TSTP Solution File: SEU294+3 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SEU294+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n012.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 07:12:12 EDT 2022
% Result : Theorem 0.66s 1.06s
% Output : Refutation 0.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SEU294+3 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : bliksem %s
% 0.13/0.33 % Computer : n012.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 : Mon Jun 20 09:19:22 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.66/1.05 *** allocated 10000 integers for termspace/termends
% 0.66/1.05 *** allocated 10000 integers for clauses
% 0.66/1.05 *** allocated 10000 integers for justifications
% 0.66/1.05 Bliksem 1.12
% 0.66/1.05
% 0.66/1.05
% 0.66/1.05 Automatic Strategy Selection
% 0.66/1.05
% 0.66/1.05
% 0.66/1.05 Clauses:
% 0.66/1.05
% 0.66/1.05 { ! in( X, Y ), ! in( Y, X ) }.
% 0.66/1.05 { ! ordinal( X ), ! element( Y, X ), epsilon_transitive( Y ) }.
% 0.66/1.05 { ! ordinal( X ), ! element( Y, X ), epsilon_connected( Y ) }.
% 0.66/1.05 { ! ordinal( X ), ! element( Y, X ), ordinal( Y ) }.
% 0.66/1.05 { ! empty( X ), finite( X ) }.
% 0.66/1.05 { ! empty( X ), function( X ) }.
% 0.66/1.05 { ! ordinal( X ), epsilon_transitive( X ) }.
% 0.66/1.05 { ! ordinal( X ), epsilon_connected( X ) }.
% 0.66/1.05 { ! empty( X ), relation( X ) }.
% 0.66/1.05 { ! empty( X ), ! ordinal( X ), alpha1( X ) }.
% 0.66/1.05 { ! empty( X ), ! ordinal( X ), natural( X ) }.
% 0.66/1.05 { ! alpha1( X ), epsilon_transitive( X ) }.
% 0.66/1.05 { ! alpha1( X ), epsilon_connected( X ) }.
% 0.66/1.05 { ! alpha1( X ), ordinal( X ) }.
% 0.66/1.05 { ! epsilon_transitive( X ), ! epsilon_connected( X ), ! ordinal( X ),
% 0.66/1.05 alpha1( X ) }.
% 0.66/1.05 { ! finite( X ), ! element( Y, powerset( X ) ), finite( Y ) }.
% 0.66/1.05 { ! relation( X ), ! empty( X ), ! function( X ), relation( X ) }.
% 0.66/1.05 { ! relation( X ), ! empty( X ), ! function( X ), function( X ) }.
% 0.66/1.05 { ! relation( X ), ! empty( X ), ! function( X ), one_to_one( X ) }.
% 0.66/1.05 { ! epsilon_transitive( X ), ! epsilon_connected( X ), ordinal( X ) }.
% 0.66/1.05 { ! empty( X ), epsilon_transitive( X ) }.
% 0.66/1.05 { ! empty( X ), epsilon_connected( X ) }.
% 0.66/1.05 { ! empty( X ), ordinal( X ) }.
% 0.66/1.05 { ! element( X, positive_rationals ), ! ordinal( X ), alpha2( X ) }.
% 0.66/1.05 { ! element( X, positive_rationals ), ! ordinal( X ), natural( X ) }.
% 0.66/1.05 { ! alpha2( X ), epsilon_transitive( X ) }.
% 0.66/1.05 { ! alpha2( X ), epsilon_connected( X ) }.
% 0.66/1.05 { ! alpha2( X ), ordinal( X ) }.
% 0.66/1.05 { ! epsilon_transitive( X ), ! epsilon_connected( X ), ! ordinal( X ),
% 0.66/1.05 alpha2( X ) }.
% 0.66/1.05 { element( skol1( X ), X ) }.
% 0.66/1.05 { empty( empty_set ) }.
% 0.66/1.05 { relation( empty_set ) }.
% 0.66/1.05 { relation_empty_yielding( empty_set ) }.
% 0.66/1.05 { ! empty( powerset( X ) ) }.
% 0.66/1.05 { empty( empty_set ) }.
% 0.66/1.05 { relation( empty_set ) }.
% 0.66/1.05 { relation_empty_yielding( empty_set ) }.
% 0.66/1.05 { function( empty_set ) }.
% 0.66/1.05 { one_to_one( empty_set ) }.
% 0.66/1.05 { empty( empty_set ) }.
% 0.66/1.05 { epsilon_transitive( empty_set ) }.
% 0.66/1.05 { epsilon_connected( empty_set ) }.
% 0.66/1.05 { ordinal( empty_set ) }.
% 0.66/1.05 { empty( empty_set ) }.
% 0.66/1.05 { relation( empty_set ) }.
% 0.66/1.05 { ! empty( positive_rationals ) }.
% 0.66/1.05 { ! empty( skol2 ) }.
% 0.66/1.05 { epsilon_transitive( skol2 ) }.
% 0.66/1.05 { epsilon_connected( skol2 ) }.
% 0.66/1.05 { ordinal( skol2 ) }.
