Consider the following premises. forall x_15: R_15(x_15) -> S_15(x_15). R_15(a_15) <-> q_9. ~S_15(a_15). Can we infer q_9 from them? If possible, name the inference rules being used at each step.
 From forall x_15: R_15(x_15) -> S_15(x_15) we can infer R_15(a_15) -> S_15(a_15) via universal instantiation. From R_15(a_15) <-> q_9 we can infer q_9 -> R_15(a_15) via biconditional elimination. From R_15(a_15) -> S_15(a_15), ~S_15(a_15) we can infer ~R_15(a_15) via modus tollens. Finally, from q_9 -> R_15(a_15), ~R_15(a_15) we can infer ~q_9 via modus tollens, which contradicts q_9. Therefore, the answer is no.