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