TSTP Solution File: GRP124-4.004 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP124-4.004 : TPTP v3.4.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art08.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 12:25:33 EDT 2009
% Result : Unsatisfiable 327.2s
% Output : Refutation 327.2s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 22
% Syntax : Number of formulae : 126 ( 60 unt; 0 def)
% Number of atoms : 333 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 419 ( 212 ~; 207 |; 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 : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 145 ( 0 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
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/GRP124-4.004.tptp',unknown),
[] ).
cnf(162936832,plain,
( ~ product(A,B,C)
| ~ product(A,D,C)
| equalish(B,D) ),
inference(rewrite,[status(thm)],[product_right_cancellation]),
[] ).
fof(product_idempotence,plain,
! [A] : product(A,A,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-4.004.tptp',unknown),
[] ).
cnf(162944728,plain,
product(A,A,A),
inference(rewrite,[status(thm)],[product_idempotence]),
[] ).
cnf(174502744,plain,
( ~ product(A,B,A)
| equalish(A,B) ),
inference(resolution,[status(thm)],[162936832,162944728]),
[] ).
fof(e_4_is_not_e_3,plain,
~ equalish(e_4,e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-4.004.tptp',unknown),
[] ).
cnf(162816416,plain,
~ equalish(e_4,e_3),
inference(rewrite,[status(thm)],[e_4_is_not_e_3]),
[] ).
cnf(174636232,plain,
~ product(e_4,e_3,e_4),
inference(resolution,[status(thm)],[174502744,162816416]),
[] ).
fof(element_4,plain,
group_element(e_4),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-4.004.tptp',unknown),
[] ).
cnf(162858008,plain,
group_element(e_4),
inference(rewrite,[status(thm)],[element_4]),
[] ).
fof(element_1,plain,
group_element(e_1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-4.004.tptp',unknown),
[] ).
cnf(162842480,plain,
group_element(e_1),
inference(rewrite,[status(thm)],[element_1]),
[] ).
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/GRP124-4.004.tptp',unknown),
[] ).
cnf(162932560,plain,
( ~ product(A,B,C)
| ~ product(A,B,D)
| equalish(C,D) ),
inference(rewrite,[status(thm)],[product_total_function2]),
[] ).
cnf(174274272,plain,
( ~ product(A,A,B)
| equalish(A,B) ),
inference(resolution,[status(thm)],[162932560,162944728]),
[] ).
fof(e_2_is_not_e_4,plain,
~ equalish(e_2,e_4),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-4.004.tptp',unknown),
[] ).
cnf(162881168,plain,
~ equalish(e_2,e_4),
inference(rewrite,[status(thm)],[e_2_is_not_e_4]),
[] ).
cnf(174365720,plain,
~ product(e_2,e_2,e_4),
inference(resolution,[status(thm)],[174274272,162881168]),
[] ).
fof(e_4_is_not_e_2,plain,
~ equalish(e_4,e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-4.004.tptp',unknown),
[] ).
cnf(162903704,plain,
~ equalish(e_4,e_2),
inference(rewrite,[status(thm)],[e_4_is_not_e_2]),
[] ).
cnf(174622864,plain,
~ product(e_4,e_2,e_4),
inference(resolution,[status(thm)],[174502744,162903704]),
[] ).
fof(element_2,plain,
group_element(e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-4.004.tptp',unknown),
[] ).
cnf(162846432,plain,
group_element(e_2),
inference(rewrite,[status(thm)],[element_2]),
[] ).
fof(qg2_2,plain,
! [A,B,C,D,E,F] :
( ~ product(A,B,C)
| ~ product(D,E,C)
| ~ product(F,A,B)
| ~ product(F,D,E)
| equalish(B,E) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-4.004.tptp',unknown),
[] ).
cnf(162957608,plain,
( ~ product(A,B,C)
| ~ product(D,E,C)
| ~ product(F,A,B)
| ~ product(F,D,E)
| equalish(B,E) ),
inference(rewrite,[status(thm)],[qg2_2]),
[] ).
cnf(176017336,plain,
( ~ product(B,C,A)
| ~ product(A,B,C)
| equalish(A,C) ),
inference(resolution,[status(thm)],[162957608,162944728]),
[] ).
cnf(176158248,plain,
( ~ product(A,e_2,e_4)
| ~ product(e_4,A,e_2) ),
inference(resolution,[status(thm)],[176017336,162903704]),
[] ).
fof(row_surjectivity,plain,
! [A,B] :
( ~ group_element(A)
| ~ group_element(B)
| product(e_1,A,B)
| product(e_2,A,B)
| product(e_3,A,B)
| product(e_4,A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-4.004.tptp',unknown),
[] ).
cnf(162828504,plain,
( ~ group_element(A)
| ~ group_element(B)
| product(e_1,A,B)
| product(e_2,A,B)
| product(e_3,A,B)
| product(e_4,A,B) ),
inference(rewrite,[status(thm)],[row_surjectivity]),
[] ).
cnf(177709528,plain,
( ~ product(e_4,e_1,e_2)
| product(e_3,e_2,e_4) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[174365720,174622864,162858008,162846432,176158248,162828504]),
[] ).
fof(e_2_is_not_e_1,plain,
~ equalish(e_2,e_1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-4.004.tptp',unknown),
[] ).
cnf(162817344,plain,
~ equalish(e_2,e_1),
inference(rewrite,[status(thm)],[e_2_is_not_e_1]),
[] ).
cnf(174338696,plain,
~ product(e_2,e_2,e_1),
inference(resolution,[status(thm)],[174274272,162817344]),
[] ).
fof(e_1_is_not_e_2,plain,
~ equalish(e_1,e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-4.004.tptp',unknown),
[] ).
cnf(162862344,plain,
~ equalish(e_1,e_2),
inference(rewrite,[status(thm)],[e_1_is_not_e_2]),
[] ).
cnf(174514776,plain,
~ product(e_1,e_2,e_1),
inference(resolution,[status(thm)],[174502744,162862344]),
[] ).
