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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
Communication formalisms for automated theorem proving tools
 PROC. OF IJCAI18 WORKSHOP ON AGENTS AND AUTOMATED REASONING
, 2003
"... This paper describes two communication formalisms for Automated Theorem Proving (ATP) tools. First, a problem and solution language has been designed. The language will be used for writing problems to be input to ATP systems, and for writing solutions output by ATP systems. Second, a hierarchy of re ..."
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This paper describes two communication formalisms for Automated Theorem Proving (ATP) tools. First, a problem and solution language has been designed. The language will be used for writing problems to be input to ATP systems, and for writing solutions output by ATP systems. Second, a hierarchy of result statuses, which adequately express the range of results output by ATP systems, has been established. These formalisms will support application and research in ATP, and will facilitate direct communication between ATP tools when they are used as embedded components in larger systems.
Yet another single law for lattices
"... Abstract. In this note we show that the equational theory of all lattices is defined by the single absorption law (((y∨x)∧x)∨(((z∧(x∨x))∨(u∧x))∧v))∧(w∨((s∨x)∧(x∨t))) = x. This identity of length 29 with 8 variables is shorter than previously known such equations defining lattices. 1. ..."
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Abstract. In this note we show that the equational theory of all lattices is defined by the single absorption law (((y∨x)∧x)∨(((z∧(x∨x))∨(u∧x))∧v))∧(w∨((s∨x)∧(x∨t))) = x. This identity of length 29 with 8 variables is shorter than previously known such equations defining lattices. 1.
Short equational bases for ortholattices
 Preprint ANL/MCSP10870903, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL
, 2004
"... Short single axioms for ortholattices, orthomodular lattices, and modular ortholattices are presented, all in terms of the Sheffer stroke. The ortholattice axiom is the shortest possible. Other equational bases in terms of the Sheffer stroke and in terms of join, meet, and complement are presented. ..."
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Short single axioms for ortholattices, orthomodular lattices, and modular ortholattices are presented, all in terms of the Sheffer stroke. The ortholattice axiom is the shortest possible. Other equational bases in terms of the Sheffer stroke and in terms of join, meet, and complement are presented. Proofs are omitted but are available in an associated technical report. Computers were used extensively to find candidates, reject candidates, and search for proofs that candidates are single axioms. The notion of computer proof is addressed. 1
Application of model search to lattice theory
 AAA Newsletter
, 2001
"... We have used the firstorder modelsearching programs MACE and SEM to study various problems in lattice theory. First, we present a case study in which the two programs are used to examine the differences between the stages along the way from lattice theory to Boolean algebra. Second, we answer seve ..."
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We have used the firstorder modelsearching programs MACE and SEM to study various problems in lattice theory. First, we present a case study in which the two programs are used to examine the differences between the stages along the way from lattice theory to Boolean algebra. Second, we answer several questions posed by Norman Megill and Mladen Pavičić on
Automated Theory Formation for Tutoring Tasks in Pure Mathematics
 In CADE18, Workshop on the Role of Automated Deduction in Mathematics
, 2002
"... The HR program forms mathematical theories from as little information as the axioms of a domain. The theories include concepts with examples and de nitions, conjectures, theorems and proofs. Moreover, HR uses third party mathematical software including automated theorem provers and model genera ..."
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The HR program forms mathematical theories from as little information as the axioms of a domain. The theories include concepts with examples and de nitions, conjectures, theorems and proofs. Moreover, HR uses third party mathematical software including automated theorem provers and model generators. We suggest that a potential role for theory formation systems such as HR is as an aid to mathematics lecturers. We discuss an application of HR to the generation of a set of group theory exercises. This forms part of a project using HR to make discoveries in Zariski spaces, which is also detailed.
Integrating HR and tptp2X into MathWeb to Compare Automated Theorem Provers
 In Proceedings of the CADE'02 Workshop on Problems and Problem sets
, 2002
"... The assessment and comparison of automated theorem proving systems (ATPs) is important for the advancement of the field. At present, the de facto assessment method is to test provers on the TPTP library of nearly 6000 theorems. We describe here a project which aims to complement the TPTP service by ..."
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The assessment and comparison of automated theorem proving systems (ATPs) is important for the advancement of the field. At present, the de facto assessment method is to test provers on the TPTP library of nearly 6000 theorems. We describe here a project which aims to complement the TPTP service by automatically generating theorems of sufficient diculty to provide a significant test for first order provers. This has been achieved by integrating the HR automated theory formation program into the MathWeb Software Bus. HR generates first order conjectures in TPTP format and passes them to a concurrent ATP service in MathWeb. MathWeb then uses the tptp2X utility to translate the conjectures into the input format of a set of provers. In this way, various ATP systems can be compared on their performance over sets of thousands of theorems they have not been previously exposed to. Our purpose here is to describe the integration of various new programs into the MathWeb architecture, rather than to present a full analysis of the performance of theorem provers. However, to demonstrate the potential of the combination of the systems, we describe some preliminary results from experiments in group theory.
Tarski Theorems on SelfDual Equational Bases for Groups
, 2004
"... We present independent selfdual equational bases of arbitrarily large finite sizes for the equational theory of groups treated as varieties of various wellknown types. Here the dual of a term f is the mirror reflection of f. For each type of group theory, we provide an independent selfdual basis ..."
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We present independent selfdual equational bases of arbitrarily large finite sizes for the equational theory of groups treated as varieties of various wellknown types. Here the dual of a term f is the mirror reflection of f. For each type of group theory, we provide an independent selfdual basis with n identities for n = 2, 3, 4. Then we develop a simple algorithmic procedure to construct independent selfdual equational bases of arbitrary finite sizes in such a way that the new larger equational bases depend explicitly on the initial bases