# Hierarchic Superposition Revisited

@inproceedings{Baumgartner2014HierarchicSR, title={Hierarchic Superposition Revisited}, author={Peter Baumgartner and Uwe Waldmann}, booktitle={PAAR@IJCAR}, year={2014} }

Many applications of automated deduction require reasoning in first-order logic modulo background theories, in particular some form of integer arithmetic. A major unsolved research challenge is to design theorem provers that are “reasonably complete” even in the presence of free function symbols ranging into a background theory sort. The hierarchic superposition calculus of Bachmair, Ganzinger, and Waldmann already supports such symbols, but, as we demonstrate, not optimally. This paper aims to…

## 8 Citations

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This work presents a framework for formal refutational completeness proofs of abstract provers that implement saturation calculi, such as ordered resolution or superposition, and relies on modular extensions of lifted redundancy criteria that extend redundancy criteria so that they cover subsumption.

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It is proved that BS( SLR) clause sets with both universally and existentially quantified verification conditions (conjectures) can be translated into BS(SLR) clauses sets over a finite set of first-order constants.

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- Computer ScienceIJCAR
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We present an Isabelle/HOL formalization of the first half of Bachmair and Ganzinger’s chapter on resolution theorem proving, culminating with a refutationally complete first-order prover based on…

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A framework for formal refutational completeness proofs of abstract provers that implement saturation calculi, such as ordered resolution or superposition, based on modular extensions of lifted redundancy criteria is presented.

J ul 2 02 1 Symbol Elimination for Parametric Second-Order Entailment Problems

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We analyze possibilities of second-order quantifier elimination for formulae containing parameters – constants or functions. For this, we use a constraint resolution calculus obtained from…

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- MathematicsSOQE@KR
- 2021

This work identifies situations in which entailment between formulae expressed using secondorder quantification can be effectively checked and identifies the weakest constraints on parameters which guarantee satisfiability.

Deciding the Bernays-Schoenfinkel Fragment over Bounded Difference Constraints by Simple Clause Learning over Theories

- MathematicsVMCAI
- 2021

SCL(T) is proved to be sound and refutationally complete for the combination of the the Bernays Schoenfinkel fragment with any compact theory and an abstract finite model property such that the size of a sufficiently large set of constants can be fixed a priori.

A Sorted Datalog Hammer for Supervisor Verification Conditions Modulo Simple Linear Arithmetic

- Computer ScienceTACAS
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This paper improves the Datalog hammer in several ways: it generalizes it to mixed real-integer arithmetic and finite first-order sorts; it extends the class of acceptable inequalities beyond variable bounds and positively grounded inequalities; and it significantly reduces the size of the hammer output by a soft typing discipline.

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