TSTP Solution File: GRP129-4.004 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP129-4.004 : TPTP v3.4.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art03.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1003MB
% OS : Linux 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May 6 12:27:29 EDT 2009
% Result : Unsatisfiable 102.3s
% Output : Refutation 102.3s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 18
% Syntax : Number of formulae : 144 ( 35 unt; 0 def)
% Number of atoms : 314 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 383 ( 213 ~; 170 |; 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 : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 156 ( 25 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
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/GRP129-4.004.tptp',unknown),
[] ).
cnf(165813496,plain,
( ~ product(A,B,C)
| ~ product(B,C,D)
| product(C,A,D) ),
inference(rewrite,[status(thm)],[qg3]),
[] ).
fof(qg3_1,plain,
! [A,B,C,D] :
( product(A,B,C)
| ~ product(C,A,D)
| ~ product(B,C,D) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP129-4.004.tptp',unknown),
[] ).
cnf(165702584,plain,
( product(A,B,C)
| ~ product(C,A,D)
| ~ product(B,C,D) ),
inference(rewrite,[status(thm)],[qg3_1]),
[] ).
cnf(180058464,plain,
( product(A,A,A)
| ~ product(A,A,B) ),
inference(resolution,[status(thm)],[165813496,165702584]),
[] ).
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/GRP129-4.004.tptp',unknown),
[] ).
cnf(165801160,plain,
( ~ product(A,B,C)
| ~ product(A,B,D)
| equalish(C,D) ),
inference(rewrite,[status(thm)],[product_total_function2]),
[] ).
fof(e_1_is_not_e_4,plain,
~ equalish(e_1,e_4),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP129-4.004.tptp',unknown),
[] ).
cnf(165738624,plain,
~ equalish(e_1,e_4),
inference(rewrite,[status(thm)],[e_1_is_not_e_4]),
[] ).
cnf(179421384,plain,
( ~ product(A,B,e_1)
| ~ product(A,B,e_4) ),
inference(resolution,[status(thm)],[165801160,165738624]),
[] ).
cnf(180256608,plain,
( ~ product(e_1,e_1,A)
| ~ product(e_1,e_1,e_4) ),
inference(resolution,[status(thm)],[180058464,179421384]),
[] ).
cnf(181159368,plain,
( ~ product(e_1,A,e_1)
| ~ product(A,e_1,e_4) ),
inference(resolution,[status(thm)],[180256608,165813496]),
[] ).
fof(e_1_is_not_e_3,plain,
~ equalish(e_1,e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP129-4.004.tptp',unknown),
[] ).
cnf(165734896,plain,
~ equalish(e_1,e_3),
inference(rewrite,[status(thm)],[e_1_is_not_e_3]),
[] ).
cnf(179385160,plain,
( ~ product(A,B,e_1)
| ~ product(A,B,e_3) ),
inference(resolution,[status(thm)],[165801160,165734896]),
[] ).
cnf(180180568,plain,
( ~ product(e_1,e_1,A)
| ~ product(e_1,e_1,e_3) ),
inference(resolution,[status(thm)],[180058464,179385160]),
[] ).
cnf(180928320,plain,
( ~ product(e_1,A,e_1)
| ~ product(A,e_1,e_3) ),
inference(resolution,[status(thm)],[180180568,165813496]),
[] ).
fof(e_1_is_not_e_2,plain,
~ equalish(e_1,e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP129-4.004.tptp',unknown),
[] ).
cnf(165730944,plain,
~ equalish(e_1,e_2),
inference(rewrite,[status(thm)],[e_1_is_not_e_2]),
[] ).
cnf(179343608,plain,
( ~ product(A,B,e_1)
| ~ product(A,B,e_2) ),
inference(resolution,[status(thm)],[165801160,165730944]),
[] ).
cnf(180116776,plain,
( ~ product(e_1,e_1,A)
| ~ product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[180058464,179343608]),
[] ).
cnf(180693672,plain,
( ~ product(e_1,A,e_1)
| ~ product(A,e_1,e_2) ),
inference(resolution,[status(thm)],[180116776,165813496]),
[] ).
fof(element_1,plain,
group_element(e_1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP129-4.004.tptp',unknown),
[] ).
cnf(165715216,plain,
group_element(e_1),
inference(rewrite,[status(thm)],[element_1]),
[] ).
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)
| product(A,B,e_4) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP129-4.004.tptp',unknown),
[] ).
cnf(165789464,plain,
( ~ group_element(A)
| ~ group_element(B)
| product(A,B,e_1)
| product(A,B,e_2)
| product(A,B,e_3)
| product(A,B,e_4) ),
inference(rewrite,[status(thm)],[product_total_function1]),
[] ).
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/GRP129-4.004.tptp',unknown),
[] ).
cnf(165805336,plain,
( ~ product(A,B,C)
| ~ product(A,D,C)
| equalish(B,D) ),
inference(rewrite,[status(thm)],[product_right_cancellation]),
[] ).
cnf(179358264,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_2,B) ),
inference(resolution,[status(thm)],[165805336,165730944]),
[] ).
cnf(180144000,plain,
( ~ product(e_1,e_1,A)
| ~ product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[180058464,179358264]),
[] ).
cnf(180746704,plain,
( ~ product(e_1,e_2,e_1)
| ~ product(A,e_1,B)
| ~ product(e_1,A,B) ),
inference(resolution,[status(thm)],[180144000,165702584]),
[] ).
cnf(286004920,plain,
( ~ group_element(A)
| ~ product(e_1,e_2,e_1)
| ~ product(e_1,A,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[181159368,180928320,180693672,165715216,165789464,180746704]),
[] ).
fof(element_2,plain,
group_element(e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP129-4.004.tptp',unknown),
[] ).
cnf(165719120,plain,
group_element(e_2),
inference(rewrite,[status(thm)],[element_2]),
[] ).
