% Mizar problem: t21_zf_model,zf_model,1245,5 
fof(t21_zf_model, conjecture,  (! [A] :  ( (v1_zf_lang(A) & m2_finseq_1(A, k4_ordinal1))  =>  (! [B] :  (m2_subset_1(B, k4_ordinal1, k1_zf_lang) =>  (! [C] :  (m2_subset_1(C, k4_ordinal1, k1_zf_lang) =>  (! [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_zf_model(D, E, k13_zf_lang(B, C, A)) <=>  (! [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)))) )  =>  ( (! [G] :  (m2_subset_1(G, k4_ordinal1, k1_zf_lang) =>  ~ ( ( ~ (k3_funct_2(k1_zf_lang, D, F, G)=k3_funct_2(k1_zf_lang, D, E, G))  &  ( ~ (B=G)  &  ~ (C=G) ) ) ) ) )  => r1_zf_model(D, F, A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(antisymmetry_r2_hidden, axiom,  (! [A, B] :  (r2_hidden(A, B) =>  ~ (r2_hidden(B, A)) ) ) ).
fof(asymmetry_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) =>  ~ (r2_tarski(B, A)) ) ) ).
fof(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_zf_lang, axiom,  (! [A] :  (m1_subset_1(A, k1_zf_lang) => v7_ordinal1(A)) ) ).
fof(cc2_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ).
fof(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(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(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(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(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_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_funct_7, axiom,  (! [A, B, C, D, E] :  ( ( (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(E, B))  =>  (v1_funct_1(k14_funct_7(A, B, C, D, E)) &  (v1_funct_2(k14_funct_7(A, B, C, D, E), A, B) & m1_subset_1(k14_funct_7(A, B, C, D, E), k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) ) ) ).
fof(dt_k14_trees_3, axiom,  (! [A] :  (v7_ordinal1(A) => m2_finseq_1(k14_trees_3(A), k4_ordinal1)) ) ).
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_xboole_0, axiom, $true).
fof(dt_k1_zf_lang, axiom, m1_subset_1(k1_zf_lang, k1_zfmisc_1(k4_ordinal1))).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_zfmisc_1, 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_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(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(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc1_zf_lang, axiom,  ~ (v1_xboole_0(k1_zf_lang)) ).
fof(fc1_zf_model, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k3_zf_model(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(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(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_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(redefinition_k14_funct_7, axiom,  (! [A, B, C, D, E] :  ( ( (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(E, B))  => k14_funct_7(A, B, C, D, E)=k1_funct_7(C, D, E)) ) ).
fof(redefinition_k14_trees_3, axiom,  (! [A] :  (v7_ordinal1(A) => k14_trees_3(A)=k5_finseq_1(A)) ) ).
fof(redefinition_k3_funct_2, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  & m1_subset_1(D, A)) )  => k3_funct_2(A, B, C, D)=k1_funct_1(C, D)) ) ).
fof(redefinition_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(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(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(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(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(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(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)) ) ) ) ) ).
