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