TSTP Solution File: GRP123-4.003 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP123-4.003 : TPTP v3.4.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art09.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 12:23:59 EDT 2009
% Result : Unsatisfiable 6.3s
% Output : Refutation 6.3s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 14
% Syntax : Number of formulae : 42 ( 24 unt; 0 def)
% Number of atoms : 81 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 87 ( 48 ~; 39 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 53 ( 0 sgn 21 !; 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/GRP123-4.003.tptp',unknown),
[] ).
cnf(162038816,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/GRP123-4.003.tptp',unknown),
[] ).
cnf(162042520,plain,
group_element(e_3),
inference(rewrite,[status(thm)],[element_3]),
[] ).
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/GRP123-4.003.tptp',unknown),
[] ).
cnf(162022768,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]),
[] ).
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/GRP123-4.003.tptp',unknown),
[] ).
cnf(162089000,plain,
( ~ product(A,B,C)
| ~ product(A,B,D)
| equalish(C,D) ),
inference(rewrite,[status(thm)],[product_total_function2]),
[] ).
fof(product_idempotence,plain,
! [A] : product(A,A,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-4.003.tptp',unknown),
[] ).
cnf(162105208,plain,
product(A,A,A),
inference(rewrite,[status(thm)],[product_idempotence]),
[] ).
cnf(172898704,plain,
( ~ product(A,A,B)
| equalish(A,B) ),
inference(resolution,[status(thm)],[162089000,162105208]),
[] ).
fof(e_3_is_not_e_2,plain,
~ equalish(e_3,e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-4.003.tptp',unknown),
[] ).
cnf(162069728,plain,
~ equalish(e_3,e_2),
inference(rewrite,[status(thm)],[e_3_is_not_e_2]),
[] ).
cnf(172991736,plain,
~ product(e_3,e_3,e_2),
inference(resolution,[status(thm)],[172898704,162069728]),
[] ).
cnf(173392480,plain,
( product(e_1,e_3,e_2)
| product(e_2,e_3,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[162038816,162042520,162022768,172991736]),
[] ).
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/GRP123-4.003.tptp',unknown),
[] ).
cnf(162097328,plain,
( ~ product(A,B,C)
| ~ product(A,D,C)
| equalish(B,D) ),
inference(rewrite,[status(thm)],[product_right_cancellation]),
[] ).
cnf(173046072,plain,
( ~ product(A,B,A)
| equalish(A,B) ),
inference(resolution,[status(thm)],[162097328,162105208]),
[] ).
fof(e_2_is_not_e_3,plain,
~ equalish(e_2,e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-4.003.tptp',unknown),
[] ).
cnf(162062224,plain,
~ equalish(e_2,e_3),
inference(rewrite,[status(thm)],[e_2_is_not_e_3]),
[] ).
cnf(173088240,plain,
~ product(e_2,e_3,e_2),
inference(resolution,[status(thm)],[173046072,162062224]),
[] ).
cnf(173413480,plain,
( product(e_1,e_3,e_2)
| product(e_3,e_3,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[162038816,162042520,162022768,173088240]),
[] ).
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/GRP123-4.003.tptp',unknown),
[] ).
cnf(162100960,plain,
( ~ product(A,B,C)
| ~ product(D,B,C)
| equalish(A,D) ),
inference(rewrite,[status(thm)],[product_left_cancellation]),
[] ).
cnf(173148368,plain,
( ~ product(e_2,A,B)
| ~ product(e_3,A,B) ),
inference(resolution,[status(thm)],[162100960,162062224]),
[] ).
cnf(174628856,plain,
product(e_1,e_3,e_2),
inference(forward_subsumption_resolution__resolution,[status(thm)],[173392480,173413480,173148368]),
[] ).
fof(e_3_is_not_e_1,plain,
~ equalish(e_3,e_1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-4.003.tptp',unknown),
[] ).
cnf(162013320,plain,
~ equalish(e_3,e_1),
inference(rewrite,[status(thm)],[e_3_is_not_e_1]),
[] ).
cnf(172978272,plain,
~ product(e_3,e_3,e_1),
inference(resolution,[status(thm)],[172898704,162013320]),
[] ).
fof(e_1_is_not_e_3,plain,
~ equalish(e_1,e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-4.003.tptp',unknown),
[] ).
cnf(162054880,plain,
~ equalish(e_1,e_3),
inference(rewrite,[status(thm)],[e_1_is_not_e_3]),
[] ).
cnf(173066464,plain,
~ product(e_1,e_3,e_1),
inference(resolution,[status(thm)],[173046072,162054880]),
[] ).
fof(element_1,plain,
group_element(e_1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-4.003.tptp',unknown),
[] ).
cnf(162034904,plain,
group_element(e_1),
inference(rewrite,[status(thm)],[element_1]),
[] ).
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/GRP123-4.003.tptp',unknown),
[] ).
cnf(162113712,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(178065848,plain,
( ~ product(B,C,A)
| ~ product(A,C,B)
| equalish(A,B) ),
inference(resolution,[status(thm)],[162113712,162105208]),
[] ).
fof(e_1_is_not_e_2,plain,
~ equalish(e_1,e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-4.003.tptp',unknown),
[] ).
cnf(162046872,plain,
~ equalish(e_1,e_2),
inference(rewrite,[status(thm)],[e_1_is_not_e_2]),
[] ).
cnf(178095264,plain,
( ~ product(e_2,A,e_1)
| ~ product(e_1,A,e_2) ),
inference(resolution,[status(thm)],[178065848,162046872]),
[] ).
cnf(178800552,plain,
( ~ product(e_1,A,e_2)
| ~ group_element(A)
| product(e_1,A,e_1)
| product(e_3,A,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[162034904,178095264,162022768]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[174628856,172978272,173066464,178800552,162042520]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 6 seconds
% START OF PROOF SEQUENCE
% fof(element_2,plain,(group_element(e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-4.003.tptp',unknown),[]).
