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156
E  A Brainiac Theorem Prover
, 2002
"... We describe the superpositionbased theorem prover E. E is a sound and complete... ..."
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Cited by 179 (23 self)
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We describe the superpositionbased theorem prover E. E is a sound and complete...
Kodkod: A relational model finder
 of Lecture
"... Abstract. The key design challenges in the construction of a SATbased relational model finder are described, and novel techniques are proposed to address them. An efficient model finder must have a mechanism for specifying partial solutions, an effective symmetry detection and breaking scheme, and ..."
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Cited by 103 (11 self)
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Abstract. The key design challenges in the construction of a SATbased relational model finder are described, and novel techniques are proposed to address them. An efficient model finder must have a mechanism for specifying partial solutions, an effective symmetry detection and breaking scheme, and an economical translation from relational to boolean logic. These desiderata are addressed with three new techniques: a symmetry detection algorithm that works in the presence of partial solutions, a sparsematrix representation of relations, and a compact representation of boolean formulas inspired by boolean expression diagrams and reduced boolean circuits. The presented techniques have been implemented and evaluated, with promising results. 1
Full functional verification of linked data structures
 In ACM Conf. Programming Language Design and Implementation (PLDI
, 2008
"... We present the first verification of full functional correctness for a range of linked data structure implementations, including mutable lists, trees, graphs, and hash tables. Specifically, we present the use of the Jahob verification system to verify formal specifications, written in classical high ..."
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Cited by 100 (19 self)
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We present the first verification of full functional correctness for a range of linked data structure implementations, including mutable lists, trees, graphs, and hash tables. Specifically, we present the use of the Jahob verification system to verify formal specifications, written in classical higherorder logic, that completely capture the desired behavior of the Java data structure implementations (with the exception of properties involving execution time and/or memory consumption). Given that the desired correctness properties include intractable constructs such as quantifiers, transitive closure, and lambda abstraction, it is a challenge to successfully prove the generated verification conditions. Our Jahob verification system uses integrated reasoning to split each verification condition into a conjunction of simpler subformulas, then apply a diverse collection of specialized decision procedures,
Solving quantified verification conditions using satisfiability modulo theories
 In CADE
, 2007
"... Abstract. First order logic provides a convenient formalism for describing a wide variety of verification conditions. Two main approaches to checking such conditions are pure first order automated theorem proving (ATP) and automated theorem proving based on satisfiability modulo theories (SMT). Trad ..."
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Cited by 50 (7 self)
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Abstract. First order logic provides a convenient formalism for describing a wide variety of verification conditions. Two main approaches to checking such conditions are pure first order automated theorem proving (ATP) and automated theorem proving based on satisfiability modulo theories (SMT). Traditional ATP systems are designed to handle quantifiers easily, but often have difficulty reasoning with respect to theories. SMT systems, on the other hand, have builtin support for many useful theories, but have a much more difficult time with quantifiers. One clue on how to get the best of both worlds can be found in the legacy system Simplify which combines builtin theory reasoning with quantifier instantiation heuristics. Inspired by Simplify and motivated by a desire to provide a competitive alternative to ATP systems, this paper describes a methodology for reasoning about quantifiers in SMT systems. We present the methodology in the context of the Abstract DPLL Modulo Theories framework. Besides adapting many of Simplify’s techniques, we also introduce a number of new heuristics. Most important is the notion of instantiation level which provides an effective mechanism for prioritizing and managing the large search space inherent in quantifier instantiation techniques. These techniques have been implemented in the SMT system CVC3. Experimental results show that our methodology enables CVC3 to solve a significant number of benchmarks that were not solvable with any previous approach. 1
Lightweight relevance filtering for machinegenerated resolution problems
 In ESCoR: Empirically Successful Computerized Reasoning
, 2006
"... Irrelevant clauses in resolution problems increase the search space, making it hard to find proofs in a reasonable time. Simple relevance filtering methods, based on counting function symbols in clauses, improve the success rate for a variety of automatic theorem provers and with various initial set ..."
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Cited by 48 (9 self)
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Irrelevant clauses in resolution problems increase the search space, making it hard to find proofs in a reasonable time. Simple relevance filtering methods, based on counting function symbols in clauses, improve the success rate for a variety of automatic theorem provers and with various initial settings. We have designed these techniques as part of a project to link automatic theorem provers to the interactive theorem prover Isabelle. They should be applicable to other situations where the resolution problems are produced mechanically and where completeness is less important than achieving a high success rate with limited processor time. 1
Modular Data Structure Verification
 EECS DEPARTMENT, MASSACHUSETTS INSTITUTE OF TECHNOLOGY
, 2007
"... This dissertation describes an approach for automatically verifying data structures, focusing on techniques for automatically proving formulas that arise in such verification. I have implemented this approach with my colleagues in a verification system called Jahob. Jahob verifies properties of Java ..."