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/GRP129-4.004.tptp',unknown),
[] ).
cnf(165808968,plain,
( ~ product(A,B,C)
| ~ product(D,B,C)
| equalish(A,D) ),
inference(rewrite,[status(thm)],[product_left_cancellation]),
[] ).
cnf(179376680,plain,
( ~ product(e_1,A,B)
| ~ product(e_2,A,B) ),
inference(resolution,[status(thm)],[165808968,165730944]),
[] ).
cnf(180172080,plain,
( ~ product(e_2,e_2,A)
| ~ product(e_1,e_2,e_2) ),
inference(resolution,[status(thm)],[180058464,179376680]),
[] ).
cnf(180884704,plain,
( ~ product(e_1,e_2,e_2)
| ~ product(e_2,B,e_2)
| ~ product(B,e_2,A) ),
inference(resolution,[status(thm)],[180172080,165813496]),
[] ).
cnf(286335720,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_4)
| ~ product(e_2,B,e_2)
| ~ product(B,e_2,A) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[286004920,165719120,165715216,165789464,180884704]),
[] ).
fof(e_2_is_not_e_4,plain,
~ equalish(e_2,e_4),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP129-4.004.tptp',unknown),
[] ).
cnf(165753856,plain,
~ equalish(e_2,e_4),
inference(rewrite,[status(thm)],[e_2_is_not_e_4]),
[] ).
cnf(179449048,plain,
( ~ product(A,B,e_2)
| ~ product(A,B,e_4) ),
inference(resolution,[status(thm)],[165801160,165753856]),
[] ).
cnf(180318808,plain,
( ~ product(e_2,e_2,A)
| ~ product(e_2,e_2,e_4) ),
inference(resolution,[status(thm)],[180058464,179449048]),
[] ).
cnf(181350368,plain,
( ~ product(e_2,A,e_2)
| ~ product(A,e_2,e_4) ),
inference(resolution,[status(thm)],[180318808,165813496]),
[] ).
fof(e_2_is_not_e_3,plain,
~ equalish(e_2,e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP129-4.004.tptp',unknown),
[] ).
cnf(165750096,plain,
~ equalish(e_2,e_3),
inference(rewrite,[status(thm)],[e_2_is_not_e_3]),
[] ).
cnf(179444536,plain,
( ~ product(A,B,e_2)
| ~ product(A,B,e_3) ),
inference(resolution,[status(thm)],[165801160,165750096]),
[] ).
cnf(180292584,plain,
( ~ product(e_2,e_2,A)
| ~ product(e_2,e_2,e_3) ),
inference(resolution,[status(thm)],[180058464,179444536]),
[] ).
cnf(181261864,plain,
( ~ product(e_2,A,e_2)
| ~ product(A,e_2,e_3) ),
inference(resolution,[status(thm)],[180292584,165813496]),
[] ).
cnf(179029680,plain,
( ~ group_element(A)
| product(e_1,A,e_1)
| product(e_1,A,e_2)
| product(e_1,A,e_3)
| product(e_1,A,e_4) ),
inference(resolution,[status(thm)],[165789464,165715216]),
[] ).
cnf(180151728,plain,
( ~ product(e_2,e_2,A)
| ~ product(e_2,e_1,e_2) ),
inference(resolution,[status(thm)],[180058464,179358264]),
[] ).
fof(qg3_2,plain,
! [A,B,C,D] :
( product(A,B,C)
| ~ product(B,D,C)
| ~ product(D,A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP129-4.004.tptp',unknown),
[] ).
cnf(165706944,plain,
( product(A,B,C)
| ~ product(B,D,C)
| ~ product(D,A,B) ),
inference(rewrite,[status(thm)],[qg3_2]),
[] ).
cnf(180793536,plain,
( ~ product(e_2,e_1,e_2)
| ~ product(e_2,B,A)
| ~ product(B,e_2,e_2) ),
inference(resolution,[status(thm)],[180151728,165706944]),
[] ).
cnf(293312736,plain,
( ~ product(e_2,e_1,e_2)
| ~ product(e_2,e_1,A) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[286335720,181350368,181261864,165719120,179029680,180793536]),
[] ).
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/GRP129-4.004.tptp',unknown),
[] ).
cnf(165685208,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(196311376,plain,
( product(e_2,e_1,e_2)
| product(e_3,e_1,e_2)
| product(e_4,e_1,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[165715216,165719120,165685208,180116776]),
[] ).
cnf(307169752,plain,
( product(e_3,e_1,e_2)
| product(e_4,e_1,e_2) ),
inference(resolution,[status(thm)],[293312736,196311376]),
[] ).
cnf(307274272,plain,
( product(e_3,e_1,e_2)
| ~ product(e_4,e_1,e_3) ),
inference(resolution,[status(thm)],[307169752,179444536]),
[] ).
cnf(182914536,plain,
( ~ product(A,e_2,e_4)
| ~ product(A,B,e_2)
| ~ product(B,e_2,e_2) ),
inference(resolution,[status(thm)],[181350368,165813496]),
[] ).
cnf(180624864,plain,
( ~ product(A,A,B)
| product(C,A,A)
| ~ product(A,C,A) ),
inference(resolution,[status(thm)],[180058464,165702584]),
[] ).
cnf(269116024,plain,
( ~ product(e_2,e_2,e_4)
| ~ product(e_2,e_2,A) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[165702584,182914536,180624864]),
[] ).
cnf(182735328,plain,
( ~ product(A,e_2,e_3)
| ~ product(A,B,e_2)
| ~ product(B,e_2,e_2) ),
inference(resolution,[status(thm)],[181261864,165813496]),
[] ).
cnf(263387256,plain,
( ~ product(e_2,e_2,e_3)
| ~ product(e_2,e_2,A) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[165702584,182735328,180624864]),
[] ).
cnf(180135280,plain,
( ~ product(e_2,e_2,A)
| ~ product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[180058464,179343608]),
[] ).
cnf(180878624,plain,
( ~ product(e_2,e_2,A)
| ~ product(e_2,B,e_2)
| ~ product(B,e_1,e_2) ),
inference(resolution,[status(thm)],[180172080,165706944]),
[] ).
cnf(286325488,plain,
( ~ product(e_2,A,e_2)
| ~ product(A,e_1,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[269116024,263387256,180135280,165719120,165789464,180878624]),
[] ).
cnf(319271560,plain,
( ~ product(e_4,e_1,e_3)
| ~ product(e_2,e_3,e_2) ),
inference(resolution,[status(thm)],[307274272,286325488]),
[] ).
