ARTIFICIAL INTELLIGENCE A Mechanical Solution of Schubert's Steamroller by Many-Sorted Resolution
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Bibliographic record
Abstract
We demonstrate the advantage of using a many-sorted resolution calculus by a mechanical solulion of automated a challenge theorem problem. provers This before. problem Our known solution as clearly 'Schubert's demonstrates Steamroller ' the power had of been a many-so unsolvedt ed bY resolution calculus. The proposed method is applicable to all resolution-based inference systems. In 1978, problem I. Schubert's Problem Schubert of the University of Alberta set up the following challenge Wolves, foxes, birds, caterpillars, and snails are animals, and there are some of each of them. Also there are some grains, and grains are plants. Every animal either likes to eat all plants or all animals much smaller than itself that like to eat some plants. Gaterpillars and snails are much smaller than birds, which are much: ' smaller than foxes, which in turn are much smaller than wolves. Wolves do not like to eat foxes or grains, while birds like to eat caterpillars but not snails. Caterpillars and snails like to eat some plants. Therefore there is an animal that likes to eat a grain-eating animal. This problem became well known since in spite of its apparent simplicity it turned out to be too hard for existing theorem provers because the search space is just too big. Using the following predicates as abbreviations: A(x): x is an animal, W(x): x is a wolf, F(x): x is a fox, B(x): x is a bird, C(x): x is a caterpillar, S(x): x is a snail, G(x): x is a grain, P(x): x is a plant, M(xy): x is much smaller than y, E(xy): x likes to eat y,
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it