Consider the following premises. forall y: ~W_3(y). forall y: U(y) <-> Q(y). exists y: Q(y) -> W_3(y). Can we infer exists y: ~U(y) from them?
 From exists y: Q(y) -> W_3(y), forall y: ~W_3(y) we can infer exists y: ~Q(y). Finally, from forall y: U(y) <-> Q(y), exists y: ~Q(y) we can infer exists y: ~U(y). Therefore, the answer is yes.