TSTP Solution File: SET082+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET082+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n003.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 22:46:44 EDT 2022
% Result : Theorem 1.57s 1.95s
% Output : Refutation 1.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET082+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.03/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Sat Jul 9 22:13:29 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.74/1.08 *** allocated 10000 integers for termspace/termends
% 0.74/1.08 *** allocated 10000 integers for clauses
% 0.74/1.08 *** allocated 10000 integers for justifications
% 0.74/1.08 Bliksem 1.12
% 0.74/1.08
% 0.74/1.08
% 0.74/1.08 Automatic Strategy Selection
% 0.74/1.08
% 0.74/1.08
% 0.74/1.08 Clauses:
% 0.74/1.08
% 0.74/1.08 { ! subclass( X, Y ), ! member( Z, X ), member( Z, Y ) }.
% 0.74/1.08 { ! member( skol1( Z, Y ), Y ), subclass( X, Y ) }.
% 0.74/1.08 { member( skol1( X, Y ), X ), subclass( X, Y ) }.
% 0.74/1.08 { subclass( X, universal_class ) }.
% 0.74/1.08 { ! X = Y, subclass( X, Y ) }.
% 0.74/1.08 { ! X = Y, subclass( Y, X ) }.
% 0.74/1.08 { ! subclass( X, Y ), ! subclass( Y, X ), X = Y }.
% 0.74/1.08 { ! member( X, unordered_pair( Y, Z ) ), member( X, universal_class ) }.
% 0.74/1.08 { ! member( X, unordered_pair( Y, Z ) ), alpha1( X, Y, Z ) }.
% 0.74/1.08 { ! member( X, universal_class ), ! alpha1( X, Y, Z ), member( X,
% 0.74/1.08 unordered_pair( Y, Z ) ) }.
% 0.74/1.08 { ! alpha1( X, Y, Z ), X = Y, X = Z }.
% 0.74/1.08 { ! X = Y, alpha1( X, Y, Z ) }.
% 0.74/1.08 { ! X = Z, alpha1( X, Y, Z ) }.
% 0.74/1.08 { member( unordered_pair( X, Y ), universal_class ) }.
% 0.74/1.08 { singleton( X ) = unordered_pair( X, X ) }.
% 0.74/1.08 { ordered_pair( X, Y ) = unordered_pair( singleton( X ), unordered_pair( X
% 0.74/1.08 , singleton( Y ) ) ) }.
% 0.74/1.08 { ! member( ordered_pair( X, Y ), cross_product( Z, T ) ), member( X, Z ) }
% 0.74/1.08 .
% 0.74/1.08 { ! member( ordered_pair( X, Y ), cross_product( Z, T ) ), member( Y, T ) }
% 0.74/1.08 .
% 0.74/1.08 { ! member( X, Z ), ! member( Y, T ), member( ordered_pair( X, Y ),
% 0.74/1.08 cross_product( Z, T ) ) }.
% 0.74/1.08 { ! member( X, universal_class ), ! member( Y, universal_class ), first(
% 0.74/1.08 ordered_pair( X, Y ) ) = X }.
% 0.74/1.08 { ! member( X, universal_class ), ! member( Y, universal_class ), second(
% 0.74/1.08 ordered_pair( X, Y ) ) = Y }.
% 0.74/1.08 { ! member( X, cross_product( Y, Z ) ), X = ordered_pair( first( X ),
% 0.74/1.08 second( X ) ) }.
% 0.74/1.08 { ! member( ordered_pair( X, Y ), element_relation ), member( Y,
% 0.74/1.08 universal_class ) }.
% 0.74/1.08 { ! member( ordered_pair( X, Y ), element_relation ), member( X, Y ) }.
% 0.74/1.08 { ! member( Y, universal_class ), ! member( X, Y ), member( ordered_pair( X
% 0.74/1.08 , Y ), element_relation ) }.
% 0.74/1.08 { subclass( element_relation, cross_product( universal_class,
% 0.74/1.08 universal_class ) ) }.
% 0.74/1.08 { ! member( Z, intersection( X, Y ) ), member( Z, X ) }.
% 0.74/1.08 { ! member( Z, intersection( X, Y ) ), member( Z, Y ) }.
% 0.74/1.08 { ! member( Z, X ), ! member( Z, Y ), member( Z, intersection( X, Y ) ) }.
% 0.74/1.08 { ! member( Y, complement( X ) ), member( Y, universal_class ) }.
% 0.74/1.08 { ! member( Y, complement( X ) ), ! member( Y, X ) }.
% 0.74/1.08 { ! member( Y, universal_class ), member( Y, X ), member( Y, complement( X
% 0.74/1.08 ) ) }.
% 0.74/1.08 { restrict( Y, X, Z ) = intersection( Y, cross_product( X, Z ) ) }.
% 0.74/1.08 { ! member( X, null_class ) }.
% 0.74/1.08 { ! member( Y, domain_of( X ) ), member( Y, universal_class ) }.
% 0.74/1.08 { ! member( Y, domain_of( X ) ), ! restrict( X, singleton( Y ),
% 0.74/1.08 universal_class ) = null_class }.
% 0.74/1.08 { ! member( Y, universal_class ), restrict( X, singleton( Y ),
% 0.74/1.08 universal_class ) = null_class, member( Y, domain_of( X ) ) }.
% 0.74/1.08 { ! member( ordered_pair( ordered_pair( Y, Z ), T ), rotate( X ) ), member
% 0.74/1.08 ( ordered_pair( ordered_pair( Y, Z ), T ), cross_product( cross_product(
% 0.74/1.08 universal_class, universal_class ), universal_class ) ) }.
% 0.74/1.08 { ! member( ordered_pair( ordered_pair( Y, Z ), T ), rotate( X ) ), member
% 0.74/1.08 ( ordered_pair( ordered_pair( Z, T ), Y ), X ) }.
% 0.74/1.08 { ! member( ordered_pair( ordered_pair( Y, Z ), T ), cross_product(
% 0.74/1.08 cross_product( universal_class, universal_class ), universal_class ) ), !
% 0.74/1.08 member( ordered_pair( ordered_pair( Z, T ), Y ), X ), member(
% 0.74/1.08 ordered_pair( ordered_pair( Y, Z ), T ), rotate( X ) ) }.
% 0.74/1.08 { subclass( rotate( X ), cross_product( cross_product( universal_class,
% 0.74/1.08 universal_class ), universal_class ) ) }.
% 0.74/1.08 { ! member( ordered_pair( ordered_pair( X, Y ), Z ), flip( T ) ), member(
% 0.74/1.08 ordered_pair( ordered_pair( X, Y ), Z ), cross_product( cross_product(
% 0.74/1.08 universal_class, universal_class ), universal_class ) ) }.
% 0.74/1.08 { ! member( ordered_pair( ordered_pair( X, Y ), Z ), flip( T ) ), member(
% 0.74/1.08 ordered_pair( ordered_pair( Y, X ), Z ), T ) }.
% 0.74/1.08 { ! member( ordered_pair( ordered_pair( X, Y ), Z ), cross_product(
% 0.74/1.08 cross_product( universal_class, universal_class ), universal_class ) ), !
% 0.74/1.08 member( ordered_pair( ordered_pair( Y, X ), Z ), T ), member(
% 0.74/1.08 ordered_pair( ordered_pair( X, Y ), Z ), flip( T ) ) }.
% 0.74/1.08 { subclass( flip( X ), cross_product( cross_product( universal_class,
% 0.74/1.26 universal_class ), universal_class ) ) }.
% 0.74/1.26 { ! member( Z, union( X, Y ) ), member( Z, X ), member( Z, Y ) }.
% 0.74/1.26 { ! member( Z, X ), member( Z, union( X, Y ) ) }.
% 0.74/1.26 { ! member( Z, Y ), member( Z, union( X, Y ) ) }.
% 0.74/1.26 { successor( X ) = union( X, singleton( X ) ) }.
% 0.74/1.26 { subclass( successor_relation, cross_product( universal_class,
% 0.74/1.26 universal_class ) ) }.
% 0.74/1.26 { ! member( ordered_pair( X, Y ), successor_relation ), member( X,
% 0.74/1.26 universal_class ) }.
% 0.74/1.26 { ! member( ordered_pair( X, Y ), successor_relation ), alpha2( X, Y ) }.
% 0.74/1.26 { ! member( X, universal_class ), ! alpha2( X, Y ), member( ordered_pair( X
% 0.74/1.26 , Y ), successor_relation ) }.
