Consider the following premises. p_1 -> q_1. q_1 -> r_1. t_3 -> p_1. Can we infer ~(t_3 -> r_1) from them? If possible, name the inference rules being used at each step.
 From p_1 -> q_1, q_1 -> r_1 we can infer p_1 -> r_1 via transitivity. Finally, from t_3 -> p_1, p_1 -> r_1 we can infer t_3 -> r_1 via transitivity, which contradicts ~(t_3 -> r_1). Therefore, the answer is no.