TSTP Solution File: SET074+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET074+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Mon Jul 18 22:46:35 EDT 2022
% Result : Theorem 5.90s 6.27s
% Output : Refutation 5.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET074+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.06/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Sat Jul 9 20:33:46 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.43/1.07 *** allocated 10000 integers for termspace/termends
% 0.43/1.07 *** allocated 10000 integers for clauses
% 0.43/1.07 *** allocated 10000 integers for justifications
% 0.43/1.07 Bliksem 1.12
% 0.43/1.07
% 0.43/1.07
% 0.43/1.07 Automatic Strategy Selection
% 0.43/1.07
% 0.43/1.07
% 0.43/1.07 Clauses:
% 0.43/1.07
% 0.43/1.07 { ! subclass( X, Y ), ! member( Z, X ), member( Z, Y ) }.
% 0.43/1.07 { ! member( skol1( Z, Y ), Y ), subclass( X, Y ) }.
% 0.43/1.07 { member( skol1( X, Y ), X ), subclass( X, Y ) }.
% 0.43/1.07 { subclass( X, universal_class ) }.
% 0.43/1.07 { ! X = Y, subclass( X, Y ) }.
% 0.43/1.07 { ! X = Y, subclass( Y, X ) }.
% 0.43/1.07 { ! subclass( X, Y ), ! subclass( Y, X ), X = Y }.
% 0.43/1.07 { ! member( X, unordered_pair( Y, Z ) ), member( X, universal_class ) }.
% 0.43/1.07 { ! member( X, unordered_pair( Y, Z ) ), alpha1( X, Y, Z ) }.
% 0.43/1.07 { ! member( X, universal_class ), ! alpha1( X, Y, Z ), member( X,
% 0.43/1.07 unordered_pair( Y, Z ) ) }.
% 0.43/1.07 { ! alpha1( X, Y, Z ), X = Y, X = Z }.
% 0.43/1.07 { ! X = Y, alpha1( X, Y, Z ) }.
% 0.43/1.07 { ! X = Z, alpha1( X, Y, Z ) }.
% 0.43/1.07 { member( unordered_pair( X, Y ), universal_class ) }.
% 0.43/1.07 { singleton( X ) = unordered_pair( X, X ) }.
% 0.43/1.07 { ordered_pair( X, Y ) = unordered_pair( singleton( X ), unordered_pair( X
% 0.43/1.07 , singleton( Y ) ) ) }.
% 0.43/1.07 { ! member( ordered_pair( X, Y ), cross_product( Z, T ) ), member( X, Z ) }
% 0.43/1.07 .
% 0.43/1.07 { ! member( ordered_pair( X, Y ), cross_product( Z, T ) ), member( Y, T ) }
% 0.43/1.07 .
% 0.43/1.07 { ! member( X, Z ), ! member( Y, T ), member( ordered_pair( X, Y ),
% 0.43/1.07 cross_product( Z, T ) ) }.
% 0.43/1.07 { ! member( X, universal_class ), ! member( Y, universal_class ), first(
% 0.43/1.07 ordered_pair( X, Y ) ) = X }.
% 0.43/1.07 { ! member( X, universal_class ), ! member( Y, universal_class ), second(
% 0.43/1.07 ordered_pair( X, Y ) ) = Y }.
% 0.43/1.07 { ! member( X, cross_product( Y, Z ) ), X = ordered_pair( first( X ),
% 0.43/1.07 second( X ) ) }.
% 0.43/1.07 { ! member( ordered_pair( X, Y ), element_relation ), member( Y,
% 0.43/1.07 universal_class ) }.
% 0.43/1.07 { ! member( ordered_pair( X, Y ), element_relation ), member( X, Y ) }.
% 0.43/1.07 { ! member( Y, universal_class ), ! member( X, Y ), member( ordered_pair( X
% 0.43/1.07 , Y ), element_relation ) }.
% 0.43/1.07 { subclass( element_relation, cross_product( universal_class,
% 0.43/1.07 universal_class ) ) }.
% 0.43/1.07 { ! member( Z, intersection( X, Y ) ), member( Z, X ) }.
% 0.43/1.07 { ! member( Z, intersection( X, Y ) ), member( Z, Y ) }.
% 0.43/1.07 { ! member( Z, X ), ! member( Z, Y ), member( Z, intersection( X, Y ) ) }.
% 0.43/1.07 { ! member( Y, complement( X ) ), member( Y, universal_class ) }.
% 0.43/1.07 { ! member( Y, complement( X ) ), ! member( Y, X ) }.
% 0.43/1.07 { ! member( Y, universal_class ), member( Y, X ), member( Y, complement( X
% 0.43/1.07 ) ) }.
% 0.43/1.07 { restrict( Y, X, Z ) = intersection( Y, cross_product( X, Z ) ) }.
% 0.43/1.07 { ! member( X, null_class ) }.
% 0.43/1.07 { ! member( Y, domain_of( X ) ), member( Y, universal_class ) }.
% 0.43/1.07 { ! member( Y, domain_of( X ) ), ! restrict( X, singleton( Y ),
% 0.43/1.07 universal_class ) = null_class }.
% 0.43/1.07 { ! member( Y, universal_class ), restrict( X, singleton( Y ),
% 0.43/1.07 universal_class ) = null_class, member( Y, domain_of( X ) ) }.
% 0.43/1.07 { ! member( ordered_pair( ordered_pair( Y, Z ), T ), rotate( X ) ), member
% 0.43/1.07 ( ordered_pair( ordered_pair( Y, Z ), T ), cross_product( cross_product(
% 0.43/1.07 universal_class, universal_class ), universal_class ) ) }.
% 0.43/1.07 { ! member( ordered_pair( ordered_pair( Y, Z ), T ), rotate( X ) ), member
% 0.43/1.07 ( ordered_pair( ordered_pair( Z, T ), Y ), X ) }.
% 0.43/1.07 { ! member( ordered_pair( ordered_pair( Y, Z ), T ), cross_product(
% 0.43/1.07 cross_product( universal_class, universal_class ), universal_class ) ), !
% 0.43/1.07 member( ordered_pair( ordered_pair( Z, T ), Y ), X ), member(
% 0.43/1.07 ordered_pair( ordered_pair( Y, Z ), T ), rotate( X ) ) }.
% 0.43/1.07 { subclass( rotate( X ), cross_product( cross_product( universal_class,
% 0.43/1.07 universal_class ), universal_class ) ) }.
% 0.43/1.07 { ! member( ordered_pair( ordered_pair( X, Y ), Z ), flip( T ) ), member(
% 0.43/1.07 ordered_pair( ordered_pair( X, Y ), Z ), cross_product( cross_product(
% 0.43/1.07 universal_class, universal_class ), universal_class ) ) }.
% 0.43/1.07 { ! member( ordered_pair( ordered_pair( X, Y ), Z ), flip( T ) ), member(
% 0.43/1.07 ordered_pair( ordered_pair( Y, X ), Z ), T ) }.
% 0.43/1.07 { ! member( ordered_pair( ordered_pair( X, Y ), Z ), cross_product(
% 0.43/1.07 cross_product( universal_class, universal_class ), universal_class ) ), !
% 0.43/1.07 member( ordered_pair( ordered_pair( Y, X ), Z ), T ), member(
% 0.43/1.07 ordered_pair( ordered_pair( X, Y ), Z ), flip( T ) ) }.
