% Mizar problem: t71_cat_8,cat_8,5074,7 
fof(t71_cat_8, conjecture,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) &  (v7_cat_8(A) &  (v8_cat_8(A) & l1_cat_6(A)) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, k5_cat_6(A)) =>  (! [C] :  (m1_subset_1(C, k5_cat_6(A)) =>  (! [D] :  (m1_subset_1(D, k5_cat_6(A)) =>  ~ ( ( ~ (k2_cat_7(A, k4_cat_8(A, D, B), C)=k1_xboole_0)  &  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, k2_cat_7(A, k4_cat_8(A, D, B), C), k2_cat_7(A, D, k15_cat_8(A, B, C))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(k2_cat_7(A, k4_cat_8(A, D, B), C), k2_cat_7(A, D, k15_cat_8(A, B, C)))))) )  =>  ~ ( ( (! [F] :  (m1_cat_7(F, A, k4_cat_8(A, D, B), C) =>  (! [G] :  (m1_cat_7(G, A, D, k15_cat_8(A, B, C)) =>  (G=k1_funct_1(E, F) => k4_cat_7(A, k4_cat_8(A, D, B), k4_cat_8(A, k15_cat_8(A, B, C), B), C, k7_cat_8(A, D, k15_cat_8(A, B, C), B, B, G, k3_cat_7(A, B)), k16_cat_8(A, B, C))=F) ) ) ) )  & v3_funct_2(E, k2_cat_7(A, k4_cat_8(A, D, B), C), k2_cat_7(A, D, k15_cat_8(A, B, 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_card_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_zfmisc_1(A))  => v3_card_1(A, 1)) ) ).
fof(cc10_ordinal1, axiom,  (! [A] :  (v6_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_ordinal1(B)) ) ) ) ).
fof(cc10_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ( ~ (v2_struct_0(A))  & v7_struct_0(A))  => v13_struct_0(A, 1)) ) ) ).
fof(cc11_card_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_card_1(A))  =>  (! [B] :  (v3_card_1(B, A) =>  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(cc11_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v7_ordinal1(A)) ) ).
fof(cc11_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, 1) =>  ( ~ (v2_struct_0(A))  & v7_struct_0(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(cc17_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(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_card_1, axiom,  (! [A] :  (v1_card_1(A) => v3_ordinal1(A)) ) ).
fof(cc1_cat_6, axiom,  (! [A] :  (l1_cat_6(A) =>  (v2_struct_0(A) =>  (v4_cat_6(A) &  (v5_cat_6(A) &  (v6_cat_6(A) &  (v7_cat_6(A) & v8_cat_6(A)) ) ) ) ) ) ) ).
fof(cc1_cat_7, axiom,  (! [A] :  (v3_ordinal1(A) =>  ~ (v1_xtuple_0(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_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v3_ordinal1(A) & v7_ordinal1(A)) ) ) ).
fof(cc1_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (v1_ordinal1(A) & v2_ordinal1(A)) ) ) ).
fof(cc1_partfun1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_partfun1(C, 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_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v7_struct_0(A)) ) ) ).
fof(cc1_xtuple_0, axiom,  (! [A] :  (v2_xtuple_0(A) => v1_xtuple_0(A)) ) ).
fof(cc20_ordinal1, axiom,  (! [A] :  ( ~ (v1_setfam_1(A))  => v10_ordinal1(A)) ) ).
fof(cc2_card_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_card_1(A)) ) ).
fof(cc2_cat_7, axiom,  (! [A] :  (l1_cat_6(A) =>  (v2_struct_0(A) => v6_cat_7(A)) ) ) ).
fof(cc2_cat_8, axiom,  (! [A] :  (l1_cat_6(A) =>  ( ( ~ (v2_struct_0(A))  &  (v7_struct_0(A) &  (v8_cat_6(A) &  (v9_cat_6(A) & v10_cat_6(A)) ) ) )  =>  (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & v3_cat_8(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_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v7_ordinal1(A) &  ~ (v3_xxreal_0(A)) ) ) ) ).
fof(cc2_ordinal1, axiom,  (! [A] :  ( (v1_ordinal1(A) & v2_ordinal1(A))  => v3_ordinal1(A)) ) ).
