TSTP Solution File: SET083+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET083+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n004.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 22:46:45 EDT 2022
% Result : Theorem 7.44s 7.87s
% Output : Refutation 7.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET083+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.12/0.14 % Command : bliksem %s
% 0.13/0.35 % Computer : n004.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % DateTime : Sat Jul 9 19:45:07 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.71/1.12 *** allocated 10000 integers for termspace/termends
% 0.71/1.12 *** allocated 10000 integers for clauses
% 0.71/1.12 *** allocated 10000 integers for justifications
% 0.71/1.12 Bliksem 1.12
% 0.71/1.12
% 0.71/1.12
% 0.71/1.12 Automatic Strategy Selection
% 0.71/1.12
% 0.71/1.12
% 0.71/1.12 Clauses:
% 0.71/1.12
% 0.71/1.12 { ! subclass( X, Y ), ! member( Z, X ), member( Z, Y ) }.
% 0.71/1.12 { ! member( skol1( Z, Y ), Y ), subclass( X, Y ) }.
% 0.71/1.12 { member( skol1( X, Y ), X ), subclass( X, Y ) }.
% 0.71/1.12 { subclass( X, universal_class ) }.
% 0.71/1.12 { ! X = Y, subclass( X, Y ) }.
% 0.71/1.12 { ! X = Y, subclass( Y, X ) }.
% 0.71/1.12 { ! subclass( X, Y ), ! subclass( Y, X ), X = Y }.
% 0.71/1.12 { ! member( X, unordered_pair( Y, Z ) ), member( X, universal_class ) }.
% 0.71/1.12 { ! member( X, unordered_pair( Y, Z ) ), alpha1( X, Y, Z ) }.
% 0.71/1.12 { ! member( X, universal_class ), ! alpha1( X, Y, Z ), member( X,
% 0.71/1.12 unordered_pair( Y, Z ) ) }.
% 0.71/1.12 { ! alpha1( X, Y, Z ), X = Y, X = Z }.
% 0.71/1.12 { ! X = Y, alpha1( X, Y, Z ) }.
% 0.71/1.12 { ! X = Z, alpha1( X, Y, Z ) }.
% 0.71/1.12 { member( unordered_pair( X, Y ), universal_class ) }.
% 0.71/1.12 { singleton( X ) = unordered_pair( X, X ) }.
% 0.71/1.12 { ordered_pair( X, Y ) = unordered_pair( singleton( X ), unordered_pair( X
% 0.71/1.12 , singleton( Y ) ) ) }.
% 0.71/1.12 { ! member( ordered_pair( X, Y ), cross_product( Z, T ) ), member( X, Z ) }
% 0.71/1.12 .
% 0.71/1.12 { ! member( ordered_pair( X, Y ), cross_product( Z, T ) ), member( Y, T ) }
% 0.71/1.12 .
% 0.71/1.12 { ! member( X, Z ), ! member( Y, T ), member( ordered_pair( X, Y ),
% 0.71/1.12 cross_product( Z, T ) ) }.
% 0.71/1.12 { ! member( X, universal_class ), ! member( Y, universal_class ), first(
% 0.71/1.12 ordered_pair( X, Y ) ) = X }.
% 0.71/1.12 { ! member( X, universal_class ), ! member( Y, universal_class ), second(
% 0.71/1.12 ordered_pair( X, Y ) ) = Y }.
% 0.71/1.12 { ! member( X, cross_product( Y, Z ) ), X = ordered_pair( first( X ),
% 0.71/1.12 second( X ) ) }.
% 0.71/1.12 { ! member( ordered_pair( X, Y ), element_relation ), member( Y,
% 0.71/1.12 universal_class ) }.
% 0.71/1.12 { ! member( ordered_pair( X, Y ), element_relation ), member( X, Y ) }.
% 0.71/1.12 { ! member( Y, universal_class ), ! member( X, Y ), member( ordered_pair( X
% 0.71/1.12 , Y ), element_relation ) }.
% 0.71/1.12 { subclass( element_relation, cross_product( universal_class,
% 0.71/1.12 universal_class ) ) }.
% 0.71/1.12 { ! member( Z, intersection( X, Y ) ), member( Z, X ) }.
% 0.71/1.12 { ! member( Z, intersection( X, Y ) ), member( Z, Y ) }.
% 0.71/1.12 { ! member( Z, X ), ! member( Z, Y ), member( Z, intersection( X, Y ) ) }.
% 0.71/1.12 { ! member( Y, complement( X ) ), member( Y, universal_class ) }.
% 0.71/1.12 { ! member( Y, complement( X ) ), ! member( Y, X ) }.
% 0.71/1.12 { ! member( Y, universal_class ), member( Y, X ), member( Y, complement( X
% 0.71/1.12 ) ) }.
% 0.71/1.12 { restrict( Y, X, Z ) = intersection( Y, cross_product( X, Z ) ) }.
% 0.71/1.12 { ! member( X, null_class ) }.
% 0.71/1.12 { ! member( Y, domain_of( X ) ), member( Y, universal_class ) }.
% 0.71/1.12 { ! member( Y, domain_of( X ) ), ! restrict( X, singleton( Y ),
% 0.71/1.12 universal_class ) = null_class }.
% 0.71/1.12 { ! member( Y, universal_class ), restrict( X, singleton( Y ),
% 0.71/1.12 universal_class ) = null_class, member( Y, domain_of( X ) ) }.
% 0.71/1.12 { ! member( ordered_pair( ordered_pair( Y, Z ), T ), rotate( X ) ), member
% 0.71/1.12 ( ordered_pair( ordered_pair( Y, Z ), T ), cross_product( cross_product(
% 0.71/1.12 universal_class, universal_class ), universal_class ) ) }.
% 0.71/1.12 { ! member( ordered_pair( ordered_pair( Y, Z ), T ), rotate( X ) ), member
% 0.71/1.12 ( ordered_pair( ordered_pair( Z, T ), Y ), X ) }.
% 0.71/1.12 { ! member( ordered_pair( ordered_pair( Y, Z ), T ), cross_product(
% 0.71/1.12 cross_product( universal_class, universal_class ), universal_class ) ), !
% 0.71/1.12 member( ordered_pair( ordered_pair( Z, T ), Y ), X ), member(
% 0.71/1.12 ordered_pair( ordered_pair( Y, Z ), T ), rotate( X ) ) }.
% 0.71/1.12 { subclass( rotate( X ), cross_product( cross_product( universal_class,
% 0.71/1.12 universal_class ), universal_class ) ) }.
% 0.71/1.12 { ! member( ordered_pair( ordered_pair( X, Y ), Z ), flip( T ) ), member(
% 0.71/1.12 ordered_pair( ordered_pair( X, Y ), Z ), cross_product( cross_product(
% 0.71/1.12 universal_class, universal_class ), universal_class ) ) }.
% 0.71/1.12 { ! member( ordered_pair( ordered_pair( X, Y ), Z ), flip( T ) ), member(
% 0.71/1.12 ordered_pair( ordered_pair( Y, X ), Z ), T ) }.
% 0.71/1.12 { ! member( ordered_pair( ordered_pair( X, Y ), Z ), cross_product(
% 0.71/1.12 cross_product( universal_class, universal_class ), universal_class ) ), !
% 0.71/1.12 member( ordered_pair( ordered_pair( Y, X ), Z ), T ), member(
% 0.71/1.12 ordered_pair( ordered_pair( X, Y ), Z ), flip( T ) ) }.
% 0.71/1.12 { subclass( flip( X ), cross_product( cross_product( universal_class,
% 0.76/1.32 universal_class ), universal_class ) ) }.
% 0.76/1.32 { ! member( Z, union( X, Y ) ), member( Z, X ), member( Z, Y ) }.
% 0.76/1.32 { ! member( Z, X ), member( Z, union( X, Y ) ) }.
% 0.76/1.32 { ! member( Z, Y ), member( Z, union( X, Y ) ) }.
% 0.76/1.32 { successor( X ) = union( X, singleton( X ) ) }.
% 0.76/1.32 { subclass( successor_relation, cross_product( universal_class,
% 0.76/1.32 universal_class ) ) }.
% 0.76/1.32 { ! member( ordered_pair( X, Y ), successor_relation ), member( X,
% 0.76/1.32 universal_class ) }.
% 0.76/1.32 { ! member( ordered_pair( X, Y ), successor_relation ), alpha2( X, Y ) }.
% 0.76/1.32 { ! member( X, universal_class ), ! alpha2( X, Y ), member( ordered_pair( X
% 0.76/1.32 , Y ), successor_relation ) }.
% 0.76/1.32 { ! alpha2( X, Y ), member( Y, universal_class ) }.
