Consider the following premises. Susan is driving a car if and only if Barbara is a carpenter. Barbara is a carpenter if and only if Jessica is sleeping. If Susan drives a car, then Jessica is sleeping. Can we infer the following from them? If we can, name the inference rule being used: The fact that Susan drives a car does not imply that Barbara is a carpenter.
 From the fact that Barbara is a carpenter if and only if Jessica is sleeping we can infer that if Jessica sleeps, then Barbara is a carpenter via biconditional elimination. Finally, from the fact that if Susan drives a car, then Jessica is sleeping, and that if Jessica sleeps, then Barbara is a carpenter we can infer that if Susan drives a car, then Barbara is a carpenter via transitivity, which contradicts that The fact that Susan drives a car does not imply that Barbara is a carpenter. Therefore, the answer is no.