% Mizar problem: t9_goedcpuc,goedcpuc,549,5 
fof(t9_goedcpuc, conjecture,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  ( (v1_henmodel(B, A) & m1_subset_1(B, k1_zfmisc_1(k3_cqc_lang(A))))  =>  (v1_henmodel(k2_xboole_0(B, k4_goedcpuc(A)), k1_goedcpuc(A)) & m1_subset_1(k2_xboole_0(B, k4_goedcpuc(A)), k1_zfmisc_1(k3_cqc_lang(k1_goedcpuc(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(cc10_finseq_1, axiom,  (! [A] :  (v3_finseq_1(A) => v6_membered(A)) ) ).
fof(cc10_ordinal1, axiom,  (! [A] :  (v6_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_ordinal1(B)) ) ) ) ).
fof(cc11_finseq_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_finseq_1(A)) ) ).
fof(cc11_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v7_ordinal1(A)) ) ).
fof(cc12_finseq_1, axiom,  (! [A] :  (v4_finseq_1(A) => v4_funct_1(A)) ) ).
fof(cc12_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v1_zfmisc_1(A)) ) ).
fof(cc13_finseq_1, axiom,  (! [A] :  (v4_finseq_1(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_finseq_1(B)) ) ) ) ).
fof(cc13_ordinal1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  ~ (v8_ordinal1(A)) ) ) ).
fof(cc14_finseq_1, axiom,  (! [A] :  (v4_finseq_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_finseq_1(B)) ) ) ) ).
fof(cc14_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc15_ordinal1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v9_ordinal1(A)) ) ) ).
fof(cc16_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v1_finset_1(A) & v2_finseq_1(A)) ) ) ) ) ).
fof(cc16_ordinal1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) )  =>  (! [B] :  (m1_subset_1(B, A) =>  ~ (v8_ordinal1(B)) ) ) ) ) ).
fof(cc17_finseq_1, axiom,  (! [A] :  (m1_finseq_1(A, k4_ordinal1) => v6_valued_0(A)) ) ).
fof(cc17_ordinal1, axiom,  (! [A] :  ( ~ (v10_ordinal1(A))  => v1_setfam_1(A)) ) ).
fof(cc18_ordinal1, axiom,  (! [A] :  (v10_ordinal1(A) =>  ~ (v1_setfam_1(A)) ) ) ).
fof(cc19_ordinal1, axiom,  (! [A] :  (v1_setfam_1(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc1_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_xboole_0(A))  =>  (v1_relat_1(A) & v1_finseq_1(A)) ) ) ).
fof(cc1_finset_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_finset_1(A)) ) ).
fof(cc1_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v3_ordinal1(A) & v7_ordinal1(A)) ) ) ).
fof(cc1_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (v1_ordinal1(A) & v2_ordinal1(A)) ) ) ).
fof(cc1_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (v1_relat_1(A) &  ~ (v1_xboole_0(A)) ) ) ) ).
fof(cc1_qc_trans, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k3_cqc_lang(A))) =>  (v1_henmodel(B, A) => v2_qc_trans(B, A, A)) ) ) ) ) ).
fof(cc1_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_relat_1(A)) ) ).
fof(cc1_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_xboole_0(B)) ) ) ) ).
fof(cc20_ordinal1, axiom,  (! [A] :  ( ~ (v1_setfam_1(A))  => v10_ordinal1(A)) ) ).
fof(cc2_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) ) ) ).
fof(cc2_finset_1, axiom,  (! [A] :  (v1_finset_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_finset_1(B)) ) ) ) ).
fof(cc2_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v7_ordinal1(A) &  ~ (v3_xxreal_0(A)) ) ) ) ).
fof(cc2_ordinal1, axiom,  (! [A] :  ( (v1_ordinal1(A) & v2_ordinal1(A))  => v3_ordinal1(A)) ) ).
fof(cc2_qc_trans, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k3_cqc_lang(A))) =>  (v2_qc_trans(B, A, A) => v1_henmodel(B, 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_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_xreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xreal_0(A)) ) ).
fof(cc3_finseq_1, axiom,  (! [A] :  (! [B] :  (m1_finseq_1(B, A) => v5_relat_1(B, A)) ) ) ).
fof(cc3_finset_1, axiom,  (! [A, B] :  (v1_finset_1(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  ( (v1_funct_1(C) & v1_funct_2(C, A, B))  =>  (v1_funct_1(C) &  (v1_funct_2(C, A, B) & v1_finset_1(C)) ) ) ) ) ) ) ).
fof(cc3_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v7_ordinal1(A) &  ~ (v3_xxreal_0(A)) ) ) ) ).
fof(cc3_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_ordinal1(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_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_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xcmplx_0(A)) ) ).
fof(cc4_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_xboole_0(A))  =>  (v1_relat_1(A) & v1_finseq_1(A)) ) ) ).
fof(cc4_finset_1, axiom,  (! [A] :  (v1_zfmisc_1(A) => v1_finset_1(A)) ) ).
fof(cc4_nat_1, axiom,  (! [A] :  ( (v7_ordinal1(A) & v8_ordinal1(A))  =>  (v7_ordinal1(A) &  ~ (v2_xxreal_0(A)) ) ) ) ).
fof(cc4_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v5_ordinal1(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_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ~ (v1_subset_1(B, A)) ) ) ) ) ).
fof(cc4_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xxreal_0(A)) ) ).
fof(cc5_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) & v1_finseq_1(A)) ) ) ) ) ).
fof(cc5_finset_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ~ (v1_zfmisc_1(A)) ) ) ).
fof(cc5_nat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v8_ordinal1(A)) ) ).
fof(cc5_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, A) => v3_ordinal1(B)) ) ) ) ).
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_subset_1, axiom,  (! [A] :  (v1_zfmisc_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_zfmisc_1(B)) ) ) ) ).
fof(cc6_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) ) ) ) ).
fof(cc6_finset_1, axiom,  (! [A] :  (v1_xboole_0(A) => v5_finset_1(A)) ) ).
fof(cc6_nat_1, axiom,  (! [A] :  ( ~ (v8_ordinal1(A))  =>  ~ (v1_xboole_0(A)) ) ) ).
fof(cc6_ordinal1, axiom,  (! [A] :  (v7_ordinal1(A) => v3_ordinal1(A)) ) ).
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(cc7_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) & v2_finseq_1(A)) ) ) ) ) ).
fof(cc7_finset_1, axiom,  (! [A] :  (v5_finset_1(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_finset_1(B)) ) ) ) ).
fof(cc7_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v7_ordinal1(A)) ) ).
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(cc8_finseq_1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_finseq_1(A)) ) ).
fof(cc8_finset_1, axiom,  (! [A] :  (v5_finset_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v5_finset_1(B)) ) ) ) ).
fof(cc8_ordinal1, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) => v7_ordinal1(A)) ) ).
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(cc9_finseq_1, axiom,  (! [A] :  (v3_finseq_1(A) => v1_finset_1(A)) ) ).
fof(cc9_finset_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v2_finset_1(A)) ) ) ).
fof(cc9_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v6_ordinal1(A)) ) ).
