TSTP Solution File: SET055+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET055+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n008.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 22:46:11 EDT 2022
% Result : Theorem 0.44s 1.07s
% Output : Refutation 0.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET055+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.03/0.12 % Command : bliksem %s
% 0.14/0.33 % Computer : n008.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % DateTime : Sat Jul 9 21:51:08 EDT 2022
% 0.14/0.33 % CPUTime :
% 0.44/1.07 *** allocated 10000 integers for termspace/termends
% 0.44/1.07 *** allocated 10000 integers for clauses
% 0.44/1.07 *** allocated 10000 integers for justifications
% 0.44/1.07 Bliksem 1.12
% 0.44/1.07
% 0.44/1.07
% 0.44/1.07 Automatic Strategy Selection
% 0.44/1.07
% 0.44/1.07
% 0.44/1.07 Clauses:
% 0.44/1.07
% 0.44/1.07 { ! subclass( X, Y ), ! member( Z, X ), member( Z, Y ) }.
% 0.44/1.07 { ! member( skol1( Z, Y ), Y ), subclass( X, Y ) }.
% 0.44/1.07 { member( skol1( X, Y ), X ), subclass( X, Y ) }.
% 0.44/1.07 { subclass( X, universal_class ) }.
% 0.44/1.07 { ! X = Y, subclass( X, Y ) }.
% 0.44/1.07 { ! X = Y, subclass( Y, X ) }.
% 0.44/1.07 { ! subclass( X, Y ), ! subclass( Y, X ), X = Y }.
% 0.44/1.07 { ! member( X, unordered_pair( Y, Z ) ), member( X, universal_class ) }.
% 0.44/1.07 { ! member( X, unordered_pair( Y, Z ) ), alpha1( X, Y, Z ) }.
% 0.44/1.07 { ! member( X, universal_class ), ! alpha1( X, Y, Z ), member( X,
% 0.44/1.07 unordered_pair( Y, Z ) ) }.
% 0.44/1.07 { ! alpha1( X, Y, Z ), X = Y, X = Z }.
% 0.44/1.07 { ! X = Y, alpha1( X, Y, Z ) }.
% 0.44/1.07 { ! X = Z, alpha1( X, Y, Z ) }.
% 0.44/1.07 { member( unordered_pair( X, Y ), universal_class ) }.
% 0.44/1.07 { singleton( X ) = unordered_pair( X, X ) }.
% 0.44/1.07 { ordered_pair( X, Y ) = unordered_pair( singleton( X ), unordered_pair( X
% 0.44/1.07 , singleton( Y ) ) ) }.
% 0.44/1.07 { ! member( ordered_pair( X, Y ), cross_product( Z, T ) ), member( X, Z ) }
% 0.44/1.07 .
% 0.44/1.07 { ! member( ordered_pair( X, Y ), cross_product( Z, T ) ), member( Y, T ) }
% 0.44/1.07 .
% 0.44/1.07 { ! member( X, Z ), ! member( Y, T ), member( ordered_pair( X, Y ),
% 0.44/1.07 cross_product( Z, T ) ) }.
% 0.44/1.07 { ! member( X, universal_class ), ! member( Y, universal_class ), first(
% 0.44/1.07 ordered_pair( X, Y ) ) = X }.
% 0.44/1.07 { ! member( X, universal_class ), ! member( Y, universal_class ), second(
% 0.44/1.07 ordered_pair( X, Y ) ) = Y }.
% 0.44/1.07 { ! member( X, cross_product( Y, Z ) ), X = ordered_pair( first( X ),
% 0.44/1.07 second( X ) ) }.
% 0.44/1.07 { ! member( ordered_pair( X, Y ), element_relation ), member( Y,
% 0.44/1.07 universal_class ) }.
% 0.44/1.07 { ! member( ordered_pair( X, Y ), element_relation ), member( X, Y ) }.
% 0.44/1.07 { ! member( Y, universal_class ), ! member( X, Y ), member( ordered_pair( X
% 0.44/1.07 , Y ), element_relation ) }.
% 0.44/1.07 { subclass( element_relation, cross_product( universal_class,
% 0.44/1.07 universal_class ) ) }.
% 0.44/1.07 { ! member( Z, intersection( X, Y ) ), member( Z, X ) }.
% 0.44/1.07 { ! member( Z, intersection( X, Y ) ), member( Z, Y ) }.
% 0.44/1.07 { ! member( Z, X ), ! member( Z, Y ), member( Z, intersection( X, Y ) ) }.
% 0.44/1.07 { ! member( Y, complement( X ) ), member( Y, universal_class ) }.
% 0.44/1.07 { ! member( Y, complement( X ) ), ! member( Y, X ) }.
% 0.44/1.07 { ! member( Y, universal_class ), member( Y, X ), member( Y, complement( X
% 0.44/1.07 ) ) }.
% 0.44/1.07 { restrict( Y, X, Z ) = intersection( Y, cross_product( X, Z ) ) }.
% 0.44/1.07 { ! member( X, null_class ) }.
% 0.44/1.07 { ! member( Y, domain_of( X ) ), member( Y, universal_class ) }.
% 0.44/1.07 { ! member( Y, domain_of( X ) ), ! restrict( X, singleton( Y ),
% 0.44/1.07 universal_class ) = null_class }.
