Consider the following premises. q <-> q_8. q_8 -> w. q or ~w. Can we infer ~(q <-> w) from them?
 From q or ~w we can infer w -> q. From q <-> q_8 we can infer q -> q_8. From q -> q_8, q_8 -> w we can infer q -> w. Finally, from q -> w, w -> q we can infer q <-> w, which contradicts ~(q <-> w). Therefore, the answer is no.