TSTP Solution File: GRA003+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GRA003+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n024.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 : Sat Jul 16 07:11:30 EDT 2022
% Result : Theorem 0.88s 1.31s
% Output : Refutation 0.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRA003+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.03/0.12 % Command : bliksem %s
% 0.13/0.33 % Computer : n024.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % DateTime : Tue May 31 02:30:51 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.43/1.07 *** allocated 10000 integers for termspace/termends
% 0.43/1.07 *** allocated 10000 integers for clauses
% 0.43/1.07 *** allocated 10000 integers for justifications
% 0.43/1.07 Bliksem 1.12
% 0.43/1.07
% 0.43/1.07
% 0.43/1.07 Automatic Strategy Selection
% 0.43/1.07
% 0.43/1.07
% 0.43/1.07 Clauses:
% 0.43/1.07
% 0.43/1.07 { ! edge( X ), ! head_of( X ) = tail_of( X ) }.
% 0.43/1.07 { ! edge( X ), vertex( head_of( X ) ) }.
% 0.43/1.07 { ! edge( X ), vertex( tail_of( X ) ) }.
% 0.43/1.07 { ! complete, ! vertex( X ), ! vertex( Y ), X = Y, edge( skol1( Z, T ) ) }
% 0.43/1.07 .
% 0.43/1.07 { ! complete, ! vertex( X ), ! vertex( Y ), X = Y, alpha11( X, Y, skol1( X
% 0.43/1.07 , Y ) ), alpha15( X, Y, skol1( X, Y ) ) }.
% 0.43/1.07 { ! alpha15( X, Y, Z ), Y = head_of( Z ) }.
% 0.43/1.07 { ! alpha15( X, Y, Z ), X = tail_of( Z ) }.
% 0.43/1.07 { ! alpha15( X, Y, Z ), ! alpha1( X, Y, Z ) }.
% 0.43/1.07 { ! Y = head_of( Z ), ! X = tail_of( Z ), alpha1( X, Y, Z ), alpha15( X, Y
% 0.43/1.07 , Z ) }.
% 0.43/1.07 { ! alpha11( X, Y, Z ), alpha1( X, Y, Z ) }.
% 0.43/1.07 { ! alpha11( X, Y, Z ), ! Y = head_of( Z ), ! X = tail_of( Z ) }.
% 0.43/1.07 { ! alpha1( X, Y, Z ), Y = head_of( Z ), alpha11( X, Y, Z ) }.
% 0.43/1.07 { ! alpha1( X, Y, Z ), X = tail_of( Z ), alpha11( X, Y, Z ) }.
% 0.43/1.07 { ! alpha1( X, Y, Z ), X = head_of( Z ) }.
% 0.43/1.07 { ! alpha1( X, Y, Z ), Y = tail_of( Z ) }.
% 0.43/1.07 { ! X = head_of( Z ), ! Y = tail_of( Z ), alpha1( X, Y, Z ) }.
% 0.43/1.07 { ! vertex( X ), ! vertex( Y ), ! edge( T ), ! X = tail_of( T ), ! Y =
% 0.43/1.07 head_of( T ), ! Z = path_cons( T, empty ), path( X, Y, Z ) }.
% 0.43/1.07 { ! vertex( X ), ! vertex( Y ), ! edge( T ), ! X = tail_of( T ), ! path(
% 0.43/1.07 head_of( T ), Y, U ), ! Z = path_cons( T, U ), path( X, Y, Z ) }.
% 0.43/1.07 { ! path( X, Y, Z ), alpha12( X, Y ) }.
% 0.43/1.07 { ! path( X, Y, Z ), alpha16( X, skol2( X, T, U ) ) }.
% 0.43/1.07 { ! path( X, Y, Z ), alpha20( Y, Z, skol2( X, Y, Z ) ) }.
% 0.43/1.07 { ! alpha20( X, Y, Z ), alpha18( X, Y, Z ), alpha21( X, Y, Z ) }.
% 0.43/1.07 { ! alpha18( X, Y, Z ), alpha20( X, Y, Z ) }.
% 0.43/1.07 { ! alpha21( X, Y, Z ), alpha20( X, Y, Z ) }.
% 0.43/1.07 { ! alpha21( X, Y, Z ), Y = path_cons( Z, skol3( T, Y, Z ) ) }.
% 0.43/1.07 { ! alpha21( X, Y, Z ), path( head_of( Z ), X, skol3( X, Y, Z ) ) }.
% 0.43/1.07 { ! alpha21( X, Y, Z ), ! alpha2( X, Y, Z ) }.
% 0.43/1.07 { ! path( head_of( Z ), X, T ), ! Y = path_cons( Z, T ), alpha2( X, Y, Z )
% 0.43/1.07 , alpha21( X, Y, Z ) }.
% 0.43/1.07 { ! alpha18( X, Y, Z ), alpha2( X, Y, Z ) }.
% 0.43/1.07 { ! alpha18( X, Y, Z ), ! path( head_of( Z ), X, T ), ! Y = path_cons( Z, T
% 0.43/1.07 ) }.
% 0.43/1.07 { ! alpha2( X, Y, Z ), Y = path_cons( Z, skol4( T, Y, Z ) ), alpha18( X, Y
% 0.43/1.07 , Z ) }.
% 0.43/1.07 { ! alpha2( X, Y, Z ), path( head_of( Z ), X, skol4( X, Y, Z ) ), alpha18(
% 0.43/1.07 X, Y, Z ) }.
% 0.43/1.07 { ! alpha16( X, Y ), edge( Y ) }.
% 0.43/1.07 { ! alpha16( X, Y ), X = tail_of( Y ) }.
% 0.43/1.07 { ! edge( Y ), ! X = tail_of( Y ), alpha16( X, Y ) }.
% 0.43/1.07 { ! alpha12( X, Y ), vertex( X ) }.
% 0.43/1.07 { ! alpha12( X, Y ), vertex( Y ) }.
% 0.43/1.07 { ! vertex( X ), ! vertex( Y ), alpha12( X, Y ) }.
% 0.43/1.07 { ! alpha2( X, Y, Z ), X = head_of( Z ) }.
% 0.43/1.07 { ! alpha2( X, Y, Z ), Y = path_cons( Z, empty ) }.
% 0.43/1.07 { ! X = head_of( Z ), ! Y = path_cons( Z, empty ), alpha2( X, Y, Z ) }.
% 0.43/1.07 { ! path( Z, T, X ), ! on_path( Y, X ), edge( Y ) }.
% 0.43/1.07 { ! path( Z, T, X ), ! on_path( Y, X ), in_path( head_of( Y ), X ) }.
% 0.43/1.07 { ! path( Z, T, X ), ! on_path( Y, X ), in_path( tail_of( Y ), X ) }.
% 0.43/1.07 { ! path( Z, T, X ), ! in_path( Y, X ), vertex( Y ) }.
% 0.43/1.07 { ! path( Z, T, X ), ! in_path( Y, X ), Y = head_of( skol5( U, Y ) ), Y =
% 0.43/1.07 tail_of( skol5( U, Y ) ) }.
% 0.43/1.07 { ! path( Z, T, X ), ! in_path( Y, X ), on_path( skol5( X, Y ), X ) }.
% 0.43/1.07 { ! sequential( X, Y ), edge( X ) }.
% 0.43/1.07 { ! sequential( X, Y ), alpha3( X, Y ) }.
% 0.43/1.07 { ! edge( X ), ! alpha3( X, Y ), sequential( X, Y ) }.
% 0.43/1.07 { ! alpha3( X, Y ), edge( Y ) }.
% 0.43/1.07 { ! alpha3( X, Y ), alpha6( X, Y ) }.
% 0.43/1.07 { ! edge( Y ), ! alpha6( X, Y ), alpha3( X, Y ) }.
% 0.43/1.07 { ! alpha6( X, Y ), ! X = Y }.
% 0.43/1.07 { ! alpha6( X, Y ), head_of( X ) = tail_of( Y ) }.
% 0.43/1.07 { X = Y, ! head_of( X ) = tail_of( Y ), alpha6( X, Y ) }.
% 0.43/1.07 { ! path( Y, Z, X ), ! on_path( T, X ), ! on_path( U, X ), ! sequential( T
% 0.43/1.07 , U ), precedes( T, U, X ) }.
% 0.43/1.07 { ! path( Y, Z, X ), ! on_path( T, X ), ! on_path( U, X ), ! sequential( T
% 0.43/1.07 , W ), ! precedes( W, U, X ), precedes( T, U, X ) }.
% 0.43/1.07 { ! path( Y, Z, X ), ! precedes( T, U, X ), alpha13( X, T, U ) }.
% 0.43/1.07 { ! path( Y, Z, X ), ! precedes( T, U, X ), alpha17( X, T, U ), alpha19( X
% 0.43/1.07 , T, U ) }.
% 0.43/1.07 { ! alpha19( X, Y, Z ), sequential( Y, skol6( T, Y, U ) ) }.
% 0.43/1.07 { ! alpha19( X, Y, Z ), precedes( skol6( X, Y, Z ), Z, X ) }.
% 0.43/1.07 { ! alpha19( X, Y, Z ), ! sequential( Y, Z ) }.
% 0.80/1.18 { ! sequential( Y, T ), ! precedes( T, Z, X ), sequential( Y, Z ), alpha19
% 0.80/1.18 ( X, Y, Z ) }.
% 0.80/1.18 { ! alpha17( X, Y, Z ), sequential( Y, Z ) }.
% 0.80/1.18 { ! alpha17( X, Y, Z ), ! sequential( Y, T ), ! precedes( T, Z, X ) }.
% 0.80/1.18 { ! sequential( Y, Z ), sequential( Y, skol7( T, Y, U ) ), alpha17( X, Y, Z
% 0.80/1.18 ) }.
% 0.80/1.18 { ! sequential( Y, Z ), precedes( skol7( X, Y, Z ), Z, X ), alpha17( X, Y,
% 0.80/1.18 Z ) }.
% 0.80/1.18 { ! alpha13( X, Y, Z ), on_path( Y, X ) }.
% 0.80/1.18 { ! alpha13( X, Y, Z ), on_path( Z, X ) }.
% 0.80/1.18 { ! on_path( Y, X ), ! on_path( Z, X ), alpha13( X, Y, Z ) }.
% 0.80/1.18 { ! shortest_path( X, Y, Z ), path( X, Y, Z ) }.
% 0.80/1.18 { ! shortest_path( X, Y, Z ), alpha4( X, Y, Z ) }.
% 0.80/1.18 { ! path( X, Y, Z ), ! alpha4( X, Y, Z ), shortest_path( X, Y, Z ) }.
% 0.80/1.18 { ! alpha4( X, Y, Z ), ! X = Y }.
% 0.80/1.18 { ! alpha4( X, Y, Z ), alpha7( X, Y, Z ) }.
% 0.80/1.18 { X = Y, ! alpha7( X, Y, Z ), alpha4( X, Y, Z ) }.
% 0.80/1.18 { ! alpha7( X, Y, Z ), ! path( X, Y, T ), less_or_equal( length_of( Z ),
% 0.80/1.18 length_of( T ) ) }.
% 0.80/1.18 { ! less_or_equal( length_of( Z ), length_of( skol8( T, U, Z ) ) ), alpha7
% 0.80/1.18 ( X, Y, Z ) }.
% 0.80/1.18 { path( X, Y, skol8( X, Y, Z ) ), alpha7( X, Y, Z ) }.
% 0.80/1.18 { ! shortest_path( T, U, Z ), ! precedes( X, Y, Z ), ! tail_of( W ) =
% 0.80/1.18 tail_of( X ), ! head_of( W ) = head_of( Y ) }.
% 0.80/1.18 { ! shortest_path( T, U, Z ), ! precedes( X, Y, Z ), ! precedes( Y, X, Z )
% 0.80/1.18 }.
% 0.80/1.18 { ! triangle( X, Y, Z ), edge( X ) }.
% 0.80/1.18 { ! triangle( X, Y, Z ), alpha5( X, Y, Z ) }.
% 0.80/1.18 { ! edge( X ), ! alpha5( X, Y, Z ), triangle( X, Y, Z ) }.
% 0.80/1.18 { ! alpha5( X, Y, Z ), edge( Y ) }.
% 0.80/1.18 { ! alpha5( X, Y, Z ), alpha8( X, Y, Z ) }.
