TPTP Problem File: GRP151-1.p
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- Solve Problem
%--------------------------------------------------------------------------
% File : GRP151-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% Domain : Group Theory (Lattice Ordered)
% Problem : Prove least upper-bound axiom using the GLB transformation
% Version : [Fuc94] (equality) axioms.
% English : This problem proves the original least upper-bound axiom from
% the equational axiomatization.
% Refs : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri
% : [Sch95] Schulz (1995), Explanation Based Learning for Distribu
% Source : [Sch95]
% Names : ax_lub2b [Sch95]
% Status : Unsatisfiable
% Rating : 0.00 v7.5.0, 0.04 v7.4.0, 0.09 v7.3.0, 0.05 v7.1.0, 0.06 v7.0.0, 0.11 v6.3.0, 0.12 v6.2.0, 0.14 v6.1.0, 0.06 v6.0.0, 0.10 v5.5.0, 0.05 v5.4.0, 0.00 v5.1.0, 0.07 v4.1.0, 0.09 v4.0.1, 0.07 v4.0.0, 0.08 v3.7.0, 0.00 v2.0.0
% Syntax : Number of clauses : 16 ( 16 unt; 0 nHn; 1 RR)
% Number of literals : 16 ( 16 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 : 33 ( 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(prove_ax_lub2b,negated_conjecture,
greatest_lower_bound(a,least_upper_bound(a,b)) != a ).
%--------------------------------------------------------------------------