TSTP Solution File: GRP130-1.003 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP130-1.003 : TPTP v3.4.2. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art01.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 12:27:33 EDT 2009
% Result : Unsatisfiable 1.5s
% Output : Refutation 1.5s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 11
% Syntax : Number of formulae : 72 ( 22 unt; 0 def)
% Number of atoms : 154 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 167 ( 85 ~; 82 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 77 ( 4 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(element_3,plain,
group_element(e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP130-1.003.tptp',unknown),
[] ).
cnf(168635408,plain,
group_element(e_3),
inference(rewrite,[status(thm)],[element_3]),
[] ).
fof(qg3,plain,
! [A,B,C,D] :
( ~ product(A,B,C)
| ~ product(A,C,D)
| product(D,B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP130-1.003.tptp',unknown),
[] ).
cnf(168702768,plain,
( ~ product(A,B,C)
| ~ product(A,C,D)
| product(D,B,A) ),
inference(rewrite,[status(thm)],[qg3]),
[] ).
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/GRP130-1.003.tptp',unknown),
[] ).
cnf(168698392,plain,
( ~ product(A,B,C)
| ~ product(D,B,C)
| equalish(A,D) ),
inference(rewrite,[status(thm)],[product_left_cancellation]),
[] ).
fof(e_1_is_not_e_3,plain,
~ equalish(e_1,e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP130-1.003.tptp',unknown),
[] ).
cnf(168643848,plain,
~ equalish(e_1,e_3),
inference(rewrite,[status(thm)],[e_1_is_not_e_3]),
[] ).
cnf(176807776,plain,
( ~ product(e_1,A,B)
| ~ product(e_3,A,B) ),
inference(resolution,[status(thm)],[168698392,168643848]),
[] ).
cnf(176912232,plain,
( ~ product(A,B,C)
| ~ product(A,C,e_3)
| ~ product(e_1,B,A) ),
inference(resolution,[status(thm)],[168702768,176807776]),
[] ).
fof(product_total_function1,plain,
! [A,B] :
( ~ group_element(A)
| ~ group_element(B)
| product(A,B,e_1)
| product(A,B,e_2)
| product(A,B,e_3) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP130-1.003.tptp',unknown),
[] ).
cnf(168674248,plain,
( ~ group_element(A)
| ~ group_element(B)
| product(A,B,e_1)
| product(A,B,e_2)
| product(A,B,e_3) ),
inference(rewrite,[status(thm)],[product_total_function1]),
[] ).
fof(element_1,plain,
group_element(e_1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP130-1.003.tptp',unknown),
[] ).
cnf(168627680,plain,
group_element(e_1),
inference(rewrite,[status(thm)],[element_1]),
[] ).
cnf(176515168,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_3) ),
inference(resolution,[status(thm)],[168674248,168627680]),
[] ).
cnf(183192856,plain,
( ~ product(e_1,A,e_1)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[176912232,176515168]),
[] ).
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/GRP130-1.003.tptp',unknown),
[] ).
cnf(168694760,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/GRP130-1.003.tptp',unknown),
[] ).
cnf(168639928,plain,
~ equalish(e_1,e_2),
inference(rewrite,[status(thm)],[e_1_is_not_e_2]),
[] ).
cnf(176701872,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_2,B) ),
inference(resolution,[status(thm)],[168694760,168639928]),
[] ).
cnf(178643856,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_3)
| ~ product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[176515168,176701872]),
[] ).
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/GRP130-1.003.tptp',unknown),
[] ).
cnf(168690528,plain,
( ~ product(A,B,C)
| ~ product(A,B,D)
| equalish(C,D) ),
inference(rewrite,[status(thm)],[product_total_function2]),
[] ).
cnf(176748336,plain,
( ~ product(A,B,e_1)
| ~ product(A,B,e_3) ),
inference(resolution,[status(thm)],[168690528,168643848]),
[] ).
cnf(187621312,plain,
( product(e_1,e_1,e_2)
| ~ product(e_1,e_2,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[183192856,178643856,176748336]),
[] ).
cnf(176734240,plain,
( ~ product(e_1,A,B)
| ~ product(e_2,A,B) ),
inference(resolution,[status(thm)],[168698392,168639928]),
[] ).
cnf(176859072,plain,
( ~ product(A,B,C)
| ~ product(A,C,e_2)
| ~ product(e_1,B,A) ),
inference(resolution,[status(thm)],[168702768,176734240]),
[] ).
cnf(178894056,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_3)
| ~ product(e_1,A,e_1) ),
inference(resolution,[status(thm)],[176515168,176859072]),
[] ).
