Consider the following premises. w -> u. q_16 and q_2. u <-> q_16. Can we infer ~u from them? If possible, name the inference rules being used at each step.
 From u <-> q_16 we can infer q_16 -> u via biconditional elimination. From q_16 and q_2 we can infer q_16 via simplification. From q_16 we can infer q_16 or w via addition. Finally, from q_16 -> u, w -> u, q_16 or w we can infer u via disjunction elimination, which contradicts ~u. Therefore, the answer is no.