Consider the following premises. forall y: W(y). forall y: W(y) <-> S_3(y). Can we infer exists y: ~S_3(y) from them?
 From forall y: W(y) <-> S_3(y) we can infer forall y: W(y) -> S_3(y). Finally, from forall y: W(y) -> S_3(y), forall y: W(y) we can infer forall y: S_3(y), which contradicts exists y: ~S_3(y). Therefore, the answer is no.