TSTP Solution File: GRP129-1.003 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP129-1.003 : TPTP v3.4.2. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art10.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 12:27:18 EDT 2009
% Result : Unsatisfiable 1.1s
% Output : Refutation 1.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 11
% Syntax : Number of formulae : 74 ( 25 unt; 0 def)
% Number of atoms : 155 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 168 ( 87 ~; 81 |; 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 : 79 ( 4 sgn 18 !; 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)
| product(A,B,e_3) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP129-1.003.tptp',unknown),
[] ).
cnf(143993384,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/GRP129-1.003.tptp',unknown),
[] ).
cnf(143942728,plain,
group_element(e_1),
inference(rewrite,[status(thm)],[element_1]),
[] ).
cnf(151853880,plain,
( ~ group_element(A)
| product(A,e_1,e_1)
| product(A,e_1,e_2)
| product(A,e_1,e_3) ),
inference(resolution,[status(thm)],[143993384,143942728]),
[] ).
fof(element_2,plain,
group_element(e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP129-1.003.tptp',unknown),
[] ).
cnf(143946680,plain,
group_element(e_2),
inference(rewrite,[status(thm)],[element_2]),
[] ).
cnf(151877088,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)],[151853880,143946680]),
[] ).
fof(qg3,plain,
! [A,B,C,D] :
( ~ product(A,B,C)
| ~ product(B,C,D)
| product(C,A,D) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP129-1.003.tptp',unknown),
[] ).
cnf(144017816,plain,
( ~ product(A,B,C)
| ~ product(B,C,D)
| product(C,A,D) ),
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/GRP129-1.003.tptp',unknown),
[] ).
cnf(144013440,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_2,plain,
~ equalish(e_1,e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP129-1.003.tptp',unknown),
[] ).
cnf(143954976,plain,
~ equalish(e_1,e_2),
inference(rewrite,[status(thm)],[e_1_is_not_e_2]),
[] ).
cnf(152020776,plain,
( ~ product(e_1,A,B)
| ~ product(e_2,A,B) ),
inference(resolution,[status(thm)],[144013440,143954976]),
[] ).
cnf(152151976,plain,
( ~ product(A,B,e_2)
| ~ product(B,e_2,C)
| ~ product(e_1,A,C) ),
inference(resolution,[status(thm)],[144017816,152020776]),
[] ).
cnf(155396768,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_3)
| ~ product(e_1,e_2,A) ),
inference(resolution,[status(thm)],[151877088,152151976]),
[] ).
cnf(151830216,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)],[143993384,143942728]),
[] ).
cnf(153711272,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_3)
| ~ product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[151830216,152020776]),
[] ).
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/GRP129-1.003.tptp',unknown),
[] ).
cnf(144009808,plain,
( ~ product(A,B,C)
| ~ product(A,D,C)
| equalish(B,D) ),
inference(rewrite,[status(thm)],[product_right_cancellation]),
[] ).
cnf(151994944,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_2,B) ),
inference(resolution,[status(thm)],[144009808,143954976]),
[] ).
cnf(152140536,plain,
( ~ product(e_2,A,B)
| ~ product(A,B,C)
| ~ product(B,e_1,C) ),
inference(resolution,[status(thm)],[144017816,151994944]),
[] ).
cnf(161258600,plain,
( product(e_1,e_1,e_3)
| ~ product(e_2,e_1,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[153711272,153711272,152140536]),
[] ).
cnf(161530832,plain,
~ product(e_2,e_1,e_1),
inference(forward_subsumption_resolution__resolution,[status(thm)],[161258600,161258600,152140536]),
[] ).
cnf(161588680,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(resolution,[status(thm)],[161530832,151877088]),
[] ).
cnf(152146632,plain,
( ~ product(A,B,e_1)
| ~ product(B,e_1,C)
| ~ product(e_2,A,C) ),
inference(resolution,[status(thm)],[144017816,152020776]),
[] ).
cnf(152441280,plain,
( ~ product(e_2,e_1,e_1)
| ~ product(e_2,A,e_2)
| ~ product(A,e_2,e_1) ),
inference(resolution,[status(thm)],[152146632,144017816]),
[] ).
cnf(161901592,plain,
( product(e_2,e_1,e_3)
| ~ product(e_1,e_2,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[155396768,161588680,152441280]),
[] ).
cnf(164640640,plain,
~ product(e_1,e_2,e_1),
inference(resolution,[status(thm)],[161901592,152146632]),
[] ).
cnf(151805904,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)],[143993384,143942728]),
[] ).
cnf(151900560,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)],[151805904,143946680]),
[] ).
cnf(164694744,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(resolution,[status(thm)],[164640640,151900560]),
[] ).
cnf(161825560,plain,
( product(e_2,e_1,e_3)
| ~ product(e_1,e_2,A) ),
inference(resolution,[status(thm)],[161588680,152151976]),
[] ).
cnf(164896880,plain,
( product(e_1,e_2,e_2)
| product(e_2,e_1,e_3) ),
inference(resolution,[status(thm)],[164694744,161825560]),
[] ).
