% Mizar problem: t31_goedelcp,goedelcp,1072,5 
fof(t31_goedelcp, conjecture,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  ( (v1_henmodel(B, A) & m1_subset_1(B, k1_zfmisc_1(k3_cqc_lang(A))))  =>  ~ ( (v4_card_3(A) &  (v1_finset_1(k6_goedelcp(A, B)) &  (! [C] :  ( (v1_henmodel(C, A) & m1_subset_1(C, k1_zfmisc_1(k3_cqc_lang(A))))  =>  ~ ( (r1_tarski(B, C) & v2_goedelcp(C, 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_finseq_1, axiom,  (! [A] :  (v3_finseq_1(A) => v6_membered(A)) ) ).
fof(cc10_ordinal1, axiom,  (! [A] :  (v6_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_ordinal1(B)) ) ) ) ).
fof(cc11_finseq_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_finseq_1(A)) ) ).
fof(cc11_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v7_ordinal1(A)) ) ).
fof(cc12_finseq_1, axiom,  (! [A] :  (v4_finseq_1(A) => v4_funct_1(A)) ) ).
fof(cc12_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v1_zfmisc_1(A)) ) ).
fof(cc13_finseq_1, axiom,  (! [A] :  (v4_finseq_1(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_finseq_1(B)) ) ) ) ).
fof(cc13_ordinal1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  ~ (v8_ordinal1(A)) ) ) ).
fof(cc14_finseq_1, axiom,  (! [A] :  (v4_finseq_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_finseq_1(B)) ) ) ) ).
fof(cc14_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc15_card_3, axiom,  (! [A] :  ( ~ (v4_card_3(A))  =>  ~ (v1_xboole_0(A)) ) ) ).
fof(cc15_ordinal1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v9_ordinal1(A)) ) ) ).
fof(cc16_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v1_finset_1(A) & v2_finseq_1(A)) ) ) ) ) ).
fof(cc16_ordinal1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) )  =>  (! [B] :  (m1_subset_1(B, A) =>  ~ (v8_ordinal1(B)) ) ) ) ) ).
fof(cc17_finseq_1, axiom,  (! [A] :  (m1_finseq_1(A, k4_ordinal1) => v6_valued_0(A)) ) ).
fof(cc17_ordinal1, axiom,  (! [A] :  ( ~ (v10_ordinal1(A))  => v1_setfam_1(A)) ) ).
fof(cc18_ordinal1, axiom,  (! [A] :  (v10_ordinal1(A) =>  ~ (v1_setfam_1(A)) ) ) ).
fof(cc19_ordinal1, axiom,  (! [A] :  (v1_setfam_1(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc1_card_3, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_card_3(A)) ) ) ) ).
fof(cc1_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_xboole_0(A))  =>  (v1_relat_1(A) & v1_finseq_1(A)) ) ) ).
fof(cc1_finset_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_finset_1(A)) ) ).
fof(cc1_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (v1_ordinal1(A) & v2_ordinal1(A)) ) ) ).
fof(cc1_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_relat_1(A)) ) ).
fof(cc1_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C)) ) ) ).
fof(cc1_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_xboole_0(B)) ) ) ) ).
fof(cc20_ordinal1, axiom,  (! [A] :  ( ~ (v1_setfam_1(A))  => v10_ordinal1(A)) ) ).
fof(cc2_card_3, axiom,  (! [A, B] :  (v1_setfam_1(B) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  ( (v1_funct_1(C) & v1_funct_2(C, A, B))  =>  (v2_relat_1(C) &  (v1_funct_1(C) & v1_funct_2(C, A, B)) ) ) ) ) ) ) ).
fof(cc2_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) ) ) ).
fof(cc2_finset_1, axiom,  (! [A] :  (v1_finset_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_finset_1(B)) ) ) ) ).
fof(cc2_ordinal1, axiom,  (! [A] :  ( (v1_ordinal1(A) & v2_ordinal1(A))  => v3_ordinal1(A)) ) ).
fof(cc2_relat_1, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_relat_1(B)) ) ) ) ).
fof(cc2_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ).
fof(cc2_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ( ~ (v1_subset_1(B, A))  =>  ~ (v1_xboole_0(B)) ) ) ) ) ) ).
fof(cc2_xreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xreal_0(A)) ) ).
fof(cc2_xxreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xxreal_0(A)) ) ).
fof(cc3_finseq_1, axiom,  (! [A] :  (! [B] :  (m1_finseq_1(B, A) => v5_relat_1(B, A)) ) ) ).
fof(cc3_finset_1, axiom,  (! [A, B] :  (v1_finset_1(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  ( (v1_funct_1(C) & v1_funct_2(C, A, B))  =>  (v1_funct_1(C) &  (v1_funct_2(C, A, B) & v1_finset_1(C)) ) ) ) ) ) ) ).
fof(cc3_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_ordinal1(A)) ) ).
fof(cc3_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v3_relat_1(A)) ) ) ).
fof(cc3_relset_1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_xboole_0(C)) ) ) ) ).
fof(cc3_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  (v1_xboole_0(B) => v1_subset_1(B, A)) ) ) ) ) ).
fof(cc3_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xcmplx_0(A)) ) ).
fof(cc3_xxreal_0, axiom,  (! [A] :  ( (v1_xxreal_0(A) & v2_xxreal_0(A))  =>  ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v3_xxreal_0(A)) ) ) ) ) ).
fof(cc4_card_3, axiom,  (! [A] :  (v5_card_3(A) =>  ( ~ (v1_finset_1(A))  & v4_card_3(A)) ) ) ).
fof(cc4_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_xboole_0(A))  =>  (v1_relat_1(A) & v1_finseq_1(A)) ) ) ).
fof(cc4_finset_1, axiom,  (! [A] :  (v1_zfmisc_1(A) => v1_finset_1(A)) ) ).
fof(cc4_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v5_ordinal1(A)) ) ).
fof(cc4_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v2_relat_1(A)) ) ) ).
fof(cc4_relset_1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A))) => v1_xboole_0(C)) ) ) ) ).
fof(cc4_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ~ (v1_subset_1(B, A)) ) ) ) ) ).
fof(cc4_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xxreal_0(A)) ) ).
fof(cc4_xxreal_0, axiom,  (! [A] :  ( ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v3_xxreal_0(A)) ) )  =>  (v1_xxreal_0(A) & v2_xxreal_0(A)) ) ) ).
fof(cc5_card_3, axiom,  (! [A] :  ( ( ~ (v1_finset_1(A))  & v4_card_3(A))  => v5_card_3(A)) ) ).
fof(cc5_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) & v1_finseq_1(A)) ) ) ) ) ).
fof(cc5_finset_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ~ (v1_zfmisc_1(A)) ) ) ).
fof(cc5_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, A) => v3_ordinal1(B)) ) ) ) ).
fof(cc5_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(B)) => v4_relat_1(C, A)) ) ) ) ).
fof(cc5_subset_1, axiom,  (! [A] :  (v1_zfmisc_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_zfmisc_1(B)) ) ) ) ).
fof(cc5_xxreal_0, axiom,  (! [A] :  ( (v1_xxreal_0(A) & v3_xxreal_0(A))  =>  ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v2_xxreal_0(A)) ) ) ) ) ).
fof(cc6_card_3, axiom,  (! [A] :  (v1_finset_1(A) => v4_card_3(A)) ) ).
fof(cc6_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) ) ) ) ).
fof(cc6_finset_1, axiom,  (! [A] :  (v1_xboole_0(A) => v5_finset_1(A)) ) ).
fof(cc6_ordinal1, axiom,  (! [A] :  (v7_ordinal1(A) => v3_ordinal1(A)) ) ).
fof(cc6_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(B)) => v5_relat_1(C, A)) ) ) ) ).
fof(cc6_xxreal_0, axiom,  (! [A] :  ( ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v2_xxreal_0(A)) ) )  =>  (v1_xxreal_0(A) & v3_xxreal_0(A)) ) ) ).
fof(cc7_card_3, axiom,  (! [A] :  (v4_card_3(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_card_3(B)) ) ) ) ).
fof(cc7_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) & v2_finseq_1(A)) ) ) ) ) ).
fof(cc7_finset_1, axiom,  (! [A] :  (v5_finset_1(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_finset_1(B)) ) ) ) ).
fof(cc7_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v7_ordinal1(A)) ) ).
fof(cc7_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  =>  (v1_xboole_0(B) &  (v1_relat_1(B) & v4_relat_1(B, A)) ) ) ) ) ) ).
fof(cc7_xxreal_0, axiom,  (! [A] :  ( (v8_ordinal1(A) & v1_xxreal_0(A))  =>  (v1_xxreal_0(A) &  ( ~ (v2_xxreal_0(A))  &  ~ (v3_xxreal_0(A)) ) ) ) ) ).
fof(cc8_card_3, axiom,  (! [A] :  (v2_card_3(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v2_card_3(B)) ) ) ) ).
fof(cc8_finseq_1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_finseq_1(A)) ) ).
fof(cc8_finset_1, axiom,  (! [A] :  (v5_finset_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v5_finset_1(B)) ) ) ) ).
fof(cc8_ordinal1, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) => v7_ordinal1(A)) ) ).
fof(cc8_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_xboole_0(B) &  (v1_relat_1(B) & v5_relat_1(B, A)) ) ) ) ) ) ).
fof(cc8_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_finseq_1, axiom,  (! [A] :  (v3_finseq_1(A) => v1_finset_1(A)) ) ).
fof(cc9_finset_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v2_finset_1(A)) ) ) ).
fof(cc9_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v6_ordinal1(A)) ) ).
fof(commutativity_k1_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & m1_subset_1(B, k4_ordinal1))  => k1_nat_1(A, B)=k1_nat_1(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_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_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(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(d12_ordinal1, axiom,  (! [A] :  (v7_ordinal1(A) <=> r2_hidden(A, k4_ordinal1)) ) ).
fof(d13_ordinal1, axiom, k5_ordinal1=k1_xboole_0).
fof(d17_ordinal1, axiom,  (! [A] : k6_ordinal1(A)=A) ).
fof(d1_henmodel, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k3_cqc_lang(A))) =>  (! [C] :  (m2_subset_1(C, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (r1_henmodel(A, B, C) <=>  (? [D] :  (m2_finseq_1(D, k3_cqc_lang(A)) &  (r1_tarski(k2_relset_1(k3_cqc_lang(A), D), B) & r4_calcul_1(A, k8_finseq_1(k3_cqc_lang(A), D, k12_finseq_1(k3_cqc_lang(A), C)))) ) ) ) ) ) ) ) ) ) ).
fof(d1_tarski, axiom,  (! [A] :  (! [B] :  (B=k1_tarski(A) <=>  (! [C] :  (r2_hidden(C, B) <=> C=A) ) ) ) ) ).
fof(d1_xboole_0, axiom,  (! [A] :  (v1_xboole_0(A) <=>  (! [B] :  ~ (r2_hidden(B, A)) ) ) ) ).
fof(d2_xboole_0, axiom, k1_xboole_0=o_0_0_xboole_0).
fof(d2_zfmisc_1, axiom,  (! [A] :  (! [B] :  (! [C] :  (C=k2_zfmisc_1(A, B) <=>  (! [D] :  (r2_hidden(D, C) <=>  (? [E] :  (? [F] :  (r2_hidden(E, A) &  (r2_hidden(F, B) & D=k4_tarski(E, F)) ) ) ) ) ) ) ) ) ) ).
