TSTP Solution File: RNG059+2 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : RNG059+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n032.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 : Mon Jul 18 20:16:14 EDT 2022
% Result : Theorem 0.72s 1.11s
% Output : Refutation 0.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : RNG059+2 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.08 % Command : bliksem %s
% 0.06/0.26 % Computer : n032.cluster.edu
% 0.06/0.26 % Model : x86_64 x86_64
% 0.06/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26 % Memory : 8042.1875MB
% 0.06/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26 % CPULimit : 300
% 0.06/0.26 % DateTime : Mon May 30 12:46:57 EDT 2022
% 0.06/0.26 % CPUTime :
% 0.45/0.86 *** allocated 10000 integers for termspace/termends
% 0.45/0.86 *** allocated 10000 integers for clauses
% 0.45/0.86 *** allocated 10000 integers for justifications
% 0.45/0.86 Bliksem 1.12
% 0.45/0.86
% 0.45/0.86
% 0.45/0.86 Automatic Strategy Selection
% 0.45/0.86
% 0.45/0.86
% 0.45/0.86 Clauses:
% 0.45/0.86
% 0.45/0.86 { && }.
% 0.45/0.86 { aNaturalNumber0( sz00 ) }.
% 0.45/0.86 { ! aNaturalNumber0( X ), aNaturalNumber0( szszuzczcdt0( X ) ) }.
% 0.45/0.86 { ! aNaturalNumber0( X ), ! szszuzczcdt0( X ) = sz00 }.
% 0.45/0.86 { ! aNaturalNumber0( X ), X = sz00, aNaturalNumber0( skol1( Y ) ) }.
% 0.45/0.86 { ! aNaturalNumber0( X ), X = sz00, X = szszuzczcdt0( skol1( X ) ) }.
% 0.45/0.86 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! szszuzczcdt0( X ) =
% 0.45/0.86 szszuzczcdt0( Y ), X = Y }.
% 0.45/0.86 { && }.
% 0.45/0.86 { ! aNaturalNumber0( X ), iLess0( X, szszuzczcdt0( X ) ) }.
% 0.45/0.86 { && }.
% 0.45/0.86 { aScalar0( sz0z00 ) }.
% 0.45/0.86 { ! aScalar0( X ), ! aScalar0( Y ), aScalar0( sdtpldt0( X, Y ) ) }.
% 0.45/0.86 { ! aScalar0( X ), ! aScalar0( Y ), aScalar0( sdtasdt0( X, Y ) ) }.
% 0.45/0.86 { ! aScalar0( X ), aScalar0( smndt0( X ) ) }.
% 0.45/0.86 { ! aScalar0( X ), alpha3( X ) }.
% 0.45/0.86 { ! aScalar0( X ), smndt0( sz0z00 ) = sz0z00 }.
% 0.45/0.86 { ! alpha3( X ), alpha5( X ) }.
% 0.45/0.86 { ! alpha3( X ), smndt0( smndt0( X ) ) = X }.
% 0.45/0.86 { ! alpha5( X ), ! smndt0( smndt0( X ) ) = X, alpha3( X ) }.
% 0.45/0.86 { ! alpha5( X ), alpha6( X ) }.
% 0.45/0.86 { ! alpha5( X ), sdtpldt0( smndt0( X ), X ) = sz0z00 }.
% 0.45/0.86 { ! alpha6( X ), ! sdtpldt0( smndt0( X ), X ) = sz0z00, alpha5( X ) }.
% 0.45/0.86 { ! alpha6( X ), alpha7( X ) }.
% 0.45/0.86 { ! alpha6( X ), sdtpldt0( X, smndt0( X ) ) = sz0z00 }.
% 0.45/0.86 { ! alpha7( X ), ! sdtpldt0( X, smndt0( X ) ) = sz0z00, alpha6( X ) }.
% 0.45/0.86 { ! alpha7( X ), alpha8( X ) }.
% 0.45/0.86 { ! alpha7( X ), sdtasdt0( sz0z00, X ) = sz0z00 }.
% 0.45/0.86 { ! alpha8( X ), ! sdtasdt0( sz0z00, X ) = sz0z00, alpha7( X ) }.
% 0.45/0.86 { ! alpha8( X ), sdtpldt0( X, sz0z00 ) = X }.
% 0.45/0.86 { ! alpha8( X ), sdtpldt0( sz0z00, X ) = X }.
% 0.45/0.86 { ! alpha8( X ), sdtasdt0( X, sz0z00 ) = sz0z00 }.
% 0.45/0.86 { ! sdtpldt0( X, sz0z00 ) = X, ! sdtpldt0( sz0z00, X ) = X, ! sdtasdt0( X,
% 0.45/0.86 sz0z00 ) = sz0z00, alpha8( X ) }.
% 0.45/0.86 { ! aScalar0( X ), ! aScalar0( Y ), ! aScalar0( Z ), alpha4( X, Y, Z ) }.
% 0.45/0.86 { ! aScalar0( X ), ! aScalar0( Y ), ! aScalar0( Z ), sdtasdt0( X, Y ) =
% 0.45/0.86 sdtasdt0( Y, X ) }.
% 0.45/0.86 { ! alpha4( X, Y, Z ), sdtpldt0( sdtpldt0( X, Y ), Z ) = sdtpldt0( X,
% 0.45/0.86 sdtpldt0( Y, Z ) ) }.
% 0.45/0.86 { ! alpha4( X, Y, Z ), sdtpldt0( X, Y ) = sdtpldt0( Y, X ) }.
% 0.45/0.86 { ! alpha4( X, Y, Z ), sdtasdt0( sdtasdt0( X, Y ), Z ) = sdtasdt0( X,
% 0.45/0.86 sdtasdt0( Y, Z ) ) }.
% 0.45/0.86 { ! sdtpldt0( sdtpldt0( X, Y ), Z ) = sdtpldt0( X, sdtpldt0( Y, Z ) ), !
% 0.45/0.86 sdtpldt0( X, Y ) = sdtpldt0( Y, X ), ! sdtasdt0( sdtasdt0( X, Y ), Z ) =
% 0.45/0.86 sdtasdt0( X, sdtasdt0( Y, Z ) ), alpha4( X, Y, Z ) }.
% 0.45/0.86 { ! aScalar0( X ), ! aScalar0( Y ), ! aScalar0( Z ), sdtasdt0( X, sdtpldt0
% 0.45/0.86 ( Y, Z ) ) = sdtpldt0( sdtasdt0( X, Y ), sdtasdt0( X, Z ) ) }.
% 0.45/0.86 { ! aScalar0( X ), ! aScalar0( Y ), ! aScalar0( Z ), sdtasdt0( sdtpldt0( X
% 0.45/0.86 , Y ), Z ) = sdtpldt0( sdtasdt0( X, Z ), sdtasdt0( Y, Z ) ) }.
% 0.45/0.86 { ! aScalar0( X ), ! aScalar0( Y ), ! aScalar0( Z ), ! aScalar0( T ),
% 0.45/0.86 sdtasdt0( sdtpldt0( X, Y ), sdtpldt0( Z, T ) ) = sdtpldt0( sdtpldt0(
% 0.45/0.86 sdtasdt0( X, Z ), sdtasdt0( X, T ) ), sdtpldt0( sdtasdt0( Y, Z ),
% 0.45/0.86 sdtasdt0( Y, T ) ) ) }.
% 0.45/0.86 { ! aScalar0( X ), ! aScalar0( Y ), sdtasdt0( X, smndt0( Y ) ) = smndt0(
% 0.45/0.86 sdtasdt0( X, Y ) ) }.
% 0.45/0.86 { ! aScalar0( X ), ! aScalar0( Y ), sdtasdt0( smndt0( X ), Y ) = smndt0(
% 0.45/0.86 sdtasdt0( X, Y ) ) }.
% 0.45/0.86 { ! aScalar0( X ), ! aScalar0( Y ), sdtasdt0( smndt0( X ), smndt0( Y ) ) =
% 0.45/0.86 sdtasdt0( X, Y ) }.
% 0.45/0.86 { && }.
% 0.45/0.86 { ! aScalar0( X ), sdtlseqdt0( X, X ) }.
% 0.45/0.86 { ! aScalar0( X ), ! aScalar0( Y ), ! sdtlseqdt0( X, Y ), ! sdtlseqdt0( Y,
% 0.45/0.86 X ), X = Y }.
% 0.45/0.86 { ! aScalar0( X ), ! aScalar0( Y ), ! aScalar0( Z ), ! sdtlseqdt0( X, Y ),
% 0.45/0.86 ! sdtlseqdt0( Y, Z ), sdtlseqdt0( X, Z ) }.
% 0.45/0.86 { ! aScalar0( X ), ! aScalar0( Y ), ! aScalar0( Z ), ! aScalar0( T ), !
% 0.45/0.86 sdtlseqdt0( X, Y ), ! sdtlseqdt0( Z, T ), sdtlseqdt0( sdtpldt0( X, Z ),
% 0.45/0.86 sdtpldt0( Y, T ) ) }.
