Karasev's colorful Tverberg conjecture for hyperplanes

Let $r$ be a positive integer. Given $r$ blue, $r$ red, and $r$ green lines in the plane in general position, where a family is in general position when the normal vectors of any two lines are linearly independent and no three lines coincide, each triple inducing a triangle. Karasev's colorful Tverberg conjecture. These lines can be split into $r$ colorful triples whose induced triangles intersect. The conjecture is a colorful hyperplane analogue of the Tverberg theorem. The paper disproves it for every $r$, so it is not open.