TSTP Solution File: SET020+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET020+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Mon Jul 18 22:45:33 EDT 2022
% Result : Theorem 3.10s 3.54s
% Output : Refutation 3.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET020+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.06/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n015.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 : Mon Jul 11 01:33:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.69/1.08 *** allocated 10000 integers for termspace/termends
% 0.69/1.08 *** allocated 10000 integers for clauses
% 0.69/1.08 *** allocated 10000 integers for justifications
% 0.69/1.08 Bliksem 1.12
% 0.69/1.08
% 0.69/1.08
% 0.69/1.08 Automatic Strategy Selection
% 0.69/1.08
% 0.69/1.08
% 0.69/1.08 Clauses:
% 0.69/1.08
% 0.69/1.08 { ! subclass( X, Y ), ! member( Z, X ), member( Z, Y ) }.
% 0.69/1.08 { ! member( skol1( Z, Y ), Y ), subclass( X, Y ) }.
% 0.69/1.08 { member( skol1( X, Y ), X ), subclass( X, Y ) }.
% 0.69/1.08 { subclass( X, universal_class ) }.
% 0.69/1.08 { ! X = Y, subclass( X, Y ) }.
% 0.69/1.08 { ! X = Y, subclass( Y, X ) }.
% 0.69/1.08 { ! subclass( X, Y ), ! subclass( Y, X ), X = Y }.
% 0.69/1.08 { ! member( X, unordered_pair( Y, Z ) ), member( X, universal_class ) }.
% 0.69/1.08 { ! member( X, unordered_pair( Y, Z ) ), alpha1( X, Y, Z ) }.
% 0.69/1.08 { ! member( X, universal_class ), ! alpha1( X, Y, Z ), member( X,
% 0.69/1.08 unordered_pair( Y, Z ) ) }.
% 0.69/1.08 { ! alpha1( X, Y, Z ), X = Y, X = Z }.
% 0.69/1.08 { ! X = Y, alpha1( X, Y, Z ) }.
% 0.69/1.08 { ! X = Z, alpha1( X, Y, Z ) }.
% 0.69/1.08 { member( unordered_pair( X, Y ), universal_class ) }.
% 0.69/1.08 { singleton( X ) = unordered_pair( X, X ) }.
% 0.69/1.08 { ordered_pair( X, Y ) = unordered_pair( singleton( X ), unordered_pair( X
% 0.69/1.08 , singleton( Y ) ) ) }.
% 0.69/1.08 { ! member( ordered_pair( X, Y ), cross_product( Z, T ) ), member( X, Z ) }
% 0.69/1.08 .
% 0.69/1.08 { ! member( ordered_pair( X, Y ), cross_product( Z, T ) ), member( Y, T ) }
% 0.69/1.08 .
% 0.69/1.08 { ! member( X, Z ), ! member( Y, T ), member( ordered_pair( X, Y ),
% 0.69/1.08 cross_product( Z, T ) ) }.
% 0.69/1.08 { ! member( X, universal_class ), ! member( Y, universal_class ), first(
% 0.69/1.08 ordered_pair( X, Y ) ) = X }.
% 0.69/1.08 { ! member( X, universal_class ), ! member( Y, universal_class ), second(
% 0.69/1.08 ordered_pair( X, Y ) ) = Y }.
% 0.69/1.08 { ! member( X, cross_product( Y, Z ) ), X = ordered_pair( first( X ),
% 0.69/1.08 second( X ) ) }.
% 0.69/1.08 { ! member( ordered_pair( X, Y ), element_relation ), member( Y,
% 0.69/1.08 universal_class ) }.
% 0.69/1.08 { ! member( ordered_pair( X, Y ), element_relation ), member( X, Y ) }.
% 0.69/1.08 { ! member( Y, universal_class ), ! member( X, Y ), member( ordered_pair( X
% 0.69/1.08 , Y ), element_relation ) }.
% 0.69/1.08 { subclass( element_relation, cross_product( universal_class,
% 0.69/1.08 universal_class ) ) }.
% 0.69/1.08 { ! member( Z, intersection( X, Y ) ), member( Z, X ) }.
% 0.69/1.08 { ! member( Z, intersection( X, Y ) ), member( Z, Y ) }.
% 0.69/1.08 { ! member( Z, X ), ! member( Z, Y ), member( Z, intersection( X, Y ) ) }.
% 0.69/1.08 { ! member( Y, complement( X ) ), member( Y, universal_class ) }.
% 0.69/1.08 { ! member( Y, complement( X ) ), ! member( Y, X ) }.
% 0.69/1.08 { ! member( Y, universal_class ), member( Y, X ), member( Y, complement( X
% 0.69/1.08 ) ) }.
% 0.69/1.08 { restrict( Y, X, Z ) = intersection( Y, cross_product( X, Z ) ) }.
% 0.69/1.08 { ! member( X, null_class ) }.
% 0.69/1.08 { ! member( Y, domain_of( X ) ), member( Y, universal_class ) }.
% 0.69/1.08 { ! member( Y, domain_of( X ) ), ! restrict( X, singleton( Y ),
% 0.69/1.08 universal_class ) = null_class }.
% 0.69/1.08 { ! member( Y, universal_class ), restrict( X, singleton( Y ),
% 0.69/1.08 universal_class ) = null_class, member( Y, domain_of( X ) ) }.
% 0.69/1.08 { ! member( ordered_pair( ordered_pair( Y, Z ), T ), rotate( X ) ), member
% 0.69/1.08 ( ordered_pair( ordered_pair( Y, Z ), T ), cross_product( cross_product(
% 0.69/1.08 universal_class, universal_class ), universal_class ) ) }.
% 0.69/1.08 { ! member( ordered_pair( ordered_pair( Y, Z ), T ), rotate( X ) ), member
% 0.69/1.08 ( ordered_pair( ordered_pair( Z, T ), Y ), X ) }.
% 0.69/1.08 { ! member( ordered_pair( ordered_pair( Y, Z ), T ), cross_product(
% 0.69/1.08 cross_product( universal_class, universal_class ), universal_class ) ), !
% 0.69/1.08 member( ordered_pair( ordered_pair( Z, T ), Y ), X ), member(
% 0.69/1.08 ordered_pair( ordered_pair( Y, Z ), T ), rotate( X ) ) }.
% 0.69/1.08 { subclass( rotate( X ), cross_product( cross_product( universal_class,
% 0.69/1.08 universal_class ), universal_class ) ) }.
% 0.69/1.08 { ! member( ordered_pair( ordered_pair( X, Y ), Z ), flip( T ) ), member(
% 0.69/1.08 ordered_pair( ordered_pair( X, Y ), Z ), cross_product( cross_product(
% 0.69/1.08 universal_class, universal_class ), universal_class ) ) }.
% 0.69/1.08 { ! member( ordered_pair( ordered_pair( X, Y ), Z ), flip( T ) ), member(
% 0.69/1.08 ordered_pair( ordered_pair( Y, X ), Z ), T ) }.
% 0.69/1.08 { ! member( ordered_pair( ordered_pair( X, Y ), Z ), cross_product(
% 0.69/1.08 cross_product( universal_class, universal_class ), universal_class ) ), !
% 0.69/1.08 member( ordered_pair( ordered_pair( Y, X ), Z ), T ), member(
% 0.69/1.08 ordered_pair( ordered_pair( X, Y ), Z ), flip( T ) ) }.
% 0.69/1.08 { subclass( flip( X ), cross_product( cross_product( universal_class,
% 0.72/1.26 universal_class ), universal_class ) ) }.
% 0.72/1.26 { ! member( Z, union( X, Y ) ), member( Z, X ), member( Z, Y ) }.
% 0.72/1.26 { ! member( Z, X ), member( Z, union( X, Y ) ) }.
% 0.72/1.26 { ! member( Z, Y ), member( Z, union( X, Y ) ) }.
% 0.72/1.26 { successor( X ) = union( X, singleton( X ) ) }.
% 0.72/1.26 { subclass( successor_relation, cross_product( universal_class,
% 0.72/1.26 universal_class ) ) }.
% 0.72/1.26 { ! member( ordered_pair( X, Y ), successor_relation ), member( X,
% 0.72/1.26 universal_class ) }.
% 0.72/1.26 { ! member( ordered_pair( X, Y ), successor_relation ), alpha2( X, Y ) }.
% 0.72/1.26 { ! member( X, universal_class ), ! alpha2( X, Y ), member( ordered_pair( X
% 0.72/1.26 , Y ), successor_relation ) }.
