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23
E  A Brainiac Theorem Prover
, 2002
"... We describe the superpositionbased theorem prover E. E is a sound and complete... ..."
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Cited by 126 (18 self)
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We describe the superpositionbased theorem prover E. E is a sound and complete...
New Techniques that Improve MACEstyle Finite Model Finding
 Proceedings of the CADE19 Workshop: Model Computation  Principles, Algorithms, Applications
, 2003
"... ..."
System description: E 0.81
 In Basin and Rusinowitch
, 2004
"... Abstract. E is an equational theorem prover for clausal logic with equality. We describe the latest version, E 0.81 Tumsong, with special emphasis on the important aspects that have changed compared to previously described versions. 1 ..."
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Cited by 44 (7 self)
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Abstract. E is an equational theorem prover for clausal logic with equality. We describe the latest version, E 0.81 Tumsong, with special emphasis on the important aspects that have changed compared to previously described versions. 1
A Decomposition Rule for Decision Procedures by Resolutionbased Calculi
 In: Proc. 11th Int. Conf. on Logic for Programming, Artificial Intelligence, and Reasoning (LPAR
, 2004
"... Abstract. Resolutionbased calculi are among the most widely used calculi for theorem proving in firstorder logic. Numerous refinements of resolution are nowadays available, such as e.g. basic superposition, a calculus highly optimized for theorem proving with equality. However, even such an advanc ..."
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Cited by 31 (10 self)
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Abstract. Resolutionbased calculi are among the most widely used calculi for theorem proving in firstorder logic. Numerous refinements of resolution are nowadays available, such as e.g. basic superposition, a calculus highly optimized for theorem proving with equality. However, even such an advanced calculus does not restrict inferences enough to obtain decision procedures for complex logics, such as SHIQ. In this paper, we present a new decomposition inference rule, which can be combined with any resolutionbased calculus compatible with the standard notion of redundancy. We combine decomposition with basic superposition to obtain three new decision procedures: (i) for the description logic SHIQ, (ii) for the description logic ALCHIQb, and (iii) for answering conjunctive queries over SHIQ knowledge bases. The first two procedures are worstcase optimal and, based on the vast experience in building efficient theorem provers, we expect them to be suitable for practical usage. 1
Tree Automata with Equality Constraints Modulo Equational Theories
 Proceedings of 3rd International Joint Conference on Automated Reasoning, IJCAR, volume 4130 of Lecture Notes in Artificial Intelligence
, 2006
"... Abstract. This paper presents new classes of tree automata combining automata with equality test and automata modulo equational theories. We believe that these classes have a good potential for application in e.g. software verification. These tree automata are obtained by extending the standard Horn ..."
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Cited by 17 (3 self)
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Abstract. This paper presents new classes of tree automata combining automata with equality test and automata modulo equational theories. We believe that these classes have a good potential for application in e.g. software verification. These tree automata are obtained by extending the standard Horn clause representations with equational conditions and rewrite systems. We show in particular that a generalized membership problem (extending the emptiness problem) is decidable by proving that the saturation of tree automata presentations with suitable paramodulation strategies terminates. Alternatively our results can be viewed as new decidable classes of firstorder formula. 1
A Comparison of Different Techniques for Grounding NearPropositional CNF Formulae
 Proc. 15th Florida Artificial Intelligence Research Symposium
, 2002
"... A nearpropositional CNF formula is a firstorder formula (in clause normal form) with a finite Herbrand universe. For this class of problems, the validity problem can be decided by a combination of grounding and propositional reasoning. However, naive approaches to grounding can generate extremely ..."
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Cited by 13 (1 self)
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A nearpropositional CNF formula is a firstorder formula (in clause normal form) with a finite Herbrand universe. For this class of problems, the validity problem can be decided by a combination of grounding and propositional reasoning. However, naive approaches to grounding can generate extremely large ground formulae. We investigate various means to reduce the number of ground instances generated and show that we can increase the number of problems that can be handled with reasonable resources.
Practical Proof Checking for Program Certification
 Proceedings of the CADE20 Workshop on Empirically Successful Classical Automated Reasoning (ESCAR’05
, 2005
"... Program certification aims to provide explicit evidence that a program meets a specified level of safety. This evidence must be independently reproducible and verifiable. We have developed a system, based on theorem proving, that generates proofs that autogenerated aerospace code adheres to a numbe ..."
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Cited by 5 (4 self)
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Program certification aims to provide explicit evidence that a program meets a specified level of safety. This evidence must be independently reproducible and verifiable. We have developed a system, based on theorem proving, that generates proofs that autogenerated aerospace code adheres to a number of safety policies. For certification purposes, these proofs need to be verified by a proof checker. Here, we describe and evaluate a semantic derivation verification approach to proof checking. The evaluation is based on 109 safety obligations that are attempted by EP and SPASS. Our system is able to verify 129 out of the 131 proofs found by the two provers. The majority of the proofs are checked completely in less than 15 seconds wall clock time. This shows that the proof checking task arising from a substantial prover application is practically tractable. 1
Finite Model Building: Improvements and Comparisons
 In: Model Computation – Principles, Algorithms, Applications, CADE19 Workshop W4
, 2003
"... The paper ivestigates nite model building for rst order logic. We consider two main categories of methods: Macetype and Falcontype methods. The paper has two goals: rst, presenting several improvements and strategies for the basic Macetype and Falcontype algorithms, second, comparing the e ..."
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Cited by 5 (0 self)
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The paper ivestigates nite model building for rst order logic. We consider two main categories of methods: Macetype and Falcontype methods. The paper has two goals: rst, presenting several improvements and strategies for the basic Macetype and Falcontype algorithms, second, comparing the eciency of dierent methods. The improvements to the Macetype algorithms are focused on decreasing the size of the propositional subtasks. A new cell selection heuristics is introduced for the Falcontype algorithms. The methods are implemented in the Gandalf theorem prover. We present both the eect of the introduced improvements and the comparison of method categories for several problem classes, based on their syntactical characteristics. Finally, several suggestions for further investigations are given.
Engineering DPLL(T) + saturation
 PROC. 4TH IJCAR
, 2008
"... Satisfiability Modulo Theories (SMT) solvers have proven highly scalable, efficient and suitable for integrated theory reasoning. The most efficient SMT solvers rely on refutationally incomplete methods for incorporating quantifier reasoning. We describe a calculus and a system that tightly integra ..."
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Cited by 5 (2 self)
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Satisfiability Modulo Theories (SMT) solvers have proven highly scalable, efficient and suitable for integrated theory reasoning. The most efficient SMT solvers rely on refutationally incomplete methods for incorporating quantifier reasoning. We describe a calculus and a system that tightly integrates Superposition and DPLL(T). In the calculus, all nonunit ground clauses are delegated to the DPLL(T) core. The integration is tight, dependencies on case splits are tracked as hypotheses in the saturation engine. The hypotheses are discharged during backtracking. The combination is refutationally complete for firstorder logic, and its implementation is competitive in performance with Ematching based SMT solvers on problems they are good at.