cnf(307270520,plain,
( product(e_4,e_1,e_2)
| ~ product(e_3,e_1,e_3) ),
inference(resolution,[status(thm)],[307169752,179444536]),
[] ).
cnf(317697728,plain,
( ~ product(e_3,e_1,e_3)
| ~ product(A,e_4,e_1)
| product(e_1,A,e_2) ),
inference(resolution,[status(thm)],[307270520,165813496]),
[] ).
cnf(179772352,plain,
( ~ product(B,C,e_1)
| ~ product(C,A,B)
| ~ product(A,B,e_2) ),
inference(resolution,[status(thm)],[165706944,179343608]),
[] ).
cnf(317854432,plain,
( ~ product(e_3,e_1,e_3)
| ~ product(e_2,e_4,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[317697728,307270520,179772352]),
[] ).
cnf(179762432,plain,
( ~ product(B,A,C)
| ~ product(A,B,C)
| product(A,A,A) ),
inference(resolution,[status(thm)],[165702584,165702584]),
[] ).
cnf(179468000,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_4,B) ),
inference(resolution,[status(thm)],[165805336,165738624]),
[] ).
cnf(180370376,plain,
( ~ product(e_1,e_1,A)
| ~ product(e_1,e_4,e_1) ),
inference(resolution,[status(thm)],[180058464,179468000]),
[] ).
cnf(179051344,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_3)
| product(e_1,e_1,e_4) ),
inference(resolution,[status(thm)],[165789464,165715216]),
[] ).
fof(e_3_is_not_e_4,plain,
~ equalish(e_3,e_4),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP129-4.004.tptp',unknown),
[] ).
cnf(165764848,plain,
~ equalish(e_3,e_4),
inference(rewrite,[status(thm)],[e_3_is_not_e_4]),
[] ).
cnf(179486832,plain,
( ~ product(A,e_3,B)
| ~ product(A,e_4,B) ),
inference(resolution,[status(thm)],[165805336,165764848]),
[] ).
cnf(179666568,plain,
( ~ product(B,A,C)
| ~ product(e_3,B,C)
| ~ product(A,e_4,B) ),
inference(resolution,[status(thm)],[165702584,179486832]),
[] ).
cnf(291527232,plain,
( ~ product(e_3,e_1,e_2)
| ~ product(e_1,e_4,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[179762432,180370376,179051344,179666568]),
[] ).
cnf(308264064,plain,
( product(e_4,e_1,e_2)
| ~ product(e_1,e_4,e_1) ),
inference(resolution,[status(thm)],[307169752,291527232]),
[] ).
cnf(307408736,plain,
( product(e_3,e_1,e_2)
| ~ product(e_1,e_4,e_1) ),
inference(resolution,[status(thm)],[307169752,180693672]),
[] ).
cnf(179520896,plain,
( ~ product(e_3,A,B)
| ~ product(e_4,A,B) ),
inference(resolution,[status(thm)],[165808968,165764848]),
[] ).
cnf(330311560,plain,
~ product(e_1,e_4,e_1),
inference(forward_subsumption_resolution__resolution,[status(thm)],[308264064,307408736,179520896]),
[] ).
fof(element_4,plain,
group_element(e_4),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP129-4.004.tptp',unknown),
[] ).
cnf(165726608,plain,
group_element(e_4),
inference(rewrite,[status(thm)],[element_4]),
[] ).
cnf(180279088,plain,
( ~ product(e_4,e_4,A)
| ~ product(e_4,e_4,e_1) ),
inference(resolution,[status(thm)],[180058464,179421384]),
[] ).
cnf(196470832,plain,
( product(e_1,e_4,e_1)
| product(e_2,e_4,e_1)
| product(e_3,e_4,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[165715216,165726608,165685208,180279088]),
[] ).
cnf(331042944,plain,
( product(e_2,e_4,e_1)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[330311560,196470832]),
[] ).
cnf(180305312,plain,
( ~ product(e_3,e_3,A)
| ~ product(e_3,e_3,e_2) ),
inference(resolution,[status(thm)],[180058464,179444536]),
[] ).
cnf(181292256,plain,
( ~ product(e_3,A,e_3)
| ~ product(A,e_3,e_2) ),
inference(resolution,[status(thm)],[180305312,165813496]),
[] ).
cnf(182808064,plain,
( ~ product(e_3,A,e_3)
| ~ product(e_3,B,A)
| ~ product(B,A,e_2) ),
inference(resolution,[status(thm)],[181292256,165813496]),
[] ).
cnf(332352144,plain,
~ product(e_3,e_1,e_3),
inference(forward_subsumption_resolution__resolution,[status(thm)],[307270520,317854432,331042944,182808064]),
[] ).
fof(element_3,plain,
group_element(e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP129-4.004.tptp',unknown),
[] ).
cnf(165722856,plain,
group_element(e_3),
inference(rewrite,[status(thm)],[element_3]),
[] ).
cnf(196392840,plain,
( product(e_2,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)],[165715216,165722856,165685208,180180568]),
[] ).
cnf(332617288,plain,
( product(e_2,e_1,e_3)
| product(e_4,e_1,e_3) ),
inference(resolution,[status(thm)],[332352144,196392840]),
[] ).
cnf(332842440,plain,
( product(e_4,e_1,e_3)
| product(A,e_2,e_3)
| ~ product(e_1,A,e_2) ),
inference(resolution,[status(thm)],[332617288,165706944]),
[] ).
cnf(179833856,plain,
( ~ product(B,C,e_3)
| ~ product(C,A,B)
| ~ product(A,B,e_2) ),
inference(resolution,[status(thm)],[165706944,179444536]),
[] ).
cnf(333138264,plain,
( product(e_4,e_1,e_3)
| ~ product(e_1,e_3,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[332842440,332617288,179833856]),
[] ).
cnf(180909160,plain,
( ~ product(e_3,e_1,A)
| ~ product(e_1,e_3,A) ),
inference(resolution,[status(thm)],[180180568,165702584]),
[] ).
