% Mizar problem: t39_isocat_1,isocat_1,1131,5 
fof(t39_isocat_1, 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] :  ( ( ~ (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, B) =>  (! [F] :  (m2_cat_1(F, A, B) =>  (! [G] :  (m2_cat_1(G, B, C) =>  (! [H] :  (m2_cat_1(H, B, C) =>  (! [I] :  (m2_cat_1(I, C, D) =>  (! [J] :  (m2_cat_1(J, C, D) =>  (! [K] :  (m2_nattra_1(K, A, B, E, F) =>  (! [L] :  (m2_nattra_1(L, B, C, G, H) =>  (! [M] :  (m2_nattra_1(M, C, D, I, J) =>  ( (r2_nattra_1(A, B, E, F) &  (r2_nattra_1(B, C, G, H) & r2_nattra_1(C, D, I, J)) )  => r2_funct_2(u1_struct_0(A), u4_struct_0(D), k6_isocat_1(A, C, D, k9_cat_1(A, B, C, E, G), k9_cat_1(A, B, C, F, H), I, J, k6_isocat_1(A, B, C, E, F, G, H, K, L), M), k6_isocat_1(A, B, D, E, F, k9_cat_1(B, C, D, G, I), k9_cat_1(B, C, D, H, J), K, k6_isocat_1(B, C, D, G, H, I, J, L, M)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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_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(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_xboole_0, axiom, k1_xboole_0=o_0_0_xboole_0).
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(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(d9_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] :  ( ( ~ (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, A, B) =>  (! [E] :  (m2_cat_1(E, A, B) =>  (! [F] :  (m2_cat_1(F, B, C) =>  (! [G] :  (m2_cat_1(G, B, C) =>  (! [H] :  (m2_nattra_1(H, A, B, D, E) =>  (! [I] :  (m2_nattra_1(I, B, C, F, G) => k6_isocat_1(A, B, C, D, E, F, G, H, I)=k5_nattra_1(A, C, k9_cat_1(A, B, C, D, F), k9_cat_1(A, B, C, E, F), k9_cat_1(A, B, C, E, G), k4_isocat_1(A, B, C, D, E, H, F), k5_isocat_1(A, B, C, F, G, E, I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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_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_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_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_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)) ) ) ) ) ) )  &  ( ( ~ (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, A, B) &  (m2_cat_1(E, A, B) &  (m2_nattra_1(F, A, B, D, E) & m2_cat_1(G, B, C)) ) ) ) ) )  => m2_nattra_1(k4_isocat_1(A, B, C, D, E, F, G), A, C, k9_cat_1(A, B, C, D, G), k9_cat_1(A, B, C, E, G))) ) ).
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_isocat_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)) ) ) ) ) ) )  &  ( ( ~ (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, B, C) &  (m2_cat_1(E, B, C) &  (m2_cat_1(F, A, B) & m2_nattra_1(G, B, C, D, E)) ) ) ) ) )  => m2_nattra_1(k5_isocat_1(A, B, C, D, E, F, G), A, C, k9_cat_1(A, B, C, F, D), k9_cat_1(A, B, C, F, E))) ) ).
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_isocat_1, axiom,  (! [A, B, C, D, E, F, G, H, I] :  ( ( ( ~ (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, A, B) &  (m2_cat_1(E, A, B) &  (m2_cat_1(F, B, C) &  (m2_cat_1(G, B, C) &  (m2_nattra_1(H, A, B, D, E) & m2_nattra_1(I, B, C, F, G)) ) ) ) ) ) ) )  => m2_nattra_1(k6_isocat_1(A, B, C, D, E, F, G, H, I), A, C, k9_cat_1(A, B, C, D, F), k9_cat_1(A, B, C, E, G))) ) ).
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_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_k9_cat_1, 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, A, B) & m2_cat_1(E, B, C)) ) ) )  => m2_cat_1(k9_cat_1(A, B, C, D, E), A, 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_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_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_0_0_xboole_0, axiom, v1_xboole_0(o_0_0_xboole_0)).
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_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(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_struct_0, axiom,  (! [A] :  ( (v2_struct_0(A) & l1_struct_0(A))  => v1_xboole_0(u1_struct_0(A))) ) ).
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_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(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_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(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(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(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(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_k9_cat_1, 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, A, B) & m2_cat_1(E, B, C)) ) ) )  => k9_cat_1(A, B, C, D, E)=k3_relat_1(D, E)) ) ).
