TSTP Solution File: GRP124-9.004 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP124-9.004 : TPTP v3.4.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art06.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 12:25:46 EDT 2009
% Result : Unsatisfiable 6.8s
% Output : Refutation 6.8s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 20
% Syntax : Number of formulae : 78 ( 46 unt; 0 def)
% Number of atoms : 128 ( 0 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 135 ( 85 ~; 50 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 63 ( 0 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(element_1,plain,
group_element(e_1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-9.004.tptp',unknown),
[] ).
cnf(159481224,plain,
group_element(e_1),
inference(rewrite,[status(thm)],[element_1]),
[] ).
fof(element_2,plain,
group_element(e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-9.004.tptp',unknown),
[] ).
cnf(159485304,plain,
group_element(e_2),
inference(rewrite,[status(thm)],[element_2]),
[] ).
fof(product1_total_function1,plain,
! [A,B] :
( ~ group_element(A)
| ~ group_element(B)
| product1(A,B,e_1)
| product1(A,B,e_2)
| product1(A,B,e_3)
| product1(A,B,e_4) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-9.004.tptp',unknown),
[] ).
cnf(159560440,plain,
( ~ group_element(A)
| ~ group_element(B)
| product1(A,B,e_1)
| product1(A,B,e_2)
| product1(A,B,e_3)
| product1(A,B,e_4) ),
inference(rewrite,[status(thm)],[product1_total_function1]),
[] ).
fof(product1_right_cancellation,plain,
! [A,B,C,D] :
( ~ product1(A,B,C)
| ~ product1(A,D,C)
| equalish(B,D) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-9.004.tptp',unknown),
[] ).
cnf(159581096,plain,
( ~ product1(A,B,C)
| ~ product1(A,D,C)
| equalish(B,D) ),
inference(rewrite,[status(thm)],[product1_right_cancellation]),
[] ).
fof(product1_idempotence,plain,
! [A] : product1(A,A,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-9.004.tptp',unknown),
[] ).
cnf(159589104,plain,
product1(A,A,A),
inference(rewrite,[status(thm)],[product1_idempotence]),
[] ).
cnf(169430440,plain,
( ~ product1(A,B,A)
| equalish(A,B) ),
inference(resolution,[status(thm)],[159581096,159589104]),
[] ).
fof(e_1_is_not_e_2,plain,
~ equalish(e_1,e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-9.004.tptp',unknown),
[] ).
cnf(159501216,plain,
~ equalish(e_1,e_2),
inference(rewrite,[status(thm)],[e_1_is_not_e_2]),
[] ).
cnf(169446360,plain,
~ product1(e_1,e_2,e_1),
inference(resolution,[status(thm)],[169430440,159501216]),
[] ).
cnf(203777440,plain,
( product1(e_1,e_2,e_2)
| product1(e_1,e_2,e_3)
| product1(e_1,e_2,e_4) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[159481224,159485304,159560440,169446360]),
[] ).
fof(product1_left_cancellation,plain,
! [A,B,C,D] :
( ~ product1(A,B,C)
| ~ product1(D,B,C)
| equalish(A,D) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-9.004.tptp',unknown),
[] ).
cnf(159584728,plain,
( ~ product1(A,B,C)
| ~ product1(D,B,C)
| equalish(A,D) ),
inference(rewrite,[status(thm)],[product1_left_cancellation]),
[] ).
cnf(169610944,plain,
( ~ product1(B,A,A)
| equalish(A,B) ),
inference(resolution,[status(thm)],[159584728,159589104]),
[] ).
fof(e_2_is_not_e_1,plain,
~ equalish(e_2,e_1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-9.004.tptp',unknown),
[] ).
cnf(159455960,plain,
~ equalish(e_2,e_1),
inference(rewrite,[status(thm)],[e_2_is_not_e_1]),
[] ).
cnf(169655568,plain,
~ product1(e_1,e_2,e_2),
inference(resolution,[status(thm)],[169610944,159455960]),
[] ).
cnf(232244384,plain,
( product1(e_1,e_2,e_3)
| product1(e_1,e_2,e_4) ),
inference(resolution,[status(thm)],[203777440,169655568]),
[] ).
fof(e_3_is_not_e_1,plain,
~ equalish(e_3,e_1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-9.004.tptp',unknown),
[] ).
