TSTP Solution File: NUM390+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : NUM390+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Mon Jul 18 06:21:53 EDT 2022
% Result : Theorem 0.74s 1.15s
% Output : Refutation 0.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM390+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : bliksem %s
% 0.13/0.33 % Computer : n019.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % DateTime : Wed Jul 6 07:12:23 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.74/1.15 *** allocated 10000 integers for termspace/termends
% 0.74/1.15 *** allocated 10000 integers for clauses
% 0.74/1.15 *** allocated 10000 integers for justifications
% 0.74/1.15 Bliksem 1.12
% 0.74/1.15
% 0.74/1.15
% 0.74/1.15 Automatic Strategy Selection
% 0.74/1.15
% 0.74/1.15
% 0.74/1.15 Clauses:
% 0.74/1.15
% 0.74/1.15 { ! in( X, Y ), ! in( Y, X ) }.
% 0.74/1.15 { ! proper_subset( X, Y ), ! proper_subset( Y, X ) }.
% 0.74/1.15 { ! empty( X ), function( X ) }.
% 0.74/1.15 { ! ordinal( X ), epsilon_transitive( X ) }.
% 0.74/1.15 { ! ordinal( X ), epsilon_connected( X ) }.
% 0.74/1.15 { ! empty( X ), relation( X ) }.
% 0.74/1.15 { ! relation( X ), ! empty( X ), ! function( X ), relation( X ) }.
% 0.74/1.15 { ! relation( X ), ! empty( X ), ! function( X ), function( X ) }.
% 0.74/1.15 { ! relation( X ), ! empty( X ), ! function( X ), one_to_one( X ) }.
% 0.74/1.15 { ! epsilon_transitive( X ), ! epsilon_connected( X ), ordinal( X ) }.
% 0.74/1.15 { ! epsilon_transitive( X ), ! in( Y, X ), subset( Y, X ) }.
% 0.74/1.15 { in( skol1( X ), X ), epsilon_transitive( X ) }.
% 0.74/1.15 { ! subset( skol1( X ), X ), epsilon_transitive( X ) }.
% 0.74/1.15 { ! proper_subset( X, Y ), subset( X, Y ) }.
% 0.74/1.15 { ! proper_subset( X, Y ), ! X = Y }.
% 0.74/1.15 { ! subset( X, Y ), X = Y, proper_subset( X, Y ) }.
% 0.74/1.15 { element( skol2( X ), X ) }.
% 0.74/1.15 { empty( empty_set ) }.
% 0.74/1.15 { relation( empty_set ) }.
% 0.74/1.15 { relation_empty_yielding( empty_set ) }.
% 0.74/1.15 { empty( empty_set ) }.
% 0.74/1.15 { empty( empty_set ) }.
% 0.74/1.15 { relation( empty_set ) }.
% 0.74/1.15 { ! proper_subset( X, X ) }.
% 0.74/1.15 { relation( skol3 ) }.
% 0.74/1.15 { function( skol3 ) }.
% 0.74/1.15 { epsilon_transitive( skol4 ) }.
% 0.74/1.15 { epsilon_connected( skol4 ) }.
% 0.74/1.15 { ordinal( skol4 ) }.
% 0.74/1.15 { empty( skol5 ) }.
% 0.74/1.15 { relation( skol5 ) }.
% 0.74/1.15 { empty( skol6 ) }.
% 0.74/1.15 { relation( skol7 ) }.
% 0.74/1.15 { empty( skol7 ) }.
% 0.74/1.15 { function( skol7 ) }.
% 0.74/1.15 { ! empty( skol8 ) }.
% 0.74/1.15 { relation( skol8 ) }.
% 0.74/1.15 { ! empty( skol9 ) }.
% 0.74/1.15 { relation( skol10 ) }.
% 0.74/1.15 { function( skol10 ) }.
% 0.74/1.15 { one_to_one( skol10 ) }.
% 0.74/1.15 { relation( skol11 ) }.
% 0.74/1.15 { relation_empty_yielding( skol11 ) }.
% 0.74/1.15 { relation( skol12 ) }.
% 0.74/1.15 { relation_empty_yielding( skol12 ) }.
% 0.74/1.15 { function( skol12 ) }.
% 0.74/1.15 { relation( skol13 ) }.
% 0.74/1.15 { relation_non_empty( skol13 ) }.
% 0.74/1.15 { function( skol13 ) }.
% 0.74/1.15 { subset( X, X ) }.
% 0.74/1.15 { ! in( X, Y ), element( X, Y ) }.
% 0.74/1.15 { ! subset( X, Z ), ! subset( Z, Y ), subset( X, Y ) }.
% 0.74/1.15 { ! epsilon_transitive( X ), ! ordinal( Y ), ! proper_subset( X, Y ), in( X
% 0.74/1.15 , Y ) }.
% 0.74/1.15 { epsilon_transitive( skol14 ) }.
% 0.74/1.15 { ordinal( skol15 ) }.
% 0.74/1.15 { ordinal( skol16 ) }.
% 0.74/1.15 { subset( skol14, skol15 ) }.
% 0.74/1.15 { in( skol15, skol16 ) }.
% 0.74/1.15 { ! in( skol14, skol16 ) }.
% 0.74/1.15 { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.74/1.15 { ! element( X, powerset( Y ) ), subset( X, Y ) }.
% 0.74/1.15 { ! subset( X, Y ), element( X, powerset( Y ) ) }.
% 0.74/1.15 { ! in( X, Z ), ! element( Z, powerset( Y ) ), element( X, Y ) }.
% 0.74/1.15 { ! in( X, Y ), ! element( Y, powerset( Z ) ), ! empty( Z ) }.
% 0.74/1.15 { ! empty( X ), X = empty_set }.
% 0.74/1.15 { ! in( X, Y ), ! empty( Y ) }.
% 0.74/1.15 { ! in( X, Y ), ! subset( Y, X ) }.
% 0.74/1.15 { ! empty( X ), X = Y, ! empty( Y ) }.
