TSTP Solution File: LCL488+1 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL488+1 : TPTP v3.4.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art09.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1003MB
% OS : Linux 2.6.17-1.2142_FC4
% CPULimit : 600s
% DateTime : Wed May 6 13:51:25 EDT 2009
% Result : Theorem 20.4s
% Output : Refutation 20.4s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 18
% Syntax : Number of formulae : 58 ( 35 unt; 0 def)
% Number of atoms : 101 ( 0 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 81 ( 38 ~; 36 |; 7 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 10 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 0 con; 1-2 aty)
% Number of variables : 76 ( 14 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(principia_op_and,plain,
op_and,
file('/tmp/SystemOnTPTP10673/LCL488+1.p',unknown),
[] ).
cnf(166713344,plain,
op_and,
inference(rewrite,[status(thm)],[principia_op_and]),
[] ).
fof(op_and,plain,
! [A,B] :
( ~ op_and
| $equal(not(or(not(A),not(B))),and(A,B)) ),
file('/tmp/SystemOnTPTP10673/LCL488+1.p',unknown),
[] ).
cnf(166639976,plain,
( ~ op_and
| $equal(not(or(not(A),not(B))),and(A,B)) ),
inference(rewrite,[status(thm)],[op_and]),
[] ).
fof(op_or,plain,
! [A,B] :
( ~ op_or
| $equal(not(and(not(A),not(B))),or(A,B)) ),
file('/tmp/SystemOnTPTP10673/LCL488+1.p',unknown),
[] ).
cnf(166622272,plain,
( ~ op_or
| $equal(not(and(not(A),not(B))),or(A,B)) ),
inference(rewrite,[status(thm)],[op_or]),
[] ).
fof(hilbert_op_or,plain,
op_or,
file('/tmp/SystemOnTPTP10673/LCL488+1.p',unknown),
[] ).
cnf(166815296,plain,
op_or,
inference(rewrite,[status(thm)],[hilbert_op_or]),
[] ).
cnf(175305528,plain,
$equal(not(and(not(A),not(B))),or(A,B)),
inference(resolution,[status(thm)],[166622272,166815296]),
[] ).
fof(op_implies_and,plain,
! [A,B] :
( ~ op_implies_and
| $equal(not(and(A,not(B))),implies(A,B)) ),
file('/tmp/SystemOnTPTP10673/LCL488+1.p',unknown),
[] ).
cnf(166657808,plain,
( ~ op_implies_and
| $equal(not(and(A,not(B))),implies(A,B)) ),
inference(rewrite,[status(thm)],[op_implies_and]),
[] ).
fof(hilbert_op_implies_and,plain,
op_implies_and,
file('/tmp/SystemOnTPTP10673/LCL488+1.p',unknown),
[] ).
cnf(166827104,plain,
op_implies_and,
inference(rewrite,[status(thm)],[hilbert_op_implies_and]),
[] ).
cnf(175309776,plain,
$equal(not(and(A,not(B))),implies(A,B)),
inference(resolution,[status(thm)],[166657808,166827104]),
[] ).
cnf(186721800,plain,
$equal(or(A,B),implies(not(A),B)),
inference(paramodulation,[status(thm)],[175305528,175309776,theory(equality)]),
[] ).
fof(r2,plain,
! [B,A] :
( ( ~ r2
| is_a_theorem(implies(B,or(A,B))) )
& ( r2
| ~ is_a_theorem(implies(q(A,B),or(p(A,B),q(A,B)))) ) ),
file('/tmp/SystemOnTPTP10673/LCL488+1.p',unknown),
[] ).
cnf(166501232,plain,
( ~ r2
| is_a_theorem(implies(B,or(A,B))) ),
inference(rewrite,[status(thm)],[r2]),
[] ).
fof(principia_r2,plain,
r2,
file('/tmp/SystemOnTPTP10673/LCL488+1.p',unknown),
[] ).
cnf(165726320,plain,
r2,
inference(rewrite,[status(thm)],[principia_r2]),
[] ).
cnf(175261352,plain,
is_a_theorem(implies(B,or(A,B))),
inference(resolution,[status(thm)],[166501232,165726320]),
[] ).
cnf(175801384,plain,
is_a_theorem(not(and(A,not(or(B,A))))),
inference(paramodulation,[status(thm)],[175309776,175261352,theory(equality)]),
[] ).
