Consider the following premises. forall z: P(z) -> T(z). forall z: S(z) or P(z). forall z: P_2(z) -> T(z). forall z: S(z) -> P_2(z). Can we infer forall z: T(z) or U_3(z) from them? If possible, name the inference rules being used at each step.
 From forall z: S(z) -> P_2(z), forall z: P_2(z) -> T(z) we can infer forall z: S(z) -> T(z) via universal transitivity. From forall z: S(z) -> T(z), forall z: P(z) -> T(z), forall z: S(z) or P(z) we can infer forall z: T(z) via universal disjunction elimination. Finally, from forall z: T(z) we can infer forall z: T(z) or U_3(z) via universal addition. Therefore, the answer is yes.