Consider the following premises. It is overcast. It is late or it is not overcast. If William climbs a mountain, then it is late. Can we infer the following from them? It is late.
 From the fact that it is overcast we can infer that it is overcast or William is climbing a mountain. From the fact that it is late or it is not overcast we can infer that if it is overcast, then it is late. Finally, from the fact that if it is overcast, then it is late, that if William climbs a mountain, then it is late, and that it is overcast or William is climbing a mountain we can infer that it is late. Therefore, the answer is yes.