TSTP Solution File: COM007+2 by Faust---1.0
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%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : COM007+2 : TPTP v3.4.2. Released v3.2.0.
% 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 11:36:35 EDT 2009
% Result : Theorem 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 12 unt; 0 def)
% Number of atoms : 62 ( 0 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 60 ( 30 ~; 28 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-3 aty)
% Number of variables : 28 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(equal_or_rewrite,plain,
! [A,B] :
( ~ reflexive_rewrite(A,B)
| $equal(B,A)
| rewrite(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+2.tptp',unknown),
[] ).
cnf(150221504,plain,
( ~ reflexive_rewrite(A,B)
| $equal(B,A)
| rewrite(A,B) ),
inference(rewrite,[status(thm)],[equal_or_rewrite]),
[] ).
fof(assumption,plain,
( reflexive_rewrite(a,b)
& reflexive_rewrite(a,c) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+2.tptp',unknown),
[] ).
cnf(150181504,plain,
reflexive_rewrite(a,b),
inference(rewrite,[status(thm)],[assumption]),
[] ).
cnf(158087728,plain,
( $equal(b,a)
| rewrite(a,b) ),
inference(resolution,[status(thm)],[150221504,150181504]),
[] ).
cnf(150174048,plain,
reflexive_rewrite(a,c),
inference(rewrite,[status(thm)],[assumption]),
[] ).
cnf(158378592,plain,
( rewrite(a,b)
| reflexive_rewrite(b,c) ),
inference(paramodulation,[status(thm)],[158087728,150174048,theory(equality)]),
[] ).
fof(goal_ax,plain,
! [A] :
( ~ reflexive_rewrite(b,A)
| ~ reflexive_rewrite(c,A)
| goal ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+2.tptp',unknown),
[] ).
cnf(150189480,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+2.tptp',unknown),
[] ).
cnf(150271768,plain,
~ goal,
inference(rewrite,[status(thm)],[goal_to_be_proved]),
[] ).
cnf(158058096,plain,
( ~ reflexive_rewrite(b,A)
| ~ reflexive_rewrite(c,A) ),
inference(resolution,[status(thm)],[150189480,150271768]),
[] ).
fof(equal_in_reflexive_rewrite,plain,
! [B,A] :
( ~ $equal(B,A)
| reflexive_rewrite(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+2.tptp',unknown),
[] ).
cnf(150203416,plain,
( ~ $equal(B,A)
| reflexive_rewrite(A,B) ),
inference(rewrite,[status(thm)],[equal_in_reflexive_rewrite]),
[] ).
cnf(158111360,plain,
reflexive_rewrite(A,A),
inference(equality_resolution,[status(thm)],[150203416]),
[] ).
cnf(158141816,plain,
~ reflexive_rewrite(b,c),
inference(resolution,[status(thm)],[158058096,158111360]),
[] ).
cnf(158447096,plain,
rewrite(a,b),
inference(resolution,[status(thm)],[158378592,158141816]),
[] ).
cnf(158073192,plain,
( $equal(c,a)
| rewrite(a,c) ),
inference(resolution,[status(thm)],[150221504,150174048]),
[] ).
cnf(158348424,plain,
( rewrite(a,c)
| reflexive_rewrite(c,b) ),
inference(paramodulation,[status(thm)],[158073192,150181504,theory(equality)]),
[] ).
cnf(158128984,plain,
~ reflexive_rewrite(c,b),
inference(resolution,[status(thm)],[158058096,158111360]),
[] ).
cnf(158410712,plain,
rewrite(a,c),
inference(resolution,[status(thm)],[158348424,158128984]),
[] ).
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+2.tptp',unknown),
[] ).
cnf(150258440,plain,
( rewrite(C,d(A,B,C))
| ~ rewrite(A,B)
| ~ rewrite(A,C) ),
inference(rewrite,[status(thm)],[rewrite_diamond]),
[] ).
cnf(150240232,plain,
( rewrite(B,d(A,B,C))
| ~ rewrite(A,B)
| ~ rewrite(A,C) ),
inference(rewrite,[status(thm)],[rewrite_diamond]),
[] ).
cnf(158502496,plain,
( rewrite(c,d(a,c,A))
| ~ rewrite(a,A) ),
inference(resolution,[status(thm)],[150240232,158410712]),
[] ).
cnf(159075944,plain,
rewrite(c,d(a,c,b)),
inference(resolution,[status(thm)],[158502496,158447096]),
[] ).
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+2.tptp',unknown),
[] ).
cnf(150210032,plain,
( ~ rewrite(A,B)
| reflexive_rewrite(A,B) ),
inference(rewrite,[status(thm)],[rewrite_in_reflexive_rewrite]),
[] ).
cnf(158183224,plain,
( ~ reflexive_rewrite(c,A)
| ~ rewrite(b,A) ),
inference(resolution,[status(thm)],[158058096,150210032]),
[] ).
cnf(158300224,plain,
( ~ rewrite(b,A)
| ~ rewrite(c,A) ),
inference(resolution,[status(thm)],[158183224,150210032]),
[] ).
cnf(159280720,plain,
~ rewrite(b,d(a,c,b)),
inference(resolution,[status(thm)],[159075944,158300224]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[158447096,158410712,150258440,159280720]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(equal_or_rewrite,plain,(~reflexive_rewrite(A,B)|$equal(B,A)|rewrite(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+2.tptp',unknown),[]).
