% Mizar problem: t27_valuat_1,valuat_1,931,5 
fof(t27_valuat_1, conjecture,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  (m2_subset_1(C, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (! [D] :  (m2_subset_1(D, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [E] :  (m1_valuat_1(E, A, B) =>  ( ~ (r2_tarski(C, k24_qc_lang1(A, D)))  =>  (! [F] :  (m2_funct_2(F, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (! [G] :  (m2_funct_2(G, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  ( (! [H] :  (m2_subset_1(H, k2_qc_lang1(A), k3_qc_lang1(A)) =>  ( ~ (C=H)  => k3_funct_2(k3_qc_lang1(A), B, G, H)=k3_funct_2(k3_qc_lang1(A), B, F, H)) ) )  => k3_funct_2(k2_valuat_1(A, B), k5_margrel1, k8_valuat_1(A, B, E, D), F)=k3_funct_2(k2_valuat_1(A, B), k5_margrel1, k8_valuat_1(A, B, E, D), G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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_funct_2, axiom,  (! [A, B] :  (! [C] :  (m1_funct_2(C, A, B) => v4_funct_1(C)) ) ) ).
fof(cc10_ordinal1, axiom,  (! [A] :  (v6_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_ordinal1(B)) ) ) ) ).
fof(cc11_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v7_ordinal1(A)) ) ).
fof(cc12_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v1_zfmisc_1(A)) ) ).
fof(cc13_ordinal1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  ~ (v8_ordinal1(A)) ) ) ).
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_ordinal1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) )  =>  (! [B] :  (m1_subset_1(B, A) =>  ~ (v8_ordinal1(B)) ) ) ) ) ).
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_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_funct_1(A)) ) ).
fof(cc1_funct_2, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_partfun1(C, A) => v1_funct_2(C, A, B)) ) ) ) ).
fof(cc1_margrel1, axiom,  (! [A] :  (v1_xboole_0(A) => v2_card_3(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_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C)) ) ) ).
fof(cc20_ordinal1, axiom,  (! [A] :  ( ~ (v1_setfam_1(A))  => v10_ordinal1(A)) ) ).
fof(cc2_funct_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ) ).
fof(cc2_funct_2, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_funct_2(C, A, B) => v1_partfun1(C, A)) ) ) ) ) ).
fof(cc2_margrel1, axiom,  (! [A] :  (m1_subset_1(A, k5_margrel1) => v1_xboolean(A)) ) ).
fof(cc2_ordinal1, axiom,  (! [A] :  ( (v1_ordinal1(A) & v2_ordinal1(A))  => v3_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(cc2_xxreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xxreal_0(A)) ) ).
fof(cc3_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_funct_1(B)) ) ) ) ).
fof(cc3_funct_2, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_funct_2(C, A, B) => v1_partfun1(C, A)) ) ) ) ) ).
fof(cc3_margrel1, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1))) =>  ( (v1_funct_1(B) & v1_funct_2(B, A, k5_margrel1))  =>  (v1_funct_1(B) &  (v1_funct_2(B, A, k5_margrel1) & v1_margrel1(B)) ) ) ) ) ) ).
fof(cc3_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_ordinal1(A)) ) ).
fof(cc3_relset_1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_xboole_0(C)) ) ) ) ).
fof(cc3_xxreal_0, axiom,  (! [A] :  ( (v1_xxreal_0(A) & v2_xxreal_0(A))  =>  ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v3_xxreal_0(A)) ) ) ) ) ).
fof(cc4_funct_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) ) ) ) ).
fof(cc4_funct_2, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, A))) =>  (v1_funct_2(B, A, A) => v1_partfun1(B, A)) ) ) ) ).
fof(cc4_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v5_ordinal1(A)) ) ).
fof(cc4_relset_1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A))) => v1_xboole_0(C)) ) ) ) ).
fof(cc4_xxreal_0, axiom,  (! [A] :  ( ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v3_xxreal_0(A)) ) )  =>  (v1_xxreal_0(A) & v2_xxreal_0(A)) ) ) ).
fof(cc5_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) )  =>  ( ~ (v1_zfmisc_1(A))  &  (v1_relat_1(A) & v1_funct_1(A)) ) ) ) ).
fof(cc5_funct_2, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A))) =>  (v1_funct_2(B, k2_zfmisc_1(A, A), A) => v1_partfun1(B, k2_zfmisc_1(A, A))) ) ) ) ).
fof(cc5_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, A) => v3_ordinal1(B)) ) ) ) ).
fof(cc5_xxreal_0, axiom,  (! [A] :  ( (v1_xxreal_0(A) & v3_xxreal_0(A))  =>  ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v2_xxreal_0(A)) ) ) ) ) ).
fof(cc6_funct_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) ) ) ) ).
fof(cc6_ordinal1, axiom,  (! [A] :  (v7_ordinal1(A) => v3_ordinal1(A)) ) ).
fof(cc6_xxreal_0, axiom,  (! [A] :  ( ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v2_xxreal_0(A)) ) )  =>  (v1_xxreal_0(A) & v3_xxreal_0(A)) ) ) ).
fof(cc7_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_funct_1(A)) ) ).
fof(cc7_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v7_ordinal1(A)) ) ).
fof(cc7_xxreal_0, axiom,  (! [A] :  ( (v8_ordinal1(A) & v1_xxreal_0(A))  =>  (v1_xxreal_0(A) &  ( ~ (v2_xxreal_0(A))  &  ~ (v3_xxreal_0(A)) ) ) ) ) ).
fof(cc8_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, A) =>  (v1_relat_1(B) & v1_funct_1(B)) ) ) ) ) ).
fof(cc8_ordinal1, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) => v7_ordinal1(A)) ) ).
fof(cc8_xxreal_0, axiom,  (! [A] :  ( (v1_xxreal_0(A) &  ( ~ (v2_xxreal_0(A))  &  ~ (v3_xxreal_0(A)) ) )  =>  (v8_ordinal1(A) & v1_xxreal_0(A)) ) ) ).
fof(cc9_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_funct_1(B)) ) ) ) ).
fof(cc9_funct_2, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  (! [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_xboole_0(C))  & v1_funct_2(C, A, B)) ) ) ) ) ) ) ).
fof(cc9_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v6_ordinal1(A)) ) ).
