TSTP Solution File: SEU238+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SEU238+1 : TPTP v8.1.0. Released v3.3.0.
% 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 : Tue Jul 19 07:11:46 EDT 2022
% Result : Theorem 3.90s 4.32s
% Output : Refutation 3.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU238+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Sat Jun 18 21:03:02 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.69/1.10 *** allocated 10000 integers for termspace/termends
% 0.69/1.10 *** allocated 10000 integers for clauses
% 0.69/1.10 *** allocated 10000 integers for justifications
% 0.69/1.10 Bliksem 1.12
% 0.69/1.10
% 0.69/1.10
% 0.69/1.10 Automatic Strategy Selection
% 0.69/1.10
% 0.69/1.10
% 0.69/1.10 Clauses:
% 0.69/1.10
% 0.69/1.10 { ! in( X, Y ), ! in( Y, X ) }.
% 0.69/1.10 { ! proper_subset( X, Y ), ! proper_subset( Y, X ) }.
% 0.69/1.10 { ! empty( X ), function( X ) }.
% 0.69/1.10 { ! ordinal( X ), epsilon_transitive( X ) }.
% 0.69/1.10 { ! ordinal( X ), epsilon_connected( X ) }.
% 0.69/1.10 { ! empty( X ), relation( X ) }.
% 0.69/1.10 { ! relation( X ), ! empty( X ), ! function( X ), relation( X ) }.
% 0.69/1.10 { ! relation( X ), ! empty( X ), ! function( X ), function( X ) }.
% 0.69/1.10 { ! relation( X ), ! empty( X ), ! function( X ), one_to_one( X ) }.
% 0.69/1.10 { ! epsilon_transitive( X ), ! epsilon_connected( X ), ordinal( X ) }.
% 0.69/1.10 { ! empty( X ), epsilon_transitive( X ) }.
% 0.69/1.10 { ! empty( X ), epsilon_connected( X ) }.
% 0.69/1.10 { ! empty( X ), ordinal( X ) }.
% 0.69/1.10 { set_union2( X, Y ) = set_union2( Y, X ) }.
% 0.69/1.10 { ! ordinal( X ), ! ordinal( Y ), ordinal_subset( X, Y ), ordinal_subset( Y
% 0.69/1.10 , X ) }.
% 0.69/1.10 { succ( X ) = set_union2( X, singleton( X ) ) }.
% 0.69/1.10 { ! proper_subset( X, Y ), subset( X, Y ) }.
% 0.69/1.10 { ! proper_subset( X, Y ), ! X = Y }.
% 0.69/1.10 { ! subset( X, Y ), X = Y, proper_subset( X, Y ) }.
% 0.69/1.10 { && }.
% 0.69/1.10 { && }.
% 0.69/1.10 { && }.
% 0.69/1.10 { && }.
% 0.69/1.10 { && }.
% 0.69/1.10 { && }.
% 0.69/1.10 { element( skol1( X ), X ) }.
% 0.69/1.10 { empty( empty_set ) }.
% 0.69/1.10 { relation( empty_set ) }.
% 0.69/1.10 { relation_empty_yielding( empty_set ) }.
% 0.69/1.10 { ! empty( succ( X ) ) }.
% 0.69/1.10 { empty( empty_set ) }.
% 0.69/1.10 { relation( empty_set ) }.
% 0.69/1.10 { relation_empty_yielding( empty_set ) }.
% 0.69/1.10 { function( empty_set ) }.
% 0.69/1.10 { one_to_one( empty_set ) }.
% 0.69/1.10 { empty( empty_set ) }.
% 0.69/1.10 { epsilon_transitive( empty_set ) }.
% 0.69/1.10 { epsilon_connected( empty_set ) }.
% 0.69/1.10 { ordinal( empty_set ) }.
% 0.69/1.10 { ! relation( X ), ! relation( Y ), relation( set_union2( X, Y ) ) }.
% 0.69/1.10 { empty( X ), ! empty( set_union2( X, Y ) ) }.
% 0.69/1.10 { ! ordinal( X ), alpha2( X ) }.
% 0.69/1.10 { ! ordinal( X ), ordinal( succ( X ) ) }.
% 0.69/1.10 { ! alpha2( X ), ! empty( succ( X ) ) }.
% 0.69/1.10 { ! alpha2( X ), epsilon_transitive( succ( X ) ) }.
% 0.69/1.10 { ! alpha2( X ), epsilon_connected( succ( X ) ) }.
% 0.69/1.10 { empty( succ( X ) ), ! epsilon_transitive( succ( X ) ), !
% 0.69/1.10 epsilon_connected( succ( X ) ), alpha2( X ) }.
% 0.69/1.10 { empty( X ), ! empty( set_union2( Y, X ) ) }.
% 0.69/1.10 { empty( empty_set ) }.
% 0.69/1.10 { relation( empty_set ) }.
% 0.69/1.10 { set_union2( X, X ) = X }.
% 0.69/1.10 { ! proper_subset( X, X ) }.
% 0.69/1.10 { relation( skol2 ) }.
% 0.69/1.10 { function( skol2 ) }.
% 0.69/1.10 { epsilon_transitive( skol3 ) }.
% 0.69/1.10 { epsilon_connected( skol3 ) }.
% 0.69/1.10 { ordinal( skol3 ) }.
% 0.69/1.10 { empty( skol4 ) }.
% 0.69/1.10 { relation( skol4 ) }.
% 0.69/1.10 { empty( skol5 ) }.
% 0.69/1.10 { relation( skol6 ) }.
% 0.69/1.10 { empty( skol6 ) }.
% 0.69/1.10 { function( skol6 ) }.
% 0.69/1.10 { relation( skol7 ) }.
% 0.69/1.10 { function( skol7 ) }.
% 0.69/1.10 { one_to_one( skol7 ) }.
% 0.69/1.10 { empty( skol7 ) }.
% 0.69/1.10 { epsilon_transitive( skol7 ) }.
% 0.69/1.10 { epsilon_connected( skol7 ) }.
% 0.69/1.10 { ordinal( skol7 ) }.
% 0.69/1.10 { ! empty( skol8 ) }.
% 0.69/1.10 { relation( skol8 ) }.
% 0.69/1.10 { ! empty( skol9 ) }.
% 0.69/1.10 { relation( skol10 ) }.
% 0.69/1.10 { function( skol10 ) }.
% 0.69/1.10 { one_to_one( skol10 ) }.
% 0.69/1.10 { ! empty( skol11 ) }.
% 0.69/1.10 { epsilon_transitive( skol11 ) }.
% 0.69/1.10 { epsilon_connected( skol11 ) }.
% 0.69/1.10 { ordinal( skol11 ) }.
% 0.69/1.10 { relation( skol12 ) }.
% 0.69/1.10 { relation_empty_yielding( skol12 ) }.
% 0.69/1.10 { relation( skol13 ) }.
% 0.69/1.10 { relation_empty_yielding( skol13 ) }.
% 0.69/1.10 { function( skol13 ) }.
% 0.69/1.10 { ! ordinal( X ), ! ordinal( Y ), ! ordinal_subset( X, Y ), subset( X, Y )
% 0.69/1.10 }.
% 0.69/1.10 { ! ordinal( X ), ! ordinal( Y ), ! subset( X, Y ), ordinal_subset( X, Y )
% 0.69/1.10 }.
% 0.69/1.10 { ! ordinal( X ), ! ordinal( Y ), ordinal_subset( X, X ) }.
% 0.69/1.10 { subset( X, X ) }.
% 0.69/1.10 { in( X, succ( X ) ) }.
% 0.69/1.10 { set_union2( X, empty_set ) = X }.
% 0.69/1.10 { ! in( X, Y ), element( X, Y ) }.
% 0.69/1.10 { ! epsilon_transitive( X ), ! ordinal( Y ), ! proper_subset( X, Y ), in( X
% 0.69/1.10 , Y ) }.
% 0.69/1.10 { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.69/1.10 { ! ordinal( X ), ! ordinal( Y ), ! in( X, Y ), ordinal_subset( succ( X ),
% 0.69/1.10 Y ) }.
% 0.69/1.10 { ! ordinal( X ), ! ordinal( Y ), ! ordinal_subset( succ( X ), Y ), in( X,
% 0.69/1.10 Y ) }.
% 0.69/1.10 { ! element( X, powerset( Y ) ), subset( X, Y ) }.
% 0.69/1.10 { ! subset( X, Y ), element( X, powerset( Y ) ) }.
% 0.69/1.10 { ! ordinal( X ), ! being_limit_ordinal( X ), ! ordinal( Y ), alpha1( X, Y
% 0.69/1.10 ) }.
% 0.69/1.10 { ! ordinal( X ), ordinal( skol14( Y ) ), being_limit_ordinal( X ) }.
% 0.69/1.10 { ! ordinal( X ), ! alpha1( X, skol14( X ) ), being_limit_ordinal( X ) }.
% 0.69/1.10 { ! alpha1( X, Y ), ! in( Y, X ), in( succ( Y ), X ) }.
% 0.69/1.10 { in( Y, X ), alpha1( X, Y ) }.
% 3.90/4.32 { ! in( succ( Y ), X ), alpha1( X, Y ) }.
% 3.90/4.32 { ordinal( skol15 ) }.
% 3.90/4.32 { alpha3( skol15 ), ordinal( skol17 ) }.
% 3.90/4.32 { alpha3( skol15 ), skol15 = succ( skol17 ) }.
% 3.90/4.32 { alpha3( skol15 ), being_limit_ordinal( skol15 ) }.
% 3.90/4.32 { ! alpha3( X ), ! being_limit_ordinal( X ) }.
% 3.90/4.32 { ! alpha3( X ), ! ordinal( Y ), ! X = succ( Y ) }.
% 3.90/4.32 { being_limit_ordinal( X ), ordinal( skol16( Y ) ), alpha3( X ) }.
% 3.90/4.32 { being_limit_ordinal( X ), X = succ( skol16( X ) ), alpha3( X ) }.
% 3.90/4.32 { ! in( X, Z ), ! element( Z, powerset( Y ) ), element( X, Y ) }.
% 3.90/4.32 { ! in( X, Y ), ! element( Y, powerset( Z ) ), ! empty( Z ) }.
% 3.90/4.32 { ! empty( X ), X = empty_set }.
% 3.90/4.32 { ! in( X, Y ), ! empty( Y ) }.
% 3.90/4.32 { ! empty( X ), X = Y, ! empty( Y ) }.
% 3.90/4.32
% 3.90/4.32 percentage equality = 0.059140, percentage horn = 0.893204
% 3.90/4.32 This is a problem with some equality
% 3.90/4.32
% 3.90/4.32
% 3.90/4.32
% 3.90/4.32 Options Used:
% 3.90/4.32
% 3.90/4.32 useres = 1
% 3.90/4.32 useparamod = 1
% 3.90/4.32 useeqrefl = 1
% 3.90/4.32 useeqfact = 1
% 3.90/4.32 usefactor = 1
% 3.90/4.32 usesimpsplitting = 0
% 3.90/4.32 usesimpdemod = 5
% 3.90/4.32 usesimpres = 3
% 3.90/4.32
% 3.90/4.32 resimpinuse = 1000
% 3.90/4.32 resimpclauses = 20000
% 3.90/4.32 substype = eqrewr
% 3.90/4.32 backwardsubs = 1
% 3.90/4.32 selectoldest = 5
% 3.90/4.32
% 3.90/4.32 litorderings [0] = split
% 3.90/4.32 litorderings [1] = extend the termordering, first sorting on arguments
% 3.90/4.32
% 3.90/4.32 termordering = kbo
% 3.90/4.32
% 3.90/4.32 litapriori = 0
% 3.90/4.32 termapriori = 1
% 3.90/4.32 litaposteriori = 0
% 3.90/4.32 termaposteriori = 0
% 3.90/4.32 demodaposteriori = 0
% 3.90/4.32 ordereqreflfact = 0
% 3.90/4.32
% 3.90/4.32 litselect = negord
% 3.90/4.32
% 3.90/4.32 maxweight = 15
% 3.90/4.32 maxdepth = 30000
% 3.90/4.32 maxlength = 115
% 3.90/4.32 maxnrvars = 195
% 3.90/4.32 excuselevel = 1
% 3.90/4.32 increasemaxweight = 1
% 3.90/4.32
% 3.90/4.32 maxselected = 10000000
% 3.90/4.32 maxnrclauses = 10000000
% 3.90/4.32
% 3.90/4.32 showgenerated = 0
% 3.90/4.32 showkept = 0
% 3.90/4.32 showselected = 0
% 3.90/4.32 showdeleted = 0
% 3.90/4.32 showresimp = 1
% 3.90/4.32 showstatus = 2000
% 3.90/4.32
% 3.90/4.32 prologoutput = 0
% 3.90/4.32 nrgoals = 5000000
% 3.90/4.32 totalproof = 1
% 3.90/4.32
% 3.90/4.32 Symbols occurring in the translation:
% 3.90/4.32
% 3.90/4.32 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 3.90/4.32 . [1, 2] (w:1, o:46, a:1, s:1, b:0),
% 3.90/4.32 && [3, 0] (w:1, o:4, a:1, s:1, b:0),
% 3.90/4.32 ! [4, 1] (w:0, o:24, a:1, s:1, b:0),
% 3.90/4.32 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 3.90/4.32 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 3.90/4.32 in [37, 2] (w:1, o:70, a:1, s:1, b:0),
% 3.90/4.32 proper_subset [38, 2] (w:1, o:72, a:1, s:1, b:0),
% 3.90/4.32 empty [39, 1] (w:1, o:29, a:1, s:1, b:0),
% 3.90/4.32 function [40, 1] (w:1, o:32, a:1, s:1, b:0),
% 3.90/4.32 ordinal [41, 1] (w:1, o:33, a:1, s:1, b:0),
% 3.90/4.32 epsilon_transitive [42, 1] (w:1, o:30, a:1, s:1, b:0),
% 3.90/4.32 epsilon_connected [43, 1] (w:1, o:31, a:1, s:1, b:0),
% 3.90/4.32 relation [44, 1] (w:1, o:34, a:1, s:1, b:0),
% 3.90/4.32 one_to_one [45, 1] (w:1, o:35, a:1, s:1, b:0),
% 3.90/4.32 set_union2 [46, 2] (w:1, o:73, a:1, s:1, b:0),
% 3.90/4.32 ordinal_subset [47, 2] (w:1, o:71, a:1, s:1, b:0),
% 3.90/4.32 succ [48, 1] (w:1, o:37, a:1, s:1, b:0),
% 3.90/4.32 singleton [49, 1] (w:1, o:38, a:1, s:1, b:0),
% 3.90/4.32 subset [50, 2] (w:1, o:74, a:1, s:1, b:0),
% 3.90/4.32 element [51, 2] (w:1, o:75, a:1, s:1, b:0),
% 3.90/4.32 empty_set [52, 0] (w:1, o:8, a:1, s:1, b:0),
% 3.90/4.32 relation_empty_yielding [53, 1] (w:1, o:36, a:1, s:1, b:0),
% 3.90/4.32 powerset [54, 1] (w:1, o:39, a:1, s:1, b:0),
% 3.90/4.32 being_limit_ordinal [55, 1] (w:1, o:42, a:1, s:1, b:0),
% 3.90/4.32 alpha1 [57, 2] (w:1, o:76, a:1, s:1, b:1),
% 3.90/4.32 alpha2 [58, 1] (w:1, o:40, a:1, s:1, b:1),
% 3.90/4.32 alpha3 [59, 1] (w:1, o:41, a:1, s:1, b:1),
% 3.90/4.32 skol1 [60, 1] (w:1, o:43, a:1, s:1, b:1),
% 3.90/4.32 skol2 [61, 0] (w:1, o:16, a:1, s:1, b:1),
% 3.90/4.32 skol3 [62, 0] (w:1, o:17, a:1, s:1, b:1),
% 3.90/4.32 skol4 [63, 0] (w:1, o:18, a:1, s:1, b:1),
% 3.90/4.32 skol5 [64, 0] (w:1, o:19, a:1, s:1, b:1),
% 3.90/4.32 skol6 [65, 0] (w:1, o:20, a:1, s:1, b:1),
% 3.90/4.32 skol7 [66, 0] (w:1, o:21, a:1, s:1, b:1),
% 3.90/4.32 skol8 [67, 0] (w:1, o:22, a:1, s:1, b:1),
% 3.90/4.32 skol9 [68, 0] (w:1, o:23, a:1, s:1, b:1),
% 3.90/4.32 skol10 [69, 0] (w:1, o:10, a:1, s:1, b:1),
% 3.90/4.32 skol11 [70, 0] (w:1, o:11, a:1, s:1, b:1),
% 3.90/4.32 skol12 [71, 0] (w:1, o:12, a:1, s:1, b:1),
% 3.90/4.32 skol13 [72, 0] (w:1, o:13, a:1, s:1, b:1),
% 3.90/4.32 skol14 [73, 1] (w:1, o:44, a:1, s:1, b:1),
% 3.90/4.32 skol15 [74, 0] (w:1, o:14, a:1, s:1, b:1),
% 3.90/4.32 skol16 [75, 1] (w:1, o:45, a:1, s:1, b:1),
% 3.90/4.32 skol17 [76, 0] (w:1, o:15, a:1, s:1, b:1).