% 0.45/0.86 { ! aScalar0( X ), ! aScalar0( Y ), ! aScalar0( Z ), ! aScalar0( T ), !
% 0.45/0.86 sdtlseqdt0( X, Y ), ! sdtlseqdt0( sz0z00, Z ), ! sdtlseqdt0( Z, T ),
% 0.45/0.86 sdtlseqdt0( sdtasdt0( X, Z ), sdtasdt0( Y, T ) ) }.
% 0.45/0.86 { ! aScalar0( X ), ! aScalar0( Y ), sdtlseqdt0( X, Y ), sdtlseqdt0( Y, X )
% 0.45/0.86 }.
% 0.45/0.86 { ! aScalar0( X ), ! aScalar0( Y ), ! sdtlseqdt0( sz0z00, X ), ! sdtlseqdt0
% 0.45/0.86 ( sz0z00, Y ), sdtlseqdt0( sz0z00, sdtpldt0( X, Y ) ) }.
% 0.72/1.11 { ! aScalar0( X ), ! aScalar0( Y ), ! sdtlseqdt0( sz0z00, X ), ! sdtlseqdt0
% 0.72/1.11 ( sz0z00, Y ), sdtlseqdt0( sz0z00, sdtasdt0( X, Y ) ) }.
% 0.72/1.11 { ! aScalar0( X ), sdtlseqdt0( sz0z00, sdtasdt0( X, X ) ) }.
% 0.72/1.11 { ! aScalar0( X ), ! aScalar0( Y ), ! sdtlseqdt0( sz0z00, X ), ! sdtlseqdt0
% 0.72/1.11 ( sz0z00, Y ), ! sdtasdt0( X, X ) = sdtasdt0( Y, Y ), X = Y }.
% 0.72/1.11 { && }.
% 0.72/1.11 { ! aVector0( X ), aNaturalNumber0( aDimensionOf0( X ) ) }.
% 0.72/1.11 { ! aVector0( X ), ! aNaturalNumber0( Y ), aScalar0( sdtlbdtrb0( X, Y ) ) }
% 0.72/1.11 .
% 0.72/1.11 { ! aVector0( X ), aDimensionOf0( X ) = sz00, ! Y = sziznziztdt0( X ),
% 0.72/1.11 aVector0( Y ) }.
% 0.72/1.11 { ! aVector0( X ), aDimensionOf0( X ) = sz00, ! Y = sziznziztdt0( X ),
% 0.72/1.11 alpha1( X, Y ) }.
% 0.72/1.11 { ! aVector0( X ), aDimensionOf0( X ) = sz00, ! aVector0( Y ), ! alpha1( X
% 0.72/1.11 , Y ), Y = sziznziztdt0( X ) }.
% 0.72/1.11 { ! alpha1( X, Y ), szszuzczcdt0( aDimensionOf0( Y ) ) = aDimensionOf0( X )
% 0.72/1.11 }.
% 0.72/1.11 { ! alpha1( X, Y ), alpha2( X, Y ) }.
% 0.72/1.11 { ! szszuzczcdt0( aDimensionOf0( Y ) ) = aDimensionOf0( X ), ! alpha2( X, Y
% 0.72/1.11 ), alpha1( X, Y ) }.
% 0.72/1.11 { ! alpha2( X, Y ), ! aNaturalNumber0( Z ), sdtlbdtrb0( Y, Z ) = sdtlbdtrb0
% 0.72/1.11 ( X, Z ) }.
% 0.72/1.11 { aNaturalNumber0( skol2( Z, T ) ), alpha2( X, Y ) }.
% 0.72/1.11 { ! sdtlbdtrb0( Y, skol2( X, Y ) ) = sdtlbdtrb0( X, skol2( X, Y ) ), alpha2
% 0.72/1.11 ( X, Y ) }.
% 0.72/1.11 { ! aVector0( X ), ! aVector0( Y ), ! aDimensionOf0( X ) = aDimensionOf0( Y
% 0.72/1.11 ), aDimensionOf0( Y ) = sz00, aDimensionOf0( sziznziztdt0( X ) ) =
% 0.72/1.11 aDimensionOf0( sziznziztdt0( Y ) ) }.
% 0.72/1.11 { ! aVector0( X ), ! aVector0( Y ), ! aDimensionOf0( X ) = aDimensionOf0( Y
% 0.72/1.11 ), aScalar0( sdtasasdt0( X, Y ) ) }.
% 0.72/1.11 { ! aVector0( X ), ! aVector0( Y ), ! aDimensionOf0( X ) = aDimensionOf0( Y
% 0.72/1.11 ), ! aDimensionOf0( Y ) = sz00, sdtasasdt0( X, Y ) = sz0z00 }.
% 0.72/1.11 { ! aVector0( X ), ! aVector0( Y ), ! aDimensionOf0( X ) = aDimensionOf0( Y
% 0.72/1.11 ), aDimensionOf0( Y ) = sz00, sdtasasdt0( X, Y ) = sdtpldt0( sdtasasdt0
% 0.72/1.11 ( sziznziztdt0( X ), sziznziztdt0( Y ) ), sdtasdt0( sdtlbdtrb0( X,
% 0.72/1.11 aDimensionOf0( X ) ), sdtlbdtrb0( Y, aDimensionOf0( Y ) ) ) ) }.
% 0.72/1.11 { ! aVector0( X ), sdtlseqdt0( sz0z00, sdtasasdt0( X, X ) ) }.
% 0.72/1.11 { aVector0( xs ) }.
% 0.72/1.11 { aVector0( xt ) }.
% 0.72/1.11 { ! aVector0( X ), ! aVector0( Y ), ! aDimensionOf0( X ) = aDimensionOf0( Y
% 0.72/1.11 ), ! iLess0( aDimensionOf0( X ), aDimensionOf0( xs ) ), sdtlseqdt0(
% 0.72/1.11 sdtasdt0( sdtasasdt0( X, Y ), sdtasasdt0( X, Y ) ), sdtasdt0( sdtasasdt0
% 0.72/1.11 ( X, X ), sdtasasdt0( Y, Y ) ) ) }.
% 0.72/1.11 { aDimensionOf0( xs ) = aDimensionOf0( xt ) }.
% 0.72/1.11 { ! aDimensionOf0( xs ) = sz00 }.
% 0.72/1.11 { aVector0( xp ) }.
% 0.72/1.11 { szszuzczcdt0( aDimensionOf0( xp ) ) = aDimensionOf0( xs ) }.
% 0.72/1.11 { ! aNaturalNumber0( X ), sdtlbdtrb0( xp, X ) = sdtlbdtrb0( xs, X ) }.
% 0.72/1.11 { xp = sziznziztdt0( xs ) }.
% 0.72/1.11 { aVector0( xq ) }.
% 0.72/1.11 { szszuzczcdt0( aDimensionOf0( xq ) ) = aDimensionOf0( xt ) }.
% 0.72/1.11 { ! aNaturalNumber0( X ), sdtlbdtrb0( xq, X ) = sdtlbdtrb0( xt, X ) }.
% 0.72/1.11 { xq = sziznziztdt0( xt ) }.
% 0.72/1.11 { aScalar0( xA ) }.
% 0.72/1.11 { xA = sdtlbdtrb0( xs, aDimensionOf0( xs ) ) }.
% 0.72/1.11 { aScalar0( xB ) }.
% 0.72/1.11 { xB = sdtlbdtrb0( xt, aDimensionOf0( xt ) ) }.
% 0.72/1.11 { aScalar0( xC ) }.
% 0.72/1.11 { xC = sdtasasdt0( xp, xp ) }.
% 0.72/1.11 { aScalar0( xD ) }.
% 0.72/1.11 { xD = sdtasasdt0( xq, xq ) }.
% 0.72/1.11 { aScalar0( xE ) }.
% 0.72/1.11 { xE = sdtasasdt0( xp, xq ) }.
% 0.72/1.11 { aScalar0( xF ) }.
% 0.72/1.11 { xF = sdtasdt0( xA, xA ) }.
% 0.72/1.11 { aScalar0( xG ) }.
% 0.72/1.11 { xG = sdtasdt0( xB, xB ) }.
% 0.72/1.11 { aScalar0( xH ) }.
% 0.72/1.11 { xH = sdtasdt0( xA, xB ) }.
% 0.72/1.11 { aScalar0( xR ) }.
% 0.72/1.11 { xR = sdtasdt0( xC, xG ) }.
% 0.72/1.11 { aScalar0( xP ) }.
% 0.72/1.11 { xP = sdtasdt0( xE, xH ) }.
% 0.72/1.11 { aScalar0( xS ) }.
% 0.72/1.11 { xS = sdtasdt0( xF, xD ) }.
% 0.72/1.11 { aScalar0( xN ) }.
% 0.72/1.11 { xN = sdtasdt0( xR, xS ) }.
% 0.72/1.11 { sdtlseqdt0( sdtasdt0( xE, xE ), sdtasdt0( xC, xD ) ) }.
% 0.72/1.11 { sdtlseqdt0( sdtasdt0( xP, xP ), xN ) }.
