%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SEU112+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n005.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 07:10:40 EDT 2022
% Result : Theorem 2.59s 3.00s
% Output : Refutation 2.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU112+1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n005.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 : Mon Jun 20 11:27:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.30/2.71 *** allocated 10000 integers for termspace/termends
% 2.30/2.71 *** allocated 10000 integers for clauses
% 2.30/2.71 *** allocated 10000 integers for justifications
% 2.30/2.71 Bliksem 1.12
% 2.30/2.71
% 2.30/2.71
% 2.30/2.71 Automatic Strategy Selection
% 2.30/2.71
% 2.30/2.71
% 2.30/2.71 Clauses:
% 2.30/2.71
% 2.30/2.71 { ! in( X, Y ), ! in( Y, X ) }.
% 2.30/2.71 { ! empty( X ), finite( X ) }.
% 2.30/2.71 { ! preboolean( X ), cup_closed( X ) }.
% 2.30/2.71 { ! preboolean( X ), diff_closed( X ) }.
% 2.30/2.71 { ! finite( X ), ! element( Y, powerset( X ) ), finite( Y ) }.
% 2.30/2.71 { ! cup_closed( X ), ! diff_closed( X ), preboolean( X ) }.
% 2.30/2.71 { ! element( X, finite_subsets( Y ) ), finite( X ) }.
% 2.30/2.71 { set_union2( X, Y ) = set_union2( Y, X ) }.
% 2.30/2.71 { preboolean( finite_subsets( X ) ) }.
% 2.30/2.71 { element( skol1( X ), X ) }.
% 2.30/2.71 { ! empty( powerset( X ) ) }.
% 2.30/2.71 { cup_closed( powerset( X ) ) }.
% 2.30/2.71 { diff_closed( powerset( X ) ) }.
% 2.30/2.71 { preboolean( powerset( X ) ) }.
% 2.30/2.71 { ! empty( powerset( X ) ) }.
% 2.30/2.71 { empty( empty_set ) }.
% 2.30/2.71 { ! empty( finite_subsets( X ) ) }.
% 2.30/2.71 { cup_closed( finite_subsets( X ) ) }.
% 2.30/2.71 { diff_closed( finite_subsets( X ) ) }.
% 2.30/2.71 { preboolean( finite_subsets( X ) ) }.
% 2.30/2.71 { empty( X ), ! empty( set_union2( X, Y ) ) }.
% 2.30/2.71 { empty( X ), ! empty( set_union2( Y, X ) ) }.
% 2.30/2.71 { ! finite( X ), ! finite( Y ), finite( set_union2( X, Y ) ) }.
% 2.30/2.71 { set_union2( X, X ) = X }.
% 2.30/2.71 { ! empty( skol2 ) }.
% 2.30/2.71 { finite( skol2 ) }.
% 2.30/2.71 { ! empty( skol3 ) }.
% 2.30/2.71 { cup_closed( skol3 ) }.
% 2.30/2.71 { cap_closed( skol3 ) }.
% 2.30/2.71 { diff_closed( skol3 ) }.
% 2.30/2.71 { preboolean( skol3 ) }.
% 2.30/2.71 { empty( X ), ! empty( skol4( Y ) ) }.
% 2.30/2.71 { empty( X ), element( skol4( X ), powerset( X ) ) }.
% 2.30/2.71 { empty( skol5 ) }.
% 2.30/2.71 { empty( skol6( Y ) ) }.
% 2.30/2.71 { relation( skol6( Y ) ) }.
% 2.30/2.71 { function( skol6( Y ) ) }.
% 2.30/2.71 { one_to_one( skol6( Y ) ) }.
% 2.30/2.71 { epsilon_transitive( skol6( Y ) ) }.
% 2.30/2.71 { epsilon_connected( skol6( Y ) ) }.
% 2.30/2.71 { ordinal( skol6( Y ) ) }.
% 2.30/2.71 { natural( skol6( Y ) ) }.
% 2.30/2.71 { finite( skol6( Y ) ) }.
% 2.30/2.71 { element( skol6( X ), powerset( X ) ) }.
% 2.30/2.71 { empty( skol7( Y ) ) }.
% 2.30/2.71 { element( skol7( X ), powerset( X ) ) }.
% 2.30/2.71 { ! empty( skol8 ) }.
% 2.30/2.71 { empty( X ), ! empty( skol9( Y ) ) }.
% 2.30/2.71 { empty( X ), finite( skol9( Y ) ) }.
% 2.30/2.71 { empty( X ), element( skol9( X ), powerset( X ) ) }.
% 2.30/2.71 { empty( X ), ! empty( skol10( Y ) ) }.
% 2.30/2.71 { empty( X ), finite( skol10( Y ) ) }.
% 2.30/2.71 { empty( X ), element( skol10( X ), powerset( X ) ) }.
% 2.30/2.71 { subset( X, X ) }.
% 2.30/2.71 { set_union2( X, empty_set ) = X }.
% 2.30/2.71 { ! in( X, Y ), element( X, Y ) }.
% 2.30/2.71 { ! subset( X, Y ), subset( finite_subsets( X ), finite_subsets( Y ) ) }.
% 2.30/2.71 { ! subset( set_union2( finite_subsets( skol11 ), finite_subsets( skol12 )
% 2.30/2.71 ), finite_subsets( set_union2( skol11, skol12 ) ) ) }.
% 2.30/2.71 { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 2.30/2.71 { ! element( X, powerset( Y ) ), subset( X, Y ) }.
% 2.30/2.71 { ! subset( X, Y ), element( X, powerset( Y ) ) }.
% 2.30/2.71 { ! in( X, Z ), ! element( Z, powerset( Y ) ), element( X, Y ) }.
% 2.30/2.71 { ! in( X, Y ), ! element( Y, powerset( Z ) ), ! empty( Z ) }.
% 2.30/2.71 { ! empty( X ), X = empty_set }.
% 2.30/2.71 { ! in( X, Y ), ! empty( Y ) }.
% 2.30/2.71 { subset( X, set_union2( X, Y ) ) }.
