% Mizar problem: t3_topalg_2,topalg_2,327,5 
fof(t3_topalg_2, conjecture,  (! [A] :  (m1_subset_1(A, k4_ordinal1) =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v1_topalg_2(B, A) & m1_pre_topc(B, k15_euclid(A))) )  =>  (! [C] :  (m1_subset_1(C, u1_struct_0(B)) =>  (! [D] :  (m1_borsuk_2(D, B, C, C) => u1_struct_0(k5_topalg_1(B, C))=k1_tarski(k6_eqrel_1(k2_topalg_1(B, C), k2_topalg_1(B, C), k4_topalg_1(B, C), D))) ) ) ) ) ) ) ) ).
fof(abstractness_v15_algstr_0, axiom,  (! [A] :  (l3_algstr_0(A) =>  (v15_algstr_0(A) => A=g3_algstr_0(u1_struct_0(A), u2_algstr_0(A))) ) ) ).
fof(abstractness_v1_pre_topc, axiom,  (! [A] :  (l1_pre_topc(A) =>  (v1_pre_topc(A) => A=g1_pre_topc(u1_struct_0(A), u1_pre_topc(A))) ) ) ).
fof(abstractness_v5_rltopsp1, axiom,  (! [A] :  (l1_rltopsp1(A) =>  (v5_rltopsp1(A) => A=g1_rltopsp1(u1_struct_0(A), u2_struct_0(A), u1_algstr_0(A), u1_rlvect_1(A), u1_pre_topc(A))) ) ) ).
fof(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_monoid_0, axiom,  (! [A] :  (l3_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v3_group_1(A) & v13_monoid_0(A)) )  =>  ( ~ (v2_struct_0(A))  &  (v1_group_1(A) & v16_monoid_0(A)) ) ) ) ) ).
fof(cc10_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ( ~ (v2_struct_0(A))  & v7_struct_0(A))  => v13_struct_0(A, 1)) ) ) ).
fof(cc10_xxreal_2, axiom,  (! [A] :  ( (v3_membered(A) & v1_xxreal_2(A))  =>  (v3_membered(A) & v3_xxreal_2(A)) ) ) ).
fof(cc11_membered, axiom,  (! [A] :  (v6_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v7_ordinal1(B)) ) ) ) ).
fof(cc11_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, 1) =>  ( ~ (v2_struct_0(A))  & v7_struct_0(A)) ) ) ) ).
fof(cc11_xxreal_2, axiom,  (! [A] :  ( (v3_membered(A) & v2_xxreal_2(A))  =>  (v3_membered(A) & v4_xxreal_2(A)) ) ) ).
fof(cc12_membered, axiom,  (! [A] :  (v1_xboole_0(A) => v6_membered(A)) ) ).
fof(cc12_xxreal_2, axiom,  (! [A] :  ( (v5_membered(A) & v5_xxreal_2(A))  =>  (v5_membered(A) & v1_finset_1(A)) ) ) ).
fof(cc13_membered, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_membered(B)) ) ) ) ).
fof(cc13_xxreal_2, axiom,  (! [A] :  ( (v6_membered(A) & v4_xxreal_2(A))  =>  (v6_membered(A) &  (v1_finset_1(A) & v4_xxreal_2(A)) ) ) ) ).
fof(cc14_membered, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v2_membered(B)) ) ) ) ).
fof(cc14_xxreal_2, axiom,  (! [A] :  ( (v2_membered(A) & v5_xxreal_2(A))  =>  (v2_membered(A) & v3_membered(A)) ) ) ).
fof(cc15_membered, axiom,  (! [A] :  (v3_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v3_membered(B)) ) ) ) ).
fof(cc15_xxreal_2, axiom,  (! [A] :  ( (v2_membered(A) & v1_xboole_0(A))  =>  (v2_membered(A) & v6_xxreal_2(A)) ) ) ).
fof(cc16_membered, axiom,  (! [A] :  (v4_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_membered(B)) ) ) ) ).
fof(cc16_xxreal_2, axiom,  (! [A] :  ( (v2_membered(A) & v1_xxreal_2(A))  =>  (v2_membered(A) &  ~ (v1_xboole_0(A)) ) ) ) ).
fof(cc17_membered, axiom,  (! [A] :  (v5_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v5_membered(B)) ) ) ) ).
fof(cc17_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc17_xxreal_2, axiom,  (! [A] :  ( (v2_membered(A) & v2_xxreal_2(A))  =>  (v2_membered(A) &  ~ (v1_xboole_0(A)) ) ) ) ).
fof(cc18_membered, axiom,  (! [A] :  (v6_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_membered(B)) ) ) ) ).
fof(cc19_membered, axiom,  (! [A] :  (v1_xboole_0(A) => v7_membered(A)) ) ).
fof(cc1_borsuk_2, axiom,  (! [A, B, C] :  ( ( (v1_borsuk_2(A) & l1_pre_topc(A))  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  =>  (! [D] :  (m1_borsuk_2(D, A, B, C) => v5_pre_topc(D, k5_topmetr, A)) ) ) ) ).
fof(cc1_funct_2, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_partfun1(C, A) => v1_funct_2(C, A, B)) ) ) ) ).
fof(cc1_jordan2b, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(k15_euclid(A))) => v5_relat_1(B, k1_numbers)) ) ) ) ).
fof(cc1_jordan2c, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) =>  (v2_compts_1(B, k15_euclid(A)) => v9_rltopsp1(B, k15_euclid(A))) ) ) ) ) ).
fof(cc1_membered, axiom,  (! [A] :  (v6_membered(A) => v5_membered(A)) ) ).
fof(cc1_monoid_0, axiom,  (! [A] :  ( (v1_monoid_0(A) & l1_struct_0(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (v1_relat_1(B) & v1_funct_1(B)) ) ) ) ) ).
fof(cc1_pre_topc, axiom,  (! [A] :  ( (v2_pre_topc(A) & l1_pre_topc(A))  =>  (! [B] :  (m1_pre_topc(B, A) => v2_pre_topc(B)) ) ) ) ).
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_rltopsp1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_rlvect_1(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (v1_xboole_0(B) => v3_rltopsp1(B, A)) ) ) ) ) ).
fof(cc1_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v7_struct_0(A)) ) ) ).
fof(cc1_topalg_2, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) =>  (! [B] :  (m1_pre_topc(B, k15_euclid(A)) =>  ( ( ~ (v2_struct_0(B))  & v1_topalg_2(B, A))  =>  ( ~ (v2_struct_0(B))  & v1_borsuk_2(B)) ) ) ) ) ) ).
fof(cc1_topmetr, axiom,  (! [A] :  ( (v3_topmetr(A) & l1_pre_topc(A))  =>  (! [B] :  (m1_pre_topc(B, A) => v3_topmetr(B)) ) ) ) ).
fof(cc1_xreal_0, axiom,  (! [A] :  (m1_subset_1(A, k1_numbers) => v1_xreal_0(A)) ) ).
fof(cc1_zfmisc_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_zfmisc_1(A)) ) ).
