% Mizar problem: t20_zf_refle,zf_refle,632,5 
fof(t20_zf_refle, conjecture,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  =>  (! [B] :  ( (v1_relat_1(B) &  (v2_relat_1(B) &  (v5_relat_1(B, A) &  (v5_ordinal1(B) &  (v1_funct_1(B) & v1_zf_refle(B, A)) ) ) ) )  =>  ( (r2_tarski(k4_ordinal1, A) &  ( (! [C] :  ( (v3_ordinal1(C) & m1_subset_1(C, A))  =>  (! [D] :  ( (v3_ordinal1(D) & m1_subset_1(D, A))  =>  (r2_tarski(C, D) => r1_tarski(k5_zf_refle(A, B, C), k5_zf_refle(A, B, D))) ) ) ) )  &  (! [C] :  ( (v3_ordinal1(C) & m1_subset_1(C, A))  =>  (v4_ordinal1(C) =>  (C=k1_xboole_0 | k5_zf_refle(A, B, C)=k3_card_3(k5_relat_1(B, C))) ) ) ) ) )  =>  (! [C] :  ( (v1_zf_lang(C) & m2_finseq_1(C, k4_ordinal1))  =>  (? [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, k2_ordinal1(A), k2_ordinal1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_ordinal1(A), k2_ordinal1(A))))) )  &  (v2_ordinal2(D) &  (v3_ordinal2(D) &  (! [E] :  ( (v3_ordinal1(E) & m1_subset_1(E, A))  =>  (k4_ordinal4(A, D, E)=E =>  (k1_xboole_0=E |  (! [F] :  ( (v1_funct_1(F) &  (v1_funct_2(F, k1_zf_lang, k5_zf_refle(A, B, E)) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang, k5_zf_refle(A, B, E))))) )  =>  (r1_zf_model(k4_zf_refle(A, B), k1_zf_lang1(k1_zf_lang, k5_zf_refle(A, B, E), k4_zf_refle(A, B), F), C) <=> r1_zf_model(k5_zf_refle(A, B, E), F, C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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(asymmetry_r2_xboole_0, axiom,  (! [A, B] :  (r2_xboole_0(A, B) =>  ~ (r2_xboole_0(B, A)) ) ) ).
fof(cc10_card_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_zfmisc_1(A))  => v3_card_1(A, 1)) ) ).
fof(cc10_ordinal1, axiom,  (! [A] :  (v6_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_ordinal1(B)) ) ) ) ).
fof(cc11_card_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_card_1(A))  =>  (! [B] :  (v3_card_1(B, A) =>  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(cc11_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v7_ordinal1(A)) ) ).
fof(cc12_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v1_zfmisc_1(A)) ) ).
fof(cc13_ordinal1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  ~ (v8_ordinal1(A)) ) ) ).
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_ordinal1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) )  =>  (! [B] :  (m1_subset_1(B, A) =>  ~ (v8_ordinal1(B)) ) ) ) ) ).
fof(cc17_ordinal1, axiom,  (! [A] :  ( ~ (v10_ordinal1(A))  => v1_setfam_1(A)) ) ).
fof(cc18_ordinal1, axiom,  (! [A] :  (v10_ordinal1(A) =>  ~ (v1_setfam_1(A)) ) ) ).
fof(cc19_ordinal1, axiom,  (! [A] :  (v1_setfam_1(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc1_card_1, axiom,  (! [A] :  (v1_card_1(A) => v3_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_card_5, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ~ (v1_xboole_0(A)) ) ) ).
fof(cc1_card_lar, axiom,  (! [A] :  ( (v3_ordinal1(A) &  ( ~ (v1_finset_1(A))  & v1_card_1(A)) )  =>  (v3_ordinal1(A) & v4_ordinal1(A)) ) ) ).
fof(cc1_classes2, axiom,  (! [A] :  (v2_classes1(A) => v1_classes1(A)) ) ).
fof(cc1_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_funct_1(A)) ) ).
fof(cc1_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (v1_ordinal1(A) & v2_ordinal1(A)) ) ) ).
fof(cc1_ordinal2, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  ( (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v5_ordinal1(B) & v1_funct_1(B)) ) )  =>  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v5_ordinal1(B) &  (v1_funct_1(B) & v1_ordinal2(B)) ) ) ) ) ) ) ) ).
fof(cc1_ordinal4, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_ordinal1(A), k2_ordinal1(A)))) =>  ( (v1_funct_1(B) & v1_funct_2(B, k2_ordinal1(A), k2_ordinal1(A)))  =>  (v5_ordinal1(B) &  (v1_funct_1(B) &  (v1_funct_2(B, k2_ordinal1(A), k2_ordinal1(A)) & v1_ordinal2(B)) ) ) ) ) ) ) ) ).
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(cc1_zf_lang, axiom,  (! [A] :  (m1_subset_1(A, k1_zf_lang) => v7_ordinal1(A)) ) ).
fof(cc20_ordinal1, axiom,  (! [A] :  ( ~ (v1_setfam_1(A))  => v10_ordinal1(A)) ) ).
fof(cc2_card_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_card_1(A)) ) ).
fof(cc2_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_card_lar, axiom,  (! [A] :  ( (v3_ordinal1(A) &  (v4_ordinal1(A) &  ~ (v1_xboole_0(A)) ) )  =>  (v3_ordinal1(A) &  ~ (v1_finset_1(A)) ) ) ) ).
fof(cc2_classes2, axiom,  (! [A] :  (v1_classes2(A) =>  (v1_ordinal1(A) & v2_classes1(A)) ) ) ).
fof(cc2_funct_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ) ).
fof(cc2_ordinal1, axiom,  (! [A] :  ( (v1_ordinal1(A) & v2_ordinal1(A))  => v3_ordinal1(A)) ) ).
fof(cc2_ordinal2, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, A) => v3_ordinal1(B)) ) ) ) ).
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(cc3_card_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_card_1(A)) ) ).
fof(cc3_card_lar, axiom,  (! [A] :  ( ( ~ (v1_finset_1(A))  &  (v1_card_1(A) &  ~ (v2_card_1(A)) ) )  =>  ( ~ (v1_finset_1(A))  &  (v1_card_1(A) &  ~ (v4_card_3(A)) ) ) ) ) ).
fof(cc3_classes2, axiom,  (! [A] :  ( (v1_ordinal1(A) & v2_classes1(A))  => v1_classes2(A)) ) ).
fof(cc3_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_funct_1(B)) ) ) ) ).
fof(cc3_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(cc4_card_1, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) => v1_finset_1(A)) ) ).
fof(cc4_card_3, axiom,  (! [A] :  (v5_card_3(A) =>  ( ~ (v1_finset_1(A))  & v4_card_3(A)) ) ) ).
fof(cc4_funct_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) ) ) ) ).
fof(cc4_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(cc5_card_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_finset_1(A)) ) ).
fof(cc5_card_3, axiom,  (! [A] :  ( ( ~ (v1_finset_1(A))  & v4_card_3(A))  => v5_card_3(A)) ) ).
fof(cc5_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) )  =>  ( ~ (v1_zfmisc_1(A))  &  (v1_relat_1(A) & v1_funct_1(A)) ) ) ) ).
fof(cc5_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(cc6_card_1, axiom,  (! [A] :  ( (v3_ordinal1(A) & v1_finset_1(A))  => v7_ordinal1(A)) ) ).
fof(cc6_card_3, axiom,  (! [A] :  (v1_finset_1(A) => v4_card_3(A)) ) ).
fof(cc6_funct_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) ) ) ) ).
fof(cc6_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(cc7_card_1, axiom,  (! [A] :  (v3_card_1(A, k5_ordinal1) => v1_xboole_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_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_funct_1(A)) ) ).
fof(cc7_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v7_ordinal1(A)) ) ).
fof(cc7_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(cc8_card_1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_card_1(A, k5_ordinal1)) ) ).
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_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, A) =>  (v1_relat_1(B) & v1_funct_1(B)) ) ) ) ) ).
fof(cc8_ordinal1, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) => v7_ordinal1(A)) ) ).
fof(cc8_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(cc9_card_1, axiom,  (! [A] :  (v3_card_1(A, 1) =>  ( ~ (v1_xboole_0(A))  & v1_zfmisc_1(A)) ) ) ).
fof(cc9_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_funct_1(B)) ) ) ) ).
fof(cc9_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v6_ordinal1(A)) ) ).
fof(commutativity_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, B)=k2_xboole_0(B, A)) ).
fof(commutativity_k3_xboole_0, axiom,  (! [A, B] : k3_xboole_0(A, B)=k3_xboole_0(B, A)) ).
fof(commutativity_k3_zf_refle, axiom,  (! [A, B, C] :  ( ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  &  ( (v3_ordinal1(B) & m1_subset_1(B, A))  &  (v3_ordinal1(C) & m1_subset_1(C, A)) ) )  => k3_zf_refle(A, B, C)=k3_zf_refle(A, C, B)) ) ).
fof(commutativity_k8_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(B, k1_zfmisc_1(A)) => k8_subset_1(A, B, C)=k8_subset_1(A, C, B)) ) ).
fof(connectedness_r1_ordinal1, axiom,  (! [A, B] :  ( (v3_ordinal1(A) & v3_ordinal1(B))  =>  (r1_ordinal1(A, B) | r1_ordinal1(B, A)) ) ) ).
fof(connectedness_r1_xxreal_0, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  =>  (r1_xxreal_0(A, B) | r1_xxreal_0(B, A)) ) ) ).
fof(d10_xboole_0, axiom,  (! [A] :  (! [B] :  (A=B <=>  (r1_tarski(A, B) & r1_tarski(B, A)) ) ) ) ).
fof(d12_ordinal2, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v5_ordinal1(A) &  (v1_funct_1(A) & v1_ordinal2(A)) ) )  =>  (v2_ordinal2(A) <=>  (! [B] :  (v3_ordinal1(B) =>  (! [C] :  (v3_ordinal1(C) =>  ( (r2_tarski(B, C) & r2_tarski(C, k9_xtuple_0(A)))  => r2_tarski(k1_funct_1(A, B), k1_funct_1(A, C))) ) ) ) ) ) ) ) ).
fof(d13_ordinal1, axiom, k5_ordinal1=k1_xboole_0).
fof(d13_ordinal2, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v5_ordinal1(A) &  (v1_funct_1(A) & v1_ordinal2(A)) ) )  =>  (v3_ordinal2(A) <=>  (! [B] :  (v3_ordinal1(B) =>  (! [C] :  (v3_ordinal1(C) =>  ( (r2_tarski(B, k9_xtuple_0(A)) &  (v4_ordinal1(B) & C=k1_funct_1(A, B)) )  =>  (B=k5_ordinal1 | r1_ordinal2(C, k5_relat_1(A, B))) ) ) ) ) ) ) ) ) ).
fof(d15_zf_lang, axiom,  (! [A] :  ( (v1_zf_lang(A) & m2_finseq_1(A, k4_ordinal1))  =>  (v7_zf_lang(A) <=>  (v2_zf_lang(A) | v3_zf_lang(A)) ) ) ) ).
fof(d1_funct_2, axiom,  (! [A] :  (! [B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  ( ( ~ (B=k1_xboole_0)  =>  (v1_funct_2(C, A, B) <=> A=k1_relset_1(A, C)) )  &  (B=k1_xboole_0 =>  (v1_funct_2(C, A, B) <=> C=k1_xboole_0) ) ) ) ) ) ) ).
fof(d1_ordinal1, axiom,  (! [A] : k1_ordinal1(A)=k2_xboole_0(A, k1_tarski(A))) ).
fof(d1_zf_lang, axiom, k1_zf_lang=a_0_0_zf_lang).
fof(d1_zf_lang1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  ( ~ (v1_xboole_0(C))  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  =>  (r1_tarski(B, C) => k1_zf_lang1(A, B, C, D)=D) ) ) ) ) ) ) ) ) ).
fof(d1_zf_refle, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  ( ( ~ (v1_xboole_0(B))  & v1_classes2(B))  =>  (! [C] :  ( (v3_ordinal1(C) & m1_subset_1(C, B))  => k1_zf_refle(A, B, C)=k3_card_3(k6_relat_1(B, k5_relat_1(A, k4_classes1(C))))) ) ) ) ) ) ).
fof(d2_funct_2, axiom,  (! [A] :  (! [B] :  (! [C] :  (C=k1_funct_2(A, B) <=>  (! [D] :  (r2_hidden(D, C) <=>  (? [E] :  ( (v1_relat_1(E) & v1_funct_1(E))  &  (D=E &  (k9_xtuple_0(E)=A & r1_tarski(k10_xtuple_0(E), B)) ) ) ) ) ) ) ) ) ) ).
fof(d2_ordinal1, axiom,  (! [A] :  (v1_ordinal1(A) <=>  (! [B] :  (r2_tarski(B, A) => r1_tarski(B, A)) ) ) ) ).
fof(d2_xboole_0, axiom, k1_xboole_0=o_0_0_xboole_0).
fof(d2_zf_refle, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  =>  (! [B] :  ( (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v5_ordinal1(B) & v1_funct_1(B)) ) )  =>  (v1_zf_refle(B, A) <=> k9_xtuple_0(B)=k2_ordinal1(A)) ) ) ) ) ).
fof(d30_zf_lang, axiom,  (! [A] :  ( (v1_zf_lang(A) & m2_finseq_1(A, k4_ordinal1))  =>  (v4_zf_lang(A) =>  (! [B] :  ( (v1_zf_lang(B) & m2_finseq_1(B, k4_ordinal1))  =>  (B=k19_zf_lang(A) <=> k5_zf_lang(B)=A) ) ) ) ) ) ).
