% Mizar problem: t15_simplex2,simplex2,1189,6 
include('Axioms/SET010^0.ax').
thf(n1_type, type, np__1: $i).
thf(g1_metric_1_type, type, g1_metric_1: $i > $i > $i).
thf(g1_rltopsp1_type, type, g1_rltopsp1: $i > $i > $i > $i > $i > $i).
thf(k13_euclid_type, type, k13_euclid: $i > $i).
thf(k14_euclid_type, type, k14_euclid: $i > $i).
thf(k15_euclid_type, type, k15_euclid: $i > $i).
thf(k1_binop_1_type, type, k1_binop_1: $i > $i > $i > $i).
thf(k1_euclid_type, type, k1_euclid: $i > $i).
thf(k1_metric_1_type, type, k1_metric_1: $i > $i > $i > $i).
thf(k1_numbers_type, type, k1_numbers: $i).
thf(k1_xboole_0_type, type, k1_xboole_0: $i).
thf(k1_zfmisc_1_type, type, k1_zfmisc_1: $i > $i).
thf(k2_tbsp_1_type, type, k2_tbsp_1: $i > $i > $i).
thf(k2_zfmisc_1_type, type, k2_zfmisc_1: $i > $i > $i).
thf(k3_convex1_type, type, k3_convex1: $i > $i > $i).
thf(k3_metric_1_type, type, k3_metric_1: $i > $i > $i > $i).
thf(k3_numbers_type, type, k3_numbers: $i).
thf(k4_finseq_2_type, type, k4_finseq_2: $i > $i > $i).
thf(k4_numbers_type, type, k4_numbers: $i).
thf(k4_ordinal1_type, type, k4_ordinal1: $i).
thf(k5_numbers_type, type, k5_numbers: $i).
thf(k5_ordinal1_type, type, k5_ordinal1: $i).
thf(k9_metric_1_type, type, k9_metric_1: $i > $i > $i > $i).
thf(u1_algstr_0_type, type, u1_algstr_0: $i > $i).
thf(u1_metric_1_type, type, u1_metric_1: $i > $i).
thf(u1_pre_topc_type, type, u1_pre_topc: $i > $i).
thf(u1_rlvect_1_type, type, u1_rlvect_1: $i > $i).
thf(u1_struct_0_type, type, u1_struct_0: $i > $i).
thf(u2_struct_0_type, type, u2_struct_0: $i > $i).
thf(l1_algstr_0_type, type, l1_algstr_0: $i > $o).
thf(l1_metric_1_type, type, l1_metric_1: $i > $o).
thf(l1_pre_topc_type, type, l1_pre_topc: $i > $o).
thf(l1_rltopsp1_type, type, l1_rltopsp1: $i > $o).
thf(l1_rlvect_1_type, type, l1_rlvect_1: $i > $o).
thf(l1_struct_0_type, type, l1_struct_0: $i > $o).
thf(l2_algstr_0_type, type, l2_algstr_0: $i > $o).
thf(l2_struct_0_type, type, l2_struct_0: $i > $o).
thf(m1_finseq_2_type, type, m1_finseq_2: $i > $i > $o).
thf(m1_subset_1_type, type, m1_subset_1: $i > $i > $o).
thf(r1_tarski_type, type, r1_tarski: $i > $i > $o).
thf(r1_xxreal_0_type, type, r1_xxreal_0: $i > $i > $o).
thf(r2_tarski_type, type, r2_tarski: $i > $i > $o).
thf(v10_ordinal1_type, type, v10_ordinal1: $i > $o).
thf(v10_pre_topc_type, type, v10_pre_topc: $i > $o).
thf(v11_pre_topc_type, type, v11_pre_topc: $i > $o).
thf(v12_pre_topc_type, type, v12_pre_topc: $i > $o).
thf(v13_algstr_0_type, type, v13_algstr_0: $i > $o).
thf(v13_struct_0_type, type, v13_struct_0: $i > $i > $o).
thf(v1_card_1_type, type, v1_card_1: $i > $o).
thf(v1_classes1_type, type, v1_classes1: $i > $o).
thf(v1_compts_1_type, type, v1_compts_1: $i > $o).
thf(v1_convex1_type, type, v1_convex1: $i > $i > $o).
thf(v1_finseq_1_type, type, v1_finseq_1: $i > $o).
thf(v1_finset_1_type, type, v1_finset_1: $i > $o).
thf(v1_funct_1_type, type, v1_funct_1: $i > $o).
thf(v1_funct_2_type, type, v1_funct_2: $i > $i > $i > $o).
thf(v1_int_1_type, type, v1_int_1: $i > $o).
thf(v1_membered_type, type, v1_membered: $i > $o).
thf(v1_metric_1_type, type, v1_metric_1: $i > $o).
thf(v1_monoid_0_type, type, v1_monoid_0: $i > $o).
thf(v1_ordinal1_type, type, v1_ordinal1: $i > $o).
thf(v1_partfun1_type, type, v1_partfun1: $i > $i > $o).
thf(v1_rat_1_type, type, v1_rat_1: $i > $o).
thf(v1_relat_1_type, type, v1_relat_1: $i > $o).
thf(v1_rlaffin1_type, type, v1_rlaffin1: $i > $i > $o).
thf(v1_rlvect_5_type, type, v1_rlvect_5: $i > $o).
thf(v1_setfam_1_type, type, v1_setfam_1: $i > $o).
thf(v1_subset_1_type, type, v1_subset_1: $i > $i > $o).
thf(v1_tdlat_3_type, type, v1_tdlat_3: $i > $o).
thf(v1_topdim_1_type, type, v1_topdim_1: $i > $i > $o).
thf(v1_topdim_2_type, type, v1_topdim_2: $i > $i > $o).
thf(v1_toprealc_type, type, v1_toprealc: $i > $o).
thf(v1_tops_2_type, type, v1_tops_2: $i > $i > $o).
thf(v1_valued_0_type, type, v1_valued_0: $i > $o).
thf(v1_valued_2_type, type, v1_valued_2: $i > $o).
thf(v1_xboole_0_type, type, v1_xboole_0: $i > $o).
thf(v1_xcmplx_0_type, type, v1_xcmplx_0: $i > $o).
thf(v1_xreal_0_type, type, v1_xreal_0: $i > $o).
thf(v1_xxreal_0_type, type, v1_xxreal_0: $i > $o).
thf(v1_xxreal_2_type, type, v1_xxreal_2: $i > $o).
thf(v1_zfmisc_1_type, type, v1_zfmisc_1: $i > $o).
thf(v2_card_1_type, type, v2_card_1: $i > $o).
thf(v2_compts_1_type, type, v2_compts_1: $i > $i > $o).
thf(v2_finseq_1_type, type, v2_finseq_1: $i > $o).
thf(v2_finset_1_type, type, v2_finset_1: $i > $o).
thf(v2_funct_1_type, type, v2_funct_1: $i > $o).
thf(v2_int_1_type, type, v2_int_1: $i > $o).
thf(v2_membered_type, type, v2_membered: $i > $o).
thf(v2_monoid_0_type, type, v2_monoid_0: $i > $o).
thf(v2_ordinal1_type, type, v2_ordinal1: $i > $o).
thf(v2_pre_topc_type, type, v2_pre_topc: $i > $o).
thf(v2_relat_1_type, type, v2_relat_1: $i > $o).
thf(v2_rlaffin1_type, type, v2_rlaffin1: $i > $i > $o).
thf(v2_rlvect_1_type, type, v2_rlvect_1: $i > $o).
thf(v2_struct_0_type, type, v2_struct_0: $i > $o).
thf(v2_topdim_1_type, type, v2_topdim_1: $i > $i > $o).
thf(v2_toprealc_type, type, v2_toprealc: $i > $o).
thf(v2_tops_1_type, type, v2_tops_1: $i > $i > $o).
thf(v2_valued_0_type, type, v2_valued_0: $i > $o).
thf(v2_xxreal_0_type, type, v2_xxreal_0: $i > $o).
thf(v2_xxreal_2_type, type, v2_xxreal_2: $i > $o).
thf(v3_card_1_type, type, v3_card_1: $i > $i > $o).
thf(v3_finseq_1_type, type, v3_finseq_1: $i > $o).
thf(v3_funct_1_type, type, v3_funct_1: $i > $o).
thf(v3_membered_type, type, v3_membered: $i > $o).
thf(v3_ordinal1_type, type, v3_ordinal1: $i > $o).
thf(v3_pcomps_1_type, type, v3_pcomps_1: $i > $o).
thf(v3_pre_topc_type, type, v3_pre_topc: $i > $i > $o).
thf(v3_relat_1_type, type, v3_relat_1: $i > $o).
thf(v3_rlvect_1_type, type, v3_rlvect_1: $i > $o).
thf(v3_topdim_1_type, type, v3_topdim_1: $i > $o).
thf(v3_topmetr_type, type, v3_topmetr: $i > $o).
thf(v3_tops_1_type, type, v3_tops_1: $i > $i > $o).
thf(v3_valued_0_type, type, v3_valued_0: $i > $o).
thf(v3_valued_2_type, type, v3_valued_2: $i > $o).
thf(v3_xxreal_0_type, type, v3_xxreal_0: $i > $o).
thf(v3_xxreal_2_type, type, v3_xxreal_2: $i > $o).
thf(v4_funct_1_type, type, v4_funct_1: $i > $o).
thf(v4_membered_type, type, v4_membered: $i > $o).
thf(v4_pre_topc_type, type, v4_pre_topc: $i > $i > $o).
thf(v4_relat_1_type, type, v4_relat_1: $i > $i > $o).
thf(v4_rlvect_1_type, type, v4_rlvect_1: $i > $o).
thf(v4_valued_0_type, type, v4_valued_0: $i > $o).
thf(v4_xxreal_2_type, type, v4_xxreal_2: $i > $o).
thf(v5_finset_1_type, type, v5_finset_1: $i > $o).
thf(v5_membered_type, type, v5_membered: $i > $o).
thf(v5_ordinal1_type, type, v5_ordinal1: $i > $o).
thf(v5_relat_1_type, type, v5_relat_1: $i > $i > $o).
thf(v5_rltopsp1_type, type, v5_rltopsp1: $i > $o).
thf(v5_rlvect_1_type, type, v5_rlvect_1: $i > $o).
thf(v5_topgen_4_type, type, v5_topgen_4: $i > $i > $o).
thf(v5_valued_0_type, type, v5_valued_0: $i > $o).
thf(v5_xxreal_2_type, type, v5_xxreal_2: $i > $o).
thf(v6_membered_type, type, v6_membered: $i > $o).
thf(v6_metric_1_type, type, v6_metric_1: $i > $o).
thf(v6_ordinal1_type, type, v6_ordinal1: $i > $o).
thf(v6_pre_topc_type, type, v6_pre_topc: $i > $o).
thf(v6_rltopsp1_type, type, v6_rltopsp1: $i > $o).
thf(v6_rlvect_1_type, type, v6_rlvect_1: $i > $o).
thf(v6_tbsp_1_type, type, v6_tbsp_1: $i > $i > $o).
thf(v6_topgen_4_type, type, v6_topgen_4: $i > $i > $o).
thf(v6_valued_0_type, type, v6_valued_0: $i > $o).
thf(v6_xxreal_2_type, type, v6_xxreal_2: $i > $o).
thf(v7_membered_type, type, v7_membered: $i > $o).
thf(v7_metric_1_type, type, v7_metric_1: $i > $o).
thf(v7_ordinal1_type, type, v7_ordinal1: $i > $o).
thf(v7_pre_topc_type, type, v7_pre_topc: $i > $o).
thf(v7_rltopsp1_type, type, v7_rltopsp1: $i > $o).
thf(v7_rlvect_1_type, type, v7_rlvect_1: $i > $o).
thf(v7_struct_0_type, type, v7_struct_0: $i > $o).
thf(v7_valued_0_type, type, v7_valued_0: $i > $o).
thf(v8_metric_1_type, type, v8_metric_1: $i > $o).
thf(v8_ordinal1_type, type, v8_ordinal1: $i > $o).
thf(v8_pre_topc_type, type, v8_pre_topc: $i > $o).
thf(v8_rlvect_1_type, type, v8_rlvect_1: $i > $o).
thf(v8_struct_0_type, type, v8_struct_0: $i > $o).
thf(v8_valued_0_type, type, v8_valued_0: $i > $o).
thf(v9_metric_1_type, type, v9_metric_1: $i > $o).
thf(v9_ordinal1_type, type, v9_ordinal1: $i > $o).
thf(v9_pre_topc_type, type, v9_pre_topc: $i > $o).
thf(v9_rltopsp1_type, type, v9_rltopsp1: $i > $i > $o).
thf(abstractness_v1_metric_1, axiom,  (! [A: $i] :  ( (l1_metric_1 @ A)  =>  ( (v1_metric_1 @ A)  =>  (A =  ( (g1_metric_1 @  (u1_struct_0 @ A) )  @  (u1_metric_1 @ A) ) ) ) ) ) , file(metric_1, v1_metric_1)).
thf(abstractness_v5_rltopsp1, axiom,  (! [A: $i] :  ( (l1_rltopsp1 @ A)  =>  ( (v5_rltopsp1 @ A)  =>  (A =  ( ( ( ( (g1_rltopsp1 @  (u1_struct_0 @ A) )  @  (u2_struct_0 @ A) )  @  (u1_algstr_0 @ A) )  @  (u1_rlvect_1 @ A) )  @  (u1_pre_topc @ A) ) ) ) ) ) , file(rltopsp1, v5_rltopsp1)).
thf(antisymmetry_r2_hidden, axiom,  (! [A: $i, B: $i] :  ( ( (r2_hidden @ A)  @ B)  =>  ~ ( ( (r2_hidden @ B)  @ A) ) ) ) , file(hidden, r2_hidden)).
thf(asymmetry_r2_tarski, axiom,  (! [A: $i, B: $i] :  ( ( (r2_tarski @ A)  @ B)  =>  ~ ( ( (r2_tarski @ B)  @ A) ) ) ) , file(tarski, r2_tarski)).
thf(cc10_card_1, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  (v1_zfmisc_1 @ A) )  =>  ( (v3_card_1 @ A)  @ np__1) ) ) , file(card_1, cc10_card_1)).
thf(cc10_finseq_1, axiom,  (! [A: $i] :  ( (v3_finseq_1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_finseq_1 @ B) ) ) ) ) , file(finseq_1, cc10_finseq_1)).
thf(cc10_membered, axiom,  (! [A: $i] :  ( (v5_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_int_1 @ B) ) ) ) ) , file(membered, cc10_membered)).
thf(cc10_ordinal1, axiom,  (! [A: $i] :  ( (v6_ordinal1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v6_ordinal1 @ B) ) ) ) ) , file(ordinal1, cc10_ordinal1)).
thf(cc10_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( ( ~ ( (v2_struct_0 @ A) )  &  (v7_struct_0 @ A) )  =>  ( (v13_struct_0 @ A)  @ np__1) ) ) ) , file(struct_0, cc10_struct_0)).
thf(cc10_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_valued_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v1_valued_0 @ B) ) ) ) ) , file(valued_0, cc10_valued_0)).
thf(cc10_xxreal_2, axiom,  (! [A: $i] :  ( ( (v3_membered @ A)  &  (v1_xxreal_2 @ A) )  =>  ( (v3_membered @ A)  &  (v3_xxreal_2 @ A) ) ) ) , file(xxreal_2, cc10_xxreal_2)).
thf(cc11_card_1, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  (v1_card_1 @ A) )  =>  (! [B: $i] :  ( ( (v3_card_1 @ B)  @ A)  =>  ~ ( (v1_xboole_0 @ B) ) ) ) ) ) , file(card_1, cc11_card_1)).
thf(cc11_finseq_1, axiom,  (! [A: $i] :  ( (v3_finseq_1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v3_finseq_1 @ B) ) ) ) ) , file(finseq_1, cc11_finseq_1)).
thf(cc11_membered, axiom,  (! [A: $i] :  ( (v6_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v7_ordinal1 @ B) ) ) ) ) , file(membered, cc11_membered)).
thf(cc11_ordinal1, axiom,  (! [A: $i] :  ( (v8_ordinal1 @ A)  =>  (v7_ordinal1 @ A) ) ) , file(ordinal1, cc11_ordinal1)).
thf(cc11_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( ( (v13_struct_0 @ A)  @ np__1)  =>  ( ~ ( (v2_struct_0 @ A) )  &  (v7_struct_0 @ A) ) ) ) ) , file(struct_0, cc11_struct_0)).
thf(cc11_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v2_valued_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v2_valued_0 @ B) ) ) ) ) , file(valued_0, cc11_valued_0)).
thf(cc11_xxreal_2, axiom,  (! [A: $i] :  ( ( (v3_membered @ A)  &  (v2_xxreal_2 @ A) )  =>  ( (v3_membered @ A)  &  (v4_xxreal_2 @ A) ) ) ) , file(xxreal_2, cc11_xxreal_2)).
thf(cc12_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v3_valued_0 @ A)  &  ( (v5_valued_0 @ A)  &  (v1_finseq_1 @ A) ) ) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_funct_1 @ A)  &  ( (v3_valued_0 @ A)  &  (v1_finseq_1 @ A) ) ) ) ) ) ) , file(finseq_1, cc12_finseq_1)).
thf(cc12_membered, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v6_membered @ A) ) ) , file(membered, cc12_membered)).
thf(cc12_ordinal1, axiom,  (! [A: $i] :  ( (v8_ordinal1 @ A)  =>  (v1_zfmisc_1 @ A) ) ) , file(ordinal1, cc12_ordinal1)).
thf(cc12_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v3_valued_0 @ B) ) ) ) ) , file(valued_0, cc12_valued_0)).
thf(cc12_xxreal_2, axiom,  (! [A: $i] :  ( ( (v5_membered @ A)  &  (v5_xxreal_2 @ A) )  =>  ( (v5_membered @ A)  &  (v1_finset_1 @ A) ) ) ) , file(xxreal_2, cc12_xxreal_2)).
