TSTP Solution File: NUM414+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : NUM414+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n003.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 06:22:01 EDT 2022
% Result : Theorem 0.42s 1.08s
% Output : Refutation 0.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : NUM414+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : bliksem %s
% 0.11/0.33 % Computer : n003.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % DateTime : Tue Jul 5 18:41:55 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.42/1.08 *** allocated 10000 integers for termspace/termends
% 0.42/1.08 *** allocated 10000 integers for clauses
% 0.42/1.08 *** allocated 10000 integers for justifications
% 0.42/1.08 Bliksem 1.12
% 0.42/1.08
% 0.42/1.08
% 0.42/1.08 Automatic Strategy Selection
% 0.42/1.08
% 0.42/1.08
% 0.42/1.08 Clauses:
% 0.42/1.08
% 0.42/1.08 { ! in( X, Y ), ! in( Y, X ) }.
% 0.42/1.08 { ! proper_subset( X, Y ), ! proper_subset( Y, X ) }.
% 0.42/1.08 { ! empty( X ), function( X ) }.
% 0.42/1.08 { ! ordinal( X ), epsilon_transitive( X ) }.
% 0.42/1.08 { ! ordinal( X ), epsilon_connected( X ) }.
% 0.42/1.08 { ! empty( X ), relation( X ) }.
% 0.42/1.08 { ! relation( X ), ! empty( X ), ! function( X ), relation( X ) }.
% 0.42/1.08 { ! relation( X ), ! empty( X ), ! function( X ), function( X ) }.
% 0.42/1.08 { ! relation( X ), ! empty( X ), ! function( X ), one_to_one( X ) }.
% 0.42/1.08 { ! epsilon_transitive( X ), ! epsilon_connected( X ), ordinal( X ) }.
% 0.42/1.08 { ! empty( X ), epsilon_transitive( X ) }.
% 0.42/1.08 { ! empty( X ), epsilon_connected( X ) }.
% 0.42/1.08 { ! empty( X ), ordinal( X ) }.
% 0.42/1.08 { ! ordinal( X ), ! ordinal( Y ), ordinal_subset( X, Y ), ordinal_subset( Y
% 0.42/1.08 , X ) }.
% 0.42/1.08 { ! proper_subset( X, Y ), subset( X, Y ) }.
% 0.42/1.08 { ! proper_subset( X, Y ), ! X = Y }.
% 0.42/1.08 { ! subset( X, Y ), X = Y, proper_subset( X, Y ) }.
% 0.42/1.08 { element( skol1( X ), X ) }.
% 0.42/1.08 { empty( empty_set ) }.
% 0.42/1.08 { relation( empty_set ) }.
% 0.42/1.08 { relation_empty_yielding( empty_set ) }.
% 0.42/1.08 { empty( empty_set ) }.
% 0.42/1.08 { relation( empty_set ) }.
% 0.42/1.08 { relation_empty_yielding( empty_set ) }.
% 0.42/1.08 { function( empty_set ) }.
% 0.42/1.08 { one_to_one( empty_set ) }.
% 0.42/1.08 { empty( empty_set ) }.
% 0.42/1.08 { epsilon_transitive( empty_set ) }.
% 0.42/1.08 { epsilon_connected( empty_set ) }.
% 0.42/1.08 { ordinal( empty_set ) }.
% 0.42/1.08 { empty( empty_set ) }.
% 0.42/1.08 { relation( empty_set ) }.
% 0.42/1.08 { ! proper_subset( X, X ) }.
% 0.42/1.08 { relation( skol2 ) }.
% 0.42/1.08 { function( skol2 ) }.
% 0.42/1.08 { epsilon_transitive( skol3 ) }.
% 0.42/1.08 { epsilon_connected( skol3 ) }.
% 0.42/1.08 { ordinal( skol3 ) }.
% 0.42/1.08 { empty( skol4 ) }.
% 0.42/1.08 { relation( skol4 ) }.
% 0.42/1.08 { empty( skol5 ) }.
% 0.42/1.08 { relation( skol6 ) }.
% 0.42/1.08 { empty( skol6 ) }.
% 0.42/1.08 { function( skol6 ) }.
% 0.42/1.08 { relation( skol7 ) }.
% 0.42/1.08 { function( skol7 ) }.
