% Mizar problem: t23_isocat_2,isocat_2,951,5 
fof(t23_isocat_2, 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] :  ( ( ~ (v2_struct_0(C))  &  ( ~ (v11_struct_0(C))  &  (v2_cat_1(C) &  (v3_cat_1(C) &  (v4_cat_1(C) &  (v5_cat_1(C) &  (v6_cat_1(C) & l1_cat_1(C)) ) ) ) ) ) )  =>  (! [D] :  (m2_cat_1(D, k6_cat_2(A, B), C) =>  (! [E] :  (m2_cat_1(E, k6_cat_2(A, B), C) =>  (r2_nattra_1(k6_cat_2(A, B), C, D, E) =>  (! [F] :  (m2_nattra_1(F, k6_cat_2(A, B), C, D, E) =>  (r2_nattra_1(A, k9_nattra_1(B, C), k5_isocat_2(A, B, C, D), k5_isocat_2(A, B, C, E)) &  (? [G] :  (m2_nattra_1(G, A, k9_nattra_1(B, C), k5_isocat_2(A, B, C, D), k5_isocat_2(A, B, C, E)) &  (! [H] :  ( (v1_funct_1(H) &  (v1_funct_2(H, k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B)), u4_struct_0(C)) & m1_subset_1(H, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B)), u4_struct_0(C))))) )  =>  (r1_funct_2(u1_struct_0(k6_cat_2(A, B)), u4_struct_0(C), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B)), u4_struct_0(C), F, H) =>  (! [I] :  (m1_subset_1(I, u1_struct_0(A)) => k2_nattra_1(A, k9_nattra_1(B, C), k5_isocat_2(A, B, C, D), k5_isocat_2(A, B, C, E), G, I)=k4_tarski(k7_cat_2(k9_nattra_1(B, C), k9_nattra_1(B, C), k8_cat_1(A, k9_nattra_1(B, C), k5_isocat_2(A, B, C, D), I), k8_cat_1(A, k9_nattra_1(B, C), k5_isocat_2(A, B, C, E), I)), k10_funct_5(u1_struct_0(A), u1_struct_0(B), u4_struct_0(C), k9_funct_2(u1_struct_0(B), u4_struct_0(C)), k11_funct_5(u1_struct_0(A), u1_struct_0(B), u4_struct_0(C), H), I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(abstractness_v1_cat_1, axiom,  (! [A] :  (l1_cat_1(A) =>  (v1_cat_1(A) => A=g1_cat_1(u1_struct_0(A), u4_struct_0(A), u1_graph_1(A), u2_graph_1(A), u1_cat_1(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_funct_2, axiom,  (! [A, B] :  (! [C] :  (m1_funct_2(C, A, B) => v4_funct_1(C)) ) ) ).
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_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, 1) =>  ( ~ (v2_struct_0(A))  & v7_struct_0(A)) ) ) ) ).
fof(cc12_struct_0, axiom,  (! [A] :  (l5_struct_0(A) =>  ( ~ (v2_struct_0(A))  => v14_struct_0(A)) ) ) ).
fof(cc13_struct_0, axiom,  (! [A] :  (l5_struct_0(A) =>  (v11_struct_0(A) => v14_struct_0(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_struct_0, axiom,  (! [A] :  (l5_struct_0(A) =>  ( ( ~ (v11_struct_0(A))  & v14_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc16_struct_0, axiom,  (! [A] :  (l5_struct_0(A) =>  (v11_struct_0(A) => v15_struct_0(A)) ) ) ).
fof(cc17_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(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_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_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(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_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_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_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_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_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_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_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_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ( ~ (v2_struct_0(A))  &  ~ (v8_struct_0(A)) ) ) ) ) ).
fof(cc6_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v7_struct_0(A) => v8_struct_0(A)) ) ) ).
fof(cc7_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ~ (v7_struct_0(A)) ) ) ) ).
fof(cc8_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v13_struct_0(A, k5_ordinal1)) ) ) ).
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_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, k5_ordinal1) => v2_struct_0(A)) ) ) ).
fof(commutativity_k2_tarski, axiom,  (! [A, B] : k2_tarski(A, B)=k2_tarski(B, 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(d17_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] :  ( ( ~ (v2_struct_0(C))  &  ( ~ (v11_struct_0(C))  &  (v1_cat_1(C) &  (v2_cat_1(C) &  (v3_cat_1(C) &  (v4_cat_1(C) &  (v5_cat_1(C) &  (v6_cat_1(C) & l1_cat_1(C)) ) ) ) ) ) ) )  =>  (C=k9_nattra_1(A, B) <=>  (u1_struct_0(C)=k4_cat_2(A, B) &  (u4_struct_0(C)=k8_nattra_1(A, B) &  ( (! [D] :  (m1_subset_1(D, u4_struct_0(C)) =>  (k3_graph_1(C, D)=k1_xtuple_0(k1_xtuple_0(D)) & k4_graph_1(C, D)=k2_xtuple_0(k1_xtuple_0(D))) ) )  &  ( (! [D] :  (m1_subset_1(D, u4_struct_0(C)) =>  (! [E] :  (m1_subset_1(E, u4_struct_0(C)) =>  (k3_graph_1(C, E)=k4_graph_1(C, D) => r2_tarski(k8_cat_2(C, C, E, D), k9_xtuple_0(u1_cat_1(C)))) ) ) ) )  &  ( (! [D] :  (m1_subset_1(D, u4_struct_0(C)) =>  (! [E] :  (m1_subset_1(E, u4_struct_0(C)) =>  ~ ( (r2_tarski(k8_cat_2(C, C, E, D), k9_xtuple_0(u1_cat_1(C))) &  (! [F] :  (m2_cat_1(F, A, B) =>  (! [G] :  (m2_cat_1(G, A, B) =>  (! [H] :  (m2_cat_1(H, A, B) =>  (! [I] :  (m2_nattra_1(I, A, B, F, G) =>  (! [J] :  (m2_nattra_1(J, A, B, G, H) =>  ~ ( (D=k4_tarski(k4_tarski(F, G), I) &  (E=k4_tarski(k4_tarski(G, H), J) & k1_funct_1(u1_cat_1(C), k8_cat_2(C, C, E, D))=k4_tarski(k4_tarski(F, H), k5_nattra_1(A, B, F, G, H, I, J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  (! [D] :  (m1_subset_1(D, u1_struct_0(C)) =>  (! [E] :  (m2_cat_1(E, A, B) =>  (E=D => k4_cat_1(C, D)=k4_tarski(k4_tarski(E, E), k4_nattra_1(A, B, E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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(d23_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)) => k8_cat_1(A, B, C, D)=k3_funct_2(u1_struct_0(A), u1_struct_0(B), k7_cat_1(A, B, C), D)) ) ) ) ) ) ) ) ).