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/GRP129-1.003.tptp',unknown),
[] ).
cnf(144005576,plain,
( ~ product(A,B,C)
| ~ product(A,B,D)
| equalish(C,D) ),
inference(rewrite,[status(thm)],[product_total_function2]),
[] ).
fof(e_2_is_not_e_3,plain,
~ equalish(e_2,e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP129-1.003.tptp',unknown),
[] ).
cnf(143966256,plain,
~ equalish(e_2,e_3),
inference(rewrite,[status(thm)],[e_2_is_not_e_3]),
[] ).
cnf(152084192,plain,
( ~ product(A,B,e_2)
| ~ product(A,B,e_3) ),
inference(resolution,[status(thm)],[144005576,143966256]),
[] ).
cnf(164351784,plain,
( ~ product(e_1,e_2,A)
| ~ product(e_2,e_1,e_2) ),
inference(resolution,[status(thm)],[161825560,152084192]),
[] ).
cnf(164916488,plain,
~ product(e_2,e_1,e_2),
inference(forward_subsumption_resolution__resolution,[status(thm)],[164896880,164351784,164694744,152140536]),
[] ).
cnf(161627760,plain,
( product(e_2,e_1,e_2)
| ~ product(e_2,e_2,e_3) ),
inference(resolution,[status(thm)],[161588680,151994944]),
[] ).
cnf(165064328,plain,
~ product(e_2,e_2,e_3),
inference(resolution,[status(thm)],[164916488,161627760]),
[] ).
cnf(152855080,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3) ),
inference(resolution,[status(thm)],[143993384,143946680]),
[] ).
cnf(165354616,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[165064328,152855080]),
[] ).
cnf(167985904,plain,
( product(e_2,e_2,e_2)
| ~ product(A,e_2,e_2)
| product(e_2,A,e_1) ),
inference(resolution,[status(thm)],[165354616,144017816]),
[] ).
cnf(151968864,plain,
( ~ product(A,B,e_1)
| ~ product(A,B,e_2) ),
inference(resolution,[status(thm)],[144005576,143954976]),
[] ).
cnf(152118000,plain,
( ~ product(A,B,C)
| ~ product(B,C,e_1)
| ~ product(C,A,e_2) ),
inference(resolution,[status(thm)],[144017816,151968864]),
[] ).
cnf(168014448,plain,
( product(e_2,e_2,e_2)
| ~ product(e_1,e_2,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[167985904,165354616,152118000]),
[] ).
cnf(164746720,plain,
( product(e_1,e_2,e_3)
| ~ product(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[164694744,152020776]),
[] ).
cnf(170508856,plain,
~ product(e_1,e_2,e_2),
inference(forward_subsumption_resolution__resolution,[status(thm)],[168014448,164746720,152084192]),
[] ).
cnf(170938792,plain,
product(e_1,e_2,e_3),
inference(resolution,[status(thm)],[170508856,164694744]),
[] ).
cnf(152111808,plain,
( ~ product(e_2,A,B)
| ~ product(e_3,A,B) ),
inference(resolution,[status(thm)],[144013440,143966256]),
[] ).
cnf(167893040,plain,
( product(e_2,e_2,e_1)
| ~ product(e_3,e_2,e_2) ),
inference(resolution,[status(thm)],[165354616,152111808]),
[] ).
fof(element_3,plain,
group_element(e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP129-1.003.tptp',unknown),
[] ).
cnf(143950456,plain,
group_element(e_3),
inference(rewrite,[status(thm)],[element_3]),
[] ).
cnf(165053416,plain,
product(e_2,e_1,e_3),
inference(resolution,[status(thm)],[164916488,161588680]),
[] ).
cnf(165177104,plain,
( ~ product(A,e_2,e_1)
| product(e_1,A,e_3) ),
inference(resolution,[status(thm)],[165053416,144017816]),
[] ).
