If we were to believe Am1, the Diels-Alder product would have a heat of formation of -7kcal/mol and the reactant +5kcal/mol, so from that criterion, Bredt's rule wouldn't apply so clearly with a 3-membered bridge.
Am1 isn't too wrong on butadiene's heat of formation. But to proceed, Diels-Alder would need an improbable conformation of the reactant.
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