% 0.80/1.18 { ! edge( Y ), ! alpha8( X, Y, Z ), alpha5( X, Y, Z ) }.
% 0.80/1.18 { ! alpha8( X, Y, Z ), edge( Z ) }.
% 0.80/1.18 { ! alpha8( X, Y, Z ), alpha9( X, Y, Z ) }.
% 0.80/1.18 { ! edge( Z ), ! alpha9( X, Y, Z ), alpha8( X, Y, Z ) }.
% 0.80/1.18 { ! alpha9( X, Y, Z ), sequential( X, Y ) }.
% 0.80/1.18 { ! alpha9( X, Y, Z ), alpha10( X, Y, Z ) }.
% 0.80/1.18 { ! sequential( X, Y ), ! alpha10( X, Y, Z ), alpha9( X, Y, Z ) }.
% 0.80/1.18 { ! alpha10( X, Y, Z ), sequential( Y, Z ) }.
% 0.80/1.18 { ! alpha10( X, Y, Z ), sequential( Z, X ) }.
% 0.80/1.18 { ! sequential( Y, Z ), ! sequential( Z, X ), alpha10( X, Y, Z ) }.
% 0.80/1.18 { ! path( Y, Z, X ), length_of( X ) = number_of_in( edges, X ) }.
% 0.80/1.18 { ! path( Y, Z, X ), number_of_in( sequential_pairs, X ) = minus( length_of
% 0.80/1.18 ( X ), n1 ) }.
% 0.80/1.18 { ! path( Y, Z, X ), alpha14( X, skol9( X ), skol11( X ) ), number_of_in(
% 0.80/1.18 sequential_pairs, X ) = number_of_in( triangles, X ) }.
% 0.80/1.18 { ! path( Y, Z, X ), ! triangle( skol9( X ), skol11( X ), T ), number_of_in
% 0.80/1.18 ( sequential_pairs, X ) = number_of_in( triangles, X ) }.
% 0.80/1.18 { ! alpha14( X, Y, Z ), on_path( Y, X ) }.
% 0.80/1.18 { ! alpha14( X, Y, Z ), on_path( Z, X ) }.
% 0.80/1.18 { ! alpha14( X, Y, Z ), sequential( Y, Z ) }.
% 0.80/1.18 { ! on_path( Y, X ), ! on_path( Z, X ), ! sequential( Y, Z ), alpha14( X, Y
% 0.80/1.18 , Z ) }.
% 0.80/1.18 { less_or_equal( number_of_in( X, Y ), number_of_in( X, graph ) ) }.
% 0.80/1.18 { shortest_path( skol10, skol12, skol15 ) }.
% 0.80/1.18 { precedes( skol13, skol14, skol15 ) }.
% 0.80/1.18 { ! vertex( skol10 ), ! vertex( skol12 ), skol10 = skol12, ! edge( skol13 )
% 0.80/1.18 , ! edge( skol14 ), skol13 = skol14, ! path( skol10, skol12, skol15 ) }.
% 0.80/1.18
% 0.80/1.18 percentage equality = 0.156997, percentage horn = 0.825688
% 0.80/1.18 This is a problem with some equality
% 0.80/1.18
% 0.80/1.18
% 0.80/1.18
% 0.80/1.18 Options Used:
% 0.80/1.18
% 0.80/1.18 useres = 1
% 0.80/1.18 useparamod = 1
% 0.80/1.18 useeqrefl = 1
% 0.80/1.18 useeqfact = 1
% 0.80/1.18 usefactor = 1
% 0.80/1.18 usesimpsplitting = 0
% 0.80/1.18 usesimpdemod = 5
% 0.80/1.18 usesimpres = 3
% 0.80/1.18
% 0.80/1.18 resimpinuse = 1000
% 0.80/1.18 resimpclauses = 20000
% 0.80/1.18 substype = eqrewr
% 0.80/1.18 backwardsubs = 1
% 0.80/1.18 selectoldest = 5
% 0.80/1.18
% 0.80/1.18 litorderings [0] = split
% 0.80/1.18 litorderings [1] = extend the termordering, first sorting on arguments
% 0.80/1.18
% 0.80/1.18 termordering = kbo
% 0.80/1.18
% 0.80/1.18 litapriori = 0
% 0.80/1.18 termapriori = 1
% 0.80/1.18 litaposteriori = 0
% 0.80/1.18 termaposteriori = 0
% 0.80/1.18 demodaposteriori = 0
% 0.80/1.18 ordereqreflfact = 0
% 0.80/1.18
% 0.80/1.18 litselect = negord
% 0.80/1.18
% 0.80/1.18 maxweight = 15
% 0.80/1.18 maxdepth = 30000
% 0.80/1.18 maxlength = 115
% 0.80/1.18 maxnrvars = 195
% 0.80/1.18 excuselevel = 1
% 0.80/1.18 increasemaxweight = 1
% 0.80/1.18
% 0.80/1.18 maxselected = 10000000
% 0.80/1.18 maxnrclauses = 10000000
% 0.80/1.18
% 0.80/1.18 showgenerated = 0
% 0.80/1.18 showkept = 0
% 0.80/1.18 showselected = 0
% 0.80/1.18 showdeleted = 0
% 0.80/1.18 showresimp = 1
% 0.80/1.18 showstatus = 2000
% 0.80/1.18
% 0.80/1.18 prologoutput = 0
% 0.80/1.18 nrgoals = 5000000
% 0.80/1.18 totalproof = 1
% 0.80/1.18
% 0.80/1.18 Symbols occurring in the translation:
% 0.88/1.31
% 0.88/1.31 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.88/1.31 . [1, 2] (w:1, o:42, a:1, s:1, b:0),
% 0.88/1.31 ! [4, 1] (w:0, o:30, a:1, s:1, b:0),
% 0.88/1.31 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.88/1.31 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.88/1.31 edge [36, 1] (w:1, o:35, a:1, s:1, b:0),
% 0.88/1.31 head_of [37, 1] (w:1, o:36, a:1, s:1, b:0),
% 0.88/1.31 tail_of [38, 1] (w:1, o:39, a:1, s:1, b:0),
% 0.88/1.31 vertex [39, 1] (w:1, o:40, a:1, s:1, b:0),
% 0.88/1.31 complete [40, 0] (w:1, o:7, a:1, s:1, b:0),
% 0.88/1.31 empty [44, 0] (w:1, o:11, a:1, s:1, b:0),
% 0.88/1.31 path_cons [45, 2] (w:1, o:69, a:1, s:1, b:0),
% 0.88/1.31 path [47, 3] (w:1, o:79, a:1, s:1, b:0),
% 0.88/1.31 on_path [48, 2] (w:1, o:68, a:1, s:1, b:0),
% 0.88/1.31 in_path [49, 2] (w:1, o:70, a:1, s:1, b:0),
% 0.88/1.31 sequential [53, 2] (w:1, o:71, a:1, s:1, b:0),
% 0.88/1.31 precedes [55, 3] (w:1, o:80, a:1, s:1, b:0),
% 0.88/1.31 shortest_path [57, 3] (w:1, o:81, a:1, s:1, b:0),
% 0.88/1.31 length_of [58, 1] (w:1, o:41, a:1, s:1, b:0),
% 0.88/1.31 less_or_equal [59, 2] (w:1, o:72, a:1, s:1, b:0),
% 0.88/1.31 triangle [60, 3] (w:1, o:88, a:1, s:1, b:0),
% 0.88/1.31 edges [61, 0] (w:1, o:18, a:1, s:1, b:0),
% 0.88/1.31 number_of_in [62, 2] (w:1, o:67, a:1, s:1, b:0),
% 0.88/1.31 sequential_pairs [63, 0] (w:1, o:19, a:1, s:1, b:0),
% 0.88/1.31 n1 [64, 0] (w:1, o:20, a:1, s:1, b:0),
% 0.88/1.31 minus [65, 2] (w:1, o:66, a:1, s:1, b:0),
% 0.88/1.31 triangles [66, 0] (w:1, o:26, a:1, s:1, b:0),
% 0.88/1.31 graph [69, 0] (w:1, o:29, a:1, s:1, b:0),
% 0.88/1.31 alpha1 [70, 3] (w:1, o:89, a:1, s:1, b:1),
% 0.88/1.31 alpha2 [71, 3] (w:1, o:98, a:1, s:1, b:1),
% 0.88/1.31 alpha3 [72, 2] (w:1, o:73, a:1, s:1, b:1),
% 0.88/1.31 alpha4 [73, 3] (w:1, o:99, a:1, s:1, b:1),
% 0.88/1.31 alpha5 [74, 3] (w:1, o:100, a:1, s:1, b:1),
% 0.88/1.31 alpha6 [75, 2] (w:1, o:74, a:1, s:1, b:1),
% 0.88/1.31 alpha7 [76, 3] (w:1, o:101, a:1, s:1, b:1),
% 0.88/1.31 alpha8 [77, 3] (w:1, o:102, a:1, s:1, b:1),
% 0.88/1.31 alpha9 [78, 3] (w:1, o:103, a:1, s:1, b:1),
% 0.88/1.31 alpha10 [79, 3] (w:1, o:90, a:1, s:1, b:1),
% 0.88/1.31 alpha11 [80, 3] (w:1, o:91, a:1, s:1, b:1),
% 0.88/1.31 alpha12 [81, 2] (w:1, o:75, a:1, s:1, b:1),
% 0.88/1.31 alpha13 [82, 3] (w:1, o:92, a:1, s:1, b:1),
% 0.88/1.31 alpha14 [83, 3] (w:1, o:93, a:1, s:1, b:1),
% 0.88/1.31 alpha15 [84, 3] (w:1, o:94, a:1, s:1, b:1),
% 0.88/1.31 alpha16 [85, 2] (w:1, o:76, a:1, s:1, b:1),
% 0.88/1.31 alpha17 [86, 3] (w:1, o:95, a:1, s:1, b:1),
% 0.88/1.31 alpha18 [87, 3] (w:1, o:96, a:1, s:1, b:1),
% 0.88/1.31 alpha19 [88, 3] (w:1, o:97, a:1, s:1, b:1),
% 0.88/1.31 alpha20 [89, 3] (w:1, o:104, a:1, s:1, b:1),
% 0.88/1.31 alpha21 [90, 3] (w:1, o:105, a:1, s:1, b:1),
% 0.88/1.31 skol1 [91, 2] (w:1, o:77, a:1, s:1, b:1),
% 0.88/1.31 skol2 [92, 3] (w:1, o:82, a:1, s:1, b:1),
% 0.88/1.31 skol3 [93, 3] (w:1, o:83, a:1, s:1, b:1),
% 0.88/1.31 skol4 [94, 3] (w:1, o:84, a:1, s:1, b:1),
% 0.88/1.31 skol5 [95, 2] (w:1, o:78, a:1, s:1, b:1),
% 0.88/1.31 skol6 [96, 3] (w:1, o:85, a:1, s:1, b:1),
% 0.88/1.31 skol7 [97, 3] (w:1, o:86, a:1, s:1, b:1),
% 0.88/1.31 skol8 [98, 3] (w:1, o:87, a:1, s:1, b:1),
% 0.88/1.31 skol9 [99, 1] (w:1, o:37, a:1, s:1, b:1),
% 0.88/1.31 skol10 [100, 0] (w:1, o:21, a:1, s:1, b:1),
% 0.88/1.31 skol11 [101, 1] (w:1, o:38, a:1, s:1, b:1),
% 0.88/1.31 skol12 [102, 0] (w:1, o:22, a:1, s:1, b:1),
% 0.88/1.31 skol13 [103, 0] (w:1, o:23, a:1, s:1, b:1),
% 0.88/1.31 skol14 [104, 0] (w:1, o:24, a:1, s:1, b:1),
% 0.88/1.31 skol15 [105, 0] (w:1, o:25, a:1, s:1, b:1).
