TSTP Solution File: SEU238+3 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SEU238+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n007.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 07:11:47 EDT 2022
% Result : Theorem 4.15s 4.54s
% Output : Refutation 4.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : SEU238+3 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n007.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 : Sun Jun 19 09:16:44 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.73/1.11 *** allocated 10000 integers for termspace/termends
% 0.73/1.11 *** allocated 10000 integers for clauses
% 0.73/1.11 *** allocated 10000 integers for justifications
% 0.73/1.11 Bliksem 1.12
% 0.73/1.11
% 0.73/1.11
% 0.73/1.11 Automatic Strategy Selection
% 0.73/1.11
% 0.73/1.11
% 0.73/1.11 Clauses:
% 0.73/1.11
% 0.73/1.11 { ! in( X, Y ), ! in( Y, X ) }.
% 0.73/1.11 { ! proper_subset( X, Y ), ! proper_subset( Y, X ) }.
% 0.73/1.11 { ! empty( X ), function( X ) }.
% 0.73/1.11 { ! ordinal( X ), epsilon_transitive( X ) }.
% 0.73/1.11 { ! ordinal( X ), epsilon_connected( X ) }.
% 0.73/1.11 { ! empty( X ), relation( X ) }.
% 0.73/1.11 { ! relation( X ), ! empty( X ), ! function( X ), relation( X ) }.
% 0.73/1.11 { ! relation( X ), ! empty( X ), ! function( X ), function( X ) }.
% 0.73/1.11 { ! relation( X ), ! empty( X ), ! function( X ), one_to_one( X ) }.
% 0.73/1.11 { ! epsilon_transitive( X ), ! epsilon_connected( X ), ordinal( X ) }.
% 0.73/1.11 { ! empty( X ), epsilon_transitive( X ) }.
% 0.73/1.11 { ! empty( X ), epsilon_connected( X ) }.
% 0.73/1.11 { ! empty( X ), ordinal( X ) }.
% 0.73/1.11 { set_union2( X, Y ) = set_union2( Y, X ) }.
% 0.73/1.11 { ! ordinal( X ), ! ordinal( Y ), ordinal_subset( X, Y ), ordinal_subset( Y
% 0.73/1.11 , X ) }.
% 0.73/1.11 { succ( X ) = set_union2( X, singleton( X ) ) }.
% 0.73/1.11 { ! proper_subset( X, Y ), subset( X, Y ) }.
% 0.73/1.11 { ! proper_subset( X, Y ), ! X = Y }.
% 0.73/1.11 { ! subset( X, Y ), X = Y, proper_subset( X, Y ) }.
% 0.73/1.11 { element( skol1( X ), X ) }.
% 0.73/1.11 { empty( empty_set ) }.
% 0.73/1.11 { relation( empty_set ) }.
% 0.73/1.11 { relation_empty_yielding( empty_set ) }.
% 0.73/1.11 { ! empty( succ( X ) ) }.
% 0.73/1.11 { empty( empty_set ) }.
% 0.73/1.11 { relation( empty_set ) }.
% 0.73/1.11 { relation_empty_yielding( empty_set ) }.
% 0.73/1.11 { function( empty_set ) }.
% 0.73/1.11 { one_to_one( empty_set ) }.
% 0.73/1.11 { empty( empty_set ) }.
% 0.73/1.11 { epsilon_transitive( empty_set ) }.
% 0.73/1.11 { epsilon_connected( empty_set ) }.
% 0.73/1.11 { ordinal( empty_set ) }.
% 0.73/1.11 { ! relation( X ), ! relation( Y ), relation( set_union2( X, Y ) ) }.
% 0.73/1.11 { empty( X ), ! empty( set_union2( X, Y ) ) }.
% 0.73/1.11 { ! ordinal( X ), alpha2( X ) }.
% 0.73/1.11 { ! ordinal( X ), ordinal( succ( X ) ) }.
% 0.73/1.11 { ! alpha2( X ), ! empty( succ( X ) ) }.
% 0.73/1.11 { ! alpha2( X ), epsilon_transitive( succ( X ) ) }.
% 0.73/1.11 { ! alpha2( X ), epsilon_connected( succ( X ) ) }.
% 0.73/1.11 { empty( succ( X ) ), ! epsilon_transitive( succ( X ) ), !
% 0.73/1.11 epsilon_connected( succ( X ) ), alpha2( X ) }.
% 0.73/1.11 { empty( X ), ! empty( set_union2( Y, X ) ) }.
% 0.73/1.11 { empty( empty_set ) }.
% 0.73/1.11 { relation( empty_set ) }.
% 0.73/1.11 { set_union2( X, X ) = X }.
% 0.73/1.11 { ! proper_subset( X, X ) }.
% 0.73/1.11 { relation( skol2 ) }.
% 0.73/1.11 { function( skol2 ) }.
% 0.73/1.11 { epsilon_transitive( skol3 ) }.
% 0.73/1.11 { epsilon_connected( skol3 ) }.
% 0.73/1.11 { ordinal( skol3 ) }.
% 0.73/1.11 { empty( skol4 ) }.
% 0.73/1.11 { relation( skol4 ) }.
% 0.73/1.11 { empty( skol5 ) }.
% 0.73/1.11 { relation( skol6 ) }.
% 0.73/1.11 { empty( skol6 ) }.
% 0.73/1.11 { function( skol6 ) }.
% 0.73/1.11 { relation( skol7 ) }.
% 0.73/1.11 { function( skol7 ) }.
% 0.73/1.11 { one_to_one( skol7 ) }.
% 0.73/1.11 { empty( skol7 ) }.
% 0.73/1.11 { epsilon_transitive( skol7 ) }.
% 0.73/1.11 { epsilon_connected( skol7 ) }.
% 0.73/1.11 { ordinal( skol7 ) }.
% 0.73/1.11 { ! empty( skol8 ) }.
% 0.73/1.11 { relation( skol8 ) }.
% 0.73/1.11 { ! empty( skol9 ) }.
% 0.73/1.11 { relation( skol10 ) }.
% 0.73/1.11 { function( skol10 ) }.
% 0.73/1.11 { one_to_one( skol10 ) }.
% 0.73/1.11 { ! empty( skol11 ) }.
% 0.73/1.11 { epsilon_transitive( skol11 ) }.
% 0.73/1.11 { epsilon_connected( skol11 ) }.
% 0.73/1.11 { ordinal( skol11 ) }.
% 0.73/1.11 { relation( skol12 ) }.
% 0.73/1.11 { relation_empty_yielding( skol12 ) }.
% 0.73/1.11 { relation( skol13 ) }.
% 0.73/1.11 { relation_empty_yielding( skol13 ) }.
% 0.73/1.11 { function( skol13 ) }.
% 0.73/1.11 { relation( skol14 ) }.
% 0.73/1.11 { relation_non_empty( skol14 ) }.
% 0.73/1.11 { function( skol14 ) }.
% 0.73/1.11 { ! ordinal( X ), ! ordinal( Y ), ! ordinal_subset( X, Y ), subset( X, Y )
% 0.73/1.11 }.
% 0.73/1.11 { ! ordinal( X ), ! ordinal( Y ), ! subset( X, Y ), ordinal_subset( X, Y )
% 0.73/1.11 }.
% 0.73/1.11 { ! ordinal( X ), ! ordinal( Y ), ordinal_subset( X, X ) }.
% 0.73/1.11 { subset( X, X ) }.
% 0.73/1.11 { in( X, succ( X ) ) }.
% 0.73/1.11 { set_union2( X, empty_set ) = X }.
% 0.73/1.11 { ! in( X, Y ), element( X, Y ) }.
% 0.73/1.11 { ! epsilon_transitive( X ), ! ordinal( Y ), ! proper_subset( X, Y ), in( X
% 0.73/1.11 , Y ) }.
% 0.73/1.11 { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.73/1.11 { ! ordinal( X ), ! ordinal( Y ), ! in( X, Y ), ordinal_subset( succ( X ),
% 0.73/1.11 Y ) }.
% 0.73/1.11 { ! ordinal( X ), ! ordinal( Y ), ! ordinal_subset( succ( X ), Y ), in( X,
% 0.73/1.11 Y ) }.
% 0.73/1.11 { ! element( X, powerset( Y ) ), subset( X, Y ) }.
% 0.73/1.11 { ! subset( X, Y ), element( X, powerset( Y ) ) }.
% 0.73/1.11 { ! ordinal( X ), ! being_limit_ordinal( X ), ! ordinal( Y ), alpha1( X, Y
% 0.73/1.11 ) }.
% 0.73/1.11 { ! ordinal( X ), ordinal( skol15( Y ) ), being_limit_ordinal( X ) }.
% 0.73/1.11 { ! ordinal( X ), ! alpha1( X, skol15( X ) ), being_limit_ordinal( X ) }.
% 0.73/1.11 { ! alpha1( X, Y ), ! in( Y, X ), in( succ( Y ), X ) }.
% 4.15/4.54 { in( Y, X ), alpha1( X, Y ) }.
% 4.15/4.54 { ! in( succ( Y ), X ), alpha1( X, Y ) }.
% 4.15/4.54 { ordinal( skol16 ) }.
% 4.15/4.54 { alpha3( skol16 ), ordinal( skol18 ) }.
% 4.15/4.54 { alpha3( skol16 ), skol16 = succ( skol18 ) }.
% 4.15/4.54 { alpha3( skol16 ), being_limit_ordinal( skol16 ) }.
% 4.15/4.54 { ! alpha3( X ), ! being_limit_ordinal( X ) }.
% 4.15/4.54 { ! alpha3( X ), ! ordinal( Y ), ! X = succ( Y ) }.
% 4.15/4.54 { being_limit_ordinal( X ), ordinal( skol17( Y ) ), alpha3( X ) }.
% 4.15/4.54 { being_limit_ordinal( X ), X = succ( skol17( X ) ), alpha3( X ) }.
% 4.15/4.54 { ! in( X, Z ), ! element( Z, powerset( Y ) ), element( X, Y ) }.
% 4.15/4.54 { ! in( X, Y ), ! element( Y, powerset( Z ) ), ! empty( Z ) }.
% 4.15/4.54 { ! empty( X ), X = empty_set }.
% 4.15/4.54 { ! in( X, Y ), ! empty( Y ) }.
% 4.15/4.54 { ! empty( X ), X = Y, ! empty( Y ) }.
% 4.15/4.54
% 4.15/4.54 percentage equality = 0.058511, percentage horn = 0.895238
% 4.15/4.54 This is a problem with some equality
% 4.15/4.54
% 4.15/4.54
% 4.15/4.54
% 4.15/4.54 Options Used:
% 4.15/4.54
% 4.15/4.54 useres = 1
% 4.15/4.54 useparamod = 1
% 4.15/4.54 useeqrefl = 1
% 4.15/4.54 useeqfact = 1
% 4.15/4.54 usefactor = 1
% 4.15/4.54 usesimpsplitting = 0
% 4.15/4.54 usesimpdemod = 5
% 4.15/4.54 usesimpres = 3
% 4.15/4.54
% 4.15/4.54 resimpinuse = 1000
% 4.15/4.54 resimpclauses = 20000
% 4.15/4.54 substype = eqrewr
% 4.15/4.54 backwardsubs = 1
% 4.15/4.54 selectoldest = 5
% 4.15/4.54
% 4.15/4.54 litorderings [0] = split
% 4.15/4.54 litorderings [1] = extend the termordering, first sorting on arguments
% 4.15/4.54
% 4.15/4.54 termordering = kbo
% 4.15/4.54
% 4.15/4.54 litapriori = 0
% 4.15/4.54 termapriori = 1
% 4.15/4.54 litaposteriori = 0
% 4.15/4.54 termaposteriori = 0
% 4.15/4.54 demodaposteriori = 0
% 4.15/4.54 ordereqreflfact = 0
% 4.15/4.54
% 4.15/4.54 litselect = negord
% 4.15/4.54
% 4.15/4.54 maxweight = 15
% 4.15/4.54 maxdepth = 30000
% 4.15/4.54 maxlength = 115
% 4.15/4.54 maxnrvars = 195
% 4.15/4.54 excuselevel = 1
% 4.15/4.54 increasemaxweight = 1
% 4.15/4.54
% 4.15/4.54 maxselected = 10000000
% 4.15/4.54 maxnrclauses = 10000000
% 4.15/4.54
% 4.15/4.54 showgenerated = 0
% 4.15/4.54 showkept = 0
% 4.15/4.54 showselected = 0
% 4.15/4.54 showdeleted = 0
% 4.15/4.54 showresimp = 1
% 4.15/4.54 showstatus = 2000
% 4.15/4.54
% 4.15/4.54 prologoutput = 0
% 4.15/4.54 nrgoals = 5000000
% 4.15/4.54 totalproof = 1
% 4.15/4.54
% 4.15/4.54 Symbols occurring in the translation:
% 4.15/4.54
% 4.15/4.54 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 4.15/4.54 . [1, 2] (w:1, o:48, a:1, s:1, b:0),
% 4.15/4.54 ! [4, 1] (w:0, o:25, a:1, s:1, b:0),
% 4.15/4.54 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 4.15/4.54 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 4.15/4.54 in [37, 2] (w:1, o:72, a:1, s:1, b:0),
% 4.15/4.54 proper_subset [38, 2] (w:1, o:74, a:1, s:1, b:0),
% 4.15/4.54 empty [39, 1] (w:1, o:30, a:1, s:1, b:0),
% 4.15/4.54 function [40, 1] (w:1, o:33, a:1, s:1, b:0),
% 4.15/4.54 ordinal [41, 1] (w:1, o:34, a:1, s:1, b:0),
% 4.15/4.54 epsilon_transitive [42, 1] (w:1, o:31, a:1, s:1, b:0),
% 4.15/4.54 epsilon_connected [43, 1] (w:1, o:32, a:1, s:1, b:0),
% 4.15/4.54 relation [44, 1] (w:1, o:35, a:1, s:1, b:0),
% 4.15/4.54 one_to_one [45, 1] (w:1, o:36, a:1, s:1, b:0),
% 4.15/4.54 set_union2 [46, 2] (w:1, o:75, a:1, s:1, b:0),
% 4.15/4.54 ordinal_subset [47, 2] (w:1, o:73, a:1, s:1, b:0),
% 4.15/4.54 succ [48, 1] (w:1, o:39, a:1, s:1, b:0),
% 4.15/4.54 singleton [49, 1] (w:1, o:40, a:1, s:1, b:0),
% 4.15/4.54 subset [50, 2] (w:1, o:76, a:1, s:1, b:0),
% 4.15/4.54 element [51, 2] (w:1, o:77, a:1, s:1, b:0),
% 4.15/4.54 empty_set [52, 0] (w:1, o:8, a:1, s:1, b:0),
% 4.15/4.54 relation_empty_yielding [53, 1] (w:1, o:37, a:1, s:1, b:0),
% 4.15/4.54 relation_non_empty [54, 1] (w:1, o:38, a:1, s:1, b:0),
% 4.15/4.54 powerset [55, 1] (w:1, o:41, a:1, s:1, b:0),
% 4.15/4.54 being_limit_ordinal [56, 1] (w:1, o:44, a:1, s:1, b:0),
% 4.15/4.54 alpha1 [58, 2] (w:1, o:78, a:1, s:1, b:1),
% 4.15/4.54 alpha2 [59, 1] (w:1, o:42, a:1, s:1, b:1),
% 4.15/4.54 alpha3 [60, 1] (w:1, o:43, a:1, s:1, b:1),
% 4.15/4.54 skol1 [61, 1] (w:1, o:45, a:1, s:1, b:1),
% 4.15/4.54 skol2 [62, 0] (w:1, o:17, a:1, s:1, b:1),
% 4.15/4.54 skol3 [63, 0] (w:1, o:18, a:1, s:1, b:1),
% 4.15/4.54 skol4 [64, 0] (w:1, o:19, a:1, s:1, b:1),
% 4.15/4.54 skol5 [65, 0] (w:1, o:20, a:1, s:1, b:1),
% 4.15/4.54 skol6 [66, 0] (w:1, o:21, a:1, s:1, b:1),
% 4.15/4.54 skol7 [67, 0] (w:1, o:22, a:1, s:1, b:1),
% 4.15/4.54 skol8 [68, 0] (w:1, o:23, a:1, s:1, b:1),
% 4.15/4.54 skol9 [69, 0] (w:1, o:24, a:1, s:1, b:1),
% 4.15/4.54 skol10 [70, 0] (w:1, o:10, a:1, s:1, b:1),
% 4.15/4.54 skol11 [71, 0] (w:1, o:11, a:1, s:1, b:1),
% 4.15/4.54 skol12 [72, 0] (w:1, o:12, a:1, s:1, b:1),
% 4.15/4.54 skol13 [73, 0] (w:1, o:13, a:1, s:1, b:1),
% 4.15/4.54 skol14 [74, 0] (w:1, o:14, a:1, s:1, b:1),
% 4.15/4.54 skol15 [75, 1] (w:1, o:46, a:1, s:1, b:1),
% 4.15/4.54 skol16 [76, 0] (w:1, o:15, a:1, s:1, b:1),
% 4.15/4.54 skol17 [77, 1] (w:1, o:47, a:1, s:1, b:1),
% 4.15/4.54 skol18 [78, 0] (w:1, o:16, a:1, s:1, b:1).
