Generalized Menger embedding conjecture

Let $K$ and $L$ be complexes of positive dimensions, each with non-zero van Kampen obstruction.

Generalized Menger embedding conjecture. The van Kampen obstruction of $K\times L$ is non-zero.

This generalizes Menger's conjecture for products of two non-planar graphs. The original conjecture was proved by Ummel and later, using simpler arguments, by M. Skopenkov; the stated generalization is presented as an open question.