TSTP Solution File: NUM489+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : NUM489+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n008.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 06:22:49 EDT 2022
% Result : Theorem 0.75s 1.32s
% Output : Refutation 0.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM489+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n008.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 : Thu Jul 7 15:29:38 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.68/1.09 *** allocated 10000 integers for termspace/termends
% 0.68/1.09 *** allocated 10000 integers for clauses
% 0.68/1.09 *** allocated 10000 integers for justifications
% 0.68/1.09 Bliksem 1.12
% 0.68/1.09
% 0.68/1.09
% 0.68/1.09 Automatic Strategy Selection
% 0.68/1.09
% 0.68/1.09
% 0.68/1.09 Clauses:
% 0.68/1.09
% 0.68/1.09 { && }.
% 0.68/1.09 { aNaturalNumber0( sz00 ) }.
% 0.68/1.09 { aNaturalNumber0( sz10 ) }.
% 0.68/1.09 { ! sz10 = sz00 }.
% 0.68/1.09 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), aNaturalNumber0( sdtpldt0
% 0.68/1.09 ( X, Y ) ) }.
% 0.68/1.09 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), aNaturalNumber0( sdtasdt0
% 0.68/1.09 ( X, Y ) ) }.
% 0.68/1.09 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), sdtpldt0( X, Y ) =
% 0.68/1.09 sdtpldt0( Y, X ) }.
% 0.68/1.09 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! aNaturalNumber0( Z ),
% 0.68/1.09 sdtpldt0( sdtpldt0( X, Y ), Z ) = sdtpldt0( X, sdtpldt0( Y, Z ) ) }.
% 0.68/1.09 { ! aNaturalNumber0( X ), sdtpldt0( X, sz00 ) = X }.
% 0.68/1.09 { ! aNaturalNumber0( X ), X = sdtpldt0( sz00, X ) }.
% 0.68/1.09 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), sdtasdt0( X, Y ) =
% 0.68/1.09 sdtasdt0( Y, X ) }.
% 0.68/1.09 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! aNaturalNumber0( Z ),
% 0.68/1.09 sdtasdt0( sdtasdt0( X, Y ), Z ) = sdtasdt0( X, sdtasdt0( Y, Z ) ) }.
% 0.68/1.09 { ! aNaturalNumber0( X ), sdtasdt0( X, sz10 ) = X }.
% 0.68/1.09 { ! aNaturalNumber0( X ), X = sdtasdt0( sz10, X ) }.
% 0.68/1.09 { ! aNaturalNumber0( X ), sdtasdt0( X, sz00 ) = sz00 }.
% 0.68/1.09 { ! aNaturalNumber0( X ), sz00 = sdtasdt0( sz00, X ) }.
% 0.68/1.09 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! aNaturalNumber0( Z ),
% 0.68/1.09 sdtasdt0( X, sdtpldt0( Y, Z ) ) = sdtpldt0( sdtasdt0( X, Y ), sdtasdt0( X
% 0.68/1.09 , Z ) ) }.
% 0.68/1.09 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! aNaturalNumber0( Z ),
% 0.68/1.09 sdtasdt0( sdtpldt0( Y, Z ), X ) = sdtpldt0( sdtasdt0( Y, X ), sdtasdt0( Z
% 0.68/1.09 , X ) ) }.
% 0.68/1.09 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! aNaturalNumber0( Z ), !
% 0.68/1.09 sdtpldt0( X, Y ) = sdtpldt0( X, Z ), Y = Z }.
% 0.68/1.09 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! aNaturalNumber0( Z ), !
% 0.68/1.09 sdtpldt0( Y, X ) = sdtpldt0( Z, X ), Y = Z }.
% 0.68/1.09 { ! aNaturalNumber0( X ), X = sz00, ! aNaturalNumber0( Y ), !
% 0.68/1.09 aNaturalNumber0( Z ), ! sdtasdt0( X, Y ) = sdtasdt0( X, Z ), Y = Z }.
% 0.68/1.09 { ! aNaturalNumber0( X ), X = sz00, ! aNaturalNumber0( Y ), !
% 0.68/1.09 aNaturalNumber0( Z ), ! sdtasdt0( Y, X ) = sdtasdt0( Z, X ), Y = Z }.
% 0.68/1.09 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! sdtpldt0( X, Y ) = sz00
% 0.68/1.09 , X = sz00 }.
% 0.68/1.09 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! sdtpldt0( X, Y ) = sz00
% 0.68/1.09 , Y = sz00 }.
% 0.68/1.09 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! sdtasdt0( X, Y ) = sz00
% 0.68/1.09 , X = sz00, Y = sz00 }.
% 0.68/1.09 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! sdtlseqdt0( X, Y ),
% 0.68/1.09 aNaturalNumber0( skol1( Z, T ) ) }.
% 0.68/1.09 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! sdtlseqdt0( X, Y ),
% 0.68/1.09 sdtpldt0( X, skol1( X, Y ) ) = Y }.
% 0.68/1.09 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! aNaturalNumber0( Z ), !
% 0.68/1.09 sdtpldt0( X, Z ) = Y, sdtlseqdt0( X, Y ) }.
% 0.68/1.09 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! sdtlseqdt0( X, Y ), ! Z
% 0.68/1.09 = sdtmndt0( Y, X ), aNaturalNumber0( Z ) }.
% 0.68/1.09 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! sdtlseqdt0( X, Y ), ! Z
% 0.68/1.09 = sdtmndt0( Y, X ), sdtpldt0( X, Z ) = Y }.
% 0.68/1.09 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! sdtlseqdt0( X, Y ), !
% 0.68/1.09 aNaturalNumber0( Z ), ! sdtpldt0( X, Z ) = Y, Z = sdtmndt0( Y, X ) }.
% 0.68/1.09 { ! aNaturalNumber0( X ), sdtlseqdt0( X, X ) }.
% 0.68/1.09 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! sdtlseqdt0( X, Y ), !
% 0.68/1.09 sdtlseqdt0( Y, X ), X = Y }.
% 0.68/1.09 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! aNaturalNumber0( Z ), !
% 0.68/1.09 sdtlseqdt0( X, Y ), ! sdtlseqdt0( Y, Z ), sdtlseqdt0( X, Z ) }.
% 0.68/1.09 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), sdtlseqdt0( X, Y ), ! Y =
% 0.68/1.09 X }.
% 0.68/1.09 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), sdtlseqdt0( X, Y ),
% 0.68/1.09 sdtlseqdt0( Y, X ) }.
% 0.68/1.09 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), X = Y, ! sdtlseqdt0( X, Y
% 0.68/1.09 ), ! aNaturalNumber0( Z ), alpha5( X, Y, Z ) }.
% 0.68/1.09 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), X = Y, ! sdtlseqdt0( X, Y
% 0.68/1.09 ), ! aNaturalNumber0( Z ), sdtlseqdt0( sdtpldt0( X, Z ), sdtpldt0( Y, Z
% 0.68/1.09 ) ) }.
% 0.68/1.09 { ! alpha5( X, Y, Z ), ! sdtpldt0( Z, X ) = sdtpldt0( Z, Y ) }.
% 0.68/1.09 { ! alpha5( X, Y, Z ), sdtlseqdt0( sdtpldt0( Z, X ), sdtpldt0( Z, Y ) ) }.
