TSTP Solution File: GRA010+1 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GRA010+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n020.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 2.43s 2.81s
% Output : Refutation 2.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : GRA010+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.13/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n020.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 23:05:08 EDT 2022
% 0.19/0.34 % CPUTime :
% 0.72/1.11 *** allocated 10000 integers for termspace/termends
% 0.72/1.11 *** allocated 10000 integers for clauses
% 0.72/1.11 *** allocated 10000 integers for justifications
% 0.72/1.11 Bliksem 1.12
% 0.72/1.11
% 0.72/1.11
% 0.72/1.11 Automatic Strategy Selection
% 0.72/1.11
% 0.72/1.11
% 0.72/1.11 Clauses:
% 0.72/1.11
% 0.72/1.11 { ! edge( X ), ! head_of( X ) = tail_of( X ) }.
% 0.72/1.11 { ! edge( X ), vertex( head_of( X ) ) }.
% 0.72/1.11 { ! edge( X ), vertex( tail_of( X ) ) }.
% 0.72/1.11 { ! complete, ! vertex( X ), ! vertex( Y ), X = Y, edge( skol1( Z, T ) ) }
% 0.72/1.11 .
% 0.72/1.11 { ! complete, ! vertex( X ), ! vertex( Y ), X = Y, alpha11( X, Y, skol1( X
% 0.72/1.11 , Y ) ), alpha15( X, Y, skol1( X, Y ) ) }.
% 0.72/1.11 { ! alpha15( X, Y, Z ), Y = head_of( Z ) }.
% 0.72/1.11 { ! alpha15( X, Y, Z ), X = tail_of( Z ) }.
% 0.72/1.11 { ! alpha15( X, Y, Z ), ! alpha1( X, Y, Z ) }.
% 0.72/1.11 { ! Y = head_of( Z ), ! X = tail_of( Z ), alpha1( X, Y, Z ), alpha15( X, Y
% 0.72/1.11 , Z ) }.
% 0.72/1.11 { ! alpha11( X, Y, Z ), alpha1( X, Y, Z ) }.
% 0.72/1.11 { ! alpha11( X, Y, Z ), ! Y = head_of( Z ), ! X = tail_of( Z ) }.
% 0.72/1.11 { ! alpha1( X, Y, Z ), Y = head_of( Z ), alpha11( X, Y, Z ) }.
% 0.72/1.11 { ! alpha1( X, Y, Z ), X = tail_of( Z ), alpha11( X, Y, Z ) }.
% 0.72/1.11 { ! alpha1( X, Y, Z ), X = head_of( Z ) }.
% 0.72/1.11 { ! alpha1( X, Y, Z ), Y = tail_of( Z ) }.
% 0.72/1.11 { ! X = head_of( Z ), ! Y = tail_of( Z ), alpha1( X, Y, Z ) }.
% 0.72/1.11 { ! vertex( X ), ! vertex( Y ), ! edge( T ), ! X = tail_of( T ), ! Y =
% 0.72/1.11 head_of( T ), ! Z = path_cons( T, empty ), path( X, Y, Z ) }.
% 0.72/1.11 { ! vertex( X ), ! vertex( Y ), ! edge( T ), ! X = tail_of( T ), ! path(
% 0.72/1.11 head_of( T ), Y, U ), ! Z = path_cons( T, U ), path( X, Y, Z ) }.
% 0.72/1.11 { ! path( X, Y, Z ), alpha12( X, Y ) }.
% 0.72/1.11 { ! path( X, Y, Z ), alpha16( X, skol2( X, T, U ) ) }.
% 0.72/1.11 { ! path( X, Y, Z ), alpha20( Y, Z, skol2( X, Y, Z ) ) }.
% 0.72/1.11 { ! alpha20( X, Y, Z ), alpha18( X, Y, Z ), alpha21( X, Y, Z ) }.
% 0.72/1.11 { ! alpha18( X, Y, Z ), alpha20( X, Y, Z ) }.
% 0.72/1.11 { ! alpha21( X, Y, Z ), alpha20( X, Y, Z ) }.
% 0.72/1.11 { ! alpha21( X, Y, Z ), Y = path_cons( Z, skol3( T, Y, Z ) ) }.
% 0.72/1.11 { ! alpha21( X, Y, Z ), path( head_of( Z ), X, skol3( X, Y, Z ) ) }.
% 0.72/1.11 { ! alpha21( X, Y, Z ), ! alpha2( X, Y, Z ) }.
% 0.72/1.11 { ! path( head_of( Z ), X, T ), ! Y = path_cons( Z, T ), alpha2( X, Y, Z )
% 0.72/1.11 , alpha21( X, Y, Z ) }.
% 0.72/1.11 { ! alpha18( X, Y, Z ), alpha2( X, Y, Z ) }.
% 0.72/1.11 { ! alpha18( X, Y, Z ), ! path( head_of( Z ), X, T ), ! Y = path_cons( Z, T
% 0.72/1.11 ) }.
% 0.72/1.11 { ! alpha2( X, Y, Z ), Y = path_cons( Z, skol4( T, Y, Z ) ), alpha18( X, Y
% 0.72/1.11 , Z ) }.
% 0.72/1.11 { ! alpha2( X, Y, Z ), path( head_of( Z ), X, skol4( X, Y, Z ) ), alpha18(
% 0.72/1.11 X, Y, Z ) }.
% 0.72/1.11 { ! alpha16( X, Y ), edge( Y ) }.
% 0.72/1.11 { ! alpha16( X, Y ), X = tail_of( Y ) }.
% 0.72/1.11 { ! edge( Y ), ! X = tail_of( Y ), alpha16( X, Y ) }.
% 0.72/1.11 { ! alpha12( X, Y ), vertex( X ) }.
% 0.72/1.11 { ! alpha12( X, Y ), vertex( Y ) }.
% 0.72/1.11 { ! vertex( X ), ! vertex( Y ), alpha12( X, Y ) }.
% 0.72/1.11 { ! alpha2( X, Y, Z ), X = head_of( Z ) }.
% 0.72/1.11 { ! alpha2( X, Y, Z ), Y = path_cons( Z, empty ) }.
% 0.72/1.11 { ! X = head_of( Z ), ! Y = path_cons( Z, empty ), alpha2( X, Y, Z ) }.
% 0.72/1.11 { ! path( Z, T, X ), ! on_path( Y, X ), edge( Y ) }.
% 0.72/1.11 { ! path( Z, T, X ), ! on_path( Y, X ), in_path( head_of( Y ), X ) }.
% 0.72/1.11 { ! path( Z, T, X ), ! on_path( Y, X ), in_path( tail_of( Y ), X ) }.
% 0.72/1.11 { ! path( Z, T, X ), ! in_path( Y, X ), vertex( Y ) }.
% 0.72/1.11 { ! path( Z, T, X ), ! in_path( Y, X ), Y = head_of( skol5( U, Y ) ), Y =
% 0.72/1.11 tail_of( skol5( U, Y ) ) }.
% 0.72/1.11 { ! path( Z, T, X ), ! in_path( Y, X ), on_path( skol5( X, Y ), X ) }.
% 0.72/1.11 { ! sequential( X, Y ), edge( X ) }.
% 0.72/1.11 { ! sequential( X, Y ), alpha3( X, Y ) }.
% 0.72/1.11 { ! edge( X ), ! alpha3( X, Y ), sequential( X, Y ) }.
% 0.72/1.11 { ! alpha3( X, Y ), edge( Y ) }.
% 0.72/1.11 { ! alpha3( X, Y ), alpha6( X, Y ) }.
% 0.72/1.11 { ! edge( Y ), ! alpha6( X, Y ), alpha3( X, Y ) }.
% 0.72/1.11 { ! alpha6( X, Y ), ! X = Y }.
% 0.72/1.11 { ! alpha6( X, Y ), head_of( X ) = tail_of( Y ) }.
% 0.72/1.11 { X = Y, ! head_of( X ) = tail_of( Y ), alpha6( X, Y ) }.
% 0.72/1.11 { ! path( Y, Z, X ), ! on_path( T, X ), ! on_path( U, X ), ! sequential( T
% 0.72/1.11 , U ), precedes( T, U, X ) }.
% 0.72/1.11 { ! path( Y, Z, X ), ! on_path( T, X ), ! on_path( U, X ), ! sequential( T
% 0.72/1.11 , W ), ! precedes( W, U, X ), precedes( T, U, X ) }.
% 0.72/1.11 { ! path( Y, Z, X ), ! precedes( T, U, X ), alpha13( X, T, U ) }.
% 0.72/1.11 { ! path( Y, Z, X ), ! precedes( T, U, X ), alpha17( X, T, U ), alpha19( X
% 0.72/1.11 , T, U ) }.
% 0.72/1.11 { ! alpha19( X, Y, Z ), sequential( Y, skol6( T, Y, U ) ) }.
% 0.72/1.11 { ! alpha19( X, Y, Z ), precedes( skol6( X, Y, Z ), Z, X ) }.
% 0.72/1.11 { ! alpha19( X, Y, Z ), ! sequential( Y, Z ) }.
% 0.75/1.22 { ! sequential( Y, T ), ! precedes( T, Z, X ), sequential( Y, Z ), alpha19
% 0.75/1.22 ( X, Y, Z ) }.
% 0.75/1.22 { ! alpha17( X, Y, Z ), sequential( Y, Z ) }.
% 0.75/1.22 { ! alpha17( X, Y, Z ), ! sequential( Y, T ), ! precedes( T, Z, X ) }.
% 0.75/1.22 { ! sequential( Y, Z ), sequential( Y, skol7( T, Y, U ) ), alpha17( X, Y, Z
% 0.75/1.22 ) }.
% 0.75/1.22 { ! sequential( Y, Z ), precedes( skol7( X, Y, Z ), Z, X ), alpha17( X, Y,
% 0.75/1.22 Z ) }.
% 0.75/1.22 { ! alpha13( X, Y, Z ), on_path( Y, X ) }.
% 0.75/1.22 { ! alpha13( X, Y, Z ), on_path( Z, X ) }.
% 0.75/1.22 { ! on_path( Y, X ), ! on_path( Z, X ), alpha13( X, Y, Z ) }.
% 0.75/1.22 { ! shortest_path( X, Y, Z ), path( X, Y, Z ) }.
% 0.75/1.22 { ! shortest_path( X, Y, Z ), alpha4( X, Y, Z ) }.
% 0.75/1.22 { ! path( X, Y, Z ), ! alpha4( X, Y, Z ), shortest_path( X, Y, Z ) }.
