TSTP Solution File: SET024+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET024+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n018.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 22:45:38 EDT 2022
% Result : Theorem 5.75s 6.12s
% Output : Refutation 5.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SET024+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.10/0.12 % Command : bliksem %s
% 0.13/0.33 % Computer : n018.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % DateTime : Sun Jul 10 09:00:12 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.43/1.08 *** allocated 10000 integers for termspace/termends
% 0.43/1.08 *** allocated 10000 integers for clauses
% 0.43/1.08 *** allocated 10000 integers for justifications
% 0.43/1.08 Bliksem 1.12
% 0.43/1.08
% 0.43/1.08
% 0.43/1.08 Automatic Strategy Selection
% 0.43/1.08
% 0.43/1.08
% 0.43/1.08 Clauses:
% 0.43/1.08
% 0.43/1.08 { ! subclass( X, Y ), ! member( Z, X ), member( Z, Y ) }.
% 0.43/1.08 { ! member( skol1( Z, Y ), Y ), subclass( X, Y ) }.
% 0.43/1.08 { member( skol1( X, Y ), X ), subclass( X, Y ) }.
% 0.43/1.08 { subclass( X, universal_class ) }.
% 0.43/1.08 { ! X = Y, subclass( X, Y ) }.
% 0.43/1.08 { ! X = Y, subclass( Y, X ) }.
% 0.43/1.08 { ! subclass( X, Y ), ! subclass( Y, X ), X = Y }.
% 0.43/1.08 { ! member( X, unordered_pair( Y, Z ) ), member( X, universal_class ) }.
% 0.43/1.08 { ! member( X, unordered_pair( Y, Z ) ), alpha1( X, Y, Z ) }.
% 0.43/1.08 { ! member( X, universal_class ), ! alpha1( X, Y, Z ), member( X,
% 0.43/1.08 unordered_pair( Y, Z ) ) }.
% 0.43/1.08 { ! alpha1( X, Y, Z ), X = Y, X = Z }.
% 0.43/1.08 { ! X = Y, alpha1( X, Y, Z ) }.
% 0.43/1.08 { ! X = Z, alpha1( X, Y, Z ) }.
% 0.43/1.08 { member( unordered_pair( X, Y ), universal_class ) }.
% 0.43/1.08 { singleton( X ) = unordered_pair( X, X ) }.
% 0.43/1.08 { ordered_pair( X, Y ) = unordered_pair( singleton( X ), unordered_pair( X
% 0.43/1.08 , singleton( Y ) ) ) }.
% 0.43/1.08 { ! member( ordered_pair( X, Y ), cross_product( Z, T ) ), member( X, Z ) }
% 0.43/1.08 .
% 0.43/1.08 { ! member( ordered_pair( X, Y ), cross_product( Z, T ) ), member( Y, T ) }
% 0.43/1.08 .
% 0.43/1.08 { ! member( X, Z ), ! member( Y, T ), member( ordered_pair( X, Y ),
% 0.43/1.08 cross_product( Z, T ) ) }.
% 0.43/1.08 { ! member( X, universal_class ), ! member( Y, universal_class ), first(
% 0.43/1.08 ordered_pair( X, Y ) ) = X }.
% 0.43/1.08 { ! member( X, universal_class ), ! member( Y, universal_class ), second(
% 0.43/1.08 ordered_pair( X, Y ) ) = Y }.
% 0.43/1.08 { ! member( X, cross_product( Y, Z ) ), X = ordered_pair( first( X ),
% 0.43/1.08 second( X ) ) }.
% 0.43/1.08 { ! member( ordered_pair( X, Y ), element_relation ), member( Y,
% 0.43/1.08 universal_class ) }.
% 0.43/1.08 { ! member( ordered_pair( X, Y ), element_relation ), member( X, Y ) }.
% 0.43/1.08 { ! member( Y, universal_class ), ! member( X, Y ), member( ordered_pair( X
% 0.43/1.08 , Y ), element_relation ) }.
% 0.43/1.08 { subclass( element_relation, cross_product( universal_class,
% 0.43/1.08 universal_class ) ) }.
% 0.43/1.08 { ! member( Z, intersection( X, Y ) ), member( Z, X ) }.
% 0.43/1.08 { ! member( Z, intersection( X, Y ) ), member( Z, Y ) }.
% 0.43/1.08 { ! member( Z, X ), ! member( Z, Y ), member( Z, intersection( X, Y ) ) }.
% 0.43/1.08 { ! member( Y, complement( X ) ), member( Y, universal_class ) }.
% 0.43/1.08 { ! member( Y, complement( X ) ), ! member( Y, X ) }.
% 0.43/1.08 { ! member( Y, universal_class ), member( Y, X ), member( Y, complement( X
% 0.43/1.08 ) ) }.
% 0.43/1.08 { restrict( Y, X, Z ) = intersection( Y, cross_product( X, Z ) ) }.
% 0.43/1.08 { ! member( X, null_class ) }.
% 0.43/1.08 { ! member( Y, domain_of( X ) ), member( Y, universal_class ) }.
% 0.43/1.08 { ! member( Y, domain_of( X ) ), ! restrict( X, singleton( Y ),
% 0.43/1.08 universal_class ) = null_class }.
% 0.43/1.08 { ! member( Y, universal_class ), restrict( X, singleton( Y ),
% 0.43/1.08 universal_class ) = null_class, member( Y, domain_of( X ) ) }.
% 0.43/1.08 { ! member( ordered_pair( ordered_pair( Y, Z ), T ), rotate( X ) ), member
% 0.43/1.08 ( ordered_pair( ordered_pair( Y, Z ), T ), cross_product( cross_product(
% 0.43/1.08 universal_class, universal_class ), universal_class ) ) }.
% 0.43/1.08 { ! member( ordered_pair( ordered_pair( Y, Z ), T ), rotate( X ) ), member
% 0.43/1.08 ( ordered_pair( ordered_pair( Z, T ), Y ), X ) }.
% 0.43/1.08 { ! member( ordered_pair( ordered_pair( Y, Z ), T ), cross_product(
% 0.43/1.08 cross_product( universal_class, universal_class ), universal_class ) ), !
% 0.43/1.08 member( ordered_pair( ordered_pair( Z, T ), Y ), X ), member(
% 0.43/1.08 ordered_pair( ordered_pair( Y, Z ), T ), rotate( X ) ) }.
% 0.43/1.08 { subclass( rotate( X ), cross_product( cross_product( universal_class,
% 0.43/1.08 universal_class ), universal_class ) ) }.
% 0.43/1.08 { ! member( ordered_pair( ordered_pair( X, Y ), Z ), flip( T ) ), member(
% 0.43/1.08 ordered_pair( ordered_pair( X, Y ), Z ), cross_product( cross_product(
% 0.43/1.08 universal_class, universal_class ), universal_class ) ) }.
% 0.43/1.08 { ! member( ordered_pair( ordered_pair( X, Y ), Z ), flip( T ) ), member(
% 0.43/1.08 ordered_pair( ordered_pair( Y, X ), Z ), T ) }.
% 0.43/1.08 { ! member( ordered_pair( ordered_pair( X, Y ), Z ), cross_product(
% 0.43/1.08 cross_product( universal_class, universal_class ), universal_class ) ), !
% 0.43/1.08 member( ordered_pair( ordered_pair( Y, X ), Z ), T ), member(
% 0.43/1.08 ordered_pair( ordered_pair( X, Y ), Z ), flip( T ) ) }.
% 0.43/1.08 { subclass( flip( X ), cross_product( cross_product( universal_class,
% 0.89/1.29 universal_class ), universal_class ) ) }.
% 0.89/1.29 { ! member( Z, union( X, Y ) ), member( Z, X ), member( Z, Y ) }.
% 0.89/1.29 { ! member( Z, X ), member( Z, union( X, Y ) ) }.
% 0.89/1.29 { ! member( Z, Y ), member( Z, union( X, Y ) ) }.
% 0.89/1.29 { successor( X ) = union( X, singleton( X ) ) }.
% 0.89/1.29 { subclass( successor_relation, cross_product( universal_class,
% 0.89/1.29 universal_class ) ) }.
% 0.89/1.29 { ! member( ordered_pair( X, Y ), successor_relation ), member( X,
% 0.89/1.29 universal_class ) }.
% 0.89/1.29 { ! member( ordered_pair( X, Y ), successor_relation ), alpha2( X, Y ) }.
% 0.89/1.29 { ! member( X, universal_class ), ! alpha2( X, Y ), member( ordered_pair( X
% 0.89/1.29 , Y ), successor_relation ) }.
