-a b^2 c^3 x^3 y - a^3 c^3 x^2 y^2 + b^3 c^3 x^2 y^2 + a c^5 x^2 y^2 -
  b c^5 x^2 y^2 + a^2 b c^3 x y^3 + a b^3 c^2 x^3 z - 
 a^3 b^2 c x^2 y z - a^2 b^3 c x^2 y z + a b^4 c x^2 y z + 
 b^5 c x^2 y z + a^3 b c^2 x^2 y z + a^2 b c^3 x^2 y z - 
 a b c^4 x^2 y z - b c^5 x^2 y z - a^5 c x y^2 z - a^4 b c x y^2 z + 
 a^3 b^2 c x y^2 z + a^2 b^3 c x y^2 z - a b^3 c^2 x y^2 z - 
 a b^2 c^3 x y^2 z + a b c^4 x y^2 z + a c^5 x y^2 z - 
 a^3 b c^2 y^3 z + a^3 b^3 x^2 z^2 - a b^5 x^2 z^2 + b^5 c x^2 z^2 - 
 b^3 c^3 x^2 z^2 + a^5 b x y z^2 - a b^5 x y z^2 + a^4 b c x y z^2 - 
 a b^4 c x y z^2 - a^3 b c^2 x y z^2 + a b^3 c^2 x y z^2 - 
 a^2 b c^3 x y z^2 + a b^2 c^3 x y z^2 + a^5 b y^2 z^2 - 
 a^3 b^3 y^2 z^2 - a^5 c y^2 z^2 + a^3 c^3 y^2 z^2 - a^2 b^3 c x z^3 +
  a^3 b^2 c y z^3 = 0