cnf(186452544,plain,
is_a_theorem(or(A,or(B,not(A)))),
inference(paramodulation,[status(thm)],[175305528,175801384,theory(equality)]),
[] ).
fof(modus_ponens,plain,
! [A,B] :
( ( ~ modus_ponens
| ~ is_a_theorem(A)
| ~ is_a_theorem(implies(A,B))
| is_a_theorem(B) )
& ( ~ is_a_theorem(y(A,B))
| modus_ponens )
& ( is_a_theorem(x(A,B))
| modus_ponens )
& ( is_a_theorem(implies(x(A,B),y(A,B)))
| modus_ponens ) ),
file('/tmp/SystemOnTPTP10673/LCL488+1.p',unknown),
[] ).
cnf(165773904,plain,
( ~ modus_ponens
| ~ is_a_theorem(A)
| ~ is_a_theorem(implies(A,B))
| is_a_theorem(B) ),
inference(rewrite,[status(thm)],[modus_ponens]),
[] ).
fof(principia_modus_ponens,plain,
modus_ponens,
file('/tmp/SystemOnTPTP10673/LCL488+1.p',unknown),
[] ).
cnf(166737232,plain,
modus_ponens,
inference(rewrite,[status(thm)],[principia_modus_ponens]),
[] ).
cnf(175229792,plain,
( ~ is_a_theorem(A)
| ~ is_a_theorem(implies(A,B))
| is_a_theorem(B) ),
inference(resolution,[status(thm)],[165773904,166737232]),
[] ).
fof(r3,plain,
! [A,B] :
( ( ~ r3
| is_a_theorem(implies(or(A,B),or(B,A))) )
& ( r3
| ~ is_a_theorem(implies(or(p(A,B),q(A,B)),or(q(A,B),p(A,B)))) ) ),
file('/tmp/SystemOnTPTP10673/LCL488+1.p',unknown),
[] ).
cnf(166531680,plain,
( ~ r3
| is_a_theorem(implies(or(A,B),or(B,A))) ),
inference(rewrite,[status(thm)],[r3]),
[] ).
fof(principia_r3,plain,
r3,
file('/tmp/SystemOnTPTP10673/LCL488+1.p',unknown),
[] ).
cnf(166770496,plain,
r3,
inference(rewrite,[status(thm)],[principia_r3]),
[] ).
cnf(175265816,plain,
is_a_theorem(implies(or(A,B),or(B,A))),
inference(resolution,[status(thm)],[166531680,166770496]),
[] ).
cnf(177720336,plain,
( ~ is_a_theorem(or(A,B))
| is_a_theorem(or(B,A)) ),
inference(resolution,[status(thm)],[175229792,175265816]),
[] ).
cnf(187675512,plain,
is_a_theorem(or(or(B,not(A)),A)),
inference(resolution,[status(thm)],[186452544,177720336]),
[] ).
cnf(188672272,plain,
is_a_theorem(implies(not(or(B,not(A))),A)),
inference(paramodulation,[status(thm)],[186721800,187675512,theory(equality)]),
[] ).
cnf(319264952,plain,
is_a_theorem(implies(and(A,B),B)),
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[166713344,166639976,188672272,theory(equality)]),
[] ).
fof(op_implies_or,plain,
! [A,B] :
( ~ op_implies_or
| $equal(or(not(A),B),implies(A,B)) ),
file('/tmp/SystemOnTPTP10673/LCL488+1.p',unknown),
[] ).
cnf(166671488,plain,
( ~ op_implies_or
| $equal(or(not(A),B),implies(A,B)) ),
inference(rewrite,[status(thm)],[op_implies_or]),
[] ).
fof(principia_op_implies_or,plain,
op_implies_or,
file('/tmp/SystemOnTPTP10673/LCL488+1.p',unknown),
[] ).
cnf(166701192,plain,
op_implies_or,
inference(rewrite,[status(thm)],[principia_op_implies_or]),
[] ).
cnf(175198464,plain,
$equal(or(not(A),B),implies(A,B)),
inference(resolution,[status(thm)],[166671488,166701192]),
[] ).
cnf(175460384,plain,
is_a_theorem(implies(B,implies(A,B))),
inference(paramodulation,[status(thm)],[175198464,175261352,theory(equality)]),
[] ).
cnf(177446704,plain,
( ~ is_a_theorem(A)
| is_a_theorem(implies(B,A)) ),
inference(resolution,[status(thm)],[175229792,175460384]),
[] ).
