  Recently, Chmutov proved that the partial-dual polynomial considered as a
function on chord diagrams satisfies the four-term relation. Deng et al. then
proved that this function on framed chord diagrams also satisfies the four-term
relation, i.e., is a framed weight system. In this paper, we extend their
results to the twist polynomial of a set system by proving that the twist
polynomial on set systems satisfies the four-term relation.
