Many people here (myslef included) can achieve the victory conditions for any given faction within 75 turns (150 years), this is only made easier when they attack you at random. If this is the one and only goal ( as many people have said) then it makes for a pretty boring game if you beat it before the mongols/turmids(sp)/america. In fact if this was the only goal, you should work towards excommunication, and ignore diplomacy entirely.
The AI should use trusted ally to expand in the other direction, go against a common enemy or attck the largest threat to themselves. They should NOT sit around till your empire is the biggest threat, then give up years of peace cause the player triggered it.
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