Consider the following premises. forall x_9: P(x_9) -> R_5(x_9). forall x_9: R_1(x_9) -> T(x_9). forall x_9: T(x_9) -> R_5(x_9). forall x_9: R_1(x_9). Can we infer R_5(a) from them? If possible, name the inference rules being used at each step.
 From forall x_9: R_1(x_9) we can infer forall x_9: R_1(x_9) or P(x_9) via universal addition. From forall x_9: R_1(x_9) -> T(x_9), forall x_9: T(x_9) -> R_5(x_9) we can infer forall x_9: R_1(x_9) -> R_5(x_9) via universal transitivity. From forall x_9: R_1(x_9) -> R_5(x_9), forall x_9: P(x_9) -> R_5(x_9), forall x_9: R_1(x_9) or P(x_9) we can infer forall x_9: R_5(x_9) via universal disjunction elimination. Finally, from forall x_9: R_5(x_9) we can infer R_5(a) via universal instantiation. Therefore, the answer is yes.