theorem
  not ex x,y,z being Rational st x^2+y^2+z^2+x+y+z = 1
  proof
    given x,y,z being Rational such that
A1: x^2+y^2+z^2+x+y+z = 1;
    (2*x+1)^2+(2*y+1)^2+(2*z+1)^2 = 7 by A1;
    hence contradiction by Th93;
  end;
