% Mizar problem: t7_frechet,frechet,314,5 
fof(t7_frechet, conjecture,  (! [A] :  (m1_subset_1(A, u1_struct_0(k7_metric_1)) =>  (! [B] :  (v1_xreal_0(B) => k8_metric_1(k7_metric_1, A, B)=k2_rcomp_1(k6_xcmplx_0(A, B), k2_xcmplx_0(A, B))) ) ) ) ).
fof(abstractness_v1_metric_1, axiom,  (! [A] :  (l1_metric_1(A) =>  (v1_metric_1(A) => A=g1_metric_1(u1_struct_0(A), u1_metric_1(A))) ) ) ).
fof(antisymmetry_r2_hidden, axiom,  (! [A, B] :  (r2_hidden(A, B) =>  ~ (r2_hidden(B, A)) ) ) ).
fof(asymmetry_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) =>  ~ (r2_tarski(B, A)) ) ) ).
fof(cc10_membered, axiom,  (! [A] :  (v5_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_int_1(B)) ) ) ) ).
fof(cc10_ordinal1, axiom,  (! [A] :  (v6_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_ordinal1(B)) ) ) ) ).
fof(cc10_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ( ~ (v2_struct_0(A))  & v7_struct_0(A))  => v13_struct_0(A, 1)) ) ) ).
fof(cc11_membered, axiom,  (! [A] :  (v6_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v7_ordinal1(B)) ) ) ) ).
fof(cc11_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v7_ordinal1(A)) ) ).
fof(cc11_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, 1) =>  ( ~ (v2_struct_0(A))  & v7_struct_0(A)) ) ) ) ).
fof(cc12_membered, axiom,  (! [A] :  (v1_xboole_0(A) => v6_membered(A)) ) ).
fof(cc12_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v1_zfmisc_1(A)) ) ).
fof(cc13_membered, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_membered(B)) ) ) ) ).
fof(cc13_ordinal1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  ~ (v8_ordinal1(A)) ) ) ).
fof(cc14_membered, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v2_membered(B)) ) ) ) ).
fof(cc14_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc15_membered, axiom,  (! [A] :  (v3_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v3_membered(B)) ) ) ) ).
fof(cc15_ordinal1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v9_ordinal1(A)) ) ) ).
fof(cc16_membered, axiom,  (! [A] :  (v4_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_membered(B)) ) ) ) ).
fof(cc16_ordinal1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) )  =>  (! [B] :  (m1_subset_1(B, A) =>  ~ (v8_ordinal1(B)) ) ) ) ) ).
fof(cc17_membered, axiom,  (! [A] :  (v5_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v5_membered(B)) ) ) ) ).
fof(cc17_ordinal1, axiom,  (! [A] :  ( ~ (v10_ordinal1(A))  => v1_setfam_1(A)) ) ).
fof(cc17_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc18_membered, axiom,  (! [A] :  (v6_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_membered(B)) ) ) ) ).
fof(cc18_ordinal1, axiom,  (! [A] :  (v10_ordinal1(A) =>  ~ (v1_setfam_1(A)) ) ) ).
fof(cc19_membered, axiom,  (! [A] :  (v1_xboole_0(A) => v7_membered(A)) ) ).
fof(cc19_ordinal1, axiom,  (! [A] :  (v1_setfam_1(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc1_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_funct_1(A)) ) ).
fof(cc1_membered, axiom,  (! [A] :  (v6_membered(A) => v5_membered(A)) ) ).
fof(cc1_metric_1, axiom,  (! [A] :  (l1_metric_1(A) =>  ( ( ~ (v2_struct_0(A))  &  (v6_metric_1(A) &  (v7_metric_1(A) &  (v8_metric_1(A) & v9_metric_1(A)) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v6_metric_1(A) &  (v7_metric_1(A) &  (v8_metric_1(A) &  (v9_metric_1(A) & v11_metric_1(A)) ) ) ) ) ) ) ) ).
fof(cc1_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v3_ordinal1(A) & v7_ordinal1(A)) ) ) ).
fof(cc1_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (v1_ordinal1(A) & v2_ordinal1(A)) ) ) ).
