TSTP Solution File: SET084+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET084+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Mon Jul 18 22:46:47 EDT 2022
% Result : Theorem 6.93s 7.34s
% Output : Refutation 6.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET084+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.07/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Sun Jul 10 03:01:46 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.73/1.09 *** allocated 10000 integers for termspace/termends
% 0.73/1.09 *** allocated 10000 integers for clauses
% 0.73/1.09 *** allocated 10000 integers for justifications
% 0.73/1.09 Bliksem 1.12
% 0.73/1.09
% 0.73/1.09
% 0.73/1.09 Automatic Strategy Selection
% 0.73/1.09
% 0.73/1.09
% 0.73/1.09 Clauses:
% 0.73/1.09
% 0.73/1.09 { ! subclass( X, Y ), ! member( Z, X ), member( Z, Y ) }.
% 0.73/1.09 { ! member( skol1( Z, Y ), Y ), subclass( X, Y ) }.
% 0.73/1.09 { member( skol1( X, Y ), X ), subclass( X, Y ) }.
% 0.73/1.09 { subclass( X, universal_class ) }.
% 0.73/1.09 { ! X = Y, subclass( X, Y ) }.
% 0.73/1.09 { ! X = Y, subclass( Y, X ) }.
% 0.73/1.09 { ! subclass( X, Y ), ! subclass( Y, X ), X = Y }.
% 0.73/1.09 { ! member( X, unordered_pair( Y, Z ) ), member( X, universal_class ) }.
% 0.73/1.09 { ! member( X, unordered_pair( Y, Z ) ), alpha1( X, Y, Z ) }.
% 0.73/1.09 { ! member( X, universal_class ), ! alpha1( X, Y, Z ), member( X,
% 0.73/1.09 unordered_pair( Y, Z ) ) }.
% 0.73/1.09 { ! alpha1( X, Y, Z ), X = Y, X = Z }.
% 0.73/1.09 { ! X = Y, alpha1( X, Y, Z ) }.
% 0.73/1.09 { ! X = Z, alpha1( X, Y, Z ) }.
% 0.73/1.09 { member( unordered_pair( X, Y ), universal_class ) }.
% 0.73/1.09 { singleton( X ) = unordered_pair( X, X ) }.
% 0.73/1.09 { ordered_pair( X, Y ) = unordered_pair( singleton( X ), unordered_pair( X
% 0.73/1.09 , singleton( Y ) ) ) }.
% 0.73/1.09 { ! member( ordered_pair( X, Y ), cross_product( Z, T ) ), member( X, Z ) }
% 0.73/1.09 .
% 0.73/1.09 { ! member( ordered_pair( X, Y ), cross_product( Z, T ) ), member( Y, T ) }
% 0.73/1.09 .
% 0.73/1.09 { ! member( X, Z ), ! member( Y, T ), member( ordered_pair( X, Y ),
% 0.73/1.09 cross_product( Z, T ) ) }.
% 0.73/1.09 { ! member( X, universal_class ), ! member( Y, universal_class ), first(
% 0.73/1.09 ordered_pair( X, Y ) ) = X }.
% 0.73/1.09 { ! member( X, universal_class ), ! member( Y, universal_class ), second(
% 0.73/1.09 ordered_pair( X, Y ) ) = Y }.
% 0.73/1.09 { ! member( X, cross_product( Y, Z ) ), X = ordered_pair( first( X ),
% 0.73/1.09 second( X ) ) }.
% 0.73/1.09 { ! member( ordered_pair( X, Y ), element_relation ), member( Y,
% 0.73/1.09 universal_class ) }.
% 0.73/1.09 { ! member( ordered_pair( X, Y ), element_relation ), member( X, Y ) }.
% 0.73/1.09 { ! member( Y, universal_class ), ! member( X, Y ), member( ordered_pair( X
% 0.73/1.09 , Y ), element_relation ) }.
% 0.73/1.09 { subclass( element_relation, cross_product( universal_class,
% 0.73/1.09 universal_class ) ) }.
% 0.73/1.09 { ! member( Z, intersection( X, Y ) ), member( Z, X ) }.
% 0.73/1.09 { ! member( Z, intersection( X, Y ) ), member( Z, Y ) }.
% 0.73/1.09 { ! member( Z, X ), ! member( Z, Y ), member( Z, intersection( X, Y ) ) }.
% 0.73/1.09 { ! member( Y, complement( X ) ), member( Y, universal_class ) }.
% 0.73/1.09 { ! member( Y, complement( X ) ), ! member( Y, X ) }.
% 0.73/1.09 { ! member( Y, universal_class ), member( Y, X ), member( Y, complement( X
% 0.73/1.09 ) ) }.
% 0.73/1.09 { restrict( Y, X, Z ) = intersection( Y, cross_product( X, Z ) ) }.
% 0.73/1.09 { ! member( X, null_class ) }.
% 0.73/1.09 { ! member( Y, domain_of( X ) ), member( Y, universal_class ) }.
% 0.73/1.09 { ! member( Y, domain_of( X ) ), ! restrict( X, singleton( Y ),
% 0.73/1.09 universal_class ) = null_class }.
% 0.73/1.09 { ! member( Y, universal_class ), restrict( X, singleton( Y ),
% 0.73/1.09 universal_class ) = null_class, member( Y, domain_of( X ) ) }.
% 0.73/1.09 { ! member( ordered_pair( ordered_pair( Y, Z ), T ), rotate( X ) ), member
% 0.73/1.09 ( ordered_pair( ordered_pair( Y, Z ), T ), cross_product( cross_product(
% 0.73/1.09 universal_class, universal_class ), universal_class ) ) }.
% 0.73/1.09 { ! member( ordered_pair( ordered_pair( Y, Z ), T ), rotate( X ) ), member
% 0.73/1.09 ( ordered_pair( ordered_pair( Z, T ), Y ), X ) }.
% 0.73/1.09 { ! member( ordered_pair( ordered_pair( Y, Z ), T ), cross_product(
% 0.73/1.09 cross_product( universal_class, universal_class ), universal_class ) ), !
% 0.73/1.09 member( ordered_pair( ordered_pair( Z, T ), Y ), X ), member(
% 0.73/1.09 ordered_pair( ordered_pair( Y, Z ), T ), rotate( X ) ) }.
% 0.73/1.09 { subclass( rotate( X ), cross_product( cross_product( universal_class,
% 0.73/1.09 universal_class ), universal_class ) ) }.
% 0.73/1.09 { ! member( ordered_pair( ordered_pair( X, Y ), Z ), flip( T ) ), member(
% 0.73/1.09 ordered_pair( ordered_pair( X, Y ), Z ), cross_product( cross_product(
% 0.73/1.09 universal_class, universal_class ), universal_class ) ) }.
% 0.73/1.09 { ! member( ordered_pair( ordered_pair( X, Y ), Z ), flip( T ) ), member(
% 0.73/1.09 ordered_pair( ordered_pair( Y, X ), Z ), T ) }.
% 0.73/1.09 { ! member( ordered_pair( ordered_pair( X, Y ), Z ), cross_product(
% 0.73/1.09 cross_product( universal_class, universal_class ), universal_class ) ), !
% 0.73/1.09 member( ordered_pair( ordered_pair( Y, X ), Z ), T ), member(
% 0.73/1.09 ordered_pair( ordered_pair( X, Y ), Z ), flip( T ) ) }.
% 0.73/1.09 { subclass( flip( X ), cross_product( cross_product( universal_class,
% 0.94/1.33 universal_class ), universal_class ) ) }.
% 0.94/1.33 { ! member( Z, union( X, Y ) ), member( Z, X ), member( Z, Y ) }.
% 0.94/1.33 { ! member( Z, X ), member( Z, union( X, Y ) ) }.
% 0.94/1.33 { ! member( Z, Y ), member( Z, union( X, Y ) ) }.
% 0.94/1.33 { successor( X ) = union( X, singleton( X ) ) }.
% 0.94/1.33 { subclass( successor_relation, cross_product( universal_class,
% 0.94/1.33 universal_class ) ) }.
% 0.94/1.33 { ! member( ordered_pair( X, Y ), successor_relation ), member( X,
% 0.94/1.33 universal_class ) }.
% 0.94/1.33 { ! member( ordered_pair( X, Y ), successor_relation ), alpha2( X, Y ) }.
% 0.94/1.33 { ! member( X, universal_class ), ! alpha2( X, Y ), member( ordered_pair( X
% 0.94/1.33 , Y ), successor_relation ) }.
