Consider the following premises. R(a_12) -> S_3(a_12). forall z: R(z) -> S_3(z). S_3(a_12) -> R(a_12). Can we infer R(a_12) <-> S_3(a_12) from them?
 From forall z: R(z) -> S_3(z) we can infer R(a_12) -> S_3(a_12). Finally, from R(a_12) -> S_3(a_12), S_3(a_12) -> R(a_12) we can infer R(a_12) <-> S_3(a_12). Therefore, the answer is yes.