Consider the following premises. forall x_1: ~Q_1(x_1). forall x_1: T_2(x_1) -> Q_1(x_1). exists x_1: T_2(x_1) or Q(x_1). Can we infer exists x_1: Q(x_1) from them? If possible, name the inference rules being used at each step.
 From forall x_1: T_2(x_1) -> Q_1(x_1), forall x_1: ~Q_1(x_1) we can infer forall x_1: ~T_2(x_1) via universal modus tollens. Finally, from exists x_1: T_2(x_1) or Q(x_1), forall x_1: ~T_2(x_1) we can infer exists x_1: Q(x_1) via existential disjunctive syllogism. Therefore, the answer is yes.