Consider the following premises. For all x_7, x_7 is a doctor or x_7 is curious. There is at least one x_7 for which x_7 is not a doctor. For all x_7, x_7 is a soldier. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, x_7 is not curious.
 From the fact that for all x_7, x_7 is a doctor or x_7 is curious, and that there is at least one x_7 for which x_7 is not a doctor we can infer that there is at least one x_7 for which x_7 is curious via existential disjunctive syllogism. From the fact that for all x_7, x_7 is a soldier, and that there is at least one x_7 for which x_7 is curious we can infer that there is at least one x_7 for which x_7 is a soldier and x_7 is curious via existential conjunction. Finally, from the fact that there is at least one x_7 for which x_7 is a soldier and x_7 is curious we can infer that there is at least one x_7 for which x_7 is a soldier via existential simplification, which contradicts that For all x_7, x_7 is not curious. Therefore, the answer is no.