% 0.88/1.31
% 0.88/1.31
% 0.88/1.31 Starting Search:
% 0.88/1.31
% 0.88/1.31 *** allocated 15000 integers for clauses
% 0.88/1.31 *** allocated 22500 integers for clauses
% 0.88/1.31 *** allocated 33750 integers for clauses
% 0.88/1.31 *** allocated 15000 integers for termspace/termends
% 0.88/1.31 *** allocated 50625 integers for clauses
% 0.88/1.31 *** allocated 22500 integers for termspace/termends
% 0.88/1.31 Resimplifying inuse:
% 0.88/1.31 Done
% 0.88/1.31
% 0.88/1.31 *** allocated 33750 integers for termspace/termends
% 0.88/1.31 *** allocated 75937 integers for clauses
% 0.88/1.31 *** allocated 50625 integers for termspace/termends
% 0.88/1.31 *** allocated 113905 integers for clauses
% 0.88/1.31
% 0.88/1.31 Intermediate Status:
% 0.88/1.31 Generated: 4179
% 0.88/1.31 Kept: 2022
% 0.88/1.31 Inuse: 165
% 0.88/1.31 Deleted: 7
% 0.88/1.31 Deletedinuse: 1
% 0.88/1.31
% 0.88/1.31 Resimplifying inuse:
% 0.88/1.31 Done
% 0.88/1.31
% 0.88/1.31 *** allocated 75937 integers for termspace/termends
% 0.88/1.31 *** allocated 170857 integers for clauses
% 0.88/1.31 Resimplifying inuse:
% 0.88/1.31 Done
% 0.88/1.31
% 0.88/1.31
% 0.88/1.31 Intermediate Status:
% 0.88/1.31 Generated: 8328
% 0.88/1.31 Kept: 4045
% 0.88/1.31 Inuse: 302
% 0.88/1.31 Deleted: 8
% 0.88/1.31 Deletedinuse: 2
% 0.88/1.31
% 0.88/1.31 Resimplifying inuse:
% 0.88/1.31 Done
% 0.88/1.31
% 0.88/1.31 *** allocated 256285 integers for clauses
% 0.88/1.31 *** allocated 113905 integers for termspace/termends
% 0.88/1.31 Resimplifying inuse:
% 0.88/1.31 Done
% 0.88/1.31
% 0.88/1.31
% 0.88/1.31 Intermediate Status:
% 0.88/1.31 Generated: 14836
% 0.88/1.31 Kept: 6080
% 0.88/1.31 Inuse: 469
% 0.88/1.31 Deleted: 15
% 0.88/1.31 Deletedinuse: 7
% 0.88/1.31
% 0.88/1.31 Resimplifying inuse:
% 0.88/1.31 Done
% 0.88/1.31
% 0.88/1.31 *** allocated 384427 integers for clauses
% 0.88/1.31 *** allocated 170857 integers for termspace/termends
% 0.88/1.31 Resimplifying inuse:
% 0.88/1.31 Done
% 0.88/1.31
% 0.88/1.31
% 0.88/1.31 Bliksems!, er is een bewijs:
% 0.88/1.31 % SZS status Theorem
% 0.88/1.31 % SZS output start Refutation
% 0.88/1.31
% 0.88/1.31 (18) {G0,W7,D2,L2,V3,M2} I { ! path( X, Y, Z ), alpha12( X, Y ) }.
% 0.88/1.31 (35) {G0,W5,D2,L2,V2,M2} I { ! alpha12( X, Y ), vertex( X ) }.
% 0.88/1.31 (36) {G0,W5,D2,L2,V2,M2} I { ! alpha12( X, Y ), vertex( Y ) }.
% 0.88/1.31 (41) {G0,W9,D2,L3,V4,M3} I { ! path( Z, T, X ), ! on_path( Y, X ), edge( Y
% 0.88/1.31 ) }.
% 0.88/1.31 (58) {G0,W12,D2,L3,V5,M3} I { ! path( Y, Z, X ), ! precedes( T, U, X ),
% 0.88/1.31 alpha13( X, T, U ) }.
% 0.88/1.31 (68) {G0,W7,D2,L2,V3,M2} I { ! alpha13( X, Y, Z ), on_path( Y, X ) }.
% 0.88/1.31 (69) {G0,W7,D2,L2,V3,M2} I { ! alpha13( X, Y, Z ), on_path( Z, X ) }.
% 0.88/1.31 (71) {G0,W8,D2,L2,V3,M2} I { ! shortest_path( X, Y, Z ), path( X, Y, Z )
% 0.88/1.31 }.
% 0.88/1.31 (72) {G0,W8,D2,L2,V3,M2} I { ! shortest_path( X, Y, Z ), alpha4( X, Y, Z )
% 0.88/1.31 }.
% 0.88/1.31 (74) {G0,W7,D2,L2,V3,M2} I { ! alpha4( X, Y, Z ), ! X = Y }.
% 0.88/1.31 (80) {G0,W18,D3,L4,V6,M4} I { ! shortest_path( T, U, Z ), ! precedes( X, Y
% 0.88/1.31 , Z ), ! tail_of( W ) = tail_of( X ), ! head_of( W ) = head_of( Y ) }.
% 0.88/1.31 (106) {G0,W4,D2,L1,V0,M1} I { shortest_path( skol10, skol12, skol15 ) }.
% 0.88/1.31 (107) {G0,W4,D2,L1,V0,M1} I { precedes( skol13, skol14, skol15 ) }.
% 0.88/1.31 (108) {G0,W18,D2,L7,V0,M7} I { ! vertex( skol10 ), ! vertex( skol12 ),
% 0.88/1.31 skol12 ==> skol10, ! edge( skol13 ), ! edge( skol14 ), skol14 ==> skol13
% 0.88/1.31 , ! path( skol10, skol12, skol15 ) }.
% 0.88/1.31 (142) {G1,W13,D3,L3,V5,M3} Q(80) { ! shortest_path( X, Y, Z ), ! precedes(
% 0.88/1.31 T, U, Z ), ! tail_of( U ) = tail_of( T ) }.
% 0.88/1.31 (143) {G2,W8,D2,L2,V4,M2} Q(142) { ! shortest_path( X, Y, Z ), ! precedes(
% 0.88/1.31 T, T, Z ) }.
% 0.88/1.31 (898) {G1,W6,D2,L2,V3,M2} R(18,35) { ! path( X, Y, Z ), vertex( X ) }.
% 0.88/1.31 (899) {G1,W6,D2,L2,V3,M2} R(18,36) { ! path( X, Y, Z ), vertex( Y ) }.
% 0.88/1.31 (2203) {G3,W4,D2,L1,V1,M1} R(143,106) { ! precedes( X, X, skol15 ) }.
% 0.88/1.31 (3438) {G1,W4,D2,L1,V0,M1} R(71,106) { path( skol10, skol12, skol15 ) }.
% 0.88/1.31 (3448) {G2,W5,D2,L2,V1,M2} R(3438,41) { ! on_path( X, skol15 ), edge( X )
% 0.88/1.31 }.
% 0.88/1.31 (3453) {G2,W2,D2,L1,V0,M1} R(3438,899) { vertex( skol12 ) }.
% 0.88/1.31 (3454) {G2,W2,D2,L1,V0,M1} R(3438,898) { vertex( skol10 ) }.
% 0.88/1.31 (3519) {G1,W4,D2,L1,V0,M1} R(72,106) { alpha4( skol10, skol12, skol15 ) }.
% 0.88/1.31 (3521) {G2,W3,D2,L1,V0,M1} R(3519,74) { ! skol12 ==> skol10 }.
% 0.88/1.31 (4000) {G3,W6,D2,L2,V2,M2} R(3448,68) { edge( X ), ! alpha13( skol15, X, Y
% 0.88/1.31 ) }.
% 0.88/1.31 (4001) {G3,W6,D2,L2,V2,M2} R(3448,69) { edge( X ), ! alpha13( skol15, Y, X
% 0.88/1.31 ) }.
% 0.88/1.31 (5183) {G3,W7,D2,L3,V0,M3} S(108);r(3454);r(3453);r(3521);r(3438) { ! edge
% 0.88/1.31 ( skol13 ), ! edge( skol14 ), skol14 ==> skol13 }.
% 0.88/1.31 (5289) {G4,W4,D2,L2,V0,M2} P(5183,107);r(2203) { ! edge( skol13 ), ! edge(
% 0.88/1.31 skol14 ) }.
% 0.88/1.31 (5295) {G5,W6,D2,L2,V1,M2} R(5289,4001) { ! edge( skol13 ), ! alpha13(
% 0.88/1.31 skol15, X, skol14 ) }.
% 0.88/1.31 (7952) {G6,W8,D2,L2,V2,M2} R(5295,4000) { ! alpha13( skol15, X, skol14 ), !
% 0.88/1.31 alpha13( skol15, skol13, Y ) }.
% 0.88/1.31 (7968) {G7,W4,D2,L1,V0,M1} F(7952) { ! alpha13( skol15, skol13, skol14 )
% 0.88/1.31 }.
% 0.88/1.31 (7969) {G8,W4,D2,L1,V2,M1} R(7968,58);r(107) { ! path( X, Y, skol15 ) }.
% 0.88/1.31 (7972) {G9,W0,D0,L0,V0,M0} R(7969,3438) { }.
% 0.88/1.31
% 0.88/1.31
% 0.88/1.31 % SZS output end Refutation
% 0.88/1.31 found a proof!
% 0.88/1.31
% 0.88/1.31
% 0.88/1.31 Unprocessed initial clauses:
% 0.88/1.31
% 0.88/1.31 (7974) {G0,W7,D3,L2,V1,M2} { ! edge( X ), ! head_of( X ) = tail_of( X )
% 0.88/1.31 }.
% 0.88/1.31 (7975) {G0,W5,D3,L2,V1,M2} { ! edge( X ), vertex( head_of( X ) ) }.
% 0.88/1.31 (7976) {G0,W5,D3,L2,V1,M2} { ! edge( X ), vertex( tail_of( X ) ) }.
% 0.88/1.31 (7977) {G0,W12,D3,L5,V4,M5} { ! complete, ! vertex( X ), ! vertex( Y ), X
% 0.88/1.31 = Y, edge( skol1( Z, T ) ) }.
% 0.88/1.31 (7978) {G0,W20,D3,L6,V2,M6} { ! complete, ! vertex( X ), ! vertex( Y ), X
% 0.88/1.31 = Y, alpha11( X, Y, skol1( X, Y ) ), alpha15( X, Y, skol1( X, Y ) ) }.
% 0.88/1.31 (7979) {G0,W8,D3,L2,V3,M2} { ! alpha15( X, Y, Z ), Y = head_of( Z ) }.
% 0.88/1.31 (7980) {G0,W8,D3,L2,V3,M2} { ! alpha15( X, Y, Z ), X = tail_of( Z ) }.
% 0.88/1.31 (7981) {G0,W8,D2,L2,V3,M2} { ! alpha15( X, Y, Z ), ! alpha1( X, Y, Z ) }.
% 0.88/1.31 (7982) {G0,W16,D3,L4,V3,M4} { ! Y = head_of( Z ), ! X = tail_of( Z ),
% 0.88/1.31 alpha1( X, Y, Z ), alpha15( X, Y, Z ) }.
% 0.88/1.31 (7983) {G0,W8,D2,L2,V3,M2} { ! alpha11( X, Y, Z ), alpha1( X, Y, Z ) }.
% 0.88/1.31 (7984) {G0,W12,D3,L3,V3,M3} { ! alpha11( X, Y, Z ), ! Y = head_of( Z ), !
% 0.88/1.31 X = tail_of( Z ) }.
% 0.88/1.31 (7985) {G0,W12,D3,L3,V3,M3} { ! alpha1( X, Y, Z ), Y = head_of( Z ),
% 0.88/1.31 alpha11( X, Y, Z ) }.
% 0.88/1.31 (7986) {G0,W12,D3,L3,V3,M3} { ! alpha1( X, Y, Z ), X = tail_of( Z ),
% 0.88/1.31 alpha11( X, Y, Z ) }.
% 0.88/1.31 (7987) {G0,W8,D3,L2,V3,M2} { ! alpha1( X, Y, Z ), X = head_of( Z ) }.
% 0.88/1.31 (7988) {G0,W8,D3,L2,V3,M2} { ! alpha1( X, Y, Z ), Y = tail_of( Z ) }.
% 0.88/1.31 (7989) {G0,W12,D3,L3,V3,M3} { ! X = head_of( Z ), ! Y = tail_of( Z ),
% 0.88/1.31 alpha1( X, Y, Z ) }.
% 0.88/1.31 (7990) {G0,W23,D3,L7,V4,M7} { ! vertex( X ), ! vertex( Y ), ! edge( T ), !
% 0.88/1.31 X = tail_of( T ), ! Y = head_of( T ), ! Z = path_cons( T, empty ), path
% 0.88/1.31 ( X, Y, Z ) }.
