TSTP Solution File: COL074-3 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : COL074-3 : TPTP v3.4.2. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art05.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 11:33:58 EDT 2009
% Result : Unsatisfiable 0.2s
% Output : Refutation 0.2s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 25 unt; 0 def)
% Number of atoms : 31 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 3 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 17 ( 7 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(extensionality1,plain,
! [B,A] :
( $equal(B,A)
| $equal(apply(eq,pair(A,B)),projection2) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL074-3.tptp',unknown),
[] ).
cnf(173812600,plain,
( $equal(B,A)
| $equal(apply(eq,pair(A,B)),projection2) ),
inference(rewrite,[status(thm)],[extensionality1]),
[] ).
fof(different_projections,plain,
~ $equal(projection2,projection1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL074-3.tptp',unknown),
[] ).
cnf(173847800,plain,
~ $equal(projection2,projection1),
inference(rewrite,[status(thm)],[different_projections]),
[] ).
cnf(184293968,plain,
$equal(apply(eq,pair(projection1,projection2)),projection2),
inference(resolution,[status(thm)],[173812600,173847800]),
[] ).
fof(k_projection2,plain,
$equal(apply(k,projection2),k_projection2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL074-3.tptp',unknown),
[] ).
cnf(173706640,plain,
$equal(apply(k,projection2),k_projection2),
inference(rewrite,[status(thm)],[k_projection2]),
[] ).
cnf(184418336,plain,
$equal(apply(k,apply(eq,pair(projection1,projection2))),k_projection2),
inference(paramodulation,[status(thm)],[184293968,173706640,theory(equality)]),
[] ).
fof(k_definition,plain,
! [A,B] : $equal(apply(apply(k,A),B),A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL074-3.tptp',unknown),
[] ).
cnf(173709216,plain,
$equal(apply(apply(k,A),B),A),
inference(rewrite,[status(thm)],[k_definition]),
[] ).
cnf(184770432,plain,
$equal(apply(k_projection2,A),apply(eq,pair(projection1,projection2))),
inference(paramodulation,[status(thm)],[184418336,173709216,theory(equality)]),
[] ).
cnf(185047320,plain,
$equal(apply(k,apply(k_projection2,A)),k_projection2),
inference(paramodulation,[status(thm)],[184770432,184418336,theory(equality)]),
[] ).
cnf(185525792,plain,
$equal(apply(k,projection2),apply(k,apply(k_projection2,A))),
inference(paramodulation,[status(thm)],[185047320,173706640,theory(equality)]),
[] ).
cnf(187143048,plain,
$equal(k_projection2,apply(k,apply(k_projection2,A))),
inference(paramodulation,[status(thm)],[185525792,173706640,theory(equality)]),
[] ).
cnf(185023392,plain,
$equal(apply(k_projection2,A),projection2),
inference(paramodulation,[status(thm)],[184770432,184293968,theory(equality)]),
[] ).
cnf(187432272,plain,
$equal(k_projection2,apply(k,projection2)),
inference(paramodulation,[status(thm)],[187143048,185023392,theory(equality)]),
[] ).
fof(self_referential,plain,
$equal(apply(eq,pair(apply(k,s),apply(k,projection2))),s),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL074-3.tptp',unknown),
[] ).
cnf(173859936,plain,
$equal(apply(eq,pair(apply(k,s),apply(k,projection2))),s),
inference(rewrite,[status(thm)],[self_referential]),
[] ).
cnf(187526632,plain,
$equal(apply(eq,pair(apply(k,s),k_projection2)),s),
inference(paramodulation,[status(thm)],[187432272,173859936,theory(equality)]),
[] ).
cnf(190729264,plain,
( $equal(k_projection2,apply(k,s))
| $equal(s,projection2) ),
inference(paramodulation,[status(thm)],[187526632,173812600,theory(equality)]),
[] ).
cnf(190929656,plain,
$equal(k_projection2,apply(k,s)),
inference(paramodulation,[status(thm)],[190729264,173706640,theory(equality)]),
[] ).
cnf(190965904,plain,
$equal(apply(k_projection2,A),s),
inference(paramodulation,[status(thm)],[190929656,173709216,theory(equality)]),
[] ).
cnf(191441104,plain,
$equal(projection2,s),
inference(paramodulation,[status(thm)],[190965904,185023392,theory(equality)]),
[] ).
cnf(191359288,plain,
$equal(apply(eq,pair(k_projection2,k_projection2)),s),
inference(paramodulation,[status(thm)],[190929656,187526632,theory(equality)]),
[] ).
fof(equality,plain,
! [A] : $equal(apply(eq,pair(A,A)),projection1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL074-3.tptp',unknown),
[] ).
cnf(173803672,plain,
$equal(apply(eq,pair(A,A)),projection1),
inference(rewrite,[status(thm)],[equality]),
[] ).
cnf(184398120,plain,
~ $equal(projection2,apply(eq,pair(A,A))),
inference(paramodulation,[status(thm)],[173847800,173803672,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[191441104,191359288,184398120,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(extensionality1,plain,($equal(B,A)|$equal(apply(eq,pair(A,B)),projection2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL074-3.tptp',unknown),[]).
