Consider the following premises. w_2 -> w. q_1 or w_2. w or ~q_1. Can we infer w or q from them? If possible, name the inference rules being used at each step.
 From w or ~q_1 we can infer q_1 -> w via rewriting. From q_1 -> w, w_2 -> w, q_1 or w_2 we can infer w via disjunction elimination. Finally, from w we can infer w or q via addition. Therefore, the answer is yes.