TSTP Solution File: GRP133-2.003 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP133-2.003 : TPTP v3.4.2. Released v1.2.0.
% 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 12:28:48 EDT 2009
% Result : Unsatisfiable 2.0s
% Output : Refutation 2.0s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 14
% Syntax : Number of formulae : 87 ( 26 unt; 0 def)
% Number of atoms : 178 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 174 ( 83 ~; 91 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 64 ( 0 sgn 21 !; 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/GRP133-2.003.tptp',unknown),
[] ).
cnf(165162904,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) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP133-2.003.tptp',unknown),
[] ).
cnf(165209464,plain,
( ~ group_element(A)
| ~ group_element(B)
| product(A,B,e_1)
| product(A,B,e_2)
| product(A,B,e_3) ),
inference(rewrite,[status(thm)],[product_total_function1]),
[] ).
fof(no_redundancy,plain,
! [A,B,C] :
( ~ product(A,e_1,B)
| ~ next(A,C)
| ~ greater(B,C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP133-2.003.tptp',unknown),
[] ).
cnf(165153960,plain,
( ~ product(A,e_1,B)
| ~ next(A,C)
| ~ greater(B,C) ),
inference(rewrite,[status(thm)],[no_redundancy]),
[] ).
fof(e_1_then_e_2,plain,
next(e_1,e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP133-2.003.tptp',unknown),
[] ).
cnf(165114120,plain,
next(e_1,e_2),
inference(rewrite,[status(thm)],[e_1_then_e_2]),
[] ).
cnf(173290536,plain,
( ~ product(e_1,e_1,A)
| ~ greater(A,e_2) ),
inference(resolution,[status(thm)],[165153960,165114120]),
[] ).
fof(e_3_greater_e_2,plain,
greater(e_3,e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP133-2.003.tptp',unknown),
[] ).
cnf(165130408,plain,
greater(e_3,e_2),
inference(rewrite,[status(thm)],[e_3_greater_e_2]),
[] ).
cnf(173651616,plain,
~ product(e_1,e_1,e_3),
inference(resolution,[status(thm)],[173290536,165130408]),
[] ).
cnf(174391664,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[165162904,165209464,173651616]),
[] ).
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/GRP133-2.003.tptp',unknown),
[] ).
cnf(165232200,plain,
( ~ product(A,B,C)
| ~ product(D,B,C)
| equalish(A,D) ),
inference(rewrite,[status(thm)],[product_left_cancellation]),
[] ).
fof(e_1_is_not_e_2,plain,
~ equalish(e_1,e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP133-2.003.tptp',unknown),
[] ).
cnf(165110864,plain,
~ equalish(e_1,e_2),
inference(rewrite,[status(thm)],[e_1_is_not_e_2]),
[] ).
cnf(173382064,plain,
( ~ product(e_1,A,B)
| ~ product(e_2,A,B) ),
inference(resolution,[status(thm)],[165232200,165110864]),
[] ).
cnf(175062368,plain,
( product(e_1,e_1,e_2)
| ~ product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[174391664,173382064]),
[] ).
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/GRP133-2.003.tptp',unknown),
[] ).
cnf(165220088,plain,
( ~ product(A,B,C)
| ~ product(A,B,D)
| equalish(C,D) ),
inference(rewrite,[status(thm)],[product_total_function2]),
[] ).
cnf(173340840,plain,
( ~ product(A,B,e_1)
| ~ product(A,B,e_2) ),
inference(resolution,[status(thm)],[165220088,165110864]),
[] ).
cnf(176676416,plain,
( ~ product(e_2,e_1,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[175062368,173340840]),
[] ).
fof(qg3,plain,
! [A,B,C,D] :
( ~ product(A,B,C)
| ~ product(B,A,D)
| product(C,D,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP133-2.003.tptp',unknown),
[] ).
cnf(165236584,plain,
( ~ product(A,B,C)
| ~ product(B,A,D)
| product(C,D,A) ),
inference(rewrite,[status(thm)],[qg3]),
[] ).
