Artificial Intelligence
The linked inference principle, I.: the formal treatment
Journal of Automated Reasoning
Gazing: an approach to the problem of definition and lemma use
Journal of Automated Reasoning
Abstraction Mappings in Mechanical Theorem Proving
Proceedings of the 5th Conference on Automated Deduction
The Linked Inference Principle, II: The User's Viewpoint
Proceedings of the 7th International Conference on Automated Deduction
Analogical Reasoning and Proof Discovery
Proceedings of the 9th International Conference on Automated Deduction
A Legacy Recalled and a Tradition Continued
Journal of Automated Reasoning
Journal of Automated Reasoning
Hilbert's Twenty-Fourth Problem
Journal of Automated Reasoning
A Shortest 2-Basis for Boolean Algebra in Terms of the Sheffer Stroke
Journal of Automated Reasoning
Automated theorem proving in quasigroup and loop theory
AI Communications - Practical Aspects of Automated Reasoning
Automated proof compression by invention of new definitions
LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
Semantic guidance for saturation provers
AISC'06 Proceedings of the 8th international conference on Artificial Intelligence and Symbolic Computation
A geometric procedure with prover9
Automated Reasoning and Mathematics
Loops with abelian inner mapping groups: an application of automated deduction
Automated Reasoning and Mathematics
Gibbard's collapse theorem for the indicative conditional: an axiomatic approach
Automated Reasoning and Mathematics
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In this article, we describe a set of procedures and strategies for searching for proofs in logical systems based on the inference rule condensed detachment. The procedures and strategies rely on the derivation of proof sketches – sequences of formulas that are used as hints to guide the search for sound proofs. In the simplest case, a proof sketch consists of a subproof – key lemmas to prove, for example – and the proof is completed by filling in the missing steps. In the more general case, a proof sketch consists of a sequence of formulas isufficient to find a proof, but it may include formulas that are not provable in the current theory. We find that even in this more general case, proof sketches can provide valuable guidance in finding sound proofs. Proof sketches have been used successfully for numerous problems coming from a variety of problem areas. We have, for example, used proof sketches to find several new two-axiom systems for Boolean algebra using the Sheffer stroke.