Relevant bibliographies by topics / Theorem proving

Academic literature on the topic 'Theorem proving'

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Published: 4 June 2021
Last updated: 8 June 2024

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Journal articles on the topic "Theorem proving"

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Gan, Wenbin, Xinguo Yu, Ting Zhang, and Mingshu Wang. "Automatically Proving Plane Geometry Theorems Stated by Text and Diagram." International Journal of Pattern Recognition and Artificial Intelligence 33, no. 07 (June 7, 2019): 1940003. http://dx.doi.org/10.1142/s0218001419400032.

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This paper presents an algorithm for proving plane geometry theorems stated by text and diagram in a complementary way. The problem of proving plane geometry theorems involves two challenging subtasks, being theorem understanding and theorem proving. This paper proposes to consider theorem understanding as a problem of extracting relations from text and diagram. A syntax–semantics (S2) model method is proposed to extract the geometric relations from theorem text, and a diagram mining method is proposed to extract geometry relations from diagram. Then, a procedure is developed to obtain a set of relations that is consistent with the given theorem with high confidence. Finally, theorem proving is conducted by using the existing proving methods which take the extracted geometric relations as input. The experimental results show that the proposed theorem proving algorithm can prove 86% of plane geometry theorems in the test dataset of 200 theorems, which is all the theorems in the popular textbook. The proposed algorithm outperforms the existing algorithms mainly because it can extract relations not only from text but also from diagram.
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Crouse, Maxwell, Ibrahim Abdelaziz, Bassem Makni, Spencer Whitehead, Cristina Cornelio, Pavan Kapanipathi, Kavitha Srinivas, Veronika Thost, Michael Witbrock, and Achille Fokoue. "A Deep Reinforcement Learning Approach to First-Order Logic Theorem Proving." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 7 (May 18, 2021): 6279–87. http://dx.doi.org/10.1609/aaai.v35i7.16780.

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Automated theorem provers have traditionally relied on manually tuned heuristics to guide how they perform proof search. Deep reinforcement learning has been proposed as a way to obviate the need for such heuristics, however, its deployment in automated theorem proving remains a challenge. In this paper we introduce TRAIL, a system that applies deep reinforcement learning to saturation-based theorem proving. TRAIL leverages (a) a novel neural representation of the state of a theorem prover and (b) a novel characterization of the inference selection process in terms of an attention-based action policy. We show through systematic analysis that these mechanisms allow TRAIL to significantly outperform previous reinforcement-learning-based theorem provers on two benchmark datasets for first-order logic automated theorem proving (proving around 15% more theorems).
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Xiao, Da, Yue Fei Zhu, Sheng Li Liu, Dong Xia Wang, and You Qiang Luo. "Digital Hardware Design Formal Verification Based on HOL System." Applied Mechanics and Materials 716-717 (December 2014): 1382–86. http://dx.doi.org/10.4028/www.scientific.net/amm.716-717.1382.

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This article selects HOL theorem proving systems for hardware Trojan detection and gives the symbol and meaning of theorem proving systems, and then introduces the symbol table, item and the meaning of HOL theorem proving systems. In order to solve the theorem proving the application of the system in hardware Trojan detection requirements, this article analyses basic hardware Trojan detection methods which applies for theorem proving systems and introduces the implementation methods and process of theorem proving about hardware Trojan detection.
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Bahodirovich, Hojiyev Dilmurodjon, Muhammadjonov Akbarshoh Akramjon Og`Li Og`Li, Muzaffarova Dilshoda Botirjon Qizi, Ibrohimjonov Islombek Ilhomjon O`G`Li, and Ahmadjonova Musharrafxon Dilmurod Qizi. "About One Theorem Of 2x2 Jordan Blocks Matrix." American Journal of Applied sciences 03, no. 06 (June 12, 2021): 28–33. http://dx.doi.org/10.37547/tajas/volume03issue06-05.

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In this paper, we have studied one theorem on 2x2 Jordan blocks matrix. There are 4 important statements which is used for proving other theorems such as in the differensial equations. In proving these statements, we have used mathematic induction, norm of matrix, Taylor series of
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Perron, Steven. "Examining Fragments of the Quantified Propositional Calculus." Journal of Symbolic Logic 73, no. 3 (September 2008): 1051–80. http://dx.doi.org/10.2178/jsl/1230396765.

