Consider the following premises. forall z_1: Q(z_1) or ~U(z_1). exists z_1: U(z_1) <-> Q(z_1). Can we infer forall z_1: ~(U(z_1) -> Q(z_1)) from them?
 From exists z_1: U(z_1) <-> Q(z_1) we can infer exists z_1: Q(z_1) -> U(z_1). Finally, from forall z_1: Q(z_1) or ~U(z_1) we can infer forall z_1: U(z_1) -> Q(z_1), which contradicts forall z_1: ~(U(z_1) -> Q(z_1)). Therefore, the answer is no.