Depth-first iterative-deepening: an optimal admissible tree search
Artificial Intelligence
A Prolog technology theorem prover: implementation by an extended Prolog computer
Journal of Automated Reasoning
Quantitative results concerning the utility of explanation-based learning
Artificial Intelligence
The Use of Lemmas in the Model Elimination Procedure
Journal of Automated Reasoning
Coupling Saturation-Based Provers by Exchanging Positive/Negative Information
RTA '98 Proceedings of the 9th International Conference on Rewriting Techniques and Applications
Goal Oriented Equational Theorem Proving Using Team Work
KI '94 Proceedings of the 18th Annual German Conference on Artificial Intelligence: Advances in Artificial Intelligence
Cooperation Between Top-Down and Bottom-Up Theorem Provers by Subgoal Clause Transfer
AISC '98 Proceedings of the International Conference on Artificial Intelligence and Symbolic Computation
DELTA - A Bottom-up Preprocessor for Top-Down Theorem Provers - System Abstract
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
Non-Horn Magic Sets to Incorporate Top-down Inference into Bottom-up Theorem Proving
CADE-14 Proceedings of the 14th International Conference on Automated Deduction
Optimizing Proof Search in Model Elimination
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
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
Cooperation of heterogeneous provers
IJCAI'99 Proceedings of the 16th international joint conference on Artifical intelligence - Volume 1
The Clause-Diffusion Methodology For Distributed Deduction
Fundamenta Informaticae
| Hi-index | 0.00 |
The use of lemmas is a major control tool for automated theorem proving. Many approaches for top-down or bottom-up theorem proving employ lemmas for improving the proof search. Commonly the lemmas used can be derived in a bottom-up manner using merely the given axioms. That is, top-down lemmas which represent decompositions of original proof goals did not receive much attention. We propose to systematically generate and use such goal decompositions. We introduce a notion of top-down lemmas, so-called subgoal clauses, and examine their potential to reduce proof lengths and searches in top-down and bottom-up theorem proving. Furthermore, we develop some heuristics so as to make the use of subgoal clauses efficient in practice. A case study conducted in TPTP domains with the state-of-the-art provers SPASS and SETHEO demonstrates the strength of our approach.