Consider the following premises. forall x: S_4(x) -> W(x). forall x: P_2(x) -> S_4(x). exists x: W(x) -> P_2(x). Can we infer forall x: ~(W(x) -> P_2(x)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.