Consider the following premises. exists x: S_2(x) -> R(x). forall x: R_1(x) or ~W(x). forall x: W_2(x) -> W(x). forall x: R(x) -> W_2(x). Can we infer exists x: S_2(x) -> R_1(x) from them?
 From forall x: R_1(x) or ~W(x) we can infer forall x: W(x) -> R_1(x). From forall x: W_2(x) -> W(x), forall x: W(x) -> R_1(x) we can infer forall x: W_2(x) -> R_1(x). From forall x: R(x) -> W_2(x), forall x: W_2(x) -> R_1(x) we can infer forall x: R(x) -> R_1(x). Finally, from exists x: S_2(x) -> R(x), forall x: R(x) -> R_1(x) we can infer exists x: S_2(x) -> R_1(x). Therefore, the answer is yes.