% Mizar problem: t3_cat_7,cat_7,132,7 
fof(t3_cat_7, conjecture,  (! [A] :  ( (v9_cat_6(A) & l1_cat_6(A))  =>  (! [B] :  (m1_subset_1(B, k1_cat_6(A)) =>  (! [C] :  (m1_subset_1(C, k1_cat_6(A)) =>  (! [D] :  (m1_subset_1(D, k1_cat_6(A)) =>  ( (r1_cat_6(A, B, C) &  (r1_cat_6(A, C, D) & v11_cat_6(C, A)) )  => r1_cat_6(A, B, D)) ) ) ) ) ) ) ) ) ).
fof(d11_cat_6, axiom,  (! [A] :  (l1_cat_6(A) =>  (v9_cat_6(A) <=>  (v6_cat_6(A) & v7_cat_6(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(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(d9_cat_6, axiom,  (! [A] :  (l1_cat_6(A) =>  (v7_cat_6(A) <=>  (! [B] :  (m1_subset_1(B, k1_cat_6(A)) =>  (! [C] :  (m1_subset_1(C, k1_cat_6(A)) =>  (! [D] :  (m1_subset_1(D, k1_cat_6(A)) =>  (r1_cat_6(A, C, D) =>  (r1_cat_6(A, B, k2_cat_6(A, C, D)) <=> r1_cat_6(A, B, C)) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_k1_cat_6, 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_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(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)) ) ).
