Consider the following premises. u <-> w_3. w_3 -> t_3. t_3 -> u. Can we infer ~(w_3 <-> u) from them?
 From w_3 -> t_3, t_3 -> u we can infer w_3 -> u. From u <-> w_3 we can infer u -> w_3. Finally, from w_3 -> u, u -> w_3 we can infer w_3 <-> u, which contradicts ~(w_3 <-> u). Therefore, the answer is no.