% Mizar problem: l7_zf_model,zf_model,883,8 
fof(l7_zf_model, conjecture,  (! [A] :  ( (v1_zf_lang(A) & m2_finseq_1(A, k4_ordinal1))  =>  (! [B] :  ( ~ (v1_xboole_0(B))  =>  ( (v2_zf_lang(A) => k4_zf_model(A, B)=a_2_2_zf_model(A, B))  &  ( (v3_zf_lang(A) => k4_zf_model(A, B)=a_2_3_zf_model(A, B))  &  ( (v4_zf_lang(A) => k4_zf_model(A, B)=k6_subset_1(k3_zf_model(B), k4_zf_model(k19_zf_lang(A), B)))  &  ( (v5_zf_lang(A) =>  (! [C] :  (! [D] :  ( (C=k4_zf_model(k20_zf_lang(A), B) & D=k4_zf_model(k21_zf_lang(A), B))  => k4_zf_model(A, B)=k3_xboole_0(C, D)) ) ) )  &  (v6_zf_lang(A) => k4_zf_model(A, B)=a_2_4_zf_model(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(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(commutativity_k3_xboole_0, axiom,  (! [A, B] : k3_xboole_0(A, B)=k3_xboole_0(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(d1_zf_lang, axiom, k1_zf_lang=a_0_0_zf_lang).
fof(d2_zf_model, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  => k3_zf_model(A)=k9_funct_2(k1_zf_lang, A)) ) ).
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(d3_zf_model, axiom,  (! [A] :  ( (v1_zf_lang(A) & m2_finseq_1(A, k4_ordinal1))  =>  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  (C=k4_zf_model(A, B) <=>  (? [D] :  ( (! [E] :  (m2_subset_1(E, k4_ordinal1, k1_zf_lang) =>  (! [F] :  (m2_subset_1(F, k4_ordinal1, k1_zf_lang) =>  (r2_hidden(k4_tarski(k3_zf_lang(E, F), a_3_0_zf_model(B, E, F)), D) & r2_hidden(k4_tarski(k4_zf_lang(E, F), a_3_1_zf_model(B, E, F)), D)) ) ) ) )  &  (r2_hidden(k4_tarski(A, C), D) &  (! [E] :  ( (v1_zf_lang(E) & m2_finseq_1(E, k4_ordinal1))  =>  (! [F] :  (r2_hidden(k4_tarski(E, F), D) =>  ( (v2_zf_lang(E) => F=a_2_0_zf_model(B, E))  &  ( (v3_zf_lang(E) => F=a_2_1_zf_model(B, E))  &  ( ~ ( (v4_zf_lang(E) &  (! [G] :  ~ ( (F=k6_subset_1(k3_zf_model(B), G) & r2_hidden(k4_tarski(k19_zf_lang(E), G), D)) ) ) ) )  &  ( ~ ( (v5_zf_lang(E) &  (! [G] :  (! [H] :  ~ ( (F=k3_xboole_0(G, H) &  (r2_hidden(k4_tarski(k20_zf_lang(E), G), D) & r2_hidden(k4_tarski(k21_zf_lang(E), H), D)) ) ) ) ) ) )  &  ~ ( (v6_zf_lang(E) &  (! [G] :  ~ ( (F=a_3_2_zf_model(B, E, G) & r2_hidden(k4_tarski(k23_zf_lang(E), G), D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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(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_funct_1, axiom, $true).
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_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_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_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_model, axiom, $true).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k4_tarski, axiom, $true).
fof(dt_k4_xboole_0, 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_model, axiom, $true).
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_k6_subset_1, axiom,  (! [A, B] : m1_subset_1(k6_subset_1(A, B), k1_zfmisc_1(A))) ).
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_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(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(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(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(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_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(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(fraenkel_a_2_0_zf_model, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(B))  &  (v1_zf_lang(C) & m2_finseq_1(C, k4_ordinal1)) )  =>  (r2_hidden(A, a_2_0_zf_model(B, C)) <=>  (? [D] :  (m1_subset_1(D, k3_zf_model(B)) &  (A=D &  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, k1_zf_lang, B) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang, B)))) )  =>  (E=D => k3_funct_2(k1_zf_lang, B, E, k17_zf_lang(C))=k3_funct_2(k1_zf_lang, B, E, k18_zf_lang(C))) ) ) ) ) ) ) ) ) ).
