% Mizar problem: t45_cat_8,cat_8,2425,7 
fof(t45_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] :  ( (v8_cat_6(C) &  (v9_cat_6(C) &  (v10_cat_6(C) & l1_cat_6(C)) ) )  =>  (! [D] :  ( (v8_cat_6(D) &  (v9_cat_6(D) &  (v10_cat_6(D) & l1_cat_6(D)) ) )  =>  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, u1_struct_0(C), u1_struct_0(A)) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C), u1_struct_0(A))))) )  =>  (! [F] :  ( (v1_funct_1(F) &  (v1_funct_2(F, u1_struct_0(C), u1_struct_0(B)) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C), u1_struct_0(B))))) )  =>  (! [G] :  ( (v1_funct_1(G) &  (v1_funct_2(G, u1_struct_0(D), u1_struct_0(A)) & m1_subset_1(G, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(D), u1_struct_0(A))))) )  =>  (! [H] :  ( (v1_funct_1(H) &  (v1_funct_2(H, u1_struct_0(D), u1_struct_0(B)) & m1_subset_1(H, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(D), u1_struct_0(B))))) )  =>  ( (v16_cat_6(E, C, A) &  (v16_cat_6(F, C, B) &  (v16_cat_6(G, D, A) &  (v16_cat_6(H, D, B) &  (r2_cat_8(A, B, C, E, F) & r2_cat_8(A, B, D, G, H)) ) ) ) )  => r2_cat_6(C, D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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(d17_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] :  ( (v8_cat_6(C) &  (v9_cat_6(C) &  (v10_cat_6(C) & l1_cat_6(C)) ) )  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(C), u1_struct_0(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C), u1_struct_0(A))))) )  =>  (v16_cat_6(D, C, A) =>  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, u1_struct_0(C), u1_struct_0(B)) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C), u1_struct_0(B))))) )  =>  (v16_cat_6(E, C, B) =>  (r2_cat_8(A, B, C, D, E) <=>  (! [F] :  ( (v8_cat_6(F) &  (v9_cat_6(F) &  (v10_cat_6(F) & l1_cat_6(F)) ) )  =>  (! [G] :  ( (v1_funct_1(G) &  (v1_funct_2(G, u1_struct_0(F), u1_struct_0(A)) & m1_subset_1(G, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(F), u1_struct_0(A))))) )  =>  (! [H] :  ( (v1_funct_1(H) &  (v1_funct_2(H, u1_struct_0(F), u1_struct_0(B)) & m1_subset_1(H, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(F), u1_struct_0(B))))) )  =>  ~ ( (v16_cat_6(G, F, A) &  (v16_cat_6(H, F, B) &  (! [I] :  ( (v1_funct_1(I) &  (v1_funct_2(I, u1_struct_0(F), u1_struct_0(C)) & m1_subset_1(I, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(F), u1_struct_0(C))))) )  =>  ~ ( (v16_cat_6(I, F, C) &  (r2_relset_1(u1_struct_0(F), u1_struct_0(A), k11_cat_6(F, C, A, I, D), G) &  (r2_relset_1(u1_struct_0(F), u1_struct_0(B), k11_cat_6(F, C, B, I, E), H) &  (! [J] :  ( (v1_funct_1(J) &  (v1_funct_2(J, u1_struct_0(F), u1_struct_0(C)) & m1_subset_1(J, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(F), u1_struct_0(C))))) )  =>  ( (v16_cat_6(J, F, C) &  (r2_relset_1(u1_struct_0(F), u1_struct_0(A), k11_cat_6(F, C, A, J, D), G) & r2_relset_1(u1_struct_0(F), u1_struct_0(B), k11_cat_6(F, C, B, J, E), H)) )  => r2_relset_1(u1_struct_0(F), u1_struct_0(C), I, J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d28_cat_6, axiom,  (! [A] :  ( (v10_cat_6(A) & l1_cat_6(A))  =>  (! [B] :  ( (v10_cat_6(B) & l1_cat_6(B))  =>  (r2_cat_6(A, 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(B), u1_struct_0(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(A))))) )  &  (v16_cat_6(C, A, B) &  (v16_cat_6(D, B, A) &  (r2_relset_1(u1_struct_0(A), u1_struct_0(A), k11_cat_6(A, B, A, C, D), k12_cat_6(A)) & r2_relset_1(u1_struct_0(B), u1_struct_0(B), k11_cat_6(B, A, B, D, C), k12_cat_6(B))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_k11_cat_6, axiom,  (! [A, B, C, D, E] :  ( ( (v10_cat_6(A) & l1_cat_6(A))  &  ( (v10_cat_6(B) & l1_cat_6(B))  &  ( (v10_cat_6(C) & l1_cat_6(C))  &  ( (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))))) )  &  (v1_funct_1(E) &  (v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C))))) ) ) ) ) )  =>  (v1_funct_1(k11_cat_6(A, B, C, D, E)) &  (v1_funct_2(k11_cat_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)) & m1_subset_1(k11_cat_6(A, B, C, D, E), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(C))))) ) ) ) ).
