TSTP Solution File: GRP131-2.002 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP131-2.002 : TPTP v3.4.2. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art02.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 12:28:37 EDT 2009
% Result : Unsatisfiable 5.0s
% Output : Refutation 5.0s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 60 ( 8 unt; 0 def)
% Number of atoms : 176 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 216 ( 100 ~; 116 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 99 ( 0 sgn 26 !; 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/GRP131-2.002.tptp',unknown),
[] ).
cnf(160967320,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/GRP131-2.002.tptp',unknown),
[] ).
cnf(160971256,plain,
group_element(e_2),
inference(rewrite,[status(thm)],[element_2]),
[] ).
fof(product_total_function1,plain,
! [A,B] :
( ~ group_element(A)
| ~ group_element(B)
| product(A,B,e_1)
| product(A,B,e_2) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP131-2.002.tptp',unknown),
[] ).
cnf(160993584,plain,
( ~ group_element(A)
| ~ group_element(B)
| product(A,B,e_1)
| product(A,B,e_2) ),
inference(rewrite,[status(thm)],[product_total_function1]),
[] ).
cnf(171464136,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[160993584,160967320]),
[] ).
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/GRP131-2.002.tptp',unknown),
[] ).
cnf(161012648,plain,
( ~ product(A,B,C)
| ~ product(A,D,C)
| equalish(B,D) ),
inference(rewrite,[status(thm)],[product_right_cancellation]),
[] ).
fof(e_1_is_not_e_2,plain,
~ equalish(e_1,e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP131-2.002.tptp',unknown),
[] ).
cnf(160927232,plain,
~ equalish(e_1,e_2),
inference(rewrite,[status(thm)],[e_1_is_not_e_2]),
[] ).
cnf(171572872,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_2,B) ),
inference(resolution,[status(thm)],[161012648,160927232]),
[] ).
cnf(171955280,plain,
( product(e_1,e_1,e_1)
| ~ product(e_1,e_2,e_2) ),
inference(resolution,[status(thm)],[171464136,171572872]),
[] ).
cnf(172894808,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_2,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[160967320,160971256,171955280,160993584]),
[] ).
cnf(171446416,plain,
( ~ group_element(A)
| product(e_1,A,e_1)
| product(e_1,A,e_2) ),
inference(resolution,[status(thm)],[160993584,160967320]),
[] ).
cnf(171517224,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2) ),
inference(resolution,[status(thm)],[171446416,160971256]),
[] ).
cnf(173141584,plain,
( product(e_1,e_2,e_1)
| ~ product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[171517224,171572872]),
[] ).
cnf(171757768,plain,
( ~ group_element(A)
| product(A,e_1,e_2)
| ~ product(A,e_2,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[160967320,160993584,171572872]),
[] ).
cnf(176658512,plain,
( ~ group_element(A)
| product(A,e_1,e_2)
| product(A,e_2,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[160971256,171757768,160993584]),
[] ).
cnf(171695608,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[160993584,160971256]),
[] ).
cnf(172164944,plain,
( product(e_2,e_2,e_1)
| ~ product(e_2,e_1,e_2) ),
inference(resolution,[status(thm)],[171695608,171572872]),
[] ).
cnf(171479680,plain,
( ~ group_element(A)
| product(A,e_1,e_1)
| product(A,e_1,e_2) ),
inference(resolution,[status(thm)],[160993584,160967320]),
[] ).
cnf(171496264,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(resolution,[status(thm)],[171479680,160971256]),
[] ).
cnf(173862760,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[172164944,171496264]),
[] ).
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/GRP131-2.002.tptp',unknown),
[] ).
cnf(161016280,plain,
( ~ product(A,B,C)
| ~ product(D,B,C)
| equalish(A,D) ),
inference(rewrite,[status(thm)],[product_left_cancellation]),
[] ).
cnf(171598640,plain,
( ~ product(e_1,A,B)
| ~ product(e_2,A,B) ),
inference(resolution,[status(thm)],[161016280,160927232]),
[] ).
cnf(174763384,plain,
( product(e_2,e_2,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[173862760,171598640]),
[] ).
fof(qg1_1,plain,
! [A,B,C,D,E,F] :
( ~ product(A,B,C)
| ~ product(D,E,C)
| ~ product(F,B,A)
| ~ product(F,E,D)
| equalish(A,D) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP131-2.002.tptp',unknown),
[] ).
