% Mizar problem: t23_index_1,index_1,1431,5 
fof(t23_index_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] :  (m2_cat_1(C, A, B) =>  (! [D] :  (m5_index_1(D, u1_struct_0(B), u4_struct_0(B), u1_graph_1(B), u2_graph_1(B), u1_cat_1(B), k7_isocat_1(B)) =>  (! [E] :  (m4_index_1(E, u1_struct_0(B), u4_struct_0(B), u1_graph_1(B), u2_graph_1(B), D) => k14_index_1(A, B, B, C, D)=k13_index_1(A, E, k9_cat_1(A, B, E, C, k9_index_1(B, D, E)))) ) ) ) ) ) ) ) ) ) ).
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_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_cat_5, axiom,  (! [A] :  (l1_cat_1(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) & v3_cat_5(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) & v1_cat_5(A)) ) ) ) ) ) ) ) ) ) ).
fof(cc1_funcop_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  ( (v1_relat_1(B) &  (v5_relat_1(B, A) & v1_funct_1(B)) )  =>  (v1_relat_1(B) &  (v1_funct_1(B) & v1_funcop_1(B)) ) ) ) ) ) ).
fof(cc1_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_funct_1(A)) ) ).
fof(cc1_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_relat_1(A)) ) ).
fof(cc1_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C)) ) ) ).
fof(cc1_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v7_struct_0(A)) ) ) ).
fof(cc2_cat_1, axiom,  (! [A] :  (l1_cat_1(A) =>  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & v15_struct_0(A)) )  =>  ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_cat_1(A) & v6_cat_1(A)) ) ) ) ) ) ).
fof(cc2_cat_5, 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) &  (v3_cat_5(A) & l1_cat_1(A)) ) ) ) ) ) ) )  =>  (! [B] :  (m3_cat_2(B, A) => v3_cat_5(B)) ) ) ) ).
fof(cc2_funcop_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funcop_1(A)) ) ) ) ).
fof(cc2_funct_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ) ).
fof(cc2_relat_1, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_relat_1(B)) ) ) ) ).
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_funcop_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_xboole_0(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) ) ) ) ).
fof(cc3_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_funct_1(B)) ) ) ) ).
fof(cc3_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v3_relat_1(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_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) ) ) ) ).
fof(cc4_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v2_relat_1(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_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) )  =>  ( ~ (v1_zfmisc_1(A))  &  (v1_relat_1(A) & v1_funct_1(A)) ) ) ) ).
fof(cc5_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(B)) => v4_relat_1(C, 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_funct_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) ) ) ) ).
fof(cc6_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(B)) => v5_relat_1(C, A)) ) ) ) ).
fof(cc6_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v7_struct_0(A) => v8_struct_0(A)) ) ) ).
fof(cc7_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_funct_1(A)) ) ).
fof(cc7_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  =>  (v1_xboole_0(B) &  (v1_relat_1(B) & v4_relat_1(B, A)) ) ) ) ) ) ).
fof(cc7_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ~ (v7_struct_0(A)) ) ) ) ).
fof(cc8_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, A) =>  (v1_relat_1(B) & v1_funct_1(B)) ) ) ) ) ).
fof(cc8_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_xboole_0(B) &  (v1_relat_1(B) & v5_relat_1(B, A)) ) ) ) ) ) ).
fof(cc8_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v13_struct_0(A, k5_ordinal1)) ) ) ).
fof(cc9_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_funct_1(B)) ) ) ) ).
fof(cc9_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, k5_ordinal1) => v2_struct_0(A)) ) ) ).
fof(d15_index_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) &  (v3_cat_5(B) & l1_cat_1(B)) ) ) ) ) ) ) )  =>  (! [C] :  (m2_cat_1(C, A, B) => k13_index_1(A, B, C)=k4_tarski(k7_cat_1(A, B, C), k12_mcart_1(C))) ) ) ) ) ) ).