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AbstractWhen restricted to proving formulas, the quantified propositional proof system is closely related to the theorems of Buss's theory . Namely, has polynomial-size proofs of the translations of theorems of , and proves that is sound. However, little is known about when proving more complex formulas. In this paper, we prove a witnessing theorem for similar in style to the KPT witnessing theorem for . This witnessing theorem is then used to show that proves is sound with respect to formulas. Note that unless the polynomial-time hierarchy collapses is the weakest theory in the S2 hierarchy for which this is true. The witnessing theorem is also used to show that is p-equivalent to a quantified version of extended-Frege for prenex formulas. This is followed by a proof that Gi, p-simulates with respect to all quantified propositional formulas. We finish by proving that S2 can be axiomatized by plus axioms stating that the cut-free version of is sound. All together this shows that the connection between and does not extend to more complex formulas.
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Jupri, Al, Siti Fatimah, and Dian Usdiyana. "Dampak Perkuliahan Geometri Pada Penalaran Deduktif Mahasiswa: Kasus Pembelajaran Teorema Ceva." AKSIOMA : Jurnal Matematika dan Pendidikan Matematika 11, no. 1 (July 15, 2020): 93–104. http://dx.doi.org/10.26877/aks.v11i1.6011.

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Geometry is one of branches of mathematics that can develop deductive thinking ability for anyone, including students of prospective mathematics teachers, who learning it. This deductive thinking ability is needed by prospective mathematics teachers for their future careers as mathematics educators. This research therefore aims to investigate the influence of the learning process of a geometry course toward deductive reasoning ability of students of prospective mathematics teachers. To do so, this qualitative research was carried out through an observation of the learning process and assessment of the geometry course, involving 56 students of prospective mathematics teachers, in one of mathematics education program, in one of state universities in Bandung. A geometry topic observed in the learning process was the Ceva’s theorem, and the assessment was in the form of an individual written test on the application of the Ceva’s theorem in a proving process. The results showed that the learning process emphasizes on proving of theorems and mathematical statements. In addition, the test revealed that ten students are able to use the Ceva’s theorem in a proving process and different strategies of proving are found, including the use of properties of similarity between triangles and of the concept of trigonometry. This indicates a creativity of student deductive thinking in proving process. In conclusion, the geometry course that emphasizes on proving of theorems and mathematical statements has influenced on filexibility of student deductive thinking in proving processes.
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Stickel, M. E. "Resolution Theorem Proving." Annual Review of Computer Science 3, no. 1 (June 1988): 285–316. http://dx.doi.org/10.1146/annurev.cs.03.060188.001441.

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Gogate, Vibhav, and Pedro Domingos. "Probabilistic theorem proving." Communications of the ACM 59, no. 7 (June 24, 2016): 107–15. http://dx.doi.org/10.1145/2936726.

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Klein, Gerwin, and Ruben Gamboa. "Interactive Theorem Proving." Journal of Automated Reasoning 56, no. 3 (February 20, 2016): 201–3. http://dx.doi.org/10.1007/s10817-016-9363-7.

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Plaisted, David A. "Automated theorem proving." Wiley Interdisciplinary Reviews: Cognitive Science 5, no. 2 (January 17, 2014): 115–28. http://dx.doi.org/10.1002/wcs.1269.

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Dissertations / Theses on the topic "Theorem proving"

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Ballarin, Clemens Michael. "Computer algebra and theorem proving." Thesis, University of Cambridge, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.624429.

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Ji, Kailiang. "Model checking and theorem proving." Sorbonne Paris Cité, 2015. http://www.theses.fr/2015USPCC250.

