% Mizar problem: t12_zfmodel1,zfmodel1,933,5 
fof(t12_zfmodel1, conjecture,  (! [A] :  (m2_subset_1(A, k4_ordinal1, k1_zf_lang) =>  (! [B] :  (m2_subset_1(B, k4_ordinal1, k1_zf_lang) =>  (! [C] :  (m2_subset_1(C, k4_ordinal1, k1_zf_lang) =>  (! [D] :  ( (v1_zf_lang(D) & m2_finseq_1(D, k4_ordinal1))  =>  (! [E] :  ( ~ (v1_xboole_0(E))  =>  (! [F] :  ( (v1_funct_1(F) &  (v1_funct_2(F, k1_zf_lang, E) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang, E)))) )  =>  ( (r1_xboole_0(k1_enumset1(A, B, C), k2_zf_model(D)) & r1_zf_model(E, F, D))  => r1_zf_model(E, F, k15_zf_lang(A, B, C, D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(antisymmetry_r2_hidden, axiom,  (! [A, B] :  (r2_hidden(A, B) =>  ~ (r2_hidden(B, A)) ) ) ).
fof(asymmetry_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) =>  ~ (r2_tarski(B, A)) ) ) ).
fof(cc10_membered, axiom,  (! [A] :  (v5_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_int_1(B)) ) ) ) ).
fof(cc11_membered, axiom,  (! [A] :  (v6_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v7_ordinal1(B)) ) ) ) ).
fof(cc12_membered, axiom,  (! [A] :  (v1_xboole_0(A) => v6_membered(A)) ) ).
fof(cc13_membered, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_membered(B)) ) ) ) ).
fof(cc14_membered, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v2_membered(B)) ) ) ) ).
fof(cc15_membered, axiom,  (! [A] :  (v3_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v3_membered(B)) ) ) ) ).
fof(cc16_membered, axiom,  (! [A] :  (v4_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_membered(B)) ) ) ) ).
fof(cc17_membered, axiom,  (! [A] :  (v5_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v5_membered(B)) ) ) ) ).
fof(cc18_membered, axiom,  (! [A] :  (v6_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_membered(B)) ) ) ) ).
fof(cc19_membered, axiom,  (! [A] :  (v1_xboole_0(A) => v7_membered(A)) ) ).
fof(cc1_membered, axiom,  (! [A] :  (v6_membered(A) => v5_membered(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(cc1_zf_lang, axiom,  (! [A] :  (m1_subset_1(A, k1_zf_lang) => v7_ordinal1(A)) ) ).
fof(cc2_membered, axiom,  (! [A] :  (v5_membered(A) => v4_membered(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_xxreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xxreal_0(A)) ) ).
fof(cc3_membered, axiom,  (! [A] :  (v4_membered(A) => v3_membered(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_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_membered, axiom,  (! [A] :  (v3_membered(A) => v2_membered(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_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_membered, axiom,  (! [A] :  (v3_membered(A) => v1_membered(A)) ) ).
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_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_membered, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xcmplx_0(B)) ) ) ) ).
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_membered, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xxreal_0(B)) ) ) ) ).
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_membered, axiom,  (! [A] :  (v3_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xreal_0(B)) ) ) ) ).
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_membered, axiom,  (! [A] :  (v4_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_rat_1(B)) ) ) ) ).
fof(commutativity_k2_tarski, axiom,  (! [A, B] : k2_tarski(A, B)=k2_tarski(B, A)) ).
fof(commutativity_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, B)=k2_xboole_0(B, A)) ).
fof(commutativity_k3_xboole_0, axiom,  (! [A, B] : k3_xboole_0(A, B)=k3_xboole_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(d1_enumset1, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  (D=k1_enumset1(A, B, C) <=>  (! [E] :  (r2_hidden(E, D) <=>  ~ ( ( ~ (E=A)  &  ( ~ (E=B)  &  ~ (E=C) ) ) ) ) ) ) ) ) ) ) ).
fof(d1_zf_lang, axiom, k1_zf_lang=a_0_0_zf_lang).
fof(d24_zf_lang, axiom,  (! [A] :  (m2_subset_1(A, k4_ordinal1, k1_zf_lang) =>  (! [B] :  (m2_subset_1(B, k4_ordinal1, k1_zf_lang) =>  (! [C] :  ( (v1_zf_lang(C) & m2_finseq_1(C, k4_ordinal1))  => k13_zf_lang(A, B, C)=k7_zf_lang(A, k7_zf_lang(B, C))) ) ) ) ) ) ).