% 0.44/1.07 { ! member( Y, universal_class ), restrict( X, singleton( Y ),
% 0.44/1.07 universal_class ) = null_class, member( Y, domain_of( X ) ) }.
% 0.44/1.07 { ! member( ordered_pair( ordered_pair( Y, Z ), T ), rotate( X ) ), member
% 0.44/1.07 ( ordered_pair( ordered_pair( Y, Z ), T ), cross_product( cross_product(
% 0.44/1.07 universal_class, universal_class ), universal_class ) ) }.
% 0.44/1.07 { ! member( ordered_pair( ordered_pair( Y, Z ), T ), rotate( X ) ), member
% 0.44/1.07 ( ordered_pair( ordered_pair( Z, T ), Y ), X ) }.
% 0.44/1.07 { ! member( ordered_pair( ordered_pair( Y, Z ), T ), cross_product(
% 0.44/1.07 cross_product( universal_class, universal_class ), universal_class ) ), !
% 0.44/1.07 member( ordered_pair( ordered_pair( Z, T ), Y ), X ), member(
% 0.44/1.07 ordered_pair( ordered_pair( Y, Z ), T ), rotate( X ) ) }.
% 0.44/1.07 { subclass( rotate( X ), cross_product( cross_product( universal_class,
% 0.44/1.07 universal_class ), universal_class ) ) }.
% 0.44/1.07 { ! member( ordered_pair( ordered_pair( X, Y ), Z ), flip( T ) ), member(
% 0.44/1.07 ordered_pair( ordered_pair( X, Y ), Z ), cross_product( cross_product(
% 0.44/1.07 universal_class, universal_class ), universal_class ) ) }.
% 0.44/1.07 { ! member( ordered_pair( ordered_pair( X, Y ), Z ), flip( T ) ), member(
% 0.44/1.07 ordered_pair( ordered_pair( Y, X ), Z ), T ) }.
% 0.44/1.07 { ! member( ordered_pair( ordered_pair( X, Y ), Z ), cross_product(
% 0.44/1.07 cross_product( universal_class, universal_class ), universal_class ) ), !
% 0.44/1.07 member( ordered_pair( ordered_pair( Y, X ), Z ), T ), member(
% 0.44/1.07 ordered_pair( ordered_pair( X, Y ), Z ), flip( T ) ) }.
% 0.44/1.07 { subclass( flip( X ), cross_product( cross_product( universal_class,
% 0.44/1.07 universal_class ), universal_class ) ) }.
% 0.44/1.07 { ! member( Z, union( X, Y ) ), member( Z, X ), member( Z, Y ) }.
% 0.44/1.07 { ! member( Z, X ), member( Z, union( X, Y ) ) }.
% 0.44/1.07 { ! member( Z, Y ), member( Z, union( X, Y ) ) }.
% 0.44/1.07 { successor( X ) = union( X, singleton( X ) ) }.
% 0.44/1.07 { subclass( successor_relation, cross_product( universal_class,
% 0.44/1.07 universal_class ) ) }.
% 0.44/1.07 { ! member( ordered_pair( X, Y ), successor_relation ), member( X,
% 0.44/1.07 universal_class ) }.
% 0.44/1.07 { ! member( ordered_pair( X, Y ), successor_relation ), alpha2( X, Y ) }.
% 0.44/1.07 { ! member( X, universal_class ), ! alpha2( X, Y ), member( ordered_pair( X
% 0.44/1.07 , Y ), successor_relation ) }.
% 0.44/1.07 { ! alpha2( X, Y ), member( Y, universal_class ) }.
% 0.44/1.07 { ! alpha2( X, Y ), successor( X ) = Y }.
% 0.44/1.07 { ! member( Y, universal_class ), ! successor( X ) = Y, alpha2( X, Y ) }.
% 0.44/1.07 { inverse( X ) = domain_of( flip( cross_product( X, universal_class ) ) ) }
% 0.44/1.07 .
% 0.44/1.07 { range_of( X ) = domain_of( inverse( X ) ) }.
% 0.44/1.07 { image( Y, X ) = range_of( restrict( Y, X, universal_class ) ) }.
% 0.44/1.07 { ! inductive( X ), member( null_class, X ) }.
% 0.44/1.07 { ! inductive( X ), subclass( image( successor_relation, X ), X ) }.
% 0.44/1.07 { ! member( null_class, X ), ! subclass( image( successor_relation, X ), X
% 0.44/1.07 ), inductive( X ) }.
% 0.44/1.07 { member( skol2, universal_class ) }.
% 0.44/1.07 { inductive( skol2 ) }.
% 0.44/1.07 { ! inductive( X ), subclass( skol2, X ) }.
% 0.44/1.07 { ! member( X, sum_class( Y ) ), member( skol3( Z, Y ), Y ) }.
% 0.44/1.07 { ! member( X, sum_class( Y ) ), member( X, skol3( X, Y ) ) }.
% 0.44/1.07 { ! member( X, Z ), ! member( Z, Y ), member( X, sum_class( Y ) ) }.
% 0.44/1.07 { ! member( X, universal_class ), member( sum_class( X ), universal_class )
% 0.44/1.07 }.
% 0.44/1.07 { ! member( X, power_class( Y ) ), member( X, universal_class ) }.
% 0.44/1.07 { ! member( X, power_class( Y ) ), subclass( X, Y ) }.
