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deep learning for math
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trivdata added the named data Feb 23, 2017

This is a dataset of 32524 examples for premise selection based on the Mizar40 experiments [1]. The proof data (without the negative part added here) served also for the DeepMath experiments described in [2].

For each conjecture the dataset contains a file with a roughly equal number of unnecessary facts and necessary facts. This is done to simplify experiments with learning methods such as neural networks.

In nnhpdata/* the examples are in this format:

C prefixformula
+ prefixformula
+ prefixformula
- prefixformula
- prefixformula

In nndata/* the examples are in this format:

C tptpformula
+ tptpformula
+ tptpformula
- tptpformula
- tptpformula

Here tptpformula is the standard FOL TPTP representation, and prefixformula is a prefix curried format using de Bruijn indeces.

C is the conjecture, + are the formulas needed for an ATP proof of C, and - are unnecessary formulas that are reasonably highly ranked by a k-nearest neighbor algorithm trained on the proofs .

To divide into training and testing, just randomly select a part (e.g. 90%) of the files to train on and test on the remaining files.

The accuracy of a simple count-based predictor evaluated incrementally on the whole dataset is 71.75%.

The mizar40 and code directories contain the data (proofs, statemnts, etc.) and the code used to generate the nndata and nnhpdata examples.



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