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24
A Prolog Technology Theorem Prover: Implementation by an Extended Prolog Compiler
 Journal of Automated Reasoning
, 1987
"... A Prolog technology theorem prover (PTTP) is an extension of Prolog that is complete for the full firstorder predicate calculus. It differs from Prolog in its use of unification with the occurs check for soundness, the modelelimination reduction rule that is added to Prolog inferences to make the ..."
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Cited by 100 (2 self)
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A Prolog technology theorem prover (PTTP) is an extension of Prolog that is complete for the full firstorder predicate calculus. It differs from Prolog in its use of unification with the occurs check for soundness, the modelelimination reduction rule that is added to Prolog inferences to make the inference system complete, and depthfirst iterativedeepening search instead of unbounded depthfirst search to make the search strategy complete. A Prolog technology theorem prover has been implemented by an extended PrologtoLISP compiler that supports these additional features. It is capable of proving theorems in the full firstorder predicate calculus at a rate of thousands of inferences per second. 1 This is a revised and expanded version of a paper presented at the 8th International Conference on Automated Deduction, Oxford, England, July 1986, and is to appear in Journal of Automated Reasoning. This research was supported by the Defense Advanced Research Projects Agency under Co...
The TPTP Problem Library
, 1999
"... This report provides a detailed description of the TPTP Problem Library for automated theorem proving systems. The library is available via Internet, and forms a common basis for development of and experimentation with automated theorem provers. This report provides: ffl the motivations for buildin ..."
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Cited by 100 (6 self)
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This report provides a detailed description of the TPTP Problem Library for automated theorem proving systems. The library is available via Internet, and forms a common basis for development of and experimentation with automated theorem provers. This report provides: ffl the motivations for building the library; ffl a discussion of the inadequacies of previous problem collections, and how these have been resolved in the TPTP; ffl a description of the library structure, including overview information; ffl descriptions of supplementary utility programs; ffl guidelines for obtaining and using the library; Contents 1 Introduction 2 1.1 Previous Problem Collections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 What is Required? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Inside the TPTP 6 2.1 The TPTP Domain Structure . . . . . . . . . . . . . . . . . . . . . ...
Caching and Lemmaizing in Model Elimination Theorem Provers
, 1992
"... Theorem provers based on model elimination have exhibited extremely high inference rates but have lacked a redundancy control mechanism such as subsumption. In this paper we report on work done to modify a model elimination theorem prover using two techniques, caching and lemmaizing, that have reduc ..."
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Cited by 49 (2 self)
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Theorem provers based on model elimination have exhibited extremely high inference rates but have lacked a redundancy control mechanism such as subsumption. In this paper we report on work done to modify a model elimination theorem prover using two techniques, caching and lemmaizing, that have reduced by more than an order of magnitude the time required to find proofs of several problems and that have enabled the prover to prove theorems previously unobtainable by topdown model elimination theorem provers.
PROTEIN: A PROver with a Theory Extension Interface
 AUTOMATED DEDUCTION  CADE12, VOLUME 814 OF LNAI
, 1994
"... PROTEIN (PROver with a Theory Extension INterface) is a PTTPbased first order theorem prover over builtin theories. Besides various standardrefinements known for model elimination, PROTEIN also offers a variant of model elimination for casebased reasoning and which does not need contrapositives. ..."
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Cited by 41 (10 self)
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PROTEIN (PROver with a Theory Extension INterface) is a PTTPbased first order theorem prover over builtin theories. Besides various standardrefinements known for model elimination, PROTEIN also offers a variant of model elimination for casebased reasoning and which does not need contrapositives.
Model Elimination without Contrapositives and its Application to PTTP
 PROCEEDINGS OF CADE12, SPRINGER LNAI 814
, 1994
"... We give modifications of model elimination which do not necessitate the use of contrapositives. These restart model elimination calculi are proven sound and complete and their implementation by PTTP is depicted. The corresponding proof procedures are evaluated by a number of runtime experiments and ..."
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Cited by 22 (8 self)
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We give modifications of model elimination which do not necessitate the use of contrapositives. These restart model elimination calculi are proven sound and complete and their implementation by PTTP is depicted. The corresponding proof procedures are evaluated by a number of runtime experiments and they are compared to other well known provers. Finally we relate our results to other calculi, namely the connection method, modified problem reduction format and NearHorn Prolog.
