Consider the following premises. u_1 <-> u. s_2 <-> u. s_2 or u_1. Can we infer ~u from them? If possible, name the inference rules being used at each step.
 From s_2 <-> u we can infer s_2 -> u via biconditional elimination. From u_1 <-> u we can infer u_1 -> u via biconditional elimination. Finally, from s_2 -> u, u_1 -> u, s_2 or u_1 we can infer u via disjunction elimination, which contradicts ~u. Therefore, the answer is no.