% 0.89/1.29 { ! alpha2( X, Y ), member( Y, universal_class ) }.
% 0.89/1.29 { ! alpha2( X, Y ), successor( X ) = Y }.
% 0.89/1.29 { ! member( Y, universal_class ), ! successor( X ) = Y, alpha2( X, Y ) }.
% 0.89/1.29 { inverse( X ) = domain_of( flip( cross_product( X, universal_class ) ) ) }
% 0.89/1.29 .
% 0.89/1.29 { range_of( X ) = domain_of( inverse( X ) ) }.
% 0.89/1.29 { image( Y, X ) = range_of( restrict( Y, X, universal_class ) ) }.
% 0.89/1.29 { ! inductive( X ), member( null_class, X ) }.
% 0.89/1.29 { ! inductive( X ), subclass( image( successor_relation, X ), X ) }.
% 0.89/1.29 { ! member( null_class, X ), ! subclass( image( successor_relation, X ), X
% 0.89/1.29 ), inductive( X ) }.
% 0.89/1.29 { member( skol2, universal_class ) }.
% 0.89/1.29 { inductive( skol2 ) }.
% 0.89/1.29 { ! inductive( X ), subclass( skol2, X ) }.
% 0.89/1.29 { ! member( X, sum_class( Y ) ), member( skol3( Z, Y ), Y ) }.
% 0.89/1.29 { ! member( X, sum_class( Y ) ), member( X, skol3( X, Y ) ) }.
% 0.89/1.29 { ! member( X, Z ), ! member( Z, Y ), member( X, sum_class( Y ) ) }.
% 0.89/1.29 { ! member( X, universal_class ), member( sum_class( X ), universal_class )
% 0.89/1.29 }.
% 0.89/1.29 { ! member( X, power_class( Y ) ), member( X, universal_class ) }.
% 0.89/1.29 { ! member( X, power_class( Y ) ), subclass( X, Y ) }.
% 0.89/1.29 { ! member( X, universal_class ), ! subclass( X, Y ), member( X,
% 0.89/1.29 power_class( Y ) ) }.
% 0.89/1.29 { ! member( X, universal_class ), member( power_class( X ), universal_class
% 0.89/1.29 ) }.
% 0.89/1.29 { subclass( compose( Y, X ), cross_product( universal_class,
% 0.89/1.29 universal_class ) ) }.
% 0.89/1.29 { ! member( ordered_pair( Z, T ), compose( Y, X ) ), member( Z,
% 0.89/1.29 universal_class ) }.
% 0.89/1.29 { ! member( ordered_pair( Z, T ), compose( Y, X ) ), member( T, image( Y,
% 0.89/1.29 image( X, singleton( Z ) ) ) ) }.
% 0.89/1.29 { ! member( Z, universal_class ), ! member( T, image( Y, image( X,
% 0.89/1.29 singleton( Z ) ) ) ), member( ordered_pair( Z, T ), compose( Y, X ) ) }.
% 0.89/1.29 { ! member( X, identity_relation ), member( skol4( Y ), universal_class ) }
% 0.89/1.29 .
% 0.89/1.29 { ! member( X, identity_relation ), X = ordered_pair( skol4( X ), skol4( X
% 0.89/1.29 ) ) }.
% 0.89/1.29 { ! member( Y, universal_class ), ! X = ordered_pair( Y, Y ), member( X,
% 0.89/1.29 identity_relation ) }.
% 0.89/1.29 { ! function( X ), subclass( X, cross_product( universal_class,
% 0.89/1.29 universal_class ) ) }.
% 0.89/1.29 { ! function( X ), subclass( compose( X, inverse( X ) ), identity_relation
% 0.89/1.29 ) }.
% 0.89/1.29 { ! subclass( X, cross_product( universal_class, universal_class ) ), !
% 0.89/1.29 subclass( compose( X, inverse( X ) ), identity_relation ), function( X )
% 0.89/1.29 }.
% 0.89/1.29 { ! member( X, universal_class ), ! function( Y ), member( image( Y, X ),
% 0.89/1.29 universal_class ) }.
% 0.89/1.29 { ! disjoint( X, Y ), ! member( Z, X ), ! member( Z, Y ) }.
% 0.89/1.29 { member( skol5( Z, Y ), Y ), disjoint( X, Y ) }.
% 0.89/1.29 { member( skol5( X, Y ), X ), disjoint( X, Y ) }.
% 0.89/1.29 { X = null_class, member( skol6( Y ), universal_class ) }.
% 0.89/1.29 { X = null_class, member( skol6( X ), X ) }.
% 0.89/1.29 { X = null_class, disjoint( skol6( X ), X ) }.
% 0.89/1.29 { apply( X, Y ) = sum_class( image( X, singleton( Y ) ) ) }.
% 0.89/1.29 { function( skol7 ) }.
% 0.89/1.29 { ! member( X, universal_class ), X = null_class, member( apply( skol7, X )
% 0.89/1.29 , X ) }.
% 0.89/1.29 { member( skol8, universal_class ) }.
% 0.89/1.29 { ! member( skol8, singleton( skol8 ) ) }.
% 0.89/1.29
% 0.89/1.29 percentage equality = 0.144330, percentage horn = 0.884211
% 0.89/1.29 This is a problem with some equality
% 0.89/1.29
% 0.89/1.29
% 0.89/1.29
% 0.89/1.29 Options Used:
% 0.89/1.29
% 0.89/1.29 useres = 1
% 0.89/1.29 useparamod = 1
% 0.89/1.29 useeqrefl = 1
% 0.89/1.29 useeqfact = 1
% 0.89/1.29 usefactor = 1
% 0.89/1.29 usesimpsplitting = 0
% 0.89/1.29 usesimpdemod = 5
% 0.89/1.29 usesimpres = 3
% 0.89/1.29
% 0.89/1.29 resimpinuse = 1000
% 0.89/1.29 resimpclauses = 20000
% 0.89/1.29 substype = eqrewr
% 0.89/1.29 backwardsubs = 1
% 0.89/1.29 selectoldest = 5
% 0.89/1.29
% 0.89/1.29 litorderings [0] = split
% 0.89/1.29 litorderings [1] = extend the termordering, first sorting on arguments
% 5.75/6.12
% 5.75/6.12 termordering = kbo
% 5.75/6.12
% 5.75/6.12 litapriori = 0
% 5.75/6.12 termapriori = 1
% 5.75/6.12 litaposteriori = 0
% 5.75/6.12 termaposteriori = 0
% 5.75/6.12 demodaposteriori = 0
% 5.75/6.12 ordereqreflfact = 0
% 5.75/6.12
% 5.75/6.12 litselect = negord
% 5.75/6.12
% 5.75/6.12 maxweight = 15
% 5.75/6.12 maxdepth = 30000
% 5.75/6.12 maxlength = 115
% 5.75/6.12 maxnrvars = 195
% 5.75/6.12 excuselevel = 1
% 5.75/6.12 increasemaxweight = 1
% 5.75/6.12
% 5.75/6.12 maxselected = 10000000
% 5.75/6.12 maxnrclauses = 10000000
% 5.75/6.12
% 5.75/6.12 showgenerated = 0
% 5.75/6.12 showkept = 0
% 5.75/6.12 showselected = 0
% 5.75/6.12 showdeleted = 0
% 5.75/6.12 showresimp = 1
% 5.75/6.12 showstatus = 2000
% 5.75/6.12
% 5.75/6.12 prologoutput = 0
% 5.75/6.12 nrgoals = 5000000
% 5.75/6.12 totalproof = 1
% 5.75/6.12
% 5.75/6.12 Symbols occurring in the translation:
% 5.75/6.12
% 5.75/6.12 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 5.75/6.12 . [1, 2] (w:1, o:44, a:1, s:1, b:0),
% 5.75/6.12 ! [4, 1] (w:0, o:23, a:1, s:1, b:0),
