% Mizar problem: l18_cqc_lang,cqc_lang,1072,5 
fof(l18_cqc_lang, conjecture,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m2_subset_1(B, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, k9_qc_lang1(A), k9_qc_lang1(A)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k9_qc_lang1(A), k9_qc_lang1(A))))) )  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, k9_qc_lang1(A), k9_qc_lang1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k9_qc_lang1(A), k9_qc_lang1(A))))) )  =>  ( ( (! [E] :  (m1_subset_1(E, k9_qc_lang1(A)) =>  (k3_funct_2(k9_qc_lang1(A), k9_qc_lang1(A), C, k5_cqc_lang(A))=k5_cqc_lang(A) &  ( (v2_qc_lang1(E, A) => k3_funct_2(k9_qc_lang1(A), k9_qc_lang1(A), C, E)=k10_qc_lang1(A, k16_qc_lang1(A, E), k1_cqc_lang(A, k17_qc_lang1(A, E), k2_cqc_lang(A, k3_qc_lang3(A, k5_numbers), B))))  &  ( (v3_qc_lang1(E, A) => k3_funct_2(k9_qc_lang1(A), k9_qc_lang1(A), C, E)=k13_qc_lang1(A, k3_funct_2(k9_qc_lang1(A), k9_qc_lang1(A), C, k18_qc_lang1(A, E))))  &  ( (v4_qc_lang1(E, A) => k3_funct_2(k9_qc_lang1(A), k9_qc_lang1(A), C, E)=k14_qc_lang1(A, k3_funct_2(k9_qc_lang1(A), k9_qc_lang1(A), C, k19_qc_lang1(A, E)), k3_funct_2(k9_qc_lang1(A), k9_qc_lang1(A), C, k20_qc_lang1(A, E))))  &  (v5_qc_lang1(E, A) => k3_funct_2(k9_qc_lang1(A), k9_qc_lang1(A), C, E)=k16_funcop_1(k9_qc_lang1(A), k21_qc_lang1(A, E), B, E, k15_qc_lang1(A, k21_qc_lang1(A, E), k3_funct_2(k9_qc_lang1(A), k9_qc_lang1(A), C, k22_qc_lang1(A, E))))) ) ) ) ) ) )  &  (! [E] :  (m1_subset_1(E, k9_qc_lang1(A)) =>  (k3_funct_2(k9_qc_lang1(A), k9_qc_lang1(A), D, k5_cqc_lang(A))=k5_cqc_lang(A) &  ( (v2_qc_lang1(E, A) => k3_funct_2(k9_qc_lang1(A), k9_qc_lang1(A), D, E)=k10_qc_lang1(A, k16_qc_lang1(A, E), k1_cqc_lang(A, k17_qc_lang1(A, E), k2_cqc_lang(A, k3_qc_lang3(A, k5_numbers), B))))  &  ( (v3_qc_lang1(E, A) => k3_funct_2(k9_qc_lang1(A), k9_qc_lang1(A), D, E)=k13_qc_lang1(A, k3_funct_2(k9_qc_lang1(A), k9_qc_lang1(A), D, k18_qc_lang1(A, E))))  &  ( (v4_qc_lang1(E, A) => k3_funct_2(k9_qc_lang1(A), k9_qc_lang1(A), D, E)=k14_qc_lang1(A, k3_funct_2(k9_qc_lang1(A), k9_qc_lang1(A), D, k19_qc_lang1(A, E)), k3_funct_2(k9_qc_lang1(A), k9_qc_lang1(A), D, k20_qc_lang1(A, E))))  &  (v5_qc_lang1(E, A) => k3_funct_2(k9_qc_lang1(A), k9_qc_lang1(A), D, E)=k16_funcop_1(k9_qc_lang1(A), k21_qc_lang1(A, E), B, E, k15_qc_lang1(A, k21_qc_lang1(A, E), k3_funct_2(k9_qc_lang1(A), k9_qc_lang1(A), D, k22_qc_lang1(A, E))))) ) ) ) ) ) ) )  => r2_funct_2(k9_qc_lang1(A), k9_qc_lang1(A), 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_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (v1_relat_1(A) &  ~ (v1_xboole_0(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(cc2_funcop_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funcop_1(A)) ) ) ) ).
fof(cc2_membered, axiom,  (! [A] :  (v5_membered(A) => v4_membered(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(cc2_xxreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xxreal_0(A)) ) ).
fof(cc3_funcop_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_xboole_0(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) ) ) ) ).
