TSTP Solution File: GRA010+2 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GRA010+2 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n026.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 07:11:32 EDT 2022
% Result : Theorem 2.34s 2.74s
% Output : Refutation 2.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRA010+2 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.10/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Mon May 30 22:53:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.45/1.14 *** allocated 10000 integers for termspace/termends
% 0.45/1.14 *** allocated 10000 integers for clauses
% 0.45/1.14 *** allocated 10000 integers for justifications
% 0.45/1.14 Bliksem 1.12
% 0.45/1.14
% 0.45/1.14
% 0.45/1.14 Automatic Strategy Selection
% 0.45/1.14
% 0.45/1.14
% 0.45/1.14 Clauses:
% 0.45/1.14
% 0.45/1.14 { ! edge( X ), ! head_of( X ) = tail_of( X ) }.
% 0.45/1.14 { ! edge( X ), vertex( head_of( X ) ) }.
% 0.45/1.14 { ! edge( X ), vertex( tail_of( X ) ) }.
% 0.45/1.14 { ! complete, ! vertex( X ), ! vertex( Y ), X = Y, edge( skol1( Z, T ) ) }
% 0.45/1.14 .
% 0.45/1.14 { ! complete, ! vertex( X ), ! vertex( Y ), X = Y, alpha11( X, Y, skol1( X
% 0.45/1.14 , Y ) ), alpha15( X, Y, skol1( X, Y ) ) }.
% 0.45/1.14 { ! alpha15( X, Y, Z ), Y = head_of( Z ) }.
% 0.45/1.14 { ! alpha15( X, Y, Z ), X = tail_of( Z ) }.
% 0.45/1.14 { ! alpha15( X, Y, Z ), ! alpha1( X, Y, Z ) }.
% 0.45/1.14 { ! Y = head_of( Z ), ! X = tail_of( Z ), alpha1( X, Y, Z ), alpha15( X, Y
% 0.45/1.14 , Z ) }.
% 0.45/1.14 { ! alpha11( X, Y, Z ), alpha1( X, Y, Z ) }.
% 0.45/1.14 { ! alpha11( X, Y, Z ), ! Y = head_of( Z ), ! X = tail_of( Z ) }.
% 0.45/1.14 { ! alpha1( X, Y, Z ), Y = head_of( Z ), alpha11( X, Y, Z ) }.
% 0.45/1.14 { ! alpha1( X, Y, Z ), X = tail_of( Z ), alpha11( X, Y, Z ) }.
% 0.45/1.14 { ! alpha1( X, Y, Z ), X = head_of( Z ) }.
% 0.45/1.14 { ! alpha1( X, Y, Z ), Y = tail_of( Z ) }.
% 0.45/1.14 { ! X = head_of( Z ), ! Y = tail_of( Z ), alpha1( X, Y, Z ) }.
% 0.45/1.14 { ! vertex( X ), ! vertex( Y ), ! edge( T ), ! X = tail_of( T ), ! Y =
% 0.45/1.14 head_of( T ), ! Z = path_cons( T, empty ), path( X, Y, Z ) }.
% 0.45/1.14 { ! vertex( X ), ! vertex( Y ), ! edge( T ), ! X = tail_of( T ), ! path(
% 0.45/1.14 head_of( T ), Y, U ), ! Z = path_cons( T, U ), path( X, Y, Z ) }.
% 0.45/1.14 { ! path( X, Y, Z ), alpha12( X, Y ) }.
% 0.45/1.14 { ! path( X, Y, Z ), alpha16( X, skol2( X, T, U ) ) }.
% 0.45/1.14 { ! path( X, Y, Z ), alpha20( Y, Z, skol2( X, Y, Z ) ) }.
% 0.45/1.14 { ! alpha20( X, Y, Z ), alpha18( X, Y, Z ), alpha21( X, Y, Z ) }.
% 0.45/1.14 { ! alpha18( X, Y, Z ), alpha20( X, Y, Z ) }.
% 0.45/1.14 { ! alpha21( X, Y, Z ), alpha20( X, Y, Z ) }.
% 0.45/1.14 { ! alpha21( X, Y, Z ), Y = path_cons( Z, skol3( T, Y, Z ) ) }.
% 0.45/1.14 { ! alpha21( X, Y, Z ), path( head_of( Z ), X, skol3( X, Y, Z ) ) }.
% 0.45/1.14 { ! alpha21( X, Y, Z ), ! alpha2( X, Y, Z ) }.
% 0.45/1.14 { ! path( head_of( Z ), X, T ), ! Y = path_cons( Z, T ), alpha2( X, Y, Z )
% 0.45/1.14 , alpha21( X, Y, Z ) }.
% 0.45/1.14 { ! alpha18( X, Y, Z ), alpha2( X, Y, Z ) }.
% 0.45/1.14 { ! alpha18( X, Y, Z ), ! path( head_of( Z ), X, T ), ! Y = path_cons( Z, T
% 0.45/1.14 ) }.
% 0.45/1.14 { ! alpha2( X, Y, Z ), Y = path_cons( Z, skol4( T, Y, Z ) ), alpha18( X, Y
% 0.45/1.14 , Z ) }.
% 0.45/1.14 { ! alpha2( X, Y, Z ), path( head_of( Z ), X, skol4( X, Y, Z ) ), alpha18(
% 0.45/1.14 X, Y, Z ) }.
% 0.45/1.14 { ! alpha16( X, Y ), edge( Y ) }.
% 0.45/1.14 { ! alpha16( X, Y ), X = tail_of( Y ) }.
% 0.45/1.14 { ! edge( Y ), ! X = tail_of( Y ), alpha16( X, Y ) }.
% 0.45/1.14 { ! alpha12( X, Y ), vertex( X ) }.
% 0.45/1.14 { ! alpha12( X, Y ), vertex( Y ) }.
% 0.45/1.14 { ! vertex( X ), ! vertex( Y ), alpha12( X, Y ) }.
% 0.45/1.14 { ! alpha2( X, Y, Z ), X = head_of( Z ) }.
% 0.45/1.14 { ! alpha2( X, Y, Z ), Y = path_cons( Z, empty ) }.
% 0.45/1.14 { ! X = head_of( Z ), ! Y = path_cons( Z, empty ), alpha2( X, Y, Z ) }.
% 0.45/1.14 { ! path( Z, T, X ), ! on_path( Y, X ), edge( Y ) }.
% 0.45/1.14 { ! path( Z, T, X ), ! on_path( Y, X ), in_path( head_of( Y ), X ) }.
% 0.45/1.14 { ! path( Z, T, X ), ! on_path( Y, X ), in_path( tail_of( Y ), X ) }.
% 0.45/1.14 { ! path( Z, T, X ), ! in_path( Y, X ), vertex( Y ) }.
% 0.45/1.14 { ! path( Z, T, X ), ! in_path( Y, X ), Y = head_of( skol5( U, Y ) ), Y =
% 0.45/1.14 tail_of( skol5( U, Y ) ) }.
% 0.45/1.14 { ! path( Z, T, X ), ! in_path( Y, X ), on_path( skol5( X, Y ), X ) }.
% 0.45/1.14 { ! sequential( X, Y ), edge( X ) }.
% 0.45/1.14 { ! sequential( X, Y ), alpha3( X, Y ) }.
% 0.45/1.14 { ! edge( X ), ! alpha3( X, Y ), sequential( X, Y ) }.
% 0.45/1.14 { ! alpha3( X, Y ), edge( Y ) }.
% 0.45/1.14 { ! alpha3( X, Y ), alpha6( X, Y ) }.
% 0.45/1.14 { ! edge( Y ), ! alpha6( X, Y ), alpha3( X, Y ) }.
% 0.45/1.14 { ! alpha6( X, Y ), ! X = Y }.
% 0.45/1.14 { ! alpha6( X, Y ), head_of( X ) = tail_of( Y ) }.
% 0.45/1.14 { X = Y, ! head_of( X ) = tail_of( Y ), alpha6( X, Y ) }.
% 0.45/1.14 { ! path( Y, Z, X ), ! on_path( T, X ), ! on_path( U, X ), ! sequential( T
% 0.45/1.14 , U ), precedes( T, U, X ) }.
% 0.45/1.14 { ! path( Y, Z, X ), ! on_path( T, X ), ! on_path( U, X ), ! sequential( T
% 0.45/1.14 , W ), ! precedes( W, U, X ), precedes( T, U, X ) }.
% 0.45/1.14 { ! path( Y, Z, X ), ! precedes( T, U, X ), alpha13( X, T, U ) }.
% 0.45/1.14 { ! path( Y, Z, X ), ! precedes( T, U, X ), alpha17( X, T, U ), alpha19( X
% 0.45/1.14 , T, U ) }.
% 0.45/1.14 { ! alpha19( X, Y, Z ), sequential( Y, skol6( T, Y, U ) ) }.
% 0.45/1.14 { ! alpha19( X, Y, Z ), precedes( skol6( X, Y, Z ), Z, X ) }.
% 0.45/1.14 { ! alpha19( X, Y, Z ), ! sequential( Y, Z ) }.
% 0.80/1.20 { ! sequential( Y, T ), ! precedes( T, Z, X ), sequential( Y, Z ), alpha19
% 0.80/1.20 ( X, Y, Z ) }.
% 0.80/1.20 { ! alpha17( X, Y, Z ), sequential( Y, Z ) }.
% 0.80/1.20 { ! alpha17( X, Y, Z ), ! sequential( Y, T ), ! precedes( T, Z, X ) }.
% 0.80/1.20 { ! sequential( Y, Z ), sequential( Y, skol7( T, Y, U ) ), alpha17( X, Y, Z
% 0.80/1.20 ) }.
% 0.80/1.20 { ! sequential( Y, Z ), precedes( skol7( X, Y, Z ), Z, X ), alpha17( X, Y,
% 0.80/1.20 Z ) }.
% 0.80/1.20 { ! alpha13( X, Y, Z ), on_path( Y, X ) }.
% 0.80/1.20 { ! alpha13( X, Y, Z ), on_path( Z, X ) }.
% 0.80/1.20 { ! on_path( Y, X ), ! on_path( Z, X ), alpha13( X, Y, Z ) }.
% 0.80/1.20 { ! shortest_path( X, Y, Z ), path( X, Y, Z ) }.
% 0.80/1.20 { ! shortest_path( X, Y, Z ), alpha4( X, Y, Z ) }.
% 0.80/1.20 { ! path( X, Y, Z ), ! alpha4( X, Y, Z ), shortest_path( X, Y, Z ) }.
% 0.80/1.20 { ! alpha4( X, Y, Z ), ! X = Y }.
