Consider the following premises. If Thomas works, then Elisabeth is cooking. For all z, z will drink water. If Thomas drinks water, then Elisabeth is cooking. Can we infer the following from them? If we can, name the inference rule being used: Elisabeth is cooking or it is late.
 From the fact that for all z, z will drink water we can infer that for all z, z will drink water or z will work via universal addition. From the fact that for all z, z will drink water or z will work we can infer that Thomas is drinking water or Thomas is working via universal instantiation. From the fact that if Thomas drinks water, then Elisabeth is cooking, that if Thomas works, then Elisabeth is cooking, and that Thomas is drinking water or Thomas is working we can infer that Elisabeth is cooking via disjunction elimination. Finally, from the fact that Elisabeth is cooking we can infer that Elisabeth is cooking or it is late via addition. Therefore, the answer is yes.