We describe some recent computer investigations with the `Constraint Logic Programming over Finite Domains' -- CLP(FD) -- library in the Prolog programming environment to search for new simple Lie algebras over the field $\GF(2)$ of $2$ elements. Motivated by a paper of Grishkov et. al., we specifically look for those with a `thin decomposition', and we settle one of their conjectures. We extrapolate from our results the existence of two new infinite families of simple Lie algebras, in addition to finding seven new sporadic examples in dimension $31$. We also better contextualise some previously discovered simple algebras, putting them into families which do not seem to have ever appeared in the literature, and give an updated table of those currently known.

翻译：我们描述了最近一些计算机调查,即“Finite Domens的严格逻辑规划”-CLP(FD)-Prolog编程环境中的图书馆,以寻找外地新的简单代数,耗资2美元。我们受到Grishkov等人的论文的启发,特别寻找那些`分解'的人,我们解决了他们的猜想之一。我们从我们的结果推断,除了在310美元方面发现了7个新的零星例子外,还发现了两个新的简单代数家庭。我们还更好地将以前发现的简单代数纳入文献中从未出现过的家庭,并给出了目前已知家庭的最新表格。