TSTP Solution File: GRP132-2.002 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP132-2.002 : TPTP v3.4.2. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art07.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 12:28:42 EDT 2009
% Result : Unsatisfiable 7.4s
% Output : Refutation 7.4s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 46 ( 10 unt; 0 def)
% Number of atoms : 124 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 145 ( 67 ~; 78 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 67 ( 0 sgn 22 !; 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/GRP132-2.002.tptp',unknown),
[] ).
cnf(148429464,plain,
group_element(e_1),
inference(rewrite,[status(thm)],[element_1]),
[] ).
fof(product_total_function1,plain,
! [A,B] :
( ~ group_element(A)
| ~ group_element(B)
| product(A,B,e_1)
| product(A,B,e_2) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP132-2.002.tptp',unknown),
[] ).
cnf(148455728,plain,
( ~ group_element(A)
| ~ group_element(B)
| product(A,B,e_1)
| product(A,B,e_2) ),
inference(rewrite,[status(thm)],[product_total_function1]),
[] ).
fof(element_2,plain,
group_element(e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP132-2.002.tptp',unknown),
[] ).
cnf(148433400,plain,
group_element(e_2),
inference(rewrite,[status(thm)],[element_2]),
[] ).
cnf(159157728,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[148455728,148433400]),
[] ).
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/GRP132-2.002.tptp',unknown),
[] ).
cnf(148474792,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/GRP132-2.002.tptp',unknown),
[] ).
cnf(148389376,plain,
~ equalish(e_1,e_2),
inference(rewrite,[status(thm)],[e_1_is_not_e_2]),
[] ).
cnf(159057752,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_2,B) ),
inference(resolution,[status(thm)],[148474792,148389376]),
[] ).
cnf(159627072,plain,
( product(e_2,e_2,e_1)
| ~ product(e_2,e_1,e_2) ),
inference(resolution,[status(thm)],[159157728,159057752]),
[] ).
cnf(158926280,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[148455728,148429464]),
[] ).
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/GRP132-2.002.tptp',unknown),
[] ).
cnf(148478424,plain,
( ~ product(A,B,C)
| ~ product(D,B,C)
| equalish(A,D) ),
inference(rewrite,[status(thm)],[product_left_cancellation]),
[] ).
cnf(159083520,plain,
( ~ product(e_1,A,B)
| ~ product(e_2,A,B) ),
inference(resolution,[status(thm)],[148478424,148389376]),
[] ).
cnf(159426176,plain,
( product(e_1,e_1,e_2)
| ~ product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[158926280,159083520]),
[] ).
cnf(160429616,plain,
( product(e_1,e_1,e_2)
| product(e_2,e_1,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[148429464,148433400,159426176,148455728]),
[] ).
cnf(161167552,plain,
( product(e_2,e_2,e_1)
| product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[159627072,160429616]),
[] ).
cnf(159404680,plain,
( product(e_1,e_1,e_2)
| ~ product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[158926280,159057752]),
[] ).
fof(qg2_2,plain,
! [A,B,C,D,E,F] :
( ~ product(A,B,C)
| ~ product(D,E,C)
| ~ product(F,A,B)
| ~ product(F,D,E)
| equalish(B,E) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP132-2.002.tptp',unknown),
[] ).
cnf(148490816,plain,
( ~ product(A,B,C)
| ~ product(D,E,C)
| ~ product(F,A,B)
| ~ product(F,D,E)
| equalish(B,E) ),
inference(rewrite,[status(thm)],[qg2_2]),
[] ).
cnf(165189112,plain,
( ~ product(A,B,e_1)
| ~ product(e_1,A,B)
| equalish(e_1,B)
| product(e_1,e_1,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[148429464,148490816,148455728]),
[] ).
cnf(165646312,plain,
( ~ product(A,e_2,e_1)
| ~ product(e_1,A,e_2)
| product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[165189112,148389376]),
[] ).
