% Mizar problem: t60_cat_8,cat_8,3322,7 
fof(t60_cat_8, conjecture,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v2_cat_1(A) &  (v3_cat_1(A) &  (v4_cat_1(A) &  (v5_cat_1(A) &  (v6_cat_1(A) & l1_cat_1(A)) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  &  (v2_cat_1(B) &  (v3_cat_1(B) &  (v4_cat_1(B) &  (v5_cat_1(B) &  (v6_cat_1(B) & l1_cat_1(B)) ) ) ) ) ) )  =>  (! [C] :  (m2_cat_1(C, A, B) =>  (! [D] :  (m2_cat_1(D, A, B) =>  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, u1_struct_0(k18_cat_6(A)), u1_struct_0(k18_cat_6(B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k18_cat_6(A)), u1_struct_0(k18_cat_6(B)))))) )  =>  (! [F] :  ( (v1_funct_1(F) &  (v1_funct_2(F, u1_struct_0(k18_cat_6(A)), u1_struct_0(k18_cat_6(B))) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k18_cat_6(A)), u1_struct_0(k18_cat_6(B)))))) )  =>  (! [G] :  ( (v1_funct_1(G) &  (v1_funct_2(G, u1_struct_0(k18_cat_6(A)), u1_struct_0(k18_cat_6(B))) & m1_subset_1(G, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k18_cat_6(A)), u1_struct_0(k18_cat_6(B)))))) )  =>  ( (r1_funct_2(u4_struct_0(A), u4_struct_0(B), u1_struct_0(k18_cat_6(A)), u1_struct_0(k18_cat_6(B)), C, E) &  (r1_funct_2(u4_struct_0(A), u4_struct_0(B), u1_struct_0(k18_cat_6(A)), u1_struct_0(k18_cat_6(B)), D, F) & r3_cat_8(k18_cat_6(A), k18_cat_6(B), E, F, G)) )  => m2_nattra_1(k4_relset_1(u1_struct_0(A), u4_struct_0(A), u1_struct_0(k18_cat_6(A)), u1_struct_0(k18_cat_6(B)), k7_isocat_1(A), G), A, B, C, D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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(cc12_struct_0, axiom,  (! [A] :  (l5_struct_0(A) =>  ( ~ (v2_struct_0(A))  => v14_struct_0(A)) ) ) ).
fof(cc13_ordinal1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  ~ (v8_ordinal1(A)) ) ) ).
fof(cc13_struct_0, axiom,  (! [A] :  (l5_struct_0(A) =>  (v11_struct_0(A) => v14_struct_0(A)) ) ) ).
fof(cc14_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc14_struct_0, axiom,  (! [A] :  (l5_struct_0(A) =>  ( (v2_struct_0(A) & v14_struct_0(A))  => v11_struct_0(A)) ) ) ).
fof(cc15_ordinal1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v9_ordinal1(A)) ) ) ).
fof(cc15_struct_0, axiom,  (! [A] :  (l5_struct_0(A) =>  ( ( ~ (v11_struct_0(A))  & v14_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc16_ordinal1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) )  =>  (! [B] :  (m1_subset_1(B, A) =>  ~ (v8_ordinal1(B)) ) ) ) ) ).
fof(cc16_struct_0, axiom,  (! [A] :  (l5_struct_0(A) =>  (v11_struct_0(A) => v15_struct_0(A)) ) ) ).
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_1, axiom,  (! [A] :  (l1_cat_1(A) =>  ( ( ~ (v2_struct_0(A))  &  (v7_struct_0(A) &  ~ (v11_struct_0(A)) ) )  =>  ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v3_cat_1(A) & v5_cat_1(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(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_1, axiom,  (! [A] :  (l1_cat_1(A) =>  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & v15_struct_0(A)) )  =>  ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_cat_1(A) & v6_cat_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_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_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_cat_3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v2_cat_1(A) &  (v3_cat_1(A) &  (v4_cat_1(A) &  (v5_cat_1(A) &  (v6_cat_1(A) & l1_cat_1(A)) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  ( ~ (k2_cat_1(A, B, C)=k1_xboole_0)  =>  (! [D] :  ( ( ~ (v2_struct_0(D))  &  ( ~ (v11_struct_0(D))  &  (v2_cat_1(D) &  (v3_cat_1(D) &  (v4_cat_1(D) &  (v5_cat_1(D) &  (v6_cat_1(D) & l1_cat_1(D)) ) ) ) ) ) )  =>  (! [E] :  (m2_cat_1(E, A, D) =>  (! [F] :  (m1_cat_1(F, A, B, C) => k9_cat_3(A, B, C, D, E, F)=k3_funct_2(u4_struct_0(A), u4_struct_0(D), E, F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d12_isocat_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v2_cat_1(A) &  (v3_cat_1(A) &  (v4_cat_1(A) &  (v5_cat_1(A) &  (v6_cat_1(A) & l1_cat_1(A)) ) ) ) ) ) )  =>  (! [B] :  ( (v1_funct_1(B) &  (v1_funct_2(B, u1_struct_0(A), u4_struct_0(A)) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u4_struct_0(A))))) )  =>  (B=k7_isocat_1(A) <=>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k3_funct_2(u1_struct_0(A), u4_struct_0(A), B, C)=k4_cat_1(A, C)) ) ) ) ) ) ) ).
