Consider the following premises. exists x_9: P(x_9) <-> P_2(x_9). forall x_9: P_2(x_9) or S_2(x_9). forall x_9: ~Q_9(x_9). forall x_9: P(x_9) -> Q_9(x_9). Can we infer exists x_9: S_2(x_9) from them? If possible, name the inference rules being used at each step.
 From forall x_9: P(x_9) -> Q_9(x_9), forall x_9: ~Q_9(x_9) we can infer forall x_9: ~P(x_9) via universal modus tollens. From exists x_9: P(x_9) <-> P_2(x_9), forall x_9: ~P(x_9) we can infer exists x_9: ~P_2(x_9) via existential biconditional elimination. Finally, from forall x_9: P_2(x_9) or S_2(x_9), exists x_9: ~P_2(x_9) we can infer exists x_9: S_2(x_9) via existential disjunctive syllogism. Therefore, the answer is yes.