% 0.68/1.09 { ! alpha5( X, Y, Z ), ! sdtpldt0( X, Z ) = sdtpldt0( Y, Z ) }.
% 0.75/1.32 { sdtpldt0( Z, X ) = sdtpldt0( Z, Y ), ! sdtlseqdt0( sdtpldt0( Z, X ),
% 0.75/1.32 sdtpldt0( Z, Y ) ), sdtpldt0( X, Z ) = sdtpldt0( Y, Z ), alpha5( X, Y, Z
% 0.75/1.32 ) }.
% 0.75/1.32 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! aNaturalNumber0( Z ), X
% 0.75/1.32 = sz00, Y = Z, ! sdtlseqdt0( Y, Z ), alpha6( X, Y, Z ) }.
% 0.75/1.32 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! aNaturalNumber0( Z ), X
% 0.75/1.32 = sz00, Y = Z, ! sdtlseqdt0( Y, Z ), sdtlseqdt0( sdtasdt0( Y, X ),
% 0.75/1.32 sdtasdt0( Z, X ) ) }.
% 0.75/1.32 { ! alpha6( X, Y, Z ), ! sdtasdt0( X, Y ) = sdtasdt0( X, Z ) }.
% 0.75/1.32 { ! alpha6( X, Y, Z ), sdtlseqdt0( sdtasdt0( X, Y ), sdtasdt0( X, Z ) ) }.
% 0.75/1.32 { ! alpha6( X, Y, Z ), ! sdtasdt0( Y, X ) = sdtasdt0( Z, X ) }.
% 0.75/1.32 { sdtasdt0( X, Y ) = sdtasdt0( X, Z ), ! sdtlseqdt0( sdtasdt0( X, Y ),
% 0.75/1.32 sdtasdt0( X, Z ) ), sdtasdt0( Y, X ) = sdtasdt0( Z, X ), alpha6( X, Y, Z
% 0.75/1.32 ) }.
% 0.75/1.32 { ! aNaturalNumber0( X ), X = sz00, X = sz10, ! sz10 = X }.
% 0.75/1.32 { ! aNaturalNumber0( X ), X = sz00, X = sz10, sdtlseqdt0( sz10, X ) }.
% 0.75/1.32 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), X = sz00, sdtlseqdt0( Y,
% 0.75/1.32 sdtasdt0( Y, X ) ) }.
% 0.75/1.32 { && }.
% 0.75/1.32 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), X = Y, ! sdtlseqdt0( X, Y
% 0.75/1.32 ), iLess0( X, Y ) }.
% 0.75/1.32 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! doDivides0( X, Y ),
% 0.75/1.32 aNaturalNumber0( skol2( Z, T ) ) }.
% 0.75/1.32 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! doDivides0( X, Y ), Y =
% 0.75/1.32 sdtasdt0( X, skol2( X, Y ) ) }.
% 0.75/1.32 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! aNaturalNumber0( Z ), !
% 0.75/1.32 Y = sdtasdt0( X, Z ), doDivides0( X, Y ) }.
% 0.75/1.32 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), X = sz00, ! doDivides0( X
% 0.75/1.32 , Y ), ! Z = sdtsldt0( Y, X ), aNaturalNumber0( Z ) }.
% 0.75/1.32 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), X = sz00, ! doDivides0( X
% 0.75/1.32 , Y ), ! Z = sdtsldt0( Y, X ), Y = sdtasdt0( X, Z ) }.
% 0.75/1.32 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), X = sz00, ! doDivides0( X
% 0.75/1.32 , Y ), ! aNaturalNumber0( Z ), ! Y = sdtasdt0( X, Z ), Z = sdtsldt0( Y, X
% 0.75/1.32 ) }.
% 0.75/1.32 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! aNaturalNumber0( Z ), !
% 0.75/1.32 doDivides0( X, Y ), ! doDivides0( Y, Z ), doDivides0( X, Z ) }.
% 0.75/1.32 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! aNaturalNumber0( Z ), !
% 0.75/1.32 doDivides0( X, Y ), ! doDivides0( X, Z ), doDivides0( X, sdtpldt0( Y, Z
% 0.75/1.32 ) ) }.
% 0.75/1.32 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! aNaturalNumber0( Z ), !
% 0.75/1.32 doDivides0( X, Y ), ! doDivides0( X, sdtpldt0( Y, Z ) ), doDivides0( X,
% 0.75/1.32 Z ) }.
% 0.75/1.32 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! doDivides0( X, Y ), Y =
% 0.75/1.32 sz00, sdtlseqdt0( X, Y ) }.
% 0.75/1.32 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), X = sz00, ! doDivides0( X
% 0.75/1.32 , Y ), ! aNaturalNumber0( Z ), sdtasdt0( Z, sdtsldt0( Y, X ) ) = sdtsldt0
% 0.75/1.32 ( sdtasdt0( Z, Y ), X ) }.
% 0.75/1.32 { ! aNaturalNumber0( X ), ! isPrime0( X ), ! X = sz00 }.
% 0.75/1.32 { ! aNaturalNumber0( X ), ! isPrime0( X ), alpha1( X ) }.
% 0.75/1.32 { ! aNaturalNumber0( X ), X = sz00, ! alpha1( X ), isPrime0( X ) }.
% 0.75/1.32 { ! alpha1( X ), ! X = sz10 }.
% 0.75/1.32 { ! alpha1( X ), alpha2( X ) }.
% 0.75/1.32 { X = sz10, ! alpha2( X ), alpha1( X ) }.
% 0.75/1.32 { ! alpha2( X ), ! alpha3( X, Y ), alpha4( X, Y ) }.
% 0.75/1.32 { alpha3( X, skol3( X ) ), alpha2( X ) }.
% 0.75/1.32 { ! alpha4( X, skol3( X ) ), alpha2( X ) }.
% 0.75/1.32 { ! alpha4( X, Y ), Y = sz10, Y = X }.
% 0.75/1.32 { ! Y = sz10, alpha4( X, Y ) }.
% 0.75/1.32 { ! Y = X, alpha4( X, Y ) }.
% 0.75/1.32 { ! alpha3( X, Y ), aNaturalNumber0( Y ) }.
% 0.75/1.32 { ! alpha3( X, Y ), doDivides0( Y, X ) }.
% 0.75/1.32 { ! aNaturalNumber0( Y ), ! doDivides0( Y, X ), alpha3( X, Y ) }.
% 0.75/1.32 { ! aNaturalNumber0( X ), X = sz00, X = sz10, aNaturalNumber0( skol4( Y ) )
% 0.75/1.32 }.
% 0.75/1.32 { ! aNaturalNumber0( X ), X = sz00, X = sz10, isPrime0( skol4( Y ) ) }.
% 0.75/1.32 { ! aNaturalNumber0( X ), X = sz00, X = sz10, doDivides0( skol4( X ), X ) }
% 0.75/1.32 .
% 0.75/1.32 { aNaturalNumber0( xn ) }.
% 0.75/1.32 { aNaturalNumber0( xm ) }.
% 0.75/1.32 { aNaturalNumber0( xp ) }.
% 0.75/1.32 { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y ), ! aNaturalNumber0( Z ), !
% 0.75/1.32 isPrime0( Z ), ! doDivides0( Z, sdtasdt0( X, Y ) ), ! iLess0( sdtpldt0(
% 0.75/1.32 sdtpldt0( X, Y ), Z ), sdtpldt0( sdtpldt0( xn, xm ), xp ) ), doDivides0(
% 0.75/1.32 Z, X ), doDivides0( Z, Y ) }.
