% Mizar problem: t14_jordan1j,jordan1j,778,5 
fof(t14_jordan1j, conjecture,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  ( (v2_compts_1(B, k15_euclid(2)) &  ( ~ (v1_sppol_1(B))  &  ( ~ (v2_sppol_1(B))  & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k15_euclid(2))))) ) )  =>  (r2_tarski(k18_pscomp_1(k3_topreal1(2, k1_jordan9(B, A))), k10_xtuple_0(k2_jordan1e(B, A))) & r2_tarski(k18_pscomp_1(k3_topreal1(2, k1_jordan9(B, A))), k3_topreal1(2, k2_jordan1e(B, 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_card_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_zfmisc_1(A))  => v3_card_1(A, 1)) ) ).
fof(cc10_finseq_1, axiom,  (! [A] :  (v3_finseq_1(A) => v6_membered(A)) ) ).
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_card_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_card_1(A))  =>  (! [B] :  (v3_card_1(B, A) =>  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(cc11_finseq_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_finseq_1(A)) ) ).
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_finseq_1, axiom,  (! [A] :  (v4_finseq_1(A) => v4_funct_1(A)) ) ).
fof(cc12_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v1_zfmisc_1(A)) ) ).
fof(cc13_finseq_1, axiom,  (! [A] :  (v4_finseq_1(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_finseq_1(B)) ) ) ) ).
fof(cc13_ordinal1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  ~ (v8_ordinal1(A)) ) ) ).
fof(cc14_finseq_1, axiom,  (! [A] :  (v4_finseq_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_finseq_1(B)) ) ) ) ).
fof(cc14_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc15_ordinal1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v9_ordinal1(A)) ) ) ).
fof(cc16_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v1_finset_1(A) & v2_finseq_1(A)) ) ) ) ) ).
fof(cc16_ordinal1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) )  =>  (! [B] :  (m1_subset_1(B, A) =>  ~ (v8_ordinal1(B)) ) ) ) ) ).
fof(cc17_finseq_1, axiom,  (! [A] :  (m1_finseq_1(A, k4_ordinal1) => v6_valued_0(A)) ) ).
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_ordinal1, axiom,  (! [A] :  (v10_ordinal1(A) =>  ~ (v1_setfam_1(A)) ) ) ).
fof(cc19_ordinal1, axiom,  (! [A] :  (v1_setfam_1(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc1_card_1, axiom,  (! [A] :  (v1_card_1(A) => v3_ordinal1(A)) ) ).
fof(cc1_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_xboole_0(A))  =>  (v1_relat_1(A) & v1_finseq_1(A)) ) ) ).
fof(cc1_finseq_6, axiom,  (! [A, B] :  (m1_finseq_1(B, A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(B)) => v2_finseq_1(C)) ) ) ) ).
fof(cc1_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_funct_1(A)) ) ).
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_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_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_sppol_2, axiom,  (! [A] :  (m1_finseq_1(A, u1_struct_0(k15_euclid(2))) =>  (v4_topreal1(A) =>  ( ~ (v1_zfmisc_1(A))  &  (v2_funct_1(A) &  (v1_topreal1(A) &  (v2_topreal1(A) & v3_topreal1(A)) ) ) ) ) ) ) ).
fof(cc1_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v7_struct_0(A)) ) ) ).
fof(cc1_topreal2, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) =>  (v1_topreal2(A) =>  ( ~ (v1_xboole_0(A))  & v2_compts_1(A, k15_euclid(2))) ) ) ) ).
fof(cc1_topreal5, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) =>  (v1_topreal2(A) =>  (v1_topreal2(A) &  ( ~ (v1_sppol_1(A))  &  ~ (v2_sppol_1(A)) ) ) ) ) ) ).
fof(cc1_topreal6, axiom,  (! [A] :  (l1_pre_topc(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (v1_xboole_0(B) => v2_connsp_1(B, A)) ) ) ) ) ).
fof(cc1_xreal_0, axiom,  (! [A] :  (m1_subset_1(A, k1_numbers) => v1_xreal_0(A)) ) ).
fof(cc20_finseq_1, axiom,  (! [A] :  (m1_finseq_1(A, k1_numbers) => v3_valued_0(A)) ) ).
fof(cc20_ordinal1, axiom,  (! [A] :  ( ~ (v1_setfam_1(A))  => v10_ordinal1(A)) ) ).
fof(cc2_card_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_card_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_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) ) ) ).
fof(cc2_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_int_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_int_1(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_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_sppol_2, axiom,  (! [A] :  (m1_finseq_1(A, u1_struct_0(k15_euclid(2))) =>  ( ( ~ (v1_zfmisc_1(A))  &  (v2_funct_1(A) &  (v1_topreal1(A) &  (v2_topreal1(A) & v3_topreal1(A)) ) ) )  => v4_topreal1(A)) ) ) ).
fof(cc2_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc2_topreal6, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) =>  ( ~ (v1_sppol_1(A))  =>  ~ (v1_xboole_0(A)) ) ) ) ).
fof(cc2_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_card_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_card_1(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_finseq_1, axiom,  (! [A] :  (! [B] :  (m1_finseq_1(B, A) => v5_relat_1(B, 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_int_1, axiom,  (! [A] :  (v1_int_1(A) => v1_xreal_0(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_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_sppol_2, axiom,  (! [A] :  (m1_finseq_1(A, u1_struct_0(k15_euclid(2))) =>  (v4_topreal1(A) =>  ~ (v1_xboole_0(A)) ) ) ) ).
