Consider the following premises. ~R_7(a_7). s_2 <-> S_7(a_7). forall x_7: R_7(x_7) <-> S_7(x_7). Can we infer s_2 from them? If possible, name the inference rules being used at each step.
 From forall x_7: R_7(x_7) <-> S_7(x_7) we can infer R_7(a_7) <-> S_7(a_7) via universal instantiation. From R_7(a_7) <-> S_7(a_7), ~R_7(a_7) we can infer ~S_7(a_7) via biconditional elimination. Finally, from s_2 <-> S_7(a_7), ~S_7(a_7) we can infer ~s_2 via biconditional elimination, which contradicts s_2. Therefore, the answer is no.