Consider the following premises. s_2 -> r. p_4 -> r. r -> p_4. p_4 -> s_2. Can we infer ~(s_2 <-> p_4) from them?
 From p_4 -> r, r -> p_4 we can infer p_4 <-> r. From p_4 <-> r we can infer r -> p_4. From s_2 -> r, r -> p_4 we can infer s_2 -> p_4. Finally, from s_2 -> p_4, p_4 -> s_2 we can infer s_2 <-> p_4, which contradicts ~(s_2 <-> p_4). Therefore, the answer is no.