% 0.75/1.32 { isPrime0( xp ) }.
% 0.75/1.32 { doDivides0( xp, sdtasdt0( xn, xm ) ) }.
% 0.75/1.32 { sdtlseqdt0( xp, xn ) }.
% 0.75/1.32 { xr = sdtmndt0( xn, xp ) }.
% 0.75/1.32 { ! xr = xn }.
% 0.75/1.32 { sdtlseqdt0( xr, xn ) }.
% 0.75/1.32 { ! xn = sdtpldt0( xp, xr ) }.
% 0.75/1.32
% 0.75/1.32 percentage equality = 0.280374, percentage horn = 0.706522
% 0.75/1.32 This is a problem with some equality
% 0.75/1.32
% 0.75/1.32
% 0.75/1.32
% 0.75/1.32 Options Used:
% 0.75/1.32
% 0.75/1.32 useres = 1
% 0.75/1.32 useparamod = 1
% 0.75/1.32 useeqrefl = 1
% 0.75/1.32 useeqfact = 1
% 0.75/1.32 usefactor = 1
% 0.75/1.32 usesimpsplitting = 0
% 0.75/1.32 usesimpdemod = 5
% 0.75/1.32 usesimpres = 3
% 0.75/1.32
% 0.75/1.32 resimpinuse = 1000
% 0.75/1.32 resimpclauses = 20000
% 0.75/1.32 substype = eqrewr
% 0.75/1.32 backwardsubs = 1
% 0.75/1.32 selectoldest = 5
% 0.75/1.32
% 0.75/1.32 litorderings [0] = split
% 0.75/1.32 litorderings [1] = extend the termordering, first sorting on arguments
% 0.75/1.32
% 0.75/1.32 termordering = kbo
% 0.75/1.32
% 0.75/1.32 litapriori = 0
% 0.75/1.32 termapriori = 1
% 0.75/1.32 litaposteriori = 0
% 0.75/1.32 termaposteriori = 0
% 0.75/1.32 demodaposteriori = 0
% 0.75/1.32 ordereqreflfact = 0
% 0.75/1.32
% 0.75/1.32 litselect = negord
% 0.75/1.32
% 0.75/1.32 maxweight = 15
% 0.75/1.32 maxdepth = 30000
% 0.75/1.32 maxlength = 115
% 0.75/1.32 maxnrvars = 195
% 0.75/1.32 excuselevel = 1
% 0.75/1.32 increasemaxweight = 1
% 0.75/1.32
% 0.75/1.32 maxselected = 10000000
% 0.75/1.32 maxnrclauses = 10000000
% 0.75/1.32
% 0.75/1.32 showgenerated = 0
% 0.75/1.32 showkept = 0
% 0.75/1.32 showselected = 0
% 0.75/1.32 showdeleted = 0
% 0.75/1.32 showresimp = 1
% 0.75/1.32 showstatus = 2000
% 0.75/1.32
% 0.75/1.32 prologoutput = 0
% 0.75/1.32 nrgoals = 5000000
% 0.75/1.32 totalproof = 1
% 0.75/1.32
% 0.75/1.32 Symbols occurring in the translation:
% 0.75/1.32
% 0.75/1.32 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.75/1.32 . [1, 2] (w:1, o:26, a:1, s:1, b:0),
% 0.75/1.32 && [3, 0] (w:1, o:4, a:1, s:1, b:0),
% 0.75/1.32 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 0.75/1.32 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.75/1.32 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.75/1.32 aNaturalNumber0 [36, 1] (w:1, o:20, a:1, s:1, b:0),
% 0.75/1.32 sz00 [37, 0] (w:1, o:7, a:1, s:1, b:0),
% 0.75/1.32 sz10 [38, 0] (w:1, o:8, a:1, s:1, b:0),
% 0.75/1.32 sdtpldt0 [40, 2] (w:1, o:50, a:1, s:1, b:0),
% 0.75/1.32 sdtasdt0 [41, 2] (w:1, o:51, a:1, s:1, b:0),
% 0.75/1.32 sdtlseqdt0 [43, 2] (w:1, o:52, a:1, s:1, b:0),
% 0.75/1.32 sdtmndt0 [44, 2] (w:1, o:53, a:1, s:1, b:0),
% 0.75/1.32 iLess0 [45, 2] (w:1, o:54, a:1, s:1, b:0),
% 0.75/1.32 doDivides0 [46, 2] (w:1, o:55, a:1, s:1, b:0),
% 0.75/1.32 sdtsldt0 [47, 2] (w:1, o:56, a:1, s:1, b:0),
% 0.75/1.32 isPrime0 [48, 1] (w:1, o:21, a:1, s:1, b:0),
% 0.75/1.32 xn [49, 0] (w:1, o:12, a:1, s:1, b:0),
% 0.75/1.32 xm [50, 0] (w:1, o:11, a:1, s:1, b:0),
% 0.75/1.32 xp [51, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.75/1.32 xr [52, 0] (w:1, o:14, a:1, s:1, b:0),
% 0.75/1.32 alpha1 [53, 1] (w:1, o:22, a:1, s:1, b:1),
% 0.75/1.32 alpha2 [54, 1] (w:1, o:23, a:1, s:1, b:1),
% 0.75/1.32 alpha3 [55, 2] (w:1, o:57, a:1, s:1, b:1),
% 0.75/1.32 alpha4 [56, 2] (w:1, o:58, a:1, s:1, b:1),
% 0.75/1.32 alpha5 [57, 3] (w:1, o:61, a:1, s:1, b:1),
% 0.75/1.32 alpha6 [58, 3] (w:1, o:62, a:1, s:1, b:1),
% 0.75/1.32 skol1 [59, 2] (w:1, o:59, a:1, s:1, b:1),
% 0.75/1.32 skol2 [60, 2] (w:1, o:60, a:1, s:1, b:1),
% 0.75/1.32 skol3 [61, 1] (w:1, o:24, a:1, s:1, b:1),
% 0.75/1.32 skol4 [62, 1] (w:1, o:25, a:1, s:1, b:1).
% 0.75/1.32
% 0.75/1.32
% 0.75/1.32 Starting Search:
% 0.75/1.32
% 0.75/1.32 *** allocated 15000 integers for clauses
% 0.75/1.32 *** allocated 22500 integers for clauses
% 0.75/1.32 *** allocated 33750 integers for clauses
% 0.75/1.32 *** allocated 15000 integers for termspace/termends
% 0.75/1.32 *** allocated 50625 integers for clauses
% 0.75/1.32 *** allocated 22500 integers for termspace/termends
% 0.75/1.32 *** allocated 75937 integers for clauses
% 0.75/1.32 Resimplifying inuse:
% 0.75/1.32 Done
% 0.75/1.32
% 0.75/1.32 *** allocated 33750 integers for termspace/termends
% 0.75/1.32 *** allocated 113905 integers for clauses
% 0.75/1.32 *** allocated 50625 integers for termspace/termends
% 0.75/1.32
% 0.75/1.32 Intermediate Status:
% 0.75/1.32 Generated: 12206
% 0.75/1.32 Kept: 2006
% 0.75/1.32 Inuse: 137
% 0.75/1.32 Deleted: 3
% 0.75/1.32 Deletedinuse: 0
% 0.75/1.32
% 0.75/1.32 Resimplifying inuse:
% 0.75/1.32
% 0.75/1.32 Bliksems!, er is een bewijs:
% 0.75/1.32 % SZS status Theorem
% 0.75/1.32 % SZS output start Refutation
% 0.75/1.32
% 0.75/1.32 (29) {G0,W17,D3,L5,V3,M5} I { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 0.75/1.32 ), ! sdtlseqdt0( X, Y ), ! Z = sdtmndt0( Y, X ), sdtpldt0( X, Z ) = Y
% 0.75/1.32 }.