fof(commutativity_k13_margrel1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_margrel1(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_margrel1(B)) ) )  => k13_margrel1(A, B)=k13_margrel1(B, A)) ) ).
fof(commutativity_k15_margrel1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(B) &  (v1_funct_2(B, A, k5_margrel1) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1)))) )  &  (v1_funct_1(C) &  (v1_funct_2(C, A, k5_margrel1) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1)))) ) ) )  => k15_margrel1(A, B, C)=k15_margrel1(A, C, B)) ) ).
fof(commutativity_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, B)=k2_xboole_0(B, A)) ).
fof(commutativity_k3_xcmplx_0, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k3_xcmplx_0(A, B)=k3_xcmplx_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_k4_xboolean, axiom,  (! [A, B] :  ( (v1_xboolean(A) & v1_xboolean(B))  => k4_xboolean(A, B)=k4_xboolean(B, A)) ) ).
fof(commutativity_k9_margrel1, axiom,  (! [A, B] :  ( (m1_subset_1(A, k5_margrel1) & m1_subset_1(B, k5_margrel1))  => k9_margrel1(A, B)=k9_margrel1(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(d12_ordinal1, axiom,  (! [A] :  (v7_ordinal1(A) <=> r2_hidden(A, k4_ordinal1)) ) ).
fof(d19_relat_1, axiom,  (! [A] :  (! [B] :  (v1_relat_1(B) =>  (v5_relat_1(B, A) <=> r1_tarski(k10_xtuple_0(B), A)) ) ) ) ).
fof(d1_qc_lang3, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m2_finseq_1(B, k2_qc_lang1(A)) =>  (! [C] :  ( ( ~ (v1_xboole_0(C))  & m1_subset_1(C, k1_zfmisc_1(k2_qc_lang1(A))))  => k1_qc_lang3(A, B, C)=a_3_0_qc_lang3(A, B, C)) ) ) ) ) ) ).
fof(d1_tarski, axiom,  (! [A] :  (! [B] :  (B=k1_tarski(A) <=>  (! [C] :  (r2_hidden(C, B) <=> C=A) ) ) ) ) ).
fof(d1_valuat_1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] : k1_valuat_1(A, B)=k1_funct_2(k3_qc_lang1(A), B)) ) ) ).
fof(d1_xboolean, axiom, k1_xboolean=k5_numbers).
fof(d2_xboolean, axiom, k2_xboolean=1).
fof(d3_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (B=k10_xtuple_0(A) <=>  (! [C] :  (r2_hidden(C, B) <=>  (? [D] :  (r2_hidden(D, k9_xtuple_0(A)) & C=k1_funct_1(A, D)) ) ) ) ) ) ) ) ).
fof(d3_valuat_1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  (v7_ordinal1(C) =>  (! [D] :  ( (v5_relat_1(D, k3_qc_lang1(A)) &  (v3_card_1(D, C) & m2_finseq_1(D, k2_qc_lang1(A))) )  =>  (! [E] :  (m2_funct_2(E, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (! [F] :  (m2_finseq_1(F, B) =>  (F=k4_valuat_1(A, B, C, D, E) <=>  (k3_finseq_1(F)=C &  (! [G] :  (v7_ordinal1(G) =>  ( (r1_xxreal_0(1, G) & r1_xxreal_0(G, C))  => k1_funct_1(F, G)=k1_funct_1(E, k1_funct_1(D, G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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(d3_xboolean, axiom,  (! [A] :  (v1_xboolean(A) <=>  (A=k1_xboolean | A=k2_xboolean) ) ) ).
fof(d4_valuat_1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  (v7_ordinal1(C) =>  (! [D] :  ( (v5_relat_1(D, k3_qc_lang1(A)) &  (v3_card_1(D, C) & m2_finseq_1(D, k2_qc_lang1(A))) )  =>  (! [E] :  (m1_subset_1(E, k2_margrel1(B)) =>  (! [F] :  (m2_funct_2(F, k2_valuat_1(A, B), k5_margrel1, k9_funct_2(k2_valuat_1(A, B), k5_margrel1)) =>  (F=k5_valuat_1(A, B, C, D, E) <=>  (! [G] :  (m2_funct_2(G, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  ( (r2_tarski(k4_valuat_1(A, B, C, D, G), E) => k3_funct_2(k2_valuat_1(A, B), k5_margrel1, F, G)=k7_margrel1)  &  ( (k3_funct_2(k2_valuat_1(A, B), k5_margrel1, F, G)=k7_margrel1 => r2_tarski(k4_valuat_1(A, B, C, D, G), E))  &  ( ( ~ (r2_tarski(k4_valuat_1(A, B, C, D, G), E))  => k3_funct_2(k2_valuat_1(A, B), k5_margrel1, F, G)=k6_margrel1)  &  ~ ( (k3_funct_2(k2_valuat_1(A, B), k5_margrel1, F, G)=k6_margrel1 & r2_tarski(k4_valuat_1(A, B, C, D, G), E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d4_xboolean, axiom,  (! [A] :  (v1_xboolean(A) => k3_xboolean(A)=k6_xcmplx_0(1, A)) ) ).
fof(d5_xboole_0, axiom,  (! [A] :  (! [B] :  (! [C] :  (C=k4_xboole_0(A, B) <=>  (! [D] :  (r2_hidden(D, C) <=>  (r2_hidden(D, A) &  ~ (r2_hidden(D, B)) ) ) ) ) ) ) ) ).
fof(d5_xboolean, axiom,  (! [A] :  (v1_xboolean(A) =>  (! [B] :  (v1_xboolean(B) => k4_xboolean(A, B)=k3_xcmplx_0(A, B)) ) ) ) ).
fof(d7_card_1, axiom,  (! [A] :  (! [B] :  (v3_card_1(B, A) <=> k1_card_1(B)=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_margrel1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_margrel1(A)) )  =>  (v1_relat_1(k12_margrel1(A)) &  (v1_funct_1(k12_margrel1(A)) & v1_margrel1(k12_margrel1(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_margrel1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_margrel1(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_margrel1(B)) ) )  =>  (v1_relat_1(k13_margrel1(A, B)) &  (v1_funct_1(k13_margrel1(A, B)) & v1_margrel1(k13_margrel1(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_margrel1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  (v1_funct_1(B) &  (v1_funct_2(B, A, k5_margrel1) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1)))) ) )  =>  (v1_funct_1(k14_margrel1(A, B)) &  (v1_funct_2(k14_margrel1(A, B), A, k5_margrel1) & m1_subset_1(k14_margrel1(A, B), k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1)))) ) ) ) ).