% 0.76/1.32 { ! alpha2( X, Y ), successor( X ) = Y }.
% 0.76/1.32 { ! member( Y, universal_class ), ! successor( X ) = Y, alpha2( X, Y ) }.
% 0.76/1.32 { inverse( X ) = domain_of( flip( cross_product( X, universal_class ) ) ) }
% 0.76/1.32 .
% 0.76/1.32 { range_of( X ) = domain_of( inverse( X ) ) }.
% 0.76/1.32 { image( Y, X ) = range_of( restrict( Y, X, universal_class ) ) }.
% 0.76/1.32 { ! inductive( X ), member( null_class, X ) }.
% 0.76/1.32 { ! inductive( X ), subclass( image( successor_relation, X ), X ) }.
% 0.76/1.32 { ! member( null_class, X ), ! subclass( image( successor_relation, X ), X
% 0.76/1.32 ), inductive( X ) }.
% 0.76/1.32 { member( skol2, universal_class ) }.
% 0.76/1.32 { inductive( skol2 ) }.
% 0.76/1.32 { ! inductive( X ), subclass( skol2, X ) }.
% 0.76/1.32 { ! member( X, sum_class( Y ) ), member( skol3( Z, Y ), Y ) }.
% 0.76/1.32 { ! member( X, sum_class( Y ) ), member( X, skol3( X, Y ) ) }.
% 0.76/1.32 { ! member( X, Z ), ! member( Z, Y ), member( X, sum_class( Y ) ) }.
% 0.76/1.32 { ! member( X, universal_class ), member( sum_class( X ), universal_class )
% 0.76/1.32 }.
% 0.76/1.32 { ! member( X, power_class( Y ) ), member( X, universal_class ) }.
% 0.76/1.32 { ! member( X, power_class( Y ) ), subclass( X, Y ) }.
% 0.76/1.32 { ! member( X, universal_class ), ! subclass( X, Y ), member( X,
% 0.76/1.32 power_class( Y ) ) }.
% 0.76/1.32 { ! member( X, universal_class ), member( power_class( X ), universal_class
% 0.76/1.32 ) }.
% 0.76/1.32 { subclass( compose( Y, X ), cross_product( universal_class,
% 0.76/1.32 universal_class ) ) }.
% 0.76/1.32 { ! member( ordered_pair( Z, T ), compose( Y, X ) ), member( Z,
% 0.76/1.32 universal_class ) }.
% 0.76/1.32 { ! member( ordered_pair( Z, T ), compose( Y, X ) ), member( T, image( Y,
% 0.76/1.32 image( X, singleton( Z ) ) ) ) }.
% 0.76/1.32 { ! member( Z, universal_class ), ! member( T, image( Y, image( X,
% 0.76/1.32 singleton( Z ) ) ) ), member( ordered_pair( Z, T ), compose( Y, X ) ) }.
% 0.76/1.32 { ! member( X, identity_relation ), member( skol4( Y ), universal_class ) }
% 0.76/1.32 .
% 0.76/1.32 { ! member( X, identity_relation ), X = ordered_pair( skol4( X ), skol4( X
% 0.76/1.32 ) ) }.
% 0.76/1.32 { ! member( Y, universal_class ), ! X = ordered_pair( Y, Y ), member( X,
% 0.76/1.32 identity_relation ) }.
% 0.76/1.32 { ! function( X ), subclass( X, cross_product( universal_class,
% 0.76/1.32 universal_class ) ) }.
% 0.76/1.32 { ! function( X ), subclass( compose( X, inverse( X ) ), identity_relation
% 0.76/1.32 ) }.
% 0.76/1.32 { ! subclass( X, cross_product( universal_class, universal_class ) ), !
% 0.76/1.32 subclass( compose( X, inverse( X ) ), identity_relation ), function( X )
% 0.76/1.32 }.
% 0.76/1.32 { ! member( X, universal_class ), ! function( Y ), member( image( Y, X ),
% 0.76/1.32 universal_class ) }.
% 0.76/1.32 { ! disjoint( X, Y ), ! member( Z, X ), ! member( Z, Y ) }.
% 0.76/1.32 { member( skol5( Z, Y ), Y ), disjoint( X, Y ) }.
% 0.76/1.32 { member( skol5( X, Y ), X ), disjoint( X, Y ) }.
% 0.76/1.32 { X = null_class, member( skol6( Y ), universal_class ) }.
% 0.76/1.32 { X = null_class, member( skol6( X ), X ) }.
% 0.76/1.32 { X = null_class, disjoint( skol6( X ), X ) }.
% 0.76/1.32 { apply( X, Y ) = sum_class( image( X, singleton( Y ) ) ) }.
% 0.76/1.32 { function( skol7 ) }.
% 0.76/1.32 { ! member( X, universal_class ), X = null_class, member( apply( skol7, X )
% 0.76/1.32 , X ) }.
% 0.76/1.32 { singleton( skol8 ) = singleton( skol9 ) }.
% 0.76/1.32 { member( skol8, universal_class ) }.
% 0.76/1.32 { ! skol8 = skol9 }.
% 0.76/1.32
% 0.76/1.32 percentage equality = 0.153846, percentage horn = 0.885417
% 0.76/1.32 This is a problem with some equality
% 0.76/1.32
% 0.76/1.32
% 0.76/1.32
% 0.76/1.32 Options Used:
% 0.76/1.32
% 0.76/1.32 useres = 1
% 0.76/1.32 useparamod = 1
% 0.76/1.32 useeqrefl = 1
% 0.76/1.32 useeqfact = 1
% 0.76/1.32 usefactor = 1
% 0.76/1.32 usesimpsplitting = 0
% 0.76/1.32 usesimpdemod = 5
% 0.76/1.32 usesimpres = 3
% 0.76/1.32
% 0.76/1.32 resimpinuse = 1000
% 0.76/1.32 resimpclauses = 20000
% 0.76/1.32 substype = eqrewr
% 0.76/1.32 backwardsubs = 1
% 0.76/1.32 selectoldest = 5
% 0.76/1.32
% 0.76/1.32 litorderings [0] = split
% 0.76/1.32 litorderings [1] = extend the termordering, first sorting on arguments
% 7.44/7.87
% 7.44/7.87 termordering = kbo
% 7.44/7.87
% 7.44/7.87 litapriori = 0
% 7.44/7.87 termapriori = 1
% 7.44/7.87 litaposteriori = 0
% 7.44/7.87 termaposteriori = 0
% 7.44/7.87 demodaposteriori = 0
% 7.44/7.87 ordereqreflfact = 0
% 7.44/7.87
% 7.44/7.87 litselect = negord
% 7.44/7.87
% 7.44/7.87 maxweight = 15
% 7.44/7.87 maxdepth = 30000
% 7.44/7.87 maxlength = 115
% 7.44/7.87 maxnrvars = 195
% 7.44/7.87 excuselevel = 1
% 7.44/7.87 increasemaxweight = 1
% 7.44/7.87
% 7.44/7.87 maxselected = 10000000
% 7.44/7.87 maxnrclauses = 10000000
% 7.44/7.87
% 7.44/7.87 showgenerated = 0
% 7.44/7.87 showkept = 0
% 7.44/7.87 showselected = 0
% 7.44/7.87 showdeleted = 0
% 7.44/7.87 showresimp = 1
% 7.44/7.87 showstatus = 2000
% 7.44/7.87
% 7.44/7.87 prologoutput = 0
% 7.44/7.87 nrgoals = 5000000
% 7.44/7.87 totalproof = 1
% 7.44/7.87
% 7.44/7.87 Symbols occurring in the translation:
% 7.44/7.87
% 7.44/7.87 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 7.44/7.87 . [1, 2] (w:1, o:45, a:1, s:1, b:0),
% 7.44/7.87 ! [4, 1] (w:0, o:24, a:1, s:1, b:0),