% 0.75/1.32 (81) {G0,W2,D2,L1,V0,M1} I { aNaturalNumber0( xn ) }.
% 0.75/1.32 (83) {G0,W2,D2,L1,V0,M1} I { aNaturalNumber0( xp ) }.
% 0.75/1.32 (87) {G0,W3,D2,L1,V0,M1} I { sdtlseqdt0( xp, xn ) }.
% 0.75/1.32 (88) {G0,W5,D3,L1,V0,M1} I { sdtmndt0( xn, xp ) ==> xr }.
% 0.75/1.32 (91) {G0,W5,D3,L1,V0,M1} I { ! sdtpldt0( xp, xr ) ==> xn }.
% 0.75/1.32 (2045) {G1,W10,D3,L3,V1,M3} R(29,87);d(88);r(83) { ! aNaturalNumber0( xn )
% 0.75/1.32 , sdtpldt0( xp, X ) ==> xn, ! X = xr }.
% 0.75/1.32 (2161) {G2,W5,D3,L1,V0,M1} Q(2045);r(81) { sdtpldt0( xp, xr ) ==> xn }.
% 0.75/1.32 (2178) {G3,W0,D0,L0,V0,M0} S(91);d(2161);q { }.
% 0.75/1.32
% 0.75/1.32
% 0.75/1.32 % SZS output end Refutation
% 0.75/1.32 found a proof!
% 0.75/1.32
% 0.75/1.32
% 0.75/1.32 Unprocessed initial clauses:
% 0.75/1.32
% 0.75/1.32 (2180) {G0,W1,D1,L1,V0,M1} { && }.
% 0.75/1.32 (2181) {G0,W2,D2,L1,V0,M1} { aNaturalNumber0( sz00 ) }.
% 0.75/1.32 (2182) {G0,W2,D2,L1,V0,M1} { aNaturalNumber0( sz10 ) }.
% 0.75/1.32 (2183) {G0,W3,D2,L1,V0,M1} { ! sz10 = sz00 }.
% 0.75/1.32 (2184) {G0,W8,D3,L3,V2,M3} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 0.75/1.32 ), aNaturalNumber0( sdtpldt0( X, Y ) ) }.
% 0.75/1.32 (2185) {G0,W8,D3,L3,V2,M3} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 0.75/1.32 ), aNaturalNumber0( sdtasdt0( X, Y ) ) }.
% 0.75/1.32 (2186) {G0,W11,D3,L3,V2,M3} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 0.75/1.32 ), sdtpldt0( X, Y ) = sdtpldt0( Y, X ) }.
% 0.75/1.32 (2187) {G0,W17,D4,L4,V3,M4} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 0.75/1.32 ), ! aNaturalNumber0( Z ), sdtpldt0( sdtpldt0( X, Y ), Z ) = sdtpldt0( X
% 0.75/1.32 , sdtpldt0( Y, Z ) ) }.
% 0.75/1.32 (2188) {G0,W7,D3,L2,V1,M2} { ! aNaturalNumber0( X ), sdtpldt0( X, sz00 ) =
% 0.75/1.32 X }.
% 0.75/1.32 (2189) {G0,W7,D3,L2,V1,M2} { ! aNaturalNumber0( X ), X = sdtpldt0( sz00, X
% 0.75/1.32 ) }.
% 0.75/1.32 (2190) {G0,W11,D3,L3,V2,M3} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 0.75/1.32 ), sdtasdt0( X, Y ) = sdtasdt0( Y, X ) }.
% 0.75/1.32 (2191) {G0,W17,D4,L4,V3,M4} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 0.75/1.32 ), ! aNaturalNumber0( Z ), sdtasdt0( sdtasdt0( X, Y ), Z ) = sdtasdt0( X
% 0.75/1.32 , sdtasdt0( Y, Z ) ) }.
% 0.75/1.32 (2192) {G0,W7,D3,L2,V1,M2} { ! aNaturalNumber0( X ), sdtasdt0( X, sz10 ) =
% 0.75/1.32 X }.
% 0.75/1.32 (2193) {G0,W7,D3,L2,V1,M2} { ! aNaturalNumber0( X ), X = sdtasdt0( sz10, X
% 0.75/1.32 ) }.
% 0.75/1.32 (2194) {G0,W7,D3,L2,V1,M2} { ! aNaturalNumber0( X ), sdtasdt0( X, sz00 ) =
% 0.75/1.32 sz00 }.
% 0.75/1.32 (2195) {G0,W7,D3,L2,V1,M2} { ! aNaturalNumber0( X ), sz00 = sdtasdt0( sz00
% 0.75/1.32 , X ) }.
% 0.75/1.32 (2196) {G0,W19,D4,L4,V3,M4} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 0.75/1.32 ), ! aNaturalNumber0( Z ), sdtasdt0( X, sdtpldt0( Y, Z ) ) = sdtpldt0(
% 0.75/1.32 sdtasdt0( X, Y ), sdtasdt0( X, Z ) ) }.
% 0.75/1.32 (2197) {G0,W19,D4,L4,V3,M4} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 0.75/1.32 ), ! aNaturalNumber0( Z ), sdtasdt0( sdtpldt0( Y, Z ), X ) = sdtpldt0(
% 0.75/1.32 sdtasdt0( Y, X ), sdtasdt0( Z, X ) ) }.
% 0.75/1.32 (2198) {G0,W16,D3,L5,V3,M5} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 0.75/1.32 ), ! aNaturalNumber0( Z ), ! sdtpldt0( X, Y ) = sdtpldt0( X, Z ), Y = Z
% 0.75/1.32 }.
% 0.75/1.32 (2199) {G0,W16,D3,L5,V3,M5} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 0.75/1.32 ), ! aNaturalNumber0( Z ), ! sdtpldt0( Y, X ) = sdtpldt0( Z, X ), Y = Z
% 0.75/1.32 }.
% 0.75/1.32 (2200) {G0,W19,D3,L6,V3,M6} { ! aNaturalNumber0( X ), X = sz00, !
% 0.75/1.32 aNaturalNumber0( Y ), ! aNaturalNumber0( Z ), ! sdtasdt0( X, Y ) =
% 0.75/1.32 sdtasdt0( X, Z ), Y = Z }.
% 0.75/1.32 (2201) {G0,W19,D3,L6,V3,M6} { ! aNaturalNumber0( X ), X = sz00, !
% 0.75/1.32 aNaturalNumber0( Y ), ! aNaturalNumber0( Z ), ! sdtasdt0( Y, X ) =
% 0.75/1.32 sdtasdt0( Z, X ), Y = Z }.
% 0.75/1.32 (2202) {G0,W12,D3,L4,V2,M4} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 0.75/1.32 ), ! sdtpldt0( X, Y ) = sz00, X = sz00 }.