% 5.75/6.12 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 5.75/6.12 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 5.75/6.12 subclass [37, 2] (w:1, o:68, a:1, s:1, b:0),
% 5.75/6.12 member [39, 2] (w:1, o:69, a:1, s:1, b:0),
% 5.75/6.12 universal_class [40, 0] (w:1, o:12, a:1, s:1, b:0),
% 5.75/6.12 unordered_pair [41, 2] (w:1, o:70, a:1, s:1, b:0),
% 5.75/6.12 singleton [42, 1] (w:1, o:30, a:1, s:1, b:0),
% 5.75/6.12 ordered_pair [43, 2] (w:1, o:71, a:1, s:1, b:0),
% 5.75/6.12 cross_product [45, 2] (w:1, o:72, a:1, s:1, b:0),
% 5.75/6.12 first [46, 1] (w:1, o:31, a:1, s:1, b:0),
% 5.75/6.12 second [47, 1] (w:1, o:32, a:1, s:1, b:0),
% 5.75/6.12 element_relation [49, 0] (w:1, o:16, a:1, s:1, b:0),
% 5.75/6.12 intersection [50, 2] (w:1, o:74, a:1, s:1, b:0),
% 5.75/6.12 complement [51, 1] (w:1, o:33, a:1, s:1, b:0),
% 5.75/6.12 restrict [53, 3] (w:1, o:83, a:1, s:1, b:0),
% 5.75/6.12 null_class [54, 0] (w:1, o:17, a:1, s:1, b:0),
% 5.75/6.12 domain_of [55, 1] (w:1, o:34, a:1, s:1, b:0),
% 5.75/6.12 rotate [57, 1] (w:1, o:28, a:1, s:1, b:0),
% 5.75/6.12 flip [58, 1] (w:1, o:35, a:1, s:1, b:0),
% 5.75/6.12 union [59, 2] (w:1, o:75, a:1, s:1, b:0),
% 5.75/6.12 successor [60, 1] (w:1, o:36, a:1, s:1, b:0),
% 5.75/6.12 successor_relation [61, 0] (w:1, o:18, a:1, s:1, b:0),
% 5.75/6.12 inverse [62, 1] (w:1, o:37, a:1, s:1, b:0),
% 5.75/6.12 range_of [63, 1] (w:1, o:29, a:1, s:1, b:0),
% 5.75/6.12 image [64, 2] (w:1, o:73, a:1, s:1, b:0),
% 5.75/6.12 inductive [65, 1] (w:1, o:38, a:1, s:1, b:0),
% 5.75/6.12 sum_class [66, 1] (w:1, o:39, a:1, s:1, b:0),
% 5.75/6.12 power_class [67, 1] (w:1, o:40, a:1, s:1, b:0),
% 5.75/6.12 compose [69, 2] (w:1, o:76, a:1, s:1, b:0),
% 5.75/6.12 identity_relation [70, 0] (w:1, o:19, a:1, s:1, b:0),
% 5.75/6.12 function [72, 1] (w:1, o:41, a:1, s:1, b:0),
% 5.75/6.12 disjoint [73, 2] (w:1, o:77, a:1, s:1, b:0),
% 5.75/6.12 apply [74, 2] (w:1, o:78, a:1, s:1, b:0),
% 5.75/6.12 alpha1 [75, 3] (w:1, o:84, a:1, s:1, b:1),
% 5.75/6.12 alpha2 [76, 2] (w:1, o:79, a:1, s:1, b:1),
% 5.75/6.12 skol1 [77, 2] (w:1, o:80, a:1, s:1, b:1),
% 5.75/6.12 skol2 [78, 0] (w:1, o:20, a:1, s:1, b:1),
% 5.75/6.12 skol3 [79, 2] (w:1, o:81, a:1, s:1, b:1),
% 5.75/6.12 skol4 [80, 1] (w:1, o:42, a:1, s:1, b:1),
% 5.75/6.12 skol5 [81, 2] (w:1, o:82, a:1, s:1, b:1),
% 5.75/6.12 skol6 [82, 1] (w:1, o:43, a:1, s:1, b:1),
% 5.75/6.12 skol7 [83, 0] (w:1, o:21, a:1, s:1, b:1),
% 5.75/6.12 skol8 [84, 0] (w:1, o:22, a:1, s:1, b:1).
% 5.75/6.12
% 5.75/6.12
% 5.75/6.12 Starting Search:
% 5.75/6.12
% 5.75/6.12 *** allocated 15000 integers for clauses
% 5.75/6.12 *** allocated 22500 integers for clauses
% 5.75/6.12 *** allocated 33750 integers for clauses
% 5.75/6.12 *** allocated 15000 integers for termspace/termends
% 5.75/6.12 *** allocated 50625 integers for clauses
% 5.75/6.12 *** allocated 22500 integers for termspace/termends
% 5.75/6.12 Resimplifying inuse:
% 5.75/6.12 Done
% 5.75/6.12
% 5.75/6.12 *** allocated 75937 integers for clauses
% 5.75/6.12 *** allocated 33750 integers for termspace/termends
% 5.75/6.12 *** allocated 113905 integers for clauses
% 5.75/6.12
% 5.75/6.12 Intermediate Status:
% 5.75/6.12 Generated: 5070
% 5.75/6.12 Kept: 2032
% 5.75/6.12 Inuse: 123
% 5.75/6.12 Deleted: 5
% 5.75/6.12 Deletedinuse: 2
% 5.75/6.12
% 5.75/6.12 Resimplifying inuse:
% 5.75/6.12 Done
% 5.75/6.12
% 5.75/6.12 *** allocated 170857 integers for clauses
% 5.75/6.12 *** allocated 50625 integers for termspace/termends
% 5.75/6.12 Resimplifying inuse:
% 5.75/6.12 Done
% 5.75/6.12
% 5.75/6.12 *** allocated 75937 integers for termspace/termends
% 5.75/6.12 *** allocated 256285 integers for clauses
% 5.75/6.12
% 5.75/6.12 Intermediate Status:
% 5.75/6.12 Generated: 9903
% 5.75/6.12 Kept: 4053
% 5.75/6.12 Inuse: 197
% 5.75/6.12 Deleted: 50
% 5.75/6.12 Deletedinuse: 19
% 5.75/6.12
% 5.75/6.12 Resimplifying inuse:
% 5.75/6.12 Done
% 5.75/6.12
% 5.75/6.12 Resimplifying inuse:
% 5.75/6.12 Done
% 5.75/6.12
% 5.75/6.12 *** allocated 113905 integers for termspace/termends
% 5.75/6.12 *** allocated 384427 integers for clauses
% 5.75/6.12
% 5.75/6.12 Intermediate Status:
% 5.75/6.12 Generated: 13665
% 5.75/6.12 Kept: 6075
% 5.75/6.12 Inuse: 252
% 5.75/6.12 Deleted: 62
% 5.75/6.12 Deletedinuse: 22
% 5.75/6.12
% 5.75/6.12 Resimplifying inuse:
% 5.75/6.12 Done
% 5.75/6.12
% 5.75/6.12 Resimplifying inuse:
% 5.75/6.12 Done
% 5.75/6.12
% 5.75/6.12
% 5.75/6.12 Intermediate Status:
% 5.75/6.12 Generated: 17460
% 5.75/6.12 Kept: 8100
% 5.75/6.12 Inuse: 312
% 5.75/6.12 Deleted: 76
% 5.75/6.12 Deletedinuse: 30
% 5.75/6.12
% 5.75/6.12 *** allocated 576640 integers for clauses
% 5.75/6.12 Resimplifying inuse:
% 5.75/6.12 Done
% 5.75/6.12
% 5.75/6.12 *** allocated 170857 integers for termspace/termends
% 5.75/6.12 Resimplifying inuse:
% 5.75/6.12 Done
% 5.75/6.12
% 5.75/6.12
% 5.75/6.12 Intermediate Status:
% 5.75/6.12 Generated: 24200
% 5.75/6.12 Kept: 10119
% 5.75/6.12 Inuse: 358
% 5.75/6.12 Deleted: 85
% 5.75/6.12 Deletedinuse: 34
% 5.75/6.12
% 5.75/6.12 Resimplifying inuse:
% 5.75/6.12 Done
% 5.75/6.12
% 5.75/6.12 *** allocated 864960 integers for clauses
% 5.75/6.12 *** allocated 256285 integers for termspace/termends
% 5.75/6.12
% 5.75/6.12 Intermediate Status:
% 5.75/6.12 Generated: 29560
% 5.75/6.12 Kept: 12908
% 5.75/6.12 Inuse: 365
% 5.75/6.12 Deleted: 87
% 5.75/6.12 Deletedinuse: 36
% 5.75/6.12
