Consider the following premises. exists x_2: P(x_2) or ~P_1(x_2). forall x_2: P(x_2) <-> W(x_2). Can we infer forall x_2: ~(P_1(x_2) -> W(x_2)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.