% 0.72/1.11 { ! sdtasdt0( smndt0( xS ), xR ) = smndt0( xN ) }.
% 0.72/1.11
% 0.72/1.11 percentage equality = 0.306202, percentage horn = 0.916667
% 0.72/1.11 This is a problem with some equality
% 0.72/1.11
% 0.72/1.11
% 0.72/1.11
% 0.72/1.11 Options Used:
% 0.72/1.11
% 0.72/1.11 useres = 1
% 0.72/1.11 useparamod = 1
% 0.72/1.11 useeqrefl = 1
% 0.72/1.11 useeqfact = 1
% 0.72/1.11 usefactor = 1
% 0.72/1.11 usesimpsplitting = 0
% 0.72/1.11 usesimpdemod = 5
% 0.72/1.11 usesimpres = 3
% 0.72/1.11
% 0.72/1.11 resimpinuse = 1000
% 0.72/1.11 resimpclauses = 20000
% 0.72/1.11 substype = eqrewr
% 0.72/1.11 backwardsubs = 1
% 0.72/1.11 selectoldest = 5
% 0.72/1.11
% 0.72/1.11 litorderings [0] = split
% 0.72/1.11 litorderings [1] = extend the termordering, first sorting on arguments
% 0.72/1.11
% 0.72/1.11 termordering = kbo
% 0.72/1.11
% 0.72/1.11 litapriori = 0
% 0.72/1.11 termapriori = 1
% 0.72/1.11 litaposteriori = 0
% 0.72/1.11 termaposteriori = 0
% 0.72/1.11 demodaposteriori = 0
% 0.72/1.11 ordereqreflfact = 0
% 0.72/1.11
% 0.72/1.11 litselect = negord
% 0.72/1.11
% 0.72/1.11 maxweight = 15
% 0.72/1.11 maxdepth = 30000
% 0.72/1.11 maxlength = 115
% 0.72/1.11 maxnrvars = 195
% 0.72/1.11 excuselevel = 1
% 0.72/1.11 increasemaxweight = 1
% 0.72/1.11
% 0.72/1.11 maxselected = 10000000
% 0.72/1.11 maxnrclauses = 10000000
% 0.72/1.11
% 0.72/1.11 showgenerated = 0
% 0.72/1.11 showkept = 0
% 0.72/1.11 showselected = 0
% 0.72/1.11 showdeleted = 0
% 0.72/1.11 showresimp = 1
% 0.72/1.11 showstatus = 2000
% 0.72/1.11
% 0.72/1.11 prologoutput = 0
% 0.72/1.11 nrgoals = 5000000
% 0.72/1.11 totalproof = 1
% 0.72/1.11
% 0.72/1.11 Symbols occurring in the translation:
% 0.72/1.11
% 0.72/1.11 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.72/1.11 . [1, 2] (w:1, o:46, a:1, s:1, b:0),
% 0.72/1.11 && [3, 0] (w:1, o:4, a:1, s:1, b:0),
% 0.72/1.11 ! [4, 1] (w:0, o:28, a:1, s:1, b:0),
% 0.72/1.11 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.72/1.11 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.72/1.11 aNaturalNumber0 [36, 1] (w:1, o:33, a:1, s:1, b:0),
% 0.72/1.11 sz00 [37, 0] (w:1, o:7, a:1, s:1, b:0),
% 0.72/1.11 szszuzczcdt0 [38, 1] (w:1, o:34, a:1, s:1, b:0),
% 0.72/1.11 iLess0 [40, 2] (w:1, o:70, a:1, s:1, b:0),
% 0.72/1.11 aScalar0 [41, 1] (w:1, o:35, a:1, s:1, b:0),
% 0.72/1.11 sz0z00 [42, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.72/1.11 sdtpldt0 [43, 2] (w:1, o:71, a:1, s:1, b:0),
% 0.72/1.11 sdtasdt0 [44, 2] (w:1, o:72, a:1, s:1, b:0),
% 0.72/1.11 smndt0 [45, 1] (w:1, o:36, a:1, s:1, b:0),
% 0.72/1.11 sdtlseqdt0 [48, 2] (w:1, o:73, a:1, s:1, b:0),
% 0.72/1.11 aVector0 [49, 1] (w:1, o:37, a:1, s:1, b:0),
% 0.72/1.11 aDimensionOf0 [50, 1] (w:1, o:38, a:1, s:1, b:0),
% 0.72/1.11 sdtlbdtrb0 [51, 2] (w:1, o:74, a:1, s:1, b:0),
% 0.72/1.11 sziznziztdt0 [52, 1] (w:1, o:39, a:1, s:1, b:0),
% 0.72/1.11 sdtasasdt0 [53, 2] (w:1, o:75, a:1, s:1, b:0),
% 0.72/1.11 xs [54, 0] (w:1, o:12, a:1, s:1, b:0),
% 0.72/1.11 xt [55, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.72/1.11 xp [56, 0] (w:1, o:14, a:1, s:1, b:0),
% 0.72/1.11 xq [57, 0] (w:1, o:15, a:1, s:1, b:0),
% 0.72/1.11 xA [58, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.72/1.11 xB [59, 0] (w:1, o:17, a:1, s:1, b:0),
% 0.72/1.11 xC [60, 0] (w:1, o:18, a:1, s:1, b:0),
% 0.72/1.11 xD [61, 0] (w:1, o:19, a:1, s:1, b:0),
% 0.72/1.11 xE [62, 0] (w:1, o:20, a:1, s:1, b:0),
% 0.72/1.11 xF [63, 0] (w:1, o:21, a:1, s:1, b:0),
% 0.72/1.11 xG [64, 0] (w:1, o:22, a:1, s:1, b:0),
% 0.72/1.11 xH [65, 0] (w:1, o:23, a:1, s:1, b:0),
% 0.72/1.11 xR [66, 0] (w:1, o:24, a:1, s:1, b:0),
% 0.72/1.11 xP [67, 0] (w:1, o:25, a:1, s:1, b:0),
% 0.72/1.11 xS [68, 0] (w:1, o:26, a:1, s:1, b:0),
% 0.72/1.11 xN [69, 0] (w:1, o:27, a:1, s:1, b:0),
% 0.72/1.11 alpha1 [70, 2] (w:1, o:76, a:1, s:1, b:1),
% 0.72/1.11 alpha2 [71, 2] (w:1, o:77, a:1, s:1, b:1),
% 0.72/1.11 alpha3 [72, 1] (w:1, o:40, a:1, s:1, b:1),
% 0.72/1.11 alpha4 [73, 3] (w:1, o:79, a:1, s:1, b:1),
% 0.72/1.11 alpha5 [74, 1] (w:1, o:41, a:1, s:1, b:1),
% 0.72/1.11 alpha6 [75, 1] (w:1, o:42, a:1, s:1, b:1),
% 0.72/1.11 alpha7 [76, 1] (w:1, o:43, a:1, s:1, b:1),
% 0.72/1.11 alpha8 [77, 1] (w:1, o:44, a:1, s:1, b:1),
% 0.72/1.11 skol1 [78, 1] (w:1, o:45, a:1, s:1, b:1),
% 0.72/1.11 skol2 [79, 2] (w:1, o:78, a:1, s:1, b:1).
% 0.72/1.11
% 0.72/1.11
% 0.72/1.11 Starting Search:
% 0.72/1.11
% 0.72/1.11 *** allocated 15000 integers for clauses
% 0.72/1.11 *** allocated 22500 integers for clauses
% 0.72/1.11 *** allocated 33750 integers for clauses
% 0.72/1.11 *** allocated 50625 integers for clauses
% 0.72/1.11 *** allocated 15000 integers for termspace/termends
% 0.72/1.11 *** allocated 75937 integers for clauses
% 0.72/1.11 *** allocated 22500 integers for termspace/termends
% 0.72/1.11 Resimplifying inuse:
% 0.72/1.11 Done
% 0.72/1.11
% 0.72/1.11 *** allocated 113905 integers for clauses
% 0.72/1.11 *** allocated 33750 integers for termspace/termends
% 0.72/1.11 *** allocated 170857 integers for clauses
% 0.72/1.11 *** allocated 50625 integers for termspace/termends
% 0.72/1.11
% 0.72/1.11 Intermediate Status:
% 0.72/1.11 Generated: 5884
% 0.72/1.11 Kept: 2085
% 0.72/1.11 Inuse: 199
% 0.72/1.11 Deleted: 4
% 0.72/1.11 Deletedinuse: 2
% 0.72/1.11
% 0.72/1.11 Resimplifying inuse:
% 0.72/1.11 Done
% 0.72/1.11
% 0.72/1.11 *** allocated 75937 integers for termspace/termends
% 0.72/1.11 *** allocated 256285 integers for clauses
% 0.72/1.11 Resimplifying inuse:
% 0.72/1.11 Done
% 0.72/1.11
% 0.72/1.11
% 0.72/1.11 Intermediate Status:
% 0.72/1.11 Generated: 14581
% 0.72/1.11 Kept: 4087
% 0.72/1.11 Inuse: 354
% 0.72/1.11 Deleted: 7
% 0.72/1.11 Deletedinuse: 3
% 0.72/1.11
% 0.72/1.11 Resimplifying inuse:
% 0.72/1.11 Done
% 0.72/1.11
% 0.72/1.11 *** allocated 113905 integers for termspace/termends
% 0.72/1.11 *** allocated 384427 integers for clauses
% 0.72/1.11
% 0.72/1.11 Bliksems!, er is een bewijs:
% 0.72/1.11 % SZS status Theorem
% 0.72/1.11 % SZS output start Refutation
% 0.72/1.11
% 0.72/1.11 (11) {G0,W5,D3,L2,V1,M2} I { ! aScalar0( X ), aScalar0( smndt0( X ) ) }.
