Consider the following premises. exists y_3: R(y_3) or ~P_2(y_3). forall y_3: W(y_3) or ~R(y_3). forall y_3: W(y_3) -> P_2(y_3). Can we infer exists y_3: P_2(y_3) -> W(y_3) from them? If possible, name the inference rules being used at each step.
 From forall y_3: W(y_3) or ~R(y_3) we can infer forall y_3: R(y_3) -> W(y_3) via universal rewriting. From exists y_3: R(y_3) or ~P_2(y_3) we can infer exists y_3: P_2(y_3) -> R(y_3) via existential rewriting. Finally, from exists y_3: P_2(y_3) -> R(y_3), forall y_3: R(y_3) -> W(y_3) we can infer exists y_3: P_2(y_3) -> W(y_3) via existential transitivity. Therefore, the answer is yes.