  We consider following geometric Ramsey problem: find the least dimension $n$
such that for any 2-coloring of edges of complete graph on the points $\{\pm
1\}^n$ there exists 4-vertex coplanar monochromatic clique. Problem was first
analyzed by Graham and Rothschild and they gave an upper bound: $n\le
F(F(F(F(F(F(F(12)))))))$, where $F(m) = 2\uparrow^m3$. In 2014 Lavrov, Lee and
Mackey greatly improved this result by giving upper bound $n<
2\uparrow\uparrow\uparrow 6 < F(5)$. In this paper we revisit their estimates
and reduce upper bound to $n< 2\uparrow\uparrow\uparrow 5$
