Consider the following premises. p <-> q_13. u -> p. u or ~s. Can we infer ~(s -> q_13) from them? If possible, name the inference rules being used at each step.
 From p <-> q_13 we can infer p -> q_13 via biconditional elimination. From u -> p, p -> q_13 we can infer u -> q_13 via transitivity. From u or ~s we can infer s -> u via rewriting. Finally, from s -> u, u -> q_13 we can infer s -> q_13 via transitivity, which contradicts ~(s -> q_13). Therefore, the answer is no.