TSTP Solution File: COM021+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : COM021+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 : Fri Jul 15 00:51:10 EDT 2022
% Result : Theorem 5.00s 5.38s
% Output : Refutation 5.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : COM021+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : bliksem %s
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Thu Jun 16 18:14:26 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.72/1.08 *** allocated 10000 integers for termspace/termends
% 0.72/1.08 *** allocated 10000 integers for clauses
% 0.72/1.08 *** allocated 10000 integers for justifications
% 0.72/1.08 Bliksem 1.12
% 0.72/1.08
% 0.72/1.08
% 0.72/1.08 Automatic Strategy Selection
% 0.72/1.08
% 0.72/1.08
% 0.72/1.08 Clauses:
% 0.72/1.08
% 0.72/1.08 { && }.
% 0.72/1.08 { && }.
% 0.72/1.08 { ! aElement0( X ), ! aRewritingSystem0( Y ), ! aReductOfIn0( Z, X, Y ),
% 0.72/1.08 aElement0( Z ) }.
% 0.72/1.08 { && }.
% 0.72/1.08 { && }.
% 0.72/1.08 { ! aElement0( X ), ! aRewritingSystem0( Y ), ! aElement0( Z ), !
% 0.72/1.08 sdtmndtplgtdt0( X, Y, Z ), aReductOfIn0( Z, X, Y ), alpha1( X, Y, Z ) }.
% 0.72/1.08 { ! aElement0( X ), ! aRewritingSystem0( Y ), ! aElement0( Z ), !
% 0.72/1.08 aReductOfIn0( Z, X, Y ), sdtmndtplgtdt0( X, Y, Z ) }.
% 0.72/1.08 { ! aElement0( X ), ! aRewritingSystem0( Y ), ! aElement0( Z ), ! alpha1( X
% 0.72/1.08 , Y, Z ), sdtmndtplgtdt0( X, Y, Z ) }.
% 0.72/1.08 { ! alpha1( X, Y, Z ), aElement0( skol1( T, U, W ) ) }.
% 0.72/1.08 { ! alpha1( X, Y, Z ), alpha6( X, Y, Z, skol1( X, Y, Z ) ) }.
% 0.72/1.08 { ! aElement0( T ), ! alpha6( X, Y, Z, T ), alpha1( X, Y, Z ) }.
% 0.72/1.08 { ! alpha6( X, Y, Z, T ), aReductOfIn0( T, X, Y ) }.
% 0.72/1.08 { ! alpha6( X, Y, Z, T ), sdtmndtplgtdt0( T, Y, Z ) }.
% 0.72/1.08 { ! aReductOfIn0( T, X, Y ), ! sdtmndtplgtdt0( T, Y, Z ), alpha6( X, Y, Z,
% 0.72/1.08 T ) }.
% 0.72/1.08 { ! aElement0( X ), ! aRewritingSystem0( Y ), ! aElement0( Z ), ! aElement0
% 0.72/1.08 ( T ), ! sdtmndtplgtdt0( X, Y, Z ), ! sdtmndtplgtdt0( Z, Y, T ),
% 0.72/1.08 sdtmndtplgtdt0( X, Y, T ) }.
% 0.72/1.08 { ! aElement0( X ), ! aRewritingSystem0( Y ), ! aElement0( Z ), !
% 0.72/1.08 sdtmndtasgtdt0( X, Y, Z ), X = Z, sdtmndtplgtdt0( X, Y, Z ) }.
% 0.72/1.08 { ! aElement0( X ), ! aRewritingSystem0( Y ), ! aElement0( Z ), ! X = Z,
% 0.72/1.08 sdtmndtasgtdt0( X, Y, Z ) }.
% 0.72/1.08 { ! aElement0( X ), ! aRewritingSystem0( Y ), ! aElement0( Z ), !
% 0.72/1.08 sdtmndtplgtdt0( X, Y, Z ), sdtmndtasgtdt0( X, Y, Z ) }.
% 0.72/1.08 { ! aElement0( X ), ! aRewritingSystem0( Y ), ! aElement0( Z ), ! aElement0
% 0.72/1.08 ( T ), ! sdtmndtasgtdt0( X, Y, Z ), ! sdtmndtasgtdt0( Z, Y, T ),
% 0.72/1.08 sdtmndtasgtdt0( X, Y, T ) }.
% 0.72/1.08 { ! aRewritingSystem0( X ), ! isConfluent0( X ), ! alpha2( X, Y, Z ),
% 0.72/1.08 alpha7( X, Y, Z ) }.
% 0.72/1.08 { ! aRewritingSystem0( X ), alpha2( X, skol2( X ), skol12( X ) ),
% 0.72/1.08 isConfluent0( X ) }.
% 0.72/1.08 { ! aRewritingSystem0( X ), ! alpha7( X, skol2( X ), skol12( X ) ),
% 0.72/1.08 isConfluent0( X ) }.
% 0.72/1.08 { ! alpha7( X, Y, Z ), aElement0( skol3( T, U, W ) ) }.
% 0.72/1.08 { ! alpha7( X, Y, Z ), alpha12( X, Y, Z, skol3( X, Y, Z ) ) }.
% 0.72/1.08 { ! aElement0( T ), ! alpha12( X, Y, Z, T ), alpha7( X, Y, Z ) }.
% 0.72/1.08 { ! alpha12( X, Y, Z, T ), sdtmndtasgtdt0( Y, X, T ) }.
% 0.72/1.08 { ! alpha12( X, Y, Z, T ), sdtmndtasgtdt0( Z, X, T ) }.
% 0.72/1.08 { ! sdtmndtasgtdt0( Y, X, T ), ! sdtmndtasgtdt0( Z, X, T ), alpha12( X, Y,
% 0.72/1.08 Z, T ) }.
% 0.72/1.08 { ! alpha2( X, Y, Z ), aElement0( skol4( T, U, W ) ) }.
% 0.72/1.08 { ! alpha2( X, Y, Z ), alpha8( X, Y, Z, skol4( X, Y, Z ) ) }.
% 0.72/1.08 { ! aElement0( T ), ! alpha8( X, Y, Z, T ), alpha2( X, Y, Z ) }.
% 0.72/1.08 { ! alpha8( X, Y, Z, T ), aElement0( Y ) }.
% 0.72/1.08 { ! alpha8( X, Y, Z, T ), alpha13( X, Y, Z, T ) }.
% 0.72/1.08 { ! aElement0( Y ), ! alpha13( X, Y, Z, T ), alpha8( X, Y, Z, T ) }.
% 0.72/1.08 { ! alpha13( X, Y, Z, T ), aElement0( Z ) }.
% 0.72/1.08 { ! alpha13( X, Y, Z, T ), alpha16( X, Y, Z, T ) }.
% 0.72/1.08 { ! aElement0( Z ), ! alpha16( X, Y, Z, T ), alpha13( X, Y, Z, T ) }.
% 0.72/1.08 { ! alpha16( X, Y, Z, T ), sdtmndtasgtdt0( T, X, Y ) }.
% 0.72/1.08 { ! alpha16( X, Y, Z, T ), sdtmndtasgtdt0( T, X, Z ) }.
% 0.72/1.08 { ! sdtmndtasgtdt0( T, X, Y ), ! sdtmndtasgtdt0( T, X, Z ), alpha16( X, Y,
% 0.72/1.08 Z, T ) }.
% 0.72/1.08 { ! aRewritingSystem0( X ), ! isLocallyConfluent0( X ), ! alpha3( X, Y, Z )
% 0.72/1.08 , alpha9( X, Y, Z ) }.
% 0.72/1.08 { ! aRewritingSystem0( X ), alpha3( X, skol5( X ), skol13( X ) ),
% 0.72/1.08 isLocallyConfluent0( X ) }.
% 0.72/1.08 { ! aRewritingSystem0( X ), ! alpha9( X, skol5( X ), skol13( X ) ),
% 0.72/1.08 isLocallyConfluent0( X ) }.
% 0.72/1.08 { ! alpha9( X, Y, Z ), aElement0( skol6( T, U, W ) ) }.
% 0.72/1.08 { ! alpha9( X, Y, Z ), alpha14( X, Y, Z, skol6( X, Y, Z ) ) }.
% 0.72/1.08 { ! aElement0( T ), ! alpha14( X, Y, Z, T ), alpha9( X, Y, Z ) }.
% 0.72/1.08 { ! alpha14( X, Y, Z, T ), sdtmndtasgtdt0( Y, X, T ) }.
% 0.72/1.08 { ! alpha14( X, Y, Z, T ), sdtmndtasgtdt0( Z, X, T ) }.
% 0.72/1.08 { ! sdtmndtasgtdt0( Y, X, T ), ! sdtmndtasgtdt0( Z, X, T ), alpha14( X, Y,
% 0.72/1.08 Z, T ) }.
% 0.72/1.08 { ! alpha3( X, Y, Z ), aElement0( skol7( T, U, W ) ) }.
% 0.72/1.08 { ! alpha3( X, Y, Z ), alpha10( X, Y, Z, skol7( X, Y, Z ) ) }.
% 0.72/1.08 { ! aElement0( T ), ! alpha10( X, Y, Z, T ), alpha3( X, Y, Z ) }.
% 0.72/1.08 { ! alpha10( X, Y, Z, T ), aElement0( Y ) }.
% 0.72/1.08 { ! alpha10( X, Y, Z, T ), alpha15( X, Y, Z, T ) }.
% 1.10/1.49 { ! aElement0( Y ), ! alpha15( X, Y, Z, T ), alpha10( X, Y, Z, T ) }.
% 1.10/1.49 { ! alpha15( X, Y, Z, T ), aElement0( Z ) }.
% 1.10/1.49 { ! alpha15( X, Y, Z, T ), alpha17( X, Y, Z, T ) }.
% 1.10/1.49 { ! aElement0( Z ), ! alpha17( X, Y, Z, T ), alpha15( X, Y, Z, T ) }.
% 1.10/1.49 { ! alpha17( X, Y, Z, T ), aReductOfIn0( Y, T, X ) }.
% 1.10/1.49 { ! alpha17( X, Y, Z, T ), aReductOfIn0( Z, T, X ) }.
% 1.10/1.49 { ! aReductOfIn0( Y, T, X ), ! aReductOfIn0( Z, T, X ), alpha17( X, Y, Z, T
% 1.10/1.49 ) }.
% 1.10/1.49 { ! aRewritingSystem0( X ), ! isTerminating0( X ), ! alpha4( Y, Z ),
% 1.10/1.49 alpha11( X, Y, Z ) }.
% 1.10/1.49 { ! aRewritingSystem0( X ), alpha4( skol8( X ), skol14( X ) ),
% 1.10/1.49 isTerminating0( X ) }.
% 1.10/1.49 { ! aRewritingSystem0( X ), ! alpha11( X, skol8( X ), skol14( X ) ),
% 1.10/1.49 isTerminating0( X ) }.
% 1.10/1.49 { ! alpha11( X, Y, Z ), ! sdtmndtplgtdt0( Y, X, Z ), iLess0( Z, Y ) }.
% 1.10/1.49 { sdtmndtplgtdt0( Y, X, Z ), alpha11( X, Y, Z ) }.
% 1.10/1.49 { ! iLess0( Z, Y ), alpha11( X, Y, Z ) }.
% 1.10/1.49 { ! alpha4( X, Y ), aElement0( X ) }.