fof(d13_cat_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v2_cat_1(A) &  (v3_cat_1(A) &  (v4_cat_1(A) &  (v5_cat_1(A) &  (v6_cat_1(A) & l1_cat_1(A)) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_cat_1(E, A, B, C) =>  (! [F] :  (m1_cat_1(F, A, C, D) =>  ~ ( ( ~ (k2_cat_1(A, B, C)=k1_xboole_0)  &  ( ~ (k2_cat_1(A, C, D)=k1_xboole_0)  &  ~ (k5_cat_1(A, B, C, D, E, F)=k1_cat_1(A, E, F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d1_cat_1, axiom,  (! [A] :  (l1_cat_1(A) =>  (! [B] :  (m1_subset_1(B, u4_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u4_struct_0(A)) =>  (r2_hidden(k4_tarski(C, B), k9_xtuple_0(u1_cat_1(A))) => k1_cat_1(A, B, C)=k1_binop_1(u1_cat_1(A), C, B)) ) ) ) ) ) ) ).
fof(d1_cat_6, axiom,  (! [A] :  (l1_cat_6(A) => k1_cat_6(A)=u1_struct_0(A)) ) ).
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(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(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(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(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_nattra_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v2_cat_1(A) &  (v3_cat_1(A) &  (v4_cat_1(A) &  (v5_cat_1(A) &  (v6_cat_1(A) & l1_cat_1(A)) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  &  (v2_cat_1(B) &  (v3_cat_1(B) &  (v4_cat_1(B) &  (v5_cat_1(B) &  (v6_cat_1(B) & l1_cat_1(B)) ) ) ) ) ) )  =>  (! [C] :  (m2_cat_1(C, A, B) =>  (! [D] :  (m2_cat_1(D, A, B) =>  (r1_nattra_1(A, B, C, D) <=>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  ~ (k2_cat_1(B, k8_cat_1(A, B, C, E), k8_cat_1(A, B, D, E))=k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d34_cat_6, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v2_cat_1(A) &  (v3_cat_1(A) &  (v4_cat_1(A) &  (v5_cat_1(A) &  (v6_cat_1(A) & l1_cat_1(A)) ) ) ) ) ) )  => k18_cat_6(A)=g1_cat_6(u4_struct_0(A), u1_cat_1(A))) ) ).
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(d3_nattra_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v2_cat_1(A) &  (v3_cat_1(A) &  (v4_cat_1(A) &  (v5_cat_1(A) &  (v6_cat_1(A) & l1_cat_1(A)) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  &  (v2_cat_1(B) &  (v3_cat_1(B) &  (v4_cat_1(B) &  (v5_cat_1(B) &  (v6_cat_1(B) & l1_cat_1(B)) ) ) ) ) ) )  =>  (! [C] :  (m2_cat_1(C, A, B) =>  (! [D] :  (m2_cat_1(D, A, B) =>  (r1_nattra_1(A, B, C, D) =>  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, u1_struct_0(A), u4_struct_0(B)) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u4_struct_0(B))))) )  =>  (m1_nattra_1(E, A, B, C, D) <=>  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) => m1_cat_1(k3_funct_2(u1_struct_0(A), u4_struct_0(B), E, F), B, k8_cat_1(A, B, C, F), k8_cat_1(A, B, D, F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d5_cat_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_cat_1(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  ( ~ (k2_cat_1(A, B, C)=k1_xboole_0)  =>  (! [D] :  (m1_subset_1(D, u4_struct_0(A)) =>  (m1_cat_1(D, A, B, C) <=> r2_tarski(D, k2_cat_1(A, B, C))) ) ) ) ) ) ) ) ) ) ).
fof(d5_nattra_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v2_cat_1(A) &  (v3_cat_1(A) &  (v4_cat_1(A) &  (v5_cat_1(A) &  (v6_cat_1(A) & l1_cat_1(A)) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  &  (v2_cat_1(B) &  (v3_cat_1(B) &  (v4_cat_1(B) &  (v5_cat_1(B) &  (v6_cat_1(B) & l1_cat_1(B)) ) ) ) ) ) )  =>  (! [C] :  (m2_cat_1(C, A, B) =>  (! [D] :  (m2_cat_1(D, A, B) =>  (r1_nattra_1(A, B, C, D) =>  (! [E] :  (m1_nattra_1(E, A, B, C, D) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) => k2_nattra_1(A, B, C, D, E, F)=k3_funct_2(u1_struct_0(A), u4_struct_0(B), E, F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d6_cat_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_cat_1(A)) )  =>  (v2_cat_1(A) <=>  (! [B] :  (m1_subset_1(B, u4_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u4_struct_0(A)) =>  (r2_hidden(k4_tarski(C, B), k9_xtuple_0(u1_cat_1(A))) <=> k3_graph_1(A, C)=k4_graph_1(A, B)) ) ) ) ) ) ) ) ).