% 0.44/1.07 { ! member( X, universal_class ), ! subclass( X, Y ), member( X,
% 0.44/1.07 power_class( Y ) ) }.
% 0.44/1.07 { ! member( X, universal_class ), member( power_class( X ), universal_class
% 0.44/1.07 ) }.
% 0.44/1.07 { subclass( compose( Y, X ), cross_product( universal_class,
% 0.44/1.07 universal_class ) ) }.
% 0.44/1.07 { ! member( ordered_pair( Z, T ), compose( Y, X ) ), member( Z,
% 0.44/1.07 universal_class ) }.
% 0.44/1.07 { ! member( ordered_pair( Z, T ), compose( Y, X ) ), member( T, image( Y,
% 0.44/1.07 image( X, singleton( Z ) ) ) ) }.
% 0.44/1.07 { ! member( Z, universal_class ), ! member( T, image( Y, image( X,
% 0.44/1.07 singleton( Z ) ) ) ), member( ordered_pair( Z, T ), compose( Y, X ) ) }.
% 0.44/1.07 { ! member( X, identity_relation ), member( skol4( Y ), universal_class ) }
% 0.44/1.07 .
% 0.44/1.07 { ! member( X, identity_relation ), X = ordered_pair( skol4( X ), skol4( X
% 0.44/1.07 ) ) }.
% 0.44/1.07 { ! member( Y, universal_class ), ! X = ordered_pair( Y, Y ), member( X,
% 0.44/1.07 identity_relation ) }.
% 0.44/1.07 { ! function( X ), subclass( X, cross_product( universal_class,
% 0.44/1.07 universal_class ) ) }.
% 0.44/1.07 { ! function( X ), subclass( compose( X, inverse( X ) ), identity_relation
% 0.44/1.07 ) }.
% 0.44/1.07 { ! subclass( X, cross_product( universal_class, universal_class ) ), !
% 0.44/1.07 subclass( compose( X, inverse( X ) ), identity_relation ), function( X )
% 0.44/1.07 }.
% 0.44/1.07 { ! member( X, universal_class ), ! function( Y ), member( image( Y, X ),
% 0.44/1.07 universal_class ) }.
% 0.44/1.07 { ! disjoint( X, Y ), ! member( Z, X ), ! member( Z, Y ) }.
% 0.44/1.07 { member( skol5( Z, Y ), Y ), disjoint( X, Y ) }.
% 0.44/1.07 { member( skol5( X, Y ), X ), disjoint( X, Y ) }.
% 0.44/1.07 { X = null_class, member( skol6( Y ), universal_class ) }.
% 0.44/1.07 { X = null_class, member( skol6( X ), X ) }.
% 0.44/1.07 { X = null_class, disjoint( skol6( X ), X ) }.
% 0.44/1.07 { apply( X, Y ) = sum_class( image( X, singleton( Y ) ) ) }.
% 0.44/1.07 { function( skol7 ) }.
% 0.44/1.07 { ! member( X, universal_class ), X = null_class, member( apply( skol7, X )
% 0.44/1.07 , X ) }.
% 0.44/1.07 { ! skol8 = skol8 }.
% 0.44/1.07
% 0.44/1.07 percentage equality = 0.150259, percentage horn = 0.882979
% 0.44/1.07 This is a problem with some equality
% 0.44/1.07
% 0.44/1.07
% 0.44/1.07
% 0.44/1.07 Options Used:
% 0.44/1.07
% 0.44/1.07 useres = 1
% 0.44/1.07 useparamod = 1
% 0.44/1.07 useeqrefl = 1
% 0.44/1.07 useeqfact = 1
% 0.44/1.07 usefactor = 1
% 0.44/1.07 usesimpsplitting = 0
% 0.44/1.07 usesimpdemod = 5
% 0.44/1.07 usesimpres = 3
% 0.44/1.07
% 0.44/1.07 resimpinuse = 1000
% 0.44/1.07 resimpclauses = 20000
% 0.44/1.07 substype = eqrewr
% 0.44/1.07 backwardsubs = 1
% 0.44/1.07 selectoldest = 5
% 0.44/1.07
% 0.44/1.07 litorderings [0] = split
% 0.44/1.07 litorderings [1] = extend the termordering, first sorting on arguments
% 0.44/1.07
% 0.44/1.07 termordering = kbo
% 0.44/1.07
% 0.44/1.07 litapriori = 0
% 0.44/1.07 termapriori = 1
% 0.44/1.07 litaposteriori = 0
% 0.44/1.07 termaposteriori = 0
% 0.44/1.07 demodaposteriori = 0
% 0.44/1.07 ordereqreflfact = 0
% 0.44/1.07
% 0.44/1.07 litselect = negord
% 0.44/1.07
% 0.44/1.07 maxweight = 15
% 0.44/1.07 maxdepth = 30000
% 0.44/1.07 maxlength = 115
% 0.44/1.07 maxnrvars = 195
% 0.44/1.07 excuselevel = 1