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_margrel1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(B) &  (v1_funct_2(B, A, k5_margrel1) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1)))) )  &  (v1_funct_1(C) &  (v1_funct_2(C, A, k5_margrel1) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1)))) ) ) )  =>  (v1_funct_1(k15_margrel1(A, B, C)) &  (v1_funct_2(k15_margrel1(A, B, C), A, k5_margrel1) & m1_subset_1(k15_margrel1(A, B, C), k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1)))) ) ) ) ).
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_k1_card_1, axiom,  (! [A] : v1_card_1(k1_card_1(A))) ).
fof(dt_k1_funct_1, axiom, $true).
fof(dt_k1_funct_2, axiom, $true).
fof(dt_k1_qc_lang3, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_finseq_1(B, k2_qc_lang1(A)) &  ( ~ (v1_xboole_0(C))  & m1_subset_1(C, k1_zfmisc_1(k2_qc_lang1(A)))) ) )  => m1_subset_1(k1_qc_lang3(A, B, C), k1_zfmisc_1(C))) ) ).
fof(dt_k1_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  => m1_subset_1(k1_relset_1(A, B), 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_xboolean, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k23_qc_lang1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_finseq_1(B, k2_qc_lang1(A)))  => m1_subset_1(k23_qc_lang1(A, B), k1_zfmisc_1(k3_qc_lang1(A)))) ) ).
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_funcop_1, axiom, $true).
fof(dt_k2_margrel1, axiom, $true).
fof(dt_k2_qc_lang1, 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_xboolean, 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_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => m1_subset_1(k3_finseq_1(A), k4_ordinal1)) ) ).
fof(dt_k3_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_relat_1, axiom,  (! [A, B] : v1_relat_1(k3_relat_1(A, B))) ).
fof(dt_k3_valuat_1, 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, k9_funct_2(k2_valuat_1(A, B), k5_margrel1))) ) )  => m2_funct_2(k3_valuat_1(A, B, C, D), k2_valuat_1(A, B), k5_margrel1, k9_funct_2(k2_valuat_1(A, B), k5_margrel1))) ) ).
fof(dt_k3_xboolean, axiom,  (! [A] :  (v1_xboolean(A) => v1_xboolean(k3_xboolean(A))) ) ).
fof(dt_k3_xcmplx_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_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => m1_subset_1(k4_finseq_1(A), k1_zfmisc_1(k4_ordinal1))) ) ).
fof(dt_k4_ordinal1, axiom, $true).
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_valuat_1, axiom,  (! [A, B, C, D, E] :  ( (m1_qc_lang1(A) &  ( ~ (v1_xboole_0(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))) )  & m1_subset_1(E, k2_valuat_1(A, B))) ) ) )  => m2_finseq_1(k4_valuat_1(A, B, C, D, E), B)) ) ).
fof(dt_k4_xboole_0, axiom, $true).
fof(dt_k4_xboolean, 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_margrel1, axiom, $true).
fof(dt_k5_numbers, axiom, m1_subset_1(k5_numbers, k4_ordinal1)).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k5_valuat_1, axiom,  (! [A, B, C, D, E] :  ( (m1_qc_lang1(A) &  ( ~ (v1_xboole_0(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))) )  & m1_subset_1(E, k2_margrel1(B))) ) ) )  => m2_funct_2(k5_valuat_1(A, B, C, D, E), k2_valuat_1(A, B), k5_margrel1, k9_funct_2(k2_valuat_1(A, B), k5_margrel1))) ) ).
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_margrel1, axiom, m1_subset_1(k6_margrel1, k5_margrel1)).
fof(dt_k6_qc_lang1, axiom, $true).
fof(dt_k6_xcmplx_0, 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_k7_margrel1, axiom, m1_subset_1(k7_margrel1, k5_margrel1)).
fof(dt_k7_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(B, k1_zfmisc_1(A)) => m1_subset_1(k7_subset_1(A, B, C), k1_zfmisc_1(A))) ) ).
fof(dt_k7_valuat_1, axiom,  (! [A, B, C, D, E] :  ( (m1_qc_lang1(A) &  ( ~ (v1_xboole_0(B))  &  (v7_ordinal1(C) &  (m1_valuat_1(D, A, B) & m1_subset_1(E, k8_qc_lang1(A, C))) ) ) )  => m1_subset_1(k7_valuat_1(A, B, C, D, E), k2_margrel1(B))) ) ).
fof(dt_k8_funcop_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(C, A))  =>  (v1_funct_1(k8_funcop_1(A, B, C)) &  (v1_funct_2(k8_funcop_1(A, B, C), B, A) & m1_subset_1(k8_funcop_1(A, B, C), k1_zfmisc_1(k2_zfmisc_1(B, A)))) ) ) ) ).
fof(dt_k8_margrel1, axiom,  (! [A] :  (m1_subset_1(A, k5_margrel1) => m1_subset_1(k8_margrel1(A), k5_margrel1)) ) ).
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_valuat_1, axiom,  (! [A, B, C, D] :  ( (m1_qc_lang1(A) &  ( ~ (v1_xboole_0(B))  &  (m1_valuat_1(C, A, B) & m1_subset_1(D, k3_cqc_lang(A))) ) )  => m2_funct_2(k8_valuat_1(A, B, C, D), k2_valuat_1(A, B), k5_margrel1, k9_funct_2(k2_valuat_1(A, B), k5_margrel1))) ) ).
fof(dt_k9_funct_2, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  => m1_funct_2(k9_funct_2(A, B), A, B)) ) ).
fof(dt_k9_margrel1, axiom,  (! [A, B] :  ( (m1_subset_1(A, k5_margrel1) & m1_subset_1(B, k5_margrel1))  => m1_subset_1(k9_margrel1(A, B), k5_margrel1)) ) ).
fof(dt_k9_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k9_qc_lang1(A))) ) ) ).
fof(dt_k9_xtuple_0, axiom, $true).
