Consider the following premises. forall x_7: ~S_2(x_7) or R(x_7). exists x_7: P_7(x_7) or S_2(x_7). forall x_7: ~P_7(x_7). Can we infer exists x_7: Q_1(x_7) or R(x_7) from them? If possible, name the inference rules being used at each step.
 From exists x_7: P_7(x_7) or S_2(x_7), forall x_7: ~P_7(x_7) we can infer exists x_7: S_2(x_7) via existential disjunctive syllogism. From exists x_7: S_2(x_7) we can infer exists x_7: S_2(x_7) or Q_1(x_7) via existential addition. Finally, from exists x_7: S_2(x_7) or Q_1(x_7), forall x_7: ~S_2(x_7) or R(x_7) we can infer exists x_7: Q_1(x_7) or R(x_7) via existential resolution. Therefore, the answer is yes.