Consider the following premises. forall z_2: P(z_2) -> S(z_2). exists z_2: P(z_2) or ~W_1(z_2). Can we infer forall z_2: ~(W_1(z_2) -> S(z_2)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.