Consider the following premises. forall x_11: R_11(x_11) -> R_9(x_11). forall x_11: R_9(x_11) -> Q(x_11). forall x_11: Q_11(x_11) -> R_9(x_11). exists x_11: P_11(x_11) or Q_11(x_11). forall x_11: ~P_11(x_11) or R_11(x_11). Can we infer exists x_11: Q(x_11) from them? If possible, name the inference rules being used at each step.
 From exists x_11: P_11(x_11) or Q_11(x_11), forall x_11: ~P_11(x_11) or R_11(x_11) we can infer exists x_11: Q_11(x_11) or R_11(x_11) via existential resolution. From forall x_11: Q_11(x_11) -> R_9(x_11), forall x_11: R_11(x_11) -> R_9(x_11), exists x_11: Q_11(x_11) or R_11(x_11) we can infer exists x_11: R_9(x_11) via existential disjunction elimination. Finally, from forall x_11: R_9(x_11) -> Q(x_11), exists x_11: R_9(x_11) we can infer exists x_11: Q(x_11) via existential modus ponens. Therefore, the answer is yes.