Consider the following premises. forall x_17: ~P_17(x_17). forall x_17: P_17(x_17) <-> Q_17(x_17). p_2 -> Q_17(a_14). Can we infer ~p_2 or q from them? If possible, name the inference rules being used at each step.
 From forall x_17: P_17(x_17) <-> Q_17(x_17), forall x_17: ~P_17(x_17) we can infer forall x_17: ~Q_17(x_17) via universal biconditional elimination. From forall x_17: ~Q_17(x_17) we can infer ~Q_17(a_14) via universal instantiation. From p_2 -> Q_17(a_14), ~Q_17(a_14) we can infer ~p_2 via modus tollens. Finally, from ~p_2 we can infer ~p_2 or q via addition. Therefore, the answer is yes.