% Mizar problem: t49_jordan21,jordan21,1273,5 
fof(t49_jordan21, conjecture,  (! [A] :  ( (v1_topreal2(A) & m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))))  =>  ~ ( (r2_tarski(k2_jordan21(A), k9_jordan6(A)) & r2_tarski(k1_jordan21(A), k9_jordan6(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_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ( ~ (v2_struct_0(A))  & v7_struct_0(A))  => v13_struct_0(A, 1)) ) ) ).
fof(cc11_membered, axiom,  (! [A] :  (v6_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v7_ordinal1(B)) ) ) ) ).
fof(cc11_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, 1) =>  ( ~ (v2_struct_0(A))  & v7_struct_0(A)) ) ) ) ).
fof(cc12_membered, axiom,  (! [A] :  (v1_xboole_0(A) => v6_membered(A)) ) ).
fof(cc13_membered, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_membered(B)) ) ) ) ).
fof(cc14_membered, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v2_membered(B)) ) ) ) ).
fof(cc15_membered, axiom,  (! [A] :  (v3_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v3_membered(B)) ) ) ) ).
fof(cc16_membered, axiom,  (! [A] :  (v4_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_membered(B)) ) ) ) ).
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(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_compts_1, axiom,  (! [A] :  (l1_pre_topc(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (v1_xboole_0(B) => v2_compts_1(B, A)) ) ) ) ) ).
fof(cc1_jordan21, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) =>  (v1_jordan21(A) =>  ~ (v1_xboole_0(A)) ) ) ) ).
fof(cc1_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_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_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(cc2_compts_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) &  (v8_pre_topc(A) & l1_pre_topc(A)) ) )  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (v2_compts_1(B, A) => v4_pre_topc(B, A)) ) ) ) ) ).
fof(cc2_euclid, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(k15_euclid(A))) => v1_finseq_1(B)) ) ) ) ).
fof(cc2_jordan21, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) =>  (v1_topreal2(A) =>  (v1_topreal2(A) & v1_jordan21(A)) ) ) ) ).
fof(cc2_membered, axiom,  (! [A] :  (v5_membered(A) => v4_membered(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_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(cc3_compts_1, axiom,  (! [A] :  (l1_pre_topc(A) =>  ( (v8_struct_0(A) & v2_pre_topc(A))  =>  (v2_pre_topc(A) & v1_compts_1(A)) ) ) ) ).
fof(cc3_euclid, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(k15_euclid(A))) => v3_valued_0(B)) ) ) ) ).
fof(cc3_membered, axiom,  (! [A] :  (v4_membered(A) => v3_membered(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_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_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(cc4_compts_1, axiom,  (! [A] :  ( (v2_pre_topc(A) & l1_pre_topc(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (v1_finset_1(B) => v2_compts_1(B, A)) ) ) ) ) ).
fof(cc4_euclid, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(k15_euclid(A))) => v3_card_1(B, A)) ) ) ) ).
fof(cc4_membered, axiom,  (! [A] :  (v3_membered(A) => v2_membered(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(cc5_compts_1, axiom,  (! [A] :  (l1_pre_topc(A) =>  (v2_struct_0(A) => v8_pre_topc(A)) ) ) ).
fof(cc5_membered, axiom,  (! [A] :  (v3_membered(A) => v1_membered(A)) ) ).
fof(cc5_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ( ~ (v2_struct_0(A))  &  ~ (v8_struct_0(A)) ) ) ) ) ).
fof(cc6_compts_1, axiom,  (! [A] :  ( (v8_pre_topc(A) & l1_pre_topc(A))  =>  (! [B] :  (m1_pre_topc(B, A) => v8_pre_topc(B)) ) ) ) ).
fof(cc6_membered, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xcmplx_0(B)) ) ) ) ).
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(cc7_membered, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xxreal_0(B)) ) ) ) ).
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(cc8_membered, axiom,  (! [A] :  (v3_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xreal_0(B)) ) ) ) ).
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(cc9_membered, axiom,  (! [A] :  (v4_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_rat_1(B)) ) ) ) ).
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_k1_valued_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_valued_0(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_valued_0(B)) ) )  => k1_valued_1(A, B)=k1_valued_1(B, A)) ) ).
fof(commutativity_k2_tarski, axiom,  (! [A, B] : k2_tarski(A, B)=k2_tarski(B, A)) ).
fof(commutativity_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, B)=k2_xboole_0(B, A)) ).
fof(commutativity_k2_xcmplx_0, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k2_xcmplx_0(A, B)=k2_xcmplx_0(B, A)) ) ).
fof(commutativity_k3_rlvect_1, axiom,  (! [A, B, C] :  ( ( (v2_rlvect_1(A) & l1_algstr_0(A))  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k3_rlvect_1(A, B, C)=k3_rlvect_1(A, C, B)) ) ).
fof(commutativity_k3_xboole_0, axiom,  (! [A, B] : k3_xboole_0(A, B)=k3_xboole_0(B, A)) ).
fof(commutativity_k3_xcmplx_0, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k3_xcmplx_0(A, B)=k3_xcmplx_0(B, A)) ) ).
fof(commutativity_k4_rvsum_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v3_valued_0(A) & v1_finseq_1(A)) ) )  &  (v1_relat_1(B) &  (v1_funct_1(B) &  (v3_valued_0(B) & v1_finseq_1(B)) ) ) )  => k4_rvsum_1(A, B)=k4_rvsum_1(B, A)) ) ).
fof(commutativity_k4_subset_1, axiom,  (! [A, B, C] :  ( (m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))  => k4_subset_1(A, B, C)=k4_subset_1(A, C, B)) ) ).
fof(commutativity_k7_domain_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  (m1_subset_1(B, A) & m1_subset_1(C, A)) )  => k7_domain_1(A, B, C)=k7_domain_1(A, C, B)) ) ).
fof(commutativity_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_jordan6, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(k15_euclid(2))) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(k15_euclid(2))) =>  (r1_jordan6(A, B, C) <=>  ~ ( ( ~ ( (r2_tarski(B, k8_jordan6(A)) &  (r2_tarski(C, k9_jordan6(A)) &  ~ (C=k18_pscomp_1(A)) ) ) )  &  ( ~ ( (r2_tarski(B, k8_jordan6(A)) &  (r2_tarski(C, k8_jordan6(A)) & r1_jordan5c(k8_jordan6(A), k18_pscomp_1(A), k22_pscomp_1(A), B, C)) ) )  &  ~ ( (r2_tarski(B, k9_jordan6(A)) &  (r2_tarski(C, k9_jordan6(A)) &  ( ~ (C=k18_pscomp_1(A))  & r1_jordan5c(k9_jordan6(A), k22_pscomp_1(A), k18_pscomp_1(A), B, C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d10_pscomp_1, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => k9_pscomp_1(A)=k1_pscomp_1(k1_pre_topc(k15_euclid(2), A), k3_pscomp_1(k15_euclid(2), k5_pscomp_1, A))) ) ).
fof(d10_xboole_0, axiom,  (! [A] :  (! [B] :  (A=B <=>  (r1_tarski(A, B) & r1_tarski(B, 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_pscomp_1, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => k12_pscomp_1(A)=k19_euclid(k8_pscomp_1(A), k7_pscomp_1(A))) ) ).
fof(d14_pscomp_1, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => k13_pscomp_1(A)=k19_euclid(k8_pscomp_1(A), k9_pscomp_1(A))) ) ).
fof(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(d17_pscomp_1, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => k16_pscomp_1(A)=k9_subset_1(u1_struct_0(k15_euclid(2)), k1_rltopsp1(k15_euclid(2), k13_pscomp_1(A), k12_pscomp_1(A)), A)) ) ).
fof(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(d1_tarski, axiom,  (! [A] :  (! [B] :  (B=k1_tarski(A) <=>  (! [C] :  (r2_hidden(C, B) <=> C=A) ) ) ) ) ).
fof(d23_pscomp_1, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => k22_pscomp_1(A)=k19_euclid(k8_pscomp_1(A), k2_pscomp_1(k1_pre_topc(k15_euclid(2), k16_pscomp_1(A)), k3_pscomp_1(k15_euclid(2), k5_pscomp_1, k16_pscomp_1(A))))) ) ).
fof(d2_jordan21, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => k1_jordan21(A)=k19_euclid(k7_xcmplx_0(k2_xcmplx_0(k8_pscomp_1(A), k6_pscomp_1(A)), 2), k2_seq_4(k7_relset_1(u1_struct_0(k15_euclid(2)), k1_numbers, k5_pscomp_1, k9_subset_1(u1_struct_0(k15_euclid(2)), A, k6_jordan6(k7_xcmplx_0(k2_xcmplx_0(k8_pscomp_1(A), k6_pscomp_1(A)), 2))))))) ) ).
fof(d2_pscomp_1, axiom,  (! [A] :  (l1_struct_0(A) =>  (! [B] :  ( (v1_funct_1(B) &  (v1_funct_2(B, u1_struct_0(A), k1_numbers) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), k1_numbers)))) )  => k2_pscomp_1(A, B)=k2_seq_4(k7_relset_1(u1_struct_0(A), k1_numbers, B, u1_struct_0(A)))) ) ) ) ).
fof(d2_rltopsp1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_rlvect_1(A) &  (v6_rlvect_1(A) &  (v7_rlvect_1(A) &  (v8_rlvect_1(A) & l1_rlvect_1(A)) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k1_rltopsp1(A, B, C)=a_3_1_rltopsp1(A, B, C)) ) ) ) ) ) ).
fof(d2_tarski, axiom,  (! [A] :  (! [B] :  (! [C] :  (C=k2_tarski(A, B) <=>  (! [D] :  (r2_hidden(D, C) <=>  (D=A | D=B) ) ) ) ) ) ) ).
fof(d3_jordan21, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => k2_jordan21(A)=k19_euclid(k7_xcmplx_0(k2_xcmplx_0(k8_pscomp_1(A), k6_pscomp_1(A)), 2), k3_seq_4(k7_relset_1(u1_struct_0(k15_euclid(2)), k1_numbers, k5_pscomp_1, k9_subset_1(u1_struct_0(k15_euclid(2)), A, k6_jordan6(k7_xcmplx_0(k2_xcmplx_0(k8_pscomp_1(A), k6_pscomp_1(A)), 2))))))) ) ).
