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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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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.
A Connectionist Control Component for the Theorem Prover SETHEO
 In ECAI94 Workshop on Combining Symbolic and Connectionist Processing
, 1994
"... Today, the power of automated theorem provers is yet too weak for proving many challinging problems. However heuristics for guiding the proof search can dramatically improve the power of such provers. Since it is very difficult to develop heuristics by hand and since they have to be developed specif ..."
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Cited by 14 (9 self)
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Today, the power of automated theorem provers is yet too weak for proving many challinging problems. However heuristics for guiding the proof search can dramatically improve the power of such provers. Since it is very difficult to develop heuristics by hand and since they have to be developed specifically for each problem domain (theory), we decided to derive heuristics automatically using machine learning techniques. Especially neural networks seem to be very suitable for the representation of heuristics because of their ability to deal with incomplete and inconsistent knowledge. In the following paper we describe our experiences with a connectionist control component for the theorem prover SETHEO. As SETHEO is very closely related to the programming language Prolog, our work might be of interest for a greater public than just the theorem proving community. 1 Introduction In automated theorem proving the goal is to find a proof for a given theorem automatically, starting from a set o...
A Structured Set of HigherOrder Problems
 Theorem Proving in Higher Order Logics: TPHOLs 2005, LNCS 3603
, 2005
"... Abstract. We present a set of problems that may support the development of calculi and theorem provers for classical higherorder logic. We propose to employ these test problems as quick and easy criteria preceding the formal soundness and completeness analysis of proof systems under development. Ou ..."
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Abstract. We present a set of problems that may support the development of calculi and theorem provers for classical higherorder logic. We propose to employ these test problems as quick and easy criteria preceding the formal soundness and completeness analysis of proof systems under development. Our set of problems is structured according to different technical issues and along different notions of semantics (including Henkin semantics) for higherorder logic. Many examples are either theorems or nontheorems depending on the choice of semantics. The examples can thus indicate the deductive strength of a proof system. 1 Motivation: Test Problems for HigherOrder Reasoning Systems Test problems are important for the practical implementation of theorem provers as well as for the preceding theoretical development of calculi, strategies and heuristics. If the test theorems can be proven (resp. the nontheorems cannot) then they ideally provide a strong indication for completeness (resp. soundness). Examples for early publications providing firstorder test problems are [21,29,23]. For more than decade now the TPTP library [28] has been developed as a systematically structured electronic repository of
Uniform Strategies: The CADE11 Theorem Proving Contest
 Journal of Automated Reasoning
, 1993
"... Abstract. At CADE10 Ross Overbeek proposed a twopart contest to stimulate and reward work in automated theorem proving. The rst part consists of seven theorems to be proved with resolution, and the second part of equational theorems. Our theorem provers Otter and its parallel child Roo proved all ..."
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Abstract. At CADE10 Ross Overbeek proposed a twopart contest to stimulate and reward work in automated theorem proving. The rst part consists of seven theorems to be proved with resolution, and the second part of equational theorems. Our theorem provers Otter and its parallel child Roo proved all of the resolution theorems and half of the equational theorems. This paper represents a family of entries in the contest.
The TPTP Problem Library (TPTP v2.1.0
 Department of Computer Science, James Cook University
, 1997
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HEUROPA: Heuristic Optimization of Parallel Computations
 In !EuroARCH '93
, 1993
"... . The performance of almost all parallel algorithms and systems can be improved by the use of heuristics that affect the parallel execution. However, since optimal guidance usually depends on many different influences, establishing such heuristics is often difficult. Due to the importance of heurist ..."
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. The performance of almost all parallel algorithms and systems can be improved by the use of heuristics that affect the parallel execution. However, since optimal guidance usually depends on many different influences, establishing such heuristics is often difficult. Due to the importance of heuristics for optimizing parallel execution, and the similarity of the problems that arise for establishing such heuristics, the HEUROPA activity was founded to attack these problems in a uniform way. To overcome the difficulties of specifying heuristics by hand, machine learning techniques have been employed to obtain heuristics automatically. This paper presents the general approach used for learning heuristics, describes the applications arising in the various subprojects, and provides a detailed case study using the approach for a particular application. 1 Introduction Parallel algorithms represent complex software, with a large number of parameters that need to be adjusted for optimal perfor...
Proving FirstOrder Equality Theorems with HyperLinking
, 1995
"... Lee and Plaisted recently developed a new automated theorem proving strategy called hyperlinking. As part of his dissertation, Lee developed a roundbyround implementation of the hyperlinking strategy, which competes well with other automated theorem provers on a wide range of theorem proving p ..."
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Lee and Plaisted recently developed a new automated theorem proving strategy called hyperlinking. As part of his dissertation, Lee developed a roundbyround implementation of the hyperlinking strategy, which competes well with other automated theorem provers on a wide range of theorem proving problems. However, Lee's roundbyround implementation of hyperlinking is not particularly well suited for the addition of special methods in support of equality. In this dissertation, we describe, as alternative to the roundbyround hyperlinking implementation of Lee, a smallest instance first implementation of hyperlinking which addresses many of the inefficiencies of roundbyround hyperlinking encountered when adding special methods in support of equality. Smallest instance first hyperlinking is based on the formalization of generating smallest clauses first, a heuristic widely used in other automated theorem provers. We prove both the soundness and logical completeness of smallest instance first hyperlinking and show that it always generates smallest clauses first under
Automated Production of Traditional Proofs in Solid Geometry
"... This paper presents a method of producing readable proofs for theorems in solid geometry. The method is for a class of constructive geometry statements about straight lines, planes, circles, and spheres. The key idea of the method is to eliminate points from the conclusion of a geometric statement u ..."
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This paper presents a method of producing readable proofs for theorems in solid geometry. The method is for a class of constructive geometry statements about straight lines, planes, circles, and spheres. The key idea of the method is to eliminate points from the conclusion of a geometric statement using several (fixed) high level basic propositions about the signed volumes of tetrahedrons and Pythagoras differences of triangles. We have implemented the algorithm and more than 80 examples from solid geometry have been used to test the program. Our program is efficient and the proofs produced by it are generally short and readable.
Automated reasoning: Real uses and . . .
"... An automated reasoning program has provided invaluable assistance in answering certain previously open questions in mathematics and in formal logic. These questions would not have been answered, at least by those who obtained the results, were it not for the program's contribution. Others have ..."
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An automated reasoning program has provided invaluable assistance in answering certain previously open questions in mathematics and in formal logic. These questions would not have been answered, at least by those who obtained the results, were it not for the program's contribution. Others have used such a program to design logic circuits, many of which proved superior (with respect to transistor count) to the existing designs, and to validate the design of other circuits. These successes establish the value of an automated reasoning program for research and suggest the value for practical applications. We thus conclude that the field of automated reasoning is on the verge of becoming one of the more significant branches of computer science. Further, we conclude that the field has already advanced from stage 1, that of potential usefulness, to stage 2, that of actual usefulness. To pass to stage 3, that of wide acceptance and use, requires, among other things, easy access to an automated reasoning program and an understanding of the various aspects of automated reasoning. In fact, an automated reasoning program is available that is portable and can be run on relatively inexpensive machines. Moreover, a system exists for producing a reasoning program tailored to given specifications. As for the requirement of understanding the aspects of automated reasoning, much research remains—research aided by access to a reasoning program. A large obstacle has thus been removed, permitting many to experiment with and find uses for a computer program that can be relied upon as a most valuable automated reasoning assistant.