reserve a,b,c,d,e,f,g,h for set;

theorem
  XOR3(a,b,c) is non empty iff ( a is non empty & not b is non empty or
  not a is non empty & b is non empty ) & not c is non empty or not ( a is non
empty & not b is non empty or not a is non empty & b is non empty ) & c is non
  empty;
