Consider the following premises. p_5 or ~q_5. ~p_2 or p. p_2 or q_5. p -> p_5. Can we infer ~p_5 from them? If possible, name the inference rules being used at each step.
 From p_5 or ~q_5 we can infer q_5 -> p_5 via rewriting. From p_2 or q_5, ~p_2 or p we can infer q_5 or p via resolution. Finally, from q_5 -> p_5, p -> p_5, q_5 or p we can infer p_5 via disjunction elimination, which contradicts ~p_5. Therefore, the answer is no.