Consider the following premises. forall x_12: Q_12(x_12) <-> Q_8(x_12). Q_8(a_5) <-> u. forall x_12: ~P_12(x_12). forall x_12: P_12(x_12) <-> Q_12(x_12). 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: Q_12(x_12) <-> Q_8(x_12), forall x_12: ~Q_12(x_12) we can infer forall x_12: ~Q_8(x_12) via universal biconditional elimination. From forall x_12: ~Q_8(x_12) we can infer ~Q_8(a_5) via universal instantiation. Finally, from Q_8(a_5) <-> u, ~Q_8(a_5) we can infer ~u via biconditional elimination. Therefore, the answer is yes.