% 0.80/1.20 { ! alpha4( X, Y, Z ), alpha7( X, Y, Z ) }.
% 0.80/1.20 { X = Y, ! alpha7( X, Y, Z ), alpha4( X, Y, Z ) }.
% 0.80/1.20 { ! alpha7( X, Y, Z ), ! path( X, Y, T ), less_or_equal( length_of( Z ),
% 0.80/1.20 length_of( T ) ) }.
% 0.80/1.20 { ! less_or_equal( length_of( Z ), length_of( skol8( T, U, Z ) ) ), alpha7
% 0.80/1.20 ( X, Y, Z ) }.
% 0.80/1.20 { path( X, Y, skol8( X, Y, Z ) ), alpha7( X, Y, Z ) }.
% 0.80/1.20 { ! shortest_path( T, U, Z ), ! precedes( X, Y, Z ), ! tail_of( W ) =
% 0.80/1.20 tail_of( X ), ! head_of( W ) = head_of( Y ) }.
% 0.80/1.20 { ! shortest_path( T, U, Z ), ! precedes( X, Y, Z ), ! precedes( Y, X, Z )
% 0.80/1.20 }.
% 0.80/1.20 { ! triangle( X, Y, Z ), edge( X ) }.
% 0.80/1.20 { ! triangle( X, Y, Z ), alpha5( X, Y, Z ) }.
% 0.80/1.20 { ! edge( X ), ! alpha5( X, Y, Z ), triangle( X, Y, Z ) }.
% 0.80/1.20 { ! alpha5( X, Y, Z ), edge( Y ) }.
% 0.80/1.20 { ! alpha5( X, Y, Z ), alpha8( X, Y, Z ) }.
% 0.80/1.20 { ! edge( Y ), ! alpha8( X, Y, Z ), alpha5( X, Y, Z ) }.
% 0.80/1.20 { ! alpha8( X, Y, Z ), edge( Z ) }.
% 0.80/1.20 { ! alpha8( X, Y, Z ), alpha9( X, Y, Z ) }.
% 0.80/1.20 { ! edge( Z ), ! alpha9( X, Y, Z ), alpha8( X, Y, Z ) }.
% 0.80/1.20 { ! alpha9( X, Y, Z ), sequential( X, Y ) }.
% 0.80/1.20 { ! alpha9( X, Y, Z ), alpha10( X, Y, Z ) }.
% 0.80/1.20 { ! sequential( X, Y ), ! alpha10( X, Y, Z ), alpha9( X, Y, Z ) }.
% 0.80/1.20 { ! alpha10( X, Y, Z ), sequential( Y, Z ) }.
% 0.80/1.20 { ! alpha10( X, Y, Z ), sequential( Z, X ) }.
% 0.80/1.20 { ! sequential( Y, Z ), ! sequential( Z, X ), alpha10( X, Y, Z ) }.
% 0.80/1.20 { ! path( Y, Z, X ), length_of( X ) = number_of_in( edges, X ) }.
% 0.80/1.20 { ! path( Y, Z, X ), number_of_in( sequential_pairs, X ) = minus( length_of
% 0.80/1.20 ( X ), n1 ) }.
% 0.80/1.20 { ! path( Y, Z, X ), alpha14( X, skol9( X ), skol12( X ) ), number_of_in(
% 0.80/1.20 sequential_pairs, X ) = number_of_in( triangles, X ) }.
% 0.80/1.20 { ! path( Y, Z, X ), ! triangle( skol9( X ), skol12( X ), T ), number_of_in
% 0.80/1.20 ( sequential_pairs, X ) = number_of_in( triangles, X ) }.
% 0.80/1.20 { ! alpha14( X, Y, Z ), on_path( Y, X ) }.
% 0.80/1.20 { ! alpha14( X, Y, Z ), on_path( Z, X ) }.
% 0.80/1.20 { ! alpha14( X, Y, Z ), sequential( Y, Z ) }.
% 0.80/1.20 { ! on_path( Y, X ), ! on_path( Z, X ), ! sequential( Y, Z ), alpha14( X, Y
% 0.80/1.20 , Z ) }.
% 0.80/1.20 { less_or_equal( number_of_in( X, Y ), number_of_in( X, graph ) ) }.
% 0.80/1.20 { ! complete, ! shortest_path( T, U, Z ), ! precedes( X, Y, Z ), !
% 0.80/1.20 sequential( X, Y ), triangle( X, Y, skol10( X, Y ) ) }.
% 0.80/1.20 { complete }.
% 0.80/1.20 { path( skol13, skol14, skol11 ) }.
% 0.80/1.20 { ! on_path( X, skol11 ), ! on_path( Y, skol11 ), ! sequential( X, Y ),
% 0.80/1.20 triangle( X, Y, skol15( X, Y ) ) }.
% 0.80/1.20 { ! number_of_in( sequential_pairs, skol11 ) = number_of_in( triangles,
% 0.80/1.20 skol11 ) }.
% 0.80/1.20
% 0.80/1.20 percentage equality = 0.152027, percentage horn = 0.837838
% 0.80/1.20 This is a problem with some equality
% 0.80/1.20
% 0.80/1.20
% 0.80/1.20
% 0.80/1.20 Options Used:
% 0.80/1.20
% 0.80/1.20 useres = 1
% 0.80/1.20 useparamod = 1
% 0.80/1.20 useeqrefl = 1
% 0.80/1.20 useeqfact = 1
% 0.80/1.20 usefactor = 1
% 0.80/1.20 usesimpsplitting = 0
% 0.80/1.20 usesimpdemod = 5
% 0.80/1.20 usesimpres = 3
% 0.80/1.20
% 0.80/1.20 resimpinuse = 1000
% 0.80/1.20 resimpclauses = 20000
% 0.80/1.20 substype = eqrewr
% 0.80/1.20 backwardsubs = 1
% 0.80/1.20 selectoldest = 5
% 0.80/1.20
% 0.80/1.20 litorderings [0] = split
% 0.80/1.20 litorderings [1] = extend the termordering, first sorting on arguments
% 0.80/1.20
% 0.80/1.20 termordering = kbo
% 0.80/1.20
% 0.80/1.20 litapriori = 0
% 0.80/1.20 termapriori = 1
% 0.80/1.20 litaposteriori = 0
% 0.80/1.20 termaposteriori = 0
% 0.80/1.20 demodaposteriori = 0
% 0.80/1.20 ordereqreflfact = 0
% 0.80/1.20
% 0.80/1.20 litselect = negord
% 0.80/1.20
% 0.80/1.20 maxweight = 15
% 0.80/1.20 maxdepth = 30000
% 0.80/1.20 maxlength = 115
% 0.80/1.20 maxnrvars = 195
% 0.80/1.20 excuselevel = 1
% 0.80/1.20 increasemaxweight = 1
% 0.80/1.20
% 0.80/1.20 maxselected = 10000000
% 0.80/1.20 maxnrclauses = 10000000
% 0.80/1.20
% 0.80/1.20 showgenerated = 0
% 0.80/1.20 showkept = 0
% 0.80/1.20 showselected = 0
% 0.80/1.20 showdeleted = 0
% 0.80/1.20 showresimp = 1
% 2.34/2.74 showstatus = 2000
% 2.34/2.74
% 2.34/2.74 prologoutput = 0
% 2.34/2.74 nrgoals = 5000000
% 2.34/2.74 totalproof = 1
% 2.34/2.74
% 2.34/2.74 Symbols occurring in the translation:
% 2.34/2.74
% 2.34/2.74 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 2.34/2.74 . [1, 2] (w:1, o:40, a:1, s:1, b:0),
% 2.34/2.74 ! [4, 1] (w:0, o:28, a:1, s:1, b:0),
% 2.34/2.74 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.34/2.74 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.34/2.74 edge [36, 1] (w:1, o:33, a:1, s:1, b:0),
% 2.34/2.74 head_of [37, 1] (w:1, o:34, a:1, s:1, b:0),
% 2.34/2.74 tail_of [38, 1] (w:1, o:37, a:1, s:1, b:0),
% 2.34/2.74 vertex [39, 1] (w:1, o:38, a:1, s:1, b:0),
% 2.34/2.74 complete [40, 0] (w:1, o:7, a:1, s:1, b:0),
% 2.34/2.74 empty [44, 0] (w:1, o:11, a:1, s:1, b:0),
% 2.34/2.74 path_cons [45, 2] (w:1, o:67, a:1, s:1, b:0),
% 2.34/2.74 path [47, 3] (w:1, o:79, a:1, s:1, b:0),
% 2.34/2.74 on_path [48, 2] (w:1, o:66, a:1, s:1, b:0),
% 2.34/2.74 in_path [49, 2] (w:1, o:68, a:1, s:1, b:0),
% 2.34/2.74 sequential [53, 2] (w:1, o:69, a:1, s:1, b:0),
% 2.34/2.74 precedes [55, 3] (w:1, o:80, a:1, s:1, b:0),
% 2.34/2.74 shortest_path [57, 3] (w:1, o:81, a:1, s:1, b:0),
% 2.34/2.74 length_of [58, 1] (w:1, o:39, a:1, s:1, b:0),
% 2.34/2.74 less_or_equal [59, 2] (w:1, o:70, a:1, s:1, b:0),
% 2.34/2.74 triangle [60, 3] (w:1, o:88, a:1, s:1, b:0),
% 2.34/2.74 edges [61, 0] (w:1, o:18, a:1, s:1, b:0),
% 2.34/2.74 number_of_in [62, 2] (w:1, o:65, a:1, s:1, b:0),
% 2.34/2.74 sequential_pairs [63, 0] (w:1, o:19, a:1, s:1, b:0),
% 2.34/2.74 n1 [64, 0] (w:1, o:20, a:1, s:1, b:0),
% 2.34/2.74 minus [65, 2] (w:1, o:64, a:1, s:1, b:0),
% 2.34/2.74 triangles [66, 0] (w:1, o:24, a:1, s:1, b:0),
% 2.34/2.74 graph [69, 0] (w:1, o:27, a:1, s:1, b:0),
% 2.34/2.74 alpha1 [70, 3] (w:1, o:89, a:1, s:1, b:1),
% 2.34/2.74 alpha2 [71, 3] (w:1, o:98, a:1, s:1, b:1),
% 2.34/2.74 alpha3 [72, 2] (w:1, o:71, a:1, s:1, b:1),
% 2.34/2.74 alpha4 [73, 3] (w:1, o:99, a:1, s:1, b:1),
% 2.34/2.74 alpha5 [74, 3] (w:1, o:100, a:1, s:1, b:1),
