Consider the following premises. forall z: Q(z) -> Q_1(z). forall z: Q_1(z) or ~T(z). forall z: Q(z). Can we infer forall z: Q_1(z) from them? If possible, name the inference rules being used at each step.
 From forall z: Q_1(z) or ~T(z) we can infer forall z: T(z) -> Q_1(z) via universal rewriting. From forall z: Q(z) we can infer forall z: Q(z) or T(z) via universal addition. Finally, from forall z: Q(z) -> Q_1(z), forall z: T(z) -> Q_1(z), forall z: Q(z) or T(z) we can infer forall z: Q_1(z) via universal disjunction elimination. Therefore, the answer is yes.