Consider the following premises. p_13 <-> r. p_6 -> p_13. s_1. p_6 or r. Can we infer ~p_13 from them? If possible, name the inference rules being used at each step.
 From p_13 <-> r we can infer r -> p_13 via biconditional elimination. Finally, from p_6 -> p_13, r -> p_13, p_6 or r we can infer p_13 via disjunction elimination, which contradicts ~p_13. Therefore, the answer is no.