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/GRP133-2.003.tptp',unknown),
[] ).
cnf(165110552,plain,
( ~ product(A,B,C)
| ~ product(A,D,C)
| equalish(B,D) ),
inference(rewrite,[status(thm)],[product_right_cancellation]),
[] ).
cnf(173356296,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_2,B) ),
inference(resolution,[status(thm)],[165110552,165110864]),
[] ).
cnf(173757824,plain,
( ~ product(A,B,C)
| ~ product(B,A,e_2)
| ~ product(C,e_1,A) ),
inference(resolution,[status(thm)],[165236584,173356296]),
[] ).
cnf(202492176,plain,
~ product(e_2,e_1,e_1),
inference(forward_subsumption_resolution__resolution,[status(thm)],[174391664,176676416,173757824,174391664]),
[] ).
fof(element_2,plain,
group_element(e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP133-2.003.tptp',unknown),
[] ).
cnf(165166872,plain,
group_element(e_2),
inference(rewrite,[status(thm)],[element_2]),
[] ).
cnf(175070080,plain,
( product(e_1,e_1,e_1)
| ~ product(e_2,e_1,e_2) ),
inference(resolution,[status(thm)],[174391664,173382064]),
[] ).
cnf(176927432,plain,
( product(e_1,e_1,e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_3) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[165162904,165166872,175070080,165209464]),
[] ).
cnf(203176856,plain,
( product(e_1,e_1,e_1)
| product(e_2,e_1,e_3) ),
inference(resolution,[status(thm)],[202492176,176927432]),
[] ).
cnf(173693536,plain,
( ~ product(e_3,A,e_1)
| ~ product(A,e_3,e_1) ),
inference(resolution,[status(thm)],[165236584,173651616]),
[] ).
cnf(173909568,plain,
( ~ product(e_1,A,e_3)
| ~ product(A,e_1,e_3) ),
inference(resolution,[status(thm)],[173693536,165236584]),
[] ).
cnf(204150216,plain,
( product(e_1,e_1,e_1)
| ~ product(e_1,e_2,e_3) ),
inference(resolution,[status(thm)],[203176856,173909568]),
[] ).
cnf(175053864,plain,
( product(e_1,e_1,e_1)
| ~ product(e_1,e_2,e_2) ),
inference(resolution,[status(thm)],[174391664,173356296]),
[] ).
cnf(176659176,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_2,e_3) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[165162904,165166872,175053864,165209464]),
[] ).
cnf(214071720,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[204150216,176659176]),
[] ).
fof(element_3,plain,
group_element(e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP133-2.003.tptp',unknown),
[] ).
cnf(165170568,plain,
group_element(e_3),
inference(rewrite,[status(thm)],[element_3]),
[] ).
cnf(174575136,plain,
( product(e_3,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[165170568,165209464,173693536]),
[] ).
cnf(202503648,plain,
( ~ product(e_2,e_1,e_3)
| product(e_3,e_3,e_3) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[174575136,173757824,174575136]),
[] ).
cnf(206391736,plain,
( product(e_3,e_3,e_3)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[202503648,203176856]),
[] ).
fof(e_1_is_not_e_3,plain,
~ equalish(e_1,e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP133-2.003.tptp',unknown),
[] ).
cnf(165179112,plain,
~ equalish(e_1,e_3),
inference(rewrite,[status(thm)],[e_1_is_not_e_3]),
[] ).
cnf(173423376,plain,
( ~ product(e_1,A,B)
| ~ product(e_3,A,B) ),
inference(resolution,[status(thm)],[165232200,165179112]),
[] ).
cnf(207085520,plain,
( product(e_1,e_1,e_1)
| ~ product(e_1,e_3,e_3) ),
inference(resolution,[status(thm)],[206391736,173423376]),
[] ).
cnf(173405008,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_3,B) ),
inference(resolution,[status(thm)],[165110552,165179112]),
[] ).
cnf(175087136,plain,
( product(e_1,e_1,e_1)
| ~ product(e_1,e_3,e_2) ),
inference(resolution,[status(thm)],[174391664,173405008]),
[] ).
cnf(177197824,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_3) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[165162904,165170568,175087136,165209464]),
[] ).
cnf(221309456,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[207085520,177197824]),
[] ).
fof(e_3_is_not_e_2,plain,
~ equalish(e_3,e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP133-2.003.tptp',unknown),
[] ).
cnf(165198000,plain,
~ equalish(e_3,e_2),
inference(rewrite,[status(thm)],[e_3_is_not_e_2]),
[] ).
cnf(173448704,plain,
( ~ product(A,e_3,B)
| ~ product(A,e_2,B) ),
inference(resolution,[status(thm)],[165110552,165198000]),
[] ).
cnf(221758808,plain,
product(e_1,e_1,e_1),
inference(forward_subsumption_resolution__resolution,[status(thm)],[214071720,221309456,173448704]),
[] ).
cnf(222070568,plain,
~ product(e_1,e_1,e_2),
inference(resolution,[status(thm)],[221758808,173340840]),
[] ).