% 0.88/1.31 (7991) {G0,W24,D3,L7,V5,M7} { ! vertex( X ), ! vertex( Y ), ! edge( T ), !
% 0.88/1.31 X = tail_of( T ), ! path( head_of( T ), Y, U ), ! Z = path_cons( T, U )
% 0.88/1.31 , path( X, Y, Z ) }.
% 0.88/1.31 (7992) {G0,W7,D2,L2,V3,M2} { ! path( X, Y, Z ), alpha12( X, Y ) }.
% 0.88/1.31 (7993) {G0,W10,D3,L2,V5,M2} { ! path( X, Y, Z ), alpha16( X, skol2( X, T,
% 0.88/1.31 U ) ) }.
% 0.88/1.31 (7994) {G0,W11,D3,L2,V3,M2} { ! path( X, Y, Z ), alpha20( Y, Z, skol2( X,
% 0.88/1.31 Y, Z ) ) }.
% 0.88/1.31 (7995) {G0,W12,D2,L3,V3,M3} { ! alpha20( X, Y, Z ), alpha18( X, Y, Z ),
% 0.88/1.31 alpha21( X, Y, Z ) }.
% 0.88/1.31 (7996) {G0,W8,D2,L2,V3,M2} { ! alpha18( X, Y, Z ), alpha20( X, Y, Z ) }.
% 0.88/1.31 (7997) {G0,W8,D2,L2,V3,M2} { ! alpha21( X, Y, Z ), alpha20( X, Y, Z ) }.
% 0.88/1.31 (7998) {G0,W12,D4,L2,V4,M2} { ! alpha21( X, Y, Z ), Y = path_cons( Z,
% 0.88/1.31 skol3( T, Y, Z ) ) }.
% 0.88/1.31 (7999) {G0,W12,D3,L2,V3,M2} { ! alpha21( X, Y, Z ), path( head_of( Z ), X
% 0.88/1.31 , skol3( X, Y, Z ) ) }.
% 0.88/1.31 (8000) {G0,W8,D2,L2,V3,M2} { ! alpha21( X, Y, Z ), ! alpha2( X, Y, Z ) }.
% 0.88/1.31 (8001) {G0,W18,D3,L4,V4,M4} { ! path( head_of( Z ), X, T ), ! Y =
% 0.88/1.31 path_cons( Z, T ), alpha2( X, Y, Z ), alpha21( X, Y, Z ) }.
% 0.88/1.31 (8002) {G0,W8,D2,L2,V3,M2} { ! alpha18( X, Y, Z ), alpha2( X, Y, Z ) }.
% 0.88/1.31 (8003) {G0,W14,D3,L3,V4,M3} { ! alpha18( X, Y, Z ), ! path( head_of( Z ),
% 0.88/1.31 X, T ), ! Y = path_cons( Z, T ) }.
% 0.88/1.31 (8004) {G0,W16,D4,L3,V4,M3} { ! alpha2( X, Y, Z ), Y = path_cons( Z, skol4
% 0.88/1.31 ( T, Y, Z ) ), alpha18( X, Y, Z ) }.
% 0.88/1.31 (8005) {G0,W16,D3,L3,V3,M3} { ! alpha2( X, Y, Z ), path( head_of( Z ), X,
% 0.88/1.31 skol4( X, Y, Z ) ), alpha18( X, Y, Z ) }.
% 0.88/1.31 (8006) {G0,W5,D2,L2,V2,M2} { ! alpha16( X, Y ), edge( Y ) }.
% 0.88/1.31 (8007) {G0,W7,D3,L2,V2,M2} { ! alpha16( X, Y ), X = tail_of( Y ) }.
% 0.88/1.31 (8008) {G0,W9,D3,L3,V2,M3} { ! edge( Y ), ! X = tail_of( Y ), alpha16( X,
% 0.88/1.31 Y ) }.
% 0.88/1.31 (8009) {G0,W5,D2,L2,V2,M2} { ! alpha12( X, Y ), vertex( X ) }.
% 0.88/1.31 (8010) {G0,W5,D2,L2,V2,M2} { ! alpha12( X, Y ), vertex( Y ) }.
% 0.88/1.31 (8011) {G0,W7,D2,L3,V2,M3} { ! vertex( X ), ! vertex( Y ), alpha12( X, Y )
% 0.88/1.31 }.
% 0.88/1.31 (8012) {G0,W8,D3,L2,V3,M2} { ! alpha2( X, Y, Z ), X = head_of( Z ) }.
% 0.88/1.31 (8013) {G0,W9,D3,L2,V3,M2} { ! alpha2( X, Y, Z ), Y = path_cons( Z, empty
% 0.88/1.31 ) }.
% 0.88/1.31 (8014) {G0,W13,D3,L3,V3,M3} { ! X = head_of( Z ), ! Y = path_cons( Z,
% 0.88/1.31 empty ), alpha2( X, Y, Z ) }.
% 0.88/1.31 (8015) {G0,W9,D2,L3,V4,M3} { ! path( Z, T, X ), ! on_path( Y, X ), edge( Y
% 0.88/1.31 ) }.
% 0.88/1.31 (8016) {G0,W11,D3,L3,V4,M3} { ! path( Z, T, X ), ! on_path( Y, X ),
% 0.88/1.31 in_path( head_of( Y ), X ) }.
% 0.88/1.31 (8017) {G0,W11,D3,L3,V4,M3} { ! path( Z, T, X ), ! on_path( Y, X ),
% 0.88/1.31 in_path( tail_of( Y ), X ) }.
% 0.88/1.31 (8018) {G0,W9,D2,L3,V4,M3} { ! path( Z, T, X ), ! in_path( Y, X ), vertex
% 0.88/1.31 ( Y ) }.
% 0.88/1.31 (8019) {G0,W19,D4,L4,V5,M4} { ! path( Z, T, X ), ! in_path( Y, X ), Y =
% 0.88/1.31 head_of( skol5( U, Y ) ), Y = tail_of( skol5( U, Y ) ) }.
% 0.88/1.31 (8020) {G0,W12,D3,L3,V4,M3} { ! path( Z, T, X ), ! in_path( Y, X ),
% 0.88/1.31 on_path( skol5( X, Y ), X ) }.
% 0.88/1.31 (8021) {G0,W5,D2,L2,V2,M2} { ! sequential( X, Y ), edge( X ) }.
% 0.88/1.31 (8022) {G0,W6,D2,L2,V2,M2} { ! sequential( X, Y ), alpha3( X, Y ) }.
% 0.88/1.31 (8023) {G0,W8,D2,L3,V2,M3} { ! edge( X ), ! alpha3( X, Y ), sequential( X
% 0.88/1.31 , Y ) }.
% 0.88/1.31 (8024) {G0,W5,D2,L2,V2,M2} { ! alpha3( X, Y ), edge( Y ) }.
% 0.88/1.31 (8025) {G0,W6,D2,L2,V2,M2} { ! alpha3( X, Y ), alpha6( X, Y ) }.
% 0.88/1.31 (8026) {G0,W8,D2,L3,V2,M3} { ! edge( Y ), ! alpha6( X, Y ), alpha3( X, Y )
% 0.88/1.31 }.
% 0.88/1.31 (8027) {G0,W6,D2,L2,V2,M2} { ! alpha6( X, Y ), ! X = Y }.
% 0.88/1.31 (8028) {G0,W8,D3,L2,V2,M2} { ! alpha6( X, Y ), head_of( X ) = tail_of( Y )
% 0.88/1.31 }.
% 0.88/1.31 (8029) {G0,W11,D3,L3,V2,M3} { X = Y, ! head_of( X ) = tail_of( Y ), alpha6
% 0.88/1.31 ( X, Y ) }.
% 0.88/1.31 (8030) {G0,W17,D2,L5,V5,M5} { ! path( Y, Z, X ), ! on_path( T, X ), !
% 0.88/1.31 on_path( U, X ), ! sequential( T, U ), precedes( T, U, X ) }.
% 0.88/1.31 (8031) {G0,W21,D2,L6,V6,M6} { ! path( Y, Z, X ), ! on_path( T, X ), !
% 0.88/1.31 on_path( U, X ), ! sequential( T, W ), ! precedes( W, U, X ), precedes( T
% 0.88/1.31 , U, X ) }.
% 0.88/1.31 (8032) {G0,W12,D2,L3,V5,M3} { ! path( Y, Z, X ), ! precedes( T, U, X ),
% 0.88/1.31 alpha13( X, T, U ) }.
% 0.88/1.31 (8033) {G0,W16,D2,L4,V5,M4} { ! path( Y, Z, X ), ! precedes( T, U, X ),
% 0.88/1.31 alpha17( X, T, U ), alpha19( X, T, U ) }.
% 0.88/1.31 (8034) {G0,W10,D3,L2,V5,M2} { ! alpha19( X, Y, Z ), sequential( Y, skol6(
% 0.88/1.31 T, Y, U ) ) }.
% 0.88/1.31 (8035) {G0,W11,D3,L2,V3,M2} { ! alpha19( X, Y, Z ), precedes( skol6( X, Y
% 0.88/1.31 , Z ), Z, X ) }.
% 0.88/1.31 (8036) {G0,W7,D2,L2,V3,M2} { ! alpha19( X, Y, Z ), ! sequential( Y, Z )
% 0.88/1.31 }.
% 0.88/1.31 (8037) {G0,W14,D2,L4,V4,M4} { ! sequential( Y, T ), ! precedes( T, Z, X )
% 0.88/1.31 , sequential( Y, Z ), alpha19( X, Y, Z ) }.
% 0.88/1.31 (8038) {G0,W7,D2,L2,V3,M2} { ! alpha17( X, Y, Z ), sequential( Y, Z ) }.
% 0.88/1.31 (8039) {G0,W11,D2,L3,V4,M3} { ! alpha17( X, Y, Z ), ! sequential( Y, T ),
% 0.88/1.31 ! precedes( T, Z, X ) }.
% 0.88/1.31 (8040) {G0,W13,D3,L3,V5,M3} { ! sequential( Y, Z ), sequential( Y, skol7(
% 0.88/1.31 T, Y, U ) ), alpha17( X, Y, Z ) }.
% 0.88/1.31 (8041) {G0,W14,D3,L3,V3,M3} { ! sequential( Y, Z ), precedes( skol7( X, Y
% 0.88/1.31 , Z ), Z, X ), alpha17( X, Y, Z ) }.
% 0.88/1.31 (8042) {G0,W7,D2,L2,V3,M2} { ! alpha13( X, Y, Z ), on_path( Y, X ) }.
% 0.88/1.31 (8043) {G0,W7,D2,L2,V3,M2} { ! alpha13( X, Y, Z ), on_path( Z, X ) }.
% 0.88/1.31 (8044) {G0,W10,D2,L3,V3,M3} { ! on_path( Y, X ), ! on_path( Z, X ),
% 0.88/1.31 alpha13( X, Y, Z ) }.
% 0.88/1.31 (8045) {G0,W8,D2,L2,V3,M2} { ! shortest_path( X, Y, Z ), path( X, Y, Z )
% 0.88/1.31 }.
% 0.88/1.31 (8046) {G0,W8,D2,L2,V3,M2} { ! shortest_path( X, Y, Z ), alpha4( X, Y, Z )
% 0.88/1.31 }.
% 0.88/1.31 (8047) {G0,W12,D2,L3,V3,M3} { ! path( X, Y, Z ), ! alpha4( X, Y, Z ),
% 0.88/1.31 shortest_path( X, Y, Z ) }.
% 0.88/1.31 (8048) {G0,W7,D2,L2,V3,M2} { ! alpha4( X, Y, Z ), ! X = Y }.
% 0.88/1.31 (8049) {G0,W8,D2,L2,V3,M2} { ! alpha4( X, Y, Z ), alpha7( X, Y, Z ) }.
% 0.88/1.31 (8050) {G0,W11,D2,L3,V3,M3} { X = Y, ! alpha7( X, Y, Z ), alpha4( X, Y, Z
% 0.88/1.31 ) }.
% 0.88/1.31 (8051) {G0,W13,D3,L3,V4,M3} { ! alpha7( X, Y, Z ), ! path( X, Y, T ),
% 0.88/1.31 less_or_equal( length_of( Z ), length_of( T ) ) }.
% 0.88/1.31 (8052) {G0,W12,D4,L2,V5,M2} { ! less_or_equal( length_of( Z ), length_of(
% 0.88/1.31 skol8( T, U, Z ) ) ), alpha7( X, Y, Z ) }.