% 0.66/1.05 { natural( skol2 ) }.
% 0.66/1.05 { ! empty( skol3 ) }.
% 0.66/1.05 { finite( skol3 ) }.
% 0.66/1.05 { relation( skol4 ) }.
% 0.66/1.05 { function( skol4 ) }.
% 0.66/1.05 { function_yielding( skol4 ) }.
% 0.66/1.05 { relation( skol5 ) }.
% 0.66/1.05 { function( skol5 ) }.
% 0.66/1.05 { epsilon_transitive( skol6 ) }.
% 0.66/1.05 { epsilon_connected( skol6 ) }.
% 0.66/1.05 { ordinal( skol6 ) }.
% 0.66/1.05 { epsilon_transitive( skol7 ) }.
% 0.66/1.05 { epsilon_connected( skol7 ) }.
% 0.66/1.05 { ordinal( skol7 ) }.
% 0.66/1.05 { being_limit_ordinal( skol7 ) }.
% 0.66/1.05 { empty( skol8 ) }.
% 0.66/1.05 { relation( skol8 ) }.
% 0.66/1.05 { empty( X ), ! empty( skol9( Y ) ) }.
% 0.66/1.05 { empty( X ), element( skol9( X ), powerset( X ) ) }.
% 0.66/1.05 { empty( skol10 ) }.
% 0.66/1.05 { element( skol11, positive_rationals ) }.
% 0.66/1.05 { ! empty( skol11 ) }.
% 0.66/1.05 { epsilon_transitive( skol11 ) }.
% 0.66/1.05 { epsilon_connected( skol11 ) }.
% 0.66/1.05 { ordinal( skol11 ) }.
% 0.66/1.05 { empty( skol12( Y ) ) }.
% 0.66/1.05 { relation( skol12( Y ) ) }.
% 0.66/1.05 { function( skol12( Y ) ) }.
% 0.66/1.05 { one_to_one( skol12( Y ) ) }.
% 0.66/1.05 { epsilon_transitive( skol12( Y ) ) }.
% 0.66/1.05 { epsilon_connected( skol12( Y ) ) }.
% 0.66/1.05 { ordinal( skol12( Y ) ) }.
% 0.66/1.05 { natural( skol12( Y ) ) }.
% 0.66/1.05 { finite( skol12( Y ) ) }.
% 0.66/1.05 { element( skol12( X ), powerset( X ) ) }.
% 0.66/1.05 { relation( skol13 ) }.
% 0.66/1.05 { empty( skol13 ) }.
% 0.66/1.05 { function( skol13 ) }.
% 0.66/1.05 { relation( skol14 ) }.
% 0.66/1.05 { function( skol14 ) }.
% 0.66/1.05 { one_to_one( skol14 ) }.
% 0.66/1.05 { empty( skol14 ) }.
% 0.66/1.05 { epsilon_transitive( skol14 ) }.
% 0.66/1.05 { epsilon_connected( skol14 ) }.
% 0.66/1.05 { ordinal( skol14 ) }.
% 0.66/1.05 { relation( skol15 ) }.
% 0.66/1.05 { function( skol15 ) }.
% 0.66/1.05 { transfinite_sequence( skol15 ) }.
% 0.66/1.05 { ordinal_yielding( skol15 ) }.
% 0.66/1.05 { ! empty( skol16 ) }.
% 0.66/1.05 { relation( skol16 ) }.
% 0.66/1.05 { empty( skol17( Y ) ) }.
% 0.66/1.05 { element( skol17( X ), powerset( X ) ) }.
% 0.66/1.05 { ! empty( skol18 ) }.
% 0.66/1.05 { element( skol19, positive_rationals ) }.
% 0.66/1.05 { empty( skol19 ) }.
% 0.66/1.05 { epsilon_transitive( skol19 ) }.
% 0.66/1.05 { epsilon_connected( skol19 ) }.
% 0.66/1.05 { ordinal( skol19 ) }.
% 0.66/1.05 { natural( skol19 ) }.
% 0.66/1.05 { empty( X ), ! empty( skol20( Y ) ) }.
% 0.66/1.05 { empty( X ), finite( skol20( Y ) ) }.
% 0.66/1.06 { empty( X ), element( skol20( X ), powerset( X ) ) }.
% 0.66/1.06 { relation( skol21 ) }.
% 0.66/1.06 { function( skol21 ) }.
% 0.66/1.06 { one_to_one( skol21 ) }.
% 0.66/1.06 { ! empty( skol22 ) }.
% 0.66/1.06 { epsilon_transitive( skol22 ) }.
% 0.66/1.06 { epsilon_connected( skol22 ) }.
% 0.66/1.06 { ordinal( skol22 ) }.
% 0.66/1.06 { relation( skol23 ) }.
% 0.66/1.06 { relation_empty_yielding( skol23 ) }.
% 0.66/1.06 { relation( skol24 ) }.
% 0.66/1.06 { relation_empty_yielding( skol24 ) }.
% 0.66/1.06 { function( skol24 ) }.