fof(cc2_borsuk_2, axiom,  (! [A] :  (l1_pre_topc(A) =>  ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & v1_borsuk_2(A)) )  =>  ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & v1_connsp_1(A)) ) ) ) ) ).
fof(cc2_euclid, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(k15_euclid(A))) => v1_finseq_1(B)) ) ) ) ).
fof(cc2_funct_2, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_funct_2(C, A, B) => v1_partfun1(C, A)) ) ) ) ) ).
fof(cc2_membered, axiom,  (! [A] :  (v5_membered(A) => v4_membered(A)) ) ).
fof(cc2_monoid_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_monoid_0(A) => v1_monoid_0(A)) ) ) ).
fof(cc2_pre_topc, axiom,  (! [A] :  ( (v2_pre_topc(A) & l1_pre_topc(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (v1_xboole_0(B) => v4_pre_topc(B, A)) ) ) ) ) ).
fof(cc2_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_rltopsp1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_rlvect_1(A) &  (v6_rlvect_1(A) &  (v7_rlvect_1(A) &  (v8_rlvect_1(A) & l1_rlvect_1(A)) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (v3_rltopsp1(B, A) => v2_rltopsp1(B, A)) ) ) ) ) ).
fof(cc2_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc2_xreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xreal_0(A)) ) ).
fof(cc2_xxreal_2, axiom,  (! [A] :  ( (v2_membered(A) &  (v1_finset_1(A) &  ~ (v1_xboole_0(A)) ) )  =>  (v2_membered(A) &  ( ~ (v1_xboole_0(A))  &  (v1_xxreal_2(A) & v2_xxreal_2(A)) ) ) ) ) ).
fof(cc2_zfmisc_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  ~ (v1_xboole_0(A)) ) ) ).
fof(cc3_euclid, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(k15_euclid(A))) => v3_valued_0(B)) ) ) ) ).
fof(cc3_funct_2, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_funct_2(C, A, B) => v1_partfun1(C, A)) ) ) ) ) ).
fof(cc3_membered, axiom,  (! [A] :  (v4_membered(A) => v3_membered(A)) ) ).
fof(cc3_monoid_0, axiom,  (! [A] :  ( (v2_monoid_0(A) & l1_struct_0(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => v1_finseq_1(B)) ) ) ) ).
fof(cc3_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_rltopsp1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_rlvect_1(A) &  (v6_rlvect_1(A) &  (v7_rlvect_1(A) &  (v8_rlvect_1(A) &  (v6_rltopsp1(A) &  (v7_rltopsp1(A) & l1_rltopsp1(A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (v1_xboole_0(B) => v9_rltopsp1(B, A)) ) ) ) ) ).
fof(cc3_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xcmplx_0(A)) ) ).
fof(cc3_xxreal_2, axiom,  (! [A] :  ( (v6_membered(A) &  ~ (v1_xboole_0(A)) )  =>  (v6_membered(A) &  ( ~ (v1_xboole_0(A))  & v1_xxreal_2(A)) ) ) ) ).
fof(cc4_euclid, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(k15_euclid(A))) => v3_card_1(B, A)) ) ) ) ).
fof(cc4_funct_2, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, A))) =>  (v1_funct_2(B, A, A) => v1_partfun1(B, A)) ) ) ) ).
fof(cc4_membered, axiom,  (! [A] :  (v3_membered(A) => v2_membered(A)) ) ).
fof(cc4_monoid_0, axiom,  (! [A] :  (l3_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) & v3_group_1(A)) )  =>  ( ~ (v2_struct_0(A))  & v13_monoid_0(A)) ) ) ) ).
fof(cc4_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_rltopsp1, axiom,  (! [A] :  (l1_rltopsp1(A) =>  ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) &  (v7_pre_topc(A) &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_rlvect_1(A) &  (v6_rlvect_1(A) &  (v7_rlvect_1(A) &  (v8_rlvect_1(A) &  (v6_rltopsp1(A) & v7_rltopsp1(A)) ) ) ) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) &  (v8_pre_topc(A) &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_rlvect_1(A) &  (v6_rlvect_1(A) &  (v7_rlvect_1(A) &  (v8_rlvect_1(A) &  (v6_rltopsp1(A) & v7_rltopsp1(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(cc4_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) =>  (v2_struct_0(A) & v8_struct_0(A)) ) ) ) ).
fof(cc4_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xxreal_0(A)) ) ).
fof(cc4_xxreal_2, axiom,  (! [A] :  ( (v2_membered(A) & v5_xxreal_2(A))  =>  (v2_membered(A) &  (v3_xxreal_2(A) & v4_xxreal_2(A)) ) ) ) ).
fof(cc5_funct_2, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A))) =>  (v1_funct_2(B, k2_zfmisc_1(A, A), A) => v1_partfun1(B, k2_zfmisc_1(A, A))) ) ) ) ).
fof(cc5_membered, axiom,  (! [A] :  (v3_membered(A) => v1_membered(A)) ) ).
fof(cc5_monoid_0, axiom,  (! [A] :  (l3_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v3_group_1(A) & v13_monoid_0(A)) )  =>  ( ~ (v2_struct_0(A))  & v2_group_1(A)) ) ) ) ).
fof(cc5_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ( ~ (v2_struct_0(A))  &  ~ (v8_struct_0(A)) ) ) ) ) ).
fof(cc5_xxreal_2, axiom,  (! [A] :  ( (v2_membered(A) &  (v3_xxreal_2(A) & v4_xxreal_2(A)) )  =>  (v2_membered(A) & v5_xxreal_2(A)) ) ) ).
fof(cc6_membered, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xcmplx_0(B)) ) ) ) ).
fof(cc6_monoid_0, axiom,  (! [A] :  (l3_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  & v13_monoid_0(A))  =>  ( ~ (v2_struct_0(A))  &  (v11_monoid_0(A) & v12_monoid_0(A)) ) ) ) ) ).
fof(cc6_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v7_struct_0(A) => v8_struct_0(A)) ) ) ).
fof(cc6_xxreal_2, axiom,  (! [A] :  ( (v3_membered(A) & v1_finset_1(A))  =>  (v3_membered(A) & v5_xxreal_2(A)) ) ) ).
fof(cc7_membered, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xxreal_0(B)) ) ) ) ).
fof(cc7_monoid_0, axiom,  (! [A] :  (l3_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v11_monoid_0(A) & v12_monoid_0(A)) )  =>  ( ~ (v2_struct_0(A))  & v13_monoid_0(A)) ) ) ) ).
fof(cc7_pre_topc, axiom,  (! [A] :  (l1_pre_topc(A) =>  (v7_pre_topc(A) => v6_pre_topc(A)) ) ) ).
fof(cc7_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ~ (v7_struct_0(A)) ) ) ) ).
fof(cc7_xxreal_2, axiom,  (! [A] :  ( (v5_membered(A) &  ( ~ (v1_xboole_0(A))  & v4_xxreal_2(A)) )  =>  (v5_membered(A) &  ( ~ (v1_xboole_0(A))  & v2_xxreal_2(A)) ) ) ) ).
fof(cc8_membered, axiom,  (! [A] :  (v3_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xreal_0(B)) ) ) ) ).
