%--------------------------------------------------------------------------
% File     : GRP124-1.003 : TPTP v9.0.0. Bugfixed v2.1.0.
% Domain   : Group Theory (Quasigroups)
% Problem  : (3,1,2) conjugate orthogonality
% Version  : [Sla93] axioms.
% English  : If ab=xy and a*b = x*y then a=x and b=y, where c*a=b iff ab=c.
%            Generate the multiplication table for the specified quasi-
%            group with 3 elements.

% Refs     : [FSB93] Fujita et al. (1993), Automatic Generation of Some Res
%          : [Sla93] Slaney (1993), Email to G. Sutcliffe
%          : [SFS95] Slaney et al. (1995), Automated Reasoning and Exhausti
% Source   : [Sla93]
% Names    : QG2 [Sla93]
%          : QG2 [FSB93]
%          : QG2 [SFS95]
%          : Bennett QG2 [TPTP]

% Status   : Unsatisfiable
% Rating   : 0.00 v2.0.0
% Syntax   :

% Comments : [Sla93]'s axiomatization has been modified for this.
%          : Substitution axioms are not needed, as any positive equality
%            literals should resolve on negative ones directly.
%          : As in GRP123-1, either one of qg2_1 or qg2_2 may be used, as
%            each implies the other in this scenario, with the help of
%            cancellation. The dependence cannot be proved, so both have
%            been left in here.
%          : tptp2X: -ftptp -s3 GRP124-1.g
% Bugfixes : v2.1.0 - Replaced by a new SOTA size.
%--------------------------------------------------------------------------