Consider the following premises. forall x_1: ~Q_3(x_1) or R(x_1). forall x_1: Q_3(x_1). Can we infer forall x_1: U(x_1) or R(x_1) from them? If possible, name the inference rules being used at each step.
 From forall x_1: Q_3(x_1) we can infer forall x_1: Q_3(x_1) or U(x_1) via universal addition. Finally, from forall x_1: Q_3(x_1) or U(x_1), forall x_1: ~Q_3(x_1) or R(x_1) we can infer forall x_1: U(x_1) or R(x_1) via universal resolution. Therefore, the answer is yes.