fof(cc8_monoid_0, axiom,  (! [A] :  (l3_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  & v16_monoid_0(A))  =>  ( ~ (v2_struct_0(A))  &  (v14_monoid_0(A) & v15_monoid_0(A)) ) ) ) ) ).
fof(cc8_pre_topc, axiom,  (! [A] :  (l1_pre_topc(A) =>  (v8_pre_topc(A) => v7_pre_topc(A)) ) ) ).
fof(cc8_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v13_struct_0(A, k5_ordinal1)) ) ) ).
fof(cc8_xxreal_2, axiom,  (! [A] :  ( (v5_membered(A) &  ( ~ (v1_xboole_0(A))  & v3_xxreal_2(A)) )  =>  (v5_membered(A) &  ( ~ (v1_xboole_0(A))  & v1_xxreal_2(A)) ) ) ) ).
fof(cc9_funct_2, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  ( (v1_funct_1(C) & v1_funct_2(C, A, B))  =>  (v1_funct_1(C) &  ( ~ (v1_xboole_0(C))  & v1_funct_2(C, A, B)) ) ) ) ) ) ) ).
fof(cc9_membered, axiom,  (! [A] :  (v4_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_rat_1(B)) ) ) ) ).
fof(cc9_monoid_0, axiom,  (! [A] :  (l3_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v14_monoid_0(A) & v15_monoid_0(A)) )  =>  ( ~ (v2_struct_0(A))  & v16_monoid_0(A)) ) ) ) ).
fof(cc9_pre_topc, axiom,  (! [A] :  (l1_pre_topc(A) =>  (v2_struct_0(A) => v6_pre_topc(A)) ) ) ).
fof(cc9_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, k5_ordinal1) => v2_struct_0(A)) ) ) ).
fof(cc9_xxreal_2, axiom,  (! [A] :  (v6_membered(A) =>  (v6_membered(A) & v3_xxreal_2(A)) ) ) ).
fof(d10_xboole_0, axiom,  (! [A] :  (! [B] :  (A=B <=>  (r1_tarski(A, B) & r1_tarski(B, A)) ) ) ) ).
fof(d1_binop_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (! [C] : k1_binop_1(A, B, C)=k1_funct_1(A, k4_tarski(B, C))) ) ) ) ).
fof(d1_tarski, axiom,  (! [A] :  (! [B] :  (B=k1_tarski(A) <=>  (! [C] :  (r2_hidden(C, B) <=> C=A) ) ) ) ) ).
fof(d1_topalg_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_pre_topc(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (D=k1_topalg_1(A, B, C) <=>  (! [E] :  (r2_hidden(E, D) <=> m1_borsuk_2(E, A, B, C)) ) ) ) ) ) ) ) ) ) ).
fof(d2_topalg_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_pre_topc(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => k2_topalg_1(A, B)=k1_topalg_1(A, B, B)) ) ) ) ).
fof(d2_xboole_0, axiom, k1_xboole_0=o_0_0_xboole_0).
fof(d3_eqrel_1, axiom,  (! [A] :  (! [B] :  ( (v3_relat_2(B) &  (v8_relat_2(B) &  (v1_partfun1(B, A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, A)))) ) )  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) =>  (C=k7_eqrel_1(A, B) <=>  (! [D] :  (m1_subset_1(D, k1_zfmisc_1(A)) =>  (r2_tarski(D, C) <=>  (? [E] :  (r2_hidden(E, A) & D=k6_eqrel_1(A, A, B, E)) ) ) ) ) ) ) ) ) ) ) ).
fof(d3_tarski, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) <=>  (! [C] :  (r2_hidden(C, A) => r2_hidden(C, B)) ) ) ) ) ).
fof(d4_topalg_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & l1_pre_topc(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => k4_topalg_1(A, B)=k3_topalg_1(A, B, B)) ) ) ) ).
fof(d5_topalg_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & l1_pre_topc(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  ( (v15_algstr_0(C) & l3_algstr_0(C))  =>  (C=k5_topalg_1(A, B) <=>  (u1_struct_0(C)=k8_eqrel_1(k2_topalg_1(A, B), k4_topalg_1(A, B)) &  (! [D] :  (m1_subset_1(D, u1_struct_0(C)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(C)) =>  (? [F] :  (m1_borsuk_2(F, A, B, B) &  (? [G] :  (m1_borsuk_2(G, A, B, B) &  (D=k6_eqrel_1(k2_topalg_1(A, B), k2_topalg_1(A, B), k4_topalg_1(A, B), F) &  (E=k6_eqrel_1(k2_topalg_1(A, B), k2_topalg_1(A, B), k4_topalg_1(A, B), G) & k4_binop_1(u1_struct_0(C), u2_algstr_0(C), D, E)=k6_eqrel_1(k2_topalg_1(A, B), k2_topalg_1(A, B), k4_topalg_1(A, B), k1_borsuk_2(A, B, B, B, F, G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d7_borsuk_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_pre_topc(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_borsuk_2(D, A, B, C) =>  (! [E] :  (m1_borsuk_2(E, A, B, C) =>  (r3_borsuk_2(A, B, C, D, E) <=>  (? [F] :  ( (v1_funct_1(F) &  (v1_funct_2(F, u1_struct_0(k2_borsuk_1(k5_topmetr, k5_topmetr)), u1_struct_0(A)) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr, k5_topmetr)), u1_struct_0(A))))) )  &  (v5_pre_topc(F, k2_borsuk_1(k5_topmetr, k5_topmetr), A) &  (! [G] :  (m1_subset_1(G, u1_struct_0(k5_topmetr)) =>  (k1_binop_1(F, G, k5_numbers)=k3_funct_2(u1_struct_0(k5_topmetr), u1_struct_0(A), D, G) &  (k1_binop_1(F, G, 1)=k3_funct_2(u1_struct_0(k5_topmetr), u1_struct_0(A), E, G) &  (k1_binop_1(F, k5_numbers, G)=B & k1_binop_1(F, 1, G)=C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_g1_pre_topc, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) =>  (v1_pre_topc(g1_pre_topc(A, B)) & l1_pre_topc(g1_pre_topc(A, B))) ) ) ).
fof(dt_g1_rltopsp1, axiom,  (! [A, B, C, D, E] :  ( (m1_subset_1(B, A) &  ( (v1_funct_1(C) &  (v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  &  ( (v1_funct_1(D) &  (v1_funct_2(D, k2_zfmisc_1(k1_numbers, A), A) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k1_numbers, A), A)))) )  & m1_subset_1(E, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  =>  (v5_rltopsp1(g1_rltopsp1(A, B, C, D, E)) & l1_rltopsp1(g1_rltopsp1(A, B, C, D, E))) ) ) ).
fof(dt_g3_algstr_0, axiom,  (! [A, B] :  ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  =>  (v15_algstr_0(g3_algstr_0(A, B)) & l3_algstr_0(g3_algstr_0(A, B))) ) ) ).
fof(dt_k15_euclid, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v5_rltopsp1(k15_euclid(A)) & l1_rltopsp1(k15_euclid(A))) ) ) ).