cnf(176677432,plain,
( ~ product(A,B,e_1)
| ~ product(A,B,e_2) ),
inference(resolution,[status(thm)],[168690528,168639928]),
[] ).
cnf(184538272,plain,
( product(e_1,e_1,e_3)
| ~ product(e_1,e_2,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[178894056,178643856,176677432]),
[] ).
fof(e_2_is_not_e_3,plain,
~ equalish(e_2,e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP130-1.003.tptp',unknown),
[] ).
cnf(168651208,plain,
~ equalish(e_2,e_3),
inference(rewrite,[status(thm)],[e_2_is_not_e_3]),
[] ).
cnf(176767360,plain,
( ~ product(A,B,e_2)
| ~ product(A,B,e_3) ),
inference(resolution,[status(thm)],[168690528,168651208]),
[] ).
cnf(187898064,plain,
~ product(e_1,e_2,e_1),
inference(forward_subsumption_resolution__resolution,[status(thm)],[187621312,184538272,176767360]),
[] ).
fof(element_2,plain,
group_element(e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP130-1.003.tptp',unknown),
[] ).
cnf(168631632,plain,
group_element(e_2),
inference(rewrite,[status(thm)],[element_2]),
[] ).
cnf(176614024,plain,
( ~ group_element(A)
| product(A,e_2,e_1)
| product(A,e_2,e_2)
| product(A,e_2,e_3) ),
inference(resolution,[status(thm)],[168674248,168631632]),
[] ).
cnf(176661544,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(resolution,[status(thm)],[176614024,168627680]),
[] ).
cnf(188037936,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(resolution,[status(thm)],[187898064,176661544]),
[] ).
cnf(188074656,plain,
( product(e_1,e_2,e_2)
| ~ product(e_1,e_1,e_3) ),
inference(resolution,[status(thm)],[188037936,176701872]),
[] ).
cnf(176982160,plain,
( product(B,B,A)
| ~ product(B,B,C)
| ~ product(B,C,A) ),
inference(resolution,[status(thm)],[168702768,168702768]),
[] ).
cnf(188229136,plain,
( product(e_1,e_2,e_2)
| ~ product(e_1,e_1,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[188074656,188037936,176982160]),
[] ).
cnf(188070152,plain,
( product(e_1,e_2,e_3)
| ~ product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[188037936,176701872]),
[] ).
cnf(189048856,plain,
~ product(e_1,e_1,e_2),
inference(forward_subsumption_resolution__resolution,[status(thm)],[188229136,188070152,176767360]),
[] ).
cnf(189185496,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_3) ),
inference(resolution,[status(thm)],[189048856,176515168]),
[] ).
cnf(189519720,plain,
( product(e_1,e_1,e_1)
| ~ product(e_1,A,e_1) ),
inference(resolution,[status(thm)],[189185496,176912232]),
[] ).
cnf(176784192,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_3,B) ),
inference(resolution,[status(thm)],[168694760,168643848]),
[] ).
cnf(189275352,plain,
( product(e_1,e_1,e_3)
| ~ product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[189185496,176784192]),
[] ).
cnf(196953048,plain,
~ product(e_1,e_3,e_1),
inference(forward_subsumption_resolution__resolution,[status(thm)],[189519720,189275352,176748336]),
[] ).
cnf(176490856,plain,
( ~ group_element(A)
| product(e_1,A,e_1)
| product(e_1,A,e_2)
| product(e_1,A,e_3) ),
inference(resolution,[status(thm)],[168674248,168627680]),
[] ).
cnf(197173816,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[168635408,196953048,176490856]),
[] ).
cnf(197367008,plain,
( product(e_1,e_3,e_2)
| ~ product(e_2,e_3,e_3) ),
inference(resolution,[status(thm)],[197173816,176734240]),
[] ).
cnf(176791048,plain,
( ~ product(A,e_2,B)
| ~ product(A,e_3,B) ),
inference(resolution,[status(thm)],[168694760,168651208]),
[] ).
cnf(188093144,plain,
( product(e_1,e_2,e_2)
| ~ product(e_1,e_3,e_3) ),
inference(resolution,[status(thm)],[188037936,176791048]),
[] ).
cnf(176898728,plain,
( ~ product(A,e_2,B)
| ~ product(A,B,C)
| ~ product(C,e_3,A) ),
inference(resolution,[status(thm)],[168702768,176791048]),
[] ).
cnf(191864176,plain,
( ~ product(e_1,e_3,e_3)
| ~ product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[188093144,176898728]),
[] ).
