%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET060+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n024.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 22:46:16 EDT 2022
% Result : Theorem 0.72s 1.14s
% Output : Refutation 0.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET060+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.03/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n024.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 16:03:28 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.72/1.08 *** allocated 10000 integers for termspace/termends
% 0.72/1.08 *** allocated 10000 integers for clauses
% 0.72/1.08 *** allocated 10000 integers for justifications
% 0.72/1.08 Bliksem 1.12
% 0.72/1.08
% 0.72/1.08
% 0.72/1.08 Automatic Strategy Selection
% 0.72/1.08
% 0.72/1.08
% 0.72/1.08 Clauses:
% 0.72/1.08
% 0.72/1.08 { ! subclass( X, Y ), ! member( Z, X ), member( Z, Y ) }.
% 0.72/1.08 { ! member( skol1( Z, Y ), Y ), subclass( X, Y ) }.
% 0.72/1.08 { member( skol1( X, Y ), X ), subclass( X, Y ) }.
% 0.72/1.08 { subclass( X, universal_class ) }.
% 0.72/1.08 { ! X = Y, subclass( X, Y ) }.
% 0.72/1.08 { ! X = Y, subclass( Y, X ) }.
% 0.72/1.08 { ! subclass( X, Y ), ! subclass( Y, X ), X = Y }.
% 0.72/1.08 { ! member( X, unordered_pair( Y, Z ) ), member( X, universal_class ) }.
% 0.72/1.08 { ! member( X, unordered_pair( Y, Z ) ), alpha1( X, Y, Z ) }.
% 0.72/1.08 { ! member( X, universal_class ), ! alpha1( X, Y, Z ), member( X,
% 0.72/1.08 unordered_pair( Y, Z ) ) }.
% 0.72/1.08 { ! alpha1( X, Y, Z ), X = Y, X = Z }.
% 0.72/1.08 { ! X = Y, alpha1( X, Y, Z ) }.
% 0.72/1.08 { ! X = Z, alpha1( X, Y, Z ) }.
% 0.72/1.08 { member( unordered_pair( X, Y ), universal_class ) }.
% 0.72/1.08 { singleton( X ) = unordered_pair( X, X ) }.
% 0.72/1.08 { ordered_pair( X, Y ) = unordered_pair( singleton( X ), unordered_pair( X
% 0.72/1.08 , singleton( Y ) ) ) }.
% 0.72/1.08 { ! member( ordered_pair( X, Y ), cross_product( Z, T ) ), member( X, Z ) }
% 0.72/1.08 .
% 0.72/1.08 { ! member( ordered_pair( X, Y ), cross_product( Z, T ) ), member( Y, T ) }
% 0.72/1.08 .
% 0.72/1.08 { ! member( X, Z ), ! member( Y, T ), member( ordered_pair( X, Y ),
% 0.72/1.08 cross_product( Z, T ) ) }.
% 0.72/1.08 { ! member( X, universal_class ), ! member( Y, universal_class ), first(
% 0.72/1.08 ordered_pair( X, Y ) ) = X }.
% 0.72/1.08 { ! member( X, universal_class ), ! member( Y, universal_class ), second(
% 0.72/1.08 ordered_pair( X, Y ) ) = Y }.
% 0.72/1.08 { ! member( X, cross_product( Y, Z ) ), X = ordered_pair( first( X ),
% 0.72/1.08 second( X ) ) }.
% 0.72/1.08 { ! member( ordered_pair( X, Y ), element_relation ), member( Y,
% 0.72/1.08 universal_class ) }.
% 0.72/1.08 { ! member( ordered_pair( X, Y ), element_relation ), member( X, Y ) }.
% 0.72/1.08 { ! member( Y, universal_class ), ! member( X, Y ), member( ordered_pair( X
% 0.72/1.08 , Y ), element_relation ) }.
% 0.72/1.08 { subclass( element_relation, cross_product( universal_class,
% 0.72/1.08 universal_class ) ) }.
% 0.72/1.08 { ! member( Z, intersection( X, Y ) ), member( Z, X ) }.
% 0.72/1.08 { ! member( Z, intersection( X, Y ) ), member( Z, Y ) }.
% 0.72/1.08 { ! member( Z, X ), ! member( Z, Y ), member( Z, intersection( X, Y ) ) }.
% 0.72/1.08 { ! member( Y, complement( X ) ), member( Y, universal_class ) }.
% 0.72/1.08 { ! member( Y, complement( X ) ), ! member( Y, X ) }.
% 0.72/1.08 { ! member( Y, universal_class ), member( Y, X ), member( Y, complement( X
% 0.72/1.08 ) ) }.
% 0.72/1.08 { restrict( Y, X, Z ) = intersection( Y, cross_product( X, Z ) ) }.
% 0.72/1.08 { ! member( X, null_class ) }.
% 0.72/1.08 { ! member( Y, domain_of( X ) ), member( Y, universal_class ) }.
% 0.72/1.08 { ! member( Y, domain_of( X ) ), ! restrict( X, singleton( Y ),
% 0.72/1.08 universal_class ) = null_class }.
% 0.72/1.08 { ! member( Y, universal_class ), restrict( X, singleton( Y ),
% 0.72/1.08 universal_class ) = null_class, member( Y, domain_of( X ) ) }.
% 0.72/1.08 { ! member( ordered_pair( ordered_pair( Y, Z ), T ), rotate( X ) ), member
% 0.72/1.08 ( ordered_pair( ordered_pair( Y, Z ), T ), cross_product( cross_product(
% 0.72/1.08 universal_class, universal_class ), universal_class ) ) }.
% 0.72/1.08 { ! member( ordered_pair( ordered_pair( Y, Z ), T ), rotate( X ) ), member
% 0.72/1.08 ( ordered_pair( ordered_pair( Z, T ), Y ), X ) }.
% 0.72/1.08 { ! member( ordered_pair( ordered_pair( Y, Z ), T ), cross_product(
% 0.72/1.08 cross_product( universal_class, universal_class ), universal_class ) ), !
% 0.72/1.08 member( ordered_pair( ordered_pair( Z, T ), Y ), X ), member(
% 0.72/1.08 ordered_pair( ordered_pair( Y, Z ), T ), rotate( X ) ) }.
% 0.72/1.08 { subclass( rotate( X ), cross_product( cross_product( universal_class,
% 0.72/1.08 universal_class ), universal_class ) ) }.