% 0.66/1.06 { relation( skol25 ) }.
% 0.66/1.06 { function( skol25 ) }.
% 0.66/1.06 { transfinite_sequence( skol25 ) }.
% 0.66/1.06 { relation( skol26 ) }.
% 0.66/1.06 { relation_non_empty( skol26 ) }.
% 0.66/1.06 { function( skol26 ) }.
% 0.66/1.06 { subset( X, X ) }.
% 0.66/1.06 { subset( skol27, skol28 ) }.
% 0.66/1.06 { finite( skol28 ) }.
% 0.66/1.06 { ! finite( skol27 ) }.
% 0.66/1.06 { ! in( X, Y ), element( X, Y ) }.
% 0.66/1.06 { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.66/1.06 { ! element( X, powerset( Y ) ), subset( X, Y ) }.
% 0.66/1.06 { ! subset( X, Y ), element( X, powerset( Y ) ) }.
% 0.66/1.06 { ! in( X, Z ), ! element( Z, powerset( Y ) ), element( X, Y ) }.
% 0.66/1.06 { ! in( X, Y ), ! element( Y, powerset( Z ) ), ! empty( Z ) }.
% 0.66/1.06 { ! empty( X ), X = empty_set }.
% 0.66/1.06 { ! in( X, Y ), ! empty( Y ) }.
% 0.66/1.06 { ! empty( X ), X = Y, ! empty( Y ) }.
% 0.66/1.06
% 0.66/1.06 percentage equality = 0.010204, percentage horn = 0.970588
% 0.66/1.06 This is a problem with some equality
% 0.66/1.06
% 0.66/1.06
% 0.66/1.06
% 0.66/1.06 Options Used:
% 0.66/1.06
% 0.66/1.06 useres = 1
% 0.66/1.06 useparamod = 1
% 0.66/1.06 useeqrefl = 1
% 0.66/1.06 useeqfact = 1
% 0.66/1.06 usefactor = 1
% 0.66/1.06 usesimpsplitting = 0
% 0.66/1.06 usesimpdemod = 5
% 0.66/1.06 usesimpres = 3
% 0.66/1.06
% 0.66/1.06 resimpinuse = 1000
% 0.66/1.06 resimpclauses = 20000
% 0.66/1.06 substype = eqrewr
% 0.66/1.06 backwardsubs = 1
% 0.66/1.06 selectoldest = 5
% 0.66/1.06
% 0.66/1.06 litorderings [0] = split
% 0.66/1.06 litorderings [1] = extend the termordering, first sorting on arguments
% 0.66/1.06
% 0.66/1.06 termordering = kbo
% 0.66/1.06
% 0.66/1.06 litapriori = 0
% 0.66/1.06 termapriori = 1
% 0.66/1.06 litaposteriori = 0
% 0.66/1.06 termaposteriori = 0
% 0.66/1.06 demodaposteriori = 0
% 0.66/1.06 ordereqreflfact = 0
% 0.66/1.06
% 0.66/1.06 litselect = negord
% 0.66/1.06
% 0.66/1.06 maxweight = 15
% 0.66/1.06 maxdepth = 30000
% 0.66/1.06 maxlength = 115
% 0.66/1.06 maxnrvars = 195
% 0.66/1.06 excuselevel = 1
% 0.66/1.06 increasemaxweight = 1
% 0.66/1.06
% 0.66/1.06 maxselected = 10000000
% 0.66/1.06 maxnrclauses = 10000000
% 0.66/1.06
% 0.66/1.06 showgenerated = 0
% 0.66/1.06 showkept = 0
% 0.66/1.06 showselected = 0
% 0.66/1.06 showdeleted = 0
% 0.66/1.06 showresimp = 1
% 0.66/1.06 showstatus = 2000
% 0.66/1.06
% 0.66/1.06 prologoutput = 0
% 0.66/1.06 nrgoals = 5000000
% 0.66/1.06 totalproof = 1
% 0.66/1.06
% 0.66/1.06 Symbols occurring in the translation:
% 0.66/1.06
% 0.66/1.06 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.66/1.06 . [1, 2] (w:1, o:62, a:1, s:1, b:0),
% 0.66/1.06 ! [4, 1] (w:0, o:34, a:1, s:1, b:0),
% 0.66/1.06 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.66/1.06 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.66/1.06 in [37, 2] (w:1, o:86, a:1, s:1, b:0),
% 0.66/1.06 ordinal [38, 1] (w:1, o:40, a:1, s:1, b:0),
% 0.66/1.06 element [39, 2] (w:1, o:87, a:1, s:1, b:0),
% 0.66/1.06 epsilon_transitive [40, 1] (w:1, o:41, a:1, s:1, b:0),
% 0.66/1.06 epsilon_connected [41, 1] (w:1, o:42, a:1, s:1, b:0),