% 0.94/1.33 { ! alpha2( X, Y ), member( Y, universal_class ) }.
% 0.94/1.33 { ! alpha2( X, Y ), successor( X ) = Y }.
% 0.94/1.33 { ! member( Y, universal_class ), ! successor( X ) = Y, alpha2( X, Y ) }.
% 0.94/1.33 { inverse( X ) = domain_of( flip( cross_product( X, universal_class ) ) ) }
% 0.94/1.33 .
% 0.94/1.33 { range_of( X ) = domain_of( inverse( X ) ) }.
% 0.94/1.33 { image( Y, X ) = range_of( restrict( Y, X, universal_class ) ) }.
% 0.94/1.33 { ! inductive( X ), member( null_class, X ) }.
% 0.94/1.33 { ! inductive( X ), subclass( image( successor_relation, X ), X ) }.
% 0.94/1.33 { ! member( null_class, X ), ! subclass( image( successor_relation, X ), X
% 0.94/1.33 ), inductive( X ) }.
% 0.94/1.33 { member( skol2, universal_class ) }.
% 0.94/1.33 { inductive( skol2 ) }.
% 0.94/1.33 { ! inductive( X ), subclass( skol2, X ) }.
% 0.94/1.33 { ! member( X, sum_class( Y ) ), member( skol3( Z, Y ), Y ) }.
% 0.94/1.33 { ! member( X, sum_class( Y ) ), member( X, skol3( X, Y ) ) }.
% 0.94/1.33 { ! member( X, Z ), ! member( Z, Y ), member( X, sum_class( Y ) ) }.
% 0.94/1.33 { ! member( X, universal_class ), member( sum_class( X ), universal_class )
% 0.94/1.33 }.
% 0.94/1.33 { ! member( X, power_class( Y ) ), member( X, universal_class ) }.
% 0.94/1.33 { ! member( X, power_class( Y ) ), subclass( X, Y ) }.
% 0.94/1.33 { ! member( X, universal_class ), ! subclass( X, Y ), member( X,
% 0.94/1.33 power_class( Y ) ) }.
% 0.94/1.33 { ! member( X, universal_class ), member( power_class( X ), universal_class
% 0.94/1.33 ) }.
% 0.94/1.33 { subclass( compose( Y, X ), cross_product( universal_class,
% 0.94/1.33 universal_class ) ) }.
% 0.94/1.33 { ! member( ordered_pair( Z, T ), compose( Y, X ) ), member( Z,
% 0.94/1.33 universal_class ) }.
% 0.94/1.33 { ! member( ordered_pair( Z, T ), compose( Y, X ) ), member( T, image( Y,
% 0.94/1.33 image( X, singleton( Z ) ) ) ) }.
% 0.94/1.33 { ! member( Z, universal_class ), ! member( T, image( Y, image( X,
% 0.94/1.33 singleton( Z ) ) ) ), member( ordered_pair( Z, T ), compose( Y, X ) ) }.
% 0.94/1.33 { ! member( X, identity_relation ), member( skol4( Y ), universal_class ) }
% 0.94/1.33 .
% 0.94/1.33 { ! member( X, identity_relation ), X = ordered_pair( skol4( X ), skol4( X
% 0.94/1.33 ) ) }.
% 0.94/1.33 { ! member( Y, universal_class ), ! X = ordered_pair( Y, Y ), member( X,
% 0.94/1.33 identity_relation ) }.
% 0.94/1.33 { ! function( X ), subclass( X, cross_product( universal_class,
% 0.94/1.33 universal_class ) ) }.
% 0.94/1.33 { ! function( X ), subclass( compose( X, inverse( X ) ), identity_relation
% 0.94/1.33 ) }.
% 0.94/1.33 { ! subclass( X, cross_product( universal_class, universal_class ) ), !
% 0.94/1.33 subclass( compose( X, inverse( X ) ), identity_relation ), function( X )
% 0.94/1.33 }.
% 0.94/1.33 { ! member( X, universal_class ), ! function( Y ), member( image( Y, X ),
% 0.94/1.33 universal_class ) }.
% 0.94/1.33 { ! disjoint( X, Y ), ! member( Z, X ), ! member( Z, Y ) }.
% 0.94/1.33 { member( skol5( Z, Y ), Y ), disjoint( X, Y ) }.
% 0.94/1.33 { member( skol5( X, Y ), X ), disjoint( X, Y ) }.
% 0.94/1.33 { X = null_class, member( skol6( Y ), universal_class ) }.
% 0.94/1.33 { X = null_class, member( skol6( X ), X ) }.
% 0.94/1.33 { X = null_class, disjoint( skol6( X ), X ) }.
% 0.94/1.33 { apply( X, Y ) = sum_class( image( X, singleton( Y ) ) ) }.
% 0.94/1.33 { function( skol7 ) }.
% 0.94/1.33 { ! member( X, universal_class ), X = null_class, member( apply( skol7, X )
% 0.94/1.33 , X ) }.
% 0.94/1.33 { singleton( skol8 ) = singleton( skol9 ) }.
% 0.94/1.33 { member( skol9, universal_class ) }.
% 0.94/1.33 { ! skol8 = skol9 }.
% 0.94/1.33
% 0.94/1.33 percentage equality = 0.153846, percentage horn = 0.885417
% 0.94/1.33 This is a problem with some equality
% 0.94/1.33
% 0.94/1.33
% 0.94/1.33
% 0.94/1.33 Options Used:
% 0.94/1.33
% 0.94/1.33 useres = 1
% 0.94/1.33 useparamod = 1
% 0.94/1.33 useeqrefl = 1
% 0.94/1.33 useeqfact = 1
% 0.94/1.33 usefactor = 1
% 0.94/1.33 usesimpsplitting = 0
% 0.94/1.33 usesimpdemod = 5
% 0.94/1.33 usesimpres = 3
% 0.94/1.33
% 0.94/1.33 resimpinuse = 1000
% 0.94/1.33 resimpclauses = 20000
% 0.94/1.33 substype = eqrewr
% 0.94/1.33 backwardsubs = 1
% 0.94/1.33 selectoldest = 5
% 0.94/1.33
% 0.94/1.33 litorderings [0] = split
% 0.94/1.33 litorderings [1] = extend the termordering, first sorting on arguments
% 6.93/7.34
% 6.93/7.34 termordering = kbo
% 6.93/7.34
% 6.93/7.34 litapriori = 0
% 6.93/7.34 termapriori = 1
% 6.93/7.34 litaposteriori = 0
% 6.93/7.34 termaposteriori = 0
% 6.93/7.34 demodaposteriori = 0
% 6.93/7.34 ordereqreflfact = 0
% 6.93/7.34
% 6.93/7.34 litselect = negord
% 6.93/7.34
% 6.93/7.34 maxweight = 15
% 6.93/7.34 maxdepth = 30000
% 6.93/7.34 maxlength = 115
% 6.93/7.34 maxnrvars = 195
% 6.93/7.34 excuselevel = 1
% 6.93/7.34 increasemaxweight = 1
% 6.93/7.34
% 6.93/7.34 maxselected = 10000000
% 6.93/7.34 maxnrclauses = 10000000
% 6.93/7.34
% 6.93/7.34 showgenerated = 0
% 6.93/7.34 showkept = 0
% 6.93/7.34 showselected = 0
% 6.93/7.34 showdeleted = 0
% 6.93/7.34 showresimp = 1
% 6.93/7.34 showstatus = 2000
% 6.93/7.34
% 6.93/7.34 prologoutput = 0
% 6.93/7.34 nrgoals = 5000000
% 6.93/7.34 totalproof = 1
% 6.93/7.34
% 6.93/7.34 Symbols occurring in the translation:
% 6.93/7.34
