TSTP Solution File: SET767+4 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET767+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Mon Jul 18 22:51:52 EDT 2022
% Result : Theorem 2.24s 2.61s
% Output : Refutation 2.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET767+4 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.13 % Command : bliksem %s
% 0.14/0.34 % Computer : n029.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % DateTime : Sat Jul 9 17:55:30 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.71/1.11 *** allocated 10000 integers for termspace/termends
% 0.71/1.11 *** allocated 10000 integers for clauses
% 0.71/1.11 *** allocated 10000 integers for justifications
% 0.71/1.11 Bliksem 1.12
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 Automatic Strategy Selection
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 Clauses:
% 0.71/1.11
% 0.71/1.11 { ! subset( X, Y ), ! member( Z, X ), member( Z, Y ) }.
% 0.71/1.11 { ! member( skol1( Z, Y ), Y ), subset( X, Y ) }.
% 0.71/1.11 { member( skol1( X, Y ), X ), subset( X, Y ) }.
% 0.71/1.11 { ! equal_set( X, Y ), subset( X, Y ) }.
% 0.71/1.11 { ! equal_set( X, Y ), subset( Y, X ) }.
% 0.71/1.11 { ! subset( X, Y ), ! subset( Y, X ), equal_set( X, Y ) }.
% 0.71/1.11 { ! member( X, power_set( Y ) ), subset( X, Y ) }.
% 0.71/1.11 { ! subset( X, Y ), member( X, power_set( Y ) ) }.
% 0.71/1.11 { ! member( X, intersection( Y, Z ) ), member( X, Y ) }.
% 0.71/1.11 { ! member( X, intersection( Y, Z ) ), member( X, Z ) }.
% 0.71/1.11 { ! member( X, Y ), ! member( X, Z ), member( X, intersection( Y, Z ) ) }.
% 0.71/1.11 { ! member( X, union( Y, Z ) ), member( X, Y ), member( X, Z ) }.
% 0.71/1.11 { ! member( X, Y ), member( X, union( Y, Z ) ) }.
% 0.71/1.11 { ! member( X, Z ), member( X, union( Y, Z ) ) }.
% 0.71/1.11 { ! member( X, empty_set ) }.
% 0.71/1.11 { ! member( X, difference( Z, Y ) ), member( X, Z ) }.
% 0.71/1.11 { ! member( X, difference( Z, Y ) ), ! member( X, Y ) }.
% 0.71/1.11 { ! member( X, Z ), member( X, Y ), member( X, difference( Z, Y ) ) }.
% 0.71/1.11 { ! member( X, singleton( Y ) ), X = Y }.
% 0.71/1.11 { ! X = Y, member( X, singleton( Y ) ) }.
% 0.71/1.11 { ! member( X, unordered_pair( Y, Z ) ), X = Y, X = Z }.
% 0.71/1.11 { ! X = Y, member( X, unordered_pair( Y, Z ) ) }.
% 0.71/1.11 { ! X = Z, member( X, unordered_pair( Y, Z ) ) }.
% 0.71/1.11 { ! member( X, sum( Y ) ), member( skol2( Z, Y ), Y ) }.
% 0.71/1.11 { ! member( X, sum( Y ) ), member( X, skol2( X, Y ) ) }.
% 0.71/1.11 { ! member( Z, Y ), ! member( X, Z ), member( X, sum( Y ) ) }.
% 0.71/1.11 { ! member( X, product( Y ) ), ! member( Z, Y ), member( X, Z ) }.
% 0.71/1.11 { member( skol3( Z, Y ), Y ), member( X, product( Y ) ) }.
% 0.71/1.11 { ! member( X, skol3( X, Y ) ), member( X, product( Y ) ) }.
% 0.71/1.11 { ! disjoint( X, Y ), ! member( Z, X ), ! member( Z, Y ) }.
% 0.71/1.11 { member( skol4( Z, Y ), Y ), disjoint( X, Y ) }.
% 0.71/1.11 { member( skol4( X, Y ), X ), disjoint( X, Y ) }.
% 0.71/1.11 { ! partition( X, Y ), alpha4( X, Y ) }.
% 0.71/1.11 { ! partition( X, Y ), alpha8( X, Y ) }.
% 0.71/1.11 { ! alpha4( X, Y ), ! alpha8( X, Y ), partition( X, Y ) }.
% 0.71/1.11 { ! alpha8( X, Y ), alpha13( X, Y ) }.
% 0.71/1.11 { ! alpha8( X, Y ), alpha1( X ) }.
% 0.71/1.11 { ! alpha13( X, Y ), ! alpha1( X ), alpha8( X, Y ) }.
% 0.71/1.11 { ! alpha13( X, Y ), ! member( Z, Y ), alpha17( X, Z ) }.
% 0.71/1.11 { member( skol5( Z, Y ), Y ), alpha13( X, Y ) }.
% 0.71/1.11 { ! alpha17( X, skol5( X, Y ) ), alpha13( X, Y ) }.
% 0.71/1.11 { ! alpha17( X, Y ), member( Y, skol6( Z, Y ) ) }.
% 0.71/1.11 { ! alpha17( X, Y ), member( skol6( X, Y ), X ) }.
% 0.71/1.11 { ! member( Z, X ), ! member( Y, Z ), alpha17( X, Y ) }.
% 0.71/1.11 { ! alpha4( X, Y ), ! member( Z, X ), subset( Z, Y ) }.
% 0.71/1.11 { ! subset( skol7( Z, Y ), Y ), alpha4( X, Y ) }.
% 0.71/1.11 { member( skol7( X, Y ), X ), alpha4( X, Y ) }.
% 0.71/1.11 { ! alpha1( X ), ! alpha9( X, Y, Z ), alpha5( Y, Z ) }.
% 0.71/1.11 { alpha9( X, skol8( X ), skol16( X ) ), alpha1( X ) }.
% 0.71/1.11 { ! alpha5( skol8( X ), skol16( X ) ), alpha1( X ) }.
% 0.71/1.11 { ! alpha9( X, Y, Z ), member( Y, X ) }.
% 0.71/1.11 { ! alpha9( X, Y, Z ), member( Z, X ) }.
% 0.71/1.11 { ! member( Y, X ), ! member( Z, X ), alpha9( X, Y, Z ) }.
% 0.71/1.11 { ! alpha5( X, Y ), ! alpha10( X, Y ), X = Y }.
% 0.71/1.11 { alpha10( X, Y ), alpha5( X, Y ) }.
% 0.71/1.11 { ! X = Y, alpha5( X, Y ) }.
% 0.71/1.11 { ! alpha10( X, Y ), member( skol9( Z, Y ), Y ) }.
% 0.71/1.11 { ! alpha10( X, Y ), member( skol9( X, Y ), X ) }.
% 0.71/1.11 { ! member( Z, X ), ! member( Z, Y ), alpha10( X, Y ) }.
% 0.71/1.11 { ! equivalence( Y, X ), alpha2( X, Y ) }.
% 0.71/1.11 { ! equivalence( Y, X ), alpha6( X, Y ) }.
% 0.71/1.11 { ! alpha2( X, Y ), ! alpha6( X, Y ), equivalence( Y, X ) }.
% 0.71/1.11 { ! alpha6( X, Y ), alpha11( X, Y ) }.
% 0.71/1.11 { ! alpha6( X, Y ), alpha14( X, Y ) }.
% 0.71/1.11 { ! alpha11( X, Y ), ! alpha14( X, Y ), alpha6( X, Y ) }.
% 0.71/1.11 { ! alpha14( X, Y ), ! alpha21( X, Z, T, U ), alpha23( Y, Z, T, U ) }.
% 0.71/1.11 { alpha21( X, skol10( X, Y ), skol17( X, Y ), skol21( X, Y ) ), alpha14( X
% 0.71/1.11 , Y ) }.
% 0.71/1.11 { ! alpha23( Y, skol10( X, Y ), skol17( X, Y ), skol21( X, Y ) ), alpha14(
% 0.71/1.11 X, Y ) }.
% 0.71/1.11 { ! alpha23( X, Y, Z, T ), ! alpha24( X, Y, Z, T ), apply( X, Y, T ) }.
