Consider the following premises. If John were a scientist, then Barbara is a cashier. John is a scientist. Karen is a police officer or Barbara is not a cashier. Can we infer the following from them? Karen is not a police officer.
 From the fact that Karen is a police officer or Barbara is not a cashier we can infer that if Barbara were a cashier, then Karen is a police officer. From the fact that if John were a scientist, then Barbara is a cashier, and that John is a scientist we can infer that Barbara is a cashier. Finally, from the fact that if Barbara were a cashier, then Karen is a police officer, and that Barbara is a cashier we can infer that Karen is a police officer, which contradicts that Karen is not a police officer. Therefore, the answer is no.