%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : NUM491+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n007.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 06:22:50 EDT 2022
% Result : Theorem 2.13s 2.56s
% Output : Refutation 2.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM491+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Wed Jul 6 19:42:13 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.75/1.16 *** allocated 10000 integers for termspace/termends
% 0.75/1.16 *** allocated 10000 integers for clauses
% 0.75/1.16 *** allocated 10000 integers for justifications
% 0.75/1.16 Bliksem 1.12
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 Automatic Strategy Selection
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 Clauses:
% 0.75/1.16
% 0.75/1.16 { && }.
% 0.75/1.16 { aNaturalNumber0( sz00 ) }.
% 0.75/1.16 { aNaturalNumber0( sz10 ) }.
% 0.75/1.16 { ! sz10 = sz00 }.
% 0.75/1.16 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), aNaturalNumber0( sdtpldt0
% 0.75/1.16 ( X, Y ) ) }.
% 0.75/1.16 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), aNaturalNumber0( sdtasdt0
% 0.75/1.16 ( X, Y ) ) }.
% 0.75/1.16 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), sdtpldt0( X, Y ) =
% 0.75/1.16 sdtpldt0( Y, X ) }.
% 0.75/1.16 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! aNaturalNumber0( Z ),
% 0.75/1.16 sdtpldt0( sdtpldt0( X, Y ), Z ) = sdtpldt0( X, sdtpldt0( Y, Z ) ) }.
% 0.75/1.16 { ! aNaturalNumber0( X ), sdtpldt0( X, sz00 ) = X }.
% 0.75/1.16 { ! aNaturalNumber0( X ), X = sdtpldt0( sz00, X ) }.
% 0.75/1.16 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), sdtasdt0( X, Y ) =
% 0.75/1.16 sdtasdt0( Y, X ) }.
% 0.75/1.16 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! aNaturalNumber0( Z ),
% 0.75/1.16 sdtasdt0( sdtasdt0( X, Y ), Z ) = sdtasdt0( X, sdtasdt0( Y, Z ) ) }.
% 0.75/1.16 { ! aNaturalNumber0( X ), sdtasdt0( X, sz10 ) = X }.
% 0.75/1.16 { ! aNaturalNumber0( X ), X = sdtasdt0( sz10, X ) }.
% 0.75/1.16 { ! aNaturalNumber0( X ), sdtasdt0( X, sz00 ) = sz00 }.
% 0.75/1.16 { ! aNaturalNumber0( X ), sz00 = sdtasdt0( sz00, X ) }.
% 0.75/1.16 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! aNaturalNumber0( Z ),
% 0.75/1.16 sdtasdt0( X, sdtpldt0( Y, Z ) ) = sdtpldt0( sdtasdt0( X, Y ), sdtasdt0( X
% 0.75/1.16 , Z ) ) }.
% 0.75/1.16 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! aNaturalNumber0( Z ),
% 0.75/1.16 sdtasdt0( sdtpldt0( Y, Z ), X ) = sdtpldt0( sdtasdt0( Y, X ), sdtasdt0( Z
% 0.75/1.16 , X ) ) }.
% 0.75/1.16 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! aNaturalNumber0( Z ), !
% 0.75/1.16 sdtpldt0( X, Y ) = sdtpldt0( X, Z ), Y = Z }.
% 0.75/1.16 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! aNaturalNumber0( Z ), !
% 0.75/1.16 sdtpldt0( Y, X ) = sdtpldt0( Z, X ), Y = Z }.
% 0.75/1.16 { ! aNaturalNumber0( X ), X = sz00, ! aNaturalNumber0( Y ), !
% 0.75/1.16 aNaturalNumber0( Z ), ! sdtasdt0( X, Y ) = sdtasdt0( X, Z ), Y = Z }.
% 0.75/1.16 { ! aNaturalNumber0( X ), X = sz00, ! aNaturalNumber0( Y ), !
% 0.75/1.16 aNaturalNumber0( Z ), ! sdtasdt0( Y, X ) = sdtasdt0( Z, X ), Y = Z }.
% 0.75/1.16 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! sdtpldt0( X, Y ) = sz00
% 0.75/1.16 , X = sz00 }.
% 0.75/1.16 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! sdtpldt0( X, Y ) = sz00
% 0.75/1.16 , Y = sz00 }.
% 0.75/1.16 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! sdtasdt0( X, Y ) = sz00
% 0.75/1.16 , X = sz00, Y = sz00 }.
% 0.75/1.16 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! sdtlseqdt0( X, Y ),
% 0.75/1.16 aNaturalNumber0( skol1( Z, T ) ) }.
% 0.75/1.16 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! sdtlseqdt0( X, Y ),
% 0.75/1.16 sdtpldt0( X, skol1( X, Y ) ) = Y }.
% 0.75/1.16 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! aNaturalNumber0( Z ), !
% 0.75/1.16 sdtpldt0( X, Z ) = Y, sdtlseqdt0( X, Y ) }.
% 0.75/1.16 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! sdtlseqdt0( X, Y ), ! Z
% 0.75/1.16 = sdtmndt0( Y, X ), aNaturalNumber0( Z ) }.
% 0.75/1.16 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! sdtlseqdt0( X, Y ), ! Z
% 0.75/1.16 = sdtmndt0( Y, X ), sdtpldt0( X, Z ) = Y }.
% 0.75/1.16 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! sdtlseqdt0( X, Y ), !
% 0.75/1.16 aNaturalNumber0( Z ), ! sdtpldt0( X, Z ) = Y, Z = sdtmndt0( Y, X ) }.
% 0.75/1.16 { ! aNaturalNumber0( X ), sdtlseqdt0( X, X ) }.
% 0.75/1.16 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! sdtlseqdt0( X, Y ), !
% 0.75/1.16 sdtlseqdt0( Y, X ), X = Y }.
% 0.75/1.16 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! aNaturalNumber0( Z ), !
% 0.75/1.16 sdtlseqdt0( X, Y ), ! sdtlseqdt0( Y, Z ), sdtlseqdt0( X, Z ) }.
% 0.75/1.16 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), sdtlseqdt0( X, Y ), ! Y =
% 0.75/1.16 X }.
% 0.75/1.16 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), sdtlseqdt0( X, Y ),
% 0.75/1.16 sdtlseqdt0( Y, X ) }.
% 0.75/1.16 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), X = Y, ! sdtlseqdt0( X, Y
% 0.75/1.16 ), ! aNaturalNumber0( Z ), alpha5( X, Y, Z ) }.
% 0.75/1.16 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), X = Y, ! sdtlseqdt0( X, Y
% 0.75/1.16 ), ! aNaturalNumber0( Z ), sdtlseqdt0( sdtpldt0( X, Z ), sdtpldt0( Y, Z
% 0.75/1.16 ) ) }.
% 0.75/1.16 { ! alpha5( X, Y, Z ), ! sdtpldt0( Z, X ) = sdtpldt0( Z, Y ) }.
% 0.75/1.16 { ! alpha5( X, Y, Z ), sdtlseqdt0( sdtpldt0( Z, X ), sdtpldt0( Z, Y ) ) }.
% 0.75/1.16 { ! alpha5( X, Y, Z ), ! sdtpldt0( X, Z ) = sdtpldt0( Y, Z ) }.
% 2.02/2.47 { sdtpldt0( Z, X ) = sdtpldt0( Z, Y ), ! sdtlseqdt0( sdtpldt0( Z, X ),
% 2.02/2.47 sdtpldt0( Z, Y ) ), sdtpldt0( X, Z ) = sdtpldt0( Y, Z ), alpha5( X, Y, Z
% 2.02/2.47 ) }.
% 2.02/2.47 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! aNaturalNumber0( Z ), X
% 2.02/2.47 = sz00, Y = Z, ! sdtlseqdt0( Y, Z ), alpha6( X, Y, Z ) }.
% 2.02/2.47 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! aNaturalNumber0( Z ), X
% 2.02/2.47 = sz00, Y = Z, ! sdtlseqdt0( Y, Z ), sdtlseqdt0( sdtasdt0( Y, X ),
% 2.02/2.47 sdtasdt0( Z, X ) ) }.
