Consider the following premises. forall z_3: ~T(z_3). exists z_3: T(z_3) <-> R_1(z_3). forall z_3: R_1(z_3) -> T(z_3). Can we infer exists z_3: ~R_1(z_3) from them?
 From exists z_3: T(z_3) <-> R_1(z_3) we can infer exists z_3: T(z_3) -> R_1(z_3). From forall z_3: R_1(z_3) -> T(z_3), exists z_3: T(z_3) -> R_1(z_3) we can infer exists z_3: R_1(z_3) <-> T(z_3). Finally, from exists z_3: R_1(z_3) <-> T(z_3), forall z_3: ~T(z_3) we can infer exists z_3: ~R_1(z_3). Therefore, the answer is yes.