thf(cc13_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_finseq_1 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v1_finset_1 @ A)  &  (v2_finseq_1 @ A) ) ) ) ) ) , file(finseq_1, cc13_finseq_1)).
thf(cc13_membered, axiom,  (! [A: $i] :  ( (v1_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v1_membered @ B) ) ) ) ) , file(membered, cc13_membered)).
thf(cc13_ordinal1, axiom,  (! [A: $i] :  ( ~ ( (v1_zfmisc_1 @ A) )  =>  ~ ( (v8_ordinal1 @ A) ) ) ) , file(ordinal1, cc13_ordinal1)).
thf(cc13_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k3_numbers) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  ( (v5_relat_1 @ B)  @ k3_numbers) ) ) ) ) , file(valued_0, cc13_valued_0)).
thf(cc13_xxreal_2, axiom,  (! [A: $i] :  ( ( (v6_membered @ A)  &  (v4_xxreal_2 @ A) )  =>  ( (v6_membered @ A)  &  ( (v1_finset_1 @ A)  &  (v4_xxreal_2 @ A) ) ) ) ) , file(xxreal_2, cc13_xxreal_2)).
thf(cc14_membered, axiom,  (! [A: $i] :  ( (v2_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v2_membered @ B) ) ) ) ) , file(membered, cc14_membered)).
thf(cc14_ordinal1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  ~ ( (v10_ordinal1 @ A) ) ) ) , file(ordinal1, cc14_ordinal1)).
thf(cc14_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k4_numbers) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  ( (v5_relat_1 @ B)  @ k4_numbers) ) ) ) ) , file(valued_0, cc14_valued_0)).
thf(cc14_xxreal_2, axiom,  (! [A: $i] :  ( ( (v2_membered @ A)  &  (v5_xxreal_2 @ A) )  =>  ( (v2_membered @ A)  &  (v3_membered @ A) ) ) ) , file(xxreal_2, cc14_xxreal_2)).
thf(cc15_membered, axiom,  (! [A: $i] :  ( (v3_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v3_membered @ B) ) ) ) ) , file(membered, cc15_membered)).
thf(cc15_ordinal1, axiom,  (! [A: $i] :  ( ( (v1_xboole_0 @ A)  &  (v1_relat_1 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v9_ordinal1 @ A) ) ) ) , file(ordinal1, cc15_ordinal1)).
thf(cc15_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v4_valued_0 @ B) ) ) ) ) , file(valued_0, cc15_valued_0)).
thf(cc15_xxreal_2, axiom,  (! [A: $i] :  ( ( (v2_membered @ A)  &  (v1_xboole_0 @ A) )  =>  ( (v2_membered @ A)  &  (v6_xxreal_2 @ A) ) ) ) , file(xxreal_2, cc15_xxreal_2)).
thf(cc16_membered, axiom,  (! [A: $i] :  ( (v4_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v4_membered @ B) ) ) ) ) , file(membered, cc16_membered)).
thf(cc16_ordinal1, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ~ ( (v10_ordinal1 @ A) ) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  ~ ( (v8_ordinal1 @ B) ) ) ) ) ) , file(ordinal1, cc16_ordinal1)).
thf(cc16_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v1_membered @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  (v1_valued_0 @ C) ) ) ) ) , file(valued_0, cc16_valued_0)).
thf(cc16_xxreal_2, axiom,  (! [A: $i] :  ( ( (v2_membered @ A)  &  (v1_xxreal_2 @ A) )  =>  ( (v2_membered @ A)  &  ~ ( (v1_xboole_0 @ A) ) ) ) ) , file(xxreal_2, cc16_xxreal_2)).
thf(cc17_membered, axiom,  (! [A: $i] :  ( (v5_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v5_membered @ B) ) ) ) ) , file(membered, cc17_membered)).
thf(cc17_ordinal1, axiom,  (! [A: $i] :  ( ~ ( (v10_ordinal1 @ A) )  =>  (v1_setfam_1 @ A) ) ) , file(ordinal1, cc17_ordinal1)).
thf(cc17_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( ~ ( (v7_struct_0 @ A) )  =>  ~ ( (v2_struct_0 @ A) ) ) ) ) , file(struct_0, cc17_struct_0)).
thf(cc17_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v2_membered @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  (v2_valued_0 @ C) ) ) ) ) , file(valued_0, cc17_valued_0)).
thf(cc17_xxreal_2, axiom,  (! [A: $i] :  ( ( (v2_membered @ A)  &  (v2_xxreal_2 @ A) )  =>  ( (v2_membered @ A)  &  ~ ( (v1_xboole_0 @ A) ) ) ) ) , file(xxreal_2, cc17_xxreal_2)).
thf(cc18_membered, axiom,  (! [A: $i] :  ( (v6_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v6_membered @ B) ) ) ) ) , file(membered, cc18_membered)).
thf(cc18_ordinal1, axiom,  (! [A: $i] :  ( (v10_ordinal1 @ A)  =>  ~ ( (v1_setfam_1 @ A) ) ) ) , file(ordinal1, cc18_ordinal1)).
thf(cc18_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v3_membered @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  (v3_valued_0 @ C) ) ) ) ) , file(valued_0, cc18_valued_0)).
thf(cc19_membered, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v7_membered @ A) ) ) , file(membered, cc19_membered)).
thf(cc19_ordinal1, axiom,  (! [A: $i] :  ( (v1_setfam_1 @ A)  =>  ~ ( (v10_ordinal1 @ A) ) ) ) , file(ordinal1, cc19_ordinal1)).
thf(cc19_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v4_membered @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( (v5_relat_1 @ C)  @ k3_numbers) ) ) ) ) , file(valued_0, cc19_valued_0)).
thf(cc1_card_1, axiom,  (! [A: $i] :  ( (v1_card_1 @ A)  =>  (v3_ordinal1 @ A) ) ) , file(card_1, cc1_card_1)).
thf(cc1_compts_1, axiom,  (! [A: $i] :  ( (l1_pre_topc @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  =>  ( (v1_xboole_0 @ B)  =>  ( (v2_compts_1 @ B)  @ A) ) ) ) ) ) , file(compts_1, cc1_compts_1)).
thf(cc1_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_euclid @ A) )  =>  ( (v3_card_1 @ B)  @ A) ) ) ) ) , file(euclid, cc1_euclid)).
thf(cc1_euclid_9, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @  (k14_euclid @ A) ) )  =>  ( (v5_relat_1 @ B)  @ k1_numbers) ) ) ) ) , file(euclid_9, cc1_euclid_9)).
thf(cc1_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_xboole_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v1_finseq_1 @ A) ) ) ) , file(finseq_1, cc1_finseq_1)).
thf(cc1_finseq_2, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  (v7_ordinal1 @ B) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  ( (k4_finseq_2 @ B)  @ A) )  =>  ( (v3_card_1 @ C)  @ B) ) ) ) ) , file(finseq_2, cc1_finseq_2)).
thf(cc1_finset_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v1_finset_1 @ A) ) ) , file(finset_1, cc1_finset_1)).
thf(cc1_funct_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v1_funct_1 @ A) ) ) , file(funct_1, cc1_funct_1)).
thf(cc1_funct_2, axiom,  (! [A: $i, B: $i] :  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( ( (v1_partfun1 @ C)  @ A)  =>  ( ( (v1_funct_2 @ C)  @ A)  @ B) ) ) ) ) , file(funct_2, cc1_funct_2)).
thf(cc1_int_1, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k4_numbers)  =>  (v1_int_1 @ A) ) ) , file(int_1, cc1_int_1)).
thf(cc1_jordan2b, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @  (k15_euclid @ A) ) )  =>  ( (v5_relat_1 @ B)  @ k1_numbers) ) ) ) ) , file(jordan2b, cc1_jordan2b)).
thf(cc1_jordan2c, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k4_ordinal1)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @  (k15_euclid @ A) ) ) )  =>  ( ( (v2_compts_1 @ B)  @  (k15_euclid @ A) )  =>  ( (v9_rltopsp1 @ B)  @  (k15_euclid @ A) ) ) ) ) ) ) , file(jordan2c, cc1_jordan2c)).
thf(cc1_membered, axiom,  (! [A: $i] :  ( (v6_membered @ A)  =>  (v5_membered @ A) ) ) , file(membered, cc1_membered)).
thf(cc1_metrizts, axiom,  (! [A: $i] :  ( (l1_pre_topc @ A)  =>  ( ( (v2_struct_0 @ A)  &  (v2_pre_topc @ A) )  =>  ( (v2_pre_topc @ A)  &  (v3_pcomps_1 @ A) ) ) ) ) , file(metrizts, cc1_metrizts)).
thf(cc1_monoid_0, axiom,  (! [A: $i] :  ( ( (v1_monoid_0 @ A)  &  (l1_struct_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  =>  ( (v1_relat_1 @ B)  &  (v1_funct_1 @ B) ) ) ) ) ) , file(monoid_0, cc1_monoid_0)).
thf(cc1_nat_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v3_ordinal1 @ A)  &  (v7_ordinal1 @ A) ) ) ) , file(nat_1, cc1_nat_1)).
thf(cc1_ordinal1, axiom,  (! [A: $i] :  ( (v3_ordinal1 @ A)  =>  ( (v1_ordinal1 @ A)  &  (v2_ordinal1 @ A) ) ) ) , file(ordinal1, cc1_ordinal1)).
thf(cc1_relat_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v1_relat_1 @ A) ) ) , file(relat_1, cc1_relat_1)).
thf(cc1_relset_1, axiom,  (! [A: $i, B: $i] :  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  (v1_relat_1 @ C) ) ) ) , file(relset_1, cc1_relset_1)).
thf(cc1_rlaffin1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v13_algstr_0 @ A)  &  ( (v2_rlvect_1 @ A)  &  ( (v3_rlvect_1 @ A)  &  ( (v4_rlvect_1 @ A)  &  ( (v5_rlvect_1 @ A)  &  ( (v6_rlvect_1 @ A)  &  ( (v7_rlvect_1 @ A)  &  ( (v8_rlvect_1 @ A)  &  (l1_rlvect_1 @ A) ) ) ) ) ) ) ) ) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  =>  ( (v1_xboole_0 @ B)  =>  ( (v1_rlaffin1 @ B)  @ A) ) ) ) ) ) , file(rlaffin1, cc1_rlaffin1)).
thf(cc1_rlaffin3, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v13_algstr_0 @ A)  &  ( (v2_rlvect_1 @ A)  &  ( (v3_rlvect_1 @ A)  &  ( (v4_rlvect_1 @ A)  &  ( (v5_rlvect_1 @ A)  &  ( (v6_rlvect_1 @ A)  &  ( (v7_rlvect_1 @ A)  &  ( (v8_rlvect_1 @ A)  &  ( (v1_rlvect_5 @ A)  &  (l1_rlvect_1 @ A) ) ) ) ) ) ) ) ) ) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  =>  ( ( (v1_rlaffin1 @ B)  @ A)  =>  ( (v1_finset_1 @ B)  &  ( (v1_rlaffin1 @ B)  @ A) ) ) ) ) ) ) , file(rlaffin3, cc1_rlaffin3)).
thf(cc1_simplex0, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v1_classes1 @ A) ) ) , file(simplex0, cc1_simplex0)).
thf(cc1_simplex2, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v6_metric_1 @ A)  &  (l1_metric_1 @ A) ) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  =>  ( (v1_finset_1 @ B)  =>  ( (v6_tbsp_1 @ B)  @ A) ) ) ) ) ) , file(simplex2, cc1_simplex2)).
thf(cc1_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( (v2_struct_0 @ A)  =>  (v7_struct_0 @ A) ) ) ) , file(struct_0, cc1_struct_0)).
thf(cc1_subset_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v1_xboole_0 @ B) ) ) ) ) , file(subset_1, cc1_subset_1)).
thf(cc1_topdim_1, axiom,  (! [A: $i] :  ( ( (v2_pre_topc @ A)  &  (l1_pre_topc @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  =>  ( (v1_finset_1 @ B)  =>  ( (v1_topdim_1 @ B)  @ A) ) ) ) ) ) , file(topdim_1, cc1_topdim_1)).
thf(cc1_topdim_2, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (k1_zfmisc_1 @ A) ) )  =>  ( (v1_finset_1 @ B)  =>  ( (v1_topdim_2 @ B)  @ A) ) ) ) ) , file(topdim_2, cc1_topdim_2)).
thf(cc1_toprealc, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( (v2_toprealc @ A)  =>  (v1_toprealc @ A) ) ) ) , file(toprealc, cc1_toprealc)).
thf(cc1_tops_1, axiom,  (! [A: $i] :  ( ( (v2_pre_topc @ A)  &  (l1_pre_topc @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  =>  ( (v1_xboole_0 @ B)  =>  ( (v3_pre_topc @ B)  @ A) ) ) ) ) ) , file(tops_1, cc1_tops_1)).
thf(cc1_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k4_numbers) ) ) ) , file(valued_0, cc1_valued_0)).
thf(cc1_xreal_0, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  (v1_xreal_0 @ A) ) ) , file(xreal_0, cc1_xreal_0)).
thf(cc1_xxreal_3, axiom,  (! [A: $i] :  ( ( (v1_xxreal_0 @ A)  &  ( ~ ( (v3_xxreal_0 @ A) )  &  ~ ( (v1_xreal_0 @ A) ) ) )  =>  ( (v1_xxreal_0 @ A)  &  (v2_xxreal_0 @ A) ) ) ) , file(xxreal_3, cc1_xxreal_3)).
thf(cc1_yellow13, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v2_pre_topc @ A)  &  ( (v7_pre_topc @ A)  &  (l1_pre_topc @ A) ) ) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  =>  ( (v1_finset_1 @ B)  =>  ( (v4_pre_topc @ B)  @ A) ) ) ) ) ) , file(yellow13, cc1_yellow13)).
thf(cc20_ordinal1, axiom,  (! [A: $i] :  ( ~ ( (v1_setfam_1 @ A) )  =>  (v10_ordinal1 @ A) ) ) , file(ordinal1, cc20_ordinal1)).
thf(cc20_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v5_membered @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( (v5_relat_1 @ C)  @ k4_numbers) ) ) ) ) , file(valued_0, cc20_valued_0)).
thf(cc21_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v6_membered @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  (v4_valued_0 @ C) ) ) ) ) , file(valued_0, cc21_valued_0)).
thf(cc22_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v1_zfmisc_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) ) ) ) ) ) ) , file(valued_0, cc22_valued_0)).
thf(cc23_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v5_valued_0 @ A) ) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v7_valued_0 @ A) ) ) ) ) ) , file(valued_0, cc23_valued_0)).
thf(cc24_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v6_valued_0 @ A) ) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v8_valued_0 @ A) ) ) ) ) ) , file(valued_0, cc24_valued_0)).
thf(cc2_card_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v1_card_1 @ A) ) ) , file(card_1, cc2_card_1)).
thf(cc2_compts_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v2_pre_topc @ A)  &  ( (v8_pre_topc @ A)  &  (l1_pre_topc @ A) ) ) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  =>  ( ( (v2_compts_1 @ B)  @ A)  =>  ( (v4_pre_topc @ B)  @ A) ) ) ) ) ) , file(compts_1, cc2_compts_1)).
thf(cc2_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @  (k15_euclid @ A) ) )  =>  (v1_finseq_1 @ B) ) ) ) ) , file(euclid, cc2_euclid)).
thf(cc2_euclid_9, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @  (k14_euclid @ A) ) )  =>  ( (v3_card_1 @ B)  @ A) ) ) ) ) , file(euclid_9, cc2_euclid_9)).
thf(cc2_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finseq_1 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finset_1 @ A) ) ) ) ) , file(finseq_1, cc2_finseq_1)).
thf(cc2_finseq_2, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_finseq_2 @ B)  @ A)  =>  (v4_funct_1 @ B) ) ) ) , file(finseq_2, cc2_finseq_2)).
thf(cc2_finset_1, axiom,  (! [A: $i] :  ( (v1_finset_1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v1_finset_1 @ B) ) ) ) ) , file(finset_1, cc2_finset_1)).
thf(cc2_funct_1, axiom,  (! [A: $i] :  ( ( (v1_xboole_0 @ A)  &  ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_funct_1 @ A) ) ) ) ) , file(funct_1, cc2_funct_1)).
thf(cc2_funct_2, axiom,  (! [A: $i, B: $i] :  ( (v1_xboole_0 @ A)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  =>  ( (v1_partfun1 @ C)  @ A) ) ) ) ) ) , file(funct_2, cc2_funct_2)).
thf(cc2_int_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v1_int_1 @ A) ) ) , file(int_1, cc2_int_1)).
thf(cc2_jordan, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k4_ordinal1)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @  (k15_euclid @ A) ) ) )  =>  ( (v1_xboole_0 @ B)  =>  ( (v9_rltopsp1 @ B)  @  (k15_euclid @ A) ) ) ) ) ) ) , file(jordan, cc2_jordan)).
thf(cc2_membered, axiom,  (! [A: $i] :  ( (v5_membered @ A)  =>  (v4_membered @ A) ) ) , file(membered, cc2_membered)).
thf(cc2_metrizts, axiom,  (! [A: $i] :  ( (l1_pre_topc @ A)  =>  ( ( (v2_pre_topc @ A)  &  (v3_pcomps_1 @ A) )  =>  ( (v2_pre_topc @ A)  &  (v12_pre_topc @ A) ) ) ) ) , file(metrizts, cc2_metrizts)).
thf(cc2_monoid_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( (v2_monoid_0 @ A)  =>  (v1_monoid_0 @ A) ) ) ) , file(monoid_0, cc2_monoid_0)).
thf(cc2_nat_1, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k4_ordinal1)  =>  ~ ( (v3_xxreal_0 @ A) ) ) ) , file(nat_1, cc2_nat_1)).