% 0.75/1.32 (2203) {G0,W12,D3,L4,V2,M4} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 0.75/1.32 ), ! sdtpldt0( X, Y ) = sz00, Y = sz00 }.
% 0.75/1.32 (2204) {G0,W15,D3,L5,V2,M5} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 0.75/1.32 ), ! sdtasdt0( X, Y ) = sz00, X = sz00, Y = sz00 }.
% 0.75/1.32 (2205) {G0,W11,D3,L4,V4,M4} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 0.75/1.32 ), ! sdtlseqdt0( X, Y ), aNaturalNumber0( skol1( Z, T ) ) }.
% 0.75/1.32 (2206) {G0,W14,D4,L4,V2,M4} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 0.75/1.32 ), ! sdtlseqdt0( X, Y ), sdtpldt0( X, skol1( X, Y ) ) = Y }.
% 0.75/1.32 (2207) {G0,W14,D3,L5,V3,M5} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 0.75/1.32 ), ! aNaturalNumber0( Z ), ! sdtpldt0( X, Z ) = Y, sdtlseqdt0( X, Y )
% 0.75/1.32 }.
% 0.75/1.32 (2208) {G0,W14,D3,L5,V3,M5} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 0.75/1.32 ), ! sdtlseqdt0( X, Y ), ! Z = sdtmndt0( Y, X ), aNaturalNumber0( Z )
% 0.75/1.32 }.
% 0.75/1.32 (2209) {G0,W17,D3,L5,V3,M5} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 0.75/1.32 ), ! sdtlseqdt0( X, Y ), ! Z = sdtmndt0( Y, X ), sdtpldt0( X, Z ) = Y
% 0.75/1.32 }.
% 0.75/1.32 (2210) {G0,W19,D3,L6,V3,M6} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 0.75/1.32 ), ! sdtlseqdt0( X, Y ), ! aNaturalNumber0( Z ), ! sdtpldt0( X, Z ) = Y
% 0.75/1.32 , Z = sdtmndt0( Y, X ) }.
% 0.75/1.32 (2211) {G0,W5,D2,L2,V1,M2} { ! aNaturalNumber0( X ), sdtlseqdt0( X, X )
% 0.75/1.32 }.
% 0.75/1.32 (2212) {G0,W13,D2,L5,V2,M5} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 0.75/1.32 ), ! sdtlseqdt0( X, Y ), ! sdtlseqdt0( Y, X ), X = Y }.
% 0.75/1.32 (2213) {G0,W15,D2,L6,V3,M6} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 0.75/1.32 ), ! aNaturalNumber0( Z ), ! sdtlseqdt0( X, Y ), ! sdtlseqdt0( Y, Z ),
% 0.75/1.32 sdtlseqdt0( X, Z ) }.
% 0.75/1.32 (2214) {G0,W10,D2,L4,V2,M4} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 0.75/1.32 ), sdtlseqdt0( X, Y ), ! Y = X }.
% 0.75/1.32 (2215) {G0,W10,D2,L4,V2,M4} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 0.75/1.32 ), sdtlseqdt0( X, Y ), sdtlseqdt0( Y, X ) }.
% 0.75/1.32 (2216) {G0,W16,D2,L6,V3,M6} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 0.75/1.32 ), X = Y, ! sdtlseqdt0( X, Y ), ! aNaturalNumber0( Z ), alpha5( X, Y, Z
% 0.75/1.32 ) }.
% 0.75/1.32 (2217) {G0,W19,D3,L6,V3,M6} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 0.75/1.32 ), X = Y, ! sdtlseqdt0( X, Y ), ! aNaturalNumber0( Z ), sdtlseqdt0(
% 0.75/1.32 sdtpldt0( X, Z ), sdtpldt0( Y, Z ) ) }.
% 0.75/1.32 (2218) {G0,W11,D3,L2,V3,M2} { ! alpha5( X, Y, Z ), ! sdtpldt0( Z, X ) =
% 0.75/1.32 sdtpldt0( Z, Y ) }.
% 0.75/1.32 (2219) {G0,W11,D3,L2,V3,M2} { ! alpha5( X, Y, Z ), sdtlseqdt0( sdtpldt0( Z
% 0.75/1.32 , X ), sdtpldt0( Z, Y ) ) }.
% 0.75/1.32 (2220) {G0,W11,D3,L2,V3,M2} { ! alpha5( X, Y, Z ), ! sdtpldt0( X, Z ) =
% 0.75/1.32 sdtpldt0( Y, Z ) }.
% 0.75/1.32 (2221) {G0,W25,D3,L4,V3,M4} { sdtpldt0( Z, X ) = sdtpldt0( Z, Y ), !
% 0.75/1.32 sdtlseqdt0( sdtpldt0( Z, X ), sdtpldt0( Z, Y ) ), sdtpldt0( X, Z ) =
% 0.75/1.32 sdtpldt0( Y, Z ), alpha5( X, Y, Z ) }.
% 0.75/1.32 (2222) {G0,W19,D2,L7,V3,M7} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 0.75/1.32 ), ! aNaturalNumber0( Z ), X = sz00, Y = Z, ! sdtlseqdt0( Y, Z ), alpha6
% 0.75/1.32 ( X, Y, Z ) }.
% 0.75/1.32 (2223) {G0,W22,D3,L7,V3,M7} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 0.75/1.32 ), ! aNaturalNumber0( Z ), X = sz00, Y = Z, ! sdtlseqdt0( Y, Z ),
% 0.75/1.32 sdtlseqdt0( sdtasdt0( Y, X ), sdtasdt0( Z, X ) ) }.
% 0.75/1.32 (2224) {G0,W11,D3,L2,V3,M2} { ! alpha6( X, Y, Z ), ! sdtasdt0( X, Y ) =
% 0.75/1.32 sdtasdt0( X, Z ) }.
% 0.75/1.32 (2225) {G0,W11,D3,L2,V3,M2} { ! alpha6( X, Y, Z ), sdtlseqdt0( sdtasdt0( X
% 0.75/1.32 , Y ), sdtasdt0( X, Z ) ) }.
% 0.75/1.32 (2226) {G0,W11,D3,L2,V3,M2} { ! alpha6( X, Y, Z ), ! sdtasdt0( Y, X ) =
% 0.75/1.32 sdtasdt0( Z, X ) }.
% 0.75/1.32 (2227) {G0,W25,D3,L4,V3,M4} { sdtasdt0( X, Y ) = sdtasdt0( X, Z ), !
% 0.75/1.32 sdtlseqdt0( sdtasdt0( X, Y ), sdtasdt0( X, Z ) ), sdtasdt0( Y, X ) =
% 0.75/1.32 sdtasdt0( Z, X ), alpha6( X, Y, Z ) }.
% 0.75/1.32 (2228) {G0,W11,D2,L4,V1,M4} { ! aNaturalNumber0( X ), X = sz00, X = sz10,
% 0.75/1.32 ! sz10 = X }.
% 0.75/1.32 (2229) {G0,W11,D2,L4,V1,M4} { ! aNaturalNumber0( X ), X = sz00, X = sz10,
% 0.75/1.32 sdtlseqdt0( sz10, X ) }.
% 0.75/1.32 (2230) {G0,W12,D3,L4,V2,M4} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 0.75/1.32 ), X = sz00, sdtlseqdt0( Y, sdtasdt0( Y, X ) ) }.