cnf(159528032,plain,
~ equalish(e_3,e_1),
inference(rewrite,[status(thm)],[e_3_is_not_e_1]),
[] ).
cnf(169675744,plain,
~ product1(e_1,e_3,e_3),
inference(resolution,[status(thm)],[169610944,159528032]),
[] ).
fof(e_1_is_not_e_3,plain,
~ equalish(e_1,e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-9.004.tptp',unknown),
[] ).
cnf(159505296,plain,
~ equalish(e_1,e_3),
inference(rewrite,[status(thm)],[e_1_is_not_e_3]),
[] ).
cnf(169454800,plain,
~ product1(e_1,e_3,e_1),
inference(resolution,[status(thm)],[169430440,159505296]),
[] ).
fof(element_3,plain,
group_element(e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-9.004.tptp',unknown),
[] ).
cnf(159493128,plain,
group_element(e_3),
inference(rewrite,[status(thm)],[element_3]),
[] ).
fof(e_2_is_not_e_3,plain,
~ equalish(e_2,e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-9.004.tptp',unknown),
[] ).
cnf(159516408,plain,
~ equalish(e_2,e_3),
inference(rewrite,[status(thm)],[e_2_is_not_e_3]),
[] ).
cnf(169667272,plain,
~ product1(e_3,e_2,e_2),
inference(resolution,[status(thm)],[169610944,159516408]),
[] ).
cnf(169433984,plain,
( ~ product1(A,B,A)
| equalish(B,A) ),
inference(resolution,[status(thm)],[159581096,159589104]),
[] ).
cnf(169571120,plain,
~ product1(e_3,e_2,e_3),
inference(resolution,[status(thm)],[169433984,159516408]),
[] ).
fof(qg2a,plain,
! [A,B,C,D] :
( ~ product1(A,B,C)
| ~ product1(C,A,D)
| product2(D,B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-9.004.tptp',unknown),
[] ).
cnf(159628744,plain,
( ~ product1(A,B,C)
| ~ product1(C,A,D)
| product2(D,B,A) ),
inference(rewrite,[status(thm)],[qg2a]),
[] ).
cnf(168727072,plain,
( ~ product1(A,A,B)
| product2(B,A,A) ),
inference(resolution,[status(thm)],[159628744,159589104]),
[] ).
fof(product2_total_function2,plain,
! [A,B,C,D] :
( ~ product2(A,B,C)
| ~ product2(A,B,D)
| equalish(C,D) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-9.004.tptp',unknown),
[] ).
cnf(159611448,plain,
( ~ product2(A,B,C)
| ~ product2(A,B,D)
| equalish(C,D) ),
inference(rewrite,[status(thm)],[product2_total_function2]),
[] ).
cnf(169860064,plain,
( ~ product1(A,A,B)
| ~ product2(B,A,C)
| equalish(A,C) ),
inference(resolution,[status(thm)],[168727072,159611448]),
[] ).
cnf(169945320,plain,
( ~ product1(e_2,e_2,A)
| ~ product2(A,e_2,e_3) ),
inference(resolution,[status(thm)],[169860064,159516408]),
[] ).
cnf(170081584,plain,
~ product2(e_2,e_2,e_3),
inference(resolution,[status(thm)],[169945320,159589104]),
[] ).
cnf(201358672,plain,
( ~ product1(e_3,e_2,A)
| ~ product1(A,e_3,e_2) ),
inference(resolution,[status(thm)],[159628744,170081584]),
[] ).
cnf(204557352,plain,
( product1(e_3,e_2,e_4)
| ~ product1(e_1,e_3,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[169667272,169571120,159493128,159485304,159560440,201358672]),
[] ).
cnf(168630592,plain,
( ~ product1(e_3,A,B)
| ~ product1(e_1,A,B) ),
inference(resolution,[status(thm)],[159584728,159528032]),
[] ).
cnf(205200640,plain,
( ~ product1(e_1,e_3,e_2)
| ~ product1(e_1,e_2,e_4) ),
inference(resolution,[status(thm)],[204557352,168630592]),
[] ).
cnf(210630976,plain,
( ~ product1(e_1,e_2,e_4)
| product1(e_1,e_3,e_4) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[169675744,169454800,159481224,159493128,205200640,159560440]),
[] ).