% 2.02/2.47 { ! alpha6( X, Y, Z ), ! sdtasdt0( X, Y ) = sdtasdt0( X, Z ) }.
% 2.02/2.47 { ! alpha6( X, Y, Z ), sdtlseqdt0( sdtasdt0( X, Y ), sdtasdt0( X, Z ) ) }.
% 2.02/2.47 { ! alpha6( X, Y, Z ), ! sdtasdt0( Y, X ) = sdtasdt0( Z, X ) }.
% 2.02/2.47 { sdtasdt0( X, Y ) = sdtasdt0( X, Z ), ! sdtlseqdt0( sdtasdt0( X, Y ),
% 2.02/2.47 sdtasdt0( X, Z ) ), sdtasdt0( Y, X ) = sdtasdt0( Z, X ), alpha6( X, Y, Z
% 2.02/2.47 ) }.
% 2.02/2.47 { ! aNaturalNumber0( X ), X = sz00, X = sz10, ! sz10 = X }.
% 2.02/2.47 { ! aNaturalNumber0( X ), X = sz00, X = sz10, sdtlseqdt0( sz10, X ) }.
% 2.02/2.47 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), X = sz00, sdtlseqdt0( Y,
% 2.02/2.47 sdtasdt0( Y, X ) ) }.
% 2.02/2.47 { && }.
% 2.02/2.47 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), X = Y, ! sdtlseqdt0( X, Y
% 2.02/2.47 ), iLess0( X, Y ) }.
% 2.02/2.47 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! doDivides0( X, Y ),
% 2.02/2.47 aNaturalNumber0( skol2( Z, T ) ) }.
% 2.02/2.47 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! doDivides0( X, Y ), Y =
% 2.02/2.47 sdtasdt0( X, skol2( X, Y ) ) }.
% 2.02/2.47 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! aNaturalNumber0( Z ), !
% 2.02/2.47 Y = sdtasdt0( X, Z ), doDivides0( X, Y ) }.
% 2.02/2.47 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), X = sz00, ! doDivides0( X
% 2.02/2.47 , Y ), ! Z = sdtsldt0( Y, X ), aNaturalNumber0( Z ) }.
% 2.02/2.47 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), X = sz00, ! doDivides0( X
% 2.02/2.47 , Y ), ! Z = sdtsldt0( Y, X ), Y = sdtasdt0( X, Z ) }.
% 2.02/2.47 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), X = sz00, ! doDivides0( X
% 2.02/2.47 , Y ), ! aNaturalNumber0( Z ), ! Y = sdtasdt0( X, Z ), Z = sdtsldt0( Y, X
% 2.02/2.47 ) }.
% 2.02/2.47 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! aNaturalNumber0( Z ), !
% 2.02/2.47 doDivides0( X, Y ), ! doDivides0( Y, Z ), doDivides0( X, Z ) }.
% 2.02/2.47 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! aNaturalNumber0( Z ), !
% 2.02/2.47 doDivides0( X, Y ), ! doDivides0( X, Z ), doDivides0( X, sdtpldt0( Y, Z
% 2.02/2.47 ) ) }.
% 2.02/2.47 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! aNaturalNumber0( Z ), !
% 2.02/2.47 doDivides0( X, Y ), ! doDivides0( X, sdtpldt0( Y, Z ) ), doDivides0( X,
% 2.02/2.47 Z ) }.
% 2.02/2.47 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! doDivides0( X, Y ), Y =
% 2.02/2.47 sz00, sdtlseqdt0( X, Y ) }.
% 2.02/2.47 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), X = sz00, ! doDivides0( X
% 2.02/2.47 , Y ), ! aNaturalNumber0( Z ), sdtasdt0( Z, sdtsldt0( Y, X ) ) = sdtsldt0
% 2.02/2.47 ( sdtasdt0( Z, Y ), X ) }.
% 2.02/2.47 { ! aNaturalNumber0( X ), ! isPrime0( X ), ! X = sz00 }.
% 2.02/2.47 { ! aNaturalNumber0( X ), ! isPrime0( X ), alpha1( X ) }.
% 2.02/2.47 { ! aNaturalNumber0( X ), X = sz00, ! alpha1( X ), isPrime0( X ) }.
% 2.02/2.47 { ! alpha1( X ), ! X = sz10 }.
% 2.02/2.47 { ! alpha1( X ), alpha2( X ) }.
% 2.02/2.47 { X = sz10, ! alpha2( X ), alpha1( X ) }.
% 2.02/2.47 { ! alpha2( X ), ! alpha3( X, Y ), alpha4( X, Y ) }.
% 2.02/2.47 { alpha3( X, skol3( X ) ), alpha2( X ) }.
% 2.02/2.47 { ! alpha4( X, skol3( X ) ), alpha2( X ) }.
% 2.02/2.47 { ! alpha4( X, Y ), Y = sz10, Y = X }.
% 2.02/2.47 { ! Y = sz10, alpha4( X, Y ) }.
% 2.02/2.47 { ! Y = X, alpha4( X, Y ) }.
% 2.02/2.47 { ! alpha3( X, Y ), aNaturalNumber0( Y ) }.
% 2.02/2.47 { ! alpha3( X, Y ), doDivides0( Y, X ) }.
% 2.02/2.47 { ! aNaturalNumber0( Y ), ! doDivides0( Y, X ), alpha3( X, Y ) }.
% 2.02/2.47 { ! aNaturalNumber0( X ), X = sz00, X = sz10, aNaturalNumber0( skol4( Y ) )
% 2.02/2.47 }.
% 2.02/2.47 { ! aNaturalNumber0( X ), X = sz00, X = sz10, isPrime0( skol4( Y ) ) }.
% 2.02/2.47 { ! aNaturalNumber0( X ), X = sz00, X = sz10, doDivides0( skol4( X ), X ) }
% 2.02/2.47 .
% 2.02/2.47 { aNaturalNumber0( xn ) }.
% 2.02/2.47 { aNaturalNumber0( xm ) }.
% 2.02/2.47 { aNaturalNumber0( xp ) }.
% 2.02/2.47 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! aNaturalNumber0( Z ), !
% 2.02/2.47 isPrime0( Z ), ! doDivides0( Z, sdtasdt0( X, Y ) ), ! iLess0( sdtpldt0(
% 2.02/2.47 sdtpldt0( X, Y ), Z ), sdtpldt0( sdtpldt0( xn, xm ), xp ) ), doDivides0(
% 2.02/2.47 Z, X ), doDivides0( Z, Y ) }.
% 2.02/2.47 { isPrime0( xp ) }.
% 2.02/2.47 { doDivides0( xp, sdtasdt0( xn, xm ) ) }.
% 2.02/2.47 { sdtlseqdt0( xp, xn ) }.
% 2.02/2.47 { xr = sdtmndt0( xn, xp ) }.
% 2.02/2.47 { ! xr = xn }.
% 2.02/2.47 { sdtlseqdt0( xr, xn ) }.
% 2.13/2.56 { xn = sdtpldt0( xp, xr ) }.
% 2.13/2.56 { sdtasdt0( xn, xm ) = sdtpldt0( sdtasdt0( xp, xm ), sdtasdt0( xr, xm ) ) }
% 2.13/2.56 .
% 2.13/2.56 { sdtasdt0( xr, xm ) = sdtmndt0( sdtasdt0( xn, xm ), sdtasdt0( xp, xm ) ) }
% 2.13/2.56 .
% 2.13/2.56 { ! doDivides0( xp, sdtasdt0( xp, xm ) ) }.
