Consider the following premises. forall x_19: ~P_19(x_19) or T_3(x_19). forall x_19: P_19(x_19) or Q_19(x_19). forall x_19: ~Q_10(x_19). exists x_19: Q_19(x_19) -> Q_10(x_19). Can we infer exists x_19: T_3(x_19) or Q(x_19) from them? If possible, name the inference rules being used at each step.
 From forall x_19: P_19(x_19) or Q_19(x_19), forall x_19: ~P_19(x_19) or T_3(x_19) we can infer forall x_19: Q_19(x_19) or T_3(x_19) via universal resolution. From exists x_19: Q_19(x_19) -> Q_10(x_19), forall x_19: ~Q_10(x_19) we can infer exists x_19: ~Q_19(x_19) via existential modus tollens. From forall x_19: Q_19(x_19) or T_3(x_19), exists x_19: ~Q_19(x_19) we can infer exists x_19: T_3(x_19) via existential disjunctive syllogism. Finally, from exists x_19: T_3(x_19) we can infer exists x_19: T_3(x_19) or Q(x_19) via existential addition. Therefore, the answer is yes.