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Extending Sledgehammer with SMT Solvers
"... Abstract. Sledgehammer is a component of Isabelle/HOL that employs firstorder automatic theorem provers (ATPs) to discharge goals arising in interactive proofs. It heuristically selects relevant facts and, if an ATP is successful, produces a snippet that replays the proof in Isabelle. We extended Sl ..."
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Abstract. Sledgehammer is a component of Isabelle/HOL that employs firstorder automatic theorem provers (ATPs) to discharge goals arising in interactive proofs. It heuristically selects relevant facts and, if an ATP is successful, produces a snippet that replays the proof in Isabelle. We extended Sledgehammer to invoke satisfiability modulo theories (SMT) solvers as well, exploiting its relevance filter and parallel architecture. Isabelle users are now pleasantly surprised by SMT proofs for problems beyond the ATPs ’ reach. Remarkably, the best SMT solver performs better than the best ATP on most of our benchmarks. 1
Three Years of Experience with Sledgehammer, a Practical Link between Automatic and Interactive Theorem Provers
"... Sledgehammer is a highly successful subsystem of Isabelle/HOL that calls automatic theorem provers to assist with interactive proof construction. It requires no user configuration: it can be invoked with a single mouse gesture at any point in a proof. It automatically finds relevant lemmas from all ..."
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Cited by 44 (7 self)
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Sledgehammer is a highly successful subsystem of Isabelle/HOL that calls automatic theorem provers to assist with interactive proof construction. It requires no user configuration: it can be invoked with a single mouse gesture at any point in a proof. It automatically finds relevant lemmas from all those currently available. An unusual aspect of its architecture is its use of unsound translations, coupled with its delivery of results as Isabelle/HOL proof scripts: its output cannot be trusted, but it does not need to be trusted. Sledgehammer works well with Isar structured proofs and allows beginners to prove challenging theorems.
Automated reasoning in higherorder logic using the TPTP THF infrastructure
 J. of Formalized Reasoning
, 2010
"... Articulate Software The Thousands of Problems for Theorem Provers (TPTP) problem library is the basis of a well known and well established infrastructure that supports research, development, and deployment of Automated Theorem Proving (ATP) systems. The extension of the TPTP from firstorder form (F ..."
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Cited by 34 (14 self)
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Articulate Software The Thousands of Problems for Theorem Provers (TPTP) problem library is the basis of a well known and well established infrastructure that supports research, development, and deployment of Automated Theorem Proving (ATP) systems. The extension of the TPTP from firstorder form (FOF) logic to typed higherorder form (THF) logic has provided a basis for new development and application of ATP systems for higherorder logic. Key developments have been the specification of the THF language, the addition of higherorder problems to the TPTP, the development of the TPTP THF infrastructure, several ATP systems for higherorder logic, and the use of higherorder ATP in a range of domains. This paper surveys these developments. 1.
2001b, ‘The CADE17 ATP System Competition
 Journal of Automated Reasoning
"... Abstract. The results of the IJCAR ATP System Competition are presented. ..."
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Abstract. The results of the IJCAR ATP System Competition are presented.
Reducing HigherOrder Theorem Proving to a Sequence of SAT Problems
, 2011
"... Abstract. We describe a complete theorem proving procedure for higherorder logic that uses SATsolving to do much of the heavy lifting. The theoretical basis for the procedure is a complete, cutfree, ground refutation calculus that incorporates a restriction on instantiations. The refined nature o ..."
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Abstract. We describe a complete theorem proving procedure for higherorder logic that uses SATsolving to do much of the heavy lifting. The theoretical basis for the procedure is a complete, cutfree, ground refutation calculus that incorporates a restriction on instantiations. The refined nature of the calculus makes it conceivable that one can search in the ground calculus itself, obtaining a complete procedure without resorting to metavariables and a higherorder lifting lemma. Once one commits to searching in a ground calculus, a natural next step is to consider ground formulas as propositional literals and the rules of the calculus as propositional clauses relating the literals. With this view in mind, we describe a theorem proving procedure that primarily generates relevant formulas along with their corresponding propositional clauses. The procedure terminates when the set of propositional clauses is unsatisfiable. We prove soundness and completeness of the procedure. The procedure has been implemented in a new higherorder theorem prover, Satallax, which makes use of the SATsolver MiniSat. We also describe the implementation and give some experimental results.
