Consider the following premises. u_3 <-> S_10(a_10). forall x_10: R_10(x_10) -> S_10(x_10). ~u_3. Can we infer ~R_10(a_10) from them? If possible, name the inference rules being used at each step.
 From forall x_10: R_10(x_10) -> S_10(x_10) we can infer R_10(a_10) -> S_10(a_10) via universal instantiation. From u_3 <-> S_10(a_10), ~u_3 we can infer ~S_10(a_10) via biconditional elimination. Finally, from R_10(a_10) -> S_10(a_10), ~S_10(a_10) we can infer ~R_10(a_10) via modus tollens. Therefore, the answer is yes.