thf(cc2_ordinal1, axiom,  (! [A: $i] :  ( ( (v1_ordinal1 @ A)  &  (v2_ordinal1 @ A) )  =>  (v3_ordinal1 @ A) ) ) , file(ordinal1, cc2_ordinal1)).
thf(cc2_pre_topc, axiom,  (! [A: $i] :  ( ( (v2_pre_topc @ A)  &  (l1_pre_topc @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  =>  ( (v1_xboole_0 @ B)  =>  ( (v4_pre_topc @ B)  @ A) ) ) ) ) ) , file(pre_topc, cc2_pre_topc)).
thf(cc2_relat_1, axiom,  (! [A: $i] :  ( (v1_relat_1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v1_relat_1 @ B) ) ) ) ) , file(relat_1, cc2_relat_1)).
thf(cc2_relset_1, axiom,  (! [A: $i, B: $i] :  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( ( (v4_relat_1 @ C)  @ A)  &  ( (v5_relat_1 @ C)  @ B) ) ) ) ) , file(relset_1, cc2_relset_1)).
thf(cc2_simplex0, axiom,  (! [A: $i] :  ( ~ ( (v1_setfam_1 @ A) )  =>  ~ ( (v1_xboole_0 @ A) ) ) ) , file(simplex0, cc2_simplex0)).
thf(cc2_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( ~ ( (v7_struct_0 @ A) )  =>  ~ ( (v2_struct_0 @ A) ) ) ) ) , file(struct_0, cc2_struct_0)).
thf(cc2_subset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  ( ~ ( ( (v1_subset_1 @ B)  @ A) )  =>  ~ ( (v1_xboole_0 @ B) ) ) ) ) ) ) , file(subset_1, cc2_subset_1)).
thf(cc2_tbsp_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_metric_1 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  =>  ( (v1_xboole_0 @ B)  =>  ( (v6_tbsp_1 @ B)  @ A) ) ) ) ) ) , file(tbsp_1, cc2_tbsp_1)).
thf(cc2_topdim_1, axiom,  (! [A: $i] :  ( ( (v2_pre_topc @ A)  &  (l1_pre_topc @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) ) )  =>  ( (v1_xboole_0 @ B)  =>  ( (v2_topdim_1 @ B)  @ A) ) ) ) ) ) , file(topdim_1, cc2_topdim_1)).
thf(cc2_tops_1, axiom,  (! [A: $i] :  ( (l1_pre_topc @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  =>  ( (v1_xboole_0 @ B)  =>  ( (v2_tops_1 @ B)  @ A) ) ) ) ) ) , file(tops_1, cc2_tops_1)).
thf(cc2_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k4_numbers) )  =>  ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k3_numbers) ) ) ) , file(valued_0, cc2_valued_0)).
thf(cc2_xreal_0, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v1_xreal_0 @ A) ) ) , file(xreal_0, cc2_xreal_0)).
thf(cc2_xxreal_0, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v1_xxreal_0 @ A) ) ) , file(xxreal_0, cc2_xxreal_0)).
thf(cc2_xxreal_2, axiom,  (! [A: $i] :  ( ( (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) ) ) ) ) ) , file(xxreal_2, cc2_xxreal_2)).
thf(cc2_xxreal_3, axiom,  (! [A: $i] :  ( ( (v1_xxreal_0 @ A)  &  ( ~ ( (v2_xxreal_0 @ A) )  &  ~ ( (v1_xreal_0 @ A) ) ) )  =>  ( (v1_xxreal_0 @ A)  &  (v3_xxreal_0 @ A) ) ) ) , file(xxreal_3, cc2_xxreal_3)).
thf(cc2_yellow13, axiom,  (! [A: $i] :  ( (l1_pre_topc @ A)  =>  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v8_struct_0 @ A)  &  ( (v2_pre_topc @ A)  &  (v7_pre_topc @ A) ) ) )  =>  ( ~ ( (v2_struct_0 @ A) )  &  ( (v2_pre_topc @ A)  &  (v1_tdlat_3 @ A) ) ) ) ) ) , file(yellow13, cc2_yellow13)).
thf(cc30_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k1_numbers) )  =>  ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) ) ) ) , file(valued_0, cc30_valued_0)).
thf(cc31_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k4_ordinal1) )  =>  ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) ) ) ) , file(valued_0, cc31_valued_0)).
thf(cc3_card_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v1_card_1 @ A) ) ) , file(card_1, cc3_card_1)).
thf(cc3_compts_1, axiom,  (! [A: $i] :  ( (l1_pre_topc @ A)  =>  ( ( (v8_struct_0 @ A)  &  (v2_pre_topc @ A) )  =>  ( (v2_pre_topc @ A)  &  (v1_compts_1 @ A) ) ) ) ) , file(compts_1, cc3_compts_1)).
thf(cc3_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @  (k15_euclid @ A) ) )  =>  (v3_valued_0 @ B) ) ) ) ) , file(euclid, cc3_euclid)).
thf(cc3_finseq_2, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_finseq_2 @ B)  @ A)  =>  (v3_finseq_1 @ B) ) ) ) , file(finseq_2, cc3_finseq_2)).
thf(cc3_finset_1, axiom,  (! [A: $i, B: $i] :  ( (v1_finset_1 @ A)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( ( (v1_funct_1 @ C)  &  ( ( (v1_funct_2 @ C)  @ A)  @ B) )  =>  ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  (v1_finset_1 @ C) ) ) ) ) ) ) ) , file(finset_1, cc3_finset_1)).
thf(cc3_funct_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v1_funct_1 @ B) ) ) ) ) , file(funct_1, cc3_funct_1)).
thf(cc3_funct_2, axiom,  (! [A: $i, B: $i] :  ( ~ ( (v1_xboole_0 @ B) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  =>  ( (v1_partfun1 @ C)  @ A) ) ) ) ) ) , file(funct_2, cc3_funct_2)).
thf(cc3_int_1, axiom,  (! [A: $i] :  ( (v1_int_1 @ A)  =>  (v1_xreal_0 @ A) ) ) , file(int_1, cc3_int_1)).
thf(cc3_jordan, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k4_ordinal1)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @  (k15_euclid @ A) ) ) )  =>  ( ~ ( ( (v9_rltopsp1 @ B)  @  (k15_euclid @ A) ) )  =>  ~ ( (v1_xboole_0 @ B) ) ) ) ) ) ) , file(jordan, cc3_jordan)).
thf(cc3_membered, axiom,  (! [A: $i] :  ( (v4_membered @ A)  =>  (v3_membered @ A) ) ) , file(membered, cc3_membered)).
thf(cc3_metrizts, axiom,  (! [A: $i] :  ( ( (v2_pre_topc @ A)  &  ( (v3_pcomps_1 @ A)  &  (l1_pre_topc @ A) ) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  =>  ( ( (v3_pre_topc @ B)  @ A)  =>  ( (v5_topgen_4 @ B)  @ A) ) ) ) ) ) , file(metrizts, cc3_metrizts)).
thf(cc3_monoid_0, axiom,  (! [A: $i] :  ( ( (v2_monoid_0 @ A)  &  (l1_struct_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  =>  (v1_finseq_1 @ B) ) ) ) ) , file(monoid_0, cc3_monoid_0)).
thf(cc3_nat_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v7_ordinal1 @ A)  &  ~ ( (v3_xxreal_0 @ A) ) ) ) ) , file(nat_1, cc3_nat_1)).
thf(cc3_ordinal1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v3_ordinal1 @ A) ) ) , file(ordinal1, cc3_ordinal1)).
thf(cc3_pre_topc, axiom,  (! [A: $i] :  ( (l1_pre_topc @ A)  =>  ( (v11_pre_topc @ A)  =>  ( (v7_pre_topc @ A)  &  (v9_pre_topc @ A) ) ) ) ) , file(pre_topc, cc3_pre_topc)).
thf(cc3_relat_1, axiom,  (! [A: $i] :  ( ( (v1_xboole_0 @ A)  &  (v1_relat_1 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v3_relat_1 @ A) ) ) ) , file(relat_1, cc3_relat_1)).
thf(cc3_relset_1, axiom,  (! [A: $i, B: $i] :  ( (v1_xboole_0 @ A)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  (v1_xboole_0 @ C) ) ) ) ) , file(relset_1, cc3_relset_1)).
thf(cc3_rlaffin1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v13_algstr_0 @ A)  &  ( (v2_rlvect_1 @ A)  &  ( (v3_rlvect_1 @ A)  &  ( (v4_rlvect_1 @ A)  &  ( (v5_rlvect_1 @ A)  &  ( (v6_rlvect_1 @ A)  &  ( (v7_rlvect_1 @ A)  &  ( (v8_rlvect_1 @ A)  &  (l1_rlvect_1 @ A) ) ) ) ) ) ) ) ) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) ) )  =>  ( (v1_xboole_0 @ B)  =>  ( (v2_rlaffin1 @ B)  @ A) ) ) ) ) ) , file(rlaffin1, cc3_rlaffin1)).
thf(cc3_simplex0, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  (v1_classes1 @ A) )  =>  ~ ( (v1_setfam_1 @ A) ) ) ) , file(simplex0, cc3_simplex0)).
thf(cc3_subset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  ( (v1_xboole_0 @ B)  =>  ( (v1_subset_1 @ B)  @ A) ) ) ) ) ) , file(subset_1, cc3_subset_1)).
thf(cc3_tbsp_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v6_metric_1 @ A)  &  ( (v8_metric_1 @ A)  &  ( (v9_metric_1 @ A)  &  (l1_metric_1 @ A) ) ) ) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  =>  ( (v1_finset_1 @ B)  =>  ( (v6_tbsp_1 @ B)  @ A) ) ) ) ) ) , file(tbsp_1, cc3_tbsp_1)).
thf(cc3_topdim_1, axiom,  (! [A: $i] :  ( (l1_pre_topc @ A)  =>  ( ( (v2_struct_0 @ A)  &  (v2_pre_topc @ A) )  =>  ( (v2_pre_topc @ A)  &  (v3_topdim_1 @ A) ) ) ) ) , file(topdim_1, cc3_topdim_1)).
thf(cc3_tops_1, axiom,  (! [A: $i] :  ( ( (v2_pre_topc @ A)  &  (l1_pre_topc @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  =>  ( (v1_xboole_0 @ B)  =>  ( (v3_tops_1 @ B)  @ A) ) ) ) ) ) , file(tops_1, cc3_tops_1)).
thf(cc3_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k4_numbers) )  =>  ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) ) ) ) , file(valued_0, cc3_valued_0)).
thf(cc3_xreal_0, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (v1_xcmplx_0 @ A) ) ) , file(xreal_0, cc3_xreal_0)).
thf(cc3_xxreal_0, axiom,  (! [A: $i] :  ( ( (v1_xxreal_0 @ A)  &  (v2_xxreal_0 @ A) )  =>  ( ~ ( (v8_ordinal1 @ A) )  &  ( (v1_xxreal_0 @ A)  &  ~ ( (v3_xxreal_0 @ A) ) ) ) ) ) , file(xxreal_0, cc3_xxreal_0)).
thf(cc3_xxreal_2, axiom,  (! [A: $i] :  ( ( (v6_membered @ A)  &  ~ ( (v1_xboole_0 @ A) ) )  =>  ( (v6_membered @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  (v1_xxreal_2 @ A) ) ) ) ) , file(xxreal_2, cc3_xxreal_2)).
thf(cc3_yellow13, axiom,  (! [A: $i] :  ( (l1_pre_topc @ A)  =>  ( ( (v8_struct_0 @ A)  &  (v2_pre_topc @ A) )  =>  ( (v2_pre_topc @ A)  &  (v1_compts_1 @ A) ) ) ) ) , file(yellow13, cc3_yellow13)).
thf(cc4_card_1, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k4_ordinal1)  =>  (v1_finset_1 @ A) ) ) , file(card_1, cc4_card_1)).
thf(cc4_compts_1, axiom,  (! [A: $i] :  ( ( (v2_pre_topc @ A)  &  (l1_pre_topc @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  =>  ( (v1_finset_1 @ B)  =>  ( (v2_compts_1 @ B)  @ A) ) ) ) ) ) , file(compts_1, cc4_compts_1)).
thf(cc4_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @  (k15_euclid @ A) ) )  =>  ( (v3_card_1 @ B)  @ A) ) ) ) ) , file(euclid, cc4_euclid)).
thf(cc4_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_xboole_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v1_finseq_1 @ A) ) ) ) , file(finseq_1, cc4_finseq_1)).
thf(cc4_finset_1, axiom,  (! [A: $i] :  ( (v1_zfmisc_1 @ A)  =>  (v1_finset_1 @ A) ) ) , file(finset_1, cc4_finset_1)).
thf(cc4_funct_1, axiom,  (! [A: $i] :  ( ( (v1_xboole_0 @ A)  &  ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v3_funct_1 @ A) ) ) ) ) , file(funct_1, cc4_funct_1)).
thf(cc4_funct_2, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) ) )  =>  ( ( ( (v1_funct_2 @ B)  @ A)  @ A)  =>  ( (v1_partfun1 @ B)  @ A) ) ) ) ) , file(funct_2, cc4_funct_2)).
thf(cc4_int_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v2_int_1 @ A) ) ) , file(int_1, cc4_int_1)).
thf(cc4_jordan, axiom,  (! [A: $i] :  ( ( ~ ( (v8_ordinal1 @ A) )  &  ( (m1_subset_1 @ A)  @ k4_ordinal1) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @  (k15_euclid @ A) ) ) )  =>  ( ( (v9_rltopsp1 @ B)  @  (k15_euclid @ A) )  =>  ( (v1_subset_1 @ B)  @  (u1_struct_0 @  (k15_euclid @ A) ) ) ) ) ) ) ) , file(jordan, cc4_jordan)).
thf(cc4_membered, axiom,  (! [A: $i] :  ( (v3_membered @ A)  =>  (v2_membered @ A) ) ) , file(membered, cc4_membered)).
thf(cc4_metrizts, axiom,  (! [A: $i] :  ( ( (v2_pre_topc @ A)  &  ( (v3_pcomps_1 @ A)  &  (l1_pre_topc @ A) ) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  =>  ( ( (v4_pre_topc @ B)  @ A)  =>  ( (v6_topgen_4 @ B)  @ A) ) ) ) ) ) , file(metrizts, cc4_metrizts)).
thf(cc4_nat_1, axiom,  (! [A: $i] :  ( ( (v7_ordinal1 @ A)  &  (v8_ordinal1 @ A) )  =>  ( (v7_ordinal1 @ A)  &  ~ ( (v2_xxreal_0 @ A) ) ) ) ) , file(nat_1, cc4_nat_1)).
thf(cc4_ordinal1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v5_ordinal1 @ A) ) ) , file(ordinal1, cc4_ordinal1)).
thf(cc4_pre_topc, axiom,  (! [A: $i] :  ( (l1_pre_topc @ A)  =>  ( ( (v7_pre_topc @ A)  &  (v9_pre_topc @ A) )  =>  (v11_pre_topc @ A) ) ) ) , file(pre_topc, cc4_pre_topc)).
thf(cc4_relat_1, axiom,  (! [A: $i] :  ( ( (v1_xboole_0 @ A)  &  (v1_relat_1 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v2_relat_1 @ A) ) ) ) , file(relat_1, cc4_relat_1)).
thf(cc4_relset_1, axiom,  (! [A: $i, B: $i] :  ( (v1_xboole_0 @ A)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ B)  @ A) ) )  =>  (v1_xboole_0 @ C) ) ) ) ) , file(relset_1, cc4_relset_1)).
thf(cc4_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( (v2_struct_0 @ A)  =>  ( (v2_struct_0 @ A)  &  (v8_struct_0 @ A) ) ) ) ) , file(struct_0, cc4_struct_0)).
thf(cc4_subset_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  ~ ( ( (v1_subset_1 @ B)  @ A) ) ) ) ) ) , file(subset_1, cc4_subset_1)).
thf(cc4_topdim_1, axiom,  (! [A: $i] :  ( ( (v2_pre_topc @ A)  &  ( (v3_topdim_1 @ A)  &  (l1_pre_topc @ A) ) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  =>  ( (v1_topdim_1 @ B)  @ A) ) ) ) ) , file(topdim_1, cc4_topdim_1)).
thf(cc4_tops_1, axiom,  (! [A: $i] :  ( ( (v2_pre_topc @ A)  &  (l1_pre_topc @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  =>  ( ( (v3_tops_1 @ B)  @ A)  =>  ( (v2_tops_1 @ B)  @ A) ) ) ) ) ) , file(tops_1, cc4_tops_1)).
thf(cc4_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k3_numbers) )  =>  ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) ) ) ) , file(valued_0, cc4_valued_0)).
thf(cc4_xreal_0, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (v1_xxreal_0 @ A) ) ) , file(xreal_0, cc4_xreal_0)).
thf(cc4_xxreal_0, axiom,  (! [A: $i] :  ( ( ~ ( (v8_ordinal1 @ A) )  &  ( (v1_xxreal_0 @ A)  &  ~ ( (v3_xxreal_0 @ A) ) ) )  =>  ( (v1_xxreal_0 @ A)  &  (v2_xxreal_0 @ A) ) ) ) , file(xxreal_0, cc4_xxreal_0)).
thf(cc4_xxreal_2, axiom,  (! [A: $i] :  ( ( (v2_membered @ A)  &  (v5_xxreal_2 @ A) )  =>  ( (v2_membered @ A)  &  ( (v3_xxreal_2 @ A)  &  (v4_xxreal_2 @ A) ) ) ) ) , file(xxreal_2, cc4_xxreal_2)).
thf(cc4_yellow13, axiom,  (! [A: $i] :  ( (l1_pre_topc @ A)  =>  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v2_pre_topc @ A)  &  (v1_tdlat_3 @ A) ) )  =>  ( (v2_pre_topc @ A)  &  ( (v7_pre_topc @ A)  &  ( (v8_pre_topc @ A)  &  ( (v9_pre_topc @ A)  &  (v10_pre_topc @ A) ) ) ) ) ) ) ) , file(yellow13, cc4_yellow13)).
