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<p><strong>Demodulating to Junk
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<p>This is a technique used in ordinary Otter, as well as in Otter-lambda, to tell the prover to discard terms of specific unwanted forms. For example, in proofs by mathematical induction, we may want to discard terms with three or more nested successors. (To see why, read the explanation at the end of <a href="Peano Arithmetic/PA-assocplus.html">assocplus</a>.) To do this, we set the weight of the atom 'junk' to some large value, more than max_weight. This will result in any term that contains 'junk' being discarded, unless we've artificially changed the weighting scheme so that some subterms might not be counted; in that case more demodulators may be required, for example, if we have changed the weights so that g-terms count like constants, then we would need: </p>
<p>s(s(s(x))) = junk.<br>
g(x,junk) = junk.<br>
g(junk,x) = junk.</p>
<p>The reason why one might want to do this is as follows: Otherwise, one might worry, Otter-lambda may say, to prove P(x) by induction, assume P(n) and try to prove P(s(n)). OK, let's try to prove P(s(n)) by induction. Fine, assume P(s(n)) and try to prove P(s(s(n)))). OK, let's try to prove P(s(s(n))) by induction. So assume P(s(s(n))) and try to prove P(s(s(s(n)))). In fact, at least on simple examples, although this phenomenon does occur, the formulae thus generated are heavy enough that they do not become the given clause often before the desired proof is generated. </p>
<p>Another case in which demodulating to junk can be used is in finding proofs in specific axiom systems for propositional logic, where it is sometimes useful to discard terms with triple negation or double negation.</p>
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