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(commutativity_k8_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(B, k1_zfmisc_1(A)) => k8_subset_1(A, B, C)=k8_subset_1(A, C, B)) ) ).
fof(commutativity_k9_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(C, k1_zfmisc_1(A)) => k9_subset_1(A, B, C)=k9_subset_1(A, C, B)) ) ).
fof(d11_calcul_1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k3_cqc_lang(A))) =>  (! [C] :  ( ~ (v1_xboole_0(C))  =>  (! [D] :  (m1_valuat_1(D, A, C) =>  (! [E] :  (m2_funct_2(E, k3_qc_lang1(A), C, k2_valuat_1(A, C)) =>  (r6_calcul_1(A, B, C, D, E) <=>  (! [F] :  (m2_subset_1(F, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (r2_tarski(F, B) => r1_valuat_1(A, C, F, D, E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d1_tarski, axiom,  (! [A] :  (! [B] :  (B=k1_tarski(A) <=>  (! [C] :  (r2_hidden(C, B) <=> C=A) ) ) ) ) ).
fof(d2_goedcpuc, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m1_goedcpuc(B, A) <=>  (! [C] :  (m2_subset_1(C, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [D] :  (m2_subset_1(D, k2_qc_lang1(A), k3_qc_lang1(A)) =>  ~ (r2_hidden(k4_tarski(B, k1_domain_1(k3_qc_lang1(A), k3_cqc_lang(A), D, C)), k1_qc_lang1(A))) ) ) ) ) ) ) ) ) ).
fof(d2_qc_trans, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m1_qc_lang1(B) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k3_cqc_lang(A))) =>  (v2_qc_trans(C, A, B) <=>  (! [D] :  (m1_subset_1(D, k1_zfmisc_1(k3_cqc_lang(B))) =>  (C=D => v1_henmodel(D, B)) ) ) ) ) ) ) ) ) ) ).
fof(d3_goedcpuc, axiom,  (! [A] :  (m1_qc_lang1(A) => k1_goedcpuc(A)=k2_zfmisc_1(k4_ordinal1, k2_xboole_0(k1_qc_lang1(A), a_1_0_goedcpuc(A)))) ) ).
fof(d3_qc_trans, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  ( (v1_qc_trans(B, A) & m1_qc_lang1(B))  =>  (! [C] :  (m2_subset_1(C, k9_qc_lang1(A), k3_cqc_lang(A)) => k1_qc_trans(A, B, C)=C) ) ) ) ) ) ).
fof(d3_tarski, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) <=>  (! [C] :  (r2_hidden(C, A) => r2_hidden(C, B)) ) ) ) ) ).
fof(d3_xboole_0, axiom,  (! [A] :  (! [B] :  (! [C] :  (C=k2_xboole_0(A, B) <=>  (! [D] :  (r2_hidden(D, C) <=>  (r2_hidden(D, A) | r2_hidden(D, B)) ) ) ) ) ) ) ).
fof(d4_goedcpuc, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m2_subset_1(B, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [C] :  (m2_subset_1(C, k2_qc_lang1(A), k3_qc_lang1(A)) => k2_goedcpuc(A, B, C)=k4_tarski(4, k4_tarski(o_1_1_goedcpuc(A), k1_domain_1(k3_qc_lang1(A), k3_cqc_lang(A), C, B)))) ) ) ) ) ) ).
fof(d4_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) => k3_qc_lang1(A)=k2_zfmisc_1(k1_tarski(4), k1_qc_lang1(A))) ) ).
fof(d5_goedcpuc, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m2_subset_1(B, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [C] :  (m2_subset_1(C, k2_qc_lang1(A), k3_qc_lang1(A)) => k3_goedcpuc(A, B, C)=k9_cqc_lang(k1_goedcpuc(A), k6_cqc_lang(k1_goedcpuc(A), k12_cqc_lang(k1_goedcpuc(A), k2_qc_trans(A, k1_goedcpuc(A), C), k1_qc_trans(A, k1_goedcpuc(A), B))), k4_substut2(k1_goedcpuc(A), k1_qc_trans(A, k1_goedcpuc(A), B), k2_qc_trans(A, k1_goedcpuc(A), C), k2_goedcpuc(A, B, C)))) ) ) ) ) ) ).
fof(d5_tarski, axiom,  (! [A] :  (! [B] : k4_tarski(A, B)=k2_tarski(k2_tarski(A, B), k1_tarski(A))) ) ).
fof(d6_goedcpuc, axiom,  (! [A] :  (m1_qc_lang1(A) => k4_goedcpuc(A)=a_1_2_goedcpuc(A)) ) ).
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_k10_xtuple_0, axiom, $true).
fof(dt_k11_cqc_lang, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k3_qc_lang1(A)) & m1_subset_1(C, k3_cqc_lang(A))) )  => m2_subset_1(k11_cqc_lang(A, B, C), k9_qc_lang1(A), k3_cqc_lang(A))) ) ).
fof(dt_k12_cqc_lang, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k3_qc_lang1(A)) & m1_subset_1(C, k3_cqc_lang(A))) )  => m2_subset_1(k12_cqc_lang(A, B, C), k9_qc_lang1(A), k3_cqc_lang(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_k12_sublemma, axiom,  (! [A, B, C, D] :  ( (m1_qc_lang1(A) &  ( ~ (v1_xboole_0(B))  &  (m1_subset_1(C, k3_qc_lang1(A)) & m1_subset_1(D, B)) ) )  =>  (v1_funct_1(k12_sublemma(A, B, C, D)) & m1_subset_1(k12_sublemma(A, B, C, D), k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B)))) ) ) ).
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_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_k17_funcop_1, axiom, $true).
fof(dt_k1_domain_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  (m1_subset_1(C, A) & m1_subset_1(D, B)) ) )  => m1_subset_1(k1_domain_1(A, B, C, D), k2_zfmisc_1(A, B))) ) ).
fof(dt_k1_funct_1, axiom, $true).
fof(dt_k1_funct_4, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) & v1_funct_1(B)) )  =>  (v1_relat_1(k1_funct_4(A, B)) & v1_funct_1(k1_funct_4(A, B))) ) ) ).
fof(dt_k1_goedcpuc, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (v1_qc_trans(k1_goedcpuc(A), A) & m1_qc_lang1(k1_goedcpuc(A))) ) ) ).
fof(dt_k1_henmodel, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k1_henmodel(A))) ) ) ).
fof(dt_k1_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k1_qc_lang1(A))) ) ) ).
fof(dt_k1_qc_trans, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  ( (v1_qc_trans(B, A) & m1_qc_lang1(B))  & m1_subset_1(C, k3_cqc_lang(A))) )  => m2_subset_1(k1_qc_trans(A, B, C), k9_qc_lang1(B), k3_cqc_lang(B))) ) ).
fof(dt_k1_sublemma, axiom,  (! [A, B, C, D] :  ( (m1_qc_lang1(A) &  ( ~ (v1_xboole_0(B))  &  (m1_subset_1(C, k2_valuat_1(A, B)) &  (v1_funct_1(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B)))) ) ) )  => m2_funct_2(k1_sublemma(A, B, C, D), k3_qc_lang1(A), B, k2_valuat_1(A, B))) ) ).
fof(dt_k1_subset_1, axiom,  (! [A] : m1_subset_1(k1_subset_1(A), k1_zfmisc_1(A))) ).
fof(dt_k1_tarski, axiom, $true).
fof(dt_k1_valuat_1, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k24_qc_lang1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k9_qc_lang1(A)))  => m1_subset_1(k24_qc_lang1(A, B), k1_zfmisc_1(k3_qc_lang1(A)))) ) ).
fof(dt_k2_goedcpuc, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k3_cqc_lang(A)) & m1_subset_1(C, k3_qc_lang1(A))) )  => m2_subset_1(k2_goedcpuc(A, B, C), k2_qc_lang1(k1_goedcpuc(A)), k3_qc_lang1(k1_goedcpuc(A)))) ) ).
