Consider the following premises. u -> q_1. q_1 -> t_2. u or w. t_2 <-> w. Can we infer ~t_2 from them?
 From t_2 <-> w we can infer w -> t_2. From u -> q_1, q_1 -> t_2 we can infer u -> t_2. Finally, from u -> t_2, w -> t_2, u or w we can infer t_2, which contradicts ~t_2. Therefore, the answer is no.