% 3.90/4.32
% 3.90/4.32
% 3.90/4.32 Starting Search:
% 3.90/4.32
% 3.90/4.32 *** allocated 15000 integers for clauses
% 3.90/4.32 *** allocated 22500 integers for clauses
% 3.90/4.32 *** allocated 33750 integers for clauses
% 3.90/4.32 *** allocated 50625 integers for clauses
% 3.90/4.32 *** allocated 15000 integers for termspace/termends
% 3.90/4.32 *** allocated 75937 integers for clauses
% 3.90/4.32 Resimplifying inuse:
% 3.90/4.32 Done
% 3.90/4.32
% 3.90/4.32 *** allocated 22500 integers for termspace/termends
% 3.90/4.32 *** allocated 113905 integers for clauses
% 3.90/4.32
% 3.90/4.32 Intermediate Status:
% 3.90/4.32 Generated: 4113
% 3.90/4.32 Kept: 2012
% 3.90/4.32 Inuse: 301
% 3.90/4.32 Deleted: 25
% 3.90/4.32 Deletedinuse: 0
% 3.90/4.32
% 3.90/4.32 Resimplifying inuse:
% 3.90/4.32 Done
% 3.90/4.32
% 3.90/4.32 *** allocated 33750 integers for termspace/termends
% 3.90/4.32 *** allocated 170857 integers for clauses
% 3.90/4.32 Resimplifying inuse:
% 3.90/4.32 Done
% 3.90/4.32
% 3.90/4.32 *** allocated 50625 integers for termspace/termends
% 3.90/4.32 *** allocated 256285 integers for clauses
% 3.90/4.32
% 3.90/4.32 Intermediate Status:
% 3.90/4.32 Generated: 10421
% 3.90/4.32 Kept: 4015
% 3.90/4.32 Inuse: 483
% 3.90/4.32 Deleted: 189
% 3.90/4.32 Deletedinuse: 113
% 3.90/4.32
% 3.90/4.32 Resimplifying inuse:
% 3.90/4.32 Done
% 3.90/4.32
% 3.90/4.32 *** allocated 75937 integers for termspace/termends
% 3.90/4.32 Resimplifying inuse:
% 3.90/4.32 Done
% 3.90/4.32
% 3.90/4.32 *** allocated 384427 integers for clauses
% 3.90/4.32
% 3.90/4.32 Intermediate Status:
% 3.90/4.32 Generated: 18928
% 3.90/4.32 Kept: 6019
% 3.90/4.32 Inuse: 718
% 3.90/4.32 Deleted: 272
% 3.90/4.32 Deletedinuse: 118
% 3.90/4.32
% 3.90/4.32 Resimplifying inuse:
% 3.90/4.32 Done
% 3.90/4.32
% 3.90/4.32 *** allocated 113905 integers for termspace/termends
% 3.90/4.32 Resimplifying inuse:
% 3.90/4.32 Done
% 3.90/4.32
% 3.90/4.32
% 3.90/4.32 Intermediate Status:
% 3.90/4.32 Generated: 25222
% 3.90/4.32 Kept: 8088
% 3.90/4.32 Inuse: 861
% 3.90/4.32 Deleted: 328
% 3.90/4.32 Deletedinuse: 128
% 3.90/4.32
% 3.90/4.32 Resimplifying inuse:
% 3.90/4.32 Done
% 3.90/4.32
% 3.90/4.32 *** allocated 576640 integers for clauses
% 3.90/4.32 Resimplifying inuse:
% 3.90/4.32 Done
% 3.90/4.32
% 3.90/4.32 *** allocated 170857 integers for termspace/termends
% 3.90/4.32
% 3.90/4.32 Intermediate Status:
% 3.90/4.32 Generated: 30247
% 3.90/4.32 Kept: 10093
% 3.90/4.32 Inuse: 916
% 3.90/4.32 Deleted: 342
% 3.90/4.32 Deletedinuse: 128
% 3.90/4.32
% 3.90/4.32 Resimplifying inuse:
% 3.90/4.32 Done
% 3.90/4.32
% 3.90/4.32 Resimplifying inuse:
% 3.90/4.32 Done
% 3.90/4.32
% 3.90/4.32
% 3.90/4.32 Intermediate Status:
% 3.90/4.32 Generated: 37595
% 3.90/4.32 Kept: 12115
% 3.90/4.32 Inuse: 1025
% 3.90/4.32 Deleted: 363
% 3.90/4.32 Deletedinuse: 128
% 3.90/4.32
% 3.90/4.32 Resimplifying inuse:
% 3.90/4.32 Done
% 3.90/4.32
% 3.90/4.32 *** allocated 864960 integers for clauses
% 3.90/4.32 Resimplifying inuse:
% 3.90/4.32 Done
% 3.90/4.32
% 3.90/4.32
% 3.90/4.32 Intermediate Status:
% 3.90/4.32 Generated: 43703
% 3.90/4.32 Kept: 14117
% 3.90/4.32 Inuse: 1094
% 3.90/4.32 Deleted: 367
% 3.90/4.32 Deletedinuse: 128
% 3.90/4.32
% 3.90/4.32 Resimplifying inuse:
% 3.90/4.32 Done
% 3.90/4.32
% 3.90/4.32 *** allocated 256285 integers for termspace/termends
% 3.90/4.32 Resimplifying inuse:
% 3.90/4.32 Done
% 3.90/4.32
% 3.90/4.32
% 3.90/4.32 Intermediate Status:
% 3.90/4.32 Generated: 49889
% 3.90/4.32 Kept: 16135
% 3.90/4.32 Inuse: 1164
% 3.90/4.32 Deleted: 369
% 3.90/4.32 Deletedinuse: 128
% 3.90/4.32
% 3.90/4.32 Resimplifying inuse:
% 3.90/4.32 Done
% 3.90/4.32
% 3.90/4.32 Resimplifying inuse:
% 3.90/4.32 Done
% 3.90/4.32
% 3.90/4.32 *** allocated 1297440 integers for clauses
% 3.90/4.32
% 3.90/4.32 Intermediate Status:
% 3.90/4.32 Generated: 55941
% 3.90/4.32 Kept: 18159
% 3.90/4.32 Inuse: 1229
% 3.90/4.32 Deleted: 378
% 3.90/4.32 Deletedinuse: 128
% 3.90/4.32
% 3.90/4.32 Resimplifying inuse:
% 3.90/4.32 Done
% 3.90/4.32
% 3.90/4.32 Resimplifying inuse:
% 3.90/4.32 Done
% 3.90/4.32
% 3.90/4.32 Resimplifying clauses:
% 3.90/4.32 Done
% 3.90/4.32
% 3.90/4.32
% 3.90/4.32 Intermediate Status:
% 3.90/4.32 Generated: 62730
% 3.90/4.32 Kept: 20169
% 3.90/4.32 Inuse: 1334
% 3.90/4.32 Deleted: 2007
% 3.90/4.32 Deletedinuse: 128
% 3.90/4.32
% 3.90/4.32 Resimplifying inuse:
% 3.90/4.32 Done
% 3.90/4.32
% 3.90/4.32 *** allocated 384427 integers for termspace/termends
% 3.90/4.32 Resimplifying inuse:
% 3.90/4.32 Done
% 3.90/4.32
% 3.90/4.32
% 3.90/4.32 Intermediate Status:
% 3.90/4.32 Generated: 72166
% 3.90/4.32 Kept: 22182
% 3.90/4.32 Inuse: 1372
% 3.90/4.32 Deleted: 2007
% 3.90/4.32 Deletedinuse: 128
% 3.90/4.32
% 3.90/4.32 Resimplifying inuse:
% 3.90/4.32 Done
% 3.90/4.32
% 3.90/4.32
% 3.90/4.32 Bliksems!, er is een bewijs:
% 3.90/4.32 % SZS status Theorem
% 3.90/4.32 % SZS output start Refutation
% 3.90/4.32
% 3.90/4.32 (0) {G0,W6,D2,L2,V2,M2} I { ! in( X, Y ), ! in( Y, X ) }.
% 3.90/4.32 (16) {G0,W9,D2,L3,V2,M3} I { ! subset( X, Y ), X = Y, proper_subset( X, Y )
% 3.90/4.32 }.
% 3.90/4.32 (19) {G0,W2,D2,L1,V0,M1} I { empty( empty_set ) }.
% 3.90/4.32 (22) {G0,W3,D3,L1,V1,M1} I { ! empty( succ( X ) ) }.
% 3.90/4.32 (27) {G0,W2,D2,L1,V0,M1} I { ordinal( empty_set ) }.
% 3.90/4.32 (30) {G0,W4,D2,L2,V1,M2} I { ! ordinal( X ), alpha2( X ) }.
% 3.90/4.32 (31) {G0,W5,D3,L2,V1,M2} I { ! ordinal( X ), ordinal( succ( X ) ) }.
% 3.90/4.32 (32) {G0,W5,D3,L2,V1,M2} I { ! alpha2( X ), epsilon_transitive( succ( X ) )
% 3.90/4.32 }.
% 3.90/4.32 (71) {G0,W10,D2,L4,V2,M4} I { ! ordinal( X ), ! ordinal( Y ), !
% 3.90/4.32 ordinal_subset( X, Y ), subset( X, Y ) }.
% 3.90/4.32 (75) {G0,W4,D3,L1,V1,M1} I { in( X, succ( X ) ) }.
% 3.90/4.32 (77) {G0,W6,D2,L2,V2,M2} I { ! in( X, Y ), element( X, Y ) }.
% 3.90/4.32 (78) {G0,W10,D2,L4,V2,M4} I { ! epsilon_transitive( X ), ! ordinal( Y ), !
% 3.90/4.32 proper_subset( X, Y ), in( X, Y ) }.
% 3.90/4.32 (79) {G0,W8,D2,L3,V2,M3} I { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 3.90/4.32 (80) {G0,W11,D3,L4,V2,M4} I { ! ordinal( X ), ! ordinal( Y ), ! in( X, Y )
% 3.90/4.32 , ordinal_subset( succ( X ), Y ) }.
% 3.90/4.32 (84) {G0,W9,D2,L4,V2,M4} I { ! ordinal( X ), ! being_limit_ordinal( X ), !
% 3.90/4.32 ordinal( Y ), alpha1( X, Y ) }.
% 3.90/4.32 (85) {G0,W7,D3,L3,V2,M3} I { ! ordinal( X ), ordinal( skol14( Y ) ),
% 3.90/4.32 being_limit_ordinal( X ) }.
% 3.90/4.32 (86) {G0,W8,D3,L3,V1,M3} I { ! ordinal( X ), ! alpha1( X, skol14( X ) ),
% 3.90/4.32 being_limit_ordinal( X ) }.
% 3.90/4.32 (87) {G0,W10,D3,L3,V2,M3} I { ! alpha1( X, Y ), ! in( Y, X ), in( succ( Y )
% 3.90/4.32 , X ) }.
% 3.90/4.32 (88) {G0,W6,D2,L2,V2,M2} I { in( Y, X ), alpha1( X, Y ) }.
% 3.90/4.32 (89) {G0,W7,D3,L2,V2,M2} I { ! in( succ( Y ), X ), alpha1( X, Y ) }.
% 3.90/4.32 (90) {G0,W2,D2,L1,V0,M1} I { ordinal( skol15 ) }.
% 3.90/4.32 (91) {G0,W4,D2,L2,V0,M2} I { alpha3( skol15 ), ordinal( skol17 ) }.
% 3.90/4.32 (92) {G0,W6,D3,L2,V0,M2} I { alpha3( skol15 ), succ( skol17 ) ==> skol15
% 3.90/4.32 }.
% 3.90/4.32 (93) {G0,W4,D2,L2,V0,M2} I { alpha3( skol15 ), being_limit_ordinal( skol15
% 3.90/4.32 ) }.
% 3.90/4.32 (94) {G0,W4,D2,L2,V1,M2} I { ! alpha3( X ), ! being_limit_ordinal( X ) }.
% 3.90/4.32 (95) {G0,W8,D3,L3,V2,M3} I { ! alpha3( X ), ! ordinal( Y ), ! X = succ( Y )
% 3.90/4.32 }.
% 3.90/4.32 (100) {G0,W5,D2,L2,V1,M2} I { ! empty( X ), X = empty_set }.
% 3.90/4.32 (101) {G0,W5,D2,L2,V2,M2} I { ! in( X, Y ), ! empty( Y ) }.
% 3.90/4.32 (102) {G0,W7,D2,L3,V2,M3} I { ! empty( X ), X = Y, ! empty( Y ) }.
% 3.90/4.32 (103) {G1,W3,D2,L1,V1,M1} F(0) { ! in( X, X ) }.
% 3.90/4.32 (546) {G1,W8,D2,L3,V1,M3} R(71,90) { ! ordinal( X ), ! ordinal_subset( X,
% 3.90/4.32 skol15 ), subset( X, skol15 ) }.
% 3.90/4.32 (643) {G1,W4,D2,L2,V0,M2} R(91,94) { ordinal( skol17 ), !
% 3.90/4.32 being_limit_ordinal( skol15 ) }.
% 3.90/4.32 (688) {G1,W4,D3,L1,V1,M1} R(77,75) { element( X, succ( X ) ) }.
% 3.90/4.32 (1090) {G2,W9,D2,L4,V1,M4} R(84,643) { ! ordinal( X ), !
% 3.90/4.32 being_limit_ordinal( X ), alpha1( X, skol17 ), ! being_limit_ordinal(
% 3.90/4.32 skol15 ) }.
% 3.90/4.32 (1134) {G3,W5,D2,L2,V0,M2} F(1090);r(90) { ! being_limit_ordinal( skol15 )
% 3.90/4.32 , alpha1( skol15, skol17 ) }.
% 3.90/4.32 (1359) {G1,W3,D2,L1,V1,M1} R(101,19) { ! in( X, empty_set ) }.
% 3.90/4.32 (1373) {G2,W3,D2,L1,V1,M1} R(88,1359) { alpha1( empty_set, X ) }.
% 3.90/4.32 (1385) {G3,W2,D2,L1,V0,M1} R(1373,86);r(27) { being_limit_ordinal(
% 3.90/4.32 empty_set ) }.
% 3.90/4.32 (1402) {G1,W6,D3,L2,V0,M2} R(92,94) { succ( skol17 ) ==> skol15, !
% 3.90/4.32 being_limit_ordinal( skol15 ) }.
% 3.90/4.32 (1405) {G2,W5,D2,L2,V0,M2} P(92,688) { element( skol17, skol15 ), alpha3(
% 3.90/4.32 skol15 ) }.
% 3.90/4.32 (1410) {G1,W4,D2,L2,V0,M2} P(92,22) { ! empty( skol15 ), alpha3( skol15 )
% 3.90/4.32 }.
% 3.90/4.32 (1580) {G2,W4,D2,L2,V0,M2} R(1410,94) { ! empty( skol15 ), !
% 3.90/4.32 being_limit_ordinal( skol15 ) }.
% 3.90/4.32 (1627) {G4,W4,D2,L2,V1,M2} P(100,1385) { being_limit_ordinal( X ), ! empty
% 3.90/4.32 ( X ) }.
% 3.90/4.32 (1649) {G5,W4,D2,L2,V1,M2} P(102,1580);f;r(1627) { ! empty( X ), ! empty(
% 3.90/4.32 skol15 ) }.
