Consider the following premises. t -> p_1. ~p_1. p_1 -> t. Can we infer ~t from them?
 From t -> p_1, p_1 -> t we can infer t <-> p_1. From t <-> p_1 we can infer t -> p_1. Finally, from t -> p_1, ~p_1 we can infer ~t. Therefore, the answer is yes.