TSTP Solution File: GRP134-2.003 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP134-2.003 : TPTP v3.4.2. Released v1.2.0.
% 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 12:28:56 EDT 2009
% Result : Unsatisfiable 0.8s
% Output : Refutation 0.8s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of formulae : 65 ( 23 unt; 0 def)
% Number of atoms : 127 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 136 ( 74 ~; 62 |; 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 : 68 ( 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/GRP134-2.003.tptp',unknown),
[] ).
cnf(164069272,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/GRP134-2.003.tptp',unknown),
[] ).
cnf(164115832,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/GRP134-2.003.tptp',unknown),
[] ).
cnf(164060328,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/GRP134-2.003.tptp',unknown),
[] ).
cnf(164020488,plain,
next(e_1,e_2),
inference(rewrite,[status(thm)],[e_1_then_e_2]),
[] ).
cnf(172196056,plain,
( ~ product(e_1,e_1,A)
| ~ greater(A,e_2) ),
inference(resolution,[status(thm)],[164060328,164020488]),
[] ).
fof(e_3_greater_e_2,plain,
greater(e_3,e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP134-2.003.tptp',unknown),
[] ).
cnf(164036776,plain,
greater(e_3,e_2),
inference(rewrite,[status(thm)],[e_3_greater_e_2]),
[] ).
cnf(172351288,plain,
~ product(e_1,e_1,e_3),
inference(resolution,[status(thm)],[172196056,164036776]),
[] ).
cnf(174057848,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[164069272,164115832,172351288]),
[] ).
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/GRP134-2.003.tptp',unknown),
[] ).
cnf(164016920,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/GRP134-2.003.tptp',unknown),
[] ).
cnf(164017232,plain,
~ equalish(e_1,e_2),
inference(rewrite,[status(thm)],[e_1_is_not_e_2]),
[] ).
cnf(172226176,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_2,B) ),
inference(resolution,[status(thm)],[164016920,164017232]),
[] ).
cnf(175057560,plain,
( product(e_1,e_1,e_1)
| ~ product(e_1,e_2,e_2) ),
inference(resolution,[status(thm)],[174057848,172226176]),
[] ).
fof(element_2,plain,
group_element(e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP134-2.003.tptp',unknown),
[] ).
cnf(164073240,plain,
group_element(e_2),
inference(rewrite,[status(thm)],[element_2]),
[] ).
cnf(175048944,plain,
( product(e_1,e_1,e_2)
| ~ product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[174057848,172226176]),
[] ).
fof(qg4,plain,
! [A,B,C,D] :
( ~ product(A,B,C)
| ~ product(B,A,D)
| product(C,D,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP134-2.003.tptp',unknown),
[] ).
cnf(164142952,plain,
( ~ product(A,B,C)
| ~ product(B,A,D)
| product(C,D,B) ),
inference(rewrite,[status(thm)],[qg4]),
[] ).
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/GRP134-2.003.tptp',unknown),
[] ).
cnf(164138568,plain,
( ~ product(A,B,C)
| ~ product(D,B,C)
| equalish(A,D) ),
inference(rewrite,[status(thm)],[product_left_cancellation]),
[] ).
cnf(172254392,plain,
( ~ product(e_1,A,B)
| ~ product(e_2,A,B) ),
inference(resolution,[status(thm)],[164138568,164017232]),
[] ).
cnf(172533096,plain,
( ~ product(A,B,e_2)
| ~ product(B,A,C)
| ~ product(e_1,C,B) ),
inference(resolution,[status(thm)],[164142952,172254392]),
[] ).
cnf(177550000,plain,
~ product(e_1,e_2,e_1),
inference(forward_subsumption_resolution__resolution,[status(thm)],[175048944,175048944,172533096]),
[] ).
cnf(177585904,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[164069272,164073240,177550000,164115832]),
[] ).
cnf(178141704,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_2,e_3) ),
inference(resolution,[status(thm)],[175057560,177585904]),
[] ).
cnf(175069696,plain,
( product(e_1,e_1,e_1)
| ~ product(e_2,e_1,e_2) ),
inference(resolution,[status(thm)],[174057848,172254392]),
[] ).
cnf(175066064,plain,
( product(e_1,e_1,e_2)
| ~ product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[174057848,172254392]),
[] ).
cnf(172521680,plain,
( ~ product(A,B,C)
| ~ product(B,A,e_2)
| ~ product(C,e_1,B) ),
inference(resolution,[status(thm)],[164142952,172226176]),
[] ).
cnf(175255328,plain,
( product(e_1,e_1,e_1)
| ~ product(e_2,e_1,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[175066064,174057848,172521680]),
[] ).