fof(d7_nattra_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v2_cat_1(A) &  (v3_cat_1(A) &  (v4_cat_1(A) &  (v5_cat_1(A) &  (v6_cat_1(A) & l1_cat_1(A)) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  &  (v2_cat_1(B) &  (v3_cat_1(B) &  (v4_cat_1(B) &  (v5_cat_1(B) &  (v6_cat_1(B) & l1_cat_1(B)) ) ) ) ) ) )  =>  (! [C] :  (m2_cat_1(C, A, B) =>  (! [D] :  (m2_cat_1(D, A, B) =>  (r2_nattra_1(A, B, C, D) <=>  (r1_nattra_1(A, B, C, D) &  (? [E] :  (m1_nattra_1(E, A, B, C, D) &  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  (! [G] :  (m1_subset_1(G, u1_struct_0(A)) =>  ( ~ (k2_cat_1(A, F, G)=k1_xboole_0)  =>  (! [H] :  (m1_cat_1(H, A, F, G) => k5_cat_1(B, k8_cat_1(A, B, C, F), k8_cat_1(A, B, C, G), k8_cat_1(A, B, D, G), k9_cat_3(A, F, G, B, C, H), k2_nattra_1(A, B, C, D, E, G))=k5_cat_1(B, k8_cat_1(A, B, C, F), k8_cat_1(A, B, D, F), k8_cat_1(A, B, D, G), k2_nattra_1(A, B, C, D, E, F), k9_cat_3(A, F, G, B, D, H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d8_nattra_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v2_cat_1(A) &  (v3_cat_1(A) &  (v4_cat_1(A) &  (v5_cat_1(A) &  (v6_cat_1(A) & l1_cat_1(A)) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  &  (v2_cat_1(B) &  (v3_cat_1(B) &  (v4_cat_1(B) &  (v5_cat_1(B) &  (v6_cat_1(B) & l1_cat_1(B)) ) ) ) ) ) )  =>  (! [C] :  (m2_cat_1(C, A, B) =>  (! [D] :  (m2_cat_1(D, A, B) =>  (r2_nattra_1(A, B, C, D) =>  (! [E] :  (m1_nattra_1(E, A, B, C, D) =>  (m2_nattra_1(E, A, B, C, D) <=>  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  (! [G] :  (m1_subset_1(G, u1_struct_0(A)) =>  ( ~ (k2_cat_1(A, F, G)=k1_xboole_0)  =>  (! [H] :  (m1_cat_1(H, A, F, G) => k5_cat_1(B, k8_cat_1(A, B, C, F), k8_cat_1(A, B, C, G), k8_cat_1(A, B, D, G), k9_cat_3(A, F, G, B, C, H), k2_nattra_1(A, B, C, D, E, G))=k5_cat_1(B, k8_cat_1(A, B, C, F), k8_cat_1(A, B, D, F), k8_cat_1(A, B, D, G), k2_nattra_1(A, B, C, D, E, F), k9_cat_3(A, F, G, B, D, H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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_k18_cat_6, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v2_cat_1(A) &  (v3_cat_1(A) &  (v4_cat_1(A) &  (v5_cat_1(A) &  (v6_cat_1(A) & l1_cat_1(A)) ) ) ) ) ) )  =>  (v1_cat_6(k18_cat_6(A)) &  (v8_cat_6(k18_cat_6(A)) &  (v9_cat_6(k18_cat_6(A)) &  (v10_cat_6(k18_cat_6(A)) & l1_cat_6(k18_cat_6(A))) ) ) ) ) ) ).
fof(dt_k1_binop_1, axiom, $true).
fof(dt_k1_cat_1, axiom,  (! [A, B, C] :  ( (l1_cat_1(A) &  (m1_subset_1(B, u4_struct_0(A)) & m1_subset_1(C, u4_struct_0(A))) )  => m1_subset_1(k1_cat_1(A, B, C), u4_struct_0(A))) ) ).
fof(dt_k1_cat_6, axiom, $true).
fof(dt_k1_funct_1, axiom, $true).
fof(dt_k1_graph_1, axiom,  (! [A, B] :  ( (l1_graph_1(A) & m1_subset_1(B, u4_struct_0(A)))  => m1_subset_1(k1_graph_1(A, B), u1_struct_0(A))) ) ).
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_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_cat_1(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k2_cat_1(A, B, C), k1_zfmisc_1(u4_struct_0(A)))) ) ).
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_graph_1, axiom,  (! [A, B] :  ( (l1_graph_1(A) & m1_subset_1(B, u4_struct_0(A)))  => m1_subset_1(k2_graph_1(A, B), u1_struct_0(A))) ) ).
fof(dt_k2_nattra_1, axiom,  (! [A, B, C, D, E, F] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v2_cat_1(A) &  (v3_cat_1(A) &  (v4_cat_1(A) &  (v5_cat_1(A) &  (v6_cat_1(A) & l1_cat_1(A)) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  &  (v2_cat_1(B) &  (v3_cat_1(B) &  (v4_cat_1(B) &  (v5_cat_1(B) &  (v6_cat_1(B) & l1_cat_1(B)) ) ) ) ) ) )  &  (m2_cat_1(C, A, B) &  (m2_cat_1(D, A, B) &  (m1_nattra_1(E, A, B, C, D) & m1_subset_1(F, u1_struct_0(A))) ) ) ) )  => m1_cat_1(k2_nattra_1(A, B, C, D, E, F), B, k8_cat_1(A, B, C, F), k8_cat_1(A, B, D, F))) ) ).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_funct_2, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  & m1_subset_1(D, A)) )  => m1_subset_1(k3_funct_2(A, B, C, D), B)) ) ).
fof(dt_k3_graph_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_graph_1(A)) )  & m1_subset_1(B, u4_struct_0(A)))  => m1_subset_1(k3_graph_1(A, B), u1_struct_0(A))) ) ).
fof(dt_k3_relat_1, axiom,  (! [A, B] : v1_relat_1(k3_relat_1(A, B))) ).
fof(dt_k4_cat_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v5_cat_1(A) &  (v6_cat_1(A) & l1_cat_1(A)) ) ) )  & m1_subset_1(B, u1_struct_0(A)))  => m1_cat_1(k4_cat_1(A, B), A, B, B)) ) ).