cnf(175045200,plain,
( product(e_1,e_1,e_2)
| ~ product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[174391664,173356296]),
[] ).
cnf(176514848,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[165162904,165166872,175045200,165209464]),
[] ).
cnf(197570512,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_2,e_2)
| ~ product(e_1,e_3,e_3) ),
inference(resolution,[status(thm)],[176514848,173448704]),
[] ).
cnf(176831440,plain,
( ~ product(e_2,e_1,e_2)
| ~ product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[175070080,173340840]),
[] ).
cnf(180146912,plain,
( ~ product(e_1,e_1,e_2)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_3) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[165162904,165166872,176831440,165209464]),
[] ).
cnf(176778816,plain,
( product(e_1,e_1,e_2)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[165162904,165166872,175062368,165209464]),
[] ).
cnf(203037520,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[180146912,176778816,173757824,176778816]),
[] ).
cnf(206382048,plain,
( product(e_3,e_3,e_3)
| product(e_2,e_1,e_2) ),
inference(resolution,[status(thm)],[202503648,203037520]),
[] ).
cnf(206566632,plain,
( product(e_2,e_1,e_2)
| ~ product(e_1,e_3,e_3) ),
inference(resolution,[status(thm)],[206382048,173423376]),
[] ).
cnf(173888168,plain,
( product(B,B,A)
| ~ product(B,C,A)
| ~ product(C,B,A) ),
inference(resolution,[status(thm)],[165236584,165236584]),
[] ).
cnf(218550432,plain,
( ~ product(e_1,e_3,e_3)
| product(e_1,e_1,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[197570512,206566632,173888168]),
[] ).
cnf(221039920,plain,
~ product(e_1,e_3,e_3),
inference(forward_subsumption_resolution__resolution,[status(thm)],[218550432,207085520,173340840]),
[] ).
cnf(173213256,plain,
( ~ group_element(A)
| product(A,e_3,e_1)
| product(A,e_3,e_2)
| product(A,e_3,e_3) ),
inference(resolution,[status(thm)],[165209464,165170568]),
[] ).
cnf(173265624,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(resolution,[status(thm)],[173213256,165162904]),
[] ).
cnf(221360056,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2) ),
inference(resolution,[status(thm)],[221039920,173265624]),
[] ).
cnf(222088864,plain,
~ product(e_1,e_3,e_1),
inference(resolution,[status(thm)],[221758808,173405008]),
[] ).
cnf(223372800,plain,
product(e_1,e_3,e_2),
inference(resolution,[status(thm)],[221360056,222088864]),
[] ).
cnf(223895480,plain,
~ product(e_3,e_1,e_2),
inference(forward_subsumption_resolution__resolution,[status(thm)],[222070568,223372800,173888168]),
[] ).
cnf(175095640,plain,
( product(e_1,e_1,e_2)
| ~ product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[174391664,173423376]),
[] ).
cnf(177315032,plain,
( product(e_1,e_1,e_2)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[165162904,165170568,175095640,165209464]),
[] ).
cnf(225780408,plain,
( product(e_1,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(resolution,[status(thm)],[223895480,177315032]),
[] ).
cnf(175079336,plain,
( product(e_1,e_1,e_2)
| ~ product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[174391664,173405008]),
[] ).
cnf(177049888,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[165162904,165170568,175079336,165209464]),
[] ).
cnf(221457824,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_3,e_2) ),
inference(resolution,[status(thm)],[221039920,177049888]),
[] ).
cnf(175369016,plain,
( product(e_3,e_3,e_2)
| ~ product(e_3,e_1,e_3) ),
inference(resolution,[status(thm)],[174575136,173405008]),
[] ).
cnf(177787160,plain,
( ~ product(e_3,e_1,e_3)
| ~ product(e_1,e_3,e_2) ),
inference(resolution,[status(thm)],[175369016,173423376]),
[] ).
cnf(226034696,plain,
product(e_1,e_1,e_2),
inference(forward_subsumption_resolution__resolution,[status(thm)],[225780408,221457824,177787160]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[226034696,222070568]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 2 seconds
% START OF PROOF SEQUENCE
% fof(element_1,plain,(group_element(e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP133-2.003.tptp',unknown),[]).
%
% cnf(165162904,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)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP133-2.003.tptp',unknown),[]).
%
% cnf(165209464,plain,(~group_element(A)|~group_element(B)|product(A,B,e_1)|product(A,B,e_2)|product(A,B,e_3)),inference(rewrite,[status(thm)],[product_total_function1]),[]).