fof(d3_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (B=k10_xtuple_0(A) <=>  (! [C] :  (r2_hidden(C, B) <=>  (? [D] :  (r2_hidden(D, k9_xtuple_0(A)) & C=k1_funct_1(A, D)) ) ) ) ) ) ) ) ).
fof(d3_goedelcp, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k3_cqc_lang(A))) =>  (B=k1_goedelcp(A) <=>  (! [C] :  (r2_tarski(C, B) <=>  (? [D] :  (m2_subset_1(D, k2_qc_lang1(A), k3_qc_lang1(A)) &  (? [E] :  (m2_subset_1(E, k9_qc_lang1(A), k3_cqc_lang(A)) & C=k12_cqc_lang(A, D, E)) ) ) ) ) ) ) ) ) ) ) ).
fof(d3_tarski, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) <=>  (! [C] :  (r2_hidden(C, A) => r2_hidden(C, B)) ) ) ) ) ).
fof(d3_xboole_0, axiom,  (! [A] :  (! [B] :  (! [C] :  (C=k2_xboole_0(A, B) <=>  (! [D] :  (r2_hidden(D, C) <=>  (r2_hidden(D, A) | r2_hidden(D, B)) ) ) ) ) ) ) ).
fof(d41_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  ( ( ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(k1_qc_lang1(A))))  => k31_qc_lang1(A, B)=o_1_2_qc_lang1(B))  &  ( ~ ( ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(k1_qc_lang1(A)))) )  => k31_qc_lang1(A, B)=k26_qc_lang1(A)) ) ) ) ) ).
fof(d4_tarski, axiom,  (! [A] :  (! [B] :  (B=k3_tarski(A) <=>  (! [C] :  (r2_hidden(C, B) <=>  (? [D] :  (r2_hidden(C, D) & r2_hidden(D, A)) ) ) ) ) ) ) ).
fof(d6_goedelcp, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  ( (v1_funct_1(B) &  (v1_funct_2(B, k4_ordinal1, k3_cqc_lang(A)) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k3_cqc_lang(A))))) )  =>  (! [C] :  (v7_ordinal1(C) =>  (! [D] :  (m2_subset_1(D, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (D=k4_goedelcp(A, B, C) <=>  (! [E] :  (m2_subset_1(E, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (E=k8_nat_1(k3_cqc_lang(A), B, C) => D=k2_goedelcp(A, E)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d7_goedelcp, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  ( (v1_funct_1(B) &  (v1_funct_2(B, k4_ordinal1, k3_cqc_lang(A)) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k3_cqc_lang(A))))) )  =>  (! [C] :  (v7_ordinal1(C) =>  (! [D] :  (m2_subset_1(D, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (D=k5_goedelcp(A, B, C) <=>  (! [E] :  (m2_subset_1(E, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (E=k8_nat_1(k3_cqc_lang(A), B, C) => D=k3_goedelcp(A, E)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d8_goedelcp, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k3_cqc_lang(A))) => k6_goedelcp(A, B)=k3_tarski(a_2_0_goedelcp(A, B))) ) ) ) ).
fof(dt_k10_xtuple_0, axiom, $true).
fof(dt_k12_cqc_lang, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k3_qc_lang1(A)) & m1_subset_1(C, k3_cqc_lang(A))) )  => m2_subset_1(k12_cqc_lang(A, B, C), k9_qc_lang1(A), k3_cqc_lang(A))) ) ).
fof(dt_k12_finseq_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(B, A))  => m2_finseq_1(k12_finseq_1(A, B), A)) ) ).
fof(dt_k12_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) => m1_subset_1(k12_qc_lang1(A), k9_qc_lang1(A))) ) ).
fof(dt_k13_qc_lang1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k9_qc_lang1(A)))  => m1_subset_1(k13_qc_lang1(A, B), k9_qc_lang1(A))) ) ).
fof(dt_k1_calcul_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_finseq_1(B, A))  => m2_finseq_1(k1_calcul_1(A, B), A)) ) ).
fof(dt_k1_card_1, axiom,  (! [A] : v1_card_1(k1_card_1(A))) ).
fof(dt_k1_domain_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  (m1_subset_1(C, A) & m1_subset_1(D, B)) ) )  => m1_subset_1(k1_domain_1(A, B, C, D), k2_zfmisc_1(A, B))) ) ).
fof(dt_k1_funct_1, axiom, $true).
fof(dt_k1_goedelcp, axiom,  (! [A] :  (m1_qc_lang1(A) => m1_subset_1(k1_goedelcp(A), k1_zfmisc_1(k3_cqc_lang(A)))) ) ).
fof(dt_k1_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & m1_subset_1(B, k4_ordinal1))  => m1_subset_1(k1_nat_1(A, B), k4_ordinal1)) ) ).
fof(dt_k1_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k1_qc_lang1(A))) ) ) ).
fof(dt_k1_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  => m1_subset_1(k1_relset_1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_k1_tarski, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_xfamily, axiom, $true).
fof(dt_k1_xtuple_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k24_qc_lang1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k9_qc_lang1(A)))  => m1_subset_1(k24_qc_lang1(A, B), k1_zfmisc_1(k3_qc_lang1(A)))) ) ).
fof(dt_k26_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) => m1_subset_1(k26_qc_lang1(A), k1_qc_lang1(A))) ) ).
fof(dt_k2_calcul_1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_finseq_1(B, k3_cqc_lang(A)))  => m2_subset_1(k2_calcul_1(A, B), k9_qc_lang1(A), k3_cqc_lang(A))) ) ).
fof(dt_k2_goedelcp, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k9_qc_lang1(A)))  => m2_subset_1(k2_goedelcp(A, B), k2_qc_lang1(A), k3_qc_lang1(A))) ) ).
fof(dt_k2_qc_lang1, axiom, $true).
fof(dt_k2_qc_lang3, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k1_qc_lang1(A)))  => m2_subset_1(k2_qc_lang3(A, B), k2_qc_lang1(A), k3_qc_lang1(A))) ) ).
fof(dt_k2_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  => m1_subset_1(k2_relset_1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_k2_xboole_0, axiom, $true).
fof(dt_k2_xcmplx_0, axiom, $true).
fof(dt_k2_xfamily, axiom, $true).
fof(dt_k2_xtuple_0, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k31_qc_lang1, axiom,  (! [A, B] :  (m1_qc_lang1(A) => m1_subset_1(k31_qc_lang1(A, B), k1_qc_lang1(A))) ) ).
fof(dt_k3_calcul_1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_finseq_1(B, k3_cqc_lang(A)))  => m1_subset_1(k3_calcul_1(A, B), k1_zfmisc_1(k3_qc_lang1(A)))) ) ).
fof(dt_k3_cqc_lang, axiom,  (! [A] :  (m1_qc_lang1(A) => m1_subset_1(k3_cqc_lang(A), k1_zfmisc_1(k9_qc_lang1(A)))) ) ).
fof(dt_k3_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => m1_subset_1(k3_finseq_1(A), k4_ordinal1)) ) ).
fof(dt_k3_funct_2, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  & m1_subset_1(D, A)) )  => m1_subset_1(k3_funct_2(A, B, C, D), B)) ) ).
fof(dt_k3_goedelcp, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k3_cqc_lang(A)))  => m2_subset_1(k3_goedelcp(A, B), k9_qc_lang1(A), k3_cqc_lang(A))) ) ).
fof(dt_k3_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) => m1_subset_1(k3_qc_lang1(A), k1_zfmisc_1(k2_qc_lang1(A)))) ) ).
fof(dt_k3_qc_lang2, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k9_qc_lang1(A)) & m1_subset_1(C, k9_qc_lang1(A))) )  => m1_subset_1(k3_qc_lang2(A, B, C), k9_qc_lang1(A))) ) ).
fof(dt_k3_tarski, axiom, $true).
fof(dt_k3_xcmplx_0, axiom, $true).
fof(dt_k4_goedelcp, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  ( (v1_funct_1(B) &  (v1_funct_2(B, k4_ordinal1, k3_cqc_lang(A)) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k3_cqc_lang(A))))) )  & v7_ordinal1(C)) )  => m2_subset_1(k4_goedelcp(A, B, C), k2_qc_lang1(A), k3_qc_lang1(A))) ) ).
fof(dt_k4_ordinal1, axiom, $true).
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_substut2, axiom,  (! [A, B, C, D] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k3_cqc_lang(A)) &  (m1_subset_1(C, k3_qc_lang1(A)) & m1_subset_1(D, k3_qc_lang1(A))) ) )  => m2_subset_1(k4_substut2(A, B, C, D), k9_qc_lang1(A), k3_cqc_lang(A))) ) ).
fof(dt_k4_tarski, axiom, $true).
fof(dt_k4_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => v1_xcmplx_0(k4_xcmplx_0(A))) ) ).
fof(dt_k5_card_1, axiom,  (! [A] :  (v7_ordinal1(A) => m1_subset_1(k5_card_1(A), k1_zfmisc_1(k4_ordinal1))) ) ).
fof(dt_k5_cqc_lang, axiom,  (! [A] :  (m1_qc_lang1(A) => m2_subset_1(k5_cqc_lang(A), k9_qc_lang1(A), k3_cqc_lang(A))) ) ).
fof(dt_k5_finseq_1, axiom, $true).
fof(dt_k5_goedelcp, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  ( (v1_funct_1(B) &  (v1_funct_2(B, k4_ordinal1, k3_cqc_lang(A)) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k3_cqc_lang(A))))) )  & v7_ordinal1(C)) )  => m2_subset_1(k5_goedelcp(A, B, C), k9_qc_lang1(A), k3_cqc_lang(A))) ) ).
fof(dt_k5_numbers, axiom, m1_subset_1(k5_numbers, k4_ordinal1)).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k5_qc_lang2, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k3_qc_lang1(A)) & m1_subset_1(C, k9_qc_lang1(A))) )  => m1_subset_1(k5_qc_lang2(A, B, C), k9_qc_lang1(A))) ) ).
fof(dt_k5_setfam_1, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) => m1_subset_1(k5_setfam_1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_k6_cqc_lang, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k3_cqc_lang(A)))  => m2_subset_1(k6_cqc_lang(A, B), k9_qc_lang1(A), k3_cqc_lang(A))) ) ).
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_goedelcp, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k1_zfmisc_1(k3_cqc_lang(A))))  => m1_subset_1(k6_goedelcp(A, B), k1_zfmisc_1(k3_qc_lang1(A)))) ) ).
fof(dt_k6_ordinal1, axiom, $true).
fof(dt_k6_xcmplx_0, axiom, $true).
fof(dt_k7_finseq_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) ) )  =>  (v1_relat_1(k7_finseq_1(A, B)) &  (v1_funct_1(k7_finseq_1(A, B)) & v1_finseq_1(k7_finseq_1(A, B))) ) ) ) ).
fof(dt_k7_xcmplx_0, axiom, $true).
fof(dt_k8_finseq_1, axiom,  (! [A, B, C] :  ( (m1_finseq_1(B, A) & m1_finseq_1(C, A))  => m2_finseq_1(k8_finseq_1(A, B, C), A)) ) ).
fof(dt_k8_nat_1, axiom,  (! [A, B, C] :  ( ( (v1_funct_1(B) &  (v1_funct_2(B, k4_ordinal1, A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, A)))) )  & v7_ordinal1(C))  => m1_subset_1(k8_nat_1(A, B, C), A)) ) ).
fof(dt_k9_cqc_lang, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k3_cqc_lang(A)) & m1_subset_1(C, k3_cqc_lang(A))) )  => m2_subset_1(k9_cqc_lang(A, B, C), k9_qc_lang1(A), k3_cqc_lang(A))) ) ).
fof(dt_k9_finseq_1, axiom,  (! [A] :  (v1_relat_1(k9_finseq_1(A)) & v1_funct_1(k9_finseq_1(A))) ) ).
fof(dt_k9_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k9_qc_lang1(A))) ) ) ).
fof(dt_k9_setfam_1, axiom,  (! [A] : m1_subset_1(k9_setfam_1(A), k1_zfmisc_1(k1_zfmisc_1(A)))) ).
fof(dt_k9_xtuple_0, axiom, $true).