%
% cnf(150221504,plain,(~reflexive_rewrite(A,B)|$equal(B,A)|rewrite(A,B)),inference(rewrite,[status(thm)],[equal_or_rewrite]),[]).
%
% fof(assumption,plain,((reflexive_rewrite(a,b)&reflexive_rewrite(a,c))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+2.tptp',unknown),[]).
%
% cnf(150181504,plain,(reflexive_rewrite(a,b)),inference(rewrite,[status(thm)],[assumption]),[]).
%
% cnf(158087728,plain,($equal(b,a)|rewrite(a,b)),inference(resolution,[status(thm)],[150221504,150181504]),[]).
%
% cnf(150174048,plain,(reflexive_rewrite(a,c)),inference(rewrite,[status(thm)],[assumption]),[]).
%
% cnf(158378592,plain,(rewrite(a,b)|reflexive_rewrite(b,c)),inference(paramodulation,[status(thm)],[158087728,150174048,theory(equality)]),[]).
%
% fof(goal_ax,plain,(~reflexive_rewrite(b,A)|~reflexive_rewrite(c,A)|goal),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+2.tptp',unknown),[]).
%
% cnf(150189480,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+2.tptp',unknown),[]).
%
% cnf(150271768,plain,(~goal),inference(rewrite,[status(thm)],[goal_to_be_proved]),[]).
%
% cnf(158058096,plain,(~reflexive_rewrite(b,A)|~reflexive_rewrite(c,A)),inference(resolution,[status(thm)],[150189480,150271768]),[]).
%
% fof(equal_in_reflexive_rewrite,plain,(~$equal(B,A)|reflexive_rewrite(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+2.tptp',unknown),[]).
%
% cnf(150203416,plain,(~$equal(B,A)|reflexive_rewrite(A,B)),inference(rewrite,[status(thm)],[equal_in_reflexive_rewrite]),[]).
%
% cnf(158111360,plain,(reflexive_rewrite(A,A)),inference(equality_resolution,[status(thm)],[150203416]),[]).
%
% cnf(158141816,plain,(~reflexive_rewrite(b,c)),inference(resolution,[status(thm)],[158058096,158111360]),[]).
%
% cnf(158447096,plain,(rewrite(a,b)),inference(resolution,[status(thm)],[158378592,158141816]),[]).
%
% cnf(158073192,plain,($equal(c,a)|rewrite(a,c)),inference(resolution,[status(thm)],[150221504,150174048]),[]).
%
% cnf(158348424,plain,(rewrite(a,c)|reflexive_rewrite(c,b)),inference(paramodulation,[status(thm)],[158073192,150181504,theory(equality)]),[]).
%
% cnf(158128984,plain,(~reflexive_rewrite(c,b)),inference(resolution,[status(thm)],[158058096,158111360]),[]).
%
% cnf(158410712,plain,(rewrite(a,c)),inference(resolution,[status(thm)],[158348424,158128984]),[]).
%
% fof(rewrite_diamond,plain,(((rewrite(C,d(A,B,C))|~rewrite(A,B)|~rewrite(A,C))&(rewrite(B,d(A,B,C))|~rewrite(A,B)|~rewrite(A,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+2.tptp',unknown),[]).
%
% cnf(150258440,plain,(rewrite(C,d(A,B,C))|~rewrite(A,B)|~rewrite(A,C)),inference(rewrite,[status(thm)],[rewrite_diamond]),[]).
%
% cnf(150240232,plain,(rewrite(B,d(A,B,C))|~rewrite(A,B)|~rewrite(A,C)),inference(rewrite,[status(thm)],[rewrite_diamond]),[]).
%
% cnf(158502496,plain,(rewrite(c,d(a,c,A))|~rewrite(a,A)),inference(resolution,[status(thm)],[150240232,158410712]),[]).
%
% cnf(159075944,plain,(rewrite(c,d(a,c,b))),inference(resolution,[status(thm)],[158502496,158447096]),[]).
%
% fof(rewrite_in_reflexive_rewrite,plain,(~rewrite(A,B)|reflexive_rewrite(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COM/COM007+2.tptp',unknown),[]).
%
% cnf(150210032,plain,(~rewrite(A,B)|reflexive_rewrite(A,B)),inference(rewrite,[status(thm)],[rewrite_in_reflexive_rewrite]),[]).
%
% cnf(158183224,plain,(~reflexive_rewrite(c,A)|~rewrite(b,A)),inference(resolution,[status(thm)],[158058096,150210032]),[]).
%
% cnf(158300224,plain,(~rewrite(b,A)|~rewrite(c,A)),inference(resolution,[status(thm)],[158183224,150210032]),[]).
%
% cnf(159280720,plain,(~rewrite(b,d(a,c,b))),inference(resolution,[status(thm)],[159075944,158300224]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[158447096,158410712,150258440,159280720]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------