% 0.74/1.26 { ! alpha2( X, Y ), member( Y, universal_class ) }.
% 0.74/1.26 { ! alpha2( X, Y ), successor( X ) = Y }.
% 0.74/1.26 { ! member( Y, universal_class ), ! successor( X ) = Y, alpha2( X, Y ) }.
% 0.74/1.26 { inverse( X ) = domain_of( flip( cross_product( X, universal_class ) ) ) }
% 0.74/1.26 .
% 0.74/1.26 { range_of( X ) = domain_of( inverse( X ) ) }.
% 0.74/1.26 { image( Y, X ) = range_of( restrict( Y, X, universal_class ) ) }.
% 0.74/1.26 { ! inductive( X ), member( null_class, X ) }.
% 0.74/1.26 { ! inductive( X ), subclass( image( successor_relation, X ), X ) }.
% 0.74/1.26 { ! member( null_class, X ), ! subclass( image( successor_relation, X ), X
% 0.74/1.26 ), inductive( X ) }.
% 0.74/1.26 { member( skol2, universal_class ) }.
% 0.74/1.26 { inductive( skol2 ) }.
% 0.74/1.26 { ! inductive( X ), subclass( skol2, X ) }.
% 0.74/1.26 { ! member( X, sum_class( Y ) ), member( skol3( Z, Y ), Y ) }.
% 0.74/1.26 { ! member( X, sum_class( Y ) ), member( X, skol3( X, Y ) ) }.
% 0.74/1.26 { ! member( X, Z ), ! member( Z, Y ), member( X, sum_class( Y ) ) }.
% 0.74/1.26 { ! member( X, universal_class ), member( sum_class( X ), universal_class )
% 0.74/1.26 }.
% 0.74/1.26 { ! member( X, power_class( Y ) ), member( X, universal_class ) }.
% 0.74/1.26 { ! member( X, power_class( Y ) ), subclass( X, Y ) }.
% 0.74/1.26 { ! member( X, universal_class ), ! subclass( X, Y ), member( X,
% 0.74/1.26 power_class( Y ) ) }.
% 0.74/1.26 { ! member( X, universal_class ), member( power_class( X ), universal_class
% 0.74/1.26 ) }.
% 0.74/1.26 { subclass( compose( Y, X ), cross_product( universal_class,
% 0.74/1.26 universal_class ) ) }.
% 0.74/1.26 { ! member( ordered_pair( Z, T ), compose( Y, X ) ), member( Z,
% 0.74/1.26 universal_class ) }.
% 0.74/1.26 { ! member( ordered_pair( Z, T ), compose( Y, X ) ), member( T, image( Y,
% 0.74/1.26 image( X, singleton( Z ) ) ) ) }.
% 0.74/1.26 { ! member( Z, universal_class ), ! member( T, image( Y, image( X,
% 0.74/1.26 singleton( Z ) ) ) ), member( ordered_pair( Z, T ), compose( Y, X ) ) }.
% 0.74/1.26 { ! member( X, identity_relation ), member( skol4( Y ), universal_class ) }
% 0.74/1.26 .
% 0.74/1.26 { ! member( X, identity_relation ), X = ordered_pair( skol4( X ), skol4( X
% 0.74/1.26 ) ) }.
% 0.74/1.26 { ! member( Y, universal_class ), ! X = ordered_pair( Y, Y ), member( X,
% 0.74/1.26 identity_relation ) }.
% 0.74/1.26 { ! function( X ), subclass( X, cross_product( universal_class,
% 0.74/1.26 universal_class ) ) }.
% 0.74/1.26 { ! function( X ), subclass( compose( X, inverse( X ) ), identity_relation
% 0.74/1.26 ) }.
% 0.74/1.26 { ! subclass( X, cross_product( universal_class, universal_class ) ), !
% 0.74/1.26 subclass( compose( X, inverse( X ) ), identity_relation ), function( X )
% 0.74/1.26 }.
% 0.74/1.26 { ! member( X, universal_class ), ! function( Y ), member( image( Y, X ),
% 0.74/1.26 universal_class ) }.
% 0.74/1.26 { ! disjoint( X, Y ), ! member( Z, X ), ! member( Z, Y ) }.
% 0.74/1.26 { member( skol5( Z, Y ), Y ), disjoint( X, Y ) }.
% 0.74/1.26 { member( skol5( X, Y ), X ), disjoint( X, Y ) }.
% 0.74/1.26 { X = null_class, member( skol6( Y ), universal_class ) }.
% 0.74/1.26 { X = null_class, member( skol6( X ), X ) }.
% 0.74/1.26 { X = null_class, disjoint( skol6( X ), X ) }.
% 0.74/1.26 { apply( X, Y ) = sum_class( image( X, singleton( Y ) ) ) }.
% 0.74/1.26 { function( skol7 ) }.
% 0.74/1.26 { ! member( X, universal_class ), X = null_class, member( apply( skol7, X )
% 0.74/1.26 , X ) }.
% 0.74/1.26 { ! member( skol8, universal_class ) }.
% 0.74/1.26 { ! singleton( skol8 ) = null_class }.
% 0.74/1.26
% 0.74/1.26 percentage equality = 0.149485, percentage horn = 0.884211
% 0.74/1.26 This is a problem with some equality
% 0.74/1.26
% 0.74/1.26
% 0.74/1.26
% 0.74/1.26 Options Used:
% 0.74/1.26
% 0.74/1.26 useres = 1
% 0.74/1.26 useparamod = 1
% 0.74/1.26 useeqrefl = 1
% 0.74/1.26 useeqfact = 1
% 0.74/1.26 usefactor = 1
% 0.74/1.26 usesimpsplitting = 0
% 0.74/1.26 usesimpdemod = 5
% 0.74/1.26 usesimpres = 3
% 0.74/1.26
% 0.74/1.26 resimpinuse = 1000
% 0.74/1.26 resimpclauses = 20000
% 0.74/1.26 substype = eqrewr
% 0.74/1.26 backwardsubs = 1
% 0.74/1.26 selectoldest = 5
% 0.74/1.26
% 0.74/1.26 litorderings [0] = split
% 0.74/1.26 litorderings [1] = extend the termordering, first sorting on arguments
% 1.57/1.94
% 1.57/1.94 termordering = kbo
% 1.57/1.94
% 1.57/1.94 litapriori = 0
% 1.57/1.94 termapriori = 1
% 1.57/1.94 litaposteriori = 0
% 1.57/1.94 termaposteriori = 0
% 1.57/1.94 demodaposteriori = 0
% 1.57/1.94 ordereqreflfact = 0
% 1.57/1.94
% 1.57/1.94 litselect = negord
% 1.57/1.94
% 1.57/1.94 maxweight = 15
% 1.57/1.94 maxdepth = 30000
% 1.57/1.94 maxlength = 115
% 1.57/1.94 maxnrvars = 195
% 1.57/1.94 excuselevel = 1
% 1.57/1.94 increasemaxweight = 1
% 1.57/1.94
% 1.57/1.94 maxselected = 10000000
% 1.57/1.94 maxnrclauses = 10000000
% 1.57/1.94
% 1.57/1.94 showgenerated = 0
% 1.57/1.94 showkept = 0
% 1.57/1.94 showselected = 0
% 1.57/1.94 showdeleted = 0
% 1.57/1.94 showresimp = 1
% 1.57/1.94 showstatus = 2000
% 1.57/1.94
% 1.57/1.94 prologoutput = 0
% 1.57/1.94 nrgoals = 5000000
% 1.57/1.94 totalproof = 1
% 1.57/1.94
% 1.57/1.94 Symbols occurring in the translation:
% 1.57/1.94
% 1.57/1.94 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.57/1.94 . [1, 2] (w:1, o:44, a:1, s:1, b:0),
% 1.57/1.94 ! [4, 1] (w:0, o:23, a:1, s:1, b:0),
% 1.57/1.94 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.57/1.94 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.57/1.94 subclass [37, 2] (w:1, o:68, a:1, s:1, b:0),
% 1.57/1.94 member [39, 2] (w:1, o:69, a:1, s:1, b:0),
% 1.57/1.94 universal_class [40, 0] (w:1, o:12, a:1, s:1, b:0),
% 1.57/1.94 unordered_pair [41, 2] (w:1, o:70, a:1, s:1, b:0),