% 2.13/2.56
% 2.13/2.56 percentage equality = 0.283951, percentage horn = 0.715789
% 2.13/2.56 This is a problem with some equality
% 2.13/2.56
% 2.13/2.56
% 2.13/2.56
% 2.13/2.56 Options Used:
% 2.13/2.56
% 2.13/2.56 useres = 1
% 2.13/2.56 useparamod = 1
% 2.13/2.56 useeqrefl = 1
% 2.13/2.56 useeqfact = 1
% 2.13/2.56 usefactor = 1
% 2.13/2.56 usesimpsplitting = 0
% 2.13/2.56 usesimpdemod = 5
% 2.13/2.56 usesimpres = 3
% 2.13/2.56
% 2.13/2.56 resimpinuse = 1000
% 2.13/2.56 resimpclauses = 20000
% 2.13/2.56 substype = eqrewr
% 2.13/2.56 backwardsubs = 1
% 2.13/2.56 selectoldest = 5
% 2.13/2.56
% 2.13/2.56 litorderings [0] = split
% 2.13/2.56 litorderings [1] = extend the termordering, first sorting on arguments
% 2.13/2.56
% 2.13/2.56 termordering = kbo
% 2.13/2.56
% 2.13/2.56 litapriori = 0
% 2.13/2.56 termapriori = 1
% 2.13/2.56 litaposteriori = 0
% 2.13/2.56 termaposteriori = 0
% 2.13/2.56 demodaposteriori = 0
% 2.13/2.56 ordereqreflfact = 0
% 2.13/2.56
% 2.13/2.56 litselect = negord
% 2.13/2.56
% 2.13/2.56 maxweight = 15
% 2.13/2.56 maxdepth = 30000
% 2.13/2.56 maxlength = 115
% 2.13/2.56 maxnrvars = 195
% 2.13/2.56 excuselevel = 1
% 2.13/2.56 increasemaxweight = 1
% 2.13/2.56
% 2.13/2.56 maxselected = 10000000
% 2.13/2.56 maxnrclauses = 10000000
% 2.13/2.56
% 2.13/2.56 showgenerated = 0
% 2.13/2.56 showkept = 0
% 2.13/2.56 showselected = 0
% 2.13/2.56 showdeleted = 0
% 2.13/2.56 showresimp = 1
% 2.13/2.56 showstatus = 2000
% 2.13/2.56
% 2.13/2.56 prologoutput = 0
% 2.13/2.56 nrgoals = 5000000
% 2.13/2.56 totalproof = 1
% 2.13/2.56
% 2.13/2.56 Symbols occurring in the translation:
% 2.13/2.56
% 2.13/2.56 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 2.13/2.56 . [1, 2] (w:1, o:26, a:1, s:1, b:0),
% 2.13/2.56 && [3, 0] (w:1, o:4, a:1, s:1, b:0),
% 2.13/2.56 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 2.13/2.56 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.13/2.56 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.13/2.56 aNaturalNumber0 [36, 1] (w:1, o:20, a:1, s:1, b:0),
% 2.13/2.56 sz00 [37, 0] (w:1, o:7, a:1, s:1, b:0),
% 2.13/2.56 sz10 [38, 0] (w:1, o:8, a:1, s:1, b:0),
% 2.13/2.56 sdtpldt0 [40, 2] (w:1, o:50, a:1, s:1, b:0),
% 2.13/2.56 sdtasdt0 [41, 2] (w:1, o:51, a:1, s:1, b:0),
% 2.13/2.56 sdtlseqdt0 [43, 2] (w:1, o:52, a:1, s:1, b:0),
% 2.13/2.56 sdtmndt0 [44, 2] (w:1, o:53, a:1, s:1, b:0),
% 2.13/2.56 iLess0 [45, 2] (w:1, o:54, a:1, s:1, b:0),
% 2.13/2.56 doDivides0 [46, 2] (w:1, o:55, a:1, s:1, b:0),
% 2.13/2.56 sdtsldt0 [47, 2] (w:1, o:56, a:1, s:1, b:0),
% 2.13/2.56 isPrime0 [48, 1] (w:1, o:21, a:1, s:1, b:0),
% 2.13/2.56 xn [49, 0] (w:1, o:12, a:1, s:1, b:0),
% 2.13/2.56 xm [50, 0] (w:1, o:11, a:1, s:1, b:0),
% 2.13/2.56 xp [51, 0] (w:1, o:13, a:1, s:1, b:0),
% 2.13/2.56 xr [52, 0] (w:1, o:14, a:1, s:1, b:0),
% 2.13/2.56 alpha1 [53, 1] (w:1, o:22, a:1, s:1, b:1),
% 2.13/2.56 alpha2 [54, 1] (w:1, o:23, a:1, s:1, b:1),
% 2.13/2.56 alpha3 [55, 2] (w:1, o:57, a:1, s:1, b:1),
% 2.13/2.56 alpha4 [56, 2] (w:1, o:58, a:1, s:1, b:1),
% 2.13/2.56 alpha5 [57, 3] (w:1, o:61, a:1, s:1, b:1),
% 2.13/2.56 alpha6 [58, 3] (w:1, o:62, a:1, s:1, b:1),
% 2.13/2.56 skol1 [59, 2] (w:1, o:59, a:1, s:1, b:1),
% 2.13/2.56 skol2 [60, 2] (w:1, o:60, a:1, s:1, b:1),
% 2.13/2.56 skol3 [61, 1] (w:1, o:24, a:1, s:1, b:1),
% 2.13/2.56 skol4 [62, 1] (w:1, o:25, a:1, s:1, b:1).
% 2.13/2.56
% 2.13/2.56
% 2.13/2.56 Starting Search:
% 2.13/2.56
% 2.13/2.56 *** allocated 15000 integers for clauses
% 2.13/2.56 *** allocated 22500 integers for clauses
% 2.13/2.56 *** allocated 33750 integers for clauses
% 2.13/2.56 *** allocated 15000 integers for termspace/termends
% 2.13/2.56 *** allocated 50625 integers for clauses
% 2.13/2.56 *** allocated 22500 integers for termspace/termends
% 2.13/2.56 *** allocated 75937 integers for clauses
% 2.13/2.56 Resimplifying inuse:
% 2.13/2.56 Done
% 2.13/2.56
% 2.13/2.56 *** allocated 33750 integers for termspace/termends
% 2.13/2.56 *** allocated 113905 integers for clauses
% 2.13/2.56 *** allocated 50625 integers for termspace/termends
% 2.13/2.56
% 2.13/2.56 Intermediate Status:
% 2.13/2.56 Generated: 13211
% 2.13/2.56 Kept: 2156
% 2.13/2.56 Inuse: 137
% 2.13/2.56 Deleted: 4
% 2.13/2.56 Deletedinuse: 0
% 2.13/2.56
% 2.13/2.56 Resimplifying inuse:
% 2.13/2.56 Done
% 2.13/2.56
% 2.13/2.56 *** allocated 170857 integers for clauses
% 2.13/2.56 *** allocated 75937 integers for termspace/termends
% 2.13/2.56 Resimplifying inuse:
% 2.13/2.56 Done
% 2.13/2.56
% 2.13/2.56 *** allocated 256285 integers for clauses
% 2.13/2.56 *** allocated 113905 integers for termspace/termends
% 2.13/2.56
% 2.13/2.56 Intermediate Status:
% 2.13/2.56 Generated: 26820
% 2.13/2.56 Kept: 4169
% 2.13/2.56 Inuse: 191
% 2.13/2.56 Deleted: 22
% 2.13/2.56 Deletedinuse: 14
% 2.13/2.56
% 2.13/2.56 Resimplifying inuse:
% 2.13/2.56 Done
% 2.13/2.56
% 2.13/2.56 Resimplifying inuse:
% 2.13/2.56 Done
% 2.13/2.56
% 2.13/2.56 *** allocated 170857 integers for termspace/termends
% 2.13/2.56 *** allocated 384427 integers for clauses
% 2.13/2.56
% 2.13/2.56 Intermediate Status:
% 2.13/2.56 Generated: 48379
% 2.13/2.56 Kept: 6600
% 2.13/2.56 Inuse: 232
% 2.13/2.56 Deleted: 28
% 2.13/2.56 Deletedinuse: 14
% 2.13/2.56
% 2.13/2.56 Resimplifying inuse:
% 2.13/2.56 Done
% 2.13/2.56
% 2.13/2.56
% 2.13/2.56 Bliksems!, er is een bewijs:
% 2.13/2.56 % SZS status Theorem
% 2.13/2.56 % SZS output start Refutation
% 2.13/2.56
% 2.13/2.56 (5) {G0,W8,D3,L3,V2,M3} I { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y )
% 2.13/2.56 , aNaturalNumber0( sdtasdt0( X, Y ) ) }.
