TSTP Solution File: GRP130-2.003 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP130-2.003 : 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 12:27:36 EDT 2009
% Result : Unsatisfiable 0.6s
% Output : Refutation 0.6s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of formulae : 56 ( 24 unt; 0 def)
% Number of atoms : 107 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 118 ( 67 ~; 51 |; 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 : 66 ( 1 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/GRP130-2.003.tptp',unknown),
[] ).
cnf(158959920,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/GRP130-2.003.tptp',unknown),
[] ).
cnf(158963888,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)
| product(A,B,e_3) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP130-2.003.tptp',unknown),
[] ).
cnf(159006480,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/GRP130-2.003.tptp',unknown),
[] ).
cnf(158950976,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/GRP130-2.003.tptp',unknown),
[] ).
cnf(158911136,plain,
next(e_1,e_2),
inference(rewrite,[status(thm)],[e_1_then_e_2]),
[] ).
cnf(167086696,plain,
( ~ product(e_1,e_1,A)
| ~ greater(A,e_2) ),
inference(resolution,[status(thm)],[158950976,158911136]),
[] ).
fof(e_3_greater_e_2,plain,
greater(e_3,e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP130-2.003.tptp',unknown),
[] ).
cnf(158927424,plain,
greater(e_3,e_2),
inference(rewrite,[status(thm)],[e_3_greater_e_2]),
[] ).
cnf(167293792,plain,
~ product(e_1,e_1,e_3),
inference(resolution,[status(thm)],[167086696,158927424]),
[] ).
cnf(169111648,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[158959920,159006480,167293792]),
[] ).
fof(qg3,plain,
! [A,B,C,D] :
( ~ product(A,B,C)
| ~ product(A,C,D)
| product(D,B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP130-2.003.tptp',unknown),
[] ).
cnf(159033600,plain,
( ~ product(A,B,C)
| ~ product(A,C,D)
| product(D,B,A) ),
inference(rewrite,[status(thm)],[qg3]),
[] ).
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/GRP130-2.003.tptp',unknown),
[] ).
cnf(159029216,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/GRP130-2.003.tptp',unknown),
[] ).
cnf(158907880,plain,
~ equalish(e_1,e_2),
inference(rewrite,[status(thm)],[e_1_is_not_e_2]),
[] ).
cnf(167188400,plain,
( ~ product(e_1,A,B)
| ~ product(e_2,A,B) ),
inference(resolution,[status(thm)],[159029216,158907880]),
[] ).
cnf(167430056,plain,
( ~ product(A,B,C)
| ~ product(A,C,e_2)
| ~ product(e_1,B,A) ),
inference(resolution,[status(thm)],[159033600,167188400]),
[] ).
cnf(170418904,plain,
( product(e_1,e_1,e_1)
| ~ product(e_1,A,e_1) ),
inference(resolution,[status(thm)],[169111648,167430056]),
[] ).
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/GRP130-2.003.tptp',unknown),
[] ).
cnf(158907568,plain,
( ~ product(A,B,C)
| ~ product(A,D,C)
| equalish(B,D) ),
inference(rewrite,[status(thm)],[product_right_cancellation]),
[] ).
cnf(167164272,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_2,B) ),
inference(resolution,[status(thm)],[158907568,158907880]),
[] ).
cnf(170209512,plain,
( product(e_1,e_1,e_2)
| ~ product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[169111648,167164272]),
[] ).
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/GRP130-2.003.tptp',unknown),
[] ).
cnf(159017104,plain,
( ~ product(A,B,C)
| ~ product(A,B,D)
| equalish(C,D) ),
inference(rewrite,[status(thm)],[product_total_function2]),
[] ).
cnf(167149616,plain,
( ~ product(A,B,e_1)
| ~ product(A,B,e_2) ),
inference(resolution,[status(thm)],[159017104,158907880]),
[] ).
cnf(173097488,plain,
~ product(e_1,e_2,e_1),
inference(forward_subsumption_resolution__resolution,[status(thm)],[170418904,170209512,167149616]),
[] ).
cnf(173219192,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[158959920,158963888,173097488,159006480]),
[] ).
fof(e_1_is_not_e_3,plain,
~ equalish(e_1,e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP130-2.003.tptp',unknown),
[] ).
cnf(158976128,plain,
~ equalish(e_1,e_3),
inference(rewrite,[status(thm)],[e_1_is_not_e_3]),
[] ).
cnf(167232992,plain,
( ~ product(e_1,A,B)
| ~ product(e_3,A,B) ),
inference(resolution,[status(thm)],[159029216,158976128]),
[] ).
cnf(173255080,plain,
( product(e_1,e_2,e_3)
| ~ product(e_3,e_2,e_2) ),
inference(resolution,[status(thm)],[173219192,167232992]),
[] ).
fof(element_3,plain,
group_element(e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP130-2.003.tptp',unknown),
[] ).
cnf(158967584,plain,
group_element(e_3),
inference(rewrite,[status(thm)],[element_3]),
[] ).