cnf(323992664,plain,
is_a_theorem(implies(C,implies(and(A,B),B))),
inference(resolution,[status(thm)],[319264952,177446704]),
[] ).
fof(and_2,plain,
! [A,B] :
( ( ~ and_2
| is_a_theorem(implies(and(A,B),B)) )
& ( and_2
| ~ is_a_theorem(implies(and(x(A,B),y(A,B)),y(A,B))) ) ),
file('/tmp/SystemOnTPTP10673/LCL488+1.p',unknown),
[] ).
cnf(165727984,plain,
( and_2
| ~ is_a_theorem(implies(and(x(A,B),y(A,B)),y(A,B))) ),
inference(rewrite,[status(thm)],[and_2]),
[] ).
fof(hilbert_and_2,plain,
~ and_2,
file('/tmp/SystemOnTPTP10673/LCL488+1.p',unknown),
[] ).
cnf(166841640,plain,
~ and_2,
inference(rewrite,[status(thm)],[hilbert_and_2]),
[] ).
cnf(175319976,plain,
~ is_a_theorem(implies(and(x(A,B),y(A,B)),y(A,B))),
inference(resolution,[status(thm)],[165727984,166841640]),
[] ).
cnf(177417072,plain,
( ~ is_a_theorem(A)
| is_a_theorem(or(B,A)) ),
inference(resolution,[status(thm)],[175229792,175261352]),
[] ).
cnf(179584808,plain,
( ~ is_a_theorem(A)
| ~ is_a_theorem(implies(or(B,A),C))
| is_a_theorem(C) ),
inference(resolution,[status(thm)],[177417072,175229792]),
[] ).
cnf(353727360,plain,
~ is_a_theorem(C),
inference(forward_subsumption_resolution__resolution,[status(thm)],[323992664,175319976,179584808]),
[] ).
fof(r1,plain,
! [A] :
( ( ~ r1
| is_a_theorem(implies(or(A,A),A)) )
& ( r1
| ~ is_a_theorem(implies(or(p(A),p(A)),p(A))) ) ),
file('/tmp/SystemOnTPTP10673/LCL488+1.p',unknown),
[] ).
cnf(166474848,plain,
( ~ r1
| is_a_theorem(implies(or(A,A),A)) ),
inference(rewrite,[status(thm)],[r1]),
[] ).
fof(principia_r1,plain,
r1,
file('/tmp/SystemOnTPTP10673/LCL488+1.p',unknown),
[] ).
cnf(166748376,plain,
r1,
inference(rewrite,[status(thm)],[principia_r1]),
[] ).
cnf(175245696,plain,
is_a_theorem(implies(or(A,A),A)),
inference(resolution,[status(thm)],[166474848,166748376]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[353727360,175245696]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 20 seconds
% START OF PROOF SEQUENCE
% fof(principia_op_and,plain,(op_and),file('/tmp/SystemOnTPTP10673/LCL488+1.p',unknown),[]).
%
% cnf(166713344,plain,(op_and),inference(rewrite,[status(thm)],[principia_op_and]),[]).
%
% fof(op_and,plain,(~op_and|$equal(not(or(not(A),not(B))),and(A,B))),file('/tmp/SystemOnTPTP10673/LCL488+1.p',unknown),[]).
%
% cnf(166639976,plain,(~op_and|$equal(not(or(not(A),not(B))),and(A,B))),inference(rewrite,[status(thm)],[op_and]),[]).
%
% fof(op_or,plain,(~op_or|$equal(not(and(not(A),not(B))),or(A,B))),file('/tmp/SystemOnTPTP10673/LCL488+1.p',unknown),[]).
%
% cnf(166622272,plain,(~op_or|$equal(not(and(not(A),not(B))),or(A,B))),inference(rewrite,[status(thm)],[op_or]),[]).
%
% fof(hilbert_op_or,plain,(op_or),file('/tmp/SystemOnTPTP10673/LCL488+1.p',unknown),[]).
%
% cnf(166815296,plain,(op_or),inference(rewrite,[status(thm)],[hilbert_op_or]),[]).
%
% cnf(175305528,plain,($equal(not(and(not(A),not(B))),or(A,B))),inference(resolution,[status(thm)],[166622272,166815296]),[]).
%
% fof(op_implies_and,plain,(~op_implies_and|$equal(not(and(A,not(B))),implies(A,B))),file('/tmp/SystemOnTPTP10673/LCL488+1.p',unknown),[]).
