%--------------------------------------------------------------------------
% File     : GRP192-1 : TPTP v8.2.0. Bugfixed v1.2.1.
% Domain   : Group Theory (Lattice Ordered)
% Problem  : Even elements implies trivial group
% Version  : [Fuc94] (equality) axioms.
% English  : The assumption all(X,1 =< X) even implies that the group is
%            trivial, i.e., all(X, X = 1).

% Refs     : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri
%          : [Sch95] Schulz (1995), Explanation Based Learning for Distribu
% Source   : [Sch95]
% Names    : p40a [Sch95]

% Status   : Unsatisfiable
% Rating   : 0.05 v8.2.0, 0.08 v8.1.0, 0.10 v7.5.0, 0.08 v7.4.0, 0.13 v7.3.0, 0.16 v7.1.0, 0.11 v6.3.0, 0.12 v6.2.0, 0.14 v6.1.0, 0.12 v6.0.0, 0.24 v5.5.0, 0.26 v5.4.0, 0.13 v5.3.0, 0.08 v5.2.0, 0.14 v5.1.0, 0.07 v4.1.0, 0.00 v4.0.1, 0.07 v4.0.0, 0.08 v3.7.0, 0.00 v3.3.0, 0.07 v3.1.0, 0.11 v2.7.0, 0.00 v2.2.1, 0.33 v2.2.0, 0.43 v2.1.0, 0.14 v2.0.0
% Syntax   : Number of clauses     :   17 (  17 unt;   0 nHn;   1 RR)
%            Number of literals    :   17 (  17 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    1 (   0 usr;   0 prp; 2-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   34 (   2 sgn)
% SPC      : CNF_UNS_RFO_PEQ_UEQ

% Comments : ORDERING LPO inverse > product > greatest_lower_bound >
%            least_upper_bound > identity > a > b
% Bugfixes : v1.2.1 - Duplicate axioms in GRP004-2.ax removed.
%--------------------------------------------------------------------------
%----Include equality group theory axioms
include('Axioms/GRP004-0.ax').
%----Include Lattice ordered group (equality) axioms
include('Axioms/GRP004-2.ax').
%--------------------------------------------------------------------------
cnf(p40a_1,hypothesis,
    least_upper_bound(identity,X) = X ).

cnf(prove_p40a,negated_conjecture,
    multiply(a,b) != multiply(b,a) ).

%--------------------------------------------------------------------------