% 1.10/1.49 { ! alpha4( X, Y ), aElement0( Y ) }.
% 1.10/1.49 { ! aElement0( X ), ! aElement0( Y ), alpha4( X, Y ) }.
% 1.10/1.49 { ! aElement0( X ), ! aRewritingSystem0( Y ), ! aNormalFormOfIn0( Z, X, Y )
% 1.10/1.49 , aElement0( Z ) }.
% 1.10/1.49 { ! aElement0( X ), ! aRewritingSystem0( Y ), ! aNormalFormOfIn0( Z, X, Y )
% 1.10/1.49 , alpha5( X, Y, Z ) }.
% 1.10/1.49 { ! aElement0( X ), ! aRewritingSystem0( Y ), ! aElement0( Z ), ! alpha5( X
% 1.10/1.49 , Y, Z ), aNormalFormOfIn0( Z, X, Y ) }.
% 1.10/1.49 { ! alpha5( X, Y, Z ), sdtmndtasgtdt0( X, Y, Z ) }.
% 1.10/1.49 { ! alpha5( X, Y, Z ), ! aReductOfIn0( T, Z, Y ) }.
% 1.10/1.49 { ! sdtmndtasgtdt0( X, Y, Z ), aReductOfIn0( skol9( Y, Z ), Z, Y ), alpha5
% 1.10/1.49 ( X, Y, Z ) }.
% 1.10/1.49 { ! aRewritingSystem0( X ), ! isTerminating0( X ), ! aElement0( Y ),
% 1.10/1.49 aNormalFormOfIn0( skol10( X, Y ), Y, X ) }.
% 1.10/1.49 { aRewritingSystem0( xR ) }.
% 1.10/1.49 { isLocallyConfluent0( xR ) }.
% 1.10/1.49 { isTerminating0( xR ) }.
% 1.10/1.49 { aElement0( xa ) }.
% 1.10/1.49 { aElement0( xb ) }.
% 1.10/1.49 { aElement0( xc ) }.
% 1.10/1.49 { ! aElement0( X ), ! aElement0( Y ), ! aElement0( Z ), ! sdtmndtasgtdt0( X
% 1.10/1.49 , xR, Y ), ! sdtmndtasgtdt0( X, xR, Z ), ! iLess0( X, xa ), aElement0(
% 1.10/1.49 skol11( T, U ) ) }.
% 1.10/1.49 { ! aElement0( X ), ! aElement0( Y ), ! aElement0( Z ), ! sdtmndtasgtdt0( X
% 1.10/1.49 , xR, Y ), ! sdtmndtasgtdt0( X, xR, Z ), ! iLess0( X, xa ),
% 1.10/1.49 sdtmndtasgtdt0( Z, xR, skol11( T, Z ) ) }.
% 1.10/1.49 { ! aElement0( X ), ! aElement0( Y ), ! aElement0( Z ), ! sdtmndtasgtdt0( X
% 1.10/1.49 , xR, Y ), ! sdtmndtasgtdt0( X, xR, Z ), ! iLess0( X, xa ),
% 1.10/1.49 sdtmndtasgtdt0( Y, xR, skol11( Y, Z ) ) }.
% 1.10/1.49 { sdtmndtplgtdt0( xa, xR, xb ) }.
% 1.10/1.49 { sdtmndtplgtdt0( xa, xR, xc ) }.
% 1.10/1.49 { aElement0( xu ) }.
% 1.10/1.49 { aReductOfIn0( xu, xa, xR ) }.
% 1.10/1.49 { sdtmndtasgtdt0( xu, xR, xb ) }.
% 1.10/1.49 { aElement0( xv ) }.
% 1.10/1.49 { aReductOfIn0( xv, xa, xR ) }.
% 1.10/1.49 { sdtmndtasgtdt0( xv, xR, xc ) }.
% 1.10/1.49 { aElement0( xw ) }.
% 1.10/1.49 { sdtmndtasgtdt0( xu, xR, xw ) }.
% 1.10/1.49 { sdtmndtasgtdt0( xv, xR, xw ) }.
% 1.10/1.49 { aNormalFormOfIn0( xd, xw, xR ) }.
% 1.10/1.49 { aElement0( xx ) }.
% 1.10/1.49 { sdtmndtasgtdt0( xb, xR, xx ) }.
% 1.10/1.49 { sdtmndtasgtdt0( xd, xR, xx ) }.
% 1.10/1.49 { ! sdtmndtasgtdt0( xb, xR, xd ) }.
% 1.10/1.49
% 1.10/1.49 percentage equality = 0.007692, percentage horn = 0.929293
% 1.10/1.49 This is a problem with some equality
% 1.10/1.49
% 1.10/1.49
% 1.10/1.49
% 1.10/1.49 Options Used:
% 1.10/1.49
% 1.10/1.49 useres = 1
% 1.10/1.49 useparamod = 1
% 1.10/1.49 useeqrefl = 1
% 1.10/1.49 useeqfact = 1
% 1.10/1.49 usefactor = 1
% 1.10/1.49 usesimpsplitting = 0
% 1.10/1.49 usesimpdemod = 5
% 1.10/1.49 usesimpres = 3
% 1.10/1.49
% 1.10/1.49 resimpinuse = 1000
% 1.10/1.49 resimpclauses = 20000
% 1.10/1.49 substype = eqrewr
% 1.10/1.49 backwardsubs = 1
% 1.10/1.49 selectoldest = 5
% 1.10/1.49
% 1.10/1.49 litorderings [0] = split
% 1.10/1.49 litorderings [1] = extend the termordering, first sorting on arguments
% 1.10/1.49
% 1.10/1.49 termordering = kbo
% 1.10/1.49
% 1.10/1.49 litapriori = 0
% 1.10/1.49 termapriori = 1
% 1.10/1.49 litaposteriori = 0
% 1.10/1.49 termaposteriori = 0
% 1.10/1.49 demodaposteriori = 0
% 1.10/1.49 ordereqreflfact = 0
% 1.10/1.49
% 1.10/1.49 litselect = negord
% 1.10/1.49
% 1.10/1.49 maxweight = 15
% 1.10/1.49 maxdepth = 30000
% 1.10/1.49 maxlength = 115
% 1.10/1.49 maxnrvars = 195
% 1.10/1.49 excuselevel = 1
% 1.10/1.49 increasemaxweight = 1
% 1.10/1.49
% 1.10/1.49 maxselected = 10000000
% 1.10/1.49 maxnrclauses = 10000000
% 1.10/1.49
% 1.10/1.49 showgenerated = 0
% 1.10/1.49 showkept = 0
% 1.10/1.49 showselected = 0
% 1.10/1.49 showdeleted = 0
% 1.10/1.49 showresimp = 1
% 1.10/1.49 showstatus = 2000
% 1.10/1.49
% 1.10/1.49 prologoutput = 0
% 1.10/1.49 nrgoals = 5000000
% 1.10/1.49 totalproof = 1
% 1.10/1.49
% 1.10/1.49 Symbols occurring in the translation:
% 1.10/1.49
% 1.10/1.49 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.10/1.49 . [1, 2] (w:1, o:36, a:1, s:1, b:0),
% 1.10/1.49 && [3, 0] (w:1, o:4, a:1, s:1, b:0),
% 5.00/5.38 ! [4, 1] (w:0, o:20, a:1, s:1, b:0),
% 5.00/5.38 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 5.00/5.38 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 5.00/5.38 aElement0 [36, 1] (w:1, o:25, a:1, s:1, b:0),
% 5.00/5.38 aRewritingSystem0 [37, 1] (w:1, o:26, a:1, s:1, b:0),
% 5.00/5.38 aReductOfIn0 [40, 3] (w:1, o:65, a:1, s:1, b:0),
% 5.00/5.38 iLess0 [41, 2] (w:1, o:60, a:1, s:1, b:0),
% 5.00/5.38 sdtmndtplgtdt0 [42, 3] (w:1, o:66, a:1, s:1, b:0),
% 5.00/5.38 sdtmndtasgtdt0 [44, 3] (w:1, o:67, a:1, s:1, b:0),
% 5.00/5.38 isConfluent0 [45, 1] (w:1, o:27, a:1, s:1, b:0),
% 5.00/5.38 isLocallyConfluent0 [47, 1] (w:1, o:28, a:1, s:1, b:0),
% 5.00/5.38 isTerminating0 [48, 1] (w:1, o:29, a:1, s:1, b:0),
% 5.00/5.38 aNormalFormOfIn0 [49, 3] (w:1, o:68, a:1, s:1, b:0),
% 5.00/5.38 xR [50, 0] (w:1, o:11, a:1, s:1, b:0),
% 5.00/5.38 xa [51, 0] (w:1, o:12, a:1, s:1, b:0),
% 5.00/5.38 xb [52, 0] (w:1, o:13, a:1, s:1, b:0),
% 5.00/5.38 xc [53, 0] (w:1, o:14, a:1, s:1, b:0),
% 5.00/5.38 xu [54, 0] (w:1, o:15, a:1, s:1, b:0),
% 5.00/5.38 xv [55, 0] (w:1, o:16, a:1, s:1, b:0),
% 5.00/5.38 xw [56, 0] (w:1, o:17, a:1, s:1, b:0),
% 5.00/5.38 xd [57, 0] (w:1, o:18, a:1, s:1, b:0),
% 5.00/5.38 xx [58, 0] (w:1, o:19, a:1, s:1, b:0),
% 5.00/5.38 alpha1 [59, 3] (w:1, o:69, a:1, s:1, b:1),
% 5.00/5.38 alpha2 [60, 3] (w:1, o:71, a:1, s:1, b:1),
% 5.00/5.38 alpha3 [61, 3] (w:1, o:72, a:1, s:1, b:1),
% 5.00/5.38 alpha4 [62, 2] (w:1, o:61, a:1, s:1, b:1),
% 5.00/5.38 alpha5 [63, 3] (w:1, o:73, a:1, s:1, b:1),
% 5.00/5.38 alpha6 [64, 4] (w:1, o:81, a:1, s:1, b:1),
% 5.00/5.38 alpha7 [65, 3] (w:1, o:74, a:1, s:1, b:1),
% 5.00/5.38 alpha8 [66, 4] (w:1, o:82, a:1, s:1, b:1),
% 5.00/5.38 alpha9 [67, 3] (w:1, o:75, a:1, s:1, b:1),
% 5.00/5.38 alpha10 [68, 4] (w:1, o:83, a:1, s:1, b:1),
% 5.00/5.38 alpha11 [69, 3] (w:1, o:70, a:1, s:1, b:1),
% 5.00/5.38 alpha12 [70, 4] (w:1, o:84, a:1, s:1, b:1),
% 5.00/5.38 alpha13 [71, 4] (w:1, o:85, a:1, s:1, b:1),
% 5.00/5.38 alpha14 [72, 4] (w:1, o:86, a:1, s:1, b:1),
% 5.00/5.38 alpha15 [73, 4] (w:1, o:87, a:1, s:1, b:1),
% 5.00/5.38 alpha16 [74, 4] (w:1, o:88, a:1, s:1, b:1),
% 5.00/5.38 alpha17 [75, 4] (w:1, o:89, a:1, s:1, b:1),
% 5.00/5.38 skol1 [76, 3] (w:1, o:76, a:1, s:1, b:1),
% 5.00/5.38 skol2 [77, 1] (w:1, o:33, a:1, s:1, b:1),
% 5.00/5.38 skol3 [78, 3] (w:1, o:77, a:1, s:1, b:1),
% 5.00/5.38 skol4 [79, 3] (w:1, o:78, a:1, s:1, b:1),
% 5.00/5.38 skol5 [80, 1] (w:1, o:34, a:1, s:1, b:1),
% 5.00/5.38 skol6 [81, 3] (w:1, o:79, a:1, s:1, b:1),
% 5.00/5.38 skol7 [82, 3] (w:1, o:80, a:1, s:1, b:1),
% 5.00/5.38 skol8 [83, 1] (w:1, o:35, a:1, s:1, b:1),
% 5.00/5.38 skol9 [84, 2] (w:1, o:62, a:1, s:1, b:1),
% 5.00/5.38 skol10 [85, 2] (w:1, o:63, a:1, s:1, b:1),
% 5.00/5.38 skol11 [86, 2] (w:1, o:64, a:1, s:1, b:1),
% 5.00/5.38 skol12 [87, 1] (w:1, o:30, a:1, s:1, b:1),
% 5.00/5.38 skol13 [88, 1] (w:1, o:31, a:1, s:1, b:1),
% 5.00/5.38 skol14 [89, 1] (w:1, o:32, a:1, s:1, b:1).