cnf(161024312,plain,
( ~ product(A,B,C)
| ~ product(D,E,C)
| ~ product(F,B,A)
| ~ product(F,E,D)
| equalish(A,D) ),
inference(rewrite,[status(thm)],[qg1_1]),
[] ).
cnf(171610720,plain,
( ~ product(e_1,A,B)
| ~ product(e_2,C,B)
| ~ product(D,A,e_1)
| ~ product(D,C,e_2) ),
inference(resolution,[status(thm)],[161024312,160927232]),
[] ).
cnf(177610008,plain,
( ~ product(e_1,A,e_2)
| ~ product(C,A,e_1)
| ~ product(C,B,e_2)
| ~ group_element(B)
| product(e_2,B,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[160971256,171610720,160993584]),
[] ).
cnf(178562032,plain,
( ~ product(e_1,A,e_2)
| ~ product(B,A,e_1)
| ~ product(B,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[177610008,160971256]),
[] ).
cnf(178620216,plain,
( ~ product(B,A,e_1)
| ~ product(B,e_2,e_2)
| product(e_2,e_2,e_1)
| ~ group_element(A)
| product(e_1,A,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[160967320,178562032,160993584]),
[] ).
cnf(178656064,plain,
( ~ product(A,e_1,e_1)
| ~ product(A,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[174763384,178620216,160967320]),
[] ).
cnf(178690104,plain,
( product(e_2,e_2,e_1)
| ~ group_element(A)
| product(A,e_1,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[176658512,160967320,178656064,160993584]),
[] ).
fof(qg1_2,plain,
! [A,B,C,D,E,F] :
( ~ product(A,B,C)
| ~ product(D,E,C)
| ~ product(F,B,A)
| ~ product(F,E,D)
| equalish(B,E) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP131-2.002.tptp',unknown),
[] ).
cnf(161028672,plain,
( ~ product(A,B,C)
| ~ product(D,E,C)
| ~ product(F,B,A)
| ~ product(F,E,D)
| equalish(B,E) ),
inference(rewrite,[status(thm)],[qg1_2]),
[] ).
cnf(171618880,plain,
( ~ product(A,e_1,B)
| ~ product(C,e_2,B)
| ~ product(D,e_1,A)
| ~ product(D,e_2,C) ),
inference(resolution,[status(thm)],[161028672,160927232]),
[] ).
cnf(177734248,plain,
( ~ product(B,e_2,e_1)
| ~ product(C,e_1,A)
| ~ product(C,e_2,B)
| ~ group_element(A)
| product(A,e_1,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[160967320,171618880,160993584]),
[] ).
cnf(178748680,plain,
( ~ product(B,e_1,A)
| ~ group_element(A)
| product(A,e_1,e_2)
| ~ group_element(B)
| product(B,e_2,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[178690104,160971256,177734248,160993584]),
[] ).
cnf(178753072,plain,
product(e_1,e_2,e_1),
inference(forward_subsumption_resolution__resolution,[status(thm)],[172894808,173141584,178748680,160967320]),
[] ).
cnf(172160424,plain,
( product(e_2,e_2,e_2)
| ~ product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[171695608,171572872]),
[] ).
cnf(171971760,plain,
( product(e_1,e_1,e_1)
| ~ product(e_2,e_1,e_2) ),
inference(resolution,[status(thm)],[171464136,171598640]),
[] ).
cnf(173037128,plain,
( product(e_1,e_1,e_1)
| product(e_2,e_1,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[160967320,160971256,171971760,160993584]),
[] ).
cnf(173765888,plain,
( product(e_2,e_2,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[172160424,173037128]),
[] ).
cnf(174649952,plain,
( product(e_1,e_1,e_1)
| ~ product(A,e_2,e_2)
| equalish(A,e_2) ),
inference(resolution,[status(thm)],[173765888,161016280]),
[] ).
cnf(174831960,plain,
( product(e_2,e_1,e_1)
| ~ product(A,e_2,e_1)
| equalish(A,e_2) ),
inference(resolution,[status(thm)],[173862760,161016280]),
[] ).
cnf(171946640,plain,
( product(e_1,e_1,e_2)
| ~ product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[171464136,171572872]),
[] ).
cnf(172608512,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_2,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[160967320,160971256,171946640,160993584]),
[] ).