fof(cc2_partfun1, 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_partfun1(C, 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_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc3_card_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_card_1(A)) ) ).
fof(cc3_cat_7, axiom,  (! [A] :  (l1_cat_6(A) =>  ( (v9_cat_6(A) &  (v10_cat_6(A) & v6_cat_7(A)) )  =>  (v8_cat_6(A) &  (v9_cat_6(A) & v10_cat_6(A)) ) ) ) ) ).
fof(cc3_cat_8, axiom,  (! [A] :  (l1_cat_6(A) =>  ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & v3_cat_8(A)) ) )  =>  ( ~ (v2_struct_0(A))  &  (v7_struct_0(A) &  (v8_cat_6(A) &  (v9_cat_6(A) & v10_cat_6(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_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v7_ordinal1(A) &  ~ (v3_xxreal_0(A)) ) ) ) ).
fof(cc3_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_ordinal1(A)) ) ).
fof(cc3_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(cc4_card_1, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) => v1_finset_1(A)) ) ).
fof(cc4_cat_8, axiom,  (! [A] :  (l1_cat_6(A) =>  ( (v2_struct_0(A) &  (v8_cat_6(A) &  (v9_cat_6(A) & v10_cat_6(A)) ) )  =>  (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & v6_cat_8(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_nat_1, axiom,  (! [A] :  ( (v7_ordinal1(A) & v8_ordinal1(A))  =>  (v7_ordinal1(A) &  ~ (v2_xxreal_0(A)) ) ) ) ).
fof(cc4_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v5_ordinal1(A)) ) ).
fof(cc4_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_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) =>  (v2_struct_0(A) & v8_struct_0(A)) ) ) ) ).
fof(cc5_card_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_finset_1(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_nat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v8_ordinal1(A)) ) ).
fof(cc5_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, A) => v3_ordinal1(B)) ) ) ) ).
fof(cc5_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ( ~ (v2_struct_0(A))  &  ~ (v8_struct_0(A)) ) ) ) ) ).
fof(cc6_card_1, axiom,  (! [A] :  ( (v3_ordinal1(A) & v1_finset_1(A))  => v7_ordinal1(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_funct_2, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  ( (v1_funct_1(C) & v3_funct_2(C, A, B))  =>  (v1_funct_1(C) &  (v2_funct_1(C) & v2_funct_2(C, B)) ) ) ) ) ) ).
fof(cc6_nat_1, axiom,  (! [A] :  ( ~ (v8_ordinal1(A))  =>  ~ (v1_xboole_0(A)) ) ) ).
fof(cc6_ordinal1, axiom,  (! [A] :  (v7_ordinal1(A) => v3_ordinal1(A)) ) ).
fof(cc6_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v7_struct_0(A) => v8_struct_0(A)) ) ) ).
fof(cc7_card_1, axiom,  (! [A] :  (v3_card_1(A, k5_ordinal1) => v1_xboole_0(A)) ) ).
fof(cc7_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_funct_1(A)) ) ).
fof(cc7_funct_2, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  ( (v1_funct_1(C) &  (v2_funct_1(C) & v2_funct_2(C, B)) )  =>  (v1_funct_1(C) & v3_funct_2(C, A, B)) ) ) ) ) ).
fof(cc7_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v7_ordinal1(A)) ) ).
fof(cc7_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ~ (v7_struct_0(A)) ) ) ) ).
fof(cc8_card_1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_card_1(A, k5_ordinal1)) ) ).
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_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v13_struct_0(A, k5_ordinal1)) ) ) ).
fof(cc9_card_1, axiom,  (! [A] :  (v3_card_1(A, 1) =>  ( ~ (v1_xboole_0(A))  & v1_zfmisc_1(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(cc9_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, k5_ordinal1) => v2_struct_0(A)) ) ) ).
fof(d10_xboole_0, axiom,  (! [A] :  (! [B] :  (A=B <=>  (r1_tarski(A, B) & r1_tarski(B, A)) ) ) ) ).