% 0.72/1.08 { ! member( ordered_pair( ordered_pair( X, Y ), Z ), flip( T ) ), member(
% 0.72/1.08 ordered_pair( ordered_pair( X, Y ), Z ), cross_product( cross_product(
% 0.72/1.08 universal_class, universal_class ), universal_class ) ) }.
% 0.72/1.08 { ! member( ordered_pair( ordered_pair( X, Y ), Z ), flip( T ) ), member(
% 0.72/1.08 ordered_pair( ordered_pair( Y, X ), Z ), T ) }.
% 0.72/1.08 { ! member( ordered_pair( ordered_pair( X, Y ), Z ), cross_product(
% 0.72/1.08 cross_product( universal_class, universal_class ), universal_class ) ), !
% 0.72/1.08 member( ordered_pair( ordered_pair( Y, X ), Z ), T ), member(
% 0.72/1.08 ordered_pair( ordered_pair( X, Y ), Z ), flip( T ) ) }.
% 0.72/1.08 { subclass( flip( X ), cross_product( cross_product( universal_class,
% 0.72/1.14 universal_class ), universal_class ) ) }.
% 0.72/1.14 { ! member( Z, union( X, Y ) ), member( Z, X ), member( Z, Y ) }.
% 0.72/1.14 { ! member( Z, X ), member( Z, union( X, Y ) ) }.
% 0.72/1.14 { ! member( Z, Y ), member( Z, union( X, Y ) ) }.
% 0.72/1.14 { successor( X ) = union( X, singleton( X ) ) }.
% 0.72/1.14 { subclass( successor_relation, cross_product( universal_class,
% 0.72/1.14 universal_class ) ) }.
% 0.72/1.14 { ! member( ordered_pair( X, Y ), successor_relation ), member( X,
% 0.72/1.14 universal_class ) }.
% 0.72/1.14 { ! member( ordered_pair( X, Y ), successor_relation ), alpha2( X, Y ) }.
% 0.72/1.14 { ! member( X, universal_class ), ! alpha2( X, Y ), member( ordered_pair( X
% 0.72/1.14 , Y ), successor_relation ) }.
% 0.72/1.14 { ! alpha2( X, Y ), member( Y, universal_class ) }.
% 0.72/1.14 { ! alpha2( X, Y ), successor( X ) = Y }.
% 0.72/1.14 { ! member( Y, universal_class ), ! successor( X ) = Y, alpha2( X, Y ) }.
% 0.72/1.14 { inverse( X ) = domain_of( flip( cross_product( X, universal_class ) ) ) }
% 0.72/1.14 .
% 0.72/1.14 { range_of( X ) = domain_of( inverse( X ) ) }.
% 0.72/1.14 { image( Y, X ) = range_of( restrict( Y, X, universal_class ) ) }.
% 0.72/1.14 { ! inductive( X ), member( null_class, X ) }.
% 0.72/1.14 { ! inductive( X ), subclass( image( successor_relation, X ), X ) }.
% 0.72/1.14 { ! member( null_class, X ), ! subclass( image( successor_relation, X ), X
% 0.72/1.14 ), inductive( X ) }.
% 0.72/1.14 { member( skol2, universal_class ) }.
% 0.72/1.14 { inductive( skol2 ) }.
% 0.72/1.14 { ! inductive( X ), subclass( skol2, X ) }.
% 0.72/1.14 { ! member( X, sum_class( Y ) ), member( skol3( Z, Y ), Y ) }.
% 0.72/1.14 { ! member( X, sum_class( Y ) ), member( X, skol3( X, Y ) ) }.
% 0.72/1.14 { ! member( X, Z ), ! member( Z, Y ), member( X, sum_class( Y ) ) }.
% 0.72/1.14 { ! member( X, universal_class ), member( sum_class( X ), universal_class )
% 0.72/1.14 }.
% 0.72/1.14 { ! member( X, power_class( Y ) ), member( X, universal_class ) }.
% 0.72/1.14 { ! member( X, power_class( Y ) ), subclass( X, Y ) }.
% 0.72/1.14 { ! member( X, universal_class ), ! subclass( X, Y ), member( X,
% 0.72/1.14 power_class( Y ) ) }.
% 0.72/1.14 { ! member( X, universal_class ), member( power_class( X ), universal_class
% 0.72/1.14 ) }.
% 0.72/1.14 { subclass( compose( Y, X ), cross_product( universal_class,
% 0.72/1.14 universal_class ) ) }.
% 0.72/1.14 { ! member( ordered_pair( Z, T ), compose( Y, X ) ), member( Z,
% 0.72/1.14 universal_class ) }.
% 0.72/1.14 { ! member( ordered_pair( Z, T ), compose( Y, X ) ), member( T, image( Y,
% 0.72/1.14 image( X, singleton( Z ) ) ) ) }.
% 0.72/1.14 { ! member( Z, universal_class ), ! member( T, image( Y, image( X,
% 0.72/1.14 singleton( Z ) ) ) ), member( ordered_pair( Z, T ), compose( Y, X ) ) }.
% 0.72/1.14 { ! member( X, identity_relation ), member( skol4( Y ), universal_class ) }
% 0.72/1.14 .
% 0.72/1.14 { ! member( X, identity_relation ), X = ordered_pair( skol4( X ), skol4( X
% 0.72/1.14 ) ) }.
% 0.72/1.14 { ! member( Y, universal_class ), ! X = ordered_pair( Y, Y ), member( X,
% 0.72/1.14 identity_relation ) }.
% 0.72/1.14 { ! function( X ), subclass( X, cross_product( universal_class,
% 0.72/1.14 universal_class ) ) }.
% 0.72/1.14 { ! function( X ), subclass( compose( X, inverse( X ) ), identity_relation
% 0.72/1.14 ) }.
% 0.72/1.14 { ! subclass( X, cross_product( universal_class, universal_class ) ), !
% 0.72/1.14 subclass( compose( X, inverse( X ) ), identity_relation ), function( X )
% 0.72/1.14 }.
% 0.72/1.14 { ! member( X, universal_class ), ! function( Y ), member( image( Y, X ),
% 0.72/1.14 universal_class ) }.
% 0.72/1.14 { ! disjoint( X, Y ), ! member( Z, X ), ! member( Z, Y ) }.
% 0.72/1.14 { member( skol5( Z, Y ), Y ), disjoint( X, Y ) }.
% 0.72/1.14 { member( skol5( X, Y ), X ), disjoint( X, Y ) }.
% 0.72/1.14 { X = null_class, member( skol6( Y ), universal_class ) }.
