Consider the following premises. If it is overcast, then it is not cloudy. If it is overcast, then it is raining. It is cold. If it rains, then it is overcast. It is cloudy. Can we infer the following from them? It is raining.
 From the fact that if it is overcast, then it is not cloudy, and that it is cloudy we can infer that it is not overcast. From the fact that if it is overcast, then it is raining, and that if it rains, then it is overcast we can infer that it is overcast if and only if it is raining. Finally, from the fact that it is overcast if and only if it is raining, and that it is not overcast we can infer that it is not raining, which contradicts that It is raining. Therefore, the answer is no.