Consider the following premises. ~R(a_2). forall x_2: R(x_2) <-> S_2(x_2). Can we infer ~S_2(a_2) from them? If possible, name the inference rules being used at each step.
 From forall x_2: R(x_2) <-> S_2(x_2) we can infer R(a_2) <-> S_2(a_2) via universal instantiation. Finally, from R(a_2) <-> S_2(a_2), ~R(a_2) we can infer ~S_2(a_2) via biconditional elimination. Therefore, the answer is yes.