% Mizar problem: l111_cat_8,cat_8,5187,7 
fof(l111_cat_8, conjecture,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) ) )  =>  (! [C] :  ( ( ~ (v2_struct_0(C))  &  (v8_cat_6(C) &  (v9_cat_6(C) &  (v10_cat_6(C) & l1_cat_6(C)) ) ) )  =>  ~ ( (A=k14_cat_8(B, C) &  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(k8_cat_8(A, B)), u1_struct_0(C)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k8_cat_8(A, B)), u1_struct_0(C))))) )  =>  ~ ( (v16_cat_6(D, k8_cat_8(A, B), C) &  (! [E] :  ( (v8_cat_6(E) &  (v9_cat_6(E) &  (v10_cat_6(E) & l1_cat_6(E)) ) )  =>  (! [F] :  ( (v1_funct_1(F) &  (v1_funct_2(F, u1_struct_0(k8_cat_8(E, B)), u1_struct_0(C)) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k8_cat_8(E, B)), u1_struct_0(C))))) )  =>  ~ ( (v16_cat_6(F, k8_cat_8(E, B), C) &  (! [G] :  ( (v1_funct_1(G) &  (v1_funct_2(G, u1_struct_0(E), u1_struct_0(A)) & m1_subset_1(G, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(E), u1_struct_0(A))))) )  =>  ~ ( (v16_cat_6(G, E, A) &  (r2_relset_1(u1_struct_0(k8_cat_8(E, B)), u1_struct_0(C), F, k11_cat_6(k8_cat_8(E, B), k8_cat_8(A, B), C, k11_cat_8(E, B, A, B, G, k12_cat_6(B)), D)) &  (! [H] :  ( (v1_funct_1(H) &  (v1_funct_2(H, u1_struct_0(E), u1_struct_0(A)) & m1_subset_1(H, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(E), u1_struct_0(A))))) )  =>  ( (v16_cat_6(H, E, A) & r2_relset_1(u1_struct_0(k8_cat_8(E, B)), u1_struct_0(C), F, k11_cat_6(k8_cat_8(E, B), k8_cat_8(A, B), C, k11_cat_8(E, B, A, B, H, k12_cat_6(B)), D)))  => r2_relset_1(u1_struct_0(E), u1_struct_0(A), G, H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(abstractness_v1_cat_6, axiom,  (! [A] :  (l1_cat_6(A) =>  (v1_cat_6(A) => A=g1_cat_6(u1_struct_0(A), u1_cat_6(A))) ) ) ).
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_cat_8, axiom,  (! [A, B] :  ( ( (v2_struct_0(A) &  (v10_cat_6(A) & l1_cat_6(A)) )  &  (v10_cat_6(B) & l1_cat_6(B)) )  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B)))) =>  ( (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)))  =>  (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v16_cat_6(C, A, B)) ) ) ) ) ) ) ).
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_partfun1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v3_relat_2(A) & v8_relat_2(A)) )  =>  (v1_relat_1(A) & v1_relat_2(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_funct_2, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, A))) =>  ( (v1_relat_2(B) &  (v1_funct_1(B) &  (v1_partfun1(B, A) & v1_funct_2(B, A, A)) ) )  =>  (v1_funct_1(B) &  (v1_funct_2(B, A, A) & v3_funct_2(B, A, A)) ) ) ) ) ) ).
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(d12_xtuple_0, axiom,  (! [A] :  (! [B] :  (B=k9_xtuple_0(A) <=>  (! [C] :  (r2_hidden(C, B) <=>  (? [D] : r2_hidden(k4_tarski(C, D), A)) ) ) ) ) ) ).
fof(d19_cat_8, axiom,  (! [A] :  ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  =>  (! [B] :  ( (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) )  => k8_cat_8(A, B)=k4_xtuple_0(o_2_0_cat_8(A, B))) ) ) ) ).
fof(d1_binop_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (! [C] : k1_binop_1(A, B, C)=k1_funct_1(A, k4_tarski(B, C))) ) ) ) ).
fof(d1_cat_6, axiom,  (! [A] :  (l1_cat_6(A) => k1_cat_6(A)=u1_struct_0(A)) ) ).
fof(d20_cat_8, axiom,  (! [A] :  ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  =>  (! [B] :  ( (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) )  => k9_cat_8(A, B)=k5_xtuple_0(o_2_0_cat_8(A, B))) ) ) ) ).
fof(d21_cat_6, axiom,  (! [A] :  ( (v10_cat_6(A) & l1_cat_6(A))  =>  (! [B] :  ( (v10_cat_6(B) & l1_cat_6(B))  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) )  =>  (! [D] :  (m1_subset_1(D, k1_cat_6(A)) =>  ( ( ~ (v2_struct_0(A))  => k9_cat_6(A, B, C, D)=k1_funct_1(C, D))  &  (v2_struct_0(A) => k9_cat_6(A, B, C, D)=o_1_2_cat_6(B)) ) ) ) ) ) ) ) ) ) ).
fof(d21_cat_8, axiom,  (! [A] :  ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  =>  (! [B] :  ( (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) )  => k10_cat_8(A, B)=k2_xtuple_0(o_2_0_cat_8(A, B))) ) ) ) ).
fof(d22_cat_6, axiom,  (! [A] :  ( (v10_cat_6(A) & l1_cat_6(A))  =>  (! [B] :  ( (v10_cat_6(B) & l1_cat_6(B))  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) )  =>  (v13_cat_6(C, A, B) <=>  (! [D] :  (m1_subset_1(D, k1_cat_6(A)) =>  (v11_cat_6(D, A) => v11_cat_6(k9_cat_6(A, B, C, D), B)) ) ) ) ) ) ) ) ) ) ).