% 0.44/1.07 increasemaxweight = 1
% 0.44/1.07
% 0.44/1.07 maxselected = 10000000
% 0.44/1.07 maxnrclauses = 10000000
% 0.44/1.07
% 0.44/1.07 showgenerated = 0
% 0.44/1.07 showkept = 0
% 0.44/1.07 showselected = 0
% 0.44/1.07 showdeleted = 0
% 0.44/1.07 showresimp = 1
% 0.44/1.07 showstatus = 2000
% 0.44/1.07
% 0.44/1.07 prologoutput = 0
% 0.44/1.07 nrgoals = 5000000
% 0.44/1.07 totalproof = 1
% 0.44/1.07
% 0.44/1.07 Symbols occurring in the translation:
% 0.44/1.07
% 0.44/1.07 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.44/1.07 . [1, 2] (w:1, o:44, a:1, s:1, b:0),
% 0.44/1.07 ! [4, 1] (w:0, o:23, a:1, s:1, b:0),
% 0.44/1.07 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.44/1.07 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.44/1.07 subclass [37, 2] (w:1, o:68, a:1, s:1, b:0),
% 0.44/1.07 member [39, 2] (w:1, o:69, a:1, s:1, b:0),
% 0.44/1.07 universal_class [40, 0] (w:1, o:12, a:1, s:1, b:0),
% 0.44/1.07 unordered_pair [41, 2] (w:1, o:70, a:1, s:1, b:0),
% 0.44/1.07 singleton [42, 1] (w:1, o:30, a:1, s:1, b:0),
% 0.44/1.07 ordered_pair [43, 2] (w:1, o:71, a:1, s:1, b:0),
% 0.44/1.07 cross_product [45, 2] (w:1, o:72, a:1, s:1, b:0),
% 0.44/1.07 first [46, 1] (w:1, o:31, a:1, s:1, b:0),
% 0.44/1.07 second [47, 1] (w:1, o:32, a:1, s:1, b:0),
% 0.44/1.07 element_relation [49, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.44/1.07 intersection [50, 2] (w:1, o:74, a:1, s:1, b:0),
% 0.44/1.07 complement [51, 1] (w:1, o:33, a:1, s:1, b:0),
% 0.44/1.07 restrict [53, 3] (w:1, o:83, a:1, s:1, b:0),
% 0.44/1.07 null_class [54, 0] (w:1, o:17, a:1, s:1, b:0),
% 0.44/1.07 domain_of [55, 1] (w:1, o:34, a:1, s:1, b:0),
% 0.44/1.07 rotate [57, 1] (w:1, o:28, a:1, s:1, b:0),
% 0.44/1.07 flip [58, 1] (w:1, o:35, a:1, s:1, b:0),
% 0.44/1.07 union [59, 2] (w:1, o:75, a:1, s:1, b:0),
% 0.44/1.07 successor [60, 1] (w:1, o:36, a:1, s:1, b:0),
% 0.44/1.07 successor_relation [61, 0] (w:1, o:18, a:1, s:1, b:0),
% 0.44/1.07 inverse [62, 1] (w:1, o:37, a:1, s:1, b:0),
% 0.44/1.07 range_of [63, 1] (w:1, o:29, a:1, s:1, b:0),
% 0.44/1.07 image [64, 2] (w:1, o:73, a:1, s:1, b:0),
% 0.44/1.07 inductive [65, 1] (w:1, o:38, a:1, s:1, b:0),
% 0.44/1.07 sum_class [66, 1] (w:1, o:39, a:1, s:1, b:0),
% 0.44/1.07 power_class [67, 1] (w:1, o:40, a:1, s:1, b:0),
% 0.44/1.07 compose [69, 2] (w:1, o:76, a:1, s:1, b:0),
% 0.44/1.07 identity_relation [70, 0] (w:1, o:19, a:1, s:1, b:0),
% 0.44/1.07 function [72, 1] (w:1, o:41, a:1, s:1, b:0),
% 0.44/1.07 disjoint [73, 2] (w:1, o:77, a:1, s:1, b:0),
% 0.44/1.07 apply [74, 2] (w:1, o:78, a:1, s:1, b:0),
% 0.44/1.07 alpha1 [75, 3] (w:1, o:84, a:1, s:1, b:1),
% 0.44/1.07 alpha2 [76, 2] (w:1, o:79, a:1, s:1, b:1),
% 0.44/1.07 skol1 [77, 2] (w:1, o:80, a:1, s:1, b:1),
% 0.44/1.07 skol2 [78, 0] (w:1, o:20, a:1, s:1, b:1),
% 0.44/1.07 skol3 [79, 2] (w:1, o:81, a:1, s:1, b:1),
% 0.44/1.07 skol4 [80, 1] (w:1, o:42, a:1, s:1, b:1),
% 0.44/1.07 skol5 [81, 2] (w:1, o:82, a:1, s:1, b:1),
% 0.44/1.07 skol6 [82, 1] (w:1, o:43, a:1, s:1, b:1),
% 0.44/1.07 skol7 [83, 0] (w:1, o:21, a:1, s:1, b:1),
% 0.44/1.07 skol8 [84, 0] (w:1, o:22, a:1, s:1, b:1).
% 0.44/1.07
% 0.44/1.07
% 0.44/1.07 Starting Search:
% 0.44/1.07
% 0.44/1.07
% 0.44/1.07 Bliksems!, er is een bewijs:
% 0.44/1.07 % SZS status Theorem
% 0.44/1.07 % SZS output start Refutation
% 0.44/1.07
% 0.44/1.07 (92) {G0,W0,D0,L0,V0,M0} I;q { }.
