Consider the following premises. forall x_10: P_10(x_10) -> Q_10(x_10). u -> P_9(a). forall x_10: ~Q_10(x_10). forall x_10: P_9(x_10) <-> P_10(x_10). Can we infer u from them? If possible, name the inference rules being used at each step.
 From forall x_10: P_10(x_10) -> Q_10(x_10), forall x_10: ~Q_10(x_10) we can infer forall x_10: ~P_10(x_10) via universal modus tollens. From forall x_10: P_9(x_10) <-> P_10(x_10), forall x_10: ~P_10(x_10) we can infer forall x_10: ~P_9(x_10) via universal biconditional elimination. From forall x_10: ~P_9(x_10) we can infer ~P_9(a) via universal instantiation. Finally, from u -> P_9(a), ~P_9(a) we can infer ~u via modus tollens, which contradicts u. Therefore, the answer is no.