% 0.74/1.15
% 0.74/1.15 percentage equality = 0.039604, percentage horn = 0.952381
% 0.74/1.15 This is a problem with some equality
% 0.74/1.15
% 0.74/1.15
% 0.74/1.15
% 0.74/1.15 Options Used:
% 0.74/1.15
% 0.74/1.15 useres = 1
% 0.74/1.15 useparamod = 1
% 0.74/1.15 useeqrefl = 1
% 0.74/1.15 useeqfact = 1
% 0.74/1.15 usefactor = 1
% 0.74/1.15 usesimpsplitting = 0
% 0.74/1.15 usesimpdemod = 5
% 0.74/1.15 usesimpres = 3
% 0.74/1.15
% 0.74/1.15 resimpinuse = 1000
% 0.74/1.15 resimpclauses = 20000
% 0.74/1.15 substype = eqrewr
% 0.74/1.15 backwardsubs = 1
% 0.74/1.15 selectoldest = 5
% 0.74/1.15
% 0.74/1.15 litorderings [0] = split
% 0.74/1.15 litorderings [1] = extend the termordering, first sorting on arguments
% 0.74/1.15
% 0.74/1.15 termordering = kbo
% 0.74/1.15
% 0.74/1.15 litapriori = 0
% 0.74/1.15 termapriori = 1
% 0.74/1.15 litaposteriori = 0
% 0.74/1.15 termaposteriori = 0
% 0.74/1.15 demodaposteriori = 0
% 0.74/1.15 ordereqreflfact = 0
% 0.74/1.15
% 0.74/1.15 litselect = negord
% 0.74/1.15
% 0.74/1.15 maxweight = 15
% 0.74/1.15 maxdepth = 30000
% 0.74/1.15 maxlength = 115
% 0.74/1.15 maxnrvars = 195
% 0.74/1.15 excuselevel = 1
% 0.74/1.15 increasemaxweight = 1
% 0.74/1.15
% 0.74/1.15 maxselected = 10000000
% 0.74/1.15 maxnrclauses = 10000000
% 0.74/1.15
% 0.74/1.15 showgenerated = 0
% 0.74/1.15 showkept = 0
% 0.74/1.15 showselected = 0
% 0.74/1.15 showdeleted = 0
% 0.74/1.15 showresimp = 1
% 0.74/1.15 showstatus = 2000
% 0.74/1.15
% 0.74/1.15 prologoutput = 0
% 0.74/1.15 nrgoals = 5000000
% 0.74/1.15 totalproof = 1
% 0.74/1.15
% 0.74/1.15 Symbols occurring in the translation:
% 0.74/1.15
% 0.74/1.15 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.74/1.15 . [1, 2] (w:1, o:41, a:1, s:1, b:0),
% 0.74/1.15 ! [4, 1] (w:0, o:24, a:1, s:1, b:0),
% 0.74/1.15 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.74/1.15 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.74/1.15 in [37, 2] (w:1, o:65, a:1, s:1, b:0),
% 0.74/1.15 proper_subset [38, 2] (w:1, o:66, a:1, s:1, b:0),
% 0.74/1.15 empty [39, 1] (w:1, o:29, a:1, s:1, b:0),
% 0.74/1.15 function [40, 1] (w:1, o:32, a:1, s:1, b:0),
% 0.74/1.15 ordinal [41, 1] (w:1, o:33, a:1, s:1, b:0),
% 0.74/1.15 epsilon_transitive [42, 1] (w:1, o:30, a:1, s:1, b:0),
% 0.74/1.15 epsilon_connected [43, 1] (w:1, o:31, a:1, s:1, b:0),
% 0.74/1.15 relation [44, 1] (w:1, o:34, a:1, s:1, b:0),
% 0.74/1.15 one_to_one [45, 1] (w:1, o:35, a:1, s:1, b:0),
% 0.74/1.15 subset [46, 2] (w:1, o:67, a:1, s:1, b:0),
% 0.74/1.15 element [47, 2] (w:1, o:68, a:1, s:1, b:0),
% 0.74/1.15 empty_set [48, 0] (w:1, o:8, a:1, s:1, b:0),
% 0.74/1.15 relation_empty_yielding [49, 1] (w:1, o:36, a:1, s:1, b:0),
% 0.74/1.15 relation_non_empty [50, 1] (w:1, o:37, a:1, s:1, b:0),
% 0.74/1.15 powerset [52, 1] (w:1, o:38, a:1, s:1, b:0),
% 0.74/1.15 skol1 [53, 1] (w:1, o:39, a:1, s:1, b:1),
% 0.74/1.15 skol2 [54, 1] (w:1, o:40, a:1, s:1, b:1),
% 0.74/1.15 skol3 [55, 0] (w:1, o:10, a:1, s:1, b:1),
% 0.74/1.15 skol4 [56, 0] (w:1, o:11, a:1, s:1, b:1),
% 0.74/1.15 skol5 [57, 0] (w:1, o:12, a:1, s:1, b:1),
% 0.74/1.15 skol6 [58, 0] (w:1, o:13, a:1, s:1, b:1),
% 0.74/1.15 skol7 [59, 0] (w:1, o:14, a:1, s:1, b:1),
% 0.74/1.15 skol8 [60, 0] (w:1, o:15, a:1, s:1, b:1),
% 0.74/1.15 skol9 [61, 0] (w:1, o:16, a:1, s:1, b:1),
% 0.74/1.15 skol10 [62, 0] (w:1, o:17, a:1, s:1, b:1),
% 0.74/1.15 skol11 [63, 0] (w:1, o:18, a:1, s:1, b:1),
% 0.74/1.15 skol12 [64, 0] (w:1, o:19, a:1, s:1, b:1),
% 0.74/1.15 skol13 [65, 0] (w:1, o:20, a:1, s:1, b:1),
% 0.74/1.15 skol14 [66, 0] (w:1, o:21, a:1, s:1, b:1),
% 0.74/1.15 skol15 [67, 0] (w:1, o:22, a:1, s:1, b:1),
% 0.74/1.15 skol16 [68, 0] (w:1, o:23, a:1, s:1, b:1).
% 0.74/1.15
% 0.74/1.15
% 0.74/1.15 Starting Search:
% 0.74/1.15
% 0.74/1.15 *** allocated 15000 integers for clauses
% 0.74/1.15 *** allocated 22500 integers for clauses
% 0.74/1.15 *** allocated 33750 integers for clauses
% 0.74/1.15 *** allocated 50625 integers for clauses
% 0.74/1.15 *** allocated 15000 integers for termspace/termends
% 0.74/1.15 *** allocated 75937 integers for clauses
% 0.74/1.15 Resimplifying inuse:
% 0.74/1.15 Done
% 0.74/1.15
% 0.74/1.15 *** allocated 22500 integers for termspace/termends
% 0.74/1.15 *** allocated 113905 integers for clauses
% 0.74/1.15 *** allocated 33750 integers for termspace/termends
% 0.74/1.15
% 0.74/1.15 Bliksems!, er is een bewijs:
% 0.74/1.15 % SZS status Theorem
% 0.74/1.15 % SZS output start Refutation
% 0.74/1.15
% 0.74/1.15 (1) {G0,W6,D2,L2,V2,M2} I { ! proper_subset( X, Y ), ! proper_subset( Y, X
% 0.74/1.15 ) }.
% 0.74/1.15 (3) {G0,W4,D2,L2,V1,M2} I { ! ordinal( X ), epsilon_transitive( X ) }.
% 0.74/1.15 (8) {G0,W8,D2,L3,V2,M3} I { ! epsilon_transitive( X ), ! in( Y, X ), subset
% 0.74/1.15 ( Y, X ) }.
% 0.74/1.15 (12) {G0,W6,D2,L2,V2,M2} I { ! proper_subset( X, Y ), ! X = Y }.
% 0.74/1.15 (13) {G0,W9,D2,L3,V2,M3} I { ! subset( X, Y ), X = Y, proper_subset( X, Y )
% 0.74/1.15 }.
% 0.74/1.15 (44) {G0,W3,D2,L1,V1,M1} I { subset( X, X ) }.
% 0.74/1.15 (45) {G0,W6,D2,L2,V2,M2} I { ! in( X, Y ), element( X, Y ) }.
% 0.74/1.15 (46) {G0,W9,D2,L3,V3,M3} I { ! subset( X, Z ), ! subset( Z, Y ), subset( X
% 0.74/1.15 , Y ) }.
% 0.74/1.15 (47) {G0,W10,D2,L4,V2,M4} I { ! epsilon_transitive( X ), ! ordinal( Y ), !
% 0.74/1.15 proper_subset( X, Y ), in( X, Y ) }.
% 0.74/1.15 (48) {G0,W2,D2,L1,V0,M1} I { epsilon_transitive( skol14 ) }.
% 0.74/1.15 (50) {G0,W2,D2,L1,V0,M1} I { ordinal( skol16 ) }.
% 0.74/1.15 (51) {G0,W3,D2,L1,V0,M1} I { subset( skol14, skol15 ) }.
% 0.74/1.15 (52) {G0,W3,D2,L1,V0,M1} I { in( skol15, skol16 ) }.
% 0.74/1.15 (53) {G0,W3,D2,L1,V0,M1} I { ! in( skol14, skol16 ) }.
% 0.74/1.15 (54) {G0,W8,D2,L3,V2,M3} I { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.74/1.15 (60) {G0,W5,D2,L2,V2,M2} I { ! in( X, Y ), ! empty( Y ) }.
% 0.74/1.15 (65) {G1,W2,D2,L1,V0,M1} R(3,50) { epsilon_transitive( skol16 ) }.
% 0.74/1.15 (82) {G2,W3,D2,L1,V0,M1} R(52,8);r(65) { subset( skol15, skol16 ) }.
% 0.74/1.15 (91) {G1,W2,D2,L1,V0,M1} R(60,52) { ! empty( skol16 ) }.
% 0.74/1.15 (98) {G1,W6,D2,L2,V0,M2} R(13,51) { skol15 ==> skol14, proper_subset(
% 0.74/1.15 skol14, skol15 ) }.
% 0.74/1.15 (99) {G3,W6,D2,L2,V0,M2} R(13,82) { skol16 ==> skol15, proper_subset(
% 0.74/1.15 skol15, skol16 ) }.
% 0.74/1.15 (101) {G1,W9,D2,L3,V2,M3} R(13,1) { ! subset( X, Y ), X = Y, !
