First-order logic and automated theorem proving (2nd ed.)
First-order logic and automated theorem proving (2nd ed.)
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
A machine program for theorem-proving
Communications of the ACM
A proof engine approach to solving combinational design automation problems
Proceedings of the 39th annual Design Automation Conference
Journal of Automated Reasoning
A Tutorial on Stålmarck‘s Proof Procedure for PropositionalLogic
Formal Methods in System Design - Special issue on formal methods for computer-added design
The Disconnection Method - A Confluent Integration of Unification in the Analytic Framework
TABLEAUX '96 Proceedings of the 5th International Workshop on Theorem Proving with Analytic Tableaux and Related Methods
E-SETHEO: An Automated3 Theorem Prover
TABLEAUX '00 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Integration of Equality Reasoning into the Disconnection Calculus
TABLEAUX '02 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
The Industrial Success of Verification Tools Based on Stålmarck's Method
CAV '97 Proceedings of the 9th International Conference on Computer Aided Verification
The Even More Liberalized delta-Rule in Free Variable Semantic Tableaux
KGC '93 Proceedings of the Third Kurt Gödel Colloquium on Computational Logic and Proof Theory
Handbook of automated reasoning
Handbook of automated reasoning
The IJCAR-2004 automated theorem proving competition
AI Communications
The model evolution calculus as a first-order DPLL method
Artificial Intelligence
Using stålmarck’s algorithm to prove inequalities
ICFEM'05 Proceedings of the 7th international conference on Formal Methods and Software Engineering
A first order extension of stålmarck’s method
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
The model evolution calculus with equality
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
A method for symbolic computation of abstract operations
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
A generalization of stålmarck's method
SAS'12 Proceedings of the 19th international conference on Static Analysis
Semantics and proof-theory of depth bounded Boolean logics
Theoretical Computer Science
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We present a proof method with a novel way of introducing universal lemmas. The method is a first order extension of Stålmarck's method, containing a branch-and-merge rule known as the dilemma rule. The dilemma rule creates two branches in a tableau-like way, but later recombines the two branches, keeping the common consequences. While the propositional version uses normal set intersection in the merges, the first order version searches for pairwise unifiable formulae in the two branches. Within branches, the system uses a special kind of variables that may not be substituted. At branch merges, these variables are replaced by universal variables, and in this way universal lemmas can be introduced. Relevant splitting formulae are found through failed unifications of variables in branches. This article presents the calculus and proof procedure, and shows soundness and completeness. Benchmarks of an implementation are also presented.