% Mizar problem: l67_grcat_1,grcat_1,1409,5 
fof(l67_grcat_1, conjecture,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  =>  (! [B] :  (m1_subset_1(B, u4_struct_0(k25_grcat_1(A))) =>  (! [C] :  (m1_subset_1(C, u4_struct_0(k25_grcat_1(A))) =>  (k3_graph_1(k25_grcat_1(A), C)=k4_graph_1(k25_grcat_1(A), B) =>  (k3_graph_1(k25_grcat_1(A), k1_cat_1(k25_grcat_1(A), B, C))=k3_graph_1(k25_grcat_1(A), B) & k4_graph_1(k25_grcat_1(A), k1_cat_1(k25_grcat_1(A), B, C))=k4_graph_1(k25_grcat_1(A), C)) ) ) ) ) ) ) ) ).
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(abstractness_v1_grcat_1, axiom,  (! [A] :  (l1_grcat_1(A) =>  (v1_grcat_1(A) => A=g1_grcat_1(u1_grcat_1(A), u2_grcat_1(A), u3_grcat_1(A))) ) ) ).
fof(abstractness_v8_algstr_0, axiom,  (! [A] :  (l2_algstr_0(A) =>  (v8_algstr_0(A) => A=g2_algstr_0(u1_struct_0(A), u1_algstr_0(A), u2_struct_0(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_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_algstr_0, axiom,  (! [A] :  ( (v13_algstr_0(A) & l2_algstr_0(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => v10_algstr_0(B, 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_algstr_0, axiom,  (! [A] :  (l1_algstr_0(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  ( (v2_algstr_0(B, A) & v3_algstr_0(B, A))  => v4_algstr_0(B, A)) ) ) ) ) ).
fof(cc1_algstr_1, axiom,  (! [A] :  (l2_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  & v4_algstr_1(A))  =>  ( ~ (v2_struct_0(A))  &  (v5_algstr_0(A) &  (v6_algstr_0(A) &  (v2_algstr_1(A) & v3_algstr_1(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_classes2, axiom,  (! [A] :  (v2_classes1(A) => v1_classes1(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_algstr_0, axiom,  (! [A] :  (l1_algstr_0(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (v4_algstr_0(B, A) =>  (v2_algstr_0(B, A) & v3_algstr_0(B, A)) ) ) ) ) ) ).
fof(cc2_algstr_1, axiom,  (! [A] :  (l2_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v5_algstr_0(A) &  (v6_algstr_0(A) &  (v2_algstr_1(A) & v3_algstr_1(A)) ) ) )  =>  ( ~ (v2_struct_0(A))  & v4_algstr_1(A)) ) ) ) ).
fof(cc2_cat_1, axiom,  (! [A] :  (l1_cat_1(A) =>  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & v15_struct_0(A)) )  =>  ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_cat_1(A) & v6_cat_1(A)) ) ) ) ) ) ).
fof(cc2_classes2, axiom,  (! [A] :  (v1_classes2(A) =>  (v1_ordinal1(A) & v2_classes1(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_algstr_0, axiom,  (! [A] :  (l1_algstr_0(A) =>  ( (v5_algstr_0(A) & v6_algstr_0(A))  => v7_algstr_0(A)) ) ) ).
fof(cc3_algstr_1, axiom,  (! [A] :  (l2_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  & v4_algstr_1(A))  =>  ( ~ (v2_struct_0(A))  & v2_algstr_1(A)) ) ) ) ).
fof(cc3_classes2, axiom,  (! [A] :  ( (v1_ordinal1(A) & v2_classes1(A))  => v1_classes2(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_algstr_0, axiom,  (! [A] :  (l1_algstr_0(A) =>  (v7_algstr_0(A) =>  (v5_algstr_0(A) & v6_algstr_0(A)) ) ) ) ).
fof(cc4_algstr_1, axiom,  (! [A] :  (l2_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) & v4_rlvect_1(A)) ) )  =>  ( ~ (v2_struct_0(A))  &  (v1_algstr_1(A) & v4_algstr_1(A)) ) ) ) ) ).