fof(e_1_is_not_e_3,plain,
~ equalish(e_1,e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP129-1.003.tptp',unknown),
[] ).
cnf(143958896,plain,
~ equalish(e_1,e_3),
inference(rewrite,[status(thm)],[e_1_is_not_e_3]),
[] ).
cnf(152033400,plain,
( ~ product(A,B,e_1)
| ~ product(A,B,e_3) ),
inference(resolution,[status(thm)],[144005576,143958896]),
[] ).
cnf(152165944,plain,
( ~ product(A,B,C)
| ~ product(B,C,e_3)
| ~ product(C,A,e_1) ),
inference(resolution,[status(thm)],[144017816,152033400]),
[] ).
cnf(165224528,plain,
~ product(e_3,e_2,e_1),
inference(forward_subsumption_resolution__resolution,[status(thm)],[165177104,165053416,152165944]),
[] ).
cnf(165521200,plain,
( product(e_3,e_2,e_2)
| product(e_3,e_2,e_3) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[143946680,143950456,165224528,143993384]),
[] ).
cnf(152103288,plain,
( ~ product(A,e_2,B)
| ~ product(A,e_3,B) ),
inference(resolution,[status(thm)],[144009808,143966256]),
[] ).
cnf(152205144,plain,
( ~ product(e_3,A,B)
| ~ product(A,B,C)
| ~ product(B,e_2,C) ),
inference(resolution,[status(thm)],[144017816,152103288]),
[] ).
cnf(169235600,plain,
( product(e_3,e_2,e_3)
| ~ product(e_2,e_2,A) ),
inference(resolution,[status(thm)],[165521200,152205144]),
[] ).
cnf(152069456,plain,
( ~ product(e_1,A,B)
| ~ product(e_3,A,B) ),
inference(resolution,[status(thm)],[144013440,143958896]),
[] ).
cnf(170504760,plain,
~ product(e_2,e_2,e_2),
inference(forward_subsumption_resolution__resolution,[status(thm)],[169235600,164746720,152069456]),
[] ).
cnf(170669384,plain,
product(e_2,e_2,e_1),
inference(resolution,[status(thm)],[170504760,165354616]),
[] ).
cnf(170886608,plain,
~ product(e_3,e_2,e_2),
inference(forward_subsumption_resolution__resolution,[status(thm)],[167893040,170669384,152205144]),
[] ).
cnf(171694056,plain,
product(e_3,e_2,e_3),
inference(resolution,[status(thm)],[170886608,165521200]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[170938792,171694056,152069456]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 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)|product(A,B,e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP129-1.003.tptp',unknown),[]).
%
% cnf(143993384,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/GRP129-1.003.tptp',unknown),[]).
%
% cnf(143942728,plain,(group_element(e_1)),inference(rewrite,[status(thm)],[element_1]),[]).
%
% cnf(151853880,plain,(~group_element(A)|product(A,e_1,e_1)|product(A,e_1,e_2)|product(A,e_1,e_3)),inference(resolution,[status(thm)],[143993384,143942728]),[]).
%
% fof(element_2,plain,(group_element(e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP129-1.003.tptp',unknown),[]).
%
% cnf(143946680,plain,(group_element(e_2)),inference(rewrite,[status(thm)],[element_2]),[]).
%
% cnf(151877088,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)],[151853880,143946680]),[]).
%
% fof(qg3,plain,(~product(A,B,C)|~product(B,C,D)|product(C,A,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP129-1.003.tptp',unknown),[]).
%
% cnf(144017816,plain,(~product(A,B,C)|~product(B,C,D)|product(C,A,D)),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/GRP129-1.003.tptp',unknown),[]).
%
% cnf(144013440,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_2,plain,(~equalish(e_1,e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP129-1.003.tptp',unknown),[]).
%
% cnf(143954976,plain,(~equalish(e_1,e_2)),inference(rewrite,[status(thm)],[e_1_is_not_e_2]),[]).
%
% cnf(152020776,plain,(~product(e_1,A,B)|~product(e_2,A,B)),inference(resolution,[status(thm)],[144013440,143954976]),[]).
%
% cnf(152151976,plain,(~product(A,B,e_2)|~product(B,e_2,C)|~product(e_1,A,C)),inference(resolution,[status(thm)],[144017816,152020776]),[]).
