Experiments with an Automatic Theorem-Prover
HavingPartial Ordering Inference Rules
Automatic theorem-provers need to be made much
more efficient.  With this in mind, Slagle has 
shown how the axioms for partial ordering can be replaced
by built-in inference rules when using a particular 
theorem-proving algorithm based upon hyper-resolution and
paramodulation.  The new rules embody the transitivity 
of partial orderings and the close relationship between
 predicates.  A program has been developed using 
a modified version of these rules.  This new theorem-prover
has been found to be very powerful for solving 
problems involving partial orderings.  This paper presents
a detailed description of the program and 
a comprehensive account of the experiments that have been performed with it.
CACM November, 1973
Slagle, J. R.
Norton, L. M.