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Cited by 44 (21 self)
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This dissertation describes an approach for automatically verifying data structures, focusing on techniques for automatically proving formulas that arise in such verification. I have implemented this approach with my colleagues in a verification system called Jahob. Jahob verifies properties of Java programs with dynamically allocated data structures. Developers write Jahob specifications in classical higherorder logic (HOL); Jahob reduces the verification problem to deciding the validity of HOL formulas. I present a new method for proving HOL formulas by combining automated reasoning techniques. My method consists of 1) splitting formulas into individual HOL conjuncts, 2) soundly approximating each HOL conjunct with a formula in a more tractable fragment and 3) proving the resulting approximation using a decision procedure or a theorem prover. I present three concrete logics; for each logic I show how to use it to approximate HOL formulas, and how to decide the validity of formulas in this logic. First, I present an approximation of HOL based on a translation to firstorder logic, which enables the use of existing resolutionbased theorem provers. Second, I present an approximation of HOL based on field constraint analysis, a new technique that enables
Computing finite models by reduction to functionfree clause logic
 Journal of Applied Logic
, 2007
"... Recent years have seen considerable interest in procedures for computing finite models of firstorder logic specifications. One of the major paradigms, MACEstyle model building, is based on reducing model search to a sequence of propositional satisfiability problems and applying (efficient) SAT sol ..."
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Cited by 34 (9 self)
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Recent years have seen considerable interest in procedures for computing finite models of firstorder logic specifications. One of the major paradigms, MACEstyle model building, is based on reducing model search to a sequence of propositional satisfiability problems and applying (efficient) SAT solvers to them. A problem with this method is that it does not scale well because the propositional formulas to be considered may become very large. We propose instead to reduce model search to a sequence of satisfiability problems consisting of functionfree firstorder clause sets, and to apply (efficient) theorem provers capable of deciding such problems. The main appeal of this method is that firstorder clause sets grow more slowly than their propositional counterparts, thus allowing for more space efficient reasoning. In this paper we describe our proposed reduction in detail and discuss how it is integrated into the Darwin prover, our implementation of the Model Evolution calculus. The results are general, however, as our approach can be used in principle with any system that decides the satisfiability of functionfree firstorder clause sets. To demonstrate its practical feasibility, we tested our approach on all satisfiable problems from the TPTP library. Our methods can solve a significant subset of these problems, which overlaps but is not included in the subset of problems solvable by stateoftheart finite model builders such as Paradox and Mace4.
SPASS Version 3.5
 In Proc. Int’l Conf. Automated Deduction (CADE
, 2009
"... Abstract. SPASS is an automated theorem prover for full firstorder logic with equality and a number of nonclassical logics. This system description provides an overview of our recent developments in SPASS 3.5 including subterm contextual rewriting, improved split backtracking, a significantly fast ..."
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Cited by 34 (3 self)
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Abstract. SPASS is an automated theorem prover for full firstorder logic with equality and a number of nonclassical logics. This system description provides an overview of our recent developments in SPASS 3.5 including subterm contextual rewriting, improved split backtracking, a significantly faster FLOTTER implementation with additional control flags, completely symmetric implementation of forward and backward redundancy criteria, faster parsing with improved support for big files, faster and extended sort module, and support for include commands in input files. Finally, SPASS 3.5 can now parse files in TPTP syntax, comes with a new converter tptp2dfg and is distributed under a BSD style license. 1
FirstOrderized ResearchCyc: Expressivity and Efficiency in a CommonSense Ontology
 In Papers from the AAAI Workshop on Contexts and Ontologies: Theory, Practice and Applications
, 2005
"... Cyc is the largest existing commonsense knowledge base. Its ontology makes heavy use of higherorder logic constructs such as a context system, first class predicates, etc. Many of these higherorder constructs are believed to be key to Cyc's ability to represent commonsense knowledge and ..."
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Cited by 33 (1 self)
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Cyc is the largest existing commonsense knowledge base. Its ontology makes heavy use of higherorder logic constructs such as a context system, first class predicates, etc. Many of these higherorder constructs are believed to be key to Cyc's ability to represent commonsense knowledge and reason with it efficiently. In this paper, we present a translation of a large part (around 90%) of the Cyc ontology into FirstOrder Logic. We discuss our methodology, and the tradeoffs between expressivity and efficiency in representation and reasoning. We also present the results of experiments using VAMPIRE, SPASS, and the E Theorem Prover on the firstorderized Cyc KB. Our results indicate that, while the use of higherorder logic is not essential to the representability of commonsense knowledge, it greatly improves the efficiency of reasoning.