GRUNGE: A Grand Unified ATP Challenge

Brown, Chad E.; Gauthier, Thibault; Kaliszyk, Cezary; Sutcliffe, Geoff; Urban, Josef

doi:10.1007/978-3-030-29436-6_8

Cited by 9 publications

(4 citation statements)

References 40 publications

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“…Remark 3 It is shown from ( 1), ( 2), ( 3), ( 4), (5) in Definition 17 that the equality predicate E in L n F(X) should satisfy properties of α-reflexity, α-symmetry, α-transitivity and α-monotonicity for function and predicate symbols, respectively.…”

Section: Remarkmentioning

confidence: 99%

“…To solve this problem, many restricted resolution methods [7] are proposed, for instance, lock resolution, hyper-resolution, semantic resolution, extension rule [19], etc. Different from restrictions on literals and clauses, contradiction separation based automated deduction [28] is an extension of binary resolution, where dynamic and multiple (two or more) clauses and literals involving in every deductive step, and its implementation CSE-E [6] also has a good performance among others [5,26].…”

Section: Introductionmentioning

confidence: 99%

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$$\alpha $$-Paramodulation method for a lattice-valued logic $$L_nF(X)$$ with equality

et al. 2020

Soft Comput

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In this paper, α-paramodulation and α-GH paramodulation methods are proposed for handling logical formulas with equality in a lattice-valued logic L n F(X), which has unique ability for representing and reasoning uncertain information from a logical point of view. As an extension of the work of [10,11], a new form of αequality axioms set is proposed. The equivalence between α-equality axioms set and E α -interpretation in L n F(X) with an appropriate level is also established, which may provide a key foundation for equality reasoning in lattice-valued logic. Based on its equivalence, E α -unsatisfiability equivalent transformation is given. Furthermore, αparamodulation and its restricted method, i.e., α-GH paramodulation are given. The soundness and completeness of the proposed methods are also obtained.

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Section: Remarkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

$$\alpha $$-Paramodulation method for a lattice-valued logic $$L_nF(X)$$ with equality

et al. 2020

Soft Comput

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“…These datasets are using different mathematical formalisms which makes it difficult to compare systems based on different logics. A recent work GRUNGE [13] addresses this problem by translating HOL4 libraries to multiple TPTP formats and logics -(un)typed/polymorphic first/higher order -providing a large unified theorem proving and machine learning challenge.…”

Section: Related Workmentioning

confidence: 99%

Towards Finding Longer Proofs

Zombori¹,

Csiszárik²,

Michalewski³

et al. 2019

Preprint

Self Cite

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We present a reinforcement learning (RL) based guidance system for automated theorem proving geared towards Finding Longer Proofs (FLoP). FLoP focuses on generalizing from short proofs to longer ones of similar structure. To achieve that, FLoP uses state-of-the-art RL approaches that were previously not applied in theorem proving. In particular, we show that curriculum learning significantly outperforms previous learning-based proof guidance on a synthetic dataset of increasingly difficult arithmetic problems.Preprint. Under review.

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“…Last but not least, we aim to explore the achieved results in the context of program equivalence [12]. placed a bounty of 1 Proofgold 6 [3] bar on each of the corresponding formal propositions. As a consequence anyone can claim 1 Proofgold bar by giving an appropriate proof term for the corresponding problem.…”

Section: Discussionmentioning

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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GRUNGE: A Grand Unified ATP Challenge

Cited by 9 publications

References 40 publications

$$\alpha $$-Paramodulation method for a lattice-valued logic $$L_nF(X)$$ with equality

$$\alpha $$-Paramodulation method for a lattice-valued logic $$L_nF(X)$$ with equality

Towards Finding Longer Proofs

A Mathematical Benchmark for Inductive Theorem Provers

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