% Mizar problem: t89_sublemma,sublemma,2829,5 
fof(t89_sublemma, conjecture,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  (m1_valuat_1(C, A, B) =>  (! [D] :  (m2_subset_1(D, k16_substut1(A), k38_substut1(A)) =>  (! [E] :  (m2_funct_2(E, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (r1_valuat_1(A, B, k39_substut1(A, D), C, E) <=> r1_sublemma(A, D, B, k1_sublemma(A, B, E, k3_sublemma(A, D, B, E)), C)) ) ) ) ) ) ) ) ) ) ) ).
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(d1_sublemma, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m2_subset_1(B, k16_substut1(A), k38_substut1(A)) =>  (! [C] :  ( ~ (v1_xboole_0(C))  =>  (! [D] :  (m2_funct_2(D, k3_qc_lang1(A), C, k2_valuat_1(A, C)) => k3_sublemma(A, B, C, D)=k4_relset_1(k3_qc_lang1(A), k3_qc_lang1(A), k3_qc_lang1(A), C, k2_substut1(A, k19_substut1(A, B)), D)) ) ) ) ) ) ) ) ).
fof(d2_sublemma, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m2_subset_1(B, k16_substut1(A), k38_substut1(A)) =>  (! [C] :  ( ~ (v1_xboole_0(C))  =>  (! [D] :  (m2_funct_2(D, k3_qc_lang1(A), C, k2_valuat_1(A, C)) =>  (! [E] :  (m1_valuat_1(E, A, C) =>  (r1_sublemma(A, B, C, D, E) <=> r1_valuat_1(A, C, k2_sublemma(A, B), E, D)) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_k16_substut1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k16_substut1(A))) ) ) ).
fof(dt_k17_substut1, axiom,  (! [A, B, C, D] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k6_qc_lang1(A)) &  (m1_finseq_1(C, k2_qc_lang1(A)) & m1_subset_1(D, k1_substut1(A))) ) )  => m1_subset_1(k17_substut1(A, B, C, D), k16_substut1(A))) ) ).
fof(dt_k19_substut1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k16_substut1(A)))  => m1_subset_1(k19_substut1(A, B), k1_substut1(A))) ) ).
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_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_substut1, axiom, $true).
fof(dt_k1_valuat_1, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_xtuple_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k20_substut1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k16_substut1(A)))  => m1_subset_1(k20_substut1(A, B), k16_substut1(A))) ) ).
fof(dt_k2_margrel1, axiom, $true).
fof(dt_k2_qc_lang1, axiom, $true).
fof(dt_k2_sublemma, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k38_substut1(A)))  => m2_subset_1(k2_sublemma(A, B), k9_qc_lang1(A), k3_cqc_lang(A))) ) ).
fof(dt_k2_substut1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k1_substut1(A)))  =>  (v1_funct_1(k2_substut1(A, B)) & m1_subset_1(k2_substut1(A, B), k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), k3_qc_lang1(A))))) ) ) ).
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_xtuple_0, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k37_substut1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k16_substut1(A)))  => m1_subset_1(k37_substut1(A, B), k9_qc_lang1(A))) ) ).
fof(dt_k38_substut1, axiom,  (! [A] :  (m1_qc_lang1(A) => m1_subset_1(k38_substut1(A), k1_zfmisc_1(k16_substut1(A)))) ) ).
fof(dt_k39_substut1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k38_substut1(A)))  => m2_subset_1(k39_substut1(A, B), k9_qc_lang1(A), k3_cqc_lang(A))) ) ).
