Consider the following premises. exists x_2: W(x_2) <-> S(x_2). forall x_2: S(x_2) or ~Q_4(x_2). Can we infer forall x_2: ~(Q_4(x_2) -> W(x_2)) from them? If possible, name the inference rules being used at each step.
 From exists x_2: W(x_2) <-> S(x_2) we can infer exists x_2: S(x_2) -> W(x_2) via existential biconditional elimination. Finally, from forall x_2: S(x_2) or ~Q_4(x_2) we can infer forall x_2: Q_4(x_2) -> S(x_2) via universal rewriting, which contradicts forall x_2: ~(Q_4(x_2) -> W(x_2)). Therefore, the answer is no.