Consider the following premises. forall x_9: R_3(x_9) -> Q_9(x_9). forall x_9: Q_9(x_9) -> R_9(x_9). forall x_9: R_3(x_9) and Q_7(x_9). Can we infer R_9(a) from them? If possible, name the inference rules being used at each step.
 From forall x_9: R_3(x_9) -> Q_9(x_9), forall x_9: Q_9(x_9) -> R_9(x_9) we can infer forall x_9: R_3(x_9) -> R_9(x_9) via universal transitivity. From forall x_9: R_3(x_9) and Q_7(x_9) we can infer forall x_9: R_3(x_9) via universal simplification. From forall x_9: R_3(x_9) -> R_9(x_9), forall x_9: R_3(x_9) we can infer forall x_9: R_9(x_9) via universal modus ponens. Finally, from forall x_9: R_9(x_9) we can infer R_9(a) via universal instantiation. Therefore, the answer is yes.