Consider the following premises. t_2 -> q_11. q_2. q_11 -> t_2. t_2 -> ~q_2. Can we infer ~q_11 from them?
 From t_2 -> q_11, q_11 -> t_2 we can infer t_2 <-> q_11. From t_2 <-> q_11 we can infer q_11 -> t_2. From t_2 -> ~q_2, q_2 we can infer ~t_2. Finally, from q_11 -> t_2, ~t_2 we can infer ~q_11. Therefore, the answer is yes.