% 0.72/1.14 { X = null_class, member( skol6( X ), X ) }.
% 0.72/1.14 { X = null_class, disjoint( skol6( X ), X ) }.
% 0.72/1.14 { apply( X, Y ) = sum_class( image( X, singleton( Y ) ) ) }.
% 0.72/1.14 { function( skol7 ) }.
% 0.72/1.14 { ! member( X, universal_class ), X = null_class, member( apply( skol7, X )
% 0.72/1.14 , X ) }.
% 0.72/1.14 { member( skol9, intersection( complement( skol8 ), skol8 ) ) }.
% 0.72/1.14
% 0.72/1.14 percentage equality = 0.145078, percentage horn = 0.882979
% 0.72/1.14 This is a problem with some equality
% 0.72/1.14
% 0.72/1.14
% 0.72/1.14
% 0.72/1.14 Options Used:
% 0.72/1.14
% 0.72/1.14 useres = 1
% 0.72/1.14 useparamod = 1
% 0.72/1.14 useeqrefl = 1
% 0.72/1.14 useeqfact = 1
% 0.72/1.14 usefactor = 1
% 0.72/1.14 usesimpsplitting = 0
% 0.72/1.14 usesimpdemod = 5
% 0.72/1.14 usesimpres = 3
% 0.72/1.14
% 0.72/1.14 resimpinuse = 1000
% 0.72/1.14 resimpclauses = 20000
% 0.72/1.14 substype = eqrewr
% 0.72/1.14 backwardsubs = 1
% 0.72/1.14 selectoldest = 5
% 0.72/1.14
% 0.72/1.14 litorderings [0] = split
% 0.72/1.14 litorderings [1] = extend the termordering, first sorting on arguments
% 0.72/1.14
% 0.72/1.14 termordering = kbo
% 0.72/1.14
% 0.72/1.14 litapriori = 0
% 0.72/1.14 termapriori = 1
% 0.72/1.14 litaposteriori = 0
% 0.72/1.14 termaposteriori = 0
% 0.72/1.14 demodaposteriori = 0
% 0.72/1.14 ordereqreflfact = 0
% 0.72/1.14
% 0.72/1.14 litselect = negord
% 0.72/1.14
% 0.72/1.14 maxweight = 15
% 0.72/1.14 maxdepth = 30000
% 0.72/1.14 maxlength = 115
% 0.72/1.14 maxnrvars = 195
% 0.72/1.14 excuselevel = 1
% 0.72/1.14 increasemaxweight = 1
% 0.72/1.14
% 0.72/1.14 maxselected = 10000000
% 0.72/1.14 maxnrclauses = 10000000
% 0.72/1.14
% 0.72/1.14 showgenerated = 0
% 0.72/1.14 showkept = 0
% 0.72/1.14 showselected = 0
% 0.72/1.14 showdeleted = 0
% 0.72/1.14 showresimp = 1
% 0.72/1.14 showstatus = 2000
% 0.72/1.14
% 0.72/1.14 prologoutput = 0
% 0.72/1.14 nrgoals = 5000000
% 0.72/1.14 totalproof = 1
% 0.72/1.14
% 0.72/1.14 Symbols occurring in the translation:
% 0.72/1.14
% 0.72/1.14 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.72/1.14 . [1, 2] (w:1, o:45, a:1, s:1, b:0),
% 0.72/1.14 ! [4, 1] (w:0, o:24, a:1, s:1, b:0),
% 0.72/1.14 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.72/1.14 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.72/1.14 subclass [37, 2] (w:1, o:69, a:1, s:1, b:0),
% 0.72/1.14 member [39, 2] (w:1, o:70, a:1, s:1, b:0),
% 0.72/1.14 universal_class [40, 0] (w:1, o:12, a:1, s:1, b:0),
% 0.72/1.14 unordered_pair [41, 2] (w:1, o:71, a:1, s:1, b:0),
% 0.72/1.14 singleton [42, 1] (w:1, o:31, a:1, s:1, b:0),
% 0.72/1.14 ordered_pair [43, 2] (w:1, o:72, a:1, s:1, b:0),
% 0.72/1.14 cross_product [45, 2] (w:1, o:73, a:1, s:1, b:0),
% 0.72/1.14 first [46, 1] (w:1, o:32, a:1, s:1, b:0),
% 0.72/1.14 second [47, 1] (w:1, o:33, a:1, s:1, b:0),
% 0.72/1.14 element_relation [49, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.72/1.14 intersection [50, 2] (w:1, o:75, a:1, s:1, b:0),
% 0.72/1.14 complement [51, 1] (w:1, o:34, a:1, s:1, b:0),
% 0.72/1.14 restrict [53, 3] (w:1, o:84, a:1, s:1, b:0),
% 0.72/1.14 null_class [54, 0] (w:1, o:17, a:1, s:1, b:0),
% 0.72/1.14 domain_of [55, 1] (w:1, o:35, a:1, s:1, b:0),
% 0.72/1.14 rotate [57, 1] (w:1, o:29, a:1, s:1, b:0),
% 0.72/1.14 flip [58, 1] (w:1, o:36, a:1, s:1, b:0),
% 0.72/1.14 union [59, 2] (w:1, o:76, a:1, s:1, b:0),
% 0.72/1.14 successor [60, 1] (w:1, o:37, a:1, s:1, b:0),
% 0.72/1.14 successor_relation [61, 0] (w:1, o:18, a:1, s:1, b:0),
% 0.72/1.14 inverse [62, 1] (w:1, o:38, a:1, s:1, b:0),
% 0.72/1.14 range_of [63, 1] (w:1, o:30, a:1, s:1, b:0),
% 0.72/1.14 image [64, 2] (w:1, o:74, a:1, s:1, b:0),
% 0.72/1.14 inductive [65, 1] (w:1, o:39, a:1, s:1, b:0),
% 0.72/1.14 sum_class [66, 1] (w:1, o:40, a:1, s:1, b:0),
% 0.72/1.14 power_class [67, 1] (w:1, o:41, a:1, s:1, b:0),
% 0.72/1.14 compose [69, 2] (w:1, o:77, a:1, s:1, b:0),
% 0.72/1.14 identity_relation [70, 0] (w:1, o:19, a:1, s:1, b:0),
% 0.72/1.14 function [72, 1] (w:1, o:42, a:1, s:1, b:0),
% 0.72/1.14 disjoint [73, 2] (w:1, o:78, a:1, s:1, b:0),
% 0.72/1.14 apply [74, 2] (w:1, o:79, a:1, s:1, b:0),
% 0.72/1.14 alpha1 [75, 3] (w:1, o:85, a:1, s:1, b:1),
% 0.72/1.14 alpha2 [76, 2] (w:1, o:80, a:1, s:1, b:1),
% 0.72/1.14 skol1 [77, 2] (w:1, o:81, a:1, s:1, b:1),
% 0.72/1.14 skol2 [78, 0] (w:1, o:20, a:1, s:1, b:1),
% 0.72/1.14 skol3 [79, 2] (w:1, o:82, a:1, s:1, b:1),
% 0.72/1.14 skol4 [80, 1] (w:1, o:43, a:1, s:1, b:1),
% 0.72/1.14 skol5 [81, 2] (w:1, o:83, a:1, s:1, b:1),
% 0.72/1.14 skol6 [82, 1] (w:1, o:44, a:1, s:1, b:1),
% 0.72/1.14 skol7 [83, 0] (w:1, o:21, a:1, s:1, b:1),
% 0.72/1.14 skol8 [84, 0] (w:1, o:22, a:1, s:1, b:1),
% 0.72/1.14 skol9 [85, 0] (w:1, o:23, a:1, s:1, b:1).
