Consider the following premises. Q_2(a_3) -> u_4. forall y: P_2(y) -> Q_2(y). ~u_4. Can we infer P_2(a_3) from them? If possible, name the inference rules being used at each step.
 From forall y: P_2(y) -> Q_2(y) we can infer P_2(a_3) -> Q_2(a_3) via universal instantiation. From Q_2(a_3) -> u_4, ~u_4 we can infer ~Q_2(a_3) via modus tollens. Finally, from P_2(a_3) -> Q_2(a_3), ~Q_2(a_3) we can infer ~P_2(a_3) via modus tollens, which contradicts P_2(a_3). Therefore, the answer is no.