% 2.13/2.56 (54) {G0,W14,D3,L5,V3,M5} I { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 2.13/2.56 ), ! aNaturalNumber0( Z ), ! Y = sdtasdt0( X, Z ), doDivides0( X, Y )
% 2.13/2.56 }.
% 2.13/2.56 (82) {G0,W2,D2,L1,V0,M1} I { aNaturalNumber0( xm ) }.
% 2.13/2.56 (83) {G0,W2,D2,L1,V0,M1} I { aNaturalNumber0( xp ) }.
% 2.13/2.56 (94) {G0,W5,D3,L1,V0,M1} I { ! doDivides0( xp, sdtasdt0( xp, xm ) ) }.
% 2.13/2.56 (258) {G1,W6,D3,L2,V1,M2} R(5,83) { ! aNaturalNumber0( X ), aNaturalNumber0
% 2.13/2.56 ( sdtasdt0( xp, X ) ) }.
% 2.13/2.56 (7119) {G1,W13,D3,L3,V1,M3} R(54,94);r(83) { ! aNaturalNumber0( sdtasdt0(
% 2.13/2.56 xp, xm ) ), ! aNaturalNumber0( X ), ! sdtasdt0( xp, xm ) = sdtasdt0( xp,
% 2.13/2.56 X ) }.
% 2.13/2.56 (7221) {G2,W2,D2,L1,V0,M1} Q(7119);r(258) { ! aNaturalNumber0( xm ) }.
% 2.13/2.56 (7257) {G3,W0,D0,L0,V0,M0} S(7221);r(82) { }.
% 2.13/2.56
% 2.13/2.56
% 2.13/2.56 % SZS output end Refutation
% 2.13/2.56 found a proof!
% 2.13/2.56
% 2.13/2.56
% 2.13/2.56 Unprocessed initial clauses:
% 2.13/2.56
% 2.13/2.56 (7259) {G0,W1,D1,L1,V0,M1} { && }.
% 2.13/2.56 (7260) {G0,W2,D2,L1,V0,M1} { aNaturalNumber0( sz00 ) }.
% 2.13/2.56 (7261) {G0,W2,D2,L1,V0,M1} { aNaturalNumber0( sz10 ) }.
% 2.13/2.56 (7262) {G0,W3,D2,L1,V0,M1} { ! sz10 = sz00 }.
% 2.13/2.56 (7263) {G0,W8,D3,L3,V2,M3} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 2.13/2.56 ), aNaturalNumber0( sdtpldt0( X, Y ) ) }.
% 2.13/2.56 (7264) {G0,W8,D3,L3,V2,M3} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 2.13/2.56 ), aNaturalNumber0( sdtasdt0( X, Y ) ) }.
% 2.13/2.56 (7265) {G0,W11,D3,L3,V2,M3} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 2.13/2.56 ), sdtpldt0( X, Y ) = sdtpldt0( Y, X ) }.
% 2.13/2.56 (7266) {G0,W17,D4,L4,V3,M4} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 2.13/2.56 ), ! aNaturalNumber0( Z ), sdtpldt0( sdtpldt0( X, Y ), Z ) = sdtpldt0( X
% 2.13/2.56 , sdtpldt0( Y, Z ) ) }.
% 2.13/2.56 (7267) {G0,W7,D3,L2,V1,M2} { ! aNaturalNumber0( X ), sdtpldt0( X, sz00 ) =
% 2.13/2.56 X }.
% 2.13/2.56 (7268) {G0,W7,D3,L2,V1,M2} { ! aNaturalNumber0( X ), X = sdtpldt0( sz00, X
% 2.13/2.56 ) }.
% 2.13/2.56 (7269) {G0,W11,D3,L3,V2,M3} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 2.13/2.56 ), sdtasdt0( X, Y ) = sdtasdt0( Y, X ) }.
% 2.13/2.56 (7270) {G0,W17,D4,L4,V3,M4} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 2.13/2.56 ), ! aNaturalNumber0( Z ), sdtasdt0( sdtasdt0( X, Y ), Z ) = sdtasdt0( X
% 2.13/2.56 , sdtasdt0( Y, Z ) ) }.
% 2.13/2.56 (7271) {G0,W7,D3,L2,V1,M2} { ! aNaturalNumber0( X ), sdtasdt0( X, sz10 ) =
% 2.13/2.56 X }.
% 2.13/2.56 (7272) {G0,W7,D3,L2,V1,M2} { ! aNaturalNumber0( X ), X = sdtasdt0( sz10, X
% 2.13/2.56 ) }.
% 2.13/2.56 (7273) {G0,W7,D3,L2,V1,M2} { ! aNaturalNumber0( X ), sdtasdt0( X, sz00 ) =
% 2.13/2.56 sz00 }.
% 2.13/2.56 (7274) {G0,W7,D3,L2,V1,M2} { ! aNaturalNumber0( X ), sz00 = sdtasdt0( sz00
% 2.13/2.56 , X ) }.
% 2.13/2.56 (7275) {G0,W19,D4,L4,V3,M4} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 2.13/2.56 ), ! aNaturalNumber0( Z ), sdtasdt0( X, sdtpldt0( Y, Z ) ) = sdtpldt0(
% 2.13/2.56 sdtasdt0( X, Y ), sdtasdt0( X, Z ) ) }.
% 2.13/2.56 (7276) {G0,W19,D4,L4,V3,M4} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 2.13/2.56 ), ! aNaturalNumber0( Z ), sdtasdt0( sdtpldt0( Y, Z ), X ) = sdtpldt0(
% 2.13/2.56 sdtasdt0( Y, X ), sdtasdt0( Z, X ) ) }.
% 2.13/2.56 (7277) {G0,W16,D3,L5,V3,M5} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 2.13/2.56 ), ! aNaturalNumber0( Z ), ! sdtpldt0( X, Y ) = sdtpldt0( X, Z ), Y = Z
% 2.13/2.56 }.
% 2.13/2.56 (7278) {G0,W16,D3,L5,V3,M5} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 2.13/2.56 ), ! aNaturalNumber0( Z ), ! sdtpldt0( Y, X ) = sdtpldt0( Z, X ), Y = Z
% 2.13/2.56 }.
% 2.13/2.56 (7279) {G0,W19,D3,L6,V3,M6} { ! aNaturalNumber0( X ), X = sz00, !
% 2.13/2.56 aNaturalNumber0( Y ), ! aNaturalNumber0( Z ), ! sdtasdt0( X, Y ) =
% 2.13/2.56 sdtasdt0( X, Z ), Y = Z }.
% 2.13/2.56 (7280) {G0,W19,D3,L6,V3,M6} { ! aNaturalNumber0( X ), X = sz00, !
% 2.13/2.56 aNaturalNumber0( Y ), ! aNaturalNumber0( Z ), ! sdtasdt0( Y, X ) =
% 2.13/2.56 sdtasdt0( Z, X ), Y = Z }.
% 2.13/2.56 (7281) {G0,W12,D3,L4,V2,M4} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 2.13/2.56 ), ! sdtpldt0( X, Y ) = sz00, X = sz00 }.
% 2.13/2.56 (7282) {G0,W12,D3,L4,V2,M4} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 2.13/2.56 ), ! sdtpldt0( X, Y ) = sz00, Y = sz00 }.
% 2.13/2.56 (7283) {G0,W15,D3,L5,V2,M5} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 2.13/2.56 ), ! sdtasdt0( X, Y ) = sz00, X = sz00, Y = sz00 }.
% 2.13/2.56 (7284) {G0,W11,D3,L4,V4,M4} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 2.13/2.56 ), ! sdtlseqdt0( X, Y ), aNaturalNumber0( skol1( Z, T ) ) }.