fof(d16_index_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] :  (m5_index_1(E, u1_struct_0(C), u4_struct_0(C), u1_graph_1(C), u2_graph_1(C), u1_cat_1(C), k7_isocat_1(C)) =>  (m3_cat_2(k4_cat_5(A, B, D), C) =>  (! [F] :  (m5_index_1(F, u1_struct_0(A), u4_struct_0(A), u1_graph_1(A), u2_graph_1(A), u1_cat_1(A), k7_isocat_1(A)) =>  (F=k14_index_1(A, B, C, D, E) <=>  (! [G] :  (m2_cat_1(G, A, C) =>  (r1_funct_2(u4_struct_0(A), u4_struct_0(C), u4_struct_0(A), u4_struct_0(B), G, D) => F=k13_index_1(A, k10_index_1(C, E), k9_cat_1(A, C, k10_index_1(C, E), G, k9_index_1(C, E, k10_index_1(C, E))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d7_funct_2, axiom,  (! [A] :  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  (! [D] :  ( ~ (v1_xboole_0(D))  =>  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, A, B) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  =>  (! [F] :  ( (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) <=>  (A=C &  (! [G] :  (m1_subset_1(G, A) => k1_funct_1(E, G)=k1_funct_1(F, G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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_index_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)) ) ) ) ) ) )  & m5_index_1(B, u1_struct_0(A), u4_struct_0(A), u1_graph_1(A), u2_graph_1(A), u1_cat_1(A), k7_isocat_1(A)))  =>  (v1_cat_1(k10_index_1(A, B)) & m4_index_1(k10_index_1(A, B), u1_struct_0(A), u4_struct_0(A), u1_graph_1(A), u2_graph_1(A), B)) ) ) ).
fof(dt_k12_mcart_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (v1_relat_1(k12_mcart_1(A)) & v1_funct_1(k12_mcart_1(A))) ) ) ).
fof(dt_k13_index_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) &  (v3_cat_5(B) & l1_cat_1(B)) ) ) ) ) ) ) )  & m2_cat_1(C, A, B)) )  => m5_index_1(k13_index_1(A, B, C), u1_struct_0(A), u4_struct_0(A), u1_graph_1(A), u2_graph_1(A), u1_cat_1(A), k7_isocat_1(A))) ) ).
fof(dt_k14_index_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) & m5_index_1(E, u1_struct_0(C), u4_struct_0(C), u1_graph_1(C), u2_graph_1(C), u1_cat_1(C), k7_isocat_1(C))) ) ) )  => m5_index_1(k14_index_1(A, B, C, D, E), u1_struct_0(A), u4_struct_0(A), u1_graph_1(A), u2_graph_1(A), u1_cat_1(A), k7_isocat_1(A))) ) ).
fof(dt_k1_funct_1, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_relat_1, axiom,  (! [A, B] : v1_relat_1(k3_relat_1(A, B))) ).
fof(dt_k4_cat_5, 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)) )  =>  (v1_cat_1(k4_cat_5(A, B, C)) & m3_cat_2(k4_cat_5(A, B, C), B)) ) ) ).
fof(dt_k4_tarski, axiom, $true).
fof(dt_k5_ordinal1, axiom, $true).
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_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_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_index_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)) ) ) ) ) ) )  &  (m5_index_1(B, u1_struct_0(A), u4_struct_0(A), u1_graph_1(A), u2_graph_1(A), u1_cat_1(A), k7_isocat_1(A)) & m4_index_1(C, u1_struct_0(A), u4_struct_0(A), u1_graph_1(A), u2_graph_1(A), B)) )  => m2_cat_1(k9_index_1(A, B, C), A, 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_index_1, axiom, $true).
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_m3_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] :  (m3_cat_2(B, 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)) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_m3_index_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( (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)))) ) ) ) )  =>  (! [E] :  (m3_index_1(E, A, B, C, D) =>  (v2_index_1(E, A, B) & m1_index_1(E, A, B)) ) ) ) ) ).
fof(dt_m4_index_1, axiom,  (! [A, B, C, D, E] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( (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)))) )  & m3_index_1(E, A, B, C, D)) ) ) )  =>  (! [F] :  (m4_index_1(F, A, B, C, D, E) =>  ( ~ (v2_struct_0(F))  &  ( ~ (v11_struct_0(F))  &  (v2_cat_1(F) &  (v3_cat_1(F) &  (v4_cat_1(F) &  (v5_cat_1(F) &  (v6_cat_1(F) &  (v3_cat_5(F) & l1_cat_1(F)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_m5_index_1, axiom,  (! [A, B, C, D, E, F] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( (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_funct_1(F) &  (v1_funct_2(F, A, B) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) ) ) ) ) )  =>  (! [G] :  (m5_index_1(G, A, B, C, D, E, F) => m3_index_1(G, A, B, C, D)) ) ) ) ).
