Consider the following premises. p -> u_2. p_13 or u. ~u or w_2. ~p_13 or t. ~t or p. u_2 or ~w_2. Can we infer ~u_2 from them? If possible, name the inference rules being used at each step.
 From p_13 or u, ~p_13 or t we can infer u or t via resolution. From u or t, ~u or w_2 we can infer t or w_2 via resolution. From u_2 or ~w_2 we can infer w_2 -> u_2 via rewriting. From t or w_2, ~t or p we can infer w_2 or p via resolution. Finally, from w_2 -> u_2, p -> u_2, w_2 or p we can infer u_2 via disjunction elimination, which contradicts ~u_2. Therefore, the answer is no.