fof(dt_k17_borsuk_1, axiom, l1_pre_topc(k17_borsuk_1)).
fof(dt_k1_binop_1, axiom, $true).
fof(dt_k1_borsuk_2, axiom,  (! [A, B, C, D, E, F] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & l1_pre_topc(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) &  (m1_subset_1(C, u1_struct_0(A)) &  (m1_subset_1(D, u1_struct_0(A)) &  (m1_borsuk_2(E, A, B, C) & m1_borsuk_2(F, A, C, D)) ) ) ) )  => m1_borsuk_2(k1_borsuk_2(A, B, C, D, E, F), A, B, D)) ) ).
fof(dt_k1_funct_1, axiom, $true).
fof(dt_k1_numbers, axiom, $true).
fof(dt_k1_tarski, axiom, $true).
fof(dt_k1_topalg_1, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_borsuk_1, axiom,  (! [A, B] :  ( ( (v2_pre_topc(A) & l1_pre_topc(A))  &  (v2_pre_topc(B) & l1_pre_topc(B)) )  =>  (v1_pre_topc(k2_borsuk_1(A, B)) &  (v2_pre_topc(k2_borsuk_1(A, B)) & l1_pre_topc(k2_borsuk_1(A, B))) ) ) ) ).
fof(dt_k2_topalg_1, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_funct_2, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  & m1_subset_1(D, A)) )  => m1_subset_1(k3_funct_2(A, B, C, D), B)) ) ).
fof(dt_k3_topalg_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & l1_pre_topc(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k3_topalg_1(A, B, C), k1_zfmisc_1(k2_zfmisc_1(k1_topalg_1(A, B, C), k1_topalg_1(A, B, C))))) ) ).
fof(dt_k3_topmetr, axiom,  (v2_pre_topc(k3_topmetr) & l1_pre_topc(k3_topmetr)) ).
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_tarski, axiom, $true).
fof(dt_k4_topalg_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & l1_pre_topc(A)) )  & m1_subset_1(B, u1_struct_0(A)))  => m1_subset_1(k4_topalg_1(A, B), k1_zfmisc_1(k2_zfmisc_1(k2_topalg_1(A, B), k2_topalg_1(A, B))))) ) ).
fof(dt_k5_numbers, axiom, m1_subset_1(k5_numbers, k4_ordinal1)).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k5_topalg_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & l1_pre_topc(A)) )  & m1_subset_1(B, u1_struct_0(A)))  =>  (v15_algstr_0(k5_topalg_1(A, B)) & l3_algstr_0(k5_topalg_1(A, B))) ) ) ).
fof(dt_k5_topmetr, axiom, m1_pre_topc(k5_topmetr, k3_topmetr)).
fof(dt_k6_eqrel_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => m1_subset_1(k6_eqrel_1(A, B, C, D), k1_zfmisc_1(B))) ) ).
fof(dt_k7_eqrel_1, axiom,  (! [A, B] :  ( (v3_relat_2(B) &  (v8_relat_2(B) &  (v1_partfun1(B, A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, A)))) ) )  => m1_subset_1(k7_eqrel_1(A, B), k1_zfmisc_1(k1_zfmisc_1(A)))) ) ).
fof(dt_k8_eqrel_1, axiom,  (! [A, B] :  ( (v3_relat_2(B) &  (v8_relat_2(B) &  (v1_partfun1(B, A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, A)))) ) )  => m1_eqrel_1(k8_eqrel_1(A, B), A)) ) ).
fof(dt_k9_relat_1, axiom, $true).
fof(dt_l1_algstr_0, axiom,  (! [A] :  (l1_algstr_0(A) => l1_struct_0(A)) ) ).
fof(dt_l1_pre_topc, axiom,  (! [A] :  (l1_pre_topc(A) => l1_struct_0(A)) ) ).
fof(dt_l1_rltopsp1, axiom,  (! [A] :  (l1_rltopsp1(A) =>  (l1_rlvect_1(A) & l1_pre_topc(A)) ) ) ).
fof(dt_l1_rlvect_1, axiom,  (! [A] :  (l1_rlvect_1(A) => l2_algstr_0(A)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_l2_algstr_0, axiom,  (! [A] :  (l2_algstr_0(A) =>  (l2_struct_0(A) & l1_algstr_0(A)) ) ) ).
fof(dt_l2_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => l1_struct_0(A)) ) ).
fof(dt_l3_algstr_0, axiom,  (! [A] :  (l3_algstr_0(A) => l1_struct_0(A)) ) ).
fof(dt_m1_borsuk_2, axiom,  (! [A, B, C] :  ( (l1_pre_topc(A) &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  =>  (! [D] :  (m1_borsuk_2(D, A, B, C) =>  (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(k5_topmetr), u1_struct_0(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr), u1_struct_0(A))))) ) ) ) ) ) ).
fof(dt_m1_eqrel_1, axiom,  (! [A] :  (! [B] :  (m1_eqrel_1(B, A) => m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) ) ).
fof(dt_m1_pre_topc, axiom,  (! [A] :  (l1_pre_topc(A) =>  (! [B] :  (m1_pre_topc(B, A) => l1_pre_topc(B)) ) ) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_o_0_0_xboole_0, axiom, v1_xboole_0(o_0_0_xboole_0)).
fof(dt_u1_algstr_0, axiom,  (! [A] :  (l1_algstr_0(A) =>  (v1_funct_1(u1_algstr_0(A)) &  (v1_funct_2(u1_algstr_0(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m1_subset_1(u1_algstr_0(A), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))) ) ) ) ).
fof(dt_u1_pre_topc, axiom,  (! [A] :  (l1_pre_topc(A) => m1_subset_1(u1_pre_topc(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))) ) ).
fof(dt_u1_rlvect_1, axiom,  (! [A] :  (l1_rlvect_1(A) =>  (v1_funct_1(u1_rlvect_1(A)) &  (v1_funct_2(u1_rlvect_1(A), k2_zfmisc_1(k1_numbers, u1_struct_0(A)), u1_struct_0(A)) & m1_subset_1(u1_rlvect_1(A), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k1_numbers, u1_struct_0(A)), u1_struct_0(A))))) ) ) ) ).
fof(dt_u1_struct_0, axiom, $true).
fof(dt_u2_algstr_0, axiom,  (! [A] :  (l3_algstr_0(A) =>  (v1_funct_1(u2_algstr_0(A)) &  (v1_funct_2(u2_algstr_0(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m1_subset_1(u2_algstr_0(A), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))) ) ) ) ).
fof(dt_u2_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => m1_subset_1(u2_struct_0(A), u1_struct_0(A))) ) ).
fof(existence_l1_algstr_0, axiom,  (? [A] : l1_algstr_0(A)) ).
fof(existence_l1_pre_topc, axiom,  (? [A] : l1_pre_topc(A)) ).
fof(existence_l1_rltopsp1, axiom,  (? [A] : l1_rltopsp1(A)) ).
fof(existence_l1_rlvect_1, axiom,  (? [A] : l1_rlvect_1(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_l2_algstr_0, axiom,  (? [A] : l2_algstr_0(A)) ).
