Consider the following premises. forall z: P(z) -> T_2(z). exists z: T_2(z) -> S(z). forall z: P(z) or ~S(z). Can we infer exists z: P(z) -> S(z) from them? If possible, name the inference rules being used at each step.
 From forall z: P(z) or ~S(z) we can infer forall z: S(z) -> P(z) via universal rewriting. Finally, from forall z: P(z) -> T_2(z), exists z: T_2(z) -> S(z) we can infer exists z: P(z) -> S(z) via existential transitivity. Therefore, the answer is yes.