% 2.13/2.56 (7285) {G0,W14,D4,L4,V2,M4} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 2.13/2.56 ), ! sdtlseqdt0( X, Y ), sdtpldt0( X, skol1( X, Y ) ) = Y }.
% 2.13/2.56 (7286) {G0,W14,D3,L5,V3,M5} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 2.13/2.56 ), ! aNaturalNumber0( Z ), ! sdtpldt0( X, Z ) = Y, sdtlseqdt0( X, Y )
% 2.13/2.56 }.
% 2.13/2.56 (7287) {G0,W14,D3,L5,V3,M5} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 2.13/2.56 ), ! sdtlseqdt0( X, Y ), ! Z = sdtmndt0( Y, X ), aNaturalNumber0( Z )
% 2.13/2.56 }.
% 2.13/2.56 (7288) {G0,W17,D3,L5,V3,M5} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 2.13/2.56 ), ! sdtlseqdt0( X, Y ), ! Z = sdtmndt0( Y, X ), sdtpldt0( X, Z ) = Y
% 2.13/2.56 }.
% 2.13/2.56 (7289) {G0,W19,D3,L6,V3,M6} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 2.13/2.56 ), ! sdtlseqdt0( X, Y ), ! aNaturalNumber0( Z ), ! sdtpldt0( X, Z ) = Y
% 2.13/2.56 , Z = sdtmndt0( Y, X ) }.
% 2.13/2.56 (7290) {G0,W5,D2,L2,V1,M2} { ! aNaturalNumber0( X ), sdtlseqdt0( X, X )
% 2.13/2.56 }.
% 2.13/2.56 (7291) {G0,W13,D2,L5,V2,M5} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 2.13/2.56 ), ! sdtlseqdt0( X, Y ), ! sdtlseqdt0( Y, X ), X = Y }.
% 2.13/2.56 (7292) {G0,W15,D2,L6,V3,M6} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 2.13/2.56 ), ! aNaturalNumber0( Z ), ! sdtlseqdt0( X, Y ), ! sdtlseqdt0( Y, Z ),
% 2.13/2.56 sdtlseqdt0( X, Z ) }.
% 2.13/2.56 (7293) {G0,W10,D2,L4,V2,M4} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 2.13/2.56 ), sdtlseqdt0( X, Y ), ! Y = X }.
% 2.13/2.56 (7294) {G0,W10,D2,L4,V2,M4} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 2.13/2.56 ), sdtlseqdt0( X, Y ), sdtlseqdt0( Y, X ) }.
% 2.13/2.56 (7295) {G0,W16,D2,L6,V3,M6} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 2.13/2.56 ), X = Y, ! sdtlseqdt0( X, Y ), ! aNaturalNumber0( Z ), alpha5( X, Y, Z
% 2.13/2.56 ) }.
% 2.13/2.56 (7296) {G0,W19,D3,L6,V3,M6} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 2.13/2.56 ), X = Y, ! sdtlseqdt0( X, Y ), ! aNaturalNumber0( Z ), sdtlseqdt0(
% 2.13/2.56 sdtpldt0( X, Z ), sdtpldt0( Y, Z ) ) }.
% 2.13/2.56 (7297) {G0,W11,D3,L2,V3,M2} { ! alpha5( X, Y, Z ), ! sdtpldt0( Z, X ) =
% 2.13/2.56 sdtpldt0( Z, Y ) }.
% 2.13/2.56 (7298) {G0,W11,D3,L2,V3,M2} { ! alpha5( X, Y, Z ), sdtlseqdt0( sdtpldt0( Z
% 2.13/2.56 , X ), sdtpldt0( Z, Y ) ) }.
% 2.13/2.56 (7299) {G0,W11,D3,L2,V3,M2} { ! alpha5( X, Y, Z ), ! sdtpldt0( X, Z ) =
% 2.13/2.56 sdtpldt0( Y, Z ) }.
% 2.13/2.56 (7300) {G0,W25,D3,L4,V3,M4} { sdtpldt0( Z, X ) = sdtpldt0( Z, Y ), !
% 2.13/2.56 sdtlseqdt0( sdtpldt0( Z, X ), sdtpldt0( Z, Y ) ), sdtpldt0( X, Z ) =
% 2.13/2.56 sdtpldt0( Y, Z ), alpha5( X, Y, Z ) }.
% 2.13/2.56 (7301) {G0,W19,D2,L7,V3,M7} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 2.13/2.56 ), ! aNaturalNumber0( Z ), X = sz00, Y = Z, ! sdtlseqdt0( Y, Z ), alpha6
% 2.13/2.56 ( X, Y, Z ) }.
% 2.13/2.56 (7302) {G0,W22,D3,L7,V3,M7} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 2.13/2.56 ), ! aNaturalNumber0( Z ), X = sz00, Y = Z, ! sdtlseqdt0( Y, Z ),
% 2.13/2.56 sdtlseqdt0( sdtasdt0( Y, X ), sdtasdt0( Z, X ) ) }.
% 2.13/2.56 (7303) {G0,W11,D3,L2,V3,M2} { ! alpha6( X, Y, Z ), ! sdtasdt0( X, Y ) =
% 2.13/2.56 sdtasdt0( X, Z ) }.
% 2.13/2.56 (7304) {G0,W11,D3,L2,V3,M2} { ! alpha6( X, Y, Z ), sdtlseqdt0( sdtasdt0( X
% 2.13/2.56 , Y ), sdtasdt0( X, Z ) ) }.
% 2.13/2.56 (7305) {G0,W11,D3,L2,V3,M2} { ! alpha6( X, Y, Z ), ! sdtasdt0( Y, X ) =
% 2.13/2.56 sdtasdt0( Z, X ) }.
% 2.13/2.56 (7306) {G0,W25,D3,L4,V3,M4} { sdtasdt0( X, Y ) = sdtasdt0( X, Z ), !
% 2.13/2.56 sdtlseqdt0( sdtasdt0( X, Y ), sdtasdt0( X, Z ) ), sdtasdt0( Y, X ) =
% 2.13/2.56 sdtasdt0( Z, X ), alpha6( X, Y, Z ) }.
% 2.13/2.56 (7307) {G0,W11,D2,L4,V1,M4} { ! aNaturalNumber0( X ), X = sz00, X = sz10,
% 2.13/2.56 ! sz10 = X }.
% 2.13/2.56 (7308) {G0,W11,D2,L4,V1,M4} { ! aNaturalNumber0( X ), X = sz00, X = sz10,
% 2.13/2.56 sdtlseqdt0( sz10, X ) }.
% 2.13/2.56 (7309) {G0,W12,D3,L4,V2,M4} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 2.13/2.56 ), X = sz00, sdtlseqdt0( Y, sdtasdt0( Y, X ) ) }.
% 2.13/2.56 (7310) {G0,W1,D1,L1,V0,M1} { && }.
% 2.13/2.56 (7311) {G0,W13,D2,L5,V2,M5} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 2.13/2.56 ), X = Y, ! sdtlseqdt0( X, Y ), iLess0( X, Y ) }.
% 2.13/2.56 (7312) {G0,W11,D3,L4,V4,M4} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 2.13/2.56 ), ! doDivides0( X, Y ), aNaturalNumber0( skol2( Z, T ) ) }.
% 2.13/2.56 (7313) {G0,W14,D4,L4,V2,M4} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 2.13/2.56 ), ! doDivides0( X, Y ), Y = sdtasdt0( X, skol2( X, Y ) ) }.
% 2.13/2.56 (7314) {G0,W14,D3,L5,V3,M5} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 2.13/2.56 ), ! aNaturalNumber0( Z ), ! Y = sdtasdt0( X, Z ), doDivides0( X, Y )
% 2.13/2.56 }.
% 2.13/2.56 (7315) {G0,W17,D3,L6,V3,M6} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 2.13/2.56 ), X = sz00, ! doDivides0( X, Y ), ! Z = sdtsldt0( Y, X ),
% 2.13/2.56 aNaturalNumber0( Z ) }.