cnf(188323592,plain,
( product(e_1,e_2,e_3)
| ~ product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[188037936,176898728]),
[] ).
cnf(197624000,plain,
~ product(e_2,e_3,e_1),
inference(forward_subsumption_resolution__resolution,[status(thm)],[191864176,188323592,197173816,176898728]),
[] ).
cnf(176562904,plain,
( ~ group_element(A)
| product(e_2,A,e_1)
| product(e_2,A,e_2)
| product(e_2,A,e_3) ),
inference(resolution,[status(thm)],[168674248,168631632]),
[] ).
cnf(197731488,plain,
( product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[168635408,197624000,176562904]),
[] ).
cnf(199265624,plain,
product(e_2,e_3,e_2),
inference(forward_subsumption_resolution__resolution,[status(thm)],[197367008,197731488,197731488,176912232]),
[] ).
cnf(176874872,plain,
( ~ product(e_2,A,B)
| ~ product(e_2,B,C)
| ~ product(C,A,e_3) ),
inference(resolution,[status(thm)],[168702768,176767360]),
[] ).
cnf(199521128,plain,
~ product(e_2,A,e_3),
inference(resolution,[status(thm)],[199265624,176874872]),
[] ).
cnf(199351920,plain,
~ product(e_2,e_1,e_2),
inference(resolution,[status(thm)],[199265624,176784192]),
[] ).
cnf(189265848,plain,
( product(e_1,e_1,e_3)
| ~ product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[189185496,176734240]),
[] ).
cnf(176847656,plain,
( ~ product(A,e_2,B)
| ~ product(A,B,C)
| ~ product(C,e_1,A) ),
inference(resolution,[status(thm)],[168702768,176701872]),
[] ).
cnf(189845704,plain,
~ product(e_2,e_1,e_1),
inference(forward_subsumption_resolution__resolution,[status(thm)],[189265848,188074656,176847656]),
[] ).
cnf(176638000,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(resolution,[status(thm)],[176562904,168627680]),
[] ).
cnf(190034792,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(resolution,[status(thm)],[189845704,176638000]),
[] ).
cnf(200265552,plain,
product(e_2,e_1,e_3),
inference(resolution,[status(thm)],[199351920,190034792]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[199521128,200265552]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 2 seconds
% START OF PROOF SEQUENCE
% fof(element_3,plain,(group_element(e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP130-1.003.tptp',unknown),[]).
%
% cnf(168635408,plain,(group_element(e_3)),inference(rewrite,[status(thm)],[element_3]),[]).
%
% fof(qg3,plain,(~product(A,B,C)|~product(A,C,D)|product(D,B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP130-1.003.tptp',unknown),[]).
%
% cnf(168702768,plain,(~product(A,B,C)|~product(A,C,D)|product(D,B,A)),inference(rewrite,[status(thm)],[qg3]),[]).
%
% 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/GRP130-1.003.tptp',unknown),[]).
%
% cnf(168698392,plain,(~product(A,B,C)|~product(D,B,C)|equalish(A,D)),inference(rewrite,[status(thm)],[product_left_cancellation]),[]).
%
% fof(e_1_is_not_e_3,plain,(~equalish(e_1,e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP130-1.003.tptp',unknown),[]).
%
% cnf(168643848,plain,(~equalish(e_1,e_3)),inference(rewrite,[status(thm)],[e_1_is_not_e_3]),[]).
%
% cnf(176807776,plain,(~product(e_1,A,B)|~product(e_3,A,B)),inference(resolution,[status(thm)],[168698392,168643848]),[]).
%
% cnf(176912232,plain,(~product(A,B,C)|~product(A,C,e_3)|~product(e_1,B,A)),inference(resolution,[status(thm)],[168702768,176807776]),[]).
%
% fof(product_total_function1,plain,(~group_element(A)|~group_element(B)|product(A,B,e_1)|product(A,B,e_2)|product(A,B,e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP130-1.003.tptp',unknown),[]).
%
% cnf(168674248,plain,(~group_element(A)|~group_element(B)|product(A,B,e_1)|product(A,B,e_2)|product(A,B,e_3)),inference(rewrite,[status(thm)],[product_total_function1]),[]).
%
% fof(element_1,plain,(group_element(e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP130-1.003.tptp',unknown),[]).
%
% cnf(168627680,plain,(group_element(e_1)),inference(rewrite,[status(thm)],[element_1]),[]).
%
% cnf(176515168,plain,(product(e_1,e_1,e_1)|product(e_1,e_1,e_2)|product(e_1,e_1,e_3)),inference(resolution,[status(thm)],[168674248,168627680]),[]).