thf(cc5_card_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v1_finset_1 @ A) ) ) , file(card_1, cc5_card_1)).
thf(cc5_compts_1, axiom,  (! [A: $i] :  ( (l1_pre_topc @ A)  =>  ( (v2_struct_0 @ A)  =>  (v8_pre_topc @ A) ) ) ) , file(compts_1, cc5_compts_1)).
thf(cc5_finseq_1, axiom,  (! [A: $i] :  ( ( (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) ) ) ) ) ) , file(finseq_1, cc5_finseq_1)).
thf(cc5_finset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_finset_1 @ A) )  =>  ~ ( (v1_zfmisc_1 @ A) ) ) ) , file(finset_1, cc5_finset_1)).
thf(cc5_funct_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ~ ( (v3_funct_1 @ A) ) ) )  =>  ( ~ ( (v1_zfmisc_1 @ A) )  &  ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) ) ) ) ) , file(funct_1, cc5_funct_1)).
thf(cc5_funct_2, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (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) ) ) ) ) ) , file(funct_2, cc5_funct_2)).
thf(cc5_int_1, axiom,  (! [A: $i] :  ( (v2_int_1 @ A)  =>  (v1_int_1 @ A) ) ) , file(int_1, cc5_int_1)).
thf(cc5_membered, axiom,  (! [A: $i] :  ( (v3_membered @ A)  =>  (v1_membered @ A) ) ) , file(membered, cc5_membered)).
thf(cc5_nat_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v8_ordinal1 @ A) ) ) , file(nat_1, cc5_nat_1)).
thf(cc5_ordinal1, axiom,  (! [A: $i] :  ( (v3_ordinal1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v3_ordinal1 @ B) ) ) ) ) , file(ordinal1, cc5_ordinal1)).
thf(cc5_pre_topc, axiom,  (! [A: $i] :  ( (l1_pre_topc @ A)  =>  ( (v12_pre_topc @ A)  =>  ( (v7_pre_topc @ A)  &  (v10_pre_topc @ A) ) ) ) ) , file(pre_topc, cc5_pre_topc)).
thf(cc5_relat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v4_relat_1 @ B)  @ A) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @ B) )  =>  ( (v4_relat_1 @ C)  @ A) ) ) ) ) , file(relat_1, cc5_relat_1)).
thf(cc5_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( ~ ( (v8_struct_0 @ A) )  =>  ( ~ ( (v2_struct_0 @ A) )  &  ~ ( (v8_struct_0 @ A) ) ) ) ) ) , file(struct_0, cc5_struct_0)).
thf(cc5_subset_1, axiom,  (! [A: $i] :  ( (v1_zfmisc_1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v1_zfmisc_1 @ B) ) ) ) ) , file(subset_1, cc5_subset_1)).
thf(cc5_tops_1, axiom,  (! [A: $i] :  ( ( (v2_pre_topc @ A)  &  (l1_pre_topc @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  =>  ( ( ( (v4_pre_topc @ B)  @ A)  &  ( (v2_tops_1 @ B)  @ A) )  =>  ( (v3_tops_1 @ B)  @ A) ) ) ) ) ) , file(tops_1, cc5_tops_1)).
thf(cc5_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v2_valued_0 @ A) ) ) ) , file(valued_0, cc5_valued_0)).
thf(cc5_xxreal_0, axiom,  (! [A: $i] :  ( ( (v1_xxreal_0 @ A)  &  (v3_xxreal_0 @ A) )  =>  ( ~ ( (v8_ordinal1 @ A) )  &  ( (v1_xxreal_0 @ A)  &  ~ ( (v2_xxreal_0 @ A) ) ) ) ) ) , file(xxreal_0, cc5_xxreal_0)).
thf(cc5_xxreal_2, axiom,  (! [A: $i] :  ( ( (v2_membered @ A)  &  ( (v3_xxreal_2 @ A)  &  (v4_xxreal_2 @ A) ) )  =>  ( (v2_membered @ A)  &  (v5_xxreal_2 @ A) ) ) ) , file(xxreal_2, cc5_xxreal_2)).
thf(cc5_yellow13, axiom,  (! [A: $i] :  ( (l1_pre_topc @ A)  =>  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v2_pre_topc @ A)  &  (v12_pre_topc @ A) ) )  =>  ( ~ ( (v2_struct_0 @ A) )  &  ( (v2_pre_topc @ A)  &  (v9_pre_topc @ A) ) ) ) ) ) , file(yellow13, cc5_yellow13)).
thf(cc6_card_1, axiom,  (! [A: $i] :  ( ( (v3_ordinal1 @ A)  &  (v1_finset_1 @ A) )  =>  (v7_ordinal1 @ A) ) ) , file(card_1, cc6_card_1)).
thf(cc6_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finseq_1 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_finseq_1 @ A) ) ) ) ) , file(finseq_1, cc6_finseq_1)).
thf(cc6_finset_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v5_finset_1 @ A) ) ) , file(finset_1, cc6_finset_1)).
thf(cc6_funct_1, axiom,  (! [A: $i] :  ( ( (v1_zfmisc_1 @ A)  &  ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v3_funct_1 @ A) ) ) ) ) , file(funct_1, cc6_funct_1)).
thf(cc6_membered, axiom,  (! [A: $i] :  ( (v1_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_xcmplx_0 @ B) ) ) ) ) , file(membered, cc6_membered)).
thf(cc6_nat_1, axiom,  (! [A: $i] :  ( ~ ( (v8_ordinal1 @ A) )  =>  ~ ( (v1_xboole_0 @ A) ) ) ) , file(nat_1, cc6_nat_1)).
thf(cc6_ordinal1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v3_ordinal1 @ A) ) ) , file(ordinal1, cc6_ordinal1)).
thf(cc6_pre_topc, axiom,  (! [A: $i] :  ( (l1_pre_topc @ A)  =>  ( ( (v7_pre_topc @ A)  &  (v10_pre_topc @ A) )  =>  (v12_pre_topc @ A) ) ) ) , file(pre_topc, cc6_pre_topc)).
thf(cc6_relat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v5_relat_1 @ B)  @ A) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @ B) )  =>  ( (v5_relat_1 @ C)  @ A) ) ) ) ) , file(relat_1, cc6_relat_1)).
thf(cc6_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( (v7_struct_0 @ A)  =>  (v8_struct_0 @ A) ) ) ) , file(struct_0, cc6_struct_0)).
thf(cc6_tops_1, axiom,  (! [A: $i] :  ( ( (v2_pre_topc @ A)  &  (l1_pre_topc @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  =>  ( ( ( (v3_pre_topc @ B)  @ A)  &  ( (v3_tops_1 @ B)  @ A) )  =>  (v1_xboole_0 @ B) ) ) ) ) ) , file(tops_1, cc6_tops_1)).
thf(cc6_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v1_valued_0 @ A) ) ) ) , file(valued_0, cc6_valued_0)).
thf(cc6_xxreal_0, axiom,  (! [A: $i] :  ( ( ~ ( (v8_ordinal1 @ A) )  &  ( (v1_xxreal_0 @ A)  &  ~ ( (v2_xxreal_0 @ A) ) ) )  =>  ( (v1_xxreal_0 @ A)  &  (v3_xxreal_0 @ A) ) ) ) , file(xxreal_0, cc6_xxreal_0)).
thf(cc6_xxreal_2, axiom,  (! [A: $i] :  ( ( (v3_membered @ A)  &  (v1_finset_1 @ A) )  =>  ( (v3_membered @ A)  &  (v5_xxreal_2 @ A) ) ) ) , file(xxreal_2, cc6_xxreal_2)).
thf(cc6_yellow13, axiom,  (! [A: $i] :  ( (l1_pre_topc @ A)  =>  ( ( (v2_pre_topc @ A)  &  (v11_pre_topc @ A) )  =>  ( (v2_pre_topc @ A)  &  (v8_pre_topc @ A) ) ) ) ) , file(yellow13, cc6_yellow13)).
thf(cc7_card_1, axiom,  (! [A: $i] :  ( ( (v3_card_1 @ A)  @ k5_ordinal1)  =>  (v1_xboole_0 @ A) ) ) , file(card_1, cc7_card_1)).
thf(cc7_finseq_1, axiom,  (! [A: $i] :  ( ( (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) ) ) ) ) ) , file(finseq_1, cc7_finseq_1)).
thf(cc7_finset_1, axiom,  (! [A: $i] :  ( (v5_finset_1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_finset_1 @ B) ) ) ) ) , file(finset_1, cc7_finset_1)).
thf(cc7_funct_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v4_funct_1 @ A) ) ) , file(funct_1, cc7_funct_1)).
thf(cc7_membered, axiom,  (! [A: $i] :  ( (v2_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_xxreal_0 @ B) ) ) ) ) , file(membered, cc7_membered)).
thf(cc7_ordinal1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v7_ordinal1 @ A) ) ) , file(ordinal1, cc7_ordinal1)).
thf(cc7_pre_topc, axiom,  (! [A: $i] :  ( (l1_pre_topc @ A)  =>  ( (v7_pre_topc @ A)  =>  (v6_pre_topc @ A) ) ) ) , file(pre_topc, cc7_pre_topc)).
thf(cc7_relat_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v4_relat_1 @ B)  @ A) )  =>  ( (v1_xboole_0 @ B)  &  ( (v1_relat_1 @ B)  &  ( (v4_relat_1 @ B)  @ A) ) ) ) ) ) ) , file(relat_1, cc7_relat_1)).
thf(cc7_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( ~ ( (v8_struct_0 @ A) )  =>  ~ ( (v7_struct_0 @ A) ) ) ) ) , file(struct_0, cc7_struct_0)).
thf(cc7_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k3_numbers) ) ) ) , file(valued_0, cc7_valued_0)).
thf(cc7_xxreal_0, axiom,  (! [A: $i] :  ( ( (v8_ordinal1 @ A)  &  (v1_xxreal_0 @ A) )  =>  ( (v1_xxreal_0 @ A)  &  ( ~ ( (v2_xxreal_0 @ A) )  &  ~ ( (v3_xxreal_0 @ A) ) ) ) ) ) , file(xxreal_0, cc7_xxreal_0)).
thf(cc7_xxreal_2, axiom,  (! [A: $i] :  ( ( (v5_membered @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  (v4_xxreal_2 @ A) ) )  =>  ( (v5_membered @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  (v2_xxreal_2 @ A) ) ) ) ) , file(xxreal_2, cc7_xxreal_2)).
thf(cc8_card_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  ( (v3_card_1 @ A)  @ k5_ordinal1) ) ) , file(card_1, cc8_card_1)).
thf(cc8_finseq_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v3_finseq_1 @ A) ) ) , file(finseq_1, cc8_finseq_1)).
thf(cc8_finset_1, axiom,  (! [A: $i] :  ( (v5_finset_1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v5_finset_1 @ B) ) ) ) ) , file(finset_1, cc8_finset_1)).
thf(cc8_funct_1, axiom,  (! [A: $i] :  ( (v4_funct_1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  ( (v1_relat_1 @ B)  &  (v1_funct_1 @ B) ) ) ) ) ) , file(funct_1, cc8_funct_1)).
thf(cc8_membered, axiom,  (! [A: $i] :  ( (v3_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_xreal_0 @ B) ) ) ) ) , file(membered, cc8_membered)).
thf(cc8_ordinal1, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k4_ordinal1)  =>  (v7_ordinal1 @ A) ) ) , file(ordinal1, cc8_ordinal1)).
thf(cc8_pre_topc, axiom,  (! [A: $i] :  ( (l1_pre_topc @ A)  =>  ( (v8_pre_topc @ A)  =>  (v7_pre_topc @ A) ) ) ) , file(pre_topc, cc8_pre_topc)).
thf(cc8_relat_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v5_relat_1 @ B)  @ A) )  =>  ( (v1_xboole_0 @ B)  &  ( (v1_relat_1 @ B)  &  ( (v5_relat_1 @ B)  @ A) ) ) ) ) ) ) , file(relat_1, cc8_relat_1)).
thf(cc8_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( (v2_struct_0 @ A)  =>  ( (v13_struct_0 @ A)  @ k5_ordinal1) ) ) ) , file(struct_0, cc8_struct_0)).
thf(cc8_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) ) ) ) , file(valued_0, cc8_valued_0)).
thf(cc8_xxreal_0, axiom,  (! [A: $i] :  ( ( (v1_xxreal_0 @ A)  &  ( ~ ( (v2_xxreal_0 @ A) )  &  ~ ( (v3_xxreal_0 @ A) ) ) )  =>  ( (v8_ordinal1 @ A)  &  (v1_xxreal_0 @ A) ) ) ) , file(xxreal_0, cc8_xxreal_0)).
thf(cc8_xxreal_2, axiom,  (! [A: $i] :  ( ( (v5_membered @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  (v3_xxreal_2 @ A) ) )  =>  ( (v5_membered @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  (v1_xxreal_2 @ A) ) ) ) ) , file(xxreal_2, cc8_xxreal_2)).
thf(cc9_card_1, axiom,  (! [A: $i] :  ( ( (v3_card_1 @ A)  @ np__1)  =>  ( ~ ( (v1_xboole_0 @ A) )  &  (v1_zfmisc_1 @ A) ) ) ) , file(card_1, cc9_card_1)).
thf(cc9_finseq_1, axiom,  (! [A: $i] :  ( (v3_finseq_1 @ A)  =>  (v4_funct_1 @ A) ) ) , file(finseq_1, cc9_finseq_1)).
thf(cc9_finset_1, axiom,  (! [A: $i] :  ( ( (v1_xboole_0 @ A)  &  (v1_relat_1 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v2_finset_1 @ A) ) ) ) , file(finset_1, cc9_finset_1)).
thf(cc9_funct_1, axiom,  (! [A: $i] :  ( (v4_funct_1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v4_funct_1 @ B) ) ) ) ) , file(funct_1, cc9_funct_1)).
thf(cc9_funct_2, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ~ ( (v1_xboole_0 @ B) ) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( ( (v1_funct_1 @ C)  &  ( ( (v1_funct_2 @ C)  @ A)  @ B) )  =>  ( (v1_funct_1 @ C)  &  ( ~ ( (v1_xboole_0 @ C) )  &  ( ( (v1_funct_2 @ C)  @ A)  @ B) ) ) ) ) ) ) ) , file(funct_2, cc9_funct_2)).
thf(cc9_membered, axiom,  (! [A: $i] :  ( (v4_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_rat_1 @ B) ) ) ) ) , file(membered, cc9_membered)).
thf(cc9_ordinal1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v6_ordinal1 @ A) ) ) , file(ordinal1, cc9_ordinal1)).
thf(cc9_pre_topc, axiom,  (! [A: $i] :  ( (l1_pre_topc @ A)  =>  ( (v2_struct_0 @ A)  =>  (v6_pre_topc @ A) ) ) ) , file(pre_topc, cc9_pre_topc)).
thf(cc9_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( ( (v13_struct_0 @ A)  @ k5_ordinal1)  =>  (v2_struct_0 @ A) ) ) ) , file(struct_0, cc9_struct_0)).
thf(cc9_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_xboole_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) ) ) ) , file(valued_0, cc9_valued_0)).
thf(cc9_xxreal_2, axiom,  (! [A: $i] :  ( (v6_membered @ A)  =>  ( (v6_membered @ A)  &  (v3_xxreal_2 @ A) ) ) ) , file(xxreal_2, cc9_xxreal_2)).
thf(commutativity_k3_metric_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v8_metric_1 @ A)  &  (l1_metric_1 @ A) )  &  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @ C)  @  (u1_struct_0 @ A) ) ) )  =>  ( ( ( (k3_metric_1 @ A)  @ B)  @ C)  =  ( ( (k3_metric_1 @ A)  @ C)  @ B) ) ) ) , file(metric_1, k3_metric_1)).
thf(connectedness_r1_xxreal_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xxreal_0 @ A)  &  (v1_xxreal_0 @ B) )  =>  ( ( (r1_xxreal_0 @ A)  @ B)  |  ( (r1_xxreal_0 @ B)  @ A) ) ) ) , file(xxreal_0, r1_xxreal_0)).
thf(d13_ordinal1, axiom,  (k5_ordinal1 = k1_xboole_0) , file(ordinal1, d13_ordinal1)).
thf(d1_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (k1_euclid @ A)  =  ( (k4_finseq_2 @ A)  @ k1_numbers) ) ) ) , file(euclid, d1_euclid)).
thf(d1_metric_1, axiom,  (! [A: $i] :  ( (l1_metric_1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (u1_struct_0 @ A) )  =>  ( ( ( (k1_metric_1 @ A)  @ B)  @ C)  =  ( ( (k1_binop_1 @  (u1_metric_1 @ A) )  @ B)  @ C) ) ) ) ) ) ) ) , file(metric_1, d1_metric_1)).
thf(d3_tarski, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (r1_tarski @ A)  @ B)  <=>  (! [C: $i] :  ( ( (r2_hidden @ C)  @ A)  =>  ( (r2_hidden @ C)  @ B) ) ) ) ) ) , file(tarski, d3_tarski)).
thf(d7_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (k14_euclid @ A)  =  ( (g1_metric_1 @  (k1_euclid @ A) )  @  (k13_euclid @ A) ) ) ) ) , file(euclid, d7_euclid)).
