TSTP Solution File: COL003-4 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : COL003-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Fri Jul 15 00:12:21 EDT 2022
% Result : Unsatisfiable 33.14s 33.54s
% Output : Refutation 33.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COL003-4 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Tue May 31 09:50:58 EDT 2022
% 0.12/0.34 % CPUTime :
% 33.14/33.54 *** allocated 10000 integers for termspace/termends
% 33.14/33.54 *** allocated 10000 integers for clauses
% 33.14/33.54 *** allocated 10000 integers for justifications
% 33.14/33.54 Bliksem 1.12
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 Automatic Strategy Selection
% 33.14/33.54
% 33.14/33.54 Clauses:
% 33.14/33.54 [
% 33.14/33.54 [ =( apply( apply( apply( b, X ), Y ), Z ), apply( X, apply( Y, Z ) ) )
% 33.14/33.54 ],
% 33.14/33.54 [ =( apply( apply( w, X ), Y ), apply( apply( X, Y ), Y ) ) ],
% 33.14/33.54 [ ~( =( apply( X, 'fixed_pt' ), apply( 'fixed_pt', apply( X, 'fixed_pt'
% 33.14/33.54 ) ) ) ), 'fixed_point'( X ) ],
% 33.14/33.54 [ ~( 'fixed_point'( apply( apply( b, apply( apply( b, apply( w, w ) ),
% 33.14/33.54 apply( apply( b, w ), b ) ) ), b ) ) ) ]
% 33.14/33.54 ] .
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 percentage equality = 0.600000, percentage horn = 1.000000
% 33.14/33.54 This is a problem with some equality
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 Options Used:
% 33.14/33.54
% 33.14/33.54 useres = 1
% 33.14/33.54 useparamod = 1
% 33.14/33.54 useeqrefl = 1
% 33.14/33.54 useeqfact = 1
% 33.14/33.54 usefactor = 1
% 33.14/33.54 usesimpsplitting = 0
% 33.14/33.54 usesimpdemod = 5
% 33.14/33.54 usesimpres = 3
% 33.14/33.54
% 33.14/33.54 resimpinuse = 1000
% 33.14/33.54 resimpclauses = 20000
% 33.14/33.54 substype = eqrewr
% 33.14/33.54 backwardsubs = 1
% 33.14/33.54 selectoldest = 5
% 33.14/33.54
% 33.14/33.54 litorderings [0] = split
% 33.14/33.54 litorderings [1] = extend the termordering, first sorting on arguments
% 33.14/33.54
% 33.14/33.54 termordering = kbo
% 33.14/33.54
% 33.14/33.54 litapriori = 0
% 33.14/33.54 termapriori = 1
% 33.14/33.54 litaposteriori = 0
% 33.14/33.54 termaposteriori = 0
% 33.14/33.54 demodaposteriori = 0
% 33.14/33.54 ordereqreflfact = 0
% 33.14/33.54
% 33.14/33.54 litselect = negord
% 33.14/33.54
% 33.14/33.54 maxweight = 15
% 33.14/33.54 maxdepth = 30000
% 33.14/33.54 maxlength = 115
% 33.14/33.54 maxnrvars = 195
% 33.14/33.54 excuselevel = 1
% 33.14/33.54 increasemaxweight = 1
% 33.14/33.54
% 33.14/33.54 maxselected = 10000000
% 33.14/33.54 maxnrclauses = 10000000
% 33.14/33.54
% 33.14/33.54 showgenerated = 0
% 33.14/33.54 showkept = 0
% 33.14/33.54 showselected = 0
% 33.14/33.54 showdeleted = 0
% 33.14/33.54 showresimp = 1
% 33.14/33.54 showstatus = 2000
% 33.14/33.54
% 33.14/33.54 prologoutput = 1
% 33.14/33.54 nrgoals = 5000000
% 33.14/33.54 totalproof = 1
% 33.14/33.54
% 33.14/33.54 Symbols occurring in the translation:
% 33.14/33.54
% 33.14/33.54 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 33.14/33.54 . [1, 2] (w:1, o:22, a:1, s:1, b:0),
% 33.14/33.54 ! [4, 1] (w:0, o:16, a:1, s:1, b:0),
% 33.14/33.54 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 33.14/33.54 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 33.14/33.54 b [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 33.14/33.54 apply [41, 2] (w:1, o:47, a:1, s:1, b:0),
% 33.14/33.54 w [44, 0] (w:1, o:13, a:1, s:1, b:0),
% 33.14/33.54 'fixed_pt' [46, 0] (w:1, o:15, a:1, s:1, b:0),
% 33.14/33.54 'fixed_point' [47, 1] (w:1, o:21, a:1, s:1, b:0).
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 Starting Search:
% 33.14/33.54
% 33.14/33.54 Resimplifying inuse:
% 33.14/33.54 Done
% 33.14/33.54
% 33.14/33.54 Failed to find proof!
% 33.14/33.54 maxweight = 15
% 33.14/33.54 maxnrclauses = 10000000
% 33.14/33.54 Generated: 1210
% 33.14/33.54 Kept: 33
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 The strategy used was not complete!
% 33.14/33.54
% 33.14/33.54 Increased maxweight to 16
% 33.14/33.54
% 33.14/33.54 Starting Search:
% 33.14/33.54
% 33.14/33.54 Resimplifying inuse:
% 33.14/33.54 Done
% 33.14/33.54
% 33.14/33.54 Failed to find proof!