% 7.44/7.87 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 7.44/7.87 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 7.44/7.87 subclass [37, 2] (w:1, o:69, a:1, s:1, b:0),
% 7.44/7.87 member [39, 2] (w:1, o:70, a:1, s:1, b:0),
% 7.44/7.87 universal_class [40, 0] (w:1, o:12, a:1, s:1, b:0),
% 7.44/7.87 unordered_pair [41, 2] (w:1, o:71, a:1, s:1, b:0),
% 7.44/7.87 singleton [42, 1] (w:1, o:31, a:1, s:1, b:0),
% 7.44/7.87 ordered_pair [43, 2] (w:1, o:72, a:1, s:1, b:0),
% 7.44/7.87 cross_product [45, 2] (w:1, o:73, a:1, s:1, b:0),
% 7.44/7.87 first [46, 1] (w:1, o:32, a:1, s:1, b:0),
% 7.44/7.87 second [47, 1] (w:1, o:33, a:1, s:1, b:0),
% 7.44/7.87 element_relation [49, 0] (w:1, o:16, a:1, s:1, b:0),
% 7.44/7.87 intersection [50, 2] (w:1, o:75, a:1, s:1, b:0),
% 7.44/7.87 complement [51, 1] (w:1, o:34, a:1, s:1, b:0),
% 7.44/7.87 restrict [53, 3] (w:1, o:84, a:1, s:1, b:0),
% 7.44/7.87 null_class [54, 0] (w:1, o:17, a:1, s:1, b:0),
% 7.44/7.87 domain_of [55, 1] (w:1, o:35, a:1, s:1, b:0),
% 7.44/7.87 rotate [57, 1] (w:1, o:29, a:1, s:1, b:0),
% 7.44/7.87 flip [58, 1] (w:1, o:36, a:1, s:1, b:0),
% 7.44/7.87 union [59, 2] (w:1, o:76, a:1, s:1, b:0),
% 7.44/7.87 successor [60, 1] (w:1, o:37, a:1, s:1, b:0),
% 7.44/7.87 successor_relation [61, 0] (w:1, o:18, a:1, s:1, b:0),
% 7.44/7.87 inverse [62, 1] (w:1, o:38, a:1, s:1, b:0),
% 7.44/7.87 range_of [63, 1] (w:1, o:30, a:1, s:1, b:0),
% 7.44/7.87 image [64, 2] (w:1, o:74, a:1, s:1, b:0),
% 7.44/7.87 inductive [65, 1] (w:1, o:39, a:1, s:1, b:0),
% 7.44/7.87 sum_class [66, 1] (w:1, o:40, a:1, s:1, b:0),
% 7.44/7.87 power_class [67, 1] (w:1, o:41, a:1, s:1, b:0),
% 7.44/7.87 compose [69, 2] (w:1, o:77, a:1, s:1, b:0),
% 7.44/7.87 identity_relation [70, 0] (w:1, o:19, a:1, s:1, b:0),
% 7.44/7.87 function [72, 1] (w:1, o:42, a:1, s:1, b:0),
% 7.44/7.87 disjoint [73, 2] (w:1, o:78, a:1, s:1, b:0),
% 7.44/7.87 apply [74, 2] (w:1, o:79, a:1, s:1, b:0),
% 7.44/7.87 alpha1 [75, 3] (w:1, o:85, a:1, s:1, b:1),
% 7.44/7.87 alpha2 [76, 2] (w:1, o:80, a:1, s:1, b:1),
% 7.44/7.87 skol1 [77, 2] (w:1, o:81, a:1, s:1, b:1),
% 7.44/7.87 skol2 [78, 0] (w:1, o:20, a:1, s:1, b:1),
% 7.44/7.87 skol3 [79, 2] (w:1, o:82, a:1, s:1, b:1),
% 7.44/7.87 skol4 [80, 1] (w:1, o:43, a:1, s:1, b:1),
% 7.44/7.87 skol5 [81, 2] (w:1, o:83, a:1, s:1, b:1),
% 7.44/7.87 skol6 [82, 1] (w:1, o:44, a:1, s:1, b:1),
% 7.44/7.87 skol7 [83, 0] (w:1, o:21, a:1, s:1, b:1),
% 7.44/7.87 skol8 [84, 0] (w:1, o:22, a:1, s:1, b:1),
% 7.44/7.87 skol9 [85, 0] (w:1, o:23, a:1, s:1, b:1).
% 7.44/7.87
% 7.44/7.87
% 7.44/7.87 Starting Search:
% 7.44/7.87
% 7.44/7.87 *** allocated 15000 integers for clauses
% 7.44/7.87 *** allocated 22500 integers for clauses
% 7.44/7.87 *** allocated 33750 integers for clauses
% 7.44/7.87 *** allocated 15000 integers for termspace/termends
% 7.44/7.87 *** allocated 50625 integers for clauses
% 7.44/7.87 Resimplifying inuse:
% 7.44/7.87 Done
% 7.44/7.87
% 7.44/7.87 *** allocated 22500 integers for termspace/termends
% 7.44/7.87 *** allocated 75937 integers for clauses
% 7.44/7.87 *** allocated 33750 integers for termspace/termends
% 7.44/7.87 *** allocated 113905 integers for clauses
% 7.44/7.87
% 7.44/7.87 Intermediate Status:
% 7.44/7.87 Generated: 5147
% 7.44/7.87 Kept: 2050
% 7.44/7.87 Inuse: 123
% 7.44/7.87 Deleted: 4
% 7.44/7.87 Deletedinuse: 1
% 7.44/7.87
% 7.44/7.87 Resimplifying inuse:
% 7.44/7.87 Done
% 7.44/7.87
% 7.44/7.87 *** allocated 170857 integers for clauses
% 7.44/7.87 *** allocated 50625 integers for termspace/termends
% 7.44/7.87 Resimplifying inuse:
% 7.44/7.87 Done
% 7.44/7.87
% 7.44/7.87 *** allocated 75937 integers for termspace/termends
% 7.44/7.87 *** allocated 256285 integers for clauses
% 7.44/7.87
% 7.44/7.87 Intermediate Status:
% 7.44/7.87 Generated: 9981
% 7.44/7.87 Kept: 4058
% 7.44/7.87 Inuse: 197
% 7.44/7.87 Deleted: 50
% 7.44/7.87 Deletedinuse: 19
% 7.44/7.87
% 7.44/7.87 Resimplifying inuse:
% 7.44/7.87 Done
% 7.44/7.87
% 7.44/7.87 Resimplifying inuse:
% 7.44/7.87 Done
% 7.44/7.87
% 7.44/7.87 *** allocated 113905 integers for termspace/termends
% 7.44/7.87 *** allocated 384427 integers for clauses
% 7.44/7.87
% 7.44/7.87 Intermediate Status:
% 7.44/7.87 Generated: 13733
% 7.44/7.87 Kept: 6071
% 7.44/7.87 Inuse: 252
% 7.44/7.87 Deleted: 62
% 7.44/7.87 Deletedinuse: 22
% 7.44/7.87
% 7.44/7.87 Resimplifying inuse:
% 7.44/7.87 Done
% 7.44/7.87
% 7.44/7.87 Resimplifying inuse:
% 7.44/7.87 Done
% 7.44/7.87
% 7.44/7.87
% 7.44/7.87 Intermediate Status:
% 7.44/7.87 Generated: 17531
% 7.44/7.87 Kept: 8099
% 7.44/7.87 Inuse: 312
% 7.44/7.87 Deleted: 75
% 7.44/7.87 Deletedinuse: 29
% 7.44/7.87
% 7.44/7.87 *** allocated 576640 integers for clauses
% 7.44/7.87 Resimplifying inuse:
% 7.44/7.87 Done
% 7.44/7.87
% 7.44/7.87 *** allocated 170857 integers for termspace/termends
% 7.44/7.87 Resimplifying inuse:
% 7.44/7.87 Done
% 7.44/7.87
% 7.44/7.87
% 7.44/7.87 Intermediate Status:
% 7.44/7.87 Generated: 24276
% 7.44/7.87 Kept: 10103
% 7.44/7.87 Inuse: 359
% 7.44/7.87 Deleted: 85
% 7.44/7.87 Deletedinuse: 34
% 7.44/7.87
% 7.44/7.87 Resimplifying inuse:
% 7.44/7.87 Done
% 7.44/7.87
% 7.44/7.87 *** allocated 864960 integers for clauses
% 7.44/7.87 *** allocated 256285 integers for termspace/termends
% 7.44/7.87
% 7.44/7.87 Intermediate Status:
% 7.44/7.87 Generated: 29598
% 7.44/7.87 Kept: 12849
% 7.44/7.87 Inuse: 365
% 7.44/7.87 Deleted: 87
