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	Automated theorem proving - Wikipedia, the free encyclopedia
		A good example of this was the machine-aided proof of the four color theorem, which was very controversial as the first claimed mathematical proof which was essentially impossible to verify by humans due to the enormous size of the program's calculation (such proofs are called non-surveyable proofs).
		E is a high-performance prover built on a purely equational calculus, developed primarily in the automated reasoning group of Technical University of Munich.
		Vampire is developed and implemented at Manchester University by Andrei Voronkov, formerly together with Alexandre Riazanov.
	en.wikipedia.org /wiki/Theorem_prover (1247 words)

	Encyclopedia :: encyclopedia : Automated theorem proving (Site not responding. Last check: 2007-11-01)
		Automated theorem proving (currently the most important subfield of automated reasoning) is the proving of mathematical theorems by a computer program.
		First-order theorem proving is one of the most mature subfields of automated theorem proving.
		Robert Stephen Boyer Co-Author of the Boyer-Moore theorem prover, co-recipient of the Herbrand Award 1999.
	www.hallencyclopedia.com /Automated_theorem_proving (1090 words)

	Automated theorem proving
		The theorems of interest may be in traditional mathematical domains, or they may be in other fields such as digital computer design.
		In reality, there is no general-purpose system that can fully automatically prove "interesting" theorems, and most theorem proving systems can be used in a variety of ways with different amounts of automation, so this distinction is often dropped and both sides of the continuum are called theorem proving.
		A good example of this was the machine-aided proof of the four color theorem, which was very controversial as the first claimed mathematical proof which was essentially impossible to check by hand.
	www.ebroadcast.com.au /lookup/encyclopedia/th/Theorem_prover.html (410 words)

	Formulation and Validation of the
		A theorem prover was used to ensure that intended consequences follow from the axioms.
		SNARK (Stickel) is a first-order-logic theorem prover with equality, associative-commutative unification, and sorts.
		Sometimes we would formulate conjectures that the theorem prover could not prove, and which on reflection turned out not to be true.
	www.ai.sri.com /daml/owl/axiomatic.htm (3085 words)

	Entrants' System Descriptions
		E 0.9 [Sch02,Sch04a] is a purely equational theorem prover.
		Equinox is a new theorem prover for pure first-order logic with equality.
		Gandalf [Tam97,Tam98] is a family of automated theorem provers, including classical, type theory, intuitionistic and linear logic provers, plus finite a model builder.
	www.cs.miami.edu /~tptp/CASC/20/SystemDescriptions.html (7158 words)

	All Information of Automated theorem proving (Site not responding. Last check: 2007-11-01)
		Automated theorem proving (currently the most important subfield of automated reasoning) is the mathematical proof of mathematical theorem s by a computer program.
		First-order logic theorem proving is one of the most mature subfields of automated theorem proving.
		- E equational theorem prover is a high-performance prover built on a purely equational calculus, developed primarily in the automated reasoning group of Technical University of Munich.
	bs_1782.bs.xvip.org (2661 words)

	Beyond Linear Arithmetic (Site not responding. Last check: 2007-11-01)
		Automatic theorem provers (ATPs) based on the resolution principle, such as SPASS and Vampire, have reached a high degree of sophistication.
		Automatic provers for higher-order logic, however, are rare: the chief ones are TPS and LEO.
		LEO is a self-contained higher-order theorem prover, but can also co-operate with a first-order prover, and this combination has already yielded significant performance improvements.
	www.cl.cam.ac.uk /~lp15/Grants/leo2.html (374 words)

	Welcome!
		The applications of theorem proving and automated reasoning in general in many domains is becoming more popular due to the advancements in hardware.
		Based on ideas from the theorem prover THEO developed by Professor Newborn, we are developing a new theorem prover which is an experimental system to demonstrate that certain major computations can be avoided by keeping track of the minor changes in linear and semi-linear resolution based theorem provers.
		The program, CARINE, that we are developing, is a first order predicate automated theorem prover which is based on an iteratively deepening depth first search algorithm.
	www.cs.mcgill.ca /~pharoun (383 words)

	Logic Group References--References
		This trace-checking may be much easier than proving the correctness of a theorem prover.
		SCOTT keeps separate the model builder and the theorem prover from semantic guidance routines to allow, in principle, a plug and play architecture.
		Its architecture is the same Discount algorithm found in Vampire and E. Written in C, it uses perfect discrimination trees (a variation on the trie) to index terms.
	logic.stanford.edu /~thinrich/references/java/tplp.html (2242 words)

	Potential Projects
		Theorem proving for classical propositional logic is quite simple to understand.
		It is often the case that the number of formulae dealt with during a proof is too large to be handled easily.
		Otter [3], SPASS [4] or Vampire [5], and to produce all the required statistics in an appropriate format.
	www.csc.liv.ac.uk /~michael/Projects/projects.html (1852 words)

