Consider the following premises. forall x_4: W(x_4) <-> P(x_4). forall x_4: W(x_4) -> T(x_4). exists x_4: T(x_4) -> P(x_4). Can we infer forall x_4: ~(P(x_4) -> W(x_4)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.