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/GRP131-2.002.tptp',unknown),
[] ).
cnf(161004248,plain,
( ~ product(A,B,C)
| ~ product(A,B,D)
| equalish(C,D) ),
inference(rewrite,[status(thm)],[product_total_function2]),
[] ).
cnf(171557608,plain,
( ~ product(A,B,e_1)
| ~ product(A,B,e_2) ),
inference(resolution,[status(thm)],[161004248,160927232]),
[] ).
cnf(172633856,plain,
( product(e_1,e_2,e_2)
| ~ product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[172608512,171557608]),
[] ).
cnf(175338008,plain,
( ~ product(e_1,e_1,e_1)
| ~ product(e_1,e_2,A)
| equalish(A,e_2) ),
inference(resolution,[status(thm)],[172633856,161004248]),
[] ).
cnf(177450136,plain,
( ~ product(C,D,e_1)
| ~ product(E,B,A)
| ~ product(E,D,C)
| equalish(A,C)
| ~ group_element(A)
| ~ group_element(B)
| product(A,B,e_2) ),
inference(resolution,[status(thm)],[161024312,160993584]),
[] ).
cnf(179558024,plain,
( ~ product(B,C,e_1)
| ~ product(D,e_2,A)
| ~ product(D,C,B)
| equalish(A,B)
| ~ group_element(A)
| product(A,e_2,e_2) ),
inference(resolution,[status(thm)],[177450136,160971256]),
[] ).
cnf(179792984,plain,
( ~ product(e_2,B,e_1)
| ~ product(C,e_2,A)
| equalish(A,e_2)
| ~ group_element(A)
| product(A,e_2,e_2)
| ~ group_element(C)
| ~ group_element(B)
| product(C,B,e_1) ),
inference(resolution,[status(thm)],[179558024,160993584]),
[] ).
cnf(183769680,plain,
( ~ product(e_1,e_2,e_1)
| equalish(e_1,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[174649952,174831960,175338008,179792984,160967320]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[178753072,183769680,160927232]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 5 seconds
% START OF PROOF SEQUENCE
% fof(element_1,plain,(group_element(e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP131-2.002.tptp',unknown),[]).
%
% cnf(160967320,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/GRP131-2.002.tptp',unknown),[]).
%
% cnf(160971256,plain,(group_element(e_2)),inference(rewrite,[status(thm)],[element_2]),[]).
%
% fof(product_total_function1,plain,(~group_element(A)|~group_element(B)|product(A,B,e_1)|product(A,B,e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP131-2.002.tptp',unknown),[]).
%
% cnf(160993584,plain,(~group_element(A)|~group_element(B)|product(A,B,e_1)|product(A,B,e_2)),inference(rewrite,[status(thm)],[product_total_function1]),[]).
%
% cnf(171464136,plain,(product(e_1,e_1,e_1)|product(e_1,e_1,e_2)),inference(resolution,[status(thm)],[160993584,160967320]),[]).
%
% 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/GRP131-2.002.tptp',unknown),[]).
%
% cnf(161012648,plain,(~product(A,B,C)|~product(A,D,C)|equalish(B,D)),inference(rewrite,[status(thm)],[product_right_cancellation]),[]).
%
% fof(e_1_is_not_e_2,plain,(~equalish(e_1,e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP131-2.002.tptp',unknown),[]).
%
% cnf(160927232,plain,(~equalish(e_1,e_2)),inference(rewrite,[status(thm)],[e_1_is_not_e_2]),[]).
%
% cnf(171572872,plain,(~product(A,e_1,B)|~product(A,e_2,B)),inference(resolution,[status(thm)],[161012648,160927232]),[]).
%
% cnf(171955280,plain,(product(e_1,e_1,e_1)|~product(e_1,e_2,e_2)),inference(resolution,[status(thm)],[171464136,171572872]),[]).
%
% cnf(172894808,plain,(product(e_1,e_1,e_1)|product(e_1,e_2,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[160967320,160971256,171955280,160993584]),[]).
%
% cnf(171446416,plain,(~group_element(A)|product(e_1,A,e_1)|product(e_1,A,e_2)),inference(resolution,[status(thm)],[160993584,160967320]),[]).