% 2.30/2.71 { ! empty( X ), X = Y, ! empty( Y ) }.
% 2.30/2.71 { ! subset( X, Y ), ! subset( Z, Y ), subset( set_union2( X, Z ), Y ) }.
% 2.30/2.71
% 2.30/2.71 percentage equality = 0.048544, percentage horn = 0.909091
% 2.30/2.71 This is a problem with some equality
% 2.30/2.71
% 2.30/2.71
% 2.30/2.71
% 2.30/2.71 Options Used:
% 2.30/2.71
% 2.30/2.71 useres = 1
% 2.30/2.71 useparamod = 1
% 2.30/2.71 useeqrefl = 1
% 2.30/2.71 useeqfact = 1
% 2.30/2.71 usefactor = 1
% 2.30/2.71 usesimpsplitting = 0
% 2.30/2.71 usesimpdemod = 5
% 2.30/2.71 usesimpres = 3
% 2.30/2.71
% 2.30/2.71 resimpinuse = 1000
% 2.30/2.71 resimpclauses = 20000
% 2.30/2.71 substype = eqrewr
% 2.30/2.71 backwardsubs = 1
% 2.30/2.71 selectoldest = 5
% 2.30/2.71
% 2.30/2.71 litorderings [0] = split
% 2.30/2.71 litorderings [1] = extend the termordering, first sorting on arguments
% 2.30/2.71
% 2.30/2.71 termordering = kbo
% 2.30/2.71
% 2.30/2.71 litapriori = 0
% 2.30/2.71 termapriori = 1
% 2.30/2.71 litaposteriori = 0
% 2.30/2.71 termaposteriori = 0
% 2.30/2.71 demodaposteriori = 0
% 2.30/2.71 ordereqreflfact = 0
% 2.30/2.71
% 2.30/2.71 litselect = negord
% 2.30/2.71
% 2.30/2.71 maxweight = 15
% 2.30/2.71 maxdepth = 30000
% 2.30/2.71 maxlength = 115
% 2.30/2.71 maxnrvars = 195
% 2.30/2.71 excuselevel = 1
% 2.30/2.71 increasemaxweight = 1
% 2.30/2.71
% 2.30/2.71 maxselected = 10000000
% 2.30/2.71 maxnrclauses = 10000000
% 2.30/2.71
% 2.30/2.71 showgenerated = 0
% 2.30/2.71 showkept = 0
% 2.30/2.71 showselected = 0
% 2.30/2.71 showdeleted = 0
% 2.30/2.71 showresimp = 1
% 2.30/2.71 showstatus = 2000
% 2.30/2.71
% 2.30/2.71 prologoutput = 0
% 2.30/2.71 nrgoals = 5000000
% 2.30/2.71 totalproof = 1
% 2.30/2.71
% 2.30/2.71 Symbols occurring in the translation:
% 2.30/2.71
% 2.30/2.71 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 2.30/2.71 . [1, 2] (w:1, o:42, a:1, s:1, b:0),
% 2.59/3.00 ! [4, 1] (w:0, o:16, a:1, s:1, b:0),
% 2.59/3.00 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.59/3.00 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.59/3.00 in [37, 2] (w:1, o:66, a:1, s:1, b:0),
% 2.59/3.00 empty [38, 1] (w:1, o:23, a:1, s:1, b:0),
% 2.59/3.00 finite [39, 1] (w:1, o:26, a:1, s:1, b:0),
% 2.59/3.00 preboolean [40, 1] (w:1, o:30, a:1, s:1, b:0),
% 2.59/3.00 cup_closed [41, 1] (w:1, o:31, a:1, s:1, b:0),
% 2.59/3.00 diff_closed [42, 1] (w:1, o:22, a:1, s:1, b:0),
% 2.59/3.00 powerset [43, 1] (w:1, o:32, a:1, s:1, b:0),
% 2.59/3.00 element [44, 2] (w:1, o:67, a:1, s:1, b:0),
% 2.59/3.00 finite_subsets [45, 1] (w:1, o:33, a:1, s:1, b:0),
% 2.59/3.00 set_union2 [46, 2] (w:1, o:68, a:1, s:1, b:0),
% 2.59/3.00 empty_set [47, 0] (w:1, o:8, a:1, s:1, b:0),
% 2.59/3.00 cap_closed [48, 1] (w:1, o:21, a:1, s:1, b:0),
% 2.59/3.00 relation [49, 1] (w:1, o:34, a:1, s:1, b:0),
% 2.59/3.00 function [50, 1] (w:1, o:35, a:1, s:1, b:0),
% 2.59/3.00 one_to_one [51, 1] (w:1, o:28, a:1, s:1, b:0),
% 2.59/3.00 epsilon_transitive [52, 1] (w:1, o:24, a:1, s:1, b:0),
% 2.59/3.00 epsilon_connected [53, 1] (w:1, o:25, a:1, s:1, b:0),
% 2.59/3.00 ordinal [54, 1] (w:1, o:29, a:1, s:1, b:0),
% 2.59/3.00 natural [55, 1] (w:1, o:27, a:1, s:1, b:0),
% 2.59/3.00 subset [56, 2] (w:1, o:69, a:1, s:1, b:0),
% 2.59/3.00 skol1 [58, 1] (w:1, o:36, a:1, s:1, b:1),
% 2.59/3.00 skol2 [59, 0] (w:1, o:12, a:1, s:1, b:1),
% 2.59/3.00 skol3 [60, 0] (w:1, o:13, a:1, s:1, b:1),
% 2.59/3.00 skol4 [61, 1] (w:1, o:37, a:1, s:1, b:1),
% 2.59/3.00 skol5 [62, 0] (w:1, o:14, a:1, s:1, b:1),
% 2.59/3.00 skol6 [63, 1] (w:1, o:38, a:1, s:1, b:1),
% 2.59/3.00 skol7 [64, 1] (w:1, o:39, a:1, s:1, b:1),
% 2.59/3.00 skol8 [65, 0] (w:1, o:15, a:1, s:1, b:1),
% 2.59/3.00 skol9 [66, 1] (w:1, o:40, a:1, s:1, b:1),
% 2.59/3.00 skol10 [67, 1] (w:1, o:41, a:1, s:1, b:1),
% 2.59/3.00 skol11 [68, 0] (w:1, o:10, a:1, s:1, b:1),
% 2.59/3.00 skol12 [69, 0] (w:1, o:11, a:1, s:1, b:1).