% 0.66/1.06 empty [42, 1] (w:1, o:43, a:1, s:1, b:0),
% 0.66/1.06 finite [43, 1] (w:1, o:44, a:1, s:1, b:0),
% 0.66/1.06 function [44, 1] (w:1, o:45, a:1, s:1, b:0),
% 0.66/1.06 relation [45, 1] (w:1, o:46, a:1, s:1, b:0),
% 0.66/1.06 natural [46, 1] (w:1, o:39, a:1, s:1, b:0),
% 0.66/1.06 powerset [47, 1] (w:1, o:49, a:1, s:1, b:0),
% 0.66/1.06 one_to_one [48, 1] (w:1, o:47, a:1, s:1, b:0),
% 0.66/1.06 positive_rationals [49, 0] (w:1, o:8, a:1, s:1, b:0),
% 0.66/1.06 empty_set [50, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.66/1.06 relation_empty_yielding [51, 1] (w:1, o:50, a:1, s:1, b:0),
% 0.66/1.06 function_yielding [52, 1] (w:1, o:51, a:1, s:1, b:0),
% 0.66/1.06 being_limit_ordinal [53, 1] (w:1, o:54, a:1, s:1, b:0),
% 0.66/1.06 transfinite_sequence [54, 1] (w:1, o:60, a:1, s:1, b:0),
% 0.66/1.06 ordinal_yielding [55, 1] (w:1, o:48, a:1, s:1, b:0),
% 0.66/1.06 relation_non_empty [56, 1] (w:1, o:61, a:1, s:1, b:0),
% 0.66/1.06 subset [57, 2] (w:1, o:88, a:1, s:1, b:0),
% 0.66/1.06 alpha1 [59, 1] (w:1, o:52, a:1, s:1, b:1),
% 0.66/1.06 alpha2 [60, 1] (w:1, o:53, a:1, s:1, b:1),
% 0.66/1.06 skol1 [61, 1] (w:1, o:55, a:1, s:1, b:1),
% 0.66/1.06 skol2 [62, 0] (w:1, o:19, a:1, s:1, b:1),
% 0.66/1.06 skol3 [63, 0] (w:1, o:28, a:1, s:1, b:1),
% 0.66/1.06 skol4 [64, 0] (w:1, o:29, a:1, s:1, b:1),
% 0.66/1.06 skol5 [65, 0] (w:1, o:30, a:1, s:1, b:1),
% 0.66/1.06 skol6 [66, 0] (w:1, o:31, a:1, s:1, b:1),
% 0.66/1.06 skol7 [67, 0] (w:1, o:32, a:1, s:1, b:1),
% 0.66/1.06 skol8 [68, 0] (w:1, o:33, a:1, s:1, b:1),
% 0.66/1.06 skol9 [69, 1] (w:1, o:56, a:1, s:1, b:1),
% 0.66/1.06 skol10 [70, 0] (w:1, o:11, a:1, s:1, b:1),
% 0.66/1.06 skol11 [71, 0] (w:1, o:12, a:1, s:1, b:1),
% 0.66/1.06 skol12 [72, 1] (w:1, o:57, a:1, s:1, b:1),
% 0.66/1.06 skol13 [73, 0] (w:1, o:13, a:1, s:1, b:1),
% 0.66/1.06 skol14 [74, 0] (w:1, o:14, a:1, s:1, b:1),
% 0.66/1.06 skol15 [75, 0] (w:1, o:15, a:1, s:1, b:1),
% 0.66/1.06 skol16 [76, 0] (w:1, o:16, a:1, s:1, b:1),
% 0.66/1.06 skol17 [77, 1] (w:1, o:58, a:1, s:1, b:1),
% 0.66/1.06 skol18 [78, 0] (w:1, o:17, a:1, s:1, b:1),
% 0.66/1.06 skol19 [79, 0] (w:1, o:18, a:1, s:1, b:1),
% 0.66/1.06 skol20 [80, 1] (w:1, o:59, a:1, s:1, b:1),
% 0.66/1.06 skol21 [81, 0] (w:1, o:20, a:1, s:1, b:1),
% 0.66/1.06 skol22 [82, 0] (w:1, o:21, a:1, s:1, b:1),
% 0.66/1.06 skol23 [83, 0] (w:1, o:22, a:1, s:1, b:1),
% 0.66/1.06 skol24 [84, 0] (w:1, o:23, a:1, s:1, b:1),
% 0.66/1.06 skol25 [85, 0] (w:1, o:24, a:1, s:1, b:1),
% 0.66/1.06 skol26 [86, 0] (w:1, o:25, a:1, s:1, b:1),
% 0.66/1.06 skol27 [87, 0] (w:1, o:26, a:1, s:1, b:1),
% 0.66/1.06 skol28 [88, 0] (w:1, o:27, a:1, s:1, b:1).
% 0.66/1.06
% 0.66/1.06
% 0.66/1.06 Starting Search:
% 0.66/1.06
% 0.66/1.06 *** allocated 15000 integers for clauses
% 0.66/1.06 *** allocated 22500 integers for clauses
% 0.66/1.06 *** allocated 33750 integers for clauses
% 0.66/1.06
% 0.66/1.06 Bliksems!, er is een bewijs:
% 0.66/1.06 % SZS status Theorem
% 0.66/1.06 % SZS output start Refutation
% 0.66/1.06
% 0.66/1.06 (15) {G0,W8,D3,L3,V2,M3} I { ! finite( X ), ! element( Y, powerset( X ) ),
% 0.66/1.06 finite( Y ) }.