fof(d3_sppol_1, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) =>  (v2_sppol_1(A) <=>  (! [B] :  (m1_subset_1(B, u1_struct_0(k15_euclid(2))) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(k15_euclid(2))) =>  ( (r2_tarski(B, A) & r2_tarski(C, A))  => k17_euclid(B)=k17_euclid(C)) ) ) ) ) ) ) ) ).
fof(d3_tarski, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) <=>  (! [C] :  (r2_hidden(C, A) => r2_hidden(C, B)) ) ) ) ) ).
fof(d4_xboole_0, axiom,  (! [A] :  (! [B] :  (! [C] :  (C=k3_xboole_0(A, B) <=>  (! [D] :  (r2_hidden(D, C) <=>  (r2_hidden(D, A) & r2_hidden(D, B)) ) ) ) ) ) ) ).
fof(d5_xboole_0, axiom,  (! [A] :  (! [B] :  (! [C] :  (C=k4_xboole_0(A, B) <=>  (! [D] :  (r2_hidden(D, C) <=>  (r2_hidden(D, A) &  ~ (r2_hidden(D, B)) ) ) ) ) ) ) ) ).
fof(d7_pscomp_1, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => k6_pscomp_1(A)=k1_pscomp_1(k1_pre_topc(k15_euclid(2), A), k3_pscomp_1(k15_euclid(2), k4_pscomp_1, A))) ) ).
fof(d7_xboole_0, axiom,  (! [A] :  (! [B] :  (r1_xboole_0(A, B) <=> k3_xboole_0(A, B)=k1_xboole_0) ) ) ).
fof(d8_jordan6, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) =>  (v1_topreal2(A) =>  (! [B] :  ( ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))))  =>  (B=k8_jordan6(A) <=>  (r1_topreal1(k15_euclid(2), k18_pscomp_1(A), k22_pscomp_1(A), B) &  (? [C] :  ( ( ~ (v1_xboole_0(C))  & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))))  &  (r1_topreal1(k15_euclid(2), k22_pscomp_1(A), k18_pscomp_1(A), C) &  (k9_subset_1(u1_struct_0(k15_euclid(2)), B, C)=k2_tarski(k18_pscomp_1(A), k22_pscomp_1(A)) &  (k4_subset_1(u1_struct_0(k15_euclid(2)), B, C)=A &  ~ (r1_xxreal_0(k18_euclid(k1_jordan5c(B, k6_jordan6(k7_xcmplx_0(k2_xcmplx_0(k6_pscomp_1(A), k8_pscomp_1(A)), 2)), k18_pscomp_1(A), k22_pscomp_1(A))), k18_euclid(k2_jordan5c(C, k6_jordan6(k7_xcmplx_0(k2_xcmplx_0(k6_pscomp_1(A), k8_pscomp_1(A)), 2)), k22_pscomp_1(A), k18_pscomp_1(A))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d8_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(d9_jordan6, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) =>  (v1_topreal2(A) =>  (! [B] :  ( ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))))  =>  (B=k9_jordan6(A) <=>  (r1_topreal1(k15_euclid(2), k22_pscomp_1(A), k18_pscomp_1(A), B) &  (k9_subset_1(u1_struct_0(k15_euclid(2)), k8_jordan6(A), B)=k2_tarski(k18_pscomp_1(A), k22_pscomp_1(A)) &  (k4_subset_1(u1_struct_0(k15_euclid(2)), k8_jordan6(A), B)=A &  ~ (r1_xxreal_0(k18_euclid(k1_jordan5c(k8_jordan6(A), k6_jordan6(k7_xcmplx_0(k2_xcmplx_0(k6_pscomp_1(A), k8_pscomp_1(A)), 2)), k18_pscomp_1(A), k22_pscomp_1(A))), k18_euclid(k2_jordan5c(B, k6_jordan6(k7_xcmplx_0(k2_xcmplx_0(k6_pscomp_1(A), k8_pscomp_1(A)), 2)), k22_pscomp_1(A), k18_pscomp_1(A))))) ) ) ) ) ) ) ) ) ) ).
fof(d9_pscomp_1, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => k8_pscomp_1(A)=k2_pscomp_1(k1_pre_topc(k15_euclid(2), A), k3_pscomp_1(k15_euclid(2), k4_pscomp_1, A))) ) ).
fof(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_rvsum_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v3_valued_0(A) & v1_finseq_1(A)) ) )  & v1_xreal_0(B))  => m2_finseq_1(k10_rvsum_1(A, B), k1_numbers)) ) ).
fof(dt_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_k12_pscomp_1, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => m1_subset_1(k12_pscomp_1(A), u1_struct_0(k15_euclid(2)))) ) ).
fof(dt_k13_pscomp_1, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => m1_subset_1(k13_pscomp_1(A), u1_struct_0(k15_euclid(2)))) ) ).
fof(dt_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_k16_pscomp_1, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => m1_subset_1(k16_pscomp_1(A), k1_zfmisc_1(u1_struct_0(k15_euclid(2))))) ) ).
fof(dt_k17_euclid, axiom,  (! [A] :  (m1_subset_1(A, u1_struct_0(k15_euclid(2))) => v1_xreal_0(k17_euclid(A))) ) ).
fof(dt_k18_euclid, axiom,  (! [A] :  (m1_subset_1(A, u1_struct_0(k15_euclid(2))) => v1_xreal_0(k18_euclid(A))) ) ).
fof(dt_k18_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_algstr_0, axiom,  (! [A, B, C] :  ( (l1_algstr_0(A) &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k1_algstr_0(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k1_jordan21, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => m1_subset_1(k1_jordan21(A), u1_struct_0(k15_euclid(2)))) ) ).
fof(dt_k1_jordan5c, axiom,  (! [A, B, C, D] :  ( (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) &  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) &  (m1_subset_1(C, u1_struct_0(k15_euclid(2))) & m1_subset_1(D, u1_struct_0(k15_euclid(2)))) ) )  => m1_subset_1(k1_jordan5c(A, B, C, D), u1_struct_0(k15_euclid(2)))) ) ).
fof(dt_k1_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_rlvect_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  & l1_rlvect_1(A))  &  (m1_subset_1(B, u1_struct_0(A)) & v1_xreal_0(C)) )  => m1_subset_1(k1_rlvect_1(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k1_tarski, axiom, $true).
fof(dt_k1_valued_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_valued_0(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_valued_0(B)) ) )  =>  (v1_relat_1(k1_valued_1(A, B)) & v1_funct_1(k1_valued_1(A, B))) ) ) ).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k22_pscomp_1, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => m1_subset_1(k22_pscomp_1(A), u1_struct_0(k15_euclid(2)))) ) ).
fof(dt_k24_valued_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_valued_0(A)) )  & v1_xcmplx_0(B))  =>  (v1_relat_1(k24_valued_1(A, B)) & v1_funct_1(k24_valued_1(A, B))) ) ) ).
fof(dt_k2_jordan21, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => m1_subset_1(k2_jordan21(A), u1_struct_0(k15_euclid(2)))) ) ).
fof(dt_k2_jordan5c, axiom,  (! [A, B, C, D] :  ( (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) &  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) &  (m1_subset_1(C, u1_struct_0(k15_euclid(2))) & m1_subset_1(D, u1_struct_0(k15_euclid(2)))) ) )  => m1_subset_1(k2_jordan5c(A, B, C, D), u1_struct_0(k15_euclid(2)))) ) ).
fof(dt_k2_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_tarski, axiom, $true).
fof(dt_k2_xboole_0, axiom, $true).
fof(dt_k2_xcmplx_0, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
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_rlvect_1, axiom,  (! [A, B, C] :  ( ( (v2_rlvect_1(A) & l1_algstr_0(A))  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k3_rlvect_1(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k3_seq_4, axiom,  (! [A] :  (v3_membered(A) => v1_xreal_0(k3_seq_4(A))) ) ).
fof(dt_k3_xboole_0, axiom, $true).
fof(dt_k3_xcmplx_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_k4_rvsum_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v3_valued_0(A) & v1_finseq_1(A)) ) )  &  (v1_relat_1(B) &  (v1_funct_1(B) &  (v3_valued_0(B) & v1_finseq_1(B)) ) ) )  => m2_finseq_1(k4_rvsum_1(A, B), k1_numbers)) ) ).
fof(dt_k4_subset_1, axiom,  (! [A, B, C] :  ( (m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))  => m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A))) ) ).
fof(dt_k4_xboole_0, axiom, $true).
fof(dt_k4_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => v1_xcmplx_0(k4_xcmplx_0(A))) ) ).
fof(dt_k5_jordan6, axiom,  (! [A, B, C, D, E] :  ( (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) &  (m1_subset_1(B, u1_struct_0(k15_euclid(2))) &  (m1_subset_1(C, u1_struct_0(k15_euclid(2))) &  (m1_subset_1(D, u1_struct_0(k15_euclid(2))) & m1_subset_1(E, u1_struct_0(k15_euclid(2)))) ) ) )  => m1_subset_1(k5_jordan6(A, B, C, D, E), k1_zfmisc_1(u1_struct_0(k15_euclid(2))))) ) ).
fof(dt_k5_numbers, axiom, m1_subset_1(k5_numbers, k4_ordinal1)).
