Consider the following premises. forall y: P(y) or ~U(y). exists y: W(y) -> U(y). forall y: W(y). Can we infer exists y: P(y) from them?
 From forall y: P(y) or ~U(y) we can infer forall y: U(y) -> P(y). From exists y: W(y) -> U(y), forall y: U(y) -> P(y) we can infer exists y: W(y) -> P(y). Finally, from exists y: W(y) -> P(y), forall y: W(y) we can infer exists y: P(y). Therefore, the answer is yes.