Consider the following premises. exists z: W_3(z) <-> W(z). forall z: W_3(z) -> W(z). Can we infer forall z: ~(W_3(z) <-> W(z)) from them?
 From exists z: W_3(z) <-> W(z) we can infer exists z: W(z) -> W_3(z). Finally, from forall z: W_3(z) -> W(z), exists z: W(z) -> W_3(z) we can infer exists z: W_3(z) <-> W(z), which contradicts forall z: ~(W_3(z) <-> W(z)). Therefore, the answer is no.