TSTP Solution File: GRP128-4.003 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP128-4.003 : TPTP v3.4.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art10.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 12:27:14 EDT 2009
% Result : Unsatisfiable 0.7s
% Output : Refutation 0.7s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 51 ( 25 unt; 0 def)
% Number of atoms : 93 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 91 ( 49 ~; 42 |; 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 : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 48 ( 0 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(element_2,plain,
group_element(e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP128-4.003.tptp',unknown),
[] ).
cnf(144078424,plain,
group_element(e_2),
inference(rewrite,[status(thm)],[element_2]),
[] ).
fof(element_3,plain,
group_element(e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP128-4.003.tptp',unknown),
[] ).
cnf(144082112,plain,
group_element(e_3),
inference(rewrite,[status(thm)],[element_3]),
[] ).
fof(element_1,plain,
group_element(e_1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP128-4.003.tptp',unknown),
[] ).
cnf(144070456,plain,
group_element(e_1),
inference(rewrite,[status(thm)],[element_1]),
[] ).
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) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP128-4.003.tptp',unknown),
[] ).
cnf(144046416,plain,
( ~ group_element(A)
| ~ group_element(B)
| product(e_1,A,B)
| product(e_2,A,B)
| product(e_3,A,B) ),
inference(rewrite,[status(thm)],[row_surjectivity]),
[] ).
cnf(157195888,plain,
( product(e_1,e_1,e_1)
| product(e_2,e_1,e_1)
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[144046416,144070456]),
[] ).
fof(qg3_2,plain,
! [A,B,C,D] :
( product(A,B,C)
| ~ product(D,A,C)
| ~ product(D,B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP128-4.003.tptp',unknown),
[] ).
cnf(144066288,plain,
( product(A,B,C)
| ~ product(D,A,C)
| ~ product(D,B,A) ),
inference(rewrite,[status(thm)],[qg3_2]),
[] ).
cnf(157821576,plain,
( ~ product(C,A,B)
| ~ product(C,B,A)
| product(B,B,B) ),
inference(resolution,[status(thm)],[144066288,144066288]),
[] ).
cnf(158825096,plain,
( product(e_1,e_1,e_1)
| product(e_3,e_1,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[157195888,157195888,157821576]),
[] ).
cnf(159042472,plain,
product(e_1,e_1,e_1),
inference(forward_subsumption_resolution__resolution,[status(thm)],[158825096,158825096,157821576]),
[] ).
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/GRP128-4.003.tptp',unknown),
[] ).
cnf(144132736,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/GRP128-4.003.tptp',unknown),
[] ).
cnf(144086464,plain,
~ equalish(e_1,e_2),
inference(rewrite,[status(thm)],[e_1_is_not_e_2]),
[] ).
cnf(157460344,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_2,B) ),
inference(resolution,[status(thm)],[144132736,144086464]),
[] ).
cnf(159054936,plain,
~ product(e_1,e_2,e_1),
inference(resolution,[status(thm)],[159042472,157460344]),
[] ).
cnf(159199768,plain,
( product(e_2,e_2,e_1)
| product(e_3,e_2,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[144070456,144078424,159054936,144046416]),
[] ).
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/GRP128-4.003.tptp',unknown),
[] ).
cnf(144128592,plain,
( ~ product(A,B,C)
| ~ product(A,B,D)
| equalish(C,D) ),
inference(rewrite,[status(thm)],[product_total_function2]),
[] ).
cnf(157445712,plain,
( ~ product(A,B,e_1)
| ~ product(A,B,e_2) ),
inference(resolution,[status(thm)],[144128592,144086464]),
[] ).
cnf(159919528,plain,
( product(e_2,e_2,e_1)
| ~ product(e_3,e_2,e_2) ),
inference(resolution,[status(thm)],[159199768,157445712]),
[] ).
cnf(159050648,plain,
~ product(e_1,e_1,e_2),
inference(resolution,[status(thm)],[159042472,157445712]),
[] ).
cnf(159168224,plain,
( product(e_2,e_1,e_2)
| product(e_3,e_1,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[144070456,144078424,159050648,144046416]),
[] ).
cnf(159640992,plain,
( product(e_3,e_1,e_2)
| ~ product(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[159168224,157460344]),
[] ).
cnf(161622960,plain,
( ~ product(e_2,e_2,e_2)
| ~ product(e_3,e_2,e_2) ),
inference(resolution,[status(thm)],[159640992,157460344]),
[] ).
cnf(159649624,plain,
( product(e_2,e_1,e_2)
| ~ product(e_3,e_2,e_2) ),
inference(resolution,[status(thm)],[159168224,157460344]),
[] ).
cnf(161896464,plain,
~ product(e_3,e_2,e_2),
inference(forward_subsumption_resolution__resolution,[status(thm)],[159919528,161622960,159649624,157821576]),
[] ).
cnf(161948416,plain,
( product(e_1,e_2,e_2)
| product(e_2,e_2,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[144078424,161896464,144046416]),
[] ).
