Consider the following premises. forall y: W_2(y) <-> P(y). forall y: W_2(y) -> T_2(y). exists y: P(y) -> W_2(y). forall y: T_2(y) -> P(y). Can we infer forall y: ~(W_2(y) <-> P(y)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.