% 4.15/4.54
% 4.15/4.54
% 4.15/4.54 Starting Search:
% 4.15/4.54
% 4.15/4.54 *** allocated 15000 integers for clauses
% 4.15/4.54 *** allocated 22500 integers for clauses
% 4.15/4.54 *** allocated 33750 integers for clauses
% 4.15/4.54 *** allocated 50625 integers for clauses
% 4.15/4.54 *** allocated 15000 integers for termspace/termends
% 4.15/4.54 *** allocated 75937 integers for clauses
% 4.15/4.54 Resimplifying inuse:
% 4.15/4.54 Done
% 4.15/4.54
% 4.15/4.54 *** allocated 22500 integers for termspace/termends
% 4.15/4.54 *** allocated 113905 integers for clauses
% 4.15/4.54
% 4.15/4.54 Intermediate Status:
% 4.15/4.54 Generated: 4053
% 4.15/4.54 Kept: 2001
% 4.15/4.54 Inuse: 298
% 4.15/4.54 Deleted: 25
% 4.15/4.54 Deletedinuse: 0
% 4.15/4.54
% 4.15/4.54 Resimplifying inuse:
% 4.15/4.54 Done
% 4.15/4.54
% 4.15/4.54 *** allocated 33750 integers for termspace/termends
% 4.15/4.54 *** allocated 170857 integers for clauses
% 4.15/4.54 Resimplifying inuse:
% 4.15/4.54 Done
% 4.15/4.54
% 4.15/4.54 *** allocated 50625 integers for termspace/termends
% 4.15/4.54 *** allocated 256285 integers for clauses
% 4.15/4.54
% 4.15/4.54 Intermediate Status:
% 4.15/4.54 Generated: 10226
% 4.15/4.54 Kept: 4002
% 4.15/4.54 Inuse: 481
% 4.15/4.54 Deleted: 191
% 4.15/4.54 Deletedinuse: 117
% 4.15/4.54
% 4.15/4.54 Resimplifying inuse:
% 4.15/4.54 Done
% 4.15/4.54
% 4.15/4.54 *** allocated 75937 integers for termspace/termends
% 4.15/4.54 Resimplifying inuse:
% 4.15/4.54 Done
% 4.15/4.54
% 4.15/4.54 *** allocated 384427 integers for clauses
% 4.15/4.54
% 4.15/4.54 Intermediate Status:
% 4.15/4.54 Generated: 18573
% 4.15/4.54 Kept: 6004
% 4.15/4.54 Inuse: 713
% 4.15/4.54 Deleted: 274
% 4.15/4.54 Deletedinuse: 122
% 4.15/4.54
% 4.15/4.54 Resimplifying inuse:
% 4.15/4.54 Done
% 4.15/4.54
% 4.15/4.54 *** allocated 113905 integers for termspace/termends
% 4.15/4.54 Resimplifying inuse:
% 4.15/4.54 Done
% 4.15/4.54
% 4.15/4.54
% 4.15/4.54 Intermediate Status:
% 4.15/4.54 Generated: 25086
% 4.15/4.54 Kept: 8011
% 4.15/4.54 Inuse: 869
% 4.15/4.54 Deleted: 327
% 4.15/4.54 Deletedinuse: 132
% 4.15/4.54
% 4.15/4.54 Resimplifying inuse:
% 4.15/4.54 Done
% 4.15/4.54
% 4.15/4.54 *** allocated 576640 integers for clauses
% 4.15/4.54 Resimplifying inuse:
% 4.15/4.54 Done
% 4.15/4.54
% 4.15/4.54 *** allocated 170857 integers for termspace/termends
% 4.15/4.54
% 4.15/4.54 Intermediate Status:
% 4.15/4.54 Generated: 29104
% 4.15/4.54 Kept: 10066
% 4.15/4.54 Inuse: 919
% 4.15/4.54 Deleted: 342
% 4.15/4.54 Deletedinuse: 132
% 4.15/4.54
% 4.15/4.54 Resimplifying inuse:
% 4.15/4.54 Done
% 4.15/4.54
% 4.15/4.54 Resimplifying inuse:
% 4.15/4.54 Done
% 4.15/4.54
% 4.15/4.54
% 4.15/4.54 Intermediate Status:
% 4.15/4.54 Generated: 35281
% 4.15/4.54 Kept: 12084
% 4.15/4.54 Inuse: 983
% 4.15/4.54 Deleted: 355
% 4.15/4.54 Deletedinuse: 132
% 4.15/4.54
% 4.15/4.54 Resimplifying inuse:
% 4.15/4.54 Done
% 4.15/4.54
% 4.15/4.54 *** allocated 864960 integers for clauses
% 4.15/4.54 Resimplifying inuse:
% 4.15/4.54 Done
% 4.15/4.54
% 4.15/4.54
% 4.15/4.54 Intermediate Status:
% 4.15/4.54 Generated: 42833
% 4.15/4.54 Kept: 14113
% 4.15/4.54 Inuse: 1097
% 4.15/4.54 Deleted: 367
% 4.15/4.54 Deletedinuse: 132
% 4.15/4.54
% 4.15/4.54 Resimplifying inuse:
% 4.15/4.54 Done
% 4.15/4.54
% 4.15/4.54 *** allocated 256285 integers for termspace/termends
% 4.15/4.54 Resimplifying inuse:
% 4.15/4.54 Done
% 4.15/4.54
% 4.15/4.54
% 4.15/4.54 Intermediate Status:
% 4.15/4.54 Generated: 48570
% 4.15/4.54 Kept: 16117
% 4.15/4.54 Inuse: 1160
% 4.15/4.54 Deleted: 371
% 4.15/4.54 Deletedinuse: 132
% 4.15/4.54
% 4.15/4.54 Resimplifying inuse:
% 4.15/4.54 Done
% 4.15/4.54
% 4.15/4.54 Resimplifying inuse:
% 4.15/4.54 Done
% 4.15/4.54
% 4.15/4.54 *** allocated 1297440 integers for clauses
% 4.15/4.54
% 4.15/4.54 Intermediate Status:
% 4.15/4.54 Generated: 54513
% 4.15/4.54 Kept: 18138
% 4.15/4.54 Inuse: 1225
% 4.15/4.54 Deleted: 375
% 4.15/4.54 Deletedinuse: 132
% 4.15/4.54
% 4.15/4.54 Resimplifying inuse:
% 4.15/4.54 Done
% 4.15/4.54
% 4.15/4.54 Resimplifying inuse:
% 4.15/4.54 Done
% 4.15/4.54
% 4.15/4.54 Resimplifying clauses:
% 4.15/4.54 Done
% 4.15/4.54
% 4.15/4.54
% 4.15/4.54 Intermediate Status:
% 4.15/4.54 Generated: 60376
% 4.15/4.54 Kept: 20241
% 4.15/4.54 Inuse: 1281
% 4.15/4.54 Deleted: 2015
% 4.15/4.54 Deletedinuse: 132
% 4.15/4.54
% 4.15/4.54 Resimplifying inuse:
% 4.15/4.54 Done
% 4.15/4.54
% 4.15/4.54 *** allocated 384427 integers for termspace/termends
% 4.15/4.54
% 4.15/4.54 Intermediate Status:
% 4.15/4.54 Generated: 70216
% 4.15/4.54 Kept: 22580
% 4.15/4.54 Inuse: 1326
% 4.15/4.54 Deleted: 2015
% 4.15/4.54 Deletedinuse: 132
% 4.15/4.54
% 4.15/4.54 Resimplifying inuse:
% 4.15/4.54 Done
% 4.15/4.54
% 4.15/4.54 Resimplifying inuse:
% 4.15/4.54 Done
% 4.15/4.54
% 4.15/4.54
% 4.15/4.54 Bliksems!, er is een bewijs:
% 4.15/4.54 % SZS status Theorem
% 4.15/4.54 % SZS output start Refutation
% 4.15/4.54
% 4.15/4.54 (0) {G0,W6,D2,L2,V2,M2} I { ! in( X, Y ), ! in( Y, X ) }.
% 4.15/4.54 (16) {G0,W9,D2,L3,V2,M3} I { ! subset( X, Y ), X = Y, proper_subset( X, Y )
% 4.15/4.54 }.
% 4.15/4.54 (18) {G0,W2,D2,L1,V0,M1} I { empty( empty_set ) }.
% 4.15/4.54 (21) {G0,W3,D3,L1,V1,M1} I { ! empty( succ( X ) ) }.
% 4.15/4.54 (26) {G0,W2,D2,L1,V0,M1} I { ordinal( empty_set ) }.
% 4.15/4.54 (29) {G0,W4,D2,L2,V1,M2} I { ! ordinal( X ), alpha2( X ) }.
% 4.15/4.54 (30) {G0,W5,D3,L2,V1,M2} I { ! ordinal( X ), ordinal( succ( X ) ) }.
% 4.15/4.54 (31) {G0,W5,D3,L2,V1,M2} I { ! alpha2( X ), epsilon_transitive( succ( X ) )
% 4.15/4.54 }.
% 4.15/4.54 (73) {G0,W10,D2,L4,V2,M4} I { ! ordinal( X ), ! ordinal( Y ), !
% 4.15/4.54 ordinal_subset( X, Y ), subset( X, Y ) }.
% 4.15/4.54 (77) {G0,W4,D3,L1,V1,M1} I { in( X, succ( X ) ) }.
% 4.15/4.54 (79) {G0,W6,D2,L2,V2,M2} I { ! in( X, Y ), element( X, Y ) }.
% 4.15/4.54 (80) {G0,W10,D2,L4,V2,M4} I { ! epsilon_transitive( X ), ! ordinal( Y ), !
% 4.15/4.54 proper_subset( X, Y ), in( X, Y ) }.
% 4.15/4.54 (81) {G0,W8,D2,L3,V2,M3} I { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 4.15/4.54 (82) {G0,W11,D3,L4,V2,M4} I { ! ordinal( X ), ! ordinal( Y ), ! in( X, Y )
% 4.15/4.54 , ordinal_subset( succ( X ), Y ) }.
% 4.15/4.54 (86) {G0,W9,D2,L4,V2,M4} I { ! ordinal( X ), ! being_limit_ordinal( X ), !
% 4.15/4.54 ordinal( Y ), alpha1( X, Y ) }.
% 4.15/4.54 (87) {G0,W7,D3,L3,V2,M3} I { ! ordinal( X ), ordinal( skol15( Y ) ),
% 4.15/4.54 being_limit_ordinal( X ) }.
% 4.15/4.54 (88) {G0,W8,D3,L3,V1,M3} I { ! ordinal( X ), ! alpha1( X, skol15( X ) ),
% 4.15/4.54 being_limit_ordinal( X ) }.
% 4.15/4.54 (89) {G0,W10,D3,L3,V2,M3} I { ! alpha1( X, Y ), ! in( Y, X ), in( succ( Y )
% 4.15/4.54 , X ) }.
% 4.15/4.54 (90) {G0,W6,D2,L2,V2,M2} I { in( Y, X ), alpha1( X, Y ) }.
% 4.15/4.54 (91) {G0,W7,D3,L2,V2,M2} I { ! in( succ( Y ), X ), alpha1( X, Y ) }.
% 4.15/4.54 (92) {G0,W2,D2,L1,V0,M1} I { ordinal( skol16 ) }.
% 4.15/4.54 (93) {G0,W4,D2,L2,V0,M2} I { alpha3( skol16 ), ordinal( skol18 ) }.
% 4.15/4.54 (94) {G0,W6,D3,L2,V0,M2} I { alpha3( skol16 ), succ( skol18 ) ==> skol16
% 4.15/4.54 }.
% 4.15/4.54 (95) {G0,W4,D2,L2,V0,M2} I { alpha3( skol16 ), being_limit_ordinal( skol16
% 4.15/4.54 ) }.
% 4.15/4.54 (96) {G0,W4,D2,L2,V1,M2} I { ! alpha3( X ), ! being_limit_ordinal( X ) }.
% 4.15/4.54 (97) {G0,W8,D3,L3,V2,M3} I { ! alpha3( X ), ! ordinal( Y ), ! X = succ( Y )
% 4.15/4.54 }.
% 4.15/4.54 (102) {G0,W5,D2,L2,V1,M2} I { ! empty( X ), X = empty_set }.
% 4.15/4.54 (103) {G0,W5,D2,L2,V2,M2} I { ! in( X, Y ), ! empty( Y ) }.
% 4.15/4.54 (104) {G0,W7,D2,L3,V2,M3} I { ! empty( X ), X = Y, ! empty( Y ) }.
% 4.15/4.54 (105) {G1,W3,D2,L1,V1,M1} F(0) { ! in( X, X ) }.
% 4.15/4.54 (552) {G1,W8,D2,L3,V1,M3} R(73,92) { ! ordinal( X ), ! ordinal_subset( X,
% 4.15/4.54 skol16 ), subset( X, skol16 ) }.
% 4.15/4.54 (656) {G1,W4,D2,L2,V0,M2} R(93,96) { ordinal( skol18 ), !
% 4.15/4.54 being_limit_ordinal( skol16 ) }.
% 4.15/4.54 (694) {G1,W4,D3,L1,V1,M1} R(79,77) { element( X, succ( X ) ) }.
% 4.15/4.54 (1077) {G2,W9,D2,L4,V1,M4} R(86,656) { ! ordinal( X ), !
% 4.15/4.54 being_limit_ordinal( X ), alpha1( X, skol18 ), ! being_limit_ordinal(
% 4.15/4.54 skol16 ) }.
% 4.15/4.54 (1121) {G3,W5,D2,L2,V0,M2} F(1077);r(92) { ! being_limit_ordinal( skol16 )
% 4.15/4.54 , alpha1( skol16, skol18 ) }.
% 4.15/4.54 (1369) {G1,W3,D2,L1,V1,M1} R(103,18) { ! in( X, empty_set ) }.
% 4.15/4.54 (1381) {G2,W3,D2,L1,V1,M1} R(1369,90) { alpha1( empty_set, X ) }.
% 4.15/4.54 (1386) {G3,W2,D2,L1,V0,M1} R(1381,88);r(26) { being_limit_ordinal(
% 4.15/4.54 empty_set ) }.