fof(cc1_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_relat_1(A)) ) ).
fof(cc1_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C)) ) ) ).
fof(cc1_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v7_struct_0(A)) ) ) ).
fof(cc1_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_xboole_0(B)) ) ) ) ).
fof(cc1_xreal_0, axiom,  (! [A] :  (m1_subset_1(A, k1_numbers) => v1_xreal_0(A)) ) ).
fof(cc20_ordinal1, axiom,  (! [A] :  ( ~ (v1_setfam_1(A))  => v10_ordinal1(A)) ) ).
fof(cc2_funct_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ) ).
fof(cc2_membered, axiom,  (! [A] :  (v5_membered(A) => v4_membered(A)) ) ).
fof(cc2_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v7_ordinal1(A) &  ~ (v3_xxreal_0(A)) ) ) ) ).
fof(cc2_ordinal1, axiom,  (! [A] :  ( (v1_ordinal1(A) & v2_ordinal1(A))  => v3_ordinal1(A)) ) ).
fof(cc2_relat_1, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_relat_1(B)) ) ) ) ).
fof(cc2_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ).
fof(cc2_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc2_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ( ~ (v1_subset_1(B, A))  =>  ~ (v1_xboole_0(B)) ) ) ) ) ) ).
fof(cc2_xreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xreal_0(A)) ) ).
fof(cc2_xxreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xxreal_0(A)) ) ).
fof(cc3_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_funct_1(B)) ) ) ) ).
fof(cc3_membered, axiom,  (! [A] :  (v4_membered(A) => v3_membered(A)) ) ).
fof(cc3_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v7_ordinal1(A) &  ~ (v3_xxreal_0(A)) ) ) ) ).
fof(cc3_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_ordinal1(A)) ) ).
fof(cc3_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v3_relat_1(A)) ) ) ).
fof(cc3_relset_1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_xboole_0(C)) ) ) ) ).
fof(cc3_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  (v1_xboole_0(B) => v1_subset_1(B, A)) ) ) ) ) ).
fof(cc3_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xcmplx_0(A)) ) ).
fof(cc3_xxreal_0, axiom,  (! [A] :  ( (v1_xxreal_0(A) & v2_xxreal_0(A))  =>  ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v3_xxreal_0(A)) ) ) ) ) ).
fof(cc4_funct_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) ) ) ) ).
fof(cc4_membered, axiom,  (! [A] :  (v3_membered(A) => v2_membered(A)) ) ).
fof(cc4_nat_1, axiom,  (! [A] :  ( (v7_ordinal1(A) & v8_ordinal1(A))  =>  (v7_ordinal1(A) &  ~ (v2_xxreal_0(A)) ) ) ) ).
fof(cc4_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v5_ordinal1(A)) ) ).
fof(cc4_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v2_relat_1(A)) ) ) ).
fof(cc4_relset_1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A))) => v1_xboole_0(C)) ) ) ) ).
fof(cc4_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) =>  (v2_struct_0(A) & v8_struct_0(A)) ) ) ) ).
fof(cc4_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ~ (v1_subset_1(B, A)) ) ) ) ) ).
fof(cc4_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xxreal_0(A)) ) ).
fof(cc4_xxreal_0, axiom,  (! [A] :  ( ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v3_xxreal_0(A)) ) )  =>  (v1_xxreal_0(A) & v2_xxreal_0(A)) ) ) ).
fof(cc5_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) )  =>  ( ~ (v1_zfmisc_1(A))  &  (v1_relat_1(A) & v1_funct_1(A)) ) ) ) ).
fof(cc5_membered, axiom,  (! [A] :  (v3_membered(A) => v1_membered(A)) ) ).
fof(cc5_nat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v8_ordinal1(A)) ) ).
fof(cc5_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, A) => v3_ordinal1(B)) ) ) ) ).
fof(cc5_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(B)) => v4_relat_1(C, A)) ) ) ) ).
fof(cc5_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ( ~ (v2_struct_0(A))  &  ~ (v8_struct_0(A)) ) ) ) ) ).
fof(cc5_subset_1, axiom,  (! [A] :  (v1_zfmisc_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_zfmisc_1(B)) ) ) ) ).