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_domain_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(B, A))  => m1_subset_1(k6_domain_1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_k6_jordan6, axiom,  (! [A] :  (v1_xreal_0(A) => m1_subset_1(k6_jordan6(A), k1_zfmisc_1(u1_struct_0(k15_euclid(2))))) ) ).
fof(dt_k6_pscomp_1, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => v1_xreal_0(k6_pscomp_1(A))) ) ).
fof(dt_k6_xcmplx_0, axiom, $true).
fof(dt_k7_domain_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  (m1_subset_1(B, A) & m1_subset_1(C, A)) )  => m1_subset_1(k7_domain_1(A, B, C), k1_zfmisc_1(A))) ) ).
fof(dt_k7_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_k7_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(B, k1_zfmisc_1(A)) => m1_subset_1(k7_subset_1(A, B, C), k1_zfmisc_1(A))) ) ).
fof(dt_k7_xcmplx_0, axiom, $true).
fof(dt_k8_jordan6, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) =>  ( ~ (v1_xboole_0(k8_jordan6(A)))  & m1_subset_1(k8_jordan6(A), k1_zfmisc_1(u1_struct_0(k15_euclid(2))))) ) ) ).
fof(dt_k8_pscomp_1, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => v1_xreal_0(k8_pscomp_1(A))) ) ).
fof(dt_k9_jordan6, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) =>  ( ~ (v1_xboole_0(k9_jordan6(A)))  & m1_subset_1(k9_jordan6(A), k1_zfmisc_1(u1_struct_0(k15_euclid(2))))) ) ) ).
fof(dt_k9_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_membered, axiom,  (! [A] :  (v1_rat_1(A) => v4_membered(k1_tarski(A))) ) ).
fof(fc10_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v2_xxreal_0(k2_xcmplx_0(A, B))) ) ) ).
fof(fc11_membered, axiom,  (! [A] :  (v1_int_1(A) => v5_membered(k1_tarski(A))) ) ).
fof(fc11_xreal_0, axiom,  (! [A, B] :  ( ( (v2_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  => v2_xxreal_0(k2_xcmplx_0(A, B))) ) ).
fof(fc12_membered, axiom,  (! [A] :  (v7_ordinal1(A) => v6_membered(k1_tarski(A))) ) ).
fof(fc12_xreal_0, axiom,  (! [A, B] :  ( ( (v2_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  => v2_xxreal_0(k2_xcmplx_0(B, A))) ) ).
fof(fc13_membered, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => v1_membered(k2_tarski(A, B))) ) ).
fof(fc13_xreal_0, axiom,  (! [A, B] :  ( ( (v3_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  => v3_xxreal_0(k2_xcmplx_0(A, B))) ) ).
fof(fc14_membered, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => v2_membered(k2_tarski(A, B))) ) ).
fof(fc14_xreal_0, axiom,  (! [A, B] :  ( ( (v3_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  => v3_xxreal_0(k2_xcmplx_0(B, A))) ) ).
fof(fc15_membered, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => v3_membered(k2_tarski(A, B))) ) ).
fof(fc15_xreal_0, axiom,  (! [A] :  ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  =>  (v1_xcmplx_0(k4_xcmplx_0(A)) &  ~ (v3_xxreal_0(k4_xcmplx_0(A))) ) ) ) ).
fof(fc16_membered, axiom,  (! [A, B] :  ( (v1_rat_1(A) & v1_rat_1(B))  => v4_membered(k2_tarski(A, B))) ) ).
fof(fc16_xreal_0, axiom,  (! [A] :  ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  =>  (v1_xcmplx_0(k4_xcmplx_0(A)) &  ~ (v2_xxreal_0(k4_xcmplx_0(A))) ) ) ) ).
fof(fc17_membered, axiom,  (! [A, B] :  ( (v1_int_1(A) & v1_int_1(B))  => v5_membered(k2_tarski(A, B))) ) ).
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_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v3_xxreal_0(k6_xcmplx_0(A, B))) ) ) ).
fof(fc18_membered, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & v7_ordinal1(B))  => v6_membered(k2_tarski(A, B))) ) ).
fof(fc18_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v2_xxreal_0(k6_xcmplx_0(B, A))) ) ) ).
fof(fc19_xreal_0, axiom,  (! [A, B] :  ( ( (v2_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  => v2_xxreal_0(k6_xcmplx_0(A, B))) ) ).
fof(fc1_jordan21, axiom,  (! [A] :  ( (v1_topreal2(A) & m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))))  =>  ( ~ (v1_xboole_0(k9_jordan6(A)))  & v1_jordan21(k9_jordan6(A))) ) ) ).
fof(fc1_jordan2c, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v5_rltopsp1(k15_euclid(A)) &  (v6_rltopsp1(k15_euclid(A)) & v7_rltopsp1(k15_euclid(A))) ) ) ) ).
fof(fc1_jordan6, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  (v1_topreal2(A) & m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2))))) )  =>  ( ~ (v1_xboole_0(k9_jordan6(A)))  & v2_compts_1(k9_jordan6(A), k15_euclid(2))) ) ) ).
fof(fc1_numbers, axiom,  ~ (v1_xboole_0(k1_numbers)) ).
fof(fc1_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v4_relat_1(B, A))  &  (v1_relat_1(C) & v4_relat_1(C, A)) )  => v4_relat_1(k2_xboole_0(B, C), A)) ) ).
fof(fc1_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(fc20_xreal_0, axiom,  (! [A, B] :  ( ( (v2_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  => v3_xxreal_0(k6_xcmplx_0(B, A))) ) ).
fof(fc21_xreal_0, axiom,  (! [A, B] :  ( ( (v3_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  => v3_xxreal_0(k6_xcmplx_0(A, B))) ) ).
fof(fc22_xreal_0, axiom,  (! [A, B] :  ( ( (v3_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  => v2_xxreal_0(k6_xcmplx_0(B, A))) ) ).
fof(fc23_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v2_xxreal_0(k3_xcmplx_0(A, B))) ) ) ).
fof(fc24_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v2_xxreal_0(k3_xcmplx_0(B, A))) ) ) ).
fof(fc25_membered, axiom,  (! [A, B] :  ( (v1_membered(A) & v1_membered(B))  => v1_membered(k2_xboole_0(A, B))) ) ).
fof(fc25_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v3_xxreal_0(k3_xcmplx_0(A, B))) ) ) ).
fof(fc26_membered, axiom,  (! [A, B] :  ( (v2_membered(A) & v2_membered(B))  => v2_membered(k2_xboole_0(A, B))) ) ).
fof(fc26_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v3_xxreal_0(k3_xcmplx_0(A, B))) ) ) ).
fof(fc27_membered, axiom,  (! [A, B] :  ( (v3_membered(A) & v3_membered(B))  => v3_membered(k2_xboole_0(A, B))) ) ).
fof(fc28_membered, axiom,  (! [A, B] :  ( (v4_membered(A) & v4_membered(B))  => v4_membered(k2_xboole_0(A, B))) ) ).
fof(fc29_membered, axiom,  (! [A, B] :  ( (v5_membered(A) & v5_membered(B))  => v5_membered(k2_xboole_0(A, B))) ) ).
fof(fc2_jordan21, axiom,  (! [A] :  ( (v1_topreal2(A) & m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))))  =>  ( ~ (v1_xboole_0(k8_jordan6(A)))  & v1_jordan21(k8_jordan6(A))) ) ) ).
fof(fc2_jordan6, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  (v1_topreal2(A) & m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2))))) )  =>  ( ~ (v1_xboole_0(k8_jordan6(A)))  & v2_compts_1(k8_jordan6(A), k15_euclid(2))) ) ) ).
fof(fc2_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_rltopsp1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_rlvect_1(A) &  (v6_rlvect_1(A) &  (v7_rlvect_1(A) &  (v8_rlvect_1(A) & l1_rlvect_1(A)) ) ) ) ) ) ) ) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  =>  ( ~ (v1_xboole_0(k1_rltopsp1(A, B, C)))  & v1_convex1(k1_rltopsp1(A, B, C), A)) ) ) ).
fof(fc2_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(fc2_xboole_0, axiom,  (! [A] :  ~ (v1_xboole_0(k1_tarski(A))) ) ).
fof(fc30_membered, axiom,  (! [A, B] :  ( (v6_membered(A) & v6_membered(B))  => v6_membered(k2_xboole_0(A, B))) ) ).
fof(fc31_membered, axiom,  (! [A, B] :  (v1_membered(A) => v1_membered(k3_xboole_0(A, B))) ) ).
fof(fc31_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v2_xxreal_0(k7_xcmplx_0(A, B))) ) ) ).
fof(fc32_membered, axiom,  (! [A, B] :  (v1_membered(A) => v1_membered(k3_xboole_0(B, A))) ) ).
fof(fc32_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v2_xxreal_0(k7_xcmplx_0(B, A))) ) ) ).
fof(fc33_membered, axiom,  (! [A, B] :  (v2_membered(A) => v2_membered(k3_xboole_0(A, B))) ) ).
fof(fc33_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v3_xxreal_0(k7_xcmplx_0(A, B))) ) ) ).
fof(fc34_membered, axiom,  (! [A, B] :  (v2_membered(A) => v2_membered(k3_xboole_0(B, A))) ) ).
fof(fc34_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v3_xxreal_0(k7_xcmplx_0(A, B))) ) ) ).
fof(fc35_membered, axiom,  (! [A, B] :  (v3_membered(A) => v3_membered(k3_xboole_0(A, B))) ) ).
fof(fc36_membered, axiom,  (! [A, B] :  (v3_membered(A) => v3_membered(k3_xboole_0(B, A))) ) ).
fof(fc37_membered, axiom,  (! [A, B] :  (v4_membered(A) => v4_membered(k3_xboole_0(A, B))) ) ).
fof(fc38_membered, axiom,  (! [A, B] :  (v4_membered(A) => v4_membered(k3_xboole_0(B, A))) ) ).
fof(fc39_membered, axiom,  (! [A, B] :  (v5_membered(A) => v5_membered(k3_xboole_0(A, B))) ) ).
fof(fc3_membered, axiom, v3_membered(k1_numbers)).
fof(fc3_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v4_relat_1(B, A))  & v1_relat_1(C))  => v4_relat_1(k4_xboole_0(B, C), A)) ) ).
fof(fc3_xboole_0, axiom,  (! [A, B] :  ~ (v1_xboole_0(k2_tarski(A, B))) ) ).
fof(fc3_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) =>  (v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A))) ) ) ).
fof(fc40_membered, axiom,  (! [A, B] :  (v5_membered(A) => v5_membered(k3_xboole_0(B, A))) ) ).
fof(fc41_membered, axiom,  (! [A, B] :  (v6_membered(A) => v6_membered(k3_xboole_0(A, B))) ) ).
fof(fc42_membered, axiom,  (! [A, B] :  (v6_membered(A) => v6_membered(k3_xboole_0(B, A))) ) ).
fof(fc43_membered, axiom,  (! [A, B] :  (v1_membered(A) => v1_membered(k4_xboole_0(A, B))) ) ).
fof(fc44_membered, axiom,  (! [A, B] :  (v2_membered(A) => v2_membered(k4_xboole_0(A, B))) ) ).
fof(fc45_membered, axiom,  (! [A, B] :  (v3_membered(A) => v3_membered(k4_xboole_0(A, B))) ) ).
fof(fc46_membered, axiom,  (! [A, B] :  (v4_membered(A) => v4_membered(k4_xboole_0(A, B))) ) ).