% 4.15/4.54 (1407) {G1,W6,D3,L2,V0,M2} R(94,96) { succ( skol18 ) ==> skol16, !
% 4.15/4.54 being_limit_ordinal( skol16 ) }.
% 4.15/4.54 (1411) {G2,W5,D2,L2,V0,M2} P(94,694) { element( skol18, skol16 ), alpha3(
% 4.15/4.54 skol16 ) }.
% 4.15/4.54 (1413) {G1,W4,D2,L2,V0,M2} P(94,21) { ! empty( skol16 ), alpha3( skol16 )
% 4.15/4.54 }.
% 4.15/4.54 (1609) {G2,W4,D2,L2,V0,M2} R(1413,96) { ! empty( skol16 ), !
% 4.15/4.54 being_limit_ordinal( skol16 ) }.
% 4.15/4.54 (1633) {G4,W4,D2,L2,V1,M2} P(102,1386) { being_limit_ordinal( X ), ! empty
% 4.15/4.54 ( X ) }.
% 4.15/4.54 (1656) {G5,W4,D2,L2,V1,M2} P(104,1609);f;r(1633) { ! empty( X ), ! empty(
% 4.15/4.54 skol16 ) }.
% 4.15/4.54 (1667) {G6,W2,D2,L1,V0,M1} F(1656) { ! empty( skol16 ) }.
% 4.15/4.54 (2634) {G3,W5,D2,L2,V0,M2} R(1411,96) { element( skol18, skol16 ), !
% 4.15/4.54 being_limit_ordinal( skol16 ) }.
% 4.15/4.54 (2643) {G7,W5,D2,L2,V0,M2} R(2634,81);r(1667) { ! being_limit_ordinal(
% 4.15/4.54 skol16 ), in( skol18, skol16 ) }.
% 4.15/4.54 (2652) {G8,W5,D2,L2,V0,M2} R(2643,89);d(1407);r(1121) { !
% 4.15/4.54 being_limit_ordinal( skol16 ), in( skol16, skol16 ) }.
% 4.15/4.54 (2661) {G9,W2,D2,L1,V0,M1} S(2652);r(105) { ! being_limit_ordinal( skol16 )
% 4.15/4.54 }.
% 4.15/4.54 (2670) {G10,W4,D3,L1,V0,M1} R(2661,88);r(92) { ! alpha1( skol16, skol15(
% 4.15/4.54 skol16 ) ) }.
% 4.15/4.54 (2671) {G10,W3,D3,L1,V1,M1} R(2661,87);r(92) { ordinal( skol15( X ) ) }.
% 4.15/4.54 (2672) {G10,W2,D2,L1,V0,M1} R(2661,95) { alpha3( skol16 ) }.
% 4.15/4.54 (2675) {G11,W6,D3,L2,V1,M2} R(2672,97) { ! ordinal( X ), ! succ( X ) ==>
% 4.15/4.54 skol16 }.
% 4.15/4.54 (2699) {G11,W4,D4,L1,V1,M1} R(2671,30) { ordinal( succ( skol15( X ) ) ) }.
% 4.15/4.54 (2700) {G11,W3,D3,L1,V1,M1} R(2671,29) { alpha2( skol15( X ) ) }.
% 4.15/4.54 (2707) {G12,W4,D4,L1,V1,M1} R(2700,31) { epsilon_transitive( succ( skol15(
% 4.15/4.54 X ) ) ) }.
% 4.15/4.54 (2719) {G11,W5,D4,L1,V0,M1} R(2670,91) { ! in( succ( skol15( skol16 ) ),
% 4.15/4.54 skol16 ) }.
% 4.15/4.54 (2720) {G11,W4,D3,L1,V0,M1} R(2670,90) { in( skol15( skol16 ), skol16 ) }.
% 4.15/4.54 (2723) {G12,W7,D4,L2,V0,M2} R(2720,82);r(2671) { ! ordinal( skol16 ),
% 4.15/4.54 ordinal_subset( succ( skol15( skol16 ) ), skol16 ) }.
% 4.15/4.54 (3972) {G13,W7,D4,L2,V0,M2} R(2719,80);r(2707) { ! ordinal( skol16 ), !
% 4.15/4.54 proper_subset( succ( skol15( skol16 ) ), skol16 ) }.
% 4.15/4.54 (5916) {G12,W5,D4,L1,V1,M1} R(2675,2671) { ! succ( skol15( X ) ) ==> skol16
% 4.15/4.54 }.
% 4.15/4.54 (20054) {G14,W5,D4,L1,V0,M1} S(3972);r(92) { ! proper_subset( succ( skol15
% 4.15/4.54 ( skol16 ) ), skol16 ) }.
% 4.15/4.54 (20062) {G13,W5,D4,L1,V0,M1} S(2723);r(92) { ordinal_subset( succ( skol15(
% 4.15/4.54 skol16 ) ), skol16 ) }.
% 4.15/4.54 (23986) {G14,W5,D4,L1,V0,M1} R(552,20062);r(2699) { subset( succ( skol15(
% 4.15/4.54 skol16 ) ), skol16 ) }.
% 4.15/4.54 (24033) {G15,W5,D4,L1,V0,M1} R(23986,16);r(20054) { succ( skol15( skol16 )
% 4.15/4.54 ) ==> skol16 }.
% 4.15/4.54 (24046) {G16,W0,D0,L0,V0,M0} S(24033);r(5916) { }.
% 4.15/4.54
% 4.15/4.54
% 4.15/4.54 % SZS output end Refutation
% 4.15/4.54 found a proof!
% 4.15/4.54
% 4.15/4.54
% 4.15/4.54 Unprocessed initial clauses:
% 4.15/4.54
% 4.15/4.54 (24048) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), ! in( Y, X ) }.
% 4.15/4.54 (24049) {G0,W6,D2,L2,V2,M2} { ! proper_subset( X, Y ), ! proper_subset( Y
% 4.15/4.54 , X ) }.
% 4.15/4.54 (24050) {G0,W4,D2,L2,V1,M2} { ! empty( X ), function( X ) }.
% 4.15/4.54 (24051) {G0,W4,D2,L2,V1,M2} { ! ordinal( X ), epsilon_transitive( X ) }.
% 4.15/4.54 (24052) {G0,W4,D2,L2,V1,M2} { ! ordinal( X ), epsilon_connected( X ) }.
% 4.15/4.54 (24053) {G0,W4,D2,L2,V1,M2} { ! empty( X ), relation( X ) }.
% 4.15/4.54 (24054) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 4.15/4.54 ), relation( X ) }.
% 4.15/4.54 (24055) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 4.15/4.54 ), function( X ) }.
% 4.15/4.54 (24056) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 4.15/4.54 ), one_to_one( X ) }.
% 4.15/4.54 (24057) {G0,W6,D2,L3,V1,M3} { ! epsilon_transitive( X ), !
% 4.15/4.54 epsilon_connected( X ), ordinal( X ) }.
% 4.15/4.54 (24058) {G0,W4,D2,L2,V1,M2} { ! empty( X ), epsilon_transitive( X ) }.
% 4.15/4.54 (24059) {G0,W4,D2,L2,V1,M2} { ! empty( X ), epsilon_connected( X ) }.
% 4.15/4.54 (24060) {G0,W4,D2,L2,V1,M2} { ! empty( X ), ordinal( X ) }.
% 4.15/4.54 (24061) {G0,W7,D3,L1,V2,M1} { set_union2( X, Y ) = set_union2( Y, X ) }.
% 4.15/4.54 (24062) {G0,W10,D2,L4,V2,M4} { ! ordinal( X ), ! ordinal( Y ),
% 4.15/4.54 ordinal_subset( X, Y ), ordinal_subset( Y, X ) }.
% 4.15/4.54 (24063) {G0,W7,D4,L1,V1,M1} { succ( X ) = set_union2( X, singleton( X ) )
% 4.15/4.54 }.
% 4.15/4.54 (24064) {G0,W6,D2,L2,V2,M2} { ! proper_subset( X, Y ), subset( X, Y ) }.
% 4.15/4.54 (24065) {G0,W6,D2,L2,V2,M2} { ! proper_subset( X, Y ), ! X = Y }.
% 4.15/4.54 (24066) {G0,W9,D2,L3,V2,M3} { ! subset( X, Y ), X = Y, proper_subset( X, Y
% 4.15/4.54 ) }.
% 4.15/4.54 (24067) {G0,W4,D3,L1,V1,M1} { element( skol1( X ), X ) }.
% 4.15/4.54 (24068) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 4.15/4.54 (24069) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 4.15/4.54 (24070) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( empty_set ) }.
% 4.15/4.54 (24071) {G0,W3,D3,L1,V1,M1} { ! empty( succ( X ) ) }.
% 4.15/4.54 (24072) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 4.15/4.54 (24073) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 4.15/4.54 (24074) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( empty_set ) }.
% 4.15/4.54 (24075) {G0,W2,D2,L1,V0,M1} { function( empty_set ) }.
% 4.15/4.54 (24076) {G0,W2,D2,L1,V0,M1} { one_to_one( empty_set ) }.
% 4.15/4.54 (24077) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 4.15/4.54 (24078) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( empty_set ) }.
% 4.15/4.54 (24079) {G0,W2,D2,L1,V0,M1} { epsilon_connected( empty_set ) }.
% 4.15/4.54 (24080) {G0,W2,D2,L1,V0,M1} { ordinal( empty_set ) }.
% 4.15/4.54 (24081) {G0,W8,D3,L3,V2,M3} { ! relation( X ), ! relation( Y ), relation(
% 4.15/4.54 set_union2( X, Y ) ) }.
% 4.15/4.54 (24082) {G0,W6,D3,L2,V2,M2} { empty( X ), ! empty( set_union2( X, Y ) )
% 4.15/4.54 }.
% 4.15/4.54 (24083) {G0,W4,D2,L2,V1,M2} { ! ordinal( X ), alpha2( X ) }.
% 4.15/4.54 (24084) {G0,W5,D3,L2,V1,M2} { ! ordinal( X ), ordinal( succ( X ) ) }.
% 4.15/4.54 (24085) {G0,W5,D3,L2,V1,M2} { ! alpha2( X ), ! empty( succ( X ) ) }.
% 4.15/4.54 (24086) {G0,W5,D3,L2,V1,M2} { ! alpha2( X ), epsilon_transitive( succ( X )
% 4.15/4.54 ) }.
% 4.15/4.54 (24087) {G0,W5,D3,L2,V1,M2} { ! alpha2( X ), epsilon_connected( succ( X )
% 4.15/4.54 ) }.
% 4.15/4.54 (24088) {G0,W11,D3,L4,V1,M4} { empty( succ( X ) ), ! epsilon_transitive(
% 4.15/4.54 succ( X ) ), ! epsilon_connected( succ( X ) ), alpha2( X ) }.
% 4.15/4.54 (24089) {G0,W6,D3,L2,V2,M2} { empty( X ), ! empty( set_union2( Y, X ) )
% 4.15/4.54 }.
% 4.15/4.54 (24090) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 4.15/4.54 (24091) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 4.15/4.54 (24092) {G0,W5,D3,L1,V1,M1} { set_union2( X, X ) = X }.
% 4.15/4.54 (24093) {G0,W3,D2,L1,V1,M1} { ! proper_subset( X, X ) }.
% 4.15/4.54 (24094) {G0,W2,D2,L1,V0,M1} { relation( skol2 ) }.
% 4.15/4.54 (24095) {G0,W2,D2,L1,V0,M1} { function( skol2 ) }.
% 4.15/4.54 (24096) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol3 ) }.
% 4.15/4.54 (24097) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol3 ) }.
% 4.15/4.54 (24098) {G0,W2,D2,L1,V0,M1} { ordinal( skol3 ) }.
% 4.15/4.54 (24099) {G0,W2,D2,L1,V0,M1} { empty( skol4 ) }.
% 4.15/4.54 (24100) {G0,W2,D2,L1,V0,M1} { relation( skol4 ) }.
% 4.15/4.54 (24101) {G0,W2,D2,L1,V0,M1} { empty( skol5 ) }.
% 4.15/4.54 (24102) {G0,W2,D2,L1,V0,M1} { relation( skol6 ) }.
% 4.15/4.54 (24103) {G0,W2,D2,L1,V0,M1} { empty( skol6 ) }.
% 4.15/4.54 (24104) {G0,W2,D2,L1,V0,M1} { function( skol6 ) }.
% 4.15/4.54 (24105) {G0,W2,D2,L1,V0,M1} { relation( skol7 ) }.
% 4.15/4.54 (24106) {G0,W2,D2,L1,V0,M1} { function( skol7 ) }.
% 4.15/4.54 (24107) {G0,W2,D2,L1,V0,M1} { one_to_one( skol7 ) }.
% 4.15/4.54 (24108) {G0,W2,D2,L1,V0,M1} { empty( skol7 ) }.
% 4.15/4.54 (24109) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol7 ) }.
% 4.15/4.54 (24110) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol7 ) }.
% 4.15/4.54 (24111) {G0,W2,D2,L1,V0,M1} { ordinal( skol7 ) }.
% 4.15/4.54 (24112) {G0,W2,D2,L1,V0,M1} { ! empty( skol8 ) }.
% 4.15/4.54 (24113) {G0,W2,D2,L1,V0,M1} { relation( skol8 ) }.
% 4.15/4.54 (24114) {G0,W2,D2,L1,V0,M1} { ! empty( skol9 ) }.
% 4.15/4.54 (24115) {G0,W2,D2,L1,V0,M1} { relation( skol10 ) }.
% 4.15/4.54 (24116) {G0,W2,D2,L1,V0,M1} { function( skol10 ) }.
% 4.15/4.54 (24117) {G0,W2,D2,L1,V0,M1} { one_to_one( skol10 ) }.
% 4.15/4.54 (24118) {G0,W2,D2,L1,V0,M1} { ! empty( skol11 ) }.
% 4.15/4.54 (24119) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol11 ) }.
% 4.15/4.54 (24120) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol11 ) }.
% 4.15/4.54 (24121) {G0,W2,D2,L1,V0,M1} { ordinal( skol11 ) }.
% 4.15/4.54 (24122) {G0,W2,D2,L1,V0,M1} { relation( skol12 ) }.
% 4.15/4.54 (24123) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( skol12 ) }.
% 4.15/4.54 (24124) {G0,W2,D2,L1,V0,M1} { relation( skol13 ) }.
% 4.15/4.54 (24125) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( skol13 ) }.
% 4.15/4.54 (24126) {G0,W2,D2,L1,V0,M1} { function( skol13 ) }.
% 4.15/4.54 (24127) {G0,W2,D2,L1,V0,M1} { relation( skol14 ) }.
% 4.15/4.54 (24128) {G0,W2,D2,L1,V0,M1} { relation_non_empty( skol14 ) }.
% 4.15/4.54 (24129) {G0,W2,D2,L1,V0,M1} { function( skol14 ) }.
% 4.15/4.54 (24130) {G0,W10,D2,L4,V2,M4} { ! ordinal( X ), ! ordinal( Y ), !
% 4.15/4.54 ordinal_subset( X, Y ), subset( X, Y ) }.
% 4.15/4.54 (24131) {G0,W10,D2,L4,V2,M4} { ! ordinal( X ), ! ordinal( Y ), ! subset( X
% 4.15/4.54 , Y ), ordinal_subset( X, Y ) }.
% 4.15/4.54 (24132) {G0,W7,D2,L3,V2,M3} { ! ordinal( X ), ! ordinal( Y ),
% 4.15/4.54 ordinal_subset( X, X ) }.
% 4.15/4.54 (24133) {G0,W3,D2,L1,V1,M1} { subset( X, X ) }.
% 4.15/4.54 (24134) {G0,W4,D3,L1,V1,M1} { in( X, succ( X ) ) }.