cnf(162125784,plain,
product(e_2,e_2,e_2),
inference(forward_subsumption_resolution__resolution,[status(thm)],[161948416,161948416,157821576]),
[] ).
fof(e_3_is_not_e_2,plain,
~ equalish(e_3,e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP128-4.003.tptp',unknown),
[] ).
cnf(144105232,plain,
~ equalish(e_3,e_2),
inference(rewrite,[status(thm)],[e_3_is_not_e_2]),
[] ).
cnf(157524904,plain,
( ~ product(A,e_3,B)
| ~ product(A,e_2,B) ),
inference(resolution,[status(thm)],[144132736,144105232]),
[] ).
cnf(162167816,plain,
~ product(e_2,e_3,e_2),
inference(resolution,[status(thm)],[162125784,157524904]),
[] ).
cnf(162685280,plain,
( product(e_1,e_3,e_2)
| product(e_3,e_3,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[144078424,144082112,162167816,144046416]),
[] ).
cnf(162201792,plain,
product(e_3,e_1,e_2),
inference(resolution,[status(thm)],[162125784,159640992]),
[] ).
fof(e_1_is_not_e_3,plain,
~ equalish(e_1,e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP128-4.003.tptp',unknown),
[] ).
cnf(144090384,plain,
~ equalish(e_1,e_3),
inference(rewrite,[status(thm)],[e_1_is_not_e_3]),
[] ).
cnf(157492648,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_3,B) ),
inference(resolution,[status(thm)],[144132736,144090384]),
[] ).
cnf(162244864,plain,
~ product(e_3,e_3,e_2),
inference(resolution,[status(thm)],[162201792,157492648]),
[] ).
cnf(164790008,plain,
product(e_1,e_3,e_2),
inference(resolution,[status(thm)],[162685280,162244864]),
[] ).
fof(qg3_1,plain,
! [A,B,C,D] :
( product(A,B,C)
| ~ product(A,C,D)
| ~ product(C,B,D) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP128-4.003.tptp',unknown),
[] ).
cnf(144061968,plain,
( product(A,B,C)
| ~ product(A,C,D)
| ~ product(C,B,D) ),
inference(rewrite,[status(thm)],[qg3_1]),
[] ).
cnf(162307528,plain,
( product(e_3,A,e_1)
| ~ product(e_1,A,e_2) ),
inference(resolution,[status(thm)],[162201792,144061968]),
[] ).
cnf(162143200,plain,
~ product(e_2,e_2,e_1),
inference(resolution,[status(thm)],[162125784,157445712]),
[] ).
cnf(162358816,plain,
product(e_3,e_2,e_1),
inference(resolution,[status(thm)],[162143200,159199768]),
[] ).
cnf(162417256,plain,
~ product(e_3,e_3,e_1),
inference(resolution,[status(thm)],[162358816,157524904]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[164790008,162307528,162417256]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(element_2,plain,(group_element(e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP128-4.003.tptp',unknown),[]).
%
% cnf(144078424,plain,(group_element(e_2)),inference(rewrite,[status(thm)],[element_2]),[]).
%
% fof(element_3,plain,(group_element(e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP128-4.003.tptp',unknown),[]).
%
% cnf(144082112,plain,(group_element(e_3)),inference(rewrite,[status(thm)],[element_3]),[]).
%
% fof(element_1,plain,(group_element(e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP128-4.003.tptp',unknown),[]).
%
% cnf(144070456,plain,(group_element(e_1)),inference(rewrite,[status(thm)],[element_1]),[]).
%
% 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)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP128-4.003.tptp',unknown),[]).
%
% cnf(144046416,plain,(~group_element(A)|~group_element(B)|product(e_1,A,B)|product(e_2,A,B)|product(e_3,A,B)),inference(rewrite,[status(thm)],[row_surjectivity]),[]).
%
% cnf(157195888,plain,(product(e_1,e_1,e_1)|product(e_2,e_1,e_1)|product(e_3,e_1,e_1)),inference(resolution,[status(thm)],[144046416,144070456]),[]).
%
% fof(qg3_2,plain,(product(A,B,C)|~product(D,A,C)|~product(D,B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP128-4.003.tptp',unknown),[]).
%
% cnf(144066288,plain,(product(A,B,C)|~product(D,A,C)|~product(D,B,A)),inference(rewrite,[status(thm)],[qg3_2]),[]).
%
% cnf(157821576,plain,(~product(C,A,B)|~product(C,B,A)|product(B,B,B)),inference(resolution,[status(thm)],[144066288,144066288]),[]).
%
% cnf(158825096,plain,(product(e_1,e_1,e_1)|product(e_3,e_1,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[157195888,157195888,157821576]),[]).
%
% cnf(159042472,plain,(product(e_1,e_1,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[158825096,158825096,157821576]),[]).
%
% 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/GRP128-4.003.tptp',unknown),[]).
%
% cnf(144132736,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/GRP128-4.003.tptp',unknown),[]).
%
% cnf(144086464,plain,(~equalish(e_1,e_2)),inference(rewrite,[status(thm)],[e_1_is_not_e_2]),[]).