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_index_1, axiom,  (! [A, B] :  (? [C] : m1_index_1(C, A, B)) ) ).
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_m3_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] : m3_cat_2(B, A)) ) ) ).
fof(existence_m3_index_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( (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)))) ) ) ) )  =>  (? [E] : m3_index_1(E, A, B, C, D)) ) ) ).
fof(existence_m4_index_1, axiom,  (! [A, B, C, D, E] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( (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)))) )  & m3_index_1(E, A, B, C, D)) ) ) )  =>  (? [F] : m4_index_1(F, A, B, C, D, E)) ) ) ).
fof(existence_m5_index_1, axiom,  (! [A, B, C, D, E, F] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( (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_funct_1(F) &  (v1_funct_2(F, A, B) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) ) ) ) ) )  =>  (? [G] : m5_index_1(G, A, B, C, D, E, F)) ) ) ).
fof(fc10_funcop_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  &  (v1_relat_1(B) & v1_funct_1(B)) )  =>  (v1_relat_1(k3_relat_1(B, A)) & v1_funcop_1(k3_relat_1(B, A))) ) ) ).
fof(fc12_relat_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v1_relat_1(B))  =>  (v1_xboole_0(k3_relat_1(A, B)) & v1_relat_1(k3_relat_1(A, B))) ) ) ).
fof(fc13_relat_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v1_relat_1(B))  =>  (v1_xboole_0(k3_relat_1(B, A)) & v1_relat_1(k3_relat_1(B, 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(fc15_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_relat_1(B) & v2_relat_1(B)) )  =>  (v1_relat_1(k3_relat_1(A, B)) & v2_relat_1(k3_relat_1(A, B))) ) ) ).
fof(fc17_funct_1, axiom,  (! [A, B, C] :  ( (v4_funct_1(A) &  (v1_relat_1(C) &  (v5_relat_1(C, A) & v1_funct_1(C)) ) )  =>  (v1_relat_1(k1_funct_1(C, B)) & v1_funct_1(k1_funct_1(C, B))) ) ) ).
fof(fc17_index_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) &  (v3_cat_5(B) & l1_cat_1(B)) ) ) ) ) ) ) )  & m2_cat_1(C, A, 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)) & v1_index_1(k7_cat_1(A, B, C))) ) ) ) ).
fof(fc19_funct_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v3_relat_1(A) & v1_funct_1(A)) )  => v1_xboole_0(k1_funct_1(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(fc1_xtuple_0, axiom,  (! [A, B] : v1_xtuple_0(k4_tarski(A, B))) ).
fof(fc20_struct_0, axiom,  (! [A] :  ( (v15_struct_0(A) & l5_struct_0(A))  => v1_zfmisc_1(u4_struct_0(A))) ) ).
fof(fc21_struct_0, axiom,  (! [A] :  ( ( ~ (v15_struct_0(A))  & l5_struct_0(A))  =>  ~ (v1_zfmisc_1(u4_struct_0(A))) ) ) ).
fof(fc29_relat_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v5_relat_1(B, A))  & v1_relat_1(C))  =>  (v1_relat_1(k3_relat_1(C, B)) & v5_relat_1(k3_relat_1(C, B), A)) ) ) ).
fof(fc2_cat_2, axiom,  (! [A, B, C, D, E] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( (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)))) ) ) ) )  =>  ( ~ (v2_struct_0(g1_cat_1(A, B, C, D, E)))  &  ( ~ (v11_struct_0(g1_cat_1(A, B, C, D, E)))  & v1_cat_1(g1_cat_1(A, B, C, D, E))) ) ) ) ).
fof(fc2_funct_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) & v1_funct_1(B)) )  =>  (v1_relat_1(k3_relat_1(A, B)) & v1_funct_1(k3_relat_1(A, B))) ) ) ).
fof(fc2_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_xboole_0(u1_struct_0(A))) ) ) ).
fof(fc30_relat_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v4_relat_1(B, A))  & v1_relat_1(C))  =>  (v1_relat_1(k3_relat_1(B, C)) & v4_relat_1(k3_relat_1(B, C), A)) ) ) ).