fof(e_3_is_not_e_2,plain,
~ equalish(e_3,e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-9.004.tptp',unknown),
[] ).
cnf(159531680,plain,
~ equalish(e_3,e_2),
inference(rewrite,[status(thm)],[e_3_is_not_e_2]),
[] ).
cnf(168685200,plain,
( ~ product1(A,e_3,B)
| ~ product1(A,e_2,B) ),
inference(resolution,[status(thm)],[159581096,159531680]),
[] ).
cnf(210688040,plain,
~ product1(e_1,e_2,e_4),
inference(resolution,[status(thm)],[210630976,168685200]),
[] ).
cnf(232599064,plain,
product1(e_1,e_2,e_3),
inference(resolution,[status(thm)],[232244384,210688040]),
[] ).
fof(e_4_is_not_e_1,plain,
~ equalish(e_4,e_1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-9.004.tptp',unknown),
[] ).
cnf(159539056,plain,
~ equalish(e_4,e_1),
inference(rewrite,[status(thm)],[e_4_is_not_e_1]),
[] ).
cnf(169699184,plain,
~ product1(e_1,e_4,e_4),
inference(resolution,[status(thm)],[169610944,159539056]),
[] ).
fof(element_4,plain,
group_element(e_4),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-9.004.tptp',unknown),
[] ).
cnf(159496880,plain,
group_element(e_4),
inference(rewrite,[status(thm)],[element_4]),
[] ).
fof(e_1_is_not_e_4,plain,
~ equalish(e_1,e_4),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-9.004.tptp',unknown),
[] ).
cnf(159509024,plain,
~ equalish(e_1,e_4),
inference(rewrite,[status(thm)],[e_1_is_not_e_4]),
[] ).
cnf(169466504,plain,
~ product1(e_1,e_4,e_1),
inference(resolution,[status(thm)],[169430440,159509024]),
[] ).
cnf(169614592,plain,
( ~ product1(A,B,B)
| equalish(A,B) ),
inference(resolution,[status(thm)],[159584728,159589104]),
[] ).
fof(e_4_is_not_e_2,plain,
~ equalish(e_4,e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-9.004.tptp',unknown),
[] ).
cnf(159542704,plain,
~ equalish(e_4,e_2),
inference(rewrite,[status(thm)],[e_4_is_not_e_2]),
[] ).
cnf(169765072,plain,
~ product1(e_4,e_2,e_2),
inference(resolution,[status(thm)],[169614592,159542704]),
[] ).
cnf(169530328,plain,
~ product1(e_4,e_2,e_4),
inference(resolution,[status(thm)],[169430440,159542704]),
[] ).
fof(e_2_is_not_e_4,plain,
~ equalish(e_2,e_4),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-9.004.tptp',unknown),
[] ).
cnf(159524256,plain,
~ equalish(e_2,e_4),
inference(rewrite,[status(thm)],[e_2_is_not_e_4]),
[] ).
cnf(169953960,plain,
( ~ product1(e_2,e_2,A)
| ~ product2(A,e_2,e_4) ),
inference(resolution,[status(thm)],[169860064,159524256]),
[] ).
cnf(170090248,plain,
~ product2(e_2,e_2,e_4),
inference(resolution,[status(thm)],[169953960,159589104]),
[] ).
cnf(201379616,plain,
( ~ product1(e_4,e_2,A)
| ~ product1(A,e_4,e_2) ),
inference(resolution,[status(thm)],[159628744,170090248]),
[] ).
cnf(204572176,plain,
( product1(e_4,e_2,e_3)
| ~ product1(e_1,e_4,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[169765072,169530328,159496880,159485304,159560440,201379616]),
[] ).
cnf(169220104,plain,
( ~ product1(e_4,A,B)
| ~ product1(e_1,A,B) ),
inference(resolution,[status(thm)],[159584728,159539056]),
[] ).
cnf(205473200,plain,
( ~ product1(e_1,e_4,e_2)
| ~ product1(e_1,e_2,e_3) ),
inference(resolution,[status(thm)],[204572176,169220104]),
[] ).
cnf(212429608,plain,
( ~ product1(e_1,e_2,e_3)
| product1(e_1,e_4,e_3) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[169699184,159496880,159481224,169466504,205473200,159560440]),
[] ).
cnf(169229088,plain,
( ~ product1(A,e_4,B)
| ~ product1(A,e_2,B) ),
inference(resolution,[status(thm)],[159581096,159542704]),
[] ).
cnf(212523896,plain,
~ product1(e_1,e_2,e_3),
inference(resolution,[status(thm)],[212429608,169229088]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[232599064,212523896]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 6 seconds
% START OF PROOF SEQUENCE
% fof(element_1,plain,(group_element(e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-9.004.tptp',unknown),[]).
