Consider the following premises. exists z: S_1(z) -> R(z). forall z: S_1(z) -> T(z). forall z: ~R(z). forall z: T(z) -> S_1(z). Can we infer exists z: ~T(z) from them?
 From exists z: S_1(z) -> R(z), forall z: ~R(z) we can infer exists z: ~S_1(z). From forall z: S_1(z) -> T(z), forall z: T(z) -> S_1(z) we can infer forall z: S_1(z) <-> T(z). Finally, from forall z: S_1(z) <-> T(z), exists z: ~S_1(z) we can infer exists z: ~T(z). Therefore, the answer is yes.