% 0.71/1.11 { alpha24( X, Y, Z, T ), alpha23( X, Y, Z, T ) }.
% 0.71/1.11 { ! apply( X, Y, T ), alpha23( X, Y, Z, T ) }.
% 0.71/1.11 { ! alpha24( X, Y, Z, T ), apply( X, Y, Z ) }.
% 0.71/1.11 { ! alpha24( X, Y, Z, T ), apply( X, Z, T ) }.
% 0.71/1.11 { ! apply( X, Y, Z ), ! apply( X, Z, T ), alpha24( X, Y, Z, T ) }.
% 0.75/1.27 { ! alpha21( X, Y, Z, T ), member( Y, X ) }.
% 0.75/1.27 { ! alpha21( X, Y, Z, T ), alpha18( X, Z, T ) }.
% 0.75/1.27 { ! member( Y, X ), ! alpha18( X, Z, T ), alpha21( X, Y, Z, T ) }.
% 0.75/1.27 { ! alpha18( X, Y, Z ), member( Y, X ) }.
% 0.75/1.27 { ! alpha18( X, Y, Z ), member( Z, X ) }.
% 0.75/1.27 { ! member( Y, X ), ! member( Z, X ), alpha18( X, Y, Z ) }.
% 0.75/1.27 { ! alpha11( X, Y ), ! alpha15( X, Z, T ), alpha19( Y, Z, T ) }.
% 0.75/1.27 { alpha15( X, skol11( X, Y ), skol18( X, Y ) ), alpha11( X, Y ) }.
% 0.75/1.27 { ! alpha19( Y, skol11( X, Y ), skol18( X, Y ) ), alpha11( X, Y ) }.
% 0.75/1.27 { ! alpha19( X, Y, Z ), ! apply( X, Y, Z ), apply( X, Z, Y ) }.
% 0.75/1.27 { apply( X, Y, Z ), alpha19( X, Y, Z ) }.
% 0.75/1.27 { ! apply( X, Z, Y ), alpha19( X, Y, Z ) }.
% 0.75/1.27 { ! alpha15( X, Y, Z ), member( Y, X ) }.
% 0.75/1.27 { ! alpha15( X, Y, Z ), member( Z, X ) }.
% 0.75/1.27 { ! member( Y, X ), ! member( Z, X ), alpha15( X, Y, Z ) }.
% 0.75/1.27 { ! alpha2( X, Y ), ! member( Z, X ), apply( Y, Z, Z ) }.
% 0.75/1.27 { ! apply( Y, skol12( Z, Y ), skol12( Z, Y ) ), alpha2( X, Y ) }.
% 0.75/1.27 { member( skol12( X, Y ), X ), alpha2( X, Y ) }.
% 0.75/1.27 { ! member( T, equivalence_class( Z, Y, X ) ), member( T, Y ) }.
% 0.75/1.27 { ! member( T, equivalence_class( Z, Y, X ) ), apply( X, Z, T ) }.
% 0.75/1.27 { ! member( T, Y ), ! apply( X, Z, T ), member( T, equivalence_class( Z, Y
% 0.75/1.27 , X ) ) }.
% 0.75/1.27 { ! pre_order( X, Y ), alpha3( X, Y ) }.
% 0.75/1.27 { ! pre_order( X, Y ), alpha7( X, Y ) }.
% 0.75/1.27 { ! alpha3( X, Y ), ! alpha7( X, Y ), pre_order( X, Y ) }.
% 0.75/1.27 { ! alpha7( X, Y ), ! alpha16( Y, Z, T, U ), alpha20( X, Z, T, U ) }.
% 0.75/1.27 { alpha16( Y, skol13( X, Y ), skol19( X, Y ), skol22( X, Y ) ), alpha7( X,
% 0.75/1.27 Y ) }.
% 0.75/1.27 { ! alpha20( X, skol13( X, Y ), skol19( X, Y ), skol22( X, Y ) ), alpha7( X
% 0.75/1.27 , Y ) }.
% 0.75/1.27 { ! alpha20( X, Y, Z, T ), ! alpha22( X, Y, Z, T ), apply( X, Y, T ) }.
% 0.75/1.27 { alpha22( X, Y, Z, T ), alpha20( X, Y, Z, T ) }.
% 0.75/1.27 { ! apply( X, Y, T ), alpha20( X, Y, Z, T ) }.
% 0.75/1.27 { ! alpha22( X, Y, Z, T ), apply( X, Y, Z ) }.
% 0.75/1.27 { ! alpha22( X, Y, Z, T ), apply( X, Z, T ) }.
% 0.75/1.27 { ! apply( X, Y, Z ), ! apply( X, Z, T ), alpha22( X, Y, Z, T ) }.
% 0.75/1.27 { ! alpha16( X, Y, Z, T ), member( Y, X ) }.
% 0.75/1.27 { ! alpha16( X, Y, Z, T ), alpha12( X, Z, T ) }.
% 0.75/1.27 { ! member( Y, X ), ! alpha12( X, Z, T ), alpha16( X, Y, Z, T ) }.
% 0.75/1.27 { ! alpha12( X, Y, Z ), member( Y, X ) }.
% 0.75/1.27 { ! alpha12( X, Y, Z ), member( Z, X ) }.
% 0.75/1.27 { ! member( Y, X ), ! member( Z, X ), alpha12( X, Y, Z ) }.
% 0.75/1.27 { ! alpha3( X, Y ), ! member( Z, Y ), apply( X, Z, Z ) }.
% 0.75/1.27 { member( skol14( Z, Y ), Y ), alpha3( X, Y ) }.
% 0.75/1.27 { ! apply( X, skol14( X, Y ), skol14( X, Y ) ), alpha3( X, Y ) }.
% 0.75/1.27 { equivalence( skol20, skol15 ) }.
% 0.75/1.27 { ! subset( equivalence_class( skol23, skol15, skol20 ), skol15 ) }.