% 1.57/1.94 singleton [42, 1] (w:1, o:30, a:1, s:1, b:0),
% 1.57/1.94 ordered_pair [43, 2] (w:1, o:71, a:1, s:1, b:0),
% 1.57/1.94 cross_product [45, 2] (w:1, o:72, a:1, s:1, b:0),
% 1.57/1.94 first [46, 1] (w:1, o:31, a:1, s:1, b:0),
% 1.57/1.94 second [47, 1] (w:1, o:32, a:1, s:1, b:0),
% 1.57/1.94 element_relation [49, 0] (w:1, o:16, a:1, s:1, b:0),
% 1.57/1.94 intersection [50, 2] (w:1, o:74, a:1, s:1, b:0),
% 1.57/1.94 complement [51, 1] (w:1, o:33, a:1, s:1, b:0),
% 1.57/1.94 restrict [53, 3] (w:1, o:83, a:1, s:1, b:0),
% 1.57/1.94 null_class [54, 0] (w:1, o:17, a:1, s:1, b:0),
% 1.57/1.94 domain_of [55, 1] (w:1, o:34, a:1, s:1, b:0),
% 1.57/1.94 rotate [57, 1] (w:1, o:28, a:1, s:1, b:0),
% 1.57/1.94 flip [58, 1] (w:1, o:35, a:1, s:1, b:0),
% 1.57/1.94 union [59, 2] (w:1, o:75, a:1, s:1, b:0),
% 1.57/1.94 successor [60, 1] (w:1, o:36, a:1, s:1, b:0),
% 1.57/1.94 successor_relation [61, 0] (w:1, o:18, a:1, s:1, b:0),
% 1.57/1.94 inverse [62, 1] (w:1, o:37, a:1, s:1, b:0),
% 1.57/1.94 range_of [63, 1] (w:1, o:29, a:1, s:1, b:0),
% 1.57/1.94 image [64, 2] (w:1, o:73, a:1, s:1, b:0),
% 1.57/1.94 inductive [65, 1] (w:1, o:38, a:1, s:1, b:0),
% 1.57/1.94 sum_class [66, 1] (w:1, o:39, a:1, s:1, b:0),
% 1.57/1.94 power_class [67, 1] (w:1, o:40, a:1, s:1, b:0),
% 1.57/1.94 compose [69, 2] (w:1, o:76, a:1, s:1, b:0),
% 1.57/1.94 identity_relation [70, 0] (w:1, o:19, a:1, s:1, b:0),
% 1.57/1.94 function [72, 1] (w:1, o:41, a:1, s:1, b:0),
% 1.57/1.94 disjoint [73, 2] (w:1, o:77, a:1, s:1, b:0),
% 1.57/1.94 apply [74, 2] (w:1, o:78, a:1, s:1, b:0),
% 1.57/1.94 alpha1 [75, 3] (w:1, o:84, a:1, s:1, b:1),
% 1.57/1.94 alpha2 [76, 2] (w:1, o:79, a:1, s:1, b:1),
% 1.57/1.94 skol1 [77, 2] (w:1, o:80, a:1, s:1, b:1),
% 1.57/1.94 skol2 [78, 0] (w:1, o:20, a:1, s:1, b:1),
% 1.57/1.94 skol3 [79, 2] (w:1, o:81, a:1, s:1, b:1),
% 1.57/1.94 skol4 [80, 1] (w:1, o:42, a:1, s:1, b:1),
% 1.57/1.94 skol5 [81, 2] (w:1, o:82, a:1, s:1, b:1),
% 1.57/1.94 skol6 [82, 1] (w:1, o:43, a:1, s:1, b:1),
% 1.57/1.94 skol7 [83, 0] (w:1, o:21, a:1, s:1, b:1),
% 1.57/1.94 skol8 [84, 0] (w:1, o:22, a:1, s:1, b:1).
% 1.57/1.94
% 1.57/1.94
% 1.57/1.94 Starting Search:
% 1.57/1.94
% 1.57/1.94 *** allocated 15000 integers for clauses
% 1.57/1.94 *** allocated 22500 integers for clauses
% 1.57/1.94 *** allocated 33750 integers for clauses
% 1.57/1.94 *** allocated 50625 integers for clauses
% 1.57/1.94 *** allocated 15000 integers for termspace/termends
% 1.57/1.94 Resimplifying inuse:
% 1.57/1.94 Done
% 1.57/1.94
% 1.57/1.94 *** allocated 75937 integers for clauses
% 1.57/1.94 *** allocated 22500 integers for termspace/termends
% 1.57/1.94 *** allocated 33750 integers for termspace/termends
% 1.57/1.94 *** allocated 113905 integers for clauses
% 1.57/1.94
% 1.57/1.94 Intermediate Status:
% 1.57/1.94 Generated: 4199
% 1.57/1.94 Kept: 2015
% 1.57/1.94 Inuse: 134
% 1.57/1.94 Deleted: 5
% 1.57/1.94 Deletedinuse: 3
% 1.57/1.94
% 1.57/1.94 Resimplifying inuse:
% 1.57/1.94 Done
% 1.57/1.94
% 1.57/1.94 *** allocated 170857 integers for clauses
% 1.57/1.94 *** allocated 50625 integers for termspace/termends
% 1.57/1.94 Resimplifying inuse:
% 1.57/1.94 Done
% 1.57/1.94
% 1.57/1.94 *** allocated 75937 integers for termspace/termends
% 1.57/1.94 *** allocated 256285 integers for clauses
% 1.57/1.94
% 1.57/1.94 Intermediate Status:
% 1.57/1.94 Generated: 9676
% 1.57/1.94 Kept: 4028
% 1.57/1.94 Inuse: 213
% 1.57/1.94 Deleted: 14
% 1.57/1.94 Deletedinuse: 8
% 1.57/1.94
% 1.57/1.94 Resimplifying inuse:
% 1.57/1.94 Done
% 1.57/1.94
% 1.57/1.94 Resimplifying inuse:
% 1.57/1.94 Done
% 1.57/1.94
% 1.57/1.94 *** allocated 113905 integers for termspace/termends
% 1.57/1.94 *** allocated 384427 integers for clauses
% 1.57/1.94
% 1.57/1.94 Intermediate Status:
% 1.57/1.95 Generated: 13473
% 1.57/1.95 Kept: 6044
% 1.57/1.95 Inuse: 276
% 1.57/1.95 Deleted: 56
% 1.57/1.95 Deletedinuse: 45
% 1.57/1.95
% 1.57/1.95 Resimplifying inuse:
% 1.57/1.95 Done
% 1.57/1.95
% 1.57/1.95 Resimplifying inuse:
% 1.57/1.95 Done
% 1.57/1.95
% 1.57/1.95
% 1.57/1.95 Intermediate Status:
% 1.57/1.95 Generated: 17199
% 1.57/1.95 Kept: 8048
% 1.57/1.95 Inuse: 346
% 1.57/1.95 Deleted: 67
% 1.57/1.95 Deletedinuse: 53
% 1.57/1.95
% 1.57/1.95 *** allocated 576640 integers for clauses
% 1.57/1.95 Resimplifying inuse:
% 1.57/1.95 Done
% 1.57/1.95
% 1.57/1.95 *** allocated 170857 integers for termspace/termends
% 1.57/1.95 Resimplifying inuse:
% 1.57/1.95 Done
% 1.57/1.95
% 1.57/1.95
% 1.57/1.95 Intermediate Status:
% 1.57/1.95 Generated: 25273
% 1.57/1.95 Kept: 11301
% 1.57/1.95 Inuse: 392
% 1.57/1.95 Deleted: 76
% 1.57/1.95 Deletedinuse: 57
% 1.57/1.95
% 1.57/1.95 Resimplifying inuse:
% 1.57/1.95 Done
% 1.57/1.95
% 1.57/1.95 *** allocated 864960 integers for clauses
% 1.57/1.95 Resimplifying inuse:
% 1.57/1.95 Done
% 1.57/1.95
% 1.57/1.95 *** allocated 256285 integers for termspace/termends
% 1.57/1.95
% 1.57/1.95 Intermediate Status:
% 1.57/1.95 Generated: 31743
% 1.57/1.95 Kept: 13827
% 1.57/1.95 Inuse: 402
% 1.57/1.95 Deleted: 78
% 1.57/1.95 Deletedinuse: 59
% 1.57/1.95
% 1.57/1.95 Resimplifying inuse:
% 1.57/1.95 Done
% 1.57/1.95
% 1.57/1.95 Resimplifying inuse:
% 1.57/1.95 Done
% 1.57/1.95
% 1.57/1.95
% 1.57/1.95 Intermediate Status:
% 1.57/1.95 Generated: 36239
% 1.57/1.95 Kept: 15848
% 1.57/1.95 Inuse: 460
% 1.57/1.95 Deleted: 84
% 1.57/1.95 Deletedinuse: 62
% 1.57/1.95
% 1.57/1.95 Resimplifying inuse:
% 1.57/1.95 Done
% 1.57/1.95
% 1.57/1.95
% 1.57/1.95 Bliksems!, er is een bewijs:
% 1.57/1.95 % SZS status Theorem
% 1.57/1.95 % SZS output start Refutation
% 1.57/1.95
% 1.57/1.95 (0) {G0,W9,D2,L3,V3,M3} I { ! subclass( X, Y ), ! member( Z, X ), member( Z
% 1.57/1.95 , Y ) }.
