Consider the following premises. forall x_4: T(x_4) -> S(x_4). forall x_4: T(x_4) <-> P(x_4). exists x_4: S(x_4) -> P(x_4). Can we infer forall x_4: ~(T(x_4) -> P(x_4)) from them?
That contradicts the premises. Therefore the answer is no.