% 2.13/2.56 (7316) {G0,W20,D3,L6,V3,M6} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 2.13/2.56 ), X = sz00, ! doDivides0( X, Y ), ! Z = sdtsldt0( Y, X ), Y = sdtasdt0
% 2.13/2.56 ( X, Z ) }.
% 2.13/2.56 (7317) {G0,W22,D3,L7,V3,M7} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 2.13/2.56 ), X = sz00, ! doDivides0( X, Y ), ! aNaturalNumber0( Z ), ! Y =
% 2.13/2.56 sdtasdt0( X, Z ), Z = sdtsldt0( Y, X ) }.
% 2.13/2.56 (7318) {G0,W15,D2,L6,V3,M6} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 2.13/2.56 ), ! aNaturalNumber0( Z ), ! doDivides0( X, Y ), ! doDivides0( Y, Z ),
% 2.13/2.56 doDivides0( X, Z ) }.
% 2.13/2.56 (7319) {G0,W17,D3,L6,V3,M6} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 2.13/2.56 ), ! aNaturalNumber0( Z ), ! doDivides0( X, Y ), ! doDivides0( X, Z ),
% 2.13/2.56 doDivides0( X, sdtpldt0( Y, Z ) ) }.
% 2.13/2.56 (7320) {G0,W17,D3,L6,V3,M6} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 2.13/2.56 ), ! aNaturalNumber0( Z ), ! doDivides0( X, Y ), ! doDivides0( X,
% 2.13/2.56 sdtpldt0( Y, Z ) ), doDivides0( X, Z ) }.
% 2.13/2.56 (7321) {G0,W13,D2,L5,V2,M5} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 2.13/2.56 ), ! doDivides0( X, Y ), Y = sz00, sdtlseqdt0( X, Y ) }.
% 2.13/2.56 (7322) {G0,W23,D4,L6,V3,M6} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 2.13/2.56 ), X = sz00, ! doDivides0( X, Y ), ! aNaturalNumber0( Z ), sdtasdt0( Z,
% 2.13/2.56 sdtsldt0( Y, X ) ) = sdtsldt0( sdtasdt0( Z, Y ), X ) }.
% 2.13/2.56 (7323) {G0,W7,D2,L3,V1,M3} { ! aNaturalNumber0( X ), ! isPrime0( X ), ! X
% 2.13/2.56 = sz00 }.
% 2.13/2.56 (7324) {G0,W6,D2,L3,V1,M3} { ! aNaturalNumber0( X ), ! isPrime0( X ),
% 2.13/2.56 alpha1( X ) }.
% 2.13/2.56 (7325) {G0,W9,D2,L4,V1,M4} { ! aNaturalNumber0( X ), X = sz00, ! alpha1( X
% 2.13/2.56 ), isPrime0( X ) }.
% 2.13/2.56 (7326) {G0,W5,D2,L2,V1,M2} { ! alpha1( X ), ! X = sz10 }.
% 2.13/2.56 (7327) {G0,W4,D2,L2,V1,M2} { ! alpha1( X ), alpha2( X ) }.
% 2.13/2.56 (7328) {G0,W7,D2,L3,V1,M3} { X = sz10, ! alpha2( X ), alpha1( X ) }.
% 2.13/2.56 (7329) {G0,W8,D2,L3,V2,M3} { ! alpha2( X ), ! alpha3( X, Y ), alpha4( X, Y
% 2.13/2.56 ) }.
% 2.13/2.56 (7330) {G0,W6,D3,L2,V1,M2} { alpha3( X, skol3( X ) ), alpha2( X ) }.
% 2.13/2.56 (7331) {G0,W6,D3,L2,V1,M2} { ! alpha4( X, skol3( X ) ), alpha2( X ) }.
% 2.13/2.56 (7332) {G0,W9,D2,L3,V2,M3} { ! alpha4( X, Y ), Y = sz10, Y = X }.
% 2.13/2.56 (7333) {G0,W6,D2,L2,V2,M2} { ! Y = sz10, alpha4( X, Y ) }.
% 2.13/2.56 (7334) {G0,W6,D2,L2,V2,M2} { ! Y = X, alpha4( X, Y ) }.
% 2.13/2.56 (7335) {G0,W5,D2,L2,V2,M2} { ! alpha3( X, Y ), aNaturalNumber0( Y ) }.
% 2.13/2.56 (7336) {G0,W6,D2,L2,V2,M2} { ! alpha3( X, Y ), doDivides0( Y, X ) }.
% 2.13/2.56 (7337) {G0,W8,D2,L3,V2,M3} { ! aNaturalNumber0( Y ), ! doDivides0( Y, X )
% 2.13/2.56 , alpha3( X, Y ) }.
% 2.13/2.56 (7338) {G0,W11,D3,L4,V2,M4} { ! aNaturalNumber0( X ), X = sz00, X = sz10,
% 2.13/2.56 aNaturalNumber0( skol4( Y ) ) }.
% 2.13/2.56 (7339) {G0,W11,D3,L4,V2,M4} { ! aNaturalNumber0( X ), X = sz00, X = sz10,
% 2.13/2.56 isPrime0( skol4( Y ) ) }.
% 2.13/2.56 (7340) {G0,W12,D3,L4,V1,M4} { ! aNaturalNumber0( X ), X = sz00, X = sz10,
% 2.13/2.56 doDivides0( skol4( X ), X ) }.
% 2.13/2.56 (7341) {G0,W2,D2,L1,V0,M1} { aNaturalNumber0( xn ) }.
% 2.13/2.56 (7342) {G0,W2,D2,L1,V0,M1} { aNaturalNumber0( xm ) }.
% 2.13/2.56 (7343) {G0,W2,D2,L1,V0,M1} { aNaturalNumber0( xp ) }.
% 2.13/2.56 (7344) {G0,W30,D4,L8,V3,M8} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 2.13/2.56 ), ! aNaturalNumber0( Z ), ! isPrime0( Z ), ! doDivides0( Z, sdtasdt0( X
% 2.13/2.56 , Y ) ), ! iLess0( sdtpldt0( sdtpldt0( X, Y ), Z ), sdtpldt0( sdtpldt0(
% 2.13/2.56 xn, xm ), xp ) ), doDivides0( Z, X ), doDivides0( Z, Y ) }.
% 2.13/2.56 (7345) {G0,W2,D2,L1,V0,M1} { isPrime0( xp ) }.
% 2.13/2.56 (7346) {G0,W5,D3,L1,V0,M1} { doDivides0( xp, sdtasdt0( xn, xm ) ) }.
% 2.13/2.56 (7347) {G0,W3,D2,L1,V0,M1} { sdtlseqdt0( xp, xn ) }.
% 2.13/2.56 (7348) {G0,W5,D3,L1,V0,M1} { xr = sdtmndt0( xn, xp ) }.
% 2.13/2.56 (7349) {G0,W3,D2,L1,V0,M1} { ! xr = xn }.
% 2.13/2.56 (7350) {G0,W3,D2,L1,V0,M1} { sdtlseqdt0( xr, xn ) }.
% 2.13/2.56 (7351) {G0,W5,D3,L1,V0,M1} { xn = sdtpldt0( xp, xr ) }.
% 2.13/2.56 (7352) {G0,W11,D4,L1,V0,M1} { sdtasdt0( xn, xm ) = sdtpldt0( sdtasdt0( xp
% 2.13/2.56 , xm ), sdtasdt0( xr, xm ) ) }.
% 2.13/2.56 (7353) {G0,W11,D4,L1,V0,M1} { sdtasdt0( xr, xm ) = sdtmndt0( sdtasdt0( xn
% 2.13/2.56 , xm ), sdtasdt0( xp, xm ) ) }.
% 2.13/2.56 (7354) {G0,W5,D3,L1,V0,M1} { ! doDivides0( xp, sdtasdt0( xp, xm ) ) }.
