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I have actually thought of a way to define a variant too large for anyone in this universe to play (whether human, alien monsters, computer programming, or whatever) and therefore is probably impossible to solve by computer too; I have defined a googolplex kind of pieces but had some trouble to define the primitives it is made from in order to ensure all of them are different (however, I think I may have figured out the solution just now).

Perhaps that isn't what you want though. Well, the answer to your question still isn't clear. Even in games where "there aren't so many moves which are at all sound", it seems to me that you should need a mathematical proof of that statement in order to correctly take advantage of it. (Still, it may be possible to make such a mathematical proof without enumerating all of the moves; it is possible to prove a lot of things about numbers which are larger than the universe.)

Email me, plz, zzo. If you have time.