% 0.75/1.22 { ! alpha4( X, Y, Z ), ! X = Y }.
% 0.75/1.22 { ! alpha4( X, Y, Z ), alpha7( X, Y, Z ) }.
% 0.75/1.22 { X = Y, ! alpha7( X, Y, Z ), alpha4( X, Y, Z ) }.
% 0.75/1.22 { ! alpha7( X, Y, Z ), ! path( X, Y, T ), less_or_equal( length_of( Z ),
% 0.75/1.22 length_of( T ) ) }.
% 0.75/1.22 { ! less_or_equal( length_of( Z ), length_of( skol8( T, U, Z ) ) ), alpha7
% 0.75/1.22 ( X, Y, Z ) }.
% 0.75/1.22 { path( X, Y, skol8( X, Y, Z ) ), alpha7( X, Y, Z ) }.
% 0.75/1.22 { ! shortest_path( T, U, Z ), ! precedes( X, Y, Z ), ! tail_of( W ) =
% 0.75/1.22 tail_of( X ), ! head_of( W ) = head_of( Y ) }.
% 0.75/1.22 { ! shortest_path( T, U, Z ), ! precedes( X, Y, Z ), ! precedes( Y, X, Z )
% 0.75/1.22 }.
% 0.75/1.22 { ! triangle( X, Y, Z ), edge( X ) }.
% 0.75/1.22 { ! triangle( X, Y, Z ), alpha5( X, Y, Z ) }.
% 0.75/1.22 { ! edge( X ), ! alpha5( X, Y, Z ), triangle( X, Y, Z ) }.
% 0.75/1.22 { ! alpha5( X, Y, Z ), edge( Y ) }.
% 0.75/1.22 { ! alpha5( X, Y, Z ), alpha8( X, Y, Z ) }.
% 0.75/1.22 { ! edge( Y ), ! alpha8( X, Y, Z ), alpha5( X, Y, Z ) }.
% 0.75/1.22 { ! alpha8( X, Y, Z ), edge( Z ) }.
% 0.75/1.22 { ! alpha8( X, Y, Z ), alpha9( X, Y, Z ) }.
% 0.75/1.22 { ! edge( Z ), ! alpha9( X, Y, Z ), alpha8( X, Y, Z ) }.
% 0.75/1.22 { ! alpha9( X, Y, Z ), sequential( X, Y ) }.
% 0.75/1.22 { ! alpha9( X, Y, Z ), alpha10( X, Y, Z ) }.
% 0.75/1.22 { ! sequential( X, Y ), ! alpha10( X, Y, Z ), alpha9( X, Y, Z ) }.
% 0.75/1.22 { ! alpha10( X, Y, Z ), sequential( Y, Z ) }.
% 0.75/1.22 { ! alpha10( X, Y, Z ), sequential( Z, X ) }.
% 0.75/1.22 { ! sequential( Y, Z ), ! sequential( Z, X ), alpha10( X, Y, Z ) }.
% 0.75/1.22 { ! path( Y, Z, X ), length_of( X ) = number_of_in( edges, X ) }.
% 0.75/1.22 { ! path( Y, Z, X ), number_of_in( sequential_pairs, X ) = minus( length_of
% 0.75/1.22 ( X ), n1 ) }.
% 0.75/1.22 { ! path( Y, Z, X ), alpha14( X, skol9( X ), skol11( X ) ), number_of_in(
% 0.75/1.22 sequential_pairs, X ) = number_of_in( triangles, X ) }.
% 0.75/1.22 { ! path( Y, Z, X ), ! triangle( skol9( X ), skol11( X ), T ), number_of_in
% 0.75/1.22 ( sequential_pairs, X ) = number_of_in( triangles, X ) }.
% 0.75/1.22 { ! alpha14( X, Y, Z ), on_path( Y, X ) }.
% 0.75/1.22 { ! alpha14( X, Y, Z ), on_path( Z, X ) }.
% 0.75/1.22 { ! alpha14( X, Y, Z ), sequential( Y, Z ) }.
% 0.75/1.22 { ! on_path( Y, X ), ! on_path( Z, X ), ! sequential( Y, Z ), alpha14( X, Y
% 0.75/1.22 , Z ) }.
% 0.75/1.22 { less_or_equal( number_of_in( X, Y ), number_of_in( X, graph ) ) }.
% 0.75/1.22 { complete }.
% 0.75/1.22 { path( skol12, skol13, skol10 ) }.
% 0.75/1.22 { ! on_path( X, skol10 ), ! on_path( Y, skol10 ), ! sequential( X, Y ),
% 0.75/1.22 triangle( X, Y, skol14( X, Y ) ) }.
% 0.75/1.22 { ! number_of_in( sequential_pairs, skol10 ) = number_of_in( triangles,
% 0.75/1.22 skol10 ) }.
% 0.75/1.22
% 0.75/1.22 percentage equality = 0.154639, percentage horn = 0.836364
% 0.75/1.22 This is a problem with some equality
% 0.75/1.22
% 0.75/1.22
% 0.75/1.22
% 0.75/1.22 Options Used:
% 0.75/1.22
% 0.75/1.22 useres = 1
% 0.75/1.22 useparamod = 1
% 0.75/1.22 useeqrefl = 1
% 0.75/1.22 useeqfact = 1
% 0.75/1.22 usefactor = 1
% 0.75/1.22 usesimpsplitting = 0
% 0.75/1.22 usesimpdemod = 5
% 0.75/1.22 usesimpres = 3
% 0.75/1.22
% 0.75/1.22 resimpinuse = 1000
% 0.75/1.22 resimpclauses = 20000
% 0.75/1.22 substype = eqrewr
% 0.75/1.22 backwardsubs = 1
% 0.75/1.22 selectoldest = 5
% 0.75/1.22
% 0.75/1.22 litorderings [0] = split
% 0.75/1.22 litorderings [1] = extend the termordering, first sorting on arguments
% 0.75/1.22
% 0.75/1.22 termordering = kbo
% 0.75/1.22
% 0.75/1.22 litapriori = 0
% 0.75/1.22 termapriori = 1
% 0.75/1.22 litaposteriori = 0
% 0.75/1.22 termaposteriori = 0
% 0.75/1.22 demodaposteriori = 0
% 0.75/1.22 ordereqreflfact = 0
% 0.75/1.22
% 0.75/1.22 litselect = negord
% 0.75/1.22
% 0.75/1.22 maxweight = 15
% 0.75/1.22 maxdepth = 30000
% 0.75/1.22 maxlength = 115
% 0.75/1.22 maxnrvars = 195
% 0.75/1.22 excuselevel = 1
% 0.75/1.22 increasemaxweight = 1
% 0.75/1.22
% 0.75/1.22 maxselected = 10000000
% 0.75/1.22 maxnrclauses = 10000000
% 0.75/1.22
% 0.75/1.22 showgenerated = 0
% 0.75/1.22 showkept = 0
% 0.75/1.22 showselected = 0
% 0.75/1.22 showdeleted = 0
% 0.75/1.22 showresimp = 1
% 0.75/1.22 showstatus = 2000
% 0.75/1.22
% 0.75/1.22 prologoutput = 0
% 0.75/1.22 nrgoals = 5000000
% 0.75/1.22 totalproof = 1
% 0.75/1.22
% 0.75/1.22 Symbols occurring in the translation:
% 2.43/2.81
% 2.43/2.81 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 2.43/2.81 . [1, 2] (w:1, o:40, a:1, s:1, b:0),
% 2.43/2.81 ! [4, 1] (w:0, o:28, a:1, s:1, b:0),
% 2.43/2.81 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.43/2.81 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.43/2.81 edge [36, 1] (w:1, o:33, a:1, s:1, b:0),
% 2.43/2.81 head_of [37, 1] (w:1, o:34, a:1, s:1, b:0),
% 2.43/2.81 tail_of [38, 1] (w:1, o:37, a:1, s:1, b:0),
% 2.43/2.81 vertex [39, 1] (w:1, o:38, a:1, s:1, b:0),
% 2.43/2.81 complete [40, 0] (w:1, o:7, a:1, s:1, b:0),
% 2.43/2.81 empty [44, 0] (w:1, o:11, a:1, s:1, b:0),
% 2.43/2.81 path_cons [45, 2] (w:1, o:67, a:1, s:1, b:0),
% 2.43/2.81 path [47, 3] (w:1, o:78, a:1, s:1, b:0),
% 2.43/2.81 on_path [48, 2] (w:1, o:66, a:1, s:1, b:0),
% 2.43/2.81 in_path [49, 2] (w:1, o:68, a:1, s:1, b:0),
% 2.43/2.81 sequential [53, 2] (w:1, o:69, a:1, s:1, b:0),
% 2.43/2.81 precedes [55, 3] (w:1, o:79, a:1, s:1, b:0),
% 2.43/2.81 shortest_path [57, 3] (w:1, o:80, a:1, s:1, b:0),
% 2.43/2.81 length_of [58, 1] (w:1, o:39, a:1, s:1, b:0),
% 2.43/2.81 less_or_equal [59, 2] (w:1, o:70, a:1, s:1, b:0),
% 2.43/2.81 triangle [60, 3] (w:1, o:87, a:1, s:1, b:0),
% 2.43/2.81 edges [61, 0] (w:1, o:18, a:1, s:1, b:0),
% 2.43/2.81 number_of_in [62, 2] (w:1, o:65, a:1, s:1, b:0),
% 2.43/2.81 sequential_pairs [63, 0] (w:1, o:19, a:1, s:1, b:0),
% 2.43/2.81 n1 [64, 0] (w:1, o:20, a:1, s:1, b:0),
% 2.43/2.81 minus [65, 2] (w:1, o:64, a:1, s:1, b:0),
% 2.43/2.81 triangles [66, 0] (w:1, o:24, a:1, s:1, b:0),
% 2.43/2.81 graph [69, 0] (w:1, o:27, a:1, s:1, b:0),
% 2.43/2.81 alpha1 [70, 3] (w:1, o:88, a:1, s:1, b:1),
% 2.43/2.81 alpha2 [71, 3] (w:1, o:97, a:1, s:1, b:1),
% 2.43/2.81 alpha3 [72, 2] (w:1, o:71, a:1, s:1, b:1),
% 2.43/2.81 alpha4 [73, 3] (w:1, o:98, a:1, s:1, b:1),
% 2.43/2.81 alpha5 [74, 3] (w:1, o:99, a:1, s:1, b:1),
% 2.43/2.81 alpha6 [75, 2] (w:1, o:72, a:1, s:1, b:1),
% 2.43/2.81 alpha7 [76, 3] (w:1, o:100, a:1, s:1, b:1),
% 2.43/2.81 alpha8 [77, 3] (w:1, o:101, a:1, s:1, b:1),
% 2.43/2.81 alpha9 [78, 3] (w:1, o:102, a:1, s:1, b:1),
% 2.43/2.81 alpha10 [79, 3] (w:1, o:89, a:1, s:1, b:1),
% 2.43/2.81 alpha11 [80, 3] (w:1, o:90, a:1, s:1, b:1),
% 2.43/2.81 alpha12 [81, 2] (w:1, o:73, a:1, s:1, b:1),
% 2.43/2.81 alpha13 [82, 3] (w:1, o:91, a:1, s:1, b:1),
% 2.43/2.81 alpha14 [83, 3] (w:1, o:92, a:1, s:1, b:1),
% 2.43/2.81 alpha15 [84, 3] (w:1, o:93, a:1, s:1, b:1),
% 2.43/2.81 alpha16 [85, 2] (w:1, o:74, a:1, s:1, b:1),
% 2.43/2.81 alpha17 [86, 3] (w:1, o:94, a:1, s:1, b:1),
% 2.43/2.81 alpha18 [87, 3] (w:1, o:95, a:1, s:1, b:1),
% 2.43/2.81 alpha19 [88, 3] (w:1, o:96, a:1, s:1, b:1),
% 2.43/2.81 alpha20 [89, 3] (w:1, o:103, a:1, s:1, b:1),
% 2.43/2.81 alpha21 [90, 3] (w:1, o:104, a:1, s:1, b:1),
% 2.43/2.81 skol1 [91, 2] (w:1, o:75, a:1, s:1, b:1),
% 2.43/2.81 skol2 [92, 3] (w:1, o:81, a:1, s:1, b:1),
% 2.43/2.81 skol3 [93, 3] (w:1, o:82, a:1, s:1, b:1),
% 2.43/2.81 skol4 [94, 3] (w:1, o:83, a:1, s:1, b:1),
% 2.43/2.81 skol5 [95, 2] (w:1, o:76, a:1, s:1, b:1),
% 2.43/2.81 skol6 [96, 3] (w:1, o:84, a:1, s:1, b:1),
% 2.43/2.81 skol7 [97, 3] (w:1, o:85, a:1, s:1, b:1),
% 2.43/2.81 skol8 [98, 3] (w:1, o:86, a:1, s:1, b:1),
% 2.43/2.81 skol9 [99, 1] (w:1, o:35, a:1, s:1, b:1),
% 2.43/2.81 skol10 [100, 0] (w:1, o:21, a:1, s:1, b:1),
% 2.43/2.81 skol11 [101, 1] (w:1, o:36, a:1, s:1, b:1),
% 2.43/2.81 skol12 [102, 0] (w:1, o:22, a:1, s:1, b:1),
% 2.43/2.81 skol13 [103, 0] (w:1, o:23, a:1, s:1, b:1),
% 2.43/2.81 skol14 [104, 2] (w:1, o:77, a:1, s:1, b:1).
