Consider the following premises. s or ~s_1. s <-> s_1. Can we infer ~(s_1 <-> s) from them?
 From s or ~s_1 we can infer s_1 -> s. From s <-> s_1 we can infer s -> s_1. Finally, from s_1 -> s, s -> s_1 we can infer s_1 <-> s, which contradicts ~(s_1 <-> s). Therefore, the answer is no.