Consider the following premises. Barbara is a writer if and only if Karen is happy. If David works, then Barbara is a writer. If John drinks water, then David is working. If Barbara were a writer, then John is drinking water. Karen is not happy. Can we infer the following from them? David is not working.
 From the fact that if Barbara were a writer, then John is drinking water, and that if John drinks water, then David is working we can infer that if Barbara were a writer, then David is working. From the fact that if Barbara were a writer, then David is working, and that if David works, then Barbara is a writer we can infer that Barbara is a writer if and only if David is working. From the fact that Barbara is a writer if and only if Karen is happy, and that Karen is not happy we can infer that Barbara is not a writer. Finally, from the fact that Barbara is a writer if and only if David is working, and that Barbara is not a writer we can infer that David is not working. Therefore, the answer is yes.