Consider the following premises. It is not cloudy or Karen is a bartender. If it is overcast, then Karen is not a bartender. It is cloudy or Karen is writing a letter. For all x_17, x_17 will not write a letter. Can we infer the following from them? It is not overcast.
 From the fact that for all x_17, x_17 will not write a letter we can infer that Karen is not writing a letter. From the fact that it is cloudy or Karen is writing a letter, and that it is not cloudy or Karen is a bartender we can infer that Karen is writing a letter or Karen is a bartender. From the fact that Karen is writing a letter or Karen is a bartender, and that Karen is not writing a letter we can infer that Karen is a bartender. Finally, from the fact that if it is overcast, then Karen is not a bartender, and that Karen is a bartender we can infer that it is not overcast. Therefore, the answer is yes.