% 0.74/1.15 proper_subset( Y, X ) }.
% 0.74/1.15 (232) {G1,W3,D2,L1,V0,M1} R(45,52) { element( skol15, skol16 ) }.
% 0.74/1.15 (252) {G1,W6,D2,L2,V1,M2} R(46,51) { ! subset( X, skol14 ), subset( X,
% 0.74/1.15 skol15 ) }.
% 0.74/1.15 (283) {G1,W5,D2,L2,V0,M2} R(47,53);r(48) { ! ordinal( skol16 ), !
% 0.74/1.15 proper_subset( skol14, skol16 ) }.
% 0.74/1.15 (326) {G2,W3,D2,L1,V0,M1} R(54,53);r(91) { ! element( skol14, skol16 ) }.
% 0.74/1.15 (888) {G2,W3,D2,L1,V0,M1} S(283);r(50) { ! proper_subset( skol14, skol16 )
% 0.74/1.15 }.
% 0.74/1.15 (894) {G3,W6,D2,L2,V0,M2} R(888,13) { ! subset( skol14, skol16 ), skol16
% 0.74/1.15 ==> skol14 }.
% 0.74/1.15 (931) {G3,W3,D2,L1,V0,M1} P(98,232);r(326) { proper_subset( skol14, skol15
% 0.74/1.15 ) }.
% 0.74/1.15 (937) {G4,W3,D2,L1,V0,M1} R(931,12) { ! skol15 ==> skol14 }.
% 0.74/1.15 (938) {G4,W3,D2,L1,V0,M1} R(931,1) { ! proper_subset( skol15, skol14 ) }.
% 0.74/1.15 (943) {G5,W9,D2,L3,V1,M3} P(13,937) { ! X = skol14, ! subset( skol15, X ),
% 0.74/1.15 proper_subset( skol15, X ) }.
% 0.74/1.15 (945) {G6,W3,D2,L1,V0,M1} Q(943);r(938) { ! subset( skol15, skol14 ) }.
% 0.74/1.15 (956) {G4,W3,D2,L1,V0,M1} P(99,888);r(931) { proper_subset( skol15, skol16
% 0.74/1.15 ) }.
% 0.74/1.15 (1265) {G7,W6,D2,L2,V1,M2} P(101,945);r(252) { ! subset( X, skol14 ), !
% 0.74/1.15 proper_subset( skol15, X ) }.
% 0.74/1.15 (1581) {G8,W3,D2,L1,V0,M1} R(1265,956) { ! subset( skol16, skol14 ) }.
% 0.74/1.15 (1604) {G9,W6,D2,L2,V1,M2} R(1581,46) { ! subset( skol16, X ), ! subset( X
% 0.74/1.15 , skol14 ) }.
% 0.74/1.15 (1787) {G10,W9,D2,L3,V2,M3} R(1604,46) { ! subset( X, skol14 ), ! subset(
% 0.74/1.15 skol16, Y ), ! subset( Y, X ) }.
% 0.74/1.15 (1801) {G11,W3,D2,L1,V0,M1} F(1787);d(894);r(44) { ! subset( skol14, skol16
% 0.74/1.15 ) }.
% 0.74/1.15 (1816) {G12,W6,D2,L2,V1,M2} R(1801,46) { ! subset( skol14, X ), ! subset( X
% 0.74/1.15 , skol16 ) }.
% 0.74/1.15 (1962) {G13,W0,D0,L0,V0,M0} R(1816,51);r(82) { }.
% 0.74/1.15
% 0.74/1.15
% 0.74/1.15 % SZS output end Refutation
% 0.74/1.15 found a proof!
% 0.74/1.15
% 0.74/1.15
% 0.74/1.15 Unprocessed initial clauses:
% 0.74/1.15
% 0.74/1.15 (1964) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), ! in( Y, X ) }.
% 0.74/1.15 (1965) {G0,W6,D2,L2,V2,M2} { ! proper_subset( X, Y ), ! proper_subset( Y,
% 0.74/1.15 X ) }.
% 0.74/1.15 (1966) {G0,W4,D2,L2,V1,M2} { ! empty( X ), function( X ) }.
% 0.74/1.15 (1967) {G0,W4,D2,L2,V1,M2} { ! ordinal( X ), epsilon_transitive( X ) }.
% 0.74/1.15 (1968) {G0,W4,D2,L2,V1,M2} { ! ordinal( X ), epsilon_connected( X ) }.
% 0.74/1.15 (1969) {G0,W4,D2,L2,V1,M2} { ! empty( X ), relation( X ) }.
% 0.74/1.15 (1970) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 0.74/1.15 ), relation( X ) }.
% 0.74/1.15 (1971) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 0.74/1.15 ), function( X ) }.
% 0.74/1.15 (1972) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 0.74/1.15 ), one_to_one( X ) }.
% 0.74/1.15 (1973) {G0,W6,D2,L3,V1,M3} { ! epsilon_transitive( X ), !
% 0.74/1.15 epsilon_connected( X ), ordinal( X ) }.
% 0.74/1.15 (1974) {G0,W8,D2,L3,V2,M3} { ! epsilon_transitive( X ), ! in( Y, X ),
% 0.74/1.15 subset( Y, X ) }.
% 0.74/1.15 (1975) {G0,W6,D3,L2,V1,M2} { in( skol1( X ), X ), epsilon_transitive( X )
% 0.74/1.15 }.
% 0.74/1.15 (1976) {G0,W6,D3,L2,V1,M2} { ! subset( skol1( X ), X ), epsilon_transitive
% 0.74/1.15 ( X ) }.
% 0.74/1.15 (1977) {G0,W6,D2,L2,V2,M2} { ! proper_subset( X, Y ), subset( X, Y ) }.
% 0.74/1.15 (1978) {G0,W6,D2,L2,V2,M2} { ! proper_subset( X, Y ), ! X = Y }.
% 0.74/1.15 (1979) {G0,W9,D2,L3,V2,M3} { ! subset( X, Y ), X = Y, proper_subset( X, Y
% 0.74/1.15 ) }.
% 0.74/1.15 (1980) {G0,W4,D3,L1,V1,M1} { element( skol2( X ), X ) }.
% 0.74/1.15 (1981) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.74/1.15 (1982) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 0.74/1.15 (1983) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( empty_set ) }.
% 0.74/1.15 (1984) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.74/1.15 (1985) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.74/1.15 (1986) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 0.74/1.15 (1987) {G0,W3,D2,L1,V1,M1} { ! proper_subset( X, X ) }.
% 0.74/1.15 (1988) {G0,W2,D2,L1,V0,M1} { relation( skol3 ) }.
% 0.74/1.15 (1989) {G0,W2,D2,L1,V0,M1} { function( skol3 ) }.
% 0.74/1.15 (1990) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol4 ) }.
% 0.74/1.15 (1991) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol4 ) }.
% 0.74/1.15 (1992) {G0,W2,D2,L1,V0,M1} { ordinal( skol4 ) }.
% 0.74/1.15 (1993) {G0,W2,D2,L1,V0,M1} { empty( skol5 ) }.
% 0.74/1.15 (1994) {G0,W2,D2,L1,V0,M1} { relation( skol5 ) }.
% 0.74/1.15 (1995) {G0,W2,D2,L1,V0,M1} { empty( skol6 ) }.
% 0.74/1.15 (1996) {G0,W2,D2,L1,V0,M1} { relation( skol7 ) }.
% 0.74/1.15 (1997) {G0,W2,D2,L1,V0,M1} { empty( skol7 ) }.
% 0.74/1.15 (1998) {G0,W2,D2,L1,V0,M1} { function( skol7 ) }.
% 0.74/1.15 (1999) {G0,W2,D2,L1,V0,M1} { ! empty( skol8 ) }.
% 0.74/1.15 (2000) {G0,W2,D2,L1,V0,M1} { relation( skol8 ) }.
% 0.74/1.15 (2001) {G0,W2,D2,L1,V0,M1} { ! empty( skol9 ) }.
% 0.74/1.15 (2002) {G0,W2,D2,L1,V0,M1} { relation( skol10 ) }.
% 0.74/1.15 (2003) {G0,W2,D2,L1,V0,M1} { function( skol10 ) }.