%
% cnf(166657808,plain,(~op_implies_and|$equal(not(and(A,not(B))),implies(A,B))),inference(rewrite,[status(thm)],[op_implies_and]),[]).
%
% fof(hilbert_op_implies_and,plain,(op_implies_and),file('/tmp/SystemOnTPTP10673/LCL488+1.p',unknown),[]).
%
% cnf(166827104,plain,(op_implies_and),inference(rewrite,[status(thm)],[hilbert_op_implies_and]),[]).
%
% cnf(175309776,plain,($equal(not(and(A,not(B))),implies(A,B))),inference(resolution,[status(thm)],[166657808,166827104]),[]).
%
% cnf(186721800,plain,($equal(or(A,B),implies(not(A),B))),inference(paramodulation,[status(thm)],[175305528,175309776,theory(equality)]),[]).
%
% fof(r2,plain,(((~r2|is_a_theorem(implies(B,or(A,B))))&(r2|~is_a_theorem(implies(q(A,B),or(p(A,B),q(A,B))))))),file('/tmp/SystemOnTPTP10673/LCL488+1.p',unknown),[]).
%
% cnf(166501232,plain,(~r2|is_a_theorem(implies(B,or(A,B)))),inference(rewrite,[status(thm)],[r2]),[]).
%
% fof(principia_r2,plain,(r2),file('/tmp/SystemOnTPTP10673/LCL488+1.p',unknown),[]).
%
% cnf(165726320,plain,(r2),inference(rewrite,[status(thm)],[principia_r2]),[]).
%
% cnf(175261352,plain,(is_a_theorem(implies(B,or(A,B)))),inference(resolution,[status(thm)],[166501232,165726320]),[]).
%
% cnf(175801384,plain,(is_a_theorem(not(and(A,not(or(B,A)))))),inference(paramodulation,[status(thm)],[175309776,175261352,theory(equality)]),[]).
%
% cnf(186452544,plain,(is_a_theorem(or(A,or(B,not(A))))),inference(paramodulation,[status(thm)],[175305528,175801384,theory(equality)]),[]).
%
% fof(modus_ponens,plain,(((~modus_ponens|~is_a_theorem(A)|~is_a_theorem(implies(A,B))|is_a_theorem(B))&(~is_a_theorem(y(A,B))|modus_ponens)&(is_a_theorem(x(A,B))|modus_ponens)&(is_a_theorem(implies(x(A,B),y(A,B)))|modus_ponens))),file('/tmp/SystemOnTPTP10673/LCL488+1.p',unknown),[]).
%
% cnf(165773904,plain,(~modus_ponens|~is_a_theorem(A)|~is_a_theorem(implies(A,B))|is_a_theorem(B)),inference(rewrite,[status(thm)],[modus_ponens]),[]).
%
% fof(principia_modus_ponens,plain,(modus_ponens),file('/tmp/SystemOnTPTP10673/LCL488+1.p',unknown),[]).
%
% cnf(166737232,plain,(modus_ponens),inference(rewrite,[status(thm)],[principia_modus_ponens]),[]).
%
% cnf(175229792,plain,(~is_a_theorem(A)|~is_a_theorem(implies(A,B))|is_a_theorem(B)),inference(resolution,[status(thm)],[165773904,166737232]),[]).
%
% fof(r3,plain,(((~r3|is_a_theorem(implies(or(A,B),or(B,A))))&(r3|~is_a_theorem(implies(or(p(A,B),q(A,B)),or(q(A,B),p(A,B))))))),file('/tmp/SystemOnTPTP10673/LCL488+1.p',unknown),[]).
%
% cnf(166531680,plain,(~r3|is_a_theorem(implies(or(A,B),or(B,A)))),inference(rewrite,[status(thm)],[r3]),[]).
%
% fof(principia_r3,plain,(r3),file('/tmp/SystemOnTPTP10673/LCL488+1.p',unknown),[]).
%
% cnf(166770496,plain,(r3),inference(rewrite,[status(thm)],[principia_r3]),[]).
%
% cnf(175265816,plain,(is_a_theorem(implies(or(A,B),or(B,A)))),inference(resolution,[status(thm)],[166531680,166770496]),[]).
%
% cnf(177720336,plain,(~is_a_theorem(or(A,B))|is_a_theorem(or(B,A))),inference(resolution,[status(thm)],[175229792,175265816]),[]).
