Consider the following premises. For all x_9, x_9 will sleep if and only if x_9 will take a plane. There is at least one x_9 for which x_9 will not write a letter. For all x_9, if x_9 goes running, then x_9 is writing a letter. For all x_9, if x_9 takes a plane, then x_9 is running. Can we infer the following from them? There is at least one x_9 for which x_9 will not write a letter.
That is one of the premises. Therefore, the answer is yes.