fof(d22_cat_8, axiom,  (! [A] :  ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  =>  (! [B] :  ( (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) )  =>  (! [C] :  ( (v8_cat_6(C) &  (v9_cat_6(C) &  (v10_cat_6(C) & l1_cat_6(C)) ) )  =>  (! [D] :  ( (v8_cat_6(D) &  (v9_cat_6(D) &  (v10_cat_6(D) & l1_cat_6(D)) ) )  =>  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, u1_struct_0(A), u1_struct_0(C)) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(C))))) )  =>  (! [F] :  ( (v1_funct_1(F) &  (v1_funct_2(F, u1_struct_0(B), u1_struct_0(D)) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(D))))) )  =>  ( (v16_cat_6(E, A, C) & v16_cat_6(F, B, D))  =>  (! [G] :  ( (v1_funct_1(G) &  (v1_funct_2(G, u1_struct_0(k8_cat_8(A, B)), u1_struct_0(k8_cat_8(C, D))) & m1_subset_1(G, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k8_cat_8(A, B)), u1_struct_0(k8_cat_8(C, D)))))) )  =>  (G=k11_cat_8(A, B, C, D, E, F) <=>  (v16_cat_6(G, k8_cat_8(A, B), k8_cat_8(C, D)) &  (r2_relset_1(u1_struct_0(k8_cat_8(A, B)), u1_struct_0(C), k11_cat_6(k8_cat_8(A, B), A, C, k9_cat_8(A, B), E), k11_cat_6(k8_cat_8(A, B), k8_cat_8(C, D), C, G, k9_cat_8(C, D))) & r2_relset_1(u1_struct_0(k8_cat_8(A, B)), u1_struct_0(D), k11_cat_6(k8_cat_8(A, B), B, D, k10_cat_8(A, B), F), k11_cat_6(k8_cat_8(A, B), k8_cat_8(C, D), D, G, k10_cat_8(C, D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d23_cat_6, axiom,  (! [A] :  ( (v10_cat_6(A) & l1_cat_6(A))  =>  (! [B] :  ( (v10_cat_6(B) & l1_cat_6(B))  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) )  =>  (v14_cat_6(C, A, B) <=>  (! [D] :  (m1_subset_1(D, k1_cat_6(A)) =>  (! [E] :  (m1_subset_1(E, k1_cat_6(A)) =>  (r1_cat_6(A, D, E) =>  (r1_cat_6(B, k9_cat_6(A, B, C, D), k9_cat_6(A, B, C, E)) & k9_cat_6(A, B, C, k2_cat_6(A, D, E))=k2_cat_6(B, k9_cat_6(A, B, C, D), k9_cat_6(A, B, C, E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d23_cat_8, axiom,  (! [A] :  ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  =>  (! [B] :  ( (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) )  =>  (! [C] :  (m1_subset_1(C, k1_cat_6(A)) =>  (! [D] :  (m1_subset_1(D, k1_cat_6(B)) =>  (! [E] :  (m1_subset_1(E, k1_cat_6(k8_cat_8(A, B))) =>  ( ~ ( ( ~ (v2_struct_0(A))  &  ( ~ (v2_struct_0(B))  &  ~ ( (E=k12_cat_8(A, B, C, D) <=>  (k9_cat_6(k8_cat_8(A, B), A, k9_cat_8(A, B), E)=C & k9_cat_6(k8_cat_8(A, B), B, k10_cat_8(A, B), E)=D) ) ) ) ) )  &  ( ~ ( ( ~ (v2_struct_0(A))  &  ~ (v2_struct_0(B)) ) )  =>  (E=k12_cat_8(A, B, C, D) <=> E=o_2_1_cat_8(A, B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d24_cat_8, axiom,  (! [A] :  ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  =>  (! [B] :  ( (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) )  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) )  =>  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) )  =>  (r3_cat_8(A, B, C, D, E) <=>  (! [F] :  (m1_subset_1(F, k1_cat_6(A)) =>  (! [G] :  (m1_subset_1(G, k1_cat_6(A)) =>  (r1_cat_6(A, F, G) =>  (r1_cat_6(B, k9_cat_6(A, B, E, F), k9_cat_6(A, B, C, G)) &  (r1_cat_6(B, k9_cat_6(A, B, D, F), k9_cat_6(A, B, E, G)) &  (k9_cat_6(A, B, E, k2_cat_6(A, F, G))=k2_cat_6(B, k9_cat_6(A, B, E, F), k9_cat_6(A, B, C, G)) & k9_cat_6(A, B, E, k2_cat_6(A, F, G))=k2_cat_6(B, k9_cat_6(A, B, D, F), k9_cat_6(A, B, E, G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d25_cat_6, axiom,  (! [A] :  ( (v10_cat_6(A) & l1_cat_6(A))  =>  (! [B] :  ( (v10_cat_6(B) & l1_cat_6(B))  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) )  =>  (v16_cat_6(C, A, B) <=>  (v13_cat_6(C, A, B) & v14_cat_6(C, A, B)) ) ) ) ) ) ) ) ).
fof(d25_cat_8, axiom,  (! [A] :  ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  =>  (! [B] :  ( (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) )  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) )  =>  (r4_cat_8(A, B, C, D) <=>  (? [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) )  & r3_cat_8(A, B, C, D, E)) ) ) ) ) ) ) ) ) ) ) ).
fof(d26_cat_8, axiom,  (! [A] :  ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  =>  (! [B] :  ( (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) )  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) )  =>  (r4_cat_8(A, B, C, D) =>  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) )  =>  (m3_cat_8(E, A, B, C, D) <=> r3_cat_8(A, B, C, D, E)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d27_cat_8, axiom,  (! [A] :  ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  =>  (! [B] :  ( (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) )  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) )  =>  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) )  =>  ( (r4_cat_8(A, B, D, C) &  (r4_cat_8(A, B, C, E) &  (v16_cat_6(C, A, B) &  (v16_cat_6(D, A, B) & v16_cat_6(E, A, B)) ) ) )  =>  (! [F] :  (m3_cat_8(F, A, B, D, C) =>  (! [G] :  (m3_cat_8(G, A, B, C, E) =>  (! [H] :  (m3_cat_8(H, A, B, D, E) =>  (H=k13_cat_8(A, B, C, D, E, F, G) <=>  (! [I] :  (m1_subset_1(I, k1_cat_6(A)) =>  (! [J] :  (m1_subset_1(J, k1_cat_6(A)) =>  (! [K] :  (m1_subset_1(K, k1_cat_6(A)) =>  ( (v11_cat_6(J, A) &  (v11_cat_6(K, A) &  (r1_cat_6(A, I, J) & r1_cat_6(A, K, I)) ) )  => k9_cat_6(A, B, H, I)=k2_cat_6(B, k2_cat_6(B, k9_cat_6(A, B, G, K), k9_cat_6(A, B, C, I)), k9_cat_6(A, B, F, J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d28_cat_8, axiom,  (! [A] :  ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  =>  (! [B] :  ( (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) )  =>  (! [C] :  ( (v1_cat_6(C) &  (v8_cat_6(C) &  (v9_cat_6(C) &  (v10_cat_6(C) & l1_cat_6(C)) ) ) )  =>  (C=k14_cat_8(A, B) <=>  (u1_struct_0(C)=a_2_2_cat_8(A, B) & u1_cat_6(C)=a_3_1_cat_8(A, B, C)) ) ) ) ) ) ) ) ).
fof(d2_cat_6, axiom,  (! [A] :  (l1_cat_6(A) =>  (! [B] :  (m1_subset_1(B, k1_cat_6(A)) =>  (! [C] :  (m1_subset_1(C, k1_cat_6(A)) =>  (r1_cat_6(A, B, C) <=> r2_hidden(k4_tarski(B, C), k1_relset_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_cat_6(A)))) ) ) ) ) ) ) ).
fof(d2_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (! [C] :  ( (r2_hidden(B, k9_xtuple_0(A)) =>  (C=k1_funct_1(A, B) <=> r2_hidden(k4_tarski(B, C), A)) )  &  ( ~ (r2_hidden(B, k9_xtuple_0(A)))  =>  (C=k1_funct_1(A, B) <=> C=k1_xboole_0) ) ) ) ) ) ) ).
fof(d3_cat_6, axiom,  (! [A] :  (l1_cat_6(A) =>  (! [B] :  (m1_subset_1(B, k1_cat_6(A)) =>  (! [C] :  (m1_subset_1(C, k1_cat_6(A)) =>  (r1_cat_6(A, B, C) => k2_cat_6(A, B, C)=k1_binop_1(u1_cat_6(A), B, C)) ) ) ) ) ) ) ).
fof(d4_struct_0, axiom,  (! [A] :  (l1_struct_0(A) => k3_struct_0(A)=k6_partfun1(u1_struct_0(A))) ) ).
fof(dt_g1_cat_6, axiom,  (! [A, B] :  ( (v1_funct_1(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A))))  =>  (v1_cat_6(g1_cat_6(A, B)) & l1_cat_6(g1_cat_6(A, B))) ) ) ).
fof(dt_k10_cat_6, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(A))  &  (v10_cat_6(A) & l1_cat_6(A)) )  &  ( ( ~ (v2_struct_0(B))  &  (v10_cat_6(B) & l1_cat_6(B)) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) &  (v16_cat_6(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) ) )  & m1_subset_1(D, k5_cat_6(A))) ) )  => m1_subset_1(k10_cat_6(A, B, C, D), k5_cat_6(B))) ) ).
fof(dt_k10_cat_8, axiom,  (! [A, B] :  ( ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  &  (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) ) )  =>  (v1_funct_1(k10_cat_8(A, B)) &  (v1_funct_2(k10_cat_8(A, B), u1_struct_0(k8_cat_8(A, B)), u1_struct_0(B)) & m1_subset_1(k10_cat_8(A, B), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k8_cat_8(A, B)), u1_struct_0(B))))) ) ) ) ).
