Consider the following premises. u_3 -> u. t <-> u. u_3. Can we infer ~t from them? If possible, name the inference rules being used at each step.
 From t <-> u we can infer u -> t via biconditional elimination. From u_3 -> u, u_3 we can infer u via modus ponens. Finally, from u -> t, u we can infer t via modus ponens, which contradicts ~t. Therefore, the answer is no.