% 7.44/7.87 Deletedinuse: 36
% 7.44/7.87
% 7.44/7.87 Resimplifying inuse:
% 7.44/7.87 Done
% 7.44/7.87
% 7.44/7.87 Resimplifying inuse:
% 7.44/7.87 Done
% 7.44/7.87
% 7.44/7.87
% 7.44/7.87 Intermediate Status:
% 7.44/7.87 Generated: 34336
% 7.44/7.87 Kept: 14874
% 7.44/7.87 Inuse: 392
% 7.44/7.87 Deleted: 88
% 7.44/7.87 Deletedinuse: 36
% 7.44/7.87
% 7.44/7.87 Resimplifying inuse:
% 7.44/7.87 Done
% 7.44/7.87
% 7.44/7.87 Resimplifying inuse:
% 7.44/7.87 Done
% 7.44/7.87
% 7.44/7.87
% 7.44/7.87 Intermediate Status:
% 7.44/7.87 Generated: 39205
% 7.44/7.87 Kept: 16931
% 7.44/7.87 Inuse: 441
% 7.44/7.87 Deleted: 94
% 7.44/7.87 Deletedinuse: 40
% 7.44/7.87
% 7.44/7.87 Resimplifying inuse:
% 7.44/7.87 Done
% 7.44/7.87
% 7.44/7.87 Resimplifying inuse:
% 7.44/7.87 Done
% 7.44/7.87
% 7.44/7.87
% 7.44/7.87 Intermediate Status:
% 7.44/7.87 Generated: 43447
% 7.44/7.87 Kept: 18945
% 7.44/7.87 Inuse: 482
% 7.44/7.87 Deleted: 94
% 7.44/7.87 Deletedinuse: 40
% 7.44/7.87
% 7.44/7.87 *** allocated 1297440 integers for clauses
% 7.44/7.87 Resimplifying inuse:
% 7.44/7.87 Done
% 7.44/7.87
% 7.44/7.87 *** allocated 384427 integers for termspace/termends
% 7.44/7.87 Resimplifying inuse:
% 7.44/7.87 Done
% 7.44/7.87
% 7.44/7.87 Resimplifying clauses:
% 7.44/7.87 Done
% 7.44/7.87
% 7.44/7.87
% 7.44/7.87 Intermediate Status:
% 7.44/7.87 Generated: 49461
% 7.44/7.87 Kept: 20962
% 7.44/7.87 Inuse: 502
% 7.44/7.87 Deleted: 902
% 7.44/7.87 Deletedinuse: 40
% 7.44/7.87
% 7.44/7.87 Resimplifying inuse:
% 7.44/7.87 Done
% 7.44/7.87
% 7.44/7.87 Resimplifying inuse:
% 7.44/7.87 Done
% 7.44/7.87
% 7.44/7.87
% 7.44/7.87 Intermediate Status:
% 7.44/7.87 Generated: 56140
% 7.44/7.87 Kept: 22990
% 7.44/7.87 Inuse: 538
% 7.44/7.87 Deleted: 905
% 7.44/7.87 Deletedinuse: 40
% 7.44/7.87
% 7.44/7.87 Resimplifying inuse:
% 7.44/7.87 Done
% 7.44/7.87
% 7.44/7.87 Resimplifying inuse:
% 7.44/7.87 Done
% 7.44/7.87
% 7.44/7.87
% 7.44/7.87 Intermediate Status:
% 7.44/7.87 Generated: 64447
% 7.44/7.87 Kept: 25138
% 7.44/7.87 Inuse: 591
% 7.44/7.87 Deleted: 907
% 7.44/7.87 Deletedinuse: 41
% 7.44/7.87
% 7.44/7.87 Resimplifying inuse:
% 7.44/7.87 Done
% 7.44/7.87
% 7.44/7.87 Resimplifying inuse:
% 7.44/7.87 Done
% 7.44/7.87
% 7.44/7.87
% 7.44/7.87 Intermediate Status:
% 7.44/7.87 Generated: 71686
% 7.44/7.87 Kept: 27138
% 7.44/7.87 Inuse: 651
% 7.44/7.87 Deleted: 907
% 7.44/7.87 Deletedinuse: 41
% 7.44/7.87
% 7.44/7.87 Resimplifying inuse:
% 7.44/7.87 Done
% 7.44/7.87
% 7.44/7.87 Resimplifying inuse:
% 7.44/7.87 Done
% 7.44/7.87
% 7.44/7.87 *** allocated 576640 integers for termspace/termends
% 7.44/7.87
% 7.44/7.87 Intermediate Status:
% 7.44/7.87 Generated: 78093
% 7.44/7.87 Kept: 29149
% 7.44/7.87 Inuse: 703
% 7.44/7.87 Deleted: 907
% 7.44/7.87 Deletedinuse: 41
% 7.44/7.87
% 7.44/7.87 *** allocated 1946160 integers for clauses
% 7.44/7.87 Resimplifying inuse:
% 7.44/7.87 Done
% 7.44/7.87
% 7.44/7.87 Resimplifying inuse:
% 7.44/7.87 Done
% 7.44/7.87
% 7.44/7.87
% 7.44/7.87 Intermediate Status:
% 7.44/7.87 Generated: 83817
% 7.44/7.87 Kept: 31168
% 7.44/7.87 Inuse: 763
% 7.44/7.87 Deleted: 907
% 7.44/7.87 Deletedinuse: 41
% 7.44/7.87
% 7.44/7.87 Resimplifying inuse:
% 7.44/7.87 Done
% 7.44/7.87
% 7.44/7.87 Resimplifying inuse:
% 7.44/7.87 Done
% 7.44/7.87
% 7.44/7.87
% 7.44/7.87 Intermediate Status:
% 7.44/7.87 Generated: 95751
% 7.44/7.87 Kept: 33176
% 7.44/7.87 Inuse: 790
% 7.44/7.87 Deleted: 907
% 7.44/7.87 Deletedinuse: 41
% 7.44/7.87
% 7.44/7.87 Resimplifying inuse:
% 7.44/7.87 Done
% 7.44/7.87
% 7.44/7.87
% 7.44/7.87 Bliksems!, er is een bewijs:
% 7.44/7.87 % SZS status Theorem
% 7.44/7.87 % SZS output start Refutation
% 7.44/7.87
% 7.44/7.87 (4) {G0,W6,D2,L2,V2,M2} I { ! X = Y, subclass( X, Y ) }.
% 7.44/7.87 (5) {G0,W9,D2,L3,V2,M3} I { ! subclass( X, Y ), ! subclass( Y, X ), X = Y
% 7.44/7.87 }.
% 7.44/7.87 (7) {G0,W9,D3,L2,V3,M2} I { ! member( X, unordered_pair( Y, Z ) ), alpha1(
% 7.44/7.87 X, Y, Z ) }.
% 7.44/7.87 (8) {G0,W12,D3,L3,V3,M3} I { ! member( X, universal_class ), ! alpha1( X, Y
% 7.44/7.87 , Z ), member( X, unordered_pair( Y, Z ) ) }.
% 7.44/7.87 (9) {G0,W10,D2,L3,V3,M3} I { ! alpha1( X, Y, Z ), X = Y, X = Z }.
% 7.44/7.87 (11) {G0,W7,D2,L2,V3,M2} I { ! X = Z, alpha1( X, Y, Z ) }.
% 7.44/7.87 (13) {G0,W6,D3,L1,V1,M1} I { unordered_pair( X, X ) ==> singleton( X ) }.
% 7.44/7.87 (92) {G0,W5,D3,L1,V0,M1} I { singleton( skol9 ) ==> singleton( skol8 ) }.
% 7.44/7.87 (93) {G0,W3,D2,L1,V0,M1} I { member( skol8, universal_class ) }.
% 7.44/7.87 (94) {G0,W3,D2,L1,V0,M1} I { ! skol9 ==> skol8 }.
% 7.44/7.87 (96) {G1,W7,D2,L2,V2,M2} F(9) { ! alpha1( X, Y, Y ), X = Y }.
% 7.44/7.87 (100) {G1,W4,D2,L1,V2,M1} Q(11) { alpha1( X, Y, X ) }.
% 7.44/7.87 (138) {G1,W6,D2,L2,V2,M2} R(5,4);r(4) { X = Y, ! Y = X }.
% 7.44/7.87 (214) {G2,W6,D2,L2,V1,M2} P(138,94) { ! X = skol8, ! X = skol9 }.
% 7.44/7.87 (246) {G1,W9,D3,L2,V2,M2} R(8,93) { ! alpha1( skol8, X, Y ), member( skol8
% 7.44/7.87 , unordered_pair( X, Y ) ) }.
% 7.44/7.87 (11228) {G3,W10,D2,L3,V2,M3} P(96,214) { ! Y = skol8, ! Y = X, ! alpha1( X
% 7.44/7.87 , skol9, skol9 ) }.
% 7.44/7.87 (11407) {G4,W7,D2,L2,V1,M2} F(11228) { ! X = skol8, ! alpha1( skol8, skol9
% 7.44/7.87 , skol9 ) }.
% 7.44/7.87 (11408) {G5,W4,D2,L1,V0,M1} Q(11407) { ! alpha1( skol8, skol9, skol9 ) }.
% 7.44/7.87 (14106) {G6,W4,D3,L1,V0,M1} R(11408,7);d(13);d(92) { ! member( skol8,
% 7.44/7.87 singleton( skol8 ) ) }.
