Consider the following premises. forall y_4: W(y_4) or ~S_3(y_4). exists y_4: S_3(y_4) and P(y_4). Can we infer exists y_4: W(y_4) from them?
 From forall y_4: W(y_4) or ~S_3(y_4) we can infer forall y_4: S_3(y_4) -> W(y_4). From exists y_4: S_3(y_4) and P(y_4) we can infer exists y_4: S_3(y_4). Finally, from forall y_4: S_3(y_4) -> W(y_4), exists y_4: S_3(y_4) we can infer exists y_4: W(y_4). Therefore, the answer is yes.