Consider the following premises. u -> q. u -> q_1. ~q_11. q_1 -> u. q <-> q_11. Can we infer ~q_1 from them?
 From q <-> q_11, ~q_11 we can infer ~q. From u -> q, ~q we can infer ~u. From u -> q_1, q_1 -> u we can infer u <-> q_1. Finally, from u <-> q_1, ~u we can infer ~q_1. Therefore, the answer is yes.