fof(dt_k2_margrel1, axiom, $true).
fof(dt_k2_partfun1, axiom,  (! [A, B, C, D] :  ( (v1_funct_1(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))  =>  (v1_funct_1(k2_partfun1(A, B, C, D)) & m1_subset_1(k2_partfun1(A, B, C, D), k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) ) ).
fof(dt_k2_qc_lang1, axiom, $true).
fof(dt_k2_qc_trans, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  ( (v1_qc_trans(B, A) & m1_qc_lang1(B))  & m1_subset_1(C, k3_qc_lang1(A))) )  => m2_subset_1(k2_qc_trans(A, B, C), k2_qc_lang1(B), k3_qc_lang1(B))) ) ).
fof(dt_k2_tarski, axiom, $true).
fof(dt_k2_valuat_1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) &  ~ (v1_xboole_0(B)) )  => m1_funct_2(k2_valuat_1(A, B), k3_qc_lang1(A), B)) ) ).
fof(dt_k2_xboole_0, 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_goedcpuc, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k3_cqc_lang(A)) & m1_subset_1(C, k3_qc_lang1(A))) )  => m2_subset_1(k3_goedcpuc(A, B, C), k9_qc_lang1(k1_goedcpuc(A)), k3_cqc_lang(k1_goedcpuc(A)))) ) ).
fof(dt_k3_henmodel, axiom,  (! [A] :  (m1_qc_lang1(A) => m2_funct_2(k3_henmodel(A), k3_qc_lang1(A), k1_henmodel(A), k2_valuat_1(A, k1_henmodel(A)))) ) ).
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_lang2, 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(k3_qc_lang2(A, B, C), k9_qc_lang1(A))) ) ).
fof(dt_k3_qc_trans, axiom,  (! [A, B, C, D] :  ( (m1_qc_lang1(A) &  ( (v1_qc_trans(B, A) & m1_qc_lang1(B))  &  (v7_ordinal1(C) & m1_subset_1(D, k8_qc_lang1(A, C))) ) )  => m2_subset_1(k3_qc_trans(A, B, C, D), k6_qc_lang1(B), k8_qc_lang1(B, C))) ) ).
fof(dt_k3_xboole_0, axiom, $true).
fof(dt_k4_cqc_lang, axiom,  (! [A, B, C, D] :  ( (v7_ordinal1(A) &  (m1_qc_lang1(B) &  (m1_subset_1(C, k8_qc_lang1(B, A)) &  (v5_relat_1(D, k3_qc_lang1(B)) &  (v3_card_1(D, A) & m1_finseq_1(D, k2_qc_lang1(B))) ) ) ) )  => m2_subset_1(k4_cqc_lang(A, B, C, D), k9_qc_lang1(B), k3_cqc_lang(B))) ) ).
fof(dt_k4_goedcpuc, axiom,  (! [A] :  (m1_qc_lang1(A) => m1_subset_1(k4_goedcpuc(A), k1_zfmisc_1(k3_cqc_lang(k1_goedcpuc(A))))) ) ).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k4_qc_trans, axiom,  (! [A, B, C, D] :  ( (m1_qc_lang1(A) &  ( (v1_qc_trans(B, A) & m1_qc_lang1(B))  &  (v7_ordinal1(C) &  (v5_relat_1(D, k3_qc_lang1(A)) &  (v3_card_1(D, C) & m1_finseq_1(D, k2_qc_lang1(A))) ) ) ) )  =>  (v5_relat_1(k4_qc_trans(A, B, C, D), k3_qc_lang1(B)) &  (v3_card_1(k4_qc_trans(A, B, C, D), C) & m2_finseq_1(k4_qc_trans(A, B, C, D), k2_qc_lang1(B))) ) ) ) ).
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_substut2, axiom,  (! [A, B, C, D] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k3_cqc_lang(A)) &  (m1_subset_1(C, k3_qc_lang1(A)) & m1_subset_1(D, k3_qc_lang1(A))) ) )  => m2_subset_1(k4_substut2(A, B, C, D), k9_qc_lang1(A), k3_cqc_lang(A))) ) ).
fof(dt_k4_tarski, axiom, $true).
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_qc_lang2, 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(k5_qc_lang2(A, B, C), k9_qc_lang1(A))) ) ).
fof(dt_k5_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => v1_relat_1(k5_relat_1(A, B))) ) ).
fof(dt_k5_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => m1_subset_1(k5_relset_1(A, B, C, D), k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) ).
fof(dt_k6_cqc_lang, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k3_cqc_lang(A)))  => m2_subset_1(k6_cqc_lang(A, B), k9_qc_lang1(A), k3_cqc_lang(A))) ) ).
fof(dt_k6_domain_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(B, A))  => m1_subset_1(k6_domain_1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_k6_goedelcp, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k1_zfmisc_1(k3_cqc_lang(A))))  => m1_subset_1(k6_goedelcp(A, B), k1_zfmisc_1(k3_qc_lang1(A)))) ) ).
fof(dt_k6_qc_lang1, axiom, $true).
fof(dt_k7_cqc_lang, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k3_cqc_lang(A)) & m1_subset_1(C, k3_cqc_lang(A))) )  => m2_subset_1(k7_cqc_lang(A, B, C), k9_qc_lang1(A), k3_cqc_lang(A))) ) ).
fof(dt_k8_qc_lang1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & v7_ordinal1(B))  => m1_subset_1(k8_qc_lang1(A, B), k1_zfmisc_1(k6_qc_lang1(A)))) ) ).
fof(dt_k8_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(B, k1_zfmisc_1(A)) => m1_subset_1(k8_subset_1(A, B, C), k1_zfmisc_1(A))) ) ).
fof(dt_k9_cqc_lang, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k3_cqc_lang(A)) & m1_subset_1(C, k3_cqc_lang(A))) )  => m2_subset_1(k9_cqc_lang(A, B, C), k9_qc_lang1(A), k3_cqc_lang(A))) ) ).
fof(dt_k9_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k9_qc_lang1(A))) ) ) ).
fof(dt_k9_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(C, k1_zfmisc_1(A)) => m1_subset_1(k9_subset_1(A, B, C), k1_zfmisc_1(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_funct_2, axiom,  (! [A, B] :  (! [C] :  (m1_funct_2(C, A, B) =>  ~ (v1_xboole_0(C)) ) ) ) ).
fof(dt_m1_goedcpuc, axiom, $true).
fof(dt_m1_henmodel, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) &  (v1_henmodel(B, A) & m1_subset_1(B, k1_zfmisc_1(k3_cqc_lang(A)))) )  =>  (! [C] :  (m1_henmodel(C, A, B) => m1_valuat_1(C, A, k1_henmodel(A))) ) ) ) ).
fof(dt_m1_qc_lang1, axiom, $true).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_m1_valuat_1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) &  ~ (v1_xboole_0(B)) )  =>  (! [C] :  (m1_valuat_1(C, A, B) =>  (v1_funct_1(C) &  (v1_funct_2(C, k6_qc_lang1(A), k2_margrel1(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k6_qc_lang1(A), k2_margrel1(B))))) ) ) ) ) ) ).
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_funct_2, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(B))  & m1_funct_2(C, A, B))  =>  (! [D] :  (m2_funct_2(D, A, B, C) =>  (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) ) ) ) ) ).