% 0.42/1.08 { one_to_one( skol7 ) }.
% 0.42/1.08 { empty( skol7 ) }.
% 0.42/1.08 { epsilon_transitive( skol7 ) }.
% 0.42/1.08 { epsilon_connected( skol7 ) }.
% 0.42/1.08 { ordinal( skol7 ) }.
% 0.42/1.08 { ! empty( skol8 ) }.
% 0.42/1.08 { relation( skol8 ) }.
% 0.42/1.08 { ! empty( skol9 ) }.
% 0.42/1.08 { relation( skol10 ) }.
% 0.42/1.08 { function( skol10 ) }.
% 0.42/1.08 { one_to_one( skol10 ) }.
% 0.42/1.08 { ! empty( skol11 ) }.
% 0.42/1.08 { epsilon_transitive( skol11 ) }.
% 0.42/1.08 { epsilon_connected( skol11 ) }.
% 0.42/1.08 { ordinal( skol11 ) }.
% 0.42/1.08 { relation( skol12 ) }.
% 0.42/1.08 { relation_empty_yielding( skol12 ) }.
% 0.42/1.08 { relation( skol13 ) }.
% 0.42/1.08 { relation_empty_yielding( skol13 ) }.
% 0.42/1.08 { function( skol13 ) }.
% 0.42/1.08 { relation( skol14 ) }.
% 0.42/1.08 { function( skol14 ) }.
% 0.42/1.08 { transfinite_sequence( skol14 ) }.
% 0.42/1.08 { relation( skol15 ) }.
% 0.42/1.08 { relation_non_empty( skol15 ) }.
% 0.42/1.08 { function( skol15 ) }.
% 0.42/1.08 { ! ordinal( X ), ! ordinal( Y ), ! ordinal_subset( X, Y ), subset( X, Y )
% 0.42/1.08 }.
% 0.42/1.08 { ! ordinal( X ), ! ordinal( Y ), ! subset( X, Y ), ordinal_subset( X, Y )
% 0.42/1.08 }.
% 0.42/1.08 { ! ordinal( X ), ! ordinal( Y ), ordinal_subset( X, X ) }.
% 0.42/1.08 { subset( X, X ) }.
% 0.42/1.08 { ! in( X, Y ), element( X, Y ) }.
% 0.42/1.08 { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.42/1.08 { ! element( X, powerset( Y ) ), subset( X, Y ) }.
% 0.42/1.08 { ! subset( X, Y ), element( X, powerset( Y ) ) }.
% 0.42/1.08 { ! in( X, Z ), ! element( Z, powerset( Y ) ), element( X, Y ) }.
% 0.42/1.08 { ordinal( skol16 ) }.
% 0.42/1.08 { ordinal( skol17 ) }.
% 0.42/1.08 { ! proper_subset( skol16, skol17 ) }.
% 0.42/1.08 { ! skol16 = skol17 }.
% 0.42/1.08 { ! proper_subset( skol17, skol16 ) }.
% 0.42/1.08 { ! in( X, Y ), ! element( Y, powerset( Z ) ), ! empty( Z ) }.
% 0.42/1.08 { ! empty( X ), X = empty_set }.
% 0.42/1.08 { ! in( X, Y ), ! empty( Y ) }.
% 0.42/1.08 { ! empty( X ), X = Y, ! empty( Y ) }.
