Consider the following premises. exists y: S_3(y) -> Q(y). forall y: S_3(y) or ~Q(y). forall y: S_3(y) -> Q(y). Can we infer forall y: ~(Q(y) -> S_3(y)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.