% Mizar problem: t50_euclid12,euclid12,922,7 
fof(t50_euclid12, conjecture,  (! [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))) =>  (! [D] :  (m2_subset_1(D, k1_zfmisc_1(k1_euclid(2)), k1_euclidlp(2)) =>  (! [E] :  (m2_subset_1(E, k1_zfmisc_1(k1_euclid(2)), k1_euclidlp(2)) =>  ~ ( (r6_euclidlp(2, D, E) &  (r2_tarski(C, k9_subset_1(k1_euclid(2), D, E)) &  (r2_tarski(A, D) &  (r2_tarski(B, E) &  ( ~ (A=C)  &  ( ~ (B=C)  &  ( ~ (k4_euclid_3(A, C, B)=k7_xcmplx_0(k28_sin_cos, 2))  &  ~ (k4_euclid_3(A, C, B)=k7_xcmplx_0(k3_xcmplx_0(3, k28_sin_cos), 2)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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_ordinal1, axiom,  (! [A] :  (v6_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_ordinal1(B)) ) ) ) ).
fof(cc10_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_valued_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_valued_0(B)) ) ) ) ).
fof(cc11_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v7_ordinal1(A)) ) ).
fof(cc11_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v2_valued_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v2_valued_0(B)) ) ) ) ).
fof(cc12_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v1_zfmisc_1(A)) ) ).
fof(cc12_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v3_valued_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v3_valued_0(B)) ) ) ) ).
fof(cc13_ordinal1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  ~ (v8_ordinal1(A)) ) ) ).
fof(cc13_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v4_valued_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_valued_0(B)) ) ) ) ).
fof(cc14_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc14_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_valued_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v5_valued_0(B)) ) ) ) ).
fof(cc15_ordinal1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v9_ordinal1(A)) ) ) ).
fof(cc15_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v6_valued_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_valued_0(B)) ) ) ) ).
fof(cc16_ordinal1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) )  =>  (! [B] :  (m1_subset_1(B, A) =>  ~ (v8_ordinal1(B)) ) ) ) ) ).
fof(cc17_ordinal1, axiom,  (! [A] :  ( ~ (v10_ordinal1(A))  => v1_setfam_1(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_euclid, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, k1_euclid(A)) => v3_card_1(B, A)) ) ) ) ).
fof(cc1_int_1, axiom,  (! [A] :  (m1_subset_1(A, k4_numbers) => v1_int_1(A)) ) ).
fof(cc1_monoid_0, axiom,  (! [A] :  ( (v1_monoid_0(A) & l1_struct_0(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (v1_relat_1(B) & v1_funct_1(B)) ) ) ) ) ).
fof(cc1_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (v1_ordinal1(A) & v2_ordinal1(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_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_xboole_0(B)) ) ) ) ).
fof(cc1_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v6_valued_0(A))  =>  (v1_relat_1(A) & v5_valued_0(A)) ) ) ).
fof(cc1_xreal_0, axiom,  (! [A] :  (m1_subset_1(A, k1_numbers) => v1_xreal_0(A)) ) ).
fof(cc1_xxreal_0, axiom,  (! [A] :  (m1_subset_1(A, k6_numbers) => v1_xxreal_0(A)) ) ).
fof(cc20_ordinal1, axiom,  (! [A] :  ( ~ (v1_setfam_1(A))  => v10_ordinal1(A)) ) ).
fof(cc22_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v1_zfmisc_1(A) & v2_valued_0(A)) ) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) &  (v7_valued_0(A) & v8_valued_0(A)) ) ) ) ) ) ).
fof(cc23_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v7_valued_0(A)) ) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v9_valued_0(A)) ) ) ) ) ).
fof(cc24_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v8_valued_0(A)) ) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v10_valued_0(A)) ) ) ) ) ).
fof(cc28_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_1(A, k2_numbers))  =>  (v1_relat_1(A) & v1_valued_0(A)) ) ) ).
fof(cc29_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_valued_0(A))  =>  (v1_relat_1(A) & v5_relat_1(A, k2_numbers)) ) ) ).
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_int_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_int_1(A)) ) ).
fof(cc2_monoid_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_monoid_0(A) => v1_monoid_0(A)) ) ) ).
fof(cc2_ordinal1, axiom,  (! [A] :  ( (v1_ordinal1(A) & v2_ordinal1(A))  => v3_ordinal1(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_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ( ~ (v1_subset_1(B, A))  =>  ~ (v1_xboole_0(B)) ) ) ) ) ) ).
fof(cc2_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_valued_0(A))  =>  (v1_relat_1(A) & v4_valued_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(cc30_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_1(A, k6_numbers))  =>  (v1_relat_1(A) & v2_valued_0(A)) ) ) ).
fof(cc31_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v2_valued_0(A))  =>  (v1_relat_1(A) & v5_relat_1(A, k6_numbers)) ) ) ).
fof(cc32_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_1(A, k1_numbers))  =>  (v1_relat_1(A) & v3_valued_0(A)) ) ) ).
fof(cc33_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v3_valued_0(A))  =>  (v1_relat_1(A) & v5_relat_1(A, k1_numbers)) ) ) ).
fof(cc34_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_1(A, k3_numbers))  =>  (v1_relat_1(A) & v4_valued_0(A)) ) ) ).
fof(cc35_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v4_valued_0(A))  =>  (v1_relat_1(A) & v5_relat_1(A, k3_numbers)) ) ) ).
fof(cc36_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_1(A, k4_numbers))  =>  (v1_relat_1(A) & v5_valued_0(A)) ) ) ).
fof(cc37_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_valued_0(A))  =>  (v1_relat_1(A) & v5_relat_1(A, k4_numbers)) ) ) ).
fof(cc38_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_1(A, k4_ordinal1))  =>  (v1_relat_1(A) & v6_valued_0(A)) ) ) ).
fof(cc39_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v6_valued_0(A))  =>  (v1_relat_1(A) & v5_relat_1(A, k4_ordinal1)) ) ) ).
