% Mizar problem: t5_altcat_3,altcat_3,173,5 
fof(t5_altcat_3, conjecture,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_altcat_1(A) &  (v11_altcat_1(A) &  (v12_altcat_1(A) & l2_altcat_1(A)) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, k1_altcat_1(A, B, C)) =>  (v3_altcat_3(D, A, B, C) =>  (v1_altcat_3(D, A, B, C) & v2_altcat_3(D, A, B, C)) ) ) ) ) ) ) ) ) ) ).
fof(d1_altcat_3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v12_altcat_1(A) & l2_altcat_1(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, k1_altcat_1(A, B, C)) =>  (! [E] :  (m1_subset_1(E, k1_altcat_1(A, C, B)) =>  (r1_altcat_3(A, B, C, D, E) <=> k5_altcat_1(A, C, B, C, E, D)=k8_altcat_1(A, C)) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_k1_altcat_1, axiom, $true).
fof(dt_k1_altcat_3, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_altcat_1(A) &  (v11_altcat_1(A) &  (v12_altcat_1(A) & l2_altcat_1(A)) ) ) )  &  (m1_subset_1(B, u1_struct_0(A)) &  (m1_subset_1(C, u1_struct_0(A)) & m1_subset_1(D, k1_altcat_1(A, B, C))) ) )  => m1_subset_1(k1_altcat_3(A, B, C, D), k1_altcat_1(A, C, B))) ) ).
fof(dt_k5_altcat_1, axiom,  (! [A, B, C, D, E, F] :  ( ( ( ~ (v2_struct_0(A))  & l2_altcat_1(A))  &  (m1_subset_1(B, u1_struct_0(A)) &  (m1_subset_1(C, u1_struct_0(A)) &  (m1_subset_1(D, u1_struct_0(A)) &  (m1_subset_1(E, k1_altcat_1(A, B, C)) & m1_subset_1(F, k1_altcat_1(A, C, D))) ) ) ) )  => m1_subset_1(k5_altcat_1(A, B, C, D, E, F), k1_altcat_1(A, B, D))) ) ).
fof(dt_k8_altcat_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v12_altcat_1(A) & l2_altcat_1(A)) )  & m1_subset_1(B, u1_struct_0(A)))  => m1_subset_1(k8_altcat_1(A, B), k1_altcat_1(A, B, B))) ) ).
fof(dt_l1_altcat_1, axiom,  (! [A] :  (l1_altcat_1(A) => l1_struct_0(A)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_l2_altcat_1, axiom,  (! [A] :  (l2_altcat_1(A) => l1_altcat_1(A)) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_u1_struct_0, axiom, $true).
fof(existence_l1_altcat_1, axiom,  (? [A] : l1_altcat_1(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_l2_altcat_1, axiom,  (? [A] : l2_altcat_1(A)) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
