A. Buch and Th. Hillenbrand. Waldmeister: development of a high performance completion-based theorem prover. SEKI-Report 96-01, Universitat Kaiserslautern, 1996.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....systems ( external systems) within Theorema session in the same way as internal Theorema provers. Currently, the following 11 external systems are supported: provers Bliksem [19] EQP [17] E [21] Gandalf [23] Otter [16] Scott [12] Setheo [15] Spass [24] Vampire [20] Waldmeister [4] and a nite model and counter example searcher Mace [18] The interface consists of two types of links direct and indirect from Theorema to an external system. The indirect link is established with Setheo, Scott and Waldmeister using rst an intermediate translation into TPTP [22] format, ....

Buch, A. and Hillenbrand, Th. Waldmeister: Development of a High Performance Completion-Based Theorem Prover, SR-96-01. Universitaet Kaiserslautern, Germany (1996).

....approach. We think that this is sensible since these systems have been developed under considerable e ort and have been tested extensively. State of the art provers employ sophisticated indexing methods [Gra96] and can cope with millions of facts eciently due to specialized storing techniques [BH96]. So in this paper we study the question how unfailing completion can be re ned in a way which is simple to implement in the mentioned systems and improves them for solving more non trivial problems, especially if AC operators are involved. For a simple example which shows the considerable ....

A. Buch and T. Hillenbrand. Waldmeister: Development of a High Performance Completion-Based Theorem Prover. SEKI-Report 96-01, Universitat Kaiserslautern, 1996.

....caused by the fact that the length of a term is not known in advance, and by the internal tree structure of terms. It appears to be the most natural solution to use techniques from Prolog. This is done in Spass [Spass99] and in Otter [McC99] However in Waldmeister other datastructures are used. [Wm95]. We have implemented 5 ways of representing terms, and compared them on two fundamental operations, matching and uni cation in unify.c. Matching is one sided uni cation, i.e. the problem of nding a substitution ; such that A = B: This is used for simpli cation and the subsumption check. We ....

....terms need this administration. The same administration is necessary if one wants to access a subterm. In order to reach the n th subterm one has to skip the rst n 1 subterms, which needs administration. Nevertheless this method also has advantages because it uses little memory. It is argued in [Wm95] that there is intrinsic advantage in a short representation. It will turn out that the pre x representation does not perform worse than the deep term with argument lists representation, which uses 3 times more memory. The pre x with ends representation is similar to the pre x representation, but ....

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A. Buch, Th. Hillenbrand, Waldmeister: Development of a High Performance Completion-Based Theorem Prover, SEKI-Report SR-96-01, 1995.

....1 Introduction Waldmeister is an automated theorem prover for unconditional equational logic. It is based on unfailing Knuth Bendix completion [1] During the rst stage of development the focus was on ecient rewriting by means of indexing and space saving techniques [2, 4]. In this paper we present two aspects of our recent work which aim at improving the system with respect to performance and ease of use. Section 2 describes a more powerful hypothesis handling. In Sect. 3 we investigate the control of the proof search and outline our current component of ....

A. Buch and Th. Hillenbrand. Waldmeister: development of a high performance completion-based theorem prover. SEKI-Report 96-01, Universitat Kaiserslautern, 1996.

....comparison of different realizations of the same functionality within the same system. This was possible because modularity has been a major principle in structuring the system. The basis for our development is the afore mentioned logical three level model of completion based theorem provers [3]. As every calculus that is given as an inference system, unfailing completion has many inherent indeterminisms. When realizing completion procedures in provers, this leads to a large family of deterministic, but parameterized algorithms. Two main parameters are typical for completion based ....

....cps are normalized to put the selection heuristic on a firmer basis. For most of these steps, there are several ways of performing them, often resulting in a completely different behaviour of the prover. We selected a setting for the competition that has proven valuable for most proof tasks (see [3]) There are many ways of aggregating the inference steps into such a sketch of algorithm. Our choice is based on an interpretation of completion as a special search process, deriving profit from the rich experience with the Discount system. Among the implemented term orderings and selection ....

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A. Buch and Th. Hillenbrand. Waldmeister: development of a high performance completion--based theorem prover. SEKI--Report 96--01, Univ. Kaiserslautern, 1996.

....simplify the hypothesis by rewriting. New facts can be derived via superposition of existing ones. Among these possible one step derivations (critical pairs or cps) one is chosen to be added to the set of facts. If the hypothesis has not become trivial by now, the next iteration cycle starts. In [BH96] we elaborate the whole design process starting from a three level system model: at the bottom the execution of single inference steps, above their aggregation into an inference machine, and at the top the overall control strategy guiding the search for promising derivations. We also give more ....

A. Buch and Th. Hillenbrand. Waldmeister: Development of a high performance completion{based theorem prover. SEKI{Report 96-01, Univ. Kaiserslautern, 1996. Available via ftp://ftp.uni-kl.de/

....skillful design of appropriate algorithms and data structures, furthermore by careful, statistically armed aggregation of the inference components into an inference machine we have gained a considerable increase in overall system performance. Our detailed analysis of this subject can be found in [BH96]. Finally, we demonstrate the power of our new prover Waldmeister by solving hard problems. 2 Fishing for eciency Supporting selection strategies is the most important requirement any inference machine has to meet, for they determine the order in which critical pairs (cps for short) are ....

A. Buch and Th. Hillenbrand. Waldmeister: Development of a high performance completion{based theorem prover. SEKI{Report 96-01, Universitat Kaiserslautern, 1996.

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