cnf(165684904,plain,
( ~ product(A,e_2,e_1)
| product(e_1,e_1,e_2)
| ~ group_element(A)
| product(e_1,A,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[148429464,165646312,148455728]),
[] ).
cnf(165703856,plain,
product(e_1,e_1,e_2),
inference(forward_subsumption_resolution__resolution,[status(thm)],[161167552,159404680,165684904,148433400]),
[] ).
cnf(159622552,plain,
( product(e_2,e_2,e_2)
| ~ product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[159157728,159057752]),
[] ).
cnf(161132920,plain,
( ~ product(e_2,e_1,e_1)
| ~ product(A,e_2,e_2)
| equalish(A,e_2) ),
inference(resolution,[status(thm)],[159622552,148478424]),
[] ).
cnf(158941824,plain,
( ~ group_element(A)
| product(A,e_1,e_1)
| product(A,e_1,e_2) ),
inference(resolution,[status(thm)],[148455728,148429464]),
[] ).
cnf(158958408,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(resolution,[status(thm)],[158941824,148433400]),
[] ).
cnf(161138752,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[159627072,158958408]),
[] ).
cnf(160066560,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_2,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[148429464,148433400,159404680,148455728]),
[] ).
cnf(160097920,plain,
( product(e_1,e_2,e_2)
| ~ product(e_2,e_1,e_2) ),
inference(resolution,[status(thm)],[160066560,159083520]),
[] ).
cnf(162738176,plain,
( product(e_1,e_2,e_2)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[160097920,158958408]),
[] ).
fof(qg2_1,plain,
! [A,B,C,D,E,F] :
( ~ product(A,B,C)
| ~ product(D,E,C)
| ~ product(F,A,B)
| ~ product(F,D,E)
| equalish(A,D) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP132-2.002.tptp',unknown),
[] ).
cnf(148486456,plain,
( ~ product(A,B,C)
| ~ product(D,E,C)
| ~ product(F,A,B)
| ~ product(F,D,E)
| equalish(A,D) ),
inference(rewrite,[status(thm)],[qg2_1]),
[] ).
cnf(159091512,plain,
( ~ product(e_1,A,B)
| ~ product(e_2,C,B)
| ~ product(D,e_1,A)
| ~ product(D,e_2,C) ),
inference(resolution,[status(thm)],[148486456,148389376]),
[] ).
cnf(165098984,plain,
product(e_1,e_2,e_2),
inference(forward_subsumption_resolution__resolution,[status(thm)],[160066560,162738176,148433400,148429464,159091512,148455728]),
[] ).
cnf(165130504,plain,
( ~ product(e_1,A,e_2)
| ~ product(C,e_1,A)
| ~ product(C,e_2,B)
| ~ group_element(B)
| product(e_2,B,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[148433400,159091512,148455728]),
[] ).
cnf(165947240,plain,
( ~ product(B,e_2,A)
| ~ group_element(A)
| product(e_2,A,e_1)
| ~ group_element(B)
| product(B,e_1,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[165098984,148429464,165130504,148455728]),
[] ).
cnf(166011096,plain,
( ~ product(e_2,e_2,A)
| ~ group_element(A)
| product(e_2,A,e_1)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[165947240,148433400]),
[] ).
cnf(166016344,plain,
product(e_2,e_1,e_1),
inference(forward_subsumption_resolution__resolution,[status(thm)],[161138752,166011096,148429464]),
[] ).
cnf(164966168,plain,
( ~ product(B,e_1,e_1)
| ~ product(A,A,B)
| equalish(A,B)
| ~ group_element(A)
| ~ group_element(B)
| product(A,B,e_2) ),
inference(resolution,[status(thm)],[148486456,148455728]),
[] ).
cnf(166289832,plain,
( ~ product(A,A,e_2)
| equalish(A,e_2)
| ~ group_element(A) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[161132920,166016344,164966168,148433400]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[148429464,165703856,166289832,148389376]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 7 seconds
% START OF PROOF SEQUENCE
% fof(element_1,plain,(group_element(e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP132-2.002.tptp',unknown),[]).