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_qc_lang1, 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_o_0_0_xboole_0, axiom, v1_xboole_0(o_0_0_xboole_0)).
fof(dt_o_1_2_qc_lang1, axiom,  (! [A] : m1_subset_1(o_1_2_qc_lang1(A), A)) ).
fof(dt_o_2_6_goedelcp, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(k1_qc_lang1(A)))) )  => m2_subset_1(o_2_6_goedelcp(A, B), k1_qc_lang1(A), B)) ) ).
fof(existence_m1_finseq_1, axiom,  (! [A] :  (? [B] : m1_finseq_1(B, A)) ) ).
fof(existence_m1_qc_lang1, axiom,  (? [A] : m1_qc_lang1(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_card_3, axiom, v5_card_3(k4_ordinal1)).
fof(fc10_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) & v9_ordinal1(A))  =>  ~ (v10_ordinal1(k10_xtuple_0(A))) ) ) ).
fof(fc10_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k9_xtuple_0(A))) ) ).
fof(fc10_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_xboole_0(k2_zfmisc_1(A, B))) ) ) ).
fof(fc10_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v2_xxreal_0(k2_xcmplx_0(A, B))) ) ) ).
fof(fc11_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) &  ~ (v9_ordinal1(A)) )  => v10_ordinal1(k10_xtuple_0(A))) ) ).
fof(fc11_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k10_xtuple_0(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_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_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) => v3_ordinal1(k6_ordinal1(A))) ) ).
fof(fc13_xreal_0, axiom,  (! [A, B] :  ( ( (v3_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  => v3_xxreal_0(k2_xcmplx_0(A, B))) ) ).
fof(fc14_finset_1, axiom,  (! [A, B] :  ( (v1_finset_1(A) & v1_finset_1(B))  => v1_finset_1(k2_zfmisc_1(A, B))) ) ).
fof(fc14_ordinal1, axiom,  (! [A] :  ( (v3_ordinal1(A) & v8_ordinal1(A))  => v1_xboole_0(k6_ordinal1(A))) ) ).
fof(fc14_xreal_0, axiom,  (! [A, B] :  ( ( (v3_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  => v3_xxreal_0(k2_xcmplx_0(B, A))) ) ).
fof(fc15_xreal_0, axiom,  (! [A] :  ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  =>  (v1_xcmplx_0(k4_xcmplx_0(A)) &  ~ (v3_xxreal_0(k4_xcmplx_0(A))) ) ) ) ).
fof(fc16_finseq_1, axiom,  (! [A] :  ( (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) )  => v3_finseq_1(k1_tarski(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_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => v3_finseq_1(k9_xtuple_0(A))) ) ).
fof(fc17_finset_1, axiom,  (! [A] :  (v1_finset_1(A) => v1_finset_1(k1_zfmisc_1(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_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) )  => v3_finseq_1(k9_xtuple_0(A))) ) ).
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_finseq_1, axiom,  (! [A, B] :  ( (v3_finseq_1(A) & v3_finseq_1(B))  => v3_finseq_1(k2_xboole_0(A, B))) ) ).
fof(fc19_finset_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_finset_1(A))  => v1_finset_1(k9_xtuple_0(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_finset_1, axiom,  (! [A] : v1_finset_1(k1_tarski(A))) ).
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_subset_1, axiom,  (! [A] :  ~ (v1_xboole_0(k1_zfmisc_1(A))) ) ).
fof(fc1_xtuple_0, axiom,  (! [A, B] : v1_xtuple_0(k4_tarski(A, B))) ).
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_finset_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_finset_1(A))  => v1_finset_1(k10_xtuple_0(A))) ) ).
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_finseq_1, axiom,  (! [A] :  ~ (v1_xboole_0(k5_finseq_1(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_finseq_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) &  ( ~ (v1_xboole_0(B))  & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k7_finseq_1(A, B)) &  (v1_funct_1(k7_finseq_1(A, B)) &  ( ~ (v1_xboole_0(k7_finseq_1(A, B)))  & v1_finseq_1(k7_finseq_1(A, B))) ) ) ) ) ).
fof(fc24_relat_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) & v1_relat_1(A))  => v1_zfmisc_1(k9_xtuple_0(A))) ) ).
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_finseq_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) &  ( ~ (v1_xboole_0(B))  & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k7_finseq_1(B, A)) &  (v1_funct_1(k7_finseq_1(B, A)) &  ( ~ (v1_xboole_0(k7_finseq_1(B, A)))  & v1_finseq_1(k7_finseq_1(B, A))) ) ) ) ) ).
fof(fc25_relat_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) & v1_relat_1(A))  => v1_zfmisc_1(k10_xtuple_0(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(fc2_cqc_lang, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k3_cqc_lang(A))) ) ) ).
fof(fc30_finset_1, axiom,  (! [A] :  (v1_finset_1(A) => v5_finset_1(k1_tarski(A))) ) ).
fof(fc31_finset_1, axiom,  (! [A] :  (v1_finset_1(A) => v5_finset_1(k1_zfmisc_1(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_finseq_1, axiom,  (! [A] : v3_card_1(k5_finseq_1(A), 1)) ).
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_finset_1, axiom,  (! [A, B] :  ( (v5_finset_1(A) & v5_finset_1(B))  => v5_finset_1(k2_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_finset_1, axiom,  (! [A] :  ( (v1_finset_1(A) & v5_finset_1(A))  => v1_finset_1(k3_tarski(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_finseq_1, axiom, v4_finseq_1(k1_tarski(k1_xboole_0))).
fof(fc35_finset_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finset_1(A)) )  => v1_finset_1(k1_funct_1(A, B))) ) ).
fof(fc36_finseq_1, axiom,  (! [A, B] :  ( (v4_finseq_1(A) & v4_finseq_1(B))  => v4_finseq_1(k2_xboole_0(A, B))) ) ).
fof(fc36_finset_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v2_finset_1(A))  => v5_finset_1(k10_xtuple_0(A))) ) ).
fof(fc38_finseq_1, axiom,  (! [A, B, C, D] :  ( (v7_ordinal1(A) &  (v7_ordinal1(B) &  ( (v1_relat_1(C) &  (v1_funct_1(C) &  (v3_card_1(C, A) & v1_finseq_1(C)) ) )  &  (v1_relat_1(D) &  (v1_funct_1(D) &  (v3_card_1(D, B) & v1_finseq_1(D)) ) ) ) ) )  =>  (v1_relat_1(k7_finseq_1(C, D)) &  (v1_funct_1(k7_finseq_1(C, D)) &  (v3_card_1(k7_finseq_1(C, D), k2_xcmplx_0(A, B)) & v1_finseq_1(k7_finseq_1(C, D))) ) ) ) ) ).
fof(fc39_finseq_1, axiom,  (! [A, B, C] :  ( (v4_finseq_1(A) &  (v1_relat_1(B) &  (v5_relat_1(B, A) & v1_funct_1(B)) ) )  => v1_finseq_1(k1_funct_1(B, C))) ) ).
fof(fc3_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) => v3_ordinal1(k3_tarski(A))) ) ).
fof(fc3_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_relat_1(B))  => v1_relat_1(k2_xboole_0(A, B))) ) ).
fof(fc3_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) =>  (v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A))) ) ) ).
fof(fc4_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v5_ordinal1(A)) )  => v3_ordinal1(k9_xtuple_0(A))) ) ).
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_xtuple_0, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k9_xtuple_0(A))) ) ).
fof(fc54_finseq_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) & v1_finseq_1(B)) ) )  &  (v1_relat_1(C) &  (v5_relat_1(C, A) &  (v1_funct_1(C) & v1_finseq_1(C)) ) ) )  =>  (v1_relat_1(k7_finseq_1(B, C)) &  (v5_relat_1(k7_finseq_1(B, C), A) &  (v1_funct_1(k7_finseq_1(B, C)) & v1_finseq_1(k7_finseq_1(B, C))) ) ) ) ) ).
fof(fc55_finseq_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v6_valued_0(A) & v1_finseq_1(A)) ) )  &  (v1_relat_1(B) &  (v1_funct_1(B) &  (v6_valued_0(B) & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k7_finseq_1(A, B)) &  (v1_funct_1(k7_finseq_1(A, B)) &  (v6_valued_0(k7_finseq_1(A, B)) & v1_finseq_1(k7_finseq_1(A, B))) ) ) ) ) ).
fof(fc58_finseq_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_relat_1(k7_finseq_1(A, B)) &  (v1_funct_1(k7_finseq_1(A, B)) &  (v3_valued_0(k7_finseq_1(A, B)) & v1_finseq_1(k7_finseq_1(A, B))) ) ) ) ) ).
fof(fc59_finseq_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v1_valued_0(A) & v1_finseq_1(A)) ) )  &  (v1_relat_1(B) &  (v1_funct_1(B) &  (v1_valued_0(B) & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k7_finseq_1(A, B)) &  (v1_funct_1(k7_finseq_1(A, B)) &  (v1_valued_0(k7_finseq_1(A, B)) & v1_finseq_1(k7_finseq_1(A, B))) ) ) ) ) ).
fof(fc5_relat_1, axiom,  (! [A, B] : v1_relat_1(k1_tarski(k4_tarski(A, B)))) ).
fof(fc5_xreal_0, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => v1_xreal_0(k2_xcmplx_0(A, B))) ) ).
fof(fc5_xtuple_0, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k10_xtuple_0(A))) ) ).
fof(fc60_finseq_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v1_finseq_1(A)) ) )  &  (v1_relat_1(B) &  (v1_funct_1(B) &  (v2_valued_0(B) & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k7_finseq_1(A, B)) &  (v1_funct_1(k7_finseq_1(A, B)) &  (v2_valued_0(k7_finseq_1(A, B)) & v1_finseq_1(k7_finseq_1(A, B))) ) ) ) ) ).
fof(fc61_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) => v6_valued_0(k5_finseq_1(A))) ) ).
fof(fc64_finseq_1, axiom,  (! [A] :  (v1_xreal_0(A) => v3_valued_0(k5_finseq_1(A))) ) ).
fof(fc65_finseq_1, axiom,  (! [A] :  (v1_xcmplx_0(A) => v1_valued_0(k5_finseq_1(A))) ) ).
fof(fc66_finseq_1, axiom,  (! [A] :  (v1_xxreal_0(A) => v2_valued_0(k5_finseq_1(A))) ) ).
fof(fc6_finseq_1, axiom,  (! [A] :  (v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A))) ) ).
fof(fc6_ordinal1, axiom,  ( ~ (v1_xboole_0(k4_ordinal1))  & v3_ordinal1(k4_ordinal1)) ).
fof(fc6_relat_1, axiom,  (! [A, B] : v1_relat_1(k2_zfmisc_1(A, B))) ).
fof(fc6_xreal_0, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => v1_xreal_0(k3_xcmplx_0(A, B))) ) ).
fof(fc7_card_3, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  => v2_card_3(k1_tarski(A))) ) ).
fof(fc7_finseq_1, axiom,  (! [A] : v1_finseq_1(k5_finseq_1(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_ordinal1, axiom, v7_ordinal1(k5_ordinal1)).
fof(fc8_relat_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_relat_1(A))  =>  ~ (v1_xboole_0(k9_xtuple_0(A))) ) ) ).
fof(fc8_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, B), C))) => v1_relat_1(k9_xtuple_0(D))) ) ).