fof(cc5_xxreal_0, axiom,  (! [A] :  ( (v1_xxreal_0(A) & v3_xxreal_0(A))  =>  ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v2_xxreal_0(A)) ) ) ) ) ).
fof(cc6_funct_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) ) ) ) ).
fof(cc6_membered, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xcmplx_0(B)) ) ) ) ).
fof(cc6_nat_1, axiom,  (! [A] :  ( ~ (v8_ordinal1(A))  =>  ~ (v1_xboole_0(A)) ) ) ).
fof(cc6_ordinal1, axiom,  (! [A] :  (v7_ordinal1(A) => v3_ordinal1(A)) ) ).
fof(cc6_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(B)) => v5_relat_1(C, A)) ) ) ) ).
fof(cc6_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v7_struct_0(A) => v8_struct_0(A)) ) ) ).
fof(cc6_xxreal_0, axiom,  (! [A] :  ( ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v2_xxreal_0(A)) ) )  =>  (v1_xxreal_0(A) & v3_xxreal_0(A)) ) ) ).
fof(cc7_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_funct_1(A)) ) ).
fof(cc7_membered, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xxreal_0(B)) ) ) ) ).
fof(cc7_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v7_ordinal1(A)) ) ).
fof(cc7_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  =>  (v1_xboole_0(B) &  (v1_relat_1(B) & v4_relat_1(B, A)) ) ) ) ) ) ).
fof(cc7_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ~ (v7_struct_0(A)) ) ) ) ).
fof(cc7_xxreal_0, axiom,  (! [A] :  ( (v8_ordinal1(A) & v1_xxreal_0(A))  =>  (v1_xxreal_0(A) &  ( ~ (v2_xxreal_0(A))  &  ~ (v3_xxreal_0(A)) ) ) ) ) ).
fof(cc8_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, A) =>  (v1_relat_1(B) & v1_funct_1(B)) ) ) ) ) ).
fof(cc8_membered, axiom,  (! [A] :  (v3_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xreal_0(B)) ) ) ) ).
fof(cc8_ordinal1, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) => v7_ordinal1(A)) ) ).
fof(cc8_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_xboole_0(B) &  (v1_relat_1(B) & v5_relat_1(B, A)) ) ) ) ) ) ).
fof(cc8_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v13_struct_0(A, k5_ordinal1)) ) ) ).
fof(cc8_xxreal_0, axiom,  (! [A] :  ( (v1_xxreal_0(A) &  ( ~ (v2_xxreal_0(A))  &  ~ (v3_xxreal_0(A)) ) )  =>  (v8_ordinal1(A) & v1_xxreal_0(A)) ) ) ).
fof(cc9_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_funct_1(B)) ) ) ) ).
fof(cc9_membered, axiom,  (! [A] :  (v4_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_rat_1(B)) ) ) ) ).
fof(cc9_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v6_ordinal1(A)) ) ).
fof(cc9_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, k5_ordinal1) => v2_struct_0(A)) ) ) ).
fof(commutativity_k2_xcmplx_0, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k2_xcmplx_0(A, B)=k2_xcmplx_0(B, A)) ) ).
fof(commutativity_k3_metric_1, axiom,  (! [A, B, C] :  ( ( (v8_metric_1(A) & l1_metric_1(A))  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k3_metric_1(A, B, C)=k3_metric_1(A, C, B)) ) ).
fof(connectedness_r1_xxreal_0, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  =>  (r1_xxreal_0(A, B) | r1_xxreal_0(B, A)) ) ) ).
fof(d10_xboole_0, axiom,  (! [A] :  (! [B] :  (A=B <=>  (r1_tarski(A, B) & r1_tarski(B, A)) ) ) ) ).
fof(d12_metric_1, axiom,  (! [A] :  ( (v1_funct_1(A) &  (v1_funct_2(A, k2_zfmisc_1(k1_numbers, k1_numbers), k1_numbers) & m1_subset_1(A, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k1_numbers, k1_numbers), k1_numbers)))) )  =>  (A=k6_metric_1 <=>  (! [B] :  (v1_xreal_0(B) =>  (! [C] :  (v1_xreal_0(C) => k1_binop_1(A, B, C)=k9_complex1(k6_xcmplx_0(B, C))) ) ) ) ) ) ) ).
