Consider the following premises. p_6 -> w. w -> r. s -> p_6. r -> s. Can we infer ~(s <-> p_6) from them?
 From p_6 -> w, w -> r we can infer p_6 -> r. From p_6 -> r, r -> s we can infer p_6 -> s. Finally, from s -> p_6, p_6 -> s we can infer s <-> p_6, which contradicts ~(s <-> p_6). Therefore, the answer is no.