% 0.88/1.31 (8053) {G0,W11,D3,L2,V3,M2} { path( X, Y, skol8( X, Y, Z ) ), alpha7( X, Y
% 0.88/1.31 , Z ) }.
% 0.88/1.31 (8054) {G0,W18,D3,L4,V6,M4} { ! shortest_path( T, U, Z ), ! precedes( X, Y
% 0.88/1.31 , Z ), ! tail_of( W ) = tail_of( X ), ! head_of( W ) = head_of( Y ) }.
% 0.88/1.31 (8055) {G0,W12,D2,L3,V5,M3} { ! shortest_path( T, U, Z ), ! precedes( X, Y
% 0.88/1.31 , Z ), ! precedes( Y, X, Z ) }.
% 0.88/1.31 (8056) {G0,W6,D2,L2,V3,M2} { ! triangle( X, Y, Z ), edge( X ) }.
% 0.88/1.31 (8057) {G0,W8,D2,L2,V3,M2} { ! triangle( X, Y, Z ), alpha5( X, Y, Z ) }.
% 0.88/1.31 (8058) {G0,W10,D2,L3,V3,M3} { ! edge( X ), ! alpha5( X, Y, Z ), triangle(
% 0.88/1.31 X, Y, Z ) }.
% 0.88/1.31 (8059) {G0,W6,D2,L2,V3,M2} { ! alpha5( X, Y, Z ), edge( Y ) }.
% 0.88/1.31 (8060) {G0,W8,D2,L2,V3,M2} { ! alpha5( X, Y, Z ), alpha8( X, Y, Z ) }.
% 0.88/1.31 (8061) {G0,W10,D2,L3,V3,M3} { ! edge( Y ), ! alpha8( X, Y, Z ), alpha5( X
% 0.88/1.31 , Y, Z ) }.
% 0.88/1.31 (8062) {G0,W6,D2,L2,V3,M2} { ! alpha8( X, Y, Z ), edge( Z ) }.
% 0.88/1.31 (8063) {G0,W8,D2,L2,V3,M2} { ! alpha8( X, Y, Z ), alpha9( X, Y, Z ) }.
% 0.88/1.31 (8064) {G0,W10,D2,L3,V3,M3} { ! edge( Z ), ! alpha9( X, Y, Z ), alpha8( X
% 0.88/1.31 , Y, Z ) }.
% 0.88/1.31 (8065) {G0,W7,D2,L2,V3,M2} { ! alpha9( X, Y, Z ), sequential( X, Y ) }.
% 0.88/1.31 (8066) {G0,W8,D2,L2,V3,M2} { ! alpha9( X, Y, Z ), alpha10( X, Y, Z ) }.
% 0.88/1.31 (8067) {G0,W11,D2,L3,V3,M3} { ! sequential( X, Y ), ! alpha10( X, Y, Z ),
% 0.88/1.31 alpha9( X, Y, Z ) }.
% 0.88/1.31 (8068) {G0,W7,D2,L2,V3,M2} { ! alpha10( X, Y, Z ), sequential( Y, Z ) }.
% 0.88/1.31 (8069) {G0,W7,D2,L2,V3,M2} { ! alpha10( X, Y, Z ), sequential( Z, X ) }.
% 0.88/1.31 (8070) {G0,W10,D2,L3,V3,M3} { ! sequential( Y, Z ), ! sequential( Z, X ),
% 0.88/1.31 alpha10( X, Y, Z ) }.
% 0.88/1.31 (8071) {G0,W10,D3,L2,V3,M2} { ! path( Y, Z, X ), length_of( X ) =
% 0.88/1.31 number_of_in( edges, X ) }.
% 0.88/1.31 (8072) {G0,W12,D4,L2,V3,M2} { ! path( Y, Z, X ), number_of_in(
% 0.88/1.31 sequential_pairs, X ) = minus( length_of( X ), n1 ) }.
% 0.88/1.31 (8073) {G0,W17,D3,L3,V3,M3} { ! path( Y, Z, X ), alpha14( X, skol9( X ),
% 0.88/1.31 skol11( X ) ), number_of_in( sequential_pairs, X ) = number_of_in(
% 0.88/1.31 triangles, X ) }.
% 0.88/1.31 (8074) {G0,W17,D3,L3,V4,M3} { ! path( Y, Z, X ), ! triangle( skol9( X ),
% 0.88/1.31 skol11( X ), T ), number_of_in( sequential_pairs, X ) = number_of_in(
% 0.88/1.31 triangles, X ) }.
% 0.88/1.31 (8075) {G0,W7,D2,L2,V3,M2} { ! alpha14( X, Y, Z ), on_path( Y, X ) }.
% 0.88/1.31 (8076) {G0,W7,D2,L2,V3,M2} { ! alpha14( X, Y, Z ), on_path( Z, X ) }.
% 0.88/1.31 (8077) {G0,W7,D2,L2,V3,M2} { ! alpha14( X, Y, Z ), sequential( Y, Z ) }.
% 0.88/1.31 (8078) {G0,W13,D2,L4,V3,M4} { ! on_path( Y, X ), ! on_path( Z, X ), !
% 0.88/1.31 sequential( Y, Z ), alpha14( X, Y, Z ) }.
% 0.88/1.31 (8079) {G0,W7,D3,L1,V2,M1} { less_or_equal( number_of_in( X, Y ),
% 0.88/1.31 number_of_in( X, graph ) ) }.
% 0.88/1.31 (8080) {G0,W4,D2,L1,V0,M1} { shortest_path( skol10, skol12, skol15 ) }.
% 0.88/1.31 (8081) {G0,W4,D2,L1,V0,M1} { precedes( skol13, skol14, skol15 ) }.
% 0.88/1.31 (8082) {G0,W18,D2,L7,V0,M7} { ! vertex( skol10 ), ! vertex( skol12 ),
% 0.88/1.31 skol10 = skol12, ! edge( skol13 ), ! edge( skol14 ), skol13 = skol14, !
% 0.88/1.31 path( skol10, skol12, skol15 ) }.
% 0.88/1.31
% 0.88/1.31
% 0.88/1.31 Total Proof:
% 0.88/1.31
% 0.88/1.31 subsumption: (18) {G0,W7,D2,L2,V3,M2} I { ! path( X, Y, Z ), alpha12( X, Y
% 0.88/1.31 ) }.
% 0.88/1.31 parent0: (7992) {G0,W7,D2,L2,V3,M2} { ! path( X, Y, Z ), alpha12( X, Y )
% 0.88/1.31 }.
% 0.88/1.31 substitution0:
% 0.88/1.31 X := X
% 0.88/1.31 Y := Y
% 0.88/1.31 Z := Z
% 0.88/1.31 end
% 0.88/1.31 permutation0:
% 0.88/1.31 0 ==> 0
% 0.88/1.31 1 ==> 1
% 0.88/1.31 end
% 0.88/1.31
% 0.88/1.31 subsumption: (35) {G0,W5,D2,L2,V2,M2} I { ! alpha12( X, Y ), vertex( X )
% 0.88/1.31 }.
% 0.88/1.31 parent0: (8009) {G0,W5,D2,L2,V2,M2} { ! alpha12( X, Y ), vertex( X ) }.
% 0.88/1.31 substitution0:
% 0.88/1.31 X := X
% 0.88/1.31 Y := Y
% 0.88/1.31 end
% 0.88/1.31 permutation0:
% 0.88/1.31 0 ==> 0
% 0.88/1.31 1 ==> 1
% 0.88/1.31 end
% 0.88/1.31
% 0.88/1.31 subsumption: (36) {G0,W5,D2,L2,V2,M2} I { ! alpha12( X, Y ), vertex( Y )
% 0.88/1.31 }.
% 0.88/1.31 parent0: (8010) {G0,W5,D2,L2,V2,M2} { ! alpha12( X, Y ), vertex( Y ) }.
% 0.88/1.31 substitution0:
% 0.88/1.31 X := X
% 0.88/1.31 Y := Y
% 0.88/1.31 end
% 0.88/1.31 permutation0:
% 0.88/1.31 0 ==> 0
% 0.88/1.31 1 ==> 1
% 0.88/1.31 end
% 0.88/1.31
% 0.88/1.31 subsumption: (41) {G0,W9,D2,L3,V4,M3} I { ! path( Z, T, X ), ! on_path( Y,
% 0.88/1.31 X ), edge( Y ) }.
% 0.88/1.31 parent0: (8015) {G0,W9,D2,L3,V4,M3} { ! path( Z, T, X ), ! on_path( Y, X )
% 0.88/1.31 , edge( Y ) }.
% 0.88/1.31 substitution0:
% 0.88/1.31 X := X
% 0.88/1.31 Y := Y
% 0.88/1.31 Z := Z
% 0.88/1.31 T := T
% 0.88/1.31 end
% 0.88/1.31 permutation0:
% 0.88/1.31 0 ==> 0
% 0.88/1.31 1 ==> 1
% 0.88/1.31 2 ==> 2
% 0.88/1.31 end
% 0.88/1.31
% 0.88/1.31 subsumption: (58) {G0,W12,D2,L3,V5,M3} I { ! path( Y, Z, X ), ! precedes( T
% 0.88/1.31 , U, X ), alpha13( X, T, U ) }.
% 0.88/1.31 parent0: (8032) {G0,W12,D2,L3,V5,M3} { ! path( Y, Z, X ), ! precedes( T, U
% 0.88/1.31 , X ), alpha13( X, T, U ) }.
% 0.88/1.31 substitution0:
% 0.88/1.31 X := X
% 0.88/1.31 Y := Y
% 0.88/1.31 Z := Z
% 0.88/1.31 T := T
% 0.88/1.31 U := U
% 0.88/1.31 end
% 0.88/1.31 permutation0:
% 0.88/1.31 0 ==> 0
% 0.88/1.31 1 ==> 1
% 0.88/1.31 2 ==> 2
% 0.88/1.31 end
% 0.88/1.31
% 0.88/1.31 subsumption: (68) {G0,W7,D2,L2,V3,M2} I { ! alpha13( X, Y, Z ), on_path( Y
% 0.88/1.31 , X ) }.
% 0.88/1.31 parent0: (8042) {G0,W7,D2,L2,V3,M2} { ! alpha13( X, Y, Z ), on_path( Y, X
% 0.88/1.31 ) }.
% 0.88/1.31 substitution0:
% 0.88/1.31 X := X
% 0.88/1.31 Y := Y
% 0.88/1.31 Z := Z
% 0.88/1.31 end
% 0.88/1.31 permutation0:
% 0.88/1.31 0 ==> 0
% 0.88/1.31 1 ==> 1
% 0.88/1.31 end
% 0.88/1.31
% 0.88/1.31 subsumption: (69) {G0,W7,D2,L2,V3,M2} I { ! alpha13( X, Y, Z ), on_path( Z
% 0.88/1.31 , X ) }.
% 0.88/1.31 parent0: (8043) {G0,W7,D2,L2,V3,M2} { ! alpha13( X, Y, Z ), on_path( Z, X
% 0.88/1.31 ) }.
% 0.88/1.31 substitution0:
% 0.88/1.31 X := X
% 0.88/1.31 Y := Y
% 0.88/1.31 Z := Z
% 0.88/1.31 end
% 0.88/1.31 permutation0:
% 0.88/1.31 0 ==> 0
% 0.88/1.31 1 ==> 1
% 0.88/1.31 end
% 0.88/1.31
% 0.88/1.31 subsumption: (71) {G0,W8,D2,L2,V3,M2} I { ! shortest_path( X, Y, Z ), path
% 0.88/1.31 ( X, Y, Z ) }.
% 0.88/1.31 parent0: (8045) {G0,W8,D2,L2,V3,M2} { ! shortest_path( X, Y, Z ), path( X
% 0.88/1.31 , Y, Z ) }.
% 0.88/1.31 substitution0:
% 0.88/1.31 X := X
% 0.88/1.31 Y := Y
% 0.88/1.31 Z := Z
% 0.88/1.31 end
% 0.88/1.31 permutation0:
% 0.88/1.31 0 ==> 0
% 0.88/1.31 1 ==> 1
% 0.88/1.31 end
% 0.88/1.31
% 0.88/1.31 subsumption: (72) {G0,W8,D2,L2,V3,M2} I { ! shortest_path( X, Y, Z ),
% 0.88/1.31 alpha4( X, Y, Z ) }.
