Consider the following premises. p_1 -> u. p_1. s_1 -> ~u. Can we infer s_1 from them? If possible, name the inference rules being used at each step.
 From p_1 -> u, p_1 we can infer u via modus ponens. Finally, from s_1 -> ~u, u we can infer ~s_1 via modus tollens, which contradicts s_1. Therefore, the answer is no.