Consider the following premises. exists y: T_3(y) -> R(y). forall y: R(y) -> T_3(y). forall y: R(y) -> T_3(y). forall y: ~R(y). Can we infer exists y: ~T_3(y) from them?
 From exists y: T_3(y) -> R(y), forall y: R(y) -> T_3(y) we can infer exists y: T_3(y) <-> R(y). From exists y: T_3(y) <-> R(y) we can infer exists y: T_3(y) -> R(y). From exists y: T_3(y) -> R(y), forall y: R(y) -> T_3(y) we can infer exists y: T_3(y) <-> R(y). Finally, from exists y: T_3(y) <-> R(y), forall y: ~R(y) we can infer exists y: ~T_3(y). Therefore, the answer is yes.