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_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(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_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_funct_2, axiom,  (! [A, B] : v4_funct_1(k1_funct_2(A, B))) ).
fof(fc10_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) & v9_ordinal1(A))  =>  ~ (v10_ordinal1(k10_xtuple_0(A))) ) ) ).
fof(fc11_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) &  ~ (v9_ordinal1(A)) )  => v10_ordinal1(k10_xtuple_0(A))) ) ).
fof(fc12_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) )  => v1_zfmisc_1(k10_xtuple_0(A))) ) ).
fof(fc12_ordinal1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v9_ordinal1(A))  & v1_relat_1(B))  =>  (v1_relat_1(k3_relat_1(B, A)) & v9_ordinal1(k3_relat_1(B, A))) ) ) ).
fof(fc13_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) )  =>  ~ (v1_zfmisc_1(k10_xtuple_0(A))) ) ) ).
fof(fc14_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  => v4_funct_1(k1_tarski(A))) ) ).
fof(fc17_funct_1, axiom,  (! [A, B, C] :  ( (v4_funct_1(A) &  (v1_relat_1(C) &  (v5_relat_1(C, A) & v1_funct_1(C)) ) )  =>  (v1_relat_1(k1_funct_1(C, B)) & v1_funct_1(k1_funct_1(C, B))) ) ) ).
fof(fc18_funct_1, axiom,  (! [A] :  ( ( ~ (v1_zfmisc_1(A))  &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  ~ (v1_zfmisc_1(k9_xtuple_0(A))) ) ) ).
fof(fc1_funct_2, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  ~ (v1_xboole_0(k1_funct_2(A, B))) ) ) ).
fof(fc1_margrel1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_margrel1(A))) ) ) ).
fof(fc1_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v4_relat_1(B, A))  &  (v1_relat_1(C) & v4_relat_1(C, A)) )  => v4_relat_1(k2_xboole_0(B, C), A)) ) ).
fof(fc1_valuat_1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) &  ~ (v1_xboole_0(B)) )  =>  (v4_funct_1(k1_valuat_1(A, B)) &  ~ (v1_xboole_0(k1_valuat_1(A, B))) ) ) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc2_cqc_lang, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k3_cqc_lang(A))) ) ) ).
fof(fc2_funct_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) & v1_funct_1(B)) )  =>  (v1_relat_1(k3_relat_1(A, B)) & v1_funct_1(k3_relat_1(A, B))) ) ) ).
fof(fc2_funct_2, axiom,  (! [A] :  ~ (v1_xboole_0(k1_funct_2(A, A))) ) ).
fof(fc2_margrel1, axiom,  ~ (v1_xboole_0(k5_margrel1)) ).
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_funct_2, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & v1_xboole_0(B))  => v1_xboole_0(k1_funct_2(A, B))) ) ).
fof(fc3_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k3_qc_lang1(A))) ) ) ).
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(fc4_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, A) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, A)))) ) )  =>  (v1_funct_1(k3_relat_1(D, C)) & v1_funct_2(k3_relat_1(D, C), A, B)) ) ) ).
fof(fc4_margrel1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_margrel1(A)) )  => v1_xboolean(k1_funct_1(A, B))) ) ).
fof(fc4_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v5_ordinal1(A)) )  => v3_ordinal1(k9_xtuple_0(A))) ) ).
fof(fc4_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v5_relat_1(B, A))  &  (v1_relat_1(C) & v5_relat_1(C, A)) )  => v5_relat_1(k2_xboole_0(B, C), A)) ) ).
fof(fc4_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(A, B))) ) ) ).
fof(fc5_funct_2, axiom,  (! [A, B, C, D] :  ( ( (v1_funct_1(C) &  (v1_funct_2(C, B, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, B)))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) )  =>  (v1_funct_1(k3_relat_1(D, C)) & v1_funct_2(k3_relat_1(D, C), A, B)) ) ) ).
fof(fc5_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(B, 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_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(fc7_funct_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v2_funct_1(B)) ) )  =>  (v1_relat_1(k3_relat_1(A, B)) & v2_funct_1(k3_relat_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(fc8_funct_2, axiom,  (! [A, B, C, D, E] :  ( ( ~ (v1_xboole_0(B))  &  ( (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(E) &  (v1_funct_2(E, B, C) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) ) ) )  =>  (v1_funct_1(k3_relat_1(D, E)) & v1_funct_2(k3_relat_1(D, E), A, C)) ) ) ).
fof(fc8_ordinal1, axiom, v7_ordinal1(k5_ordinal1)).
fof(fc8_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, B), C))) => v1_relat_1(k9_xtuple_0(D))) ) ).
fof(fc9_ordinal1, axiom, v8_ordinal1(k5_ordinal1)).
fof(fc9_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, k2_zfmisc_1(B, C)))) => v1_relat_1(k10_xtuple_0(D))) ) ).
fof(fraenkel_a_3_0_qc_lang3, axiom,  (! [A, B, C, D] :  ( (m1_qc_lang1(B) &  (m2_finseq_1(C, k2_qc_lang1(B)) &  ( ~ (v1_xboole_0(D))  & m1_subset_1(D, k1_zfmisc_1(k2_qc_lang1(B)))) ) )  =>  (r2_hidden(A, a_3_0_qc_lang3(B, C, D)) <=>  (? [E] :  (v7_ordinal1(E) &  (A=k1_funct_1(C, E) &  (r1_xxreal_0(1, E) &  (r1_xxreal_0(E, k3_finseq_1(C)) & r2_tarski(k1_funct_1(C, E), D)) ) ) ) ) ) ) ) ).
fof(fraenkel_a_3_0_valuat_1, axiom,  (! [A, B, C, D] :  ( (m1_qc_lang1(B) &  (v7_ordinal1(C) &  (v5_relat_1(D, k3_qc_lang1(B)) &  (v3_card_1(D, C) & m2_finseq_1(D, k2_qc_lang1(B))) ) ) )  =>  (r2_hidden(A, a_3_0_valuat_1(B, C, D)) <=>  (? [E] :  (v7_ordinal1(E) &  (A=k1_funct_1(D, E) &  (r1_xxreal_0(1, E) &  (r1_xxreal_0(E, k3_finseq_1(D)) & r2_tarski(k1_funct_1(D, E), k3_qc_lang1(B))) ) ) ) ) ) ) ) ).