fof(cc3_topreal6, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) =>  ( ~ (v2_sppol_1(A))  =>  ~ (v1_xboole_0(A)) ) ) ) ).
fof(cc3_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_card_1, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) => v1_finset_1(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_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_xboole_0(A))  =>  (v1_relat_1(A) & v1_finseq_1(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_int_1, axiom,  (! [A] :  (v7_ordinal1(A) => v2_int_1(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_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_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_card_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_finset_1(A)) ) ).
fof(cc5_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) & v1_finseq_1(A)) ) ) ) ) ).
fof(cc5_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_int_1, axiom,  (! [A] :  (v2_int_1(A) => v1_int_1(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_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ( ~ (v2_struct_0(A))  &  ~ (v8_struct_0(A)) ) ) ) ) ).
fof(cc5_xxreal_0, axiom,  (! [A] :  ( (v1_xxreal_0(A) & v3_xxreal_0(A))  =>  ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v2_xxreal_0(A)) ) ) ) ) ).
fof(cc6_card_1, axiom,  (! [A] :  ( (v3_ordinal1(A) & v1_finset_1(A))  => v7_ordinal1(A)) ) ).
fof(cc6_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) ) ) ) ).
fof(cc6_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_nat_1, axiom,  (! [A] :  ( ~ (v8_ordinal1(A))  =>  ~ (v1_xboole_0(A)) ) ) ).
fof(cc6_ordinal1, axiom,  (! [A] :  (v7_ordinal1(A) => v3_ordinal1(A)) ) ).
fof(cc6_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v7_struct_0(A) => v8_struct_0(A)) ) ) ).
fof(cc6_topreal6, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) =>  (v1_xboole_0(A) => v1_sppol_1(A)) ) ) ).
fof(cc6_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_card_1, axiom,  (! [A] :  (v3_card_1(A, k5_ordinal1) => v1_xboole_0(A)) ) ).
fof(cc7_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) & v2_finseq_1(A)) ) ) ) ) ).
fof(cc7_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_funct_1(A)) ) ).
fof(cc7_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v7_ordinal1(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_topreal6, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) =>  (v1_xboole_0(A) => v2_sppol_1(A)) ) ) ).
fof(cc7_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_card_1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_card_1(A, k5_ordinal1)) ) ).
fof(cc8_finseq_1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_finseq_1(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_ordinal1, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) => v7_ordinal1(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_topreal6, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) =>  (v1_topreal2(A) => v2_connsp_1(A, k15_euclid(2))) ) ) ).
fof(cc8_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_card_1, axiom,  (! [A] :  (v3_card_1(A, 1) =>  ( ~ (v1_xboole_0(A))  & v1_zfmisc_1(A)) ) ) ).
fof(cc9_finseq_1, axiom,  (! [A] :  (v3_finseq_1(A) => v1_finset_1(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_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v6_ordinal1(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(commutativity_k1_rltopsp1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_rlvect_1(A) &  (v6_rlvect_1(A) &  (v7_rlvect_1(A) &  (v8_rlvect_1(A) & l1_rlvect_1(A)) ) ) ) ) ) ) ) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k1_rltopsp1(A, B, C)=k1_rltopsp1(A, C, B)) ) ).
fof(commutativity_k3_xboole_0, axiom,  (! [A, B] : k3_xboole_0(A, B)=k3_xboole_0(B, A)) ).
fof(commutativity_k9_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(C, k1_zfmisc_1(A)) => k9_subset_1(A, B, C)=k9_subset_1(A, C, B)) ) ).
fof(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_pscomp_1, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => k9_pscomp_1(A)=k1_pscomp_1(k1_pre_topc(k15_euclid(2), A), k3_pscomp_1(k15_euclid(2), k5_pscomp_1, A))) ) ).
fof(d11_pscomp_1, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => k10_pscomp_1(A)=k19_euclid(k6_pscomp_1(A), k9_pscomp_1(A))) ) ).
fof(d12_pscomp_1, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => k11_pscomp_1(A)=k19_euclid(k6_pscomp_1(A), k7_pscomp_1(A))) ) ).
fof(d13_ordinal1, axiom, k5_ordinal1=k1_xboole_0).
fof(d15_pscomp_1, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => k14_pscomp_1(A)=k9_subset_1(u1_struct_0(k15_euclid(2)), k1_rltopsp1(k15_euclid(2), k10_pscomp_1(A), k11_pscomp_1(A)), A)) ) ).
fof(d19_pscomp_1, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => k18_pscomp_1(A)=k19_euclid(k6_pscomp_1(A), k1_pscomp_1(k1_pre_topc(k15_euclid(2), k14_pscomp_1(A)), k3_pscomp_1(k15_euclid(2), k5_pscomp_1, k14_pscomp_1(A))))) ) ).
fof(d1_pscomp_1, axiom,  (! [A] :  (l1_struct_0(A) =>  (! [B] :  ( (v1_funct_1(B) &  (v1_funct_2(B, u1_struct_0(A), k1_numbers) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), k1_numbers)))) )  => k1_pscomp_1(A, B)=k3_seq_4(k7_relset_1(u1_struct_0(A), k1_numbers, B, u1_struct_0(A)))) ) ) ) ).
fof(d2_pscomp_1, axiom,  (! [A] :  (l1_struct_0(A) =>  (! [B] :  ( (v1_funct_1(B) &  (v1_funct_2(B, u1_struct_0(A), k1_numbers) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), k1_numbers)))) )  => k2_pscomp_1(A, B)=k2_seq_4(k7_relset_1(u1_struct_0(A), k1_numbers, B, u1_struct_0(A)))) ) ) ) ).