%
% cnf(157460344,plain,(~product(A,e_1,B)|~product(A,e_2,B)),inference(resolution,[status(thm)],[144132736,144086464]),[]).
%
% cnf(159054936,plain,(~product(e_1,e_2,e_1)),inference(resolution,[status(thm)],[159042472,157460344]),[]).
%
% cnf(159199768,plain,(product(e_2,e_2,e_1)|product(e_3,e_2,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[144070456,144078424,159054936,144046416]),[]).
%
% 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/GRP128-4.003.tptp',unknown),[]).
%
% cnf(144128592,plain,(~product(A,B,C)|~product(A,B,D)|equalish(C,D)),inference(rewrite,[status(thm)],[product_total_function2]),[]).
%
% cnf(157445712,plain,(~product(A,B,e_1)|~product(A,B,e_2)),inference(resolution,[status(thm)],[144128592,144086464]),[]).
%
% cnf(159919528,plain,(product(e_2,e_2,e_1)|~product(e_3,e_2,e_2)),inference(resolution,[status(thm)],[159199768,157445712]),[]).
%
% cnf(159050648,plain,(~product(e_1,e_1,e_2)),inference(resolution,[status(thm)],[159042472,157445712]),[]).
%
% cnf(159168224,plain,(product(e_2,e_1,e_2)|product(e_3,e_1,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[144070456,144078424,159050648,144046416]),[]).
%
% cnf(159640992,plain,(product(e_3,e_1,e_2)|~product(e_2,e_2,e_2)),inference(resolution,[status(thm)],[159168224,157460344]),[]).
%
% cnf(161622960,plain,(~product(e_2,e_2,e_2)|~product(e_3,e_2,e_2)),inference(resolution,[status(thm)],[159640992,157460344]),[]).
%
% cnf(159649624,plain,(product(e_2,e_1,e_2)|~product(e_3,e_2,e_2)),inference(resolution,[status(thm)],[159168224,157460344]),[]).
%
% cnf(161896464,plain,(~product(e_3,e_2,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[159919528,161622960,159649624,157821576]),[]).
%
% cnf(161948416,plain,(product(e_1,e_2,e_2)|product(e_2,e_2,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[144078424,161896464,144046416]),[]).
%
% cnf(162125784,plain,(product(e_2,e_2,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[161948416,161948416,157821576]),[]).
%
% fof(e_3_is_not_e_2,plain,(~equalish(e_3,e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP128-4.003.tptp',unknown),[]).
%
% cnf(144105232,plain,(~equalish(e_3,e_2)),inference(rewrite,[status(thm)],[e_3_is_not_e_2]),[]).
%
% cnf(157524904,plain,(~product(A,e_3,B)|~product(A,e_2,B)),inference(resolution,[status(thm)],[144132736,144105232]),[]).
%
% cnf(162167816,plain,(~product(e_2,e_3,e_2)),inference(resolution,[status(thm)],[162125784,157524904]),[]).
%
% cnf(162685280,plain,(product(e_1,e_3,e_2)|product(e_3,e_3,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[144078424,144082112,162167816,144046416]),[]).
%
% cnf(162201792,plain,(product(e_3,e_1,e_2)),inference(resolution,[status(thm)],[162125784,159640992]),[]).
%
% fof(e_1_is_not_e_3,plain,(~equalish(e_1,e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP128-4.003.tptp',unknown),[]).
%
% cnf(144090384,plain,(~equalish(e_1,e_3)),inference(rewrite,[status(thm)],[e_1_is_not_e_3]),[]).
%
% cnf(157492648,plain,(~product(A,e_1,B)|~product(A,e_3,B)),inference(resolution,[status(thm)],[144132736,144090384]),[]).
%
% cnf(162244864,plain,(~product(e_3,e_3,e_2)),inference(resolution,[status(thm)],[162201792,157492648]),[]).
%
% cnf(164790008,plain,(product(e_1,e_3,e_2)),inference(resolution,[status(thm)],[162685280,162244864]),[]).
%
% fof(qg3_1,plain,(product(A,B,C)|~product(A,C,D)|~product(C,B,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP128-4.003.tptp',unknown),[]).
%
% cnf(144061968,plain,(product(A,B,C)|~product(A,C,D)|~product(C,B,D)),inference(rewrite,[status(thm)],[qg3_1]),[]).
%
% cnf(162307528,plain,(product(e_3,A,e_1)|~product(e_1,A,e_2)),inference(resolution,[status(thm)],[162201792,144061968]),[]).
%
% cnf(162143200,plain,(~product(e_2,e_2,e_1)),inference(resolution,[status(thm)],[162125784,157445712]),[]).
%
% cnf(162358816,plain,(product(e_3,e_2,e_1)),inference(resolution,[status(thm)],[162143200,159199768]),[]).
%
% cnf(162417256,plain,(~product(e_3,e_3,e_1)),inference(resolution,[status(thm)],[162358816,157524904]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[164790008,162307528,162417256]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------