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_tarski, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) <=>  (! [C] :  (r2_hidden(C, A) => r2_hidden(C, B)) ) ) ) ) ).
fof(d3_zf_lang, axiom,  (! [A] :  (m2_subset_1(A, k4_ordinal1, k1_zf_lang) =>  (! [B] :  (m2_subset_1(B, k4_ordinal1, k1_zf_lang) => k3_zf_lang(A, B)=k8_finseq_1(k4_ordinal1, k8_finseq_1(k4_ordinal1, k14_trees_3(k5_numbers), k14_trees_3(A)), k14_trees_3(B))) ) ) ) ).
fof(d4_card_3, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  => k3_card_3(A)=k3_tarski(k10_xtuple_0(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(d4_xboole_0, axiom,  (! [A] :  (! [B] :  (! [C] :  (C=k3_xboole_0(A, B) <=>  (! [D] :  (r2_hidden(D, C) <=>  (r2_hidden(D, A) & r2_hidden(D, B)) ) ) ) ) ) ) ).
fof(d4_zf_lang, axiom,  (! [A] :  (m2_subset_1(A, k4_ordinal1, k1_zf_lang) =>  (! [B] :  (m2_subset_1(B, k4_ordinal1, k1_zf_lang) => k4_zf_lang(A, B)=k8_finseq_1(k4_ordinal1, k8_finseq_1(k4_ordinal1, k14_trees_3(1), k14_trees_3(A)), k14_trees_3(B))) ) ) ) ).
fof(d5_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (v3_ordinal1(B) =>  (r1_ordinal1(A, B) <=>  (! [C] :  (v3_ordinal1(C) =>  (r2_tarski(C, A) => r2_tarski(C, B)) ) ) ) ) ) ) ) ).
fof(d5_ordinal2, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v5_ordinal1(A) & v1_funct_1(A)) )  => k4_ordinal2(A)=k3_ordinal2(k10_xtuple_0(A))) ) ).
fof(d5_zf_lang, axiom,  (! [A] :  (m2_finseq_1(A, k4_ordinal1) => k5_zf_lang(A)=k8_finseq_1(k4_ordinal1, k14_trees_3(2), A)) ) ).
fof(d6_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (! [C] :  (C=k7_relat_1(A, B) <=>  (! [D] :  (r2_hidden(D, C) <=>  (? [E] :  (r2_hidden(E, k9_xtuple_0(A)) &  (r2_hidden(E, B) & D=k1_funct_1(A, E)) ) ) ) ) ) ) ) ) ) ).
fof(d6_tarski, axiom,  (! [A] :  (! [B] :  (r3_tarski(A, B) <=>  (? [C] :  ( (! [D] :  ~ ( (r2_hidden(D, A) &  (! [E] :  ~ ( (r2_hidden(E, B) & r2_hidden(k4_tarski(D, E), C)) ) ) ) ) )  &  ( (! [D] :  ~ ( (r2_hidden(D, B) &  (! [E] :  ~ ( (r2_hidden(E, A) & r2_hidden(k4_tarski(E, D), C)) ) ) ) ) )  &  (! [D] :  (! [E] :  (! [F] :  (! [G] :  ( (r2_hidden(k4_tarski(D, E), C) & r2_hidden(k4_tarski(F, G), C))  =>  (D=F <=> E=G) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d6_zf_lang, axiom,  (! [A] :  (m2_finseq_1(A, k4_ordinal1) =>  (! [B] :  (m2_finseq_1(B, k4_ordinal1) => k6_zf_lang(A, B)=k8_finseq_1(k4_ordinal1, k8_finseq_1(k4_ordinal1, k14_trees_3(3), A), B)) ) ) ) ).
fof(d7_ordinal1, axiom,  (! [A] :  (v5_ordinal1(A) <=> v3_ordinal1(k9_xtuple_0(A))) ) ).
fof(d7_zf_lang, axiom,  (! [A] :  (m2_subset_1(A, k4_ordinal1, k1_zf_lang) =>  (! [B] :  (m2_finseq_1(B, k4_ordinal1) => k7_zf_lang(A, B)=k8_finseq_1(k4_ordinal1, k8_finseq_1(k4_ordinal1, k14_trees_3(4), k14_trees_3(A)), B)) ) ) ) ).
fof(d8_xboole_0, axiom,  (! [A] :  (! [B] :  (r2_xboole_0(A, B) <=>  (r1_tarski(A, B) &  ~ (A=B) ) ) ) ) ).
fof(d9_ordinal1, axiom,  (! [A] :  (! [B] :  (B=k2_ordinal1(A) <=>  (! [C] :  (r2_hidden(C, B) <=>  (r2_hidden(C, A) & v3_ordinal1(C)) ) ) ) ) ) ).
fof(dt_k10_xtuple_0, axiom, $true).
fof(dt_k14_trees_3, axiom,  (! [A] :  (v7_ordinal1(A) => m2_finseq_1(k14_trees_3(A), k4_ordinal1)) ) ).
fof(dt_k17_zf_lang, axiom,  (! [A] :  ( (v1_zf_lang(A) & m1_finseq_1(A, k4_ordinal1))  => m2_subset_1(k17_zf_lang(A), k4_ordinal1, k1_zf_lang)) ) ).
fof(dt_k18_zf_lang, axiom,  (! [A] :  ( (v1_zf_lang(A) & m1_finseq_1(A, k4_ordinal1))  => m2_subset_1(k18_zf_lang(A), k4_ordinal1, k1_zf_lang)) ) ).
fof(dt_k19_zf_lang, axiom,  (! [A] :  ( (v1_zf_lang(A) & m1_finseq_1(A, k4_ordinal1))  =>  (v1_zf_lang(k19_zf_lang(A)) & m2_finseq_1(k19_zf_lang(A), k4_ordinal1)) ) ) ).
fof(dt_k1_card_1, axiom,  (! [A] : v1_card_1(k1_card_1(A))) ).
fof(dt_k1_funct_1, axiom, $true).
fof(dt_k1_funct_2, axiom, $true).
fof(dt_k1_funct_7, axiom,  (! [A, B, C] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (v1_relat_1(k1_funct_7(A, B, C)) & v1_funct_1(k1_funct_7(A, B, C))) ) ) ).
fof(dt_k1_ordinal1, axiom, $true).
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_zf_lang, axiom, m1_subset_1(k1_zf_lang, k1_zfmisc_1(k4_ordinal1))).
fof(dt_k1_zf_lang1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  &  (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) ) ) )  =>  (v1_funct_1(k1_zf_lang1(A, B, C, D)) &  (v1_funct_2(k1_zf_lang1(A, B, C, D), A, C) & m1_subset_1(k1_zf_lang1(A, B, C, D), k1_zfmisc_1(k2_zfmisc_1(A, C)))) ) ) ) ).
fof(dt_k1_zf_model, axiom, $true).
fof(dt_k1_zf_refle, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k20_zf_lang, axiom,  (! [A] :  ( (v1_zf_lang(A) & m1_finseq_1(A, k4_ordinal1))  =>  (v1_zf_lang(k20_zf_lang(A)) & m2_finseq_1(k20_zf_lang(A), k4_ordinal1)) ) ) ).
fof(dt_k21_zf_lang, axiom,  (! [A] :  ( (v1_zf_lang(A) & m1_finseq_1(A, k4_ordinal1))  =>  (v1_zf_lang(k21_zf_lang(A)) & m2_finseq_1(k21_zf_lang(A), k4_ordinal1)) ) ) ).
fof(dt_k22_zf_lang, axiom,  (! [A] :  ( (v1_zf_lang(A) & m1_finseq_1(A, k4_ordinal1))  => m2_subset_1(k22_zf_lang(A), k4_ordinal1, k1_zf_lang)) ) ).
fof(dt_k23_zf_lang, axiom,  (! [A] :  ( (v1_zf_lang(A) & m1_finseq_1(A, k4_ordinal1))  =>  (v1_zf_lang(k23_zf_lang(A)) & m2_finseq_1(k23_zf_lang(A), k4_ordinal1)) ) ) ).
fof(dt_k2_ordinal1, axiom, $true).
fof(dt_k2_ordinal4, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  =>  (v3_ordinal1(k2_ordinal4(A)) & m1_subset_1(k2_ordinal4(A), 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_zf_lang1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(B) &  (v1_funct_2(B, k1_zf_lang, A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang, A)))) )  &  (m1_subset_1(C, k1_zf_lang) & m1_subset_1(D, A)) ) )  =>  (v1_funct_1(k2_zf_lang1(A, B, C, D)) &  (v1_funct_2(k2_zf_lang1(A, B, C, D), k1_zf_lang, A) & m1_subset_1(k2_zf_lang1(A, B, C, D), k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang, A)))) ) ) ) ).
fof(dt_k2_zf_model, axiom,  (! [A] :  ( (v1_zf_lang(A) & m1_finseq_1(A, k4_ordinal1))  => m1_subset_1(k2_zf_model(A), k1_zfmisc_1(k1_zf_lang))) ) ).
fof(dt_k2_zf_refle, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(A) &  (v5_ordinal1(A) &  (v1_funct_1(A) & v1_ordinal2(A)) ) )  &  ( ( ~ (v1_xboole_0(B))  & v1_classes2(B))  &  (v3_ordinal1(C) & m1_subset_1(C, B)) ) )  =>  (v3_ordinal1(k2_zf_refle(A, B, C)) & m1_subset_1(k2_zf_refle(A, B, C), B)) ) ) ).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_card_3, axiom, $true).
fof(dt_k3_funct_2, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  & m1_subset_1(D, A)) )  => m1_subset_1(k3_funct_2(A, B, C, D), B)) ) ).
fof(dt_k3_ordinal2, axiom,  (! [A] : v3_ordinal1(k3_ordinal2(A))) ).
fof(dt_k3_ordinal4, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  =>  (v3_ordinal1(k3_ordinal4(A)) &  ( ~ (v1_xboole_0(k3_ordinal4(A)))  & m1_subset_1(k3_ordinal4(A), A)) ) ) ) ).
fof(dt_k3_relat_1, axiom,  (! [A, B] : v1_relat_1(k3_relat_1(A, B))) ).
fof(dt_k3_tarski, axiom, $true).
fof(dt_k3_xboole_0, axiom, $true).
fof(dt_k3_zf_lang, axiom,  (! [A, B] :  ( (m1_subset_1(A, k1_zf_lang) & m1_subset_1(B, k1_zf_lang))  => m2_finseq_1(k3_zf_lang(A, B), k4_ordinal1)) ) ).
fof(dt_k3_zf_refle, axiom,  (! [A, B, C] :  ( ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  &  ( (v3_ordinal1(B) & m1_subset_1(B, A))  &  (v3_ordinal1(C) & m1_subset_1(C, A)) ) )  =>  (v3_ordinal1(k3_zf_refle(A, B, C)) & m1_subset_1(k3_zf_refle(A, B, C), A)) ) ) ).
fof(dt_k4_classes1, axiom, $true).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k4_ordinal2, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v5_ordinal1(A) & v1_funct_1(A)) )  => v3_ordinal1(k4_ordinal2(A))) ) ).
fof(dt_k4_ordinal4, axiom,  (! [A, B, C] :  ( ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  &  ( (v1_funct_1(B) &  (v1_funct_2(B, k2_ordinal1(A), k2_ordinal1(A)) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_ordinal1(A), k2_ordinal1(A))))) )  &  (v3_ordinal1(C) & m1_subset_1(C, A)) ) )  =>  (v3_ordinal1(k4_ordinal4(A, B, C)) & m1_subset_1(k4_ordinal4(A, B, C), A)) ) ) ).
fof(dt_k4_relat_1, axiom,  (! [A] : v1_relat_1(k4_relat_1(A))) ).
fof(dt_k4_tarski, axiom, $true).
fof(dt_k4_zf_lang, axiom,  (! [A, B] :  ( (m1_subset_1(A, k1_zf_lang) & m1_subset_1(B, k1_zf_lang))  => m2_finseq_1(k4_zf_lang(A, B), k4_ordinal1)) ) ).
fof(dt_k4_zf_refle, axiom,  (! [A, B] :  ( ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  &  (v1_relat_1(B) &  (v2_relat_1(B) &  (v5_relat_1(B, A) &  (v5_ordinal1(B) &  (v1_funct_1(B) & v1_zf_refle(B, A)) ) ) ) ) )  =>  ( ~ (v1_xboole_0(k4_zf_refle(A, B)))  & m1_subset_1(k4_zf_refle(A, B), k1_zfmisc_1(A))) ) ) ).
