Consider the following premises. It is cold. John is running or Sarah is not a soldier. If it is cold, then Sarah is a soldier. Can we infer the following from them? John is running.
 From the fact that John is running or Sarah is not a soldier we can infer that if Sarah were a soldier, then John is running. From the fact that if it is cold, then Sarah is a soldier, and that it is cold we can infer that Sarah is a soldier. Finally, from the fact that if Sarah were a soldier, then John is running, and that Sarah is a soldier we can infer that John is running. Therefore, the answer is yes.