Consider the following premises. w -> r_8. r_8 -> p_8. ~p_5. p_8 -> w. p_5 <-> r_8. Can we infer ~p_8 from them? If possible, name the inference rules being used at each step.
 From p_8 -> w, w -> r_8 we can infer p_8 -> r_8 via transitivity. From p_5 <-> r_8, ~p_5 we can infer ~r_8 via biconditional elimination. From p_8 -> r_8, r_8 -> p_8 we can infer p_8 <-> r_8 via biconditional introduction. Finally, from p_8 <-> r_8, ~r_8 we can infer ~p_8 via biconditional elimination. Therefore, the answer is yes.