Consider the following premises. If it is overcast, then Mary is sleeping. Mary is not writing a letter. For all x_11, x_11 will write a letter if and only if x_11 will sleep. Can we infer the following from them? It is overcast.
 From the fact that for all x_11, x_11 will write a letter if and only if x_11 will sleep we can infer that Mary is writing a letter if and only if Mary is sleeping. From the fact that Mary is writing a letter if and only if Mary is sleeping, and that Mary is not writing a letter we can infer that Mary is not sleeping. Finally, from the fact that if it is overcast, then Mary is sleeping, and that Mary is not sleeping we can infer that it is not overcast, which contradicts that It is overcast. Therefore, the answer is no.