The Maple handbook: Maple V Release 4
The Maple handbook: Maple V Release 4
Boosting combinatorial search through randomization
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
Knowledge-based proof planning
Artificial Intelligence
Integrating Computer Algebra into Proof Planning
Journal of Automated Reasoning
The Use of Explicit Plans to Guide Inductive Proofs
Proceedings of the 9th International Conference on Automated Deduction
Exploring Abstract Algebra in Constructive Type Theory
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
Non-Trivial Symbolic Computations in Proof Planning
FroCoS '00 Proceedings of the Third International Workshop on Frontiers of Combining Systems
Omega: Towards a Mathematical Assistant
CADE-14 Proceedings of the 14th International Conference on Automated Deduction
Proof Development with Omega-MEGA: sqrt(2) Is Irrational
LPAR '02 Proceedings of the 9th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Employing Theory Formation to Guide Proof Planning
AISC '02/Calculemus '02 Proceedings of the Joint International Conferences on Artificial Intelligence, Automated Reasoning, and Symbolic Computation
Constraint Solving for Proof Planning
Journal of Automated Reasoning
Failure Reasoning in Multiple-Strategy Proof Planning
Electronic Notes in Theoretical Computer Science (ENTCS)
On the Comparison of Proof Planning Systems: , Ωmega and IsaPlanner
Electronic Notes in Theoretical Computer Science (ENTCS)
Impasse-driven reasoning in proof planning
MKM'05 Proceedings of the 4th international conference on Mathematical Knowledge Management
System description: MULTI a multi-strategy proof planner
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
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We report on a case study on combining proof planning with computer algebra systems. We construct proofs for basic algebraic properties of residue classes as well as for isomorphisms between residue classes using different proof techniques, which are implemented as strategies in a multi-strategy proof planner. The search space of the proof planner can be drastically reduced by employing computations of two computer algebra systems during the planning process. To test the effectiveness of our approach we carried out a large number of experiments and also compared it with some alternative approaches. In particular, we experimented with substituting computer algebra by model generation and by proving theorems with a first-order equational theorem prover instead of a proof planner.