fof(d13_cat_8, axiom,  (! [A] :  ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) &  (v7_cat_8(A) & l1_cat_6(A)) ) ) )  =>  (! [B] :  (m1_subset_1(B, k5_cat_6(A)) =>  (! [C] :  (m1_subset_1(C, k5_cat_6(A)) => k4_cat_8(A, B, C)=k4_xtuple_0(o_3_0_cat_8(A, B, C))) ) ) ) ) ) ).
fof(d1_funct_2, axiom,  (! [A] :  (! [B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  ( ( ~ (B=k1_xboole_0)  =>  (v1_funct_2(C, A, B) <=> A=k1_relset_1(A, C)) )  &  (B=k1_xboole_0 =>  (v1_funct_2(C, A, B) <=> C=k1_xboole_0) ) ) ) ) ) ) ).
fof(d1_xboole_0, axiom,  (! [A] :  (v1_xboole_0(A) <=>  (! [B] :  ~ (r2_hidden(B, A)) ) ) ) ).
fof(d29_cat_8, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) &  (v7_cat_8(A) & l1_cat_6(A)) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, k5_cat_6(A)) =>  (! [C] :  (m1_subset_1(C, k5_cat_6(A)) =>  (! [D] :  (m1_subset_1(D, k5_cat_6(A)) =>  (! [E] :  (m1_cat_7(E, A, k4_cat_8(A, D, B), C) =>  ( ~ (k2_cat_7(A, k4_cat_8(A, D, B), C)=k1_xboole_0)  =>  (r5_cat_8(A, B, C, D, E) <=>  (! [F] :  (m1_subset_1(F, k5_cat_6(A)) =>  (! [G] :  (m1_cat_7(G, A, k4_cat_8(A, F, B), C) =>  ( ~ (k2_cat_7(A, k4_cat_8(A, F, B), C)=k1_xboole_0)  =>  ( ~ (k2_cat_7(A, F, D)=k1_xboole_0)  &  (? [H] :  (m1_cat_7(H, A, F, D) &  (G=k4_cat_7(A, k4_cat_8(A, F, B), k4_cat_8(A, D, B), C, k7_cat_8(A, F, D, B, B, H, k3_cat_7(A, B)), E) &  (! [I] :  (m1_cat_7(I, A, F, D) =>  (G=k4_cat_7(A, k4_cat_8(A, F, B), k4_cat_8(A, D, B), C, k7_cat_8(A, F, D, B, B, I, k3_cat_7(A, B)), E) => H=I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d32_cat_8, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) &  (v7_cat_8(A) &  (v8_cat_8(A) & l1_cat_6(A)) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, k5_cat_6(A)) =>  (! [C] :  (m1_subset_1(C, k5_cat_6(A)) => k15_cat_8(A, B, C)=k1_xtuple_0(o_3_2_cat_8(A, B, C))) ) ) ) ) ) ).
fof(d33_cat_8, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) &  (v7_cat_8(A) &  (v8_cat_8(A) & l1_cat_6(A)) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, k5_cat_6(A)) =>  (! [C] :  (m1_subset_1(C, k5_cat_6(A)) => k16_cat_8(A, B, C)=k2_xtuple_0(o_3_2_cat_8(A, B, C))) ) ) ) ) ) ).
fof(d3_cat_7, axiom,  (! [A] :  (l1_cat_6(A) =>  (! [B] :  (m1_subset_1(B, k5_cat_6(A)) =>  (! [C] :  (m1_subset_1(C, k5_cat_6(A)) =>  ( ~ (k1_cat_7(A, B, C)=k1_xboole_0)  =>  (! [D] :  (m1_subset_1(D, k1_cat_6(A)) =>  (m1_cat_7(D, A, B, C) <=> r2_tarski(D, k1_cat_7(A, B, C))) ) ) ) ) ) ) ) ) ) ).
fof(d3_funct_2, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v2_funct_2(B, A) <=> k2_relset_1(A, B)=A) ) ) ) ).
fof(d3_tarski, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) <=>  (! [C] :  (r2_hidden(C, A) => r2_hidden(C, B)) ) ) ) ) ).
fof(dt_k10_xtuple_0, axiom, $true).
