Consider the following premises. ~r_8. u <-> p_8. w -> r_8. r_8 -> p_8. p_8 -> w. Can we infer u 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 r_8 -> p_8, p_8 -> r_8 we can infer r_8 <-> p_8 via biconditional introduction. From r_8 <-> p_8, ~r_8 we can infer ~p_8 via biconditional elimination. Finally, from u <-> p_8, ~p_8 we can infer ~u via biconditional elimination, which contradicts u. Therefore, the answer is no.