Consider the following premises. ~p. forall x_7: R_7(x_7) <-> S_7(x_7). R_7(a_7) -> p. Can we infer S_7(a_7) 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) -> p, ~p we can infer ~R_7(a_7) via modus tollens. Finally, from R_7(a_7) <-> S_7(a_7), ~R_7(a_7) we can infer ~S_7(a_7) via biconditional elimination, which contradicts S_7(a_7). Therefore, the answer is no.