fof(dt_k15_cat_8, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) &  (v7_cat_8(A) &  (v8_cat_8(A) & l1_cat_6(A)) ) ) ) ) )  &  (m1_subset_1(B, k5_cat_6(A)) & m1_subset_1(C, k5_cat_6(A))) )  => m1_subset_1(k15_cat_8(A, B, C), k5_cat_6(A))) ) ).
fof(dt_k16_cat_8, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) &  (v7_cat_8(A) &  (v8_cat_8(A) & l1_cat_6(A)) ) ) ) ) )  &  (m1_subset_1(B, k5_cat_6(A)) & m1_subset_1(C, k5_cat_6(A))) )  => m1_cat_7(k16_cat_8(A, B, C), A, k4_cat_8(A, k15_cat_8(A, B, C), B), C)) ) ).
fof(dt_k1_cat_6, axiom, $true).
fof(dt_k1_cat_7, axiom,  (! [A, B, C] :  ( (l1_cat_6(A) &  (m1_subset_1(B, k5_cat_6(A)) & m1_subset_1(C, k5_cat_6(A))) )  => m1_subset_1(k1_cat_7(A, B, C), k1_zfmisc_1(k1_cat_6(A)))) ) ).
fof(dt_k1_funct_1, axiom, $true).
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_xboole_0, axiom, $true).
fof(dt_k1_xtuple_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_cat_7, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  &  (m1_subset_1(B, k5_cat_6(A)) & m1_subset_1(C, k5_cat_6(A))) )  => m1_subset_1(k2_cat_7(A, B, C), k1_zfmisc_1(k1_cat_6(A)))) ) ).
fof(dt_k2_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  => m1_subset_1(k2_relset_1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_k2_xtuple_0, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_cat_7, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v10_cat_6(A) & l1_cat_6(A)) )  & m1_subset_1(B, k5_cat_6(A)))  => m1_cat_7(k3_cat_7(A, B), A, B, B)) ) ).
fof(dt_k4_cat_7, axiom,  (! [A, B, C, D, E, F] :  ( ( (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) )  &  (m1_subset_1(B, k5_cat_6(A)) &  (m1_subset_1(C, k5_cat_6(A)) &  (m1_subset_1(D, k5_cat_6(A)) &  (m1_cat_7(E, A, B, C) & m1_cat_7(F, A, C, D)) ) ) ) )  => m1_cat_7(k4_cat_7(A, B, C, D, E, F), A, B, D)) ) ).
fof(dt_k4_cat_8, axiom,  (! [A, B, C] :  ( ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) &  (v7_cat_8(A) & l1_cat_6(A)) ) ) )  &  (m1_subset_1(B, k5_cat_6(A)) & m1_subset_1(C, k5_cat_6(A))) )  => m1_subset_1(k4_cat_8(A, B, C), k5_cat_6(A))) ) ).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k4_xtuple_0, axiom, $true).
fof(dt_k5_cat_6, axiom,  (! [A] :  (l1_cat_6(A) => m1_subset_1(k5_cat_6(A), k1_zfmisc_1(k1_cat_6(A)))) ) ).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k7_cat_8, axiom,  (! [A, B, C, D, E, F, G] :  ( ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) &  (v7_cat_8(A) & l1_cat_6(A)) ) ) )  &  (m1_subset_1(B, k5_cat_6(A)) &  (m1_subset_1(C, k5_cat_6(A)) &  (m1_subset_1(D, k5_cat_6(A)) &  (m1_subset_1(E, k5_cat_6(A)) &  (m1_cat_7(F, A, B, C) & m1_cat_7(G, A, D, E)) ) ) ) ) )  => m1_cat_7(k7_cat_8(A, B, C, D, E, F, G), A, k4_cat_8(A, B, D), k4_cat_8(A, C, E))) ) ).
fof(dt_k8_cat_6, axiom,  (! [A, B] :  ( ( (v10_cat_6(A) & l1_cat_6(A))  & m1_subset_1(B, k5_cat_6(A)))  => m1_subset_1(k8_cat_6(A, B), k1_cat_6(A))) ) ).
fof(dt_k9_xtuple_0, axiom, $true).