% 5.75/6.12 Resimplifying inuse:
% 5.75/6.12 Done
% 5.75/6.12
% 5.75/6.12 Resimplifying inuse:
% 5.75/6.12 Done
% 5.75/6.12
% 5.75/6.12
% 5.75/6.12 Intermediate Status:
% 5.75/6.12 Generated: 34284
% 5.75/6.12 Kept: 14916
% 5.75/6.12 Inuse: 390
% 5.75/6.12 Deleted: 88
% 5.75/6.12 Deletedinuse: 36
% 5.75/6.12
% 5.75/6.12 Resimplifying inuse:
% 5.75/6.12 Done
% 5.75/6.12
% 5.75/6.12 Resimplifying inuse:
% 5.75/6.12 Done
% 5.75/6.12
% 5.75/6.12
% 5.75/6.12 Intermediate Status:
% 5.75/6.12 Generated: 39248
% 5.75/6.12 Kept: 16969
% 5.75/6.12 Inuse: 437
% 5.75/6.12 Deleted: 94
% 5.75/6.12 Deletedinuse: 40
% 5.75/6.12
% 5.75/6.12 Resimplifying inuse:
% 5.75/6.12 Done
% 5.75/6.12
% 5.75/6.12 Resimplifying inuse:
% 5.75/6.12 Done
% 5.75/6.12
% 5.75/6.12
% 5.75/6.12 Intermediate Status:
% 5.75/6.12 Generated: 43441
% 5.75/6.12 Kept: 19040
% 5.75/6.12 Inuse: 482
% 5.75/6.12 Deleted: 94
% 5.75/6.12 Deletedinuse: 40
% 5.75/6.12
% 5.75/6.12 *** allocated 1297440 integers for clauses
% 5.75/6.12 Resimplifying inuse:
% 5.75/6.12 Done
% 5.75/6.12
% 5.75/6.12 *** allocated 384427 integers for termspace/termends
% 5.75/6.12 Resimplifying clauses:
% 5.75/6.12 Done
% 5.75/6.12
% 5.75/6.12 Resimplifying inuse:
% 5.75/6.12 Done
% 5.75/6.12
% 5.75/6.12
% 5.75/6.12 Intermediate Status:
% 5.75/6.12 Generated: 49302
% 5.75/6.12 Kept: 21315
% 5.75/6.12 Inuse: 509
% 5.75/6.12 Deleted: 908
% 5.75/6.12 Deletedinuse: 40
% 5.75/6.12
% 5.75/6.12 Resimplifying inuse:
% 5.75/6.12 Done
% 5.75/6.12
% 5.75/6.12 Resimplifying inuse:
% 5.75/6.12 Done
% 5.75/6.12
% 5.75/6.12
% 5.75/6.12 Intermediate Status:
% 5.75/6.12 Generated: 57096
% 5.75/6.12 Kept: 23327
% 5.75/6.12 Inuse: 544
% 5.75/6.12 Deleted: 908
% 5.75/6.12 Deletedinuse: 40
% 5.75/6.12
% 5.75/6.12 Resimplifying inuse:
% 5.75/6.12 Done
% 5.75/6.12
% 5.75/6.12 Resimplifying inuse:
% 5.75/6.12 Done
% 5.75/6.12
% 5.75/6.12
% 5.75/6.12 Intermediate Status:
% 5.75/6.12 Generated: 65094
% 5.75/6.12 Kept: 25350
% 5.75/6.12 Inuse: 595
% 5.75/6.12 Deleted: 910
% 5.75/6.12 Deletedinuse: 41
% 5.75/6.12
% 5.75/6.12 Resimplifying inuse:
% 5.75/6.12 Done
% 5.75/6.12
% 5.75/6.12 Resimplifying inuse:
% 5.75/6.12 Done
% 5.75/6.12
% 5.75/6.12
% 5.75/6.12 Intermediate Status:
% 5.75/6.12 Generated: 71846
% 5.75/6.12 Kept: 27352
% 5.75/6.12 Inuse: 652
% 5.75/6.12 Deleted: 910
% 5.75/6.12 Deletedinuse: 41
% 5.75/6.12
% 5.75/6.12 Resimplifying inuse:
% 5.75/6.12 Done
% 5.75/6.12
% 5.75/6.12 Resimplifying inuse:
% 5.75/6.12 Done
% 5.75/6.12
% 5.75/6.12 *** allocated 576640 integers for termspace/termends
% 5.75/6.12 *** allocated 1946160 integers for clauses
% 5.75/6.12
% 5.75/6.12 Intermediate Status:
% 5.75/6.12 Generated: 78050
% 5.75/6.12 Kept: 29381
% 5.75/6.12 Inuse: 710
% 5.75/6.12 Deleted: 910
% 5.75/6.12 Deletedinuse: 41
% 5.75/6.12
% 5.75/6.12 Resimplifying inuse:
% 5.75/6.12 Done
% 5.75/6.12
% 5.75/6.12 Resimplifying inuse:
% 5.75/6.12 Done
% 5.75/6.12
% 5.75/6.12
% 5.75/6.12 Intermediate Status:
% 5.75/6.12 Generated: 84622
% 5.75/6.12 Kept: 31428
% 5.75/6.12 Inuse: 775
% 5.75/6.12 Deleted: 939
% 5.75/6.12 Deletedinuse: 57
% 5.75/6.12
% 5.75/6.12 Resimplifying inuse:
% 5.75/6.12 Done
% 5.75/6.12
% 5.75/6.12 Resimplifying inuse:
% 5.75/6.12 Done
% 5.75/6.12
% 5.75/6.12
% 5.75/6.12 Intermediate Status:
% 5.75/6.12 Generated: 90000
% 5.75/6.12 Kept: 33468
% 5.75/6.12 Inuse: 821
% 5.75/6.12 Deleted: 956
% 5.75/6.12 Deletedinuse: 67
% 5.75/6.12
% 5.75/6.12 Resimplifying inuse:
% 5.75/6.12 Done
% 5.75/6.12
% 5.75/6.12
% 5.75/6.12 Bliksems!, er is een bewijs:
% 5.75/6.12 % SZS status Theorem
% 5.75/6.12 % SZS output start Refutation
% 5.75/6.12
% 5.75/6.12 (2) {G0,W8,D3,L2,V2,M2} I { member( skol1( X, Y ), X ), subclass( X, Y )
% 5.75/6.12 }.
% 5.75/6.12 (4) {G0,W6,D2,L2,V2,M2} I { ! X = Y, subclass( X, Y ) }.
% 5.75/6.12 (5) {G0,W9,D2,L3,V2,M3} I { ! subclass( X, Y ), ! subclass( Y, X ), X = Y
% 5.75/6.12 }.
% 5.75/6.12 (7) {G0,W9,D3,L2,V3,M2} I { ! member( X, unordered_pair( Y, Z ) ), alpha1(
% 5.75/6.12 X, Y, Z ) }.
% 5.75/6.12 (8) {G0,W12,D3,L3,V3,M3} I { ! member( X, universal_class ), ! alpha1( X, Y
% 5.75/6.12 , Z ), member( X, unordered_pair( Y, Z ) ) }.
% 5.75/6.12 (9) {G0,W10,D2,L3,V3,M3} I { ! alpha1( X, Y, Z ), X = Y, X = Z }.
% 5.75/6.12 (11) {G0,W7,D2,L2,V3,M2} I { ! X = Z, alpha1( X, Y, Z ) }.
% 5.75/6.12 (13) {G0,W6,D3,L1,V1,M1} I { unordered_pair( X, X ) ==> singleton( X ) }.
% 5.75/6.12 (32) {G0,W3,D2,L1,V1,M1} I { ! member( X, null_class ) }.
% 5.75/6.12 (92) {G0,W3,D2,L1,V0,M1} I { member( skol8, universal_class ) }.
% 5.75/6.12 (93) {G0,W4,D3,L1,V0,M1} I { ! member( skol8, singleton( skol8 ) ) }.
% 5.75/6.12 (95) {G1,W7,D2,L2,V2,M2} F(9) { ! alpha1( X, Y, Y ), X = Y }.
% 5.75/6.12 (99) {G1,W4,D2,L1,V2,M1} Q(11) { alpha1( X, Y, X ) }.
% 5.75/6.12 (126) {G1,W3,D2,L1,V1,M1} R(2,32) { subclass( null_class, X ) }.
% 5.75/6.12 (144) {G1,W6,D2,L2,V2,M2} R(5,4);r(4) { X = Y, ! Y = X }.
% 5.75/6.12 (146) {G2,W6,D2,L2,V1,M2} R(5,126) { ! subclass( X, null_class ),
% 5.75/6.12 null_class = X }.
% 5.75/6.12 (188) {G1,W13,D4,L2,V3,M2} R(7,2) { alpha1( skol1( unordered_pair( X, Y ),
% 5.75/6.12 Z ), X, Y ), subclass( unordered_pair( X, Y ), Z ) }.
% 5.75/6.12 (223) {G2,W11,D3,L3,V3,M3} P(144,2) { member( Z, X ), subclass( X, Y ), ! Z
% 5.75/6.12 = skol1( X, Y ) }.
% 5.75/6.12 (251) {G1,W9,D3,L2,V2,M2} R(8,92) { ! alpha1( skol8, X, Y ), member( skol8
% 5.75/6.12 , unordered_pair( X, Y ) ) }.