% 2.43/2.81
% 2.43/2.81
% 2.43/2.81 Starting Search:
% 2.43/2.81
% 2.43/2.81 *** allocated 15000 integers for clauses
% 2.43/2.81 *** allocated 22500 integers for clauses
% 2.43/2.81 *** allocated 33750 integers for clauses
% 2.43/2.81 *** allocated 15000 integers for termspace/termends
% 2.43/2.81 *** allocated 50625 integers for clauses
% 2.43/2.81 *** allocated 22500 integers for termspace/termends
% 2.43/2.81 Resimplifying inuse:
% 2.43/2.81 Done
% 2.43/2.81
% 2.43/2.81 *** allocated 75937 integers for clauses
% 2.43/2.81 *** allocated 33750 integers for termspace/termends
% 2.43/2.81 *** allocated 113905 integers for clauses
% 2.43/2.81
% 2.43/2.81 Intermediate Status:
% 2.43/2.81 Generated: 4116
% 2.43/2.81 Kept: 2008
% 2.43/2.81 Inuse: 193
% 2.43/2.81 Deleted: 5
% 2.43/2.81 Deletedinuse: 1
% 2.43/2.81
% 2.43/2.81 Resimplifying inuse:
% 2.43/2.81 Done
% 2.43/2.81
% 2.43/2.81 *** allocated 50625 integers for termspace/termends
% 2.43/2.81 *** allocated 170857 integers for clauses
% 2.43/2.81 Resimplifying inuse:
% 2.43/2.81 Done
% 2.43/2.81
% 2.43/2.81 *** allocated 75937 integers for termspace/termends
% 2.43/2.81
% 2.43/2.81 Intermediate Status:
% 2.43/2.81 Generated: 8804
% 2.43/2.81 Kept: 4012
% 2.43/2.81 Inuse: 330
% 2.43/2.81 Deleted: 9
% 2.43/2.81 Deletedinuse: 3
% 2.43/2.81
% 2.43/2.81 Resimplifying inuse:
% 2.43/2.81 Done
% 2.43/2.81
% 2.43/2.81 *** allocated 256285 integers for clauses
% 2.43/2.81 *** allocated 113905 integers for termspace/termends
% 2.43/2.81 Resimplifying inuse:
% 2.43/2.81 Done
% 2.43/2.81
% 2.43/2.81
% 2.43/2.81 Intermediate Status:
% 2.43/2.81 Generated: 15850
% 2.43/2.81 Kept: 6017
% 2.43/2.81 Inuse: 515
% 2.43/2.81 Deleted: 21
% 2.43/2.81 Deletedinuse: 6
% 2.43/2.81
% 2.43/2.81 Resimplifying inuse:
% 2.43/2.81 Done
% 2.43/2.81
% 2.43/2.81 *** allocated 384427 integers for clauses
% 2.43/2.81 Resimplifying inuse:
% 2.43/2.81 Done
% 2.43/2.81
% 2.43/2.81 *** allocated 170857 integers for termspace/termends
% 2.43/2.81
% 2.43/2.81 Intermediate Status:
% 2.43/2.81 Generated: 23488
% 2.43/2.81 Kept: 8036
% 2.43/2.81 Inuse: 624
% 2.43/2.81 Deleted: 36
% 2.43/2.81 Deletedinuse: 9
% 2.43/2.81
% 2.43/2.81 Resimplifying inuse:
% 2.43/2.81 Done
% 2.43/2.81
% 2.43/2.81 Resimplifying inuse:
% 2.43/2.81 Done
% 2.43/2.81
% 2.43/2.81 *** allocated 576640 integers for clauses
% 2.43/2.81
% 2.43/2.81 Intermediate Status:
% 2.43/2.81 Generated: 30967
% 2.43/2.81 Kept: 10043
% 2.43/2.81 Inuse: 757
% 2.43/2.81 Deleted: 45
% 2.43/2.81 Deletedinuse: 9
% 2.43/2.81
% 2.43/2.81 Resimplifying inuse:
% 2.43/2.81 Done
% 2.43/2.81
% 2.43/2.81 Resimplifying inuse:
% 2.43/2.81 Done
% 2.43/2.81
% 2.43/2.81 *** allocated 256285 integers for termspace/termends
% 2.43/2.81
% 2.43/2.81 Intermediate Status:
% 2.43/2.81 Generated: 37569
% 2.43/2.81 Kept: 12177
% 2.43/2.81 Inuse: 838
% 2.43/2.81 Deleted: 48
% 2.43/2.81 Deletedinuse: 9
% 2.43/2.81
% 2.43/2.81 Resimplifying inuse:
% 2.43/2.81 Done
% 2.43/2.81
% 2.43/2.81 Resimplifying inuse:
% 2.43/2.81 Done
% 2.43/2.81
% 2.43/2.81
% 2.43/2.81 Intermediate Status:
% 2.43/2.81 Generated: 52634
% 2.43/2.81 Kept: 14513
% 2.43/2.81 Inuse: 1159
% 2.43/2.81 Deleted: 69
% 2.43/2.81 Deletedinuse: 9
% 2.43/2.81
% 2.43/2.81 Resimplifying inuse:
% 2.43/2.81 Done
% 2.43/2.81
% 2.43/2.81 *** allocated 864960 integers for clauses
% 2.43/2.81 Resimplifying inuse:
% 2.43/2.81 Done
% 2.43/2.81
% 2.43/2.81
% 2.43/2.81 Intermediate Status:
% 2.43/2.81 Generated: 83469
% 2.43/2.81 Kept: 16561
% 2.43/2.81 Inuse: 1391
% 2.43/2.81 Deleted: 113
% 2.43/2.81 Deletedinuse: 41
% 2.43/2.81
% 2.43/2.81 Resimplifying inuse:
% 2.43/2.81 Done
% 2.43/2.81
% 2.43/2.81 *** allocated 384427 integers for termspace/termends
% 2.43/2.81 Resimplifying inuse:
% 2.43/2.81 Done
% 2.43/2.81
% 2.43/2.81
% 2.43/2.81 Intermediate Status:
% 2.43/2.81 Generated: 104006
% 2.43/2.81 Kept: 18569
% 2.43/2.81 Inuse: 1522
% 2.43/2.81 Deleted: 120
% 2.43/2.81 Deletedinuse: 45
% 2.43/2.81
% 2.43/2.81 Resimplifying inuse:
% 2.43/2.81 Done
% 2.43/2.81
% 2.43/2.81 Resimplifying inuse:
% 2.43/2.81 Done
% 2.43/2.81
% 2.43/2.81 Resimplifying clauses:
% 2.43/2.81
% 2.43/2.81 Bliksems!, er is een bewijs:
% 2.43/2.81 % SZS status Theorem
% 2.43/2.81 % SZS output start Refutation
% 2.43/2.81
% 2.43/2.81 (99) {G0,W17,D3,L3,V3,M3} I { ! path( Y, Z, X ), alpha14( X, skol9( X ),
% 2.43/2.81 skol11( X ) ), number_of_in( triangles, X ) ==> number_of_in(
% 2.43/2.81 sequential_pairs, X ) }.
% 2.43/2.81 (100) {G0,W17,D3,L3,V4,M3} I { ! path( Y, Z, X ), ! triangle( skol9( X ),
% 2.43/2.81 skol11( X ), T ), number_of_in( triangles, X ) ==> number_of_in(
% 2.43/2.81 sequential_pairs, X ) }.
% 2.43/2.81 (101) {G0,W7,D2,L2,V3,M2} I { ! alpha14( X, Y, Z ), on_path( Y, X ) }.
