Consider the following premises. forall z_3: W_1(z_3) <-> Q(z_3). exists z_3: W_1(z_3) -> U(z_3). forall z_3: W_1(z_3) -> Q(z_3). Can we infer forall z_3: ~(Q(z_3) -> U(z_3)) from them?
That contradicts the premises. Therefore the answer is no.