cnf(307414656,plain,
( product(e_4,e_1,e_2)
| ~ product(e_1,e_3,e_2) ),
inference(resolution,[status(thm)],[307169752,180909160]),
[] ).
cnf(335303512,plain,
~ product(e_1,e_3,e_2),
inference(forward_subsumption_resolution__resolution,[status(thm)],[333138264,307414656,179444536]),
[] ).
cnf(196489472,plain,
( product(e_1,e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_4,e_3,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[165719120,165722856,165685208,180305312]),
[] ).
cnf(336057224,plain,
( product(e_2,e_3,e_2)
| product(e_4,e_3,e_2) ),
inference(resolution,[status(thm)],[335303512,196489472]),
[] ).
cnf(181136184,plain,
( ~ product(e_4,e_1,A)
| ~ product(e_1,e_4,A) ),
inference(resolution,[status(thm)],[180256608,165702584]),
[] ).
cnf(182456984,plain,
( ~ product(e_4,e_1,A)
| ~ product(A,e_1,B)
| ~ product(e_4,A,B) ),
inference(resolution,[status(thm)],[181136184,165702584]),
[] ).
cnf(337109056,plain,
~ product(e_4,e_1,e_3),
inference(forward_subsumption_resolution__resolution,[status(thm)],[307274272,319271560,336057224,182456984]),
[] ).
cnf(337475832,plain,
product(e_2,e_1,e_3),
inference(resolution,[status(thm)],[337109056,332617288]),
[] ).
cnf(179456784,plain,
( ~ product(A,B,e_3)
| ~ product(A,B,e_4) ),
inference(resolution,[status(thm)],[165801160,165764848]),
[] ).
cnf(337581288,plain,
~ product(e_2,e_1,e_4),
inference(resolution,[status(thm)],[337475832,179456784]),
[] ).
cnf(307282280,plain,
( product(e_3,e_1,e_2)
| ~ product(e_4,e_1,e_4) ),
inference(resolution,[status(thm)],[307169752,179449048]),
[] ).
cnf(320818784,plain,
( ~ product(e_4,e_1,e_4)
| ~ product(A,e_3,e_1)
| product(e_1,A,e_2) ),
inference(resolution,[status(thm)],[307282280,165813496]),
[] ).
cnf(320976960,plain,
( ~ product(e_4,e_1,e_4)
| ~ product(e_2,e_3,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[320818784,307282280,179772352]),
[] ).
cnf(179394688,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_3,B) ),
inference(resolution,[status(thm)],[165805336,165734896]),
[] ).
cnf(180214256,plain,
( ~ product(e_1,e_1,A)
| ~ product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[180058464,179394688]),
[] ).
cnf(179678488,plain,
( ~ product(B,A,C)
| ~ product(e_4,B,C)
| ~ product(A,e_3,B) ),
inference(resolution,[status(thm)],[165702584,179486832]),
[] ).
cnf(291531728,plain,
( ~ product(e_4,e_1,e_2)
| ~ product(e_1,e_3,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[179762432,180214256,179051344,179678488]),
[] ).
cnf(308268480,plain,
( product(e_3,e_1,e_2)
| ~ product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[307169752,291531728]),
[] ).
cnf(307405136,plain,
( product(e_4,e_1,e_2)
| ~ product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[307169752,180693672]),
[] ).
cnf(325516104,plain,
~ product(e_1,e_3,e_1),
inference(forward_subsumption_resolution__resolution,[status(thm)],[308268480,307405136,179520896]),
[] ).
cnf(180205536,plain,
( ~ product(e_3,e_3,A)
| ~ product(e_3,e_3,e_1) ),
inference(resolution,[status(thm)],[180058464,179385160]),
[] ).
cnf(196402952,plain,
( product(e_1,e_3,e_1)
| product(e_2,e_3,e_1)
| product(e_4,e_3,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[165715216,165722856,165685208,180205536]),
[] ).
cnf(326200464,plain,
( product(e_2,e_3,e_1)
| product(e_4,e_3,e_1) ),
inference(resolution,[status(thm)],[325516104,196402952]),
[] ).
cnf(180331504,plain,
( ~ product(e_4,e_4,A)
| ~ product(e_4,e_4,e_2) ),
inference(resolution,[status(thm)],[180058464,179449048]),
[] ).
cnf(181380728,plain,
( ~ product(e_4,A,e_4)
| ~ product(A,e_4,e_2) ),
inference(resolution,[status(thm)],[180331504,165813496]),
[] ).
cnf(182987248,plain,
( ~ product(e_4,A,e_4)
| ~ product(e_4,B,A)
| ~ product(B,A,e_2) ),
inference(resolution,[status(thm)],[181380728,165813496]),
[] ).
cnf(327456024,plain,
~ product(e_4,e_1,e_4),
inference(forward_subsumption_resolution__resolution,[status(thm)],[307282280,320976960,326200464,182987248]),
[] ).
cnf(196461608,plain,
( product(e_2,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)],[165715216,165726608,165685208,180256608]),
[] ).
cnf(327653352,plain,
( product(e_2,e_1,e_4)
| product(e_3,e_1,e_4) ),
inference(resolution,[status(thm)],[327456024,196461608]),
[] ).
cnf(338821136,plain,
product(e_3,e_1,e_4),
inference(resolution,[status(thm)],[337581288,327653352]),
[] ).
cnf(181492928,plain,
( ~ product(e_1,e_1,A)
| ~ product(e_4,B,e_1)
| ~ product(B,e_1,e_4) ),
inference(resolution,[status(thm)],[180370376,165706944]),
[] ).
cnf(286739504,plain,
( ~ product(e_4,A,e_1)
| ~ product(A,e_1,e_4) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[180116776,180180568,180256608,165715216,165789464,181492928]),
[] ).
cnf(339526824,plain,
~ product(e_4,e_3,e_1),
inference(resolution,[status(thm)],[338821136,286739504]),
[] ).
cnf(342762248,plain,
product(e_2,e_3,e_1),
inference(resolution,[status(thm)],[339526824,326200464]),
[] ).
cnf(307278592,plain,
( product(e_4,e_1,e_2)
| ~ product(e_3,e_1,e_4) ),
inference(resolution,[status(thm)],[307169752,179449048]),
[] ).
cnf(328358448,plain,
( product(e_2,e_1,e_4)
| product(e_4,e_1,e_2) ),
inference(resolution,[status(thm)],[327653352,307278592]),
[] ).
cnf(338825488,plain,
product(e_4,e_1,e_2),
inference(resolution,[status(thm)],[337581288,328358448]),
[] ).
cnf(339836400,plain,
~ product(e_4,e_3,e_2),
inference(resolution,[status(thm)],[338825488,179394688]),
[] ).
cnf(344124760,plain,
product(e_2,e_3,e_2),
inference(resolution,[status(thm)],[339836400,336057224]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[342762248,344124760,179343608]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 102 seconds
% START OF PROOF SEQUENCE
% fof(qg3,plain,(~product(A,B,C)|~product(B,C,D)|product(C,A,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP129-4.004.tptp',unknown),[]).