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Le model checking est une technique de vérification automatique de propriétés de correction de systèmes finis. Normalement, les outils de model checking ont deux caractéristiques remarquables : ils sont automatisés et ils produisent un contre-exemple si le système ne satisfait pas la propriété. La Déduction Modulo est une reformulation de la logique des prédicats où certains axiomes---possiblement tous---sont remplacés par des règles de réécriture. Le but de cette dissertation est de donner un encodage de propriétés temporelles exprimées en CTL en des formules du premier ordre, en exprimant l'équivalence logique entre les opérateurs temporels avec des règles de réécriture. De cette manière, les algorithmes de recherche de preuve conçus pour la Déduction Modulo, tels que la Résolution Modulo ou les Tableaux Modulo, peuvent être utilisés pour vérifier des propriétés temporelles de systèmes de transition finis. Afin d'accomplir le but de résoudre des problèmes de model checking avec un prouveur automatique quelconque, trois travaux sont inclus dans cette dissertation. Premièrement, nous abordons le problème de parcours de graphes en model checking avec des prouveurs automatiques. Nous proposons une façon d'encoder un graphe en tant que formule de manière à ce que le parcours du graphe correspond aux étapes de résolution. Nous présentons ensuite comment formuler les problèmes de model checking comme des formules du premier ordre en Déduction Modulo. La correction et la complétude de notre méthode montre que résoudre des problèmes de model checking CTL avec des prouveurs automatiques est faisable. Enfin, en nous appuyant sur la base théorique du deuxième travail, nous proposons une méthode de model checking symbolique. Cette méthode est implantée dans iProver Modulo, qui est un prouveur automatique du premier ordre qui utilise la Résolution Modulo Polarisée
Model checking is a technique for automatically verifying correctness properties of finite systems. Normally, model checking tools enjoy two remarkable features: they are fully automatic and a counterexample will be produced if the system fails to satisfy the property. . Deduction Modulo is a reformulation of Predicate Logic where some axioms- - - possibly ail---are replaced by rewrite rules. The focus of this dissertation is to give an encoding of temporal properties expressed in CTL as first -order formulas, by translating the logical equivalence between temporal operators into rewrite rules. This way, proof -search algorithms designed for Deduction Modulo, such as Resolution Modulo or Tableaux Modulo, can be used to verify temporal properties of finite transition systems. To achieve the aim of solving model checking problems with an off-the-shelf automated theorem proyer, three works are included in this dissertation. First, we address the graph traversai problems in model checking with automated theorem provers. As a preparation work, we propose a way of encoding a graph as a formula such that the traversal of the graph corresponds to resolution steps. Then we present the way of translating model checking problems as proving first-order formulas in Deduction Modulo. The soundness and completeness of our method shows that solving CTL model checking problems with automated theorem provers is feasible. At last, based on the theoretical basis in the second work, we propose a symbolic model checking method. This method is implemented in iProver Modulo, which is a first-order theorem proyer uses Polarized Resolution Modulo
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Kakkad, Aman. "Machine Learning for Automated Theorem Proving." Scholarly Repository, 2009. http://scholarlyrepository.miami.edu/oa_theses/223.

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Developing logic in machines has always been an area of concern for scientists. Automated Theorem Proving is a field that has implemented the concept of logical consequence to a certain level. However, if the number of available axioms is very large then the probability of getting a proof for a conjecture in a reasonable time limit can be very small. This is where the ability to learn from previously proved theorems comes into play. If we see in our own lives, whenever a new situation S(NEW) is encountered we try to recollect all old scenarios S(OLD) in our neural system similar to the new one. Based on them we then try to find a solution for S(NEW) with the help of all related facts F(OLD) to S(OLD). Similar is the concept in this research. The thesis deals with developing a solution and finally implementing it in a tool that tries to prove a failed conjecture (a problem that the ATP system failed to prove) by extracting a sufficient set of axioms (we call it Refined Axiom Set (RAS)) from a large pool of available axioms. The process is carried out by measuring the similarity of a failed conjecture with solved theorems (already proved) of the same domain. We call it "process1", which is based on syntactic selection of axioms. After process1, RAS may still have irrelevant axioms, which motivated us to apply semantic selection approach on RAS so as to refine it to a much finer level. We call this approach as "process2". We then try to prove failed conjecture either from the output of process1 or process2, depending upon whichever approach is selected by the user. As for our testing result domain, we picked all FOF problems from the TPTP problem domain called SWC, which consisted of 24 broken conjectures (problems for which the ATP system is able to show that proof exists but not able to find it because of limited resources), 124 failed conjectures and 274 solved theorems. The results are produced by keeping in account both the broken and failed problems. The percentage of broken conjectures being solved with respect to the failed conjectures is obviously higher and the tool has shown a success of 100 % on the broken set and 19.5 % on the failed ones.
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Folkler, Andreas. "Automated Theorem Proving : Resolution vs. Tableaux." Thesis, Blekinge Tekniska Högskola, Institutionen för programvaruteknik och datavetenskap, 2002. http://urn.kb.se/resolve?urn=urn:nbn:se:bth-5531.

