TSTP Solution File: COM007+1 by Faust---1.0
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%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : COM007+1 : TPTP v3.4.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art08.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 11:36:32 EDT 2009
% Result : Theorem 0.5s
% Output : Refutation 0.5s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 42 ( 16 unt; 0 def)
% Number of atoms : 80 ( 0 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 78 ( 40 ~; 36 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-3 aty)
% Number of variables : 42 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(substitution,plain,
! [A,B,C] :
( ~ equalish(A,B)
| ~ reflexive_rewrite(B,C)
| reflexive_rewrite(A,C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+1.tptp',unknown),
[] ).
cnf(140626528,plain,
( ~ equalish(A,B)
| ~ reflexive_rewrite(B,C)
| reflexive_rewrite(A,C) ),
inference(rewrite,[status(thm)],[substitution]),
[] ).
fof(assumption,plain,
( reflexive_rewrite(a,b)
& reflexive_rewrite(a,c) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+1.tptp',unknown),
[] ).
cnf(140588888,plain,
reflexive_rewrite(a,c),
inference(rewrite,[status(thm)],[assumption]),
[] ).
cnf(148513904,plain,
( ~ equalish(A,a)
| reflexive_rewrite(A,c) ),
inference(resolution,[status(thm)],[140626528,140588888]),
[] ).
fof(goal_ax,plain,
! [A] :
( ~ reflexive_rewrite(b,A)
| ~ reflexive_rewrite(c,A)
| goal ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+1.tptp',unknown),
[] ).
cnf(140604320,plain,
( ~ reflexive_rewrite(b,A)
| ~ reflexive_rewrite(c,A)
| goal ),
inference(rewrite,[status(thm)],[goal_ax]),
[] ).
fof(goal_to_be_proved,plain,
~ goal,
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+1.tptp',unknown),
[] ).
cnf(140702712,plain,
~ goal,
inference(rewrite,[status(thm)],[goal_to_be_proved]),
[] ).
cnf(148480928,plain,
( ~ reflexive_rewrite(b,A)
| ~ reflexive_rewrite(c,A) ),
inference(resolution,[status(thm)],[140604320,140702712]),
[] ).
fof(equalish_in_reflexive_rewrite,plain,
! [A,B] :
( ~ equalish(A,B)
| reflexive_rewrite(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+1.tptp',unknown),
[] ).
cnf(140631464,plain,
( ~ equalish(A,B)
| reflexive_rewrite(A,B) ),
inference(rewrite,[status(thm)],[equalish_in_reflexive_rewrite]),
[] ).
fof(reflexivity,plain,
! [A] : equalish(A,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+1.tptp',unknown),
[] ).
cnf(140609168,plain,
equalish(A,A),
inference(rewrite,[status(thm)],[reflexivity]),
[] ).
cnf(148550528,plain,
reflexive_rewrite(A,A),
inference(resolution,[status(thm)],[140631464,140609168]),
[] ).
cnf(148599552,plain,
~ reflexive_rewrite(b,c),
inference(resolution,[status(thm)],[148480928,148550528]),
[] ).
cnf(149500848,plain,
~ equalish(b,a),
inference(resolution,[status(thm)],[148513904,148599552]),
[] ).
fof(equalish_or_rewrite,plain,
! [A,B] :
( ~ reflexive_rewrite(A,B)
| equalish(A,B)
| rewrite(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+1.tptp',unknown),
[] ).
cnf(140645120,plain,
( ~ reflexive_rewrite(A,B)
| equalish(A,B)
| rewrite(A,B) ),
inference(rewrite,[status(thm)],[equalish_or_rewrite]),
[] ).
cnf(140596344,plain,
reflexive_rewrite(a,b),
inference(rewrite,[status(thm)],[assumption]),
[] ).
cnf(148530720,plain,
( equalish(a,b)
| rewrite(a,b) ),
inference(resolution,[status(thm)],[140645120,140596344]),
[] ).
fof(symmtery,plain,
! [A,B] :
( ~ equalish(A,B)
| equalish(B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+1.tptp',unknown),
[] ).
cnf(140615784,plain,
( ~ equalish(A,B)
| equalish(B,A) ),
inference(rewrite,[status(thm)],[symmtery]),
[] ).
cnf(149011920,plain,
( rewrite(a,b)
| equalish(b,a) ),
inference(resolution,[status(thm)],[148530720,140615784]),
[] ).
cnf(149583888,plain,
rewrite(a,b),
inference(resolution,[status(thm)],[149500848,149011920]),
[] ).
cnf(148541056,plain,
( ~ equalish(A,a)
| reflexive_rewrite(A,b) ),
inference(resolution,[status(thm)],[140626528,140596344]),
[] ).