% 7.44/7.87 (35019) {G2,W13,D3,L3,V3,M3} P(96,246) { ! alpha1( X, Y, Z ), member( X,
% 7.44/7.87 unordered_pair( Y, Z ) ), ! alpha1( skol8, X, X ) }.
% 7.44/7.87 (35029) {G3,W4,D3,L1,V0,M1} F(35019);d(13);r(100) { member( skol8,
% 7.44/7.87 singleton( skol8 ) ) }.
% 7.44/7.87 (35030) {G7,W0,D0,L0,V0,M0} S(35029);r(14106) { }.
% 7.44/7.87
% 7.44/7.87
% 7.44/7.87 % SZS output end Refutation
% 7.44/7.87 found a proof!
% 7.44/7.87
% 7.44/7.87
% 7.44/7.87 Unprocessed initial clauses:
% 7.44/7.87
% 7.44/7.87 (35032) {G0,W9,D2,L3,V3,M3} { ! subclass( X, Y ), ! member( Z, X ), member
% 7.44/7.87 ( Z, Y ) }.
% 7.44/7.87 (35033) {G0,W8,D3,L2,V3,M2} { ! member( skol1( Z, Y ), Y ), subclass( X, Y
% 7.44/7.87 ) }.
% 7.44/7.87 (35034) {G0,W8,D3,L2,V2,M2} { member( skol1( X, Y ), X ), subclass( X, Y )
% 7.44/7.87 }.
% 7.44/7.87 (35035) {G0,W3,D2,L1,V1,M1} { subclass( X, universal_class ) }.
% 7.44/7.87 (35036) {G0,W6,D2,L2,V2,M2} { ! X = Y, subclass( X, Y ) }.
% 7.44/7.87 (35037) {G0,W6,D2,L2,V2,M2} { ! X = Y, subclass( Y, X ) }.
% 7.44/7.87 (35038) {G0,W9,D2,L3,V2,M3} { ! subclass( X, Y ), ! subclass( Y, X ), X =
% 7.44/7.87 Y }.
% 7.44/7.87 (35039) {G0,W8,D3,L2,V3,M2} { ! member( X, unordered_pair( Y, Z ) ),
% 7.44/7.87 member( X, universal_class ) }.
% 7.44/7.87 (35040) {G0,W9,D3,L2,V3,M2} { ! member( X, unordered_pair( Y, Z ) ),
% 7.44/7.87 alpha1( X, Y, Z ) }.
% 7.44/7.87 (35041) {G0,W12,D3,L3,V3,M3} { ! member( X, universal_class ), ! alpha1( X
% 7.44/7.87 , Y, Z ), member( X, unordered_pair( Y, Z ) ) }.
% 7.44/7.87 (35042) {G0,W10,D2,L3,V3,M3} { ! alpha1( X, Y, Z ), X = Y, X = Z }.
% 7.44/7.87 (35043) {G0,W7,D2,L2,V3,M2} { ! X = Y, alpha1( X, Y, Z ) }.
% 7.44/7.87 (35044) {G0,W7,D2,L2,V3,M2} { ! X = Z, alpha1( X, Y, Z ) }.
% 7.44/7.87 (35045) {G0,W5,D3,L1,V2,M1} { member( unordered_pair( X, Y ),
% 7.44/7.87 universal_class ) }.
% 7.44/7.87 (35046) {G0,W6,D3,L1,V1,M1} { singleton( X ) = unordered_pair( X, X ) }.
% 7.44/7.87 (35047) {G0,W11,D5,L1,V2,M1} { ordered_pair( X, Y ) = unordered_pair(
% 7.44/7.87 singleton( X ), unordered_pair( X, singleton( Y ) ) ) }.
% 7.44/7.87 (35048) {G0,W10,D3,L2,V4,M2} { ! member( ordered_pair( X, Y ),
% 7.44/7.87 cross_product( Z, T ) ), member( X, Z ) }.
% 7.44/7.87 (35049) {G0,W10,D3,L2,V4,M2} { ! member( ordered_pair( X, Y ),
% 7.44/7.87 cross_product( Z, T ) ), member( Y, T ) }.
% 7.44/7.87 (35050) {G0,W13,D3,L3,V4,M3} { ! member( X, Z ), ! member( Y, T ), member
% 7.44/7.87 ( ordered_pair( X, Y ), cross_product( Z, T ) ) }.
% 7.44/7.87 (35051) {G0,W12,D4,L3,V2,M3} { ! member( X, universal_class ), ! member( Y
% 7.44/7.87 , universal_class ), first( ordered_pair( X, Y ) ) = X }.
% 7.44/7.87 (35052) {G0,W12,D4,L3,V2,M3} { ! member( X, universal_class ), ! member( Y
% 7.44/7.87 , universal_class ), second( ordered_pair( X, Y ) ) = Y }.
% 7.44/7.87 (35053) {G0,W12,D4,L2,V3,M2} { ! member( X, cross_product( Y, Z ) ), X =
% 7.44/7.87 ordered_pair( first( X ), second( X ) ) }.
% 7.44/7.87 (35054) {G0,W8,D3,L2,V2,M2} { ! member( ordered_pair( X, Y ),
% 7.44/7.87 element_relation ), member( Y, universal_class ) }.
% 7.44/7.87 (35055) {G0,W8,D3,L2,V2,M2} { ! member( ordered_pair( X, Y ),
% 7.44/7.87 element_relation ), member( X, Y ) }.
% 7.44/7.87 (35056) {G0,W11,D3,L3,V2,M3} { ! member( Y, universal_class ), ! member( X
% 7.44/7.87 , Y ), member( ordered_pair( X, Y ), element_relation ) }.
% 7.44/7.87 (35057) {G0,W5,D3,L1,V0,M1} { subclass( element_relation, cross_product(
% 7.44/7.87 universal_class, universal_class ) ) }.
% 7.44/7.87 (35058) {G0,W8,D3,L2,V3,M2} { ! member( Z, intersection( X, Y ) ), member
% 7.44/7.87 ( Z, X ) }.
% 7.44/7.87 (35059) {G0,W8,D3,L2,V3,M2} { ! member( Z, intersection( X, Y ) ), member
% 7.44/7.87 ( Z, Y ) }.
% 7.44/7.87 (35060) {G0,W11,D3,L3,V3,M3} { ! member( Z, X ), ! member( Z, Y ), member
% 7.44/7.87 ( Z, intersection( X, Y ) ) }.
% 7.44/7.87 (35061) {G0,W7,D3,L2,V2,M2} { ! member( Y, complement( X ) ), member( Y,
% 7.44/7.87 universal_class ) }.
% 7.44/7.87 (35062) {G0,W7,D3,L2,V2,M2} { ! member( Y, complement( X ) ), ! member( Y
% 7.44/7.87 , X ) }.
% 7.44/7.87 (35063) {G0,W10,D3,L3,V2,M3} { ! member( Y, universal_class ), member( Y,
% 7.44/7.87 X ), member( Y, complement( X ) ) }.
% 7.44/7.87 (35064) {G0,W10,D4,L1,V3,M1} { restrict( Y, X, Z ) = intersection( Y,
% 7.44/7.87 cross_product( X, Z ) ) }.
% 7.44/7.87 (35065) {G0,W3,D2,L1,V1,M1} { ! member( X, null_class ) }.
% 7.44/7.87 (35066) {G0,W7,D3,L2,V2,M2} { ! member( Y, domain_of( X ) ), member( Y,
% 7.44/7.87 universal_class ) }.
% 7.44/7.87 (35067) {G0,W11,D4,L2,V2,M2} { ! member( Y, domain_of( X ) ), ! restrict(
% 7.44/7.87 X, singleton( Y ), universal_class ) = null_class }.
% 7.44/7.87 (35068) {G0,W14,D4,L3,V2,M3} { ! member( Y, universal_class ), restrict( X
% 7.44/7.87 , singleton( Y ), universal_class ) = null_class, member( Y, domain_of( X
% 7.44/7.87 ) ) }.
% 7.44/7.87 (35069) {G0,W19,D4,L2,V4,M2} { ! member( ordered_pair( ordered_pair( Y, Z
% 7.44/7.87 ), T ), rotate( X ) ), member( ordered_pair( ordered_pair( Y, Z ), T ),
% 7.44/7.87 cross_product( cross_product( universal_class, universal_class ),
% 7.44/7.87 universal_class ) ) }.
% 7.44/7.87 (35070) {G0,W15,D4,L2,V4,M2} { ! member( ordered_pair( ordered_pair( Y, Z
% 7.44/7.87 ), T ), rotate( X ) ), member( ordered_pair( ordered_pair( Z, T ), Y ),
% 7.44/7.87 X ) }.
