Consider the following premises. forall z: Q(z) or ~S_4(z). forall z: Q(z) -> S_4(z). Can we infer forall z: S_4(z) -> Q(z) from them? If possible, name the inference rules being used at each step.
We can infer forall z: S_4(z) -> Q(z) via the universal rewriting rule. Therefore, the answer is yes.