% 2.59/3.00
% 2.59/3.00
% 2.59/3.00 Starting Search:
% 2.59/3.00
% 2.59/3.00 *** allocated 15000 integers for clauses
% 2.59/3.00 *** allocated 22500 integers for clauses
% 2.59/3.00 *** allocated 33750 integers for clauses
% 2.59/3.00 *** allocated 50625 integers for clauses
% 2.59/3.00 *** allocated 75937 integers for clauses
% 2.59/3.00 *** allocated 15000 integers for termspace/termends
% 2.59/3.00 Resimplifying inuse:
% 2.59/3.00 Done
% 2.59/3.00
% 2.59/3.00 *** allocated 22500 integers for termspace/termends
% 2.59/3.00 *** allocated 113905 integers for clauses
% 2.59/3.00
% 2.59/3.00 Intermediate Status:
% 2.59/3.00 Generated: 5659
% 2.59/3.00 Kept: 2009
% 2.59/3.00 Inuse: 303
% 2.59/3.00 Deleted: 36
% 2.59/3.00 Deletedinuse: 21
% 2.59/3.00
% 2.59/3.00 Resimplifying inuse:
% 2.59/3.00 Done
% 2.59/3.00
% 2.59/3.00 *** allocated 33750 integers for termspace/termends
% 2.59/3.00 *** allocated 170857 integers for clauses
% 2.59/3.00 *** allocated 50625 integers for termspace/termends
% 2.59/3.00 Resimplifying inuse:
% 2.59/3.00 Done
% 2.59/3.00
% 2.59/3.00 *** allocated 256285 integers for clauses
% 2.59/3.00
% 2.59/3.00 Intermediate Status:
% 2.59/3.00 Generated: 11538
% 2.59/3.00 Kept: 4009
% 2.59/3.00 Inuse: 406
% 2.59/3.00 Deleted: 49
% 2.59/3.00 Deletedinuse: 21
% 2.59/3.00
% 2.59/3.00 Resimplifying inuse:
% 2.59/3.00 Done
% 2.59/3.00
% 2.59/3.00 *** allocated 75937 integers for termspace/termends
% 2.59/3.00 Resimplifying inuse:
% 2.59/3.00 Done
% 2.59/3.00
% 2.59/3.00 *** allocated 384427 integers for clauses
% 2.59/3.00
% 2.59/3.00 Intermediate Status:
% 2.59/3.00 Generated: 17118
% 2.59/3.00 Kept: 6011
% 2.59/3.00 Inuse: 489
% 2.59/3.00 Deleted: 49
% 2.59/3.00 Deletedinuse: 21
% 2.59/3.00
% 2.59/3.00 Resimplifying inuse:
% 2.59/3.00 Done
% 2.59/3.00
% 2.59/3.00 *** allocated 113905 integers for termspace/termends
% 2.59/3.00 Resimplifying inuse:
% 2.59/3.00 Done
% 2.59/3.00
% 2.59/3.00
% 2.59/3.00 Intermediate Status:
% 2.59/3.00 Generated: 27504
% 2.59/3.00 Kept: 8013
% 2.59/3.00 Inuse: 608
% 2.59/3.00 Deleted: 61
% 2.59/3.00 Deletedinuse: 21
% 2.59/3.00
% 2.59/3.00 *** allocated 576640 integers for clauses
% 2.59/3.00 Resimplifying inuse:
% 2.59/3.00 Done
% 2.59/3.00
% 2.59/3.00 Resimplifying inuse:
% 2.59/3.00 Done
% 2.59/3.00
% 2.59/3.00 *** allocated 170857 integers for termspace/termends
% 2.59/3.00
% 2.59/3.00 Intermediate Status:
% 2.59/3.00 Generated: 38227
% 2.59/3.00 Kept: 10060
% 2.59/3.00 Inuse: 729
% 2.59/3.00 Deleted: 103
% 2.59/3.00 Deletedinuse: 36
% 2.59/3.00
% 2.59/3.00 Resimplifying inuse:
% 2.59/3.00 Done
% 2.59/3.00
% 2.59/3.00 Resimplifying inuse:
% 2.59/3.00 Done
% 2.59/3.00
% 2.59/3.00
% 2.59/3.00 Intermediate Status:
% 2.59/3.00 Generated: 50901
% 2.59/3.00 Kept: 12063
% 2.59/3.00 Inuse: 836
% 2.59/3.00 Deleted: 103
% 2.59/3.00 Deletedinuse: 36
% 2.59/3.00
% 2.59/3.00 Resimplifying inuse:
% 2.59/3.00 Done
% 2.59/3.00
% 2.59/3.00 *** allocated 864960 integers for clauses
% 2.59/3.00 Resimplifying inuse:
% 2.59/3.00 Done
% 2.59/3.00
% 2.59/3.00 *** allocated 256285 integers for termspace/termends
% 2.59/3.00
% 2.59/3.00 Intermediate Status:
% 2.59/3.00 Generated: 65264
% 2.59/3.00 Kept: 14083
% 2.59/3.00 Inuse: 876
% 2.59/3.00 Deleted: 106
% 2.59/3.00 Deletedinuse: 36
% 2.59/3.00
% 2.59/3.00 Resimplifying inuse:
% 2.59/3.00 Done
% 2.59/3.00
% 2.59/3.00 Resimplifying inuse:
% 2.59/3.00 Done
% 2.59/3.00
% 2.59/3.00
% 2.59/3.00 Intermediate Status:
% 2.59/3.00 Generated: 80792
% 2.59/3.00 Kept: 16096
% 2.59/3.00 Inuse: 1023
% 2.59/3.00 Deleted: 142
% 2.59/3.00 Deletedinuse: 36
% 2.59/3.00
% 2.59/3.00 Resimplifying inuse:
% 2.59/3.00 Done
% 2.59/3.00
% 2.59/3.00 Resimplifying inuse:
% 2.59/3.00 Done
% 2.59/3.00
% 2.59/3.00
% 2.59/3.00 Intermediate Status:
% 2.59/3.00 Generated: 90703
% 2.59/3.00 Kept: 18115
% 2.59/3.00 Inuse: 1111
% 2.59/3.00 Deleted: 143
% 2.59/3.00 Deletedinuse: 37
% 2.59/3.00
% 2.59/3.00 *** allocated 1297440 integers for clauses
% 2.59/3.00 Resimplifying inuse:
% 2.59/3.00 Done
% 2.59/3.00
% 2.59/3.00 Resimplifying inuse:
% 2.59/3.00 Done
% 2.59/3.00
% 2.59/3.00
% 2.59/3.00 Intermediate Status:
% 2.59/3.00 Generated: 102176
% 2.59/3.00 Kept: 20169
% 2.59/3.00 Inuse: 1215
% 2.59/3.00 Deleted: 143
% 2.59/3.00 Deletedinuse: 37
% 2.59/3.00
% 2.59/3.00 Resimplifying clauses:
% 2.59/3.00
% 2.59/3.00 Bliksems!, er is een bewijs:
% 2.59/3.00 % SZS status Theorem
% 2.59/3.00 % SZS output start Refutation
% 2.59/3.00
% 2.59/3.00 (7) {G0,W7,D3,L1,V2,M1} I { set_union2( X, Y ) = set_union2( Y, X ) }.