% 3.90/4.32 (1659) {G6,W2,D2,L1,V0,M1} F(1649) { ! empty( skol15 ) }.
% 3.90/4.32 (2146) {G3,W5,D2,L2,V0,M2} R(1405,94) { element( skol17, skol15 ), !
% 3.90/4.32 being_limit_ordinal( skol15 ) }.
% 3.90/4.32 (2155) {G7,W5,D2,L2,V0,M2} R(2146,79);r(1659) { ! being_limit_ordinal(
% 3.90/4.32 skol15 ), in( skol17, skol15 ) }.
% 3.90/4.32 (2164) {G8,W5,D2,L2,V0,M2} R(2155,87);d(1402);r(1134) { !
% 3.90/4.32 being_limit_ordinal( skol15 ), in( skol15, skol15 ) }.
% 3.90/4.32 (2174) {G9,W2,D2,L1,V0,M1} S(2164);r(103) { ! being_limit_ordinal( skol15 )
% 3.90/4.32 }.
% 3.90/4.32 (2590) {G10,W4,D3,L1,V0,M1} R(2174,86);r(90) { ! alpha1( skol15, skol14(
% 3.90/4.32 skol15 ) ) }.
% 3.90/4.32 (2591) {G10,W3,D3,L1,V1,M1} R(2174,85);r(90) { ordinal( skol14( X ) ) }.
% 3.90/4.32 (2592) {G10,W2,D2,L1,V0,M1} R(2174,93) { alpha3( skol15 ) }.
% 3.90/4.32 (2595) {G11,W6,D3,L2,V1,M2} R(2592,95) { ! ordinal( X ), ! succ( X ) ==>
% 3.90/4.32 skol15 }.
% 3.90/4.32 (2619) {G11,W4,D4,L1,V1,M1} R(2591,31) { ordinal( succ( skol14( X ) ) ) }.
% 3.90/4.32 (2620) {G11,W3,D3,L1,V1,M1} R(2591,30) { alpha2( skol14( X ) ) }.
% 3.90/4.32 (2627) {G12,W4,D4,L1,V1,M1} R(2620,32) { epsilon_transitive( succ( skol14(
% 3.90/4.32 X ) ) ) }.
% 3.90/4.32 (2699) {G11,W5,D4,L1,V0,M1} R(2590,89) { ! in( succ( skol14( skol15 ) ),
% 3.90/4.32 skol15 ) }.
% 3.90/4.32 (2700) {G11,W4,D3,L1,V0,M1} R(2590,88) { in( skol14( skol15 ), skol15 ) }.
% 3.90/4.32 (2707) {G12,W7,D4,L2,V0,M2} R(2700,80);r(2591) { ! ordinal( skol15 ),
% 3.90/4.32 ordinal_subset( succ( skol14( skol15 ) ), skol15 ) }.
% 3.90/4.32 (4006) {G13,W7,D4,L2,V0,M2} R(2699,78);r(2627) { ! ordinal( skol15 ), !
% 3.90/4.32 proper_subset( succ( skol14( skol15 ) ), skol15 ) }.
% 3.90/4.32 (5947) {G12,W5,D4,L1,V1,M1} R(2595,2591) { ! succ( skol14( X ) ) ==> skol15
% 3.90/4.32 }.
% 3.90/4.32 (20074) {G14,W5,D4,L1,V0,M1} S(4006);r(90) { ! proper_subset( succ( skol14
% 3.90/4.32 ( skol15 ) ), skol15 ) }.
% 3.90/4.32 (20082) {G13,W5,D4,L1,V0,M1} S(2707);r(90) { ordinal_subset( succ( skol14(
% 3.90/4.32 skol15 ) ), skol15 ) }.
% 3.90/4.32 (23211) {G14,W5,D4,L1,V0,M1} R(20082,546);r(2619) { subset( succ( skol14(
% 3.90/4.32 skol15 ) ), skol15 ) }.
% 3.90/4.32 (23229) {G15,W5,D4,L1,V0,M1} R(23211,16);r(20074) { succ( skol14( skol15 )
% 3.90/4.32 ) ==> skol15 }.
% 3.90/4.32 (23242) {G16,W0,D0,L0,V0,M0} S(23229);r(5947) { }.
% 3.90/4.32
% 3.90/4.32
% 3.90/4.32 % SZS output end Refutation
% 3.90/4.32 found a proof!
% 3.90/4.32
% 3.90/4.32
% 3.90/4.32 Unprocessed initial clauses:
% 3.90/4.32
% 3.90/4.32 (23244) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), ! in( Y, X ) }.
% 3.90/4.32 (23245) {G0,W6,D2,L2,V2,M2} { ! proper_subset( X, Y ), ! proper_subset( Y
% 3.90/4.32 , X ) }.
% 3.90/4.32 (23246) {G0,W4,D2,L2,V1,M2} { ! empty( X ), function( X ) }.
% 3.90/4.32 (23247) {G0,W4,D2,L2,V1,M2} { ! ordinal( X ), epsilon_transitive( X ) }.
% 3.90/4.32 (23248) {G0,W4,D2,L2,V1,M2} { ! ordinal( X ), epsilon_connected( X ) }.
% 3.90/4.32 (23249) {G0,W4,D2,L2,V1,M2} { ! empty( X ), relation( X ) }.
% 3.90/4.32 (23250) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 3.90/4.32 ), relation( X ) }.
% 3.90/4.32 (23251) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 3.90/4.32 ), function( X ) }.
% 3.90/4.32 (23252) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 3.90/4.32 ), one_to_one( X ) }.
% 3.90/4.32 (23253) {G0,W6,D2,L3,V1,M3} { ! epsilon_transitive( X ), !
% 3.90/4.32 epsilon_connected( X ), ordinal( X ) }.
% 3.90/4.32 (23254) {G0,W4,D2,L2,V1,M2} { ! empty( X ), epsilon_transitive( X ) }.
% 3.90/4.32 (23255) {G0,W4,D2,L2,V1,M2} { ! empty( X ), epsilon_connected( X ) }.
% 3.90/4.32 (23256) {G0,W4,D2,L2,V1,M2} { ! empty( X ), ordinal( X ) }.
% 3.90/4.32 (23257) {G0,W7,D3,L1,V2,M1} { set_union2( X, Y ) = set_union2( Y, X ) }.
% 3.90/4.32 (23258) {G0,W10,D2,L4,V2,M4} { ! ordinal( X ), ! ordinal( Y ),
% 3.90/4.32 ordinal_subset( X, Y ), ordinal_subset( Y, X ) }.
% 3.90/4.32 (23259) {G0,W7,D4,L1,V1,M1} { succ( X ) = set_union2( X, singleton( X ) )
% 3.90/4.32 }.
% 3.90/4.32 (23260) {G0,W6,D2,L2,V2,M2} { ! proper_subset( X, Y ), subset( X, Y ) }.
% 3.90/4.32 (23261) {G0,W6,D2,L2,V2,M2} { ! proper_subset( X, Y ), ! X = Y }.
% 3.90/4.32 (23262) {G0,W9,D2,L3,V2,M3} { ! subset( X, Y ), X = Y, proper_subset( X, Y
% 3.90/4.32 ) }.
% 3.90/4.32 (23263) {G0,W1,D1,L1,V0,M1} { && }.
% 3.90/4.32 (23264) {G0,W1,D1,L1,V0,M1} { && }.
% 3.90/4.32 (23265) {G0,W1,D1,L1,V0,M1} { && }.
% 3.90/4.32 (23266) {G0,W1,D1,L1,V0,M1} { && }.
% 3.90/4.32 (23267) {G0,W1,D1,L1,V0,M1} { && }.
% 3.90/4.32 (23268) {G0,W1,D1,L1,V0,M1} { && }.
% 3.90/4.32 (23269) {G0,W4,D3,L1,V1,M1} { element( skol1( X ), X ) }.
% 3.90/4.32 (23270) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 3.90/4.32 (23271) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 3.90/4.32 (23272) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( empty_set ) }.
% 3.90/4.32 (23273) {G0,W3,D3,L1,V1,M1} { ! empty( succ( X ) ) }.
% 3.90/4.32 (23274) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 3.90/4.32 (23275) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 3.90/4.32 (23276) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( empty_set ) }.
% 3.90/4.32 (23277) {G0,W2,D2,L1,V0,M1} { function( empty_set ) }.
% 3.90/4.32 (23278) {G0,W2,D2,L1,V0,M1} { one_to_one( empty_set ) }.
% 3.90/4.32 (23279) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 3.90/4.32 (23280) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( empty_set ) }.
% 3.90/4.32 (23281) {G0,W2,D2,L1,V0,M1} { epsilon_connected( empty_set ) }.
% 3.90/4.32 (23282) {G0,W2,D2,L1,V0,M1} { ordinal( empty_set ) }.
% 3.90/4.32 (23283) {G0,W8,D3,L3,V2,M3} { ! relation( X ), ! relation( Y ), relation(
% 3.90/4.32 set_union2( X, Y ) ) }.
% 3.90/4.32 (23284) {G0,W6,D3,L2,V2,M2} { empty( X ), ! empty( set_union2( X, Y ) )
% 3.90/4.32 }.
% 3.90/4.32 (23285) {G0,W4,D2,L2,V1,M2} { ! ordinal( X ), alpha2( X ) }.
% 3.90/4.32 (23286) {G0,W5,D3,L2,V1,M2} { ! ordinal( X ), ordinal( succ( X ) ) }.
% 3.90/4.32 (23287) {G0,W5,D3,L2,V1,M2} { ! alpha2( X ), ! empty( succ( X ) ) }.
% 3.90/4.32 (23288) {G0,W5,D3,L2,V1,M2} { ! alpha2( X ), epsilon_transitive( succ( X )
% 3.90/4.32 ) }.
% 3.90/4.32 (23289) {G0,W5,D3,L2,V1,M2} { ! alpha2( X ), epsilon_connected( succ( X )
% 3.90/4.32 ) }.
% 3.90/4.32 (23290) {G0,W11,D3,L4,V1,M4} { empty( succ( X ) ), ! epsilon_transitive(
% 3.90/4.32 succ( X ) ), ! epsilon_connected( succ( X ) ), alpha2( X ) }.
% 3.90/4.32 (23291) {G0,W6,D3,L2,V2,M2} { empty( X ), ! empty( set_union2( Y, X ) )
% 3.90/4.32 }.
% 3.90/4.32 (23292) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 3.90/4.32 (23293) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 3.90/4.32 (23294) {G0,W5,D3,L1,V1,M1} { set_union2( X, X ) = X }.
% 3.90/4.32 (23295) {G0,W3,D2,L1,V1,M1} { ! proper_subset( X, X ) }.
% 3.90/4.32 (23296) {G0,W2,D2,L1,V0,M1} { relation( skol2 ) }.
% 3.90/4.32 (23297) {G0,W2,D2,L1,V0,M1} { function( skol2 ) }.
% 3.90/4.32 (23298) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol3 ) }.
% 3.90/4.32 (23299) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol3 ) }.
% 3.90/4.32 (23300) {G0,W2,D2,L1,V0,M1} { ordinal( skol3 ) }.
% 3.90/4.32 (23301) {G0,W2,D2,L1,V0,M1} { empty( skol4 ) }.
% 3.90/4.32 (23302) {G0,W2,D2,L1,V0,M1} { relation( skol4 ) }.
% 3.90/4.32 (23303) {G0,W2,D2,L1,V0,M1} { empty( skol5 ) }.
% 3.90/4.32 (23304) {G0,W2,D2,L1,V0,M1} { relation( skol6 ) }.
% 3.90/4.32 (23305) {G0,W2,D2,L1,V0,M1} { empty( skol6 ) }.
% 3.90/4.32 (23306) {G0,W2,D2,L1,V0,M1} { function( skol6 ) }.
% 3.90/4.32 (23307) {G0,W2,D2,L1,V0,M1} { relation( skol7 ) }.
% 3.90/4.32 (23308) {G0,W2,D2,L1,V0,M1} { function( skol7 ) }.
% 3.90/4.32 (23309) {G0,W2,D2,L1,V0,M1} { one_to_one( skol7 ) }.
% 3.90/4.32 (23310) {G0,W2,D2,L1,V0,M1} { empty( skol7 ) }.
% 3.90/4.32 (23311) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol7 ) }.
% 3.90/4.32 (23312) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol7 ) }.
% 3.90/4.32 (23313) {G0,W2,D2,L1,V0,M1} { ordinal( skol7 ) }.
% 3.90/4.32 (23314) {G0,W2,D2,L1,V0,M1} { ! empty( skol8 ) }.
% 3.90/4.32 (23315) {G0,W2,D2,L1,V0,M1} { relation( skol8 ) }.
% 3.90/4.32 (23316) {G0,W2,D2,L1,V0,M1} { ! empty( skol9 ) }.
% 3.90/4.32 (23317) {G0,W2,D2,L1,V0,M1} { relation( skol10 ) }.
% 3.90/4.32 (23318) {G0,W2,D2,L1,V0,M1} { function( skol10 ) }.
% 3.90/4.32 (23319) {G0,W2,D2,L1,V0,M1} { one_to_one( skol10 ) }.
% 3.90/4.32 (23320) {G0,W2,D2,L1,V0,M1} { ! empty( skol11 ) }.
% 3.90/4.32 (23321) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol11 ) }.
% 3.90/4.32 (23322) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol11 ) }.
% 3.90/4.32 (23323) {G0,W2,D2,L1,V0,M1} { ordinal( skol11 ) }.
% 3.90/4.32 (23324) {G0,W2,D2,L1,V0,M1} { relation( skol12 ) }.
% 3.90/4.32 (23325) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( skol12 ) }.
% 3.90/4.32 (23326) {G0,W2,D2,L1,V0,M1} { relation( skol13 ) }.
% 3.90/4.32 (23327) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( skol13 ) }.
% 3.90/4.32 (23328) {G0,W2,D2,L1,V0,M1} { function( skol13 ) }.
% 3.90/4.32 (23329) {G0,W10,D2,L4,V2,M4} { ! ordinal( X ), ! ordinal( Y ), !
% 3.90/4.32 ordinal_subset( X, Y ), subset( X, Y ) }.
% 3.90/4.32 (23330) {G0,W10,D2,L4,V2,M4} { ! ordinal( X ), ! ordinal( Y ), ! subset( X
% 3.90/4.32 , Y ), ordinal_subset( X, Y ) }.
% 3.90/4.32 (23331) {G0,W7,D2,L3,V2,M3} { ! ordinal( X ), ! ordinal( Y ),
% 3.90/4.32 ordinal_subset( X, X ) }.
% 3.90/4.32 (23332) {G0,W3,D2,L1,V1,M1} { subset( X, X ) }.
% 3.90/4.32 (23333) {G0,W4,D3,L1,V1,M1} { in( X, succ( X ) ) }.
% 3.90/4.32 (23334) {G0,W5,D3,L1,V1,M1} { set_union2( X, empty_set ) = X }.
% 3.90/4.32 (23335) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), element( X, Y ) }.
% 3.90/4.32 (23336) {G0,W10,D2,L4,V2,M4} { ! epsilon_transitive( X ), ! ordinal( Y ),
% 3.90/4.32 ! proper_subset( X, Y ), in( X, Y ) }.
% 3.90/4.32 (23337) {G0,W8,D2,L3,V2,M3} { ! element( X, Y ), empty( Y ), in( X, Y )
% 3.90/4.32 }.
% 3.90/4.32 (23338) {G0,W11,D3,L4,V2,M4} { ! ordinal( X ), ! ordinal( Y ), ! in( X, Y
% 3.90/4.32 ), ordinal_subset( succ( X ), Y ) }.
% 3.90/4.32 (23339) {G0,W11,D3,L4,V2,M4} { ! ordinal( X ), ! ordinal( Y ), !
% 3.90/4.32 ordinal_subset( succ( X ), Y ), in( X, Y ) }.
% 3.90/4.32 (23340) {G0,W7,D3,L2,V2,M2} { ! element( X, powerset( Y ) ), subset( X, Y
% 3.90/4.32 ) }.
% 3.90/4.32 (23341) {G0,W7,D3,L2,V2,M2} { ! subset( X, Y ), element( X, powerset( Y )
% 3.90/4.32 ) }.
% 3.90/4.32 (23342) {G0,W9,D2,L4,V2,M4} { ! ordinal( X ), ! being_limit_ordinal( X ),
% 3.90/4.32 ! ordinal( Y ), alpha1( X, Y ) }.
