Consider the following premises. u_4. s -> u_4. s or ~u_4. Can we infer ~s from them? If possible, name the inference rules being used at each step.
 From s or ~u_4 we can infer u_4 -> s via rewriting. From s -> u_4, u_4 -> s we can infer s <-> u_4 via biconditional introduction. From s <-> u_4 we can infer u_4 -> s via biconditional elimination. Finally, from u_4 -> s, u_4 we can infer s via modus ponens, which contradicts ~s. Therefore, the answer is no.