% 0.74/1.15 (2004) {G0,W2,D2,L1,V0,M1} { one_to_one( skol10 ) }.
% 0.74/1.15 (2005) {G0,W2,D2,L1,V0,M1} { relation( skol11 ) }.
% 0.74/1.15 (2006) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( skol11 ) }.
% 0.74/1.15 (2007) {G0,W2,D2,L1,V0,M1} { relation( skol12 ) }.
% 0.74/1.15 (2008) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( skol12 ) }.
% 0.74/1.15 (2009) {G0,W2,D2,L1,V0,M1} { function( skol12 ) }.
% 0.74/1.15 (2010) {G0,W2,D2,L1,V0,M1} { relation( skol13 ) }.
% 0.74/1.15 (2011) {G0,W2,D2,L1,V0,M1} { relation_non_empty( skol13 ) }.
% 0.74/1.15 (2012) {G0,W2,D2,L1,V0,M1} { function( skol13 ) }.
% 0.74/1.15 (2013) {G0,W3,D2,L1,V1,M1} { subset( X, X ) }.
% 0.74/1.15 (2014) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), element( X, Y ) }.
% 0.74/1.15 (2015) {G0,W9,D2,L3,V3,M3} { ! subset( X, Z ), ! subset( Z, Y ), subset( X
% 0.74/1.15 , Y ) }.
% 0.74/1.15 (2016) {G0,W10,D2,L4,V2,M4} { ! epsilon_transitive( X ), ! ordinal( Y ), !
% 0.74/1.15 proper_subset( X, Y ), in( X, Y ) }.
% 0.74/1.15 (2017) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol14 ) }.
% 0.74/1.15 (2018) {G0,W2,D2,L1,V0,M1} { ordinal( skol15 ) }.
% 0.74/1.15 (2019) {G0,W2,D2,L1,V0,M1} { ordinal( skol16 ) }.
% 0.74/1.15 (2020) {G0,W3,D2,L1,V0,M1} { subset( skol14, skol15 ) }.
% 0.74/1.15 (2021) {G0,W3,D2,L1,V0,M1} { in( skol15, skol16 ) }.
% 0.74/1.15 (2022) {G0,W3,D2,L1,V0,M1} { ! in( skol14, skol16 ) }.
% 0.74/1.15 (2023) {G0,W8,D2,L3,V2,M3} { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.74/1.15 (2024) {G0,W7,D3,L2,V2,M2} { ! element( X, powerset( Y ) ), subset( X, Y )
% 0.74/1.15 }.
% 0.74/1.15 (2025) {G0,W7,D3,L2,V2,M2} { ! subset( X, Y ), element( X, powerset( Y ) )
% 0.74/1.15 }.
% 0.74/1.15 (2026) {G0,W10,D3,L3,V3,M3} { ! in( X, Z ), ! element( Z, powerset( Y ) )
% 0.74/1.15 , element( X, Y ) }.
% 0.74/1.15 (2027) {G0,W9,D3,L3,V3,M3} { ! in( X, Y ), ! element( Y, powerset( Z ) ),
% 0.74/1.15 ! empty( Z ) }.
% 0.74/1.15 (2028) {G0,W5,D2,L2,V1,M2} { ! empty( X ), X = empty_set }.
% 0.74/1.15 (2029) {G0,W5,D2,L2,V2,M2} { ! in( X, Y ), ! empty( Y ) }.
% 0.74/1.15 (2030) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), ! subset( Y, X ) }.
% 0.74/1.15 (2031) {G0,W7,D2,L3,V2,M3} { ! empty( X ), X = Y, ! empty( Y ) }.
% 0.74/1.15
% 0.74/1.15
% 0.74/1.15 Total Proof:
% 0.74/1.15
% 0.74/1.15 subsumption: (1) {G0,W6,D2,L2,V2,M2} I { ! proper_subset( X, Y ), !
% 0.74/1.15 proper_subset( Y, X ) }.
% 0.74/1.15 parent0: (1965) {G0,W6,D2,L2,V2,M2} { ! proper_subset( X, Y ), !
% 0.74/1.15 proper_subset( Y, X ) }.
% 0.74/1.15 substitution0:
% 0.74/1.15 X := X
% 0.74/1.15 Y := Y
% 0.74/1.15 end
% 0.74/1.15 permutation0:
% 0.74/1.15 0 ==> 0
% 0.74/1.15 1 ==> 1
% 0.74/1.15 end
% 0.74/1.15
% 0.74/1.15 subsumption: (3) {G0,W4,D2,L2,V1,M2} I { ! ordinal( X ), epsilon_transitive
% 0.74/1.15 ( X ) }.
% 0.74/1.15 parent0: (1967) {G0,W4,D2,L2,V1,M2} { ! ordinal( X ), epsilon_transitive(
% 0.74/1.15 X ) }.
% 0.74/1.15 substitution0:
% 0.74/1.15 X := X
% 0.74/1.15 end
% 0.74/1.15 permutation0:
% 0.74/1.15 0 ==> 0
% 0.74/1.15 1 ==> 1
% 0.74/1.15 end
% 0.74/1.15
% 0.74/1.15 subsumption: (8) {G0,W8,D2,L3,V2,M3} I { ! epsilon_transitive( X ), ! in( Y
% 0.74/1.15 , X ), subset( Y, X ) }.
% 0.74/1.15 parent0: (1974) {G0,W8,D2,L3,V2,M3} { ! epsilon_transitive( X ), ! in( Y,
% 0.74/1.15 X ), subset( Y, X ) }.
% 0.74/1.15 substitution0:
% 0.74/1.15 X := X
% 0.74/1.15 Y := Y
% 0.74/1.15 end
% 0.74/1.15 permutation0:
% 0.74/1.15 0 ==> 0
% 0.74/1.15 1 ==> 1
% 0.74/1.15 2 ==> 2
% 0.74/1.15 end
% 0.74/1.15
% 0.74/1.15 subsumption: (12) {G0,W6,D2,L2,V2,M2} I { ! proper_subset( X, Y ), ! X = Y
% 0.74/1.15 }.
% 0.74/1.15 parent0: (1978) {G0,W6,D2,L2,V2,M2} { ! proper_subset( X, Y ), ! X = Y }.
% 0.74/1.15 substitution0:
% 0.74/1.15 X := X
% 0.74/1.15 Y := Y
% 0.74/1.15 end
% 0.74/1.15 permutation0:
% 0.74/1.15 0 ==> 0
% 0.74/1.15 1 ==> 1
% 0.74/1.15 end
% 0.74/1.15
% 0.74/1.15 subsumption: (13) {G0,W9,D2,L3,V2,M3} I { ! subset( X, Y ), X = Y,
% 0.74/1.15 proper_subset( X, Y ) }.
% 0.74/1.15 parent0: (1979) {G0,W9,D2,L3,V2,M3} { ! subset( X, Y ), X = Y,
% 0.74/1.15 proper_subset( X, Y ) }.
% 0.74/1.15 substitution0:
% 0.74/1.15 X := X
% 0.74/1.15 Y := Y
% 0.74/1.15 end
% 0.74/1.15 permutation0:
% 0.74/1.15 0 ==> 0
% 0.74/1.15 1 ==> 1
% 0.74/1.15 2 ==> 2
% 0.74/1.15 end
% 0.74/1.15
% 0.74/1.15 subsumption: (44) {G0,W3,D2,L1,V1,M1} I { subset( X, X ) }.
% 0.74/1.15 parent0: (2013) {G0,W3,D2,L1,V1,M1} { subset( X, X ) }.
% 0.74/1.15 substitution0:
% 0.74/1.15 X := X
% 0.74/1.15 end
% 0.74/1.15 permutation0:
% 0.74/1.15 0 ==> 0
% 0.74/1.15 end
% 0.74/1.15
% 0.74/1.15 subsumption: (45) {G0,W6,D2,L2,V2,M2} I { ! in( X, Y ), element( X, Y ) }.
% 0.74/1.15 parent0: (2014) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), element( X, Y ) }.