thf(d8_tbsp_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v6_metric_1 @ A)  &  (l1_metric_1 @ A) ) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  =>  ( ( (v6_tbsp_1 @ B)  @ A)  =>  (! [C: $i] :  ( (v1_xreal_0 @ C)  =>  ( ( ~ ( (B = k1_xboole_0) )  =>  ( (C =  ( (k2_tbsp_1 @ A)  @ B) )  <=>  ( (! [D: $i] :  ( ( (m1_subset_1 @ D)  @  (u1_struct_0 @ A) )  =>  (! [E: $i] :  ( ( (m1_subset_1 @ E)  @  (u1_struct_0 @ A) )  =>  ( ( ( (r2_tarski @ D)  @ B)  &  ( (r2_tarski @ E)  @ B) )  =>  ( (r1_xxreal_0 @  ( ( (k1_metric_1 @ A)  @ D)  @ E) )  @ C) ) ) ) ) )  &  (! [D: $i] :  ( (v1_xreal_0 @ D)  =>  ( (! [E: $i] :  ( ( (m1_subset_1 @ E)  @  (u1_struct_0 @ A) )  =>  (! [F: $i] :  ( ( (m1_subset_1 @ F)  @  (u1_struct_0 @ A) )  =>  ( ( ( (r2_tarski @ E)  @ B)  &  ( (r2_tarski @ F)  @ B) )  =>  ( (r1_xxreal_0 @  ( ( (k1_metric_1 @ A)  @ E)  @ F) )  @ D) ) ) ) ) )  =>  ( (r1_xxreal_0 @ C)  @ D) ) ) ) ) ) )  &  ( (B = k1_xboole_0)  =>  ( (C =  ( (k2_tbsp_1 @ A)  @ B) )  <=>  (C = k5_numbers) ) ) ) ) ) ) ) ) ) ) , file(tbsp_1, d8_tbsp_1)).
thf(dt_g1_metric_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_funct_1 @ B)  &  ( ( ( (v1_funct_2 @ B)  @  ( (k2_zfmisc_1 @ A)  @ A) )  @ k1_numbers)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) )  @ k1_numbers) ) ) ) )  =>  ( (v1_metric_1 @  ( (g1_metric_1 @ A)  @ B) )  &  (l1_metric_1 @  ( (g1_metric_1 @ A)  @ B) ) ) ) ) , file(metric_1, g1_metric_1)).
thf(dt_g1_rltopsp1, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( ( (m1_subset_1 @ B)  @ A)  &  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @  ( (k2_zfmisc_1 @ A)  @ A) )  @ A)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) )  @ A) ) ) ) )  &  ( ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @  ( (k2_zfmisc_1 @ k1_numbers)  @ A) )  @ A)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ A) )  @ A) ) ) ) )  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  (k1_zfmisc_1 @ A) ) ) ) ) )  =>  ( (v5_rltopsp1 @  ( ( ( ( (g1_rltopsp1 @ A)  @ B)  @ C)  @ D)  @ E) )  &  (l1_rltopsp1 @  ( ( ( ( (g1_rltopsp1 @ A)  @ B)  @ C)  @ D)  @ E) ) ) ) ) , file(rltopsp1, g1_rltopsp1)).
thf(dt_k13_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v1_funct_1 @  (k13_euclid @ A) )  &  ( ( ( (v1_funct_2 @  (k13_euclid @ A) )  @  ( (k2_zfmisc_1 @  (k1_euclid @ A) )  @  (k1_euclid @ A) ) )  @ k1_numbers)  &  ( (m1_subset_1 @  (k13_euclid @ A) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @  (k1_euclid @ A) )  @  (k1_euclid @ A) ) )  @ k1_numbers) ) ) ) ) ) ) , file(euclid, k13_euclid)).
thf(dt_k14_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v1_metric_1 @  (k14_euclid @ A) )  &  ( (v6_metric_1 @  (k14_euclid @ A) )  &  ( (v7_metric_1 @  (k14_euclid @ A) )  &  ( (v8_metric_1 @  (k14_euclid @ A) )  &  ( (v9_metric_1 @  (k14_euclid @ A) )  &  (l1_metric_1 @  (k14_euclid @ A) ) ) ) ) ) ) ) ) , file(euclid, k14_euclid)).
thf(dt_k15_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v5_rltopsp1 @  (k15_euclid @ A) )  &  (l1_rltopsp1 @  (k15_euclid @ A) ) ) ) ) , file(euclid, k15_euclid)).
thf(dt_k1_binop_1, axiom, $true, file(binop_1, k1_binop_1)).
thf(dt_k1_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (m1_finseq_2 @  (k1_euclid @ A) )  @ k1_numbers) ) ) , file(euclid, k1_euclid)).
thf(dt_k1_metric_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (l1_metric_1 @ A)  &  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @ C)  @  (u1_struct_0 @ A) ) ) )  =>  (v1_xreal_0 @  ( ( (k1_metric_1 @ A)  @ B)  @ C) ) ) ) , file(metric_1, k1_metric_1)).
thf(dt_k1_numbers, axiom, $true, file(numbers, k1_numbers)).
thf(dt_k1_xboole_0, axiom, $true, file(xboole_0, k1_xboole_0)).
thf(dt_k1_zfmisc_1, axiom, $true, file(zfmisc_1, k1_zfmisc_1)).
thf(dt_k2_tbsp_1, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v6_metric_1 @ A)  &  (l1_metric_1 @ A) ) )  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) ) )  =>  (v1_xreal_0 @  ( (k2_tbsp_1 @ A)  @ B) ) ) ) , file(tbsp_1, k2_tbsp_1)).
thf(dt_k2_zfmisc_1, axiom, $true, file(zfmisc_1, k2_zfmisc_1)).
thf(dt_k3_convex1, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_rlvect_1 @ A) )  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) ) )  =>  ( ( (v1_convex1 @  ( (k3_convex1 @ A)  @ B) )  @ A)  &  ( (m1_subset_1 @  ( (k3_convex1 @ A)  @ B) )  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) ) ) ) ) , file(convex1, k3_convex1)).
thf(dt_k3_metric_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v8_metric_1 @ A)  &  (l1_metric_1 @ A) )  &  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @ C)  @  (u1_struct_0 @ A) ) ) )  =>  (v1_xreal_0 @  ( ( (k3_metric_1 @ A)  @ B)  @ C) ) ) ) , file(metric_1, k3_metric_1)).
thf(dt_k3_numbers, axiom, $true, file(numbers, k3_numbers)).
thf(dt_k4_finseq_2, axiom,  (! [A: $i, B: $i] :  ( (v7_ordinal1 @ A)  =>  ( (m1_finseq_2 @  ( (k4_finseq_2 @ A)  @ B) )  @ B) ) ) , file(finseq_2, k4_finseq_2)).
thf(dt_k4_numbers, axiom, $true, file(numbers, k4_numbers)).
thf(dt_k4_ordinal1, axiom, $true, file(ordinal1, k4_ordinal1)).
thf(dt_k5_numbers, axiom,  ( (m1_subset_1 @ k5_numbers)  @ k4_ordinal1) , file(numbers, k5_numbers)).
thf(dt_k5_ordinal1, axiom, $true, file(ordinal1, k5_ordinal1)).
thf(dt_k9_metric_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (l1_metric_1 @ A)  &  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  &  (v1_xreal_0 @ C) ) )  =>  ( (m1_subset_1 @  ( ( (k9_metric_1 @ A)  @ B)  @ C) )  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) ) ) ) , file(metric_1, k9_metric_1)).
thf(dt_l1_algstr_0, axiom,  (! [A: $i] :  ( (l1_algstr_0 @ A)  =>  (l1_struct_0 @ A) ) ) , file(algstr_0, l1_algstr_0)).
thf(dt_l1_metric_1, axiom,  (! [A: $i] :  ( (l1_metric_1 @ A)  =>  (l1_struct_0 @ A) ) ) , file(metric_1, l1_metric_1)).
thf(dt_l1_pre_topc, axiom,  (! [A: $i] :  ( (l1_pre_topc @ A)  =>  (l1_struct_0 @ A) ) ) , file(pre_topc, l1_pre_topc)).
thf(dt_l1_rltopsp1, axiom,  (! [A: $i] :  ( (l1_rltopsp1 @ A)  =>  ( (l1_rlvect_1 @ A)  &  (l1_pre_topc @ A) ) ) ) , file(rltopsp1, l1_rltopsp1)).
thf(dt_l1_rlvect_1, axiom,  (! [A: $i] :  ( (l1_rlvect_1 @ A)  =>  (l2_algstr_0 @ A) ) ) , file(rlvect_1, l1_rlvect_1)).
thf(dt_l1_struct_0, axiom, $true, file(struct_0, l1_struct_0)).
thf(dt_l2_algstr_0, axiom,  (! [A: $i] :  ( (l2_algstr_0 @ A)  =>  ( (l2_struct_0 @ A)  &  (l1_algstr_0 @ A) ) ) ) , file(algstr_0, l2_algstr_0)).
thf(dt_l2_struct_0, axiom,  (! [A: $i] :  ( (l2_struct_0 @ A)  =>  (l1_struct_0 @ A) ) ) , file(struct_0, l2_struct_0)).
thf(dt_m1_finseq_2, axiom, $true, file(finseq_2, m1_finseq_2)).
thf(dt_m1_subset_1, axiom, $true, file(subset_1, m1_subset_1)).
thf(dt_u1_algstr_0, axiom,  (! [A: $i] :  ( (l1_algstr_0 @ A)  =>  ( (v1_funct_1 @  (u1_algstr_0 @ A) )  &  ( ( ( (v1_funct_2 @  (u1_algstr_0 @ A) )  @  ( (k2_zfmisc_1 @  (u1_struct_0 @ A) )  @  (u1_struct_0 @ A) ) )  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @  (u1_algstr_0 @ A) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @  (u1_struct_0 @ A) )  @  (u1_struct_0 @ A) ) )  @  (u1_struct_0 @ A) ) ) ) ) ) ) ) , file(algstr_0, u1_algstr_0)).
thf(dt_u1_metric_1, axiom,  (! [A: $i] :  ( (l1_metric_1 @ A)  =>  ( (v1_funct_1 @  (u1_metric_1 @ A) )  &  ( ( ( (v1_funct_2 @  (u1_metric_1 @ A) )  @  ( (k2_zfmisc_1 @  (u1_struct_0 @ A) )  @  (u1_struct_0 @ A) ) )  @ k1_numbers)  &  ( (m1_subset_1 @  (u1_metric_1 @ A) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @  (u1_struct_0 @ A) )  @  (u1_struct_0 @ A) ) )  @ k1_numbers) ) ) ) ) ) ) , file(metric_1, u1_metric_1)).
thf(dt_u1_pre_topc, axiom,  (! [A: $i] :  ( (l1_pre_topc @ A)  =>  ( (m1_subset_1 @  (u1_pre_topc @ A) )  @  (k1_zfmisc_1 @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) ) ) ) ) , file(pre_topc, u1_pre_topc)).
thf(dt_u1_rlvect_1, axiom,  (! [A: $i] :  ( (l1_rlvect_1 @ A)  =>  ( (v1_funct_1 @  (u1_rlvect_1 @ A) )  &  ( ( ( (v1_funct_2 @  (u1_rlvect_1 @ A) )  @  ( (k2_zfmisc_1 @ k1_numbers)  @  (u1_struct_0 @ A) ) )  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @  (u1_rlvect_1 @ A) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @  (u1_struct_0 @ A) ) )  @  (u1_struct_0 @ A) ) ) ) ) ) ) ) , file(rlvect_1, u1_rlvect_1)).
thf(dt_u1_struct_0, axiom, $true, file(struct_0, u1_struct_0)).
thf(dt_u2_struct_0, axiom,  (! [A: $i] :  ( (l2_struct_0 @ A)  =>  ( (m1_subset_1 @  (u2_struct_0 @ A) )  @  (u1_struct_0 @ A) ) ) ) , file(struct_0, u2_struct_0)).
thf(existence_l1_algstr_0, axiom,  (? [A: $i] :  (l1_algstr_0 @ A) ) , file(algstr_0, l1_algstr_0)).
thf(existence_l1_metric_1, axiom,  (? [A: $i] :  (l1_metric_1 @ A) ) , file(metric_1, l1_metric_1)).
thf(existence_l1_pre_topc, axiom,  (? [A: $i] :  (l1_pre_topc @ A) ) , file(pre_topc, l1_pre_topc)).
thf(existence_l1_rltopsp1, axiom,  (? [A: $i] :  (l1_rltopsp1 @ A) ) , file(rltopsp1, l1_rltopsp1)).
thf(existence_l1_rlvect_1, axiom,  (? [A: $i] :  (l1_rlvect_1 @ A) ) , file(rlvect_1, l1_rlvect_1)).
thf(existence_l1_struct_0, axiom,  (? [A: $i] :  (l1_struct_0 @ A) ) , file(struct_0, l1_struct_0)).
thf(existence_l2_algstr_0, axiom,  (? [A: $i] :  (l2_algstr_0 @ A) ) , file(algstr_0, l2_algstr_0)).
thf(existence_l2_struct_0, axiom,  (? [A: $i] :  (l2_struct_0 @ A) ) , file(struct_0, l2_struct_0)).
thf(existence_m1_finseq_2, axiom,  (! [A: $i] :  (? [B: $i] :  ( (m1_finseq_2 @ B)  @ A) ) ) , file(finseq_2, m1_finseq_2)).
thf(existence_m1_subset_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (m1_subset_1 @ B)  @ A) ) ) , file(subset_1, m1_subset_1)).
thf(fc10_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v3_valued_2 @  (k1_euclid @ A) ) ) ) , file(euclid, fc10_euclid)).
thf(fc10_subset_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ~ ( (v1_xboole_0 @ B) ) )  =>  ~ ( (v1_xboole_0 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) ) , file(subset_1, fc10_subset_1)).
thf(fc10_toprealc, axiom,  ( (v7_struct_0 @  (k15_euclid @ k5_numbers) )  &  (v5_rltopsp1 @  (k15_euclid @ k5_numbers) ) ) , file(toprealc, fc10_toprealc)).
thf(fc11_toprealc, axiom,  (! [A: $i] :  ( ( (v1_toprealc @ A)  &  (l1_struct_0 @ A) )  =>  (v1_valued_2 @  (u1_struct_0 @ A) ) ) ) , file(toprealc, fc11_toprealc)).
thf(fc11_xxreal_2, axiom,  ( ~ ( (v3_xxreal_2 @ k1_numbers) )  &  ~ ( (v4_xxreal_2 @ k1_numbers) ) ) , file(xxreal_2, fc11_xxreal_2)).
thf(fc12_card_1, axiom,  (! [A: $i] :  ( ~ ( (v1_finset_1 @ A) )  =>  ~ ( (v1_finset_1 @  (k1_zfmisc_1 @ A) ) ) ) ) , file(card_1, fc12_card_1)).
thf(fc12_toprealc, axiom,  (! [A: $i] :  ( ( (v2_toprealc @ A)  &  (l1_struct_0 @ A) )  =>  (v3_valued_2 @  (u1_struct_0 @ A) ) ) ) , file(toprealc, fc12_toprealc)).
thf(fc13_card_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_finset_1 @ A) )  &  ~ ( (v1_xboole_0 @ B) ) )  =>  ~ ( (v1_finset_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) ) , file(card_1, fc13_card_1)).
thf(fc14_card_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_finset_1 @ A) )  &  ~ ( (v1_xboole_0 @ B) ) )  =>  ~ ( (v1_finset_1 @  ( (k2_zfmisc_1 @ B)  @ A) ) ) ) ) , file(card_1, fc14_card_1)).
thf(fc14_finset_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_finset_1 @ A)  &  (v1_finset_1 @ B) )  =>  (v1_finset_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) , file(finset_1, fc14_finset_1)).
thf(fc17_finset_1, axiom,  (! [A: $i] :  ( (v1_finset_1 @ A)  =>  (v1_finset_1 @  (k1_zfmisc_1 @ A) ) ) ) , file(finset_1, fc17_finset_1)).
thf(fc17_toprealc, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v1_metric_1 @  (k14_euclid @ A) )  &  ( (v6_metric_1 @  (k14_euclid @ A) )  &  ( (v7_metric_1 @  (k14_euclid @ A) )  &  ( (v8_metric_1 @  (k14_euclid @ A) )  &  ( (v9_metric_1 @  (k14_euclid @ A) )  &  (v2_toprealc @  (k14_euclid @ A) ) ) ) ) ) ) ) ) , file(toprealc, fc17_toprealc)).
thf(fc17_xxreal_2, axiom,  (v6_xxreal_2 @ k1_numbers) , file(xxreal_2, fc17_xxreal_2)).
thf(fc19_struct_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_card_1 @ A)  &  ( ( (v13_struct_0 @ B)  @ A)  &  (l1_struct_0 @ B) ) )  =>  ( (v3_card_1 @  (u1_struct_0 @ B) )  @ A) ) ) , file(struct_0, fc19_struct_0)).
thf(fc1_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ~ ( (v1_xboole_0 @  (k1_euclid @ A) ) ) ) ) , file(euclid, fc1_euclid)).
thf(fc1_jordan, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v6_metric_1 @ A)  &  ( (v8_metric_1 @ A)  &  ( (v9_metric_1 @ A)  &  (l1_metric_1 @ A) ) ) )  &  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @ C)  @  (u1_struct_0 @ A) ) ) )  =>  ( (v1_xreal_0 @  ( ( (k1_metric_1 @ A)  @ B)  @ C) )  &  ~ ( (v3_xxreal_0 @  ( ( (k1_metric_1 @ A)  @ B)  @ C) ) ) ) ) ) , file(jordan, fc1_jordan)).
thf(fc1_jordan2c, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v5_rltopsp1 @  (k15_euclid @ A) )  &  ( (v6_rltopsp1 @  (k15_euclid @ A) )  &  (v7_rltopsp1 @  (k15_euclid @ A) ) ) ) ) ) , file(jordan2c, fc1_jordan2c)).
thf(fc1_numbers, axiom,  ~ ( (v1_xboole_0 @ k1_numbers) ) , file(numbers, fc1_numbers)).
thf(fc1_pre_topc, axiom,  (! [A: $i] :  ( ( (v2_pre_topc @ A)  &  (l1_pre_topc @ A) )  =>  ~ ( (v1_xboole_0 @  (u1_pre_topc @ A) ) ) ) ) , file(pre_topc, fc1_pre_topc)).