fof(d3_tarski, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) <=>  (! [C] :  (r2_hidden(C, A) => r2_hidden(C, B)) ) ) ) ) ).
fof(d7_pscomp_1, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => k6_pscomp_1(A)=k1_pscomp_1(k1_pre_topc(k15_euclid(2), A), k3_pscomp_1(k15_euclid(2), k4_pscomp_1, A))) ) ).
fof(d8_pscomp_1, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => k7_pscomp_1(A)=k2_pscomp_1(k1_pre_topc(k15_euclid(2), A), k3_pscomp_1(k15_euclid(2), k5_pscomp_1, A))) ) ).
fof(d8_topreal1, axiom,  (! [A] :  (m2_finseq_1(A, u1_struct_0(k15_euclid(2))) =>  (v4_topreal1(A) <=>  (v2_funct_1(A) &  (r1_xxreal_0(2, k3_finseq_1(A)) &  (v2_topreal1(A) &  (v3_topreal1(A) & v1_topreal1(A)) ) ) ) ) ) ) ).
fof(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_k10_finseq_1, axiom, $true).
fof(dt_k10_pscomp_1, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => m1_subset_1(k10_pscomp_1(A), u1_struct_0(k15_euclid(2)))) ) ).
fof(dt_k10_xtuple_0, axiom, $true).
fof(dt_k11_pscomp_1, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => m1_subset_1(k11_pscomp_1(A), u1_struct_0(k15_euclid(2)))) ) ).
fof(dt_k14_pscomp_1, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => m1_subset_1(k14_pscomp_1(A), k1_zfmisc_1(u1_struct_0(k15_euclid(2))))) ) ).
fof(dt_k15_euclid, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v5_rltopsp1(k15_euclid(A)) & l1_rltopsp1(k15_euclid(A))) ) ) ).
fof(dt_k18_pscomp_1, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => m1_subset_1(k18_pscomp_1(A), u1_struct_0(k15_euclid(2)))) ) ).
fof(dt_k19_euclid, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => m1_subset_1(k19_euclid(A, B), u1_struct_0(k15_euclid(2)))) ) ).
fof(dt_k1_card_1, axiom,  (! [A] : v1_card_1(k1_card_1(A))) ).
fof(dt_k1_jordan9, axiom,  (! [A, B] :  ( ( ( ~ (v1_xboole_0(A))  &  (v2_compts_1(A, k15_euclid(2)) &  ( ~ (v1_sppol_1(A))  &  ( ~ (v2_sppol_1(A))  & m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2))))) ) ) )  & v7_ordinal1(B))  =>  ( ~ (v1_xboole_0(k1_jordan9(A, B)))  &  ( ~ (v3_funct_1(k1_jordan9(A, B)))  &  (v1_finseq_6(k1_jordan9(A, B), u1_struct_0(k15_euclid(2))) &  (v1_topreal1(k1_jordan9(A, B)) &  (v2_topreal1(k1_jordan9(A, B)) &  (v1_goboard5(k1_jordan9(A, B)) &  (v2_goboard5(k1_jordan9(A, B)) &  (v1_sprect_2(k1_jordan9(A, B)) & m2_finseq_1(k1_jordan9(A, B), u1_struct_0(k15_euclid(2)))) ) ) ) ) ) ) ) ) ) ).
fof(dt_k1_numbers, axiom, $true).
fof(dt_k1_pre_topc, axiom,  (! [A, B] :  ( (l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))  =>  (v1_pre_topc(k1_pre_topc(A, B)) & m1_pre_topc(k1_pre_topc(A, B), A)) ) ) ).
fof(dt_k1_pscomp_1, axiom,  (! [A, B] :  ( (l1_struct_0(A) &  (v1_funct_1(B) &  (v1_funct_2(B, u1_struct_0(A), k1_numbers) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), k1_numbers)))) ) )  => v1_xreal_0(k1_pscomp_1(A, B))) ) ).
fof(dt_k1_rltopsp1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_rlvect_1(A) &  (v6_rlvect_1(A) &  (v7_rlvect_1(A) &  (v8_rlvect_1(A) & l1_rlvect_1(A)) ) ) ) ) ) ) ) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k1_rltopsp1(A, B, C), k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_jordan1e, axiom,  (! [A, B] :  ( ( (v2_compts_1(A, k15_euclid(2)) &  ( ~ (v1_sppol_1(A))  &  ( ~ (v2_sppol_1(A))  & m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2))))) ) )  & v7_ordinal1(B))  => m2_finseq_1(k2_jordan1e(A, B), u1_struct_0(k15_euclid(2)))) ) ).
fof(dt_k2_pscomp_1, axiom,  (! [A, B] :  ( (l1_struct_0(A) &  (v1_funct_1(B) &  (v1_funct_2(B, u1_struct_0(A), k1_numbers) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), k1_numbers)))) ) )  => v1_xreal_0(k2_pscomp_1(A, B))) ) ).
fof(dt_k2_seq_4, axiom,  (! [A] :  (v3_membered(A) => v1_xreal_0(k2_seq_4(A))) ) ).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => m1_subset_1(k3_finseq_1(A), k4_ordinal1)) ) ).