cnf(175605040,plain,
( ~ group_element(A)
| ~ group_element(B)
| product(e_1,A,B)
| product(e_2,A,B)
| product(e_4,A,B)
| ~ product(e_3,A,C)
| equalish(B,C) ),
inference(resolution,[status(thm)],[162828504,162932560]),
[] ).
fof(e_1_is_not_e_4,plain,
~ equalish(e_1,e_4),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-4.004.tptp',unknown),
[] ).
cnf(162870024,plain,
~ equalish(e_1,e_4),
inference(rewrite,[status(thm)],[e_1_is_not_e_4]),
[] ).
cnf(184965496,plain,
( ~ group_element(A)
| product(e_1,A,e_1)
| product(e_2,A,e_1)
| product(e_4,A,e_1)
| ~ product(e_3,A,e_4) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[162842480,175605040,162870024]),
[] ).
cnf(185146920,plain,
( product(e_4,e_2,e_1)
| ~ product(e_3,e_2,e_4) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[174338696,174514776,184965496,162846432]),
[] ).
cnf(174308984,plain,
~ product(e_1,e_1,e_2),
inference(resolution,[status(thm)],[174274272,162862344]),
[] ).
cnf(174540016,plain,
~ product(e_2,e_1,e_2),
inference(resolution,[status(thm)],[174502744,162817344]),
[] ).
cnf(174079808,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_2,B) ),
inference(resolution,[status(thm)],[162936832,162862344]),
[] ).
cnf(174114208,plain,
( ~ product(A,e_1,B)
| ~ product(C,e_2,B)
| ~ product(D,A,e_1)
| ~ product(D,C,e_2) ),
inference(resolution,[status(thm)],[162957608,162862344]),
[] ).
cnf(178091544,plain,
( ~ product(A,e_1,B)
| ~ product(C,e_2,B)
| ~ product(e_3,C,e_2)
| ~ group_element(A)
| product(e_1,A,e_1)
| product(e_2,A,e_1)
| product(e_4,A,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[162842480,174114208,162828504]),
[] ).
cnf(203822096,plain,
( ~ product(e_2,e_1,A)
| ~ product(B,e_2,A)
| ~ product(e_3,B,e_2)
| product(e_4,e_2,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[174338696,174514776,178091544,162846432]),
[] ).
cnf(203847056,plain,
( ~ product(e_2,e_1,A)
| ~ product(e_3,e_1,e_2)
| product(e_4,e_2,e_1)
| ~ group_element(A)
| product(e_3,e_2,A)
| product(e_4,e_2,A) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[174079808,162846432,203822096,162828504]),
[] ).
cnf(203885816,plain,
( ~ product(e_2,e_1,A)
| product(e_4,e_2,e_1)
| ~ group_element(A)
| product(e_3,e_2,A)
| product(e_4,e_2,A)
| product(e_4,e_1,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[162842480,162846432,174308984,174540016,203847056,162828504]),
[] ).
cnf(203897848,plain,
( ~ product(e_2,e_1,e_4)
| product(e_4,e_2,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[177709528,185146920,174622864,203885816,162858008]),
[] ).
cnf(203926744,plain,
( product(e_4,e_2,e_1)
| product(e_1,e_1,e_4)
| product(e_3,e_1,e_4)
| product(e_4,e_1,e_4) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[162858008,162842480,203897848,162828504]),
[] ).
fof(e_4_is_not_e_1,plain,
~ equalish(e_4,e_1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-4.004.tptp',unknown),
[] ).
cnf(162900056,plain,
~ equalish(e_4,e_1),
inference(rewrite,[status(thm)],[e_4_is_not_e_1]),
[] ).
cnf(174609496,plain,
~ product(e_4,e_1,e_4),
inference(resolution,[status(thm)],[174502744,162900056]),
[] ).
cnf(174330160,plain,
~ product(e_1,e_1,e_4),
inference(resolution,[status(thm)],[174274272,162870024]),
[] ).
cnf(174162904,plain,
( ~ product(A,e_1,B)
| ~ product(C,e_4,B)
| ~ product(D,A,e_1)
| ~ product(D,C,e_4) ),
inference(resolution,[status(thm)],[162957608,162870024]),
[] ).
cnf(178577880,plain,
( ~ product(B,e_4,A)
| ~ product(C,e_2,e_1)
| ~ product(C,B,e_4)
| ~ group_element(A)
| product(e_1,e_1,A)
| product(e_3,e_1,A)
| product(e_4,e_1,A) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[162842480,174162904,162828504]),
[] ).
cnf(205075840,plain,
product(e_3,e_1,e_4),
inference(forward_subsumption_resolution__resolution,[status(thm)],[203926744,174609496,174330160,162858008,178577880,162944728]),
[] ).
fof(e_1_is_not_e_3,plain,
~ equalish(e_1,e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-4.004.tptp',unknown),
[] ).
cnf(162866296,plain,
~ equalish(e_1,e_3),
inference(rewrite,[status(thm)],[e_1_is_not_e_3]),
[] ).
cnf(174468336,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_3,B) ),
inference(resolution,[status(thm)],[162936832,162866296]),
[] ).
fof(element_3,plain,
group_element(e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-4.004.tptp',unknown),
[] ).
cnf(162850168,plain,
group_element(e_3),
inference(rewrite,[status(thm)],[element_3]),
[] ).
cnf(175619232,plain,
( ~ group_element(A)
| ~ group_element(B)
| product(e_1,A,B)
| product(e_2,A,B)
| product(e_3,A,B)
| ~ product(e_4,A,C)
| equalish(B,C) ),
inference(resolution,[status(thm)],[162828504,162932560]),
[] ).
cnf(185432264,plain,
( ~ group_element(A)
| product(e_1,A,e_1)
| product(e_2,A,e_1)
| product(e_3,A,e_1)
| ~ product(e_4,A,e_3) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[162842480,175619232,162866296]),
[] ).