cnf(167356824,plain,
( ~ product(e_3,e_1,A)
| ~ product(e_3,A,e_1) ),
inference(resolution,[status(thm)],[159033600,167293792]),
[] ).
cnf(169283592,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[158959920,158967584,159006480,167356824]),
[] ).
fof(e_2_is_not_e_3,plain,
~ equalish(e_2,e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP130-2.003.tptp',unknown),
[] ).
cnf(158983472,plain,
~ equalish(e_2,e_3),
inference(rewrite,[status(thm)],[e_2_is_not_e_3]),
[] ).
cnf(167306632,plain,
( ~ product(A,B,e_2)
| ~ product(A,B,e_3) ),
inference(resolution,[status(thm)],[159017104,158983472]),
[] ).
cnf(167474904,plain,
( ~ product(e_3,A,B)
| ~ product(e_3,B,C)
| ~ product(C,A,e_2) ),
inference(resolution,[status(thm)],[159033600,167306632]),
[] ).
cnf(170948776,plain,
( product(e_3,e_1,e_3)
| ~ product(e_3,e_2,e_3) ),
inference(resolution,[status(thm)],[169283592,167474904]),
[] ).
cnf(170685496,plain,
( product(e_3,e_1,e_2)
| ~ product(e_3,e_2,e_3) ),
inference(resolution,[status(thm)],[169283592,167164272]),
[] ).
cnf(178900960,plain,
~ product(e_3,e_2,e_3),
inference(forward_subsumption_resolution__resolution,[status(thm)],[170948776,170685496,167306632]),
[] ).
cnf(179049240,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[158963888,158967584,178900960,159006480]),
[] ).
cnf(179292608,plain,
product(e_3,e_2,e_1),
inference(forward_subsumption_resolution__resolution,[status(thm)],[173255080,179049240,179049240,167430056]),
[] ).
cnf(167196936,plain,
( ~ product(A,B,e_1)
| ~ product(A,B,e_3) ),
inference(resolution,[status(thm)],[159017104,158976128]),
[] ).
cnf(167441384,plain,
( ~ product(e_3,A,B)
| ~ product(e_3,B,C)
| ~ product(C,A,e_1) ),
inference(resolution,[status(thm)],[159033600,167196936]),
[] ).
cnf(179531392,plain,
~ product(e_3,e_1,e_3),
inference(resolution,[status(thm)],[179292608,167441384]),
[] ).
cnf(179408256,plain,
~ product(e_3,e_1,e_2),
inference(resolution,[status(thm)],[179292608,167356824]),
[] ).
cnf(179750776,plain,
product(e_3,e_1,e_3),
inference(resolution,[status(thm)],[179408256,169283592]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[179531392,179750776]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(element_1,plain,(group_element(e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP130-2.003.tptp',unknown),[]).
%
% cnf(158959920,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/GRP130-2.003.tptp',unknown),[]).
%
% cnf(158963888,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)|product(A,B,e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP130-2.003.tptp',unknown),[]).
%
% cnf(159006480,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/GRP130-2.003.tptp',unknown),[]).
%
% cnf(158950976,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/GRP130-2.003.tptp',unknown),[]).
%
% cnf(158911136,plain,(next(e_1,e_2)),inference(rewrite,[status(thm)],[e_1_then_e_2]),[]).
%
% cnf(167086696,plain,(~product(e_1,e_1,A)|~greater(A,e_2)),inference(resolution,[status(thm)],[158950976,158911136]),[]).
%
% fof(e_3_greater_e_2,plain,(greater(e_3,e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP130-2.003.tptp',unknown),[]).
%
% cnf(158927424,plain,(greater(e_3,e_2)),inference(rewrite,[status(thm)],[e_3_greater_e_2]),[]).
%
% cnf(167293792,plain,(~product(e_1,e_1,e_3)),inference(resolution,[status(thm)],[167086696,158927424]),[]).
%
% cnf(169111648,plain,(product(e_1,e_1,e_1)|product(e_1,e_1,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[158959920,159006480,167293792]),[]).
%
% fof(qg3,plain,(~product(A,B,C)|~product(A,C,D)|product(D,B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP130-2.003.tptp',unknown),[]).
%
% cnf(159033600,plain,(~product(A,B,C)|~product(A,C,D)|product(D,B,A)),inference(rewrite,[status(thm)],[qg3]),[]).
%
% 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/GRP130-2.003.tptp',unknown),[]).
%
% cnf(159029216,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/GRP130-2.003.tptp',unknown),[]).
%
% cnf(158907880,plain,(~equalish(e_1,e_2)),inference(rewrite,[status(thm)],[e_1_is_not_e_2]),[]).
%
% cnf(167188400,plain,(~product(e_1,A,B)|~product(e_2,A,B)),inference(resolution,[status(thm)],[159029216,158907880]),[]).
%
% cnf(167430056,plain,(~product(A,B,C)|~product(A,C,e_2)|~product(e_1,B,A)),inference(resolution,[status(thm)],[159033600,167188400]),[]).
