Consider the following premises. t_3 -> w. w <-> q. q -> t_3. Can we infer ~(w <-> t_3) from them?
 From w <-> q we can infer w -> q. From w -> q, q -> t_3 we can infer w -> t_3. Finally, from w -> t_3, t_3 -> w we can infer w <-> t_3, which contradicts ~(w <-> t_3). Therefore, the answer is no.