% 5.75/6.12 (26740) {G2,W10,D4,L2,V2,M2} R(188,95);d(13);d(13) { subclass( singleton( X
% 5.75/6.12 ), Y ), skol1( singleton( X ), Y ) ==> X }.
% 5.75/6.12 (30601) {G3,W4,D3,L1,V1,M1} R(223,93);d(26740);q { subclass( singleton(
% 5.75/6.12 skol8 ), X ) }.
% 5.75/6.12 (30645) {G4,W4,D3,L1,V0,M1} R(30601,146) { singleton( skol8 ) ==>
% 5.75/6.12 null_class }.
% 5.75/6.12 (31152) {G5,W8,D3,L2,V1,M2} P(95,30645) { singleton( X ) ==> null_class, !
% 5.75/6.12 alpha1( skol8, X, X ) }.
% 5.75/6.12 (34484) {G2,W13,D3,L3,V3,M3} P(95,251) { ! alpha1( X, Y, Z ), member( X,
% 5.75/6.12 unordered_pair( Y, Z ) ), ! alpha1( skol8, X, X ) }.
% 5.75/6.12 (34494) {G6,W3,D2,L1,V0,M1} F(34484);d(13);d(31152);r(99) { member( skol8,
% 5.75/6.12 null_class ) }.
% 5.75/6.12 (34495) {G7,W0,D0,L0,V0,M0} S(34494);r(32) { }.
% 5.75/6.12
% 5.75/6.12
% 5.75/6.12 % SZS output end Refutation
% 5.75/6.12 found a proof!
% 5.75/6.12
% 5.75/6.12
% 5.75/6.12 Unprocessed initial clauses:
% 5.75/6.12
% 5.75/6.12 (34497) {G0,W9,D2,L3,V3,M3} { ! subclass( X, Y ), ! member( Z, X ), member
% 5.75/6.12 ( Z, Y ) }.
% 5.75/6.12 (34498) {G0,W8,D3,L2,V3,M2} { ! member( skol1( Z, Y ), Y ), subclass( X, Y
% 5.75/6.12 ) }.
% 5.75/6.12 (34499) {G0,W8,D3,L2,V2,M2} { member( skol1( X, Y ), X ), subclass( X, Y )
% 5.75/6.12 }.
% 5.75/6.12 (34500) {G0,W3,D2,L1,V1,M1} { subclass( X, universal_class ) }.
% 5.75/6.12 (34501) {G0,W6,D2,L2,V2,M2} { ! X = Y, subclass( X, Y ) }.
% 5.75/6.12 (34502) {G0,W6,D2,L2,V2,M2} { ! X = Y, subclass( Y, X ) }.
% 5.75/6.12 (34503) {G0,W9,D2,L3,V2,M3} { ! subclass( X, Y ), ! subclass( Y, X ), X =
% 5.75/6.12 Y }.
% 5.75/6.12 (34504) {G0,W8,D3,L2,V3,M2} { ! member( X, unordered_pair( Y, Z ) ),
% 5.75/6.12 member( X, universal_class ) }.
% 5.75/6.12 (34505) {G0,W9,D3,L2,V3,M2} { ! member( X, unordered_pair( Y, Z ) ),
% 5.75/6.12 alpha1( X, Y, Z ) }.
% 5.75/6.12 (34506) {G0,W12,D3,L3,V3,M3} { ! member( X, universal_class ), ! alpha1( X
% 5.75/6.12 , Y, Z ), member( X, unordered_pair( Y, Z ) ) }.
% 5.75/6.12 (34507) {G0,W10,D2,L3,V3,M3} { ! alpha1( X, Y, Z ), X = Y, X = Z }.
% 5.75/6.12 (34508) {G0,W7,D2,L2,V3,M2} { ! X = Y, alpha1( X, Y, Z ) }.
% 5.75/6.12 (34509) {G0,W7,D2,L2,V3,M2} { ! X = Z, alpha1( X, Y, Z ) }.
% 5.75/6.12 (34510) {G0,W5,D3,L1,V2,M1} { member( unordered_pair( X, Y ),
% 5.75/6.12 universal_class ) }.
% 5.75/6.12 (34511) {G0,W6,D3,L1,V1,M1} { singleton( X ) = unordered_pair( X, X ) }.
% 5.75/6.12 (34512) {G0,W11,D5,L1,V2,M1} { ordered_pair( X, Y ) = unordered_pair(
% 5.75/6.12 singleton( X ), unordered_pair( X, singleton( Y ) ) ) }.
% 5.75/6.12 (34513) {G0,W10,D3,L2,V4,M2} { ! member( ordered_pair( X, Y ),
% 5.75/6.12 cross_product( Z, T ) ), member( X, Z ) }.
% 5.75/6.12 (34514) {G0,W10,D3,L2,V4,M2} { ! member( ordered_pair( X, Y ),
% 5.75/6.12 cross_product( Z, T ) ), member( Y, T ) }.
% 5.75/6.12 (34515) {G0,W13,D3,L3,V4,M3} { ! member( X, Z ), ! member( Y, T ), member
% 5.75/6.12 ( ordered_pair( X, Y ), cross_product( Z, T ) ) }.
% 5.75/6.12 (34516) {G0,W12,D4,L3,V2,M3} { ! member( X, universal_class ), ! member( Y
% 5.75/6.12 , universal_class ), first( ordered_pair( X, Y ) ) = X }.
% 5.75/6.12 (34517) {G0,W12,D4,L3,V2,M3} { ! member( X, universal_class ), ! member( Y
% 5.75/6.12 , universal_class ), second( ordered_pair( X, Y ) ) = Y }.
% 5.75/6.12 (34518) {G0,W12,D4,L2,V3,M2} { ! member( X, cross_product( Y, Z ) ), X =
% 5.75/6.12 ordered_pair( first( X ), second( X ) ) }.
% 5.75/6.12 (34519) {G0,W8,D3,L2,V2,M2} { ! member( ordered_pair( X, Y ),
% 5.75/6.12 element_relation ), member( Y, universal_class ) }.
% 5.75/6.12 (34520) {G0,W8,D3,L2,V2,M2} { ! member( ordered_pair( X, Y ),
% 5.75/6.12 element_relation ), member( X, Y ) }.
% 5.75/6.12 (34521) {G0,W11,D3,L3,V2,M3} { ! member( Y, universal_class ), ! member( X
% 5.75/6.12 , Y ), member( ordered_pair( X, Y ), element_relation ) }.
% 5.75/6.12 (34522) {G0,W5,D3,L1,V0,M1} { subclass( element_relation, cross_product(
% 5.75/6.12 universal_class, universal_class ) ) }.
% 5.75/6.12 (34523) {G0,W8,D3,L2,V3,M2} { ! member( Z, intersection( X, Y ) ), member
% 5.75/6.12 ( Z, X ) }.
% 5.75/6.12 (34524) {G0,W8,D3,L2,V3,M2} { ! member( Z, intersection( X, Y ) ), member
% 5.75/6.12 ( Z, Y ) }.
% 5.75/6.12 (34525) {G0,W11,D3,L3,V3,M3} { ! member( Z, X ), ! member( Z, Y ), member
% 5.75/6.12 ( Z, intersection( X, Y ) ) }.
% 5.75/6.12 (34526) {G0,W7,D3,L2,V2,M2} { ! member( Y, complement( X ) ), member( Y,
% 5.75/6.12 universal_class ) }.
% 5.75/6.12 (34527) {G0,W7,D3,L2,V2,M2} { ! member( Y, complement( X ) ), ! member( Y
% 5.75/6.12 , X ) }.
% 5.75/6.12 (34528) {G0,W10,D3,L3,V2,M3} { ! member( Y, universal_class ), member( Y,
% 5.75/6.12 X ), member( Y, complement( X ) ) }.
% 5.75/6.12 (34529) {G0,W10,D4,L1,V3,M1} { restrict( Y, X, Z ) = intersection( Y,
% 5.75/6.12 cross_product( X, Z ) ) }.
% 5.75/6.12 (34530) {G0,W3,D2,L1,V1,M1} { ! member( X, null_class ) }.
% 5.75/6.12 (34531) {G0,W7,D3,L2,V2,M2} { ! member( Y, domain_of( X ) ), member( Y,
% 5.75/6.12 universal_class ) }.
% 5.75/6.12 (34532) {G0,W11,D4,L2,V2,M2} { ! member( Y, domain_of( X ) ), ! restrict(
% 5.75/6.12 X, singleton( Y ), universal_class ) = null_class }.