% 33.14/33.54 maxweight = 16
% 33.14/33.54 maxnrclauses = 10000000
% 33.14/33.54 Generated: 1210
% 33.14/33.54 Kept: 33
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 The strategy used was not complete!
% 33.14/33.54
% 33.14/33.54 Increased maxweight to 17
% 33.14/33.54
% 33.14/33.54 Starting Search:
% 33.14/33.54
% 33.14/33.54 Resimplifying inuse:
% 33.14/33.54 Done
% 33.14/33.54
% 33.14/33.54 Failed to find proof!
% 33.14/33.54 maxweight = 17
% 33.14/33.54 maxnrclauses = 10000000
% 33.14/33.54 Generated: 3933
% 33.14/33.54 Kept: 78
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 The strategy used was not complete!
% 33.14/33.54
% 33.14/33.54 Increased maxweight to 18
% 33.14/33.54
% 33.14/33.54 Starting Search:
% 33.14/33.54
% 33.14/33.54 Resimplifying inuse:
% 33.14/33.54 Done
% 33.14/33.54
% 33.14/33.54 Failed to find proof!
% 33.14/33.54 maxweight = 18
% 33.14/33.54 maxnrclauses = 10000000
% 33.14/33.54 Generated: 3939
% 33.14/33.54 Kept: 79
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 The strategy used was not complete!
% 33.14/33.54
% 33.14/33.54 Increased maxweight to 19
% 33.14/33.54
% 33.14/33.54 Starting Search:
% 33.14/33.54
% 33.14/33.54 Resimplifying inuse:
% 33.14/33.54 Done
% 33.14/33.54
% 33.14/33.54 Failed to find proof!
% 33.14/33.54 maxweight = 19
% 33.14/33.54 maxnrclauses = 10000000
% 33.14/33.54 Generated: 104337
% 33.14/33.54 Kept: 252
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 The strategy used was not complete!
% 33.14/33.54
% 33.14/33.54 Increased maxweight to 20
% 33.14/33.54
% 33.14/33.54 Starting Search:
% 33.14/33.54
% 33.14/33.54 Resimplifying inuse:
% 33.14/33.54 Done
% 33.14/33.54
% 33.14/33.54 Failed to find proof!
% 33.14/33.54 maxweight = 20
% 33.14/33.54 maxnrclauses = 10000000
% 33.14/33.54 Generated: 104344
% 33.14/33.54 Kept: 253
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 The strategy used was not complete!
% 33.14/33.54
% 33.14/33.54 Increased maxweight to 21
% 33.14/33.54
% 33.14/33.54 Starting Search:
% 33.14/33.54
% 33.14/33.54 Resimplifying inuse:
% 33.14/33.54 Done
% 33.14/33.54
% 33.14/33.54 Failed to find proof!
% 33.14/33.54 maxweight = 21
% 33.14/33.54 maxnrclauses = 10000000
% 33.14/33.54 Generated: 482671
% 33.14/33.54 Kept: 682
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 The strategy used was not complete!
% 33.14/33.54
% 33.14/33.54 Increased maxweight to 22
% 33.14/33.54
% 33.14/33.54 Starting Search:
% 33.14/33.54
% 33.14/33.54 Resimplifying inuse:
% 33.14/33.54 Done
% 33.14/33.54
% 33.14/33.54 Failed to find proof!
% 33.14/33.54 maxweight = 22
% 33.14/33.54 maxnrclauses = 10000000
% 33.14/33.54 Generated: 482671
% 33.14/33.54 Kept: 682
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 The strategy used was not complete!
% 33.14/33.54
% 33.14/33.54 Increased maxweight to 23
% 33.14/33.54
% 33.14/33.54 Starting Search:
% 33.14/33.54
% 33.14/33.54 Resimplifying inuse:
% 33.14/33.54 Done
% 33.14/33.54
% 33.14/33.54 Resimplifying inuse:
% 33.14/33.54 Done
% 33.14/33.54
% 33.14/33.54 Failed to find proof!
% 33.14/33.54 maxweight = 23
% 33.14/33.54 maxnrclauses = 10000000
% 33.14/33.54 Generated: 2239233
% 33.14/33.54 Kept: 1766
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 The strategy used was not complete!
% 33.14/33.54
% 33.14/33.54 Increased maxweight to 24
% 33.14/33.54
% 33.14/33.54 Starting Search:
% 33.14/33.54
% 33.14/33.54 Resimplifying inuse:
% 33.14/33.54 Done
% 33.14/33.54
% 33.14/33.54 Resimplifying inuse:
% 33.14/33.54 Done
% 33.14/33.54
% 33.14/33.54 Failed to find proof!
% 33.14/33.54 maxweight = 24
% 33.14/33.54 maxnrclauses = 10000000
% 33.14/33.54 Generated: 2239529
% 33.14/33.54 Kept: 1775
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 The strategy used was not complete!
% 33.14/33.54
% 33.14/33.54 Increased maxweight to 25
% 33.14/33.54
% 33.14/33.54 Starting Search:
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 Bliksems!, er is een bewijs:
% 33.14/33.54 % SZS status Unsatisfiable
% 33.14/33.54 % SZS output start Refutation
% 33.14/33.54
% 33.14/33.54 clause( 0, [ =( apply( apply( apply( b, X ), Y ), Z ), apply( X, apply( Y,
% 33.14/33.54 Z ) ) ) ] )
% 33.14/33.54 .