% 2.43/2.81 (102) {G0,W7,D2,L2,V3,M2} I { ! alpha14( X, Y, Z ), on_path( Z, X ) }.
% 2.43/2.81 (103) {G0,W7,D2,L2,V3,M2} I { ! alpha14( X, Y, Z ), sequential( Y, Z ) }.
% 2.43/2.81 (107) {G0,W4,D2,L1,V0,M1} I { path( skol12, skol13, skol10 ) }.
% 2.43/2.81 (108) {G0,W15,D3,L4,V2,M4} I { ! on_path( X, skol10 ), ! on_path( Y, skol10
% 2.43/2.81 ), ! sequential( X, Y ), triangle( X, Y, skol14( X, Y ) ) }.
% 2.43/2.81 (109) {G0,W7,D3,L1,V0,M1} I { ! number_of_in( triangles, skol10 ) ==>
% 2.43/2.81 number_of_in( sequential_pairs, skol10 ) }.
% 2.43/2.81 (4734) {G1,W6,D3,L1,V0,M1} R(99,107);r(109) { alpha14( skol10, skol9(
% 2.43/2.81 skol10 ), skol11( skol10 ) ) }.
% 2.43/2.81 (4767) {G2,W4,D3,L1,V0,M1} R(4734,101) { on_path( skol9( skol10 ), skol10 )
% 2.43/2.81 }.
% 2.43/2.81 (4768) {G2,W4,D3,L1,V0,M1} R(4734,102) { on_path( skol11( skol10 ), skol10
% 2.43/2.81 ) }.
% 2.43/2.81 (4774) {G2,W5,D3,L1,V0,M1} R(4734,103) { sequential( skol9( skol10 ),
% 2.43/2.81 skol11( skol10 ) ) }.
% 2.43/2.81 (4876) {G1,W6,D3,L1,V1,M1} R(100,107);r(109) { ! triangle( skol9( skol10 )
% 2.43/2.81 , skol11( skol10 ), X ) }.
% 2.43/2.81 (5223) {G3,W9,D3,L2,V0,M2} R(4876,108);r(4767) { ! on_path( skol11( skol10
% 2.43/2.81 ), skol10 ), ! sequential( skol9( skol10 ), skol11( skol10 ) ) }.
% 2.43/2.81 (20104) {G4,W0,D0,L0,V0,M0} S(5223);r(4768);r(4774) { }.
% 2.43/2.81
% 2.43/2.81
% 2.43/2.81 % SZS output end Refutation
% 2.43/2.81 found a proof!
% 2.43/2.81
% 2.43/2.81
% 2.43/2.81 Unprocessed initial clauses:
% 2.43/2.81
% 2.43/2.81 (20106) {G0,W7,D3,L2,V1,M2} { ! edge( X ), ! head_of( X ) = tail_of( X )
% 2.43/2.81 }.
% 2.43/2.81 (20107) {G0,W5,D3,L2,V1,M2} { ! edge( X ), vertex( head_of( X ) ) }.
% 2.43/2.81 (20108) {G0,W5,D3,L2,V1,M2} { ! edge( X ), vertex( tail_of( X ) ) }.
% 2.43/2.81 (20109) {G0,W12,D3,L5,V4,M5} { ! complete, ! vertex( X ), ! vertex( Y ), X
% 2.43/2.81 = Y, edge( skol1( Z, T ) ) }.
% 2.43/2.81 (20110) {G0,W20,D3,L6,V2,M6} { ! complete, ! vertex( X ), ! vertex( Y ), X
% 2.43/2.81 = Y, alpha11( X, Y, skol1( X, Y ) ), alpha15( X, Y, skol1( X, Y ) ) }.
% 2.43/2.81 (20111) {G0,W8,D3,L2,V3,M2} { ! alpha15( X, Y, Z ), Y = head_of( Z ) }.
% 2.43/2.81 (20112) {G0,W8,D3,L2,V3,M2} { ! alpha15( X, Y, Z ), X = tail_of( Z ) }.
% 2.43/2.81 (20113) {G0,W8,D2,L2,V3,M2} { ! alpha15( X, Y, Z ), ! alpha1( X, Y, Z )
% 2.43/2.81 }.
% 2.43/2.81 (20114) {G0,W16,D3,L4,V3,M4} { ! Y = head_of( Z ), ! X = tail_of( Z ),
% 2.43/2.81 alpha1( X, Y, Z ), alpha15( X, Y, Z ) }.
% 2.43/2.81 (20115) {G0,W8,D2,L2,V3,M2} { ! alpha11( X, Y, Z ), alpha1( X, Y, Z ) }.
% 2.43/2.81 (20116) {G0,W12,D3,L3,V3,M3} { ! alpha11( X, Y, Z ), ! Y = head_of( Z ), !
% 2.43/2.81 X = tail_of( Z ) }.
% 2.43/2.81 (20117) {G0,W12,D3,L3,V3,M3} { ! alpha1( X, Y, Z ), Y = head_of( Z ),
% 2.43/2.81 alpha11( X, Y, Z ) }.
% 2.43/2.81 (20118) {G0,W12,D3,L3,V3,M3} { ! alpha1( X, Y, Z ), X = tail_of( Z ),
% 2.43/2.81 alpha11( X, Y, Z ) }.
% 2.43/2.81 (20119) {G0,W8,D3,L2,V3,M2} { ! alpha1( X, Y, Z ), X = head_of( Z ) }.
% 2.43/2.81 (20120) {G0,W8,D3,L2,V3,M2} { ! alpha1( X, Y, Z ), Y = tail_of( Z ) }.
% 2.43/2.81 (20121) {G0,W12,D3,L3,V3,M3} { ! X = head_of( Z ), ! Y = tail_of( Z ),
% 2.43/2.81 alpha1( X, Y, Z ) }.
% 2.43/2.81 (20122) {G0,W23,D3,L7,V4,M7} { ! vertex( X ), ! vertex( Y ), ! edge( T ),
% 2.43/2.81 ! X = tail_of( T ), ! Y = head_of( T ), ! Z = path_cons( T, empty ), path
% 2.43/2.81 ( X, Y, Z ) }.
% 2.43/2.81 (20123) {G0,W24,D3,L7,V5,M7} { ! vertex( X ), ! vertex( Y ), ! edge( T ),
% 2.43/2.81 ! X = tail_of( T ), ! path( head_of( T ), Y, U ), ! Z = path_cons( T, U )
% 2.43/2.81 , path( X, Y, Z ) }.
% 2.43/2.81 (20124) {G0,W7,D2,L2,V3,M2} { ! path( X, Y, Z ), alpha12( X, Y ) }.
% 2.43/2.81 (20125) {G0,W10,D3,L2,V5,M2} { ! path( X, Y, Z ), alpha16( X, skol2( X, T
% 2.43/2.81 , U ) ) }.
% 2.43/2.81 (20126) {G0,W11,D3,L2,V3,M2} { ! path( X, Y, Z ), alpha20( Y, Z, skol2( X
% 2.43/2.81 , Y, Z ) ) }.
% 2.43/2.81 (20127) {G0,W12,D2,L3,V3,M3} { ! alpha20( X, Y, Z ), alpha18( X, Y, Z ),
% 2.43/2.81 alpha21( X, Y, Z ) }.
% 2.43/2.81 (20128) {G0,W8,D2,L2,V3,M2} { ! alpha18( X, Y, Z ), alpha20( X, Y, Z ) }.
% 2.43/2.81 (20129) {G0,W8,D2,L2,V3,M2} { ! alpha21( X, Y, Z ), alpha20( X, Y, Z ) }.
% 2.43/2.81 (20130) {G0,W12,D4,L2,V4,M2} { ! alpha21( X, Y, Z ), Y = path_cons( Z,
% 2.43/2.81 skol3( T, Y, Z ) ) }.
% 2.43/2.81 (20131) {G0,W12,D3,L2,V3,M2} { ! alpha21( X, Y, Z ), path( head_of( Z ), X
% 2.43/2.81 , skol3( X, Y, Z ) ) }.
% 2.43/2.81 (20132) {G0,W8,D2,L2,V3,M2} { ! alpha21( X, Y, Z ), ! alpha2( X, Y, Z )
% 2.43/2.81 }.
% 2.43/2.81 (20133) {G0,W18,D3,L4,V4,M4} { ! path( head_of( Z ), X, T ), ! Y =
% 2.43/2.81 path_cons( Z, T ), alpha2( X, Y, Z ), alpha21( X, Y, Z ) }.
% 2.43/2.81 (20134) {G0,W8,D2,L2,V3,M2} { ! alpha18( X, Y, Z ), alpha2( X, Y, Z ) }.
% 2.43/2.81 (20135) {G0,W14,D3,L3,V4,M3} { ! alpha18( X, Y, Z ), ! path( head_of( Z )
% 2.43/2.81 , X, T ), ! Y = path_cons( Z, T ) }.
% 2.43/2.81 (20136) {G0,W16,D4,L3,V4,M3} { ! alpha2( X, Y, Z ), Y = path_cons( Z,
% 2.43/2.81 skol4( T, Y, Z ) ), alpha18( X, Y, Z ) }.
% 2.43/2.81 (20137) {G0,W16,D3,L3,V3,M3} { ! alpha2( X, Y, Z ), path( head_of( Z ), X
% 2.43/2.81 , skol4( X, Y, Z ) ), alpha18( X, Y, Z ) }.
% 2.43/2.81 (20138) {G0,W5,D2,L2,V2,M2} { ! alpha16( X, Y ), edge( Y ) }.
% 2.43/2.81 (20139) {G0,W7,D3,L2,V2,M2} { ! alpha16( X, Y ), X = tail_of( Y ) }.
% 2.43/2.81 (20140) {G0,W9,D3,L3,V2,M3} { ! edge( Y ), ! X = tail_of( Y ), alpha16( X
% 2.43/2.81 , Y ) }.
% 2.43/2.81 (20141) {G0,W5,D2,L2,V2,M2} { ! alpha12( X, Y ), vertex( X ) }.
% 2.43/2.81 (20142) {G0,W5,D2,L2,V2,M2} { ! alpha12( X, Y ), vertex( Y ) }.
% 2.43/2.81 (20143) {G0,W7,D2,L3,V2,M3} { ! vertex( X ), ! vertex( Y ), alpha12( X, Y
% 2.43/2.81 ) }.
% 2.43/2.81 (20144) {G0,W8,D3,L2,V3,M2} { ! alpha2( X, Y, Z ), X = head_of( Z ) }.