	Vaishnava blog feeds » Blog Archive » IJCAI day 1
		He’s been working on this system for the past 10 years and it is by far the fastest 1st-order logic reasoning system in the world.
		A small change in the parameters will often allow the prover to answer a problem that was taking 24 hours before in a couple of seconds.
		Intel has been verifying all their chips in a similar fashion after the embarrassing bug in the original Pentium processor that caused it to give the incorrect answer on a few simple division operations.
	www.prabhupada.org /rama/?p=381 (531 words)

	Introduction
		The Tau theorem prover and knowledge base (a formal theory repository), is aiming to be the first interactive, easy-to-use, and comprehensive prover of its kind on the Internet.
		The proof trace shows how the theorem was broken down into sub-proofs and how the formulas were rewritten and normalized to facilitate the proof.
		The Tau prover is a hybrid which is indirect, at its core, and operates by saturation of the quantified formulas in the proof, and unification/resolution.
	www.hsinfosystems.com /taujay/doc/Introduction.html (1222 words)

	Resolution Theorem Proving
		Automated theorem proving is the application of rules of deduction to the problem of proving that a theorem statement follows from a set of axioms which are taken to be true.
		None of these theorems were known to the user when they were reported, and each one takes around 10 lines, and a fair bit of number theoretic knowledge, to prove.
		Proof planning has been particularly useful for proving theorems inductively, i.e., using the the principal of mathematical induction (not to be confused with the type of inductive reasoning we will be covering in the lectures on machine learning).
	www.doc.ic.ac.uk /~sgc/teaching/v231/lecture9.html (4853 words)

	The University of Manchester :: People :: Professor Andrei Voronkov (Site not responding. Last check: 2007-11-01)
		Andrei with his students implemented a system for automated reasoning in first-order logic (a theorem prover) Vampire.
		Vampire has been the winner at six world cups in theorem proving (CASC), winning altogether nine titles in the two main divisions of the competition.
		(1) The adaptation of the theorem prover Vampire for various applications, such as reasoning with ontologies in the Semantic Web project, software and hardware verification.
	www.knowledgehorizons.manchester.ac.uk /people/index.asp?personID=174 (250 words)

	Max-Planck-Institut für Informatik - Automation of Logic: Spass
		The father of all todays modern theorem provers is Otter developed by Bill McCune.
		The FDPLL prover is a first-order version of the Davis-Putnam-Logeman-Loveland procedure, developed by Peter Baumgartner at the University of Koblenz.
		One of the very best systems for purely equational reasoning is the Waldmeister theorem prover developed at the Max-Planck Institut für Informatik.
	spass.mpi-sb.mpg.de /links.html (317 words)

	Horizons of Truth :: Goedel Centenary 2006
		Traditionally, theorem provers have been used to prove theorems with relatively small axiomatisations.
		The recent development of large ontologies poses a non-trivial challenge of reasoning with axiomatisations consisting of hundreds of thousands (and in the near future hundreds of millions) axioms.
		In the talk we describe an adaptation of the theorem prover Vampire for reasoning with large ontologies using expressive logics.
	www.logic.at /goedel2006/abstract.php?voronkov (197 words)

	[No title]
		INVITED TALK The Anatomy of Vampire: New Directions in Efficient Implementation of Logical Inference Andrei Voronkov Computer Science Department University of Uppsala voronkov@csd.uu.se We discuss an implementation technique, called code trees, for a class of bottom-up procedures.
		It is applicable to many procedures, including resolution-based procedures, the inverse method, bottom-up evaluation of logic programs and theorem proving methods which use lemmaizing.
		Vampire is considerably faster than Otter, when both use the same logical methods.
	www.cs.cmu.edu /Groups/AI/events/meetings/lpar94 (2025 words)

	Dracula Information Website - Bram Stokers Dracula, the misterious vampire legend. » 2006 » January (Site not responding. Last check: 2007-11-01)
		In the anime series Hellsing, the vampire Alucard (note: Dracula spelled backwards) is Dracula himself, having been magically bound into servitude by the Hellsing family rather than being destroyed outright.
		Cartoon vampires based upon Dracula also include Count Duckula and Count Chocula, the animated mascot of the breakfast cereal of the same name.
		As popular as vampires may seem, they occupy a kind of niche in mostly modestly budgeted horror movies (the first three titles on this list notwithstanding).
	www.info-dracula.com /2006/01 (1659 words)