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_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_sublemma, axiom,  (! [A, B, C, D] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k38_substut1(A)) &  ( ~ (v1_xboole_0(C))  & m1_subset_1(D, k2_valuat_1(A, C))) ) )  =>  (v1_funct_1(k3_sublemma(A, B, C, D)) & m1_subset_1(k3_sublemma(A, B, C, D), k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A), C)))) ) ) ).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k4_relset_1, axiom,  (! [A, B, C, D, E, F] :  ( (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(C, D))))  => m1_subset_1(k4_relset_1(A, B, C, D, E, F), k1_zfmisc_1(k2_zfmisc_1(A, D)))) ) ).
fof(dt_k4_sublemma, axiom,  (! [A, B, C, D, E] :  ( (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))) )  & m1_subset_1(E, k1_substut1(B))) ) ) )  => m2_subset_1(k4_sublemma(A, B, C, D, E), k16_substut1(B), k38_substut1(B))) ) ).
fof(dt_k4_tarski, axiom, $true).
fof(dt_k5_sublemma, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k38_substut1(A)))  => m2_subset_1(k5_sublemma(A, B), k16_substut1(A), k38_substut1(A))) ) ).
fof(dt_k6_qc_lang1, axiom, $true).
fof(dt_k6_sublemma, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k38_substut1(A)) & m1_subset_1(C, k38_substut1(A))) )  => m2_subset_1(k6_sublemma(A, B, C), k16_substut1(A), k38_substut1(A))) ) ).
fof(dt_k7_sublemma, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k38_substut1(A)) & m1_subset_1(C, k3_qc_lang1(A))) )  =>  (v1_sublemma(k7_sublemma(A, B, C), A) & m1_subset_1(k7_sublemma(A, B, C), k2_zfmisc_1(k16_substut1(A), k3_qc_lang1(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_sublemma, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  ( (v1_sublemma(B, A) & m1_subset_1(B, k2_zfmisc_1(k16_substut1(A), k3_qc_lang1(A))))  & m1_substut1(C, A, B)) )  => m2_subset_1(k9_sublemma(A, B, C), k16_substut1(A), k38_substut1(A))) ) ).
fof(dt_m1_finseq_1, axiom,  (! [A] :  (! [B] :  (m1_finseq_1(B, A) =>  (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) ) ) ) ) ).
fof(dt_m1_funct_2, axiom,  (! [A, B] :  (! [C] :  (m1_funct_2(C, A, B) =>  ~ (v1_xboole_0(C)) ) ) ) ).
fof(dt_m1_qc_lang1, axiom, $true).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_m1_substut1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k2_zfmisc_1(k16_substut1(A), k3_qc_lang1(A))))  =>  (! [C] :  (m1_substut1(C, A, B) => m1_subset_1(C, k1_substut1(A))) ) ) ) ).
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_substut1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k2_zfmisc_1(k16_substut1(A), k3_qc_lang1(A))))  =>  (? [C] : m1_substut1(C, A, B)) ) ) ).
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_funcop_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  &  (v1_relat_1(B) & v1_funct_1(B)) )  =>  (v1_relat_1(k3_relat_1(B, A)) & v1_funcop_1(k3_relat_1(B, 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_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(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(fc12_relat_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v1_relat_1(B))  =>  (v1_xboole_0(k3_relat_1(A, B)) & v1_relat_1(k3_relat_1(A, B))) ) ) ).
fof(fc13_relat_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v1_relat_1(B))  =>  (v1_xboole_0(k3_relat_1(B, A)) & v1_relat_1(k3_relat_1(B, A))) ) ) ).
fof(fc15_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_relat_1(B) & v2_relat_1(B)) )  =>  (v1_relat_1(k3_relat_1(A, B)) & v2_relat_1(k3_relat_1(A, B))) ) ) ).
fof(fc1_subset_1, axiom,  (! [A] :  ~ (v1_xboole_0(k1_zfmisc_1(A))) ) ).
fof(fc1_substut1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k1_substut1(A))) ) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc1_xtuple_0, axiom,  (! [A, B] : v1_xtuple_0(k4_tarski(A, B))) ).
fof(fc29_relat_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v5_relat_1(B, A))  & v1_relat_1(C))  =>  (v1_relat_1(k3_relat_1(C, B)) & v5_relat_1(k3_relat_1(C, B), A)) ) ) ).