fof(fc47_membered, axiom,  (! [A, B] :  (v5_membered(A) => v5_membered(k4_xboole_0(A, B))) ) ).
fof(fc48_membered, axiom,  (! [A, B] :  (v6_membered(A) => v6_membered(k4_xboole_0(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(fc4_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v5_relat_1(B, A))  &  (v1_relat_1(C) & v5_relat_1(C, A)) )  => v5_relat_1(k2_xboole_0(B, C), A)) ) ).
fof(fc4_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(A, B))) ) ) ).
fof(fc56_membered, axiom, v7_membered(k1_numbers)).
fof(fc59_membered, axiom, v7_membered(k4_ordinal1)).
fof(fc5_compts_1, axiom,  (! [A] :  (l1_pre_topc(A) => v1_tops_2(u1_pre_topc(A), A)) ) ).
fof(fc5_euclid, axiom,  (! [A] :  (v7_ordinal1(A) =>  ( ~ (v2_struct_0(k15_euclid(A)))  & v5_rltopsp1(k15_euclid(A))) ) ) ).
fof(fc5_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v5_relat_1(B, A))  & v1_relat_1(C))  => v5_relat_1(k3_xboole_0(B, C), A)) ) ).
fof(fc5_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_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(B, A))) ) ) ).
fof(fc5_xreal_0, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => v1_xreal_0(k2_xcmplx_0(A, B))) ) ).
fof(fc6_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_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v5_relat_1(B, A))  & v1_relat_1(C))  => v5_relat_1(k4_xboole_0(B, C), A)) ) ).
fof(fc6_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(fc6_xreal_0, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => v1_xreal_0(k3_xcmplx_0(A, B))) ) ).
fof(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_struct_0, axiom,  (! [A] :  ( (v7_struct_0(A) & l1_struct_0(A))  => v1_zfmisc_1(u1_struct_0(A))) ) ).
fof(fc7_xreal_0, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => v1_xreal_0(k6_xcmplx_0(A, B))) ) ).
fof(fc8_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_xreal_0, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => v1_xreal_0(k7_xcmplx_0(A, B))) ) ).
fof(fc9_membered, axiom,  (! [A] :  (v1_xreal_0(A) => v3_membered(k1_tarski(A))) ) ).
fof(fc9_struct_0, axiom,  (! [A] :  ( ( ~ (v8_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_finset_1(u1_struct_0(A))) ) ) ).
fof(fc9_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v3_xxreal_0(k2_xcmplx_0(A, B))) ) ) ).
fof(fraenkel_a_3_1_rltopsp1, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v5_rlvect_1(B) &  (v6_rlvect_1(B) &  (v7_rlvect_1(B) &  (v8_rlvect_1(B) & l1_rlvect_1(B)) ) ) ) ) ) ) ) )  &  (m1_subset_1(C, u1_struct_0(B)) & m1_subset_1(D, u1_struct_0(B))) )  =>  (r2_hidden(A, a_3_1_rltopsp1(B, C, D)) <=>  (? [E] :  (v1_xreal_0(E) &  (A=k3_rlvect_1(B, k1_rlvect_1(B, C, k6_xcmplx_0(1, E)), k1_rlvect_1(B, D, E)) &  (r1_xxreal_0(k5_numbers, E) & r1_xxreal_0(E, 1)) ) ) ) ) ) ) ).
fof(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_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, A)=A) ).
fof(idempotence_k3_xboole_0, axiom,  (! [A, B] : k3_xboole_0(A, A)=A) ).
fof(idempotence_k4_subset_1, axiom,  (! [A, B, C] :  ( (m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))  => k4_subset_1(A, B, B)=B) ) ).
fof(idempotence_k9_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(C, k1_zfmisc_1(A)) => k9_subset_1(A, B, B)=B) ) ).
fof(ie1_euclid, axiom,  (! [A, B, C, D, E] :  ( (v1_xreal_0(A) &  (v1_xreal_0(B) &  (v7_ordinal1(C) &  (m1_subset_1(D, u1_struct_0(k15_euclid(C))) &  (v1_relat_1(E) &  (v1_funct_1(E) &  (v1_finseq_1(E) & v3_valued_0(E)) ) ) ) ) ) )  =>  ( (A=B & D=E)  => k1_rlvect_1(k15_euclid(C), D, A)=k10_rvsum_1(E, B)) ) ) ).
fof(ie2_euclid, axiom,  (! [A, B, C, D, E] :  ( (v7_ordinal1(A) &  (m1_subset_1(B, u1_struct_0(k15_euclid(A))) &  (m1_subset_1(C, u1_struct_0(k15_euclid(A))) &  ( (v1_relat_1(D) &  (v1_funct_1(D) &  (v1_finseq_1(D) & v3_valued_0(D)) ) )  &  (v1_relat_1(E) &  (v1_funct_1(E) &  (v1_finseq_1(E) & v3_valued_0(E)) ) ) ) ) ) )  =>  ( (B=D & C=E)  => k3_rlvect_1(k15_euclid(A), B, C)=k4_rvsum_1(D, E)) ) ) ).
fof(involutiveness_k4_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => k4_xcmplx_0(k4_xcmplx_0(A))=A) ) ).
fof(irreflexivity_r1_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (r1_subset_1(A, A)) ) ) ).
fof(irreflexivity_r2_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (r2_subset_1(A, A)) ) ) ).
fof(l3_jordan21, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  ~ ( (r2_tarski(A, k2_xboole_0(k2_xboole_0(B, C), D)) &  ( ~ (r2_tarski(A, B))  &  ( ~ (r2_tarski(A, C))  &  ~ (r2_tarski(A, D)) ) ) ) ) ) ) ) ) ).
fof(l4_jordan21, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  ( (r1_xboole_0(A, D) &  (r1_xboole_0(B, D) & r1_xboole_0(C, D)) )  => r1_xboole_0(k2_xboole_0(k2_xboole_0(A, B), C), D)) ) ) ) ) ).
fof(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_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(rc1_compts_1, axiom,  (? [A] :  (l1_pre_topc(A) &  ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & v8_pre_topc(A)) ) ) ) ).
fof(rc1_jordan21, axiom,  (? [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) &  ( ~ (v1_xboole_0(A))  &  (v4_pre_topc(A, k15_euclid(2)) &  (v2_connsp_1(A, k15_euclid(2)) &  (v2_compts_1(A, k15_euclid(2)) &  (v9_rltopsp1(A, k15_euclid(2)) &  ( ~ (v1_sppol_1(A))  &  ( ~ (v2_sppol_1(A))  &  (v1_topreal2(A) & v1_jordan21(A)) ) ) ) ) ) ) ) ) ) ).
fof(rc1_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v6_membered(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_topreal2, axiom,  (? [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) &  (v4_funct_1(A) &  ( ~ (v1_xboole_0(A))  & v1_topreal2(A)) ) ) ) ).
fof(rc1_topreal6, axiom,  (? [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) &  ( ~ (v1_xboole_0(A))  & v1_convex1(A, k15_euclid(2))) ) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc1_xreal_0, axiom,  (? [A] : v1_xreal_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(rc2_compts_1, axiom,  (? [A] :  (l1_pre_topc(A) &  ( ~ (v2_struct_0(A))  &  (v8_struct_0(A) &  (v1_pre_topc(A) & v2_pre_topc(A)) ) ) ) ) ).
fof(rc2_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v6_membered(A)) ) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc2_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc3_compts_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & l1_pre_topc(A)) )  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  & v2_compts_1(B, A)) ) ) ) ) ).
fof(rc3_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v6_membered(A) & v7_membered(A)) ) ) ).
fof(rc3_rltopsp1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_rlvect_1(A) &  (v6_rlvect_1(A) &  (v7_rlvect_1(A) &  (v8_rlvect_1(A) & l1_rlvect_1(A)) ) ) ) ) ) ) ) )  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  & v2_rltopsp1(B, A)) ) ) ) ) ).
fof(rc3_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v2_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc4_compts_1, axiom,  (! [A] :  ( (v2_pre_topc(A) & l1_pre_topc(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) &  ( ~ (v1_xboole_0(B))  & v1_tops_2(B, A)) ) ) ) ) ).
fof(rc4_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_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v3_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc6_rltopsp1, axiom,  (? [A] :  (l1_rltopsp1(A) & v5_rltopsp1(A)) ) ).
fof(rc7_rltopsp1, axiom,  (? [A] :  (l1_rltopsp1(A) &  ( ~ (v2_struct_0(A))  & v5_rltopsp1(A)) ) ) ).
fof(rc8_rltopsp1, axiom,  (? [A] :  (l1_rltopsp1(A) &  ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_rlvect_1(A) &  (v6_rlvect_1(A) &  (v7_rlvect_1(A) &  (v8_rlvect_1(A) &  (v5_rltopsp1(A) &  (v6_rltopsp1(A) & v7_rltopsp1(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(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_k10_rvsum_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v3_valued_0(A) & v1_finseq_1(A)) ) )  & v1_xreal_0(B))  => k10_rvsum_1(A, B)=k24_valued_1(A, B)) ) ).
fof(redefinition_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_pscomp_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  & l1_pre_topc(A))  &  ( (v1_funct_1(B) &  (v1_funct_2(B, u1_struct_0(A), k1_numbers) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), k1_numbers)))) )  & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) )  => k3_pscomp_1(A, B, C)=k5_relat_1(B, C)) ) ).
fof(redefinition_k3_rlvect_1, axiom,  (! [A, B, C] :  ( ( (v2_rlvect_1(A) & l1_algstr_0(A))  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k3_rlvect_1(A, B, C)=k1_algstr_0(A, B, C)) ) ).
fof(redefinition_k4_rvsum_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v3_valued_0(A) & v1_finseq_1(A)) ) )  &  (v1_relat_1(B) &  (v1_funct_1(B) &  (v3_valued_0(B) & v1_finseq_1(B)) ) ) )  => k4_rvsum_1(A, B)=k1_valued_1(A, B)) ) ).
fof(redefinition_k4_subset_1, axiom,  (! [A, B, C] :  ( (m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))  => k4_subset_1(A, B, C)=k2_xboole_0(B, C)) ) ).
fof(redefinition_k5_numbers, axiom, k5_numbers=k5_ordinal1).
fof(redefinition_k6_domain_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(B, A))  => k6_domain_1(A, B)=k1_tarski(B)) ) ).
