Different Proofs are Good Proofs

In order to compare the quality of proofs, it is necessary to measure artifacts of the proofs, and evaluate the measurements to determine dierences between the proofs. This paper discounts the approach of ranking proofs by their measured proof artifacts, and takes the position that dierent proofs are good proofs . The position is based on proofs in the TSTP solution library, which are generated by Automated Theorem Proving (ATP) systems applied to rst-order logic problems in the TPTP problem library.

[1]  P. Jaccard,et al.  Etude comparative de la distribution florale dans une portion des Alpes et des Jura , 1901 .

[2]  G Sutcliffe,et al.  The practice of clausification in automatic theorem proving , 1996 .

[3]  Christoph Weidenbach,et al.  Computing Small Clause Normal Forms , 2001, Handbook of Automated Reasoning.

[4]  Stephan Schulz A Comparison of Different Techniques for Grounding Near-Propositional CNF Formulae , 2002, FLAIRS Conference.

[5]  Andrei Voronkov,et al.  The design and implementation of VAMPIRE , 2002, AI Commun..

[6]  J. Hurd First-Order Proof Tactics in Higher-Order Logic Theorem Provers In Proc , 2003 .

[7]  G. Bancerek,et al.  Journal of Formalized Mathematics on the Characterizations of Compactness , 2022 .

[8]  John K. Slaney,et al.  Guiding a Theorem Prover with Soft Constraints , 2004, ECAI.

[9]  Christoph Benzmüller,et al.  A Generic Modular Data Structure for Proof Attempts Alternating on Ideas and Granularity , 2005, MKM.

[10]  Josef Urban,et al.  MPTP 0.2: Design, Implementation, and Initial Experiments , 2006, Journal of Automated Reasoning.

[11]  Deborah L. McGuinness,et al.  A proof markup language for Semantic Web services , 2006, Inf. Syst..

[12]  Koen Claessen,et al.  Using the TPTP Language for Writing Derivations and Finite Interpretations , 2006, IJCAR.

[13]  Yi Gao,et al.  Automated Generation of Interesting Theorems , 2006, FLAIRS.

[14]  Deborah L. McGuinness,et al.  Knowledge-Worker Requirements for Next Generation Query Answering & Explanation Systems , 2006 .

[15]  Geoff Sutcliffe The SZS Ontologies for Automated Reasoning Software , 2008, LPAR Workshops.

[16]  Geoff Sutcliffe The CADE-21 automated theorem proving system competition , 2008, AI Commun..

[17]  Deborah L. McGuinness,et al.  Presenting TSTP Proofs with Inference Web Tools , 2008, PAAR/ESHOL.

[18]  Geoff Sutcliffe The TPTP Problem Library and Associated Infrastructure , 2009, Journal of Automated Reasoning.

[19]  Christoph Weidenbach,et al.  SPASS Version 3.5 , 2009, CADE.

[20]  Christoph Benzmüller,et al.  Presenting Proofs with Adapted Granularity , 2009, KI.

[21]  Tore Opsahl,et al.  Clustering in weighted networks , 2009, Soc. Networks.