%
% cnf(159481224,plain,(group_element(e_1)),inference(rewrite,[status(thm)],[element_1]),[]).
%
% fof(element_2,plain,(group_element(e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-9.004.tptp',unknown),[]).
%
% cnf(159485304,plain,(group_element(e_2)),inference(rewrite,[status(thm)],[element_2]),[]).
%
% fof(product1_total_function1,plain,(~group_element(A)|~group_element(B)|product1(A,B,e_1)|product1(A,B,e_2)|product1(A,B,e_3)|product1(A,B,e_4)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-9.004.tptp',unknown),[]).
%
% cnf(159560440,plain,(~group_element(A)|~group_element(B)|product1(A,B,e_1)|product1(A,B,e_2)|product1(A,B,e_3)|product1(A,B,e_4)),inference(rewrite,[status(thm)],[product1_total_function1]),[]).
%
% fof(product1_right_cancellation,plain,(~product1(A,B,C)|~product1(A,D,C)|equalish(B,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-9.004.tptp',unknown),[]).
%
% cnf(159581096,plain,(~product1(A,B,C)|~product1(A,D,C)|equalish(B,D)),inference(rewrite,[status(thm)],[product1_right_cancellation]),[]).
%
% fof(product1_idempotence,plain,(product1(A,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-9.004.tptp',unknown),[]).
%
% cnf(159589104,plain,(product1(A,A,A)),inference(rewrite,[status(thm)],[product1_idempotence]),[]).
%
% cnf(169430440,plain,(~product1(A,B,A)|equalish(A,B)),inference(resolution,[status(thm)],[159581096,159589104]),[]).
%
% fof(e_1_is_not_e_2,plain,(~equalish(e_1,e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-9.004.tptp',unknown),[]).
%
% cnf(159501216,plain,(~equalish(e_1,e_2)),inference(rewrite,[status(thm)],[e_1_is_not_e_2]),[]).
%
% cnf(169446360,plain,(~product1(e_1,e_2,e_1)),inference(resolution,[status(thm)],[169430440,159501216]),[]).
%
% cnf(203777440,plain,(product1(e_1,e_2,e_2)|product1(e_1,e_2,e_3)|product1(e_1,e_2,e_4)),inference(forward_subsumption_resolution__resolution,[status(thm)],[159481224,159485304,159560440,169446360]),[]).
%
% fof(product1_left_cancellation,plain,(~product1(A,B,C)|~product1(D,B,C)|equalish(A,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-9.004.tptp',unknown),[]).
%
% cnf(159584728,plain,(~product1(A,B,C)|~product1(D,B,C)|equalish(A,D)),inference(rewrite,[status(thm)],[product1_left_cancellation]),[]).
%
% cnf(169610944,plain,(~product1(B,A,A)|equalish(A,B)),inference(resolution,[status(thm)],[159584728,159589104]),[]).
%
% fof(e_2_is_not_e_1,plain,(~equalish(e_2,e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-9.004.tptp',unknown),[]).
%
% cnf(159455960,plain,(~equalish(e_2,e_1)),inference(rewrite,[status(thm)],[e_2_is_not_e_1]),[]).
%
% cnf(169655568,plain,(~product1(e_1,e_2,e_2)),inference(resolution,[status(thm)],[169610944,159455960]),[]).
%
% cnf(232244384,plain,(product1(e_1,e_2,e_3)|product1(e_1,e_2,e_4)),inference(resolution,[status(thm)],[203777440,169655568]),[]).
%
% fof(e_3_is_not_e_1,plain,(~equalish(e_3,e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-9.004.tptp',unknown),[]).
