## Cancellative superposition decides the theory of divisible torsion-free abelian groups

**Uwe Waldmann**
In Harald Ganzinger, David McAllester, and Andrei Voronkov, editors,
*Logic for Programming and Automated Reasoning,
6th International Conference, LPAR'99*, LNAI 1705, pages 131-147,
Tbilisi, Georgia, September 6-10, 1999. Springer-Verlag.

*Earlier version:* Technical Report MPI-I-1999-2-003, Max-Planck-Institut
für Informatik, Saarbrücken, March 1999.
[Postscript file, 140 kB]

**Abstract:**
In divisible torsion-free abelian groups, the efficiency
of the cancellative superposition calculus can be greatly increased
by combining it with a variable elimination algorithm that transforms
every clause into an equivalent clause without unshielded variables.
We show that the resulting calculus is not only refutationally
complete (even in the presence of arbitrary free function symbols),
but that it is also a decision procedure for the theory of divisible
torsion-free abelian groups.

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Uwe Waldmann
<

uwe@mpi-inf.mpg.de>,
2001-06-20.