TSTP Solution File: GRP125-4.003 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP125-4.003 : TPTP v3.4.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art01.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 12:26:03 EDT 2009
% Result : Unsatisfiable 4.1s
% Output : Refutation 4.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 12
% Syntax : Number of formulae : 36 ( 24 unt; 0 def)
% Number of atoms : 60 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 58 ( 34 ~; 24 |; 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 : 35 ( 0 sgn 15 !; 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/GRP125-4.003.tptp',unknown),
[] ).
cnf(151189656,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/GRP125-4.003.tptp',unknown),
[] ).
cnf(151197624,plain,
group_element(e_2),
inference(rewrite,[status(thm)],[element_2]),
[] ).
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/GRP125-4.003.tptp',unknown),
[] ).
cnf(151165616,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/GRP125-4.003.tptp',unknown),
[] ).
cnf(151247792,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/GRP125-4.003.tptp',unknown),
[] ).
cnf(151259056,plain,
product(A,A,A),
inference(rewrite,[status(thm)],[product_idempotence]),
[] ).
cnf(164704016,plain,
( ~ product(A,A,B)
| equalish(A,B) ),
inference(resolution,[status(thm)],[151247792,151259056]),
[] ).
fof(e_1_is_not_e_2,plain,
~ equalish(e_1,e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP125-4.003.tptp',unknown),
[] ).
cnf(151205664,plain,
~ equalish(e_1,e_2),
inference(rewrite,[status(thm)],[e_1_is_not_e_2]),
[] ).
cnf(164729616,plain,
~ product(e_1,e_1,e_2),
inference(resolution,[status(thm)],[164704016,151205664]),
[] ).
cnf(182442368,plain,
( product(e_2,e_1,e_2)
| product(e_3,e_1,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[151189656,151197624,151165616,164729616]),
[] ).
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/GRP125-4.003.tptp',unknown),
[] ).
cnf(151251936,plain,
( ~ product(A,B,C)
| ~ product(A,D,C)
| equalish(B,D) ),
inference(rewrite,[status(thm)],[product_right_cancellation]),
[] ).
cnf(164834144,plain,
( ~ product(A,B,A)
| equalish(A,B) ),
inference(resolution,[status(thm)],[151251936,151259056]),
[] ).
fof(e_2_is_not_e_1,plain,
~ equalish(e_2,e_1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP125-4.003.tptp',unknown),
[] ).
cnf(151213360,plain,
~ equalish(e_2,e_1),
inference(rewrite,[status(thm)],[e_2_is_not_e_1]),
[] ).
cnf(164866976,plain,
~ product(e_2,e_1,e_2),
inference(resolution,[status(thm)],[164834144,151213360]),
[] ).
cnf(185101104,plain,
product(e_3,e_1,e_2),
inference(resolution,[status(thm)],[182442368,164866976]),
[] ).
fof(e_3_is_not_e_1,plain,
~ equalish(e_3,e_1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP125-4.003.tptp',unknown),
[] ).
cnf(151156168,plain,
~ equalish(e_3,e_1),
inference(rewrite,[status(thm)],[e_3_is_not_e_1]),
[] ).
cnf(164893720,plain,
~ product(e_3,e_1,e_3),
inference(resolution,[status(thm)],[164834144,151156168]),
[] ).
fof(e_1_is_not_e_3,plain,
~ equalish(e_1,e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP125-4.003.tptp',unknown),
[] ).
cnf(151209584,plain,
~ equalish(e_1,e_3),
inference(rewrite,[status(thm)],[e_1_is_not_e_3]),
[] ).
cnf(164738200,plain,
~ product(e_1,e_1,e_3),
inference(resolution,[status(thm)],[164704016,151209584]),
[] ).
fof(element_3,plain,
group_element(e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP125-4.003.tptp',unknown),
[] ).
cnf(151201312,plain,
group_element(e_3),
inference(rewrite,[status(thm)],[element_3]),
[] ).
fof(qg3_2,plain,
! [A,B,C,D] :
( product(A,B,C)
| ~ product(D,C,B)
| ~ product(B,A,D) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP125-4.003.tptp',unknown),
[] ).
cnf(151185488,plain,
( product(A,B,C)
| ~ product(D,C,B)
| ~ product(B,A,D) ),
inference(rewrite,[status(thm)],[qg3_2]),
[] ).
cnf(164858536,plain,
~ product(e_1,e_3,e_1),
inference(resolution,[status(thm)],[164834144,151209584]),
[] ).
cnf(165620776,plain,
( ~ product(A,e_1,e_3)
| ~ product(e_3,e_1,A) ),
inference(resolution,[status(thm)],[151185488,164858536]),
[] ).
cnf(183287544,plain,
~ product(e_3,e_1,e_2),
inference(forward_subsumption_resolution__resolution,[status(thm)],[164893720,164738200,151201312,151189656,151165616,165620776]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[185101104,183287544]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 4 seconds
% START OF PROOF SEQUENCE
% fof(element_1,plain,(group_element(e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP125-4.003.tptp',unknown),[]).
