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Clipping Thousands of Intersecting Polygons in the same Shapefile ArcGIS 10.1

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I have seen this question asked multiple times without any answers.
Does anyone know if there is a model, tool or a python script script to remove thousands of polygon intersections within the same shapefile?
I am working with sewer mains and need to analyze each main's buffered sewered area. As you could understand, every single sewer main now has 100 ft radius of intersect with the upstream and downstream mains. I want to delete these just the same as creating a Flat Buffer that is only available in the advanced licenses.
I am not very familiar with any of the modelbuilders or scripts, so if you could be extensive and elaborate in the response, I would appreciate it.


Thanks.

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