TSTP Solution File: GRP131-1.002 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP131-1.002 : TPTP v3.4.2. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art04.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2794MHz
% Memory : 1003MB
% OS : Linux 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May 6 12:28:34 EDT 2009
% Result : Unsatisfiable 5.1s
% Output : Refutation 5.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 63 ( 8 unt; 0 def)
% Number of atoms : 183 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 223 ( 103 ~; 120 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 100 ( 0 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(product_total_function1,plain,
! [A,B] :
( ~ group_element(A)
| ~ group_element(B)
| product(A,B,e_1)
| product(A,B,e_2) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP131-1.002.tptp',unknown),
[] ).
cnf(156556992,plain,
( ~ group_element(A)
| ~ group_element(B)
| product(A,B,e_1)
| product(A,B,e_2) ),
inference(rewrite,[status(thm)],[product_total_function1]),
[] ).
fof(element_1,plain,
group_element(e_1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP131-1.002.tptp',unknown),
[] ).
cnf(156534904,plain,
group_element(e_1),
inference(rewrite,[status(thm)],[element_1]),
[] ).
cnf(167007344,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[156556992,156534904]),
[] ).
fof(product_right_cancellation,plain,
! [A,B,C,D] :
( ~ product(A,B,C)
| ~ product(A,D,C)
| equalish(B,D) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP131-1.002.tptp',unknown),
[] ).
cnf(156577528,plain,
( ~ product(A,B,C)
| ~ product(A,D,C)
| equalish(B,D) ),
inference(rewrite,[status(thm)],[product_right_cancellation]),
[] ).
fof(e_1_is_not_e_2,plain,
~ equalish(e_1,e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP131-1.002.tptp',unknown),
[] ).
cnf(156543344,plain,
~ equalish(e_1,e_2),
inference(rewrite,[status(thm)],[e_1_is_not_e_2]),
[] ).
cnf(167103048,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_2,B) ),
inference(resolution,[status(thm)],[156577528,156543344]),
[] ).
cnf(167387416,plain,
( product(e_1,e_1,e_1)
| ~ product(e_1,e_2,e_2) ),
inference(resolution,[status(thm)],[167007344,167103048]),
[] ).
cnf(166989688,plain,
( ~ group_element(A)
| product(e_1,A,e_1)
| product(e_1,A,e_2) ),
inference(resolution,[status(thm)],[156556992,156534904]),
[] ).
fof(element_2,plain,
group_element(e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP131-1.002.tptp',unknown),
[] ).
cnf(156538824,plain,
group_element(e_2),
inference(rewrite,[status(thm)],[element_2]),
[] ).
cnf(167061984,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2) ),
inference(resolution,[status(thm)],[166989688,156538824]),
[] ).
cnf(168043912,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[167387416,167061984]),
[] ).
cnf(167965928,plain,
( product(e_1,e_2,e_1)
| ~ product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[167061984,167103048]),
[] ).
cnf(167228624,plain,
( ~ group_element(A)
| product(A,e_1,e_2)
| ~ product(A,e_2,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[156534904,156556992,167103048]),
[] ).
cnf(167217528,plain,
( ~ group_element(A)
| product(A,e_2,e_1)
| product(A,e_2,e_2) ),
inference(resolution,[status(thm)],[156556992,156538824]),
[] ).
cnf(170879696,plain,
( ~ group_element(A)
| product(A,e_1,e_2)
| product(A,e_2,e_2) ),
inference(resolution,[status(thm)],[167228624,167217528]),
[] ).
cnf(167378736,plain,
( product(e_1,e_1,e_2)
| ~ product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[167007344,167103048]),
[] ).
cnf(167735400,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_2,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[156534904,156538824,167378736,156556992]),
[] ).
fof(product_total_function2,plain,
! [A,B,C,D] :
( ~ product(A,B,C)
| ~ product(A,B,D)
| equalish(C,D) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP131-1.002.tptp',unknown),
[] ).
