Consider the following premises. ~p. p <-> q_12. ~q_12 <-> s_2. Can we infer ~s_2 from them? If possible, name the inference rules being used at each step.
 From p <-> q_12, ~p we can infer ~q_12 via biconditional elimination. From ~q_12 <-> s_2 we can infer ~q_12 -> s_2 via biconditional elimination. Finally, from ~q_12 -> s_2, ~q_12 we can infer s_2 via modus ponens, which contradicts ~s_2. Therefore, the answer is no.