% 0.88/1.31 parent0: (8046) {G0,W8,D2,L2,V3,M2} { ! shortest_path( X, Y, Z ), alpha4(
% 0.88/1.31 X, Y, Z ) }.
% 0.88/1.31 substitution0:
% 0.88/1.31 X := X
% 0.88/1.31 Y := Y
% 0.88/1.31 Z := Z
% 0.88/1.31 end
% 0.88/1.31 permutation0:
% 0.88/1.31 0 ==> 0
% 0.88/1.31 1 ==> 1
% 0.88/1.31 end
% 0.88/1.31
% 0.88/1.31 subsumption: (74) {G0,W7,D2,L2,V3,M2} I { ! alpha4( X, Y, Z ), ! X = Y }.
% 0.88/1.31 parent0: (8048) {G0,W7,D2,L2,V3,M2} { ! alpha4( X, Y, Z ), ! X = Y }.
% 0.88/1.31 substitution0:
% 0.88/1.31 X := X
% 0.88/1.31 Y := Y
% 0.88/1.31 Z := Z
% 0.88/1.31 end
% 0.88/1.31 permutation0:
% 0.88/1.31 0 ==> 0
% 0.88/1.31 1 ==> 1
% 0.88/1.31 end
% 0.88/1.31
% 0.88/1.31 subsumption: (80) {G0,W18,D3,L4,V6,M4} I { ! shortest_path( T, U, Z ), !
% 0.88/1.31 precedes( X, Y, Z ), ! tail_of( W ) = tail_of( X ), ! head_of( W ) =
% 0.88/1.31 head_of( Y ) }.
% 0.88/1.31 parent0: (8054) {G0,W18,D3,L4,V6,M4} { ! shortest_path( T, U, Z ), !
% 0.88/1.32 precedes( X, Y, Z ), ! tail_of( W ) = tail_of( X ), ! head_of( W ) =
% 0.88/1.32 head_of( Y ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := X
% 0.88/1.32 Y := Y
% 0.88/1.32 Z := Z
% 0.88/1.32 T := T
% 0.88/1.32 U := U
% 0.88/1.32 W := W
% 0.88/1.32 end
% 0.88/1.32 permutation0:
% 0.88/1.32 0 ==> 0
% 0.88/1.32 1 ==> 1
% 0.88/1.32 2 ==> 2
% 0.88/1.32 3 ==> 3
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 subsumption: (106) {G0,W4,D2,L1,V0,M1} I { shortest_path( skol10, skol12,
% 0.88/1.32 skol15 ) }.
% 0.88/1.32 parent0: (8080) {G0,W4,D2,L1,V0,M1} { shortest_path( skol10, skol12,
% 0.88/1.32 skol15 ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 end
% 0.88/1.32 permutation0:
% 0.88/1.32 0 ==> 0
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 subsumption: (107) {G0,W4,D2,L1,V0,M1} I { precedes( skol13, skol14, skol15
% 0.88/1.32 ) }.
% 0.88/1.32 parent0: (8081) {G0,W4,D2,L1,V0,M1} { precedes( skol13, skol14, skol15 )
% 0.88/1.32 }.
% 0.88/1.32 substitution0:
% 0.88/1.32 end
% 0.88/1.32 permutation0:
% 0.88/1.32 0 ==> 0
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 eqswap: (9393) {G0,W18,D2,L7,V0,M7} { skol14 = skol13, ! vertex( skol10 )
% 0.88/1.32 , ! vertex( skol12 ), skol10 = skol12, ! edge( skol13 ), ! edge( skol14 )
% 0.88/1.32 , ! path( skol10, skol12, skol15 ) }.
% 0.88/1.32 parent0[5]: (8082) {G0,W18,D2,L7,V0,M7} { ! vertex( skol10 ), ! vertex(
% 0.88/1.32 skol12 ), skol10 = skol12, ! edge( skol13 ), ! edge( skol14 ), skol13 =
% 0.88/1.32 skol14, ! path( skol10, skol12, skol15 ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 eqswap: (9394) {G0,W18,D2,L7,V0,M7} { skol12 = skol10, skol14 = skol13, !
% 0.88/1.32 vertex( skol10 ), ! vertex( skol12 ), ! edge( skol13 ), ! edge( skol14 )
% 0.88/1.32 , ! path( skol10, skol12, skol15 ) }.
% 0.88/1.32 parent0[3]: (9393) {G0,W18,D2,L7,V0,M7} { skol14 = skol13, ! vertex(
% 0.88/1.32 skol10 ), ! vertex( skol12 ), skol10 = skol12, ! edge( skol13 ), ! edge(
% 0.88/1.32 skol14 ), ! path( skol10, skol12, skol15 ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 subsumption: (108) {G0,W18,D2,L7,V0,M7} I { ! vertex( skol10 ), ! vertex(
% 0.88/1.32 skol12 ), skol12 ==> skol10, ! edge( skol13 ), ! edge( skol14 ), skol14
% 0.88/1.32 ==> skol13, ! path( skol10, skol12, skol15 ) }.
% 0.88/1.32 parent0: (9394) {G0,W18,D2,L7,V0,M7} { skol12 = skol10, skol14 = skol13, !
% 0.88/1.32 vertex( skol10 ), ! vertex( skol12 ), ! edge( skol13 ), ! edge( skol14 )
% 0.88/1.32 , ! path( skol10, skol12, skol15 ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 end
% 0.88/1.32 permutation0:
% 0.88/1.32 0 ==> 2
% 0.88/1.32 1 ==> 5
% 0.88/1.32 2 ==> 0
% 0.88/1.32 3 ==> 1
% 0.88/1.32 4 ==> 3
% 0.88/1.32 5 ==> 4
% 0.88/1.32 6 ==> 6
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 eqswap: (9395) {G0,W18,D3,L4,V6,M4} { ! tail_of( Y ) = tail_of( X ), !
% 0.88/1.32 shortest_path( Z, T, U ), ! precedes( Y, W, U ), ! head_of( X ) = head_of
% 0.88/1.32 ( W ) }.
% 0.88/1.32 parent0[2]: (80) {G0,W18,D3,L4,V6,M4} I { ! shortest_path( T, U, Z ), !
% 0.88/1.32 precedes( X, Y, Z ), ! tail_of( W ) = tail_of( X ), ! head_of( W ) =
% 0.88/1.32 head_of( Y ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := Y
% 0.88/1.32 Y := W
% 0.88/1.32 Z := U
% 0.88/1.32 T := Z
% 0.88/1.32 U := T
% 0.88/1.32 W := X
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 eqrefl: (9399) {G0,W13,D3,L3,V5,M3} { ! tail_of( X ) = tail_of( Y ), !
% 0.88/1.32 shortest_path( Z, T, U ), ! precedes( X, Y, U ) }.
% 0.88/1.32 parent0[3]: (9395) {G0,W18,D3,L4,V6,M4} { ! tail_of( Y ) = tail_of( X ), !
% 0.88/1.32 shortest_path( Z, T, U ), ! precedes( Y, W, U ), ! head_of( X ) =
% 0.88/1.32 head_of( W ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := Y
% 0.88/1.32 Y := X
% 0.88/1.32 Z := Z
% 0.88/1.32 T := T
% 0.88/1.32 U := U
% 0.88/1.32 W := Y
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 eqswap: (9400) {G0,W13,D3,L3,V5,M3} { ! tail_of( Y ) = tail_of( X ), !
% 0.88/1.32 shortest_path( Z, T, U ), ! precedes( X, Y, U ) }.
% 0.88/1.32 parent0[0]: (9399) {G0,W13,D3,L3,V5,M3} { ! tail_of( X ) = tail_of( Y ), !
% 0.88/1.32 shortest_path( Z, T, U ), ! precedes( X, Y, U ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := X
% 0.88/1.32 Y := Y
% 0.88/1.32 Z := Z
% 0.88/1.32 T := T
% 0.88/1.32 U := U
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 subsumption: (142) {G1,W13,D3,L3,V5,M3} Q(80) { ! shortest_path( X, Y, Z )
% 0.88/1.32 , ! precedes( T, U, Z ), ! tail_of( U ) = tail_of( T ) }.
% 0.88/1.32 parent0: (9400) {G0,W13,D3,L3,V5,M3} { ! tail_of( Y ) = tail_of( X ), !
% 0.88/1.32 shortest_path( Z, T, U ), ! precedes( X, Y, U ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := T
% 0.88/1.32 Y := U
% 0.88/1.32 Z := X
% 0.88/1.32 T := Y
% 0.88/1.32 U := Z
% 0.88/1.32 end
% 0.88/1.32 permutation0:
% 0.88/1.32 0 ==> 2
% 0.88/1.32 1 ==> 0
% 0.88/1.32 2 ==> 1
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 eqswap: (9402) {G1,W13,D3,L3,V5,M3} { ! tail_of( Y ) = tail_of( X ), !
% 0.88/1.32 shortest_path( Z, T, U ), ! precedes( Y, X, U ) }.
% 0.88/1.32 parent0[2]: (142) {G1,W13,D3,L3,V5,M3} Q(80) { ! shortest_path( X, Y, Z ),
% 0.88/1.32 ! precedes( T, U, Z ), ! tail_of( U ) = tail_of( T ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := Z
% 0.88/1.32 Y := T
% 0.88/1.32 Z := U
% 0.88/1.32 T := Y
% 0.88/1.32 U := X
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 eqrefl: (9403) {G0,W8,D2,L2,V4,M2} { ! shortest_path( Y, Z, T ), !
% 0.88/1.32 precedes( X, X, T ) }.
% 0.88/1.32 parent0[0]: (9402) {G1,W13,D3,L3,V5,M3} { ! tail_of( Y ) = tail_of( X ), !
% 0.88/1.32 shortest_path( Z, T, U ), ! precedes( Y, X, U ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := X
% 0.88/1.32 Y := X
% 0.88/1.32 Z := Y
% 0.88/1.32 T := Z
% 0.88/1.32 U := T
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 subsumption: (143) {G2,W8,D2,L2,V4,M2} Q(142) { ! shortest_path( X, Y, Z )
% 0.88/1.32 , ! precedes( T, T, Z ) }.
% 0.88/1.32 parent0: (9403) {G0,W8,D2,L2,V4,M2} { ! shortest_path( Y, Z, T ), !
% 0.88/1.32 precedes( X, X, T ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := T
% 0.88/1.32 Y := X
% 0.88/1.32 Z := Y
% 0.88/1.32 T := Z
% 0.88/1.32 end
% 0.88/1.32 permutation0:
% 0.88/1.32 0 ==> 0
% 0.88/1.32 1 ==> 1
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 resolution: (9404) {G1,W6,D2,L2,V3,M2} { vertex( X ), ! path( X, Y, Z )
% 0.88/1.32 }.
% 0.88/1.32 parent0[0]: (35) {G0,W5,D2,L2,V2,M2} I { ! alpha12( X, Y ), vertex( X ) }.
% 0.88/1.32 parent1[1]: (18) {G0,W7,D2,L2,V3,M2} I { ! path( X, Y, Z ), alpha12( X, Y )
% 0.88/1.32 }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := X
% 0.88/1.32 Y := Y
% 0.88/1.32 end
% 0.88/1.32 substitution1:
% 0.88/1.32 X := X
% 0.88/1.32 Y := Y
% 0.88/1.32 Z := Z
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 subsumption: (898) {G1,W6,D2,L2,V3,M2} R(18,35) { ! path( X, Y, Z ), vertex
% 0.88/1.32 ( X ) }.
% 0.88/1.32 parent0: (9404) {G1,W6,D2,L2,V3,M2} { vertex( X ), ! path( X, Y, Z ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := X
% 0.88/1.32 Y := Y
% 0.88/1.32 Z := Z
% 0.88/1.32 end
% 0.88/1.32 permutation0:
% 0.88/1.32 0 ==> 1
% 0.88/1.32 1 ==> 0
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 resolution: (9405) {G1,W6,D2,L2,V3,M2} { vertex( Y ), ! path( X, Y, Z )
% 0.88/1.32 }.
% 0.88/1.32 parent0[0]: (36) {G0,W5,D2,L2,V2,M2} I { ! alpha12( X, Y ), vertex( Y ) }.