fof(idempotence_k13_margrel1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_margrel1(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_margrel1(B)) ) )  => k13_margrel1(A, A)=A) ) ).
fof(idempotence_k15_margrel1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(B) &  (v1_funct_2(B, A, k5_margrel1) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1)))) )  &  (v1_funct_1(C) &  (v1_funct_2(C, A, k5_margrel1) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1)))) ) ) )  => k15_margrel1(A, B, B)=B) ) ).
fof(idempotence_k2_xboole_0, axiom,  (! [A, B] : k2_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_k4_xboolean, axiom,  (! [A, B] :  ( (v1_xboolean(A) & v1_xboolean(B))  => k4_xboolean(A, A)=A) ) ).
fof(idempotence_k9_margrel1, axiom,  (! [A, B] :  ( (m1_subset_1(A, k5_margrel1) & m1_subset_1(B, k5_margrel1))  => k9_margrel1(A, A)=A) ) ).
fof(involutiveness_k12_margrel1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_margrel1(A)) )  => k12_margrel1(k12_margrel1(A))=A) ) ).
fof(involutiveness_k14_margrel1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  (v1_funct_1(B) &  (v1_funct_2(B, A, k5_margrel1) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1)))) ) )  => k14_margrel1(A, k14_margrel1(A, B))=B) ) ).
fof(involutiveness_k3_xboolean, axiom,  (! [A] :  (v1_xboolean(A) => k3_xboolean(k3_xboolean(A))=A) ) ).
fof(involutiveness_k8_margrel1, axiom,  (! [A] :  (m1_subset_1(A, k5_margrel1) => k8_margrel1(k8_margrel1(A))=A) ) ).
fof(l10_valuat_1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m2_subset_1(B, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [C] :  ( ~ (v1_xboole_0(C))  =>  (! [D] :  (m1_valuat_1(D, A, C) =>  (r2_funct_2(k2_valuat_1(A, C), k5_margrel1, k8_valuat_1(A, C, D, k5_cqc_lang(A)), k8_funcop_1(k5_margrel1, k2_valuat_1(A, C), k7_margrel1)) &  ( (! [E] :  (v7_ordinal1(E) =>  (! [F] :  ( (v5_relat_1(F, k3_qc_lang1(A)) &  (v3_card_1(F, E) & m2_finseq_1(F, k2_qc_lang1(A))) )  =>  (! [G] :  (m2_subset_1(G, k6_qc_lang1(A), k8_qc_lang1(A, E)) => r2_funct_2(k2_valuat_1(A, C), k5_margrel1, k8_valuat_1(A, C, D, k4_cqc_lang(E, A, G, F)), k5_valuat_1(A, C, E, F, k7_valuat_1(A, C, E, D, G)))) ) ) ) ) )  &  ( (! [E] :  (m2_subset_1(E, k9_qc_lang1(A), k3_cqc_lang(A)) => r2_funct_2(k2_valuat_1(A, C), k5_margrel1, k8_valuat_1(A, C, D, k6_cqc_lang(A, E)), k14_margrel1(k2_valuat_1(A, C), k8_valuat_1(A, C, D, E)))) )  &  ( (! [E] :  (m2_subset_1(E, k9_qc_lang1(A), k3_cqc_lang(A)) => r2_funct_2(k2_valuat_1(A, C), k5_margrel1, k8_valuat_1(A, C, D, k7_cqc_lang(A, B, E)), k15_margrel1(k2_valuat_1(A, C), k8_valuat_1(A, C, D, B), k8_valuat_1(A, C, D, E)))) )  &  (! [E] :  (m2_subset_1(E, k2_qc_lang1(A), k3_qc_lang1(A)) => r2_funct_2(k2_valuat_1(A, C), k5_margrel1, k8_valuat_1(A, C, D, k11_cqc_lang(A, E, B)), k3_valuat_1(A, C, E, k8_valuat_1(A, C, D, B)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(l36_valuat_1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [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] :  (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)) =>  (? [G] :  (m2_funct_2(G, k3_qc_lang1(A), B, k2_valuat_1(A, B)) &  ( (! [H] :  (m2_subset_1(H, k2_qc_lang1(A), k3_qc_lang1(A)) =>  ( ~ (H=C)  => k3_funct_2(k3_qc_lang1(A), B, G, H)=k3_funct_2(k3_qc_lang1(A), B, E, H)) ) )  & k3_funct_2(k3_qc_lang1(A), B, G, C)=k3_funct_2(k3_qc_lang1(A), B, F, D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(projectivity_k1_card_1, axiom,  (! [A] : k1_card_1(k1_card_1(A))=k1_card_1(A)) ).
fof(projectivity_k3_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => k3_finseq_1(k3_finseq_1(A))=k3_finseq_1(A)) ) ).
fof(rc10_ordinal1, axiom,  (? [A] :  ~ (v8_ordinal1(A)) ) ).
fof(rc11_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) ) ) ).
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(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_funct_1, axiom,  (? [A] :  (v1_relat_1(A) & v1_funct_1(A)) ) ).
fof(rc1_funct_2, axiom,  (! [A, 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_funct_2(C, A, B)) ) ) ) ) ) ) ).
fof(rc1_ordinal1, axiom,  (? [A] :  (v1_ordinal1(A) & v2_ordinal1(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_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ).
fof(rc2_margrel1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v1_margrel1(A)) ) ) ).
fof(rc2_ordinal1, axiom,  (? [A] : v3_ordinal1(A)) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc2_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(rc3_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_ordinal1(A) &  (v2_ordinal1(A) & v3_ordinal1(A)) ) ) ) ).
fof(rc3_xxreal_0, axiom,  (? [A] :  (v1_xxreal_0(A) & v2_xxreal_0(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_xxreal_0, axiom,  (? [A] :  (v1_xxreal_0(A) & v3_xxreal_0(A)) ) ).
fof(rc5_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) ) ) ).
fof(rc5_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc5_xxreal_0, axiom,  (? [A] :  (v8_ordinal1(A) & v1_xxreal_0(A)) ) ).
fof(rc6_funct_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) & v1_funct_1(C)) ) ) ) ) ).
fof(rc6_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc7_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v4_funct_1(A)) ) ).
fof(rc7_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v7_ordinal1(A)) ) ).
fof(rc8_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rc9_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
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_k14_margrel1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  (v1_funct_1(B) &  (v1_funct_2(B, A, k5_margrel1) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1)))) ) )  => k14_margrel1(A, B)=k12_margrel1(B)) ) ).
fof(redefinition_k15_margrel1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(B) &  (v1_funct_2(B, A, k5_margrel1) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1)))) )  &  (v1_funct_1(C) &  (v1_funct_2(C, A, k5_margrel1) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1)))) ) ) )  => k15_margrel1(A, B, C)=k13_margrel1(B, C)) ) ).
fof(redefinition_k1_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  => k1_relset_1(A, B)=k9_xtuple_0(B)) ) ).