% 6.93/7.34 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 6.93/7.34 . [1, 2] (w:1, o:45, a:1, s:1, b:0),
% 6.93/7.34 ! [4, 1] (w:0, o:24, a:1, s:1, b:0),
% 6.93/7.34 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 6.93/7.34 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 6.93/7.34 subclass [37, 2] (w:1, o:69, a:1, s:1, b:0),
% 6.93/7.34 member [39, 2] (w:1, o:70, a:1, s:1, b:0),
% 6.93/7.34 universal_class [40, 0] (w:1, o:12, a:1, s:1, b:0),
% 6.93/7.34 unordered_pair [41, 2] (w:1, o:71, a:1, s:1, b:0),
% 6.93/7.34 singleton [42, 1] (w:1, o:31, a:1, s:1, b:0),
% 6.93/7.34 ordered_pair [43, 2] (w:1, o:72, a:1, s:1, b:0),
% 6.93/7.34 cross_product [45, 2] (w:1, o:73, a:1, s:1, b:0),
% 6.93/7.34 first [46, 1] (w:1, o:32, a:1, s:1, b:0),
% 6.93/7.34 second [47, 1] (w:1, o:33, a:1, s:1, b:0),
% 6.93/7.34 element_relation [49, 0] (w:1, o:16, a:1, s:1, b:0),
% 6.93/7.34 intersection [50, 2] (w:1, o:75, a:1, s:1, b:0),
% 6.93/7.34 complement [51, 1] (w:1, o:34, a:1, s:1, b:0),
% 6.93/7.34 restrict [53, 3] (w:1, o:84, a:1, s:1, b:0),
% 6.93/7.34 null_class [54, 0] (w:1, o:17, a:1, s:1, b:0),
% 6.93/7.34 domain_of [55, 1] (w:1, o:35, a:1, s:1, b:0),
% 6.93/7.34 rotate [57, 1] (w:1, o:29, a:1, s:1, b:0),
% 6.93/7.34 flip [58, 1] (w:1, o:36, a:1, s:1, b:0),
% 6.93/7.34 union [59, 2] (w:1, o:76, a:1, s:1, b:0),
% 6.93/7.34 successor [60, 1] (w:1, o:37, a:1, s:1, b:0),
% 6.93/7.34 successor_relation [61, 0] (w:1, o:18, a:1, s:1, b:0),
% 6.93/7.34 inverse [62, 1] (w:1, o:38, a:1, s:1, b:0),
% 6.93/7.34 range_of [63, 1] (w:1, o:30, a:1, s:1, b:0),
% 6.93/7.34 image [64, 2] (w:1, o:74, a:1, s:1, b:0),
% 6.93/7.34 inductive [65, 1] (w:1, o:39, a:1, s:1, b:0),
% 6.93/7.34 sum_class [66, 1] (w:1, o:40, a:1, s:1, b:0),
% 6.93/7.34 power_class [67, 1] (w:1, o:41, a:1, s:1, b:0),
% 6.93/7.34 compose [69, 2] (w:1, o:77, a:1, s:1, b:0),
% 6.93/7.34 identity_relation [70, 0] (w:1, o:19, a:1, s:1, b:0),
% 6.93/7.34 function [72, 1] (w:1, o:42, a:1, s:1, b:0),
% 6.93/7.34 disjoint [73, 2] (w:1, o:78, a:1, s:1, b:0),
% 6.93/7.34 apply [74, 2] (w:1, o:79, a:1, s:1, b:0),
% 6.93/7.34 alpha1 [75, 3] (w:1, o:85, a:1, s:1, b:1),
% 6.93/7.34 alpha2 [76, 2] (w:1, o:80, a:1, s:1, b:1),
% 6.93/7.34 skol1 [77, 2] (w:1, o:81, a:1, s:1, b:1),
% 6.93/7.34 skol2 [78, 0] (w:1, o:20, a:1, s:1, b:1),
% 6.93/7.34 skol3 [79, 2] (w:1, o:82, a:1, s:1, b:1),
% 6.93/7.34 skol4 [80, 1] (w:1, o:43, a:1, s:1, b:1),
% 6.93/7.34 skol5 [81, 2] (w:1, o:83, a:1, s:1, b:1),
% 6.93/7.34 skol6 [82, 1] (w:1, o:44, a:1, s:1, b:1),
% 6.93/7.34 skol7 [83, 0] (w:1, o:21, a:1, s:1, b:1),
% 6.93/7.34 skol8 [84, 0] (w:1, o:22, a:1, s:1, b:1),
% 6.93/7.34 skol9 [85, 0] (w:1, o:23, a:1, s:1, b:1).
% 6.93/7.34
% 6.93/7.34
% 6.93/7.34 Starting Search:
% 6.93/7.34
% 6.93/7.34 *** allocated 15000 integers for clauses
% 6.93/7.34 *** allocated 22500 integers for clauses
% 6.93/7.34 *** allocated 33750 integers for clauses
% 6.93/7.34 *** allocated 15000 integers for termspace/termends
% 6.93/7.34 *** allocated 50625 integers for clauses
% 6.93/7.34 Resimplifying inuse:
% 6.93/7.34 Done
% 6.93/7.34
% 6.93/7.34 *** allocated 22500 integers for termspace/termends
% 6.93/7.34 *** allocated 75937 integers for clauses
% 6.93/7.34 *** allocated 33750 integers for termspace/termends
% 6.93/7.34 *** allocated 113905 integers for clauses
% 6.93/7.34
% 6.93/7.34 Intermediate Status:
% 6.93/7.34 Generated: 5147
% 6.93/7.34 Kept: 2050
% 6.93/7.34 Inuse: 123
% 6.93/7.34 Deleted: 4
% 6.93/7.34 Deletedinuse: 1
% 6.93/7.34
% 6.93/7.34 Resimplifying inuse:
% 6.93/7.34 Done
% 6.93/7.34
% 6.93/7.34 *** allocated 170857 integers for clauses
% 6.93/7.34 *** allocated 50625 integers for termspace/termends
% 6.93/7.34 Resimplifying inuse:
% 6.93/7.34 Done
% 6.93/7.34
% 6.93/7.34 *** allocated 75937 integers for termspace/termends
% 6.93/7.34 *** allocated 256285 integers for clauses
% 6.93/7.34
% 6.93/7.34 Intermediate Status:
% 6.93/7.34 Generated: 9981
% 6.93/7.34 Kept: 4057
% 6.93/7.34 Inuse: 197
% 6.93/7.34 Deleted: 50
% 6.93/7.34 Deletedinuse: 19
% 6.93/7.34
% 6.93/7.34 Resimplifying inuse:
% 6.93/7.34 Done
% 6.93/7.34
% 6.93/7.34 Resimplifying inuse:
% 6.93/7.34 Done
% 6.93/7.34
% 6.93/7.34 *** allocated 113905 integers for termspace/termends
% 6.93/7.34 *** allocated 384427 integers for clauses
% 6.93/7.34
% 6.93/7.34 Intermediate Status:
% 6.93/7.34 Generated: 13733
% 6.93/7.34 Kept: 6070
% 6.93/7.34 Inuse: 252
% 6.93/7.34 Deleted: 62
% 6.93/7.34 Deletedinuse: 22
% 6.93/7.34
% 6.93/7.34 Resimplifying inuse:
% 6.93/7.34 Done
% 6.93/7.34
% 6.93/7.34 Resimplifying inuse:
% 6.93/7.34 Done
% 6.93/7.34
% 6.93/7.34
% 6.93/7.34 Intermediate Status:
% 6.93/7.34 Generated: 17467
% 6.93/7.34 Kept: 8077
% 6.93/7.34 Inuse: 311
% 6.93/7.34 Deleted: 75
% 6.93/7.34 Deletedinuse: 29
% 6.93/7.34
% 6.93/7.34 Resimplifying inuse:
% 6.93/7.34 Done
% 6.93/7.34
% 6.93/7.34 *** allocated 576640 integers for clauses
% 6.93/7.34 *** allocated 170857 integers for termspace/termends
% 6.93/7.34 Resimplifying inuse:
% 6.93/7.34 Done
% 6.93/7.34
% 6.93/7.34
% 6.93/7.34 Intermediate Status:
% 6.93/7.34 Generated: 24190
% 6.93/7.34 Kept: 10077
% 6.93/7.34 Inuse: 358
% 6.93/7.34 Deleted: 85
% 6.93/7.34 Deletedinuse: 34
% 6.93/7.34
% 6.93/7.34 Resimplifying inuse:
% 6.93/7.34 Done
% 6.93/7.34
% 6.93/7.34 Resimplifying inuse:
% 6.93/7.34 Done
% 6.93/7.34
