% Mizar problem: t61_cat_8,cat_8,3484,7 
fof(t61_cat_8, conjecture,  (! [A] :  ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  =>  (! [B] :  ( (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) )  =>  (v16_cat_6(C, A, B) => r3_cat_8(A, B, C, C, C)) ) ) ) ) ) ) ).
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(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(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(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(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(d14_cat_6, axiom,  (! [A] :  (l1_cat_6(A) =>  (! [B] :  (m1_subset_1(B, k1_cat_6(A)) =>  (v11_cat_6(B, A) <=>  (v2_cat_6(B, A) & v3_cat_6(B, A)) ) ) ) ) ) ).
fof(d23_cat_6, axiom,  (! [A] :  ( (v10_cat_6(A) & l1_cat_6(A))  =>  (! [B] :  ( (v10_cat_6(B) & l1_cat_6(B))  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) )  =>  (v14_cat_6(C, A, B) <=>  (! [D] :  (m1_subset_1(D, k1_cat_6(A)) =>  (! [E] :  (m1_subset_1(E, k1_cat_6(A)) =>  (r1_cat_6(A, D, E) =>  (r1_cat_6(B, k9_cat_6(A, B, C, D), k9_cat_6(A, B, C, E)) & k9_cat_6(A, B, C, k2_cat_6(A, D, E))=k2_cat_6(B, k9_cat_6(A, B, C, D), k9_cat_6(A, B, C, E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d24_cat_8, axiom,  (! [A] :  ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  =>  (! [B] :  ( (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) )  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) )  =>  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) )  =>  (r3_cat_8(A, B, C, D, E) <=>  (! [F] :  (m1_subset_1(F, k1_cat_6(A)) =>  (! [G] :  (m1_subset_1(G, k1_cat_6(A)) =>  (r1_cat_6(A, F, G) =>  (r1_cat_6(B, k9_cat_6(A, B, E, F), k9_cat_6(A, B, C, G)) &  (r1_cat_6(B, k9_cat_6(A, B, D, F), k9_cat_6(A, B, E, G)) &  (k9_cat_6(A, B, E, k2_cat_6(A, F, G))=k2_cat_6(B, k9_cat_6(A, B, E, F), k9_cat_6(A, B, C, G)) & k9_cat_6(A, B, E, k2_cat_6(A, F, G))=k2_cat_6(B, k9_cat_6(A, B, D, F), k9_cat_6(A, B, E, G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d25_cat_6, axiom,  (! [A] :  ( (v10_cat_6(A) & l1_cat_6(A))  =>  (! [B] :  ( (v10_cat_6(B) & l1_cat_6(B))  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) )  =>  (v16_cat_6(C, A, B) <=>  (v13_cat_6(C, A, B) & v14_cat_6(C, A, B)) ) ) ) ) ) ) ) ).
fof(d4_cat_6, axiom,  (! [A] :  (l1_cat_6(A) =>  (! [B] :  (m1_subset_1(B, k1_cat_6(A)) =>  (v2_cat_6(B, A) <=>  (! [C] :  (m1_subset_1(C, k1_cat_6(A)) =>  (r1_cat_6(A, B, C) => k2_cat_6(A, B, C)=C) ) ) ) ) ) ) ) ).
fof(d5_cat_6, axiom,  (! [A] :  (l1_cat_6(A) =>  (! [B] :  (m1_subset_1(B, k1_cat_6(A)) =>  (v3_cat_6(B, A) <=>  (! [C] :  (m1_subset_1(C, k1_cat_6(A)) =>  (r1_cat_6(A, C, B) => k2_cat_6(A, C, B)=C) ) ) ) ) ) ) ) ).
fof(dt_k1_cat_6, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_cat_6, axiom,  (! [A, B, C] :  ( (l1_cat_6(A) &  (m1_subset_1(B, k1_cat_6(A)) & m1_subset_1(C, k1_cat_6(A))) )  => m1_subset_1(k2_cat_6(A, B, C), k1_cat_6(A))) ) ).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k9_cat_6, axiom,  (! [A, B, C, D] :  ( ( (v10_cat_6(A) & l1_cat_6(A))  &  ( (v10_cat_6(B) & l1_cat_6(B))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) )  & m1_subset_1(D, k1_cat_6(A))) ) )  => m1_subset_1(k9_cat_6(A, B, C, D), k1_cat_6(B))) ) ).
fof(dt_l1_cat_6, axiom,  (! [A] :  (l1_cat_6(A) => l1_struct_0(A)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_u1_struct_0, axiom, $true).
fof(existence_l1_cat_6, axiom,  (? [A] : l1_cat_6(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(rc14_cat_6, axiom,  (! [A, B] :  ( ( (v10_cat_6(A) & l1_cat_6(A))  &  (v10_cat_6(B) & l1_cat_6(B)) )  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B)))) &  (v1_relat_1(C) &  (v4_relat_1(C, u1_struct_0(A)) &  (v5_relat_1(C, u1_struct_0(B)) &  (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v13_cat_6(C, A, B)) ) ) ) ) ) ) ) ) ).
fof(rc1_funct_1, axiom,  (? [A] :  (v1_relat_1(A) & v1_funct_1(A)) ) ).
fof(rc1_funct_2, axiom,  (! [A, B] :  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_funct_2(C, A, B)) ) ) ) ) ) ) ).
fof(rc1_partfun1, axiom,  (! [A, B] :  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) & v1_funct_1(C)) ) ) ) ) ) ).
fof(rc6_cat_6, axiom,  (? [A] :  (l1_cat_6(A) &  ( ~ (v8_cat_6(A))  &  (v9_cat_6(A) & v10_cat_6(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(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t58_cat_8, axiom,  (! [A] :  ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  =>  (! [B] :  ( (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) )  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) )  =>  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) )  =>  ( (v16_cat_6(C, A, B) & v16_cat_6(D, A, B))  =>  (r3_cat_8(A, B, C, D, E) <=>  (! [F] :  (m1_subset_1(F, k1_cat_6(A)) =>  (! [G] :  (m1_subset_1(G, k1_cat_6(A)) =>  (! [H] :  (m1_subset_1(H, k1_cat_6(A)) =>  ( (v11_cat_6(G, A) &  (v11_cat_6(H, A) &  (r1_cat_6(A, G, F) & r1_cat_6(A, F, H)) ) )  =>  (r1_cat_6(B, k9_cat_6(A, B, E, G), k9_cat_6(A, B, C, F)) &  (r1_cat_6(B, k9_cat_6(A, B, D, F), k9_cat_6(A, B, E, H)) &  (k9_cat_6(A, B, E, F)=k2_cat_6(B, k9_cat_6(A, B, E, G), k9_cat_6(A, B, C, F)) & k9_cat_6(A, B, E, F)=k2_cat_6(B, k9_cat_6(A, B, D, F), k9_cat_6(A, B, E, H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