fof(cc3_membered, axiom,  (! [A] :  (v4_membered(A) => v3_membered(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(cc4_membered, axiom,  (! [A] :  (v3_membered(A) => v2_membered(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(cc5_membered, axiom,  (! [A] :  (v3_membered(A) => v1_membered(A)) ) ).
fof(cc6_membered, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xcmplx_0(B)) ) ) ) ).
fof(cc7_membered, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xxreal_0(B)) ) ) ) ).
fof(cc8_membered, axiom,  (! [A] :  (v3_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xreal_0(B)) ) ) ) ).
fof(cc9_membered, axiom,  (! [A] :  (v4_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_rat_1(B)) ) ) ) ).
fof(d2_cqc_lang, axiom,  (! [A] :  (m1_qc_lang1(A) => k3_cqc_lang(A)=a_1_0_cqc_lang(A)) ) ).
fof(d2_funcop_1, axiom,  (! [A] :  (! [B] : k2_funcop_1(A, B)=k2_zfmisc_1(A, k1_tarski(B))) ) ).
fof(d9_funcop_1, axiom,  (! [A] :  (! [B] : k17_funcop_1(A, B)=k7_funcop_1(k1_tarski(A), B)) ) ).
fof(dt_k10_qc_lang1, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k6_qc_lang1(A)) & m1_finseq_1(C, k2_qc_lang1(A))) )  => m1_subset_1(k10_qc_lang1(A, B, C), k9_qc_lang1(A))) ) ).
fof(dt_k12_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) => m1_subset_1(k12_qc_lang1(A), k9_qc_lang1(A))) ) ).
fof(dt_k13_qc_lang1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k9_qc_lang1(A)))  => m1_subset_1(k13_qc_lang1(A, B), k9_qc_lang1(A))) ) ).
fof(dt_k14_funcop_1, axiom, $true).
fof(dt_k14_qc_lang1, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k9_qc_lang1(A)) & m1_subset_1(C, k9_qc_lang1(A))) )  => m1_subset_1(k14_qc_lang1(A, B, C), k9_qc_lang1(A))) ) ).
fof(dt_k15_qc_lang1, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k3_qc_lang1(A)) & m1_subset_1(C, k9_qc_lang1(A))) )  => m1_subset_1(k15_qc_lang1(A, B, C), k9_qc_lang1(A))) ) ).
fof(dt_k16_funcop_1, axiom,  (! [A, B, C, D, E] :  ( (m1_subset_1(D, A) & m1_subset_1(E, A))  => m1_subset_1(k16_funcop_1(A, B, C, D, E), A)) ) ).
fof(dt_k16_qc_lang1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k9_qc_lang1(A)))  => m1_subset_1(k16_qc_lang1(A, B), k6_qc_lang1(A))) ) ).
fof(dt_k17_funcop_1, axiom, $true).
fof(dt_k17_qc_lang1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k9_qc_lang1(A)))  => m2_finseq_1(k17_qc_lang1(A, B), k2_qc_lang1(A))) ) ).
fof(dt_k18_qc_lang1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k9_qc_lang1(A)))  => m1_subset_1(k18_qc_lang1(A, B), k9_qc_lang1(A))) ) ).
fof(dt_k19_qc_lang1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k9_qc_lang1(A)))  => m1_subset_1(k19_qc_lang1(A, B), k9_qc_lang1(A))) ) ).
fof(dt_k1_cqc_lang, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_finseq_1(B, k2_qc_lang1(A)) &  (v1_funct_1(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k5_qc_lang1(A), k2_qc_lang1(A))))) ) )  => m2_finseq_1(k1_cqc_lang(A, B, C), k2_qc_lang1(A))) ) ).
fof(dt_k1_funct_1, axiom, $true).
fof(dt_k1_tarski, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k20_qc_lang1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k9_qc_lang1(A)))  => m1_subset_1(k20_qc_lang1(A, B), k9_qc_lang1(A))) ) ).
fof(dt_k21_qc_lang1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k9_qc_lang1(A)))  => m2_subset_1(k21_qc_lang1(A, B), k2_qc_lang1(A), k3_qc_lang1(A))) ) ).
fof(dt_k22_qc_lang1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k9_qc_lang1(A)))  => m1_subset_1(k22_qc_lang1(A, B), k9_qc_lang1(A))) ) ).
fof(dt_k2_cqc_lang, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k5_qc_lang1(A)) & m1_subset_1(C, k3_qc_lang1(A))) )  =>  (v1_funct_1(k2_cqc_lang(A, B, C)) & m1_subset_1(k2_cqc_lang(A, B, C), k1_zfmisc_1(k2_zfmisc_1(k5_qc_lang1(A), k2_qc_lang1(A))))) ) ) ).
fof(dt_k2_funcop_1, axiom, $true).
fof(dt_k2_qc_lang1, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_cqc_lang, axiom,  (! [A] :  (m1_qc_lang1(A) => m1_subset_1(k3_cqc_lang(A), k1_zfmisc_1(k9_qc_lang1(A)))) ) ).