% 0.43/1.07 { subclass( flip( X ), cross_product( cross_product( universal_class,
% 0.73/1.24 universal_class ), universal_class ) ) }.
% 0.73/1.24 { ! member( Z, union( X, Y ) ), member( Z, X ), member( Z, Y ) }.
% 0.73/1.24 { ! member( Z, X ), member( Z, union( X, Y ) ) }.
% 0.73/1.24 { ! member( Z, Y ), member( Z, union( X, Y ) ) }.
% 0.73/1.24 { successor( X ) = union( X, singleton( X ) ) }.
% 0.73/1.24 { subclass( successor_relation, cross_product( universal_class,
% 0.73/1.24 universal_class ) ) }.
% 0.73/1.24 { ! member( ordered_pair( X, Y ), successor_relation ), member( X,
% 0.73/1.24 universal_class ) }.
% 0.73/1.24 { ! member( ordered_pair( X, Y ), successor_relation ), alpha2( X, Y ) }.
% 0.73/1.24 { ! member( X, universal_class ), ! alpha2( X, Y ), member( ordered_pair( X
% 0.73/1.24 , Y ), successor_relation ) }.
% 0.73/1.24 { ! alpha2( X, Y ), member( Y, universal_class ) }.
% 0.73/1.24 { ! alpha2( X, Y ), successor( X ) = Y }.
% 0.73/1.24 { ! member( Y, universal_class ), ! successor( X ) = Y, alpha2( X, Y ) }.
% 0.73/1.24 { inverse( X ) = domain_of( flip( cross_product( X, universal_class ) ) ) }
% 0.73/1.24 .
% 0.73/1.24 { range_of( X ) = domain_of( inverse( X ) ) }.
% 0.73/1.24 { image( Y, X ) = range_of( restrict( Y, X, universal_class ) ) }.
% 0.73/1.24 { ! inductive( X ), member( null_class, X ) }.
% 0.73/1.24 { ! inductive( X ), subclass( image( successor_relation, X ), X ) }.
% 0.73/1.24 { ! member( null_class, X ), ! subclass( image( successor_relation, X ), X
% 0.73/1.24 ), inductive( X ) }.
% 0.73/1.24 { member( skol2, universal_class ) }.
% 0.73/1.24 { inductive( skol2 ) }.
% 0.73/1.24 { ! inductive( X ), subclass( skol2, X ) }.
% 0.73/1.24 { ! member( X, sum_class( Y ) ), member( skol3( Z, Y ), Y ) }.
% 0.73/1.24 { ! member( X, sum_class( Y ) ), member( X, skol3( X, Y ) ) }.
% 0.73/1.24 { ! member( X, Z ), ! member( Z, Y ), member( X, sum_class( Y ) ) }.
% 0.73/1.24 { ! member( X, universal_class ), member( sum_class( X ), universal_class )
% 0.73/1.24 }.
% 0.73/1.24 { ! member( X, power_class( Y ) ), member( X, universal_class ) }.
% 0.73/1.24 { ! member( X, power_class( Y ) ), subclass( X, Y ) }.
% 0.73/1.24 { ! member( X, universal_class ), ! subclass( X, Y ), member( X,
% 0.73/1.24 power_class( Y ) ) }.
% 0.73/1.24 { ! member( X, universal_class ), member( power_class( X ), universal_class
% 0.73/1.24 ) }.
% 0.73/1.24 { subclass( compose( Y, X ), cross_product( universal_class,
% 0.73/1.24 universal_class ) ) }.
% 0.73/1.24 { ! member( ordered_pair( Z, T ), compose( Y, X ) ), member( Z,
% 0.73/1.24 universal_class ) }.
% 0.73/1.24 { ! member( ordered_pair( Z, T ), compose( Y, X ) ), member( T, image( Y,
% 0.73/1.24 image( X, singleton( Z ) ) ) ) }.
% 0.73/1.24 { ! member( Z, universal_class ), ! member( T, image( Y, image( X,
% 0.73/1.24 singleton( Z ) ) ) ), member( ordered_pair( Z, T ), compose( Y, X ) ) }.
% 0.73/1.24 { ! member( X, identity_relation ), member( skol4( Y ), universal_class ) }
% 0.73/1.24 .
% 0.73/1.24 { ! member( X, identity_relation ), X = ordered_pair( skol4( X ), skol4( X
% 0.73/1.24 ) ) }.
% 0.73/1.24 { ! member( Y, universal_class ), ! X = ordered_pair( Y, Y ), member( X,
% 0.73/1.24 identity_relation ) }.
% 0.73/1.24 { ! function( X ), subclass( X, cross_product( universal_class,
% 0.73/1.24 universal_class ) ) }.
% 0.73/1.24 { ! function( X ), subclass( compose( X, inverse( X ) ), identity_relation
% 0.73/1.24 ) }.
% 0.73/1.24 { ! subclass( X, cross_product( universal_class, universal_class ) ), !
% 0.73/1.24 subclass( compose( X, inverse( X ) ), identity_relation ), function( X )
% 0.73/1.24 }.
% 0.73/1.24 { ! member( X, universal_class ), ! function( Y ), member( image( Y, X ),
% 0.73/1.24 universal_class ) }.
% 0.73/1.24 { ! disjoint( X, Y ), ! member( Z, X ), ! member( Z, Y ) }.
% 0.73/1.24 { member( skol5( Z, Y ), Y ), disjoint( X, Y ) }.
% 0.73/1.24 { member( skol5( X, Y ), X ), disjoint( X, Y ) }.
% 0.73/1.24 { X = null_class, member( skol6( Y ), universal_class ) }.
% 0.73/1.24 { X = null_class, member( skol6( X ), X ) }.
% 0.73/1.24 { X = null_class, disjoint( skol6( X ), X ) }.
% 0.73/1.24 { apply( X, Y ) = sum_class( image( X, singleton( Y ) ) ) }.
% 0.73/1.24 { function( skol7 ) }.
% 0.73/1.24 { ! member( X, universal_class ), X = null_class, member( apply( skol7, X )
% 0.73/1.24 , X ) }.
% 0.73/1.24 { member( skol8, universal_class ) }.
% 0.73/1.24 { unordered_pair( skol9, skol8 ) = null_class }.
