%% 1. Title: First-order theorem proving %% %% 2. Sources: %% %% (a) James P Bridge, Sean B Holden and Lawrence C Paulson %% %% University of Cambridge %% Computer Laboratory %% William Gates Building %% 15 JJ Thomson Avenue %% Cambridge CB3 0FD %% UK %% %% +44 (0)1223 763500 %% forename.surname@cl.cam.ac.uk %% %% (b) Sean B Holden - details as (a). %% %% (c) Date: 17th April 2013 %% %% 3. Past Usage: %% %% (a) Machine learning for first-order theorem proving: learning to %% select a good heuristic James P Bridge, Sean B Holden and %% Lawrence C Paulson Submitted for publication in the Journal of %% Automated Reasoning, Springer 2012/13. %% %% Please include a citation if you use this data. %% %% (b) We wish to predict which of a set of five heuristics will %% provide the fastest proof, given features derived from a %% theorem to be proved. A sixth possible prediction is to decline %% to attempt a proof, should the theorem be assessed as too %% difficult. %% %% (c) In prediction terms this is a challenging problem. However we %% can do better than any individual heuristic and obtain %% performance comparable to that of a hand-crafted selection %% mechanism employing around 75 addition heuristics. The ability %% to decline a proof is also beneficial. %% %% 4. Relevant Information Paragraph: %% %% Files: %% %% Expanding the tarball ml-prove.tar produces a directory ml-prove/ %% containing the files: %% %% all-data-raw.csv - raw data used to derive training, %% validation and test data. %% all-data-raw-statistics.txt - min, max, mean and standard deviation %% for raw data. (Tabulated below.) %% train.csv - actual training, validation and test %% validation.csv sets used. %% test.csv %% all-data-statistics.txt - min, max and correlation data for %% combined actual data. (Tabulated below.) %% %% Raw data: %% %% Columns 1 to 14 are the static features and columns 15 to 53 are %% the dynamic features. (See the paper for a description of static %% and dynamic features.) The final five columns denote the time in %% seconds taken by each of the five heuristics to prove the relevant %% theorem. There was a time limit of 100 seconds. An entry of -100 %% denotes failure to obtain a proof within the time limit. The first %% half of this data corresponds to the training data used. The second %% half was permuted and split to obtain the validation and test sets. %% %% Training, validation and test data: %% %% These are the sets used in the reported experiments. Two redundant %% features (static feature 5 and dynamic feature 21 in the raw data) %% were removed. The features in the training set are normalised to %% zero mean and unit variance. Validation/test data was normalized %% using the coefficients computed for the training set. Labels are in %% the final six columns. The first five of those correspond to the %% five heuristics (H1 to H5) and contain +1 if the corresponding %% heuristic found a proof and was the fastest to do so, and -1 %% otherwise. The final column contains +1 where no heuristic finds a %% proof within the time limit and -1 otherwise (H0 in the paper). %% %% 5. Number of Instances: %% %% 6118 in the raw data. %% %% The training, validation and test sets have 3059, 1529 and 1530 %% respectively. %% %% 6. Number of Attributes: %% %% There are 13 static and 38 dynamic features for each instance. (See %% the paper for details regarding static/dynamic features. The raw %% data has two more features, which are redundant.) Columns 1 %% to 13 contain static features and columns 14 to 51 dynamic %% features. %% %% 7. Description of attributes: %% %% The full names for each attribute are provided in the paper, tables %% 2 and 3. %% %% Raw data: all attributes are numeric. Attributes 5, 9, 11, 13 %% and 35 are integer-valued. All other attributes are continuous. %% %% Training, validation and test data: all data are numeric and %% continuous on account of being normalized. %% %% 8. Missing Attribute Values: %% %% There are no missing values. %% %% 9. Class Distribution: number of positive instances in the sets for %% each heuristic (H1 to H5) and the "decline" option H0. %% %% H1 H2 H3 H4 H5 H0 %% Training set: 556 229 373 303 312 1286 %% Validation set: 260 133 187 146 159 644 %% Test set: 273 124 188 168 153 624 %% @relation first-order-theorem @attribute V1 numeric @attribute V2 numeric @attribute V3 numeric @attribute V4 numeric @attribute V5 numeric @attribute V6 numeric @attribute V7 numeric @attribute V8 numeric @attribute V9 numeric @attribute V10 numeric @attribute V11 numeric @attribute V12 numeric @attribute V13 numeric @attribute V14 numeric @attribute V15 numeric @attribute V16 numeric @attribute V17 numeric @attribute V18 numeric @attribute V19 numeric @attribute V20 numeric @attribute V21 numeric @attribute V22 numeric @attribute V23 numeric @attribute V24 numeric @attribute V25 numeric @attribute V26 numeric @attribute V27 numeric @attribute V28 numeric @attribute V29 numeric @attribute V30 numeric @attribute V31 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