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