% 0.75/1.27
% 0.75/1.27 percentage equality = 0.029630, percentage horn = 0.838983
% 0.75/1.27 This is a problem with some equality
% 0.75/1.27
% 0.75/1.27
% 0.75/1.27
% 0.75/1.27 Options Used:
% 0.75/1.27
% 0.75/1.27 useres = 1
% 0.75/1.27 useparamod = 1
% 0.75/1.27 useeqrefl = 1
% 0.75/1.27 useeqfact = 1
% 0.75/1.27 usefactor = 1
% 0.75/1.27 usesimpsplitting = 0
% 0.75/1.27 usesimpdemod = 5
% 0.75/1.27 usesimpres = 3
% 0.75/1.27
% 0.75/1.27 resimpinuse = 1000
% 0.75/1.27 resimpclauses = 20000
% 0.75/1.27 substype = eqrewr
% 0.75/1.27 backwardsubs = 1
% 0.75/1.27 selectoldest = 5
% 0.75/1.27
% 0.75/1.27 litorderings [0] = split
% 0.75/1.27 litorderings [1] = extend the termordering, first sorting on arguments
% 0.75/1.27
% 0.75/1.27 termordering = kbo
% 0.75/1.27
% 0.75/1.27 litapriori = 0
% 0.75/1.27 termapriori = 1
% 0.75/1.28 litaposteriori = 0
% 0.75/1.28 termaposteriori = 0
% 0.75/1.28 demodaposteriori = 0
% 0.75/1.28 ordereqreflfact = 0
% 0.75/1.28
% 0.75/1.28 litselect = negord
% 0.75/1.28
% 0.75/1.28 maxweight = 15
% 0.75/1.28 maxdepth = 30000
% 0.75/1.28 maxlength = 115
% 0.75/1.28 maxnrvars = 195
% 0.75/1.28 excuselevel = 1
% 0.75/1.28 increasemaxweight = 1
% 0.75/1.28
% 0.75/1.28 maxselected = 10000000
% 0.75/1.28 maxnrclauses = 10000000
% 0.75/1.28
% 0.75/1.28 showgenerated = 0
% 0.75/1.28 showkept = 0
% 0.75/1.28 showselected = 0
% 0.75/1.28 showdeleted = 0
% 0.75/1.28 showresimp = 1
% 0.75/1.28 showstatus = 2000
% 0.75/1.28
% 0.75/1.28 prologoutput = 0
% 0.75/1.28 nrgoals = 5000000
% 0.75/1.28 totalproof = 1
% 0.75/1.28
% 0.75/1.28 Symbols occurring in the translation:
% 0.75/1.28
% 0.75/1.28 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.75/1.28 . [1, 2] (w:1, o:29, a:1, s:1, b:0),
% 0.75/1.28 ! [4, 1] (w:0, o:17, a:1, s:1, b:0),
% 0.75/1.28 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.75/1.28 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.75/1.28 subset [37, 2] (w:1, o:53, a:1, s:1, b:0),
% 0.75/1.28 member [39, 2] (w:1, o:54, a:1, s:1, b:0),
% 0.75/1.28 equal_set [40, 2] (w:1, o:57, a:1, s:1, b:0),
% 0.75/1.28 power_set [41, 1] (w:1, o:22, a:1, s:1, b:0),
% 0.75/1.28 intersection [42, 2] (w:1, o:58, a:1, s:1, b:0),
% 2.24/2.60 union [43, 2] (w:1, o:59, a:1, s:1, b:0),
% 2.24/2.60 empty_set [44, 0] (w:1, o:9, a:1, s:1, b:0),
% 2.24/2.60 difference [46, 2] (w:1, o:55, a:1, s:1, b:0),
% 2.24/2.60 singleton [47, 1] (w:1, o:23, a:1, s:1, b:0),
% 2.24/2.60 unordered_pair [48, 2] (w:1, o:60, a:1, s:1, b:0),
% 2.24/2.60 sum [49, 1] (w:1, o:24, a:1, s:1, b:0),
% 2.24/2.60 product [51, 1] (w:1, o:25, a:1, s:1, b:0),
% 2.24/2.60 disjoint [52, 2] (w:1, o:56, a:1, s:1, b:0),
% 2.24/2.60 partition [53, 2] (w:1, o:61, a:1, s:1, b:0),
% 2.24/2.60 equivalence [56, 2] (w:1, o:62, a:1, s:1, b:0),
% 2.24/2.60 apply [57, 3] (w:1, o:94, a:1, s:1, b:0),
% 2.24/2.60 equivalence_class [58, 3] (w:1, o:95, a:1, s:1, b:0),
% 2.24/2.60 pre_order [59, 2] (w:1, o:63, a:1, s:1, b:0),
% 2.24/2.60 alpha1 [60, 1] (w:1, o:26, a:1, s:1, b:1),
% 2.24/2.60 alpha2 [61, 2] (w:1, o:69, a:1, s:1, b:1),
% 2.24/2.60 alpha3 [62, 2] (w:1, o:70, a:1, s:1, b:1),
% 2.24/2.60 alpha4 [63, 2] (w:1, o:71, a:1, s:1, b:1),
% 2.24/2.60 alpha5 [64, 2] (w:1, o:72, a:1, s:1, b:1),
% 2.24/2.60 alpha6 [65, 2] (w:1, o:73, a:1, s:1, b:1),
% 2.24/2.60 alpha7 [66, 2] (w:1, o:74, a:1, s:1, b:1),
% 2.24/2.60 alpha8 [67, 2] (w:1, o:75, a:1, s:1, b:1),
% 2.24/2.60 alpha9 [68, 3] (w:1, o:96, a:1, s:1, b:1),
% 2.24/2.60 alpha10 [69, 2] (w:1, o:64, a:1, s:1, b:1),
% 2.24/2.60 alpha11 [70, 2] (w:1, o:65, a:1, s:1, b:1),
% 2.24/2.60 alpha12 [71, 3] (w:1, o:97, a:1, s:1, b:1),
% 2.24/2.60 alpha13 [72, 2] (w:1, o:66, a:1, s:1, b:1),
% 2.24/2.60 alpha14 [73, 2] (w:1, o:67, a:1, s:1, b:1),
% 2.24/2.60 alpha15 [74, 3] (w:1, o:98, a:1, s:1, b:1),
% 2.24/2.60 alpha16 [75, 4] (w:1, o:101, a:1, s:1, b:1),
% 2.24/2.60 alpha17 [76, 2] (w:1, o:68, a:1, s:1, b:1),
% 2.24/2.60 alpha18 [77, 3] (w:1, o:99, a:1, s:1, b:1),
% 2.24/2.60 alpha19 [78, 3] (w:1, o:100, a:1, s:1, b:1),
% 2.24/2.60 alpha20 [79, 4] (w:1, o:102, a:1, s:1, b:1),
% 2.24/2.60 alpha21 [80, 4] (w:1, o:103, a:1, s:1, b:1),
% 2.24/2.60 alpha22 [81, 4] (w:1, o:104, a:1, s:1, b:1),
% 2.24/2.60 alpha23 [82, 4] (w:1, o:105, a:1, s:1, b:1),
% 2.24/2.60 alpha24 [83, 4] (w:1, o:106, a:1, s:1, b:1),
% 2.24/2.60 skol1 [84, 2] (w:1, o:76, a:1, s:1, b:1),
% 2.24/2.60 skol2 [85, 2] (w:1, o:85, a:1, s:1, b:1),
% 2.24/2.60 skol3 [86, 2] (w:1, o:88, a:1, s:1, b:1),
% 2.24/2.60 skol4 [87, 2] (w:1, o:89, a:1, s:1, b:1),
% 2.24/2.60 skol5 [88, 2] (w:1, o:90, a:1, s:1, b:1),
% 2.24/2.60 skol6 [89, 2] (w:1, o:91, a:1, s:1, b:1),
% 2.24/2.60 skol7 [90, 2] (w:1, o:92, a:1, s:1, b:1),
% 2.24/2.60 skol8 [91, 1] (w:1, o:27, a:1, s:1, b:1),
% 2.24/2.60 skol9 [92, 2] (w:1, o:93, a:1, s:1, b:1),
% 2.24/2.60 skol10 [93, 2] (w:1, o:77, a:1, s:1, b:1),
% 2.24/2.60 skol11 [94, 2] (w:1, o:78, a:1, s:1, b:1),
% 2.24/2.60 skol12 [95, 2] (w:1, o:79, a:1, s:1, b:1),
% 2.24/2.60 skol13 [96, 2] (w:1, o:80, a:1, s:1, b:1),
% 2.24/2.60 skol14 [97, 2] (w:1, o:81, a:1, s:1, b:1),
% 2.24/2.60 skol15 [98, 0] (w:1, o:14, a:1, s:1, b:1),
% 2.24/2.60 skol16 [99, 1] (w:1, o:28, a:1, s:1, b:1),
% 2.24/2.60 skol17 [100, 2] (w:1, o:82, a:1, s:1, b:1),
% 2.24/2.60 skol18 [101, 2] (w:1, o:83, a:1, s:1, b:1),
% 2.24/2.60 skol19 [102, 2] (w:1, o:84, a:1, s:1, b:1),
% 2.24/2.60 skol20 [103, 0] (w:1, o:15, a:1, s:1, b:1),
% 2.24/2.60 skol21 [104, 2] (w:1, o:86, a:1, s:1, b:1),
% 2.24/2.60 skol22 [105, 2] (w:1, o:87, a:1, s:1, b:1),
% 2.24/2.60 skol23 [106, 0] (w:1, o:16, a:1, s:1, b:1).
