Consider the following premises. forall x_9: Q_2(x_9) -> S(x_9). exists x_9: Q(x_9) <-> S(x_9). forall x_9: T(x_9) -> S(x_9). forall x_9: T(x_9) or Q_2(x_9). Can we infer exists x_9: Q(x_9) from them? If possible, name the inference rules being used at each step.
 From forall x_9: T(x_9) -> S(x_9), forall x_9: Q_2(x_9) -> S(x_9), forall x_9: T(x_9) or Q_2(x_9) we can infer forall x_9: S(x_9) via universal disjunction elimination. From exists x_9: Q(x_9) <-> S(x_9) we can infer exists x_9: S(x_9) -> Q(x_9) via existential biconditional elimination. Finally, from exists x_9: S(x_9) -> Q(x_9), forall x_9: S(x_9) we can infer exists x_9: Q(x_9) via existential modus ponens. Therefore, the answer is yes.