% 0.44/1.07
% 0.44/1.07
% 0.44/1.07 % SZS output end Refutation
% 0.44/1.07 found a proof!
% 0.44/1.07
% 0.44/1.07
% 0.44/1.07 Unprocessed initial clauses:
% 0.44/1.07
% 0.44/1.07 (94) {G0,W9,D2,L3,V3,M3} { ! subclass( X, Y ), ! member( Z, X ), member( Z
% 0.44/1.07 , Y ) }.
% 0.44/1.07 (95) {G0,W8,D3,L2,V3,M2} { ! member( skol1( Z, Y ), Y ), subclass( X, Y )
% 0.44/1.07 }.
% 0.44/1.07 (96) {G0,W8,D3,L2,V2,M2} { member( skol1( X, Y ), X ), subclass( X, Y )
% 0.44/1.07 }.
% 0.44/1.07 (97) {G0,W3,D2,L1,V1,M1} { subclass( X, universal_class ) }.
% 0.44/1.07 (98) {G0,W6,D2,L2,V2,M2} { ! X = Y, subclass( X, Y ) }.
% 0.44/1.07 (99) {G0,W6,D2,L2,V2,M2} { ! X = Y, subclass( Y, X ) }.
% 0.44/1.07 (100) {G0,W9,D2,L3,V2,M3} { ! subclass( X, Y ), ! subclass( Y, X ), X = Y
% 0.44/1.07 }.
% 0.44/1.07 (101) {G0,W8,D3,L2,V3,M2} { ! member( X, unordered_pair( Y, Z ) ), member
% 0.44/1.07 ( X, universal_class ) }.
% 0.44/1.07 (102) {G0,W9,D3,L2,V3,M2} { ! member( X, unordered_pair( Y, Z ) ), alpha1
% 0.44/1.07 ( X, Y, Z ) }.
% 0.44/1.07 (103) {G0,W12,D3,L3,V3,M3} { ! member( X, universal_class ), ! alpha1( X,
% 0.44/1.07 Y, Z ), member( X, unordered_pair( Y, Z ) ) }.
% 0.44/1.07 (104) {G0,W10,D2,L3,V3,M3} { ! alpha1( X, Y, Z ), X = Y, X = Z }.
% 0.44/1.07 (105) {G0,W7,D2,L2,V3,M2} { ! X = Y, alpha1( X, Y, Z ) }.
% 0.44/1.07 (106) {G0,W7,D2,L2,V3,M2} { ! X = Z, alpha1( X, Y, Z ) }.
% 0.44/1.07 (107) {G0,W5,D3,L1,V2,M1} { member( unordered_pair( X, Y ),
% 0.44/1.07 universal_class ) }.
% 0.44/1.07 (108) {G0,W6,D3,L1,V1,M1} { singleton( X ) = unordered_pair( X, X ) }.
% 0.44/1.07 (109) {G0,W11,D5,L1,V2,M1} { ordered_pair( X, Y ) = unordered_pair(
% 0.44/1.07 singleton( X ), unordered_pair( X, singleton( Y ) ) ) }.
% 0.44/1.07 (110) {G0,W10,D3,L2,V4,M2} { ! member( ordered_pair( X, Y ), cross_product
% 0.44/1.07 ( Z, T ) ), member( X, Z ) }.
% 0.44/1.07 (111) {G0,W10,D3,L2,V4,M2} { ! member( ordered_pair( X, Y ), cross_product
% 0.44/1.07 ( Z, T ) ), member( Y, T ) }.
% 0.44/1.07 (112) {G0,W13,D3,L3,V4,M3} { ! member( X, Z ), ! member( Y, T ), member(
% 0.44/1.07 ordered_pair( X, Y ), cross_product( Z, T ) ) }.
% 0.44/1.07 (113) {G0,W12,D4,L3,V2,M3} { ! member( X, universal_class ), ! member( Y,
% 0.44/1.07 universal_class ), first( ordered_pair( X, Y ) ) = X }.
% 0.44/1.07 (114) {G0,W12,D4,L3,V2,M3} { ! member( X, universal_class ), ! member( Y,
% 0.44/1.07 universal_class ), second( ordered_pair( X, Y ) ) = Y }.
% 0.44/1.07 (115) {G0,W12,D4,L2,V3,M2} { ! member( X, cross_product( Y, Z ) ), X =
% 0.44/1.07 ordered_pair( first( X ), second( X ) ) }.
% 0.44/1.07 (116) {G0,W8,D3,L2,V2,M2} { ! member( ordered_pair( X, Y ),
% 0.44/1.07 element_relation ), member( Y, universal_class ) }.
% 0.44/1.07 (117) {G0,W8,D3,L2,V2,M2} { ! member( ordered_pair( X, Y ),
% 0.44/1.07 element_relation ), member( X, Y ) }.
% 0.44/1.07 (118) {G0,W11,D3,L3,V2,M3} { ! member( Y, universal_class ), ! member( X,
% 0.44/1.07 Y ), member( ordered_pair( X, Y ), element_relation ) }.
% 0.44/1.07 (119) {G0,W5,D3,L1,V0,M1} { subclass( element_relation, cross_product(
% 0.44/1.07 universal_class, universal_class ) ) }.