fof(dt_k3_pscomp_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  & l1_pre_topc(A))  &  ( (v1_funct_1(B) &  (v1_funct_2(B, u1_struct_0(A), k1_numbers) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), k1_numbers)))) )  & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) )  =>  (v1_funct_1(k3_pscomp_1(A, B, C)) &  (v1_funct_2(k3_pscomp_1(A, B, C), u1_struct_0(k1_pre_topc(A, C)), k1_numbers) & m1_subset_1(k3_pscomp_1(A, B, C), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k1_pre_topc(A, C)), k1_numbers)))) ) ) ) ).
fof(dt_k3_seq_4, axiom,  (! [A] :  (v3_membered(A) => v1_xreal_0(k3_seq_4(A))) ) ).
fof(dt_k3_topreal1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & m1_finseq_1(B, u1_struct_0(k15_euclid(A))))  => m1_subset_1(k3_topreal1(A, B), k1_zfmisc_1(u1_struct_0(k15_euclid(A))))) ) ).
fof(dt_k3_xboole_0, axiom, $true).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k4_pscomp_1, axiom,  (v1_funct_1(k4_pscomp_1) &  (v1_funct_2(k4_pscomp_1, u1_struct_0(k15_euclid(2)), k1_numbers) & m1_subset_1(k4_pscomp_1, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k15_euclid(2)), k1_numbers)))) ) ).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k5_pscomp_1, axiom,  (v1_funct_1(k5_pscomp_1) &  (v1_funct_2(k5_pscomp_1, u1_struct_0(k15_euclid(2)), k1_numbers) & m1_subset_1(k5_pscomp_1, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k15_euclid(2)), k1_numbers)))) ) ).
fof(dt_k5_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => v1_relat_1(k5_relat_1(A, B))) ) ).
fof(dt_k6_pscomp_1, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => v1_xreal_0(k6_pscomp_1(A))) ) ).
fof(dt_k7_partfun1, axiom,  (! [A, B, C] :  ( (v1_relat_1(B) &  (v5_relat_1(B, A) & v1_funct_1(B)) )  => m1_subset_1(k7_partfun1(A, B, C), A)) ) ).
fof(dt_k7_pscomp_1, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => v1_xreal_0(k7_pscomp_1(A))) ) ).
fof(dt_k7_relat_1, axiom, $true).
fof(dt_k7_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => m1_subset_1(k7_relset_1(A, B, C, D), k1_zfmisc_1(B))) ) ).
fof(dt_k9_pscomp_1, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => v1_xreal_0(k9_pscomp_1(A))) ) ).
fof(dt_k9_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(C, k1_zfmisc_1(A)) => m1_subset_1(k9_subset_1(A, B, C), k1_zfmisc_1(A))) ) ).
fof(dt_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_m1_finseq_1, axiom,  (! [A] :  (! [B] :  (m1_finseq_1(B, A) =>  (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) ) ) ) ) ).
fof(dt_m1_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_m2_finseq_1, axiom,  (! [A] :  (! [B] :  (m2_finseq_1(B, A) =>  (v1_funct_1(B) &  (v1_finseq_1(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, A)))) ) ) ) ) ).
fof(dt_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_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_m1_finseq_1, axiom,  (! [A] :  (? [B] : m1_finseq_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(existence_m2_finseq_1, axiom,  (! [A] :  (? [B] : m2_finseq_1(B, A)) ) ).
fof(fc10_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ( ~ (v1_finset_1(k1_card_1(A)))  & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc10_finseq_1, axiom,  (! [A, B] : v1_finseq_1(k10_finseq_1(A, B))) ).
fof(fc10_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) & v9_ordinal1(A))  =>  ~ (v10_ordinal1(k10_xtuple_0(A))) ) ) ).
fof(fc11_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) &  ~ (v9_ordinal1(A)) )  => v10_ordinal1(k10_xtuple_0(A))) ) ).
fof(fc12_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ~ (v1_finset_1(k1_zfmisc_1(A))) ) ) ).
fof(fc12_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) )  => v1_zfmisc_1(k10_xtuple_0(A))) ) ).
fof(fc13_card_1, axiom,  (! [A, B] :  ( ( ~ (v1_finset_1(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_finset_1(k2_zfmisc_1(A, B))) ) ) ).
fof(fc13_finseq_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) )  =>  (v1_relat_1(k5_relat_1(A, B)) & v2_finseq_1(k5_relat_1(A, B))) ) ) ).
fof(fc13_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) )  =>  ~ (v1_zfmisc_1(k10_xtuple_0(A))) ) ) ).
fof(fc13_sppol_2, axiom,  (! [A, B, C] :  ( (m1_subset_1(A, k4_ordinal1) &  (m1_subset_1(B, u1_struct_0(k15_euclid(A))) & m1_subset_1(C, u1_struct_0(k15_euclid(A)))) )  => v2_compts_1(k1_rltopsp1(k15_euclid(A), B, C), k15_euclid(A))) ) ).
fof(fc14_card_1, axiom,  (! [A, B] :  ( ( ~ (v1_finset_1(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_finset_1(k2_zfmisc_1(B, A))) ) ) ).
fof(fc19_struct_0, axiom,  (! [A, B] :  ( (v1_card_1(A) &  (v13_struct_0(B, A) & l1_struct_0(B)) )  => v3_card_1(u1_struct_0(B), A)) ) ).
fof(fc1_card_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (v1_xboole_0(k1_card_1(A)) & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc1_jordan2c, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v5_rltopsp1(k15_euclid(A)) &  (v6_rltopsp1(k15_euclid(A)) & v7_rltopsp1(k15_euclid(A))) ) ) ) ).
