Consider the following premises. q or q_13. ~q. p_13 <-> q_13. Can we infer ~p_13 from them? If possible, name the inference rules being used at each step.
 From p_13 <-> q_13 we can infer q_13 -> p_13 via biconditional elimination. From q or q_13, ~q we can infer q_13 via disjunctive syllogism. Finally, from q_13 -> p_13, q_13 we can infer p_13 via modus ponens, which contradicts ~p_13. Therefore, the answer is no.