% 0.72/1.14
% 0.72/1.14
% 0.72/1.14 Starting Search:
% 0.72/1.14
% 0.72/1.14 *** allocated 15000 integers for clauses
% 0.72/1.14 *** allocated 22500 integers for clauses
% 0.72/1.14 *** allocated 33750 integers for clauses
% 0.72/1.14 *** allocated 15000 integers for termspace/termends
% 0.72/1.14 *** allocated 50625 integers for clauses
% 0.72/1.14 Resimplifying inuse:
% 0.72/1.14 Done
% 0.72/1.14
% 0.72/1.14 *** allocated 22500 integers for termspace/termends
% 0.72/1.14 *** allocated 75937 integers for clauses
% 0.72/1.14 *** allocated 33750 integers for termspace/termends
% 0.72/1.14 *** allocated 113905 integers for clauses
% 0.72/1.14
% 0.72/1.14 Intermediate Status:
% 0.72/1.14 Generated: 5288
% 0.72/1.14 Kept: 2132
% 0.72/1.14 Inuse: 125
% 0.72/1.14 Deleted: 2
% 0.72/1.14 Deletedinuse: 1
% 0.72/1.14
% 0.72/1.14 Resimplifying inuse:
% 0.72/1.14 Done
% 0.72/1.14
% 0.72/1.14
% 0.72/1.14 Bliksems!, er is een bewijs:
% 0.72/1.14 % SZS status Theorem
% 0.72/1.14 % SZS output start Refutation
% 0.72/1.14
% 0.72/1.14 (25) {G0,W8,D3,L2,V3,M2} I { ! member( Z, intersection( X, Y ) ), member( Z
% 0.72/1.14 , X ) }.
% 0.72/1.14 (26) {G0,W8,D3,L2,V3,M2} I { ! member( Z, intersection( X, Y ) ), member( Z
% 0.72/1.14 , Y ) }.
% 0.72/1.14 (29) {G0,W7,D3,L2,V2,M2} I { ! member( Y, complement( X ) ), ! member( Y, X
% 0.72/1.14 ) }.
% 0.72/1.14 (92) {G0,W6,D4,L1,V0,M1} I { member( skol9, intersection( complement( skol8
% 0.72/1.14 ), skol8 ) ) }.
% 0.72/1.14 (1777) {G1,W4,D3,L1,V0,M1} R(25,92) { member( skol9, complement( skol8 ) )
% 0.72/1.14 }.
% 0.72/1.14 (1910) {G1,W3,D2,L1,V0,M1} R(26,92) { member( skol9, skol8 ) }.
% 0.72/1.14 (2209) {G2,W0,D0,L0,V0,M0} R(29,1910);r(1777) { }.
% 0.72/1.14
% 0.72/1.14
% 0.72/1.14 % SZS output end Refutation
% 0.72/1.14 found a proof!
% 0.72/1.14
% 0.72/1.14
% 0.72/1.14 Unprocessed initial clauses:
% 0.72/1.14
% 0.72/1.14 (2211) {G0,W9,D2,L3,V3,M3} { ! subclass( X, Y ), ! member( Z, X ), member
% 0.72/1.14 ( Z, Y ) }.
% 0.72/1.14 (2212) {G0,W8,D3,L2,V3,M2} { ! member( skol1( Z, Y ), Y ), subclass( X, Y
% 0.72/1.14 ) }.
% 0.72/1.14 (2213) {G0,W8,D3,L2,V2,M2} { member( skol1( X, Y ), X ), subclass( X, Y )
% 0.72/1.14 }.
% 0.72/1.14 (2214) {G0,W3,D2,L1,V1,M1} { subclass( X, universal_class ) }.
% 0.72/1.14 (2215) {G0,W6,D2,L2,V2,M2} { ! X = Y, subclass( X, Y ) }.
% 0.72/1.14 (2216) {G0,W6,D2,L2,V2,M2} { ! X = Y, subclass( Y, X ) }.
% 0.72/1.14 (2217) {G0,W9,D2,L3,V2,M3} { ! subclass( X, Y ), ! subclass( Y, X ), X = Y
% 0.72/1.14 }.
% 0.72/1.14 (2218) {G0,W8,D3,L2,V3,M2} { ! member( X, unordered_pair( Y, Z ) ), member
% 0.72/1.14 ( X, universal_class ) }.
% 0.72/1.14 (2219) {G0,W9,D3,L2,V3,M2} { ! member( X, unordered_pair( Y, Z ) ), alpha1
% 0.72/1.14 ( X, Y, Z ) }.
% 0.72/1.14 (2220) {G0,W12,D3,L3,V3,M3} { ! member( X, universal_class ), ! alpha1( X
% 0.72/1.14 , Y, Z ), member( X, unordered_pair( Y, Z ) ) }.
% 0.72/1.14 (2221) {G0,W10,D2,L3,V3,M3} { ! alpha1( X, Y, Z ), X = Y, X = Z }.
% 0.72/1.14 (2222) {G0,W7,D2,L2,V3,M2} { ! X = Y, alpha1( X, Y, Z ) }.
% 0.72/1.14 (2223) {G0,W7,D2,L2,V3,M2} { ! X = Z, alpha1( X, Y, Z ) }.
