Minimality conjecture for semisimple subgroup foliations on semi-Riemannian Lie groups

Let $(G,g)$ be a semi-Riemannian Lie group with a subgroup $K$ generating a left-invariant conformal foliation $\mathcal F$ on $G$ of codimension two. Semisimple subgroup minimality conjecture. If $K$ is semisimple, then the foliation $\mathcal F$ is minimal. The conjecture extends the corresponding Riemannian claim to semi-Riemannian Lie groups. The paper states that its results produce examples contradicting this claim, so it is refuted.