Consider the following premises. forall x_5: R(x_5) -> S_5(x_5). forall x_9: R(x_9) and P(x_9). Can we infer S_5(a_6) from them? If possible, name the inference rules being used at each step.
 From forall x_9: R(x_9) and P(x_9) we can infer forall x_9: R(x_9) via universal simplification. From forall x_9: R(x_9) we can infer R(a_6) via universal instantiation. From forall x_5: R(x_5) -> S_5(x_5) we can infer R(a_6) -> S_5(a_6) via universal instantiation. Finally, from R(a_6) -> S_5(a_6), R(a_6) we can infer S_5(a_6) via modus ponens. Therefore, the answer is yes.