%
% cnf(165813496,plain,(~product(A,B,C)|~product(B,C,D)|product(C,A,D)),inference(rewrite,[status(thm)],[qg3]),[]).
%
% fof(qg3_1,plain,(product(A,B,C)|~product(C,A,D)|~product(B,C,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP129-4.004.tptp',unknown),[]).
%
% cnf(165702584,plain,(product(A,B,C)|~product(C,A,D)|~product(B,C,D)),inference(rewrite,[status(thm)],[qg3_1]),[]).
%
% cnf(180058464,plain,(product(A,A,A)|~product(A,A,B)),inference(resolution,[status(thm)],[165813496,165702584]),[]).
%
% 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/GRP129-4.004.tptp',unknown),[]).
%
% cnf(165801160,plain,(~product(A,B,C)|~product(A,B,D)|equalish(C,D)),inference(rewrite,[status(thm)],[product_total_function2]),[]).
%
% fof(e_1_is_not_e_4,plain,(~equalish(e_1,e_4)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP129-4.004.tptp',unknown),[]).
%
% cnf(165738624,plain,(~equalish(e_1,e_4)),inference(rewrite,[status(thm)],[e_1_is_not_e_4]),[]).
%
% cnf(179421384,plain,(~product(A,B,e_1)|~product(A,B,e_4)),inference(resolution,[status(thm)],[165801160,165738624]),[]).
%
% cnf(180256608,plain,(~product(e_1,e_1,A)|~product(e_1,e_1,e_4)),inference(resolution,[status(thm)],[180058464,179421384]),[]).
%
% cnf(181159368,plain,(~product(e_1,A,e_1)|~product(A,e_1,e_4)),inference(resolution,[status(thm)],[180256608,165813496]),[]).
%
% fof(e_1_is_not_e_3,plain,(~equalish(e_1,e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP129-4.004.tptp',unknown),[]).
%
% cnf(165734896,plain,(~equalish(e_1,e_3)),inference(rewrite,[status(thm)],[e_1_is_not_e_3]),[]).
%
% cnf(179385160,plain,(~product(A,B,e_1)|~product(A,B,e_3)),inference(resolution,[status(thm)],[165801160,165734896]),[]).
%
% cnf(180180568,plain,(~product(e_1,e_1,A)|~product(e_1,e_1,e_3)),inference(resolution,[status(thm)],[180058464,179385160]),[]).
%
% cnf(180928320,plain,(~product(e_1,A,e_1)|~product(A,e_1,e_3)),inference(resolution,[status(thm)],[180180568,165813496]),[]).
%
% fof(e_1_is_not_e_2,plain,(~equalish(e_1,e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP129-4.004.tptp',unknown),[]).
%
% cnf(165730944,plain,(~equalish(e_1,e_2)),inference(rewrite,[status(thm)],[e_1_is_not_e_2]),[]).
%
% cnf(179343608,plain,(~product(A,B,e_1)|~product(A,B,e_2)),inference(resolution,[status(thm)],[165801160,165730944]),[]).
%
% cnf(180116776,plain,(~product(e_1,e_1,A)|~product(e_1,e_1,e_2)),inference(resolution,[status(thm)],[180058464,179343608]),[]).
%
% cnf(180693672,plain,(~product(e_1,A,e_1)|~product(A,e_1,e_2)),inference(resolution,[status(thm)],[180116776,165813496]),[]).
%
% fof(element_1,plain,(group_element(e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP129-4.004.tptp',unknown),[]).
%
% cnf(165715216,plain,(group_element(e_1)),inference(rewrite,[status(thm)],[element_1]),[]).
%
% 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)|product(A,B,e_4)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP129-4.004.tptp',unknown),[]).
%
% cnf(165789464,plain,(~group_element(A)|~group_element(B)|product(A,B,e_1)|product(A,B,e_2)|product(A,B,e_3)|product(A,B,e_4)),inference(rewrite,[status(thm)],[product_total_function1]),[]).
%
% 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/GRP129-4.004.tptp',unknown),[]).
%
% cnf(165805336,plain,(~product(A,B,C)|~product(A,D,C)|equalish(B,D)),inference(rewrite,[status(thm)],[product_right_cancellation]),[]).
%
% cnf(179358264,plain,(~product(A,e_1,B)|~product(A,e_2,B)),inference(resolution,[status(thm)],[165805336,165730944]),[]).
%
% cnf(180144000,plain,(~product(e_1,e_1,A)|~product(e_1,e_2,e_1)),inference(resolution,[status(thm)],[180058464,179358264]),[]).
%
% cnf(180746704,plain,(~product(e_1,e_2,e_1)|~product(A,e_1,B)|~product(e_1,A,B)),inference(resolution,[status(thm)],[180144000,165702584]),[]).
%
% cnf(286004920,plain,(~group_element(A)|~product(e_1,e_2,e_1)|~product(e_1,A,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[181159368,180928320,180693672,165715216,165789464,180746704]),[]).
%
% fof(element_2,plain,(group_element(e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP129-4.004.tptp',unknown),[]).
%
% cnf(165719120,plain,(group_element(e_2)),inference(rewrite,[status(thm)],[element_2]),[]).
%
% 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/GRP129-4.004.tptp',unknown),[]).