fof(existence_l2_struct_0, axiom,  (? [A] : l2_struct_0(A)) ).
fof(existence_l3_algstr_0, axiom,  (? [A] : l3_algstr_0(A)) ).
fof(existence_m1_borsuk_2, axiom,  (! [A, B, C] :  ( (l1_pre_topc(A) &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  =>  (? [D] : m1_borsuk_2(D, A, B, C)) ) ) ).
fof(existence_m1_eqrel_1, axiom,  (! [A] :  (? [B] : m1_eqrel_1(B, A)) ) ).
fof(existence_m1_pre_topc, axiom,  (! [A] :  (l1_pre_topc(A) =>  (? [B] : m1_pre_topc(B, A)) ) ) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc10_membered, axiom,  (! [A] :  (v1_rat_1(A) => v4_membered(k1_tarski(A))) ) ).
fof(fc11_membered, axiom,  (! [A] :  (v1_int_1(A) => v5_membered(k1_tarski(A))) ) ).
fof(fc11_xxreal_2, axiom,  ( ~ (v3_xxreal_2(k1_numbers))  &  ~ (v4_xxreal_2(k1_numbers)) ) ).
fof(fc12_membered, axiom,  (! [A] :  (v7_ordinal1(A) => v6_membered(k1_tarski(A))) ) ).
fof(fc17_rltopsp1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_rlvect_1(A) &  (v6_rlvect_1(A) &  (v7_rlvect_1(A) &  (v8_rlvect_1(A) & l1_rlvect_1(A)) ) ) ) ) ) ) ) )  & m1_subset_1(B, u1_struct_0(A)))  => v10_rltopsp1(k1_tarski(B), A)) ) ).
fof(fc17_xxreal_2, axiom, v6_xxreal_2(k1_numbers)).
fof(fc1_jordan2c, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v5_rltopsp1(k15_euclid(A)) &  (v6_rltopsp1(k15_euclid(A)) & v7_rltopsp1(k15_euclid(A))) ) ) ) ).
fof(fc1_numbers, axiom,  ~ (v1_xboole_0(k1_numbers)) ).
fof(fc1_pre_topc, axiom,  (! [A] :  ( (v2_pre_topc(A) & l1_pre_topc(A))  =>  ~ (v1_xboole_0(u1_pre_topc(A))) ) ) ).
fof(fc1_struct_0, axiom,  (! [A] :  ( (v2_struct_0(A) & l1_struct_0(A))  => v1_xboole_0(u1_struct_0(A))) ) ).
fof(fc1_topalg_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  & l1_pre_topc(A))  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  =>  ~ (v1_xboole_0(k1_topalg_1(A, B, C))) ) ) ).
fof(fc1_zfmisc_1, axiom,  (! [A] : v1_zfmisc_1(k1_tarski(A))) ).
fof(fc2_borsuk_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & l1_pre_topc(A)) )  & m1_subset_1(B, u1_struct_0(A)))  => v2_compts_1(k1_tarski(B), A)) ) ).
fof(fc2_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_xboole_0(u1_struct_0(A))) ) ) ).
fof(fc2_topalg_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l1_pre_topc(A))  & m1_subset_1(B, u1_struct_0(A)))  =>  ~ (v1_xboole_0(k2_topalg_1(A, B))) ) ) ).
fof(fc2_topmetr, axiom,  ( ~ (v2_struct_0(k3_topmetr))  &  (v1_pre_topc(k3_topmetr) & v2_pre_topc(k3_topmetr)) ) ).
fof(fc2_zfmisc_1, axiom,  (! [A, B] :  (v1_xboole_0(B) => v1_xboole_0(k2_zfmisc_1(A, B))) ) ).
fof(fc3_borsuk_1, axiom,  (! [A, B] :  ( ( (v2_pre_topc(A) & l1_pre_topc(A))  &  (v2_struct_0(B) &  (v2_pre_topc(B) & l1_pre_topc(B)) ) )  =>  (v2_struct_0(k2_borsuk_1(A, B)) &  (v1_pre_topc(k2_borsuk_1(A, B)) & v2_pre_topc(k2_borsuk_1(A, B))) ) ) ) ).
fof(fc3_membered, axiom, v3_membered(k1_numbers)).
fof(fc3_topalg_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & l1_pre_topc(A)) )  & m1_subset_1(B, u1_struct_0(A)))  =>  ( ~ (v1_xboole_0(k4_topalg_1(A, B)))  &  (v1_partfun1(k4_topalg_1(A, B), k2_topalg_1(A, B)) &  (v3_relat_2(k4_topalg_1(A, B)) & v8_relat_2(k4_topalg_1(A, B))) ) ) ) ) ).
fof(fc3_topmetr, axiom, v3_topmetr(k17_borsuk_1)).
fof(fc3_zfmisc_1, axiom,  (! [A, B] :  (v1_xboole_0(A) => v1_xboole_0(k2_zfmisc_1(A, B))) ) ).
fof(fc4_borsuk_1, axiom,  (! [A, B] :  ( ( (v2_pre_topc(A) & l1_pre_topc(A))  &  (v2_struct_0(B) &  (v2_pre_topc(B) & l1_pre_topc(B)) ) )  =>  (v2_struct_0(k2_borsuk_1(B, A)) &  (v1_pre_topc(k2_borsuk_1(B, A)) & v2_pre_topc(k2_borsuk_1(B, A))) ) ) ) ).
fof(fc4_topalg_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & l1_pre_topc(A)) )  & m1_subset_1(B, u1_struct_0(A)))  =>  ( ~ (v2_struct_0(k5_topalg_1(A, B)))  & v15_algstr_0(k5_topalg_1(A, B))) ) ) ).
fof(fc4_topmetr, axiom,  (! [A] :  ( (v3_topmetr(A) & l1_struct_0(A))  => v3_membered(u1_struct_0(A))) ) ).
fof(fc4_zfmisc_1, axiom,  (! [A, B] :  ( (v1_zfmisc_1(A) & v1_zfmisc_1(B))  => v1_zfmisc_1(k2_zfmisc_1(A, B))) ) ).
fof(fc56_membered, axiom, v7_membered(k1_numbers)).
fof(fc59_membered, axiom, v7_membered(k4_ordinal1)).
fof(fc5_borsuk_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & l1_pre_topc(A)) )  &  ( ~ (v2_struct_0(B))  &  (v2_pre_topc(B) & l1_pre_topc(B)) ) )  =>  ( ~ (v2_struct_0(k2_borsuk_1(A, B)))  &  (v1_pre_topc(k2_borsuk_1(A, B)) & v2_pre_topc(k2_borsuk_1(A, B))) ) ) ) ).
fof(fc5_borsuk_2, axiom,  (! [A, B] :  ( ( (v2_pre_topc(A) &  (v6_pre_topc(A) & l1_pre_topc(A)) )  &  (v2_pre_topc(B) &  (v6_pre_topc(B) & l1_pre_topc(B)) ) )  =>  (v1_pre_topc(k2_borsuk_1(A, B)) &  (v2_pre_topc(k2_borsuk_1(A, B)) & v6_pre_topc(k2_borsuk_1(A, B))) ) ) ) ).