% 0.66/1.06 (124) {G0,W3,D2,L1,V0,M1} I { subset( skol27, skol28 ) }.
% 0.66/1.06 (125) {G0,W2,D2,L1,V0,M1} I { finite( skol28 ) }.
% 0.66/1.06 (126) {G0,W2,D2,L1,V0,M1} I { ! finite( skol27 ) }.
% 0.66/1.06 (130) {G0,W7,D3,L2,V2,M2} I { ! subset( X, Y ), element( X, powerset( Y ) )
% 0.66/1.06 }.
% 0.66/1.06 (409) {G1,W4,D3,L1,V0,M1} R(130,124) { element( skol27, powerset( skol28 )
% 0.66/1.06 ) }.
% 0.66/1.06 (669) {G2,W2,D2,L1,V0,M1} R(409,15);r(125) { finite( skol27 ) }.
% 0.66/1.06 (675) {G3,W0,D0,L0,V0,M0} S(669);r(126) { }.
% 0.66/1.06
% 0.66/1.06
% 0.66/1.06 % SZS output end Refutation
% 0.66/1.06 found a proof!
% 0.66/1.06
% 0.66/1.06
% 0.66/1.06 Unprocessed initial clauses:
% 0.66/1.06
% 0.66/1.06 (677) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), ! in( Y, X ) }.
% 0.66/1.06 (678) {G0,W7,D2,L3,V2,M3} { ! ordinal( X ), ! element( Y, X ),
% 0.66/1.06 epsilon_transitive( Y ) }.
% 0.66/1.06 (679) {G0,W7,D2,L3,V2,M3} { ! ordinal( X ), ! element( Y, X ),
% 0.66/1.06 epsilon_connected( Y ) }.
% 0.66/1.06 (680) {G0,W7,D2,L3,V2,M3} { ! ordinal( X ), ! element( Y, X ), ordinal( Y
% 0.66/1.06 ) }.
% 0.66/1.06 (681) {G0,W4,D2,L2,V1,M2} { ! empty( X ), finite( X ) }.
% 0.66/1.06 (682) {G0,W4,D2,L2,V1,M2} { ! empty( X ), function( X ) }.
% 0.66/1.06 (683) {G0,W4,D2,L2,V1,M2} { ! ordinal( X ), epsilon_transitive( X ) }.
% 0.66/1.06 (684) {G0,W4,D2,L2,V1,M2} { ! ordinal( X ), epsilon_connected( X ) }.
% 0.66/1.06 (685) {G0,W4,D2,L2,V1,M2} { ! empty( X ), relation( X ) }.
% 0.66/1.06 (686) {G0,W6,D2,L3,V1,M3} { ! empty( X ), ! ordinal( X ), alpha1( X ) }.
% 0.66/1.06 (687) {G0,W6,D2,L3,V1,M3} { ! empty( X ), ! ordinal( X ), natural( X ) }.
% 0.66/1.06 (688) {G0,W4,D2,L2,V1,M2} { ! alpha1( X ), epsilon_transitive( X ) }.
% 0.66/1.06 (689) {G0,W4,D2,L2,V1,M2} { ! alpha1( X ), epsilon_connected( X ) }.
% 0.66/1.06 (690) {G0,W4,D2,L2,V1,M2} { ! alpha1( X ), ordinal( X ) }.
% 0.66/1.06 (691) {G0,W8,D2,L4,V1,M4} { ! epsilon_transitive( X ), ! epsilon_connected
% 0.66/1.06 ( X ), ! ordinal( X ), alpha1( X ) }.
% 0.66/1.06 (692) {G0,W8,D3,L3,V2,M3} { ! finite( X ), ! element( Y, powerset( X ) ),
% 0.66/1.06 finite( Y ) }.
% 0.66/1.06 (693) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X )
% 0.66/1.07 , relation( X ) }.
% 0.66/1.07 (694) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X )
% 0.66/1.07 , function( X ) }.
% 0.66/1.07 (695) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X )
% 0.66/1.07 , one_to_one( X ) }.
% 0.66/1.07 (696) {G0,W6,D2,L3,V1,M3} { ! epsilon_transitive( X ), ! epsilon_connected
% 0.66/1.07 ( X ), ordinal( X ) }.
% 0.66/1.07 (697) {G0,W4,D2,L2,V1,M2} { ! empty( X ), epsilon_transitive( X ) }.
% 0.66/1.07 (698) {G0,W4,D2,L2,V1,M2} { ! empty( X ), epsilon_connected( X ) }.
% 0.66/1.07 (699) {G0,W4,D2,L2,V1,M2} { ! empty( X ), ordinal( X ) }.
% 0.66/1.07 (700) {G0,W7,D2,L3,V1,M3} { ! element( X, positive_rationals ), ! ordinal
% 0.66/1.07 ( X ), alpha2( X ) }.
