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