MySQL Query on bad designed table with multiple Selfjoins
Looking at your Query, I have a few suggestions: 


Get rid of the "OR"s.  you can do this by checking if the
addition of all the fields > 0... OR's are a killer.
as Jkavalik mentioned, use a distinct  instead of a group by... better perf.
The "AND"s of Values 2 to 6 can also be an addition = 0
Do you absolutely need the Left joins? Can they be replaced with inner joins?  


As for the logic, I'm not sure I understand the whole concept.