% 0.66/1.07 (701) {G0,W7,D2,L3,V1,M3} { ! element( X, positive_rationals ), ! ordinal
% 0.66/1.07 ( X ), natural( X ) }.
% 0.66/1.07 (702) {G0,W4,D2,L2,V1,M2} { ! alpha2( X ), epsilon_transitive( X ) }.
% 0.66/1.07 (703) {G0,W4,D2,L2,V1,M2} { ! alpha2( X ), epsilon_connected( X ) }.
% 0.66/1.07 (704) {G0,W4,D2,L2,V1,M2} { ! alpha2( X ), ordinal( X ) }.
% 0.66/1.07 (705) {G0,W8,D2,L4,V1,M4} { ! epsilon_transitive( X ), ! epsilon_connected
% 0.66/1.07 ( X ), ! ordinal( X ), alpha2( X ) }.
% 0.66/1.07 (706) {G0,W4,D3,L1,V1,M1} { element( skol1( X ), X ) }.
% 0.66/1.07 (707) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.66/1.07 (708) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 0.66/1.07 (709) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( empty_set ) }.
% 0.66/1.07 (710) {G0,W3,D3,L1,V1,M1} { ! empty( powerset( X ) ) }.
% 0.66/1.07 (711) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.66/1.07 (712) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 0.66/1.07 (713) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( empty_set ) }.
% 0.66/1.07 (714) {G0,W2,D2,L1,V0,M1} { function( empty_set ) }.
% 0.66/1.07 (715) {G0,W2,D2,L1,V0,M1} { one_to_one( empty_set ) }.
% 0.66/1.07 (716) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.66/1.07 (717) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( empty_set ) }.
% 0.66/1.07 (718) {G0,W2,D2,L1,V0,M1} { epsilon_connected( empty_set ) }.
% 0.66/1.07 (719) {G0,W2,D2,L1,V0,M1} { ordinal( empty_set ) }.
% 0.66/1.07 (720) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.66/1.07 (721) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 0.66/1.07 (722) {G0,W2,D2,L1,V0,M1} { ! empty( positive_rationals ) }.
% 0.66/1.07 (723) {G0,W2,D2,L1,V0,M1} { ! empty( skol2 ) }.
% 0.66/1.07 (724) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol2 ) }.
% 0.66/1.07 (725) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol2 ) }.
% 0.66/1.07 (726) {G0,W2,D2,L1,V0,M1} { ordinal( skol2 ) }.
% 0.66/1.07 (727) {G0,W2,D2,L1,V0,M1} { natural( skol2 ) }.
% 0.66/1.07 (728) {G0,W2,D2,L1,V0,M1} { ! empty( skol3 ) }.
% 0.66/1.07 (729) {G0,W2,D2,L1,V0,M1} { finite( skol3 ) }.
% 0.66/1.07 (730) {G0,W2,D2,L1,V0,M1} { relation( skol4 ) }.
% 0.66/1.07 (731) {G0,W2,D2,L1,V0,M1} { function( skol4 ) }.
% 0.66/1.07 (732) {G0,W2,D2,L1,V0,M1} { function_yielding( skol4 ) }.
% 0.66/1.07 (733) {G0,W2,D2,L1,V0,M1} { relation( skol5 ) }.
% 0.66/1.07 (734) {G0,W2,D2,L1,V0,M1} { function( skol5 ) }.
% 0.66/1.07 (735) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol6 ) }.
% 0.66/1.07 (736) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol6 ) }.
% 0.66/1.07 (737) {G0,W2,D2,L1,V0,M1} { ordinal( skol6 ) }.
% 0.66/1.07 (738) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol7 ) }.
% 0.66/1.07 (739) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol7 ) }.
% 0.66/1.07 (740) {G0,W2,D2,L1,V0,M1} { ordinal( skol7 ) }.
% 0.66/1.07 (741) {G0,W2,D2,L1,V0,M1} { being_limit_ordinal( skol7 ) }.
% 0.66/1.07 (742) {G0,W2,D2,L1,V0,M1} { empty( skol8 ) }.
% 0.66/1.07 (743) {G0,W2,D2,L1,V0,M1} { relation( skol8 ) }.
% 0.66/1.07 (744) {G0,W5,D3,L2,V2,M2} { empty( X ), ! empty( skol9( Y ) ) }.
% 0.66/1.07 (745) {G0,W7,D3,L2,V1,M2} { empty( X ), element( skol9( X ), powerset( X )
% 0.66/1.07 ) }.
% 0.66/1.07 (746) {G0,W2,D2,L1,V0,M1} { empty( skol10 ) }.
% 0.66/1.07 (747) {G0,W3,D2,L1,V0,M1} { element( skol11, positive_rationals ) }.
% 0.66/1.07 (748) {G0,W2,D2,L1,V0,M1} { ! empty( skol11 ) }.
% 0.66/1.07 (749) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol11 ) }.
% 0.66/1.07 (750) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol11 ) }.
