Consider the following premises. p_1 <-> u. t <-> ~p_1. ~u. Can we infer ~t from them? If possible, name the inference rules being used at each step.
 From p_1 <-> u, ~u we can infer ~p_1 via biconditional elimination. From t <-> ~p_1 we can infer ~p_1 -> t via biconditional elimination. Finally, from ~p_1 -> t, ~p_1 we can infer t via modus ponens, which contradicts ~t. Therefore, the answer is no.