Consider the following premises. forall x_18: P_18(x_18). forall x_18: Q_18(x_18) -> R_3(x_18). forall x_18: P_18(x_18) <-> R_3(x_18). Can we infer R_3(a_9) or p_2 from them? If possible, name the inference rules being used at each step.
 From forall x_18: P_18(x_18) we can infer forall x_18: P_18(x_18) or Q_18(x_18) via universal addition. From forall x_18: P_18(x_18) <-> R_3(x_18) we can infer forall x_18: P_18(x_18) -> R_3(x_18) via universal biconditional elimination. From forall x_18: P_18(x_18) -> R_3(x_18), forall x_18: Q_18(x_18) -> R_3(x_18), forall x_18: P_18(x_18) or Q_18(x_18) we can infer forall x_18: R_3(x_18) via universal disjunction elimination. From forall x_18: R_3(x_18) we can infer R_3(a_9) via universal instantiation. Finally, from R_3(a_9) we can infer R_3(a_9) or p_2 via addition. Therefore, the answer is yes.