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_1_1_goedcpuc, axiom,  (! [A] :  (m1_qc_lang1(A) => m1_goedcpuc(o_1_1_goedcpuc(A), 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_goedcpuc, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (? [B] : m1_goedcpuc(B, A)) ) ) ).
fof(existence_m1_henmodel, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) &  (v1_henmodel(B, A) & m1_subset_1(B, k1_zfmisc_1(k3_cqc_lang(A)))) )  =>  (? [C] : m1_henmodel(C, A, B)) ) ) ).
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_m1_valuat_1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) &  ~ (v1_xboole_0(B)) )  =>  (? [C] : m1_valuat_1(C, A, B)) ) ) ).
fof(existence_m2_finseq_1, axiom,  (! [A] :  (? [B] : m2_finseq_1(B, A)) ) ).
fof(existence_m2_funct_2, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(B))  & m1_funct_2(C, A, B))  =>  (? [D] : m2_funct_2(D, A, B, C)) ) ) ).
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_finset_1, axiom,  (! [A, B] :  (v1_finset_1(B) => v1_finset_1(k3_xboole_0(A, B))) ) ).
fof(fc10_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) & v9_ordinal1(A))  =>  ~ (v10_ordinal1(k10_xtuple_0(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_finset_1, axiom,  (! [A, B] :  (v1_finset_1(A) => v1_finset_1(k3_xboole_0(A, B))) ) ).
fof(fc11_nat_1, axiom,  (! [A] :  ( ~ (v8_ordinal1(A))  => v1_setfam_1(k1_tarski(A))) ) ).
fof(fc11_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) &  ~ (v9_ordinal1(A)) )  => v10_ordinal1(k10_xtuple_0(A))) ) ).
fof(fc11_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k10_xtuple_0(A))) ) ).
fof(fc12_nat_1, axiom,  (! [A, B] :  ( ( ~ (v8_ordinal1(A))  &  ~ (v8_ordinal1(B)) )  => v1_setfam_1(k2_tarski(A, B))) ) ).
fof(fc13_finseq_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) )  =>  (v1_relat_1(k5_relat_1(A, B)) & v2_finseq_1(k5_relat_1(A, B))) ) ) ).
fof(fc13_subset_1, axiom,  (! [A] : v1_xboole_0(k1_subset_1(A))) ).
fof(fc14_finset_1, axiom,  (! [A, B] :  ( (v1_finset_1(A) & v1_finset_1(B))  => v1_finset_1(k2_zfmisc_1(A, B))) ) ).
fof(fc16_finseq_1, axiom,  (! [A] :  ( (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) )  => v3_finseq_1(k1_tarski(A))) ) ).
fof(fc16_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_xboole_0(B))  =>  (v1_xboole_0(k5_relat_1(A, B)) & v1_relat_1(k5_relat_1(A, B))) ) ) ).
fof(fc17_finset_1, axiom,  (! [A] :  (v1_finset_1(A) => v1_finset_1(k1_zfmisc_1(A))) ) ).
fof(fc17_relat_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_xboole_0(k5_relat_1(A, B)) & v1_relat_1(k5_relat_1(A, B))) ) ) ).
fof(fc19_finseq_1, axiom,  (! [A, B] :  ( (v3_finseq_1(A) & v3_finseq_1(B))  => v3_finseq_1(k2_xboole_0(A, B))) ) ).
fof(fc1_finset_1, axiom,  (! [A] : v1_finset_1(k1_tarski(A))) ).
fof(fc1_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k1_qc_lang1(A))) ) ) ).
fof(fc1_qc_trans, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) &  (v1_finset_1(B) & m1_subset_1(B, k1_zfmisc_1(k3_cqc_lang(A)))) )  => v1_finset_1(k6_goedelcp(A, B))) ) ).
fof(fc1_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => v1_relat_1(k3_xboole_0(A, B))) ) ).
fof(fc1_subset_1, axiom,  (! [A] :  ~ (v1_xboole_0(k1_zfmisc_1(A))) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc1_xtuple_0, axiom,  (! [A, B] : v1_xtuple_0(k4_tarski(A, B))) ).
fof(fc21_finseq_1, axiom,  (! [A, B] :  (v3_finseq_1(A) => v3_finseq_1(k3_xboole_0(A, B))) ) ).
fof(fc21_finset_1, axiom,  (! [A, B] : v1_finset_1(k17_funcop_1(A, B))) ).
fof(fc22_finset_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_finset_1(A))  => v1_finset_1(k10_xtuple_0(A))) ) ).
fof(fc23_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v3_relat_1(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v3_relat_1(k5_relat_1(A, B))) ) ) ).
fof(fc24_finset_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finset_1(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_finset_1(B)) ) )  =>  (v1_relat_1(k1_funct_4(A, B)) &  (v1_funct_1(k1_funct_4(A, B)) & v1_finset_1(k1_funct_4(A, B))) ) ) ) ).
fof(fc25_relat_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) & v1_relat_1(A))  => v1_zfmisc_1(k10_xtuple_0(A))) ) ).
fof(fc26_finset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v1_finset_1(B))  =>  (v1_relat_1(k5_relat_1(B, A)) & v1_finset_1(k5_relat_1(B, A))) ) ) ).
fof(fc26_relat_1, axiom,  (! [A, B, C] :  ( (v1_relat_1(C) & v5_relat_1(C, B))  =>  (v1_relat_1(k5_relat_1(C, A)) & v5_relat_1(k5_relat_1(C, A), B)) ) ) ).
fof(fc27_finset_1, axiom,  (! [A, B] :  ( (v1_finset_1(A) &  (v1_relat_1(B) & v1_funct_1(B)) )  =>  (v1_relat_1(k5_relat_1(B, A)) & v1_finset_1(k5_relat_1(B, A))) ) ) ).
fof(fc27_relat_1, axiom,  (! [A, B, C] :  ( (v1_relat_1(C) & v4_relat_1(C, B))  =>  (v1_relat_1(k5_relat_1(C, A)) &  (v4_relat_1(k5_relat_1(C, A), A) & v4_relat_1(k5_relat_1(C, A), B)) ) ) ) ).
fof(fc2_cqc_lang, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k3_cqc_lang(A))) ) ) ).
fof(fc2_finset_1, axiom,  (! [A, B] : v1_finset_1(k2_tarski(A, B))) ).
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(fc30_finset_1, axiom,  (! [A] :  (v1_finset_1(A) => v5_finset_1(k1_tarski(A))) ) ).
fof(fc31_finset_1, axiom,  (! [A] :  (v1_finset_1(A) => v5_finset_1(k1_zfmisc_1(A))) ) ).
fof(fc32_finset_1, axiom,  (! [A, B] :  ( (v1_finset_1(A) & v1_finset_1(B))  => v5_finset_1(k2_tarski(A, B))) ) ).
fof(fc33_finset_1, axiom,  (! [A, B] :  ( (v5_finset_1(A) & v5_finset_1(B))  => v5_finset_1(k2_xboole_0(A, B))) ) ).
fof(fc33_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v2_relat_1(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v2_relat_1(k5_relat_1(A, B))) ) ) ).
fof(fc35_finseq_1, axiom, v4_finseq_1(k1_tarski(k1_xboole_0))).
fof(fc35_finset_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finset_1(A)) )  => v1_finset_1(k1_funct_1(A, B))) ) ).
fof(fc36_finseq_1, axiom,  (! [A, B] :  ( (v4_finseq_1(A) & v4_finseq_1(B))  => v4_finseq_1(k2_xboole_0(A, B))) ) ).
fof(fc36_finset_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v2_finset_1(A))  => v5_finset_1(k10_xtuple_0(A))) ) ).
fof(fc39_finseq_1, axiom,  (! [A, B, C] :  ( (v4_finseq_1(A) &  (v1_relat_1(B) &  (v5_relat_1(B, A) & v1_funct_1(B)) ) )  => v1_finseq_1(k1_funct_1(B, C))) ) ).
fof(fc3_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k3_qc_lang1(A))) ) ) ).
