Consider the following premises. forall x: W(x). forall x: U(x) -> ~R_4(x). forall x: W(x) -> R_4(x). Can we infer exists x: U(x) from them?
 From forall x: W(x) -> R_4(x), forall x: W(x) we can infer forall x: R_4(x). Finally, from forall x: U(x) -> ~R_4(x), forall x: R_4(x) we can infer forall x: ~U(x), which contradicts exists x: U(x). Therefore, the answer is no.