%
% fof(no_redundancy,plain,(~product(A,e_1,B)|~next(A,C)|~greater(B,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP133-2.003.tptp',unknown),[]).
%
% cnf(165153960,plain,(~product(A,e_1,B)|~next(A,C)|~greater(B,C)),inference(rewrite,[status(thm)],[no_redundancy]),[]).
%
% fof(e_1_then_e_2,plain,(next(e_1,e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP133-2.003.tptp',unknown),[]).
%
% cnf(165114120,plain,(next(e_1,e_2)),inference(rewrite,[status(thm)],[e_1_then_e_2]),[]).
%
% cnf(173290536,plain,(~product(e_1,e_1,A)|~greater(A,e_2)),inference(resolution,[status(thm)],[165153960,165114120]),[]).
%
% fof(e_3_greater_e_2,plain,(greater(e_3,e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP133-2.003.tptp',unknown),[]).
%
% cnf(165130408,plain,(greater(e_3,e_2)),inference(rewrite,[status(thm)],[e_3_greater_e_2]),[]).
%
% cnf(173651616,plain,(~product(e_1,e_1,e_3)),inference(resolution,[status(thm)],[173290536,165130408]),[]).
%
% cnf(174391664,plain,(product(e_1,e_1,e_1)|product(e_1,e_1,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[165162904,165209464,173651616]),[]).
%
% 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/GRP133-2.003.tptp',unknown),[]).
%
% cnf(165232200,plain,(~product(A,B,C)|~product(D,B,C)|equalish(A,D)),inference(rewrite,[status(thm)],[product_left_cancellation]),[]).
%
% fof(e_1_is_not_e_2,plain,(~equalish(e_1,e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP133-2.003.tptp',unknown),[]).
%
% cnf(165110864,plain,(~equalish(e_1,e_2)),inference(rewrite,[status(thm)],[e_1_is_not_e_2]),[]).
%
% cnf(173382064,plain,(~product(e_1,A,B)|~product(e_2,A,B)),inference(resolution,[status(thm)],[165232200,165110864]),[]).
%
% cnf(175062368,plain,(product(e_1,e_1,e_2)|~product(e_2,e_1,e_1)),inference(resolution,[status(thm)],[174391664,173382064]),[]).
%
% 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/GRP133-2.003.tptp',unknown),[]).
%
% cnf(165220088,plain,(~product(A,B,C)|~product(A,B,D)|equalish(C,D)),inference(rewrite,[status(thm)],[product_total_function2]),[]).
%
% cnf(173340840,plain,(~product(A,B,e_1)|~product(A,B,e_2)),inference(resolution,[status(thm)],[165220088,165110864]),[]).
%
% cnf(176676416,plain,(~product(e_2,e_1,e_1)|~product(e_1,e_1,e_1)),inference(resolution,[status(thm)],[175062368,173340840]),[]).
%
% fof(qg3,plain,(~product(A,B,C)|~product(B,A,D)|product(C,D,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP133-2.003.tptp',unknown),[]).
%
% cnf(165236584,plain,(~product(A,B,C)|~product(B,A,D)|product(C,D,A)),inference(rewrite,[status(thm)],[qg3]),[]).
%
% 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/GRP133-2.003.tptp',unknown),[]).
%
% cnf(165110552,plain,(~product(A,B,C)|~product(A,D,C)|equalish(B,D)),inference(rewrite,[status(thm)],[product_right_cancellation]),[]).
%
% cnf(173356296,plain,(~product(A,e_1,B)|~product(A,e_2,B)),inference(resolution,[status(thm)],[165110552,165110864]),[]).
%
% cnf(173757824,plain,(~product(A,B,C)|~product(B,A,e_2)|~product(C,e_1,A)),inference(resolution,[status(thm)],[165236584,173356296]),[]).
%
% cnf(202492176,plain,(~product(e_2,e_1,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[174391664,176676416,173757824,174391664]),[]).
%
% fof(element_2,plain,(group_element(e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP133-2.003.tptp',unknown),[]).
%
% cnf(165166872,plain,(group_element(e_2)),inference(rewrite,[status(thm)],[element_2]),[]).
%
% cnf(175070080,plain,(product(e_1,e_1,e_1)|~product(e_2,e_1,e_2)),inference(resolution,[status(thm)],[174391664,173382064]),[]).
%
% cnf(176927432,plain,(product(e_1,e_1,e_1)|product(e_2,e_1,e_1)|product(e_2,e_1,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[165162904,165166872,175070080,165209464]),[]).
