Consider the following premises. exists x_7: P_7(x_7) or ~Q_7(x_7). forall x_7: P_2(x_7) or ~P_7(x_7). Can we infer forall x_7: ~(Q_7(x_7) -> P_2(x_7)) from them? If possible, name the inference rules being used at each step.
 From exists x_7: P_7(x_7) or ~Q_7(x_7) we can infer exists x_7: Q_7(x_7) -> P_7(x_7) via existential rewriting. Finally, from forall x_7: P_2(x_7) or ~P_7(x_7) we can infer forall x_7: P_7(x_7) -> P_2(x_7) via universal rewriting, which contradicts forall x_7: ~(Q_7(x_7) -> P_2(x_7)). Therefore, the answer is no.