Consider the following premises. p_11 -> u. t_4 -> r_2. q_3 -> p_11. u -> r_11. r_11 -> t_4. Can we infer ~(q_3 -> r_2) from them? If possible, name the inference rules being used at each step.
 From p_11 -> u, u -> r_11 we can infer p_11 -> r_11 via transitivity. From q_3 -> p_11, p_11 -> r_11 we can infer q_3 -> r_11 via transitivity. From r_11 -> t_4, t_4 -> r_2 we can infer r_11 -> r_2 via transitivity. Finally, from q_3 -> r_11, r_11 -> r_2 we can infer q_3 -> r_2 via transitivity, which contradicts ~(q_3 -> r_2). Therefore, the answer is no.