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/GRP134-2.003.tptp',unknown),
[] ).
cnf(164126456,plain,
( ~ product(A,B,C)
| ~ product(A,B,D)
| equalish(C,D) ),
inference(rewrite,[status(thm)],[product_total_function2]),
[] ).
cnf(172211520,plain,
( ~ product(A,B,e_1)
| ~ product(A,B,e_2) ),
inference(resolution,[status(thm)],[164126456,164017232]),
[] ).
cnf(178691008,plain,
~ product(e_2,e_1,e_1),
inference(forward_subsumption_resolution__resolution,[status(thm)],[175255328,175066064,172211520]),
[] ).
cnf(178803392,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[164069272,164073240,178691008,164115832]),
[] ).
cnf(179965224,plain,
( product(e_1,e_1,e_1)
| product(e_2,e_1,e_3) ),
inference(resolution,[status(thm)],[175069696,178803392]),
[] ).
cnf(172458968,plain,
( ~ product(A,e_3,e_1)
| ~ product(e_3,A,e_1) ),
inference(resolution,[status(thm)],[164142952,172351288]),
[] ).
cnf(172678320,plain,
( ~ product(A,e_1,e_3)
| ~ product(e_1,A,e_3) ),
inference(resolution,[status(thm)],[172458968,164142952]),
[] ).
cnf(180525208,plain,
product(e_1,e_1,e_1),
inference(forward_subsumption_resolution__resolution,[status(thm)],[178141704,179965224,172678320]),
[] ).
cnf(180775600,plain,
( ~ product(e_1,e_1,A)
| product(A,e_1,e_1) ),
inference(resolution,[status(thm)],[180525208,164142952]),
[] ).
cnf(172504664,plain,
( ~ product(A,e_1,B)
| ~ product(e_1,A,C)
| ~ product(B,C,e_2) ),
inference(resolution,[status(thm)],[164142952,172211520]),
[] ).
cnf(181678016,plain,
~ product(e_1,e_1,e_2),
inference(forward_subsumption_resolution__resolution,[status(thm)],[180775600,175255328,172504664]),
[] ).
fof(element_3,plain,
group_element(e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP134-2.003.tptp',unknown),
[] ).
cnf(164076936,plain,
group_element(e_3),
inference(rewrite,[status(thm)],[element_3]),
[] ).
fof(e_1_is_not_e_3,plain,
~ equalish(e_1,e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP134-2.003.tptp',unknown),
[] ).
cnf(164085480,plain,
~ equalish(e_1,e_3),
inference(rewrite,[status(thm)],[e_1_is_not_e_3]),
[] ).
cnf(172414064,plain,
( ~ product(e_1,A,B)
| ~ product(e_3,A,B) ),
inference(resolution,[status(thm)],[164138568,164085480]),
[] ).
cnf(180703488,plain,
~ product(e_3,e_1,e_1),
inference(resolution,[status(thm)],[180525208,172414064]),
[] ).
cnf(181040912,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[164069272,164076936,180703488,164115832]),
[] ).
cnf(172653664,plain,
( product(B,B,A)
| ~ product(C,B,A)
| ~ product(B,C,A) ),
inference(resolution,[status(thm)],[164142952,164142952]),
[] ).
cnf(182689272,plain,
( product(e_3,e_1,e_3)
| ~ product(e_1,e_3,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[181678016,181040912,172653664]),
[] ).
cnf(174220600,plain,
( product(e_3,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[164076936,164115832,172458968]),
[] ).
cnf(172390480,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_3,B) ),
inference(resolution,[status(thm)],[164016920,164085480]),
[] ).
cnf(175512792,plain,
( product(e_3,e_3,e_2)
| ~ product(e_3,e_1,e_3) ),
inference(resolution,[status(thm)],[174220600,172390480]),
[] ).
cnf(183755096,plain,
~ product(e_1,e_3,e_2),
inference(forward_subsumption_resolution__resolution,[status(thm)],[182689272,175512792,172414064]),
[] ).
cnf(182555616,plain,
( product(e_3,e_1,e_2)
| ~ product(e_1,e_3,e_3) ),
inference(resolution,[status(thm)],[181040912,172678320]),
[] ).
cnf(175509216,plain,
( product(e_3,e_3,e_3)
| ~ product(e_3,e_1,e_2) ),
inference(resolution,[status(thm)],[174220600,172390480]),
[] ).
cnf(183281696,plain,
~ product(e_1,e_3,e_3),
inference(forward_subsumption_resolution__resolution,[status(thm)],[182555616,175509216,172414064]),
[] ).
cnf(183578976,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[164069272,164076936,183281696,164115832]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[183755096,180525208,183578976,172390480]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(element_1,plain,(group_element(e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP134-2.003.tptp',unknown),[]).