fof(d26_zf_lang, axiom,  (! [A] :  (m2_subset_1(A, k4_ordinal1, k1_zf_lang) =>  (! [B] :  (m2_subset_1(B, k4_ordinal1, k1_zf_lang) =>  (! [C] :  (m2_subset_1(C, k4_ordinal1, k1_zf_lang) =>  (! [D] :  ( (v1_zf_lang(D) & m2_finseq_1(D, k4_ordinal1))  => k15_zf_lang(A, B, C, D)=k7_zf_lang(A, k13_zf_lang(B, C, D))) ) ) ) ) ) ) ) ).
fof(d2_tarski, axiom,  (! [A] :  (! [B] :  (! [C] :  (C=k2_tarski(A, B) <=>  (! [D] :  (r2_hidden(D, C) <=>  (D=A | D=B) ) ) ) ) ) ) ).
fof(d2_xboole_0, axiom, k1_xboole_0=o_0_0_xboole_0).
fof(d2_zf_model, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  => k3_zf_model(A)=k9_funct_2(k1_zf_lang, A)) ) ).
fof(d4_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) <=> r2_tarski(B, k5_zf_model(C, A))) ) ) ) ) ) ) ).
fof(d5_xboole_0, axiom,  (! [A] :  (! [B] :  (! [C] :  (C=k4_xboole_0(A, B) <=>  (! [D] :  (r2_hidden(D, C) <=>  (r2_hidden(D, A) &  ~ (r2_hidden(D, B)) ) ) ) ) ) ) ) ).
fof(d7_xboole_0, axiom,  (! [A] :  (! [B] :  (r1_xboole_0(A, B) <=> k3_xboole_0(A, B)=k1_xboole_0) ) ) ).
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(dt_k13_zf_lang, axiom,  (! [A, B, C] :  ( (m1_subset_1(A, k1_zf_lang) &  (m1_subset_1(B, k1_zf_lang) &  (v1_zf_lang(C) & m1_finseq_1(C, k4_ordinal1)) ) )  =>  (v1_zf_lang(k13_zf_lang(A, B, C)) & m2_finseq_1(k13_zf_lang(A, B, C), k4_ordinal1)) ) ) ).
fof(dt_k14_trees_3, axiom,  (! [A] :  (v7_ordinal1(A) => m2_finseq_1(k14_trees_3(A), k4_ordinal1)) ) ).
fof(dt_k15_zf_lang, axiom,  (! [A, B, C, D] :  ( (m1_subset_1(A, k1_zf_lang) &  (m1_subset_1(B, k1_zf_lang) &  (m1_subset_1(C, k1_zf_lang) &  (v1_zf_lang(D) & m1_finseq_1(D, k4_ordinal1)) ) ) )  =>  (v1_zf_lang(k15_zf_lang(A, B, C, D)) & m2_finseq_1(k15_zf_lang(A, B, C, D), 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_enumset1, axiom, $true).
fof(dt_k1_funct_2, axiom, $true).
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_model, 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_tarski, axiom, $true).
fof(dt_k2_xboole_0, axiom, $true).
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_zfmisc_1, axiom, $true).
fof(dt_k3_xboole_0, axiom, $true).
fof(dt_k3_zf_model, axiom, $true).
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_xboole_0, axiom, $true).
fof(dt_k4_zf_model, axiom, $true).
fof(dt_k5_finseq_1, axiom, $true).
fof(dt_k5_zf_model, axiom,  (! [A, B] :  ( ( (v1_zf_lang(A) & m1_finseq_1(A, k4_ordinal1))  &  ~ (v1_xboole_0(B)) )  => m1_subset_1(k5_zf_model(A, B), k1_zfmisc_1(k3_zf_model(B)))) ) ).
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_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(B, k1_zfmisc_1(A)) => m1_subset_1(k7_subset_1(A, B, C), k1_zfmisc_1(A))) ) ).
fof(dt_k7_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_k9_funct_2, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  => m1_funct_2(k9_funct_2(A, B), A, B)) ) ).
