Consider the following premises. forall y: S_3(y) or ~S_2(y). forall y: Q(y) -> S_2(y). forall y: S_3(y) -> Q(y). Can we infer forall y: S_3(y) -> S_2(y) from them? If possible, name the inference rules being used at each step.
We can infer forall y: S_3(y) -> S_2(y) via the universal transitivity rule. Therefore, the answer is yes.