thf(fc1_rlaffin1, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_rlvect_1 @ A) )  &  ( (v1_xboole_0 @ B)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) ) ) )  =>  ( (v1_xboole_0 @  ( (k3_convex1 @ A)  @ B) )  &  ( (v1_convex1 @  ( (k3_convex1 @ A)  @ B) )  @ A) ) ) ) , file(rlaffin1, fc1_rlaffin1)).
thf(fc1_rlaffin3, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v5_rltopsp1 @  (k15_euclid @ A) )  &  ( (v6_rltopsp1 @  (k15_euclid @ A) )  &  (v7_rltopsp1 @  (k15_euclid @ A) ) ) ) ) ) , file(rlaffin3, fc1_rlaffin3)).
thf(fc1_struct_0, axiom,  (! [A: $i] :  ( ( (v2_struct_0 @ A)  &  (l1_struct_0 @ A) )  =>  (v1_xboole_0 @  (u1_struct_0 @ A) ) ) ) , file(struct_0, fc1_struct_0)).
thf(fc1_subset_1, axiom,  (! [A: $i] :  ~ ( (v1_xboole_0 @  (k1_zfmisc_1 @ A) ) ) ) , file(subset_1, fc1_subset_1)).
thf(fc1_xboole_0, axiom,  (v1_xboole_0 @ k1_xboole_0) , file(xboole_0, fc1_xboole_0)).
thf(fc20_euclid_9, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v2_monoid_0 @  (k14_euclid @ A) )  &  ( (v1_metric_1 @  (k14_euclid @ A) )  &  ( (v6_metric_1 @  (k14_euclid @ A) )  &  ( (v7_metric_1 @  (k14_euclid @ A) )  &  ( (v8_metric_1 @  (k14_euclid @ A) )  &  (v9_metric_1 @  (k14_euclid @ A) ) ) ) ) ) ) ) ) , file(euclid_9, fc20_euclid_9)).
thf(fc2_rlaffin1, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_rlvect_1 @ A) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) ) ) )  =>  ( ~ ( (v1_xboole_0 @  ( (k3_convex1 @ A)  @ B) ) )  &  ( (v1_convex1 @  ( (k3_convex1 @ A)  @ B) )  @ A) ) ) ) , file(rlaffin1, fc2_rlaffin1)).
thf(fc2_rlaffin3, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v5_rltopsp1 @  (k15_euclid @ A) )  &  (v1_rlvect_5 @  (k15_euclid @ A) ) ) ) ) , file(rlaffin3, fc2_rlaffin3)).
thf(fc2_struct_0, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_struct_0 @ A) )  =>  ~ ( (v1_xboole_0 @  (u1_struct_0 @ A) ) ) ) ) , file(struct_0, fc2_struct_0)).
thf(fc31_finset_1, axiom,  (! [A: $i] :  ( (v1_finset_1 @ A)  =>  (v5_finset_1 @  (k1_zfmisc_1 @ A) ) ) ) , file(finset_1, fc31_finset_1)).
thf(fc3_membered, axiom,  (v3_membered @ k1_numbers) , file(membered, fc3_membered)).
thf(fc3_numbers, axiom,  ~ ( (v1_xboole_0 @ k3_numbers) ) , file(numbers, fc3_numbers)).
thf(fc4_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( ~ ( (v2_struct_0 @  (k14_euclid @ A) ) )  &  ( (v1_metric_1 @  (k14_euclid @ A) )  &  ( (v6_metric_1 @  (k14_euclid @ A) )  &  ( (v7_metric_1 @  (k14_euclid @ A) )  &  ( (v8_metric_1 @  (k14_euclid @ A) )  &  (v9_metric_1 @  (k14_euclid @ A) ) ) ) ) ) ) ) ) , file(euclid, fc4_euclid)).
thf(fc4_membered, axiom,  (v4_membered @ k3_numbers) , file(membered, fc4_membered)).
thf(fc4_numbers, axiom,  ~ ( (v1_xboole_0 @ k4_numbers) ) , file(numbers, fc4_numbers)).
thf(fc4_topmetr, axiom,  (! [A: $i] :  ( ( (v3_topmetr @ A)  &  (l1_struct_0 @ A) )  =>  (v3_membered @  (u1_struct_0 @ A) ) ) ) , file(topmetr, fc4_topmetr)).
thf(fc56_membered, axiom,  (v7_membered @ k1_numbers) , file(membered, fc56_membered)).
thf(fc57_membered, axiom,  (v7_membered @ k3_numbers) , file(membered, fc57_membered)).
thf(fc58_membered, axiom,  (v7_membered @ k4_numbers) , file(membered, fc58_membered)).
thf(fc59_membered, axiom,  (v7_membered @ k4_ordinal1) , file(membered, fc59_membered)).
thf(fc5_compts_1, axiom,  (! [A: $i] :  ( (l1_pre_topc @ A)  =>  ( (v1_tops_2 @  (u1_pre_topc @ A) )  @ A) ) ) , file(compts_1, fc5_compts_1)).
thf(fc5_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( ~ ( (v2_struct_0 @  (k15_euclid @ A) ) )  &  (v5_rltopsp1 @  (k15_euclid @ A) ) ) ) ) , file(euclid, fc5_euclid)).
thf(fc5_finseq_2, axiom,  (! [A: $i, B: $i] :  ( ( (v7_ordinal1 @ A)  &  ~ ( (v1_xboole_0 @ B) ) )  =>  ~ ( (v1_xboole_0 @  ( (k4_finseq_2 @ A)  @ B) ) ) ) ) , file(finseq_2, fc5_finseq_2)).
thf(fc5_membered, axiom,  (v5_membered @ k4_numbers) , file(membered, fc5_membered)).
thf(fc5_topdim_2, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v5_rltopsp1 @  (k15_euclid @ A) )  &  (v3_topdim_1 @  (k15_euclid @ A) ) ) ) ) , file(topdim_2, fc5_topdim_2)).
thf(fc6_card_1, axiom,  (v1_card_1 @ k4_ordinal1) , file(card_1, fc6_card_1)).
thf(fc6_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v2_pre_topc @  (k15_euclid @ A) )  &  ( (v13_algstr_0 @  (k15_euclid @ A) )  &  ( (v2_rlvect_1 @  (k15_euclid @ A) )  &  ( (v3_rlvect_1 @  (k15_euclid @ A) )  &  ( (v4_rlvect_1 @  (k15_euclid @ A) )  &  ( (v5_rlvect_1 @  (k15_euclid @ A) )  &  ( (v6_rlvect_1 @  (k15_euclid @ A) )  &  ( (v7_rlvect_1 @  (k15_euclid @ A) )  &  ( (v8_rlvect_1 @  (k15_euclid @ A) )  &  (v5_rltopsp1 @  (k15_euclid @ A) ) ) ) ) ) ) ) ) ) ) ) ) , file(euclid, fc6_euclid)).
thf(fc6_membered, axiom,  (v6_membered @ k4_ordinal1) , file(membered, fc6_membered)).
thf(fc6_numbers, axiom,  ~ ( (v1_finset_1 @ k4_numbers) ) , file(numbers, fc6_numbers)).
thf(fc6_ordinal1, axiom,  ( ~ ( (v1_xboole_0 @ k4_ordinal1) )  &  (v3_ordinal1 @ k4_ordinal1) ) , file(ordinal1, fc6_ordinal1)).
thf(fc6_relat_1, axiom,  (! [A: $i, B: $i] :  (v1_relat_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) , file(relat_1, fc6_relat_1)).
thf(fc6_struct_0, axiom,  (! [A: $i] :  ( ( ~ ( (v7_struct_0 @ A) )  &  (l1_struct_0 @ A) )  =>  ~ ( (v1_zfmisc_1 @  (u1_struct_0 @ A) ) ) ) ) , file(struct_0, fc6_struct_0)).
thf(fc7_card_1, axiom,  (v2_card_1 @ k4_ordinal1) , file(card_1, fc7_card_1)).
thf(fc7_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v2_monoid_0 @  (k15_euclid @ A) )  &  (v5_rltopsp1 @  (k15_euclid @ A) ) ) ) ) , file(euclid, fc7_euclid)).
thf(fc7_numbers, axiom,  ~ ( (v1_finset_1 @ k3_numbers) ) , file(numbers, fc7_numbers)).
thf(fc7_rlaffin3, axiom,  (! [A: $i, B: $i] :  ( ( (v7_ordinal1 @ A)  &  ( ( (v1_rlaffin1 @ B)  @  (k15_euclid @ A) )  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @  (k15_euclid @ A) ) ) ) ) )  =>  ( ( (v1_convex1 @  ( (k3_convex1 @  (k15_euclid @ A) )  @ B) )  @  (k15_euclid @ A) )  &  ( (v4_pre_topc @  ( (k3_convex1 @  (k15_euclid @ A) )  @ B) )  @  (k15_euclid @ A) ) ) ) ) , file(rlaffin3, fc7_rlaffin3)).
thf(fc7_struct_0, axiom,  (! [A: $i] :  ( ( (v7_struct_0 @ A)  &  (l1_struct_0 @ A) )  =>  (v1_zfmisc_1 @  (u1_struct_0 @ A) ) ) ) , file(struct_0, fc7_struct_0)).
thf(fc85_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v1_membered @ B)  =>  (v1_valued_0 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) , file(valued_0, fc85_valued_0)).
thf(fc86_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v2_membered @ B)  =>  (v2_valued_0 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) , file(valued_0, fc86_valued_0)).
thf(fc87_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v3_membered @ B)  =>  (v3_valued_0 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) , file(valued_0, fc87_valued_0)).
thf(fc88_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v4_membered @ B)  =>  ( (v5_relat_1 @  ( (k2_zfmisc_1 @ A)  @ B) )  @ k3_numbers) ) ) , file(valued_0, fc88_valued_0)).
thf(fc89_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v5_membered @ B)  =>  ( (v5_relat_1 @  ( (k2_zfmisc_1 @ A)  @ B) )  @ k4_numbers) ) ) , file(valued_0, fc89_valued_0)).
thf(fc8_euclid, axiom,  (! [A: $i, B: $i] :  ( (v7_ordinal1 @ A)  =>  (v3_finseq_1 @  ( (k4_finseq_2 @ A)  @ B) ) ) ) , file(euclid, fc8_euclid)).
thf(fc8_numbers, axiom,  ~ ( (v1_finset_1 @ k1_numbers) ) , file(numbers, fc8_numbers)).
thf(fc8_ordinal1, axiom,  (v7_ordinal1 @ k5_ordinal1) , file(ordinal1, fc8_ordinal1)).
thf(fc8_struct_0, axiom,  (! [A: $i] :  ( ( (v8_struct_0 @ A)  &  (l1_struct_0 @ A) )  =>  (v1_finset_1 @  (u1_struct_0 @ A) ) ) ) , file(struct_0, fc8_struct_0)).
thf(fc8_toprealc, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v5_rltopsp1 @  (k15_euclid @ A) )  &  (v2_toprealc @  (k15_euclid @ A) ) ) ) ) , file(toprealc, fc8_toprealc)).
thf(fc90_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v6_membered @ B)  =>  (v4_valued_0 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) , file(valued_0, fc90_valued_0)).
thf(fc9_card_1, axiom,  ~ ( (v1_finset_1 @ k4_ordinal1) ) , file(card_1, fc9_card_1)).
thf(fc9_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v3_finseq_1 @  (k1_euclid @ A) ) ) ) , file(euclid, fc9_euclid)).
thf(fc9_ordinal1, axiom,  (v8_ordinal1 @ k5_ordinal1) , file(ordinal1, fc9_ordinal1)).
thf(fc9_struct_0, axiom,  (! [A: $i] :  ( ( ~ ( (v8_struct_0 @ A) )  &  (l1_struct_0 @ A) )  =>  ~ ( (v1_finset_1 @  (u1_struct_0 @ A) ) ) ) ) , file(struct_0, fc9_struct_0)).
thf(fc9_toprealc, axiom,  ( (v5_rltopsp1 @  (k15_euclid @ k5_numbers) )  &  (v3_topmetr @  (k15_euclid @ k5_numbers) ) ) , file(toprealc, fc9_toprealc)).
thf(free_g1_metric_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_funct_1 @ B)  &  ( ( ( (v1_funct_2 @ B)  @  ( (k2_zfmisc_1 @ A)  @ A) )  @ k1_numbers)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) )  @ k1_numbers) ) ) ) )  =>  (! [C: $i, D: $i] :  ( ( ( (g1_metric_1 @ A)  @ B)  =  ( (g1_metric_1 @ C)  @ D) )  =>  ( (A = C)  &  (B = D) ) ) ) ) ) , file(metric_1, g1_metric_1)).
thf(free_g1_rltopsp1, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( ( (m1_subset_1 @ B)  @ A)  &  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @  ( (k2_zfmisc_1 @ A)  @ A) )  @ A)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) )  @ A) ) ) ) )  &  ( ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @  ( (k2_zfmisc_1 @ k1_numbers)  @ A) )  @ A)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ A) )  @ A) ) ) ) )  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  (k1_zfmisc_1 @ A) ) ) ) ) )  =>  (! [F: $i, G: $i, H: $i, I: $i, J: $i] :  ( ( ( ( ( ( (g1_rltopsp1 @ A)  @ B)  @ C)  @ D)  @ E)  =  ( ( ( ( (g1_rltopsp1 @ F)  @ G)  @ H)  @ I)  @ J) )  =>  ( (A = F)  &  ( (B = G)  &  ( (C = H)  &  ( (D = I)  &  (E = J) ) ) ) ) ) ) ) ) , file(rltopsp1, g1_rltopsp1)).
thf(rc10_finset_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_finset_1 @ A) ) ) ) ) , file(finset_1, rc10_finset_1)).
thf(rc10_ordinal1, axiom,  (? [A: $i] :  (v8_ordinal1 @ A) ) , file(ordinal1, rc10_ordinal1)).
thf(rc10_pre_topc, axiom,  (! [A: $i] :  ( ( (v2_pre_topc @ A)  &  (l1_pre_topc @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  &  ( (v3_pre_topc @ B)  @ A) ) ) ) ) , file(pre_topc, rc10_pre_topc)).
thf(rc11_finseq_1, axiom,  (? [A: $i] :  ( (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) ) ) ) ) ) ) ) , file(finseq_1, rc11_finseq_1)).
thf(rc11_ordinal1, axiom,  (? [A: $i] :  ~ ( (v8_ordinal1 @ A) ) ) , file(ordinal1, rc11_ordinal1)).
thf(rc12_ordinal1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ~ ( (v10_ordinal1 @ A) ) ) ) , file(ordinal1, rc12_ordinal1)).
thf(rc13_finseq_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k4_ordinal1)  &  ( (v1_funct_1 @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_finset_1 @ A)  &  ( (v4_valued_0 @ A)  &  ( (v1_finseq_1 @ A)  &  (v2_finseq_1 @ A) ) ) ) ) ) ) ) ) , file(finseq_1, rc13_finseq_1)).
thf(rc13_ordinal1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  (v9_ordinal1 @ A) ) ) , file(ordinal1, rc13_ordinal1)).
thf(rc14_ordinal1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ~ ( (v9_ordinal1 @ A) ) ) ) , file(ordinal1, rc14_ordinal1)).
thf(rc1_card_1, axiom,  (? [A: $i] :  (v1_card_1 @ A) ) , file(card_1, rc1_card_1)).
thf(rc1_compts_1, axiom,  (? [A: $i] :  ( (l1_pre_topc @ A)  &  ( ~ ( (v2_struct_0 @ A) )  &  ( (v2_pre_topc @ A)  &  (v8_pre_topc @ A) ) ) ) ) , file(compts_1, rc1_compts_1)).
thf(rc1_finseq_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( ( (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) ) ) ) ) ) , file(finseq_1, rc1_finseq_1)).
thf(rc1_finseq_2, axiom,  (! [A: $i] :  (? [B: $i] :  ( ( (m1_finseq_2 @ B)  @ A)  &  ~ ( (v1_xboole_0 @ B) ) ) ) ) , file(finseq_2, rc1_finseq_2)).
thf(rc1_finset_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v1_finset_1 @ A) ) ) , file(finset_1, rc1_finset_1)).
thf(rc1_funct_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) ) ) , file(funct_1, rc1_funct_1)).
thf(rc1_funct_2, axiom,  (! [A: $i, B: $i] :  (? [C: $i] :  ( ( (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) ) ) ) ) ) ) ) , file(funct_2, rc1_funct_2)).
thf(rc1_int_1, axiom,  (? [A: $i] :  ( (v1_xxreal_0 @ A)  &  ( (v1_xcmplx_0 @ A)  &  ( (v1_xreal_0 @ A)  &  (v1_int_1 @ A) ) ) ) ) , file(int_1, rc1_int_1)).
thf(rc1_jordan, axiom,  (! [A: $i] :  ( ( (v7_ordinal1 @ A)  &  ~ ( (v8_ordinal1 @ A) ) )  =>  (? [B: $i] :  ( ( (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) ) ) ) ) ) ) ) ) ) , file(jordan, rc1_jordan)).
thf(rc1_jordan2c, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_metric_1 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  &  ( (v6_tbsp_1 @ B)  @ A) ) ) ) ) , file(jordan2c, rc1_jordan2c)).
thf(rc1_membered, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v6_membered @ A) ) ) , file(membered, rc1_membered)).
thf(rc1_monoid_0, axiom,  (? [A: $i] :  ( (l1_struct_0 @ A)  &  (v1_monoid_0 @ A) ) ) , file(monoid_0, rc1_monoid_0)).
thf(rc1_nat_1, axiom,  (? [A: $i] :  (v7_ordinal1 @ A) ) , file(nat_1, rc1_nat_1)).
thf(rc1_ordinal1, axiom,  (? [A: $i] :  ( (v1_ordinal1 @ A)  &  (v2_ordinal1 @ A) ) ) , file(ordinal1, rc1_ordinal1)).
thf(rc1_relat_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v1_relat_1 @ A) ) ) , file(relat_1, rc1_relat_1)).