%
% cnf(203176856,plain,(product(e_1,e_1,e_1)|product(e_2,e_1,e_3)),inference(resolution,[status(thm)],[202492176,176927432]),[]).
%
% cnf(173693536,plain,(~product(e_3,A,e_1)|~product(A,e_3,e_1)),inference(resolution,[status(thm)],[165236584,173651616]),[]).
%
% cnf(173909568,plain,(~product(e_1,A,e_3)|~product(A,e_1,e_3)),inference(resolution,[status(thm)],[173693536,165236584]),[]).
%
% cnf(204150216,plain,(product(e_1,e_1,e_1)|~product(e_1,e_2,e_3)),inference(resolution,[status(thm)],[203176856,173909568]),[]).
%
% cnf(175053864,plain,(product(e_1,e_1,e_1)|~product(e_1,e_2,e_2)),inference(resolution,[status(thm)],[174391664,173356296]),[]).
%
% cnf(176659176,plain,(product(e_1,e_1,e_1)|product(e_1,e_2,e_1)|product(e_1,e_2,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[165162904,165166872,175053864,165209464]),[]).
%
% cnf(214071720,plain,(product(e_1,e_1,e_1)|product(e_1,e_2,e_1)),inference(resolution,[status(thm)],[204150216,176659176]),[]).
%
% fof(element_3,plain,(group_element(e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP133-2.003.tptp',unknown),[]).
%
% cnf(165170568,plain,(group_element(e_3)),inference(rewrite,[status(thm)],[element_3]),[]).
%
% cnf(174575136,plain,(product(e_3,e_3,e_2)|product(e_3,e_3,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[165170568,165209464,173693536]),[]).
%
% cnf(202503648,plain,(~product(e_2,e_1,e_3)|product(e_3,e_3,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[174575136,173757824,174575136]),[]).
%
% cnf(206391736,plain,(product(e_3,e_3,e_3)|product(e_1,e_1,e_1)),inference(resolution,[status(thm)],[202503648,203176856]),[]).
%
% fof(e_1_is_not_e_3,plain,(~equalish(e_1,e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP133-2.003.tptp',unknown),[]).
%
% cnf(165179112,plain,(~equalish(e_1,e_3)),inference(rewrite,[status(thm)],[e_1_is_not_e_3]),[]).
%
% cnf(173423376,plain,(~product(e_1,A,B)|~product(e_3,A,B)),inference(resolution,[status(thm)],[165232200,165179112]),[]).
%
% cnf(207085520,plain,(product(e_1,e_1,e_1)|~product(e_1,e_3,e_3)),inference(resolution,[status(thm)],[206391736,173423376]),[]).
%
% cnf(173405008,plain,(~product(A,e_1,B)|~product(A,e_3,B)),inference(resolution,[status(thm)],[165110552,165179112]),[]).
%
% cnf(175087136,plain,(product(e_1,e_1,e_1)|~product(e_1,e_3,e_2)),inference(resolution,[status(thm)],[174391664,173405008]),[]).
%
% cnf(177197824,plain,(product(e_1,e_1,e_1)|product(e_1,e_3,e_1)|product(e_1,e_3,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[165162904,165170568,175087136,165209464]),[]).
%
% cnf(221309456,plain,(product(e_1,e_1,e_1)|product(e_1,e_3,e_1)),inference(resolution,[status(thm)],[207085520,177197824]),[]).
%
% fof(e_3_is_not_e_2,plain,(~equalish(e_3,e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP133-2.003.tptp',unknown),[]).
%
% cnf(165198000,plain,(~equalish(e_3,e_2)),inference(rewrite,[status(thm)],[e_3_is_not_e_2]),[]).
%
% cnf(173448704,plain,(~product(A,e_3,B)|~product(A,e_2,B)),inference(resolution,[status(thm)],[165110552,165198000]),[]).
%
% cnf(221758808,plain,(product(e_1,e_1,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[214071720,221309456,173448704]),[]).
%
% cnf(222070568,plain,(~product(e_1,e_1,e_2)),inference(resolution,[status(thm)],[221758808,173340840]),[]).
%
% cnf(175045200,plain,(product(e_1,e_1,e_2)|~product(e_1,e_2,e_1)),inference(resolution,[status(thm)],[174391664,173356296]),[]).
%
% cnf(176514848,plain,(product(e_1,e_1,e_2)|product(e_1,e_2,e_2)|product(e_1,e_2,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[165162904,165166872,175045200,165209464]),[]).
