TSTP Solution File: GRP123-2.003 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP123-2.003 : TPTP v3.4.2. Released v1.2.0.
% 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 12:23:51 EDT 2009
% Result : Unsatisfiable 33.1s
% Output : Refutation 33.1s
% 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_1,plain,
group_element(e_1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-2.003.tptp',unknown),
[] ).
cnf(166539936,plain,
group_element(e_1),
inference(rewrite,[status(thm)],[element_1]),
[] ).
fof(element_3,plain,
group_element(e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-2.003.tptp',unknown),
[] ).
cnf(166547600,plain,
group_element(e_3),
inference(rewrite,[status(thm)],[element_3]),
[] ).
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/GRP123-2.003.tptp',unknown),
[] ).
cnf(166586496,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(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/GRP123-2.003.tptp',unknown),
[] ).
cnf(166487584,plain,
( ~ product(A,B,C)
| ~ product(A,D,C)
| equalish(B,D) ),
inference(rewrite,[status(thm)],[product_right_cancellation]),
[] ).
fof(product_idempotence,plain,
! [A] : product(A,A,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-2.003.tptp',unknown),
[] ).
cnf(166613584,plain,
product(A,A,A),
inference(rewrite,[status(thm)],[product_idempotence]),
[] ).
cnf(177665600,plain,
( ~ product(A,B,A)
| equalish(A,B) ),
inference(resolution,[status(thm)],[166487584,166613584]),
[] ).
fof(e_1_is_not_e_3,plain,
~ equalish(e_1,e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-2.003.tptp',unknown),
[] ).
cnf(166556144,plain,
~ equalish(e_1,e_3),
inference(rewrite,[status(thm)],[e_1_is_not_e_3]),
[] ).
cnf(177695776,plain,
~ product(e_1,e_3,e_1),
inference(resolution,[status(thm)],[177665600,166556144]),
[] ).
cnf(178049480,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[166539936,166547600,166586496,177695776]),
[] ).
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/GRP123-2.003.tptp',unknown),
[] ).
cnf(166609232,plain,
( ~ product(A,B,C)
| ~ product(D,B,C)
| equalish(A,D) ),
inference(rewrite,[status(thm)],[product_left_cancellation]),
[] ).
cnf(177781456,plain,
( ~ product(B,A,A)
| equalish(A,B) ),
inference(resolution,[status(thm)],[166609232,166613584]),
[] ).
fof(e_3_is_not_e_1,plain,
~ equalish(e_3,e_1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-2.003.tptp',unknown),
[] ).
cnf(166571384,plain,
~ equalish(e_3,e_1),
inference(rewrite,[status(thm)],[e_3_is_not_e_1]),
[] ).
cnf(177846040,plain,
~ product(e_1,e_3,e_3),
inference(resolution,[status(thm)],[177781456,166571384]),
[] ).
cnf(178118168,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[166539936,166547600,166586496,177846040]),
[] ).
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/GRP123-2.003.tptp',unknown),
[] ).
cnf(166597120,plain,
( ~ product(A,B,C)
| ~ product(A,B,D)
| equalish(C,D) ),
inference(rewrite,[status(thm)],[product_total_function2]),
[] ).
cnf(177297608,plain,
( ~ product(A,B,e_1)
| ~ product(A,B,e_3) ),
inference(resolution,[status(thm)],[166597120,166556144]),
[] ).
cnf(180275328,plain,
product(e_1,e_3,e_2),
inference(forward_subsumption_resolution__resolution,[status(thm)],[178049480,178118168,177297608]),
[] ).
fof(e_3_is_not_e_2,plain,
~ equalish(e_3,e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-2.003.tptp',unknown),
[] ).
cnf(166575032,plain,
~ equalish(e_3,e_2),
inference(rewrite,[status(thm)],[e_3_is_not_e_2]),
[] ).
cnf(177859416,plain,
~ product(e_2,e_3,e_3),
inference(resolution,[status(thm)],[177781456,166575032]),
[] ).
fof(e_2_is_not_e_3,plain,
~ equalish(e_2,e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-2.003.tptp',unknown),
[] ).
cnf(166563488,plain,
~ equalish(e_2,e_3),
inference(rewrite,[status(thm)],[e_2_is_not_e_3]),
[] ).
cnf(177718384,plain,
~ product(e_2,e_3,e_2),
inference(resolution,[status(thm)],[177665600,166563488]),
[] ).
fof(element_2,plain,
group_element(e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-2.003.tptp',unknown),
[] ).
cnf(166543904,plain,
group_element(e_2),
inference(rewrite,[status(thm)],[element_2]),
[] ).
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/GRP123-2.003.tptp',unknown),
[] ).
cnf(166622152,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(182967656,plain,
( ~ product(B,C,A)
| ~ product(A,C,B)
| equalish(A,B) ),
inference(resolution,[status(thm)],[166622152,166613584]),
[] ).
fof(e_1_is_not_e_2,plain,
~ equalish(e_1,e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-2.003.tptp',unknown),
[] ).
cnf(166487896,plain,
~ equalish(e_1,e_2),
inference(rewrite,[status(thm)],[e_1_is_not_e_2]),
[] ).
cnf(182997072,plain,
( ~ product(e_2,A,e_1)
| ~ product(e_1,A,e_2) ),
inference(resolution,[status(thm)],[182967656,166487896]),
[] ).
cnf(183714456,plain,
( ~ product(e_1,A,e_2)
| ~ group_element(A)
| product(e_2,A,e_2)
| product(e_2,A,e_3) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[166543904,182997072,166586496]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[180275328,177859416,177718384,183714456,166547600]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 33 seconds
% START OF PROOF SEQUENCE
% fof(element_1,plain,(group_element(e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-2.003.tptp',unknown),[]).
