Consider the following premises. u or ~t. p_1 -> r. t or p_1. r -> u. Can we infer u from them? If possible, name the inference rules being used at each step.
 From u or ~t we can infer t -> u via rewriting. From p_1 -> r, r -> u we can infer p_1 -> u via transitivity. Finally, from t -> u, p_1 -> u, t or p_1 we can infer u via disjunction elimination. Therefore, the answer is yes.