Consider the following premises. forall y: P(y) -> U_2(y). exists y: Q(y) -> U_2(y). forall y: R(y) or Q(y). forall y: ~R(y) or P_1(y). forall y: P_1(y) -> P(y). Can we infer forall y: ~U_2(y) from them?
 From forall y: P_1(y) -> P(y), forall y: P(y) -> U_2(y) we can infer forall y: P_1(y) -> U_2(y). From forall y: R(y) or Q(y), forall y: ~R(y) or P_1(y) we can infer forall y: Q(y) or P_1(y). Finally, from exists y: Q(y) -> U_2(y), forall y: P_1(y) -> U_2(y), forall y: Q(y) or P_1(y) we can infer exists y: U_2(y), which contradicts forall y: ~U_2(y). Therefore, the answer is no.