Consider the following premises. If it is late, then it is snowing. It is cloudy. It is snowing or Michael is not a poet. Michael is a poet or it is late. Can we infer the following from them? It is snowing and it is cloudy.
 From the fact that it is snowing or Michael is not a poet we can infer that if Michael were a poet, then it is snowing. From the fact that if Michael were a poet, then it is snowing, that if it is late, then it is snowing, and that Michael is a poet or it is late we can infer that it is snowing. Finally, from the fact that it is snowing, and that it is cloudy we can infer that it is snowing and it is cloudy. Therefore, the answer is yes.