Consider the following premises. If it is cloudy, then Karen is an astronaut. It is cloudy. If Karen were an astronaut, then it is cloudy. Can we infer the following from them? If we can, name the inference rule being used: Karen is not an astronaut.
 From the fact that if Karen were an astronaut, then it is cloudy, and that if it is cloudy, then Karen is an astronaut we can infer that Karen is an astronaut if and only if it is cloudy via biconditional introduction. From the fact that Karen is an astronaut if and only if it is cloudy we can infer that if it is cloudy, then Karen is an astronaut via biconditional elimination. Finally, from the fact that if it is cloudy, then Karen is an astronaut, and that it is cloudy we can infer that Karen is an astronaut via modus ponens, which contradicts that Karen is not an astronaut. Therefore, the answer is no.