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_int_1, axiom,  (! [A] :  (v1_int_1(A) => v1_xreal_0(A)) ) ).
fof(cc3_monoid_0, axiom,  (! [A] :  ( (v2_monoid_0(A) & l1_struct_0(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => v1_finseq_1(B)) ) ) ) ).
fof(cc3_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_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  (v1_xboole_0(B) => v1_subset_1(B, A)) ) ) ) ) ).
fof(cc3_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_valued_0(A))  =>  (v1_relat_1(A) & v3_valued_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_euclid, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(k15_euclid(A))) => v3_card_1(B, A)) ) ) ) ).
fof(cc4_int_1, axiom,  (! [A] :  (v7_ordinal1(A) => v2_int_1(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_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ~ (v1_subset_1(B, A)) ) ) ) ) ).
fof(cc4_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v4_valued_0(A))  =>  (v1_relat_1(A) & v3_valued_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_int_1, axiom,  (! [A] :  (v2_int_1(A) => v1_int_1(A)) ) ).
fof(cc5_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, A) => v3_ordinal1(B)) ) ) ) ).
fof(cc5_subset_1, axiom,  (! [A] :  (v1_zfmisc_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_zfmisc_1(B)) ) ) ) ).
fof(cc5_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v3_valued_0(A))  =>  (v1_relat_1(A) & v2_valued_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_ordinal1, axiom,  (! [A] :  (v7_ordinal1(A) => v3_ordinal1(A)) ) ).
fof(cc6_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v3_valued_0(A))  =>  (v1_relat_1(A) & v1_valued_0(A)) ) ) ).
fof(cc6_xxreal_0, axiom,  (! [A] :  ( ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v2_xxreal_0(A)) ) )  =>  (v1_xxreal_0(A) & v3_xxreal_0(A)) ) ) ).
fof(cc7_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v7_ordinal1(A)) ) ).
fof(cc7_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v6_valued_0(A))  =>  (v1_relat_1(A) & v4_valued_0(A)) ) ) ).
fof(cc7_xxreal_0, axiom,  (! [A] :  ( (v8_ordinal1(A) & v1_xxreal_0(A))  =>  (v1_xxreal_0(A) &  ( ~ (v2_xxreal_0(A))  &  ~ (v3_xxreal_0(A)) ) ) ) ) ).
fof(cc8_ordinal1, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) => v7_ordinal1(A)) ) ).
fof(cc8_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v6_valued_0(A))  =>  (v1_relat_1(A) & v3_valued_0(A)) ) ) ).
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_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v6_ordinal1(A)) ) ).
fof(cc9_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_xboole_0(A))  =>  (v1_relat_1(A) & v6_valued_0(A)) ) ) ).
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_k22_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)) ) ) )  => k22_rvsum_1(A, B)=k22_rvsum_1(B, A)) ) ).
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_k5_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))) )  => k5_rltopsp1(A, B, C)=k5_rltopsp1(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(d1_euclid, axiom,  (! [A] :  (v7_ordinal1(A) => k1_euclid(A)=k4_finseq_2(A, k1_numbers)) ) ).
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(d6_valued_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_valued_0(A)) )  => k30_valued_1(A)=k24_valued_1(A, k4_xcmplx_0(1))) ) ).
fof(d8_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) =>  (! [B] :  (v1_xcmplx_0(B) => k7_xcmplx_0(A, B)=k3_xcmplx_0(A, k5_xcmplx_0(B))) ) ) ) ).
fof(d9_valued_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_valued_0(A)) )  =>  (! [B] :  ( (v1_relat_1(B) &  (v1_funct_1(B) & v1_valued_0(B)) )  => k45_valued_1(A, B)=k1_valued_1(A, k30_valued_1(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_k15_euclid, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v5_rltopsp1(k15_euclid(A)) & l1_rltopsp1(k15_euclid(A))) ) ) ).
fof(dt_k1_euclid, axiom,  (! [A] :  (v7_ordinal1(A) => m1_finseq_2(k1_euclid(A), k1_numbers)) ) ).
fof(dt_k1_euclidlp, axiom,  (! [A] :  (v7_ordinal1(A) => m1_subset_1(k1_euclidlp(A), k1_zfmisc_1(k1_zfmisc_1(k1_euclid(A))))) ) ).
fof(dt_k1_numbers, 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_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)) ) ) )  => v1_xreal_0(k22_rvsum_1(A, B))) ) ).