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_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) => m1_subset_1(k3_qc_lang1(A), k1_zfmisc_1(k2_qc_lang1(A)))) ) ).
fof(dt_k3_qc_lang3, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & v7_ordinal1(B))  => m2_subset_1(k3_qc_lang3(A, B), k2_qc_lang1(A), k5_qc_lang1(A))) ) ).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k4_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) => m1_subset_1(k4_qc_lang1(A), k1_zfmisc_1(k2_qc_lang1(A)))) ) ).
fof(dt_k5_cqc_lang, axiom,  (! [A] :  (m1_qc_lang1(A) => m2_subset_1(k5_cqc_lang(A), k9_qc_lang1(A), k3_cqc_lang(A))) ) ).
fof(dt_k5_numbers, axiom, m1_subset_1(k5_numbers, k4_ordinal1)).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k5_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) => m1_subset_1(k5_qc_lang1(A), k1_zfmisc_1(k2_qc_lang1(A)))) ) ).
fof(dt_k5_qc_lang3, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k9_qc_lang1(A)))  => m1_subset_1(k5_qc_lang3(A, B), k1_zfmisc_1(k5_qc_lang1(A)))) ) ).
fof(dt_k6_qc_lang1, axiom, $true).
fof(dt_k6_qc_lang3, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k9_qc_lang1(A)))  => m1_subset_1(k6_qc_lang3(A, B), k1_zfmisc_1(k4_qc_lang1(A)))) ) ).
fof(dt_k7_funcop_1, axiom,  (! [A, B] :  (v1_funct_1(k7_funcop_1(A, B)) &  (v1_funct_2(k7_funcop_1(A, B), A, k1_tarski(B)) & m1_subset_1(k7_funcop_1(A, B), k1_zfmisc_1(k2_zfmisc_1(A, k1_tarski(B))))) ) ) ).
fof(dt_k9_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k9_qc_lang1(A))) ) ) ).
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_qc_lang1, axiom, $true).
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_qc_lang1, axiom,  (? [A] : m1_qc_lang1(A)) ).
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(fc11_funcop_1, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  => v2_relat_1(k2_funcop_1(A, B))) ) ).
fof(fc11_membered, axiom,  (! [A] :  (v1_int_1(A) => v5_membered(k1_tarski(A))) ) ).
fof(fc12_funcop_1, axiom,  (! [A, B] :  (v1_relat_1(k17_funcop_1(A, B)) & v1_funct_1(k17_funcop_1(A, B))) ) ).
fof(fc12_membered, axiom,  (! [A] :  (v7_ordinal1(A) => v6_membered(k1_tarski(A))) ) ).
fof(fc13_funcop_1, axiom,  (! [A, B] : v2_funct_1(k17_funcop_1(A, B))) ).
fof(fc15_funcop_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v1_funct_1(B))  => v1_funcop_1(k2_funcop_1(A, B))) ) ).
fof(fc16_funcop_1, axiom,  (! [A, B] : v3_funct_1(k2_funcop_1(A, B))) ).
fof(fc18_funcop_1, axiom,  (! [A, B] : v4_relat_1(k2_funcop_1(A, B), A)) ).
fof(fc19_funcop_1, axiom,  (! [A, B] : v4_relat_1(k17_funcop_1(A, B), k1_tarski(A))) ).
fof(fc1_funcop_1, axiom,  (! [A, B] :  (v1_relat_1(k2_funcop_1(A, B)) & v1_funct_1(k2_funcop_1(A, B))) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc20_funcop_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v1_funct_1(B))  => v1_funcop_1(k17_funcop_1(A, B))) ) ).
fof(fc21_funcop_1, axiom,  (! [A, B] :  (v1_relat_1(k2_funcop_1(A, B)) &  (v4_relat_1(k2_funcop_1(A, B), A) &  (v1_funct_1(k2_funcop_1(A, B)) & v1_partfun1(k2_funcop_1(A, B), A)) ) ) ) ).