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_xboole_0, axiom,  (! [A, B] :  ~ (v1_xboole_0(k2_tarski(A, B))) ) ).
fof(fc4_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(A, B))) ) ) ).
fof(fc5_ordinal1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v5_ordinal1(A)) )  & v3_ordinal1(B))  =>  (v1_relat_1(k5_relat_1(A, B)) &  (v5_relat_1(k5_relat_1(A, B), k10_xtuple_0(A)) & v5_ordinal1(k5_relat_1(A, B))) ) ) ) ).
fof(fc5_relat_1, axiom,  (! [A, B] : v1_relat_1(k1_tarski(k4_tarski(A, B)))) ).
fof(fc5_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(B, A))) ) ) ).
fof(fc5_xtuple_0, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k10_xtuple_0(A))) ) ).
fof(fc6_ordinal1, axiom,  ( ~ (v1_xboole_0(k4_ordinal1))  & v3_ordinal1(k4_ordinal1)) ).
fof(fc6_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k6_qc_lang1(A))) ) ) ).
fof(fc6_relat_1, axiom,  (! [A, B] : v1_relat_1(k2_zfmisc_1(A, B))) ).
fof(fc7_qc_lang1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & m1_qc_lang1(B))  =>  ~ (v1_xboole_0(k8_qc_lang1(B, A))) ) ) ).
fof(fc7_relat_1, axiom,  (! [A, B, C, D] : v1_relat_1(k2_tarski(k4_tarski(A, B), k4_tarski(C, D)))) ).
fof(fc9_finset_1, axiom,  (! [A, B] :  ( (v1_finset_1(A) & v1_finset_1(B))  => v1_finset_1(k2_xboole_0(A, B))) ) ).
fof(fc9_relat_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_relat_1(A))  =>  ~ (v1_xboole_0(k10_xtuple_0(A))) ) ) ).
fof(fraenkel_a_1_0_goedcpuc, axiom,  (! [A, B] :  (m1_qc_lang1(B) =>  (r2_hidden(A, a_1_0_goedcpuc(B)) <=>  (? [C, D] :  ( (m2_subset_1(C, k9_qc_lang1(B), k3_cqc_lang(B)) & m2_subset_1(D, k2_qc_lang1(B), k3_qc_lang1(B)))  & A=k4_tarski(o_1_1_goedcpuc(B), k1_domain_1(k3_qc_lang1(B), k3_cqc_lang(B), D, C))) ) ) ) ) ).
fof(fraenkel_a_1_2_goedcpuc, axiom,  (! [A, B] :  (m1_qc_lang1(B) =>  (r2_hidden(A, a_1_2_goedcpuc(B)) <=>  (? [C, D] :  ( (m2_subset_1(C, k9_qc_lang1(B), k3_cqc_lang(B)) & m2_subset_1(D, k2_qc_lang1(B), k3_qc_lang1(B)))  & A=k3_goedcpuc(B, C, D)) ) ) ) ) ).
fof(idempotence_k1_funct_4, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) & v1_funct_1(B)) )  => k1_funct_4(A, A)=A) ) ).
fof(idempotence_k1_sublemma, axiom,  (! [A, B, C, D] :  ( (m1_qc_lang1(A) &  ( ~ (v1_xboole_0(B))  &  (m1_subset_1(C, k2_valuat_1(A, B)) &  (v1_funct_1(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B)))) ) ) )  => k1_sublemma(A, B, C, C)=C) ) ).
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(idempotence_k8_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(B, k1_zfmisc_1(A)) => k8_subset_1(A, B, B)=B) ) ).
fof(idempotence_k9_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(C, k1_zfmisc_1(A)) => k9_subset_1(A, B, B)=B) ) ).
fof(rc10_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v1_funct_1(B) &  (v1_finset_1(B) &  (v3_card_1(B, A) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ) ).
fof(rc10_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v1_funct_1(A) & v2_finset_1(A)) ) ) ) ).
fof(rc10_ordinal1, axiom,  (? [A] :  ~ (v8_ordinal1(A)) ) ).
fof(rc11_finseq_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v4_finseq_1(A)) ) ).
fof(rc11_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) ) ) ).
fof(rc12_finseq_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v1_finset_1(B) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ).
fof(rc12_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) & v9_ordinal1(A)) ) ).
fof(rc13_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) &  ~ (v9_ordinal1(A)) ) ) ).
fof(rc16_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) &  (v6_valued_0(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ) ).
fof(rc1_cqc_lang, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & v7_ordinal1(B))  =>  (? [C] :  (m1_finseq_1(C, k2_qc_lang1(A)) &  (v1_relat_1(C) &  (v4_relat_1(C, k4_ordinal1) &  (v5_relat_1(C, k2_qc_lang1(A)) &  (v5_relat_1(C, k3_qc_lang1(A)) &  (v1_funct_1(C) &  (v3_card_1(C, B) & v1_finseq_1(C)) ) ) ) ) ) ) ) ) ) ).
fof(rc1_finseq_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, A))) &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) ) ) ) ) ).
fof(rc1_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_finset_1(A)) ) ).
fof(rc1_nat_1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc1_ordinal1, axiom,  (? [A] :  (v1_ordinal1(A) & v2_ordinal1(A)) ) ).
fof(rc1_qc_lang1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & m1_qc_lang1(B))  =>  (? [C] :  (m1_finseq_1(C, k2_qc_lang1(B)) &  (v1_relat_1(C) &  (v4_relat_1(C, k4_ordinal1) &  (v5_relat_1(C, k2_qc_lang1(B)) &  (v1_funct_1(C) &  (v1_finset_1(C) &  (v3_card_1(C, A) &  (v1_finseq_1(C) & v2_finseq_1(C)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc1_qc_trans, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (? [B] :  (m1_qc_lang1(B) &  ( ~ (v1_xboole_0(B))  &  (v1_relat_1(B) & v1_qc_trans(B, A)) ) ) ) ) ) ).
fof(rc1_relat_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_relat_1(A)) ) ).
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_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc1_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc1_xtuple_0, axiom,  (? [A] : v1_xtuple_0(A)) ).
fof(rc2_finseq_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v1_finset_1(B) & v1_finseq_1(B)) ) ) ) ) ) ).
fof(rc2_finset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_finset_1(B)) ) ) ).
fof(rc2_nat_1, axiom,  (? [A] :  (v7_ordinal1(A) & v8_ordinal1(A)) ) ).
fof(rc2_ordinal1, axiom,  (? [A] : v3_ordinal1(A)) ).
fof(rc2_qc_trans, axiom,  (! [A, B] :  ( ( (v4_card_3(A) & m1_qc_lang1(A))  &  (v4_card_3(B) & m1_qc_lang1(B)) )  =>  (? [C] :  (m1_qc_lang1(C) &  ( ~ (v1_xboole_0(C))  &  (v1_relat_1(C) &  (v4_card_3(C) &  (v1_qc_trans(C, A) & v1_qc_trans(C, B)) ) ) ) ) ) ) ) ).