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_k28_sin_cos, axiom, v1_xreal_0(k28_sin_cos)).
fof(dt_k2_numbers, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k30_valued_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_valued_0(A)) )  =>  (v1_relat_1(k30_valued_1(A)) &  (v1_funct_1(k30_valued_1(A)) & v1_valued_0(k30_valued_1(A))) ) ) ) ).
fof(dt_k3_numbers, axiom, $true).
fof(dt_k3_xboole_0, axiom, $true).
fof(dt_k3_xcmplx_0, axiom, $true).
fof(dt_k45_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(k45_valued_1(A, B)) & v1_funct_1(k45_valued_1(A, B))) ) ) ).
fof(dt_k4_euclid_3, axiom,  (! [A, B, C] :  ( (m1_subset_1(A, 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)))) )  => v1_xreal_0(k4_euclid_3(A, B, C))) ) ).
fof(dt_k4_finseq_2, axiom,  (! [A, B] :  (v7_ordinal1(A) => m1_finseq_2(k4_finseq_2(A, B), B)) ) ).
fof(dt_k4_numbers, axiom, $true).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k4_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => v1_xcmplx_0(k4_xcmplx_0(A))) ) ).
fof(dt_k5_algstr_0, axiom,  (! [A, B, C] :  ( (l2_algstr_0(A) &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k5_algstr_0(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k5_numbers, axiom, m1_subset_1(k5_numbers, k4_ordinal1)).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k5_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(k5_rltopsp1(A, B, C), k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k5_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => v1_xcmplx_0(k5_xcmplx_0(A))) ) ).
fof(dt_k6_numbers, axiom, $true).
fof(dt_k7_xcmplx_0, axiom, $true).
fof(dt_k8_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(k8_rvsum_1(A, B), k1_numbers)) ) ).
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_finseq_2, axiom, $true).
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_m2_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(A))) )  =>  (! [C] :  (m2_subset_1(C, A, B) => m1_subset_1(C, 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_finseq_2, axiom,  (! [A] :  (? [B] : m1_finseq_2(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(existence_m2_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(A))) )  =>  (? [C] : m2_subset_1(C, A, B)) ) ) ).
fof(fc10_euclid, axiom,  (! [A] :  (v7_ordinal1(A) => v3_valued_2(k1_euclid(A))) ) ).
fof(fc10_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_xboole_0(k2_zfmisc_1(A, B))) ) ) ).
fof(fc13_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_valued_0(A))  & v1_relat_1(B))  => v1_valued_0(k3_xboole_0(A, B))) ) ).
fof(fc15_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v2_valued_0(A))  & v1_relat_1(B))  => v2_valued_0(k3_xboole_0(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_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_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v3_valued_0(A))  & v1_relat_1(B))  => v3_valued_0(k3_xboole_0(A, B))) ) ).
fof(fc19_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v4_valued_0(A))  & v1_relat_1(B))  => v4_valued_0(k3_xboole_0(A, B))) ) ).
fof(fc1_euclid, axiom,  (! [A] :  (v7_ordinal1(A) =>  ~ (v1_xboole_0(k1_euclid(A))) ) ) ).
fof(fc1_euclidlp, axiom,  (! [A] :  (v7_ordinal1(A) =>  ~ (v1_xboole_0(k1_euclidlp(A))) ) ) ).
fof(fc1_subset_1, axiom,  (! [A] :  ~ (v1_xboole_0(k1_zfmisc_1(A))) ) ).
fof(fc21_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v5_valued_0(A))  & v1_relat_1(B))  => v5_valued_0(k3_xboole_0(A, B))) ) ).
fof(fc23_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v6_valued_0(A))  & v1_relat_1(B))  => v6_valued_0(k3_xboole_0(A, B))) ) ).
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_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_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_xreal_0, axiom,  (! [A] :  ( (v2_xxreal_0(A) & v1_xreal_0(A))  =>  (v1_xcmplx_0(k5_xcmplx_0(A)) & v2_xxreal_0(k5_xcmplx_0(A))) ) ) ).
fof(fc28_xreal_0, axiom,  (! [A] :  ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  =>  (v1_xcmplx_0(k5_xcmplx_0(A)) &  ~ (v2_xxreal_0(k5_xcmplx_0(A))) ) ) ) ).
fof(fc29_xreal_0, axiom,  (! [A] :  ( (v3_xxreal_0(A) & v1_xreal_0(A))  =>  (v1_xcmplx_0(k5_xcmplx_0(A)) & v3_xxreal_0(k5_xcmplx_0(A))) ) ) ).
fof(fc2_int_1, axiom,  (! [A, B] :  ( (v1_int_1(A) & v1_int_1(B))  => v1_int_1(k3_xcmplx_0(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(fc30_xreal_0, axiom,  (! [A] :  ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  =>  (v1_xcmplx_0(k5_xcmplx_0(A)) &  ~ (v3_xxreal_0(k5_xcmplx_0(A))) ) ) ) ).
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_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_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_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(fc3_int_1, axiom,  (! [A] :  (v1_int_1(A) =>  (v1_xcmplx_0(k4_xcmplx_0(A)) & v1_int_1(k4_xcmplx_0(A))) ) ) ).
fof(fc3_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) =>  (v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A))) ) ) ).
fof(fc4_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) =>  (v1_xcmplx_0(k5_xcmplx_0(A)) & v1_xreal_0(k5_xcmplx_0(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(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_int_1, axiom, v2_int_1(k4_xcmplx_0(1))).
fof(fc6_ordinal1, axiom,  ( ~ (v1_xboole_0(k4_ordinal1))  & v3_ordinal1(k4_ordinal1)) ).
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(fc8_euclid, axiom,  (! [A, B] :  (v7_ordinal1(A) => v4_finseq_1(k4_finseq_2(A, B))) ) ).
fof(fc8_ordinal1, axiom, v7_ordinal1(k5_ordinal1)).
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_euclid, axiom,  (! [A] :  (v7_ordinal1(A) => v4_finseq_1(k1_euclid(A))) ) ).
fof(fc9_ordinal1, axiom, v8_ordinal1(k5_ordinal1)).
