A PROLOG technology theorem prover: implementation by an extended PROLOG compiler
Proc. of the 8th international conference on Automated deduction
Journal of Automated Reasoning
A Prolog technology theorem prover: implementation by an extended Prolog computer
Journal of Automated Reasoning
PARTHEO: a high-performance parallel theorem prover
CADE-10 Proceedings of the tenth international conference on Automated deduction
Warren's abstract machine: a tutorial reconstruction
Warren's abstract machine: a tutorial reconstruction
Parthenon: a parallel theorem prover for non-Horn clauses
Journal of Automated Reasoning
SETHEO: a high-performance theorem prover
Journal of Automated Reasoning
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
Efficiency and Completeness of the Set of Support Strategy in Theorem Proving
Journal of the ACM (JACM)
Mechanical Theorem-Proving by Model Elimination
Journal of the ACM (JACM)
A Simplified Format for the Model Elimination Theorem-Proving Procedure
Journal of the ACM (JACM)
An Implementation of the Model Elimination Proof Procedure
Journal of the ACM (JACM)
Symbolic Logic and Mechanical Theorem Proving
Symbolic Logic and Mechanical Theorem Proving
Variable Elimination and Chaining in a Resolution-based Prover for Inequalities
Proceedings of the 5th Conference on Automated Deduction
Proceedings of the 10th International Conference on Automated Deduction
The Central Variable Strategy of Str+ve
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
Caching and Lemmaizing in Model Elimination Theorem Provers
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
LIM+ Challenge Problems by RUE Hyper-Resolution
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
Semantically Guided First-Order Theorem Proving using Hyper-Linking
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
The Search Efficiency of Theorem Proving Strategies
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
Investigations in Model Elimination Based Theorem Proving
Investigations in Model Elimination Based Theorem Proving
Automated theorem proving: A logical basis (Fundamental studies in computer science)
Automated theorem proving: A logical basis (Fundamental studies in computer science)
A propositional theorem prover to solve planning and other problems
Annals of Mathematics and Artificial Intelligence
Lemma and cut strategies for propositional model elimination
Annals of Mathematics and Artificial Intelligence
Autarky Pruning in Propositional Model Elimination Reduces Failure Redundancy
Journal of Automated Reasoning
Lemma Generalization and Non-unit Lemma Matching for Model Elimination
ASIAN '99 Proceedings of the 5th Asian Computing Science Conference on Advances in Computing Science
Strategy Parallel Use of Model Elimination with Lemmata (System Abstract)
TABLEAUX '99 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Conditional Pure Literal Graphs
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
Persistent and Quasi-Persistent Lemmas in Propositional Model Elimination
Annals of Mathematics and Artificial Intelligence
Cooperation between top-down and bottom-up theorem provers
Journal of Artificial Intelligence Research
Lemma generation for model elimination by combining top-down and bottom-up inference
IJCAI'99 Proceedings of the 16th international joint conference on Artifical intelligence - Volume 1
Towards a unified model of search in theorem-proving: subgoal-reduction strategies
Journal of Symbolic Computation
A taxonomy of theorem-proving strategies
Artificial intelligence today
On the Use of Subgoal Clauses in Bottom-up and Top-down Calculi
Fundamenta Informaticae
Hi-index | 0.00 |
When the model elimination (ME) procedure was first proposed, the notion of lemma was put forth as a promising augmentation to the basic complete proof procedure. Here the lemmas that are used are also discovered by the procedure in the same proof run. Several implementations of ME now exist, but only a 1970s implementation explicitly examined this lemma mechanism, with indifferent results. We report on the successful use of lemmas using the METEOR implementation of ME. Not only does the lemma device permit METEOR to obtain proofs not otherwise obtainable by METEOR, or any other ME prover not using lemmas, but some well-known challenge problems are solved. We discuss several of these more difficult problems, including two challenge problems for uniform general-purpose provers, where METEOR was first in obtaining the proof. The problems are not selected simply to show off the lemma device, but rather to understand it better. Thus, we choose problems with widely different characteristics, including one where very few lemmas are created automatically, the opposite of normal behavior. This selection points out the potential of, and the problems with, lemma use. The biggest problem normally is the selection of appropriate lemmas to retain from the large number generated.