% 33.14/33.54 clause( 1, [ =( apply( apply( w, X ), Y ), apply( apply( X, Y ), Y ) ) ] )
% 33.14/33.54 .
% 33.14/33.54 clause( 2, [ ~( =( apply( 'fixed_pt', apply( X, 'fixed_pt' ) ), apply( X,
% 33.14/33.54 'fixed_pt' ) ) ), 'fixed_point'( X ) ] )
% 33.14/33.54 .
% 33.14/33.54 clause( 3, [ ~( 'fixed_point'( apply( apply( b, apply( apply( b, apply( w,
% 33.14/33.54 w ) ), apply( apply( b, w ), b ) ) ), b ) ) ) ] )
% 33.14/33.54 .
% 33.14/33.54 clause( 4, [ =( apply( apply( w, w ), X ), apply( apply( X, X ), X ) ) ] )
% 33.14/33.54 .
% 33.14/33.54 clause( 18, [ =( apply( apply( w, apply( b, X ) ), Y ), apply( X, apply( Y
% 33.14/33.54 , Y ) ) ) ] )
% 33.14/33.54 .
% 33.14/33.54 clause( 26, [ =( apply( apply( apply( w, apply( b, apply( b, X ) ) ), Y ),
% 33.14/33.54 Z ), apply( X, apply( apply( Y, Y ), Z ) ) ) ] )
% 33.14/33.54 .
% 33.14/33.54 clause( 40, [ ~( =( apply( 'fixed_pt', apply( apply( w, w ), apply( w,
% 33.14/33.54 apply( b, apply( b, 'fixed_pt' ) ) ) ) ), apply( apply( w, w ), apply( w
% 33.14/33.54 , apply( b, apply( b, 'fixed_pt' ) ) ) ) ) ) ] )
% 33.14/33.54 .
% 33.14/33.54 clause( 668, [ =( apply( X, apply( apply( w, w ), apply( w, apply( b, apply(
% 33.14/33.54 b, X ) ) ) ) ), apply( apply( w, w ), apply( w, apply( b, apply( b, X ) )
% 33.14/33.54 ) ) ) ] )
% 33.14/33.54 .
% 33.14/33.54 clause( 975, [] )
% 33.14/33.54 .
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 % SZS output end Refutation
% 33.14/33.54 found a proof!
% 33.14/33.54
% 33.14/33.54 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 33.14/33.54
% 33.14/33.54 initialclauses(
% 33.14/33.54 [ clause( 977, [ =( apply( apply( apply( b, X ), Y ), Z ), apply( X, apply(
% 33.14/33.54 Y, Z ) ) ) ] )
% 33.14/33.54 , clause( 978, [ =( apply( apply( w, X ), Y ), apply( apply( X, Y ), Y ) )
% 33.14/33.54 ] )
% 33.14/33.54 , clause( 979, [ ~( =( apply( X, 'fixed_pt' ), apply( 'fixed_pt', apply( X
% 33.14/33.54 , 'fixed_pt' ) ) ) ), 'fixed_point'( X ) ] )
% 33.14/33.54 , clause( 980, [ ~( 'fixed_point'( apply( apply( b, apply( apply( b, apply(
% 33.14/33.54 w, w ) ), apply( apply( b, w ), b ) ) ), b ) ) ) ] )
% 33.14/33.54 ] ).
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 subsumption(
% 33.14/33.54 clause( 0, [ =( apply( apply( apply( b, X ), Y ), Z ), apply( X, apply( Y,
% 33.14/33.54 Z ) ) ) ] )
% 33.14/33.54 , clause( 977, [ =( apply( apply( apply( b, X ), Y ), Z ), apply( X, apply(
% 33.14/33.54 Y, Z ) ) ) ] )
% 33.14/33.54 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 33.14/33.54 permutation( 0, [ ==>( 0, 0 )] ) ).
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 subsumption(
% 33.14/33.54 clause( 1, [ =( apply( apply( w, X ), Y ), apply( apply( X, Y ), Y ) ) ] )
% 33.14/33.54 , clause( 978, [ =( apply( apply( w, X ), Y ), apply( apply( X, Y ), Y ) )
% 33.14/33.54 ] )
% 33.14/33.54 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 33.14/33.54 )] ) ).
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 eqswap(
% 33.14/33.54 clause( 986, [ ~( =( apply( 'fixed_pt', apply( X, 'fixed_pt' ) ), apply( X
% 33.14/33.54 , 'fixed_pt' ) ) ), 'fixed_point'( X ) ] )
% 33.14/33.54 , clause( 979, [ ~( =( apply( X, 'fixed_pt' ), apply( 'fixed_pt', apply( X
% 33.14/33.54 , 'fixed_pt' ) ) ) ), 'fixed_point'( X ) ] )
% 33.14/33.54 , 0, substitution( 0, [ :=( X, X )] )).
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 subsumption(
% 33.14/33.54 clause( 2, [ ~( =( apply( 'fixed_pt', apply( X, 'fixed_pt' ) ), apply( X,
% 33.14/33.54 'fixed_pt' ) ) ), 'fixed_point'( X ) ] )
% 33.14/33.54 , clause( 986, [ ~( =( apply( 'fixed_pt', apply( X, 'fixed_pt' ) ), apply(
% 33.14/33.54 X, 'fixed_pt' ) ) ), 'fixed_point'( X ) ] )
% 33.14/33.54 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 33.14/33.54 1 )] ) ).