% 0.75/1.32 (2231) {G0,W1,D1,L1,V0,M1} { && }.
% 0.75/1.32 (2232) {G0,W13,D2,L5,V2,M5} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 0.75/1.32 ), X = Y, ! sdtlseqdt0( X, Y ), iLess0( X, Y ) }.
% 0.75/1.32 (2233) {G0,W11,D3,L4,V4,M4} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 0.75/1.32 ), ! doDivides0( X, Y ), aNaturalNumber0( skol2( Z, T ) ) }.
% 0.75/1.32 (2234) {G0,W14,D4,L4,V2,M4} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 0.75/1.32 ), ! doDivides0( X, Y ), Y = sdtasdt0( X, skol2( X, Y ) ) }.
% 0.75/1.32 (2235) {G0,W14,D3,L5,V3,M5} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 0.75/1.32 ), ! aNaturalNumber0( Z ), ! Y = sdtasdt0( X, Z ), doDivides0( X, Y )
% 0.75/1.32 }.
% 0.75/1.32 (2236) {G0,W17,D3,L6,V3,M6} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 0.75/1.32 ), X = sz00, ! doDivides0( X, Y ), ! Z = sdtsldt0( Y, X ),
% 0.75/1.32 aNaturalNumber0( Z ) }.
% 0.75/1.32 (2237) {G0,W20,D3,L6,V3,M6} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 0.75/1.32 ), X = sz00, ! doDivides0( X, Y ), ! Z = sdtsldt0( Y, X ), Y = sdtasdt0
% 0.75/1.32 ( X, Z ) }.
% 0.75/1.32 (2238) {G0,W22,D3,L7,V3,M7} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 0.75/1.32 ), X = sz00, ! doDivides0( X, Y ), ! aNaturalNumber0( Z ), ! Y =
% 0.75/1.32 sdtasdt0( X, Z ), Z = sdtsldt0( Y, X ) }.
% 0.75/1.32 (2239) {G0,W15,D2,L6,V3,M6} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 0.75/1.32 ), ! aNaturalNumber0( Z ), ! doDivides0( X, Y ), ! doDivides0( Y, Z ),
% 0.75/1.32 doDivides0( X, Z ) }.
% 0.75/1.32 (2240) {G0,W17,D3,L6,V3,M6} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 0.75/1.32 ), ! aNaturalNumber0( Z ), ! doDivides0( X, Y ), ! doDivides0( X, Z ),
% 0.75/1.32 doDivides0( X, sdtpldt0( Y, Z ) ) }.
% 0.75/1.32 (2241) {G0,W17,D3,L6,V3,M6} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 0.75/1.32 ), ! aNaturalNumber0( Z ), ! doDivides0( X, Y ), ! doDivides0( X,
% 0.75/1.33 sdtpldt0( Y, Z ) ), doDivides0( X, Z ) }.
% 0.75/1.33 (2242) {G0,W13,D2,L5,V2,M5} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 0.75/1.33 ), ! doDivides0( X, Y ), Y = sz00, sdtlseqdt0( X, Y ) }.
% 0.75/1.33 (2243) {G0,W23,D4,L6,V3,M6} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 0.75/1.33 ), X = sz00, ! doDivides0( X, Y ), ! aNaturalNumber0( Z ), sdtasdt0( Z,
% 0.75/1.33 sdtsldt0( Y, X ) ) = sdtsldt0( sdtasdt0( Z, Y ), X ) }.
% 0.75/1.33 (2244) {G0,W7,D2,L3,V1,M3} { ! aNaturalNumber0( X ), ! isPrime0( X ), ! X
% 0.75/1.33 = sz00 }.
% 0.75/1.33 (2245) {G0,W6,D2,L3,V1,M3} { ! aNaturalNumber0( X ), ! isPrime0( X ),
% 0.75/1.33 alpha1( X ) }.
% 0.75/1.33 (2246) {G0,W9,D2,L4,V1,M4} { ! aNaturalNumber0( X ), X = sz00, ! alpha1( X
% 0.75/1.33 ), isPrime0( X ) }.
% 0.75/1.33 (2247) {G0,W5,D2,L2,V1,M2} { ! alpha1( X ), ! X = sz10 }.
% 0.75/1.33 (2248) {G0,W4,D2,L2,V1,M2} { ! alpha1( X ), alpha2( X ) }.
% 0.75/1.33 (2249) {G0,W7,D2,L3,V1,M3} { X = sz10, ! alpha2( X ), alpha1( X ) }.
% 0.75/1.33 (2250) {G0,W8,D2,L3,V2,M3} { ! alpha2( X ), ! alpha3( X, Y ), alpha4( X, Y
% 0.75/1.33 ) }.
% 0.75/1.33 (2251) {G0,W6,D3,L2,V1,M2} { alpha3( X, skol3( X ) ), alpha2( X ) }.
% 0.75/1.33 (2252) {G0,W6,D3,L2,V1,M2} { ! alpha4( X, skol3( X ) ), alpha2( X ) }.
% 0.75/1.33 (2253) {G0,W9,D2,L3,V2,M3} { ! alpha4( X, Y ), Y = sz10, Y = X }.
% 0.75/1.33 (2254) {G0,W6,D2,L2,V2,M2} { ! Y = sz10, alpha4( X, Y ) }.
% 0.75/1.33 (2255) {G0,W6,D2,L2,V2,M2} { ! Y = X, alpha4( X, Y ) }.
% 0.75/1.33 (2256) {G0,W5,D2,L2,V2,M2} { ! alpha3( X, Y ), aNaturalNumber0( Y ) }.
% 0.75/1.33 (2257) {G0,W6,D2,L2,V2,M2} { ! alpha3( X, Y ), doDivides0( Y, X ) }.
% 0.75/1.33 (2258) {G0,W8,D2,L3,V2,M3} { ! aNaturalNumber0( Y ), ! doDivides0( Y, X )
% 0.75/1.33 , alpha3( X, Y ) }.
% 0.75/1.33 (2259) {G0,W11,D3,L4,V2,M4} { ! aNaturalNumber0( X ), X = sz00, X = sz10,
% 0.75/1.33 aNaturalNumber0( skol4( Y ) ) }.
% 0.75/1.33 (2260) {G0,W11,D3,L4,V2,M4} { ! aNaturalNumber0( X ), X = sz00, X = sz10,
% 0.75/1.33 isPrime0( skol4( Y ) ) }.
% 0.75/1.33 (2261) {G0,W12,D3,L4,V1,M4} { ! aNaturalNumber0( X ), X = sz00, X = sz10,
% 0.75/1.33 doDivides0( skol4( X ), X ) }.
% 0.75/1.33 (2262) {G0,W2,D2,L1,V0,M1} { aNaturalNumber0( xn ) }.
% 0.75/1.33 (2263) {G0,W2,D2,L1,V0,M1} { aNaturalNumber0( xm ) }.
% 0.75/1.33 (2264) {G0,W2,D2,L1,V0,M1} { aNaturalNumber0( xp ) }.
