Consider the following premises. forall x_5: P_5(x_5) or Q_5(x_5). forall x_5: ~P_5(x_5). forall x_5: Q_3(x_5). Can we infer Q_3(a_2) from them? If possible, name the inference rules being used at each step.
 From forall x_5: P_5(x_5) or Q_5(x_5), forall x_5: ~P_5(x_5) we can infer forall x_5: Q_5(x_5) via universal disjunctive syllogism. From forall x_5: Q_5(x_5), forall x_5: Q_3(x_5) we can infer forall x_5: Q_5(x_5) and Q_3(x_5) via universal conjunction. From forall x_5: Q_5(x_5) and Q_3(x_5) we can infer Q_5(a_2) and Q_3(a_2) via universal instantiation. Finally, from Q_5(a_2) and Q_3(a_2) we can infer Q_3(a_2) via simplification. Therefore, the answer is yes.