Consider the following premises. p_9 -> t. t -> p_9. r -> t. ~p_7 or r. p_7 or p_9. Can we infer ~t from them? If possible, name the inference rules being used at each step.
 From p_9 -> t, t -> p_9 we can infer p_9 <-> t via biconditional introduction. From p_7 or p_9, ~p_7 or r we can infer p_9 or r via resolution. From p_9 <-> t we can infer p_9 -> t via biconditional elimination. Finally, from p_9 -> t, r -> t, p_9 or r we can infer t via disjunction elimination, which contradicts ~t. Therefore, the answer is no.