% 0.44/1.07 (120) {G0,W8,D3,L2,V3,M2} { ! member( Z, intersection( X, Y ) ), member( Z
% 0.44/1.07 , X ) }.
% 0.44/1.07 (121) {G0,W8,D3,L2,V3,M2} { ! member( Z, intersection( X, Y ) ), member( Z
% 0.44/1.07 , Y ) }.
% 0.44/1.07 (122) {G0,W11,D3,L3,V3,M3} { ! member( Z, X ), ! member( Z, Y ), member( Z
% 0.44/1.07 , intersection( X, Y ) ) }.
% 0.44/1.07 (123) {G0,W7,D3,L2,V2,M2} { ! member( Y, complement( X ) ), member( Y,
% 0.44/1.07 universal_class ) }.
% 0.44/1.07 (124) {G0,W7,D3,L2,V2,M2} { ! member( Y, complement( X ) ), ! member( Y, X
% 0.44/1.07 ) }.
% 0.44/1.07 (125) {G0,W10,D3,L3,V2,M3} { ! member( Y, universal_class ), member( Y, X
% 0.44/1.07 ), member( Y, complement( X ) ) }.
% 0.44/1.07 (126) {G0,W10,D4,L1,V3,M1} { restrict( Y, X, Z ) = intersection( Y,
% 0.44/1.07 cross_product( X, Z ) ) }.
% 0.44/1.07 (127) {G0,W3,D2,L1,V1,M1} { ! member( X, null_class ) }.
% 0.44/1.07 (128) {G0,W7,D3,L2,V2,M2} { ! member( Y, domain_of( X ) ), member( Y,
% 0.44/1.07 universal_class ) }.
% 0.44/1.07 (129) {G0,W11,D4,L2,V2,M2} { ! member( Y, domain_of( X ) ), ! restrict( X
% 0.44/1.07 , singleton( Y ), universal_class ) = null_class }.
% 0.44/1.07 (130) {G0,W14,D4,L3,V2,M3} { ! member( Y, universal_class ), restrict( X,
% 0.44/1.07 singleton( Y ), universal_class ) = null_class, member( Y, domain_of( X )
% 0.44/1.07 ) }.
% 0.44/1.07 (131) {G0,W19,D4,L2,V4,M2} { ! member( ordered_pair( ordered_pair( Y, Z )
% 0.44/1.07 , T ), rotate( X ) ), member( ordered_pair( ordered_pair( Y, Z ), T ),
% 0.44/1.07 cross_product( cross_product( universal_class, universal_class ),
% 0.44/1.07 universal_class ) ) }.
% 0.44/1.07 (132) {G0,W15,D4,L2,V4,M2} { ! member( ordered_pair( ordered_pair( Y, Z )
% 0.44/1.07 , T ), rotate( X ) ), member( ordered_pair( ordered_pair( Z, T ), Y ), X
% 0.44/1.07 ) }.
% 0.44/1.07 (133) {G0,W26,D4,L3,V4,M3} { ! member( ordered_pair( ordered_pair( Y, Z )
% 0.44/1.07 , T ), cross_product( cross_product( universal_class, universal_class ),
% 0.44/1.07 universal_class ) ), ! member( ordered_pair( ordered_pair( Z, T ), Y ), X
% 0.44/1.07 ), member( ordered_pair( ordered_pair( Y, Z ), T ), rotate( X ) ) }.
% 0.44/1.07 (134) {G0,W8,D4,L1,V1,M1} { subclass( rotate( X ), cross_product(
% 0.44/1.07 cross_product( universal_class, universal_class ), universal_class ) )
% 0.44/1.07 }.
% 0.44/1.07 (135) {G0,W19,D4,L2,V4,M2} { ! member( ordered_pair( ordered_pair( X, Y )
% 0.44/1.07 , Z ), flip( T ) ), member( ordered_pair( ordered_pair( X, Y ), Z ),
% 0.44/1.07 cross_product( cross_product( universal_class, universal_class ),
% 0.44/1.07 universal_class ) ) }.
% 0.44/1.07 (136) {G0,W15,D4,L2,V4,M2} { ! member( ordered_pair( ordered_pair( X, Y )
% 0.44/1.07 , Z ), flip( T ) ), member( ordered_pair( ordered_pair( Y, X ), Z ), T )
% 0.44/1.07 }.
% 0.44/1.07 (137) {G0,W26,D4,L3,V4,M3} { ! member( ordered_pair( ordered_pair( X, Y )
% 0.44/1.07 , Z ), cross_product( cross_product( universal_class, universal_class ),
% 0.44/1.07 universal_class ) ), ! member( ordered_pair( ordered_pair( Y, X ), Z ), T
% 0.44/1.07 ), member( ordered_pair( ordered_pair( X, Y ), Z ), flip( T ) ) }.
% 0.44/1.07 (138) {G0,W8,D4,L1,V1,M1} { subclass( flip( X ), cross_product(
% 0.44/1.07 cross_product( universal_class, universal_class ), universal_class ) )
% 0.44/1.07 }.
% 0.44/1.07 (139) {G0,W11,D3,L3,V3,M3} { ! member( Z, union( X, Y ) ), member( Z, X )
% 0.44/1.07 , member( Z, Y ) }.
% 0.44/1.07 (140) {G0,W8,D3,L2,V3,M2} { ! member( Z, X ), member( Z, union( X, Y ) )
% 0.44/1.07 }.
