Consider the following premises. There is at least one x_2 for which if x_2 were bored, then x_2 is an astronaut. For all x_2, if x_2 were an electrician, then x_2 is an astronaut. For all x_2, if x_2 were a cashier, then x_2 is bored. For all x_2, x_2 is an electrician or x_2 is a cashier. Can we infer the following from them? For all x_2, x_2 is not an astronaut.
 From the fact that for all x_2, if x_2 were a cashier, then x_2 is bored, and that there is at least one x_2 for which if x_2 were bored, then x_2 is an astronaut we can infer that there is at least one x_2 for which if x_2 were a cashier, then x_2 is an astronaut. Finally, from the fact that for all x_2, if x_2 were an electrician, then x_2 is an astronaut, that there is at least one x_2 for which if x_2 were a cashier, then x_2 is an astronaut, and that for all x_2, x_2 is an electrician or x_2 is a cashier we can infer that there is at least one x_2 for which x_2 is an astronaut, which contradicts that For all x_2, x_2 is not an astronaut. Therefore, the answer is no.