fof(fraenkel_a_2_1_zf_model, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(B))  &  (v1_zf_lang(C) & m2_finseq_1(C, k4_ordinal1)) )  =>  (r2_hidden(A, a_2_1_zf_model(B, C)) <=>  (? [D] :  (m1_subset_1(D, k3_zf_model(B)) &  (A=D &  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, k1_zf_lang, B) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang, B)))) )  =>  (E=D => r2_tarski(k3_funct_2(k1_zf_lang, B, E, k17_zf_lang(C)), k3_funct_2(k1_zf_lang, B, E, k18_zf_lang(C)))) ) ) ) ) ) ) ) ) ).
fof(fraenkel_a_2_2_zf_model, axiom,  (! [A, B, C] :  ( ( (v1_zf_lang(B) & m2_finseq_1(B, k4_ordinal1))  &  ~ (v1_xboole_0(C)) )  =>  (r2_hidden(A, a_2_2_zf_model(B, C)) <=>  (? [D] :  (m1_subset_1(D, k3_zf_model(C)) &  (A=D &  (! [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)))) )  =>  (E=D => k3_funct_2(k1_zf_lang, C, E, k17_zf_lang(B))=k3_funct_2(k1_zf_lang, C, E, k18_zf_lang(B))) ) ) ) ) ) ) ) ) ).
fof(fraenkel_a_2_3_zf_model, axiom,  (! [A, B, C] :  ( ( (v1_zf_lang(B) & m2_finseq_1(B, k4_ordinal1))  &  ~ (v1_xboole_0(C)) )  =>  (r2_hidden(A, a_2_3_zf_model(B, C)) <=>  (? [D] :  (m1_subset_1(D, k3_zf_model(C)) &  (A=D &  (! [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)))) )  =>  (E=D => r2_tarski(k3_funct_2(k1_zf_lang, C, E, k17_zf_lang(B)), k3_funct_2(k1_zf_lang, C, E, k18_zf_lang(B)))) ) ) ) ) ) ) ) ) ).
fof(fraenkel_a_2_4_zf_model, axiom,  (! [A, B, C] :  ( ( (v1_zf_lang(B) & m2_finseq_1(B, k4_ordinal1))  &  ~ (v1_xboole_0(C)) )  =>  (r2_hidden(A, a_2_4_zf_model(B, C)) <=>  (? [D] :  (m1_subset_1(D, k3_zf_model(C)) &  (A=D &  (! [E] :  (! [F] :  ( (v1_funct_1(F) &  (v1_funct_2(F, k1_zf_lang, C) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang, C)))) )  =>  ( (E=k4_zf_model(k23_zf_lang(B), C) & F=D)  =>  (r2_tarski(F, E) &  (! [G] :  ( (v1_funct_1(G) &  (v1_funct_2(G, k1_zf_lang, C) & m1_subset_1(G, k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang, C)))) )  =>  ( (! [H] :  (m2_subset_1(H, k4_ordinal1, k1_zf_lang) =>  ( ~ (k3_funct_2(k1_zf_lang, C, G, H)=k3_funct_2(k1_zf_lang, C, F, H))  => k22_zf_lang(B)=H) ) )  => r2_tarski(G, E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(fraenkel_a_3_0_zf_model, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(B))  &  (m2_subset_1(C, k4_ordinal1, k1_zf_lang) & m2_subset_1(D, k4_ordinal1, k1_zf_lang)) )  =>  (r2_hidden(A, a_3_0_zf_model(B, C, D)) <=>  (? [E] :  (m1_subset_1(E, k3_zf_model(B)) &  (A=E &  (! [F] :  ( (v1_funct_1(F) &  (v1_funct_2(F, k1_zf_lang, B) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang, B)))) )  =>  (F=E => k3_funct_2(k1_zf_lang, B, F, C)=k3_funct_2(k1_zf_lang, B, F, D)) ) ) ) ) ) ) ) ) ).
fof(fraenkel_a_3_1_zf_model, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(B))  &  (m2_subset_1(C, k4_ordinal1, k1_zf_lang) & m2_subset_1(D, k4_ordinal1, k1_zf_lang)) )  =>  (r2_hidden(A, a_3_1_zf_model(B, C, D)) <=>  (? [E] :  (m1_subset_1(E, k3_zf_model(B)) &  (A=E &  (! [F] :  ( (v1_funct_1(F) &  (v1_funct_2(F, k1_zf_lang, B) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang, B)))) )  =>  (F=E => r2_tarski(k3_funct_2(k1_zf_lang, B, F, C), k3_funct_2(k1_zf_lang, B, F, D))) ) ) ) ) ) ) ) ) ).
