Consider the following premises. exists x: P_3(x) -> T(x). forall x: T(x) or ~P(x). forall x: P_3(x). Can we infer forall x: ~T(x) from them?
 From forall x: T(x) or ~P(x) we can infer forall x: P(x) -> T(x). From forall x: P_3(x) we can infer forall x: P_3(x) or P(x). Finally, from exists x: P_3(x) -> T(x), forall x: P(x) -> T(x), forall x: P_3(x) or P(x) we can infer exists x: T(x), which contradicts forall x: ~T(x). Therefore, the answer is no.