cnf(185604408,plain,
( product(e_3,e_2,e_1)
| ~ product(e_4,e_2,e_3) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[174338696,174514776,185432264,162846432]),
[] ).
fof(e_3_is_not_e_2,plain,
~ equalish(e_3,e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-4.004.tptp',unknown),
[] ).
cnf(162892680,plain,
~ equalish(e_3,e_2),
inference(rewrite,[status(thm)],[e_3_is_not_e_2]),
[] ).
cnf(174587720,plain,
~ product(e_3,e_2,e_3),
inference(resolution,[status(thm)],[174502744,162892680]),
[] ).
fof(qg2_1,plain,
! [A,B,C,D,E,F] :
( ~ product(A,B,C)
| ~ product(D,E,C)
| ~ product(F,A,B)
| ~ product(F,D,E)
| equalish(A,D) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-4.004.tptp',unknown),
[] ).
cnf(162953248,plain,
( ~ product(A,B,C)
| ~ product(D,E,C)
| ~ product(F,A,B)
| ~ product(F,D,E)
| equalish(A,D) ),
inference(rewrite,[status(thm)],[qg2_1]),
[] ).
cnf(175814504,plain,
( ~ product(B,C,A)
| ~ product(A,B,C)
| equalish(A,B) ),
inference(resolution,[status(thm)],[162953248,162944728]),
[] ).
cnf(175979864,plain,
( ~ product(e_2,A,e_4)
| ~ product(e_4,e_2,A) ),
inference(resolution,[status(thm)],[175814504,162903704]),
[] ).
cnf(185005264,plain,
( ~ group_element(A)
| product(e_1,A,e_4)
| product(e_2,A,e_4)
| product(e_4,A,e_4)
| ~ product(e_3,A,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[162858008,175605040,162903704]),
[] ).
cnf(185275120,plain,
( product(e_2,e_1,e_4)
| ~ product(e_3,e_1,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[174609496,174330160,185005264,162842480]),
[] ).
cnf(203854136,plain,
~ product(e_3,e_1,e_2),
inference(forward_subsumption_resolution__resolution,[status(thm)],[185146920,175979864,185275120,174622864,203847056,162858008]),
[] ).
cnf(178106072,plain,
( ~ product(A,e_1,B)
| ~ product(C,e_2,B)
| ~ product(e_4,C,e_2)
| ~ group_element(A)
| product(e_1,A,e_1)
| product(e_2,A,e_1)
| product(e_3,A,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[162842480,174114208,162828504]),
[] ).
cnf(203938832,plain,
( ~ product(e_2,e_1,A)
| ~ product(B,e_2,A)
| ~ product(e_4,B,e_2)
| product(e_3,e_2,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[174338696,174514776,178106072,162846432]),
[] ).
cnf(203959632,plain,
( ~ product(e_2,e_1,A)
| ~ product(e_4,e_1,e_2)
| product(e_3,e_2,e_1)
| ~ group_element(A)
| product(e_3,e_2,A)
| product(e_4,e_2,A) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[174079808,162846432,203938832,162828504]),
[] ).
cnf(204003960,plain,
( ~ product(e_2,e_1,A)
| product(e_3,e_2,e_1)
| ~ group_element(A)
| product(e_3,e_2,A)
| product(e_4,e_2,A) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[162842480,162846432,174308984,174540016,203854136,203959632,162828504]),
[] ).
cnf(204013336,plain,
( ~ product(e_2,e_1,e_3)
| product(e_3,e_2,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[185604408,174587720,204003960,162850168]),
[] ).
cnf(204035328,plain,
( product(e_3,e_2,e_1)
| product(e_1,e_1,e_3)
| product(e_3,e_1,e_3)
| product(e_4,e_1,e_3) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[162850168,162842480,204013336,162828504]),
[] ).
fof(e_3_is_not_e_1,plain,
~ equalish(e_3,e_1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-4.004.tptp',unknown),
[] ).
cnf(162889032,plain,
~ equalish(e_3,e_1),
inference(rewrite,[status(thm)],[e_3_is_not_e_1]),
[] ).
cnf(174579280,plain,
~ product(e_3,e_1,e_3),
inference(resolution,[status(thm)],[174502744,162889032]),
[] ).
cnf(174321592,plain,
~ product(e_1,e_1,e_3),
inference(resolution,[status(thm)],[174274272,162866296]),
[] ).
cnf(175754480,plain,
( ~ product(A,e_3,B)
| ~ product(C,e_1,B)
| ~ product(D,A,e_3)
| ~ product(D,C,e_1) ),
inference(resolution,[status(thm)],[162957608,162889032]),
[] ).
cnf(181540240,plain,
( ~ product(A,e_3,B)
| ~ product(C,A,e_3)
| ~ product(C,e_2,e_1)
| ~ group_element(B)
| product(e_1,e_1,B)
| product(e_3,e_1,B)
| product(e_4,e_1,B) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[162842480,175754480,162828504]),
[] ).
cnf(209518992,plain,
product(e_4,e_1,e_3),
inference(forward_subsumption_resolution__resolution,[status(thm)],[204035328,174579280,174321592,162850168,181540240,162944728]),
[] ).
cnf(174374288,plain,
~ product(e_3,e_3,e_1),
inference(resolution,[status(thm)],[174274272,162889032]),
[] ).
cnf(174424120,plain,
~ product(e_4,e_4,e_2),
inference(resolution,[status(thm)],[174274272,162903704]),
[] ).
cnf(176098336,plain,
( ~ product(A,e_4,e_2)
| ~ product(e_2,A,e_4) ),
inference(resolution,[status(thm)],[176017336,162881168]),
[] ).
cnf(175869344,plain,
( ~ product(e_4,A,e_1)
| ~ product(e_1,e_4,A) ),
inference(resolution,[status(thm)],[175814504,162870024]),
[] ).
cnf(177075032,plain,
( ~ product(e_1,e_4,A)
| ~ group_element(A)
| product(e_1,A,e_1)
| product(e_2,A,e_1)
| product(e_3,A,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[162842480,175869344,162828504]),
[] ).