%
% cnf(165808968,plain,(~product(A,B,C)|~product(D,B,C)|equalish(A,D)),inference(rewrite,[status(thm)],[product_left_cancellation]),[]).
%
% cnf(179376680,plain,(~product(e_1,A,B)|~product(e_2,A,B)),inference(resolution,[status(thm)],[165808968,165730944]),[]).
%
% cnf(180172080,plain,(~product(e_2,e_2,A)|~product(e_1,e_2,e_2)),inference(resolution,[status(thm)],[180058464,179376680]),[]).
%
% cnf(180884704,plain,(~product(e_1,e_2,e_2)|~product(e_2,B,e_2)|~product(B,e_2,A)),inference(resolution,[status(thm)],[180172080,165813496]),[]).
%
% cnf(286335720,plain,(product(e_1,e_2,e_3)|product(e_1,e_2,e_4)|~product(e_2,B,e_2)|~product(B,e_2,A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[286004920,165719120,165715216,165789464,180884704]),[]).
%
% fof(e_2_is_not_e_4,plain,(~equalish(e_2,e_4)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP129-4.004.tptp',unknown),[]).
%
% cnf(165753856,plain,(~equalish(e_2,e_4)),inference(rewrite,[status(thm)],[e_2_is_not_e_4]),[]).
%
% cnf(179449048,plain,(~product(A,B,e_2)|~product(A,B,e_4)),inference(resolution,[status(thm)],[165801160,165753856]),[]).
%
% cnf(180318808,plain,(~product(e_2,e_2,A)|~product(e_2,e_2,e_4)),inference(resolution,[status(thm)],[180058464,179449048]),[]).
%
% cnf(181350368,plain,(~product(e_2,A,e_2)|~product(A,e_2,e_4)),inference(resolution,[status(thm)],[180318808,165813496]),[]).
%
% fof(e_2_is_not_e_3,plain,(~equalish(e_2,e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP129-4.004.tptp',unknown),[]).
%
% cnf(165750096,plain,(~equalish(e_2,e_3)),inference(rewrite,[status(thm)],[e_2_is_not_e_3]),[]).
%
% cnf(179444536,plain,(~product(A,B,e_2)|~product(A,B,e_3)),inference(resolution,[status(thm)],[165801160,165750096]),[]).
%
% cnf(180292584,plain,(~product(e_2,e_2,A)|~product(e_2,e_2,e_3)),inference(resolution,[status(thm)],[180058464,179444536]),[]).
%
% cnf(181261864,plain,(~product(e_2,A,e_2)|~product(A,e_2,e_3)),inference(resolution,[status(thm)],[180292584,165813496]),[]).
%
% cnf(179029680,plain,(~group_element(A)|product(e_1,A,e_1)|product(e_1,A,e_2)|product(e_1,A,e_3)|product(e_1,A,e_4)),inference(resolution,[status(thm)],[165789464,165715216]),[]).
%
% cnf(180151728,plain,(~product(e_2,e_2,A)|~product(e_2,e_1,e_2)),inference(resolution,[status(thm)],[180058464,179358264]),[]).
%
% fof(qg3_2,plain,(product(A,B,C)|~product(B,D,C)|~product(D,A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP129-4.004.tptp',unknown),[]).
%
% cnf(165706944,plain,(product(A,B,C)|~product(B,D,C)|~product(D,A,B)),inference(rewrite,[status(thm)],[qg3_2]),[]).
%
% cnf(180793536,plain,(~product(e_2,e_1,e_2)|~product(e_2,B,A)|~product(B,e_2,e_2)),inference(resolution,[status(thm)],[180151728,165706944]),[]).
%
% cnf(293312736,plain,(~product(e_2,e_1,e_2)|~product(e_2,e_1,A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[286335720,181350368,181261864,165719120,179029680,180793536]),[]).
%
% 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/GRP129-4.004.tptp',unknown),[]).
%
% cnf(165685208,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(196311376,plain,(product(e_2,e_1,e_2)|product(e_3,e_1,e_2)|product(e_4,e_1,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[165715216,165719120,165685208,180116776]),[]).
%
% cnf(307169752,plain,(product(e_3,e_1,e_2)|product(e_4,e_1,e_2)),inference(resolution,[status(thm)],[293312736,196311376]),[]).
%
% cnf(307274272,plain,(product(e_3,e_1,e_2)|~product(e_4,e_1,e_3)),inference(resolution,[status(thm)],[307169752,179444536]),[]).
%
% cnf(182914536,plain,(~product(A,e_2,e_4)|~product(A,B,e_2)|~product(B,e_2,e_2)),inference(resolution,[status(thm)],[181350368,165813496]),[]).
%
% cnf(180624864,plain,(~product(A,A,B)|product(C,A,A)|~product(A,C,A)),inference(resolution,[status(thm)],[180058464,165702584]),[]).
%
% cnf(269116024,plain,(~product(e_2,e_2,e_4)|~product(e_2,e_2,A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[165702584,182914536,180624864]),[]).
%
% cnf(182735328,plain,(~product(A,e_2,e_3)|~product(A,B,e_2)|~product(B,e_2,e_2)),inference(resolution,[status(thm)],[181261864,165813496]),[]).
%
% cnf(263387256,plain,(~product(e_2,e_2,e_3)|~product(e_2,e_2,A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[165702584,182735328,180624864]),[]).
%
% cnf(180135280,plain,(~product(e_2,e_2,A)|~product(e_2,e_2,e_1)),inference(resolution,[status(thm)],[180058464,179343608]),[]).
%
% cnf(180878624,plain,(~product(e_2,e_2,A)|~product(e_2,B,e_2)|~product(B,e_1,e_2)),inference(resolution,[status(thm)],[180172080,165706944]),[]).
%
% cnf(286325488,plain,(~product(e_2,A,e_2)|~product(A,e_1,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[269116024,263387256,180135280,165719120,165789464,180878624]),[]).
%
% cnf(319271560,plain,(~product(e_4,e_1,e_3)|~product(e_2,e_3,e_2)),inference(resolution,[status(thm)],[307274272,286325488]),[]).
%
% cnf(307270520,plain,(product(e_4,e_1,e_2)|~product(e_3,e_1,e_3)),inference(resolution,[status(thm)],[307169752,179444536]),[]).
