Consider the following premises. forall x: Q_4(x) <-> W(x). forall x: W(x) -> Q_4(x). forall x: Q_4(x). exists x: ~W(x). Can we infer forall x: ~P_2(x) from them? If possible, name the inference rules being used at each step.
The premises are contradictory and we can infer anything from them. Therefore, the answer is yes.