% 5.00/5.38
% 5.00/5.38
% 5.00/5.38 Starting Search:
% 5.00/5.38
% 5.00/5.38 *** allocated 15000 integers for clauses
% 5.00/5.38 *** allocated 22500 integers for clauses
% 5.00/5.38 *** allocated 15000 integers for termspace/termends
% 5.00/5.38 *** allocated 33750 integers for clauses
% 5.00/5.38 *** allocated 50625 integers for clauses
% 5.00/5.38 *** allocated 22500 integers for termspace/termends
% 5.00/5.38 Resimplifying inuse:
% 5.00/5.38 Done
% 5.00/5.38
% 5.00/5.38 *** allocated 75937 integers for clauses
% 5.00/5.38 *** allocated 33750 integers for termspace/termends
% 5.00/5.38 *** allocated 113905 integers for clauses
% 5.00/5.38
% 5.00/5.38 Intermediate Status:
% 5.00/5.38 Generated: 8177
% 5.00/5.38 Kept: 2004
% 5.00/5.38 Inuse: 276
% 5.00/5.38 Deleted: 1
% 5.00/5.38 Deletedinuse: 1
% 5.00/5.38
% 5.00/5.38 Resimplifying inuse:
% 5.00/5.38 Done
% 5.00/5.38
% 5.00/5.38 *** allocated 50625 integers for termspace/termends
% 5.00/5.38 *** allocated 170857 integers for clauses
% 5.00/5.38 Resimplifying inuse:
% 5.00/5.38 Done
% 5.00/5.38
% 5.00/5.38 *** allocated 75937 integers for termspace/termends
% 5.00/5.38 *** allocated 256285 integers for clauses
% 5.00/5.38
% 5.00/5.38 Intermediate Status:
% 5.00/5.38 Generated: 15361
% 5.00/5.38 Kept: 4017
% 5.00/5.38 Inuse: 541
% 5.00/5.38 Deleted: 19
% 5.00/5.38 Deletedinuse: 6
% 5.00/5.38
% 5.00/5.38 Resimplifying inuse:
% 5.00/5.38 Done
% 5.00/5.38
% 5.00/5.38 Resimplifying inuse:
% 5.00/5.38 Done
% 5.00/5.38
% 5.00/5.38 *** allocated 113905 integers for termspace/termends
% 5.00/5.38 *** allocated 384427 integers for clauses
% 5.00/5.38
% 5.00/5.38 Intermediate Status:
% 5.00/5.38 Generated: 24507
% 5.00/5.38 Kept: 6047
% 5.00/5.38 Inuse: 719
% 5.00/5.38 Deleted: 56
% 5.00/5.38 Deletedinuse: 17
% 5.00/5.38
% 5.00/5.38 Resimplifying inuse:
% 5.00/5.38 Done
% 5.00/5.38
% 5.00/5.38 Resimplifying inuse:
% 5.00/5.38 Done
% 5.00/5.38
% 5.00/5.38
% 5.00/5.38 Intermediate Status:
% 5.00/5.38 Generated: 49659
% 5.00/5.38 Kept: 8047
% 5.00/5.38 Inuse: 860
% 5.00/5.38 Deleted: 80
% 5.00/5.38 Deletedinuse: 17
% 5.00/5.38
% 5.00/5.38 Resimplifying inuse:
% 5.00/5.38 Done
% 5.00/5.38
% 5.00/5.38 *** allocated 170857 integers for termspace/termends
% 5.00/5.38 Resimplifying inuse:
% 5.00/5.38 Done
% 5.00/5.38
% 5.00/5.38 *** allocated 576640 integers for clauses
% 5.00/5.38
% 5.00/5.38 Intermediate Status:
% 5.00/5.38 Generated: 70960
% 5.00/5.38 Kept: 10098
% 5.00/5.38 Inuse: 1093
% 5.00/5.38 Deleted: 90
% 5.00/5.38 Deletedinuse: 17
% 5.00/5.38
% 5.00/5.38 Resimplifying inuse:
% 5.00/5.38 Done
% 5.00/5.38
% 5.00/5.38 Resimplifying inuse:
% 5.00/5.38 Done
% 5.00/5.38
% 5.00/5.38
% 5.00/5.38 Intermediate Status:
% 5.00/5.38 Generated: 83409
% 5.00/5.38 Kept: 12147
% 5.00/5.38 Inuse: 1255
% 5.00/5.38 Deleted: 92
% 5.00/5.38 Deletedinuse: 17
% 5.00/5.38
% 5.00/5.38 Resimplifying inuse:
% 5.00/5.38 Done
% 5.00/5.38
% 5.00/5.38 *** allocated 256285 integers for termspace/termends
% 5.00/5.38 Resimplifying inuse:
% 5.00/5.38 Done
% 5.00/5.38
% 5.00/5.38 *** allocated 864960 integers for clauses
% 5.00/5.38
% 5.00/5.38 Intermediate Status:
% 5.00/5.38 Generated: 180201
% 5.00/5.38 Kept: 14191
% 5.00/5.38 Inuse: 1641
% 5.00/5.38 Deleted: 107
% 5.00/5.38 Deletedinuse: 22
% 5.00/5.38
% 5.00/5.38 Resimplifying inuse:
% 5.00/5.38 Done
% 5.00/5.38
% 5.00/5.38 Resimplifying inuse:
% 5.00/5.38 Done
% 5.00/5.38
% 5.00/5.38
% 5.00/5.38 Intermediate Status:
% 5.00/5.38 Generated: 278833
% 5.00/5.38 Kept: 16191
% 5.00/5.38 Inuse: 1969
% 5.00/5.38 Deleted: 122
% 5.00/5.38 Deletedinuse: 30
% 5.00/5.38
% 5.00/5.38 Resimplifying inuse:
% 5.00/5.38 Done
% 5.00/5.38
% 5.00/5.38 Resimplifying inuse:
% 5.00/5.38 Done
% 5.00/5.38
% 5.00/5.38 *** allocated 384427 integers for termspace/termends
% 5.00/5.38
% 5.00/5.38 Intermediate Status:
% 5.00/5.38 Generated: 348881
% 5.00/5.38 Kept: 18203
% 5.00/5.38 Inuse: 2298
% 5.00/5.38 Deleted: 128
% 5.00/5.38 Deletedinuse: 30
% 5.00/5.38
% 5.00/5.38 Resimplifying inuse:
% 5.00/5.38 Done
% 5.00/5.38
% 5.00/5.38 Resimplifying inuse:
% 5.00/5.38 Done
% 5.00/5.38
% 5.00/5.38 Resimplifying clauses:
% 5.00/5.38
% 5.00/5.38 Bliksems!, er is een bewijs:
% 5.00/5.38 % SZS status Theorem
% 5.00/5.38 % SZS output start Refutation
% 5.00/5.38
% 5.00/5.38 (2) {G0,W18,D2,L6,V3,M6} I { ! aElement0( X ), ! aRewritingSystem0( Y ), !
% 5.00/5.38 aElement0( Z ), ! sdtmndtplgtdt0( X, Y, Z ), aReductOfIn0( Z, X, Y ),
% 5.00/5.38 alpha1( X, Y, Z ) }.
% 5.00/5.38 (6) {G0,W12,D3,L2,V3,M2} I { ! alpha1( X, Y, Z ), alpha6( X, Y, Z, skol1( X
% 5.00/5.38 , Y, Z ) ) }.
% 5.00/5.38 (8) {G0,W9,D2,L2,V4,M2} I { ! alpha6( X, Y, Z, T ), aReductOfIn0( T, X, Y )
% 5.00/5.38 }.
% 5.00/5.38 (12) {G0,W17,D2,L6,V3,M6} I { ! aElement0( X ), ! aRewritingSystem0( Y ), !
% 5.00/5.38 aElement0( Z ), ! sdtmndtasgtdt0( X, Y, Z ), X = Z, sdtmndtplgtdt0( X, Y
% 5.00/5.38 , Z ) }.
% 5.00/5.38 (67) {G0,W10,D2,L4,V3,M4} I { ! aElement0( X ), ! aRewritingSystem0( Y ), !
% 5.00/5.38 aNormalFormOfIn0( Z, X, Y ), aElement0( Z ) }.
% 5.00/5.38 (68) {G0,W12,D2,L4,V3,M4} I { ! aElement0( X ), ! aRewritingSystem0( Y ), !
% 5.00/5.38 aNormalFormOfIn0( Z, X, Y ), alpha5( X, Y, Z ) }.
% 5.00/5.38 (71) {G0,W8,D2,L2,V4,M2} I { ! alpha5( X, Y, Z ), ! aReductOfIn0( T, Z, Y )
% 5.00/5.38 }.
% 5.00/5.38 (74) {G0,W2,D2,L1,V0,M1} I { aRewritingSystem0( xR ) }.
% 5.00/5.38 (91) {G0,W2,D2,L1,V0,M1} I { aElement0( xw ) }.
% 5.00/5.38 (94) {G0,W4,D2,L1,V0,M1} I { aNormalFormOfIn0( xd, xw, xR ) }.
% 5.00/5.38 (95) {G0,W2,D2,L1,V0,M1} I { aElement0( xx ) }.
% 5.00/5.38 (96) {G0,W4,D2,L1,V0,M1} I { sdtmndtasgtdt0( xb, xR, xx ) }.
% 5.00/5.38 (97) {G0,W4,D2,L1,V0,M1} I { sdtmndtasgtdt0( xd, xR, xx ) }.
% 5.00/5.38 (98) {G0,W4,D2,L1,V0,M1} I { ! sdtmndtasgtdt0( xb, xR, xd ) }.
% 5.00/5.38 (143) {G1,W16,D2,L5,V2,M5} R(74,2) { ! aElement0( X ), ! aElement0( Y ), !
% 5.00/5.38 sdtmndtplgtdt0( X, xR, Y ), aReductOfIn0( Y, X, xR ), alpha1( X, xR, Y )
% 5.00/5.38 }.
% 5.00/5.38 (427) {G1,W11,D2,L4,V0,M4} R(12,97);r(74) { ! aElement0( xd ), ! aElement0
% 5.00/5.38 ( xx ), xx ==> xd, sdtmndtplgtdt0( xd, xR, xx ) }.
