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