Consider the following premises. For all x_4, x_4 is not an electrician. There is at least one x_4 for which x_4 is an electrician or x_4 is a janitor. For all x_4, x_4 is an astronaut. Can we infer the following from them? If we can, name the inference rule being used: For all x_4, either x_4 is an astronaut or x_4 is a janitor are not true.
 From the fact that there is at least one x_4 for which x_4 is an electrician or x_4 is a janitor, and that for all x_4, x_4 is not an electrician we can infer that there is at least one x_4 for which x_4 is a janitor via existential disjunctive syllogism. Finally, from the fact that for all x_4, x_4 is an astronaut, and that there is at least one x_4 for which x_4 is a janitor we can infer that there is at least one x_4 for which x_4 is an astronaut and x_4 is a janitor via existential conjunction, which contradicts that For all x_4, either x_4 is an astronaut or x_4 is a janitor are not true. Therefore, the answer is no.