% 0.72/1.26 { ! alpha2( X, Y ), member( Y, universal_class ) }.
% 0.72/1.26 { ! alpha2( X, Y ), successor( X ) = Y }.
% 0.72/1.26 { ! member( Y, universal_class ), ! successor( X ) = Y, alpha2( X, Y ) }.
% 0.72/1.26 { inverse( X ) = domain_of( flip( cross_product( X, universal_class ) ) ) }
% 0.72/1.26 .
% 0.72/1.26 { range_of( X ) = domain_of( inverse( X ) ) }.
% 0.72/1.26 { image( Y, X ) = range_of( restrict( Y, X, universal_class ) ) }.
% 0.72/1.26 { ! inductive( X ), member( null_class, X ) }.
% 0.72/1.26 { ! inductive( X ), subclass( image( successor_relation, X ), X ) }.
% 0.72/1.26 { ! member( null_class, X ), ! subclass( image( successor_relation, X ), X
% 0.72/1.26 ), inductive( X ) }.
% 0.72/1.26 { member( skol2, universal_class ) }.
% 0.72/1.26 { inductive( skol2 ) }.
% 0.72/1.26 { ! inductive( X ), subclass( skol2, X ) }.
% 0.72/1.26 { ! member( X, sum_class( Y ) ), member( skol3( Z, Y ), Y ) }.
% 0.72/1.26 { ! member( X, sum_class( Y ) ), member( X, skol3( X, Y ) ) }.
% 0.72/1.26 { ! member( X, Z ), ! member( Z, Y ), member( X, sum_class( Y ) ) }.
% 0.72/1.26 { ! member( X, universal_class ), member( sum_class( X ), universal_class )
% 0.72/1.26 }.
% 0.72/1.26 { ! member( X, power_class( Y ) ), member( X, universal_class ) }.
% 0.72/1.26 { ! member( X, power_class( Y ) ), subclass( X, Y ) }.
% 0.72/1.26 { ! member( X, universal_class ), ! subclass( X, Y ), member( X,
% 0.72/1.26 power_class( Y ) ) }.
% 0.72/1.26 { ! member( X, universal_class ), member( power_class( X ), universal_class
% 0.72/1.26 ) }.
% 0.72/1.26 { subclass( compose( Y, X ), cross_product( universal_class,
% 0.72/1.26 universal_class ) ) }.
% 0.72/1.26 { ! member( ordered_pair( Z, T ), compose( Y, X ) ), member( Z,
% 0.72/1.26 universal_class ) }.
% 0.72/1.26 { ! member( ordered_pair( Z, T ), compose( Y, X ) ), member( T, image( Y,
% 0.72/1.26 image( X, singleton( Z ) ) ) ) }.
% 0.72/1.26 { ! member( Z, universal_class ), ! member( T, image( Y, image( X,
% 0.72/1.26 singleton( Z ) ) ) ), member( ordered_pair( Z, T ), compose( Y, X ) ) }.
% 0.72/1.26 { ! member( X, identity_relation ), member( skol4( Y ), universal_class ) }
% 0.72/1.26 .
% 0.72/1.26 { ! member( X, identity_relation ), X = ordered_pair( skol4( X ), skol4( X
% 0.72/1.26 ) ) }.
% 0.72/1.26 { ! member( Y, universal_class ), ! X = ordered_pair( Y, Y ), member( X,
% 0.72/1.26 identity_relation ) }.
% 0.72/1.26 { ! function( X ), subclass( X, cross_product( universal_class,
% 0.72/1.26 universal_class ) ) }.
% 0.72/1.26 { ! function( X ), subclass( compose( X, inverse( X ) ), identity_relation
% 0.72/1.26 ) }.
% 0.72/1.26 { ! subclass( X, cross_product( universal_class, universal_class ) ), !
% 0.72/1.26 subclass( compose( X, inverse( X ) ), identity_relation ), function( X )
% 0.72/1.26 }.
% 0.72/1.26 { ! member( X, universal_class ), ! function( Y ), member( image( Y, X ),
% 0.72/1.26 universal_class ) }.
% 0.72/1.26 { ! disjoint( X, Y ), ! member( Z, X ), ! member( Z, Y ) }.
% 0.72/1.26 { member( skol5( Z, Y ), Y ), disjoint( X, Y ) }.
% 0.72/1.26 { member( skol5( X, Y ), X ), disjoint( X, Y ) }.
% 0.72/1.26 { X = null_class, member( skol6( Y ), universal_class ) }.
% 0.72/1.26 { X = null_class, member( skol6( X ), X ) }.
% 0.72/1.26 { X = null_class, disjoint( skol6( X ), X ) }.
% 0.72/1.26 { apply( X, Y ) = sum_class( image( X, singleton( Y ) ) ) }.
% 0.72/1.26 { function( skol7 ) }.
% 0.72/1.26 { ! member( X, universal_class ), X = null_class, member( apply( skol7, X )
% 0.72/1.26 , X ) }.
% 0.72/1.26 { member( skol8, universal_class ) }.
% 0.72/1.26 { member( skol9, universal_class ) }.
% 0.72/1.26 { skol10 = ordered_pair( skol8, skol9 ) }.
% 0.72/1.26 { ! first( skol10 ) = skol8, ! second( skol10 ) = skol9 }.
% 0.72/1.26
% 0.72/1.26 percentage equality = 0.157360, percentage horn = 0.886598
% 0.72/1.26 This is a problem with some equality
% 0.72/1.26
% 0.72/1.26
% 0.72/1.26
% 0.72/1.26 Options Used:
% 0.72/1.26
% 0.72/1.26 useres = 1
% 0.72/1.26 useparamod = 1
% 0.72/1.26 useeqrefl = 1
% 0.72/1.26 useeqfact = 1
% 0.72/1.26 usefactor = 1
% 0.72/1.26 usesimpsplitting = 0
% 0.72/1.26 usesimpdemod = 5
% 0.72/1.26 usesimpres = 3
% 0.72/1.26
% 0.72/1.26 resimpinuse = 1000
% 0.72/1.26 resimpclauses = 20000
% 0.72/1.26 substype = eqrewr
% 0.72/1.26 backwardsubs = 1
% 3.10/3.54 selectoldest = 5
% 3.10/3.54
% 3.10/3.54 litorderings [0] = split
% 3.10/3.54 litorderings [1] = extend the termordering, first sorting on arguments
% 3.10/3.54
% 3.10/3.54 termordering = kbo
% 3.10/3.54
% 3.10/3.54 litapriori = 0
% 3.10/3.54 termapriori = 1
% 3.10/3.54 litaposteriori = 0
% 3.10/3.54 termaposteriori = 0
% 3.10/3.54 demodaposteriori = 0
% 3.10/3.54 ordereqreflfact = 0
% 3.10/3.54
% 3.10/3.54 litselect = negord
% 3.10/3.54
% 3.10/3.54 maxweight = 15
% 3.10/3.54 maxdepth = 30000
% 3.10/3.54 maxlength = 115
% 3.10/3.54 maxnrvars = 195
% 3.10/3.54 excuselevel = 1
% 3.10/3.54 increasemaxweight = 1
% 3.10/3.54
% 3.10/3.54 maxselected = 10000000
% 3.10/3.54 maxnrclauses = 10000000
% 3.10/3.54
% 3.10/3.54 showgenerated = 0
% 3.10/3.54 showkept = 0
% 3.10/3.54 showselected = 0
% 3.10/3.54 showdeleted = 0
% 3.10/3.54 showresimp = 1
% 3.10/3.54 showstatus = 2000
% 3.10/3.54
% 3.10/3.54 prologoutput = 0
% 3.10/3.54 nrgoals = 5000000
% 3.10/3.54 totalproof = 1
% 3.10/3.54
% 3.10/3.54 Symbols occurring in the translation:
% 3.10/3.54
% 3.10/3.54 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 3.10/3.54 . [1, 2] (w:1, o:46, a:1, s:1, b:0),
% 3.10/3.54 ! [4, 1] (w:0, o:25, a:1, s:1, b:0),
% 3.10/3.54 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 3.10/3.54 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 3.10/3.54 subclass [37, 2] (w:1, o:70, a:1, s:1, b:0),
% 3.10/3.54 member [39, 2] (w:1, o:71, a:1, s:1, b:0),
% 3.10/3.54 universal_class [40, 0] (w:1, o:12, a:1, s:1, b:0),
% 3.10/3.54 unordered_pair [41, 2] (w:1, o:72, a:1, s:1, b:0),
% 3.10/3.54 singleton [42, 1] (w:1, o:32, a:1, s:1, b:0),
% 3.10/3.54 ordered_pair [43, 2] (w:1, o:73, a:1, s:1, b:0),
% 3.10/3.54 cross_product [45, 2] (w:1, o:74, a:1, s:1, b:0),
% 3.10/3.54 first [46, 1] (w:1, o:33, a:1, s:1, b:0),
% 3.10/3.54 second [47, 1] (w:1, o:34, a:1, s:1, b:0),
% 3.10/3.54 element_relation [49, 0] (w:1, o:16, a:1, s:1, b:0),
