Consider the following premises. exists z_1: U(z_1) <-> Q(z_1). forall z_1: T(z_1) -> Q(z_1). forall z_1: Q(z_1) -> T(z_1). Can we infer forall z_1: ~(U(z_1) -> T(z_1)) from them?
That contradicts the premises. Therefore the answer is no.