Consider the following premises. If William were a poet, then William is sleeping. If William sleeps, then William is a poet. It is cloudy if and only if William is a poet. Can we infer the following from them? The fact that William sleeps does not imply that it is cloudy.
 From the fact that if William were a poet, then William is sleeping, and that if William sleeps, then William is a poet we can infer that William is a poet if and only if William is sleeping. From the fact that William is a poet if and only if William is sleeping we can infer that if William sleeps, then William is a poet. From the fact that it is cloudy if and only if William is a poet we can infer that if William were a poet, then it is cloudy. Finally, from the fact that if William sleeps, then William is a poet, and that if William were a poet, then it is cloudy we can infer that if William sleeps, then it is cloudy, which contradicts that The fact that William sleeps does not imply that it is cloudy. Therefore, the answer is no.