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(ie4_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)  => k5_algstr_0(k15_euclid(A), B, C)=k8_rvsum_1(D, E)) ) ) ).
fof(involutiveness_k30_valued_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_valued_0(A)) )  => k30_valued_1(k30_valued_1(A))=A) ) ).
fof(involutiveness_k4_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => k4_xcmplx_0(k4_xcmplx_0(A))=A) ) ).
fof(involutiveness_k5_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => k5_xcmplx_0(k5_xcmplx_0(A))=A) ) ).
fof(rc10_ordinal1, axiom,  (? [A] :  ~ (v8_ordinal1(A)) ) ).
fof(rc11_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) ) ) ).
fof(rc12_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) & v9_ordinal1(A)) ) ).
fof(rc13_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) &  ~ (v9_ordinal1(A)) ) ) ).
fof(rc1_int_1, axiom,  (? [A] :  (v1_xxreal_0(A) &  (v1_xcmplx_0(A) &  (v1_xreal_0(A) & v1_int_1(A)) ) ) ) ).
fof(rc1_monoid_0, axiom,  (? [A] :  (l1_struct_0(A) & v1_monoid_0(A)) ) ).
fof(rc1_ordinal1, axiom,  (? [A] :  (v1_ordinal1(A) & v2_ordinal1(A)) ) ).
fof(rc1_relset_1, axiom,  (! [A, B] :  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_xboole_0(C) &  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ) ) ).
fof(rc1_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc1_valued_0, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v6_valued_0(A)) ) ) ).
fof(rc1_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc1_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(rc2_int_1, axiom,  (? [A] : v1_int_1(A)) ).
fof(rc2_monoid_0, axiom,  (? [A] :  (l1_struct_0(A) & v2_monoid_0(A)) ) ).
fof(rc2_ordinal1, axiom,  (? [A] : v3_ordinal1(A)) ).
fof(rc2_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_xboole_0(B)) ) ) ).
fof(rc2_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc2_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(rc3_int_1, axiom,  (? [A] : v2_int_1(A)) ).
fof(rc3_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_ordinal1(A) &  (v2_ordinal1(A) & v3_ordinal1(A)) ) ) ) ).
fof(rc3_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_subset_1(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(rc3_xxreal_0, axiom,  (? [A] :  (v1_xxreal_0(A) & v2_xxreal_0(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_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_subset_1(B, A)) ) ) ) ).
fof(rc4_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v3_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc4_xxreal_0, axiom,  (? [A] :  (v1_xxreal_0(A) & v3_xxreal_0(A)) ) ).
fof(rc5_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc5_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc5_xreal_0, axiom,  (? [A] :  (v8_ordinal1(A) &  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc5_xxreal_0, axiom,  (? [A] :  (v8_ordinal1(A) & v1_xxreal_0(A)) ) ).
fof(rc6_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc6_subset_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc7_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v7_ordinal1(A)) ) ).
fof(rc8_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rc9_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(redefinition_k5_numbers, axiom, k5_numbers=k5_ordinal1).
fof(redefinition_k8_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)) ) ) )  => k8_rvsum_1(A, B)=k45_valued_1(A, B)) ) ).
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_m2_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(A))) )  =>  (! [C] :  (m2_subset_1(C, A, B) <=> m1_subset_1(C, 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(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_r3_rn1d3, axiom, k7_xcmplx_0(1, 3)=k7_xcmplx_0(1, 3)).
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_rm3_rnm1d3, axiom, k7_xcmplx_0(1, k4_xcmplx_0(3))=k7_xcmplx_0(k4_xcmplx_0(1), 3)).
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_rn1d3_r3, axiom, k7_xcmplx_0(1, k7_xcmplx_0(1, 3))=3).
fof(rqRealDiv__k7_xcmplx_0__r1_rn2d3_rn3d2, axiom, k7_xcmplx_0(1, k7_xcmplx_0(2, 3))=k7_xcmplx_0(3, 2)).
fof(rqRealDiv__k7_xcmplx_0__r1_rn3d2_rn2d3, axiom, k7_xcmplx_0(1, k7_xcmplx_0(3, 2))=k7_xcmplx_0(2, 3)).
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__r1_rnm1d3_rm3, axiom, k7_xcmplx_0(1, k7_xcmplx_0(k4_xcmplx_0(1), 3))=k4_xcmplx_0(3)).
fof(rqRealDiv__k7_xcmplx_0__r1_rnm2d3_rnm3d2, axiom, k7_xcmplx_0(1, k7_xcmplx_0(k4_xcmplx_0(2), 3))=k7_xcmplx_0(k4_xcmplx_0(3), 2)).
fof(rqRealDiv__k7_xcmplx_0__r1_rnm3d2_rnm2d3, axiom, k7_xcmplx_0(1, k7_xcmplx_0(k4_xcmplx_0(3), 2))=k7_xcmplx_0(k4_xcmplx_0(2), 3)).
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__r2_r3_rn2d3, axiom, k7_xcmplx_0(2, 3)=k7_xcmplx_0(2, 3)).
fof(rqRealDiv__k7_xcmplx_0__r3_r1_r3, axiom, k7_xcmplx_0(3, 1)=3).
fof(rqRealDiv__k7_xcmplx_0__r3_r2_rn3d2, axiom, k7_xcmplx_0(3, 2)=k7_xcmplx_0(3, 2)).
fof(rqRealDiv__k7_xcmplx_0__r3_r3_r1, axiom, k7_xcmplx_0(3, 3)=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(rqRealDiv__k7_xcmplx_0__rn1d2_rn1d2_r1, axiom, k7_xcmplx_0(k7_xcmplx_0(1, 2), k7_xcmplx_0(1, 2))=1).
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_r3_r3, axiom, k3_xcmplx_0(1, 3)=3).