fof(dt_k11_cat_6, axiom,  (! [A, B, C, D, E] :  ( ( (v10_cat_6(A) & l1_cat_6(A))  &  ( (v10_cat_6(B) & l1_cat_6(B))  &  ( (v10_cat_6(C) & l1_cat_6(C))  &  ( (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) )  &  (v1_funct_1(E) &  (v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C))))) ) ) ) ) )  =>  (v1_funct_1(k11_cat_6(A, B, C, D, E)) &  (v1_funct_2(k11_cat_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)) & m1_subset_1(k11_cat_6(A, B, C, D, E), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(C))))) ) ) ) ).
fof(dt_k11_cat_8, axiom,  (! [A, B, C, D, E, F] :  ( ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  &  ( (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) )  &  ( (v8_cat_6(C) &  (v9_cat_6(C) &  (v10_cat_6(C) & l1_cat_6(C)) ) )  &  ( (v8_cat_6(D) &  (v9_cat_6(D) &  (v10_cat_6(D) & l1_cat_6(D)) ) )  &  ( (v1_funct_1(E) &  (v1_funct_2(E, u1_struct_0(A), u1_struct_0(C)) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(C))))) )  &  (v1_funct_1(F) &  (v1_funct_2(F, u1_struct_0(B), u1_struct_0(D)) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(D))))) ) ) ) ) ) )  =>  (v1_funct_1(k11_cat_8(A, B, C, D, E, F)) &  (v1_funct_2(k11_cat_8(A, B, C, D, E, F), u1_struct_0(k8_cat_8(A, B)), u1_struct_0(k8_cat_8(C, D))) & m1_subset_1(k11_cat_8(A, B, C, D, E, F), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k8_cat_8(A, B)), u1_struct_0(k8_cat_8(C, D)))))) ) ) ) ).
fof(dt_k12_cat_6, axiom,  (! [A] :  ( (v10_cat_6(A) & l1_cat_6(A))  =>  (v1_funct_1(k12_cat_6(A)) &  (v1_funct_2(k12_cat_6(A), u1_struct_0(A), u1_struct_0(A)) & m1_subset_1(k12_cat_6(A), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A))))) ) ) ) ).
fof(dt_k12_cat_8, axiom,  (! [A, B, C, D] :  ( ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  &  ( (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) )  &  (m1_subset_1(C, k1_cat_6(A)) & m1_subset_1(D, k1_cat_6(B))) ) )  => m1_subset_1(k12_cat_8(A, B, C, D), k1_cat_6(k8_cat_8(A, B)))) ) ).
fof(dt_k13_cat_8, axiom,  (! [A, B, C, D, E, F, G] :  ( ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  &  ( (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) )  &  ( (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) )  &  ( (v1_funct_1(E) &  (v1_funct_2(E, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) )  &  (m3_cat_8(F, A, B, D, C) & m3_cat_8(G, A, B, C, E)) ) ) ) ) )  => m3_cat_8(k13_cat_8(A, B, C, D, E, F, G), A, B, D, E)) ) ).
fof(dt_k14_cat_8, axiom,  (! [A, B] :  ( ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  &  (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) ) )  =>  (v1_cat_6(k14_cat_8(A, B)) &  (v8_cat_6(k14_cat_8(A, B)) &  (v9_cat_6(k14_cat_8(A, B)) &  (v10_cat_6(k14_cat_8(A, B)) & l1_cat_6(k14_cat_8(A, B))) ) ) ) ) ) ).
fof(dt_k1_binop_1, axiom, $true).
fof(dt_k1_cat_6, axiom, $true).
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_zfmisc_1, axiom, $true).
fof(dt_k2_cat_6, axiom,  (! [A, B, C] :  ( (l1_cat_6(A) &  (m1_subset_1(B, k1_cat_6(A)) & m1_subset_1(C, k1_cat_6(A))) )  => m1_subset_1(k2_cat_6(A, B, C), k1_cat_6(A))) ) ).
fof(dt_k2_xtuple_0, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v1_funct_1(k3_struct_0(A)) &  (v1_funct_2(k3_struct_0(A), u1_struct_0(A), u1_struct_0(A)) & m1_subset_1(k3_struct_0(A), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A))))) ) ) ) ).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k4_relat_1, axiom,  (! [A] : v1_relat_1(k4_relat_1(A))) ).
fof(dt_k4_tarski, 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_k5_xtuple_0, axiom, $true).
fof(dt_k6_cat_6, axiom,  (! [A, B] :  ( ( (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) )  & m1_subset_1(B, k1_cat_6(A)))  => m1_subset_1(k6_cat_6(A, B), k5_cat_6(A))) ) ).
fof(dt_k6_partfun1, axiom,  (! [A] :  (v1_partfun1(k6_partfun1(A), A) & m1_subset_1(k6_partfun1(A), k1_zfmisc_1(k2_zfmisc_1(A, A)))) ) ).
fof(dt_k7_cat_6, axiom,  (! [A, B] :  ( ( (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) )  & m1_subset_1(B, k1_cat_6(A)))  => m1_subset_1(k7_cat_6(A, B), k5_cat_6(A))) ) ).
fof(dt_k8_cat_8, axiom,  (! [A, B] :  ( ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  &  (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) ) )  =>  (v1_cat_6(k8_cat_8(A, B)) &  (v8_cat_6(k8_cat_8(A, B)) &  (v9_cat_6(k8_cat_8(A, B)) &  (v10_cat_6(k8_cat_8(A, B)) & l1_cat_6(k8_cat_8(A, B))) ) ) ) ) ) ).
fof(dt_k9_cat_6, axiom,  (! [A, B, C, D] :  ( ( (v10_cat_6(A) & l1_cat_6(A))  &  ( (v10_cat_6(B) & l1_cat_6(B))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) )  & m1_subset_1(D, k1_cat_6(A))) ) )  => m1_subset_1(k9_cat_6(A, B, C, D), k1_cat_6(B))) ) ).
fof(dt_k9_cat_8, axiom,  (! [A, B] :  ( ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  &  (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) ) )  =>  (v1_funct_1(k9_cat_8(A, B)) &  (v1_funct_2(k9_cat_8(A, B), u1_struct_0(k8_cat_8(A, B)), u1_struct_0(A)) & m1_subset_1(k9_cat_8(A, B), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k8_cat_8(A, B)), u1_struct_0(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_subset_1, axiom, $true).
fof(dt_m2_cat_8, axiom,  (! [A, B] :  ( ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  &  (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) ) )  =>  (! [C] :  (m2_cat_8(C, A, B) => v2_xtuple_0(C)) ) ) ) ).
fof(dt_m3_cat_8, axiom,  (! [A, B, C, D] :  ( ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  &  ( (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) ) ) ) )  =>  (! [E] :  (m3_cat_8(E, A, B, C, D) =>  (v1_funct_1(E) &  (v1_funct_2(E, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) ) ) ) ) ) ).
fof(dt_o_1_2_cat_6, axiom,  (! [A] :  ( (v10_cat_6(A) & l1_cat_6(A))  => m1_subset_1(o_1_2_cat_6(A), k5_cat_6(A))) ) ).
fof(dt_o_2_0_cat_8, axiom,  (! [A, B] :  ( ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  &  (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) ) )  => m2_cat_8(o_2_0_cat_8(A, B), A, B)) ) ).
fof(dt_o_2_13_cat_8, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) ) )  &  (v2_struct_0(B) &  (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) ) ) )  =>  (v1_funct_1(o_2_13_cat_8(A, B)) &  (v1_funct_2(o_2_13_cat_8(A, B), u1_struct_0(B), u1_struct_0(A)) &  (v16_cat_6(o_2_13_cat_8(A, B), B, A) & m1_subset_1(o_2_13_cat_8(A, B), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(A))))) ) ) ) ) ).
fof(dt_o_2_1_cat_8, axiom,  (! [A, B] :  ( ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  &  (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) ) )  => m1_subset_1(o_2_1_cat_8(A, B), k1_cat_6(k8_cat_8(A, B)))) ) ).
fof(dt_u1_cat_6, axiom,  (! [A] :  (l1_cat_6(A) =>  (v1_funct_1(u1_cat_6(A)) & m1_subset_1(u1_cat_6(A), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))) ) ) ).
fof(dt_u1_struct_0, axiom, $true).