The Search Efficiency of Theorem Proving Strategies: An Analytical Comparison
, 1994
"... We analyze the search efficiency of a number of common refutational theorem proving strategies for firstorder logic. Search efficiency is concerned with the total number of proofs and partial proofs generated, rather than with the sizes of the proofs. We show that most common strategies produce sea ..."
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Cited by 22 (3 self)
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We analyze the search efficiency of a number of common refutational theorem proving strategies for firstorder logic. Search efficiency is concerned with the total number of proofs and partial proofs generated, rather than with the sizes of the proofs. We show that most common strategies produce search spaces of exponential size even on simple sets of clauses, or else are not sensitive to the goal. However, clause linking, which uses a reduction to propositional calculus, has behavior that is more favorable in some respects, a property that it shares with methods that cache subgoals. A strategy which is of interest for termrewriting based theorem proving is the Aordering strategy, and we discuss it in some detail. We show some advantages of Aordering over other strategies, which may help to explain its efficiency in practice. We also point out some of its combinatorial inefficiencies, especially in relation to goalsensitivity and irrelevant clauses. In addition, SLDreso...
METEOR: Exploring Model Elimination Theorem Proving
 Journal of Automated Reasoning
, 1992
"... In this paper we describe the theorem prover METEOR which is a highperformance Model Elimination prover running in sequential, parallel and distributed computing environments. METEOR has a very high inference rate, but as is the case with better chessplaying programs speed alone is not suffici ..."
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Cited by 12 (1 self)
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In this paper we describe the theorem prover METEOR which is a highperformance Model Elimination prover running in sequential, parallel and distributed computing environments. METEOR has a very high inference rate, but as is the case with better chessplaying programs speed alone is not sufficient when exploring large search spaces; intelligent search is necessary. We describe modifications to traditional iterative deepening search mechanisms whose implementation in METEOR result in performance improvements of several orders of magnitude and that have permitted the discovery of proofs unobtainable by topdown Model Elimination provers. 1 Introduction Model Elimination (ME) [Lov68, Lov69, Lov78] is the basis for the underlying inference mechanism of several highperformance theorem provers. The design of these provers is adapted from the architecture of the WAM (Warren Abstract Machine) [War83]  the de facto standard for efficient Prolog implementations. Such provers includ...
Paramodulation without Duplication
 Proceedings 10th IEEE Symposium on Logic in Computer Science, San Diego (Ca., USA
, 1995
"... The resolution (and paramodulation) inference systems are theorem proving procedures for firstorder logic (with equality), but they can run exponentially long for subclasses which have polynomial time decision procedures, as in the case of SLD resolution and the KnuthBendix completion procedure, b ..."
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Cited by 11 (6 self)
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The resolution (and paramodulation) inference systems are theorem proving procedures for firstorder logic (with equality), but they can run exponentially long for subclasses which have polynomial time decision procedures, as in the case of SLD resolution and the KnuthBendix completion procedure, both in the ground case. Specialized methods run in polynomial time, but have not been extended to the full firstorder case. We show a form of Paramodulation which does not copy literals, which runs in polynomial time for the ground case of the following four subclasses: Horn Clauses with any selection rule, any set of Unit Equalities (this includes Completion), Equational Horn Clauses with a certain selection rule, and Conditional Narrowing.
Model Elimination, Logic Programming and Computing Answers
 University of Koblenz
, 1995
"... We demonstrate that theorem provers using model elimination (ME) can be used as answer complete interpreters for disjunctive logic programming. More specifically, we introduce a mechanism for computing answers into the restart variant of ME. Building on this, we develop a new calculus called ancestr ..."
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Cited by 10 (5 self)
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We demonstrate that theorem provers using model elimination (ME) can be used as answer complete interpreters for disjunctive logic programming. More specifically, we introduce a mechanism for computing answers into the restart variant of ME. Building on this, we develop a new calculus called ancestry restart ME. This variant admits a more restrictive regularity restriction than restart ME, and, as a side effect, it is in particular attractive for computing definite answers. The presented calculi can also be used successfully in the context of automated theorem proving. We demonstrate experimentally that it is more difficult to compute (nontrivial) answers to goals, instead of only proving the existence of answers.