fof(d13_metric_1, axiom, k7_metric_1=g1_metric_1(k1_numbers, k6_metric_1)).
fof(d13_ordinal1, axiom, k5_ordinal1=k1_xboole_0).
fof(d1_metric_1, axiom,  (! [A] :  (l1_metric_1(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k1_metric_1(A, B, C)=k1_binop_1(u1_metric_1(A), B, C)) ) ) ) ) ) ).
fof(d3_tarski, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) <=>  (! [C] :  (r2_hidden(C, A) => r2_hidden(C, B)) ) ) ) ) ).
fof(d7_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) =>  (! [B] :  (v1_xcmplx_0(B) => k6_xcmplx_0(A, B)=k2_xcmplx_0(A, k4_xcmplx_0(B))) ) ) ) ).
fof(dt_g1_metric_1, axiom,  (! [A, B] :  ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(A, A), k1_numbers) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), k1_numbers)))) )  =>  (v1_metric_1(g1_metric_1(A, B)) & l1_metric_1(g1_metric_1(A, B))) ) ) ).
fof(dt_k1_binop_1, axiom, $true).
fof(dt_k1_metric_1, axiom,  (! [A, B, C] :  ( (l1_metric_1(A) &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => v1_xreal_0(k1_metric_1(A, B, C))) ) ).
fof(dt_k1_numbers, axiom, $true).
fof(dt_k1_real_1, axiom,  (! [A] :  (m1_subset_1(A, k1_numbers) => m1_subset_1(k1_real_1(A), k1_numbers)) ) ).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_rcomp_1, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => m1_subset_1(k2_rcomp_1(A, B), k1_zfmisc_1(k1_numbers))) ) ).
fof(dt_k2_xcmplx_0, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_metric_1, axiom,  (! [A, B, C] :  ( ( (v8_metric_1(A) & l1_metric_1(A))  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => v1_xreal_0(k3_metric_1(A, B, C))) ) ).
fof(dt_k4_binop_1, axiom,  (! [A, B, C, D] :  ( ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  &  (m1_subset_1(C, A) & m1_subset_1(D, A)) )  => m1_subset_1(k4_binop_1(A, B, C, D), A)) ) ).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k4_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => v1_xcmplx_0(k4_xcmplx_0(A))) ) ).
fof(dt_k4_xxreal_1, axiom, $true).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k5_real_1, axiom,  (! [A, B] :  ( (m1_subset_1(A, k1_numbers) & m1_subset_1(B, k1_numbers))  => m1_subset_1(k5_real_1(A, B), k1_numbers)) ) ).
fof(dt_k6_metric_1, axiom,  (v1_funct_1(k6_metric_1) &  (v1_funct_2(k6_metric_1, k2_zfmisc_1(k1_numbers, k1_numbers), k1_numbers) & m1_subset_1(k6_metric_1, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k1_numbers, k1_numbers), k1_numbers)))) ) ).
fof(dt_k6_xcmplx_0, axiom, $true).
fof(dt_k7_metric_1, axiom,  (v1_metric_1(k7_metric_1) & l1_metric_1(k7_metric_1)) ).
fof(dt_k8_metric_1, axiom,  (! [A, B, C] :  ( (l1_metric_1(A) &  (m1_subset_1(B, u1_struct_0(A)) & v1_xreal_0(C)) )  => m1_subset_1(k8_metric_1(A, B, C), k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k9_complex1, axiom,  (! [A] :  (v1_xcmplx_0(A) => v1_xreal_0(k9_complex1(A))) ) ).
fof(dt_l1_metric_1, axiom,  (! [A] :  (l1_metric_1(A) => l1_struct_0(A)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_u1_metric_1, axiom,  (! [A] :  (l1_metric_1(A) =>  (v1_funct_1(u1_metric_1(A)) &  (v1_funct_2(u1_metric_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), k1_numbers) & m1_subset_1(u1_metric_1(A), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), k1_numbers)))) ) ) ) ).
fof(dt_u1_struct_0, axiom, $true).
