Consider the following premises. forall z: U(z) <-> T(z). forall z: U(z) -> ~W_1(z). forall z: W_1(z). Can we infer exists z: T(z) from them?
 From forall z: U(z) -> ~W_1(z), forall z: W_1(z) we can infer forall z: ~U(z). Finally, from forall z: U(z) <-> T(z), forall z: ~U(z) we can infer forall z: ~T(z), which contradicts exists z: T(z). Therefore, the answer is no.