Consider the following premises. forall x: W_1(x). forall x: S(x) or ~W_1(x). Can we infer exists x: ~(S(x) or U(x)) from them?
 From forall x: S(x) or ~W_1(x) we can infer forall x: W_1(x) -> S(x). From forall x: W_1(x) -> S(x), forall x: W_1(x) we can infer forall x: S(x). Finally, from forall x: S(x) we can infer forall x: S(x) or U(x), which contradicts exists x: ~(S(x) or U(x)). Therefore, the answer is no.