Consider the following premises. forall z: R(z) -> P(z). forall z: P(z) -> S(z). forall z: S(z) -> R(z). Can we infer P(a_2) -> S(a_2) from them? If possible, name the inference rules being used at each step.
 From forall z: S(z) -> R(z), forall z: R(z) -> P(z) we can infer forall z: S(z) -> P(z) via universal transitivity. From forall z: S(z) -> P(z), forall z: P(z) -> S(z) we can infer forall z: S(z) <-> P(z) via universal biconditional introduction. From forall z: S(z) <-> P(z) we can infer S(a_2) <-> P(a_2) via universal instantiation. Finally, from S(a_2) <-> P(a_2) we can infer P(a_2) -> S(a_2) via biconditional elimination. Therefore, the answer is yes.