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_rm3_rm3, axiom, k3_xcmplx_0(1, k4_xcmplx_0(3))=k4_xcmplx_0(3)).
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_rn1d3_rn1d3, axiom, k3_xcmplx_0(1, k7_xcmplx_0(1, 3))=k7_xcmplx_0(1, 3)).
fof(rqRealMult__k3_xcmplx_0__r1_rn2d3_rn2d3, axiom, k3_xcmplx_0(1, k7_xcmplx_0(2, 3))=k7_xcmplx_0(2, 3)).
fof(rqRealMult__k3_xcmplx_0__r1_rn3d2_rn3d2, axiom, k3_xcmplx_0(1, k7_xcmplx_0(3, 2))=k7_xcmplx_0(3, 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__r1_rnm1d3_rnm1d3, axiom, k3_xcmplx_0(1, k7_xcmplx_0(k4_xcmplx_0(1), 3))=k7_xcmplx_0(k4_xcmplx_0(1), 3)).
fof(rqRealMult__k3_xcmplx_0__r1_rnm2d3_rnm2d3, axiom, k3_xcmplx_0(1, k7_xcmplx_0(k4_xcmplx_0(2), 3))=k7_xcmplx_0(k4_xcmplx_0(2), 3)).
fof(rqRealMult__k3_xcmplx_0__r1_rnm3d2_rnm3d2, axiom, k3_xcmplx_0(1, k7_xcmplx_0(k4_xcmplx_0(3), 2))=k7_xcmplx_0(k4_xcmplx_0(3), 2)).
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_rn1d3_rn2d3, axiom, k3_xcmplx_0(2, k7_xcmplx_0(1, 3))=k7_xcmplx_0(2, 3)).
fof(rqRealMult__k3_xcmplx_0__r2_rn3d2_r3, axiom, k3_xcmplx_0(2, k7_xcmplx_0(3, 2))=3).
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__r2_rnm1d3_rnm2d3, axiom, k3_xcmplx_0(2, k7_xcmplx_0(k4_xcmplx_0(1), 3))=k7_xcmplx_0(k4_xcmplx_0(2), 3)).
fof(rqRealMult__k3_xcmplx_0__r2_rnm3d2_rm3, axiom, k3_xcmplx_0(2, k7_xcmplx_0(k4_xcmplx_0(3), 2))=k4_xcmplx_0(3)).
fof(rqRealMult__k3_xcmplx_0__r3_r1_r3, axiom, k3_xcmplx_0(3, 1)=3).
fof(rqRealMult__k3_xcmplx_0__r3_rn1d2_rn3d2, axiom, k3_xcmplx_0(3, k7_xcmplx_0(1, 2))=k7_xcmplx_0(3, 2)).
fof(rqRealMult__k3_xcmplx_0__r3_rn1d3_r1, axiom, k3_xcmplx_0(3, k7_xcmplx_0(1, 3))=1).
fof(rqRealMult__k3_xcmplx_0__r3_rn2d3_r2, axiom, k3_xcmplx_0(3, k7_xcmplx_0(2, 3))=2).
fof(rqRealMult__k3_xcmplx_0__r3_rnm1d2_rnm3d2, axiom, k3_xcmplx_0(3, k7_xcmplx_0(k4_xcmplx_0(1), 2))=k7_xcmplx_0(k4_xcmplx_0(3), 2)).
fof(rqRealMult__k3_xcmplx_0__r3_rnm1d3_rm1, axiom, k3_xcmplx_0(3, k7_xcmplx_0(k4_xcmplx_0(1), 3))=k4_xcmplx_0(1)).
fof(rqRealMult__k3_xcmplx_0__r3_rnm2d3_rm2, axiom, k3_xcmplx_0(3, k7_xcmplx_0(k4_xcmplx_0(2), 3))=k4_xcmplx_0(2)).
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_rn1d3_rnm2d3, axiom, k3_xcmplx_0(k4_xcmplx_0(2), k7_xcmplx_0(1, 3))=k7_xcmplx_0(k4_xcmplx_0(2), 3)).
fof(rqRealMult__k3_xcmplx_0__rm2_rn3d2_rm3, axiom, k3_xcmplx_0(k4_xcmplx_0(2), k7_xcmplx_0(3, 2))=k4_xcmplx_0(3)).
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__rm2_rnm1d3_rn2d3, axiom, k3_xcmplx_0(k4_xcmplx_0(2), k7_xcmplx_0(k4_xcmplx_0(1), 3))=k7_xcmplx_0(2, 3)).
fof(rqRealMult__k3_xcmplx_0__rm2_rnm3d2_r3, axiom, k3_xcmplx_0(k4_xcmplx_0(2), k7_xcmplx_0(k4_xcmplx_0(3), 2))=3).
fof(rqRealMult__k3_xcmplx_0__rm3_r1_rm3, axiom, k3_xcmplx_0(k4_xcmplx_0(3), 1)=k4_xcmplx_0(3)).
fof(rqRealMult__k3_xcmplx_0__rm3_rn1d2_rnm3d2, axiom, k3_xcmplx_0(k4_xcmplx_0(3), k7_xcmplx_0(1, 2))=k7_xcmplx_0(k4_xcmplx_0(3), 2)).
fof(rqRealMult__k3_xcmplx_0__rm3_rn1d3_rm1, axiom, k3_xcmplx_0(k4_xcmplx_0(3), k7_xcmplx_0(1, 3))=k4_xcmplx_0(1)).