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 subsumption(
% 33.14/33.54 clause( 3, [ ~( 'fixed_point'( apply( apply( b, apply( apply( b, apply( w,
% 33.14/33.54 w ) ), apply( apply( b, w ), b ) ) ), b ) ) ) ] )
% 33.14/33.54 , clause( 980, [ ~( 'fixed_point'( apply( apply( b, apply( apply( b, apply(
% 33.14/33.54 w, w ) ), apply( apply( b, w ), b ) ) ), b ) ) ) ] )
% 33.14/33.54 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 eqswap(
% 33.14/33.54 clause( 990, [ =( apply( apply( X, Y ), Y ), apply( apply( w, X ), Y ) ) ]
% 33.14/33.54 )
% 33.14/33.54 , clause( 1, [ =( apply( apply( w, X ), Y ), apply( apply( X, Y ), Y ) ) ]
% 33.14/33.54 )
% 33.14/33.54 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 eqswap(
% 33.14/33.54 clause( 991, [ =( apply( apply( X, Y ), Y ), apply( apply( w, X ), Y ) ) ]
% 33.14/33.54 )
% 33.14/33.54 , clause( 1, [ =( apply( apply( w, X ), Y ), apply( apply( X, Y ), Y ) ) ]
% 33.14/33.54 )
% 33.14/33.54 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 paramod(
% 33.14/33.54 clause( 994, [ =( apply( apply( X, X ), X ), apply( apply( w, w ), X ) ) ]
% 33.14/33.54 )
% 33.14/33.54 , clause( 990, [ =( apply( apply( X, Y ), Y ), apply( apply( w, X ), Y ) )
% 33.14/33.54 ] )
% 33.14/33.54 , 0, clause( 991, [ =( apply( apply( X, Y ), Y ), apply( apply( w, X ), Y )
% 33.14/33.54 ) ] )
% 33.14/33.54 , 0, 6, substitution( 0, [ :=( X, w ), :=( Y, X )] ), substitution( 1, [
% 33.14/33.54 :=( X, X ), :=( Y, X )] )).
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 eqswap(
% 33.14/33.54 clause( 1000, [ =( apply( apply( w, w ), X ), apply( apply( X, X ), X ) ) ]
% 33.14/33.54 )
% 33.14/33.54 , clause( 994, [ =( apply( apply( X, X ), X ), apply( apply( w, w ), X ) )
% 33.14/33.54 ] )
% 33.14/33.54 , 0, substitution( 0, [ :=( X, X )] )).
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 subsumption(
% 33.14/33.54 clause( 4, [ =( apply( apply( w, w ), X ), apply( apply( X, X ), X ) ) ] )
% 33.14/33.54 , clause( 1000, [ =( apply( apply( w, w ), X ), apply( apply( X, X ), X ) )
% 33.14/33.54 ] )
% 33.14/33.54 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 eqswap(
% 33.14/33.54 clause( 1001, [ =( apply( X, apply( Y, Z ) ), apply( apply( apply( b, X ),
% 33.14/33.54 Y ), Z ) ) ] )
% 33.14/33.54 , clause( 0, [ =( apply( apply( apply( b, X ), Y ), Z ), apply( X, apply( Y
% 33.14/33.54 , Z ) ) ) ] )
% 33.14/33.54 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 eqswap(
% 33.14/33.54 clause( 1002, [ =( apply( apply( X, Y ), Y ), apply( apply( w, X ), Y ) ) ]
% 33.14/33.54 )
% 33.14/33.54 , clause( 1, [ =( apply( apply( w, X ), Y ), apply( apply( X, Y ), Y ) ) ]
% 33.14/33.54 )
% 33.14/33.54 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 paramod(
% 33.14/33.54 clause( 1005, [ =( apply( X, apply( Y, Y ) ), apply( apply( w, apply( b, X
% 33.14/33.54 ) ), Y ) ) ] )
% 33.14/33.54 , clause( 1002, [ =( apply( apply( X, Y ), Y ), apply( apply( w, X ), Y ) )
% 33.14/33.54 ] )
% 33.14/33.54 , 0, clause( 1001, [ =( apply( X, apply( Y, Z ) ), apply( apply( apply( b,
% 33.14/33.54 X ), Y ), Z ) ) ] )
% 33.14/33.54 , 0, 6, substitution( 0, [ :=( X, apply( b, X ) ), :=( Y, Y )] ),
% 33.14/33.54 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Y )] )).
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 eqswap(
% 33.14/33.54 clause( 1009, [ =( apply( apply( w, apply( b, X ) ), Y ), apply( X, apply(
% 33.14/33.54 Y, Y ) ) ) ] )
% 33.14/33.54 , clause( 1005, [ =( apply( X, apply( Y, Y ) ), apply( apply( w, apply( b,
% 33.14/33.54 X ) ), Y ) ) ] )
% 33.14/33.54 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 subsumption(
% 33.14/33.54 clause( 18, [ =( apply( apply( w, apply( b, X ) ), Y ), apply( X, apply( Y
% 33.14/33.54 , Y ) ) ) ] )
% 33.14/33.54 , clause( 1009, [ =( apply( apply( w, apply( b, X ) ), Y ), apply( X, apply(
% 33.14/33.54 Y, Y ) ) ) ] )
% 33.14/33.54 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 33.14/33.54 )] ) ).
