Consider the following premises. exists x: P(x) or ~W(x). forall x: P(x) -> S_2(x). Can we infer exists x: W(x) -> S_2(x) from them? If possible, name the inference rules being used at each step.
 From exists x: P(x) or ~W(x) we can infer exists x: W(x) -> P(x) via existential rewriting. Finally, from exists x: W(x) -> P(x), forall x: P(x) -> S_2(x) we can infer exists x: W(x) -> S_2(x) via existential transitivity. Therefore, the answer is yes.