Consider the following premises. p_6 -> r. r -> q. s_4 -> p_6. q -> s_4. Can we infer ~(p_6 <-> s_4) from them?
 From p_6 -> r, r -> q we can infer p_6 -> q. From p_6 -> q, q -> s_4 we can infer p_6 -> s_4. Finally, from p_6 -> s_4, s_4 -> p_6 we can infer p_6 <-> s_4, which contradicts ~(p_6 <-> s_4). Therefore, the answer is no.