TSTP Solution File: GRP132-1.002 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP132-1.002 : TPTP v3.4.2. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art02.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 12:28:40 EDT 2009
% Result : Unsatisfiable 7.4s
% Output : Refutation 7.4s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 51 ( 10 unt; 0 def)
% Number of atoms : 136 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 159 ( 74 ~; 85 |; 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 : 77 ( 0 sgn 26 !; 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/GRP132-1.002.tptp',unknown),
[] ).
cnf(144033912,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/GRP132-1.002.tptp',unknown),
[] ).
cnf(144037832,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) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP132-1.002.tptp',unknown),
[] ).
cnf(144056000,plain,
( ~ group_element(A)
| ~ group_element(B)
| product(A,B,e_1)
| product(A,B,e_2) ),
inference(rewrite,[status(thm)],[product_total_function1]),
[] ).
cnf(154506352,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[144056000,144033912]),
[] ).
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/GRP132-1.002.tptp',unknown),
[] ).
cnf(144080168,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/GRP132-1.002.tptp',unknown),
[] ).
cnf(144042352,plain,
~ equalish(e_1,e_2),
inference(rewrite,[status(thm)],[e_1_is_not_e_2]),
[] ).
cnf(154679880,plain,
( ~ product(e_1,A,B)
| ~ product(e_2,A,B) ),
inference(resolution,[status(thm)],[144080168,144042352]),
[] ).
cnf(154894944,plain,
( product(e_1,e_1,e_2)
| ~ product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[154506352,154679880]),
[] ).
cnf(155691672,plain,
( product(e_1,e_1,e_2)
| product(e_2,e_1,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[144033912,144037832,154894944,144056000]),
[] ).
cnf(154561800,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[144056000,144037832]),
[] ).
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/GRP132-1.002.tptp',unknown),
[] ).
cnf(144076536,plain,
( ~ product(A,B,C)
| ~ product(A,D,C)
| equalish(B,D) ),
inference(rewrite,[status(thm)],[product_right_cancellation]),
[] ).
cnf(154651600,plain,
( ~ product(A,e_1,B)
| ~ product(A,e_2,B) ),
inference(resolution,[status(thm)],[144076536,144042352]),
[] ).
cnf(155000328,plain,
( product(e_2,e_2,e_1)
| ~ product(e_2,e_1,e_2) ),
inference(resolution,[status(thm)],[154561800,154651600]),
[] ).
cnf(156313920,plain,
( product(e_1,e_1,e_2)
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[155691672,155000328]),
[] ).
cnf(154877760,plain,
( product(e_1,e_1,e_2)
| ~ product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[154506352,154651600]),
[] ).
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/GRP132-1.002.tptp',unknown),
[] ).
cnf(144092496,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(159577760,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)],[144033912,144092496,144056000]),
[] ).
cnf(160070632,plain,
( ~ product(A,e_2,e_1)
| ~ product(e_1,A,e_2)
| product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[159577760,144042352]),
[] ).
cnf(160105104,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)],[144033912,160070632,144056000]),
[] ).
cnf(160128136,plain,
product(e_1,e_1,e_2),
inference(forward_subsumption_resolution__resolution,[status(thm)],[156313920,154877760,160105104,144037832]),
[] ).
cnf(154991640,plain,
( product(e_2,e_2,e_2)
| ~ product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[154561800,154651600]),
[] ).
cnf(156076848,plain,
( ~ product(e_2,e_1,e_1)
| ~ product(A,e_2,e_2)
| equalish(A,e_2) ),
inference(resolution,[status(thm)],[154991640,144080168]),
[] ).
cnf(154545056,plain,
( ~ group_element(A)
| product(e_2,A,e_1)
| product(e_2,A,e_2) ),
inference(resolution,[status(thm)],[144056000,144037832]),
[] ).
cnf(154595280,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference(resolution,[status(thm)],[154545056,144033912]),
[] ).
cnf(156087568,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[155000328,154595280]),
[] ).
cnf(155305712,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_2,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[144033912,144037832,154877760,144056000]),
[] ).