% 2.59/3.00 (54) {G0,W8,D3,L2,V2,M2} I { ! subset( X, Y ), subset( finite_subsets( X )
% 2.59/3.00 , finite_subsets( Y ) ) }.
% 2.59/3.00 (55) {G0,W10,D4,L1,V0,M1} I { ! subset( set_union2( finite_subsets( skol11
% 2.59/3.00 ), finite_subsets( skol12 ) ), finite_subsets( set_union2( skol11,
% 2.59/3.00 skol12 ) ) ) }.
% 2.59/3.00 (63) {G0,W5,D3,L1,V2,M1} I { subset( X, set_union2( X, Y ) ) }.
% 2.59/3.00 (65) {G0,W11,D3,L3,V3,M3} I { ! subset( X, Y ), ! subset( Z, Y ), subset(
% 2.59/3.00 set_union2( X, Z ), Y ) }.
% 2.59/3.00 (210) {G1,W5,D3,L1,V2,M1} P(7,63) { subset( X, set_union2( Y, X ) ) }.
% 2.59/3.00 (347) {G2,W7,D4,L1,V2,M1} R(54,210) { subset( finite_subsets( X ),
% 2.59/3.00 finite_subsets( set_union2( Y, X ) ) ) }.
% 2.59/3.00 (348) {G1,W7,D4,L1,V2,M1} R(54,63) { subset( finite_subsets( X ),
% 2.59/3.00 finite_subsets( set_union2( X, Y ) ) ) }.
% 2.59/3.00 (369) {G1,W10,D4,L1,V0,M1} P(7,55) { ! subset( set_union2( finite_subsets(
% 2.59/3.00 skol11 ), finite_subsets( skol12 ) ), finite_subsets( set_union2( skol12
% 2.59/3.00 , skol11 ) ) ) }.
% 2.59/3.00 (16786) {G3,W7,D4,L1,V0,M1} R(369,65);r(347) { ! subset( finite_subsets(
% 2.59/3.00 skol12 ), finite_subsets( set_union2( skol12, skol11 ) ) ) }.
% 2.59/3.00 (20169) {G4,W0,D0,L0,V0,M0} S(16786);r(348) { }.
% 2.59/3.00
% 2.59/3.00
% 2.59/3.00 % SZS output end Refutation
% 2.59/3.00 found a proof!
% 2.59/3.00
% 2.59/3.00
% 2.59/3.00 Unprocessed initial clauses:
% 2.59/3.00
% 2.59/3.00 (20171) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), ! in( Y, X ) }.
% 2.59/3.00 (20172) {G0,W4,D2,L2,V1,M2} { ! empty( X ), finite( X ) }.
% 2.59/3.00 (20173) {G0,W4,D2,L2,V1,M2} { ! preboolean( X ), cup_closed( X ) }.
% 2.59/3.00 (20174) {G0,W4,D2,L2,V1,M2} { ! preboolean( X ), diff_closed( X ) }.
% 2.59/3.00 (20175) {G0,W8,D3,L3,V2,M3} { ! finite( X ), ! element( Y, powerset( X ) )
% 2.59/3.00 , finite( Y ) }.
% 2.59/3.00 (20176) {G0,W6,D2,L3,V1,M3} { ! cup_closed( X ), ! diff_closed( X ),
% 2.59/3.00 preboolean( X ) }.
% 2.59/3.00 (20177) {G0,W6,D3,L2,V2,M2} { ! element( X, finite_subsets( Y ) ), finite
% 2.59/3.00 ( X ) }.
% 2.59/3.00 (20178) {G0,W7,D3,L1,V2,M1} { set_union2( X, Y ) = set_union2( Y, X ) }.
% 2.59/3.00 (20179) {G0,W3,D3,L1,V1,M1} { preboolean( finite_subsets( X ) ) }.
% 2.59/3.00 (20180) {G0,W4,D3,L1,V1,M1} { element( skol1( X ), X ) }.
% 2.59/3.00 (20181) {G0,W3,D3,L1,V1,M1} { ! empty( powerset( X ) ) }.
% 2.59/3.00 (20182) {G0,W3,D3,L1,V1,M1} { cup_closed( powerset( X ) ) }.
% 2.59/3.00 (20183) {G0,W3,D3,L1,V1,M1} { diff_closed( powerset( X ) ) }.