%
% cnf(155396768,plain,(product(e_2,e_1,e_1)|product(e_2,e_1,e_3)|~product(e_1,e_2,A)),inference(resolution,[status(thm)],[151877088,152151976]),[]).
%
% cnf(151830216,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)],[143993384,143942728]),[]).
%
% cnf(153711272,plain,(product(e_1,e_1,e_2)|product(e_1,e_1,e_3)|~product(e_2,e_1,e_1)),inference(resolution,[status(thm)],[151830216,152020776]),[]).
%
% 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/GRP129-1.003.tptp',unknown),[]).
%
% cnf(144009808,plain,(~product(A,B,C)|~product(A,D,C)|equalish(B,D)),inference(rewrite,[status(thm)],[product_right_cancellation]),[]).
%
% cnf(151994944,plain,(~product(A,e_1,B)|~product(A,e_2,B)),inference(resolution,[status(thm)],[144009808,143954976]),[]).
%
% cnf(152140536,plain,(~product(e_2,A,B)|~product(A,B,C)|~product(B,e_1,C)),inference(resolution,[status(thm)],[144017816,151994944]),[]).
%
% cnf(161258600,plain,(product(e_1,e_1,e_3)|~product(e_2,e_1,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[153711272,153711272,152140536]),[]).
%
% cnf(161530832,plain,(~product(e_2,e_1,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[161258600,161258600,152140536]),[]).
%
% cnf(161588680,plain,(product(e_2,e_1,e_2)|product(e_2,e_1,e_3)),inference(resolution,[status(thm)],[161530832,151877088]),[]).
%
% cnf(152146632,plain,(~product(A,B,e_1)|~product(B,e_1,C)|~product(e_2,A,C)),inference(resolution,[status(thm)],[144017816,152020776]),[]).
%
% cnf(152441280,plain,(~product(e_2,e_1,e_1)|~product(e_2,A,e_2)|~product(A,e_2,e_1)),inference(resolution,[status(thm)],[152146632,144017816]),[]).
%
% cnf(161901592,plain,(product(e_2,e_1,e_3)|~product(e_1,e_2,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[155396768,161588680,152441280]),[]).
%
% cnf(164640640,plain,(~product(e_1,e_2,e_1)),inference(resolution,[status(thm)],[161901592,152146632]),[]).
%
% cnf(151805904,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)],[143993384,143942728]),[]).
%
% cnf(151900560,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)],[151805904,143946680]),[]).
%
% cnf(164694744,plain,(product(e_1,e_2,e_2)|product(e_1,e_2,e_3)),inference(resolution,[status(thm)],[164640640,151900560]),[]).
%
% cnf(161825560,plain,(product(e_2,e_1,e_3)|~product(e_1,e_2,A)),inference(resolution,[status(thm)],[161588680,152151976]),[]).
%
% cnf(164896880,plain,(product(e_1,e_2,e_2)|product(e_2,e_1,e_3)),inference(resolution,[status(thm)],[164694744,161825560]),[]).
%
% 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/GRP129-1.003.tptp',unknown),[]).
%
% cnf(144005576,plain,(~product(A,B,C)|~product(A,B,D)|equalish(C,D)),inference(rewrite,[status(thm)],[product_total_function2]),[]).
%
% fof(e_2_is_not_e_3,plain,(~equalish(e_2,e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP129-1.003.tptp',unknown),[]).
%
% cnf(143966256,plain,(~equalish(e_2,e_3)),inference(rewrite,[status(thm)],[e_2_is_not_e_3]),[]).
%
% cnf(152084192,plain,(~product(A,B,e_2)|~product(A,B,e_3)),inference(resolution,[status(thm)],[144005576,143966256]),[]).
%
% cnf(164351784,plain,(~product(e_1,e_2,A)|~product(e_2,e_1,e_2)),inference(resolution,[status(thm)],[161825560,152084192]),[]).
%
% cnf(164916488,plain,(~product(e_2,e_1,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[164896880,164351784,164694744,152140536]),[]).
%
% cnf(161627760,plain,(product(e_2,e_1,e_2)|~product(e_2,e_2,e_3)),inference(resolution,[status(thm)],[161588680,151994944]),[]).
%
% cnf(165064328,plain,(~product(e_2,e_2,e_3)),inference(resolution,[status(thm)],[164916488,161627760]),[]).
%
% cnf(152855080,plain,(product(e_2,e_2,e_1)|product(e_2,e_2,e_2)|product(e_2,e_2,e_3)),inference(resolution,[status(thm)],[143993384,143946680]),[]).