% 2.13/2.56
% 2.13/2.56
% 2.13/2.56 Total Proof:
% 2.13/2.56
% 2.13/2.56 subsumption: (5) {G0,W8,D3,L3,V2,M3} I { ! aNaturalNumber0( X ), !
% 2.13/2.56 aNaturalNumber0( Y ), aNaturalNumber0( sdtasdt0( X, Y ) ) }.
% 2.13/2.57 parent0: (7264) {G0,W8,D3,L3,V2,M3} { ! aNaturalNumber0( X ), !
% 2.13/2.57 aNaturalNumber0( Y ), aNaturalNumber0( sdtasdt0( X, Y ) ) }.
% 2.13/2.57 substitution0:
% 2.13/2.57 X := X
% 2.13/2.57 Y := Y
% 2.13/2.57 end
% 2.13/2.57 permutation0:
% 2.13/2.57 0 ==> 0
% 2.13/2.57 1 ==> 1
% 2.13/2.57 2 ==> 2
% 2.13/2.57 end
% 2.13/2.57
% 2.13/2.57 subsumption: (54) {G0,W14,D3,L5,V3,M5} I { ! aNaturalNumber0( X ), !
% 2.13/2.57 aNaturalNumber0( Y ), ! aNaturalNumber0( Z ), ! Y = sdtasdt0( X, Z ),
% 2.13/2.57 doDivides0( X, Y ) }.
% 2.13/2.57 parent0: (7314) {G0,W14,D3,L5,V3,M5} { ! aNaturalNumber0( X ), !
% 2.13/2.57 aNaturalNumber0( Y ), ! aNaturalNumber0( Z ), ! Y = sdtasdt0( X, Z ),
% 2.13/2.57 doDivides0( X, Y ) }.
% 2.13/2.57 substitution0:
% 2.13/2.57 X := X
% 2.13/2.57 Y := Y
% 2.13/2.57 Z := Z
% 2.13/2.57 end
% 2.13/2.57 permutation0:
% 2.13/2.57 0 ==> 0
% 2.13/2.57 1 ==> 1
% 2.13/2.57 2 ==> 2
% 2.13/2.57 3 ==> 3
% 2.13/2.57 4 ==> 4
% 2.13/2.57 end
% 2.13/2.57
% 2.13/2.57 subsumption: (82) {G0,W2,D2,L1,V0,M1} I { aNaturalNumber0( xm ) }.
% 2.13/2.57 parent0: (7342) {G0,W2,D2,L1,V0,M1} { aNaturalNumber0( xm ) }.
% 2.13/2.57 substitution0:
% 2.13/2.57 end
% 2.13/2.57 permutation0:
% 2.13/2.57 0 ==> 0
% 2.13/2.57 end
% 2.13/2.57
% 2.13/2.57 *** allocated 256285 integers for termspace/termends
% 2.13/2.57 subsumption: (83) {G0,W2,D2,L1,V0,M1} I { aNaturalNumber0( xp ) }.
% 2.13/2.57 parent0: (7343) {G0,W2,D2,L1,V0,M1} { aNaturalNumber0( xp ) }.
% 2.13/2.57 substitution0:
% 2.13/2.57 end
% 2.13/2.57 permutation0:
% 2.13/2.57 0 ==> 0
% 2.13/2.57 end
% 2.13/2.57
% 2.13/2.57 subsumption: (94) {G0,W5,D3,L1,V0,M1} I { ! doDivides0( xp, sdtasdt0( xp,
% 2.13/2.57 xm ) ) }.
% 2.13/2.57 parent0: (7354) {G0,W5,D3,L1,V0,M1} { ! doDivides0( xp, sdtasdt0( xp, xm )
% 2.13/2.57 ) }.
% 2.13/2.57 substitution0:
% 2.13/2.57 end
% 2.13/2.57 permutation0:
% 2.13/2.57 0 ==> 0
% 2.13/2.57 end
% 2.13/2.57
% 2.13/2.57 resolution: (8929) {G1,W6,D3,L2,V1,M2} { ! aNaturalNumber0( X ),
% 2.13/2.57 aNaturalNumber0( sdtasdt0( xp, X ) ) }.
% 2.13/2.57 parent0[0]: (5) {G0,W8,D3,L3,V2,M3} I { ! aNaturalNumber0( X ), !
% 2.13/2.57 aNaturalNumber0( Y ), aNaturalNumber0( sdtasdt0( X, Y ) ) }.
% 2.13/2.57 parent1[0]: (83) {G0,W2,D2,L1,V0,M1} I { aNaturalNumber0( xp ) }.
% 2.13/2.57 substitution0:
% 2.13/2.57 X := xp
% 2.13/2.57 Y := X
% 2.13/2.57 end
% 2.13/2.57 substitution1:
% 2.13/2.57 end
% 2.13/2.57
% 2.13/2.57 subsumption: (258) {G1,W6,D3,L2,V1,M2} R(5,83) { ! aNaturalNumber0( X ),
% 2.13/2.57 aNaturalNumber0( sdtasdt0( xp, X ) ) }.
% 2.13/2.57 parent0: (8929) {G1,W6,D3,L2,V1,M2} { ! aNaturalNumber0( X ),
% 2.13/2.57 aNaturalNumber0( sdtasdt0( xp, X ) ) }.
% 2.13/2.57 substitution0:
% 2.13/2.57 X := X
% 2.13/2.57 end
% 2.13/2.57 permutation0:
% 2.13/2.57 0 ==> 0
% 2.13/2.57 1 ==> 1
% 2.13/2.57 end
% 2.13/2.57
% 2.13/2.57 eqswap: (8931) {G0,W14,D3,L5,V3,M5} { ! sdtasdt0( Y, Z ) = X, !
% 2.13/2.57 aNaturalNumber0( Y ), ! aNaturalNumber0( X ), ! aNaturalNumber0( Z ),
% 2.13/2.57 doDivides0( Y, X ) }.
% 2.13/2.57 parent0[3]: (54) {G0,W14,D3,L5,V3,M5} I { ! aNaturalNumber0( X ), !
% 2.13/2.57 aNaturalNumber0( Y ), ! aNaturalNumber0( Z ), ! Y = sdtasdt0( X, Z ),
% 2.13/2.57 doDivides0( X, Y ) }.
% 2.13/2.57 substitution0:
% 2.13/2.57 X := Y
% 2.13/2.57 Y := X
% 2.13/2.57 Z := Z
% 2.13/2.57 end
% 2.13/2.57
% 2.13/2.57 resolution: (8932) {G1,W15,D3,L4,V1,M4} { ! sdtasdt0( xp, X ) = sdtasdt0(
% 2.13/2.57 xp, xm ), ! aNaturalNumber0( xp ), ! aNaturalNumber0( sdtasdt0( xp, xm )
% 2.13/2.57 ), ! aNaturalNumber0( X ) }.
% 2.13/2.57 parent0[0]: (94) {G0,W5,D3,L1,V0,M1} I { ! doDivides0( xp, sdtasdt0( xp, xm
% 2.13/2.57 ) ) }.
% 2.13/2.57 parent1[4]: (8931) {G0,W14,D3,L5,V3,M5} { ! sdtasdt0( Y, Z ) = X, !
% 2.13/2.57 aNaturalNumber0( Y ), ! aNaturalNumber0( X ), ! aNaturalNumber0( Z ),
% 2.13/2.57 doDivides0( Y, X ) }.
% 2.13/2.57 substitution0:
% 2.13/2.57 end
% 2.13/2.57 substitution1:
% 2.13/2.57 X := sdtasdt0( xp, xm )
% 2.13/2.57 Y := xp
% 2.13/2.57 Z := X
% 2.13/2.57 end
% 2.13/2.57
% 2.13/2.57 resolution: (8939) {G1,W13,D3,L3,V1,M3} { ! sdtasdt0( xp, X ) = sdtasdt0(
% 2.13/2.57 xp, xm ), ! aNaturalNumber0( sdtasdt0( xp, xm ) ), ! aNaturalNumber0( X )
% 2.13/2.57 }.
