Consider the following premises. u -> r_1. p_9 -> u. p_9 <-> q_9. Can we infer ~(q_9 -> r_1) from them? If possible, name the inference rules being used at each step.
 From p_9 <-> q_9 we can infer q_9 -> p_9 via biconditional elimination. From p_9 -> u, u -> r_1 we can infer p_9 -> r_1 via transitivity. Finally, from q_9 -> p_9, p_9 -> r_1 we can infer q_9 -> r_1 via transitivity, which contradicts ~(q_9 -> r_1). Therefore, the answer is no.