1984 - A Mechanical Solution of Schubert's Steamroller by Many-Sorted Resolution

We demonstrate the advantage of using a many-sorted resolution calculus by a mechanical solution of a challenge problem. This problem known as "Schubert's Steamroller" had been unsolved by automated theorem provers until now. Our solution clearly demonstrates the power of a many-sorted resolution calculus. The proposed method is applicable to all resolution-based inference systems. 1, SCHUBERT'S PROBLEM In 1978, L. Schubert of the University of Alberta set up the following challenge problem: Wolves, foxes, birds, caterpillars, and snails are animals, and there are someof each of them. Also there are some grains, and grains are plants. Every animaleither likes to eat all plants or all animals much smaller than itself that like to eat some plants. Caterpillars 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 an abbreviation: A(x) -xisananimal 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) xis a snail GM xisagrain p (xl xis aplant M(xy)-x is much smaller than y E(xy)-x likes to eaty we obtain the following set of clauses as a predicate logic formulation of the problem: