Consider the following premises. forall x_21: Q_21(x_21) -> R_21(x_21). forall x_21: P_21(x_21) or Q_21(x_21). forall x_21: R_21(x_21) <-> Q_16(x_21). forall x_21: P_21(x_21) -> R_21(x_21). Can we infer Q_16(a_9) or p_2 from them? If possible, name the inference rules being used at each step.
 From forall x_21: P_21(x_21) -> R_21(x_21), forall x_21: Q_21(x_21) -> R_21(x_21), forall x_21: P_21(x_21) or Q_21(x_21) we can infer forall x_21: R_21(x_21) via universal disjunction elimination. From forall x_21: R_21(x_21) <-> Q_16(x_21) we can infer forall x_21: R_21(x_21) -> Q_16(x_21) via universal biconditional elimination. From forall x_21: R_21(x_21) -> Q_16(x_21), forall x_21: R_21(x_21) we can infer forall x_21: Q_16(x_21) via universal modus ponens. From forall x_21: Q_16(x_21) we can infer Q_16(a_9) via universal instantiation. Finally, from Q_16(a_9) we can infer Q_16(a_9) or p_2 via addition. Therefore, the answer is yes.