fof(existence_l1_metric_1, axiom,  (? [A] : l1_metric_1(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc10_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_xboole_0(k2_zfmisc_1(A, B))) ) ) ).
fof(fc10_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v2_xxreal_0(k2_xcmplx_0(A, B))) ) ) ).
fof(fc11_xreal_0, axiom,  (! [A, B] :  ( ( (v2_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  => v2_xxreal_0(k2_xcmplx_0(A, B))) ) ).
fof(fc12_xreal_0, axiom,  (! [A, B] :  ( ( (v2_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  => v2_xxreal_0(k2_xcmplx_0(B, A))) ) ).
fof(fc13_xreal_0, axiom,  (! [A, B] :  ( ( (v3_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  => v3_xxreal_0(k2_xcmplx_0(A, B))) ) ).
fof(fc14_xreal_0, axiom,  (! [A, B] :  ( ( (v3_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  => v3_xxreal_0(k2_xcmplx_0(B, A))) ) ).
fof(fc15_xreal_0, axiom,  (! [A] :  ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  =>  (v1_xcmplx_0(k4_xcmplx_0(A)) &  ~ (v3_xxreal_0(k4_xcmplx_0(A))) ) ) ) ).
fof(fc16_xreal_0, axiom,  (! [A] :  ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  =>  (v1_xcmplx_0(k4_xcmplx_0(A)) &  ~ (v2_xxreal_0(k4_xcmplx_0(A))) ) ) ) ).
fof(fc17_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v3_xxreal_0(k6_xcmplx_0(A, B))) ) ) ).
fof(fc18_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v2_xxreal_0(k6_xcmplx_0(B, A))) ) ) ).
fof(fc19_xreal_0, axiom,  (! [A, B] :  ( ( (v2_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  => v2_xxreal_0(k6_xcmplx_0(A, B))) ) ).
fof(fc1_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & v7_ordinal1(B))  => v7_ordinal1(k2_xcmplx_0(A, B))) ) ).
fof(fc1_numbers, axiom,  ~ (v1_xboole_0(k1_numbers)) ).
fof(fc1_struct_0, axiom,  (! [A] :  ( (v2_struct_0(A) & l1_struct_0(A))  => v1_xboole_0(u1_struct_0(A))) ) ).
fof(fc1_subset_1, axiom,  (! [A] :  ~ (v1_xboole_0(k1_zfmisc_1(A))) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc20_xreal_0, axiom,  (! [A, B] :  ( ( (v2_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  => v3_xxreal_0(k6_xcmplx_0(B, A))) ) ).
fof(fc21_xreal_0, axiom,  (! [A, B] :  ( ( (v3_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  => v3_xxreal_0(k6_xcmplx_0(A, B))) ) ).
fof(fc22_xreal_0, axiom,  (! [A, B] :  ( ( (v3_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  => v2_xxreal_0(k6_xcmplx_0(B, A))) ) ).
fof(fc2_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_xboole_0(u1_struct_0(A))) ) ) ).
fof(fc3_membered, axiom, v3_membered(k1_numbers)).
fof(fc3_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) &  (v7_ordinal1(B) &  ~ (v8_ordinal1(B)) ) )  =>  ~ (v8_ordinal1(k2_xcmplx_0(A, B))) ) ) ).
fof(fc3_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) =>  (v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A))) ) ) ).
fof(fc4_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) &  (v7_ordinal1(B) &  ~ (v8_ordinal1(B)) ) )  =>  ~ (v8_ordinal1(k2_xcmplx_0(B, A))) ) ) ).
fof(fc4_topmetr, axiom,  (! [A] :  ( (v3_topmetr(A) & l1_struct_0(A))  => v3_membered(u1_struct_0(A))) ) ).
fof(fc56_membered, axiom, v7_membered(k1_numbers)).
fof(fc59_membered, axiom, v7_membered(k4_ordinal1)).
fof(fc5_metric_1, axiom,  ( ~ (v2_struct_0(k7_metric_1))  & v1_metric_1(k7_metric_1)) ).
fof(fc5_xreal_0, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => v1_xreal_0(k2_xcmplx_0(A, B))) ) ).