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 eqswap(
% 33.14/33.54 clause( 1011, [ =( apply( X, apply( Y, Y ) ), apply( apply( w, apply( b, X
% 33.14/33.54 ) ), Y ) ) ] )
% 33.14/33.54 , clause( 18, [ =( apply( apply( w, apply( b, X ) ), Y ), apply( X, apply(
% 33.14/33.54 Y, Y ) ) ) ] )
% 33.14/33.54 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 eqswap(
% 33.14/33.54 clause( 1012, [ =( apply( X, apply( Y, Z ) ), apply( apply( apply( b, X ),
% 33.14/33.54 Y ), Z ) ) ] )
% 33.14/33.54 , clause( 0, [ =( apply( apply( apply( b, X ), Y ), Z ), apply( X, apply( Y
% 33.14/33.54 , Z ) ) ) ] )
% 33.14/33.54 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 paramod(
% 33.14/33.54 clause( 1016, [ =( apply( X, apply( apply( Y, Y ), Z ) ), apply( apply(
% 33.14/33.54 apply( w, apply( b, apply( b, X ) ) ), Y ), Z ) ) ] )
% 33.14/33.54 , clause( 1011, [ =( apply( X, apply( Y, Y ) ), apply( apply( w, apply( b,
% 33.14/33.54 X ) ), Y ) ) ] )
% 33.14/33.54 , 0, clause( 1012, [ =( apply( X, apply( Y, Z ) ), apply( apply( apply( b,
% 33.14/33.54 X ), Y ), Z ) ) ] )
% 33.14/33.54 , 0, 9, substitution( 0, [ :=( X, apply( b, X ) ), :=( Y, Y )] ),
% 33.14/33.54 substitution( 1, [ :=( X, X ), :=( Y, apply( Y, Y ) ), :=( Z, Z )] )).
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 eqswap(
% 33.14/33.54 clause( 1024, [ =( apply( apply( apply( w, apply( b, apply( b, X ) ) ), Y )
% 33.14/33.54 , Z ), apply( X, apply( apply( Y, Y ), Z ) ) ) ] )
% 33.14/33.54 , clause( 1016, [ =( apply( X, apply( apply( Y, Y ), Z ) ), apply( apply(
% 33.14/33.54 apply( w, apply( b, apply( b, X ) ) ), Y ), Z ) ) ] )
% 33.14/33.54 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 subsumption(
% 33.14/33.54 clause( 26, [ =( apply( apply( apply( w, apply( b, apply( b, X ) ) ), Y ),
% 33.14/33.54 Z ), apply( X, apply( apply( Y, Y ), Z ) ) ) ] )
% 33.14/33.54 , clause( 1024, [ =( apply( apply( apply( w, apply( b, apply( b, X ) ) ), Y
% 33.14/33.54 ), Z ), apply( X, apply( apply( Y, Y ), Z ) ) ) ] )
% 33.14/33.54 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 33.14/33.54 permutation( 0, [ ==>( 0, 0 )] ) ).
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 eqswap(
% 33.14/33.54 clause( 1027, [ ~( =( apply( X, 'fixed_pt' ), apply( 'fixed_pt', apply( X,
% 33.14/33.54 'fixed_pt' ) ) ) ), 'fixed_point'( X ) ] )
% 33.14/33.54 , clause( 2, [ ~( =( apply( 'fixed_pt', apply( X, 'fixed_pt' ) ), apply( X
% 33.14/33.54 , 'fixed_pt' ) ) ), 'fixed_point'( X ) ] )
% 33.14/33.54 , 0, substitution( 0, [ :=( X, X )] )).
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 resolution(
% 33.14/33.54 clause( 1031, [ ~( =( apply( apply( apply( b, apply( apply( b, apply( w, w
% 33.14/33.54 ) ), apply( apply( b, w ), b ) ) ), b ), 'fixed_pt' ), apply( 'fixed_pt'
% 33.14/33.54 , apply( apply( apply( b, apply( apply( b, apply( w, w ) ), apply( apply(
% 33.14/33.54 b, w ), b ) ) ), b ), 'fixed_pt' ) ) ) ) ] )
% 33.14/33.54 , clause( 3, [ ~( 'fixed_point'( apply( apply( b, apply( apply( b, apply( w
% 33.14/33.54 , w ) ), apply( apply( b, w ), b ) ) ), b ) ) ) ] )
% 33.14/33.54 , 0, clause( 1027, [ ~( =( apply( X, 'fixed_pt' ), apply( 'fixed_pt', apply(
% 33.14/33.54 X, 'fixed_pt' ) ) ) ), 'fixed_point'( X ) ] )
% 33.14/33.54 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, apply( apply( b,
% 33.14/33.54 apply( apply( b, apply( w, w ) ), apply( apply( b, w ), b ) ) ), b ) )] )
% 33.14/33.54 ).
