Consider the following premises. forall y_4: S_4(y_4) or ~R(y_4). forall y_4: R(y_4) <-> P_3(y_4). Can we infer forall y_4: P_3(y_4) -> S_4(y_4) from them?
 From forall y_4: R(y_4) <-> P_3(y_4) we can infer forall y_4: P_3(y_4) -> R(y_4). From forall y_4: S_4(y_4) or ~R(y_4) we can infer forall y_4: R(y_4) -> S_4(y_4). Finally, from forall y_4: P_3(y_4) -> R(y_4), forall y_4: R(y_4) -> S_4(y_4) we can infer forall y_4: P_3(y_4) -> S_4(y_4). Therefore, the answer is yes.