% 2.59/3.00 (20184) {G0,W3,D3,L1,V1,M1} { preboolean( powerset( X ) ) }.
% 2.59/3.00 (20185) {G0,W3,D3,L1,V1,M1} { ! empty( powerset( X ) ) }.
% 2.59/3.00 (20186) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 2.59/3.00 (20187) {G0,W3,D3,L1,V1,M1} { ! empty( finite_subsets( X ) ) }.
% 2.59/3.00 (20188) {G0,W3,D3,L1,V1,M1} { cup_closed( finite_subsets( X ) ) }.
% 2.59/3.00 (20189) {G0,W3,D3,L1,V1,M1} { diff_closed( finite_subsets( X ) ) }.
% 2.59/3.00 (20190) {G0,W3,D3,L1,V1,M1} { preboolean( finite_subsets( X ) ) }.
% 2.59/3.00 (20191) {G0,W6,D3,L2,V2,M2} { empty( X ), ! empty( set_union2( X, Y ) )
% 2.59/3.00 }.
% 2.59/3.00 (20192) {G0,W6,D3,L2,V2,M2} { empty( X ), ! empty( set_union2( Y, X ) )
% 2.59/3.00 }.
% 2.59/3.00 (20193) {G0,W8,D3,L3,V2,M3} { ! finite( X ), ! finite( Y ), finite(
% 2.59/3.00 set_union2( X, Y ) ) }.
% 2.59/3.00 (20194) {G0,W5,D3,L1,V1,M1} { set_union2( X, X ) = X }.
% 2.59/3.00 (20195) {G0,W2,D2,L1,V0,M1} { ! empty( skol2 ) }.
% 2.59/3.00 (20196) {G0,W2,D2,L1,V0,M1} { finite( skol2 ) }.
% 2.59/3.00 (20197) {G0,W2,D2,L1,V0,M1} { ! empty( skol3 ) }.
% 2.59/3.00 (20198) {G0,W2,D2,L1,V0,M1} { cup_closed( skol3 ) }.
% 2.59/3.00 (20199) {G0,W2,D2,L1,V0,M1} { cap_closed( skol3 ) }.
% 2.59/3.00 (20200) {G0,W2,D2,L1,V0,M1} { diff_closed( skol3 ) }.
% 2.59/3.00 (20201) {G0,W2,D2,L1,V0,M1} { preboolean( skol3 ) }.
% 2.59/3.00 (20202) {G0,W5,D3,L2,V2,M2} { empty( X ), ! empty( skol4( Y ) ) }.
% 2.59/3.00 (20203) {G0,W7,D3,L2,V1,M2} { empty( X ), element( skol4( X ), powerset( X
% 2.59/3.00 ) ) }.
% 2.59/3.00 (20204) {G0,W2,D2,L1,V0,M1} { empty( skol5 ) }.
% 2.59/3.00 (20205) {G0,W3,D3,L1,V1,M1} { empty( skol6( Y ) ) }.
% 2.59/3.00 (20206) {G0,W3,D3,L1,V1,M1} { relation( skol6( Y ) ) }.
% 2.59/3.00 (20207) {G0,W3,D3,L1,V1,M1} { function( skol6( Y ) ) }.
% 2.59/3.00 (20208) {G0,W3,D3,L1,V1,M1} { one_to_one( skol6( Y ) ) }.
% 2.59/3.00 (20209) {G0,W3,D3,L1,V1,M1} { epsilon_transitive( skol6( Y ) ) }.
% 2.59/3.00 (20210) {G0,W3,D3,L1,V1,M1} { epsilon_connected( skol6( Y ) ) }.
% 2.59/3.00 (20211) {G0,W3,D3,L1,V1,M1} { ordinal( skol6( Y ) ) }.
% 2.59/3.00 (20212) {G0,W3,D3,L1,V1,M1} { natural( skol6( Y ) ) }.
% 2.59/3.00 (20213) {G0,W3,D3,L1,V1,M1} { finite( skol6( Y ) ) }.
% 2.59/3.00 (20214) {G0,W5,D3,L1,V1,M1} { element( skol6( X ), powerset( X ) ) }.
% 2.59/3.00 (20215) {G0,W3,D3,L1,V1,M1} { empty( skol7( Y ) ) }.
% 2.59/3.00 (20216) {G0,W5,D3,L1,V1,M1} { element( skol7( X ), powerset( X ) ) }.
% 2.59/3.00 (20217) {G0,W2,D2,L1,V0,M1} { ! empty( skol8 ) }.
% 2.59/3.00 (20218) {G0,W5,D3,L2,V2,M2} { empty( X ), ! empty( skol9( Y ) ) }.
% 2.59/3.00 (20219) {G0,W5,D3,L2,V2,M2} { empty( X ), finite( skol9( Y ) ) }.
% 2.59/3.00 (20220) {G0,W7,D3,L2,V1,M2} { empty( X ), element( skol9( X ), powerset( X
% 2.59/3.00 ) ) }.
% 2.59/3.00 (20221) {G0,W5,D3,L2,V2,M2} { empty( X ), ! empty( skol10( Y ) ) }.
% 2.59/3.00 (20222) {G0,W5,D3,L2,V2,M2} { empty( X ), finite( skol10( Y ) ) }.
% 2.59/3.00 (20223) {G0,W7,D3,L2,V1,M2} { empty( X ), element( skol10( X ), powerset(
% 2.59/3.00 X ) ) }.
% 2.59/3.00 (20224) {G0,W3,D2,L1,V1,M1} { subset( X, X ) }.
% 2.59/3.00 (20225) {G0,W5,D3,L1,V1,M1} { set_union2( X, empty_set ) = X }.
% 2.59/3.00 (20226) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), element( X, Y ) }.
% 2.59/3.00 (20227) {G0,W8,D3,L2,V2,M2} { ! subset( X, Y ), subset( finite_subsets( X
% 2.59/3.00 ), finite_subsets( Y ) ) }.
% 2.59/3.00 (20228) {G0,W10,D4,L1,V0,M1} { ! subset( set_union2( finite_subsets(
% 2.59/3.00 skol11 ), finite_subsets( skol12 ) ), finite_subsets( set_union2( skol11
% 2.59/3.00 , skol12 ) ) ) }.
