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