fof(dt_l1_cat_6, axiom,  (! [A] :  (l1_cat_6(A) => l1_struct_0(A)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_m1_cat_7, axiom,  (! [A, B, C] :  ( (l1_cat_6(A) &  (m1_subset_1(B, k5_cat_6(A)) & m1_subset_1(C, k5_cat_6(A))) )  =>  (! [D] :  (m1_cat_7(D, A, B, C) => m1_subset_1(D, k1_cat_6(A))) ) ) ) ).
fof(dt_m1_cat_8, axiom,  (! [A, B, C] :  ( ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) &  (v7_cat_8(A) & l1_cat_6(A)) ) ) )  &  (m1_subset_1(B, k5_cat_6(A)) & m1_subset_1(C, k5_cat_6(A))) )  =>  (! [D] :  (m1_cat_8(D, A, B, C) => v2_xtuple_0(D)) ) ) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_m4_cat_8, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) &  (v7_cat_8(A) &  (v8_cat_8(A) & l1_cat_6(A)) ) ) ) ) )  &  (m1_subset_1(B, k5_cat_6(A)) & m1_subset_1(C, k5_cat_6(A))) )  =>  (! [D] :  (m4_cat_8(D, A, B, C) => v1_xtuple_0(D)) ) ) ) ).
fof(dt_o_3_0_cat_8, axiom,  (! [A, B, C] :  ( ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) &  (v7_cat_8(A) & l1_cat_6(A)) ) ) )  &  (m1_subset_1(B, k5_cat_6(A)) & m1_subset_1(C, k5_cat_6(A))) )  => m1_cat_8(o_3_0_cat_8(A, B, C), A, B, C)) ) ).
fof(dt_o_3_2_cat_8, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) &  (v7_cat_8(A) &  (v8_cat_8(A) & l1_cat_6(A)) ) ) ) ) )  &  (m1_subset_1(B, k5_cat_6(A)) & m1_subset_1(C, k5_cat_6(A))) )  => m4_cat_8(o_3_2_cat_8(A, B, C), A, B, C)) ) ).
fof(existence_l1_cat_6, axiom,  (? [A] : l1_cat_6(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_m1_cat_7, axiom,  (! [A, B, C] :  ( (l1_cat_6(A) &  (m1_subset_1(B, k5_cat_6(A)) & m1_subset_1(C, k5_cat_6(A))) )  =>  (? [D] : m1_cat_7(D, A, B, C)) ) ) ).
fof(existence_m1_cat_8, axiom,  (! [A, B, C] :  ( ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) &  (v7_cat_8(A) & l1_cat_6(A)) ) ) )  &  (m1_subset_1(B, k5_cat_6(A)) & m1_subset_1(C, k5_cat_6(A))) )  =>  (? [D] : m1_cat_8(D, A, B, C)) ) ) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(existence_m4_cat_8, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) &  (v7_cat_8(A) &  (v8_cat_8(A) & l1_cat_6(A)) ) ) ) ) )  &  (m1_subset_1(B, k5_cat_6(A)) & m1_subset_1(C, k5_cat_6(A))) )  =>  (? [D] : m4_cat_8(D, A, B, C)) ) ) ).
fof(fc10_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) & v9_ordinal1(A))  =>  ~ (v10_ordinal1(k10_xtuple_0(A))) ) ) ).
fof(fc11_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) &  ~ (v9_ordinal1(A)) )  => v10_ordinal1(k10_xtuple_0(A))) ) ).
fof(fc12_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ~ (v1_finset_1(k1_zfmisc_1(A))) ) ) ).
fof(fc12_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) )  => v1_zfmisc_1(k10_xtuple_0(A))) ) ).
fof(fc13_card_1, axiom,  (! [A, B] :  ( ( ~ (v1_finset_1(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_finset_1(k2_zfmisc_1(A, B))) ) ) ).
fof(fc13_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) )  =>  ~ (v1_zfmisc_1(k10_xtuple_0(A))) ) ) ).
fof(fc14_card_1, axiom,  (! [A, B] :  ( ( ~ (v1_finset_1(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_finset_1(k2_zfmisc_1(B, A))) ) ) ).
