Consider the following premises. q_1 -> t_2. s -> t_2. q_1 -> s. t_2 -> q_1. Can we infer ~(t_2 <-> q_1) from them?
 From q_1 -> s, s -> t_2 we can infer q_1 -> t_2. Finally, from t_2 -> q_1, q_1 -> t_2 we can infer t_2 <-> q_1, which contradicts ~(t_2 <-> q_1). Therefore, the answer is no.