We show that the problem of finding a Resolution refutation that is at most polynomially longer than a shortest one is NP-hard. In the parlance of proof complexity, Resolution is not automatable unless P = NP. Indeed, we show that it is NP-hard to distinguish between formulas that have Resolution refutations of polynomial length and those that do not have subexponential length refutations. This also implies that Resolution is not automatable in subexponential time or quasi-polynomial time unless NP is included in SUBEXP or QP, respectively.

中文翻译：

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自动解决是 NP-Hard

我们表明，找到一个最多比最短多项式更长的解析反驳的问题是 NP 难的。用证明复杂性的说法，除非 P = NP，否则解析是不可自动化的。事实上，我们表明，区分具有多项式长度的分辨率反驳的公式和没有次指数长度反驳的公式是 NP 困难的。这也意味着除非 NP 分别包含在 SUBEXP 或 QP 中，否则分辨率在次指数时间或准多项式时间内是不可自动化的。