Consider the following premises. exists x_9: ~R_9(x_9). forall x_9: W(x_9) or U_1(x_9). forall x_9: W(x_9) -> Q_9(x_9). forall x_9: Q_9(x_9) -> R_9(x_9). Can we infer forall x_9: ~U_1(x_9) from them? If possible, name the inference rules being used at each step.
 From forall x_9: W(x_9) -> Q_9(x_9), forall x_9: Q_9(x_9) -> R_9(x_9) we can infer forall x_9: W(x_9) -> R_9(x_9) via universal transitivity. From forall x_9: W(x_9) -> R_9(x_9), exists x_9: ~R_9(x_9) we can infer exists x_9: ~W(x_9) via existential modus tollens. Finally, from forall x_9: W(x_9) or U_1(x_9), exists x_9: ~W(x_9) we can infer exists x_9: U_1(x_9) via existential disjunctive syllogism, which contradicts forall x_9: ~U_1(x_9). Therefore, the answer is no.