% 5.00/5.38 (2106) {G1,W4,D2,L2,V0,M2} R(67,94);r(91) { ! aRewritingSystem0( xR ),
% 5.00/5.38 aElement0( xd ) }.
% 5.00/5.38 (2146) {G1,W6,D2,L2,V0,M2} R(68,94);r(91) { ! aRewritingSystem0( xR ),
% 5.00/5.38 alpha5( xw, xR, xd ) }.
% 5.00/5.38 (2476) {G2,W2,D2,L1,V0,M1} S(2106);r(74) { aElement0( xd ) }.
% 5.00/5.38 (4568) {G2,W4,D2,L1,V0,M1} S(2146);r(74) { alpha5( xw, xR, xd ) }.
% 5.00/5.38 (4569) {G3,W4,D2,L1,V1,M1} R(4568,71) { ! aReductOfIn0( X, xd, xR ) }.
% 5.00/5.38 (4582) {G4,W5,D2,L1,V2,M1} R(4569,8) { ! alpha6( xd, xR, X, Y ) }.
% 5.00/5.38 (4598) {G5,W4,D2,L1,V1,M1} R(4582,6) { ! alpha1( xd, xR, X ) }.
% 5.00/5.38 (14452) {G3,W7,D2,L2,V0,M2} S(427);r(2476);r(95) { xx ==> xd,
% 5.00/5.38 sdtmndtplgtdt0( xd, xR, xx ) }.
% 5.00/5.38 (14478) {G4,W4,D2,L1,V0,M1} P(14452,96);r(98) { sdtmndtplgtdt0( xd, xR, xx
% 5.00/5.38 ) }.
% 5.00/5.38 (14523) {G5,W10,D2,L3,V0,M3} R(14478,143);r(2476) { ! aElement0( xx ),
% 5.00/5.38 aReductOfIn0( xx, xd, xR ), alpha1( xd, xR, xx ) }.
% 5.00/5.38 (20520) {G6,W0,D0,L0,V0,M0} S(14523);r(95);r(4569);r(4598) { }.
% 5.00/5.38
% 5.00/5.38
% 5.00/5.38 % SZS output end Refutation
% 5.00/5.38 found a proof!
% 5.00/5.38
% 5.00/5.38
% 5.00/5.38 Unprocessed initial clauses:
% 5.00/5.38
% 5.00/5.38 (20522) {G0,W1,D1,L1,V0,M1} { && }.
% 5.00/5.38 (20523) {G0,W1,D1,L1,V0,M1} { && }.
% 5.00/5.38 (20524) {G0,W10,D2,L4,V3,M4} { ! aElement0( X ), ! aRewritingSystem0( Y )
% 5.00/5.38 , ! aReductOfIn0( Z, X, Y ), aElement0( Z ) }.
% 5.00/5.38 (20525) {G0,W1,D1,L1,V0,M1} { && }.
% 5.00/5.38 (20526) {G0,W1,D1,L1,V0,M1} { && }.
% 5.00/5.38 (20527) {G0,W18,D2,L6,V3,M6} { ! aElement0( X ), ! aRewritingSystem0( Y )
% 5.00/5.38 , ! aElement0( Z ), ! sdtmndtplgtdt0( X, Y, Z ), aReductOfIn0( Z, X, Y )
% 5.00/5.38 , alpha1( X, Y, Z ) }.
% 5.00/5.38 (20528) {G0,W14,D2,L5,V3,M5} { ! aElement0( X ), ! aRewritingSystem0( Y )
% 5.00/5.38 , ! aElement0( Z ), ! aReductOfIn0( Z, X, Y ), sdtmndtplgtdt0( X, Y, Z )
% 5.00/5.38 }.
% 5.00/5.38 (20529) {G0,W14,D2,L5,V3,M5} { ! aElement0( X ), ! aRewritingSystem0( Y )
% 5.00/5.38 , ! aElement0( Z ), ! alpha1( X, Y, Z ), sdtmndtplgtdt0( X, Y, Z ) }.
% 5.00/5.38 (20530) {G0,W9,D3,L2,V6,M2} { ! alpha1( X, Y, Z ), aElement0( skol1( T, U
% 5.00/5.38 , W ) ) }.
% 5.00/5.38 (20531) {G0,W12,D3,L2,V3,M2} { ! alpha1( X, Y, Z ), alpha6( X, Y, Z, skol1
% 5.00/5.38 ( X, Y, Z ) ) }.
% 5.00/5.38 (20532) {G0,W11,D2,L3,V4,M3} { ! aElement0( T ), ! alpha6( X, Y, Z, T ),
% 5.00/5.38 alpha1( X, Y, Z ) }.
% 5.00/5.38 (20533) {G0,W9,D2,L2,V4,M2} { ! alpha6( X, Y, Z, T ), aReductOfIn0( T, X,
% 5.00/5.38 Y ) }.
% 5.00/5.38 (20534) {G0,W9,D2,L2,V4,M2} { ! alpha6( X, Y, Z, T ), sdtmndtplgtdt0( T, Y
% 5.00/5.38 , Z ) }.
% 5.00/5.38 (20535) {G0,W13,D2,L3,V4,M3} { ! aReductOfIn0( T, X, Y ), ! sdtmndtplgtdt0
% 5.00/5.38 ( T, Y, Z ), alpha6( X, Y, Z, T ) }.
% 5.00/5.38 (20536) {G0,W20,D2,L7,V4,M7} { ! aElement0( X ), ! aRewritingSystem0( Y )
% 5.00/5.38 , ! aElement0( Z ), ! aElement0( T ), ! sdtmndtplgtdt0( X, Y, Z ), !
% 5.00/5.38 sdtmndtplgtdt0( Z, Y, T ), sdtmndtplgtdt0( X, Y, T ) }.
% 5.00/5.38 (20537) {G0,W17,D2,L6,V3,M6} { ! aElement0( X ), ! aRewritingSystem0( Y )
% 5.00/5.38 , ! aElement0( Z ), ! sdtmndtasgtdt0( X, Y, Z ), X = Z, sdtmndtplgtdt0( X
% 5.00/5.38 , Y, Z ) }.
% 5.00/5.38 (20538) {G0,W13,D2,L5,V3,M5} { ! aElement0( X ), ! aRewritingSystem0( Y )
% 5.00/5.38 , ! aElement0( Z ), ! X = Z, sdtmndtasgtdt0( X, Y, Z ) }.
% 5.00/5.38 (20539) {G0,W14,D2,L5,V3,M5} { ! aElement0( X ), ! aRewritingSystem0( Y )
% 5.00/5.38 , ! aElement0( Z ), ! sdtmndtplgtdt0( X, Y, Z ), sdtmndtasgtdt0( X, Y, Z
% 5.00/5.38 ) }.
% 5.00/5.38 (20540) {G0,W20,D2,L7,V4,M7} { ! aElement0( X ), ! aRewritingSystem0( Y )
% 5.00/5.38 , ! aElement0( Z ), ! aElement0( T ), ! sdtmndtasgtdt0( X, Y, Z ), !
% 5.00/5.38 sdtmndtasgtdt0( Z, Y, T ), sdtmndtasgtdt0( X, Y, T ) }.
% 5.00/5.38 (20541) {G0,W12,D2,L4,V3,M4} { ! aRewritingSystem0( X ), ! isConfluent0( X
% 5.00/5.38 ), ! alpha2( X, Y, Z ), alpha7( X, Y, Z ) }.
% 5.00/5.38 (20542) {G0,W10,D3,L3,V1,M3} { ! aRewritingSystem0( X ), alpha2( X, skol2
% 5.00/5.38 ( X ), skol12( X ) ), isConfluent0( X ) }.
% 5.00/5.38 (20543) {G0,W10,D3,L3,V1,M3} { ! aRewritingSystem0( X ), ! alpha7( X,
% 5.00/5.38 skol2( X ), skol12( X ) ), isConfluent0( X ) }.
% 5.00/5.38 (20544) {G0,W9,D3,L2,V6,M2} { ! alpha7( X, Y, Z ), aElement0( skol3( T, U
% 5.00/5.38 , W ) ) }.
% 5.00/5.38 (20545) {G0,W12,D3,L2,V3,M2} { ! alpha7( X, Y, Z ), alpha12( X, Y, Z,
% 5.00/5.38 skol3( X, Y, Z ) ) }.
% 5.00/5.38 (20546) {G0,W11,D2,L3,V4,M3} { ! aElement0( T ), ! alpha12( X, Y, Z, T ),
% 5.00/5.38 alpha7( X, Y, Z ) }.
% 5.00/5.38 (20547) {G0,W9,D2,L2,V4,M2} { ! alpha12( X, Y, Z, T ), sdtmndtasgtdt0( Y,
% 5.00/5.38 X, T ) }.
% 5.00/5.38 (20548) {G0,W9,D2,L2,V4,M2} { ! alpha12( X, Y, Z, T ), sdtmndtasgtdt0( Z,
% 5.00/5.38 X, T ) }.
% 5.00/5.38 (20549) {G0,W13,D2,L3,V4,M3} { ! sdtmndtasgtdt0( Y, X, T ), !
% 5.00/5.38 sdtmndtasgtdt0( Z, X, T ), alpha12( X, Y, Z, T ) }.
% 5.00/5.38 (20550) {G0,W9,D3,L2,V6,M2} { ! alpha2( X, Y, Z ), aElement0( skol4( T, U
% 5.00/5.38 , W ) ) }.
% 5.00/5.38 (20551) {G0,W12,D3,L2,V3,M2} { ! alpha2( X, Y, Z ), alpha8( X, Y, Z, skol4
% 5.00/5.38 ( X, Y, Z ) ) }.
% 5.00/5.38 (20552) {G0,W11,D2,L3,V4,M3} { ! aElement0( T ), ! alpha8( X, Y, Z, T ),
% 5.00/5.38 alpha2( X, Y, Z ) }.
% 5.00/5.38 (20553) {G0,W7,D2,L2,V4,M2} { ! alpha8( X, Y, Z, T ), aElement0( Y ) }.
% 5.00/5.38 (20554) {G0,W10,D2,L2,V4,M2} { ! alpha8( X, Y, Z, T ), alpha13( X, Y, Z, T
% 5.00/5.38 ) }.
% 5.00/5.38 (20555) {G0,W12,D2,L3,V4,M3} { ! aElement0( Y ), ! alpha13( X, Y, Z, T ),
% 5.00/5.38 alpha8( X, Y, Z, T ) }.
% 5.00/5.38 (20556) {G0,W7,D2,L2,V4,M2} { ! alpha13( X, Y, Z, T ), aElement0( Z ) }.
% 5.00/5.38 (20557) {G0,W10,D2,L2,V4,M2} { ! alpha13( X, Y, Z, T ), alpha16( X, Y, Z,
% 5.00/5.38 T ) }.
% 5.00/5.38 (20558) {G0,W12,D2,L3,V4,M3} { ! aElement0( Z ), ! alpha16( X, Y, Z, T ),
% 5.00/5.38 alpha13( X, Y, Z, T ) }.
% 5.00/5.38 (20559) {G0,W9,D2,L2,V4,M2} { ! alpha16( X, Y, Z, T ), sdtmndtasgtdt0( T,
% 5.00/5.38 X, Y ) }.
% 5.00/5.38 (20560) {G0,W9,D2,L2,V4,M2} { ! alpha16( X, Y, Z, T ), sdtmndtasgtdt0( T,
% 5.00/5.38 X, Z ) }.