%
% cnf(148429464,plain,(group_element(e_1)),inference(rewrite,[status(thm)],[element_1]),[]).
%
% fof(product_total_function1,plain,(~group_element(A)|~group_element(B)|product(A,B,e_1)|product(A,B,e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP132-2.002.tptp',unknown),[]).
%
% cnf(148455728,plain,(~group_element(A)|~group_element(B)|product(A,B,e_1)|product(A,B,e_2)),inference(rewrite,[status(thm)],[product_total_function1]),[]).
%
% fof(element_2,plain,(group_element(e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP132-2.002.tptp',unknown),[]).
%
% cnf(148433400,plain,(group_element(e_2)),inference(rewrite,[status(thm)],[element_2]),[]).
%
% cnf(159157728,plain,(product(e_2,e_2,e_1)|product(e_2,e_2,e_2)),inference(resolution,[status(thm)],[148455728,148433400]),[]).
%
% 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/GRP132-2.002.tptp',unknown),[]).
%
% cnf(148474792,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/GRP132-2.002.tptp',unknown),[]).
%
% cnf(148389376,plain,(~equalish(e_1,e_2)),inference(rewrite,[status(thm)],[e_1_is_not_e_2]),[]).
%
% cnf(159057752,plain,(~product(A,e_1,B)|~product(A,e_2,B)),inference(resolution,[status(thm)],[148474792,148389376]),[]).
%
% cnf(159627072,plain,(product(e_2,e_2,e_1)|~product(e_2,e_1,e_2)),inference(resolution,[status(thm)],[159157728,159057752]),[]).
%
% cnf(158926280,plain,(product(e_1,e_1,e_1)|product(e_1,e_1,e_2)),inference(resolution,[status(thm)],[148455728,148429464]),[]).
%
% 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/GRP132-2.002.tptp',unknown),[]).
%
% cnf(148478424,plain,(~product(A,B,C)|~product(D,B,C)|equalish(A,D)),inference(rewrite,[status(thm)],[product_left_cancellation]),[]).
%
% cnf(159083520,plain,(~product(e_1,A,B)|~product(e_2,A,B)),inference(resolution,[status(thm)],[148478424,148389376]),[]).
%
% cnf(159426176,plain,(product(e_1,e_1,e_2)|~product(e_2,e_1,e_1)),inference(resolution,[status(thm)],[158926280,159083520]),[]).
%
% cnf(160429616,plain,(product(e_1,e_1,e_2)|product(e_2,e_1,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[148429464,148433400,159426176,148455728]),[]).
%
% cnf(161167552,plain,(product(e_2,e_2,e_1)|product(e_1,e_1,e_2)),inference(resolution,[status(thm)],[159627072,160429616]),[]).
%
% cnf(159404680,plain,(product(e_1,e_1,e_2)|~product(e_1,e_2,e_1)),inference(resolution,[status(thm)],[158926280,159057752]),[]).
%
% fof(qg2_2,plain,(~product(A,B,C)|~product(D,E,C)|~product(F,A,B)|~product(F,D,E)|equalish(B,E)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP132-2.002.tptp',unknown),[]).
%
% cnf(148490816,plain,(~product(A,B,C)|~product(D,E,C)|~product(F,A,B)|~product(F,D,E)|equalish(B,E)),inference(rewrite,[status(thm)],[qg2_2]),[]).
%
% cnf(165189112,plain,(~product(A,B,e_1)|~product(e_1,A,B)|equalish(e_1,B)|product(e_1,e_1,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[148429464,148490816,148455728]),[]).
%
% cnf(165646312,plain,(~product(A,e_2,e_1)|~product(e_1,A,e_2)|product(e_1,e_1,e_2)),inference(resolution,[status(thm)],[165189112,148389376]),[]).