fof(fc22_funcop_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(C, A))  => v5_relat_1(k17_funcop_1(B, C), A)) ) ).
fof(fc23_funcop_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(B))  & m1_subset_1(C, B))  => v5_relat_1(k2_funcop_1(A, C), B)) ) ).
fof(fc24_funcop_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(B, A))  => v4_relat_1(k17_funcop_1(B, C), A)) ) ).
fof(fc2_cqc_lang, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k3_cqc_lang(A))) ) ) ).
fof(fc2_funcop_1, axiom,  (! [A] : v1_xboole_0(k2_funcop_1(k1_xboole_0, A))) ).
fof(fc2_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k2_qc_lang1(A))) ) ) ).
fof(fc2_xboole_0, axiom,  (! [A] :  ~ (v1_xboole_0(k1_tarski(A))) ) ).
fof(fc3_funcop_1, axiom,  (! [A, B] :  (v1_xboole_0(B) => v1_xboole_0(k2_funcop_1(B, A))) ) ).
fof(fc3_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k3_qc_lang1(A))) ) ) ).
fof(fc4_funcop_1, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  ~ (v1_xboole_0(k2_funcop_1(B, A))) ) ) ).
fof(fc4_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k4_qc_lang1(A))) ) ) ).
fof(fc59_membered, axiom, v7_membered(k4_ordinal1)).
fof(fc5_funcop_1, axiom,  (! [A] : v3_relat_1(k2_funcop_1(A, k1_xboole_0))) ).
fof(fc5_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k5_qc_lang1(A))) ) ) ).
fof(fc6_membered, axiom, v6_membered(k4_ordinal1)).
fof(fc6_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k6_qc_lang1(A))) ) ) ).
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_funcop_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(k1_funct_1(A, B)) & v1_funct_1(k1_funct_1(A, B))) ) ) ).
fof(fc9_membered, axiom,  (! [A] :  (v1_xreal_0(A) => v3_membered(k1_tarski(A))) ) ).
fof(fraenkel_a_1_0_cqc_lang, axiom,  (! [A, B] :  (m1_qc_lang1(B) =>  (r2_hidden(A, a_1_0_cqc_lang(B)) <=>  (? [C] :  (m1_subset_1(C, k9_qc_lang1(B)) &  (A=C &  (k6_qc_lang3(B, C)=k1_xboole_0 & k5_qc_lang3(B, C)=k1_xboole_0) ) ) ) ) ) ) ).
fof(rc1_funcop_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) ) ) ).
fof(rc1_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v6_membered(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(rc1_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(rc2_funcop_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  (v3_funct_1(A) &  ~ (v1_xboole_0(A)) ) ) ) ) ).
fof(rc2_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v6_membered(A)) ) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc2_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(rc3_funcop_1, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) &  (v3_funct_1(C) &  (v1_partfun1(C, A) & v1_funct_2(C, A, B)) ) ) ) ) ) ) ) ) ) ).
fof(rc3_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v6_membered(A) & v7_membered(A)) ) ) ).
fof(rc4_funcop_1, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) ) ) ) ) ) ).
fof(rc5_funcop_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) ) ) ) ).
fof(rd1_funcop_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(C, A))  => k1_funct_1(k2_funcop_1(A, B), C)=B) ) ).
fof(redefinition_k16_funcop_1, axiom,  (! [A, B, C, D, E] :  ( (m1_subset_1(D, A) & m1_subset_1(E, A))  => k16_funcop_1(A, B, C, D, E)=k14_funcop_1(B, C, D, E)) ) ).
fof(redefinition_k2_cqc_lang, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k5_qc_lang1(A)) & m1_subset_1(C, k3_qc_lang1(A))) )  => k2_cqc_lang(A, B, C)=k17_funcop_1(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_k5_cqc_lang, axiom,  (! [A] :  (m1_qc_lang1(A) => k5_cqc_lang(A)=k12_qc_lang1(A)) ) ).
fof(redefinition_k5_numbers, axiom, k5_numbers=k5_ordinal1).