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_finset_1, axiom,  (! [A, B] :  ( (v1_finset_1(A) & v1_finset_1(B))  => v1_finset_1(k2_xboole_0(A, B))) ) ).
fof(fc9_ordinal1, axiom, v8_ordinal1(k5_ordinal1)).
fof(fc9_relat_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_relat_1(A))  =>  ~ (v1_xboole_0(k10_xtuple_0(A))) ) ) ).
fof(fc9_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, k2_zfmisc_1(B, C)))) => v1_relat_1(k10_xtuple_0(D))) ) ).
fof(fc9_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_2_0_goedelcp, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(B) & m1_subset_1(C, k1_zfmisc_1(k3_cqc_lang(B))))  =>  (r2_hidden(A, a_2_0_goedelcp(B, C)) <=>  (? [D] :  (m2_subset_1(D, k9_qc_lang1(B), k3_cqc_lang(B)) &  (A=k24_qc_lang1(B, D) & r2_tarski(D, C)) ) ) ) ) ) ).
fof(fraenkel_a_2_3_goedelcp, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(B) & m1_subset_1(C, k1_zfmisc_1(k3_qc_lang1(B))))  =>  (r2_hidden(A, a_2_3_goedelcp(B, C)) <=>  (? [D] :  (m1_subset_1(D, k1_qc_lang1(B)) &  (A=D &  ~ (r2_tarski(k2_qc_lang3(B, D), C)) ) ) ) ) ) ) ).
fof(fraenkel_a_2_4_goedelcp, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(B) &  (v1_funct_1(C) &  (v1_funct_2(C, k4_ordinal1, k2_zfmisc_1(k3_cqc_lang(B), k1_zfmisc_1(k3_qc_lang1(B)))) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k2_zfmisc_1(k3_cqc_lang(B), k1_zfmisc_1(k3_qc_lang1(B))))))) ) )  =>  (r2_hidden(A, a_2_4_goedelcp(B, C)) <=>  (? [D] :  (v7_ordinal1(D) & A=k1_xfamily(k8_nat_1(k2_zfmisc_1(k3_cqc_lang(B), k1_zfmisc_1(k3_qc_lang1(B))), C, D))) ) ) ) ) ).
fof(fraenkel_a_2_5_goedelcp, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(B) &  (v1_funct_1(C) &  (v1_funct_2(C, k4_ordinal1, k2_zfmisc_1(k3_cqc_lang(B), k1_zfmisc_1(k3_qc_lang1(B)))) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k2_zfmisc_1(k3_cqc_lang(B), k1_zfmisc_1(k3_qc_lang1(B))))))) ) )  =>  (r2_hidden(A, a_2_5_goedelcp(B, C)) <=>  (? [D] :  (v7_ordinal1(D) &  (A=k1_xfamily(k8_nat_1(k2_zfmisc_1(k3_cqc_lang(B), k1_zfmisc_1(k3_qc_lang1(B))), C, D)) & r2_tarski(D, k5_numbers)) ) ) ) ) ) ).
fof(fraenkel_a_3_2_goedelcp, axiom,  (! [A, B, C, D] :  ( (m1_qc_lang1(B) &  ( (v1_henmodel(C, B) & m1_subset_1(C, k1_zfmisc_1(k3_cqc_lang(B))))  &  (v1_funct_1(D) &  (v1_funct_2(D, k4_ordinal1, k3_cqc_lang(B)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k3_cqc_lang(B))))) ) ) )  =>  (r2_hidden(A, a_3_2_goedelcp(B, C, D)) <=>  (? [E] :  (m1_subset_1(E, k1_qc_lang1(B)) &  (A=E &  ~ (r2_tarski(k2_qc_lang3(B, E), k6_goedelcp(B, k4_subset_1(k3_cqc_lang(B), C, k6_domain_1(k3_cqc_lang(B), k3_funct_2(k4_ordinal1, k3_cqc_lang(B), D, k5_numbers)))))) ) ) ) ) ) ) ).
fof(fraenkel_a_3_3_goedelcp, axiom,  (! [A, B, C, D] :  ( (m1_qc_lang1(B) &  (v1_funct_1(C) &  (v1_funct_2(C, k4_ordinal1, k2_zfmisc_1(k3_cqc_lang(B), k1_zfmisc_1(k3_qc_lang1(B)))) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k2_zfmisc_1(k3_cqc_lang(B), k1_zfmisc_1(k3_qc_lang1(B))))))) ) )  =>  (r2_hidden(A, a_3_3_goedelcp(B, C, D)) <=>  (? [E] :  (v7_ordinal1(E) &  (A=k1_xfamily(k8_nat_1(k2_zfmisc_1(k3_cqc_lang(B), k1_zfmisc_1(k3_qc_lang1(B))), C, E)) & r2_tarski(E, D)) ) ) ) ) ) ).
fof(fraenkel_a_3_4_goedelcp, axiom,  (! [A, B, C, D] :  ( (m1_qc_lang1(B) &  ( (v1_funct_1(C) &  (v1_funct_2(C, k4_ordinal1, k2_zfmisc_1(k3_cqc_lang(B), k1_zfmisc_1(k3_qc_lang1(B)))) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k2_zfmisc_1(k3_cqc_lang(B), k1_zfmisc_1(k3_qc_lang1(B))))))) )  & v7_ordinal1(D)) )  =>  (r2_hidden(A, a_3_4_goedelcp(B, C, D)) <=>  (? [E] :  (v7_ordinal1(E) &  (A=k1_xfamily(k8_nat_1(k2_zfmisc_1(k3_cqc_lang(B), k1_zfmisc_1(k3_qc_lang1(B))), C, E)) & r2_tarski(E, k1_nat_1(D, 1))) ) ) ) ) ) ).
fof(fraenkel_a_3_5_goedelcp, axiom,  (! [A, B, C, D] :  ( (m1_qc_lang1(B) &  ( (v1_funct_1(C) &  (v1_funct_2(C, k4_ordinal1, k2_zfmisc_1(k3_cqc_lang(B), k1_zfmisc_1(k3_qc_lang1(B)))) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k2_zfmisc_1(k3_cqc_lang(B), k1_zfmisc_1(k3_qc_lang1(B))))))) )  & m1_subset_1(D, k4_ordinal1)) )  =>  (r2_hidden(A, a_3_5_goedelcp(B, C, D)) <=>  (? [E] :  (v7_ordinal1(E) &  (A=k1_xfamily(k8_nat_1(k2_zfmisc_1(k3_cqc_lang(B), k1_zfmisc_1(k3_qc_lang1(B))), C, E)) & r2_tarski(E, D)) ) ) ) ) ) ).
fof(fraenkel_a_3_6_goedelcp, axiom,  (! [A, B, C, D] :  ( (m1_qc_lang1(B) &  ( (v1_funct_1(C) &  (v1_funct_2(C, k4_ordinal1, k2_zfmisc_1(k3_cqc_lang(B), k1_zfmisc_1(k3_qc_lang1(B)))) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k2_zfmisc_1(k3_cqc_lang(B), k1_zfmisc_1(k3_qc_lang1(B))))))) )  & v7_ordinal1(D)) )  =>  (r2_hidden(A, a_3_6_goedelcp(B, C, D)) <=>  (? [E] :  (v7_ordinal1(E) &  (A=k1_xfamily(k8_nat_1(k2_zfmisc_1(k3_cqc_lang(B), k1_zfmisc_1(k3_qc_lang1(B))), C, E)) & r2_tarski(E, D)) ) ) ) ) ) ).
fof(fraenkel_a_3_7_goedelcp, axiom,  (! [A, B, C, D] :  ( (m1_qc_lang1(B) &  ( (v1_funct_1(C) &  (v1_funct_2(C, k4_ordinal1, k3_cqc_lang(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k3_cqc_lang(B))))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, k4_ordinal1, k2_zfmisc_1(k3_cqc_lang(B), k1_zfmisc_1(k3_qc_lang1(B)))) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k2_zfmisc_1(k3_cqc_lang(B), k1_zfmisc_1(k3_qc_lang1(B))))))) ) ) )  =>  (r2_hidden(A, a_3_7_goedelcp(B, C, D)) <=>  (? [E] :  (m1_subset_1(E, k1_qc_lang1(B)) &  (A=E &  ~ (r2_tarski(k2_qc_lang3(B, E), k2_xboole_0(k6_goedelcp(B, k6_domain_1(k3_cqc_lang(B), k3_funct_2(k4_ordinal1, k3_cqc_lang(B), C, k1_nat_1(k5_numbers, 1)))), k2_xfamily(k8_nat_1(k2_zfmisc_1(k3_cqc_lang(B), k1_zfmisc_1(k3_qc_lang1(B))), D, k5_numbers))))) ) ) ) ) ) ) ).
fof(fraenkel_a_3_8_goedelcp, axiom,  (! [A, B, C, D] :  ( (m1_qc_lang1(B) &  (m2_subset_1(C, k9_qc_lang1(B), k3_cqc_lang(B)) & m1_subset_1(D, k1_zfmisc_1(k3_qc_lang1(B)))) )  =>  (r2_hidden(A, a_3_8_goedelcp(B, C, D)) <=>  (? [E] :  (m1_subset_1(E, k1_qc_lang1(B)) &  (A=E &  ~ (r2_tarski(k2_qc_lang3(B, E), k4_subset_1(k3_qc_lang1(B), k6_goedelcp(B, k6_domain_1(k3_cqc_lang(B), C)), D))) ) ) ) ) ) ) ).
fof(fraenkel_a_3_9_goedelcp, axiom,  (! [A, B, C, D] :  ( (m1_qc_lang1(B) &  ( (v1_henmodel(C, B) & m1_subset_1(C, k1_zfmisc_1(k3_cqc_lang(B))))  & m2_subset_1(D, k9_qc_lang1(B), k3_cqc_lang(B))) )  =>  (r2_hidden(A, a_3_9_goedelcp(B, C, D)) <=>  (? [E] :  (m1_subset_1(E, k1_qc_lang1(B)) &  (A=E &  ~ (r2_tarski(k2_qc_lang3(B, E), k6_goedelcp(B, k4_subset_1(k3_cqc_lang(B), C, k6_domain_1(k3_cqc_lang(B), D))))) ) ) ) ) ) ) ).
fof(fraenkel_a_4_0_goedelcp, axiom,  (! [A, B, C, D, E] :  ( (m1_qc_lang1(B) &  ( (v1_funct_1(C) &  (v1_funct_2(C, k4_ordinal1, k3_cqc_lang(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k3_cqc_lang(B))))) )  &  (v7_ordinal1(D) & m1_subset_1(E, k1_zfmisc_1(k3_qc_lang1(B)))) ) )  =>  (r2_hidden(A, a_4_0_goedelcp(B, C, D, E)) <=>  (? [F] :  (m1_subset_1(F, k1_qc_lang1(B)) &  (A=F &  ~ (r2_tarski(k2_qc_lang3(B, F), k4_subset_1(k3_qc_lang1(B), E, k6_goedelcp(B, k6_domain_1(k3_cqc_lang(B), k3_funct_2(k4_ordinal1, k3_cqc_lang(B), C, k1_nat_1(D, 1))))))) ) ) ) ) ) ) ).
