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xor === (p and not q) or (q and not p) 

...
     nor ((q nor q) nor ((p nor p) nor (p nor p))))
    nor (((q nor q) nor ((p nor p) nor (p nor p))) 
     nor ((p nor p) nor ((q nor q) nor (q nor q))))

    === (((p nor p) nor q) nor ((q nor q) nor p)) 
    nor (((q nor q) nor p) nor ((p nor p) nor q))