Consider the following premises. forall x_5: R(x_5) <-> Q(x_5). forall x_5: ~Q_5(x_5). forall x_5: P_5(x_5) -> Q_5(x_5). forall x_5: R(x_5) -> P_5(x_5). Can we infer forall x_5: ~Q(x_5) from them? If possible, name the inference rules being used at each step.
 From forall x_5: P_5(x_5) -> Q_5(x_5), forall x_5: ~Q_5(x_5) we can infer forall x_5: ~P_5(x_5) via universal modus tollens. From forall x_5: R(x_5) -> P_5(x_5), forall x_5: ~P_5(x_5) we can infer forall x_5: ~R(x_5) via universal modus tollens. Finally, from forall x_5: R(x_5) <-> Q(x_5), forall x_5: ~R(x_5) we can infer forall x_5: ~Q(x_5) via universal biconditional elimination. Therefore, the answer is yes.