%
% cnf(165354616,plain,(product(e_2,e_2,e_1)|product(e_2,e_2,e_2)),inference(resolution,[status(thm)],[165064328,152855080]),[]).
%
% cnf(167985904,plain,(product(e_2,e_2,e_2)|~product(A,e_2,e_2)|product(e_2,A,e_1)),inference(resolution,[status(thm)],[165354616,144017816]),[]).
%
% cnf(151968864,plain,(~product(A,B,e_1)|~product(A,B,e_2)),inference(resolution,[status(thm)],[144005576,143954976]),[]).
%
% cnf(152118000,plain,(~product(A,B,C)|~product(B,C,e_1)|~product(C,A,e_2)),inference(resolution,[status(thm)],[144017816,151968864]),[]).
%
% cnf(168014448,plain,(product(e_2,e_2,e_2)|~product(e_1,e_2,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[167985904,165354616,152118000]),[]).
%
% cnf(164746720,plain,(product(e_1,e_2,e_3)|~product(e_2,e_2,e_2)),inference(resolution,[status(thm)],[164694744,152020776]),[]).
%
% cnf(170508856,plain,(~product(e_1,e_2,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[168014448,164746720,152084192]),[]).
%
% cnf(170938792,plain,(product(e_1,e_2,e_3)),inference(resolution,[status(thm)],[170508856,164694744]),[]).
%
% cnf(152111808,plain,(~product(e_2,A,B)|~product(e_3,A,B)),inference(resolution,[status(thm)],[144013440,143966256]),[]).
%
% cnf(167893040,plain,(product(e_2,e_2,e_1)|~product(e_3,e_2,e_2)),inference(resolution,[status(thm)],[165354616,152111808]),[]).
%
% fof(element_3,plain,(group_element(e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP129-1.003.tptp',unknown),[]).
%
% cnf(143950456,plain,(group_element(e_3)),inference(rewrite,[status(thm)],[element_3]),[]).
%
% cnf(165053416,plain,(product(e_2,e_1,e_3)),inference(resolution,[status(thm)],[164916488,161588680]),[]).
%
% cnf(165177104,plain,(~product(A,e_2,e_1)|product(e_1,A,e_3)),inference(resolution,[status(thm)],[165053416,144017816]),[]).
%
% fof(e_1_is_not_e_3,plain,(~equalish(e_1,e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP129-1.003.tptp',unknown),[]).
%
% cnf(143958896,plain,(~equalish(e_1,e_3)),inference(rewrite,[status(thm)],[e_1_is_not_e_3]),[]).
%
% cnf(152033400,plain,(~product(A,B,e_1)|~product(A,B,e_3)),inference(resolution,[status(thm)],[144005576,143958896]),[]).
%
% cnf(152165944,plain,(~product(A,B,C)|~product(B,C,e_3)|~product(C,A,e_1)),inference(resolution,[status(thm)],[144017816,152033400]),[]).
%
% cnf(165224528,plain,(~product(e_3,e_2,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[165177104,165053416,152165944]),[]).
%
% cnf(165521200,plain,(product(e_3,e_2,e_2)|product(e_3,e_2,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[143946680,143950456,165224528,143993384]),[]).
%
% cnf(152103288,plain,(~product(A,e_2,B)|~product(A,e_3,B)),inference(resolution,[status(thm)],[144009808,143966256]),[]).
%
% cnf(152205144,plain,(~product(e_3,A,B)|~product(A,B,C)|~product(B,e_2,C)),inference(resolution,[status(thm)],[144017816,152103288]),[]).
%
% cnf(169235600,plain,(product(e_3,e_2,e_3)|~product(e_2,e_2,A)),inference(resolution,[status(thm)],[165521200,152205144]),[]).
%
% cnf(152069456,plain,(~product(e_1,A,B)|~product(e_3,A,B)),inference(resolution,[status(thm)],[144013440,143958896]),[]).
%
% cnf(170504760,plain,(~product(e_2,e_2,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[169235600,164746720,152069456]),[]).
%
% cnf(170669384,plain,(product(e_2,e_2,e_1)),inference(resolution,[status(thm)],[170504760,165354616]),[]).
%
% cnf(170886608,plain,(~product(e_3,e_2,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[167893040,170669384,152205144]),[]).
%
% cnf(171694056,plain,(product(e_3,e_2,e_3)),inference(resolution,[status(thm)],[170886608,165521200]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[170938792,171694056,152069456]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------