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_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(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_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_membered, axiom,  (! [A] :  (v1_rat_1(A) => v4_membered(k1_tarski(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(fc11_membered, axiom,  (! [A] :  (v1_int_1(A) => v5_membered(k1_tarski(A))) ) ).
fof(fc12_membered, axiom,  (! [A] :  (v7_ordinal1(A) => v6_membered(k1_tarski(A))) ) ).
fof(fc13_membered, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => v1_membered(k2_tarski(A, B))) ) ).
fof(fc14_membered, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => v2_membered(k2_tarski(A, B))) ) ).
fof(fc15_membered, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => v3_membered(k2_tarski(A, B))) ) ).
fof(fc16_membered, axiom,  (! [A, B] :  ( (v1_rat_1(A) & v1_rat_1(B))  => v4_membered(k2_tarski(A, B))) ) ).
fof(fc17_membered, axiom,  (! [A, B] :  ( (v1_int_1(A) & v1_int_1(B))  => v5_membered(k2_tarski(A, B))) ) ).
fof(fc18_membered, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & v7_ordinal1(B))  => v6_membered(k2_tarski(A, B))) ) ).
fof(fc19_membered, axiom,  (! [A, B, C] :  ( (v1_xcmplx_0(A) &  (v1_xcmplx_0(B) & v1_xcmplx_0(C)) )  => v1_membered(k1_enumset1(A, B, C))) ) ).
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(fc20_membered, axiom,  (! [A, B, C] :  ( (v1_xxreal_0(A) &  (v1_xxreal_0(B) & v1_xxreal_0(C)) )  => v2_membered(k1_enumset1(A, B, C))) ) ).
fof(fc21_membered, axiom,  (! [A, B, C] :  ( (v1_xreal_0(A) &  (v1_xreal_0(B) & v1_xreal_0(C)) )  => v3_membered(k1_enumset1(A, B, C))) ) ).
fof(fc22_membered, axiom,  (! [A, B, C] :  ( (v1_rat_1(A) &  (v1_rat_1(B) & v1_rat_1(C)) )  => v4_membered(k1_enumset1(A, B, C))) ) ).
fof(fc23_membered, axiom,  (! [A, B, C] :  ( (v1_int_1(A) &  (v1_int_1(B) & v1_int_1(C)) )  => v5_membered(k1_enumset1(A, B, C))) ) ).
fof(fc24_membered, axiom,  (! [A, B, C] :  ( (v7_ordinal1(A) &  (v7_ordinal1(B) & v7_ordinal1(C)) )  => v6_membered(k1_enumset1(A, B, C))) ) ).
fof(fc25_membered, axiom,  (! [A, B] :  ( (v1_membered(A) & v1_membered(B))  => v1_membered(k2_xboole_0(A, B))) ) ).
fof(fc26_membered, axiom,  (! [A, B] :  ( (v2_membered(A) & v2_membered(B))  => v2_membered(k2_xboole_0(A, B))) ) ).
fof(fc27_membered, axiom,  (! [A, B] :  ( (v3_membered(A) & v3_membered(B))  => v3_membered(k2_xboole_0(A, B))) ) ).
fof(fc28_membered, axiom,  (! [A, B] :  ( (v4_membered(A) & v4_membered(B))  => v4_membered(k2_xboole_0(A, B))) ) ).
fof(fc29_membered, axiom,  (! [A, B] :  ( (v5_membered(A) & v5_membered(B))  => v5_membered(k2_xboole_0(A, B))) ) ).
fof(fc2_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => v1_relat_1(k4_xboole_0(A, B))) ) ).
fof(fc2_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v4_relat_1(B, A))  & v1_relat_1(C))  => v4_relat_1(k3_xboole_0(B, C), A)) ) ).
fof(fc2_subset_1, axiom,  (! [A, B, C] :  ~ (v1_xboole_0(k1_enumset1(A, B, C))) ) ).
fof(fc30_membered, axiom,  (! [A, B] :  ( (v6_membered(A) & v6_membered(B))  => v6_membered(k2_xboole_0(A, B))) ) ).
fof(fc31_membered, axiom,  (! [A, B] :  (v1_membered(A) => v1_membered(k3_xboole_0(A, B))) ) ).
fof(fc32_membered, axiom,  (! [A, B] :  (v1_membered(A) => v1_membered(k3_xboole_0(B, A))) ) ).
fof(fc33_membered, axiom,  (! [A, B] :  (v2_membered(A) => v2_membered(k3_xboole_0(A, B))) ) ).
