Consider the following premises. P_9(a_5) or t. forall x_13: ~Q_13(x_13). forall x_13: P_13(x_13) <-> Q_13(x_13). forall x_13: P_9(x_13) <-> P_13(x_13). Can we infer t from them? If possible, name the inference rules being used at each step.
 From forall x_13: P_13(x_13) <-> Q_13(x_13), forall x_13: ~Q_13(x_13) we can infer forall x_13: ~P_13(x_13) via universal biconditional elimination. From forall x_13: P_9(x_13) <-> P_13(x_13), forall x_13: ~P_13(x_13) we can infer forall x_13: ~P_9(x_13) via universal biconditional elimination. From forall x_13: ~P_9(x_13) we can infer ~P_9(a_5) via universal instantiation. Finally, from P_9(a_5) or t, ~P_9(a_5) we can infer t via disjunctive syllogism. Therefore, the answer is yes.