%
% cnf(317697728,plain,(~product(e_3,e_1,e_3)|~product(A,e_4,e_1)|product(e_1,A,e_2)),inference(resolution,[status(thm)],[307270520,165813496]),[]).
%
% cnf(179772352,plain,(~product(B,C,e_1)|~product(C,A,B)|~product(A,B,e_2)),inference(resolution,[status(thm)],[165706944,179343608]),[]).
%
% cnf(317854432,plain,(~product(e_3,e_1,e_3)|~product(e_2,e_4,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[317697728,307270520,179772352]),[]).
%
% cnf(179762432,plain,(~product(B,A,C)|~product(A,B,C)|product(A,A,A)),inference(resolution,[status(thm)],[165702584,165702584]),[]).
%
% cnf(179468000,plain,(~product(A,e_1,B)|~product(A,e_4,B)),inference(resolution,[status(thm)],[165805336,165738624]),[]).
%
% cnf(180370376,plain,(~product(e_1,e_1,A)|~product(e_1,e_4,e_1)),inference(resolution,[status(thm)],[180058464,179468000]),[]).
%
% cnf(179051344,plain,(product(e_1,e_1,e_1)|product(e_1,e_1,e_2)|product(e_1,e_1,e_3)|product(e_1,e_1,e_4)),inference(resolution,[status(thm)],[165789464,165715216]),[]).
%
% fof(e_3_is_not_e_4,plain,(~equalish(e_3,e_4)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP129-4.004.tptp',unknown),[]).
%
% cnf(165764848,plain,(~equalish(e_3,e_4)),inference(rewrite,[status(thm)],[e_3_is_not_e_4]),[]).
%
% cnf(179486832,plain,(~product(A,e_3,B)|~product(A,e_4,B)),inference(resolution,[status(thm)],[165805336,165764848]),[]).
%
% cnf(179666568,plain,(~product(B,A,C)|~product(e_3,B,C)|~product(A,e_4,B)),inference(resolution,[status(thm)],[165702584,179486832]),[]).
%
% cnf(291527232,plain,(~product(e_3,e_1,e_2)|~product(e_1,e_4,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[179762432,180370376,179051344,179666568]),[]).
%
% cnf(308264064,plain,(product(e_4,e_1,e_2)|~product(e_1,e_4,e_1)),inference(resolution,[status(thm)],[307169752,291527232]),[]).
%
% cnf(307408736,plain,(product(e_3,e_1,e_2)|~product(e_1,e_4,e_1)),inference(resolution,[status(thm)],[307169752,180693672]),[]).
%
% cnf(179520896,plain,(~product(e_3,A,B)|~product(e_4,A,B)),inference(resolution,[status(thm)],[165808968,165764848]),[]).
%
% cnf(330311560,plain,(~product(e_1,e_4,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[308264064,307408736,179520896]),[]).
%
% fof(element_4,plain,(group_element(e_4)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP129-4.004.tptp',unknown),[]).
%
% cnf(165726608,plain,(group_element(e_4)),inference(rewrite,[status(thm)],[element_4]),[]).
%
% cnf(180279088,plain,(~product(e_4,e_4,A)|~product(e_4,e_4,e_1)),inference(resolution,[status(thm)],[180058464,179421384]),[]).
%
% cnf(196470832,plain,(product(e_1,e_4,e_1)|product(e_2,e_4,e_1)|product(e_3,e_4,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[165715216,165726608,165685208,180279088]),[]).
%
% cnf(331042944,plain,(product(e_2,e_4,e_1)|product(e_3,e_4,e_1)),inference(resolution,[status(thm)],[330311560,196470832]),[]).
%
% cnf(180305312,plain,(~product(e_3,e_3,A)|~product(e_3,e_3,e_2)),inference(resolution,[status(thm)],[180058464,179444536]),[]).
%
% cnf(181292256,plain,(~product(e_3,A,e_3)|~product(A,e_3,e_2)),inference(resolution,[status(thm)],[180305312,165813496]),[]).
%
% cnf(182808064,plain,(~product(e_3,A,e_3)|~product(e_3,B,A)|~product(B,A,e_2)),inference(resolution,[status(thm)],[181292256,165813496]),[]).
%
% cnf(332352144,plain,(~product(e_3,e_1,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[307270520,317854432,331042944,182808064]),[]).
%
% fof(element_3,plain,(group_element(e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP129-4.004.tptp',unknown),[]).
%
% cnf(165722856,plain,(group_element(e_3)),inference(rewrite,[status(thm)],[element_3]),[]).
%
% cnf(196392840,plain,(product(e_2,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)],[165715216,165722856,165685208,180180568]),[]).
%
% cnf(332617288,plain,(product(e_2,e_1,e_3)|product(e_4,e_1,e_3)),inference(resolution,[status(thm)],[332352144,196392840]),[]).
%
% cnf(332842440,plain,(product(e_4,e_1,e_3)|product(A,e_2,e_3)|~product(e_1,A,e_2)),inference(resolution,[status(thm)],[332617288,165706944]),[]).
%
% cnf(179833856,plain,(~product(B,C,e_3)|~product(C,A,B)|~product(A,B,e_2)),inference(resolution,[status(thm)],[165706944,179444536]),[]).
%
% cnf(333138264,plain,(product(e_4,e_1,e_3)|~product(e_1,e_3,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[332842440,332617288,179833856]),[]).
%
% cnf(180909160,plain,(~product(e_3,e_1,A)|~product(e_1,e_3,A)),inference(resolution,[status(thm)],[180180568,165702584]),[]).
%
% cnf(307414656,plain,(product(e_4,e_1,e_2)|~product(e_1,e_3,e_2)),inference(resolution,[status(thm)],[307169752,180909160]),[]).
%
% cnf(335303512,plain,(~product(e_1,e_3,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[333138264,307414656,179444536]),[]).
%
% cnf(196489472,plain,(product(e_1,e_3,e_2)|product(e_2,e_3,e_2)|product(e_4,e_3,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[165719120,165722856,165685208,180305312]),[]).