% 0.42/1.08
% 0.42/1.08 percentage equality = 0.040323, percentage horn = 0.963415
% 0.42/1.08 This is a problem with some equality
% 0.42/1.08
% 0.42/1.08
% 0.42/1.08
% 0.42/1.08 Options Used:
% 0.42/1.08
% 0.42/1.08 useres = 1
% 0.42/1.08 useparamod = 1
% 0.42/1.08 useeqrefl = 1
% 0.42/1.08 useeqfact = 1
% 0.42/1.08 usefactor = 1
% 0.42/1.08 usesimpsplitting = 0
% 0.42/1.08 usesimpdemod = 5
% 0.42/1.08 usesimpres = 3
% 0.42/1.08
% 0.42/1.08 resimpinuse = 1000
% 0.42/1.08 resimpclauses = 20000
% 0.42/1.08 substype = eqrewr
% 0.42/1.08 backwardsubs = 1
% 0.42/1.08 selectoldest = 5
% 0.42/1.08
% 0.42/1.08 litorderings [0] = split
% 0.42/1.08 litorderings [1] = extend the termordering, first sorting on arguments
% 0.42/1.08
% 0.42/1.08 termordering = kbo
% 0.42/1.08
% 0.42/1.08 litapriori = 0
% 0.42/1.08 termapriori = 1
% 0.42/1.08 litaposteriori = 0
% 0.42/1.08 termaposteriori = 0
% 0.42/1.08 demodaposteriori = 0
% 0.42/1.08 ordereqreflfact = 0
% 0.42/1.08
% 0.42/1.08 litselect = negord
% 0.42/1.08
% 0.42/1.08 maxweight = 15
% 0.42/1.08 maxdepth = 30000
% 0.42/1.08 maxlength = 115
% 0.42/1.08 maxnrvars = 195
% 0.42/1.08 excuselevel = 1
% 0.42/1.08 increasemaxweight = 1
% 0.42/1.08
% 0.42/1.08 maxselected = 10000000
% 0.42/1.08 maxnrclauses = 10000000
% 0.42/1.08
% 0.42/1.08 showgenerated = 0
% 0.42/1.08 showkept = 0
% 0.42/1.08 showselected = 0
% 0.42/1.08 showdeleted = 0
% 0.42/1.08 showresimp = 1
% 0.42/1.08 showstatus = 2000
% 0.42/1.08
% 0.42/1.08 prologoutput = 0
% 0.42/1.08 nrgoals = 5000000
% 0.42/1.08 totalproof = 1
% 0.42/1.08
% 0.42/1.08 Symbols occurring in the translation:
% 0.42/1.08
% 0.42/1.08 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.42/1.08 . [1, 2] (w:1, o:43, a:1, s:1, b:0),
% 0.42/1.08 ! [4, 1] (w:0, o:26, a:1, s:1, b:0),
% 0.42/1.08 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.42/1.08 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.42/1.08 in [37, 2] (w:1, o:67, a:1, s:1, b:0),
% 0.42/1.08 proper_subset [38, 2] (w:1, o:69, a:1, s:1, b:0),
% 0.42/1.08 empty [39, 1] (w:1, o:31, a:1, s:1, b:0),
% 0.42/1.08 function [40, 1] (w:1, o:34, a:1, s:1, b:0),
% 0.42/1.08 ordinal [41, 1] (w:1, o:35, a:1, s:1, b:0),
% 0.42/1.08 epsilon_transitive [42, 1] (w:1, o:32, a:1, s:1, b:0),
% 0.42/1.08 epsilon_connected [43, 1] (w:1, o:33, a:1, s:1, b:0),
% 0.42/1.08 relation [44, 1] (w:1, o:36, a:1, s:1, b:0),
% 0.42/1.08 one_to_one [45, 1] (w:1, o:37, a:1, s:1, b:0),
% 0.42/1.08 ordinal_subset [46, 2] (w:1, o:68, a:1, s:1, b:0),
% 0.42/1.08 subset [47, 2] (w:1, o:70, a:1, s:1, b:0),
% 0.42/1.08 element [48, 2] (w:1, o:71, a:1, s:1, b:0),
% 0.42/1.08 empty_set [49, 0] (w:1, o:8, a:1, s:1, b:0),
% 0.42/1.08 relation_empty_yielding [50, 1] (w:1, o:38, a:1, s:1, b:0),
