Consider the following premises. p_5 or q_5. ~q_5 or q. q -> q_4. q_7 -> q_4. p -> q_7. ~p_5 or p. Can we infer q_4 from them? If possible, name the inference rules being used at each step.
 From p -> q_7, q_7 -> q_4 we can infer p -> q_4 via transitivity. From p_5 or q_5, ~p_5 or p we can infer q_5 or p via resolution. From q_5 or p, ~q_5 or q we can infer p or q via resolution. Finally, from p -> q_4, q -> q_4, p or q we can infer q_4 via disjunction elimination. Therefore, the answer is yes.