cnf(148586720,plain,
~ reflexive_rewrite(c,b),
inference(resolution,[status(thm)],[148480928,148550528]),
[] ).
cnf(149610696,plain,
~ equalish(c,a),
inference(resolution,[status(thm)],[148541056,148586720]),
[] ).
cnf(148493608,plain,
( equalish(a,c)
| rewrite(a,c) ),
inference(resolution,[status(thm)],[140645120,140588888]),
[] ).
cnf(148939792,plain,
( rewrite(a,c)
| equalish(c,a) ),
inference(resolution,[status(thm)],[148493608,140615784]),
[] ).
cnf(149665160,plain,
rewrite(a,c),
inference(resolution,[status(thm)],[149610696,148939792]),
[] ).
fof(rewrite_diamond,plain,
! [C,A,B] :
( ( rewrite(C,d(A,B,C))
| ~ rewrite(A,B)
| ~ rewrite(A,C) )
& ( rewrite(B,d(A,B,C))
| ~ rewrite(A,B)
| ~ rewrite(A,C) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+1.tptp',unknown),
[] ).
cnf(140663840,plain,
( rewrite(B,d(A,B,C))
| ~ rewrite(A,B)
| ~ rewrite(A,C) ),
inference(rewrite,[status(thm)],[rewrite_diamond]),
[] ).
cnf(151899736,plain,
( rewrite(b,d(a,b,A))
| ~ rewrite(a,A) ),
inference(resolution,[status(thm)],[140663840,149583888]),
[] ).
cnf(155908512,plain,
rewrite(b,d(a,b,c)),
inference(resolution,[status(thm)],[151899736,149665160]),
[] ).
fof(rewrite_in_reflexive_rewrite,plain,
! [A,B] :
( ~ rewrite(A,B)
| reflexive_rewrite(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+1.tptp',unknown),
[] ).
cnf(140637744,plain,
( ~ rewrite(A,B)
| reflexive_rewrite(A,B) ),
inference(rewrite,[status(thm)],[rewrite_in_reflexive_rewrite]),
[] ).
cnf(148637680,plain,
( ~ reflexive_rewrite(c,A)
| ~ rewrite(b,A) ),
inference(resolution,[status(thm)],[148480928,140637744]),
[] ).
cnf(148791816,plain,
( ~ rewrite(b,A)
| ~ rewrite(c,A) ),
inference(resolution,[status(thm)],[148637680,140637744]),
[] ).
cnf(156282824,plain,
~ rewrite(c,d(a,b,c)),
inference(resolution,[status(thm)],[155908512,148791816]),
[] ).
cnf(140689384,plain,
( rewrite(C,d(A,B,C))
| ~ rewrite(A,B)
| ~ rewrite(A,C) ),
inference(rewrite,[status(thm)],[rewrite_diamond]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[149583888,149665160,156282824,140689384]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(substitution,plain,(~equalish(A,B)|~reflexive_rewrite(B,C)|reflexive_rewrite(A,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+1.tptp',unknown),[]).
%
% cnf(140626528,plain,(~equalish(A,B)|~reflexive_rewrite(B,C)|reflexive_rewrite(A,C)),inference(rewrite,[status(thm)],[substitution]),[]).
%
% fof(assumption,plain,((reflexive_rewrite(a,b)&reflexive_rewrite(a,c))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+1.tptp',unknown),[]).
%
% cnf(140588888,plain,(reflexive_rewrite(a,c)),inference(rewrite,[status(thm)],[assumption]),[]).
%
% cnf(148513904,plain,(~equalish(A,a)|reflexive_rewrite(A,c)),inference(resolution,[status(thm)],[140626528,140588888]),[]).
%
% fof(goal_ax,plain,(~reflexive_rewrite(b,A)|~reflexive_rewrite(c,A)|goal),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+1.tptp',unknown),[]).
%
% cnf(140604320,plain,(~reflexive_rewrite(b,A)|~reflexive_rewrite(c,A)|goal),inference(rewrite,[status(thm)],[goal_ax]),[]).
%
% fof(goal_to_be_proved,plain,(~goal),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+1.tptp',unknown),[]).
%
% cnf(140702712,plain,(~goal),inference(rewrite,[status(thm)],[goal_to_be_proved]),[]).
%
% cnf(148480928,plain,(~reflexive_rewrite(b,A)|~reflexive_rewrite(c,A)),inference(resolution,[status(thm)],[140604320,140702712]),[]).
%
% fof(equalish_in_reflexive_rewrite,plain,(~equalish(A,B)|reflexive_rewrite(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+1.tptp',unknown),[]).
%
% cnf(140631464,plain,(~equalish(A,B)|reflexive_rewrite(A,B)),inference(rewrite,[status(thm)],[equalish_in_reflexive_rewrite]),[]).
