Complex sentence: The Doctor proves this by having the scientists read their copies of the base's manual that each had been issued, in which they find that the first word of any chosen page is different for each of them, rather than identical as it should be.
Split into simpler sentences: The Doctor proves this by having the scientists individually read copies of the base's manual that each had been issued. They find that the first word of any chosen page is different for each of them, rather than identical as it should be.