fof(d2_isocat_2, 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] :  ( ( ~ (v2_struct_0(C))  &  ( ~ (v11_struct_0(C))  &  (v2_cat_1(C) &  (v3_cat_1(C) &  (v4_cat_1(C) &  (v5_cat_1(C) &  (v6_cat_1(C) & l1_cat_1(C)) ) ) ) ) ) )  =>  (! [D] :  (m2_cat_1(D, k6_cat_2(A, B), C) =>  (! [E] :  (m1_subset_1(E, u4_struct_0(A)) => k3_isocat_2(A, B, C, D, E)=k1_funct_1(k1_funct_5(D), E)) ) ) ) ) ) ) ) ) ) ).
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(d3_isocat_2, 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] :  ( ( ~ (v2_struct_0(C))  &  ( ~ (v11_struct_0(C))  &  (v2_cat_1(C) &  (v3_cat_1(C) &  (v4_cat_1(C) &  (v5_cat_1(C) &  (v6_cat_1(C) & l1_cat_1(C)) ) ) ) ) ) )  =>  (! [D] :  (m2_cat_1(D, k6_cat_2(A, B), C) =>  (! [E] :  (m1_subset_1(E, u4_struct_0(A)) => k4_isocat_2(A, B, C, D, E)=k1_partfun1(u1_struct_0(B), u4_struct_0(B), u4_struct_0(B), u4_struct_0(C), k7_isocat_1(B), k3_isocat_2(A, B, C, D, E))) ) ) ) ) ) ) ) ) ) ).
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(d4_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)=a_3_0_cat_1(A, B, C)) ) ) ) ) ) ).
fof(d4_isocat_2, 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] :  ( ( ~ (v2_struct_0(C))  &  ( ~ (v11_struct_0(C))  &  (v2_cat_1(C) &  (v3_cat_1(C) &  (v4_cat_1(C) &  (v5_cat_1(C) &  (v6_cat_1(C) & l1_cat_1(C)) ) ) ) ) ) )  =>  (! [D] :  (m2_cat_1(D, k6_cat_2(A, B), C) =>  (! [E] :  (m2_cat_1(E, A, k9_nattra_1(B, C)) =>  (E=k5_isocat_2(A, B, C, D) <=>  (! [F] :  (m1_subset_1(F, u4_struct_0(A)) => k3_funct_2(u4_struct_0(A), u4_struct_0(k9_nattra_1(B, C)), E, F)=k4_tarski(k4_tarski(k10_cat_2(A, B, C, D, k3_graph_1(A, F)), k10_cat_2(A, B, C, D, k4_graph_1(A, F))), k4_isocat_2(A, B, C, 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(d5_tarski, axiom,  (! [A] :  (! [B] : k4_tarski(A, B)=k2_tarski(k2_tarski(A, B), k1_tarski(A))) ) ).
fof(d7_cat_2, 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)) ) ) ) ) ) )  => k6_cat_2(A, B)=g1_cat_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B)), k2_zfmisc_1(u4_struct_0(A), u4_struct_0(B)), k16_funct_3(u4_struct_0(A), u4_struct_0(B), u1_struct_0(A), u1_struct_0(B), u1_graph_1(A), u1_graph_1(B)), k16_funct_3(u4_struct_0(A), u4_struct_0(B), u1_struct_0(A), u1_struct_0(B), u2_graph_1(A), u2_graph_1(B)), k10_funct_4(u4_struct_0(A), u4_struct_0(B), u1_cat_1(A), u1_cat_1(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_cat_2, 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] :  ( ( ~ (v2_struct_0(C))  &  ( ~ (v11_struct_0(C))  &  (v2_cat_1(C) &  (v3_cat_1(C) &  (v4_cat_1(C) &  (v5_cat_1(C) &  (v6_cat_1(C) & l1_cat_1(C)) ) ) ) ) ) )  =>  (! [D] :  (m2_cat_1(D, k6_cat_2(A, B), C) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) => k10_cat_2(A, B, C, D, E)=k1_funct_1(k1_funct_5(D), k4_cat_1(A, E))) ) ) ) ) ) ) ) ) ) ).