% 3.10/3.54 intersection [50, 2] (w:1, o:76, a:1, s:1, b:0),
% 3.10/3.54 complement [51, 1] (w:1, o:35, a:1, s:1, b:0),
% 3.10/3.54 restrict [53, 3] (w:1, o:85, a:1, s:1, b:0),
% 3.10/3.54 null_class [54, 0] (w:1, o:17, a:1, s:1, b:0),
% 3.10/3.54 domain_of [55, 1] (w:1, o:36, a:1, s:1, b:0),
% 3.10/3.54 rotate [57, 1] (w:1, o:30, a:1, s:1, b:0),
% 3.10/3.54 flip [58, 1] (w:1, o:37, a:1, s:1, b:0),
% 3.10/3.54 union [59, 2] (w:1, o:77, a:1, s:1, b:0),
% 3.10/3.54 successor [60, 1] (w:1, o:38, a:1, s:1, b:0),
% 3.10/3.54 successor_relation [61, 0] (w:1, o:18, a:1, s:1, b:0),
% 3.10/3.54 inverse [62, 1] (w:1, o:39, a:1, s:1, b:0),
% 3.10/3.54 range_of [63, 1] (w:1, o:31, a:1, s:1, b:0),
% 3.10/3.54 image [64, 2] (w:1, o:75, a:1, s:1, b:0),
% 3.10/3.54 inductive [65, 1] (w:1, o:40, a:1, s:1, b:0),
% 3.10/3.54 sum_class [66, 1] (w:1, o:41, a:1, s:1, b:0),
% 3.10/3.54 power_class [67, 1] (w:1, o:42, a:1, s:1, b:0),
% 3.10/3.54 compose [69, 2] (w:1, o:78, a:1, s:1, b:0),
% 3.10/3.54 identity_relation [70, 0] (w:1, o:19, a:1, s:1, b:0),
% 3.10/3.54 function [72, 1] (w:1, o:43, a:1, s:1, b:0),
% 3.10/3.54 disjoint [73, 2] (w:1, o:79, a:1, s:1, b:0),
% 3.10/3.54 apply [74, 2] (w:1, o:80, a:1, s:1, b:0),
% 3.10/3.54 alpha1 [75, 3] (w:1, o:86, a:1, s:1, b:1),
% 3.10/3.54 alpha2 [76, 2] (w:1, o:81, a:1, s:1, b:1),
% 3.10/3.54 skol1 [77, 2] (w:1, o:82, a:1, s:1, b:1),
% 3.10/3.54 skol2 [78, 0] (w:1, o:21, a:1, s:1, b:1),
% 3.10/3.54 skol3 [79, 2] (w:1, o:83, a:1, s:1, b:1),
% 3.10/3.54 skol4 [80, 1] (w:1, o:44, a:1, s:1, b:1),
% 3.10/3.54 skol5 [81, 2] (w:1, o:84, a:1, s:1, b:1),
% 3.10/3.54 skol6 [82, 1] (w:1, o:45, a:1, s:1, b:1),
% 3.10/3.54 skol7 [83, 0] (w:1, o:22, a:1, s:1, b:1),
% 3.10/3.54 skol8 [84, 0] (w:1, o:23, a:1, s:1, b:1),
% 3.10/3.54 skol9 [85, 0] (w:1, o:24, a:1, s:1, b:1),
% 3.10/3.54 skol10 [86, 0] (w:1, o:20, a:1, s:1, b:1).
% 3.10/3.54
% 3.10/3.54
% 3.10/3.54 Starting Search:
% 3.10/3.54
% 3.10/3.54 *** allocated 15000 integers for clauses
% 3.10/3.54 *** allocated 22500 integers for clauses
% 3.10/3.54 *** allocated 33750 integers for clauses
% 3.10/3.54 *** allocated 15000 integers for termspace/termends
% 3.10/3.54 *** allocated 50625 integers for clauses
% 3.10/3.54 *** allocated 22500 integers for termspace/termends
% 3.10/3.54 Resimplifying inuse:
% 3.10/3.54 Done
% 3.10/3.54
% 3.10/3.54 *** allocated 75937 integers for clauses
% 3.10/3.54 *** allocated 33750 integers for termspace/termends
% 3.10/3.54 *** allocated 113905 integers for clauses
% 3.10/3.54
% 3.10/3.54 Intermediate Status:
% 3.10/3.54 Generated: 5271
% 3.10/3.54 Kept: 2095
% 3.10/3.54 Inuse: 125
% 3.10/3.54 Deleted: 3
% 3.10/3.54 Deletedinuse: 2
% 3.10/3.54
% 3.10/3.54 Resimplifying inuse:
% 3.10/3.54 Done
% 3.10/3.54
% 3.10/3.54 *** allocated 170857 integers for clauses
% 3.10/3.54 *** allocated 50625 integers for termspace/termends
% 3.10/3.54 Resimplifying inuse:
% 3.10/3.54 Done
% 3.10/3.54
% 3.10/3.54 *** allocated 75937 integers for termspace/termends
% 3.10/3.54 *** allocated 256285 integers for clauses
% 3.10/3.54
% 3.10/3.54 Intermediate Status:
% 3.10/3.54 Generated: 10009
% 3.10/3.54 Kept: 4114
% 3.10/3.54 Inuse: 193
% 3.10/3.54 Deleted: 42
% 3.10/3.54 Deletedinuse: 18
% 3.10/3.54
% 3.10/3.54 Resimplifying inuse:
% 3.10/3.54 Done
% 3.10/3.54
% 3.10/3.54 Resimplifying inuse:
% 3.10/3.54 Done
% 3.10/3.54
% 3.10/3.54 *** allocated 113905 integers for termspace/termends
% 3.10/3.54 *** allocated 384427 integers for clauses
% 3.10/3.54
% 3.10/3.54 Intermediate Status:
% 3.10/3.54 Generated: 14174
% 3.10/3.54 Kept: 6363
% 3.10/3.54 Inuse: 257
% 3.10/3.54 Deleted: 49
% 3.10/3.54 Deletedinuse: 20
% 3.10/3.54
% 3.10/3.54 Resimplifying inuse:
% 3.10/3.54 Done
% 3.10/3.54
% 3.10/3.54 Resimplifying inuse:
% 3.10/3.54 Done
% 3.10/3.54
% 3.10/3.54 *** allocated 576640 integers for clauses
% 3.10/3.54 *** allocated 170857 integers for termspace/termends
% 3.10/3.54
% 3.10/3.54 Intermediate Status:
% 3.10/3.54 Generated: 17991
% 3.10/3.54 Kept: 8392
% 3.10/3.54 Inuse: 316
% 3.10/3.54 Deleted: 68
% 3.10/3.54 Deletedinuse: 28
% 3.10/3.54
% 3.10/3.54 Resimplifying inuse:
% 3.10/3.54 Done
% 3.10/3.54
% 3.10/3.54 Resimplifying inuse:
% 3.10/3.54 Done
% 3.10/3.54
% 3.10/3.54
% 3.10/3.54 Intermediate Status:
% 3.10/3.54 Generated: 25116
% 3.10/3.54 Kept: 10717
% 3.10/3.54 Inuse: 362
% 3.10/3.54 Deleted: 76
% 3.10/3.54 Deletedinuse: 32
% 3.10/3.54
% 3.10/3.54 Resimplifying inuse:
% 3.10/3.54 Done
% 3.10/3.54
% 3.10/3.54 *** allocated 864960 integers for clauses
% 3.10/3.54 Resimplifying inuse:
% 3.10/3.54 Done
% 3.10/3.54
% 3.10/3.54 *** allocated 256285 integers for termspace/termends
% 3.10/3.54
% 3.10/3.54 Intermediate Status:
% 3.10/3.54 Generated: 31228
% 3.10/3.54 Kept: 13965
% 3.10/3.54 Inuse: 377
% 3.10/3.54 Deleted: 79
% 3.10/3.54 Deletedinuse: 35
% 3.10/3.54
% 3.10/3.54 Resimplifying inuse:
% 3.10/3.54 Done
% 3.10/3.54
% 3.10/3.54 Resimplifying inuse:
% 3.10/3.54 Done
% 3.10/3.54
% 3.10/3.54
% 3.10/3.54 Intermediate Status:
% 3.10/3.54 Generated: 35923
% 3.10/3.54 Kept: 15987
% 3.10/3.54 Inuse: 398
% 3.10/3.54 Deleted: 79
% 3.10/3.54 Deletedinuse: 35
% 3.10/3.54
% 3.10/3.54 Resimplifying inuse:
% 3.10/3.54 Done
% 3.10/3.54
% 3.10/3.54 Resimplifying inuse:
% 3.10/3.54 Done
% 3.10/3.54
% 3.10/3.54
% 3.10/3.54 Intermediate Status:
% 3.10/3.54 Generated: 40605
% 3.10/3.54 Kept: 17997
% 3.10/3.54 Inuse: 444
% 3.10/3.54 Deleted: 86
% 3.10/3.54 Deletedinuse: 39
% 3.10/3.54
% 3.10/3.54 Resimplifying inuse:
% 3.10/3.54 Done
% 3.10/3.54
% 3.10/3.54 *** allocated 1297440 integers for clauses
% 3.10/3.54 Resimplifying inuse:
% 3.10/3.54 Done
% 3.10/3.54
% 3.10/3.54 *** allocated 384427 integers for termspace/termends
% 3.10/3.54
% 3.10/3.54 Intermediate Status:
% 3.10/3.54 Generated: 44865
% 3.10/3.54 Kept: 20003
% 3.10/3.54 Inuse: 485
% 3.10/3.54 Deleted: 86
% 3.10/3.54 Deletedinuse: 39
% 3.10/3.54
% 3.10/3.54 Resimplifying clauses:
% 3.10/3.54 Done
% 3.10/3.54
% 3.10/3.54
% 3.10/3.54 Bliksems!, er is een bewijs:
% 3.10/3.54 % SZS status Theorem
% 3.10/3.54 % SZS output start Refutation
% 3.10/3.54
% 3.10/3.54 (18) {G0,W12,D4,L3,V2,M3} I { ! member( X, universal_class ), ! member( Y,
% 3.10/3.54 universal_class ), first( ordered_pair( X, Y ) ) ==> X }.