cnf(182410552,plain,
( ~ product(e_1,e_4,e_2)
| product(e_3,e_2,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[174338696,174514776,177075032,162846432]),
[] ).
cnf(175941008,plain,
( ~ product(e_2,A,e_3)
| ~ product(e_3,e_2,A) ),
inference(resolution,[status(thm)],[175814504,162892680]),
[] ).
cnf(185463272,plain,
( ~ group_element(A)
| product(e_1,A,e_3)
| product(e_2,A,e_3)
| product(e_3,A,e_3)
| ~ product(e_4,A,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[162850168,175619232,162892680]),
[] ).
cnf(185719480,plain,
( product(e_2,e_1,e_3)
| ~ product(e_4,e_1,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[174579280,174321592,185463272,162842480]),
[] ).
cnf(203966616,plain,
~ product(e_4,e_1,e_2),
inference(forward_subsumption_resolution__resolution,[status(thm)],[185604408,175941008,185719480,174587720,203959632,162850168]),
[] ).
cnf(174136040,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_4,B) ),
inference(resolution,[status(thm)],[162936832,162870024]),
[] ).
cnf(178733376,plain,
( ~ product(A,e_1,B)
| ~ product(C,e_4,B)
| ~ product(e_3,A,e_1)
| ~ group_element(C)
| product(e_1,C,e_4)
| product(e_2,C,e_4)
| product(e_4,C,e_4) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[162858008,174162904,162828504]),
[] ).
cnf(205984216,plain,
( ~ product(A,e_1,B)
| ~ product(e_1,e_4,B)
| ~ product(e_3,A,e_1)
| product(e_2,e_1,e_4) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[174609496,174330160,178733376,162842480]),
[] ).
cnf(206022600,plain,
( ~ product(e_1,e_4,A)
| ~ product(e_3,e_2,e_1)
| product(e_2,e_1,e_4)
| ~ group_element(A)
| product(e_3,e_1,A)
| product(e_4,e_1,A) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[174136040,162842480,205984216,162828504]),
[] ).
cnf(206033584,plain,
~ product(e_1,e_4,e_2),
inference(forward_subsumption_resolution__resolution,[status(thm)],[176098336,182410552,203854136,203966616,206022600,162846432]),
[] ).
cnf(174566720,plain,
~ product(e_2,e_4,e_2),
inference(resolution,[status(thm)],[174502744,162881168]),
[] ).
fof(e_3_is_not_e_4,plain,
~ equalish(e_3,e_4),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-4.004.tptp',unknown),
[] ).
cnf(162896248,plain,
~ equalish(e_3,e_4),
inference(rewrite,[status(thm)],[e_3_is_not_e_4]),
[] ).
cnf(174212848,plain,
( ~ product(e_3,A,B)
| ~ product(e_4,C,B)
| ~ product(D,e_3,A)
| ~ product(D,e_4,C) ),
inference(resolution,[status(thm)],[162953248,162896248]),
[] ).
cnf(178976944,plain,
( ~ product(e_3,A,B)
| ~ product(e_4,C,B)
| ~ product(e_3,e_3,A)
| ~ group_element(C)
| product(e_1,e_4,C)
| product(e_2,e_4,C)
| product(e_4,e_4,C) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[162858008,174212848,162828504]),
[] ).
cnf(206671632,plain,
( ~ product(e_3,A,B)
| ~ product(e_4,e_2,B)
| ~ product(e_3,e_3,A) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[174424120,206033584,174566720,178976944,162846432]),
[] ).
cnf(206692456,plain,
~ product(e_4,e_2,e_3),
inference(resolution,[status(thm)],[206671632,162944728]),
[] ).
fof(e_2_is_not_e_3,plain,
~ equalish(e_2,e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-4.004.tptp',unknown),
[] ).
cnf(162877408,plain,
~ equalish(e_2,e_3),
inference(rewrite,[status(thm)],[e_2_is_not_e_3]),
[] ).
cnf(174352192,plain,
~ product(e_2,e_2,e_3),
inference(resolution,[status(thm)],[174274272,162877408]),
[] ).
cnf(181575648,plain,
( ~ product(A,e_3,B)
| ~ product(C,e_1,B)
| ~ product(e_1,C,e_1)
| ~ group_element(A)
| product(e_2,A,e_3)
| product(e_3,A,e_3)
| product(e_4,A,e_3) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[162850168,175754480,162828504]),
[] ).
cnf(209733704,plain,
( ~ product(e_2,e_3,A)
| ~ product(B,e_1,A)
| ~ product(e_1,B,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[174587720,206692456,174352192,181575648,162846432]),
[] ).
cnf(209775632,plain,
~ product(e_2,e_3,e_1),
inference(resolution,[status(thm)],[209733704,162944728]),
[] ).
cnf(174523136,plain,
~ product(e_1,e_3,e_1),
inference(resolution,[status(thm)],[174502744,162866296]),
[] ).
cnf(181648808,plain,
( ~ product(A,e_3,B)
| ~ product(C,e_1,B)
| ~ product(e_4,A,e_3)
| ~ group_element(C)
| product(e_1,C,e_1)
| product(e_2,C,e_1)
| product(e_3,C,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[162842480,175754480,162828504]),
[] ).
cnf(210258192,plain,
( ~ product(A,e_3,B)
| ~ product(e_3,e_1,B)
| ~ product(e_4,A,e_3) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[174374288,209775632,174523136,181648808,162850168]),
[] ).
cnf(210271848,plain,
( ~ product(e_3,e_1,A)
| ~ group_element(A)
| product(e_2,e_3,A)
| product(e_4,e_3,A) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[174468336,209518992,162850168,210258192,162828504]),
[] ).
cnf(210270120,plain,
product(e_2,e_3,e_4),
inference(forward_subsumption_resolution__resolution,[status(thm)],[174636232,205075840,210271848,162858008]),
[] ).
cnf(175778312,plain,
( ~ product(A,e_4,B)
| ~ product(C,e_2,B)
| ~ product(D,A,e_4)
| ~ product(D,C,e_2) ),
inference(resolution,[status(thm)],[162957608,162903704]),
[] ).
cnf(181810288,plain,
( ~ product(B,e_2,A)
| ~ product(C,e_3,e_4)
| ~ product(C,B,e_2)
| ~ group_element(A)
| product(e_1,e_4,A)
| product(e_2,e_4,A)
| product(e_4,e_4,A) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[162858008,175778312,162828504]),
[] ).
cnf(211873824,plain,
( ~ product(A,e_2,e_2)
| ~ product(B,e_3,e_4)
| ~ product(B,A,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[174424120,174566720,206033584,181810288,162846432]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[210270120,211873824,162944728]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 328 seconds
% START OF PROOF SEQUENCE
% 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/GRP124-4.004.tptp',unknown),[]).