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_1, axiom,  (! [A, B, C, D, E] :  ( ( (v1_funct_1(C) &  (v1_funct_2(C, B, A) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A)))) )  &  ( (v1_funct_1(D) &  (v1_funct_2(D, B, A) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(B, A)))) )  &  (v1_funct_1(E) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(B, B), B)))) ) )  =>  (v1_cat_1(g1_cat_1(A, B, C, D, E)) & l1_cat_1(g1_cat_1(A, B, C, D, E))) ) ) ).
fof(dt_k10_cat_2, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (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(C))  &  ( ~ (v11_struct_0(C))  &  (v2_cat_1(C) &  (v3_cat_1(C) &  (v4_cat_1(C) &  (v5_cat_1(C) &  (v6_cat_1(C) & l1_cat_1(C)) ) ) ) ) ) )  &  (m2_cat_1(D, k6_cat_2(A, B), C) & m1_subset_1(E, u1_struct_0(A))) ) ) )  => m2_cat_1(k10_cat_2(A, B, C, D, E), B, C)) ) ).
fof(dt_k10_funct_2, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  (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(k10_funct_2(A, B, C, D), B)) ) ).
fof(dt_k10_funct_4, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( (v1_funct_1(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A))))  &  (v1_funct_1(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(B, B), B)))) ) ) )  =>  (v1_funct_1(k10_funct_4(A, B, C, D)) & m1_subset_1(k10_funct_4(A, B, C, D), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, B), k2_zfmisc_1(A, B)), k2_zfmisc_1(A, B))))) ) ) ).
fof(dt_k10_funct_5, axiom,  (! [A, B, C, D, E, F] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(C))  &  (m1_funct_2(D, B, C) &  ( (v1_funct_1(E) &  (v1_funct_2(E, A, D) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, D)))) )  & m1_subset_1(F, A)) ) ) )  => m2_funct_2(k10_funct_5(A, B, C, D, E, F), B, C, D)) ) ).
fof(dt_k11_funct_5, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  &  (v1_funct_1(D) &  (v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, B), C)))) ) ) ) )  =>  (v1_funct_1(k11_funct_5(A, B, C, D)) &  (v1_funct_2(k11_funct_5(A, B, C, D), A, k9_funct_2(B, C)) & m1_subset_1(k11_funct_5(A, B, C, D), k1_zfmisc_1(k2_zfmisc_1(A, k9_funct_2(B, C))))) ) ) ) ).
fof(dt_k15_funct_3, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) & v1_funct_1(B)) )  =>  (v1_relat_1(k15_funct_3(A, B)) & v1_funct_1(k15_funct_3(A, B))) ) ) ).
fof(dt_k16_funct_3, axiom,  (! [A, B, C, D, E, F] :  ( ( (v1_funct_1(E) &  (v1_funct_2(E, A, C) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, C)))) )  &  (v1_funct_1(F) &  (v1_funct_2(F, B, D) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(B, D)))) ) )  =>  (v1_funct_1(k16_funct_3(A, B, C, D, E, F)) &  (v1_funct_2(k16_funct_3(A, B, C, D, E, F), k2_zfmisc_1(A, B), k2_zfmisc_1(C, D)) & m1_subset_1(k16_funct_3(A, B, C, D, E, F), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, B), k2_zfmisc_1(C, D))))) ) ) ) ).
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_funct_1, axiom, $true).
fof(dt_k1_funct_2, axiom, $true).
fof(dt_k1_funct_5, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (v1_relat_1(k1_funct_5(A)) & v1_funct_1(k1_funct_5(A))) ) ) ).
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_nattra_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)) ) ) ) ) ) )  &  ( ( ~ (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_nattra_1(k1_nattra_1(A, B, C), A, B, C, C)) ) ).
fof(dt_k1_partfun1, axiom,  (! [A, B, C, D, E, F] :  ( ( (v1_funct_1(E) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))))  &  (v1_funct_1(F) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(C, D)))) )  =>  (v1_funct_1(k1_partfun1(A, B, C, D, E, F)) & m1_subset_1(k1_partfun1(A, B, C, D, E, F), k1_zfmisc_1(k2_zfmisc_1(A, D)))) ) ) ).
fof(dt_k1_tarski, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_xtuple_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_binop_1, axiom,  (! [A, B, C, D, E, F] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( (v1_funct_1(D) &  (v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, B), C)))) )  &  (m1_subset_1(E, A) & m1_subset_1(F, B)) ) ) )  => m1_subset_1(k2_binop_1(A, B, C, D, E, F), C)) ) ).
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_2, axiom, $true).
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_tarski, axiom, $true).
fof(dt_k2_xtuple_0, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_funct_2, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  & m1_subset_1(D, A)) )  => m1_subset_1(k3_funct_2(A, B, C, D), B)) ) ).
fof(dt_k3_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_isocat_2, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (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(C))  &  ( ~ (v11_struct_0(C))  &  (v2_cat_1(C) &  (v3_cat_1(C) &  (v4_cat_1(C) &  (v5_cat_1(C) &  (v6_cat_1(C) & l1_cat_1(C)) ) ) ) ) ) )  &  (m2_cat_1(D, k6_cat_2(A, B), C) & m1_subset_1(E, u4_struct_0(A))) ) ) )  =>  (v1_funct_1(k3_isocat_2(A, B, C, D, E)) &  (v1_funct_2(k3_isocat_2(A, B, C, D, E), u4_struct_0(B), u4_struct_0(C)) & m1_subset_1(k3_isocat_2(A, B, C, D, E), k1_zfmisc_1(k2_zfmisc_1(u4_struct_0(B), u4_struct_0(C))))) ) ) ) ).
