Consider the following premises. S_12(a_12) -> ~r. r. S_12(a_12) -> R_12(a_12). forall x_12: R_12(x_12) -> S_12(x_12). Can we infer ~R_12(a_12) from them? If possible, name the inference rules being used at each step.
 From forall x_12: R_12(x_12) -> S_12(x_12) we can infer R_12(a_12) -> S_12(a_12) via universal instantiation. From S_12(a_12) -> ~r, r we can infer ~S_12(a_12) via modus tollens. From S_12(a_12) -> R_12(a_12), R_12(a_12) -> S_12(a_12) we can infer S_12(a_12) <-> R_12(a_12) via biconditional introduction. Finally, from S_12(a_12) <-> R_12(a_12), ~S_12(a_12) we can infer ~R_12(a_12) via biconditional elimination. Therefore, the answer is yes.