Consider the following premises. forall x: W_1(x) -> P(x). exists x: T(x) <-> W_1(x). forall x: P(x) <-> T(x). Can we infer forall x: ~(T(x) <-> W_1(x)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.