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_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k2_qc_lang1(A))) ) ) ).
fof(fc2_substut1, axiom,  (! [A] :  (m1_qc_lang1(A) => v4_funct_1(k1_substut1(A))) ) ).
fof(fc30_relat_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v4_relat_1(B, A))  & v1_relat_1(C))  =>  (v1_relat_1(k3_relat_1(B, C)) & v4_relat_1(k3_relat_1(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_substut1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ( ~ (v1_xboole_0(k16_substut1(A)))  & v1_substut1(k16_substut1(A), 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_substut1, axiom,  (! [A, B, C, D, E] :  ( (m1_qc_lang1(A) &  (v7_ordinal1(B) &  (m1_subset_1(C, k8_qc_lang1(A, B)) &  ( (v3_card_1(D, B) & m1_finseq_1(D, k2_qc_lang1(A)))  & m1_subset_1(E, k1_substut1(A))) ) ) )  => v4_substut1(k17_substut1(A, C, D, E), 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(fc6_substut1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k16_substut1(A)))  => v5_substut1(k20_substut1(A, B), 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_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(fc7_substut1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k38_substut1(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(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(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_sublemma, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (? [B] :  (m1_subset_1(B, k2_zfmisc_1(k16_substut1(A), k3_qc_lang1(A))) & v1_sublemma(B, A)) ) ) ) ).
fof(rc1_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc1_xtuple_0, axiom,  (? [A] : v1_xtuple_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_substut1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (? [B] :  ( ~ (v1_xboole_0(B))  & v1_substut1(B, A)) ) ) ) ).
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(rd1_xtuple_0, axiom,  (! [A, B] : k1_xtuple_0(k4_tarski(A, B))=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(rd2_xtuple_0, axiom,  (! [A, B] : k2_xtuple_0(k4_tarski(A, B))=B) ).
fof(rd3_xtuple_0, axiom,  (! [A] :  (v1_xtuple_0(A) => k4_tarski(k1_xtuple_0(A), k2_xtuple_0(A))=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_k19_substut1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k16_substut1(A)))  => k19_substut1(A, B)=k2_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_sublemma, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k38_substut1(A)))  => k2_sublemma(A, B)=k1_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_k39_substut1, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k38_substut1(A)))  => k39_substut1(A, B)=k37_substut1(A, B)) ) ).
fof(redefinition_k4_relset_1, axiom,  (! [A, B, C, D, E, F] :  ( (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(C, D))))  => k4_relset_1(A, B, C, D, E, F)=k3_relat_1(E, F)) ) ).
fof(redefinition_k4_sublemma, axiom,  (! [A, B, C, D, E] :  ( (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))) )  & m1_subset_1(E, k1_substut1(B))) ) ) )  => k4_sublemma(A, B, C, D, E)=k17_substut1(B, C, D, E)) ) ).
fof(redefinition_k5_sublemma, axiom,  (! [A, B] :  ( (m1_qc_lang1(A) & m1_subset_1(B, k38_substut1(A)))  => k5_sublemma(A, B)=k20_substut1(A, B)) ) ).