% 0.72/1.11 (31) {G0,W13,D3,L4,V3,M4} I { ! aScalar0( X ), ! aScalar0( Y ), ! aScalar0
% 0.72/1.11 ( Z ), sdtasdt0( X, Y ) = sdtasdt0( Y, X ) }.
% 0.72/1.11 (39) {G0,W13,D4,L3,V2,M3} I { ! aScalar0( X ), ! aScalar0( Y ), sdtasdt0( X
% 0.72/1.11 , smndt0( Y ) ) ==> smndt0( sdtasdt0( X, Y ) ) }.
% 0.72/1.11 (97) {G0,W2,D2,L1,V0,M1} I { aScalar0( xR ) }.
% 0.72/1.11 (101) {G0,W2,D2,L1,V0,M1} I { aScalar0( xS ) }.
% 0.72/1.11 (104) {G0,W5,D3,L1,V0,M1} I { sdtasdt0( xR, xS ) ==> xN }.
% 0.72/1.11 (107) {G0,W7,D4,L1,V0,M1} I { ! sdtasdt0( smndt0( xS ), xR ) ==> smndt0( xN
% 0.72/1.11 ) }.
% 0.72/1.11 (115) {G1,W11,D3,L3,V2,M3} F(31) { ! aScalar0( X ), ! aScalar0( Y ),
% 0.72/1.11 sdtasdt0( X, Y ) = sdtasdt0( Y, X ) }.
% 0.72/1.11 (406) {G1,W3,D3,L1,V0,M1} R(11,101) { aScalar0( smndt0( xS ) ) }.
% 0.72/1.11 (1261) {G1,W11,D4,L2,V1,M2} R(39,101) { ! aScalar0( X ), sdtasdt0( X,
% 0.72/1.11 smndt0( xS ) ) ==> smndt0( sdtasdt0( X, xS ) ) }.
% 0.72/1.11 (5087) {G2,W2,D2,L1,V0,M1} P(115,107);d(1261);d(104);q;r(406) { ! aScalar0
% 0.72/1.11 ( xR ) }.
% 0.72/1.11 (5096) {G3,W0,D0,L0,V0,M0} S(5087);r(97) { }.
% 0.72/1.11
% 0.72/1.11
% 0.72/1.11 % SZS output end Refutation
% 0.72/1.11 found a proof!
% 0.72/1.11
% 0.72/1.11
% 0.72/1.11 Unprocessed initial clauses:
% 0.72/1.11
% 0.72/1.11 (5098) {G0,W1,D1,L1,V0,M1} { && }.
% 0.72/1.11 (5099) {G0,W2,D2,L1,V0,M1} { aNaturalNumber0( sz00 ) }.
% 0.72/1.11 (5100) {G0,W5,D3,L2,V1,M2} { ! aNaturalNumber0( X ), aNaturalNumber0(
% 0.72/1.11 szszuzczcdt0( X ) ) }.
% 0.72/1.11 (5101) {G0,W6,D3,L2,V1,M2} { ! aNaturalNumber0( X ), ! szszuzczcdt0( X ) =
% 0.72/1.11 sz00 }.
% 0.72/1.11 (5102) {G0,W8,D3,L3,V2,M3} { ! aNaturalNumber0( X ), X = sz00,
% 0.72/1.11 aNaturalNumber0( skol1( Y ) ) }.
% 0.72/1.11 (5103) {G0,W10,D4,L3,V1,M3} { ! aNaturalNumber0( X ), X = sz00, X =
% 0.72/1.11 szszuzczcdt0( skol1( X ) ) }.
% 0.72/1.11 (5104) {G0,W12,D3,L4,V2,M4} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 0.72/1.11 ), ! szszuzczcdt0( X ) = szszuzczcdt0( Y ), X = Y }.
% 0.72/1.11 (5105) {G0,W1,D1,L1,V0,M1} { && }.
% 0.72/1.11 (5106) {G0,W6,D3,L2,V1,M2} { ! aNaturalNumber0( X ), iLess0( X,
% 0.72/1.11 szszuzczcdt0( X ) ) }.
% 0.72/1.11 (5107) {G0,W1,D1,L1,V0,M1} { && }.
% 0.72/1.11 (5108) {G0,W2,D2,L1,V0,M1} { aScalar0( sz0z00 ) }.
% 0.72/1.11 (5109) {G0,W8,D3,L3,V2,M3} { ! aScalar0( X ), ! aScalar0( Y ), aScalar0(
% 0.72/1.11 sdtpldt0( X, Y ) ) }.
% 0.72/1.11 (5110) {G0,W8,D3,L3,V2,M3} { ! aScalar0( X ), ! aScalar0( Y ), aScalar0(
% 0.72/1.11 sdtasdt0( X, Y ) ) }.
% 0.72/1.11 (5111) {G0,W5,D3,L2,V1,M2} { ! aScalar0( X ), aScalar0( smndt0( X ) ) }.
% 0.72/1.11 (5112) {G0,W4,D2,L2,V1,M2} { ! aScalar0( X ), alpha3( X ) }.
% 0.72/1.11 (5113) {G0,W6,D3,L2,V1,M2} { ! aScalar0( X ), smndt0( sz0z00 ) = sz0z00
% 0.72/1.11 }.
% 0.72/1.11 (5114) {G0,W4,D2,L2,V1,M2} { ! alpha3( X ), alpha5( X ) }.
% 0.72/1.11 (5115) {G0,W7,D4,L2,V1,M2} { ! alpha3( X ), smndt0( smndt0( X ) ) = X }.
% 0.72/1.11 (5116) {G0,W9,D4,L3,V1,M3} { ! alpha5( X ), ! smndt0( smndt0( X ) ) = X,
% 0.72/1.11 alpha3( X ) }.
% 0.72/1.11 (5117) {G0,W4,D2,L2,V1,M2} { ! alpha5( X ), alpha6( X ) }.
% 0.72/1.11 (5118) {G0,W8,D4,L2,V1,M2} { ! alpha5( X ), sdtpldt0( smndt0( X ), X ) =
% 0.72/1.11 sz0z00 }.
% 0.72/1.11 (5119) {G0,W10,D4,L3,V1,M3} { ! alpha6( X ), ! sdtpldt0( smndt0( X ), X )
% 0.72/1.11 = sz0z00, alpha5( X ) }.
% 0.72/1.11 (5120) {G0,W4,D2,L2,V1,M2} { ! alpha6( X ), alpha7( X ) }.
% 0.72/1.11 (5121) {G0,W8,D4,L2,V1,M2} { ! alpha6( X ), sdtpldt0( X, smndt0( X ) ) =
% 0.72/1.11 sz0z00 }.
% 0.72/1.11 (5122) {G0,W10,D4,L3,V1,M3} { ! alpha7( X ), ! sdtpldt0( X, smndt0( X ) )
% 0.72/1.11 = sz0z00, alpha6( X ) }.
% 0.72/1.11 (5123) {G0,W4,D2,L2,V1,M2} { ! alpha7( X ), alpha8( X ) }.
% 0.72/1.11 (5124) {G0,W7,D3,L2,V1,M2} { ! alpha7( X ), sdtasdt0( sz0z00, X ) = sz0z00
% 0.72/1.11 }.
% 0.72/1.11 (5125) {G0,W9,D3,L3,V1,M3} { ! alpha8( X ), ! sdtasdt0( sz0z00, X ) =
% 0.72/1.11 sz0z00, alpha7( X ) }.
% 0.72/1.11 (5126) {G0,W7,D3,L2,V1,M2} { ! alpha8( X ), sdtpldt0( X, sz0z00 ) = X }.
% 0.72/1.11 (5127) {G0,W7,D3,L2,V1,M2} { ! alpha8( X ), sdtpldt0( sz0z00, X ) = X }.
% 0.72/1.11 (5128) {G0,W7,D3,L2,V1,M2} { ! alpha8( X ), sdtasdt0( X, sz0z00 ) = sz0z00
% 0.72/1.11 }.
% 0.72/1.11 (5129) {G0,W17,D3,L4,V1,M4} { ! sdtpldt0( X, sz0z00 ) = X, ! sdtpldt0(
% 0.72/1.11 sz0z00, X ) = X, ! sdtasdt0( X, sz0z00 ) = sz0z00, alpha8( X ) }.
