Consider the following premises. If it is cloudy, then David is a politician. For all x_15, if x_15 were a poet, then x_15 is running. David is a politician if and only if Karen is a poet. Karen is not running. Can we infer the following from them? It is not cloudy.
 From the fact that for all x_15, if x_15 were a poet, then x_15 is running we can infer that if Karen were a poet, then Karen is running. From the fact that if Karen were a poet, then Karen is running, and that Karen is not running we can infer that Karen is not a poet. From the fact that David is a politician if and only if Karen is a poet, and that Karen is not a poet we can infer that David is not a politician. Finally, from the fact that if it is cloudy, then David is a politician, and that David is not a politician we can infer that it is not cloudy. Therefore, the answer is yes.