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/GRP132-1.002.tptp',unknown),
[] ).
cnf(144068248,plain,
( ~ product(A,B,C)
| ~ product(A,B,D)
| equalish(C,D) ),
inference(rewrite,[status(thm)],[product_total_function2]),
[] ).
cnf(154627288,plain,
( ~ product(A,B,e_1)
| ~ product(A,B,e_2) ),
inference(resolution,[status(thm)],[144068248,144042352]),
[] ).
cnf(155317304,plain,
( product(e_1,e_2,e_2)
| ~ product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[155305712,154627288]),
[] ).
cnf(154902656,plain,
( product(e_1,e_1,e_1)
| ~ product(e_2,e_1,e_2) ),
inference(resolution,[status(thm)],[154506352,154679880]),
[] ).
cnf(155751816,plain,
( product(e_1,e_1,e_1)
| product(e_2,e_1,e_1) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[144033912,144037832,154902656,144056000]),
[] ).
cnf(156958808,plain,
( product(e_1,e_2,e_2)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[155317304,155751816]),
[] ).
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/GRP132-1.002.tptp',unknown),
[] ).
cnf(144088200,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(154687872,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)],[144088200,144042352]),
[] ).
cnf(159486800,plain,
product(e_1,e_2,e_2),
inference(forward_subsumption_resolution__resolution,[status(thm)],[155305712,156958808,144037832,144033912,154687872,144056000]),
[] ).
cnf(159522352,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)],[144037832,154687872,144056000]),
[] ).
cnf(160332320,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)],[159486800,144033912,159522352,144056000]),
[] ).
cnf(160377168,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)],[160332320,144037832]),
[] ).
cnf(160382416,plain,
product(e_2,e_1,e_1),
inference(forward_subsumption_resolution__resolution,[status(thm)],[156087568,160377168,144033912]),
[] ).
cnf(159358184,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)],[144088200,144056000]),
[] ).
cnf(160599568,plain,
( ~ product(A,A,e_2)
| equalish(A,e_2)
| ~ group_element(A) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[156076848,160382416,159358184,144037832]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[144033912,160128136,160599568,144042352]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 8 seconds
% START OF PROOF SEQUENCE
% fof(element_1,plain,(group_element(e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP132-1.002.tptp',unknown),[]).
%
% cnf(144033912,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/GRP132-1.002.tptp',unknown),[]).
%
% cnf(144037832,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)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP132-1.002.tptp',unknown),[]).
%
% cnf(144056000,plain,(~group_element(A)|~group_element(B)|product(A,B,e_1)|product(A,B,e_2)),inference(rewrite,[status(thm)],[product_total_function1]),[]).
%
% cnf(154506352,plain,(product(e_1,e_1,e_1)|product(e_1,e_1,e_2)),inference(resolution,[status(thm)],[144056000,144033912]),[]).
%
% 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/GRP132-1.002.tptp',unknown),[]).
%
% cnf(144080168,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/GRP132-1.002.tptp',unknown),[]).
%
% cnf(144042352,plain,(~equalish(e_1,e_2)),inference(rewrite,[status(thm)],[e_1_is_not_e_2]),[]).
%
% cnf(154679880,plain,(~product(e_1,A,B)|~product(e_2,A,B)),inference(resolution,[status(thm)],[144080168,144042352]),[]).
%
% cnf(154894944,plain,(product(e_1,e_1,e_2)|~product(e_2,e_1,e_1)),inference(resolution,[status(thm)],[154506352,154679880]),[]).
%
% cnf(155691672,plain,(product(e_1,e_1,e_2)|product(e_2,e_1,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[144033912,144037832,154894944,144056000]),[]).
%
% cnf(154561800,plain,(product(e_2,e_2,e_1)|product(e_2,e_2,e_2)),inference(resolution,[status(thm)],[144056000,144037832]),[]).
%
% 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/GRP132-1.002.tptp',unknown),[]).
%
% cnf(144076536,plain,(~product(A,B,C)|~product(A,D,C)|equalish(B,D)),inference(rewrite,[status(thm)],[product_right_cancellation]),[]).
%
% cnf(154651600,plain,(~product(A,e_1,B)|~product(A,e_2,B)),inference(resolution,[status(thm)],[144076536,144042352]),[]).
%
% cnf(155000328,plain,(product(e_2,e_2,e_1)|~product(e_2,e_1,e_2)),inference(resolution,[status(thm)],[154561800,154651600]),[]).