% 0.72/1.11 (5130) {G0,W10,D2,L4,V3,M4} { ! aScalar0( X ), ! aScalar0( Y ), ! aScalar0
% 0.72/1.11 ( Z ), alpha4( X, Y, Z ) }.
% 0.72/1.11 (5131) {G0,W13,D3,L4,V3,M4} { ! aScalar0( X ), ! aScalar0( Y ), ! aScalar0
% 0.72/1.11 ( Z ), sdtasdt0( X, Y ) = sdtasdt0( Y, X ) }.
% 0.72/1.11 (5132) {G0,W15,D4,L2,V3,M2} { ! alpha4( X, Y, Z ), sdtpldt0( sdtpldt0( X,
% 0.72/1.11 Y ), Z ) = sdtpldt0( X, sdtpldt0( Y, Z ) ) }.
% 0.72/1.11 (5133) {G0,W11,D3,L2,V3,M2} { ! alpha4( X, Y, Z ), sdtpldt0( X, Y ) =
% 0.72/1.11 sdtpldt0( Y, X ) }.
% 0.72/1.11 (5134) {G0,W15,D4,L2,V3,M2} { ! alpha4( X, Y, Z ), sdtasdt0( sdtasdt0( X,
% 0.72/1.11 Y ), Z ) = sdtasdt0( X, sdtasdt0( Y, Z ) ) }.
% 0.72/1.11 (5135) {G0,W33,D4,L4,V3,M4} { ! sdtpldt0( sdtpldt0( X, Y ), Z ) = sdtpldt0
% 0.72/1.11 ( X, sdtpldt0( Y, Z ) ), ! sdtpldt0( X, Y ) = sdtpldt0( Y, X ), !
% 0.72/1.11 sdtasdt0( sdtasdt0( X, Y ), Z ) = sdtasdt0( X, sdtasdt0( Y, Z ) ), alpha4
% 0.72/1.11 ( X, Y, Z ) }.
% 0.72/1.11 (5136) {G0,W19,D4,L4,V3,M4} { ! aScalar0( X ), ! aScalar0( Y ), ! aScalar0
% 0.72/1.11 ( Z ), sdtasdt0( X, sdtpldt0( Y, Z ) ) = sdtpldt0( sdtasdt0( X, Y ),
% 0.72/1.11 sdtasdt0( X, Z ) ) }.
% 0.72/1.11 (5137) {G0,W19,D4,L4,V3,M4} { ! aScalar0( X ), ! aScalar0( Y ), ! aScalar0
% 0.72/1.11 ( Z ), sdtasdt0( sdtpldt0( X, Y ), Z ) = sdtpldt0( sdtasdt0( X, Z ),
% 0.72/1.11 sdtasdt0( Y, Z ) ) }.
% 0.72/1.11 (5138) {G0,W31,D5,L5,V4,M5} { ! aScalar0( X ), ! aScalar0( Y ), ! aScalar0
% 0.72/1.11 ( Z ), ! aScalar0( T ), sdtasdt0( sdtpldt0( X, Y ), sdtpldt0( Z, T ) ) =
% 0.72/1.11 sdtpldt0( sdtpldt0( sdtasdt0( X, Z ), sdtasdt0( X, T ) ), sdtpldt0(
% 0.72/1.11 sdtasdt0( Y, Z ), sdtasdt0( Y, T ) ) ) }.
% 0.72/1.11 (5139) {G0,W13,D4,L3,V2,M3} { ! aScalar0( X ), ! aScalar0( Y ), sdtasdt0(
% 0.72/1.11 X, smndt0( Y ) ) = smndt0( sdtasdt0( X, Y ) ) }.
% 0.72/1.11 (5140) {G0,W13,D4,L3,V2,M3} { ! aScalar0( X ), ! aScalar0( Y ), sdtasdt0(
% 0.72/1.11 smndt0( X ), Y ) = smndt0( sdtasdt0( X, Y ) ) }.
% 0.72/1.11 (5141) {G0,W13,D4,L3,V2,M3} { ! aScalar0( X ), ! aScalar0( Y ), sdtasdt0(
% 0.72/1.11 smndt0( X ), smndt0( Y ) ) = sdtasdt0( X, Y ) }.
% 0.72/1.11 (5142) {G0,W1,D1,L1,V0,M1} { && }.
% 0.72/1.11 (5143) {G0,W5,D2,L2,V1,M2} { ! aScalar0( X ), sdtlseqdt0( X, X ) }.
% 0.72/1.11 (5144) {G0,W13,D2,L5,V2,M5} { ! aScalar0( X ), ! aScalar0( Y ), !
% 0.72/1.11 sdtlseqdt0( X, Y ), ! sdtlseqdt0( Y, X ), X = Y }.
% 0.72/1.11 (5145) {G0,W15,D2,L6,V3,M6} { ! aScalar0( X ), ! aScalar0( Y ), ! aScalar0
% 0.72/1.11 ( Z ), ! sdtlseqdt0( X, Y ), ! sdtlseqdt0( Y, Z ), sdtlseqdt0( X, Z ) }.
% 0.72/1.11 (5146) {G0,W21,D3,L7,V4,M7} { ! aScalar0( X ), ! aScalar0( Y ), ! aScalar0
% 0.72/1.11 ( Z ), ! aScalar0( T ), ! sdtlseqdt0( X, Y ), ! sdtlseqdt0( Z, T ),
% 0.72/1.11 sdtlseqdt0( sdtpldt0( X, Z ), sdtpldt0( Y, T ) ) }.
% 0.72/1.11 (5147) {G0,W24,D3,L8,V4,M8} { ! aScalar0( X ), ! aScalar0( Y ), ! aScalar0
% 0.72/1.11 ( Z ), ! aScalar0( T ), ! sdtlseqdt0( X, Y ), ! sdtlseqdt0( sz0z00, Z ),
% 0.72/1.11 ! sdtlseqdt0( Z, T ), sdtlseqdt0( sdtasdt0( X, Z ), sdtasdt0( Y, T ) )
% 0.72/1.11 }.
% 0.72/1.11 (5148) {G0,W10,D2,L4,V2,M4} { ! aScalar0( X ), ! aScalar0( Y ), sdtlseqdt0
% 0.72/1.11 ( X, Y ), sdtlseqdt0( Y, X ) }.
% 0.72/1.11 (5149) {G0,W15,D3,L5,V2,M5} { ! aScalar0( X ), ! aScalar0( Y ), !
% 0.72/1.11 sdtlseqdt0( sz0z00, X ), ! sdtlseqdt0( sz0z00, Y ), sdtlseqdt0( sz0z00,
% 0.72/1.11 sdtpldt0( X, Y ) ) }.
% 0.72/1.11 (5150) {G0,W15,D3,L5,V2,M5} { ! aScalar0( X ), ! aScalar0( Y ), !
% 0.72/1.11 sdtlseqdt0( sz0z00, X ), ! sdtlseqdt0( sz0z00, Y ), sdtlseqdt0( sz0z00,
% 0.72/1.11 sdtasdt0( X, Y ) ) }.
% 0.72/1.11 (5151) {G0,W7,D3,L2,V1,M2} { ! aScalar0( X ), sdtlseqdt0( sz0z00, sdtasdt0
% 0.72/1.11 ( X, X ) ) }.
% 0.72/1.11 (5152) {G0,W20,D3,L6,V2,M6} { ! aScalar0( X ), ! aScalar0( Y ), !
% 0.72/1.11 sdtlseqdt0( sz0z00, X ), ! sdtlseqdt0( sz0z00, Y ), ! sdtasdt0( X, X ) =
% 0.72/1.11 sdtasdt0( Y, Y ), X = Y }.
% 0.72/1.11 (5153) {G0,W1,D1,L1,V0,M1} { && }.
% 0.72/1.11 (5154) {G0,W5,D3,L2,V1,M2} { ! aVector0( X ), aNaturalNumber0(
% 0.72/1.11 aDimensionOf0( X ) ) }.
% 0.72/1.11 (5155) {G0,W8,D3,L3,V2,M3} { ! aVector0( X ), ! aNaturalNumber0( Y ),
% 0.72/1.11 aScalar0( sdtlbdtrb0( X, Y ) ) }.
% 0.72/1.11 (5156) {G0,W12,D3,L4,V2,M4} { ! aVector0( X ), aDimensionOf0( X ) = sz00,
% 0.72/1.11 ! Y = sziznziztdt0( X ), aVector0( Y ) }.
% 0.72/1.11 (5157) {G0,W13,D3,L4,V2,M4} { ! aVector0( X ), aDimensionOf0( X ) = sz00,
% 0.72/1.11 ! Y = sziznziztdt0( X ), alpha1( X, Y ) }.
% 0.72/1.11 (5158) {G0,W15,D3,L5,V2,M5} { ! aVector0( X ), aDimensionOf0( X ) = sz00,
% 0.72/1.11 ! aVector0( Y ), ! alpha1( X, Y ), Y = sziznziztdt0( X ) }.
% 0.72/1.11 (5159) {G0,W9,D4,L2,V2,M2} { ! alpha1( X, Y ), szszuzczcdt0( aDimensionOf0
% 0.72/1.11 ( Y ) ) = aDimensionOf0( X ) }.