Embedding and automating conditional logics in classical higherorder logic
 Annals of Mathematics and Artificial Intelligence. In Print. DOI
, 2012
"... Abstract. A sound and complete embedding of conditional logics into classical higherorder logic is presented. This embedding enables the application of offtheshelf higherorder automated theorem provers and model finders for reasoning within and about conditional logics. 1 ..."
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Abstract. A sound and complete embedding of conditional logics into classical higherorder logic is presented. This embedding enables the application of offtheshelf higherorder automated theorem provers and model finders for reasoning within and about conditional logics. 1
Understanding LEOII’s proofs
 International Workshop on the Implementation of Logics (IWIL2012
, 2012
"... The Leo and LeoII provers have pioneered the integration of higherorder and firstorder automated theoremproving. To date, the LeoII system is, to our knowledge, the only automated higherorder theoremprover which is capable of generating joint higherorder–firstorder proof objects in TPTP for ..."
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Cited by 5 (4 self)
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The Leo and LeoII provers have pioneered the integration of higherorder and firstorder automated theoremproving. To date, the LeoII system is, to our knowledge, the only automated higherorder theoremprover which is capable of generating joint higherorder–firstorder proof objects in TPTP format. This paper discusses LeoII’s proof objects. The target audience are practitioners with an interest in using LeoII proofs within other systems. 1
Higherorder aspects and context in SUMO
 Journal of Web Semantics (Special Issue on Reasoning with context in the Semantic Web
, 2012
"... This article addresses the automation of higherorder aspects in expressive ontologies such as the Suggested Upper Merged Ontology SUMO. Evidence is provided that modern higherorder automated theorem provers like LEOII can be fruitfully employed for the task. A particular focus is on embedded for ..."
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This article addresses the automation of higherorder aspects in expressive ontologies such as the Suggested Upper Merged Ontology SUMO. Evidence is provided that modern higherorder automated theorem provers like LEOII can be fruitfully employed for the task. A particular focus is on embedded formulas (formulas as terms), which are used in SUMO, for example, for modeling temporal, epistemic, or doxastic contexts. This modeling is partly in conflict with SUMO’s assumption of a bivalent, classical semantics and it may hence lead to counterintuitive reasoning results with automated theorem provers in practice. A solution is proposed that maps SUMO to quantified multimodal logic which is in turn modeled as a fragment of classical higherorder logic. This way automated higherorder theorem provers can be safely applied for reasoning about modal contexts in SUMO. Our findings are of wider relevance as they analogously apply to other expressive ontologies and knowledge representation formalisms.
Combining and Automating Classical and NonClassical Logics in Classical HigherOrder Logics
 ANNALS OF MATHEMATICS AND ARTIFICIAL INTELLIGENCE (PREFINAL VERSION)
"... Numerous classical and nonclassical logics can be elegantly embedded in Church’s simple type theory, also known as classical higherorder logic. Examples include propositional and quantified multimodal logics, intuitionistic logics, logics for security, and logics for spatial reasoning. Furthermor ..."
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Cited by 5 (5 self)
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Numerous classical and nonclassical logics can be elegantly embedded in Church’s simple type theory, also known as classical higherorder logic. Examples include propositional and quantified multimodal logics, intuitionistic logics, logics for security, and logics for spatial reasoning. Furthermore, simple type theory is sufficiently expressive to model combinations of embedded logics and it has a well understood semantics. Offtheshelf reasoning systems for simple type theory exist that can be uniformly employed for reasoning within and about embedded logics and logics combinations. In this article we focus on combinations of (quantified) epistemic and doxastic logics and study their application for modeling and automating the reasoning of rational agents. We present illustrating example problems and report on experiments with offtheshelf higherorder automated theorem provers.
LEOII version 1.5
"... LeoII cooperates with other theoremprovers to prove theorems in classical higherorder logic. It returns hybrid proofs, which contain inferences made by LeoII as well as the backend provers with which it cooperates. This article describes recent improvements made to LeoII. 1 ..."
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LeoII cooperates with other theoremprovers to prove theorems in classical higherorder logic. It returns hybrid proofs, which contain inferences made by LeoII as well as the backend provers with which it cooperates. This article describes recent improvements made to LeoII. 1