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