Consider the following premises. forall x_5: Q(x_5) or ~U(x_5). forall x_5: T(x_5) -> Q(x_5). forall x_5: U(x_5). Can we infer forall x_5: Q(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 T(x_5) via universal addition. From forall x_5: Q(x_5) or ~U(x_5) we can infer forall x_5: U(x_5) -> Q(x_5) via universal rewriting. Finally, from forall x_5: U(x_5) -> Q(x_5), forall x_5: T(x_5) -> Q(x_5), forall x_5: U(x_5) or T(x_5) we can infer forall x_5: Q(x_5) via universal disjunction elimination. Therefore, the answer is yes.