fof(fc34_membered, axiom,  (! [A, B] :  (v2_membered(A) => v2_membered(k3_xboole_0(B, A))) ) ).
fof(fc35_membered, axiom,  (! [A, B] :  (v3_membered(A) => v3_membered(k3_xboole_0(A, B))) ) ).
fof(fc36_membered, axiom,  (! [A, B] :  (v3_membered(A) => v3_membered(k3_xboole_0(B, A))) ) ).
fof(fc37_membered, axiom,  (! [A, B] :  (v4_membered(A) => v4_membered(k3_xboole_0(A, B))) ) ).
fof(fc38_membered, axiom,  (! [A, B] :  (v4_membered(A) => v4_membered(k3_xboole_0(B, A))) ) ).
fof(fc39_membered, axiom,  (! [A, B] :  (v5_membered(A) => v5_membered(k3_xboole_0(A, B))) ) ).
fof(fc3_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_relat_1(B))  => v1_relat_1(k2_xboole_0(A, B))) ) ).
fof(fc3_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v4_relat_1(B, A))  & v1_relat_1(C))  => v4_relat_1(k4_xboole_0(B, C), A)) ) ).
fof(fc40_membered, axiom,  (! [A, B] :  (v5_membered(A) => v5_membered(k3_xboole_0(B, A))) ) ).
fof(fc41_membered, axiom,  (! [A, B] :  (v6_membered(A) => v6_membered(k3_xboole_0(A, B))) ) ).
fof(fc42_membered, axiom,  (! [A, B] :  (v6_membered(A) => v6_membered(k3_xboole_0(B, A))) ) ).
fof(fc43_membered, axiom,  (! [A, B] :  (v1_membered(A) => v1_membered(k4_xboole_0(A, B))) ) ).
fof(fc44_membered, axiom,  (! [A, B] :  (v2_membered(A) => v2_membered(k4_xboole_0(A, B))) ) ).
fof(fc45_membered, axiom,  (! [A, B] :  (v3_membered(A) => v3_membered(k4_xboole_0(A, B))) ) ).
fof(fc46_membered, axiom,  (! [A, B] :  (v4_membered(A) => v4_membered(k4_xboole_0(A, B))) ) ).
fof(fc47_membered, axiom,  (! [A, B] :  (v5_membered(A) => v5_membered(k4_xboole_0(A, B))) ) ).
fof(fc48_membered, axiom,  (! [A, B] :  (v6_membered(A) => v6_membered(k4_xboole_0(A, B))) ) ).
fof(fc4_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(fc59_membered, axiom, v7_membered(k4_ordinal1)).
fof(fc5_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v5_relat_1(B, A))  & v1_relat_1(C))  => v5_relat_1(k3_xboole_0(B, C), A)) ) ).
fof(fc6_membered, axiom, v6_membered(k4_ordinal1)).
fof(fc6_relat_1, axiom,  (! [A, B] : v1_relat_1(k2_zfmisc_1(A, B))) ).
fof(fc6_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v5_relat_1(B, A))  & v1_relat_1(C))  => v5_relat_1(k4_xboole_0(B, C), A)) ) ).
fof(fc6_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_membered, axiom,  (! [A] :  (v1_xcmplx_0(A) => v1_membered(k1_tarski(A))) ) ).
fof(fc8_membered, axiom,  (! [A] :  (v1_xxreal_0(A) => v2_membered(k1_tarski(A))) ) ).
fof(fc9_membered, axiom,  (! [A] :  (v1_xreal_0(A) => v3_membered(k1_tarski(A))) ) ).
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_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(l12_zfmodel1, axiom,  (! [A] :  (m2_subset_1(A, k4_ordinal1, k1_zf_lang) =>  (! [B] :  ( (v1_zf_lang(B) & m2_finseq_1(B, k4_ordinal1))  =>  (r2_relset_1(k4_ordinal1, k4_ordinal1, k23_zf_lang(k7_zf_lang(A, B)), B) & k22_zf_lang(k7_zf_lang(A, B))=A) ) ) ) ) ).
fof(rc1_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v6_membered(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_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(rc2_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v6_membered(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_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(rc3_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v6_membered(A) & v7_membered(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_xxreal_0, axiom,  (? [A] :  (v1_xxreal_0(A) & v2_xxreal_0(A)) ) ).
