Consider the following premises. Patricia is not playing a game. Karen is fast. If Karen were fast, then Patricia is playing a game. Can we infer the following from them? Patricia is a soldier.
 From the fact that if Karen were fast, then Patricia is playing a game, and that Patricia is not playing a game we can infer that Karen is not fast. From the fact that Karen is fast we can infer that Karen is fast or Patricia is a soldier. Finally, from the fact that Karen is fast or Patricia is a soldier, and that Karen is not fast we can infer that Patricia is a soldier. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.