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Proving Harder Theorems by Axiom Reduction

机译:通过公理归约证明更难的定理

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摘要

Automated Theorem Proving (ATP) problems may contain unnecessary axioms, either because some of the axiomati-zation of the theory is irrelevant to the particular theorem, or because the axiomatization is redundant by design. ATP systems do not have effective techniques for detecting that axioms are unnecessary (or unlikely to be necessary) to the proof of a theorem. Axiom reduction removes combinations of axioms from an ATP problem, and submits the resultant axiom-reduced problems to an object ATP system. When a combination of only unnecessary axioms is removed, the problem may be quickly solved.
机译:自动定理证明(ATP)问题可能包含不必要的公理,这可能是由于该理论的某些公理化与特定定理无关,或者是因为公理化在设计上是多余的。 ATP系统没有有效的技术来检测公理对于定理的证明是不必要的(或不太可能是必要的)。公理减少可从ATP问题中删除公理的组合,并将由此产生的公理减少的问题提交给目标ATP系统。当仅去除不必要的公理的组合时,可以快速解决该问题。

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