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DOFD is not the first date you were ever late on the account.
It is the date you went delinquent and never caught up prior to to charge off/collection/other similar action.
It might be removed 7 years from date it was closed, since it was a negative account.
However, the lates will fall off one by one as they reach 7 years, and the account could end up being a positive account, which will report for 10 years from date closed.
When were the lates? When was it closed?