Consider the following premises. forall x_5: Q_5(x_5) -> T_2(x_5). exists x_5: Q_1(x_5). forall x_5: U(x_5) -> T_2(x_5). forall x_5: U(x_5). Can we infer exists x_5: Q_1(x_5) and T_2(x_5) from them? If possible, name the inference rules being used at each step.
 From forall x_5: U(x_5) we can infer forall x_5: U(x_5) or Q_5(x_5) via universal addition. From forall x_5: U(x_5) -> T_2(x_5), forall x_5: Q_5(x_5) -> T_2(x_5), forall x_5: U(x_5) or Q_5(x_5) we can infer forall x_5: T_2(x_5) via universal disjunction elimination. Finally, from exists x_5: Q_1(x_5), forall x_5: T_2(x_5) we can infer exists x_5: Q_1(x_5) and T_2(x_5) via existential conjunction. Therefore, the answer is yes.