% 2.24/2.60
% 2.24/2.60
% 2.24/2.60 Starting Search:
% 2.24/2.60
% 2.24/2.60 *** allocated 15000 integers for clauses
% 2.24/2.60 *** allocated 22500 integers for clauses
% 2.24/2.60 *** allocated 33750 integers for clauses
% 2.24/2.60 *** allocated 50625 integers for clauses
% 2.24/2.60 *** allocated 15000 integers for termspace/termends
% 2.24/2.60 *** allocated 75937 integers for clauses
% 2.24/2.60 *** allocated 22500 integers for termspace/termends
% 2.24/2.60 Resimplifying inuse:
% 2.24/2.60 Done
% 2.24/2.60
% 2.24/2.60 *** allocated 113905 integers for clauses
% 2.24/2.60 *** allocated 33750 integers for termspace/termends
% 2.24/2.60
% 2.24/2.60 Intermediate Status:
% 2.24/2.60 Generated: 2878
% 2.24/2.60 Kept: 2012
% 2.24/2.60 Inuse: 125
% 2.24/2.60 Deleted: 4
% 2.24/2.60 Deletedinuse: 0
% 2.24/2.60
% 2.24/2.60 Resimplifying inuse:
% 2.24/2.60 Done
% 2.24/2.60
% 2.24/2.60 *** allocated 170857 integers for clauses
% 2.24/2.60 *** allocated 50625 integers for termspace/termends
% 2.24/2.60 Resimplifying inuse:
% 2.24/2.60 Done
% 2.24/2.60
% 2.24/2.60 *** allocated 256285 integers for clauses
% 2.24/2.60 *** allocated 75937 integers for termspace/termends
% 2.24/2.60
% 2.24/2.60 Intermediate Status:
% 2.24/2.60 Generated: 5871
% 2.24/2.60 Kept: 4366
% 2.24/2.60 Inuse: 242
% 2.24/2.60 Deleted: 4
% 2.24/2.60 Deletedinuse: 0
% 2.24/2.60
% 2.24/2.60 Resimplifying inuse:
% 2.24/2.60 Done
% 2.24/2.60
% 2.24/2.60 Resimplifying inuse:
% 2.24/2.60 Done
% 2.24/2.60
% 2.24/2.60 *** allocated 384427 integers for clauses
% 2.24/2.60 *** allocated 113905 integers for termspace/termends
% 2.24/2.61
% 2.24/2.61 Intermediate Status:
% 2.24/2.61 Generated: 11128
% 2.24/2.61 Kept: 6368
% 2.24/2.61 Inuse: 447
% 2.24/2.61 Deleted: 6
% 2.24/2.61 Deletedinuse: 0
% 2.24/2.61
% 2.24/2.61 Resimplifying inuse:
% 2.24/2.61 Done
% 2.24/2.61
% 2.24/2.61 Resimplifying inuse:
% 2.24/2.61 Done
% 2.24/2.61
% 2.24/2.61 *** allocated 576640 integers for clauses
% 2.24/2.61 *** allocated 170857 integers for termspace/termends
% 2.24/2.61
% 2.24/2.61 Intermediate Status:
% 2.24/2.61 Generated: 15842
% 2.24/2.61 Kept: 8953
% 2.24/2.61 Inuse: 530
% 2.24/2.61 Deleted: 8
% 2.24/2.61 Deletedinuse: 2
% 2.24/2.61
% 2.24/2.61 Resimplifying inuse:
% 2.24/2.61 Done
% 2.24/2.61
% 2.24/2.61 Resimplifying inuse:
% 2.24/2.61 Done
% 2.24/2.61
% 2.24/2.61
% 2.24/2.61 Intermediate Status:
% 2.24/2.61 Generated: 21738
% 2.24/2.61 Kept: 11373
% 2.24/2.61 Inuse: 610
% 2.24/2.61 Deleted: 9
% 2.24/2.61 Deletedinuse: 2
% 2.24/2.61
% 2.24/2.61 Resimplifying inuse:
% 2.24/2.61 Done
% 2.24/2.61
% 2.24/2.61 Resimplifying inuse:
% 2.24/2.61 Done
% 2.24/2.61
% 2.24/2.61 *** allocated 256285 integers for termspace/termends
% 2.24/2.61 *** allocated 864960 integers for clauses
% 2.24/2.61
% 2.24/2.61 Intermediate Status:
% 2.24/2.61 Generated: 25675
% 2.24/2.61 Kept: 13382
% 2.24/2.61 Inuse: 652
% 2.24/2.61 Deleted: 13
% 2.24/2.61 Deletedinuse: 6
% 2.24/2.61
% 2.24/2.61 Resimplifying inuse:
% 2.24/2.61 Done
% 2.24/2.61
% 2.24/2.61 Resimplifying inuse:
% 2.24/2.61 Done
% 2.24/2.61
% 2.24/2.61
% 2.24/2.61 Intermediate Status:
% 2.24/2.61 Generated: 30987
% 2.24/2.61 Kept: 15396
% 2.24/2.61 Inuse: 734
% 2.24/2.61 Deleted: 13
% 2.24/2.61 Deletedinuse: 6
% 2.24/2.61
% 2.24/2.61 Resimplifying inuse:
% 2.24/2.61 Done
% 2.24/2.61
% 2.24/2.61 Resimplifying inuse:
% 2.24/2.61 Done
% 2.24/2.61
% 2.24/2.61
% 2.24/2.61 Intermediate Status:
% 2.24/2.61 Generated: 35143
% 2.24/2.61 Kept: 17417
% 2.24/2.61 Inuse: 805
% 2.24/2.61 Deleted: 24
% 2.24/2.61 Deletedinuse: 6
% 2.24/2.61
% 2.24/2.61 Resimplifying inuse:
% 2.24/2.61 Done
% 2.24/2.61
% 2.24/2.61 Resimplifying inuse:
% 2.24/2.61 Done
% 2.24/2.61
% 2.24/2.61 *** allocated 384427 integers for termspace/termends
% 2.24/2.61
% 2.24/2.61 Intermediate Status:
% 2.24/2.61 Generated: 38818
% 2.24/2.61 Kept: 19455
% 2.24/2.61 Inuse: 862
% 2.24/2.61 Deleted: 25
% 2.24/2.61 Deletedinuse: 6
% 2.24/2.61
% 2.24/2.61 Resimplifying inuse:
% 2.24/2.61 Done
% 2.24/2.61
% 2.24/2.61 Resimplifying clauses:
% 2.24/2.61
% 2.24/2.61 Bliksems!, er is een bewijs:
% 2.24/2.61 % SZS status Theorem
% 2.24/2.61 % SZS output start Refutation
% 2.24/2.61
% 2.24/2.61 (1) {G0,W8,D3,L2,V3,M2} I { ! member( skol1( Z, Y ), Y ), subset( X, Y )
% 2.24/2.61 }.
% 2.24/2.61 (2) {G0,W8,D3,L2,V2,M2} I { member( skol1( X, Y ), X ), subset( X, Y ) }.
% 2.24/2.61 (92) {G0,W9,D3,L2,V4,M2} I { ! member( T, equivalence_class( Z, Y, X ) ),
% 2.24/2.61 member( T, Y ) }.
% 2.24/2.61 (117) {G0,W6,D3,L1,V0,M1} I { ! subset( equivalence_class( skol23, skol15,
% 2.24/2.61 skol20 ), skol15 ) }.
% 2.24/2.61 (1533) {G1,W11,D4,L1,V0,M1} R(117,2) { member( skol1( equivalence_class(
% 2.24/2.61 skol23, skol15, skol20 ), skol15 ), equivalence_class( skol23, skol15,
% 2.24/2.61 skol20 ) ) }.
% 2.24/2.61 (1534) {G1,W5,D3,L1,V1,M1} R(117,1) { ! member( skol1( X, skol15 ), skol15
% 2.24/2.61 ) }.
% 2.24/2.61 (5913) {G2,W8,D3,L1,V3,M1} R(92,1534) { ! member( skol1( X, skol15 ),
% 2.24/2.61 equivalence_class( Y, skol15, Z ) ) }.
% 2.24/2.61 (20058) {G3,W0,D0,L0,V0,M0} S(1533);r(5913) { }.
% 2.24/2.61
% 2.24/2.61
% 2.24/2.61 % SZS output end Refutation
% 2.24/2.61 found a proof!
% 2.24/2.61
% 2.24/2.61
% 2.24/2.61 Unprocessed initial clauses:
% 2.24/2.61
% 2.24/2.61 (20060) {G0,W9,D2,L3,V3,M3} { ! subset( X, Y ), ! member( Z, X ), member(
% 2.24/2.61 Z, Y ) }.
% 2.24/2.61 (20061) {G0,W8,D3,L2,V3,M2} { ! member( skol1( Z, Y ), Y ), subset( X, Y )
% 2.24/2.61 }.
