Consider the following premises. t_3 or u. p_9 or ~t_3. p_9 <-> u. Can we infer ~p_9 from them? If possible, name the inference rules being used at each step.
 From p_9 <-> u we can infer u -> p_9 via biconditional elimination. From p_9 or ~t_3 we can infer t_3 -> p_9 via rewriting. Finally, from t_3 -> p_9, u -> p_9, t_3 or u we can infer p_9 via disjunction elimination, which contradicts ~p_9. Therefore, the answer is no.