fof(dt_k5_finseq_1, axiom, $true).
fof(dt_k5_numbers, axiom, m1_subset_1(k5_numbers, k4_ordinal1)).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k5_ordinal4, axiom,  (! [A, B, C] :  ( ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  &  ( (v1_funct_1(B) &  (v1_funct_2(B, k2_ordinal1(A), k2_ordinal1(A)) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_ordinal1(A), k2_ordinal1(A))))) )  &  (v1_funct_1(C) &  (v1_funct_2(C, k2_ordinal1(A), k2_ordinal1(A)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_ordinal1(A), k2_ordinal1(A))))) ) ) )  =>  (v1_funct_1(k5_ordinal4(A, B, C)) &  (v1_funct_2(k5_ordinal4(A, B, C), k2_ordinal1(A), k2_ordinal1(A)) & m1_subset_1(k5_ordinal4(A, B, C), k1_zfmisc_1(k2_zfmisc_1(k2_ordinal1(A), k2_ordinal1(A))))) ) ) ) ).
fof(dt_k5_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => v1_relat_1(k5_relat_1(A, B))) ) ).
fof(dt_k5_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => m1_subset_1(k5_relset_1(A, B, C, D), k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) ).
fof(dt_k5_zf_lang, axiom,  (! [A] :  (m1_finseq_1(A, k4_ordinal1) => m2_finseq_1(k5_zf_lang(A), k4_ordinal1)) ) ).
fof(dt_k5_zf_refle, axiom,  (! [A, B, C] :  ( ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  &  ( (v1_relat_1(B) &  (v2_relat_1(B) &  (v5_relat_1(B, A) &  (v5_ordinal1(B) &  (v1_funct_1(B) & v1_zf_refle(B, A)) ) ) ) )  &  (v3_ordinal1(C) & m1_subset_1(C, A)) ) )  =>  ( ~ (v1_xboole_0(k5_zf_refle(A, B, C)))  & m1_subset_1(k5_zf_refle(A, B, C), A)) ) ) ).
fof(dt_k6_ordinal4, axiom,  (! [A, B] :  ( ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  &  (v3_ordinal1(B) & m1_subset_1(B, A)) )  =>  (v3_ordinal1(k6_ordinal4(A, B)) &  ( ~ (v1_xboole_0(k6_ordinal4(A, B)))  & m1_subset_1(k6_ordinal4(A, B), A)) ) ) ) ).
fof(dt_k6_relat_1, axiom,  (! [A, B] :  (v1_relat_1(B) => v1_relat_1(k6_relat_1(A, B))) ) ).
fof(dt_k6_zf_lang, axiom,  (! [A, B] :  ( (m1_finseq_1(A, k4_ordinal1) & m1_finseq_1(B, k4_ordinal1))  => m2_finseq_1(k6_zf_lang(A, B), k4_ordinal1)) ) ).
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_relat_1, axiom, $true).
fof(dt_k7_zf_lang, axiom,  (! [A, B] :  ( (m1_subset_1(A, k1_zf_lang) & m1_finseq_1(B, k4_ordinal1))  => m2_finseq_1(k7_zf_lang(A, B), k4_ordinal1)) ) ).
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_ordinal2, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v5_ordinal1(A) &  (v1_funct_1(A) & v1_ordinal2(A)) ) )  => v3_ordinal1(k8_ordinal2(A))) ) ).
fof(dt_k8_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(B, k1_zfmisc_1(A)) => m1_subset_1(k8_subset_1(A, B, C), k1_zfmisc_1(A))) ) ).
fof(dt_k9_funct_2, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  => m1_funct_2(k9_funct_2(A, B), A, B)) ) ).
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_funct_2, axiom,  (! [A, B] :  (! [C] :  (m1_funct_2(C, A, B) =>  ~ (v1_xboole_0(C)) ) ) ) ).
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_funct_2, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(B))  & m1_funct_2(C, A, B))  =>  (! [D] :  (m2_funct_2(D, A, B, C) =>  (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) ) ) ) ) ).
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_3_0_zf_refle, axiom,  (! [A, B, C] :  ( ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  &  ( (v1_relat_1(B) &  (v2_relat_1(B) &  (v5_relat_1(B, A) &  (v5_ordinal1(B) &  (v1_funct_1(B) & v1_zf_refle(B, A)) ) ) ) )  &  (v3_ordinal1(C) & m1_subset_1(C, A)) ) )  => m1_subset_1(o_3_0_zf_refle(A, B, C), k5_zf_refle(A, B, C))) ) ).
fof(existence_m1_finseq_1, axiom,  (! [A] :  (? [B] : m1_finseq_1(B, A)) ) ).
fof(existence_m1_funct_2, axiom,  (! [A, B] :  (? [C] : m1_funct_2(C, A, B)) ) ).
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_funct_2, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(B))  & m1_funct_2(C, A, B))  =>  (? [D] : m2_funct_2(D, A, B, C)) ) ) ).
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_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ( ~ (v1_finset_1(k1_card_1(A)))  & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc10_card_3, axiom, v5_card_3(k4_ordinal1)).
fof(fc10_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) )  => v1_setfam_1(k10_xtuple_0(A))) ) ).
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_relset_1, axiom,  (! [A, B] :  ( ( ( ~ (v1_xboole_0(A))  & v1_relat_1(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(k9_xtuple_0(A)))) )  =>  ( ~ (v1_xboole_0(k5_relat_1(A, B)))  & v1_relat_1(k5_relat_1(A, B))) ) ) ).
fof(fc10_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_xboole_0(k2_zfmisc_1(A, B))) ) ) ).
fof(fc11_funct_1, axiom,  (! [A, B] :  ( ( ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) ) )  & m1_subset_1(B, k9_xtuple_0(A)))  =>  ~ (v1_xboole_0(k1_funct_1(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_relset_1, axiom,  (! [A, B] :  ( ( ( ~ (v1_xboole_0(A))  & v1_relat_1(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(k9_xtuple_0(A)))) )  =>  ~ (v1_xboole_0(k7_relat_1(A, B))) ) ) ).
fof(fc12_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ~ (v1_finset_1(k1_zfmisc_1(A))) ) ) ).
fof(fc12_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) )  => v1_zfmisc_1(k10_xtuple_0(A))) ) ).
fof(fc12_ordinal1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v9_ordinal1(A))  & v1_relat_1(B))  =>  (v1_relat_1(k3_relat_1(B, A)) & v9_ordinal1(k3_relat_1(B, A))) ) ) ).
fof(fc12_relat_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v1_relat_1(B))  =>  (v1_xboole_0(k3_relat_1(A, B)) & v1_relat_1(k3_relat_1(A, B))) ) ) ).
fof(fc13_card_1, axiom,  (! [A, B] :  ( ( ~ (v1_finset_1(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_finset_1(k2_zfmisc_1(A, B))) ) ) ).
fof(fc13_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) )  =>  ~ (v1_zfmisc_1(k10_xtuple_0(A))) ) ) ).
fof(fc13_relat_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v1_relat_1(B))  =>  (v1_xboole_0(k3_relat_1(B, A)) & v1_relat_1(k3_relat_1(B, A))) ) ) ).
fof(fc14_card_1, axiom,  (! [A, B] :  ( ( ~ (v1_finset_1(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_finset_1(k2_zfmisc_1(B, A))) ) ) ).
fof(fc14_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  => v4_funct_1(k1_tarski(A))) ) ).
fof(fc15_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_relat_1(B) & v2_relat_1(B)) )  =>  (v1_relat_1(k3_relat_1(A, B)) & v2_relat_1(k3_relat_1(A, B))) ) ) ).
fof(fc16_card_1, axiom,  (! [A] : v3_card_1(k1_tarski(A), 1)) ).
fof(fc16_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_xboole_0(B))  =>  (v1_xboole_0(k5_relat_1(A, B)) & v1_relat_1(k5_relat_1(A, B))) ) ) ).
fof(fc17_card_1, axiom,  (! [A, B] :  ( (v1_card_1(A) &  (v1_relat_1(B) &  (v1_funct_1(B) & v3_card_1(B, A)) ) )  => v3_card_1(k9_xtuple_0(B), A)) ) ).
fof(fc17_funct_1, axiom,  (! [A, B, C] :  ( (v4_funct_1(A) &  (v1_relat_1(C) &  (v5_relat_1(C, A) & v1_funct_1(C)) ) )  =>  (v1_relat_1(k1_funct_1(C, B)) & v1_funct_1(k1_funct_1(C, B))) ) ) ).
fof(fc17_relat_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_xboole_0(k5_relat_1(A, B)) & v1_relat_1(k5_relat_1(A, B))) ) ) ).
fof(fc18_funct_1, axiom,  (! [A] :  ( ( ~ (v1_zfmisc_1(A))  &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  ~ (v1_zfmisc_1(k9_xtuple_0(A))) ) ) ).
fof(fc18_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_xboole_0(B))  =>  (v1_xboole_0(k6_relat_1(B, A)) & v1_relat_1(k6_relat_1(B, A))) ) ) ).
fof(fc19_funct_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v3_relat_1(A) & v1_funct_1(A)) )  => v1_xboole_0(k1_funct_1(A, B))) ) ).
fof(fc19_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_xboole_0(B))  => v1_xboole_0(k7_relat_1(A, B))) ) ).
fof(fc1_card_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (v1_xboole_0(k1_card_1(A)) & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc1_card_3, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_card_3(A)) )  =>  (v1_relat_1(k5_relat_1(A, B)) & v1_card_3(k5_relat_1(A, B))) ) ) ).
fof(fc1_card_5, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v5_ordinal1(A) & v1_ordinal2(A)) ) )  => v3_ordinal1(k3_card_3(A))) ) ).
fof(fc1_card_lar, axiom,  (! [A] :  ( (v3_ordinal1(A) &  ~ (v1_xboole_0(A)) )  =>  ~ (v1_xboole_0(k4_classes1(A))) ) ) ).
fof(fc1_funct_1, axiom,  (! [A, B] : v1_funct_1(k1_tarski(k4_tarski(A, B)))) ).
fof(fc1_ordinal1, axiom,  (! [A] :  ~ (v1_xboole_0(k1_ordinal1(A))) ) ).
fof(fc1_ordinal2, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v5_ordinal1(A) &  (v1_funct_1(A) & v1_ordinal2(A)) ) )  & v3_ordinal1(B))  =>  (v1_relat_1(k5_relat_1(A, B)) & v1_ordinal2(k5_relat_1(A, B))) ) ) ).
fof(fc1_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => v1_relat_1(k3_xboole_0(A, B))) ) ).
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_zf_lang, axiom,  ~ (v1_xboole_0(k1_zf_lang)) ).
fof(fc1_zf_lang1, axiom,  (! [A] :  ( (v1_zf_lang(A) & m1_finseq_1(A, k4_ordinal1))  => v1_finset_1(k1_zf_model(A))) ) ).
fof(fc20_relat_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v1_relat_1(A))  => v1_xboole_0(k7_relat_1(A, B))) ) ).
fof(fc23_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v3_relat_1(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v3_relat_1(k5_relat_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(fc25_relat_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) & v1_relat_1(A))  => v1_zfmisc_1(k10_xtuple_0(A))) ) ).
fof(fc26_relat_1, axiom,  (! [A, B, C] :  ( (v1_relat_1(C) & v5_relat_1(C, B))  =>  (v1_relat_1(k5_relat_1(C, A)) & v5_relat_1(k5_relat_1(C, A), B)) ) ) ).
fof(fc27_relat_1, axiom,  (! [A, B, C] :  ( (v1_relat_1(C) & v4_relat_1(C, B))  =>  (v1_relat_1(k5_relat_1(C, A)) &  (v4_relat_1(k5_relat_1(C, A), A) & v4_relat_1(k5_relat_1(C, A), B)) ) ) ) ).
fof(fc28_relat_1, axiom,  (! [A] :  (v1_relat_1(k4_relat_1(A)) &  (v4_relat_1(k4_relat_1(A), A) & v5_relat_1(k4_relat_1(A), A)) ) ) ).
fof(fc29_relat_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v5_relat_1(B, A))  & v1_relat_1(C))  =>  (v1_relat_1(k3_relat_1(C, B)) & v5_relat_1(k3_relat_1(C, B), A)) ) ) ).
fof(fc2_card_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (v8_ordinal1(k1_card_1(A)) & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc2_classes1, axiom,  (! [A] :  (v3_ordinal1(A) => v1_ordinal1(k4_classes1(A))) ) ).
fof(fc2_classes2, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  => v3_ordinal1(k2_ordinal1(A))) ) ).
fof(fc2_funct_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) & v1_funct_1(B)) )  =>  (v1_relat_1(k3_relat_1(A, B)) & v1_funct_1(k3_relat_1(A, B))) ) ) ).
