The determination of $ES(7)$ is the first open case of the planar Erdős--Szekeres problem, where the general conjecture predicts $ES(7)=33$. We present a SAT encoding for the 33-point case based on triple-orientation variables and a 4-set convexity criterion for excluding convex 7-gons, together with convex-layer anchoring constraints. The framework yields UNSAT certificates for a collection of anchored subfamilies. We also report pronounced runtime variability across configurations, including heavy-tailed behavior that currently dominates the computational effort and motivates further encoding refinements.

翻译：$ES(7)$的确定是平面Erdős--Szekeres问题中首个悬而未决的情形，该问题的一般猜想预测$ES(7)=33$。本文提出一种基于三元定向变量的33点情形SAT编码方法，结合用于排除凸七边形的四集凸性判定准则以及凸层锚定约束。该框架为一组锚定子族生成UNSAT可满足性证明。我们还观察到不同配置间存在显著的运行时间差异，包括当前主导计算开销的重尾行为，这为后续编码优化提供了方向。