%
% cnf(166539936,plain,(group_element(e_1)),inference(rewrite,[status(thm)],[element_1]),[]).
%
% fof(element_3,plain,(group_element(e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-2.003.tptp',unknown),[]).
%
% cnf(166547600,plain,(group_element(e_3)),inference(rewrite,[status(thm)],[element_3]),[]).
%
% 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/GRP123-2.003.tptp',unknown),[]).
%
% cnf(166586496,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(product_right_cancellation,plain,(~product(A,B,C)|~product(A,D,C)|equalish(B,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-2.003.tptp',unknown),[]).
%
% cnf(166487584,plain,(~product(A,B,C)|~product(A,D,C)|equalish(B,D)),inference(rewrite,[status(thm)],[product_right_cancellation]),[]).
%
% fof(product_idempotence,plain,(product(A,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-2.003.tptp',unknown),[]).
%
% cnf(166613584,plain,(product(A,A,A)),inference(rewrite,[status(thm)],[product_idempotence]),[]).
%
% cnf(177665600,plain,(~product(A,B,A)|equalish(A,B)),inference(resolution,[status(thm)],[166487584,166613584]),[]).
%
% fof(e_1_is_not_e_3,plain,(~equalish(e_1,e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-2.003.tptp',unknown),[]).
%
% cnf(166556144,plain,(~equalish(e_1,e_3)),inference(rewrite,[status(thm)],[e_1_is_not_e_3]),[]).
%
% cnf(177695776,plain,(~product(e_1,e_3,e_1)),inference(resolution,[status(thm)],[177665600,166556144]),[]).
%
% cnf(178049480,plain,(product(e_1,e_3,e_2)|product(e_1,e_3,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[166539936,166547600,166586496,177695776]),[]).
%
% 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/GRP123-2.003.tptp',unknown),[]).
%
% cnf(166609232,plain,(~product(A,B,C)|~product(D,B,C)|equalish(A,D)),inference(rewrite,[status(thm)],[product_left_cancellation]),[]).
%
% cnf(177781456,plain,(~product(B,A,A)|equalish(A,B)),inference(resolution,[status(thm)],[166609232,166613584]),[]).
%
% fof(e_3_is_not_e_1,plain,(~equalish(e_3,e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-2.003.tptp',unknown),[]).
%
% cnf(166571384,plain,(~equalish(e_3,e_1)),inference(rewrite,[status(thm)],[e_3_is_not_e_1]),[]).
%
% cnf(177846040,plain,(~product(e_1,e_3,e_3)),inference(resolution,[status(thm)],[177781456,166571384]),[]).
%
% cnf(178118168,plain,(product(e_1,e_3,e_1)|product(e_1,e_3,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[166539936,166547600,166586496,177846040]),[]).
%
% 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/GRP123-2.003.tptp',unknown),[]).
%
% cnf(166597120,plain,(~product(A,B,C)|~product(A,B,D)|equalish(C,D)),inference(rewrite,[status(thm)],[product_total_function2]),[]).
%
% cnf(177297608,plain,(~product(A,B,e_1)|~product(A,B,e_3)),inference(resolution,[status(thm)],[166597120,166556144]),[]).
%
% cnf(180275328,plain,(product(e_1,e_3,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[178049480,178118168,177297608]),[]).
%
% fof(e_3_is_not_e_2,plain,(~equalish(e_3,e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-2.003.tptp',unknown),[]).
%
% cnf(166575032,plain,(~equalish(e_3,e_2)),inference(rewrite,[status(thm)],[e_3_is_not_e_2]),[]).
%
% cnf(177859416,plain,(~product(e_2,e_3,e_3)),inference(resolution,[status(thm)],[177781456,166575032]),[]).
%
% fof(e_2_is_not_e_3,plain,(~equalish(e_2,e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-2.003.tptp',unknown),[]).
%
% cnf(166563488,plain,(~equalish(e_2,e_3)),inference(rewrite,[status(thm)],[e_2_is_not_e_3]),[]).
%
% cnf(177718384,plain,(~product(e_2,e_3,e_2)),inference(resolution,[status(thm)],[177665600,166563488]),[]).
%
% fof(element_2,plain,(group_element(e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-2.003.tptp',unknown),[]).
%
% cnf(166543904,plain,(group_element(e_2)),inference(rewrite,[status(thm)],[element_2]),[]).
%
% 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/GRP123-2.003.tptp',unknown),[]).
%
% cnf(166622152,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(182967656,plain,(~product(B,C,A)|~product(A,C,B)|equalish(A,B)),inference(resolution,[status(thm)],[166622152,166613584]),[]).
%
% fof(e_1_is_not_e_2,plain,(~equalish(e_1,e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-2.003.tptp',unknown),[]).
%
% cnf(166487896,plain,(~equalish(e_1,e_2)),inference(rewrite,[status(thm)],[e_1_is_not_e_2]),[]).
%
% cnf(182997072,plain,(~product(e_2,A,e_1)|~product(e_1,A,e_2)),inference(resolution,[status(thm)],[182967656,166487896]),[]).
%
% cnf(183714456,plain,(~product(e_1,A,e_2)|~group_element(A)|product(e_2,A,e_2)|product(e_2,A,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[166543904,182997072,166586496]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[180275328,177859416,177718384,183714456,166547600]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------