We show how to aggressively add uninferred constraints, in a controlled manner, to formulae for finding Van der Waerden numbers during search. We show that doing so can improve the performance of standard SAT solvers on these formulae by orders of magnitude. We obtain a new and much greater lower bound for one of the Van der Waerden numbers, specifically a bound of 1132 for W(2,6). We believe this bound to actually be the number we seek. The structure of propositional formulae for solving Van der Waerden numbers is similar to that of formulae arising from Bounded Model Checking. Therefore, we view this as a preliminary investigation into solving hard formulae in the area of Formal Verification.
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机译：我们展示了如何在搜索过程中以受控方式积极地将未推断的约束添加到用于查找Van der Waerden数的公式中。我们表明，这样做可以将这些公式上的标准SAT解算器的性能提高几个数量级。我们获得范德华登数之一的新的更大的下界，特别是W（2,6）的下界1132。我们相信这实际上是我们寻求的数量。求解范德瓦尔登数的命题公式的结构类似于由边界模型检查产生的公式的结构。因此，我们认为这是对形式验证领域中的硬公式求解的初步研究。
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