%
% cnf(151189656,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/GRP125-4.003.tptp',unknown),[]).
%
% cnf(151197624,plain,(group_element(e_2)),inference(rewrite,[status(thm)],[element_2]),[]).
%
% 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/GRP125-4.003.tptp',unknown),[]).
%
% cnf(151165616,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/GRP125-4.003.tptp',unknown),[]).
%
% cnf(151247792,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/GRP125-4.003.tptp',unknown),[]).
%
% cnf(151259056,plain,(product(A,A,A)),inference(rewrite,[status(thm)],[product_idempotence]),[]).
%
% cnf(164704016,plain,(~product(A,A,B)|equalish(A,B)),inference(resolution,[status(thm)],[151247792,151259056]),[]).
%
% fof(e_1_is_not_e_2,plain,(~equalish(e_1,e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP125-4.003.tptp',unknown),[]).
%
% cnf(151205664,plain,(~equalish(e_1,e_2)),inference(rewrite,[status(thm)],[e_1_is_not_e_2]),[]).
%
% cnf(164729616,plain,(~product(e_1,e_1,e_2)),inference(resolution,[status(thm)],[164704016,151205664]),[]).
%
% cnf(182442368,plain,(product(e_2,e_1,e_2)|product(e_3,e_1,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[151189656,151197624,151165616,164729616]),[]).
%
% 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/GRP125-4.003.tptp',unknown),[]).
%
% cnf(151251936,plain,(~product(A,B,C)|~product(A,D,C)|equalish(B,D)),inference(rewrite,[status(thm)],[product_right_cancellation]),[]).
%
% cnf(164834144,plain,(~product(A,B,A)|equalish(A,B)),inference(resolution,[status(thm)],[151251936,151259056]),[]).
%
% fof(e_2_is_not_e_1,plain,(~equalish(e_2,e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP125-4.003.tptp',unknown),[]).
%
% cnf(151213360,plain,(~equalish(e_2,e_1)),inference(rewrite,[status(thm)],[e_2_is_not_e_1]),[]).
%
% cnf(164866976,plain,(~product(e_2,e_1,e_2)),inference(resolution,[status(thm)],[164834144,151213360]),[]).
%
% cnf(185101104,plain,(product(e_3,e_1,e_2)),inference(resolution,[status(thm)],[182442368,164866976]),[]).
%
% fof(e_3_is_not_e_1,plain,(~equalish(e_3,e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP125-4.003.tptp',unknown),[]).
%
% cnf(151156168,plain,(~equalish(e_3,e_1)),inference(rewrite,[status(thm)],[e_3_is_not_e_1]),[]).
%
% cnf(164893720,plain,(~product(e_3,e_1,e_3)),inference(resolution,[status(thm)],[164834144,151156168]),[]).
%
% fof(e_1_is_not_e_3,plain,(~equalish(e_1,e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP125-4.003.tptp',unknown),[]).
%
% cnf(151209584,plain,(~equalish(e_1,e_3)),inference(rewrite,[status(thm)],[e_1_is_not_e_3]),[]).
%
% cnf(164738200,plain,(~product(e_1,e_1,e_3)),inference(resolution,[status(thm)],[164704016,151209584]),[]).
%
% fof(element_3,plain,(group_element(e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP125-4.003.tptp',unknown),[]).
%
% cnf(151201312,plain,(group_element(e_3)),inference(rewrite,[status(thm)],[element_3]),[]).
%
% fof(qg3_2,plain,(product(A,B,C)|~product(D,C,B)|~product(B,A,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP125-4.003.tptp',unknown),[]).
%
% cnf(151185488,plain,(product(A,B,C)|~product(D,C,B)|~product(B,A,D)),inference(rewrite,[status(thm)],[qg3_2]),[]).
%
% cnf(164858536,plain,(~product(e_1,e_3,e_1)),inference(resolution,[status(thm)],[164834144,151209584]),[]).
%
% cnf(165620776,plain,(~product(A,e_1,e_3)|~product(e_3,e_1,A)),inference(resolution,[status(thm)],[151185488,164858536]),[]).
%
% cnf(183287544,plain,(~product(e_3,e_1,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[164893720,164738200,151201312,151189656,151165616,165620776]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[185101104,183287544]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------