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_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc2_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc3_finseq_1, axiom,  (! [A] :  (? [B] :  (m1_finseq_1(B, A) &  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v1_xboole_0(B) &  (v1_finset_1(B) & v1_finseq_1(B)) ) ) ) ) ) ) ) ).
fof(rc3_finset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_xboole_0(B))  & v1_finset_1(B)) ) ) ) ) ).
fof(rc3_nat_1, axiom,  (? [A] :  (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) ) ) ).
fof(rc3_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_ordinal1(A) &  (v2_ordinal1(A) & v3_ordinal1(A)) ) ) ) ).
fof(rc3_qc_trans, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k3_cqc_lang(A))) &  ( ~ (v1_xboole_0(B))  & v1_henmodel(B, 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_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v2_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc4_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) ) ) ).
fof(rc4_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) ) ) ).
fof(rc4_ordinal1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) & v5_ordinal1(B)) ) ) ) ) ).
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_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v3_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc5_finseq_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v3_finseq_1(A)) ) ).
fof(rc5_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc5_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc5_xreal_0, axiom,  (? [A] :  (v8_ordinal1(A) &  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc6_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ).
fof(rc6_finset_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_finset_1(C)) ) ) ) ) ) ).
fof(rc6_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc6_subset_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc7_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v2_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ) ).
fof(rc7_finset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  (? [C] :  ( ~ (v1_xboole_0(C))  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_finset_1(C)) ) ) ) ) ) ) ) ).
fof(rc7_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v7_ordinal1(A)) ) ).
fof(rc8_finseq_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_finseq_1(B, A) &  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  ( ~ (v1_xboole_0(B))  &  (v1_finset_1(B) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc8_finset_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_zfmisc_1(B))  & v1_finset_1(B)) ) ) ) ) ).
fof(rc8_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rc9_finseq_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  ( ~ (v1_xboole_0(B))  &  (v1_finset_1(B) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ) ) ).
fof(rc9_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) & v5_finset_1(A)) ) ) ).
fof(rc9_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rd5_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => k5_relat_1(k5_relat_1(A, B), B)=k5_relat_1(A, B)) ) ).
fof(rd8_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  => k5_relat_1(B, A)=B) ) ).
fof(redefinition_k11_cqc_lang, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k3_qc_lang1(A)) & m1_subset_1(C, k3_cqc_lang(A))) )  => k11_cqc_lang(A, B, C)=k15_qc_lang1(A, B, C)) ) ).
fof(redefinition_k12_cqc_lang, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k3_qc_lang1(A)) & m1_subset_1(C, k3_cqc_lang(A))) )  => k12_cqc_lang(A, B, C)=k5_qc_lang2(A, B, C)) ) ).
fof(redefinition_k12_sublemma, axiom,  (! [A, B, C, D] :  ( (m1_qc_lang1(A) &  ( ~ (v1_xboole_0(B))  &  (m1_subset_1(C, k3_qc_lang1(A)) & m1_subset_1(D, B)) ) )  => k12_sublemma(A, B, C, D)=k17_funcop_1(C, D)) ) ).
fof(redefinition_k1_domain_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  (m1_subset_1(C, A) & m1_subset_1(D, B)) ) )  => k1_domain_1(A, B, C, D)=k4_tarski(C, D)) ) ).
fof(redefinition_k1_sublemma, axiom,  (! [A, B, C, D] :  ( (m1_qc_lang1(A) &  ( ~ (v1_xboole_0(B))  &  (m1_subset_1(C, k2_valuat_1(A, B)) &  (v1_funct_1(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B)))) ) ) )  => k1_sublemma(A, B, C, D)=k1_funct_4(C, D)) ) ).
fof(redefinition_k2_partfun1, axiom,  (! [A, B, C, D] :  ( (v1_funct_1(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))  => k2_partfun1(A, B, C, D)=k5_relat_1(C, D)) ) ).
fof(redefinition_k2_valuat_1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) &  ~ (v1_xboole_0(B)) )  => k2_valuat_1(A, B)=k1_valuat_1(A, B)) ) ).
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_k4_cqc_lang, axiom,  (! [A, B, C, D] :  ( (v7_ordinal1(A) &  (m1_qc_lang1(B) &  (m1_subset_1(C, k8_qc_lang1(B, A)) &  (v5_relat_1(D, k3_qc_lang1(B)) &  (v3_card_1(D, A) & m1_finseq_1(D, k2_qc_lang1(B))) ) ) ) )  => k4_cqc_lang(A, B, C, D)=k10_qc_lang1(B, C, D)) ) ).
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_cqc_lang, axiom,  (! [A] :  (m1_qc_lang1(A) => k5_cqc_lang(A)=k12_qc_lang1(A)) ) ).
fof(redefinition_k5_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => k5_relset_1(A, B, C, D)=k5_relat_1(C, D)) ) ).
fof(redefinition_k6_cqc_lang, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k3_cqc_lang(A)))  => k6_cqc_lang(A, B)=k13_qc_lang1(A, B)) ) ).
fof(redefinition_k6_domain_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(B, A))  => k6_domain_1(A, B)=k1_tarski(B)) ) ).
fof(redefinition_k7_cqc_lang, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k3_cqc_lang(A)) & m1_subset_1(C, k3_cqc_lang(A))) )  => k7_cqc_lang(A, B, C)=k14_qc_lang1(A, B, C)) ) ).
fof(redefinition_k8_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(B, k1_zfmisc_1(A)) => k8_subset_1(A, B, C)=k3_xboole_0(B, C)) ) ).
fof(redefinition_k9_cqc_lang, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k3_cqc_lang(A)) & m1_subset_1(C, k3_cqc_lang(A))) )  => k9_cqc_lang(A, B, C)=k3_qc_lang2(A, B, C)) ) ).
fof(redefinition_k9_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(C, k1_zfmisc_1(A)) => k9_subset_1(A, B, C)=k3_xboole_0(B, C)) ) ).
fof(redefinition_m2_finseq_1, axiom,  (! [A] :  (! [B] :  (m2_finseq_1(B, A) <=> m1_finseq_1(B, A)) ) ) ).
fof(redefinition_m2_funct_2, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(B))  & m1_funct_2(C, A, B))  =>  (! [D] :  (m2_funct_2(D, A, B, C) <=> m1_subset_1(D, C)) ) ) ) ).
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_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(s2_finset_1__e5_19_2_3__goedcpuc, axiom,  (! [A, B, C, D] :  ( (m1_qc_lang1(A) &  ( (v1_qc_trans(B, A) & m1_qc_lang1(B))  &  (m1_subset_1(C, k1_zfmisc_1(k3_cqc_lang(B))) & m1_subset_1(D, k1_zfmisc_1(k3_cqc_lang(B)))) ) )  =>  ( (v1_finset_1(D) &  ( (? [E] :  ( ~ (v1_xboole_0(E))  &  (? [F] :  (m1_valuat_1(F, B, E) &  (? [G] :  (m2_funct_2(G, k3_qc_lang1(B), E, k2_valuat_1(B, E)) &  (? [H] :  (m1_subset_1(H, k1_zfmisc_1(k3_cqc_lang(B))) &  (H=k1_xboole_0 & r6_calcul_1(B, k4_subset_1(k3_cqc_lang(B), C, H), E, F, G)) ) ) ) ) ) ) ) )  &  (! [I] :  (! [J] :  ( (r2_tarski(I, D) &  (r1_tarski(J, D) &  (? [K] :  ( ~ (v1_xboole_0(K))  &  (? [L] :  (m1_valuat_1(L, B, K) &  (? [M] :  (m2_funct_2(M, k3_qc_lang1(B), K, k2_valuat_1(B, K)) &  (? [N] :  (m1_subset_1(N, k1_zfmisc_1(k3_cqc_lang(B))) &  (N=J & r6_calcul_1(B, k4_subset_1(k3_cqc_lang(B), C, N), K, L, M)) ) ) ) ) ) ) ) ) ) )  =>  (? [O] :  ( ~ (v1_xboole_0(O))  &  (? [P] :  (m1_valuat_1(P, B, O) &  (? [Q] :  (m2_funct_2(Q, k3_qc_lang1(B), O, k2_valuat_1(B, O)) &  (? [R] :  (m1_subset_1(R, k1_zfmisc_1(k3_cqc_lang(B))) &  (R=k2_xboole_0(J, k1_tarski(I)) & r6_calcul_1(B, k4_subset_1(k3_cqc_lang(B), C, R), O, P, Q)) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (? [S] :  ( ~ (v1_xboole_0(S))  &  (? [T] :  (m1_valuat_1(T, B, S) &  (? [U] :  (m2_funct_2(U, k3_qc_lang1(B), S, k2_valuat_1(B, S)) &  (? [V] :  (m1_subset_1(V, k1_zfmisc_1(k3_cqc_lang(B))) &  (V=D & r6_calcul_1(B, k4_subset_1(k3_cqc_lang(B), C, V), S, T, U)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(spc4_boole, axiom,  ~ (v1_xboole_0(4)) ).