fof(cc4_funct_2, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, A))) =>  (v1_funct_2(B, A, A) => v1_partfun1(B, A)) ) ) ) ).
fof(cc4_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_algstr_0, axiom,  (! [A] :  ( (v5_algstr_0(A) & l1_algstr_0(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => v2_algstr_0(B, 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_algstr_0, axiom,  (! [A] :  ( (v6_algstr_0(A) & l1_algstr_0(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => v3_algstr_0(B, A)) ) ) ) ).
fof(cc6_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v7_struct_0(A) => v8_struct_0(A)) ) ) ).
fof(cc7_algstr_1, axiom,  (! [A] :  (l2_algstr_0(A) =>  (v13_struct_0(A, 1) =>  (v13_struct_0(A, 1) &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) & v4_rlvect_1(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(d10_grcat_1, axiom,  (! [A] :  (l1_grcat_1(A) => k8_grcat_1(A)=u2_grcat_1(A)) ) ).
fof(d13_ordinal1, axiom, k5_ordinal1=k1_xboole_0).
fof(d30_grcat_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  => k25_grcat_1(A)=g1_cat_1(k17_grcat_1(A), k18_grcat_1(k17_grcat_1(A)), k22_grcat_1(k17_grcat_1(A)), k23_grcat_1(k17_grcat_1(A)), k24_grcat_1(k17_grcat_1(A)))) ) ).
fof(d3_graph_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_graph_1(A)) )  =>  (! [B] :  (m1_subset_1(B, u4_struct_0(A)) => k3_graph_1(A, B)=k3_funct_2(u4_struct_0(A), u1_struct_0(A), u1_graph_1(A), B)) ) ) ) ).
fof(d4_graph_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_graph_1(A)) )  =>  (! [B] :  (m1_subset_1(B, u4_struct_0(A)) => k4_graph_1(A, B)=k3_funct_2(u4_struct_0(A), u1_struct_0(A), u2_graph_1(A), B)) ) ) ) ).
fof(d9_grcat_1, axiom,  (! [A] :  (l1_grcat_1(A) => k7_grcat_1(A)=u1_grcat_1(A)) ) ).
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_g1_grcat_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l2_algstr_0(A)) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l2_algstr_0(B)) ) ) )  &  (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) ) ) )  =>  (v1_grcat_1(g1_grcat_1(A, B, C)) & l1_grcat_1(g1_grcat_1(A, B, C))) ) ) ).
fof(dt_g2_algstr_0, axiom,  (! [A, B, C] :  ( ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  & m1_subset_1(C, A))  =>  (v8_algstr_0(g2_algstr_0(A, B, C)) & l2_algstr_0(g2_algstr_0(A, B, C))) ) ) ).
fof(dt_k13_grcat_1, axiom,  (! [A, B] :  ( ( (v2_grcat_1(A) & l1_grcat_1(A))  &  (v2_grcat_1(B) & l1_grcat_1(B)) )  =>  (v1_grcat_1(k13_grcat_1(A, B)) &  (v2_grcat_1(k13_grcat_1(A, B)) & l1_grcat_1(k13_grcat_1(A, B))) ) ) ) ).
fof(dt_k17_grcat_1, axiom, $true).
fof(dt_k18_grcat_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v3_grcat_1(A))  =>  ( ~ (v1_xboole_0(k18_grcat_1(A)))  & v4_grcat_1(k18_grcat_1(A))) ) ) ).
fof(dt_k19_grcat_1, axiom,  (! [A, B] :  ( ( ( ~ (v1_xboole_0(A))  & v3_grcat_1(A))  & m1_subset_1(B, k18_grcat_1(A)))  =>  (v8_algstr_0(k19_grcat_1(A, B)) & m2_grcat_1(k19_grcat_1(A, B), A)) ) ) ).
