Consider the following premises. It is cloudy or Charles is sleeping. If Elisabeth were a politician, then it is overcast. Elisabeth is a politician or Charles is not sleeping. If it is cloudy, then Elisabeth is a politician. Can we infer the following from them? It is overcast.
 From the fact that Elisabeth is a politician or Charles is not sleeping we can infer that if Charles sleeps, then Elisabeth is a politician. From the fact that if it is cloudy, then Elisabeth is a politician, that if Charles sleeps, then Elisabeth is a politician, and that it is cloudy or Charles is sleeping we can infer that Elisabeth is a politician. Finally, from the fact that if Elisabeth were a politician, then it is overcast, and that Elisabeth is a politician we can infer that it is overcast. Therefore, the answer is yes.