Consider the following premises. For all x_7, x_7 will sleep and x_7 will play squash. For all x_7, if x_7 were a taxi driver, then x_7 is not sleeping. There is at least one x_7 for which x_7 will write a letter if and only if x_7 is a taxi driver. Can we infer the following from them? There is at least one x_7 for which x_7 will not write a letter.
 From the fact that for all x_7, x_7 will sleep and x_7 will play squash we can infer that for all x_7, x_7 will sleep. From the fact that for all x_7, if x_7 were a taxi driver, then x_7 is not sleeping, and that for all x_7, x_7 will sleep we can infer that for all x_7, x_7 is not a taxi driver. Finally, from the fact that there is at least one x_7 for which x_7 will write a letter if and only if x_7 is a taxi driver, and that for all x_7, x_7 is not a taxi driver we can infer that there is at least one x_7 for which x_7 will not write a letter. Therefore, the answer is yes.