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ENIGMA: Efficient Learning-Based Inference Guiding Machine

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Intelligent Computer Mathematics (CICM 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10383))

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Abstract

ENIGMA is a learning-based method for guiding given clause selection in saturation-based theorem provers. Clauses from many previous proof searches are classified as positive and negative based on their participation in the proofs. An efficient classification model is trained on this data, classifying a clause as useful or un-useful for the proof search. This learned classification is used to guide next proof searches prioritizing useful clauses among other generated clauses. The approach is evaluated on the E prover and the CASC 2016 AIM benchmark, showing a large increase of E’s performance.

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Notes

  1. 1.

    We use E Prover 1.9.1 (http://www.eprover.org/).

  2. 2.

    We use .

  3. 3.

    AIM is a long-term and large-scale project [15] in applied automated deduction concerned with proving open algebraic conjectures by Kinyon and Veroff.

  4. 4.

    Different proof search settings (term orderings, rewriting settings, etc.) may largely change the proof search and make training examples incompatible. That is to say, a classifier trained on proofs produced with some proof search settings should be used only with the same settings. In our case, the proof search settings used to produce competition proofs are not known. Thus we resort to a single E prover strategy and generate compatible training data ourselves.

  5. 5.

    All the experiments were performed at Intel Xeon 2.3 GHz workstation.

  6. 6.

    We use Vampire 4.0 in CASC mode.

  7. 7.

    In an initial experiment, a simple nearest-neighbor selection of training problems for the learning further decreases the solving times and proves one more AIM problem unsolved by Prover9.

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Acknowledgments

We thank Stephan Schulz for his open and modular implementation of E and its many features that allowed us to do this work. We also thank the Machine Learning Group at National Taiwan University for making LIBLINEAR openly available. This work was supported by the ERC Consolidator grant no. 649043 AI4REASON.

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Authors and Affiliations

  1. Czech Technical University in Prague, Prague, Czech Republic

    Jan Jakubův & Josef Urban

Authors
  1. Jan Jakubův
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  2. Josef Urban
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Correspondence to Jan Jakubův .

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Editors and Affiliations

  1. Radboud University, Nijmegen, The Netherlands

    Herman Geuvers

  2. Coventry University, Coventry, United Kingdom

    Matthew England

  3. National University of Sciences and Technology, Islamabad, Pakistan

    Osman Hasan

  4. Jacobs University Bremen, Bremen, Germany

    Florian Rabe

  5. FIZ Karlsruhe, Berlin, Germany

    Olaf Teschke

The E Prover Strategy Used in Experiments

The E Prover Strategy Used in Experiments

The following fixed E strategy \(S_0\), described by its command line arguments, was used in the experiments:

figure a

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Jakubův, J., Urban, J. (2017). ENIGMA: Efficient Learning-Based Inference Guiding Machine. In: Geuvers, H., England, M., Hasan, O., Rabe, F., Teschke, O. (eds) Intelligent Computer Mathematics. CICM 2017. Lecture Notes in Computer Science(), vol 10383. Springer, Cham. https://doi.org/10.1007/978-3-319-62075-6_20

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  • DOI: https://doi.org/10.1007/978-3-319-62075-6_20

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