Abstract
We investigate the integration of SAT technology into clausal connection-tableau systems for classical first-order logic. Clauses present in tableaux during backtracking search are heuristically grounded and added to an incremental SAT solver. If the solver reports an unsatisfiable set of ground clauses at any point, search may be halted and a proof reported. This technique alone is surprisingly effective, but also supports further refinements “for free”. In particular we further investigate depth control of randomised search based on grounded clauses, and a kind of ground lemmata rule derived from the partial SAT model.
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Notes
- 1.
- 2.
Unless there are no such clauses or all clauses stem from the conjecture, in which case positive clauses are used instead.
- 3.
pseudo-random shuffle such that results are reproducible.
- 4.
https://github.com/MichaelRawson/satcop commit 65122a99e08648f5b2e331280d0a0011e73a0836 is discussed here.
- 5.
It is interesting to note that the saturation-based Vampire theorem prover also fails to solve this problem in reasonable time without support from a SAT solver.
- 6.
run with SWI Prolog 7.6.4 [50].
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Rawson, M., Reger, G. (2021). Eliminating Models During Model Elimination. In: Das, A., Negri, S. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2021. Lecture Notes in Computer Science(), vol 12842. Springer, Cham. https://doi.org/10.1007/978-3-030-86059-2_15
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