% 0.72/1.11 (5160) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), alpha2( X, Y ) }.
% 0.72/1.11 (5161) {G0,W12,D4,L3,V2,M3} { ! szszuzczcdt0( aDimensionOf0( Y ) ) =
% 0.72/1.11 aDimensionOf0( X ), ! alpha2( X, Y ), alpha1( X, Y ) }.
% 0.72/1.11 (5162) {G0,W12,D3,L3,V3,M3} { ! alpha2( X, Y ), ! aNaturalNumber0( Z ),
% 0.72/1.11 sdtlbdtrb0( Y, Z ) = sdtlbdtrb0( X, Z ) }.
% 0.72/1.11 (5163) {G0,W7,D3,L2,V4,M2} { aNaturalNumber0( skol2( Z, T ) ), alpha2( X,
% 0.72/1.11 Y ) }.
% 0.72/1.11 (5164) {G0,W14,D4,L2,V2,M2} { ! sdtlbdtrb0( Y, skol2( X, Y ) ) =
% 0.72/1.11 sdtlbdtrb0( X, skol2( X, Y ) ), alpha2( X, Y ) }.
% 0.72/1.11 (5165) {G0,W20,D4,L5,V2,M5} { ! aVector0( X ), ! aVector0( Y ), !
% 0.72/1.11 aDimensionOf0( X ) = aDimensionOf0( Y ), aDimensionOf0( Y ) = sz00,
% 0.72/1.11 aDimensionOf0( sziznziztdt0( X ) ) = aDimensionOf0( sziznziztdt0( Y ) )
% 0.72/1.11 }.
% 0.72/1.11 (5166) {G0,W13,D3,L4,V2,M4} { ! aVector0( X ), ! aVector0( Y ), !
% 0.72/1.11 aDimensionOf0( X ) = aDimensionOf0( Y ), aScalar0( sdtasasdt0( X, Y ) )
% 0.72/1.11 }.
% 0.72/1.11 (5167) {G0,W18,D3,L5,V2,M5} { ! aVector0( X ), ! aVector0( Y ), !
% 0.72/1.11 aDimensionOf0( X ) = aDimensionOf0( Y ), ! aDimensionOf0( Y ) = sz00,
% 0.72/1.11 sdtasasdt0( X, Y ) = sz0z00 }.
% 0.72/1.11 (5168) {G0,W32,D6,L5,V2,M5} { ! aVector0( X ), ! aVector0( Y ), !
% 0.72/1.11 aDimensionOf0( X ) = aDimensionOf0( Y ), aDimensionOf0( Y ) = sz00,
% 0.72/1.11 sdtasasdt0( X, Y ) = sdtpldt0( sdtasasdt0( sziznziztdt0( X ),
% 0.72/1.11 sziznziztdt0( Y ) ), sdtasdt0( sdtlbdtrb0( X, aDimensionOf0( X ) ),
% 0.72/1.11 sdtlbdtrb0( Y, aDimensionOf0( Y ) ) ) ) }.
% 0.72/1.11 (5169) {G0,W7,D3,L2,V1,M2} { ! aVector0( X ), sdtlseqdt0( sz0z00,
% 0.72/1.11 sdtasasdt0( X, X ) ) }.
% 0.72/1.11 (5170) {G0,W2,D2,L1,V0,M1} { aVector0( xs ) }.
% 0.72/1.11 (5171) {G0,W2,D2,L1,V0,M1} { aVector0( xt ) }.
% 0.72/1.11 (5172) {G0,W29,D4,L5,V2,M5} { ! aVector0( X ), ! aVector0( Y ), !
% 0.72/1.11 aDimensionOf0( X ) = aDimensionOf0( Y ), ! iLess0( aDimensionOf0( X ),
% 0.72/1.11 aDimensionOf0( xs ) ), sdtlseqdt0( sdtasdt0( sdtasasdt0( X, Y ),
% 0.72/1.11 sdtasasdt0( X, Y ) ), sdtasdt0( sdtasasdt0( X, X ), sdtasasdt0( Y, Y ) )
% 0.72/1.11 ) }.
% 0.72/1.11 (5173) {G0,W5,D3,L1,V0,M1} { aDimensionOf0( xs ) = aDimensionOf0( xt ) }.
% 0.72/1.11 (5174) {G0,W4,D3,L1,V0,M1} { ! aDimensionOf0( xs ) = sz00 }.
% 0.72/1.11 (5175) {G0,W2,D2,L1,V0,M1} { aVector0( xp ) }.
% 0.72/1.11 (5176) {G0,W6,D4,L1,V0,M1} { szszuzczcdt0( aDimensionOf0( xp ) ) =
% 0.72/1.11 aDimensionOf0( xs ) }.
% 0.72/1.11 (5177) {G0,W9,D3,L2,V1,M2} { ! aNaturalNumber0( X ), sdtlbdtrb0( xp, X ) =
% 0.72/1.11 sdtlbdtrb0( xs, X ) }.
% 0.72/1.11 (5178) {G0,W4,D3,L1,V0,M1} { xp = sziznziztdt0( xs ) }.
% 0.72/1.11 (5179) {G0,W2,D2,L1,V0,M1} { aVector0( xq ) }.
% 0.72/1.11 (5180) {G0,W6,D4,L1,V0,M1} { szszuzczcdt0( aDimensionOf0( xq ) ) =
% 0.72/1.11 aDimensionOf0( xt ) }.
% 0.72/1.11 (5181) {G0,W9,D3,L2,V1,M2} { ! aNaturalNumber0( X ), sdtlbdtrb0( xq, X ) =
% 0.72/1.11 sdtlbdtrb0( xt, X ) }.
% 0.72/1.11 (5182) {G0,W4,D3,L1,V0,M1} { xq = sziznziztdt0( xt ) }.
% 0.72/1.11 (5183) {G0,W2,D2,L1,V0,M1} { aScalar0( xA ) }.
% 0.72/1.11 (5184) {G0,W6,D4,L1,V0,M1} { xA = sdtlbdtrb0( xs, aDimensionOf0( xs ) )
% 0.72/1.11 }.
% 0.72/1.11 (5185) {G0,W2,D2,L1,V0,M1} { aScalar0( xB ) }.
% 0.72/1.11 (5186) {G0,W6,D4,L1,V0,M1} { xB = sdtlbdtrb0( xt, aDimensionOf0( xt ) )
% 0.72/1.11 }.
% 0.72/1.11 (5187) {G0,W2,D2,L1,V0,M1} { aScalar0( xC ) }.
% 0.72/1.11 (5188) {G0,W5,D3,L1,V0,M1} { xC = sdtasasdt0( xp, xp ) }.
% 0.72/1.11 (5189) {G0,W2,D2,L1,V0,M1} { aScalar0( xD ) }.
% 0.72/1.11 (5190) {G0,W5,D3,L1,V0,M1} { xD = sdtasasdt0( xq, xq ) }.
% 0.72/1.11 (5191) {G0,W2,D2,L1,V0,M1} { aScalar0( xE ) }.
% 0.72/1.11 (5192) {G0,W5,D3,L1,V0,M1} { xE = sdtasasdt0( xp, xq ) }.
% 0.72/1.11 (5193) {G0,W2,D2,L1,V0,M1} { aScalar0( xF ) }.
% 0.72/1.11 (5194) {G0,W5,D3,L1,V0,M1} { xF = sdtasdt0( xA, xA ) }.
% 0.72/1.11 (5195) {G0,W2,D2,L1,V0,M1} { aScalar0( xG ) }.
% 0.72/1.11 (5196) {G0,W5,D3,L1,V0,M1} { xG = sdtasdt0( xB, xB ) }.
% 0.72/1.11 (5197) {G0,W2,D2,L1,V0,M1} { aScalar0( xH ) }.
% 0.72/1.11 (5198) {G0,W5,D3,L1,V0,M1} { xH = sdtasdt0( xA, xB ) }.
% 0.72/1.11 (5199) {G0,W2,D2,L1,V0,M1} { aScalar0( xR ) }.
% 0.72/1.11 (5200) {G0,W5,D3,L1,V0,M1} { xR = sdtasdt0( xC, xG ) }.
% 0.72/1.11 (5201) {G0,W2,D2,L1,V0,M1} { aScalar0( xP ) }.
% 0.72/1.11 (5202) {G0,W5,D3,L1,V0,M1} { xP = sdtasdt0( xE, xH ) }.
% 0.72/1.11 (5203) {G0,W2,D2,L1,V0,M1} { aScalar0( xS ) }.
% 0.72/1.11 (5204) {G0,W5,D3,L1,V0,M1} { xS = sdtasdt0( xF, xD ) }.
% 0.72/1.11 (5205) {G0,W2,D2,L1,V0,M1} { aScalar0( xN ) }.
% 0.72/1.11 (5206) {G0,W5,D3,L1,V0,M1} { xN = sdtasdt0( xR, xS ) }.