fof(dt_k4_graph_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_graph_1(A)) )  & m1_subset_1(B, u4_struct_0(A)))  => m1_subset_1(k4_graph_1(A, B), u1_struct_0(A))) ) ).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k4_relset_1, axiom,  (! [A, B, C, D, E, F] :  ( (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(C, D))))  => m1_subset_1(k4_relset_1(A, B, C, D, E, F), k1_zfmisc_1(k2_zfmisc_1(A, D)))) ) ).
fof(dt_k4_tarski, axiom, $true).
fof(dt_k5_cat_1, axiom,  (! [A, B, C, D, E, F] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v2_cat_1(A) &  (v3_cat_1(A) &  (v4_cat_1(A) &  (v5_cat_1(A) &  (v6_cat_1(A) & l1_cat_1(A)) ) ) ) ) ) )  &  (m1_subset_1(B, u1_struct_0(A)) &  (m1_subset_1(C, u1_struct_0(A)) &  (m1_subset_1(D, u1_struct_0(A)) &  (m1_cat_1(E, A, B, C) & m1_cat_1(F, A, C, D)) ) ) ) )  => m1_cat_1(k5_cat_1(A, B, C, D, E, F), A, B, D)) ) ).
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_k6_cat_2, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v2_cat_1(A) &  (v3_cat_1(A) &  (v4_cat_1(A) &  (v5_cat_1(A) &  (v6_cat_1(A) & l1_cat_1(A)) ) ) ) ) ) )  &  ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  &  (v2_cat_1(B) &  (v3_cat_1(B) &  (v4_cat_1(B) &  (v5_cat_1(B) &  (v6_cat_1(B) & l1_cat_1(B)) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(k6_cat_2(A, B)))  &  ( ~ (v11_struct_0(k6_cat_2(A, B)))  &  (v2_cat_1(k6_cat_2(A, B)) &  (v3_cat_1(k6_cat_2(A, B)) &  (v4_cat_1(k6_cat_2(A, B)) &  (v5_cat_1(k6_cat_2(A, B)) &  (v6_cat_1(k6_cat_2(A, B)) & l1_cat_1(k6_cat_2(A, B))) ) ) ) ) ) ) ) ) ).
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_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_k7_isocat_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v2_cat_1(A) &  (v3_cat_1(A) &  (v4_cat_1(A) &  (v5_cat_1(A) &  (v6_cat_1(A) & l1_cat_1(A)) ) ) ) ) ) )  =>  (v1_funct_1(k7_isocat_1(A)) &  (v1_funct_2(k7_isocat_1(A), u1_struct_0(A), u4_struct_0(A)) & m1_subset_1(k7_isocat_1(A), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u4_struct_0(A))))) ) ) ) ).
fof(dt_k8_cat_1, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v2_cat_1(A) &  (v3_cat_1(A) &  (v4_cat_1(A) &  (v5_cat_1(A) &  (v6_cat_1(A) & l1_cat_1(A)) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  &  (v2_cat_1(B) &  (v3_cat_1(B) &  (v4_cat_1(B) &  (v5_cat_1(B) &  (v6_cat_1(B) & l1_cat_1(B)) ) ) ) ) ) )  &  (m2_cat_1(C, A, B) & m1_subset_1(D, u1_struct_0(A))) ) )  => m1_subset_1(k8_cat_1(A, B, C, D), u1_struct_0(B))) ) ).
fof(dt_k8_cat_2, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v2_cat_1(A) &  (v3_cat_1(A) &  (v4_cat_1(A) &  (v5_cat_1(A) &  (v6_cat_1(A) & l1_cat_1(A)) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  &  (v2_cat_1(B) &  (v3_cat_1(B) &  (v4_cat_1(B) &  (v5_cat_1(B) &  (v6_cat_1(B) & l1_cat_1(B)) ) ) ) ) ) )  &  (m1_subset_1(C, u4_struct_0(A)) & m1_subset_1(D, u4_struct_0(B))) ) )  => m1_subset_1(k8_cat_2(A, B, C, D), u4_struct_0(k6_cat_2(A, B)))) ) ).
fof(dt_k9_cat_3, axiom,  (! [A, B, C, D, E, F] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v2_cat_1(A) &  (v3_cat_1(A) &  (v4_cat_1(A) &  (v5_cat_1(A) &  (v6_cat_1(A) & l1_cat_1(A)) ) ) ) ) ) )  &  (m1_subset_1(B, u1_struct_0(A)) &  (m1_subset_1(C, u1_struct_0(A)) &  ( ( ~ (v2_struct_0(D))  &  ( ~ (v11_struct_0(D))  &  (v2_cat_1(D) &  (v3_cat_1(D) &  (v4_cat_1(D) &  (v5_cat_1(D) &  (v6_cat_1(D) & l1_cat_1(D)) ) ) ) ) ) )  &  (m2_cat_1(E, A, D) & m1_cat_1(F, A, B, C)) ) ) ) )  => m1_cat_1(k9_cat_3(A, B, C, D, E, F), D, k8_cat_1(A, D, E, B), k8_cat_1(A, D, E, C))) ) ).