% 0.72/1.14 (2224) {G0,W5,D3,L1,V2,M1} { member( unordered_pair( X, Y ),
% 0.72/1.14 universal_class ) }.
% 0.72/1.14 (2225) {G0,W6,D3,L1,V1,M1} { singleton( X ) = unordered_pair( X, X ) }.
% 0.72/1.14 (2226) {G0,W11,D5,L1,V2,M1} { ordered_pair( X, Y ) = unordered_pair(
% 0.72/1.14 singleton( X ), unordered_pair( X, singleton( Y ) ) ) }.
% 0.72/1.14 (2227) {G0,W10,D3,L2,V4,M2} { ! member( ordered_pair( X, Y ),
% 0.72/1.14 cross_product( Z, T ) ), member( X, Z ) }.
% 0.72/1.14 (2228) {G0,W10,D3,L2,V4,M2} { ! member( ordered_pair( X, Y ),
% 0.72/1.14 cross_product( Z, T ) ), member( Y, T ) }.
% 0.72/1.14 (2229) {G0,W13,D3,L3,V4,M3} { ! member( X, Z ), ! member( Y, T ), member(
% 0.72/1.14 ordered_pair( X, Y ), cross_product( Z, T ) ) }.
% 0.72/1.14 (2230) {G0,W12,D4,L3,V2,M3} { ! member( X, universal_class ), ! member( Y
% 0.72/1.14 , universal_class ), first( ordered_pair( X, Y ) ) = X }.
% 0.72/1.14 (2231) {G0,W12,D4,L3,V2,M3} { ! member( X, universal_class ), ! member( Y
% 0.72/1.14 , universal_class ), second( ordered_pair( X, Y ) ) = Y }.
% 0.72/1.14 (2232) {G0,W12,D4,L2,V3,M2} { ! member( X, cross_product( Y, Z ) ), X =
% 0.72/1.14 ordered_pair( first( X ), second( X ) ) }.
% 0.72/1.14 (2233) {G0,W8,D3,L2,V2,M2} { ! member( ordered_pair( X, Y ),
% 0.72/1.14 element_relation ), member( Y, universal_class ) }.
% 0.72/1.14 (2234) {G0,W8,D3,L2,V2,M2} { ! member( ordered_pair( X, Y ),
% 0.72/1.14 element_relation ), member( X, Y ) }.
% 0.72/1.14 (2235) {G0,W11,D3,L3,V2,M3} { ! member( Y, universal_class ), ! member( X
% 0.72/1.14 , Y ), member( ordered_pair( X, Y ), element_relation ) }.
% 0.72/1.14 (2236) {G0,W5,D3,L1,V0,M1} { subclass( element_relation, cross_product(
% 0.72/1.14 universal_class, universal_class ) ) }.
% 0.72/1.14 (2237) {G0,W8,D3,L2,V3,M2} { ! member( Z, intersection( X, Y ) ), member(
% 0.72/1.14 Z, X ) }.
% 0.72/1.14 (2238) {G0,W8,D3,L2,V3,M2} { ! member( Z, intersection( X, Y ) ), member(
% 0.72/1.14 Z, Y ) }.
% 0.72/1.14 (2239) {G0,W11,D3,L3,V3,M3} { ! member( Z, X ), ! member( Z, Y ), member(
% 0.72/1.14 Z, intersection( X, Y ) ) }.
% 0.72/1.14 (2240) {G0,W7,D3,L2,V2,M2} { ! member( Y, complement( X ) ), member( Y,
% 0.72/1.14 universal_class ) }.
% 0.72/1.14 (2241) {G0,W7,D3,L2,V2,M2} { ! member( Y, complement( X ) ), ! member( Y,
% 0.72/1.14 X ) }.
% 0.72/1.14 (2242) {G0,W10,D3,L3,V2,M3} { ! member( Y, universal_class ), member( Y, X
% 0.72/1.14 ), member( Y, complement( X ) ) }.
% 0.72/1.14 (2243) {G0,W10,D4,L1,V3,M1} { restrict( Y, X, Z ) = intersection( Y,
% 0.72/1.14 cross_product( X, Z ) ) }.
% 0.72/1.14 (2244) {G0,W3,D2,L1,V1,M1} { ! member( X, null_class ) }.
% 0.72/1.14 (2245) {G0,W7,D3,L2,V2,M2} { ! member( Y, domain_of( X ) ), member( Y,
% 0.72/1.14 universal_class ) }.
% 0.72/1.14 (2246) {G0,W11,D4,L2,V2,M2} { ! member( Y, domain_of( X ) ), ! restrict( X
% 0.72/1.14 , singleton( Y ), universal_class ) = null_class }.
% 0.72/1.14 (2247) {G0,W14,D4,L3,V2,M3} { ! member( Y, universal_class ), restrict( X
% 0.72/1.14 , singleton( Y ), universal_class ) = null_class, member( Y, domain_of( X
% 0.72/1.14 ) ) }.
% 0.72/1.14 (2248) {G0,W19,D4,L2,V4,M2} { ! member( ordered_pair( ordered_pair( Y, Z )
% 0.72/1.14 , T ), rotate( X ) ), member( ordered_pair( ordered_pair( Y, Z ), T ),
% 0.72/1.14 cross_product( cross_product( universal_class, universal_class ),
% 0.72/1.14 universal_class ) ) }.
% 0.72/1.14 (2249) {G0,W15,D4,L2,V4,M2} { ! member( ordered_pair( ordered_pair( Y, Z )
% 0.72/1.14 , T ), rotate( X ) ), member( ordered_pair( ordered_pair( Z, T ), Y ), X
% 0.72/1.14 ) }.
% 0.72/1.14 (2250) {G0,W26,D4,L3,V4,M3} { ! member( ordered_pair( ordered_pair( Y, Z )
% 0.72/1.14 , T ), cross_product( cross_product( universal_class, universal_class ),
% 0.72/1.14 universal_class ) ), ! member( ordered_pair( ordered_pair( Z, T ), Y ), X
% 0.72/1.14 ), member( ordered_pair( ordered_pair( Y, Z ), T ), rotate( X ) ) }.
% 0.72/1.14 (2251) {G0,W8,D4,L1,V1,M1} { subclass( rotate( X ), cross_product(
% 0.72/1.14 cross_product( universal_class, universal_class ), universal_class ) )
% 0.72/1.14 }.