% 0.42/1.08 transfinite_sequence [51, 1] (w:1, o:40, a:1, s:1, b:0),
% 0.42/1.08 relation_non_empty [52, 1] (w:1, o:41, a:1, s:1, b:0),
% 0.42/1.08 powerset [53, 1] (w:1, o:42, a:1, s:1, b:0),
% 0.42/1.08 skol1 [55, 1] (w:1, o:39, a:1, s:1, b:1),
% 0.42/1.08 skol2 [56, 0] (w:1, o:18, a:1, s:1, b:1),
% 0.42/1.08 skol3 [57, 0] (w:1, o:19, a:1, s:1, b:1),
% 0.42/1.08 skol4 [58, 0] (w:1, o:20, a:1, s:1, b:1),
% 0.42/1.08 skol5 [59, 0] (w:1, o:21, a:1, s:1, b:1),
% 0.42/1.08 skol6 [60, 0] (w:1, o:22, a:1, s:1, b:1),
% 0.42/1.08 skol7 [61, 0] (w:1, o:23, a:1, s:1, b:1),
% 0.42/1.08 skol8 [62, 0] (w:1, o:24, a:1, s:1, b:1),
% 0.42/1.08 skol9 [63, 0] (w:1, o:25, a:1, s:1, b:1),
% 0.42/1.08 skol10 [64, 0] (w:1, o:10, a:1, s:1, b:1),
% 0.42/1.08 skol11 [65, 0] (w:1, o:11, a:1, s:1, b:1),
% 0.42/1.08 skol12 [66, 0] (w:1, o:12, a:1, s:1, b:1),
% 0.42/1.08 skol13 [67, 0] (w:1, o:13, a:1, s:1, b:1),
% 0.42/1.08 skol14 [68, 0] (w:1, o:14, a:1, s:1, b:1),
% 0.42/1.08 skol15 [69, 0] (w:1, o:15, a:1, s:1, b:1),
% 0.42/1.08 skol16 [70, 0] (w:1, o:16, a:1, s:1, b:1),
% 0.42/1.08 skol17 [71, 0] (w:1, o:17, a:1, s:1, b:1).
% 0.42/1.08
% 0.42/1.08
% 0.42/1.08 Starting Search:
% 0.42/1.08
% 0.42/1.08 *** allocated 15000 integers for clauses
% 0.42/1.08 *** allocated 22500 integers for clauses
% 0.42/1.08 *** allocated 33750 integers for clauses
% 0.42/1.08 *** allocated 50625 integers for clauses
% 0.42/1.08
% 0.42/1.08 Bliksems!, er is een bewijs:
% 0.42/1.08 % SZS status Theorem
% 0.42/1.08 % SZS output start Refutation
% 0.42/1.08
% 0.42/1.08 (11) {G0,W10,D2,L4,V2,M4} I { ! ordinal( X ), ! ordinal( Y ),
% 0.42/1.08 ordinal_subset( X, Y ), ordinal_subset( Y, X ) }.
% 0.42/1.08 (14) {G0,W9,D2,L3,V2,M3} I { ! subset( X, Y ), X = Y, proper_subset( X, Y )
% 0.42/1.08 }.
% 0.42/1.08 (24) {G0,W3,D2,L1,V1,M1} I { ! proper_subset( X, X ) }.
% 0.42/1.08 (64) {G0,W10,D2,L4,V2,M4} I { ! ordinal( X ), ! ordinal( Y ), !
% 0.42/1.08 ordinal_subset( X, Y ), subset( X, Y ) }.
% 0.42/1.08 (73) {G0,W2,D2,L1,V0,M1} I { ordinal( skol16 ) }.
% 0.42/1.08 (74) {G0,W2,D2,L1,V0,M1} I { ordinal( skol17 ) }.
% 0.42/1.08 (75) {G0,W3,D2,L1,V0,M1} I { ! proper_subset( skol16, skol17 ) }.
% 0.42/1.08 (76) {G0,W3,D2,L1,V0,M1} I { ! skol17 ==> skol16 }.
% 0.42/1.08 (77) {G0,W3,D2,L1,V0,M1} I { ! proper_subset( skol17, skol16 ) }.
% 0.42/1.08 (323) {G1,W6,D2,L2,V0,M2} R(77,14) { ! subset( skol17, skol16 ), skol17 ==>
% 0.42/1.08 skol16 }.
% 0.42/1.08 (328) {G1,W9,D2,L3,V1,M3} P(14,76) { ! X = skol16, ! subset( skol17, X ),
% 0.42/1.08 proper_subset( skol17, X ) }.
% 0.42/1.08 (329) {G1,W9,D2,L3,V1,M3} P(14,76) { ! X = skol16, ! subset( X, skol17 ),
% 0.42/1.08 proper_subset( X, skol17 ) }.
% 0.42/1.08 (330) {G2,W3,D2,L1,V0,M1} Q(329);r(75) { ! subset( skol16, skol17 ) }.
