Consider the following premises. ~u or r. u or q_12. r <-> w. w <-> q_12. Can we infer ~w from them? If possible, name the inference rules being used at each step.
 From u or q_12, ~u or r we can infer q_12 or r via resolution. From r <-> w we can infer r -> w via biconditional elimination. From w <-> q_12 we can infer q_12 -> w via biconditional elimination. Finally, from q_12 -> w, r -> w, q_12 or r we can infer w via disjunction elimination, which contradicts ~w. Therefore, the answer is no.