Consider the following premises. forall x: ~P(x). forall x: T_1(x) or W_4(x). forall x: W_4(x) -> P(x). forall x: ~T_1(x) or Q(x). forall x: P(x) -> W_4(x). Can we infer forall x: ~P(x) from them? If possible, name the inference rules being used at each step.
That is one of the premises. Therefore, the answer is yes.