  We consider two CSP problems: the first CSP encodes 2D Sperner's lemma for
the standard triangulation of the right triangle on $n^2$ small triangles; the
second CSP encodes the fact that it is impossible to match cells of $n \times
n$ square to arrows (two horizontal, two vertical and four diagonal) such that
arrows in two cells with a common edge differ by at most $45^\circ$, and all
arrows on the boundary of the square do not look outside (this fact is a
corollary of the Brower's fixed point theorem). We prove that the tree-like
resolution complexities of these CSPs are $2^{\Theta(n)}$. For Sperner's lemma
our result implies $\Omega(n)$ lower bound on the number of request to colors
of vertices that is enough to make in order to find a trichromatic triangle;
this lower bound was originally proved by Crescenzi and Silvestri.
  CSP based on Sperner's lemma is related with the $\rm PPAD$-complete problem.
We show that CSP corresponding to arrows is also related with a $\rm
PPAD$-complete problem.
