Consider the following premises. r_2 or Q_7(a_5). forall x_7: P_7(x_7) or ~Q_7(x_7). r_2 -> P_7(a_5). Can we infer P_7(a_5) from them? If possible, name the inference rules being used at each step.
 From forall x_7: P_7(x_7) or ~Q_7(x_7) we can infer forall x_7: Q_7(x_7) -> P_7(x_7) via universal rewriting. From forall x_7: Q_7(x_7) -> P_7(x_7) we can infer Q_7(a_5) -> P_7(a_5) via universal instantiation. Finally, from r_2 -> P_7(a_5), Q_7(a_5) -> P_7(a_5), r_2 or Q_7(a_5) we can infer P_7(a_5) via disjunction elimination. Therefore, the answer is yes.