Consider the following premises. ~q_4. q_11 -> r. q_4 <-> r. r -> q_11. Can we infer ~q_11 from them?
 From r -> q_11, q_11 -> r we can infer r <-> q_11. From q_4 <-> r we can infer r -> q_4. From r -> q_4, ~q_4 we can infer ~r. Finally, from r <-> q_11, ~r we can infer ~q_11. Therefore, the answer is yes.