Consider the following premises. ~w. w -> P(a). forall x: T_4(x) -> P(x). P(a) -> w. Can we infer ~T_4(a) from them?
 From forall x: T_4(x) -> P(x) we can infer T_4(a) -> P(a). From P(a) -> w, w -> P(a) we can infer P(a) <-> w. From P(a) <-> w, ~w we can infer ~P(a). Finally, from T_4(a) -> P(a), ~P(a) we can infer ~T_4(a). Therefore, the answer is yes.