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Practical Proof Checking for Program Certification
 Proceedings of the CADE20 Workshop on Empirically Successful Classical Automated Reasoning (ESCAR’05
, 2005
"... Program certification aims to provide explicit evidence that a program meets a specified level of safety. This evidence must be independently reproducible and verifiable. We have developed a system, based on theorem proving, that generates proofs that autogenerated aerospace code adheres to a numbe ..."
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Program certification aims to provide explicit evidence that a program meets a specified level of safety. This evidence must be independently reproducible and verifiable. We have developed a system, based on theorem proving, that generates proofs that autogenerated aerospace code adheres to a number of safety policies. For certification purposes, these proofs need to be verified by a proof checker. Here, we describe and evaluate a semantic derivation verification approach to proof checking. The evaluation is based on 109 safety obligations that are attempted by EP and SPASS. Our system is able to verify 129 out of the 131 proofs found by the two provers. The majority of the proofs are checked completely in less than 15 seconds wall clock time. This shows that the proof checking task arising from a substantial prover application is practically tractable. 1
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.
CLASSIFICATION RESULTS IN QUASIGROUP AND LOOP THEORY VIA A COMBINATION OF AUTOMATED REASONING TOOLS
"... Abstract. We present some novel classification results in quasigroup and loop theory. For quasigroups up to size 5 and loops up to size 7, we describe a unique property which determines the isomorphism (and in the case of loops, the isotopism) class for any example. These invariant properties were g ..."
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Abstract. We present some novel classification results in quasigroup and loop theory. For quasigroups up to size 5 and loops up to size 7, we describe a unique property which determines the isomorphism (and in the case of loops, the isotopism) class for any example. These invariant properties were generated using a variety of automated techniques – including machine learning and computer algebra – which we present here. Moreover, each result has been automatically verified, again using a variety of techniques – including automated theorem proving, computer algebra and satisfiability solving – and we describe our bootstrapping approach to the generation and verification of these classification results. 1.
Discrete Event Calculus Deduction using FirstOrder Automated Theorem Proving
"... Abstract. The event calculus is a powerful and highly usable formalism for reasoning about action and change. The discrete event calculus limits time to integers. This paper shows how discrete event calculus problems can be encoded in firstorder logic, and solved using a firstorder logic automated ..."
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Abstract. The event calculus is a powerful and highly usable formalism for reasoning about action and change. The discrete event calculus limits time to integers. This paper shows how discrete event calculus problems can be encoded in firstorder logic, and solved using a firstorder logic automated theorem proving system. The following techniques are discussed: reification is used to convert event and fluent atoms into firstorder terms, uniquenessofnames axioms are generated to ensure uniqueness of event and fluent terms, predicate completion is used to convert secondorder circumscriptions into firstorder formulae, and a limited firstorder axiomatization of integer arithmetic is developed. The performance of firstorder automated theorem proving is compared to that of satisfiability solving. 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
RESTRUCTURING FORMAL MATHEMATICS FOR NATURAL TEXTS
, 2004
"... In the presence of growing collections of formal mathematics, and renewed interest in formal mathematics and automated theorem proving for new domains such as hardware or code verification, it is vital to be able to present formal content accessibly to broad audiences. We propose a novel approach to ..."
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In the presence of growing collections of formal mathematics, and renewed interest in formal mathematics and automated theorem proving for new domains such as hardware or code verification, it is vital to be able to present formal content accessibly to broad audiences. We propose a novel approach to constructing a content planner for formal mathematics produced by a tacticstyle prover which capitalizes on the inherent structure of the formal proofs. Though it had been posited that highlevel formal structure is unsuitable as a source of information for text generation, due to its heuristic nature and necessary lack of details, we are able to show that this is not the case. Tacticstyle proofs share significant structural commonality with the discourse structure of corresponding texts. These commonalities allow a content planner to be constructed which need only use lowlevel logical content as a supplementary information source to the generation process. To show that this is the case, we collected two corpora of texts generated to communicate the proof content of a series of formal proofs produced by the Nuprl
Proof Generation for Saturating FirstOrder Theorem Provers
"... Firstorder Automated Theorem Proving (ATP) is one of the oldest and most developed areas of automated reasoning. Today, the most widely used firstorder provers are fully automatic and process firstorder logic with equality. Many stateoftheart ATP systems consist of a clausifier, translating a ..."
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Firstorder Automated Theorem Proving (ATP) is one of the oldest and most developed areas of automated reasoning. Today, the most widely used firstorder provers are fully automatic and process firstorder logic with equality. Many stateoftheart ATP systems consist of a clausifier, translating a full firstorder