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 paramod(
% 33.14/33.54 clause( 1033, [ ~( =( apply( apply( apply( b, apply( apply( b, apply( w, w
% 33.14/33.54 ) ), apply( apply( b, w ), b ) ) ), b ), 'fixed_pt' ), apply( 'fixed_pt'
% 33.14/33.54 , apply( apply( apply( b, apply( w, w ) ), apply( apply( b, w ), b ) ),
% 33.14/33.54 apply( b, 'fixed_pt' ) ) ) ) ) ] )
% 33.14/33.54 , clause( 0, [ =( apply( apply( apply( b, X ), Y ), Z ), apply( X, apply( Y
% 33.14/33.54 , Z ) ) ) ] )
% 33.14/33.54 , 0, clause( 1031, [ ~( =( apply( apply( apply( b, apply( apply( b, apply(
% 33.14/33.54 w, w ) ), apply( apply( b, w ), b ) ) ), b ), 'fixed_pt' ), apply(
% 33.14/33.54 'fixed_pt', apply( apply( apply( b, apply( apply( b, apply( w, w ) ),
% 33.14/33.54 apply( apply( b, w ), b ) ) ), b ), 'fixed_pt' ) ) ) ) ] )
% 33.14/33.54 , 0, 21, substitution( 0, [ :=( X, apply( apply( b, apply( w, w ) ), apply(
% 33.14/33.54 apply( b, w ), b ) ) ), :=( Y, b ), :=( Z, 'fixed_pt' )] ),
% 33.14/33.54 substitution( 1, [] )).
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 paramod(
% 33.14/33.54 clause( 1045, [ ~( =( apply( apply( apply( b, apply( apply( b, apply( w, w
% 33.14/33.54 ) ), apply( apply( b, w ), b ) ) ), b ), 'fixed_pt' ), apply( 'fixed_pt'
% 33.14/33.54 , apply( apply( w, w ), apply( apply( apply( b, w ), b ), apply( b,
% 33.14/33.54 'fixed_pt' ) ) ) ) ) ) ] )
% 33.14/33.54 , clause( 0, [ =( apply( apply( apply( b, X ), Y ), Z ), apply( X, apply( Y
% 33.14/33.54 , Z ) ) ) ] )
% 33.14/33.54 , 0, clause( 1033, [ ~( =( apply( apply( apply( b, apply( apply( b, apply(
% 33.14/33.54 w, w ) ), apply( apply( b, w ), b ) ) ), b ), 'fixed_pt' ), apply(
% 33.14/33.54 'fixed_pt', apply( apply( apply( b, apply( w, w ) ), apply( apply( b, w )
% 33.14/33.54 , b ) ), apply( b, 'fixed_pt' ) ) ) ) ) ] )
% 33.14/33.54 , 0, 21, substitution( 0, [ :=( X, apply( w, w ) ), :=( Y, apply( apply( b
% 33.14/33.54 , w ), b ) ), :=( Z, apply( b, 'fixed_pt' ) )] ), substitution( 1, [] )
% 33.14/33.54 ).
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 paramod(
% 33.14/33.54 clause( 1056, [ ~( =( apply( apply( apply( b, apply( apply( b, apply( w, w
% 33.14/33.54 ) ), apply( apply( b, w ), b ) ) ), b ), 'fixed_pt' ), apply( 'fixed_pt'
% 33.14/33.54 , apply( apply( w, w ), apply( w, apply( b, apply( b, 'fixed_pt' ) ) ) )
% 33.14/33.54 ) ) ) ] )
% 33.14/33.54 , clause( 0, [ =( apply( apply( apply( b, X ), Y ), Z ), apply( X, apply( Y
% 33.14/33.54 , Z ) ) ) ] )
% 33.14/33.54 , 0, clause( 1045, [ ~( =( apply( apply( apply( b, apply( apply( b, apply(
% 33.14/33.54 w, w ) ), apply( apply( b, w ), b ) ) ), b ), 'fixed_pt' ), apply(
% 33.14/33.54 'fixed_pt', apply( apply( w, w ), apply( apply( apply( b, w ), b ), apply(
% 33.14/33.54 b, 'fixed_pt' ) ) ) ) ) ) ] )
% 33.14/33.54 , 0, 25, substitution( 0, [ :=( X, w ), :=( Y, b ), :=( Z, apply( b,
% 33.14/33.54 'fixed_pt' ) )] ), substitution( 1, [] )).
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 paramod(
% 33.14/33.54 clause( 1057, [ ~( =( apply( apply( apply( b, apply( w, w ) ), apply( apply(
% 33.14/33.54 b, w ), b ) ), apply( b, 'fixed_pt' ) ), apply( 'fixed_pt', apply( apply(
% 33.14/33.54 w, w ), apply( w, apply( b, apply( b, 'fixed_pt' ) ) ) ) ) ) ) ] )
% 33.14/33.54 , clause( 0, [ =( apply( apply( apply( b, X ), Y ), Z ), apply( X, apply( Y
% 33.14/33.54 , Z ) ) ) ] )
% 33.14/33.54 , 0, clause( 1056, [ ~( =( apply( apply( apply( b, apply( apply( b, apply(
% 33.14/33.54 w, w ) ), apply( apply( b, w ), b ) ) ), b ), 'fixed_pt' ), apply(
% 33.14/33.54 'fixed_pt', apply( apply( w, w ), apply( w, apply( b, apply( b,
% 33.14/33.54 'fixed_pt' ) ) ) ) ) ) ) ] )
% 33.14/33.54 , 0, 2, substitution( 0, [ :=( X, apply( apply( b, apply( w, w ) ), apply(
% 33.14/33.54 apply( b, w ), b ) ) ), :=( Y, b ), :=( Z, 'fixed_pt' )] ),
% 33.14/33.54 substitution( 1, [] )).