% 1.57/1.95 (2) {G0,W8,D3,L2,V2,M2} I { member( skol1( X, Y ), X ), subclass( X, Y )
% 1.57/1.95 }.
% 1.57/1.95 (3) {G0,W3,D2,L1,V1,M1} I { subclass( X, universal_class ) }.
% 1.57/1.95 (4) {G0,W6,D2,L2,V2,M2} I { ! X = Y, subclass( X, Y ) }.
% 1.57/1.95 (5) {G0,W9,D2,L3,V2,M3} I { ! subclass( X, Y ), ! subclass( Y, X ), X = Y
% 1.57/1.95 }.
% 1.57/1.95 (7) {G0,W9,D3,L2,V3,M2} I { ! member( X, unordered_pair( Y, Z ) ), alpha1(
% 1.57/1.95 X, Y, Z ) }.
% 1.57/1.95 (9) {G0,W10,D2,L3,V3,M3} I { ! alpha1( X, Y, Z ), X = Y, X = Z }.
% 1.57/1.95 (13) {G0,W6,D3,L1,V1,M1} I { unordered_pair( X, X ) ==> singleton( X ) }.
% 1.57/1.95 (32) {G0,W3,D2,L1,V1,M1} I { ! member( X, null_class ) }.
% 1.57/1.95 (58) {G0,W5,D2,L2,V1,M2} I { ! inductive( X ), member( null_class, X ) }.
% 1.57/1.95 (62) {G0,W2,D2,L1,V0,M1} I { inductive( skol2 ) }.
% 1.57/1.95 (83) {G0,W9,D2,L3,V3,M3} I { ! disjoint( X, Y ), ! member( Z, X ), ! member
% 1.57/1.95 ( Z, Y ) }.
% 1.57/1.95 (84) {G0,W8,D3,L2,V3,M2} I { member( skol5( Z, Y ), Y ), disjoint( X, Y )
% 1.57/1.95 }.
% 1.57/1.95 (86) {G0,W7,D3,L2,V2,M2} I { X = null_class, member( skol6( Y ),
% 1.57/1.95 universal_class ) }.
% 1.57/1.95 (87) {G0,W7,D3,L2,V1,M2} I { X = null_class, member( skol6( X ), X ) }.
% 1.57/1.95 (92) {G0,W3,D2,L1,V0,M1} I { ! member( skol8, universal_class ) }.
% 1.57/1.95 (93) {G0,W4,D3,L1,V0,M1} I { ! singleton( skol8 ) ==> null_class }.
% 1.57/1.95 (95) {G1,W7,D2,L2,V2,M2} F(9) { ! alpha1( X, Y, Y ), X = Y }.
% 1.57/1.95 (113) {G1,W6,D2,L2,V2,M2} R(0,3) { ! member( X, Y ), member( X,
% 1.57/1.95 universal_class ) }.
% 1.57/1.95 (115) {G1,W3,D2,L1,V1,M1} R(92,0);r(3) { ! member( skol8, X ) }.
% 1.57/1.95 (122) {G1,W3,D2,L1,V0,M1} R(58,62) { member( null_class, skol2 ) }.
% 1.57/1.95 (125) {G1,W3,D2,L1,V1,M1} R(2,32) { subclass( null_class, X ) }.
% 1.57/1.95 (131) {G2,W3,D2,L1,V0,M1} R(113,122) { member( null_class, universal_class
% 1.57/1.95 ) }.
% 1.57/1.95 (137) {G1,W6,D2,L2,V2,M2} R(5,4);r(4) { X = Y, ! Y = X }.
% 1.57/1.95 (209) {G2,W6,D2,L2,V2,M2} P(137,125) { subclass( X, Y ), ! X = null_class
% 1.57/1.95 }.
% 1.57/1.95 (218) {G2,W6,D2,L2,V2,M2} P(137,115) { ! member( X, Y ), ! X = skol8 }.
% 1.57/1.95 (235) {G3,W3,D2,L1,V0,M1} R(218,131) { ! skol8 ==> null_class }.
% 1.57/1.95 (253) {G4,W6,D2,L2,V1,M2} P(5,235);r(209) { ! X = null_class, ! subclass(
% 1.57/1.95 skol8, X ) }.
% 1.57/1.95 (254) {G5,W3,D2,L1,V0,M1} Q(253) { ! subclass( skol8, null_class ) }.
% 1.57/1.95 (255) {G6,W5,D3,L1,V0,M1} R(254,2) { member( skol1( skol8, null_class ),
% 1.57/1.95 skol8 ) }.
% 1.57/1.95 (8516) {G2,W9,D2,L3,V3,M3} R(83,113) { ! disjoint( universal_class, X ), !
% 1.57/1.95 member( Y, X ), ! member( Y, Z ) }.
% 1.57/1.95 (8533) {G3,W6,D2,L2,V2,M2} F(8516) { ! disjoint( universal_class, X ), !
% 1.57/1.95 member( Y, X ) }.
% 1.57/1.95 (8604) {G7,W3,D2,L1,V0,M1} R(8533,255) { ! disjoint( universal_class, skol8
% 1.57/1.95 ) }.
% 1.57/1.95 (8660) {G8,W5,D3,L1,V1,M1} R(84,8604) { member( skol5( X, skol8 ), skol8 )
% 1.57/1.95 }.
% 1.57/1.95 (8904) {G9,W4,D3,L1,V1,M1} P(86,8660);r(32) { member( skol6( Y ),
% 1.57/1.95 universal_class ) }.
% 1.57/1.95 (8962) {G10,W4,D3,L1,V1,M1} R(8904,218) { ! skol6( X ) ==> skol8 }.
% 1.57/1.95 (10076) {G11,W8,D3,L2,V2,M2} P(95,8962) { ! Y = skol8, ! alpha1( skol6( X )
% 1.57/1.95 , Y, Y ) }.
% 1.57/1.95 (11294) {G12,W5,D3,L1,V1,M1} Q(10076) { ! alpha1( skol6( X ), skol8, skol8
% 1.57/1.95 ) }.
% 1.57/1.95 (15903) {G13,W5,D3,L1,V1,M1} R(11294,7);d(13) { ! member( skol6( X ),
% 1.57/1.95 singleton( skol8 ) ) }.
% 1.57/1.95 (15956) {G14,W4,D3,L1,V0,M1} R(15903,87) { singleton( skol8 ) ==>
% 1.57/1.95 null_class }.
% 1.57/1.95 (15970) {G15,W0,D0,L0,V0,M0} S(15956);r(93) { }.
% 1.57/1.95
% 1.57/1.95
% 1.57/1.95 % SZS output end Refutation
% 1.57/1.95 found a proof!
% 1.57/1.95
% 1.57/1.95
% 1.57/1.95 Unprocessed initial clauses:
% 1.57/1.95
% 1.57/1.95 (15972) {G0,W9,D2,L3,V3,M3} { ! subclass( X, Y ), ! member( Z, X ), member
% 1.57/1.95 ( Z, Y ) }.
% 1.57/1.95 (15973) {G0,W8,D3,L2,V3,M2} { ! member( skol1( Z, Y ), Y ), subclass( X, Y
% 1.57/1.95 ) }.
% 1.57/1.95 (15974) {G0,W8,D3,L2,V2,M2} { member( skol1( X, Y ), X ), subclass( X, Y )
% 1.57/1.95 }.
% 1.57/1.95 (15975) {G0,W3,D2,L1,V1,M1} { subclass( X, universal_class ) }.
% 1.57/1.95 (15976) {G0,W6,D2,L2,V2,M2} { ! X = Y, subclass( X, Y ) }.