% 2.34/2.74 alpha6 [75, 2] (w:1, o:72, a:1, s:1, b:1),
% 2.34/2.74 alpha7 [76, 3] (w:1, o:101, a:1, s:1, b:1),
% 2.34/2.74 alpha8 [77, 3] (w:1, o:102, a:1, s:1, b:1),
% 2.34/2.74 alpha9 [78, 3] (w:1, o:103, a:1, s:1, b:1),
% 2.34/2.74 alpha10 [79, 3] (w:1, o:90, a:1, s:1, b:1),
% 2.34/2.74 alpha11 [80, 3] (w:1, o:91, a:1, s:1, b:1),
% 2.34/2.74 alpha12 [81, 2] (w:1, o:73, a:1, s:1, b:1),
% 2.34/2.74 alpha13 [82, 3] (w:1, o:92, a:1, s:1, b:1),
% 2.34/2.74 alpha14 [83, 3] (w:1, o:93, a:1, s:1, b:1),
% 2.34/2.74 alpha15 [84, 3] (w:1, o:94, a:1, s:1, b:1),
% 2.34/2.74 alpha16 [85, 2] (w:1, o:74, a:1, s:1, b:1),
% 2.34/2.74 alpha17 [86, 3] (w:1, o:95, a:1, s:1, b:1),
% 2.34/2.74 alpha18 [87, 3] (w:1, o:96, a:1, s:1, b:1),
% 2.34/2.74 alpha19 [88, 3] (w:1, o:97, a:1, s:1, b:1),
% 2.34/2.74 alpha20 [89, 3] (w:1, o:104, a:1, s:1, b:1),
% 2.34/2.74 alpha21 [90, 3] (w:1, o:105, a:1, s:1, b:1),
% 2.34/2.74 skol1 [91, 2] (w:1, o:75, a:1, s:1, b:1),
% 2.34/2.74 skol2 [92, 3] (w:1, o:82, a:1, s:1, b:1),
% 2.34/2.74 skol3 [93, 3] (w:1, o:83, a:1, s:1, b:1),
% 2.34/2.74 skol4 [94, 3] (w:1, o:84, a:1, s:1, b:1),
% 2.34/2.74 skol5 [95, 2] (w:1, o:76, a:1, s:1, b:1),
% 2.34/2.74 skol6 [96, 3] (w:1, o:85, a:1, s:1, b:1),
% 2.34/2.74 skol7 [97, 3] (w:1, o:86, a:1, s:1, b:1),
% 2.34/2.74 skol8 [98, 3] (w:1, o:87, a:1, s:1, b:1),
% 2.34/2.74 skol9 [99, 1] (w:1, o:35, a:1, s:1, b:1),
% 2.34/2.74 skol10 [100, 2] (w:1, o:77, a:1, s:1, b:1),
% 2.34/2.74 skol11 [101, 0] (w:1, o:21, a:1, s:1, b:1),
% 2.34/2.74 skol12 [102, 1] (w:1, o:36, a:1, s:1, b:1),
% 2.34/2.74 skol13 [103, 0] (w:1, o:22, a:1, s:1, b:1),
% 2.34/2.74 skol14 [104, 0] (w:1, o:23, a:1, s:1, b:1),
% 2.34/2.74 skol15 [105, 2] (w:1, o:78, a:1, s:1, b:1).
% 2.34/2.74
% 2.34/2.74
% 2.34/2.74 Starting Search:
% 2.34/2.74
% 2.34/2.74 *** allocated 15000 integers for clauses
% 2.34/2.74 *** allocated 22500 integers for clauses
% 2.34/2.74 *** allocated 33750 integers for clauses
% 2.34/2.74 *** allocated 15000 integers for termspace/termends
% 2.34/2.74 *** allocated 50625 integers for clauses
% 2.34/2.74 *** allocated 22500 integers for termspace/termends
% 2.34/2.74 Resimplifying inuse:
% 2.34/2.74 Done
% 2.34/2.74
% 2.34/2.74 *** allocated 75937 integers for clauses
% 2.34/2.74 *** allocated 33750 integers for termspace/termends
% 2.34/2.74 *** allocated 113905 integers for clauses
% 2.34/2.74
% 2.34/2.74 Intermediate Status:
% 2.34/2.74 Generated: 4117
% 2.34/2.74 Kept: 2009
% 2.34/2.74 Inuse: 193
% 2.34/2.74 Deleted: 5
% 2.34/2.74 Deletedinuse: 1
% 2.34/2.74
% 2.34/2.74 Resimplifying inuse:
% 2.34/2.74 Done
% 2.34/2.74
% 2.34/2.74 *** allocated 50625 integers for termspace/termends
% 2.34/2.74 *** allocated 170857 integers for clauses
% 2.34/2.74 Resimplifying inuse:
% 2.34/2.74 Done
% 2.34/2.74
% 2.34/2.74 *** allocated 75937 integers for termspace/termends
% 2.34/2.74
% 2.34/2.74 Intermediate Status:
% 2.34/2.74 Generated: 8805
% 2.34/2.74 Kept: 4013
% 2.34/2.74 Inuse: 330
% 2.34/2.74 Deleted: 9
% 2.34/2.74 Deletedinuse: 3
% 2.34/2.74
% 2.34/2.74 Resimplifying inuse:
% 2.34/2.74 Done
% 2.34/2.74
% 2.34/2.74 *** allocated 256285 integers for clauses
% 2.34/2.74 *** allocated 113905 integers for termspace/termends
% 2.34/2.74 Resimplifying inuse:
% 2.34/2.74 Done
% 2.34/2.74
% 2.34/2.74
% 2.34/2.74 Intermediate Status:
% 2.34/2.74 Generated: 15852
% 2.34/2.74 Kept: 6019
% 2.34/2.74 Inuse: 515
% 2.34/2.74 Deleted: 21
% 2.34/2.74 Deletedinuse: 6
% 2.34/2.74
% 2.34/2.74 Resimplifying inuse:
% 2.34/2.74 Done
% 2.34/2.74
% 2.34/2.74 *** allocated 384427 integers for clauses
% 2.34/2.74 Resimplifying inuse:
% 2.34/2.74 Done
% 2.34/2.74
% 2.34/2.74 *** allocated 170857 integers for termspace/termends
% 2.34/2.74
% 2.34/2.74 Intermediate Status:
% 2.34/2.74 Generated: 23535
% 2.34/2.74 Kept: 8134
% 2.34/2.74 Inuse: 624
% 2.34/2.74 Deleted: 37
% 2.34/2.74 Deletedinuse: 9
% 2.34/2.74
% 2.34/2.74 Resimplifying inuse:
% 2.34/2.74 Done
% 2.34/2.74
% 2.34/2.74 Resimplifying inuse:
% 2.34/2.74 Done
% 2.34/2.74
% 2.34/2.74 *** allocated 576640 integers for clauses
% 2.34/2.74
% 2.34/2.74 Intermediate Status:
% 2.34/2.74 Generated: 31304
% 2.34/2.74 Kept: 10145
% 2.34/2.74 Inuse: 764
% 2.34/2.74 Deleted: 46
% 2.34/2.74 Deletedinuse: 9
% 2.34/2.74
% 2.34/2.74 Resimplifying inuse:
% 2.34/2.74 Done
% 2.34/2.74
% 2.34/2.74 Resimplifying inuse:
% 2.34/2.74 Done
% 2.34/2.74
% 2.34/2.74 *** allocated 256285 integers for termspace/termends
% 2.34/2.74
% 2.34/2.74 Intermediate Status:
% 2.34/2.74 Generated: 37331
% 2.34/2.74 Kept: 12176
% 2.34/2.74 Inuse: 837
% 2.34/2.74 Deleted: 49
% 2.34/2.74 Deletedinuse: 9
% 2.34/2.74
% 2.34/2.74 Resimplifying inuse:
% 2.34/2.74 Done
% 2.34/2.74
% 2.34/2.74 Resimplifying inuse:
% 2.34/2.74 Done
% 2.34/2.74
% 2.34/2.74
% 2.34/2.74 Intermediate Status:
% 2.34/2.74 Generated: 52636
% 2.34/2.74 Kept: 14516
% 2.34/2.74 Inuse: 1159
% 2.34/2.74 Deleted: 69
% 2.34/2.74 Deletedinuse: 9
% 2.34/2.74
% 2.34/2.74 Resimplifying inuse:
% 2.34/2.74 Done
% 2.34/2.74
% 2.34/2.74 *** allocated 864960 integers for clauses
% 2.34/2.74 Resimplifying inuse:
% 2.34/2.74 Done
% 2.34/2.74
% 2.34/2.74
% 2.34/2.74 Intermediate Status:
% 2.34/2.74 Generated: 83215
% 2.34/2.74 Kept: 16553
% 2.34/2.74 Inuse: 1390
% 2.34/2.74 Deleted: 114
% 2.34/2.74 Deletedinuse: 41
% 2.34/2.74
% 2.34/2.74 Resimplifying inuse:
% 2.34/2.74 Done
% 2.34/2.74
% 2.34/2.74 *** allocated 384427 integers for termspace/termends
% 2.34/2.74 Resimplifying inuse:
% 2.34/2.74 Done
% 2.34/2.74
% 2.34/2.74
% 2.34/2.74 Intermediate Status:
% 2.34/2.74 Generated: 104129
% 2.34/2.74 Kept: 18569
% 2.34/2.74 Inuse: 1525
% 2.34/2.74 Deleted: 121
% 2.34/2.74 Deletedinuse: 45
% 2.34/2.74
% 2.34/2.74 Resimplifying inuse:
% 2.34/2.74 Done
% 2.34/2.74
% 2.34/2.74 Resimplifying inuse:
% 2.34/2.74 Done
% 2.34/2.74
% 2.34/2.74 Resimplifying clauses:
% 2.34/2.74
% 2.34/2.74 Bliksems!, er is een bewijs:
% 2.34/2.74 % SZS status Theorem
% 2.34/2.74 % SZS output start Refutation
% 2.34/2.74
% 2.34/2.74 (99) {G0,W17,D3,L3,V3,M3} I { ! path( Y, Z, X ), alpha14( X, skol9( X ),
% 2.34/2.74 skol12( X ) ), number_of_in( triangles, X ) ==> number_of_in(
% 2.34/2.74 sequential_pairs, X ) }.
% 2.34/2.74 (100) {G0,W17,D3,L3,V4,M3} I { ! path( Y, Z, X ), ! triangle( skol9( X ),
% 2.34/2.74 skol12( X ), T ), number_of_in( triangles, X ) ==> number_of_in(
% 2.34/2.74 sequential_pairs, X ) }.