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_xtuple_0, axiom, $true).
fof(dt_l1_cat_1, axiom,  (! [A] :  (l1_cat_1(A) => l1_graph_1(A)) ) ).
fof(dt_l1_cat_6, axiom,  (! [A] :  (l1_cat_6(A) => l1_struct_0(A)) ) ).
fof(dt_l1_graph_1, axiom,  (! [A] :  (l1_graph_1(A) => l5_struct_0(A)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_l5_struct_0, axiom,  (! [A] :  (l5_struct_0(A) => l1_struct_0(A)) ) ).
fof(dt_m1_cat_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_cat_1(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  =>  (! [D] :  (m1_cat_1(D, A, B, C) => m1_subset_1(D, u4_struct_0(A))) ) ) ) ).
fof(dt_m1_nattra_1, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v2_cat_1(A) &  (v3_cat_1(A) &  (v4_cat_1(A) &  (v5_cat_1(A) &  (v6_cat_1(A) & l1_cat_1(A)) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  &  (v2_cat_1(B) &  (v3_cat_1(B) &  (v4_cat_1(B) &  (v5_cat_1(B) &  (v6_cat_1(B) & l1_cat_1(B)) ) ) ) ) ) )  &  (m2_cat_1(C, A, B) & m2_cat_1(D, A, B)) ) )  =>  (! [E] :  (m1_nattra_1(E, A, B, C, D) =>  (v1_funct_1(E) &  (v1_funct_2(E, u1_struct_0(A), u4_struct_0(B)) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u4_struct_0(B))))) ) ) ) ) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_m2_cat_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v2_cat_1(A) &  (v3_cat_1(A) &  (v4_cat_1(A) &  (v5_cat_1(A) &  (v6_cat_1(A) & l1_cat_1(A)) ) ) ) ) ) )  &  ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  &  (v2_cat_1(B) &  (v3_cat_1(B) &  (v4_cat_1(B) &  (v5_cat_1(B) &  (v6_cat_1(B) & l1_cat_1(B)) ) ) ) ) ) ) )  =>  (! [C] :  (m2_cat_1(C, A, B) =>  (v1_funct_1(C) &  (v1_funct_2(C, u4_struct_0(A), u4_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u4_struct_0(A), u4_struct_0(B))))) ) ) ) ) ) ).
fof(dt_m2_nattra_1, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v2_cat_1(A) &  (v3_cat_1(A) &  (v4_cat_1(A) &  (v5_cat_1(A) &  (v6_cat_1(A) & l1_cat_1(A)) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  &  (v2_cat_1(B) &  (v3_cat_1(B) &  (v4_cat_1(B) &  (v5_cat_1(B) &  (v6_cat_1(B) & l1_cat_1(B)) ) ) ) ) ) )  &  (m2_cat_1(C, A, B) & m2_cat_1(D, A, B)) ) )  =>  (! [E] :  (m2_nattra_1(E, A, B, C, D) => m1_nattra_1(E, A, B, C, D)) ) ) ) ).
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_u1_cat_1, axiom,  (! [A] :  (l1_cat_1(A) =>  (v1_funct_1(u1_cat_1(A)) & m1_subset_1(u1_cat_1(A), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u4_struct_0(A), u4_struct_0(A)), u4_struct_0(A))))) ) ) ).
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(dt_u4_struct_0, axiom, $true).
fof(existence_l1_cat_1, axiom,  (? [A] : l1_cat_1(A)) ).
fof(existence_l1_cat_6, axiom,  (? [A] : l1_cat_6(A)) ).
fof(existence_l1_graph_1, axiom,  (? [A] : l1_graph_1(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_l5_struct_0, axiom,  (? [A] : l5_struct_0(A)) ).
fof(existence_m1_cat_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_cat_1(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  =>  (? [D] : m1_cat_1(D, A, B, C)) ) ) ).
fof(existence_m1_nattra_1, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v2_cat_1(A) &  (v3_cat_1(A) &  (v4_cat_1(A) &  (v5_cat_1(A) &  (v6_cat_1(A) & l1_cat_1(A)) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  &  (v2_cat_1(B) &  (v3_cat_1(B) &  (v4_cat_1(B) &  (v5_cat_1(B) &  (v6_cat_1(B) & l1_cat_1(B)) ) ) ) ) ) )  &  (m2_cat_1(C, A, B) & m2_cat_1(D, A, B)) ) )  =>  (? [E] : m1_nattra_1(E, A, B, C, D)) ) ) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(existence_m2_cat_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v2_cat_1(A) &  (v3_cat_1(A) &  (v4_cat_1(A) &  (v5_cat_1(A) &  (v6_cat_1(A) & l1_cat_1(A)) ) ) ) ) ) )  &  ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  &  (v2_cat_1(B) &  (v3_cat_1(B) &  (v4_cat_1(B) &  (v5_cat_1(B) &  (v6_cat_1(B) & l1_cat_1(B)) ) ) ) ) ) ) )  =>  (? [C] : m2_cat_1(C, A, B)) ) ) ).
fof(existence_m2_nattra_1, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v2_cat_1(A) &  (v3_cat_1(A) &  (v4_cat_1(A) &  (v5_cat_1(A) &  (v6_cat_1(A) & l1_cat_1(A)) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  &  (v2_cat_1(B) &  (v3_cat_1(B) &  (v4_cat_1(B) &  (v5_cat_1(B) &  (v6_cat_1(B) & l1_cat_1(B)) ) ) ) ) ) )  &  (m2_cat_1(C, A, B) & m2_cat_1(D, A, B)) ) )  =>  (? [E] : m2_nattra_1(E, A, B, C, D)) ) ) ).
fof(fc12_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ~ (v1_finset_1(k1_zfmisc_1(A))) ) ) ).
fof(fc12_ordinal1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v9_ordinal1(A))  & v1_relat_1(B))  =>  (v1_relat_1(k3_relat_1(B, A)) & v9_ordinal1(k3_relat_1(B, A))) ) ) ).
fof(fc13_card_1, axiom,  (! [A, B] :  ( ( ~ (v1_finset_1(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_finset_1(k2_zfmisc_1(A, B))) ) ) ).
