Consider the following premises. Mary is a taxi driver or it is sunny. If Mary were a taxi driver, then it is overcast. It is overcast or it is not sunny. If it is overcast, then it is raining. Can we infer the following from them? If we can, name the inference rule being used: It is not raining.
 From the fact that it is overcast or it is not sunny we can infer that if it is sunny, then it is overcast via rewriting. From the fact that if Mary were a taxi driver, then it is overcast, that if it is sunny, then it is overcast, and that Mary is a taxi driver or it is sunny we can infer that it is overcast via disjunction elimination. Finally, from the fact that if it is overcast, then it is raining, and that it is overcast we can infer that it is raining via modus ponens, which contradicts that It is not raining. Therefore, the answer is no.