Consider the following premises. r_2 or ~p_4. p -> ~r_2. p_6 -> r_2. p_6 or p_4. Can we infer ~p from them? If possible, name the inference rules being used at each step.
 From r_2 or ~p_4 we can infer p_4 -> r_2 via rewriting. From p_6 -> r_2, p_4 -> r_2, p_6 or p_4 we can infer r_2 via disjunction elimination. Finally, from p -> ~r_2, r_2 we can infer ~p via modus tollens. Therefore, the answer is yes.