Proceedings of the 31st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
An interpolating theorem prover
Theoretical Computer Science - Tools and algorithms for the construction and analysis of systems (TACAS 2004)
Interpolation for data structures
Proceedings of the 14th ACM SIGSOFT international symposium on Foundations of software engineering
The design and implementation of VAMPIRE
AI Communications - CASC
Interpolation and Symbol Elimination
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Splitting without backtracking
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
The TPTP Problem Library and Associated Infrastructure
Journal of Automated Reasoning
Array abstractions from proofs
CAV'07 Proceedings of the 19th international conference on Computer aided verification
TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
Quantified invariant generation using an interpolating saturation prover
TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
Interpolating quantifier-free Presburger arithmetic
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
Beyond quantifier-free interpolation in extensions of Presburger arithmetic
VMCAI'11 Proceedings of the 12th international conference on Verification, model checking, and abstract interpretation
Efficient interpolant generation in satisfiability modulo linear integer arithmetic
TACAS'11/ETAPS'11 Proceedings of the 17th international conference on Tools and algorithms for the construction and analysis of systems: part of the joint European conferences on theory and practice of software
KRATOS: a software model checker for SystemC
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
VMCAI'10 Proceedings of the 11th international conference on Verification, Model Checking, and Abstract Interpretation
A fast linear-arithmetic solver for DPLL(T)
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
Interpolation and symbol elimination in vampire
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
An interpolating sequent calculus for quantifier-free presburger arithmetic
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
A practical and complete approach to predicate refinement
TACAS'06 Proceedings of the 12th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Complete instantiation-based interpolation
POPL '13 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
First-Order theorem proving and vampire
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
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Interpolation is an important technique in verification and static analysis of programs. In particular, interpolants extracted from proofs of various properties are used in invariant generation and bounded model checking. A number of recent papers studies interpolation in various theories and also extraction of smaller interpolants from proofs. In particular, there are several algorithms for extracting of interpolants from so-called local proofs. The main contribution of this paper is a technique of minimising interpolants based on transformations of what we call the "grey area" of local proofs. Another contribution is a technique of transforming, under certain common conditions, arbitrary proofs into local ones. Unlike many other interpolation techniques, our technique is very general and applies to arbitrary theories. Our approach is implemented in the theorem prover Vampire and evaluated on a large number of benchmarks coming from first-order theorem proving and bounded model checking using logic with equality, uninterpreted functions and linear integer arithmetic. Our experiments demonstrate the power of the new techniques: for example, it is not unusual that our proof transformation gives more than a tenfold reduction in the size of interpolants.