fof(rqRealMult__k3_xcmplx_0__rm3_rn2d3_rm2, axiom, k3_xcmplx_0(k4_xcmplx_0(3), k7_xcmplx_0(2, 3))=k4_xcmplx_0(2)).
fof(rqRealMult__k3_xcmplx_0__rm3_rnm1d2_rn3d2, axiom, k3_xcmplx_0(k4_xcmplx_0(3), k7_xcmplx_0(k4_xcmplx_0(1), 2))=k7_xcmplx_0(3, 2)).
fof(rqRealMult__k3_xcmplx_0__rm3_rnm1d3_r1, axiom, k3_xcmplx_0(k4_xcmplx_0(3), k7_xcmplx_0(k4_xcmplx_0(1), 3))=1).
fof(rqRealMult__k3_xcmplx_0__rm3_rnm2d3_r2, axiom, k3_xcmplx_0(k4_xcmplx_0(3), k7_xcmplx_0(k4_xcmplx_0(2), 3))=2).
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_r3_rn3d2, axiom, k3_xcmplx_0(k7_xcmplx_0(1, 2), 3)=k7_xcmplx_0(3, 2)).
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__rn1d2_rm3_rnm3d2, axiom, k3_xcmplx_0(k7_xcmplx_0(1, 2), k4_xcmplx_0(3))=k7_xcmplx_0(k4_xcmplx_0(3), 2)).
fof(rqRealMult__k3_xcmplx_0__rn1d2_rn2d3_rn1d3, axiom, k3_xcmplx_0(k7_xcmplx_0(1, 2), k7_xcmplx_0(2, 3))=k7_xcmplx_0(1, 3)).
fof(rqRealMult__k3_xcmplx_0__rn1d2_rnm2d3_rnm1d3, axiom, k3_xcmplx_0(k7_xcmplx_0(1, 2), k7_xcmplx_0(k4_xcmplx_0(2), 3))=k7_xcmplx_0(k4_xcmplx_0(1), 3)).
fof(rqRealMult__k3_xcmplx_0__rn1d3_r1_rn1d3, axiom, k3_xcmplx_0(k7_xcmplx_0(1, 3), 1)=k7_xcmplx_0(1, 3)).
fof(rqRealMult__k3_xcmplx_0__rn1d3_r2_rn2d3, axiom, k3_xcmplx_0(k7_xcmplx_0(1, 3), 2)=k7_xcmplx_0(2, 3)).
fof(rqRealMult__k3_xcmplx_0__rn1d3_r3_r1, axiom, k3_xcmplx_0(k7_xcmplx_0(1, 3), 3)=1).
fof(rqRealMult__k3_xcmplx_0__rn1d3_rm2_rnm2d3, axiom, k3_xcmplx_0(k7_xcmplx_0(1, 3), k4_xcmplx_0(2))=k7_xcmplx_0(k4_xcmplx_0(2), 3)).
fof(rqRealMult__k3_xcmplx_0__rn1d3_rm3_rm1, axiom, k3_xcmplx_0(k7_xcmplx_0(1, 3), k4_xcmplx_0(3))=k4_xcmplx_0(1)).
fof(rqRealMult__k3_xcmplx_0__rn1d3_rn3d2_rn1d2, axiom, k3_xcmplx_0(k7_xcmplx_0(1, 3), k7_xcmplx_0(3, 2))=k7_xcmplx_0(1, 2)).
fof(rqRealMult__k3_xcmplx_0__rn1d3_rnm3d2_rnm1d2, axiom, k3_xcmplx_0(k7_xcmplx_0(1, 3), k7_xcmplx_0(k4_xcmplx_0(3), 2))=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealMult__k3_xcmplx_0__rn2d3_r1_rn2d3, axiom, k3_xcmplx_0(k7_xcmplx_0(2, 3), 1)=k7_xcmplx_0(2, 3)).
fof(rqRealMult__k3_xcmplx_0__rn2d3_r3_r2, axiom, k3_xcmplx_0(k7_xcmplx_0(2, 3), 3)=2).
fof(rqRealMult__k3_xcmplx_0__rn2d3_rm3_rm2, axiom, k3_xcmplx_0(k7_xcmplx_0(2, 3), k4_xcmplx_0(3))=k4_xcmplx_0(2)).
fof(rqRealMult__k3_xcmplx_0__rn2d3_rn1d2_rn1d3, axiom, k3_xcmplx_0(k7_xcmplx_0(2, 3), k7_xcmplx_0(1, 2))=k7_xcmplx_0(1, 3)).
fof(rqRealMult__k3_xcmplx_0__rn2d3_rn3d2_r1, axiom, k3_xcmplx_0(k7_xcmplx_0(2, 3), k7_xcmplx_0(3, 2))=1).
fof(rqRealMult__k3_xcmplx_0__rn2d3_rnm1d2_rnm1d3, axiom, k3_xcmplx_0(k7_xcmplx_0(2, 3), k7_xcmplx_0(k4_xcmplx_0(1), 2))=k7_xcmplx_0(k4_xcmplx_0(1), 3)).
fof(rqRealMult__k3_xcmplx_0__rn2d3_rnm3d2_rm1, axiom, k3_xcmplx_0(k7_xcmplx_0(2, 3), k7_xcmplx_0(k4_xcmplx_0(3), 2))=k4_xcmplx_0(1)).
fof(rqRealMult__k3_xcmplx_0__rn3d2_r1_rn3d2, axiom, k3_xcmplx_0(k7_xcmplx_0(3, 2), 1)=k7_xcmplx_0(3, 2)).
fof(rqRealMult__k3_xcmplx_0__rn3d2_r2_r3, axiom, k3_xcmplx_0(k7_xcmplx_0(3, 2), 2)=3).
