Consider the following premises. forall x_18: Q_14(x_18) -> Q_18(x_18). forall x_18: P_18(x_18) <-> Q_18(x_18). forall x_18: P_18(x_18). Can we infer Q_18(a_9) or q from them? If possible, name the inference rules being used at each step.
 From forall x_18: P_18(x_18) <-> Q_18(x_18) we can infer forall x_18: P_18(x_18) -> Q_18(x_18) via universal biconditional elimination. From forall x_18: P_18(x_18) we can infer forall x_18: P_18(x_18) or Q_14(x_18) via universal addition. From forall x_18: P_18(x_18) -> Q_18(x_18), forall x_18: Q_14(x_18) -> Q_18(x_18), forall x_18: P_18(x_18) or Q_14(x_18) we can infer forall x_18: Q_18(x_18) via universal disjunction elimination. From forall x_18: Q_18(x_18) we can infer Q_18(a_9) via universal instantiation. Finally, from Q_18(a_9) we can infer Q_18(a_9) or q via addition. Therefore, the answer is yes.