Consider the following premises. Q_4(a_3) -> u. P_4(a_3) -> u. forall x_4: P_4(x_4). Can we infer ~u from them? If possible, name the inference rules being used at each step.
 From forall x_4: P_4(x_4) we can infer forall x_4: P_4(x_4) or Q_4(x_4) via universal addition. From forall x_4: P_4(x_4) or Q_4(x_4) we can infer P_4(a_3) or Q_4(a_3) via universal instantiation. Finally, from P_4(a_3) -> u, Q_4(a_3) -> u, P_4(a_3) or Q_4(a_3) we can infer u via disjunction elimination, which contradicts ~u. Therefore, the answer is no.