Consider the following premises. forall y: W(y) -> Q_4(y). forall y: Q_4(y) -> W(y). Can we infer exists y: ~(Q_4(y) -> W(y)) from them?
 From forall y: Q_4(y) -> W(y), forall y: W(y) -> Q_4(y) we can infer forall y: Q_4(y) <-> W(y). Finally, from forall y: Q_4(y) <-> W(y) we can infer forall y: Q_4(y) -> W(y), which contradicts exists y: ~(Q_4(y) -> W(y)). Therefore, the answer is no.