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_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)) ) ) ) ) ) ) )  => m1_cat_2(k4_cat_2(A, B), A, 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_isocat_2, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (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(C))  &  ( ~ (v11_struct_0(C))  &  (v2_cat_1(C) &  (v3_cat_1(C) &  (v4_cat_1(C) &  (v5_cat_1(C) &  (v6_cat_1(C) & l1_cat_1(C)) ) ) ) ) ) )  &  (m2_cat_1(D, k6_cat_2(A, B), C) & m1_subset_1(E, u4_struct_0(A))) ) ) )  => m2_nattra_1(k4_isocat_2(A, B, C, D, E), B, C, k10_cat_2(A, B, C, D, k3_graph_1(A, E)), k10_cat_2(A, B, C, D, k4_graph_1(A, E)))) ) ).
fof(dt_k4_nattra_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)) ) ) ) ) ) )  &  ( ( ~ (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_nattra_1(k4_nattra_1(A, B, C), A, B, C, C)) ) ).
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_funct_4, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) & v1_funct_1(B)) )  =>  (v1_relat_1(k5_funct_4(A, B)) & v1_funct_1(k5_funct_4(A, B))) ) ) ).
fof(dt_k5_isocat_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)) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(C))  &  ( ~ (v11_struct_0(C))  &  (v2_cat_1(C) &  (v3_cat_1(C) &  (v4_cat_1(C) &  (v5_cat_1(C) &  (v6_cat_1(C) & l1_cat_1(C)) ) ) ) ) ) )  & m2_cat_1(D, k6_cat_2(A, B), C)) ) )  => m2_cat_1(k5_isocat_2(A, B, C, D), A, k9_nattra_1(B, C))) ) ).
fof(dt_k5_nattra_1, axiom,  (! [A, B, C, D, E, F, G] :  ( ( ( ~ (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) &  (m2_cat_1(E, A, B) &  (m2_nattra_1(F, A, B, C, D) & m2_nattra_1(G, A, B, D, E)) ) ) ) ) )  => m2_nattra_1(k5_nattra_1(A, B, C, D, E, F, G), A, B, C, E)) ) ).
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_k7_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)) ) ) ) ) ) )  &  ( ( ~ (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)) ) ) ) ) ) )  &  (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))))) ) ) )  =>  (v1_funct_1(k7_cat_1(A, B, C)) &  (v1_funct_2(k7_cat_1(A, B, C), u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(k7_cat_1(A, B, C), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) ) ) ) ).
fof(dt_k7_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, u1_struct_0(A)) & m1_subset_1(D, u1_struct_0(B))) ) )  => m1_subset_1(k7_cat_2(A, B, C, D), u1_struct_0(k6_cat_2(A, B)))) ) ).
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_k7_partfun1, axiom,  (! [A, B, C] :  ( (v1_relat_1(B) &  (v5_relat_1(B, A) & v1_funct_1(B)) )  => m1_subset_1(k7_partfun1(A, B, C), 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_k8_nattra_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)) ) ) ) ) ) ) )  => m4_nattra_1(k8_nattra_1(A, B), A, B)) ) ).
fof(dt_k9_cat_2, 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)) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(C))  &  ( ~ (v11_struct_0(C))  &  (v2_cat_1(C) &  (v3_cat_1(C) &  (v4_cat_1(C) &  (v5_cat_1(C) &  (v6_cat_1(C) & l1_cat_1(C)) ) ) ) ) ) )  &  (m2_cat_1(D, k6_cat_2(A, B), C) &  (m1_subset_1(E, u4_struct_0(A)) & m1_subset_1(F, u4_struct_0(B))) ) ) ) )  => m1_subset_1(k9_cat_2(A, B, C, D, E, F), u4_struct_0(C))) ) ).
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_funct_2, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  => m1_funct_2(k9_funct_2(A, B), A, B)) ) ).
fof(dt_k9_nattra_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)) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(k9_nattra_1(A, B)))  &  ( ~ (v11_struct_0(k9_nattra_1(A, B)))  &  (v1_cat_1(k9_nattra_1(A, B)) &  (v2_cat_1(k9_nattra_1(A, B)) &  (v3_cat_1(k9_nattra_1(A, B)) &  (v4_cat_1(k9_nattra_1(A, B)) &  (v5_cat_1(k9_nattra_1(A, B)) &  (v6_cat_1(k9_nattra_1(A, B)) & l1_cat_1(k9_nattra_1(A, 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_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_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)) ) ) ) ) ) ) )  =>  (! [C] :  (m1_cat_2(C, A, B) =>  ~ (v1_xboole_0(C)) ) ) ) ) ).
fof(dt_m1_funct_2, axiom,  (! [A, B] :  (! [C] :  (m1_funct_2(C, A, B) =>  ~ (v1_xboole_0(C)) ) ) ) ).
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_funct_2, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(B))  & m1_funct_2(C, A, B))  =>  (! [D] :  (m2_funct_2(D, A, B, C) =>  (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) ) ) ) ) ).
fof(dt_m2_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_m4_nattra_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] :  (m4_nattra_1(C, A, B) =>  ~ (v1_xboole_0(C)) ) ) ) ) ).
