Consider the following premises. forall x_9: Q_1(x_9) -> ~Q(x_9). forall x_9: Q_3(x_9) -> Q(x_9). exists x_9: Q_3(x_9) or Q_9(x_9). forall x_9: Q_9(x_9) -> Q(x_9). Can we infer forall x_9: Q_1(x_9) from them? If possible, name the inference rules being used at each step.
 From forall x_9: Q_3(x_9) -> Q(x_9), forall x_9: Q_9(x_9) -> Q(x_9), exists x_9: Q_3(x_9) or Q_9(x_9) we can infer exists x_9: Q(x_9) via existential disjunction elimination. Finally, from forall x_9: Q_1(x_9) -> ~Q(x_9), exists x_9: Q(x_9) we can infer exists x_9: ~Q_1(x_9) via existential modus tollens, which contradicts forall x_9: Q_1(x_9). Therefore, the answer is no.