Consider the following premises. q_6 -> w. q -> q_6. q <-> w. Can we infer ~(w <-> q) from them?
 From q -> q_6, q_6 -> w we can infer q -> w. From q <-> w we can infer w -> q. Finally, from w -> q, q -> w we can infer w <-> q, which contradicts ~(w <-> q). Therefore, the answer is no.