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_graph_1, axiom,  (! [A] :  (l1_graph_1(A) =>  (v1_funct_1(u1_graph_1(A)) &  (v1_funct_2(u1_graph_1(A), u4_struct_0(A), u1_struct_0(A)) & m1_subset_1(u1_graph_1(A), k1_zfmisc_1(k2_zfmisc_1(u4_struct_0(A), u1_struct_0(A))))) ) ) ) ).
fof(dt_u1_struct_0, axiom, $true).
fof(dt_u2_graph_1, axiom,  (! [A] :  (l1_graph_1(A) =>  (v1_funct_1(u2_graph_1(A)) &  (v1_funct_2(u2_graph_1(A), u4_struct_0(A), u1_struct_0(A)) & m1_subset_1(u2_graph_1(A), k1_zfmisc_1(k2_zfmisc_1(u4_struct_0(A), u1_struct_0(A))))) ) ) ) ).
fof(dt_u4_struct_0, axiom, $true).
fof(existence_l1_cat_1, axiom,  (? [A] : l1_cat_1(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_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)) ) ) ) ) ) ) )  =>  (? [C] : m1_cat_2(C, A, B)) ) ) ).
fof(existence_m1_funct_2, axiom,  (! [A, B] :  (? [C] : m1_funct_2(C, A, B)) ) ).
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_funct_2, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(B))  & m1_funct_2(C, A, B))  =>  (? [D] : m2_funct_2(D, A, B, C)) ) ) ).
fof(existence_m2_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(existence_m4_nattra_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] : m4_nattra_1(C, A, B)) ) ) ).
fof(fc10_funct_2, axiom,  (! [A, B] : v4_funct_1(k1_funct_2(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_struct_0, axiom,  (! [A] :  ( ( ~ (v11_struct_0(A))  & l5_struct_0(A))  =>  ~ (v1_xboole_0(u4_struct_0(A))) ) ) ).
fof(fc1_funct_2, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  ~ (v1_xboole_0(k1_funct_2(A, B))) ) ) ).
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(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_funct_2, axiom,  (! [A] :  ~ (v1_xboole_0(k1_funct_2(A, A))) ) ).
fof(fc2_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_xboole_0(u1_struct_0(A))) ) ) ).
fof(fc2_xboole_0, axiom,  (! [A] :  ~ (v1_xboole_0(k1_tarski(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_funct_2, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & v1_xboole_0(B))  => v1_xboole_0(k1_funct_2(A, B))) ) ).
fof(fc3_xboole_0, axiom,  (! [A, B] :  ~ (v1_xboole_0(k2_tarski(A, B))) ) ).
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(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_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_zfmisc_1(u1_struct_0(A))) ) ) ).
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_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_struct_0, axiom,  (! [A] :  ( ( ~ (v8_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_finset_1(u1_struct_0(A))) ) ) ).
fof(fraenkel_a_3_0_cat_1, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  & l1_cat_1(B)) )  &  (m1_subset_1(C, u1_struct_0(B)) & m1_subset_1(D, u1_struct_0(B))) )  =>  (r2_hidden(A, a_3_0_cat_1(B, C, D)) <=>  (? [E] :  (m1_subset_1(E, u4_struct_0(B)) &  (A=E &  (k3_graph_1(B, E)=C & k4_graph_1(B, E)=D) ) ) ) ) ) ) ).
fof(free_g1_cat_1, axiom,  (! [A, B, C, D, E] :  ( ( (v1_funct_1(C) &  (v1_funct_2(C, B, A) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A)))) )  &  ( (v1_funct_1(D) &  (v1_funct_2(D, B, A) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(B, A)))) )  &  (v1_funct_1(E) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(B, B), B)))) ) )  =>  (! [F, G, H, I, J] :  (g1_cat_1(A, B, C, D, E)=g1_cat_1(F, G, H, I, J) =>  (A=F &  (B=G &  (C=H &  (D=I & E=J) ) ) ) ) ) ) ) ).
fof(ie1_funct_2, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( (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)) ) )  => k7_partfun1(B, C, D)=k3_funct_2(A, B, C, D)) ) ).
fof(l24_isocat_2, 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)) => r2_tarski(k2_nattra_1(A, B, C, D, E, F), k2_cat_1(B, k8_cat_1(A, B, C, F), k8_cat_1(A, B, D, F)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc1_cat_1, axiom,  (? [A] :  (l1_cat_1(A) & v1_cat_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_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(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(rc25_struct_0, axiom,  (? [A] :  (l5_struct_0(A) &  ~ (v15_struct_0(A)) ) ) ).
fof(rc2_cat_1, axiom,  (? [A] :  (l1_cat_1(A) &  ( ~ (v2_struct_0(A))  &  ~ (v11_struct_0(A)) ) ) ) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc3_cat_1, axiom,  (? [A] :  (l1_cat_1(A) &  ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v14_struct_0(A) &  (v1_cat_1(A) &  (v2_cat_1(A) &  (v3_cat_1(A) &  (v4_cat_1(A) &  (v5_cat_1(A) & v6_cat_1(A)) ) ) ) ) ) ) ) ) ) ).
