Consider the following premises. w <-> q_13. u or q_13. u -> w. q. Can we infer ~w from them? If possible, name the inference rules being used at each step.
 From w <-> q_13 we can infer q_13 -> w via biconditional elimination. Finally, from u -> w, q_13 -> w, u or q_13 we can infer w via disjunction elimination, which contradicts ~w. Therefore, the answer is no.