% 4.15/4.54 (24135) {G0,W5,D3,L1,V1,M1} { set_union2( X, empty_set ) = X }.
% 4.15/4.54 (24136) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), element( X, Y ) }.
% 4.15/4.54 (24137) {G0,W10,D2,L4,V2,M4} { ! epsilon_transitive( X ), ! ordinal( Y ),
% 4.15/4.54 ! proper_subset( X, Y ), in( X, Y ) }.
% 4.15/4.54 (24138) {G0,W8,D2,L3,V2,M3} { ! element( X, Y ), empty( Y ), in( X, Y )
% 4.15/4.54 }.
% 4.15/4.54 (24139) {G0,W11,D3,L4,V2,M4} { ! ordinal( X ), ! ordinal( Y ), ! in( X, Y
% 4.15/4.54 ), ordinal_subset( succ( X ), Y ) }.
% 4.15/4.54 (24140) {G0,W11,D3,L4,V2,M4} { ! ordinal( X ), ! ordinal( Y ), !
% 4.15/4.54 ordinal_subset( succ( X ), Y ), in( X, Y ) }.
% 4.15/4.54 (24141) {G0,W7,D3,L2,V2,M2} { ! element( X, powerset( Y ) ), subset( X, Y
% 4.15/4.54 ) }.
% 4.15/4.54 (24142) {G0,W7,D3,L2,V2,M2} { ! subset( X, Y ), element( X, powerset( Y )
% 4.15/4.54 ) }.
% 4.15/4.54 (24143) {G0,W9,D2,L4,V2,M4} { ! ordinal( X ), ! being_limit_ordinal( X ),
% 4.15/4.54 ! ordinal( Y ), alpha1( X, Y ) }.
% 4.15/4.54 (24144) {G0,W7,D3,L3,V2,M3} { ! ordinal( X ), ordinal( skol15( Y ) ),
% 4.15/4.54 being_limit_ordinal( X ) }.
% 4.15/4.54 (24145) {G0,W8,D3,L3,V1,M3} { ! ordinal( X ), ! alpha1( X, skol15( X ) ),
% 4.15/4.54 being_limit_ordinal( X ) }.
% 4.15/4.54 (24146) {G0,W10,D3,L3,V2,M3} { ! alpha1( X, Y ), ! in( Y, X ), in( succ( Y
% 4.15/4.54 ), X ) }.
% 4.15/4.54 (24147) {G0,W6,D2,L2,V2,M2} { in( Y, X ), alpha1( X, Y ) }.
% 4.15/4.54 (24148) {G0,W7,D3,L2,V2,M2} { ! in( succ( Y ), X ), alpha1( X, Y ) }.
% 4.15/4.54 (24149) {G0,W2,D2,L1,V0,M1} { ordinal( skol16 ) }.
% 4.15/4.54 (24150) {G0,W4,D2,L2,V0,M2} { alpha3( skol16 ), ordinal( skol18 ) }.
% 4.15/4.54 (24151) {G0,W6,D3,L2,V0,M2} { alpha3( skol16 ), skol16 = succ( skol18 )
% 4.15/4.54 }.
% 4.15/4.54 (24152) {G0,W4,D2,L2,V0,M2} { alpha3( skol16 ), being_limit_ordinal(
% 4.15/4.54 skol16 ) }.
% 4.15/4.54 (24153) {G0,W4,D2,L2,V1,M2} { ! alpha3( X ), ! being_limit_ordinal( X )
% 4.15/4.54 }.
% 4.15/4.54 (24154) {G0,W8,D3,L3,V2,M3} { ! alpha3( X ), ! ordinal( Y ), ! X = succ( Y
% 4.15/4.54 ) }.
% 4.15/4.54 (24155) {G0,W7,D3,L3,V2,M3} { being_limit_ordinal( X ), ordinal( skol17( Y
% 4.15/4.54 ) ), alpha3( X ) }.
% 4.15/4.54 (24156) {G0,W9,D4,L3,V1,M3} { being_limit_ordinal( X ), X = succ( skol17(
% 4.15/4.54 X ) ), alpha3( X ) }.
% 4.15/4.54 (24157) {G0,W10,D3,L3,V3,M3} { ! in( X, Z ), ! element( Z, powerset( Y ) )
% 4.15/4.54 , element( X, Y ) }.
% 4.15/4.54 (24158) {G0,W9,D3,L3,V3,M3} { ! in( X, Y ), ! element( Y, powerset( Z ) )
% 4.15/4.54 , ! empty( Z ) }.
% 4.15/4.54 (24159) {G0,W5,D2,L2,V1,M2} { ! empty( X ), X = empty_set }.
% 4.15/4.54 (24160) {G0,W5,D2,L2,V2,M2} { ! in( X, Y ), ! empty( Y ) }.
% 4.15/4.54 (24161) {G0,W7,D2,L3,V2,M3} { ! empty( X ), X = Y, ! empty( Y ) }.
% 4.15/4.54
% 4.15/4.54
% 4.15/4.54 Total Proof:
% 4.15/4.54
% 4.15/4.54 subsumption: (0) {G0,W6,D2,L2,V2,M2} I { ! in( X, Y ), ! in( Y, X ) }.
% 4.15/4.54 parent0: (24048) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), ! in( Y, X ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 X := X
% 4.15/4.54 Y := Y
% 4.15/4.54 end
% 4.15/4.54 permutation0:
% 4.15/4.54 0 ==> 0
% 4.15/4.54 1 ==> 1
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 subsumption: (16) {G0,W9,D2,L3,V2,M3} I { ! subset( X, Y ), X = Y,
% 4.15/4.54 proper_subset( X, Y ) }.
% 4.15/4.54 parent0: (24066) {G0,W9,D2,L3,V2,M3} { ! subset( X, Y ), X = Y,
% 4.15/4.54 proper_subset( X, Y ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 X := X
% 4.15/4.54 Y := Y
% 4.15/4.54 end
% 4.15/4.54 permutation0:
% 4.15/4.54 0 ==> 0
% 4.15/4.54 1 ==> 1
% 4.15/4.54 2 ==> 2
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 subsumption: (18) {G0,W2,D2,L1,V0,M1} I { empty( empty_set ) }.
% 4.15/4.54 parent0: (24068) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 end
% 4.15/4.54 permutation0:
% 4.15/4.54 0 ==> 0
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 subsumption: (21) {G0,W3,D3,L1,V1,M1} I { ! empty( succ( X ) ) }.
% 4.15/4.54 parent0: (24071) {G0,W3,D3,L1,V1,M1} { ! empty( succ( X ) ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 X := X
% 4.15/4.54 end
% 4.15/4.54 permutation0:
% 4.15/4.54 0 ==> 0
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 subsumption: (26) {G0,W2,D2,L1,V0,M1} I { ordinal( empty_set ) }.
% 4.15/4.54 parent0: (24080) {G0,W2,D2,L1,V0,M1} { ordinal( empty_set ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 end
% 4.15/4.54 permutation0:
% 4.15/4.54 0 ==> 0
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 subsumption: (29) {G0,W4,D2,L2,V1,M2} I { ! ordinal( X ), alpha2( X ) }.
% 4.15/4.54 parent0: (24083) {G0,W4,D2,L2,V1,M2} { ! ordinal( X ), alpha2( X ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 X := X
% 4.15/4.54 end
% 4.15/4.54 permutation0:
% 4.15/4.54 0 ==> 0
% 4.15/4.54 1 ==> 1
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 subsumption: (30) {G0,W5,D3,L2,V1,M2} I { ! ordinal( X ), ordinal( succ( X
% 4.15/4.54 ) ) }.
% 4.15/4.54 parent0: (24084) {G0,W5,D3,L2,V1,M2} { ! ordinal( X ), ordinal( succ( X )
% 4.15/4.54 ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 X := X
% 4.15/4.54 end
% 4.15/4.54 permutation0:
% 4.15/4.54 0 ==> 0
% 4.15/4.54 1 ==> 1
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 subsumption: (31) {G0,W5,D3,L2,V1,M2} I { ! alpha2( X ), epsilon_transitive
% 4.15/4.54 ( succ( X ) ) }.
% 4.15/4.54 parent0: (24086) {G0,W5,D3,L2,V1,M2} { ! alpha2( X ), epsilon_transitive(
% 4.15/4.54 succ( X ) ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 X := X
% 4.15/4.54 end
% 4.15/4.54 permutation0:
% 4.15/4.54 0 ==> 0
% 4.15/4.54 1 ==> 1
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 subsumption: (73) {G0,W10,D2,L4,V2,M4} I { ! ordinal( X ), ! ordinal( Y ),
% 4.15/4.54 ! ordinal_subset( X, Y ), subset( X, Y ) }.
% 4.15/4.54 parent0: (24130) {G0,W10,D2,L4,V2,M4} { ! ordinal( X ), ! ordinal( Y ), !
% 4.15/4.54 ordinal_subset( X, Y ), subset( X, Y ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 X := X
% 4.15/4.54 Y := Y
% 4.15/4.54 end
% 4.15/4.54 permutation0:
% 4.15/4.54 0 ==> 0
% 4.15/4.54 1 ==> 1
% 4.15/4.54 2 ==> 2
% 4.15/4.54 3 ==> 3
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 subsumption: (77) {G0,W4,D3,L1,V1,M1} I { in( X, succ( X ) ) }.
% 4.15/4.54 parent0: (24134) {G0,W4,D3,L1,V1,M1} { in( X, succ( X ) ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 X := X
% 4.15/4.54 end
% 4.15/4.54 permutation0:
% 4.15/4.54 0 ==> 0
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 subsumption: (79) {G0,W6,D2,L2,V2,M2} I { ! in( X, Y ), element( X, Y ) }.
% 4.15/4.54 parent0: (24136) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), element( X, Y ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 X := X
% 4.15/4.54 Y := Y
% 4.15/4.54 end
% 4.15/4.54 permutation0:
% 4.15/4.54 0 ==> 0
% 4.15/4.54 1 ==> 1
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 subsumption: (80) {G0,W10,D2,L4,V2,M4} I { ! epsilon_transitive( X ), !
% 4.15/4.54 ordinal( Y ), ! proper_subset( X, Y ), in( X, Y ) }.
% 4.15/4.54 parent0: (24137) {G0,W10,D2,L4,V2,M4} { ! epsilon_transitive( X ), !
% 4.15/4.54 ordinal( Y ), ! proper_subset( X, Y ), in( X, Y ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 X := X
% 4.15/4.54 Y := Y
% 4.15/4.54 end
% 4.15/4.54 permutation0:
% 4.15/4.54 0 ==> 0
% 4.15/4.54 1 ==> 1
% 4.15/4.54 2 ==> 2
% 4.15/4.54 3 ==> 3
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 subsumption: (81) {G0,W8,D2,L3,V2,M3} I { ! element( X, Y ), empty( Y ), in
% 4.15/4.54 ( X, Y ) }.
% 4.15/4.54 parent0: (24138) {G0,W8,D2,L3,V2,M3} { ! element( X, Y ), empty( Y ), in(
% 4.15/4.54 X, Y ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 X := X
% 4.15/4.54 Y := Y
% 4.15/4.54 end
% 4.15/4.54 permutation0:
% 4.15/4.54 0 ==> 0
% 4.15/4.54 1 ==> 1
% 4.15/4.54 2 ==> 2
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 subsumption: (82) {G0,W11,D3,L4,V2,M4} I { ! ordinal( X ), ! ordinal( Y ),
% 4.15/4.54 ! in( X, Y ), ordinal_subset( succ( X ), Y ) }.
% 4.15/4.54 parent0: (24139) {G0,W11,D3,L4,V2,M4} { ! ordinal( X ), ! ordinal( Y ), !
% 4.15/4.54 in( X, Y ), ordinal_subset( succ( X ), Y ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 X := X
% 4.15/4.54 Y := Y
% 4.15/4.54 end
% 4.15/4.54 permutation0:
% 4.15/4.54 0 ==> 0
% 4.15/4.54 1 ==> 1
% 4.15/4.54 2 ==> 2
% 4.15/4.54 3 ==> 3
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 subsumption: (86) {G0,W9,D2,L4,V2,M4} I { ! ordinal( X ), !
% 4.15/4.54 being_limit_ordinal( X ), ! ordinal( Y ), alpha1( X, Y ) }.
% 4.15/4.54 parent0: (24143) {G0,W9,D2,L4,V2,M4} { ! ordinal( X ), !
% 4.15/4.54 being_limit_ordinal( X ), ! ordinal( Y ), alpha1( X, Y ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 X := X
% 4.15/4.54 Y := Y
% 4.15/4.54 end
% 4.15/4.54 permutation0:
% 4.15/4.54 0 ==> 0
% 4.15/4.54 1 ==> 1
% 4.15/4.54 2 ==> 2
% 4.15/4.54 3 ==> 3
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 subsumption: (87) {G0,W7,D3,L3,V2,M3} I { ! ordinal( X ), ordinal( skol15(
% 4.15/4.54 Y ) ), being_limit_ordinal( X ) }.
% 4.15/4.54 parent0: (24144) {G0,W7,D3,L3,V2,M3} { ! ordinal( X ), ordinal( skol15( Y
% 4.15/4.54 ) ), being_limit_ordinal( X ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 X := X
% 4.15/4.54 Y := Y
% 4.15/4.54 end
% 4.15/4.54 permutation0:
% 4.15/4.54 0 ==> 0
% 4.15/4.54 1 ==> 1
% 4.15/4.54 2 ==> 2
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 subsumption: (88) {G0,W8,D3,L3,V1,M3} I { ! ordinal( X ), ! alpha1( X,
% 4.15/4.54 skol15( X ) ), being_limit_ordinal( X ) }.
% 4.15/4.54 parent0: (24145) {G0,W8,D3,L3,V1,M3} { ! ordinal( X ), ! alpha1( X, skol15
% 4.15/4.54 ( X ) ), being_limit_ordinal( X ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 X := X
% 4.15/4.54 end
% 4.15/4.54 permutation0:
% 4.15/4.54 0 ==> 0
% 4.15/4.54 1 ==> 1
% 4.15/4.54 2 ==> 2
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 subsumption: (89) {G0,W10,D3,L3,V2,M3} I { ! alpha1( X, Y ), ! in( Y, X ),
% 4.15/4.54 in( succ( Y ), X ) }.
% 4.15/4.54 parent0: (24146) {G0,W10,D3,L3,V2,M3} { ! alpha1( X, Y ), ! in( Y, X ), in
% 4.15/4.54 ( succ( Y ), X ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 X := X
% 4.15/4.54 Y := Y
% 4.15/4.54 end
% 4.15/4.54 permutation0:
% 4.15/4.54 0 ==> 0
% 4.15/4.54 1 ==> 1
% 4.15/4.54 2 ==> 2
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 subsumption: (90) {G0,W6,D2,L2,V2,M2} I { in( Y, X ), alpha1( X, Y ) }.
% 4.15/4.54 parent0: (24147) {G0,W6,D2,L2,V2,M2} { in( Y, X ), alpha1( X, Y ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 X := X
% 4.15/4.54 Y := Y
% 4.15/4.54 end
% 4.15/4.54 permutation0:
% 4.15/4.54 0 ==> 0
% 4.15/4.54 1 ==> 1
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 subsumption: (91) {G0,W7,D3,L2,V2,M2} I { ! in( succ( Y ), X ), alpha1( X,
% 4.15/4.54 Y ) }.
% 4.15/4.54 parent0: (24148) {G0,W7,D3,L2,V2,M2} { ! in( succ( Y ), X ), alpha1( X, Y
% 4.15/4.54 ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 X := X
% 4.15/4.54 Y := Y
% 4.15/4.54 end
% 4.15/4.54 permutation0:
% 4.15/4.54 0 ==> 0
% 4.15/4.54 1 ==> 1
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 subsumption: (92) {G0,W2,D2,L1,V0,M1} I { ordinal( skol16 ) }.
