Consider the following premises. exists z: U(z). forall z: T(z). forall z: U(z) -> W(z). Can we infer exists z: W(z) and T(z) from them?
 From forall z: U(z) -> W(z), exists z: U(z) we can infer exists z: W(z). Finally, from exists z: W(z), forall z: T(z) we can infer exists z: W(z) and T(z). Therefore, the answer is yes.