% 3.90/4.32 (23343) {G0,W7,D3,L3,V2,M3} { ! ordinal( X ), ordinal( skol14( Y ) ),
% 3.90/4.32 being_limit_ordinal( X ) }.
% 3.90/4.32 (23344) {G0,W8,D3,L3,V1,M3} { ! ordinal( X ), ! alpha1( X, skol14( X ) ),
% 3.90/4.32 being_limit_ordinal( X ) }.
% 3.90/4.32 (23345) {G0,W10,D3,L3,V2,M3} { ! alpha1( X, Y ), ! in( Y, X ), in( succ( Y
% 3.90/4.32 ), X ) }.
% 3.90/4.32 (23346) {G0,W6,D2,L2,V2,M2} { in( Y, X ), alpha1( X, Y ) }.
% 3.90/4.32 (23347) {G0,W7,D3,L2,V2,M2} { ! in( succ( Y ), X ), alpha1( X, Y ) }.
% 3.90/4.32 (23348) {G0,W2,D2,L1,V0,M1} { ordinal( skol15 ) }.
% 3.90/4.32 (23349) {G0,W4,D2,L2,V0,M2} { alpha3( skol15 ), ordinal( skol17 ) }.
% 3.90/4.32 (23350) {G0,W6,D3,L2,V0,M2} { alpha3( skol15 ), skol15 = succ( skol17 )
% 3.90/4.32 }.
% 3.90/4.32 (23351) {G0,W4,D2,L2,V0,M2} { alpha3( skol15 ), being_limit_ordinal(
% 3.90/4.32 skol15 ) }.
% 3.90/4.32 (23352) {G0,W4,D2,L2,V1,M2} { ! alpha3( X ), ! being_limit_ordinal( X )
% 3.90/4.32 }.
% 3.90/4.32 (23353) {G0,W8,D3,L3,V2,M3} { ! alpha3( X ), ! ordinal( Y ), ! X = succ( Y
% 3.90/4.32 ) }.
% 3.90/4.32 (23354) {G0,W7,D3,L3,V2,M3} { being_limit_ordinal( X ), ordinal( skol16( Y
% 3.90/4.32 ) ), alpha3( X ) }.
% 3.90/4.32 (23355) {G0,W9,D4,L3,V1,M3} { being_limit_ordinal( X ), X = succ( skol16(
% 3.90/4.32 X ) ), alpha3( X ) }.
% 3.90/4.32 (23356) {G0,W10,D3,L3,V3,M3} { ! in( X, Z ), ! element( Z, powerset( Y ) )
% 3.90/4.32 , element( X, Y ) }.
% 3.90/4.32 (23357) {G0,W9,D3,L3,V3,M3} { ! in( X, Y ), ! element( Y, powerset( Z ) )
% 3.90/4.32 , ! empty( Z ) }.
% 3.90/4.32 (23358) {G0,W5,D2,L2,V1,M2} { ! empty( X ), X = empty_set }.
% 3.90/4.32 (23359) {G0,W5,D2,L2,V2,M2} { ! in( X, Y ), ! empty( Y ) }.
% 3.90/4.32 (23360) {G0,W7,D2,L3,V2,M3} { ! empty( X ), X = Y, ! empty( Y ) }.
% 3.90/4.32
% 3.90/4.32
% 3.90/4.32 Total Proof:
% 3.90/4.32
% 3.90/4.32 subsumption: (0) {G0,W6,D2,L2,V2,M2} I { ! in( X, Y ), ! in( Y, X ) }.
% 3.90/4.32 parent0: (23244) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), ! in( Y, X ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 X := X
% 3.90/4.32 Y := Y
% 3.90/4.32 end
% 3.90/4.32 permutation0:
% 3.90/4.32 0 ==> 0
% 3.90/4.32 1 ==> 1
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 subsumption: (16) {G0,W9,D2,L3,V2,M3} I { ! subset( X, Y ), X = Y,
% 3.90/4.32 proper_subset( X, Y ) }.
% 3.90/4.32 parent0: (23262) {G0,W9,D2,L3,V2,M3} { ! subset( X, Y ), X = Y,
% 3.90/4.32 proper_subset( X, Y ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 X := X
% 3.90/4.32 Y := Y
% 3.90/4.32 end
% 3.90/4.32 permutation0:
% 3.90/4.32 0 ==> 0
% 3.90/4.32 1 ==> 1
% 3.90/4.32 2 ==> 2
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 subsumption: (19) {G0,W2,D2,L1,V0,M1} I { empty( empty_set ) }.
% 3.90/4.32 parent0: (23270) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 end
% 3.90/4.32 permutation0:
% 3.90/4.32 0 ==> 0
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 subsumption: (22) {G0,W3,D3,L1,V1,M1} I { ! empty( succ( X ) ) }.
% 3.90/4.32 parent0: (23273) {G0,W3,D3,L1,V1,M1} { ! empty( succ( X ) ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 X := X
% 3.90/4.32 end
% 3.90/4.32 permutation0:
% 3.90/4.32 0 ==> 0
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 subsumption: (27) {G0,W2,D2,L1,V0,M1} I { ordinal( empty_set ) }.
% 3.90/4.32 parent0: (23282) {G0,W2,D2,L1,V0,M1} { ordinal( empty_set ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 end
% 3.90/4.32 permutation0:
% 3.90/4.32 0 ==> 0
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 subsumption: (30) {G0,W4,D2,L2,V1,M2} I { ! ordinal( X ), alpha2( X ) }.
% 3.90/4.32 parent0: (23285) {G0,W4,D2,L2,V1,M2} { ! ordinal( X ), alpha2( X ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 X := X
% 3.90/4.32 end
% 3.90/4.32 permutation0:
% 3.90/4.32 0 ==> 0
% 3.90/4.32 1 ==> 1
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 subsumption: (31) {G0,W5,D3,L2,V1,M2} I { ! ordinal( X ), ordinal( succ( X
% 3.90/4.32 ) ) }.
% 3.90/4.32 parent0: (23286) {G0,W5,D3,L2,V1,M2} { ! ordinal( X ), ordinal( succ( X )
% 3.90/4.32 ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 X := X
% 3.90/4.32 end
% 3.90/4.32 permutation0:
% 3.90/4.32 0 ==> 0
% 3.90/4.32 1 ==> 1
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 subsumption: (32) {G0,W5,D3,L2,V1,M2} I { ! alpha2( X ), epsilon_transitive
% 3.90/4.32 ( succ( X ) ) }.
% 3.90/4.32 parent0: (23288) {G0,W5,D3,L2,V1,M2} { ! alpha2( X ), epsilon_transitive(
% 3.90/4.32 succ( X ) ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 X := X
% 3.90/4.32 end
% 3.90/4.32 permutation0:
% 3.90/4.32 0 ==> 0
% 3.90/4.32 1 ==> 1
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 subsumption: (71) {G0,W10,D2,L4,V2,M4} I { ! ordinal( X ), ! ordinal( Y ),
% 3.90/4.32 ! ordinal_subset( X, Y ), subset( X, Y ) }.
% 3.90/4.32 parent0: (23329) {G0,W10,D2,L4,V2,M4} { ! ordinal( X ), ! ordinal( Y ), !
% 3.90/4.32 ordinal_subset( X, Y ), subset( X, Y ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 X := X
% 3.90/4.32 Y := Y
% 3.90/4.32 end
% 3.90/4.32 permutation0:
% 3.90/4.32 0 ==> 0
% 3.90/4.32 1 ==> 1
% 3.90/4.32 2 ==> 2
% 3.90/4.32 3 ==> 3
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 subsumption: (75) {G0,W4,D3,L1,V1,M1} I { in( X, succ( X ) ) }.
% 3.90/4.32 parent0: (23333) {G0,W4,D3,L1,V1,M1} { in( X, succ( X ) ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 X := X
% 3.90/4.32 end
% 3.90/4.32 permutation0:
% 3.90/4.32 0 ==> 0
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 subsumption: (77) {G0,W6,D2,L2,V2,M2} I { ! in( X, Y ), element( X, Y ) }.
% 3.90/4.32 parent0: (23335) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), element( X, Y ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 X := X
% 3.90/4.32 Y := Y
% 3.90/4.32 end
% 3.90/4.32 permutation0:
% 3.90/4.32 0 ==> 0
% 3.90/4.32 1 ==> 1
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 subsumption: (78) {G0,W10,D2,L4,V2,M4} I { ! epsilon_transitive( X ), !
% 3.90/4.32 ordinal( Y ), ! proper_subset( X, Y ), in( X, Y ) }.
% 3.90/4.32 parent0: (23336) {G0,W10,D2,L4,V2,M4} { ! epsilon_transitive( X ), !
% 3.90/4.32 ordinal( Y ), ! proper_subset( X, Y ), in( X, Y ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 X := X
% 3.90/4.32 Y := Y
% 3.90/4.32 end
% 3.90/4.32 permutation0:
% 3.90/4.32 0 ==> 0
% 3.90/4.32 1 ==> 1
% 3.90/4.32 2 ==> 2
% 3.90/4.32 3 ==> 3
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 subsumption: (79) {G0,W8,D2,L3,V2,M3} I { ! element( X, Y ), empty( Y ), in
% 3.90/4.32 ( X, Y ) }.
% 3.90/4.32 parent0: (23337) {G0,W8,D2,L3,V2,M3} { ! element( X, Y ), empty( Y ), in(
% 3.90/4.32 X, Y ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 X := X
% 3.90/4.32 Y := Y
% 3.90/4.32 end
% 3.90/4.32 permutation0:
% 3.90/4.32 0 ==> 0
% 3.90/4.32 1 ==> 1
% 3.90/4.32 2 ==> 2
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 subsumption: (80) {G0,W11,D3,L4,V2,M4} I { ! ordinal( X ), ! ordinal( Y ),
% 3.90/4.32 ! in( X, Y ), ordinal_subset( succ( X ), Y ) }.
% 3.90/4.32 parent0: (23338) {G0,W11,D3,L4,V2,M4} { ! ordinal( X ), ! ordinal( Y ), !
% 3.90/4.32 in( X, Y ), ordinal_subset( succ( X ), Y ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 X := X
% 3.90/4.32 Y := Y
% 3.90/4.32 end
% 3.90/4.32 permutation0:
% 3.90/4.32 0 ==> 0
% 3.90/4.32 1 ==> 1
% 3.90/4.32 2 ==> 2
% 3.90/4.32 3 ==> 3
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 subsumption: (84) {G0,W9,D2,L4,V2,M4} I { ! ordinal( X ), !
% 3.90/4.32 being_limit_ordinal( X ), ! ordinal( Y ), alpha1( X, Y ) }.
% 3.90/4.32 parent0: (23342) {G0,W9,D2,L4,V2,M4} { ! ordinal( X ), !
% 3.90/4.32 being_limit_ordinal( X ), ! ordinal( Y ), alpha1( X, Y ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 X := X
% 3.90/4.32 Y := Y
% 3.90/4.32 end
% 3.90/4.32 permutation0:
% 3.90/4.32 0 ==> 0
% 3.90/4.32 1 ==> 1
% 3.90/4.32 2 ==> 2
% 3.90/4.32 3 ==> 3
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 subsumption: (85) {G0,W7,D3,L3,V2,M3} I { ! ordinal( X ), ordinal( skol14(
% 3.90/4.32 Y ) ), being_limit_ordinal( X ) }.
% 3.90/4.32 parent0: (23343) {G0,W7,D3,L3,V2,M3} { ! ordinal( X ), ordinal( skol14( Y
% 3.90/4.32 ) ), being_limit_ordinal( X ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 X := X
% 3.90/4.32 Y := Y
% 3.90/4.32 end
% 3.90/4.32 permutation0:
% 3.90/4.32 0 ==> 0
% 3.90/4.32 1 ==> 1
% 3.90/4.32 2 ==> 2
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 subsumption: (86) {G0,W8,D3,L3,V1,M3} I { ! ordinal( X ), ! alpha1( X,
% 3.90/4.32 skol14( X ) ), being_limit_ordinal( X ) }.
% 3.90/4.32 parent0: (23344) {G0,W8,D3,L3,V1,M3} { ! ordinal( X ), ! alpha1( X, skol14
% 3.90/4.32 ( X ) ), being_limit_ordinal( X ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 X := X
% 3.90/4.32 end
% 3.90/4.32 permutation0:
% 3.90/4.32 0 ==> 0
% 3.90/4.32 1 ==> 1
% 3.90/4.32 2 ==> 2
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 subsumption: (87) {G0,W10,D3,L3,V2,M3} I { ! alpha1( X, Y ), ! in( Y, X ),
% 3.90/4.32 in( succ( Y ), X ) }.
% 3.90/4.32 parent0: (23345) {G0,W10,D3,L3,V2,M3} { ! alpha1( X, Y ), ! in( Y, X ), in
% 3.90/4.32 ( succ( Y ), X ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 X := X
% 3.90/4.32 Y := Y
% 3.90/4.32 end
% 3.90/4.32 permutation0:
% 3.90/4.32 0 ==> 0
% 3.90/4.32 1 ==> 1
% 3.90/4.32 2 ==> 2
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 subsumption: (88) {G0,W6,D2,L2,V2,M2} I { in( Y, X ), alpha1( X, Y ) }.
% 3.90/4.32 parent0: (23346) {G0,W6,D2,L2,V2,M2} { in( Y, X ), alpha1( X, Y ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 X := X
% 3.90/4.32 Y := Y
% 3.90/4.32 end
% 3.90/4.32 permutation0:
% 3.90/4.32 0 ==> 0
% 3.90/4.32 1 ==> 1
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 subsumption: (89) {G0,W7,D3,L2,V2,M2} I { ! in( succ( Y ), X ), alpha1( X,
% 3.90/4.32 Y ) }.
% 3.90/4.32 parent0: (23347) {G0,W7,D3,L2,V2,M2} { ! in( succ( Y ), X ), alpha1( X, Y
% 3.90/4.32 ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 X := X
% 3.90/4.32 Y := Y
% 3.90/4.32 end
% 3.90/4.32 permutation0:
% 3.90/4.32 0 ==> 0
% 3.90/4.32 1 ==> 1
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 subsumption: (90) {G0,W2,D2,L1,V0,M1} I { ordinal( skol15 ) }.
% 3.90/4.32 parent0: (23348) {G0,W2,D2,L1,V0,M1} { ordinal( skol15 ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 end
% 3.90/4.32 permutation0:
% 3.90/4.32 0 ==> 0
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 subsumption: (91) {G0,W4,D2,L2,V0,M2} I { alpha3( skol15 ), ordinal( skol17
% 3.90/4.32 ) }.
% 3.90/4.32 parent0: (23349) {G0,W4,D2,L2,V0,M2} { alpha3( skol15 ), ordinal( skol17 )
% 3.90/4.32 }.
% 3.90/4.32 substitution0:
% 3.90/4.32 end
% 3.90/4.32 permutation0:
% 3.90/4.32 0 ==> 0
% 3.90/4.32 1 ==> 1
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 eqswap: (23655) {G0,W6,D3,L2,V0,M2} { succ( skol17 ) = skol15, alpha3(
% 3.90/4.32 skol15 ) }.
% 3.90/4.32 parent0[1]: (23350) {G0,W6,D3,L2,V0,M2} { alpha3( skol15 ), skol15 = succ
% 3.90/4.32 ( skol17 ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 subsumption: (92) {G0,W6,D3,L2,V0,M2} I { alpha3( skol15 ), succ( skol17 )
% 3.90/4.32 ==> skol15 }.
% 3.90/4.32 parent0: (23655) {G0,W6,D3,L2,V0,M2} { succ( skol17 ) = skol15, alpha3(
% 3.90/4.32 skol15 ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 end
% 3.90/4.32 permutation0:
% 3.90/4.32 0 ==> 1
% 3.90/4.32 1 ==> 0
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 subsumption: (93) {G0,W4,D2,L2,V0,M2} I { alpha3( skol15 ),
% 3.90/4.32 being_limit_ordinal( skol15 ) }.
% 3.90/4.32 parent0: (23351) {G0,W4,D2,L2,V0,M2} { alpha3( skol15 ),
% 3.90/4.32 being_limit_ordinal( skol15 ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 end
% 3.90/4.32 permutation0:
% 3.90/4.32 0 ==> 0
% 3.90/4.32 1 ==> 1
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 subsumption: (94) {G0,W4,D2,L2,V1,M2} I { ! alpha3( X ), !