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_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => k3_finseq_1(A)=k1_card_1(A)) ) ).
fof(redefinition_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_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => k4_finseq_1(A)=k9_xtuple_0(A)) ) ).
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_k4_valuat_1, axiom,  (! [A, B, C, D, E] :  ( (m1_qc_lang1(A) &  ( ~ (v1_xboole_0(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))) )  & m1_subset_1(E, k2_valuat_1(A, B))) ) ) )  => k4_valuat_1(A, B, C, D, E)=k3_relat_1(D, E)) ) ).
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_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_margrel1, axiom, k6_margrel1=k1_xboolean).
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_k7_margrel1, axiom, k7_margrel1=k2_xboolean).
fof(redefinition_k7_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(B, k1_zfmisc_1(A)) => k7_subset_1(A, B, C)=k4_xboole_0(B, C)) ) ).
fof(redefinition_k7_valuat_1, axiom,  (! [A, B, C, D, E] :  ( (m1_qc_lang1(A) &  ( ~ (v1_xboole_0(B))  &  (v7_ordinal1(C) &  (m1_valuat_1(D, A, B) & m1_subset_1(E, k8_qc_lang1(A, C))) ) ) )  => k7_valuat_1(A, B, C, D, E)=k1_funct_1(D, E)) ) ).
fof(redefinition_k8_funcop_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(C, A))  => k8_funcop_1(A, B, C)=k2_funcop_1(B, C)) ) ).
fof(redefinition_k8_margrel1, axiom,  (! [A] :  (m1_subset_1(A, k5_margrel1) => k8_margrel1(A)=k3_xboolean(A)) ) ).
fof(redefinition_k9_funct_2, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  => k9_funct_2(A, B)=k1_funct_2(A, B)) ) ).
fof(redefinition_k9_margrel1, axiom,  (! [A, B] :  ( (m1_subset_1(A, k5_margrel1) & m1_subset_1(B, k5_margrel1))  => k9_margrel1(A, B)=k4_xboolean(A, B)) ) ).
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_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_r1_xxreal_0, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => r1_xxreal_0(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_cqc_lang__e2_35__valuat_1, axiom,  (! [A, B, C, D] :  ( (m1_qc_lang1(A) &  ( ~ (v1_xboole_0(B))  &  (m2_subset_1(C, k2_qc_lang1(A), k3_qc_lang1(A)) & m1_valuat_1(D, A, B)) ) )  =>  ( (! [E] :  (m2_subset_1(E, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [F] :  (m2_subset_1(F, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [G] :  (m2_subset_1(G, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (! [H] :  (v7_ordinal1(H) =>  (! [I] :  ( (v5_relat_1(I, k3_qc_lang1(A)) &  (v3_card_1(I, H) & m2_finseq_1(I, k2_qc_lang1(A))) )  =>  (! [J] :  (m2_subset_1(J, k6_qc_lang1(A), k8_qc_lang1(A, H)) =>  ( ( ~ (r2_tarski(C, k24_qc_lang1(A, k5_cqc_lang(A))))  =>  (! [K] :  (m2_funct_2(K, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (! [L] :  (m2_funct_2(L, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  ( (! [M] :  (m2_subset_1(M, k2_qc_lang1(A), k3_qc_lang1(A)) =>  ( ~ (C=M)  => k3_funct_2(k3_qc_lang1(A), B, L, M)=k3_funct_2(k3_qc_lang1(A), B, K, M)) ) )  => k3_funct_2(k2_valuat_1(A, B), k5_margrel1, k8_valuat_1(A, B, D, k5_cqc_lang(A)), K)=k3_funct_2(k2_valuat_1(A, B), k5_margrel1, k8_valuat_1(A, B, D, k5_cqc_lang(A)), L)) ) ) ) ) )  &  ( ( ~ (r2_tarski(C, k24_qc_lang1(A, k4_cqc_lang(H, A, J, I))))  =>  (! [N] :  (m2_funct_2(N, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (! [O] :  (m2_funct_2(O, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  ( (! [P] :  (m2_subset_1(P, k2_qc_lang1(A), k3_qc_lang1(A)) =>  ( ~ (C=P)  => k3_funct_2(k3_qc_lang1(A), B, O, P)=k3_funct_2(k3_qc_lang1(A), B, N, P)) ) )  => k3_funct_2(k2_valuat_1(A, B), k5_margrel1, k8_valuat_1(A, B, D, k4_cqc_lang(H, A, J, I)), N)=k3_funct_2(k2_valuat_1(A, B), k5_margrel1, k8_valuat_1(A, B, D, k4_cqc_lang(H, A, J, I)), O)) ) ) ) ) )  &  ( ( ( ~ (r2_tarski(C, k24_qc_lang1(A, E)))  =>  (! [Q] :  (m2_funct_2(Q, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (! [R] :  (m2_funct_2(R, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  ( (! [S] :  (m2_subset_1(S, k2_qc_lang1(A), k3_qc_lang1(A)) =>  ( ~ (C=S)  => k3_funct_2(k3_qc_lang1(A), B, R, S)=k3_funct_2(k3_qc_lang1(A), B, Q, S)) ) )  => k3_funct_2(k2_valuat_1(A, B), k5_margrel1, k8_valuat_1(A, B, D, E), Q)=k3_funct_2(k2_valuat_1(A, B), k5_margrel1, k8_valuat_1(A, B, D, E), R)) ) ) ) ) )  =>  ( ~ (r2_tarski(C, k24_qc_lang1(A, k6_cqc_lang(A, E))))  =>  (! [T] :  (m2_funct_2(T, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (! [U] :  (m2_funct_2(U, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  ( (! [V] :  (m2_subset_1(V, k2_qc_lang1(A), k3_qc_lang1(A)) =>  ( ~ (C=V)  => k3_funct_2(k3_qc_lang1(A), B, U, V)=k3_funct_2(k3_qc_lang1(A), B, T, V)) ) )  => k3_funct_2(k2_valuat_1(A, B), k5_margrel1, k8_valuat_1(A, B, D, k6_cqc_lang(A, E)), T)=k3_funct_2(k2_valuat_1(A, B), k5_margrel1, k8_valuat_1(A, B, D, k6_cqc_lang(A, E)), U)) ) ) ) ) ) )  &  ( ( ( ( ~ (r2_tarski(C, k24_qc_lang1(A, E)))  =>  (! [W] :  (m2_funct_2(W, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (! [X] :  (m2_funct_2(X, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  ( (! [Y] :  (m2_subset_1(Y, k2_qc_lang1(A), k3_qc_lang1(A)) =>  ( ~ (C=Y)  => k3_funct_2(k3_qc_lang1(A), B, X, Y)=k3_funct_2(k3_qc_lang1(A), B, W, Y)) ) )  => k3_funct_2(k2_valuat_1(A, B), k5_margrel1, k8_valuat_1(A, B, D, E), W)=k3_funct_2(k2_valuat_1(A, B), k5_margrel1, k8_valuat_1(A, B, D, E), X)) ) ) ) ) )  &  ( ~ (r2_tarski(C, k24_qc_lang1(A, F)))  =>  (! [Z] :  (m2_funct_2(Z, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (! [A1] :  (m2_funct_2(A1, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  ( (! [B1] :  (m2_subset_1(B1, k2_qc_lang1(A), k3_qc_lang1(A)) =>  ( ~ (C=B1)  => k3_funct_2(k3_qc_lang1(A), B, A1, B1)=k3_funct_2(k3_qc_lang1(A), B, Z, B1)) ) )  => k3_funct_2(k2_valuat_1(A, B), k5_margrel1, k8_valuat_1(A, B, D, F), Z)=k3_funct_2(k2_valuat_1(A, B), k5_margrel1, k8_valuat_1(A, B, D, F), A1)) ) ) ) ) ) )  =>  ( ~ (r2_tarski(C, k24_qc_lang1(A, k7_cqc_lang(A, E, F))))  =>  (! [C1] :  (m2_funct_2(C1, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (! [D1] :  (m2_funct_2(D1, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  ( (! [E1] :  (m2_subset_1(E1, k2_qc_lang1(A), k3_qc_lang1(A)) =>  ( ~ (C=E1)  => k3_funct_2(k3_qc_lang1(A), B, D1, E1)=k3_funct_2(k3_qc_lang1(A), B, C1, E1)) ) )  => k3_funct_2(k2_valuat_1(A, B), k5_margrel1, k8_valuat_1(A, B, D, k7_cqc_lang(A, E, F)), C1)=k3_funct_2(k2_valuat_1(A, B), k5_margrel1, k8_valuat_1(A, B, D, k7_cqc_lang(A, E, F)), D1)) ) ) ) ) ) )  &  ( ( ~ (r2_tarski(C, k24_qc_lang1(A, E)))  =>  (! [F1] :  (m2_funct_2(F1, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (! [G1] :  (m2_funct_2(G1, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  ( (! [H1] :  (m2_subset_1(H1, k2_qc_lang1(A), k3_qc_lang1(A)) =>  ( ~ (C=H1)  => k3_funct_2(k3_qc_lang1(A), B, G1, H1)=k3_funct_2(k3_qc_lang1(A), B, F1, H1)) ) )  => k3_funct_2(k2_valuat_1(A, B), k5_margrel1, k8_valuat_1(A, B, D, E), F1)=k3_funct_2(k2_valuat_1(A, B), k5_margrel1, k8_valuat_1(A, B, D, E), G1)) ) ) ) ) )  =>  ( ~ (r2_tarski(C, k24_qc_lang1(A, k11_cqc_lang(A, G, E))))  =>  (! [I1] :  (m2_funct_2(I1, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (! [J1] :  (m2_funct_2(J1, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  ( (! [K1] :  (m2_subset_1(K1, k2_qc_lang1(A), k3_qc_lang1(A)) =>  ( ~ (C=K1)  => k3_funct_2(k3_qc_lang1(A), B, J1, K1)=k3_funct_2(k3_qc_lang1(A), B, I1, K1)) ) )  => k3_funct_2(k2_valuat_1(A, B), k5_margrel1, k8_valuat_1(A, B, D, k11_cqc_lang(A, G, E)), I1)=k3_funct_2(k2_valuat_1(A, B), k5_margrel1, k8_valuat_1(A, B, D, k11_cqc_lang(A, G, E)), J1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [E] :  (m2_subset_1(E, k9_qc_lang1(A), k3_cqc_lang(A)) =>  ( ~ (r2_tarski(C, k24_qc_lang1(A, E)))  =>  (! [L1] :  (m2_funct_2(L1, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (! [M1] :  (m2_funct_2(M1, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  ( (! [N1] :  (m2_subset_1(N1, k2_qc_lang1(A), k3_qc_lang1(A)) =>  ( ~ (C=N1)  => k3_funct_2(k3_qc_lang1(A), B, M1, N1)=k3_funct_2(k3_qc_lang1(A), B, L1, N1)) ) )  => k3_funct_2(k2_valuat_1(A, B), k5_margrel1, k8_valuat_1(A, B, D, E), L1)=k3_funct_2(k2_valuat_1(A, B), k5_margrel1, k8_valuat_1(A, B, D, E), M1)) ) ) ) ) ) ) ) ) ) ) ).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(spc1_numerals, axiom,  (v2_xxreal_0(1) & m1_subset_1(1, k4_ordinal1)) ).
