Consider the following premises. For all x_6, x_6 will work or x_6 is not sad. For all x_6, x_6 is a writer. For all x_6, if x_6 were a cashier, then x_6 is working. For all x_6, x_6 is a cashier or x_6 is sad. Can we infer the following from them? There is at least one x_6 for which either x_6 is a writer or x_6 will work are not true.
 From the fact that for all x_6, x_6 will work or x_6 is not sad we can infer that for all x_6, if x_6 were sad, then x_6 is working. From the fact that for all x_6, if x_6 were a cashier, then x_6 is working, that for all x_6, if x_6 were sad, then x_6 is working, and that for all x_6, x_6 is a cashier or x_6 is sad we can infer that for all x_6, x_6 will work. Finally, from the fact that for all x_6, x_6 is a writer, and that for all x_6, x_6 will work we can infer that for all x_6, x_6 is a writer and x_6 will work, which contradicts that There is at least one x_6 for which either x_6 is a writer or x_6 will work are not true. Therefore, the answer is no.