% 0.73/1.24
% 0.73/1.24 percentage equality = 0.149485, percentage horn = 0.884211
% 0.73/1.24 This is a problem with some equality
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 Options Used:
% 0.73/1.24
% 0.73/1.24 useres = 1
% 0.73/1.24 useparamod = 1
% 0.73/1.24 useeqrefl = 1
% 0.73/1.24 useeqfact = 1
% 0.73/1.24 usefactor = 1
% 0.73/1.24 usesimpsplitting = 0
% 0.73/1.24 usesimpdemod = 5
% 0.73/1.24 usesimpres = 3
% 0.73/1.24
% 0.73/1.24 resimpinuse = 1000
% 0.73/1.24 resimpclauses = 20000
% 0.73/1.24 substype = eqrewr
% 0.73/1.24 backwardsubs = 1
% 0.73/1.24 selectoldest = 5
% 0.73/1.24
% 0.73/1.24 litorderings [0] = split
% 0.73/1.24 litorderings [1] = extend the termordering, first sorting on arguments
% 5.90/6.27
% 5.90/6.27 termordering = kbo
% 5.90/6.27
% 5.90/6.27 litapriori = 0
% 5.90/6.27 termapriori = 1
% 5.90/6.27 litaposteriori = 0
% 5.90/6.27 termaposteriori = 0
% 5.90/6.27 demodaposteriori = 0
% 5.90/6.27 ordereqreflfact = 0
% 5.90/6.27
% 5.90/6.27 litselect = negord
% 5.90/6.27
% 5.90/6.27 maxweight = 15
% 5.90/6.27 maxdepth = 30000
% 5.90/6.27 maxlength = 115
% 5.90/6.27 maxnrvars = 195
% 5.90/6.27 excuselevel = 1
% 5.90/6.27 increasemaxweight = 1
% 5.90/6.27
% 5.90/6.27 maxselected = 10000000
% 5.90/6.27 maxnrclauses = 10000000
% 5.90/6.27
% 5.90/6.27 showgenerated = 0
% 5.90/6.27 showkept = 0
% 5.90/6.27 showselected = 0
% 5.90/6.27 showdeleted = 0
% 5.90/6.27 showresimp = 1
% 5.90/6.27 showstatus = 2000
% 5.90/6.27
% 5.90/6.27 prologoutput = 0
% 5.90/6.27 nrgoals = 5000000
% 5.90/6.27 totalproof = 1
% 5.90/6.27
% 5.90/6.27 Symbols occurring in the translation:
% 5.90/6.27
% 5.90/6.27 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 5.90/6.27 . [1, 2] (w:1, o:45, a:1, s:1, b:0),
% 5.90/6.27 ! [4, 1] (w:0, o:24, a:1, s:1, b:0),
% 5.90/6.27 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 5.90/6.27 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 5.90/6.27 subclass [37, 2] (w:1, o:69, a:1, s:1, b:0),
% 5.90/6.27 member [39, 2] (w:1, o:70, a:1, s:1, b:0),
% 5.90/6.27 universal_class [40, 0] (w:1, o:12, a:1, s:1, b:0),
% 5.90/6.27 unordered_pair [41, 2] (w:1, o:71, a:1, s:1, b:0),
% 5.90/6.27 singleton [42, 1] (w:1, o:31, a:1, s:1, b:0),
% 5.90/6.27 ordered_pair [43, 2] (w:1, o:72, a:1, s:1, b:0),
% 5.90/6.27 cross_product [45, 2] (w:1, o:73, a:1, s:1, b:0),
% 5.90/6.27 first [46, 1] (w:1, o:32, a:1, s:1, b:0),
% 5.90/6.27 second [47, 1] (w:1, o:33, a:1, s:1, b:0),
% 5.90/6.27 element_relation [49, 0] (w:1, o:16, a:1, s:1, b:0),
% 5.90/6.27 intersection [50, 2] (w:1, o:75, a:1, s:1, b:0),
% 5.90/6.27 complement [51, 1] (w:1, o:34, a:1, s:1, b:0),
% 5.90/6.27 restrict [53, 3] (w:1, o:84, a:1, s:1, b:0),
% 5.90/6.27 null_class [54, 0] (w:1, o:17, a:1, s:1, b:0),
% 5.90/6.27 domain_of [55, 1] (w:1, o:35, a:1, s:1, b:0),
% 5.90/6.27 rotate [57, 1] (w:1, o:29, a:1, s:1, b:0),
% 5.90/6.27 flip [58, 1] (w:1, o:36, a:1, s:1, b:0),
% 5.90/6.27 union [59, 2] (w:1, o:76, a:1, s:1, b:0),
% 5.90/6.27 successor [60, 1] (w:1, o:37, a:1, s:1, b:0),
% 5.90/6.27 successor_relation [61, 0] (w:1, o:18, a:1, s:1, b:0),
% 5.90/6.27 inverse [62, 1] (w:1, o:38, a:1, s:1, b:0),
% 5.90/6.27 range_of [63, 1] (w:1, o:30, a:1, s:1, b:0),
% 5.90/6.27 image [64, 2] (w:1, o:74, a:1, s:1, b:0),
% 5.90/6.27 inductive [65, 1] (w:1, o:39, a:1, s:1, b:0),
% 5.90/6.27 sum_class [66, 1] (w:1, o:40, a:1, s:1, b:0),
% 5.90/6.27 power_class [67, 1] (w:1, o:41, a:1, s:1, b:0),
% 5.90/6.27 compose [69, 2] (w:1, o:77, a:1, s:1, b:0),
% 5.90/6.27 identity_relation [70, 0] (w:1, o:19, a:1, s:1, b:0),
% 5.90/6.27 function [72, 1] (w:1, o:42, a:1, s:1, b:0),
% 5.90/6.27 disjoint [73, 2] (w:1, o:78, a:1, s:1, b:0),
% 5.90/6.27 apply [74, 2] (w:1, o:79, a:1, s:1, b:0),
% 5.90/6.27 alpha1 [75, 3] (w:1, o:85, a:1, s:1, b:1),
% 5.90/6.27 alpha2 [76, 2] (w:1, o:80, a:1, s:1, b:1),
% 5.90/6.27 skol1 [77, 2] (w:1, o:81, a:1, s:1, b:1),
% 5.90/6.27 skol2 [78, 0] (w:1, o:20, a:1, s:1, b:1),
% 5.90/6.27 skol3 [79, 2] (w:1, o:82, a:1, s:1, b:1),
% 5.90/6.27 skol4 [80, 1] (w:1, o:43, a:1, s:1, b:1),
% 5.90/6.27 skol5 [81, 2] (w:1, o:83, a:1, s:1, b:1),
% 5.90/6.27 skol6 [82, 1] (w:1, o:44, a:1, s:1, b:1),
% 5.90/6.27 skol7 [83, 0] (w:1, o:21, a:1, s:1, b:1),
% 5.90/6.27 skol8 [84, 0] (w:1, o:22, a:1, s:1, b:1),
% 5.90/6.27 skol9 [85, 0] (w:1, o:23, a:1, s:1, b:1).