fof(fraenkel_a_4_1_goedelcp, axiom,  (! [A, B, C, D, E] :  ( (m1_qc_lang1(B) &  ( (v1_funct_1(C) &  (v1_funct_2(C, k4_ordinal1, k2_zfmisc_1(k3_cqc_lang(B), k1_zfmisc_1(k3_qc_lang1(B)))) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k2_zfmisc_1(k3_cqc_lang(B), k1_zfmisc_1(k3_qc_lang1(B))))))) )  &  (m2_subset_1(D, k9_qc_lang1(B), k3_cqc_lang(B)) & v7_ordinal1(E)) ) )  =>  (r2_hidden(A, a_4_1_goedelcp(B, C, D, E)) <=>  (? [F] :  (m1_subset_1(F, k1_qc_lang1(B)) &  (A=F &  ~ (r2_tarski(k2_qc_lang3(B, F), k2_xboole_0(k6_goedelcp(B, k6_domain_1(k3_cqc_lang(B), D)), k2_xfamily(k8_nat_1(k2_zfmisc_1(k3_cqc_lang(B), k1_zfmisc_1(k3_qc_lang1(B))), C, E))))) ) ) ) ) ) ) ).
fof(fraenkel_a_4_2_goedelcp, axiom,  (! [A, B, C, D, E] :  ( (m1_qc_lang1(B) &  ( (v1_funct_1(C) &  (v1_funct_2(C, k4_ordinal1, k3_cqc_lang(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k3_cqc_lang(B))))) )  &  ( (v1_funct_1(D) &  (v1_funct_2(D, k4_ordinal1, k2_zfmisc_1(k3_cqc_lang(B), k1_zfmisc_1(k3_qc_lang1(B)))) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k2_zfmisc_1(k3_cqc_lang(B), k1_zfmisc_1(k3_qc_lang1(B))))))) )  & v7_ordinal1(E)) ) )  =>  (r2_hidden(A, a_4_2_goedelcp(B, C, D, E)) <=>  (? [F] :  (m1_subset_1(F, k1_qc_lang1(B)) &  (A=F &  ~ (r2_tarski(k2_qc_lang3(B, F), k2_xboole_0(k6_goedelcp(B, k6_domain_1(k3_cqc_lang(B), k3_funct_2(k4_ordinal1, k3_cqc_lang(B), C, k1_nat_1(E, 1)))), k2_xfamily(k8_nat_1(k2_zfmisc_1(k3_cqc_lang(B), k1_zfmisc_1(k3_qc_lang1(B))), D, E))))) ) ) ) ) ) ) ).
fof(fraenkel_a_4_3_goedelcp, axiom,  (! [A, B, C, D, E] :  ( (m1_qc_lang1(B) &  ( (v1_funct_1(C) &  (v1_funct_2(C, k4_ordinal1, k3_cqc_lang(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k3_cqc_lang(B))))) )  &  ( (v1_funct_1(D) &  (v1_funct_2(D, k4_ordinal1, k2_zfmisc_1(k3_cqc_lang(B), k1_zfmisc_1(k3_qc_lang1(B)))) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k2_zfmisc_1(k3_cqc_lang(B), k1_zfmisc_1(k3_qc_lang1(B))))))) )  & v7_ordinal1(E)) ) )  =>  (r2_hidden(A, a_4_3_goedelcp(B, C, D, E)) <=>  (? [F] :  (m1_subset_1(F, k1_qc_lang1(B)) &  (A=F &  ~ (r2_tarski(k2_qc_lang3(B, F), k2_xboole_0(k6_goedelcp(B, k6_domain_1(k3_cqc_lang(B), k3_funct_2(k4_ordinal1, k3_cqc_lang(B), C, k1_nat_1(k1_nat_1(E, 1), 1)))), k2_xfamily(k8_nat_1(k2_zfmisc_1(k3_cqc_lang(B), k1_zfmisc_1(k3_qc_lang1(B))), D, k1_nat_1(E, 1)))))) ) ) ) ) ) ) ).
fof(fraenkel_a_4_4_goedelcp, axiom,  (! [A, B, C, D, E] :  ( (m1_qc_lang1(B) &  ( (v1_funct_1(C) &  (v1_funct_2(C, k4_ordinal1, k3_cqc_lang(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k3_cqc_lang(B))))) )  &  ( (v1_funct_1(D) &  (v1_funct_2(D, k4_ordinal1, k2_zfmisc_1(k3_cqc_lang(B), k1_zfmisc_1(k3_qc_lang1(B)))) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k2_zfmisc_1(k3_cqc_lang(B), k1_zfmisc_1(k3_qc_lang1(B))))))) )  & v7_ordinal1(E)) ) )  =>  (r2_hidden(A, a_4_4_goedelcp(B, C, D, E)) <=>  (? [F] :  (m1_subset_1(F, k1_qc_lang1(B)) &  (A=F &  ~ (r2_tarski(k2_qc_lang3(B, F), k2_xboole_0(k2_xfamily(k8_nat_1(k2_zfmisc_1(k3_cqc_lang(B), k1_zfmisc_1(k3_qc_lang1(B))), D, E)), k6_goedelcp(B, k6_domain_1(k3_cqc_lang(B), k3_funct_2(k4_ordinal1, k3_cqc_lang(B), C, k1_nat_1(E, 1))))))) ) ) ) ) ) ) ).
fof(idempotence_k2_xboole_0, axiom,  (! [A, B] : k2_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(involutiveness_k4_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => k4_xcmplx_0(k4_xcmplx_0(A))=A) ) ).
fof(l24_goedelcp, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  ~ ( (v4_card_3(A) &  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  ~ ( (k9_xtuple_0(B)=k4_ordinal1 & A=k10_xtuple_0(B)) ) ) ) ) ) ) ) ).
fof(projectivity_k1_card_1, axiom,  (! [A] : k1_card_1(k1_card_1(A))=k1_card_1(A)) ).
fof(projectivity_k3_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => k3_finseq_1(k3_finseq_1(A))=k3_finseq_1(A)) ) ).
fof(rc10_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v1_funct_1(B) &  (v1_finset_1(B) &  (v3_card_1(B, A) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ) ).
fof(rc10_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v1_funct_1(A) & v2_finset_1(A)) ) ) ) ).
fof(rc10_ordinal1, axiom,  (? [A] :  ~ (v8_ordinal1(A)) ) ).
fof(rc11_finseq_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v4_finseq_1(A)) ) ).
fof(rc11_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) ) ) ).
fof(rc12_finseq_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v1_finset_1(B) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ).
fof(rc12_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) & v9_ordinal1(A)) ) ).
fof(rc13_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) &  ~ (v9_ordinal1(A)) ) ) ).
fof(rc16_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) &  (v6_valued_0(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ) ).
fof(rc1_card_3, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v1_card_3(A)) ) ) ).
fof(rc1_cqc_lang, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & v7_ordinal1(B))  =>  (? [C] :  (m1_finseq_1(C, k2_qc_lang1(A)) &  (v1_relat_1(C) &  (v4_relat_1(C, k4_ordinal1) &  (v5_relat_1(C, k2_qc_lang1(A)) &  (v5_relat_1(C, k3_qc_lang1(A)) &  (v1_funct_1(C) &  (v3_card_1(C, B) & v1_finseq_1(C)) ) ) ) ) ) ) ) ) ) ).
fof(rc1_finseq_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, A))) &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) ) ) ) ) ).
fof(rc1_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_finset_1(A)) ) ).
fof(rc1_goedelcp, axiom,  (? [A] :  (m1_qc_lang1(A) & v4_card_3(A)) ) ).
fof(rc1_henmodel, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k3_cqc_lang(A))) & v1_henmodel(B, A)) ) ) ) ).
fof(rc1_ordinal1, axiom,  (? [A] :  (v1_ordinal1(A) & v2_ordinal1(A)) ) ).
fof(rc1_relat_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_relat_1(A)) ) ).
fof(rc1_relset_1, axiom,  (! [A, B] :  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_xboole_0(C) &  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ) ) ).
fof(rc1_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc1_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc1_xtuple_0, axiom,  (? [A] : v1_xtuple_0(A)) ).
fof(rc1_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(rc2_finseq_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v1_finset_1(B) & v1_finseq_1(B)) ) ) ) ) ) ).
fof(rc2_finset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_finset_1(B)) ) ) ).
fof(rc2_ordinal1, axiom,  (? [A] : v3_ordinal1(A)) ).
fof(rc2_relat_1, axiom,  (? [A] :  (v1_relat_1(A) & v2_relat_1(A)) ) ).
fof(rc2_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_xboole_0(B)) ) ) ).
fof(rc2_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc2_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(rc3_card_3, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v4_funct_1(A) & v2_card_3(A)) ) ) ).
fof(rc3_finseq_1, axiom,  (! [A] :  (? [B] :  (m1_finseq_1(B, A) &  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v1_xboole_0(B) &  (v1_finset_1(B) & v1_finseq_1(B)) ) ) ) ) ) ) ) ).
fof(rc3_finset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_xboole_0(B))  & v1_finset_1(B)) ) ) ) ) ).
fof(rc3_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_ordinal1(A) &  (v2_ordinal1(A) & v3_ordinal1(A)) ) ) ) ).
fof(rc3_relat_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ).
fof(rc3_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_subset_1(B, A)) ) ) ) ).
fof(rc3_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_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) ) ) ).
fof(rc4_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v1_funct_1(A) & v1_finset_1(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_card_3, axiom,  (? [A] : v5_card_3(A)) ).
fof(rc5_finseq_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v3_finseq_1(A)) ) ).
fof(rc5_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc5_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc5_xreal_0, axiom,  (? [A] :  (v8_ordinal1(A) &  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc5_xxreal_0, axiom,  (? [A] :  (v8_ordinal1(A) & v1_xxreal_0(A)) ) ).
fof(rc6_card_3, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v1_finset_1(A)) ) ) ) ).
fof(rc6_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ).
fof(rc6_finset_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_finset_1(C)) ) ) ) ) ) ).
fof(rc6_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc6_subset_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc7_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v2_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ) ).
fof(rc7_finset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  (? [C] :  ( ~ (v1_xboole_0(C))  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_finset_1(C)) ) ) ) ) ) ) ) ).
fof(rc7_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v7_ordinal1(A)) ) ).
fof(rc8_finseq_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_finseq_1(B, A) &  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  ( ~ (v1_xboole_0(B))  &  (v1_finset_1(B) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc8_finset_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_zfmisc_1(B))  & v1_finset_1(B)) ) ) ) ) ).
fof(rc8_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rc9_finseq_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  ( ~ (v1_xboole_0(B))  &  (v1_finset_1(B) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ) ) ).
fof(rc9_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) & v5_finset_1(A)) ) ) ).
fof(rc9_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rd1_finseq_1, axiom,  (! [A] : k1_funct_1(k9_finseq_1(A), 1)=A) ).
fof(rd1_xtuple_0, axiom,  (! [A, B] : k1_xtuple_0(k4_tarski(A, B))=A) ).
fof(rd2_xtuple_0, axiom,  (! [A, B] : k2_xtuple_0(k4_tarski(A, B))=B) ).
