Consider the following premises. ~Q(a_3) or t. forall x_7: P_7(x_7) or Q_7(x_7). forall x_7: ~P_7(x_7) or Q(x_7). forall x_7: ~Q_7(x_7) or R_5(x_7). Can we infer R_5(a_3) or t 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), forall x_7: ~P_7(x_7) or Q(x_7) we can infer forall x_7: Q_7(x_7) or Q(x_7) via universal resolution. From forall x_7: Q_7(x_7) or Q(x_7), forall x_7: ~Q_7(x_7) or R_5(x_7) we can infer forall x_7: Q(x_7) or R_5(x_7) via universal resolution. From forall x_7: Q(x_7) or R_5(x_7) we can infer Q(a_3) or R_5(a_3) via universal instantiation. Finally, from Q(a_3) or R_5(a_3), ~Q(a_3) or t we can infer R_5(a_3) or t via resolution. Therefore, the answer is yes.