Consider the following premises. exists y: P(y) -> U(y). forall y: P(y). forall y: W(y). Can we infer forall y: ~(U(y) and W(y)) from them?
 From exists y: P(y) -> U(y), forall y: P(y) we can infer exists y: U(y). Finally, from exists y: U(y), forall y: W(y) we can infer exists y: U(y) and W(y), which contradicts forall y: ~(U(y) and W(y)). Therefore, the answer is no.