% 3.90/4.32 being_limit_ordinal( X ) }.
% 3.90/4.32 parent0: (23352) {G0,W4,D2,L2,V1,M2} { ! alpha3( X ), !
% 3.90/4.32 being_limit_ordinal( X ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 X := X
% 3.90/4.32 end
% 3.90/4.32 permutation0:
% 3.90/4.32 0 ==> 0
% 3.90/4.32 1 ==> 1
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 subsumption: (95) {G0,W8,D3,L3,V2,M3} I { ! alpha3( X ), ! ordinal( Y ), !
% 3.90/4.32 X = succ( Y ) }.
% 3.90/4.32 parent0: (23353) {G0,W8,D3,L3,V2,M3} { ! alpha3( X ), ! ordinal( Y ), ! X
% 3.90/4.32 = succ( Y ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 X := X
% 3.90/4.32 Y := Y
% 3.90/4.32 end
% 3.90/4.32 permutation0:
% 3.90/4.32 0 ==> 0
% 3.90/4.32 1 ==> 1
% 3.90/4.32 2 ==> 2
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 subsumption: (100) {G0,W5,D2,L2,V1,M2} I { ! empty( X ), X = empty_set }.
% 3.90/4.32 parent0: (23358) {G0,W5,D2,L2,V1,M2} { ! empty( X ), X = empty_set }.
% 3.90/4.32 substitution0:
% 3.90/4.32 X := X
% 3.90/4.32 end
% 3.90/4.32 permutation0:
% 3.90/4.32 0 ==> 0
% 3.90/4.32 1 ==> 1
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 subsumption: (101) {G0,W5,D2,L2,V2,M2} I { ! in( X, Y ), ! empty( Y ) }.
% 3.90/4.32 parent0: (23359) {G0,W5,D2,L2,V2,M2} { ! in( X, Y ), ! empty( Y ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 X := X
% 3.90/4.32 Y := Y
% 3.90/4.32 end
% 3.90/4.32 permutation0:
% 3.90/4.32 0 ==> 0
% 3.90/4.32 1 ==> 1
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 subsumption: (102) {G0,W7,D2,L3,V2,M3} I { ! empty( X ), X = Y, ! empty( Y
% 3.90/4.32 ) }.
% 3.90/4.32 parent0: (23360) {G0,W7,D2,L3,V2,M3} { ! empty( X ), X = Y, ! empty( Y )
% 3.90/4.32 }.
% 3.90/4.32 substitution0:
% 3.90/4.32 X := X
% 3.90/4.32 Y := Y
% 3.90/4.32 end
% 3.90/4.32 permutation0:
% 3.90/4.32 0 ==> 0
% 3.90/4.32 1 ==> 1
% 3.90/4.32 2 ==> 2
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 factor: (23775) {G0,W3,D2,L1,V1,M1} { ! in( X, X ) }.
% 3.90/4.32 parent0[0, 1]: (0) {G0,W6,D2,L2,V2,M2} I { ! in( X, Y ), ! in( Y, X ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 X := X
% 3.90/4.32 Y := X
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 subsumption: (103) {G1,W3,D2,L1,V1,M1} F(0) { ! in( X, X ) }.
% 3.90/4.32 parent0: (23775) {G0,W3,D2,L1,V1,M1} { ! in( X, X ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 X := X
% 3.90/4.32 end
% 3.90/4.32 permutation0:
% 3.90/4.32 0 ==> 0
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 resolution: (23777) {G1,W8,D2,L3,V1,M3} { ! ordinal( X ), ! ordinal_subset
% 3.90/4.32 ( X, skol15 ), subset( X, skol15 ) }.
% 3.90/4.32 parent0[1]: (71) {G0,W10,D2,L4,V2,M4} I { ! ordinal( X ), ! ordinal( Y ), !
% 3.90/4.32 ordinal_subset( X, Y ), subset( X, Y ) }.
% 3.90/4.32 parent1[0]: (90) {G0,W2,D2,L1,V0,M1} I { ordinal( skol15 ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 X := X
% 3.90/4.32 Y := skol15
% 3.90/4.32 end
% 3.90/4.32 substitution1:
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 subsumption: (546) {G1,W8,D2,L3,V1,M3} R(71,90) { ! ordinal( X ), !
% 3.90/4.32 ordinal_subset( X, skol15 ), subset( X, skol15 ) }.
% 3.90/4.32 parent0: (23777) {G1,W8,D2,L3,V1,M3} { ! ordinal( X ), ! ordinal_subset( X
% 3.90/4.32 , skol15 ), subset( X, skol15 ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 X := X
% 3.90/4.32 end
% 3.90/4.32 permutation0:
% 3.90/4.32 0 ==> 0
% 3.90/4.32 1 ==> 1
% 3.90/4.32 2 ==> 2
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 resolution: (23778) {G1,W4,D2,L2,V0,M2} { ! being_limit_ordinal( skol15 )
% 3.90/4.32 , ordinal( skol17 ) }.
% 3.90/4.32 parent0[0]: (94) {G0,W4,D2,L2,V1,M2} I { ! alpha3( X ), !
% 3.90/4.32 being_limit_ordinal( X ) }.
% 3.90/4.32 parent1[0]: (91) {G0,W4,D2,L2,V0,M2} I { alpha3( skol15 ), ordinal( skol17
% 3.90/4.32 ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 X := skol15
% 3.90/4.32 end
% 3.90/4.32 substitution1:
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 subsumption: (643) {G1,W4,D2,L2,V0,M2} R(91,94) { ordinal( skol17 ), !
% 3.90/4.32 being_limit_ordinal( skol15 ) }.
% 3.90/4.32 parent0: (23778) {G1,W4,D2,L2,V0,M2} { ! being_limit_ordinal( skol15 ),
% 3.90/4.32 ordinal( skol17 ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 end
% 3.90/4.32 permutation0:
% 3.90/4.32 0 ==> 1
% 3.90/4.32 1 ==> 0
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 resolution: (23779) {G1,W4,D3,L1,V1,M1} { element( X, succ( X ) ) }.
% 3.90/4.32 parent0[0]: (77) {G0,W6,D2,L2,V2,M2} I { ! in( X, Y ), element( X, Y ) }.
% 3.90/4.32 parent1[0]: (75) {G0,W4,D3,L1,V1,M1} I { in( X, succ( X ) ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 X := X
% 3.90/4.32 Y := succ( X )
% 3.90/4.32 end
% 3.90/4.32 substitution1:
% 3.90/4.32 X := X
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 subsumption: (688) {G1,W4,D3,L1,V1,M1} R(77,75) { element( X, succ( X ) )
% 3.90/4.32 }.
% 3.90/4.32 parent0: (23779) {G1,W4,D3,L1,V1,M1} { element( X, succ( X ) ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 X := X
% 3.90/4.32 end
% 3.90/4.32 permutation0:
% 3.90/4.32 0 ==> 0
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 resolution: (23781) {G1,W9,D2,L4,V1,M4} { ! ordinal( X ), !
% 3.90/4.32 being_limit_ordinal( X ), alpha1( X, skol17 ), ! being_limit_ordinal(
% 3.90/4.32 skol15 ) }.
% 3.90/4.32 parent0[2]: (84) {G0,W9,D2,L4,V2,M4} I { ! ordinal( X ), !
% 3.90/4.32 being_limit_ordinal( X ), ! ordinal( Y ), alpha1( X, Y ) }.
% 3.90/4.32 parent1[0]: (643) {G1,W4,D2,L2,V0,M2} R(91,94) { ordinal( skol17 ), !
% 3.90/4.32 being_limit_ordinal( skol15 ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 X := X
% 3.90/4.32 Y := skol17
% 3.90/4.32 end
% 3.90/4.32 substitution1:
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 subsumption: (1090) {G2,W9,D2,L4,V1,M4} R(84,643) { ! ordinal( X ), !
% 3.90/4.32 being_limit_ordinal( X ), alpha1( X, skol17 ), ! being_limit_ordinal(
% 3.90/4.32 skol15 ) }.
% 3.90/4.32 parent0: (23781) {G1,W9,D2,L4,V1,M4} { ! ordinal( X ), !
% 3.90/4.32 being_limit_ordinal( X ), alpha1( X, skol17 ), ! being_limit_ordinal(
% 3.90/4.32 skol15 ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 X := X
% 3.90/4.32 end
% 3.90/4.32 permutation0:
% 3.90/4.32 0 ==> 0
% 3.90/4.32 1 ==> 1
% 3.90/4.32 2 ==> 2
% 3.90/4.32 3 ==> 3
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 factor: (23783) {G2,W7,D2,L3,V0,M3} { ! ordinal( skol15 ), !
% 3.90/4.32 being_limit_ordinal( skol15 ), alpha1( skol15, skol17 ) }.
% 3.90/4.32 parent0[1, 3]: (1090) {G2,W9,D2,L4,V1,M4} R(84,643) { ! ordinal( X ), !
% 3.90/4.32 being_limit_ordinal( X ), alpha1( X, skol17 ), ! being_limit_ordinal(
% 3.90/4.32 skol15 ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 X := skol15
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 resolution: (23784) {G1,W5,D2,L2,V0,M2} { ! being_limit_ordinal( skol15 )
% 3.90/4.32 , alpha1( skol15, skol17 ) }.
% 3.90/4.32 parent0[0]: (23783) {G2,W7,D2,L3,V0,M3} { ! ordinal( skol15 ), !
% 3.90/4.32 being_limit_ordinal( skol15 ), alpha1( skol15, skol17 ) }.
% 3.90/4.32 parent1[0]: (90) {G0,W2,D2,L1,V0,M1} I { ordinal( skol15 ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 end
% 3.90/4.32 substitution1:
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 subsumption: (1134) {G3,W5,D2,L2,V0,M2} F(1090);r(90) { !
% 3.90/4.32 being_limit_ordinal( skol15 ), alpha1( skol15, skol17 ) }.
% 3.90/4.32 parent0: (23784) {G1,W5,D2,L2,V0,M2} { ! being_limit_ordinal( skol15 ),
% 3.90/4.32 alpha1( skol15, skol17 ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 end
% 3.90/4.32 permutation0:
% 3.90/4.32 0 ==> 0
% 3.90/4.32 1 ==> 1
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 resolution: (23785) {G1,W3,D2,L1,V1,M1} { ! in( X, empty_set ) }.
% 3.90/4.32 parent0[1]: (101) {G0,W5,D2,L2,V2,M2} I { ! in( X, Y ), ! empty( Y ) }.
% 3.90/4.32 parent1[0]: (19) {G0,W2,D2,L1,V0,M1} I { empty( empty_set ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 X := X
% 3.90/4.32 Y := empty_set
% 3.90/4.32 end
% 3.90/4.32 substitution1:
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 subsumption: (1359) {G1,W3,D2,L1,V1,M1} R(101,19) { ! in( X, empty_set )
% 3.90/4.32 }.
% 3.90/4.32 parent0: (23785) {G1,W3,D2,L1,V1,M1} { ! in( X, empty_set ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 X := X
% 3.90/4.32 end
% 3.90/4.32 permutation0:
% 3.90/4.32 0 ==> 0
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 resolution: (23786) {G1,W3,D2,L1,V1,M1} { alpha1( empty_set, X ) }.
% 3.90/4.32 parent0[0]: (1359) {G1,W3,D2,L1,V1,M1} R(101,19) { ! in( X, empty_set ) }.
% 3.90/4.32 parent1[0]: (88) {G0,W6,D2,L2,V2,M2} I { in( Y, X ), alpha1( X, Y ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 X := X
% 3.90/4.32 end
% 3.90/4.32 substitution1:
% 3.90/4.32 X := empty_set
% 3.90/4.32 Y := X
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 subsumption: (1373) {G2,W3,D2,L1,V1,M1} R(88,1359) { alpha1( empty_set, X )
% 3.90/4.32 }.
% 3.90/4.32 parent0: (23786) {G1,W3,D2,L1,V1,M1} { alpha1( empty_set, X ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 X := X
% 3.90/4.32 end
% 3.90/4.32 permutation0:
% 3.90/4.32 0 ==> 0
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 resolution: (23787) {G1,W4,D2,L2,V0,M2} { ! ordinal( empty_set ),
% 3.90/4.32 being_limit_ordinal( empty_set ) }.
% 3.90/4.32 parent0[1]: (86) {G0,W8,D3,L3,V1,M3} I { ! ordinal( X ), ! alpha1( X,
% 3.90/4.32 skol14( X ) ), being_limit_ordinal( X ) }.
% 3.90/4.32 parent1[0]: (1373) {G2,W3,D2,L1,V1,M1} R(88,1359) { alpha1( empty_set, X )
% 3.90/4.32 }.
% 3.90/4.32 substitution0:
% 3.90/4.32 X := empty_set
% 3.90/4.32 end
% 3.90/4.32 substitution1:
% 3.90/4.32 X := skol14( empty_set )
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 resolution: (23788) {G1,W2,D2,L1,V0,M1} { being_limit_ordinal( empty_set )
% 3.90/4.32 }.
% 3.90/4.32 parent0[0]: (23787) {G1,W4,D2,L2,V0,M2} { ! ordinal( empty_set ),
% 3.90/4.32 being_limit_ordinal( empty_set ) }.
% 3.90/4.32 parent1[0]: (27) {G0,W2,D2,L1,V0,M1} I { ordinal( empty_set ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 end
% 3.90/4.32 substitution1:
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 subsumption: (1385) {G3,W2,D2,L1,V0,M1} R(1373,86);r(27) {
% 3.90/4.32 being_limit_ordinal( empty_set ) }.
% 3.90/4.32 parent0: (23788) {G1,W2,D2,L1,V0,M1} { being_limit_ordinal( empty_set )
% 3.90/4.32 }.
% 3.90/4.32 substitution0:
% 3.90/4.32 end
% 3.90/4.32 permutation0:
% 3.90/4.32 0 ==> 0
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 eqswap: (23789) {G0,W6,D3,L2,V0,M2} { skol15 ==> succ( skol17 ), alpha3(
% 3.90/4.32 skol15 ) }.
% 3.90/4.32 parent0[1]: (92) {G0,W6,D3,L2,V0,M2} I { alpha3( skol15 ), succ( skol17 )
% 3.90/4.32 ==> skol15 }.
% 3.90/4.32 substitution0:
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 resolution: (23790) {G1,W6,D3,L2,V0,M2} { ! being_limit_ordinal( skol15 )
% 3.90/4.32 , skol15 ==> succ( skol17 ) }.
% 3.90/4.32 parent0[0]: (94) {G0,W4,D2,L2,V1,M2} I { ! alpha3( X ), !
% 3.90/4.32 being_limit_ordinal( X ) }.
% 3.90/4.32 parent1[1]: (23789) {G0,W6,D3,L2,V0,M2} { skol15 ==> succ( skol17 ),
% 3.90/4.32 alpha3( skol15 ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 X := skol15
% 3.90/4.32 end
% 3.90/4.32 substitution1:
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 eqswap: (23791) {G1,W6,D3,L2,V0,M2} { succ( skol17 ) ==> skol15, !
% 3.90/4.32 being_limit_ordinal( skol15 ) }.
% 3.90/4.32 parent0[1]: (23790) {G1,W6,D3,L2,V0,M2} { ! being_limit_ordinal( skol15 )
% 3.90/4.32 , skol15 ==> succ( skol17 ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 subsumption: (1402) {G1,W6,D3,L2,V0,M2} R(92,94) { succ( skol17 ) ==>
% 3.90/4.32 skol15, ! being_limit_ordinal( skol15 ) }.
% 3.90/4.32 parent0: (23791) {G1,W6,D3,L2,V0,M2} { succ( skol17 ) ==> skol15, !
% 3.90/4.32 being_limit_ordinal( skol15 ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 end
% 3.90/4.32 permutation0:
% 3.90/4.32 0 ==> 0
% 3.90/4.32 1 ==> 1
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 paramod: (23793) {G1,W5,D2,L2,V0,M2} { element( skol17, skol15 ), alpha3(
% 3.90/4.32 skol15 ) }.
% 3.90/4.32 parent0[1]: (92) {G0,W6,D3,L2,V0,M2} I { alpha3( skol15 ), succ( skol17 )
% 3.90/4.32 ==> skol15 }.
