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\begin{document}

\title{Given Clause Loops}
\author{Jasmin Blanchette \and Qi Qiu \and Sophie Tourret}
\maketitle

\begin{abstract}
\noindent
This Isabelle/HOL formalization extends the
\verb|Saturation_|\allowbreak\verb|Framework| and
\verb|Saturation_|\allowbreak\verb|Framework_|\allowbreak\verb|Extensions|
entries of the \emph{Archive of Formal Proofs} with the specification and
verification of four semiabstract given clause procedures, or ``loops'':\ the
DISCOUNT, Otter, iProver, and Zipperposition loops. For each loop, (dynamic)
refutational completeness is proved under the assumption that the underlying
calculus is (statically) refutationally complete and that the used queue data
structures are fair.

The formalization is inspired by the proof sketches found in the article ``A
comprehensive framework for saturation theorem proving'' by Uwe Waldmann, Sophie
Tourret, Simon Robillard, and Jasmin Blanchette (\emph{Journal of Automated
Reasoning} \textbf{66}(4): 499--539, 2022). A paper titled ``Verified given
clause procedures'' about the present formalization is in the works.
\end{abstract}

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\end{document}

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