Consider the following premises. For all x_6, x_6 will sleep if and only if x_6 is a mechanic. For all x_6, if x_6 were an office clerk, then x_6 is a mechanic. There is at least one x_6 for which x_6 will not sleep. For all x_6, if x_6 sleeps, then x_6 is an office clerk. Can we infer the following from them? For all x_6, x_6 is a mechanic.
 From the fact that for all x_6, if x_6 sleeps, then x_6 is an office clerk, and that for all x_6, if x_6 were an office clerk, then x_6 is a mechanic we can infer that for all x_6, if x_6 sleeps, then x_6 is a mechanic. From the fact that for all x_6, x_6 will sleep if and only if x_6 is a mechanic we can infer that for all x_6, if x_6 were a mechanic, then x_6 is sleeping. From the fact that for all x_6, if x_6 sleeps, then x_6 is a mechanic, and that for all x_6, if x_6 were a mechanic, then x_6 is sleeping we can infer that for all x_6, x_6 will sleep if and only if x_6 is a mechanic. Finally, from the fact that for all x_6, x_6 will sleep if and only if x_6 is a mechanic, and that there is at least one x_6 for which x_6 will not sleep we can infer that there is at least one x_6 for which x_6 is not a mechanic, which contradicts that For all x_6, x_6 is a mechanic. Therefore, the answer is no.