% 2.43/2.81 (20145) {G0,W9,D3,L2,V3,M2} { ! alpha2( X, Y, Z ), Y = path_cons( Z, empty
% 2.43/2.81 ) }.
% 2.43/2.81 (20146) {G0,W13,D3,L3,V3,M3} { ! X = head_of( Z ), ! Y = path_cons( Z,
% 2.43/2.81 empty ), alpha2( X, Y, Z ) }.
% 2.43/2.81 (20147) {G0,W9,D2,L3,V4,M3} { ! path( Z, T, X ), ! on_path( Y, X ), edge(
% 2.43/2.81 Y ) }.
% 2.43/2.81 (20148) {G0,W11,D3,L3,V4,M3} { ! path( Z, T, X ), ! on_path( Y, X ),
% 2.43/2.81 in_path( head_of( Y ), X ) }.
% 2.43/2.81 (20149) {G0,W11,D3,L3,V4,M3} { ! path( Z, T, X ), ! on_path( Y, X ),
% 2.43/2.81 in_path( tail_of( Y ), X ) }.
% 2.43/2.81 (20150) {G0,W9,D2,L3,V4,M3} { ! path( Z, T, X ), ! in_path( Y, X ), vertex
% 2.43/2.81 ( Y ) }.
% 2.43/2.81 (20151) {G0,W19,D4,L4,V5,M4} { ! path( Z, T, X ), ! in_path( Y, X ), Y =
% 2.43/2.81 head_of( skol5( U, Y ) ), Y = tail_of( skol5( U, Y ) ) }.
% 2.43/2.81 (20152) {G0,W12,D3,L3,V4,M3} { ! path( Z, T, X ), ! in_path( Y, X ),
% 2.43/2.81 on_path( skol5( X, Y ), X ) }.
% 2.43/2.81 (20153) {G0,W5,D2,L2,V2,M2} { ! sequential( X, Y ), edge( X ) }.
% 2.43/2.81 (20154) {G0,W6,D2,L2,V2,M2} { ! sequential( X, Y ), alpha3( X, Y ) }.
% 2.43/2.81 (20155) {G0,W8,D2,L3,V2,M3} { ! edge( X ), ! alpha3( X, Y ), sequential( X
% 2.43/2.81 , Y ) }.
% 2.43/2.81 (20156) {G0,W5,D2,L2,V2,M2} { ! alpha3( X, Y ), edge( Y ) }.
% 2.43/2.81 (20157) {G0,W6,D2,L2,V2,M2} { ! alpha3( X, Y ), alpha6( X, Y ) }.
% 2.43/2.81 (20158) {G0,W8,D2,L3,V2,M3} { ! edge( Y ), ! alpha6( X, Y ), alpha3( X, Y
% 2.43/2.81 ) }.
% 2.43/2.81 (20159) {G0,W6,D2,L2,V2,M2} { ! alpha6( X, Y ), ! X = Y }.
% 2.43/2.81 (20160) {G0,W8,D3,L2,V2,M2} { ! alpha6( X, Y ), head_of( X ) = tail_of( Y
% 2.43/2.81 ) }.
% 2.43/2.81 (20161) {G0,W11,D3,L3,V2,M3} { X = Y, ! head_of( X ) = tail_of( Y ),
% 2.43/2.81 alpha6( X, Y ) }.
% 2.43/2.81 (20162) {G0,W17,D2,L5,V5,M5} { ! path( Y, Z, X ), ! on_path( T, X ), !
% 2.43/2.81 on_path( U, X ), ! sequential( T, U ), precedes( T, U, X ) }.
% 2.43/2.81 (20163) {G0,W21,D2,L6,V6,M6} { ! path( Y, Z, X ), ! on_path( T, X ), !
% 2.43/2.81 on_path( U, X ), ! sequential( T, W ), ! precedes( W, U, X ), precedes( T
% 2.43/2.81 , U, X ) }.
% 2.43/2.81 (20164) {G0,W12,D2,L3,V5,M3} { ! path( Y, Z, X ), ! precedes( T, U, X ),
% 2.43/2.81 alpha13( X, T, U ) }.
% 2.43/2.81 (20165) {G0,W16,D2,L4,V5,M4} { ! path( Y, Z, X ), ! precedes( T, U, X ),
% 2.43/2.81 alpha17( X, T, U ), alpha19( X, T, U ) }.
% 2.43/2.81 (20166) {G0,W10,D3,L2,V5,M2} { ! alpha19( X, Y, Z ), sequential( Y, skol6
% 2.43/2.81 ( T, Y, U ) ) }.
% 2.43/2.81 (20167) {G0,W11,D3,L2,V3,M2} { ! alpha19( X, Y, Z ), precedes( skol6( X, Y
% 2.43/2.81 , Z ), Z, X ) }.
% 2.43/2.81 (20168) {G0,W7,D2,L2,V3,M2} { ! alpha19( X, Y, Z ), ! sequential( Y, Z )
% 2.43/2.81 }.
% 2.43/2.81 (20169) {G0,W14,D2,L4,V4,M4} { ! sequential( Y, T ), ! precedes( T, Z, X )
% 2.43/2.81 , sequential( Y, Z ), alpha19( X, Y, Z ) }.
% 2.43/2.81 (20170) {G0,W7,D2,L2,V3,M2} { ! alpha17( X, Y, Z ), sequential( Y, Z ) }.
% 2.43/2.81 (20171) {G0,W11,D2,L3,V4,M3} { ! alpha17( X, Y, Z ), ! sequential( Y, T )
% 2.43/2.81 , ! precedes( T, Z, X ) }.
% 2.43/2.81 (20172) {G0,W13,D3,L3,V5,M3} { ! sequential( Y, Z ), sequential( Y, skol7
% 2.43/2.81 ( T, Y, U ) ), alpha17( X, Y, Z ) }.
% 2.43/2.81 (20173) {G0,W14,D3,L3,V3,M3} { ! sequential( Y, Z ), precedes( skol7( X, Y
% 2.43/2.81 , Z ), Z, X ), alpha17( X, Y, Z ) }.
% 2.43/2.81 (20174) {G0,W7,D2,L2,V3,M2} { ! alpha13( X, Y, Z ), on_path( Y, X ) }.
% 2.43/2.81 (20175) {G0,W7,D2,L2,V3,M2} { ! alpha13( X, Y, Z ), on_path( Z, X ) }.
% 2.43/2.81 (20176) {G0,W10,D2,L3,V3,M3} { ! on_path( Y, X ), ! on_path( Z, X ),
% 2.43/2.81 alpha13( X, Y, Z ) }.
% 2.43/2.81 (20177) {G0,W8,D2,L2,V3,M2} { ! shortest_path( X, Y, Z ), path( X, Y, Z )
% 2.43/2.81 }.
% 2.43/2.81 (20178) {G0,W8,D2,L2,V3,M2} { ! shortest_path( X, Y, Z ), alpha4( X, Y, Z
% 2.43/2.81 ) }.
% 2.43/2.81 (20179) {G0,W12,D2,L3,V3,M3} { ! path( X, Y, Z ), ! alpha4( X, Y, Z ),
% 2.43/2.81 shortest_path( X, Y, Z ) }.
% 2.43/2.81 (20180) {G0,W7,D2,L2,V3,M2} { ! alpha4( X, Y, Z ), ! X = Y }.
% 2.43/2.81 (20181) {G0,W8,D2,L2,V3,M2} { ! alpha4( X, Y, Z ), alpha7( X, Y, Z ) }.
% 2.43/2.81 (20182) {G0,W11,D2,L3,V3,M3} { X = Y, ! alpha7( X, Y, Z ), alpha4( X, Y, Z
% 2.43/2.81 ) }.
% 2.43/2.81 (20183) {G0,W13,D3,L3,V4,M3} { ! alpha7( X, Y, Z ), ! path( X, Y, T ),
% 2.43/2.81 less_or_equal( length_of( Z ), length_of( T ) ) }.
% 2.43/2.81 (20184) {G0,W12,D4,L2,V5,M2} { ! less_or_equal( length_of( Z ), length_of
% 2.43/2.81 ( skol8( T, U, Z ) ) ), alpha7( X, Y, Z ) }.
% 2.43/2.81 (20185) {G0,W11,D3,L2,V3,M2} { path( X, Y, skol8( X, Y, Z ) ), alpha7( X,
% 2.43/2.81 Y, Z ) }.
% 2.43/2.81 (20186) {G0,W18,D3,L4,V6,M4} { ! shortest_path( T, U, Z ), ! precedes( X,
% 2.43/2.81 Y, Z ), ! tail_of( W ) = tail_of( X ), ! head_of( W ) = head_of( Y ) }.
% 2.43/2.81 (20187) {G0,W12,D2,L3,V5,M3} { ! shortest_path( T, U, Z ), ! precedes( X,
% 2.43/2.81 Y, Z ), ! precedes( Y, X, Z ) }.
% 2.43/2.81 (20188) {G0,W6,D2,L2,V3,M2} { ! triangle( X, Y, Z ), edge( X ) }.
% 2.43/2.81 (20189) {G0,W8,D2,L2,V3,M2} { ! triangle( X, Y, Z ), alpha5( X, Y, Z ) }.
% 2.43/2.81 (20190) {G0,W10,D2,L3,V3,M3} { ! edge( X ), ! alpha5( X, Y, Z ), triangle
% 2.43/2.81 ( X, Y, Z ) }.
% 2.43/2.81 (20191) {G0,W6,D2,L2,V3,M2} { ! alpha5( X, Y, Z ), edge( Y ) }.
% 2.43/2.81 (20192) {G0,W8,D2,L2,V3,M2} { ! alpha5( X, Y, Z ), alpha8( X, Y, Z ) }.
% 2.43/2.81 (20193) {G0,W10,D2,L3,V3,M3} { ! edge( Y ), ! alpha8( X, Y, Z ), alpha5( X
% 2.43/2.81 , Y, Z ) }.
% 2.43/2.81 (20194) {G0,W6,D2,L2,V3,M2} { ! alpha8( X, Y, Z ), edge( Z ) }.
% 2.43/2.81 (20195) {G0,W8,D2,L2,V3,M2} { ! alpha8( X, Y, Z ), alpha9( X, Y, Z ) }.
% 2.43/2.81 (20196) {G0,W10,D2,L3,V3,M3} { ! edge( Z ), ! alpha9( X, Y, Z ), alpha8( X
% 2.43/2.81 , Y, Z ) }.
% 2.43/2.81 (20197) {G0,W7,D2,L2,V3,M2} { ! alpha9( X, Y, Z ), sequential( X, Y ) }.
