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  Automatic proofs and counterexamples for some ortholattice identities (1998) [20 citations — 2 self]

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by William Mccune
Information Processing Letters
ftp://ftp.ese-metz.fr/pub/ThProving/Otter/www-misc/ortholattice-submitted.ps.gz
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Abstract:

This note answers questions on whether three identities known to hold for orthomodular lattices are true also for ortholattices. One identity is shown to fail by MACE, a program that searches for counterexamples, an the other two are proved to hold by EQP, an equational theorem prover. The problems, from work in quantum logic, were given to us by Norman Megill.

Citations

263 Otter 3.0 Reference Manual and Guide – McCune - 1994
70 Basic Paramodulation and Superposition – Bachmair, Ganzinger, et al. - 1992
70 A Davis-Putnam program and its application to finite first-order model search – McCune - 1994
28 Otter--the CADE-13 competition incarnations – McCune, Wos - 1997
24 33 basic test problems: a practical evaluation of some paramodulation strategies – McCune - 1997
19 R.: Automated deduction in equational logic and cubic curves – McCune, Padmanablan - 1996
8 Orthomodularity is not elementary – Goldblatt - 1984
4 Binary Orthologic with Modus Ponens Is either Orthomodular or Distributive, Helv – Pavicic, Megill - 1998
1 Orthomodular structures and physical theory – Marlow - 1977
1 Correspondence by electronic mail – Megill, Sept - 1997
1 Correspondence by electronic mail. Fortunately, two of the larger equations (associativity of meet and x (y y ) = y y ) could be omitted, because they depend on the other axioms and lemmas; this allowed the search to run in less than 70 megabytes – Megill, Sept - 1997
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