TPTP Problem File: GRP017-1.p
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%--------------------------------------------------------------------------
% File : GRP017-1 : TPTP v9.0.0. Released v1.0.0.
% Domain : Group Theory
% Problem : The inverse of each element is unique
% Version : [MOW76] axioms.
% English : i.e., if ab=ba=identity and ac=ca=identity then b=c
% Refs : [MOW76] McCharen et al. (1976), Problems and Experiments for a
% Source : [ANL]
% Names : G2 [MOW76]
% : invers1.ver1.in [ANL]
% Status : Unsatisfiable
% Rating : 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, 0.00 v2.0.0
% Syntax : Number of clauses : 13 ( 10 unt; 0 nHn; 8 RR)
% Number of literals : 21 ( 2 equ; 9 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 2-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn)
% SPC : CNF_UNS_RFO_SEQ_HRN
% Comments :
%--------------------------------------------------------------------------
%----Include group theory axioms
include('Axioms/GRP003-0.ax').
%--------------------------------------------------------------------------
cnf(a_times_b_is_identity,hypothesis,
product(a,b,identity) ).
cnf(b_times_a_is_identity,hypothesis,
product(b,a,identity) ).
cnf(a_times_c_is_identity,hypothesis,
product(a,c,identity) ).
cnf(c_times_a_is_identity,hypothesis,
product(c,a,identity) ).
cnf(prove_b_equals_c,negated_conjecture,
b != c ).
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