%
% cnf(171517224,plain,(product(e_1,e_2,e_1)|product(e_1,e_2,e_2)),inference(resolution,[status(thm)],[171446416,160971256]),[]).
%
% cnf(173141584,plain,(product(e_1,e_2,e_1)|~product(e_1,e_1,e_2)),inference(resolution,[status(thm)],[171517224,171572872]),[]).
%
% cnf(171757768,plain,(~group_element(A)|product(A,e_1,e_2)|~product(A,e_2,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[160967320,160993584,171572872]),[]).
%
% cnf(176658512,plain,(~group_element(A)|product(A,e_1,e_2)|product(A,e_2,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[160971256,171757768,160993584]),[]).
%
% cnf(171695608,plain,(product(e_2,e_2,e_1)|product(e_2,e_2,e_2)),inference(resolution,[status(thm)],[160993584,160971256]),[]).
%
% cnf(172164944,plain,(product(e_2,e_2,e_1)|~product(e_2,e_1,e_2)),inference(resolution,[status(thm)],[171695608,171572872]),[]).
%
% cnf(171479680,plain,(~group_element(A)|product(A,e_1,e_1)|product(A,e_1,e_2)),inference(resolution,[status(thm)],[160993584,160967320]),[]).
%
% cnf(171496264,plain,(product(e_2,e_1,e_1)|product(e_2,e_1,e_2)),inference(resolution,[status(thm)],[171479680,160971256]),[]).
%
% cnf(173862760,plain,(product(e_2,e_2,e_1)|product(e_2,e_1,e_1)),inference(resolution,[status(thm)],[172164944,171496264]),[]).
%
% 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/GRP131-2.002.tptp',unknown),[]).
%
% cnf(161016280,plain,(~product(A,B,C)|~product(D,B,C)|equalish(A,D)),inference(rewrite,[status(thm)],[product_left_cancellation]),[]).
%
% cnf(171598640,plain,(~product(e_1,A,B)|~product(e_2,A,B)),inference(resolution,[status(thm)],[161016280,160927232]),[]).
%
% cnf(174763384,plain,(product(e_2,e_2,e_1)|~product(e_1,e_1,e_1)),inference(resolution,[status(thm)],[173862760,171598640]),[]).
%
% fof(qg1_1,plain,(~product(A,B,C)|~product(D,E,C)|~product(F,B,A)|~product(F,E,D)|equalish(A,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP131-2.002.tptp',unknown),[]).
%
% cnf(161024312,plain,(~product(A,B,C)|~product(D,E,C)|~product(F,B,A)|~product(F,E,D)|equalish(A,D)),inference(rewrite,[status(thm)],[qg1_1]),[]).
%
% cnf(171610720,plain,(~product(e_1,A,B)|~product(e_2,C,B)|~product(D,A,e_1)|~product(D,C,e_2)),inference(resolution,[status(thm)],[161024312,160927232]),[]).
%
% cnf(177610008,plain,(~product(e_1,A,e_2)|~product(C,A,e_1)|~product(C,B,e_2)|~group_element(B)|product(e_2,B,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[160971256,171610720,160993584]),[]).
%
% cnf(178562032,plain,(~product(e_1,A,e_2)|~product(B,A,e_1)|~product(B,e_2,e_2)|product(e_2,e_2,e_1)),inference(resolution,[status(thm)],[177610008,160971256]),[]).
%
% cnf(178620216,plain,(~product(B,A,e_1)|~product(B,e_2,e_2)|product(e_2,e_2,e_1)|~group_element(A)|product(e_1,A,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[160967320,178562032,160993584]),[]).
%
% cnf(178656064,plain,(~product(A,e_1,e_1)|~product(A,e_2,e_2)|product(e_2,e_2,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[174763384,178620216,160967320]),[]).
%
% cnf(178690104,plain,(product(e_2,e_2,e_1)|~group_element(A)|product(A,e_1,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[176658512,160967320,178656064,160993584]),[]).
%
% fof(qg1_2,plain,(~product(A,B,C)|~product(D,E,C)|~product(F,B,A)|~product(F,E,D)|equalish(B,E)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP131-2.002.tptp',unknown),[]).