% 5.75/6.12 (34533) {G0,W14,D4,L3,V2,M3} { ! member( Y, universal_class ), restrict( X
% 5.75/6.12 , singleton( Y ), universal_class ) = null_class, member( Y, domain_of( X
% 5.75/6.12 ) ) }.
% 5.75/6.12 (34534) {G0,W19,D4,L2,V4,M2} { ! member( ordered_pair( ordered_pair( Y, Z
% 5.75/6.12 ), T ), rotate( X ) ), member( ordered_pair( ordered_pair( Y, Z ), T ),
% 5.75/6.12 cross_product( cross_product( universal_class, universal_class ),
% 5.75/6.12 universal_class ) ) }.
% 5.75/6.12 (34535) {G0,W15,D4,L2,V4,M2} { ! member( ordered_pair( ordered_pair( Y, Z
% 5.75/6.12 ), T ), rotate( X ) ), member( ordered_pair( ordered_pair( Z, T ), Y ),
% 5.75/6.12 X ) }.
% 5.75/6.12 (34536) {G0,W26,D4,L3,V4,M3} { ! member( ordered_pair( ordered_pair( Y, Z
% 5.75/6.12 ), T ), cross_product( cross_product( universal_class, universal_class )
% 5.75/6.12 , universal_class ) ), ! member( ordered_pair( ordered_pair( Z, T ), Y )
% 5.75/6.12 , X ), member( ordered_pair( ordered_pair( Y, Z ), T ), rotate( X ) ) }.
% 5.75/6.12 (34537) {G0,W8,D4,L1,V1,M1} { subclass( rotate( X ), cross_product(
% 5.75/6.12 cross_product( universal_class, universal_class ), universal_class ) )
% 5.75/6.12 }.
% 5.75/6.12 (34538) {G0,W19,D4,L2,V4,M2} { ! member( ordered_pair( ordered_pair( X, Y
% 5.75/6.12 ), Z ), flip( T ) ), member( ordered_pair( ordered_pair( X, Y ), Z ),
% 5.75/6.12 cross_product( cross_product( universal_class, universal_class ),
% 5.75/6.12 universal_class ) ) }.
% 5.75/6.12 (34539) {G0,W15,D4,L2,V4,M2} { ! member( ordered_pair( ordered_pair( X, Y
% 5.75/6.12 ), Z ), flip( T ) ), member( ordered_pair( ordered_pair( Y, X ), Z ), T
% 5.75/6.12 ) }.
% 5.75/6.12 (34540) {G0,W26,D4,L3,V4,M3} { ! member( ordered_pair( ordered_pair( X, Y
% 5.75/6.12 ), Z ), cross_product( cross_product( universal_class, universal_class )
% 5.75/6.12 , universal_class ) ), ! member( ordered_pair( ordered_pair( Y, X ), Z )
% 5.75/6.12 , T ), member( ordered_pair( ordered_pair( X, Y ), Z ), flip( T ) ) }.
% 5.75/6.12 (34541) {G0,W8,D4,L1,V1,M1} { subclass( flip( X ), cross_product(
% 5.75/6.12 cross_product( universal_class, universal_class ), universal_class ) )
% 5.75/6.12 }.
% 5.75/6.12 (34542) {G0,W11,D3,L3,V3,M3} { ! member( Z, union( X, Y ) ), member( Z, X
% 5.75/6.12 ), member( Z, Y ) }.
% 5.75/6.12 (34543) {G0,W8,D3,L2,V3,M2} { ! member( Z, X ), member( Z, union( X, Y ) )
% 5.75/6.12 }.
% 5.75/6.12 (34544) {G0,W8,D3,L2,V3,M2} { ! member( Z, Y ), member( Z, union( X, Y ) )
% 5.75/6.12 }.
% 5.75/6.12 (34545) {G0,W7,D4,L1,V1,M1} { successor( X ) = union( X, singleton( X ) )
% 5.75/6.12 }.
% 5.75/6.12 (34546) {G0,W5,D3,L1,V0,M1} { subclass( successor_relation, cross_product
% 5.75/6.12 ( universal_class, universal_class ) ) }.
% 5.75/6.12 (34547) {G0,W8,D3,L2,V2,M2} { ! member( ordered_pair( X, Y ),
% 5.75/6.12 successor_relation ), member( X, universal_class ) }.
% 5.75/6.12 (34548) {G0,W8,D3,L2,V2,M2} { ! member( ordered_pair( X, Y ),
% 5.75/6.12 successor_relation ), alpha2( X, Y ) }.
% 5.75/6.12 (34549) {G0,W11,D3,L3,V2,M3} { ! member( X, universal_class ), ! alpha2( X
% 5.75/6.12 , Y ), member( ordered_pair( X, Y ), successor_relation ) }.
% 5.75/6.12 (34550) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), member( Y, universal_class
% 5.75/6.12 ) }.
% 5.75/6.12 (34551) {G0,W7,D3,L2,V2,M2} { ! alpha2( X, Y ), successor( X ) = Y }.
% 5.75/6.12 (34552) {G0,W10,D3,L3,V2,M3} { ! member( Y, universal_class ), ! successor
% 5.75/6.12 ( X ) = Y, alpha2( X, Y ) }.
% 5.75/6.12 (34553) {G0,W8,D5,L1,V1,M1} { inverse( X ) = domain_of( flip(
% 5.75/6.12 cross_product( X, universal_class ) ) ) }.
% 5.75/6.12 (34554) {G0,W6,D4,L1,V1,M1} { range_of( X ) = domain_of( inverse( X ) )
% 5.75/6.12 }.
% 5.75/6.12 (34555) {G0,W9,D4,L1,V2,M1} { image( Y, X ) = range_of( restrict( Y, X,
% 5.75/6.12 universal_class ) ) }.
% 5.75/6.12 (34556) {G0,W5,D2,L2,V1,M2} { ! inductive( X ), member( null_class, X )
% 5.75/6.12 }.
% 5.75/6.12 (34557) {G0,W7,D3,L2,V1,M2} { ! inductive( X ), subclass( image(
% 5.75/6.12 successor_relation, X ), X ) }.
% 5.75/6.12 (34558) {G0,W10,D3,L3,V1,M3} { ! member( null_class, X ), ! subclass(
% 5.75/6.12 image( successor_relation, X ), X ), inductive( X ) }.
% 5.75/6.12 (34559) {G0,W3,D2,L1,V0,M1} { member( skol2, universal_class ) }.
% 5.75/6.12 (34560) {G0,W2,D2,L1,V0,M1} { inductive( skol2 ) }.
% 5.75/6.12 (34561) {G0,W5,D2,L2,V1,M2} { ! inductive( X ), subclass( skol2, X ) }.
% 5.75/6.12 (34562) {G0,W9,D3,L2,V3,M2} { ! member( X, sum_class( Y ) ), member( skol3
% 5.75/6.12 ( Z, Y ), Y ) }.
% 5.75/6.12 (34563) {G0,W9,D3,L2,V2,M2} { ! member( X, sum_class( Y ) ), member( X,
% 5.75/6.12 skol3( X, Y ) ) }.
% 5.75/6.12 (34564) {G0,W10,D3,L3,V3,M3} { ! member( X, Z ), ! member( Z, Y ), member
% 5.75/6.12 ( X, sum_class( Y ) ) }.
% 5.75/6.12 (34565) {G0,W7,D3,L2,V1,M2} { ! member( X, universal_class ), member(
% 5.75/6.12 sum_class( X ), universal_class ) }.
% 5.75/6.12 (34566) {G0,W7,D3,L2,V2,M2} { ! member( X, power_class( Y ) ), member( X,
% 5.75/6.12 universal_class ) }.
% 5.75/6.12 (34567) {G0,W7,D3,L2,V2,M2} { ! member( X, power_class( Y ) ), subclass( X
% 5.75/6.12 , Y ) }.
% 5.75/6.12 (34568) {G0,W10,D3,L3,V2,M3} { ! member( X, universal_class ), ! subclass
% 5.75/6.12 ( X, Y ), member( X, power_class( Y ) ) }.
% 5.75/6.12 (34569) {G0,W7,D3,L2,V1,M2} { ! member( X, universal_class ), member(
% 5.75/6.12 power_class( X ), universal_class ) }.
% 5.75/6.12 (34570) {G0,W7,D3,L1,V2,M1} { subclass( compose( Y, X ), cross_product(
% 5.75/6.12 universal_class, universal_class ) ) }.
% 5.75/6.12 (34571) {G0,W10,D3,L2,V4,M2} { ! member( ordered_pair( Z, T ), compose( Y
% 5.75/6.12 , X ) ), member( Z, universal_class ) }.
