Consider the following premises. exists x_12: ~P_12(x_12) or R_12(x_12). forall x_12: R_9(x_12) -> Q(x_12). forall x_12: R_12(x_12) -> R_9(x_12). forall x_12: P_12(x_12) or Q_12(x_12). forall x_12: Q_12(x_12) -> R_9(x_12). Can we infer forall x_12: ~Q(x_12) from them? If possible, name the inference rules being used at each step.
 From forall x_12: P_12(x_12) or Q_12(x_12), exists x_12: ~P_12(x_12) or R_12(x_12) we can infer exists x_12: Q_12(x_12) or R_12(x_12) via existential resolution. From forall x_12: Q_12(x_12) -> R_9(x_12), forall x_12: R_12(x_12) -> R_9(x_12), exists x_12: Q_12(x_12) or R_12(x_12) we can infer exists x_12: R_9(x_12) via existential disjunction elimination. Finally, from forall x_12: R_9(x_12) -> Q(x_12), exists x_12: R_9(x_12) we can infer exists x_12: Q(x_12) via existential modus ponens, which contradicts forall x_12: ~Q(x_12). Therefore, the answer is no.