In this paper, we examine Quigley's "A Polynomial Time Algorithm for 3SAT" [Qui24]. Quigley claims to construct an algorithm that runs in polynomial time and determines whether a boolean formula in 3CNF form is satisfiable. Such a result would prove that 3SAT $\in \text{P}$ and thus $\text{P} = \text{NP}$. We show Quigley's argument is flawed by providing counterexamples to several lemmas he attempts to use to justify the correctness of his algorithm. We also provide an infinite class of 3CNF formulas that are unsatisfiable but are classified as satisfiable by Quigley's algorithm. In doing so, we prove that Quigley's algorithm fails on certain inputs, and thus his claim that $\text{P} = \text{NP}$ is not established by his paper.

翻译：本文对Quigley的《3SAT多项式时间算法》[Qui24]进行了审视。Quigley声称构建了一种在多项式时间内运行、能判定3CNF形式布尔公式可满足性的算法。该结果若能成立，将证明3SAT $\in \text{P}$，进而得出$\text{P} = \text{NP}$的结论。我们通过对其论证过程中若干引理提出反例，揭示了Quigley论证的缺陷。此外，我们构造了一类被Quigley算法错误判定为可满足、实则不可满足的3CNF公式无限集合。由此证明Quigley算法在特定输入上失效，其关于$\text{P} = \text{NP}$的主张未能通过该论文得到确证。