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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...
SpecificationBased Browsing of Software Component Libraries
 in Proceedings of ASE
, 1999
"... . Specificationbased retrieval provides exact contentoriented access to component libraries but requires too much deductive power. Specificationbased browsing evades this bottleneck by moving any deduction into an offline indexing phase. In this paper, we show how match relations are used to bui ..."
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Cited by 31 (2 self)
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. Specificationbased retrieval provides exact contentoriented access to component libraries but requires too much deductive power. Specificationbased browsing evades this bottleneck by moving any deduction into an offline indexing phase. In this paper, we show how match relations are used to build an appropriate index and how formal concept analysis is used to build a suitable navigation structure. This structure has the singlefocus property (i.e., any sensible subset of a library is represented by a single node) and supports attributebased (via explicit component properties) and objectbased (via implicit component similarities) navigation styles. It thus combines the exact semantics of formal methods with the interactive navigation possibilities of informal methods. Experiments show that current theorem provers can solve enough of the emerging proof problems to make browsing feasible. The navigation structure also indicates situations where additional abstractions are required ...
AgentOriented Integration of Distributed Mathematical Services
 Journal of Universal Computer Science
, 1999
"... Realworld applications of automated theorem proving require modern software environments that enable modularisation, networked interoperability, robustness, and scalability. These requirements are met by the AgentOriented Programming paradigm of Distributed Artificial Intelligence. We argue that ..."
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Cited by 19 (10 self)
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Realworld applications of automated theorem proving require modern software environments that enable modularisation, networked interoperability, robustness, and scalability. These requirements are met by the AgentOriented Programming paradigm of Distributed Artificial Intelligence. We argue that a reasonable framework for automated theorem proving in the large regards typical mathematical services as autonomous agents that provide internal functionality to the outside and that, in turn, are able to access a variety of existing external services. This article describes...
PSETHEO: Strategy Parallel Automated Theorem Proving
 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX98
, 1998
"... One of the key issues in Automated Theorem Proving is the search for optimal proof strategies. Since there is not one uniform strategy which works optimal on all proof tasks, one is faced with the difficult problem of selecting a good strategy for a given task. In this paper, we discuss a way of cir ..."
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Cited by 10 (1 self)
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One of the key issues in Automated Theorem Proving is the search for optimal proof strategies. Since there is not one uniform strategy which works optimal on all proof tasks, one is faced with the difficult problem of selecting a good strategy for a given task. In this paper, we discuss a way of circumventing this strategy selection problem by using strategy parallelism. In this approach, a proof task is attempted in parallel by a set of uniform strategies while distributing the given amount of computing resources according to a certain schedule. We discuss important issues of strategy parallelism like search space partitioning, schedule computation, and scalability. In order to evaluate the potential of the method experimentally, we have implemented the strategy parallel theorem prover pSETHEO, which is also described in the paper. The experimental results obtained with the system justify our approach. 1 Introduction Automated Theorem Proving (ATP) is the subfield of theoretical co...
Simple and Efficient Clause Subsumption with Feature Vector Indexing
 Proc. of the IJCAR2004 Workshop on Empirically Successful FirstOrder Theorem Proving
"... Abstract. This paper describes feature vector indexing, a new, nonperfect indexing method for clause subsumption. It is suitable for both forward (i.e., finding a subsuming clause in a set) and backward (finding all subsumed clauses in a set) subsumption. Moreover, it is easy to implement, but still ..."
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Cited by 9 (3 self)
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Abstract. This paper describes feature vector indexing, a new, nonperfect indexing method for clause subsumption. It is suitable for both forward (i.e., finding a subsuming clause in a set) and backward (finding all subsumed clauses in a set) subsumption. Moreover, it is easy to implement, but still yields excellent performance in practice. As an added benefit, by restricting the selection of features used in the index, our technique immediately adapts to indexing modulo arbitrary AC theories with only minor loss of efficiency. Alternatively, the feature selection can be restricted to result in set subsumption. Feature vector indexing has been implemented in our equational theorem prover E, and has enabled us to integrate new simplification techniques making heavy use of subsumption. We experimentally compare the performance of the prover for a number of strategies using feature vector indexing and conventional sequential subsumption.