fof(spc4_numerals, axiom,  (v2_xxreal_0(4) & m1_subset_1(4, k4_ordinal1)) ).
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(t12_henmodel, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k3_cqc_lang(A))) =>  (! [C] :  ( ~ (v1_xboole_0(C))  =>  ( ~ (v1_henmodel(B, A))  =>  (! [D] :  (m1_valuat_1(D, A, C) =>  (! [E] :  (m2_funct_2(E, k3_qc_lang1(A), C, k2_valuat_1(A, C)) =>  ~ (r6_calcul_1(A, B, C, D, E)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t12_qc_trans, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  ( (v1_qc_trans(B, A) & m1_qc_lang1(B))  =>  (! [C] :  (m2_subset_1(C, k9_qc_lang1(A), k3_cqc_lang(A)) => k24_qc_lang1(A, C)=k24_qc_lang1(B, k1_qc_trans(A, B, C))) ) ) ) ) ) ).
fof(t17_valuat_1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  (m2_funct_2(C, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (! [D] :  (m2_subset_1(D, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [E] :  (m1_valuat_1(E, A, B) =>  (r1_valuat_1(A, B, k6_cqc_lang(A, D), E, C) <=>  ~ (r1_valuat_1(A, B, D, E, C)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t18_qc_trans, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  ( (v1_qc_trans(B, A) & m1_qc_lang1(B))  =>  (! [C] :  ( (v1_henmodel(C, B) & m1_subset_1(C, k1_zfmisc_1(k3_cqc_lang(B))))  =>  (m1_subset_1(C, k1_zfmisc_1(k3_cqc_lang(A))) => v2_qc_trans(C, B, A)) ) ) ) ) ) ) ).
fof(t18_xboole_1, axiom,  (! [A] :  (! [B] :  (! [C] :  (r1_tarski(A, k3_xboole_0(B, C)) => r1_tarski(A, B)) ) ) ) ).
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_xboole_1, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r1_tarski(A, B) & r1_tarski(B, C))  => r1_tarski(A, C)) ) ) ) ).
fof(t1_xtuple_0, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  (k4_tarski(A, B)=k4_tarski(C, D) =>  (A=C & B=D) ) ) ) ) ) ).
fof(t20_qc_trans, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  ( (v1_finset_1(B) & m1_subset_1(B, k1_zfmisc_1(k3_cqc_lang(A))))  =>  (? [C] :  ( (v4_card_3(C) & m1_qc_lang1(C))  &  ( (v1_finset_1(B) & m1_subset_1(B, k1_zfmisc_1(k3_cqc_lang(C))))  & v1_qc_trans(A, C)) ) ) ) ) ) ) ).
fof(t21_qc_trans, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  ( (v1_henmodel(B, A) & m1_subset_1(B, k1_zfmisc_1(k3_cqc_lang(A))))  =>  (! [C] :  ( (v1_qc_trans(C, A) & m1_qc_lang1(C))  =>  (! [D] :  (m1_subset_1(D, k1_zfmisc_1(k3_cqc_lang(C))) =>  (B=D =>  (! [E] :  ( ~ (v1_xboole_0(E))  =>  (! [F] :  (m1_valuat_1(F, A, E) =>  (! [G] :  (m2_funct_2(G, k3_qc_lang1(A), E, k2_valuat_1(A, E)) =>  ~ ( (r6_calcul_1(A, B, E, F, G) &  (! [H] :  ( ~ (v1_xboole_0(H))  =>  (! [I] :  (m1_valuat_1(I, C, H) =>  (! [J] :  (m2_funct_2(J, k3_qc_lang1(C), H, k2_valuat_1(C, H)) =>  ~ (r6_calcul_1(C, D, H, I, J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t22_qc_trans, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  ( (v1_henmodel(B, A) & m1_subset_1(B, k1_zfmisc_1(k3_cqc_lang(A))))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k3_cqc_lang(A))) =>  (r1_tarski(C, B) => v1_henmodel(C, A)) ) ) ) ) ) ) ).
fof(t23_qc_trans, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  ( (v1_henmodel(B, A) & m1_subset_1(B, k1_zfmisc_1(k3_cqc_lang(A))))  =>  (! [C] :  ( (v1_qc_trans(C, A) & m1_qc_lang1(C))  => v2_qc_trans(B, A, C)) ) ) ) ) ) ).
fof(t23_xboole_1, axiom,  (! [A] :  (! [B] :  (! [C] : k3_xboole_0(A, k2_xboole_0(B, C))=k2_xboole_0(k3_xboole_0(A, B), k3_xboole_0(A, C))) ) ) ).
fof(t24_calcul_1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m2_subset_1(B, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [C] :  (m2_subset_1(C, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (! [D] :  (m2_subset_1(D, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (! [E] :  ( ~ (v1_xboole_0(E))  =>  (! [F] :  (m1_valuat_1(F, A, E) =>  (! [G] :  (m2_funct_2(G, k3_qc_lang1(A), E, k2_valuat_1(A, E)) =>  (r1_valuat_1(A, E, k4_substut2(A, B, C, D), F, G) <=>  (? [H] :  (m1_subset_1(H, E) &  (k3_funct_2(k3_qc_lang1(A), E, G, D)=H & r1_valuat_1(A, E, B, F, k1_sublemma(A, E, G, k12_sublemma(A, E, C, H)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t26_calcul_1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m2_subset_1(B, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (! [C] :  ( ~ (v1_xboole_0(C))  =>  (! [D] :  (m2_funct_2(D, k3_qc_lang1(A), C, k2_valuat_1(A, C)) =>  (! [E] :  (m1_subset_1(E, C) =>  (! [F] :  (r1_tarski(F, k3_qc_lang1(A)) =>  (r2_tarski(B, F) | r2_relset_1(k3_qc_lang1(A), C, k2_partfun1(k3_qc_lang1(A), C, k1_sublemma(A, C, D, k12_sublemma(A, C, B, E)), F), k2_partfun1(k3_qc_lang1(A), C, D, F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t28_xboole_1, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) => k3_xboole_0(A, B)=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(t34_goedelcp, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  ( (v1_henmodel(B, A) & m1_subset_1(B, k1_zfmisc_1(k3_cqc_lang(A))))  =>  ~ ( (v4_card_3(A) &  (v1_finset_1(k6_goedelcp(A, B)) &  (! [C] :  ( (v1_henmodel(C, A) & m1_subset_1(C, k1_zfmisc_1(k3_cqc_lang(A))))  =>  (! [D] :  (m1_henmodel(D, A, C) =>  ~ (r6_calcul_1(A, B, k1_henmodel(A), D, k3_henmodel(A))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t48_sublemma, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (! [C] :  (m2_subset_1(C, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (! [D] :  ( ~ (v1_xboole_0(D))  =>  (! [E] :  (m2_funct_2(E, k3_qc_lang1(A), D, k2_valuat_1(A, D)) =>  (! [F] :  (m1_subset_1(F, D) =>  ( ~ (C=B)  => k1_funct_1(k1_sublemma(A, D, E, k12_sublemma(A, D, C, F)), B)=k1_funct_1(E, B)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t49_sublemma, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m2_subset_1(B, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (! [C] :  (m2_subset_1(C, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (! [D] :  ( ~ (v1_xboole_0(D))  =>  (! [E] :  (m2_funct_2(E, k3_qc_lang1(A), D, k2_valuat_1(A, D)) =>  (! [F] :  (m1_subset_1(F, D) =>  (B=C => k3_funct_2(k3_qc_lang1(A), D, k1_sublemma(A, D, E, k12_sublemma(A, D, B, F)), C)=F) ) ) ) ) ) ) ) ) ) ) ) ) ).