% 2.43/2.81 (20198) {G0,W8,D2,L2,V3,M2} { ! alpha9( X, Y, Z ), alpha10( X, Y, Z ) }.
% 2.43/2.81 (20199) {G0,W11,D2,L3,V3,M3} { ! sequential( X, Y ), ! alpha10( X, Y, Z )
% 2.43/2.81 , alpha9( X, Y, Z ) }.
% 2.43/2.81 (20200) {G0,W7,D2,L2,V3,M2} { ! alpha10( X, Y, Z ), sequential( Y, Z ) }.
% 2.43/2.81 (20201) {G0,W7,D2,L2,V3,M2} { ! alpha10( X, Y, Z ), sequential( Z, X ) }.
% 2.43/2.81 (20202) {G0,W10,D2,L3,V3,M3} { ! sequential( Y, Z ), ! sequential( Z, X )
% 2.43/2.81 , alpha10( X, Y, Z ) }.
% 2.43/2.81 (20203) {G0,W10,D3,L2,V3,M2} { ! path( Y, Z, X ), length_of( X ) =
% 2.43/2.81 number_of_in( edges, X ) }.
% 2.43/2.81 (20204) {G0,W12,D4,L2,V3,M2} { ! path( Y, Z, X ), number_of_in(
% 2.43/2.81 sequential_pairs, X ) = minus( length_of( X ), n1 ) }.
% 2.43/2.81 (20205) {G0,W17,D3,L3,V3,M3} { ! path( Y, Z, X ), alpha14( X, skol9( X ),
% 2.43/2.81 skol11( X ) ), number_of_in( sequential_pairs, X ) = number_of_in(
% 2.43/2.81 triangles, X ) }.
% 2.43/2.81 (20206) {G0,W17,D3,L3,V4,M3} { ! path( Y, Z, X ), ! triangle( skol9( X ),
% 2.43/2.81 skol11( X ), T ), number_of_in( sequential_pairs, X ) = number_of_in(
% 2.43/2.81 triangles, X ) }.
% 2.43/2.81 (20207) {G0,W7,D2,L2,V3,M2} { ! alpha14( X, Y, Z ), on_path( Y, X ) }.
% 2.43/2.81 (20208) {G0,W7,D2,L2,V3,M2} { ! alpha14( X, Y, Z ), on_path( Z, X ) }.
% 2.43/2.81 (20209) {G0,W7,D2,L2,V3,M2} { ! alpha14( X, Y, Z ), sequential( Y, Z ) }.
% 2.43/2.81 (20210) {G0,W13,D2,L4,V3,M4} { ! on_path( Y, X ), ! on_path( Z, X ), !
% 2.43/2.81 sequential( Y, Z ), alpha14( X, Y, Z ) }.
% 2.43/2.81 (20211) {G0,W7,D3,L1,V2,M1} { less_or_equal( number_of_in( X, Y ),
% 2.43/2.81 number_of_in( X, graph ) ) }.
% 2.43/2.81 (20212) {G0,W1,D1,L1,V0,M1} { complete }.
% 2.43/2.81 (20213) {G0,W4,D2,L1,V0,M1} { path( skol12, skol13, skol10 ) }.
% 2.43/2.81 (20214) {G0,W15,D3,L4,V2,M4} { ! on_path( X, skol10 ), ! on_path( Y,
% 2.43/2.81 skol10 ), ! sequential( X, Y ), triangle( X, Y, skol14( X, Y ) ) }.
% 2.43/2.81 (20215) {G0,W7,D3,L1,V0,M1} { ! number_of_in( sequential_pairs, skol10 ) =
% 2.43/2.81 number_of_in( triangles, skol10 ) }.
% 2.43/2.81
% 2.43/2.81
% 2.43/2.81 Total Proof:
% 2.43/2.81
% 2.43/2.81 eqswap: (20321) {G0,W17,D3,L3,V3,M3} { number_of_in( triangles, X ) =
% 2.43/2.81 number_of_in( sequential_pairs, X ), ! path( Y, Z, X ), alpha14( X, skol9
% 2.43/2.81 ( X ), skol11( X ) ) }.
% 2.43/2.81 parent0[2]: (20205) {G0,W17,D3,L3,V3,M3} { ! path( Y, Z, X ), alpha14( X,
% 2.43/2.81 skol9( X ), skol11( X ) ), number_of_in( sequential_pairs, X ) =
% 2.43/2.81 number_of_in( triangles, X ) }.
% 2.43/2.81 substitution0:
% 2.43/2.81 X := X
% 2.43/2.81 Y := Y
% 2.43/2.81 Z := Z
% 2.43/2.81 end
% 2.43/2.81
% 2.43/2.81 subsumption: (99) {G0,W17,D3,L3,V3,M3} I { ! path( Y, Z, X ), alpha14( X,
% 2.43/2.81 skol9( X ), skol11( X ) ), number_of_in( triangles, X ) ==> number_of_in
% 2.43/2.81 ( sequential_pairs, X ) }.
% 2.43/2.81 parent0: (20321) {G0,W17,D3,L3,V3,M3} { number_of_in( triangles, X ) =
% 2.43/2.81 number_of_in( sequential_pairs, X ), ! path( Y, Z, X ), alpha14( X, skol9
% 2.43/2.81 ( X ), skol11( X ) ) }.
% 2.43/2.81 substitution0:
% 2.43/2.81 X := X
% 2.43/2.81 Y := Y
% 2.43/2.81 Z := Z
% 2.43/2.81 end
% 2.43/2.81 permutation0:
% 2.43/2.81 0 ==> 2
% 2.43/2.81 1 ==> 0
% 2.43/2.81 2 ==> 1
% 2.43/2.81 end
% 2.43/2.81
% 2.43/2.81 eqswap: (20428) {G0,W17,D3,L3,V4,M3} { number_of_in( triangles, X ) =
% 2.43/2.81 number_of_in( sequential_pairs, X ), ! path( Y, Z, X ), ! triangle( skol9
% 2.43/2.81 ( X ), skol11( X ), T ) }.
% 2.43/2.81 parent0[2]: (20206) {G0,W17,D3,L3,V4,M3} { ! path( Y, Z, X ), ! triangle(
% 2.43/2.81 skol9( X ), skol11( X ), T ), number_of_in( sequential_pairs, X ) =
% 2.43/2.81 number_of_in( triangles, X ) }.
% 2.43/2.81 substitution0:
% 2.43/2.81 X := X
% 2.43/2.81 Y := Y
% 2.43/2.81 Z := Z
% 2.43/2.81 T := T
% 2.43/2.81 end
% 2.43/2.81
% 2.43/2.81 subsumption: (100) {G0,W17,D3,L3,V4,M3} I { ! path( Y, Z, X ), ! triangle(
% 2.43/2.81 skol9( X ), skol11( X ), T ), number_of_in( triangles, X ) ==>
% 2.43/2.81 number_of_in( sequential_pairs, X ) }.
% 2.43/2.81 parent0: (20428) {G0,W17,D3,L3,V4,M3} { number_of_in( triangles, X ) =
% 2.43/2.81 number_of_in( sequential_pairs, X ), ! path( Y, Z, X ), ! triangle( skol9
% 2.43/2.81 ( X ), skol11( X ), T ) }.
% 2.43/2.81 substitution0:
% 2.43/2.81 X := X
% 2.43/2.81 Y := Y
% 2.43/2.81 Z := Z
% 2.43/2.81 T := T
% 2.43/2.81 end
% 2.43/2.81 permutation0:
% 2.43/2.81 0 ==> 2
% 2.43/2.81 1 ==> 0
% 2.43/2.81 2 ==> 1
% 2.43/2.81 end
% 2.43/2.81
% 2.43/2.81 subsumption: (101) {G0,W7,D2,L2,V3,M2} I { ! alpha14( X, Y, Z ), on_path( Y
% 2.43/2.81 , X ) }.
% 2.43/2.81 parent0: (20207) {G0,W7,D2,L2,V3,M2} { ! alpha14( X, Y, Z ), on_path( Y, X
% 2.43/2.81 ) }.
% 2.43/2.81 substitution0:
% 2.43/2.81 X := X
% 2.43/2.81 Y := Y
% 2.43/2.81 Z := Z
% 2.43/2.81 end
% 2.43/2.81 permutation0:
% 2.43/2.81 0 ==> 0
% 2.43/2.81 1 ==> 1
% 2.43/2.81 end
% 2.43/2.81
% 2.43/2.81 subsumption: (102) {G0,W7,D2,L2,V3,M2} I { ! alpha14( X, Y, Z ), on_path( Z
% 2.43/2.81 , X ) }.
% 2.43/2.81 parent0: (20208) {G0,W7,D2,L2,V3,M2} { ! alpha14( X, Y, Z ), on_path( Z, X
% 2.43/2.81 ) }.
% 2.43/2.81 substitution0:
% 2.43/2.81 X := X
% 2.43/2.81 Y := Y
% 2.43/2.81 Z := Z
% 2.43/2.81 end
% 2.43/2.81 permutation0:
% 2.43/2.81 0 ==> 0
% 2.43/2.81 1 ==> 1
% 2.43/2.81 end
% 2.43/2.81
% 2.43/2.81 subsumption: (103) {G0,W7,D2,L2,V3,M2} I { ! alpha14( X, Y, Z ), sequential
% 2.43/2.81 ( Y, Z ) }.
% 2.43/2.81 parent0: (20209) {G0,W7,D2,L2,V3,M2} { ! alpha14( X, Y, Z ), sequential( Y
% 2.43/2.81 , Z ) }.
% 2.43/2.81 substitution0:
% 2.43/2.81 X := X
% 2.43/2.81 Y := Y
% 2.43/2.81 Z := Z
% 2.43/2.81 end
% 2.43/2.81 permutation0:
% 2.43/2.81 0 ==> 0
% 2.43/2.81 1 ==> 1
% 2.43/2.81 end
% 2.43/2.81
% 2.43/2.81 subsumption: (107) {G0,W4,D2,L1,V0,M1} I { path( skol12, skol13, skol10 )
% 2.43/2.81 }.
% 2.43/2.81 parent0: (20213) {G0,W4,D2,L1,V0,M1} { path( skol12, skol13, skol10 ) }.
% 2.43/2.81 substitution0:
% 2.43/2.81 end
% 2.43/2.81 permutation0:
% 2.43/2.81 0 ==> 0
% 2.43/2.81 end
% 2.43/2.81
% 2.43/2.81 subsumption: (108) {G0,W15,D3,L4,V2,M4} I { ! on_path( X, skol10 ), !