fof(redefinition_k7_sublemma, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  (m1_subset_1(B, k38_substut1(A)) & m1_subset_1(C, k3_qc_lang1(A))) )  => k7_sublemma(A, B, C)=k4_tarski(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_sublemma__e2_110__sublemma, axiom,  (! [A, B, C] :  ( (m1_qc_lang1(A) &  ( ~ (v1_xboole_0(B))  & m1_valuat_1(C, A, B)) )  =>  ( (! [D] :  (m2_subset_1(D, k16_substut1(A), k38_substut1(A)) =>  (! [E] :  (m2_subset_1(E, k16_substut1(A), k38_substut1(A)) =>  (! [F] :  (m2_subset_1(F, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (! [G] :  (m1_substut1(G, A, k7_sublemma(A, D, F)) =>  (! [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)) =>  (! [K] :  (m1_subset_1(K, k1_substut1(A)) =>  ( (! [L] :  (m2_funct_2(L, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (r1_valuat_1(A, B, k39_substut1(A, k4_sublemma(H, A, J, I, K)), C, L) <=> r1_sublemma(A, k4_sublemma(H, A, J, I, K), B, k1_sublemma(A, B, L, k3_sublemma(A, k4_sublemma(H, A, J, I, K), B, L)), C)) ) )  &  ( (v2_substut1(D, A) =>  (! [M] :  (m2_funct_2(M, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (r1_valuat_1(A, B, k39_substut1(A, D), C, M) <=> r1_sublemma(A, D, B, k1_sublemma(A, B, M, k3_sublemma(A, D, B, M)), C)) ) ) )  &  ( ( (! [N] :  (m2_funct_2(N, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (r1_valuat_1(A, B, k39_substut1(A, D), C, N) <=> r1_sublemma(A, D, B, k1_sublemma(A, B, N, k3_sublemma(A, D, B, N)), C)) ) )  =>  (! [O] :  (m2_funct_2(O, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (r1_valuat_1(A, B, k39_substut1(A, k5_sublemma(A, D)), C, O) <=> r1_sublemma(A, k5_sublemma(A, D), B, k1_sublemma(A, B, O, k3_sublemma(A, k5_sublemma(A, D), B, O)), C)) ) ) )  &  ( ( (k19_substut1(A, D)=k19_substut1(A, E) &  ( (! [P] :  (m2_funct_2(P, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (r1_valuat_1(A, B, k39_substut1(A, D), C, P) <=> r1_sublemma(A, D, B, k1_sublemma(A, B, P, k3_sublemma(A, D, B, P)), C)) ) )  &  (! [Q] :  (m2_funct_2(Q, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (r1_valuat_1(A, B, k39_substut1(A, E), C, Q) <=> r1_sublemma(A, E, B, k1_sublemma(A, B, Q, k3_sublemma(A, E, B, Q)), C)) ) ) ) )  =>  (! [R] :  (m2_funct_2(R, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (r1_valuat_1(A, B, k39_substut1(A, k6_sublemma(A, D, E)), C, R) <=> r1_sublemma(A, k6_sublemma(A, D, E), B, k1_sublemma(A, B, R, k3_sublemma(A, k6_sublemma(A, D, E), B, R)), C)) ) ) )  &  ( (v3_substut1(k7_sublemma(A, D, F), A) &  (! [S] :  (m2_funct_2(S, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (r1_valuat_1(A, B, k39_substut1(A, D), C, S) <=> r1_sublemma(A, D, B, k1_sublemma(A, B, S, k3_sublemma(A, D, B, S)), C)) ) ) )  =>  (! [T] :  (m2_funct_2(T, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (r1_valuat_1(A, B, k39_substut1(A, k9_sublemma(A, k7_sublemma(A, D, F), G)), C, T) <=> r1_sublemma(A, k9_sublemma(A, k7_sublemma(A, D, F), G), B, k1_sublemma(A, B, T, k3_sublemma(A, k9_sublemma(A, k7_sublemma(A, D, F), G), B, T)), C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [D] :  (m2_subset_1(D, k16_substut1(A), k38_substut1(A)) =>  (! [U] :  (m2_funct_2(U, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (r1_valuat_1(A, B, k39_substut1(A, D), C, U) <=> r1_sublemma(A, D, B, k1_sublemma(A, B, U, k3_sublemma(A, D, B, U)), C)) ) ) ) ) ) ) ) ).
