TSTP Solution File: GRP123-1.003 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP123-1.003 : 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 12:23:48 EDT 2009
% Result : Unsatisfiable 31.6s
% Output : Refutation 31.6s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 12
% Syntax : Number of formulae : 35 ( 22 unt; 0 def)
% Number of atoms : 65 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 68 ( 38 ~; 30 |; 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 : 42 ( 0 sgn 17 !; 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/GRP123-1.003.tptp',unknown),
[] ).
cnf(169530264,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/GRP123-1.003.tptp',unknown),
[] ).
cnf(169534040,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/GRP123-1.003.tptp',unknown),
[] ).
cnf(169572880,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/GRP123-1.003.tptp',unknown),
[] ).
cnf(169589304,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/GRP123-1.003.tptp',unknown),
[] ).
cnf(169597280,plain,
product(A,A,A),
inference(rewrite,[status(thm)],[product_idempotence]),
[] ).
cnf(180482408,plain,
( ~ product(A,B,A)
| equalish(A,B) ),
inference(resolution,[status(thm)],[169589304,169597280]),
[] ).
fof(e_3_is_not_e_2,plain,
~ equalish(e_3,e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-1.003.tptp',unknown),
[] ).
cnf(169561384,plain,
~ equalish(e_3,e_2),
inference(rewrite,[status(thm)],[e_3_is_not_e_2]),
[] ).
cnf(180559480,plain,
~ product(e_3,e_2,e_3),
inference(resolution,[status(thm)],[180482408,169561384]),
[] ).
cnf(180864776,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_2) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[169530264,169534040,169572880,180559480]),
[] ).
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/GRP123-1.003.tptp',unknown),
[] ).
cnf(169592936,plain,
( ~ product(A,B,C)
| ~ product(D,B,C)
| equalish(A,D) ),
inference(rewrite,[status(thm)],[product_left_cancellation]),
[] ).
cnf(180615408,plain,
( ~ product(B,A,A)
| equalish(A,B) ),
inference(resolution,[status(thm)],[169592936,169597280]),
[] ).
fof(e_2_is_not_e_3,plain,
~ equalish(e_2,e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-1.003.tptp',unknown),
[] ).
cnf(169549840,plain,
~ equalish(e_2,e_3),
inference(rewrite,[status(thm)],[e_2_is_not_e_3]),
[] ).
cnf(180662528,plain,
~ product(e_3,e_2,e_2),
inference(resolution,[status(thm)],[180615408,169549840]),
[] ).
cnf(182383504,plain,
product(e_3,e_2,e_1),
inference(resolution,[status(thm)],[180864776,180662528]),
[] ).
fof(e_2_is_not_e_1,plain,
~ equalish(e_2,e_1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-1.003.tptp',unknown),
[] ).
cnf(169546272,plain,
~ equalish(e_2,e_1),
inference(rewrite,[status(thm)],[e_2_is_not_e_1]),
[] ).
cnf(180649184,plain,
~ product(e_1,e_2,e_2),
inference(resolution,[status(thm)],[180615408,169546272]),
[] ).
fof(e_1_is_not_e_2,plain,
~ equalish(e_1,e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-1.003.tptp',unknown),
[] ).
cnf(169538560,plain,
~ equalish(e_1,e_2),
inference(rewrite,[status(thm)],[e_1_is_not_e_2]),
[] ).
cnf(180494440,plain,
~ product(e_1,e_2,e_1),
inference(resolution,[status(thm)],[180482408,169538560]),
[] ).
fof(element_1,plain,
group_element(e_1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-1.003.tptp',unknown),
[] ).
cnf(169526312,plain,
group_element(e_1),
inference(rewrite,[status(thm)],[element_1]),
[] ).
fof(qg1_2,plain,
! [A,B,C,D,E,F] :
( ~ product(A,B,C)
| ~ product(D,E,C)
| ~ product(F,B,A)
| ~ product(F,E,D)
| equalish(B,E) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-1.003.tptp',unknown),
[] ).
cnf(169614200,plain,
( ~ product(A,B,C)
| ~ product(D,E,C)
| ~ product(F,B,A)
| ~ product(F,E,D)
| equalish(B,E) ),
inference(rewrite,[status(thm)],[qg1_2]),
[] ).
cnf(185622280,plain,
( ~ product(B,C,A)
| ~ product(A,C,B)
| equalish(A,C) ),
inference(resolution,[status(thm)],[169614200,169597280]),
[] ).
cnf(185638488,plain,
( ~ product(A,e_2,e_1)
| ~ product(e_1,e_2,A) ),
inference(resolution,[status(thm)],[185622280,169538560]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[182383504,180649184,180494440,169526312,169530264,185638488,169572880]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 31 seconds
% START OF PROOF SEQUENCE
% fof(element_2,plain,(group_element(e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-1.003.tptp',unknown),[]).