% 5.00/5.38 (20561) {G0,W13,D2,L3,V4,M3} { ! sdtmndtasgtdt0( T, X, Y ), !
% 5.00/5.38 sdtmndtasgtdt0( T, X, Z ), alpha16( X, Y, Z, T ) }.
% 5.00/5.38 (20562) {G0,W12,D2,L4,V3,M4} { ! aRewritingSystem0( X ), !
% 5.00/5.38 isLocallyConfluent0( X ), ! alpha3( X, Y, Z ), alpha9( X, Y, Z ) }.
% 5.00/5.38 (20563) {G0,W10,D3,L3,V1,M3} { ! aRewritingSystem0( X ), alpha3( X, skol5
% 5.00/5.38 ( X ), skol13( X ) ), isLocallyConfluent0( X ) }.
% 5.00/5.38 (20564) {G0,W10,D3,L3,V1,M3} { ! aRewritingSystem0( X ), ! alpha9( X,
% 5.00/5.38 skol5( X ), skol13( X ) ), isLocallyConfluent0( X ) }.
% 5.00/5.38 (20565) {G0,W9,D3,L2,V6,M2} { ! alpha9( X, Y, Z ), aElement0( skol6( T, U
% 5.00/5.38 , W ) ) }.
% 5.00/5.38 (20566) {G0,W12,D3,L2,V3,M2} { ! alpha9( X, Y, Z ), alpha14( X, Y, Z,
% 5.00/5.38 skol6( X, Y, Z ) ) }.
% 5.00/5.38 (20567) {G0,W11,D2,L3,V4,M3} { ! aElement0( T ), ! alpha14( X, Y, Z, T ),
% 5.00/5.38 alpha9( X, Y, Z ) }.
% 5.00/5.38 (20568) {G0,W9,D2,L2,V4,M2} { ! alpha14( X, Y, Z, T ), sdtmndtasgtdt0( Y,
% 5.00/5.38 X, T ) }.
% 5.00/5.38 (20569) {G0,W9,D2,L2,V4,M2} { ! alpha14( X, Y, Z, T ), sdtmndtasgtdt0( Z,
% 5.00/5.38 X, T ) }.
% 5.00/5.38 (20570) {G0,W13,D2,L3,V4,M3} { ! sdtmndtasgtdt0( Y, X, T ), !
% 5.00/5.38 sdtmndtasgtdt0( Z, X, T ), alpha14( X, Y, Z, T ) }.
% 5.00/5.38 (20571) {G0,W9,D3,L2,V6,M2} { ! alpha3( X, Y, Z ), aElement0( skol7( T, U
% 5.00/5.38 , W ) ) }.
% 5.00/5.38 (20572) {G0,W12,D3,L2,V3,M2} { ! alpha3( X, Y, Z ), alpha10( X, Y, Z,
% 5.00/5.38 skol7( X, Y, Z ) ) }.
% 5.00/5.38 (20573) {G0,W11,D2,L3,V4,M3} { ! aElement0( T ), ! alpha10( X, Y, Z, T ),
% 5.00/5.38 alpha3( X, Y, Z ) }.
% 5.00/5.38 (20574) {G0,W7,D2,L2,V4,M2} { ! alpha10( X, Y, Z, T ), aElement0( Y ) }.
% 5.00/5.38 (20575) {G0,W10,D2,L2,V4,M2} { ! alpha10( X, Y, Z, T ), alpha15( X, Y, Z,
% 5.00/5.38 T ) }.
% 5.00/5.38 (20576) {G0,W12,D2,L3,V4,M3} { ! aElement0( Y ), ! alpha15( X, Y, Z, T ),
% 5.00/5.38 alpha10( X, Y, Z, T ) }.
% 5.00/5.38 (20577) {G0,W7,D2,L2,V4,M2} { ! alpha15( X, Y, Z, T ), aElement0( Z ) }.
% 5.00/5.38 (20578) {G0,W10,D2,L2,V4,M2} { ! alpha15( X, Y, Z, T ), alpha17( X, Y, Z,
% 5.00/5.38 T ) }.
% 5.00/5.38 (20579) {G0,W12,D2,L3,V4,M3} { ! aElement0( Z ), ! alpha17( X, Y, Z, T ),
% 5.00/5.38 alpha15( X, Y, Z, T ) }.
% 5.00/5.38 (20580) {G0,W9,D2,L2,V4,M2} { ! alpha17( X, Y, Z, T ), aReductOfIn0( Y, T
% 5.00/5.38 , X ) }.
% 5.00/5.38 (20581) {G0,W9,D2,L2,V4,M2} { ! alpha17( X, Y, Z, T ), aReductOfIn0( Z, T
% 5.00/5.38 , X ) }.
% 5.00/5.38 (20582) {G0,W13,D2,L3,V4,M3} { ! aReductOfIn0( Y, T, X ), ! aReductOfIn0(
% 5.00/5.38 Z, T, X ), alpha17( X, Y, Z, T ) }.
% 5.00/5.38 (20583) {G0,W11,D2,L4,V3,M4} { ! aRewritingSystem0( X ), ! isTerminating0
% 5.00/5.38 ( X ), ! alpha4( Y, Z ), alpha11( X, Y, Z ) }.
% 5.00/5.38 (20584) {G0,W9,D3,L3,V1,M3} { ! aRewritingSystem0( X ), alpha4( skol8( X )
% 5.00/5.38 , skol14( X ) ), isTerminating0( X ) }.
% 5.00/5.38 (20585) {G0,W10,D3,L3,V1,M3} { ! aRewritingSystem0( X ), ! alpha11( X,
% 5.00/5.38 skol8( X ), skol14( X ) ), isTerminating0( X ) }.
% 5.00/5.38 (20586) {G0,W11,D2,L3,V3,M3} { ! alpha11( X, Y, Z ), ! sdtmndtplgtdt0( Y,
% 5.00/5.38 X, Z ), iLess0( Z, Y ) }.
% 5.00/5.38 (20587) {G0,W8,D2,L2,V3,M2} { sdtmndtplgtdt0( Y, X, Z ), alpha11( X, Y, Z
% 5.00/5.38 ) }.
% 5.00/5.38 (20588) {G0,W7,D2,L2,V3,M2} { ! iLess0( Z, Y ), alpha11( X, Y, Z ) }.
% 5.00/5.38 (20589) {G0,W5,D2,L2,V2,M2} { ! alpha4( X, Y ), aElement0( X ) }.
% 5.00/5.38 (20590) {G0,W5,D2,L2,V2,M2} { ! alpha4( X, Y ), aElement0( Y ) }.
% 5.00/5.38 (20591) {G0,W7,D2,L3,V2,M3} { ! aElement0( X ), ! aElement0( Y ), alpha4(
% 5.00/5.38 X, Y ) }.
% 5.00/5.38 (20592) {G0,W10,D2,L4,V3,M4} { ! aElement0( X ), ! aRewritingSystem0( Y )
% 5.00/5.38 , ! aNormalFormOfIn0( Z, X, Y ), aElement0( Z ) }.
% 5.00/5.38 (20593) {G0,W12,D2,L4,V3,M4} { ! aElement0( X ), ! aRewritingSystem0( Y )
% 5.00/5.38 , ! aNormalFormOfIn0( Z, X, Y ), alpha5( X, Y, Z ) }.
% 5.00/5.38 (20594) {G0,W14,D2,L5,V3,M5} { ! aElement0( X ), ! aRewritingSystem0( Y )
% 5.00/5.38 , ! aElement0( Z ), ! alpha5( X, Y, Z ), aNormalFormOfIn0( Z, X, Y ) }.
% 5.00/5.38 (20595) {G0,W8,D2,L2,V3,M2} { ! alpha5( X, Y, Z ), sdtmndtasgtdt0( X, Y, Z
% 5.00/5.38 ) }.
% 5.00/5.38 (20596) {G0,W8,D2,L2,V4,M2} { ! alpha5( X, Y, Z ), ! aReductOfIn0( T, Z, Y
% 5.00/5.38 ) }.
% 5.00/5.38 (20597) {G0,W14,D3,L3,V3,M3} { ! sdtmndtasgtdt0( X, Y, Z ), aReductOfIn0(
% 5.00/5.38 skol9( Y, Z ), Z, Y ), alpha5( X, Y, Z ) }.
% 5.00/5.38 (20598) {G0,W12,D3,L4,V2,M4} { ! aRewritingSystem0( X ), ! isTerminating0
% 5.00/5.38 ( X ), ! aElement0( Y ), aNormalFormOfIn0( skol10( X, Y ), Y, X ) }.
% 5.00/5.38 (20599) {G0,W2,D2,L1,V0,M1} { aRewritingSystem0( xR ) }.
% 5.00/5.38 (20600) {G0,W2,D2,L1,V0,M1} { isLocallyConfluent0( xR ) }.
% 5.00/5.38 (20601) {G0,W2,D2,L1,V0,M1} { isTerminating0( xR ) }.
% 5.00/5.38 (20602) {G0,W2,D2,L1,V0,M1} { aElement0( xa ) }.
% 5.00/5.38 (20603) {G0,W2,D2,L1,V0,M1} { aElement0( xb ) }.
% 5.00/5.38 (20604) {G0,W2,D2,L1,V0,M1} { aElement0( xc ) }.
% 5.00/5.38 (20605) {G0,W21,D3,L7,V5,M7} { ! aElement0( X ), ! aElement0( Y ), !
% 5.00/5.38 aElement0( Z ), ! sdtmndtasgtdt0( X, xR, Y ), ! sdtmndtasgtdt0( X, xR, Z
% 5.00/5.38 ), ! iLess0( X, xa ), aElement0( skol11( T, U ) ) }.
% 5.00/5.38 (20606) {G0,W23,D3,L7,V4,M7} { ! aElement0( X ), ! aElement0( Y ), !
% 5.00/5.38 aElement0( Z ), ! sdtmndtasgtdt0( X, xR, Y ), ! sdtmndtasgtdt0( X, xR, Z
% 5.00/5.38 ), ! iLess0( X, xa ), sdtmndtasgtdt0( Z, xR, skol11( T, Z ) ) }.
% 5.00/5.38 (20607) {G0,W23,D3,L7,V3,M7} { ! aElement0( X ), ! aElement0( Y ), !
% 5.00/5.38 aElement0( Z ), ! sdtmndtasgtdt0( X, xR, Y ), ! sdtmndtasgtdt0( X, xR, Z
% 5.00/5.38 ), ! iLess0( X, xa ), sdtmndtasgtdt0( Y, xR, skol11( Y, Z ) ) }.
% 5.00/5.38 (20608) {G0,W4,D2,L1,V0,M1} { sdtmndtplgtdt0( xa, xR, xb ) }.
% 5.00/5.38 (20609) {G0,W4,D2,L1,V0,M1} { sdtmndtplgtdt0( xa, xR, xc ) }.
% 5.00/5.38 (20610) {G0,W2,D2,L1,V0,M1} { aElement0( xu ) }.
% 5.00/5.38 (20611) {G0,W4,D2,L1,V0,M1} { aReductOfIn0( xu, xa, xR ) }.
% 5.00/5.38 (20612) {G0,W4,D2,L1,V0,M1} { sdtmndtasgtdt0( xu, xR, xb ) }.
% 5.00/5.38 (20613) {G0,W2,D2,L1,V0,M1} { aElement0( xv ) }.