% 5.90/6.27
% 5.90/6.27
% 5.90/6.27 Starting Search:
% 5.90/6.27
% 5.90/6.27 *** allocated 15000 integers for clauses
% 5.90/6.27 *** allocated 22500 integers for clauses
% 5.90/6.27 *** allocated 33750 integers for clauses
% 5.90/6.27 *** allocated 15000 integers for termspace/termends
% 5.90/6.27 *** allocated 50625 integers for clauses
% 5.90/6.27 *** allocated 22500 integers for termspace/termends
% 5.90/6.27 Resimplifying inuse:
% 5.90/6.27 Done
% 5.90/6.27
% 5.90/6.27 *** allocated 75937 integers for clauses
% 5.90/6.27 *** allocated 33750 integers for termspace/termends
% 5.90/6.27 *** allocated 113905 integers for clauses
% 5.90/6.27
% 5.90/6.27 Intermediate Status:
% 5.90/6.27 Generated: 5070
% 5.90/6.27 Kept: 2025
% 5.90/6.27 Inuse: 122
% 5.90/6.27 Deleted: 6
% 5.90/6.27 Deletedinuse: 2
% 5.90/6.27
% 5.90/6.27 Resimplifying inuse:
% 5.90/6.27 Done
% 5.90/6.27
% 5.90/6.27 *** allocated 170857 integers for clauses
% 5.90/6.27 *** allocated 50625 integers for termspace/termends
% 5.90/6.27 Resimplifying inuse:
% 5.90/6.27 Done
% 5.90/6.27
% 5.90/6.27 *** allocated 75937 integers for termspace/termends
% 5.90/6.27 *** allocated 256285 integers for clauses
% 5.90/6.27
% 5.90/6.27 Intermediate Status:
% 5.90/6.27 Generated: 9896
% 5.90/6.27 Kept: 4029
% 5.90/6.27 Inuse: 196
% 5.90/6.27 Deleted: 59
% 5.90/6.27 Deletedinuse: 19
% 5.90/6.27
% 5.90/6.27 Resimplifying inuse:
% 5.90/6.27 Done
% 5.90/6.27
% 5.90/6.27 Resimplifying inuse:
% 5.90/6.27 Done
% 5.90/6.27
% 5.90/6.27 *** allocated 113905 integers for termspace/termends
% 5.90/6.27 *** allocated 384427 integers for clauses
% 5.90/6.27
% 5.90/6.27 Intermediate Status:
% 5.90/6.27 Generated: 13604
% 5.90/6.27 Kept: 6035
% 5.90/6.27 Inuse: 251
% 5.90/6.27 Deleted: 78
% 5.90/6.27 Deletedinuse: 25
% 5.90/6.27
% 5.90/6.27 Resimplifying inuse:
% 5.90/6.27 Done
% 5.90/6.27
% 5.90/6.27 Resimplifying inuse:
% 5.90/6.27 Done
% 5.90/6.27
% 5.90/6.27
% 5.90/6.27 Intermediate Status:
% 5.90/6.27 Generated: 17505
% 5.90/6.27 Kept: 8080
% 5.90/6.27 Inuse: 311
% 5.90/6.27 Deleted: 88
% 5.90/6.27 Deletedinuse: 33
% 5.90/6.27
% 5.90/6.27 *** allocated 576640 integers for clauses
% 5.90/6.27 Resimplifying inuse:
% 5.90/6.27 Done
% 5.90/6.27
% 5.90/6.27 *** allocated 170857 integers for termspace/termends
% 5.90/6.27 Resimplifying inuse:
% 5.90/6.27 Done
% 5.90/6.27
% 5.90/6.27
% 5.90/6.27 Intermediate Status:
% 5.90/6.27 Generated: 25294
% 5.90/6.27 Kept: 11152
% 5.90/6.27 Inuse: 352
% 5.90/6.27 Deleted: 96
% 5.90/6.27 Deletedinuse: 37
% 5.90/6.27
% 5.90/6.27 Resimplifying inuse:
% 5.90/6.27 Done
% 5.90/6.27
% 5.90/6.27 Resimplifying inuse:
% 5.90/6.27 Done
% 5.90/6.27
% 5.90/6.27 *** allocated 864960 integers for clauses
% 5.90/6.27 *** allocated 256285 integers for termspace/termends
% 5.90/6.27
% 5.90/6.27 Intermediate Status:
% 5.90/6.27 Generated: 31590
% 5.90/6.27 Kept: 13636
% 5.90/6.27 Inuse: 362
% 5.90/6.27 Deleted: 98
% 5.90/6.27 Deletedinuse: 39
% 5.90/6.27
% 5.90/6.27 Resimplifying inuse:
% 5.90/6.27 Done
% 5.90/6.27
% 5.90/6.27 Resimplifying inuse:
% 5.90/6.27 Done
% 5.90/6.27
% 5.90/6.27
% 5.90/6.27 Intermediate Status:
% 5.90/6.27 Generated: 36155
% 5.90/6.27 Kept: 15654
% 5.90/6.27 Inuse: 415
% 5.90/6.27 Deleted: 104
% 5.90/6.27 Deletedinuse: 42
% 5.90/6.27
% 5.90/6.27 Resimplifying inuse:
% 5.90/6.27 Done
% 5.90/6.27
% 5.90/6.27 Resimplifying inuse:
% 5.90/6.27 Done
% 5.90/6.27
% 5.90/6.27
% 5.90/6.27 Intermediate Status:
% 5.90/6.27 Generated: 40451
% 5.90/6.27 Kept: 17688
% 5.90/6.27 Inuse: 457
% 5.90/6.27 Deleted: 105
% 5.90/6.27 Deletedinuse: 43
% 5.90/6.27
% 5.90/6.27 Resimplifying inuse:
% 5.90/6.27 Done
% 5.90/6.27
% 5.90/6.27 Resimplifying inuse:
% 5.90/6.27 Done
% 5.90/6.27
% 5.90/6.27 *** allocated 1297440 integers for clauses
% 5.90/6.27 *** allocated 384427 integers for termspace/termends
% 5.90/6.27
% 5.90/6.27 Intermediate Status:
% 5.90/6.27 Generated: 45079
% 5.90/6.27 Kept: 19725
% 5.90/6.27 Inuse: 495
% 5.90/6.27 Deleted: 108
% 5.90/6.27 Deletedinuse: 43
% 5.90/6.27
% 5.90/6.27 Resimplifying inuse:
% 5.90/6.27 Done
% 5.90/6.27
% 5.90/6.27 Resimplifying inuse:
% 5.90/6.27 Done
% 5.90/6.27
% 5.90/6.27 Resimplifying clauses:
% 5.90/6.27 Done
% 5.90/6.27
% 5.90/6.27
% 5.90/6.27 Intermediate Status:
% 5.90/6.27 Generated: 52576
% 5.90/6.27 Kept: 21910
% 5.90/6.27 Inuse: 508
% 5.90/6.27 Deleted: 955
% 5.90/6.27 Deletedinuse: 43
% 5.90/6.27
% 5.90/6.27 Resimplifying inuse:
% 5.90/6.27 Done
% 5.90/6.27
% 5.90/6.27 Resimplifying inuse:
% 5.90/6.27 Done
% 5.90/6.27
% 5.90/6.27
% 5.90/6.27 Intermediate Status:
% 5.90/6.27 Generated: 59957
% 5.90/6.27 Kept: 23923
% 5.90/6.27 Inuse: 571
% 5.90/6.27 Deleted: 957
% 5.90/6.27 Deletedinuse: 44
% 5.90/6.27
% 5.90/6.27 Resimplifying inuse:
% 5.90/6.27 Done
% 5.90/6.27
% 5.90/6.27 Resimplifying inuse:
% 5.90/6.27 Done
% 5.90/6.27
% 5.90/6.27
% 5.90/6.27 Intermediate Status:
% 5.90/6.27 Generated: 68685
% 5.90/6.27 Kept: 25952
% 5.90/6.27 Inuse: 629
% 5.90/6.27 Deleted: 957
% 5.90/6.27 Deletedinuse: 44
% 5.90/6.27
% 5.90/6.27 Resimplifying inuse:
% 5.90/6.27 Done
% 5.90/6.27
% 5.90/6.27 Resimplifying inuse:
% 5.90/6.27 Done
% 5.90/6.27
% 5.90/6.27
% 5.90/6.27 Intermediate Status:
% 5.90/6.27 Generated: 74239
% 5.90/6.27 Kept: 27964
% 5.90/6.27 Inuse: 678
% 5.90/6.27 Deleted: 957
% 5.90/6.27 Deletedinuse: 44
% 5.90/6.27
% 5.90/6.27 Resimplifying inuse:
% 5.90/6.27 Done
% 5.90/6.27
% 5.90/6.27 *** allocated 576640 integers for termspace/termends
% 5.90/6.27 Resimplifying inuse:
% 5.90/6.27 Done
% 5.90/6.27
% 5.90/6.27 *** allocated 1946160 integers for clauses
% 5.90/6.27
% 5.90/6.27 Intermediate Status:
% 5.90/6.27 Generated: 81350
% 5.90/6.27 Kept: 30004
% 5.90/6.27 Inuse: 757
% 5.90/6.27 Deleted: 960
% 5.90/6.27 Deletedinuse: 44
% 5.90/6.27
% 5.90/6.27 Resimplifying inuse:
% 5.90/6.27 Done
% 5.90/6.27
% 5.90/6.27 Resimplifying inuse:
% 5.90/6.27 Done
% 5.90/6.27
% 5.90/6.27
% 5.90/6.27 Intermediate Status:
% 5.90/6.27 Generated: 86831
% 5.90/6.27 Kept: 32049
% 5.90/6.27 Inuse: 796
% 5.90/6.27 Deleted: 960
% 5.90/6.27 Deletedinuse: 44
% 5.90/6.27
% 5.90/6.27 Resimplifying inuse:
% 5.90/6.27 Done
% 5.90/6.27
% 5.90/6.27 Resimplifying inuse:
% 5.90/6.27 Done
% 5.90/6.27
% 5.90/6.27
% 5.90/6.27 Intermediate Status:
% 5.90/6.27 Generated: 92271
% 5.90/6.27 Kept: 34089
% 5.90/6.27 Inuse: 852
% 5.90/6.27 Deleted: 963
% 5.90/6.27 Deletedinuse: 45
% 5.90/6.27
% 5.90/6.27
% 5.90/6.27 Bliksems!, er is een bewijs:
% 5.90/6.27 % SZS status Theorem
% 5.90/6.27 % SZS output start Refutation
% 5.90/6.27
% 5.90/6.27 (4) {G0,W6,D2,L2,V2,M2} I { ! X = Y, subclass( X, Y ) }.