% 0.74/1.15 substitution0:
% 0.74/1.15 X := X
% 0.74/1.15 Y := Y
% 0.74/1.15 end
% 0.74/1.15 permutation0:
% 0.74/1.15 0 ==> 0
% 0.74/1.15 1 ==> 1
% 0.74/1.15 end
% 0.74/1.15
% 0.74/1.15 subsumption: (46) {G0,W9,D2,L3,V3,M3} I { ! subset( X, Z ), ! subset( Z, Y
% 0.74/1.15 ), subset( X, Y ) }.
% 0.74/1.15 parent0: (2015) {G0,W9,D2,L3,V3,M3} { ! subset( X, Z ), ! subset( Z, Y ),
% 0.74/1.15 subset( X, Y ) }.
% 0.74/1.15 substitution0:
% 0.74/1.15 X := X
% 0.74/1.15 Y := Y
% 0.74/1.15 Z := Z
% 0.74/1.15 end
% 0.74/1.15 permutation0:
% 0.74/1.15 0 ==> 0
% 0.74/1.15 1 ==> 1
% 0.74/1.15 2 ==> 2
% 0.74/1.15 end
% 0.74/1.15
% 0.74/1.15 subsumption: (47) {G0,W10,D2,L4,V2,M4} I { ! epsilon_transitive( X ), !
% 0.74/1.15 ordinal( Y ), ! proper_subset( X, Y ), in( X, Y ) }.
% 0.74/1.15 parent0: (2016) {G0,W10,D2,L4,V2,M4} { ! epsilon_transitive( X ), !
% 0.74/1.15 ordinal( Y ), ! proper_subset( X, Y ), in( X, Y ) }.
% 0.74/1.15 substitution0:
% 0.74/1.15 X := X
% 0.74/1.15 Y := Y
% 0.74/1.15 end
% 0.74/1.15 permutation0:
% 0.74/1.15 0 ==> 0
% 0.74/1.15 1 ==> 1
% 0.74/1.15 2 ==> 2
% 0.74/1.15 3 ==> 3
% 0.74/1.15 end
% 0.74/1.15
% 0.74/1.15 subsumption: (48) {G0,W2,D2,L1,V0,M1} I { epsilon_transitive( skol14 ) }.
% 0.74/1.15 parent0: (2017) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol14 ) }.
% 0.74/1.15 substitution0:
% 0.74/1.15 end
% 0.74/1.15 permutation0:
% 0.74/1.15 0 ==> 0
% 0.74/1.15 end
% 0.74/1.15
% 0.74/1.15 subsumption: (50) {G0,W2,D2,L1,V0,M1} I { ordinal( skol16 ) }.
% 0.74/1.15 parent0: (2019) {G0,W2,D2,L1,V0,M1} { ordinal( skol16 ) }.
% 0.74/1.15 substitution0:
% 0.74/1.15 end
% 0.74/1.15 permutation0:
% 0.74/1.15 0 ==> 0
% 0.74/1.15 end
% 0.74/1.15
% 0.74/1.15 subsumption: (51) {G0,W3,D2,L1,V0,M1} I { subset( skol14, skol15 ) }.
% 0.74/1.15 parent0: (2020) {G0,W3,D2,L1,V0,M1} { subset( skol14, skol15 ) }.
% 0.74/1.15 substitution0:
% 0.74/1.15 end
% 0.74/1.15 permutation0:
% 0.74/1.15 0 ==> 0
% 0.74/1.15 end
% 0.74/1.15
% 0.74/1.15 subsumption: (52) {G0,W3,D2,L1,V0,M1} I { in( skol15, skol16 ) }.
% 0.74/1.15 parent0: (2021) {G0,W3,D2,L1,V0,M1} { in( skol15, skol16 ) }.
% 0.74/1.15 substitution0:
% 0.74/1.15 end
% 0.74/1.15 permutation0:
% 0.74/1.15 0 ==> 0
% 0.74/1.15 end
% 0.74/1.15
% 0.74/1.15 subsumption: (53) {G0,W3,D2,L1,V0,M1} I { ! in( skol14, skol16 ) }.
% 0.74/1.15 parent0: (2022) {G0,W3,D2,L1,V0,M1} { ! in( skol14, skol16 ) }.
% 0.74/1.15 substitution0:
% 0.74/1.15 end
% 0.74/1.15 permutation0:
% 0.74/1.15 0 ==> 0
% 0.74/1.15 end
% 0.74/1.15
% 0.74/1.15 subsumption: (54) {G0,W8,D2,L3,V2,M3} I { ! element( X, Y ), empty( Y ), in
% 0.74/1.15 ( X, Y ) }.
% 0.74/1.15 parent0: (2023) {G0,W8,D2,L3,V2,M3} { ! element( X, Y ), empty( Y ), in( X
% 0.74/1.15 , Y ) }.
% 0.74/1.15 substitution0:
% 0.74/1.15 X := X
% 0.74/1.15 Y := Y
% 0.74/1.15 end
% 0.74/1.15 permutation0:
% 0.74/1.15 0 ==> 0
% 0.74/1.15 1 ==> 1
% 0.74/1.15 2 ==> 2
% 0.74/1.15 end
% 0.74/1.15
% 0.74/1.15 subsumption: (60) {G0,W5,D2,L2,V2,M2} I { ! in( X, Y ), ! empty( Y ) }.
% 0.74/1.15 parent0: (2029) {G0,W5,D2,L2,V2,M2} { ! in( X, Y ), ! empty( Y ) }.
% 0.74/1.15 substitution0:
% 0.74/1.15 X := X
% 0.74/1.15 Y := Y
% 0.74/1.15 end
% 0.74/1.15 permutation0:
% 0.74/1.15 0 ==> 0
% 0.74/1.15 1 ==> 1
% 0.74/1.15 end
% 0.74/1.15
% 0.74/1.15 resolution: (2099) {G1,W2,D2,L1,V0,M1} { epsilon_transitive( skol16 ) }.
% 0.74/1.15 parent0[0]: (3) {G0,W4,D2,L2,V1,M2} I { ! ordinal( X ), epsilon_transitive
% 0.74/1.15 ( X ) }.
% 0.74/1.15 parent1[0]: (50) {G0,W2,D2,L1,V0,M1} I { ordinal( skol16 ) }.
% 0.74/1.15 substitution0:
% 0.74/1.15 X := skol16
% 0.74/1.15 end
% 0.74/1.15 substitution1:
% 0.74/1.15 end
% 0.74/1.15
% 0.74/1.15 subsumption: (65) {G1,W2,D2,L1,V0,M1} R(3,50) { epsilon_transitive( skol16
% 0.74/1.15 ) }.
% 0.74/1.15 parent0: (2099) {G1,W2,D2,L1,V0,M1} { epsilon_transitive( skol16 ) }.
% 0.74/1.15 substitution0:
% 0.74/1.15 end
% 0.74/1.15 permutation0:
% 0.74/1.15 0 ==> 0
% 0.74/1.15 end
% 0.74/1.15
% 0.74/1.15 resolution: (2100) {G1,W5,D2,L2,V0,M2} { ! epsilon_transitive( skol16 ),
% 0.74/1.15 subset( skol15, skol16 ) }.
% 0.74/1.15 parent0[1]: (8) {G0,W8,D2,L3,V2,M3} I { ! epsilon_transitive( X ), ! in( Y
% 0.74/1.15 , X ), subset( Y, X ) }.
% 0.74/1.15 parent1[0]: (52) {G0,W3,D2,L1,V0,M1} I { in( skol15, skol16 ) }.
% 0.74/1.15 substitution0:
% 0.74/1.15 X := skol16
% 0.74/1.15 Y := skol15
% 0.74/1.15 end
% 0.74/1.15 substitution1:
% 0.74/1.15 end
% 0.74/1.15
% 0.74/1.15 resolution: (2101) {G2,W3,D2,L1,V0,M1} { subset( skol15, skol16 ) }.
% 0.74/1.15 parent0[0]: (2100) {G1,W5,D2,L2,V0,M2} { ! epsilon_transitive( skol16 ),
% 0.74/1.15 subset( skol15, skol16 ) }.
% 0.74/1.15 parent1[0]: (65) {G1,W2,D2,L1,V0,M1} R(3,50) { epsilon_transitive( skol16 )
% 0.74/1.15 }.