fof(fc17_card_1, axiom,  (! [A, B] :  ( (v1_card_1(A) &  (v1_relat_1(B) &  (v1_funct_1(B) & v3_card_1(B, A)) ) )  => v3_card_1(k9_xtuple_0(B), A)) ) ).
fof(fc17_funct_1, axiom,  (! [A, B, C] :  ( (v4_funct_1(A) &  (v1_relat_1(C) &  (v5_relat_1(C, A) & v1_funct_1(C)) ) )  =>  (v1_relat_1(k1_funct_1(C, B)) & v1_funct_1(k1_funct_1(C, B))) ) ) ).
fof(fc18_funct_1, axiom,  (! [A] :  ( ( ~ (v1_zfmisc_1(A))  &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  ~ (v1_zfmisc_1(k9_xtuple_0(A))) ) ) ).
fof(fc1_cat_6, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_cat_6(A) & l1_cat_6(A)) )  =>  ~ (v1_xboole_0(k5_cat_6(A))) ) ) ).
fof(fc1_cat_7, axiom,  (! [A] :  ( (v2_struct_0(A) & l1_cat_6(A))  => v1_xboole_0(k1_cat_6(A))) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc2_cat_7, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_cat_6(A))  =>  ~ (v1_xboole_0(k1_cat_6(A))) ) ) ).
fof(fc3_cat_7, axiom,  (! [A] :  ( (v2_struct_0(A) &  (v10_cat_6(A) & l1_cat_6(A)) )  => v1_xboole_0(k5_cat_6(A))) ) ).
fof(fc4_cat_7, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_cat_6(A) & l1_cat_6(A)) )  =>  ~ (v1_xboole_0(k5_cat_6(A))) ) ) ).
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_cat_7, axiom,  (! [A, B] :  ( ( (v10_cat_6(A) & l1_cat_6(A))  & m1_subset_1(B, k5_cat_6(A)))  => v11_cat_6(k8_cat_6(A, B), A)) ) ).
fof(fc5_xtuple_0, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k10_xtuple_0(A))) ) ).
fof(fc6_card_1, axiom, v1_card_1(k4_ordinal1)).
fof(fc6_cat_7, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v10_cat_6(A) & l1_cat_6(A)) )  & m1_subset_1(B, k5_cat_6(A)))  =>  ~ (v1_xboole_0(k1_cat_7(A, B, B))) ) ) ).
fof(fc6_ordinal1, axiom,  ( ~ (v1_xboole_0(k4_ordinal1))  & v3_ordinal1(k4_ordinal1)) ).
fof(fc7_card_1, axiom, v2_card_1(k4_ordinal1)).
fof(fc8_ordinal1, axiom, v7_ordinal1(k5_ordinal1)).
fof(fc8_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, B), C))) => v1_relat_1(k9_xtuple_0(D))) ) ).
fof(fc9_card_1, axiom,  ~ (v1_finset_1(k4_ordinal1)) ).
fof(fc9_ordinal1, axiom, v8_ordinal1(k5_ordinal1)).
fof(fc9_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, k2_zfmisc_1(B, C)))) => v1_relat_1(k10_xtuple_0(D))) ) ).
fof(rc10_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_card_1(B)) ) ) ) ).
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_card_1, axiom,  (? [A] : v1_card_1(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_nat_1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc1_ordinal1, axiom,  (? [A] :  (v1_ordinal1(A) & v2_ordinal1(A)) ) ).
fof(rc1_partfun1, 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)) ) ) ) ) ) ).
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_xtuple_0, axiom,  (? [A] : v1_xtuple_0(A)) ).
fof(rc23_struct_0, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] :  (l1_struct_0(B) & v13_struct_0(B, A)) ) ) ) ).
fof(rc2_card_1, axiom,  (? [A] :  (v1_ordinal1(A) &  (v2_ordinal1(A) &  (v3_ordinal1(A) &  (v1_finset_1(A) & v1_card_1(A)) ) ) ) ) ).
fof(rc2_cat_6, axiom,  (? [A] :  (l1_cat_6(A) &  (v4_cat_6(A) &  ( ~ (v5_cat_6(A))  &  (v8_cat_6(A) & v9_cat_6(A)) ) ) ) ) ).