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The purpose of this master thesis was to investigate which of the two methods, resolution and tableaux, that is the most appropriate for automated theorem proving. This was done by implementing an automated theorem prover, comparing and documenting implementation problems, and measuring proving efficiency. In this thesis, I conclude that the resolution method might be more suitable for an automated theorem prover than tableaux, in the aspect of ease of implementation. Regarding the efficiency, the test results indicate that resolution is the better choice.
Syftet med detta magisterarbete var att undersöka vilken av de två metoderna, resolution och tablå, som är mest lämpad för automatisk teorembevisning. Detta gjordes genom att implementera en automatisk teorembevisare, jämföra och dokumentera problem, samt att mäta prestanda för bevisning. I detta arbete drar jag slutsatsen att resolutionsmetoden förmodligen är mer lämpad än tablåmetoden för en automatisk teorembevisare, med avseende på hur svår den är att implementera. När det gäller prestanda indikerar utförda tester att resolutionsmetoden är det bästa valet.
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Amjad, Hasan. "Combining model checking and theorem proving." Thesis, University of Cambridge, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.616074.

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Bridge, J. P. "Machine learning and automated theorem proving." Thesis, University of Cambridge, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.596901.

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Computer programs to find formal proofs of theorems were originally designed as tools for mathematicians, but modern applications are much more diverse. In particular they are used in formal methods to verify software and hardware designs to prevent errors being introduced into systems. Despite this, the high level of human expertise required in their use means that theorem proving tools are not widely used by non-specialists. The work described in this dissertation addresses one aspect of this problem, that of heuristic selection. In theory theorem provers should be automatic; in practice the heuristics used in the proof search are not universally optimal for all problems so human expertise is required to determie heuristic choice and to set parameter values. Modern machine learning has been applied to the automation of heuristic selection in a first order logic theorem prover. One objective was to find if there are any features of a proof problem that are both easy to measure and provide useful information for determining heuristic choice. Another was to determine and demonstrate a practical approach to making theorem provers truly automatic. In the experimental work, heuristic selection based on features of the conjecture to be proved and the associated axioms is shown to do better than any single heuristic. Additionally a comparison has been made between static features, measured prior to the proof search process, and dynamic features that measure changes arising in the early stages of proof search. Further work was done on determining which features are important, demonstrating that good results are obtained with only a few features required.
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Hou, Tie. "Interactive theorem proving and program extraction." Thesis, Swansea University, 2014. https://cronfa.swan.ac.uk/Record/cronfa42845.

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Syme, Donald Robert. "Declarative theorem proving for operational semantics." Thesis, University of Cambridge, 1999. https://www.repository.cam.ac.uk/handle/1810/252967.

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This dissertation is concerned with techniques for formally checking properties of systems that are described by operational semantics. We describe innovations and tools for tackling this problem, and a large case study in the application of these tools. The innovations centre on the notion of "declarative theorem proving", and in particular techniques for declarative proof description. We define what we mean by this, assess its costs and benefits, and describe the impact of this approach with respect to four fundamental areas of theorem prover design: specification, proof description, automated reasoning and interaction. We have implemented our techniques as the DECLARE system, which we use to demonstrate how our principles translate into practice. With regard to specification we briefly describe the range of specification devices employed, and present a technique for validating operational specifications against their informal requirements. The proof language is based on just three major devices: decomposition, justification by automation and second order schema application, and we describe these in detail. We also specify the requirements for an automated reasoning engine in the context of declarative proof and operational semantics. We describe the engine we have implemented and assess how it does and does not meet these requirements. The case study is a formally checked proof of the type soundness of a subset of the Java language, and is an interesting result in its own right. We define an operational semantics for this subset, based on Drossopoulou and Eisenbach's work in this field, and then outline the structure of our type soundness proot which is based on a notion of conformance. Some errors in the Java Language Specification and Drossopoulou and Eisenbach's work were discovered during this process, and these are described. Finally, we argue why declarative techniques substantially improved the quality of the results achieved, particularly with respect to maintainability and readability.
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Harrison, John Robert. "Theorem proving with the real numbers." Thesis, University of Cambridge, 1996. https://www.repository.cam.ac.uk/handle/1810/265488.

