Consider the following premises. forall x_12: P_12(x_12) -> ~Q_12(x_12). P_12(a_10) <-> t. forall x_12: Q_12(x_12). Can we infer ~t 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: Q_12(x_12) we can infer forall x_12: ~P_12(x_12) via universal modus tollens. From forall x_12: ~P_12(x_12) we can infer ~P_12(a_10) via universal instantiation. From P_12(a_10) <-> t we can infer t -> P_12(a_10) via biconditional elimination. Finally, from t -> P_12(a_10), ~P_12(a_10) we can infer ~t via modus tollens. Therefore, the answer is yes.