fof(rd3_xtuple_0, axiom,  (! [A] :  (v1_xtuple_0(A) => k4_tarski(k1_xtuple_0(A), k2_xtuple_0(A))=A) ) ).
fof(redefinition_k12_cqc_lang, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k3_qc_lang1(A)) & m1_subset_1(C, k3_cqc_lang(A))) )  => k12_cqc_lang(A, B, C)=k5_qc_lang2(A, B, C)) ) ).
fof(redefinition_k12_finseq_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(B, A))  => k12_finseq_1(A, B)=k5_finseq_1(B)) ) ).
fof(redefinition_k1_domain_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  (m1_subset_1(C, A) & m1_subset_1(D, B)) ) )  => k1_domain_1(A, B, C, D)=k4_tarski(C, D)) ) ).
fof(redefinition_k1_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & m1_subset_1(B, k4_ordinal1))  => k1_nat_1(A, B)=k2_xcmplx_0(A, B)) ) ).
fof(redefinition_k1_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  => k1_relset_1(A, B)=k9_xtuple_0(B)) ) ).
fof(redefinition_k1_xfamily, axiom,  (! [A] : k1_xfamily(A)=k1_xtuple_0(A)) ).
fof(redefinition_k2_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  => k2_relset_1(A, B)=k10_xtuple_0(B)) ) ).
fof(redefinition_k2_xfamily, axiom,  (! [A] : k2_xfamily(A)=k2_xtuple_0(A)) ).
fof(redefinition_k3_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => k3_finseq_1(A)=k1_card_1(A)) ) ).
fof(redefinition_k3_funct_2, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  & m1_subset_1(D, A)) )  => k3_funct_2(A, B, C, D)=k1_funct_1(C, D)) ) ).
fof(redefinition_k4_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_card_1, axiom,  (! [A] :  (v7_ordinal1(A) => k5_card_1(A)=k6_ordinal1(A)) ) ).
fof(redefinition_k5_cqc_lang, axiom,  (! [A] :  (m1_qc_lang1(A) => k5_cqc_lang(A)=k12_qc_lang1(A)) ) ).
fof(redefinition_k5_numbers, axiom, k5_numbers=k5_ordinal1).
fof(redefinition_k5_setfam_1, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) => k5_setfam_1(A, B)=k3_tarski(B)) ) ).
fof(redefinition_k6_cqc_lang, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k3_cqc_lang(A)))  => k6_cqc_lang(A, B)=k13_qc_lang1(A, B)) ) ).
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_k8_finseq_1, axiom,  (! [A, B, C] :  ( (m1_finseq_1(B, A) & m1_finseq_1(C, A))  => k8_finseq_1(A, B, C)=k7_finseq_1(B, C)) ) ).
fof(redefinition_k8_nat_1, axiom,  (! [A, B, C] :  ( ( (v1_funct_1(B) &  (v1_funct_2(B, k4_ordinal1, A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, A)))) )  & v7_ordinal1(C))  => k8_nat_1(A, B, C)=k1_funct_1(B, C)) ) ).
fof(redefinition_k9_cqc_lang, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k3_cqc_lang(A)) & m1_subset_1(C, k3_cqc_lang(A))) )  => k9_cqc_lang(A, B, C)=k3_qc_lang2(A, B, C)) ) ).
fof(redefinition_k9_finseq_1, axiom,  (! [A] : k9_finseq_1(A)=k5_finseq_1(A)) ).
fof(redefinition_k9_setfam_1, axiom,  (! [A] : k9_setfam_1(A)=k1_zfmisc_1(A)) ).
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_relset_1, axiom,  (! [A, B, C, D] :  ( (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))  =>  (r2_relset_1(A, B, C, D) <=> C=D) ) ) ).
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(reflexivity_r2_relset_1, axiom,  (! [A, B, C, D] :  ( (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))  => r2_relset_1(A, B, C, C)) ) ).
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(s2_nat_1__e26_37__goedelcp, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) &  (v1_funct_1(B) &  (v1_funct_2(B, k4_ordinal1, k2_zfmisc_1(k3_cqc_lang(A), k1_zfmisc_1(k3_qc_lang1(A)))) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k2_zfmisc_1(k3_cqc_lang(A), k1_zfmisc_1(k3_qc_lang1(A))))))) ) )  =>  ( ( (v1_finset_1(k2_xfamily(k8_nat_1(k2_zfmisc_1(k3_cqc_lang(A), k1_zfmisc_1(k3_qc_lang1(A))), B, k5_numbers))) & m1_subset_1(k2_xfamily(k8_nat_1(k2_zfmisc_1(k3_cqc_lang(A), k1_zfmisc_1(k3_qc_lang1(A))), B, k5_numbers)), k1_zfmisc_1(k3_qc_lang1(A))))  &  (! [C] :  (v7_ordinal1(C) =>  ( (v1_finset_1(k2_xfamily(k8_nat_1(k2_zfmisc_1(k3_cqc_lang(A), k1_zfmisc_1(k3_qc_lang1(A))), B, C))) & m1_subset_1(k2_xfamily(k8_nat_1(k2_zfmisc_1(k3_cqc_lang(A), k1_zfmisc_1(k3_qc_lang1(A))), B, C)), k1_zfmisc_1(k3_qc_lang1(A))))  =>  (v1_finset_1(k2_xfamily(k8_nat_1(k2_zfmisc_1(k3_cqc_lang(A), k1_zfmisc_1(k3_qc_lang1(A))), B, k1_nat_1(C, 1)))) & m1_subset_1(k2_xfamily(k8_nat_1(k2_zfmisc_1(k3_cqc_lang(A), k1_zfmisc_1(k3_qc_lang1(A))), B, k1_nat_1(C, 1))), k1_zfmisc_1(k3_qc_lang1(A)))) ) ) ) )  =>  (! [C] :  (v7_ordinal1(C) =>  (v1_finset_1(k2_xfamily(k8_nat_1(k2_zfmisc_1(k3_cqc_lang(A), k1_zfmisc_1(k3_qc_lang1(A))), B, C))) & m1_subset_1(k2_xfamily(k8_nat_1(k2_zfmisc_1(k3_cqc_lang(A), k1_zfmisc_1(k3_qc_lang1(A))), B, C)), k1_zfmisc_1(k3_qc_lang1(A)))) ) ) ) ) ) ).
fof(s2_nat_1__e33_37__goedelcp, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) &  (v1_funct_1(B) &  (v1_funct_2(B, k4_ordinal1, k1_zfmisc_1(k3_cqc_lang(A))) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k1_zfmisc_1(k3_cqc_lang(A)))))) ) )  =>  ( (v1_henmodel(k8_nat_1(k1_zfmisc_1(k3_cqc_lang(A)), B, k5_numbers), A) &  (! [C] :  (v7_ordinal1(C) =>  (v1_henmodel(k8_nat_1(k1_zfmisc_1(k3_cqc_lang(A)), B, C), A) => v1_henmodel(k8_nat_1(k1_zfmisc_1(k3_cqc_lang(A)), B, k1_nat_1(C, 1)), A)) ) ) )  =>  (! [C] :  (v7_ordinal1(C) => v1_henmodel(k8_nat_1(k1_zfmisc_1(k3_cqc_lang(A)), B, C), A)) ) ) ) ) ).
fof(s2_nat_1__e3_37_11__goedelcp, axiom,  (! [A, B, C, D] :  ( (m1_qc_lang1(A) &  ( (v1_funct_1(B) &  (v1_funct_2(B, k4_ordinal1, k3_cqc_lang(A)) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k3_cqc_lang(A))))) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, k4_ordinal1, k2_zfmisc_1(k3_cqc_lang(A), k1_zfmisc_1(k3_qc_lang1(A)))) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k2_zfmisc_1(k3_cqc_lang(A), k1_zfmisc_1(k3_qc_lang1(A))))))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, k4_ordinal1, k1_zfmisc_1(k3_cqc_lang(A))) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k1_zfmisc_1(k3_cqc_lang(A)))))) ) ) ) )  =>  ( ( (r1_tarski(k6_goedelcp(A, k3_funct_2(k4_ordinal1, k1_zfmisc_1(k3_cqc_lang(A)), D, k1_nat_1(k5_numbers, 1))), k2_xfamily(k8_nat_1(k2_zfmisc_1(k3_cqc_lang(A), k1_zfmisc_1(k3_qc_lang1(A))), C, k5_numbers))) &  ~ (r2_tarski(k2_qc_lang3(A, k31_qc_lang1(A, a_3_7_goedelcp(A, B, C))), k6_goedelcp(A, k4_subset_1(k3_cqc_lang(A), k3_funct_2(k4_ordinal1, k1_zfmisc_1(k3_cqc_lang(A)), D, k1_nat_1(k5_numbers, 1)), k6_domain_1(k3_cqc_lang(A), k3_funct_2(k4_ordinal1, k3_cqc_lang(A), B, k1_nat_1(k5_numbers, 1))))))) )  &  (! [E] :  (v7_ordinal1(E) =>  ( (r1_tarski(k6_goedelcp(A, k3_funct_2(k4_ordinal1, k1_zfmisc_1(k3_cqc_lang(A)), D, k1_nat_1(E, 1))), k2_xfamily(k8_nat_1(k2_zfmisc_1(k3_cqc_lang(A), k1_zfmisc_1(k3_qc_lang1(A))), C, E))) &  ~ (r2_tarski(k2_qc_lang3(A, k31_qc_lang1(A, a_4_2_goedelcp(A, B, C, E))), k6_goedelcp(A, k4_subset_1(k3_cqc_lang(A), k3_funct_2(k4_ordinal1, k1_zfmisc_1(k3_cqc_lang(A)), D, k1_nat_1(E, 1)), k6_domain_1(k3_cqc_lang(A), k3_funct_2(k4_ordinal1, k3_cqc_lang(A), B, k1_nat_1(E, 1))))))) )  =>  (r1_tarski(k6_goedelcp(A, k3_funct_2(k4_ordinal1, k1_zfmisc_1(k3_cqc_lang(A)), D, k1_nat_1(k1_nat_1(E, 1), 1))), k2_xfamily(k8_nat_1(k2_zfmisc_1(k3_cqc_lang(A), k1_zfmisc_1(k3_qc_lang1(A))), C, k1_nat_1(E, 1)))) &  ~ (r2_tarski(k2_qc_lang3(A, k31_qc_lang1(A, a_4_3_goedelcp(A, B, C, E))), k6_goedelcp(A, k4_subset_1(k3_cqc_lang(A), k3_funct_2(k4_ordinal1, k1_zfmisc_1(k3_cqc_lang(A)), D, k1_nat_1(k1_nat_1(E, 1), 1)), k6_domain_1(k3_cqc_lang(A), k3_funct_2(k4_ordinal1, k3_cqc_lang(A), B, k1_nat_1(k1_nat_1(E, 1), 1))))))) ) ) ) ) )  =>  (! [E] :  (v7_ordinal1(E) =>  (r1_tarski(k6_goedelcp(A, k3_funct_2(k4_ordinal1, k1_zfmisc_1(k3_cqc_lang(A)), D, k1_nat_1(E, 1))), k2_xfamily(k8_nat_1(k2_zfmisc_1(k3_cqc_lang(A), k1_zfmisc_1(k3_qc_lang1(A))), C, E))) &  ~ (r2_tarski(k2_qc_lang3(A, k31_qc_lang1(A, a_4_2_goedelcp(A, B, C, E))), k6_goedelcp(A, k4_subset_1(k3_cqc_lang(A), k3_funct_2(k4_ordinal1, k1_zfmisc_1(k3_cqc_lang(A)), D, k1_nat_1(E, 1)), k6_domain_1(k3_cqc_lang(A), k3_funct_2(k4_ordinal1, k3_cqc_lang(A), B, k1_nat_1(E, 1))))))) ) ) ) ) ) ) ).