cnf(156569240,plain,
( ~ product(A,B,C)
| ~ product(A,B,D)
| equalish(C,D) ),
inference(rewrite,[status(thm)],[product_total_function2]),
[] ).
cnf(167077096,plain,
( ~ product(A,B,e_1)
| ~ product(A,B,e_2) ),
inference(resolution,[status(thm)],[156569240,156543344]),
[] ).
cnf(167782928,plain,
( product(e_1,e_2,e_2)
| ~ product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[167735400,167077096]),
[] ).
cnf(167202208,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[156556992,156538824]),
[] ).
fof(product_left_cancellation,plain,
! [A,B,C,D] :
( ~ product(A,B,C)
| ~ product(D,B,C)
| equalish(A,D) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP131-1.002.tptp',unknown),
[] ).
cnf(156581160,plain,
( ~ product(A,B,C)
| ~ product(D,B,C)
| equalish(A,D) ),
inference(rewrite,[status(thm)],[product_left_cancellation]),
[] ).
cnf(167128880,plain,
( ~ product(e_1,A,B)
| ~ product(e_2,A,B) ),
inference(resolution,[status(thm)],[156581160,156543344]),
[] ).
cnf(167567224,plain,
( product(e_2,e_2,e_1)
| ~ product(e_1,e_2,e_2) ),
inference(resolution,[status(thm)],[167202208,167128880]),
[] ).
cnf(169104656,plain,
( ~ product(e_1,e_1,e_1)
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[167782928,167567224]),
[] ).
fof(qg1_1,plain,
! [A,B,C,D,E,F] :
( ~ product(A,B,C)
| ~ product(D,E,C)
| ~ product(F,B,A)
| ~ product(F,E,D)
| equalish(A,D) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP131-1.002.tptp',unknown),
[] ).
cnf(156589192,plain,
( ~ product(A,B,C)
| ~ product(D,E,C)
| ~ product(F,B,A)
| ~ product(F,E,D)
| equalish(A,D) ),
inference(rewrite,[status(thm)],[qg1_1]),
[] ).
cnf(167136872,plain,
( ~ product(e_1,A,B)
| ~ product(e_2,C,B)
| ~ product(D,A,e_1)
| ~ product(D,C,e_2) ),
inference(resolution,[status(thm)],[156589192,156543344]),
[] ).
cnf(171930368,plain,
( ~ product(e_1,A,e_2)
| ~ product(C,A,e_1)
| ~ product(C,B,e_2)
| ~ group_element(B)
| product(e_2,B,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[156538824,167136872,156556992]),
[] ).
cnf(172992336,plain,
( ~ product(e_1,A,e_2)
| ~ product(B,A,e_1)
| ~ product(B,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[171930368,156538824]),
[] ).
cnf(173044632,plain,
( ~ product(B,A,e_1)
| ~ product(B,e_2,e_2)
| product(e_2,e_2,e_1)
| ~ group_element(A)
| product(e_1,A,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[156534904,172992336,156556992]),
[] ).
cnf(173088648,plain,
( ~ product(A,e_1,e_1)
| ~ product(A,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[169104656,173044632,156534904]),
[] ).
cnf(173122688,plain,
( product(e_2,e_2,e_1)
| ~ group_element(A)
| product(A,e_1,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[170879696,156534904,173088648,156556992]),
[] ).
fof(qg1_2,plain,
! [A,B,C,D,E,F] :
( ~ product(A,B,C)
| ~ product(D,E,C)
| ~ product(F,B,A)
| ~ product(F,E,D)
| equalish(B,E) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP131-1.002.tptp',unknown),
[] ).
cnf(156593488,plain,
( ~ product(A,B,C)
| ~ product(D,E,C)
| ~ product(F,B,A)
| ~ product(F,E,D)
| equalish(B,E) ),
inference(rewrite,[status(thm)],[qg1_2]),
[] ).