% 5.75/6.12 (34572) {G0,W15,D5,L2,V4,M2} { ! member( ordered_pair( Z, T ), compose( Y
% 5.75/6.12 , X ) ), member( T, image( Y, image( X, singleton( Z ) ) ) ) }.
% 5.75/6.12 (34573) {G0,W18,D5,L3,V4,M3} { ! member( Z, universal_class ), ! member( T
% 5.75/6.12 , image( Y, image( X, singleton( Z ) ) ) ), member( ordered_pair( Z, T )
% 5.75/6.12 , compose( Y, X ) ) }.
% 5.75/6.12 (34574) {G0,W7,D3,L2,V2,M2} { ! member( X, identity_relation ), member(
% 5.75/6.12 skol4( Y ), universal_class ) }.
% 5.75/6.12 (34575) {G0,W10,D4,L2,V1,M2} { ! member( X, identity_relation ), X =
% 5.75/6.12 ordered_pair( skol4( X ), skol4( X ) ) }.
% 5.75/6.12 (34576) {G0,W11,D3,L3,V2,M3} { ! member( Y, universal_class ), ! X =
% 5.75/6.12 ordered_pair( Y, Y ), member( X, identity_relation ) }.
% 5.75/6.12 (34577) {G0,W7,D3,L2,V1,M2} { ! function( X ), subclass( X, cross_product
% 5.75/6.12 ( universal_class, universal_class ) ) }.
% 5.75/6.12 (34578) {G0,W8,D4,L2,V1,M2} { ! function( X ), subclass( compose( X,
% 5.75/6.12 inverse( X ) ), identity_relation ) }.
% 5.75/6.12 (34579) {G0,W13,D4,L3,V1,M3} { ! subclass( X, cross_product(
% 5.75/6.12 universal_class, universal_class ) ), ! subclass( compose( X, inverse( X
% 5.75/6.12 ) ), identity_relation ), function( X ) }.
% 5.75/6.12 (34580) {G0,W10,D3,L3,V2,M3} { ! member( X, universal_class ), ! function
% 5.75/6.12 ( Y ), member( image( Y, X ), universal_class ) }.
% 5.75/6.12 (34581) {G0,W9,D2,L3,V3,M3} { ! disjoint( X, Y ), ! member( Z, X ), !
% 5.75/6.12 member( Z, Y ) }.
% 5.75/6.12 (34582) {G0,W8,D3,L2,V3,M2} { member( skol5( Z, Y ), Y ), disjoint( X, Y )
% 5.75/6.12 }.
% 5.75/6.12 (34583) {G0,W8,D3,L2,V2,M2} { member( skol5( X, Y ), X ), disjoint( X, Y )
% 5.75/6.12 }.
% 5.75/6.12 (34584) {G0,W7,D3,L2,V2,M2} { X = null_class, member( skol6( Y ),
% 5.75/6.12 universal_class ) }.
% 5.75/6.12 (34585) {G0,W7,D3,L2,V1,M2} { X = null_class, member( skol6( X ), X ) }.
% 5.75/6.12 (34586) {G0,W7,D3,L2,V1,M2} { X = null_class, disjoint( skol6( X ), X )
% 5.75/6.12 }.
% 5.75/6.12 (34587) {G0,W9,D5,L1,V2,M1} { apply( X, Y ) = sum_class( image( X,
% 5.75/6.12 singleton( Y ) ) ) }.
% 5.75/6.12 (34588) {G0,W2,D2,L1,V0,M1} { function( skol7 ) }.
% 5.75/6.12 (34589) {G0,W11,D3,L3,V1,M3} { ! member( X, universal_class ), X =
% 5.75/6.12 null_class, member( apply( skol7, X ), X ) }.
% 5.75/6.12 (34590) {G0,W3,D2,L1,V0,M1} { member( skol8, universal_class ) }.
% 5.75/6.12 (34591) {G0,W4,D3,L1,V0,M1} { ! member( skol8, singleton( skol8 ) ) }.
% 5.75/6.12
% 5.75/6.12
% 5.75/6.12 Total Proof:
% 5.75/6.12
% 5.75/6.12 subsumption: (2) {G0,W8,D3,L2,V2,M2} I { member( skol1( X, Y ), X ),
% 5.75/6.12 subclass( X, Y ) }.
% 5.75/6.12 parent0: (34499) {G0,W8,D3,L2,V2,M2} { member( skol1( X, Y ), X ),
% 5.75/6.12 subclass( X, Y ) }.
% 5.75/6.12 substitution0:
% 5.75/6.12 X := X
% 5.75/6.12 Y := Y
% 5.75/6.12 end
% 5.75/6.12 permutation0:
% 5.75/6.12 0 ==> 0
% 5.75/6.12 1 ==> 1
% 5.75/6.12 end
% 5.75/6.12
% 5.75/6.12 subsumption: (4) {G0,W6,D2,L2,V2,M2} I { ! X = Y, subclass( X, Y ) }.
% 5.75/6.12 parent0: (34501) {G0,W6,D2,L2,V2,M2} { ! X = Y, subclass( X, Y ) }.
% 5.75/6.12 substitution0:
% 5.75/6.12 X := X
% 5.75/6.12 Y := Y
% 5.75/6.12 end
% 5.75/6.12 permutation0:
% 5.75/6.12 0 ==> 0
% 5.75/6.12 1 ==> 1
% 5.75/6.12 end
% 5.75/6.12
% 5.75/6.12 subsumption: (5) {G0,W9,D2,L3,V2,M3} I { ! subclass( X, Y ), ! subclass( Y
% 5.75/6.12 , X ), X = Y }.
% 5.75/6.12 parent0: (34503) {G0,W9,D2,L3,V2,M3} { ! subclass( X, Y ), ! subclass( Y,
% 5.75/6.12 X ), X = Y }.
% 5.75/6.12 substitution0:
% 5.75/6.12 X := X
% 5.75/6.12 Y := Y
% 5.75/6.12 end
% 5.75/6.12 permutation0:
% 5.75/6.12 0 ==> 0
% 5.75/6.12 1 ==> 1
% 5.75/6.12 2 ==> 2
% 5.75/6.12 end
% 5.75/6.12
% 5.75/6.12 subsumption: (7) {G0,W9,D3,L2,V3,M2} I { ! member( X, unordered_pair( Y, Z
% 5.75/6.12 ) ), alpha1( X, Y, Z ) }.
% 5.75/6.12 parent0: (34505) {G0,W9,D3,L2,V3,M2} { ! member( X, unordered_pair( Y, Z )
% 5.75/6.12 ), alpha1( X, Y, Z ) }.
% 5.75/6.12 substitution0:
% 5.75/6.12 X := X
% 5.75/6.12 Y := Y
% 5.75/6.12 Z := Z
% 5.75/6.12 end
% 5.75/6.12 permutation0:
% 5.75/6.12 0 ==> 0
% 5.75/6.12 1 ==> 1
% 5.75/6.12 end
% 5.75/6.12
% 5.75/6.12 subsumption: (8) {G0,W12,D3,L3,V3,M3} I { ! member( X, universal_class ), !
% 5.75/6.12 alpha1( X, Y, Z ), member( X, unordered_pair( Y, Z ) ) }.
% 5.75/6.12 parent0: (34506) {G0,W12,D3,L3,V3,M3} { ! member( X, universal_class ), !
% 5.75/6.12 alpha1( X, Y, Z ), member( X, unordered_pair( Y, Z ) ) }.
% 5.75/6.12 substitution0:
% 5.75/6.12 X := X
% 5.75/6.12 Y := Y
% 5.75/6.12 Z := Z
% 5.75/6.12 end
% 5.75/6.12 permutation0:
% 5.75/6.12 0 ==> 0
% 5.75/6.12 1 ==> 1
% 5.75/6.12 2 ==> 2
% 5.75/6.12 end
% 5.75/6.12
% 5.75/6.12 subsumption: (9) {G0,W10,D2,L3,V3,M3} I { ! alpha1( X, Y, Z ), X = Y, X = Z
% 5.75/6.12 }.
% 5.75/6.12 parent0: (34507) {G0,W10,D2,L3,V3,M3} { ! alpha1( X, Y, Z ), X = Y, X = Z
% 5.75/6.12 }.
% 5.75/6.12 substitution0:
% 5.75/6.12 X := X
% 5.75/6.12 Y := Y
% 5.75/6.12 Z := Z
% 5.75/6.12 end
% 5.75/6.12 permutation0:
% 5.75/6.12 0 ==> 0
% 5.75/6.12 1 ==> 1
% 5.75/6.12 2 ==> 2
% 5.75/6.12 end
% 5.75/6.12
% 5.75/6.12 subsumption: (11) {G0,W7,D2,L2,V3,M2} I { ! X = Z, alpha1( X, Y, Z ) }.
