Consider the following premises. r_6 -> r. t_2 -> q. q -> u. u -> r_6. Can we infer ~(t_2 -> r) from them? If possible, name the inference rules being used at each step.
 From q -> u, u -> r_6 we can infer q -> r_6 via transitivity. From t_2 -> q, q -> r_6 we can infer t_2 -> r_6 via transitivity. Finally, from t_2 -> r_6, r_6 -> r we can infer t_2 -> r via transitivity, which contradicts ~(t_2 -> r). Therefore, the answer is no.