%
% cnf(164069272,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/GRP134-2.003.tptp',unknown),[]).
%
% cnf(164115832,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/GRP134-2.003.tptp',unknown),[]).
%
% cnf(164060328,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/GRP134-2.003.tptp',unknown),[]).
%
% cnf(164020488,plain,(next(e_1,e_2)),inference(rewrite,[status(thm)],[e_1_then_e_2]),[]).
%
% cnf(172196056,plain,(~product(e_1,e_1,A)|~greater(A,e_2)),inference(resolution,[status(thm)],[164060328,164020488]),[]).
%
% fof(e_3_greater_e_2,plain,(greater(e_3,e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP134-2.003.tptp',unknown),[]).
%
% cnf(164036776,plain,(greater(e_3,e_2)),inference(rewrite,[status(thm)],[e_3_greater_e_2]),[]).
%
% cnf(172351288,plain,(~product(e_1,e_1,e_3)),inference(resolution,[status(thm)],[172196056,164036776]),[]).
%
% cnf(174057848,plain,(product(e_1,e_1,e_1)|product(e_1,e_1,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[164069272,164115832,172351288]),[]).
%
% 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/GRP134-2.003.tptp',unknown),[]).
%
% cnf(164016920,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/GRP134-2.003.tptp',unknown),[]).
%
% cnf(164017232,plain,(~equalish(e_1,e_2)),inference(rewrite,[status(thm)],[e_1_is_not_e_2]),[]).
%
% cnf(172226176,plain,(~product(A,e_1,B)|~product(A,e_2,B)),inference(resolution,[status(thm)],[164016920,164017232]),[]).
%
% cnf(175057560,plain,(product(e_1,e_1,e_1)|~product(e_1,e_2,e_2)),inference(resolution,[status(thm)],[174057848,172226176]),[]).
%
% fof(element_2,plain,(group_element(e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP134-2.003.tptp',unknown),[]).
%
% cnf(164073240,plain,(group_element(e_2)),inference(rewrite,[status(thm)],[element_2]),[]).
%
% cnf(175048944,plain,(product(e_1,e_1,e_2)|~product(e_1,e_2,e_1)),inference(resolution,[status(thm)],[174057848,172226176]),[]).
%
% fof(qg4,plain,(~product(A,B,C)|~product(B,A,D)|product(C,D,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP134-2.003.tptp',unknown),[]).
%
% cnf(164142952,plain,(~product(A,B,C)|~product(B,A,D)|product(C,D,B)),inference(rewrite,[status(thm)],[qg4]),[]).
%
% 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/GRP134-2.003.tptp',unknown),[]).
%
% cnf(164138568,plain,(~product(A,B,C)|~product(D,B,C)|equalish(A,D)),inference(rewrite,[status(thm)],[product_left_cancellation]),[]).
%
% cnf(172254392,plain,(~product(e_1,A,B)|~product(e_2,A,B)),inference(resolution,[status(thm)],[164138568,164017232]),[]).
%
% cnf(172533096,plain,(~product(A,B,e_2)|~product(B,A,C)|~product(e_1,C,B)),inference(resolution,[status(thm)],[164142952,172254392]),[]).
%
% cnf(177550000,plain,(~product(e_1,e_2,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[175048944,175048944,172533096]),[]).
%
% cnf(177585904,plain,(product(e_1,e_2,e_2)|product(e_1,e_2,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[164069272,164073240,177550000,164115832]),[]).
%
% cnf(178141704,plain,(product(e_1,e_1,e_1)|product(e_1,e_2,e_3)),inference(resolution,[status(thm)],[175057560,177585904]),[]).
%
% cnf(175069696,plain,(product(e_1,e_1,e_1)|~product(e_2,e_1,e_2)),inference(resolution,[status(thm)],[174057848,172254392]),[]).
%
% cnf(175066064,plain,(product(e_1,e_1,e_2)|~product(e_2,e_1,e_1)),inference(resolution,[status(thm)],[174057848,172254392]),[]).
%
% cnf(172521680,plain,(~product(A,B,C)|~product(B,A,e_2)|~product(C,e_1,B)),inference(resolution,[status(thm)],[164142952,172226176]),[]).
