% Mizar problem: t81_sublemma,sublemma,2332,5 
fof(t81_sublemma, conjecture,  (! [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] :  ( (v1_funct_1(F) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B))))  =>  (! [G] :  ( (v1_funct_1(G) & m1_subset_1(G, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B))))  =>  (! [H] :  ( (v1_funct_1(H) & m1_subset_1(H, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B))))  =>  ( ( (! [I] :  (m2_subset_1(I, k2_qc_lang1(A), k3_qc_lang1(A)) =>  ~ ( (r2_tarski(I, k1_relset_1(k3_qc_lang1(A), G)) & r2_tarski(I, k24_qc_lang1(A, D))) ) ) )  &  ( (! [I] :  (m2_subset_1(I, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (r2_tarski(I, k1_relset_1(k3_qc_lang1(A), H)) => k1_funct_1(H, I)=k3_funct_2(k3_qc_lang1(A), B, E, I)) ) )  & r1_xboole_0(k1_relset_1(k3_qc_lang1(A), F), k1_relset_1(k3_qc_lang1(A), H))) )  =>  (r1_valuat_1(A, B, D, C, k1_sublemma(A, B, E, F)) <=> r1_valuat_1(A, B, D, C, k1_sublemma(A, B, E, k14_sublemma(A, B, k14_sublemma(A, B, F, G), H)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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_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_funcop_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  ( (v1_relat_1(B) &  (v5_relat_1(B, A) & v1_funct_1(B)) )  =>  (v1_relat_1(B) &  (v1_funct_1(B) & v1_funcop_1(B)) ) ) ) ) ) ).
fof(cc1_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_funct_1(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_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_relat_1(A)) ) ).
fof(cc1_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C)) ) ) ).
fof(cc1_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_funcop_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funcop_1(A)) ) ) ) ).
fof(cc2_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_ordinal1, axiom,  (! [A] :  ( (v1_ordinal1(A) & v2_ordinal1(A))  => v3_ordinal1(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_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_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_xxreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xxreal_0(A)) ) ).
fof(cc3_funcop_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_xboole_0(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) ) ) ) ).
fof(cc3_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_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_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_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_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_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_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_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ~ (v1_subset_1(B, A)) ) ) ) ) ).
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_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(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_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(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_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(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_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(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_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v6_ordinal1(A)) ) ).
fof(commutativity_k3_xboole_0, axiom,  (! [A, B] : k3_xboole_0(A, B)=k3_xboole_0(B, A)) ).
fof(d7_xboole_0, axiom,  (! [A] :  (! [B] :  (r1_xboole_0(A, B) <=> k3_xboole_0(A, B)=k1_xboole_0) ) ) ).
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_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_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) => m1_subset_1(k12_qc_lang1(A), k9_qc_lang1(A))) ) ).
fof(dt_k13_qc_lang1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k9_qc_lang1(A)))  => m1_subset_1(k13_qc_lang1(A, B), k9_qc_lang1(A))) ) ).
fof(dt_k14_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_k14_sublemma, axiom,  (! [A, B, C, D] :  ( (m1_qc_lang1(A) &  ( ~ (v1_xboole_0(B))  &  ( (v1_funct_1(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B))))  &  (v1_funct_1(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B)))) ) ) )  =>  (v1_funct_1(k14_sublemma(A, B, C, D)) & m1_subset_1(k14_sublemma(A, B, C, D), k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B)))) ) ) ).
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_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_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_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_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_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_zfmisc_1, axiom, $true).
fof(dt_k3_cqc_lang, axiom,  (! [A] :  (m1_qc_lang1(A) => m1_subset_1(k3_cqc_lang(A), k1_zfmisc_1(k9_qc_lang1(A)))) ) ).
fof(dt_k3_funct_2, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  & m1_subset_1(D, A)) )  => m1_subset_1(k3_funct_2(A, B, C, D), B)) ) ).
fof(dt_k3_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) => m1_subset_1(k3_qc_lang1(A), k1_zfmisc_1(k2_qc_lang1(A)))) ) ).
fof(dt_k3_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_ordinal1, 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_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_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_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_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k9_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_funct_1, axiom,  (! [A, B] :  ( ( ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) ) )  & m1_subset_1(B, k9_xtuple_0(A)))  =>  ~ (v1_xboole_0(k1_funct_1(A, B))) ) ) ).
fof(fc11_funct_4, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v5_relat_1(B, A) & v1_funct_1(B)) )  &  (v1_relat_1(C) &  (v5_relat_1(C, A) & v1_funct_1(C)) ) )  =>  (v1_relat_1(k1_funct_4(B, C)) &  (v5_relat_1(k1_funct_4(B, C), A) & v1_funct_1(k1_funct_4(B, C))) ) ) ) ).