fof(fc3_index_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_index_1(B)) ) )  =>  (v1_relat_1(k3_relat_1(A, B)) & v1_index_1(k3_relat_1(A, B))) ) ) ).
fof(fc6_relat_1, axiom,  (! [A, B] : v1_relat_1(k2_zfmisc_1(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_funct_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v2_funct_1(B)) ) )  =>  (v1_relat_1(k3_relat_1(A, B)) & v2_funct_1(k3_relat_1(A, B))) ) ) ).
fof(fc7_struct_0, axiom,  (! [A] :  ( (v7_struct_0(A) & l1_struct_0(A))  => v1_zfmisc_1(u1_struct_0(A))) ) ).
fof(fc8_struct_0, axiom,  (! [A] :  ( (v8_struct_0(A) & l1_struct_0(A))  => v1_finset_1(u1_struct_0(A))) ) ).
fof(fc9_funcop_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(k1_funct_1(A, B)) & v1_funct_1(k1_funct_1(A, B))) ) ) ).
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(rc1_cat_1, axiom,  (? [A] :  (l1_cat_1(A) & v1_cat_1(A)) ) ).
fof(rc1_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] :  (m3_cat_2(B, A) &  ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  &  (v14_struct_0(B) &  (v1_cat_1(B) &  (v2_cat_1(B) &  (v3_cat_1(B) &  (v4_cat_1(B) &  (v5_cat_1(B) & v6_cat_1(B)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc1_cat_5, 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) & v1_cat_5(A)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc1_funcop_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) ) ) ).
fof(rc1_funct_1, axiom,  (? [A] :  (v1_relat_1(A) & v1_funct_1(A)) ) ).
fof(rc1_relat_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_relat_1(A)) ) ).
fof(rc1_relset_1, axiom,  (! [A, B] :  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_xboole_0(C) &  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc1_xtuple_0, axiom,  (? [A] : v1_xtuple_0(A)) ).
fof(rc21_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc22_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(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_funcop_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  (v3_funct_1(A) &  ~ (v1_xboole_0(A)) ) ) ) ) ).
fof(rc2_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ).
fof(rc2_index_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v1_index_1(A)) ) ) ).
fof(rc2_relat_1, axiom,  (? [A] :  (v1_relat_1(A) & v2_relat_1(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(rc3_cat_5, 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) & v3_cat_5(A)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc3_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) ) ) ).
fof(rc3_relat_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ).
fof(rc4_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_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(rc5_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) ) ) ).
fof(rc6_funct_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) & v1_funct_1(C)) ) ) ) ) ).
fof(rc7_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v4_funct_1(A)) ) ).
fof(rc9_funct_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) & v1_funct_1(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_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_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_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
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(t11_index_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] :  (m5_index_1(B, u1_struct_0(A), u4_struct_0(A), u1_graph_1(A), u2_graph_1(A), u1_cat_1(A), k7_isocat_1(A)) =>  (! [C] :  (m4_index_1(C, u1_struct_0(A), u4_struct_0(A), u1_graph_1(A), u2_graph_1(A), B) =>  (! [D] :  (m4_index_1(D, u1_struct_0(A), u4_struct_0(A), u1_graph_1(A), u2_graph_1(A), B) =>  (r1_funct_2(u4_struct_0(A), u4_struct_0(C), u4_struct_0(A), u4_struct_0(D), k9_index_1(A, B, C), k9_index_1(A, B, D)) & r1_funct_2(u1_struct_0(A), u1_struct_0(C), u1_struct_0(A), u1_struct_0(D), k7_cat_1(A, C, k9_index_1(A, B, C)), k7_cat_1(A, D, k9_index_1(A, B, D)))) ) ) ) ) ) ) ) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t2_index_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) &  (v3_cat_5(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) &  (v3_cat_5(C) & l1_cat_1(C)) ) ) ) ) ) ) )  =>  (! [D] :  (m2_cat_1(D, A, B) =>  (! [E] :  (m2_cat_1(E, A, C) =>  (r1_funct_2(u4_struct_0(A), u4_struct_0(B), u4_struct_0(A), u4_struct_0(C), D, E) => r1_funct_2(u1_struct_0(A), u1_struct_0(B), u1_struct_0(A), u1_struct_0(C), k7_cat_1(A, B, D), k7_cat_1(A, C, E))) ) ) ) ) ) ) ) ) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(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)) ) ) ) ) ).
