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The TPTP Problem Library
, 1999
"... This report provides a detailed description of the TPTP Problem Library for automated theorem proving systems. The library is available via Internet, and forms a common basis for development of and experimentation with automated theorem provers. This report provides: ffl the motivations for buildin ..."
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Cited by 100 (6 self)
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This report provides a detailed description of the TPTP Problem Library for automated theorem proving systems. The library is available via Internet, and forms a common basis for development of and experimentation with automated theorem provers. This report provides: ffl the motivations for building the library; ffl a discussion of the inadequacies of previous problem collections, and how these have been resolved in the TPTP; ffl a description of the library structure, including overview information; ffl descriptions of supplementary utility programs; ffl guidelines for obtaining and using the library; Contents 1 Introduction 2 1.1 Previous Problem Collections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 What is Required? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Inside the TPTP 6 2.1 The TPTP Domain Structure . . . . . . . . . . . . . . . . . . . . . ...
Proving Java Type Soundness
, 1997
"... This technical report describes a machine checked proof of the type soundness of a subset of the Java language called Java S . A formal semantics for this subset has been developed by Drossopoulou and Eisenbach, and they have sketched an outline of the type soundness proof. The formulation developed ..."
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Cited by 86 (2 self)
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This technical report describes a machine checked proof of the type soundness of a subset of the Java language called Java S . A formal semantics for this subset has been developed by Drossopoulou and Eisenbach, and they have sketched an outline of the type soundness proof. The formulation developed here complements their written semantics and proof by correcting and clarifying significant details; and it demonstrates the utility of formal, machine checking when exploring a large and detailed proof based on operational semantics. The development also serves as a case study in the application of `declarative' proof techniques to a major property of an operational system. Contents 1 Introduction 2 1.1 Java . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 What is Type Soundness for Java? . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 The Tool: DECLARE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Outl...
Controlled Integrations of the Cut Rule into Connection Tableau Calculi
"... In this paper techniques are developed and compared which increase the inferential power of tableau systems for classical firstorder logic. The mechanisms are formulated in the framework of connection tableaux, which is an amalgamation of the connection method and the tableau calculus, and a genera ..."
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Cited by 61 (3 self)
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In this paper techniques are developed and compared which increase the inferential power of tableau systems for classical firstorder logic. The mechanisms are formulated in the framework of connection tableaux, which is an amalgamation of the connection method and the tableau calculus, and a generalization of model elimination. Since connection tableau calculi are among the weakest proof systems with respect to proof compactness, and the (backward) cut rule is not suitable for the firstorder case, we study alternative methods for shortening proofs. The techniques we investigate are the folding up and the folding down operation. Folding up represents an efficient way of supporting the basic calculus, which is topdown oriented, with lemmata derived in a bottomup manner. It is shown that both techniques can also be viewed as controlled integrations of the cut rule. In order to remedy the additional redundancy imported into tableau proof procedures by the new inference rules, we develop and apply an extension of the regularity condition on tableaux and the mechanism of antilemmata which realizes a subsumption concept on tableaux. Using the framework of the theorem prover SETHEO, we have implemented three new proof procedures which overcome the deductive weakness of cutfree tableau systems. Experimental results demonstrate the superiority of the systems with folding up over the cutfree variant and the one with folding down.
Firstorder proof tactics in higherorder logic theorem provers
 Design and Application of Strategies/Tactics in Higher Order Logics, number NASA/CP2003212448 in NASA Technical Reports
, 2003
"... Abstract. In this paper we evaluate the effectiveness of firstorder proof procedures when used as tactics for proving subgoals in a higherorder logic interactive theorem prover. We first motivate why such firstorder proof tactics are useful, and then describe the core integrating technology: an ‘ ..."
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Cited by 50 (4 self)
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Abstract. In this paper we evaluate the effectiveness of firstorder proof procedures when used as tactics for proving subgoals in a higherorder logic interactive theorem prover. We first motivate why such firstorder proof tactics are useful, and then describe the core integrating technology: an ‘LCFstyle’ logical kernel for clausal firstorder logic. This allows the choice of different logical mappings between higherorder logic and firstorder logic to be used depending on the subgoal, and also enables several different firstorder proof procedures to cooperate on constructing the proof. This work was carried out using the HOL4 theorem prover; we comment on the ease of transferring the technology to other higherorder logic theorem provers. 1
Caching and Lemmaizing in Model Elimination Theorem Provers
, 1992
"... Theorem provers based on model elimination have exhibited extremely high inference rates but have lacked a redundancy control mechanism such as subsumption. In this paper we report on work done to modify a model elimination theorem prover using two techniques, caching and lemmaizing, that have reduc ..."
