Consider the following premises. If David were rich, then it is overcast. It is overcast or Richard is not sad. Richard is sad or it is windy. If it is windy, then David is rich. Can we infer the following from them? If we can, name the inference rule being used: It is not overcast.
 From the fact that if it is windy, then David is rich, and that if David were rich, then it is overcast we can infer that if it is windy, then it is overcast via transitivity. From the fact that it is overcast or Richard is not sad we can infer that if Richard were sad, then it is overcast via rewriting. Finally, from the fact that if Richard were sad, then it is overcast, that if it is windy, then it is overcast, and that Richard is sad or it is windy we can infer that it is overcast via disjunction elimination, which contradicts that It is not overcast. Therefore, the answer is no.