% 0.66/1.07 (751) {G0,W2,D2,L1,V0,M1} { ordinal( skol11 ) }.
% 0.66/1.07 (752) {G0,W3,D3,L1,V1,M1} { empty( skol12( Y ) ) }.
% 0.66/1.07 (753) {G0,W3,D3,L1,V1,M1} { relation( skol12( Y ) ) }.
% 0.66/1.07 (754) {G0,W3,D3,L1,V1,M1} { function( skol12( Y ) ) }.
% 0.66/1.07 (755) {G0,W3,D3,L1,V1,M1} { one_to_one( skol12( Y ) ) }.
% 0.66/1.07 (756) {G0,W3,D3,L1,V1,M1} { epsilon_transitive( skol12( Y ) ) }.
% 0.66/1.07 (757) {G0,W3,D3,L1,V1,M1} { epsilon_connected( skol12( Y ) ) }.
% 0.66/1.07 (758) {G0,W3,D3,L1,V1,M1} { ordinal( skol12( Y ) ) }.
% 0.66/1.07 (759) {G0,W3,D3,L1,V1,M1} { natural( skol12( Y ) ) }.
% 0.66/1.07 (760) {G0,W3,D3,L1,V1,M1} { finite( skol12( Y ) ) }.
% 0.66/1.07 (761) {G0,W5,D3,L1,V1,M1} { element( skol12( X ), powerset( X ) ) }.
% 0.66/1.07 (762) {G0,W2,D2,L1,V0,M1} { relation( skol13 ) }.
% 0.66/1.07 (763) {G0,W2,D2,L1,V0,M1} { empty( skol13 ) }.
% 0.66/1.07 (764) {G0,W2,D2,L1,V0,M1} { function( skol13 ) }.
% 0.66/1.07 (765) {G0,W2,D2,L1,V0,M1} { relation( skol14 ) }.
% 0.66/1.07 (766) {G0,W2,D2,L1,V0,M1} { function( skol14 ) }.
% 0.66/1.07 (767) {G0,W2,D2,L1,V0,M1} { one_to_one( skol14 ) }.
% 0.66/1.07 (768) {G0,W2,D2,L1,V0,M1} { empty( skol14 ) }.
% 0.66/1.07 (769) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol14 ) }.
% 0.66/1.07 (770) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol14 ) }.
% 0.66/1.07 (771) {G0,W2,D2,L1,V0,M1} { ordinal( skol14 ) }.
% 0.66/1.07 (772) {G0,W2,D2,L1,V0,M1} { relation( skol15 ) }.
% 0.66/1.07 (773) {G0,W2,D2,L1,V0,M1} { function( skol15 ) }.
% 0.66/1.07 (774) {G0,W2,D2,L1,V0,M1} { transfinite_sequence( skol15 ) }.
% 0.66/1.07 (775) {G0,W2,D2,L1,V0,M1} { ordinal_yielding( skol15 ) }.
% 0.66/1.07 (776) {G0,W2,D2,L1,V0,M1} { ! empty( skol16 ) }.
% 0.66/1.07 (777) {G0,W2,D2,L1,V0,M1} { relation( skol16 ) }.
% 0.66/1.07 (778) {G0,W3,D3,L1,V1,M1} { empty( skol17( Y ) ) }.
% 0.66/1.07 (779) {G0,W5,D3,L1,V1,M1} { element( skol17( X ), powerset( X ) ) }.
% 0.66/1.07 (780) {G0,W2,D2,L1,V0,M1} { ! empty( skol18 ) }.
% 0.66/1.07 (781) {G0,W3,D2,L1,V0,M1} { element( skol19, positive_rationals ) }.
% 0.66/1.07 (782) {G0,W2,D2,L1,V0,M1} { empty( skol19 ) }.
% 0.66/1.07 (783) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol19 ) }.
% 0.66/1.07 (784) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol19 ) }.
% 0.66/1.07 (785) {G0,W2,D2,L1,V0,M1} { ordinal( skol19 ) }.
% 0.66/1.07 (786) {G0,W2,D2,L1,V0,M1} { natural( skol19 ) }.
% 0.66/1.07 (787) {G0,W5,D3,L2,V2,M2} { empty( X ), ! empty( skol20( Y ) ) }.
% 0.66/1.07 (788) {G0,W5,D3,L2,V2,M2} { empty( X ), finite( skol20( Y ) ) }.
% 0.66/1.07 (789) {G0,W7,D3,L2,V1,M2} { empty( X ), element( skol20( X ), powerset( X
% 0.66/1.07 ) ) }.
% 0.66/1.07 (790) {G0,W2,D2,L1,V0,M1} { relation( skol21 ) }.
% 0.66/1.07 (791) {G0,W2,D2,L1,V0,M1} { function( skol21 ) }.
% 0.66/1.07 (792) {G0,W2,D2,L1,V0,M1} { one_to_one( skol21 ) }.
% 0.66/1.07 (793) {G0,W2,D2,L1,V0,M1} { ! empty( skol22 ) }.
% 0.66/1.07 (794) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol22 ) }.