% 4.15/4.54 parent0: (24149) {G0,W2,D2,L1,V0,M1} { ordinal( skol16 ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 end
% 4.15/4.54 permutation0:
% 4.15/4.54 0 ==> 0
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 subsumption: (93) {G0,W4,D2,L2,V0,M2} I { alpha3( skol16 ), ordinal( skol18
% 4.15/4.54 ) }.
% 4.15/4.54 parent0: (24150) {G0,W4,D2,L2,V0,M2} { alpha3( skol16 ), ordinal( skol18 )
% 4.15/4.54 }.
% 4.15/4.54 substitution0:
% 4.15/4.54 end
% 4.15/4.54 permutation0:
% 4.15/4.54 0 ==> 0
% 4.15/4.54 1 ==> 1
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 eqswap: (24456) {G0,W6,D3,L2,V0,M2} { succ( skol18 ) = skol16, alpha3(
% 4.15/4.54 skol16 ) }.
% 4.15/4.54 parent0[1]: (24151) {G0,W6,D3,L2,V0,M2} { alpha3( skol16 ), skol16 = succ
% 4.15/4.54 ( skol18 ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 subsumption: (94) {G0,W6,D3,L2,V0,M2} I { alpha3( skol16 ), succ( skol18 )
% 4.15/4.54 ==> skol16 }.
% 4.15/4.54 parent0: (24456) {G0,W6,D3,L2,V0,M2} { succ( skol18 ) = skol16, alpha3(
% 4.15/4.54 skol16 ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 end
% 4.15/4.54 permutation0:
% 4.15/4.54 0 ==> 1
% 4.15/4.54 1 ==> 0
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 subsumption: (95) {G0,W4,D2,L2,V0,M2} I { alpha3( skol16 ),
% 4.15/4.54 being_limit_ordinal( skol16 ) }.
% 4.15/4.54 parent0: (24152) {G0,W4,D2,L2,V0,M2} { alpha3( skol16 ),
% 4.15/4.54 being_limit_ordinal( skol16 ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 end
% 4.15/4.54 permutation0:
% 4.15/4.54 0 ==> 0
% 4.15/4.54 1 ==> 1
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 subsumption: (96) {G0,W4,D2,L2,V1,M2} I { ! alpha3( X ), !
% 4.15/4.54 being_limit_ordinal( X ) }.
% 4.15/4.54 parent0: (24153) {G0,W4,D2,L2,V1,M2} { ! alpha3( X ), !
% 4.15/4.54 being_limit_ordinal( X ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 X := X
% 4.15/4.54 end
% 4.15/4.54 permutation0:
% 4.15/4.54 0 ==> 0
% 4.15/4.54 1 ==> 1
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 subsumption: (97) {G0,W8,D3,L3,V2,M3} I { ! alpha3( X ), ! ordinal( Y ), !
% 4.15/4.54 X = succ( Y ) }.
% 4.15/4.54 parent0: (24154) {G0,W8,D3,L3,V2,M3} { ! alpha3( X ), ! ordinal( Y ), ! X
% 4.15/4.54 = succ( Y ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 X := X
% 4.15/4.54 Y := Y
% 4.15/4.54 end
% 4.15/4.54 permutation0:
% 4.15/4.54 0 ==> 0
% 4.15/4.54 1 ==> 1
% 4.15/4.54 2 ==> 2
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 subsumption: (102) {G0,W5,D2,L2,V1,M2} I { ! empty( X ), X = empty_set }.
% 4.15/4.54 parent0: (24159) {G0,W5,D2,L2,V1,M2} { ! empty( X ), X = empty_set }.
% 4.15/4.54 substitution0:
% 4.15/4.54 X := X
% 4.15/4.54 end
% 4.15/4.54 permutation0:
% 4.15/4.54 0 ==> 0
% 4.15/4.54 1 ==> 1
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 subsumption: (103) {G0,W5,D2,L2,V2,M2} I { ! in( X, Y ), ! empty( Y ) }.
% 4.15/4.54 parent0: (24160) {G0,W5,D2,L2,V2,M2} { ! in( X, Y ), ! empty( Y ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 X := X
% 4.15/4.54 Y := Y
% 4.15/4.54 end
% 4.15/4.54 permutation0:
% 4.15/4.54 0 ==> 0
% 4.15/4.54 1 ==> 1
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 subsumption: (104) {G0,W7,D2,L3,V2,M3} I { ! empty( X ), X = Y, ! empty( Y
% 4.15/4.54 ) }.
% 4.15/4.54 parent0: (24161) {G0,W7,D2,L3,V2,M3} { ! empty( X ), X = Y, ! empty( Y )
% 4.15/4.54 }.
% 4.15/4.54 substitution0:
% 4.15/4.54 X := X
% 4.15/4.54 Y := Y
% 4.15/4.54 end
% 4.15/4.54 permutation0:
% 4.15/4.54 0 ==> 0
% 4.15/4.54 1 ==> 1
% 4.15/4.54 2 ==> 2
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 factor: (24576) {G0,W3,D2,L1,V1,M1} { ! in( X, X ) }.
% 4.15/4.54 parent0[0, 1]: (0) {G0,W6,D2,L2,V2,M2} I { ! in( X, Y ), ! in( Y, X ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 X := X
% 4.15/4.54 Y := X
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 subsumption: (105) {G1,W3,D2,L1,V1,M1} F(0) { ! in( X, X ) }.
% 4.15/4.54 parent0: (24576) {G0,W3,D2,L1,V1,M1} { ! in( X, X ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 X := X
% 4.15/4.54 end
% 4.15/4.54 permutation0:
% 4.15/4.54 0 ==> 0
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 resolution: (24578) {G1,W8,D2,L3,V1,M3} { ! ordinal( X ), ! ordinal_subset
% 4.15/4.54 ( X, skol16 ), subset( X, skol16 ) }.
% 4.15/4.54 parent0[1]: (73) {G0,W10,D2,L4,V2,M4} I { ! ordinal( X ), ! ordinal( Y ), !
% 4.15/4.54 ordinal_subset( X, Y ), subset( X, Y ) }.
% 4.15/4.54 parent1[0]: (92) {G0,W2,D2,L1,V0,M1} I { ordinal( skol16 ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 X := X
% 4.15/4.54 Y := skol16
% 4.15/4.54 end
% 4.15/4.54 substitution1:
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 subsumption: (552) {G1,W8,D2,L3,V1,M3} R(73,92) { ! ordinal( X ), !
% 4.15/4.54 ordinal_subset( X, skol16 ), subset( X, skol16 ) }.
% 4.15/4.54 parent0: (24578) {G1,W8,D2,L3,V1,M3} { ! ordinal( X ), ! ordinal_subset( X
% 4.15/4.54 , skol16 ), subset( X, skol16 ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 X := X
% 4.15/4.54 end
% 4.15/4.54 permutation0:
% 4.15/4.54 0 ==> 0
% 4.15/4.54 1 ==> 1
% 4.15/4.54 2 ==> 2
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 resolution: (24579) {G1,W4,D2,L2,V0,M2} { ! being_limit_ordinal( skol16 )
% 4.15/4.54 , ordinal( skol18 ) }.
% 4.15/4.54 parent0[0]: (96) {G0,W4,D2,L2,V1,M2} I { ! alpha3( X ), !
% 4.15/4.54 being_limit_ordinal( X ) }.
% 4.15/4.54 parent1[0]: (93) {G0,W4,D2,L2,V0,M2} I { alpha3( skol16 ), ordinal( skol18
% 4.15/4.54 ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 X := skol16
% 4.15/4.54 end
% 4.15/4.54 substitution1:
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 subsumption: (656) {G1,W4,D2,L2,V0,M2} R(93,96) { ordinal( skol18 ), !
% 4.15/4.54 being_limit_ordinal( skol16 ) }.
% 4.15/4.54 parent0: (24579) {G1,W4,D2,L2,V0,M2} { ! being_limit_ordinal( skol16 ),
% 4.15/4.54 ordinal( skol18 ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 end
% 4.15/4.54 permutation0:
% 4.15/4.54 0 ==> 1
% 4.15/4.54 1 ==> 0
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 resolution: (24580) {G1,W4,D3,L1,V1,M1} { element( X, succ( X ) ) }.
% 4.15/4.54 parent0[0]: (79) {G0,W6,D2,L2,V2,M2} I { ! in( X, Y ), element( X, Y ) }.
% 4.15/4.54 parent1[0]: (77) {G0,W4,D3,L1,V1,M1} I { in( X, succ( X ) ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 X := X
% 4.15/4.54 Y := succ( X )
% 4.15/4.54 end
% 4.15/4.54 substitution1:
% 4.15/4.54 X := X
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 subsumption: (694) {G1,W4,D3,L1,V1,M1} R(79,77) { element( X, succ( X ) )
% 4.15/4.54 }.
% 4.15/4.54 parent0: (24580) {G1,W4,D3,L1,V1,M1} { element( X, succ( X ) ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 X := X
% 4.15/4.54 end
% 4.15/4.54 permutation0:
% 4.15/4.54 0 ==> 0
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 resolution: (24582) {G1,W9,D2,L4,V1,M4} { ! ordinal( X ), !
% 4.15/4.54 being_limit_ordinal( X ), alpha1( X, skol18 ), ! being_limit_ordinal(
% 4.15/4.54 skol16 ) }.
% 4.15/4.54 parent0[2]: (86) {G0,W9,D2,L4,V2,M4} I { ! ordinal( X ), !
% 4.15/4.54 being_limit_ordinal( X ), ! ordinal( Y ), alpha1( X, Y ) }.
% 4.15/4.54 parent1[0]: (656) {G1,W4,D2,L2,V0,M2} R(93,96) { ordinal( skol18 ), !
% 4.15/4.54 being_limit_ordinal( skol16 ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 X := X
% 4.15/4.54 Y := skol18
% 4.15/4.54 end
% 4.15/4.54 substitution1:
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 subsumption: (1077) {G2,W9,D2,L4,V1,M4} R(86,656) { ! ordinal( X ), !
% 4.15/4.54 being_limit_ordinal( X ), alpha1( X, skol18 ), ! being_limit_ordinal(
% 4.15/4.54 skol16 ) }.
% 4.15/4.54 parent0: (24582) {G1,W9,D2,L4,V1,M4} { ! ordinal( X ), !
% 4.15/4.54 being_limit_ordinal( X ), alpha1( X, skol18 ), ! being_limit_ordinal(
% 4.15/4.54 skol16 ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 X := X
% 4.15/4.54 end
% 4.15/4.54 permutation0:
% 4.15/4.54 0 ==> 0
% 4.15/4.54 1 ==> 1
% 4.15/4.54 2 ==> 2
% 4.15/4.54 3 ==> 3
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 factor: (24584) {G2,W7,D2,L3,V0,M3} { ! ordinal( skol16 ), !
% 4.15/4.54 being_limit_ordinal( skol16 ), alpha1( skol16, skol18 ) }.
% 4.15/4.54 parent0[1, 3]: (1077) {G2,W9,D2,L4,V1,M4} R(86,656) { ! ordinal( X ), !
% 4.15/4.54 being_limit_ordinal( X ), alpha1( X, skol18 ), ! being_limit_ordinal(
% 4.15/4.54 skol16 ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 X := skol16
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 resolution: (24585) {G1,W5,D2,L2,V0,M2} { ! being_limit_ordinal( skol16 )
% 4.15/4.54 , alpha1( skol16, skol18 ) }.
% 4.15/4.54 parent0[0]: (24584) {G2,W7,D2,L3,V0,M3} { ! ordinal( skol16 ), !
% 4.15/4.54 being_limit_ordinal( skol16 ), alpha1( skol16, skol18 ) }.
% 4.15/4.54 parent1[0]: (92) {G0,W2,D2,L1,V0,M1} I { ordinal( skol16 ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 end
% 4.15/4.54 substitution1:
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 subsumption: (1121) {G3,W5,D2,L2,V0,M2} F(1077);r(92) { !
% 4.15/4.54 being_limit_ordinal( skol16 ), alpha1( skol16, skol18 ) }.
% 4.15/4.54 parent0: (24585) {G1,W5,D2,L2,V0,M2} { ! being_limit_ordinal( skol16 ),
% 4.15/4.54 alpha1( skol16, skol18 ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 end
% 4.15/4.54 permutation0:
% 4.15/4.54 0 ==> 0
% 4.15/4.54 1 ==> 1
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 resolution: (24586) {G1,W3,D2,L1,V1,M1} { ! in( X, empty_set ) }.
% 4.15/4.54 parent0[1]: (103) {G0,W5,D2,L2,V2,M2} I { ! in( X, Y ), ! empty( Y ) }.
% 4.15/4.54 parent1[0]: (18) {G0,W2,D2,L1,V0,M1} I { empty( empty_set ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 X := X
% 4.15/4.54 Y := empty_set
% 4.15/4.54 end
% 4.15/4.54 substitution1:
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 subsumption: (1369) {G1,W3,D2,L1,V1,M1} R(103,18) { ! in( X, empty_set )
% 4.15/4.54 }.
% 4.15/4.54 parent0: (24586) {G1,W3,D2,L1,V1,M1} { ! in( X, empty_set ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 X := X
% 4.15/4.54 end
% 4.15/4.54 permutation0:
% 4.15/4.54 0 ==> 0
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 resolution: (24587) {G1,W3,D2,L1,V1,M1} { alpha1( empty_set, X ) }.
% 4.15/4.54 parent0[0]: (1369) {G1,W3,D2,L1,V1,M1} R(103,18) { ! in( X, empty_set ) }.
% 4.15/4.54 parent1[0]: (90) {G0,W6,D2,L2,V2,M2} I { in( Y, X ), alpha1( X, Y ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 X := X
% 4.15/4.54 end
% 4.15/4.54 substitution1:
% 4.15/4.54 X := empty_set
% 4.15/4.54 Y := X
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 subsumption: (1381) {G2,W3,D2,L1,V1,M1} R(1369,90) { alpha1( empty_set, X )
% 4.15/4.54 }.
% 4.15/4.54 parent0: (24587) {G1,W3,D2,L1,V1,M1} { alpha1( empty_set, X ) }.
% 4.15/4.54 substitution0:
% 4.15/4.54 X := X
% 4.15/4.54 end
% 4.15/4.54 permutation0:
% 4.15/4.54 0 ==> 0
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 resolution: (24588) {G1,W4,D2,L2,V0,M2} { ! ordinal( empty_set ),
% 4.15/4.54 being_limit_ordinal( empty_set ) }.
% 4.15/4.54 parent0[1]: (88) {G0,W8,D3,L3,V1,M3} I { ! ordinal( X ), ! alpha1( X,
% 4.15/4.54 skol15( X ) ), being_limit_ordinal( X ) }.
% 4.15/4.54 parent1[0]: (1381) {G2,W3,D2,L1,V1,M1} R(1369,90) { alpha1( empty_set, X )
% 4.15/4.54 }.
% 4.15/4.54 substitution0:
% 4.15/4.54 X := empty_set
% 4.15/4.54 end
% 4.15/4.54 substitution1:
% 4.15/4.54 X := skol15( empty_set )
% 4.15/4.54 end
% 4.15/4.54
% 4.15/4.54 resolution: (24589) {G1,W2,D2,L1,V0,M1} { being_limit_ordinal( empty_set )
% 4.15/4.54 }.
% 4.15/4.54 parent0[0]: (24588) {G1,W4,D2,L2,V0,M2} { ! ordinal( empty_set ),
% 4.15/4.54 being_limit_ordinal( empty_set ) }.
% 4.15/4.54 parent1[0]: (26) {G0,W2,D2,L1,V0,M1} I { ordinal( empty_set ) }.
