Consider the following premises. q <-> t_4. p_2 or ~t_4. Can we infer ~(q -> p_2) from them?
 From q <-> t_4 we can infer q -> t_4. From p_2 or ~t_4 we can infer t_4 -> p_2. Finally, from q -> t_4, t_4 -> p_2 we can infer q -> p_2, which contradicts ~(q -> p_2). Therefore, the answer is no.