% 0.74/1.15 substitution0:
% 0.74/1.15 end
% 0.74/1.15 substitution1:
% 0.74/1.15 end
% 0.74/1.15
% 0.74/1.15 subsumption: (82) {G2,W3,D2,L1,V0,M1} R(52,8);r(65) { subset( skol15,
% 0.74/1.15 skol16 ) }.
% 0.74/1.15 parent0: (2101) {G2,W3,D2,L1,V0,M1} { subset( skol15, skol16 ) }.
% 0.74/1.15 substitution0:
% 0.74/1.15 end
% 0.74/1.15 permutation0:
% 0.74/1.15 0 ==> 0
% 0.74/1.15 end
% 0.74/1.15
% 0.74/1.15 resolution: (2102) {G1,W2,D2,L1,V0,M1} { ! empty( skol16 ) }.
% 0.74/1.15 parent0[0]: (60) {G0,W5,D2,L2,V2,M2} I { ! in( X, Y ), ! empty( Y ) }.
% 0.74/1.15 parent1[0]: (52) {G0,W3,D2,L1,V0,M1} I { in( skol15, skol16 ) }.
% 0.74/1.15 substitution0:
% 0.74/1.15 X := skol15
% 0.74/1.15 Y := skol16
% 0.74/1.15 end
% 0.74/1.15 substitution1:
% 0.74/1.15 end
% 0.74/1.15
% 0.74/1.15 subsumption: (91) {G1,W2,D2,L1,V0,M1} R(60,52) { ! empty( skol16 ) }.
% 0.74/1.15 parent0: (2102) {G1,W2,D2,L1,V0,M1} { ! empty( skol16 ) }.
% 0.74/1.15 substitution0:
% 0.74/1.15 end
% 0.74/1.15 permutation0:
% 0.74/1.15 0 ==> 0
% 0.74/1.15 end
% 0.74/1.15
% 0.74/1.15 eqswap: (2103) {G0,W9,D2,L3,V2,M3} { Y = X, ! subset( X, Y ),
% 0.74/1.15 proper_subset( X, Y ) }.
% 0.74/1.15 parent0[1]: (13) {G0,W9,D2,L3,V2,M3} I { ! subset( X, Y ), X = Y,
% 0.74/1.15 proper_subset( X, Y ) }.
% 0.74/1.15 substitution0:
% 0.74/1.15 X := X
% 0.74/1.15 Y := Y
% 0.74/1.15 end
% 0.74/1.15
% 0.74/1.15 resolution: (2104) {G1,W6,D2,L2,V0,M2} { skol15 = skol14, proper_subset(
% 0.74/1.15 skol14, skol15 ) }.
% 0.74/1.15 parent0[1]: (2103) {G0,W9,D2,L3,V2,M3} { Y = X, ! subset( X, Y ),
% 0.74/1.15 proper_subset( X, Y ) }.
% 0.74/1.15 parent1[0]: (51) {G0,W3,D2,L1,V0,M1} I { subset( skol14, skol15 ) }.
% 0.74/1.15 substitution0:
% 0.74/1.15 X := skol14
% 0.74/1.15 Y := skol15
% 0.74/1.15 end
% 0.74/1.15 substitution1:
% 0.74/1.15 end
% 0.74/1.15
% 0.74/1.15 subsumption: (98) {G1,W6,D2,L2,V0,M2} R(13,51) { skol15 ==> skol14,
% 0.74/1.15 proper_subset( skol14, skol15 ) }.
% 0.74/1.15 parent0: (2104) {G1,W6,D2,L2,V0,M2} { skol15 = skol14, proper_subset(
% 0.74/1.15 skol14, skol15 ) }.
% 0.74/1.15 substitution0:
% 0.74/1.15 end
% 0.74/1.15 permutation0:
% 0.74/1.15 0 ==> 0
% 0.74/1.15 1 ==> 1
% 0.74/1.15 end
% 0.74/1.15
% 0.74/1.15 eqswap: (2106) {G0,W9,D2,L3,V2,M3} { Y = X, ! subset( X, Y ),
% 0.74/1.15 proper_subset( X, Y ) }.
% 0.74/1.15 parent0[1]: (13) {G0,W9,D2,L3,V2,M3} I { ! subset( X, Y ), X = Y,
% 0.74/1.15 proper_subset( X, Y ) }.
% 0.74/1.15 substitution0:
% 0.74/1.15 X := X
% 0.74/1.15 Y := Y
% 0.74/1.15 end
% 0.74/1.15
% 0.74/1.15 resolution: (2107) {G1,W6,D2,L2,V0,M2} { skol16 = skol15, proper_subset(
% 0.74/1.15 skol15, skol16 ) }.
% 0.74/1.15 parent0[1]: (2106) {G0,W9,D2,L3,V2,M3} { Y = X, ! subset( X, Y ),
% 0.74/1.15 proper_subset( X, Y ) }.
% 0.74/1.15 parent1[0]: (82) {G2,W3,D2,L1,V0,M1} R(52,8);r(65) { subset( skol15, skol16
% 0.74/1.15 ) }.
% 0.74/1.15 substitution0:
% 0.74/1.15 X := skol15
% 0.74/1.15 Y := skol16
% 0.74/1.15 end
% 0.74/1.15 substitution1:
% 0.74/1.15 end
% 0.74/1.15
% 0.74/1.15 subsumption: (99) {G3,W6,D2,L2,V0,M2} R(13,82) { skol16 ==> skol15,
% 0.74/1.15 proper_subset( skol15, skol16 ) }.
% 0.74/1.15 parent0: (2107) {G1,W6,D2,L2,V0,M2} { skol16 = skol15, proper_subset(
% 0.74/1.15 skol15, skol16 ) }.
% 0.74/1.15 substitution0:
% 0.74/1.15 end
% 0.74/1.15 permutation0:
% 0.74/1.15 0 ==> 0
% 0.74/1.15 1 ==> 1
% 0.74/1.15 end
% 0.74/1.15
% 0.74/1.15 eqswap: (2109) {G0,W9,D2,L3,V2,M3} { Y = X, ! subset( X, Y ),
% 0.74/1.15 proper_subset( X, Y ) }.
% 0.74/1.15 parent0[1]: (13) {G0,W9,D2,L3,V2,M3} I { ! subset( X, Y ), X = Y,
% 0.74/1.15 proper_subset( X, Y ) }.
% 0.74/1.15 substitution0:
% 0.74/1.15 X := X
% 0.74/1.15 Y := Y
% 0.74/1.15 end
% 0.74/1.15
% 0.74/1.15 resolution: (2110) {G1,W9,D2,L3,V2,M3} { ! proper_subset( Y, X ), Y = X, !
% 0.74/1.15 subset( X, Y ) }.
% 0.74/1.15 parent0[0]: (1) {G0,W6,D2,L2,V2,M2} I { ! proper_subset( X, Y ), !
% 0.74/1.15 proper_subset( Y, X ) }.
% 0.74/1.15 parent1[2]: (2109) {G0,W9,D2,L3,V2,M3} { Y = X, ! subset( X, Y ),
% 0.74/1.15 proper_subset( X, Y ) }.
% 0.74/1.15 substitution0:
% 0.74/1.15 X := X
% 0.74/1.15 Y := Y
% 0.74/1.15 end
% 0.74/1.15 substitution1:
% 0.74/1.15 X := X
% 0.74/1.15 Y := Y
% 0.74/1.15 end
% 0.74/1.15
% 0.74/1.15 eqswap: (2111) {G1,W9,D2,L3,V2,M3} { Y = X, ! proper_subset( X, Y ), !
% 0.74/1.15 subset( Y, X ) }.
% 0.74/1.15 parent0[1]: (2110) {G1,W9,D2,L3,V2,M3} { ! proper_subset( Y, X ), Y = X, !
% 0.74/1.15 subset( X, Y ) }.
% 0.74/1.15 substitution0:
% 0.74/1.15 X := Y
% 0.74/1.15 Y := X
% 0.74/1.15 end
% 0.74/1.15
% 0.74/1.15 subsumption: (101) {G1,W9,D2,L3,V2,M3} R(13,1) { ! subset( X, Y ), X = Y, !
% 0.74/1.15 proper_subset( Y, X ) }.
