twee-0.1: tests/semigroup2.p

% File     : GRP'1'96'-''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 ('1'998), Email to G. Sutcliffe
%          : [MP96]  McCune & Padmanabhan ('1'996), Automated Deduction in Eq
%          : [McC95] McCune ('1'995), Four Challenge Problems in Equational L
% Source   : [McC98]
% Names    : CS'-'3 [MP96]
%          : Problem B [McC95]
% Status   : Unsatisfiable
% Rating   : '1'.'0''0' v4.'0'.'1', '0'.93 v4.'0'.'0', '0'.92 v3.7.'0', '0'.89 v3.4.'0', '1'.'0''0' v3.3.'0', '0'.93 v3.'1'.'0', '1'.'0''0' 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    :   '1'8 (   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(a, axiom, '*'('*'(A,B),C)='*'(A,'*'(B,C))).
cnf(a, axiom, '*'(A,'*'(B,'*'(B,B)))='*'(B,'*'(B,'*'(B,A)))).
cnf(a, axiom, '*'(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)))))))))))))))))).