% Mizar problem: t2_valuat_1,valuat_1,128,5 
fof(t2_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_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(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(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_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, k2_valuat_1(A, B), k5_margrel1, k9_funct_2(k2_valuat_1(A, B), k5_margrel1)) =>  (! [E] :  (m2_funct_2(E, k2_valuat_1(A, B), k5_margrel1, k9_funct_2(k2_valuat_1(A, B), k5_margrel1)) =>  (E=k3_valuat_1(A, B, C, D) <=>  (! [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)=k11_margrel1(a_5_0_valuat_1(A, B, C, D, F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d2_xboolean, axiom, k2_xboolean=1).
fof(dt_k10_margrel1, axiom, $true).
fof(dt_k11_margrel1, axiom,  (! [A] : m1_subset_1(k11_margrel1(A), k5_margrel1)) ).
fof(dt_k1_funct_1, axiom, $true).
fof(dt_k1_funct_2, 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_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_xboolean, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
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_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_k4_ordinal1, axiom, $true).
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_k6_margrel1, axiom, m1_subset_1(k6_margrel1, k5_margrel1)).
fof(dt_k7_margrel1, axiom, m1_subset_1(k7_margrel1, 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_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_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_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_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(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(fc1_funct_2, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  ~ (v1_xboole_0(k1_funct_2(A, B))) ) ) ).
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_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(fc3_funct_2, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & v1_xboole_0(B))  => v1_xboole_0(k1_funct_2(A, B))) ) ).
fof(fc3_margrel1, axiom,  (! [A] : v1_xboolean(k10_margrel1(A))) ).
fof(fc3_qc_lang1, axiom,  (! [A] :  (m1_qc_lang1(A) =>  ~ (v1_xboole_0(k3_qc_lang1(A))) ) ) ).
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(fc6_ordinal1, axiom,  ( ~ (v1_xboole_0(k4_ordinal1))  & v3_ordinal1(k4_ordinal1)) ).
fof(fc8_ordinal1, axiom, v7_ordinal1(k5_ordinal1)).
fof(fc9_ordinal1, axiom, v8_ordinal1(k5_ordinal1)).
fof(fraenkel_a_5_0_valuat_1, axiom,  (! [A, B, C, D, E, F] :  ( (m1_qc_lang1(B) &  ( ~ (v1_xboole_0(C))  &  (m2_subset_1(D, k2_qc_lang1(B), k3_qc_lang1(B)) &  (m2_funct_2(E, k2_valuat_1(B, C), k5_margrel1, k9_funct_2(k2_valuat_1(B, C), k5_margrel1)) & m2_funct_2(F, k3_qc_lang1(B), C, k2_valuat_1(B, C))) ) ) )  =>  (r2_hidden(A, a_5_0_valuat_1(B, C, D, E, F)) <=>  (? [G] :  (m2_funct_2(G, k3_qc_lang1(B), C, k2_valuat_1(B, C)) &  (A=k3_funct_2(k2_valuat_1(B, C), k5_margrel1, E, G) &  (! [H] :  (m2_subset_1(H, k2_qc_lang1(B), k3_qc_lang1(B)) =>  ( ~ (D=H)  => k3_funct_2(k3_qc_lang1(B), C, G, H)=k3_funct_2(k3_qc_lang1(B), C, F, H)) ) ) ) ) ) ) ) ) ).
fof(fraenkel_a_5_2_valuat_1, axiom,  (! [A, B, C, D, E, F] :  ( (m1_qc_lang1(B) &  ( ~ (v1_xboole_0(C))  &  (m2_subset_1(D, k2_qc_lang1(B), k3_qc_lang1(B)) &  (m2_funct_2(E, k3_qc_lang1(B), C, k2_valuat_1(B, C)) & m2_funct_2(F, k2_valuat_1(B, C), k5_margrel1, k9_funct_2(k2_valuat_1(B, C), k5_margrel1))) ) ) )  =>  (r2_hidden(A, a_5_2_valuat_1(B, C, D, E, F)) <=>  (? [G] :  (m2_funct_2(G, k3_qc_lang1(B), C, k2_valuat_1(B, C)) &  (A=k3_funct_2(k2_valuat_1(B, C), k5_margrel1, F, G) &  (! [H] :  (m2_subset_1(H, k2_qc_lang1(B), k3_qc_lang1(B)) =>  ( ~ (D=H)  => k3_funct_2(k3_qc_lang1(B), C, G, H)=k3_funct_2(k3_qc_lang1(B), C, E, H)) ) ) ) ) ) ) ) ) ).
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_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_margrel1, axiom,  (! [A] : k11_margrel1(A)=k10_margrel1(A)) ).
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_k5_numbers, axiom, k5_numbers=k5_ordinal1).
fof(redefinition_k6_margrel1, axiom, k6_margrel1=k1_xboolean).
fof(redefinition_k7_margrel1, axiom, k7_margrel1=k2_xboolean).
fof(redefinition_k9_funct_2, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  => k9_funct_2(A, B)=k1_funct_2(A, B)) ) ).
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(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(spc1_numerals, axiom,  (v2_xxreal_0(1) & m1_subset_1(1, k4_ordinal1)) ).
fof(t17_margrel1, axiom,  (! [A] :  ( ( ~ (r2_tarski(k6_margrel1, A))  => k11_margrel1(A)=k7_margrel1)  &  ( ~ ( (k11_margrel1(A)=k7_margrel1 & r2_tarski(k6_margrel1, A)) )  &  ( (r2_tarski(k6_margrel1, A) => k11_margrel1(A)=k6_margrel1)  &  (k11_margrel1(A)=k6_margrel1 => r2_tarski(k6_margrel1, 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_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t2_tarski, axiom,  (! [A] :  (! [B] :  ( (! [C] :  (r2_hidden(C, A) <=> r2_hidden(C, B)) )  => A=B) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t4_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r2_tarski(A, B) & m1_subset_1(B, k1_zfmisc_1(C)))  => m1_subset_1(A, C)) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