%
% cnf(162936832,plain,(~product(A,B,C)|~product(A,D,C)|equalish(B,D)),inference(rewrite,[status(thm)],[product_right_cancellation]),[]).
%
% fof(product_idempotence,plain,(product(A,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-4.004.tptp',unknown),[]).
%
% cnf(162944728,plain,(product(A,A,A)),inference(rewrite,[status(thm)],[product_idempotence]),[]).
%
% cnf(174502744,plain,(~product(A,B,A)|equalish(A,B)),inference(resolution,[status(thm)],[162936832,162944728]),[]).
%
% fof(e_4_is_not_e_3,plain,(~equalish(e_4,e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-4.004.tptp',unknown),[]).
%
% cnf(162816416,plain,(~equalish(e_4,e_3)),inference(rewrite,[status(thm)],[e_4_is_not_e_3]),[]).
%
% cnf(174636232,plain,(~product(e_4,e_3,e_4)),inference(resolution,[status(thm)],[174502744,162816416]),[]).
%
% fof(element_4,plain,(group_element(e_4)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-4.004.tptp',unknown),[]).
%
% cnf(162858008,plain,(group_element(e_4)),inference(rewrite,[status(thm)],[element_4]),[]).
%
% fof(element_1,plain,(group_element(e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-4.004.tptp',unknown),[]).
%
% cnf(162842480,plain,(group_element(e_1)),inference(rewrite,[status(thm)],[element_1]),[]).
%
% 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/GRP124-4.004.tptp',unknown),[]).
%
% cnf(162932560,plain,(~product(A,B,C)|~product(A,B,D)|equalish(C,D)),inference(rewrite,[status(thm)],[product_total_function2]),[]).
%
% cnf(174274272,plain,(~product(A,A,B)|equalish(A,B)),inference(resolution,[status(thm)],[162932560,162944728]),[]).
%
% fof(e_2_is_not_e_4,plain,(~equalish(e_2,e_4)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-4.004.tptp',unknown),[]).
%
% cnf(162881168,plain,(~equalish(e_2,e_4)),inference(rewrite,[status(thm)],[e_2_is_not_e_4]),[]).
%
% cnf(174365720,plain,(~product(e_2,e_2,e_4)),inference(resolution,[status(thm)],[174274272,162881168]),[]).
%
% fof(e_4_is_not_e_2,plain,(~equalish(e_4,e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-4.004.tptp',unknown),[]).
%
% cnf(162903704,plain,(~equalish(e_4,e_2)),inference(rewrite,[status(thm)],[e_4_is_not_e_2]),[]).
%
% cnf(174622864,plain,(~product(e_4,e_2,e_4)),inference(resolution,[status(thm)],[174502744,162903704]),[]).
%
% fof(element_2,plain,(group_element(e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-4.004.tptp',unknown),[]).
%
% cnf(162846432,plain,(group_element(e_2)),inference(rewrite,[status(thm)],[element_2]),[]).
%
% fof(qg2_2,plain,(~product(A,B,C)|~product(D,E,C)|~product(F,A,B)|~product(F,D,E)|equalish(B,E)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-4.004.tptp',unknown),[]).
%
% cnf(162957608,plain,(~product(A,B,C)|~product(D,E,C)|~product(F,A,B)|~product(F,D,E)|equalish(B,E)),inference(rewrite,[status(thm)],[qg2_2]),[]).
%
% cnf(176017336,plain,(~product(B,C,A)|~product(A,B,C)|equalish(A,C)),inference(resolution,[status(thm)],[162957608,162944728]),[]).
%
% cnf(176158248,plain,(~product(A,e_2,e_4)|~product(e_4,A,e_2)),inference(resolution,[status(thm)],[176017336,162903704]),[]).
%
% fof(row_surjectivity,plain,(~group_element(A)|~group_element(B)|product(e_1,A,B)|product(e_2,A,B)|product(e_3,A,B)|product(e_4,A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-4.004.tptp',unknown),[]).
%
% cnf(162828504,plain,(~group_element(A)|~group_element(B)|product(e_1,A,B)|product(e_2,A,B)|product(e_3,A,B)|product(e_4,A,B)),inference(rewrite,[status(thm)],[row_surjectivity]),[]).
%
% cnf(177709528,plain,(~product(e_4,e_1,e_2)|product(e_3,e_2,e_4)),inference(forward_subsumption_resolution__resolution,[status(thm)],[174365720,174622864,162858008,162846432,176158248,162828504]),[]).
%
% fof(e_2_is_not_e_1,plain,(~equalish(e_2,e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-4.004.tptp',unknown),[]).
%
% cnf(162817344,plain,(~equalish(e_2,e_1)),inference(rewrite,[status(thm)],[e_2_is_not_e_1]),[]).
%
% cnf(174338696,plain,(~product(e_2,e_2,e_1)),inference(resolution,[status(thm)],[174274272,162817344]),[]).
%
% fof(e_1_is_not_e_2,plain,(~equalish(e_1,e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-4.004.tptp',unknown),[]).
%
% cnf(162862344,plain,(~equalish(e_1,e_2)),inference(rewrite,[status(thm)],[e_1_is_not_e_2]),[]).
