Abstract
Modern first-order resolution and superposition theorem provers use saturation algorithms to search for a refutation in clauses derivable from the input clauses. On hard problems, this search space often grows rapidly and performance degrades especially fast when long and heavy clauses are generated. One approach that has proved successful in taming the search space is splitting where clauses are split into components with disjoint variables and the components are asserted in turn. This reduces the length and weight of clauses in the search space at the cost of keeping track of splitting decisions.
This paper considers the new AVATAR (Advanced Vampire Architecture for Theories And Resolution) approach to splitting which places a SAT (or SMT) solver at the centre of the theorem prover and uses it to direct the exploration of the search space. Using such an approach also allows the propositional part of the search space to be dealt with outside of the first-order prover.
AVATAR has proved very successful, especially for problems coming from applications such as program verification and program analysis as these commonly contain clauses suitable for splitting. However, AVATAR is still a new idea and there is much left to understand. This paper presents an in-depth exploration of this new architecture, introducing new, highly experimental, options that allow us to vary the operation and interaction of the various components. It then extensively evaluates these new options, using the TPTP library, to gain an insight into which of these options are essential and how AVATAR can be optimally applied.
A. Voronkov—Partially supported by the EPSRC grant "Reasoning for Verification and Security".
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Notes
- 1.
This useful optimization is not derictly available for non-ground components. Negating a non-ground component would require skolemization and is not considered in this paper.
- 2.
A list of the selected problems, the executable of our prover as well as the results of the experiment are available from http://vprover.org.
- 3.
Note that previous experiments [3] used longer time limits.
- 4.
- 5.
Only runs which took at least one second to complete are considered here.
- 6.
A different statistic, not shown in the table, is the performance of strategies at the 10Â % mark from each end of the sorted order (quantiles), which were 865 and 1072, respectively.
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Reger, G., Suda, M., Voronkov, A. (2015). Playing with AVATAR. In: Felty, A., Middeldorp, A. (eds) Automated Deduction - CADE-25. CADE 2015. Lecture Notes in Computer Science(), vol 9195. Springer, Cham. https://doi.org/10.1007/978-3-319-21401-6_28
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