fof(fc2_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  ( ~ (v1_xboole_0(k1_ordinal1(A)))  & v3_ordinal1(k1_ordinal1(A))) ) ) ).
fof(fc2_ordinal2, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v5_ordinal1(A) &  (v1_funct_1(A) & v1_ordinal2(A)) ) )  => v3_ordinal1(k1_funct_1(A, B))) ) ).
fof(fc2_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v4_relat_1(B, A))  & v1_relat_1(C))  => v4_relat_1(k3_xboole_0(B, C), A)) ) ).
fof(fc2_zf_lang, axiom,  (! [A, B] :  ( (m1_subset_1(A, k1_zf_lang) & m1_subset_1(B, k1_zf_lang))  => v1_zf_lang(k3_zf_lang(A, B))) ) ).
fof(fc30_relat_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v4_relat_1(B, A))  & v1_relat_1(C))  =>  (v1_relat_1(k3_relat_1(B, C)) & v4_relat_1(k3_relat_1(B, C), A)) ) ) ).
fof(fc31_relat_1, axiom,  (! [A, B, C] :  ( (v1_relat_1(C) & v4_relat_1(C, A))  =>  (v1_relat_1(k6_relat_1(B, C)) & v4_relat_1(k6_relat_1(B, C), A)) ) ) ).
fof(fc32_relat_1, axiom,  (! [A, B, C] :  ( (v1_relat_1(C) & v5_relat_1(C, B))  =>  (v1_relat_1(k6_relat_1(A, C)) &  (v5_relat_1(k6_relat_1(A, C), A) & v5_relat_1(k6_relat_1(A, C), B)) ) ) ) ).
fof(fc33_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v2_relat_1(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v2_relat_1(k5_relat_1(A, B))) ) ) ).
fof(fc3_card_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  ( ~ (v1_xboole_0(k1_card_1(A)))  & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc3_funct_1, axiom,  (! [A] :  (v1_relat_1(k4_relat_1(A)) & v1_funct_1(k4_relat_1(A))) ) ).
fof(fc3_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) => v3_ordinal1(k3_tarski(A))) ) ).
fof(fc3_ordinal4, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  =>  ~ (v1_xboole_0(k2_ordinal1(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_zf_lang, axiom,  (! [A, B] :  ( (m1_subset_1(A, k1_zf_lang) & m1_subset_1(B, k1_zf_lang))  => v1_zf_lang(k4_zf_lang(A, B))) ) ).
fof(fc4_card_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  ( ~ (v8_ordinal1(k1_card_1(A)))  & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc4_funct_1, axiom,  (! [A] :  (v1_relat_1(k4_relat_1(A)) & v2_funct_1(k4_relat_1(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_zf_lang, axiom,  (! [A] :  ( (v1_zf_lang(A) & m1_finseq_1(A, k4_ordinal1))  => v1_zf_lang(k5_zf_lang(A))) ) ).
fof(fc5_ordinal1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v5_ordinal1(A)) )  & v3_ordinal1(B))  =>  (v1_relat_1(k5_relat_1(A, B)) &  (v5_relat_1(k5_relat_1(A, B), k10_xtuple_0(A)) & v5_ordinal1(k5_relat_1(A, B))) ) ) ) ).
fof(fc5_relat_1, axiom,  (! [A, B] : v1_relat_1(k1_tarski(k4_tarski(A, B)))) ).
fof(fc5_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v5_relat_1(B, A))  & v1_relat_1(C))  => v5_relat_1(k3_xboole_0(B, C), A)) ) ).
fof(fc5_zf_lang, axiom,  (! [A, B] :  ( ( (v1_zf_lang(A) & m1_finseq_1(A, k4_ordinal1))  &  (v1_zf_lang(B) & m1_finseq_1(B, k4_ordinal1)) )  => v1_zf_lang(k6_zf_lang(A, B))) ) ).
fof(fc6_card_1, axiom, v1_card_1(k4_ordinal1)).
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_zf_lang, axiom,  (! [A, B] :  ( (m1_subset_1(A, k1_zf_lang) &  (v1_zf_lang(B) & m1_finseq_1(B, k4_ordinal1)) )  => v1_zf_lang(k7_zf_lang(A, B))) ) ).
fof(fc7_card_1, axiom, v2_card_1(k4_ordinal1)).
fof(fc7_card_3, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  => v2_card_3(k1_tarski(A))) ) ).
fof(fc7_funct_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v2_funct_1(B)) ) )  =>  (v1_relat_1(k3_relat_1(A, B)) & v2_funct_1(k3_relat_1(A, B))) ) ) ).
fof(fc7_ordinal1, axiom,  (! [A] :  ( (v3_ordinal1(A) & v7_ordinal1(A))  => v7_ordinal1(k1_ordinal1(A))) ) ).
fof(fc7_relset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  ( ~ (v1_xboole_0(k4_relat_1(A)))  & v1_relat_1(k4_relat_1(A))) ) ) ).
fof(fc8_card_1, axiom,  (! [A] :  (v1_finset_1(A) =>  (v1_finset_1(k1_card_1(A)) & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc8_funct_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v1_funct_1(k5_relat_1(A, B))) ) ) ).
fof(fc8_ordinal1, axiom, v7_ordinal1(k5_ordinal1)).
fof(fc8_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(fc9_card_1, axiom,  ~ (v1_finset_1(k4_ordinal1)) ).
fof(fc9_funct_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (v1_relat_1(k6_relat_1(A, B)) & v1_funct_1(k6_relat_1(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(fraenkel_a_0_0_zf_lang, axiom,  (! [A] :  (r2_hidden(A, a_0_0_zf_lang) <=>  (? [B] :  (m1_subset_1(B, k4_ordinal1) &  (A=B & r1_xxreal_0(5, B)) ) ) ) ) ).
fof(idempotence_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, A)=A) ).
fof(idempotence_k3_xboole_0, axiom,  (! [A, B] : k3_xboole_0(A, A)=A) ).
fof(idempotence_k3_zf_refle, axiom,  (! [A, B, C] :  ( ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  &  ( (v3_ordinal1(B) & m1_subset_1(B, A))  &  (v3_ordinal1(C) & m1_subset_1(C, A)) ) )  => k3_zf_refle(A, B, B)=B) ) ).
fof(idempotence_k8_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(B, k1_zfmisc_1(A)) => k8_subset_1(A, B, B)=B) ) ).
fof(irreflexivity_r2_xboole_0, axiom,  (! [A, B] :  ~ (r2_xboole_0(A, A)) ) ).
fof(projectivity_k1_card_1, axiom,  (! [A] : k1_card_1(k1_card_1(A))=k1_card_1(A)) ).
fof(rc10_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_card_1(B)) ) ) ) ).
fof(rc10_ordinal1, axiom,  (? [A] :  ~ (v8_ordinal1(A)) ) ).
fof(rc11_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) ) ) ).
fof(rc12_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) & v9_ordinal1(A)) ) ).
fof(rc13_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) &  ~ (v9_ordinal1(A)) ) ) ).
fof(rc1_card_1, axiom,  (? [A] : v1_card_1(A)) ).
fof(rc1_card_3, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v1_card_3(A)) ) ) ).
fof(rc1_card_5, axiom,  (? [A] :  (v1_ordinal1(A) &  (v2_ordinal1(A) &  (v3_ordinal1(A) &  ( ~ (v1_finset_1(A))  & v1_card_1(A)) ) ) ) ) ).
fof(rc1_classes2, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_classes2(A)) ) ).
fof(rc1_funct_1, axiom,  (? [A] :  (v1_relat_1(A) & v1_funct_1(A)) ) ).
fof(rc1_ordinal1, axiom,  (? [A] :  (v1_ordinal1(A) & v2_ordinal1(A)) ) ).
fof(rc1_ordinal2, axiom,  (? [A] :  (v1_ordinal1(A) &  (v2_ordinal1(A) &  (v3_ordinal1(A) & v4_ordinal1(A)) ) ) ) ).
fof(rc1_ordinal4, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  =>  (? [B] :  (m1_subset_1(B, A) & v3_ordinal1(B)) ) ) ) ).
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_zf_refle, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  =>  (? [B] :  (m1_subset_1(B, A) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc2_card_1, axiom,  (? [A] :  (v1_ordinal1(A) &  (v2_ordinal1(A) &  (v3_ordinal1(A) &  (v1_finset_1(A) & v1_card_1(A)) ) ) ) ) ).
fof(rc2_card_lar, axiom,  (! [A] :  ( ( ~ (v1_finset_1(A))  &  (v1_card_1(A) &  ~ (v4_card_3(A)) ) )  =>  (? [B] :  (m1_subset_1(B, A) &  (v1_ordinal1(B) &  (v2_ordinal1(B) &  (v3_ordinal1(B) &  ( ~ (v1_finset_1(B))  & v1_card_1(B)) ) ) ) ) ) ) ) ).
fof(rc2_classes2, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  =>  (? [B] :  (m1_subset_1(B, A) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc2_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ).
fof(rc2_ordinal1, axiom,  (? [A] : v3_ordinal1(A)) ).
fof(rc2_ordinal2, axiom,  (? [A] :  (v1_relat_1(A) &  (v5_ordinal1(A) &  (v1_funct_1(A) & v1_ordinal2(A)) ) ) ) ).
fof(rc2_ordinal4, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  =>  (? [B] :  (m1_subset_1(B, A) &  (v1_ordinal1(B) &  (v2_ordinal1(B) &  (v3_ordinal1(B) &  ~ (v1_xboole_0(B)) ) ) ) ) ) ) ) ).
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_zf_refle, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  =>  (? [B] :  (v1_relat_1(B) &  (v2_relat_1(B) &  (v5_relat_1(B, A) &  (v5_ordinal1(B) &  (v1_funct_1(B) & v1_zf_refle(B, A)) ) ) ) ) ) ) ) ).
fof(rc3_card_1, axiom,  (? [A] :  ~ (v1_finset_1(A)) ) ).
fof(rc3_card_3, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v4_funct_1(A) & v2_card_3(A)) ) ) ).
fof(rc3_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) ) ) ).
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(rc4_card_1, axiom,  (? [A] :  (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) ) ) ).
fof(rc4_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_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(rc5_card_1, axiom,  (? [A] :  (v1_ordinal1(A) &  (v2_ordinal1(A) &  (v3_ordinal1(A) &  (v7_ordinal1(A) &  ( ~ (v8_ordinal1(A))  & v1_card_1(A)) ) ) ) ) ) ).
fof(rc5_card_3, axiom,  (? [A] : v5_card_3(A)) ).
fof(rc5_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_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(rc6_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_finset_1(B)) ) ) ) ) ).
fof(rc6_card_3, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v1_finset_1(A)) ) ) ) ).
fof(rc6_funct_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) & v1_funct_1(C)) ) ) ) ) ).
fof(rc6_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc6_subset_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc7_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] : v3_card_1(B, A)) ) ) ).
fof(rc7_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v4_funct_1(A)) ) ).
fof(rc7_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v7_ordinal1(A)) ) ).
fof(rc8_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] :  (v1_relat_1(B) &  (v1_funct_1(B) & v3_card_1(B, A)) ) ) ) ) ).
fof(rc8_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rc9_card_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v3_card_1(B, 1)) ) ) ) ).
fof(rc9_funct_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) & v1_funct_1(B)) ) ) ) ) ).
fof(rc9_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rd1_card_1, axiom,  (! [A] :  (v1_card_1(A) => k1_card_1(A)=A) ) ).
fof(rd1_funct_1, axiom,  (! [A, B] :  (m1_subset_1(B, A) => k1_funct_1(k4_relat_1(A), B)=B) ) ).
fof(rd1_relat_1, axiom,  (! [A] : k9_xtuple_0(k4_relat_1(A))=A) ).
fof(rd2_relat_1, axiom,  (! [A] : k10_xtuple_0(k4_relat_1(A))=A) ).
fof(rd4_relat_1, axiom,  (! [A] :  (v1_relat_1(A) => k5_relat_1(A, k9_xtuple_0(A))=A) ) ).
fof(rd5_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => k5_relat_1(k5_relat_1(A, B), B)=k5_relat_1(A, B)) ) ).
fof(rd6_relat_1, axiom,  (! [A] :  (v1_relat_1(A) => k6_relat_1(k10_xtuple_0(A), A)=A) ) ).
fof(rd7_relat_1, axiom,  (! [A, B] :  (v1_relat_1(B) => k6_relat_1(A, k6_relat_1(A, B))=k6_relat_1(A, B)) ) ).
fof(rd8_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  => k5_relat_1(B, A)=B) ) ).
fof(rd9_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  => k6_relat_1(A, B)=B) ) ).
fof(redefinition_k14_trees_3, axiom,  (! [A] :  (v7_ordinal1(A) => k14_trees_3(A)=k5_finseq_1(A)) ) ).