%
% cnf(174514776,plain,(~product(e_1,e_2,e_1)),inference(resolution,[status(thm)],[174502744,162862344]),[]).
%
% cnf(175605040,plain,(~group_element(A)|~group_element(B)|product(e_1,A,B)|product(e_2,A,B)|product(e_4,A,B)|~product(e_3,A,C)|equalish(B,C)),inference(resolution,[status(thm)],[162828504,162932560]),[]).
%
% fof(e_1_is_not_e_4,plain,(~equalish(e_1,e_4)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-4.004.tptp',unknown),[]).
%
% cnf(162870024,plain,(~equalish(e_1,e_4)),inference(rewrite,[status(thm)],[e_1_is_not_e_4]),[]).
%
% cnf(184965496,plain,(~group_element(A)|product(e_1,A,e_1)|product(e_2,A,e_1)|product(e_4,A,e_1)|~product(e_3,A,e_4)),inference(forward_subsumption_resolution__resolution,[status(thm)],[162842480,175605040,162870024]),[]).
%
% cnf(185146920,plain,(product(e_4,e_2,e_1)|~product(e_3,e_2,e_4)),inference(forward_subsumption_resolution__resolution,[status(thm)],[174338696,174514776,184965496,162846432]),[]).
%
% cnf(174308984,plain,(~product(e_1,e_1,e_2)),inference(resolution,[status(thm)],[174274272,162862344]),[]).
%
% cnf(174540016,plain,(~product(e_2,e_1,e_2)),inference(resolution,[status(thm)],[174502744,162817344]),[]).
%
% cnf(174079808,plain,(~product(A,e_1,B)|~product(A,e_2,B)),inference(resolution,[status(thm)],[162936832,162862344]),[]).
%
% cnf(174114208,plain,(~product(A,e_1,B)|~product(C,e_2,B)|~product(D,A,e_1)|~product(D,C,e_2)),inference(resolution,[status(thm)],[162957608,162862344]),[]).
%
% cnf(178091544,plain,(~product(A,e_1,B)|~product(C,e_2,B)|~product(e_3,C,e_2)|~group_element(A)|product(e_1,A,e_1)|product(e_2,A,e_1)|product(e_4,A,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[162842480,174114208,162828504]),[]).
%
% cnf(203822096,plain,(~product(e_2,e_1,A)|~product(B,e_2,A)|~product(e_3,B,e_2)|product(e_4,e_2,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[174338696,174514776,178091544,162846432]),[]).
%
% cnf(203847056,plain,(~product(e_2,e_1,A)|~product(e_3,e_1,e_2)|product(e_4,e_2,e_1)|~group_element(A)|product(e_3,e_2,A)|product(e_4,e_2,A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[174079808,162846432,203822096,162828504]),[]).
%
% cnf(203885816,plain,(~product(e_2,e_1,A)|product(e_4,e_2,e_1)|~group_element(A)|product(e_3,e_2,A)|product(e_4,e_2,A)|product(e_4,e_1,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[162842480,162846432,174308984,174540016,203847056,162828504]),[]).
%
% cnf(203897848,plain,(~product(e_2,e_1,e_4)|product(e_4,e_2,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[177709528,185146920,174622864,203885816,162858008]),[]).
%
% cnf(203926744,plain,(product(e_4,e_2,e_1)|product(e_1,e_1,e_4)|product(e_3,e_1,e_4)|product(e_4,e_1,e_4)),inference(forward_subsumption_resolution__resolution,[status(thm)],[162858008,162842480,203897848,162828504]),[]).
%
% fof(e_4_is_not_e_1,plain,(~equalish(e_4,e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-4.004.tptp',unknown),[]).
%
% cnf(162900056,plain,(~equalish(e_4,e_1)),inference(rewrite,[status(thm)],[e_4_is_not_e_1]),[]).
%
% cnf(174609496,plain,(~product(e_4,e_1,e_4)),inference(resolution,[status(thm)],[174502744,162900056]),[]).
%
% cnf(174330160,plain,(~product(e_1,e_1,e_4)),inference(resolution,[status(thm)],[174274272,162870024]),[]).
%
% cnf(174162904,plain,(~product(A,e_1,B)|~product(C,e_4,B)|~product(D,A,e_1)|~product(D,C,e_4)),inference(resolution,[status(thm)],[162957608,162870024]),[]).
%
% cnf(178577880,plain,(~product(B,e_4,A)|~product(C,e_2,e_1)|~product(C,B,e_4)|~group_element(A)|product(e_1,e_1,A)|product(e_3,e_1,A)|product(e_4,e_1,A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[162842480,174162904,162828504]),[]).
%
% cnf(205075840,plain,(product(e_3,e_1,e_4)),inference(forward_subsumption_resolution__resolution,[status(thm)],[203926744,174609496,174330160,162858008,178577880,162944728]),[]).
%
% fof(e_1_is_not_e_3,plain,(~equalish(e_1,e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-4.004.tptp',unknown),[]).
%
% cnf(162866296,plain,(~equalish(e_1,e_3)),inference(rewrite,[status(thm)],[e_1_is_not_e_3]),[]).
%
% cnf(174468336,plain,(~product(A,e_1,B)|~product(A,e_3,B)),inference(resolution,[status(thm)],[162936832,162866296]),[]).
%
% fof(element_3,plain,(group_element(e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-4.004.tptp',unknown),[]).
%
% cnf(162850168,plain,(group_element(e_3)),inference(rewrite,[status(thm)],[element_3]),[]).
%
% cnf(175619232,plain,(~group_element(A)|~group_element(B)|product(e_1,A,B)|product(e_2,A,B)|product(e_3,A,B)|~product(e_4,A,C)|equalish(B,C)),inference(resolution,[status(thm)],[162828504,162932560]),[]).
%
% cnf(185432264,plain,(~group_element(A)|product(e_1,A,e_1)|product(e_2,A,e_1)|product(e_3,A,e_1)|~product(e_4,A,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[162842480,175619232,162866296]),[]).
