Consider the following premises. forall z: Q_1(z) or ~W(z). exists z: W(z) or ~Q_1(z). Can we infer forall z: ~(Q_1(z) -> W(z)) from them?
 From exists z: W(z) or ~Q_1(z) we can infer exists z: Q_1(z) -> W(z). Finally, from forall z: Q_1(z) or ~W(z) we can infer forall z: W(z) -> Q_1(z), which contradicts forall z: ~(Q_1(z) -> W(z)). Therefore, the answer is no.