fof(fc6_membered, axiom, v6_membered(k4_ordinal1)).
fof(fc6_metric_1, axiom,  (v1_metric_1(k7_metric_1) &  (v6_metric_1(k7_metric_1) &  (v7_metric_1(k7_metric_1) &  (v8_metric_1(k7_metric_1) & v9_metric_1(k7_metric_1)) ) ) ) ).
fof(fc6_ordinal1, axiom,  ( ~ (v1_xboole_0(k4_ordinal1))  & v3_ordinal1(k4_ordinal1)) ).
fof(fc6_relat_1, axiom,  (! [A, B] : v1_relat_1(k2_zfmisc_1(A, B))) ).
fof(fc6_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(fc6_topmetr, axiom,  (v1_metric_1(k7_metric_1) & v3_topmetr(k7_metric_1)) ).
fof(fc7_struct_0, axiom,  (! [A] :  ( (v7_struct_0(A) & l1_struct_0(A))  => v1_zfmisc_1(u1_struct_0(A))) ) ).
fof(fc7_xreal_0, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => v1_xreal_0(k6_xcmplx_0(A, B))) ) ).
fof(fc8_numbers, axiom,  ~ (v1_finset_1(k1_numbers)) ).
fof(fc8_ordinal1, axiom, v7_ordinal1(k5_ordinal1)).
fof(fc8_struct_0, axiom,  (! [A] :  ( (v8_struct_0(A) & l1_struct_0(A))  => v1_finset_1(u1_struct_0(A))) ) ).
fof(fc9_ordinal1, axiom, v8_ordinal1(k5_ordinal1)).
fof(fc9_struct_0, axiom,  (! [A] :  ( ( ~ (v8_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_finset_1(u1_struct_0(A))) ) ) ).
fof(fc9_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v3_xxreal_0(k2_xcmplx_0(A, B))) ) ) ).
fof(free_g1_metric_1, axiom,  (! [A, B] :  ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(A, A), k1_numbers) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), k1_numbers)))) )  =>  (! [C, D] :  (g1_metric_1(A, B)=g1_metric_1(C, D) =>  (A=C & B=D) ) ) ) ) ).
fof(involutiveness_k1_real_1, axiom,  (! [A] :  (m1_subset_1(A, k1_numbers) => k1_real_1(k1_real_1(A))=A) ) ).
fof(involutiveness_k4_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => k4_xcmplx_0(k4_xcmplx_0(A))=A) ) ).
fof(projectivity_k9_complex1, axiom,  (! [A] :  (v1_xcmplx_0(A) => k9_complex1(k9_complex1(A))=k9_complex1(A)) ) ).
fof(rc10_ordinal1, axiom,  (? [A] :  ~ (v8_ordinal1(A)) ) ).
fof(rc11_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) ) ) ).
fof(rc12_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) & v9_ordinal1(A)) ) ).
fof(rc13_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) &  ~ (v9_ordinal1(A)) ) ) ).
fof(rc1_funct_1, axiom,  (? [A] :  (v1_relat_1(A) & v1_funct_1(A)) ) ).
fof(rc1_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v6_membered(A)) ) ).
fof(rc1_metric_1, axiom,  (? [A] :  (l1_metric_1(A) & v1_metric_1(A)) ) ).
fof(rc1_nat_1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc1_ordinal1, axiom,  (? [A] :  (v1_ordinal1(A) & v2_ordinal1(A)) ) ).
fof(rc1_relat_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_relat_1(A)) ) ).
fof(rc1_relset_1, axiom,  (! [A, B] :  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_xboole_0(C) &  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ) ) ).
fof(rc1_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc1_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc1_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(rc21_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc22_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc2_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ).
fof(rc2_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v6_membered(A)) ) ).
fof(rc2_metric_1, axiom,  (? [A] :  (l1_metric_1(A) &  ( ~ (v2_struct_0(A))  & v1_metric_1(A)) ) ) ).
fof(rc2_nat_1, axiom,  (? [A] :  (v7_ordinal1(A) & v8_ordinal1(A)) ) ).
fof(rc2_ordinal1, axiom,  (? [A] : v3_ordinal1(A)) ).
