Consider the following premises. John is sleeping or James is not working. It is not sunny. It is sunny or James is working. Can we infer the following from them? If we can, name the inference rule being used: John is not sleeping.
 From the fact that it is sunny or James is working, and that it is not sunny we can infer that James is working via disjunctive syllogism. From the fact that John is sleeping or James is not working we can infer that if James works, then John is sleeping via rewriting. Finally, from the fact that if James works, then John is sleeping, and that James is working we can infer that John is sleeping via modus ponens, which contradicts that John is not sleeping. Therefore, the answer is no.