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_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(existence_m2_cat_8, axiom,  (! [A, B] :  ( ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  &  (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) ) )  =>  (? [C] : m2_cat_8(C, A, B)) ) ) ).
fof(existence_m3_cat_8, axiom,  (! [A, B, C, D] :  ( ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  &  ( (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) ) ) ) )  =>  (? [E] : m3_cat_8(E, A, B, C, D)) ) ) ).
fof(fc10_cat_8, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) ) )  &  ( ~ (v2_struct_0(B))  &  (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) ) ) )  =>  ( ~ (v2_struct_0(k14_cat_8(A, B)))  &  (v1_cat_6(k14_cat_8(A, B)) &  (v8_cat_6(k14_cat_8(A, B)) &  (v9_cat_6(k14_cat_8(A, B)) & v10_cat_6(k14_cat_8(A, B))) ) ) ) ) ) ).
fof(fc11_funct_2, axiom,  (! [A] :  (v1_relat_1(k4_relat_1(A)) &  (v4_relat_1(k4_relat_1(A), A) &  (v1_funct_1(k4_relat_1(A)) & v1_partfun1(k4_relat_1(A), A)) ) ) ) ).
fof(fc12_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ~ (v1_finset_1(k1_zfmisc_1(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(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(fc19_struct_0, axiom,  (! [A, B] :  ( (v1_card_1(A) &  (v13_struct_0(B, A) & l1_struct_0(B)) )  => v3_card_1(u1_struct_0(B), 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_struct_0, axiom,  (! [A] :  ( (v2_struct_0(A) & l1_struct_0(A))  => v1_xboole_0(u1_struct_0(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(fc2_cat_6, axiom,  (! [A] :  ( (v10_cat_6(A) & l1_cat_6(A))  =>  (v1_funct_1(k3_struct_0(A)) &  (v1_funct_2(k3_struct_0(A), u1_struct_0(A), u1_struct_0(A)) & v16_cat_6(k3_struct_0(A), A, A)) ) ) ) ).
fof(fc2_cat_7, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_cat_6(A))  =>  ~ (v1_xboole_0(k1_cat_6(A))) ) ) ).
fof(fc2_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_xboole_0(u1_struct_0(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(fc3_cat_8, axiom,  (! [A, B] :  ( ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  &  (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) ) )  =>  (v1_funct_1(k9_cat_8(A, B)) &  (v1_funct_2(k9_cat_8(A, B), u1_struct_0(k8_cat_8(A, B)), u1_struct_0(A)) & v16_cat_6(k9_cat_8(A, B), k8_cat_8(A, B), A)) ) ) ) ).
fof(fc3_funct_1, axiom,  (! [A] :  (v1_relat_1(k4_relat_1(A)) & v1_funct_1(k4_relat_1(A))) ) ).
fof(fc3_partfun1, axiom,  (! [A] :  (v1_relat_1(k4_relat_1(A)) &  (v3_relat_2(k4_relat_1(A)) &  (v4_relat_2(k4_relat_1(A)) & v8_relat_2(k4_relat_1(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_cat_8, axiom,  (! [A, B] :  ( ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  &  (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) ) )  =>  (v1_funct_1(k10_cat_8(A, B)) &  (v1_funct_2(k10_cat_8(A, B), u1_struct_0(k8_cat_8(A, B)), u1_struct_0(B)) & v16_cat_6(k10_cat_8(A, B), k8_cat_8(A, B), B)) ) ) ) ).
fof(fc4_funct_1, axiom,  (! [A] :  (v1_relat_1(k4_relat_1(A)) & v2_funct_1(k4_relat_1(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_8, axiom,  (! [A, B] :  ( ( (v2_struct_0(A) &  (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) ) )  &  (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) ) )  =>  (v2_struct_0(k8_cat_8(A, B)) &  (v1_cat_6(k8_cat_8(A, B)) &  (v8_cat_6(k8_cat_8(A, B)) &  (v9_cat_6(k8_cat_8(A, B)) & v10_cat_6(k8_cat_8(A, B))) ) ) ) ) ) ).
fof(fc6_card_1, axiom, v1_card_1(k4_ordinal1)).
fof(fc6_cat_8, axiom,  (! [A, B] :  ( ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  &  (v2_struct_0(B) &  (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) ) ) )  =>  (v2_struct_0(k8_cat_8(A, B)) &  (v1_cat_6(k8_cat_8(A, B)) &  (v8_cat_6(k8_cat_8(A, B)) &  (v9_cat_6(k8_cat_8(A, B)) & v10_cat_6(k8_cat_8(A, B))) ) ) ) ) ) ).
fof(fc6_ordinal1, axiom,  ( ~ (v1_xboole_0(k4_ordinal1))  & v3_ordinal1(k4_ordinal1)) ).
fof(fc6_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(fc7_card_1, axiom, v2_card_1(k4_ordinal1)).
fof(fc7_cat_8, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) ) )  &  ( ~ (v2_struct_0(B))  &  (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) ) ) )  =>  ( ~ (v2_struct_0(k8_cat_8(A, B)))  &  (v1_cat_6(k8_cat_8(A, B)) &  (v8_cat_6(k8_cat_8(A, B)) &  (v9_cat_6(k8_cat_8(A, B)) & v10_cat_6(k8_cat_8(A, B))) ) ) ) ) ) ).
fof(fc7_relset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  ( ~ (v1_xboole_0(k4_relat_1(A)))  & v1_relat_1(k4_relat_1(A))) ) ) ).
fof(fc7_struct_0, axiom,  (! [A] :  ( (v7_struct_0(A) & l1_struct_0(A))  => v1_zfmisc_1(u1_struct_0(A))) ) ).
fof(fc8_cat_8, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) ) )  &  (v2_struct_0(B) &  (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) ) ) )  =>  (v2_struct_0(k14_cat_8(A, B)) &  (v1_cat_6(k14_cat_8(A, B)) &  (v8_cat_6(k14_cat_8(A, B)) &  (v9_cat_6(k14_cat_8(A, B)) & v10_cat_6(k14_cat_8(A, B))) ) ) ) ) ) ).
