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