%
% cnf(185604408,plain,(product(e_3,e_2,e_1)|~product(e_4,e_2,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[174338696,174514776,185432264,162846432]),[]).
%
% fof(e_3_is_not_e_2,plain,(~equalish(e_3,e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-4.004.tptp',unknown),[]).
%
% cnf(162892680,plain,(~equalish(e_3,e_2)),inference(rewrite,[status(thm)],[e_3_is_not_e_2]),[]).
%
% cnf(174587720,plain,(~product(e_3,e_2,e_3)),inference(resolution,[status(thm)],[174502744,162892680]),[]).
%
% fof(qg2_1,plain,(~product(A,B,C)|~product(D,E,C)|~product(F,A,B)|~product(F,D,E)|equalish(A,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-4.004.tptp',unknown),[]).
%
% cnf(162953248,plain,(~product(A,B,C)|~product(D,E,C)|~product(F,A,B)|~product(F,D,E)|equalish(A,D)),inference(rewrite,[status(thm)],[qg2_1]),[]).
%
% cnf(175814504,plain,(~product(B,C,A)|~product(A,B,C)|equalish(A,B)),inference(resolution,[status(thm)],[162953248,162944728]),[]).
%
% cnf(175979864,plain,(~product(e_2,A,e_4)|~product(e_4,e_2,A)),inference(resolution,[status(thm)],[175814504,162903704]),[]).
%
% cnf(185005264,plain,(~group_element(A)|product(e_1,A,e_4)|product(e_2,A,e_4)|product(e_4,A,e_4)|~product(e_3,A,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[162858008,175605040,162903704]),[]).
%
% cnf(185275120,plain,(product(e_2,e_1,e_4)|~product(e_3,e_1,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[174609496,174330160,185005264,162842480]),[]).
%
% cnf(203854136,plain,(~product(e_3,e_1,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[185146920,175979864,185275120,174622864,203847056,162858008]),[]).
%
% cnf(178106072,plain,(~product(A,e_1,B)|~product(C,e_2,B)|~product(e_4,C,e_2)|~group_element(A)|product(e_1,A,e_1)|product(e_2,A,e_1)|product(e_3,A,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[162842480,174114208,162828504]),[]).
%
% cnf(203938832,plain,(~product(e_2,e_1,A)|~product(B,e_2,A)|~product(e_4,B,e_2)|product(e_3,e_2,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[174338696,174514776,178106072,162846432]),[]).
%
% cnf(203959632,plain,(~product(e_2,e_1,A)|~product(e_4,e_1,e_2)|product(e_3,e_2,e_1)|~group_element(A)|product(e_3,e_2,A)|product(e_4,e_2,A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[174079808,162846432,203938832,162828504]),[]).
%
% cnf(204003960,plain,(~product(e_2,e_1,A)|product(e_3,e_2,e_1)|~group_element(A)|product(e_3,e_2,A)|product(e_4,e_2,A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[162842480,162846432,174308984,174540016,203854136,203959632,162828504]),[]).
%
% cnf(204013336,plain,(~product(e_2,e_1,e_3)|product(e_3,e_2,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[185604408,174587720,204003960,162850168]),[]).
%
% cnf(204035328,plain,(product(e_3,e_2,e_1)|product(e_1,e_1,e_3)|product(e_3,e_1,e_3)|product(e_4,e_1,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[162850168,162842480,204013336,162828504]),[]).
%
% fof(e_3_is_not_e_1,plain,(~equalish(e_3,e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-4.004.tptp',unknown),[]).
%
% cnf(162889032,plain,(~equalish(e_3,e_1)),inference(rewrite,[status(thm)],[e_3_is_not_e_1]),[]).
%
% cnf(174579280,plain,(~product(e_3,e_1,e_3)),inference(resolution,[status(thm)],[174502744,162889032]),[]).
%
% cnf(174321592,plain,(~product(e_1,e_1,e_3)),inference(resolution,[status(thm)],[174274272,162866296]),[]).
%
% cnf(175754480,plain,(~product(A,e_3,B)|~product(C,e_1,B)|~product(D,A,e_3)|~product(D,C,e_1)),inference(resolution,[status(thm)],[162957608,162889032]),[]).
%
% cnf(181540240,plain,(~product(A,e_3,B)|~product(C,A,e_3)|~product(C,e_2,e_1)|~group_element(B)|product(e_1,e_1,B)|product(e_3,e_1,B)|product(e_4,e_1,B)),inference(forward_subsumption_resolution__resolution,[status(thm)],[162842480,175754480,162828504]),[]).
%
% cnf(209518992,plain,(product(e_4,e_1,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[204035328,174579280,174321592,162850168,181540240,162944728]),[]).
%
% cnf(174374288,plain,(~product(e_3,e_3,e_1)),inference(resolution,[status(thm)],[174274272,162889032]),[]).
%
% cnf(174424120,plain,(~product(e_4,e_4,e_2)),inference(resolution,[status(thm)],[174274272,162903704]),[]).
%
% cnf(176098336,plain,(~product(A,e_4,e_2)|~product(e_2,A,e_4)),inference(resolution,[status(thm)],[176017336,162881168]),[]).
%
% cnf(175869344,plain,(~product(e_4,A,e_1)|~product(e_1,e_4,A)),inference(resolution,[status(thm)],[175814504,162870024]),[]).
%
% cnf(177075032,plain,(~product(e_1,e_4,A)|~group_element(A)|product(e_1,A,e_1)|product(e_2,A,e_1)|product(e_3,A,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[162842480,175869344,162828504]),[]).
%
% cnf(182410552,plain,(~product(e_1,e_4,e_2)|product(e_3,e_2,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[174338696,174514776,177075032,162846432]),[]).
%
% cnf(175941008,plain,(~product(e_2,A,e_3)|~product(e_3,e_2,A)),inference(resolution,[status(thm)],[175814504,162892680]),[]).
