Knowledge-based proof planning
Artificial Intelligence
On the notion of interestingness in automated mathematical discovery
International Journal of Human-Computer Studies - Special issue on Machine Discovery
Exploring properties of residue classes
Symbolic computation and automated reasoning
Comparing approaches to the exploration of the domain of residue classes
Journal of Symbolic Computation - Integrated reasoning and algebra systems
Automatic Identification of Mathematical Concepts
ICML '00 Proceedings of the Seventeenth International Conference on Machine Learning
Proof Planning with Multiple Strategies
CL '00 Proceedings of the First International Conference on Computational Logic
The Use of Explicit Plans to Guide Inductive Proofs
Proceedings of the 9th International Conference on Automated Deduction
CADE-17 Proceedings of the 17th International Conference on Automated Deduction
Classifying Isomorphic Residue Classes
Computer Aided Systems Theory - EUROCAST 2001-Revised Papers
Omega: Towards a Mathematical Assistant
CADE-14 Proceedings of the 14th International Conference on Automated Deduction
SEM: a system for enumerating models
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Mathematical applications of inductive logic programming
Machine Learning
Proof planning with multiple strategies
Artificial Intelligence
The TM System for Repairing Non-Theorems
Electronic Notes in Theoretical Computer Science (ENTCS)
System description: MULTI a multi-strategy proof planner
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
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The invention of suitable concepts to characterise mathematical structures is one of the most challenging tasks for both human mathematicians and automated theorem provers alike. We present an approach where automatic concept formation is used to guide nonisomorphism proofs in the residue class domain. The main idea behind the proof is to automatically identify discriminants for two given structures to show that they are not isomorphic. Suitable discriminants are generated by a theory formation system; the overall proof is constructed by a proof planner with the additional support of traditional automated theorem provers and a computer algebra system.