Consider the following premises. For all x_17, if x_17 sleeps, then x_17 is writing a letter. For all x_17, if x_17 were poor, then x_17 is a nurse. For all x_17, if x_17 were a nurse, then x_17 is poor. For all x_17, if x_17 writes a letter, then x_17 is a nurse. There is at least one x_17 for which x_17 is not poor. Can we infer the following from them? If we can, name the inference rule being used: For all x_17, x_17 will sleep.
 From the fact that for all x_17, if x_17 were poor, then x_17 is a nurse, and that for all x_17, if x_17 were a nurse, then x_17 is poor we can infer that for all x_17, x_17 is poor if and only if x_17 is a nurse via universal biconditional introduction. From the fact that for all x_17, x_17 is poor if and only if x_17 is a nurse, and that there is at least one x_17 for which x_17 is not poor we can infer that there is at least one x_17 for which x_17 is not a nurse via existential biconditional elimination. From the fact that for all x_17, if x_17 writes a letter, then x_17 is a nurse, and that there is at least one x_17 for which x_17 is not a nurse we can infer that there is at least one x_17 for which x_17 will not write a letter via existential modus tollens. Finally, from the fact that for all x_17, if x_17 sleeps, then x_17 is writing a letter, and that there is at least one x_17 for which x_17 will not write a letter we can infer that there is at least one x_17 for which x_17 will not sleep via existential modus tollens, which contradicts that For all x_17, x_17 will sleep. Therefore, the answer is no.