% 0.42/1.08 (331) {G2,W3,D2,L1,V0,M1} Q(328);d(323);r(24) { ! subset( skol17, skol16 )
% 0.42/1.08 }.
% 0.42/1.08 (337) {G3,W5,D2,L2,V0,M2} R(330,64);r(73) { ! ordinal( skol17 ), !
% 0.42/1.08 ordinal_subset( skol16, skol17 ) }.
% 0.42/1.08 (702) {G4,W3,D2,L1,V0,M1} S(337);r(74) { ! ordinal_subset( skol16, skol17 )
% 0.42/1.08 }.
% 0.42/1.08 (707) {G5,W5,D2,L2,V0,M2} R(702,11);r(73) { ! ordinal( skol17 ),
% 0.42/1.08 ordinal_subset( skol17, skol16 ) }.
% 0.42/1.08 (753) {G6,W3,D2,L1,V0,M1} S(707);r(74) { ordinal_subset( skol17, skol16 )
% 0.42/1.08 }.
% 0.42/1.08 (754) {G7,W5,D2,L2,V0,M2} R(753,64);r(74) { ! ordinal( skol16 ), subset(
% 0.42/1.08 skol17, skol16 ) }.
% 0.42/1.08 (768) {G8,W0,D0,L0,V0,M0} S(754);r(73);r(331) { }.
% 0.42/1.08
% 0.42/1.08
% 0.42/1.08 % SZS output end Refutation
% 0.42/1.08 found a proof!
% 0.42/1.08
% 0.42/1.08
% 0.42/1.08 Unprocessed initial clauses:
% 0.42/1.08
% 0.42/1.08 (770) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), ! in( Y, X ) }.
% 0.42/1.08 (771) {G0,W6,D2,L2,V2,M2} { ! proper_subset( X, Y ), ! proper_subset( Y, X
% 0.42/1.08 ) }.
% 0.42/1.08 (772) {G0,W4,D2,L2,V1,M2} { ! empty( X ), function( X ) }.
% 0.42/1.08 (773) {G0,W4,D2,L2,V1,M2} { ! ordinal( X ), epsilon_transitive( X ) }.
% 0.42/1.08 (774) {G0,W4,D2,L2,V1,M2} { ! ordinal( X ), epsilon_connected( X ) }.
% 0.42/1.08 (775) {G0,W4,D2,L2,V1,M2} { ! empty( X ), relation( X ) }.
% 0.42/1.08 (776) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X )
% 0.42/1.08 , relation( X ) }.
% 0.42/1.08 (777) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X )
% 0.42/1.08 , function( X ) }.
% 0.42/1.08 (778) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X )
% 0.42/1.08 , one_to_one( X ) }.
% 0.42/1.08 (779) {G0,W6,D2,L3,V1,M3} { ! epsilon_transitive( X ), ! epsilon_connected
% 0.42/1.08 ( X ), ordinal( X ) }.
% 0.42/1.08 (780) {G0,W4,D2,L2,V1,M2} { ! empty( X ), epsilon_transitive( X ) }.
% 0.42/1.08 (781) {G0,W4,D2,L2,V1,M2} { ! empty( X ), epsilon_connected( X ) }.
% 0.42/1.08 (782) {G0,W4,D2,L2,V1,M2} { ! empty( X ), ordinal( X ) }.
% 0.42/1.08 (783) {G0,W10,D2,L4,V2,M4} { ! ordinal( X ), ! ordinal( Y ),
% 0.42/1.08 ordinal_subset( X, Y ), ordinal_subset( Y, X ) }.
% 0.42/1.08 (784) {G0,W6,D2,L2,V2,M2} { ! proper_subset( X, Y ), subset( X, Y ) }.
% 0.42/1.08 (785) {G0,W6,D2,L2,V2,M2} { ! proper_subset( X, Y ), ! X = Y }.
% 0.42/1.08 (786) {G0,W9,D2,L3,V2,M3} { ! subset( X, Y ), X = Y, proper_subset( X, Y )
% 0.42/1.08 }.
% 0.42/1.08 (787) {G0,W4,D3,L1,V1,M1} { element( skol1( X ), X ) }.
% 0.42/1.08 (788) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.42/1.08 (789) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 0.42/1.08 (790) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( empty_set ) }.