%
% cnf(187675512,plain,(is_a_theorem(or(or(B,not(A)),A))),inference(resolution,[status(thm)],[186452544,177720336]),[]).
%
% cnf(188672272,plain,(is_a_theorem(implies(not(or(B,not(A))),A))),inference(paramodulation,[status(thm)],[186721800,187675512,theory(equality)]),[]).
%
% cnf(319264952,plain,(is_a_theorem(implies(and(A,B),B))),inference(forward_subsumption_resolution__paramodulation,[status(thm)],[166713344,166639976,188672272,theory(equality)]),[]).
%
% fof(op_implies_or,plain,(~op_implies_or|$equal(or(not(A),B),implies(A,B))),file('/tmp/SystemOnTPTP10673/LCL488+1.p',unknown),[]).
%
% cnf(166671488,plain,(~op_implies_or|$equal(or(not(A),B),implies(A,B))),inference(rewrite,[status(thm)],[op_implies_or]),[]).
%
% fof(principia_op_implies_or,plain,(op_implies_or),file('/tmp/SystemOnTPTP10673/LCL488+1.p',unknown),[]).
%
% cnf(166701192,plain,(op_implies_or),inference(rewrite,[status(thm)],[principia_op_implies_or]),[]).
%
% cnf(175198464,plain,($equal(or(not(A),B),implies(A,B))),inference(resolution,[status(thm)],[166671488,166701192]),[]).
%
% cnf(175460384,plain,(is_a_theorem(implies(B,implies(A,B)))),inference(paramodulation,[status(thm)],[175198464,175261352,theory(equality)]),[]).
%
% cnf(177446704,plain,(~is_a_theorem(A)|is_a_theorem(implies(B,A))),inference(resolution,[status(thm)],[175229792,175460384]),[]).
%
% cnf(323992664,plain,(is_a_theorem(implies(C,implies(and(A,B),B)))),inference(resolution,[status(thm)],[319264952,177446704]),[]).
%
% fof(and_2,plain,(((~and_2|is_a_theorem(implies(and(A,B),B)))&(and_2|~is_a_theorem(implies(and(x(A,B),y(A,B)),y(A,B)))))),file('/tmp/SystemOnTPTP10673/LCL488+1.p',unknown),[]).
%
% cnf(165727984,plain,(and_2|~is_a_theorem(implies(and(x(A,B),y(A,B)),y(A,B)))),inference(rewrite,[status(thm)],[and_2]),[]).
%
% fof(hilbert_and_2,plain,(~and_2),file('/tmp/SystemOnTPTP10673/LCL488+1.p',unknown),[]).
%
% cnf(166841640,plain,(~and_2),inference(rewrite,[status(thm)],[hilbert_and_2]),[]).
%
% cnf(175319976,plain,(~is_a_theorem(implies(and(x(A,B),y(A,B)),y(A,B)))),inference(resolution,[status(thm)],[165727984,166841640]),[]).
%
% cnf(177417072,plain,(~is_a_theorem(A)|is_a_theorem(or(B,A))),inference(resolution,[status(thm)],[175229792,175261352]),[]).
%
% cnf(179584808,plain,(~is_a_theorem(A)|~is_a_theorem(implies(or(B,A),C))|is_a_theorem(C)),inference(resolution,[status(thm)],[177417072,175229792]),[]).
%
% cnf(353727360,plain,(~is_a_theorem(C)),inference(forward_subsumption_resolution__resolution,[status(thm)],[323992664,175319976,179584808]),[]).
%
% fof(r1,plain,(((~r1|is_a_theorem(implies(or(A,A),A)))&(r1|~is_a_theorem(implies(or(p(A),p(A)),p(A)))))),file('/tmp/SystemOnTPTP10673/LCL488+1.p',unknown),[]).
%
% cnf(166474848,plain,(~r1|is_a_theorem(implies(or(A,A),A))),inference(rewrite,[status(thm)],[r1]),[]).
%
% fof(principia_r1,plain,(r1),file('/tmp/SystemOnTPTP10673/LCL488+1.p',unknown),[]).
%
% cnf(166748376,plain,(r1),inference(rewrite,[status(thm)],[principia_r1]),[]).
%
% cnf(175245696,plain,(is_a_theorem(implies(or(A,A),A))),inference(resolution,[status(thm)],[166474848,166748376]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[353727360,175245696]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------