fof(redefinition_k7_funcop_1, axiom,  (! [A, B] : k7_funcop_1(A, B)=k2_funcop_1(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_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_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_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(s1_qc_lang3__e5_38__cqc_lang, axiom,  (! [A, B, C, D] :  ( (m1_qc_lang1(A) &  (m2_subset_1(B, k2_qc_lang1(A), k3_qc_lang1(A)) &  ( (v1_funct_1(C) &  (v1_funct_2(C, k9_qc_lang1(A), k9_qc_lang1(A)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k9_qc_lang1(A), k9_qc_lang1(A))))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, k9_qc_lang1(A), k9_qc_lang1(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k9_qc_lang1(A), k9_qc_lang1(A))))) ) ) ) )  =>  ( ( (! [E] :  (m1_subset_1(E, k9_qc_lang1(A)) =>  (! [F] :  (m1_subset_1(F, k9_qc_lang1(A)) =>  (! [G] :  (m1_subset_1(G, k9_qc_lang1(A)) =>  ( (E=k12_qc_lang1(A) => k3_funct_2(k9_qc_lang1(A), k9_qc_lang1(A), C, E)=k5_cqc_lang(A))  &  ( (v2_qc_lang1(E, A) => k3_funct_2(k9_qc_lang1(A), k9_qc_lang1(A), C, E)=k10_qc_lang1(A, k16_qc_lang1(A, E), k1_cqc_lang(A, k17_qc_lang1(A, E), k2_cqc_lang(A, k3_qc_lang3(A, k5_numbers), B))))  &  ( ( (v3_qc_lang1(E, A) & F=k3_funct_2(k9_qc_lang1(A), k9_qc_lang1(A), C, k18_qc_lang1(A, E)))  => k3_funct_2(k9_qc_lang1(A), k9_qc_lang1(A), C, E)=k13_qc_lang1(A, F))  &  ( ( (v4_qc_lang1(E, A) &  (F=k3_funct_2(k9_qc_lang1(A), k9_qc_lang1(A), C, k19_qc_lang1(A, E)) & G=k3_funct_2(k9_qc_lang1(A), k9_qc_lang1(A), C, k20_qc_lang1(A, E))) )  => k3_funct_2(k9_qc_lang1(A), k9_qc_lang1(A), C, E)=k14_qc_lang1(A, F, G))  &  ( (v5_qc_lang1(E, A) & F=k3_funct_2(k9_qc_lang1(A), k9_qc_lang1(A), C, k22_qc_lang1(A, E)))  => k3_funct_2(k9_qc_lang1(A), k9_qc_lang1(A), C, E)=k16_funcop_1(k9_qc_lang1(A), k21_qc_lang1(A, E), B, E, k15_qc_lang1(A, k21_qc_lang1(A, E), F))) ) ) ) ) ) ) ) ) ) )  &  (! [E] :  (m1_subset_1(E, k9_qc_lang1(A)) =>  (! [F] :  (m1_subset_1(F, k9_qc_lang1(A)) =>  (! [G] :  (m1_subset_1(G, k9_qc_lang1(A)) =>  ( (E=k12_qc_lang1(A) => k3_funct_2(k9_qc_lang1(A), k9_qc_lang1(A), D, E)=k5_cqc_lang(A))  &  ( (v2_qc_lang1(E, A) => k3_funct_2(k9_qc_lang1(A), k9_qc_lang1(A), D, E)=k10_qc_lang1(A, k16_qc_lang1(A, E), k1_cqc_lang(A, k17_qc_lang1(A, E), k2_cqc_lang(A, k3_qc_lang3(A, k5_numbers), B))))  &  ( ( (v3_qc_lang1(E, A) & F=k3_funct_2(k9_qc_lang1(A), k9_qc_lang1(A), D, k18_qc_lang1(A, E)))  => k3_funct_2(k9_qc_lang1(A), k9_qc_lang1(A), D, E)=k13_qc_lang1(A, F))  &  ( ( (v4_qc_lang1(E, A) &  (F=k3_funct_2(k9_qc_lang1(A), k9_qc_lang1(A), D, k19_qc_lang1(A, E)) & G=k3_funct_2(k9_qc_lang1(A), k9_qc_lang1(A), D, k20_qc_lang1(A, E))) )  => k3_funct_2(k9_qc_lang1(A), k9_qc_lang1(A), D, E)=k14_qc_lang1(A, F, G))  &  ( (v5_qc_lang1(E, A) & F=k3_funct_2(k9_qc_lang1(A), k9_qc_lang1(A), D, k22_qc_lang1(A, E)))  => k3_funct_2(k9_qc_lang1(A), k9_qc_lang1(A), D, E)=k16_funcop_1(k9_qc_lang1(A), k21_qc_lang1(A, E), B, E, k15_qc_lang1(A, k21_qc_lang1(A, E), F))) ) ) ) ) ) ) ) ) ) ) )  => r2_funct_2(k9_qc_lang1(A), k9_qc_lang1(A), C, D)) ) ) ).
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(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)) ) ) ) ) ).