fof(redefinition_k7_domain_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  (m1_subset_1(B, A) & m1_subset_1(C, A)) )  => k7_domain_1(A, B, C)=k2_tarski(B, C)) ) ).
fof(redefinition_k7_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => k7_relset_1(A, B, C, D)=k7_relat_1(C, D)) ) ).
fof(redefinition_k7_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(B, k1_zfmisc_1(A)) => k7_subset_1(A, B, C)=k4_xboole_0(B, C)) ) ).
fof(redefinition_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_r1_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  (r1_subset_1(A, B) <=> r1_xboole_0(A, B)) ) ) ).
fof(redefinition_r2_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  (r2_subset_1(A, B) <=> r1_xboole_0(A, B)) ) ) ).
fof(redefinition_r2_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__r0_r0, axiom, r1_xxreal_0(0, 0)).
fof(rqLessOrEqual__r1_xxreal_0__r0_r1, axiom, r1_xxreal_0(0, 1)).
fof(rqLessOrEqual__r1_xxreal_0__r0_r2, axiom, r1_xxreal_0(0, 2)).
fof(rqLessOrEqual__r1_xxreal_0__r0_rm1, axiom,  ~ (r1_xxreal_0(0, k4_xcmplx_0(1))) ).
fof(rqLessOrEqual__r1_xxreal_0__r0_rm2, axiom,  ~ (r1_xxreal_0(0, k4_xcmplx_0(2))) ).
fof(rqLessOrEqual__r1_xxreal_0__r0_rn1d2, axiom, r1_xxreal_0(0, k7_xcmplx_0(1, 2))).
fof(rqLessOrEqual__r1_xxreal_0__r0_rnm1d2, axiom,  ~ (r1_xxreal_0(0, k7_xcmplx_0(k4_xcmplx_0(1), 2))) ).
fof(rqLessOrEqual__r1_xxreal_0__r1_r0, axiom,  ~ (r1_xxreal_0(1, 0)) ).
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__r1_rm1, axiom,  ~ (r1_xxreal_0(1, k4_xcmplx_0(1))) ).
fof(rqLessOrEqual__r1_xxreal_0__r1_rm2, axiom,  ~ (r1_xxreal_0(1, k4_xcmplx_0(2))) ).
fof(rqLessOrEqual__r1_xxreal_0__r1_rn1d2, axiom,  ~ (r1_xxreal_0(1, k7_xcmplx_0(1, 2))) ).
fof(rqLessOrEqual__r1_xxreal_0__r1_rnm1d2, axiom,  ~ (r1_xxreal_0(1, k7_xcmplx_0(k4_xcmplx_0(1), 2))) ).
fof(rqLessOrEqual__r1_xxreal_0__r2_r0, axiom,  ~ (r1_xxreal_0(2, 0)) ).
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(rqLessOrEqual__r1_xxreal_0__r2_rm1, axiom,  ~ (r1_xxreal_0(2, k4_xcmplx_0(1))) ).
fof(rqLessOrEqual__r1_xxreal_0__r2_rm2, axiom,  ~ (r1_xxreal_0(2, k4_xcmplx_0(2))) ).
fof(rqLessOrEqual__r1_xxreal_0__r2_rn1d2, axiom,  ~ (r1_xxreal_0(2, k7_xcmplx_0(1, 2))) ).
fof(rqLessOrEqual__r1_xxreal_0__r2_rnm1d2, axiom,  ~ (r1_xxreal_0(2, k7_xcmplx_0(k4_xcmplx_0(1), 2))) ).
fof(rqLessOrEqual__r1_xxreal_0__rm1_r0, axiom, r1_xxreal_0(k4_xcmplx_0(1), 0)).
fof(rqLessOrEqual__r1_xxreal_0__rm1_r1, axiom, r1_xxreal_0(k4_xcmplx_0(1), 1)).
fof(rqLessOrEqual__r1_xxreal_0__rm1_r2, axiom, r1_xxreal_0(k4_xcmplx_0(1), 2)).
fof(rqLessOrEqual__r1_xxreal_0__rm1_rm1, axiom, r1_xxreal_0(k4_xcmplx_0(1), k4_xcmplx_0(1))).
fof(rqLessOrEqual__r1_xxreal_0__rm1_rm2, axiom,  ~ (r1_xxreal_0(k4_xcmplx_0(1), k4_xcmplx_0(2))) ).
fof(rqLessOrEqual__r1_xxreal_0__rm1_rn1d2, axiom, r1_xxreal_0(k4_xcmplx_0(1), k7_xcmplx_0(1, 2))).
fof(rqLessOrEqual__r1_xxreal_0__rm1_rnm1d2, axiom, r1_xxreal_0(k4_xcmplx_0(1), k7_xcmplx_0(k4_xcmplx_0(1), 2))).
fof(rqLessOrEqual__r1_xxreal_0__rm2_r0, axiom, r1_xxreal_0(k4_xcmplx_0(2), 0)).
fof(rqLessOrEqual__r1_xxreal_0__rm2_r1, axiom, r1_xxreal_0(k4_xcmplx_0(2), 1)).
fof(rqLessOrEqual__r1_xxreal_0__rm2_r2, axiom, r1_xxreal_0(k4_xcmplx_0(2), 2)).
fof(rqLessOrEqual__r1_xxreal_0__rm2_rm1, axiom, r1_xxreal_0(k4_xcmplx_0(2), k4_xcmplx_0(1))).
fof(rqLessOrEqual__r1_xxreal_0__rm2_rm2, axiom, r1_xxreal_0(k4_xcmplx_0(2), k4_xcmplx_0(2))).
fof(rqLessOrEqual__r1_xxreal_0__rm2_rn1d2, axiom, r1_xxreal_0(k4_xcmplx_0(2), k7_xcmplx_0(1, 2))).
fof(rqLessOrEqual__r1_xxreal_0__rn1d2_r0, axiom,  ~ (r1_xxreal_0(k7_xcmplx_0(1, 2), 0)) ).
fof(rqLessOrEqual__r1_xxreal_0__rn1d2_r1, axiom, r1_xxreal_0(k7_xcmplx_0(1, 2), 1)).
fof(rqLessOrEqual__r1_xxreal_0__rn1d2_r2, axiom, r1_xxreal_0(k7_xcmplx_0(1, 2), 2)).
fof(rqLessOrEqual__r1_xxreal_0__rn1d2_rm1, axiom,  ~ (r1_xxreal_0(k7_xcmplx_0(1, 2), k4_xcmplx_0(1))) ).
fof(rqLessOrEqual__r1_xxreal_0__rn1d2_rm2, axiom,  ~ (r1_xxreal_0(k7_xcmplx_0(1, 2), k4_xcmplx_0(2))) ).
fof(rqLessOrEqual__r1_xxreal_0__rn1d2_rn1d2, axiom, r1_xxreal_0(k7_xcmplx_0(1, 2), k7_xcmplx_0(1, 2))).
fof(rqLessOrEqual__r1_xxreal_0__rn1d2_rnm1d2, axiom,  ~ (r1_xxreal_0(k7_xcmplx_0(1, 2), k7_xcmplx_0(k4_xcmplx_0(1), 2))) ).
fof(rqLessOrEqual__r1_xxreal_0__rnm1d2_r0, axiom, r1_xxreal_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), 0)).
fof(rqLessOrEqual__r1_xxreal_0__rnm1d2_r1, axiom, r1_xxreal_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), 1)).
fof(rqLessOrEqual__r1_xxreal_0__rnm1d2_r2, axiom, r1_xxreal_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), 2)).
fof(rqLessOrEqual__r1_xxreal_0__rnm1d2_rm1, axiom,  ~ (r1_xxreal_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), k4_xcmplx_0(1))) ).
fof(rqLessOrEqual__r1_xxreal_0__rnm1d2_rn1d2, axiom, r1_xxreal_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), k7_xcmplx_0(1, 2))).
fof(rqLessOrEqual__r1_xxreal_0__rnm1d2_rnm1d2, axiom, r1_xxreal_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), k7_xcmplx_0(k4_xcmplx_0(1), 2))).
fof(rqRealAdd__k2_xcmplx_0__r0_r0_r0, axiom, k2_xcmplx_0(0, 0)=0).
fof(rqRealAdd__k2_xcmplx_0__r0_r1_r1, axiom, k2_xcmplx_0(0, 1)=1).
fof(rqRealAdd__k2_xcmplx_0__r0_r2_r2, axiom, k2_xcmplx_0(0, 2)=2).
fof(rqRealAdd__k2_xcmplx_0__r0_rm1_rm1, axiom, k2_xcmplx_0(0, k4_xcmplx_0(1))=k4_xcmplx_0(1)).
fof(rqRealAdd__k2_xcmplx_0__r0_rm2_rm2, axiom, k2_xcmplx_0(0, k4_xcmplx_0(2))=k4_xcmplx_0(2)).
fof(rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2, axiom, k2_xcmplx_0(0, k7_xcmplx_0(1, 2))=k7_xcmplx_0(1, 2)).
fof(rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2, axiom, k2_xcmplx_0(0, k7_xcmplx_0(k4_xcmplx_0(1), 2))=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealAdd__k2_xcmplx_0__r1_r0_r1, axiom, k2_xcmplx_0(1, 0)=1).
fof(rqRealAdd__k2_xcmplx_0__r1_r1_r2, axiom, k2_xcmplx_0(1, 1)=2).
fof(rqRealAdd__k2_xcmplx_0__r1_rm1_r0, axiom, k2_xcmplx_0(1, k4_xcmplx_0(1))=0).
fof(rqRealAdd__k2_xcmplx_0__r1_rm2_rm1, axiom, k2_xcmplx_0(1, k4_xcmplx_0(2))=k4_xcmplx_0(1)).
fof(rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2, axiom, k2_xcmplx_0(1, k7_xcmplx_0(k4_xcmplx_0(1), 2))=k7_xcmplx_0(1, 2)).
fof(rqRealAdd__k2_xcmplx_0__r2_r0_r2, axiom, k2_xcmplx_0(2, 0)=2).
fof(rqRealAdd__k2_xcmplx_0__r2_rm1_r1, axiom, k2_xcmplx_0(2, k4_xcmplx_0(1))=1).
fof(rqRealAdd__k2_xcmplx_0__r2_rm2_r0, axiom, k2_xcmplx_0(2, k4_xcmplx_0(2))=0).
