Consider the following premises. exists x_3: W_3(x_3) -> ~Q_3(x_3). forall x_3: Q(x_3) -> W_3(x_3). forall x_3: Q_3(x_3). Can we infer exists x_3: ~Q(x_3) from them? If possible, name the inference rules being used at each step.
 From exists x_3: W_3(x_3) -> ~Q_3(x_3), forall x_3: Q_3(x_3) we can infer exists x_3: ~W_3(x_3) via existential modus tollens. Finally, from forall x_3: Q(x_3) -> W_3(x_3), exists x_3: ~W_3(x_3) we can infer exists x_3: ~Q(x_3) via existential modus tollens. Therefore, the answer is yes.