Consider the following premises. forall x_12: ~P_12(x_12). forall x_12: P_12(x_12) <-> Q_12(x_12). forall x_12: P_6(x_12) -> Q_12(x_12). P_6(a_5) or u. Can we infer u from them? If possible, name the inference rules being used at each step.
 From forall x_12: P_12(x_12) <-> Q_12(x_12), forall x_12: ~P_12(x_12) we can infer forall x_12: ~Q_12(x_12) via universal biconditional elimination. From forall x_12: P_6(x_12) -> Q_12(x_12), forall x_12: ~Q_12(x_12) we can infer forall x_12: ~P_6(x_12) via universal modus tollens. From forall x_12: ~P_6(x_12) we can infer ~P_6(a_5) via universal instantiation. Finally, from P_6(a_5) or u, ~P_6(a_5) we can infer u via disjunctive syllogism. Therefore, the answer is yes.