Geoprocessing tools fail though CRS same, prj-file ok, edit mode off, topology valid,

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For my layers none of the QGIS geoproccesing tools (difference, intersection, etc. all give empty attribute tables) work, though I've checked for all (?) error sources (as in the title). Then I tried to do a manual edit of my polygon-geometry (adding a ring) and this is what happend (the data is in my Dropbox):

I'm using QGIS 2.10.0 on Win7



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