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Automated Theorem Proving in Quasigroup and Loop Theory

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ATP <strong>in</strong> <strong>Quasigroup</strong>s <strong>and</strong> <strong>Loop</strong>s<br />

Phillips, Stanovský<br />

[MPV03] W. McCune, R. Padmanabhan, R. Veroff, Yet another s<strong>in</strong>gle law for lattices, Algebra Universalis 50<br />

(2003), no. 2, 165–169.<br />

[MVFHFW02] W. McCune, R. Veroff, B. Fitelson, K. Harris, A. Feist, L. Wos, Short s<strong>in</strong>gle axioms for Boolean<br />

algebra, J. Automat. Reason. 29 (2002), no. 1, 1–16.<br />

[Nag08] G. P. Nagy. A class of f<strong>in</strong>ite simple Bol loops of exponent 2, to appear <strong>in</strong> Trans. Amer. Math. Soc., 2008.<br />

[NV07] G. P. Nagy <strong>and</strong> P. Vojtěchovský, Comput<strong>in</strong>g with small quasigroups <strong>and</strong> loops, <strong>Quasigroup</strong>s <strong>and</strong> Related<br />

Systems 15 (2007), 77–94.<br />

[Pfl90] H. O. Pflugfelder, <strong>Quasigroup</strong>s <strong>and</strong> <strong>Loop</strong>s: Introduction, Sigma Series <strong>in</strong> Pure Mathematics 7, Heldermann<br />

Verlag Berl<strong>in</strong>, 1990.<br />

[Pfl00] H. O. Pflugfelder, Historical notes on loop theory, Comment. Math. Univ. Carol<strong>in</strong>. 41/2 (2000), 359–370.<br />

[Phi03] J.D. Phillips, See Otter digg<strong>in</strong>g for algebraic pearls, <strong>Quasigroup</strong>s <strong>and</strong> Related Systems, 10 (2003), 95–<br />

114.<br />

[Phi06] J.D. Phillips, A short basis for the variety of WIP PACC-loops, <strong>Quasigroup</strong>s <strong>and</strong> Related Systems, 14<br />

(2006), 73–80.<br />

[Phi06b] J.D. Phillips, Short equational bases for two varieties of groupoids associated with <strong>in</strong>voluted restrictive<br />

bisemigroups of b<strong>in</strong>ary relations, Semigroup Forum 73, No. 2, 308-312 (2006).<br />

[Pud07] P. Pudlák, Semantic Selection of Premisses for <strong>Automated</strong> <strong>Theorem</strong> <strong>Prov<strong>in</strong>g</strong>, proceed<strong>in</strong>gs of the ESARLT<br />

Workshop, Bremen, 2007.<br />

[PS08] J.D. Phillips, D. Stanovský, <strong>Automated</strong> theorem prov<strong>in</strong>g <strong>in</strong> loop theory, proceed<strong>in</strong>gs of the ESARM<br />

workshop, Birm<strong>in</strong>gham, 2008.<br />

[PSxx] J.D. Phillips, D. Stanovský, <strong>Loop</strong>s with abelian <strong>in</strong>ner mapp<strong>in</strong>g groups, work <strong>in</strong> progress.<br />

[PV05a] J.D. Phillips <strong>and</strong> P. Vojtěchovský, The varieties of loops of Bol-Moufang type, Algebra Universalis, 54<br />

(3) (2005), 259–271.<br />

[PV05b] J.D. Phillips <strong>and</strong> P. Vojtěchovský, The varieties of quasigroups of Bol-Moufang type: an equational<br />

reason<strong>in</strong>g approach, Journal of Algebra, 293 (2005), 17–33.<br />

[PV05c] J.D. Phillips <strong>and</strong> P. Vojtěchovský, L<strong>in</strong>ear groupoids <strong>and</strong> the associated wreath products, Journal of Symbolic<br />

Computation, 40 (3), (2005), 1106–1125.<br />

[PV06] J.D. Phillips <strong>and</strong> P. Vojtěchovský, C-loops: an <strong>in</strong>troduction, Publicationes Mathematicae Debrecen,<br />

68/1–2 (2006), p. 115–137.<br />

[PV08] J.D. Phillips <strong>and</strong> P. Vojtěchovský, A scoop from groups: new equational foundations for loops, Commentationes<br />

Mathematicae Universitatis Carol<strong>in</strong>ae, 49/2 (2008), 279–290.<br />

[RV02] A. Riazanov, A. Voronkov, The Design <strong>and</strong> Implementation of Vampire, AI Communications 15(2-3)<br />

(2002), 91–110.<br />

[S] http://www.spass-prover.org/<br />

[Sch02] S. Schulz, E: A Bra<strong>in</strong>iac <strong>Theorem</strong> Prover, AI Communications 15(2-3) (2002), 111–126.<br />

[SV08] M. Sp<strong>in</strong>ks, R. Veroff, Constructive logic with strong negation is a substructural logic, Studia Logica 88/3<br />

(2008), 325–348.<br />

[Sta08] D. Stanovský, Distributive groupoids are symmetric-by-medial: An elementary proof, Comment. Math.<br />

Univ. Carol<strong>in</strong>ae 49/4 (2008), 541–546.<br />

[SS98] G. Sutcliffe, C. Suttner, The TPTP Problem Library: CNF Release v1.2.1, Journal of <strong>Automated</strong> Reason<strong>in</strong>g,<br />

21/2 (1998), 177–203.<br />

[SS06] G. Sutcliffe, C. Suttner, The State of CASC, AI Communications 19/1 (2006), 35–48.<br />

[Tam97] T. Tammet, G<strong>and</strong>alf, J. of <strong>Automated</strong> Reason<strong>in</strong>g 18/2 (1997), 199–204.<br />

[Ver01] R. Veroff, Solv<strong>in</strong>g open questions <strong>and</strong> other challenge problems us<strong>in</strong>g proof sketches, J. <strong>Automated</strong><br />

Reason<strong>in</strong>g 27(2) (2001), 157–174.<br />

[VM] R. Veroff, W. McCune, http://www.cs.unm.edu/~veroff/MEDIAN ALGEBRA/<br />

[VS06] R. Veroff, M. Sp<strong>in</strong>ks, Axiomatiz<strong>in</strong>g the skew Boolean propositional calculus, J. Automat. Reason. 37<br />

(2006), no. 1-2, 3–20 (2007).<br />

20

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