% 6.93/7.34 *** allocated 864960 integers for clauses
% 6.93/7.34 *** allocated 256285 integers for termspace/termends
% 6.93/7.34
% 6.93/7.34 Intermediate Status:
% 6.93/7.34 Generated: 29588
% 6.93/7.34 Kept: 12863
% 6.93/7.34 Inuse: 365
% 6.93/7.34 Deleted: 87
% 6.93/7.34 Deletedinuse: 36
% 6.93/7.34
% 6.93/7.34 Resimplifying inuse:
% 6.93/7.34 Done
% 6.93/7.34
% 6.93/7.34 Resimplifying inuse:
% 6.93/7.34 Done
% 6.93/7.34
% 6.93/7.34
% 6.93/7.34 Intermediate Status:
% 6.93/7.34 Generated: 34336
% 6.93/7.34 Kept: 14897
% 6.93/7.34 Inuse: 392
% 6.93/7.34 Deleted: 88
% 6.93/7.34 Deletedinuse: 36
% 6.93/7.34
% 6.93/7.34 Resimplifying inuse:
% 6.93/7.34 Done
% 6.93/7.34
% 6.93/7.34 Resimplifying inuse:
% 6.93/7.34 Done
% 6.93/7.34
% 6.93/7.34
% 6.93/7.34 Intermediate Status:
% 6.93/7.34 Generated: 39186
% 6.93/7.34 Kept: 16926
% 6.93/7.34 Inuse: 441
% 6.93/7.34 Deleted: 94
% 6.93/7.34 Deletedinuse: 40
% 6.93/7.34
% 6.93/7.34 Resimplifying inuse:
% 6.93/7.34 Done
% 6.93/7.34
% 6.93/7.34 Resimplifying inuse:
% 6.93/7.34 Done
% 6.93/7.34
% 6.93/7.34
% 6.93/7.34 Intermediate Status:
% 6.93/7.34 Generated: 43439
% 6.93/7.34 Kept: 18965
% 6.93/7.34 Inuse: 482
% 6.93/7.34 Deleted: 94
% 6.93/7.34 Deletedinuse: 40
% 6.93/7.34
% 6.93/7.34 *** allocated 1297440 integers for clauses
% 6.93/7.34 Resimplifying inuse:
% 6.93/7.34 Done
% 6.93/7.34
% 6.93/7.34 *** allocated 384427 integers for termspace/termends
% 6.93/7.34 Resimplifying inuse:
% 6.93/7.34 Done
% 6.93/7.34
% 6.93/7.34 Resimplifying clauses:
% 6.93/7.34 Done
% 6.93/7.34
% 6.93/7.34
% 6.93/7.34 Intermediate Status:
% 6.93/7.34 Generated: 49453
% 6.93/7.34 Kept: 20986
% 6.93/7.34 Inuse: 502
% 6.93/7.34 Deleted: 906
% 6.93/7.34 Deletedinuse: 40
% 6.93/7.34
% 6.93/7.34 Resimplifying inuse:
% 6.93/7.34 Done
% 6.93/7.34
% 6.93/7.34 Resimplifying inuse:
% 6.93/7.34 Done
% 6.93/7.34
% 6.93/7.34
% 6.93/7.34 Intermediate Status:
% 6.93/7.34 Generated: 55966
% 6.93/7.34 Kept: 22986
% 6.93/7.34 Inuse: 537
% 6.93/7.34 Deleted: 909
% 6.93/7.34 Deletedinuse: 40
% 6.93/7.34
% 6.93/7.34 Resimplifying inuse:
% 6.93/7.34 Done
% 6.93/7.34
% 6.93/7.34 Resimplifying inuse:
% 6.93/7.34 Done
% 6.93/7.34
% 6.93/7.34
% 6.93/7.34 Intermediate Status:
% 6.93/7.34 Generated: 64439
% 6.93/7.34 Kept: 25166
% 6.93/7.34 Inuse: 591
% 6.93/7.34 Deleted: 911
% 6.93/7.34 Deletedinuse: 41
% 6.93/7.34
% 6.93/7.34 Resimplifying inuse:
% 6.93/7.34 Done
% 6.93/7.34
% 6.93/7.34 Resimplifying inuse:
% 6.93/7.34 Done
% 6.93/7.34
% 6.93/7.34
% 6.93/7.34 Intermediate Status:
% 6.93/7.34 Generated: 71678
% 6.93/7.34 Kept: 27168
% 6.93/7.34 Inuse: 651
% 6.93/7.34 Deleted: 911
% 6.93/7.34 Deletedinuse: 41
% 6.93/7.34
% 6.93/7.34 Resimplifying inuse:
% 6.93/7.34 Done
% 6.93/7.34
% 6.93/7.34 Resimplifying inuse:
% 6.93/7.34 Done
% 6.93/7.34
% 6.93/7.34 *** allocated 576640 integers for termspace/termends
% 6.93/7.34
% 6.93/7.34 Intermediate Status:
% 6.93/7.34 Generated: 78085
% 6.93/7.34 Kept: 29179
% 6.93/7.34 Inuse: 703
% 6.93/7.34 Deleted: 911
% 6.93/7.34 Deletedinuse: 41
% 6.93/7.34
% 6.93/7.34 *** allocated 1946160 integers for clauses
% 6.93/7.34 Resimplifying inuse:
% 6.93/7.34 Done
% 6.93/7.34
% 6.93/7.34 Resimplifying inuse:
% 6.93/7.34 Done
% 6.93/7.34
% 6.93/7.34
% 6.93/7.34 Intermediate Status:
% 6.93/7.34 Generated: 83809
% 6.93/7.34 Kept: 31198
% 6.93/7.34 Inuse: 763
% 6.93/7.34 Deleted: 911
% 6.93/7.34 Deletedinuse: 41
% 6.93/7.34
% 6.93/7.34 Resimplifying inuse:
% 6.93/7.34 Done
% 6.93/7.34
% 6.93/7.34 Resimplifying inuse:
% 6.93/7.34 Done
% 6.93/7.34
% 6.93/7.34
% 6.93/7.34 Intermediate Status:
% 6.93/7.34 Generated: 95746
% 6.93/7.34 Kept: 33211
% 6.93/7.34 Inuse: 790
% 6.93/7.34 Deleted: 911
% 6.93/7.34 Deletedinuse: 41
% 6.93/7.34
% 6.93/7.34 Resimplifying inuse:
% 6.93/7.34 Done
% 6.93/7.34
% 6.93/7.34
% 6.93/7.34 Bliksems!, er is een bewijs:
% 6.93/7.34 % SZS status Theorem
% 6.93/7.34 % SZS output start Refutation
% 6.93/7.34
% 6.93/7.34 (7) {G0,W9,D3,L2,V3,M2} I { ! member( X, unordered_pair( Y, Z ) ), alpha1(
% 6.93/7.34 X, Y, Z ) }.
% 6.93/7.34 (8) {G0,W12,D3,L3,V3,M3} I { ! member( X, universal_class ), ! alpha1( X, Y
% 6.93/7.34 , Z ), member( X, unordered_pair( Y, Z ) ) }.
% 6.93/7.34 (9) {G0,W10,D2,L3,V3,M3} I { ! alpha1( X, Y, Z ), X = Y, X = Z }.
% 6.93/7.34 (10) {G0,W7,D2,L2,V3,M2} I { ! X = Y, alpha1( X, Y, Z ) }.
% 6.93/7.34 (13) {G0,W6,D3,L1,V1,M1} I { unordered_pair( X, X ) ==> singleton( X ) }.
% 6.93/7.34 (92) {G0,W5,D3,L1,V0,M1} I { singleton( skol9 ) ==> singleton( skol8 ) }.
% 6.93/7.34 (93) {G0,W3,D2,L1,V0,M1} I { member( skol9, universal_class ) }.
% 6.93/7.34 (94) {G0,W3,D2,L1,V0,M1} I { ! skol9 ==> skol8 }.
% 6.93/7.34 (96) {G1,W7,D2,L2,V2,M2} F(9) { ! alpha1( X, Y, Y ), X = Y }.
% 6.93/7.34 (99) {G1,W4,D2,L1,V2,M1} Q(10) { alpha1( X, X, Y ) }.
% 6.93/7.34 (246) {G1,W9,D3,L2,V2,M2} R(8,93) { ! alpha1( skol9, X, Y ), member( skol9
% 6.93/7.34 , unordered_pair( X, Y ) ) }.
% 6.93/7.34 (11406) {G2,W7,D2,L2,V1,M2} P(96,94) { ! X = skol8, ! alpha1( skol9, X, X )
% 6.93/7.34 }.
% 6.93/7.34 (11411) {G3,W4,D2,L1,V0,M1} Q(11406) { ! alpha1( skol9, skol8, skol8 ) }.
% 6.93/7.34 (14240) {G4,W4,D3,L1,V0,M1} R(11411,7);d(13) { ! member( skol9, singleton(
% 6.93/7.34 skol8 ) ) }.
% 6.93/7.34 (14264) {G5,W8,D3,L2,V1,M2} P(96,14240) { ! member( X, singleton( skol8 ) )
% 6.93/7.34 , ! alpha1( X, skol9, skol9 ) }.