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(t4_xboole_1, axiom,  (! [A] :  (! [B] :  (! [C] : k2_xboole_0(k2_xboole_0(A, B), C)=k2_xboole_0(A, k2_xboole_0(B, 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(t64_sublemma, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m2_subset_1(B, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [C] :  (m2_subset_1(C, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (! [D] :  ( ~ (v1_xboole_0(D))  =>  (! [E] :  (m2_funct_2(E, k3_qc_lang1(A), D, k2_valuat_1(A, D)) =>  (! [F] :  (m2_funct_2(F, k3_qc_lang1(A), D, k2_valuat_1(A, D)) =>  (! [G] :  (m1_subset_1(G, D) =>  (r2_relset_1(k3_qc_lang1(A), D, k5_relset_1(k3_qc_lang1(A), D, E, k24_qc_lang1(A, B)), k5_relset_1(k3_qc_lang1(A), D, F, k24_qc_lang1(A, B))) => r2_relset_1(k3_qc_lang1(A), D, k5_relset_1(k3_qc_lang1(A), D, k1_sublemma(A, D, E, k12_sublemma(A, D, C, G)), k24_qc_lang1(A, B)), k5_relset_1(k3_qc_lang1(A), D, k1_sublemma(A, D, F, k12_sublemma(A, D, C, G)), k24_qc_lang1(A, B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t68_sublemma, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  (m1_valuat_1(C, A, B) =>  (! [D] :  (m2_subset_1(D, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [E] :  (m2_funct_2(E, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (! [F] :  (m2_funct_2(F, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (r2_relset_1(k3_qc_lang1(A), B, k5_relset_1(k3_qc_lang1(A), B, E, k24_qc_lang1(A, D)), k5_relset_1(k3_qc_lang1(A), B, F, k24_qc_lang1(A, D))) =>  (r1_valuat_1(A, B, D, C, E) <=> r1_valuat_1(A, B, D, C, F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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(t7_goedcpuc, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  ( (v1_qc_trans(B, A) & m1_qc_lang1(B))  =>  (! [C] :  (m2_subset_1(C, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [D] :  (m2_subset_1(D, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [E] :  (m2_subset_1(E, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (k1_qc_trans(A, B, k9_cqc_lang(A, C, D))=k9_cqc_lang(B, k1_qc_trans(A, B, C), k1_qc_trans(A, B, D)) & k1_qc_trans(A, B, k12_cqc_lang(A, E, C))=k12_cqc_lang(B, k2_qc_trans(A, B, E), k1_qc_trans(A, B, C))) ) ) ) ) ) ) ) ) ) ) ).
fof(t7_henmodel, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k3_cqc_lang(A))) =>  ~ ( ( ~ (v1_henmodel(B, A))  &  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k3_cqc_lang(A))) =>  ~ ( (r1_tarski(C, B) &  (v1_finset_1(C) &  ~ (v1_henmodel(C, A)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t7_qc_trans, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  ( (v1_qc_trans(B, A) & m1_qc_lang1(B))  =>  (! [C] :  (m2_subset_1(C, k9_qc_lang1(A), k3_cqc_lang(A)) => m2_subset_1(C, k9_qc_lang1(B), k3_cqc_lang(B))) ) ) ) ) ) ).
fof(t87_zfmisc_1, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  (r2_hidden(k4_tarski(C, D), k2_zfmisc_1(A, B)) <=>  (r2_hidden(C, A) & r2_hidden(D, B)) ) ) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
fof(t8_goedcpuc, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m2_subset_1(B, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [C] :  (m2_subset_1(C, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [D] :  ( ~ (v1_xboole_0(D))  =>  (! [E] :  (m1_valuat_1(E, A, D) =>  (! [F] :  (m2_funct_2(F, k3_qc_lang1(A), D, k2_valuat_1(A, D)) =>  ( (r1_valuat_1(A, D, B, E, F) | r1_valuat_1(A, D, C, E, F))  <=> r1_valuat_1(A, D, k9_cqc_lang(A, B, C), E, F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t8_qc_trans, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (v7_ordinal1(B) =>  (! [C] :  (m2_subset_1(C, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [D] :  (m2_subset_1(D, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [E] :  (m2_subset_1(E, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (! [F] :  (m2_subset_1(F, k6_qc_lang1(A), k8_qc_lang1(A, B)) =>  (! [G] :  ( (v5_relat_1(G, k3_qc_lang1(A)) &  (v3_card_1(G, B) & m2_finseq_1(G, k2_qc_lang1(A))) )  =>  (! [H] :  ( (v1_qc_trans(H, A) & m1_qc_lang1(H))  =>  (k1_qc_trans(A, H, k5_cqc_lang(A))=k5_cqc_lang(H) &  (k1_qc_trans(A, H, k4_cqc_lang(B, A, F, G))=k4_cqc_lang(B, H, k3_qc_trans(A, H, B, F), k4_qc_trans(A, H, B, G)) &  (k1_qc_trans(A, H, k6_cqc_lang(A, C))=k6_cqc_lang(H, k1_qc_trans(A, H, C)) &  (k1_qc_trans(A, H, k7_cqc_lang(A, C, D))=k7_cqc_lang(H, k1_qc_trans(A, H, C), k1_qc_trans(A, H, D)) & k1_qc_trans(A, H, k11_cqc_lang(A, E, C))=k11_cqc_lang(H, k2_qc_trans(A, H, E), k1_qc_trans(A, H, C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t8_xboole_1, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r1_tarski(A, C) & r1_tarski(B, C))  => r1_tarski(k2_xboole_0(A, B), C)) ) ) ) ).
fof(t9_goedelcp, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m2_subset_1(B, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [C] :  (m2_subset_1(C, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (! [D] :  ( ~ (v1_xboole_0(D))  =>  (! [E] :  (m1_valuat_1(E, A, D) =>  (! [F] :  (m2_funct_2(F, k3_qc_lang1(A), D, k2_valuat_1(A, D)) =>  (r1_valuat_1(A, D, k12_cqc_lang(A, C, B), E, F) <=>  (? [G] :  (m1_subset_1(G, D) & r1_valuat_1(A, D, B, E, k1_sublemma(A, D, F, k12_sublemma(A, D, C, G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