% 2.59/3.00 (20229) {G0,W8,D2,L3,V2,M3} { ! element( X, Y ), empty( Y ), in( X, Y )
% 2.59/3.00 }.
% 2.59/3.00 (20230) {G0,W7,D3,L2,V2,M2} { ! element( X, powerset( Y ) ), subset( X, Y
% 2.59/3.00 ) }.
% 2.59/3.00 (20231) {G0,W7,D3,L2,V2,M2} { ! subset( X, Y ), element( X, powerset( Y )
% 2.59/3.00 ) }.
% 2.59/3.00 (20232) {G0,W10,D3,L3,V3,M3} { ! in( X, Z ), ! element( Z, powerset( Y ) )
% 2.59/3.00 , element( X, Y ) }.
% 2.59/3.00 (20233) {G0,W9,D3,L3,V3,M3} { ! in( X, Y ), ! element( Y, powerset( Z ) )
% 2.59/3.00 , ! empty( Z ) }.
% 2.59/3.00 (20234) {G0,W5,D2,L2,V1,M2} { ! empty( X ), X = empty_set }.
% 2.59/3.00 (20235) {G0,W5,D2,L2,V2,M2} { ! in( X, Y ), ! empty( Y ) }.
% 2.59/3.00 (20236) {G0,W5,D3,L1,V2,M1} { subset( X, set_union2( X, Y ) ) }.
% 2.59/3.00 (20237) {G0,W7,D2,L3,V2,M3} { ! empty( X ), X = Y, ! empty( Y ) }.
% 2.59/3.00 (20238) {G0,W11,D3,L3,V3,M3} { ! subset( X, Y ), ! subset( Z, Y ), subset
% 2.59/3.00 ( set_union2( X, Z ), Y ) }.
% 2.59/3.00
% 2.59/3.00
% 2.59/3.00 Total Proof:
% 2.59/3.00
% 2.59/3.00 subsumption: (7) {G0,W7,D3,L1,V2,M1} I { set_union2( X, Y ) = set_union2( Y
% 2.59/3.00 , X ) }.
% 2.59/3.00 parent0: (20178) {G0,W7,D3,L1,V2,M1} { set_union2( X, Y ) = set_union2( Y
% 2.59/3.00 , X ) }.
% 2.59/3.00 substitution0:
% 2.59/3.00 X := X
% 2.59/3.00 Y := Y
% 2.59/3.00 end
% 2.59/3.00 permutation0:
% 2.59/3.00 0 ==> 0
% 2.59/3.00 end
% 2.59/3.00
% 2.59/3.00 subsumption: (54) {G0,W8,D3,L2,V2,M2} I { ! subset( X, Y ), subset(
% 2.59/3.00 finite_subsets( X ), finite_subsets( Y ) ) }.
% 2.59/3.00 parent0: (20227) {G0,W8,D3,L2,V2,M2} { ! subset( X, Y ), subset(
% 2.59/3.00 finite_subsets( X ), finite_subsets( Y ) ) }.
% 2.59/3.00 substitution0:
% 2.59/3.00 X := X
% 2.59/3.00 Y := Y
% 2.59/3.00 end
% 2.59/3.00 permutation0:
% 2.59/3.00 0 ==> 0
% 2.59/3.00 1 ==> 1
% 2.59/3.00 end
% 2.59/3.00
% 2.59/3.00 subsumption: (55) {G0,W10,D4,L1,V0,M1} I { ! subset( set_union2(
% 2.59/3.00 finite_subsets( skol11 ), finite_subsets( skol12 ) ), finite_subsets(
% 2.59/3.00 set_union2( skol11, skol12 ) ) ) }.
% 2.59/3.00 parent0: (20228) {G0,W10,D4,L1,V0,M1} { ! subset( set_union2(
% 2.59/3.00 finite_subsets( skol11 ), finite_subsets( skol12 ) ), finite_subsets(
% 2.59/3.00 set_union2( skol11, skol12 ) ) ) }.
% 2.59/3.00 substitution0:
% 2.59/3.00 end
% 2.59/3.00 permutation0:
% 2.59/3.00 0 ==> 0
% 2.59/3.00 end
% 2.59/3.00
% 2.59/3.00 subsumption: (63) {G0,W5,D3,L1,V2,M1} I { subset( X, set_union2( X, Y ) )
% 2.59/3.00 }.
% 2.59/3.00 parent0: (20236) {G0,W5,D3,L1,V2,M1} { subset( X, set_union2( X, Y ) ) }.
% 2.59/3.00 substitution0:
% 2.59/3.00 X := X
% 2.59/3.00 Y := Y
% 2.59/3.00 end
% 2.59/3.00 permutation0:
% 2.59/3.00 0 ==> 0
% 2.59/3.00 end
% 2.59/3.00
% 2.59/3.00 subsumption: (65) {G0,W11,D3,L3,V3,M3} I { ! subset( X, Y ), ! subset( Z, Y
% 2.59/3.00 ), subset( set_union2( X, Z ), Y ) }.
% 2.59/3.00 parent0: (20238) {G0,W11,D3,L3,V3,M3} { ! subset( X, Y ), ! subset( Z, Y )
% 2.59/3.00 , subset( set_union2( X, Z ), Y ) }.
% 2.59/3.00 substitution0:
% 2.59/3.00 X := X
% 2.59/3.00 Y := Y
% 2.59/3.00 Z := Z
% 2.59/3.00 end
% 2.59/3.00 permutation0:
% 2.59/3.00 0 ==> 0
% 2.59/3.00 1 ==> 1
% 2.59/3.00 2 ==> 2
% 2.59/3.00 end
% 2.59/3.00
% 2.59/3.00 paramod: (20260) {G1,W5,D3,L1,V2,M1} { subset( X, set_union2( Y, X ) ) }.
% 2.59/3.00 parent0[0]: (7) {G0,W7,D3,L1,V2,M1} I { set_union2( X, Y ) = set_union2( Y
% 2.59/3.00 , X ) }.