%
% cnf(161028672,plain,(~product(A,B,C)|~product(D,E,C)|~product(F,B,A)|~product(F,E,D)|equalish(B,E)),inference(rewrite,[status(thm)],[qg1_2]),[]).
%
% cnf(171618880,plain,(~product(A,e_1,B)|~product(C,e_2,B)|~product(D,e_1,A)|~product(D,e_2,C)),inference(resolution,[status(thm)],[161028672,160927232]),[]).
%
% cnf(177734248,plain,(~product(B,e_2,e_1)|~product(C,e_1,A)|~product(C,e_2,B)|~group_element(A)|product(A,e_1,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[160967320,171618880,160993584]),[]).
%
% cnf(178748680,plain,(~product(B,e_1,A)|~group_element(A)|product(A,e_1,e_2)|~group_element(B)|product(B,e_2,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[178690104,160971256,177734248,160993584]),[]).
%
% cnf(178753072,plain,(product(e_1,e_2,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[172894808,173141584,178748680,160967320]),[]).
%
% cnf(172160424,plain,(product(e_2,e_2,e_2)|~product(e_2,e_1,e_1)),inference(resolution,[status(thm)],[171695608,171572872]),[]).
%
% cnf(171971760,plain,(product(e_1,e_1,e_1)|~product(e_2,e_1,e_2)),inference(resolution,[status(thm)],[171464136,171598640]),[]).
%
% cnf(173037128,plain,(product(e_1,e_1,e_1)|product(e_2,e_1,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[160967320,160971256,171971760,160993584]),[]).
%
% cnf(173765888,plain,(product(e_2,e_2,e_2)|product(e_1,e_1,e_1)),inference(resolution,[status(thm)],[172160424,173037128]),[]).
%
% cnf(174649952,plain,(product(e_1,e_1,e_1)|~product(A,e_2,e_2)|equalish(A,e_2)),inference(resolution,[status(thm)],[173765888,161016280]),[]).
%
% cnf(174831960,plain,(product(e_2,e_1,e_1)|~product(A,e_2,e_1)|equalish(A,e_2)),inference(resolution,[status(thm)],[173862760,161016280]),[]).
%
% cnf(171946640,plain,(product(e_1,e_1,e_2)|~product(e_1,e_2,e_1)),inference(resolution,[status(thm)],[171464136,171572872]),[]).
%
% cnf(172608512,plain,(product(e_1,e_1,e_2)|product(e_1,e_2,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[160967320,160971256,171946640,160993584]),[]).
%
% 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/GRP131-2.002.tptp',unknown),[]).
%
% cnf(161004248,plain,(~product(A,B,C)|~product(A,B,D)|equalish(C,D)),inference(rewrite,[status(thm)],[product_total_function2]),[]).
%
% cnf(171557608,plain,(~product(A,B,e_1)|~product(A,B,e_2)),inference(resolution,[status(thm)],[161004248,160927232]),[]).
%
% cnf(172633856,plain,(product(e_1,e_2,e_2)|~product(e_1,e_1,e_1)),inference(resolution,[status(thm)],[172608512,171557608]),[]).
%
% cnf(175338008,plain,(~product(e_1,e_1,e_1)|~product(e_1,e_2,A)|equalish(A,e_2)),inference(resolution,[status(thm)],[172633856,161004248]),[]).
%
% cnf(177450136,plain,(~product(C,D,e_1)|~product(E,B,A)|~product(E,D,C)|equalish(A,C)|~group_element(A)|~group_element(B)|product(A,B,e_2)),inference(resolution,[status(thm)],[161024312,160993584]),[]).
%
% cnf(179558024,plain,(~product(B,C,e_1)|~product(D,e_2,A)|~product(D,C,B)|equalish(A,B)|~group_element(A)|product(A,e_2,e_2)),inference(resolution,[status(thm)],[177450136,160971256]),[]).
%
% cnf(179792984,plain,(~product(e_2,B,e_1)|~product(C,e_2,A)|equalish(A,e_2)|~group_element(A)|product(A,e_2,e_2)|~group_element(C)|~group_element(B)|product(C,B,e_1)),inference(resolution,[status(thm)],[179558024,160993584]),[]).
%
% cnf(183769680,plain,(~product(e_1,e_2,e_1)|equalish(e_1,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[174649952,174831960,175338008,179792984,160967320]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[178753072,183769680,160927232]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------