% 0.88/1.32 parent1[1]: (18) {G0,W7,D2,L2,V3,M2} I { ! path( X, Y, Z ), alpha12( X, Y )
% 0.88/1.32 }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := X
% 0.88/1.32 Y := Y
% 0.88/1.32 end
% 0.88/1.32 substitution1:
% 0.88/1.32 X := X
% 0.88/1.32 Y := Y
% 0.88/1.32 Z := Z
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 subsumption: (899) {G1,W6,D2,L2,V3,M2} R(18,36) { ! path( X, Y, Z ), vertex
% 0.88/1.32 ( Y ) }.
% 0.88/1.32 parent0: (9405) {G1,W6,D2,L2,V3,M2} { vertex( Y ), ! path( X, Y, Z ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := X
% 0.88/1.32 Y := Y
% 0.88/1.32 Z := Z
% 0.88/1.32 end
% 0.88/1.32 permutation0:
% 0.88/1.32 0 ==> 1
% 0.88/1.32 1 ==> 0
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 resolution: (9406) {G1,W4,D2,L1,V1,M1} { ! precedes( X, X, skol15 ) }.
% 0.88/1.32 parent0[0]: (143) {G2,W8,D2,L2,V4,M2} Q(142) { ! shortest_path( X, Y, Z ),
% 0.88/1.32 ! precedes( T, T, Z ) }.
% 0.88/1.32 parent1[0]: (106) {G0,W4,D2,L1,V0,M1} I { shortest_path( skol10, skol12,
% 0.88/1.32 skol15 ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := skol10
% 0.88/1.32 Y := skol12
% 0.88/1.32 Z := skol15
% 0.88/1.32 T := X
% 0.88/1.32 end
% 0.88/1.32 substitution1:
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 subsumption: (2203) {G3,W4,D2,L1,V1,M1} R(143,106) { ! precedes( X, X,
% 0.88/1.32 skol15 ) }.
% 0.88/1.32 parent0: (9406) {G1,W4,D2,L1,V1,M1} { ! precedes( X, X, skol15 ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := X
% 0.88/1.32 end
% 0.88/1.32 permutation0:
% 0.88/1.32 0 ==> 0
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 resolution: (9407) {G1,W4,D2,L1,V0,M1} { path( skol10, skol12, skol15 )
% 0.88/1.32 }.
% 0.88/1.32 parent0[0]: (71) {G0,W8,D2,L2,V3,M2} I { ! shortest_path( X, Y, Z ), path(
% 0.88/1.32 X, Y, Z ) }.
% 0.88/1.32 parent1[0]: (106) {G0,W4,D2,L1,V0,M1} I { shortest_path( skol10, skol12,
% 0.88/1.32 skol15 ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := skol10
% 0.88/1.32 Y := skol12
% 0.88/1.32 Z := skol15
% 0.88/1.32 end
% 0.88/1.32 substitution1:
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 subsumption: (3438) {G1,W4,D2,L1,V0,M1} R(71,106) { path( skol10, skol12,
% 0.88/1.32 skol15 ) }.
% 0.88/1.32 parent0: (9407) {G1,W4,D2,L1,V0,M1} { path( skol10, skol12, skol15 ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 end
% 0.88/1.32 permutation0:
% 0.88/1.32 0 ==> 0
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 resolution: (9408) {G1,W5,D2,L2,V1,M2} { ! on_path( X, skol15 ), edge( X )
% 0.88/1.32 }.
% 0.88/1.32 parent0[0]: (41) {G0,W9,D2,L3,V4,M3} I { ! path( Z, T, X ), ! on_path( Y, X
% 0.88/1.32 ), edge( Y ) }.
% 0.88/1.32 parent1[0]: (3438) {G1,W4,D2,L1,V0,M1} R(71,106) { path( skol10, skol12,
% 0.88/1.32 skol15 ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := skol15
% 0.88/1.32 Y := X
% 0.88/1.32 Z := skol10
% 0.88/1.32 T := skol12
% 0.88/1.32 end
% 0.88/1.32 substitution1:
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 subsumption: (3448) {G2,W5,D2,L2,V1,M2} R(3438,41) { ! on_path( X, skol15 )
% 0.88/1.32 , edge( X ) }.
% 0.88/1.32 parent0: (9408) {G1,W5,D2,L2,V1,M2} { ! on_path( X, skol15 ), edge( X )
% 0.88/1.32 }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := X
% 0.88/1.32 end
% 0.88/1.32 permutation0:
% 0.88/1.32 0 ==> 0
% 0.88/1.32 1 ==> 1
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 resolution: (9409) {G2,W2,D2,L1,V0,M1} { vertex( skol12 ) }.
% 0.88/1.32 parent0[0]: (899) {G1,W6,D2,L2,V3,M2} R(18,36) { ! path( X, Y, Z ), vertex
% 0.88/1.32 ( Y ) }.
% 0.88/1.32 parent1[0]: (3438) {G1,W4,D2,L1,V0,M1} R(71,106) { path( skol10, skol12,
% 0.88/1.32 skol15 ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := skol10
% 0.88/1.32 Y := skol12
% 0.88/1.32 Z := skol15
% 0.88/1.32 end
% 0.88/1.32 substitution1:
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 subsumption: (3453) {G2,W2,D2,L1,V0,M1} R(3438,899) { vertex( skol12 ) }.
% 0.88/1.32 parent0: (9409) {G2,W2,D2,L1,V0,M1} { vertex( skol12 ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 end
% 0.88/1.32 permutation0:
% 0.88/1.32 0 ==> 0
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 resolution: (9410) {G2,W2,D2,L1,V0,M1} { vertex( skol10 ) }.
% 0.88/1.32 parent0[0]: (898) {G1,W6,D2,L2,V3,M2} R(18,35) { ! path( X, Y, Z ), vertex
% 0.88/1.32 ( X ) }.
% 0.88/1.32 parent1[0]: (3438) {G1,W4,D2,L1,V0,M1} R(71,106) { path( skol10, skol12,
% 0.88/1.32 skol15 ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := skol10
% 0.88/1.32 Y := skol12
% 0.88/1.32 Z := skol15
% 0.88/1.32 end
% 0.88/1.32 substitution1:
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 subsumption: (3454) {G2,W2,D2,L1,V0,M1} R(3438,898) { vertex( skol10 ) }.
% 0.88/1.32 parent0: (9410) {G2,W2,D2,L1,V0,M1} { vertex( skol10 ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 end
% 0.88/1.32 permutation0:
% 0.88/1.32 0 ==> 0
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 resolution: (9411) {G1,W4,D2,L1,V0,M1} { alpha4( skol10, skol12, skol15 )
% 0.88/1.32 }.
% 0.88/1.32 parent0[0]: (72) {G0,W8,D2,L2,V3,M2} I { ! shortest_path( X, Y, Z ), alpha4
% 0.88/1.32 ( X, Y, Z ) }.
% 0.88/1.32 parent1[0]: (106) {G0,W4,D2,L1,V0,M1} I { shortest_path( skol10, skol12,
% 0.88/1.32 skol15 ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := skol10
% 0.88/1.32 Y := skol12
% 0.88/1.32 Z := skol15
% 0.88/1.32 end
% 0.88/1.32 substitution1:
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 subsumption: (3519) {G1,W4,D2,L1,V0,M1} R(72,106) { alpha4( skol10, skol12
% 0.88/1.32 , skol15 ) }.
% 0.88/1.32 parent0: (9411) {G1,W4,D2,L1,V0,M1} { alpha4( skol10, skol12, skol15 ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 end
% 0.88/1.32 permutation0:
% 0.88/1.32 0 ==> 0
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 eqswap: (9412) {G0,W7,D2,L2,V3,M2} { ! Y = X, ! alpha4( X, Y, Z ) }.
% 0.88/1.32 parent0[1]: (74) {G0,W7,D2,L2,V3,M2} I { ! alpha4( X, Y, Z ), ! X = Y }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := X
% 0.88/1.32 Y := Y
% 0.88/1.32 Z := Z
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 resolution: (9413) {G1,W3,D2,L1,V0,M1} { ! skol12 = skol10 }.
% 0.88/1.32 parent0[1]: (9412) {G0,W7,D2,L2,V3,M2} { ! Y = X, ! alpha4( X, Y, Z ) }.
% 0.88/1.32 parent1[0]: (3519) {G1,W4,D2,L1,V0,M1} R(72,106) { alpha4( skol10, skol12,
% 0.88/1.32 skol15 ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := skol10
% 0.88/1.32 Y := skol12
% 0.88/1.32 Z := skol15
% 0.88/1.32 end
% 0.88/1.32 substitution1:
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 subsumption: (3521) {G2,W3,D2,L1,V0,M1} R(3519,74) { ! skol12 ==> skol10
% 0.88/1.32 }.
% 0.88/1.32 parent0: (9413) {G1,W3,D2,L1,V0,M1} { ! skol12 = skol10 }.
% 0.88/1.32 substitution0:
% 0.88/1.32 end
% 0.88/1.32 permutation0:
% 0.88/1.32 0 ==> 0
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 resolution: (9415) {G1,W6,D2,L2,V2,M2} { edge( X ), ! alpha13( skol15, X,
% 0.88/1.32 Y ) }.
% 0.88/1.32 parent0[0]: (3448) {G2,W5,D2,L2,V1,M2} R(3438,41) { ! on_path( X, skol15 )
% 0.88/1.32 , edge( X ) }.
% 0.88/1.32 parent1[1]: (68) {G0,W7,D2,L2,V3,M2} I { ! alpha13( X, Y, Z ), on_path( Y,
% 0.88/1.32 X ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := X
% 0.88/1.32 end
% 0.88/1.32 substitution1:
% 0.88/1.32 X := skol15
% 0.88/1.32 Y := X
% 0.88/1.32 Z := Y
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 subsumption: (4000) {G3,W6,D2,L2,V2,M2} R(3448,68) { edge( X ), ! alpha13(
% 0.88/1.32 skol15, X, Y ) }.
% 0.88/1.32 parent0: (9415) {G1,W6,D2,L2,V2,M2} { edge( X ), ! alpha13( skol15, X, Y )
% 0.88/1.32 }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := X
% 0.88/1.32 Y := Y
% 0.88/1.32 end
% 0.88/1.32 permutation0:
% 0.88/1.32 0 ==> 0
% 0.88/1.32 1 ==> 1
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 resolution: (9416) {G1,W6,D2,L2,V2,M2} { edge( X ), ! alpha13( skol15, Y,
% 0.88/1.32 X ) }.
% 0.88/1.32 parent0[0]: (3448) {G2,W5,D2,L2,V1,M2} R(3438,41) { ! on_path( X, skol15 )
% 0.88/1.32 , edge( X ) }.
% 0.88/1.32 parent1[1]: (69) {G0,W7,D2,L2,V3,M2} I { ! alpha13( X, Y, Z ), on_path( Z,
% 0.88/1.32 X ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := X
% 0.88/1.32 end
% 0.88/1.32 substitution1:
% 0.88/1.32 X := skol15
% 0.88/1.32 Y := Y
% 0.88/1.32 Z := X
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 subsumption: (4001) {G3,W6,D2,L2,V2,M2} R(3448,69) { edge( X ), ! alpha13(
% 0.88/1.32 skol15, Y, X ) }.
% 0.88/1.32 parent0: (9416) {G1,W6,D2,L2,V2,M2} { edge( X ), ! alpha13( skol15, Y, X )
% 0.88/1.32 }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := X
% 0.88/1.32 Y := Y
% 0.88/1.32 end
% 0.88/1.32 permutation0:
% 0.88/1.32 0 ==> 0
% 0.88/1.32 1 ==> 1
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 resolution: (9421) {G1,W16,D2,L6,V0,M6} { ! vertex( skol12 ), skol12 ==>
% 0.88/1.32 skol10, ! edge( skol13 ), ! edge( skol14 ), skol14 ==> skol13, ! path(
% 0.88/1.32 skol10, skol12, skol15 ) }.
% 0.88/1.32 parent0[0]: (108) {G0,W18,D2,L7,V0,M7} I { ! vertex( skol10 ), ! vertex(
% 0.88/1.32 skol12 ), skol12 ==> skol10, ! edge( skol13 ), ! edge( skol14 ), skol14
% 0.88/1.32 ==> skol13, ! path( skol10, skol12, skol15 ) }.
