% Mizar problem: t48_cat_8,cat_8,2617,7 
fof(t48_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)) ) )  => r2_cat_8(A, B, k8_cat_8(A, B), k9_cat_8(A, B), k10_cat_8(A, B))) ) ) ) ).
fof(abstractness_v1_cat_6, axiom,  (! [A] :  (l1_cat_6(A) =>  (v1_cat_6(A) => A=g1_cat_6(u1_struct_0(A), u1_cat_6(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_xtuple_0, axiom,  (! [A] :  (v2_xtuple_0(A) => v1_xtuple_0(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(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(d18_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] :  (v2_xtuple_0(C) =>  (m2_cat_8(C, A, B) <=>  (? [D] :  ( (v1_cat_6(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(D), u1_struct_0(A)) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(D), u1_struct_0(A))))) )  &  (? [F] :  ( (v1_funct_1(F) &  (v1_funct_2(F, u1_struct_0(D), u1_struct_0(B)) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(D), u1_struct_0(B))))) )  &  (C=k3_xtuple_0(D, E, F) &  (v16_cat_6(E, D, A) &  (v16_cat_6(F, D, B) & r2_cat_8(A, B, D, E, F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d19_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)) ) )  => k8_cat_8(A, B)=k4_xtuple_0(o_2_0_cat_8(A, B))) ) ) ) ).
fof(d20_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)) ) )  => k9_cat_8(A, B)=k5_xtuple_0(o_2_0_cat_8(A, B))) ) ) ) ).
fof(d21_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)) ) )  => k10_cat_8(A, B)=k2_xtuple_0(o_2_0_cat_8(A, B))) ) ) ) ).
fof(dt_g1_cat_6, axiom,  (! [A, B] :  ( (v1_funct_1(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A))))  =>  (v1_cat_6(g1_cat_6(A, B)) & l1_cat_6(g1_cat_6(A, B))) ) ) ).
fof(dt_k10_cat_8, axiom,  (! [A, B] :  ( ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  &  (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) ) )  =>  (v1_funct_1(k10_cat_8(A, B)) &  (v1_funct_2(k10_cat_8(A, B), u1_struct_0(k8_cat_8(A, B)), u1_struct_0(B)) & m1_subset_1(k10_cat_8(A, B), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k8_cat_8(A, B)), u1_struct_0(B))))) ) ) ) ).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_xtuple_0, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_xtuple_0, axiom, $true).
fof(dt_k4_xtuple_0, axiom, $true).
fof(dt_k5_xtuple_0, axiom, $true).
fof(dt_k8_cat_8, axiom,  (! [A, B] :  ( ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  &  (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) ) )  =>  (v1_cat_6(k8_cat_8(A, B)) &  (v8_cat_6(k8_cat_8(A, B)) &  (v9_cat_6(k8_cat_8(A, B)) &  (v10_cat_6(k8_cat_8(A, B)) & l1_cat_6(k8_cat_8(A, B))) ) ) ) ) ) ).
fof(dt_k9_cat_8, axiom,  (! [A, B] :  ( ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  &  (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) ) )  =>  (v1_funct_1(k9_cat_8(A, B)) &  (v1_funct_2(k9_cat_8(A, B), u1_struct_0(k8_cat_8(A, B)), u1_struct_0(A)) & m1_subset_1(k9_cat_8(A, B), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k8_cat_8(A, B)), 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_m2_cat_8, axiom,  (! [A, B] :  ( ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  &  (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) ) )  =>  (! [C] :  (m2_cat_8(C, A, B) => v2_xtuple_0(C)) ) ) ) ).
fof(dt_o_2_0_cat_8, axiom,  (! [A, B] :  ( ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  &  (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) ) )  => m2_cat_8(o_2_0_cat_8(A, B), A, B)) ) ).
fof(dt_u1_cat_6, axiom,  (! [A] :  (l1_cat_6(A) =>  (v1_funct_1(u1_cat_6(A)) & m1_subset_1(u1_cat_6(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_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(existence_m2_cat_8, axiom,  (! [A, B] :  ( ( (v8_cat_6(A) &  (v9_cat_6(A) &  (v10_cat_6(A) & l1_cat_6(A)) ) )  &  (v8_cat_6(B) &  (v9_cat_6(B) &  (v10_cat_6(B) & l1_cat_6(B)) ) ) )  =>  (? [C] : m2_cat_8(C, A, B)) ) ) ).
fof(fc2_xtuple_0, axiom,  (! [A, B, C] : v2_xtuple_0(k3_xtuple_0(A, B, C))) ).
fof(free_g1_cat_6, axiom,  (! [A, B] :  ( (v1_funct_1(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A))))  =>  (! [C, D] :  (g1_cat_6(A, B)=g1_cat_6(C, D) =>  (A=C & B=D) ) ) ) ) ).
fof(rc11_cat_6, axiom,  (? [A] :  (l1_cat_6(A) &  (v1_cat_6(A) &  (v8_cat_6(A) &  (v9_cat_6(A) & v10_cat_6(A)) ) ) ) ) ).
fof(rc1_cat_6, axiom,  (? [A] :  (l1_cat_6(A) & v1_cat_6(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(rc1_xtuple_0, axiom,  (? [A] : v1_xtuple_0(A)) ).
fof(rc2_xtuple_0, axiom,  (? [A] : v2_xtuple_0(A)) ).
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(rc9_cat_6, axiom,  (? [A] :  (l1_cat_6(A) &  (v1_cat_6(A) &  (v8_cat_6(A) &  (v9_cat_6(A) & v10_cat_6(A)) ) ) ) ) ).
fof(rd4_xtuple_0, axiom,  (! [A, B, C] : k4_xtuple_0(k3_xtuple_0(A, B, C))=A) ).
fof(rd5_xtuple_0, axiom,  (! [A, B, C] : k5_xtuple_0(k3_xtuple_0(A, B, C))=B) ).
fof(rd6_xtuple_0, axiom,  (! [A, B, C] : k2_xtuple_0(k3_xtuple_0(A, B, C))=C) ).
fof(rd7_xtuple_0, axiom,  (! [A] :  (v2_xtuple_0(A) => k3_xtuple_0(k4_xtuple_0(A), k5_xtuple_0(A), k2_xtuple_0(A))=A) ) ).
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)) ) ) ).