% 2.24/2.61 (20062) {G0,W8,D3,L2,V2,M2} { member( skol1( X, Y ), X ), subset( X, Y )
% 2.24/2.61 }.
% 2.24/2.61 (20063) {G0,W6,D2,L2,V2,M2} { ! equal_set( X, Y ), subset( X, Y ) }.
% 2.24/2.61 (20064) {G0,W6,D2,L2,V2,M2} { ! equal_set( X, Y ), subset( Y, X ) }.
% 2.24/2.61 (20065) {G0,W9,D2,L3,V2,M3} { ! subset( X, Y ), ! subset( Y, X ),
% 2.24/2.61 equal_set( X, Y ) }.
% 2.24/2.61 (20066) {G0,W7,D3,L2,V2,M2} { ! member( X, power_set( Y ) ), subset( X, Y
% 2.24/2.61 ) }.
% 2.24/2.61 (20067) {G0,W7,D3,L2,V2,M2} { ! subset( X, Y ), member( X, power_set( Y )
% 2.24/2.61 ) }.
% 2.24/2.61 (20068) {G0,W8,D3,L2,V3,M2} { ! member( X, intersection( Y, Z ) ), member
% 2.24/2.61 ( X, Y ) }.
% 2.24/2.61 (20069) {G0,W8,D3,L2,V3,M2} { ! member( X, intersection( Y, Z ) ), member
% 2.24/2.61 ( X, Z ) }.
% 2.24/2.61 (20070) {G0,W11,D3,L3,V3,M3} { ! member( X, Y ), ! member( X, Z ), member
% 2.24/2.61 ( X, intersection( Y, Z ) ) }.
% 2.24/2.61 (20071) {G0,W11,D3,L3,V3,M3} { ! member( X, union( Y, Z ) ), member( X, Y
% 2.24/2.61 ), member( X, Z ) }.
% 2.24/2.61 (20072) {G0,W8,D3,L2,V3,M2} { ! member( X, Y ), member( X, union( Y, Z ) )
% 2.24/2.61 }.
% 2.24/2.61 (20073) {G0,W8,D3,L2,V3,M2} { ! member( X, Z ), member( X, union( Y, Z ) )
% 2.24/2.61 }.
% 2.24/2.61 (20074) {G0,W3,D2,L1,V1,M1} { ! member( X, empty_set ) }.
% 2.24/2.61 (20075) {G0,W8,D3,L2,V3,M2} { ! member( X, difference( Z, Y ) ), member( X
% 2.24/2.61 , Z ) }.
% 2.24/2.61 (20076) {G0,W8,D3,L2,V3,M2} { ! member( X, difference( Z, Y ) ), ! member
% 2.24/2.61 ( X, Y ) }.
% 2.24/2.61 (20077) {G0,W11,D3,L3,V3,M3} { ! member( X, Z ), member( X, Y ), member( X
% 2.24/2.61 , difference( Z, Y ) ) }.
% 2.24/2.61 (20078) {G0,W7,D3,L2,V2,M2} { ! member( X, singleton( Y ) ), X = Y }.
% 2.24/2.61 (20079) {G0,W7,D3,L2,V2,M2} { ! X = Y, member( X, singleton( Y ) ) }.
% 2.24/2.61 (20080) {G0,W11,D3,L3,V3,M3} { ! member( X, unordered_pair( Y, Z ) ), X =
% 2.24/2.61 Y, X = Z }.
% 2.24/2.61 (20081) {G0,W8,D3,L2,V3,M2} { ! X = Y, member( X, unordered_pair( Y, Z ) )
% 2.24/2.61 }.
% 2.24/2.61 (20082) {G0,W8,D3,L2,V3,M2} { ! X = Z, member( X, unordered_pair( Y, Z ) )
% 2.24/2.61 }.
% 2.24/2.61 (20083) {G0,W9,D3,L2,V3,M2} { ! member( X, sum( Y ) ), member( skol2( Z, Y
% 2.24/2.61 ), Y ) }.
% 2.24/2.61 (20084) {G0,W9,D3,L2,V2,M2} { ! member( X, sum( Y ) ), member( X, skol2( X
% 2.24/2.61 , Y ) ) }.
% 2.24/2.61 (20085) {G0,W10,D3,L3,V3,M3} { ! member( Z, Y ), ! member( X, Z ), member
% 2.24/2.61 ( X, sum( Y ) ) }.
% 2.24/2.61 (20086) {G0,W10,D3,L3,V3,M3} { ! member( X, product( Y ) ), ! member( Z, Y
% 2.24/2.61 ), member( X, Z ) }.
% 2.24/2.61 (20087) {G0,W9,D3,L2,V3,M2} { member( skol3( Z, Y ), Y ), member( X,
% 2.24/2.61 product( Y ) ) }.
% 2.24/2.61 (20088) {G0,W9,D3,L2,V2,M2} { ! member( X, skol3( X, Y ) ), member( X,
% 2.24/2.61 product( Y ) ) }.
% 2.24/2.61 (20089) {G0,W9,D2,L3,V3,M3} { ! disjoint( X, Y ), ! member( Z, X ), !
% 2.24/2.61 member( Z, Y ) }.
% 2.24/2.61 (20090) {G0,W8,D3,L2,V3,M2} { member( skol4( Z, Y ), Y ), disjoint( X, Y )
% 2.24/2.61 }.
% 2.24/2.61 (20091) {G0,W8,D3,L2,V2,M2} { member( skol4( X, Y ), X ), disjoint( X, Y )
% 2.24/2.61 }.
% 2.24/2.61 (20092) {G0,W6,D2,L2,V2,M2} { ! partition( X, Y ), alpha4( X, Y ) }.
% 2.24/2.61 (20093) {G0,W6,D2,L2,V2,M2} { ! partition( X, Y ), alpha8( X, Y ) }.
% 2.24/2.61 (20094) {G0,W9,D2,L3,V2,M3} { ! alpha4( X, Y ), ! alpha8( X, Y ),
% 2.24/2.61 partition( X, Y ) }.
% 2.24/2.61 (20095) {G0,W6,D2,L2,V2,M2} { ! alpha8( X, Y ), alpha13( X, Y ) }.
% 2.24/2.61 (20096) {G0,W5,D2,L2,V2,M2} { ! alpha8( X, Y ), alpha1( X ) }.
% 2.24/2.61 (20097) {G0,W8,D2,L3,V2,M3} { ! alpha13( X, Y ), ! alpha1( X ), alpha8( X
% 2.24/2.61 , Y ) }.
% 2.24/2.61 (20098) {G0,W9,D2,L3,V3,M3} { ! alpha13( X, Y ), ! member( Z, Y ), alpha17
% 2.24/2.61 ( X, Z ) }.
% 2.24/2.61 (20099) {G0,W8,D3,L2,V3,M2} { member( skol5( Z, Y ), Y ), alpha13( X, Y )
% 2.24/2.61 }.
% 2.24/2.61 (20100) {G0,W8,D3,L2,V2,M2} { ! alpha17( X, skol5( X, Y ) ), alpha13( X, Y
% 2.24/2.61 ) }.
% 2.24/2.61 (20101) {G0,W8,D3,L2,V3,M2} { ! alpha17( X, Y ), member( Y, skol6( Z, Y )
% 2.24/2.61 ) }.
% 2.24/2.61 (20102) {G0,W8,D3,L2,V2,M2} { ! alpha17( X, Y ), member( skol6( X, Y ), X
% 2.24/2.61 ) }.
% 2.24/2.61 (20103) {G0,W9,D2,L3,V3,M3} { ! member( Z, X ), ! member( Y, Z ), alpha17
% 2.24/2.61 ( X, Y ) }.
% 2.24/2.61 (20104) {G0,W9,D2,L3,V3,M3} { ! alpha4( X, Y ), ! member( Z, X ), subset(
% 2.24/2.61 Z, Y ) }.
% 2.24/2.61 (20105) {G0,W8,D3,L2,V3,M2} { ! subset( skol7( Z, Y ), Y ), alpha4( X, Y )
% 2.24/2.61 }.