% 0.74/1.15 parent0: (2111) {G1,W9,D2,L3,V2,M3} { Y = X, ! proper_subset( X, Y ), !
% 0.74/1.15 subset( Y, X ) }.
% 0.74/1.15 substitution0:
% 0.74/1.15 X := Y
% 0.74/1.15 Y := X
% 0.74/1.15 end
% 0.74/1.15 permutation0:
% 0.74/1.15 0 ==> 1
% 0.74/1.15 1 ==> 2
% 0.74/1.15 2 ==> 0
% 0.74/1.15 end
% 0.74/1.15
% 0.74/1.15 resolution: (2112) {G1,W3,D2,L1,V0,M1} { element( skol15, skol16 ) }.
% 0.74/1.15 parent0[0]: (45) {G0,W6,D2,L2,V2,M2} I { ! in( X, Y ), element( X, Y ) }.
% 0.74/1.15 parent1[0]: (52) {G0,W3,D2,L1,V0,M1} I { in( skol15, skol16 ) }.
% 0.74/1.15 substitution0:
% 0.74/1.15 X := skol15
% 0.74/1.15 Y := skol16
% 0.74/1.15 end
% 0.74/1.15 substitution1:
% 0.74/1.15 end
% 0.74/1.15
% 0.74/1.15 subsumption: (232) {G1,W3,D2,L1,V0,M1} R(45,52) { element( skol15, skol16 )
% 0.74/1.15 }.
% 0.74/1.15 parent0: (2112) {G1,W3,D2,L1,V0,M1} { element( skol15, skol16 ) }.
% 0.74/1.15 substitution0:
% 0.74/1.15 end
% 0.74/1.15 permutation0:
% 0.74/1.15 0 ==> 0
% 0.74/1.15 end
% 0.74/1.15
% 0.74/1.15 resolution: (2114) {G1,W6,D2,L2,V1,M2} { ! subset( X, skol14 ), subset( X
% 0.74/1.15 , skol15 ) }.
% 0.74/1.15 parent0[1]: (46) {G0,W9,D2,L3,V3,M3} I { ! subset( X, Z ), ! subset( Z, Y )
% 0.74/1.15 , subset( X, Y ) }.
% 0.74/1.15 parent1[0]: (51) {G0,W3,D2,L1,V0,M1} I { subset( skol14, skol15 ) }.
% 0.74/1.15 substitution0:
% 0.74/1.15 X := X
% 0.74/1.15 Y := skol15
% 0.74/1.15 Z := skol14
% 0.74/1.15 end
% 0.74/1.15 substitution1:
% 0.74/1.15 end
% 0.74/1.15
% 0.74/1.15 subsumption: (252) {G1,W6,D2,L2,V1,M2} R(46,51) { ! subset( X, skol14 ),
% 0.74/1.15 subset( X, skol15 ) }.
% 0.74/1.15 parent0: (2114) {G1,W6,D2,L2,V1,M2} { ! subset( X, skol14 ), subset( X,
% 0.74/1.15 skol15 ) }.
% 0.74/1.15 substitution0:
% 0.74/1.15 X := X
% 0.74/1.15 end
% 0.74/1.15 permutation0:
% 0.74/1.15 0 ==> 0
% 0.74/1.15 1 ==> 1
% 0.74/1.15 end
% 0.74/1.15
% 0.74/1.15 resolution: (2115) {G1,W7,D2,L3,V0,M3} { ! epsilon_transitive( skol14 ), !
% 0.74/1.15 ordinal( skol16 ), ! proper_subset( skol14, skol16 ) }.
% 0.74/1.15 parent0[0]: (53) {G0,W3,D2,L1,V0,M1} I { ! in( skol14, skol16 ) }.
% 0.74/1.15 parent1[3]: (47) {G0,W10,D2,L4,V2,M4} I { ! epsilon_transitive( X ), !
% 0.74/1.15 ordinal( Y ), ! proper_subset( X, Y ), in( X, Y ) }.
% 0.74/1.15 substitution0:
% 0.74/1.15 end
% 0.74/1.15 substitution1:
% 0.74/1.15 X := skol14
% 0.74/1.15 Y := skol16
% 0.74/1.15 end
% 0.74/1.15
% 0.74/1.15 resolution: (2116) {G1,W5,D2,L2,V0,M2} { ! ordinal( skol16 ), !
% 0.74/1.15 proper_subset( skol14, skol16 ) }.
% 0.74/1.15 parent0[0]: (2115) {G1,W7,D2,L3,V0,M3} { ! epsilon_transitive( skol14 ), !
% 0.74/1.15 ordinal( skol16 ), ! proper_subset( skol14, skol16 ) }.
% 0.74/1.15 parent1[0]: (48) {G0,W2,D2,L1,V0,M1} I { epsilon_transitive( skol14 ) }.
% 0.74/1.15 substitution0:
% 0.74/1.15 end
% 0.74/1.15 substitution1:
% 0.74/1.15 end
% 0.74/1.15
% 0.74/1.15 subsumption: (283) {G1,W5,D2,L2,V0,M2} R(47,53);r(48) { ! ordinal( skol16 )
% 0.74/1.15 , ! proper_subset( skol14, skol16 ) }.
% 0.74/1.15 parent0: (2116) {G1,W5,D2,L2,V0,M2} { ! ordinal( skol16 ), ! proper_subset
% 0.74/1.15 ( skol14, skol16 ) }.
% 0.74/1.15 substitution0:
% 0.74/1.15 end
% 0.74/1.15 permutation0:
% 0.74/1.15 0 ==> 0
% 0.74/1.15 1 ==> 1
% 0.74/1.15 end
% 0.74/1.15
% 0.74/1.15 resolution: (2117) {G1,W5,D2,L2,V0,M2} { ! element( skol14, skol16 ),
% 0.74/1.15 empty( skol16 ) }.
% 0.74/1.15 parent0[0]: (53) {G0,W3,D2,L1,V0,M1} I { ! in( skol14, skol16 ) }.
% 0.74/1.15 parent1[2]: (54) {G0,W8,D2,L3,V2,M3} I { ! element( X, Y ), empty( Y ), in
% 0.74/1.15 ( X, Y ) }.
% 0.74/1.15 substitution0:
% 0.74/1.15 end
% 0.74/1.15 substitution1:
% 0.74/1.15 X := skol14
% 0.74/1.15 Y := skol16
% 0.74/1.15 end
% 0.74/1.15
% 0.74/1.15 resolution: (2118) {G2,W3,D2,L1,V0,M1} { ! element( skol14, skol16 ) }.
% 0.74/1.44 parent0[0]: (91) {G1,W2,D2,L1,V0,M1} R(60,52) { ! empty( skol16 ) }.
% 0.74/1.44 parent1[1]: (2117) {G1,W5,D2,L2,V0,M2} { ! element( skol14, skol16 ),
% 0.74/1.44 empty( skol16 ) }.
% 0.74/1.44 substitution0:
% 0.74/1.44 end
% 0.74/1.44 substitution1:
% 0.74/1.44 end
% 0.74/1.44
% 0.74/1.44 subsumption: (326) {G2,W3,D2,L1,V0,M1} R(54,53);r(91) { ! element( skol14,
% 0.74/1.44 skol16 ) }.
% 0.74/1.44 parent0: (2118) {G2,W3,D2,L1,V0,M1} { ! element( skol14, skol16 ) }.
% 0.74/1.44 substitution0:
% 0.74/1.44 end
% 0.74/1.44 permutation0:
% 0.74/1.44 0 ==> 0
% 0.74/1.44 end
% 0.74/1.44
% 0.74/1.44 resolution: (2119) {G1,W3,D2,L1,V0,M1} { ! proper_subset( skol14, skol16 )
% 0.74/1.44 }.
% 0.74/1.44 parent0[0]: (283) {G1,W5,D2,L2,V0,M2} R(47,53);r(48) { ! ordinal( skol16 )
% 0.74/1.44 , ! proper_subset( skol14, skol16 ) }.
% 0.74/1.44 parent1[0]: (50) {G0,W2,D2,L1,V0,M1} I { ordinal( skol16 ) }.