% 1.57/1.95 (15977) {G0,W6,D2,L2,V2,M2} { ! X = Y, subclass( Y, X ) }.
% 1.57/1.95 (15978) {G0,W9,D2,L3,V2,M3} { ! subclass( X, Y ), ! subclass( Y, X ), X =
% 1.57/1.95 Y }.
% 1.57/1.95 (15979) {G0,W8,D3,L2,V3,M2} { ! member( X, unordered_pair( Y, Z ) ),
% 1.57/1.95 member( X, universal_class ) }.
% 1.57/1.95 (15980) {G0,W9,D3,L2,V3,M2} { ! member( X, unordered_pair( Y, Z ) ),
% 1.57/1.95 alpha1( X, Y, Z ) }.
% 1.57/1.95 (15981) {G0,W12,D3,L3,V3,M3} { ! member( X, universal_class ), ! alpha1( X
% 1.57/1.95 , Y, Z ), member( X, unordered_pair( Y, Z ) ) }.
% 1.57/1.95 (15982) {G0,W10,D2,L3,V3,M3} { ! alpha1( X, Y, Z ), X = Y, X = Z }.
% 1.57/1.95 (15983) {G0,W7,D2,L2,V3,M2} { ! X = Y, alpha1( X, Y, Z ) }.
% 1.57/1.95 (15984) {G0,W7,D2,L2,V3,M2} { ! X = Z, alpha1( X, Y, Z ) }.
% 1.57/1.95 (15985) {G0,W5,D3,L1,V2,M1} { member( unordered_pair( X, Y ),
% 1.57/1.95 universal_class ) }.
% 1.57/1.95 (15986) {G0,W6,D3,L1,V1,M1} { singleton( X ) = unordered_pair( X, X ) }.
% 1.57/1.95 (15987) {G0,W11,D5,L1,V2,M1} { ordered_pair( X, Y ) = unordered_pair(
% 1.57/1.95 singleton( X ), unordered_pair( X, singleton( Y ) ) ) }.
% 1.57/1.95 (15988) {G0,W10,D3,L2,V4,M2} { ! member( ordered_pair( X, Y ),
% 1.57/1.95 cross_product( Z, T ) ), member( X, Z ) }.
% 1.57/1.95 (15989) {G0,W10,D3,L2,V4,M2} { ! member( ordered_pair( X, Y ),
% 1.57/1.95 cross_product( Z, T ) ), member( Y, T ) }.
% 1.57/1.95 (15990) {G0,W13,D3,L3,V4,M3} { ! member( X, Z ), ! member( Y, T ), member
% 1.57/1.95 ( ordered_pair( X, Y ), cross_product( Z, T ) ) }.
% 1.57/1.95 (15991) {G0,W12,D4,L3,V2,M3} { ! member( X, universal_class ), ! member( Y
% 1.57/1.95 , universal_class ), first( ordered_pair( X, Y ) ) = X }.
% 1.57/1.95 (15992) {G0,W12,D4,L3,V2,M3} { ! member( X, universal_class ), ! member( Y
% 1.57/1.95 , universal_class ), second( ordered_pair( X, Y ) ) = Y }.
% 1.57/1.95 (15993) {G0,W12,D4,L2,V3,M2} { ! member( X, cross_product( Y, Z ) ), X =
% 1.57/1.95 ordered_pair( first( X ), second( X ) ) }.
% 1.57/1.95 (15994) {G0,W8,D3,L2,V2,M2} { ! member( ordered_pair( X, Y ),
% 1.57/1.95 element_relation ), member( Y, universal_class ) }.
% 1.57/1.95 (15995) {G0,W8,D3,L2,V2,M2} { ! member( ordered_pair( X, Y ),
% 1.57/1.95 element_relation ), member( X, Y ) }.
% 1.57/1.95 (15996) {G0,W11,D3,L3,V2,M3} { ! member( Y, universal_class ), ! member( X
% 1.57/1.95 , Y ), member( ordered_pair( X, Y ), element_relation ) }.
% 1.57/1.95 (15997) {G0,W5,D3,L1,V0,M1} { subclass( element_relation, cross_product(
% 1.57/1.95 universal_class, universal_class ) ) }.
% 1.57/1.95 (15998) {G0,W8,D3,L2,V3,M2} { ! member( Z, intersection( X, Y ) ), member
% 1.57/1.95 ( Z, X ) }.
% 1.57/1.95 (15999) {G0,W8,D3,L2,V3,M2} { ! member( Z, intersection( X, Y ) ), member
% 1.57/1.95 ( Z, Y ) }.
% 1.57/1.95 (16000) {G0,W11,D3,L3,V3,M3} { ! member( Z, X ), ! member( Z, Y ), member
% 1.57/1.95 ( Z, intersection( X, Y ) ) }.
% 1.57/1.95 (16001) {G0,W7,D3,L2,V2,M2} { ! member( Y, complement( X ) ), member( Y,
% 1.57/1.95 universal_class ) }.
% 1.57/1.95 (16002) {G0,W7,D3,L2,V2,M2} { ! member( Y, complement( X ) ), ! member( Y
% 1.57/1.95 , X ) }.
% 1.57/1.95 (16003) {G0,W10,D3,L3,V2,M3} { ! member( Y, universal_class ), member( Y,
% 1.57/1.95 X ), member( Y, complement( X ) ) }.
% 1.57/1.95 (16004) {G0,W10,D4,L1,V3,M1} { restrict( Y, X, Z ) = intersection( Y,
% 1.57/1.95 cross_product( X, Z ) ) }.
% 1.57/1.95 (16005) {G0,W3,D2,L1,V1,M1} { ! member( X, null_class ) }.
% 1.57/1.95 (16006) {G0,W7,D3,L2,V2,M2} { ! member( Y, domain_of( X ) ), member( Y,
% 1.57/1.95 universal_class ) }.
% 1.57/1.95 (16007) {G0,W11,D4,L2,V2,M2} { ! member( Y, domain_of( X ) ), ! restrict(
% 1.57/1.95 X, singleton( Y ), universal_class ) = null_class }.
% 1.57/1.95 (16008) {G0,W14,D4,L3,V2,M3} { ! member( Y, universal_class ), restrict( X
% 1.57/1.95 , singleton( Y ), universal_class ) = null_class, member( Y, domain_of( X
% 1.57/1.95 ) ) }.
% 1.57/1.95 (16009) {G0,W19,D4,L2,V4,M2} { ! member( ordered_pair( ordered_pair( Y, Z
% 1.57/1.95 ), T ), rotate( X ) ), member( ordered_pair( ordered_pair( Y, Z ), T ),
% 1.57/1.95 cross_product( cross_product( universal_class, universal_class ),
% 1.57/1.95 universal_class ) ) }.
% 1.57/1.95 (16010) {G0,W15,D4,L2,V4,M2} { ! member( ordered_pair( ordered_pair( Y, Z
% 1.57/1.95 ), T ), rotate( X ) ), member( ordered_pair( ordered_pair( Z, T ), Y ),
% 1.57/1.95 X ) }.
% 1.57/1.95 (16011) {G0,W26,D4,L3,V4,M3} { ! member( ordered_pair( ordered_pair( Y, Z
% 1.57/1.95 ), T ), cross_product( cross_product( universal_class, universal_class )
% 1.57/1.95 , universal_class ) ), ! member( ordered_pair( ordered_pair( Z, T ), Y )
% 1.57/1.95 , X ), member( ordered_pair( ordered_pair( Y, Z ), T ), rotate( X ) ) }.
% 1.57/1.95 (16012) {G0,W8,D4,L1,V1,M1} { subclass( rotate( X ), cross_product(
% 1.57/1.95 cross_product( universal_class, universal_class ), universal_class ) )
% 1.57/1.95 }.
% 1.57/1.95 (16013) {G0,W19,D4,L2,V4,M2} { ! member( ordered_pair( ordered_pair( X, Y
% 1.57/1.95 ), Z ), flip( T ) ), member( ordered_pair( ordered_pair( X, Y ), Z ),
% 1.57/1.95 cross_product( cross_product( universal_class, universal_class ),
% 1.57/1.95 universal_class ) ) }.
% 1.57/1.95 (16014) {G0,W15,D4,L2,V4,M2} { ! member( ordered_pair( ordered_pair( X, Y
% 1.57/1.95 ), Z ), flip( T ) ), member( ordered_pair( ordered_pair( Y, X ), Z ), T
% 1.57/1.95 ) }.