% 2.24/2.61 (20106) {G0,W8,D3,L2,V2,M2} { member( skol7( X, Y ), X ), alpha4( X, Y )
% 2.24/2.61 }.
% 2.24/2.61 (20107) {G0,W9,D2,L3,V3,M3} { ! alpha1( X ), ! alpha9( X, Y, Z ), alpha5(
% 2.24/2.61 Y, Z ) }.
% 2.24/2.61 (20108) {G0,W8,D3,L2,V1,M2} { alpha9( X, skol8( X ), skol16( X ) ), alpha1
% 2.24/2.61 ( X ) }.
% 2.24/2.61 (20109) {G0,W7,D3,L2,V1,M2} { ! alpha5( skol8( X ), skol16( X ) ), alpha1
% 2.24/2.61 ( X ) }.
% 2.24/2.61 (20110) {G0,W7,D2,L2,V3,M2} { ! alpha9( X, Y, Z ), member( Y, X ) }.
% 2.24/2.61 (20111) {G0,W7,D2,L2,V3,M2} { ! alpha9( X, Y, Z ), member( Z, X ) }.
% 2.24/2.61 (20112) {G0,W10,D2,L3,V3,M3} { ! member( Y, X ), ! member( Z, X ), alpha9
% 2.24/2.61 ( X, Y, Z ) }.
% 2.24/2.61 (20113) {G0,W9,D2,L3,V2,M3} { ! alpha5( X, Y ), ! alpha10( X, Y ), X = Y
% 2.24/2.61 }.
% 2.24/2.61 (20114) {G0,W6,D2,L2,V2,M2} { alpha10( X, Y ), alpha5( X, Y ) }.
% 2.24/2.61 (20115) {G0,W6,D2,L2,V2,M2} { ! X = Y, alpha5( X, Y ) }.
% 2.24/2.61 (20116) {G0,W8,D3,L2,V3,M2} { ! alpha10( X, Y ), member( skol9( Z, Y ), Y
% 2.24/2.61 ) }.
% 2.24/2.61 (20117) {G0,W8,D3,L2,V2,M2} { ! alpha10( X, Y ), member( skol9( X, Y ), X
% 2.24/2.61 ) }.
% 2.24/2.61 (20118) {G0,W9,D2,L3,V3,M3} { ! member( Z, X ), ! member( Z, Y ), alpha10
% 2.24/2.61 ( X, Y ) }.
% 2.24/2.61 (20119) {G0,W6,D2,L2,V2,M2} { ! equivalence( Y, X ), alpha2( X, Y ) }.
% 2.24/2.61 (20120) {G0,W6,D2,L2,V2,M2} { ! equivalence( Y, X ), alpha6( X, Y ) }.
% 2.24/2.61 (20121) {G0,W9,D2,L3,V2,M3} { ! alpha2( X, Y ), ! alpha6( X, Y ),
% 2.24/2.61 equivalence( Y, X ) }.
% 2.24/2.61 (20122) {G0,W6,D2,L2,V2,M2} { ! alpha6( X, Y ), alpha11( X, Y ) }.
% 2.24/2.61 (20123) {G0,W6,D2,L2,V2,M2} { ! alpha6( X, Y ), alpha14( X, Y ) }.
% 2.24/2.61 (20124) {G0,W9,D2,L3,V2,M3} { ! alpha11( X, Y ), ! alpha14( X, Y ), alpha6
% 2.24/2.61 ( X, Y ) }.
% 2.24/2.61 (20125) {G0,W13,D2,L3,V5,M3} { ! alpha14( X, Y ), ! alpha21( X, Z, T, U )
% 2.24/2.61 , alpha23( Y, Z, T, U ) }.
% 2.24/2.61 (20126) {G0,W14,D3,L2,V2,M2} { alpha21( X, skol10( X, Y ), skol17( X, Y )
% 2.24/2.61 , skol21( X, Y ) ), alpha14( X, Y ) }.
% 2.24/2.61 (20127) {G0,W14,D3,L2,V2,M2} { ! alpha23( Y, skol10( X, Y ), skol17( X, Y
% 2.24/2.61 ), skol21( X, Y ) ), alpha14( X, Y ) }.
% 2.24/2.61 (20128) {G0,W14,D2,L3,V4,M3} { ! alpha23( X, Y, Z, T ), ! alpha24( X, Y, Z
% 2.24/2.61 , T ), apply( X, Y, T ) }.
% 2.24/2.61 (20129) {G0,W10,D2,L2,V4,M2} { alpha24( X, Y, Z, T ), alpha23( X, Y, Z, T
% 2.24/2.61 ) }.
% 2.24/2.61 (20130) {G0,W9,D2,L2,V4,M2} { ! apply( X, Y, T ), alpha23( X, Y, Z, T )
% 2.24/2.61 }.
% 2.24/2.61 (20131) {G0,W9,D2,L2,V4,M2} { ! alpha24( X, Y, Z, T ), apply( X, Y, Z )
% 2.24/2.61 }.
% 2.24/2.61 (20132) {G0,W9,D2,L2,V4,M2} { ! alpha24( X, Y, Z, T ), apply( X, Z, T )
% 2.24/2.61 }.
% 2.24/2.61 (20133) {G0,W13,D2,L3,V4,M3} { ! apply( X, Y, Z ), ! apply( X, Z, T ),
% 2.24/2.61 alpha24( X, Y, Z, T ) }.
% 2.24/2.61 (20134) {G0,W8,D2,L2,V4,M2} { ! alpha21( X, Y, Z, T ), member( Y, X ) }.
% 2.24/2.61 (20135) {G0,W9,D2,L2,V4,M2} { ! alpha21( X, Y, Z, T ), alpha18( X, Z, T )
% 2.24/2.61 }.
% 2.24/2.61 (20136) {G0,W12,D2,L3,V4,M3} { ! member( Y, X ), ! alpha18( X, Z, T ),
% 2.24/2.61 alpha21( X, Y, Z, T ) }.
% 2.24/2.61 (20137) {G0,W7,D2,L2,V3,M2} { ! alpha18( X, Y, Z ), member( Y, X ) }.
% 2.24/2.61 (20138) {G0,W7,D2,L2,V3,M2} { ! alpha18( X, Y, Z ), member( Z, X ) }.
% 2.24/2.61 (20139) {G0,W10,D2,L3,V3,M3} { ! member( Y, X ), ! member( Z, X ), alpha18
% 2.24/2.61 ( X, Y, Z ) }.
% 2.24/2.61 (20140) {G0,W11,D2,L3,V4,M3} { ! alpha11( X, Y ), ! alpha15( X, Z, T ),
% 2.24/2.61 alpha19( Y, Z, T ) }.
% 2.24/2.61 (20141) {G0,W11,D3,L2,V2,M2} { alpha15( X, skol11( X, Y ), skol18( X, Y )
% 2.24/2.61 ), alpha11( X, Y ) }.
% 2.24/2.61 (20142) {G0,W11,D3,L2,V2,M2} { ! alpha19( Y, skol11( X, Y ), skol18( X, Y
% 2.24/2.61 ) ), alpha11( X, Y ) }.
% 2.24/2.61 (20143) {G0,W12,D2,L3,V3,M3} { ! alpha19( X, Y, Z ), ! apply( X, Y, Z ),
% 2.24/2.61 apply( X, Z, Y ) }.
% 2.24/2.61 (20144) {G0,W8,D2,L2,V3,M2} { apply( X, Y, Z ), alpha19( X, Y, Z ) }.
% 2.24/2.61 (20145) {G0,W8,D2,L2,V3,M2} { ! apply( X, Z, Y ), alpha19( X, Y, Z ) }.
% 2.24/2.61 (20146) {G0,W7,D2,L2,V3,M2} { ! alpha15( X, Y, Z ), member( Y, X ) }.
% 2.24/2.61 (20147) {G0,W7,D2,L2,V3,M2} { ! alpha15( X, Y, Z ), member( Z, X ) }.
% 2.24/2.61 (20148) {G0,W10,D2,L3,V3,M3} { ! member( Y, X ), ! member( Z, X ), alpha15
% 2.24/2.61 ( X, Y, Z ) }.
