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We consider two CSP problems: the first CSP encodes 2D Sperner's lemma forthe standard triangulation of the right triangle on $n^2$ small triangles; thesecond CSP encodes the fact that it is impossible to match cells of $n \timesn$ square to arrows (two horizontal, two vertical and four diagonal) such thatarrows in two cells with a common edge differ by at most $45^\circ$, and allarrows on the boundary of the square do not look outside (this fact is acorollary of the Brower's fixed point theorem). We prove that the tree-likeresolution complexities of these CSPs are $2^{\Theta(n)}$. For Sperner's lemmaour result implies $\Omega(n)$ lower bound on the number of request to colorsof 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 $\rmPPAD$-complete problem.

Tree-like resolution complexity of two planar problems