Consider the following premises. ~u. u. Can we infer q_4 from them? If possible, name the inference rules being used at each step.
 From u we can infer u or q_4 via addition. Finally, from u or q_4, ~u we can infer q_4 via disjunctive syllogism. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.