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_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_k20_grcat_1, axiom,  (! [A, B] :  ( ( ( ~ (v1_xboole_0(A))  & v3_grcat_1(A))  & m1_subset_1(B, k18_grcat_1(A)))  =>  (v8_algstr_0(k20_grcat_1(A, B)) & m2_grcat_1(k20_grcat_1(A, B), A)) ) ) ).
fof(dt_k22_grcat_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v3_grcat_1(A))  =>  (v1_funct_1(k22_grcat_1(A)) &  (v1_funct_2(k22_grcat_1(A), k18_grcat_1(A), A) & m1_subset_1(k22_grcat_1(A), k1_zfmisc_1(k2_zfmisc_1(k18_grcat_1(A), A)))) ) ) ) ).
fof(dt_k23_grcat_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v3_grcat_1(A))  =>  (v1_funct_1(k23_grcat_1(A)) &  (v1_funct_2(k23_grcat_1(A), k18_grcat_1(A), A) & m1_subset_1(k23_grcat_1(A), k1_zfmisc_1(k2_zfmisc_1(k18_grcat_1(A), A)))) ) ) ) ).
fof(dt_k24_grcat_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v3_grcat_1(A))  =>  (v1_funct_1(k24_grcat_1(A)) & m1_subset_1(k24_grcat_1(A), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k18_grcat_1(A), k18_grcat_1(A)), k18_grcat_1(A))))) ) ) ).
fof(dt_k25_grcat_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  =>  ( ~ (v2_struct_0(k25_grcat_1(A)))  &  ( ~ (v11_struct_0(k25_grcat_1(A)))  &  (v1_cat_1(k25_grcat_1(A)) & l1_cat_1(k25_grcat_1(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_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_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_tarski, axiom, $true).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k7_grcat_1, axiom,  (! [A] :  (l1_grcat_1(A) =>  ( ~ (v2_struct_0(k7_grcat_1(A)))  &  (v13_algstr_0(k7_grcat_1(A)) &  (v3_rlvect_1(k7_grcat_1(A)) &  (v4_rlvect_1(k7_grcat_1(A)) & l2_algstr_0(k7_grcat_1(A))) ) ) ) ) ) ).
fof(dt_k8_grcat_1, axiom,  (! [A] :  (l1_grcat_1(A) =>  ( ~ (v2_struct_0(k8_grcat_1(A)))  &  (v13_algstr_0(k8_grcat_1(A)) &  (v3_rlvect_1(k8_grcat_1(A)) &  (v4_rlvect_1(k8_grcat_1(A)) & l2_algstr_0(k8_grcat_1(A))) ) ) ) ) ) ).
fof(dt_k9_xtuple_0, axiom, $true).
fof(dt_l1_algstr_0, axiom,  (! [A] :  (l1_algstr_0(A) => l1_struct_0(A)) ) ).
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_grcat_1, axiom, $true).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_l2_algstr_0, axiom,  (! [A] :  (l2_algstr_0(A) =>  (l2_struct_0(A) & l1_algstr_0(A)) ) ) ).
fof(dt_l2_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => l1_struct_0(A)) ) ).
fof(dt_l5_struct_0, axiom,  (! [A] :  (l5_struct_0(A) => l1_struct_0(A)) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_m2_grcat_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v3_grcat_1(A))  =>  (! [B] :  (m2_grcat_1(B, A) =>  ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l2_algstr_0(B)) ) ) ) ) ) ) ) ).
fof(dt_m3_grcat_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v4_grcat_1(A))  =>  (! [B] :  (m3_grcat_1(B, A) =>  (v2_grcat_1(B) & l1_grcat_1(B)) ) ) ) ) ).
fof(dt_u1_algstr_0, axiom,  (! [A] :  (l1_algstr_0(A) =>  (v1_funct_1(u1_algstr_0(A)) &  (v1_funct_2(u1_algstr_0(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m1_subset_1(u1_algstr_0(A), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))) ) ) ) ).
fof(dt_u1_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_grcat_1, axiom,  (! [A] :  (l1_grcat_1(A) =>  ( ~ (v2_struct_0(u1_grcat_1(A)))  &  (v13_algstr_0(u1_grcat_1(A)) &  (v3_rlvect_1(u1_grcat_1(A)) &  (v4_rlvect_1(u1_grcat_1(A)) & l2_algstr_0(u1_grcat_1(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_u2_grcat_1, axiom,  (! [A] :  (l1_grcat_1(A) =>  ( ~ (v2_struct_0(u2_grcat_1(A)))  &  (v13_algstr_0(u2_grcat_1(A)) &  (v3_rlvect_1(u2_grcat_1(A)) &  (v4_rlvect_1(u2_grcat_1(A)) & l2_algstr_0(u2_grcat_1(A))) ) ) ) ) ) ).
