Consider the following premises. ~Q_5(b) or w. forall x_5: ~P_5(x_5) or R_5(x_5). forall x_5: P_5(x_5) or Q_5(x_5). Can we infer R_5(b) or w 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) or R_5(x_5) we can infer forall x_5: Q_5(x_5) or R_5(x_5) via universal resolution. From forall x_5: Q_5(x_5) or R_5(x_5) we can infer Q_5(b) or R_5(b) via universal instantiation. Finally, from Q_5(b) or R_5(b), ~Q_5(b) or w we can infer R_5(b) or w via resolution. Therefore, the answer is yes.