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_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_zf_lang1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(B) &  (v1_funct_2(B, k1_zf_lang, A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang, A)))) )  &  (m1_subset_1(C, k1_zf_lang) & m1_subset_1(D, A)) ) )  => k2_zf_lang1(A, B, C, D)=k1_funct_7(B, C, D)) ) ).
fof(redefinition_k2_zf_model, axiom,  (! [A] :  ( (v1_zf_lang(A) & m1_finseq_1(A, k4_ordinal1))  => k2_zf_model(A)=k1_zf_model(A)) ) ).
fof(redefinition_k2_zf_refle, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(A) &  (v5_ordinal1(A) &  (v1_funct_1(A) & v1_ordinal2(A)) ) )  &  ( ( ~ (v1_xboole_0(B))  & v1_classes2(B))  &  (v3_ordinal1(C) & m1_subset_1(C, B)) ) )  => k2_zf_refle(A, B, C)=k1_zf_refle(A, B, C)) ) ).
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_k3_zf_refle, axiom,  (! [A, B, C] :  ( ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  &  ( (v3_ordinal1(B) & m1_subset_1(B, A))  &  (v3_ordinal1(C) & m1_subset_1(C, A)) ) )  => k3_zf_refle(A, B, C)=k2_xboole_0(B, C)) ) ).
fof(redefinition_k4_ordinal4, axiom,  (! [A, B, C] :  ( ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  &  ( (v1_funct_1(B) &  (v1_funct_2(B, k2_ordinal1(A), k2_ordinal1(A)) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_ordinal1(A), k2_ordinal1(A))))) )  &  (v3_ordinal1(C) & m1_subset_1(C, A)) ) )  => k4_ordinal4(A, B, C)=k1_funct_1(B, C)) ) ).
fof(redefinition_k4_zf_refle, axiom,  (! [A, B] :  ( ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  &  (v1_relat_1(B) &  (v2_relat_1(B) &  (v5_relat_1(B, A) &  (v5_ordinal1(B) &  (v1_funct_1(B) & v1_zf_refle(B, A)) ) ) ) ) )  => k4_zf_refle(A, B)=k3_card_3(B)) ) ).
fof(redefinition_k5_numbers, axiom, k5_numbers=k5_ordinal1).
fof(redefinition_k5_ordinal4, axiom,  (! [A, B, C] :  ( ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  &  ( (v1_funct_1(B) &  (v1_funct_2(B, k2_ordinal1(A), k2_ordinal1(A)) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_ordinal1(A), k2_ordinal1(A))))) )  &  (v1_funct_1(C) &  (v1_funct_2(C, k2_ordinal1(A), k2_ordinal1(A)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_ordinal1(A), k2_ordinal1(A))))) ) ) )  => k5_ordinal4(A, B, C)=k3_relat_1(B, C)) ) ).
fof(redefinition_k5_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => k5_relset_1(A, B, C, D)=k5_relat_1(C, D)) ) ).
fof(redefinition_k5_zf_refle, axiom,  (! [A, B, C] :  ( ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  &  ( (v1_relat_1(B) &  (v2_relat_1(B) &  (v5_relat_1(B, A) &  (v5_ordinal1(B) &  (v1_funct_1(B) & v1_zf_refle(B, A)) ) ) ) )  &  (v3_ordinal1(C) & m1_subset_1(C, A)) ) )  => k5_zf_refle(A, B, C)=k1_funct_1(B, C)) ) ).
fof(redefinition_k6_ordinal4, axiom,  (! [A, B] :  ( ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  &  (v3_ordinal1(B) & m1_subset_1(B, A)) )  => k6_ordinal4(A, B)=k1_ordinal1(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_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(B, k1_zfmisc_1(A)) => k8_subset_1(A, B, C)=k3_xboole_0(B, C)) ) ).
fof(redefinition_k9_funct_2, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  => k9_funct_2(A, B)=k1_funct_2(A, B)) ) ).
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_funct_2, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(B))  & m1_funct_2(C, A, B))  =>  (! [D] :  (m2_funct_2(D, A, B, C) <=> m1_subset_1(D, C)) ) ) ) ).
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_r1_funct_2, axiom,  (! [A, B, C, D, E, F] :  ( ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(D))  &  ( (v1_funct_1(E) &  (v1_funct_2(E, A, B) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(F) &  (v1_funct_2(F, C, D) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(C, D)))) ) ) ) )  =>  (r1_funct_2(A, B, C, D, E, F) <=> E=F) ) ) ).
fof(redefinition_r1_ordinal1, axiom,  (! [A, B] :  ( (v3_ordinal1(A) & v3_ordinal1(B))  =>  (r1_ordinal1(A, B) <=> r1_tarski(A, B)) ) ) ).
fof(redefinition_r2_funct_2, axiom,  (! [A, B, C, D] :  ( ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) )  =>  (r2_funct_2(A, B, C, D) <=> C=D) ) ) ).
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(redefinition_r2_wellord2, axiom,  (! [A, B] :  (r2_wellord2(A, B) <=> r3_tarski(A, B)) ) ).
fof(reflexivity_r1_funct_2, axiom,  (! [A, B, C, D, E, F] :  ( ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(D))  &  ( (v1_funct_1(E) &  (v1_funct_2(E, A, B) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(F) &  (v1_funct_2(F, C, D) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(C, D)))) ) ) ) )  => r1_funct_2(A, B, C, D, E, E)) ) ).
fof(reflexivity_r1_ordinal1, axiom,  (! [A, B] :  ( (v3_ordinal1(A) & v3_ordinal1(B))  => r1_ordinal1(A, A)) ) ).
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_funct_2, axiom,  (! [A, B, C, D] :  ( ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) )  => r2_funct_2(A, B, C, C)) ) ).
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(reflexivity_r2_wellord2, axiom,  (! [A, B] : r2_wellord2(A, A)) ).
fof(s1_partfun1__e31_30_1_5__zf_refle, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  &  ( (v1_relat_1(B) &  (v2_relat_1(B) &  (v5_relat_1(B, A) &  (v5_ordinal1(B) &  (v1_funct_1(B) & v1_zf_refle(B, A)) ) ) ) )  &  ( (v1_zf_lang(C) & m2_finseq_1(C, k4_ordinal1))  &  ( (v1_funct_1(D) &  (v1_funct_2(D, k1_zf_lang, k4_zf_refle(A, B)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang, k4_zf_refle(A, B))))) )  &  (v3_ordinal1(E) & m1_subset_1(E, A)) ) ) ) )  =>  (? [F] :  ( (v1_relat_1(F) & v1_funct_1(F))  &  (k9_xtuple_0(F)=k1_zf_lang &  (! [G] :  (r2_hidden(G, k1_zf_lang) =>  ( (r2_hidden(G, k2_zf_model(k5_zf_lang(k23_zf_lang(C)))) => k1_funct_1(F, G)=k1_funct_1(D, G))  &  ( ~ (r2_hidden(G, k2_zf_model(k5_zf_lang(k23_zf_lang(C)))))  => k1_funct_1(F, G)=o_3_0_zf_refle(A, B, E)) ) ) ) ) ) ) ) ) ).
fof(s1_zf_lang__e10_30__zf_refle, axiom,  (! [A, B] :  ( ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  &  (v1_relat_1(B) &  (v2_relat_1(B) &  (v5_relat_1(B, A) &  (v5_ordinal1(B) &  (v1_funct_1(B) & v1_zf_refle(B, A)) ) ) ) ) )  =>  ( ( (! [C] :  ( (v1_zf_lang(C) & m2_finseq_1(C, k4_ordinal1))  =>  (v7_zf_lang(C) =>  (? [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, k2_ordinal1(A), k2_ordinal1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_ordinal1(A), k2_ordinal1(A))))) )  &  (v2_ordinal2(D) &  (v3_ordinal2(D) &  (! [E] :  ( (v3_ordinal1(E) & m1_subset_1(E, A))  =>  (k4_ordinal4(A, D, E)=E =>  (k1_xboole_0=E |  (! [F] :  ( (v1_funct_1(F) &  (v1_funct_2(F, k1_zf_lang, k5_zf_refle(A, B, E)) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang, k5_zf_refle(A, B, E))))) )  =>  (r1_zf_model(k4_zf_refle(A, B), k1_zf_lang1(k1_zf_lang, k5_zf_refle(A, B, E), k4_zf_refle(A, B), F), C) <=> r1_zf_model(k5_zf_refle(A, B, E), F, C)) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [C] :  ( (v1_zf_lang(C) & m2_finseq_1(C, k4_ordinal1))  =>  ( (v4_zf_lang(C) &  (? [G] :  ( (v1_funct_1(G) &  (v1_funct_2(G, k2_ordinal1(A), k2_ordinal1(A)) & m1_subset_1(G, k1_zfmisc_1(k2_zfmisc_1(k2_ordinal1(A), k2_ordinal1(A))))) )  &  (v2_ordinal2(G) &  (v3_ordinal2(G) &  (! [H] :  ( (v3_ordinal1(H) & m1_subset_1(H, A))  =>  (k4_ordinal4(A, G, H)=H =>  (k1_xboole_0=H |  (! [I] :  ( (v1_funct_1(I) &  (v1_funct_2(I, k1_zf_lang, k5_zf_refle(A, B, H)) & m1_subset_1(I, k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang, k5_zf_refle(A, B, H))))) )  =>  (r1_zf_model(k4_zf_refle(A, B), k1_zf_lang1(k1_zf_lang, k5_zf_refle(A, B, H), k4_zf_refle(A, B), I), k19_zf_lang(C)) <=> r1_zf_model(k5_zf_refle(A, B, H), I, k19_zf_lang(C))) ) ) ) ) ) ) ) ) ) ) )  =>  (? [J] :  ( (v1_funct_1(J) &  (v1_funct_2(J, k2_ordinal1(A), k2_ordinal1(A)) & m1_subset_1(J, k1_zfmisc_1(k2_zfmisc_1(k2_ordinal1(A), k2_ordinal1(A))))) )  &  (v2_ordinal2(J) &  (v3_ordinal2(J) &  (! [K] :  ( (v3_ordinal1(K) & m1_subset_1(K, A))  =>  (k4_ordinal4(A, J, K)=K =>  (k1_xboole_0=K |  (! [L] :  ( (v1_funct_1(L) &  (v1_funct_2(L, k1_zf_lang, k5_zf_refle(A, B, K)) & m1_subset_1(L, k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang, k5_zf_refle(A, B, K))))) )  =>  (r1_zf_model(k4_zf_refle(A, B), k1_zf_lang1(k1_zf_lang, k5_zf_refle(A, B, K), k4_zf_refle(A, B), L), C) <=> r1_zf_model(k5_zf_refle(A, B, K), L, C)) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [C] :  ( (v1_zf_lang(C) & m2_finseq_1(C, k4_ordinal1))  =>  ( (v5_zf_lang(C) &  ( (? [M] :  ( (v1_funct_1(M) &  (v1_funct_2(M, k2_ordinal1(A), k2_ordinal1(A)) & m1_subset_1(M, k1_zfmisc_1(k2_zfmisc_1(k2_ordinal1(A), k2_ordinal1(A))))) )  &  (v2_ordinal2(M) &  (v3_ordinal2(M) &  (! [N] :  ( (v3_ordinal1(N) & m1_subset_1(N, A))  =>  (k4_ordinal4(A, M, N)=N =>  (k1_xboole_0=N |  (! [O] :  ( (v1_funct_1(O) &  (v1_funct_2(O, k1_zf_lang, k5_zf_refle(A, B, N)) & m1_subset_1(O, k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang, k5_zf_refle(A, B, N))))) )  =>  (r1_zf_model(k4_zf_refle(A, B), k1_zf_lang1(k1_zf_lang, k5_zf_refle(A, B, N), k4_zf_refle(A, B), O), k20_zf_lang(C)) <=> r1_zf_model(k5_zf_refle(A, B, N), O, k20_zf_lang(C))) ) ) ) ) ) ) ) ) ) )  &  (? [P] :  ( (v1_funct_1(P) &  (v1_funct_2(P, k2_ordinal1(A), k2_ordinal1(A)) & m1_subset_1(P, k1_zfmisc_1(k2_zfmisc_1(k2_ordinal1(A), k2_ordinal1(A))))) )  &  (v2_ordinal2(P) &  (v3_ordinal2(P) &  (! [Q] :  ( (v3_ordinal1(Q) & m1_subset_1(Q, A))  =>  (k4_ordinal4(A, P, Q)=Q =>  (k1_xboole_0=Q |  (! [R] :  ( (v1_funct_1(R) &  (v1_funct_2(R, k1_zf_lang, k5_zf_refle(A, B, Q)) & m1_subset_1(R, k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang, k5_zf_refle(A, B, Q))))) )  =>  (r1_zf_model(k4_zf_refle(A, B), k1_zf_lang1(k1_zf_lang, k5_zf_refle(A, B, Q), k4_zf_refle(A, B), R), k21_zf_lang(C)) <=> r1_zf_model(k5_zf_refle(A, B, Q), R, k21_zf_lang(C))) ) ) ) ) ) ) ) ) ) ) ) )  =>  (? [S] :  ( (v1_funct_1(S) &  (v1_funct_2(S, k2_ordinal1(A), k2_ordinal1(A)) & m1_subset_1(S, k1_zfmisc_1(k2_zfmisc_1(k2_ordinal1(A), k2_ordinal1(A))))) )  &  (v2_ordinal2(S) &  (v3_ordinal2(S) &  (! [T] :  ( (v3_ordinal1(T) & m1_subset_1(T, A))  =>  (k4_ordinal4(A, S, T)=T =>  (k1_xboole_0=T |  (! [U] :  ( (v1_funct_1(U) &  (v1_funct_2(U, k1_zf_lang, k5_zf_refle(A, B, T)) & m1_subset_1(U, k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang, k5_zf_refle(A, B, T))))) )  =>  (r1_zf_model(k4_zf_refle(A, B), k1_zf_lang1(k1_zf_lang, k5_zf_refle(A, B, T), k4_zf_refle(A, B), U), C) <=> r1_zf_model(k5_zf_refle(A, B, T), U, C)) ) ) ) ) ) ) ) ) ) ) ) ) )  &  (! [C] :  ( (v1_zf_lang(C) & m2_finseq_1(C, k4_ordinal1))  =>  ( (v6_zf_lang(C) &  (? [V] :  ( (v1_funct_1(V) &  (v1_funct_2(V, k2_ordinal1(A), k2_ordinal1(A)) & m1_subset_1(V, k1_zfmisc_1(k2_zfmisc_1(k2_ordinal1(A), k2_ordinal1(A))))) )  &  (v2_ordinal2(V) &  (v3_ordinal2(V) &  (! [W] :  ( (v3_ordinal1(W) & m1_subset_1(W, A))  =>  (k4_ordinal4(A, V, W)=W =>  (k1_xboole_0=W |  (! [X] :  ( (v1_funct_1(X) &  (v1_funct_2(X, k1_zf_lang, k5_zf_refle(A, B, W)) & m1_subset_1(X, k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang, k5_zf_refle(A, B, W))))) )  =>  (r1_zf_model(k4_zf_refle(A, B), k1_zf_lang1(k1_zf_lang, k5_zf_refle(A, B, W), k4_zf_refle(A, B), X), k23_zf_lang(C)) <=> r1_zf_model(k5_zf_refle(A, B, W), X, k23_zf_lang(C))) ) ) ) ) ) ) ) ) ) ) )  =>  (? [Y] :  ( (v1_funct_1(Y) &  (v1_funct_2(Y, k2_ordinal1(A), k2_ordinal1(A)) & m1_subset_1(Y, k1_zfmisc_1(k2_zfmisc_1(k2_ordinal1(A), k2_ordinal1(A))))) )  &  (v2_ordinal2(Y) &  (v3_ordinal2(Y) &  (! [Z] :  ( (v3_ordinal1(Z) & m1_subset_1(Z, A))  =>  (k4_ordinal4(A, Y, Z)=Z =>  (k1_xboole_0=Z |  (! [A1] :  ( (v1_funct_1(A1) &  (v1_funct_2(A1, k1_zf_lang, k5_zf_refle(A, B, Z)) & m1_subset_1(A1, k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang, k5_zf_refle(A, B, Z))))) )  =>  (r1_zf_model(k4_zf_refle(A, B), k1_zf_lang1(k1_zf_lang, k5_zf_refle(A, B, Z), k4_zf_refle(A, B), A1), C) <=> r1_zf_model(k5_zf_refle(A, B, Z), A1, C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C] :  ( (v1_zf_lang(C) & m2_finseq_1(C, k4_ordinal1))  =>  (? [B1] :  ( (v1_funct_1(B1) &  (v1_funct_2(B1, k2_ordinal1(A), k2_ordinal1(A)) & m1_subset_1(B1, k1_zfmisc_1(k2_zfmisc_1(k2_ordinal1(A), k2_ordinal1(A))))) )  &  (v2_ordinal2(B1) &  (v3_ordinal2(B1) &  (! [C1] :  ( (v3_ordinal1(C1) & m1_subset_1(C1, A))  =>  (k4_ordinal4(A, B1, C1)=C1 =>  (k1_xboole_0=C1 |  (! [D1] :  ( (v1_funct_1(D1) &  (v1_funct_2(D1, k1_zf_lang, k5_zf_refle(A, B, C1)) & m1_subset_1(D1, k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang, k5_zf_refle(A, B, C1))))) )  =>  (r1_zf_model(k4_zf_refle(A, B), k1_zf_lang1(k1_zf_lang, k5_zf_refle(A, B, C1), k4_zf_refle(A, B), D1), C) <=> r1_zf_model(k5_zf_refle(A, B, C1), D1, C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(s1_zf_refle__e4_30_1__zf_refle, axiom,  (! [A, B, C] :  ( ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  &  ( (v1_relat_1(B) &  (v2_relat_1(B) &  (v5_relat_1(B, A) &  (v5_ordinal1(B) &  (v1_funct_1(B) & v1_zf_refle(B, A)) ) ) ) )  &  (v1_zf_lang(C) & m2_finseq_1(C, k4_ordinal1)) ) )  =>  ( (! [D] :  (m1_subset_1(D, k9_funct_2(k1_zf_lang, k4_zf_refle(A, B))) =>  (? [E] :  ( (v3_ordinal1(E) & m1_subset_1(E, A))  &  (? [F] :  ( (v1_funct_1(F) &  (v1_funct_2(F, k1_zf_lang, k4_zf_refle(A, B)) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang, k4_zf_refle(A, B))))) )  &  (D=F &  ~ ( ( (! [G] :  (m2_subset_1(G, A, k4_zf_refle(A, B)) =>  ~ ( (r2_tarski(G, k1_funct_1(B, E)) & r1_zf_model(k4_zf_refle(A, B), k2_zf_lang1(k4_zf_refle(A, B), F, k22_zf_lang(C), G), k5_zf_lang(k23_zf_lang(C)))) ) ) )  &  ~ ( (E=k2_ordinal4(A) &  (! [G] :  (m2_subset_1(G, A, k4_zf_refle(A, B)) =>  ~ (r1_zf_model(k4_zf_refle(A, B), k2_zf_lang1(k4_zf_refle(A, B), F, k22_zf_lang(C), G), k5_zf_lang(k23_zf_lang(C)))) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (? [D] :  ( (v1_relat_1(D) & v1_funct_1(D))  &  (k9_xtuple_0(D)=k9_funct_2(k1_zf_lang, k4_zf_refle(A, B)) &  (! [E] :  (m1_subset_1(E, k9_funct_2(k1_zf_lang, k4_zf_refle(A, B))) =>  (? [H] :  ( (v3_ordinal1(H) & m1_subset_1(H, A))  &  (H=k1_funct_1(D, E) &  ( (? [I] :  ( (v1_funct_1(I) &  (v1_funct_2(I, k1_zf_lang, k4_zf_refle(A, B)) & m1_subset_1(I, k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang, k4_zf_refle(A, B))))) )  &  (E=I &  ~ ( ( (! [J] :  (m2_subset_1(J, A, k4_zf_refle(A, B)) =>  ~ ( (r2_tarski(J, k1_funct_1(B, H)) & r1_zf_model(k4_zf_refle(A, B), k2_zf_lang1(k4_zf_refle(A, B), I, k22_zf_lang(C), J), k5_zf_lang(k23_zf_lang(C)))) ) ) )  &  ~ ( (H=k2_ordinal4(A) &  (! [J] :  (m2_subset_1(J, A, k4_zf_refle(A, B)) =>  ~ (r1_zf_model(k4_zf_refle(A, B), k2_zf_lang1(k4_zf_refle(A, B), I, k22_zf_lang(C), J), k5_zf_lang(k23_zf_lang(C)))) ) ) ) ) ) ) ) ) )  &  (! [K] :  ( (v3_ordinal1(K) & m1_subset_1(K, A))  =>  ( (? [L] :  ( (v1_funct_1(L) &  (v1_funct_2(L, k1_zf_lang, k4_zf_refle(A, B)) & m1_subset_1(L, k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang, k4_zf_refle(A, B))))) )  &  (E=L &  ~ ( ( (! [M] :  (m2_subset_1(M, A, k4_zf_refle(A, B)) =>  ~ ( (r2_tarski(M, k1_funct_1(B, K)) & r1_zf_model(k4_zf_refle(A, B), k2_zf_lang1(k4_zf_refle(A, B), L, k22_zf_lang(C), M), k5_zf_lang(k23_zf_lang(C)))) ) ) )  &  ~ ( (K=k2_ordinal4(A) &  (! [M] :  (m2_subset_1(M, A, k4_zf_refle(A, B)) =>  ~ (r1_zf_model(k4_zf_refle(A, B), k2_zf_lang1(k4_zf_refle(A, B), L, k22_zf_lang(C), M), k5_zf_lang(k23_zf_lang(C)))) ) ) ) ) ) ) ) ) )  => r1_ordinal1(H, K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(s2_card_2__e6_30_1_5_1__zf_refle, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  &  ( (v1_relat_1(B) &  (v2_relat_1(B) &  (v5_relat_1(B, A) &  (v5_ordinal1(B) &  (v1_funct_1(B) & v1_zf_refle(B, A)) ) ) ) )  &  ( (v1_zf_lang(C) & m2_finseq_1(C, k4_ordinal1))  &  (v1_funct_1(D) &  (v1_funct_2(D, k1_zf_lang, k4_zf_refle(A, B)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang, k4_zf_refle(A, B))))) ) ) ) )  =>  ( ( ~ (k2_zf_model(k5_zf_lang(k23_zf_lang(C)))=k1_xboole_0)  &  ( (! [E] :  (! [F] :  ( (! [G] :  ( (v3_ordinal1(G) & m1_subset_1(G, A))  =>  (r2_tarski(k1_funct_1(D, E), k5_zf_refle(A, B, G)) => r2_tarski(k1_funct_1(D, F), k5_zf_refle(A, B, G))) ) )  |  (! [H] :  ( (v3_ordinal1(H) & m1_subset_1(H, A))  =>  (r2_tarski(k1_funct_1(D, F), k5_zf_refle(A, B, H)) => r2_tarski(k1_funct_1(D, E), k5_zf_refle(A, B, H))) ) ) ) ) )  &  (! [E] :  (! [F] :  (! [I] :  ( ( (! [J] :  ( (v3_ordinal1(J) & m1_subset_1(J, A))  =>  (r2_tarski(k1_funct_1(D, E), k5_zf_refle(A, B, J)) => r2_tarski(k1_funct_1(D, F), k5_zf_refle(A, B, J))) ) )  &  (! [K] :  ( (v3_ordinal1(K) & m1_subset_1(K, A))  =>  (r2_tarski(k1_funct_1(D, F), k5_zf_refle(A, B, K)) => r2_tarski(k1_funct_1(D, I), k5_zf_refle(A, B, K))) ) ) )  =>  (! [L] :  ( (v3_ordinal1(L) & m1_subset_1(L, A))  =>  (r2_tarski(k1_funct_1(D, E), k5_zf_refle(A, B, L)) => r2_tarski(k1_funct_1(D, I), k5_zf_refle(A, B, L))) ) ) ) ) ) ) ) )  =>  (? [E] :  (r2_hidden(E, k2_zf_model(k5_zf_lang(k23_zf_lang(C)))) &  (! [F] :  (r2_hidden(F, k2_zf_model(k5_zf_lang(k23_zf_lang(C)))) =>  (! [M] :  ( (v3_ordinal1(M) & m1_subset_1(M, A))  =>  (r2_tarski(k1_funct_1(D, E), k5_zf_refle(A, B, M)) => r2_tarski(k1_funct_1(D, F), k5_zf_refle(A, B, M))) ) ) ) ) ) ) ) ) ) ).
fof(s2_zf_refle__e8_30_1__zf_refle, axiom,  (! [A, B, C] :  ( ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  &  ( (v1_relat_1(B) &  (v2_relat_1(B) &  (v5_relat_1(B, A) &  (v5_ordinal1(B) &  (v1_funct_1(B) & v1_zf_refle(B, A)) ) ) ) )  &  (v1_relat_1(C) & v1_funct_1(C)) ) )  =>  ( (! [D] :  ( (v3_ordinal1(D) & m1_subset_1(D, A))  =>  (? [E] :  ( (v3_ordinal1(E) & m1_subset_1(E, A))  & E=k3_ordinal2(k7_relat_1(C, k9_funct_2(k1_zf_lang, k5_zf_refle(A, B, D))))) ) ) )  =>  (? [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, k2_ordinal1(A), k2_ordinal1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_ordinal1(A), k2_ordinal1(A))))) )  &  (! [E] :  ( (v3_ordinal1(E) & m1_subset_1(E, A))  => k4_ordinal4(A, D, E)=k3_ordinal2(k7_relat_1(C, k9_funct_2(k1_zf_lang, k5_zf_refle(A, B, E))))) ) ) ) ) ) ) ).
