Consider the following premises. forall x_2: S(x_2) <-> S_2(x_2). ~S(a_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: S(x_2) <-> S_2(x_2) we can infer S(a_2) <-> S_2(a_2) via universal instantiation. Finally, from S(a_2) <-> S_2(a_2), ~S(a_2) we can infer ~S_2(a_2) via biconditional elimination, which contradicts S_2(a_2). Therefore, the answer is no.