Consider the following premises. forall x_2: T_4(x_2) -> Q_2(x_2). forall x_2: Q(x_2) -> R_2(x_2). exists x_2: Q_2(x_2) -> R_2(x_2). forall x_2: T_4(x_2) or Q(x_2). Can we infer exists x_2: R_2(x_2) from them? If possible, name the inference rules being used at each step.
 From forall x_2: T_4(x_2) -> Q_2(x_2), exists x_2: Q_2(x_2) -> R_2(x_2) we can infer exists x_2: T_4(x_2) -> R_2(x_2) via existential transitivity. Finally, from exists x_2: T_4(x_2) -> R_2(x_2), forall x_2: Q(x_2) -> R_2(x_2), forall x_2: T_4(x_2) or Q(x_2) we can infer exists x_2: R_2(x_2) via existential disjunction elimination. Therefore, the answer is yes.