The trivial units conjecture for torsion-free groups

Let $G$ be a torsion-free group and let $R$ be an integral domain. The trivial units conjecture. $G$ satisfies the trivial units property for $R$, meaning that the only units in the group ring $R[G]$ are elements of the form $rg$, where $g\in G$ and $r$ is a unit of $R$. The conjecture was refuted by Gardam; variants and extensions produced non-trivial units over fields of every characteristic, while the original formulation for integral group rings remains open.