First leaves: a tutorial introduction to Maple V
First leaves: a tutorial introduction to Maple V
Introduction to HOL: a theorem proving environment for higher order logic
Introduction to HOL: a theorem proving environment for higher order logic
Knowledge-based proof planning
Artificial Intelligence
MBase: representing knowledge and context for the intergration of mathematical software systems
Journal of Symbolic Computation - Calculemus-99: integrating computation and deduction
Comparing approaches to the exploration of the domain of residue classes
Journal of Symbolic Computation - Integrated reasoning and algebra systems
Proceedings of the Third International Workshop on Frontiers of Combining Systems
FroCoS '00 Proceedings of the Third International Workshop on Frontiers of Combining Systems
Proceedings of the 12th International Conference on Automated Deduction
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
Proceedings of the 15th International Conference on Automated Deduction: Automated Deduction
CADE-15 Proceedings of the 15th International Conference on Automated Deduction: Automated Deduction
Proceedings of the 17th International Conference on Automated Deduction
CADE-17 Proceedings of the 17th International Conference on Automated Deduction
Proceedings of the 18th International Conference on Automated Deduction
CADE-18 Proceedings of the 18th 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
Integrating Constraint Solving into Proof Planning
FroCoS '00 Proceedings of the Third International Workshop on Frontiers of Combining Systems
Planning Diagonalization Proofs
KI '97 Proceedings of the 21st Annual German Conference on Artificial Intelligence: Advances in Artificial Intelligence
PVS: Combining Specification, Proof Checking, and Model Checking
CAV '96 Proceedings of the 8th International Conference on Computer Aided Verification
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
System Description: The MathWeb Software Bus for Distributed Mathematical Reasoning
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
The Use of Explicit Plans to Guide Inductive Proofs
Proceedings of the 9th International Conference on Automated Deduction
Reconstruction Proofs at the Assertion Level
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
Selectively Instantiating Definitions
CADE-15 Proceedings of the 15th International Conference on Automated Deduction: Automated Deduction
System Description: Proof Planning in Higher-Order Logic with Lambda-Clam
CADE-15 Proceedings of the 15th International Conference on Automated Deduction: Automated Deduction
The Nuprl Open Logical Environment
CADE-17 Proceedings of the 17th International Conference on Automated Deduction
System Description: MBASE, an Open Mathematical Knowledge Base
CADE-17 Proceedings of the 17th International Conference on Automated Deduction
P.rex: An Interactive Proof Explainer
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
Non-Trivial Symbolic Computations in Proof Planning
FroCoS '00 Proceedings of the Third International Workshop on Frontiers of Combining Systems
System Description: LEO - A Higher-Order Theorem Prover
CADE-15 Proceedings of the 15th International Conference on Automated Deduction: 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
Authoring Verified Documents by Interactive Proof Construction and Verification in Text-Editors
Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
Formal Proof: Reconciling Correctness and Understanding
Calculemus '09/MKM '09 Proceedings of the 16th Symposium, 8th International Conference. Held as Part of CICM '09 on Intelligent Computer Mathematics
A generic modular data structure for proof attempts alternating on ideas and granularity
MKM'05 Proceedings of the 4th international conference on Mathematical Knowledge Management
A User-friendly Interface for a Lightweight Verification System
Electronic Notes in Theoretical Computer Science (ENTCS)
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Freek Wiedijk proposed the well-known theorem about the irrationality of √2 as a case study and used this theorem for a comparison of fifteen (interactive) theorem proving systems, which were asked to present their solution (see [48]). This represents an important shift of emphasis in the field of automated deduction away from the somehow artificial problems of the past as represented, for example, in the test set of the TPTP library [45] back to real mathematical challenges. In this paper we present an overview of the ΩMEGA system as far as it is relevant for the purpose of this paper and show the development of a proof for this theorem.