Consider the following premises. forall x_15: Q_15(x_15). u_3 -> ~Q_11(a_9). forall x_15: P_15(x_15) or Q_11(x_15). forall x_15: P_15(x_15) -> ~Q_15(x_15). Can we infer ~u_3 from them? If possible, name the inference rules being used at each step.
 From forall x_15: P_15(x_15) -> ~Q_15(x_15), forall x_15: Q_15(x_15) we can infer forall x_15: ~P_15(x_15) via universal modus tollens. From forall x_15: P_15(x_15) or Q_11(x_15), forall x_15: ~P_15(x_15) we can infer forall x_15: Q_11(x_15) via universal disjunctive syllogism. From forall x_15: Q_11(x_15) we can infer Q_11(a_9) via universal instantiation. Finally, from u_3 -> ~Q_11(a_9), Q_11(a_9) we can infer ~u_3 via modus tollens. Therefore, the answer is yes.