Consider the following premises. forall x_9: ~P_9(x_9) or R_9(x_9). forall x_9: P_3(x_9). forall x_9: ~Q_9(x_9). forall x_9: P_9(x_9) or Q_9(x_9). Can we infer ~R_9(a_2) from them? If possible, name the inference rules being used at each step.
 From forall x_9: P_9(x_9) or Q_9(x_9), forall x_9: ~P_9(x_9) or R_9(x_9) we can infer forall x_9: Q_9(x_9) or R_9(x_9) via universal resolution. Finally, from forall x_9: Q_9(x_9) or R_9(x_9), forall x_9: ~Q_9(x_9) we can infer forall x_9: R_9(x_9) via universal disjunctive syllogism, which contradicts ~R_9(a_2). Therefore, the answer is no.