fof(dt_u2_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => m1_subset_1(u2_struct_0(A), u1_struct_0(A))) ) ).
fof(dt_u3_grcat_1, axiom,  (! [A] :  (l1_grcat_1(A) =>  (v1_funct_1(u3_grcat_1(A)) &  (v1_funct_2(u3_grcat_1(A), u1_struct_0(u1_grcat_1(A)), u1_struct_0(u2_grcat_1(A))) & m1_subset_1(u3_grcat_1(A), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(u1_grcat_1(A)), u1_struct_0(u2_grcat_1(A)))))) ) ) ) ).
fof(dt_u4_struct_0, axiom, $true).
fof(existence_l1_algstr_0, axiom,  (? [A] : l1_algstr_0(A)) ).
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_grcat_1, axiom,  (? [A] : l1_grcat_1(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_l2_algstr_0, axiom,  (? [A] : l2_algstr_0(A)) ).
fof(existence_l2_struct_0, axiom,  (? [A] : l2_struct_0(A)) ).
fof(existence_l5_struct_0, axiom,  (? [A] : l5_struct_0(A)) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(existence_m2_grcat_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v3_grcat_1(A))  =>  (? [B] : m2_grcat_1(B, A)) ) ) ).
fof(existence_m3_grcat_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v4_grcat_1(A))  =>  (? [B] : m3_grcat_1(B, A)) ) ) ).
fof(fc11_grcat_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  =>  ~ (v1_xboole_0(k17_grcat_1(A))) ) ) ).
fof(fc12_grcat_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  => v3_grcat_1(k17_grcat_1(A))) ) ).
fof(fc13_grcat_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  =>  ( ~ (v2_struct_0(k25_grcat_1(A)))  &  ( ~ (v11_struct_0(k25_grcat_1(A)))  & v1_cat_1(k25_grcat_1(A))) ) ) ) ).
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(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_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_xboole_0(u1_struct_0(A))) ) ) ).
fof(fc6_algstr_0, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  & m1_subset_1(C, A)) )  =>  ( ~ (v2_struct_0(g2_algstr_0(A, B, C)))  & v8_algstr_0(g2_algstr_0(A, B, C))) ) ) ).
fof(fc6_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(fc7_algstr_0, axiom,  (! [A, B, C] :  ( (v1_zfmisc_1(A) &  ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  & m1_subset_1(C, A)) )  =>  (v7_struct_0(g2_algstr_0(A, B, C)) & v8_algstr_0(g2_algstr_0(A, B, C))) ) ) ).
fof(fc7_struct_0, axiom,  (! [A] :  ( (v7_struct_0(A) & l1_struct_0(A))  => v1_zfmisc_1(u1_struct_0(A))) ) ).
fof(fc8_algstr_0, axiom,  (! [A, B, C] :  ( ( ~ (v1_zfmisc_1(A))  &  ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  & m1_subset_1(C, A)) )  =>  ( ~ (v7_struct_0(g2_algstr_0(A, B, C)))  & v8_algstr_0(g2_algstr_0(A, B, 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(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(free_g1_grcat_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l2_algstr_0(A)) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l2_algstr_0(B)) ) ) )  &  (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) ) ) )  =>  (! [D, E, F] :  (g1_grcat_1(A, B, C)=g1_grcat_1(D, E, F) =>  (A=D &  (B=E & C=F) ) ) ) ) ) ).
fof(free_g2_algstr_0, axiom,  (! [A, B, C] :  ( ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  & m1_subset_1(C, A))  =>  (! [D, E, F] :  (g2_algstr_0(A, B, C)=g2_algstr_0(D, E, F) =>  (A=D &  (B=E & C=F) ) ) ) ) ) ).
