Consider the following premises. r_11 -> p. u -> q_11. t -> u. p -> r_1. q_11 -> r_11. Can we infer ~(t -> r_1) from them? If possible, name the inference rules being used at each step.
 From u -> q_11, q_11 -> r_11 we can infer u -> r_11 via transitivity. From t -> u, u -> r_11 we can infer t -> r_11 via transitivity. From r_11 -> p, p -> r_1 we can infer r_11 -> r_1 via transitivity. Finally, from t -> r_11, r_11 -> r_1 we can infer t -> r_1 via transitivity, which contradicts ~(t -> r_1). Therefore, the answer is no.