%
% cnf(162038816,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/GRP123-4.003.tptp',unknown),[]).
%
% cnf(162042520,plain,(group_element(e_3)),inference(rewrite,[status(thm)],[element_3]),[]).
%
% 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/GRP123-4.003.tptp',unknown),[]).
%
% cnf(162022768,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]),[]).
%
% 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/GRP123-4.003.tptp',unknown),[]).
%
% cnf(162089000,plain,(~product(A,B,C)|~product(A,B,D)|equalish(C,D)),inference(rewrite,[status(thm)],[product_total_function2]),[]).
%
% fof(product_idempotence,plain,(product(A,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-4.003.tptp',unknown),[]).
%
% cnf(162105208,plain,(product(A,A,A)),inference(rewrite,[status(thm)],[product_idempotence]),[]).
%
% cnf(172898704,plain,(~product(A,A,B)|equalish(A,B)),inference(resolution,[status(thm)],[162089000,162105208]),[]).
%
% fof(e_3_is_not_e_2,plain,(~equalish(e_3,e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-4.003.tptp',unknown),[]).
%
% cnf(162069728,plain,(~equalish(e_3,e_2)),inference(rewrite,[status(thm)],[e_3_is_not_e_2]),[]).
%
% cnf(172991736,plain,(~product(e_3,e_3,e_2)),inference(resolution,[status(thm)],[172898704,162069728]),[]).
%
% cnf(173392480,plain,(product(e_1,e_3,e_2)|product(e_2,e_3,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[162038816,162042520,162022768,172991736]),[]).
%
% 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/GRP123-4.003.tptp',unknown),[]).
%
% cnf(162097328,plain,(~product(A,B,C)|~product(A,D,C)|equalish(B,D)),inference(rewrite,[status(thm)],[product_right_cancellation]),[]).
%
% cnf(173046072,plain,(~product(A,B,A)|equalish(A,B)),inference(resolution,[status(thm)],[162097328,162105208]),[]).
%
% fof(e_2_is_not_e_3,plain,(~equalish(e_2,e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-4.003.tptp',unknown),[]).
%
% cnf(162062224,plain,(~equalish(e_2,e_3)),inference(rewrite,[status(thm)],[e_2_is_not_e_3]),[]).
%
% cnf(173088240,plain,(~product(e_2,e_3,e_2)),inference(resolution,[status(thm)],[173046072,162062224]),[]).
%
% cnf(173413480,plain,(product(e_1,e_3,e_2)|product(e_3,e_3,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[162038816,162042520,162022768,173088240]),[]).
%
% 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/GRP123-4.003.tptp',unknown),[]).
%
% cnf(162100960,plain,(~product(A,B,C)|~product(D,B,C)|equalish(A,D)),inference(rewrite,[status(thm)],[product_left_cancellation]),[]).
%
% cnf(173148368,plain,(~product(e_2,A,B)|~product(e_3,A,B)),inference(resolution,[status(thm)],[162100960,162062224]),[]).
%
% cnf(174628856,plain,(product(e_1,e_3,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[173392480,173413480,173148368]),[]).
%
% fof(e_3_is_not_e_1,plain,(~equalish(e_3,e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-4.003.tptp',unknown),[]).
%
% cnf(162013320,plain,(~equalish(e_3,e_1)),inference(rewrite,[status(thm)],[e_3_is_not_e_1]),[]).
%
% cnf(172978272,plain,(~product(e_3,e_3,e_1)),inference(resolution,[status(thm)],[172898704,162013320]),[]).
%
% fof(e_1_is_not_e_3,plain,(~equalish(e_1,e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-4.003.tptp',unknown),[]).
%
% cnf(162054880,plain,(~equalish(e_1,e_3)),inference(rewrite,[status(thm)],[e_1_is_not_e_3]),[]).
%
% cnf(173066464,plain,(~product(e_1,e_3,e_1)),inference(resolution,[status(thm)],[173046072,162054880]),[]).
%
% fof(element_1,plain,(group_element(e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-4.003.tptp',unknown),[]).
%
% cnf(162034904,plain,(group_element(e_1)),inference(rewrite,[status(thm)],[element_1]),[]).
%
% 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/GRP123-4.003.tptp',unknown),[]).
%
% cnf(162113712,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(178065848,plain,(~product(B,C,A)|~product(A,C,B)|equalish(A,B)),inference(resolution,[status(thm)],[162113712,162105208]),[]).
%
% fof(e_1_is_not_e_2,plain,(~equalish(e_1,e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-4.003.tptp',unknown),[]).
%
% cnf(162046872,plain,(~equalish(e_1,e_2)),inference(rewrite,[status(thm)],[e_1_is_not_e_2]),[]).
%
% cnf(178095264,plain,(~product(e_2,A,e_1)|~product(e_1,A,e_2)),inference(resolution,[status(thm)],[178065848,162046872]),[]).
%
% cnf(178800552,plain,(~product(e_1,A,e_2)|~group_element(A)|product(e_1,A,e_1)|product(e_3,A,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[162034904,178095264,162022768]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[174628856,172978272,173066464,178800552,162042520]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------