Communications of the ACM
A Structure-preserving Clause Form Translation
Journal of Symbolic Computation
A strong problem reduction method based on function introduction
ISSAC '90 Proceedings of the international symposium on Symbolic and algebraic computation
Reduction rules for resolution-based systems
Artificial Intelligence
Relative complexities of first order calculi
Relative complexities of first order calculi
Removing redundancy from a clause
Artificial Intelligence
On the efficiency of subsumption algorithms
Journal of the ACM (JACM)
A Mechanical Proof Procedure and its Realization in an Electronic Computer
Journal of the ACM (JACM)
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
Resolution Strategies as Decision Procedures
Journal of the ACM (JACM)
Theorem Proving via General Matings
Journal of the ACM (JACM)
Shortening Proofs by Quantifier Introduction
LPAR '92 Proceedings of the International Conference on Logic Programming and Automated Reasoning
On Different Concepts of Function Introduction
KGC '93 Proceedings of the Third Kurt Gödel Colloquium on Computational Logic and Proof Theory
Abstraction Using Generalization Functions
Proceedings of the 8th International Conference on Automated Deduction
The Crisis in Finite Mathematics: Automated Reasoning as Cause and Cure
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
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Resolution proofs are unstructured by their very nature, since theycannot use substantial lemmata. To impose structure on given resolutionproofs and thereby improve their readability we will introduce new lemmatain a postprocessing step. As these lemmata cannot be generated byresolution, we will employ function introduction rules as presented by Baazand Leitsch and give a correct and complete criterion for theirapplicability to the proofs. Applying function introduction rules toresolution proofs enables us to detect and eliminate certain homomorphicsubproofs immune to the known redundancy elimination rules. For the caseswhen the criterion is satisfied we will characterize the transformation oftree resolution proofs to their condensation-reduced functional extensions,which may result in a double exponential reduction of proof height.Moreover, the proofs obtained by this transformation are more structured andhence more intelligible.