% 3.10/3.54 (19) {G0,W12,D4,L3,V2,M3} I { ! member( X, universal_class ), ! member( Y,
% 3.10/3.54 universal_class ), second( ordered_pair( X, Y ) ) ==> Y }.
% 3.10/3.54 (92) {G0,W3,D2,L1,V0,M1} I { member( skol8, universal_class ) }.
% 3.10/3.54 (93) {G0,W3,D2,L1,V0,M1} I { member( skol9, universal_class ) }.
% 3.10/3.54 (94) {G0,W5,D3,L1,V0,M1} I { ordered_pair( skol8, skol9 ) ==> skol10 }.
% 3.10/3.54 (95) {G0,W8,D3,L2,V0,M2} I { ! first( skol10 ) ==> skol8, ! second( skol10
% 3.10/3.54 ) ==> skol9 }.
% 3.10/3.54 (1048) {G1,W7,D3,L2,V0,M2} P(94,18);r(92) { ! member( skol9,
% 3.10/3.54 universal_class ), first( skol10 ) ==> skol8 }.
% 3.10/3.54 (1162) {G1,W7,D3,L2,V0,M2} P(94,19);r(92) { ! member( skol9,
% 3.10/3.54 universal_class ), second( skol10 ) ==> skol9 }.
% 3.10/3.54 (20037) {G2,W4,D3,L1,V0,M1} S(1162);r(93) { second( skol10 ) ==> skol9 }.
% 3.10/3.54 (20038) {G2,W4,D3,L1,V0,M1} S(1048);r(93) { first( skol10 ) ==> skol8 }.
% 3.10/3.54 (20039) {G3,W0,D0,L0,V0,M0} R(20037,95);d(20038);q { }.
% 3.10/3.54
% 3.10/3.54
% 3.10/3.54 % SZS output end Refutation
% 3.10/3.54 found a proof!
% 3.10/3.54
% 3.10/3.54
% 3.10/3.54 Unprocessed initial clauses:
% 3.10/3.54
% 3.10/3.54 (20041) {G0,W9,D2,L3,V3,M3} { ! subclass( X, Y ), ! member( Z, X ), member
% 3.10/3.54 ( Z, Y ) }.
% 3.10/3.54 (20042) {G0,W8,D3,L2,V3,M2} { ! member( skol1( Z, Y ), Y ), subclass( X, Y
% 3.10/3.54 ) }.
% 3.10/3.54 (20043) {G0,W8,D3,L2,V2,M2} { member( skol1( X, Y ), X ), subclass( X, Y )
% 3.10/3.54 }.
% 3.10/3.54 (20044) {G0,W3,D2,L1,V1,M1} { subclass( X, universal_class ) }.
% 3.10/3.54 (20045) {G0,W6,D2,L2,V2,M2} { ! X = Y, subclass( X, Y ) }.
% 3.10/3.54 (20046) {G0,W6,D2,L2,V2,M2} { ! X = Y, subclass( Y, X ) }.
% 3.10/3.54 (20047) {G0,W9,D2,L3,V2,M3} { ! subclass( X, Y ), ! subclass( Y, X ), X =
% 3.10/3.54 Y }.
% 3.10/3.54 (20048) {G0,W8,D3,L2,V3,M2} { ! member( X, unordered_pair( Y, Z ) ),
% 3.10/3.54 member( X, universal_class ) }.
% 3.10/3.54 (20049) {G0,W9,D3,L2,V3,M2} { ! member( X, unordered_pair( Y, Z ) ),
% 3.10/3.54 alpha1( X, Y, Z ) }.
% 3.10/3.54 (20050) {G0,W12,D3,L3,V3,M3} { ! member( X, universal_class ), ! alpha1( X
% 3.10/3.54 , Y, Z ), member( X, unordered_pair( Y, Z ) ) }.
% 3.10/3.54 (20051) {G0,W10,D2,L3,V3,M3} { ! alpha1( X, Y, Z ), X = Y, X = Z }.
% 3.10/3.54 (20052) {G0,W7,D2,L2,V3,M2} { ! X = Y, alpha1( X, Y, Z ) }.
% 3.10/3.54 (20053) {G0,W7,D2,L2,V3,M2} { ! X = Z, alpha1( X, Y, Z ) }.
% 3.10/3.54 (20054) {G0,W5,D3,L1,V2,M1} { member( unordered_pair( X, Y ),
% 3.10/3.54 universal_class ) }.
% 3.10/3.54 (20055) {G0,W6,D3,L1,V1,M1} { singleton( X ) = unordered_pair( X, X ) }.
% 3.10/3.54 (20056) {G0,W11,D5,L1,V2,M1} { ordered_pair( X, Y ) = unordered_pair(
% 3.10/3.54 singleton( X ), unordered_pair( X, singleton( Y ) ) ) }.
% 3.10/3.54 (20057) {G0,W10,D3,L2,V4,M2} { ! member( ordered_pair( X, Y ),
% 3.10/3.54 cross_product( Z, T ) ), member( X, Z ) }.
% 3.10/3.54 (20058) {G0,W10,D3,L2,V4,M2} { ! member( ordered_pair( X, Y ),
% 3.10/3.54 cross_product( Z, T ) ), member( Y, T ) }.
% 3.10/3.54 (20059) {G0,W13,D3,L3,V4,M3} { ! member( X, Z ), ! member( Y, T ), member
% 3.10/3.54 ( ordered_pair( X, Y ), cross_product( Z, T ) ) }.
% 3.10/3.54 (20060) {G0,W12,D4,L3,V2,M3} { ! member( X, universal_class ), ! member( Y
% 3.10/3.54 , universal_class ), first( ordered_pair( X, Y ) ) = X }.
% 3.10/3.54 (20061) {G0,W12,D4,L3,V2,M3} { ! member( X, universal_class ), ! member( Y
% 3.10/3.54 , universal_class ), second( ordered_pair( X, Y ) ) = Y }.
% 3.10/3.54 (20062) {G0,W12,D4,L2,V3,M2} { ! member( X, cross_product( Y, Z ) ), X =
% 3.10/3.54 ordered_pair( first( X ), second( X ) ) }.
% 3.10/3.54 (20063) {G0,W8,D3,L2,V2,M2} { ! member( ordered_pair( X, Y ),
% 3.10/3.54 element_relation ), member( Y, universal_class ) }.