fof(rc2_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ).
fof(rc2_funct_2, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, A))) &  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) &  (v1_funct_2(B, A, A) & v3_funct_2(B, A, A)) ) ) ) ) ) ) ) ) ).
fof(rc2_nat_1, axiom,  (? [A] :  (v7_ordinal1(A) & v8_ordinal1(A)) ) ).
fof(rc2_ordinal1, axiom,  (? [A] : v3_ordinal1(A)) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc2_xtuple_0, axiom,  (? [A] : v2_xtuple_0(A)) ).
fof(rc3_card_1, axiom,  (? [A] :  ~ (v1_finset_1(A)) ) ).
fof(rc3_cat_6, axiom,  (? [A] :  (l1_cat_6(A) &  ( ~ (v4_cat_6(A))  &  (v5_cat_6(A) &  (v8_cat_6(A) & v9_cat_6(A)) ) ) ) ) ).
fof(rc3_nat_1, axiom,  (? [A] :  (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) ) ) ).
fof(rc3_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_ordinal1(A) &  (v2_ordinal1(A) & v3_ordinal1(A)) ) ) ) ).
fof(rc3_partfun1, 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_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) &  ~ (v1_xboole_0(C)) ) ) ) ) ) ) ) ) ).
fof(rc4_card_1, axiom,  (? [A] :  (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) ) ) ).
fof(rc4_cat_6, axiom,  (? [A] :  (l1_cat_6(A) &  ( ~ (v6_cat_6(A))  &  (v7_cat_6(A) &  (v8_cat_6(A) & v10_cat_6(A)) ) ) ) ) ).
fof(rc4_ordinal1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) & v5_ordinal1(B)) ) ) ) ) ).
fof(rc5_card_1, axiom,  (? [A] :  (v1_ordinal1(A) &  (v2_ordinal1(A) &  (v3_ordinal1(A) &  (v7_ordinal1(A) &  ( ~ (v8_ordinal1(A))  & v1_card_1(A)) ) ) ) ) ) ).
fof(rc5_cat_6, axiom,  (? [A] :  (l1_cat_6(A) &  (v6_cat_6(A) &  ( ~ (v7_cat_6(A))  &  (v8_cat_6(A) & v10_cat_6(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(rc6_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_finset_1(B)) ) ) ) ) ).
fof(rc6_cat_6, axiom,  (? [A] :  (l1_cat_6(A) &  ( ~ (v8_cat_6(A))  &  (v9_cat_6(A) & v10_cat_6(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_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] : v3_card_1(B, A)) ) ) ).
fof(rc7_cat_6, axiom,  (? [A] :  (l1_cat_6(A) & v2_struct_0(A)) ) ).
fof(rc7_cat_8, axiom,  (? [A] :  (l1_cat_6(A) &  ( ~ (v2_struct_0(A))  &  (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & v7_cat_8(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_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] :  (v1_relat_1(B) &  (v1_funct_1(B) & v3_card_1(B, A)) ) ) ) ) ).
fof(rc8_cat_8, axiom,  (? [A] :  (l1_cat_6(A) &  ( ~ (v2_struct_0(A))  &  (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) &  (v7_cat_8(A) & v8_cat_8(A)) ) ) ) ) ) ) ).
fof(rc8_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rc9_card_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v3_card_1(B, 1)) ) ) ) ).
fof(rc9_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(redefinition_k1_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  => k1_relset_1(A, B)=k9_xtuple_0(B)) ) ).
fof(redefinition_k2_cat_7, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  &  (m1_subset_1(B, k5_cat_6(A)) & m1_subset_1(C, k5_cat_6(A))) )  => k2_cat_7(A, B, C)=k1_cat_7(A, B, C)) ) ).
fof(redefinition_k2_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  => k2_relset_1(A, B)=k10_xtuple_0(B)) ) ).
