Consider the following premises. forall x: Q_4(x) <-> S_1(x). forall x: Q_4(x) or ~P(x). forall x: S_1(x) -> P(x). Can we infer forall x: P(x) -> S_1(x) from them?
 From forall x: Q_4(x) or ~P(x) we can infer forall x: P(x) -> Q_4(x). From forall x: Q_4(x) <-> S_1(x) we can infer forall x: Q_4(x) -> S_1(x). Finally, from forall x: P(x) -> Q_4(x), forall x: Q_4(x) -> S_1(x) we can infer forall x: P(x) -> S_1(x). Therefore, the answer is yes.