fof(rc1_algstr_1, axiom,  (? [A] :  (l2_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  (v8_algstr_0(A) &  (v4_rlvect_1(A) &  (v1_algstr_1(A) & v4_algstr_1(A)) ) ) ) ) ) ).
fof(rc1_cat_1, axiom,  (? [A] :  (l1_cat_1(A) & v1_cat_1(A)) ) ).
fof(rc1_classes2, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_classes2(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(rc20_struct_0, axiom,  (? [A] :  (l2_struct_0(A) &  ( ~ (v2_struct_0(A))  & v7_struct_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_algstr_1, axiom,  (? [A] :  (l2_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  (v5_algstr_0(A) &  (v6_algstr_0(A) &  (v7_algstr_0(A) &  (v8_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v1_algstr_1(A) &  (v2_algstr_1(A) &  (v3_algstr_1(A) & v4_algstr_1(A)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc2_cat_1, axiom,  (? [A] :  (l1_cat_1(A) &  ( ~ (v2_struct_0(A))  &  ~ (v11_struct_0(A)) ) ) ) ).
fof(rc2_classes2, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  =>  (? [B] :  (m1_subset_1(B, A) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc2_grcat_1, axiom,  (? [A] :  (l1_grcat_1(A) & v1_grcat_1(A)) ) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc3_algstr_1, axiom,  (? [A] :  (l2_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  (v5_algstr_0(A) &  (v6_algstr_0(A) &  (v7_algstr_0(A) &  (v8_algstr_0(A) &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v1_algstr_1(A) &  (v2_algstr_1(A) &  (v3_algstr_1(A) & v4_algstr_1(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc3_grcat_1, axiom,  (? [A] :  (l1_grcat_1(A) &  (v1_grcat_1(A) & v2_grcat_1(A)) ) ) ).
fof(rc4_algstr_0, axiom,  (? [A] :  (l2_algstr_0(A) & v8_algstr_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(rc5_algstr_0, axiom,  (? [A] :  (l2_algstr_0(A) &  (v13_struct_0(A, 1) & v8_algstr_0(A)) ) ) ).
fof(rc5_grcat_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v3_grcat_1(A)) ) ).
fof(rc6_grcat_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v3_grcat_1(A))  =>  (? [B] :  (m1_subset_1(B, A) &  ( ~ (v2_struct_0(B))  &  (v5_algstr_0(B) &  (v6_algstr_0(B) &  (v7_algstr_0(B) &  (v8_algstr_0(B) &  (v13_algstr_0(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v1_algstr_1(B) &  (v2_algstr_1(B) &  (v3_algstr_1(B) & v4_algstr_1(B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc7_grcat_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v4_grcat_1(A)) ) ).
fof(rc8_grcat_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v4_grcat_1(A))  =>  (? [B] :  (m1_subset_1(B, A) &  (v1_grcat_1(B) & v2_grcat_1(B)) ) ) ) ) ).
fof(redefinition_k19_grcat_1, axiom,  (! [A, B] :  ( ( ( ~ (v1_xboole_0(A))  & v3_grcat_1(A))  & m1_subset_1(B, k18_grcat_1(A)))  => k19_grcat_1(A, B)=k7_grcat_1(B)) ) ).
fof(redefinition_k20_grcat_1, axiom,  (! [A, B] :  ( ( ( ~ (v1_xboole_0(A))  & v3_grcat_1(A))  & m1_subset_1(B, k18_grcat_1(A)))  => k20_grcat_1(A, B)=k8_grcat_1(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_m2_grcat_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v3_grcat_1(A))  =>  (! [B] :  (m2_grcat_1(B, A) <=> m1_subset_1(B, A)) ) ) ) ).