%
% cnf(173812600,plain,($equal(B,A)|$equal(apply(eq,pair(A,B)),projection2)),inference(rewrite,[status(thm)],[extensionality1]),[]).
%
% fof(different_projections,plain,(~$equal(projection2,projection1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL074-3.tptp',unknown),[]).
%
% cnf(173847800,plain,(~$equal(projection2,projection1)),inference(rewrite,[status(thm)],[different_projections]),[]).
%
% cnf(184293968,plain,($equal(apply(eq,pair(projection1,projection2)),projection2)),inference(resolution,[status(thm)],[173812600,173847800]),[]).
%
% fof(k_projection2,plain,($equal(apply(k,projection2),k_projection2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL074-3.tptp',unknown),[]).
%
% cnf(173706640,plain,($equal(apply(k,projection2),k_projection2)),inference(rewrite,[status(thm)],[k_projection2]),[]).
%
% cnf(184418336,plain,($equal(apply(k,apply(eq,pair(projection1,projection2))),k_projection2)),inference(paramodulation,[status(thm)],[184293968,173706640,theory(equality)]),[]).
%
% fof(k_definition,plain,($equal(apply(apply(k,A),B),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL074-3.tptp',unknown),[]).
%
% cnf(173709216,plain,($equal(apply(apply(k,A),B),A)),inference(rewrite,[status(thm)],[k_definition]),[]).
%
% cnf(184770432,plain,($equal(apply(k_projection2,A),apply(eq,pair(projection1,projection2)))),inference(paramodulation,[status(thm)],[184418336,173709216,theory(equality)]),[]).
%
% cnf(185047320,plain,($equal(apply(k,apply(k_projection2,A)),k_projection2)),inference(paramodulation,[status(thm)],[184770432,184418336,theory(equality)]),[]).
%
% cnf(185525792,plain,($equal(apply(k,projection2),apply(k,apply(k_projection2,A)))),inference(paramodulation,[status(thm)],[185047320,173706640,theory(equality)]),[]).
%
% cnf(187143048,plain,($equal(k_projection2,apply(k,apply(k_projection2,A)))),inference(paramodulation,[status(thm)],[185525792,173706640,theory(equality)]),[]).
%
% cnf(185023392,plain,($equal(apply(k_projection2,A),projection2)),inference(paramodulation,[status(thm)],[184770432,184293968,theory(equality)]),[]).
%
% cnf(187432272,plain,($equal(k_projection2,apply(k,projection2))),inference(paramodulation,[status(thm)],[187143048,185023392,theory(equality)]),[]).
%
% fof(self_referential,plain,($equal(apply(eq,pair(apply(k,s),apply(k,projection2))),s)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL074-3.tptp',unknown),[]).
%
% cnf(173859936,plain,($equal(apply(eq,pair(apply(k,s),apply(k,projection2))),s)),inference(rewrite,[status(thm)],[self_referential]),[]).
%
% cnf(187526632,plain,($equal(apply(eq,pair(apply(k,s),k_projection2)),s)),inference(paramodulation,[status(thm)],[187432272,173859936,theory(equality)]),[]).
%
% cnf(190729264,plain,($equal(k_projection2,apply(k,s))|$equal(s,projection2)),inference(paramodulation,[status(thm)],[187526632,173812600,theory(equality)]),[]).
%
% cnf(190929656,plain,($equal(k_projection2,apply(k,s))),inference(paramodulation,[status(thm)],[190729264,173706640,theory(equality)]),[]).
%
% cnf(190965904,plain,($equal(apply(k_projection2,A),s)),inference(paramodulation,[status(thm)],[190929656,173709216,theory(equality)]),[]).
%
% cnf(191441104,plain,($equal(projection2,s)),inference(paramodulation,[status(thm)],[190965904,185023392,theory(equality)]),[]).
%
% cnf(191359288,plain,($equal(apply(eq,pair(k_projection2,k_projection2)),s)),inference(paramodulation,[status(thm)],[190929656,187526632,theory(equality)]),[]).
%
% fof(equality,plain,($equal(apply(eq,pair(A,A)),projection1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL074-3.tptp',unknown),[]).
%
% cnf(173803672,plain,($equal(apply(eq,pair(A,A)),projection1)),inference(rewrite,[status(thm)],[equality]),[]).
%
% cnf(184398120,plain,(~$equal(projection2,apply(eq,pair(A,A)))),inference(paramodulation,[status(thm)],[173847800,173803672,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[191441104,191359288,184398120,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------