	Let's COMPIT! - Useful Links
		More on Vampire, the theorem prover, can be found on the Vampire Home Page.
		More on the Waldmeister theorem prover you find on the Waldmeister Home Page.
		A collection of further readings on Waldmeister as well as on theorem proving you find on Thomas Hillenbrand's publications page.
	www.mpi-sb.mpg.de /~hillen/compit/links.htm (107 words)

	FRDCSA: Current packages, sorted alphabetically (Site not responding. Last check: 2007-11-01)
		We intended to use Vampire as a theorem prover to allow answering CELT questions.
		YES/NO questions would be answered by trying to prove that a formula is a theorem (i.e., that something is indeed the case).
		Vampire 6.0 is better selection of best strategies based on extensive experiments.
	frdcsa.onshore.net /frdcsa/binary/index.html (5254 words)

	[No title] (Site not responding. Last check: 2007-11-01)
		Athena is an interactive theorem prover for multi-sorted first-order logic with equality.
		To prove an implication, Athena provides syntactic constructs that temporarily add the implication hypothesis to the assumption base during the scope of the proof for the implication conclusion.
		SPASS - An Automated Theorem Prover for First-Order Logic with Equality.
	athena-dpl.sourceforge.net (302 words)

	Alexandre Riazanov: Splitting without Backtracking (Site not responding. Last check: 2007-11-01)
		The case analysis principle is the core of tableau-based theorem proving.
		Is can also be integrated into saturation-based theorem proving in the form of the splitting rule
		This form of splitting is implemented in our resolution-and superposition-based theorem prover Vampire.
	www.cs.bham.ac.uk /~exr/dag01/riazanov.html (141 words)

	Highlights from the Manufacturing Engineering Laboratory
		A daunting field of research - that of developing and examining proofs of formal logical statements - has just become a little easier.
		This tool provides a graphical user interface to the open source version (version 2) of the Vampire Theorem Prover (http://en.wikipedia.org/wiki/Vampire_theorem_prover).
		The system provides formatted presentation of the proof generated by Vampire.
	www.mel.nist.gov /wnew/hilights/2006/hlmarch.htm (656 words)

	MIV - Minimal Interface to Vampire - Products and Tools - Manufacturing Systems Integration Division
		This tool provides a graphical user interface to the open source version (version 2) of the Vampire Theorem Prover.
		A more sophisticated Tomcat-based (web-based) interface to Vampire is provided through the Sigma Knowledge Engineering Environment.
		In no case does such identification imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the products are necessarily the best available for the purpose.
	www.mel.nist.gov /msid/MIV.html (254 words)

	Implementing an Efficient Theorem Prover - Riazanov (ResearchIndex) (Site not responding. Last check: 2007-11-01)
		Abstract: Since the invention of resolution and paramodulation calculi, theoretical research in the area of resolution-based theorem proving has achieved a remarkable progress in constructing inference systems based on various refinements of these calculi.
		The developed theory has a significant but not yet fully realised potential for such applications as formal hardware and software development, computer algebra, and assisting human mathematicians.
		10 a Brainiac Theorem Prover (context) - Schulz - 2002
	citeseer.ist.psu.edu /riazanov03implementing.html (1059 words)

	Web Links. -- Theorem Provers
		Vampire A Theorem Prover for First-Order Classical Logic
		ProteinPROTEIN is an automated theorem prover for first-order clause logic.
		It follows Loveland's Model Elimination procedure and is implemented according to Stickel's PTTP-Technique, i.e.
	www0.risc.uni-linz.ac.at /people/irents/links/links_7.html (86 words)

	E - A Brainiac Theorem Prover (ResearchIndex) (Site not responding. Last check: 2007-11-01)
		If your firewall is blocking outgoing connections to port 3125, you can use these links to download local copies.
		Describes implementation and performance of first-order prover E. Abstract: We describe the superposition-based theorem prover E. E is a sound and complete...
		11 The Anatomy of Vampire: Implementing Bottom-Up Procedures wi..
	citeseer.ist.psu.edu /560030.html (505 words)

	MICAI-2006 (Site not responding. Last check: 2007-11-01)
		This talk will provide a general overview of this field, including its history, its most significant developments, some of its most important application areas and its current challenges.
		The recent development of large ontologies poses a non-trivial challenge of reasoning with axiomatisations consisting of hundreds of thousands axioms.
		These ontologies will be created by large groups of people and by computer programs and will contain knowledge of varying quality.
	www.cicling.org /micai/2006 (1796 words)

	Conference Information System (Site not responding. Last check: 2007-11-01)
		The theory and practice of automated reasoning in first-order.
		We give an overview of automated theorem proving in first-order logic including the theory, implementation and applications.
		The overview will be accompanied by demos of the theorem prover Vampire.
	www-sbras.nsc.ru /ws/show_abstract.dhtml?en+102+9110 (59 words)

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