fof(rqRealMult__k3_xcmplx_0__rn3d2_rm2_rm3, axiom, k3_xcmplx_0(k7_xcmplx_0(3, 2), k4_xcmplx_0(2))=k4_xcmplx_0(3)).
fof(rqRealMult__k3_xcmplx_0__rn3d2_rn1d3_rn1d2, axiom, k3_xcmplx_0(k7_xcmplx_0(3, 2), k7_xcmplx_0(1, 3))=k7_xcmplx_0(1, 2)).
fof(rqRealMult__k3_xcmplx_0__rn3d2_rn2d3_r1, axiom, k3_xcmplx_0(k7_xcmplx_0(3, 2), k7_xcmplx_0(2, 3))=1).
fof(rqRealMult__k3_xcmplx_0__rn3d2_rnm1d3_rnm1d2, axiom, k3_xcmplx_0(k7_xcmplx_0(3, 2), k7_xcmplx_0(k4_xcmplx_0(1), 3))=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealMult__k3_xcmplx_0__rn3d2_rnm2d3_rm1, axiom, k3_xcmplx_0(k7_xcmplx_0(3, 2), k7_xcmplx_0(k4_xcmplx_0(2), 3))=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_r3_rnm3d2, axiom, k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), 3)=k7_xcmplx_0(k4_xcmplx_0(3), 2)).
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(rqRealMult__k3_xcmplx_0__rnm1d2_rm3_rn3d2, axiom, k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), k4_xcmplx_0(3))=k7_xcmplx_0(3, 2)).
fof(rqRealMult__k3_xcmplx_0__rnm1d2_rn2d3_rnm1d3, axiom, k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), k7_xcmplx_0(2, 3))=k7_xcmplx_0(k4_xcmplx_0(1), 3)).
fof(rqRealMult__k3_xcmplx_0__rnm1d2_rnm2d3_rn1d3, axiom, k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), k7_xcmplx_0(k4_xcmplx_0(2), 3))=k7_xcmplx_0(1, 3)).
fof(rqRealMult__k3_xcmplx_0__rnm1d3_r1_rnm1d3, axiom, k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 3), 1)=k7_xcmplx_0(k4_xcmplx_0(1), 3)).
fof(rqRealMult__k3_xcmplx_0__rnm1d3_r2_rnm2d3, axiom, k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 3), 2)=k7_xcmplx_0(k4_xcmplx_0(2), 3)).
fof(rqRealMult__k3_xcmplx_0__rnm1d3_r3_rm1, axiom, k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 3), 3)=k4_xcmplx_0(1)).
fof(rqRealMult__k3_xcmplx_0__rnm1d3_rm2_rn2d3, axiom, k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 3), k4_xcmplx_0(2))=k7_xcmplx_0(2, 3)).
fof(rqRealMult__k3_xcmplx_0__rnm1d3_rm3_r1, axiom, k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 3), k4_xcmplx_0(3))=1).
fof(rqRealMult__k3_xcmplx_0__rnm1d3_rn3d2_rnm1d2, axiom, k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 3), k7_xcmplx_0(3, 2))=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealMult__k3_xcmplx_0__rnm1d3_rnm3d2_rn1d2, axiom, k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 3), k7_xcmplx_0(k4_xcmplx_0(3), 2))=k7_xcmplx_0(1, 2)).
fof(rqRealMult__k3_xcmplx_0__rnm2d3_r1_rnm2d3, axiom, k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(2), 3), 1)=k7_xcmplx_0(k4_xcmplx_0(2), 3)).
fof(rqRealMult__k3_xcmplx_0__rnm2d3_r3_rm2, axiom, k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(2), 3), 3)=k4_xcmplx_0(2)).
fof(rqRealMult__k3_xcmplx_0__rnm2d3_rm3_r2, axiom, k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(2), 3), k4_xcmplx_0(3))=2).
fof(rqRealMult__k3_xcmplx_0__rnm2d3_rn1d2_rnm1d3, axiom, k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(2), 3), k7_xcmplx_0(1, 2))=k7_xcmplx_0(k4_xcmplx_0(1), 3)).
fof(rqRealMult__k3_xcmplx_0__rnm2d3_rn3d2_rm1, axiom, k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(2), 3), k7_xcmplx_0(3, 2))=k4_xcmplx_0(1)).
fof(rqRealMult__k3_xcmplx_0__rnm2d3_rnm1d2_rn1d3, axiom, k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(2), 3), k7_xcmplx_0(k4_xcmplx_0(1), 2))=k7_xcmplx_0(1, 3)).
fof(rqRealMult__k3_xcmplx_0__rnm2d3_rnm3d2_r1, axiom, k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(2), 3), k7_xcmplx_0(k4_xcmplx_0(3), 2))=1).
fof(rqRealMult__k3_xcmplx_0__rnm3d2_r1_rnm3d2, axiom, k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3), 2), 1)=k7_xcmplx_0(k4_xcmplx_0(3), 2)).
fof(rqRealMult__k3_xcmplx_0__rnm3d2_r2_rm3, axiom, k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3), 2), 2)=k4_xcmplx_0(3)).
fof(rqRealMult__k3_xcmplx_0__rnm3d2_rm2_r3, axiom, k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3), 2), k4_xcmplx_0(2))=3).
fof(rqRealMult__k3_xcmplx_0__rnm3d2_rn1d3_rnm1d2, axiom, k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3), 2), k7_xcmplx_0(1, 3))=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealMult__k3_xcmplx_0__rnm3d2_rn2d3_rm1, axiom, k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3), 2), k7_xcmplx_0(2, 3))=k4_xcmplx_0(1)).
fof(rqRealMult__k3_xcmplx_0__rnm3d2_rnm1d3_rn1d2, axiom, k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3), 2), k7_xcmplx_0(k4_xcmplx_0(1), 3))=k7_xcmplx_0(1, 2)).
fof(rqRealMult__k3_xcmplx_0__rnm3d2_rnm2d3_r1, axiom, k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3), 2), k7_xcmplx_0(k4_xcmplx_0(2), 3))=1).
