Consider the following premises. forall z: S_4(z) -> P_3(z). exists z: P_3(z) -> S_4(z). forall z: S_4(z) or ~P_3(z). Can we infer forall z: ~(P_3(z) -> S_4(z)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.