thf(rc1_relset_1, axiom,  (! [A: $i, B: $i] :  (? [C: $i] :  ( ( (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) ) ) ) ) ) ) , file(relset_1, rc1_relset_1)).
thf(rc1_rlaffin1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v13_algstr_0 @ A)  &  ( (v2_rlvect_1 @ A)  &  ( (v3_rlvect_1 @ A)  &  ( (v4_rlvect_1 @ A)  &  ( (v5_rlvect_1 @ A)  &  ( (v6_rlvect_1 @ A)  &  ( (v7_rlvect_1 @ A)  &  ( (v8_rlvect_1 @ A)  &  (l1_rlvect_1 @ A) ) ) ) ) ) ) ) ) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  &  ( ( (v3_card_1 @ B)  @ np__1)  &  ( (v1_rlaffin1 @ B)  @ A) ) ) ) ) ) , file(rlaffin1, rc1_rlaffin1)).
thf(rc1_seq_4, axiom,  (? [A: $i] :  ( ( (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) ) ) ) ) ) ) ) , file(seq_4, rc1_seq_4)).
thf(rc1_subset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ~ ( (v1_xboole_0 @ B) ) ) ) ) ) , file(subset_1, rc1_subset_1)).
thf(rc1_topdim_1, axiom,  (! [A: $i] :  ( ( (v2_pre_topc @ A)  &  (l1_pre_topc @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) ) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( (v2_topdim_1 @ B)  @ A) ) ) ) ) ) , file(topdim_1, rc1_topdim_1)).
thf(rc1_topdim_2, axiom,  (! [A: $i] :  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (k1_zfmisc_1 @ A) ) )  &  ( (v1_topdim_2 @ B)  @ A) ) ) ) , file(topdim_2, rc1_topdim_2)).
thf(rc1_tops_1, axiom,  (! [A: $i] :  ( ( (v2_pre_topc @ A)  &  (l1_pre_topc @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  &  ( (v3_pre_topc @ B)  @ A) ) ) ) ) , file(tops_1, rc1_tops_1)).
thf(rc1_valued_0, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v4_valued_0 @ A) ) ) ) , file(valued_0, rc1_valued_0)).
thf(rc1_valued_1, axiom,  (? [A: $i] :  ( (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) ) ) ) ) ) ) ) , file(valued_1, rc1_valued_1)).
thf(rc1_xboole_0, axiom,  (? [A: $i] :  (v1_xboole_0 @ A) ) , file(xboole_0, rc1_xboole_0)).
thf(rc1_xreal_0, axiom,  (? [A: $i] :  (v1_xreal_0 @ A) ) , file(xreal_0, rc1_xreal_0)).
thf(rc1_xxreal_0, axiom,  (? [A: $i] :  (v1_xxreal_0 @ A) ) , file(xxreal_0, rc1_xxreal_0)).
thf(rc1_xxreal_2, axiom,  (? [A: $i] :  ( (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) ) ) ) ) ) ) ) ) ) , file(xxreal_2, rc1_xxreal_2)).
thf(rc1_xxreal_3, axiom,  (? [A: $i] :  ( (v1_xxreal_0 @ A)  &  ( (v2_xxreal_0 @ A)  &  ~ ( (v1_xreal_0 @ A) ) ) ) ) , file(xxreal_3, rc1_xxreal_3)).
thf(rc20_struct_0, axiom,  (? [A: $i] :  ( (l2_struct_0 @ A)  &  ( ~ ( (v2_struct_0 @ A) )  &  (v7_struct_0 @ A) ) ) ) , file(struct_0, rc20_struct_0)).
thf(rc21_struct_0, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_struct_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  (v1_zfmisc_1 @ B) ) ) ) ) ) , file(struct_0, rc21_struct_0)).
thf(rc22_struct_0, axiom,  (! [A: $i] :  ( ( ~ ( (v7_struct_0 @ A) )  &  (l1_struct_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  &  ~ ( (v1_zfmisc_1 @ B) ) ) ) ) ) , file(struct_0, rc22_struct_0)).
thf(rc23_struct_0, axiom,  (! [A: $i] :  ( (v1_card_1 @ A)  =>  (? [B: $i] :  ( (l1_struct_0 @ B)  &  ( (v13_struct_0 @ B)  @ A) ) ) ) ) , file(struct_0, rc23_struct_0)).
thf(rc2_card_1, axiom,  (? [A: $i] :  ( (v1_ordinal1 @ A)  &  ( (v2_ordinal1 @ A)  &  ( (v3_ordinal1 @ A)  &  ( (v1_finset_1 @ A)  &  (v1_card_1 @ A) ) ) ) ) ) , file(card_1, rc2_card_1)).
thf(rc2_finset_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  (v1_finset_1 @ B) ) ) ) , file(finset_1, rc2_finset_1)).
thf(rc2_funct_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_funct_1 @ A) ) ) ) , file(funct_1, rc2_funct_1)).
thf(rc2_int_1, axiom,  (? [A: $i] :  (v1_int_1 @ A) ) , file(int_1, rc2_int_1)).
thf(rc2_jordan, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k4_ordinal1)  =>  (? [B: $i] :  ( ( (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) ) ) ) ) ) ) ) ) ) , file(jordan, rc2_jordan)).
thf(rc2_membered, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v6_membered @ A) ) ) , file(membered, rc2_membered)).
thf(rc2_monoid_0, axiom,  (? [A: $i] :  ( (l1_struct_0 @ A)  &  (v2_monoid_0 @ A) ) ) , file(monoid_0, rc2_monoid_0)).
thf(rc2_nat_1, axiom,  (? [A: $i] :  ( (v7_ordinal1 @ A)  &  (v8_ordinal1 @ A) ) ) , file(nat_1, rc2_nat_1)).
thf(rc2_ordinal1, axiom,  (? [A: $i] :  (v3_ordinal1 @ A) ) , file(ordinal1, rc2_ordinal1)).
thf(rc2_relat_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  (v2_relat_1 @ A) ) ) , file(relat_1, rc2_relat_1)).
thf(rc2_rlaffin1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v13_algstr_0 @ A)  &  ( (v2_rlvect_1 @ A)  &  ( (v3_rlvect_1 @ A)  &  ( (v4_rlvect_1 @ A)  &  ( (v5_rlvect_1 @ A)  &  ( (v6_rlvect_1 @ A)  &  ( (v7_rlvect_1 @ A)  &  ( (v8_rlvect_1 @ A)  &  (l1_rlvect_1 @ A) ) ) ) ) ) ) ) ) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) ) )  &  ( (v1_xboole_0 @ B)  &  ( (v2_rlaffin1 @ B)  @ A) ) ) ) ) ) , file(rlaffin1, rc2_rlaffin1)).
thf(rc2_simplex0, axiom,  (! [A: $i] :  ( (l1_pre_topc @ A)  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) ) )  &  ( (v1_xboole_0 @ B)  &  ( (v1_tops_2 @ B)  @ A) ) ) ) ) ) , file(simplex0, rc2_simplex0)).
thf(rc2_subset_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  (v1_xboole_0 @ B) ) ) ) , file(subset_1, rc2_subset_1)).
thf(rc2_tbsp_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_metric_1 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  &  ( (v6_tbsp_1 @ B)  @ A) ) ) ) ) , file(tbsp_1, rc2_tbsp_1)).
thf(rc2_topdim_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v2_pre_topc @ A)  &  (l1_pre_topc @ A) ) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( (v1_topdim_1 @ B)  @ A) ) ) ) ) ) , file(topdim_1, rc2_topdim_1)).
thf(rc2_tops_1, axiom,  (! [A: $i] :  ( ( (v2_pre_topc @ A)  &  (l1_pre_topc @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  &  ( ( (v3_pre_topc @ B)  @ A)  &  ( (v4_pre_topc @ B)  @ A) ) ) ) ) ) , file(tops_1, rc2_tops_1)).
thf(rc2_valued_0, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( ( (v5_relat_1 @ A)  @ k3_numbers)  &  ( ( (v5_relat_1 @ A)  @ k4_numbers)  &  ( (v1_funct_1 @ A)  &  ( (v3_funct_1 @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  (v4_valued_0 @ A) ) ) ) ) ) ) ) , file(valued_0, rc2_valued_0)).
thf(rc2_valued_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k4_ordinal1)  &  ( (v1_funct_1 @ A)  &  ~ ( (v1_xboole_0 @ A) ) ) ) ) ) , file(valued_1, rc2_valued_1)).
thf(rc2_xboole_0, axiom,  (? [A: $i] :  ~ ( (v1_xboole_0 @ A) ) ) , file(xboole_0, rc2_xboole_0)).
thf(rc2_xreal_0, axiom,  (? [A: $i] :  (v1_xreal_0 @ A) ) , file(xreal_0, rc2_xreal_0)).
thf(rc2_xxreal_0, axiom,  (? [A: $i] :  (v1_xxreal_0 @ A) ) , file(xxreal_0, rc2_xxreal_0)).
thf(rc2_xxreal_2, axiom,  (? [A: $i] :  ( (v6_membered @ A)  &  ( (v1_finset_1 @ A)  &  ~ ( (v1_xboole_0 @ A) ) ) ) ) , file(xxreal_2, rc2_xxreal_2)).
thf(rc2_xxreal_3, axiom,  (? [A: $i] :  ( (v1_xxreal_0 @ A)  &  ( (v3_xxreal_0 @ A)  &  ~ ( (v1_xreal_0 @ A) ) ) ) ) , file(xxreal_3, rc2_xxreal_3)).
thf(rc3_card_1, axiom,  (? [A: $i] :  ~ ( (v1_finset_1 @ A) ) ) , file(card_1, rc3_card_1)).
thf(rc3_compts_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v2_pre_topc @ A)  &  (l1_pre_topc @ A) ) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( (v2_compts_1 @ B)  @ A) ) ) ) ) ) , file(compts_1, rc3_compts_1)).
thf(rc3_finseq_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_finseq_1 @ A) ) ) ) , file(finseq_1, rc3_finseq_1)).
thf(rc3_finset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  (v1_finset_1 @ B) ) ) ) ) ) , file(finset_1, rc3_finset_1)).
thf(rc3_funct_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( (v2_relat_1 @ A)  &  (v1_funct_1 @ A) ) ) ) , file(funct_1, rc3_funct_1)).
thf(rc3_int_1, axiom,  (? [A: $i] :  (v2_int_1 @ A) ) , file(int_1, rc3_int_1)).
thf(rc3_jordan, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k4_ordinal1)  =>  (? [B: $i] :  ( ( (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) ) ) ) ) ) ) ) ) ) , file(jordan, rc3_jordan)).
thf(rc3_membered, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v6_membered @ A)  &  (v7_membered @ A) ) ) ) , file(membered, rc3_membered)).
thf(rc3_nat_1, axiom,  (? [A: $i] :  ( (v7_ordinal1 @ A)  &  ~ ( (v8_ordinal1 @ A) ) ) ) , file(nat_1, rc3_nat_1)).
thf(rc3_ordinal1, axiom,  (? [A: $i] :  (v3_ordinal1 @ A) ) , file(ordinal1, rc3_ordinal1)).
thf(rc3_relat_1, axiom,  (! [A: $i, B: $i] :  (? [C: $i] :  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ A)  &  ( (v5_relat_1 @ C)  @ B) ) ) ) ) , file(relat_1, rc3_relat_1)).
thf(rc3_rlaffin1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v13_algstr_0 @ A)  &  ( (v2_rlvect_1 @ A)  &  ( (v3_rlvect_1 @ A)  &  ( (v4_rlvect_1 @ A)  &  ( (v5_rlvect_1 @ A)  &  ( (v6_rlvect_1 @ A)  &  ( (v7_rlvect_1 @ A)  &  ( (v8_rlvect_1 @ A)  &  (l1_rlvect_1 @ A) ) ) ) ) ) ) ) ) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) ) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( (v2_rlaffin1 @ B)  @ A) ) ) ) ) ) , file(rlaffin1, rc3_rlaffin1)).
thf(rc3_simplex1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v13_algstr_0 @ A)  &  ( (v2_rlvect_1 @ A)  &  ( (v3_rlvect_1 @ A)  &  ( (v4_rlvect_1 @ A)  &  ( (v5_rlvect_1 @ A)  &  ( (v6_rlvect_1 @ A)  &  ( (v7_rlvect_1 @ A)  &  ( (v8_rlvect_1 @ A)  &  (l1_rlvect_1 @ A) ) ) ) ) ) ) ) ) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  &  ( ( (v3_card_1 @ B)  @ np__1)  &  ( (v1_rlaffin1 @ B)  @ A) ) ) ) ) ) , file(simplex1, rc3_simplex1)).
thf(rc3_subset_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ~ ( ( (v1_subset_1 @ B)  @ A) ) ) ) ) , file(subset_1, rc3_subset_1)).
thf(rc3_tbsp_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v6_metric_1 @ A)  &  ( (v8_metric_1 @ A)  &  ( (v9_metric_1 @ A)  &  (l1_metric_1 @ A) ) ) ) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  (v1_finset_1 @ B) ) ) ) ) ) , file(tbsp_1, rc3_tbsp_1)).
thf(rc3_topdim_1, axiom,  (? [A: $i] :  ( (l1_pre_topc @ A)  &  ( ~ ( (v2_struct_0 @ A) )  &  ( (v2_pre_topc @ A)  &  (v3_topdim_1 @ A) ) ) ) ) , file(topdim_1, rc3_topdim_1)).
thf(rc3_topmetr, axiom,  (? [A: $i] :  ( (l1_struct_0 @ A)  &  ( ~ ( (v2_struct_0 @ A) )  &  (v3_topmetr @ A) ) ) ) , file(topmetr, rc3_topmetr)).
thf(rc3_tops_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v2_pre_topc @ A)  &  (l1_pre_topc @ A) ) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( ( (v3_pre_topc @ B)  @ A)  &  ( (v4_pre_topc @ B)  @ A) ) ) ) ) ) ) , file(tops_1, rc3_tops_1)).
thf(rc3_valued_0, axiom,  (? [A: $i] :  ( ( (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) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(valued_0, rc3_valued_0)).
thf(rc3_valued_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k4_ordinal1)  &  ( (v1_funct_1 @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  (v1_finset_1 @ A) ) ) ) ) ) , file(valued_1, rc3_valued_1)).
thf(rc3_xreal_0, axiom,  (? [A: $i] :  ( (v1_xcmplx_0 @ A)  &  ( (v1_xxreal_0 @ A)  &  ( (v2_xxreal_0 @ A)  &  (v1_xreal_0 @ A) ) ) ) ) , file(xreal_0, rc3_xreal_0)).
thf(rc3_xxreal_0, axiom,  (? [A: $i] :  ( (v1_xxreal_0 @ A)  &  (v2_xxreal_0 @ A) ) ) , file(xxreal_0, rc3_xxreal_0)).
thf(rc3_xxreal_2, axiom,  (? [A: $i] :  ( (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) ) ) ) ) ) ) ) ) ) , file(xxreal_2, rc3_xxreal_2)).
thf(rc4_card_1, axiom,  (? [A: $i] :  ( (v7_ordinal1 @ A)  &  ~ ( (v8_ordinal1 @ A) ) ) ) , file(card_1, rc4_card_1)).
thf(rc4_compts_1, axiom,  (! [A: $i] :  ( ( (v2_pre_topc @ A)  &  (l1_pre_topc @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) ) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( (v1_tops_2 @ B)  @ A) ) ) ) ) ) , file(compts_1, rc4_compts_1)).
thf(rc4_finseq_1, axiom,  (? [A: $i] :  ( (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) ) ) ) ) ) ) ) , file(finseq_1, rc4_finseq_1)).
thf(rc4_finset_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finset_1 @ A) ) ) ) ) , file(finset_1, rc4_finset_1)).
thf(rc4_funct_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_relat_1 @ A)  &  ( (v2_relat_1 @ A)  &  (v1_funct_1 @ A) ) ) ) ) , file(funct_1, rc4_funct_1)).
thf(rc4_nat_1, axiom,  (? [A: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @ k1_numbers) )  &  ( ~ ( (v1_xboole_0 @ A) )  &  (v3_ordinal1 @ A) ) ) ) , file(nat_1, rc4_nat_1)).
thf(rc4_ordinal1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_ordinal1 @ A)  &  ( (v2_ordinal1 @ A)  &  (v3_ordinal1 @ A) ) ) ) ) , file(ordinal1, rc4_ordinal1)).
thf(rc4_struct_0, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_struct_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  &  ~ ( (v1_xboole_0 @ B) ) ) ) ) ) , file(struct_0, rc4_struct_0)).
thf(rc4_subset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ( (v1_subset_1 @ B)  @ A) ) ) ) ) , file(subset_1, rc4_subset_1)).
thf(rc4_valued_0, axiom,  (! [A: $i] :  (? [B: $i] :  ( ( (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) ) ) ) ) ) ) ) ) , file(valued_0, rc4_valued_0)).
thf(rc4_valued_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k4_ordinal1)  &  ( (v1_funct_1 @ A)  &  ( (v1_finset_1 @ A)  &  ( (v3_card_1 @ A)  @ np__1) ) ) ) ) ) , file(valued_1, rc4_valued_1)).
thf(rc4_xreal_0, axiom,  (? [A: $i] :  ( (v1_xcmplx_0 @ A)  &  ( (v1_xxreal_0 @ A)  &  ( (v3_xxreal_0 @ A)  &  (v1_xreal_0 @ A) ) ) ) ) , file(xreal_0, rc4_xreal_0)).
thf(rc4_xxreal_0, axiom,  (? [A: $i] :  ( (v1_xxreal_0 @ A)  &  (v3_xxreal_0 @ A) ) ) , file(xxreal_0, rc4_xxreal_0)).
thf(rc4_xxreal_2, axiom,  (? [A: $i] :  ( (v2_membered @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  (v6_xxreal_2 @ A) ) ) ) , file(xxreal_2, rc4_xxreal_2)).