fof(fc1_pre_topc, axiom,  (! [A] :  ( (v2_pre_topc(A) & l1_pre_topc(A))  =>  ~ (v1_xboole_0(u1_pre_topc(A))) ) ) ).
fof(fc1_revrot_1, axiom,  (! [A] :  ( (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) )  =>  ( ~ (v7_struct_0(k15_euclid(A)))  & v5_rltopsp1(k15_euclid(A))) ) ) ).
fof(fc1_sprect_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) &  ( ~ (v1_zfmisc_1(B))  & m1_finseq_1(B, u1_struct_0(k15_euclid(A)))) )  =>  ~ (v1_xboole_0(k3_topreal1(A, B))) ) ) ).
fof(fc1_struct_0, axiom,  (! [A] :  ( (v2_struct_0(A) & l1_struct_0(A))  => v1_xboole_0(u1_struct_0(A))) ) ).
fof(fc1_topreal1, axiom,  (! [A] :  (v7_ordinal1(A) => v4_funct_1(u1_struct_0(k15_euclid(A)))) ) ).
fof(fc1_topreal6, axiom,  (! [A, B] :  ( (l1_pre_topc(A) &  (v1_finset_1(B) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) )  =>  (v8_struct_0(k1_pre_topc(A, B)) & v1_pre_topc(k1_pre_topc(A, B))) ) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc21_finseq_1, axiom,  (! [A, B] :  (v3_finseq_1(A) => v3_finseq_1(k3_xboole_0(A, B))) ) ).
fof(fc26_finseq_1, axiom,  (! [A, B] :  ~ (v1_xboole_0(k10_finseq_1(A, B))) ) ).
fof(fc2_card_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (v8_ordinal1(k1_card_1(A)) & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc2_finseq_5, axiom,  (! [A, B] :  ~ (v1_zfmisc_1(k10_finseq_1(A, B))) ) ).
fof(fc2_jordan1e, axiom,  (! [A, B] :  ( ( (v2_compts_1(A, k15_euclid(2)) &  ( ~ (v1_sppol_1(A))  &  ( ~ (v2_sppol_1(A))  & m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2))))) ) )  & v7_ordinal1(B))  =>  ~ (v1_xboole_0(k2_jordan1e(A, B))) ) ) ).
fof(fc2_pre_topc, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l1_pre_topc(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) )  =>  ( ~ (v2_struct_0(k1_pre_topc(A, B)))  & v1_pre_topc(k1_pre_topc(A, B))) ) ) ).
fof(fc2_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v4_relat_1(B, A))  & v1_relat_1(C))  => v4_relat_1(k3_xboole_0(B, C), A)) ) ).
fof(fc2_sprect_1, axiom,  (! [A] :  (m1_finseq_1(A, u1_struct_0(k15_euclid(2))) => v2_compts_1(k3_topreal1(2, A), k15_euclid(2))) ) ).
fof(fc2_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_xboole_0(u1_struct_0(A))) ) ) ).
fof(fc2_topreal1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v8_pre_topc(k15_euclid(A)) & v5_rltopsp1(k15_euclid(A))) ) ) ).
fof(fc2_topreal6, axiom,  (! [A, B] :  ( (m1_subset_1(A, u1_struct_0(k15_euclid(2))) & m1_subset_1(B, u1_struct_0(k15_euclid(2))))  => v2_connsp_1(k1_rltopsp1(k15_euclid(2), A, B), k15_euclid(2))) ) ).
fof(fc33_finseq_1, axiom,  (! [A, B] : v3_card_1(k10_finseq_1(A, B), 2)) ).
fof(fc3_card_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  ( ~ (v1_xboole_0(k1_card_1(A)))  & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc3_jordan1g, axiom,  (! [A, B] :  ( ( (v2_connsp_1(A, k15_euclid(2)) &  (v2_compts_1(A, k15_euclid(2)) &  ( ~ (v1_sppol_1(A))  &  ( ~ (v2_sppol_1(A))  & m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2))))) ) ) )  & v7_ordinal1(B))  => v2_goboard5(k2_jordan1e(A, B))) ) ).
fof(fc3_pre_topc, axiom,  (! [A, B] :  ( ( (v2_pre_topc(A) & l1_pre_topc(A))  & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))  =>  (v1_pre_topc(k1_pre_topc(A, B)) & v2_pre_topc(k1_pre_topc(A, B))) ) ) ).
fof(fc3_sprect_2, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v3_funct_1(A))  &  (v1_finseq_6(A, u1_struct_0(k15_euclid(2))) &  (v1_topreal1(A) &  (v2_topreal1(A) &  (v1_goboard5(A) &  (v2_goboard5(A) & m1_finseq_1(A, u1_struct_0(k15_euclid(2)))) ) ) ) ) ) )  => v1_topreal2(k3_topreal1(2, A))) ) ).
fof(fc4_card_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  ( ~ (v8_ordinal1(k1_card_1(A)))  & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc4_jordan1e, axiom,  (! [A, B] :  ( ( (v2_compts_1(A, k15_euclid(2)) &  ( ~ (v1_sppol_1(A))  &  ( ~ (v2_sppol_1(A))  & m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2))))) ) )  & v7_ordinal1(B))  =>  (v2_funct_1(k2_jordan1e(A, B)) &  (v1_topreal1(k2_jordan1e(A, B)) &  (v2_topreal1(k2_jordan1e(A, B)) & v3_topreal1(k2_jordan1e(A, B))) ) ) ) ) ).