%
% cnf(185463272,plain,(~group_element(A)|product(e_1,A,e_3)|product(e_2,A,e_3)|product(e_3,A,e_3)|~product(e_4,A,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[162850168,175619232,162892680]),[]).
%
% cnf(185719480,plain,(product(e_2,e_1,e_3)|~product(e_4,e_1,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[174579280,174321592,185463272,162842480]),[]).
%
% cnf(203966616,plain,(~product(e_4,e_1,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[185604408,175941008,185719480,174587720,203959632,162850168]),[]).
%
% cnf(174136040,plain,(~product(A,e_1,B)|~product(A,e_4,B)),inference(resolution,[status(thm)],[162936832,162870024]),[]).
%
% cnf(178733376,plain,(~product(A,e_1,B)|~product(C,e_4,B)|~product(e_3,A,e_1)|~group_element(C)|product(e_1,C,e_4)|product(e_2,C,e_4)|product(e_4,C,e_4)),inference(forward_subsumption_resolution__resolution,[status(thm)],[162858008,174162904,162828504]),[]).
%
% cnf(205984216,plain,(~product(A,e_1,B)|~product(e_1,e_4,B)|~product(e_3,A,e_1)|product(e_2,e_1,e_4)),inference(forward_subsumption_resolution__resolution,[status(thm)],[174609496,174330160,178733376,162842480]),[]).
%
% cnf(206022600,plain,(~product(e_1,e_4,A)|~product(e_3,e_2,e_1)|product(e_2,e_1,e_4)|~group_element(A)|product(e_3,e_1,A)|product(e_4,e_1,A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[174136040,162842480,205984216,162828504]),[]).
%
% cnf(206033584,plain,(~product(e_1,e_4,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[176098336,182410552,203854136,203966616,206022600,162846432]),[]).
%
% cnf(174566720,plain,(~product(e_2,e_4,e_2)),inference(resolution,[status(thm)],[174502744,162881168]),[]).
%
% fof(e_3_is_not_e_4,plain,(~equalish(e_3,e_4)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-4.004.tptp',unknown),[]).
%
% cnf(162896248,plain,(~equalish(e_3,e_4)),inference(rewrite,[status(thm)],[e_3_is_not_e_4]),[]).
%
% cnf(174212848,plain,(~product(e_3,A,B)|~product(e_4,C,B)|~product(D,e_3,A)|~product(D,e_4,C)),inference(resolution,[status(thm)],[162953248,162896248]),[]).
%
% cnf(178976944,plain,(~product(e_3,A,B)|~product(e_4,C,B)|~product(e_3,e_3,A)|~group_element(C)|product(e_1,e_4,C)|product(e_2,e_4,C)|product(e_4,e_4,C)),inference(forward_subsumption_resolution__resolution,[status(thm)],[162858008,174212848,162828504]),[]).
%
% cnf(206671632,plain,(~product(e_3,A,B)|~product(e_4,e_2,B)|~product(e_3,e_3,A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[174424120,206033584,174566720,178976944,162846432]),[]).
%
% cnf(206692456,plain,(~product(e_4,e_2,e_3)),inference(resolution,[status(thm)],[206671632,162944728]),[]).
%
% fof(e_2_is_not_e_3,plain,(~equalish(e_2,e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-4.004.tptp',unknown),[]).
%
% cnf(162877408,plain,(~equalish(e_2,e_3)),inference(rewrite,[status(thm)],[e_2_is_not_e_3]),[]).
%
% cnf(174352192,plain,(~product(e_2,e_2,e_3)),inference(resolution,[status(thm)],[174274272,162877408]),[]).
%
% cnf(181575648,plain,(~product(A,e_3,B)|~product(C,e_1,B)|~product(e_1,C,e_1)|~group_element(A)|product(e_2,A,e_3)|product(e_3,A,e_3)|product(e_4,A,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[162850168,175754480,162828504]),[]).
%
% cnf(209733704,plain,(~product(e_2,e_3,A)|~product(B,e_1,A)|~product(e_1,B,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[174587720,206692456,174352192,181575648,162846432]),[]).
%
% cnf(209775632,plain,(~product(e_2,e_3,e_1)),inference(resolution,[status(thm)],[209733704,162944728]),[]).
%
% cnf(174523136,plain,(~product(e_1,e_3,e_1)),inference(resolution,[status(thm)],[174502744,162866296]),[]).
%
% cnf(181648808,plain,(~product(A,e_3,B)|~product(C,e_1,B)|~product(e_4,A,e_3)|~group_element(C)|product(e_1,C,e_1)|product(e_2,C,e_1)|product(e_3,C,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[162842480,175754480,162828504]),[]).
%
% cnf(210258192,plain,(~product(A,e_3,B)|~product(e_3,e_1,B)|~product(e_4,A,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[174374288,209775632,174523136,181648808,162850168]),[]).
%
% cnf(210271848,plain,(~product(e_3,e_1,A)|~group_element(A)|product(e_2,e_3,A)|product(e_4,e_3,A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[174468336,209518992,162850168,210258192,162828504]),[]).
%
% cnf(210270120,plain,(product(e_2,e_3,e_4)),inference(forward_subsumption_resolution__resolution,[status(thm)],[174636232,205075840,210271848,162858008]),[]).
%
% cnf(175778312,plain,(~product(A,e_4,B)|~product(C,e_2,B)|~product(D,A,e_4)|~product(D,C,e_2)),inference(resolution,[status(thm)],[162957608,162903704]),[]).
%
% cnf(181810288,plain,(~product(B,e_2,A)|~product(C,e_3,e_4)|~product(C,B,e_2)|~group_element(A)|product(e_1,e_4,A)|product(e_2,e_4,A)|product(e_4,e_4,A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[162858008,175778312,162828504]),[]).
%
% cnf(211873824,plain,(~product(A,e_2,e_2)|~product(B,e_3,e_4)|~product(B,A,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[174424120,174566720,206033584,181810288,162846432]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[210270120,211873824,162944728]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------