% 0.42/1.08 (791) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.42/1.08 (792) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 0.42/1.08 (793) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( empty_set ) }.
% 0.42/1.08 (794) {G0,W2,D2,L1,V0,M1} { function( empty_set ) }.
% 0.42/1.08 (795) {G0,W2,D2,L1,V0,M1} { one_to_one( empty_set ) }.
% 0.42/1.08 (796) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.42/1.08 (797) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( empty_set ) }.
% 0.42/1.08 (798) {G0,W2,D2,L1,V0,M1} { epsilon_connected( empty_set ) }.
% 0.42/1.08 (799) {G0,W2,D2,L1,V0,M1} { ordinal( empty_set ) }.
% 0.42/1.08 (800) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.42/1.08 (801) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 0.42/1.08 (802) {G0,W3,D2,L1,V1,M1} { ! proper_subset( X, X ) }.
% 0.42/1.08 (803) {G0,W2,D2,L1,V0,M1} { relation( skol2 ) }.
% 0.42/1.08 (804) {G0,W2,D2,L1,V0,M1} { function( skol2 ) }.
% 0.42/1.08 (805) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol3 ) }.
% 0.42/1.08 (806) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol3 ) }.
% 0.42/1.08 (807) {G0,W2,D2,L1,V0,M1} { ordinal( skol3 ) }.
% 0.42/1.08 (808) {G0,W2,D2,L1,V0,M1} { empty( skol4 ) }.
% 0.42/1.08 (809) {G0,W2,D2,L1,V0,M1} { relation( skol4 ) }.
% 0.42/1.08 (810) {G0,W2,D2,L1,V0,M1} { empty( skol5 ) }.
% 0.42/1.08 (811) {G0,W2,D2,L1,V0,M1} { relation( skol6 ) }.
% 0.42/1.08 (812) {G0,W2,D2,L1,V0,M1} { empty( skol6 ) }.
% 0.42/1.08 (813) {G0,W2,D2,L1,V0,M1} { function( skol6 ) }.
% 0.42/1.08 (814) {G0,W2,D2,L1,V0,M1} { relation( skol7 ) }.
% 0.42/1.08 (815) {G0,W2,D2,L1,V0,M1} { function( skol7 ) }.
% 0.42/1.08 (816) {G0,W2,D2,L1,V0,M1} { one_to_one( skol7 ) }.
% 0.42/1.08 (817) {G0,W2,D2,L1,V0,M1} { empty( skol7 ) }.
% 0.42/1.08 (818) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol7 ) }.
% 0.42/1.08 (819) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol7 ) }.
% 0.42/1.08 (820) {G0,W2,D2,L1,V0,M1} { ordinal( skol7 ) }.
% 0.42/1.08 (821) {G0,W2,D2,L1,V0,M1} { ! empty( skol8 ) }.
% 0.42/1.08 (822) {G0,W2,D2,L1,V0,M1} { relation( skol8 ) }.
% 0.42/1.08 (823) {G0,W2,D2,L1,V0,M1} { ! empty( skol9 ) }.
% 0.42/1.08 (824) {G0,W2,D2,L1,V0,M1} { relation( skol10 ) }.
% 0.42/1.08 (825) {G0,W2,D2,L1,V0,M1} { function( skol10 ) }.
% 0.42/1.08 (826) {G0,W2,D2,L1,V0,M1} { one_to_one( skol10 ) }.
% 0.42/1.08 (827) {G0,W2,D2,L1,V0,M1} { ! empty( skol11 ) }.
% 0.42/1.08 (828) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol11 ) }.
% 0.42/1.08 (829) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol11 ) }.
% 0.42/1.08 (830) {G0,W2,D2,L1,V0,M1} { ordinal( skol11 ) }.
% 0.42/1.08 (831) {G0,W2,D2,L1,V0,M1} { relation( skol12 ) }.
% 0.42/1.08 (832) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( skol12 ) }.
% 0.42/1.08 (833) {G0,W2,D2,L1,V0,M1} { relation( skol13 ) }.
% 0.42/1.08 (834) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( skol13 ) }.
% 0.42/1.08 (835) {G0,W2,D2,L1,V0,M1} { function( skol13 ) }.