% 4.15/4.55 substitution0:
% 4.15/4.55 end
% 4.15/4.55 substitution1:
% 4.15/4.55 end
% 4.15/4.55
% 4.15/4.55 subsumption: (1386) {G3,W2,D2,L1,V0,M1} R(1381,88);r(26) {
% 4.15/4.55 being_limit_ordinal( empty_set ) }.
% 4.15/4.55 parent0: (24589) {G1,W2,D2,L1,V0,M1} { being_limit_ordinal( empty_set )
% 4.15/4.55 }.
% 4.15/4.55 substitution0:
% 4.15/4.55 end
% 4.15/4.55 permutation0:
% 4.15/4.55 0 ==> 0
% 4.15/4.55 end
% 4.15/4.55
% 4.15/4.55 eqswap: (24590) {G0,W6,D3,L2,V0,M2} { skol16 ==> succ( skol18 ), alpha3(
% 4.15/4.55 skol16 ) }.
% 4.15/4.55 parent0[1]: (94) {G0,W6,D3,L2,V0,M2} I { alpha3( skol16 ), succ( skol18 )
% 4.15/4.55 ==> skol16 }.
% 4.15/4.55 substitution0:
% 4.15/4.55 end
% 4.15/4.55
% 4.15/4.55 resolution: (24591) {G1,W6,D3,L2,V0,M2} { ! being_limit_ordinal( skol16 )
% 4.15/4.55 , skol16 ==> succ( skol18 ) }.
% 4.15/4.55 parent0[0]: (96) {G0,W4,D2,L2,V1,M2} I { ! alpha3( X ), !
% 4.15/4.55 being_limit_ordinal( X ) }.
% 4.15/4.55 parent1[1]: (24590) {G0,W6,D3,L2,V0,M2} { skol16 ==> succ( skol18 ),
% 4.15/4.55 alpha3( skol16 ) }.
% 4.15/4.55 substitution0:
% 4.15/4.55 X := skol16
% 4.15/4.55 end
% 4.15/4.55 substitution1:
% 4.15/4.55 end
% 4.15/4.55
% 4.15/4.55 eqswap: (24592) {G1,W6,D3,L2,V0,M2} { succ( skol18 ) ==> skol16, !
% 4.15/4.55 being_limit_ordinal( skol16 ) }.
% 4.15/4.55 parent0[1]: (24591) {G1,W6,D3,L2,V0,M2} { ! being_limit_ordinal( skol16 )
% 4.15/4.55 , skol16 ==> succ( skol18 ) }.
% 4.15/4.55 substitution0:
% 4.15/4.55 end
% 4.15/4.55
% 4.15/4.55 subsumption: (1407) {G1,W6,D3,L2,V0,M2} R(94,96) { succ( skol18 ) ==>
% 4.15/4.55 skol16, ! being_limit_ordinal( skol16 ) }.
% 4.15/4.55 parent0: (24592) {G1,W6,D3,L2,V0,M2} { succ( skol18 ) ==> skol16, !
% 4.15/4.55 being_limit_ordinal( skol16 ) }.
% 4.15/4.55 substitution0:
% 4.15/4.55 end
% 4.15/4.55 permutation0:
% 4.15/4.55 0 ==> 0
% 4.15/4.55 1 ==> 1
% 4.15/4.55 end
% 4.15/4.55
% 4.15/4.55 paramod: (24594) {G1,W5,D2,L2,V0,M2} { element( skol18, skol16 ), alpha3(
% 4.15/4.55 skol16 ) }.
% 4.15/4.55 parent0[1]: (94) {G0,W6,D3,L2,V0,M2} I { alpha3( skol16 ), succ( skol18 )
% 4.15/4.55 ==> skol16 }.
% 4.15/4.55 parent1[0; 2]: (694) {G1,W4,D3,L1,V1,M1} R(79,77) { element( X, succ( X ) )
% 4.15/4.55 }.
% 4.15/4.55 substitution0:
% 4.15/4.55 end
% 4.15/4.55 substitution1:
% 4.15/4.55 X := skol18
% 4.15/4.55 end
% 4.15/4.55
% 4.15/4.55 subsumption: (1411) {G2,W5,D2,L2,V0,M2} P(94,694) { element( skol18, skol16
% 4.15/4.55 ), alpha3( skol16 ) }.
% 4.15/4.55 parent0: (24594) {G1,W5,D2,L2,V0,M2} { element( skol18, skol16 ), alpha3(
% 4.15/4.55 skol16 ) }.
% 4.15/4.55 substitution0:
% 4.15/4.55 end
% 4.15/4.55 permutation0:
% 4.15/4.55 0 ==> 0
% 4.15/4.55 1 ==> 1
% 4.15/4.55 end
% 4.15/4.55
% 4.15/4.55 paramod: (24596) {G1,W4,D2,L2,V0,M2} { ! empty( skol16 ), alpha3( skol16 )
% 4.15/4.55 }.
% 4.15/4.55 parent0[1]: (94) {G0,W6,D3,L2,V0,M2} I { alpha3( skol16 ), succ( skol18 )
% 4.15/4.55 ==> skol16 }.
% 4.15/4.55 parent1[0; 2]: (21) {G0,W3,D3,L1,V1,M1} I { ! empty( succ( X ) ) }.
% 4.15/4.55 substitution0:
% 4.15/4.55 end
% 4.15/4.55 substitution1:
% 4.15/4.55 X := skol18
% 4.15/4.55 end
% 4.15/4.55
% 4.15/4.55 subsumption: (1413) {G1,W4,D2,L2,V0,M2} P(94,21) { ! empty( skol16 ),
% 4.15/4.55 alpha3( skol16 ) }.
% 4.15/4.55 parent0: (24596) {G1,W4,D2,L2,V0,M2} { ! empty( skol16 ), alpha3( skol16 )
% 4.15/4.55 }.
% 4.15/4.55 substitution0:
% 4.15/4.55 end
% 4.15/4.55 permutation0:
% 4.15/4.55 0 ==> 0
% 4.15/4.55 1 ==> 1
% 4.15/4.55 end
% 4.15/4.55
% 4.15/4.55 resolution: (24597) {G1,W4,D2,L2,V0,M2} { ! being_limit_ordinal( skol16 )
% 4.15/4.55 , ! empty( skol16 ) }.
% 4.15/4.55 parent0[0]: (96) {G0,W4,D2,L2,V1,M2} I { ! alpha3( X ), !
% 4.15/4.55 being_limit_ordinal( X ) }.
% 4.15/4.55 parent1[1]: (1413) {G1,W4,D2,L2,V0,M2} P(94,21) { ! empty( skol16 ), alpha3
% 4.15/4.55 ( skol16 ) }.
% 4.15/4.55 substitution0:
% 4.15/4.55 X := skol16
% 4.15/4.55 end
% 4.15/4.55 substitution1:
% 4.15/4.55 end
% 4.15/4.55
% 4.15/4.55 subsumption: (1609) {G2,W4,D2,L2,V0,M2} R(1413,96) { ! empty( skol16 ), !
% 4.15/4.55 being_limit_ordinal( skol16 ) }.
% 4.15/4.55 parent0: (24597) {G1,W4,D2,L2,V0,M2} { ! being_limit_ordinal( skol16 ), !
% 4.15/4.55 empty( skol16 ) }.
% 4.15/4.55 substitution0:
% 4.15/4.55 end
% 4.15/4.55 permutation0:
% 4.15/4.55 0 ==> 1
% 4.15/4.55 1 ==> 0
% 4.15/4.55 end
% 4.15/4.55
% 4.15/4.55 eqswap: (24598) {G0,W5,D2,L2,V1,M2} { empty_set = X, ! empty( X ) }.
% 4.15/4.57 parent0[1]: (102) {G0,W5,D2,L2,V1,M2} I { ! empty( X ), X = empty_set }.
% 4.15/4.57 substitution0:
% 4.15/4.57 X := X
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 paramod: (24599) {G1,W4,D2,L2,V1,M2} { being_limit_ordinal( X ), ! empty(
% 4.15/4.57 X ) }.
% 4.15/4.57 parent0[0]: (24598) {G0,W5,D2,L2,V1,M2} { empty_set = X, ! empty( X ) }.
% 4.15/4.57 parent1[0; 1]: (1386) {G3,W2,D2,L1,V0,M1} R(1381,88);r(26) {
% 4.15/4.57 being_limit_ordinal( empty_set ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 X := X
% 4.15/4.57 end
% 4.15/4.57 substitution1:
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 subsumption: (1633) {G4,W4,D2,L2,V1,M2} P(102,1386) { being_limit_ordinal(
% 4.15/4.57 X ), ! empty( X ) }.
% 4.15/4.57 parent0: (24599) {G1,W4,D2,L2,V1,M2} { being_limit_ordinal( X ), ! empty(
% 4.15/4.57 X ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 X := X
% 4.15/4.57 end
% 4.15/4.57 permutation0:
% 4.15/4.57 0 ==> 0
% 4.15/4.57 1 ==> 1
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 paramod: (24600) {G1,W8,D2,L4,V1,M4} { ! empty( X ), ! empty( skol16 ), !
% 4.15/4.57 empty( X ), ! being_limit_ordinal( skol16 ) }.
% 4.15/4.57 parent0[1]: (104) {G0,W7,D2,L3,V2,M3} I { ! empty( X ), X = Y, ! empty( Y )
% 4.15/4.57 }.
% 4.15/4.57 parent1[0; 2]: (1609) {G2,W4,D2,L2,V0,M2} R(1413,96) { ! empty( skol16 ), !
% 4.15/4.57 being_limit_ordinal( skol16 ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 X := skol16
% 4.15/4.57 Y := X
% 4.15/4.57 end
% 4.15/4.57 substitution1:
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 resolution: (24625) {G2,W8,D2,L4,V1,M4} { ! empty( X ), ! empty( skol16 )
% 4.15/4.57 , ! empty( X ), ! empty( skol16 ) }.
% 4.15/4.57 parent0[3]: (24600) {G1,W8,D2,L4,V1,M4} { ! empty( X ), ! empty( skol16 )
% 4.15/4.57 , ! empty( X ), ! being_limit_ordinal( skol16 ) }.
% 4.15/4.57 parent1[0]: (1633) {G4,W4,D2,L2,V1,M2} P(102,1386) { being_limit_ordinal( X
% 4.15/4.57 ), ! empty( X ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 X := X
% 4.15/4.57 end
% 4.15/4.57 substitution1:
% 4.15/4.57 X := skol16
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 factor: (24626) {G2,W6,D2,L3,V0,M3} { ! empty( skol16 ), ! empty( skol16 )
% 4.15/4.57 , ! empty( skol16 ) }.
% 4.15/4.57 parent0[0, 1]: (24625) {G2,W8,D2,L4,V1,M4} { ! empty( X ), ! empty( skol16
% 4.15/4.57 ), ! empty( X ), ! empty( skol16 ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 X := skol16
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 factor: (24627) {G2,W4,D2,L2,V0,M2} { ! empty( skol16 ), ! empty( skol16 )
% 4.15/4.57 }.
% 4.15/4.57 parent0[0, 1]: (24626) {G2,W6,D2,L3,V0,M3} { ! empty( skol16 ), ! empty(
% 4.15/4.57 skol16 ), ! empty( skol16 ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 subsumption: (1656) {G5,W4,D2,L2,V1,M2} P(104,1609);f;r(1633) { ! empty( X
% 4.15/4.57 ), ! empty( skol16 ) }.
% 4.15/4.57 parent0: (24627) {G2,W4,D2,L2,V0,M2} { ! empty( skol16 ), ! empty( skol16
% 4.15/4.57 ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 end
% 4.15/4.57 permutation0:
% 4.15/4.57 0 ==> 1
% 4.15/4.57 1 ==> 1
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 factor: (24629) {G5,W2,D2,L1,V0,M1} { ! empty( skol16 ) }.
% 4.15/4.57 parent0[0, 1]: (1656) {G5,W4,D2,L2,V1,M2} P(104,1609);f;r(1633) { ! empty(
% 4.15/4.57 X ), ! empty( skol16 ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 X := skol16
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 subsumption: (1667) {G6,W2,D2,L1,V0,M1} F(1656) { ! empty( skol16 ) }.
% 4.15/4.57 parent0: (24629) {G5,W2,D2,L1,V0,M1} { ! empty( skol16 ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 end
% 4.15/4.57 permutation0:
% 4.15/4.57 0 ==> 0
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 resolution: (24630) {G1,W5,D2,L2,V0,M2} { ! being_limit_ordinal( skol16 )
% 4.15/4.57 , element( skol18, skol16 ) }.
% 4.15/4.57 parent0[0]: (96) {G0,W4,D2,L2,V1,M2} I { ! alpha3( X ), !
% 4.15/4.57 being_limit_ordinal( X ) }.
% 4.15/4.57 parent1[1]: (1411) {G2,W5,D2,L2,V0,M2} P(94,694) { element( skol18, skol16
% 4.15/4.57 ), alpha3( skol16 ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 X := skol16
% 4.15/4.57 end
% 4.15/4.57 substitution1:
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 subsumption: (2634) {G3,W5,D2,L2,V0,M2} R(1411,96) { element( skol18,
% 4.15/4.57 skol16 ), ! being_limit_ordinal( skol16 ) }.
% 4.15/4.57 parent0: (24630) {G1,W5,D2,L2,V0,M2} { ! being_limit_ordinal( skol16 ),
% 4.15/4.57 element( skol18, skol16 ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 end
% 4.15/4.57 permutation0:
% 4.15/4.57 0 ==> 1
% 4.15/4.57 1 ==> 0
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 resolution: (24631) {G1,W7,D2,L3,V0,M3} { empty( skol16 ), in( skol18,
% 4.15/4.57 skol16 ), ! being_limit_ordinal( skol16 ) }.
% 4.15/4.57 parent0[0]: (81) {G0,W8,D2,L3,V2,M3} I { ! element( X, Y ), empty( Y ), in
% 4.15/4.57 ( X, Y ) }.
% 4.15/4.57 parent1[0]: (2634) {G3,W5,D2,L2,V0,M2} R(1411,96) { element( skol18, skol16
% 4.15/4.57 ), ! being_limit_ordinal( skol16 ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 X := skol18
% 4.15/4.57 Y := skol16
% 4.15/4.57 end
% 4.15/4.57 substitution1:
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 resolution: (24632) {G2,W5,D2,L2,V0,M2} { in( skol18, skol16 ), !
% 4.15/4.57 being_limit_ordinal( skol16 ) }.
% 4.15/4.57 parent0[0]: (1667) {G6,W2,D2,L1,V0,M1} F(1656) { ! empty( skol16 ) }.
% 4.15/4.57 parent1[0]: (24631) {G1,W7,D2,L3,V0,M3} { empty( skol16 ), in( skol18,
% 4.15/4.57 skol16 ), ! being_limit_ordinal( skol16 ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 end
% 4.15/4.57 substitution1:
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 subsumption: (2643) {G7,W5,D2,L2,V0,M2} R(2634,81);r(1667) { !
% 4.15/4.57 being_limit_ordinal( skol16 ), in( skol18, skol16 ) }.
% 4.15/4.57 parent0: (24632) {G2,W5,D2,L2,V0,M2} { in( skol18, skol16 ), !
% 4.15/4.57 being_limit_ordinal( skol16 ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 end
% 4.15/4.57 permutation0:
% 4.15/4.57 0 ==> 1
% 4.15/4.57 1 ==> 0
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 resolution: (24634) {G1,W9,D3,L3,V0,M3} { ! alpha1( skol16, skol18 ), in(
% 4.15/4.57 succ( skol18 ), skol16 ), ! being_limit_ordinal( skol16 ) }.