fof(fc13_struct_0, axiom,  (! [A] :  ( (v11_struct_0(A) & l5_struct_0(A))  => v1_xboole_0(u4_struct_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(fc14_struct_0, axiom,  (! [A] :  ( ( ~ (v11_struct_0(A))  & l5_struct_0(A))  =>  ~ (v1_xboole_0(u4_struct_0(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(fc20_struct_0, axiom,  (! [A] :  ( (v15_struct_0(A) & l5_struct_0(A))  => v1_zfmisc_1(u4_struct_0(A))) ) ).
fof(fc21_struct_0, axiom,  (! [A] :  ( ( ~ (v15_struct_0(A))  & l5_struct_0(A))  =>  ~ (v1_zfmisc_1(u4_struct_0(A))) ) ) ).
fof(fc2_cat_7, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_cat_6(A))  =>  ~ (v1_xboole_0(k1_cat_6(A))) ) ) ).
fof(fc2_funct_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) & v1_funct_1(B)) )  =>  (v1_relat_1(k3_relat_1(A, B)) & v1_funct_1(k3_relat_1(A, B))) ) ) ).
fof(fc2_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_xboole_0(u1_struct_0(A))) ) ) ).
fof(fc3_cat_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v5_cat_1(A) & l1_cat_1(A)) ) )  & m1_subset_1(B, u1_struct_0(A)))  =>  ~ (v1_xboole_0(k2_cat_1(A, B, B))) ) ) ).
fof(fc3_cat_6, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v2_cat_1(A) &  (v3_cat_1(A) &  (v4_cat_1(A) &  (v5_cat_1(A) &  (v6_cat_1(A) & l1_cat_1(A)) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(k18_cat_6(A)))  &  (v1_cat_6(k18_cat_6(A)) &  (v8_cat_6(k18_cat_6(A)) &  (v9_cat_6(k18_cat_6(A)) & v10_cat_6(k18_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_funct_2, axiom,  (! [A, B, C, D] :  ( ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, A, A) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, A)))) ) )  =>  (v1_funct_1(k3_relat_1(D, C)) & v1_funct_2(k3_relat_1(D, C), A, B)) ) ) ).
fof(fc4_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v5_ordinal1(A)) )  => v3_ordinal1(k9_xtuple_0(A))) ) ).
fof(fc4_xtuple_0, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k9_xtuple_0(A))) ) ).
fof(fc5_funct_2, axiom,  (! [A, B, C, D] :  ( ( (v1_funct_1(C) &  (v1_funct_2(C, B, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, B)))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) )  =>  (v1_funct_1(k3_relat_1(D, C)) & v1_funct_2(k3_relat_1(D, C), A, B)) ) ) ).
fof(fc6_card_1, axiom, v1_card_1(k4_ordinal1)).
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_funct_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v2_funct_1(B)) ) )  =>  (v1_relat_1(k3_relat_1(A, B)) & v2_funct_1(k3_relat_1(A, B))) ) ) ).
fof(fc7_struct_0, axiom,  (! [A] :  ( (v7_struct_0(A) & l1_struct_0(A))  => v1_zfmisc_1(u1_struct_0(A))) ) ).
fof(fc8_funct_2, axiom,  (! [A, B, C, D, E] :  ( ( ~ (v1_xboole_0(B))  &  ( (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(E) &  (v1_funct_2(E, B, C) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) ) ) )  =>  (v1_funct_1(k3_relat_1(D, E)) & v1_funct_2(k3_relat_1(D, E), A, C)) ) ) ).
fof(fc8_nat_1, axiom,  (! [A, B, C] :  ( ( (v1_funct_1(A) &  (v1_funct_2(A, k4_ordinal1, k4_ordinal1) & m1_subset_1(A, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k4_ordinal1)))) )  &  ( ~ (v1_xboole_0(B))  &  (v1_funct_1(C) &  (v1_funct_2(C, k4_ordinal1, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, B)))) ) ) )  =>  (v1_relat_1(k3_relat_1(A, C)) &  (v4_relat_1(k3_relat_1(A, C), k4_ordinal1) &  (v5_relat_1(k3_relat_1(A, C), B) & v1_funct_1(k3_relat_1(A, C))) ) ) ) ) ).
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_nat_1, axiom,  (! [A, B, C] :  ( ( (v1_funct_1(A) &  (v1_funct_2(A, k4_ordinal1, k4_ordinal1) & m1_subset_1(A, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k4_ordinal1)))) )  &  ( ~ (v1_xboole_0(B))  &  (v1_funct_1(C) &  (v1_funct_2(C, k4_ordinal1, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, B)))) ) ) )  =>  (v1_relat_1(k3_relat_1(A, C)) & v1_partfun1(k3_relat_1(A, C), k4_ordinal1)) ) ) ).
