Consider the following premises. For all x_6, x_6 is an astronaut or x_6 will cook. For all x_6, x_6 is not an astronaut. For all x_6, x_6 is excited and x_6 is a lawyer. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which either x_6 will cook or x_6 is excited are not true.
 From the fact that for all x_6, x_6 is an astronaut or x_6 will cook, and that for all x_6, x_6 is not an astronaut we can infer that for all x_6, x_6 will cook via universal disjunctive syllogism. From the fact that for all x_6, x_6 is excited and x_6 is a lawyer we can infer that for all x_6, x_6 is excited via universal simplification. Finally, from the fact that for all x_6, x_6 will cook, and that for all x_6, x_6 is excited we can infer that for all x_6, x_6 will cook and x_6 is excited via universal conjunction, which contradicts that There is at least one x_6 for which either x_6 will cook or x_6 is excited are not true. Therefore, the answer is no.