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