% 6.93/7.34 (35055) {G2,W13,D3,L3,V3,M3} P(96,246) { ! alpha1( X, Y, Z ), member( X,
% 6.93/7.34 unordered_pair( Y, Z ) ), ! alpha1( X, skol9, skol9 ) }.
% 6.93/7.34 (35063) {G6,W4,D2,L1,V1,M1} F(35055);d(13);d(92);r(14264) { ! alpha1( X,
% 6.93/7.34 skol9, skol9 ) }.
% 6.93/7.34 (35070) {G7,W0,D0,L0,V0,M0} R(35063,99) { }.
% 6.93/7.34
% 6.93/7.34
% 6.93/7.34 % SZS output end Refutation
% 6.93/7.34 found a proof!
% 6.93/7.34
% 6.93/7.34
% 6.93/7.34 Unprocessed initial clauses:
% 6.93/7.34
% 6.93/7.34 (35072) {G0,W9,D2,L3,V3,M3} { ! subclass( X, Y ), ! member( Z, X ), member
% 6.93/7.34 ( Z, Y ) }.
% 6.93/7.34 (35073) {G0,W8,D3,L2,V3,M2} { ! member( skol1( Z, Y ), Y ), subclass( X, Y
% 6.93/7.34 ) }.
% 6.93/7.34 (35074) {G0,W8,D3,L2,V2,M2} { member( skol1( X, Y ), X ), subclass( X, Y )
% 6.93/7.34 }.
% 6.93/7.34 (35075) {G0,W3,D2,L1,V1,M1} { subclass( X, universal_class ) }.
% 6.93/7.34 (35076) {G0,W6,D2,L2,V2,M2} { ! X = Y, subclass( X, Y ) }.
% 6.93/7.34 (35077) {G0,W6,D2,L2,V2,M2} { ! X = Y, subclass( Y, X ) }.
% 6.93/7.34 (35078) {G0,W9,D2,L3,V2,M3} { ! subclass( X, Y ), ! subclass( Y, X ), X =
% 6.93/7.34 Y }.
% 6.93/7.34 (35079) {G0,W8,D3,L2,V3,M2} { ! member( X, unordered_pair( Y, Z ) ),
% 6.93/7.34 member( X, universal_class ) }.
% 6.93/7.34 (35080) {G0,W9,D3,L2,V3,M2} { ! member( X, unordered_pair( Y, Z ) ),
% 6.93/7.34 alpha1( X, Y, Z ) }.
% 6.93/7.34 (35081) {G0,W12,D3,L3,V3,M3} { ! member( X, universal_class ), ! alpha1( X
% 6.93/7.34 , Y, Z ), member( X, unordered_pair( Y, Z ) ) }.
% 6.93/7.34 (35082) {G0,W10,D2,L3,V3,M3} { ! alpha1( X, Y, Z ), X = Y, X = Z }.
% 6.93/7.34 (35083) {G0,W7,D2,L2,V3,M2} { ! X = Y, alpha1( X, Y, Z ) }.
% 6.93/7.34 (35084) {G0,W7,D2,L2,V3,M2} { ! X = Z, alpha1( X, Y, Z ) }.
% 6.93/7.34 (35085) {G0,W5,D3,L1,V2,M1} { member( unordered_pair( X, Y ),
% 6.93/7.34 universal_class ) }.
% 6.93/7.34 (35086) {G0,W6,D3,L1,V1,M1} { singleton( X ) = unordered_pair( X, X ) }.
% 6.93/7.34 (35087) {G0,W11,D5,L1,V2,M1} { ordered_pair( X, Y ) = unordered_pair(
% 6.93/7.34 singleton( X ), unordered_pair( X, singleton( Y ) ) ) }.
% 6.93/7.34 (35088) {G0,W10,D3,L2,V4,M2} { ! member( ordered_pair( X, Y ),
% 6.93/7.34 cross_product( Z, T ) ), member( X, Z ) }.
% 6.93/7.34 (35089) {G0,W10,D3,L2,V4,M2} { ! member( ordered_pair( X, Y ),
% 6.93/7.34 cross_product( Z, T ) ), member( Y, T ) }.
% 6.93/7.34 (35090) {G0,W13,D3,L3,V4,M3} { ! member( X, Z ), ! member( Y, T ), member
% 6.93/7.34 ( ordered_pair( X, Y ), cross_product( Z, T ) ) }.
% 6.93/7.34 (35091) {G0,W12,D4,L3,V2,M3} { ! member( X, universal_class ), ! member( Y
% 6.93/7.34 , universal_class ), first( ordered_pair( X, Y ) ) = X }.
% 6.93/7.34 (35092) {G0,W12,D4,L3,V2,M3} { ! member( X, universal_class ), ! member( Y
% 6.93/7.34 , universal_class ), second( ordered_pair( X, Y ) ) = Y }.
% 6.93/7.34 (35093) {G0,W12,D4,L2,V3,M2} { ! member( X, cross_product( Y, Z ) ), X =
% 6.93/7.34 ordered_pair( first( X ), second( X ) ) }.
% 6.93/7.34 (35094) {G0,W8,D3,L2,V2,M2} { ! member( ordered_pair( X, Y ),
% 6.93/7.34 element_relation ), member( Y, universal_class ) }.
% 6.93/7.34 (35095) {G0,W8,D3,L2,V2,M2} { ! member( ordered_pair( X, Y ),
% 6.93/7.34 element_relation ), member( X, Y ) }.
% 6.93/7.34 (35096) {G0,W11,D3,L3,V2,M3} { ! member( Y, universal_class ), ! member( X
% 6.93/7.34 , Y ), member( ordered_pair( X, Y ), element_relation ) }.
% 6.93/7.34 (35097) {G0,W5,D3,L1,V0,M1} { subclass( element_relation, cross_product(
% 6.93/7.34 universal_class, universal_class ) ) }.
% 6.93/7.34 (35098) {G0,W8,D3,L2,V3,M2} { ! member( Z, intersection( X, Y ) ), member
% 6.93/7.34 ( Z, X ) }.
% 6.93/7.34 (35099) {G0,W8,D3,L2,V3,M2} { ! member( Z, intersection( X, Y ) ), member
% 6.93/7.34 ( Z, Y ) }.
% 6.93/7.34 (35100) {G0,W11,D3,L3,V3,M3} { ! member( Z, X ), ! member( Z, Y ), member
% 6.93/7.34 ( Z, intersection( X, Y ) ) }.
% 6.93/7.34 (35101) {G0,W7,D3,L2,V2,M2} { ! member( Y, complement( X ) ), member( Y,
% 6.93/7.34 universal_class ) }.
% 6.93/7.34 (35102) {G0,W7,D3,L2,V2,M2} { ! member( Y, complement( X ) ), ! member( Y
% 6.93/7.34 , X ) }.
% 6.93/7.34 (35103) {G0,W10,D3,L3,V2,M3} { ! member( Y, universal_class ), member( Y,
% 6.93/7.34 X ), member( Y, complement( X ) ) }.
% 6.93/7.34 (35104) {G0,W10,D4,L1,V3,M1} { restrict( Y, X, Z ) = intersection( Y,
% 6.93/7.34 cross_product( X, Z ) ) }.
% 6.93/7.34 (35105) {G0,W3,D2,L1,V1,M1} { ! member( X, null_class ) }.
% 6.93/7.34 (35106) {G0,W7,D3,L2,V2,M2} { ! member( Y, domain_of( X ) ), member( Y,
% 6.93/7.34 universal_class ) }.
% 6.93/7.34 (35107) {G0,W11,D4,L2,V2,M2} { ! member( Y, domain_of( X ) ), ! restrict(
% 6.93/7.34 X, singleton( Y ), universal_class ) = null_class }.
% 6.93/7.34 (35108) {G0,W14,D4,L3,V2,M3} { ! member( Y, universal_class ), restrict( X
% 6.93/7.34 , singleton( Y ), universal_class ) = null_class, member( Y, domain_of( X
% 6.93/7.34 ) ) }.
% 6.93/7.34 (35109) {G0,W19,D4,L2,V4,M2} { ! member( ordered_pair( ordered_pair( Y, Z
% 6.93/7.34 ), T ), rotate( X ) ), member( ordered_pair( ordered_pair( Y, Z ), T ),
% 6.93/7.34 cross_product( cross_product( universal_class, universal_class ),
% 6.93/7.34 universal_class ) ) }.