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(fc19_funct_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v3_relat_1(A) & v1_funct_1(A)) )  => v1_xboole_0(k1_funct_1(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(fc24_relat_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) & v1_relat_1(A))  => v1_zfmisc_1(k9_xtuple_0(A))) ) ).
fof(fc2_cqc_lang, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k3_cqc_lang(A))) ) ) ).
fof(fc2_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k2_qc_lang1(A))) ) ) ).
fof(fc2_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v4_relat_1(B, A))  & v1_relat_1(C))  => v4_relat_1(k3_xboole_0(B, C), A)) ) ).
fof(fc3_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k3_qc_lang1(A))) ) ) ).
fof(fc4_funct_4, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) &  (v1_funct_1(B) &  ~ (v1_xboole_0(B)) ) ) )  =>  (v1_relat_1(k1_funct_4(A, B)) &  (v1_funct_1(k1_funct_4(A, B)) &  ~ (v1_xboole_0(k1_funct_4(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_xtuple_0, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k9_xtuple_0(A))) ) ).
fof(fc5_funct_4, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) &  (v1_funct_1(B) &  ~ (v1_xboole_0(B)) ) ) )  =>  (v1_relat_1(k1_funct_4(B, A)) &  (v1_funct_1(k1_funct_4(B, A)) &  ~ (v1_xboole_0(k1_funct_4(B, A))) ) ) ) ) ).
fof(fc5_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v5_relat_1(B, A))  & v1_relat_1(C))  => v5_relat_1(k3_xboole_0(B, C), A)) ) ).
fof(fc6_funct_4, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) )  &  (v1_relat_1(B) &  (v2_relat_1(B) & v1_funct_1(B)) ) )  =>  (v1_relat_1(k1_funct_4(A, B)) &  (v2_relat_1(k1_funct_4(A, B)) & v1_funct_1(k1_funct_4(A, B))) ) ) ) ).
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_funct_4, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_funcop_1(B)) ) )  =>  (v1_relat_1(k1_funct_4(A, B)) &  (v1_funct_1(k1_funct_4(A, B)) & v1_funcop_1(k1_funct_4(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_4, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) & v1_funct_1(B)) )  &  (v1_relat_1(C) &  (v4_relat_1(C, A) & v1_funct_1(C)) ) )  =>  (v1_relat_1(k1_funct_4(B, C)) &  (v4_relat_1(k1_funct_4(B, C), A) & v1_funct_1(k1_funct_4(B, C))) ) ) ) ).
fof(fc8_relat_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_relat_1(A))  =>  ~ (v1_xboole_0(k9_xtuple_0(A))) ) ) ).
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_funcop_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(k1_funct_1(A, B)) & v1_funct_1(k1_funct_1(A, B))) ) ) ).
fof(idempotence_k14_sublemma, axiom,  (! [A, B, C, D] :  ( (m1_qc_lang1(A) &  ( ~ (v1_xboole_0(B))  &  ( (v1_funct_1(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B))))  &  (v1_funct_1(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B)))) ) ) )  => k14_sublemma(A, B, C, C)=C) ) ).
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_k3_xboole_0, axiom,  (! [A, B] : k3_xboole_0(A, A)=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_funcop_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) ) ) ).
fof(rc1_funct_1, axiom,  (? [A] :  (v1_relat_1(A) & v1_funct_1(A)) ) ).
fof(rc1_ordinal1, axiom,  (? [A] :  (v1_ordinal1(A) & v2_ordinal1(A)) ) ).
fof(rc1_relat_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_relat_1(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_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_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(rc2_funcop_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  (v3_funct_1(A) &  ~ (v1_xboole_0(A)) ) ) ) ) ).
fof(rc2_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ).
fof(rc2_ordinal1, axiom,  (? [A] : v3_ordinal1(A)) ).
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_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(rc3_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) ) ) ).
fof(rc3_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_ordinal1(A) &  (v2_ordinal1(A) & v3_ordinal1(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_xxreal_0, axiom,  (? [A] :  (v1_xxreal_0(A) & v2_xxreal_0(A)) ) ).
fof(rc4_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_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_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_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_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(rc6_subset_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
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_funct_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) & v1_funct_1(B)) ) ) ) ) ).
fof(rc9_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rd1_funct_4, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_xboole_0(B)) ) )  => k1_funct_4(B, A)=A) ) ).
fof(rd2_funct_4, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_xboole_0(B)) ) )  => k1_funct_4(A, B)=A) ) ).
fof(rd4_funct_4, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) & v1_funct_1(B)) )  => k1_funct_4(k1_funct_4(A, B), B)=k1_funct_4(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_k14_sublemma, axiom,  (! [A, B, C, D] :  ( (m1_qc_lang1(A) &  ( ~ (v1_xboole_0(B))  &  ( (v1_funct_1(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B))))  &  (v1_funct_1(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B)))) ) ) )  => k14_sublemma(A, B, C, D)=k1_funct_4(C, D)) ) ).