%
% cnf(165684904,plain,(~product(A,e_2,e_1)|product(e_1,e_1,e_2)|~group_element(A)|product(e_1,A,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[148429464,165646312,148455728]),[]).
%
% cnf(165703856,plain,(product(e_1,e_1,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[161167552,159404680,165684904,148433400]),[]).
%
% cnf(159622552,plain,(product(e_2,e_2,e_2)|~product(e_2,e_1,e_1)),inference(resolution,[status(thm)],[159157728,159057752]),[]).
%
% cnf(161132920,plain,(~product(e_2,e_1,e_1)|~product(A,e_2,e_2)|equalish(A,e_2)),inference(resolution,[status(thm)],[159622552,148478424]),[]).
%
% cnf(158941824,plain,(~group_element(A)|product(A,e_1,e_1)|product(A,e_1,e_2)),inference(resolution,[status(thm)],[148455728,148429464]),[]).
%
% cnf(158958408,plain,(product(e_2,e_1,e_1)|product(e_2,e_1,e_2)),inference(resolution,[status(thm)],[158941824,148433400]),[]).
%
% cnf(161138752,plain,(product(e_2,e_2,e_1)|product(e_2,e_1,e_1)),inference(resolution,[status(thm)],[159627072,158958408]),[]).
%
% cnf(160066560,plain,(product(e_1,e_1,e_2)|product(e_1,e_2,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[148429464,148433400,159404680,148455728]),[]).
%
% cnf(160097920,plain,(product(e_1,e_2,e_2)|~product(e_2,e_1,e_2)),inference(resolution,[status(thm)],[160066560,159083520]),[]).
%
% cnf(162738176,plain,(product(e_1,e_2,e_2)|product(e_2,e_1,e_1)),inference(resolution,[status(thm)],[160097920,158958408]),[]).
%
% fof(qg2_1,plain,(~product(A,B,C)|~product(D,E,C)|~product(F,A,B)|~product(F,D,E)|equalish(A,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP132-2.002.tptp',unknown),[]).
%
% cnf(148486456,plain,(~product(A,B,C)|~product(D,E,C)|~product(F,A,B)|~product(F,D,E)|equalish(A,D)),inference(rewrite,[status(thm)],[qg2_1]),[]).
%
% cnf(159091512,plain,(~product(e_1,A,B)|~product(e_2,C,B)|~product(D,e_1,A)|~product(D,e_2,C)),inference(resolution,[status(thm)],[148486456,148389376]),[]).
%
% cnf(165098984,plain,(product(e_1,e_2,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[160066560,162738176,148433400,148429464,159091512,148455728]),[]).
%
% cnf(165130504,plain,(~product(e_1,A,e_2)|~product(C,e_1,A)|~product(C,e_2,B)|~group_element(B)|product(e_2,B,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[148433400,159091512,148455728]),[]).
%
% cnf(165947240,plain,(~product(B,e_2,A)|~group_element(A)|product(e_2,A,e_1)|~group_element(B)|product(B,e_1,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[165098984,148429464,165130504,148455728]),[]).
%
% cnf(166011096,plain,(~product(e_2,e_2,A)|~group_element(A)|product(e_2,A,e_1)|product(e_2,e_1,e_1)),inference(resolution,[status(thm)],[165947240,148433400]),[]).
%
% cnf(166016344,plain,(product(e_2,e_1,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[161138752,166011096,148429464]),[]).
%
% cnf(164966168,plain,(~product(B,e_1,e_1)|~product(A,A,B)|equalish(A,B)|~group_element(A)|~group_element(B)|product(A,B,e_2)),inference(resolution,[status(thm)],[148486456,148455728]),[]).
%
% cnf(166289832,plain,(~product(A,A,e_2)|equalish(A,e_2)|~group_element(A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[161132920,166016344,164966168,148433400]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[148429464,165703856,166289832,148389376]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------