fof(s2_recdef_1__e10_37__goedelcp, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  ( (v1_funct_1(B) &  (v1_funct_2(B, k4_ordinal1, k3_cqc_lang(A)) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k3_cqc_lang(A))))) )  & m1_subset_1(C, k2_zfmisc_1(k3_cqc_lang(A), k1_zfmisc_1(k3_qc_lang1(A))))) )  =>  ( (! [D] :  (v7_ordinal1(D) =>  (! [E] :  (m1_subset_1(E, k2_zfmisc_1(k3_cqc_lang(A), k1_zfmisc_1(k3_qc_lang1(A)))) =>  (? [F] :  (m1_subset_1(F, k2_zfmisc_1(k3_cqc_lang(A), k1_zfmisc_1(k3_qc_lang1(A)))) &  (? [G] :  (m1_subset_1(G, k1_zfmisc_1(k3_qc_lang1(A))) &  (? [H] :  (m1_subset_1(H, k1_zfmisc_1(k3_qc_lang1(A))) &  (G=k2_xfamily(E) &  (H=k4_subset_1(k3_qc_lang1(A), G, k6_goedelcp(A, k6_domain_1(k3_cqc_lang(A), k3_funct_2(k4_ordinal1, k3_cqc_lang(A), B, k1_nat_1(D, 1))))) & F=k1_domain_1(k3_cqc_lang(A), k1_zfmisc_1(k3_qc_lang1(A)), k9_cqc_lang(A, k6_cqc_lang(A, k3_funct_2(k4_ordinal1, k3_cqc_lang(A), B, k1_nat_1(D, 1))), k4_substut2(A, k5_goedelcp(A, B, k1_nat_1(D, 1)), k4_goedelcp(A, B, k1_nat_1(D, 1)), k2_qc_lang3(A, k31_qc_lang1(A, a_2_3_goedelcp(A, H))))), k4_subset_1(k3_qc_lang1(A), G, k24_qc_lang1(A, k9_cqc_lang(A, k6_cqc_lang(A, k3_funct_2(k4_ordinal1, k3_cqc_lang(A), B, k1_nat_1(D, 1))), k4_substut2(A, k5_goedelcp(A, B, k1_nat_1(D, 1)), k4_goedelcp(A, B, k1_nat_1(D, 1)), k2_qc_lang3(A, k31_qc_lang1(A, a_2_3_goedelcp(A, H))))))))) ) ) ) ) ) ) ) ) ) ) )  =>  (? [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, k4_ordinal1, k2_zfmisc_1(k3_cqc_lang(A), k1_zfmisc_1(k3_qc_lang1(A)))) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k2_zfmisc_1(k3_cqc_lang(A), k1_zfmisc_1(k3_qc_lang1(A))))))) )  &  (k3_funct_2(k4_ordinal1, k2_zfmisc_1(k3_cqc_lang(A), k1_zfmisc_1(k3_qc_lang1(A))), D, k5_numbers)=C &  (! [E] :  (v7_ordinal1(E) =>  (? [I] :  (m1_subset_1(I, k1_zfmisc_1(k3_qc_lang1(A))) &  (? [J] :  (m1_subset_1(J, k1_zfmisc_1(k3_qc_lang1(A))) &  (I=k2_xfamily(k1_funct_1(D, E)) &  (J=k4_subset_1(k3_qc_lang1(A), I, k6_goedelcp(A, k6_domain_1(k3_cqc_lang(A), k3_funct_2(k4_ordinal1, k3_cqc_lang(A), B, k1_nat_1(E, 1))))) & k3_funct_2(k4_ordinal1, k2_zfmisc_1(k3_cqc_lang(A), k1_zfmisc_1(k3_qc_lang1(A))), D, k1_nat_1(E, 1))=k1_domain_1(k3_cqc_lang(A), k1_zfmisc_1(k3_qc_lang1(A)), k9_cqc_lang(A, k6_cqc_lang(A, k3_funct_2(k4_ordinal1, k3_cqc_lang(A), B, k1_nat_1(E, 1))), k4_substut2(A, k5_goedelcp(A, B, k1_nat_1(E, 1)), k4_goedelcp(A, B, k1_nat_1(E, 1)), k2_qc_lang3(A, k31_qc_lang1(A, a_2_3_goedelcp(A, J))))), k4_subset_1(k3_qc_lang1(A), I, k24_qc_lang1(A, k9_cqc_lang(A, k6_cqc_lang(A, k3_funct_2(k4_ordinal1, k3_cqc_lang(A), B, k1_nat_1(E, 1))), k4_substut2(A, k5_goedelcp(A, B, k1_nat_1(E, 1)), k4_goedelcp(A, B, k1_nat_1(E, 1)), k2_qc_lang3(A, k31_qc_lang1(A, a_2_3_goedelcp(A, J))))))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(s5_funct_1__e15_37__goedelcp, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  ( (v1_henmodel(B, A) & m1_subset_1(B, k1_zfmisc_1(k3_cqc_lang(A))))  &  (v1_funct_1(C) &  (v1_funct_2(C, k4_ordinal1, k2_zfmisc_1(k3_cqc_lang(A), k1_zfmisc_1(k3_qc_lang1(A)))) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k2_zfmisc_1(k3_cqc_lang(A), k1_zfmisc_1(k3_qc_lang1(A))))))) ) ) )  =>  (? [D] :  ( (v1_relat_1(D) & v1_funct_1(D))  &  (k9_xtuple_0(D)=k4_ordinal1 &  (! [E] :  (r2_tarski(E, k4_ordinal1) => k1_funct_1(D, E)=k2_xboole_0(B, a_3_3_goedelcp(A, C, E))) ) ) ) ) ) ) ).
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_r2_relset_1, axiom,  (! [A, B, C, D] :  ( (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))  =>  (r2_relset_1(A, B, C, D) => r2_relset_1(A, B, D, C)) ) ) ).
fof(t10_calcul_1, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) )  =>  (r1_xxreal_0(1, k3_finseq_1(k7_finseq_1(B, k9_finseq_1(A)))) & r2_tarski(k3_finseq_1(k7_finseq_1(B, k9_finseq_1(A))), k1_relset_1(k4_ordinal1, k7_finseq_1(B, k9_finseq_1(A))))) ) ) ) ).
fof(t10_mcart_1, axiom,  (! [A] :  (! [B] :  (! [C] :  (r2_hidden(A, k2_zfmisc_1(B, C)) =>  (r2_hidden(k1_xtuple_0(A), B) & r2_hidden(k2_xtuple_0(A), C)) ) ) ) ) ).
fof(t11_henmodel, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  ( (v1_funct_1(B) &  (v1_funct_2(B, k4_ordinal1, k9_setfam_1(k3_cqc_lang(A))) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k9_setfam_1(k3_cqc_lang(A)))))) )  =>  ( (! [C] :  (v7_ordinal1(C) =>  (! [D] :  (v7_ordinal1(D) =>  ( (r2_tarski(D, k1_relset_1(k4_ordinal1, B)) & r2_tarski(C, k1_relset_1(k4_ordinal1, B)))  =>  (r1_xxreal_0(D, C) |  (v1_henmodel(k8_nat_1(k9_setfam_1(k3_cqc_lang(A)), B, C), A) & r1_tarski(k8_nat_1(k9_setfam_1(k3_cqc_lang(A)), B, C), k8_nat_1(k9_setfam_1(k3_cqc_lang(A)), B, D))) ) ) ) ) ) )  => v1_henmodel(k5_setfam_1(k3_cqc_lang(A), k2_relset_1(k9_setfam_1(k3_cqc_lang(A)), B)), A)) ) ) ) ) ).
fof(t11_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  (v7_ordinal1(B) => r1_xxreal_0(A, k2_xcmplx_0(A, B))) ) ) ) ).
fof(t13_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  (v7_ordinal1(B) =>  ( ~ (r1_xxreal_0(k1_nat_1(B, 1), A))  <=> r1_xxreal_0(A, B)) ) ) ) ) ).
fof(t19_cqc_sim1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m1_subset_1(B, k9_qc_lang1(A)) => v1_finset_1(k24_qc_lang1(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_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ( (r1_xxreal_0(A, B) & v2_xxreal_0(A))  => v2_xxreal_0(B)) ) ) ) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t20_goedelcp, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (v4_card_3(A) =>  ( ~ (v1_xboole_0(k1_goedelcp(A)))  & v4_card_3(k1_goedelcp(A))) ) ) ) ).
fof(t21_calcul_2, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m2_subset_1(B, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [C] :  (m2_finseq_1(C, k3_cqc_lang(A)) => r4_calcul_1(A, k8_finseq_1(k3_cqc_lang(A), k8_finseq_1(k3_cqc_lang(A), C, k12_finseq_1(k3_cqc_lang(A), B)), k12_finseq_1(k3_cqc_lang(A), B)))) ) ) ) ) ) ).
fof(t21_goedelcp, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k3_cqc_lang(A))) =>  (! [C] :  (m2_subset_1(C, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (r2_tarski(C, B) => r1_henmodel(A, B, C)) ) ) ) ) ) ) ).
fof(t22_goedelcp, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m2_subset_1(B, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [C] :  (m2_subset_1(C, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (k2_goedelcp(A, k12_cqc_lang(A, C, B))=C & k3_goedelcp(A, k12_cqc_lang(A, C, B))=B) ) ) ) ) ) ) ).
fof(t24_calcul_2, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m2_subset_1(B, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [C] :  (m2_subset_1(C, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [D] :  (m2_finseq_1(D, k3_cqc_lang(A)) =>  ( (r4_calcul_1(A, k8_finseq_1(k3_cqc_lang(A), D, k12_finseq_1(k3_cqc_lang(A), B))) & r4_calcul_1(A, k8_finseq_1(k3_cqc_lang(A), k8_finseq_1(k3_cqc_lang(A), D, k12_finseq_1(k3_cqc_lang(A), B)), k12_finseq_1(k3_cqc_lang(A), C))))  => r4_calcul_1(A, k8_finseq_1(k3_cqc_lang(A), D, k12_finseq_1(k3_cqc_lang(A), C)))) ) ) ) ) ) ) ) ) ).
fof(t24_goedelcp, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k3_cqc_lang(A))) =>  (r1_henmodel(A, B, k6_cqc_lang(A, k5_cqc_lang(A))) <=>  ~ (v1_henmodel(B, A)) ) ) ) ) ) ).
fof(t25_goedelcp, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m2_subset_1(B, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [C] :  (m2_finseq_1(C, k3_cqc_lang(A)) =>  (! [D] :  (m2_finseq_1(D, k3_cqc_lang(A)) =>  (r4_calcul_1(A, k8_finseq_1(k3_cqc_lang(A), C, k12_finseq_1(k3_cqc_lang(A), B))) =>  (r1_xxreal_0(k3_finseq_1(C), k5_numbers) | r4_calcul_1(A, k8_finseq_1(k3_cqc_lang(A), k8_finseq_1(k3_cqc_lang(A), k8_finseq_1(k3_cqc_lang(A), k1_calcul_1(k3_cqc_lang(A), C), D), k12_finseq_1(k3_cqc_lang(A), k2_calcul_1(A, C))), k12_finseq_1(k3_cqc_lang(A), B)))) ) ) ) ) ) ) ) ) ) ).