%
% cnf(183192856,plain,(~product(e_1,A,e_1)|product(e_1,e_1,e_1)|product(e_1,e_1,e_2)),inference(resolution,[status(thm)],[176912232,176515168]),[]).
%
% 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/GRP130-1.003.tptp',unknown),[]).
%
% cnf(168694760,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/GRP130-1.003.tptp',unknown),[]).
%
% cnf(168639928,plain,(~equalish(e_1,e_2)),inference(rewrite,[status(thm)],[e_1_is_not_e_2]),[]).
%
% cnf(176701872,plain,(~product(A,e_1,B)|~product(A,e_2,B)),inference(resolution,[status(thm)],[168694760,168639928]),[]).
%
% cnf(178643856,plain,(product(e_1,e_1,e_2)|product(e_1,e_1,e_3)|~product(e_1,e_2,e_1)),inference(resolution,[status(thm)],[176515168,176701872]),[]).
%
% 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/GRP130-1.003.tptp',unknown),[]).
%
% cnf(168690528,plain,(~product(A,B,C)|~product(A,B,D)|equalish(C,D)),inference(rewrite,[status(thm)],[product_total_function2]),[]).
%
% cnf(176748336,plain,(~product(A,B,e_1)|~product(A,B,e_3)),inference(resolution,[status(thm)],[168690528,168643848]),[]).
%
% cnf(187621312,plain,(product(e_1,e_1,e_2)|~product(e_1,e_2,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[183192856,178643856,176748336]),[]).
%
% cnf(176734240,plain,(~product(e_1,A,B)|~product(e_2,A,B)),inference(resolution,[status(thm)],[168698392,168639928]),[]).
%
% cnf(176859072,plain,(~product(A,B,C)|~product(A,C,e_2)|~product(e_1,B,A)),inference(resolution,[status(thm)],[168702768,176734240]),[]).
%
% cnf(178894056,plain,(product(e_1,e_1,e_1)|product(e_1,e_1,e_3)|~product(e_1,A,e_1)),inference(resolution,[status(thm)],[176515168,176859072]),[]).
%
% cnf(176677432,plain,(~product(A,B,e_1)|~product(A,B,e_2)),inference(resolution,[status(thm)],[168690528,168639928]),[]).
%
% cnf(184538272,plain,(product(e_1,e_1,e_3)|~product(e_1,e_2,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[178894056,178643856,176677432]),[]).
%
% fof(e_2_is_not_e_3,plain,(~equalish(e_2,e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP130-1.003.tptp',unknown),[]).
%
% cnf(168651208,plain,(~equalish(e_2,e_3)),inference(rewrite,[status(thm)],[e_2_is_not_e_3]),[]).
%
% cnf(176767360,plain,(~product(A,B,e_2)|~product(A,B,e_3)),inference(resolution,[status(thm)],[168690528,168651208]),[]).
%
% cnf(187898064,plain,(~product(e_1,e_2,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[187621312,184538272,176767360]),[]).
%
% fof(element_2,plain,(group_element(e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP130-1.003.tptp',unknown),[]).
%
% cnf(168631632,plain,(group_element(e_2)),inference(rewrite,[status(thm)],[element_2]),[]).
%
% cnf(176614024,plain,(~group_element(A)|product(A,e_2,e_1)|product(A,e_2,e_2)|product(A,e_2,e_3)),inference(resolution,[status(thm)],[168674248,168631632]),[]).
%
% cnf(176661544,plain,(product(e_1,e_2,e_1)|product(e_1,e_2,e_2)|product(e_1,e_2,e_3)),inference(resolution,[status(thm)],[176614024,168627680]),[]).
%
% cnf(188037936,plain,(product(e_1,e_2,e_2)|product(e_1,e_2,e_3)),inference(resolution,[status(thm)],[187898064,176661544]),[]).
%
% cnf(188074656,plain,(product(e_1,e_2,e_2)|~product(e_1,e_1,e_3)),inference(resolution,[status(thm)],[188037936,176701872]),[]).
%
% cnf(176982160,plain,(product(B,B,A)|~product(B,B,C)|~product(B,C,A)),inference(resolution,[status(thm)],[168702768,168702768]),[]).
%
% cnf(188229136,plain,(product(e_1,e_2,e_2)|~product(e_1,e_1,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[188074656,188037936,176982160]),[]).
%
% cnf(188070152,plain,(product(e_1,e_2,e_3)|~product(e_1,e_1,e_2)),inference(resolution,[status(thm)],[188037936,176701872]),[]).
