Consider the following premises. p_12. p_12 <-> u. Can we infer ~u from them? If possible, name the inference rules being used at each step.
 From p_12 <-> u we can infer p_12 -> u via biconditional elimination. Finally, from p_12 -> u, p_12 we can infer u via modus ponens, which contradicts ~u. Therefore, the answer is no.