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