fof(rqRealAdd__k2_xcmplx_0__rm1_r0_rm1, axiom, k2_xcmplx_0(k4_xcmplx_0(1), 0)=k4_xcmplx_0(1)).
fof(rqRealAdd__k2_xcmplx_0__rm1_r1_r0, axiom, k2_xcmplx_0(k4_xcmplx_0(1), 1)=0).
fof(rqRealAdd__k2_xcmplx_0__rm1_r2_r1, axiom, k2_xcmplx_0(k4_xcmplx_0(1), 2)=1).
fof(rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2, axiom, k2_xcmplx_0(k4_xcmplx_0(1), k4_xcmplx_0(1))=k4_xcmplx_0(2)).
fof(rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2, axiom, k2_xcmplx_0(k4_xcmplx_0(1), k7_xcmplx_0(1, 2))=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealAdd__k2_xcmplx_0__rm2_r0_rm2, axiom, k2_xcmplx_0(k4_xcmplx_0(2), 0)=k4_xcmplx_0(2)).
fof(rqRealAdd__k2_xcmplx_0__rm2_r1_rm1, axiom, k2_xcmplx_0(k4_xcmplx_0(2), 1)=k4_xcmplx_0(1)).
fof(rqRealAdd__k2_xcmplx_0__rm2_r2_r0, axiom, k2_xcmplx_0(k4_xcmplx_0(2), 2)=0).
fof(rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2, axiom, k2_xcmplx_0(k7_xcmplx_0(1, 2), 0)=k7_xcmplx_0(1, 2)).
fof(rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2, axiom, k2_xcmplx_0(k7_xcmplx_0(1, 2), k4_xcmplx_0(1))=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1, axiom, k2_xcmplx_0(k7_xcmplx_0(1, 2), k7_xcmplx_0(1, 2))=1).
fof(rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0, axiom, k2_xcmplx_0(k7_xcmplx_0(1, 2), k7_xcmplx_0(k4_xcmplx_0(1), 2))=0).
fof(rqRealAdd__k2_xcmplx_0__rnm1d2_r0_rnm1d2, axiom, k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), 0)=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2, axiom, k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), 1)=k7_xcmplx_0(1, 2)).
fof(rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0, axiom, k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), k7_xcmplx_0(1, 2))=0).
fof(rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1, axiom, k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), k7_xcmplx_0(k4_xcmplx_0(1), 2))=k4_xcmplx_0(1)).
fof(rqRealDiff__k6_xcmplx_0__r0_r0_r0, axiom, k6_xcmplx_0(0, 0)=0).
fof(rqRealDiff__k6_xcmplx_0__r0_r1_rm1, axiom, k6_xcmplx_0(0, 1)=k4_xcmplx_0(1)).
fof(rqRealDiff__k6_xcmplx_0__r0_r2_rm2, axiom, k6_xcmplx_0(0, 2)=k4_xcmplx_0(2)).
fof(rqRealDiff__k6_xcmplx_0__r0_rm1_r1, axiom, k6_xcmplx_0(0, k4_xcmplx_0(1))=1).
fof(rqRealDiff__k6_xcmplx_0__r0_rm2_r2, axiom, k6_xcmplx_0(0, k4_xcmplx_0(2))=2).
fof(rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2, axiom, k6_xcmplx_0(0, k7_xcmplx_0(1, 2))=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2, axiom, k6_xcmplx_0(0, k7_xcmplx_0(k4_xcmplx_0(1), 2))=k7_xcmplx_0(1, 2)).
fof(rqRealDiff__k6_xcmplx_0__r1_r0_r1, axiom, k6_xcmplx_0(1, 0)=1).
fof(rqRealDiff__k6_xcmplx_0__r1_r1_r0, axiom, k6_xcmplx_0(1, 1)=0).
fof(rqRealDiff__k6_xcmplx_0__r1_r2_rm1, axiom, k6_xcmplx_0(1, 2)=k4_xcmplx_0(1)).
fof(rqRealDiff__k6_xcmplx_0__r1_rm1_r2, axiom, k6_xcmplx_0(1, k4_xcmplx_0(1))=2).
fof(rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2, axiom, k6_xcmplx_0(1, k7_xcmplx_0(1, 2))=k7_xcmplx_0(1, 2)).
fof(rqRealDiff__k6_xcmplx_0__r2_r0_r2, axiom, k6_xcmplx_0(2, 0)=2).
fof(rqRealDiff__k6_xcmplx_0__r2_r1_r1, axiom, k6_xcmplx_0(2, 1)=1).
fof(rqRealDiff__k6_xcmplx_0__r2_r2_r0, axiom, k6_xcmplx_0(2, 2)=0).
fof(rqRealDiff__k6_xcmplx_0__rm1_r0_rm1, axiom, k6_xcmplx_0(k4_xcmplx_0(1), 0)=k4_xcmplx_0(1)).
fof(rqRealDiff__k6_xcmplx_0__rm1_r1_rm2, axiom, k6_xcmplx_0(k4_xcmplx_0(1), 1)=k4_xcmplx_0(2)).
fof(rqRealDiff__k6_xcmplx_0__rm1_rm1_r0, axiom, k6_xcmplx_0(k4_xcmplx_0(1), k4_xcmplx_0(1))=0).
fof(rqRealDiff__k6_xcmplx_0__rm1_rm2_r1, axiom, k6_xcmplx_0(k4_xcmplx_0(1), k4_xcmplx_0(2))=1).
fof(rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2, axiom, k6_xcmplx_0(k4_xcmplx_0(1), k7_xcmplx_0(k4_xcmplx_0(1), 2))=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealDiff__k6_xcmplx_0__rm2_r0_rm2, axiom, k6_xcmplx_0(k4_xcmplx_0(2), 0)=k4_xcmplx_0(2)).
fof(rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1, axiom, k6_xcmplx_0(k4_xcmplx_0(2), k4_xcmplx_0(1))=k4_xcmplx_0(1)).
fof(rqRealDiff__k6_xcmplx_0__rm2_rm2_r0, axiom, k6_xcmplx_0(k4_xcmplx_0(2), k4_xcmplx_0(2))=0).
fof(rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2, axiom, k6_xcmplx_0(k7_xcmplx_0(1, 2), 0)=k7_xcmplx_0(1, 2)).
fof(rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2, axiom, k6_xcmplx_0(k7_xcmplx_0(1, 2), 1)=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0, axiom, k6_xcmplx_0(k7_xcmplx_0(1, 2), k7_xcmplx_0(1, 2))=0).
fof(rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1, axiom, k6_xcmplx_0(k7_xcmplx_0(1, 2), k7_xcmplx_0(k4_xcmplx_0(1), 2))=1).
fof(rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2, axiom, k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), 0)=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2, axiom, k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), k4_xcmplx_0(1))=k7_xcmplx_0(1, 2)).
fof(rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1, axiom, k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), k7_xcmplx_0(1, 2))=k4_xcmplx_0(1)).
fof(rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0, axiom, k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), k7_xcmplx_0(k4_xcmplx_0(1), 2))=0).
fof(rqRealDiv__k7_xcmplx_0__r1_r1_r1, axiom, k7_xcmplx_0(1, 1)=1).
fof(rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2, axiom, k7_xcmplx_0(1, 2)=k7_xcmplx_0(1, 2)).
fof(rqRealDiv__k7_xcmplx_0__r1_rm1_rm1, axiom, k7_xcmplx_0(1, k4_xcmplx_0(1))=k4_xcmplx_0(1)).
fof(rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2, axiom, k7_xcmplx_0(1, k4_xcmplx_0(2))=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2, axiom, k7_xcmplx_0(1, k7_xcmplx_0(1, 2))=2).
fof(rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2, axiom, k7_xcmplx_0(1, k7_xcmplx_0(k4_xcmplx_0(1), 2))=k4_xcmplx_0(2)).
fof(rqRealDiv__k7_xcmplx_0__r2_r1_r2, axiom, k7_xcmplx_0(2, 1)=2).
fof(rqRealDiv__k7_xcmplx_0__r2_r2_r1, axiom, k7_xcmplx_0(2, 2)=1).
fof(rqRealDiv__k7_xcmplx_0__rm1_r1_rm1, axiom, k7_xcmplx_0(k4_xcmplx_0(1), 1)=k4_xcmplx_0(1)).
fof(rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2, axiom, k7_xcmplx_0(k4_xcmplx_0(1), 2)=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealDiv__k7_xcmplx_0__rm2_r2_rm1, axiom, k7_xcmplx_0(k4_xcmplx_0(2), 2)=k4_xcmplx_0(1)).
fof(rqRealMult__k3_xcmplx_0__r0_r0_r0, axiom, k3_xcmplx_0(0, 0)=0).
fof(rqRealMult__k3_xcmplx_0__r0_r1_r0, axiom, k3_xcmplx_0(0, 1)=0).
fof(rqRealMult__k3_xcmplx_0__r0_r2_r0, axiom, k3_xcmplx_0(0, 2)=0).
fof(rqRealMult__k3_xcmplx_0__r0_rm2_r0, axiom, k3_xcmplx_0(0, k4_xcmplx_0(2))=0).
fof(rqRealMult__k3_xcmplx_0__r0_rn1d2_r0, axiom, k3_xcmplx_0(0, k7_xcmplx_0(1, 2))=0).
fof(rqRealMult__k3_xcmplx_0__r1_r0_r0, axiom, k3_xcmplx_0(1, 0)=0).
fof(rqRealMult__k3_xcmplx_0__r1_r1_r1, axiom, k3_xcmplx_0(1, 1)=1).
fof(rqRealMult__k3_xcmplx_0__r1_r2_r2, axiom, k3_xcmplx_0(1, 2)=2).
fof(rqRealMult__k3_xcmplx_0__r1_rm2_rm2, axiom, k3_xcmplx_0(1, k4_xcmplx_0(2))=k4_xcmplx_0(2)).
fof(rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2, axiom, k3_xcmplx_0(1, k7_xcmplx_0(1, 2))=k7_xcmplx_0(1, 2)).
fof(rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2, axiom, k3_xcmplx_0(1, k7_xcmplx_0(k4_xcmplx_0(1), 2))=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealMult__k3_xcmplx_0__r2_r0_r0, axiom, k3_xcmplx_0(2, 0)=0).
