Consider the following premises. forall x_9: Q_9(x_9). forall x_9: Q(x_9) -> Q_5(x_9). forall x_9: Q_5(x_9) -> R_1(x_9). forall x_9: Q(x_9). Can we infer exists x_9: ~R_1(x_9) from them? If possible, name the inference rules being used at each step.
 From forall x_9: Q(x_9), forall x_9: Q_9(x_9) we can infer forall x_9: Q(x_9) and Q_9(x_9) via universal conjunction. From forall x_9: Q(x_9) -> Q_5(x_9), forall x_9: Q_5(x_9) -> R_1(x_9) we can infer forall x_9: Q(x_9) -> R_1(x_9) via universal transitivity. From forall x_9: Q(x_9) and Q_9(x_9) we can infer forall x_9: Q(x_9) via universal simplification. Finally, from forall x_9: Q(x_9) -> R_1(x_9), forall x_9: Q(x_9) we can infer forall x_9: R_1(x_9) via universal modus ponens, which contradicts exists x_9: ~R_1(x_9). Therefore, the answer is no.