% 3.10/3.54 (20064) {G0,W8,D3,L2,V2,M2} { ! member( ordered_pair( X, Y ),
% 3.10/3.54 element_relation ), member( X, Y ) }.
% 3.10/3.54 (20065) {G0,W11,D3,L3,V2,M3} { ! member( Y, universal_class ), ! member( X
% 3.10/3.54 , Y ), member( ordered_pair( X, Y ), element_relation ) }.
% 3.10/3.54 (20066) {G0,W5,D3,L1,V0,M1} { subclass( element_relation, cross_product(
% 3.10/3.54 universal_class, universal_class ) ) }.
% 3.10/3.54 (20067) {G0,W8,D3,L2,V3,M2} { ! member( Z, intersection( X, Y ) ), member
% 3.10/3.54 ( Z, X ) }.
% 3.10/3.54 (20068) {G0,W8,D3,L2,V3,M2} { ! member( Z, intersection( X, Y ) ), member
% 3.10/3.54 ( Z, Y ) }.
% 3.10/3.54 (20069) {G0,W11,D3,L3,V3,M3} { ! member( Z, X ), ! member( Z, Y ), member
% 3.10/3.54 ( Z, intersection( X, Y ) ) }.
% 3.10/3.54 (20070) {G0,W7,D3,L2,V2,M2} { ! member( Y, complement( X ) ), member( Y,
% 3.10/3.54 universal_class ) }.
% 3.10/3.54 (20071) {G0,W7,D3,L2,V2,M2} { ! member( Y, complement( X ) ), ! member( Y
% 3.10/3.54 , X ) }.
% 3.10/3.54 (20072) {G0,W10,D3,L3,V2,M3} { ! member( Y, universal_class ), member( Y,
% 3.10/3.54 X ), member( Y, complement( X ) ) }.
% 3.10/3.54 (20073) {G0,W10,D4,L1,V3,M1} { restrict( Y, X, Z ) = intersection( Y,
% 3.10/3.54 cross_product( X, Z ) ) }.
% 3.10/3.54 (20074) {G0,W3,D2,L1,V1,M1} { ! member( X, null_class ) }.
% 3.10/3.54 (20075) {G0,W7,D3,L2,V2,M2} { ! member( Y, domain_of( X ) ), member( Y,
% 3.10/3.54 universal_class ) }.
% 3.10/3.54 (20076) {G0,W11,D4,L2,V2,M2} { ! member( Y, domain_of( X ) ), ! restrict(
% 3.10/3.54 X, singleton( Y ), universal_class ) = null_class }.
% 3.10/3.54 (20077) {G0,W14,D4,L3,V2,M3} { ! member( Y, universal_class ), restrict( X
% 3.10/3.54 , singleton( Y ), universal_class ) = null_class, member( Y, domain_of( X
% 3.10/3.54 ) ) }.
% 3.10/3.54 (20078) {G0,W19,D4,L2,V4,M2} { ! member( ordered_pair( ordered_pair( Y, Z
% 3.10/3.54 ), T ), rotate( X ) ), member( ordered_pair( ordered_pair( Y, Z ), T ),
% 3.10/3.54 cross_product( cross_product( universal_class, universal_class ),
% 3.10/3.54 universal_class ) ) }.
% 3.10/3.54 (20079) {G0,W15,D4,L2,V4,M2} { ! member( ordered_pair( ordered_pair( Y, Z
% 3.10/3.54 ), T ), rotate( X ) ), member( ordered_pair( ordered_pair( Z, T ), Y ),
% 3.10/3.54 X ) }.
% 3.10/3.54 (20080) {G0,W26,D4,L3,V4,M3} { ! member( ordered_pair( ordered_pair( Y, Z
% 3.10/3.54 ), T ), cross_product( cross_product( universal_class, universal_class )
% 3.10/3.54 , universal_class ) ), ! member( ordered_pair( ordered_pair( Z, T ), Y )
% 3.10/3.54 , X ), member( ordered_pair( ordered_pair( Y, Z ), T ), rotate( X ) ) }.
% 3.10/3.54 (20081) {G0,W8,D4,L1,V1,M1} { subclass( rotate( X ), cross_product(
% 3.10/3.54 cross_product( universal_class, universal_class ), universal_class ) )
% 3.10/3.54 }.
% 3.10/3.54 (20082) {G0,W19,D4,L2,V4,M2} { ! member( ordered_pair( ordered_pair( X, Y
% 3.10/3.54 ), Z ), flip( T ) ), member( ordered_pair( ordered_pair( X, Y ), Z ),
% 3.10/3.54 cross_product( cross_product( universal_class, universal_class ),
% 3.10/3.54 universal_class ) ) }.
% 3.10/3.54 (20083) {G0,W15,D4,L2,V4,M2} { ! member( ordered_pair( ordered_pair( X, Y
% 3.10/3.54 ), Z ), flip( T ) ), member( ordered_pair( ordered_pair( Y, X ), Z ), T
% 3.10/3.54 ) }.
% 3.10/3.54 (20084) {G0,W26,D4,L3,V4,M3} { ! member( ordered_pair( ordered_pair( X, Y
% 3.10/3.54 ), Z ), cross_product( cross_product( universal_class, universal_class )
% 3.10/3.54 , universal_class ) ), ! member( ordered_pair( ordered_pair( Y, X ), Z )
% 3.10/3.54 , T ), member( ordered_pair( ordered_pair( X, Y ), Z ), flip( T ) ) }.
% 3.10/3.54 (20085) {G0,W8,D4,L1,V1,M1} { subclass( flip( X ), cross_product(
% 3.10/3.54 cross_product( universal_class, universal_class ), universal_class ) )
% 3.10/3.54 }.
% 3.10/3.54 (20086) {G0,W11,D3,L3,V3,M3} { ! member( Z, union( X, Y ) ), member( Z, X
% 3.10/3.54 ), member( Z, Y ) }.
% 3.10/3.54 (20087) {G0,W8,D3,L2,V3,M2} { ! member( Z, X ), member( Z, union( X, Y ) )
% 3.10/3.54 }.
% 3.10/3.54 (20088) {G0,W8,D3,L2,V3,M2} { ! member( Z, Y ), member( Z, union( X, Y ) )
% 3.10/3.54 }.
% 3.10/3.54 (20089) {G0,W7,D4,L1,V1,M1} { successor( X ) = union( X, singleton( X ) )
% 3.10/3.54 }.
% 3.10/3.54 (20090) {G0,W5,D3,L1,V0,M1} { subclass( successor_relation, cross_product
% 3.10/3.54 ( universal_class, universal_class ) ) }.
% 3.10/3.54 (20091) {G0,W8,D3,L2,V2,M2} { ! member( ordered_pair( X, Y ),
% 3.10/3.54 successor_relation ), member( X, universal_class ) }.
% 3.10/3.54 (20092) {G0,W8,D3,L2,V2,M2} { ! member( ordered_pair( X, Y ),
% 3.10/3.54 successor_relation ), alpha2( X, Y ) }.
% 3.10/3.54 (20093) {G0,W11,D3,L3,V2,M3} { ! member( X, universal_class ), ! alpha2( X
% 3.10/3.54 , Y ), member( ordered_pair( X, Y ), successor_relation ) }.
% 3.10/3.54 (20094) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), member( Y, universal_class
% 3.10/3.54 ) }.
% 3.10/3.54 (20095) {G0,W7,D3,L2,V2,M2} { ! alpha2( X, Y ), successor( X ) = Y }.
% 3.10/3.54 (20096) {G0,W10,D3,L3,V2,M3} { ! member( Y, universal_class ), ! successor
% 3.10/3.54 ( X ) = Y, alpha2( X, Y ) }.
% 3.10/3.54 (20097) {G0,W8,D5,L1,V1,M1} { inverse( X ) = domain_of( flip(
% 3.10/3.54 cross_product( X, universal_class ) ) ) }.
% 3.10/3.54 (20098) {G0,W6,D4,L1,V1,M1} { range_of( X ) = domain_of( inverse( X ) )
% 3.10/3.54 }.
% 3.10/3.54 (20099) {G0,W9,D4,L1,V2,M1} { image( Y, X ) = range_of( restrict( Y, X,
% 3.10/3.54 universal_class ) ) }.
% 3.10/3.54 (20100) {G0,W5,D2,L2,V1,M2} { ! inductive( X ), member( null_class, X )
% 3.10/3.54 }.
% 3.10/3.54 (20101) {G0,W7,D3,L2,V1,M2} { ! inductive( X ), subclass( image(
% 3.10/3.54 successor_relation, X ), X ) }.