fof(fc4_jordan2c, axiom,  (! [A, B] :  ( (m1_subset_1(A, u1_struct_0(k15_euclid(2))) & m1_subset_1(B, u1_struct_0(k15_euclid(2))))  => v2_tops_1(k1_rltopsp1(k15_euclid(2), A, B), k15_euclid(2))) ) ).
fof(fc5_euclid, axiom,  (! [A] :  (v7_ordinal1(A) =>  ( ~ (v2_struct_0(k15_euclid(A)))  & v5_rltopsp1(k15_euclid(A))) ) ) ).
fof(fc5_jordan2c, axiom,  (! [A] :  (m1_finseq_1(A, u1_struct_0(k15_euclid(2))) => v2_tops_1(k3_topreal1(2, A), k15_euclid(2))) ) ).
fof(fc5_ordinal1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v5_ordinal1(A)) )  & v3_ordinal1(B))  =>  (v1_relat_1(k5_relat_1(A, B)) &  (v5_relat_1(k5_relat_1(A, B), k10_xtuple_0(A)) & v5_ordinal1(k5_relat_1(A, B))) ) ) ) ).
fof(fc5_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v5_relat_1(B, A))  & v1_relat_1(C))  => v5_relat_1(k3_xboole_0(B, C), A)) ) ).
fof(fc6_card_1, axiom, v1_card_1(k4_ordinal1)).
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_jordan1e, axiom,  (! [A, B] :  ( ( (v2_compts_1(A, k15_euclid(2)) &  ( ~ (v1_sppol_1(A))  &  ( ~ (v2_sppol_1(A))  & m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2))))) ) )  & v7_ordinal1(B))  => v4_topreal1(k2_jordan1e(A, B))) ) ).
fof(fc6_ordinal1, axiom,  ( ~ (v1_xboole_0(k4_ordinal1))  & v3_ordinal1(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_card_1, axiom, v2_card_1(k4_ordinal1)).
fof(fc7_euclid, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v2_monoid_0(k15_euclid(A)) & v5_rltopsp1(k15_euclid(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_card_1, axiom,  (! [A] :  (v1_finset_1(A) =>  (v1_finset_1(k1_card_1(A)) & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc8_finseq_1, axiom,  (! [A, B] :  (v1_relat_1(k10_finseq_1(A, B)) & v1_funct_1(k10_finseq_1(A, B))) ) ).
fof(fc8_funct_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v1_funct_1(k5_relat_1(A, B))) ) ) ).
fof(fc8_ordinal1, axiom, v7_ordinal1(k5_ordinal1)).
fof(fc8_pre_topc, axiom,  (! [A, B] :  ( (l1_pre_topc(A) &  (v1_xboole_0(B) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) )  =>  (v2_struct_0(k1_pre_topc(A, B)) & v1_pre_topc(k1_pre_topc(A, B))) ) ) ).
fof(fc8_struct_0, axiom,  (! [A] :  ( (v8_struct_0(A) & l1_struct_0(A))  => v1_finset_1(u1_struct_0(A))) ) ).
fof(fc9_card_1, axiom,  ~ (v1_finset_1(k4_ordinal1)) ).
fof(fc9_ordinal1, axiom, v8_ordinal1(k5_ordinal1)).
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_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, k2_zfmisc_1(B, C)))) => v1_relat_1(k10_xtuple_0(D))) ) ).
fof(fc9_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(idempotence_k3_xboole_0, axiom,  (! [A, B] : k3_xboole_0(A, A)=A) ).
fof(idempotence_k9_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(C, k1_zfmisc_1(A)) => k9_subset_1(A, B, B)=B) ) ).
fof(projectivity_k1_card_1, axiom,  (! [A] : k1_card_1(k1_card_1(A))=k1_card_1(A)) ).
fof(projectivity_k3_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => k3_finseq_1(k3_finseq_1(A))=k3_finseq_1(A)) ) ).
fof(rc10_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_card_1(B)) ) ) ) ).
fof(rc10_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v1_funct_1(B) &  (v1_finset_1(B) &  (v3_card_1(B, A) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ) ).
fof(rc10_ordinal1, axiom,  (? [A] :  ~ (v8_ordinal1(A)) ) ).
fof(rc11_finseq_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v4_finseq_1(A)) ) ).
fof(rc11_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) ) ) ).
fof(rc11_pre_topc, axiom,  (? [A] :  (l1_pre_topc(A) &  (v2_struct_0(A) & v1_pre_topc(A)) ) ) ).
fof(rc12_finseq_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v1_finset_1(B) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ).
fof(rc12_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) & v9_ordinal1(A)) ) ).
fof(rc12_pre_topc, axiom,  (? [A] :  (l1_pre_topc(A) &  (v2_struct_0(A) &  (v1_pre_topc(A) & v2_pre_topc(A)) ) ) ) ).
fof(rc13_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) &  ~ (v9_ordinal1(A)) ) ) ).
fof(rc14_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  (v2_funct_1(A) &  (v1_finset_1(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ).
fof(rc15_finseq_1, axiom,  (! [A] :  (? [B] :  (m1_finseq_1(B, A) &  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v2_funct_1(B) &  (v1_finset_1(B) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ) ) ).
fof(rc16_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) &  (v6_valued_0(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ) ).
fof(rc1_card_1, axiom,  (? [A] : v1_card_1(A)) ).
fof(rc1_finseq_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, A))) &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) ) ) ) ) ).