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_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(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
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(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t22_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] :  ( ( ~ (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, A, B) =>  (! [E] :  (m2_cat_1(E, A, B) =>  (! [F] :  (m2_cat_1(F, B, C) =>  (! [G] :  (m2_cat_1(G, B, C) =>  ( (r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))  => r2_nattra_1(A, C, k9_cat_1(A, B, C, D, F), k9_cat_1(A, B, C, E, G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t26_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_cat_1(F, A, B) =>  (! [G] :  (m2_nattra_1(G, A, B, C, D) =>  (! [H] :  (m2_nattra_1(H, A, B, D, E) =>  ( (r2_nattra_1(A, B, C, D) &  (r2_nattra_1(A, B, D, E) & r2_nattra_1(A, B, E, F)) )  =>  (! [I] :  (m2_nattra_1(I, A, B, E, F) => r2_funct_2(u1_struct_0(A), u4_struct_0(B), k5_nattra_1(A, B, C, D, F, G, k5_nattra_1(A, B, D, E, F, H, I)), k5_nattra_1(A, B, C, E, F, k5_nattra_1(A, B, C, D, E, G, H), I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t27_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] :  ( ( ~ (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, A, B) =>  (! [E] :  (m2_cat_1(E, A, B) =>  (! [F] :  (m2_cat_1(F, A, B) =>  (! [G] :  (m2_cat_1(G, B, C) =>  (! [H] :  (m2_nattra_1(H, A, B, D, E) =>  (! [I] :  (m2_nattra_1(I, A, B, E, F) =>  ( (r2_nattra_1(A, B, D, E) & r2_nattra_1(A, B, E, F))  => r2_funct_2(u1_struct_0(A), u4_struct_0(C), k4_isocat_1(A, B, C, D, F, k5_nattra_1(A, B, D, E, F, H, I), G), k5_nattra_1(A, C, k9_cat_1(A, B, C, D, G), k9_cat_1(A, B, C, E, G), k9_cat_1(A, B, C, F, G), k4_isocat_1(A, B, C, D, E, H, G), k4_isocat_1(A, B, C, E, F, I, G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t28_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] :  ( ( ~ (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, A, B) =>  (! [E] :  (m2_cat_1(E, B, C) =>  (! [F] :  (m2_cat_1(F, B, C) =>  (! [G] :  (m2_cat_1(G, B, C) =>  (! [H] :  (m2_nattra_1(H, B, C, E, F) =>  (! [I] :  (m2_nattra_1(I, B, C, F, G) =>  ( (r2_nattra_1(B, C, E, F) & r2_nattra_1(B, C, F, G))  => r2_funct_2(u1_struct_0(A), u4_struct_0(C), k5_isocat_1(A, B, C, E, G, D, k5_nattra_1(B, C, E, F, G, H, I)), k5_nattra_1(A, C, k9_cat_1(A, B, C, D, E), k9_cat_1(A, B, C, D, F), k9_cat_1(A, B, C, D, G), k5_isocat_1(A, B, C, E, F, D, H), k5_isocat_1(A, B, C, F, G, D, I)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t29_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] :  ( ( ~ (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] :  ( ( ~ (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, B) =>  (! [F] :  (m2_cat_1(F, B, C) =>  (! [G] :  (m2_cat_1(G, C, D) =>  (! [H] :  (m2_cat_1(H, C, D) =>  (! [I] :  (m2_nattra_1(I, C, D, G, H) =>  (r2_nattra_1(C, D, G, H) => r2_funct_2(u1_struct_0(A), u4_struct_0(D), k5_isocat_1(A, B, D, k9_cat_1(B, C, D, F, G), k9_cat_1(B, C, D, F, H), E, k5_isocat_1(B, C, D, G, H, F, I)), k5_isocat_1(A, C, D, G, H, k9_cat_1(A, B, C, E, F), I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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(t30_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] :  ( ( ~ (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] :  ( ( ~ (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, B) =>  (! [F] :  (m2_cat_1(F, B, C) =>  (! [G] :  (m2_cat_1(G, B, C) =>  (! [H] :  (m2_cat_1(H, C, D) =>  (! [I] :  (m2_nattra_1(I, B, C, F, G) =>  (r2_nattra_1(B, C, F, G) => r2_funct_2(u1_struct_0(A), u4_struct_0(D), k5_isocat_1(A, B, D, k9_cat_1(B, C, D, F, H), k9_cat_1(B, C, D, G, H), E, k4_isocat_1(B, C, D, F, G, I, H)), k4_isocat_1(A, C, D, k9_cat_1(A, B, C, E, F), k9_cat_1(A, B, C, E, G), k5_isocat_1(A, B, C, F, G, E, I), H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t31_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] :  ( ( ~ (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] :  ( ( ~ (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, B) =>  (! [F] :  (m2_cat_1(F, A, B) =>  (! [G] :  (m2_cat_1(G, B, C) =>  (! [H] :  (m2_cat_1(H, C, D) =>  (! [I] :  (m2_nattra_1(I, A, B, E, F) =>  (r2_nattra_1(A, B, E, F) => r2_funct_2(u1_struct_0(A), u4_struct_0(D), k4_isocat_1(A, B, D, E, F, I, k9_cat_1(B, C, D, G, H)), k4_isocat_1(A, C, D, k9_cat_1(A, B, C, E, G), k9_cat_1(A, B, C, F, G), k4_isocat_1(A, B, C, E, F, I, G), H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t36_relat_1, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (v1_relat_1(B) =>  (! [C] :  (v1_relat_1(C) => k3_relat_1(k3_relat_1(A, C), B)=k3_relat_1(A, k3_relat_1(C, B))) ) ) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t4_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r2_tarski(A, B) & m1_subset_1(B, k1_zfmisc_1(C)))  => m1_subset_1(A, C)) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
