Consider the following premises. For all x_15, x_15 is excited if and only if x_15 is a musician. For all x_15, x_15 will sleep if and only if x_15 will write a letter. For all x_15, if x_15 were an artist, then x_15 is writing a letter. For all x_15, x_15 is a musician or x_15 is an artist. For all x_15, if x_15 were excited, then x_15 is sleeping. Can we infer the following from them? There is at least one x_15 for which x_15 will not write a letter.
 From the fact that for all x_15, x_15 will sleep if and only if x_15 will write a letter we can infer that for all x_15, if x_15 sleeps, then x_15 is writing a letter. From the fact that for all x_15, x_15 is excited if and only if x_15 is a musician we can infer that for all x_15, if x_15 were a musician, then x_15 is excited. From the fact that for all x_15, if x_15 were excited, then x_15 is sleeping, and that for all x_15, if x_15 sleeps, then x_15 is writing a letter we can infer that for all x_15, if x_15 were excited, then x_15 is writing a letter. From the fact that for all x_15, if x_15 were a musician, then x_15 is excited, and that for all x_15, if x_15 were excited, then x_15 is writing a letter we can infer that for all x_15, if x_15 were a musician, then x_15 is writing a letter. Finally, from the fact that for all x_15, if x_15 were a musician, then x_15 is writing a letter, that for all x_15, if x_15 were an artist, then x_15 is writing a letter, and that for all x_15, x_15 is a musician or x_15 is an artist we can infer that for all x_15, x_15 will write a letter, which contradicts that There is at least one x_15 for which x_15 will not write a letter. Therefore, the answer is no.