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19
Solution of the Robbins Problem
 Journal of Automated Reasoning
, 1997
"... . In this article we show that the three equations known as commutativity, associativity, and the Robbins equation are a basis for the variety of Boolean algebras. The problem was posed by Herbert Robbins in the 1930s. The proof was found automatically by EQP, a theoremproving program for equationa ..."
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Cited by 129 (3 self)
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. In this article we show that the three equations known as commutativity, associativity, and the Robbins equation are a basis for the variety of Boolean algebras. The problem was posed by Herbert Robbins in the 1930s. The proof was found automatically by EQP, a theoremproving program for equational logic. We present the proof and the search strategies that enabled the program to find the proof. Key words: Associativecommutative unification, Boolean algebra, EQP, equational logic, paramodulation, Robbins algebra, Robbins problem. 1. Introduction This article contains the answer to the Robbins question of whether all Robbins algebras are Boolean. The answer is yes, all Robbins algebras are Boolean. The proof that answers the question was found by EQP, an automated theoremproving program for equational logic. In 1933, E. V. Huntington presented the following three equations as a basis for Boolean algebra [6, 5]: x + y = y + x, (commutativity) (x + y) + z = x + (y + z), (associativit...
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 128 (18 self)
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We describe the superpositionbased theorem prover E. E is a sound and complete...
Otter: The CADE13 Competition Incarnations
 JOURNAL OF AUTOMATED REASONING
, 1997
"... This article discusses the two incarnations of Otter entered in the CADE13 Automated Theorem Proving Competition. Also presented are some historical background, a summary of applications that have led to new results in mathematics and logic, and a general discussion of Otter. ..."
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Cited by 44 (3 self)
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This article discusses the two incarnations of Otter entered in the CADE13 Automated Theorem Proving Competition. Also presented are some historical background, a summary of applications that have led to new results in mathematics and logic, and a general discussion of Otter.
Automatic Proofs and Counterexamples for Some Ortholattice Identities
 Information Processing Letters
, 1998
"... This note answers questions on whether three identities known to hold for orthomodular lattices are true also for ortholattices. One identity is shown to fail by MACE, a program that searches for counterexamples, an the other two are proved to hold by EQP, an equational theorem prover. The problems, ..."
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Cited by 22 (2 self)
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This note answers questions on whether three identities known to hold for orthomodular lattices are true also for ortholattices. One identity is shown to fail by MACE, a program that searches for counterexamples, an the other two are proved to hold by EQP, an equational theorem prover. The problems, from work in quantum logic, were given to us by Norman Megill. Keywords: Automatic theorem proving, ortholattice, quantum logic, theory of computation. 1 Introduction An ortholattice is an algebra with a binary operation (join) and a unary operation 0 (complement) satisfying the following (independent) set of identities. x y = (x 0 y 0 ) 0 (definition of meet) x y = y x (x y) z = x (y z) x (x y) = x x 00 = x x (y y 0 ) = y y 0 Supported by the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Computational and Technology Research, U.S. Department of Energy, under Contract W31109Eng38. From these identities one can...
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...
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 10 (4 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.
Citius altius fortius: Lessons learned from the Theorem Prover Waldmeister
 Proceedings of the 4th International Workshop on FirstOrder Theorem Proving, number 86.1 in Electronic Notes in Theoretical Computer Science
, 2003
"... In the last years, the development of automated theorem provers has been advancing in a so to speak Olympic spirit, following the motto "faster, higher, stronger"; and the Waldmeister system has been a part of that endeavour. We will survey the concepts underlying this prover, which implements Knuth ..."
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Cited by 8 (0 self)
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In the last years, the development of automated theorem provers has been advancing in a so to speak Olympic spirit, following the motto "faster, higher, stronger"; and the Waldmeister system has been a part of that endeavour. We will survey the concepts underlying this prover, which implements KnuthBendix completion in its unfailing variant. The system architecture is based on a strict separation of active and passive facts, and is realized via speci cally tailored representations for each of the central data structures: indexing for the active facts, setbased compression for the passive facts, successor sets for the conjectures. In order to cope with large search spaces, specialized redundancy criteria are employed, and the empirically gained control knowledge is integrated to ease the use of the system. We conclude with a discussion of strengths and weaknesses, and a view of future prospects.
The Next WALDMEISTER Loop
 Proceedings of the 18th International Conference on Automated Deduction, LNAI
, 2001
"... In saturationbased theorem provers, the reasoning process consists in constructing the closure of an axiom set under inferences. ..."
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Cited by 7 (1 self)
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In saturationbased theorem provers, the reasoning process consists in constructing the closure of an axiom set under inferences.
Experiments With Subdivision of Search in Distributed Theorem Proving
 Proc. of PASCO97
, 1997
"... We introduce the distributed theorem prover Peersmcd for networks of workstations. Peersmcd is the parallelization of the Argonne prover EQP, according to our ClauseDiffusion methodology for distributed deduction. The new features of Peersmcd include the AGO (AncestorGraph Oriented) heuristic c ..."
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Cited by 6 (2 self)
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We introduce the distributed theorem prover Peersmcd for networks of workstations. Peersmcd is the parallelization of the Argonne prover EQP, according to our ClauseDiffusion methodology for distributed deduction. The new features of Peersmcd include the AGO (AncestorGraph Oriented) heuristic criteria for subdividing the search space among parallel processes. We report the performance of Peersmcd on several experiments, including problems which require days of sequential computation. In these experiments Peersmcd achieves considerable, sometime superlinear, speedup over EQP. We analyze these results by examining several statistics produced by the provers. The analysis shows that the AGO criteria partitions the search space effectively, enabling Peersmcd to achieve superlinear speedup by parallel search. 1 Introduction Distributed deduction is concerned with the problem of proving difficult theorems by distributing the work among networked computers. The motivation is to st...