% 0.44/1.07 (141) {G0,W8,D3,L2,V3,M2} { ! member( Z, Y ), member( Z, union( X, Y ) )
% 0.44/1.07 }.
% 0.44/1.07 (142) {G0,W7,D4,L1,V1,M1} { successor( X ) = union( X, singleton( X ) )
% 0.44/1.07 }.
% 0.44/1.07 (143) {G0,W5,D3,L1,V0,M1} { subclass( successor_relation, cross_product(
% 0.44/1.07 universal_class, universal_class ) ) }.
% 0.44/1.07 (144) {G0,W8,D3,L2,V2,M2} { ! member( ordered_pair( X, Y ),
% 0.44/1.07 successor_relation ), member( X, universal_class ) }.
% 0.44/1.07 (145) {G0,W8,D3,L2,V2,M2} { ! member( ordered_pair( X, Y ),
% 0.44/1.07 successor_relation ), alpha2( X, Y ) }.
% 0.44/1.07 (146) {G0,W11,D3,L3,V2,M3} { ! member( X, universal_class ), ! alpha2( X,
% 0.44/1.07 Y ), member( ordered_pair( X, Y ), successor_relation ) }.
% 0.44/1.07 (147) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), member( Y, universal_class )
% 0.44/1.07 }.
% 0.44/1.07 (148) {G0,W7,D3,L2,V2,M2} { ! alpha2( X, Y ), successor( X ) = Y }.
% 0.44/1.07 (149) {G0,W10,D3,L3,V2,M3} { ! member( Y, universal_class ), ! successor(
% 0.44/1.07 X ) = Y, alpha2( X, Y ) }.
% 0.44/1.07 (150) {G0,W8,D5,L1,V1,M1} { inverse( X ) = domain_of( flip( cross_product
% 0.44/1.07 ( X, universal_class ) ) ) }.
% 0.44/1.07 (151) {G0,W6,D4,L1,V1,M1} { range_of( X ) = domain_of( inverse( X ) ) }.
% 0.44/1.07 (152) {G0,W9,D4,L1,V2,M1} { image( Y, X ) = range_of( restrict( Y, X,
% 0.44/1.07 universal_class ) ) }.
% 0.44/1.07 (153) {G0,W5,D2,L2,V1,M2} { ! inductive( X ), member( null_class, X ) }.
% 0.44/1.07 (154) {G0,W7,D3,L2,V1,M2} { ! inductive( X ), subclass( image(
% 0.44/1.07 successor_relation, X ), X ) }.
% 0.44/1.07 (155) {G0,W10,D3,L3,V1,M3} { ! member( null_class, X ), ! subclass( image
% 0.44/1.07 ( successor_relation, X ), X ), inductive( X ) }.
% 0.44/1.07 (156) {G0,W3,D2,L1,V0,M1} { member( skol2, universal_class ) }.
% 0.44/1.07 (157) {G0,W2,D2,L1,V0,M1} { inductive( skol2 ) }.
% 0.44/1.07 (158) {G0,W5,D2,L2,V1,M2} { ! inductive( X ), subclass( skol2, X ) }.
% 0.44/1.07 (159) {G0,W9,D3,L2,V3,M2} { ! member( X, sum_class( Y ) ), member( skol3(
% 0.44/1.07 Z, Y ), Y ) }.
% 0.44/1.07 (160) {G0,W9,D3,L2,V2,M2} { ! member( X, sum_class( Y ) ), member( X,
% 0.44/1.07 skol3( X, Y ) ) }.
% 0.44/1.07 (161) {G0,W10,D3,L3,V3,M3} { ! member( X, Z ), ! member( Z, Y ), member( X
% 0.44/1.07 , sum_class( Y ) ) }.
% 0.44/1.07 (162) {G0,W7,D3,L2,V1,M2} { ! member( X, universal_class ), member(
% 0.44/1.07 sum_class( X ), universal_class ) }.
% 0.44/1.07 (163) {G0,W7,D3,L2,V2,M2} { ! member( X, power_class( Y ) ), member( X,
% 0.44/1.07 universal_class ) }.
% 0.44/1.07 (164) {G0,W7,D3,L2,V2,M2} { ! member( X, power_class( Y ) ), subclass( X,
% 0.44/1.07 Y ) }.
% 0.44/1.07 (165) {G0,W10,D3,L3,V2,M3} { ! member( X, universal_class ), ! subclass( X
% 0.44/1.07 , Y ), member( X, power_class( Y ) ) }.
% 0.44/1.07 (166) {G0,W7,D3,L2,V1,M2} { ! member( X, universal_class ), member(
% 0.44/1.07 power_class( X ), universal_class ) }.
% 0.44/1.07 (167) {G0,W7,D3,L1,V2,M1} { subclass( compose( Y, X ), cross_product(
% 0.44/1.07 universal_class, universal_class ) ) }.
% 0.44/1.07 (168) {G0,W10,D3,L2,V4,M2} { ! member( ordered_pair( Z, T ), compose( Y, X
% 0.44/1.07 ) ), member( Z, universal_class ) }.
% 0.44/1.07 (169) {G0,W15,D5,L2,V4,M2} { ! member( ordered_pair( Z, T ), compose( Y, X
% 0.44/1.07 ) ), member( T, image( Y, image( X, singleton( Z ) ) ) ) }.