% 3.10/3.54 (20102) {G0,W10,D3,L3,V1,M3} { ! member( null_class, X ), ! subclass(
% 3.10/3.54 image( successor_relation, X ), X ), inductive( X ) }.
% 3.10/3.54 (20103) {G0,W3,D2,L1,V0,M1} { member( skol2, universal_class ) }.
% 3.10/3.54 (20104) {G0,W2,D2,L1,V0,M1} { inductive( skol2 ) }.
% 3.10/3.54 (20105) {G0,W5,D2,L2,V1,M2} { ! inductive( X ), subclass( skol2, X ) }.
% 3.10/3.54 (20106) {G0,W9,D3,L2,V3,M2} { ! member( X, sum_class( Y ) ), member( skol3
% 3.10/3.54 ( Z, Y ), Y ) }.
% 3.10/3.54 (20107) {G0,W9,D3,L2,V2,M2} { ! member( X, sum_class( Y ) ), member( X,
% 3.10/3.54 skol3( X, Y ) ) }.
% 3.10/3.54 (20108) {G0,W10,D3,L3,V3,M3} { ! member( X, Z ), ! member( Z, Y ), member
% 3.10/3.54 ( X, sum_class( Y ) ) }.
% 3.10/3.54 (20109) {G0,W7,D3,L2,V1,M2} { ! member( X, universal_class ), member(
% 3.10/3.54 sum_class( X ), universal_class ) }.
% 3.10/3.54 (20110) {G0,W7,D3,L2,V2,M2} { ! member( X, power_class( Y ) ), member( X,
% 3.10/3.54 universal_class ) }.
% 3.10/3.54 (20111) {G0,W7,D3,L2,V2,M2} { ! member( X, power_class( Y ) ), subclass( X
% 3.10/3.54 , Y ) }.
% 3.10/3.54 (20112) {G0,W10,D3,L3,V2,M3} { ! member( X, universal_class ), ! subclass
% 3.10/3.54 ( X, Y ), member( X, power_class( Y ) ) }.
% 3.10/3.54 (20113) {G0,W7,D3,L2,V1,M2} { ! member( X, universal_class ), member(
% 3.10/3.54 power_class( X ), universal_class ) }.
% 3.10/3.54 (20114) {G0,W7,D3,L1,V2,M1} { subclass( compose( Y, X ), cross_product(
% 3.10/3.54 universal_class, universal_class ) ) }.
% 3.10/3.54 (20115) {G0,W10,D3,L2,V4,M2} { ! member( ordered_pair( Z, T ), compose( Y
% 3.10/3.54 , X ) ), member( Z, universal_class ) }.
% 3.10/3.54 (20116) {G0,W15,D5,L2,V4,M2} { ! member( ordered_pair( Z, T ), compose( Y
% 3.10/3.54 , X ) ), member( T, image( Y, image( X, singleton( Z ) ) ) ) }.
% 3.10/3.54 (20117) {G0,W18,D5,L3,V4,M3} { ! member( Z, universal_class ), ! member( T
% 3.10/3.54 , image( Y, image( X, singleton( Z ) ) ) ), member( ordered_pair( Z, T )
% 3.10/3.54 , compose( Y, X ) ) }.
% 3.10/3.54 (20118) {G0,W7,D3,L2,V2,M2} { ! member( X, identity_relation ), member(
% 3.10/3.54 skol4( Y ), universal_class ) }.
% 3.10/3.54 (20119) {G0,W10,D4,L2,V1,M2} { ! member( X, identity_relation ), X =
% 3.10/3.54 ordered_pair( skol4( X ), skol4( X ) ) }.
% 3.10/3.54 (20120) {G0,W11,D3,L3,V2,M3} { ! member( Y, universal_class ), ! X =
% 3.10/3.54 ordered_pair( Y, Y ), member( X, identity_relation ) }.
% 3.10/3.54 (20121) {G0,W7,D3,L2,V1,M2} { ! function( X ), subclass( X, cross_product
% 3.10/3.54 ( universal_class, universal_class ) ) }.
% 3.10/3.54 (20122) {G0,W8,D4,L2,V1,M2} { ! function( X ), subclass( compose( X,
% 3.10/3.54 inverse( X ) ), identity_relation ) }.
% 3.10/3.54 (20123) {G0,W13,D4,L3,V1,M3} { ! subclass( X, cross_product(
% 3.10/3.54 universal_class, universal_class ) ), ! subclass( compose( X, inverse( X
% 3.10/3.54 ) ), identity_relation ), function( X ) }.
% 3.10/3.54 (20124) {G0,W10,D3,L3,V2,M3} { ! member( X, universal_class ), ! function
% 3.10/3.54 ( Y ), member( image( Y, X ), universal_class ) }.
% 3.10/3.54 (20125) {G0,W9,D2,L3,V3,M3} { ! disjoint( X, Y ), ! member( Z, X ), !
% 3.10/3.54 member( Z, Y ) }.
% 3.10/3.54 (20126) {G0,W8,D3,L2,V3,M2} { member( skol5( Z, Y ), Y ), disjoint( X, Y )
% 3.10/3.54 }.
% 3.10/3.54 (20127) {G0,W8,D3,L2,V2,M2} { member( skol5( X, Y ), X ), disjoint( X, Y )
% 3.10/3.54 }.
% 3.10/3.54 (20128) {G0,W7,D3,L2,V2,M2} { X = null_class, member( skol6( Y ),
% 3.10/3.54 universal_class ) }.
% 3.10/3.54 (20129) {G0,W7,D3,L2,V1,M2} { X = null_class, member( skol6( X ), X ) }.
% 3.10/3.54 (20130) {G0,W7,D3,L2,V1,M2} { X = null_class, disjoint( skol6( X ), X )
% 3.10/3.54 }.
% 3.10/3.54 (20131) {G0,W9,D5,L1,V2,M1} { apply( X, Y ) = sum_class( image( X,
% 3.10/3.54 singleton( Y ) ) ) }.
% 3.10/3.54 (20132) {G0,W2,D2,L1,V0,M1} { function( skol7 ) }.
% 3.10/3.54 (20133) {G0,W11,D3,L3,V1,M3} { ! member( X, universal_class ), X =
% 3.10/3.54 null_class, member( apply( skol7, X ), X ) }.
% 3.10/3.54 (20134) {G0,W3,D2,L1,V0,M1} { member( skol8, universal_class ) }.
% 3.10/3.54 (20135) {G0,W3,D2,L1,V0,M1} { member( skol9, universal_class ) }.
% 3.10/3.54 (20136) {G0,W5,D3,L1,V0,M1} { skol10 = ordered_pair( skol8, skol9 ) }.
% 3.10/3.54 (20137) {G0,W8,D3,L2,V0,M2} { ! first( skol10 ) = skol8, ! second( skol10
% 3.10/3.54 ) = skol9 }.
% 3.10/3.54
% 3.10/3.54
% 3.10/3.54 Total Proof:
% 3.10/3.54
% 3.10/3.54 subsumption: (18) {G0,W12,D4,L3,V2,M3} I { ! member( X, universal_class ),
% 3.10/3.54 ! member( Y, universal_class ), first( ordered_pair( X, Y ) ) ==> X }.
% 3.10/3.54 parent0: (20060) {G0,W12,D4,L3,V2,M3} { ! member( X, universal_class ), !
% 3.10/3.54 member( Y, universal_class ), first( ordered_pair( X, Y ) ) = X }.
% 3.10/3.54 substitution0:
% 3.10/3.54 X := X
% 3.10/3.54 Y := Y
% 3.10/3.54 end
% 3.10/3.54 permutation0:
% 3.10/3.54 0 ==> 0
% 3.10/3.54 1 ==> 1
% 3.10/3.54 2 ==> 2
% 3.10/3.54 end
% 3.10/3.54
% 3.10/3.54 subsumption: (19) {G0,W12,D4,L3,V2,M3} I { ! member( X, universal_class ),
% 3.10/3.54 ! member( Y, universal_class ), second( ordered_pair( X, Y ) ) ==> Y }.
% 3.10/3.54 parent0: (20061) {G0,W12,D4,L3,V2,M3} { ! member( X, universal_class ), !
% 3.10/3.54 member( Y, universal_class ), second( ordered_pair( X, Y ) ) = Y }.
