  We show that the Identity Problem is decidable in polynomial time for
finitely generated sub-semigroups of the group $\mathsf{UT}(4, \mathbb{Z})$ of
$4 \times 4$ unitriangular integer matrices. As a byproduct of our proof, we
also show the polynomial-time decidability of several subset reachability
problems in $\mathsf{UT}(4, \mathbb{Z})$.
