Consider the following premises. w_1 <-> q_12. q_12 -> s_1. w_1. Can we infer ~s_1 from them?
 From w_1 <-> q_12 we can infer w_1 -> q_12. From w_1 -> q_12, w_1 we can infer q_12. Finally, from q_12 -> s_1, q_12 we can infer s_1, which contradicts ~s_1. Therefore, the answer is no.