fof(rc2_relat_1, axiom,  (? [A] :  (v1_relat_1(A) & v2_relat_1(A)) ) ).
fof(rc2_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_xboole_0(B)) ) ) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc2_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc2_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(rc3_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) ) ) ).
fof(rc3_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v6_membered(A) & v7_membered(A)) ) ) ).
fof(rc3_metric_1, axiom,  (? [A] :  (l1_metric_1(A) &  ( ~ (v2_struct_0(A))  &  (v1_metric_1(A) &  (v6_metric_1(A) &  (v7_metric_1(A) &  (v8_metric_1(A) & v9_metric_1(A)) ) ) ) ) ) ) ).
fof(rc3_nat_1, axiom,  (? [A] :  (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) ) ) ).
fof(rc3_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_ordinal1(A) &  (v2_ordinal1(A) & v3_ordinal1(A)) ) ) ) ).
fof(rc3_relat_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ).
fof(rc3_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_subset_1(B, A)) ) ) ) ).
fof(rc3_topmetr, axiom,  (? [A] :  (l1_struct_0(A) &  ( ~ (v2_struct_0(A))  & v3_topmetr(A)) ) ) ).
fof(rc3_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v2_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc3_xxreal_0, axiom,  (? [A] :  (v1_xxreal_0(A) & v2_xxreal_0(A)) ) ).
fof(rc4_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) ) ) ) ).
fof(rc4_nat_1, axiom,  (? [A] :  (m1_subset_1(A, k1_zfmisc_1(k1_numbers)) &  ( ~ (v1_xboole_0(A))  & v3_ordinal1(A)) ) ) ).
fof(rc4_ordinal1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) & v5_ordinal1(B)) ) ) ) ) ).
fof(rc4_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc4_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_subset_1(B, A)) ) ) ) ).
fof(rc4_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v3_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc4_xxreal_0, axiom,  (? [A] :  (v1_xxreal_0(A) & v3_xxreal_0(A)) ) ).
fof(rc5_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) ) ) ).
fof(rc5_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc5_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc5_xreal_0, axiom,  (? [A] :  (v8_ordinal1(A) &  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc5_xxreal_0, axiom,  (? [A] :  (v8_ordinal1(A) & v1_xxreal_0(A)) ) ).
fof(rc6_funct_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) & v1_funct_1(C)) ) ) ) ) ).
fof(rc6_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc6_subset_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc7_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v4_funct_1(A)) ) ).
fof(rc7_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v7_ordinal1(A)) ) ).
fof(rc8_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rc9_funct_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) & v1_funct_1(B)) ) ) ) ) ).
fof(rc9_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(redefinition_k1_real_1, axiom,  (! [A] :  (m1_subset_1(A, k1_numbers) => k1_real_1(A)=k4_xcmplx_0(A)) ) ).
fof(redefinition_k2_rcomp_1, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => k2_rcomp_1(A, B)=k4_xxreal_1(A, B)) ) ).
fof(redefinition_k3_metric_1, axiom,  (! [A, B, C] :  ( ( (v8_metric_1(A) & l1_metric_1(A))  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k3_metric_1(A, B, C)=k1_metric_1(A, B, C)) ) ).
fof(redefinition_k4_binop_1, axiom,  (! [A, B, C, D] :  ( ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  &  (m1_subset_1(C, A) & m1_subset_1(D, A)) )  => k4_binop_1(A, B, C, D)=k1_binop_1(B, C, D)) ) ).
fof(redefinition_k5_real_1, axiom,  (! [A, B] :  ( (m1_subset_1(A, k1_numbers) & m1_subset_1(B, k1_numbers))  => k5_real_1(A, B)=k6_xcmplx_0(A, B)) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(reflexivity_r1_xxreal_0, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => r1_xxreal_0(A, A)) ) ).
fof(rqLessOrEqual__r1_xxreal_0__r1_r1, axiom, r1_xxreal_0(1, 1)).
fof(rqLessOrEqual__r1_xxreal_0__r1_rm1, axiom,  ~ (r1_xxreal_0(1, k4_xcmplx_0(1))) ).
fof(rqLessOrEqual__r1_xxreal_0__rm1_r1, axiom, r1_xxreal_0(k4_xcmplx_0(1), 1)).
