A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
Knowledge-based proof planning
Artificial Intelligence
Automatic derivation of the irrationality of e
Journal of Symbolic Computation - Calculemus-99: integrating computation and deduction
Handbook of Automated Reasoning: Volume 1
Handbook of Automated Reasoning: Volume 1
Proof Planning with Multiple Strategies
CL '00 Proceedings of the First International Conference on Computational Logic
Automatic Generation of Epsilon-Delta Proofs of Continuity
AISC '98 Proceedings of the International Conference on Artificial Intelligence and Symbolic Computation
The Use of Explicit Plans to Guide Inductive Proofs
Proceedings of the 9th International Conference on Automated Deduction
Constraint Solving for Proof Planning
Journal of Automated Reasoning
Proof planning with multiple strategies
Artificial Intelligence
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Sometimes it is pragmatically useful to prove a theorem by contradiction rather than finding a direct proof. Some reductio ad absurdum arguments have made mathematical history and the general issue if and how a proof by contradiction can be replaced by a direct proof touches upon deep foundational issues such as the legitimacy of tertium non datur arguments in classical vs. intuitionistic foundations. In this paper we are interested in the pragmatic issue when and how to use this proof strategy in everyday mathematics in general and in particular in automated proof planning. Proof planning is a general technique in automated theorem proving that captures and makes explicit proof patterns and mathematical search control. So, how can we proof plan an argument by reductio ad absurdum and when is it useful to do so? What are the methods and decision involved?