fof(t15_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] :  (m1_subset_1(G, k1_substut1(A)) =>  (! [H] :  (m2_funct_2(H, k3_qc_lang1(A), C, k2_valuat_1(A, C)) =>  (r1_valuat_1(A, C, k39_substut1(A, k4_sublemma(B, A, E, F, G)), D, H) <=> r1_sublemma(A, k4_sublemma(B, A, E, F, G), C, k1_sublemma(A, C, H, k3_sublemma(A, k4_sublemma(B, A, E, F, G), C, H)), D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t19_sublemma, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  (m1_valuat_1(C, A, B) =>  (! [D] :  (m2_subset_1(D, k16_substut1(A), k38_substut1(A)) =>  ( (! [E] :  (m2_funct_2(E, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (r1_valuat_1(A, B, k39_substut1(A, D), C, E) <=> r1_sublemma(A, D, B, k1_sublemma(A, B, E, k3_sublemma(A, D, B, E)), C)) ) )  =>  (! [E] :  (m2_funct_2(E, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (r1_valuat_1(A, B, k39_substut1(A, k5_sublemma(A, D)), C, E) <=> r1_sublemma(A, k5_sublemma(A, D), B, k1_sublemma(A, B, E, k3_sublemma(A, k5_sublemma(A, D), B, E)), C)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t1_numerals, axiom, m1_subset_1(k1_xboole_0, k4_ordinal1)).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t25_sublemma, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  (m1_valuat_1(C, A, B) =>  (! [D] :  (m2_subset_1(D, k16_substut1(A), k38_substut1(A)) =>  (! [E] :  (m2_subset_1(E, k16_substut1(A), k38_substut1(A)) =>  ( (k19_substut1(A, D)=k19_substut1(A, E) &  ( (! [F] :  (m2_funct_2(F, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (r1_valuat_1(A, B, k39_substut1(A, D), C, F) <=> r1_sublemma(A, D, B, k1_sublemma(A, B, F, k3_sublemma(A, D, B, F)), C)) ) )  &  (! [F] :  (m2_funct_2(F, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (r1_valuat_1(A, B, k39_substut1(A, E), C, F) <=> r1_sublemma(A, E, B, k1_sublemma(A, B, F, k3_sublemma(A, E, B, F)), C)) ) ) ) )  =>  (! [F] :  (m2_funct_2(F, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (r1_valuat_1(A, B, k39_substut1(A, k6_sublemma(A, D, E)), C, F) <=> r1_sublemma(A, k6_sublemma(A, D, E), B, k1_sublemma(A, B, F, k3_sublemma(A, k6_sublemma(A, D, E), B, F)), C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t4_sublemma, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  (m1_valuat_1(C, A, B) =>  (! [D] :  (m2_subset_1(D, k16_substut1(A), k38_substut1(A)) =>  (v2_substut1(D, A) =>  (! [E] :  (m2_funct_2(E, k3_qc_lang1(A), B, k2_valuat_1(A, B)) =>  (r1_valuat_1(A, B, k39_substut1(A, D), C, E) <=> r1_sublemma(A, D, B, k1_sublemma(A, B, E, k3_sublemma(A, D, B, E)), C)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t4_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r2_tarski(A, B) & m1_subset_1(B, k1_zfmisc_1(C)))  => m1_subset_1(A, C)) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t88_sublemma, axiom,  (! [A] :  (m1_qc_lang1(A) =>  (! [B] :  (m2_subset_1(B, k2_qc_lang1(A), k3_qc_lang1(A)) =>  (! [C] :  ( ~ (v1_xboole_0(C))  =>  (! [D] :  (m1_valuat_1(D, A, C) =>  (! [E] :  (m2_subset_1(E, k16_substut1(A), k38_substut1(A)) =>  (! [F] :  (m1_substut1(F, A, k7_sublemma(A, E, B)) =>  ( (v3_substut1(k7_sublemma(A, E, B), A) &  (! [G] :  (m2_funct_2(G, k3_qc_lang1(A), C, k2_valuat_1(A, C)) =>  (r1_valuat_1(A, C, k39_substut1(A, E), D, G) <=> r1_sublemma(A, E, C, k1_sublemma(A, C, G, k3_sublemma(A, E, C, G)), D)) ) ) )  =>  (! [G] :  (m2_funct_2(G, k3_qc_lang1(A), C, k2_valuat_1(A, C)) =>  (r1_valuat_1(A, C, k39_substut1(A, k9_sublemma(A, k7_sublemma(A, E, B), F)), D, G) <=> r1_sublemma(A, k9_sublemma(A, k7_sublemma(A, E, B), F), C, k1_sublemma(A, C, G, k3_sublemma(A, k9_sublemma(A, k7_sublemma(A, E, B), F), C, G)), D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