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Cited by 49 (2 self)
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Theorem provers based on model elimination have exhibited extremely high inference rates but have lacked a redundancy control mechanism such as subsumption. In this paper we report on work done to modify a model elimination theorem prover using two techniques, caching and lemmaizing, that have reduced by more than an order of magnitude the time required to find proofs of several problems and that have enabled the prover to prove theorems previously unobtainable by topdown model elimination theorem provers.
A FirstOrder Logic DavisPutnamLogemannLoveland Procedure
"... The DavisPutnamLogemannLoveland procedure (DPLL) was introduced in the early ..."
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Cited by 38 (6 self)
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The DavisPutnamLogemannLoveland procedure (DPLL) was introduced in the early
Model Elimination without Contrapositives and its Application to PTTP
 PROCEEDINGS OF CADE12, SPRINGER LNAI 814
, 1994
"... We give modifications of model elimination which do not necessitate the use of contrapositives. These restart model elimination calculi are proven sound and complete and their implementation by PTTP is depicted. The corresponding proof procedures are evaluated by a number of runtime experiments and ..."
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Cited by 22 (8 self)
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We give modifications of model elimination which do not necessitate the use of contrapositives. These restart model elimination calculi are proven sound and complete and their implementation by PTTP is depicted. The corresponding proof procedures are evaluated by a number of runtime experiments and they are compared to other well known provers. Finally we relate our results to other calculi, namely the connection method, modified problem reduction format and NearHorn Prolog.
leanCoP: Lean ConnectionBased Theorem Proving
 UNIVERSITY OF KOBLENZ
, 2000
"... The Prolog program "prove(M,I) : append(Q,[CR],M), "+member(,C), append(Q,R,S), prove([!],[[!C]S],[],I). prove([],,,). prove([LC],M,P,I) : (N=L; L=N) ? (member(N,P); append(Q,[DR],M), copyterm(D,E), append(A,[NB],E), append(A,B,F), (D==E ? append(R,Q,S); length(P,K), ..."
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Cited by 19 (7 self)
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The Prolog program "prove(M,I) : append(Q,[CR],M), "+member(,C), append(Q,R,S), prove([!],[[!C]S],[],I). prove([],,,). prove([LC],M,P,I) : (N=L; L=N) ? (member(N,P); append(Q,[DR],M), copyterm(D,E), append(A,[NB],E), append(A,B,F), (D==E ? append(R,Q,S); length(P,K), K!I, append(R,[DQ],S)), prove(F,S,[LP],I)), prove(C,M,P,I)." implements a theorem prover for classical firstorder (clausal) logic which is based on the connection calculus. It is sound, complete (if one more line is added), and demonstrates a comparatively strong performance.
Deduction Systems Based on Resolution
, 1991
"... A general theory of deduction systems is presented. The theory is illustrated with deduction systems based on the resolution calculus, in particular with clause graphs. This theory distinguishes four constituents of a deduction system: ffl the logic, which establishes a notion of semantic entailmen ..."
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Cited by 19 (0 self)
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A general theory of deduction systems is presented. The theory is illustrated with deduction systems based on the resolution calculus, in particular with clause graphs. This theory distinguishes four constituents of a deduction system: ffl the logic, which establishes a notion of semantic entailment; ffl the calculus, whose rules of inference provide the syntactic counterpart of entailment; ffl the logical state transition system, which determines the representation of formulae or sets of formulae together with their interrelationships, and also may allow additional operations reducing the search space; ffl the control, which comprises the criteria used to choose the most promising from among all applicable inference steps. Much of the standard material on resolution is presented in this framework. For the last two levels many alternatives are discussed. Appropriately adjusted notions of soundness, completeness, confluence, and Noetherianness are introduced in order to characterize...