There is no 4562. I do have a "Schedule of Mineral Interest Properties-Alternative Minimum Tax" form. The property descriptions are things like "Occidental Permian" and "Texland Petroleum" so I don't think that helps you. The carryover numbers are in a column titles "(4) AMT Depletion Adjustment". I think there must be some place to enter them where they carry over to 6251 part 1 somehow.