% 7.44/7.87 (35071) {G0,W26,D4,L3,V4,M3} { ! member( ordered_pair( ordered_pair( Y, Z
% 7.44/7.87 ), T ), cross_product( cross_product( universal_class, universal_class )
% 7.44/7.87 , universal_class ) ), ! member( ordered_pair( ordered_pair( Z, T ), Y )
% 7.44/7.87 , X ), member( ordered_pair( ordered_pair( Y, Z ), T ), rotate( X ) ) }.
% 7.44/7.87 (35072) {G0,W8,D4,L1,V1,M1} { subclass( rotate( X ), cross_product(
% 7.44/7.87 cross_product( universal_class, universal_class ), universal_class ) )
% 7.44/7.87 }.
% 7.44/7.87 (35073) {G0,W19,D4,L2,V4,M2} { ! member( ordered_pair( ordered_pair( X, Y
% 7.44/7.87 ), Z ), flip( T ) ), member( ordered_pair( ordered_pair( X, Y ), Z ),
% 7.44/7.87 cross_product( cross_product( universal_class, universal_class ),
% 7.44/7.87 universal_class ) ) }.
% 7.44/7.87 (35074) {G0,W15,D4,L2,V4,M2} { ! member( ordered_pair( ordered_pair( X, Y
% 7.44/7.87 ), Z ), flip( T ) ), member( ordered_pair( ordered_pair( Y, X ), Z ), T
% 7.44/7.87 ) }.
% 7.44/7.87 (35075) {G0,W26,D4,L3,V4,M3} { ! member( ordered_pair( ordered_pair( X, Y
% 7.44/7.87 ), Z ), cross_product( cross_product( universal_class, universal_class )
% 7.44/7.87 , universal_class ) ), ! member( ordered_pair( ordered_pair( Y, X ), Z )
% 7.44/7.87 , T ), member( ordered_pair( ordered_pair( X, Y ), Z ), flip( T ) ) }.
% 7.44/7.87 (35076) {G0,W8,D4,L1,V1,M1} { subclass( flip( X ), cross_product(
% 7.44/7.87 cross_product( universal_class, universal_class ), universal_class ) )
% 7.44/7.87 }.
% 7.44/7.87 (35077) {G0,W11,D3,L3,V3,M3} { ! member( Z, union( X, Y ) ), member( Z, X
% 7.44/7.87 ), member( Z, Y ) }.
% 7.44/7.87 (35078) {G0,W8,D3,L2,V3,M2} { ! member( Z, X ), member( Z, union( X, Y ) )
% 7.44/7.87 }.
% 7.44/7.87 (35079) {G0,W8,D3,L2,V3,M2} { ! member( Z, Y ), member( Z, union( X, Y ) )
% 7.44/7.87 }.
% 7.44/7.87 (35080) {G0,W7,D4,L1,V1,M1} { successor( X ) = union( X, singleton( X ) )
% 7.44/7.87 }.
% 7.44/7.87 (35081) {G0,W5,D3,L1,V0,M1} { subclass( successor_relation, cross_product
% 7.44/7.87 ( universal_class, universal_class ) ) }.
% 7.44/7.87 (35082) {G0,W8,D3,L2,V2,M2} { ! member( ordered_pair( X, Y ),
% 7.44/7.87 successor_relation ), member( X, universal_class ) }.
% 7.44/7.87 (35083) {G0,W8,D3,L2,V2,M2} { ! member( ordered_pair( X, Y ),
% 7.44/7.87 successor_relation ), alpha2( X, Y ) }.
% 7.44/7.87 (35084) {G0,W11,D3,L3,V2,M3} { ! member( X, universal_class ), ! alpha2( X
% 7.44/7.87 , Y ), member( ordered_pair( X, Y ), successor_relation ) }.
% 7.44/7.87 (35085) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), member( Y, universal_class
% 7.44/7.87 ) }.
% 7.44/7.87 (35086) {G0,W7,D3,L2,V2,M2} { ! alpha2( X, Y ), successor( X ) = Y }.
% 7.44/7.87 (35087) {G0,W10,D3,L3,V2,M3} { ! member( Y, universal_class ), ! successor
% 7.44/7.87 ( X ) = Y, alpha2( X, Y ) }.
% 7.44/7.87 (35088) {G0,W8,D5,L1,V1,M1} { inverse( X ) = domain_of( flip(
% 7.44/7.87 cross_product( X, universal_class ) ) ) }.
% 7.44/7.87 (35089) {G0,W6,D4,L1,V1,M1} { range_of( X ) = domain_of( inverse( X ) )
% 7.44/7.87 }.
% 7.44/7.87 (35090) {G0,W9,D4,L1,V2,M1} { image( Y, X ) = range_of( restrict( Y, X,
% 7.44/7.87 universal_class ) ) }.
% 7.44/7.87 (35091) {G0,W5,D2,L2,V1,M2} { ! inductive( X ), member( null_class, X )
% 7.44/7.87 }.
% 7.44/7.87 (35092) {G0,W7,D3,L2,V1,M2} { ! inductive( X ), subclass( image(
% 7.44/7.87 successor_relation, X ), X ) }.
% 7.44/7.87 (35093) {G0,W10,D3,L3,V1,M3} { ! member( null_class, X ), ! subclass(
% 7.44/7.87 image( successor_relation, X ), X ), inductive( X ) }.
% 7.44/7.87 (35094) {G0,W3,D2,L1,V0,M1} { member( skol2, universal_class ) }.
% 7.44/7.87 (35095) {G0,W2,D2,L1,V0,M1} { inductive( skol2 ) }.
% 7.44/7.87 (35096) {G0,W5,D2,L2,V1,M2} { ! inductive( X ), subclass( skol2, X ) }.
% 7.44/7.87 (35097) {G0,W9,D3,L2,V3,M2} { ! member( X, sum_class( Y ) ), member( skol3
% 7.44/7.87 ( Z, Y ), Y ) }.
% 7.44/7.87 (35098) {G0,W9,D3,L2,V2,M2} { ! member( X, sum_class( Y ) ), member( X,
% 7.44/7.87 skol3( X, Y ) ) }.
% 7.44/7.87 (35099) {G0,W10,D3,L3,V3,M3} { ! member( X, Z ), ! member( Z, Y ), member
% 7.44/7.87 ( X, sum_class( Y ) ) }.
% 7.44/7.87 (35100) {G0,W7,D3,L2,V1,M2} { ! member( X, universal_class ), member(
% 7.44/7.87 sum_class( X ), universal_class ) }.
% 7.44/7.87 (35101) {G0,W7,D3,L2,V2,M2} { ! member( X, power_class( Y ) ), member( X,
% 7.44/7.87 universal_class ) }.
% 7.44/7.87 (35102) {G0,W7,D3,L2,V2,M2} { ! member( X, power_class( Y ) ), subclass( X
% 7.44/7.87 , Y ) }.
% 7.44/7.87 (35103) {G0,W10,D3,L3,V2,M3} { ! member( X, universal_class ), ! subclass
% 7.44/7.87 ( X, Y ), member( X, power_class( Y ) ) }.
% 7.44/7.87 (35104) {G0,W7,D3,L2,V1,M2} { ! member( X, universal_class ), member(
% 7.44/7.87 power_class( X ), universal_class ) }.
% 7.44/7.87 (35105) {G0,W7,D3,L1,V2,M1} { subclass( compose( Y, X ), cross_product(
% 7.44/7.87 universal_class, universal_class ) ) }.
% 7.44/7.87 (35106) {G0,W10,D3,L2,V4,M2} { ! member( ordered_pair( Z, T ), compose( Y
% 7.44/7.87 , X ) ), member( Z, universal_class ) }.
% 7.44/7.87 (35107) {G0,W15,D5,L2,V4,M2} { ! member( ordered_pair( Z, T ), compose( Y
% 7.44/7.87 , X ) ), member( T, image( Y, image( X, singleton( Z ) ) ) ) }.
% 7.44/7.87 (35108) {G0,W18,D5,L3,V4,M3} { ! member( Z, universal_class ), ! member( T
% 7.44/7.87 , image( Y, image( X, singleton( Z ) ) ) ), member( ordered_pair( Z, T )
% 7.44/7.87 , compose( Y, X ) ) }.
% 7.44/7.87 (35109) {G0,W7,D3,L2,V2,M2} { ! member( X, identity_relation ), member(
% 7.44/7.87 skol4( Y ), universal_class ) }.
% 7.44/7.87 (35110) {G0,W10,D4,L2,V1,M2} { ! member( X, identity_relation ), X =
% 7.44/7.87 ordered_pair( skol4( X ), skol4( X ) ) }.
