Consider the following premises. If it is late, then it is raining. It is not raining. It is late. Can we infer the following from them? It is overcast.
 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 it is not late we can infer that it is not late or it is overcast. Finally, from the fact that it is not late or it is overcast, and that it is late we can infer that it is overcast. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.