% 5.90/6.27 (5) {G0,W9,D2,L3,V2,M3} I { ! subclass( X, Y ), ! subclass( Y, X ), X = Y
% 5.90/6.27 }.
% 5.90/6.27 (8) {G0,W12,D3,L3,V3,M3} I { ! member( X, universal_class ), ! alpha1( X, Y
% 5.90/6.27 , Z ), member( X, unordered_pair( Y, Z ) ) }.
% 5.90/6.27 (11) {G0,W7,D2,L2,V3,M2} I { ! X = Z, alpha1( X, Y, Z ) }.
% 5.90/6.27 (32) {G0,W3,D2,L1,V1,M1} I { ! member( X, null_class ) }.
% 5.90/6.27 (92) {G0,W3,D2,L1,V0,M1} I { member( skol8, universal_class ) }.
% 5.90/6.27 (93) {G0,W5,D3,L1,V0,M1} I { unordered_pair( skol9, skol8 ) ==> null_class
% 5.90/6.27 }.
% 5.90/6.27 (99) {G1,W4,D2,L1,V2,M1} Q(11) { alpha1( X, Y, X ) }.
% 5.90/6.27 (145) {G1,W6,D2,L2,V2,M2} R(5,4);r(4) { X = Y, ! Y = X }.
% 5.90/6.27 (219) {G2,W8,D3,L2,V1,M2} P(145,93) { unordered_pair( X, skol8 ) ==>
% 5.90/6.27 null_class, ! X = skol9 }.
% 5.90/6.27 (252) {G1,W9,D3,L2,V2,M2} R(8,92) { ! alpha1( skol8, X, Y ), member( skol8
% 5.90/6.27 , unordered_pair( X, Y ) ) }.
% 5.90/6.27 (34187) {G3,W6,D2,L2,V1,M2} P(219,252);r(99) { member( skol8, null_class )
% 5.90/6.27 , ! X = skol9 }.
% 5.90/6.27 (34204) {G4,W0,D0,L0,V0,M0} Q(34187);r(32) { }.
% 5.90/6.27
% 5.90/6.27
% 5.90/6.27 % SZS output end Refutation
% 5.90/6.27 found a proof!
% 5.90/6.27
% 5.90/6.27
% 5.90/6.27 Unprocessed initial clauses:
% 5.90/6.27
% 5.90/6.27 (34206) {G0,W9,D2,L3,V3,M3} { ! subclass( X, Y ), ! member( Z, X ), member
% 5.90/6.27 ( Z, Y ) }.
% 5.90/6.27 (34207) {G0,W8,D3,L2,V3,M2} { ! member( skol1( Z, Y ), Y ), subclass( X, Y
% 5.90/6.27 ) }.
% 5.90/6.27 (34208) {G0,W8,D3,L2,V2,M2} { member( skol1( X, Y ), X ), subclass( X, Y )
% 5.90/6.27 }.
% 5.90/6.27 (34209) {G0,W3,D2,L1,V1,M1} { subclass( X, universal_class ) }.
% 5.90/6.27 (34210) {G0,W6,D2,L2,V2,M2} { ! X = Y, subclass( X, Y ) }.
% 5.90/6.27 (34211) {G0,W6,D2,L2,V2,M2} { ! X = Y, subclass( Y, X ) }.
% 5.90/6.27 (34212) {G0,W9,D2,L3,V2,M3} { ! subclass( X, Y ), ! subclass( Y, X ), X =
% 5.90/6.27 Y }.
% 5.90/6.27 (34213) {G0,W8,D3,L2,V3,M2} { ! member( X, unordered_pair( Y, Z ) ),
% 5.90/6.27 member( X, universal_class ) }.
% 5.90/6.27 (34214) {G0,W9,D3,L2,V3,M2} { ! member( X, unordered_pair( Y, Z ) ),
% 5.90/6.27 alpha1( X, Y, Z ) }.
% 5.90/6.27 (34215) {G0,W12,D3,L3,V3,M3} { ! member( X, universal_class ), ! alpha1( X
% 5.90/6.27 , Y, Z ), member( X, unordered_pair( Y, Z ) ) }.
% 5.90/6.27 (34216) {G0,W10,D2,L3,V3,M3} { ! alpha1( X, Y, Z ), X = Y, X = Z }.
% 5.90/6.27 (34217) {G0,W7,D2,L2,V3,M2} { ! X = Y, alpha1( X, Y, Z ) }.
% 5.90/6.27 (34218) {G0,W7,D2,L2,V3,M2} { ! X = Z, alpha1( X, Y, Z ) }.
% 5.90/6.27 (34219) {G0,W5,D3,L1,V2,M1} { member( unordered_pair( X, Y ),
% 5.90/6.27 universal_class ) }.
% 5.90/6.27 (34220) {G0,W6,D3,L1,V1,M1} { singleton( X ) = unordered_pair( X, X ) }.
% 5.90/6.27 (34221) {G0,W11,D5,L1,V2,M1} { ordered_pair( X, Y ) = unordered_pair(
% 5.90/6.27 singleton( X ), unordered_pair( X, singleton( Y ) ) ) }.
% 5.90/6.27 (34222) {G0,W10,D3,L2,V4,M2} { ! member( ordered_pair( X, Y ),
% 5.90/6.27 cross_product( Z, T ) ), member( X, Z ) }.