% 3.10/3.54 substitution0:
% 3.10/3.54 X := X
% 3.10/3.54 Y := Y
% 3.10/3.54 end
% 3.10/3.54 permutation0:
% 3.10/3.54 0 ==> 0
% 3.10/3.54 1 ==> 1
% 3.10/3.54 2 ==> 2
% 3.10/3.54 end
% 3.10/3.54
% 3.10/3.54 subsumption: (92) {G0,W3,D2,L1,V0,M1} I { member( skol8, universal_class )
% 3.10/3.54 }.
% 3.10/3.54 parent0: (20134) {G0,W3,D2,L1,V0,M1} { member( skol8, universal_class )
% 3.10/3.54 }.
% 3.10/3.54 substitution0:
% 3.10/3.54 end
% 3.10/3.54 permutation0:
% 3.10/3.54 0 ==> 0
% 3.10/3.54 end
% 3.10/3.54
% 3.10/3.54 subsumption: (93) {G0,W3,D2,L1,V0,M1} I { member( skol9, universal_class )
% 3.10/3.54 }.
% 3.10/3.54 parent0: (20135) {G0,W3,D2,L1,V0,M1} { member( skol9, universal_class )
% 3.10/3.54 }.
% 3.10/3.54 substitution0:
% 3.10/3.54 end
% 3.10/3.54 permutation0:
% 3.10/3.54 0 ==> 0
% 3.10/3.54 end
% 3.10/3.54
% 3.10/3.54 eqswap: (20302) {G0,W5,D3,L1,V0,M1} { ordered_pair( skol8, skol9 ) =
% 3.10/3.54 skol10 }.
% 3.10/3.54 parent0[0]: (20136) {G0,W5,D3,L1,V0,M1} { skol10 = ordered_pair( skol8,
% 3.10/3.54 skol9 ) }.
% 3.10/3.54 substitution0:
% 3.10/3.54 end
% 3.10/3.54
% 3.10/3.54 subsumption: (94) {G0,W5,D3,L1,V0,M1} I { ordered_pair( skol8, skol9 ) ==>
% 3.10/3.54 skol10 }.
% 3.10/3.54 parent0: (20302) {G0,W5,D3,L1,V0,M1} { ordered_pair( skol8, skol9 ) =
% 3.10/3.54 skol10 }.
% 3.10/3.54 substitution0:
% 3.10/3.54 end
% 3.10/3.54 permutation0:
% 3.10/3.54 0 ==> 0
% 3.10/3.54 end
% 3.10/3.54
% 3.10/3.54 subsumption: (95) {G0,W8,D3,L2,V0,M2} I { ! first( skol10 ) ==> skol8, !
% 3.10/3.54 second( skol10 ) ==> skol9 }.
% 3.10/3.54 parent0: (20137) {G0,W8,D3,L2,V0,M2} { ! first( skol10 ) = skol8, ! second
% 3.10/3.54 ( skol10 ) = skol9 }.
% 3.10/3.54 substitution0:
% 3.10/3.54 end
% 3.10/3.54 permutation0:
% 3.10/3.54 0 ==> 0
% 3.10/3.54 1 ==> 1
% 3.10/3.54 end
% 3.10/3.54
% 3.10/3.54 eqswap: (20351) {G0,W12,D4,L3,V2,M3} { X ==> first( ordered_pair( X, Y ) )
% 3.10/3.54 , ! member( X, universal_class ), ! member( Y, universal_class ) }.
% 3.10/3.54 parent0[2]: (18) {G0,W12,D4,L3,V2,M3} I { ! member( X, universal_class ), !
% 3.10/3.54 member( Y, universal_class ), first( ordered_pair( X, Y ) ) ==> X }.
% 3.10/3.54 substitution0:
% 3.10/3.54 X := X
% 3.10/3.54 Y := Y
% 3.10/3.54 end
% 3.10/3.54
% 3.10/3.54 paramod: (20352) {G1,W10,D3,L3,V0,M3} { skol8 ==> first( skol10 ), !
% 3.10/3.54 member( skol8, universal_class ), ! member( skol9, universal_class ) }.
% 3.10/3.54 parent0[0]: (94) {G0,W5,D3,L1,V0,M1} I { ordered_pair( skol8, skol9 ) ==>
% 3.10/3.54 skol10 }.
% 3.10/3.54 parent1[0; 3]: (20351) {G0,W12,D4,L3,V2,M3} { X ==> first( ordered_pair( X
% 3.10/3.54 , Y ) ), ! member( X, universal_class ), ! member( Y, universal_class )
% 3.10/3.54 }.
% 3.10/3.54 substitution0:
% 3.10/3.54 end
% 3.10/3.54 substitution1:
% 3.10/3.54 X := skol8
% 3.10/3.54 Y := skol9
% 3.10/3.54 end
% 3.10/3.54
% 3.10/3.54 resolution: (20353) {G1,W7,D3,L2,V0,M2} { skol8 ==> first( skol10 ), !
% 3.10/3.54 member( skol9, universal_class ) }.
% 3.10/3.54 parent0[1]: (20352) {G1,W10,D3,L3,V0,M3} { skol8 ==> first( skol10 ), !
% 3.10/3.54 member( skol8, universal_class ), ! member( skol9, universal_class ) }.
% 3.10/3.54 parent1[0]: (92) {G0,W3,D2,L1,V0,M1} I { member( skol8, universal_class )
% 3.10/3.54 }.
% 3.10/3.54 substitution0:
% 3.10/3.54 end
% 3.10/3.54 substitution1:
% 3.10/3.54 end
% 3.10/3.54
% 3.10/3.54 eqswap: (20354) {G1,W7,D3,L2,V0,M2} { first( skol10 ) ==> skol8, ! member
% 3.10/3.54 ( skol9, universal_class ) }.
% 3.10/3.54 parent0[0]: (20353) {G1,W7,D3,L2,V0,M2} { skol8 ==> first( skol10 ), !
% 3.10/3.54 member( skol9, universal_class ) }.
% 3.10/3.54 substitution0:
% 3.10/3.54 end
% 3.10/3.54
% 3.10/3.54 subsumption: (1048) {G1,W7,D3,L2,V0,M2} P(94,18);r(92) { ! member( skol9,
% 3.10/3.54 universal_class ), first( skol10 ) ==> skol8 }.
% 3.10/3.54 parent0: (20354) {G1,W7,D3,L2,V0,M2} { first( skol10 ) ==> skol8, ! member
% 3.10/3.54 ( skol9, universal_class ) }.
% 3.10/3.54 substitution0:
% 3.10/3.54 end
% 3.10/3.54 permutation0:
% 3.10/3.54 0 ==> 1
% 3.10/3.54 1 ==> 0
% 3.10/3.54 end
% 3.10/3.54
% 3.10/3.54 eqswap: (20356) {G0,W12,D4,L3,V2,M3} { Y ==> second( ordered_pair( X, Y )
% 3.10/3.54 ), ! member( X, universal_class ), ! member( Y, universal_class ) }.
% 3.10/3.54 parent0[2]: (19) {G0,W12,D4,L3,V2,M3} I { ! member( X, universal_class ), !
% 3.10/3.54 member( Y, universal_class ), second( ordered_pair( X, Y ) ) ==> Y }.
% 3.10/3.54 substitution0:
% 3.10/3.54 X := X
% 3.10/3.54 Y := Y
% 3.10/3.54 end
% 3.10/3.54
% 3.10/3.54 paramod: (20357) {G1,W10,D3,L3,V0,M3} { skol9 ==> second( skol10 ), !
% 3.10/3.54 member( skol8, universal_class ), ! member( skol9, universal_class ) }.
% 3.10/3.54 parent0[0]: (94) {G0,W5,D3,L1,V0,M1} I { ordered_pair( skol8, skol9 ) ==>
% 3.10/3.54 skol10 }.
% 3.10/3.54 parent1[0; 3]: (20356) {G0,W12,D4,L3,V2,M3} { Y ==> second( ordered_pair(
% 3.10/3.54 X, Y ) ), ! member( X, universal_class ), ! member( Y, universal_class )
% 3.10/3.54 }.
% 3.10/3.54 substitution0:
% 3.10/3.54 end
% 3.10/3.54 substitution1:
% 3.10/3.54 X := skol8
% 3.10/3.54 Y := skol9
% 3.10/3.54 end
% 3.10/3.54
% 3.10/3.54 resolution: (20358) {G1,W7,D3,L2,V0,M2} { skol9 ==> second( skol10 ), !
% 3.10/3.54 member( skol9, universal_class ) }.
% 3.10/3.54 parent0[1]: (20357) {G1,W10,D3,L3,V0,M3} { skol9 ==> second( skol10 ), !
% 3.10/3.54 member( skol8, universal_class ), ! member( skol9, universal_class ) }.