% 6.93/7.34 (35110) {G0,W15,D4,L2,V4,M2} { ! member( ordered_pair( ordered_pair( Y, Z
% 6.93/7.34 ), T ), rotate( X ) ), member( ordered_pair( ordered_pair( Z, T ), Y ),
% 6.93/7.34 X ) }.
% 6.93/7.34 (35111) {G0,W26,D4,L3,V4,M3} { ! member( ordered_pair( ordered_pair( Y, Z
% 6.93/7.34 ), T ), cross_product( cross_product( universal_class, universal_class )
% 6.93/7.34 , universal_class ) ), ! member( ordered_pair( ordered_pair( Z, T ), Y )
% 6.93/7.34 , X ), member( ordered_pair( ordered_pair( Y, Z ), T ), rotate( X ) ) }.
% 6.93/7.34 (35112) {G0,W8,D4,L1,V1,M1} { subclass( rotate( X ), cross_product(
% 6.93/7.34 cross_product( universal_class, universal_class ), universal_class ) )
% 6.93/7.34 }.
% 6.93/7.34 (35113) {G0,W19,D4,L2,V4,M2} { ! member( ordered_pair( ordered_pair( X, Y
% 6.93/7.34 ), Z ), flip( T ) ), member( ordered_pair( ordered_pair( X, Y ), Z ),
% 6.93/7.34 cross_product( cross_product( universal_class, universal_class ),
% 6.93/7.34 universal_class ) ) }.
% 6.93/7.34 (35114) {G0,W15,D4,L2,V4,M2} { ! member( ordered_pair( ordered_pair( X, Y
% 6.93/7.34 ), Z ), flip( T ) ), member( ordered_pair( ordered_pair( Y, X ), Z ), T
% 6.93/7.34 ) }.
% 6.93/7.34 (35115) {G0,W26,D4,L3,V4,M3} { ! member( ordered_pair( ordered_pair( X, Y
% 6.93/7.34 ), Z ), cross_product( cross_product( universal_class, universal_class )
% 6.93/7.34 , universal_class ) ), ! member( ordered_pair( ordered_pair( Y, X ), Z )
% 6.93/7.34 , T ), member( ordered_pair( ordered_pair( X, Y ), Z ), flip( T ) ) }.
% 6.93/7.34 (35116) {G0,W8,D4,L1,V1,M1} { subclass( flip( X ), cross_product(
% 6.93/7.34 cross_product( universal_class, universal_class ), universal_class ) )
% 6.93/7.34 }.
% 6.93/7.34 (35117) {G0,W11,D3,L3,V3,M3} { ! member( Z, union( X, Y ) ), member( Z, X
% 6.93/7.34 ), member( Z, Y ) }.
% 6.93/7.34 (35118) {G0,W8,D3,L2,V3,M2} { ! member( Z, X ), member( Z, union( X, Y ) )
% 6.93/7.34 }.
% 6.93/7.34 (35119) {G0,W8,D3,L2,V3,M2} { ! member( Z, Y ), member( Z, union( X, Y ) )
% 6.93/7.34 }.
% 6.93/7.34 (35120) {G0,W7,D4,L1,V1,M1} { successor( X ) = union( X, singleton( X ) )
% 6.93/7.34 }.
% 6.93/7.34 (35121) {G0,W5,D3,L1,V0,M1} { subclass( successor_relation, cross_product
% 6.93/7.34 ( universal_class, universal_class ) ) }.
% 6.93/7.34 (35122) {G0,W8,D3,L2,V2,M2} { ! member( ordered_pair( X, Y ),
% 6.93/7.34 successor_relation ), member( X, universal_class ) }.
% 6.93/7.34 (35123) {G0,W8,D3,L2,V2,M2} { ! member( ordered_pair( X, Y ),
% 6.93/7.34 successor_relation ), alpha2( X, Y ) }.
% 6.93/7.34 (35124) {G0,W11,D3,L3,V2,M3} { ! member( X, universal_class ), ! alpha2( X
% 6.93/7.34 , Y ), member( ordered_pair( X, Y ), successor_relation ) }.
% 6.93/7.34 (35125) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), member( Y, universal_class
% 6.93/7.34 ) }.
% 6.93/7.34 (35126) {G0,W7,D3,L2,V2,M2} { ! alpha2( X, Y ), successor( X ) = Y }.
% 6.93/7.34 (35127) {G0,W10,D3,L3,V2,M3} { ! member( Y, universal_class ), ! successor
% 6.93/7.34 ( X ) = Y, alpha2( X, Y ) }.
% 6.93/7.34 (35128) {G0,W8,D5,L1,V1,M1} { inverse( X ) = domain_of( flip(
% 6.93/7.34 cross_product( X, universal_class ) ) ) }.
% 6.93/7.34 (35129) {G0,W6,D4,L1,V1,M1} { range_of( X ) = domain_of( inverse( X ) )
% 6.93/7.34 }.
% 6.93/7.34 (35130) {G0,W9,D4,L1,V2,M1} { image( Y, X ) = range_of( restrict( Y, X,
% 6.93/7.34 universal_class ) ) }.
% 6.93/7.34 (35131) {G0,W5,D2,L2,V1,M2} { ! inductive( X ), member( null_class, X )
% 6.93/7.34 }.
% 6.93/7.34 (35132) {G0,W7,D3,L2,V1,M2} { ! inductive( X ), subclass( image(
% 6.93/7.34 successor_relation, X ), X ) }.
% 6.93/7.34 (35133) {G0,W10,D3,L3,V1,M3} { ! member( null_class, X ), ! subclass(
% 6.93/7.34 image( successor_relation, X ), X ), inductive( X ) }.
% 6.93/7.34 (35134) {G0,W3,D2,L1,V0,M1} { member( skol2, universal_class ) }.
% 6.93/7.34 (35135) {G0,W2,D2,L1,V0,M1} { inductive( skol2 ) }.
% 6.93/7.34 (35136) {G0,W5,D2,L2,V1,M2} { ! inductive( X ), subclass( skol2, X ) }.
% 6.93/7.34 (35137) {G0,W9,D3,L2,V3,M2} { ! member( X, sum_class( Y ) ), member( skol3
% 6.93/7.34 ( Z, Y ), Y ) }.
% 6.93/7.34 (35138) {G0,W9,D3,L2,V2,M2} { ! member( X, sum_class( Y ) ), member( X,
% 6.93/7.34 skol3( X, Y ) ) }.
% 6.93/7.34 (35139) {G0,W10,D3,L3,V3,M3} { ! member( X, Z ), ! member( Z, Y ), member
% 6.93/7.34 ( X, sum_class( Y ) ) }.
% 6.93/7.34 (35140) {G0,W7,D3,L2,V1,M2} { ! member( X, universal_class ), member(
% 6.93/7.34 sum_class( X ), universal_class ) }.
% 6.93/7.34 (35141) {G0,W7,D3,L2,V2,M2} { ! member( X, power_class( Y ) ), member( X,
% 6.93/7.34 universal_class ) }.
% 6.93/7.34 (35142) {G0,W7,D3,L2,V2,M2} { ! member( X, power_class( Y ) ), subclass( X
% 6.93/7.34 , Y ) }.
% 6.93/7.34 (35143) {G0,W10,D3,L3,V2,M3} { ! member( X, universal_class ), ! subclass
% 6.93/7.34 ( X, Y ), member( X, power_class( Y ) ) }.
% 6.93/7.34 (35144) {G0,W7,D3,L2,V1,M2} { ! member( X, universal_class ), member(
% 6.93/7.34 power_class( X ), universal_class ) }.
% 6.93/7.34 (35145) {G0,W7,D3,L1,V2,M1} { subclass( compose( Y, X ), cross_product(
% 6.93/7.34 universal_class, universal_class ) ) }.
% 6.93/7.34 (35146) {G0,W10,D3,L2,V4,M2} { ! member( ordered_pair( Z, T ), compose( Y
% 6.93/7.34 , X ) ), member( Z, universal_class ) }.
% 6.93/7.34 (35147) {G0,W15,D5,L2,V4,M2} { ! member( ordered_pair( Z, T ), compose( Y
% 6.93/7.34 , X ) ), member( T, image( Y, image( X, singleton( Z ) ) ) ) }.
% 6.93/7.34 (35148) {G0,W18,D5,L3,V4,M3} { ! member( Z, universal_class ), ! member( T
% 6.93/7.34 , image( Y, image( X, singleton( Z ) ) ) ), member( ordered_pair( Z, T )
% 6.93/7.34 , compose( Y, X ) ) }.
