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tut comments on Open Thread - Aug 24 - Aug 30 - Less Wrong Discussion
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{All possible proofs} has infinitely many elements longer than zero, so your algorithm will (might) run forever on some programs that do halt, so it is not a halting oracle.
If a program halts, it's easy to prove that it halts. Just run it until it halts. The problem is proving that some programs won't halt.