% 0.72/1.14 (2252) {G0,W19,D4,L2,V4,M2} { ! member( ordered_pair( ordered_pair( X, Y )
% 0.72/1.14 , Z ), flip( T ) ), member( ordered_pair( ordered_pair( X, Y ), Z ),
% 0.72/1.14 cross_product( cross_product( universal_class, universal_class ),
% 0.72/1.14 universal_class ) ) }.
% 0.72/1.14 (2253) {G0,W15,D4,L2,V4,M2} { ! member( ordered_pair( ordered_pair( X, Y )
% 0.72/1.14 , Z ), flip( T ) ), member( ordered_pair( ordered_pair( Y, X ), Z ), T )
% 0.72/1.14 }.
% 0.72/1.14 (2254) {G0,W26,D4,L3,V4,M3} { ! member( ordered_pair( ordered_pair( X, Y )
% 0.72/1.14 , Z ), cross_product( cross_product( universal_class, universal_class ),
% 0.72/1.14 universal_class ) ), ! member( ordered_pair( ordered_pair( Y, X ), Z ), T
% 0.72/1.14 ), member( ordered_pair( ordered_pair( X, Y ), Z ), flip( T ) ) }.
% 0.72/1.14 (2255) {G0,W8,D4,L1,V1,M1} { subclass( flip( X ), cross_product(
% 0.72/1.14 cross_product( universal_class, universal_class ), universal_class ) )
% 0.72/1.14 }.
% 0.72/1.14 (2256) {G0,W11,D3,L3,V3,M3} { ! member( Z, union( X, Y ) ), member( Z, X )
% 0.72/1.14 , member( Z, Y ) }.
% 0.72/1.14 (2257) {G0,W8,D3,L2,V3,M2} { ! member( Z, X ), member( Z, union( X, Y ) )
% 0.72/1.14 }.
% 0.72/1.14 (2258) {G0,W8,D3,L2,V3,M2} { ! member( Z, Y ), member( Z, union( X, Y ) )
% 0.72/1.14 }.
% 0.72/1.14 (2259) {G0,W7,D4,L1,V1,M1} { successor( X ) = union( X, singleton( X ) )
% 0.72/1.14 }.
% 0.72/1.14 (2260) {G0,W5,D3,L1,V0,M1} { subclass( successor_relation, cross_product(
% 0.72/1.14 universal_class, universal_class ) ) }.
% 0.72/1.14 (2261) {G0,W8,D3,L2,V2,M2} { ! member( ordered_pair( X, Y ),
% 0.72/1.14 successor_relation ), member( X, universal_class ) }.
% 0.72/1.14 (2262) {G0,W8,D3,L2,V2,M2} { ! member( ordered_pair( X, Y ),
% 0.72/1.14 successor_relation ), alpha2( X, Y ) }.
% 0.72/1.14 (2263) {G0,W11,D3,L3,V2,M3} { ! member( X, universal_class ), ! alpha2( X
% 0.72/1.14 , Y ), member( ordered_pair( X, Y ), successor_relation ) }.
% 0.72/1.14 (2264) {G0,W6,D2,L2,V2,M2} { ! alpha2( X, Y ), member( Y, universal_class
% 0.72/1.14 ) }.
% 0.72/1.14 (2265) {G0,W7,D3,L2,V2,M2} { ! alpha2( X, Y ), successor( X ) = Y }.
% 0.72/1.14 (2266) {G0,W10,D3,L3,V2,M3} { ! member( Y, universal_class ), ! successor
% 0.72/1.14 ( X ) = Y, alpha2( X, Y ) }.
% 0.72/1.14 (2267) {G0,W8,D5,L1,V1,M1} { inverse( X ) = domain_of( flip( cross_product
% 0.72/1.14 ( X, universal_class ) ) ) }.
% 0.72/1.14 (2268) {G0,W6,D4,L1,V1,M1} { range_of( X ) = domain_of( inverse( X ) ) }.
% 0.72/1.14 (2269) {G0,W9,D4,L1,V2,M1} { image( Y, X ) = range_of( restrict( Y, X,
% 0.72/1.14 universal_class ) ) }.
% 0.72/1.14 (2270) {G0,W5,D2,L2,V1,M2} { ! inductive( X ), member( null_class, X ) }.
% 0.72/1.14 (2271) {G0,W7,D3,L2,V1,M2} { ! inductive( X ), subclass( image(
% 0.72/1.14 successor_relation, X ), X ) }.
% 0.72/1.14 (2272) {G0,W10,D3,L3,V1,M3} { ! member( null_class, X ), ! subclass( image
% 0.72/1.15 ( successor_relation, X ), X ), inductive( X ) }.
% 0.72/1.15 (2273) {G0,W3,D2,L1,V0,M1} { member( skol2, universal_class ) }.
% 0.72/1.15 (2274) {G0,W2,D2,L1,V0,M1} { inductive( skol2 ) }.
% 0.72/1.15 (2275) {G0,W5,D2,L2,V1,M2} { ! inductive( X ), subclass( skol2, X ) }.
% 0.72/1.15 (2276) {G0,W9,D3,L2,V3,M2} { ! member( X, sum_class( Y ) ), member( skol3
% 0.72/1.15 ( Z, Y ), Y ) }.
% 0.72/1.15 (2277) {G0,W9,D3,L2,V2,M2} { ! member( X, sum_class( Y ) ), member( X,
% 0.72/1.15 skol3( X, Y ) ) }.
% 0.72/1.15 (2278) {G0,W10,D3,L3,V3,M3} { ! member( X, Z ), ! member( Z, Y ), member(
% 0.72/1.15 X, sum_class( Y ) ) }.
% 0.72/1.15 (2279) {G0,W7,D3,L2,V1,M2} { ! member( X, universal_class ), member(
% 0.72/1.15 sum_class( X ), universal_class ) }.
% 0.72/1.15 (2280) {G0,W7,D3,L2,V2,M2} { ! member( X, power_class( Y ) ), member( X,
% 0.72/1.15 universal_class ) }.
% 0.72/1.15 (2281) {G0,W7,D3,L2,V2,M2} { ! member( X, power_class( Y ) ), subclass( X
% 0.72/1.15 , Y ) }.
% 0.72/1.15 (2282) {G0,W10,D3,L3,V2,M3} { ! member( X, universal_class ), ! subclass(
% 0.72/1.15 X, Y ), member( X, power_class( Y ) ) }.
% 0.72/1.15 (2283) {G0,W7,D3,L2,V1,M2} { ! member( X, universal_class ), member(
% 0.72/1.15 power_class( X ), universal_class ) }.