% 4.15/4.57 parent0[1]: (89) {G0,W10,D3,L3,V2,M3} I { ! alpha1( X, Y ), ! in( Y, X ),
% 4.15/4.57 in( succ( Y ), X ) }.
% 4.15/4.57 parent1[1]: (2643) {G7,W5,D2,L2,V0,M2} R(2634,81);r(1667) { !
% 4.15/4.57 being_limit_ordinal( skol16 ), in( skol18, skol16 ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 X := skol16
% 4.15/4.57 Y := skol18
% 4.15/4.57 end
% 4.15/4.57 substitution1:
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 paramod: (24635) {G2,W10,D2,L4,V0,M4} { in( skol16, skol16 ), !
% 4.15/4.57 being_limit_ordinal( skol16 ), ! alpha1( skol16, skol18 ), !
% 4.15/4.57 being_limit_ordinal( skol16 ) }.
% 4.15/4.57 parent0[0]: (1407) {G1,W6,D3,L2,V0,M2} R(94,96) { succ( skol18 ) ==> skol16
% 4.15/4.57 , ! being_limit_ordinal( skol16 ) }.
% 4.15/4.57 parent1[1; 1]: (24634) {G1,W9,D3,L3,V0,M3} { ! alpha1( skol16, skol18 ),
% 4.15/4.57 in( succ( skol18 ), skol16 ), ! being_limit_ordinal( skol16 ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 end
% 4.15/4.57 substitution1:
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 factor: (24636) {G2,W8,D2,L3,V0,M3} { in( skol16, skol16 ), !
% 4.15/4.57 being_limit_ordinal( skol16 ), ! alpha1( skol16, skol18 ) }.
% 4.15/4.57 parent0[1, 3]: (24635) {G2,W10,D2,L4,V0,M4} { in( skol16, skol16 ), !
% 4.15/4.57 being_limit_ordinal( skol16 ), ! alpha1( skol16, skol18 ), !
% 4.15/4.57 being_limit_ordinal( skol16 ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 resolution: (24637) {G3,W7,D2,L3,V0,M3} { in( skol16, skol16 ), !
% 4.15/4.57 being_limit_ordinal( skol16 ), ! being_limit_ordinal( skol16 ) }.
% 4.15/4.57 parent0[2]: (24636) {G2,W8,D2,L3,V0,M3} { in( skol16, skol16 ), !
% 4.15/4.57 being_limit_ordinal( skol16 ), ! alpha1( skol16, skol18 ) }.
% 4.15/4.57 parent1[1]: (1121) {G3,W5,D2,L2,V0,M2} F(1077);r(92) { !
% 4.15/4.57 being_limit_ordinal( skol16 ), alpha1( skol16, skol18 ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 end
% 4.15/4.57 substitution1:
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 factor: (24638) {G3,W5,D2,L2,V0,M2} { in( skol16, skol16 ), !
% 4.15/4.57 being_limit_ordinal( skol16 ) }.
% 4.15/4.57 parent0[1, 2]: (24637) {G3,W7,D2,L3,V0,M3} { in( skol16, skol16 ), !
% 4.15/4.57 being_limit_ordinal( skol16 ), ! being_limit_ordinal( skol16 ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 subsumption: (2652) {G8,W5,D2,L2,V0,M2} R(2643,89);d(1407);r(1121) { !
% 4.15/4.57 being_limit_ordinal( skol16 ), in( skol16, skol16 ) }.
% 4.15/4.57 parent0: (24638) {G3,W5,D2,L2,V0,M2} { in( skol16, skol16 ), !
% 4.15/4.57 being_limit_ordinal( skol16 ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 end
% 4.15/4.57 permutation0:
% 4.15/4.57 0 ==> 1
% 4.15/4.57 1 ==> 0
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 resolution: (24639) {G2,W2,D2,L1,V0,M1} { ! being_limit_ordinal( skol16 )
% 4.15/4.57 }.
% 4.15/4.57 parent0[0]: (105) {G1,W3,D2,L1,V1,M1} F(0) { ! in( X, X ) }.
% 4.15/4.57 parent1[1]: (2652) {G8,W5,D2,L2,V0,M2} R(2643,89);d(1407);r(1121) { !
% 4.15/4.57 being_limit_ordinal( skol16 ), in( skol16, skol16 ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 X := skol16
% 4.15/4.57 end
% 4.15/4.57 substitution1:
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 subsumption: (2661) {G9,W2,D2,L1,V0,M1} S(2652);r(105) { !
% 4.15/4.57 being_limit_ordinal( skol16 ) }.
% 4.15/4.57 parent0: (24639) {G2,W2,D2,L1,V0,M1} { ! being_limit_ordinal( skol16 ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 end
% 4.15/4.57 permutation0:
% 4.15/4.57 0 ==> 0
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 resolution: (24640) {G1,W6,D3,L2,V0,M2} { ! ordinal( skol16 ), ! alpha1(
% 4.15/4.57 skol16, skol15( skol16 ) ) }.
% 4.15/4.57 parent0[0]: (2661) {G9,W2,D2,L1,V0,M1} S(2652);r(105) { !
% 4.15/4.57 being_limit_ordinal( skol16 ) }.
% 4.15/4.57 parent1[2]: (88) {G0,W8,D3,L3,V1,M3} I { ! ordinal( X ), ! alpha1( X,
% 4.15/4.57 skol15( X ) ), being_limit_ordinal( X ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 end
% 4.15/4.57 substitution1:
% 4.15/4.57 X := skol16
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 resolution: (24641) {G1,W4,D3,L1,V0,M1} { ! alpha1( skol16, skol15( skol16
% 4.15/4.57 ) ) }.
% 4.15/4.57 parent0[0]: (24640) {G1,W6,D3,L2,V0,M2} { ! ordinal( skol16 ), ! alpha1(
% 4.15/4.57 skol16, skol15( skol16 ) ) }.
% 4.15/4.57 parent1[0]: (92) {G0,W2,D2,L1,V0,M1} I { ordinal( skol16 ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 end
% 4.15/4.57 substitution1:
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 subsumption: (2670) {G10,W4,D3,L1,V0,M1} R(2661,88);r(92) { ! alpha1(
% 4.15/4.57 skol16, skol15( skol16 ) ) }.
% 4.15/4.57 parent0: (24641) {G1,W4,D3,L1,V0,M1} { ! alpha1( skol16, skol15( skol16 )
% 4.15/4.57 ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 end
% 4.15/4.57 permutation0:
% 4.15/4.57 0 ==> 0
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 resolution: (24642) {G1,W5,D3,L2,V1,M2} { ! ordinal( skol16 ), ordinal(
% 4.15/4.57 skol15( X ) ) }.
% 4.15/4.57 parent0[0]: (2661) {G9,W2,D2,L1,V0,M1} S(2652);r(105) { !
% 4.15/4.57 being_limit_ordinal( skol16 ) }.
% 4.15/4.57 parent1[2]: (87) {G0,W7,D3,L3,V2,M3} I { ! ordinal( X ), ordinal( skol15( Y
% 4.15/4.57 ) ), being_limit_ordinal( X ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 end
% 4.15/4.57 substitution1:
% 4.15/4.57 X := skol16
% 4.15/4.57 Y := X
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 resolution: (24643) {G1,W3,D3,L1,V1,M1} { ordinal( skol15( X ) ) }.
% 4.15/4.57 parent0[0]: (24642) {G1,W5,D3,L2,V1,M2} { ! ordinal( skol16 ), ordinal(
% 4.15/4.57 skol15( X ) ) }.
% 4.15/4.57 parent1[0]: (92) {G0,W2,D2,L1,V0,M1} I { ordinal( skol16 ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 X := X
% 4.15/4.57 end
% 4.15/4.57 substitution1:
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 subsumption: (2671) {G10,W3,D3,L1,V1,M1} R(2661,87);r(92) { ordinal( skol15
% 4.15/4.57 ( X ) ) }.
% 4.15/4.57 parent0: (24643) {G1,W3,D3,L1,V1,M1} { ordinal( skol15( X ) ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 X := X
% 4.15/4.57 end
% 4.15/4.57 permutation0:
% 4.15/4.57 0 ==> 0
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 resolution: (24644) {G1,W2,D2,L1,V0,M1} { alpha3( skol16 ) }.
% 4.15/4.57 parent0[0]: (2661) {G9,W2,D2,L1,V0,M1} S(2652);r(105) { !
% 4.15/4.57 being_limit_ordinal( skol16 ) }.
% 4.15/4.57 parent1[1]: (95) {G0,W4,D2,L2,V0,M2} I { alpha3( skol16 ),
% 4.15/4.57 being_limit_ordinal( skol16 ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 end
% 4.15/4.57 substitution1:
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 subsumption: (2672) {G10,W2,D2,L1,V0,M1} R(2661,95) { alpha3( skol16 ) }.
% 4.15/4.57 parent0: (24644) {G1,W2,D2,L1,V0,M1} { alpha3( skol16 ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 end
% 4.15/4.57 permutation0:
% 4.15/4.57 0 ==> 0
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 eqswap: (24645) {G0,W8,D3,L3,V2,M3} { ! succ( Y ) = X, ! alpha3( X ), !
% 4.15/4.57 ordinal( Y ) }.
% 4.15/4.57 parent0[2]: (97) {G0,W8,D3,L3,V2,M3} I { ! alpha3( X ), ! ordinal( Y ), ! X
% 4.15/4.57 = succ( Y ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 X := X
% 4.15/4.57 Y := Y
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 resolution: (24646) {G1,W6,D3,L2,V1,M2} { ! succ( X ) = skol16, ! ordinal
% 4.15/4.57 ( X ) }.
% 4.15/4.57 parent0[1]: (24645) {G0,W8,D3,L3,V2,M3} { ! succ( Y ) = X, ! alpha3( X ),
% 4.15/4.57 ! ordinal( Y ) }.
% 4.15/4.57 parent1[0]: (2672) {G10,W2,D2,L1,V0,M1} R(2661,95) { alpha3( skol16 ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 X := skol16
% 4.15/4.57 Y := X
% 4.15/4.57 end
% 4.15/4.57 substitution1:
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 subsumption: (2675) {G11,W6,D3,L2,V1,M2} R(2672,97) { ! ordinal( X ), !
% 4.15/4.57 succ( X ) ==> skol16 }.
% 4.15/4.57 parent0: (24646) {G1,W6,D3,L2,V1,M2} { ! succ( X ) = skol16, ! ordinal( X
% 4.15/4.57 ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 X := X
% 4.15/4.57 end
% 4.15/4.57 permutation0:
% 4.15/4.57 0 ==> 1
% 4.15/4.57 1 ==> 0
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 resolution: (24648) {G1,W4,D4,L1,V1,M1} { ordinal( succ( skol15( X ) ) )
% 4.15/4.57 }.
% 4.15/4.57 parent0[0]: (30) {G0,W5,D3,L2,V1,M2} I { ! ordinal( X ), ordinal( succ( X )
% 4.15/4.57 ) }.
% 4.15/4.57 parent1[0]: (2671) {G10,W3,D3,L1,V1,M1} R(2661,87);r(92) { ordinal( skol15
% 4.15/4.57 ( X ) ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 X := skol15( X )
% 4.15/4.57 end
% 4.15/4.57 substitution1:
% 4.15/4.57 X := X
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 subsumption: (2699) {G11,W4,D4,L1,V1,M1} R(2671,30) { ordinal( succ( skol15
% 4.15/4.57 ( X ) ) ) }.
% 4.15/4.57 parent0: (24648) {G1,W4,D4,L1,V1,M1} { ordinal( succ( skol15( X ) ) ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 X := X
% 4.15/4.57 end
% 4.15/4.57 permutation0:
% 4.15/4.57 0 ==> 0
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 resolution: (24649) {G1,W3,D3,L1,V1,M1} { alpha2( skol15( X ) ) }.
% 4.15/4.57 parent0[0]: (29) {G0,W4,D2,L2,V1,M2} I { ! ordinal( X ), alpha2( X ) }.
% 4.15/4.57 parent1[0]: (2671) {G10,W3,D3,L1,V1,M1} R(2661,87);r(92) { ordinal( skol15
% 4.15/4.57 ( X ) ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 X := skol15( X )
% 4.15/4.57 end
% 4.15/4.57 substitution1:
% 4.15/4.57 X := X
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 subsumption: (2700) {G11,W3,D3,L1,V1,M1} R(2671,29) { alpha2( skol15( X ) )
% 4.15/4.57 }.
% 4.15/4.57 parent0: (24649) {G1,W3,D3,L1,V1,M1} { alpha2( skol15( X ) ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 X := X
% 4.15/4.57 end
% 4.15/4.57 permutation0:
% 4.15/4.57 0 ==> 0
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 resolution: (24650) {G1,W4,D4,L1,V1,M1} { epsilon_transitive( succ( skol15
% 4.15/4.57 ( X ) ) ) }.
% 4.15/4.57 parent0[0]: (31) {G0,W5,D3,L2,V1,M2} I { ! alpha2( X ), epsilon_transitive
% 4.15/4.57 ( succ( X ) ) }.
% 4.15/4.57 parent1[0]: (2700) {G11,W3,D3,L1,V1,M1} R(2671,29) { alpha2( skol15( X ) )
% 4.15/4.57 }.
% 4.15/4.57 substitution0:
% 4.15/4.57 X := skol15( X )
% 4.15/4.57 end
% 4.15/4.57 substitution1:
% 4.15/4.57 X := X
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 subsumption: (2707) {G12,W4,D4,L1,V1,M1} R(2700,31) { epsilon_transitive(
% 4.15/4.57 succ( skol15( X ) ) ) }.
% 4.15/4.57 parent0: (24650) {G1,W4,D4,L1,V1,M1} { epsilon_transitive( succ( skol15( X
% 4.15/4.57 ) ) ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 X := X
% 4.15/4.57 end
% 4.15/4.57 permutation0:
% 4.15/4.57 0 ==> 0
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 resolution: (24651) {G1,W5,D4,L1,V0,M1} { ! in( succ( skol15( skol16 ) ),
% 4.15/4.57 skol16 ) }.
% 4.15/4.57 parent0[0]: (2670) {G10,W4,D3,L1,V0,M1} R(2661,88);r(92) { ! alpha1( skol16
% 4.15/4.57 , skol15( skol16 ) ) }.
% 4.15/4.57 parent1[1]: (91) {G0,W7,D3,L2,V2,M2} I { ! in( succ( Y ), X ), alpha1( X, Y
% 4.15/4.57 ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 end
% 4.15/4.57 substitution1:
% 4.15/4.57 X := skol16
% 4.15/4.57 Y := skol15( skol16 )
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 subsumption: (2719) {G11,W5,D4,L1,V0,M1} R(2670,91) { ! in( succ( skol15(
% 4.15/4.57 skol16 ) ), skol16 ) }.
% 4.15/4.57 parent0: (24651) {G1,W5,D4,L1,V0,M1} { ! in( succ( skol15( skol16 ) ),
% 4.15/4.57 skol16 ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 end
% 4.15/4.57 permutation0:
% 4.15/4.57 0 ==> 0
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 resolution: (24652) {G1,W4,D3,L1,V0,M1} { in( skol15( skol16 ), skol16 )
% 4.15/4.57 }.
% 4.15/4.57 parent0[0]: (2670) {G10,W4,D3,L1,V0,M1} R(2661,88);r(92) { ! alpha1( skol16
% 4.15/4.57 , skol15( skol16 ) ) }.
% 4.15/4.57 parent1[1]: (90) {G0,W6,D2,L2,V2,M2} I { in( Y, X ), alpha1( X, Y ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 end
% 4.15/4.57 substitution1:
% 4.15/4.57 X := skol16
% 4.15/4.57 Y := skol15( skol16 )
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 subsumption: (2720) {G11,W4,D3,L1,V0,M1} R(2670,90) { in( skol15( skol16 )
% 4.15/4.57 , skol16 ) }.
