. The model should output correct solution at least 75% of the time it is suitably prompted.

The ability should be demonstrated before 1st Jan 2027 in order for this market to resolve YES, but if there is an exceptionally strong suspicion that a specific non-public LM should be able to solve it, I'll wait until I can test it on that or another very similar model. However, if someone finds a prompt setup which makes say GPT-4 solve it correctly, but they find it after 2026, this market still resolves NO. 

The model is allowed to be arbitrarily prompted, as long as

The model should ideally be able to explain its reasoning in detail, which I would then check. If the model produces erroneous reasoning but gets it right (despite errors or perhaps without thinking out loud), I'll default to assuming that it's just a leak since the solution can be found online – but if there is a strong reason to suspect that it is not a leak (e.g. the model is known to display very strong logical reasoning in other contexts), I'll create variations on the test and see whether model can solve them correctly.