fof(redefinition_k3_cat_7, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v10_cat_6(A) & l1_cat_6(A)) )  & m1_subset_1(B, k5_cat_6(A)))  => k3_cat_7(A, B)=k8_cat_6(A, 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_funct_2__e4_126__cat_8, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(A))  &  (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) &  (v7_cat_8(A) &  (v8_cat_8(A) & l1_cat_6(A)) ) ) ) ) )  &  (m1_subset_1(B, k5_cat_6(A)) &  (m1_subset_1(C, k5_cat_6(A)) & m1_subset_1(D, k5_cat_6(A))) ) )  =>  ( (! [E] :  ~ ( (r2_hidden(E, k2_cat_7(A, k4_cat_8(A, D, B), C)) &  (! [F] :  ~ ( (r2_hidden(F, k2_cat_7(A, D, k15_cat_8(A, B, C))) &  (! [G] :  (m1_cat_7(G, A, k4_cat_8(A, D, B), C) =>  ~ ( (G=E &  (! [H] :  (m1_cat_7(H, A, D, k15_cat_8(A, B, C)) =>  ~ ( (H=F &  (G=k4_cat_7(A, k4_cat_8(A, D, B), k4_cat_8(A, k15_cat_8(A, B, C), B), C, k7_cat_8(A, D, k15_cat_8(A, B, C), B, B, H, k3_cat_7(A, B)), k16_cat_8(A, B, C)) &  (! [I] :  (m1_cat_7(I, A, D, k15_cat_8(A, B, C)) =>  (G=k4_cat_7(A, k4_cat_8(A, D, B), k4_cat_8(A, k15_cat_8(A, B, C), B), C, k7_cat_8(A, D, k15_cat_8(A, B, C), B, B, I, k3_cat_7(A, B)), k16_cat_8(A, B, C)) => H=I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (? [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, k2_cat_7(A, k4_cat_8(A, D, B), C), k2_cat_7(A, D, k15_cat_8(A, B, C))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(k2_cat_7(A, k4_cat_8(A, D, B), C), k2_cat_7(A, D, k15_cat_8(A, B, C)))))) )  &  (! [F] :  (r2_hidden(F, k2_cat_7(A, k4_cat_8(A, D, B), C)) =>  (! [J] :  (m1_cat_7(J, A, k4_cat_8(A, D, B), C) =>  ~ ( (J=F &  (! [K] :  (m1_cat_7(K, A, D, k15_cat_8(A, B, C)) =>  ~ ( (K=k1_funct_1(E, F) &  (J=k4_cat_7(A, k4_cat_8(A, D, B), k4_cat_8(A, k15_cat_8(A, B, C), B), C, k7_cat_8(A, D, k15_cat_8(A, B, C), B, B, K, k3_cat_7(A, B)), k16_cat_8(A, B, C)) &  (! [L] :  (m1_cat_7(L, A, D, k15_cat_8(A, B, C)) =>  (J=k4_cat_7(A, k4_cat_8(A, D, B), k4_cat_8(A, k15_cat_8(A, B, C), B), C, k7_cat_8(A, D, k15_cat_8(A, B, C), B, B, L, k3_cat_7(A, B)), k16_cat_8(A, B, C)) => K=L) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(spc1_numerals, axiom,  (v2_xxreal_0(1) & m1_subset_1(1, k4_ordinal1)) ).
fof(t19_funct_2, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  =>  ( (B=k1_xboole_0 => A=k1_xboole_0)  =>  (v2_funct_1(C) <=>  (! [D] :  (! [E] :  ( (r2_hidden(D, A) &  (r2_hidden(E, A) & k1_funct_1(C, D)=k1_funct_1(C, E)) )  => D=E) ) ) ) ) ) ) ) ) ).
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(t3_funct_1, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (r2_hidden(A, k9_xtuple_0(B)) => r2_tarski(k1_funct_1(B, A), k10_xtuple_0(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(t70_cat_8, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) &  (v7_cat_8(A) &  (v8_cat_8(A) & l1_cat_6(A)) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, k5_cat_6(A)) =>  (! [C] :  (m1_subset_1(C, k5_cat_6(A)) =>  ( ~ (k2_cat_7(A, k4_cat_8(A, k15_cat_8(A, B, C), B), C)=k1_xboole_0)  & r5_cat_8(A, B, C, k15_cat_8(A, B, C), k16_cat_8(A, B, C))) ) ) ) ) ) ) ).
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)) ) ) ) ) ).