% 0.44/1.07 (170) {G0,W18,D5,L3,V4,M3} { ! member( Z, universal_class ), ! member( T,
% 0.44/1.07 image( Y, image( X, singleton( Z ) ) ) ), member( ordered_pair( Z, T ),
% 0.44/1.07 compose( Y, X ) ) }.
% 0.44/1.07 (171) {G0,W7,D3,L2,V2,M2} { ! member( X, identity_relation ), member(
% 0.44/1.07 skol4( Y ), universal_class ) }.
% 0.44/1.07 (172) {G0,W10,D4,L2,V1,M2} { ! member( X, identity_relation ), X =
% 0.44/1.07 ordered_pair( skol4( X ), skol4( X ) ) }.
% 0.44/1.07 (173) {G0,W11,D3,L3,V2,M3} { ! member( Y, universal_class ), ! X =
% 0.44/1.07 ordered_pair( Y, Y ), member( X, identity_relation ) }.
% 0.44/1.07 (174) {G0,W7,D3,L2,V1,M2} { ! function( X ), subclass( X, cross_product(
% 0.44/1.07 universal_class, universal_class ) ) }.
% 0.44/1.07 (175) {G0,W8,D4,L2,V1,M2} { ! function( X ), subclass( compose( X, inverse
% 0.44/1.07 ( X ) ), identity_relation ) }.
% 0.44/1.07 (176) {G0,W13,D4,L3,V1,M3} { ! subclass( X, cross_product( universal_class
% 0.44/1.07 , universal_class ) ), ! subclass( compose( X, inverse( X ) ),
% 0.44/1.07 identity_relation ), function( X ) }.
% 0.44/1.07 (177) {G0,W10,D3,L3,V2,M3} { ! member( X, universal_class ), ! function( Y
% 0.44/1.07 ), member( image( Y, X ), universal_class ) }.
% 0.44/1.07 (178) {G0,W9,D2,L3,V3,M3} { ! disjoint( X, Y ), ! member( Z, X ), ! member
% 0.44/1.07 ( Z, Y ) }.
% 0.44/1.07 (179) {G0,W8,D3,L2,V3,M2} { member( skol5( Z, Y ), Y ), disjoint( X, Y )
% 0.44/1.07 }.
% 0.44/1.07 (180) {G0,W8,D3,L2,V2,M2} { member( skol5( X, Y ), X ), disjoint( X, Y )
% 0.44/1.07 }.
% 0.44/1.07 (181) {G0,W7,D3,L2,V2,M2} { X = null_class, member( skol6( Y ),
% 0.44/1.07 universal_class ) }.
% 0.44/1.07 (182) {G0,W7,D3,L2,V1,M2} { X = null_class, member( skol6( X ), X ) }.
% 0.44/1.07 (183) {G0,W7,D3,L2,V1,M2} { X = null_class, disjoint( skol6( X ), X ) }.
% 0.44/1.07 (184) {G0,W9,D5,L1,V2,M1} { apply( X, Y ) = sum_class( image( X, singleton
% 0.44/1.07 ( Y ) ) ) }.
% 0.44/1.07 (185) {G0,W2,D2,L1,V0,M1} { function( skol7 ) }.
% 0.44/1.07 (186) {G0,W11,D3,L3,V1,M3} { ! member( X, universal_class ), X =
% 0.44/1.07 null_class, member( apply( skol7, X ), X ) }.
% 0.44/1.07 (187) {G0,W3,D2,L1,V0,M1} { ! skol8 = skol8 }.
% 0.44/1.07
% 0.44/1.07
% 0.44/1.07 Total Proof:
% 0.44/1.07
% 0.44/1.07 eqrefl: (232) {G0,W0,D0,L0,V0,M0} { }.
% 0.44/1.07 parent0[0]: (187) {G0,W3,D2,L1,V0,M1} { ! skol8 = skol8 }.
% 0.44/1.07 substitution0:
% 0.44/1.07 end
% 0.44/1.07
% 0.44/1.07 subsumption: (92) {G0,W0,D0,L0,V0,M0} I;q { }.
% 0.44/1.07 parent0: (232) {G0,W0,D0,L0,V0,M0} { }.
% 0.44/1.07 substitution0:
% 0.44/1.07 end
% 0.44/1.07 permutation0:
% 0.44/1.07 end
% 0.44/1.07
% 0.44/1.07 Proof check complete!
% 0.44/1.07
% 0.44/1.07 Memory use:
% 0.44/1.07
% 0.44/1.07 space for terms: 2860
% 0.44/1.07 space for clauses: 6301
% 0.44/1.07
% 0.44/1.07
% 0.44/1.07 clauses generated: 94
% 0.44/1.07 clauses kept: 93
% 0.44/1.07 clauses selected: 0
% 0.44/1.07 clauses deleted: 0
% 0.44/1.07 clauses inuse deleted: 0
% 0.44/1.07
% 0.44/1.07 subsentry: 115
% 0.44/1.07 literals s-matched: 69
% 0.44/1.07 literals matched: 67
% 0.44/1.07 full subsumption: 25
% 0.44/1.07
% 0.44/1.07 checksum: -578514360
% 0.44/1.07
% 0.44/1.07
% 0.44/1.07 Bliksem ended
%------------------------------------------------------------------------------