% 5.00/5.38 (20614) {G0,W4,D2,L1,V0,M1} { aReductOfIn0( xv, xa, xR ) }.
% 5.00/5.38 (20615) {G0,W4,D2,L1,V0,M1} { sdtmndtasgtdt0( xv, xR, xc ) }.
% 5.00/5.38 (20616) {G0,W2,D2,L1,V0,M1} { aElement0( xw ) }.
% 5.00/5.38 (20617) {G0,W4,D2,L1,V0,M1} { sdtmndtasgtdt0( xu, xR, xw ) }.
% 5.00/5.38 (20618) {G0,W4,D2,L1,V0,M1} { sdtmndtasgtdt0( xv, xR, xw ) }.
% 5.00/5.38 (20619) {G0,W4,D2,L1,V0,M1} { aNormalFormOfIn0( xd, xw, xR ) }.
% 5.00/5.38 (20620) {G0,W2,D2,L1,V0,M1} { aElement0( xx ) }.
% 5.00/5.38 (20621) {G0,W4,D2,L1,V0,M1} { sdtmndtasgtdt0( xb, xR, xx ) }.
% 5.00/5.38 (20622) {G0,W4,D2,L1,V0,M1} { sdtmndtasgtdt0( xd, xR, xx ) }.
% 5.00/5.38 (20623) {G0,W4,D2,L1,V0,M1} { ! sdtmndtasgtdt0( xb, xR, xd ) }.
% 5.00/5.38
% 5.00/5.38
% 5.00/5.38 Total Proof:
% 5.00/5.38
% 5.00/5.38 subsumption: (2) {G0,W18,D2,L6,V3,M6} I { ! aElement0( X ), !
% 5.00/5.38 aRewritingSystem0( Y ), ! aElement0( Z ), ! sdtmndtplgtdt0( X, Y, Z ),
% 5.00/5.38 aReductOfIn0( Z, X, Y ), alpha1( X, Y, Z ) }.
% 5.00/5.38 parent0: (20527) {G0,W18,D2,L6,V3,M6} { ! aElement0( X ), !
% 5.00/5.38 aRewritingSystem0( Y ), ! aElement0( Z ), ! sdtmndtplgtdt0( X, Y, Z ),
% 5.00/5.38 aReductOfIn0( Z, X, Y ), alpha1( X, Y, Z ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 X := X
% 5.00/5.38 Y := Y
% 5.00/5.38 Z := Z
% 5.00/5.38 end
% 5.00/5.38 permutation0:
% 5.00/5.38 0 ==> 0
% 5.00/5.38 1 ==> 1
% 5.00/5.38 2 ==> 2
% 5.00/5.38 3 ==> 3
% 5.00/5.38 4 ==> 4
% 5.00/5.38 5 ==> 5
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 subsumption: (6) {G0,W12,D3,L2,V3,M2} I { ! alpha1( X, Y, Z ), alpha6( X, Y
% 5.00/5.38 , Z, skol1( X, Y, Z ) ) }.
% 5.00/5.38 parent0: (20531) {G0,W12,D3,L2,V3,M2} { ! alpha1( X, Y, Z ), alpha6( X, Y
% 5.00/5.38 , Z, skol1( X, Y, Z ) ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 X := X
% 5.00/5.38 Y := Y
% 5.00/5.38 Z := Z
% 5.00/5.38 end
% 5.00/5.38 permutation0:
% 5.00/5.38 0 ==> 0
% 5.00/5.38 1 ==> 1
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 subsumption: (8) {G0,W9,D2,L2,V4,M2} I { ! alpha6( X, Y, Z, T ),
% 5.00/5.38 aReductOfIn0( T, X, Y ) }.
% 5.00/5.38 parent0: (20533) {G0,W9,D2,L2,V4,M2} { ! alpha6( X, Y, Z, T ),
% 5.00/5.38 aReductOfIn0( T, X, Y ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 X := X
% 5.00/5.38 Y := Y
% 5.00/5.38 Z := Z
% 5.00/5.38 T := T
% 5.00/5.38 end
% 5.00/5.38 permutation0:
% 5.00/5.38 0 ==> 0
% 5.00/5.38 1 ==> 1
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 subsumption: (12) {G0,W17,D2,L6,V3,M6} I { ! aElement0( X ), !
% 5.00/5.38 aRewritingSystem0( Y ), ! aElement0( Z ), ! sdtmndtasgtdt0( X, Y, Z ), X
% 5.00/5.38 = Z, sdtmndtplgtdt0( X, Y, Z ) }.
% 5.00/5.38 parent0: (20537) {G0,W17,D2,L6,V3,M6} { ! aElement0( X ), !
% 5.00/5.38 aRewritingSystem0( Y ), ! aElement0( Z ), ! sdtmndtasgtdt0( X, Y, Z ), X
% 5.00/5.38 = Z, sdtmndtplgtdt0( X, Y, Z ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 X := X
% 5.00/5.38 Y := Y
% 5.00/5.38 Z := Z
% 5.00/5.38 end
% 5.00/5.38 permutation0:
% 5.00/5.38 0 ==> 0
% 5.00/5.38 1 ==> 1
% 5.00/5.38 2 ==> 2
% 5.00/5.38 3 ==> 3
% 5.00/5.38 4 ==> 4
% 5.00/5.38 5 ==> 5
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 subsumption: (67) {G0,W10,D2,L4,V3,M4} I { ! aElement0( X ), !
% 5.00/5.38 aRewritingSystem0( Y ), ! aNormalFormOfIn0( Z, X, Y ), aElement0( Z ) }.
% 5.00/5.38 parent0: (20592) {G0,W10,D2,L4,V3,M4} { ! aElement0( X ), !
% 5.00/5.38 aRewritingSystem0( Y ), ! aNormalFormOfIn0( Z, X, Y ), aElement0( Z ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 X := X
% 5.00/5.38 Y := Y
% 5.00/5.38 Z := Z
% 5.00/5.38 end
% 5.00/5.38 permutation0:
% 5.00/5.38 0 ==> 0
% 5.00/5.38 1 ==> 1
% 5.00/5.38 2 ==> 2
% 5.00/5.38 3 ==> 3
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 subsumption: (68) {G0,W12,D2,L4,V3,M4} I { ! aElement0( X ), !
% 5.00/5.38 aRewritingSystem0( Y ), ! aNormalFormOfIn0( Z, X, Y ), alpha5( X, Y, Z )
% 5.00/5.38 }.
% 5.00/5.38 parent0: (20593) {G0,W12,D2,L4,V3,M4} { ! aElement0( X ), !
% 5.00/5.38 aRewritingSystem0( Y ), ! aNormalFormOfIn0( Z, X, Y ), alpha5( X, Y, Z )
% 5.00/5.38 }.
% 5.00/5.38 substitution0:
% 5.00/5.38 X := X
% 5.00/5.38 Y := Y
% 5.00/5.38 Z := Z
% 5.00/5.38 end
% 5.00/5.38 permutation0:
% 5.00/5.38 0 ==> 0
% 5.00/5.38 1 ==> 1
% 5.00/5.38 2 ==> 2
% 5.00/5.38 3 ==> 3
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 subsumption: (71) {G0,W8,D2,L2,V4,M2} I { ! alpha5( X, Y, Z ), !
% 5.00/5.38 aReductOfIn0( T, Z, Y ) }.
% 5.00/5.38 parent0: (20596) {G0,W8,D2,L2,V4,M2} { ! alpha5( X, Y, Z ), ! aReductOfIn0
% 5.00/5.38 ( T, Z, Y ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 X := X
% 5.00/5.38 Y := Y
% 5.00/5.38 Z := Z
% 5.00/5.38 T := T
% 5.00/5.38 end
% 5.00/5.38 permutation0:
% 5.00/5.38 0 ==> 0
% 5.00/5.38 1 ==> 1
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 subsumption: (74) {G0,W2,D2,L1,V0,M1} I { aRewritingSystem0( xR ) }.
% 5.00/5.38 parent0: (20599) {G0,W2,D2,L1,V0,M1} { aRewritingSystem0( xR ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 end
% 5.00/5.38 permutation0:
% 5.00/5.38 0 ==> 0
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 subsumption: (91) {G0,W2,D2,L1,V0,M1} I { aElement0( xw ) }.
% 5.00/5.38 parent0: (20616) {G0,W2,D2,L1,V0,M1} { aElement0( xw ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 end
% 5.00/5.38 permutation0:
% 5.00/5.38 0 ==> 0
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 subsumption: (94) {G0,W4,D2,L1,V0,M1} I { aNormalFormOfIn0( xd, xw, xR )
% 5.00/5.38 }.
% 5.00/5.38 parent0: (20619) {G0,W4,D2,L1,V0,M1} { aNormalFormOfIn0( xd, xw, xR ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 end
% 5.00/5.38 permutation0:
% 5.00/5.38 0 ==> 0
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 subsumption: (95) {G0,W2,D2,L1,V0,M1} I { aElement0( xx ) }.
% 5.00/5.38 parent0: (20620) {G0,W2,D2,L1,V0,M1} { aElement0( xx ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 end
% 5.00/5.38 permutation0:
% 5.00/5.38 0 ==> 0
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 subsumption: (96) {G0,W4,D2,L1,V0,M1} I { sdtmndtasgtdt0( xb, xR, xx ) }.
% 5.00/5.38 parent0: (20621) {G0,W4,D2,L1,V0,M1} { sdtmndtasgtdt0( xb, xR, xx ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 end
% 5.00/5.38 permutation0:
% 5.00/5.38 0 ==> 0
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 subsumption: (97) {G0,W4,D2,L1,V0,M1} I { sdtmndtasgtdt0( xd, xR, xx ) }.
% 5.00/5.38 parent0: (20622) {G0,W4,D2,L1,V0,M1} { sdtmndtasgtdt0( xd, xR, xx ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 end
% 5.00/5.38 permutation0:
% 5.00/5.38 0 ==> 0
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 subsumption: (98) {G0,W4,D2,L1,V0,M1} I { ! sdtmndtasgtdt0( xb, xR, xd )
% 5.00/5.38 }.
% 5.00/5.38 parent0: (20623) {G0,W4,D2,L1,V0,M1} { ! sdtmndtasgtdt0( xb, xR, xd ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 end
% 5.00/5.38 permutation0:
% 5.00/5.38 0 ==> 0
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 resolution: (21014) {G1,W16,D2,L5,V2,M5} { ! aElement0( X ), ! aElement0(
% 5.00/5.38 Y ), ! sdtmndtplgtdt0( X, xR, Y ), aReductOfIn0( Y, X, xR ), alpha1( X,
% 5.00/5.38 xR, Y ) }.
% 5.00/5.38 parent0[1]: (2) {G0,W18,D2,L6,V3,M6} I { ! aElement0( X ), !
% 5.00/5.38 aRewritingSystem0( Y ), ! aElement0( Z ), ! sdtmndtplgtdt0( X, Y, Z ),
% 5.00/5.38 aReductOfIn0( Z, X, Y ), alpha1( X, Y, Z ) }.
% 5.00/5.38 parent1[0]: (74) {G0,W2,D2,L1,V0,M1} I { aRewritingSystem0( xR ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 X := X
% 5.00/5.38 Y := xR
% 5.00/5.38 Z := Y
% 5.00/5.38 end
% 5.00/5.38 substitution1:
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 subsumption: (143) {G1,W16,D2,L5,V2,M5} R(74,2) { ! aElement0( X ), !