fof(fc5_euclid, axiom,  (! [A] :  (v7_ordinal1(A) =>  ( ~ (v2_struct_0(k15_euclid(A)))  & v5_rltopsp1(k15_euclid(A))) ) ) ).
fof(fc5_rltopsp1, axiom,  (! [A, B, C, D, E] :  ( ( ~ (v1_xboole_0(A))  &  (m1_subset_1(B, A) &  ( (v1_funct_1(C) &  (v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  &  ( (v1_funct_1(D) &  (v1_funct_2(D, k2_zfmisc_1(k1_numbers, A), A) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k1_numbers, A), A)))) )  & m1_subset_1(E, k1_zfmisc_1(k1_zfmisc_1(A)))) ) ) )  =>  ( ~ (v2_struct_0(g1_rltopsp1(A, B, C, D, E)))  & v5_rltopsp1(g1_rltopsp1(A, B, C, D, E))) ) ) ).
fof(fc5_topalg_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & l1_pre_topc(A)) )  & m1_subset_1(B, u1_struct_0(A)))  =>  (v15_algstr_0(k5_topalg_1(A, B)) &  (v2_group_1(k5_topalg_1(A, B)) & v3_group_1(k5_topalg_1(A, B))) ) ) ) ).
fof(fc5_topmetr, axiom,  (v2_pre_topc(k3_topmetr) & v3_topmetr(k3_topmetr)) ).
fof(fc6_borsuk_2, axiom,  (! [A, B] :  ( ( (v2_pre_topc(A) &  (v7_pre_topc(A) & l1_pre_topc(A)) )  &  (v2_pre_topc(B) &  (v7_pre_topc(B) & l1_pre_topc(B)) ) )  =>  (v1_pre_topc(k2_borsuk_1(A, B)) &  (v2_pre_topc(k2_borsuk_1(A, B)) & v7_pre_topc(k2_borsuk_1(A, B))) ) ) ) ).
fof(fc6_euclid, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v2_pre_topc(k15_euclid(A)) &  (v13_algstr_0(k15_euclid(A)) &  (v2_rlvect_1(k15_euclid(A)) &  (v3_rlvect_1(k15_euclid(A)) &  (v4_rlvect_1(k15_euclid(A)) &  (v5_rlvect_1(k15_euclid(A)) &  (v6_rlvect_1(k15_euclid(A)) &  (v7_rlvect_1(k15_euclid(A)) &  (v8_rlvect_1(k15_euclid(A)) & v5_rltopsp1(k15_euclid(A))) ) ) ) ) ) ) ) ) ) ) ).
fof(fc6_membered, axiom, v6_membered(k4_ordinal1)).
fof(fc6_pre_topc, axiom,  (! [A] :  ( (v2_pre_topc(A) & l1_pre_topc(A))  =>  (v1_pre_topc(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A))) & v2_pre_topc(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)))) ) ) ).
fof(fc6_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(fc7_borsuk_2, axiom,  (! [A, B] :  ( ( (v2_pre_topc(A) &  (v8_pre_topc(A) & l1_pre_topc(A)) )  &  (v2_pre_topc(B) &  (v8_pre_topc(B) & l1_pre_topc(B)) ) )  =>  (v1_pre_topc(k2_borsuk_1(A, B)) &  (v2_pre_topc(k2_borsuk_1(A, B)) & v8_pre_topc(k2_borsuk_1(A, B))) ) ) ) ).
fof(fc7_euclid, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v2_monoid_0(k15_euclid(A)) & v5_rltopsp1(k15_euclid(A))) ) ) ).
fof(fc7_membered, axiom,  (! [A] :  (v1_xcmplx_0(A) => v1_membered(k1_tarski(A))) ) ).
fof(fc7_pre_topc, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_pre_topc(A))  =>  ( ~ (v2_struct_0(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A))))  & v1_pre_topc(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)))) ) ) ).
fof(fc7_struct_0, axiom,  (! [A] :  ( (v7_struct_0(A) & l1_struct_0(A))  => v1_zfmisc_1(u1_struct_0(A))) ) ).
fof(fc8_borsuk_2, axiom,  (v8_pre_topc(k17_borsuk_1) & v1_compts_1(k17_borsuk_1)) ).
fof(fc8_membered, axiom,  (! [A] :  (v1_xxreal_0(A) => v2_membered(k1_tarski(A))) ) ).
fof(fc8_numbers, axiom,  ~ (v1_finset_1(k1_numbers)) ).
fof(fc8_struct_0, axiom,  (! [A] :  ( (v8_struct_0(A) & l1_struct_0(A))  => v1_finset_1(u1_struct_0(A))) ) ).
fof(fc8_topalg_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & m1_subset_1(B, u1_struct_0(k15_euclid(A))))  =>  (v7_struct_0(k5_topalg_1(k15_euclid(A), B)) & v15_algstr_0(k5_topalg_1(k15_euclid(A), B))) ) ) ).
fof(fc9_borsuk_1, axiom,  ( ~ (v2_struct_0(k17_borsuk_1))  &  (v1_pre_topc(k17_borsuk_1) & v2_pre_topc(k17_borsuk_1)) ) ).
fof(fc9_borsuk_2, axiom, v1_borsuk_2(k17_borsuk_1)).
fof(fc9_membered, axiom,  (! [A] :  (v1_xreal_0(A) => v3_membered(k1_tarski(A))) ) ).
fof(fc9_pre_topc, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))))  =>  ( ~ (v2_struct_0(g1_pre_topc(A, B)))  & v1_pre_topc(g1_pre_topc(A, B))) ) ) ).
fof(fc9_struct_0, axiom,  (! [A] :  ( ( ~ (v8_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_finset_1(u1_struct_0(A))) ) ) ).
fof(free_g1_pre_topc, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) =>  (! [C, D] :  (g1_pre_topc(A, B)=g1_pre_topc(C, D) =>  (A=C & B=D) ) ) ) ) ).
fof(free_g1_rltopsp1, axiom,  (! [A, B, C, D, E] :  ( (m1_subset_1(B, A) &  ( (v1_funct_1(C) &  (v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  &  ( (v1_funct_1(D) &  (v1_funct_2(D, k2_zfmisc_1(k1_numbers, A), A) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k1_numbers, A), A)))) )  & m1_subset_1(E, k1_zfmisc_1(k1_zfmisc_1(A)))) ) )  =>  (! [F, G, H, I, J] :  (g1_rltopsp1(A, B, C, D, E)=g1_rltopsp1(F, G, H, I, J) =>  (A=F &  (B=G &  (C=H &  (D=I & E=J) ) ) ) ) ) ) ) ).
fof(free_g3_algstr_0, axiom,  (! [A, B] :  ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  =>  (! [C, D] :  (g3_algstr_0(A, B)=g3_algstr_0(C, D) =>  (A=C & B=D) ) ) ) ) ).