% 2.34/2.74 (101) {G0,W7,D2,L2,V3,M2} I { ! alpha14( X, Y, Z ), on_path( Y, X ) }.
% 2.34/2.74 (102) {G0,W7,D2,L2,V3,M2} I { ! alpha14( X, Y, Z ), on_path( Z, X ) }.
% 2.34/2.74 (103) {G0,W7,D2,L2,V3,M2} I { ! alpha14( X, Y, Z ), sequential( Y, Z ) }.
% 2.34/2.74 (108) {G0,W4,D2,L1,V0,M1} I { path( skol13, skol14, skol11 ) }.
% 2.34/2.74 (109) {G0,W15,D3,L4,V2,M4} I { ! on_path( X, skol11 ), ! on_path( Y, skol11
% 2.34/2.74 ), ! sequential( X, Y ), triangle( X, Y, skol15( X, Y ) ) }.
% 2.34/2.74 (110) {G0,W7,D3,L1,V0,M1} I { ! number_of_in( triangles, skol11 ) ==>
% 2.34/2.74 number_of_in( sequential_pairs, skol11 ) }.
% 2.34/2.74 (4735) {G1,W6,D3,L1,V0,M1} R(99,108);r(110) { alpha14( skol11, skol9(
% 2.34/2.74 skol11 ), skol12( skol11 ) ) }.
% 2.34/2.74 (4768) {G2,W4,D3,L1,V0,M1} R(4735,101) { on_path( skol9( skol11 ), skol11 )
% 2.34/2.74 }.
% 2.34/2.74 (4769) {G2,W4,D3,L1,V0,M1} R(4735,102) { on_path( skol12( skol11 ), skol11
% 2.34/2.74 ) }.
% 2.34/2.74 (4775) {G2,W5,D3,L1,V0,M1} R(4735,103) { sequential( skol9( skol11 ),
% 2.34/2.74 skol12( skol11 ) ) }.
% 2.34/2.74 (4877) {G1,W6,D3,L1,V1,M1} R(100,108);r(110) { ! triangle( skol9( skol11 )
% 2.34/2.74 , skol12( skol11 ), X ) }.
% 2.34/2.74 (5225) {G3,W9,D3,L2,V0,M2} R(4877,109);r(4768) { ! on_path( skol12( skol11
% 2.34/2.74 ), skol11 ), ! sequential( skol9( skol11 ), skol12( skol11 ) ) }.
% 2.34/2.74 (20216) {G4,W0,D0,L0,V0,M0} S(5225);r(4769);r(4775) { }.
% 2.34/2.74
% 2.34/2.74
% 2.34/2.74 % SZS output end Refutation
% 2.34/2.74 found a proof!
% 2.34/2.74
% 2.34/2.74
% 2.34/2.74 Unprocessed initial clauses:
% 2.34/2.74
% 2.34/2.74 (20218) {G0,W7,D3,L2,V1,M2} { ! edge( X ), ! head_of( X ) = tail_of( X )
% 2.34/2.74 }.
% 2.34/2.74 (20219) {G0,W5,D3,L2,V1,M2} { ! edge( X ), vertex( head_of( X ) ) }.
% 2.34/2.74 (20220) {G0,W5,D3,L2,V1,M2} { ! edge( X ), vertex( tail_of( X ) ) }.
% 2.34/2.74 (20221) {G0,W12,D3,L5,V4,M5} { ! complete, ! vertex( X ), ! vertex( Y ), X
% 2.34/2.74 = Y, edge( skol1( Z, T ) ) }.
% 2.34/2.74 (20222) {G0,W20,D3,L6,V2,M6} { ! complete, ! vertex( X ), ! vertex( Y ), X
% 2.34/2.74 = Y, alpha11( X, Y, skol1( X, Y ) ), alpha15( X, Y, skol1( X, Y ) ) }.
% 2.34/2.74 (20223) {G0,W8,D3,L2,V3,M2} { ! alpha15( X, Y, Z ), Y = head_of( Z ) }.
% 2.34/2.74 (20224) {G0,W8,D3,L2,V3,M2} { ! alpha15( X, Y, Z ), X = tail_of( Z ) }.
% 2.34/2.74 (20225) {G0,W8,D2,L2,V3,M2} { ! alpha15( X, Y, Z ), ! alpha1( X, Y, Z )
% 2.34/2.74 }.
% 2.34/2.74 (20226) {G0,W16,D3,L4,V3,M4} { ! Y = head_of( Z ), ! X = tail_of( Z ),
% 2.34/2.74 alpha1( X, Y, Z ), alpha15( X, Y, Z ) }.
% 2.34/2.74 (20227) {G0,W8,D2,L2,V3,M2} { ! alpha11( X, Y, Z ), alpha1( X, Y, Z ) }.
% 2.34/2.74 (20228) {G0,W12,D3,L3,V3,M3} { ! alpha11( X, Y, Z ), ! Y = head_of( Z ), !
% 2.34/2.74 X = tail_of( Z ) }.
% 2.34/2.74 (20229) {G0,W12,D3,L3,V3,M3} { ! alpha1( X, Y, Z ), Y = head_of( Z ),
% 2.34/2.74 alpha11( X, Y, Z ) }.
% 2.34/2.74 (20230) {G0,W12,D3,L3,V3,M3} { ! alpha1( X, Y, Z ), X = tail_of( Z ),
% 2.34/2.74 alpha11( X, Y, Z ) }.
% 2.34/2.74 (20231) {G0,W8,D3,L2,V3,M2} { ! alpha1( X, Y, Z ), X = head_of( Z ) }.
% 2.34/2.74 (20232) {G0,W8,D3,L2,V3,M2} { ! alpha1( X, Y, Z ), Y = tail_of( Z ) }.
% 2.34/2.74 (20233) {G0,W12,D3,L3,V3,M3} { ! X = head_of( Z ), ! Y = tail_of( Z ),
% 2.34/2.74 alpha1( X, Y, Z ) }.
% 2.34/2.74 (20234) {G0,W23,D3,L7,V4,M7} { ! vertex( X ), ! vertex( Y ), ! edge( T ),
% 2.34/2.74 ! X = tail_of( T ), ! Y = head_of( T ), ! Z = path_cons( T, empty ), path
% 2.34/2.74 ( X, Y, Z ) }.
% 2.34/2.74 (20235) {G0,W24,D3,L7,V5,M7} { ! vertex( X ), ! vertex( Y ), ! edge( T ),
% 2.34/2.74 ! X = tail_of( T ), ! path( head_of( T ), Y, U ), ! Z = path_cons( T, U )
% 2.34/2.74 , path( X, Y, Z ) }.
% 2.34/2.74 (20236) {G0,W7,D2,L2,V3,M2} { ! path( X, Y, Z ), alpha12( X, Y ) }.
% 2.34/2.74 (20237) {G0,W10,D3,L2,V5,M2} { ! path( X, Y, Z ), alpha16( X, skol2( X, T
% 2.34/2.74 , U ) ) }.
% 2.34/2.74 (20238) {G0,W11,D3,L2,V3,M2} { ! path( X, Y, Z ), alpha20( Y, Z, skol2( X
% 2.34/2.74 , Y, Z ) ) }.
% 2.34/2.74 (20239) {G0,W12,D2,L3,V3,M3} { ! alpha20( X, Y, Z ), alpha18( X, Y, Z ),
% 2.34/2.74 alpha21( X, Y, Z ) }.
% 2.34/2.74 (20240) {G0,W8,D2,L2,V3,M2} { ! alpha18( X, Y, Z ), alpha20( X, Y, Z ) }.
% 2.34/2.74 (20241) {G0,W8,D2,L2,V3,M2} { ! alpha21( X, Y, Z ), alpha20( X, Y, Z ) }.
% 2.34/2.74 (20242) {G0,W12,D4,L2,V4,M2} { ! alpha21( X, Y, Z ), Y = path_cons( Z,
% 2.34/2.74 skol3( T, Y, Z ) ) }.
% 2.34/2.74 (20243) {G0,W12,D3,L2,V3,M2} { ! alpha21( X, Y, Z ), path( head_of( Z ), X
% 2.34/2.74 , skol3( X, Y, Z ) ) }.
% 2.34/2.74 (20244) {G0,W8,D2,L2,V3,M2} { ! alpha21( X, Y, Z ), ! alpha2( X, Y, Z )
% 2.34/2.74 }.
% 2.34/2.74 (20245) {G0,W18,D3,L4,V4,M4} { ! path( head_of( Z ), X, T ), ! Y =
% 2.34/2.74 path_cons( Z, T ), alpha2( X, Y, Z ), alpha21( X, Y, Z ) }.
% 2.34/2.74 (20246) {G0,W8,D2,L2,V3,M2} { ! alpha18( X, Y, Z ), alpha2( X, Y, Z ) }.
% 2.34/2.74 (20247) {G0,W14,D3,L3,V4,M3} { ! alpha18( X, Y, Z ), ! path( head_of( Z )
% 2.34/2.74 , X, T ), ! Y = path_cons( Z, T ) }.
% 2.34/2.74 (20248) {G0,W16,D4,L3,V4,M3} { ! alpha2( X, Y, Z ), Y = path_cons( Z,
% 2.34/2.74 skol4( T, Y, Z ) ), alpha18( X, Y, Z ) }.
% 2.34/2.74 (20249) {G0,W16,D3,L3,V3,M3} { ! alpha2( X, Y, Z ), path( head_of( Z ), X
% 2.34/2.74 , skol4( X, Y, Z ) ), alpha18( X, Y, Z ) }.
% 2.34/2.74 (20250) {G0,W5,D2,L2,V2,M2} { ! alpha16( X, Y ), edge( Y ) }.
% 2.34/2.74 (20251) {G0,W7,D3,L2,V2,M2} { ! alpha16( X, Y ), X = tail_of( Y ) }.
% 2.34/2.74 (20252) {G0,W9,D3,L3,V2,M3} { ! edge( Y ), ! X = tail_of( Y ), alpha16( X
% 2.34/2.74 , Y ) }.
% 2.34/2.74 (20253) {G0,W5,D2,L2,V2,M2} { ! alpha12( X, Y ), vertex( X ) }.
% 2.34/2.74 (20254) {G0,W5,D2,L2,V2,M2} { ! alpha12( X, Y ), vertex( Y ) }.
% 2.34/2.74 (20255) {G0,W7,D2,L3,V2,M3} { ! vertex( X ), ! vertex( Y ), alpha12( X, Y
% 2.34/2.74 ) }.
% 2.34/2.74 (20256) {G0,W8,D3,L2,V3,M2} { ! alpha2( X, Y, Z ), X = head_of( Z ) }.