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(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_k10_funct_2, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) ) )  => k10_funct_2(A, B, C, D)=k7_partfun1(B, C, D)) ) ).
fof(redefinition_k10_funct_4, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( (v1_funct_1(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A))))  &  (v1_funct_1(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(B, B), B)))) ) ) )  => k10_funct_4(A, B, C, D)=k5_funct_4(C, D)) ) ).
fof(redefinition_k10_funct_5, axiom,  (! [A, B, C, D, E, F] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(C))  &  (m1_funct_2(D, B, C) &  ( (v1_funct_1(E) &  (v1_funct_2(E, A, D) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, D)))) )  & m1_subset_1(F, A)) ) ) )  => k10_funct_5(A, B, C, D, E, F)=k1_funct_1(E, F)) ) ).
fof(redefinition_k11_funct_5, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  &  (v1_funct_1(D) &  (v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, B), C)))) ) ) ) )  => k11_funct_5(A, B, C, D)=k1_funct_5(D)) ) ).
fof(redefinition_k16_funct_3, axiom,  (! [A, B, C, D, E, F] :  ( ( (v1_funct_1(E) &  (v1_funct_2(E, A, C) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, C)))) )  &  (v1_funct_1(F) &  (v1_funct_2(F, B, D) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(B, D)))) ) )  => k16_funct_3(A, B, C, D, E, F)=k15_funct_3(E, F)) ) ).
fof(redefinition_k1_partfun1, axiom,  (! [A, B, C, D, E, F] :  ( ( (v1_funct_1(E) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))))  &  (v1_funct_1(F) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(C, D)))) )  => k1_partfun1(A, B, C, D, E, F)=k3_relat_1(E, F)) ) ).
fof(redefinition_k2_binop_1, axiom,  (! [A, B, C, D, E, F] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( (v1_funct_1(D) &  (v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, B), C)))) )  &  (m1_subset_1(E, A) & m1_subset_1(F, B)) ) ) )  => k2_binop_1(A, B, C, D, E, F)=k1_binop_1(D, E, F)) ) ).
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_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)) ) ) ) ) ) ) )  => k4_cat_2(A, B)=k2_cat_2(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_nattra_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)) ) ) ) ) ) )  &  ( ( ~ (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)) )  => k4_nattra_1(A, B, C)=k1_nattra_1(A, B, C)) ) ).
fof(redefinition_k7_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, u1_struct_0(A)) & m1_subset_1(D, u1_struct_0(B))) ) )  => k7_cat_2(A, B, C, D)=k4_tarski(C, D)) ) ).
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_k9_cat_2, 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)) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(C))  &  ( ~ (v11_struct_0(C))  &  (v2_cat_1(C) &  (v3_cat_1(C) &  (v4_cat_1(C) &  (v5_cat_1(C) &  (v6_cat_1(C) & l1_cat_1(C)) ) ) ) ) ) )  &  (m2_cat_1(D, k6_cat_2(A, B), C) &  (m1_subset_1(E, u4_struct_0(A)) & m1_subset_1(F, u4_struct_0(B))) ) ) ) )  => k9_cat_2(A, B, C, D, E, F)=k1_binop_1(D, E, F)) ) ).
fof(redefinition_k9_funct_2, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  => k9_funct_2(A, B)=k1_funct_2(A, B)) ) ).
fof(redefinition_m2_funct_2, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(B))  & m1_funct_2(C, A, B))  =>  (! [D] :  (m2_funct_2(D, A, B, C) <=> m1_subset_1(D, C)) ) ) ) ).
fof(redefinition_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_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, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) )  =>  (r2_funct_2(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_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, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) )  => r2_funct_2(A, B, C, C)) ) ).
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(s1_funct_2__e9_29__isocat_2, 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)) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(C))  &  ( ~ (v11_struct_0(C))  &  (v2_cat_1(C) &  (v3_cat_1(C) &  (v4_cat_1(C) &  (v5_cat_1(C) &  (v6_cat_1(C) & l1_cat_1(C)) ) ) ) ) ) )  &  (m2_cat_1(D, k6_cat_2(A, B), C) &  (m2_cat_1(E, k6_cat_2(A, B), C) & m2_nattra_1(F, k6_cat_2(A, B), C, D, E)) ) ) ) )  =>  ( (! [G] :  ~ ( (r2_hidden(G, u1_struct_0(A)) &  (! [H] :  ~ ( (r2_hidden(H, u4_struct_0(k9_nattra_1(B, C))) &  (! [I] :  (m1_subset_1(I, u1_struct_0(A)) =>  (! [J] :  ( (v1_funct_1(J) &  (v1_funct_2(J, k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B)), u4_struct_0(C)) & m1_subset_1(J, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B)), u4_struct_0(C))))) )  =>  ( (r1_funct_2(u1_struct_0(k6_cat_2(A, B)), u4_struct_0(C), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B)), u4_struct_0(C), F, J) & G=I)  => H=k4_tarski(k7_cat_2(k9_nattra_1(B, C), k9_nattra_1(B, C), k8_cat_1(A, k9_nattra_1(B, C), k5_isocat_2(A, B, C, D), I), k8_cat_1(A, k9_nattra_1(B, C), k5_isocat_2(A, B, C, E), I)), k10_funct_5(u1_struct_0(A), u1_struct_0(B), u4_struct_0(C), k9_funct_2(u1_struct_0(B), u4_struct_0(C)), k11_funct_5(u1_struct_0(A), u1_struct_0(B), u4_struct_0(C), J), I))) ) ) ) ) ) ) ) ) ) )  =>  (? [G] :  ( (v1_funct_1(G) &  (v1_funct_2(G, u1_struct_0(A), u4_struct_0(k9_nattra_1(B, C))) & m1_subset_1(G, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u4_struct_0(k9_nattra_1(B, C)))))) )  &  (! [H] :  (r2_hidden(H, u1_struct_0(A)) =>  (! [K] :  (m1_subset_1(K, u1_struct_0(A)) =>  (! [L] :  ( (v1_funct_1(L) &  (v1_funct_2(L, k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B)), u4_struct_0(C)) & m1_subset_1(L, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B)), u4_struct_0(C))))) )  =>  ( (r1_funct_2(u1_struct_0(k6_cat_2(A, B)), u4_struct_0(C), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B)), u4_struct_0(C), F, L) & H=K)  => k1_funct_1(G, H)=k4_tarski(k7_cat_2(k9_nattra_1(B, C), k9_nattra_1(B, C), k8_cat_1(A, k9_nattra_1(B, C), k5_isocat_2(A, B, C, D), K), k8_cat_1(A, k9_nattra_1(B, C), k5_isocat_2(A, B, C, E), K)), k10_funct_5(u1_struct_0(A), u1_struct_0(B), u4_struct_0(C), k9_funct_2(u1_struct_0(B), u4_struct_0(C)), k11_funct_5(u1_struct_0(A), u1_struct_0(B), u4_struct_0(C), L), K))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
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_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, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) )  =>  (r2_funct_2(A, B, C, D) => r2_funct_2(A, B, D, C)) ) ) ).
