Consider the following premises. Thomas is a poet or it is not raining. If Joseph works, then Thomas is a poet. If Thomas were a poet, then Joseph is working. Joseph is not working. Can we infer the following from them? It is not raining.
 From the fact that if Joseph works, then Thomas is a poet, and that if Thomas were a poet, then Joseph is working we can infer that Joseph is working if and only if Thomas is a poet. From the fact that Thomas is a poet or it is not raining we can infer that if it rains, then Thomas is a poet. From the fact that Joseph is working if and only if Thomas is a poet we can infer that if Thomas were a poet, then Joseph is working. From the fact that if it rains, then Thomas is a poet, and that if Thomas were a poet, then Joseph is working we can infer that if it rains, then Joseph is working. Finally, from the fact that if it rains, then Joseph is working, and that Joseph is not working we can infer that it is not raining. Therefore, the answer is yes.