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PROTEIN: A PROver with a Theory Extension Interface
 AUTOMATED DEDUCTION  CADE12, VOLUME 814 OF LNAI
, 1994
"... PROTEIN (PROver with a Theory Extension INterface) is a PTTPbased first order theorem prover over builtin theories. Besides various standardrefinements known for model elimination, PROTEIN also offers a variant of model elimination for casebased reasoning and which does not need contrapositives. ..."
Abstract

Cited by 41 (10 self)
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PROTEIN (PROver with a Theory Extension INterface) is a PTTPbased first order theorem prover over builtin theories. Besides various standardrefinements known for model elimination, PROTEIN also offers a variant of model elimination for casebased reasoning and which does not need contrapositives.
Simultaneous Rigid EUnification is Undecidable
 Computer Science Logic. 9th International Workshop, CSL'95
, 1995
"... Simultaneous rigid Eunification has been introduced in the area of theorem proving with equality. It is used in extension procedures, like the tableau method or the connection method. Many articles in this area assume the existence of an algorithm for simultaneous rigid Eunification. There were se ..."
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Cited by 18 (9 self)
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Simultaneous rigid Eunification has been introduced in the area of theorem proving with equality. It is used in extension procedures, like the tableau method or the connection method. Many articles in this area assume the existence of an algorithm for simultaneous rigid Eunification. There were several faulty proofs of the decidability of this problem. In this paper we prove that simultaneous rigid Eunification is undecidable. As a consequence we obtain the undecidability of the 9 fragment of intuitionistic logic with equality. 1 Introduction Simultaneous rigid Eunification plays a crucial role in extending to first order languages with equality automatic proof methods based on sequent calculi, such as semantic tableaux [Fitting 88], the connection method [Bibel 82] (also known as the mating method [Andrews 81]), model elimination [Loveland 68] and a dozen other procedures. The usability of simultaneous rigid Eunification has been explained in [Bibel 87, GaRaSn 87]. Since ...
Consolution as a Framework for Comparing Calculi
 JOURNAL OF SYMBOLIC COMPUTATION
, 1994
"... In this paper, stepwise and nearly stepwise simulation results for a number of firstorder proof calculi are presented and an overview is given that illustrates the relations between these calculi. For this purpose, we modify the consolution calculus in such a way that it can be instantiated to reso ..."
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Cited by 14 (10 self)
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In this paper, stepwise and nearly stepwise simulation results for a number of firstorder proof calculi are presented and an overview is given that illustrates the relations between these calculi. For this purpose, we modify the consolution calculus in such a way that it can be instantiated to resolution, tableaux model elimination, a connection method and Loveland's model elimination.
Refinements of Theory Model Elimination and a Variant without Contrapositives
 University of Koblenz, Institute for Computer Science
, 1994
"... Theory Reasoning means to buildin certain knowledge about a problem domain into a deduction system or calculus, which is in our case model elimination. Several versions of theory model elimination (TME) calculi are presented and proven complete: on the one hand we have highly restricted versions of ..."
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Cited by 8 (6 self)
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Theory Reasoning means to buildin certain knowledge about a problem domain into a deduction system or calculus, which is in our case model elimination. Several versions of theory model elimination (TME) calculi are presented and proven complete: on the one hand we have highly restricted versions of total and partial TME. These restrictions allow (1) to keep fewer path literals in extension steps than in related calculi, and (2) discard proof attempts with multiple occurrences of literals along a path (i.e. regularity holds). On the other hand, we obtain by small modifications to TME versions which do not need contrapositives (a la NearHorn Prolog). We show that regularity can be adapted for these versions. The independence of the goal computation rule holds for all variants. Comparative runtime results for our PTTPimplementations are supplied. 1 Introduction The model elimination calculus (ME calculus) has been developed already in the early days of automated theorem proving [Lovel...