%
% cnf(169530264,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/GRP123-1.003.tptp',unknown),[]).
%
% cnf(169534040,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/GRP123-1.003.tptp',unknown),[]).
%
% cnf(169572880,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/GRP123-1.003.tptp',unknown),[]).
%
% cnf(169589304,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/GRP123-1.003.tptp',unknown),[]).
%
% cnf(169597280,plain,(product(A,A,A)),inference(rewrite,[status(thm)],[product_idempotence]),[]).
%
% cnf(180482408,plain,(~product(A,B,A)|equalish(A,B)),inference(resolution,[status(thm)],[169589304,169597280]),[]).
%
% fof(e_3_is_not_e_2,plain,(~equalish(e_3,e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-1.003.tptp',unknown),[]).
%
% cnf(169561384,plain,(~equalish(e_3,e_2)),inference(rewrite,[status(thm)],[e_3_is_not_e_2]),[]).
%
% cnf(180559480,plain,(~product(e_3,e_2,e_3)),inference(resolution,[status(thm)],[180482408,169561384]),[]).
%
% cnf(180864776,plain,(product(e_3,e_2,e_1)|product(e_3,e_2,e_2)),inference(forward_subsumption_resolution__resolution,[status(thm)],[169530264,169534040,169572880,180559480]),[]).
%
% 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/GRP123-1.003.tptp',unknown),[]).
%
% cnf(169592936,plain,(~product(A,B,C)|~product(D,B,C)|equalish(A,D)),inference(rewrite,[status(thm)],[product_left_cancellation]),[]).
%
% cnf(180615408,plain,(~product(B,A,A)|equalish(A,B)),inference(resolution,[status(thm)],[169592936,169597280]),[]).
%
% fof(e_2_is_not_e_3,plain,(~equalish(e_2,e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-1.003.tptp',unknown),[]).
%
% cnf(169549840,plain,(~equalish(e_2,e_3)),inference(rewrite,[status(thm)],[e_2_is_not_e_3]),[]).
%
% cnf(180662528,plain,(~product(e_3,e_2,e_2)),inference(resolution,[status(thm)],[180615408,169549840]),[]).
%
% cnf(182383504,plain,(product(e_3,e_2,e_1)),inference(resolution,[status(thm)],[180864776,180662528]),[]).
%
% fof(e_2_is_not_e_1,plain,(~equalish(e_2,e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-1.003.tptp',unknown),[]).
%
% cnf(169546272,plain,(~equalish(e_2,e_1)),inference(rewrite,[status(thm)],[e_2_is_not_e_1]),[]).
%
% cnf(180649184,plain,(~product(e_1,e_2,e_2)),inference(resolution,[status(thm)],[180615408,169546272]),[]).
%
% fof(e_1_is_not_e_2,plain,(~equalish(e_1,e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-1.003.tptp',unknown),[]).
%
% cnf(169538560,plain,(~equalish(e_1,e_2)),inference(rewrite,[status(thm)],[e_1_is_not_e_2]),[]).
%
% cnf(180494440,plain,(~product(e_1,e_2,e_1)),inference(resolution,[status(thm)],[180482408,169538560]),[]).
%
% fof(element_1,plain,(group_element(e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-1.003.tptp',unknown),[]).
%
% cnf(169526312,plain,(group_element(e_1)),inference(rewrite,[status(thm)],[element_1]),[]).
%
% fof(qg1_2,plain,(~product(A,B,C)|~product(D,E,C)|~product(F,B,A)|~product(F,E,D)|equalish(B,E)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-1.003.tptp',unknown),[]).
%
% cnf(169614200,plain,(~product(A,B,C)|~product(D,E,C)|~product(F,B,A)|~product(F,E,D)|equalish(B,E)),inference(rewrite,[status(thm)],[qg1_2]),[]).
%
% cnf(185622280,plain,(~product(B,C,A)|~product(A,C,B)|equalish(A,C)),inference(resolution,[status(thm)],[169614200,169597280]),[]).
%
% cnf(185638488,plain,(~product(A,e_2,e_1)|~product(e_1,e_2,A)),inference(resolution,[status(thm)],[185622280,169538560]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[182383504,180649184,180494440,169526312,169530264,185638488,169572880]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------