%
% cnf(175255328,plain,(product(e_1,e_1,e_1)|~product(e_2,e_1,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[175066064,174057848,172521680]),[]).
%
% 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/GRP134-2.003.tptp',unknown),[]).
%
% cnf(164126456,plain,(~product(A,B,C)|~product(A,B,D)|equalish(C,D)),inference(rewrite,[status(thm)],[product_total_function2]),[]).
%
% cnf(172211520,plain,(~product(A,B,e_1)|~product(A,B,e_2)),inference(resolution,[status(thm)],[164126456,164017232]),[]).
%
% cnf(178691008,plain,(~product(e_2,e_1,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[175255328,175066064,172211520]),[]).
%
% cnf(178803392,plain,(product(e_2,e_1,e_2)|product(e_2,e_1,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[164069272,164073240,178691008,164115832]),[]).
%
% cnf(179965224,plain,(product(e_1,e_1,e_1)|product(e_2,e_1,e_3)),inference(resolution,[status(thm)],[175069696,178803392]),[]).
%
% cnf(172458968,plain,(~product(A,e_3,e_1)|~product(e_3,A,e_1)),inference(resolution,[status(thm)],[164142952,172351288]),[]).
%
% cnf(172678320,plain,(~product(A,e_1,e_3)|~product(e_1,A,e_3)),inference(resolution,[status(thm)],[172458968,164142952]),[]).
%
% cnf(180525208,plain,(product(e_1,e_1,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[178141704,179965224,172678320]),[]).
%
% cnf(180775600,plain,(~product(e_1,e_1,A)|product(A,e_1,e_1)),inference(resolution,[status(thm)],[180525208,164142952]),[]).
%
% cnf(172504664,plain,(~product(A,e_1,B)|~product(e_1,A,C)|~product(B,C,e_2)),inference(resolution,[status(thm)],[164142952,172211520]),[]).
%
% cnf(181678016,plain,(~product(e_1,e_1,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[180775600,175255328,172504664]),[]).
%
% fof(element_3,plain,(group_element(e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP134-2.003.tptp',unknown),[]).
%
% cnf(164076936,plain,(group_element(e_3)),inference(rewrite,[status(thm)],[element_3]),[]).
%
% fof(e_1_is_not_e_3,plain,(~equalish(e_1,e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP134-2.003.tptp',unknown),[]).
%
% cnf(164085480,plain,(~equalish(e_1,e_3)),inference(rewrite,[status(thm)],[e_1_is_not_e_3]),[]).
%
% cnf(172414064,plain,(~product(e_1,A,B)|~product(e_3,A,B)),inference(resolution,[status(thm)],[164138568,164085480]),[]).
%
% cnf(180703488,plain,(~product(e_3,e_1,e_1)),inference(resolution,[status(thm)],[180525208,172414064]),[]).
%
% cnf(181040912,plain,(product(e_3,e_1,e_2)|product(e_3,e_1,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[164069272,164076936,180703488,164115832]),[]).
%
% cnf(172653664,plain,(product(B,B,A)|~product(C,B,A)|~product(B,C,A)),inference(resolution,[status(thm)],[164142952,164142952]),[]).
%
% cnf(182689272,plain,(product(e_3,e_1,e_3)|~product(e_1,e_3,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[181678016,181040912,172653664]),[]).
%
% cnf(174220600,plain,(product(e_3,e_3,e_2)|product(e_3,e_3,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[164076936,164115832,172458968]),[]).
%
% cnf(172390480,plain,(~product(A,e_1,B)|~product(A,e_3,B)),inference(resolution,[status(thm)],[164016920,164085480]),[]).
%
% cnf(175512792,plain,(product(e_3,e_3,e_2)|~product(e_3,e_1,e_3)),inference(resolution,[status(thm)],[174220600,172390480]),[]).
%
% cnf(183755096,plain,(~product(e_1,e_3,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[182689272,175512792,172414064]),[]).
%
% cnf(182555616,plain,(product(e_3,e_1,e_2)|~product(e_1,e_3,e_3)),inference(resolution,[status(thm)],[181040912,172678320]),[]).
%
% cnf(175509216,plain,(product(e_3,e_3,e_3)|~product(e_3,e_1,e_2)),inference(resolution,[status(thm)],[174220600,172390480]),[]).
%
% cnf(183281696,plain,(~product(e_1,e_3,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[182555616,175509216,172414064]),[]).
%
% cnf(183578976,plain,(product(e_1,e_3,e_1)|product(e_1,e_3,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[164069272,164076936,183281696,164115832]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[183755096,180525208,183578976,172390480]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------