Consider the following premises. u -> t. p -> t_3. q_3 -> u. q -> q_3. t_3 -> q. Can we infer ~(p -> t) from them? If possible, name the inference rules being used at each step.
 From q_3 -> u, u -> t we can infer q_3 -> t via transitivity. From t_3 -> q, q -> q_3 we can infer t_3 -> q_3 via transitivity. From t_3 -> q_3, q_3 -> t we can infer t_3 -> t via transitivity. Finally, from p -> t_3, t_3 -> t we can infer p -> t via transitivity, which contradicts ~(p -> t). Therefore, the answer is no.