% 5.90/6.27 (34223) {G0,W10,D3,L2,V4,M2} { ! member( ordered_pair( X, Y ),
% 5.90/6.27 cross_product( Z, T ) ), member( Y, T ) }.
% 5.90/6.27 (34224) {G0,W13,D3,L3,V4,M3} { ! member( X, Z ), ! member( Y, T ), member
% 5.90/6.27 ( ordered_pair( X, Y ), cross_product( Z, T ) ) }.
% 5.90/6.27 (34225) {G0,W12,D4,L3,V2,M3} { ! member( X, universal_class ), ! member( Y
% 5.90/6.27 , universal_class ), first( ordered_pair( X, Y ) ) = X }.
% 5.90/6.27 (34226) {G0,W12,D4,L3,V2,M3} { ! member( X, universal_class ), ! member( Y
% 5.90/6.27 , universal_class ), second( ordered_pair( X, Y ) ) = Y }.
% 5.90/6.27 (34227) {G0,W12,D4,L2,V3,M2} { ! member( X, cross_product( Y, Z ) ), X =
% 5.90/6.27 ordered_pair( first( X ), second( X ) ) }.
% 5.90/6.27 (34228) {G0,W8,D3,L2,V2,M2} { ! member( ordered_pair( X, Y ),
% 5.90/6.27 element_relation ), member( Y, universal_class ) }.
% 5.90/6.27 (34229) {G0,W8,D3,L2,V2,M2} { ! member( ordered_pair( X, Y ),
% 5.90/6.27 element_relation ), member( X, Y ) }.
% 5.90/6.27 (34230) {G0,W11,D3,L3,V2,M3} { ! member( Y, universal_class ), ! member( X
% 5.90/6.27 , Y ), member( ordered_pair( X, Y ), element_relation ) }.
% 5.90/6.27 (34231) {G0,W5,D3,L1,V0,M1} { subclass( element_relation, cross_product(
% 5.90/6.27 universal_class, universal_class ) ) }.
% 5.90/6.27 (34232) {G0,W8,D3,L2,V3,M2} { ! member( Z, intersection( X, Y ) ), member
% 5.90/6.27 ( Z, X ) }.
% 5.90/6.27 (34233) {G0,W8,D3,L2,V3,M2} { ! member( Z, intersection( X, Y ) ), member
% 5.90/6.27 ( Z, Y ) }.
% 5.90/6.27 (34234) {G0,W11,D3,L3,V3,M3} { ! member( Z, X ), ! member( Z, Y ), member
% 5.90/6.27 ( Z, intersection( X, Y ) ) }.
% 5.90/6.27 (34235) {G0,W7,D3,L2,V2,M2} { ! member( Y, complement( X ) ), member( Y,
% 5.90/6.27 universal_class ) }.
% 5.90/6.27 (34236) {G0,W7,D3,L2,V2,M2} { ! member( Y, complement( X ) ), ! member( Y
% 5.90/6.27 , X ) }.
% 5.90/6.27 (34237) {G0,W10,D3,L3,V2,M3} { ! member( Y, universal_class ), member( Y,
% 5.90/6.27 X ), member( Y, complement( X ) ) }.
% 5.90/6.27 (34238) {G0,W10,D4,L1,V3,M1} { restrict( Y, X, Z ) = intersection( Y,
% 5.90/6.27 cross_product( X, Z ) ) }.
% 5.90/6.27 (34239) {G0,W3,D2,L1,V1,M1} { ! member( X, null_class ) }.
% 5.90/6.27 (34240) {G0,W7,D3,L2,V2,M2} { ! member( Y, domain_of( X ) ), member( Y,
% 5.90/6.27 universal_class ) }.
% 5.90/6.27 (34241) {G0,W11,D4,L2,V2,M2} { ! member( Y, domain_of( X ) ), ! restrict(
% 5.90/6.27 X, singleton( Y ), universal_class ) = null_class }.
% 5.90/6.27 (34242) {G0,W14,D4,L3,V2,M3} { ! member( Y, universal_class ), restrict( X
% 5.90/6.27 , singleton( Y ), universal_class ) = null_class, member( Y, domain_of( X
% 5.90/6.27 ) ) }.
% 5.90/6.27 (34243) {G0,W19,D4,L2,V4,M2} { ! member( ordered_pair( ordered_pair( Y, Z
% 5.90/6.27 ), T ), rotate( X ) ), member( ordered_pair( ordered_pair( Y, Z ), T ),
% 5.90/6.27 cross_product( cross_product( universal_class, universal_class ),
% 5.90/6.27 universal_class ) ) }.
% 5.90/6.27 (34244) {G0,W15,D4,L2,V4,M2} { ! member( ordered_pair( ordered_pair( Y, Z
% 5.90/6.27 ), T ), rotate( X ) ), member( ordered_pair( ordered_pair( Z, T ), Y ),
% 5.90/6.27 X ) }.
% 5.90/6.27 (34245) {G0,W26,D4,L3,V4,M3} { ! member( ordered_pair( ordered_pair( Y, Z
% 5.90/6.27 ), T ), cross_product( cross_product( universal_class, universal_class )
% 5.90/6.27 , universal_class ) ), ! member( ordered_pair( ordered_pair( Z, T ), Y )
% 5.90/6.27 , X ), member( ordered_pair( ordered_pair( Y, Z ), T ), rotate( X ) ) }.
% 5.90/6.27 (34246) {G0,W8,D4,L1,V1,M1} { subclass( rotate( X ), cross_product(
% 5.90/6.27 cross_product( universal_class, universal_class ), universal_class ) )
% 5.90/6.27 }.
% 5.90/6.27 (34247) {G0,W19,D4,L2,V4,M2} { ! member( ordered_pair( ordered_pair( X, Y
% 5.90/6.27 ), Z ), flip( T ) ), member( ordered_pair( ordered_pair( X, Y ), Z ),
% 5.90/6.27 cross_product( cross_product( universal_class, universal_class ),
% 5.90/6.27 universal_class ) ) }.
% 5.90/6.27 (34248) {G0,W15,D4,L2,V4,M2} { ! member( ordered_pair( ordered_pair( X, Y
% 5.90/6.27 ), Z ), flip( T ) ), member( ordered_pair( ordered_pair( Y, X ), Z ), T
% 5.90/6.27 ) }.
% 5.90/6.27 (34249) {G0,W26,D4,L3,V4,M3} { ! member( ordered_pair( ordered_pair( X, Y
% 5.90/6.27 ), Z ), cross_product( cross_product( universal_class, universal_class )
% 5.90/6.27 , universal_class ) ), ! member( ordered_pair( ordered_pair( Y, X ), Z )
% 5.90/6.27 , T ), member( ordered_pair( ordered_pair( X, Y ), Z ), flip( T ) ) }.
% 5.90/6.27 (34250) {G0,W8,D4,L1,V1,M1} { subclass( flip( X ), cross_product(
% 5.90/6.27 cross_product( universal_class, universal_class ), universal_class ) )
% 5.90/6.27 }.
% 5.90/6.27 (34251) {G0,W11,D3,L3,V3,M3} { ! member( Z, union( X, Y ) ), member( Z, X
% 5.90/6.27 ), member( Z, Y ) }.