% 3.90/4.32 parent1[0; 2]: (688) {G1,W4,D3,L1,V1,M1} R(77,75) { element( X, succ( X ) )
% 3.90/4.32 }.
% 3.90/4.32 substitution0:
% 3.90/4.32 end
% 3.90/4.32 substitution1:
% 3.90/4.32 X := skol17
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 subsumption: (1405) {G2,W5,D2,L2,V0,M2} P(92,688) { element( skol17, skol15
% 3.90/4.32 ), alpha3( skol15 ) }.
% 3.90/4.32 parent0: (23793) {G1,W5,D2,L2,V0,M2} { element( skol17, skol15 ), alpha3(
% 3.90/4.32 skol15 ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 end
% 3.90/4.32 permutation0:
% 3.90/4.32 0 ==> 0
% 3.90/4.32 1 ==> 1
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 paramod: (23795) {G1,W4,D2,L2,V0,M2} { ! empty( skol15 ), alpha3( skol15 )
% 3.90/4.32 }.
% 3.90/4.32 parent0[1]: (92) {G0,W6,D3,L2,V0,M2} I { alpha3( skol15 ), succ( skol17 )
% 3.90/4.32 ==> skol15 }.
% 3.90/4.32 parent1[0; 2]: (22) {G0,W3,D3,L1,V1,M1} I { ! empty( succ( X ) ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 end
% 3.90/4.32 substitution1:
% 3.90/4.32 X := skol17
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 subsumption: (1410) {G1,W4,D2,L2,V0,M2} P(92,22) { ! empty( skol15 ),
% 3.90/4.32 alpha3( skol15 ) }.
% 3.90/4.32 parent0: (23795) {G1,W4,D2,L2,V0,M2} { ! empty( skol15 ), alpha3( skol15 )
% 3.90/4.32 }.
% 3.90/4.32 substitution0:
% 3.90/4.32 end
% 3.90/4.32 permutation0:
% 3.90/4.32 0 ==> 0
% 3.90/4.32 1 ==> 1
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 resolution: (23796) {G1,W4,D2,L2,V0,M2} { ! being_limit_ordinal( skol15 )
% 3.90/4.32 , ! empty( skol15 ) }.
% 3.90/4.32 parent0[0]: (94) {G0,W4,D2,L2,V1,M2} I { ! alpha3( X ), !
% 3.90/4.32 being_limit_ordinal( X ) }.
% 3.90/4.32 parent1[1]: (1410) {G1,W4,D2,L2,V0,M2} P(92,22) { ! empty( skol15 ), alpha3
% 3.90/4.32 ( skol15 ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 X := skol15
% 3.90/4.32 end
% 3.90/4.32 substitution1:
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 subsumption: (1580) {G2,W4,D2,L2,V0,M2} R(1410,94) { ! empty( skol15 ), !
% 3.90/4.32 being_limit_ordinal( skol15 ) }.
% 3.90/4.32 parent0: (23796) {G1,W4,D2,L2,V0,M2} { ! being_limit_ordinal( skol15 ), !
% 3.90/4.32 empty( skol15 ) }.
% 3.90/4.32 substitution0:
% 3.90/4.32 end
% 3.90/4.32 permutation0:
% 3.90/4.32 0 ==> 1
% 3.90/4.32 1 ==> 0
% 3.90/4.32 end
% 3.90/4.32
% 3.90/4.32 eqswap: (23797) {G0,W5,D2,L2,V1,M2} { empty_set = X, ! empty( X ) }.
% 3.90/4.32 parent0[1]: (100) {G0,W5,D2,L2,V1,M2} I { ! empty( X ), X = empty_set }.
% 3.90/4.34 substitution0:
% 3.90/4.34 X := X
% 3.90/4.34 end
% 3.90/4.34
% 3.90/4.34 paramod: (23798) {G1,W4,D2,L2,V1,M2} { being_limit_ordinal( X ), ! empty(
% 3.90/4.34 X ) }.
% 3.90/4.34 parent0[0]: (23797) {G0,W5,D2,L2,V1,M2} { empty_set = X, ! empty( X ) }.
% 3.90/4.34 parent1[0; 1]: (1385) {G3,W2,D2,L1,V0,M1} R(1373,86);r(27) {
% 3.90/4.34 being_limit_ordinal( empty_set ) }.
% 3.90/4.34 substitution0:
% 3.90/4.34 X := X
% 3.90/4.34 end
% 3.90/4.34 substitution1:
% 3.90/4.34 end
% 3.90/4.34
% 3.90/4.34 subsumption: (1627) {G4,W4,D2,L2,V1,M2} P(100,1385) { being_limit_ordinal(
% 3.90/4.34 X ), ! empty( X ) }.
% 3.90/4.34 parent0: (23798) {G1,W4,D2,L2,V1,M2} { being_limit_ordinal( X ), ! empty(
% 3.90/4.34 X ) }.
% 3.90/4.34 substitution0:
% 3.90/4.34 X := X
% 3.90/4.34 end
% 3.90/4.34 permutation0:
% 3.90/4.34 0 ==> 0
% 3.90/4.34 1 ==> 1
% 3.90/4.34 end
% 3.90/4.34
% 3.90/4.34 paramod: (23799) {G1,W8,D2,L4,V1,M4} { ! empty( X ), ! empty( skol15 ), !
% 3.90/4.34 empty( X ), ! being_limit_ordinal( skol15 ) }.
% 3.90/4.34 parent0[1]: (102) {G0,W7,D2,L3,V2,M3} I { ! empty( X ), X = Y, ! empty( Y )
% 3.90/4.34 }.
% 3.90/4.34 parent1[0; 2]: (1580) {G2,W4,D2,L2,V0,M2} R(1410,94) { ! empty( skol15 ), !
% 3.90/4.34 being_limit_ordinal( skol15 ) }.
% 3.90/4.34 substitution0:
% 3.90/4.34 X := skol15
% 3.90/4.34 Y := X
% 3.90/4.34 end
% 3.90/4.34 substitution1:
% 3.90/4.34 end
% 3.90/4.34
% 3.90/4.34 resolution: (23824) {G2,W8,D2,L4,V1,M4} { ! empty( X ), ! empty( skol15 )
% 3.90/4.34 , ! empty( X ), ! empty( skol15 ) }.
% 3.90/4.34 parent0[3]: (23799) {G1,W8,D2,L4,V1,M4} { ! empty( X ), ! empty( skol15 )
% 3.90/4.34 , ! empty( X ), ! being_limit_ordinal( skol15 ) }.
% 3.90/4.34 parent1[0]: (1627) {G4,W4,D2,L2,V1,M2} P(100,1385) { being_limit_ordinal( X
% 3.90/4.34 ), ! empty( X ) }.
% 3.90/4.34 substitution0:
% 3.90/4.34 X := X
% 3.90/4.34 end
% 3.90/4.34 substitution1:
% 3.90/4.34 X := skol15
% 3.90/4.34 end
% 3.90/4.34
% 3.90/4.34 factor: (23825) {G2,W6,D2,L3,V0,M3} { ! empty( skol15 ), ! empty( skol15 )
% 3.90/4.34 , ! empty( skol15 ) }.
% 3.90/4.34 parent0[0, 1]: (23824) {G2,W8,D2,L4,V1,M4} { ! empty( X ), ! empty( skol15
% 3.90/4.34 ), ! empty( X ), ! empty( skol15 ) }.
% 3.90/4.34 substitution0:
% 3.90/4.34 X := skol15
% 3.90/4.34 end
% 3.90/4.34
% 3.90/4.34 factor: (23826) {G2,W4,D2,L2,V0,M2} { ! empty( skol15 ), ! empty( skol15 )
% 3.90/4.34 }.
% 3.90/4.34 parent0[0, 1]: (23825) {G2,W6,D2,L3,V0,M3} { ! empty( skol15 ), ! empty(
% 3.90/4.34 skol15 ), ! empty( skol15 ) }.
% 3.90/4.34 substitution0:
% 3.90/4.34 end
% 3.90/4.34
% 3.90/4.34 subsumption: (1649) {G5,W4,D2,L2,V1,M2} P(102,1580);f;r(1627) { ! empty( X
% 3.90/4.34 ), ! empty( skol15 ) }.
% 3.90/4.34 parent0: (23826) {G2,W4,D2,L2,V0,M2} { ! empty( skol15 ), ! empty( skol15
% 3.90/4.34 ) }.
% 3.90/4.34 substitution0:
% 3.90/4.34 end
% 3.90/4.34 permutation0:
% 3.90/4.34 0 ==> 1
% 3.90/4.34 1 ==> 1
% 3.90/4.34 end
% 3.90/4.34
% 3.90/4.34 factor: (23828) {G5,W2,D2,L1,V0,M1} { ! empty( skol15 ) }.
% 3.90/4.34 parent0[0, 1]: (1649) {G5,W4,D2,L2,V1,M2} P(102,1580);f;r(1627) { ! empty(
% 3.90/4.34 X ), ! empty( skol15 ) }.
% 3.90/4.34 substitution0:
% 3.90/4.34 X := skol15
% 3.90/4.34 end
% 3.90/4.34
% 3.90/4.34 subsumption: (1659) {G6,W2,D2,L1,V0,M1} F(1649) { ! empty( skol15 ) }.
% 3.90/4.34 parent0: (23828) {G5,W2,D2,L1,V0,M1} { ! empty( skol15 ) }.
% 3.90/4.34 substitution0:
% 3.90/4.34 end
% 3.90/4.34 permutation0:
% 3.90/4.34 0 ==> 0
% 3.90/4.34 end
% 3.90/4.34
% 3.90/4.34 resolution: (23829) {G1,W5,D2,L2,V0,M2} { ! being_limit_ordinal( skol15 )
% 3.90/4.34 , element( skol17, skol15 ) }.
% 3.90/4.34 parent0[0]: (94) {G0,W4,D2,L2,V1,M2} I { ! alpha3( X ), !
% 3.90/4.34 being_limit_ordinal( X ) }.
% 3.90/4.34 parent1[1]: (1405) {G2,W5,D2,L2,V0,M2} P(92,688) { element( skol17, skol15
% 3.90/4.34 ), alpha3( skol15 ) }.
% 3.90/4.34 substitution0:
% 3.90/4.34 X := skol15
% 3.90/4.34 end
% 3.90/4.34 substitution1:
% 3.90/4.34 end
% 3.90/4.34
% 3.90/4.34 subsumption: (2146) {G3,W5,D2,L2,V0,M2} R(1405,94) { element( skol17,
% 3.90/4.34 skol15 ), ! being_limit_ordinal( skol15 ) }.
% 3.90/4.34 parent0: (23829) {G1,W5,D2,L2,V0,M2} { ! being_limit_ordinal( skol15 ),
% 3.90/4.34 element( skol17, skol15 ) }.
% 3.90/4.34 substitution0:
% 3.90/4.34 end
% 3.90/4.34 permutation0:
% 3.90/4.34 0 ==> 1
% 3.90/4.34 1 ==> 0
% 3.90/4.34 end
% 3.90/4.34
% 3.90/4.34 resolution: (23830) {G1,W7,D2,L3,V0,M3} { empty( skol15 ), in( skol17,
% 3.90/4.34 skol15 ), ! being_limit_ordinal( skol15 ) }.
% 3.90/4.34 parent0[0]: (79) {G0,W8,D2,L3,V2,M3} I { ! element( X, Y ), empty( Y ), in
% 3.90/4.34 ( X, Y ) }.
% 3.90/4.34 parent1[0]: (2146) {G3,W5,D2,L2,V0,M2} R(1405,94) { element( skol17, skol15
% 3.90/4.34 ), ! being_limit_ordinal( skol15 ) }.
% 3.90/4.34 substitution0:
% 3.90/4.34 X := skol17
% 3.90/4.34 Y := skol15
% 3.90/4.34 end
% 3.90/4.34 substitution1:
% 3.90/4.34 end
% 3.90/4.34
% 3.90/4.34 resolution: (23831) {G2,W5,D2,L2,V0,M2} { in( skol17, skol15 ), !
% 3.90/4.34 being_limit_ordinal( skol15 ) }.
% 3.90/4.34 parent0[0]: (1659) {G6,W2,D2,L1,V0,M1} F(1649) { ! empty( skol15 ) }.
% 3.90/4.34 parent1[0]: (23830) {G1,W7,D2,L3,V0,M3} { empty( skol15 ), in( skol17,
% 3.90/4.34 skol15 ), ! being_limit_ordinal( skol15 ) }.
% 3.90/4.34 substitution0:
% 3.90/4.34 end
% 3.90/4.34 substitution1:
% 3.90/4.34 end
% 3.90/4.34
% 3.90/4.34 subsumption: (2155) {G7,W5,D2,L2,V0,M2} R(2146,79);r(1659) { !
% 3.90/4.34 being_limit_ordinal( skol15 ), in( skol17, skol15 ) }.
% 3.90/4.34 parent0: (23831) {G2,W5,D2,L2,V0,M2} { in( skol17, skol15 ), !
% 3.90/4.34 being_limit_ordinal( skol15 ) }.
% 3.90/4.34 substitution0:
% 3.90/4.34 end
% 3.90/4.34 permutation0:
% 3.90/4.34 0 ==> 1
% 3.90/4.34 1 ==> 0
% 3.90/4.34 end
% 3.90/4.34
% 3.90/4.34 resolution: (23833) {G1,W9,D3,L3,V0,M3} { ! alpha1( skol15, skol17 ), in(
% 3.90/4.34 succ( skol17 ), skol15 ), ! being_limit_ordinal( skol15 ) }.
% 3.90/4.34 parent0[1]: (87) {G0,W10,D3,L3,V2,M3} I { ! alpha1( X, Y ), ! in( Y, X ),
% 3.90/4.34 in( succ( Y ), X ) }.
% 3.90/4.34 parent1[1]: (2155) {G7,W5,D2,L2,V0,M2} R(2146,79);r(1659) { !
% 3.90/4.34 being_limit_ordinal( skol15 ), in( skol17, skol15 ) }.
% 3.90/4.34 substitution0:
% 3.90/4.34 X := skol15
% 3.90/4.34 Y := skol17
% 3.90/4.34 end
% 3.90/4.34 substitution1:
% 3.90/4.34 end
% 3.90/4.34
% 3.90/4.34 paramod: (23834) {G2,W10,D2,L4,V0,M4} { in( skol15, skol15 ), !
% 3.90/4.34 being_limit_ordinal( skol15 ), ! alpha1( skol15, skol17 ), !
% 3.90/4.34 being_limit_ordinal( skol15 ) }.
% 3.90/4.34 parent0[0]: (1402) {G1,W6,D3,L2,V0,M2} R(92,94) { succ( skol17 ) ==> skol15
% 3.90/4.34 , ! being_limit_ordinal( skol15 ) }.
% 3.90/4.34 parent1[1; 1]: (23833) {G1,W9,D3,L3,V0,M3} { ! alpha1( skol15, skol17 ),
% 3.90/4.34 in( succ( skol17 ), skol15 ), ! being_limit_ordinal( skol15 ) }.
% 3.90/4.34 substitution0:
% 3.90/4.34 end
% 3.90/4.34 substitution1:
% 3.90/4.34 end
% 3.90/4.34
% 3.90/4.34 factor: (23835) {G2,W8,D2,L3,V0,M3} { in( skol15, skol15 ), !
% 3.90/4.34 being_limit_ordinal( skol15 ), ! alpha1( skol15, skol17 ) }.
% 3.90/4.34 parent0[1, 3]: (23834) {G2,W10,D2,L4,V0,M4} { in( skol15, skol15 ), !
% 3.90/4.34 being_limit_ordinal( skol15 ), ! alpha1( skol15, skol17 ), !
% 3.90/4.34 being_limit_ordinal( skol15 ) }.
% 3.90/4.34 substitution0:
% 3.90/4.34 end
% 3.90/4.34
% 3.90/4.34 resolution: (23836) {G3,W7,D2,L3,V0,M3} { in( skol15, skol15 ), !
% 3.90/4.34 being_limit_ordinal( skol15 ), ! being_limit_ordinal( skol15 ) }.
% 3.90/4.34 parent0[2]: (23835) {G2,W8,D2,L3,V0,M3} { in( skol15, skol15 ), !
