Consider the following premises. For all x_5, x_5 will not sleep. There is at least one x_5 for which x_5 is a lawyer if and only if x_5 is sad. For all x_5, if x_5 were a lawyer, then x_5 is sleeping. For all x_5, if x_5 sleeps, then x_5 is a lawyer. Can we infer the following from them? There is at least one x_5 for which x_5 is not sad.
 From the fact that for all x_5, if x_5 sleeps, then x_5 is a lawyer, and that for all x_5, if x_5 were a lawyer, then x_5 is sleeping we can infer that for all x_5, x_5 will sleep if and only if x_5 is a lawyer. From the fact that for all x_5, x_5 will sleep if and only if x_5 is a lawyer, and that for all x_5, x_5 will not sleep we can infer that for all x_5, x_5 is not a lawyer. Finally, from the fact that there is at least one x_5 for which x_5 is a lawyer if and only if x_5 is sad, and that for all x_5, x_5 is not a lawyer we can infer that there is at least one x_5 for which x_5 is not sad. Therefore, the answer is yes.