fof(s3_zf_refle__e10_30_1__zf_refle, axiom,  (! [A, B] :  ( ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  &  (v1_funct_1(B) &  (v1_funct_2(B, k2_ordinal1(A), k2_ordinal1(A)) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_ordinal1(A), k2_ordinal1(A))))) ) )  =>  (? [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, k2_ordinal1(A), k2_ordinal1(A)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_ordinal1(A), k2_ordinal1(A))))) )  &  (k4_ordinal4(A, C, k2_ordinal4(A))=k4_ordinal4(A, B, k2_ordinal4(A)) &  ( (! [D] :  ( (v3_ordinal1(D) & m1_subset_1(D, A))  => k4_ordinal4(A, C, k6_ordinal4(A, D))=k6_ordinal4(A, k3_zf_refle(A, k4_ordinal4(A, B, k6_ordinal4(A, D)), k4_ordinal4(A, C, D)))) )  &  (! [D] :  ( (v3_ordinal1(D) & m1_subset_1(D, A))  =>  (v4_ordinal1(D) =>  (D=k2_ordinal4(A) | k4_ordinal4(A, C, D)=k2_zf_refle(k5_relset_1(k2_ordinal1(A), k2_ordinal1(A), C, D), A, D)) ) ) ) ) ) ) ) ) ) ).
fof(s4_zf_refle__e25_30_1__zf_refle, axiom,  (! [A, B, C] :  ( ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  &  ( (v1_funct_1(B) &  (v1_funct_2(B, k2_ordinal1(A), k2_ordinal1(A)) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_ordinal1(A), k2_ordinal1(A))))) )  &  (v1_funct_1(C) &  (v1_funct_2(C, k2_ordinal1(A), k2_ordinal1(A)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_ordinal1(A), k2_ordinal1(A))))) ) ) )  =>  ( (r1_ordinal1(k1_funct_1(B, k2_ordinal4(A)), k1_funct_1(C, k2_ordinal4(A))) &  ( (! [D] :  ( (v3_ordinal1(D) & m1_subset_1(D, A))  =>  (r1_ordinal1(k1_funct_1(B, D), k1_funct_1(C, D)) => r1_ordinal1(k1_funct_1(B, k6_ordinal4(A, D)), k1_funct_1(C, k6_ordinal4(A, D)))) ) )  &  (! [D] :  ( (v3_ordinal1(D) & m1_subset_1(D, A))  =>  ( (v4_ordinal1(D) &  (! [E] :  ( (v3_ordinal1(E) & m1_subset_1(E, A))  =>  (r2_tarski(E, D) => r1_ordinal1(k1_funct_1(B, E), k1_funct_1(C, E))) ) ) )  =>  (D=k2_ordinal4(A) | r1_ordinal1(k1_funct_1(B, D), k1_funct_1(C, D))) ) ) ) ) )  =>  (! [D] :  ( (v3_ordinal1(D) & m1_subset_1(D, A))  => r1_ordinal1(k1_funct_1(B, D), k1_funct_1(C, D))) ) ) ) ) ).
fof(s4_zf_refle__e8_30_1_3__zf_refle, axiom,  (! [A, B, C] :  ( ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  &  ( (v1_funct_1(B) &  (v1_funct_2(B, k2_ordinal1(A), k2_ordinal1(A)) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_ordinal1(A), k2_ordinal1(A))))) )  &  (v3_ordinal1(C) & m1_subset_1(C, A)) ) )  =>  ( ( (r2_tarski(C, k2_ordinal4(A)) => r2_tarski(k4_ordinal4(A, B, C), k4_ordinal4(A, B, k2_ordinal4(A))))  &  ( (! [D] :  ( (v3_ordinal1(D) & m1_subset_1(D, A))  =>  ( (r2_tarski(C, D) => r2_tarski(k4_ordinal4(A, B, C), k4_ordinal4(A, B, D)))  =>  (r2_tarski(C, k6_ordinal4(A, D)) => r2_tarski(k4_ordinal4(A, B, C), k4_ordinal4(A, B, k6_ordinal4(A, D)))) ) ) )  &  (! [D] :  ( (v3_ordinal1(D) & m1_subset_1(D, A))  =>  ( (v4_ordinal1(D) &  (! [E] :  ( (v3_ordinal1(E) & m1_subset_1(E, A))  =>  (r2_tarski(E, D) =>  (r2_tarski(C, E) => r2_tarski(k4_ordinal4(A, B, C), k4_ordinal4(A, B, E))) ) ) ) )  =>  (D=k2_ordinal4(A) |  (r2_tarski(C, D) => r2_tarski(k4_ordinal4(A, B, C), k4_ordinal4(A, B, D))) ) ) ) ) ) )  =>  (! [D] :  ( (v3_ordinal1(D) & m1_subset_1(D, A))  =>  (r2_tarski(C, D) => r2_tarski(k4_ordinal4(A, B, C), k4_ordinal4(A, B, D))) ) ) ) ) ) ).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(spc1_numerals, axiom,  (v2_xxreal_0(1) & m1_subset_1(1, k4_ordinal1)) ).
fof(spc2_boole, axiom,  ~ (v1_xboole_0(2)) ).
fof(spc2_numerals, axiom,  (v2_xxreal_0(2) & m1_subset_1(2, k4_ordinal1)) ).
fof(spc3_boole, axiom,  ~ (v1_xboole_0(3)) ).
fof(spc3_numerals, axiom,  (v2_xxreal_0(3) & m1_subset_1(3, k4_ordinal1)) ).
fof(spc4_boole, axiom,  ~ (v1_xboole_0(4)) ).
fof(spc4_numerals, axiom,  (v2_xxreal_0(4) & m1_subset_1(4, k4_ordinal1)) ).
fof(spc5_boole, axiom,  ~ (v1_xboole_0(5)) ).
fof(spc5_numerals, axiom,  (v2_xxreal_0(5) & m1_subset_1(5, k4_ordinal1)) ).
fof(symmetry_r1_funct_2, axiom,  (! [A, B, C, D, E, F] :  ( ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(D))  &  ( (v1_funct_1(E) &  (v1_funct_2(E, A, B) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(F) &  (v1_funct_2(F, C, D) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(C, D)))) ) ) ) )  =>  (r1_funct_2(A, B, C, D, E, F) => r1_funct_2(A, B, C, D, F, E)) ) ) ).
fof(symmetry_r2_funct_2, axiom,  (! [A, B, C, D] :  ( ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) )  =>  (r2_funct_2(A, B, C, D) => r2_funct_2(A, B, D, C)) ) ) ).
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(symmetry_r2_wellord2, axiom,  (! [A, B] :  (r2_wellord2(A, B) => r2_wellord2(B, A)) ) ).
fof(t10_ordinal1, axiom,  (! [A] :  (! [B] :  (! [C] :  (v1_ordinal1(C) =>  ( (r2_tarski(A, B) & r2_tarski(B, C))  => r2_tarski(A, C)) ) ) ) ) ).
fof(t10_ordinal4, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v5_ordinal1(A) &  (v1_funct_1(A) & v1_ordinal2(A)) ) )  =>  (! [B] :  (v3_ordinal1(B) =>  ( (v2_ordinal2(A) & r2_tarski(B, k9_xtuple_0(A)))  => r1_ordinal1(B, k1_funct_1(A, B))) ) ) ) ) ).
fof(t10_zfmodel1, axiom,  (! [A] :  (m2_subset_1(A, k4_ordinal1, k1_zf_lang) =>  (! [B] :  ( (v1_zf_lang(B) & m2_finseq_1(B, k4_ordinal1))  =>  (! [C] :  ( ~ (v1_xboole_0(C))  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, k1_zf_lang, C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang, C)))) )  =>  (r1_zf_model(C, D, B) =>  (r2_tarski(A, k2_zf_model(B)) | r1_zf_model(C, D, k7_zf_lang(A, B))) ) ) ) ) ) ) ) ) ) ).
fof(t11_ordinal1, axiom,  (! [A] :  (v1_ordinal1(A) =>  (! [B] :  (v3_ordinal1(B) =>  (r2_xboole_0(A, B) => r2_tarski(A, B)) ) ) ) ) ).
fof(t128_funct_7, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  =>  (! [D] :  (m1_subset_1(D, A) =>  (! [E] : k1_funct_1(k1_funct_7(C, D, E), D)=E) ) ) ) ) ) ) ) ) ).
fof(t12_funct_1, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (! [C] :  ( (v1_relat_1(C) & v1_funct_1(C))  =>  (r2_hidden(A, k9_xtuple_0(k3_relat_1(B, C))) => k1_funct_1(k3_relat_1(B, C), A)=k1_funct_1(C, k1_funct_1(B, A))) ) ) ) ) ) ).
fof(t12_ordinal1, axiom,  (! [A] :  (v1_ordinal1(A) =>  (! [B] :  (v3_ordinal1(B) =>  (! [C] :  (v3_ordinal1(C) =>  ( (r1_tarski(A, B) & r2_tarski(B, C))  => r2_tarski(A, C)) ) ) ) ) ) ) ).
fof(t12_zf_model, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_funct_1(B) &  (v1_funct_2(B, k1_zf_lang, A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang, A)))) )  =>  (! [C] :  (m2_subset_1(C, k4_ordinal1, k1_zf_lang) =>  (! [D] :  (m2_subset_1(D, k4_ordinal1, k1_zf_lang) =>  (r1_zf_model(A, B, k3_zf_lang(C, D)) <=> k3_funct_2(k1_zf_lang, A, B, C)=k3_funct_2(k1_zf_lang, A, B, D)) ) ) ) ) ) ) ) ) ).
fof(t13_ordinal4, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v5_ordinal1(A) &  (v1_funct_1(A) & v1_ordinal2(A)) ) )  =>  (! [B] :  ( (v1_relat_1(B) &  (v5_ordinal1(B) &  (v1_funct_1(B) & v1_ordinal2(B)) ) )  =>  ~ ( (v2_ordinal2(A) &  (v2_ordinal2(B) &  (! [C] :  ( (v1_relat_1(C) &  (v5_ordinal1(C) &  (v1_funct_1(C) & v1_ordinal2(C)) ) )  =>  ~ ( (C=k3_relat_1(B, A) & v2_ordinal2(C)) ) ) ) ) ) ) ) ) ) ) ).
fof(t13_zf_model, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_funct_1(B) &  (v1_funct_2(B, k1_zf_lang, A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang, A)))) )  =>  (! [C] :  (m2_subset_1(C, k4_ordinal1, k1_zf_lang) =>  (! [D] :  (m2_subset_1(D, k4_ordinal1, k1_zf_lang) =>  (r1_zf_model(A, B, k4_zf_lang(C, D)) <=> r2_tarski(k3_funct_2(k1_zf_lang, A, B, C), k3_funct_2(k1_zf_lang, A, B, D))) ) ) ) ) ) ) ) ) ).
fof(t14_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (v3_ordinal1(B) =>  ~ ( ( ~ (r2_tarski(A, B))  &  ( ~ (A=B)  &  ~ (r2_tarski(B, A)) ) ) ) ) ) ) ) ).
fof(t14_zf_model, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_funct_1(B) &  (v1_funct_2(B, k1_zf_lang, A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang, A)))) )  =>  (! [C] :  ( (v1_zf_lang(C) & m2_finseq_1(C, k4_ordinal1))  =>  (r1_zf_model(A, B, C) <=>  ~ (r1_zf_model(A, B, k5_zf_lang(C))) ) ) ) ) ) ) ) ).
fof(t14_zf_refle, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  =>  (! [B] :  ( (v3_ordinal1(B) & m1_subset_1(B, A))  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, k2_ordinal1(A), k2_ordinal1(A)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_ordinal1(A), k2_ordinal1(A))))) )  =>  (k2_zf_refle(C, A, B)=k3_card_3(k5_relset_1(k2_ordinal1(A), k2_ordinal1(A), C, B)) & k2_zf_refle(k5_relset_1(k2_ordinal1(A), k2_ordinal1(A), C, B), A, B)=k3_card_3(k5_relset_1(k2_ordinal1(A), k2_ordinal1(A), C, B))) ) ) ) ) ) ) ).
fof(t15_ordinal4, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v5_ordinal1(A) &  (v1_funct_1(A) & v1_ordinal2(A)) ) )  =>  (! [B] :  (v3_ordinal1(B) =>  (v2_ordinal2(A) => v2_ordinal2(k5_relat_1(A, B))) ) ) ) ) ).
fof(t15_zf_model, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_funct_1(B) &  (v1_funct_2(B, k1_zf_lang, A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang, A)))) )  =>  (! [C] :  ( (v1_zf_lang(C) & m2_finseq_1(C, k4_ordinal1))  =>  (! [D] :  ( (v1_zf_lang(D) & m2_finseq_1(D, k4_ordinal1))  =>  (r1_zf_model(A, B, k6_zf_lang(C, D)) <=>  (r1_zf_model(A, B, C) & r1_zf_model(A, B, D)) ) ) ) ) ) ) ) ) ) ).