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(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(rc25_struct_0, axiom,  (? [A] :  (l5_struct_0(A) &  ~ (v15_struct_0(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_1, axiom,  (? [A] :  (l1_cat_1(A) &  ( ~ (v2_struct_0(A))  &  ~ (v11_struct_0(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_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(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_cat_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v2_cat_1(A) &  (v3_cat_1(A) &  (v4_cat_1(A) &  (v5_cat_1(A) &  (v6_cat_1(A) & l1_cat_1(A)) ) ) ) ) ) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_cat_1(C, A, B, B)) )  => k5_cat_1(A, B, B, B, k4_cat_1(A, B), C)=C) ) ).
fof(rd2_cat_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v2_cat_1(A) &  (v3_cat_1(A) &  (v4_cat_1(A) &  (v5_cat_1(A) &  (v6_cat_1(A) & l1_cat_1(A)) ) ) ) ) ) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_cat_1(C, A, B, B)) )  => k5_cat_1(A, B, B, B, C, k4_cat_1(A, B))=C) ) ).
fof(rd3_cat_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v2_cat_1(A) &  (v3_cat_1(A) &  (v4_cat_1(A) &  (v5_cat_1(A) &  (v6_cat_1(A) & l1_cat_1(A)) ) ) ) ) ) )  & m1_subset_1(B, u1_struct_0(A)))  => k3_graph_1(A, k4_cat_1(A, B))=B) ) ).
fof(rd4_cat_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v2_cat_1(A) &  (v3_cat_1(A) &  (v4_cat_1(A) &  (v5_cat_1(A) &  (v6_cat_1(A) & l1_cat_1(A)) ) ) ) ) ) )  & m1_subset_1(B, u1_struct_0(A)))  => k4_graph_1(A, k4_cat_1(A, B))=B) ) ).
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_k3_funct_2, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  & m1_subset_1(D, A)) )  => k3_funct_2(A, B, C, D)=k1_funct_1(C, D)) ) ).
fof(redefinition_k3_graph_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_graph_1(A)) )  & m1_subset_1(B, u4_struct_0(A)))  => k3_graph_1(A, B)=k1_graph_1(A, B)) ) ).
fof(redefinition_k4_graph_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_graph_1(A)) )  & m1_subset_1(B, u4_struct_0(A)))  => k4_graph_1(A, B)=k2_graph_1(A, B)) ) ).
fof(redefinition_k4_relset_1, axiom,  (! [A, B, C, D, E, F] :  ( (m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(C, D))))  => k4_relset_1(A, B, C, D, E, F)=k3_relat_1(E, F)) ) ).
fof(redefinition_k8_cat_2, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v2_cat_1(A) &  (v3_cat_1(A) &  (v4_cat_1(A) &  (v5_cat_1(A) &  (v6_cat_1(A) & l1_cat_1(A)) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  &  (v2_cat_1(B) &  (v3_cat_1(B) &  (v4_cat_1(B) &  (v5_cat_1(B) &  (v6_cat_1(B) & l1_cat_1(B)) ) ) ) ) ) )  &  (m1_subset_1(C, u4_struct_0(A)) & m1_subset_1(D, u4_struct_0(B))) ) )  => k8_cat_2(A, B, C, D)=k4_tarski(C, D)) ) ).
fof(redefinition_r1_funct_2, axiom,  (! [A, B, C, D, E, F] :  ( ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(D))  &  ( (v1_funct_1(E) &  (v1_funct_2(E, A, B) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(F) &  (v1_funct_2(F, C, D) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(C, D)))) ) ) ) )  =>  (r1_funct_2(A, B, C, D, E, F) <=> E=F) ) ) ).
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_funct_2, axiom,  (! [A, B, C, D, E, F] :  ( ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(D))  &  ( (v1_funct_1(E) &  (v1_funct_2(E, A, B) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(F) &  (v1_funct_2(F, C, D) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(C, D)))) ) ) ) )  => r1_funct_2(A, B, C, D, E, E)) ) ).
fof(reflexivity_r1_nattra_1, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v2_cat_1(A) &  (v3_cat_1(A) &  (v4_cat_1(A) &  (v5_cat_1(A) &  (v6_cat_1(A) & l1_cat_1(A)) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  &  (v2_cat_1(B) &  (v3_cat_1(B) &  (v4_cat_1(B) &  (v5_cat_1(B) &  (v6_cat_1(B) & l1_cat_1(B)) ) ) ) ) ) )  &  (m2_cat_1(C, A, B) & m2_cat_1(D, A, B)) ) )  => r1_nattra_1(A, B, C, C)) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(reflexivity_r2_nattra_1, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v2_cat_1(A) &  (v3_cat_1(A) &  (v4_cat_1(A) &  (v5_cat_1(A) &  (v6_cat_1(A) & l1_cat_1(A)) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  &  (v2_cat_1(B) &  (v3_cat_1(B) &  (v4_cat_1(B) &  (v5_cat_1(B) &  (v6_cat_1(B) & l1_cat_1(B)) ) ) ) ) ) )  &  (m2_cat_1(C, A, B) & m2_cat_1(D, A, B)) ) )  => r2_nattra_1(A, B, C, C)) ) ).
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(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(spc1_numerals, axiom,  (v2_xxreal_0(1) & m1_subset_1(1, k4_ordinal1)) ).
fof(symmetry_r1_funct_2, axiom,  (! [A, B, C, D, E, F] :  ( ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(D))  &  ( (v1_funct_1(E) &  (v1_funct_2(E, A, B) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(F) &  (v1_funct_2(F, C, D) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(C, D)))) ) ) ) )  =>  (r1_funct_2(A, B, C, D, E, F) => r1_funct_2(A, B, C, D, F, E)) ) ) ).
