Satallax: An Automatic Higher-Order Prover

Brown, Chad E.

doi:10.1007/978-3-642-31365-3_11

Cited by 95 publications

(107 citation statements)

References 9 publications

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“…This allows experimenting with higher-order ATPs like LEO2 [10] and Satallax [20], in addition to the standard ATPs working in the first-order formalism. The translation to THF needs to perform only one step: monomorphisation.…”

Section: Translations To Higher-order Formatsmentioning

confidence: 99%

“…1897 of the 16082 named theorems do not have a proof (those are definitions and axioms). For all the remaining 14185 named theorems the corresponding re-proving ATP problems were created, and are available online 20 in the FOF, THF, and TFF1 formats. These problems are used for the ATP re-proving experiments described in Section 5.1.…”

Section: The Data Set Of Atp Re-proving Problemsmentioning

confidence: 99%

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Learning-Assisted Automated Reasoning with Flyspeck

2014

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The considerable mathematical knowledge encoded by the Flyspeck project is combined with external automated theorem provers (ATPs) and machine-learning premise selection methods trained on the Flyspeck proofs, producing an AI system capable of proving a wide range of mathematical conjectures automatically. The performance of this architecture is evaluated in a bootstrapping scenario emulating the development of Flyspeck from axioms to the last theorem, each time using only the previous theorems and proofs. It is shown that 39 % of the 14185 theorems could be proved in a push-button mode (without any high-level advice and user interaction) in 30 seconds of real time on a fourteen-CPU workstation. The necessary work involves: (i) an implementation of sound translations of the HOL Light logic to ATP formalisms: untyped first-order, polymorphic typed first-order, and typed higher-order, (ii) export of the dependency information from HOL Light and ATP proofs for the machine learners, and (iii) choice of suitable representations and methods for learning from previous proofs, and their integration as advisors with HOL Light. This work is described and discussed here, and an initial analysis of the body of proofs that were found fully automatically is provided.

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Section: Translations To Higher-order Formatsmentioning

confidence: 99%

Section: The Data Set Of Atp Re-proving Problemsmentioning

confidence: 99%

Learning-Assisted Automated Reasoning with Flyspeck

2014

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“…In the experiments the following HOL provers were applied: Satallax (2.6) [6], Isabelle (2012) [10], LEO-II [4] (1.5.0), Nitpick (2012) [5] and agsyHOL (1.0) [9]. Isabelle, Satallax, LEO-II and agsyHOL are theorem provers.…”

Section: The Prover Hol-pmentioning

confidence: 99%

“…This meta-prover exploits the SystemOnTPTP infrastructure [15] and sequentially schedules the HOL reasoners LEO-II [4], Satallax [6], Isabelle [10], agsyHOL [9] and Nitpick [5]. HOL-P is evaluated with respect to 580 benchmark problems in the QMLTP library [13].…”

Section: Introductionmentioning

confidence: 99%

HOL Based First-Order Modal Logic Provers

Benzmüller

Raths

2013

Logic for Programming, Artificial Intelligence, and Reasoning

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Abstract. First-order modal logics (FMLs) can be modeled as natural fragments of classical higher-order logic (HOL). The FMLtoHOL tool exploits this fact and it enables the application of off-the-shelf HOL provers and model finders for reasoning within FMLs. The tool bridges between the qmf-syntax for FML and the TPTP thf0-syntax for HOL. It currently supports logics K, K4, D, D4, T, S4, and S5 with respect to constant, varying and cumulative domain semantics. The approach is evaluated in combination with a meta-prover for HOL, which sequentially schedules various HOL reasoners. The resulting system is very competitive.

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“…The paper thus provides useful and relevant information for evaluations of competitor systems based on the direct approach. Moreover, some light is shed on the collective and individual performances of the higher-order automated theorem provers LEO-II [5], Satallax [7], Isabelle [10], agsyHOL [9] and Nitpick [6].…”

Section: Introductionmentioning

confidence: 99%

HOL Provers for First-order Modal Logics --- Experiments

Benzmüller¹

EPiC Series in Computing

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Satallax: An Automatic Higher-Order Prover

Cited by 95 publications

References 9 publications

Learning-Assisted Automated Reasoning with Flyspeck

Learning-Assisted Automated Reasoning with Flyspeck

HOL Based First-Order Modal Logic Provers

HOL Provers for First-order Modal Logics --- Experiments

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