∀ {a b c d e f a' b' c' d' e' f' : ℤ} {S : Set (ℤ × ℤ)},
  S = {(0, 0), (1, 1), (-1, -1), (1, 2), (2, 1), (-1, -2), (-2, -1), (1, 3), (3, 1), (-1, -3), (-3, -1)} →
    (a, a') ∈ S →
      (b, b') ∈ S →
        (c, c') ∈ S →
          (d, d') ∈ S →
            (e, e') ∈ S →
              (f, f') ∈ S →
                c = a + 3 * b →
                  c' = a' + b' →
                    d = 2 * a + 3 * b →
                      d' = 2 * a' + b' →
                        e = a + b → e' = 3 * a' + b' → f = a + 2 * b → f' = 3 * a' + 2 * b' → a = 0 ∧ b = 0