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This thesis discusses the use of the real numbers in theorem proving. Typically, theorem provers only support a few 'discrete' datatypes such as the natural numbers. However the availability of the real numbers opens up many interesting and important application areas, such as the verification of floating point hardware and hybrid systems. It also allows the formalization of many more branches of classical mathematics, which is particularly relevant for attempts to inject more rigour into computer algebra systems. Our work is conducted in a version of the HOL theorem prover. We describe the rigorous definitional construction of the real numbers, using a new version of Cantor's method, and the formalization of a significant portion of real analysis. We also describe . an advanced derived decision procedure for the 'Tarski subset' of real algebra as well as some more modest but practically useful tools for automating explicit calculations and routine linear arithmetic reasoning. Finally, we consider in more detail two interesting application areas. We discuss the desirability of combining the rigour of theorem provers with the power and convenience of computer algebra systems, and explain a method we have used in practice to achieve this. We then move on to the verification of floating point hardware. After a careful discussion of possible correctness specifications, we report on two case studies, one involving a transcendental function. We aim to show that a theory of real numbers is useful in practice and interesting in theory, and that the 'LCF style' of theorem proving is well suited to the kind of work we describe. As for verification applications, we hope to convince the reader that the verification of real industrial designs is well within the abilities of current theorem proving .technology.
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Haufe, Sebastian. "Automated Theorem Proving for General Game Playing." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-89998.

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While automated game playing systems like Deep Blue perform excellent within their domain, handling a different game or even a slight change of rules is impossible without intervention of the programmer. Considered a great challenge for Artificial Intelligence, General Game Playing is concerned with the development of techniques that enable computer programs to play arbitrary, possibly unknown n-player games given nothing but the game rules in a tailor-made description language. A key to success in this endeavour is the ability to reliably extract hidden game-specific features from a given game description automatically. An informed general game player can efficiently play a game by exploiting structural game properties to choose the currently most appropriate algorithm, to construct a suited heuristic, or to apply techniques that reduce the search space. In addition, an automated method for property extraction can provide valuable assistance for the discovery of specification bugs during game design by providing information about the mechanics of the currently specified game description. The recent extension of the description language to games with incomplete information and elements of chance further induces the need for the detection of game properties involving player knowledge in several stages of the game. In this thesis, we develop a formal proof method for the automatic acquisition of rich game-specific invariance properties. To this end, we first introduce a simple yet expressive property description language to address knowledge-free game properties which may involve arbitrary finite sequences of successive game states. We specify a semantic based on state transition systems over the Game Description Language, and develop a provably correct formal theory which allows to show the validity of game properties with respect to their semantic across all reachable game states. Our proof theory does not require to visit every single reachable state. Instead, it applies an induction principle on the game rules based on the generation of answer set programs, allowing to apply any off-the-shelf answer set solver to practically verify invariance properties even in complex games whose state space cannot totally be explored. To account for the recent extension of the description language to games with incomplete information and elements of chance, we correctly extend our induction method to properties involving player knowledge. With an extensive evaluation we show its practical applicability even in complex games.
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Books on the topic "Theorem proving"

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Beringer, Lennart, and Amy Felty, eds. Interactive Theorem Proving. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-32347-8.

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Bibel, Wolfgang. Automated Theorem Proving. Wiesbaden: Vieweg+Teubner Verlag, 1987. http://dx.doi.org/10.1007/978-3-322-90102-6.

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Ayala-Rincón, Mauricio, and César A. Muñoz, eds. Interactive Theorem Proving. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-66107-0.