% 2.34/2.74 (20257) {G0,W9,D3,L2,V3,M2} { ! alpha2( X, Y, Z ), Y = path_cons( Z, empty
% 2.34/2.74 ) }.
% 2.34/2.74 (20258) {G0,W13,D3,L3,V3,M3} { ! X = head_of( Z ), ! Y = path_cons( Z,
% 2.34/2.74 empty ), alpha2( X, Y, Z ) }.
% 2.34/2.74 (20259) {G0,W9,D2,L3,V4,M3} { ! path( Z, T, X ), ! on_path( Y, X ), edge(
% 2.34/2.74 Y ) }.
% 2.34/2.74 (20260) {G0,W11,D3,L3,V4,M3} { ! path( Z, T, X ), ! on_path( Y, X ),
% 2.34/2.74 in_path( head_of( Y ), X ) }.
% 2.34/2.74 (20261) {G0,W11,D3,L3,V4,M3} { ! path( Z, T, X ), ! on_path( Y, X ),
% 2.34/2.74 in_path( tail_of( Y ), X ) }.
% 2.34/2.74 (20262) {G0,W9,D2,L3,V4,M3} { ! path( Z, T, X ), ! in_path( Y, X ), vertex
% 2.34/2.74 ( Y ) }.
% 2.34/2.74 (20263) {G0,W19,D4,L4,V5,M4} { ! path( Z, T, X ), ! in_path( Y, X ), Y =
% 2.34/2.74 head_of( skol5( U, Y ) ), Y = tail_of( skol5( U, Y ) ) }.
% 2.34/2.74 (20264) {G0,W12,D3,L3,V4,M3} { ! path( Z, T, X ), ! in_path( Y, X ),
% 2.34/2.74 on_path( skol5( X, Y ), X ) }.
% 2.34/2.74 (20265) {G0,W5,D2,L2,V2,M2} { ! sequential( X, Y ), edge( X ) }.
% 2.34/2.74 (20266) {G0,W6,D2,L2,V2,M2} { ! sequential( X, Y ), alpha3( X, Y ) }.
% 2.34/2.74 (20267) {G0,W8,D2,L3,V2,M3} { ! edge( X ), ! alpha3( X, Y ), sequential( X
% 2.34/2.74 , Y ) }.
% 2.34/2.74 (20268) {G0,W5,D2,L2,V2,M2} { ! alpha3( X, Y ), edge( Y ) }.
% 2.34/2.74 (20269) {G0,W6,D2,L2,V2,M2} { ! alpha3( X, Y ), alpha6( X, Y ) }.
% 2.34/2.74 (20270) {G0,W8,D2,L3,V2,M3} { ! edge( Y ), ! alpha6( X, Y ), alpha3( X, Y
% 2.34/2.74 ) }.
% 2.34/2.74 (20271) {G0,W6,D2,L2,V2,M2} { ! alpha6( X, Y ), ! X = Y }.
% 2.34/2.74 (20272) {G0,W8,D3,L2,V2,M2} { ! alpha6( X, Y ), head_of( X ) = tail_of( Y
% 2.34/2.74 ) }.
% 2.34/2.74 (20273) {G0,W11,D3,L3,V2,M3} { X = Y, ! head_of( X ) = tail_of( Y ),
% 2.34/2.74 alpha6( X, Y ) }.
% 2.34/2.74 (20274) {G0,W17,D2,L5,V5,M5} { ! path( Y, Z, X ), ! on_path( T, X ), !
% 2.34/2.74 on_path( U, X ), ! sequential( T, U ), precedes( T, U, X ) }.
% 2.34/2.74 (20275) {G0,W21,D2,L6,V6,M6} { ! path( Y, Z, X ), ! on_path( T, X ), !
% 2.34/2.74 on_path( U, X ), ! sequential( T, W ), ! precedes( W, U, X ), precedes( T
% 2.34/2.74 , U, X ) }.
% 2.34/2.74 (20276) {G0,W12,D2,L3,V5,M3} { ! path( Y, Z, X ), ! precedes( T, U, X ),
% 2.34/2.74 alpha13( X, T, U ) }.
% 2.34/2.74 (20277) {G0,W16,D2,L4,V5,M4} { ! path( Y, Z, X ), ! precedes( T, U, X ),
% 2.34/2.74 alpha17( X, T, U ), alpha19( X, T, U ) }.
% 2.34/2.74 (20278) {G0,W10,D3,L2,V5,M2} { ! alpha19( X, Y, Z ), sequential( Y, skol6
% 2.34/2.74 ( T, Y, U ) ) }.
% 2.34/2.74 (20279) {G0,W11,D3,L2,V3,M2} { ! alpha19( X, Y, Z ), precedes( skol6( X, Y
% 2.34/2.74 , Z ), Z, X ) }.
% 2.34/2.74 (20280) {G0,W7,D2,L2,V3,M2} { ! alpha19( X, Y, Z ), ! sequential( Y, Z )
% 2.34/2.74 }.
% 2.34/2.74 (20281) {G0,W14,D2,L4,V4,M4} { ! sequential( Y, T ), ! precedes( T, Z, X )
% 2.34/2.74 , sequential( Y, Z ), alpha19( X, Y, Z ) }.
% 2.34/2.74 (20282) {G0,W7,D2,L2,V3,M2} { ! alpha17( X, Y, Z ), sequential( Y, Z ) }.
% 2.34/2.74 (20283) {G0,W11,D2,L3,V4,M3} { ! alpha17( X, Y, Z ), ! sequential( Y, T )
% 2.34/2.74 , ! precedes( T, Z, X ) }.
% 2.34/2.74 (20284) {G0,W13,D3,L3,V5,M3} { ! sequential( Y, Z ), sequential( Y, skol7
% 2.34/2.74 ( T, Y, U ) ), alpha17( X, Y, Z ) }.
% 2.34/2.74 (20285) {G0,W14,D3,L3,V3,M3} { ! sequential( Y, Z ), precedes( skol7( X, Y
% 2.34/2.74 , Z ), Z, X ), alpha17( X, Y, Z ) }.
% 2.34/2.74 (20286) {G0,W7,D2,L2,V3,M2} { ! alpha13( X, Y, Z ), on_path( Y, X ) }.
% 2.34/2.74 (20287) {G0,W7,D2,L2,V3,M2} { ! alpha13( X, Y, Z ), on_path( Z, X ) }.
% 2.34/2.74 (20288) {G0,W10,D2,L3,V3,M3} { ! on_path( Y, X ), ! on_path( Z, X ),
% 2.34/2.74 alpha13( X, Y, Z ) }.
% 2.34/2.74 (20289) {G0,W8,D2,L2,V3,M2} { ! shortest_path( X, Y, Z ), path( X, Y, Z )
% 2.34/2.74 }.
% 2.34/2.74 (20290) {G0,W8,D2,L2,V3,M2} { ! shortest_path( X, Y, Z ), alpha4( X, Y, Z
% 2.34/2.74 ) }.
% 2.34/2.74 (20291) {G0,W12,D2,L3,V3,M3} { ! path( X, Y, Z ), ! alpha4( X, Y, Z ),
% 2.34/2.74 shortest_path( X, Y, Z ) }.
% 2.34/2.74 (20292) {G0,W7,D2,L2,V3,M2} { ! alpha4( X, Y, Z ), ! X = Y }.
% 2.34/2.74 (20293) {G0,W8,D2,L2,V3,M2} { ! alpha4( X, Y, Z ), alpha7( X, Y, Z ) }.
% 2.34/2.74 (20294) {G0,W11,D2,L3,V3,M3} { X = Y, ! alpha7( X, Y, Z ), alpha4( X, Y, Z
% 2.34/2.74 ) }.
% 2.34/2.74 (20295) {G0,W13,D3,L3,V4,M3} { ! alpha7( X, Y, Z ), ! path( X, Y, T ),
% 2.34/2.74 less_or_equal( length_of( Z ), length_of( T ) ) }.
% 2.34/2.74 (20296) {G0,W12,D4,L2,V5,M2} { ! less_or_equal( length_of( Z ), length_of
% 2.34/2.74 ( skol8( T, U, Z ) ) ), alpha7( X, Y, Z ) }.
% 2.34/2.74 (20297) {G0,W11,D3,L2,V3,M2} { path( X, Y, skol8( X, Y, Z ) ), alpha7( X,
% 2.34/2.74 Y, Z ) }.
% 2.34/2.74 (20298) {G0,W18,D3,L4,V6,M4} { ! shortest_path( T, U, Z ), ! precedes( X,
% 2.34/2.74 Y, Z ), ! tail_of( W ) = tail_of( X ), ! head_of( W ) = head_of( Y ) }.
% 2.34/2.74 (20299) {G0,W12,D2,L3,V5,M3} { ! shortest_path( T, U, Z ), ! precedes( X,
% 2.34/2.74 Y, Z ), ! precedes( Y, X, Z ) }.
% 2.34/2.74 (20300) {G0,W6,D2,L2,V3,M2} { ! triangle( X, Y, Z ), edge( X ) }.
% 2.34/2.74 (20301) {G0,W8,D2,L2,V3,M2} { ! triangle( X, Y, Z ), alpha5( X, Y, Z ) }.
% 2.34/2.74 (20302) {G0,W10,D2,L3,V3,M3} { ! edge( X ), ! alpha5( X, Y, Z ), triangle
% 2.34/2.74 ( X, Y, Z ) }.
% 2.34/2.74 (20303) {G0,W6,D2,L2,V3,M2} { ! alpha5( X, Y, Z ), edge( Y ) }.
% 2.34/2.74 (20304) {G0,W8,D2,L2,V3,M2} { ! alpha5( X, Y, Z ), alpha8( X, Y, Z ) }.
% 2.34/2.74 (20305) {G0,W10,D2,L3,V3,M3} { ! edge( Y ), ! alpha8( X, Y, Z ), alpha5( X
% 2.34/2.74 , Y, Z ) }.
% 2.34/2.74 (20306) {G0,W6,D2,L2,V3,M2} { ! alpha8( X, Y, Z ), edge( Z ) }.
% 2.34/2.74 (20307) {G0,W8,D2,L2,V3,M2} { ! alpha8( X, Y, Z ), alpha9( X, Y, Z ) }.
% 2.34/2.74 (20308) {G0,W10,D2,L3,V3,M3} { ! edge( Z ), ! alpha9( X, Y, Z ), alpha8( X
% 2.34/2.74 , Y, Z ) }.
% 2.34/2.74 (20309) {G0,W7,D2,L2,V3,M2} { ! alpha9( X, Y, Z ), sequential( X, Y ) }.