% 7.44/7.87 (35111) {G0,W11,D3,L3,V2,M3} { ! member( Y, universal_class ), ! X =
% 7.44/7.87 ordered_pair( Y, Y ), member( X, identity_relation ) }.
% 7.44/7.87 (35112) {G0,W7,D3,L2,V1,M2} { ! function( X ), subclass( X, cross_product
% 7.44/7.87 ( universal_class, universal_class ) ) }.
% 7.44/7.87 (35113) {G0,W8,D4,L2,V1,M2} { ! function( X ), subclass( compose( X,
% 7.44/7.87 inverse( X ) ), identity_relation ) }.
% 7.44/7.87 (35114) {G0,W13,D4,L3,V1,M3} { ! subclass( X, cross_product(
% 7.44/7.87 universal_class, universal_class ) ), ! subclass( compose( X, inverse( X
% 7.44/7.87 ) ), identity_relation ), function( X ) }.
% 7.44/7.87 (35115) {G0,W10,D3,L3,V2,M3} { ! member( X, universal_class ), ! function
% 7.44/7.87 ( Y ), member( image( Y, X ), universal_class ) }.
% 7.44/7.87 (35116) {G0,W9,D2,L3,V3,M3} { ! disjoint( X, Y ), ! member( Z, X ), !
% 7.44/7.87 member( Z, Y ) }.
% 7.44/7.87 (35117) {G0,W8,D3,L2,V3,M2} { member( skol5( Z, Y ), Y ), disjoint( X, Y )
% 7.44/7.87 }.
% 7.44/7.87 (35118) {G0,W8,D3,L2,V2,M2} { member( skol5( X, Y ), X ), disjoint( X, Y )
% 7.44/7.87 }.
% 7.44/7.87 (35119) {G0,W7,D3,L2,V2,M2} { X = null_class, member( skol6( Y ),
% 7.44/7.87 universal_class ) }.
% 7.44/7.87 (35120) {G0,W7,D3,L2,V1,M2} { X = null_class, member( skol6( X ), X ) }.
% 7.44/7.87 (35121) {G0,W7,D3,L2,V1,M2} { X = null_class, disjoint( skol6( X ), X )
% 7.44/7.87 }.
% 7.44/7.87 (35122) {G0,W9,D5,L1,V2,M1} { apply( X, Y ) = sum_class( image( X,
% 7.44/7.87 singleton( Y ) ) ) }.
% 7.44/7.87 (35123) {G0,W2,D2,L1,V0,M1} { function( skol7 ) }.
% 7.44/7.87 (35124) {G0,W11,D3,L3,V1,M3} { ! member( X, universal_class ), X =
% 7.44/7.87 null_class, member( apply( skol7, X ), X ) }.
% 7.44/7.87 (35125) {G0,W5,D3,L1,V0,M1} { singleton( skol8 ) = singleton( skol9 ) }.
% 7.44/7.87 (35126) {G0,W3,D2,L1,V0,M1} { member( skol8, universal_class ) }.
% 7.44/7.87 (35127) {G0,W3,D2,L1,V0,M1} { ! skol8 = skol9 }.
% 7.44/7.87
% 7.44/7.87
% 7.44/7.87 Total Proof:
% 7.44/7.87
% 7.44/7.87 subsumption: (4) {G0,W6,D2,L2,V2,M2} I { ! X = Y, subclass( X, Y ) }.
% 7.44/7.87 parent0: (35036) {G0,W6,D2,L2,V2,M2} { ! X = Y, subclass( X, Y ) }.
% 7.44/7.87 substitution0:
% 7.44/7.87 X := X
% 7.44/7.87 Y := Y
% 7.44/7.87 end
% 7.44/7.87 permutation0:
% 7.44/7.87 0 ==> 0
% 7.44/7.87 1 ==> 1
% 7.44/7.87 end
% 7.44/7.87
% 7.44/7.87 subsumption: (5) {G0,W9,D2,L3,V2,M3} I { ! subclass( X, Y ), ! subclass( Y
% 7.44/7.87 , X ), X = Y }.
% 7.44/7.87 parent0: (35038) {G0,W9,D2,L3,V2,M3} { ! subclass( X, Y ), ! subclass( Y,
% 7.44/7.87 X ), X = Y }.
% 7.44/7.87 substitution0:
% 7.44/7.87 X := X
% 7.44/7.87 Y := Y
% 7.44/7.87 end
% 7.44/7.87 permutation0:
% 7.44/7.87 0 ==> 0
% 7.44/7.87 1 ==> 1
% 7.44/7.87 2 ==> 2
% 7.44/7.87 end
% 7.44/7.87
% 7.44/7.87 subsumption: (7) {G0,W9,D3,L2,V3,M2} I { ! member( X, unordered_pair( Y, Z
% 7.44/7.87 ) ), alpha1( X, Y, Z ) }.
% 7.44/7.87 parent0: (35040) {G0,W9,D3,L2,V3,M2} { ! member( X, unordered_pair( Y, Z )
% 7.44/7.87 ), alpha1( X, Y, Z ) }.
% 7.44/7.87 substitution0:
% 7.44/7.87 X := X
% 7.44/7.87 Y := Y
% 7.44/7.87 Z := Z
% 7.44/7.87 end
% 7.44/7.87 permutation0:
% 7.44/7.87 0 ==> 0
% 7.44/7.87 1 ==> 1
% 7.44/7.87 end
% 7.44/7.87
% 7.44/7.87 subsumption: (8) {G0,W12,D3,L3,V3,M3} I { ! member( X, universal_class ), !
% 7.44/7.87 alpha1( X, Y, Z ), member( X, unordered_pair( Y, Z ) ) }.
% 7.44/7.87 parent0: (35041) {G0,W12,D3,L3,V3,M3} { ! member( X, universal_class ), !
% 7.44/7.87 alpha1( X, Y, Z ), member( X, unordered_pair( Y, Z ) ) }.
% 7.44/7.87 substitution0:
% 7.44/7.87 X := X
% 7.44/7.87 Y := Y
% 7.44/7.87 Z := Z
% 7.44/7.87 end
% 7.44/7.87 permutation0:
% 7.44/7.87 0 ==> 0
% 7.44/7.87 1 ==> 1
% 7.44/7.87 2 ==> 2
% 7.44/7.87 end
% 7.44/7.87
% 7.44/7.87 subsumption: (9) {G0,W10,D2,L3,V3,M3} I { ! alpha1( X, Y, Z ), X = Y, X = Z
% 7.44/7.87 }.
% 7.44/7.87 parent0: (35042) {G0,W10,D2,L3,V3,M3} { ! alpha1( X, Y, Z ), X = Y, X = Z
% 7.44/7.87 }.
% 7.44/7.87 substitution0:
% 7.44/7.87 X := X
% 7.44/7.87 Y := Y
% 7.44/7.87 Z := Z
% 7.44/7.87 end
% 7.44/7.87 permutation0:
% 7.44/7.87 0 ==> 0
% 7.44/7.87 1 ==> 1
% 7.44/7.87 2 ==> 2
% 7.44/7.87 end
% 7.44/7.87
% 7.44/7.87 subsumption: (11) {G0,W7,D2,L2,V3,M2} I { ! X = Z, alpha1( X, Y, Z ) }.
% 7.44/7.87 parent0: (35044) {G0,W7,D2,L2,V3,M2} { ! X = Z, alpha1( X, Y, Z ) }.
% 7.44/7.87 substitution0:
% 7.44/7.87 X := X
% 7.44/7.87 Y := Y
% 7.44/7.87 Z := Z
% 7.44/7.87 end
% 7.44/7.87 permutation0:
% 7.44/7.87 0 ==> 0
% 7.44/7.87 1 ==> 1
% 7.44/7.87 end
% 7.44/7.87
% 7.44/7.87 eqswap: (35166) {G0,W6,D3,L1,V1,M1} { unordered_pair( X, X ) = singleton(
% 7.44/7.87 X ) }.
% 7.44/7.87 parent0[0]: (35046) {G0,W6,D3,L1,V1,M1} { singleton( X ) = unordered_pair
% 7.44/7.87 ( X, X ) }.
% 7.44/7.87 substitution0:
% 7.44/7.87 X := X
% 7.44/7.87 end
% 7.44/7.87
% 7.44/7.87 subsumption: (13) {G0,W6,D3,L1,V1,M1} I { unordered_pair( X, X ) ==>
% 7.44/7.87 singleton( X ) }.
% 7.44/7.87 parent0: (35166) {G0,W6,D3,L1,V1,M1} { unordered_pair( X, X ) = singleton
% 7.44/7.87 ( X ) }.