% 2.24/2.61 (20149) {G0,W10,D2,L3,V3,M3} { ! alpha2( X, Y ), ! member( Z, X ), apply(
% 2.24/2.61 Y, Z, Z ) }.
% 2.24/2.61 (20150) {G0,W11,D3,L2,V3,M2} { ! apply( Y, skol12( Z, Y ), skol12( Z, Y )
% 2.24/2.61 ), alpha2( X, Y ) }.
% 2.24/2.61 (20151) {G0,W8,D3,L2,V2,M2} { member( skol12( X, Y ), X ), alpha2( X, Y )
% 2.24/2.61 }.
% 2.24/2.61 (20152) {G0,W9,D3,L2,V4,M2} { ! member( T, equivalence_class( Z, Y, X ) )
% 2.24/2.61 , member( T, Y ) }.
% 2.24/2.61 (20153) {G0,W10,D3,L2,V4,M2} { ! member( T, equivalence_class( Z, Y, X ) )
% 2.24/2.61 , apply( X, Z, T ) }.
% 2.24/2.61 (20154) {G0,W13,D3,L3,V4,M3} { ! member( T, Y ), ! apply( X, Z, T ),
% 2.24/2.61 member( T, equivalence_class( Z, Y, X ) ) }.
% 2.24/2.61 (20155) {G0,W6,D2,L2,V2,M2} { ! pre_order( X, Y ), alpha3( X, Y ) }.
% 2.24/2.61 (20156) {G0,W6,D2,L2,V2,M2} { ! pre_order( X, Y ), alpha7( X, Y ) }.
% 2.24/2.61 (20157) {G0,W9,D2,L3,V2,M3} { ! alpha3( X, Y ), ! alpha7( X, Y ),
% 2.24/2.61 pre_order( X, Y ) }.
% 2.24/2.61 (20158) {G0,W13,D2,L3,V5,M3} { ! alpha7( X, Y ), ! alpha16( Y, Z, T, U ),
% 2.24/2.61 alpha20( X, Z, T, U ) }.
% 2.24/2.61 (20159) {G0,W14,D3,L2,V2,M2} { alpha16( Y, skol13( X, Y ), skol19( X, Y )
% 2.24/2.61 , skol22( X, Y ) ), alpha7( X, Y ) }.
% 2.24/2.61 (20160) {G0,W14,D3,L2,V2,M2} { ! alpha20( X, skol13( X, Y ), skol19( X, Y
% 2.24/2.61 ), skol22( X, Y ) ), alpha7( X, Y ) }.
% 2.24/2.61 (20161) {G0,W14,D2,L3,V4,M3} { ! alpha20( X, Y, Z, T ), ! alpha22( X, Y, Z
% 2.24/2.61 , T ), apply( X, Y, T ) }.
% 2.24/2.61 (20162) {G0,W10,D2,L2,V4,M2} { alpha22( X, Y, Z, T ), alpha20( X, Y, Z, T
% 2.24/2.61 ) }.
% 2.24/2.61 (20163) {G0,W9,D2,L2,V4,M2} { ! apply( X, Y, T ), alpha20( X, Y, Z, T )
% 2.24/2.61 }.
% 2.24/2.61 (20164) {G0,W9,D2,L2,V4,M2} { ! alpha22( X, Y, Z, T ), apply( X, Y, Z )
% 2.24/2.61 }.
% 2.24/2.61 (20165) {G0,W9,D2,L2,V4,M2} { ! alpha22( X, Y, Z, T ), apply( X, Z, T )
% 2.24/2.61 }.
% 2.24/2.61 (20166) {G0,W13,D2,L3,V4,M3} { ! apply( X, Y, Z ), ! apply( X, Z, T ),
% 2.24/2.61 alpha22( X, Y, Z, T ) }.
% 2.24/2.61 (20167) {G0,W8,D2,L2,V4,M2} { ! alpha16( X, Y, Z, T ), member( Y, X ) }.
% 2.24/2.61 (20168) {G0,W9,D2,L2,V4,M2} { ! alpha16( X, Y, Z, T ), alpha12( X, Z, T )
% 2.24/2.61 }.
% 2.24/2.61 (20169) {G0,W12,D2,L3,V4,M3} { ! member( Y, X ), ! alpha12( X, Z, T ),
% 2.24/2.61 alpha16( X, Y, Z, T ) }.
% 2.24/2.61 (20170) {G0,W7,D2,L2,V3,M2} { ! alpha12( X, Y, Z ), member( Y, X ) }.
% 2.24/2.61 (20171) {G0,W7,D2,L2,V3,M2} { ! alpha12( X, Y, Z ), member( Z, X ) }.
% 2.24/2.61 (20172) {G0,W10,D2,L3,V3,M3} { ! member( Y, X ), ! member( Z, X ), alpha12
% 2.24/2.61 ( X, Y, Z ) }.
% 2.24/2.61 (20173) {G0,W10,D2,L3,V3,M3} { ! alpha3( X, Y ), ! member( Z, Y ), apply(
% 2.24/2.61 X, Z, Z ) }.
% 2.24/2.61 (20174) {G0,W8,D3,L2,V3,M2} { member( skol14( Z, Y ), Y ), alpha3( X, Y )
% 2.24/2.61 }.
% 2.24/2.61 (20175) {G0,W11,D3,L2,V2,M2} { ! apply( X, skol14( X, Y ), skol14( X, Y )
% 2.24/2.61 ), alpha3( X, Y ) }.
% 2.24/2.61 (20176) {G0,W3,D2,L1,V0,M1} { equivalence( skol20, skol15 ) }.
% 2.24/2.61 (20177) {G0,W6,D3,L1,V0,M1} { ! subset( equivalence_class( skol23, skol15
% 2.24/2.61 , skol20 ), skol15 ) }.
% 2.24/2.61
% 2.24/2.61
% 2.24/2.61 Total Proof:
% 2.24/2.61
% 2.24/2.61 subsumption: (1) {G0,W8,D3,L2,V3,M2} I { ! member( skol1( Z, Y ), Y ),
% 2.24/2.61 subset( X, Y ) }.
% 2.24/2.61 parent0: (20061) {G0,W8,D3,L2,V3,M2} { ! member( skol1( Z, Y ), Y ),
% 2.24/2.61 subset( X, Y ) }.
% 2.24/2.61 substitution0:
% 2.24/2.61 X := X
% 2.24/2.61 Y := Y
% 2.24/2.61 Z := Z
% 2.24/2.61 end
% 2.24/2.61 permutation0:
% 2.24/2.61 0 ==> 0
% 2.24/2.61 1 ==> 1
% 2.24/2.61 end
% 2.24/2.61
% 2.24/2.61 subsumption: (2) {G0,W8,D3,L2,V2,M2} I { member( skol1( X, Y ), X ), subset
% 2.24/2.61 ( X, Y ) }.
% 2.24/2.61 parent0: (20062) {G0,W8,D3,L2,V2,M2} { member( skol1( X, Y ), X ), subset
% 2.24/2.61 ( X, Y ) }.
% 2.24/2.61 substitution0:
% 2.24/2.61 X := X
% 2.24/2.61 Y := Y
% 2.24/2.61 end
% 2.24/2.61 permutation0:
% 2.24/2.61 0 ==> 0
% 2.24/2.61 1 ==> 1
% 2.24/2.61 end
% 2.24/2.61
% 2.24/2.61 subsumption: (92) {G0,W9,D3,L2,V4,M2} I { ! member( T, equivalence_class( Z
% 2.24/2.61 , Y, X ) ), member( T, Y ) }.
% 2.24/2.61 parent0: (20152) {G0,W9,D3,L2,V4,M2} { ! member( T, equivalence_class( Z,
% 2.24/2.61 Y, X ) ), member( T, Y ) }.
% 2.24/2.61 substitution0:
% 2.24/2.61 X := X
% 2.24/2.61 Y := Y
% 2.24/2.61 Z := Z
% 2.24/2.61 T := T
% 2.24/2.61 end
% 2.24/2.61 permutation0:
% 2.24/2.61 0 ==> 0
% 2.24/2.61 1 ==> 1
% 2.24/2.61 end
% 2.24/2.61
% 2.24/2.61 subsumption: (117) {G0,W6,D3,L1,V0,M1} I { ! subset( equivalence_class(
% 2.24/2.61 skol23, skol15, skol20 ), skol15 ) }.