fof(rc10_rltopsp1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_rlvect_1(A) &  (v6_rlvect_1(A) &  (v7_rlvect_1(A) &  (v8_rlvect_1(A) & l1_rlvect_1(A)) ) ) ) ) ) ) ) )  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v10_rltopsp1(B, A)) ) ) ) ).
fof(rc11_pre_topc, axiom,  (? [A] :  (l1_pre_topc(A) &  (v2_struct_0(A) & v1_pre_topc(A)) ) ) ).
fof(rc11_rltopsp1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v7_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_rlvect_1(A) &  (v6_rlvect_1(A) &  (v7_rlvect_1(A) &  (v8_rlvect_1(A) & l1_rlvect_1(A)) ) ) ) ) ) ) ) ) )  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_zfmisc_1(B))  & v10_rltopsp1(B, A)) ) ) ) ) ).
fof(rc12_pre_topc, axiom,  (? [A] :  (l1_pre_topc(A) &  (v2_struct_0(A) &  (v1_pre_topc(A) & v2_pre_topc(A)) ) ) ) ).
fof(rc1_funct_2, axiom,  (! [A, B] :  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_funct_2(C, A, B)) ) ) ) ) ) ) ).
fof(rc1_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v6_membered(A)) ) ).
fof(rc1_monoid_0, axiom,  (? [A] :  (l1_struct_0(A) & v1_monoid_0(A)) ) ).
fof(rc1_pre_topc, axiom,  (? [A] :  (l1_pre_topc(A) & v1_pre_topc(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_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc1_xxreal_2, axiom,  (? [A] :  (v1_membered(A) &  (v2_membered(A) &  (v3_membered(A) &  (v4_membered(A) &  (v5_membered(A) &  (v6_membered(A) &  ( ~ (v1_xboole_0(A))  &  (v1_xxreal_2(A) & v2_xxreal_2(A)) ) ) ) ) ) ) ) ) ).
fof(rc1_zfmisc_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_zfmisc_1(A)) ) ).
fof(rc20_struct_0, axiom,  (? [A] :  (l2_struct_0(A) &  ( ~ (v2_struct_0(A))  & v7_struct_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_borsuk_2, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & l1_pre_topc(A)) )  & m1_subset_1(B, u1_struct_0(A)))  =>  (? [C] :  (m1_borsuk_2(C, A, B, B) &  ( ~ (v1_xboole_0(C))  &  (v1_relat_1(C) &  (v4_relat_1(C, u1_struct_0(k5_topmetr)) &  (v5_relat_1(C, u1_struct_0(A)) &  (v1_funct_1(C) &  (v1_partfun1(C, u1_struct_0(k5_topmetr)) &  (v1_funct_2(C, u1_struct_0(k5_topmetr), u1_struct_0(A)) & v5_pre_topc(C, k5_topmetr, A)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc2_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v6_membered(A)) ) ).
fof(rc2_monoid_0, axiom,  (? [A] :  (l1_struct_0(A) & v2_monoid_0(A)) ) ).
fof(rc2_pre_topc, axiom,  (? [A] :  (l1_pre_topc(A) &  ( ~ (v2_struct_0(A))  &  (v1_pre_topc(A) & v2_pre_topc(A)) ) ) ) ).
fof(rc2_topalg_2, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) =>  (? [B] :  (m1_pre_topc(B, k15_euclid(A)) &  ( ~ (v2_struct_0(B))  &  (v1_pre_topc(B) &  (v2_pre_topc(B) & v1_topalg_2(B, A)) ) ) ) ) ) ) ).
fof(rc2_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc2_xxreal_2, axiom,  (? [A] :  (v6_membered(A) &  (v1_finset_1(A) &  ~ (v1_xboole_0(A)) ) ) ) ).
fof(rc2_zfmisc_1, axiom,  (? [A] :  ~ (v1_zfmisc_1(A)) ) ).
fof(rc3_borsuk_2, axiom,  (? [A] :  (l1_pre_topc(A) &  ( ~ (v2_struct_0(A))  &  (v1_pre_topc(A) &  (v2_pre_topc(A) & v1_borsuk_2(A)) ) ) ) ) ).
fof(rc3_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v6_membered(A) & v7_membered(A)) ) ) ).
fof(rc3_pre_topc, axiom,  (! [A] :  (l1_pre_topc(A) =>  (? [B] :  (m1_pre_topc(B, A) & v1_pre_topc(B)) ) ) ) ).
fof(rc3_rltopsp1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_rlvect_1(A) &  (v6_rlvect_1(A) &  (v7_rlvect_1(A) &  (v8_rlvect_1(A) & l1_rlvect_1(A)) ) ) ) ) ) ) ) )  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  & v2_rltopsp1(B, A)) ) ) ) ) ).
fof(rc3_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_2, axiom,  (? [A] :  (v1_membered(A) &  (v2_membered(A) &  (v3_membered(A) &  (v4_membered(A) &  (v5_membered(A) &  (v6_membered(A) &  ( ~ (v1_xboole_0(A))  &  (v1_xxreal_2(A) & v5_xxreal_2(A)) ) ) ) ) ) ) ) ) ).
fof(rc4_pre_topc, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_pre_topc(A))  =>  (? [B] :  (m1_pre_topc(B, A) &  ( ~ (v2_struct_0(B))  & v1_pre_topc(B)) ) ) ) ) ).
fof(rc4_rltopsp1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_rlvect_1(A) &  (v6_rlvect_1(A) &  (v7_rlvect_1(A) &  (v8_rlvect_1(A) & l1_rlvect_1(A)) ) ) ) ) ) ) ) )  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  & v3_rltopsp1(B, A)) ) ) ) ) ).
fof(rc4_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_topmetr, axiom,  (? [A] :  (l1_pre_topc(A) &  ( ~ (v2_struct_0(A))  &  (v1_pre_topc(A) &  (v2_pre_topc(A) & v3_topmetr(A)) ) ) ) ) ).
fof(rc4_xxreal_2, axiom,  (? [A] :  (v2_membered(A) &  ( ~ (v1_xboole_0(A))  & v6_xxreal_2(A)) ) ) ).
fof(rc5_pre_topc, axiom,  (! [A] :  ( (v2_pre_topc(A) & l1_pre_topc(A))  =>  (? [B] :  (m1_pre_topc(B, A) &  (v1_pre_topc(B) & v2_pre_topc(B)) ) ) ) ) ).
fof(rc5_xxreal_2, axiom,  (? [A] :  (v2_membered(A) &  (v1_xxreal_2(A) &  (v2_xxreal_2(A) & v6_xxreal_2(A)) ) ) ) ).
fof(rc6_pre_topc, axiom,  (! [A] :  ( (v2_pre_topc(A) & l1_pre_topc(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(B, A)) ) ) ) ).
fof(rc6_rltopsp1, axiom,  (? [A] :  (l1_rltopsp1(A) & v5_rltopsp1(A)) ) ).
fof(rc6_xxreal_2, axiom,  (? [A] :  (v2_membered(A) &  ( ~ (v1_xxreal_2(A))  &  (v2_xxreal_2(A) & v6_xxreal_2(A)) ) ) ) ).
fof(rc7_pre_topc, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & l1_pre_topc(A)) )  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  & v4_pre_topc(B, A)) ) ) ) ) ).
