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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 . . . . . . . . . . . . . . . . . . . . . ...
The Model Evolution Calculus
, 2003
"... The DPLL procedure is the basis of some of the most successful propositional satisfiability solvers to date. Although originally devised as a proofprocedure for firstorder logic, it has been used almost exclusively for propositional logic so far because of its highly inefficient treatment of quanti ..."
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Cited by 87 (14 self)
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The DPLL procedure is the basis of some of the most successful propositional satisfiability solvers to date. Although originally devised as a proofprocedure for firstorder logic, it has been used almost exclusively for propositional logic so far because of its highly inefficient treatment of quantifiers, based on instantiation into ground formulas. The recent FDPLL calculus by Baumgartner was the first successful attempt to lift the procedure to the firstorder level without resorting to ground instantiations. FDPLL lifts to the firstorder case the core of the DPLL procedure, the splitting rule, but ignores other aspects of the procedure that, although not necessary for completeness, are crucial for its effectiveness in practice. In this paper, we present a new calculus loosely based on FDPLL that lifts these aspects as well. In addition to being a more faithful litfing of the DPLL procedure, the new calculus contains a more systematic treatment of universal literals, one of FDPLL's optimizations, and so has the potential of leading to much faster implementations.
Using CSP LookBack Techniques to Solve Exceptionally Hard SAT Instances
 Principles and Practice of Constraint Programming
, 1996
"... Abstract. While CNF propositional satisfiability (SAT) is a subclass of the more general constraint satisfaction problem (CSP), conventional wisdom has it that some wellknown CSP lookback techniques including backjumping and learning are of little use for SAT. We enhance the Tableau SAT algor ..."
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Cited by 34 (1 self)
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Abstract. While CNF propositional satisfiability (SAT) is a subclass of the more general constraint satisfaction problem (CSP), conventional wisdom has it that some wellknown CSP lookback techniques including backjumping and learning are of little use for SAT. We enhance the Tableau SAT algorithm of Crawford and Auton with lookback techniques and evaluate its performance on problems specifically designed to challenge it. The Random 3SAT problem space has commonly been used to benchmark SAT algorithms because consistently difficult instances can be found near a region known as the phase transition. We modify Random 3SAT in two ways which make instances even harder. First, we evaluate problems with structural regularities and find that CSP lookback techniques offer little advantage. Second, we evaluate problems in which a hard unsatisfiable instance of medium size is embedded in a larger instance, and we find the lookback enhancements to be indispensable. Without them, most instances are “exceptionally hard ”orders of magnitude harder than typical Random 3SAT instances with the same surface characteristics.
FDPLL – A FirstOrder DavisPutnamLogemanLoveland Procedure
 CADE17 – The 17th International Conference on Automated Deduction, volume 1831 of Lecture Notes in Artificial Intelligence
, 2000
"... Abstract. FDPLL is a directly lifted version of the wellknown DavisPutnamLogemanLoveland (DPLL) procedure. While DPLL is based on a splitting rule for case analysis wrt. ground and complementary literals, FDPLL uses a lifted splitting rule, i.e. the case analysis is made wrt. nonground and comp ..."
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Cited by 33 (8 self)
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Abstract. FDPLL is a directly lifted version of the wellknown DavisPutnamLogemanLoveland (DPLL) procedure. While DPLL is based on a splitting rule for case analysis wrt. ground and complementary literals, FDPLL uses a lifted splitting rule, i.e. the case analysis is made wrt. nonground and complementary literals now. The motivation for this lifting is to bring together successful firstorder techniques like unification and subsumption to the propositionally successful DPLL procedure. At the heart of the method is a new technique to represent firstorder interpretations, where a literal specifies truth values for all its ground instances, unless there is a more specific literal specifying opposite truth values. Based on this idea, the FDPLL calculus is developed and proven as strongly complete. 1
Ordered Semantic HyperLinking
, 1994
"... We propose a method for combining the clause linking theorem proving method with theorem proving methods based on orderings. This may be useful for incorporating termrewriting based approaches into clause linking. In this way, some of the propositional inefficiencies of orderingbased approaches ..."