fof(dt_k12_cat_6, axiom,  (! [A] :  ( (v10_cat_6(A) & l1_cat_6(A))  =>  (v1_funct_1(k12_cat_6(A)) &  (v1_funct_2(k12_cat_6(A), u1_struct_0(A), u1_struct_0(A)) & m1_subset_1(k12_cat_6(A), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A))))) ) ) ) ).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v1_funct_1(k3_struct_0(A)) &  (v1_funct_2(k3_struct_0(A), u1_struct_0(A), u1_struct_0(A)) & m1_subset_1(k3_struct_0(A), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A))))) ) ) ) ).
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(fc2_cat_6, axiom,  (! [A] :  ( (v10_cat_6(A) & l1_cat_6(A))  =>  (v1_funct_1(k3_struct_0(A)) &  (v1_funct_2(k3_struct_0(A), u1_struct_0(A), u1_struct_0(A)) & v16_cat_6(k3_struct_0(A), A, A)) ) ) ) ).
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(redefinition_k12_cat_6, axiom,  (! [A] :  ( (v10_cat_6(A) & l1_cat_6(A))  => k12_cat_6(A)=k3_struct_0(A)) ) ).
fof(redefinition_r2_relset_1, axiom,  (! [A, B, C, D] :  ( (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))  =>  (r2_relset_1(A, B, C, D) <=> C=D) ) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(reflexivity_r2_cat_6, axiom,  (! [A, B] :  ( ( (v10_cat_6(A) & l1_cat_6(A))  &  (v10_cat_6(B) & l1_cat_6(B)) )  => r2_cat_6(A, A)) ) ).
fof(reflexivity_r2_relset_1, axiom,  (! [A, B, C, D] :  ( (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))  => r2_relset_1(A, B, C, C)) ) ).
fof(symmetry_r2_cat_6, axiom,  (! [A, B] :  ( ( (v10_cat_6(A) & l1_cat_6(A))  &  (v10_cat_6(B) & l1_cat_6(B)) )  =>  (r2_cat_6(A, B) => r2_cat_6(B, A)) ) ) ).
fof(symmetry_r2_relset_1, axiom,  (! [A, B, C, D] :  ( (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))))  =>  (r2_relset_1(A, B, C, D) => r2_relset_1(A, B, D, C)) ) ) ).
fof(t10_cat_7, 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] :  ( (v8_cat_6(C) &  (v9_cat_6(C) &  (v10_cat_6(C) & l1_cat_6(C)) ) )  =>  (! [D] :  ( (v8_cat_6(D) &  (v9_cat_6(D) &  (v10_cat_6(D) & l1_cat_6(D)) ) )  =>  (! [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))))) )  =>  (! [F] :  ( (v1_funct_1(F) &  (v1_funct_2(F, u1_struct_0(B), u1_struct_0(C)) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C))))) )  =>  (! [G] :  ( (v1_funct_1(G) &  (v1_funct_2(G, u1_struct_0(C), u1_struct_0(D)) & m1_subset_1(G, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C), u1_struct_0(D))))) )  =>  ( (v16_cat_6(E, A, B) &  (v16_cat_6(F, B, C) & v16_cat_6(G, C, D)) )  => r2_relset_1(u1_struct_0(A), u1_struct_0(D), k11_cat_6(A, C, D, k11_cat_6(A, B, C, E, F), G), k11_cat_6(A, B, D, E, k11_cat_6(B, C, D, F, G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t11_cat_7, 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))))) )  =>  (v16_cat_6(C, A, B) =>  (r2_relset_1(u1_struct_0(A), u1_struct_0(B), k11_cat_6(A, A, B, k12_cat_6(A), C), C) & r2_relset_1(u1_struct_0(A), u1_struct_0(B), k11_cat_6(A, B, B, C, k12_cat_6(B)), C)) ) ) ) ) ) ) ) ).
fof(t35_cat_6, axiom,  (! [A] :  ( (v10_cat_6(A) & l1_cat_6(A))  =>  (! [B] :  ( (v10_cat_6(B) & l1_cat_6(B))  =>  (! [C] :  ( (v10_cat_6(C) & l1_cat_6(C))  =>  (! [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(B), u1_struct_0(C)) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C))))) )  =>  ( (v16_cat_6(D, A, B) & v16_cat_6(E, B, C))  => v16_cat_6(k11_cat_6(A, B, C, D, E), A, C)) ) ) ) ) ) ) ) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
