# I-Terms in Ordered Resolution and Superposition Calculi: Retrieving Lost Completeness

• Hicham Bensaid
• Ricardo Caferra
• Nicolas Peltier
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6167)

## Abstract

Ordered resolution and superposition are the state-of-the-art proof procedures used in saturation-based theorem proving, for non equational and equational clause sets respectively. In this paper, we present extensions of these calculi that permit one to reason about formulae built from terms with integer exponents (or I-terms), a schematisation language allowing one to denote infinite sequences of iterated terms [8]. We prove that the ordered resolution calculus is still refutationally complete when applied on (non equational) clauses containing I-terms. In the equational case, we prove that the superposition calculus is not complete in the presence of I-terms and we devise a new inference rule, called H-superposition, that restores completeness.

### Keywords

Automated reasoning term schematisation terms with integer exponents resolution and superposition calculi refutational completeness

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## Authors and Affiliations

• Hicham Bensaid
• 1
• 2
• Ricardo Caferra
• 2
• Nicolas Peltier
• 2
1. 1.INPT/LIGRabatMorocco
2. 2.LIG, Grenoble INP/CNRSSaint Martin d’HèresFrance