% 2.34/2.74 (20310) {G0,W8,D2,L2,V3,M2} { ! alpha9( X, Y, Z ), alpha10( X, Y, Z ) }.
% 2.34/2.74 (20311) {G0,W11,D2,L3,V3,M3} { ! sequential( X, Y ), ! alpha10( X, Y, Z )
% 2.34/2.74 , alpha9( X, Y, Z ) }.
% 2.34/2.74 (20312) {G0,W7,D2,L2,V3,M2} { ! alpha10( X, Y, Z ), sequential( Y, Z ) }.
% 2.34/2.74 (20313) {G0,W7,D2,L2,V3,M2} { ! alpha10( X, Y, Z ), sequential( Z, X ) }.
% 2.34/2.74 (20314) {G0,W10,D2,L3,V3,M3} { ! sequential( Y, Z ), ! sequential( Z, X )
% 2.34/2.74 , alpha10( X, Y, Z ) }.
% 2.34/2.74 (20315) {G0,W10,D3,L2,V3,M2} { ! path( Y, Z, X ), length_of( X ) =
% 2.34/2.74 number_of_in( edges, X ) }.
% 2.34/2.74 (20316) {G0,W12,D4,L2,V3,M2} { ! path( Y, Z, X ), number_of_in(
% 2.34/2.74 sequential_pairs, X ) = minus( length_of( X ), n1 ) }.
% 2.34/2.74 (20317) {G0,W17,D3,L3,V3,M3} { ! path( Y, Z, X ), alpha14( X, skol9( X ),
% 2.34/2.74 skol12( X ) ), number_of_in( sequential_pairs, X ) = number_of_in(
% 2.34/2.74 triangles, X ) }.
% 2.34/2.74 (20318) {G0,W17,D3,L3,V4,M3} { ! path( Y, Z, X ), ! triangle( skol9( X ),
% 2.34/2.74 skol12( X ), T ), number_of_in( sequential_pairs, X ) = number_of_in(
% 2.34/2.74 triangles, X ) }.
% 2.34/2.74 (20319) {G0,W7,D2,L2,V3,M2} { ! alpha14( X, Y, Z ), on_path( Y, X ) }.
% 2.34/2.74 (20320) {G0,W7,D2,L2,V3,M2} { ! alpha14( X, Y, Z ), on_path( Z, X ) }.
% 2.34/2.74 (20321) {G0,W7,D2,L2,V3,M2} { ! alpha14( X, Y, Z ), sequential( Y, Z ) }.
% 2.34/2.74 (20322) {G0,W13,D2,L4,V3,M4} { ! on_path( Y, X ), ! on_path( Z, X ), !
% 2.34/2.74 sequential( Y, Z ), alpha14( X, Y, Z ) }.
% 2.34/2.74 (20323) {G0,W7,D3,L1,V2,M1} { less_or_equal( number_of_in( X, Y ),
% 2.34/2.74 number_of_in( X, graph ) ) }.
% 2.34/2.74 (20324) {G0,W18,D3,L5,V5,M5} { ! complete, ! shortest_path( T, U, Z ), !
% 2.34/2.74 precedes( X, Y, Z ), ! sequential( X, Y ), triangle( X, Y, skol10( X, Y )
% 2.34/2.74 ) }.
% 2.34/2.74 (20325) {G0,W1,D1,L1,V0,M1} { complete }.
% 2.34/2.74 (20326) {G0,W4,D2,L1,V0,M1} { path( skol13, skol14, skol11 ) }.
% 2.34/2.74 (20327) {G0,W15,D3,L4,V2,M4} { ! on_path( X, skol11 ), ! on_path( Y,
% 2.34/2.74 skol11 ), ! sequential( X, Y ), triangle( X, Y, skol15( X, Y ) ) }.
% 2.34/2.74 (20328) {G0,W7,D3,L1,V0,M1} { ! number_of_in( sequential_pairs, skol11 ) =
% 2.34/2.74 number_of_in( triangles, skol11 ) }.
% 2.34/2.74
% 2.34/2.74
% 2.34/2.74 Total Proof:
% 2.34/2.74
% 2.34/2.74 eqswap: (20434) {G0,W17,D3,L3,V3,M3} { number_of_in( triangles, X ) =
% 2.34/2.74 number_of_in( sequential_pairs, X ), ! path( Y, Z, X ), alpha14( X, skol9
% 2.34/2.74 ( X ), skol12( X ) ) }.
% 2.34/2.74 parent0[2]: (20317) {G0,W17,D3,L3,V3,M3} { ! path( Y, Z, X ), alpha14( X,
% 2.34/2.74 skol9( X ), skol12( X ) ), number_of_in( sequential_pairs, X ) =
% 2.34/2.74 number_of_in( triangles, X ) }.
% 2.34/2.74 substitution0:
% 2.34/2.74 X := X
% 2.34/2.74 Y := Y
% 2.34/2.74 Z := Z
% 2.34/2.74 end
% 2.34/2.74
% 2.34/2.74 subsumption: (99) {G0,W17,D3,L3,V3,M3} I { ! path( Y, Z, X ), alpha14( X,
% 2.34/2.74 skol9( X ), skol12( X ) ), number_of_in( triangles, X ) ==> number_of_in
% 2.34/2.74 ( sequential_pairs, X ) }.
% 2.34/2.74 parent0: (20434) {G0,W17,D3,L3,V3,M3} { number_of_in( triangles, X ) =
% 2.34/2.74 number_of_in( sequential_pairs, X ), ! path( Y, Z, X ), alpha14( X, skol9
% 2.34/2.74 ( X ), skol12( X ) ) }.
% 2.34/2.74 substitution0:
% 2.34/2.74 X := X
% 2.34/2.74 Y := Y
% 2.34/2.74 Z := Z
% 2.34/2.74 end
% 2.34/2.74 permutation0:
% 2.34/2.74 0 ==> 2
% 2.34/2.74 1 ==> 0
% 2.34/2.74 2 ==> 1
% 2.34/2.74 end
% 2.34/2.74
% 2.34/2.74 eqswap: (20541) {G0,W17,D3,L3,V4,M3} { number_of_in( triangles, X ) =
% 2.34/2.74 number_of_in( sequential_pairs, X ), ! path( Y, Z, X ), ! triangle( skol9
% 2.34/2.74 ( X ), skol12( X ), T ) }.
% 2.34/2.74 parent0[2]: (20318) {G0,W17,D3,L3,V4,M3} { ! path( Y, Z, X ), ! triangle(
% 2.34/2.74 skol9( X ), skol12( X ), T ), number_of_in( sequential_pairs, X ) =
% 2.34/2.74 number_of_in( triangles, X ) }.
% 2.34/2.74 substitution0:
% 2.34/2.74 X := X
% 2.34/2.74 Y := Y
% 2.34/2.74 Z := Z
% 2.34/2.74 T := T
% 2.34/2.74 end
% 2.34/2.74
% 2.34/2.74 subsumption: (100) {G0,W17,D3,L3,V4,M3} I { ! path( Y, Z, X ), ! triangle(
% 2.34/2.74 skol9( X ), skol12( X ), T ), number_of_in( triangles, X ) ==>
% 2.34/2.74 number_of_in( sequential_pairs, X ) }.
% 2.34/2.74 parent0: (20541) {G0,W17,D3,L3,V4,M3} { number_of_in( triangles, X ) =
% 2.34/2.74 number_of_in( sequential_pairs, X ), ! path( Y, Z, X ), ! triangle( skol9
% 2.34/2.74 ( X ), skol12( X ), T ) }.
% 2.34/2.74 substitution0:
% 2.34/2.74 X := X
% 2.34/2.74 Y := Y
% 2.34/2.74 Z := Z
% 2.34/2.74 T := T
% 2.34/2.74 end
% 2.34/2.74 permutation0:
% 2.34/2.74 0 ==> 2
% 2.34/2.74 1 ==> 0
% 2.34/2.74 2 ==> 1
% 2.34/2.74 end
% 2.34/2.74
% 2.34/2.74 subsumption: (101) {G0,W7,D2,L2,V3,M2} I { ! alpha14( X, Y, Z ), on_path( Y
% 2.34/2.74 , X ) }.
% 2.34/2.74 parent0: (20319) {G0,W7,D2,L2,V3,M2} { ! alpha14( X, Y, Z ), on_path( Y, X
% 2.34/2.74 ) }.
% 2.34/2.74 substitution0:
% 2.34/2.74 X := X
% 2.34/2.74 Y := Y
% 2.34/2.74 Z := Z
% 2.34/2.74 end
% 2.34/2.74 permutation0:
% 2.34/2.74 0 ==> 0
% 2.34/2.74 1 ==> 1
% 2.34/2.74 end
% 2.34/2.74
% 2.34/2.74 subsumption: (102) {G0,W7,D2,L2,V3,M2} I { ! alpha14( X, Y, Z ), on_path( Z
% 2.34/2.74 , X ) }.
% 2.34/2.74 parent0: (20320) {G0,W7,D2,L2,V3,M2} { ! alpha14( X, Y, Z ), on_path( Z, X
% 2.34/2.74 ) }.
% 2.34/2.74 substitution0:
% 2.34/2.74 X := X
% 2.34/2.74 Y := Y
% 2.34/2.74 Z := Z
% 2.34/2.74 end
% 2.34/2.74 permutation0:
% 2.34/2.74 0 ==> 0
% 2.34/2.74 1 ==> 1
% 2.34/2.74 end
% 2.34/2.74
% 2.34/2.74 subsumption: (103) {G0,W7,D2,L2,V3,M2} I { ! alpha14( X, Y, Z ), sequential
% 2.34/2.74 ( Y, Z ) }.
% 2.34/2.74 parent0: (20321) {G0,W7,D2,L2,V3,M2} { ! alpha14( X, Y, Z ), sequential( Y
% 2.34/2.74 , Z ) }.
% 2.34/2.74 substitution0:
% 2.34/2.74 X := X
% 2.34/2.74 Y := Y
% 2.34/2.74 Z := Z
% 2.34/2.74 end
% 2.34/2.74 permutation0:
% 2.34/2.74 0 ==> 0
% 2.34/2.74 1 ==> 1
% 2.34/2.74 end
% 2.34/2.74
% 2.34/2.74 subsumption: (108) {G0,W4,D2,L1,V0,M1} I { path( skol13, skol14, skol11 )
% 2.34/2.74 }.
% 2.34/2.74 parent0: (20326) {G0,W4,D2,L1,V0,M1} { path( skol13, skol14, skol11 ) }.
