Consider the following premises. If Thomas plays a game, then it is late. It is not raining. If it is late, then Thomas is playing a game. If it is late, then it is raining. Can we infer the following from them? Thomas is not playing a game.
 From the fact that if it is late, then it is raining, and that it is not raining we can infer that it is not late. From the fact that if it is late, then Thomas is playing a game, and that if Thomas plays a game, then it is late we can infer that it is late if and only if Thomas is playing a game. Finally, from the fact that it is late if and only if Thomas is playing a game, and that it is not late we can infer that Thomas is not playing a game. Therefore, the answer is yes.