fof(t10_isocat_2, 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] :  ( ( ~ (v2_struct_0(C))  &  ( ~ (v11_struct_0(C))  &  (v2_cat_1(C) &  (v3_cat_1(C) &  (v4_cat_1(C) &  (v5_cat_1(C) &  (v6_cat_1(C) & l1_cat_1(C)) ) ) ) ) ) )  =>  (! [D] :  (m2_cat_1(D, k6_cat_2(A, B), C) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(B)) => k8_cat_1(B, C, k10_cat_2(A, B, C, D, E), F)=k8_cat_1(k6_cat_2(A, B), C, D, k7_cat_2(A, B, E, F))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t11_isocat_2, 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] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(B)) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(B)) =>  ( ( ~ (k2_cat_1(A, C, D)=k1_xboole_0)  &  ~ (k2_cat_1(B, E, F)=k1_xboole_0) )  <=>  ~ (k2_cat_1(k6_cat_2(A, B), k7_cat_2(A, B, C, E), k7_cat_2(A, B, D, F))=k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t13_isocat_2, 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] :  ( ( ~ (v2_struct_0(C))  &  ( ~ (v11_struct_0(C))  &  (v2_cat_1(C) &  (v3_cat_1(C) &  (v4_cat_1(C) &  (v5_cat_1(C) &  (v6_cat_1(C) & l1_cat_1(C)) ) ) ) ) ) )  =>  (! [D] :  (m2_cat_1(D, k6_cat_2(A, B), C) =>  (! [E] :  (m2_cat_1(E, k6_cat_2(A, B), C) =>  (r2_nattra_1(k6_cat_2(A, B), C, D, E) =>  (! [F] :  (m2_nattra_1(F, k6_cat_2(A, B), C, D, E) =>  (! [G] :  (m1_subset_1(G, u1_struct_0(A)) =>  (r2_nattra_1(B, C, k10_cat_2(A, B, C, D, G), k10_cat_2(A, B, C, E, G)) & m2_nattra_1(k1_funct_1(k1_funct_5(F), G), B, C, k10_cat_2(A, B, C, D, G), k10_cat_2(A, B, C, E, G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t15_funct_2, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  =>  (! [E] :  ( (v1_relat_1(E) & v1_funct_1(E))  =>  (r2_hidden(C, A) =>  (B=k1_xboole_0 | k1_funct_1(k3_relat_1(D, E), C)=k1_funct_1(E, k1_funct_1(D, C))) ) ) ) ) ) ) ) ) ).
fof(t15_isocat_2, 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] :  ( ( ~ (v2_struct_0(C))  &  ( ~ (v11_struct_0(C))  &  (v2_cat_1(C) &  (v3_cat_1(C) &  (v4_cat_1(C) &  (v5_cat_1(C) &  (v6_cat_1(C) & l1_cat_1(C)) ) ) ) ) ) )  =>  (! [D] :  (m2_cat_1(D, k6_cat_2(A, B), C) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  ( ~ (k2_cat_1(A, E, F)=k1_xboole_0)  =>  (! [G] :  (m1_cat_1(G, A, E, F) =>  (r2_nattra_1(B, C, k10_cat_2(A, B, C, D, E), k10_cat_2(A, B, C, D, F)) & m2_nattra_1(k1_partfun1(u1_struct_0(B), u4_struct_0(B), u4_struct_0(B), u4_struct_0(C), k7_isocat_1(B), k3_isocat_2(A, B, C, D, G)), B, C, k10_cat_2(A, B, C, D, E), k10_cat_2(A, B, C, D, F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t18_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) =>  (! [E] :  (m2_cat_1(E, A, B) =>  ( (r1_nattra_1(A, B, C, D) & r1_nattra_1(A, B, D, E))  => r1_nattra_1(A, B, C, E)) ) ) ) ) ) ) ) ) ) ) ).
fof(t19_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_nattra_1(F, A, B, C, D) =>  ( (! [G] :  (m1_subset_1(G, u1_struct_0(A)) => k2_nattra_1(A, B, C, D, E, G)=k2_nattra_1(A, B, C, D, F, G)) )  => r2_funct_2(u1_struct_0(A), u4_struct_0(B), E, F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t20_isocat_2, 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] :  ( ( ~ (v2_struct_0(C))  &  ( ~ (v11_struct_0(C))  &  (v2_cat_1(C) &  (v3_cat_1(C) &  (v4_cat_1(C) &  (v5_cat_1(C) &  (v6_cat_1(C) & l1_cat_1(C)) ) ) ) ) ) )  =>  (! [D] :  (m2_cat_1(D, k6_cat_2(A, B), C) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) => k8_cat_1(A, k9_nattra_1(B, C), k5_isocat_2(A, B, C, D), E)=k10_cat_2(A, B, C, D, E)) ) ) ) ) ) ) ) ) ) ).
