Consider the following premises. forall z: U_1(z) -> T(z). forall z: S_3(z) -> U_1(z). forall z: T(z) -> S_3(z). exists z: ~U_1(z). Can we infer exists z: ~T(z) from them?
 From forall z: T(z) -> S_3(z), forall z: S_3(z) -> U_1(z) we can infer forall z: T(z) -> U_1(z). From forall z: U_1(z) -> T(z), forall z: T(z) -> U_1(z) we can infer forall z: U_1(z) <-> T(z). Finally, from forall z: U_1(z) <-> T(z), exists z: ~U_1(z) we can infer exists z: ~T(z). Therefore, the answer is yes.