Consider the following premises. forall x_12: R_12(x_12) <-> S_12(x_12). w_4 <-> s. ~R_12(a_12). w_4 -> S_12(a_12). Can we infer ~s 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 R_12(a_12) <-> S_12(a_12), ~R_12(a_12) we can infer ~S_12(a_12) via biconditional elimination. From w_4 -> S_12(a_12), ~S_12(a_12) we can infer ~w_4 via modus tollens. Finally, from w_4 <-> s, ~w_4 we can infer ~s via biconditional elimination. Therefore, the answer is yes.