% 6.93/7.34 (35149) {G0,W7,D3,L2,V2,M2} { ! member( X, identity_relation ), member(
% 6.93/7.34 skol4( Y ), universal_class ) }.
% 6.93/7.34 (35150) {G0,W10,D4,L2,V1,M2} { ! member( X, identity_relation ), X =
% 6.93/7.34 ordered_pair( skol4( X ), skol4( X ) ) }.
% 6.93/7.34 (35151) {G0,W11,D3,L3,V2,M3} { ! member( Y, universal_class ), ! X =
% 6.93/7.34 ordered_pair( Y, Y ), member( X, identity_relation ) }.
% 6.93/7.34 (35152) {G0,W7,D3,L2,V1,M2} { ! function( X ), subclass( X, cross_product
% 6.93/7.34 ( universal_class, universal_class ) ) }.
% 6.93/7.34 (35153) {G0,W8,D4,L2,V1,M2} { ! function( X ), subclass( compose( X,
% 6.93/7.34 inverse( X ) ), identity_relation ) }.
% 6.93/7.34 (35154) {G0,W13,D4,L3,V1,M3} { ! subclass( X, cross_product(
% 6.93/7.34 universal_class, universal_class ) ), ! subclass( compose( X, inverse( X
% 6.93/7.34 ) ), identity_relation ), function( X ) }.
% 6.93/7.34 (35155) {G0,W10,D3,L3,V2,M3} { ! member( X, universal_class ), ! function
% 6.93/7.34 ( Y ), member( image( Y, X ), universal_class ) }.
% 6.93/7.34 (35156) {G0,W9,D2,L3,V3,M3} { ! disjoint( X, Y ), ! member( Z, X ), !
% 6.93/7.34 member( Z, Y ) }.
% 6.93/7.34 (35157) {G0,W8,D3,L2,V3,M2} { member( skol5( Z, Y ), Y ), disjoint( X, Y )
% 6.93/7.34 }.
% 6.93/7.34 (35158) {G0,W8,D3,L2,V2,M2} { member( skol5( X, Y ), X ), disjoint( X, Y )
% 6.93/7.34 }.
% 6.93/7.34 (35159) {G0,W7,D3,L2,V2,M2} { X = null_class, member( skol6( Y ),
% 6.93/7.34 universal_class ) }.
% 6.93/7.34 (35160) {G0,W7,D3,L2,V1,M2} { X = null_class, member( skol6( X ), X ) }.
% 6.93/7.34 (35161) {G0,W7,D3,L2,V1,M2} { X = null_class, disjoint( skol6( X ), X )
% 6.93/7.34 }.
% 6.93/7.34 (35162) {G0,W9,D5,L1,V2,M1} { apply( X, Y ) = sum_class( image( X,
% 6.93/7.34 singleton( Y ) ) ) }.
% 6.93/7.34 (35163) {G0,W2,D2,L1,V0,M1} { function( skol7 ) }.
% 6.93/7.34 (35164) {G0,W11,D3,L3,V1,M3} { ! member( X, universal_class ), X =
% 6.93/7.34 null_class, member( apply( skol7, X ), X ) }.
% 6.93/7.34 (35165) {G0,W5,D3,L1,V0,M1} { singleton( skol8 ) = singleton( skol9 ) }.
% 6.93/7.34 (35166) {G0,W3,D2,L1,V0,M1} { member( skol9, universal_class ) }.
% 6.93/7.34 (35167) {G0,W3,D2,L1,V0,M1} { ! skol8 = skol9 }.
% 6.93/7.34
% 6.93/7.34
% 6.93/7.34 Total Proof:
% 6.93/7.34
% 6.93/7.34 subsumption: (7) {G0,W9,D3,L2,V3,M2} I { ! member( X, unordered_pair( Y, Z
% 6.93/7.34 ) ), alpha1( X, Y, Z ) }.
% 6.93/7.34 parent0: (35080) {G0,W9,D3,L2,V3,M2} { ! member( X, unordered_pair( Y, Z )
% 6.93/7.34 ), alpha1( X, Y, Z ) }.
% 6.93/7.34 substitution0:
% 6.93/7.34 X := X
% 6.93/7.34 Y := Y
% 6.93/7.34 Z := Z
% 6.93/7.34 end
% 6.93/7.34 permutation0:
% 6.93/7.34 0 ==> 0
% 6.93/7.34 1 ==> 1
% 6.93/7.34 end
% 6.93/7.34
% 6.93/7.34 subsumption: (8) {G0,W12,D3,L3,V3,M3} I { ! member( X, universal_class ), !
% 6.93/7.34 alpha1( X, Y, Z ), member( X, unordered_pair( Y, Z ) ) }.
% 6.93/7.34 parent0: (35081) {G0,W12,D3,L3,V3,M3} { ! member( X, universal_class ), !
% 6.93/7.34 alpha1( X, Y, Z ), member( X, unordered_pair( Y, Z ) ) }.
% 6.93/7.34 substitution0:
% 6.93/7.34 X := X
% 6.93/7.34 Y := Y
% 6.93/7.34 Z := Z
% 6.93/7.34 end
% 6.93/7.34 permutation0:
% 6.93/7.34 0 ==> 0
% 6.93/7.34 1 ==> 1
% 6.93/7.34 2 ==> 2
% 6.93/7.34 end
% 6.93/7.34
% 6.93/7.34 subsumption: (9) {G0,W10,D2,L3,V3,M3} I { ! alpha1( X, Y, Z ), X = Y, X = Z
% 6.93/7.34 }.
% 6.93/7.34 parent0: (35082) {G0,W10,D2,L3,V3,M3} { ! alpha1( X, Y, Z ), X = Y, X = Z
% 6.93/7.34 }.
% 6.93/7.34 substitution0:
% 6.93/7.34 X := X
% 6.93/7.34 Y := Y
% 6.93/7.34 Z := Z
% 6.93/7.34 end
% 6.93/7.34 permutation0:
% 6.93/7.34 0 ==> 0
% 6.93/7.34 1 ==> 1
% 6.93/7.34 2 ==> 2
% 6.93/7.34 end
% 6.93/7.34
% 6.93/7.34 subsumption: (10) {G0,W7,D2,L2,V3,M2} I { ! X = Y, alpha1( X, Y, Z ) }.
% 6.93/7.34 parent0: (35083) {G0,W7,D2,L2,V3,M2} { ! X = Y, alpha1( X, Y, Z ) }.
% 6.93/7.34 substitution0:
% 6.93/7.34 X := X
% 6.93/7.34 Y := Y
% 6.93/7.34 Z := Z
% 6.93/7.34 end
% 6.93/7.34 permutation0:
% 6.93/7.34 0 ==> 0
% 6.93/7.34 1 ==> 1
% 6.93/7.34 end
% 6.93/7.34
% 6.93/7.34 eqswap: (35201) {G0,W6,D3,L1,V1,M1} { unordered_pair( X, X ) = singleton(
% 6.93/7.34 X ) }.
% 6.93/7.34 parent0[0]: (35086) {G0,W6,D3,L1,V1,M1} { singleton( X ) = unordered_pair
% 6.93/7.34 ( X, X ) }.
% 6.93/7.34 substitution0:
% 6.93/7.34 X := X
% 6.93/7.34 end
% 6.93/7.34
% 6.93/7.34 subsumption: (13) {G0,W6,D3,L1,V1,M1} I { unordered_pair( X, X ) ==>
% 6.93/7.34 singleton( X ) }.
% 263.60/264.01 parent0: (35201) {G0,W6,D3,L1,V1,M1} { unordered_pair( X, X ) = singleton
% 263.60/264.01 ( X ) }.
% 263.60/264.01 substitution0:
% 263.60/264.01 X := X
% 263.60/264.01 end
% 263.60/264.01 permutation0:
% 263.60/264.01 0 ==> 0
% 263.60/264.01 end
% 263.60/264.01
% 263.60/264.01 eqswap: (35245) {G0,W5,D3,L1,V0,M1} { singleton( skol9 ) = singleton(
% 263.60/264.01 skol8 ) }.
% 263.60/264.01 parent0[0]: (35165) {G0,W5,D3,L1,V0,M1} { singleton( skol8 ) = singleton(
% 263.60/264.01 skol9 ) }.
% 263.60/264.01 substitution0:
% 263.60/264.01 end
% 263.60/264.01
% 263.60/264.01 subsumption: (92) {G0,W5,D3,L1,V0,M1} I { singleton( skol9 ) ==> singleton
% 263.60/264.01 ( skol8 ) }.
