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Full Idea
Jordain made consistent and ill-starred efforts to prove the Axiom of Choice.
Gist of Idea
Efforts to prove the Axiom of Choice have failed
Source
Penelope Maddy (Believing the Axioms I [1988], §1.7)
Book Ref
-: 'Journal of Symbolic Logic' [-], p.487
A Reaction
This would appear to be the fate of most axioms. You would presumably have to use a different system from the one you are engaged with to achieve your proof.