% 5.00/5.38 aElement0( Y ), ! sdtmndtplgtdt0( X, xR, Y ), aReductOfIn0( Y, X, xR ),
% 5.00/5.38 alpha1( X, xR, Y ) }.
% 5.00/5.38 parent0: (21014) {G1,W16,D2,L5,V2,M5} { ! aElement0( X ), ! aElement0( Y )
% 5.00/5.38 , ! sdtmndtplgtdt0( X, xR, Y ), aReductOfIn0( Y, X, xR ), alpha1( X, xR,
% 5.00/5.38 Y ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 X := X
% 5.00/5.38 Y := Y
% 5.00/5.38 end
% 5.00/5.38 permutation0:
% 5.00/5.38 0 ==> 0
% 5.00/5.38 1 ==> 1
% 5.00/5.38 2 ==> 2
% 5.00/5.38 3 ==> 3
% 5.00/5.38 4 ==> 4
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 eqswap: (21016) {G0,W17,D2,L6,V3,M6} { Y = X, ! aElement0( X ), !
% 5.00/5.38 aRewritingSystem0( Z ), ! aElement0( Y ), ! sdtmndtasgtdt0( X, Z, Y ),
% 5.00/5.38 sdtmndtplgtdt0( X, Z, Y ) }.
% 5.00/5.38 parent0[4]: (12) {G0,W17,D2,L6,V3,M6} I { ! aElement0( X ), !
% 5.00/5.38 aRewritingSystem0( Y ), ! aElement0( Z ), ! sdtmndtasgtdt0( X, Y, Z ), X
% 5.00/5.38 = Z, sdtmndtplgtdt0( X, Y, Z ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 X := X
% 5.00/5.38 Y := Z
% 5.00/5.38 Z := Y
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 resolution: (21017) {G1,W13,D2,L5,V0,M5} { xx = xd, ! aElement0( xd ), !
% 5.00/5.38 aRewritingSystem0( xR ), ! aElement0( xx ), sdtmndtplgtdt0( xd, xR, xx )
% 5.00/5.38 }.
% 5.00/5.38 parent0[4]: (21016) {G0,W17,D2,L6,V3,M6} { Y = X, ! aElement0( X ), !
% 5.00/5.38 aRewritingSystem0( Z ), ! aElement0( Y ), ! sdtmndtasgtdt0( X, Z, Y ),
% 5.00/5.38 sdtmndtplgtdt0( X, Z, Y ) }.
% 5.00/5.38 parent1[0]: (97) {G0,W4,D2,L1,V0,M1} I { sdtmndtasgtdt0( xd, xR, xx ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 X := xd
% 5.00/5.38 Y := xx
% 5.00/5.38 Z := xR
% 5.00/5.38 end
% 5.00/5.38 substitution1:
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 resolution: (21018) {G1,W11,D2,L4,V0,M4} { xx = xd, ! aElement0( xd ), !
% 5.00/5.38 aElement0( xx ), sdtmndtplgtdt0( xd, xR, xx ) }.
% 5.00/5.38 parent0[2]: (21017) {G1,W13,D2,L5,V0,M5} { xx = xd, ! aElement0( xd ), !
% 5.00/5.38 aRewritingSystem0( xR ), ! aElement0( xx ), sdtmndtplgtdt0( xd, xR, xx )
% 5.00/5.38 }.
% 5.00/5.38 parent1[0]: (74) {G0,W2,D2,L1,V0,M1} I { aRewritingSystem0( xR ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 end
% 5.00/5.38 substitution1:
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 subsumption: (427) {G1,W11,D2,L4,V0,M4} R(12,97);r(74) { ! aElement0( xd )
% 5.00/5.38 , ! aElement0( xx ), xx ==> xd, sdtmndtplgtdt0( xd, xR, xx ) }.
% 5.00/5.38 parent0: (21018) {G1,W11,D2,L4,V0,M4} { xx = xd, ! aElement0( xd ), !
% 5.00/5.38 aElement0( xx ), sdtmndtplgtdt0( xd, xR, xx ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 end
% 5.00/5.38 permutation0:
% 5.00/5.38 0 ==> 2
% 5.00/5.38 1 ==> 0
% 5.00/5.38 2 ==> 1
% 5.00/5.38 3 ==> 3
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 resolution: (21020) {G1,W6,D2,L3,V0,M3} { ! aElement0( xw ), !
% 5.00/5.38 aRewritingSystem0( xR ), aElement0( xd ) }.
% 5.00/5.38 parent0[2]: (67) {G0,W10,D2,L4,V3,M4} I { ! aElement0( X ), !
% 5.00/5.38 aRewritingSystem0( Y ), ! aNormalFormOfIn0( Z, X, Y ), aElement0( Z ) }.
% 5.00/5.38 parent1[0]: (94) {G0,W4,D2,L1,V0,M1} I { aNormalFormOfIn0( xd, xw, xR ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 X := xw
% 5.00/5.38 Y := xR
% 5.00/5.38 Z := xd
% 5.00/5.38 end
% 5.00/5.38 substitution1:
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 resolution: (21021) {G1,W4,D2,L2,V0,M2} { ! aRewritingSystem0( xR ),
% 5.00/5.38 aElement0( xd ) }.
% 5.00/5.38 parent0[0]: (21020) {G1,W6,D2,L3,V0,M3} { ! aElement0( xw ), !
% 5.00/5.38 aRewritingSystem0( xR ), aElement0( xd ) }.
% 5.00/5.38 parent1[0]: (91) {G0,W2,D2,L1,V0,M1} I { aElement0( xw ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 end
% 5.00/5.38 substitution1:
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 subsumption: (2106) {G1,W4,D2,L2,V0,M2} R(67,94);r(91) { !
% 5.00/5.38 aRewritingSystem0( xR ), aElement0( xd ) }.
% 5.00/5.38 parent0: (21021) {G1,W4,D2,L2,V0,M2} { ! aRewritingSystem0( xR ),
% 5.00/5.38 aElement0( xd ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 end
% 5.00/5.38 permutation0:
% 5.00/5.38 0 ==> 0
% 5.00/5.38 1 ==> 1
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 resolution: (21022) {G1,W8,D2,L3,V0,M3} { ! aElement0( xw ), !
% 5.00/5.38 aRewritingSystem0( xR ), alpha5( xw, xR, xd ) }.
% 5.00/5.38 parent0[2]: (68) {G0,W12,D2,L4,V3,M4} I { ! aElement0( X ), !
% 5.00/5.38 aRewritingSystem0( Y ), ! aNormalFormOfIn0( Z, X, Y ), alpha5( X, Y, Z )
% 5.00/5.38 }.
% 5.00/5.38 parent1[0]: (94) {G0,W4,D2,L1,V0,M1} I { aNormalFormOfIn0( xd, xw, xR ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 X := xw
% 5.00/5.38 Y := xR
% 5.00/5.38 Z := xd
% 5.00/5.38 end
% 5.00/5.38 substitution1:
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 resolution: (21023) {G1,W6,D2,L2,V0,M2} { ! aRewritingSystem0( xR ),
% 5.00/5.38 alpha5( xw, xR, xd ) }.
% 5.00/5.38 parent0[0]: (21022) {G1,W8,D2,L3,V0,M3} { ! aElement0( xw ), !
% 5.00/5.38 aRewritingSystem0( xR ), alpha5( xw, xR, xd ) }.
% 5.00/5.38 parent1[0]: (91) {G0,W2,D2,L1,V0,M1} I { aElement0( xw ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 end
% 5.00/5.38 substitution1:
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 subsumption: (2146) {G1,W6,D2,L2,V0,M2} R(68,94);r(91) { !
% 5.00/5.38 aRewritingSystem0( xR ), alpha5( xw, xR, xd ) }.
% 5.00/5.38 parent0: (21023) {G1,W6,D2,L2,V0,M2} { ! aRewritingSystem0( xR ), alpha5(
% 5.00/5.38 xw, xR, xd ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 end
% 5.00/5.38 permutation0:
% 5.00/5.38 0 ==> 0
% 5.00/5.38 1 ==> 1
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 resolution: (21024) {G1,W2,D2,L1,V0,M1} { aElement0( xd ) }.
% 5.00/5.38 parent0[0]: (2106) {G1,W4,D2,L2,V0,M2} R(67,94);r(91) { ! aRewritingSystem0
% 5.00/5.38 ( xR ), aElement0( xd ) }.
% 5.00/5.38 parent1[0]: (74) {G0,W2,D2,L1,V0,M1} I { aRewritingSystem0( xR ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 end
% 5.00/5.38 substitution1:
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 subsumption: (2476) {G2,W2,D2,L1,V0,M1} S(2106);r(74) { aElement0( xd ) }.
% 5.00/5.38 parent0: (21024) {G1,W2,D2,L1,V0,M1} { aElement0( xd ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 end
% 5.00/5.38 permutation0:
% 5.00/5.38 0 ==> 0
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 resolution: (21025) {G1,W4,D2,L1,V0,M1} { alpha5( xw, xR, xd ) }.
% 5.00/5.38 parent0[0]: (2146) {G1,W6,D2,L2,V0,M2} R(68,94);r(91) { ! aRewritingSystem0
% 5.00/5.38 ( xR ), alpha5( xw, xR, xd ) }.
% 5.00/5.38 parent1[0]: (74) {G0,W2,D2,L1,V0,M1} I { aRewritingSystem0( xR ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 end
% 5.00/5.38 substitution1:
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 subsumption: (4568) {G2,W4,D2,L1,V0,M1} S(2146);r(74) { alpha5( xw, xR, xd
% 5.00/5.38 ) }.
% 5.00/5.38 parent0: (21025) {G1,W4,D2,L1,V0,M1} { alpha5( xw, xR, xd ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 end
% 5.00/5.38 permutation0:
% 5.00/5.38 0 ==> 0
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 resolution: (21026) {G1,W4,D2,L1,V1,M1} { ! aReductOfIn0( X, xd, xR ) }.
% 5.00/5.38 parent0[0]: (71) {G0,W8,D2,L2,V4,M2} I { ! alpha5( X, Y, Z ), !
% 5.00/5.38 aReductOfIn0( T, Z, Y ) }.
% 5.00/5.38 parent1[0]: (4568) {G2,W4,D2,L1,V0,M1} S(2146);r(74) { alpha5( xw, xR, xd )
% 5.00/5.38 }.
% 5.00/5.38 substitution0:
% 5.00/5.38 X := xw
% 5.00/5.38 Y := xR
% 5.00/5.38 Z := xd
% 5.00/5.38 T := X
% 5.00/5.38 end
% 5.00/5.38 substitution1:
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 subsumption: (4569) {G3,W4,D2,L1,V1,M1} R(4568,71) { ! aReductOfIn0( X, xd
% 5.00/5.38 , xR ) }.
% 5.00/5.38 parent0: (21026) {G1,W4,D2,L1,V1,M1} { ! aReductOfIn0( X, xd, xR ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 X := X
% 5.00/5.38 end
% 5.00/5.38 permutation0:
% 5.00/5.38 0 ==> 0
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 resolution: (21027) {G1,W5,D2,L1,V2,M1} { ! alpha6( xd, xR, Y, X ) }.
% 5.00/5.38 parent0[0]: (4569) {G3,W4,D2,L1,V1,M1} R(4568,71) { ! aReductOfIn0( X, xd,
% 5.00/5.38 xR ) }.