% 0.72/1.15 (2284) {G0,W7,D3,L1,V2,M1} { subclass( compose( Y, X ), cross_product(
% 0.72/1.15 universal_class, universal_class ) ) }.
% 0.72/1.15 (2285) {G0,W10,D3,L2,V4,M2} { ! member( ordered_pair( Z, T ), compose( Y,
% 0.72/1.15 X ) ), member( Z, universal_class ) }.
% 0.72/1.15 (2286) {G0,W15,D5,L2,V4,M2} { ! member( ordered_pair( Z, T ), compose( Y,
% 0.72/1.15 X ) ), member( T, image( Y, image( X, singleton( Z ) ) ) ) }.
% 0.72/1.15 (2287) {G0,W18,D5,L3,V4,M3} { ! member( Z, universal_class ), ! member( T
% 0.72/1.15 , image( Y, image( X, singleton( Z ) ) ) ), member( ordered_pair( Z, T )
% 0.72/1.15 , compose( Y, X ) ) }.
% 0.72/1.15 (2288) {G0,W7,D3,L2,V2,M2} { ! member( X, identity_relation ), member(
% 0.72/1.15 skol4( Y ), universal_class ) }.
% 0.72/1.15 (2289) {G0,W10,D4,L2,V1,M2} { ! member( X, identity_relation ), X =
% 0.72/1.15 ordered_pair( skol4( X ), skol4( X ) ) }.
% 0.72/1.15 (2290) {G0,W11,D3,L3,V2,M3} { ! member( Y, universal_class ), ! X =
% 0.72/1.15 ordered_pair( Y, Y ), member( X, identity_relation ) }.
% 0.72/1.15 (2291) {G0,W7,D3,L2,V1,M2} { ! function( X ), subclass( X, cross_product(
% 0.72/1.15 universal_class, universal_class ) ) }.
% 0.72/1.15 (2292) {G0,W8,D4,L2,V1,M2} { ! function( X ), subclass( compose( X,
% 0.72/1.15 inverse( X ) ), identity_relation ) }.
% 0.72/1.15 (2293) {G0,W13,D4,L3,V1,M3} { ! subclass( X, cross_product(
% 0.72/1.15 universal_class, universal_class ) ), ! subclass( compose( X, inverse( X
% 0.72/1.15 ) ), identity_relation ), function( X ) }.
% 0.72/1.15 (2294) {G0,W10,D3,L3,V2,M3} { ! member( X, universal_class ), ! function(
% 0.72/1.15 Y ), member( image( Y, X ), universal_class ) }.
% 0.72/1.15 (2295) {G0,W9,D2,L3,V3,M3} { ! disjoint( X, Y ), ! member( Z, X ), !
% 0.72/1.15 member( Z, Y ) }.
% 0.72/1.15 (2296) {G0,W8,D3,L2,V3,M2} { member( skol5( Z, Y ), Y ), disjoint( X, Y )
% 0.72/1.15 }.
% 0.72/1.15 (2297) {G0,W8,D3,L2,V2,M2} { member( skol5( X, Y ), X ), disjoint( X, Y )
% 0.72/1.15 }.
% 0.72/1.15 (2298) {G0,W7,D3,L2,V2,M2} { X = null_class, member( skol6( Y ),
% 0.72/1.15 universal_class ) }.
% 0.72/1.15 (2299) {G0,W7,D3,L2,V1,M2} { X = null_class, member( skol6( X ), X ) }.
% 0.72/1.15 (2300) {G0,W7,D3,L2,V1,M2} { X = null_class, disjoint( skol6( X ), X ) }.
% 0.72/1.15 (2301) {G0,W9,D5,L1,V2,M1} { apply( X, Y ) = sum_class( image( X,
% 0.72/1.15 singleton( Y ) ) ) }.
% 0.72/1.15 (2302) {G0,W2,D2,L1,V0,M1} { function( skol7 ) }.
% 0.72/1.15 (2303) {G0,W11,D3,L3,V1,M3} { ! member( X, universal_class ), X =
% 0.72/1.15 null_class, member( apply( skol7, X ), X ) }.
% 0.72/1.15 (2304) {G0,W6,D4,L1,V0,M1} { member( skol9, intersection( complement(
% 0.72/1.15 skol8 ), skol8 ) ) }.
% 0.72/1.15
% 0.72/1.15
% 0.72/1.15 Total Proof:
% 0.72/1.15
% 0.72/1.15 subsumption: (25) {G0,W8,D3,L2,V3,M2} I { ! member( Z, intersection( X, Y )
% 0.72/1.15 ), member( Z, X ) }.
% 0.72/1.15 parent0: (2237) {G0,W8,D3,L2,V3,M2} { ! member( Z, intersection( X, Y ) )
% 0.72/1.15 , member( Z, X ) }.
% 0.72/1.15 substitution0:
% 0.72/1.15 X := X
% 0.72/1.15 Y := Y
% 0.72/1.15 Z := Z
% 0.72/1.15 end
% 0.72/1.15 permutation0:
% 0.72/1.15 0 ==> 0
% 0.72/1.15 1 ==> 1
% 0.72/1.15 end
% 0.72/1.15
% 0.72/1.15 subsumption: (26) {G0,W8,D3,L2,V3,M2} I { ! member( Z, intersection( X, Y )
% 0.72/1.15 ), member( Z, Y ) }.
% 0.72/1.15 parent0: (2238) {G0,W8,D3,L2,V3,M2} { ! member( Z, intersection( X, Y ) )
% 0.72/1.15 , member( Z, Y ) }.
% 0.72/1.15 substitution0:
% 0.72/1.15 X := X
% 0.72/1.15 Y := Y
% 0.72/1.15 Z := Z
% 0.72/1.15 end
% 0.72/1.15 permutation0:
% 0.72/1.15 0 ==> 0
% 0.72/1.15 1 ==> 1
% 0.72/1.15 end
% 0.72/1.15
% 0.72/1.15 subsumption: (29) {G0,W7,D3,L2,V2,M2} I { ! member( Y, complement( X ) ), !
% 0.72/1.15 member( Y, X ) }.
% 0.72/1.15 parent0: (2241) {G0,W7,D3,L2,V2,M2} { ! member( Y, complement( X ) ), !
% 0.72/1.15 member( Y, X ) }.
