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