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Newborn, Monty. Automated Theorem Proving. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4613-0089-2.

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Klein, Gerwin, and Ruben Gamboa, eds. Interactive Theorem Proving. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-08970-6.

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Blazy, Sandrine, Christine Paulin-Mohring, and David Pichardie, eds. Interactive Theorem Proving. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-39634-2.

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Kaufmann, Matt, and Lawrence C. Paulson, eds. Interactive Theorem Proving. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-14052-5.

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van Eekelen, Marko, Herman Geuvers, Julien Schmaltz, and Freek Wiedijk, eds. Interactive Theorem Proving. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-22863-6.

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Urban, Christian, and Xingyuan Zhang, eds. Interactive Theorem Proving. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-22102-1.

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Avigad, Jeremy, and Assia Mahboubi, eds. Interactive Theorem Proving. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94821-8.

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Book chapters on the topic "Theorem proving"

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Abadi, Martín, and Zohar Manna. "Modal theorem proving." In 8th International Conference on Automated Deduction, 172–89. Berlin, Heidelberg: Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/3-540-16780-3_89.

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Li, Hongbo. "Automated Theorem Proving." In Geometric Algebra with Applications in Science and Engineering, 110–19. Boston, MA: Birkhäuser Boston, 2001. http://dx.doi.org/10.1007/978-1-4612-0159-5_6.

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Stachniak, Zbigniew. "Theorem Proving Strategies." In Automated Reasoning Series, 103–31. Dordrecht: Springer Netherlands, 1996. http://dx.doi.org/10.1007/978-94-009-1677-7_5.

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Lynch, Christopher. "Unsound Theorem Proving." In Computer Science Logic, 473–87. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-30124-0_36.

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Dowek, Gilles. "Automated Theorem Proving." In Proofs and Algorithms, 117–38. London: Springer London, 2011. http://dx.doi.org/10.1007/978-0-85729-121-9_6.

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Bonacina, Maria Paola. "Parallel Theorem Proving." In Handbook of Parallel Constraint Reasoning, 179–235. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-63516-3_6.

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Fleuriot, Jacques. "Geometry Theorem Proving." In A Combination of Geometry Theorem Proving and Nonstandard Analysis with Application to Newton’s Principia, 11–30. London: Springer London, 2001. http://dx.doi.org/10.1007/978-0-85729-329-9_2.

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Ahmed, Asad, Osman Hasan, Falah Awwad, and Nabil Bastaki. "Interactive Theorem Proving." In Formal Analysis of Future Energy Systems Using Interactive Theorem Proving, 23–29. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-78409-6_2.

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Reif, Wolfgang, and Gerhard Schellhorn. "Theorem Proving in Large Theories." In Applied Logic Series, 225–41. Dordrecht: Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-017-0437-3_9.

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Aspinall, David, and Cezary Kaliszyk. "What’s in a Theorem Name?" In Interactive Theorem Proving, 459–65. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-43144-4_28.

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Conference papers on the topic "Theorem proving"

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Niknafs-Kermani, Amir, Boris Konev, and Michael Fisher. "Symmetric Temporal Theorem Proving." In 2012 19th International Symposium on Temporal Representation and Reasoning (TIME). IEEE, 2012. http://dx.doi.org/10.1109/time.2012.20.

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Gonthier, Georges. "Combinatorics for theorem proving." In the 1st Workshop. New York, New York, USA: ACM Press, 2009. http://dx.doi.org/10.1145/1735813.1735814.

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Yorsh, Greta, Thomas Ball, and Mooly Sagiv. "Testing, abstraction, theorem proving." In the 2006 international symposium. New York, New York, USA: ACM Press, 2006. http://dx.doi.org/10.1145/1146238.1146255.

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Chen, Chiyan, and Hongwei Xi. "Combining programming with theorem proving." In the tenth ACM SIGPLAN international conference. New York, New York, USA: ACM Press, 2005. http://dx.doi.org/10.1145/1086365.1086375.

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Weirich, Stephanie. "Session details: Automated theorem proving." In ICFP'12: ACM SIGPLAN International Conference on Functional Programming. New York, NY, USA: ACM, 2012. http://dx.doi.org/10.1145/3249893.

