Consider the following premises. q -> u. r -> w_4. r. w_4 or ~u. Can we infer w_4 from them? If possible, name the inference rules being used at each step.
 From r we can infer r or q via addition. From w_4 or ~u we can infer u -> w_4 via rewriting. From q -> u, u -> w_4 we can infer q -> w_4 via transitivity. Finally, from r -> w_4, q -> w_4, r or q we can infer w_4 via disjunction elimination. Therefore, the answer is yes.