Consider the following premises. forall x_1: Q_3(x_1) -> W(x_1). forall x_1: S_1(x_1) -> W(x_1). exists x_1: Q_3(x_1). Can we infer exists x_1: W(x_1) from them? If possible, name the inference rules being used at each step.
 From exists x_1: Q_3(x_1) we can infer exists x_1: Q_3(x_1) or S_1(x_1) via existential addition. Finally, from forall x_1: Q_3(x_1) -> W(x_1), forall x_1: S_1(x_1) -> W(x_1), exists x_1: Q_3(x_1) or S_1(x_1) we can infer exists x_1: W(x_1) via existential disjunction elimination. Therefore, the answer is yes.