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__r3_rm3, axiom, k4_xcmplx_0(3)=k4_xcmplx_0(3)).
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__rm3_r3, axiom, k4_xcmplx_0(k4_xcmplx_0(3))=3).
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__rn1d3_rnm1d3, axiom, k4_xcmplx_0(k7_xcmplx_0(1, 3))=k7_xcmplx_0(k4_xcmplx_0(1), 3)).
fof(rqRealNeg__k4_xcmplx_0__rn2d3_rnm2d3, axiom, k4_xcmplx_0(k7_xcmplx_0(2, 3))=k7_xcmplx_0(k4_xcmplx_0(2), 3)).
fof(rqRealNeg__k4_xcmplx_0__rn3d2_rnm3d2, axiom, k4_xcmplx_0(k7_xcmplx_0(3, 2))=k7_xcmplx_0(k4_xcmplx_0(3), 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(rqRealNeg__k4_xcmplx_0__rnm1d3_rn1d3, axiom, k4_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 3))=k7_xcmplx_0(1, 3)).
fof(rqRealNeg__k4_xcmplx_0__rnm2d3_rn2d3, axiom, k4_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(2), 3))=k7_xcmplx_0(2, 3)).
fof(rqRealNeg__k4_xcmplx_0__rnm3d2_rn3d2, axiom, k4_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(3), 2))=k7_xcmplx_0(3, 2)).
fof(spc10_arithm, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k3_xcmplx_0(k5_xcmplx_0(A), k5_xcmplx_0(B))=k5_xcmplx_0(k3_xcmplx_0(A, B))) ) ).
fof(spc11_arithm, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k7_xcmplx_0(k5_xcmplx_0(A), k5_xcmplx_0(B))=k7_xcmplx_0(B, A)) ) ).
fof(spc12_arithm, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k3_xcmplx_0(A, k5_xcmplx_0(B))=k7_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(spc3_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k7_xcmplx_0(1, A)=k5_xcmplx_0(A)) ) ).
fof(spc3_boole, axiom,  ~ (v1_xboole_0(3)) ).
fof(spc3_numerals, axiom,  (v2_xxreal_0(3) & m1_subset_1(3, 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(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(symmetry_r6_euclidlp, axiom,  (! [A, B, C] :  ( (v7_ordinal1(A) &  (m1_subset_1(B, k1_euclidlp(A)) & m1_subset_1(C, k1_euclidlp(A))) )  =>  (r6_euclidlp(A, B, C) => r6_euclidlp(A, C, B)) ) ) ).
fof(t1_numerals, axiom, m1_subset_1(k1_xboole_0, k4_ordinal1)).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t2_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_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t3_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k3_xcmplx_0(1, A)=A) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t45_euclid_3, 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))) =>  ~ ( ( ~ (A=B)  &  ( ~ (C=B)  &  ~ ( (k22_rvsum_1(k5_algstr_0(k15_euclid(2), A, B), k5_algstr_0(k15_euclid(2), C, B))=k5_numbers <=>  (k4_euclid_3(A, B, C)=k7_xcmplx_0(k28_sin_cos, 2) | k4_euclid_3(A, B, C)=k3_xcmplx_0(k7_xcmplx_0(3, 2), k28_sin_cos)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t48_euclid12, 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))) =>  (! [D] :  (m2_subset_1(D, k1_zfmisc_1(k1_euclid(2)), k1_euclidlp(2)) =>  (! [E] :  (m2_subset_1(E, k1_zfmisc_1(k1_euclid(2)), k1_euclidlp(2)) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(k15_euclid(2))) =>  ( (r6_euclidlp(2, D, E) &  (D=k5_rltopsp1(k15_euclid(2), A, B) & E=k5_rltopsp1(k15_euclid(2), C, F)) )  => k22_rvsum_1(k5_algstr_0(k15_euclid(2), B, A), k5_algstr_0(k15_euclid(2), F, C))=k5_ordinal1) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t49_euclid12, axiom,  (! [A] :  (m1_subset_1(A, u1_struct_0(k15_euclid(2))) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(k15_euclid(2))) =>  (! [C] :  (m2_subset_1(C, k1_zfmisc_1(k1_euclid(2)), k1_euclidlp(2)) =>  ( (v1_euclid_4(C, 2) &  (r2_tarski(A, C) & r2_tarski(B, C)) )  =>  (A=B | C=k5_rltopsp1(k15_euclid(2), A, B)) ) ) ) ) ) ) ) ).
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_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k7_xcmplx_0(k5_numbers, A)=k5_numbers) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t67_euclidlp, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  (m2_subset_1(B, k1_zfmisc_1(k1_euclid(A)), k1_euclidlp(A)) =>  (! [C] :  (m2_subset_1(C, k1_zfmisc_1(k1_euclid(A)), k1_euclidlp(A)) =>  (r6_euclidlp(A, B, C) =>  (v1_euclid_4(B, A) & v1_euclid_4(C, A)) ) ) ) ) ) ) ) ).
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(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