% 2.59/3.00 parent1[0; 2]: (63) {G0,W5,D3,L1,V2,M1} I { subset( X, set_union2( X, Y ) )
% 2.59/3.00 }.
% 2.59/3.00 substitution0:
% 2.59/3.00 X := X
% 2.59/3.00 Y := Y
% 2.59/3.00 end
% 2.59/3.00 substitution1:
% 2.59/3.00 X := X
% 2.59/3.00 Y := Y
% 2.59/3.00 end
% 2.59/3.00
% 2.59/3.00 subsumption: (210) {G1,W5,D3,L1,V2,M1} P(7,63) { subset( X, set_union2( Y,
% 2.59/3.00 X ) ) }.
% 2.59/3.00 parent0: (20260) {G1,W5,D3,L1,V2,M1} { subset( X, set_union2( Y, X ) ) }.
% 2.59/3.00 substitution0:
% 2.59/3.00 X := X
% 2.59/3.00 Y := Y
% 2.59/3.00 end
% 2.59/3.00 permutation0:
% 2.59/3.00 0 ==> 0
% 2.59/3.00 end
% 2.59/3.00
% 2.59/3.00 resolution: (20262) {G1,W7,D4,L1,V2,M1} { subset( finite_subsets( X ),
% 2.59/3.00 finite_subsets( set_union2( Y, X ) ) ) }.
% 2.59/3.00 parent0[0]: (54) {G0,W8,D3,L2,V2,M2} I { ! subset( X, Y ), subset(
% 2.59/3.00 finite_subsets( X ), finite_subsets( Y ) ) }.
% 2.59/3.00 parent1[0]: (210) {G1,W5,D3,L1,V2,M1} P(7,63) { subset( X, set_union2( Y, X
% 2.59/3.00 ) ) }.
% 2.59/3.00 substitution0:
% 2.59/3.00 X := X
% 2.59/3.00 Y := set_union2( Y, X )
% 2.59/3.00 end
% 2.59/3.00 substitution1:
% 2.59/3.00 X := X
% 2.59/3.00 Y := Y
% 2.59/3.00 end
% 2.59/3.00
% 2.59/3.00 subsumption: (347) {G2,W7,D4,L1,V2,M1} R(54,210) { subset( finite_subsets(
% 2.59/3.00 X ), finite_subsets( set_union2( Y, X ) ) ) }.
% 2.59/3.00 parent0: (20262) {G1,W7,D4,L1,V2,M1} { subset( finite_subsets( X ),
% 2.59/3.00 finite_subsets( set_union2( Y, X ) ) ) }.
% 2.59/3.00 substitution0:
% 2.59/3.00 X := X
% 2.59/3.00 Y := Y
% 2.59/3.00 end
% 2.59/3.00 permutation0:
% 2.59/3.00 0 ==> 0
% 2.59/3.00 end
% 2.59/3.00
% 2.59/3.00 resolution: (20263) {G1,W7,D4,L1,V2,M1} { subset( finite_subsets( X ),
% 2.59/3.00 finite_subsets( set_union2( X, Y ) ) ) }.
% 2.59/3.00 parent0[0]: (54) {G0,W8,D3,L2,V2,M2} I { ! subset( X, Y ), subset(
% 2.59/3.00 finite_subsets( X ), finite_subsets( Y ) ) }.
% 2.59/3.00 parent1[0]: (63) {G0,W5,D3,L1,V2,M1} I { subset( X, set_union2( X, Y ) )
% 2.59/3.00 }.
% 2.59/3.00 substitution0:
% 2.59/3.00 X := X
% 2.59/3.00 Y := set_union2( X, Y )
% 2.59/3.00 end
% 2.59/3.00 substitution1:
% 2.59/3.00 X := X
% 2.59/3.00 Y := Y
% 2.59/3.00 end
% 2.59/3.00
% 2.59/3.00 subsumption: (348) {G1,W7,D4,L1,V2,M1} R(54,63) { subset( finite_subsets( X
% 2.59/3.00 ), finite_subsets( set_union2( X, Y ) ) ) }.
% 2.59/3.00 parent0: (20263) {G1,W7,D4,L1,V2,M1} { subset( finite_subsets( X ),
% 2.59/3.00 finite_subsets( set_union2( X, Y ) ) ) }.
% 2.59/3.00 substitution0:
% 2.59/3.00 X := X
% 2.59/3.00 Y := Y
% 2.59/3.00 end
% 2.59/3.00 permutation0:
% 2.59/3.00 0 ==> 0
% 2.59/3.00 end
% 2.59/3.00
% 2.59/3.00 paramod: (20265) {G1,W10,D4,L1,V0,M1} { ! subset( set_union2(
% 2.59/3.00 finite_subsets( skol11 ), finite_subsets( skol12 ) ), finite_subsets(
% 2.59/3.00 set_union2( skol12, skol11 ) ) ) }.
% 2.59/3.00 parent0[0]: (7) {G0,W7,D3,L1,V2,M1} I { set_union2( X, Y ) = set_union2( Y
% 2.59/3.00 , X ) }.
% 2.59/3.00 parent1[0; 8]: (55) {G0,W10,D4,L1,V0,M1} I { ! subset( set_union2(
% 2.59/3.00 finite_subsets( skol11 ), finite_subsets( skol12 ) ), finite_subsets(
% 2.59/3.00 set_union2( skol11, skol12 ) ) ) }.
% 2.59/3.00 substitution0:
% 2.59/3.00 X := skol11
% 2.59/3.00 Y := skol12
% 2.59/3.00 end
% 2.59/3.00 substitution1:
% 2.59/3.00 end
% 2.59/3.00
% 2.59/3.00 subsumption: (369) {G1,W10,D4,L1,V0,M1} P(7,55) { ! subset( set_union2(
% 2.59/3.00 finite_subsets( skol11 ), finite_subsets( skol12 ) ), finite_subsets(
% 2.59/3.00 set_union2( skol12, skol11 ) ) ) }.
