Consider the following premises. forall y: ~W(y). exists y: W(y) -> S_4(y). forall y: S(y) <-> S_4(y). forall y: S(y) -> W(y). Can we infer exists y: ~S(y) from them?
 From forall y: S(y) <-> S_4(y) we can infer forall y: S_4(y) -> S(y). From exists y: W(y) -> S_4(y), forall y: S_4(y) -> S(y) we can infer exists y: W(y) -> S(y). From forall y: S(y) -> W(y), exists y: W(y) -> S(y) we can infer exists y: S(y) <-> W(y). Finally, from exists y: S(y) <-> W(y), forall y: ~W(y) we can infer exists y: ~S(y). Therefore, the answer is yes.