Consider the following premises. forall x_13: P_13(x_13) or Q_13(x_13). forall x_13: T_1(x_13) <-> Q(x_13). exists x_13: ~P_13(x_13). forall x_13: Q(x_13) -> ~Q_13(x_13). Can we infer exists x_13: ~T_1(x_13) from them? If possible, name the inference rules being used at each step.
 From forall x_13: P_13(x_13) or Q_13(x_13), exists x_13: ~P_13(x_13) we can infer exists x_13: Q_13(x_13) via existential disjunctive syllogism. From forall x_13: Q(x_13) -> ~Q_13(x_13), exists x_13: Q_13(x_13) we can infer exists x_13: ~Q(x_13) via existential modus tollens. Finally, from forall x_13: T_1(x_13) <-> Q(x_13), exists x_13: ~Q(x_13) we can infer exists x_13: ~T_1(x_13) via existential biconditional elimination. Therefore, the answer is yes.