Selecting the Selection
Modern saturation-based Automated Theorem Provers typically implement the superposition calculus for reasoning about first-order logic with or without equality. Practical implementations of this calculus use a variety of literal selections and term orderings to tame the growth of the search space and help steer proof search. This paper introduces the notion of lookahead selection that estimates (looks ahead) the effect of selecting a particular literal on the number of immediate children of the given clause and selects to minimize this value. There is also a case made for the use of incomplete selection strategies that attempt to restrict the search space instead of satisfying some completeness criteria. Experimental evaluation in the Vampire theorem prover shows that both lookahead selection and incomplete selection significantly contribute to solving hard problems unsolvable by other methods.