Induction and Skolemization in saturation theorem proving

Quantifier-free induction for lists

“…This conjecture is particularly interesting for the methods presented in [15,16,25]. As shown in [19,31] these methods carry out induction on literals and clauses. However, the results in [19,31] are formulated for induction over natural numbers and need to be adapted to the case for induction over lists and other recursive datatypes.…”

“…As shown in [19,31] these methods carry out induction on literals and clauses. However, the results in [19,31] are formulated for induction over natural numbers and need to be adapted to the case for induction over lists and other recursive datatypes. A positive answer to the conjecture above together with analogues of the results [19,31] would provide a formal justification for the necessity to implement more powerful induction rules that handle conjunction and quantification such as described in [16].…”

“…However, the results in [19,31] are formulated for induction over natural numbers and need to be adapted to the case for induction over lists and other recursive datatypes. A positive answer to the conjecture above together with analogues of the results [19,31] would provide a formal justification for the necessity to implement more powerful induction rules that handle conjunction and quantification such as described in [16]. As a byproduct, the formulas I X m A(X ) with m ≥ 1 form a set of benchmark problems of increasing difficulty for automated theorem provers.…”

“…So far the work in this research program [17][18][19][20]31] has concentrated on induction for natural numbers only. However, since lists and other inductive data types are fundamental structures of computer science, it is of paramount importance for the subject of AITP to analyze the mechanical properties of these inductive datatypes.…”