fof(rqRealMult__k3_xcmplx_0__r2_r1_r2, axiom, k3_xcmplx_0(2, 1)=2).
fof(rqRealMult__k3_xcmplx_0__r2_rn1d2_r1, axiom, k3_xcmplx_0(2, k7_xcmplx_0(1, 2))=1).
fof(rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1, axiom, k3_xcmplx_0(2, k7_xcmplx_0(k4_xcmplx_0(1), 2))=k4_xcmplx_0(1)).
fof(rqRealMult__k3_xcmplx_0__rm2_r0_r0, axiom, k3_xcmplx_0(k4_xcmplx_0(2), 0)=0).
fof(rqRealMult__k3_xcmplx_0__rm2_r1_rm2, axiom, k3_xcmplx_0(k4_xcmplx_0(2), 1)=k4_xcmplx_0(2)).
fof(rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1, axiom, k3_xcmplx_0(k4_xcmplx_0(2), k7_xcmplx_0(1, 2))=k4_xcmplx_0(1)).
fof(rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1, axiom, k3_xcmplx_0(k4_xcmplx_0(2), k7_xcmplx_0(k4_xcmplx_0(1), 2))=1).
fof(rqRealMult__k3_xcmplx_0__rn1d2_r0_r0, axiom, k3_xcmplx_0(k7_xcmplx_0(1, 2), 0)=0).
fof(rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2, axiom, k3_xcmplx_0(k7_xcmplx_0(1, 2), 1)=k7_xcmplx_0(1, 2)).
fof(rqRealMult__k3_xcmplx_0__rn1d2_r2_r1, axiom, k3_xcmplx_0(k7_xcmplx_0(1, 2), 2)=1).
fof(rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1, axiom, k3_xcmplx_0(k7_xcmplx_0(1, 2), k4_xcmplx_0(2))=k4_xcmplx_0(1)).
fof(rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2, axiom, k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), 1)=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1, axiom, k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), 2)=k4_xcmplx_0(1)).
fof(rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1, axiom, k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), k4_xcmplx_0(2))=1).
fof(rqRealNeg__k4_xcmplx_0__r0_r0, axiom, k4_xcmplx_0(0)=0).
fof(rqRealNeg__k4_xcmplx_0__r1_rm1, axiom, k4_xcmplx_0(1)=k4_xcmplx_0(1)).
fof(rqRealNeg__k4_xcmplx_0__r2_rm2, axiom, k4_xcmplx_0(2)=k4_xcmplx_0(2)).
fof(rqRealNeg__k4_xcmplx_0__rm1_r1, axiom, k4_xcmplx_0(k4_xcmplx_0(1))=1).
fof(rqRealNeg__k4_xcmplx_0__rm2_r2, axiom, k4_xcmplx_0(k4_xcmplx_0(2))=2).
fof(rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2, axiom, k4_xcmplx_0(k7_xcmplx_0(1, 2))=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2, axiom, k4_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2))=k7_xcmplx_0(1, 2)).
fof(spc0_boole, axiom, v1_xboole_0(0)).
fof(spc0_numerals, axiom, m1_subset_1(0, k4_ordinal1)).
fof(spc1_arithm, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k2_xcmplx_0(A, k4_xcmplx_0(B))=k6_xcmplx_0(A, B)) ) ).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(spc1_numerals, axiom,  (v2_xxreal_0(1) & m1_subset_1(1, k4_ordinal1)) ).
fof(spc2_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k3_xcmplx_0(A, k4_xcmplx_0(1))=k4_xcmplx_0(A)) ) ).
fof(spc2_boole, axiom,  ~ (v1_xboole_0(2)) ).
fof(spc2_numerals, axiom,  (v2_xxreal_0(2) & m1_subset_1(2, k4_ordinal1)) ).
fof(spc4_arithm, axiom,  (! [A, B, C] :  ( (v1_xcmplx_0(A) &  (v1_xcmplx_0(B) & v1_xcmplx_0(C)) )  => k3_xcmplx_0(A, k7_xcmplx_0(B, C))=k7_xcmplx_0(k3_xcmplx_0(A, B), C)) ) ).
fof(spc5_arithm, axiom,  (! [A, B, C] :  ( (v1_xcmplx_0(A) &  (v1_xcmplx_0(B) & v1_xcmplx_0(C)) )  => k3_xcmplx_0(k2_xcmplx_0(A, B), C)=k2_xcmplx_0(k3_xcmplx_0(A, C), k3_xcmplx_0(B, C))) ) ).
fof(spc6_arithm, axiom,  (! [A, B, C] :  ( (v1_xcmplx_0(A) &  (v1_xcmplx_0(B) & v1_xcmplx_0(C)) )  => k2_xcmplx_0(k2_xcmplx_0(A, B), C)=k2_xcmplx_0(A, k2_xcmplx_0(B, C))) ) ).
fof(spc7_arithm, axiom,  (! [A, B, C] :  ( (v1_xcmplx_0(A) &  (v1_xcmplx_0(B) & v1_xcmplx_0(C)) )  => k3_xcmplx_0(k3_xcmplx_0(A, B), C)=k3_xcmplx_0(A, k3_xcmplx_0(B, C))) ) ).
fof(spc8_arithm, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k2_xcmplx_0(k4_xcmplx_0(A), k4_xcmplx_0(B))=k4_xcmplx_0(k2_xcmplx_0(A, B))) ) ).
fof(spc9_arithm, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k6_xcmplx_0(k4_xcmplx_0(A), k4_xcmplx_0(B))=k6_xcmplx_0(B, A)) ) ).
fof(symmetry_r1_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  (r1_subset_1(A, B) => r1_subset_1(B, A)) ) ) ).
fof(symmetry_r1_xboole_0, axiom,  (! [A, B] :  (r1_xboole_0(A, B) => r1_xboole_0(B, A)) ) ).
fof(symmetry_r2_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  (r2_subset_1(A, B) => r2_subset_1(B, A)) ) ) ).
fof(t10_topreal1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(k15_euclid(A))) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(k15_euclid(A))) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(k15_euclid(A))) =>  ( (r1_topreal1(k15_euclid(A), C, D, B) & k9_subset_1(u1_struct_0(k15_euclid(A)), B, k1_rltopsp1(k15_euclid(A), D, E))=k1_tarski(D))  => r1_topreal1(k15_euclid(A), C, E, k4_subset_1(u1_struct_0(k15_euclid(A)), B, k1_rltopsp1(k15_euclid(A), D, E)))) ) ) ) ) ) ) ) ) ) ) ).
fof(t11_jordan21, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(k15_euclid(2))) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(k15_euclid(2))) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(k15_euclid(2))) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(k15_euclid(2))) =>  (r1_topreal1(k15_euclid(2), B, C, A) =>  (B=D |  (C=E |  ( ~ (r2_tarski(B, k5_jordan6(A, B, C, D, E)))  &  ~ (r2_tarski(C, k5_jordan6(A, B, C, D, E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t11_topreal1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(k15_euclid(A))) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(k15_euclid(A))) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(k15_euclid(A))) =>  ( (r1_topreal1(k15_euclid(A), D, C, B) & k9_subset_1(u1_struct_0(k15_euclid(A)), k1_rltopsp1(k15_euclid(A), E, D), B)=k1_tarski(D))  => r1_topreal1(k15_euclid(A), E, C, k4_subset_1(u1_struct_0(k15_euclid(A)), k1_rltopsp1(k15_euclid(A), E, D), B))) ) ) ) ) ) ) ) ) ) ) ).
fof(t14_jordan5b, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(k15_euclid(A))) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(k15_euclid(A))) =>  (r1_topreal1(k15_euclid(A), C, D, B) => r1_topreal1(k15_euclid(A), D, C, B)) ) ) ) ) ) ) ) ) ).
fof(t16_sppol_1, axiom,  (! [A] :  (m1_subset_1(A, u1_struct_0(k15_euclid(2))) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(k15_euclid(2))) =>  (k17_euclid(A)=k17_euclid(B) <=> v2_sppol_1(k1_rltopsp1(k15_euclid(2), A, B))) ) ) ) ) ).
fof(t1_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k2_xcmplx_0(A, k5_numbers)=A) ) ).
fof(t1_boole, axiom,  (! [A] : k2_xboole_0(A, k1_xboole_0)=A) ).
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(t21_jordan16, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(k15_euclid(2))) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(k15_euclid(2))) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(k15_euclid(2))) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(k15_euclid(2))) =>  ( (r1_topreal1(k15_euclid(2), B, C, A) & r1_jordan5c(A, B, C, D, E))  =>  (D=E | r1_topreal1(k15_euclid(2), D, E, k5_jordan6(A, B, C, D, E))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t226_xreal_1, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ( ~ (r1_xxreal_0(B, A))  =>  ( ~ (r1_xxreal_0(k7_xcmplx_0(k2_xcmplx_0(A, B), 2), A))  &  ~ (r1_xxreal_0(B, k7_xcmplx_0(k2_xcmplx_0(A, B), 2))) ) ) ) ) ) ) ).
fof(t23_xboole_1, axiom,  (! [A] :  (! [B] :  (! [C] : k3_xboole_0(A, k2_xboole_0(B, C))=k2_xboole_0(k3_xboole_0(A, B), k3_xboole_0(A, C))) ) ) ).
fof(t24_jordan21, axiom,  (! [A] :  ( (v2_compts_1(A, k15_euclid(2)) &  ( ~ (v2_sppol_1(A))  & m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2))))) )  =>  ~ (k1_jordan21(A)=k18_pscomp_1(A)) ) ) ).
fof(t24_pscomp_1, axiom,  (! [A] :  (m1_subset_1(A, u1_struct_0(k15_euclid(2))) =>  (! [B] :  ( ( ~ (v1_xboole_0(B))  &  (v2_compts_1(B, k15_euclid(2)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k15_euclid(2))))) )  =>  (r2_tarski(A, B) =>  (r1_xxreal_0(k6_pscomp_1(B), k17_euclid(A)) &  (r1_xxreal_0(k17_euclid(A), k8_pscomp_1(B)) &  (r1_xxreal_0(k9_pscomp_1(B), k18_euclid(A)) & r1_xxreal_0(k18_euclid(A), k7_pscomp_1(B))) ) ) ) ) ) ) ) ).
