Consider the following premises. forall x_5: U(x_5) and Q_5(x_5). exists x_5: ~U(x_5) or R(x_5). Can we infer exists x_5: Q_1(x_5) or R(x_5) from them? If possible, name the inference rules being used at each step.
 From forall x_5: U(x_5) and Q_5(x_5) we can infer forall x_5: U(x_5) via universal simplification. From forall x_5: U(x_5) we can infer forall x_5: U(x_5) or Q_1(x_5) via universal addition. Finally, from forall x_5: U(x_5) or Q_1(x_5), exists x_5: ~U(x_5) or R(x_5) we can infer exists x_5: Q_1(x_5) or R(x_5) via existential resolution. Therefore, the answer is yes.