%
% cnf(336057224,plain,(product(e_2,e_3,e_2)|product(e_4,e_3,e_2)),inference(resolution,[status(thm)],[335303512,196489472]),[]).
%
% cnf(181136184,plain,(~product(e_4,e_1,A)|~product(e_1,e_4,A)),inference(resolution,[status(thm)],[180256608,165702584]),[]).
%
% cnf(182456984,plain,(~product(e_4,e_1,A)|~product(A,e_1,B)|~product(e_4,A,B)),inference(resolution,[status(thm)],[181136184,165702584]),[]).
%
% cnf(337109056,plain,(~product(e_4,e_1,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[307274272,319271560,336057224,182456984]),[]).
%
% cnf(337475832,plain,(product(e_2,e_1,e_3)),inference(resolution,[status(thm)],[337109056,332617288]),[]).
%
% cnf(179456784,plain,(~product(A,B,e_3)|~product(A,B,e_4)),inference(resolution,[status(thm)],[165801160,165764848]),[]).
%
% cnf(337581288,plain,(~product(e_2,e_1,e_4)),inference(resolution,[status(thm)],[337475832,179456784]),[]).
%
% cnf(307282280,plain,(product(e_3,e_1,e_2)|~product(e_4,e_1,e_4)),inference(resolution,[status(thm)],[307169752,179449048]),[]).
%
% cnf(320818784,plain,(~product(e_4,e_1,e_4)|~product(A,e_3,e_1)|product(e_1,A,e_2)),inference(resolution,[status(thm)],[307282280,165813496]),[]).
%
% cnf(320976960,plain,(~product(e_4,e_1,e_4)|~product(e_2,e_3,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[320818784,307282280,179772352]),[]).
%
% cnf(179394688,plain,(~product(A,e_1,B)|~product(A,e_3,B)),inference(resolution,[status(thm)],[165805336,165734896]),[]).
%
% cnf(180214256,plain,(~product(e_1,e_1,A)|~product(e_1,e_3,e_1)),inference(resolution,[status(thm)],[180058464,179394688]),[]).
%
% cnf(179678488,plain,(~product(B,A,C)|~product(e_4,B,C)|~product(A,e_3,B)),inference(resolution,[status(thm)],[165702584,179486832]),[]).
%
% cnf(291531728,plain,(~product(e_4,e_1,e_2)|~product(e_1,e_3,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[179762432,180214256,179051344,179678488]),[]).
%
% cnf(308268480,plain,(product(e_3,e_1,e_2)|~product(e_1,e_3,e_1)),inference(resolution,[status(thm)],[307169752,291531728]),[]).
%
% cnf(307405136,plain,(product(e_4,e_1,e_2)|~product(e_1,e_3,e_1)),inference(resolution,[status(thm)],[307169752,180693672]),[]).
%
% cnf(325516104,plain,(~product(e_1,e_3,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[308268480,307405136,179520896]),[]).
%
% cnf(180205536,plain,(~product(e_3,e_3,A)|~product(e_3,e_3,e_1)),inference(resolution,[status(thm)],[180058464,179385160]),[]).
%
% cnf(196402952,plain,(product(e_1,e_3,e_1)|product(e_2,e_3,e_1)|product(e_4,e_3,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[165715216,165722856,165685208,180205536]),[]).
%
% cnf(326200464,plain,(product(e_2,e_3,e_1)|product(e_4,e_3,e_1)),inference(resolution,[status(thm)],[325516104,196402952]),[]).
%
% cnf(180331504,plain,(~product(e_4,e_4,A)|~product(e_4,e_4,e_2)),inference(resolution,[status(thm)],[180058464,179449048]),[]).
%
% cnf(181380728,plain,(~product(e_4,A,e_4)|~product(A,e_4,e_2)),inference(resolution,[status(thm)],[180331504,165813496]),[]).
%
% cnf(182987248,plain,(~product(e_4,A,e_4)|~product(e_4,B,A)|~product(B,A,e_2)),inference(resolution,[status(thm)],[181380728,165813496]),[]).
%
% cnf(327456024,plain,(~product(e_4,e_1,e_4)),inference(forward_subsumption_resolution__resolution,[status(thm)],[307282280,320976960,326200464,182987248]),[]).
%
% cnf(196461608,plain,(product(e_2,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)],[165715216,165726608,165685208,180256608]),[]).
%
% cnf(327653352,plain,(product(e_2,e_1,e_4)|product(e_3,e_1,e_4)),inference(resolution,[status(thm)],[327456024,196461608]),[]).
%
% cnf(338821136,plain,(product(e_3,e_1,e_4)),inference(resolution,[status(thm)],[337581288,327653352]),[]).
%
% cnf(181492928,plain,(~product(e_1,e_1,A)|~product(e_4,B,e_1)|~product(B,e_1,e_4)),inference(resolution,[status(thm)],[180370376,165706944]),[]).
%
% cnf(286739504,plain,(~product(e_4,A,e_1)|~product(A,e_1,e_4)),inference(forward_subsumption_resolution__resolution,[status(thm)],[180116776,180180568,180256608,165715216,165789464,181492928]),[]).
%
% cnf(339526824,plain,(~product(e_4,e_3,e_1)),inference(resolution,[status(thm)],[338821136,286739504]),[]).
%
% cnf(342762248,plain,(product(e_2,e_3,e_1)),inference(resolution,[status(thm)],[339526824,326200464]),[]).
%
% cnf(307278592,plain,(product(e_4,e_1,e_2)|~product(e_3,e_1,e_4)),inference(resolution,[status(thm)],[307169752,179449048]),[]).
%
% cnf(328358448,plain,(product(e_2,e_1,e_4)|product(e_4,e_1,e_2)),inference(resolution,[status(thm)],[327653352,307278592]),[]).
%
% cnf(338825488,plain,(product(e_4,e_1,e_2)),inference(resolution,[status(thm)],[337581288,328358448]),[]).
%
% cnf(339836400,plain,(~product(e_4,e_3,e_2)),inference(resolution,[status(thm)],[338825488,179394688]),[]).
%
% cnf(344124760,plain,(product(e_2,e_3,e_2)),inference(resolution,[status(thm)],[339836400,336057224]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[342762248,344124760,179343608]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------