Consider the following premises. If Robert sleeps, then Michael is sad. Michael is not sad. If James cooks, then Robert is sleeping. Robert is sleeping or Michael is not sad. Can we infer the following from them? If we can, name the inference rule being used: James is cooking.
 From the fact that Robert is sleeping or Michael is not sad we can infer that if Michael were sad, then Robert is sleeping via rewriting. From the fact that if Robert sleeps, then Michael is sad, and that if Michael were sad, then Robert is sleeping we can infer that Robert is sleeping if and only if Michael is sad via biconditional introduction. From the fact that Robert is sleeping if and only if Michael is sad, and that Michael is not sad we can infer that Robert is not sleeping via biconditional elimination. Finally, from the fact that if James cooks, then Robert is sleeping, and that Robert is not sleeping we can infer that James is not cooking via modus tollens, which contradicts that James is cooking. Therefore, the answer is no.