% 3.90/4.34 being_limit_ordinal( skol15 ), ! alpha1( skol15, skol17 ) }.
% 3.90/4.34 parent1[1]: (1134) {G3,W5,D2,L2,V0,M2} F(1090);r(90) { !
% 3.90/4.34 being_limit_ordinal( skol15 ), alpha1( skol15, skol17 ) }.
% 3.90/4.34 substitution0:
% 3.90/4.34 end
% 3.90/4.34 substitution1:
% 3.90/4.34 end
% 3.90/4.34
% 3.90/4.34 factor: (23837) {G3,W5,D2,L2,V0,M2} { in( skol15, skol15 ), !
% 3.90/4.34 being_limit_ordinal( skol15 ) }.
% 3.90/4.34 parent0[1, 2]: (23836) {G3,W7,D2,L3,V0,M3} { in( skol15, skol15 ), !
% 3.90/4.34 being_limit_ordinal( skol15 ), ! being_limit_ordinal( skol15 ) }.
% 3.90/4.34 substitution0:
% 3.90/4.34 end
% 3.90/4.34
% 3.90/4.34 subsumption: (2164) {G8,W5,D2,L2,V0,M2} R(2155,87);d(1402);r(1134) { !
% 3.90/4.34 being_limit_ordinal( skol15 ), in( skol15, skol15 ) }.
% 3.90/4.34 parent0: (23837) {G3,W5,D2,L2,V0,M2} { in( skol15, skol15 ), !
% 3.90/4.34 being_limit_ordinal( skol15 ) }.
% 3.90/4.34 substitution0:
% 3.90/4.34 end
% 3.90/4.34 permutation0:
% 3.90/4.34 0 ==> 1
% 3.90/4.34 1 ==> 0
% 3.90/4.34 end
% 3.90/4.34
% 3.90/4.34 resolution: (23838) {G2,W2,D2,L1,V0,M1} { ! being_limit_ordinal( skol15 )
% 3.90/4.34 }.
% 3.90/4.34 parent0[0]: (103) {G1,W3,D2,L1,V1,M1} F(0) { ! in( X, X ) }.
% 3.90/4.34 parent1[1]: (2164) {G8,W5,D2,L2,V0,M2} R(2155,87);d(1402);r(1134) { !
% 3.90/4.34 being_limit_ordinal( skol15 ), in( skol15, skol15 ) }.
% 3.90/4.34 substitution0:
% 3.90/4.34 X := skol15
% 3.90/4.34 end
% 3.90/4.34 substitution1:
% 3.90/4.34 end
% 3.90/4.34
% 3.90/4.34 subsumption: (2174) {G9,W2,D2,L1,V0,M1} S(2164);r(103) { !
% 3.90/4.34 being_limit_ordinal( skol15 ) }.
% 3.90/4.34 parent0: (23838) {G2,W2,D2,L1,V0,M1} { ! being_limit_ordinal( skol15 ) }.
% 3.90/4.34 substitution0:
% 3.90/4.34 end
% 3.90/4.34 permutation0:
% 3.90/4.34 0 ==> 0
% 3.90/4.34 end
% 3.90/4.34
% 3.90/4.34 resolution: (23839) {G1,W6,D3,L2,V0,M2} { ! ordinal( skol15 ), ! alpha1(
% 3.90/4.34 skol15, skol14( skol15 ) ) }.
% 3.90/4.34 parent0[0]: (2174) {G9,W2,D2,L1,V0,M1} S(2164);r(103) { !
% 3.90/4.34 being_limit_ordinal( skol15 ) }.
% 3.90/4.34 parent1[2]: (86) {G0,W8,D3,L3,V1,M3} I { ! ordinal( X ), ! alpha1( X,
% 3.90/4.35 skol14( X ) ), being_limit_ordinal( X ) }.
% 3.90/4.35 substitution0:
% 3.90/4.35 end
% 3.90/4.35 substitution1:
% 3.90/4.35 X := skol15
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 resolution: (23840) {G1,W4,D3,L1,V0,M1} { ! alpha1( skol15, skol14( skol15
% 3.90/4.35 ) ) }.
% 3.90/4.35 parent0[0]: (23839) {G1,W6,D3,L2,V0,M2} { ! ordinal( skol15 ), ! alpha1(
% 3.90/4.35 skol15, skol14( skol15 ) ) }.
% 3.90/4.35 parent1[0]: (90) {G0,W2,D2,L1,V0,M1} I { ordinal( skol15 ) }.
% 3.90/4.35 substitution0:
% 3.90/4.35 end
% 3.90/4.35 substitution1:
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 subsumption: (2590) {G10,W4,D3,L1,V0,M1} R(2174,86);r(90) { ! alpha1(
% 3.90/4.35 skol15, skol14( skol15 ) ) }.
% 3.90/4.35 parent0: (23840) {G1,W4,D3,L1,V0,M1} { ! alpha1( skol15, skol14( skol15 )
% 3.90/4.35 ) }.
% 3.90/4.35 substitution0:
% 3.90/4.35 end
% 3.90/4.35 permutation0:
% 3.90/4.35 0 ==> 0
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 resolution: (23841) {G1,W5,D3,L2,V1,M2} { ! ordinal( skol15 ), ordinal(
% 3.90/4.35 skol14( X ) ) }.
% 3.90/4.35 parent0[0]: (2174) {G9,W2,D2,L1,V0,M1} S(2164);r(103) { !
% 3.90/4.35 being_limit_ordinal( skol15 ) }.
% 3.90/4.35 parent1[2]: (85) {G0,W7,D3,L3,V2,M3} I { ! ordinal( X ), ordinal( skol14( Y
% 3.90/4.35 ) ), being_limit_ordinal( X ) }.
% 3.90/4.35 substitution0:
% 3.90/4.35 end
% 3.90/4.35 substitution1:
% 3.90/4.35 X := skol15
% 3.90/4.35 Y := X
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 resolution: (23842) {G1,W3,D3,L1,V1,M1} { ordinal( skol14( X ) ) }.
% 3.90/4.35 parent0[0]: (23841) {G1,W5,D3,L2,V1,M2} { ! ordinal( skol15 ), ordinal(
% 3.90/4.35 skol14( X ) ) }.
% 3.90/4.35 parent1[0]: (90) {G0,W2,D2,L1,V0,M1} I { ordinal( skol15 ) }.
% 3.90/4.35 substitution0:
% 3.90/4.35 X := X
% 3.90/4.35 end
% 3.90/4.35 substitution1:
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 subsumption: (2591) {G10,W3,D3,L1,V1,M1} R(2174,85);r(90) { ordinal( skol14
% 3.90/4.35 ( X ) ) }.
% 3.90/4.35 parent0: (23842) {G1,W3,D3,L1,V1,M1} { ordinal( skol14( X ) ) }.
% 3.90/4.35 substitution0:
% 3.90/4.35 X := X
% 3.90/4.35 end
% 3.90/4.35 permutation0:
% 3.90/4.35 0 ==> 0
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 resolution: (23843) {G1,W2,D2,L1,V0,M1} { alpha3( skol15 ) }.
% 3.90/4.35 parent0[0]: (2174) {G9,W2,D2,L1,V0,M1} S(2164);r(103) { !
% 3.90/4.35 being_limit_ordinal( skol15 ) }.
% 3.90/4.35 parent1[1]: (93) {G0,W4,D2,L2,V0,M2} I { alpha3( skol15 ),
% 3.90/4.35 being_limit_ordinal( skol15 ) }.
% 3.90/4.35 substitution0:
% 3.90/4.35 end
% 3.90/4.35 substitution1:
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 subsumption: (2592) {G10,W2,D2,L1,V0,M1} R(2174,93) { alpha3( skol15 ) }.
% 3.90/4.35 parent0: (23843) {G1,W2,D2,L1,V0,M1} { alpha3( skol15 ) }.
% 3.90/4.35 substitution0:
% 3.90/4.35 end
% 3.90/4.35 permutation0:
% 3.90/4.35 0 ==> 0
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 eqswap: (23844) {G0,W8,D3,L3,V2,M3} { ! succ( Y ) = X, ! alpha3( X ), !
% 3.90/4.35 ordinal( Y ) }.
% 3.90/4.35 parent0[2]: (95) {G0,W8,D3,L3,V2,M3} I { ! alpha3( X ), ! ordinal( Y ), ! X
% 3.90/4.35 = succ( Y ) }.
% 3.90/4.35 substitution0:
% 3.90/4.35 X := X
% 3.90/4.35 Y := Y
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 resolution: (23845) {G1,W6,D3,L2,V1,M2} { ! succ( X ) = skol15, ! ordinal
% 3.90/4.35 ( X ) }.
% 3.90/4.35 parent0[1]: (23844) {G0,W8,D3,L3,V2,M3} { ! succ( Y ) = X, ! alpha3( X ),
% 3.90/4.35 ! ordinal( Y ) }.
% 3.90/4.35 parent1[0]: (2592) {G10,W2,D2,L1,V0,M1} R(2174,93) { alpha3( skol15 ) }.
% 3.90/4.35 substitution0:
% 3.90/4.35 X := skol15
% 3.90/4.35 Y := X
% 3.90/4.35 end
% 3.90/4.35 substitution1:
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 subsumption: (2595) {G11,W6,D3,L2,V1,M2} R(2592,95) { ! ordinal( X ), !
% 3.90/4.35 succ( X ) ==> skol15 }.
% 3.90/4.35 parent0: (23845) {G1,W6,D3,L2,V1,M2} { ! succ( X ) = skol15, ! ordinal( X
% 3.90/4.35 ) }.
% 3.90/4.35 substitution0:
% 3.90/4.35 X := X
% 3.90/4.35 end
% 3.90/4.35 permutation0:
% 3.90/4.35 0 ==> 1
% 3.90/4.35 1 ==> 0
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 resolution: (23847) {G1,W4,D4,L1,V1,M1} { ordinal( succ( skol14( X ) ) )
% 3.90/4.35 }.
% 3.90/4.35 parent0[0]: (31) {G0,W5,D3,L2,V1,M2} I { ! ordinal( X ), ordinal( succ( X )
% 3.90/4.35 ) }.
% 3.90/4.35 parent1[0]: (2591) {G10,W3,D3,L1,V1,M1} R(2174,85);r(90) { ordinal( skol14
% 3.90/4.35 ( X ) ) }.
% 3.90/4.35 substitution0:
% 3.90/4.35 X := skol14( X )
% 3.90/4.35 end
% 3.90/4.35 substitution1:
% 3.90/4.35 X := X
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 subsumption: (2619) {G11,W4,D4,L1,V1,M1} R(2591,31) { ordinal( succ( skol14
% 3.90/4.35 ( X ) ) ) }.
% 3.90/4.35 parent0: (23847) {G1,W4,D4,L1,V1,M1} { ordinal( succ( skol14( X ) ) ) }.
% 3.90/4.35 substitution0:
% 3.90/4.35 X := X
% 3.90/4.35 end
% 3.90/4.35 permutation0:
% 3.90/4.35 0 ==> 0
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 resolution: (23848) {G1,W3,D3,L1,V1,M1} { alpha2( skol14( X ) ) }.
% 3.90/4.35 parent0[0]: (30) {G0,W4,D2,L2,V1,M2} I { ! ordinal( X ), alpha2( X ) }.
% 3.90/4.35 parent1[0]: (2591) {G10,W3,D3,L1,V1,M1} R(2174,85);r(90) { ordinal( skol14
% 3.90/4.35 ( X ) ) }.
% 3.90/4.35 substitution0:
% 3.90/4.35 X := skol14( X )
% 3.90/4.35 end
% 3.90/4.35 substitution1:
% 3.90/4.35 X := X
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 subsumption: (2620) {G11,W3,D3,L1,V1,M1} R(2591,30) { alpha2( skol14( X ) )
% 3.90/4.35 }.
% 3.90/4.35 parent0: (23848) {G1,W3,D3,L1,V1,M1} { alpha2( skol14( X ) ) }.
% 3.90/4.35 substitution0:
% 3.90/4.35 X := X
% 3.90/4.35 end
% 3.90/4.35 permutation0:
% 3.90/4.35 0 ==> 0
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 resolution: (23849) {G1,W4,D4,L1,V1,M1} { epsilon_transitive( succ( skol14
% 3.90/4.35 ( X ) ) ) }.
% 3.90/4.35 parent0[0]: (32) {G0,W5,D3,L2,V1,M2} I { ! alpha2( X ), epsilon_transitive
% 3.90/4.35 ( succ( X ) ) }.
% 3.90/4.35 parent1[0]: (2620) {G11,W3,D3,L1,V1,M1} R(2591,30) { alpha2( skol14( X ) )
% 3.90/4.35 }.
% 3.90/4.35 substitution0:
% 3.90/4.35 X := skol14( X )
% 3.90/4.35 end
% 3.90/4.35 substitution1:
% 3.90/4.35 X := X
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 subsumption: (2627) {G12,W4,D4,L1,V1,M1} R(2620,32) { epsilon_transitive(
% 3.90/4.35 succ( skol14( X ) ) ) }.
% 3.90/4.35 parent0: (23849) {G1,W4,D4,L1,V1,M1} { epsilon_transitive( succ( skol14( X
% 3.90/4.35 ) ) ) }.
% 3.90/4.35 substitution0:
% 3.90/4.35 X := X
% 3.90/4.35 end
% 3.90/4.35 permutation0:
% 3.90/4.35 0 ==> 0
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 resolution: (23850) {G1,W5,D4,L1,V0,M1} { ! in( succ( skol14( skol15 ) ),
% 3.90/4.35 skol15 ) }.
% 3.90/4.35 parent0[0]: (2590) {G10,W4,D3,L1,V0,M1} R(2174,86);r(90) { ! alpha1( skol15
% 3.90/4.35 , skol14( skol15 ) ) }.
% 3.90/4.35 parent1[1]: (89) {G0,W7,D3,L2,V2,M2} I { ! in( succ( Y ), X ), alpha1( X, Y
% 3.90/4.35 ) }.
% 3.90/4.35 substitution0:
% 3.90/4.35 end
% 3.90/4.35 substitution1:
% 3.90/4.35 X := skol15
% 3.90/4.35 Y := skol14( skol15 )
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 subsumption: (2699) {G11,W5,D4,L1,V0,M1} R(2590,89) { ! in( succ( skol14(
% 3.90/4.35 skol15 ) ), skol15 ) }.
% 3.90/4.35 parent0: (23850) {G1,W5,D4,L1,V0,M1} { ! in( succ( skol14( skol15 ) ),
% 3.90/4.35 skol15 ) }.
% 3.90/4.35 substitution0:
% 3.90/4.35 end
% 3.90/4.35 permutation0:
% 3.90/4.35 0 ==> 0
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 resolution: (23851) {G1,W4,D3,L1,V0,M1} { in( skol14( skol15 ), skol15 )
% 3.90/4.35 }.
% 3.90/4.35 parent0[0]: (2590) {G10,W4,D3,L1,V0,M1} R(2174,86);r(90) { ! alpha1( skol15
% 3.90/4.35 , skol14( skol15 ) ) }.
% 3.90/4.35 parent1[1]: (88) {G0,W6,D2,L2,V2,M2} I { in( Y, X ), alpha1( X, Y ) }.
% 3.90/4.35 substitution0:
% 3.90/4.35 end
% 3.90/4.35 substitution1:
% 3.90/4.35 X := skol15
% 3.90/4.35 Y := skol14( skol15 )
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 subsumption: (2700) {G11,W4,D3,L1,V0,M1} R(2590,88) { in( skol14( skol15 )
% 3.90/4.35 , skol15 ) }.
% 3.90/4.35 parent0: (23851) {G1,W4,D3,L1,V0,M1} { in( skol14( skol15 ), skol15 ) }.
% 3.90/4.35 substitution0:
% 3.90/4.35 end
% 3.90/4.35 permutation0:
% 3.90/4.35 0 ==> 0
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 resolution: (23852) {G1,W10,D4,L3,V0,M3} { ! ordinal( skol14( skol15 ) ),
% 3.90/4.35 ! ordinal( skol15 ), ordinal_subset( succ( skol14( skol15 ) ), skol15 )
% 3.90/4.35 }.
% 3.90/4.35 parent0[2]: (80) {G0,W11,D3,L4,V2,M4} I { ! ordinal( X ), ! ordinal( Y ), !
