Consider the following premises. forall x_10: Q_10(x_10) -> T_2(x_10). exists x_10: P_10(x_10) -> Q_10(x_10). forall x_10: P_10(x_10). Can we infer exists x_10: T_2(x_10) or Q(x_10) from them? If possible, name the inference rules being used at each step.
 From exists x_10: P_10(x_10) -> Q_10(x_10), forall x_10: Q_10(x_10) -> T_2(x_10) we can infer exists x_10: P_10(x_10) -> T_2(x_10) via existential transitivity. From exists x_10: P_10(x_10) -> T_2(x_10), forall x_10: P_10(x_10) we can infer exists x_10: T_2(x_10) via existential modus ponens. Finally, from exists x_10: T_2(x_10) we can infer exists x_10: T_2(x_10) or Q(x_10) via existential addition. Therefore, the answer is yes.