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(fc8_struct_0, axiom,  (! [A] :  ( (v8_struct_0(A) & l1_struct_0(A))  => v1_finset_1(u1_struct_0(A))) ) ).
fof(fc9_card_1, axiom,  ~ (v1_finset_1(k4_ordinal1)) ).
fof(fc9_cat_8, axiom,  (! [A, B] :  ( ( (v2_struct_0(A) &  (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) ) )  &  (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) ) )  =>  ( ~ (v2_struct_0(k14_cat_8(A, B)))  &  (v7_struct_0(k14_cat_8(A, B)) &  (v1_cat_6(k14_cat_8(A, B)) &  (v8_cat_6(k14_cat_8(A, B)) &  (v9_cat_6(k14_cat_8(A, B)) & v10_cat_6(k14_cat_8(A, B))) ) ) ) ) ) ) ).
fof(fc9_ordinal1, axiom, v8_ordinal1(k5_ordinal1)).
fof(fc9_struct_0, axiom,  (! [A] :  ( ( ~ (v8_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_finset_1(u1_struct_0(A))) ) ) ).
fof(fraenkel_a_2_11_cat_8, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(B))  &  (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) ) )  &  ( ~ (v2_struct_0(C))  &  (v8_cat_6(C) &  (v9_cat_6(C) &  (v10_cat_6(C) & l1_cat_6(C)) ) ) ) )  =>  (r2_hidden(A, a_2_11_cat_8(B, C)) <=>  (? [D, E, F] :  ( ( (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(B), u1_struct_0(C)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C))))) )  &  ( (v1_funct_1(E) &  (v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C))))) )  & m3_cat_8(F, B, C, D, E)) )  &  (A=k4_tarski(k4_tarski(D, E), F) &  (v16_cat_6(D, B, C) &  (v16_cat_6(E, B, C) & r4_cat_8(B, C, D, E)) ) ) ) ) ) ) ) ).
fof(fraenkel_a_2_2_cat_8, axiom,  (! [A, B, C] :  ( ( (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) )  &  (v8_cat_6(C) &  (v9_cat_6(C) &  (v10_cat_6(C) & l1_cat_6(C)) ) ) )  =>  (r2_hidden(A, a_2_2_cat_8(B, C)) <=>  (? [D, E, F] :  ( ( (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(B), u1_struct_0(C)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C))))) )  &  ( (v1_funct_1(E) &  (v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C))))) )  & m3_cat_8(F, B, C, D, E)) )  &  (A=k4_tarski(k4_tarski(D, E), F) &  (v16_cat_6(D, B, C) &  (v16_cat_6(E, B, C) & r4_cat_8(B, C, D, E)) ) ) ) ) ) ) ) ).
fof(fraenkel_a_3_1_cat_8, axiom,  (! [A, B, C, D] :  ( ( (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) )  &  ( (v8_cat_6(C) &  (v9_cat_6(C) &  (v10_cat_6(C) & l1_cat_6(C)) ) )  &  (v1_cat_6(D) &  (v8_cat_6(D) &  (v9_cat_6(D) &  (v10_cat_6(D) & l1_cat_6(D)) ) ) ) ) )  =>  (r2_hidden(A, a_3_1_cat_8(B, C, D)) <=>  (? [E, F, G] :  ( (m1_subset_1(E, u1_struct_0(D)) &  (m1_subset_1(F, u1_struct_0(D)) & m1_subset_1(G, u1_struct_0(D))) )  &  (A=k4_tarski(k4_tarski(F, E), G) &  (? [H] :  ( (v1_funct_1(H) &  (v1_funct_2(H, u1_struct_0(B), u1_struct_0(C)) & m1_subset_1(H, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C))))) )  &  (? [I] :  ( (v1_funct_1(I) &  (v1_funct_2(I, u1_struct_0(B), u1_struct_0(C)) & m1_subset_1(I, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C))))) )  &  (? [J] :  ( (v1_funct_1(J) &  (v1_funct_2(J, u1_struct_0(B), u1_struct_0(C)) & m1_subset_1(J, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C))))) )  &  (? [K] :  (m3_cat_8(K, B, C, H, I) &  (? [L] :  (m3_cat_8(L, B, C, I, J) &  (E=k4_tarski(k4_tarski(H, I), K) &  (F=k4_tarski(k4_tarski(I, J), L) & G=k4_tarski(k4_tarski(H, J), k13_cat_8(B, C, I, H, J, K, L))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(fraenkel_a_3_9_cat_8, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(B))  &  (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) ) )  &  ( ( ~ (v2_struct_0(C))  &  (v8_cat_6(C) &  (v9_cat_6(C) &  (v10_cat_6(C) & l1_cat_6(C)) ) ) )  &  ( ~ (v2_struct_0(D))  &  (v8_cat_6(D) &  (v9_cat_6(D) &  (v10_cat_6(D) & l1_cat_6(D)) ) ) ) ) )  =>  (r2_hidden(A, a_3_9_cat_8(B, C, D)) <=>  (? [E, F, G] :  ( (m1_subset_1(E, u1_struct_0(B)) &  (m1_subset_1(F, u1_struct_0(B)) & m1_subset_1(G, u1_struct_0(B))) )  &  (A=k4_tarski(k4_tarski(F, E), G) &  (? [H] :  ( (v1_funct_1(H) &  (v1_funct_2(H, u1_struct_0(C), u1_struct_0(D)) & m1_subset_1(H, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C), u1_struct_0(D))))) )  &  (? [I] :  ( (v1_funct_1(I) &  (v1_funct_2(I, u1_struct_0(C), u1_struct_0(D)) & m1_subset_1(I, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C), u1_struct_0(D))))) )  &  (? [J] :  ( (v1_funct_1(J) &  (v1_funct_2(J, u1_struct_0(C), u1_struct_0(D)) & m1_subset_1(J, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C), u1_struct_0(D))))) )  &  (? [K] :  (m3_cat_8(K, C, D, H, I) &  (? [L] :  (m3_cat_8(L, C, D, I, J) &  (E=k4_tarski(k4_tarski(H, I), K) &  (F=k4_tarski(k4_tarski(I, J), L) & G=k4_tarski(k4_tarski(H, J), k13_cat_8(C, D, I, H, J, K, L))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(free_g1_cat_6, axiom,  (! [A, B] :  ( (v1_funct_1(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A))))  =>  (! [C, D] :  (g1_cat_6(A, B)=g1_cat_6(C, D) =>  (A=C & B=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_cat_6, axiom,  (? [A] :  (l1_cat_6(A) &  (v1_cat_6(A) &  (v8_cat_6(A) &  (v9_cat_6(A) & v10_cat_6(A)) ) ) ) ) ).
fof(rc11_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) ) ) ).
fof(rc12_cat_6, axiom,  (? [A] :  (l1_cat_6(A) &  (v2_struct_0(A) &  (v1_cat_6(A) &  (v8_cat_6(A) &  (v9_cat_6(A) & v10_cat_6(A)) ) ) ) ) ) ).
fof(rc12_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) & v9_ordinal1(A)) ) ).
fof(rc13_cat_6, axiom,  (? [A] :  (l1_cat_6(A) &  ( ~ (v2_struct_0(A))  &  (v1_cat_6(A) &  (v8_cat_6(A) &  (v9_cat_6(A) & v10_cat_6(A)) ) ) ) ) ) ).
fof(rc13_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) &  ~ (v9_ordinal1(A)) ) ) ).
fof(rc14_cat_6, axiom,  (! [A, B] :  ( ( (v10_cat_6(A) & l1_cat_6(A))  &  (v10_cat_6(B) & l1_cat_6(B)) )  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B)))) &  (v1_relat_1(C) &  (v4_relat_1(C, u1_struct_0(A)) &  (v5_relat_1(C, u1_struct_0(B)) &  (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v13_cat_6(C, A, B)) ) ) ) ) ) ) ) ) ).
fof(rc1_card_1, axiom,  (? [A] : v1_card_1(A)) ).
fof(rc1_cat_6, axiom,  (? [A] :  (l1_cat_6(A) & v1_cat_6(A)) ) ).
