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RichardKennaway comments on Prisoner's dilemma tournament results - Less Wrong
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What happens if the two sets of axioms are individually consistent, but together are inconsistent?
Deem both of the agents to have not terminated?
How will you know? The set of consistent axiom systems is undecidable. (Though the set of inconsistent axioms systems is computably enumerable.)
You just run the Prolog (or whatever logic system implements all this), and it either terminates with a failure or does not terminate within the time allowed by the competition. The time limit renders everything practically decidable.
Perhaps it terminates in the time required proving that A defects and B cooperates, even though the axioms were inconsistent, and one could also have proved that A cooperates and B defects.
The competitors know the deterministic proof-search algorithm (e.g. that of Prolog), and the first answer that produces within the time limit, that is the answer.