Consider the following premises. forall y_3: P(y_3) -> T(y_3). exists y_3: T(y_3) -> P(y_3). forall y_3: ~T(y_3). Can we infer exists y_3: ~P(y_3) from them?
 From exists y_3: T(y_3) -> P(y_3), forall y_3: P(y_3) -> T(y_3) we can infer exists y_3: T(y_3) <-> P(y_3). From exists y_3: T(y_3) <-> P(y_3) we can infer exists y_3: P(y_3) -> T(y_3). Finally, from exists y_3: P(y_3) -> T(y_3), forall y_3: ~T(y_3) we can infer exists y_3: ~P(y_3). Therefore, the answer is yes.