% 0.75/1.33 (2265) {G0,W30,D4,L8,V3,M8} { ! aNaturalNumber0( X ), ! aNaturalNumber0( Y
% 0.75/1.33 ), ! aNaturalNumber0( Z ), ! isPrime0( Z ), ! doDivides0( Z, sdtasdt0( X
% 0.75/1.33 , Y ) ), ! iLess0( sdtpldt0( sdtpldt0( X, Y ), Z ), sdtpldt0( sdtpldt0(
% 0.75/1.33 xn, xm ), xp ) ), doDivides0( Z, X ), doDivides0( Z, Y ) }.
% 0.75/1.33 (2266) {G0,W2,D2,L1,V0,M1} { isPrime0( xp ) }.
% 0.75/1.33 (2267) {G0,W5,D3,L1,V0,M1} { doDivides0( xp, sdtasdt0( xn, xm ) ) }.
% 0.75/1.33 (2268) {G0,W3,D2,L1,V0,M1} { sdtlseqdt0( xp, xn ) }.
% 0.75/1.33 (2269) {G0,W5,D3,L1,V0,M1} { xr = sdtmndt0( xn, xp ) }.
% 0.75/1.33 (2270) {G0,W3,D2,L1,V0,M1} { ! xr = xn }.
% 0.75/1.33 (2271) {G0,W3,D2,L1,V0,M1} { sdtlseqdt0( xr, xn ) }.
% 0.75/1.33 (2272) {G0,W5,D3,L1,V0,M1} { ! xn = sdtpldt0( xp, xr ) }.
% 0.75/1.33
% 0.75/1.33
% 0.75/1.33 Total Proof:
% 0.75/1.33
% 0.75/1.33 *** allocated 170857 integers for clauses
% 0.75/1.33 subsumption: (29) {G0,W17,D3,L5,V3,M5} I { ! aNaturalNumber0( X ), !
% 0.75/1.33 aNaturalNumber0( Y ), ! sdtlseqdt0( X, Y ), ! Z = sdtmndt0( Y, X ),
% 0.75/1.33 sdtpldt0( X, Z ) = Y }.
% 0.75/1.33 parent0: (2209) {G0,W17,D3,L5,V3,M5} { ! aNaturalNumber0( X ), !
% 0.75/1.33 aNaturalNumber0( Y ), ! sdtlseqdt0( X, Y ), ! Z = sdtmndt0( Y, X ),
% 0.75/1.33 sdtpldt0( X, Z ) = Y }.
% 0.75/1.33 substitution0:
% 0.75/1.33 X := X
% 0.75/1.33 Y := Y
% 0.75/1.33 Z := Z
% 0.75/1.33 end
% 0.75/1.33 permutation0:
% 0.75/1.33 0 ==> 0
% 0.75/1.33 1 ==> 1
% 0.75/1.33 2 ==> 2
% 0.75/1.33 3 ==> 3
% 0.75/1.33 4 ==> 4
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 *** allocated 75937 integers for termspace/termends
% 0.75/1.33 subsumption: (81) {G0,W2,D2,L1,V0,M1} I { aNaturalNumber0( xn ) }.
% 0.75/1.33 parent0: (2262) {G0,W2,D2,L1,V0,M1} { aNaturalNumber0( xn ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 end
% 0.75/1.33 permutation0:
% 0.75/1.33 0 ==> 0
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 subsumption: (83) {G0,W2,D2,L1,V0,M1} I { aNaturalNumber0( xp ) }.
% 0.75/1.33 parent0: (2264) {G0,W2,D2,L1,V0,M1} { aNaturalNumber0( xp ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 end
% 0.75/1.33 permutation0:
% 0.75/1.33 0 ==> 0
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 subsumption: (87) {G0,W3,D2,L1,V0,M1} I { sdtlseqdt0( xp, xn ) }.
% 0.75/1.33 parent0: (2268) {G0,W3,D2,L1,V0,M1} { sdtlseqdt0( xp, xn ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 end
% 0.75/1.33 permutation0:
% 0.75/1.33 0 ==> 0
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 *** allocated 113905 integers for termspace/termends
% 0.75/1.33 eqswap: (4130) {G0,W5,D3,L1,V0,M1} { sdtmndt0( xn, xp ) = xr }.
% 0.75/1.33 parent0[0]: (2269) {G0,W5,D3,L1,V0,M1} { xr = sdtmndt0( xn, xp ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 subsumption: (88) {G0,W5,D3,L1,V0,M1} I { sdtmndt0( xn, xp ) ==> xr }.
% 0.75/1.33 parent0: (4130) {G0,W5,D3,L1,V0,M1} { sdtmndt0( xn, xp ) = xr }.
% 0.75/1.33 substitution0:
% 0.75/1.33 end
% 0.75/1.33 permutation0:
% 0.75/1.33 0 ==> 0
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 eqswap: (4559) {G0,W5,D3,L1,V0,M1} { ! sdtpldt0( xp, xr ) = xn }.
% 0.75/1.33 parent0[0]: (2272) {G0,W5,D3,L1,V0,M1} { ! xn = sdtpldt0( xp, xr ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 subsumption: (91) {G0,W5,D3,L1,V0,M1} I { ! sdtpldt0( xp, xr ) ==> xn }.
% 0.75/1.33 parent0: (4559) {G0,W5,D3,L1,V0,M1} { ! sdtpldt0( xp, xr ) = xn }.
% 0.75/1.33 substitution0:
% 0.75/1.33 end
% 0.75/1.33 permutation0:
% 0.75/1.33 0 ==> 0
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 eqswap: (4560) {G0,W17,D3,L5,V3,M5} { ! sdtmndt0( Y, Z ) = X, !
% 0.75/1.33 aNaturalNumber0( Z ), ! aNaturalNumber0( Y ), ! sdtlseqdt0( Z, Y ),
% 0.75/1.33 sdtpldt0( Z, X ) = Y }.
% 0.75/1.33 parent0[3]: (29) {G0,W17,D3,L5,V3,M5} I { ! aNaturalNumber0( X ), !
% 0.75/1.33 aNaturalNumber0( Y ), ! sdtlseqdt0( X, Y ), ! Z = sdtmndt0( Y, X ),
% 0.75/1.33 sdtpldt0( X, Z ) = Y }.
% 0.75/1.33 substitution0:
% 0.75/1.33 X := Z
% 0.75/1.33 Y := Y
% 0.75/1.33 Z := X
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 resolution: (4564) {G1,W14,D3,L4,V1,M4} { ! sdtmndt0( xn, xp ) = X, !
% 0.75/1.33 aNaturalNumber0( xp ), ! aNaturalNumber0( xn ), sdtpldt0( xp, X ) = xn
% 0.75/1.33 }.
% 0.75/1.33 parent0[3]: (4560) {G0,W17,D3,L5,V3,M5} { ! sdtmndt0( Y, Z ) = X, !
% 0.75/1.33 aNaturalNumber0( Z ), ! aNaturalNumber0( Y ), ! sdtlseqdt0( Z, Y ),
% 0.75/1.33 sdtpldt0( Z, X ) = Y }.
% 0.75/1.33 parent1[0]: (87) {G0,W3,D2,L1,V0,M1} I { sdtlseqdt0( xp, xn ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 X := X
% 0.75/1.33 Y := xn
% 0.75/1.33 Z := xp
% 0.75/1.33 end
% 0.75/1.33 substitution1:
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 paramod: (4565) {G1,W12,D3,L4,V1,M4} { ! xr = X, ! aNaturalNumber0( xp ),
% 0.75/1.33 ! aNaturalNumber0( xn ), sdtpldt0( xp, X ) = xn }.