% 5.75/6.12 parent0: (34509) {G0,W7,D2,L2,V3,M2} { ! X = Z, alpha1( X, Y, Z ) }.
% 5.75/6.12 substitution0:
% 5.75/6.12 X := X
% 5.75/6.12 Y := Y
% 5.75/6.12 Z := Z
% 5.75/6.12 end
% 5.75/6.12 permutation0:
% 5.75/6.12 0 ==> 0
% 5.75/6.12 1 ==> 1
% 5.75/6.12 end
% 5.75/6.12
% 5.75/6.12 eqswap: (34630) {G0,W6,D3,L1,V1,M1} { unordered_pair( X, X ) = singleton(
% 5.75/6.12 X ) }.
% 5.75/6.12 parent0[0]: (34511) {G0,W6,D3,L1,V1,M1} { singleton( X ) = unordered_pair
% 5.75/6.12 ( X, X ) }.
% 5.75/6.12 substitution0:
% 5.75/6.12 X := X
% 5.75/6.12 end
% 5.75/6.12
% 5.75/6.12 subsumption: (13) {G0,W6,D3,L1,V1,M1} I { unordered_pair( X, X ) ==>
% 5.75/6.12 singleton( X ) }.
% 5.75/6.12 parent0: (34630) {G0,W6,D3,L1,V1,M1} { unordered_pair( X, X ) = singleton
% 5.75/6.12 ( X ) }.
% 5.75/6.12 substitution0:
% 5.75/6.12 X := X
% 5.75/6.12 end
% 5.75/6.12 permutation0:
% 5.75/6.12 0 ==> 0
% 5.75/6.12 end
% 5.75/6.12
% 5.75/6.12 subsumption: (32) {G0,W3,D2,L1,V1,M1} I { ! member( X, null_class ) }.
% 5.75/6.12 parent0: (34530) {G0,W3,D2,L1,V1,M1} { ! member( X, null_class ) }.
% 5.75/6.12 substitution0:
% 5.75/6.12 X := X
% 5.75/6.12 end
% 5.75/6.12 permutation0:
% 5.75/6.12 0 ==> 0
% 5.75/6.12 end
% 5.75/6.12
% 5.75/6.12 subsumption: (92) {G0,W3,D2,L1,V0,M1} I { member( skol8, universal_class )
% 5.75/6.12 }.
% 5.75/6.12 parent0: (34590) {G0,W3,D2,L1,V0,M1} { member( skol8, universal_class )
% 5.75/6.12 }.
% 5.75/6.12 substitution0:
% 5.75/6.12 end
% 5.75/6.12 permutation0:
% 5.75/6.12 0 ==> 0
% 5.75/6.12 end
% 5.75/6.12
% 5.75/6.12 subsumption: (93) {G0,W4,D3,L1,V0,M1} I { ! member( skol8, singleton( skol8
% 5.75/6.12 ) ) }.
% 5.75/6.12 parent0: (34591) {G0,W4,D3,L1,V0,M1} { ! member( skol8, singleton( skol8 )
% 5.75/6.12 ) }.
% 5.75/6.12 substitution0:
% 5.75/6.12 end
% 5.75/6.12 permutation0:
% 5.75/6.12 0 ==> 0
% 5.75/6.12 end
% 5.75/6.12
% 5.75/6.12 factor: (34743) {G0,W7,D2,L2,V2,M2} { ! alpha1( X, Y, Y ), X = Y }.
% 5.75/6.12 parent0[1, 2]: (9) {G0,W10,D2,L3,V3,M3} I { ! alpha1( X, Y, Z ), X = Y, X =
% 5.75/6.12 Z }.
% 5.75/6.12 substitution0:
% 5.75/6.12 X := X
% 5.75/6.12 Y := Y
% 5.75/6.12 Z := Y
% 5.75/6.12 end
% 5.75/6.12
% 5.75/6.12 subsumption: (95) {G1,W7,D2,L2,V2,M2} F(9) { ! alpha1( X, Y, Y ), X = Y }.
% 5.75/6.12 parent0: (34743) {G0,W7,D2,L2,V2,M2} { ! alpha1( X, Y, Y ), X = Y }.
% 5.75/6.12 substitution0:
% 5.75/6.12 X := X
% 5.75/6.12 Y := Y
% 5.75/6.12 end
% 5.75/6.12 permutation0:
% 5.75/6.12 0 ==> 0
% 5.75/6.12 1 ==> 1
% 5.75/6.12 end
% 5.75/6.12
% 5.75/6.12 eqswap: (34745) {G0,W7,D2,L2,V3,M2} { ! Y = X, alpha1( X, Z, Y ) }.
% 5.75/6.12 parent0[0]: (11) {G0,W7,D2,L2,V3,M2} I { ! X = Z, alpha1( X, Y, Z ) }.
% 5.75/6.12 substitution0:
% 5.75/6.12 X := X
% 5.75/6.12 Y := Z
% 5.75/6.12 Z := Y
% 5.75/6.12 end
% 5.75/6.12
% 5.75/6.12 eqrefl: (34746) {G0,W4,D2,L1,V2,M1} { alpha1( X, Y, X ) }.
% 5.75/6.12 parent0[0]: (34745) {G0,W7,D2,L2,V3,M2} { ! Y = X, alpha1( X, Z, Y ) }.
% 5.75/6.12 substitution0:
% 5.75/6.12 X := X
% 5.75/6.12 Y := X
% 5.75/6.12 Z := Y
% 5.75/6.12 end
% 5.75/6.12
% 5.75/6.12 subsumption: (99) {G1,W4,D2,L1,V2,M1} Q(11) { alpha1( X, Y, X ) }.
% 5.75/6.12 parent0: (34746) {G0,W4,D2,L1,V2,M1} { alpha1( X, Y, X ) }.
% 5.75/6.12 substitution0:
% 5.75/6.12 X := X
% 5.75/6.12 Y := Y
% 5.75/6.12 end
% 5.75/6.12 permutation0:
% 5.75/6.12 0 ==> 0
% 5.75/6.12 end
% 5.75/6.12
% 5.75/6.12 resolution: (34747) {G1,W3,D2,L1,V1,M1} { subclass( null_class, X ) }.
% 5.75/6.12 parent0[0]: (32) {G0,W3,D2,L1,V1,M1} I { ! member( X, null_class ) }.
% 5.75/6.12 parent1[0]: (2) {G0,W8,D3,L2,V2,M2} I { member( skol1( X, Y ), X ),
% 5.75/6.12 subclass( X, Y ) }.
% 5.75/6.12 substitution0:
% 5.75/6.12 X := skol1( null_class, X )
% 5.75/6.12 end
% 5.75/6.12 substitution1:
% 5.75/6.12 X := null_class
% 5.75/6.12 Y := X
% 5.75/6.12 end
% 5.75/6.12
% 5.75/6.12 subsumption: (126) {G1,W3,D2,L1,V1,M1} R(2,32) { subclass( null_class, X )
% 5.75/6.12 }.
% 5.75/6.12 parent0: (34747) {G1,W3,D2,L1,V1,M1} { subclass( null_class, X ) }.
% 5.75/6.12 substitution0:
% 5.75/6.12 X := X
% 5.75/6.12 end
% 5.75/6.12 permutation0:
% 5.75/6.12 0 ==> 0
% 5.75/6.12 end
% 5.75/6.12
% 5.75/6.12 eqswap: (34748) {G0,W6,D2,L2,V2,M2} { ! Y = X, subclass( X, Y ) }.
% 5.75/6.12 parent0[0]: (4) {G0,W6,D2,L2,V2,M2} I { ! X = Y, subclass( X, Y ) }.
% 5.75/6.12 substitution0:
% 5.75/6.12 X := X
% 5.75/6.12 Y := Y
% 5.75/6.12 end
% 5.75/6.12
% 5.75/6.12 eqswap: (34749) {G0,W6,D2,L2,V2,M2} { ! Y = X, subclass( X, Y ) }.
% 5.75/6.12 parent0[0]: (4) {G0,W6,D2,L2,V2,M2} I { ! X = Y, subclass( X, Y ) }.
% 5.75/6.12 substitution0:
% 5.75/6.12 X := X
% 5.75/6.12 Y := Y
% 5.75/6.12 end
% 5.75/6.12
% 5.75/6.12 resolution: (34750) {G1,W9,D2,L3,V2,M3} { ! subclass( Y, X ), X = Y, ! Y =
% 5.75/6.12 X }.
% 5.75/6.12 parent0[0]: (5) {G0,W9Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------