%
% cnf(159528032,plain,(~equalish(e_3,e_1)),inference(rewrite,[status(thm)],[e_3_is_not_e_1]),[]).
%
% cnf(169675744,plain,(~product1(e_1,e_3,e_3)),inference(resolution,[status(thm)],[169610944,159528032]),[]).
%
% fof(e_1_is_not_e_3,plain,(~equalish(e_1,e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-9.004.tptp',unknown),[]).
%
% cnf(159505296,plain,(~equalish(e_1,e_3)),inference(rewrite,[status(thm)],[e_1_is_not_e_3]),[]).
%
% cnf(169454800,plain,(~product1(e_1,e_3,e_1)),inference(resolution,[status(thm)],[169430440,159505296]),[]).
%
% fof(element_3,plain,(group_element(e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-9.004.tptp',unknown),[]).
%
% cnf(159493128,plain,(group_element(e_3)),inference(rewrite,[status(thm)],[element_3]),[]).
%
% fof(e_2_is_not_e_3,plain,(~equalish(e_2,e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-9.004.tptp',unknown),[]).
%
% cnf(159516408,plain,(~equalish(e_2,e_3)),inference(rewrite,[status(thm)],[e_2_is_not_e_3]),[]).
%
% cnf(169667272,plain,(~product1(e_3,e_2,e_2)),inference(resolution,[status(thm)],[169610944,159516408]),[]).
%
% cnf(169433984,plain,(~product1(A,B,A)|equalish(B,A)),inference(resolution,[status(thm)],[159581096,159589104]),[]).
%
% cnf(169571120,plain,(~product1(e_3,e_2,e_3)),inference(resolution,[status(thm)],[169433984,159516408]),[]).
%
% fof(qg2a,plain,(~product1(A,B,C)|~product1(C,A,D)|product2(D,B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-9.004.tptp',unknown),[]).
%
% cnf(159628744,plain,(~product1(A,B,C)|~product1(C,A,D)|product2(D,B,A)),inference(rewrite,[status(thm)],[qg2a]),[]).
%
% cnf(168727072,plain,(~product1(A,A,B)|product2(B,A,A)),inference(resolution,[status(thm)],[159628744,159589104]),[]).
%
% fof(product2_total_function2,plain,(~product2(A,B,C)|~product2(A,B,D)|equalish(C,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-9.004.tptp',unknown),[]).
%
% cnf(159611448,plain,(~product2(A,B,C)|~product2(A,B,D)|equalish(C,D)),inference(rewrite,[status(thm)],[product2_total_function2]),[]).
%
% cnf(169860064,plain,(~product1(A,A,B)|~product2(B,A,C)|equalish(A,C)),inference(resolution,[status(thm)],[168727072,159611448]),[]).
%
% cnf(169945320,plain,(~product1(e_2,e_2,A)|~product2(A,e_2,e_3)),inference(resolution,[status(thm)],[169860064,159516408]),[]).
%
% cnf(170081584,plain,(~product2(e_2,e_2,e_3)),inference(resolution,[status(thm)],[169945320,159589104]),[]).
%
% cnf(201358672,plain,(~product1(e_3,e_2,A)|~product1(A,e_3,e_2)),inference(resolution,[status(thm)],[159628744,170081584]),[]).
%
% cnf(204557352,plain,(product1(e_3,e_2,e_4)|~product1(e_1,e_3,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[169667272,169571120,159493128,159485304,159560440,201358672]),[]).
%
% cnf(168630592,plain,(~product1(e_3,A,B)|~product1(e_1,A,B)),inference(resolution,[status(thm)],[159584728,159528032]),[]).
%
% cnf(205200640,plain,(~product1(e_1,e_3,e_2)|~product1(e_1,e_2,e_4)),inference(resolution,[status(thm)],[204557352,168630592]),[]).
%
% cnf(210630976,plain,(~product1(e_1,e_2,e_4)|product1(e_1,e_3,e_4)),inference(forward_subsumption_resolution__resolution,[status(thm)],[169675744,169454800,159481224,159493128,205200640,159560440]),[]).
%
% fof(e_3_is_not_e_2,plain,(~equalish(e_3,e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-9.004.tptp',unknown),[]).
%
% cnf(159531680,plain,(~equalish(e_3,e_2)),inference(rewrite,[status(thm)],[e_3_is_not_e_2]),[]).
