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