Consider the following premises. forall x_4: Q(x_4) -> Q_3(x_4). Q_3(a_4) -> Q(a_4). Q(a_4) -> Q_3(a_4). Can we infer ~(Q_3(a_4) <-> Q(a_4)) from them? If possible, name the inference rules being used at each step.
 From forall x_4: Q(x_4) -> Q_3(x_4) we can infer Q(a_4) -> Q_3(a_4) via universal instantiation. Finally, from Q_3(a_4) -> Q(a_4), Q(a_4) -> Q_3(a_4) we can infer Q_3(a_4) <-> Q(a_4) via biconditional introduction, which contradicts ~(Q_3(a_4) <-> Q(a_4)). Therefore, the answer is no.