Consider the following premises. exists y: T_3(y) -> P(y). forall y: P(y) -> T_3(y). forall y: T_3(y). Can we infer forall y: ~P(y) from them?
 From exists y: T_3(y) -> P(y), forall y: P(y) -> T_3(y) we can infer exists y: T_3(y) <-> P(y). From exists y: T_3(y) <-> P(y) we can infer exists y: T_3(y) -> P(y). Finally, from exists y: T_3(y) -> P(y), forall y: T_3(y) we can infer exists y: P(y), which contradicts forall y: ~P(y). Therefore, the answer is no.