fof(fraenkel_a_3_2_zf_model, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(B))  &  (v1_zf_lang(C) & m2_finseq_1(C, k4_ordinal1)) )  =>  (r2_hidden(A, a_3_2_zf_model(B, C, D)) <=>  (? [E] :  (m1_subset_1(E, k3_zf_model(B)) &  (A=E &  (! [F] :  (! [G] :  ( (v1_funct_1(G) &  (v1_funct_2(G, k1_zf_lang, B) & m1_subset_1(G, k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang, B)))) )  =>  ( (F=D & G=E)  =>  (r2_tarski(G, F) &  (! [H] :  ( (v1_funct_1(H) &  (v1_funct_2(H, k1_zf_lang, B) & m1_subset_1(H, k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang, B)))) )  =>  ( (! [I] :  (m2_subset_1(I, k4_ordinal1, k1_zf_lang) =>  ( ~ (k3_funct_2(k1_zf_lang, B, H, I)=k3_funct_2(k1_zf_lang, B, G, I))  => k22_zf_lang(C)=I) ) )  => r2_tarski(H, F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(idempotence_k3_xboole_0, axiom,  (! [A, B] : k3_xboole_0(A, A)=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_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
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_numbers, axiom, k5_numbers=k5_ordinal1).
fof(redefinition_k6_subset_1, axiom,  (! [A, B] : k6_subset_1(A, B)=k4_xboole_0(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(s3_zf_model__e2_12__zf_model, axiom,  (! [A, B] :  ( ( (v1_zf_lang(A) & m2_finseq_1(A, k4_ordinal1))  &  ~ (v1_xboole_0(B)) )  =>  ( (! [C] :  ( (v1_zf_lang(C) & m2_finseq_1(C, k4_ordinal1))  =>  (! [D] :  (D=k4_zf_model(C, B) <=>  (? [E] :  ( (! [F] :  (m2_subset_1(F, k4_ordinal1, k1_zf_lang) =>  (! [G] :  (m2_subset_1(G, k4_ordinal1, k1_zf_lang) =>  (r2_hidden(k4_tarski(k3_zf_lang(F, G), a_3_0_zf_model(B, F, G)), E) & r2_hidden(k4_tarski(k4_zf_lang(F, G), a_3_1_zf_model(B, F, G)), E)) ) ) ) )  &  (r2_hidden(k4_tarski(C, D), E) &  (! [F] :  ( (v1_zf_lang(F) & m2_finseq_1(F, k4_ordinal1))  =>  (! [G] :  (r2_hidden(k4_tarski(F, G), E) =>  ( (v2_zf_lang(F) => G=a_2_0_zf_model(B, F))  &  ( (v3_zf_lang(F) => G=a_2_1_zf_model(B, F))  &  ( ~ ( (v4_zf_lang(F) &  (! [H] :  ~ ( (G=k6_subset_1(k3_zf_model(B), H) & r2_hidden(k4_tarski(k19_zf_lang(F), H), E)) ) ) ) )  &  ( ~ ( (v5_zf_lang(F) &  (! [H] :  (! [I] :  ~ ( (G=k3_xboole_0(H, I) &  (r2_hidden(k4_tarski(k20_zf_lang(F), H), E) & r2_hidden(k4_tarski(k21_zf_lang(F), I), E)) ) ) ) ) ) )  &  ~ ( (v6_zf_lang(F) &  (! [H] :  ~ ( (G=a_3_2_zf_model(B, F, H) & r2_hidden(k4_tarski(k23_zf_lang(F), H), E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (v2_zf_lang(A) => k4_zf_model(A, B)=a_2_2_zf_model(A, B))  &  ( (v3_zf_lang(A) => k4_zf_model(A, B)=a_2_3_zf_model(A, B))  &  ( (v4_zf_lang(A) => k4_zf_model(A, B)=k6_subset_1(k3_zf_model(B), k4_zf_model(k19_zf_lang(A), B)))  &  ( (v5_zf_lang(A) =>  (! [C] :  (! [D] :  ( (C=k4_zf_model(k20_zf_lang(A), B) & D=k4_zf_model(k21_zf_lang(A), B))  => k4_zf_model(A, B)=k3_xboole_0(C, D)) ) ) )  &  (v6_zf_lang(A) => k4_zf_model(A, B)=a_2_4_zf_model(A, B)) ) ) ) ) ) ) ) ).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(spc1_numerals, axiom,  (v2_xxreal_0(1) & m1_subset_1(1, k4_ordinal1)) ).
fof(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_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(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)) ) ) ) ) ).
