Consider the following premises. For all x_10, x_10 will sleep or x_10 is not a mechanic. Robert is not an electrician or Elisabeth is a mechanic. If Thomas were happy, then Elisabeth is sleeping. Robert is an electrician or Thomas is happy. Can we infer the following from them? If we can, name the inference rule being used: Elisabeth is not sleeping.
 From the fact that for all x_10, x_10 will sleep or x_10 is not a mechanic we can infer that for all x_10, if x_10 were a mechanic, then x_10 is sleeping via universal rewriting. From the fact that for all x_10, if x_10 were a mechanic, then x_10 is sleeping we can infer that if Elisabeth were a mechanic, then Elisabeth is sleeping via universal instantiation. From the fact that Robert is an electrician or Thomas is happy, and that Robert is not an electrician or Elisabeth is a mechanic we can infer that Thomas is happy or Elisabeth is a mechanic via resolution. Finally, from the fact that if Thomas were happy, then Elisabeth is sleeping, that if Elisabeth were a mechanic, then Elisabeth is sleeping, and that Thomas is happy or Elisabeth is a mechanic we can infer that Elisabeth is sleeping via disjunction elimination, which contradicts that Elisabeth is not sleeping. Therefore, the answer is no.