Consider the following premises. t_2 -> t. q_8 -> t_2. ~t_2. s_1 <-> t. t -> q_8. Can we infer s_1 from them? If possible, name the inference rules being used at each step.
 From t -> q_8, q_8 -> t_2 we can infer t -> t_2 via transitivity. From t_2 -> t, t -> t_2 we can infer t_2 <-> t via biconditional introduction. From t_2 <-> t, ~t_2 we can infer ~t via biconditional elimination. Finally, from s_1 <-> t, ~t we can infer ~s_1 via biconditional elimination, which contradicts s_1. Therefore, the answer is no.