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