cnf(167149056,plain,
( ~ product(A,e_1,B)
| ~ product(C,e_2,B)
| ~ product(D,e_1,A)
| ~ product(D,e_2,C) ),
inference(resolution,[status(thm)],[156593488,156543344]),
[] ).
cnf(172054576,plain,
( ~ product(B,e_2,e_1)
| ~ product(C,e_1,A)
| ~ product(C,e_2,B)
| ~ group_element(A)
| product(A,e_1,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[156534904,167149056,156556992]),
[] ).
cnf(173181264,plain,
( ~ product(B,e_1,A)
| ~ group_element(A)
| product(A,e_1,e_2)
| ~ group_element(B)
| product(B,e_2,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[173122688,156538824,172054576,156556992]),
[] ).
cnf(173185592,plain,
product(e_1,e_2,e_1),
inference(forward_subsumption_resolution__resolution,[status(thm)],[168043912,167965928,173181264,156534904]),
[] ).
cnf(167554728,plain,
( product(e_2,e_2,e_2)
| ~ product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[167202208,167103048]),
[] ).
cnf(167407720,plain,
( product(e_1,e_1,e_1)
| ~ product(e_2,e_1,e_2) ),
inference(resolution,[status(thm)],[167007344,167128880]),
[] ).
cnf(168223144,plain,
( product(e_1,e_1,e_1)
| product(e_2,e_1,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[156534904,156538824,167407720,156556992]),
[] ).
cnf(168675312,plain,
( product(e_2,e_2,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[167554728,168223144]),
[] ).
cnf(169046872,plain,
( product(e_1,e_1,e_1)
| ~ product(A,e_2,e_2)
| equalish(A,e_2) ),
inference(resolution,[status(thm)],[168675312,156581160]),
[] ).
cnf(167559248,plain,
( product(e_2,e_2,e_1)
| ~ product(e_2,e_1,e_2) ),
inference(resolution,[status(thm)],[167202208,167103048]),
[] ).
cnf(167024464,plain,
( ~ group_element(A)
| product(A,e_1,e_1)
| product(A,e_1,e_2) ),
inference(resolution,[status(thm)],[156556992,156534904]),
[] ).
cnf(167041048,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(resolution,[status(thm)],[167024464,156538824]),
[] ).
cnf(168719736,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[167559248,167041048]),
[] ).
cnf(169264288,plain,
( product(e_2,e_1,e_1)
| ~ product(A,e_2,e_1)
| equalish(A,e_2) ),
inference(resolution,[status(thm)],[168719736,156581160]),
[] ).
cnf(168579672,plain,
( product(e_2,e_1,e_1)
| ~ product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[168223144,167103048]),
[] ).
cnf(170825440,plain,
( ~ product(e_1,e_2,e_1)
| ~ product(A,e_1,e_1)
| equalish(A,e_2) ),
inference(resolution,[status(thm)],[168579672,156581160]),
[] ).
cnf(171766600,plain,
( ~ product(C,D,e_1)
| ~ product(E,B,A)
| ~ product(E,D,C)
| equalish(A,C)
| ~ group_element(A)
| ~ group_element(B)
| product(A,B,e_2) ),
inference(resolution,[status(thm)],[156589192,156556992]),
[] ).
cnf(173947840,plain,
( ~ product(B,C,e_1)
| ~ product(D,e_2,A)
| ~ product(D,C,B)
| equalish(A,B)
| ~ group_element(A)
| product(A,e_2,e_2) ),
inference(resolution,[status(thm)],[171766600,156538824]),
[] ).
cnf(174186704,plain,
( ~ product(e_2,B,e_1)
| ~ product(C,e_2,A)
| equalish(A,e_2)
| ~ group_element(A)
| product(A,e_2,e_2)
| ~ group_element(C)
| ~ group_element(B)
| product(C,B,e_1) ),
inference(resolution,[status(thm)],[173947840,156556992]),
[] ).
cnf(178151632,plain,
( ~ product(e_1,e_2,e_1)
| equalish(e_1,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[169046872,169264288,170825440,174186704,156534904]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[173185592,178151632,156543344]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 5 seconds
% START OF PROOF SEQUENCE
% fof(product_total_function1,plain,(~group_element(A)|~group_element(B)|product(A,B,e_1)|product(A,B,e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP131-1.002.tptp',unknown),[]).
