Consider the following premises. forall z_4: P(z_4) -> T(z_4). forall z_4: P(z_4). forall z_4: T(z_4) -> P(z_4). Can we infer ~T(a_9) from them?
 From forall z_4: T(z_4) -> P(z_4), forall z_4: P(z_4) -> T(z_4) we can infer forall z_4: T(z_4) <-> P(z_4). From forall z_4: T(z_4) <-> P(z_4) we can infer forall z_4: P(z_4) -> T(z_4). Finally, from forall z_4: P(z_4) -> T(z_4), forall z_4: P(z_4) we can infer forall z_4: T(z_4), which contradicts ~T(a_9). Therefore, the answer is no.