% 2.13/2.57 parent0[1]: (8932) {G1,W15,D3,L4,V1,M4} { ! sdtasdt0( xp, X ) = sdtasdt0(
% 2.13/2.57 xp, xm ), ! aNaturalNumber0( xp ), ! aNaturalNumber0( sdtasdt0( xp, xm )
% 2.13/2.57 ), ! aNaturalNumber0( X ) }.
% 2.13/2.57 parent1[0]: (83) {G0,W2,D2,L1,V0,M1} I { aNaturalNumber0( xp ) }.
% 2.13/2.57 substitution0:
% 2.13/2.57 X := X
% 2.13/2.57 end
% 2.13/2.57 substitution1:
% 2.13/2.57 end
% 2.13/2.57
% 2.13/2.57 eqswap: (8940) {G1,W13,D3,L3,V1,M3} { ! sdtasdt0( xp, xm ) = sdtasdt0( xp
% 2.13/2.57 , X ), ! aNaturalNumber0( sdtasdt0( xp, xm ) ), ! aNaturalNumber0( X )
% 2.13/2.57 }.
% 2.13/2.57 parent0[0]: (8939) {G1,W13,D3,L3,V1,M3} { ! sdtasdt0( xp, X ) = sdtasdt0(
% 2.13/2.57 xp, xm ), ! aNaturalNumber0( sdtasdt0( xp, xm ) ), ! aNaturalNumber0( X )
% 2.13/2.57 }.
% 2.13/2.57 substitution0:
% 2.13/2.57 X := X
% 2.13/2.57 end
% 2.13/2.57
% 2.13/2.57 subsumption: (7119) {G1,W13,D3,L3,V1,M3} R(54,94);r(83) { ! aNaturalNumber0
% 2.13/2.57 ( sdtasdt0( xp, xm ) ), ! aNaturalNumber0( X ), ! sdtasdt0( xp, xm ) =
% 2.13/2.57 sdtasdt0( xp, X ) }.
% 2.13/2.57 parent0: (8940) {G1,W13,D3,L3,V1,M3} { ! sdtasdt0( xp, xm ) = sdtasdt0( xp
% 2.13/2.57 , X ), ! aNaturalNumber0( sdtasdt0( xp, xm ) ), ! aNaturalNumber0( X )
% 2.13/2.57 }.
% 2.13/2.57 substitution0:
% 2.13/2.57 X := X
% 2.13/2.57 end
% 2.13/2.57 permutation0:
% 2.13/2.57 0 ==> 2
% 2.13/2.57 1 ==> 0
% 2.13/2.57 2 ==> 1
% 2.13/2.57 end
% 2.13/2.57
% 2.13/2.57 eqswap: (8943) {G1,W13,D3,L3,V1,M3} { ! sdtasdt0( xp, X ) = sdtasdt0( xp,
% 2.13/2.57 xm ), ! aNaturalNumber0( sdtasdt0( xp, xm ) ), ! aNaturalNumber0( X ) }.
% 2.13/2.57 parent0[2]: (7119) {G1,W13,D3,L3,V1,M3} R(54,94);r(83) { ! aNaturalNumber0
% 2.13/2.57 ( sdtasdt0( xp, xm ) ), ! aNaturalNumber0( X ), ! sdtasdt0( xp, xm ) =
% 2.13/2.57 sdtasdt0( xp, X ) }.
% 2.13/2.57 substitution0:
% 2.13/2.57 X := X
% 2.13/2.57 end
% 2.13/2.57
% 2.13/2.57 eqrefl: (8944) {G0,W6,D3,L2,V0,M2} { ! aNaturalNumber0( sdtasdt0( xp, xm )
% 2.13/2.57 ), ! aNaturalNumber0( xm ) }.
% 2.13/2.57 parent0[0]: (8943) {G1,W13,D3,L3,V1,M3} { ! sdtasdt0( xp, X ) = sdtasdt0(
% 2.13/2.57 xp, xm ), ! aNaturalNumber0( sdtasdt0( xp, xm ) ), ! aNaturalNumber0( X )
% 2.13/2.57 }.
% 2.13/2.57 substitution0:
% 2.13/2.57 X := xm
% 2.13/2.57 end
% 2.13/2.57
% 2.13/2.57 resolution: (8945) {G1,W4,D2,L2,V0,M2} { ! aNaturalNumber0( xm ), !
% 2.13/2.57 aNaturalNumber0( xm ) }.
% 2.13/2.57 parent0[0]: (8944) {G0,W6,D3,L2,V0,M2} { ! aNaturalNumber0( sdtasdt0( xp,
% 2.13/2.57 xm ) ), ! aNaturalNumber0( xm ) }.
% 2.13/2.57 parent1[1]: (258) {G1,W6,D3,L2,V1,M2} R(5,83) { ! aNaturalNumber0( X ),
% 2.13/2.57 aNaturalNumber0( sdtasdt0( xp, X ) ) }.
% 2.13/2.57 substitution0:
% 2.13/2.57 end
% 2.13/2.57 substitution1:
% 2.13/2.57 X := xm
% 2.13/2.57 end
% 2.13/2.57
% 2.13/2.57 factor: (8946) {G1,W2,D2,L1,V0,M1} { ! aNaturalNumber0( xm ) }.
% 2.13/2.57 parent0[0, 1]: (8945) {G1,W4,D2,L2,V0,M2} { ! aNaturalNumber0( xm ), !
% 2.13/2.57 aNaturalNumber0( xm ) }.
% 2.13/2.57 substitution0:
% 2.13/2.57 end
% 2.13/2.57
% 2.13/2.57 subsumption: (7221) {G2,W2,D2,L1,V0,M1} Q(7119);r(258) { ! aNaturalNumber0
% 2.13/2.57 ( xm ) }.
% 2.13/2.57 parent0: (8946) {G1,W2,D2,L1,V0,M1} { ! aNaturalNumber0( xm ) }.
% 2.13/2.57 substitution0:
% 2.13/2.57 end
% 2.13/2.57 permutation0:
% 2.13/2.57 0 ==> 0
% 2.13/2.57 end
% 2.13/2.57
% 2.13/2.57 resolution: (8947) {G1,W0,D0,L0,V0,M0} { }.
% 2.13/2.57 parent0[0]: (7221) {G2,W2,D2,L1,V0,M1} Q(7119);r(258) { ! aNaturalNumber0(
% 2.13/2.57 xm ) }.
% 2.13/2.57 parent1[0]: (82) {G0,W2,D2,L1,V0,M1} I { aNaturalNumber0( xm ) }.
% 2.13/2.57 substitution0:
% 2.13/2.57 end
% 2.13/2.57 substitution1:
% 2.13/2.57 end
% 2.13/2.57
% 2.13/2.57 subsumption: (7257) {G3,W0,D0,L0,V0,M0} S(7221);r(82) { }.
% 2.13/2.57 parent0: (8947) {G1,W0,D0,L0,V0,M0} { }.
% 2.13/2.57 substitution0:
% 2.13/2.57 end
% 2.13/2.57 permutation0:
% 2.13/2.57 end
% 2.13/2.57
% 2.13/2.57 Proof check complete!
% 2.13/2.57
% 2.13/2.57 Memory use:
% 2.13/2.57
% 2.13/2.57 space for terms: 154778
% 2.13/2.57 space for clauses: 326641
% 2.13/2.57
% 2.13/2.57
% 2.13/2.57 clauses generated: 51655
% 2.13/2.57 clauses kept: 7258
% 2.13/2.57 clauses selected: 247
% 2.13/2.57 clauses deleted: 31
% 2.13/2.57 clauses inuse deleted: 16
% 2.13/2.57
% 2.13/2.57 subsentry: 136217
% 2.13/2.57 literals s-matched: 87262
% 2.13/2.57 literals matched: 70387
% 2.13/2.57 full subsumption: 57746
% 2.13/2.57
% 2.13/2.57 checksum: -2050023483
% 2.13/2.57
% 2.13/2.57
% 2.13/2.57 Bliksem ended
%------------------------------------------------------------------------------