fof(t21_isocat_2, 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] :  ( ( ~ (v2_struct_0(C))  &  ( ~ (v11_struct_0(C))  &  (v2_cat_1(C) &  (v3_cat_1(C) &  (v4_cat_1(C) &  (v5_cat_1(C) &  (v6_cat_1(C) & l1_cat_1(C)) ) ) ) ) ) )  =>  (! [D] :  (m2_cat_1(D, k6_cat_2(A, B), C) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) => m2_cat_1(k8_cat_1(A, k9_nattra_1(B, C), k5_isocat_2(A, B, C, D), E), B, C)) ) ) ) ) ) ) ) ) ) ).
fof(t25_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) =>  (! [E] :  (m2_cat_1(E, A, B) =>  ( (r2_nattra_1(A, B, C, D) & r2_nattra_1(A, B, D, E))  =>  (! [F] :  (m2_nattra_1(F, A, B, C, D) =>  (! [G] :  (m2_nattra_1(G, A, B, D, E) =>  (! [H] :  (m1_subset_1(H, u1_struct_0(A)) => k2_nattra_1(A, B, C, E, k5_nattra_1(A, B, C, D, E, F, G), H)=k5_cat_1(B, k8_cat_1(A, B, C, H), k8_cat_1(A, B, D, H), k8_cat_1(A, B, E, H), k2_nattra_1(A, B, C, D, F, H), k2_nattra_1(A, B, D, E, G, H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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_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) =>  (! [E] :  (m2_nattra_1(E, A, B, C, D) =>  (r2_nattra_1(A, B, C, D) <=> r2_hidden(k4_tarski(k4_tarski(C, D), E), k8_nattra_1(A, B))) ) ) ) ) ) ) ) ) ) ) ).
fof(t33_cat_2, 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] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_cat_1(E, A, C, D) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(B)) =>  (! [G] :  (m1_subset_1(G, u1_struct_0(B)) =>  (! [H] :  (m1_cat_1(H, B, F, G) =>  ~ ( ( ~ (k2_cat_1(A, C, D)=k1_xboole_0)  &  ( ~ (k2_cat_1(B, F, G)=k1_xboole_0)  &  ~ (m1_cat_1(k8_cat_2(A, B, E, H), k6_cat_2(A, B), k7_cat_2(A, B, C, F), k7_cat_2(A, B, D, G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t33_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) =>  (! [E] :  (m2_nattra_1(E, A, B, C, D) =>  (! [F] :  (m1_subset_1(F, u4_struct_0(k9_nattra_1(A, B))) =>  (F=k4_tarski(k4_tarski(C, D), E) =>  (k3_graph_1(k9_nattra_1(A, B), F)=C & k4_graph_1(k9_nattra_1(A, B), F)=D) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t36_cat_2, 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] :  ( ( ~ (v2_struct_0(C))  &  ( ~ (v11_struct_0(C))  &  (v2_cat_1(C) &  (v3_cat_1(C) &  (v4_cat_1(C) &  (v5_cat_1(C) &  (v6_cat_1(C) & l1_cat_1(C)) ) ) ) ) ) )  =>  (! [D] :  (m2_cat_1(D, k6_cat_2(A, C), B) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (! [F] :  (m1_subset_1(F, u4_struct_0(C)) => k3_funct_2(u4_struct_0(C), u4_struct_0(B), k10_cat_2(A, C, B, D, E), F)=k9_cat_2(A, C, B, D, k4_cat_1(A, E), F)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t36_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) =>  (! [E] :  (m2_cat_1(E, A, B) =>  (! [F] :  (m2_nattra_1(F, A, B, C, D) =>  (! [G] :  (m2_nattra_1(G, A, B, D, E) =>  (! [H] :  (m1_subset_1(H, u4_struct_0(k9_nattra_1(A, B))) =>  (! [I] :  (m1_subset_1(I, u4_struct_0(k9_nattra_1(A, B))) =>  ( (H=k4_tarski(k4_tarski(C, D), F) & I=k4_tarski(k4_tarski(D, E), G))  => k1_cat_1(k9_nattra_1(A, B), H, I)=k4_tarski(k4_tarski(C, E), k5_nattra_1(A, B, C, D, E, F, G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t4_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r2_tarski(A, B) & m1_subset_1(B, k1_zfmisc_1(C)))  => m1_subset_1(A, C)) ) ) ) ).
fof(t5_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)) =>  (! [D] :  (m1_cat_1(D, A, B, C) =>  ( ~ (k2_cat_1(A, B, C)=k1_xboole_0)  =>  (k3_graph_1(A, D)=B & k4_graph_1(A, D)=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(t69_funct_5, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  ( ~ (v1_xboole_0(C))  =>  (! [D] :  (m1_subset_1(D, A) =>  (! [E] :  (m1_subset_1(E, B) =>  (! [F] :  ( (v1_funct_1(F) &  (v1_funct_2(F, k2_zfmisc_1(A, B), C) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, B), C)))) )  => k2_binop_1(A, B, C, F, D, E)=k3_funct_2(B, C, k10_funct_5(A, B, C, k9_funct_2(B, C), k11_funct_5(A, B, C, F), D), 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(t84_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)  & k2_cat_1(B, k8_cat_1(A, B, C, D), k8_cat_1(A, B, C, E))=k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