fof(t26_calcul_2, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m2_subset_1(B, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [C] :  (m2_subset_1(C, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [D] :  (m2_finseq_1(D, k3_cqc_lang(A)) =>  ( (r4_calcul_1(A, k8_finseq_1(k3_cqc_lang(A), k8_finseq_1(k3_cqc_lang(A), D, k12_finseq_1(k3_cqc_lang(A), B)), k12_finseq_1(k3_cqc_lang(A), C))) & r4_calcul_1(A, k8_finseq_1(k3_cqc_lang(A), k8_finseq_1(k3_cqc_lang(A), D, k12_finseq_1(k3_cqc_lang(A), k6_cqc_lang(A, B))), k12_finseq_1(k3_cqc_lang(A), C))))  => r4_calcul_1(A, k8_finseq_1(k3_cqc_lang(A), D, k12_finseq_1(k3_cqc_lang(A), C)))) ) ) ) ) ) ) ) ) ).
fof(t26_goedelcp, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m2_subset_1(B, k9_qc_lang1(A), k3_cqc_lang(A)) => k6_goedelcp(A, k6_domain_1(k3_cqc_lang(A), B))=k24_qc_lang1(A, B)) ) ) ) ).
fof(t27_goedelcp, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k3_cqc_lang(A))) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k3_cqc_lang(A))) => k6_goedelcp(A, k4_subset_1(k3_cqc_lang(A), B, C))=k4_subset_1(k3_qc_lang1(A), k6_goedelcp(A, B), k6_goedelcp(A, C))) ) ) ) ) ) ).
fof(t28_goedelcp, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k3_qc_lang1(A))) =>  ~ ( (v1_finset_1(B) &  (! [C] :  (m2_subset_1(C, k2_qc_lang1(A), k3_qc_lang1(A)) => r2_tarski(C, B)) ) ) ) ) ) ) ) ).
fof(t29_goedelcp, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k3_cqc_lang(A))) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k3_cqc_lang(A))) =>  (r1_tarski(B, C) => r1_tarski(k6_goedelcp(A, B), k6_goedelcp(A, C))) ) ) ) ) ) ) ).
fof(t2_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k3_xcmplx_0(A, k5_numbers)=k5_numbers) ) ).
fof(t2_funct_2, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (r1_tarski(k10_xtuple_0(B), A) =>  (v1_funct_1(B) &  (v1_funct_2(B, k9_xtuple_0(B), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k9_xtuple_0(B), A)))) ) ) ) ) ) ).
fof(t2_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ( (r1_xxreal_0(A, B) & v3_xxreal_0(B))  => v3_xxreal_0(A)) ) ) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(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_goedelcp, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m2_finseq_1(B, k3_cqc_lang(A)) => k6_goedelcp(A, k2_relset_1(k3_cqc_lang(A), B))=k3_calcul_1(A, B)) ) ) ) ).
fof(t30_qc_lang3, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m2_subset_1(B, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (? [C] :  (m1_subset_1(C, k1_qc_lang1(A)) & k2_qc_lang3(A, C)=B) ) ) ) ) ) ).
fof(t3_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k3_xcmplx_0(1, A)=A) ) ).
fof(t3_funct_1, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (r2_hidden(A, k9_xtuple_0(B)) => r2_tarski(k1_funct_1(B, A), k10_xtuple_0(B))) ) ) ) ).
fof(t3_qc_lang3, axiom,  (! [A] :  (m1_qc_lang1(A) => k24_qc_lang1(A, k12_qc_lang1(A))=k1_xboole_0) ) ).
fof(t3_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( (r1_xxreal_0(A, B) &  ( ~ (v3_xxreal_0(A))  & v3_xxreal_0(B)) ) ) ) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t44_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  (v7_ordinal1(B) =>  (r2_hidden(A, k5_card_1(B)) <=>  ~ (r1_xxreal_0(B, A)) ) ) ) ) ) ).
fof(t4_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k6_xcmplx_0(A, k5_numbers)=A) ) ).
fof(t4_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( (r1_xxreal_0(A, B) &  ( ~ (v2_xxreal_0(B))  & v2_xxreal_0(A)) ) ) ) ) ) ) ).
fof(t4_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r2_tarski(A, B) & m1_subset_1(B, k1_zfmisc_1(C)))  => m1_subset_1(A, C)) ) ) ) ).
fof(t4_xboole_1, axiom,  (! [A] :  (! [B] :  (! [C] : k2_xboole_0(k2_xboole_0(A, B), C)=k2_xboole_0(A, k2_xboole_0(B, C))) ) ) ).
fof(t51_calcul_1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m2_subset_1(B, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [C] :  (m2_subset_1(C, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [D] :  (m2_finseq_1(D, k3_cqc_lang(A)) =>  (r4_calcul_1(A, k8_finseq_1(k3_cqc_lang(A), D, k12_finseq_1(k3_cqc_lang(A), B))) => r4_calcul_1(A, k8_finseq_1(k3_cqc_lang(A), D, k12_finseq_1(k3_cqc_lang(A), k9_cqc_lang(A, B, C))))) ) ) ) ) ) ) ) ) ).
fof(t52_calcul_1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m2_subset_1(B, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [C] :  (m2_subset_1(C, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [D] :  (m2_finseq_1(D, k3_cqc_lang(A)) =>  (r4_calcul_1(A, k8_finseq_1(k3_cqc_lang(A), D, k12_finseq_1(k3_cqc_lang(A), C))) => r4_calcul_1(A, k8_finseq_1(k3_cqc_lang(A), D, k12_finseq_1(k3_cqc_lang(A), k9_cqc_lang(A, B, C))))) ) ) ) ) ) ) ) ) ).
fof(t59_calcul_1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m2_finseq_1(B, k3_cqc_lang(A)) =>  (! [C] :  (m2_finseq_1(C, k3_cqc_lang(A)) => k3_calcul_1(A, k8_finseq_1(k3_cqc_lang(A), B, C))=k4_subset_1(k3_qc_lang1(A), k3_calcul_1(A, B), k3_calcul_1(A, C))) ) ) ) ) ) ).
fof(t5_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k7_xcmplx_0(k5_numbers, A)=k5_numbers) ) ).
fof(t5_calcul_1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m2_subset_1(B, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [C] :  (m2_finseq_1(C, k3_cqc_lang(A)) =>  (k2_calcul_1(A, k8_finseq_1(k3_cqc_lang(A), C, k12_finseq_1(k3_cqc_lang(A), B)))=B & r2_relset_1(k4_ordinal1, k3_cqc_lang(A), k1_calcul_1(k3_cqc_lang(A), k8_finseq_1(k3_cqc_lang(A), C, k12_finseq_1(k3_cqc_lang(A), B))), C)) ) ) ) ) ) ) ).
fof(t5_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  (r1_xxreal_0(A, B) =>  (v8_ordinal1(B) |  (v3_xxreal_0(A) | v2_xxreal_0(B)) ) ) ) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t60_calcul_1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m2_subset_1(B, k9_qc_lang1(A), k3_cqc_lang(A)) => k3_calcul_1(A, k12_finseq_1(k3_cqc_lang(A), B))=k24_qc_lang1(A, B)) ) ) ) ).
fof(t61_calcul_1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m2_subset_1(B, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [C] :  (m2_subset_1(C, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [D] :  (m2_subset_1(D, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (! [E] :  (m2_subset_1(E, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (! [F] :  (m2_finseq_1(F, k3_cqc_lang(A)) =>  (r4_calcul_1(A, k8_finseq_1(k3_cqc_lang(A), k8_finseq_1(k3_cqc_lang(A), F, k12_finseq_1(k3_cqc_lang(A), k4_substut2(A, B, D, E))), k12_finseq_1(k3_cqc_lang(A), C))) =>  (r2_tarski(E, k3_calcul_1(A, k8_finseq_1(k3_cqc_lang(A), k8_finseq_1(k3_cqc_lang(A), F, k12_finseq_1(k3_cqc_lang(A), k12_cqc_lang(A, D, B))), k12_finseq_1(k3_cqc_lang(A), C)))) | r4_calcul_1(A, k8_finseq_1(k3_cqc_lang(A), k8_finseq_1(k3_cqc_lang(A), F, k12_finseq_1(k3_cqc_lang(A), k12_cqc_lang(A, D, B))), k12_finseq_1(k3_cqc_lang(A), 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(t6_henmodel, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k3_cqc_lang(A))) =>  ( ~ (v1_henmodel(B, A))  <=>  (! [C] :  (m2_subset_1(C, k9_qc_lang1(A), k3_cqc_lang(A)) => r1_henmodel(A, B, C)) ) ) ) ) ) ) ).
fof(t6_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  ~ ( ( ~ (A=k5_numbers)  &  (! [B] :  (v7_ordinal1(B) =>  ~ (A=k1_nat_1(B, 1)) ) ) ) ) ) ) ).
fof(t6_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  (r1_xxreal_0(A, B) =>  (v8_ordinal1(A) |  (v2_xxreal_0(B) | v3_xxreal_0(A)) ) ) ) ) ) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t7_qc_lang3, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m1_subset_1(B, k9_qc_lang1(A)) => k24_qc_lang1(A, k13_qc_lang1(A, B))=k24_qc_lang1(A, B)) ) ) ) ).
fof(t7_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( ( ~ (r1_xxreal_0(A, B))  &  ( ~ (v2_xxreal_0(A))  &  ~ (v3_xxreal_0(B)) ) ) ) ) ) ) ) ).
fof(t7_xboole_1, axiom,  (! [A] :  (! [B] : r1_tarski(A, k2_xboole_0(A, B))) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
fof(t8_henmodel, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k3_cqc_lang(A))) =>  (! [C] :  (m2_subset_1(C, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [D] :  (m2_subset_1(D, k9_qc_lang1(A), k3_cqc_lang(A)) =>  ~ ( (r1_henmodel(A, k4_subset_1(k3_cqc_lang(A), B, k6_domain_1(k3_cqc_lang(A), C)), D) &  (! [E] :  (m2_finseq_1(E, k3_cqc_lang(A)) =>  ~ ( (r1_tarski(k2_relset_1(k3_cqc_lang(A), E), B) & r4_calcul_1(A, k8_finseq_1(k3_cqc_lang(A), k8_finseq_1(k3_cqc_lang(A), E, k12_finseq_1(k3_cqc_lang(A), C)), k12_finseq_1(k3_cqc_lang(A), D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t8_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  (v7_ordinal1(B) =>  ~ ( (r1_xxreal_0(A, k1_nat_1(B, 1)) &  ( ~ (r1_xxreal_0(A, B))  &  ~ (A=k1_nat_1(B, 1)) ) ) ) ) ) ) ) ).
fof(t8_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( ( ~ (r1_xxreal_0(A, B))  &  ( ~ (v3_xxreal_0(B))  &  ~ (v2_xxreal_0(A)) ) ) ) ) ) ) ) ).
fof(t8_xboole_1, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r1_tarski(A, C) & r1_tarski(B, C))  => r1_tarski(k2_xboole_0(A, B), C)) ) ) ) ).
fof(t9_xboole_1, axiom,  (! [A] :  (! [B] :  (! [C] :  (r1_tarski(A, B) => r1_tarski(k2_xboole_0(A, C), k2_xboole_0(B, C))) ) ) ) ).
