Consider the following premises. exists z: W_2(z) or ~Q_1(z). forall z: W_2(z) -> Q_1(z). Can we infer forall z: ~(Q_1(z) <-> W_2(z)) from them?
 From exists z: W_2(z) or ~Q_1(z) we can infer exists z: Q_1(z) -> W_2(z). Finally, from exists z: Q_1(z) -> W_2(z), forall z: W_2(z) -> Q_1(z) we can infer exists z: Q_1(z) <-> W_2(z), which contradicts forall z: ~(Q_1(z) <-> W_2(z)). Therefore, the answer is no.