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 paramod(
% 33.14/33.54 clause( 1058, [ ~( =( apply( apply( w, w ), apply( apply( apply( b, w ), b
% 33.14/33.54 ), apply( b, 'fixed_pt' ) ) ), apply( 'fixed_pt', apply( apply( w, w ),
% 33.14/33.54 apply( w, apply( b, apply( b, 'fixed_pt' ) ) ) ) ) ) ) ] )
% 33.14/33.54 , clause( 0, [ =( apply( apply( apply( b, X ), Y ), Z ), apply( X, apply( Y
% 33.14/33.54 , Z ) ) ) ] )
% 33.14/33.54 , 0, clause( 1057, [ ~( =( apply( apply( apply( b, apply( w, w ) ), apply(
% 33.14/33.54 apply( b, w ), b ) ), apply( b, 'fixed_pt' ) ), apply( 'fixed_pt', apply(
% 33.14/33.54 apply( w, w ), apply( w, apply( b, apply( b, 'fixed_pt' ) ) ) ) ) ) ) ]
% 33.14/33.54 )
% 33.14/33.54 , 0, 2, substitution( 0, [ :=( X, apply( w, w ) ), :=( Y, apply( apply( b,
% 33.14/33.54 w ), b ) ), :=( Z, apply( b, 'fixed_pt' ) )] ), substitution( 1, [] )
% 33.14/33.54 ).
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 paramod(
% 33.14/33.54 clause( 1059, [ ~( =( apply( apply( w, w ), apply( w, apply( b, apply( b,
% 33.14/33.54 'fixed_pt' ) ) ) ), apply( 'fixed_pt', apply( apply( w, w ), apply( w,
% 33.14/33.54 apply( b, apply( b, 'fixed_pt' ) ) ) ) ) ) ) ] )
% 33.14/33.54 , clause( 0, [ =( apply( apply( apply( b, X ), Y ), Z ), apply( X, apply( Y
% 33.14/33.54 , Z ) ) ) ] )
% 33.14/33.54 , 0, clause( 1058, [ ~( =( apply( apply( w, w ), apply( apply( apply( b, w
% 33.14/33.54 ), b ), apply( b, 'fixed_pt' ) ) ), apply( 'fixed_pt', apply( apply( w,
% 33.14/33.54 w ), apply( w, apply( b, apply( b, 'fixed_pt' ) ) ) ) ) ) ) ] )
% 33.14/33.54 , 0, 6, substitution( 0, [ :=( X, w ), :=( Y, b ), :=( Z, apply( b,
% 33.14/33.54 'fixed_pt' ) )] ), substitution( 1, [] )).
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 eqswap(
% 33.14/33.54 clause( 1065, [ ~( =( apply( 'fixed_pt', apply( apply( w, w ), apply( w,
% 33.14/33.54 apply( b, apply( b, 'fixed_pt' ) ) ) ) ), apply( apply( w, w ), apply( w
% 33.14/33.54 , apply( b, apply( b, 'fixed_pt' ) ) ) ) ) ) ] )
% 33.14/33.54 , clause( 1059, [ ~( =( apply( apply( w, w ), apply( w, apply( b, apply( b
% 33.14/33.54 , 'fixed_pt' ) ) ) ), apply( 'fixed_pt', apply( apply( w, w ), apply( w,
% 33.14/33.54 apply( b, apply( b, 'fixed_pt' ) ) ) ) ) ) ) ] )
% 33.14/33.54 , 0, substitution( 0, [] )).
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 subsumption(
% 33.14/33.54 clause( 40, [ ~( =( apply( 'fixed_pt', apply( apply( w, w ), apply( w,
% 33.14/33.54 apply( b, apply( b, 'fixed_pt' ) ) ) ) ), apply( apply( w, w ), apply( w
% 33.14/33.54 , apply( b, apply( b, 'fixed_pt' ) ) ) ) ) ) ] )
% 33.14/33.54 , clause( 1065, [ ~( =( apply( 'fixed_pt', apply( apply( w, w ), apply( w,
% 33.14/33.54 apply( b, apply( b, 'fixed_pt' ) ) ) ) ), apply( apply( w, w ), apply( w
% 33.14/33.54 , apply( b, apply( b, 'fixed_pt' ) ) ) ) ) ) ] )
% 33.14/33.54 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 eqswap(
% 33.14/33.54 clause( 1069, [ =( apply( apply( X, X ), X ), apply( apply( w, w ), X ) ) ]
% 33.14/33.54 )
% 33.14/33.54 , clause( 4, [ =( apply( apply( w, w ), X ), apply( apply( X, X ), X ) ) ]
% 33.14/33.54 )
% 33.14/33.54 , 0, substitution( 0, [ :=( X, X )] )).
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 eqswap(
% 33.14/33.54 clause( 1070, [ =( apply( X, apply( apply( Y, Y ), Z ) ), apply( apply(
% 33.14/33.54 apply( w, apply( b, apply( b, X ) ) ), Y ), Z ) ) ] )
% 33.14/33.54 , clause( 26, [ =( apply( apply( apply( w, apply( b, apply( b, X ) ) ), Y )
% 33.14/33.54 , Z ), apply( X, apply( apply( Y, Y ), Z ) ) ) ] )
% 33.14/33.54 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 paramod(
% 33.14/33.54 clause( 1073, [ =( apply( X, apply( apply( apply( w, apply( b, apply( b, X
% 33.14/33.54 ) ) ), apply( w, apply( b, apply( b, X ) ) ) ), apply( w, apply( b,
% 33.14/33.54 apply( b, X ) ) ) ) ), apply( apply( w, w ), apply( w, apply( b, apply( b
% 33.14/33.54 , X ) ) ) ) ) ] )
% 33.14/33.54 , clause( 1069, [ =( apply( apply( X, X ), X ), apply( apply( w, w ), X ) )
% 33.14/33.54 ] )
% 33.14/33.54 , 0, clause( 1070, [ =( apply( X, apply( apply( Y, Y ), Z ) ), apply( apply(
% 33.14/33.54 apply( w, apply( b, apply( b, X ) ) ), Y ), Z ) ) ] )
% 33.14/33.54 , 0, 26, substitution( 0, [ :=( X, apply( w, apply( b, apply( b, X ) ) ) )] )
% 33.14/33.54 , substitution( 1, [ :=( X, X ), :=( Y, apply( w, apply( b, apply( b, X )
% 33.14/33.54 ) ) ), :=( Z, apply( w, apply( b, apply( b, X ) ) ) )] )).
