Inductive Benchmarks for Automated Reasoning

Hajdu, Marton; Hozzová, Petra; Kovács, Laura; Schoisswohl, Johannes; Воронков, Андрей

doi:10.1007/978-3-030-81097-9_9

Cited by 3 publications

(2 citation statements)

References 14 publications

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“…In the following experiments, we test the performance of three state-of-the-art provers Vampire [17], CVC5 [18,1] and Z3 [7] on our benchmark. Vampire is run with an induction schedule [15,13] suggested by its developers; CVC5 is run with its induction flag on [20]. The addition of support for arithmetical induction is recent in these two provers.…”

Section: Methodsmentioning

confidence: 99%

A Mathematical Benchmark for Inductive Theorem Provers

Gauthier¹,

Brown²,

Janota³

et al.

EPiC Series in Computing

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We present a benchmark of 29687 problems derived from the On-Line Encyclopedia of Integer Sequences (OEIS). Each problem expresses the equivalence of two syntactically different programs generating the same OEIS sequence. Such programs were conjectured by a learning-guided synthesis system using a language with looping operators. The operators implement recursion, and thus many of the proofs require induction on natural numbers. The benchmark contains problems of varying difficulty from a wide area of mathematical domains. We believe that these characteristics will make it an effective judge for the progress of inductive theorem provers in this domain for years to come.

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Section: Methodsmentioning

confidence: 99%

A Mathematical Benchmark for Inductive Theorem Provers

Gauthier¹,

Brown²,

Janota³

et al.

EPiC Series in Computing

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show abstract

“…See Appendix C of our extended paper[22] 6. https://github.com/vprover/vampire/commit/16a38442515f8385…”

mentioning

confidence: 99%

Rewriting and Inductive Reasoning

Hajdu,

Kovács,

Rawson

EPiC Series in Computing

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Rewriting techniques based on reduction orderings generate “just enough” consequences to retain first-order completeness. This is ideal for superposition-based first-order theorem proving, but for at least one approach to inductive reasoning we show that we are miss- ing crucial consequences. We therefore extend the superposition calculus with rewriting- based techniques to generate sufficient consequences for automating induction in satura- tion. When applying our work within the unit-equational fragment, our experiments with the theorem prover Vampire show significant improvements for inductive reasoning.

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