% 0.88/1.32 parent1[0]: (3454) {G2,W2,D2,L1,V0,M1} R(3438,898) { vertex( skol10 ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 end
% 0.88/1.32 substitution1:
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 resolution: (9422) {G2,W14,D2,L5,V0,M5} { skol12 ==> skol10, ! edge(
% 0.88/1.32 skol13 ), ! edge( skol14 ), skol14 ==> skol13, ! path( skol10, skol12,
% 0.88/1.32 skol15 ) }.
% 0.88/1.32 parent0[0]: (9421) {G1,W16,D2,L6,V0,M6} { ! vertex( skol12 ), skol12 ==>
% 0.88/1.32 skol10, ! edge( skol13 ), ! edge( skol14 ), skol14 ==> skol13, ! path(
% 0.88/1.32 skol10, skol12, skol15 ) }.
% 0.88/1.32 parent1[0]: (3453) {G2,W2,D2,L1,V0,M1} R(3438,899) { vertex( skol12 ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 end
% 0.88/1.32 substitution1:
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 resolution: (9423) {G3,W11,D2,L4,V0,M4} { ! edge( skol13 ), ! edge( skol14
% 0.88/1.32 ), skol14 ==> skol13, ! path( skol10, skol12, skol15 ) }.
% 0.88/1.32 parent0[0]: (3521) {G2,W3,D2,L1,V0,M1} R(3519,74) { ! skol12 ==> skol10 }.
% 0.88/1.32 parent1[0]: (9422) {G2,W14,D2,L5,V0,M5} { skol12 ==> skol10, ! edge(
% 0.88/1.32 skol13 ), ! edge( skol14 ), skol14 ==> skol13, ! path( skol10, skol12,
% 0.88/1.32 skol15 ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 end
% 0.88/1.32 substitution1:
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 resolution: (9424) {G2,W7,D2,L3,V0,M3} { ! edge( skol13 ), ! edge( skol14
% 0.88/1.32 ), skol14 ==> skol13 }.
% 0.88/1.32 parent0[3]: (9423) {G3,W11,D2,L4,V0,M4} { ! edge( skol13 ), ! edge( skol14
% 0.88/1.32 ), skol14 ==> skol13, ! path( skol10, skol12, skol15 ) }.
% 0.88/1.32 parent1[0]: (3438) {G1,W4,D2,L1,V0,M1} R(71,106) { path( skol10, skol12,
% 0.88/1.32 skol15 ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 end
% 0.88/1.32 substitution1:
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 subsumption: (5183) {G3,W7,D2,L3,V0,M3} S(108);r(3454);r(3453);r(3521);r(
% 0.88/1.32 3438) { ! edge( skol13 ), ! edge( skol14 ), skol14 ==> skol13 }.
% 0.88/1.32 parent0: (9424) {G2,W7,D2,L3,V0,M3} { ! edge( skol13 ), ! edge( skol14 ),
% 0.88/1.32 skol14 ==> skol13 }.
% 0.88/1.32 substitution0:
% 0.88/1.32 end
% 0.88/1.32 permutation0:
% 0.88/1.32 0 ==> 0
% 0.88/1.32 1 ==> 1
% 0.88/1.32 2 ==> 2
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 paramod: (9427) {G1,W8,D2,L3,V0,M3} { precedes( skol13, skol13, skol15 ),
% 0.88/1.32 ! edge( skol13 ), ! edge( skol14 ) }.
% 0.88/1.32 parent0[2]: (5183) {G3,W7,D2,L3,V0,M3} S(108);r(3454);r(3453);r(3521);r(
% 0.88/1.32 3438) { ! edge( skol13 ), ! edge( skol14 ), skol14 ==> skol13 }.
% 0.88/1.32 parent1[0; 2]: (107) {G0,W4,D2,L1,V0,M1} I { precedes( skol13, skol14,
% 0.88/1.32 skol15 ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 end
% 0.88/1.32 substitution1:
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 resolution: (9448) {G2,W4,D2,L2,V0,M2} { ! edge( skol13 ), ! edge( skol14
% 0.88/1.32 ) }.
% 0.88/1.32 parent0[0]: (2203) {G3,W4,D2,L1,V1,M1} R(143,106) { ! precedes( X, X,
% 0.88/1.32 skol15 ) }.
% 0.88/1.32 parent1[0]: (9427) {G1,W8,D2,L3,V0,M3} { precedes( skol13, skol13, skol15
% 0.88/1.32 ), ! edge( skol13 ), ! edge( skol14 ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := skol13
% 0.88/1.32 end
% 0.88/1.32 substitution1:
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 subsumption: (5289) {G4,W4,D2,L2,V0,M2} P(5183,107);r(2203) { ! edge(
% 0.88/1.32 skol13 ), ! edge( skol14 ) }.
% 0.88/1.32 parent0: (9448) {G2,W4,D2,L2,V0,M2} { ! edge( skol13 ), ! edge( skol14 )
% 0.88/1.32 }.
% 0.88/1.32 substitution0:
% 0.88/1.32 end
% 0.88/1.32 permutation0:
% 0.88/1.32 0 ==> 0
% 0.88/1.32 1 ==> 1
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 resolution: (9450) {G4,W6,D2,L2,V1,M2} { ! edge( skol13 ), ! alpha13(
% 0.88/1.32 skol15, X, skol14 ) }.
% 0.88/1.32 parent0[1]: (5289) {G4,W4,D2,L2,V0,M2} P(5183,107);r(2203) { ! edge( skol13
% 0.88/1.32 ), ! edge( skol14 ) }.
% 0.88/1.32 parent1[0]: (4001) {G3,W6,D2,L2,V2,M2} R(3448,69) { edge( X ), ! alpha13(
% 0.88/1.32 skol15, Y, X ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 end
% 0.88/1.32 substitution1:
% 0.88/1.32 X := skol14
% 0.88/1.32 Y := X
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 subsumption: (5295) {G5,W6,D2,L2,V1,M2} R(5289,4001) { ! edge( skol13 ), !
% 0.88/1.32 alpha13( skol15, X, skol14 ) }.
% 0.88/1.32 parent0: (9450) {G4,W6,D2,L2,V1,M2} { ! edge( skol13 ), ! alpha13( skol15
% 0.88/1.32 , X, skol14 ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := X
% 0.88/1.32 end
% 0.88/1.32 permutation0:
% 0.88/1.32 0 ==> 0
% 0.88/1.32 1 ==> 1
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 resolution: (9451) {G4,W8,D2,L2,V2,M2} { ! alpha13( skol15, X, skol14 ), !
% 0.88/1.32 alpha13( skol15, skol13, Y ) }.
% 0.88/1.32 parent0[0]: (5295) {G5,W6,D2,L2,V1,M2} R(5289,4001) { ! edge( skol13 ), !
% 0.88/1.32 alpha13( skol15, X, skol14 ) }.
% 0.88/1.32 parent1[0]: (4000) {G3,W6,D2,L2,V2,M2} R(3448,68) { edge( X ), ! alpha13(
% 0.88/1.32 skol15, X, Y ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := X
% 0.88/1.32 end
% 0.88/1.32 substitution1:
% 0.88/1.32 X := skol13
% 0.88/1.32 Y := Y
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 subsumption: (7952) {G6,W8,D2,L2,V2,M2} R(5295,4000) { ! alpha13( skol15, X
% 0.88/1.32 , skol14 ), ! alpha13( skol15, skol13, Y ) }.
% 0.88/1.32 parent0: (9451) {G4,W8,D2,L2,V2,M2} { ! alpha13( skol15, X, skol14 ), !
% 0.88/1.32 alpha13( skol15, skol13, Y ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := X
% 0.88/1.32 Y := Y
% 0.88/1.32 end
% 0.88/1.32 permutation0:
% 0.88/1.32 0 ==> 0
% 0.88/1.32 1 ==> 1
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 factor: (9453) {G6,W4,D2,L1,V0,M1} { ! alpha13( skol15, skol13, skol14 )
% 0.88/1.32 }.
% 0.88/1.32 parent0[0, 1]: (7952) {G6,W8,D2,L2,V2,M2} R(5295,4000) { ! alpha13( skol15
% 0.88/1.32 , X, skol14 ), ! alpha13( skol15, skol13, Y ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := skol13
% 0.88/1.32 Y := skol14
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 subsumption: (7968) {G7,W4,D2,L1,V0,M1} F(7952) { ! alpha13( skol15, skol13
% 0.88/1.32 , skol14 ) }.
% 0.88/1.32 parent0: (9453) {G6,W4,D2,L1,V0,M1} { ! alpha13( skol15, skol13, skol14 )
% 0.88/1.32 }.
% 0.88/1.32 substitution0:
% 0.88/1.32 end
% 0.88/1.32 permutation0:
% 0.88/1.32 0 ==> 0
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 resolution: (9454) {G1,W8,D2,L2,V2,M2} { ! path( X, Y, skol15 ), !
% 0.88/1.32 precedes( skol13, skol14, skol15 ) }.
% 0.88/1.32 parent0[0]: (7968) {G7,W4,D2,L1,V0,M1} F(7952) { ! alpha13( skol15, skol13
% 0.88/1.32 , skol14 ) }.
% 0.88/1.32 parent1[2]: (58) {G0,W12,D2,L3,V5,M3} I { ! path( Y, Z, X ), ! precedes( T
% 0.88/1.32 , U, X ), alpha13( X, T, U ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 end
% 0.88/1.32 substitution1:
% 0.88/1.32 X := skol15
% 0.88/1.32 Y := X
% 0.88/1.32 Z := Y
% 0.88/1.32 T := skol13
% 0.88/1.32 U := skol14
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 resolution: (9455) {G1,W4,D2,L1,V2,M1} { ! path( X, Y, skol15 ) }.
% 0.88/1.32 parent0[1]: (9454) {G1,W8,D2,L2,V2,M2} { ! path( X, Y, skol15 ), !
% 0.88/1.32 precedes( skol13, skol14, skol15 ) }.
% 0.88/1.32 parent1[0]: (107) {G0,W4,D2,L1,V0,M1} I { precedes( skol13, skol14, skol15
% 0.88/1.32 ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := X
% 0.88/1.32 Y := Y
% 0.88/1.32 end
% 0.88/1.32 substitution1:
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 subsumption: (7969) {G8,W4,D2,L1,V2,M1} R(7968,58);r(107) { ! path( X, Y,
% 0.88/1.32 skol15 ) }.
% 0.88/1.32 parent0: (9455) {G1,W4,D2,L1,V2,M1} { ! path( X, Y, skol15 ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := X
% 0.88/1.32 Y := Y
% 0.88/1.32 end
% 0.88/1.32 permutation0:
% 0.88/1.32 0 ==> 0
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 resolution: (9456) {G2,W0,D0,L0,V0,M0} { }.
% 0.88/1.32 parent0[0]: (7969) {G8,W4,D2,L1,V2,M1} R(7968,58);r(107) { ! path( X, Y,
% 0.88/1.32 skol15 ) }.
% 0.88/1.32 parent1[0]: (3438) {G1,W4,D2,L1,V0,M1} R(71,106) { path( skol10, skol12,
% 0.88/1.32 skol15 ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := skol10
% 0.88/1.32 Y := skol12
% 0.88/1.32 end
% 0.88/1.32 substitution1:
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 subsumption: (7972) {G9,W0,D0,L0,V0,M0} R(7969,3438) { }.
% 0.88/1.32 parent0: (9456) {G2,W0,D0,L0,V0,M0} { }.
% 0.88/1.32 substitution0:
% 0.88/1.32 end
% 0.88/1.32 permutation0:
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 Proof check complete!
% 0.88/1.32
% 0.88/1.32 Memory use:
% 0.88/1.32
% 0.88/1.32 space for terms: 127670
% 0.88/1.32 space for clauses: 309218
% 0.88/1.32
% 0.88/1.32
% 0.88/1.32 clauses generated: 19164
% 0.88/1.32 clauses kept: 7973
% 0.88/1.32 clauses selected: 556
% 0.88/1.32 clauses deleted: 22
% 0.88/1.32 clauses inuse deleted: 9
% 0.88/1.32
% 0.88/1.32 subsentry: 39442
% 0.88/1.32 literals s-matched: 26465
% 0.88/1.32 literals matched: 24828
% 0.88/1.32 full subsumption: 5455
% 0.88/1.32
% 0.88/1.32 checksum: 1946840850
% 0.88/1.32
% 0.88/1.32
% 0.88/1.32 Bliksem ended
%------------------------------------------------------------------------------