%
% cnf(170418904,plain,(product(e_1,e_1,e_1)|~product(e_1,A,e_1)),inference(resolution,[status(thm)],[169111648,167430056]),[]).
%
% 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/GRP130-2.003.tptp',unknown),[]).
%
% cnf(158907568,plain,(~product(A,B,C)|~product(A,D,C)|equalish(B,D)),inference(rewrite,[status(thm)],[product_right_cancellation]),[]).
%
% cnf(167164272,plain,(~product(A,e_1,B)|~product(A,e_2,B)),inference(resolution,[status(thm)],[158907568,158907880]),[]).
%
% cnf(170209512,plain,(product(e_1,e_1,e_2)|~product(e_1,e_2,e_1)),inference(resolution,[status(thm)],[169111648,167164272]),[]).
%
% 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/GRP130-2.003.tptp',unknown),[]).
%
% cnf(159017104,plain,(~product(A,B,C)|~product(A,B,D)|equalish(C,D)),inference(rewrite,[status(thm)],[product_total_function2]),[]).
%
% cnf(167149616,plain,(~product(A,B,e_1)|~product(A,B,e_2)),inference(resolution,[status(thm)],[159017104,158907880]),[]).
%
% cnf(173097488,plain,(~product(e_1,e_2,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[170418904,170209512,167149616]),[]).
%
% cnf(173219192,plain,(product(e_1,e_2,e_2)|product(e_1,e_2,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[158959920,158963888,173097488,159006480]),[]).
%
% fof(e_1_is_not_e_3,plain,(~equalish(e_1,e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP130-2.003.tptp',unknown),[]).
%
% cnf(158976128,plain,(~equalish(e_1,e_3)),inference(rewrite,[status(thm)],[e_1_is_not_e_3]),[]).
%
% cnf(167232992,plain,(~product(e_1,A,B)|~product(e_3,A,B)),inference(resolution,[status(thm)],[159029216,158976128]),[]).
%
% cnf(173255080,plain,(product(e_1,e_2,e_3)|~product(e_3,e_2,e_2)),inference(resolution,[status(thm)],[173219192,167232992]),[]).
%
% fof(element_3,plain,(group_element(e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP130-2.003.tptp',unknown),[]).
%
% cnf(158967584,plain,(group_element(e_3)),inference(rewrite,[status(thm)],[element_3]),[]).
%
% cnf(167356824,plain,(~product(e_3,e_1,A)|~product(e_3,A,e_1)),inference(resolution,[status(thm)],[159033600,167293792]),[]).
%
% cnf(169283592,plain,(product(e_3,e_1,e_2)|product(e_3,e_1,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[158959920,158967584,159006480,167356824]),[]).
%
% fof(e_2_is_not_e_3,plain,(~equalish(e_2,e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP130-2.003.tptp',unknown),[]).
%
% cnf(158983472,plain,(~equalish(e_2,e_3)),inference(rewrite,[status(thm)],[e_2_is_not_e_3]),[]).
%
% cnf(167306632,plain,(~product(A,B,e_2)|~product(A,B,e_3)),inference(resolution,[status(thm)],[159017104,158983472]),[]).
%
% cnf(167474904,plain,(~product(e_3,A,B)|~product(e_3,B,C)|~product(C,A,e_2)),inference(resolution,[status(thm)],[159033600,167306632]),[]).
%
% cnf(170948776,plain,(product(e_3,e_1,e_3)|~product(e_3,e_2,e_3)),inference(resolution,[status(thm)],[169283592,167474904]),[]).
%
% cnf(170685496,plain,(product(e_3,e_1,e_2)|~product(e_3,e_2,e_3)),inference(resolution,[status(thm)],[169283592,167164272]),[]).
%
% cnf(178900960,plain,(~product(e_3,e_2,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[170948776,170685496,167306632]),[]).
%
% cnf(179049240,plain,(product(e_3,e_2,e_1)|product(e_3,e_2,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[158963888,158967584,178900960,159006480]),[]).
%
% cnf(179292608,plain,(product(e_3,e_2,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[173255080,179049240,179049240,167430056]),[]).
%
% cnf(167196936,plain,(~product(A,B,e_1)|~product(A,B,e_3)),inference(resolution,[status(thm)],[159017104,158976128]),[]).
%
% cnf(167441384,plain,(~product(e_3,A,B)|~product(e_3,B,C)|~product(C,A,e_1)),inference(resolution,[status(thm)],[159033600,167196936]),[]).
%
% cnf(179531392,plain,(~product(e_3,e_1,e_3)),inference(resolution,[status(thm)],[179292608,167441384]),[]).
%
% cnf(179408256,plain,(~product(e_3,e_1,e_2)),inference(resolution,[status(thm)],[179292608,167356824]),[]).
%
% cnf(179750776,plain,(product(e_3,e_1,e_3)),inference(resolution,[status(thm)],[179408256,169283592]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[179531392,179750776]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------