fof(t16_zf_model, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_funct_1(B) &  (v1_funct_2(B, k1_zf_lang, A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang, A)))) )  =>  (! [C] :  ( (v1_zf_lang(C) & m2_finseq_1(C, k4_ordinal1))  =>  (! [D] :  (m2_subset_1(D, k4_ordinal1, k1_zf_lang) =>  (r1_zf_model(A, B, k7_zf_lang(D, C)) <=>  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, k1_zf_lang, A) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang, A)))) )  =>  ( (! [F] :  (m2_subset_1(F, k4_ordinal1, k1_zf_lang) =>  ( ~ (k3_funct_2(k1_zf_lang, A, E, F)=k3_funct_2(k1_zf_lang, A, B, F))  => D=F) ) )  => r1_zf_model(A, E, C)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t16_zf_refle, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  =>  (! [B] :  ( (v3_ordinal1(B) & m1_subset_1(B, A))  =>  (! [C] :  ( (v1_relat_1(C) &  (v2_relat_1(C) &  (v5_relat_1(C, A) &  (v5_ordinal1(C) &  (v1_funct_1(C) & v1_zf_refle(C, A)) ) ) ) )  => r1_tarski(k5_zf_refle(A, C, B), k4_zf_refle(A, C))) ) ) ) ) ) ).
fof(t17_ordinal4, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v5_ordinal1(A) &  (v1_funct_1(A) & v1_ordinal2(A)) ) )  =>  (! [B] :  ( (v1_relat_1(B) &  (v5_ordinal1(B) &  (v1_funct_1(B) & v1_ordinal2(B)) ) )  =>  (! [C] :  ( (v1_relat_1(C) &  (v5_ordinal1(C) &  (v1_funct_1(C) & v1_ordinal2(C)) ) )  =>  ( (v2_ordinal2(B) &  (v3_ordinal2(B) &  (v3_ordinal2(C) & A=k3_relat_1(B, C)) ) )  => v3_ordinal2(A)) ) ) ) ) ) ) ).
fof(t17_zf_refle, axiom, r3_tarski(k4_ordinal1, k1_zf_lang)).
fof(t18_funct_1, axiom,  (! [A] :  (! [B] :  (r2_hidden(B, A) => k1_funct_1(k4_relat_1(A), B)=B) ) ) ).
fof(t18_ordinal2, axiom,  (! [A] :  (v3_ordinal1(A) => k3_ordinal2(A)=A) ) ).
fof(t19_ordinal2, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (r2_tarski(A, B) => r2_tarski(A, k3_ordinal2(B))) ) ) ) ).
fof(t19_zf_refle, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  =>  (! [B] :  (r2_tarski(B, A) => r2_tarski(k3_ordinal2(B), A)) ) ) ) ).
fof(t1_boole, axiom,  (! [A] : k2_xboole_0(A, k1_xboole_0)=A) ).
fof(t1_classes1, axiom,  (! [A] :  (v2_classes1(A) <=>  (v1_classes1(A) &  ( (! [B] :  (r2_tarski(B, A) => r2_tarski(k9_setfam_1(B), A)) )  &  (! [B] :  ( (r1_tarski(B, A) & r2_tarski(k1_card_1(B), k1_card_1(A)))  => r2_tarski(B, A)) ) ) ) ) ) ).
fof(t1_classes2, axiom,  (! [A] :  (! [B] :  ( (v1_classes1(B) & r2_tarski(A, B))  =>  ( ~ (r3_tarski(A, B))  & r2_tarski(k1_card_1(A), k1_card_1(B))) ) ) ) ).
fof(t1_numerals, axiom, m1_subset_1(k1_xboole_0, k4_ordinal1)).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t1_xboole_1, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r1_tarski(A, B) & r1_tarski(B, C))  => r1_tarski(A, C)) ) ) ) ).
fof(t21_ordinal2, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  ~ ( (r2_tarski(A, k3_ordinal2(B)) &  (! [C] :  (v3_ordinal1(C) =>  ~ ( (r2_tarski(C, B) & r1_ordinal1(A, C)) ) ) ) ) ) ) ) ) ).
fof(t22_funct_1, axiom,  (! [A] :  (! [B] : k3_relat_1(k4_relat_1(B), k4_relat_1(A))=k4_relat_1(k3_xboole_0(A, B))) ) ).
fof(t22_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (v3_ordinal1(B) =>  (r2_tarski(A, k1_ordinal1(B)) <=> r1_ordinal1(A, B)) ) ) ) ) ).
fof(t28_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (v4_ordinal1(A) <=>  (! [B] :  (v3_ordinal1(B) =>  (r2_tarski(B, A) => r2_tarski(k1_ordinal1(B), A)) ) ) ) ) ) ).
fof(t28_xboole_1, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) => k3_xboole_0(A, B)=A) ) ) ).
fof(t2_boole, axiom,  (! [A] : k3_xboole_0(A, k1_xboole_0)=k1_xboole_0) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t2_tarski, axiom,  (! [A] :  (! [B] :  ( (! [C] :  (r2_hidden(C, A) <=> r2_hidden(C, B)) )  => A=B) ) ) ).
fof(t32_funct_7, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (! [C] :  (! [D] :  ( ~ (C=D)  => k1_funct_1(k1_funct_7(A, C, B), D)=k1_funct_1(A, D)) ) ) ) ) ) ).
fof(t33_ordinal4, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  =>  (k2_ordinal4(A)=k1_xboole_0 & k3_ordinal4(A)=1) ) ) ).
fof(t34_ordinal4, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  =>  (! [B] :  ( (v3_ordinal1(B) & m1_subset_1(B, A))  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, k2_ordinal1(A), k2_ordinal1(A)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_ordinal1(A), k2_ordinal1(A))))) )  => r2_tarski(B, k9_xtuple_0(C))) ) ) ) ) ) ).
fof(t36_zf_lang, axiom,  (! [A] :  ( (v1_zf_lang(A) & m2_finseq_1(A, k4_ordinal1))  =>  (v2_zf_lang(A) => A=k3_zf_lang(k17_zf_lang(A), k18_zf_lang(A))) ) ) ).
fof(t37_zf_lang, axiom,  (! [A] :  ( (v1_zf_lang(A) & m2_finseq_1(A, k4_ordinal1))  =>  (v3_zf_lang(A) => A=k4_zf_lang(k17_zf_lang(A), k18_zf_lang(A))) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t40_zf_lang, axiom,  (! [A] :  ( (v1_zf_lang(A) & m2_finseq_1(A, k4_ordinal1))  =>  (v5_zf_lang(A) => A=k6_zf_lang(k20_zf_lang(A), k21_zf_lang(A))) ) ) ).
fof(t44_zf_lang, axiom,  (! [A] :  ( (v1_zf_lang(A) & m2_finseq_1(A, k4_ordinal1))  =>  (v6_zf_lang(A) => A=k7_zf_lang(k22_zf_lang(A), k23_zf_lang(A))) ) ) ).
fof(t47_funct_1, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (v1_relat_1(C) & v1_funct_1(C))  =>  (r2_hidden(B, k9_xtuple_0(k5_relat_1(C, A))) => k1_funct_1(k5_relat_1(C, A), B)=k1_funct_1(C, B)) ) ) ) ) ).
fof(t49_funct_1, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (v1_relat_1(C) & v1_funct_1(C))  =>  (r2_hidden(B, A) => k1_funct_1(k5_relat_1(C, A), B)=k1_funct_1(C, B)) ) ) ) ) ).
fof(t4_relset_1, axiom,  (! [A] :  (! [B] :  (! [C] :  (v1_relat_1(C) =>  ( (r1_tarski(k9_xtuple_0(C), A) & r1_tarski(k10_xtuple_0(C), B))  => m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) ) ) ) ).
fof(t4_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r2_tarski(A, B) & m1_subset_1(B, k1_zfmisc_1(C)))  => m1_subset_1(A, C)) ) ) ) ).
fof(t50_funct_1, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (v1_relat_1(C) & v1_funct_1(C))  =>  ( (r2_hidden(B, k9_xtuple_0(C)) & r2_hidden(B, A))  => r2_tarski(k1_funct_1(C, B), k10_xtuple_0(k5_relat_1(C, A)))) ) ) ) ) ).
fof(t56_funct_5, axiom,  (! [A] :  (! [B] :  (! [C] :  (r1_tarski(A, B) => r1_tarski(k1_funct_2(C, A), k1_funct_2(C, B))) ) ) ) ).
fof(t57_relat_1, axiom,  (! [A] :  (! [B] :  (! [C] :  (v1_relat_1(C) =>  (r2_hidden(B, k9_xtuple_0(k5_relat_1(C, A))) <=>  (r2_hidden(B, A) & r2_hidden(B, k9_xtuple_0(C))) ) ) ) ) ) ).
fof(t58_relat_1, axiom,  (! [A] :  (! [B] :  (v1_relat_1(B) => r1_tarski(k9_xtuple_0(k5_relat_1(B, A)), A)) ) ) ).
fof(t5_card_1, axiom,  (! [A] :  (! [B] :  (r2_wellord2(A, B) <=> k1_card_1(A)=k1_card_1(B)) ) ) ).
fof(t5_ordinal1, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(B, A) & r1_tarski(A, 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(t61_classes2, axiom,  (! [A] :  (! [B] :  (! [C] :  ( ( ~ (v1_xboole_0(C))  & v1_classes2(C))  =>  ( (r2_tarski(A, C) & r2_tarski(B, C))  =>  (r2_tarski(k2_zfmisc_1(A, B), C) & r2_tarski(k1_funct_2(A, B), C)) ) ) ) ) ) ).
fof(t61_funct_5, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  ( (k1_card_1(A)=k1_card_1(C) & k1_card_1(B)=k1_card_1(D))  => k1_card_1(k1_funct_2(A, B))=k1_card_1(k1_funct_2(C, D))) ) ) ) ) ).
fof(t61_relat_1, axiom,  (! [A] :  (! [B] :  (v1_relat_1(B) => k9_xtuple_0(k5_relat_1(B, A))=k3_xboole_0(k9_xtuple_0(B), A)) ) ) ).
fof(t62_relat_1, axiom,  (! [A] :  (! [B] :  (v1_relat_1(B) =>  (r1_tarski(A, k9_xtuple_0(B)) => k9_xtuple_0(k5_relat_1(B, A))=A) ) ) ) ).
fof(t65_relat_1, axiom,  (! [A] :  (! [B] :  (v1_relat_1(B) => k5_relat_1(B, A)=k3_relat_1(k4_relat_1(A), B)) ) ) ).
fof(t67_card_1, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  => r1_ordinal1(k1_card_1(k7_relat_1(B, A)), k1_card_1(A))) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t6_ordinal1, axiom,  (! [A] : r2_tarski(A, k1_ordinal1(A))) ).
fof(t70_relat_1, axiom,  (! [A] :  (! [B] :  (v1_relat_1(B) => r1_tarski(k10_xtuple_0(k5_relat_1(B, A)), k10_xtuple_0(B))) ) ) ).
fof(t71_zf_lang1, axiom,  (! [A] :  ( (v1_zf_lang(A) & m2_finseq_1(A, k4_ordinal1))  =>  (! [B] :  (m2_subset_1(B, k4_ordinal1, k1_zf_lang) =>  (! [C] :  ( ~ (v1_xboole_0(C))  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, k1_zf_lang, C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang, C)))) )  =>  (r1_zf_model(C, D, k7_zf_lang(B, A)) <=>  (! [E] :  (m1_subset_1(E, C) => r1_zf_model(C, k2_zf_lang1(C, D, B, E), A)) ) ) ) ) ) ) ) ) ) ) ).
fof(t75_zf_lang1, axiom,  (! [A] :  ( (v1_zf_lang(A) & m2_finseq_1(A, k4_ordinal1))  =>  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, k1_zf_lang, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang, B)))) )  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, k1_zf_lang, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang, B)))) )  =>  ( ( (! [E] :  (m2_subset_1(E, k4_ordinal1, k1_zf_lang) =>  (r2_tarski(E, k2_zf_model(A)) => k3_funct_2(k1_zf_lang, B, D, E)=k3_funct_2(k1_zf_lang, B, C, E)) ) )  & r1_zf_model(B, C, A))  => r1_zf_model(B, D, A)) ) ) ) ) ) ) ) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_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_funct_2, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  =>  ( (B=k1_xboole_0 => A=k1_xboole_0)  => r2_tarski(C, k1_funct_2(A, B))) ) ) ) ) ).
fof(t8_ordinal3, axiom,  (! [A] :  (v3_ordinal1(A) =>  ( ~ (A=k1_xboole_0)  => r2_tarski(k1_xboole_0, A)) ) ) ).
fof(t8_ordinal4, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v5_ordinal1(A) &  (v1_funct_1(A) & v1_ordinal2(A)) ) )  =>  ( (v4_ordinal1(k9_xtuple_0(A)) & v2_ordinal2(A))  =>  (k9_xtuple_0(A)=k1_xboole_0 |  (r1_ordinal2(k4_ordinal2(A), A) & k8_ordinal2(A)=k4_ordinal2(A)) ) ) ) ) ).