% 3.90/4.35 in( X, Y ), ordinal_subset( succ( X ), Y ) }.
% 3.90/4.35 parent1[0]: (2700) {G11,W4,D3,L1,V0,M1} R(2590,88) { in( skol14( skol15 ),
% 3.90/4.35 skol15 ) }.
% 3.90/4.35 substitution0:
% 3.90/4.35 X := skol14( skol15 )
% 3.90/4.35 Y := skol15
% 3.90/4.35 end
% 3.90/4.35 substitution1:
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 resolution: (23853) {G2,W7,D4,L2,V0,M2} { ! ordinal( skol15 ),
% 3.90/4.35 ordinal_subset( succ( skol14( skol15 ) ), skol15 ) }.
% 3.90/4.35 parent0[0]: (23852) {G1,W10,D4,L3,V0,M3} { ! ordinal( skol14( skol15 ) ),
% 3.90/4.35 ! ordinal( skol15 ), ordinal_subset( succ( skol14( skol15 ) ), skol15 )
% 3.90/4.35 }.
% 3.90/4.35 parent1[0]: (2591) {G10,W3,D3,L1,V1,M1} R(2174,85);r(90) { ordinal( skol14
% 3.90/4.35 ( X ) ) }.
% 3.90/4.35 substitution0:
% 3.90/4.35 end
% 3.90/4.35 substitution1:
% 3.90/4.35 X := skol15
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 subsumption: (2707) {G12,W7,D4,L2,V0,M2} R(2700,80);r(2591) { ! ordinal(
% 3.90/4.35 skol15 ), ordinal_subset( succ( skol14( skol15 ) ), skol15 ) }.
% 3.90/4.35 parent0: (23853) {G2,W7,D4,L2,V0,M2} { ! ordinal( skol15 ), ordinal_subset
% 3.90/4.35 ( succ( skol14( skol15 ) ), skol15 ) }.
% 3.90/4.35 substitution0:
% 3.90/4.35 end
% 3.90/4.35 permutation0:
% 3.90/4.35 0 ==> 0
% 3.90/4.35 1 ==> 1
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 resolution: (23854) {G1,W11,D4,L3,V0,M3} { ! epsilon_transitive( succ(
% 3.90/4.35 skol14( skol15 ) ) ), ! ordinal( skol15 ), ! proper_subset( succ( skol14
% 3.90/4.35 ( skol15 ) ), skol15 ) }.
% 3.90/4.35 parent0[0]: (2699) {G11,W5,D4,L1,V0,M1} R(2590,89) { ! in( succ( skol14(
% 3.90/4.35 skol15 ) ), skol15 ) }.
% 3.90/4.35 parent1[3]: (78) {G0,W10,D2,L4,V2,M4} I { ! epsilon_transitive( X ), !
% 3.90/4.35 ordinal( Y ), ! proper_subset( X, Y ), in( X, Y ) }.
% 3.90/4.35 substitution0:
% 3.90/4.35 end
% 3.90/4.35 substitution1:
% 3.90/4.35 X := succ( skol14( skol15 ) )
% 3.90/4.35 Y := skol15
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 resolution: (23855) {G2,W7,D4,L2,V0,M2} { ! ordinal( skol15 ), !
% 3.90/4.35 proper_subset( succ( skol14( skol15 ) ), skol15 ) }.
% 3.90/4.35 parent0[0]: (23854) {G1,W11,D4,L3,V0,M3} { ! epsilon_transitive( succ(
% 3.90/4.35 skol14( skol15 ) ) ), ! ordinal( skol15 ), ! proper_subset( succ( skol14
% 3.90/4.35 ( skol15 ) ), skol15 ) }.
% 3.90/4.35 parent1[0]: (2627) {G12,W4,D4,L1,V1,M1} R(2620,32) { epsilon_transitive(
% 3.90/4.35 succ( skol14( X ) ) ) }.
% 3.90/4.35 substitution0:
% 3.90/4.35 end
% 3.90/4.35 substitution1:
% 3.90/4.35 X := skol15
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 subsumption: (4006) {G13,W7,D4,L2,V0,M2} R(2699,78);r(2627) { ! ordinal(
% 3.90/4.35 skol15 ), ! proper_subset( succ( skol14( skol15 ) ), skol15 ) }.
% 3.90/4.35 parent0: (23855) {G2,W7,D4,L2,V0,M2} { ! ordinal( skol15 ), !
% 3.90/4.35 proper_subset( succ( skol14( skol15 ) ), skol15 ) }.
% 3.90/4.35 substitution0:
% 3.90/4.35 end
% 3.90/4.35 permutation0:
% 3.90/4.35 0 ==> 0
% 3.90/4.35 1 ==> 1
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 eqswap: (23856) {G11,W6,D3,L2,V1,M2} { ! skol15 ==> succ( X ), ! ordinal(
% 3.90/4.35 X ) }.
% 3.90/4.35 parent0[1]: (2595) {G11,W6,D3,L2,V1,M2} R(2592,95) { ! ordinal( X ), ! succ
% 3.90/4.35 ( X ) ==> skol15 }.
% 3.90/4.35 substitution0:
% 3.90/4.35 X := X
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 resolution: (23857) {G11,W5,D4,L1,V1,M1} { ! skol15 ==> succ( skol14( X )
% 3.90/4.35 ) }.
% 3.90/4.35 parent0[1]: (23856) {G11,W6,D3,L2,V1,M2} { ! skol15 ==> succ( X ), !
% 3.90/4.35 ordinal( X ) }.
% 3.90/4.35 parent1[0]: (2591) {G10,W3,D3,L1,V1,M1} R(2174,85);r(90) { ordinal( skol14
% 3.90/4.35 ( X ) ) }.
% 3.90/4.35 substitution0:
% 3.90/4.35 X := skol14( X )
% 3.90/4.35 end
% 3.90/4.35 substitution1:
% 3.90/4.35 X := X
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 eqswap: (23858) {G11,W5,D4,L1,V1,M1} { ! succ( skol14( X ) ) ==> skol15
% 3.90/4.35 }.
% 3.90/4.35 parent0[0]: (23857) {G11,W5,D4,L1,V1,M1} { ! skol15 ==> succ( skol14( X )
% 3.90/4.35 ) }.
% 3.90/4.35 substitution0:
% 3.90/4.35 X := X
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 subsumption: (5947) {G12,W5,D4,L1,V1,M1} R(2595,2591) { ! succ( skol14( X )
% 3.90/4.35 ) ==> skol15 }.
% 3.90/4.35 parent0: (23858) {G11,W5,D4,L1,V1,M1} { ! succ( skol14( X ) ) ==> skol15
% 3.90/4.35 }.
% 3.90/4.35 substitution0:
% 3.90/4.35 X := X
% 3.90/4.35 end
% 3.90/4.35 permutation0:
% 3.90/4.35 0 ==> 0
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 resolution: (23859) {G1,W5,D4,L1,V0,M1} { ! proper_subset( succ( skol14(
% 3.90/4.35 skol15 ) ), skol15 ) }.
% 3.90/4.35 parent0[0]: (4006) {G13,W7,D4,L2,V0,M2} R(2699,78);r(2627) { ! ordinal(
% 3.90/4.35 skol15 ), ! proper_subset( succ( skol14( skol15 ) ), skol15 ) }.
% 3.90/4.35 parent1[0]: (90) {G0,W2,D2,L1,V0,M1} I { ordinal( skol15 ) }.
% 3.90/4.35 substitution0:
% 3.90/4.35 end
% 3.90/4.35 substitution1:
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 subsumption: (20074) {G14,W5,D4,L1,V0,M1} S(4006);r(90) { ! proper_subset(
% 3.90/4.35 succ( skol14( skol15 ) ), skol15 ) }.
% 3.90/4.35 parent0: (23859) {G1,W5,D4,L1,V0,M1} { ! proper_subset( succ( skol14(
% 3.90/4.35 skol15 ) ), skol15 ) }.
% 3.90/4.35 substitution0:
% 3.90/4.35 end
% 3.90/4.35 permutation0:
% 3.90/4.35 0 ==> 0
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 resolution: (23860) {G1,W5,D4,L1,V0,M1} { ordinal_subset( succ( skol14(
% 3.90/4.35 skol15 ) ), skol15 ) }.
% 3.90/4.35 parent0[0]: (2707) {G12,W7,D4,L2,V0,M2} R(2700,80);r(2591) { ! ordinal(
% 3.90/4.35 skol15 ), ordinal_subset( succ( skol14( skol15 ) ), skol15 ) }.
% 3.90/4.35 parent1[0]: (90) {G0,W2,D2,L1,V0,M1} I { ordinal( skol15 ) }.
% 3.90/4.35 substitution0:
% 3.90/4.35 end
% 3.90/4.35 substitution1:
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 subsumption: (20082) {G13,W5,D4,L1,V0,M1} S(2707);r(90) { ordinal_subset(
% 3.90/4.35 succ( skol14( skol15 ) ), skol15 ) }.
% 3.90/4.35 parent0: (23860) {G1,W5,D4,L1,V0,M1} { ordinal_subset( succ( skol14(
% 3.90/4.35 skol15 ) ), skol15 ) }.
% 3.90/4.35 substitution0:
% 3.90/4.35 end
% 3.90/4.35 permutation0:
% 3.90/4.35 0 ==> 0
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 resolution: (23861) {G2,W9,D4,L2,V0,M2} { ! ordinal( succ( skol14( skol15
% 3.90/4.35 ) ) ), subset( succ( skol14( skol15 ) ), skol15 ) }.
% 3.90/4.35 parent0[1]: (546) {G1,W8,D2,L3,V1,M3} R(71,90) { ! ordinal( X ), !
% 3.90/4.35 ordinal_subset( X, skol15 ), subset( X, skol15 ) }.
% 3.90/4.35 parent1[0]: (20082) {G13,W5,D4,L1,V0,M1} S(2707);r(90) { ordinal_subset(
% 3.90/4.35 succ( skol14( skol15 ) ), skol15 ) }.
% 3.90/4.35 substitution0:
% 3.90/4.35 X := succ( skol14( skol15 ) )
% 3.90/4.35 end
% 3.90/4.35 substitution1:
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 resolution: (23862) {G3,W5,D4,L1,V0,M1} { subset( succ( skol14( skol15 ) )
% 3.90/4.35 , skol15 ) }.
% 3.90/4.35 parent0[0]: (23861) {G2,W9,D4,L2,V0,M2} { ! ordinal( succ( skol14( skol15
% 3.90/4.35 ) ) ), subset( succ( skol14( skol15 ) ), skol15 ) }.
% 3.90/4.35 parent1[0]: (2619) {G11,W4,D4,L1,V1,M1} R(2591,31) { ordinal( succ( skol14
% 3.90/4.35 ( X ) ) ) }.
% 3.90/4.35 substitution0:
% 3.90/4.35 end
% 3.90/4.35 substitution1:
% 3.90/4.35 X := skol15
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 subsumption: (23211) {G14,W5,D4,L1,V0,M1} R(20082,546);r(2619) { subset(
% 3.90/4.35 succ( skol14( skol15 ) ), skol15 ) }.
% 3.90/4.35 parent0: (23862) {G3,W5,D4,L1,V0,M1} { subset( succ( skol14( skol15 ) ),
% 3.90/4.35 skol15 ) }.
% 3.90/4.35 substitution0:
% 3.90/4.35 end
% 3.90/4.35 permutation0:
% 3.90/4.35 0 ==> 0
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 eqswap: (23863) {G0,W9,D2,L3,V2,M3} { Y = X, ! subset( X, Y ),
% 3.90/4.35 proper_subset( X, Y ) }.
% 3.90/4.35 parent0[1]: (16) {G0,W9,D2,L3,V2,M3} I { ! subset( X, Y ), X = Y,
% 3.90/4.35 proper_subset( X, Y ) }.
% 3.90/4.35 substitution0:
% 3.90/4.35 X := X
% 3.90/4.35 Y := Y
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 resolution: (23864) {G1,W10,D4,L2,V0,M2} { skol15 = succ( skol14( skol15 )
% 3.90/4.35 ), proper_subset( succ( skol14( skol15 ) ), skol15 ) }.
% 3.90/4.35 parent0[1]: (23863) {G0,W9,D2,L3,V2,M3} { Y = X, ! subset( X, Y ),
% 3.90/4.35 proper_subset( X, Y ) }.
% 3.90/4.35 parent1[0]: (23211) {G14,W5,D4,L1,V0,M1} R(20082,546);r(2619) { subset(
% 3.90/4.35 succ( skol14( skol15 ) ), skol15 ) }.
% 3.90/4.35 substitution0:
% 3.90/4.35 X := succ( skol14( skol15 ) )
% 3.90/4.35 Y := skol15
% 3.90/4.35 end
% 3.90/4.35 substitution1:
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 resolution: (23865) {G2,W5,D4,L1,V0,M1} { skol15 = succ( skol14( skol15 )
% 3.90/4.35 ) }.
% 3.90/4.35 parent0[0]: (20074) {G14,W5,D4,L1,V0,M1} S(4006);r(90) { ! proper_subset(
% 3.90/4.35 succ( skol14( skol15 ) ), skol15 ) }.
% 3.90/4.35 parent1[1]: (23864) {G1,W10,D4,L2,V0,M2} { skol15 = succ( skol14( skol15 )
% 3.90/4.35 ), proper_subset( succ( skol14( skol15 ) ), skol15 ) }.
% 3.90/4.35 substitution0:
% 3.90/4.35 end
% 3.90/4.35 substitution1:
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 eqswap: (23866) {G2,W5,D4,L1,V0,M1} { succ( skol14( skol15 ) ) = skol15
% 3.90/4.35 }.
% 3.90/4.35 parent0[0]: (23865) {G2,W5,D4,L1,V0,M1} { skol15 = succ( skol14( skol15 )
% 3.90/4.35 ) }.
% 3.90/4.35 substitution0:
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 subsumption: (23229) {G15,W5,D4,L1,V0,M1} R(23211,16);r(20074) { succ(
% 3.90/4.35 skol14( skol15 ) ) ==> skol15 }.
% 3.90/4.35 parent0: (23866) {G2,W5,D4,L1,V0,M1} { succ( skol14( skol15 ) ) = skol15
% 3.90/4.35 }.
% 3.90/4.35 substitution0:
% 3.90/4.35 end
% 3.90/4.35 permutation0:
% 3.90/4.35 0 ==> 0
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 resolution: (23869) {G13,W0,D0,L0,V0,M0} { }.
% 3.90/4.35 parent0[0]: (5947) {G12,W5,D4,L1,V1,M1} R(2595,2591) { ! succ( skol14( X )
% 3.90/4.35 ) ==> skol15 }.
% 3.90/4.35 parent1[0]: (23229) {G15,W5,D4,L1,V0,M1} R(23211,16);r(20074) { succ(
% 3.90/4.35 skol14( skol15 ) ) ==> skol15 }.
% 3.90/4.35 substitution0:
% 3.90/4.35 X := skol15
% 3.90/4.35 end
% 3.90/4.35 substitution1:
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 subsumption: (23242) {G16,W0,D0,L0,V0,M0} S(23229);r(5947) { }.
% 3.90/4.35 parent0: (23869) {G13,W0,D0,L0,V0,M0} { }.
% 3.90/4.35 substitution0:
% 3.90/4.35 end
% 3.90/4.35 permutation0:
% 3.90/4.35 end
% 3.90/4.35
% 3.90/4.35 Proof check complete!
% 3.90/4.35
% 3.90/4.35 Memory use:
% 3.90/4.35
% 3.90/4.35 space for terms: 286215
% 3.90/4.35 space for clauses: 1081834
% 3.90/4.35
% 3.90/4.35
% 3.90/4.35 clauses generated: 76424
% 3.90/4.35 clauses kept: 23243
% 3.90/4.35 clauses selected: 1420
% 3.90/4.35 clauses deleted: 2010
% 3.90/4.35 clauses inuse deleted: 128
% 3.90/4.35
% 3.90/4.35 subsentry: 226819
% 3.90/4.35 literals s-matched: 131050
% 3.90/4.35 literals matched: 124379
% 3.90/4.35 full subsumption: 24452
% 3.90/4.35
% 3.90/4.35 checksum: 64859768
% 3.90/4.35
% 3.90/4.35
% 3.90/4.35 Bliksem ended
%------------------------------------------------------------------------------