% 2.34/2.74 substitution0:
% 2.34/2.74 end
% 2.34/2.74 permutation0:
% 2.34/2.74 0 ==> 0
% 2.34/2.74 end
% 2.34/2.74
% 2.34/2.74 subsumption: (109) {G0,W15,D3,L4,V2,M4} I { ! on_path( X, skol11 ), !
% 2.34/2.74 on_path( Y, skol11 ), ! sequential( X, Y ), triangle( X, Y, skol15( X, Y
% 2.34/2.74 ) ) }.
% 2.34/2.74 parent0: (20327) {G0,W15,D3,L4,V2,M4} { ! on_path( X, skol11 ), ! on_path
% 2.34/2.74 ( Y, skol11 ), ! sequential( X, Y ), triangle( X, Y, skol15( X, Y ) ) }.
% 2.34/2.74 substitution0:
% 2.34/2.74 X := X
% 2.34/2.74 Y := Y
% 2.34/2.74 end
% 2.34/2.74 permutation0:
% 2.34/2.74 0 ==> 0
% 2.34/2.74 1 ==> 1
% 2.34/2.74 2 ==> 2
% 2.34/2.74 3 ==> 3
% 2.34/2.74 end
% 2.34/2.74
% 2.34/2.74 eqswap: (21189) {G0,W7,D3,L1,V0,M1} { ! number_of_in( triangles, skol11 )
% 2.34/2.74 = number_of_in( sequential_pairs, skol11 ) }.
% 2.34/2.74 parent0[0]: (20328) {G0,W7,D3,L1,V0,M1} { ! number_of_in( sequential_pairs
% 2.34/2.74 , skol11 ) = number_of_in( triangles, skol11 ) }.
% 2.34/2.74 substitution0:
% 2.34/2.74 end
% 2.34/2.74
% 2.34/2.74 subsumption: (110) {G0,W7,D3,L1,V0,M1} I { ! number_of_in( triangles,
% 2.34/2.74 skol11 ) ==> number_of_in( sequential_pairs, skol11 ) }.
% 2.34/2.74 parent0: (21189) {G0,W7,D3,L1,V0,M1} { ! number_of_in( triangles, skol11 )
% 2.34/2.74 = number_of_in( sequential_pairs, skol11 ) }.
% 2.34/2.74 substitution0:
% 2.34/2.74 end
% 2.34/2.74 permutation0:
% 2.34/2.74 0 ==> 0
% 2.34/2.74 end
% 2.34/2.74
% 2.34/2.74 eqswap: (21190) {G0,W17,D3,L3,V3,M3} { number_of_in( sequential_pairs, X )
% 2.34/2.74 ==> number_of_in( triangles, X ), ! path( Y, Z, X ), alpha14( X, skol9(
% 2.34/2.74 X ), skol12( X ) ) }.
% 2.34/2.74 parent0[2]: (99) {G0,W17,D3,L3,V3,M3} I { ! path( Y, Z, X ), alpha14( X,
% 2.34/2.74 skol9( X ), skol12( X ) ), number_of_in( triangles, X ) ==> number_of_in
% 2.34/2.74 ( sequential_pairs, X ) }.
% 2.34/2.74 substitution0:
% 2.34/2.74 X := X
% 2.34/2.74 Y := Y
% 2.34/2.74 Z := Z
% 2.34/2.74 end
% 2.34/2.74
% 2.34/2.74 eqswap: (21191) {G0,W7,D3,L1,V0,M1} { ! number_of_in( sequential_pairs,
% 2.34/2.74 skol11 ) ==> number_of_in( triangles, skol11 ) }.
% 2.34/2.74 parent0[0]: (110) {G0,W7,D3,L1,V0,M1} I { ! number_of_in( triangles, skol11
% 2.34/2.74 ) ==> number_of_in( sequential_pairs, skol11 ) }.
% 2.34/2.74 substitution0:
% 2.34/2.74 end
% 2.34/2.74
% 2.34/2.74 resolution: (21192) {G1,W13,D3,L2,V0,M2} { number_of_in( sequential_pairs
% 2.34/2.74 , skol11 ) ==> number_of_in( triangles, skol11 ), alpha14( skol11, skol9
% 2.34/2.74 ( skol11 ), skol12( skol11 ) ) }.
% 2.34/2.74 parent0[1]: (21190) {G0,W17,D3,L3,V3,M3} { number_of_in( sequential_pairs
% 2.34/2.74 , X ) ==> number_of_in( triangles, X ), ! path( Y, Z, X ), alpha14( X,
% 2.34/2.74 skol9( X ), skol12( X ) ) }.
% 2.34/2.74 parent1[0]: (108) {G0,W4,D2,L1,V0,M1} I { path( skol13, skol14, skol11 )
% 2.34/2.74 }.
% 2.34/2.74 substitution0:
% 2.34/2.74 X := skol11
% 2.34/2.74 Y := skol13
% 2.34/2.74 Z := skol14
% 2.34/2.74 end
% 2.34/2.74 substitution1:
% 2.34/2.74 end
% 2.34/2.74
% 2.34/2.74 resolution: (21193) {G1,W6,D3,L1,V0,M1} { alpha14( skol11, skol9( skol11 )
% 2.34/2.74 , skol12( skol11 ) ) }.
% 2.34/2.74 parent0[0]: (21191) {G0,W7,D3,L1,V0,M1} { ! number_of_in( sequential_pairs
% 2.34/2.74 , skol11 ) ==> number_of_in( triangles, skol11 ) }.
% 2.34/2.74 parent1[0]: (21192) {G1,W13,D3,L2,V0,M2} { number_of_in( sequential_pairs
% 2.34/2.74 , skol11 ) ==> number_of_in( triangles, skol11 ), alpha14( skol11, skol9
% 2.34/2.74 ( skol11 ), skol12( skol11 ) ) }.
% 2.34/2.74 substitution0:
% 2.34/2.74 end
% 2.34/2.74 substitution1:
% 2.34/2.74 end
% 2.34/2.74
% 2.34/2.74 subsumption: (4735) {G1,W6,D3,L1,V0,M1} R(99,108);r(110) { alpha14( skol11
% 2.34/2.74 , skol9( skol11 ), skol12( skol11 ) ) }.
% 2.34/2.74 parent0: (21193) {G1,W6,D3,L1,V0,M1} { alpha14( skol11, skol9( skol11 ),
% 2.34/2.74 skol12( skol11 ) ) }.
% 2.34/2.74 substitution0:
% 2.34/2.74 end
% 2.34/2.74 permutation0:
% 2.34/2.74 0 ==> 0
% 2.34/2.74 end
% 2.34/2.74
% 2.34/2.74 resolution: (21194) {G1,W4,D3,L1,V0,M1} { on_path( skol9( skol11 ), skol11
% 2.34/2.74 ) }.
% 2.34/2.74 parent0[0]: (101) {G0,W7,D2,L2,V3,M2} I { ! alpha14( X, Y, Z ), on_path( Y
% 2.34/2.74 , X ) }.
% 2.34/2.74 parent1[0]: (4735) {G1,W6,D3,L1,V0,M1} R(99,108);r(110) { alpha14( skol11,
% 2.34/2.74 skol9( skol11 ), skol12( skol11 ) ) }.
% 2.34/2.74 substitution0:
% 2.34/2.74 X := skol11
% 2.34/2.74 Y := skol9( skol11 )
% 2.34/2.74 Z := skol12( skol11 )
% 2.34/2.74 end
% 2.34/2.74 substitution1:
% 2.34/2.74 end
% 2.34/2.74
% 2.34/2.74 subsumption: (4768) {G2,W4,D3,L1,V0,M1} R(4735,101) { on_path( skol9(
% 2.34/2.74 skol11 ), skol11 ) }.
% 2.34/2.74 parent0: (21194) {G1,W4,D3,L1,V0,M1} { on_path( skol9( skol11 ), skol11 )
% 2.34/2.74 }.
% 2.34/2.74 substitution0:
% 2.34/2.74 end
% 2.34/2.74 permutation0:
% 2.34/2.74 0 ==> 0
% 2.34/2.74 end
% 2.34/2.74
% 2.34/2.74 resolution: (21195) {G1,W4,D3,L1,V0,M1} { on_path( skol12( skol11 ),
% 2.34/2.74 skol11 ) }.
% 2.34/2.74 parent0[0]: (102) {G0,W7,D2,L2,V3,M2} I { ! alpha14( X, Y, Z ), on_path( Z
% 2.34/2.74 , X ) }.
% 2.34/2.74 parent1[0]: (4735) {G1,W6,D3,L1,V0,M1} R(99,108);r(110) { alpha14( skol11,
% 2.34/2.74 skol9( skol11 ), skol12( skol11 ) ) }.
% 2.34/2.74 substitution0:
% 2.34/2.74 X := skol11
% 2.34/2.74 Y := skol9( skol11 )
% 2.34/2.74 Z := skol12( skol11 )
% 2.34/2.74 end
% 2.34/2.74 substitution1:
% 2.34/2.74 end
% 2.34/2.74
% 2.34/2.74 subsumption: (4769) {G2,W4,D3,L1,V0,M1} R(4735,102) { on_path( skol12(
% 2.34/2.74 skol11 ), skol11 ) }.
% 2.34/2.74 parent0: (21195) {G1,W4,D3,L1,V0,M1} { on_path( skol12( skol11 ), skol11 )
% 2.34/2.74 }.
% 2.34/2.74 substitution0:
% 2.34/2.74 end
% 2.34/2.74 permutation0:
% 2.34/2.74 0 ==> 0
% 2.34/2.74 end
% 2.34/2.74
% 2.34/2.74 resolution: (21196) {G1,W5,D3,L1,V0,M1} { sequential( skol9( skol11 ),
% 2.34/2.74 skol12( skol11 ) ) }.
% 2.34/2.74 parent0[0]: (103) {G0,W7,D2,L2,V3,M2} I { ! alpha14( X, Y, Z ), sequential
% 2.34/2.74 ( Y, Z ) }.
% 2.34/2.74 parent1[0]: (4735) {G1,W6,D3,L1,V0,M1} R(99,108);r(110) { alpha14( skol11,
% 2.34/2.74 skol9( skol11 ), skol12( skol11 ) ) }.
% 2.34/2.74 substitution0:
% 2.34/2.74 X := skol11
% 2.34/2.74 Y := skol9( skol11 )
% 2.34/2.74 Z := skol12( skol11 )
% 2.34/2.74 end
% 2.34/2.74 substitution1:
% 2.34/2.74 end
% 2.34/2.74
% 2.34/2.74 subsumption: (4775) {G2,W5,D3,L1,V0,M1} R(4735,103) { sequential( skol9(
% 2.34/2.74 skol11 ), skol12( skol11 ) ) }.