% 4.15/4.57 parent0: (24652) {G1,W4,D3,L1,V0,M1} { in( skol15( skol16 ), skol16 ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 end
% 4.15/4.57 permutation0:
% 4.15/4.57 0 ==> 0
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 resolution: (24653) {G1,W10,D4,L3,V0,M3} { ! ordinal( skol15( skol16 ) ),
% 4.15/4.57 ! ordinal( skol16 ), ordinal_subset( succ( skol15( skol16 ) ), skol16 )
% 4.15/4.57 }.
% 4.15/4.57 parent0[2]: (82) {G0,W11,D3,L4,V2,M4} I { ! ordinal( X ), ! ordinal( Y ), !
% 4.15/4.57 in( X, Y ), ordinal_subset( succ( X ), Y ) }.
% 4.15/4.57 parent1[0]: (2720) {G11,W4,D3,L1,V0,M1} R(2670,90) { in( skol15( skol16 ),
% 4.15/4.57 skol16 ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 X := skol15( skol16 )
% 4.15/4.57 Y := skol16
% 4.15/4.57 end
% 4.15/4.57 substitution1:
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 resolution: (24654) {G2,W7,D4,L2,V0,M2} { ! ordinal( skol16 ),
% 4.15/4.57 ordinal_subset( succ( skol15( skol16 ) ), skol16 ) }.
% 4.15/4.57 parent0[0]: (24653) {G1,W10,D4,L3,V0,M3} { ! ordinal( skol15( skol16 ) ),
% 4.15/4.57 ! ordinal( skol16 ), ordinal_subset( succ( skol15( skol16 ) ), skol16 )
% 4.15/4.57 }.
% 4.15/4.57 parent1[0]: (2671) {G10,W3,D3,L1,V1,M1} R(2661,87);r(92) { ordinal( skol15
% 4.15/4.57 ( X ) ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 end
% 4.15/4.57 substitution1:
% 4.15/4.57 X := skol16
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 subsumption: (2723) {G12,W7,D4,L2,V0,M2} R(2720,82);r(2671) { ! ordinal(
% 4.15/4.57 skol16 ), ordinal_subset( succ( skol15( skol16 ) ), skol16 ) }.
% 4.15/4.57 parent0: (24654) {G2,W7,D4,L2,V0,M2} { ! ordinal( skol16 ), ordinal_subset
% 4.15/4.57 ( succ( skol15( skol16 ) ), skol16 ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 end
% 4.15/4.57 permutation0:
% 4.15/4.57 0 ==> 0
% 4.15/4.57 1 ==> 1
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 resolution: (24655) {G1,W11,D4,L3,V0,M3} { ! epsilon_transitive( succ(
% 4.15/4.57 skol15( skol16 ) ) ), ! ordinal( skol16 ), ! proper_subset( succ( skol15
% 4.15/4.57 ( skol16 ) ), skol16 ) }.
% 4.15/4.57 parent0[0]: (2719) {G11,W5,D4,L1,V0,M1} R(2670,91) { ! in( succ( skol15(
% 4.15/4.57 skol16 ) ), skol16 ) }.
% 4.15/4.57 parent1[3]: (80) {G0,W10,D2,L4,V2,M4} I { ! epsilon_transitive( X ), !
% 4.15/4.57 ordinal( Y ), ! proper_subset( X, Y ), in( X, Y ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 end
% 4.15/4.57 substitution1:
% 4.15/4.57 X := succ( skol15( skol16 ) )
% 4.15/4.57 Y := skol16
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 resolution: (24656) {G2,W7,D4,L2,V0,M2} { ! ordinal( skol16 ), !
% 4.15/4.57 proper_subset( succ( skol15( skol16 ) ), skol16 ) }.
% 4.15/4.57 parent0[0]: (24655) {G1,W11,D4,L3,V0,M3} { ! epsilon_transitive( succ(
% 4.15/4.57 skol15( skol16 ) ) ), ! ordinal( skol16 ), ! proper_subset( succ( skol15
% 4.15/4.57 ( skol16 ) ), skol16 ) }.
% 4.15/4.57 parent1[0]: (2707) {G12,W4,D4,L1,V1,M1} R(2700,31) { epsilon_transitive(
% 4.15/4.57 succ( skol15( X ) ) ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 end
% 4.15/4.57 substitution1:
% 4.15/4.57 X := skol16
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 subsumption: (3972) {G13,W7,D4,L2,V0,M2} R(2719,80);r(2707) { ! ordinal(
% 4.15/4.57 skol16 ), ! proper_subset( succ( skol15( skol16 ) ), skol16 ) }.
% 4.15/4.57 parent0: (24656) {G2,W7,D4,L2,V0,M2} { ! ordinal( skol16 ), !
% 4.15/4.57 proper_subset( succ( skol15( skol16 ) ), skol16 ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 end
% 4.15/4.57 permutation0:
% 4.15/4.57 0 ==> 0
% 4.15/4.57 1 ==> 1
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 eqswap: (24657) {G11,W6,D3,L2,V1,M2} { ! skol16 ==> succ( X ), ! ordinal(
% 4.15/4.57 X ) }.
% 4.15/4.57 parent0[1]: (2675) {G11,W6,D3,L2,V1,M2} R(2672,97) { ! ordinal( X ), ! succ
% 4.15/4.57 ( X ) ==> skol16 }.
% 4.15/4.57 substitution0:
% 4.15/4.57 X := X
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 resolution: (24658) {G11,W5,D4,L1,V1,M1} { ! skol16 ==> succ( skol15( X )
% 4.15/4.57 ) }.
% 4.15/4.57 parent0[1]: (24657) {G11,W6,D3,L2,V1,M2} { ! skol16 ==> succ( X ), !
% 4.15/4.57 ordinal( X ) }.
% 4.15/4.57 parent1[0]: (2671) {G10,W3,D3,L1,V1,M1} R(2661,87);r(92) { ordinal( skol15
% 4.15/4.57 ( X ) ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 X := skol15( X )
% 4.15/4.57 end
% 4.15/4.57 substitution1:
% 4.15/4.57 X := X
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 eqswap: (24659) {G11,W5,D4,L1,V1,M1} { ! succ( skol15( X ) ) ==> skol16
% 4.15/4.57 }.
% 4.15/4.57 parent0[0]: (24658) {G11,W5,D4,L1,V1,M1} { ! skol16 ==> succ( skol15( X )
% 4.15/4.57 ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 X := X
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 subsumption: (5916) {G12,W5,D4,L1,V1,M1} R(2675,2671) { ! succ( skol15( X )
% 4.15/4.57 ) ==> skol16 }.
% 4.15/4.57 parent0: (24659) {G11,W5,D4,L1,V1,M1} { ! succ( skol15( X ) ) ==> skol16
% 4.15/4.57 }.
% 4.15/4.57 substitution0:
% 4.15/4.57 X := X
% 4.15/4.57 end
% 4.15/4.57 permutation0:
% 4.15/4.57 0 ==> 0
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 resolution: (24660) {G1,W5,D4,L1,V0,M1} { ! proper_subset( succ( skol15(
% 4.15/4.57 skol16 ) ), skol16 ) }.
% 4.15/4.57 parent0[0]: (3972) {G13,W7,D4,L2,V0,M2} R(2719,80);r(2707) { ! ordinal(
% 4.15/4.57 skol16 ), ! proper_subset( succ( skol15( skol16 ) ), skol16 ) }.
% 4.15/4.57 parent1[0]: (92) {G0,W2,D2,L1,V0,M1} I { ordinal( skol16 ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 end
% 4.15/4.57 substitution1:
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 subsumption: (20054) {G14,W5,D4,L1,V0,M1} S(3972);r(92) { ! proper_subset(
% 4.15/4.57 succ( skol15( skol16 ) ), skol16 ) }.
% 4.15/4.57 parent0: (24660) {G1,W5,D4,L1,V0,M1} { ! proper_subset( succ( skol15(
% 4.15/4.57 skol16 ) ), skol16 ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 end
% 4.15/4.57 permutation0:
% 4.15/4.57 0 ==> 0
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 resolution: (24661) {G1,W5,D4,L1,V0,M1} { ordinal_subset( succ( skol15(
% 4.15/4.57 skol16 ) ), skol16 ) }.
% 4.15/4.57 parent0[0]: (2723) {G12,W7,D4,L2,V0,M2} R(2720,82);r(2671) { ! ordinal(
% 4.15/4.57 skol16 ), ordinal_subset( succ( skol15( skol16 ) ), skol16 ) }.
% 4.15/4.57 parent1[0]: (92) {G0,W2,D2,L1,V0,M1} I { ordinal( skol16 ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 end
% 4.15/4.57 substitution1:
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 subsumption: (20062) {G13,W5,D4,L1,V0,M1} S(2723);r(92) { ordinal_subset(
% 4.15/4.57 succ( skol15( skol16 ) ), skol16 ) }.
% 4.15/4.57 parent0: (24661) {G1,W5,D4,L1,V0,M1} { ordinal_subset( succ( skol15(
% 4.15/4.57 skol16 ) ), skol16 ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 end
% 4.15/4.57 permutation0:
% 4.15/4.57 0 ==> 0
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 resolution: (24662) {G2,W9,D4,L2,V0,M2} { ! ordinal( succ( skol15( skol16
% 4.15/4.57 ) ) ), subset( succ( skol15( skol16 ) ), skol16 ) }.
% 4.15/4.57 parent0[1]: (552) {G1,W8,D2,L3,V1,M3} R(73,92) { ! ordinal( X ), !
% 4.15/4.57 ordinal_subset( X, skol16 ), subset( X, skol16 ) }.
% 4.15/4.57 parent1[0]: (20062) {G13,W5,D4,L1,V0,M1} S(2723);r(92) { ordinal_subset(
% 4.15/4.57 succ( skol15( skol16 ) ), skol16 ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 X := succ( skol15( skol16 ) )
% 4.15/4.57 end
% 4.15/4.57 substitution1:
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 resolution: (24663) {G3,W5,D4,L1,V0,M1} { subset( succ( skol15( skol16 ) )
% 4.15/4.57 , skol16 ) }.
% 4.15/4.57 parent0[0]: (24662) {G2,W9,D4,L2,V0,M2} { ! ordinal( succ( skol15( skol16
% 4.15/4.57 ) ) ), subset( succ( skol15( skol16 ) ), skol16 ) }.
% 4.15/4.57 parent1[0]: (2699) {G11,W4,D4,L1,V1,M1} R(2671,30) { ordinal( succ( skol15
% 4.15/4.57 ( X ) ) ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 end
% 4.15/4.57 substitution1:
% 4.15/4.57 X := skol16
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 subsumption: (23986) {G14,W5,D4,L1,V0,M1} R(552,20062);r(2699) { subset(
% 4.15/4.57 succ( skol15( skol16 ) ), skol16 ) }.
% 4.15/4.57 parent0: (24663) {G3,W5,D4,L1,V0,M1} { subset( succ( skol15( skol16 ) ),
% 4.15/4.57 skol16 ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 end
% 4.15/4.57 permutation0:
% 4.15/4.57 0 ==> 0
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 eqswap: (24664) {G0,W9,D2,L3,V2,M3} { Y = X, ! subset( X, Y ),
% 4.15/4.57 proper_subset( X, Y ) }.
% 4.15/4.57 parent0[1]: (16) {G0,W9,D2,L3,V2,M3} I { ! subset( X, Y ), X = Y,
% 4.15/4.57 proper_subset( X, Y ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 X := X
% 4.15/4.57 Y := Y
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 resolution: (24665) {G1,W10,D4,L2,V0,M2} { skol16 = succ( skol15( skol16 )
% 4.15/4.57 ), proper_subset( succ( skol15( skol16 ) ), skol16 ) }.
% 4.15/4.57 parent0[1]: (24664) {G0,W9,D2,L3,V2,M3} { Y = X, ! subset( X, Y ),
% 4.15/4.57 proper_subset( X, Y ) }.
% 4.15/4.57 parent1[0]: (23986) {G14,W5,D4,L1,V0,M1} R(552,20062);r(2699) { subset(
% 4.15/4.57 succ( skol15( skol16 ) ), skol16 ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 X := succ( skol15( skol16 ) )
% 4.15/4.57 Y := skol16
% 4.15/4.57 end
% 4.15/4.57 substitution1:
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 resolution: (24666) {G2,W5,D4,L1,V0,M1} { skol16 = succ( skol15( skol16 )
% 4.15/4.57 ) }.
% 4.15/4.57 parent0[0]: (20054) {G14,W5,D4,L1,V0,M1} S(3972);r(92) { ! proper_subset(
% 4.15/4.57 succ( skol15( skol16 ) ), skol16 ) }.
% 4.15/4.57 parent1[1]: (24665) {G1,W10,D4,L2,V0,M2} { skol16 = succ( skol15( skol16 )
% 4.15/4.57 ), proper_subset( succ( skol15( skol16 ) ), skol16 ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 end
% 4.15/4.57 substitution1:
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 eqswap: (24667) {G2,W5,D4,L1,V0,M1} { succ( skol15( skol16 ) ) = skol16
% 4.15/4.57 }.
% 4.15/4.57 parent0[0]: (24666) {G2,W5,D4,L1,V0,M1} { skol16 = succ( skol15( skol16 )
% 4.15/4.57 ) }.
% 4.15/4.57 substitution0:
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 subsumption: (24033) {G15,W5,D4,L1,V0,M1} R(23986,16);r(20054) { succ(
% 4.15/4.57 skol15( skol16 ) ) ==> skol16 }.
% 4.15/4.57 parent0: (24667) {G2,W5,D4,L1,V0,M1} { succ( skol15( skol16 ) ) = skol16
% 4.15/4.57 }.
% 4.15/4.57 substitution0:
% 4.15/4.57 end
% 4.15/4.57 permutation0:
% 4.15/4.57 0 ==> 0
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 resolution: (24670) {G13,W0,D0,L0,V0,M0} { }.
% 4.15/4.57 parent0[0]: (5916) {G12,W5,D4,L1,V1,M1} R(2675,2671) { ! succ( skol15( X )
% 4.15/4.57 ) ==> skol16 }.
% 4.15/4.57 parent1[0]: (24033) {G15,W5,D4,L1,V0,M1} R(23986,16);r(20054) { succ(
% 4.15/4.57 skol15( skol16 ) ) ==> skol16 }.
% 4.15/4.57 substitution0:
% 4.15/4.57 X := skol16
% 4.15/4.57 end
% 4.15/4.57 substitution1:
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 subsumption: (24046) {G16,W0,D0,L0,V0,M0} S(24033);r(5916) { }.
% 4.15/4.57 parent0: (24670) {G13,W0,D0,L0,V0,M0} { }.
% 4.15/4.57 substitution0:
% 4.15/4.57 end
% 4.15/4.57 permutation0:
% 4.15/4.57 end
% 4.15/4.57
% 4.15/4.57 Proof check complete!
% 4.15/4.57
% 4.15/4.57 Memory use:
% 4.15/4.57
% 4.15/4.57 space for terms: 292208
% 4.15/4.57 space for clauses: 1116294
% 4.15/4.57
% 4.15/4.57
% 4.15/4.57 clauses generated: 77148
% 4.15/4.57 clauses kept: 24047
% 4.15/4.57 clauses selected: 1391
% 4.15/4.57 clauses deleted: 2022
% 4.15/4.57 clauses inuse deleted: 136
% 4.15/4.57
% 4.15/4.57 subsentry: 220636
% 4.15/4.57 literals s-matched: 126952
% 4.15/4.57 literals matched: 120573
% 4.15/4.57 full subsumption: 25034
% 4.15/4.57
% 4.15/4.57 checksum: 1719278678
% 4.15/4.57
% 4.15/4.57
% 4.15/4.57 Bliksem ended
%------------------------------------------------------------------------------