thf(rc5_card_1, axiom,  (? [A: $i] :  ( (v1_ordinal1 @ A)  &  ( (v2_ordinal1 @ A)  &  ( (v3_ordinal1 @ A)  &  ( (v7_ordinal1 @ A)  &  ( ~ ( (v8_ordinal1 @ A) )  &  (v1_card_1 @ A) ) ) ) ) ) ) , file(card_1, rc5_card_1)).
thf(rc5_finseq_1, axiom,  (? [A: $i] :  ( (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) ) ) ) ) ) ) ) ) , file(finseq_1, rc5_finseq_1)).
thf(rc5_funct_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ~ ( (v3_funct_1 @ A) ) ) ) ) , file(funct_1, rc5_funct_1)).
thf(rc5_nat_1, axiom,  (? [A: $i] :  ( ( (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) ) ) ) ) ) ) ) ) ) ) ) , file(nat_1, rc5_nat_1)).
thf(rc5_ordinal1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( ( (v5_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  (v5_ordinal1 @ B) ) ) ) ) ) , file(ordinal1, rc5_ordinal1)).
thf(rc5_subset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  (v1_zfmisc_1 @ B) ) ) ) ) ) , file(subset_1, rc5_subset_1)).
thf(rc5_tops_1, axiom,  (! [A: $i] :  ( (l1_pre_topc @ A)  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  &  ( (v2_tops_1 @ B)  @ A) ) ) ) ) , file(tops_1, rc5_tops_1)).
thf(rc5_valued_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (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) ) ) ) ) ) ) ) ) ) ) , file(valued_1, rc5_valued_1)).
thf(rc5_xreal_0, axiom,  (? [A: $i] :  ( (v8_ordinal1 @ A)  &  ( (v1_xcmplx_0 @ A)  &  ( (v1_xxreal_0 @ A)  &  (v1_xreal_0 @ A) ) ) ) ) , file(xreal_0, rc5_xreal_0)).
thf(rc5_xxreal_0, axiom,  (? [A: $i] :  ( (v8_ordinal1 @ A)  &  (v1_xxreal_0 @ A) ) ) , file(xxreal_0, rc5_xxreal_0)).
thf(rc5_xxreal_2, axiom,  (? [A: $i] :  ( (v2_membered @ A)  &  ( (v1_xxreal_2 @ A)  &  ( (v2_xxreal_2 @ A)  &  (v6_xxreal_2 @ A) ) ) ) ) , file(xxreal_2, rc5_xxreal_2)).
thf(rc6_card_1, axiom,  (! [A: $i] :  ( ~ ( (v1_finset_1 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ~ ( (v1_finset_1 @ B) ) ) ) ) ) , file(card_1, rc6_card_1)).
thf(rc6_finset_1, axiom,  (! [A: $i, B: $i] :  (? [C: $i] :  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ A)  &  ( ( (v5_relat_1 @ C)  @ B)  &  ( (v1_funct_1 @ C)  &  (v1_finset_1 @ C) ) ) ) ) ) ) , file(finset_1, rc6_finset_1)).
thf(rc6_funct_1, axiom,  (! [A: $i, B: $i] :  (? [C: $i] :  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ A)  &  ( ( (v5_relat_1 @ C)  @ B)  &  (v1_funct_1 @ C) ) ) ) ) ) , file(funct_1, rc6_funct_1)).
thf(rc6_ordinal1, axiom,  (? [A: $i] :  (v7_ordinal1 @ A) ) , file(ordinal1, rc6_ordinal1)).
thf(rc6_pre_topc, axiom,  (! [A: $i] :  ( ( (v2_pre_topc @ A)  &  (l1_pre_topc @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  &  ( (v4_pre_topc @ B)  @ A) ) ) ) ) , file(pre_topc, rc6_pre_topc)).
thf(rc6_subset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_zfmisc_1 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ~ ( (v1_zfmisc_1 @ B) ) ) ) ) ) , file(subset_1, rc6_subset_1)).
thf(rc6_tops_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v2_pre_topc @ A)  &  (l1_pre_topc @ A) ) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ~ ( ( (v2_tops_1 @ B)  @ A) ) ) ) ) ) ) , file(tops_1, rc6_tops_1)).
thf(rc6_valued_0, axiom,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( ( (v1_partfun1 @ B)  @ A)  &  (v4_valued_0 @ B) ) ) ) ) ) ) , file(valued_0, rc6_valued_0)).
thf(rc6_xxreal_2, axiom,  (? [A: $i] :  ( (v2_membered @ A)  &  ( ~ ( (v1_xxreal_2 @ A) )  &  ( (v2_xxreal_2 @ A)  &  (v6_xxreal_2 @ A) ) ) ) ) , file(xxreal_2, rc6_xxreal_2)).
thf(rc7_card_1, axiom,  (! [A: $i] :  ( (v1_card_1 @ A)  =>  (? [B: $i] :  ( (v3_card_1 @ B)  @ A) ) ) ) , file(card_1, rc7_card_1)).
thf(rc7_finseq_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (? [B: $i] :  ( (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) ) ) ) ) ) ) ) ) ) , file(finseq_1, rc7_finseq_1)).
thf(rc7_finset_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ~ ( (v1_xboole_0 @ B) ) )  =>  (? [C: $i] :  ( ~ ( (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) ) ) ) ) ) ) ) ) , file(finset_1, rc7_finset_1)).
thf(rc7_funct_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v4_funct_1 @ A) ) ) , file(funct_1, rc7_funct_1)).
thf(rc7_ordinal1, axiom,  (? [A: $i] :  (v7_ordinal1 @ A) ) , file(ordinal1, rc7_ordinal1)).
thf(rc7_pre_topc, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v2_pre_topc @ A)  &  (l1_pre_topc @ A) ) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( (v4_pre_topc @ B)  @ A) ) ) ) ) ) , file(pre_topc, rc7_pre_topc)).
thf(rc7_tops_1, axiom,  (! [A: $i] :  ( ( (v2_pre_topc @ A)  &  (l1_pre_topc @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  &  ( (v3_tops_1 @ B)  @ A) ) ) ) ) , file(tops_1, rc7_tops_1)).
thf(rc7_xxreal_2, axiom,  (? [A: $i] :  ( (v2_membered @ A)  &  ( (v1_xxreal_2 @ A)  &  ( ~ ( (v2_xxreal_2 @ A) )  &  (v6_xxreal_2 @ A) ) ) ) ) , file(xxreal_2, rc7_xxreal_2)).
thf(rc8_card_1, axiom,  (! [A: $i] :  ( (v1_card_1 @ A)  =>  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v3_card_1 @ B)  @ A) ) ) ) ) ) , file(card_1, rc8_card_1)).
thf(rc8_finseq_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v3_finseq_1 @ A) ) ) , file(finseq_1, rc8_finseq_1)).
thf(rc8_finset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_zfmisc_1 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ( ~ ( (v1_zfmisc_1 @ B) )  &  (v1_finset_1 @ B) ) ) ) ) ) , file(finset_1, rc8_finset_1)).
thf(rc8_ordinal1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v7_ordinal1 @ A) ) ) , file(ordinal1, rc8_ordinal1)).
thf(rc8_xxreal_2, axiom,  (? [A: $i] :  ( (v2_membered @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  ( ~ ( (v1_xxreal_2 @ A) )  &  ( ~ ( (v2_xxreal_2 @ A) )  &  (v6_xxreal_2 @ A) ) ) ) ) ) , file(xxreal_2, rc8_xxreal_2)).
thf(rc9_card_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ( (v3_card_1 @ B)  @ np__1) ) ) ) ) , file(card_1, rc9_card_1)).
thf(rc9_finseq_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (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) ) ) ) ) ) ) ) ) , file(finseq_1, rc9_finseq_1)).
thf(rc9_finset_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_finset_1 @ A)  &  (v5_finset_1 @ A) ) ) ) , file(finset_1, rc9_finset_1)).
thf(rc9_funct_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( (v2_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  (v1_funct_1 @ B) ) ) ) ) ) , file(funct_1, rc9_funct_1)).
thf(rc9_ordinal1, axiom,  (? [A: $i] :  (v8_ordinal1 @ A) ) , file(ordinal1, rc9_ordinal1)).
thf(rc9_pre_topc, axiom,  (? [A: $i] :  ( (l1_pre_topc @ A)  &  ( ~ ( (v2_struct_0 @ A) )  &  ( (v2_pre_topc @ A)  &  (v7_pre_topc @ A) ) ) ) ) , file(pre_topc, rc9_pre_topc)).
thf(redefinition_k3_metric_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v8_metric_1 @ A)  &  (l1_metric_1 @ A) )  &  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @ C)  @  (u1_struct_0 @ A) ) ) )  =>  ( ( ( (k3_metric_1 @ A)  @ B)  @ C)  =  ( ( (k1_metric_1 @ A)  @ B)  @ C) ) ) ) , file(metric_1, k3_metric_1)).
thf(redefinition_k5_numbers, axiom,  (k5_numbers = k5_ordinal1) , file(numbers, k5_numbers)).
thf(redefinition_r2_tarski, axiom,  (! [A: $i, B: $i] :  ( ( (r2_tarski @ A)  @ B)  <=>  ( (r2_hidden @ A)  @ B) ) ) , file(tarski, r2_tarski)).
thf(reflexivity_r1_tarski, axiom,  (! [A: $i, B: $i] :  ( (r1_tarski @ A)  @ A) ) , file(tarski, r1_tarski)).
thf(reflexivity_r1_xxreal_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xxreal_0 @ A)  &  (v1_xxreal_0 @ B) )  =>  ( (r1_xxreal_0 @ A)  @ A) ) ) , file(xxreal_0, r1_xxreal_0)).
thf(rqLessOrEqual__r1_xxreal_0__r1_r1, axiom,  ( (r1_xxreal_0 @ np__1)  @ np__1) , file(arithm, rqLessOrEqual__r1_xxreal_0__r1_r1)).
thf(spc1_boole, axiom,  ~ ( (v1_xboole_0 @ np__1) ) , file(boole, spc1_boole)).
thf(spc1_numerals, axiom,  ( (v2_xxreal_0 @ np__1)  &  ( (m1_subset_1 @ np__1)  @ k4_ordinal1) ) , file(numerals, spc1_numerals)).
thf(t12_metric_1, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (l1_metric_1 @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (u1_struct_0 @ B) )  =>  (! [D: $i] :  ( ( (m1_subset_1 @ D)  @  (u1_struct_0 @ B) )  =>  ( ( (r2_tarski @ D)  @  ( ( (k9_metric_1 @ B)  @ C)  @ A) )  <=>  ( ~ ( (v2_struct_0 @ B) )  &  ( (r1_xxreal_0 @  ( ( (k1_metric_1 @ B)  @ C)  @ D) )  @ A) ) ) ) ) ) ) ) ) ) ) , file(metric_1, t12_metric_1)).
thf(t13_simplex2, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @  (k15_euclid @ A) ) ) )  =>  (! [C: $i] :  ( ( ( (v6_tbsp_1 @ C)  @  (k14_euclid @ A) )  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  (u1_struct_0 @  (k14_euclid @ A) ) ) ) )  =>  ( (C = B)  =>  (! [D: $i] :  ( ( (m1_subset_1 @ D)  @  (u1_struct_0 @  (k14_euclid @ A) ) )  =>  ( ( (r2_tarski @ D)  @  ( (k3_convex1 @  (k15_euclid @ A) )  @ B) )  =>  ( (r1_tarski @  ( (k3_convex1 @  (k15_euclid @ A) )  @ B) )  @  ( ( (k9_metric_1 @  (k14_euclid @ A) )  @ D)  @  ( (k2_tbsp_1 @  (k14_euclid @ A) )  @ C) ) ) ) ) ) ) ) ) ) ) ) ) , file(simplex2, t13_simplex2)).
thf(t1_numerals, axiom,  ( (m1_subset_1 @ k1_xboole_0)  @ k4_ordinal1) , file(numerals, t1_numerals)).
thf(t1_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ( ( ( (r1_xxreal_0 @ A)  @ B)  &  (v2_xxreal_0 @ A) )  =>  (v2_xxreal_0 @ B) ) ) ) ) ) , file(real, t1_real)).
thf(t1_subset, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (r2_tarski @ A)  @ B)  =>  ( (m1_subset_1 @ A)  @ B) ) ) ) , file(subset, t1_subset)).
thf(t1_xxreal_0, axiom,  (! [A: $i] :  ( (v1_xxreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xxreal_0 @ B)  =>  ( ( ( (r1_xxreal_0 @ A)  @ B)  &  ( (r1_xxreal_0 @ B)  @ A) )  =>  (A = B) ) ) ) ) ) , file(xxreal_0, t1_xxreal_0)).
thf(t24_tbsp_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v6_metric_1 @ A)  &  (l1_metric_1 @ A) ) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  =>  ( ( ( (v6_tbsp_1 @ B)  @ A)  &  ( (r1_tarski @ C)  @ B) )  =>  ( (r1_xxreal_0 @  ( (k2_tbsp_1 @ A)  @ C) )  @  ( (k2_tbsp_1 @ A)  @ B) ) ) ) ) ) ) ) ) , file(tbsp_1, t24_tbsp_1)).
thf(t2_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ( ( ( (r1_xxreal_0 @ A)  @ B)  &  (v3_xxreal_0 @ B) )  =>  (v3_xxreal_0 @ A) ) ) ) ) ) , file(real, t2_real)).
thf(t2_subset, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_subset_1 @ A)  @ B)  =>  ( (v1_xboole_0 @ B)  |  ( (r2_tarski @ A)  @ B) ) ) ) ) , file(subset, t2_subset)).
thf(t3_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ~ ( ( ( (r1_xxreal_0 @ A)  @ B)  &  ( ~ ( (v3_xxreal_0 @ A) )  &  (v3_xxreal_0 @ B) ) ) ) ) ) ) ) , file(real, t3_real)).
thf(t3_subset, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @ B) )  <=>  ( (r1_tarski @ A)  @ B) ) ) ) , file(subset, t3_subset)).
thf(t41_convex1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v13_algstr_0 @ A)  &  ( (v2_rlvect_1 @ A)  &  ( (v3_rlvect_1 @ A)  &  ( (v4_rlvect_1 @ A)  &  ( (v5_rlvect_1 @ A)  &  ( (v6_rlvect_1 @ A)  &  ( (v7_rlvect_1 @ A)  &  ( (v8_rlvect_1 @ A)  &  (l1_rlvect_1 @ A) ) ) ) ) ) ) ) ) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  =>  ( (r1_tarski @ B)  @  ( (k3_convex1 @ A)  @ B) ) ) ) ) ) , file(convex1, t41_convex1)).
thf(t4_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ~ ( ( ( (r1_xxreal_0 @ A)  @ B)  &  ( ~ ( (v2_xxreal_0 @ B) )  &  (v2_xxreal_0 @ A) ) ) ) ) ) ) ) , file(real, t4_real)).
thf(t4_subset, axiom,  (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  ( ( ( (r2_tarski @ A)  @ B)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ C) ) )  =>  ( (m1_subset_1 @ A)  @ C) ) ) ) ) , file(subset, t4_subset)).
thf(t5_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ( ( (r1_xxreal_0 @ A)  @ B)  =>  ( (v8_ordinal1 @ B)  |  ( (v3_xxreal_0 @ A)  |  (v2_xxreal_0 @ B) ) ) ) ) ) ) ) , file(real, t5_real)).
thf(t5_subset, axiom,  (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  ~ ( ( ( (r2_tarski @ A)  @ B)  &  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ C) )  &  (v1_xboole_0 @ C) ) ) ) ) ) ) , file(subset, t5_subset)).
thf(t6_boole, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (A = k1_xboole_0) ) ) , file(boole, t6_boole)).
thf(t6_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ( ( (r1_xxreal_0 @ A)  @ B)  =>  ( (v8_ordinal1 @ A)  |  ( (v2_xxreal_0 @ B)  |  (v3_xxreal_0 @ A) ) ) ) ) ) ) ) , file(real, t6_real)).
thf(t7_boole, axiom,  (! [A: $i] :  (! [B: $i] :  ~ ( ( ( (r2_tarski @ A)  @ B)  &  (v1_xboole_0 @ B) ) ) ) ) , file(boole, t7_boole)).
thf(t7_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ~ ( ( ~ ( ( (r1_xxreal_0 @ A)  @ B) )  &  ( ~ ( (v2_xxreal_0 @ A) )  &  ~ ( (v3_xxreal_0 @ B) ) ) ) ) ) ) ) ) , file(real, t7_real)).
thf(t8_boole, axiom,  (! [A: $i] :  (! [B: $i] :  ~ ( ( (v1_xboole_0 @ A)  &  ( ~ ( (A = B) )  &  (v1_xboole_0 @ B) ) ) ) ) ) , file(boole, t8_boole)).
thf(t8_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ~ ( ( ~ ( ( (r1_xxreal_0 @ A)  @ B) )  &  ( ~ ( (v3_xxreal_0 @ B) )  &  ~ ( (v2_xxreal_0 @ A) ) ) ) ) ) ) ) ) , file(real, t8_real)).
thf(t15_simplex2, conjecture,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @  (k15_euclid @ A) ) ) )  =>  (! [C: $i] :  ( ( ( (v6_tbsp_1 @ C)  @  (k14_euclid @ A) )  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  (u1_struct_0 @  (k14_euclid @ A) ) ) ) )  =>  (! [D: $i] :  ( ( ( (v6_tbsp_1 @ D)  @  (k14_euclid @ A) )  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  (u1_struct_0 @  (k14_euclid @ A) ) ) ) )  =>  ( ( (D =  ( (k3_convex1 @  (k15_euclid @ A) )  @ B) )  &  (C = B) )  =>  ( ( (k2_tbsp_1 @  (k14_euclid @ A) )  @ C)  =  ( (k2_tbsp_1 @  (k14_euclid @ A) )  @ D) ) ) ) ) ) ) ) ) ) ) , file(simplex2, t15_simplex2)).