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"THEOREM PROVING IN THE ONTOLOGY LIFECYCLE." In International Conference on Knowledge Engineering and Ontology Development. SciTePress - Science and and Technology Publications, 2010. http://dx.doi.org/10.5220/0003076400370049.

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Otten, Jens. "nanoCoP: Natural Non-clausal Theorem Proving." In Twenty-Sixth International Joint Conference on Artificial Intelligence. California: International Joint Conferences on Artificial Intelligence Organization, 2017. http://dx.doi.org/10.24963/ijcai.2017/695.

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Abstract:
Most efficient fully automated theorem provers implement proof search calculi that require the input formula to be in a clausal form, i.e. disjunctive or conjunctive normal form. The translation into clausal form introduces a significant overhead to the proof search and modifies the structure of the original formula. Translating a proof in clausal form back into a more readable non-clausal proof of the original formula is not straightforward. This paper presents a non-clausal automated theorem prover for classical first-order logic. It is based on a non-clausal connection calculus and implemented with a few lines of Prolog code. Working entirely on the original structure of the input formula yields not only a speed up of the proof search, but the resulting non-clausal proofs are also shorter.
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Paulson, Lawrence C. "Automated theorem proving for special functions." In the 2014 Symposium. New York, New York, USA: ACM Press, 2014. http://dx.doi.org/10.1145/2631948.2631950.

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Munoz Toriz, Juan Pablo, Ivan Martinez Ruiz, and Jose Arrazola Ramirez. "On Automatic Theorem Proving with ML." In 2014 13th Mexican International Conference on Artificial Intelligence (MICAI). IEEE, 2014. http://dx.doi.org/10.1109/micai.2014.42.

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Bonacina, Maria Paola. "On theorem proving for program checking." In the 12th international ACM SIGPLAN symposium. New York, New York, USA: ACM Press, 2010. http://dx.doi.org/10.1145/1836089.1836090.

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Reports on the topic "Theorem proving"

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Abadi, Martin, and Zohar Manna. Modal Theorem Proving,. Fort Belvoir, VA: Defense Technical Information Center, May 1986. http://dx.doi.org/10.21236/ada325959.

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Shankar, Natarajan. PVS Theorem Proving Enhancements. Fort Belvoir, VA: Defense Technical Information Center, June 1997. http://dx.doi.org/10.21236/ada326917.

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Avigad, Jeremy, and Robert Harper. Type Theory, Computation and Interactive Theorem Proving. Fort Belvoir, VA: Defense Technical Information Center, September 2015. http://dx.doi.org/10.21236/ad1003773.

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Bellin, Gianluigi, and Jussi Ketonen. Experiments in Automatic Theorem Proving. Fort Belvoir, VA: Defense Technical Information Center, December 1986. http://dx.doi.org/10.21236/ada327449.

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Archer, Myla, and Constance Heitmeyer. Human-Style Theorem Proving Using PVS. Fort Belvoir, VA: Defense Technical Information Center, August 1997. http://dx.doi.org/10.21236/ada464276.

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Lusk, E., and W. McCune. An entry in the 1992 Overbeek theorem-proving contest. Office of Scientific and Technical Information (OSTI), November 1992. http://dx.doi.org/10.2172/6940861.

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Lusk, E. L., and W. W. McCune. An entry in the 1992 Overbeek theorem-proving contest. Office of Scientific and Technical Information (OSTI), November 1992. http://dx.doi.org/10.2172/10114594.

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Clarke, Edmund, and Xudong Zhao. Analytica - An Experiment in Combining Theorem Proving and Symbolic Computation. Fort Belvoir, VA: Defense Technical Information Center, October 1992. http://dx.doi.org/10.21236/ada258656.

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McCune, W. A case study in automated theorem proving: A difficult problem about commutators. Office of Scientific and Technical Information (OSTI), February 1995. http://dx.doi.org/10.2172/27057.

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Wos, L., and W. McCune. Searching for fixed point combinators by using automated theorem proving: A preliminary report. Office of Scientific and Technical Information (OSTI), September 1988. http://dx.doi.org/10.2172/6852789.

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