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_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_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_k5_cqc_lang, axiom,  (! [A] :  (m1_qc_lang1(A) => k5_cqc_lang(A)=k12_qc_lang1(A)) ) ).
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_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_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_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(s1_cqc_lang__e2_99__sublemma, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  ( ~ (v1_xboole_0(B))  & m1_valuat_1(C, 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] :  (m2_subset_1(F, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (! [G] :  (v7_ordinal1(G) =>  (! [H] :  ( (v5_relat_1(H, k3_qc_lang1(A)) &  (v3_card_1(H, G) & m2_finseq_1(H, k2_qc_lang1(A))) )  =>  (! [I] :  (m2_subset_1(I, k6_qc_lang1(A), k8_qc_lang1(A, G)) =>  ( (! [J] :  (m2_funct_2(J, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (! [K] :  ( (v1_funct_1(K) & m1_subset_1(K, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B))))  =>  (! [L] :  ( (v1_funct_1(L) & m1_subset_1(L, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B))))  =>  (! [M] :  ( (v1_funct_1(M) & m1_subset_1(M, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B))))  =>  ( ( (! [N] :  (m2_subset_1(N, k2_qc_lang1(A), k3_qc_lang1(A)) =>  ~ ( (r2_tarski(N, k1_relset_1(k3_qc_lang1(A), L)) & r2_tarski(N, k24_qc_lang1(A, k5_cqc_lang(A)))) ) ) )  &  ( (! [N] :  (m2_subset_1(N, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (r2_tarski(N, k1_relset_1(k3_qc_lang1(A), M)) => k1_funct_1(M, N)=k3_funct_2(k3_qc_lang1(A), B, J, N)) ) )  & r1_xboole_0(k1_relset_1(k3_qc_lang1(A), K), k1_relset_1(k3_qc_lang1(A), M))) )  =>  (r1_valuat_1(A, B, k5_cqc_lang(A), C, k1_sublemma(A, B, J, K)) <=> r1_valuat_1(A, B, k5_cqc_lang(A), C, k1_sublemma(A, B, J, k14_sublemma(A, B, k14_sublemma(A, B, K, L), M)))) ) ) ) ) ) ) ) ) )  &  ( (! [O] :  (m2_funct_2(O, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (! [P] :  ( (v1_funct_1(P) & m1_subset_1(P, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B))))  =>  (! [Q] :  ( (v1_funct_1(Q) & m1_subset_1(Q, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B))))  =>  (! [R] :  ( (v1_funct_1(R) & m1_subset_1(R, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B))))  =>  ( ( (! [S] :  (m2_subset_1(S, k2_qc_lang1(A), k3_qc_lang1(A)) =>  ~ ( (r2_tarski(S, k1_relset_1(k3_qc_lang1(A), Q)) & r2_tarski(S, k24_qc_lang1(A, k4_cqc_lang(G, A, I, H)))) ) ) )  &  ( (! [S] :  (m2_subset_1(S, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (r2_tarski(S, k1_relset_1(k3_qc_lang1(A), R)) => k1_funct_1(R, S)=k3_funct_2(k3_qc_lang1(A), B, O, S)) ) )  & r1_xboole_0(k1_relset_1(k3_qc_lang1(A), P), k1_relset_1(k3_qc_lang1(A), R))) )  =>  (r1_valuat_1(A, B, k4_cqc_lang(G, A, I, H), C, k1_sublemma(A, B, O, P)) <=> r1_valuat_1(A, B, k4_cqc_lang(G, A, I, H), C, k1_sublemma(A, B, O, k14_sublemma(A, B, k14_sublemma(A, B, P, Q), R)))) ) ) ) ) ) ) ) ) )  &  ( ( (! [T] :  (m2_funct_2(T, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (! [U] :  ( (v1_funct_1(U) & m1_subset_1(U, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B))))  =>  (! [V] :  ( (v1_funct_1(V) & m1_subset_1(V, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B))))  =>  (! [W] :  ( (v1_funct_1(W) & m1_subset_1(W, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B))))  =>  ( ( (! [X] :  (m2_subset_1(X, k2_qc_lang1(A), k3_qc_lang1(A)) =>  ~ ( (r2_tarski(X, k1_relset_1(k3_qc_lang1(A), V)) & r2_tarski(X, k24_qc_lang1(A, D))) ) ) )  &  ( (! [X] :  (m2_subset_1(X, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (r2_tarski(X, k1_relset_1(k3_qc_lang1(A), W)) => k1_funct_1(W, X)=k3_funct_2(k3_qc_lang1(A), B, T, X)) ) )  & r1_xboole_0(k1_relset_1(k3_qc_lang1(A), U), k1_relset_1(k3_qc_lang1(A), W))) )  =>  (r1_valuat_1(A, B, D, C, k1_sublemma(A, B, T, U)) <=> r1_valuat_1(A, B, D, C, k1_sublemma(A, B, T, k14_sublemma(A, B, k14_sublemma(A, B, U, V), W)))) ) ) ) ) ) ) ) ) )  =>  (! [Y] :  (m2_funct_2(Y, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (! [Z] :  ( (v1_funct_1(Z) & m1_subset_1(Z, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B))))  =>  (! [A1] :  ( (v1_funct_1(A1) & m1_subset_1(A1, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B))))  =>  (! [B1] :  ( (v1_funct_1(B1) & m1_subset_1(B1, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B))))  =>  ( ( (! [C1] :  (m2_subset_1(C1, k2_qc_lang1(A), k3_qc_lang1(A)) =>  ~ ( (r2_tarski(C1, k1_relset_1(k3_qc_lang1(A), A1)) & r2_tarski(C1, k24_qc_lang1(A, k6_cqc_lang(A, D)))) ) ) )  &  ( (! [C1] :  (m2_subset_1(C1, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (r2_tarski(C1, k1_relset_1(k3_qc_lang1(A), B1)) => k1_funct_1(B1, C1)=k3_funct_2(k3_qc_lang1(A), B, Y, C1)) ) )  & r1_xboole_0(k1_relset_1(k3_qc_lang1(A), Z), k1_relset_1(k3_qc_lang1(A), B1))) )  =>  (r1_valuat_1(A, B, k6_cqc_lang(A, D), C, k1_sublemma(A, B, Y, Z)) <=> r1_valuat_1(A, B, k6_cqc_lang(A, D), C, k1_sublemma(A, B, Y, k14_sublemma(A, B, k14_sublemma(A, B, Z, A1), B1)))) ) ) ) ) ) ) ) ) ) )  &  ( ( ( (! [D1] :  (m2_funct_2(D1, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (! [E1] :  ( (v1_funct_1(E1) & m1_subset_1(E1, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B))))  =>  (! [F1] :  ( (v1_funct_1(F1) & m1_subset_1(F1, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B))))  =>  (! [G1] :  ( (v1_funct_1(G1) & m1_subset_1(G1, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B))))  =>  ( ( (! [H1] :  (m2_subset_1(H1, k2_qc_lang1(A), k3_qc_lang1(A)) =>  ~ ( (r2_tarski(H1, k1_relset_1(k3_qc_lang1(A), F1)) & r2_tarski(H1, k24_qc_lang1(A, D))) ) ) )  &  ( (! [H1] :  (m2_subset_1(H1, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (r2_tarski(H1, k1_relset_1(k3_qc_lang1(A), G1)) => k1_funct_1(G1, H1)=k3_funct_2(k3_qc_lang1(A), B, D1, H1)) ) )  & r1_xboole_0(k1_relset_1(k3_qc_lang1(A), E1), k1_relset_1(k3_qc_lang1(A), G1))) )  =>  (r1_valuat_1(A, B, D, C, k1_sublemma(A, B, D1, E1)) <=> r1_valuat_1(A, B, D, C, k1_sublemma(A, B, D1, k14_sublemma(A, B, k14_sublemma(A, B, E1, F1), G1)))) ) ) ) ) ) ) ) ) )  &  (! [I1] :  (m2_funct_2(I1, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (! [J1] :  ( (v1_funct_1(J1) & m1_subset_1(J1, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B))))  =>  (! [K1] :  ( (v1_funct_1(K1) & m1_subset_1(K1, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B))))  =>  (! [L1] :  ( (v1_funct_1(L1) & m1_subset_1(L1, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B))))  =>  ( ( (! [M1] :  (m2_subset_1(M1, k2_qc_lang1(A), k3_qc_lang1(A)) =>  ~ ( (r2_tarski(M1, k1_relset_1(k3_qc_lang1(A), K1)) & r2_tarski(M1, k24_qc_lang1(A, E))) ) ) )  &  ( (! [M1] :  (m2_subset_1(M1, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (r2_tarski(M1, k1_relset_1(k3_qc_lang1(A), L1)) => k1_funct_1(L1, M1)=k3_funct_2(k3_qc_lang1(A), B, I1, M1)) ) )  & r1_xboole_0(k1_relset_1(k3_qc_lang1(A), J1), k1_relset_1(k3_qc_lang1(A), L1))) )  =>  (r1_valuat_1(A, B, E, C, k1_sublemma(A, B, I1, J1)) <=> r1_valuat_1(A, B, E, C, k1_sublemma(A, B, I1, k14_sublemma(A, B, k14_sublemma(A, B, J1, K1), L1)))) ) ) ) ) ) ) ) ) ) )  =>  (! [N1] :  (m2_funct_2(N1, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (! [O1] :  ( (v1_funct_1(O1) & m1_subset_1(O1, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B))))  =>  (! [P1] :  ( (v1_funct_1(P1) & m1_subset_1(P1, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B))))  =>  (! [Q1] :  ( (v1_funct_1(Q1) & m1_subset_1(Q1, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B))))  =>  ( ( (! [R1] :  (m2_subset_1(R1, k2_qc_lang1(A), k3_qc_lang1(A)) =>  ~ ( (r2_tarski(R1, k1_relset_1(k3_qc_lang1(A), P1)) & r2_tarski(R1, k24_qc_lang1(A, k7_cqc_lang(A, D, E)))) ) ) )  &  ( (! [R1] :  (m2_subset_1(R1, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (r2_tarski(R1, k1_relset_1(k3_qc_lang1(A), Q1)) => k1_funct_1(Q1, R1)=k3_funct_2(k3_qc_lang1(A), B, N1, R1)) ) )  & r1_xboole_0(k1_relset_1(k3_qc_lang1(A), O1), k1_relset_1(k3_qc_lang1(A), Q1))) )  =>  (r1_valuat_1(A, B, k7_cqc_lang(A, D, E), C, k1_sublemma(A, B, N1, O1)) <=> r1_valuat_1(A, B, k7_cqc_lang(A, D, E), C, k1_sublemma(A, B, N1, k14_sublemma(A, B, k14_sublemma(A, B, O1, P1), Q1)))) ) ) ) ) ) ) ) ) ) )  &  ( (! [S1] :  (m2_funct_2(S1, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (! [T1] :  ( (v1_funct_1(T1) & m1_subset_1(T1, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B))))  =>  (! [U1] :  ( (v1_funct_1(U1) & m1_subset_1(U1, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B))))  =>  (! [V1] :  ( (v1_funct_1(V1) & m1_subset_1(V1, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B))))  =>  ( ( (! [W1] :  (m2_subset_1(W1, k2_qc_lang1(A), k3_qc_lang1(A)) =>  ~ ( (r2_tarski(W1, k1_relset_1(k3_qc_lang1(A), U1)) & r2_tarski(W1, k24_qc_lang1(A, D))) ) ) )  &  ( (! [W1] :  (m2_subset_1(W1, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (r2_tarski(W1, k1_relset_1(k3_qc_lang1(A), V1)) => k1_funct_1(V1, W1)=k3_funct_2(k3_qc_lang1(A), B, S1, W1)) ) )  & r1_xboole_0(k1_relset_1(k3_qc_lang1(A), T1), k1_relset_1(k3_qc_lang1(A), V1))) )  =>  (r1_valuat_1(A, B, D, C, k1_sublemma(A, B, S1, T1)) <=> r1_valuat_1(A, B, D, C, k1_sublemma(A, B, S1, k14_sublemma(A, B, k14_sublemma(A, B, T1, U1), V1)))) ) ) ) ) ) ) ) ) )  =>  (! [X1] :  (m2_funct_2(X1, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (! [Y1] :  ( (v1_funct_1(Y1) & m1_subset_1(Y1, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B))))  =>  (! [Z1] :  ( (v1_funct_1(Z1) & m1_subset_1(Z1, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B))))  =>  (! [A2] :  ( (v1_funct_1(A2) & m1_subset_1(A2, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B))))  =>  ( ( (! [B2] :  (m2_subset_1(B2, k2_qc_lang1(A), k3_qc_lang1(A)) =>  ~ ( (r2_tarski(B2, k1_relset_1(k3_qc_lang1(A), Z1)) & r2_tarski(B2, k24_qc_lang1(A, k11_cqc_lang(A, F, D)))) ) ) )  &  ( (! [B2] :  (m2_subset_1(B2, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (r2_tarski(B2, k1_relset_1(k3_qc_lang1(A), A2)) => k1_funct_1(A2, B2)=k3_funct_2(k3_qc_lang1(A), B, X1, B2)) ) )  & r1_xboole_0(k1_relset_1(k3_qc_lang1(A), Y1), k1_relset_1(k3_qc_lang1(A), A2))) )  =>  (r1_valuat_1(A, B, k11_cqc_lang(A, F, D), C, k1_sublemma(A, B, X1, Y1)) <=> r1_valuat_1(A, B, k11_cqc_lang(A, F, D), C, k1_sublemma(A, B, X1, k14_sublemma(A, B, k14_sublemma(A, B, Y1, Z1), A2)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D] :  (m2_subset_1(D, k9_qc_lang1(A), k3_cqc_lang(A)) =>  (! [C2] :  (m2_funct_2(C2, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (! [D2] :  ( (v1_funct_1(D2) & m1_subset_1(D2, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B))))  =>  (! [E2] :  ( (v1_funct_1(E2) & m1_subset_1(E2, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B))))  =>  (! [F2] :  ( (v1_funct_1(F2) & m1_subset_1(F2, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), B))))  =>  ( ( (! [G2] :  (m2_subset_1(G2, k2_qc_lang1(A), k3_qc_lang1(A)) =>  ~ ( (r2_tarski(G2, k1_relset_1(k3_qc_lang1(A), E2)) & r2_tarski(G2, k24_qc_lang1(A, D))) ) ) )  &  ( (! [G2] :  (m2_subset_1(G2, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (r2_tarski(G2, k1_relset_1(k3_qc_lang1(A), F2)) => k1_funct_1(F2, G2)=k3_funct_2(k3_qc_lang1(A), B, C2, G2)) ) )  & r1_xboole_0(k1_relset_1(k3_qc_lang1(A), D2), k1_relset_1(k3_qc_lang1(A), F2))) )  =>  (r1_valuat_1(A, B, D, C, k1_sublemma(A, B, C2, D2)) <=> r1_valuat_1(A, B, D, C, k1_sublemma(A, B, C2, k14_sublemma(A, B, k14_sublemma(A, B, D2, E2), F2)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(symmetry_r1_xboole_0, axiom,  (! [A, B] :  (r1_xboole_0(A, B) => r1_xboole_0(B, 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(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(t32_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) => r1_valuat_1(A, B, k5_cqc_lang(A), D, C)) ) ) ) ) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t4_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r2_tarski(A, B) & m1_subset_1(B, k1_zfmisc_1(C)))  => m1_subset_1(A, C)) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t75_sublemma, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (v7_ordinal1(B) =>  (! [C] :  ( ~ (v1_xboole_0(C))  =>  (! [D] :  (m1_valuat_1(D, A, C) =>  (! [E] :  (m2_subset_1(E, k6_qc_lang1(A), k8_qc_lang1(A, B)) =>  (! [F] :  ( (v5_relat_1(F, k3_qc_lang1(A)) &  (v3_card_1(F, B) & m2_finseq_1(F, k2_qc_lang1(A))) )  =>  (! [G] :  (m2_funct_2(G, k3_qc_lang1(A), C, k2_valuat_1(A, C)) =>  (! [H] :  ( (v1_funct_1(H) & m1_subset_1(H, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), C))))  =>  (! [I] :  ( (v1_funct_1(I) & m1_subset_1(I, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), C))))  =>  (! [J] :  ( (v1_funct_1(J) & m1_subset_1(J, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), C))))  =>  ( ( (! [K] :  (m2_subset_1(K, k2_qc_lang1(A), k3_qc_lang1(A)) =>  ~ ( (r2_tarski(K, k1_relset_1(k3_qc_lang1(A), I)) & r2_tarski(K, k24_qc_lang1(A, k4_cqc_lang(B, A, E, F)))) ) ) )  &  ( (! [K] :  (m2_subset_1(K, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (r2_tarski(K, k1_relset_1(k3_qc_lang1(A), J)) => k1_funct_1(J, K)=k3_funct_2(k3_qc_lang1(A), C, G, K)) ) )  & r1_xboole_0(k1_relset_1(k3_qc_lang1(A), H), k1_relset_1(k3_qc_lang1(A), J))) )  =>  (r1_valuat_1(A, C, k4_cqc_lang(B, A, E, F), D, k1_sublemma(A, C, G, H)) <=> r1_valuat_1(A, C, k4_cqc_lang(B, A, E, F), D, k1_sublemma(A, C, G, k14_sublemma(A, C, k14_sublemma(A, C, H, I), J)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t76_sublemma, 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) =>  ( (! [E] :  (m2_funct_2(E, k3_qc_lang1(A), C, k2_valuat_1(A, C)) =>  (! [F] :  ( (v1_funct_1(F) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), C))))  =>  (! [G] :  ( (v1_funct_1(G) & m1_subset_1(G, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), C))))  =>  (! [H] :  ( (v1_funct_1(H) & m1_subset_1(H, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), C))))  =>  ( ( (! [I] :  (m2_subset_1(I, k2_qc_lang1(A), k3_qc_lang1(A)) =>  ~ ( (r2_tarski(I, k1_relset_1(k3_qc_lang1(A), G)) & r2_tarski(I, k24_qc_lang1(A, B))) ) ) )  &  ( (! [I] :  (m2_subset_1(I, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (r2_tarski(I, k1_relset_1(k3_qc_lang1(A), H)) => k1_funct_1(H, I)=k3_funct_2(k3_qc_lang1(A), C, E, I)) ) )  & r1_xboole_0(k1_relset_1(k3_qc_lang1(A), F), k1_relset_1(k3_qc_lang1(A), H))) )  =>  (r1_valuat_1(A, C, B, D, k1_sublemma(A, C, E, F)) <=> r1_valuat_1(A, C, B, D, k1_sublemma(A, C, E, k14_sublemma(A, C, k14_sublemma(A, C, F, G), H)))) ) ) ) ) ) ) ) ) )  =>  (! [E] :  (m2_funct_2(E, k3_qc_lang1(A), C, k2_valuat_1(A, C)) =>  (! [F] :  ( (v1_funct_1(F) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), C))))  =>  (! [G] :  ( (v1_funct_1(G) & m1_subset_1(G, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), C))))  =>  (! [H] :  ( (v1_funct_1(H) & m1_subset_1(H, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), C))))  =>  ( ( (! [I] :  (m2_subset_1(I, k2_qc_lang1(A), k3_qc_lang1(A)) =>  ~ ( (r2_tarski(I, k1_relset_1(k3_qc_lang1(A), G)) & r2_tarski(I, k24_qc_lang1(A, k6_cqc_lang(A, B)))) ) ) )  &  ( (! [I] :  (m2_subset_1(I, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (r2_tarski(I, k1_relset_1(k3_qc_lang1(A), H)) => k1_funct_1(H, I)=k3_funct_2(k3_qc_lang1(A), C, E, I)) ) )  & r1_xboole_0(k1_relset_1(k3_qc_lang1(A), F), k1_relset_1(k3_qc_lang1(A), H))) )  =>  (r1_valuat_1(A, C, k6_cqc_lang(A, B), D, k1_sublemma(A, C, E, F)) <=> r1_valuat_1(A, C, k6_cqc_lang(A, B), D, k1_sublemma(A, C, E, k14_sublemma(A, C, k14_sublemma(A, C, F, G), H)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t77_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, 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)) =>  (! [G] :  ( (v1_funct_1(G) & m1_subset_1(G, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), D))))  =>  (! [H] :  ( (v1_funct_1(H) & m1_subset_1(H, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), D))))  =>  (! [I] :  ( (v1_funct_1(I) & m1_subset_1(I, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), D))))  =>  ( ( (! [J] :  (m2_subset_1(J, k2_qc_lang1(A), k3_qc_lang1(A)) =>  ~ ( (r2_tarski(J, k1_relset_1(k3_qc_lang1(A), H)) & r2_tarski(J, k24_qc_lang1(A, B))) ) ) )  &  ( (! [J] :  (m2_subset_1(J, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (r2_tarski(J, k1_relset_1(k3_qc_lang1(A), I)) => k1_funct_1(I, J)=k3_funct_2(k3_qc_lang1(A), D, F, J)) ) )  & r1_xboole_0(k1_relset_1(k3_qc_lang1(A), G), k1_relset_1(k3_qc_lang1(A), I))) )  =>  (r1_valuat_1(A, D, B, E, k1_sublemma(A, D, F, G)) <=> r1_valuat_1(A, D, B, E, k1_sublemma(A, D, F, k14_sublemma(A, D, k14_sublemma(A, D, G, H), I)))) ) ) ) ) ) ) ) ) )  &  (! [F] :  (m2_funct_2(F, k3_qc_lang1(A), D, k2_valuat_1(A, D)) =>  (! [G] :  ( (v1_funct_1(G) & m1_subset_1(G, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), D))))  =>  (! [H] :  ( (v1_funct_1(H) & m1_subset_1(H, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), D))))  =>  (! [I] :  ( (v1_funct_1(I) & m1_subset_1(I, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), D))))  =>  ( ( (! [J] :  (m2_subset_1(J, k2_qc_lang1(A), k3_qc_lang1(A)) =>  ~ ( (r2_tarski(J, k1_relset_1(k3_qc_lang1(A), H)) & r2_tarski(J, k24_qc_lang1(A, C))) ) ) )  &  ( (! [J] :  (m2_subset_1(J, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (r2_tarski(J, k1_relset_1(k3_qc_lang1(A), I)) => k1_funct_1(I, J)=k3_funct_2(k3_qc_lang1(A), D, F, J)) ) )  & r1_xboole_0(k1_relset_1(k3_qc_lang1(A), G), k1_relset_1(k3_qc_lang1(A), I))) )  =>  (r1_valuat_1(A, D, C, E, k1_sublemma(A, D, F, G)) <=> r1_valuat_1(A, D, C, E, k1_sublemma(A, D, F, k14_sublemma(A, D, k14_sublemma(A, D, G, H), I)))) ) ) ) ) ) ) ) ) ) )  =>  (! [F] :  (m2_funct_2(F, k3_qc_lang1(A), D, k2_valuat_1(A, D)) =>  (! [G] :  ( (v1_funct_1(G) & m1_subset_1(G, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), D))))  =>  (! [H] :  ( (v1_funct_1(H) & m1_subset_1(H, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), D))))  =>  (! [I] :  ( (v1_funct_1(I) & m1_subset_1(I, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), D))))  =>  ( ( (! [J] :  (m2_subset_1(J, k2_qc_lang1(A), k3_qc_lang1(A)) =>  ~ ( (r2_tarski(J, k1_relset_1(k3_qc_lang1(A), H)) & r2_tarski(J, k24_qc_lang1(A, k7_cqc_lang(A, B, C)))) ) ) )  &  ( (! [J] :  (m2_subset_1(J, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (r2_tarski(J, k1_relset_1(k3_qc_lang1(A), I)) => k1_funct_1(I, J)=k3_funct_2(k3_qc_lang1(A), D, F, J)) ) )  & r1_xboole_0(k1_relset_1(k3_qc_lang1(A), G), k1_relset_1(k3_qc_lang1(A), I))) )  =>  (r1_valuat_1(A, D, k7_cqc_lang(A, B, C), E, k1_sublemma(A, D, F, G)) <=> r1_valuat_1(A, D, k7_cqc_lang(A, B, C), E, k1_sublemma(A, D, F, k14_sublemma(A, D, k14_sublemma(A, D, G, H), I)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t80_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] :  (m1_valuat_1(E, A, D) =>  ( (! [F] :  (m2_funct_2(F, k3_qc_lang1(A), D, k2_valuat_1(A, D)) =>  (! [G] :  ( (v1_funct_1(G) & m1_subset_1(G, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), D))))  =>  (! [H] :  ( (v1_funct_1(H) & m1_subset_1(H, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), D))))  =>  (! [I] :  ( (v1_funct_1(I) & m1_subset_1(I, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), D))))  =>  ( ( (! [J] :  (m2_subset_1(J, k2_qc_lang1(A), k3_qc_lang1(A)) =>  ~ ( (r2_tarski(J, k1_relset_1(k3_qc_lang1(A), H)) & r2_tarski(J, k24_qc_lang1(A, B))) ) ) )  &  ( (! [J] :  (m2_subset_1(J, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (r2_tarski(J, k1_relset_1(k3_qc_lang1(A), I)) => k1_funct_1(I, J)=k3_funct_2(k3_qc_lang1(A), D, F, J)) ) )  & r1_xboole_0(k1_relset_1(k3_qc_lang1(A), G), k1_relset_1(k3_qc_lang1(A), I))) )  =>  (r1_valuat_1(A, D, B, E, k1_sublemma(A, D, F, G)) <=> r1_valuat_1(A, D, B, E, k1_sublemma(A, D, F, k14_sublemma(A, D, k14_sublemma(A, D, G, H), I)))) ) ) ) ) ) ) ) ) )  =>  (! [F] :  (m2_funct_2(F, k3_qc_lang1(A), D, k2_valuat_1(A, D)) =>  (! [G] :  ( (v1_funct_1(G) & m1_subset_1(G, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), D))))  =>  (! [H] :  ( (v1_funct_1(H) & m1_subset_1(H, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), D))))  =>  (! [I] :  ( (v1_funct_1(I) & m1_subset_1(I, k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), D))))  =>  ( ( (! [J] :  (m2_subset_1(J, k2_qc_lang1(A), k3_qc_lang1(A)) =>  ~ ( (r2_tarski(J, k1_relset_1(k3_qc_lang1(A), H)) & r2_tarski(J, k24_qc_lang1(A, k11_cqc_lang(A, C, B)))) ) ) )  &  ( (! [J] :  (m2_subset_1(J, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (r2_tarski(J, k1_relset_1(k3_qc_lang1(A), I)) => k1_funct_1(I, J)=k3_funct_2(k3_qc_lang1(A), D, F, J)) ) )  & r1_xboole_0(k1_relset_1(k3_qc_lang1(A), G), k1_relset_1(k3_qc_lang1(A), I))) )  =>  (r1_valuat_1(A, D, k11_cqc_lang(A, C, B), E, k1_sublemma(A, D, F, G)) <=> r1_valuat_1(A, D, k11_cqc_lang(A, C, B), E, k1_sublemma(A, D, F, k14_sublemma(A, D, k14_sublemma(A, D, G, H), I)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