% 0.72/1.15 substitution0:
% 0.72/1.15 X := X
% 0.72/1.15 Y := Y
% 0.72/1.15 end
% 0.72/1.15 permutation0:
% 0.72/1.15 0 ==> 0
% 0.72/1.15 1 ==> 1
% 0.72/1.15 end
% 0.72/1.15
% 0.72/1.15 subsumption: (92) {G0,W6,D4,L1,V0,M1} I { member( skol9, intersection(
% 0.72/1.15 complement( skol8 ), skol8 ) ) }.
% 0.72/1.15 parent0: (2304) {G0,W6,D4,L1,V0,M1} { member( skol9, intersection(
% 0.72/1.15 complement( skol8 ), skol8 ) ) }.
% 0.72/1.15 substitution0:
% 0.72/1.15 end
% 0.72/1.15 permutation0:
% 0.72/1.15 0 ==> 0
% 0.72/1.15 end
% 0.72/1.15
% 0.72/1.15 resolution: (2412) {G1,W4,D3,L1,V0,M1} { member( skol9, complement( skol8
% 0.72/1.15 ) ) }.
% 0.72/1.15 parent0[0]: (25) {G0,W8,D3,L2,V3,M2} I { ! member( Z, intersection( X, Y )
% 0.72/1.15 ), member( Z, X ) }.
% 0.72/1.15 parent1[0]: (92) {G0,W6,D4,L1,V0,M1} I { member( skol9, intersection(
% 0.72/1.15 complement( skol8 ), skol8 ) ) }.
% 0.72/1.15 substitution0:
% 0.72/1.15 X := complement( skol8 )
% 0.72/1.15 Y := skol8
% 0.72/1.15 Z := skol9
% 0.72/1.15 end
% 0.72/1.15 substitution1:
% 0.72/1.15 end
% 0.72/1.15
% 0.72/1.15 subsumption: (1777) {G1,W4,D3,L1,V0,M1} R(25,92) { member( skol9,
% 0.72/1.15 complement( skol8 ) ) }.
% 0.72/1.15 parent0: (2412) {G1,W4,D3,L1,V0,M1} { member( skol9, complement( skol8 ) )
% 0.72/1.15 }.
% 0.72/1.15 substitution0:
% 0.72/1.15 end
% 0.72/1.15 permutation0:
% 0.72/1.15 0 ==> 0
% 0.72/1.15 end
% 0.72/1.15
% 0.72/1.15 resolution: (2413) {G1,W3,D2,L1,V0,M1} { member( skol9, skol8 ) }.
% 0.72/1.15 parent0[0]: (26) {G0,W8,D3,L2,V3,M2} I { ! member( Z, intersection( X, Y )
% 0.72/1.15 ), member( Z, Y ) }.
% 0.72/1.15 parent1[0]: (92) {G0,W6,D4,L1,V0,M1} I { member( skol9, intersection(
% 0.72/1.15 complement( skol8 ), skol8 ) ) }.
% 0.72/1.15 substitution0:
% 0.72/1.15 X := complement( skol8 )
% 0.72/1.15 Y := skol8
% 0.72/1.15 Z := skol9
% 0.72/1.15 end
% 0.72/1.15 substitution1:
% 0.72/1.15 end
% 0.72/1.15
% 0.72/1.15 subsumption: (1910) {G1,W3,D2,L1,V0,M1} R(26,92) { member( skol9, skol8 )
% 0.72/1.15 }.
% 0.72/1.15 parent0: (2413) {G1,W3,D2,L1,V0,M1} { member( skol9, skol8 ) }.
% 0.72/1.15 substitution0:
% 0.72/1.15 end
% 0.72/1.15 permutation0:
% 0.72/1.15 0 ==> 0
% 0.72/1.15 end
% 0.72/1.15
% 0.72/1.15 resolution: (2414) {G1,W4,D3,L1,V0,M1} { ! member( skol9, complement(
% 0.72/1.15 skol8 ) ) }.
% 0.72/1.15 parent0[1]: (29) {G0,W7,D3,L2,V2,M2} I { ! member( Y, complement( X ) ), !
% 0.72/1.15 member( Y, X ) }.
% 0.72/1.15 parent1[0]: (1910) {G1,W3,D2,L1,V0,M1} R(26,92) { member( skol9, skol8 )
% 0.72/1.15 }.
% 0.72/1.15 substitution0:
% 0.72/1.15 X := skol8
% 0.72/1.15 Y := skol9
% 0.72/1.15 end
% 0.72/1.15 substitution1:
% 0.72/1.15 end
% 0.72/1.15
% 0.72/1.15 resolution: (2415) {G2,W0,D0,L0,V0,M0} { }.
% 0.72/1.15 parent0[0]: (2414) {G1,W4,D3,L1,V0,M1} { ! member( skol9, complement(
% 0.72/1.15 skol8 ) ) }.
% 0.72/1.15 parent1[0]: (1777) {G1,W4,D3,L1,V0,M1} R(25,92) { member( skol9, complement
% 0.72/1.15 ( skol8 ) ) }.
% 0.72/1.15 substitution0:
% 0.72/1.15 end
% 0.72/1.15 substitution1:
% 0.72/1.15 end
% 0.72/1.15
% 0.72/1.15 subsumption: (2209) {G2,W0,D0,L0,V0,M0} R(29,1910);r(1777) { }.
% 0.72/1.15 parent0: (2415) {G2,W0,D0,L0,V0,M0} { }.
% 0.72/1.15 substitution0:
% 0.72/1.15 end
% 0.72/1.15 permutation0:
% 0.72/1.15 end
% 0.72/1.15
% 0.72/1.15 Proof check complete!
% 0.72/1.15
% 0.72/1.15 Memory use:
% 0.72/1.15
% 0.72/1.15 space for terms: 30453
% 0.72/1.15 space for clauses: 103176
% 0.72/1.15
% 0.72/1.15
% 0.72/1.15 clauses generated: 5508
% 0.72/1.15 clauses kept: 2210
% 0.72/1.15 clauses selected: 132
% 0.72/1.15 clauses deleted: 8
% 0.72/1.15 clauses inuse deleted: 4
% 0.72/1.15
% 0.72/1.15 subsentry: 12217
% 0.72/1.15 literals s-matched: 10131
% 0.72/1.15 literals matched: 10123
% 0.72/1.15 full subsumption: 5021
% 0.72/1.15
% 0.72/1.15 checksum: 2133268233
% 0.72/1.15
% 0.72/1.15
% 0.72/1.15 Bliksem ended
%------------------------------------------------------------------------------