Consider the following premises. forall x_4: W(x_4) -> ~Q_4(x_4). exists x_4: Q_4(x_4). forall x_4: W(x_4) <-> U(x_4). Can we infer exists x_4: ~U(x_4) from them? If possible, name the inference rules being used at each step.
 From forall x_4: W(x_4) -> ~Q_4(x_4), exists x_4: Q_4(x_4) we can infer exists x_4: ~W(x_4) via existential modus tollens. Finally, from forall x_4: W(x_4) <-> U(x_4), exists x_4: ~W(x_4) we can infer exists x_4: ~U(x_4) via existential biconditional elimination. Therefore, the answer is yes.