Consider the following premises. forall x_5: P_5(x_5) or Q_4(x_5). forall x_5: Q_4(x_5) -> Q(x_5). forall x_5: P_5(x_5) -> Q_5(x_5). forall x_5: Q_5(x_5) -> Q(x_5). forall x_5: U(x_5). Can we infer forall x_5: U(x_5) and Q(x_5) from them? If possible, name the inference rules being used at each step.
 From forall x_5: P_5(x_5) -> Q_5(x_5), forall x_5: Q_5(x_5) -> Q(x_5) we can infer forall x_5: P_5(x_5) -> Q(x_5) via universal transitivity. From forall x_5: P_5(x_5) -> Q(x_5), forall x_5: Q_4(x_5) -> Q(x_5), forall x_5: P_5(x_5) or Q_4(x_5) we can infer forall x_5: Q(x_5) via universal disjunction elimination. Finally, from forall x_5: U(x_5), forall x_5: Q(x_5) we can infer forall x_5: U(x_5) and Q(x_5) via universal conjunction. Therefore, the answer is yes.