TPTP Problem File: GRP031-1.p
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%--------------------------------------------------------------------------
% File : GRP031-1 : TPTP v9.0.0. Released v1.0.0.
% Domain : Group Theory (Semigroups)
% Problem : In semigroups, left inverse and id => right inverse exists
% Version : [MOW76] axioms.
% English : If there are left inverses and left identity, then every
% element has a right inverse.
% Refs : [Wos65] Wos (1965), Unpublished Note
% : [MOW76] McCharen et al. (1976), Problems and Experiments for a
% : [WM76] Wilson & Minker (1976), Resolution, Refinements, and S
% Source : [SPRFN]
% Names : Problem 5 [Wos65]
% : wos5 [WM76]
% : G4 [MOW76]
% : invers2.ver1.t [ANL]
% Status : Unsatisfiable
% Rating : 0.08 v9.0.0, 0.06 v8.2.0, 0.00 v6.0.0, 0.11 v5.5.0, 0.06 v5.4.0, 0.07 v5.3.0, 0.17 v5.2.0, 0.12 v5.1.0, 0.14 v5.0.0, 0.00 v2.0.0
% Syntax : Number of clauses : 7 ( 4 unt; 0 nHn; 4 RR)
% Number of literals : 15 ( 1 equ; 9 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 2-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 21 ( 1 sgn)
% SPC : CNF_UNS_RFO_SEQ_HRN
% Comments : This can also be viewed as a group theory problem, showing
% that the right inverse axiom is dependant on the rest of the
% axiom set; i.e., if there is a left inverse then there
% is a right inverse.
%--------------------------------------------------------------------------
%----Include semi-group axioms
include('Axioms/GRP002-0.ax').
%--------------------------------------------------------------------------
cnf(left_identity,hypothesis,
product(identity,A,A) ).
cnf(left_inverse,hypothesis,
product(inverse(A),A,identity) ).
cnf(prove_a_has_an_inverse,negated_conjecture,
~ product(a,A,identity) ).
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