% 2.59/3.00 parent0: (20265) {G1,W10,D4,L1,V0,M1} { ! subset( set_union2(
% 2.59/3.00 finite_subsets( skol11 ), finite_subsets( skol12 ) ), finite_subsets(
% 2.59/3.00 set_union2( skol12, skol11 ) ) ) }.
% 2.59/3.00 substitution0:
% 2.59/3.00 end
% 2.59/3.00 permutation0:
% 2.59/3.00 0 ==> 0
% 2.59/3.00 end
% 2.59/3.00
% 2.59/3.00 resolution: (20268) {G1,W14,D4,L2,V0,M2} { ! subset( finite_subsets(
% 2.59/3.00 skol11 ), finite_subsets( set_union2( skol12, skol11 ) ) ), ! subset(
% 2.59/3.00 finite_subsets( skol12 ), finite_subsets( set_union2( skol12, skol11 ) )
% 2.59/3.00 ) }.
% 2.59/3.00 parent0[0]: (369) {G1,W10,D4,L1,V0,M1} P(7,55) { ! subset( set_union2(
% 2.59/3.00 finite_subsets( skol11 ), finite_subsets( skol12 ) ), finite_subsets(
% 2.59/3.00 set_union2( skol12, skol11 ) ) ) }.
% 2.59/3.00 parent1[2]: (65) {G0,W11,D3,L3,V3,M3} I { ! subset( X, Y ), ! subset( Z, Y
% 2.59/3.00 ), subset( set_union2( X, Z ), Y ) }.
% 2.59/3.00 substitution0:
% 2.59/3.00 end
% 2.59/3.00 substitution1:
% 2.59/3.00 X := finite_subsets( skol11 )
% 2.59/3.00 Y := finite_subsets( set_union2( skol12, skol11 ) )
% 2.59/3.00 Z := finite_subsets( skol12 )
% 2.59/3.00 end
% 2.59/3.00
% 2.59/3.00 resolution: (20269) {G2,W7,D4,L1,V0,M1} { ! subset( finite_subsets( skol12
% 2.59/3.00 ), finite_subsets( set_union2( skol12, skol11 ) ) ) }.
% 2.59/3.00 parent0[0]: (20268) {G1,W14,D4,L2,V0,M2} { ! subset( finite_subsets(
% 2.59/3.00 skol11 ), finite_subsets( set_union2( skol12, skol11 ) ) ), ! subset(
% 2.59/3.00 finite_subsets( skol12 ), finite_subsets( set_union2( skol12, skol11 ) )
% 2.59/3.00 ) }.
% 2.59/3.00 parent1[0]: (347) {G2,W7,D4,L1,V2,M1} R(54,210) { subset( finite_subsets( X
% 2.59/3.00 ), finite_subsets( set_union2( Y, X ) ) ) }.
% 2.59/3.00 substitution0:
% 2.59/3.00 end
% 2.59/3.00 substitution1:
% 2.59/3.00 X := skol11
% 2.59/3.00 Y := skol12
% 2.59/3.00 end
% 2.59/3.00
% 2.59/3.00 subsumption: (16786) {G3,W7,D4,L1,V0,M1} R(369,65);r(347) { ! subset(
% 2.59/3.00 finite_subsets( skol12 ), finite_subsets( set_union2( skol12, skol11 ) )
% 2.59/3.00 ) }.
% 2.59/3.00 parent0: (20269) {G2,W7,D4,L1,V0,M1} { ! subset( finite_subsets( skol12 )
% 2.59/3.00 , finite_subsets( set_union2( skol12, skol11 ) ) ) }.
% 2.59/3.00 substitution0:
% 2.59/3.00 end
% 2.59/3.00 permutation0:
% 2.59/3.00 0 ==> 0
% 2.59/3.00 end
% 2.59/3.00
% 2.59/3.00 resolution: (20270) {G2,W0,D0,L0,V0,M0} { }.
% 2.59/3.00 parent0[0]: (16786) {G3,W7,D4,L1,V0,M1} R(369,65);r(347) { ! subset(
% 2.59/3.00 finite_subsets( skol12 ), finite_subsets( set_union2( skol12, skol11 ) )
% 2.59/3.00 ) }.
% 2.59/3.00 parent1[0]: (348) {G1,W7,D4,L1,V2,M1} R(54,63) { subset( finite_subsets( X
% 2.59/3.00 ), finite_subsets( set_union2( X, Y ) ) ) }.
% 2.59/3.00 substitution0:
% 2.59/3.00 end
% 2.59/3.00 substitution1:
% 2.59/3.00 X := skol12
% 2.59/3.00 Y := skol11
% 2.59/3.00 end
% 2.59/3.00
% 2.59/3.00 subsumption: (20169) {G4,W0,D0,L0,V0,M0} S(16786);r(348) { }.
% 2.59/3.00 parent0: (20270) {G2,W0,D0,L0,V0,M0} { }.
% 2.59/3.00 substitution0:
% 2.59/3.00 end
% 2.59/3.00 permutation0:
% 2.59/3.00 end
% 2.59/3.00
% 2.59/3.00 Proof check complete!
% 2.59/3.00
% 2.59/3.00 Memory use:
% 2.59/3.00
% 2.59/3.00 space for terms: 247520
% 2.59/3.00 space for clauses: 951374
% 2.59/3.00
% 2.59/3.00
% 2.59/3.00 clauses generated: 102177
% 2.59/3.00 clauses kept: 20170
% 2.59/3.00 clauses selected: 1215
% 2.59/3.00 clauses deleted: 163
% 2.59/3.00 clauses inuse deleted: 37
% 2.59/3.00
% 2.59/3.00 subsentry: 428436
% 2.59/3.00 literals s-matched: 262451
% 2.59/3.00 literals matched: 247538
% 2.59/3.00 full subsumption: 26689
% 2.59/3.00
% 2.59/3.00 checksum: 246553980
% 2.59/3.00
% 2.59/3.00
% 2.59/3.00 Bliksem ended
%------------------------------------------------------------------------------