Consider the following premises. forall y_3: S_2(y_3) -> T(y_3). exists y_3: T(y_3) -> S_2(y_3). forall y_3: S_2(y_3) -> T(y_3). forall y_3: ~S_2(y_3). Can we infer forall y_3: T(y_3) from them?
 From exists y_3: T(y_3) -> S_2(y_3), forall y_3: S_2(y_3) -> T(y_3) we can infer exists y_3: T(y_3) <-> S_2(y_3). From exists y_3: T(y_3) <-> S_2(y_3) we can infer exists y_3: T(y_3) -> S_2(y_3). From exists y_3: T(y_3) -> S_2(y_3), forall y_3: S_2(y_3) -> T(y_3) we can infer exists y_3: T(y_3) <-> S_2(y_3). Finally, from exists y_3: T(y_3) <-> S_2(y_3), forall y_3: ~S_2(y_3) we can infer exists y_3: ~T(y_3), which contradicts forall y_3: T(y_3). Therefore, the answer is no.