Consider the following premises. forall x_9: P_9(x_9) or ~R(x_9). forall x_9: R(x_9) or ~P_9(x_9). Can we infer R(a) -> P_9(a) from them? If possible, name the inference rules being used at each step.
 From forall x_9: P_9(x_9) or ~R(x_9) we can infer forall x_9: R(x_9) -> P_9(x_9) via universal rewriting. From forall x_9: R(x_9) or ~P_9(x_9) we can infer forall x_9: P_9(x_9) -> R(x_9) via universal rewriting. From forall x_9: R(x_9) -> P_9(x_9), forall x_9: P_9(x_9) -> R(x_9) we can infer forall x_9: R(x_9) <-> P_9(x_9) via universal biconditional introduction. From forall x_9: R(x_9) <-> P_9(x_9) we can infer R(a) <-> P_9(a) via universal instantiation. Finally, from R(a) <-> P_9(a) we can infer R(a) -> P_9(a) via biconditional elimination. Therefore, the answer is yes.