Consider the following premises. exists y: P_2(y) or ~T_2(y). forall y: T_2(y) or W(y). forall y: W(y) -> P_2(y). Can we infer forall y: ~(P_2(y) or P(y)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.