No, a rejected tax return doesn't count as an e-file until it is fixed and accepted.
You can check on the other returns that have been e-filed under this license code.
For each tax return that was e-filed there will be an Electronic Postmark Report which has the date/time the federal tax return was e-filed and the date it was accepted by the IRS, if accepted.
You will have to Continue each tax return and then click on Forms. When in Forms mode on the left side of the screen at the bottom of the list for federal tax forms, schedules and worksheets will be the Postmark Report. Click on the report to open.
If you are still having trouble with this issue and the five free e-files definitely haven't been used, you can follow this link for Support.
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