%
% cnf(156556992,plain,(~group_element(A)|~group_element(B)|product(A,B,e_1)|product(A,B,e_2)),inference(rewrite,[status(thm)],[product_total_function1]),[]).
%
% fof(element_1,plain,(group_element(e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP131-1.002.tptp',unknown),[]).
%
% cnf(156534904,plain,(group_element(e_1)),inference(rewrite,[status(thm)],[element_1]),[]).
%
% cnf(167007344,plain,(product(e_1,e_1,e_1)|product(e_1,e_1,e_2)),inference(resolution,[status(thm)],[156556992,156534904]),[]).
%
% fof(product_right_cancellation,plain,(~product(A,B,C)|~product(A,D,C)|equalish(B,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP131-1.002.tptp',unknown),[]).
%
% cnf(156577528,plain,(~product(A,B,C)|~product(A,D,C)|equalish(B,D)),inference(rewrite,[status(thm)],[product_right_cancellation]),[]).
%
% fof(e_1_is_not_e_2,plain,(~equalish(e_1,e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP131-1.002.tptp',unknown),[]).
%
% cnf(156543344,plain,(~equalish(e_1,e_2)),inference(rewrite,[status(thm)],[e_1_is_not_e_2]),[]).
%
% cnf(167103048,plain,(~product(A,e_1,B)|~product(A,e_2,B)),inference(resolution,[status(thm)],[156577528,156543344]),[]).
%
% cnf(167387416,plain,(product(e_1,e_1,e_1)|~product(e_1,e_2,e_2)),inference(resolution,[status(thm)],[167007344,167103048]),[]).
%
% cnf(166989688,plain,(~group_element(A)|product(e_1,A,e_1)|product(e_1,A,e_2)),inference(resolution,[status(thm)],[156556992,156534904]),[]).
%
% fof(element_2,plain,(group_element(e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP131-1.002.tptp',unknown),[]).
%
% cnf(156538824,plain,(group_element(e_2)),inference(rewrite,[status(thm)],[element_2]),[]).
%
% cnf(167061984,plain,(product(e_1,e_2,e_1)|product(e_1,e_2,e_2)),inference(resolution,[status(thm)],[166989688,156538824]),[]).
%
% cnf(168043912,plain,(product(e_1,e_1,e_1)|product(e_1,e_2,e_1)),inference(resolution,[status(thm)],[167387416,167061984]),[]).
%
% cnf(167965928,plain,(product(e_1,e_2,e_1)|~product(e_1,e_1,e_2)),inference(resolution,[status(thm)],[167061984,167103048]),[]).
%
% cnf(167228624,plain,(~group_element(A)|product(A,e_1,e_2)|~product(A,e_2,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[156534904,156556992,167103048]),[]).
%
% cnf(167217528,plain,(~group_element(A)|product(A,e_2,e_1)|product(A,e_2,e_2)),inference(resolution,[status(thm)],[156556992,156538824]),[]).
%
% cnf(170879696,plain,(~group_element(A)|product(A,e_1,e_2)|product(A,e_2,e_2)),inference(resolution,[status(thm)],[167228624,167217528]),[]).
%
% cnf(167378736,plain,(product(e_1,e_1,e_2)|~product(e_1,e_2,e_1)),inference(resolution,[status(thm)],[167007344,167103048]),[]).
%
% cnf(167735400,plain,(product(e_1,e_1,e_2)|product(e_1,e_2,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[156534904,156538824,167378736,156556992]),[]).
%
% fof(product_total_function2,plain,(~product(A,B,C)|~product(A,B,D)|equalish(C,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP131-1.002.tptp',unknown),[]).
