The supersymmetric symmetry criterion for integrability

Let $\mathcal{L}_1$ be a maximal finite-dimensional superalgebra of Lie point symmetries of a nonlinear system of partial differential equations, and let $\mathcal{L}_2$ be a maximal finite-dimensional superalgebra of Lie point symmetries of its associated linear system. Let $\pi$ be a projection operator such that

$$\pi(\mathcal{L}_2)=\mathcal{L}_2\omega,$$

where $\omega$ involves all independent bosonic and fermionic variables and all dependent bosonic and fermionic superfields. The supersymmetric symmetry criterion. If $\mathcal{L}_1=\pi(\mathcal{L}_2)$, then the nonlinear system is not integrable. If $\pi(\mathcal{L}_2)$ is a proper subset of $\mathcal{L}_1$, a free parameter can be introduced into the linear system using a symmetry transformation generated by a vector field in $\mathcal{L}_4=\mathcal{L}_1\backslash\{\mathcal{L}_1\cap\pi(\mathcal{L}_2)\}$, and that transformation acts nontrivially, meaning that it cannot be eliminated through an $\mathcal{L}_1$-valued gauge matrix function, then the nonlinear system is a candidate to be integrable. This is presented as the supersymmetric extension of the classical symmetry criterion. The supplied text gives no evidence that the criterion itself has been proved or disproved.