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(t10_qc_lang3, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m1_subset_1(B, k9_qc_lang1(A)) =>  (! [C] :  (m1_subset_1(C, k9_qc_lang1(A)) => k24_qc_lang1(A, k14_qc_lang1(A, B, C))=k4_subset_1(k3_qc_lang1(A), k24_qc_lang1(A, B), k24_qc_lang1(A, C))) ) ) ) ) ) ).
fof(t10_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) => k3_funct_2(k2_valuat_1(A, B), k5_margrel1, k8_valuat_1(A, B, E, k6_cqc_lang(A, D)), C)=k8_margrel1(k3_funct_2(k2_valuat_1(A, B), k5_margrel1, k8_valuat_1(A, B, E, D), C))) ) ) ) ) ) ) ) ) ) ).
fof(t11_margrel1, axiom,  (! [A] :  (v1_xboolean(A) =>  ( (A=k6_margrel1 => k3_xboolean(A)=k7_margrel1)  &  ( (k3_xboolean(A)=k7_margrel1 => A=k6_margrel1)  &  ( (A=k7_margrel1 => k3_xboolean(A)=k6_margrel1)  &  (k3_xboolean(A)=k6_margrel1 => A=k7_margrel1) ) ) ) ) ) ).
fof(t12_margrel1, axiom,  (! [A] :  (v1_xboolean(A) =>  (! [B] :  (v1_xboolean(B) =>  ( (k4_xboolean(A, B)=k7_margrel1 =>  (A=k7_margrel1 & B=k7_margrel1) )  &  ( ( (A=k7_margrel1 & B=k7_margrel1)  => k4_xboolean(A, B)=k7_margrel1)  &  ( ~ ( (k4_xboolean(A, B)=k6_margrel1 &  ( ~ (A=k6_margrel1)  &  ~ (B=k6_margrel1) ) ) )  &  ( (A=k6_margrel1 | B=k6_margrel1)  => k4_xboolean(A, B)=k6_margrel1) ) ) ) ) ) ) ) ).
fof(t12_qc_lang3, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m2_subset_1(B, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (! [C] :  (m1_subset_1(C, k9_qc_lang1(A)) => k24_qc_lang1(A, k15_qc_lang1(A, B, C))=k7_subset_1(k3_qc_lang1(A), k24_qc_lang1(A, C), k1_tarski(B))) ) ) ) ) ) ).
fof(t12_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] :  (m2_subset_1(E, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [F] :  (m1_valuat_1(F, A, B) => k3_funct_2(k2_valuat_1(A, B), k5_margrel1, k8_valuat_1(A, B, F, k7_cqc_lang(A, D, E)), C)=k9_margrel1(k3_funct_2(k2_valuat_1(A, B), k5_margrel1, k8_valuat_1(A, B, F, D), C), k3_funct_2(k2_valuat_1(A, B), k5_margrel1, k8_valuat_1(A, B, F, E), C))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t14_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (! [B] :  ( (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) )  =>  ( (k3_finseq_1(A)=k3_finseq_1(B) &  (! [C] :  (v7_ordinal1(C) =>  ( (r1_xxreal_0(1, C) & r1_xxreal_0(C, k3_finseq_1(A)))  => k1_funct_1(A, C)=k1_funct_1(B, C)) ) ) )  => 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(t25_finseq_3, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (! [B] :  (v7_ordinal1(B) =>  (r2_tarski(B, k1_relset_1(k4_ordinal1, A)) <=>  (r1_xxreal_0(1, B) & r1_xxreal_0(B, k3_finseq_1(A))) ) ) ) ) ) ).
fof(t2_qc_lang3, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m2_finseq_1(B, k2_qc_lang1(A)) => k23_qc_lang1(A, B)=k1_qc_lang3(A, B, k3_qc_lang1(A))) ) ) ) ).
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(t2_valuat_1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  (m2_subset_1(C, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (! [D] :  (m2_funct_2(D, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (! [E] :  (m2_funct_2(E, k2_valuat_1(A, B), k5_margrel1, k9_funct_2(k2_valuat_1(A, B), k5_margrel1)) =>  (k3_funct_2(k2_valuat_1(A, B), k5_margrel1, k3_valuat_1(A, B, C, E), D)=k6_margrel1 <=>  (? [F] :  (m2_funct_2(F, k3_qc_lang1(A), B, k2_valuat_1(A, B)) &  (k3_funct_2(k2_valuat_1(A, B), k5_margrel1, E, F)=k6_margrel1 &  (! [G] :  (m2_subset_1(G, k2_qc_lang1(A), k3_qc_lang1(A)) =>  ( ~ (C=G)  => k3_funct_2(k3_qc_lang1(A), B, F, G)=k3_funct_2(k3_qc_lang1(A), B, D, G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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(t3_valuat_1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  (m2_subset_1(C, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (! [D] :  (m2_funct_2(D, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (! [E] :  (m2_funct_2(E, k2_valuat_1(A, B), k5_margrel1, k9_funct_2(k2_valuat_1(A, B), k5_margrel1)) =>  (k3_funct_2(k2_valuat_1(A, B), k5_margrel1, k3_valuat_1(A, B, C, E), D)=k7_margrel1 <=>  (! [F] :  (m2_funct_2(F, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  ( (! [G] :  (m2_subset_1(G, k2_qc_lang1(A), k3_qc_lang1(A)) =>  ( ~ (C=G)  => k3_funct_2(k3_qc_lang1(A), B, F, G)=k3_funct_2(k3_qc_lang1(A), B, D, G)) ) )  => k3_funct_2(k2_valuat_1(A, B), k5_margrel1, E, F)=k7_margrel1) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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_qc_lang3, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  (m1_qc_lang1(B) =>  (! [C] :  (m2_subset_1(C, k6_qc_lang1(B), k8_qc_lang1(B, A)) =>  (! [D] :  ( (v3_card_1(D, A) & m2_finseq_1(D, k2_qc_lang1(B)))  => k24_qc_lang1(B, k10_qc_lang1(B, C, D))=k23_qc_lang1(B, D)) ) ) ) ) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t5_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] :  (m1_valuat_1(D, A, B) => k3_funct_2(k2_valuat_1(A, B), k5_margrel1, k8_valuat_1(A, B, D, k5_cqc_lang(A)), C)=k7_margrel1) ) ) ) ) ) ) ) ).
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_qc_lang3, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m1_subset_1(B, k9_qc_lang1(A)) => k24_qc_lang1(A, k13_qc_lang1(A, B))=k24_qc_lang1(A, B)) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