%
% cnf(156569240,plain,(~product(A,B,C)|~product(A,B,D)|equalish(C,D)),inference(rewrite,[status(thm)],[product_total_function2]),[]).
%
% cnf(167077096,plain,(~product(A,B,e_1)|~product(A,B,e_2)),inference(resolution,[status(thm)],[156569240,156543344]),[]).
%
% cnf(167782928,plain,(product(e_1,e_2,e_2)|~product(e_1,e_1,e_1)),inference(resolution,[status(thm)],[167735400,167077096]),[]).
%
% cnf(167202208,plain,(product(e_2,e_2,e_1)|product(e_2,e_2,e_2)),inference(resolution,[status(thm)],[156556992,156538824]),[]).
%
% fof(product_left_cancellation,plain,(~product(A,B,C)|~product(D,B,C)|equalish(A,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP131-1.002.tptp',unknown),[]).
%
% cnf(156581160,plain,(~product(A,B,C)|~product(D,B,C)|equalish(A,D)),inference(rewrite,[status(thm)],[product_left_cancellation]),[]).
%
% cnf(167128880,plain,(~product(e_1,A,B)|~product(e_2,A,B)),inference(resolution,[status(thm)],[156581160,156543344]),[]).
%
% cnf(167567224,plain,(product(e_2,e_2,e_1)|~product(e_1,e_2,e_2)),inference(resolution,[status(thm)],[167202208,167128880]),[]).
%
% cnf(169104656,plain,(~product(e_1,e_1,e_1)|product(e_2,e_2,e_1)),inference(resolution,[status(thm)],[167782928,167567224]),[]).
%
% fof(qg1_1,plain,(~product(A,B,C)|~product(D,E,C)|~product(F,B,A)|~product(F,E,D)|equalish(A,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP131-1.002.tptp',unknown),[]).
%
% cnf(156589192,plain,(~product(A,B,C)|~product(D,E,C)|~product(F,B,A)|~product(F,E,D)|equalish(A,D)),inference(rewrite,[status(thm)],[qg1_1]),[]).
%
% cnf(167136872,plain,(~product(e_1,A,B)|~product(e_2,C,B)|~product(D,A,e_1)|~product(D,C,e_2)),inference(resolution,[status(thm)],[156589192,156543344]),[]).
%
% cnf(171930368,plain,(~product(e_1,A,e_2)|~product(C,A,e_1)|~product(C,B,e_2)|~group_element(B)|product(e_2,B,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[156538824,167136872,156556992]),[]).
%
% cnf(172992336,plain,(~product(e_1,A,e_2)|~product(B,A,e_1)|~product(B,e_2,e_2)|product(e_2,e_2,e_1)),inference(resolution,[status(thm)],[171930368,156538824]),[]).
%
% cnf(173044632,plain,(~product(B,A,e_1)|~product(B,e_2,e_2)|product(e_2,e_2,e_1)|~group_element(A)|product(e_1,A,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[156534904,172992336,156556992]),[]).
%
% cnf(173088648,plain,(~product(A,e_1,e_1)|~product(A,e_2,e_2)|product(e_2,e_2,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[169104656,173044632,156534904]),[]).
%
% cnf(173122688,plain,(product(e_2,e_2,e_1)|~group_element(A)|product(A,e_1,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[170879696,156534904,173088648,156556992]),[]).
%
% fof(qg1_2,plain,(~product(A,B,C)|~product(D,E,C)|~product(F,B,A)|~product(F,E,D)|equalish(B,E)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP131-1.002.tptp',unknown),[]).
%
% cnf(156593488,plain,(~product(A,B,C)|~product(D,E,C)|~product(F,B,A)|~product(F,E,D)|equalish(B,E)),inference(rewrite,[status(thm)],[qg1_2]),[]).
%
% cnf(167149056,plain,(~product(A,e_1,B)|~product(C,e_2,B)|~product(D,e_1,A)|~product(D,e_2,C)),inference(resolution,[status(thm)],[156593488,156543344]),[]).