% 1.57/1.95 (16015) {G0,W26,D4,L3,V4,M3} { ! member( ordered_pair( ordered_pair( X, Y
% 1.57/1.95 ), Z ), cross_product( cross_product( universal_class, universal_class )
% 1.57/1.95 , universal_class ) ), ! member( ordered_pair( ordered_pair( Y, X ), Z )
% 1.57/1.95 , T ), member( ordered_pair( ordered_pair( X, Y ), Z ), flip( T ) ) }.
% 1.57/1.95 (16016) {G0,W8,D4,L1,V1,M1} { subclass( flip( X ), cross_product(
% 1.57/1.95 cross_product( universal_class, universal_class ), universal_class ) )
% 1.57/1.95 }.
% 1.57/1.95 (16017) {G0,W11,D3,L3,V3,M3} { ! member( Z, union( X, Y ) ), member( Z, X
% 1.57/1.95 ), member( Z, Y ) }.
% 1.57/1.95 (16018) {G0,W8,D3,L2,V3,M2} { ! member( Z, X ), member( Z, union( X, Y ) )
% 1.57/1.95 }.
% 1.57/1.95 (16019) {G0,W8,D3,L2,V3,M2} { ! member( Z, Y ), member( Z, union( X, Y ) )
% 1.57/1.95 }.
% 1.57/1.95 (16020) {G0,W7,D4,L1,V1,M1} { successor( X ) = union( X, singleton( X ) )
% 1.57/1.95 }.
% 1.57/1.95 (16021) {G0,W5,D3,L1,V0,M1} { subclass( successor_relation, cross_product
% 1.57/1.95 ( universal_class, universal_class ) ) }.
% 1.57/1.95 (16022) {G0,W8,D3,L2,V2,M2} { ! member( ordered_pair( X, Y ),
% 1.57/1.95 successor_relation ), member( X, universal_class ) }.
% 1.57/1.95 (16023) {G0,W8,D3,L2,V2,M2} { ! member( ordered_pair( X, Y ),
% 1.57/1.95 successor_relation ), alpha2( X, Y ) }.
% 1.57/1.95 (16024) {G0,W11,D3,L3,V2,M3} { ! member( X, universal_class ), ! alpha2( X
% 1.57/1.95 , Y ), member( ordered_pair( X, Y ), successor_relation ) }.
% 1.57/1.95 (16025) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), member( Y, universal_class
% 1.57/1.95 ) }.
% 1.57/1.95 (16026) {G0,W7,D3,L2,V2,M2} { ! alpha2( X, Y ), successor( X ) = Y }.
% 1.57/1.95 (16027) {G0,W10,D3,L3,V2,M3} { ! member( Y, universal_class ), ! successor
% 1.57/1.95 ( X ) = Y, alpha2( X, Y ) }.
% 1.57/1.95 (16028) {G0,W8,D5,L1,V1,M1} { inverse( X ) = domain_of( flip(
% 1.57/1.95 cross_product( X, universal_class ) ) ) }.
% 1.57/1.95 (16029) {G0,W6,D4,L1,V1,M1} { range_of( X ) = domain_of( inverse( X ) )
% 1.57/1.95 }.
% 1.57/1.95 (16030) {G0,W9,D4,L1,V2,M1} { image( Y, X ) = range_of( restrict( Y, X,
% 1.57/1.95 universal_class ) ) }.
% 1.57/1.95 (16031) {G0,W5,D2,L2,V1,M2} { ! inductive( X ), member( null_class, X )
% 1.57/1.95 }.
% 1.57/1.95 (16032) {G0,W7,D3,L2,V1,M2} { ! inductive( X ), subclass( image(
% 1.57/1.95 successor_relation, X ), X ) }.
% 1.57/1.95 (16033) {G0,W10,D3,L3,V1,M3} { ! member( null_class, X ), ! subclass(
% 1.57/1.95 image( successor_relation, X ), X ), inductive( X ) }.
% 1.57/1.95 (16034) {G0,W3,D2,L1,V0,M1} { member( skol2, universal_class ) }.
% 1.57/1.95 (16035) {G0,W2,D2,L1,V0,M1} { inductive( skol2 ) }.
% 1.57/1.95 (16036) {G0,W5,D2,L2,V1,M2} { ! inductive( X ), subclass( skol2, X ) }.
% 1.57/1.95 (16037) {G0,W9,D3,L2,V3,M2} { ! member( X, sum_class( Y ) ), member( skol3
% 1.57/1.95 ( Z, Y ), Y ) }.
% 1.57/1.95 (16038) {G0,W9,D3,L2,V2,M2} { ! member( X, sum_class( Y ) ), member( X,
% 1.57/1.95 skol3( X, Y ) ) }.
% 1.57/1.95 (16039) {G0,W10,D3,L3,V3,M3} { ! member( X, Z ), ! member( Z, Y ), member
% 1.57/1.95 ( X, sum_class( Y ) ) }.
% 1.57/1.95 (16040) {G0,W7,D3,L2,V1,M2} { ! member( X, universal_class ), member(
% 1.57/1.95 sum_class( X ), universal_class ) }.
% 1.57/1.95 (16041) {G0,W7,D3,L2,V2,M2} { ! member( X, power_class( Y ) ), member( X,
% 1.57/1.95 universal_class ) }.
% 1.57/1.95 (16042) {G0,W7,D3,L2,V2,M2} { ! member( X, power_class( Y ) ), subclass( X
% 1.57/1.95 , Y ) }.
% 1.57/1.95 (16043) {G0,W10,D3,L3,V2,M3} { ! member( X, universal_class ), ! subclass
% 1.57/1.95 ( X, Y ), member( X, power_class( Y ) ) }.
% 1.57/1.95 (16044) {G0,W7,D3,L2,V1,M2} { ! member( X, universal_class ), member(
% 1.57/1.95 power_class( X ), universal_class ) }.
% 1.57/1.95 (16045) {G0,W7,D3,L1,V2,M1} { subclass( compose( Y, X ), cross_product(
% 1.57/1.95 universal_class, universal_class ) ) }.
% 1.57/1.95 (16046) {G0,W10,D3,L2,V4,M2} { ! member( ordered_pair( Z, T ), compose( Y
% 1.57/1.95 , X ) ), member( Z, universal_class ) }.
% 1.57/1.95 (16047) {G0,W15,D5,L2,V4,M2} { ! member( ordered_pair( Z, T ), compose( Y
% 1.57/1.95 , X ) ), member( T, image( Y, image( X, singleton( Z ) ) ) ) }.
% 1.57/1.95 (16048) {G0,W18,D5,L3,V4,M3} { ! member( Z, universal_class ), ! member( T
% 1.57/1.95 , image( Y, image( X, singleton( Z ) ) ) ), member( ordered_pair( Z, T )
% 1.57/1.95 , compose( Y, X ) ) }.
% 1.57/1.95 (16049) {G0,W7,D3,L2,V2,M2} { ! member( X, identity_relation ), member(
% 1.57/1.95 skol4( Y ), universal_class ) }.
% 1.57/1.95 (16050) {G0,W10,D4,L2,V1,M2} { ! member( X, identity_relation ), X =
% 1.57/1.95 ordered_pair( skol4( X ), skol4( X ) ) }.
% 1.57/1.95 (16051) {G0,W11,D3,L3,V2,M3} { ! member( Y, universal_class ), ! X =
% 1.57/1.95 ordered_pair( Y, Y ), member( X, identity_relation ) }.
% 1.57/1.95 (16052) {G0,W7,D3,L2,V1,M2} { ! function( X ), subclass( X, cross_product
% 1.57/1.95 ( universal_class, universal_class ) ) }.
% 1.57/1.95 (16053) {G0,W8,D4,L2,V1,M2} { ! function( X ), subclass( compose( X,
% 1.57/1.95 inverse( X ) ), identity_relation ) }.
% 1.57/1.95 (16054) {G0,W13,D4,L3,V1,M3} { ! subclass( X, cross_product(
% 1.57/1.95 universal_class, universal_class ) ), ! subclass( compose( X, inverse( X
% 1.57/1.95 ) ), identity_relation ), function( X ) }.
% 1.57/1.95 (16055) {G0,W10,D3,L3,V2,M3} { ! member( X, universal_class ), ! function
% 1.57/1.95 ( Y ), member( image( Y, X ), universal_class ) }.
% 1.57/1.95 (16056) {G0,W9,D2,L3,V3,M3} { ! disjoint( X, Y ), ! member( Z, X ), !