fof(rc1_cat_7, axiom,  (? [A] :  (l1_cat_6(A) &  (v1_cat_6(A) & v6_cat_7(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(rc21_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc22_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
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_cat_8, axiom,  (? [A] :  (l1_cat_6(A) &  ( ~ (v2_struct_0(A))  &  (v1_cat_6(A) &  (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & v3_cat_8(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_partfun1, 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_relat_2(B) &  (v3_relat_2(B) &  (v4_relat_2(B) &  (v8_relat_2(B) & v1_partfun1(B, 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_cat_8, axiom,  (? [A] :  (l1_cat_6(A) &  (v1_cat_6(A) &  (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) &  ~ (v3_cat_8(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(rc4_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ~ (v1_xboole_0(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_cat_8, axiom,  (? [A] :  (l1_cat_6(A) &  (v2_struct_0(A) &  (v1_cat_6(A) &  (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & v6_cat_8(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_cat_8, axiom,  (? [A] :  (l1_cat_6(A) &  (v1_cat_6(A) &  (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) &  ~ (v6_cat_8(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_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_6, axiom,  (? [A] :  (l1_cat_6(A) &  (v1_cat_6(A) &  (v4_cat_6(A) &  (v5_cat_6(A) &  (v6_cat_6(A) &  (v7_cat_6(A) & v8_cat_6(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_cat_6, axiom,  (? [A] :  (l1_cat_6(A) &  (v1_cat_6(A) &  (v8_cat_6(A) &  (v9_cat_6(A) & v10_cat_6(A)) ) ) ) ) ).
fof(rc9_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rd1_funct_1, axiom,  (! [A, B] :  (m1_subset_1(B, A) => k1_funct_1(k4_relat_1(A), B)=B) ) ).
fof(rd2_xtuple_0, axiom,  (! [A, B] : k2_xtuple_0(k4_tarski(A, B))=B) ).
fof(redefinition_k10_cat_6, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(A))  &  (v10_cat_6(A) & l1_cat_6(A)) )  &  ( ( ~ (v2_struct_0(B))  &  (v10_cat_6(B) & l1_cat_6(B)) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) &  (v16_cat_6(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) ) )  & m1_subset_1(D, k5_cat_6(A))) ) )  => k10_cat_6(A, B, C, D)=k1_funct_1(C, D)) ) ).
fof(redefinition_k12_cat_6, axiom,  (! [A] :  ( (v10_cat_6(A) & l1_cat_6(A))  => k12_cat_6(A)=k3_struct_0(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_k6_partfun1, axiom,  (! [A] : k6_partfun1(A)=k4_relat_1(A)) ).
fof(redefinition_r2_relset_1, axiom,  (! [A, B, C, D] :  ( (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))  =>  (r2_relset_1(A, B, C, D) <=> C=D) ) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(reflexivity_r2_relset_1, axiom,  (! [A, B, C, D] :  ( (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))  => r2_relset_1(A, B, C, C)) ) ).
fof(s1_funct_2__e2_128_5_2_1__cat_8, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (v2_struct_0(A))  &  (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) ) )  &  ( (v8_cat_6(C) &  (v9_cat_6(C) &  (v10_cat_6(C) & l1_cat_6(C)) ) )  &  ( (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(k8_cat_8(C, A)), u1_struct_0(B)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k8_cat_8(C, A)), u1_struct_0(B))))) )  & m1_subset_1(E, k1_cat_6(C))) ) ) )  =>  ( (! [F] :  ~ ( (r2_hidden(F, u1_struct_0(A)) &  (! [G] :  ~ ( (r2_hidden(G, u1_struct_0(B)) &  (? [H] :  (m1_subset_1(H, k1_cat_6(A)) &  (F=H & G=k9_cat_6(k8_cat_8(C, A), B, D, k12_cat_8(C, A, E, H))) ) ) ) ) ) ) ) )  =>  (? [F] :  ( (v1_funct_1(F) &  (v1_funct_2(F, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) )  &  (! [G] :  (r2_hidden(G, u1_struct_0(A)) =>  (? [I] :  (m1_subset_1(I, k1_cat_6(A)) &  (G=I & k1_funct_1(F, G)=k9_cat_6(k8_cat_8(C, A), B, D, k12_cat_8(C, A, E, I))) ) ) ) ) ) ) ) ) ) ).
fof(s1_funct_2__e3_128__cat_8, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) ) )  &  ( ~ (v2_struct_0(C))  &  (v8_cat_6(C) &  (v9_cat_6(C) &  (v10_cat_6(C) & l1_cat_6(C)) ) ) ) ) )  =>  ( (! [D] :  ~ ( (r2_hidden(D, u1_struct_0(k8_cat_8(A, B))) &  (! [E] :  ~ ( (r2_hidden(E, u1_struct_0(C)) &  (? [F] :  (m1_subset_1(F, k1_cat_6(A)) &  (? [G] :  (m1_subset_1(G, k1_cat_6(B)) &  (? [H] :  (m1_subset_1(H, k1_cat_6(k8_cat_8(A, B))) &  (? [I] :  (m1_subset_1(I, k1_cat_6(C)) &  (? [J] :  ( (v1_funct_1(J) &  (v1_funct_2(J, u1_struct_0(B), u1_struct_0(C)) & m1_subset_1(J, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C))))) )  &  (H=k12_cat_8(A, B, F, G) &  (D=H &  (E=I &  (I=k9_cat_6(B, C, J, G) & J=k2_xtuple_0(F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (? [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(k8_cat_8(A, B)), u1_struct_0(C)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k8_cat_8(A, B)), u1_struct_0(C))))) )  &  (! [E] :  (r2_hidden(E, u1_struct_0(k8_cat_8(A, B))) =>  (? [K] :  (m1_subset_1(K, k1_cat_6(A)) &  (? [L] :  (m1_subset_1(L, k1_cat_6(B)) &  (? [M] :  (m1_subset_1(M, k1_cat_6(k8_cat_8(A, B))) &  (? [N] :  (m1_subset_1(N, k1_cat_6(C)) &  (? [O] :  ( (v1_funct_1(O) &  (v1_funct_2(O, u1_struct_0(B), u1_struct_0(C)) & m1_subset_1(O, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C))))) )  &  (M=k12_cat_8(A, B, K, L) &  (E=M &  (k1_funct_1(D, E)=N &  (N=k9_cat_6(B, C, O, L) & O=k2_xtuple_0(K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(s1_funct_2__e4_128_5_2__cat_8, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (v2_struct_0(A))  &  (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) ) )  &  ( ( ~ (v2_struct_0(C))  &  (v8_cat_6(C) &  (v9_cat_6(C) &  (v10_cat_6(C) & l1_cat_6(C)) ) ) )  &  ( (v8_cat_6(D) &  (v9_cat_6(D) &  (v10_cat_6(D) & l1_cat_6(D)) ) )  &  (v1_funct_1(E) &  (v1_funct_2(E, u1_struct_0(k8_cat_8(D, B)), u1_struct_0(C)) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k8_cat_8(D, B)), u1_struct_0(C))))) ) ) ) ) )  =>  ( (! [F] :  ~ ( (r2_hidden(F, u1_struct_0(D)) &  (! [G] :  ~ ( (r2_hidden(G, u1_struct_0(A)) &  (? [H] :  (m1_subset_1(H, k1_cat_6(D)) &  (? [I] :  (m1_subset_1(I, k1_cat_6(D)) &  (? [J] :  (m1_subset_1(J, k1_cat_6(D)) &  (? [K] :  ( (v1_funct_1(K) &  (v1_funct_2(K, u1_struct_0(B), u1_struct_0(C)) & m1_subset_1(K, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C))))) )  &  (? [L] :  ( (v1_funct_1(L) &  (v1_funct_2(L, u1_struct_0(B), u1_struct_0(C)) & m1_subset_1(L, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C))))) )  &  (? [M] :  (m3_cat_8(M, B, C, K, L) &  (F=H &  (r1_cat_6(D, J, H) &  (r1_cat_6(D, H, I) &  (v11_cat_6(I, D) &  (v11_cat_6(J, D) &  (G=k4_tarski(k4_tarski(K, L), M) &  (v16_cat_6(K, B, C) &  (v16_cat_6(L, B, C) &  (r4_cat_8(B, C, K, L) &  (! [N] :  (m1_subset_1(N, k1_cat_6(B)) =>  (k9_cat_6(B, C, K, N)=k9_cat_6(k8_cat_8(D, B), C, E, k12_cat_8(D, B, I, N)) &  (k9_cat_6(B, C, L, N)=k9_cat_6(k8_cat_8(D, B), C, E, k12_cat_8(D, B, J, N)) & k9_cat_6(B, C, M, N)=k9_cat_6(k8_cat_8(D, B), C, E, k12_cat_8(D, B, H, N))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (? [F] :  ( (v1_funct_1(F) &  (v1_funct_2(F, u1_struct_0(D), u1_struct_0(A)) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(D), u1_struct_0(A))))) )  &  (! [G] :  (r2_hidden(G, u1_struct_0(D)) =>  (? [O] :  (m1_subset_1(O, k1_cat_6(D)) &  (? [P] :  (m1_subset_1(P, k1_cat_6(D)) &  (? [Q] :  (m1_subset_1(Q, k1_cat_6(D)) &  (? [R] :  ( (v1_funct_1(R) &  (v1_funct_2(R, u1_struct_0(B), u1_struct_0(C)) & m1_subset_1(R, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C))))) )  &  (? [S] :  ( (v1_funct_1(S) &  (v1_funct_2(S, u1_struct_0(B), u1_struct_0(C)) & m1_subset_1(S, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C))))) )  &  (? [T] :  (m3_cat_8(T, B, C, R, S) &  (G=O &  (r1_cat_6(D, Q, O) &  (r1_cat_6(D, O, P) &  (v11_cat_6(P, D) &  (v11_cat_6(Q, D) &  (k1_funct_1(F, G)=k4_tarski(k4_tarski(R, S), T) &  (v16_cat_6(R, B, C) &  (v16_cat_6(S, B, C) &  (r4_cat_8(B, C, R, S) &  (! [U] :  (m1_subset_1(U, k1_cat_6(B)) =>  (k9_cat_6(B, C, R, U)=k9_cat_6(k8_cat_8(D, B), C, E, k12_cat_8(D, B, P, U)) &  (k9_cat_6(B, C, S, U)=k9_cat_6(k8_cat_8(D, B), C, E, k12_cat_8(D, B, Q, U)) & k9_cat_6(B, C, T, U)=k9_cat_6(k8_cat_8(D, B), C, E, k12_cat_8(D, B, O, U))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(spc1_numerals, axiom,  (v2_xxreal_0(1) & m1_subset_1(1, k4_ordinal1)) ).
fof(symmetry_r2_relset_1, axiom,  (! [A, B, C, D] :  ( (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))  =>  (r2_relset_1(A, B, C, D) => r2_relset_1(A, B, D, C)) ) ) ).
fof(t12_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)))) )  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  =>  ( (! [E] :  (r2_hidden(E, A) => k1_funct_1(C, E)=k1_funct_1(D, E)) )  => r2_relset_1(A, B, C, D)) ) ) ) ) ) ) ).
fof(t18_funct_1, axiom,  (! [A] :  (! [B] :  (r2_hidden(B, A) => k1_funct_1(k4_relat_1(A), B)=B) ) ) ).
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(t1_xtuple_0, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  (k4_tarski(A, B)=k4_tarski(C, D) =>  (A=C & B=D) ) ) ) ) ) ).
fof(t24_cat_6, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_cat_6(A) & l1_cat_6(A)) )  =>  (! [B] :  (m1_subset_1(B, k1_cat_6(A)) =>  (v11_cat_6(B, A) => r1_cat_6(A, B, B)) ) ) ) ) ).
fof(t26_cat_6, axiom,  (! [A] :  ( (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) )  =>  (! [B] :  (m1_subset_1(B, k1_cat_6(A)) =>  (! [C] :  (m1_subset_1(C, k1_cat_6(A)) =>  ( (r1_cat_6(A, B, C) & v11_cat_6(C, A))  => k6_cat_6(A, B)=C) ) ) ) ) ) ) ).
fof(t27_cat_6, axiom,  (! [A] :  ( (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) )  =>  (! [B] :  (m1_subset_1(B, k1_cat_6(A)) =>  (! [C] :  (m1_subset_1(C, k1_cat_6(A)) =>  ( (r1_cat_6(A, C, B) & v11_cat_6(C, A))  => k7_cat_6(A, B)=C) ) ) ) ) ) ) ).
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(t32_cat_6, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) &  (v16_cat_6(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) ) )  =>  (! [D] :  (m1_subset_1(D, k1_cat_6(A)) =>  (k10_cat_6(A, B, C, k6_cat_6(A, D))=k6_cat_6(B, k9_cat_6(A, B, C, D)) & k10_cat_6(A, B, C, k7_cat_6(A, D))=k7_cat_6(B, k9_cat_6(A, B, C, D))) ) ) ) ) ) ) ) ) ).
fof(t34_cat_6, axiom,  (! [A] :  ( (v10_cat_6(A) & l1_cat_6(A))  =>  (! [B] :  ( (v10_cat_6(B) & l1_cat_6(B))  =>  (! [C] :  ( (v10_cat_6(C) & l1_cat_6(C))  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) )  =>  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C))))) )  =>  (! [F] :  (m1_subset_1(F, k1_cat_6(A)) =>  ( (v16_cat_6(D, A, B) & v16_cat_6(E, B, C))  =>  (v2_struct_0(A) | k9_cat_6(A, C, k11_cat_6(A, B, C, D, E), F)=k9_cat_6(B, C, E, k9_cat_6(A, B, D, F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t4_cat_7, axiom,  (! [A] :  ( (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) )  =>  (! [B] :  (m1_subset_1(B, k1_cat_6(A)) =>  (! [C] :  (m1_subset_1(C, k1_cat_6(A)) =>  (r1_cat_6(A, B, C) =>  (k6_cat_6(A, k2_cat_6(A, B, C))=k6_cat_6(A, C) & k7_cat_6(A, k2_cat_6(A, B, C))=k7_cat_6(A, B)) ) ) ) ) ) ) ) ).
fof(t4_cat_8, axiom,  (! [A] :  ( (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) )  =>  (! [B] :  (m1_subset_1(B, k1_cat_6(A)) =>  (! [C] :  (m1_subset_1(C, k1_cat_6(A)) =>  (r1_cat_6(A, B, C) =>  ( (v11_cat_6(B, A) => k2_cat_6(A, B, C)=C)  &  (v11_cat_6(C, A) => k2_cat_6(A, B, C)=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(t52_cat_8, axiom,  (! [A] :  ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  =>  (! [B] :  ( (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) )  =>  (! [C] :  (m1_subset_1(C, k1_cat_6(k8_cat_8(A, B))) =>  (? [D] :  (m1_subset_1(D, k1_cat_6(A)) &  (? [E] :  (m1_subset_1(E, k1_cat_6(B)) & C=k12_cat_8(A, B, D, E)) ) ) ) ) ) ) ) ) ) ).