% 2.43/2.81 on_path( Y, skol10 ), ! sequential( X, Y ), triangle( X, Y, skol14( X, Y
% 2.43/2.81 ) ) }.
% 2.43/2.81 parent0: (20214) {G0,W15,D3,L4,V2,M4} { ! on_path( X, skol10 ), ! on_path
% 2.43/2.81 ( Y, skol10 ), ! sequential( X, Y ), triangle( X, Y, skol14( X, Y ) ) }.
% 2.43/2.81 substitution0:
% 2.43/2.81 X := X
% 2.43/2.81 Y := Y
% 2.43/2.81 end
% 2.43/2.81 permutation0:
% 2.43/2.81 0 ==> 0
% 2.43/2.81 1 ==> 1
% 2.43/2.81 2 ==> 2
% 2.43/2.81 3 ==> 3
% 2.43/2.81 end
% 2.43/2.81
% 2.43/2.81 eqswap: (21076) {G0,W7,D3,L1,V0,M1} { ! number_of_in( triangles, skol10 )
% 2.43/2.81 = number_of_in( sequential_pairs, skol10 ) }.
% 2.43/2.81 parent0[0]: (20215) {G0,W7,D3,L1,V0,M1} { ! number_of_in( sequential_pairs
% 2.43/2.81 , skol10 ) = number_of_in( triangles, skol10 ) }.
% 2.43/2.81 substitution0:
% 2.43/2.81 end
% 2.43/2.81
% 2.43/2.81 subsumption: (109) {G0,W7,D3,L1,V0,M1} I { ! number_of_in( triangles,
% 2.43/2.81 skol10 ) ==> number_of_in( sequential_pairs, skol10 ) }.
% 2.43/2.81 parent0: (21076) {G0,W7,D3,L1,V0,M1} { ! number_of_in( triangles, skol10 )
% 2.43/2.81 = number_of_in( sequential_pairs, skol10 ) }.
% 2.43/2.81 substitution0:
% 2.43/2.81 end
% 2.43/2.81 permutation0:
% 2.43/2.81 0 ==> 0
% 2.43/2.81 end
% 2.43/2.81
% 2.43/2.81 eqswap: (21077) {G0,W17,D3,L3,V3,M3} { number_of_in( sequential_pairs, X )
% 2.43/2.81 ==> number_of_in( triangles, X ), ! path( Y, Z, X ), alpha14( X, skol9(
% 2.43/2.81 X ), skol11( X ) ) }.
% 2.43/2.81 parent0[2]: (99) {G0,W17,D3,L3,V3,M3} I { ! path( Y, Z, X ), alpha14( X,
% 2.43/2.81 skol9( X ), skol11( X ) ), number_of_in( triangles, X ) ==> number_of_in
% 2.43/2.81 ( sequential_pairs, X ) }.
% 2.43/2.81 substitution0:
% 2.43/2.81 X := X
% 2.43/2.81 Y := Y
% 2.43/2.81 Z := Z
% 2.43/2.81 end
% 2.43/2.81
% 2.43/2.81 eqswap: (21078) {G0,W7,D3,L1,V0,M1} { ! number_of_in( sequential_pairs,
% 2.43/2.81 skol10 ) ==> number_of_in( triangles, skol10 ) }.
% 2.43/2.81 parent0[0]: (109) {G0,W7,D3,L1,V0,M1} I { ! number_of_in( triangles, skol10
% 2.43/2.81 ) ==> number_of_in( sequential_pairs, skol10 ) }.
% 2.43/2.81 substitution0:
% 2.43/2.81 end
% 2.43/2.81
% 2.43/2.81 resolution: (21079) {G1,W13,D3,L2,V0,M2} { number_of_in( sequential_pairs
% 2.43/2.81 , skol10 ) ==> number_of_in( triangles, skol10 ), alpha14( skol10, skol9
% 2.43/2.81 ( skol10 ), skol11( skol10 ) ) }.
% 2.43/2.81 parent0[1]: (21077) {G0,W17,D3,L3,V3,M3} { number_of_in( sequential_pairs
% 2.43/2.81 , X ) ==> number_of_in( triangles, X ), ! path( Y, Z, X ), alpha14( X,
% 2.43/2.81 skol9( X ), skol11( X ) ) }.
% 2.43/2.81 parent1[0]: (107) {G0,W4,D2,L1,V0,M1} I { path( skol12, skol13, skol10 )
% 2.43/2.81 }.
% 2.43/2.81 substitution0:
% 2.43/2.81 X := skol10
% 2.43/2.81 Y := skol12
% 2.43/2.81 Z := skol13
% 2.43/2.81 end
% 2.43/2.81 substitution1:
% 2.43/2.81 end
% 2.43/2.81
% 2.43/2.81 resolution: (21080) {G1,W6,D3,L1,V0,M1} { alpha14( skol10, skol9( skol10 )
% 2.43/2.81 , skol11( skol10 ) ) }.
% 2.43/2.81 parent0[0]: (21078) {G0,W7,D3,L1,V0,M1} { ! number_of_in( sequential_pairs
% 2.43/2.81 , skol10 ) ==> number_of_in( triangles, skol10 ) }.
% 2.43/2.81 parent1[0]: (21079) {G1,W13,D3,L2,V0,M2} { number_of_in( sequential_pairs
% 2.43/2.81 , skol10 ) ==> number_of_in( triangles, skol10 ), alpha14( skol10, skol9
% 2.43/2.81 ( skol10 ), skol11( skol10 ) ) }.
% 2.43/2.81 substitution0:
% 2.43/2.81 end
% 2.43/2.81 substitution1:
% 2.43/2.81 end
% 2.43/2.81
% 2.43/2.81 subsumption: (4734) {G1,W6,D3,L1,V0,M1} R(99,107);r(109) { alpha14( skol10
% 2.43/2.81 , skol9( skol10 ), skol11( skol10 ) ) }.
% 2.43/2.81 parent0: (21080) {G1,W6,D3,L1,V0,M1} { alpha14( skol10, skol9( skol10 ),
% 2.43/2.81 skol11( skol10 ) ) }.
% 2.43/2.81 substitution0:
% 2.43/2.81 end
% 2.43/2.81 permutation0:
% 2.43/2.81 0 ==> 0
% 2.43/2.81 end
% 2.43/2.81
% 2.43/2.81 resolution: (21081) {G1,W4,D3,L1,V0,M1} { on_path( skol9( skol10 ), skol10
% 2.43/2.81 ) }.
% 2.43/2.81 parent0[0]: (101) {G0,W7,D2,L2,V3,M2} I { ! alpha14( X, Y, Z ), on_path( Y
% 2.43/2.81 , X ) }.
% 2.43/2.81 parent1[0]: (4734) {G1,W6,D3,L1,V0,M1} R(99,107);r(109) { alpha14( skol10,
% 2.43/2.81 skol9( skol10 ), skol11( skol10 ) ) }.
% 2.43/2.81 substitution0:
% 2.43/2.81 X := skol10
% 2.43/2.81 Y := skol9( skol10 )
% 2.43/2.81 Z := skol11( skol10 )
% 2.43/2.81 end
% 2.43/2.81 substitution1:
% 2.43/2.81 end
% 2.43/2.81
% 2.43/2.81 subsumption: (4767) {G2,W4,D3,L1,V0,M1} R(4734,101) { on_path( skol9(
% 2.43/2.81 skol10 ), skol10 ) }.
% 2.43/2.81 parent0: (21081) {G1,W4,D3,L1,V0,M1} { on_path( skol9( skol10 ), skol10 )
% 2.43/2.81 }.
% 2.43/2.81 substitution0:
% 2.43/2.81 end
% 2.43/2.81 permutation0:
% 2.43/2.81 0 ==> 0
% 2.43/2.81 end
% 2.43/2.81
% 2.43/2.81 resolution: (21082) {G1,W4,D3,L1,V0,M1} { on_path( skol11( skol10 ),
% 2.43/2.81 skol10 ) }.
% 2.43/2.81 parent0[0]: (102) {G0,W7,D2,L2,V3,M2} I { ! alpha14( X, Y, Z ), on_path( Z
% 2.43/2.81 , X ) }.
% 2.43/2.81 parent1[0]: (4734) {G1,W6,D3,L1,V0,M1} R(99,107);r(109) { alpha14( skol10,
% 2.43/2.81 skol9( skol10 ), skol11( skol10 ) ) }.
% 2.43/2.81 substitution0:
% 2.43/2.81 X := skol10
% 2.43/2.81 Y := skol9( skol10 )
% 2.43/2.81 Z := skol11( skol10 )
% 2.43/2.81 end
% 2.43/2.81 substitution1:
% 2.43/2.81 end
% 2.43/2.81
% 2.43/2.81 subsumption: (4768) {G2,W4,D3,L1,V0,M1} R(4734,102) { on_path( skol11(
% 2.43/2.81 skol10 ), skol10 ) }.
% 2.43/2.81 parent0: (21082) {G1,W4,D3,L1,V0,M1} { on_path( skol11( skol10 ), skol10 )
% 2.43/2.81 }.
% 2.43/2.81 substitution0:
% 2.43/2.81 end
% 2.43/2.81 permutation0:
% 2.43/2.81 0 ==> 0
% 2.43/2.81 end
% 2.43/2.81
% 2.43/2.81 resolution: (21083) {G1,W5,D3,L1,V0,M1} { sequential( skol9( skol10 ),
% 2.43/2.81 skol11( skol10 ) ) }.
% 2.43/2.81 parent0[0]: (103) {G0,W7,D2,L2,V3,M2} I { ! alpha14( X, Y, Z ), sequential
% 2.43/2.81 ( Y, Z ) }.
% 2.43/2.81 parent1[0]: (4734) {G1,W6,D3,L1,V0,M1} R(99,107);r(109) { alpha14( skol10,
% 2.43/2.81 skol9( skol10 ), skol11( skol10 ) ) }.
% 2.43/2.81 substitution0:
% 2.43/2.81 X := skol10
% 2.43/2.81 Y := skol9( skol10 )
% 2.43/2.81 Z := skol11( skol10 )
% 2.43/2.81 end
% 2.43/2.81 substitution1:
% 2.43/2.81 end
% 2.43/2.81
% 2.43/2.81 subsumption: (4774) {G2,W5,D3,L1,V0,M1} R(4734,103) { sequential( skol9(
% 2.43/2.81 skol10 ), skol11( skol10 ) ) }.