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_xxreal_0, axiom,  (? [A] :  (v1_xxreal_0(A) & v3_xxreal_0(A)) ) ).
fof(rc5_xxreal_0, axiom,  (? [A] :  (v8_ordinal1(A) & v1_xxreal_0(A)) ) ).
fof(redefinition_k14_trees_3, axiom,  (! [A] :  (v7_ordinal1(A) => k14_trees_3(A)=k5_finseq_1(A)) ) ).
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_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_zf_model, axiom,  (! [A, B] :  ( ( (v1_zf_lang(A) & m1_finseq_1(A, k4_ordinal1))  &  ~ (v1_xboole_0(B)) )  => k5_zf_model(A, B)=k4_zf_model(A, B)) ) ).
fof(redefinition_k7_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(B, k1_zfmisc_1(A)) => k7_subset_1(A, B, C)=k4_xboole_0(B, C)) ) ).
fof(redefinition_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_k9_funct_2, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  => k9_funct_2(A, B)=k1_funct_2(A, B)) ) ).
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__r4_r4, axiom, r1_xxreal_0(4, 4)).
fof(rqLessOrEqual__r1_xxreal_0__r4_r5, axiom, r1_xxreal_0(4, 5)).
fof(rqLessOrEqual__r1_xxreal_0__r5_r4, axiom,  ~ (r1_xxreal_0(5, 4)) ).
fof(rqLessOrEqual__r1_xxreal_0__r5_r5, axiom, r1_xxreal_0(5, 5)).
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_xboole_0, axiom,  (! [A, B] :  (r1_xboole_0(A, B) => r1_xboole_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_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_zfmodel1, axiom,  (! [A] :  (m2_subset_1(A, k4_ordinal1, k1_zf_lang) =>  (! [B] :  (m2_subset_1(B, k4_ordinal1, k1_zf_lang) =>  (! [C] :  ( (v1_zf_lang(C) & m2_finseq_1(C, k4_ordinal1))  =>  (! [D] :  ( ~ (v1_xboole_0(D))  =>  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, k1_zf_lang, D) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang, D)))) )  =>  ( (r1_xboole_0(k2_tarski(A, B), k2_zf_model(C)) & r1_zf_model(D, E, C))  => r1_zf_model(D, E, k13_zf_lang(A, B, C))) ) ) ) ) ) ) ) ) ) ) ).
fof(t1_boole, axiom,  (! [A] : k2_xboole_0(A, k1_xboole_0)=A) ).
fof(t1_numerals, axiom, m1_subset_1(k1_xboole_0, k4_ordinal1)).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t1_zf_model, axiom,  (! [A] :  ( (v1_zf_lang(A) & m2_finseq_1(A, k4_ordinal1))  =>  ( (v2_zf_lang(A) => k2_zf_model(A)=k2_tarski(k17_zf_lang(A), k18_zf_lang(A)))  &  ( (v3_zf_lang(A) => k2_zf_model(A)=k2_tarski(k17_zf_lang(A), k18_zf_lang(A)))  &  ( (v4_zf_lang(A) => k2_zf_model(A)=k2_zf_model(k19_zf_lang(A)))  &  ( (v5_zf_lang(A) => k2_zf_model(A)=k4_subset_1(k1_zf_lang, k2_zf_model(k20_zf_lang(A)), k2_zf_model(k21_zf_lang(A))))  &  (v6_zf_lang(A) => k2_zf_model(A)=k7_subset_1(k1_zf_lang, k2_zf_model(k23_zf_lang(A)), k1_tarski(k22_zf_lang(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(t3_boole, axiom,  (! [A] : k4_xboole_0(A, k1_xboole_0)=A) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t3_xboole_0, axiom,  (! [A] :  (! [B] :  ( ~ ( ( ~ (r1_xboole_0(A, B))  &  (! [C] :  ~ ( (r2_hidden(C, A) & r2_hidden(C, B)) ) ) ) )  &  ~ ( ( (? [C] :  (r2_hidden(C, A) & r2_hidden(C, B)) )  & r1_xboole_0(A, B)) ) ) ) ) ).
fof(t4_boole, axiom,  (! [A] : k4_xboole_0(k1_xboole_0, A)=k1_xboole_0) ).
fof(t4_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r2_tarski(A, B) & m1_subset_1(B, k1_zfmisc_1(C)))  => m1_subset_1(A, C)) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
