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A Resolution Theorem Prover for Intuitionistic Logic
 Proceedings of CADE13
, 1996
"... We use the general scheme of building resolution calculi (also called the inverse method) originating from S.Maslov and G.Mints to design and implement a resolution theorem prover for intuitionistic logic. A number of search strategies is introduced and proved complete. The resolution method is show ..."
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We use the general scheme of building resolution calculi (also called the inverse method) originating from S.Maslov and G.Mints to design and implement a resolution theorem prover for intuitionistic logic. A number of search strategies is introduced and proved complete. The resolution method is shown to be a decision procedure for a new syntactically described decidable class of intuitionistic logic. We compare the search strategies suitable for the resolution method with strategies suitable for the tableau method. The performance of our prover is compared with the performance of a tableau prover for intuitionistic logic presented in [17].
Towards efficient subsumption
 Conference on Automated Deduction
, 1998
"... Abstract. We propose several methods for writing efficient subsumption procedures for nonunit clauses, tested in practice as parts incorporated into the Gandalf family of theorem provers. Versions of Gandalf exist for classical logic, first order intuitionistic logic and type theory. Subsumption is ..."
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Abstract. We propose several methods for writing efficient subsumption procedures for nonunit clauses, tested in practice as parts incorporated into the Gandalf family of theorem provers. Versions of Gandalf exist for classical logic, first order intuitionistic logic and type theory. Subsumption is one of the most important techniques for cutting down search space in resolution theorem proving. However, for many problem categories most of the proof search time is spent on subsumption. While acceptable efficiency has been achieved for subsuming unit clauses (see [7], [2]), the nonunit subsumption tends to slow provers down prohibitively. We propose several methods for writing efficient subsumption procedures for nonunit clauses, succesfully tested in practice as parts built into the Gandalf family of theorem provers: – ordering literals according to a certain subsumption measure – indexing first two literals of each nonunit clause – precomputed properties of terms, literals and clauses – a hierarchy of fast filters for clausetoclause subsumption – combining subsumption with clause simplification – linear search among the strongly reduced number of candidates for back subsumption The presented methods for substitution were among the key techniques enabling the classical version of Gandalf to win the MIX division of the CASC14 prover contest in 1997. The approach of the paper is purely empirical, presenting the methods and bringing some statistical evidence. 1 Gandalf Family of Provers Before continuing with the details of the subsumption methods we will present an overview of the Gandalf family of provers. We use the name Gandalf for the interdependent, codesharing, resolutionbased automated theorem provers we are developing: a resolution prover for firstorder intuitionistic logic Tammet [9], for a fragment of MartinLöf’s type theory Tammet [10] and for firstorder
Some tools for computerassisted theorem proving in MartinLöf type theory
 TPHOLS  SUPPLEMENTAL PROCEEDINGS. UNIVERSITY OF EDINBURGH
, 2001
"... We propose some tools facilitating interactive proof and program development in the proof editor Alfa based on MartinLöf Type Theory, in particular a tool for equality reasoning supported by tools for deriving equality (and proofs or its properties) for inductive datatypes as well as automated pr ..."
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We propose some tools facilitating interactive proof and program development in the proof editor Alfa based on MartinLöf Type Theory, in particular a tool for equality reasoning supported by tools for deriving equality (and proofs or its properties) for inductive datatypes as well as automated proofsearch.
development in MartinLöf Type Theory (extended abstract)
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Gandalf
, 1997
"... . We give a brief overview of the first order classical logic component in the Gandalf family of resolutionbased automated theorem provers for classical and intuitionistic logics. The main strength of the described version is a sophisticated algorithm for nonunit subsumption. Key words: Automated ..."
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. We give a brief overview of the first order classical logic component in the Gandalf family of resolutionbased automated theorem provers for classical and intuitionistic logics. The main strength of the described version is a sophisticated algorithm for nonunit subsumption. Key words: Automated theorem proving, competition, Gandalf, resolution, subsumption. 1. Introduction We use the name Gandalf for the family of interdependent, codesharing, resolutionbased automated theorem provers we are currently developing: \Gamma A resolution prover for the full firstorder intuitionistic logic, see [4]. \Gamma A prover for a fragment of MartinLof's type theory, see [5]. The prover converts type theory formulas to first order logic, searches for the proof, then converts proofs back to type theory. A special component for automated induction is included. \Gamma A resolution prover for firstorder classical logic. prover is described in the current paper. 1.1. Motivation The motivation ...
Reference Manual. Gandalf
, 1997
"... 3 1 Introduction 3 1.1 Implemented strategies : : : : : : : : : : : : : : : : : : : : : : : : : : 4 1.2 Other versions of Gandalf : : : : : : : : : : : : : : : : : : : : : : : : 5 1.3 Why "Gandalf " : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 5 1.4 Performance : : : : : : ..."
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3 1 Introduction 3 1.1 Implemented strategies : : : : : : : : : : : : : : : : : : : : : : : : : : 4 1.2 Other versions of Gandalf : : : : : : : : : : : : : : : : : : : : : : : : 5 1.3 Why "Gandalf " : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 5 1.4 Performance : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 5 1.5 History : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 6 1.6 Future improvements : : : : : : : : : : : : : : : : : : : : : : : : : : : 6 2 Outline of Gandalf's Inference Process 6 3 Obtaining Gandalf 7 4 Running Gandalf 8 5 Syntax 8 5.1 Preparing TPTP problem files : : : : : : : : : : : : : : : : : : : : : 9 5.2 Incorrect syntax : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 9 5.3 Comments : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 9 5.4 Names for Symbols : : : : : : : : : : : : : : : : : : : : : : : : : : : : 9 5.5 Term and Clause Syntax : : : : : : : : : : : : : : : : : : : : : : : : : ...