% 5.90/6.27 (34252) {G0,W8,D3,L2,V3,M2} { ! member( Z, X ), member( Z, union( X, Y ) )
% 5.90/6.27 }.
% 5.90/6.27 (34253) {G0,W8,D3,L2,V3,M2} { ! member( Z, Y ), member( Z, union( X, Y ) )
% 5.90/6.27 }.
% 5.90/6.27 (34254) {G0,W7,D4,L1,V1,M1} { successor( X ) = union( X, singleton( X ) )
% 5.90/6.27 }.
% 5.90/6.27 (34255) {G0,W5,D3,L1,V0,M1} { subclass( successor_relation, cross_product
% 5.90/6.27 ( universal_class, universal_class ) ) }.
% 5.90/6.27 (34256) {G0,W8,D3,L2,V2,M2} { ! member( ordered_pair( X, Y ),
% 5.90/6.27 successor_relation ), member( X, universal_class ) }.
% 5.90/6.27 (34257) {G0,W8,D3,L2,V2,M2} { ! member( ordered_pair( X, Y ),
% 5.90/6.27 successor_relation ), alpha2( X, Y ) }.
% 5.90/6.27 (34258) {G0,W11,D3,L3,V2,M3} { ! member( X, universal_class ), ! alpha2( X
% 5.90/6.27 , Y ), member( ordered_pair( X, Y ), successor_relation ) }.
% 5.90/6.27 (34259) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), member( Y, universal_class
% 5.90/6.27 ) }.
% 5.90/6.27 (34260) {G0,W7,D3,L2,V2,M2} { ! alpha2( X, Y ), successor( X ) = Y }.
% 5.90/6.27 (34261) {G0,W10,D3,L3,V2,M3} { ! member( Y, universal_class ), ! successor
% 5.90/6.27 ( X ) = Y, alpha2( X, Y ) }.
% 5.90/6.27 (34262) {G0,W8,D5,L1,V1,M1} { inverse( X ) = domain_of( flip(
% 5.90/6.27 cross_product( X, universal_class ) ) ) }.
% 5.90/6.27 (34263) {G0,W6,D4,L1,V1,M1} { range_of( X ) = domain_of( inverse( X ) )
% 5.90/6.27 }.
% 5.90/6.27 (34264) {G0,W9,D4,L1,V2,M1} { image( Y, X ) = range_of( restrict( Y, X,
% 5.90/6.27 universal_class ) ) }.
% 5.90/6.27 (34265) {G0,W5,D2,L2,V1,M2} { ! inductive( X ), member( null_class, X )
% 5.90/6.27 }.
% 5.90/6.27 (34266) {G0,W7,D3,L2,V1,M2} { ! inductive( X ), subclass( image(
% 5.90/6.27 successor_relation, X ), X ) }.
% 5.90/6.27 (34267) {G0,W10,D3,L3,V1,M3} { ! member( null_class, X ), ! subclass(
% 5.90/6.27 image( successor_relation, X ), X ), inductive( X ) }.
% 5.90/6.27 (34268) {G0,W3,D2,L1,V0,M1} { member( skol2, universal_class ) }.
% 5.90/6.27 (34269) {G0,W2,D2,L1,V0,M1} { inductive( skol2 ) }.
% 5.90/6.27 (34270) {G0,W5,D2,L2,V1,M2} { ! inductive( X ), subclass( skol2, X ) }.
% 5.90/6.27 (34271) {G0,W9,D3,L2,V3,M2} { ! member( X, sum_class( Y ) ), member( skol3
% 5.90/6.27 ( Z, Y ), Y ) }.
% 5.90/6.27 (34272) {G0,W9,D3,L2,V2,M2} { ! member( X, sum_class( Y ) ), member( X,
% 5.90/6.27 skol3( X, Y ) ) }.
% 5.90/6.27 (34273) {G0,W10,D3,L3,V3,M3} { ! member( X, Z ), ! member( Z, Y ), member
% 5.90/6.27 ( X, sum_class( Y ) ) }.
% 5.90/6.27 (34274) {G0,W7,D3,L2,V1,M2} { ! member( X, universal_class ), member(
% 5.90/6.27 sum_class( X ), universal_class ) }.
% 5.90/6.27 (34275) {G0,W7,D3,L2,V2,M2} { ! member( X, power_class( Y ) ), member( X,
% 5.90/6.27 universal_class ) }.
% 5.90/6.27 (34276) {G0,W7,D3,L2,V2,M2} { ! member( X, power_class( Y ) ), subclass( X
% 5.90/6.27 , Y ) }.
% 5.90/6.27 (34277) {G0,W10,D3,L3,V2,M3} { ! member( X, universal_class ), ! subclass
% 5.90/6.27 ( X, Y ), member( X, power_class( Y ) ) }.
% 5.90/6.27 (34278) {G0,W7,D3,L2,V1,M2} { ! member( X, universal_class ), member(
% 5.90/6.27 power_class( X ), universal_class ) }.
% 5.90/6.27 (34279) {G0,W7,D3,L1,V2,M1} { subclass( compose( Y, X ), cross_product(
% 5.90/6.27 universal_class, universal_class ) ) }.
% 5.90/6.27 (34280) {G0,W10,D3,L2,V4,M2} { ! member( ordered_pair( Z, T ), compose( Y
% 5.90/6.27 , X ) ), member( Z, universal_class ) }.
% 5.90/6.27 (34281) {G0,W15,D5,L2,V4,M2} { ! member( ordered_pair( Z, T ), compose( Y
% 5.90/6.27 , X ) ), member( T, image( Y, image( X, singleton( Z ) ) ) ) }.
% 5.90/6.27 (34282) {G0,W18,D5,L3,V4,M3} { ! member( Z, universal_class ), ! member( T
% 5.90/6.27 , image( Y, image( X, singleton( Z ) ) ) ), member( ordered_pair( Z, T )
% 5.90/6.27 , compose( Y, X ) ) }.
% 5.90/6.27 (34283) {G0,W7,D3,L2,V2,M2} { ! member( X, identity_relation ), member(
% 5.90/6.27 skol4( Y ), universal_class ) }.
% 5.90/6.27 (34284) {G0,W10,D4,L2,V1,M2} { ! member( X, identity_relation ), X =
% 5.90/6.27 ordered_pair( skol4( X ), skol4( X ) ) }.
% 5.90/6.27 (34285) {G0,W11,D3,L3,V2,M3} { ! member( Y, universal_class ), ! X =
% 5.90/6.27 ordered_pair( Y, Y ), member( X, identity_relation ) }.
% 5.90/6.27 (34286) {G0,W7,D3,L2,V1,M2} { ! function( X ), subclass( X, cross_product
% 5.90/6.27 ( universal_class, universal_class ) ) }.
% 5.90/6.27 (34287) {G0,W8,D4,L2,V1,M2} { ! function( X ), subclass( compose( X,
% 5.90/6.27 inverse( X ) ), identity_relation ) }.
% 5.90/6.27 (34288) {G0,W13,D4,L3,V1,M3} { ! subclass( X, cross_product(
% 5.90/6.27 universal_class, universal_class ) ), ! subclass( compose( X, inverse( X
% 5.90/6.27 ) ), identity_relation ), function( X ) }.
% 5.90/6.27 (34289) {G0,W10,D3,L3,V2,M3} { ! member( X, universal_class ), ! function
% 5.90/6.27 ( Y ), member( image( Y, X ), universal_class ) }.
