Consider the following premises. p_2 or ~q_11. p or q_11. ~p. Can we infer ~p_2 from them? If possible, name the inference rules being used at each step.
 From p_2 or ~q_11 we can infer q_11 -> p_2 via rewriting. From p or q_11, ~p we can infer q_11 via disjunctive syllogism. Finally, from q_11 -> p_2, q_11 we can infer p_2 via modus ponens, which contradicts ~p_2. Therefore, the answer is no.