Consider the following premises. s or ~q_8. u <-> q_8. Can we infer ~(u -> s) from them? If possible, name the inference rules being used at each step.
 From u <-> q_8 we can infer u -> q_8 via biconditional elimination. From s or ~q_8 we can infer q_8 -> s via rewriting. Finally, from u -> q_8, q_8 -> s we can infer u -> s via transitivity, which contradicts ~(u -> s). Therefore, the answer is no.