fof(redefinition_m3_grcat_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v4_grcat_1(A))  =>  (! [B] :  (m3_grcat_1(B, A) <=> m1_subset_1(B, A)) ) ) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t20_grcat_1, axiom,  (! [A] :  ( (v1_grcat_1(A) &  (v2_grcat_1(A) & l1_grcat_1(A)) )  =>  (! [B] :  ( (v1_grcat_1(B) &  (v2_grcat_1(B) & l1_grcat_1(B)) )  =>  (k7_grcat_1(B)=k8_grcat_1(A) =>  (k7_grcat_1(k13_grcat_1(B, A))=k7_grcat_1(A) & k8_grcat_1(k13_grcat_1(B, A))=k8_grcat_1(B)) ) ) ) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t32_grcat_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v3_grcat_1(A))  =>  (! [B] :  (m3_grcat_1(B, k18_grcat_1(A)) =>  (! [C] :  (m3_grcat_1(C, k18_grcat_1(A)) =>  (k19_grcat_1(A, B)=k20_grcat_1(A, C) => r2_tarski(k13_grcat_1(B, C), k18_grcat_1(A))) ) ) ) ) ) ) ).
fof(t34_grcat_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  =>  (! [B] :  (m1_subset_1(B, u4_struct_0(k25_grcat_1(A))) =>  (! [C] :  (m3_grcat_1(C, k18_grcat_1(k17_grcat_1(A))) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(k25_grcat_1(A))) =>  (! [E] :  (m2_grcat_1(E, k17_grcat_1(A)) =>  ( (v1_grcat_1(B) & m3_grcat_1(B, k18_grcat_1(k17_grcat_1(A))))  &  (m1_subset_1(C, u4_struct_0(k25_grcat_1(A))) &  ( (v8_algstr_0(D) & m2_grcat_1(D, k17_grcat_1(A)))  & m1_subset_1(E, u1_struct_0(k25_grcat_1(A)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t36_grcat_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  =>  (! [B] :  (m1_subset_1(B, u4_struct_0(k25_grcat_1(A))) =>  (! [C] :  (m1_subset_1(C, u4_struct_0(k25_grcat_1(A))) =>  (! [D] :  (m3_grcat_1(D, k18_grcat_1(k17_grcat_1(A))) =>  (! [E] :  (m3_grcat_1(E, k18_grcat_1(k17_grcat_1(A))) =>  ( (B=D & C=E)  =>  ( (k3_graph_1(k25_grcat_1(A), C)=k4_graph_1(k25_grcat_1(A), B) => k19_grcat_1(k17_grcat_1(A), E)=k20_grcat_1(k17_grcat_1(A), D))  &  ( (k19_grcat_1(k17_grcat_1(A), E)=k20_grcat_1(k17_grcat_1(A), D) => k3_graph_1(k25_grcat_1(A), C)=k4_graph_1(k25_grcat_1(A), B))  &  ( (k3_graph_1(k25_grcat_1(A), C)=k4_graph_1(k25_grcat_1(A), B) => r2_hidden(k4_tarski(E, D), k9_xtuple_0(k24_grcat_1(k17_grcat_1(A)))))  &  ( (r2_hidden(k4_tarski(E, D), k9_xtuple_0(k24_grcat_1(k17_grcat_1(A)))) => k3_graph_1(k25_grcat_1(A), C)=k4_graph_1(k25_grcat_1(A), B))  &  ( (k3_graph_1(k25_grcat_1(A), C)=k4_graph_1(k25_grcat_1(A), B) => k1_cat_1(k25_grcat_1(A), B, C)=k13_grcat_1(E, D))  &  ( (k3_graph_1(k25_grcat_1(A), B)=k3_graph_1(k25_grcat_1(A), C) => k19_grcat_1(k17_grcat_1(A), D)=k19_grcat_1(k17_grcat_1(A), E))  &  ( (k19_grcat_1(k17_grcat_1(A), D)=k19_grcat_1(k17_grcat_1(A), E) => k3_graph_1(k25_grcat_1(A), B)=k3_graph_1(k25_grcat_1(A), C))  &  ( (k4_graph_1(k25_grcat_1(A), B)=k4_graph_1(k25_grcat_1(A), C) => k20_grcat_1(k17_grcat_1(A), D)=k20_grcat_1(k17_grcat_1(A), E))  &  (k20_grcat_1(k17_grcat_1(A), D)=k20_grcat_1(k17_grcat_1(A), E) => k4_graph_1(k25_grcat_1(A), B)=k4_graph_1(k25_grcat_1(A), C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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)) ) ) ) ) ).