%
% cnf(197570512,plain,(product(e_1,e_1,e_2)|product(e_1,e_2,e_2)|~product(e_1,e_3,e_3)),inference(resolution,[status(thm)],[176514848,173448704]),[]).
%
% cnf(176831440,plain,(~product(e_2,e_1,e_2)|~product(e_1,e_1,e_2)),inference(resolution,[status(thm)],[175070080,173340840]),[]).
%
% cnf(180146912,plain,(~product(e_1,e_1,e_2)|product(e_2,e_1,e_1)|product(e_2,e_1,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[165162904,165166872,176831440,165209464]),[]).
%
% cnf(176778816,plain,(product(e_1,e_1,e_2)|product(e_2,e_1,e_2)|product(e_2,e_1,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[165162904,165166872,175062368,165209464]),[]).
%
% cnf(203037520,plain,(product(e_2,e_1,e_2)|product(e_2,e_1,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[180146912,176778816,173757824,176778816]),[]).
%
% cnf(206382048,plain,(product(e_3,e_3,e_3)|product(e_2,e_1,e_2)),inference(resolution,[status(thm)],[202503648,203037520]),[]).
%
% cnf(206566632,plain,(product(e_2,e_1,e_2)|~product(e_1,e_3,e_3)),inference(resolution,[status(thm)],[206382048,173423376]),[]).
%
% cnf(173888168,plain,(product(B,B,A)|~product(B,C,A)|~product(C,B,A)),inference(resolution,[status(thm)],[165236584,165236584]),[]).
%
% cnf(218550432,plain,(~product(e_1,e_3,e_3)|product(e_1,e_1,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[197570512,206566632,173888168]),[]).
%
% cnf(221039920,plain,(~product(e_1,e_3,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[218550432,207085520,173340840]),[]).
%
% cnf(173213256,plain,(~group_element(A)|product(A,e_3,e_1)|product(A,e_3,e_2)|product(A,e_3,e_3)),inference(resolution,[status(thm)],[165209464,165170568]),[]).
%
% cnf(173265624,plain,(product(e_1,e_3,e_1)|product(e_1,e_3,e_2)|product(e_1,e_3,e_3)),inference(resolution,[status(thm)],[173213256,165162904]),[]).
%
% cnf(221360056,plain,(product(e_1,e_3,e_1)|product(e_1,e_3,e_2)),inference(resolution,[status(thm)],[221039920,173265624]),[]).
%
% cnf(222088864,plain,(~product(e_1,e_3,e_1)),inference(resolution,[status(thm)],[221758808,173405008]),[]).
%
% cnf(223372800,plain,(product(e_1,e_3,e_2)),inference(resolution,[status(thm)],[221360056,222088864]),[]).
%
% cnf(223895480,plain,(~product(e_3,e_1,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[222070568,223372800,173888168]),[]).
%
% cnf(175095640,plain,(product(e_1,e_1,e_2)|~product(e_3,e_1,e_1)),inference(resolution,[status(thm)],[174391664,173423376]),[]).
%
% cnf(177315032,plain,(product(e_1,e_1,e_2)|product(e_3,e_1,e_2)|product(e_3,e_1,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[165162904,165170568,175095640,165209464]),[]).
%
% cnf(225780408,plain,(product(e_1,e_1,e_2)|product(e_3,e_1,e_3)),inference(resolution,[status(thm)],[223895480,177315032]),[]).
%
% cnf(175079336,plain,(product(e_1,e_1,e_2)|~product(e_1,e_3,e_1)),inference(resolution,[status(thm)],[174391664,173405008]),[]).
%
% cnf(177049888,plain,(product(e_1,e_1,e_2)|product(e_1,e_3,e_2)|product(e_1,e_3,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[165162904,165170568,175079336,165209464]),[]).
%
% cnf(221457824,plain,(product(e_1,e_1,e_2)|product(e_1,e_3,e_2)),inference(resolution,[status(thm)],[221039920,177049888]),[]).
%
% cnf(175369016,plain,(product(e_3,e_3,e_2)|~product(e_3,e_1,e_3)),inference(resolution,[status(thm)],[174575136,173405008]),[]).
%
% cnf(177787160,plain,(~product(e_3,e_1,e_3)|~product(e_1,e_3,e_2)),inference(resolution,[status(thm)],[175369016,173423376]),[]).
%
% cnf(226034696,plain,(product(e_1,e_1,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[225780408,221457824,177787160]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[226034696,222070568]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------