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 paramod(
% 33.14/33.54 clause( 1074, [ =( apply( X, apply( apply( w, w ), apply( w, apply( b,
% 33.14/33.54 apply( b, X ) ) ) ) ), apply( apply( w, w ), apply( w, apply( b, apply( b
% 33.14/33.54 , X ) ) ) ) ) ] )
% 33.14/33.54 , clause( 1069, [ =( apply( apply( X, X ), X ), apply( apply( w, w ), X ) )
% 33.14/33.54 ] )
% 33.14/33.54 , 0, clause( 1073, [ =( apply( X, apply( apply( apply( w, apply( b, apply(
% 33.14/33.54 b, X ) ) ), apply( w, apply( b, apply( b, X ) ) ) ), apply( w, apply( b,
% 33.14/33.54 apply( b, X ) ) ) ) ), apply( apply( w, w ), apply( w, apply( b, apply( b
% 33.14/33.54 , X ) ) ) ) ) ] )
% 33.14/33.54 , 0, 3, substitution( 0, [ :=( X, apply( w, apply( b, apply( b, X ) ) ) )] )
% 33.14/33.54 , substitution( 1, [ :=( X, X )] )).
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 subsumption(
% 33.14/33.54 clause( 668, [ =( apply( X, apply( apply( w, w ), apply( w, apply( b, apply(
% 33.14/33.54 b, X ) ) ) ) ), apply( apply( w, w ), apply( w, apply( b, apply( b, X ) )
% 33.14/33.54 ) ) ) ] )
% 33.14/33.54 , clause( 1074, [ =( apply( X, apply( apply( w, w ), apply( w, apply( b,
% 33.14/33.54 apply( b, X ) ) ) ) ), apply( apply( w, w ), apply( w, apply( b, apply( b
% 33.14/33.54 , X ) ) ) ) ) ] )
% 33.14/33.54 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 paramod(
% 33.14/33.54 clause( 1081, [ ~( =( apply( apply( w, w ), apply( w, apply( b, apply( b,
% 33.14/33.54 'fixed_pt' ) ) ) ), apply( apply( w, w ), apply( w, apply( b, apply( b,
% 33.14/33.54 'fixed_pt' ) ) ) ) ) ) ] )
% 33.14/33.54 , clause( 668, [ =( apply( X, apply( apply( w, w ), apply( w, apply( b,
% 33.14/33.54 apply( b, X ) ) ) ) ), apply( apply( w, w ), apply( w, apply( b, apply( b
% 33.14/33.54 , X ) ) ) ) ) ] )
% 33.14/33.54 , 0, clause( 40, [ ~( =( apply( 'fixed_pt', apply( apply( w, w ), apply( w
% 33.14/33.54 , apply( b, apply( b, 'fixed_pt' ) ) ) ) ), apply( apply( w, w ), apply(
% 33.14/33.54 w, apply( b, apply( b, 'fixed_pt' ) ) ) ) ) ) ] )
% 33.14/33.54 , 0, 2, substitution( 0, [ :=( X, 'fixed_pt' )] ), substitution( 1, [] )
% 33.14/33.54 ).
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 eqrefl(
% 33.14/33.54 clause( 1082, [] )
% 33.14/33.54 , clause( 1081, [ ~( =( apply( apply( w, w ), apply( w, apply( b, apply( b
% 33.14/33.54 , 'fixed_pt' ) ) ) ), apply( apply( w, w ), apply( w, apply( b, apply( b
% 33.14/33.54 , 'fixed_pt' ) ) ) ) ) ) ] )
% 33.14/33.54 , 0, substitution( 0, [] )).
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 subsumption(
% 33.14/33.54 clause( 975, [] )
% 33.14/33.54 , clause( 1082, [] )
% 33.14/33.54 , substitution( 0, [] ), permutation( 0, [] ) ).
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 end.
% 33.14/33.54
% 33.14/33.54 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 33.14/33.54
% 33.14/33.54 Memory use:
% 33.14/33.54
% 33.14/33.54 space for terms: 22023
% 33.14/33.54 space for clauses: 136755
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 clauses generated: 12298
% 33.14/33.54 clauses kept: 976
% 33.14/33.54 clauses selected: 95
% 33.14/33.54 clauses deleted: 26
% 33.14/33.54 clauses inuse deleted: 0
% 33.14/33.54
% 33.14/33.54 subsentry: 3246
% 33.14/33.54 literals s-matched: 2596
% 33.14/33.54 literals matched: 2588
% 33.14/33.54 full subsumption: 0
% 33.14/33.54
% 33.14/33.54 checksum: 294014780
% 33.14/33.54
% 33.14/33.54
% 33.14/33.54 Bliksem ended
%------------------------------------------------------------------------------