% 0.74/1.44 substitution0:
% 0.74/1.44 end
% 0.74/1.44 substitution1:
% 0.74/1.44 end
% 0.74/1.44
% 0.74/1.44 subsumption: (888) {G2,W3,D2,L1,V0,M1} S(283);r(50) { ! proper_subset(
% 0.74/1.44 skol14, skol16 ) }.
% 0.74/1.44 parent0: (2119) {G1,W3,D2,L1,V0,M1} { ! proper_subset( skol14, skol16 )
% 0.74/1.44 }.
% 0.74/1.44 substitution0:
% 0.74/1.44 end
% 0.74/1.44 permutation0:
% 0.74/1.44 0 ==> 0
% 0.74/1.44 end
% 0.74/1.44
% 0.74/1.44 eqswap: (2120) {G0,W9,D2,L3,V2,M3} { Y = X, ! subset( X, Y ),
% 0.74/1.44 proper_subset( X, Y ) }.
% 0.74/1.44 parent0[1]: (13) {G0,W9,D2,L3,V2,M3} I { ! subset( X, Y ), X = Y,
% 0.74/1.44 proper_subset( X, Y ) }.
% 0.74/1.44 substitution0:
% 0.74/1.44 X := X
% 0.74/1.44 Y := Y
% 0.74/1.44 end
% 0.74/1.44
% 0.74/1.44 resolution: (2121) {G1,W6,D2,L2,V0,M2} { skol16 = skol14, ! subset( skol14
% 0.74/1.44 , skol16 ) }.
% 0.74/1.44 parent0[0]: (888) {G2,W3,D2,L1,V0,M1} S(283);r(50) { ! proper_subset(
% 0.74/1.44 skol14, skol16 ) }.
% 0.74/1.44 parent1[2]: (2120) {G0,W9,D2,L3,V2,M3} { Y = X, ! subset( X, Y ),
% 0.74/1.44 proper_subset( X, Y ) }.
% 0.74/1.44 substitution0:
% 0.74/1.44 end
% 0.74/1.44 substitution1:
% 0.74/1.44 X := skol14
% 0.74/1.44 Y := skol16
% 0.74/1.44 end
% 0.74/1.44
% 0.74/1.44 subsumption: (894) {G3,W6,D2,L2,V0,M2} R(888,13) { ! subset( skol14, skol16
% 0.74/1.44 ), skol16 ==> skol14 }.
% 0.74/1.44 parent0: (2121) {G1,W6,D2,L2,V0,M2} { skol16 = skol14, ! subset( skol14,
% 0.74/1.44 skol16 ) }.
% 0.74/1.44 substitution0:
% 0.74/1.44 end
% 0.74/1.44 permutation0:
% 0.74/1.44 0 ==> 1
% 0.74/1.44 1 ==> 0
% 0.74/1.44 end
% 0.74/1.44
% 0.74/1.44 paramod: (2124) {G2,W6,D2,L2,V0,M2} { element( skol14, skol16 ),
% 0.74/1.44 proper_subset( skol14, skol15 ) }.
% 0.74/1.44 parent0[0]: (98) {G1,W6,D2,L2,V0,M2} R(13,51) { skol15 ==> skol14,
% 0.74/1.44 proper_subset( skol14, skol15 ) }.
% 0.74/1.44 parent1[0; 1]: (232) {G1,W3,D2,L1,V0,M1} R(45,52) { element( skol15, skol16
% 0.74/1.44 ) }.
% 0.74/1.44 substitution0:
% 0.74/1.44 end
% 0.74/1.44 substitution1:
% 0.74/1.44 end
% 0.74/1.44
% 0.74/1.44 resolution: (2135) {G3,W3,D2,L1,V0,M1} { proper_subset( skol14, skol15 )
% 0.74/1.44 }.
% 0.74/1.44 parent0[0]: (326) {G2,W3,D2,L1,V0,M1} R(54,53);r(91) { ! element( skol14,
% 0.74/1.44 skol16 ) }.
% 0.74/1.44 parent1[0]: (2124) {G2,W6,D2,L2,V0,M2} { element( skol14, skol16 ),
% 0.74/1.44 proper_subset( skol14, skol15 ) }.
% 0.74/1.44 substitution0:
% 0.74/1.44 end
% 0.74/1.44 substitution1:
% 0.74/1.44 end
% 0.74/1.44
% 0.74/1.44 subsumption: (931) {G3,W3,D2,L1,V0,M1} P(98,232);r(326) { proper_subset(
% 0.74/1.44 skol14, skol15 ) }.
% 0.74/1.44 parent0: (2135) {G3,W3,D2,L1,V0,M1} { proper_subset( skol14, skol15 ) }.
% 0.74/1.44 substitution0:
% 0.74/1.44 end
% 0.74/1.44 permutation0:
% 0.74/1.44 0 ==> 0
% 0.74/1.44 end
% 0.74/1.44
% 0.74/1.44 eqswap: (2136) {G0,W6,D2,L2,V2,M2} { ! Y = X, ! proper_subset( X, Y ) }.
% 0.74/1.44 parent0[1]: (12) {G0,W6,D2,L2,V2,M2} I { ! proper_subset( X, Y ), ! X = Y
% 0.74/1.44 }.
% 0.74/1.44 substitution0:
% 0.74/1.44 X := X
% 0.74/1.44 Y := Y
% 0.74/1.44 end
% 0.74/1.44
% 0.74/1.44 resolution: (2137) {G1,W3,D2,L1,V0,M1} { ! skol15 = skol14 }.
% 0.74/1.44 parent0[1]: (2136) {G0,W6,D2,L2,V2,M2} { ! Y = X, ! proper_subset( X, Y )
% 0.74/1.44 }.
% 0.74/1.44 parent1[0]: (931) {G3,W3,D2,L1,V0,M1} P(98,232);r(326) { proper_subset(
% 0.74/1.44 skol14, skol15 ) }.
% 0.74/1.44 substitution0:
% 0.74/1.44 X := skol14
% 0.74/1.44 Y := skol15
% 0.74/1.44 end
% 0.74/1.44 substitution1:
% 0.74/1.44 end
% 0.74/1.44
% 0.74/1.44 subsumption: (937) {G4,W3,D2,L1,V0,M1} R(931,12) { ! skol15 ==> skol14 }.
% 0.74/1.44 parent0: (2137) {G1,W3,D2,L1,V0,M1} { ! skol15 = skol14 }.
% 0.74/1.44 substitution0:
% 0.74/1.44 end
% 0.74/1.44 permutation0:
% 0.74/1.44 0 ==> 0
% 0.74/1.44 end
% 0.74/1.44
% 0.74/1.44 resolution: (2139) {G1,W3,D2,L1,V0,M1} { ! proper_subset( skol15, skol14 )
% 0.74/1.44 }.
% 0.74/1.44 parent0[0]: (1) {G0,W6,D2,L2,V2,M2} I { ! proper_subset( X, Y ), !
% 0.74/1.44 proper_subset( Y, X ) }.
% 0.74/1.44 parent1[0]: (931) {G3,W3,D2,L1,V0,M1} P(98,232);r(326) { proper_subset(
% 0.74/1.44 skol14, skol15 ) }.
% 0.74/1.44 substitution0:
% 0.74/1.44 X := skol14
% 0.74/1.44 Y := skol15
% 0.74/1.44 end
% 0.74/1.44 substitution1:
% 0.74/1.44 end
% 0.74/1.44
% 0.74/1.44 subsumption: (938) {G4,W3,D2,L1,V0,M1} R(931,1) { ! proper_subset( skol15,
% 0.74/1.44 skol14 ) }.
% 0.74/1.44 parent0: (2139) {G1,W3,D2,L1,V0,M1} { ! proper_subset( skol15, skol14 )
% 0.74/1.44 }.
% 0.74/1.44 substitution0:
% 0.74/1.44 end
% 0.74/1.44 permutation0:
% 0.74/1.44 0 ==> 0
% 0.74/1.44 end
% 0.74/1.44
% 0.74/1.44 *** allocated 50625 integers for termspace/termends
% 0.74/1.44 *** allocated 15000 integers for justifications
% 0.74/1.44 *** allocated 22500 integers for justifications
% 0.74/1.44 *** allocated 75937 integers for termspace/termendCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------