% 0.42/1.08 (836) {G0,W2,D2,L1,V0,M1} { relation( skol14 ) }.
% 0.42/1.08 (837) {G0,W2,D2,L1,V0,M1} { function( skol14 ) }.
% 0.42/1.08 (838) {G0,W2,D2,L1,V0,M1} { transfinite_sequence( skol14 ) }.
% 0.42/1.08 (839) {G0,W2,D2,L1,V0,M1} { relation( skol15 ) }.
% 0.42/1.08 (840) {G0,W2,D2,L1,V0,M1} { relation_non_empty( skol15 ) }.
% 0.42/1.08 (841) {G0,W2,D2,L1,V0,M1} { function( skol15 ) }.
% 0.42/1.08 (842) {G0,W10,D2,L4,V2,M4} { ! ordinal( X ), ! ordinal( Y ), !
% 0.42/1.08 ordinal_subset( X, Y ), subset( X, Y ) }.
% 0.42/1.08 (843) {G0,W10,D2,L4,V2,M4} { ! ordinal( X ), ! ordinal( Y ), ! subset( X,
% 0.42/1.08 Y ), ordinal_subset( X, Y ) }.
% 0.42/1.08 (844) {G0,W7,D2,L3,V2,M3} { ! ordinal( X ), ! ordinal( Y ), ordinal_subset
% 0.42/1.08 ( X, X ) }.
% 0.42/1.08 (845) {G0,W3,D2,L1,V1,M1} { subset( X, X ) }.
% 0.42/1.08 (846) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), element( X, Y ) }.
% 0.42/1.08 (847) {G0,W8,D2,L3,V2,M3} { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.42/1.08 (848) {G0,W7,D3,L2,V2,M2} { ! element( X, powerset( Y ) ), subset( X, Y )
% 0.42/1.08 }.
% 0.42/1.08 (849) {G0,W7,D3,L2,V2,M2} { ! subset( X, Y ), element( X, powerset( Y ) )
% 0.42/1.08 }.
% 0.42/1.08 (850) {G0,W10,D3,L3,V3,M3} { ! in( X, Z ), ! element( Z, powerset( Y ) ),
% 0.42/1.08 element( X, Y ) }.
% 0.42/1.08 (851) {G0,W2,D2,L1,V0,M1} { ordinal( skol16 ) }.
% 0.42/1.08 (852) {G0,W2,D2,L1,V0,M1} { ordinal( skol17 ) }.
% 0.42/1.08 (853) {G0,W3,D2,L1,V0,M1} { ! proper_subset( skol16, skol17 ) }.
% 0.42/1.08 (854) {G0,W3,D2,L1,V0,M1} { ! skol16 = skol17 }.
% 0.42/1.08 (855) {G0,W3,D2,L1,V0,M1} { ! proper_subset( skol17, skol16 ) }.
% 0.42/1.08 (856) {G0,W9,D3,L3,V3,M3} { ! in( X, Y ), ! element( Y, powerset( Z ) ), !
% 0.42/1.08 empty( Z ) }.
% 0.42/1.08 (857) {G0,W5,D2,L2,V1,M2} { ! empty( X ), X = empty_set }.
% 0.42/1.08 (858) {G0,W5,D2,L2,V2,M2} { ! in( X, Y ), ! empty( Y ) }.
% 0.42/1.08 (859) {G0,W7,D2,L3,V2,M3} { ! empty( X ), X = Y, ! empty( Y ) }.
% 0.42/1.08
% 0.42/1.08
% 0.42/1.08 Total Proof:
% 0.42/1.08
% 0.42/1.08 subsumption: (11) {G0,W10,D2,L4,V2,M4} I { ! ordinal( X ), ! ordinal( Y ),
% 0.42/1.08 ordinal_subset( X, Y ), ordinal_subset( Y, X ) }.
% 0.42/1.08 parent0: (783) {G0,W10,D2,L4,V2,M4} { ! ordinal( X ), ! ordinal( Y ),
% 0.42/1.08 ordinal_subset( X, Y ), ordinal_subset( Y, X ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := X
% 0.42/1.08 Y := Y
% 0.42/1.08 end
% 0.42/1.08 permutation0:
% 0.42/1.08 0 ==> 0
% 0.42/1.08 1 ==> 1
% 0.42/1.08 2 ==> 2
% 0.42/1.08 3 ==> 3
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 subsumption: (14) {G0,W9,D2,L3,V2,M3} I { ! subset( X, Y ), X = Y,
% 0.42/1.08 proper_subset( X, Y ) }.
