
Analyzing Individual Proofs as the Basis of Interoperability between Proof Systems
We describe the first results of a project of analyzing in which theorie...
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Learning to Prove Theorems via Interacting with Proof Assistants
Humans prove theorems by relying on substantial highlevel reasoning and...
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Finding Proofs in Tarskian Geometry
We report on a project to use a theorem prover to find proofs of the the...
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Automatically Proving Mathematical Theorems with Evolutionary Algorithms and Proof Assistants
Mathematical theorems are human knowledge able to be accumulated in the ...
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A New Conjecture About Identity of Proofs
A central problem in prooftheory is that of finding criteria for identi...
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A Spectrum of Applications of Automated Reasoning
The likelihood of an automated reasoning program being of substantial as...
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Towards Automated Proof Strategy Generalisation
The ability to automatically generalise (interactive) proofs and use suc...
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Learning from Łukasiewicz and Meredith: Investigations into Proof Structures (Extended Version)
The material presented in this paper contributes to establishing a basis deemed essential for substantial progress in Automated Deduction. It identifies and studies global features in selected problems and their proofs which offer the potential of guiding proof search in a more direct way. The studied problems are of the widespread form of "axiom(s) and rule(s) imply goal(s)". The features include the wellknown concept of lemmas. For their elaboration both human and automated proofs of selected theorems are taken into a close comparative consideration. The study at the same time accounts for a coherent and comprehensive formal reconstruction of historical work by Łukasiewicz, Meredith and others. First experiments resulting from the study indicate novel ways of lemma generation to supplement automated firstorder provers of various families, strengthening in particular their ability to find short proofs.
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