%
% cnf(189048856,plain,(~product(e_1,e_1,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[188229136,188070152,176767360]),[]).
%
% cnf(189185496,plain,(product(e_1,e_1,e_1)|product(e_1,e_1,e_3)),inference(resolution,[status(thm)],[189048856,176515168]),[]).
%
% cnf(189519720,plain,(product(e_1,e_1,e_1)|~product(e_1,A,e_1)),inference(resolution,[status(thm)],[189185496,176912232]),[]).
%
% cnf(176784192,plain,(~product(A,e_1,B)|~product(A,e_3,B)),inference(resolution,[status(thm)],[168694760,168643848]),[]).
%
% cnf(189275352,plain,(product(e_1,e_1,e_3)|~product(e_1,e_3,e_1)),inference(resolution,[status(thm)],[189185496,176784192]),[]).
%
% cnf(196953048,plain,(~product(e_1,e_3,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[189519720,189275352,176748336]),[]).
%
% cnf(176490856,plain,(~group_element(A)|product(e_1,A,e_1)|product(e_1,A,e_2)|product(e_1,A,e_3)),inference(resolution,[status(thm)],[168674248,168627680]),[]).
%
% cnf(197173816,plain,(product(e_1,e_3,e_2)|product(e_1,e_3,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[168635408,196953048,176490856]),[]).
%
% cnf(197367008,plain,(product(e_1,e_3,e_2)|~product(e_2,e_3,e_3)),inference(resolution,[status(thm)],[197173816,176734240]),[]).
%
% cnf(176791048,plain,(~product(A,e_2,B)|~product(A,e_3,B)),inference(resolution,[status(thm)],[168694760,168651208]),[]).
%
% cnf(188093144,plain,(product(e_1,e_2,e_2)|~product(e_1,e_3,e_3)),inference(resolution,[status(thm)],[188037936,176791048]),[]).
%
% cnf(176898728,plain,(~product(A,e_2,B)|~product(A,B,C)|~product(C,e_3,A)),inference(resolution,[status(thm)],[168702768,176791048]),[]).
%
% cnf(191864176,plain,(~product(e_1,e_3,e_3)|~product(e_2,e_3,e_1)),inference(resolution,[status(thm)],[188093144,176898728]),[]).
%
% cnf(188323592,plain,(product(e_1,e_2,e_3)|~product(e_2,e_3,e_1)),inference(resolution,[status(thm)],[188037936,176898728]),[]).
%
% cnf(197624000,plain,(~product(e_2,e_3,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[191864176,188323592,197173816,176898728]),[]).
%
% cnf(176562904,plain,(~group_element(A)|product(e_2,A,e_1)|product(e_2,A,e_2)|product(e_2,A,e_3)),inference(resolution,[status(thm)],[168674248,168631632]),[]).
%
% cnf(197731488,plain,(product(e_2,e_3,e_2)|product(e_2,e_3,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[168635408,197624000,176562904]),[]).
%
% cnf(199265624,plain,(product(e_2,e_3,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[197367008,197731488,197731488,176912232]),[]).
%
% cnf(176874872,plain,(~product(e_2,A,B)|~product(e_2,B,C)|~product(C,A,e_3)),inference(resolution,[status(thm)],[168702768,176767360]),[]).
%
% cnf(199521128,plain,(~product(e_2,A,e_3)),inference(resolution,[status(thm)],[199265624,176874872]),[]).
%
% cnf(199351920,plain,(~product(e_2,e_1,e_2)),inference(resolution,[status(thm)],[199265624,176784192]),[]).
%
% cnf(189265848,plain,(product(e_1,e_1,e_3)|~product(e_2,e_1,e_1)),inference(resolution,[status(thm)],[189185496,176734240]),[]).
%
% cnf(176847656,plain,(~product(A,e_2,B)|~product(A,B,C)|~product(C,e_1,A)),inference(resolution,[status(thm)],[168702768,176701872]),[]).
%
% cnf(189845704,plain,(~product(e_2,e_1,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[189265848,188074656,176847656]),[]).
%
% cnf(176638000,plain,(product(e_2,e_1,e_1)|product(e_2,e_1,e_2)|product(e_2,e_1,e_3)),inference(resolution,[status(thm)],[176562904,168627680]),[]).
%
% cnf(190034792,plain,(product(e_2,e_1,e_2)|product(e_2,e_1,e_3)),inference(resolution,[status(thm)],[189845704,176638000]),[]).
%
% cnf(200265552,plain,(product(e_2,e_1,e_3)),inference(resolution,[status(thm)],[199351920,190034792]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[199521128,200265552]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------