Consider the following premises. For all x_13, if x_13 were fast, then x_13 is excited. For all x_13, if x_13 were fast, then x_13 is a police officer. For all x_13, if x_13 were a police officer, then x_13 is fast. For all x_13, x_13 will write a letter if and only if x_13 is a police officer. Can we infer the following from them? There is at least one x_13 for which the fact that x_13 writes a letter does not imply that x_13 is excited.
 From the fact that for all x_13, if x_13 were fast, then x_13 is a police officer, and that for all x_13, if x_13 were a police officer, then x_13 is fast we can infer that for all x_13, x_13 is fast if and only if x_13 is a police officer. From the fact that for all x_13, x_13 will write a letter if and only if x_13 is a police officer we can infer that for all x_13, if x_13 writes a letter, then x_13 is a police officer. From the fact that for all x_13, x_13 is fast if and only if x_13 is a police officer we can infer that for all x_13, if x_13 were a police officer, then x_13 is fast. From the fact that for all x_13, if x_13 writes a letter, then x_13 is a police officer, and that for all x_13, if x_13 were a police officer, then x_13 is fast we can infer that for all x_13, if x_13 writes a letter, then x_13 is fast. Finally, from the fact that for all x_13, if x_13 writes a letter, then x_13 is fast, and that for all x_13, if x_13 were fast, then x_13 is excited we can infer that for all x_13, if x_13 writes a letter, then x_13 is excited, which contradicts that There is at least one x_13 for which the fact that x_13 writes a letter does not imply that x_13 is excited. Therefore, the answer is no.