% 3.10/3.54 parent1[0]: (92) {G0,W3,D2,L1,V0,M1} I { member( skol8, universal_class )
% 3.10/3.54 }.
% 3.10/3.54 substitution0:
% 3.10/3.54 end
% 3.10/3.54 substitution1:
% 3.10/3.54 end
% 3.10/3.54
% 3.10/3.54 eqswap: (20359) {G1,W7,D3,L2,V0,M2} { second( skol10 ) ==> skol9, ! member
% 3.10/3.54 ( skol9, universal_class ) }.
% 3.10/3.54 parent0[0]: (20358) {G1,W7,D3,L2,V0,M2} { skol9 ==> second( skol10 ), !
% 3.10/3.54 member( skol9, universal_class ) }.
% 3.10/3.54 substitution0:
% 3.10/3.54 end
% 3.10/3.54
% 3.10/3.54 subsumption: (1162) {G1,W7,D3,L2,V0,M2} P(94,19);r(92) { ! member( skol9,
% 3.10/3.54 universal_class ), second( skol10 ) ==> skol9 }.
% 3.10/3.54 parent0: (20359) {G1,W7,D3,L2,V0,M2} { second( skol10 ) ==> skol9, !
% 3.10/3.54 member( skol9, universal_class ) }.
% 3.10/3.54 substitution0:
% 3.10/3.54 end
% 3.10/3.54 permutation0:
% 3.10/3.54 0 ==> 1
% 3.10/3.54 1 ==> 0
% 3.10/3.54 end
% 3.10/3.54
% 3.10/3.54 resolution: (20361) {G1,W4,D3,L1,V0,M1} { second( skol10 ) ==> skol9 }.
% 3.10/3.54 parent0[0]: (1162) {G1,W7,D3,L2,V0,M2} P(94,19);r(92) { ! member( skol9,
% 3.10/3.54 universal_class ), second( skol10 ) ==> skol9 }.
% 3.10/3.54 parent1[0]: (93) {G0,W3,D2,L1,V0,M1} I { member( skol9, universal_class )
% 3.10/3.54 }.
% 3.10/3.54 substitution0:
% 3.10/3.54 end
% 3.10/3.54 substitution1:
% 3.10/3.54 end
% 3.10/3.54
% 3.10/3.54 subsumption: (20037) {G2,W4,D3,L1,V0,M1} S(1162);r(93) { second( skol10 )
% 3.10/3.54 ==> skol9 }.
% 3.10/3.54 parent0: (20361) {G1,W4,D3,L1,V0,M1} { second( skol10 ) ==> skol9 }.
% 3.10/3.54 substitution0:
% 3.10/3.54 end
% 3.10/3.54 permutation0:
% 3.10/3.54 0 ==> 0
% 3.10/3.54 end
% 3.10/3.54
% 3.10/3.54 resolution: (20364) {G1,W4,D3,L1,V0,M1} { first( skol10 ) ==> skol8 }.
% 3.10/3.54 parent0[0]: (1048) {G1,W7,D3,L2,V0,M2} P(94,18);r(92) { ! member( skol9,
% 3.10/3.54 universal_class ), first( skol10 ) ==> skol8 }.
% 3.10/3.54 parent1[0]: (93) {G0,W3,D2,L1,V0,M1} I { member( skol9, universal_class )
% 3.10/3.54 }.
% 3.10/3.54 substitution0:
% 3.10/3.54 end
% 3.10/3.54 substitution1:
% 3.10/3.54 end
% 3.10/3.54
% 3.10/3.54 subsumption: (20038) {G2,W4,D3,L1,V0,M1} S(1048);r(93) { first( skol10 )
% 3.10/3.54 ==> skol8 }.
% 3.10/3.54 parent0: (20364) {G1,W4,D3,L1,V0,M1} { first( skol10 ) ==> skol8 }.
% 3.10/3.54 substitution0:
% 3.10/3.54 end
% 3.10/3.54 permutation0:
% 3.10/3.54 0 ==> 0
% 3.10/3.54 end
% 3.10/3.54
% 3.10/3.54 eqswap: (20366) {G2,W4,D3,L1,V0,M1} { skol9 ==> second( skol10 ) }.
% 3.10/3.54 parent0[0]: (20037) {G2,W4,D3,L1,V0,M1} S(1162);r(93) { second( skol10 )
% 3.10/3.54 ==> skol9 }.
% 3.10/3.54 substitution0:
% 3.10/3.54 end
% 3.10/3.54
% 3.10/3.54 eqswap: (20368) {G0,W8,D3,L2,V0,M2} { ! skol9 ==> second( skol10 ), !
% 3.10/3.54 first( skol10 ) ==> skol8 }.
% 3.10/3.54 parent0[1]: (95) {G0,W8,D3,L2,V0,M2} I { ! first( skol10 ) ==> skol8, !
% 3.10/3.54 second( skol10 ) ==> skol9 }.
% 3.10/3.54 substitution0:
% 3.10/3.54 end
% 3.10/3.54
% 3.10/3.54 eqswap: (20369) {G0,W8,D3,L2,V0,M2} { ! skol8 ==> first( skol10 ), ! skol9
% 3.10/3.54 ==> second( skol10 ) }.
% 3.10/3.54 parent0[1]: (20368) {G0,W8,D3,L2,V0,M2} { ! skol9 ==> second( skol10 ), !
% 3.10/3.54 first( skol10 ) ==> skol8 }.
% 3.10/3.54 substitution0:
% 3.10/3.54 end
% 3.10/3.54
% 3.10/3.54 resolution: (20371) {G1,W4,D3,L1,V0,M1} { ! skol8 ==> first( skol10 ) }.
% 3.10/3.54 parent0[1]: (20369) {G0,W8,D3,L2,V0,M2} { ! skol8 ==> first( skol10 ), !
% 3.10/3.54 skol9 ==> second( skol10 ) }.
% 3.10/3.54 parent1[0]: (20366) {G2,W4,D3,L1,V0,M1} { skol9 ==> second( skol10 ) }.
% 3.10/3.54 substitution0:
% 3.10/3.54 end
% 3.10/3.54 substitution1:
% 3.10/3.54 end
% 3.10/3.54
% 3.10/3.54 paramod: (20372) {G2,W3,D2,L1,V0,M1} { ! skol8 ==> skol8 }.
% 3.10/3.54 parent0[0]: (20038) {G2,W4,D3,L1,V0,M1} S(1048);r(93) { first( skol10 ) ==>
% 3.10/3.54 skol8 }.
% 3.10/3.54 parent1[0; 3]: (20371) {G1,W4,D3,L1,V0,M1} { ! skol8 ==> first( skol10 )
% 3.10/3.54 }.
% 3.10/3.54 substitution0:
% 3.10/3.54 end
% 3.10/3.54 substitution1:
% 3.10/3.54 end
% 3.10/3.54
% 3.10/3.54 eqrefl: (20373) {G0,W0,D0,L0,V0,M0} { }.
% 3.10/3.54 parent0[0]: (20372) {G2,W3,D2,L1,V0,M1} { ! skol8 ==> skol8 }.
% 3.10/3.54 substitution0:
% 3.10/3.54 end
% 3.10/3.54
% 3.10/3.54 subsumption: (20039) {G3,W0,D0,L0,V0,M0} R(20037,95);d(20038);q { }.
% 3.10/3.54 parent0: (20373) {G0,W0,D0,L0,V0,M0} { }.
% 3.10/3.54 substitution0:
% 3.10/3.54 end
% 3.10/3.54 permutation0:
% 3.10/3.54 end
% 3.10/3.54
% 3.10/3.54 Proof check complete!
% 3.10/3.54
% 3.10/3.54 Memory use:
% 3.10/3.54
% 3.10/3.54 space for terms: 262243
% 3.10/3.54 space for clauses: 916191
% 3.10/3.54
% 3.10/3.54
% 3.10/3.54 clauses generated: 45058
% 3.10/3.54 clauses kept: 20040
% 3.10/3.54 clauses selected: 486
% 3.10/3.54 clauses deleted: 871
% 3.10/3.54 clauses inuse deleted: 39
% 3.10/3.54
% 3.10/3.54 subsentry: 188524
% 3.10/3.54 literals s-matched: 115822
% 3.10/3.54 literals matched: 112549
% 3.10/3.54 full subsumption: 54959
% 3.10/3.54
% 3.10/3.54 checksum: -746473034
% 3.10/3.54
% 3.10/3.54
% 3.10/3.54 Bliksem ended
%------------------------------------------------------------------------------