%
% fof(reflexivity,plain,(equalish(A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+1.tptp',unknown),[]).
%
% cnf(140609168,plain,(equalish(A,A)),inference(rewrite,[status(thm)],[reflexivity]),[]).
%
% cnf(148550528,plain,(reflexive_rewrite(A,A)),inference(resolution,[status(thm)],[140631464,140609168]),[]).
%
% cnf(148599552,plain,(~reflexive_rewrite(b,c)),inference(resolution,[status(thm)],[148480928,148550528]),[]).
%
% cnf(149500848,plain,(~equalish(b,a)),inference(resolution,[status(thm)],[148513904,148599552]),[]).
%
% fof(equalish_or_rewrite,plain,(~reflexive_rewrite(A,B)|equalish(A,B)|rewrite(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+1.tptp',unknown),[]).
%
% cnf(140645120,plain,(~reflexive_rewrite(A,B)|equalish(A,B)|rewrite(A,B)),inference(rewrite,[status(thm)],[equalish_or_rewrite]),[]).
%
% cnf(140596344,plain,(reflexive_rewrite(a,b)),inference(rewrite,[status(thm)],[assumption]),[]).
%
% cnf(148530720,plain,(equalish(a,b)|rewrite(a,b)),inference(resolution,[status(thm)],[140645120,140596344]),[]).
%
% fof(symmtery,plain,(~equalish(A,B)|equalish(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+1.tptp',unknown),[]).
%
% cnf(140615784,plain,(~equalish(A,B)|equalish(B,A)),inference(rewrite,[status(thm)],[symmtery]),[]).
%
% cnf(149011920,plain,(rewrite(a,b)|equalish(b,a)),inference(resolution,[status(thm)],[148530720,140615784]),[]).
%
% cnf(149583888,plain,(rewrite(a,b)),inference(resolution,[status(thm)],[149500848,149011920]),[]).
%
% cnf(148541056,plain,(~equalish(A,a)|reflexive_rewrite(A,b)),inference(resolution,[status(thm)],[140626528,140596344]),[]).
%
% cnf(148586720,plain,(~reflexive_rewrite(c,b)),inference(resolution,[status(thm)],[148480928,148550528]),[]).
%
% cnf(149610696,plain,(~equalish(c,a)),inference(resolution,[status(thm)],[148541056,148586720]),[]).
%
% cnf(148493608,plain,(equalish(a,c)|rewrite(a,c)),inference(resolution,[status(thm)],[140645120,140588888]),[]).
%
% cnf(148939792,plain,(rewrite(a,c)|equalish(c,a)),inference(resolution,[status(thm)],[148493608,140615784]),[]).
%
% cnf(149665160,plain,(rewrite(a,c)),inference(resolution,[status(thm)],[149610696,148939792]),[]).
%
% fof(rewrite_diamond,plain,(((rewrite(C,d(A,B,C))|~rewrite(A,B)|~rewrite(A,C))&(rewrite(B,d(A,B,C))|~rewrite(A,B)|~rewrite(A,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+1.tptp',unknown),[]).
%
% cnf(140663840,plain,(rewrite(B,d(A,B,C))|~rewrite(A,B)|~rewrite(A,C)),inference(rewrite,[status(thm)],[rewrite_diamond]),[]).
%
% cnf(151899736,plain,(rewrite(b,d(a,b,A))|~rewrite(a,A)),inference(resolution,[status(thm)],[140663840,149583888]),[]).
%
% cnf(155908512,plain,(rewrite(b,d(a,b,c))),inference(resolution,[status(thm)],[151899736,149665160]),[]).
%
% fof(rewrite_in_reflexive_rewrite,plain,(~rewrite(A,B)|reflexive_rewrite(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+1.tptp',unknown),[]).
%
% cnf(140637744,plain,(~rewrite(A,B)|reflexive_rewrite(A,B)),inference(rewrite,[status(thm)],[rewrite_in_reflexive_rewrite]),[]).
%
% cnf(148637680,plain,(~reflexive_rewrite(c,A)|~rewrite(b,A)),inference(resolution,[status(thm)],[148480928,140637744]),[]).
%
% cnf(148791816,plain,(~rewrite(b,A)|~rewrite(c,A)),inference(resolution,[status(thm)],[148637680,140637744]),[]).
%
% cnf(156282824,plain,(~rewrite(c,d(a,b,c))),inference(resolution,[status(thm)],[155908512,148791816]),[]).
%
% cnf(140689384,plain,(rewrite(C,d(A,B,C))|~rewrite(A,B)|~rewrite(A,C)),inference(rewrite,[status(thm)],[rewrite_diamond]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[149583888,149665160,156282824,140689384]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------