Consider the following premises. forall x_9: Q_7(x_9). forall x_9: ~P_9(x_9). forall x_9: ~W(x_9) or R(x_9). forall x_9: P_9(x_9) or W(x_9). Can we infer forall x_9: U(x_9) or R(x_9) from them? If possible, name the inference rules being used at each step.
 From forall x_9: P_9(x_9) or W(x_9), forall x_9: ~P_9(x_9) we can infer forall x_9: W(x_9) via universal disjunctive syllogism. From forall x_9: W(x_9), forall x_9: Q_7(x_9) we can infer forall x_9: W(x_9) and Q_7(x_9) via universal conjunction. From forall x_9: W(x_9) and Q_7(x_9) we can infer forall x_9: W(x_9) via universal simplification. From forall x_9: W(x_9) we can infer forall x_9: W(x_9) or U(x_9) via universal addition. Finally, from forall x_9: W(x_9) or U(x_9), forall x_9: ~W(x_9) or R(x_9) we can infer forall x_9: U(x_9) or R(x_9) via universal resolution. Therefore, the answer is yes.