% 263.60/264.01 parent0: (35245) {G0,W5,D3,L1,V0,M1} { singleton( skol9 ) = singleton(
% 263.60/264.01 skol8 ) }.
% 263.60/264.01 substitution0:
% 263.60/264.01 end
% 263.60/264.01 permutation0:
% 263.60/264.01 0 ==> 0
% 263.60/264.01 end
% 263.60/264.01
% 263.60/264.01 subsumption: (93) {G0,W3,D2,L1,V0,M1} I { member( skol9, universal_class )
% 263.60/264.01 }.
% 263.60/264.01 parent0: (35166) {G0,W3,D2,L1,V0,M1} { member( skol9, universal_class )
% 263.60/264.01 }.
% 263.60/264.01 substitution0:
% 263.60/264.01 end
% 263.60/264.01 permutation0:
% 263.60/264.01 0 ==> 0
% 263.60/264.01 end
% 263.60/264.01
% 263.60/264.01 eqswap: (35334) {G0,W3,D2,L1,V0,M1} { ! skol9 = skol8 }.
% 263.60/264.01 parent0[0]: (35167) {G0,W3,D2,L1,V0,M1} { ! skol8 = skol9 }.
% 263.60/264.01 substitution0:
% 263.60/264.01 end
% 263.60/264.01
% 263.60/264.01 subsumption: (94) {G0,W3,D2,L1,V0,M1} I { ! skol9 ==> skol8 }.
% 263.60/264.01 parent0: (35334) {G0,W3,D2,L1,V0,M1} { ! skol9 = skol8 }.
% 263.60/264.01 substitution0:
% 263.60/264.01 end
% 263.60/264.01 permutation0:
% 263.60/264.01 0 ==> 0
% 263.60/264.01 end
% 263.60/264.01
% 263.60/264.01 factor: (35338) {G0,W7,D2,L2,V2,M2} { ! alpha1( X, Y, Y ), X = Y }.
% 263.60/264.01 parent0[1, 2]: (9) {G0,W10,D2,L3,V3,M3} I { ! alpha1( X, Y, Z ), X = Y, X =
% 263.60/264.01 Z }.
% 263.60/264.01 substitution0:
% 263.60/264.01 X := X
% 263.60/264.01 Y := Y
% 263.60/264.01 Z := Y
% 263.60/264.01 end
% 263.60/264.01
% 263.60/264.01 subsumption: (96) {G1,W7,D2,L2,V2,M2} F(9) { ! alpha1( X, Y, Y ), X = Y }.
% 263.60/264.01 parent0: (35338) {G0,W7,D2,L2,V2,M2} { ! alpha1( X, Y, Y ), X = Y }.
% 263.60/264.01 substitution0:
% 263.60/264.01 X := X
% 263.60/264.01 Y := Y
% 263.60/264.01 end
% 263.60/264.01 permutation0:
% 263.60/264.01 0 ==> 0
% 263.60/264.01 1 ==> 1
% 263.60/264.01 end
% 263.60/264.01
% 263.60/264.01 eqswap: (35340) {G0,W7,D2,L2,V3,M2} { ! Y = X, alpha1( X, Y, Z ) }.
% 263.60/264.01 parent0[0]: (10) {G0,W7,D2,L2,V3,M2} I { ! X = Y, alpha1( X, Y, Z ) }.
% 263.60/264.01 substitution0:
% 263.60/264.01 X := X
% 263.60/264.01 Y := Y
% 263.60/264.01 Z := Z
% 263.60/264.01 end
% 263.60/264.01
% 263.60/264.01 eqrefl: (35341) {G0,W4,D2,L1,V2,M1} { alpha1( X, X, Y ) }.
% 263.60/264.01 parent0[0]: (35340) {G0,W7,D2,L2,V3,M2} { ! Y = X, alpha1( X, Y, Z ) }.
% 263.60/264.01 substitution0:
% 263.60/264.01 X := X
% 263.60/264.01 Y := X
% 263.60/264.01 Z := Y
% 263.60/264.01 end
% 263.60/264.01
% 263.60/264.01 subsumption: (99) {G1,W4,D2,L1,V2,M1} Q(10) { alpha1( X, X, Y ) }.
% 263.60/264.01 parent0: (35341) {G0,W4,D2,L1,V2,M1} { alpha1( X, X, Y ) }.
% 263.60/264.01 substitution0:
% 263.60/264.01 X := X
% 263.60/264.01 Y := Y
% 263.60/264.01 end
% 263.60/264.01 permutation0:
% 263.60/264.01 0 ==> 0
% 263.60/264.01 end
% 263.60/264.01
% 263.60/264.01 resolution: (35342) {G1,W9,D3,L2,V2,M2} { ! alpha1( skol9, X, Y ), member
% 263.60/264.01 ( skol9, unordered_pair( X, Y ) ) }.
% 263.60/264.01 parent0[0]: (8) {G0,W12,D3,L3,V3,M3} I { ! member( X, universal_class ), !
% 263.60/264.01 alpha1( X, Y, Z ), member( X, unordered_pair( Y, Z ) ) }.
% 263.60/264.01 parent1[0]: (93) {G0,W3,D2,L1,V0,M1} I { member( skol9, universal_class )
% 263.60/264.01 }.
% 263.60/264.01 substitution0:
% 263.60/264.01 X := skol9
% 263.60/264.01 Y := X
% 263.60/264.01 Z := Y
% 263.60/264.01 end
% 263.60/264.01 substitution1:
% 263.60/264.01 end
% 263.60/264.01
% 263.60/264.01 subsumption: (246) {G1,W9,D3,L2,V2,M2} R(8,93) { ! alpha1( skol9, X, Y ),
% 263.60/264.01 member( skol9, unordered_pair( X, Y ) ) }.
% 263.60/264.01 parent0: (35342) {G1,W9,D3,L2,V2,M2} { ! alpha1( skol9, X, Y ), member(
% 263.60/264.01 skol9, unordered_pair( X, Y ) ) }.
% 263.60/264.01 substitution0:
% 263.60/264.01 X := X
% 263.60/264.01 Y := Y
% 263.60/264.01 end
% 263.60/264.01 permutation0:
% 263.60/264.01 0 ==> 0
% 263.60/264.01 1 ==> 1
% 263.60/264.01 end
% 263.60/264.01
% 263.60/264.01 *** allocated 15000 integers for justifications
% 263.60/264.01 *** allocated 22500 integers for justifications
% 263.60/264.01 *** allocated 33750 integers for justifications
% 263.60/264.01 *** allocated 50625 integers for justifications
% 263.60/264.01 *** allocated 75937 integers for justifications
% 263.60/264.01 *** allocated 113905 integers for justifications
% 263.60/264.01 *** allocated 864960 integers for termspace/termends
% 263.60/264.01 *** allocated 170857 integers for justifications
% 263.60/264.01 *** allocated 256285 integers for justifications
% 263.60/264.01 *** allocated 384427 integers for justifications
% 263.60/264.01 *** allocated 1297440 integers for termspace/termends
% 263.60/264.01 *** allocated 576640 integers for justifications
% 263.60/264.01 *** allocated 2919240 integers for clauses
% 263.60/264.01 *** allocated 864960 integers for justifications
% 263.60/264.01 *** allocated 1946160 integers for termspace/termends
% 263.60/264.01 *** allocated 1297440 integers for justifications
% 263.60/264.01 eqswap: (35344) {G0,W3,D2,L1,V0,M1} { ! skol8 ==> skol9 }.
% 263.60/264.01 parent0[0]: (94) {G0,W3,D2,L1,V0,M1} I { ! skol9 ==> skol8 }.
% 263.60/264.01 substitution0:
% 263.60/264.01 end
% 263.60/264.01
% 263.60/264.01 paramod: (99092) {G1,W7,D2,L2,V1,M2} { ! skol8 ==> X, ! alpha1( skol9, X,
% 263.60/264.01 X ) }.
% 263.60/264.01 parent0[1]: (96) {G1,W7,D2,L2,V2,M2} F(9) { ! alpha1( X, Y, Y ), X = Y }.
% 263.60/264.01 parent1[0; 3]: (35344) {G0,W3,D2,L1,V0,M1} { ! skol8 ==> skol9 }.
% 263.60/264.01 substitution0:
% 263.60/264.01 X := skol9
% 263.60/264.01 Y := X
% 263.60/264.01 end
% 263.60/264.01 substitution1:
% 263.60/264.01 end
% 263.60/264.01
% 263.60/264.01 eqswap: (99134) {G1,W7,D2,L2,V1,M2} { ! X ==> skol8, ! alpha1( Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------