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(t13_funct_1, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (! [C] :  ( (v1_relat_1(C) & v1_funct_1(C))  =>  (r2_hidden(A, k9_xtuple_0(B)) => k1_funct_1(k3_relat_1(B, C), A)=k1_funct_1(C, k1_funct_1(B, A))) ) ) ) ) ) ).
fof(t14_cat_8, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v2_cat_1(A) &  (v3_cat_1(A) &  (v4_cat_1(A) &  (v5_cat_1(A) &  (v6_cat_1(A) & l1_cat_1(A)) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u4_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, k1_cat_6(k18_cat_6(A))) =>  (B=C =>  (k6_cat_6(k18_cat_6(A), C)=k4_cat_1(A, k3_graph_1(A, B)) & k7_cat_6(k18_cat_6(A), C)=k4_cat_1(A, k4_graph_1(A, B))) ) ) ) ) ) ) ) ).
fof(t15_cat_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v2_cat_1(A) &  (v3_cat_1(A) &  (v4_cat_1(A) &  (v5_cat_1(A) &  (v6_cat_1(A) & l1_cat_1(A)) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u4_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u4_struct_0(A)) =>  (k3_graph_1(A, C)=k4_graph_1(A, B) <=> r2_hidden(k4_tarski(C, B), k9_xtuple_0(u1_cat_1(A)))) ) ) ) ) ) ) ).
fof(t1_cat_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_cat_1(A)) )  =>  (! [B] :  (m1_subset_1(B, u4_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (r2_tarski(B, k2_cat_1(A, C, D)) <=>  (k3_graph_1(A, B)=C & k4_graph_1(A, B)=D) ) ) ) ) ) ) ) ) ) ).
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(t21_cat_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v2_cat_1(A) &  (v3_cat_1(A) &  (v4_cat_1(A) &  (v5_cat_1(A) &  (v6_cat_1(A) & l1_cat_1(A)) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u4_struct_0(A)) =>  (k4_graph_1(A, C)=B => k1_cat_1(A, C, k4_cat_1(A, B))=C) ) ) ) ) ) ) ).
fof(t22_cat_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v2_cat_1(A) &  (v3_cat_1(A) &  (v4_cat_1(A) &  (v5_cat_1(A) &  (v6_cat_1(A) & l1_cat_1(A)) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u4_struct_0(A)) =>  (k3_graph_1(A, C)=B => k1_cat_1(A, k4_cat_1(A, B), C)=C) ) ) ) ) ) ) ).
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(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t40_cat_6, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v2_cat_1(A) &  (v3_cat_1(A) &  (v4_cat_1(A) &  (v5_cat_1(A) &  (v6_cat_1(A) & l1_cat_1(A)) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u4_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u4_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, k1_cat_6(k18_cat_6(A))) =>  (! [E] :  (m1_subset_1(E, k1_cat_6(k18_cat_6(A))) =>  ( (B=D &  (C=E & r2_tarski(k8_cat_2(A, A, B, C), k1_relset_1(k2_zfmisc_1(u4_struct_0(A), u4_struct_0(A)), u1_cat_1(A)))) )  => k1_cat_1(A, C, B)=k2_cat_6(k18_cat_6(A), D, E)) ) ) ) ) ) ) ) ) ) ) ).
fof(t41_cat_6, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v2_cat_1(A) &  (v3_cat_1(A) &  (v4_cat_1(A) &  (v5_cat_1(A) &  (v6_cat_1(A) & l1_cat_1(A)) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, k1_cat_6(k18_cat_6(A))) =>  (v11_cat_6(B, k18_cat_6(A)) <=>  (? [C] :  (m1_subset_1(C, u1_struct_0(A)) & B=k4_cat_1(A, C)) ) ) ) ) ) ) ).
fof(t42_cat_6, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v2_cat_1(A) &  (v3_cat_1(A) &  (v4_cat_1(A) &  (v5_cat_1(A) &  (v6_cat_1(A) & l1_cat_1(A)) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  &  (v2_cat_1(B) &  (v3_cat_1(B) &  (v4_cat_1(B) &  (v5_cat_1(B) &  (v6_cat_1(B) & l1_cat_1(B)) ) ) ) ) ) )  =>  (! [C] :  (m2_cat_1(C, A, B) =>  (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(k18_cat_6(A)), u1_struct_0(k18_cat_6(B))) &  (v16_cat_6(C, k18_cat_6(A), k18_cat_6(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k18_cat_6(A)), u1_struct_0(k18_cat_6(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_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v2_cat_1(A) &  (v3_cat_1(A) &  (v4_cat_1(A) &  (v5_cat_1(A) &  (v6_cat_1(A) & l1_cat_1(A)) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  &  (v2_cat_1(B) &  (v3_cat_1(B) &  (v4_cat_1(B) &  (v5_cat_1(B) &  (v6_cat_1(B) & l1_cat_1(B)) ) ) ) ) ) )  =>  (! [C] :  (m2_cat_1(C, A, B) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(B)) =>  (k3_funct_2(u4_struct_0(A), u4_struct_0(B), C, k4_cat_1(A, D))=k4_cat_1(B, E) => k8_cat_1(A, B, C, D)=E) ) ) ) ) ) ) ) ) ) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t82_cat_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v2_cat_1(A) &  (v3_cat_1(A) &  (v4_cat_1(A) &  (v5_cat_1(A) &  (v6_cat_1(A) & l1_cat_1(A)) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  &  (v2_cat_1(B) &  (v3_cat_1(B) &  (v4_cat_1(B) &  (v5_cat_1(B) &  (v6_cat_1(B) & l1_cat_1(B)) ) ) ) ) ) )  =>  (! [C] :  (m2_cat_1(C, A, B) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  ( ~ (k2_cat_1(A, D, E)=k1_xboole_0)  =>  (! [F] :  (m1_cat_1(F, A, D, E) => r2_tarski(k3_funct_2(u4_struct_0(A), u4_struct_0(B), C, F), k2_cat_1(B, k8_cat_1(A, B, C, D), k8_cat_1(A, B, C, E)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
