Consider the following premises. forall y: P_2(y) and W(y). forall y: P_2(y) -> S_3(y). Can we infer exists y: ~S_3(y) from them? If possible, name the inference rules being used at each step.
 From forall y: P_2(y) and W(y) we can infer forall y: P_2(y) via universal simplification. Finally, from forall y: P_2(y) -> S_3(y), forall y: P_2(y) we can infer forall y: S_3(y) via universal modus ponens, which contradicts exists y: ~S_3(y). Therefore, the answer is no.