Consider the following premises. q_15 or ~R_12(a_12). ~p_15. forall x_12: R_12(x_12) <-> S_12(x_12). p_15 <-> q_15. Can we infer S_12(a_12) from them? If possible, name the inference rules being used at each step.
 From p_15 <-> q_15, ~p_15 we can infer ~q_15 via biconditional elimination. 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 q_15 or ~R_12(a_12) we can infer R_12(a_12) -> q_15 via rewriting. From R_12(a_12) -> q_15, ~q_15 we can infer ~R_12(a_12) via modus tollens. Finally, from R_12(a_12) <-> S_12(a_12), ~R_12(a_12) we can infer ~S_12(a_12) via biconditional elimination, which contradicts S_12(a_12). Therefore, the answer is no.