% 2.24/2.61 parent0: (20177) {G0,W6,D3,L1,V0,M1} { ! subset( equivalence_class( skol23
% 2.24/2.61 , skol15, skol20 ), skol15 ) }.
% 2.24/2.61 substitution0:
% 2.24/2.61 end
% 2.24/2.61 permutation0:
% 2.24/2.61 0 ==> 0
% 2.24/2.61 end
% 2.24/2.61
% 2.24/2.61 resolution: (20224) {G1,W11,D4,L1,V0,M1} { member( skol1(
% 2.24/2.61 equivalence_class( skol23, skol15, skol20 ), skol15 ), equivalence_class
% 2.24/2.61 ( skol23, skol15, skol20 ) ) }.
% 2.24/2.61 parent0[0]: (117) {G0,W6,D3,L1,V0,M1} I { ! subset( equivalence_class(
% 2.24/2.61 skol23, skol15, skol20 ), skol15 ) }.
% 2.24/2.61 parent1[1]: (2) {G0,W8,D3,L2,V2,M2} I { member( skol1( X, Y ), X ), subset
% 2.24/2.61 ( X, Y ) }.
% 2.24/2.61 substitution0:
% 2.24/2.61 end
% 2.24/2.61 substitution1:
% 2.24/2.61 X := equivalence_class( skol23, skol15, skol20 )
% 2.24/2.61 Y := skol15
% 2.24/2.61 end
% 2.24/2.61
% 2.24/2.61 subsumption: (1533) {G1,W11,D4,L1,V0,M1} R(117,2) { member( skol1(
% 2.24/2.61 equivalence_class( skol23, skol15, skol20 ), skol15 ), equivalence_class
% 2.24/2.61 ( skol23, skol15, skol20 ) ) }.
% 2.24/2.61 parent0: (20224) {G1,W11,D4,L1,V0,M1} { member( skol1( equivalence_class(
% 2.24/2.61 skol23, skol15, skol20 ), skol15 ), equivalence_class( skol23, skol15,
% 2.24/2.61 skol20 ) ) }.
% 2.24/2.61 substitution0:
% 2.24/2.61 end
% 2.24/2.61 permutation0:
% 2.24/2.61 0 ==> 0
% 2.24/2.61 end
% 2.24/2.61
% 2.24/2.61 resolution: (20225) {G1,W5,D3,L1,V1,M1} { ! member( skol1( X, skol15 ),
% 2.24/2.61 skol15 ) }.
% 2.24/2.61 parent0[0]: (117) {G0,W6,D3,L1,V0,M1} I { ! subset( equivalence_class(
% 2.24/2.61 skol23, skol15, skol20 ), skol15 ) }.
% 2.24/2.61 parent1[1]: (1) {G0,W8,D3,L2,V3,M2} I { ! member( skol1( Z, Y ), Y ),
% 2.24/2.61 subset( X, Y ) }.
% 2.24/2.61 substitution0:
% 2.24/2.61 end
% 2.24/2.61 substitution1:
% 2.24/2.61 X := equivalence_class( skol23, skol15, skol20 )
% 2.24/2.61 Y := skol15
% 2.24/2.61 Z := X
% 2.24/2.61 end
% 2.24/2.61
% 2.24/2.61 subsumption: (1534) {G1,W5,D3,L1,V1,M1} R(117,1) { ! member( skol1( X,
% 2.24/2.61 skol15 ), skol15 ) }.
% 2.24/2.61 parent0: (20225) {G1,W5,D3,L1,V1,M1} { ! member( skol1( X, skol15 ),
% 2.24/2.61 skol15 ) }.
% 2.24/2.61 substitution0:
% 2.24/2.61 X := X
% 2.24/2.61 end
% 2.24/2.61 permutation0:
% 2.24/2.61 0 ==> 0
% 2.24/2.61 end
% 2.24/2.61
% 2.24/2.61 resolution: (20226) {G1,W8,D3,L1,V3,M1} { ! member( skol1( X, skol15 ),
% 2.24/2.61 equivalence_class( Y, skol15, Z ) ) }.
% 2.24/2.61 parent0[0]: (1534) {G1,W5,D3,L1,V1,M1} R(117,1) { ! member( skol1( X,
% 2.24/2.61 skol15 ), skol15 ) }.
% 2.24/2.61 parent1[1]: (92) {G0,W9,D3,L2,V4,M2} I { ! member( T, equivalence_class( Z
% 2.24/2.61 , Y, X ) ), member( T, Y ) }.
% 2.24/2.61 substitution0:
% 2.24/2.61 X := X
% 2.24/2.61 end
% 2.24/2.61 substitution1:
% 2.24/2.61 X := Z
% 2.24/2.61 Y := skol15
% 2.24/2.61 Z := Y
% 2.24/2.61 T := skol1( X, skol15 )
% 2.24/2.61 end
% 2.24/2.61
% 2.24/2.61 subsumption: (5913) {G2,W8,D3,L1,V3,M1} R(92,1534) { ! member( skol1( X,
% 2.24/2.61 skol15 ), equivalence_class( Y, skol15, Z ) ) }.
% 2.24/2.61 parent0: (20226) {G1,W8,D3,L1,V3,M1} { ! member( skol1( X, skol15 ),
% 2.24/2.61 equivalence_class( Y, skol15, Z ) ) }.
% 2.24/2.61 substitution0:
% 2.24/2.61 X := X
% 2.24/2.61 Y := Y
% 2.24/2.61 Z := Z
% 2.24/2.61 end
% 2.24/2.61 permutation0:
% 2.24/2.61 0 ==> 0
% 2.24/2.61 end
% 2.24/2.61
% 2.24/2.61 resolution: (20227) {G2,W0,D0,L0,V0,M0} { }.
% 2.24/2.61 parent0[0]: (5913) {G2,W8,D3,L1,V3,M1} R(92,1534) { ! member( skol1( X,
% 2.24/2.61 skol15 ), equivalence_class( Y, skol15, Z ) ) }.
% 2.24/2.61 parent1[0]: (1533) {G1,W11,D4,L1,V0,M1} R(117,2) { member( skol1(
% 2.24/2.61 equivalence_class( skol23, skol15, skol20 ), skol15 ), equivalence_class
% 2.24/2.61 ( skol23, skol15, skol20 ) ) }.
% 2.24/2.61 substitution0:
% 2.24/2.61 X := equivalence_class( skol23, skol15, skol20 )
% 2.24/2.61 Y := skol23
% 2.24/2.61 Z := skol20
% 2.24/2.61 end
% 2.24/2.61 substitution1:
% 2.24/2.61 end
% 2.24/2.61
% 2.24/2.61 subsumption: (20058) {G3,W0,D0,L0,V0,M0} S(1533);r(5913) { }.
% 2.24/2.61 parent0: (20227) {G2,W0,D0,L0,V0,M0} { }.
% 2.24/2.61 substitution0:
% 2.24/2.61 end
% 2.24/2.61 permutation0:
% 2.24/2.61 end
% 2.24/2.61
% 2.24/2.61 Proof check complete!
% 2.24/2.61
% 2.24/2.61 Memory use:
% 2.24/2.61
% 2.24/2.61 space for terms: 265257
% 2.24/2.61 space for clauses: 857511
% 2.24/2.61
% 2.24/2.61
% 2.24/2.61 clauses generated: 39858
% 2.24/2.61 clauses kept: 20059
% 2.24/2.61 clauses selected: 871
% 2.24/2.61 clauses deleted: 677
% 2.24/2.61 clauses inuse deleted: 6
% 2.24/2.61
% 2.24/2.61 subsentry: 208412
% 2.24/2.61 literals s-matched: 135824
% 2.24/2.61 literals matched: 122175
% 2.24/2.61 full subsumption: 44041
% 2.24/2.61
% 2.24/2.61 checksum: -1144613142
% 2.24/2.61
% 2.24/2.61
% 2.24/2.61 Bliksem ended
%------------------------------------------------------------------------------