Vogel's antisymmetry conjecture for three-legged diagrams

Let $\mathcal{X}^3$ be the space of fixed Jacobi diagrams with three legs, and let $\Lambda\subseteq\mathcal{X}^3$ be the subspace of elements antisymmetric under permutations of their legs. Vogel's antisymmetry conjecture.

$$\Lambda=\mathcal{X}^3,$$

that is, any fixed diagram with three legs is antisymmetric with respect to leg permutations. The statement is presented as conjectural in the text, with no resolution supplied.