fof(rc1_finseq_5, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  ( ~ (v1_xboole_0(A))  &  (v1_funct_1(A) &  (v2_funct_1(A) &  (v1_finset_1(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ) ).
fof(rc1_finseq_6, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_finseq_1(B, A) &  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v1_finset_1(B) &  (v3_card_1(B, 1) &  (v1_finseq_1(B) &  (v2_finseq_1(B) & v1_finseq_6(B, A)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc1_funct_1, axiom,  (? [A] :  (v1_relat_1(A) & v1_funct_1(A)) ) ).
fof(rc1_int_1, axiom,  (? [A] :  (v1_xxreal_0(A) &  (v1_xcmplx_0(A) &  (v1_xreal_0(A) & v1_int_1(A)) ) ) ) ).
fof(rc1_jordan1g, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_zfmisc_1(A) &  (v1_funct_1(A) &  (v1_finset_1(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ).
fof(rc1_nat_1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc1_ordinal1, axiom,  (? [A] :  (v1_ordinal1(A) & v2_ordinal1(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_sppol_2, axiom,  (? [A] :  (m1_finseq_1(A, u1_struct_0(k15_euclid(2))) &  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v5_relat_1(A, u1_struct_0(k15_euclid(2))) &  (v1_funct_1(A) &  (v1_finset_1(A) &  (v1_finseq_1(A) &  (v2_finseq_1(A) & v4_topreal1(A)) ) ) ) ) ) ) ) ) ).
fof(rc1_sprect_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  ( ~ (v1_xboole_0(A))  &  (v1_funct_1(A) &  (v3_funct_1(A) &  (v1_finset_1(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ) ).
fof(rc1_sprect_2, axiom,  (? [A] :  (m1_finseq_1(A, u1_struct_0(k15_euclid(2))) &  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v5_relat_1(A, u1_struct_0(k15_euclid(2))) &  ( ~ (v1_xboole_0(A))  &  ( ~ (v1_zfmisc_1(A))  &  ( ~ (v8_ordinal1(A))  &  (v1_funct_1(A) &  ( ~ (v3_funct_1(A))  &  (v1_finset_1(A) &  (v1_finseq_1(A) &  (v2_finseq_1(A) &  (v1_finseq_6(A, u1_struct_0(k15_euclid(2))) &  (v1_topreal1(A) &  (v2_topreal1(A) &  (v1_goboard5(A) &  (v2_goboard5(A) & v1_sprect_2(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc1_topreal2, axiom,  (? [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) &  (v4_funct_1(A) &  ( ~ (v1_xboole_0(A))  & v1_topreal2(A)) ) ) ) ).
fof(rc1_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(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(rc23_struct_0, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] :  (l1_struct_0(B) & v13_struct_0(B, A)) ) ) ) ).
fof(rc2_card_1, axiom,  (? [A] :  (v1_ordinal1(A) &  (v2_ordinal1(A) &  (v3_ordinal1(A) &  (v1_finset_1(A) & v1_card_1(A)) ) ) ) ) ).
fof(rc2_finseq_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v1_finset_1(B) & v1_finseq_1(B)) ) ) ) ) ) ).
fof(rc2_finseq_5, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_finseq_1(B, A) &  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, A) &  ( ~ (v1_xboole_0(B))  &  (v1_funct_1(B) &  (v2_funct_1(B) &  (v1_finset_1(B) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc2_finseq_6, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_finseq_1(B, A) &  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, A) &  ( ~ (v1_zfmisc_1(B))  &  (v1_funct_1(B) &  (v1_finset_1(B) &  (v1_finseq_1(B) &  (v2_finseq_1(B) & v1_finseq_6(B, A)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc2_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ).
fof(rc2_int_1, axiom,  (? [A] : v1_int_1(A)) ).
fof(rc2_nat_1, axiom,  (? [A] :  (v7_ordinal1(A) & v8_ordinal1(A)) ) ).
fof(rc2_ordinal1, axiom,  (? [A] : v3_ordinal1(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_sppol_2, axiom,  (? [A] :  (m1_finseq_1(A, u1_struct_0(k15_euclid(2))) &  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v5_relat_1(A, u1_struct_0(k15_euclid(2))) &  ( ~ (v1_zfmisc_1(A))  &  (v1_funct_1(A) &  (v2_funct_1(A) &  (v1_finset_1(A) &  (v1_finseq_1(A) &  (v2_finseq_1(A) &  (v1_topreal1(A) &  (v2_topreal1(A) & v3_topreal1(A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc2_sprect_1, axiom,  (? [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) &  ( ~ (v1_xboole_0(A))  &  (v2_compts_1(A, k15_euclid(2)) &  ( ~ (v1_sppol_1(A))  &  ~ (v2_sppol_1(A)) ) ) ) ) ) ).
fof(rc2_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_card_1, axiom,  (? [A] :  ~ (v1_finset_1(A)) ) ).
fof(rc3_finseq_1, axiom,  (! [A] :  (? [B] :  (m1_finseq_1(B, A) &  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v1_xboole_0(B) &  (v1_finset_1(B) & v1_finseq_1(B)) ) ) ) ) ) ) ) ).
fof(rc3_finseq_5, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  ( ~ (v1_zfmisc_1(A))  &  (v1_funct_1(A) &  (v1_finset_1(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ).
fof(rc3_int_1, axiom,  (? [A] : v2_int_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_pre_topc, axiom,  (! [A] :  (l1_pre_topc(A) =>  (? [B] :  (m1_pre_topc(B, A) & v1_pre_topc(B)) ) ) ) ).