% 0.75/1.33 parent0[0]: (88) {G0,W5,D3,L1,V0,M1} I { sdtmndt0( xn, xp ) ==> xr }.
% 0.75/1.33 parent1[0; 2]: (4564) {G1,W14,D3,L4,V1,M4} { ! sdtmndt0( xn, xp ) = X, !
% 0.75/1.33 aNaturalNumber0( xp ), ! aNaturalNumber0( xn ), sdtpldt0( xp, X ) = xn
% 0.75/1.33 }.
% 0.75/1.33 substitution0:
% 0.75/1.33 end
% 0.75/1.33 substitution1:
% 0.75/1.33 X := X
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 resolution: (4566) {G1,W10,D3,L3,V1,M3} { ! xr = X, ! aNaturalNumber0( xn
% 0.75/1.33 ), sdtpldt0( xp, X ) = xn }.
% 0.75/1.33 parent0[1]: (4565) {G1,W12,D3,L4,V1,M4} { ! xr = X, ! aNaturalNumber0( xp
% 0.75/1.33 ), ! aNaturalNumber0( xn ), sdtpldt0( xp, X ) = xn }.
% 0.75/1.33 parent1[0]: (83) {G0,W2,D2,L1,V0,M1} I { aNaturalNumber0( xp ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 X := X
% 0.75/1.33 end
% 0.75/1.33 substitution1:
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 eqswap: (4567) {G1,W10,D3,L3,V1,M3} { ! X = xr, ! aNaturalNumber0( xn ),
% 0.75/1.33 sdtpldt0( xp, X ) = xn }.
% 0.75/1.33 parent0[0]: (4566) {G1,W10,D3,L3,V1,M3} { ! xr = X, ! aNaturalNumber0( xn
% 0.75/1.33 ), sdtpldt0( xp, X ) = xn }.
% 0.75/1.33 substitution0:
% 0.75/1.33 X := X
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 subsumption: (2045) {G1,W10,D3,L3,V1,M3} R(29,87);d(88);r(83) { !
% 0.75/1.33 aNaturalNumber0( xn ), sdtpldt0( xp, X ) ==> xn, ! X = xr }.
% 0.75/1.33 parent0: (4567) {G1,W10,D3,L3,V1,M3} { ! X = xr, ! aNaturalNumber0( xn ),
% 0.75/1.33 sdtpldt0( xp, X ) = xn }.
% 0.75/1.33 substitution0:
% 0.75/1.33 X := X
% 0.75/1.33 end
% 0.75/1.33 permutation0:
% 0.75/1.33 0 ==> 2
% 0.75/1.33 1 ==> 0
% 0.75/1.33 2 ==> 1
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 eqswap: (4570) {G1,W10,D3,L3,V1,M3} { xn ==> sdtpldt0( xp, X ), !
% 0.75/1.33 aNaturalNumber0( xn ), ! X = xr }.
% 0.75/1.33 parent0[1]: (2045) {G1,W10,D3,L3,V1,M3} R(29,87);d(88);r(83) { !
% 0.75/1.33 aNaturalNumber0( xn ), sdtpldt0( xp, X ) ==> xn, ! X = xr }.
% 0.75/1.33 substitution0:
% 0.75/1.33 X := X
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 eqrefl: (4573) {G0,W7,D3,L2,V0,M2} { xn ==> sdtpldt0( xp, xr ), !
% 0.75/1.33 aNaturalNumber0( xn ) }.
% 0.75/1.33 parent0[2]: (4570) {G1,W10,D3,L3,V1,M3} { xn ==> sdtpldt0( xp, X ), !
% 0.75/1.33 aNaturalNumber0( xn ), ! X = xr }.
% 0.75/1.33 substitution0:
% 0.75/1.33 X := xr
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 resolution: (4574) {G1,W5,D3,L1,V0,M1} { xn ==> sdtpldt0( xp, xr ) }.
% 0.75/1.33 parent0[1]: (4573) {G0,W7,D3,L2,V0,M2} { xn ==> sdtpldt0( xp, xr ), !
% 0.75/1.33 aNaturalNumber0( xn ) }.
% 0.75/1.33 parent1[0]: (81) {G0,W2,D2,L1,V0,M1} I { aNaturalNumber0( xn ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 end
% 0.75/1.33 substitution1:
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 eqswap: (4575) {G1,W5,D3,L1,V0,M1} { sdtpldt0( xp, xr ) ==> xn }.
% 0.75/1.33 parent0[0]: (4574) {G1,W5,D3,L1,V0,M1} { xn ==> sdtpldt0( xp, xr ) }.
% 0.75/1.33 substitution0:
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 subsumption: (2161) {G2,W5,D3,L1,V0,M1} Q(2045);r(81) { sdtpldt0( xp, xr )
% 0.75/1.33 ==> xn }.
% 0.75/1.33 parent0: (4575) {G1,W5,D3,L1,V0,M1} { sdtpldt0( xp, xr ) ==> xn }.
% 0.75/1.33 substitution0:
% 0.75/1.33 end
% 0.75/1.33 permutation0:
% 0.75/1.33 0 ==> 0
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 paramod: (4578) {G1,W3,D2,L1,V0,M1} { ! xn ==> xn }.
% 0.75/1.33 parent0[0]: (2161) {G2,W5,D3,L1,V0,M1} Q(2045);r(81) { sdtpldt0( xp, xr )
% 0.75/1.33 ==> xn }.
% 0.75/1.33 parent1[0; 2]: (91) {G0,W5,D3,L1,V0,M1} I { ! sdtpldt0( xp, xr ) ==> xn }.
% 0.75/1.33 substitution0:
% 0.75/1.33 end
% 0.75/1.33 substitution1:
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 eqrefl: (4579) {G0,W0,D0,L0,V0,M0} { }.
% 0.75/1.33 parent0[0]: (4578) {G1,W3,D2,L1,V0,M1} { ! xn ==> xn }.
% 0.75/1.33 substitution0:
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 subsumption: (2178) {G3,W0,D0,L0,V0,M0} S(91);d(2161);q { }.
% 0.75/1.33 parent0: (4579) {G0,W0,D0,L0,V0,M0} { }.
% 0.75/1.33 substitution0:
% 0.75/1.33 end
% 0.75/1.33 permutation0:
% 0.75/1.33 end
% 0.75/1.33
% 0.75/1.33 Proof check complete!
% 0.75/1.33
% 0.75/1.33 Memory use:
% 0.75/1.33
% 0.75/1.33 space for terms: 42119
% 0.75/1.33 space for clauses: 110971
% 0.75/1.33
% 0.75/1.33
% 0.75/1.33 clauses generated: 13282
% 0.75/1.33 clauses kept: 2179
% 0.75/1.33 clauses selected: 138
% 0.75/1.33 clauses deleted: 9
% 0.75/1.33 clauses inuse deleted: 6
% 0.75/1.33
% 0.75/1.33 subsentry: 35242
% 0.75/1.33 literals s-matched: 17026
% 0.75/1.33 literals matched: 14058
% 0.75/1.33 full subsumption: 9337
% 0.75/1.33
% 0.75/1.33 checksum: 924783659
% 0.75/1.33
% 0.75/1.33
% 0.75/1.33 Bliksem ended
%------------------------------------------------------------------------------