%
% cnf(156313920,plain,(product(e_1,e_1,e_2)|product(e_2,e_2,e_1)),inference(resolution,[status(thm)],[155691672,155000328]),[]).
%
% cnf(154877760,plain,(product(e_1,e_1,e_2)|~product(e_1,e_2,e_1)),inference(resolution,[status(thm)],[154506352,154651600]),[]).
%
% 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/GRP132-1.002.tptp',unknown),[]).
%
% cnf(144092496,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(159577760,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)],[144033912,144092496,144056000]),[]).
%
% cnf(160070632,plain,(~product(A,e_2,e_1)|~product(e_1,A,e_2)|product(e_1,e_1,e_2)),inference(resolution,[status(thm)],[159577760,144042352]),[]).
%
% cnf(160105104,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)],[144033912,160070632,144056000]),[]).
%
% cnf(160128136,plain,(product(e_1,e_1,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[156313920,154877760,160105104,144037832]),[]).
%
% cnf(154991640,plain,(product(e_2,e_2,e_2)|~product(e_2,e_1,e_1)),inference(resolution,[status(thm)],[154561800,154651600]),[]).
%
% cnf(156076848,plain,(~product(e_2,e_1,e_1)|~product(A,e_2,e_2)|equalish(A,e_2)),inference(resolution,[status(thm)],[154991640,144080168]),[]).
%
% cnf(154545056,plain,(~group_element(A)|product(e_2,A,e_1)|product(e_2,A,e_2)),inference(resolution,[status(thm)],[144056000,144037832]),[]).
%
% cnf(154595280,plain,(product(e_2,e_1,e_1)|product(e_2,e_1,e_2)),inference(resolution,[status(thm)],[154545056,144033912]),[]).
%
% cnf(156087568,plain,(product(e_2,e_2,e_1)|product(e_2,e_1,e_1)),inference(resolution,[status(thm)],[155000328,154595280]),[]).
%
% cnf(155305712,plain,(product(e_1,e_1,e_2)|product(e_1,e_2,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[144033912,144037832,154877760,144056000]),[]).
%
% 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/GRP132-1.002.tptp',unknown),[]).
%
% cnf(144068248,plain,(~product(A,B,C)|~product(A,B,D)|equalish(C,D)),inference(rewrite,[status(thm)],[product_total_function2]),[]).
%
% cnf(154627288,plain,(~product(A,B,e_1)|~product(A,B,e_2)),inference(resolution,[status(thm)],[144068248,144042352]),[]).
%
% cnf(155317304,plain,(product(e_1,e_2,e_2)|~product(e_1,e_1,e_1)),inference(resolution,[status(thm)],[155305712,154627288]),[]).
%
% cnf(154902656,plain,(product(e_1,e_1,e_1)|~product(e_2,e_1,e_2)),inference(resolution,[status(thm)],[154506352,154679880]),[]).
%
% cnf(155751816,plain,(product(e_1,e_1,e_1)|product(e_2,e_1,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[144033912,144037832,154902656,144056000]),[]).
%
% cnf(156958808,plain,(product(e_1,e_2,e_2)|product(e_2,e_1,e_1)),inference(resolution,[status(thm)],[155317304,155751816]),[]).
%
% 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/GRP132-1.002.tptp',unknown),[]).
%
% cnf(144088200,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(154687872,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)],[144088200,144042352]),[]).
%
% cnf(159486800,plain,(product(e_1,e_2,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[155305712,156958808,144037832,144033912,154687872,144056000]),[]).
%
% cnf(159522352,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)],[144037832,154687872,144056000]),[]).
%
% cnf(160332320,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)],[159486800,144033912,159522352,144056000]),[]).
%
% cnf(160377168,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)],[160332320,144037832]),[]).
%
% cnf(160382416,plain,(product(e_2,e_1,e_1)),inference(forward_subsumption_resolution__resolution,[status(thm)],[156087568,160377168,144033912]),[]).
%
% cnf(159358184,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)],[144088200,144056000]),[]).
%
% cnf(160599568,plain,(~product(A,A,e_2)|equalish(A,e_2)|~group_element(A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[156076848,160382416,159358184,144037832]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[144033912,160128136,160599568,144042352]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------