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