fof(rqLessOrEqual__r1_xxreal_0__rm1_rm1, axiom, r1_xxreal_0(k4_xcmplx_0(1), k4_xcmplx_0(1))).
fof(rqRealNeg__k4_xcmplx_0__r1_rm1, axiom, k4_xcmplx_0(1)=k4_xcmplx_0(1)).
fof(rqRealNeg__k4_xcmplx_0__rm1_r1, axiom, k4_xcmplx_0(k4_xcmplx_0(1))=1).
fof(spc1_arithm, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k2_xcmplx_0(A, k4_xcmplx_0(B))=k6_xcmplx_0(A, B)) ) ).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(spc1_numerals, axiom,  (v2_xxreal_0(1) & m1_subset_1(1, k4_ordinal1)) ).
fof(spc6_arithm, axiom,  (! [A, B, C] :  ( (v1_xcmplx_0(A) &  (v1_xcmplx_0(B) & v1_xcmplx_0(C)) )  => k2_xcmplx_0(k2_xcmplx_0(A, B), C)=k2_xcmplx_0(A, k2_xcmplx_0(B, C))) ) ).
fof(spc8_arithm, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k2_xcmplx_0(k4_xcmplx_0(A), k4_xcmplx_0(B))=k4_xcmplx_0(k2_xcmplx_0(A, B))) ) ).
fof(spc9_arithm, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k6_xcmplx_0(k4_xcmplx_0(A), k4_xcmplx_0(B))=k6_xcmplx_0(B, A)) ) ).
fof(t11_metric_1, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (l1_metric_1(B) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(B)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(B)) =>  (r2_tarski(D, k8_metric_1(B, C, A)) <=>  ( ~ (v2_struct_0(B))  &  ~ (r1_xxreal_0(A, k1_metric_1(B, C, D))) ) ) ) ) ) ) ) ) ) ) ).
fof(t1_numerals, axiom, m1_subset_1(k1_xboole_0, k4_ordinal1)).
fof(t1_rcomp_1, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  (! [C] :  (v1_xreal_0(C) =>  (r2_hidden(B, k2_rcomp_1(k6_xcmplx_0(C, A), k2_xcmplx_0(C, A))) <=>  ~ (r1_xxreal_0(A, k9_complex1(k6_xcmplx_0(B, C)))) ) ) ) ) ) ) ) ).
fof(t1_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ( (r1_xxreal_0(A, B) & v2_xxreal_0(A))  => v2_xxreal_0(B)) ) ) ) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t2_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ( (r1_xxreal_0(A, B) & v3_xxreal_0(B))  => v3_xxreal_0(A)) ) ) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t3_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( (r1_xxreal_0(A, B) &  ( ~ (v3_xxreal_0(A))  & v3_xxreal_0(B)) ) ) ) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t4_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( (r1_xxreal_0(A, B) &  ( ~ (v2_xxreal_0(B))  & v2_xxreal_0(A)) ) ) ) ) ) ) ).
fof(t4_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r2_tarski(A, B) & m1_subset_1(B, k1_zfmisc_1(C)))  => m1_subset_1(A, C)) ) ) ) ).
fof(t52_complex1, axiom,  (! [A] :  (v1_xcmplx_0(A) => k9_complex1(k4_xcmplx_0(A))=k9_complex1(A)) ) ).
fof(t5_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  (r1_xxreal_0(A, B) =>  (v8_ordinal1(B) |  (v3_xxreal_0(A) | v2_xxreal_0(B)) ) ) ) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t6_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  (r1_xxreal_0(A, B) =>  (v8_ordinal1(A) |  (v2_xxreal_0(B) | v3_xxreal_0(A)) ) ) ) ) ) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t7_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( ( ~ (r1_xxreal_0(A, B))  &  ( ~ (v2_xxreal_0(A))  &  ~ (v3_xxreal_0(B)) ) ) ) ) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
fof(t8_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( ( ~ (r1_xxreal_0(A, B))  &  ( ~ (v3_xxreal_0(B))  &  ~ (v2_xxreal_0(A)) ) ) ) ) ) ) ) ).
