Consider the following premises. q_1 -> s. s -> q_1. q_1 -> s. Can we infer ~(s <-> q_1) from them?
 From q_1 -> s, s -> q_1 we can infer q_1 <-> s. From q_1 <-> s we can infer s -> q_1. Finally, from s -> q_1, q_1 -> s we can infer s <-> q_1, which contradicts ~(s <-> q_1). Therefore, the answer is no.