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