% 1.57/1.95 member( Z, Y ) }.
% 1.57/1.95 (16057) {G0,W8,D3,L2,V3,M2} { member( skol5( Z, Y ), Y ), disjoint( X, Y )
% 1.57/1.95 }.
% 1.57/1.95 (16058) {G0,W8,D3,L2,V2,M2} { member( skol5( X, Y ), X ), disjoint( X, Y )
% 1.57/1.95 }.
% 1.57/1.95 (16059) {G0,W7,D3,L2,V2,M2} { X = null_class, member( skol6( Y ),
% 1.57/1.95 universal_class ) }.
% 1.57/1.95 (16060) {G0,W7,D3,L2,V1,M2} { X = null_class, member( skol6( X ), X ) }.
% 1.57/1.95 (16061) {G0,W7,D3,L2,V1,M2} { X = null_class, disjoint( skol6( X ), X )
% 1.57/1.95 }.
% 1.57/1.95 (16062) {G0,W9,D5,L1,V2,M1} { apply( X, Y ) = sum_class( image( X,
% 1.57/1.95 singleton( Y ) ) ) }.
% 1.57/1.95 (16063) {G0,W2,D2,L1,V0,M1} { function( skol7 ) }.
% 1.57/1.95 (16064) {G0,W11,D3,L3,V1,M3} { ! member( X, universal_class ), X =
% 1.57/1.95 null_class, member( apply( skol7, X ), X ) }.
% 1.57/1.95 (16065) {G0,W3,D2,L1,V0,M1} { ! member( skol8, universal_class ) }.
% 1.57/1.95 (16066) {G0,W4,D3,L1,V0,M1} { ! singleton( skol8 ) = null_class }.
% 1.57/1.95
% 1.57/1.95
% 1.57/1.95 Total Proof:
% 1.57/1.95
% 1.57/1.95 subsumption: (0) {G0,W9,D2,L3,V3,M3} I { ! subclass( X, Y ), ! member( Z, X
% 1.57/1.95 ), member( Z, Y ) }.
% 1.57/1.95 parent0: (15972) {G0,W9,D2,L3,V3,M3} { ! subclass( X, Y ), ! member( Z, X
% 1.57/1.95 ), member( Z, Y ) }.
% 1.57/1.95 substitution0:
% 1.57/1.95 X := X
% 1.57/1.95 Y := Y
% 1.57/1.95 Z := Z
% 1.57/1.95 end
% 1.57/1.95 permutation0:
% 1.57/1.95 0 ==> 0
% 1.57/1.95 1 ==> 1
% 1.57/1.95 2 ==> 2
% 1.57/1.95 end
% 1.57/1.95
% 1.57/1.95 subsumption: (2) {G0,W8,D3,L2,V2,M2} I { member( skol1( X, Y ), X ),
% 1.57/1.95 subclass( X, Y ) }.
% 1.57/1.95 parent0: (15974) {G0,W8,D3,L2,V2,M2} { member( skol1( X, Y ), X ),
% 1.57/1.95 subclass( X, Y ) }.
% 1.57/1.95 substitution0:
% 1.57/1.95 X := X
% 1.57/1.95 Y := Y
% 1.57/1.95 end
% 1.57/1.95 permutation0:
% 1.57/1.95 0 ==> 0
% 1.57/1.95 1 ==> 1
% 1.57/1.95 end
% 1.57/1.95
% 1.57/1.95 subsumption: (3) {G0,W3,D2,L1,V1,M1} I { subclass( X, universal_class ) }.
% 1.57/1.95 parent0: (15975) {G0,W3,D2,L1,V1,M1} { subclass( X, universal_class ) }.
% 1.57/1.95 substitution0:
% 1.57/1.95 X := X
% 1.57/1.95 end
% 1.57/1.95 permutation0:
% 1.57/1.95 0 ==> 0
% 1.57/1.95 end
% 1.57/1.95
% 1.57/1.95 subsumption: (4) {G0,W6,D2,L2,V2,M2} I { ! X = Y, subclass( X, Y ) }.
% 1.57/1.95 parent0: (15976) {G0,W6,D2,L2,V2,M2} { ! X = Y, subclass( X, Y ) }.
% 1.57/1.95 substitution0:
% 1.57/1.95 X := X
% 1.57/1.95 Y := Y
% 1.57/1.95 end
% 1.57/1.95 permutation0:
% 1.57/1.95 0 ==> 0
% 1.57/1.95 1 ==> 1
% 1.57/1.95 end
% 1.57/1.95
% 1.57/1.95 subsumption: (5) {G0,W9,D2,L3,V2,M3} I { ! subclass( X, Y ), ! subclass( Y
% 1.57/1.95 , X ), X = Y }.
% 1.57/1.95 parent0: (15978) {G0,W9,D2,L3,V2,M3} { ! subclass( X, Y ), ! subclass( Y,
% 1.57/1.95 X ), X = Y }.
% 1.57/1.95 substitution0:
% 1.57/1.95 X := X
% 1.57/1.95 Y := Y
% 1.57/1.95 end
% 1.57/1.95 permutation0:
% 1.57/1.95 0 ==> 0
% 1.57/1.95 1 ==> 1
% 1.57/1.95 2 ==> 2
% 1.57/1.95 end
% 1.57/1.95
% 1.57/1.95 subsumption: (7) {G0,W9,D3,L2,V3,M2} I { ! member( X, unordered_pair( Y, Z
% 1.57/1.95 ) ), alpha1( X, Y, Z ) }.
% 1.57/1.95 parent0: (15980) {G0,W9,D3,L2,V3,M2} { ! member( X, unordered_pair( Y, Z )
% 1.57/1.95 ), alpha1( X, Y, Z ) }.
% 1.57/1.95 substitution0:
% 1.57/1.95 X := X
% 1.57/1.95 Y := Y
% 1.57/1.95 Z := Z
% 1.57/1.95 end
% 1.57/1.95 permutation0:
% 1.57/1.95 0 ==> 0
% 1.57/1.95 1 ==> 1
% 1.57/1.95 end
% 1.57/1.95
% 1.57/1.95 subsumption: (9) {G0,W10,D2,L3,V3,M3} I { ! alpha1( X, Y, Z ), X = Y, X = Z
% 1.57/1.95 }.
% 1.57/1.95 parent0: (15982) {G0,W10,D2,L3,V3,M3} { ! alpha1( X, Y, Z ), X = Y, X = Z
% 1.57/1.95 }.
% 1.57/1.95 substitution0:
% 1.57/1.95 X := X
% 1.57/1.95 Y := Y
% 1.57/1.95 Z := Z
% 1.57/1.95 end
% 1.57/1.95 permutation0:
% 1.57/1.95 0 ==> 0
% 1.57/1.95 1 ==> 1
% 1.57/1.95 2 ==> 2
% 1.57/1.95 end
% 1.57/1.95
% 1.57/1.95 eqswap: (16092) {G0,W6,D3,L1,V1,M1} { unordered_pair( X, X ) = singleton(
% 1.57/1.95 X ) }.
% 1.57/1.95 parent0[0]: (15986) {G0,W6,D3,L1,V1,M1} { singleton( X ) = unordered_pair
% 1.57/1.95 ( X, X ) }.
% 1.57/1.95 substitution0:
% 1.57/1.95 X := X
% 1.57/1.95 end
% 1.57/1.95
% 1.57/1.95 subsumption: (13) {G0,W6,D3,L1,V1,M1} I { unordered_pair( X, X ) ==>
% 1.57/1.95 singleton( X ) }.
% 1.57/1.95 parent0: (16092) {G0,W6,D3,L1,V1,M1} { unordered_pair( X, X ) = singleton
% 1.57/1.95 ( X ) }.
% 1.57/1.95 substitution0:
% 1.57/1.95 X := X
% 1.57/1.95 end
% 1.57/1.95 permutation0:
% 1.57/1.95 0 ==> 0
% 1.57/1.95 end
% 1.57/1.95
% 1.57/1.95 subsumption: (32) {G0,W3,D2,L1,V1,M1} I { ! member( X, null_class ) }.
% 1.57/1.95 parent0: (16005) {G0,W3,D2,L1,V1,M1} { ! member( X, null_class ) }.