% 2.43/2.81 parent0: (21083) {G1,W5,D3,L1,V0,M1} { sequential( skol9( skol10 ), skol11
% 2.43/2.81 ( skol10 ) ) }.
% 2.43/2.81 substitution0:
% 2.43/2.81 end
% 2.43/2.81 permutation0:
% 2.43/2.81 0 ==> 0
% 2.43/2.81 end
% 2.43/2.81
% 2.43/2.81 eqswap: (21084) {G0,W17,D3,L3,V4,M3} { number_of_in( sequential_pairs, X )
% 2.43/2.81 ==> number_of_in( triangles, X ), ! path( Y, Z, X ), ! triangle( skol9(
% 2.43/2.81 X ), skol11( X ), T ) }.
% 2.43/2.81 parent0[2]: (100) {G0,W17,D3,L3,V4,M3} I { ! path( Y, Z, X ), ! triangle(
% 2.43/2.81 skol9( X ), skol11( X ), T ), number_of_in( triangles, X ) ==>
% 2.43/2.81 number_of_in( sequential_pairs, X ) }.
% 2.43/2.81 substitution0:
% 2.43/2.81 X := X
% 2.43/2.81 Y := Y
% 2.43/2.81 Z := Z
% 2.43/2.81 T := T
% 2.43/2.81 end
% 2.43/2.81
% 2.43/2.81 eqswap: (21085) {G0,W7,D3,L1,V0,M1} { ! number_of_in( sequential_pairs,
% 2.43/2.81 skol10 ) ==> number_of_in( triangles, skol10 ) }.
% 2.43/2.81 parent0[0]: (109) {G0,W7,D3,L1,V0,M1} I { ! number_of_in( triangles, skol10
% 2.43/2.81 ) ==> number_of_in( sequential_pairs, skol10 ) }.
% 2.43/2.81 substitution0:
% 2.43/2.81 end
% 2.43/2.81
% 2.43/2.81 resolution: (21086) {G1,W13,D3,L2,V1,M2} { number_of_in( sequential_pairs
% 2.43/2.81 , skol10 ) ==> number_of_in( triangles, skol10 ), ! triangle( skol9(
% 2.43/2.81 skol10 ), skol11( skol10 ), X ) }.
% 2.43/2.81 parent0[1]: (21084) {G0,W17,D3,L3,V4,M3} { number_of_in( sequential_pairs
% 2.43/2.81 , X ) ==> number_of_in( triangles, X ), ! path( Y, Z, X ), ! triangle(
% 2.43/2.81 skol9( X ), skol11( X ), T ) }.
% 2.43/2.81 parent1[0]: (107) {G0,W4,D2,L1,V0,M1} I { path( skol12, skol13, skol10 )
% 2.43/2.81 }.
% 2.43/2.81 substitution0:
% 2.43/2.81 X := skol10
% 2.43/2.81 Y := skol12
% 2.43/2.81 Z := skol13
% 2.43/2.81 T := X
% 2.43/2.81 end
% 2.43/2.81 substitution1:
% 2.43/2.81 end
% 2.43/2.81
% 2.43/2.81 resolution: (21087) {G1,W6,D3,L1,V1,M1} { ! triangle( skol9( skol10 ),
% 2.43/2.81 skol11( skol10 ), X ) }.
% 2.43/2.81 parent0[0]: (21085) {G0,W7,D3,L1,V0,M1} { ! number_of_in( sequential_pairs
% 2.43/2.81 , skol10 ) ==> number_of_in( triangles, skol10 ) }.
% 2.43/2.81 parent1[0]: (21086) {G1,W13,D3,L2,V1,M2} { number_of_in( sequential_pairs
% 2.43/2.81 , skol10 ) ==> number_of_in( triangles, skol10 ), ! triangle( skol9(
% 2.43/2.81 skol10 ), skol11( skol10 ), X ) }.
% 2.43/2.81 substitution0:
% 2.43/2.81 end
% 2.43/2.81 substitution1:
% 2.43/2.81 X := X
% 2.43/2.81 end
% 2.43/2.81
% 2.43/2.81 subsumption: (4876) {G1,W6,D3,L1,V1,M1} R(100,107);r(109) { ! triangle(
% 2.43/2.81 skol9( skol10 ), skol11( skol10 ), X ) }.
% 2.43/2.81 parent0: (21087) {G1,W6,D3,L1,V1,M1} { ! triangle( skol9( skol10 ), skol11
% 2.43/2.81 ( skol10 ), X ) }.
% 2.43/2.81 substitution0:
% 2.43/2.81 X := X
% 2.43/2.81 end
% 2.43/2.81 permutation0:
% 2.43/2.81 0 ==> 0
% 2.43/2.81 end
% 2.43/2.81
% 2.43/2.81 resolution: (21088) {G1,W13,D3,L3,V0,M3} { ! on_path( skol9( skol10 ),
% 2.43/2.81 skol10 ), ! on_path( skol11( skol10 ), skol10 ), ! sequential( skol9(
% 2.43/2.81 skol10 ), skol11( skol10 ) ) }.
% 2.43/2.81 parent0[0]: (4876) {G1,W6,D3,L1,V1,M1} R(100,107);r(109) { ! triangle(
% 2.43/2.81 skol9( skol10 ), skol11( skol10 ), X ) }.
% 2.43/2.81 parent1[3]: (108) {G0,W15,D3,L4,V2,M4} I { ! on_path( X, skol10 ), !
% 2.43/2.81 on_path( Y, skol10 ), ! sequential( X, Y ), triangle( X, Y, skol14( X, Y
% 2.43/2.81 ) ) }.
% 2.43/2.81 substitution0:
% 2.43/2.81 X := skol14( skol9( skol10 ), skol11( skol10 ) )
% 2.43/2.81 end
% 2.43/2.81 substitution1:
% 2.43/2.81 X := skol9( skol10 )
% 2.43/2.81 Y := skol11( skol10 )
% 2.43/2.81 end
% 2.43/2.81
% 2.43/2.81 resolution: (21089) {G2,W9,D3,L2,V0,M2} { ! on_path( skol11( skol10 ),
% 2.43/2.81 skol10 ), ! sequential( skol9( skol10 ), skol11( skol10 ) ) }.
% 2.43/2.81 parent0[0]: (21088) {G1,W13,D3,L3,V0,M3} { ! on_path( skol9( skol10 ),
% 2.43/2.81 skol10 ), ! on_path( skol11( skol10 ), skol10 ), ! sequential( skol9(
% 2.43/2.81 skol10 ), skol11( skol10 ) ) }.
% 2.43/2.81 parent1[0]: (4767) {G2,W4,D3,L1,V0,M1} R(4734,101) { on_path( skol9( skol10
% 2.43/2.81 ), skol10 ) }.
% 2.43/2.81 substitution0:
% 2.43/2.81 end
% 2.43/2.81 substitution1:
% 2.43/2.81 end
% 2.43/2.81
% 2.43/2.81 subsumption: (5223) {G3,W9,D3,L2,V0,M2} R(4876,108);r(4767) { ! on_path(
% 2.43/2.81 skol11( skol10 ), skol10 ), ! sequential( skol9( skol10 ), skol11( skol10
% 2.43/2.81 ) ) }.
% 2.43/2.81 parent0: (21089) {G2,W9,D3,L2,V0,M2} { ! on_path( skol11( skol10 ), skol10
% 2.43/2.81 ), ! sequential( skol9( skol10 ), skol11( skol10 ) ) }.
% 2.43/2.81 substitution0:
% 2.43/2.81 end
% 2.43/2.81 permutation0:
% 2.43/2.81 0 ==> 0
% 2.43/2.81 1 ==> 1
% 2.43/2.81 end
% 2.43/2.81
% 2.43/2.81 resolution: (21090) {G3,W5,D3,L1,V0,M1} { ! sequential( skol9( skol10 ),
% 2.43/2.81 skol11( skol10 ) ) }.
% 2.43/2.81 parent0[0]: (5223) {G3,W9,D3,L2,V0,M2} R(4876,108);r(4767) { ! on_path(
% 2.43/2.81 skol11( skol10 ), skol10 ), ! sequential( skol9( skol10 ), skol11( skol10
% 2.43/2.81 ) ) }.
% 2.43/2.81 parent1[0]: (4768) {G2,W4,D3,L1,V0,M1} R(4734,102) { on_path( skol11(
% 2.43/2.81 skol10 ), skol10 ) }.
% 2.43/2.81 substitution0:
% 2.43/2.81 end
% 2.43/2.81 substitution1:
% 2.43/2.81 end
% 2.43/2.81
% 2.43/2.81 resolution: (21091) {G3,W0,D0,L0,V0,M0} { }.
% 2.43/2.81 parent0[0]: (21090) {G3,W5,D3,L1,V0,M1} { ! sequential( skol9( skol10 ),
% 2.43/2.81 skol11( skol10 ) ) }.
% 2.43/2.81 parent1[0]: (4774) {G2,W5,D3,L1,V0,M1} R(4734,103) { sequential( skol9(
% 2.43/2.81 skol10 ), skol11( skol10 ) ) }.
% 2.43/2.81 substitution0:
% 2.43/2.81 end
% 2.43/2.81 substitution1:
% 2.43/2.81 end
% 2.43/2.81
% 2.43/2.81 subsumption: (20104) {G4,W0,D0,L0,V0,M0} S(5223);r(4768);r(4774) { }.
% 2.43/2.81 parent0: (21091) {G3,W0,D0,L0,V0,M0} { }.
% 2.43/2.81 substitution0:
% 2.43/2.81 end
% 2.43/2.81 permutation0:
% 2.43/2.81 end
% 2.43/2.81
% 2.43/2.81 Proof check complete!
% 2.43/2.81
% 2.43/2.81 Memory use:
% 2.43/2.81
% 2.43/2.81 space for terms: 294735
% 2.43/2.81 space for clauses: 758680
% 2.43/2.81
% 2.43/2.81
% 2.43/2.81 clauses generated: 114479
% 2.43/2.81 clauses kept: 20105
% 2.43/2.81 clauses selected: 1601
% 2.43/2.81 clauses deleted: 1022
% 2.43/2.81 clauses inuse deleted: 45
% 2.43/2.81
% 2.43/2.81 subsentry: 277880
% 2.43/2.81 literals s-matched: 223357
% 2.43/2.81 literals matched: 199173
% 2.43/2.81 full subsumption: 38965
% 2.43/2.81
% 2.43/2.81 checksum: 31550481
% 2.43/2.81
% 2.43/2.81
% 2.43/2.81 Bliksem ended
%------------------------------------------------------------------------------