% 5.00/5.38 parent1[1]: (8) {G0,W9,D2,L2,V4,M2} I { ! alpha6( X, Y, Z, T ),
% 5.00/5.38 aReductOfIn0( T, X, Y ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 X := X
% 5.00/5.38 end
% 5.00/5.38 substitution1:
% 5.00/5.38 X := xd
% 5.00/5.38 Y := xR
% 5.00/5.38 Z := Y
% 5.00/5.38 T := X
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 subsumption: (4582) {G4,W5,D2,L1,V2,M1} R(4569,8) { ! alpha6( xd, xR, X, Y
% 5.00/5.38 ) }.
% 5.00/5.38 parent0: (21027) {G1,W5,D2,L1,V2,M1} { ! alpha6( xd, xR, Y, X ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 X := Y
% 5.00/5.38 Y := X
% 5.00/5.38 end
% 5.00/5.38 permutation0:
% 5.00/5.38 0 ==> 0
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 resolution: (21028) {G1,W4,D2,L1,V1,M1} { ! alpha1( xd, xR, X ) }.
% 5.00/5.38 parent0[0]: (4582) {G4,W5,D2,L1,V2,M1} R(4569,8) { ! alpha6( xd, xR, X, Y )
% 5.00/5.38 }.
% 5.00/5.38 parent1[1]: (6) {G0,W12,D3,L2,V3,M2} I { ! alpha1( X, Y, Z ), alpha6( X, Y
% 5.00/5.38 , Z, skol1( X, Y, Z ) ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 X := X
% 5.00/5.38 Y := skol1( xd, xR, X )
% 5.00/5.38 end
% 5.00/5.38 substitution1:
% 5.00/5.38 X := xd
% 5.00/5.38 Y := xR
% 5.00/5.38 Z := X
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 subsumption: (4598) {G5,W4,D2,L1,V1,M1} R(4582,6) { ! alpha1( xd, xR, X )
% 5.00/5.38 }.
% 5.00/5.38 parent0: (21028) {G1,W4,D2,L1,V1,M1} { ! alpha1( xd, xR, X ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 X := X
% 5.00/5.38 end
% 5.00/5.38 permutation0:
% 5.00/5.38 0 ==> 0
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 resolution: (21030) {G2,W9,D2,L3,V0,M3} { ! aElement0( xx ), xx ==> xd,
% 5.00/5.38 sdtmndtplgtdt0( xd, xR, xx ) }.
% 5.00/5.38 parent0[0]: (427) {G1,W11,D2,L4,V0,M4} R(12,97);r(74) { ! aElement0( xd ),
% 5.00/5.38 ! aElement0( xx ), xx ==> xd, sdtmndtplgtdt0( xd, xR, xx ) }.
% 5.00/5.38 parent1[0]: (2476) {G2,W2,D2,L1,V0,M1} S(2106);r(74) { aElement0( xd ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 end
% 5.00/5.38 substitution1:
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 resolution: (21031) {G1,W7,D2,L2,V0,M2} { xx ==> xd, sdtmndtplgtdt0( xd,
% 5.00/5.38 xR, xx ) }.
% 5.00/5.38 parent0[0]: (21030) {G2,W9,D2,L3,V0,M3} { ! aElement0( xx ), xx ==> xd,
% 5.00/5.38 sdtmndtplgtdt0( xd, xR, xx ) }.
% 5.00/5.38 parent1[0]: (95) {G0,W2,D2,L1,V0,M1} I { aElement0( xx ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 end
% 5.00/5.38 substitution1:
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 subsumption: (14452) {G3,W7,D2,L2,V0,M2} S(427);r(2476);r(95) { xx ==> xd,
% 5.00/5.38 sdtmndtplgtdt0( xd, xR, xx ) }.
% 5.00/5.38 parent0: (21031) {G1,W7,D2,L2,V0,M2} { xx ==> xd, sdtmndtplgtdt0( xd, xR,
% 5.00/5.38 xx ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 end
% 5.00/5.38 permutation0:
% 5.00/5.38 0 ==> 0
% 5.00/5.38 1 ==> 1
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 paramod: (21034) {G1,W8,D2,L2,V0,M2} { sdtmndtasgtdt0( xb, xR, xd ),
% 5.00/5.38 sdtmndtplgtdt0( xd, xR, xx ) }.
% 5.00/5.38 parent0[0]: (14452) {G3,W7,D2,L2,V0,M2} S(427);r(2476);r(95) { xx ==> xd,
% 5.00/5.38 sdtmndtplgtdt0( xd, xR, xx ) }.
% 5.00/5.38 parent1[0; 3]: (96) {G0,W4,D2,L1,V0,M1} I { sdtmndtasgtdt0( xb, xR, xx )
% 5.00/5.38 }.
% 5.00/5.38 substitution0:
% 5.00/5.38 end
% 5.00/5.38 substitution1:
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 resolution: (21045) {G1,W4,D2,L1,V0,M1} { sdtmndtplgtdt0( xd, xR, xx ) }.
% 5.00/5.38 parent0[0]: (98) {G0,W4,D2,L1,V0,M1} I { ! sdtmndtasgtdt0( xb, xR, xd ) }.
% 5.00/5.38 parent1[0]: (21034) {G1,W8,D2,L2,V0,M2} { sdtmndtasgtdt0( xb, xR, xd ),
% 5.00/5.38 sdtmndtplgtdt0( xd, xR, xx ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 end
% 5.00/5.38 substitution1:
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 subsumption: (14478) {G4,W4,D2,L1,V0,M1} P(14452,96);r(98) { sdtmndtplgtdt0
% 5.00/5.38 ( xd, xR, xx ) }.
% 5.00/5.38 parent0: (21045) {G1,W4,D2,L1,V0,M1} { sdtmndtplgtdt0( xd, xR, xx ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 end
% 5.00/5.38 permutation0:
% 5.00/5.38 0 ==> 0
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 resolution: (21046) {G2,W12,D2,L4,V0,M4} { ! aElement0( xd ), ! aElement0
% 5.00/5.38 ( xx ), aReductOfIn0( xx, xd, xR ), alpha1( xd, xR, xx ) }.
% 5.00/5.38 parent0[2]: (143) {G1,W16,D2,L5,V2,M5} R(74,2) { ! aElement0( X ), !
% 5.00/5.38 aElement0( Y ), ! sdtmndtplgtdt0( X, xR, Y ), aReductOfIn0( Y, X, xR ),
% 5.00/5.38 alpha1( X, xR, Y ) }.
% 5.00/5.38 parent1[0]: (14478) {G4,W4,D2,L1,V0,M1} P(14452,96);r(98) { sdtmndtplgtdt0
% 5.00/5.38 ( xd, xR, xx ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 X := xd
% 5.00/5.38 Y := xx
% 5.00/5.38 end
% 5.00/5.38 substitution1:
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 resolution: (21047) {G3,W10,D2,L3,V0,M3} { ! aElement0( xx ), aReductOfIn0
% 5.00/5.38 ( xx, xd, xR ), alpha1( xd, xR, xx ) }.
% 5.00/5.38 parent0[0]: (21046) {G2,W12,D2,L4,V0,M4} { ! aElement0( xd ), ! aElement0
% 5.00/5.38 ( xx ), aReductOfIn0( xx, xd, xR ), alpha1( xd, xR, xx ) }.
% 5.00/5.38 parent1[0]: (2476) {G2,W2,D2,L1,V0,M1} S(2106);r(74) { aElement0( xd ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 end
% 5.00/5.38 substitution1:
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 subsumption: (14523) {G5,W10,D2,L3,V0,M3} R(14478,143);r(2476) { !
% 5.00/5.38 aElement0( xx ), aReductOfIn0( xx, xd, xR ), alpha1( xd, xR, xx ) }.
% 5.00/5.38 parent0: (21047) {G3,W10,D2,L3,V0,M3} { ! aElement0( xx ), aReductOfIn0(
% 5.00/5.38 xx, xd, xR ), alpha1( xd, xR, xx ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 end
% 5.00/5.38 permutation0:
% 5.00/5.38 0 ==> 0
% 5.00/5.38 1 ==> 1
% 5.00/5.38 2 ==> 2
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 resolution: (21048) {G1,W8,D2,L2,V0,M2} { aReductOfIn0( xx, xd, xR ),
% 5.00/5.38 alpha1( xd, xR, xx ) }.
% 5.00/5.38 parent0[0]: (14523) {G5,W10,D2,L3,V0,M3} R(14478,143);r(2476) { ! aElement0
% 5.00/5.38 ( xx ), aReductOfIn0( xx, xd, xR ), alpha1( xd, xR, xx ) }.
% 5.00/5.38 parent1[0]: (95) {G0,W2,D2,L1,V0,M1} I { aElement0( xx ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 end
% 5.00/5.38 substitution1:
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 resolution: (21049) {G2,W4,D2,L1,V0,M1} { alpha1( xd, xR, xx ) }.
% 5.00/5.38 parent0[0]: (4569) {G3,W4,D2,L1,V1,M1} R(4568,71) { ! aReductOfIn0( X, xd,
% 5.00/5.38 xR ) }.
% 5.00/5.38 parent1[0]: (21048) {G1,W8,D2,L2,V0,M2} { aReductOfIn0( xx, xd, xR ),
% 5.00/5.38 alpha1( xd, xR, xx ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 X := xx
% 5.00/5.38 end
% 5.00/5.38 substitution1:
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 resolution: (21050) {G3,W0,D0,L0,V0,M0} { }.
% 5.00/5.38 parent0[0]: (4598) {G5,W4,D2,L1,V1,M1} R(4582,6) { ! alpha1( xd, xR, X )
% 5.00/5.38 }.
% 5.00/5.38 parent1[0]: (21049) {G2,W4,D2,L1,V0,M1} { alpha1( xd, xR, xx ) }.
% 5.00/5.38 substitution0:
% 5.00/5.38 X := xx
% 5.00/5.38 end
% 5.00/5.38 substitution1:
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 subsumption: (20520) {G6,W0,D0,L0,V0,M0} S(14523);r(95);r(4569);r(4598) {
% 5.00/5.38 }.
% 5.00/5.38 parent0: (21050) {G3,W0,D0,L0,V0,M0} { }.
% 5.00/5.38 substitution0:
% 5.00/5.38 end
% 5.00/5.38 permutation0:
% 5.00/5.38 end
% 5.00/5.38
% 5.00/5.38 Proof check complete!
% 5.00/5.38
% 5.00/5.38 Memory use:
% 5.00/5.38
% 5.00/5.38 space for terms: 297253
% 5.00/5.38 space for clauses: 819633
% 5.00/5.38
% 5.00/5.38
% 5.00/5.38 clauses generated: 382582
% 5.00/5.38 clauses kept: 20521
% 5.00/5.38 clauses selected: 2447
% 5.00/5.38 clauses deleted: 1155
% 5.00/5.38 clauses inuse deleted: 30
% 5.00/5.38
% 5.00/5.38 subsentry: 528340
% 5.00/5.38 literals s-matched: 436561
% 5.00/5.38 literals matched: 336285
% 5.00/5.38 full subsumption: 15429
% 5.00/5.38
% 5.00/5.38 checksum: -486896214
% 5.00/5.38
% 5.00/5.38
% 5.00/5.38 Bliksem ended
%------------------------------------------------------------------------------