% 5.90/6.27 (34290) {G0,W9,D2,L3,V3,M3} { ! disjoint( X, Y ), ! member( Z, X ), !
% 5.90/6.27 member( Z, Y ) }.
% 5.90/6.27 (34291) {G0,W8,D3,L2,V3,M2} { member( skol5( Z, Y ), Y ), disjoint( X, Y )
% 5.90/6.27 }.
% 5.90/6.27 (34292) {G0,W8,D3,L2,V2,M2} { member( skol5( X, Y ), X ), disjoint( X, Y )
% 5.90/6.27 }.
% 5.90/6.27 (34293) {G0,W7,D3,L2,V2,M2} { X = null_class, member( skol6( Y ),
% 5.90/6.27 universal_class ) }.
% 5.90/6.27 (34294) {G0,W7,D3,L2,V1,M2} { X = null_class, member( skol6( X ), X ) }.
% 5.90/6.27 (34295) {G0,W7,D3,L2,V1,M2} { X = null_class, disjoint( skol6( X ), X )
% 5.90/6.27 }.
% 5.90/6.27 (34296) {G0,W9,D5,L1,V2,M1} { apply( X, Y ) = sum_class( image( X,
% 5.90/6.27 singleton( Y ) ) ) }.
% 5.90/6.27 (34297) {G0,W2,D2,L1,V0,M1} { function( skol7 ) }.
% 5.90/6.27 (34298) {G0,W11,D3,L3,V1,M3} { ! member( X, universal_class ), X =
% 5.90/6.27 null_class, member( apply( skol7, X ), X ) }.
% 5.90/6.27 (34299) {G0,W3,D2,L1,V0,M1} { member( skol8, universal_class ) }.
% 5.90/6.27 (34300) {G0,W5,D3,L1,V0,M1} { unordered_pair( skol9, skol8 ) = null_class
% 5.90/6.27 }.
% 5.90/6.27
% 5.90/6.27
% 5.90/6.27 Total Proof:
% 5.90/6.27
% 5.90/6.27 subsumption: (4) {G0,W6,D2,L2,V2,M2} I { ! X = Y, subclass( X, Y ) }.
% 5.90/6.27 parent0: (34210) {G0,W6,D2,L2,V2,M2} { ! X = Y, subclass( X, Y ) }.
% 5.90/6.27 substitution0:
% 5.90/6.27 X := X
% 5.90/6.27 Y := Y
% 5.90/6.27 end
% 5.90/6.27 permutation0:
% 5.90/6.27 0 ==> 0
% 5.90/6.27 1 ==> 1
% 5.90/6.27 end
% 5.90/6.27
% 5.90/6.27 subsumption: (5) {G0,W9,D2,L3,V2,M3} I { ! subclass( X, Y ), ! subclass( Y
% 5.90/6.27 , X ), X = Y }.
% 5.90/6.27 parent0: (34212) {G0,W9,D2,L3,V2,M3} { ! subclass( X, Y ), ! subclass( Y,
% 5.90/6.27 X ), X = Y }.
% 5.90/6.27 substitution0:
% 5.90/6.27 X := X
% 5.90/6.27 Y := Y
% 5.90/6.27 end
% 5.90/6.27 permutation0:
% 5.90/6.27 0 ==> 0
% 5.90/6.27 1 ==> 1
% 5.90/6.27 2 ==> 2
% 5.90/6.27 end
% 5.90/6.27
% 5.90/6.27 subsumption: (8) {G0,W12,D3,L3,V3,M3} I { ! member( X, universal_class ), !
% 5.90/6.27 alpha1( X, Y, Z ), member( X, unordered_pair( Y, Z ) ) }.
% 5.90/6.27 parent0: (34215) {G0,W12,D3,L3,V3,M3} { ! member( X, universal_class ), !
% 5.90/6.27 alpha1( X, Y, Z ), member( X, unordered_pair( Y, Z ) ) }.
% 5.90/6.27 substitution0:
% 5.90/6.27 X := X
% 5.90/6.27 Y := Y
% 5.90/6.27 Z := Z
% 5.90/6.27 end
% 5.90/6.27 permutation0:
% 5.90/6.27 0 ==> 0
% 5.90/6.27 1 ==> 1
% 5.90/6.27 2 ==> 2
% 5.90/6.27 end
% 5.90/6.27
% 5.90/6.27 subsumption: (11) {G0,W7,D2,L2,V3,M2} I { ! X = Z, alpha1( X, Y, Z ) }.
% 5.90/6.27 parent0: (34218) {G0,W7,D2,L2,V3,M2} { ! X = Z, alpha1( X, Y, Z ) }.
% 5.90/6.27 substitution0:
% 5.90/6.27 X := X
% 5.90/6.27 Y := Y
% 5.90/6.27 Z := Z
% 5.90/6.27 end
% 5.90/6.27 permutation0:
% 5.90/6.27 0 ==> 0
% 5.90/6.27 1 ==> 1
% 5.90/6.27 end
% 5.90/6.27
% 5.90/6.27 subsumption: (32) {G0,W3,D2,L1,V1,M1} I { ! member( X, null_class ) }.
% 5.90/6.27 parent0: (34239) {G0,W3,D2,L1,V1,M1} { ! member( X, null_class ) }.
% 5.90/6.27 substitution0:
% 5.90/6.27 X := X
% 5.90/6.27 end
% 5.90/6.27 permutation0:
% 5.90/6.27 0 ==> 0
% 5.90/6.27 end
% 5.90/6.27
% 5.90/6.27 subsumption: (92) {G0,W3,D2,L1,V0,M1} I { member( skol8, universal_class )
% 5.90/6.27 }.
% 5.90/6.27 parent0: (34299) {G0,W3,D2,L1,V0,M1} { member( skol8, universal_class )
% 5.90/6.27 }.
% 5.90/6.27 substitution0:
% 5.90/6.27 end
% 5.90/6.27 permutation0:
% 5.90/6.27 0 ==> 0
% 5.90/6.27 end
% 5.90/6.27
% 5.90/6.27 subsumption: (93) {G0,W5,D3,L1,V0,M1} I { unordered_pair( skol9, skol8 )
% 5.90/6.27 ==> null_class }.
% 5.90/6.27 parent0: (34300) {G0,W5,D3,L1,V0,M1} { unordered_pair( skol9, skol8 ) =
% 5.90/6.27 null_class }.
% 5.90/6.27 substitution0:
% 5.90/6.27 end
% 5.90/6.27 permutation0:
% 5.90/6.27 0 ==> 0
% 5.90/6.27 end
% 5.90/6.27
% 5.90/6.27 eqswap: (34428) {G0,W7,D2,L2,V3,M2} { ! Y = X, alpha1( X, Z, Y ) }.
% 5.90/6.27 parent0[0]: (11) {G0,W7,D2,L2,V3,M2} I { ! X = Z, alpha1( X, Y, Z ) }.
% 5.90/6.27 substitution0:
% 5.90/6.27 X := X
% 5.90/6.27 Y := Z
% 5.90/6.27 Z := Y
% 5.90/6.27 end
% 5.90/6.27
% 5.90/6.27 eqrefl: (34429) {G0,W4,D2,L1,V2,M1} { alpha1( X, Y, X ) }.
% 5.90/6.27 parent0[Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------