% 7.44/7.87 substitution0:
% 7.44/7.87 X := X
% 7.44/7.87 end
% 7.44/7.87 permutation0:
% 7.44/7.87 0 ==> 0
% 7.44/7.87 end
% 7.44/7.87
% 7.44/7.87 eqswap: (35210) {G0,W5,D3,L1,V0,M1} { singleton( skol9 ) = singleton(
% 7.44/7.87 skol8 ) }.
% 7.44/7.87 parent0[0]: (35125) {G0,W5,D3,L1,V0,M1} { singleton( skol8 ) = singleton(
% 7.44/7.87 skol9 ) }.
% 7.44/7.87 substitution0:
% 7.44/7.87 end
% 7.44/7.87
% 7.44/7.87 subsumption: (92) {G0,W5,D3,L1,V0,M1} I { singleton( skol9 ) ==> singleton
% 7.44/7.87 ( skol8 ) }.
% 7.44/7.87 parent0: (35210) {G0,W5,D3,L1,V0,M1} { singleton( skol9 ) = singleton(
% 7.44/7.87 skol8 ) }.
% 7.44/7.87 substitution0:
% 7.44/7.87 end
% 7.44/7.87 permutation0:
% 7.44/7.87 0 ==> 0
% 7.44/7.87 end
% 7.44/7.87
% 7.44/7.87 subsumption: (93) {G0,W3,D2,L1,V0,M1} I { member( skol8, universal_class )
% 7.44/7.87 }.
% 7.44/7.87 parent0: (35126) {G0,W3,D2,L1,V0,M1} { member( skol8, universal_class )
% 7.44/7.87 }.
% 7.44/7.87 substitution0:
% 7.44/7.87 end
% 7.44/7.87 permutation0:
% 7.44/7.87 0 ==> 0
% 7.44/7.87 end
% 7.44/7.87
% 7.44/7.87 eqswap: (35299) {G0,W3,D2,L1,V0,M1} { ! skol9 = skol8 }.
% 7.44/7.87 parent0[0]: (35127) {G0,W3,D2,L1,V0,M1} { ! skol8 = skol9 }.
% 7.44/7.87 substitution0:
% 7.44/7.87 end
% 7.44/7.87
% 7.44/7.87 subsumption: (94) {G0,W3,D2,L1,V0,M1} I { ! skol9 ==> skol8 }.
% 7.44/7.87 parent0: (35299) {G0,W3,D2,L1,V0,M1} { ! skol9 = skol8 }.
% 7.44/7.87 substitution0:
% 7.44/7.87 end
% 7.44/7.87 permutation0:
% 7.44/7.87 0 ==> 0
% 7.44/7.87 end
% 7.44/7.87
% 7.44/7.87 factor: (35303) {G0,W7,D2,L2,V2,M2} { ! alpha1( X, Y, Y ), X = Y }.
% 7.44/7.87 parent0[1, 2]: (9) {G0,W10,D2,L3,V3,M3} I { ! alpha1( X, Y, Z ), X = Y, X =
% 7.44/7.87 Z }.
% 7.44/7.87 substitution0:
% 7.44/7.87 X := X
% 7.44/7.87 Y := Y
% 7.44/7.87 Z := Y
% 7.44/7.87 end
% 7.44/7.87
% 7.44/7.87 subsumption: (96) {G1,W7,D2,L2,V2,M2} F(9) { ! alpha1( X, Y, Y ), X = Y }.
% 7.44/7.87 parent0: (35303) {G0,W7,D2,L2,V2,M2} { ! alpha1( X, Y, Y ), X = Y }.
% 7.44/7.87 substitution0:
% 7.44/7.87 X := X
% 7.44/7.87 Y := Y
% 7.44/7.87 end
% 7.44/7.87 permutation0:
% 7.44/7.87 0 ==> 0
% 7.44/7.87 1 ==> 1
% 7.44/7.87 end
% 7.44/7.87
% 7.44/7.87 eqswap: (35305) {G0,W7,D2,L2,V3,M2} { ! Y = X, alpha1( X, Z, Y ) }.
% 7.44/7.87 parent0[0]: (11) {G0,W7,D2,L2,V3,M2} I { ! X = Z, alpha1( X, Y, Z ) }.
% 7.44/7.87 substitution0:
% 7.44/7.87 X := X
% 7.44/7.87 Y := Z
% 7.44/7.87 Z := Y
% 7.44/7.87 end
% 7.44/7.87
% 7.44/7.87 eqrefl: (35306) {G0,W4,D2,L1,V2,M1} { alpha1( X, Y, X ) }.
% 7.44/7.87 parent0[0]: (35305) {G0,W7,D2,L2,V3,M2} { ! Y = X, alpha1( X, Z, Y ) }.
% 7.44/7.87 substitution0:
% 7.44/7.87 X := X
% 7.44/7.87 Y := X
% 7.44/7.87 Z := Y
% 7.44/7.87 end
% 7.44/7.87
% 7.44/7.87 subsumption: (100) {G1,W4,D2,L1,V2,M1} Q(11) { alpha1( X, Y, X ) }.
% 7.44/7.87 parent0: (35306) {G0,W4,D2,L1,V2,M1} { alpha1( X, Y, X ) }.
% 7.44/7.87 substitution0:
% 7.44/7.87 X := X
% 7.44/7.87 Y := Y
% 7.44/7.87 end
% 7.44/7.87 permutation0:
% 7.44/7.87 0 ==> 0
% 7.44/7.87 end
% 7.44/7.87
% 7.44/7.87 eqswap: (35307) {G0,W6,D2,L2,V2,M2} { ! Y = X, subclass( X, Y ) }.
% 7.44/7.87 parent0[0]: (4) {G0,W6,D2,L2,V2,M2} I { ! X = Y, subclass( X, Y ) }.
% 7.44/7.87 substitution0:
% 7.44/7.87 X := X
% 7.44/7.87 Y := Y
% 7.44/7.87 end
% 7.44/7.87
% 7.44/7.87 eqswap: (35308) {G0,W6,D2,L2,V2,M2} { ! Y = X, subclass( X, Y ) }.
% 7.44/7.87 parent0[0]: (4) {G0,W6,D2,L2,V2,M2} I { ! X = Y, subclass( X, Y ) }.
% 7.44/7.87 substitution0:
% 7.44/7.87 X := X
% 7.44/7.87 Y := Y
% 7.44/7.87 end
% 7.44/7.87
% 7.44/7.87 resolution: (35309) {G1,W9,D2,L3,V2,M3} { ! subclass( Y, X ), X = Y, ! Y =
% 7.44/7.87 X }.
% 7.44/7.87 parent0[0]: (5) {G0,W9,D2,L3,V2,M3} I { ! subclass( X, Y ), ! subclass( Y,
% 7.44/7.87 X ), X = Y }.
% 7.44/7.87 parent1[1]: (35307) {G0,W6,D2,L2,V2,M2} { ! Y = X, subclass( X, Y ) }.
% 7.44/7.87 substitution0:
% 7.44/7.87 X := X
% 7.44/7.87 Y := Y
% 7.44/7.87 end
% 7.44/7.87 substitution1:
% 7.44/7.87 X := X
% 7.44/7.87 Y := Y
% 7.44/7.87 end
% 7.44/7.87
% 7.44/7.87 resolution: (35311) {G1,W9,D2,L3,V2,M3} { Y = X, ! X = Y, ! Y = X }.
% 7.44/7.87 parent0[0]: (35309) {G1,W9,D2,L3,V2,M3} { ! subclass( Y, X ), X = Y, ! Y =
% 7.44/7.87 X }.
% 7.44/7.87 parent1[1]: (35308) {G0,W6,D2,L2,V2,M2} { ! Y = X, subclass( X, Y ) }.
% 7.44/7.87 substitution0:
% 7.44/7.87 X := Y
% 7.44/7.87 Y := X
% 7.44/7.87 end
% 7.44/7.87 substitution1:
% 7.44/7.87 X := X
% 7.44/7.87 Y := Y
% 7.44/7.87 end
% 7.44/7.87
% 7.44/7.87 eqswap: (35313) {G1,W9,D2,L3,V2,M3} { ! Y = X, X = Y, ! Y = X }.
% 7.44/7.87 parent0[2]: (35311) {G1,W9,D2,L3,V2,M3} { Y = X, ! X = Y, ! Y = X }.
% 7.44/7.87 substitution0:
% 7.44/7.87 X := Y
% 7.44/7.87 Y := X
% 7.44/7.87 end
% 7.44/7.87
% 7.44/7.87 factor: (35315) {G1,W6,D2,L2,V2,M2} { ! X = Y, Y = X }.
% 7.44/7.87 parent0[0, 2]: (35313) {G1,W9,D2,L3,V2,M3} {Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------