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