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Cited by 24 (3 self)
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We propose a method for combining the clause linking theorem proving method with theorem proving methods based on orderings. This may be useful for incorporating termrewriting based approaches into clause linking. In this way, some of the propositional inefficiencies of orderingbased approaches may be overcome, while at the same time incorporating the advantages of ordering methods into clause linking. The combination also provides a natural way to combine resolution on nonground clauses, with the clause linking method, which is essentially a ground method. We describe the method, prove completeness, and show that the enumeration part of clause linking with semantics can be reduced to polynomial time in certain cases. We analyze the complexity of the proposed method, and also give some plausibility arguments concerning its expected performance. 1 Introduction There are at least two basic approaches to the study of automated deduction. One approach concentrates on solving...
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...
Proof Lengths for Equational Completion
 Information and Computation
, 1995
"... We first show that ground termrewriting systems can be completed in a polynomial number of rewriting steps, if the appropriate data structure for terms is used. We then apply this result to study the lengths of critical pair proofs in nonground systems, and obtain bounds on the lengths of critical ..."
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Cited by 15 (1 self)
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We first show that ground termrewriting systems can be completed in a polynomial number of rewriting steps, if the appropriate data structure for terms is used. We then apply this result to study the lengths of critical pair proofs in nonground systems, and obtain bounds on the lengths of critical pair proofs in the nonground case. We show how these bounds depend on the types of inference steps that are allowed in the proofs. 1 Introduction We are interested in developing theoretical techniques for evaluating the efficiency of automated inference methods. This includes bounding proof sizes, as well as bounding the size of the total search space generated. Such investigations can provide insights into the comparative strengths of various inference systems, insights that might otherwise be missed. This can also aid in the development of new methods and new inference rules, as we will show. We first consider equational deduction for systems of ground equations. We note that in general...
A Taxonomy of Parallel Strategies for Deduction
 Annals of Mathematics and Artificial Intelligence
, 1999
"... This paper presents a taxonomy of parallel theoremproving methods based on the control of search (e.g., masterslaves versus peer processes), the granularity of parallelism (e.g., fine, medium and coarse grain) and the nature of the method (e.g., orderingbased versus subgoalreduction) . We anal ..."
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Cited by 14 (1 self)
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This paper presents a taxonomy of parallel theoremproving methods based on the control of search (e.g., masterslaves versus peer processes), the granularity of parallelism (e.g., fine, medium and coarse grain) and the nature of the method (e.g., orderingbased versus subgoalreduction) . We analyze how the di#erent approaches to parallelization a#ect the control of search: while fine and mediumgrain methods, as well as masterslaves methods, generally do not modify the sequential search plan, parallelsearch methods may combine sequential search plans (multisearch) or extend the search plan with the capability of subdividing the search space (distributed search). Precisely because the search plan is modified, the latter methods may produce radically di#erent searches than their sequential base, as exemplified by the first distributed proof of the Robbins theorem generated by the Modified ClauseDi#usion prover Peersmcd. An overview of the state of the field and directions...
Partial Instantiation Methods for Inference in First Order Logic
 Journal of Automated Reasoning
, 2000
"... Satisfiability algorithms for propositional logic have improved enormously in recently years. This increases the attractiveness of satisfiability methods for first order logic that reduce the problem to a series of groundlevel satisfiability problems. R. Jeroslow introduced a partial instantiati ..."
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Cited by 12 (0 self)
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Satisfiability algorithms for propositional logic have improved enormously in recently years. This increases the attractiveness of satisfiability methods for first order logic that reduce the problem to a series of groundlevel satisfiability problems. R. Jeroslow introduced a partial instantiation method of this kind that differs radically from the standard resolutionbased methods. This paper lays the theoretical groundwork for an extension of his method that is general enough and efficient enough for general logic programming with indefinite clauses. In particular we improve Jeroslow's approach by (a) extending it to logic with functions, (b) accelerating it through the use of satisfiers, as introduced by Gallo and Rago, and (c) simplifying it to obtain further speedup. We provide a similar development for a "dual" partial instantiation approach defined by Hooker and suggest a primal/dual strategy. We prove correctness of the primal and dual algorithms for full firstorder ...
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.