%
% cnf(168685200,plain,(~product1(A,e_3,B)|~product1(A,e_2,B)),inference(resolution,[status(thm)],[159581096,159531680]),[]).
%
% cnf(210688040,plain,(~product1(e_1,e_2,e_4)),inference(resolution,[status(thm)],[210630976,168685200]),[]).
%
% cnf(232599064,plain,(product1(e_1,e_2,e_3)),inference(resolution,[status(thm)],[232244384,210688040]),[]).
%
% fof(e_4_is_not_e_1,plain,(~equalish(e_4,e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-9.004.tptp',unknown),[]).
%
% cnf(159539056,plain,(~equalish(e_4,e_1)),inference(rewrite,[status(thm)],[e_4_is_not_e_1]),[]).
%
% cnf(169699184,plain,(~product1(e_1,e_4,e_4)),inference(resolution,[status(thm)],[169610944,159539056]),[]).
%
% fof(element_4,plain,(group_element(e_4)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-9.004.tptp',unknown),[]).
%
% cnf(159496880,plain,(group_element(e_4)),inference(rewrite,[status(thm)],[element_4]),[]).
%
% fof(e_1_is_not_e_4,plain,(~equalish(e_1,e_4)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-9.004.tptp',unknown),[]).
%
% cnf(159509024,plain,(~equalish(e_1,e_4)),inference(rewrite,[status(thm)],[e_1_is_not_e_4]),[]).
%
% cnf(169466504,plain,(~product1(e_1,e_4,e_1)),inference(resolution,[status(thm)],[169430440,159509024]),[]).
%
% cnf(169614592,plain,(~product1(A,B,B)|equalish(A,B)),inference(resolution,[status(thm)],[159584728,159589104]),[]).
%
% fof(e_4_is_not_e_2,plain,(~equalish(e_4,e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-9.004.tptp',unknown),[]).
%
% cnf(159542704,plain,(~equalish(e_4,e_2)),inference(rewrite,[status(thm)],[e_4_is_not_e_2]),[]).
%
% cnf(169765072,plain,(~product1(e_4,e_2,e_2)),inference(resolution,[status(thm)],[169614592,159542704]),[]).
%
% cnf(169530328,plain,(~product1(e_4,e_2,e_4)),inference(resolution,[status(thm)],[169430440,159542704]),[]).
%
% fof(e_2_is_not_e_4,plain,(~equalish(e_2,e_4)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP124-9.004.tptp',unknown),[]).
%
% cnf(159524256,plain,(~equalish(e_2,e_4)),inference(rewrite,[status(thm)],[e_2_is_not_e_4]),[]).
%
% cnf(169953960,plain,(~product1(e_2,e_2,A)|~product2(A,e_2,e_4)),inference(resolution,[status(thm)],[169860064,159524256]),[]).
%
% cnf(170090248,plain,(~product2(e_2,e_2,e_4)),inference(resolution,[status(thm)],[169953960,159589104]),[]).
%
% cnf(201379616,plain,(~product1(e_4,e_2,A)|~product1(A,e_4,e_2)),inference(resolution,[status(thm)],[159628744,170090248]),[]).
%
% cnf(204572176,plain,(product1(e_4,e_2,e_3)|~product1(e_1,e_4,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[169765072,169530328,159496880,159485304,159560440,201379616]),[]).
%
% cnf(169220104,plain,(~product1(e_4,A,B)|~product1(e_1,A,B)),inference(resolution,[status(thm)],[159584728,159539056]),[]).
%
% cnf(205473200,plain,(~product1(e_1,e_4,e_2)|~product1(e_1,e_2,e_3)),inference(resolution,[status(thm)],[204572176,169220104]),[]).
%
% cnf(212429608,plain,(~product1(e_1,e_2,e_3)|product1(e_1,e_4,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[169699184,159496880,159481224,169466504,205473200,159560440]),[]).
%
% cnf(169229088,plain,(~product1(A,e_4,B)|~product1(A,e_2,B)),inference(resolution,[status(thm)],[159581096,159542704]),[]).
%
% cnf(212523896,plain,(~product1(e_1,e_2,e_3)),inference(resolution,[status(thm)],[212429608,169229088]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[232599064,212523896]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------