An Evaluation of Shared Rewriting
 PROCEEDINGS OF THE SECOND INTERNATIONAL WORKSHOP ON IMPLEMENTATION OF LOGICS, TECHNICAL REPORT MPII20012006
, 2001
"... We present an experimental study on the use of shared rewriting in equational theorem proving. We identify the main effects that lead to term sharing in the proof state and experimentally show their influence. Besides the ..."
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Cited by 5 (4 self)
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We present an experimental study on the use of shared rewriting in equational theorem proving. We identify the main effects that lead to term sharing in the proof state and experimentally show their influence. Besides the
Towards Concurrent Resource Managed Deduction
 UNIVERSITY OF BIRMINGHAM, SCHOOL OF COMPUTER SCIENCE. URL
, 1999
"... In this paper, we describe an architecture for resource guided concurrent mechanised deduction which is motivated by some findings in cognitive science. Its benefits are illustrated by comparing it with traditional proof search techniques. In particular, we introduce the notion of focused search ..."
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Cited by 3 (2 self)
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In this paper, we describe an architecture for resource guided concurrent mechanised deduction which is motivated by some findings in cognitive science. Its benefits are illustrated by comparing it with traditional proof search techniques. In particular, we introduce the notion of focused search and show that a reasoning system can be built as the cooperative collection of concurrently acting specialised problem solvers. These reasoners typically perform well in a particular problem domain. The system architecture that we describe assesses the subgoals of a theorem and distributes them to the specialised solvers that look the most promising. Furthermore it allocates resources (above all computation time and memory) to the specialised reasoners. This technique is referred to as resource management. Each reasoner terminates its search for a solution of a given subgoal when the solution is found or when it runs out of its assigned resources. We argue that the effect of resource ma...
Using Term Space Maps to Capture Search Control Knowledge
 IN EQUATIONAL THEOREM PROVING. PROC. FLAIRS99
, 1999
"... We describe a learning inference control heuristic for an equational theorem prover. The heuristic selects a number of problems similar to a new problem from a knowledge base and compiles information about good search decisions for these selected problems into a term space map, which is used to eval ..."
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Cited by 2 (1 self)
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We describe a learning inference control heuristic for an equational theorem prover. The heuristic selects a number of problems similar to a new problem from a knowledge base and compiles information about good search decisions for these selected problems into a term space map, which is used to evaluate the search alternatives at an important choice point in the theorem prover. Experiments on the TPTP problem library show the improvements possible with this new approach.
Automated Reasoning: Past Story and New Trends*
"... We overview the development of firstorder automated reasoning systems starting from their early years. Based on the analysis of current and potential applications of such systems, we also try to predict new trends in firstorder automated reasoning. Our presentation will be centered around two main ..."
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Cited by 2 (0 self)
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We overview the development of firstorder automated reasoning systems starting from their early years. Based on the analysis of current and potential applications of such systems, we also try to predict new trends in firstorder automated reasoning. Our presentation will be centered around two main motives: efficiency and usefulness for existing and future potential applications. This paper expresses the views of the author on past, present, and future of theorem proving in firstorder logic gained during ten years of working on the development, implementation, and applications of the theorem prover Vampire, see [Riazanov and Voronkov, 2002a]. It reflects our recent experience with applications of Vampire in verification, proof assistants, theorem proving, and semantic Web, as well as the analysis of future potential applications. 1 Theorem Proving in FirstOrder Logic The idea of automatic theorem proving has a long history both in mathematics and computer science. For a long time, it was believed by many that hard theorems in mathematics can be proved in a completely automatic way, using the ability of computers to perform fast combinatorial calculations. The very first experiments in automated theorem proving have shown that the purely combinatorial methods of proving firstorder theorems are too week even for proving theorems regarded as relatively easy by mathematicians. Provability in firstorder logic is a very hard combinatorial problem. Firstorder logic is undecidable, which means that there is no terminating procedure checking provability of formulas. There are decidable classes of firstorder formulas but formulas of these classes do not often arise in applications. Due to undecidability, very short formulas may turn out to be extremely complex, while very long ones rather easy. Sometimes firstorder provers find proofs consisting of several thousand steps in a few seconds, but sometimes it takes hours to find a tenstep proof. The theory of firstorder reasoning is centered around the completeness theorems while in practice completeness is often not an issue due to the intrinsic * Partially supported by a grant from EPSRC.