% 0.72/1.11 (5207) {G0,W7,D3,L1,V0,M1} { sdtlseqdt0( sdtasdt0( xE, xE ), sdtasdt0( xC
% 0.72/1.11 , xD ) ) }.
% 0.72/1.11 (5208) {G0,W5,D3,L1,V0,M1} { sdtlseqdt0( sdtasdt0( xP, xP ), xN ) }.
% 0.72/1.11 (5209) {G0,W7,D4,L1,V0,M1} { ! sdtasdt0( smndt0( xS ), xR ) = smndt0( xN )
% 0.72/1.11 }.
% 0.72/1.11
% 0.72/1.11
% 0.72/1.11 Total Proof:
% 0.72/1.11
% 0.72/1.11 subsumption: (11) {G0,W5,D3,L2,V1,M2} I { ! aScalar0( X ), aScalar0( smndt0
% 0.72/1.11 ( X ) ) }.
% 0.72/1.11 parent0: (5111) {G0,W5,D3,L2,V1,M2} { ! aScalar0( X ), aScalar0( smndt0( X
% 0.72/1.11 ) ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := X
% 0.72/1.11 end
% 0.72/1.11 permutation0:
% 0.72/1.11 0 ==> 0
% 0.72/1.11 1 ==> 1
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 subsumption: (31) {G0,W13,D3,L4,V3,M4} I { ! aScalar0( X ), ! aScalar0( Y )
% 0.72/1.11 , ! aScalar0( Z ), sdtasdt0( X, Y ) = sdtasdt0( Y, X ) }.
% 0.72/1.11 parent0: (5131) {G0,W13,D3,L4,V3,M4} { ! aScalar0( X ), ! aScalar0( Y ), !
% 0.72/1.11 aScalar0( Z ), sdtasdt0( X, Y ) = sdtasdt0( Y, X ) }.
% 0.72/1.12 substitution0:
% 0.72/1.12 X := X
% 0.72/1.12 Y := Y
% 0.72/1.12 Z := X
% 0.72/1.12 end
% 0.72/1.12 permutation0:
% 0.72/1.12 0 ==> 0
% 0.72/1.12 1 ==> 1
% 0.72/1.12 2 ==> 0
% 0.72/1.12 3 ==> 3
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 subsumption: (39) {G0,W13,D4,L3,V2,M3} I { ! aScalar0( X ), ! aScalar0( Y )
% 0.72/1.12 , sdtasdt0( X, smndt0( Y ) ) ==> smndt0( sdtasdt0( X, Y ) ) }.
% 0.72/1.12 parent0: (5139) {G0,W13,D4,L3,V2,M3} { ! aScalar0( X ), ! aScalar0( Y ),
% 0.72/1.12 sdtasdt0( X, smndt0( Y ) ) = smndt0( sdtasdt0( X, Y ) ) }.
% 0.72/1.12 substitution0:
% 0.72/1.12 X := X
% 0.72/1.12 Y := Y
% 0.72/1.12 end
% 0.72/1.12 permutation0:
% 0.72/1.12 0 ==> 0
% 0.72/1.12 1 ==> 1
% 0.72/1.12 2 ==> 2
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 subsumption: (97) {G0,W2,D2,L1,V0,M1} I { aScalar0( xR ) }.
% 0.72/1.12 parent0: (5199) {G0,W2,D2,L1,V0,M1} { aScalar0( xR ) }.
% 0.72/1.12 substitution0:
% 0.72/1.12 end
% 0.72/1.12 permutation0:
% 0.72/1.12 0 ==> 0
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 subsumption: (101) {G0,W2,D2,L1,V0,M1} I { aScalar0( xS ) }.
% 0.72/1.12 parent0: (5203) {G0,W2,D2,L1,V0,M1} { aScalar0( xS ) }.
% 0.72/1.12 substitution0:
% 0.72/1.12 end
% 0.72/1.12 permutation0:
% 0.72/1.12 0 ==> 0
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 eqswap: (6112) {G0,W5,D3,L1,V0,M1} { sdtasdt0( xR, xS ) = xN }.
% 0.72/1.12 parent0[0]: (5206) {G0,W5,D3,L1,V0,M1} { xN = sdtasdt0( xR, xS ) }.
% 0.72/1.12 substitution0:
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 subsumption: (104) {G0,W5,D3,L1,V0,M1} I { sdtasdt0( xR, xS ) ==> xN }.
% 0.72/1.12 parent0: (6112) {G0,W5,D3,L1,V0,M1} { sdtasdt0( xR, xS ) = xN }.
% 0.72/1.12 substitution0:
% 0.72/1.12 end
% 0.72/1.12 permutation0:
% 0.72/1.12 0 ==> 0
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 subsumption: (107) {G0,W7,D4,L1,V0,M1} I { ! sdtasdt0( smndt0( xS ), xR )
% 0.72/1.12 ==> smndt0( xN ) }.
% 0.72/1.12 parent0: (5209) {G0,W7,D4,L1,V0,M1} { ! sdtasdt0( smndt0( xS ), xR ) =
% 0.72/1.12 smndt0( xN ) }.
% 0.72/1.12 substitution0:
% 0.72/1.12 end
% 0.72/1.12 permutation0:
% 0.72/1.12 0 ==> 0
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 factor: (6369) {G0,W11,D3,L3,V2,M3} { ! aScalar0( X ), ! aScalar0( Y ),
% 0.72/1.12 sdtasdt0( X, Y ) = sdtasdt0( Y, X ) }.
% 0.72/1.12 parent0[0, 2]: (31) {G0,W13,D3,L4,V3,M4} I { ! aScalar0( X ), ! aScalar0( Y
% 0.72/1.12 ), ! aScalar0( Z ), sdtasdt0( X, Y ) = sdtasdt0( Y, X ) }.
% 0.72/1.12 substitution0:
% 0.72/1.12 X := X
% 0.72/1.12 Y := Y
% 0.72/1.12 Z := X
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 subsumption: (115) {G1,W11,D3,L3,V2,M3} F(31) { ! aScalar0( X ), ! aScalar0
% 0.72/1.12 ( Y ), sdtasdt0( X, Y ) = sdtasdt0( Y, X ) }.
% 0.72/1.12 parent0: (6369) {G0,W11,D3,L3,V2,M3} { ! aScalar0( X ), ! aScalar0( Y ),
% 0.72/1.12 sdtasdt0( X, Y ) = sdtasdt0( Y, X ) }.
% 0.72/1.12 substitution0:
% 0.72/1.12 X := X
% 0.72/1.12 Y := Y
% 0.72/1.12 end
% 0.72/1.12 permutation0:
% 0.72/1.12 0 ==> 0
% 0.72/1.12 1 ==> 1
% 0.72/1.12 2 ==> 2
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 resolution: (6371) {G1,W3,D3,L1,V0,M1} { aScalar0( smndt0( xS ) ) }.
% 0.72/1.12 parent0[0]: (11) {G0,W5,D3,L2,V1,M2} I { ! aScalar0( X ), aScalar0( smndt0
% 0.72/1.12 ( X ) ) }.
% 0.72/1.12 parent1[0]: (101) {G0,W2,D2,L1,V0,M1} I { aScalar0( xS ) }.
% 0.72/1.12 substitution0:
% 0.72/1.12 X := xS
% 0.72/1.12 end
% 0.72/1.12 substitution1:
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 subsumption: (406) {G1,W3,D3,L1,V0,M1} R(11,101) { aScalar0( smndt0( xS ) )
% 0.72/1.12 }.
% 0.72/1.12 parent0: (6371) {G1,W3,D3,L1,V0,M1} { aScalar0( smndt0( xS ) ) }.
% 0.72/1.12 substitution0:
% 0.72/1.12 end
% 0.72/1.12 permutation0:
% 0.72/1.12 0 ==> 0
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 eqswap: (6372) {G0,W13,D4,L3,V2,M3} { smndt0( sdtasdt0( X, Y ) ) ==>
% 0.72/1.12 sdtasdt0( X, smndt0( Y ) ), ! aScalar0( X ), ! aScalar0( Y ) }.
% 0.72/1.12 parent0[2]: (39) {G0,W13,D4,L3,V2,M3} I { ! aScalar0( X ), ! aScalar0( Y )
% 0.72/1.12 , sdtasdt0( X, smndt0( Y ) ) ==> smndt0( sdtasdt0( X, Y ) ) }.
% 0.72/1.12 substitution0:
% 0.72/1.12 X := X
% 0.72/1.12 Y := Y
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 resolution: (6374) {G1,W11,D4,L2,V1,M2} { smndt0( sdtasdt0( X, xS ) ) ==>
% 0.72/1.12 sdtasdt0( X, smndt0( xS ) ), ! aScalar0( X ) }.
% 0.72/1.12 parent0[2]: (6372) {G0,W13,D4,L3,V2,M3} { smndt0( sdtasdt0( X, Y ) ) ==>
% 0.72/1.12 sdtasdt0( X, smndt0( Y ) ), ! aScalar0( X ), ! aScalar0( Y ) }.
% 0.72/1.12 parent1[0]: (101) {G0,W2,D2,L1,V0,M1} I { aScalar0( xS ) }.
