Consider the following premises. forall z: T(z) -> U_4(z). forall z: T(z) <-> S(z). exists z: ~U_4(z). Can we infer exists z: ~S(z) from them?
 From forall z: T(z) -> U_4(z), exists z: ~U_4(z) we can infer exists z: ~T(z). Finally, from forall z: T(z) <-> S(z), exists z: ~T(z) we can infer exists z: ~S(z). Therefore, the answer is yes.