% 1.57/1.95 substitution0:
% 1.57/1.95 X := X
% 1.57/1.95 end
% 1.57/1.95 permutation0:
% 1.57/1.95 0 ==> 0
% 1.57/1.95 end
% 1.57/1.95
% 1.57/1.95 subsumption: (58) {G0,W5,D2,L2,V1,M2} I { ! inductive( X ), member(
% 1.57/1.95 null_class, X ) }.
% 1.57/1.95 parent0: (16031) {G0,W5,D2,L2,V1,M2} { ! inductive( X ), member(
% 1.57/1.95 null_class, X ) }.
% 1.57/1.95 substitution0:
% 1.57/1.95 X := X
% 1.57/1.95 end
% 1.57/1.95 permutation0:
% 1.57/1.95 0 ==> 0
% 1.57/1.95 1 ==> 1
% 1.57/1.95 end
% 1.57/1.95
% 1.57/1.95 subsumption: (62) {G0,W2,D2,L1,V0,M1} I { inductive( skol2 ) }.
% 1.57/1.95 parent0: (16035) {G0,W2,D2,L1,V0,M1} { inductive( skol2 ) }.
% 1.57/1.95 substitution0:
% 1.57/1.95 end
% 1.57/1.95 permutation0:
% 1.57/1.95 0 ==> 0
% 1.57/1.95 end
% 1.57/1.95
% 1.57/1.95 subsumption: (83) {G0,W9,D2,L3,V3,M3} I { ! disjoint( X, Y ), ! member( Z,
% 1.57/1.95 X ), ! member( Z, Y ) }.
% 1.57/1.95 parent0: (16056) {G0,W9,D2,L3,V3,M3} { ! disjoint( X, Y ), ! member( Z, X
% 1.57/1.95 ), ! member( Z, Y ) }.
% 1.57/1.95 substitution0:
% 1.57/1.95 X := X
% 1.57/1.95 Y := Y
% 1.57/1.95 Z := Z
% 1.57/1.95 end
% 1.57/1.95 permutation0:
% 1.57/1.95 0 ==> 0
% 1.57/1.95 1 ==> 1
% 1.57/1.95 2 ==> 2
% 1.57/1.95 end
% 1.57/1.95
% 1.57/1.95 subsumption: (84) {G0,W8,D3,L2,V3,M2} I { member( skol5( Z, Y ), Y ),
% 1.57/1.95 disjoint( X, Y ) }.
% 1.57/1.95 parent0: (16057) {G0,W8,D3,L2,V3,M2} { member( skol5( Z, Y ), Y ),
% 1.57/1.95 disjoint( X, Y ) }.
% 1.57/1.95 substitution0:
% 1.57/1.95 X := X
% 1.57/1.95 Y := Y
% 1.57/1.95 Z := Z
% 1.57/1.95 end
% 1.57/1.95 permutation0:
% 1.57/1.95 0 ==> 0
% 1.57/1.95 1 ==> 1
% 1.57/1.95 end
% 1.57/1.95
% 1.57/1.95 subsumption: (86) {G0,W7,D3,L2,V2,M2} I { X = null_class, member( skol6( Y
% 1.57/1.95 ), universal_class ) }.
% 1.57/1.95 parent0: (16059) {G0,W7,D3,L2,V2,M2} { X = null_class, member( skol6( Y )
% 1.57/1.95 , universal_class ) }.
% 1.57/1.95 substitution0:
% 1.57/1.95 X := X
% 1.57/1.95 Y := Y
% 1.57/1.95 end
% 1.57/1.95 permutation0:
% 1.57/1.95 0 ==> 0
% 1.57/1.95 1 ==> 1
% 1.57/1.95 end
% 1.57/1.95
% 1.57/1.95 subsumption: (87) {G0,W7,D3,L2,V1,M2} I { X = null_class, member( skol6( X
% 1.57/1.95 ), X ) }.
% 1.57/1.95 parent0: (16060) {G0,W7,D3,L2,V1,M2} { X = null_class, member( skol6( X )
% 1.57/1.95 , X ) }.
% 1.57/1.95 substitution0:
% 1.57/1.95 X := X
% 1.57/1.95 end
% 1.57/1.95 permutation0:
% 1.57/1.95 0 ==> 0
% 1.57/1.95 1 ==> 1
% 1.57/1.95 end
% 1.57/1.95
% 1.57/1.95 subsumption: (92) {G0,W3,D2,L1,V0,M1} I { ! member( skol8, universal_class
% 1.57/1.95 ) }.
% 1.57/1.95 parent0: (16065) {G0,W3,D2,L1,V0,M1} { ! member( skol8, universal_class )
% 1.57/1.95 }.
% 1.57/1.95 substitution0:
% 1.57/1.95 end
% 1.57/1.95 permutation0:
% 1.57/1.95 0 ==> 0
% 1.57/1.95 end
% 1.57/1.95
% 1.57/1.95 subsumption: (93) {G0,W4,D3,L1,V0,M1} I { ! singleton( skol8 ) ==>
% 1.57/1.95 null_class }.
% 1.57/1.95 parent0: (16066) {G0,W4,D3,L1,V0,M1} { ! singleton( skol8 ) = null_class
% 1.57/1.95 }.
% 1.57/1.95 substitution0:
% 1.57/1.95 end
% 1.57/1.95 permutation0:
% 1.57/1.95 0 ==> 0
% 1.57/1.95 end
% 1.57/1.95
% 1.57/1.95 factor: (16429) {G0,W7,D2,L2,V2,M2} { ! alpha1( X, Y, Y ), X = Y }.
% 1.57/1.95 parent0[1, 2]: (9) {G0,W10,D2,L3,V3,M3} I { ! alpha1( X, Y, Z ), X = Y, X =
% 1.57/1.95 Z }.
% 1.57/1.95 substitution0:
% 1.57/1.95 X := X
% 1.57/1.95 Y := Y
% 1.57/1.95 Z := Y
% 1.57/1.95 end
% 1.57/1.95
% 1.57/1.95 subsumption: (95) {G1,W7,D2,L2,V2,M2} F(9) { ! alpha1( X, Y, Y ), X = Y }.
% 1.57/1.95 parent0: (16429) {G0,W7,D2,L2,V2,M2} { ! alpha1( X, Y, Y ), X = Y }.
% 1.57/1.95 substitution0:
% 1.57/1.95 X := X
% 1.57/1.95 Y := Y
% 1.57/1.95 end
% 1.57/1.95 permutation0:
% 1.57/1.95 0 ==> 0
% 1.57/1.95 1 ==> 1
% 1.57/1.95 end
% 1.57/1.95
% 1.57/1.95 resolution: (16431) {G1,W6,D2,L2,V2,M2} { ! member( Y, X ), member( Y,
% 1.57/1.95 universal_class ) }.
% 1.57/1.95 parent0[0]: (0) {G0,W9,D2,L3,V3,M3} I { ! subclass( X, Y ), ! member( Z, X
% 1.57/1.95 ), member( Z, Y ) }.
% 1.57/1.95 parent1[0]: (3) {G0,W3,D2,L1,V1,M1} I { subclass( X, universal_class ) }.
% 1.57/1.95 substitution0:
% 1.57/1.95 X := X
% 1.57/1.95 Y := universal_class
% 1.57/1.95 Z := Y
% 1.57/1.95 end
% 1.57/1.95 substitution1:
% 1.57/1.95 X := X
% 1.57/1.95 end
% 1.57/1.95
% 1.57/1.95 subsumption: (113) {G1,W6,D2,L2,V2,M2} R(0,3) { ! member( X, Y ), member( X
% 1.57/1.95 , universal_class ) }.
% 1.57/1.95 parent0: (16431) {G1,W6,D2,L2,V2,M2} { ! member( Y, X ), member( Y,
% 1.57/1.95 universal_class ) }.
% 1.57/1.95 substitution0:
% 1.57/1.95 X := Y
% 1.57/1.95 Y := X
% 1.57/1.95 end
% 1.57/1.95 permutation0:
% 1.57/1.95 0 ==> 0
% 1.57/1.95 1 ==> 1
% 1.57/1.95 end
% 1.57/1.95
% 1.57/1.95 resolution: (16432) {G1,W6,D2,L2,V1,M2} { ! subclass( X, universal_class )
% 1.57/1.95 , ! member( skol8, X ) }.
% 1.57/1.95 parent0[0]: (92) {G0,W3,D2,L1,V0,M1} I { ! member( skol8, universal_class )
% 1.57/1.95 }.
% 1.57/1.95 parent1[2]: (0) {G0,W9,D2,L3,V3,M3} I { ! subclass( X, Y ), ! member( Z, Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------