% Mizar problem: t10_zfmodel1,zfmodel1,898,5 
fof(t10_zfmodel1, conjecture,  (! [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(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(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_zf_lang, axiom, k1_zf_lang=a_0_0_zf_lang).
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(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_k14_trees_3, axiom,  (! [A] :  (v7_ordinal1(A) => m2_finseq_1(k14_trees_3(A), k4_ordinal1)) ) ).
fof(dt_k1_card_1, axiom,  (! [A] : v1_card_1(k1_card_1(A))) ).
fof(dt_k1_funct_2, 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_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_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => m1_subset_1(k3_finseq_1(A), k4_ordinal1)) ) ).
fof(dt_k3_zf_model, axiom, $true).
fof(dt_k4_ordinal1, 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_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_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_xboole_0(k2_zfmisc_1(A, B))) ) ) ).
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(fc59_membered, axiom, v7_membered(k4_ordinal1)).
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_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(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(l10_zfmodel1, axiom,  (! [A] :  (v7_ordinal1(A) =>  ( (! [B] :  (v7_ordinal1(B) =>  ( ~ (r1_xxreal_0(A, B))  =>  (! [C] :  (m2_subset_1(C, k4_ordinal1, k1_zf_lang) =>  (! [D] :  ( ~ (v1_xboole_0(D))  =>  (! [E] :  ( (v1_zf_lang(E) & m2_finseq_1(E, k4_ordinal1))  =>  (! [F] :  ( (v1_funct_1(F) &  (v1_funct_2(F, k1_zf_lang, D) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang, D)))) )  =>  ( (k3_finseq_1(E)=B & r1_zf_model(D, F, E))  =>  (r2_tarski(C, k2_zf_model(E)) | r1_zf_model(D, F, k7_zf_lang(C, E))) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m2_subset_1(B, k4_ordinal1, k1_zf_lang) =>  (! [C] :  ( ~ (v1_xboole_0(C))  =>  (! [D] :  ( (v1_zf_lang(D) & m2_finseq_1(D, k4_ordinal1))  =>  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, k1_zf_lang, C) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang, C)))) )  =>  ( (k3_finseq_1(D)=A & r1_zf_model(C, E, D))  =>  (r2_tarski(B, k2_zf_model(D)) | r1_zf_model(C, E, k7_zf_lang(B, D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(projectivity_k1_card_1, axiom,  (! [A] : k1_card_1(k1_card_1(A))=k1_card_1(A)) ).
fof(projectivity_k3_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => k3_finseq_1(k3_finseq_1(A))=k3_finseq_1(A)) ) ).
fof(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_k3_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => k3_finseq_1(A)=k1_card_1(A)) ) ).
fof(redefinition_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_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_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(reflexivity_r1_xxreal_0, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => r1_xxreal_0(A, A)) ) ).
fof(rqLessOrEqual__r1_xxreal_0__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(s4_nat_1__e2_11__zfmodel1, axiom,  ( (! [A] :  (v7_ordinal1(A) =>  ( (! [B] :  (v7_ordinal1(B) =>  ( ~ (r1_xxreal_0(A, B))  =>  (! [C] :  (m2_subset_1(C, k4_ordinal1, k1_zf_lang) =>  (! [D] :  ( ~ (v1_xboole_0(D))  =>  (! [E] :  ( (v1_zf_lang(E) & m2_finseq_1(E, k4_ordinal1))  =>  (! [F] :  ( (v1_funct_1(F) &  (v1_funct_2(F, k1_zf_lang, D) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang, D)))) )  =>  ( (k3_finseq_1(E)=B & r1_zf_model(D, F, E))  =>  (r2_tarski(C, k2_zf_model(E)) | r1_zf_model(D, F, k7_zf_lang(C, E))) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [G] :  (m2_subset_1(G, k4_ordinal1, k1_zf_lang) =>  (! [H] :  ( ~ (v1_xboole_0(H))  =>  (! [I] :  ( (v1_zf_lang(I) & m2_finseq_1(I, k4_ordinal1))  =>  (! [J] :  ( (v1_funct_1(J) &  (v1_funct_2(J, k1_zf_lang, H) & m1_subset_1(J, k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang, H)))) )  =>  ( (k3_finseq_1(I)=A & r1_zf_model(H, J, I))  =>  (r2_tarski(G, k2_zf_model(I)) | r1_zf_model(H, J, k7_zf_lang(G, I))) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [A] :  (v7_ordinal1(A) =>  (! [K] :  (m2_subset_1(K, k4_ordinal1, k1_zf_lang) =>  (! [L] :  ( ~ (v1_xboole_0(L))  =>  (! [M] :  ( (v1_zf_lang(M) & m2_finseq_1(M, k4_ordinal1))  =>  (! [N] :  ( (v1_funct_1(N) &  (v1_funct_2(N, k1_zf_lang, L) & m1_subset_1(N, k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang, L)))) )  =>  ( (k3_finseq_1(M)=A & r1_zf_model(L, N, M))  =>  (r2_tarski(K, k2_zf_model(M)) | r1_zf_model(L, N, k7_zf_lang(K, M))) ) ) ) ) ) ) ) ) ) ) ) ) ).
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(t1_numerals, axiom, m1_subset_1(k1_xboole_0, k4_ordinal1)).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t2_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_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t4_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r2_tarski(A, B) & m1_subset_1(B, k1_zfmisc_1(C)))  => m1_subset_1(A, C)) ) ) ) ).
fof(t5_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)) ) ) ) ) ).