fof(t25_jordan21, axiom,  (! [A] :  ( (v2_compts_1(A, k15_euclid(2)) &  ( ~ (v2_sppol_1(A))  & m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2))))) )  =>  ~ (k1_jordan21(A)=k22_pscomp_1(A)) ) ) ).
fof(t26_jordan21, axiom,  (! [A] :  ( (v2_compts_1(A, k15_euclid(2)) &  ( ~ (v2_sppol_1(A))  & m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2))))) )  =>  ~ (k2_jordan21(A)=k18_pscomp_1(A)) ) ) ).
fof(t26_xboole_1, axiom,  (! [A] :  (! [B] :  (! [C] :  (r1_tarski(A, B) => r1_tarski(k3_xboole_0(A, C), k3_xboole_0(B, C))) ) ) ) ).
fof(t27_jordan21, axiom,  (! [A] :  ( (v2_compts_1(A, k15_euclid(2)) &  ( ~ (v2_sppol_1(A))  & m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2))))) )  =>  ~ (k2_jordan21(A)=k22_pscomp_1(A)) ) ) ).
fof(t2_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k3_xcmplx_0(A, k5_numbers)=k5_numbers) ) ).
fof(t2_boole, axiom,  (! [A] : k3_xboole_0(A, k1_xboole_0)=k1_xboole_0) ).
fof(t2_jordan16, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(k15_euclid(2))) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(k15_euclid(2))) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(k15_euclid(2))) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(k15_euclid(2))) => r1_tarski(k5_jordan6(A, B, C, D, E), A)) ) ) ) ) ) ) ) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t2_tarski, axiom,  (! [A] :  (! [B] :  ( (! [C] :  (r2_hidden(C, A) <=> r2_hidden(C, B)) )  => A=B) ) ) ).
fof(t2_xxreal_0, axiom,  (! [A] :  (v1_xxreal_0(A) =>  (! [B] :  (v1_xxreal_0(B) =>  (! [C] :  (v1_xxreal_0(C) =>  ( (r1_xxreal_0(A, B) & r1_xxreal_0(B, C))  => r1_xxreal_0(A, C)) ) ) ) ) ) ) ).
fof(t30_jordan21, axiom,  (! [A] :  ( (v2_compts_1(A, k15_euclid(2)) &  (v1_jordan21(A) & m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2))))) )  => r2_tarski(k1_jordan21(A), A)) ) ).
fof(t31_jordan21, axiom,  (! [A] :  ( (v2_compts_1(A, k15_euclid(2)) &  (v1_jordan21(A) & m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2))))) )  => r2_tarski(k2_jordan21(A), A)) ) ).
fof(t31_sprect_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  (v2_compts_1(A, k15_euclid(2)) &  ( ~ (v2_sppol_1(A))  & m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2))))) ) )  =>  ~ (r1_xxreal_0(k8_pscomp_1(A), k6_pscomp_1(A))) ) ) ).
fof(t34_jordan21, axiom,  (! [A] :  ( (v2_compts_1(A, k15_euclid(2)) &  (v1_jordan21(A) & m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2))))) )  => k9_subset_1(u1_struct_0(k15_euclid(2)), k1_rltopsp1(k15_euclid(2), k1_jordan21(A), k19_euclid(k7_xcmplx_0(k2_xcmplx_0(k6_pscomp_1(A), k8_pscomp_1(A)), 2), k7_pscomp_1(A))), A)=k6_domain_1(u1_struct_0(k15_euclid(2)), k1_jordan21(A))) ) ).
fof(t35_jordan21, axiom,  (! [A] :  ( (v2_compts_1(A, k15_euclid(2)) &  (v1_jordan21(A) & m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2))))) )  => k9_subset_1(u1_struct_0(k15_euclid(2)), k1_rltopsp1(k15_euclid(2), k2_jordan21(A), k19_euclid(k7_xcmplx_0(k2_xcmplx_0(k6_pscomp_1(A), k8_pscomp_1(A)), 2), k9_pscomp_1(A))), A)=k6_domain_1(u1_struct_0(k15_euclid(2)), k2_jordan21(A))) ) ).
fof(t37_jordan21, axiom,  (! [A] :  ( (v1_topreal2(A) & m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))))  =>  ~ (k1_jordan21(A)=k2_jordan21(A)) ) ) ).
fof(t38_jordan21, axiom,  (! [A] :  ( (v1_topreal2(A) & m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))))  =>  ~ (r1_xxreal_0(k18_euclid(k1_jordan21(A)), k9_pscomp_1(A))) ) ) ).
fof(t39_jordan21, axiom,  (! [A] :  ( (v1_topreal2(A) & m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))))  => r1_xxreal_0(k18_euclid(k1_jordan21(A)), k7_pscomp_1(A))) ) ).
fof(t3_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k3_xcmplx_0(1, A)=A) ) ).
fof(t3_boole, axiom,  (! [A] : k4_xboole_0(A, k1_xboole_0)=A) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t3_xboole_0, axiom,  (! [A] :  (! [B] :  ( ~ ( ( ~ (r1_xboole_0(A, B))  &  (! [C] :  ~ ( (r2_hidden(C, A) & r2_hidden(C, B)) ) ) ) )  &  ~ ( ( (? [C] :  (r2_hidden(C, A) & r2_hidden(C, B)) )  & r1_xboole_0(A, B)) ) ) ) ) ).
fof(t40_jordan21, axiom,  (! [A] :  ( (v1_topreal2(A) & m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))))  => r1_xxreal_0(k9_pscomp_1(A), k18_euclid(k2_jordan21(A)))) ) ).
fof(t41_jordan21, axiom,  (! [A] :  ( (v1_topreal2(A) & m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))))  =>  ~ (r1_xxreal_0(k7_pscomp_1(A), k18_euclid(k2_jordan21(A)))) ) ) ).
fof(t42_jordan21, axiom,  (! [A] :  ( (v1_topreal2(A) & m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))))  => r1_subset_1(k1_rltopsp1(k15_euclid(2), k1_jordan21(A), k19_euclid(k7_xcmplx_0(k2_xcmplx_0(k6_pscomp_1(A), k8_pscomp_1(A)), 2), k7_pscomp_1(A))), k1_rltopsp1(k15_euclid(2), k2_jordan21(A), k19_euclid(k7_xcmplx_0(k2_xcmplx_0(k6_pscomp_1(A), k8_pscomp_1(A)), 2), k9_pscomp_1(A))))) ) ).
fof(t44_jgraph_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))))  =>  (! [B] :  ( ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))))  =>  (! [C] :  (m1_subset_1(C, u1_struct_0(k15_euclid(2))) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(k15_euclid(2))) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(k15_euclid(2))) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(k15_euclid(2))) =>  ~ ( (r1_topreal1(k15_euclid(2), C, D, A) &  (r1_topreal1(k15_euclid(2), E, F, B) &  ( (! [G] :  (m1_subset_1(G, u1_struct_0(k15_euclid(2))) =>  (r2_tarski(G, A) =>  (r1_xxreal_0(k17_euclid(C), k17_euclid(G)) & r1_xxreal_0(k17_euclid(G), k17_euclid(D))) ) ) )  &  ( (! [G] :  (m1_subset_1(G, u1_struct_0(k15_euclid(2))) =>  (r2_tarski(G, B) =>  (r1_xxreal_0(k17_euclid(C), k17_euclid(G)) & r1_xxreal_0(k17_euclid(G), k17_euclid(D))) ) ) )  &  ( (! [G] :  (m1_subset_1(G, u1_struct_0(k15_euclid(2))) =>  (r2_tarski(G, A) =>  (r1_xxreal_0(k18_euclid(E), k18_euclid(G)) & r1_xxreal_0(k18_euclid(G), k18_euclid(F))) ) ) )  &  ( (! [G] :  (m1_subset_1(G, u1_struct_0(k15_euclid(2))) =>  (r2_tarski(G, B) =>  (r1_xxreal_0(k18_euclid(E), k18_euclid(G)) & r1_xxreal_0(k18_euclid(G), k18_euclid(F))) ) ) )  & r2_subset_1(A, B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t4_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k6_xcmplx_0(A, k5_numbers)=A) ) ).
fof(t4_boole, axiom,  (! [A] : k4_xboole_0(k1_xboole_0, A)=k1_xboole_0) ).
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(t4_topreal1, axiom,  (! [A] :  (m1_subset_1(A, u1_struct_0(k15_euclid(2))) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(k15_euclid(2))) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(k15_euclid(2))) =>  ( (r1_xxreal_0(k18_euclid(B), k18_euclid(C)) & r2_tarski(A, k1_rltopsp1(k15_euclid(2), B, C)))  =>  (r1_xxreal_0(k18_euclid(B), k18_euclid(A)) & r1_xxreal_0(k18_euclid(A), k18_euclid(C))) ) ) ) ) ) ) ) ).
fof(t52_euclid, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  (k17_euclid(k19_euclid(A, B))=A & k18_euclid(k19_euclid(A, B))=B) ) ) ) ) ).
fof(t5_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k7_xcmplx_0(k5_numbers, A)=k5_numbers) ) ).
fof(t5_jordan16, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(k15_euclid(2))) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(k15_euclid(2))) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(k15_euclid(2))) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(k15_euclid(2))) =>  (r1_jordan5c(A, B, C, D, E) =>  (r2_tarski(D, k5_jordan6(A, B, C, D, E)) & r2_tarski(E, k5_jordan6(A, B, C, D, E))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t61_jordan6, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  (v1_topreal2(A) & m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2))))) )  =>  (r1_tarski(k9_jordan6(A), A) & r1_tarski(k8_jordan6(A), A)) ) ) ).
fof(t68_rltopsp1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_rlvect_1(A) &  (v6_rlvect_1(A) &  (v7_rlvect_1(A) &  (v8_rlvect_1(A) & l1_rlvect_1(A)) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => r2_tarski(B, k1_rltopsp1(A, B, C))) ) ) ) ) ) ).
fof(t6_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k7_xcmplx_0(A, 1)=A) ) ).
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(t7_jordan16, axiom,  (! [A] :  ( (v1_topreal2(A) & m1_subset_1(A, k1_zfmisc_1(u1_struct_0(k15_euclid(2)))))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(k15_euclid(2))) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(k15_euclid(2))) =>  ~ ( (r2_tarski(B, A) &  (r2_tarski(C, A) &  ( ~ (r1_jordan6(A, B, C))  &  ~ (r1_jordan6(A, C, B)) ) ) ) ) ) ) ) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