fof(t53_cat_8, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) ) )  =>  (! [C] :  (m1_subset_1(C, k1_cat_6(A)) =>  (! [D] :  (m1_subset_1(D, k1_cat_6(A)) =>  (! [E] :  (m1_subset_1(E, k1_cat_6(B)) =>  (! [F] :  (m1_subset_1(F, k1_cat_6(B)) =>  (k12_cat_8(A, B, C, E)=k12_cat_8(A, B, D, F) =>  (C=D & E=F) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t54_cat_8, axiom,  (! [A] :  ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  =>  (! [B] :  ( (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) )  =>  (! [C] :  (m1_subset_1(C, k1_cat_6(A)) =>  (! [D] :  (m1_subset_1(D, k1_cat_6(A)) =>  (! [E] :  (m1_subset_1(E, k1_cat_6(B)) =>  (! [F] :  (m1_subset_1(F, k1_cat_6(B)) =>  (r1_cat_6(k8_cat_8(A, B), k12_cat_8(A, B, C, E), k12_cat_8(A, B, D, F)) <=>  (r1_cat_6(A, C, D) & r1_cat_6(B, E, F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t55_cat_8, axiom,  (! [A] :  ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  =>  (! [B] :  ( (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) )  =>  (! [C] :  (m1_subset_1(C, k1_cat_6(A)) =>  (! [D] :  (m1_subset_1(D, k1_cat_6(A)) =>  (! [E] :  (m1_subset_1(E, k1_cat_6(B)) =>  (! [F] :  (m1_subset_1(F, k1_cat_6(B)) =>  ( (r1_cat_6(A, C, D) & r1_cat_6(B, E, F))  => k2_cat_6(k8_cat_8(A, B), k12_cat_8(A, B, C, E), k12_cat_8(A, B, D, F))=k12_cat_8(A, B, k2_cat_6(A, C, D), k2_cat_6(B, E, F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t56_cat_8, axiom,  (! [A] :  ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  =>  (! [B] :  ( (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) )  =>  (! [C] :  (m1_subset_1(C, k1_cat_6(A)) =>  (! [D] :  (m1_subset_1(D, k1_cat_6(B)) =>  (! [E] :  (m1_subset_1(E, k1_cat_6(k8_cat_8(A, B))) =>  (E=k12_cat_8(A, B, C, D) =>  (v2_struct_0(A) |  (v2_struct_0(B) |  (v11_cat_6(E, k8_cat_8(A, B)) <=>  (v11_cat_6(C, A) & v11_cat_6(D, B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t57_cat_8, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) ) )  =>  (! [C] :  ( (v8_cat_6(C) &  (v9_cat_6(C) &  (v10_cat_6(C) & l1_cat_6(C)) ) )  =>  (! [D] :  ( (v8_cat_6(D) &  (v9_cat_6(D) &  (v10_cat_6(D) & l1_cat_6(D)) ) )  =>  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, u1_struct_0(A), u1_struct_0(C)) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(C))))) )  =>  (! [F] :  ( (v1_funct_1(F) &  (v1_funct_2(F, u1_struct_0(B), u1_struct_0(D)) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(D))))) )  =>  (! [G] :  (m1_subset_1(G, k1_cat_6(A)) =>  (! [H] :  (m1_subset_1(H, k1_cat_6(B)) =>  ( (v16_cat_6(E, A, C) & v16_cat_6(F, B, D))  => k9_cat_6(k8_cat_8(A, B), k8_cat_8(C, D), k11_cat_8(A, B, C, D, E, F), k12_cat_8(A, B, G, H))=k12_cat_8(C, D, k9_cat_6(A, C, E, G), k9_cat_6(B, D, F, H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t58_cat_8, axiom,  (! [A] :  ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  =>  (! [B] :  ( (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) )  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) )  =>  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) )  =>  ( (v16_cat_6(C, A, B) & v16_cat_6(D, A, B))  =>  (r3_cat_8(A, B, C, D, E) <=>  (! [F] :  (m1_subset_1(F, k1_cat_6(A)) =>  (! [G] :  (m1_subset_1(G, k1_cat_6(A)) =>  (! [H] :  (m1_subset_1(H, k1_cat_6(A)) =>  ( (v11_cat_6(G, A) &  (v11_cat_6(H, A) &  (r1_cat_6(A, G, F) & r1_cat_6(A, F, H)) ) )  =>  (r1_cat_6(B, k9_cat_6(A, B, E, G), k9_cat_6(A, B, C, F)) &  (r1_cat_6(B, k9_cat_6(A, B, D, F), k9_cat_6(A, B, E, H)) &  (k9_cat_6(A, B, E, F)=k2_cat_6(B, k9_cat_6(A, B, E, G), k9_cat_6(A, B, C, F)) & k9_cat_6(A, B, E, F)=k2_cat_6(B, k9_cat_6(A, B, D, F), k9_cat_6(A, B, E, H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t5_cat_7, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  =>  (! [B] :  (m1_subset_1(B, k1_cat_6(A)) =>  (! [C] :  (m1_subset_1(C, k1_cat_6(A)) =>  (r1_cat_6(A, B, C) <=> k6_cat_6(A, B)=k7_cat_6(A, C)) ) ) ) ) ) ) ).
fof(t5_cat_8, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_cat_6(A) & l1_cat_6(A)) )  =>  (! [B] :  (m1_subset_1(B, k1_cat_6(A)) =>  (? [C] :  (m1_subset_1(C, k1_cat_6(A)) &  (? [D] :  (m1_subset_1(D, k1_cat_6(A)) &  (v11_cat_6(C, A) &  (v11_cat_6(D, A) &  (r1_cat_6(A, C, B) & r1_cat_6(A, B, D)) ) ) ) ) ) ) ) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t63_cat_8, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) ) )  =>  (! [C] :  (m1_subset_1(C, k1_cat_6(k14_cat_8(A, B))) =>  (! [D] :  (m1_subset_1(D, k1_cat_6(k14_cat_8(A, B))) =>  (r1_cat_6(k14_cat_8(A, B), C, D) <=>  (? [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, u1_struct_0(A), u1_struct_0(B)) &  (v16_cat_6(E, A, B) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) ) )  &  (? [F] :  ( (v1_funct_1(F) &  (v1_funct_2(F, u1_struct_0(A), u1_struct_0(B)) &  (v16_cat_6(F, A, B) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) ) )  &  (? [G] :  ( (v1_funct_1(G) &  (v1_funct_2(G, u1_struct_0(A), u1_struct_0(B)) &  (v16_cat_6(G, A, B) & m1_subset_1(G, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) ) )  &  (? [H] :  (m3_cat_8(H, A, B, F, E) &  (? [I] :  (m3_cat_8(I, A, B, E, G) &  (C=k4_tarski(k4_tarski(E, G), I) &  (D=k4_tarski(k4_tarski(F, E), H) &  (k2_cat_6(k14_cat_8(A, B), C, D)=k4_tarski(k4_tarski(F, G), k13_cat_8(A, B, E, F, G, H, I)) &  (! [J] :  (m1_subset_1(J, k1_cat_6(A)) =>  (! [K] :  (m1_subset_1(K, k1_cat_6(A)) =>  (r1_cat_6(A, K, J) =>  (r1_cat_6(B, k9_cat_6(A, B, I, K), k9_cat_6(A, B, H, J)) & k9_cat_6(A, B, k13_cat_8(A, B, E, F, G, H, I), k2_cat_6(A, K, J))=k2_cat_6(B, k9_cat_6(A, B, I, K), k9_cat_6(A, B, H, J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t64_cat_8, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) ) )  =>  (! [C] :  (m1_subset_1(C, k1_cat_6(k14_cat_8(A, B))) =>  (v11_cat_6(C, k14_cat_8(A, B)) <=>  (? [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) &  (v16_cat_6(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) ) )  & C=k4_tarski(k4_tarski(D, D), D)) ) ) ) ) ) ) ) ) ).
fof(t65_cat_8, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) ) )  =>  (! [C] :  (m1_subset_1(C, k1_cat_6(k14_cat_8(A, B))) =>  (? [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) &  (v16_cat_6(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) ) )  &  (? [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, u1_struct_0(A), u1_struct_0(B)) &  (v16_cat_6(E, A, B) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) ) )  &  (? [F] :  (m3_cat_8(F, A, B, D, E) &  (C=k4_tarski(k4_tarski(D, E), F) &  (k6_cat_6(k14_cat_8(A, B), C)=k4_tarski(k4_tarski(D, D), D) & k7_cat_6(k14_cat_8(A, B), C)=k4_tarski(k4_tarski(E, E), E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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)) ) ) ) ) ).
