Michal,
I split the polygons into 4 shapefiles manually: I simply selected first one non-overlapping set covering as much of the original 'lines" file as possible right click copied the selection, deleted them and pasted them into another shapefile using create features and Target: the second shapefile, then repeat the process with the remaining outlines and a new shapefile until the remainder was a non-overlapping set. I then copied and pasted and merged each set in a scratch file and ran the "Autocomplete Polygons" process on each merged set with the Target being a Polygon shapefile.. Actually, the other polyline shapefiles were not strictly necessary except to make it easy to see that I had 4 non-overlapping sets or if one used the Copy Features tool to preserve attributes.
I am not familiar with the ET geowizards Polyline to Polygon tool, but I expect it would works the same as "Autocomplete Polygons" and the new functions in ArcGIS 10 that produce polygons from all the intersecting outlined areas rather than one per record.
Hardolph