% 2.34/2.74 parent0: (21196) {G1,W5,D3,L1,V0,M1} { sequential( skol9( skol11 ), skol12
% 2.34/2.74 ( skol11 ) ) }.
% 2.34/2.74 substitution0:
% 2.34/2.74 end
% 2.34/2.74 permutation0:
% 2.34/2.74 0 ==> 0
% 2.34/2.74 end
% 2.34/2.74
% 2.34/2.74 eqswap: (21197) {G0,W17,D3,L3,V4,M3} { number_of_in( sequential_pairs, X )
% 2.34/2.74 ==> number_of_in( triangles, X ), ! path( Y, Z, X ), ! triangle( skol9(
% 2.34/2.74 X ), skol12( X ), T ) }.
% 2.34/2.74 parent0[2]: (100) {G0,W17,D3,L3,V4,M3} I { ! path( Y, Z, X ), ! triangle(
% 2.34/2.74 skol9( X ), skol12( X ), T ), number_of_in( triangles, X ) ==>
% 2.34/2.74 number_of_in( sequential_pairs, X ) }.
% 2.34/2.74 substitution0:
% 2.34/2.74 X := X
% 2.34/2.74 Y := Y
% 2.34/2.74 Z := Z
% 2.34/2.74 T := T
% 2.34/2.74 end
% 2.34/2.74
% 2.34/2.74 eqswap: (21198) {G0,W7,D3,L1,V0,M1} { ! number_of_in( sequential_pairs,
% 2.34/2.74 skol11 ) ==> number_of_in( triangles, skol11 ) }.
% 2.34/2.74 parent0[0]: (110) {G0,W7,D3,L1,V0,M1} I { ! number_of_in( triangles, skol11
% 2.34/2.74 ) ==> number_of_in( sequential_pairs, skol11 ) }.
% 2.34/2.74 substitution0:
% 2.34/2.74 end
% 2.34/2.74
% 2.34/2.74 resolution: (21199) {G1,W13,D3,L2,V1,M2} { number_of_in( sequential_pairs
% 2.34/2.74 , skol11 ) ==> number_of_in( triangles, skol11 ), ! triangle( skol9(
% 2.34/2.74 skol11 ), skol12( skol11 ), X ) }.
% 2.34/2.74 parent0[1]: (21197) {G0,W17,D3,L3,V4,M3} { number_of_in( sequential_pairs
% 2.34/2.74 , X ) ==> number_of_in( triangles, X ), ! path( Y, Z, X ), ! triangle(
% 2.34/2.74 skol9( X ), skol12( X ), T ) }.
% 2.34/2.74 parent1[0]: (108) {G0,W4,D2,L1,V0,M1} I { path( skol13, skol14, skol11 )
% 2.34/2.74 }.
% 2.34/2.74 substitution0:
% 2.34/2.74 X := skol11
% 2.34/2.74 Y := skol13
% 2.34/2.74 Z := skol14
% 2.34/2.74 T := X
% 2.34/2.74 end
% 2.34/2.74 substitution1:
% 2.34/2.74 end
% 2.34/2.74
% 2.34/2.74 resolution: (21200) {G1,W6,D3,L1,V1,M1} { ! triangle( skol9( skol11 ),
% 2.34/2.74 skol12( skol11 ), X ) }.
% 2.34/2.74 parent0[0]: (21198) {G0,W7,D3,L1,V0,M1} { ! number_of_in( sequential_pairs
% 2.34/2.74 , skol11 ) ==> number_of_in( triangles, skol11 ) }.
% 2.34/2.74 parent1[0]: (21199) {G1,W13,D3,L2,V1,M2} { number_of_in( sequential_pairs
% 2.34/2.74 , skol11 ) ==> number_of_in( triangles, skol11 ), ! triangle( skol9(
% 2.34/2.74 skol11 ), skol12( skol11 ), X ) }.
% 2.34/2.74 substitution0:
% 2.34/2.74 end
% 2.34/2.74 substitution1:
% 2.34/2.74 X := X
% 2.34/2.74 end
% 2.34/2.74
% 2.34/2.74 subsumption: (4877) {G1,W6,D3,L1,V1,M1} R(100,108);r(110) { ! triangle(
% 2.34/2.74 skol9( skol11 ), skol12( skol11 ), X ) }.
% 2.34/2.74 parent0: (21200) {G1,W6,D3,L1,V1,M1} { ! triangle( skol9( skol11 ), skol12
% 2.34/2.74 ( skol11 ), X ) }.
% 2.34/2.74 substitution0:
% 2.34/2.74 X := X
% 2.34/2.74 end
% 2.34/2.74 permutation0:
% 2.34/2.74 0 ==> 0
% 2.34/2.74 end
% 2.34/2.74
% 2.34/2.74 resolution: (21201) {G1,W13,D3,L3,V0,M3} { ! on_path( skol9( skol11 ),
% 2.34/2.74 skol11 ), ! on_path( skol12( skol11 ), skol11 ), ! sequential( skol9(
% 2.34/2.74 skol11 ), skol12( skol11 ) ) }.
% 2.34/2.74 parent0[0]: (4877) {G1,W6,D3,L1,V1,M1} R(100,108);r(110) { ! triangle(
% 2.34/2.74 skol9( skol11 ), skol12( skol11 ), X ) }.
% 2.34/2.74 parent1[3]: (109) {G0,W15,D3,L4,V2,M4} I { ! on_path( X, skol11 ), !
% 2.34/2.74 on_path( Y, skol11 ), ! sequential( X, Y ), triangle( X, Y, skol15( X, Y
% 2.34/2.74 ) ) }.
% 2.34/2.74 substitution0:
% 2.34/2.74 X := skol15( skol9( skol11 ), skol12( skol11 ) )
% 2.34/2.74 end
% 2.34/2.74 substitution1:
% 2.34/2.74 X := skol9( skol11 )
% 2.34/2.74 Y := skol12( skol11 )
% 2.34/2.74 end
% 2.34/2.74
% 2.34/2.74 resolution: (21202) {G2,W9,D3,L2,V0,M2} { ! on_path( skol12( skol11 ),
% 2.34/2.74 skol11 ), ! sequential( skol9( skol11 ), skol12( skol11 ) ) }.
% 2.34/2.74 parent0[0]: (21201) {G1,W13,D3,L3,V0,M3} { ! on_path( skol9( skol11 ),
% 2.34/2.74 skol11 ), ! on_path( skol12( skol11 ), skol11 ), ! sequential( skol9(
% 2.34/2.74 skol11 ), skol12( skol11 ) ) }.
% 2.34/2.74 parent1[0]: (4768) {G2,W4,D3,L1,V0,M1} R(4735,101) { on_path( skol9( skol11
% 2.34/2.74 ), skol11 ) }.
% 2.34/2.74 substitution0:
% 2.34/2.74 end
% 2.34/2.74 substitution1:
% 2.34/2.74 end
% 2.34/2.74
% 2.34/2.74 subsumption: (5225) {G3,W9,D3,L2,V0,M2} R(4877,109);r(4768) { ! on_path(
% 2.34/2.74 skol12( skol11 ), skol11 ), ! sequential( skol9( skol11 ), skol12( skol11
% 2.34/2.74 ) ) }.
% 2.34/2.74 parent0: (21202) {G2,W9,D3,L2,V0,M2} { ! on_path( skol12( skol11 ), skol11
% 2.34/2.74 ), ! sequential( skol9( skol11 ), skol12( skol11 ) ) }.
% 2.34/2.74 substitution0:
% 2.34/2.74 end
% 2.34/2.74 permutation0:
% 2.34/2.74 0 ==> 0
% 2.34/2.74 1 ==> 1
% 2.34/2.74 end
% 2.34/2.74
% 2.34/2.74 resolution: (21203) {G3,W5,D3,L1,V0,M1} { ! sequential( skol9( skol11 ),
% 2.34/2.74 skol12( skol11 ) ) }.
% 2.34/2.74 parent0[0]: (5225) {G3,W9,D3,L2,V0,M2} R(4877,109);r(4768) { ! on_path(
% 2.34/2.74 skol12( skol11 ), skol11 ), ! sequential( skol9( skol11 ), skol12( skol11
% 2.34/2.74 ) ) }.
% 2.34/2.74 parent1[0]: (4769) {G2,W4,D3,L1,V0,M1} R(4735,102) { on_path( skol12(
% 2.34/2.74 skol11 ), skol11 ) }.
% 2.34/2.74 substitution0:
% 2.34/2.74 end
% 2.34/2.74 substitution1:
% 2.34/2.74 end
% 2.34/2.74
% 2.34/2.74 resolution: (21204) {G3,W0,D0,L0,V0,M0} { }.
% 2.34/2.74 parent0[0]: (21203) {G3,W5,D3,L1,V0,M1} { ! sequential( skol9( skol11 ),
% 2.34/2.74 skol12( skol11 ) ) }.
% 2.34/2.74 parent1[0]: (4775) {G2,W5,D3,L1,V0,M1} R(4735,103) { sequential( skol9(
% 2.34/2.74 skol11 ), skol12( skol11 ) ) }.
% 2.34/2.74 substitution0:
% 2.34/2.74 end
% 2.34/2.74 substitution1:
% 2.34/2.74 end
% 2.34/2.74
% 2.34/2.74 subsumption: (20216) {G4,W0,D0,L0,V0,M0} S(5225);r(4769);r(4775) { }.
% 2.34/2.74 parent0: (21204) {G3,W0,D0,L0,V0,M0} { }.
% 2.34/2.74 substitution0:
% 2.34/2.74 end
% 2.34/2.74 permutation0:
% 2.34/2.74 end
% 2.34/2.74
% 2.34/2.74 Proof check complete!
% 2.34/2.74
% 2.34/2.74 Memory use:
% 2.34/2.74
% 2.34/2.74 space for terms: 295958
% 2.34/2.74 space for clauses: 762648
% 2.34/2.74
% 2.34/2.74
% 2.34/2.74 clauses generated: 114077
% 2.34/2.74 clauses kept: 20217
% 2.34/2.74 clauses selected: 1601
% 2.34/2.74 clauses deleted: 1088
% 2.34/2.74 clauses inuse deleted: 45
% 2.34/2.74
% 2.34/2.74 subsentry: 276032
% 2.34/2.74 literals s-matched: 222991
% 2.34/2.74 literals matched: 199021
% 2.34/2.74 full subsumption: 39609
% 2.34/2.74
% 2.34/2.74 checksum: -649025931
% 2.34/2.74
% 2.34/2.74
% 2.34/2.74 Bliksem ended
%------------------------------------------------------------------------------