Consider the following premises. forall x_7: Q_7(x_7) -> P_3(x_7). exists x_7: P_7(x_7) -> P_3(x_7). forall x_7: P_3(x_7) -> Q(x_7). forall x_7: P_7(x_7) or Q_7(x_7). Can we infer exists x_7: Q(x_7) from them? If possible, name the inference rules being used at each step.
 From exists x_7: P_7(x_7) -> P_3(x_7), forall x_7: Q_7(x_7) -> P_3(x_7), forall x_7: P_7(x_7) or Q_7(x_7) we can infer exists x_7: P_3(x_7) via existential disjunction elimination. Finally, from forall x_7: P_3(x_7) -> Q(x_7), exists x_7: P_3(x_7) we can infer exists x_7: Q(x_7) via existential modus ponens. Therefore, the answer is yes.