I'm reviewing this part and It seems to me that the sole purpose of his "Herculean labors"
was to refute the oracle. He didn't believe himself that he was the wisest man on earth,
so he embarked on a journey to prove the oracle wrong.
The opposite result of these labors, the oracle being irrefutable, is the purpose of presenting them to the jury.
It was never the purpose of the labors themselves.
Perhaps I'm misreading this commentary by William Seymour Tyler:http://www.archive.org/stream/platosapo ... 3/mode/2up
But by his explanation, why wouldn't it be subjunctive?