twee-lib-2.1: tests/semigroup2.p

% File     : GRP196-1 : TPTP v6.1.0. Released v2.2.0.
% Domain   : Group Theory (Semigroups)
% Problem  : In semigroups, xyyy=yyyx -> (uy)^9 = u^9v^9.
% Version  : [MP96] (equality) axioms.
% English  :
% Refs     : [McC98] McCune (1998), Email to G. Sutcliffe
%          : [MP96]  McCune & Padmanabhan (1996), Automated Deduction in Eq
%          : [McC95] McCune (1995), Four Challenge Problems in Equational L
% Source   : [McC98]
% Names    : CS-3 [MP96]
%          : Problem B [McC95]
% Status   : Unsatisfiable
% Rating   : 1.00 v4.0.1, 0.93 v4.0.0, 0.92 v3.7.0, 0.89 v3.4.0, 1.00 v3.3.0, 0.93 v3.1.0, 1.00 v2.2.1
% Syntax   : Number of clauses     :    3 (   0 non-Horn;   3 unit;   1 RR)
%            Number of atoms       :    3 (   3 equality)
%            Maximal clause size   :    1 (   1 average)
%            Number of predicates  :    1 (   0 propositional; 2-2 arity)
%            Number of functors    :    3 (   2 constant; 0-2 arity)
%            Number of variables   :    5 (   0 singleton)
%            Maximal term depth    :   18 (   8 average)
% SPC      : CNF_UNS_RFO_PEQ_UEQ
% Comments : The problem was originally posed for cancellative semigroups,
%            Otter does this with a nonstandard representation [MP96].
cnf(assoc, axiom, '*'('*'(A,B),C)='*'(A,'*'(B,C))).
cnf(twiddle, axiom, '*'(A,'*'(B,'*'(B,B)))='*'(B,'*'(B,'*'(B,A)))).
cnf(conjecture, negated_conjecture, '*'(a,'*'(b,'*'(a,'*'(b,'*'(a,'*'(b,'*'(a,'*'(b,'*'(a,'*'(b,'*'(a,'*'(b,'*'(a,'*'(b,'*'(a,'*'(b,'*'(a,b))))))))))))))))) != '*'(a,'*'(a,'*'(a,'*'(a,'*'(a,'*'(a,'*'(a,'*'(a,'*'(a,'*'(b,'*'(b,'*'(b,'*'(b,'*'(b,'*'(b,'*'(b,'*'(b,b)))))))))))))))))).