%
% cnf(172054576,plain,(~product(B,e_2,e_1)|~product(C,e_1,A)|~product(C,e_2,B)|~group_element(A)|product(A,e_1,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[156534904,167149056,156556992]),[]).
%
% cnf(173181264,plain,(~product(B,e_1,A)|~group_element(A)|product(A,e_1,e_2)|~group_element(B)|product(B,e_2,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[173122688,156538824,172054576,156556992]),[]).
%
% cnf(173185592,plain,(product(e_1,e_2,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[168043912,167965928,173181264,156534904]),[]).
%
% cnf(167554728,plain,(product(e_2,e_2,e_2)|~product(e_2,e_1,e_1)),inference(resolution,[status(thm)],[167202208,167103048]),[]).
%
% cnf(167407720,plain,(product(e_1,e_1,e_1)|~product(e_2,e_1,e_2)),inference(resolution,[status(thm)],[167007344,167128880]),[]).
%
% cnf(168223144,plain,(product(e_1,e_1,e_1)|product(e_2,e_1,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[156534904,156538824,167407720,156556992]),[]).
%
% cnf(168675312,plain,(product(e_2,e_2,e_2)|product(e_1,e_1,e_1)),inference(resolution,[status(thm)],[167554728,168223144]),[]).
%
% cnf(169046872,plain,(product(e_1,e_1,e_1)|~product(A,e_2,e_2)|equalish(A,e_2)),inference(resolution,[status(thm)],[168675312,156581160]),[]).
%
% cnf(167559248,plain,(product(e_2,e_2,e_1)|~product(e_2,e_1,e_2)),inference(resolution,[status(thm)],[167202208,167103048]),[]).
%
% cnf(167024464,plain,(~group_element(A)|product(A,e_1,e_1)|product(A,e_1,e_2)),inference(resolution,[status(thm)],[156556992,156534904]),[]).
%
% cnf(167041048,plain,(product(e_2,e_1,e_1)|product(e_2,e_1,e_2)),inference(resolution,[status(thm)],[167024464,156538824]),[]).
%
% cnf(168719736,plain,(product(e_2,e_2,e_1)|product(e_2,e_1,e_1)),inference(resolution,[status(thm)],[167559248,167041048]),[]).
%
% cnf(169264288,plain,(product(e_2,e_1,e_1)|~product(A,e_2,e_1)|equalish(A,e_2)),inference(resolution,[status(thm)],[168719736,156581160]),[]).
%
% cnf(168579672,plain,(product(e_2,e_1,e_1)|~product(e_1,e_2,e_1)),inference(resolution,[status(thm)],[168223144,167103048]),[]).
%
% cnf(170825440,plain,(~product(e_1,e_2,e_1)|~product(A,e_1,e_1)|equalish(A,e_2)),inference(resolution,[status(thm)],[168579672,156581160]),[]).
%
% cnf(171766600,plain,(~product(C,D,e_1)|~product(E,B,A)|~product(E,D,C)|equalish(A,C)|~group_element(A)|~group_element(B)|product(A,B,e_2)),inference(resolution,[status(thm)],[156589192,156556992]),[]).
%
% cnf(173947840,plain,(~product(B,C,e_1)|~product(D,e_2,A)|~product(D,C,B)|equalish(A,B)|~group_element(A)|product(A,e_2,e_2)),inference(resolution,[status(thm)],[171766600,156538824]),[]).
%
% cnf(174186704,plain,(~product(e_2,B,e_1)|~product(C,e_2,A)|equalish(A,e_2)|~group_element(A)|product(A,e_2,e_2)|~group_element(C)|~group_element(B)|product(C,B,e_1)),inference(resolution,[status(thm)],[173947840,156556992]),[]).
%
% cnf(178151632,plain,(~product(e_1,e_2,e_1)|equalish(e_1,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[169046872,169264288,170825440,174186704,156534904]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[173185592,178151632,156543344]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------