Consider the following premises. p -> p_1. p_1 -> t. t -> t_2. Can we infer ~(p -> t_2) from them? If possible, name the inference rules being used at each step.
 From p_1 -> t, t -> t_2 we can infer p_1 -> t_2 via transitivity. Finally, from p -> p_1, p_1 -> t_2 we can infer p -> t_2 via transitivity, which contradicts ~(p -> t_2). Therefore, the answer is no.