Efficiency and Completeness of the Set of Support Strategy in Theorem Proving
Journal of the ACM (JACM)
Labelled deduction
SATIRE: a new incremental satisfiability engine
Proceedings of the 38th annual Design Automation Conference
A simplifier based on efficient decision algorithms
POPL '78 Proceedings of the 5th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Parametric shape analysis via 3-valued logic
ACM Transactions on Programming Languages and Systems (TOPLAS)
TVLA: A System for Implementing Static Analyses
SAS '00 Proceedings of the 7th International Symposium on Static Analysis
Construction of Abstract State Graphs with PVS
CAV '97 Proceedings of the 9th International Conference on Computer Aided Verification
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
Boolean and Cartesian Abstraction for Model Checking C Programs
TACAS 2001 Proceedings of the 7th International Conference on Tools and Algorithms for the Construction and Analysis of Systems
Combining superposition, sorts and splitting
Handbook of automated reasoning
The design and implementation of VAMPIRE
AI Communications - CASC
AI Communications - CASC
Splitting without backtracking
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Towards a unified model of search in theorem-proving: subgoal-reduction strategies
Journal of Symbolic Computation
Decision procedures for SAT, SAT modulo theories and beyond. the barcelogictools
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Predicate abstraction via symbolic decision procedures
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
Abstraction refinement via inductive learning
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
Superposition-based analysis of first-order probabilistic timed automata
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
Labelled superposition for PLTL
LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
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We add labels to first-order clauses to simultaneously apply superpositions to several proof obligations inside one clause set. From a theoretical perspective, the approach unifies a variety of deduction modes. These include different strategies such as set of support, as well as explicit case analysis, e.g., splitting. From a practical perspective, labelled clauses offer advantages in the case of related proof obligations resulting from multiple conjectures over the same axiom set or from a single conjecture that is a large conjunction. Here we can share clauses (e.g., the axioms and clauses deduced from them, share Skolem symbols), share deduced clause variants, and transfer lemmas between the different obligations. Motivated by software verification, we have created a prototype implementation of labelled clauses that supports multiple conjectures, and we provide convincing experiments for the benefits.