fof(rc7_rltopsp1, axiom,  (? [A] :  (l1_rltopsp1(A) &  ( ~ (v2_struct_0(A))  & v5_rltopsp1(A)) ) ) ).
fof(rc7_xxreal_2, axiom,  (? [A] :  (v2_membered(A) &  (v1_xxreal_2(A) &  ( ~ (v2_xxreal_2(A))  & v6_xxreal_2(A)) ) ) ) ).
fof(rc8_pre_topc, axiom,  (! [A, B] :  ( ( (v2_pre_topc(A) & l1_pre_topc(A))  &  ( ~ (v2_struct_0(B))  &  (v2_pre_topc(B) & l1_pre_topc(B)) ) )  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B)))) &  (v1_relat_1(C) &  (v4_relat_1(C, u1_struct_0(A)) &  (v5_relat_1(C, u1_struct_0(B)) &  (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B)) ) ) ) ) ) ) ) ) ).
fof(rc8_rltopsp1, axiom,  (? [A] :  (l1_rltopsp1(A) &  ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_rlvect_1(A) &  (v6_rlvect_1(A) &  (v7_rlvect_1(A) &  (v8_rlvect_1(A) &  (v5_rltopsp1(A) &  (v6_rltopsp1(A) & v7_rltopsp1(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc8_xxreal_2, axiom,  (? [A] :  (v2_membered(A) &  ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xxreal_2(A))  &  ( ~ (v2_xxreal_2(A))  & v6_xxreal_2(A)) ) ) ) ) ).
fof(rc9_pre_topc, axiom,  (? [A] :  (l1_pre_topc(A) &  ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & v7_pre_topc(A)) ) ) ) ).
fof(rc9_rltopsp1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_rlvect_1(A) &  (v6_rlvect_1(A) &  (v7_rlvect_1(A) &  (v8_rlvect_1(A) &  (v6_rltopsp1(A) &  (v7_rltopsp1(A) & l1_rltopsp1(A)) ) ) ) ) ) ) ) ) ) ) )  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v9_rltopsp1(B, A)) ) ) ) ).
fof(redefinition_k3_funct_2, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  & m1_subset_1(D, A)) )  => k3_funct_2(A, B, C, D)=k1_funct_1(C, D)) ) ).
fof(redefinition_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_numbers, axiom, k5_numbers=k5_ordinal1).
fof(redefinition_k5_topmetr, axiom, k5_topmetr=k17_borsuk_1).
fof(redefinition_k6_eqrel_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => k6_eqrel_1(A, B, C, D)=k9_relat_1(C, D)) ) ).
fof(redefinition_k8_eqrel_1, axiom,  (! [A, B] :  ( (v3_relat_2(B) &  (v8_relat_2(B) &  (v1_partfun1(B, A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, A)))) ) )  => k8_eqrel_1(A, B)=k7_eqrel_1(A, B)) ) ).
fof(redefinition_r1_borsuk_6, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & l1_pre_topc(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  =>  (r1_borsuk_6(A, B, C) <=> r1_borsuk_2(A, B, C)) ) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(redefinition_r4_borsuk_2, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) &  (v1_borsuk_2(A) & l1_pre_topc(A)) ) )  &  (m1_subset_1(B, u1_struct_0(A)) &  (m1_subset_1(C, u1_struct_0(A)) &  (m1_borsuk_2(D, A, B, C) & m1_borsuk_2(E, A, B, C)) ) ) )  =>  (r4_borsuk_2(A, B, C, D, E) <=> r3_borsuk_2(A, B, C, D, E)) ) ) ).
fof(reflexivity_r1_borsuk_6, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & l1_pre_topc(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => r1_borsuk_6(A, B, B)) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(reflexivity_r4_borsuk_2, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) &  (v1_borsuk_2(A) & l1_pre_topc(A)) ) )  &  (m1_subset_1(B, u1_struct_0(A)) &  (m1_subset_1(C, u1_struct_0(A)) &  (m1_borsuk_2(D, A, B, C) & m1_borsuk_2(E, A, B, C)) ) ) )  => r4_borsuk_2(A, B, C, D, D)) ) ).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(spc1_numerals, axiom,  (v2_xxreal_0(1) & m1_subset_1(1, k4_ordinal1)) ).
fof(symmetry_r1_borsuk_6, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & l1_pre_topc(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  =>  (r1_borsuk_6(A, B, C) => r1_borsuk_6(A, C, B)) ) ) ).
fof(symmetry_r3_borsuk_2, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (v2_struct_0(A))  & l1_pre_topc(A))  &  (m1_subset_1(B, u1_struct_0(A)) &  (m1_subset_1(C, u1_struct_0(A)) &  (m1_borsuk_2(D, A, B, C) & m1_borsuk_2(E, A, B, C)) ) ) )  =>  (r3_borsuk_2(A, B, C, D, E) => r3_borsuk_2(A, B, C, E, D)) ) ) ).
fof(symmetry_r4_borsuk_2, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) &  (v1_borsuk_2(A) & l1_pre_topc(A)) ) )  &  (m1_subset_1(B, u1_struct_0(A)) &  (m1_subset_1(C, u1_struct_0(A)) &  (m1_borsuk_2(D, A, B, C) & m1_borsuk_2(E, A, B, C)) ) ) )  =>  (r4_borsuk_2(A, B, C, D, E) => r4_borsuk_2(A, B, C, E, D)) ) ) ).
fof(t1_numerals, axiom, m1_subset_1(k1_xboole_0, k4_ordinal1)).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t2_topalg_2, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v1_topalg_2(B, A) & m1_pre_topc(B, k15_euclid(A))) )  =>  (! [C] :  (m1_subset_1(C, u1_struct_0(B)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(B)) =>  (! [E] :  (m1_borsuk_2(E, B, C, D) =>  (! [F] :  (m1_borsuk_2(F, B, C, D) => r4_borsuk_2(B, C, D, E, F)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t46_topalg_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & l1_pre_topc(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (r1_borsuk_6(A, B, C) =>  (! [D] :  (m1_borsuk_2(D, A, B, C) =>  (! [E] :  (m1_borsuk_2(E, A, B, C) =>  (k6_eqrel_1(k1_topalg_1(A, B, C), k1_topalg_1(A, B, C), k3_topalg_1(A, B, C), D)=k6_eqrel_1(k1_topalg_1(A, B, C), k1_topalg_1(A, B, C), k3_topalg_1(A, B, C), E) <=> r3_borsuk_2(A, B, C, D, E)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t47_topalg_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & l1_pre_topc(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (r2_tarski(C, u1_struct_0(k5_topalg_1(A, B))) <=>  (? [D] :  (m1_borsuk_2(D, A, B, B) & C=k6_eqrel_1(k2_topalg_1(A, B), k2_topalg_1(A, B), k4_topalg_1(A, B), D)) ) ) ) ) ) ) ) ).
fof(t4_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r2_tarski(A, B) & m1_subset_1(B, k1_zfmisc_1(C)))  => m1_subset_1(A, C)) ) ) ) ).
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(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