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_card_1, axiom,  (? [A] :  (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) ) ) ).
fof(rc4_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) ) ) ).
fof(rc4_finseq_6, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  (? [B] :  (m1_finseq_1(B, A) &  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  ( ~ (v3_funct_1(B))  &  (v1_finset_1(B) &  (v1_finseq_1(B) &  (v2_finseq_1(B) & v1_finseq_6(B, A)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(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_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_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_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_card_1, axiom,  (? [A] :  (v1_ordinal1(A) &  (v2_ordinal1(A) &  (v3_ordinal1(A) &  (v7_ordinal1(A) &  ( ~ (v8_ordinal1(A))  & v1_card_1(A)) ) ) ) ) ) ).
fof(rc5_finseq_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v3_finseq_1(A)) ) ).
fof(rc5_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) ) ) ).
fof(rc5_nat_1, axiom,  (? [A] :  (m1_subset_1(A, k4_ordinal1) &  (v1_ordinal1(A) &  (v2_ordinal1(A) &  (v3_ordinal1(A) &  (v7_ordinal1(A) &  ( ~ (v8_ordinal1(A))  &  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v1_xreal_0(A) &  (v1_finset_1(A) & v1_card_1(A)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc5_ordinal1, axiom,  (? [A] : v7_ordinal1(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_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_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_finset_1(B)) ) ) ) ) ).
fof(rc6_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ).
fof(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_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(rc7_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] : v3_card_1(B, A)) ) ) ).
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(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(rc8_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] :  (v1_relat_1(B) &  (v1_funct_1(B) & v3_card_1(B, A)) ) ) ) ) ).
fof(rc8_finseq_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_finseq_1(B, A) &  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  ( ~ (v1_xboole_0(B))  &  (v1_finset_1(B) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc8_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rc9_card_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v3_card_1(B, 1)) ) ) ) ).
fof(rc9_finseq_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  ( ~ (v1_xboole_0(B))  &  (v1_finset_1(B) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ) ) ).
fof(rc9_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rc9_pre_topc, axiom,  (? [A] :  (l1_pre_topc(A) &  ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & v7_pre_topc(A)) ) ) ) ).
fof(rd1_card_1, axiom,  (! [A] :  (v1_card_1(A) => k1_card_1(A)=A) ) ).
fof(redefinition_k19_euclid, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => k19_euclid(A, B)=k10_finseq_1(A, B)) ) ).
fof(redefinition_k3_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => k3_finseq_1(A)=k1_card_1(A)) ) ).
fof(redefinition_k3_pscomp_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  & l1_pre_topc(A))  &  ( (v1_funct_1(B) &  (v1_funct_2(B, u1_struct_0(A), k1_numbers) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), k1_numbers)))) )  & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) )  => k3_pscomp_1(A, B, C)=k5_relat_1(B, C)) ) ).
fof(redefinition_k7_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => k7_relset_1(A, B, C, D)=k7_relat_1(C, D)) ) ).
fof(redefinition_k9_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(C, k1_zfmisc_1(A)) => k9_subset_1(A, B, C)=k3_xboole_0(B, C)) ) ).
fof(redefinition_m2_finseq_1, axiom,  (! [A] :  (! [B] :  (m2_finseq_1(B, A) <=> m1_finseq_1(B, A)) ) ) ).
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_r2, axiom, r1_xxreal_0(1, 2)).
fof(rqLessOrEqual__r1_xxreal_0__r2_r1, axiom,  ~ (r1_xxreal_0(2, 1)) ).
fof(rqLessOrEqual__r1_xxreal_0__r2_r2, axiom, r1_xxreal_0(2, 2)).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(spc1_numerals, axiom,  (v2_xxreal_0(1) & m1_subset_1(1, k4_ordinal1)) ).
fof(spc2_boole, axiom,  ~ (v1_xboole_0(2)) ).
fof(spc2_numerals, axiom,  (v2_xxreal_0(2) & m1_subset_1(2, k4_ordinal1)) ).
fof(t168_finseq_6, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ( ~ (v1_xboole_0(B))  & m2_finseq_1(B, A))  => r2_tarski(k7_partfun1(A, B, k3_finseq_1(B)), k10_xtuple_0(B))) ) ) ) ).
fof(t18_sppol_2, axiom,  (! [A] :  (m2_finseq_1(A, u1_struct_0(k15_euclid(2))) =>  (r1_xxreal_0(2, k3_finseq_1(A)) => r1_tarski(k10_xtuple_0(A), k3_topreal1(2, A))) ) ) ).
fof(t1_numerals, axiom, m1_subset_1(k1_xboole_0, k4_ordinal1)).
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_boole, axiom,  (! [A] : k3_xboole_0(A, k1_xboole_0)=k1_xboole_0) ).
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(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_jordan1f, axiom,  (! [A] :  ( (v2_compts_1(A, k15_euclid(2)) &  ( ~ (v1_sppol_1(A))  &  ( ~ (v2_sppol_1(A))  & m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2))))) ) )  =>  (! [B] :  (v7_ordinal1(B) => k7_partfun1(u1_struct_0(k15_euclid(2)), k2_jordan1e(A, B), k3_finseq_1(k2_jordan1e(A, B)))=k18_pscomp_1(k3_topreal1(2, k1_jordan9(A, B)))) ) ) ) ).
fof(t8_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( ( ~ (r1_xxreal_0(A, B))  &  ( ~ (v3_xxreal_0(B))  &  ~ (v2_xxreal_0(A)) ) ) ) ) ) ) ) ).
