Consider the following premises. u <-> q_8. u <-> q_4. Can we infer ~(q_4 -> q_8) from them?
 From u <-> q_8 we can infer u -> q_8. From u <-> q_4 we can infer q_4 -> u. Finally, from q_4 -> u, u -> q_8 we can infer q_4 -> q_8, which contradicts ~(q_4 -> q_8). Therefore, the answer is no.