% 0.42/1.08 parent0: (786) {G0,W9,D2,L3,V2,M3} { ! subset( X, Y ), X = Y,
% 0.42/1.08 proper_subset( X, Y ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := X
% 0.42/1.08 Y := Y
% 0.42/1.08 end
% 0.42/1.08 permutation0:
% 0.42/1.08 0 ==> 0
% 0.42/1.08 1 ==> 1
% 0.42/1.08 2 ==> 2
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 factor: (873) {G0,W3,D2,L1,V1,M1} { ! proper_subset( X, X ) }.
% 0.42/1.08 parent0[0, 1]: (771) {G0,W6,D2,L2,V2,M2} { ! proper_subset( X, Y ), !
% 0.42/1.08 proper_subset( Y, X ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := X
% 0.42/1.08 Y := X
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 subsumption: (24) {G0,W3,D2,L1,V1,M1} I { ! proper_subset( X, X ) }.
% 0.42/1.08 parent0: (873) {G0,W3,D2,L1,V1,M1} { ! proper_subset( X, X ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := X
% 0.42/1.08 end
% 0.42/1.08 permutation0:
% 0.42/1.08 0 ==> 0
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 subsumption: (64) {G0,W10,D2,L4,V2,M4} I { ! ordinal( X ), ! ordinal( Y ),
% 0.42/1.08 ! ordinal_subset( X, Y ), subset( X, Y ) }.
% 0.42/1.08 parent0: (842) {G0,W10,D2,L4,V2,M4} { ! ordinal( X ), ! ordinal( Y ), !
% 0.42/1.08 ordinal_subset( X, Y ), subset( X, Y ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 X := X
% 0.42/1.08 Y := Y
% 0.42/1.08 end
% 0.42/1.08 permutation0:
% 0.42/1.08 0 ==> 0
% 0.42/1.08 1 ==> 1
% 0.42/1.08 2 ==> 2
% 0.42/1.08 3 ==> 3
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 subsumption: (73) {G0,W2,D2,L1,V0,M1} I { ordinal( skol16 ) }.
% 0.42/1.08 parent0: (851) {G0,W2,D2,L1,V0,M1} { ordinal( skol16 ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 end
% 0.42/1.08 permutation0:
% 0.42/1.08 0 ==> 0
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 subsumption: (74) {G0,W2,D2,L1,V0,M1} I { ordinal( skol17 ) }.
% 0.42/1.08 parent0: (852) {G0,W2,D2,L1,V0,M1} { ordinal( skol17 ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 end
% 0.42/1.08 permutation0:
% 0.42/1.08 0 ==> 0
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 subsumption: (75) {G0,W3,D2,L1,V0,M1} I { ! proper_subset( skol16, skol17 )
% 0.42/1.08 }.
% 0.42/1.08 parent0: (853) {G0,W3,D2,L1,V0,M1} { ! proper_subset( skol16, skol17 ) }.
% 0.42/1.08 substitution0:
% 0.42/1.08 end
% 0.42/1.08 permutation0:
% 0.42/1.08 0 ==> 0
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 eqswap: (922) {G0,W3,D2,L1,V0,M1} { ! skol17 = skol16 }.
% 0.42/1.08 parent0[0]: (854) {G0,W3,D2,L1,V0,M1} { ! skol16 = skol17 }.
% 0.42/1.08 substitution0:
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 subsumption: (76) {G0,W3,D2,L1,V0,M1} I { ! skol17 ==> skol16 }.
% 0.42/1.08 parent0: (922) {G0,W3,D2,L1,V0,M1} { ! skol17 = skol16 }.
% 0.42/1.08 substitution0:
% 0.42/1.08 end
% 0.42/1.08 permutation0:
% 0.42/1.08 0 ==> 0
% 0.42/1.08 end
% 0.42/1.08
% 0.42/1.08 subsumption: (77) {G0,W3,D2,L1,V0,M1} I { ! proper_subset( skol17, skol16 )
% 0.42/1.08 Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------