Consider the following premises. u -> t_1. w -> u. t -> w. ~t_1. Can we infer t from them? If possible, name the inference rules being used at each step.
 From u -> t_1, ~t_1 we can infer ~u via modus tollens. From t -> w, w -> u we can infer t -> u via transitivity. Finally, from t -> u, ~u we can infer ~t via modus tollens, which contradicts t. Therefore, the answer is no.