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OTTER 3.3 Reference Manual
"... by the United States Government and operated by The University of Chicago under the provisions of a contract with the Department of Energy. DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any a ..."
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by the United States Government and operated by The University of Chicago under the provisions of a contract with the Department of Energy. DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor The University of Chicago, nor any of their employees or officers, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privatelyowned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of document authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof, Argonne National Laboratory, or The University of Chicago. ii
A formal system for Euclid's Elements
, 2009
"... We present a formal system, E, which provides a faithful model of the proofs in Euclid’s Elements, including the use of diagrammatic reasoning. ..."
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We present a formal system, E, which provides a faithful model of the proofs in Euclid’s Elements, including the use of diagrammatic reasoning.
A Shortest 2Basis for Boolean Algebra in Terms of the Sheffer Stroke
 J. Automated Reasoning
, 2003
"... In this article, we present a short 2basis for Boolean algebra in terms of the Sheffer stroke and prove that no such 2basis can be shorter. We also prove that the new 2basis is unique (for its length) up to applications of commutativity. Our proof of the 2basis was found by using the method of p ..."
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In this article, we present a short 2basis for Boolean algebra in terms of the Sheffer stroke and prove that no such 2basis can be shorter. We also prove that the new 2basis is unique (for its length) up to applications of commutativity. Our proof of the 2basis was found by using the method of proof sketches and relied on the use of an automated reasoning program.
Automated Proof Compression by Invention of New Definitions
"... Stateoftheart automated theorem provers (ATPs) are today able to solve relatively complicated mathematical problems. But as ATPs become stronger and more used by mathematicians, the length and human unreadability of the automatically found proofs become a serious problem for the ATP users. One re ..."
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Stateoftheart automated theorem provers (ATPs) are today able to solve relatively complicated mathematical problems. But as ATPs become stronger and more used by mathematicians, the length and human unreadability of the automatically found proofs become a serious problem for the ATP users. One remedy is automated proof compression by invention of new definitions. We propose a new algorithm for automated compression of arbitrary sets of terms (like mathematical proofs) by invention of new definitions, using a heuristics based on substitution trees. The algorithm has been implemented and tested on a number of automatically found proofs. The results of the tests are included. 1 Introduction, motivation, and related work Stateoftheart automated theorem provers (ATPs) are today able to solve relatively complicated mathematical problems [McC97], [PS08], and are becoming a standard part of interactive theorem provers and verification tools [MP08], [Urb08]. But as ATPs become stronger and more used by mathematicians, understanding and refactoring the automatically found proofs becomes more and more important.
Axiomatizing the Skew Boolean Propositional Calculus
, 2007
"... Abstract. The skew Boolean propositional calculus (SBP C) is a generalization of the classical propositional calculus that arises naturally in the study of certain wellknown deductive systems. In this article, we consider a candidate presentation of SBP C and prove it constitutes a Hilbertstyle ax ..."
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Abstract. The skew Boolean propositional calculus (SBP C) is a generalization of the classical propositional calculus that arises naturally in the study of certain wellknown deductive systems. In this article, we consider a candidate presentation of SBP C and prove it constitutes a Hilbertstyle axiomatization. The problem reduces to establishing that the logic presented by the candidate axiomatization is algebraizable in the sense of Blok and Pigozzi. In turn, this is equivalent to verifying four particular formulas are derivable from the candidate presentation. Automated deduction methods played a central role in proving these four theorems. In particular, our approach relied heavily on the method of proof sketches. 1.
Automated theorem proving in loop theory
 proceedings of the ESARM workshop
, 2008
"... In this paper we compare the performance of various automated theorem provers on nearly all of the theorems in loop theory known to have been obtained with the assistance of automated theorem provers. Our analysis yields some surprising results, e.g., the theorem prover most often used by loop theor ..."
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In this paper we compare the performance of various automated theorem provers on nearly all of the theorems in loop theory known to have been obtained with the assistance of automated theorem provers. Our analysis yields some surprising results, e.g., the theorem prover most often used by loop theorists doesn’t necessarily yield the best performance. 1
Automated theorem proving in quasigroup and loop theory
 NORTHERN MICHIGAN UNIVERSITY, MARQUETTE, MI 49855 USA
"... We survey all known results in the area of quasigroup and loop theory to have been obtained with the assistance of automated theorem provers. We provide both informal and formal descriptions of selected problems, and compare the performance of selected stateofthe art first order theorem provers on ..."
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We survey all known results in the area of quasigroup and loop theory to have been obtained with the assistance of automated theorem provers. We provide both informal and formal descriptions of selected problems, and compare the performance of selected stateofthe art first order theorem provers on them. Our analysis yields some surprising results, e.g., the theorem prover most often used by loop theorists does not necessarily yield the best performance.
Automated discovery of single axioms for ortholattices
 Algebra Universalis
, 2005
"... Abstract. We present short single axioms for ortholattices, orthomodular lattices, and modular ortholattices, all in terms of the Sheffer stroke. The ortholattice axiom is the shortest possible. We also give multiequation bases in terms of the Sheffer stroke and in terms of join, meet, and complemen ..."
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Abstract. We present short single axioms for ortholattices, orthomodular lattices, and modular ortholattices, all in terms of the Sheffer stroke. The ortholattice axiom is the shortest possible. We also give multiequation bases in terms of the Sheffer stroke and in terms of join, meet, and complementation. Proofs are omitted but are available in an associated technical report and on the Web. We used computers extensively to find candidates, reject candidates, and search for proofs that candidates are single axioms. 1.
ON A HOMOMORPHISM PROPERTY OF HOOPS
"... Abstract. We present a syntactic proof that equation e → (b · c) = (e → b) · (e → c) is satisfied in a hoop A for any idempotent e ∈ A and all b, c ∈ A. The theorem both answers a question and generalizes a result of Ferreirim [6]. 1. ..."
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Abstract. We present a syntactic proof that equation e → (b · c) = (e → b) · (e → c) is satisfied in a hoop A for any idempotent e ∈ A and all b, c ∈ A. The theorem both answers a question and generalizes a result of Ferreirim [6]. 1.
P.: Loops with abelian inner mapping groups: An application of automated deduction
 McCune Festschrift, Lecture Notes in Artificial Intelligence
, 2013
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