% 0.72/1.12 substitution0:
% 0.72/1.12 X := X
% 0.72/1.12 Y := xS
% 0.72/1.12 end
% 0.72/1.12 substitution1:
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 eqswap: (6375) {G1,W11,D4,L2,V1,M2} { sdtasdt0( X, smndt0( xS ) ) ==>
% 0.72/1.12 smndt0( sdtasdt0( X, xS ) ), ! aScalar0( X ) }.
% 0.72/1.12 parent0[0]: (6374) {G1,W11,D4,L2,V1,M2} { smndt0( sdtasdt0( X, xS ) ) ==>
% 0.72/1.12 sdtasdt0( X, smndt0( xS ) ), ! aScalar0( X ) }.
% 0.72/1.12 substitution0:
% 0.72/1.12 X := X
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 subsumption: (1261) {G1,W11,D4,L2,V1,M2} R(39,101) { ! aScalar0( X ),
% 0.72/1.12 sdtasdt0( X, smndt0( xS ) ) ==> smndt0( sdtasdt0( X, xS ) ) }.
% 0.72/1.12 parent0: (6375) {G1,W11,D4,L2,V1,M2} { sdtasdt0( X, smndt0( xS ) ) ==>
% 0.72/1.12 smndt0( sdtasdt0( X, xS ) ), ! aScalar0( X ) }.
% 0.72/1.12 substitution0:
% 0.72/1.12 X := X
% 0.72/1.12 end
% 0.72/1.12 permutation0:
% 0.72/1.12 0 ==> 1
% 0.72/1.12 1 ==> 0
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 eqswap: (6377) {G0,W7,D4,L1,V0,M1} { ! smndt0( xN ) ==> sdtasdt0( smndt0(
% 0.72/1.12 xS ), xR ) }.
% 0.72/1.12 parent0[0]: (107) {G0,W7,D4,L1,V0,M1} I { ! sdtasdt0( smndt0( xS ), xR )
% 0.72/1.12 ==> smndt0( xN ) }.
% 0.72/1.12 substitution0:
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 paramod: (6380) {G1,W12,D4,L3,V0,M3} { ! smndt0( xN ) ==> sdtasdt0( xR,
% 0.72/1.12 smndt0( xS ) ), ! aScalar0( smndt0( xS ) ), ! aScalar0( xR ) }.
% 0.72/1.12 parent0[2]: (115) {G1,W11,D3,L3,V2,M3} F(31) { ! aScalar0( X ), ! aScalar0
% 0.72/1.12 ( Y ), sdtasdt0( X, Y ) = sdtasdt0( Y, X ) }.
% 0.72/1.12 parent1[0; 4]: (6377) {G0,W7,D4,L1,V0,M1} { ! smndt0( xN ) ==> sdtasdt0(
% 0.72/1.12 smndt0( xS ), xR ) }.
% 0.72/1.12 substitution0:
% 0.72/1.12 X := smndt0( xS )
% 0.72/1.12 Y := xR
% 0.72/1.12 end
% 0.72/1.12 substitution1:
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 paramod: (6437) {G2,W14,D4,L4,V0,M4} { ! smndt0( xN ) ==> smndt0( sdtasdt0
% 0.72/1.12 ( xR, xS ) ), ! aScalar0( xR ), ! aScalar0( smndt0( xS ) ), ! aScalar0(
% 0.72/1.12 xR ) }.
% 0.72/1.12 parent0[1]: (1261) {G1,W11,D4,L2,V1,M2} R(39,101) { ! aScalar0( X ),
% 0.72/1.12 sdtasdt0( X, smndt0( xS ) ) ==> smndt0( sdtasdt0( X, xS ) ) }.
% 0.72/1.12 parent1[0; 4]: (6380) {G1,W12,D4,L3,V0,M3} { ! smndt0( xN ) ==> sdtasdt0(
% 0.72/1.12 xR, smndt0( xS ) ), ! aScalar0( smndt0( xS ) ), ! aScalar0( xR ) }.
% 0.72/1.12 substitution0:
% 0.72/1.12 X := xR
% 0.72/1.12 end
% 0.72/1.12 substitution1:
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 factor: (6438) {G2,W12,D4,L3,V0,M3} { ! smndt0( xN ) ==> smndt0( sdtasdt0
% 0.72/1.12 ( xR, xS ) ), ! aScalar0( xR ), ! aScalar0( smndt0( xS ) ) }.
% 0.72/1.12 parent0[1, 3]: (6437) {G2,W14,D4,L4,V0,M4} { ! smndt0( xN ) ==> smndt0(
% 0.72/1.12 sdtasdt0( xR, xS ) ), ! aScalar0( xR ), ! aScalar0( smndt0( xS ) ), !
% 0.72/1.12 aScalar0( xR ) }.
% 0.72/1.12 substitution0:
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 paramod: (6439) {G1,W10,D3,L3,V0,M3} { ! smndt0( xN ) ==> smndt0( xN ), !
% 0.72/1.12 aScalar0( xR ), ! aScalar0( smndt0( xS ) ) }.
% 0.72/1.12 parent0[0]: (104) {G0,W5,D3,L1,V0,M1} I { sdtasdt0( xR, xS ) ==> xN }.
% 0.72/1.12 parent1[0; 5]: (6438) {G2,W12,D4,L3,V0,M3} { ! smndt0( xN ) ==> smndt0(
% 0.72/1.12 sdtasdt0( xR, xS ) ), ! aScalar0( xR ), ! aScalar0( smndt0( xS ) ) }.
% 0.72/1.12 substitution0:
% 0.72/1.12 end
% 0.72/1.12 substitution1:
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 eqrefl: (6440) {G0,W5,D3,L2,V0,M2} { ! aScalar0( xR ), ! aScalar0( smndt0
% 0.72/1.12 ( xS ) ) }.
% 0.72/1.12 parent0[0]: (6439) {G1,W10,D3,L3,V0,M3} { ! smndt0( xN ) ==> smndt0( xN )
% 0.72/1.12 , ! aScalar0( xR ), ! aScalar0( smndt0( xS ) ) }.
% 0.72/1.12 substitution0:
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 resolution: (6441) {G1,W2,D2,L1,V0,M1} { ! aScalar0( xR ) }.
% 0.72/1.12 parent0[1]: (6440) {G0,W5,D3,L2,V0,M2} { ! aScalar0( xR ), ! aScalar0(
% 0.72/1.12 smndt0( xS ) ) }.
% 0.72/1.12 parent1[0]: (406) {G1,W3,D3,L1,V0,M1} R(11,101) { aScalar0( smndt0( xS ) )
% 0.72/1.12 }.
% 0.72/1.12 substitution0:
% 0.72/1.12 end
% 0.72/1.12 substitution1:
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 subsumption: (5087) {G2,W2,D2,L1,V0,M1} P(115,107);d(1261);d(104);q;r(406)
% 0.72/1.12 { ! aScalar0( xR ) }.
% 0.72/1.12 parent0: (6441) {G1,W2,D2,L1,V0,M1} { ! aScalar0( xR ) }.
% 0.72/1.12 substitution0:
% 0.72/1.12 end
% 0.72/1.12 permutation0:
% 0.72/1.12 0 ==> 0
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 resolution: (6442) {G1,W0,D0,L0,V0,M0} { }.
% 0.72/1.12 parent0[0]: (5087) {G2,W2,D2,L1,V0,M1} P(115,107);d(1261);d(104);q;r(406)
% 0.72/1.12 { ! aScalar0( xR ) }.
% 0.72/1.12 parent1[0]: (97) {G0,W2,D2,L1,V0,M1} I { aScalar0( xR ) }.
% 0.72/1.12 substitution0:
% 0.72/1.12 end
% 0.72/1.12 substitution1:
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 subsumption: (5096) {G3,W0,D0,L0,V0,M0} S(5087);r(97) { }.
% 0.72/1.12 parent0: (6442) {G1,W0,D0,L0,V0,M0} { }.
% 0.72/1.12 substitution0:
% 0.72/1.12 end
% 0.72/1.12 permutation0:
% 0.72/1.12 end
% 0.72/1.12
% 0.72/1.12 Proof check complete!
% 0.72/1.12
% 0.72/1.12 Memory use:
% 0.72/1.12
% 0.72/1.12 space for terms: 86555
% 0.72/1.12 space for clauses: 296274
% 0.72/1.12
% 0.72/1.12
% 0.72/1.12 clauses generated: 18026
% 0.72/1.12 clauses kept: 5097
% 0.72/1.12 clauses selected: 436
% 0.72/1.12 clauses deleted: 17
% 0.72/1.12 clauses inuse deleted: 11
% 0.72/1.12
% 0.72/1.12 subsentry: 49633
% 0.72/1.12 literals s-matched: 24005
% 0.72/1.12 literals matched: 19312
% 0.72/1.12 full subsumption: 10772
% 0.72/1.12
% 0.72/1.12 checksum: 608221200
% 0.72/1.12
% 0.72/1.12
% 0.72/1.12 Bliksem ended
%------------------------------------------------------------------------------