Consider the following premises. exists x_1: Q_3(x_1). forall x_1: Q_3(x_1) -> Q_1(x_1). forall x_1: Q_1(x_1) -> W(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 forall x_1: Q_3(x_1) -> Q_1(x_1), forall x_1: Q_1(x_1) -> W(x_1) we can infer forall x_1: Q_3(x_1) -> W(x_1) via universal transitivity. Finally, from forall x_1: Q_3(x_1) -> W(x_1), exists x_1: Q_3(x_1) we can infer exists x_1: W(x_1) via existential modus ponens. Therefore, the answer is yes.