Consider the following premises. forall x_13: T_2(x_13) -> Q_13(x_13). forall x_13: ~P_13(x_13). exists x_13: P_13(x_13) <-> Q_13(x_13). Can we infer exists x_13: ~T_2(x_13) from them? If possible, name the inference rules being used at each step.
 From exists x_13: P_13(x_13) <-> Q_13(x_13) we can infer exists x_13: Q_13(x_13) -> P_13(x_13) via existential biconditional elimination. From exists x_13: Q_13(x_13) -> P_13(x_13), forall x_13: ~P_13(x_13) we can infer exists x_13: ~Q_13(x_13) via existential modus tollens. Finally, from forall x_13: T_2(x_13) -> Q_13(x_13), exists x_13: ~Q_13(x_13) we can infer exists x_13: ~T_2(x_13) via existential modus tollens. Therefore, the answer is yes.