% 0.66/1.07 (795) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol22 ) }.
% 0.66/1.07 (796) {G0,W2,D2,L1,V0,M1} { ordinal( skol22 ) }.
% 0.66/1.07 (797) {G0,W2,D2,L1,V0,M1} { relation( skol23 ) }.
% 0.66/1.07 (798) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( skol23 ) }.
% 0.66/1.07 (799) {G0,W2,D2,L1,V0,M1} { relation( skol24 ) }.
% 0.66/1.07 (800) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( skol24 ) }.
% 0.66/1.07 (801) {G0,W2,D2,L1,V0,M1} { function( skol24 ) }.
% 0.66/1.07 (802) {G0,W2,D2,L1,V0,M1} { relation( skol25 ) }.
% 0.66/1.07 (803) {G0,W2,D2,L1,V0,M1} { function( skol25 ) }.
% 0.66/1.07 (804) {G0,W2,D2,L1,V0,M1} { transfinite_sequence( skol25 ) }.
% 0.66/1.07 (805) {G0,W2,D2,L1,V0,M1} { relation( skol26 ) }.
% 0.66/1.07 (806) {G0,W2,D2,L1,V0,M1} { relation_non_empty( skol26 ) }.
% 0.66/1.07 (807) {G0,W2,D2,L1,V0,M1} { function( skol26 ) }.
% 0.66/1.07 (808) {G0,W3,D2,L1,V1,M1} { subset( X, X ) }.
% 0.66/1.07 (809) {G0,W3,D2,L1,V0,M1} { subset( skol27, skol28 ) }.
% 0.66/1.07 (810) {G0,W2,D2,L1,V0,M1} { finite( skol28 ) }.
% 0.66/1.07 (811) {G0,W2,D2,L1,V0,M1} { ! finite( skol27 ) }.
% 0.66/1.07 (812) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), element( X, Y ) }.
% 0.66/1.07 (813) {G0,W8,D2,L3,V2,M3} { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.66/1.07 (814) {G0,W7,D3,L2,V2,M2} { ! element( X, powerset( Y ) ), subset( X, Y )
% 0.66/1.07 }.
% 0.66/1.07 (815) {G0,W7,D3,L2,V2,M2} { ! subset( X, Y ), element( X, powerset( Y ) )
% 0.66/1.07 }.
% 0.66/1.07 (816) {G0,W10,D3,L3,V3,M3} { ! in( X, Z ), ! element( Z, powerset( Y ) ),
% 0.66/1.07 element( X, Y ) }.
% 0.66/1.07 (817) {G0,W9,D3,L3,V3,M3} { ! in( X, Y ), ! element( Y, powerset( Z ) ), !
% 0.66/1.07 empty( Z ) }.
% 0.66/1.07 (818) {G0,W5,D2,L2,V1,M2} { ! empty( X ), X = empty_set }.
% 0.66/1.07 (819) {G0,W5,D2,L2,V2,M2} { ! in( X, Y ), ! empty( Y ) }.
% 0.66/1.07 (820) {G0,W7,D2,L3,V2,M3} { ! empty( X ), X = Y, ! empty( Y ) }.
% 0.66/1.07
% 0.66/1.07
% 0.66/1.07 Total Proof:
% 0.66/1.07
% 0.66/1.07 subsumption: (15) {G0,W8,D3,L3,V2,M3} I { ! finite( X ), ! element( Y,
% 0.66/1.07 powerset( X ) ), finite( Y ) }.
% 0.66/1.07 parent0: (692) {G0,W8,D3,L3,V2,M3} { ! finite( X ), ! element( Y, powerset
% 0.66/1.07 ( X ) ), finite( Y ) }.
% 0.66/1.07 substitution0:
% 0.66/1.07 X := X
% 0.66/1.07 Y := Y
% 0.66/1.07 end
% 0.66/1.07 permutation0:
% 0.66/1.07 0 ==> 0
% 0.66/1.07 1 ==> 1
% 0.66/1.07 2 ==> 2
% 0.66/1.07 end
% 0.66/1.07
% 0.66/1.07 subsumption: (124) {G0,W3,D2,L1,V0,M1} I { subset( skol27, skol28 ) }.
% 0.66/1.07 parent0: (809) {G0,W3,D2,L1,V0,M1} { subset( skol27, skol28 ) }.
% 0.66/1.07 substitution0:
% 0.66/1.07 end
% 0.66/1.07 permutation0:
% 0.66/1.07 0 ==> 0
% 0.66/1.07 end
% 0.66/1.07
% 0.66/1.07 subsumption: (125) {G0,W2,D2,L1,V0,M1} I { finite( skol28 ) }.
% 0.66/1.07 parent0: (810) {G0,W2,D2,L1,V0,M1} { finite( skol28 ) }.
% 0.66/1.07 substitution0:
% 0.66/1.07 end
% 0.66/1.07 permutation0:
% 0.66/1.07 0 ==> 0
% 0.66/1.07 end
% 0.66/1.07
% 0.66/1.07 subsumption: (126) {G0,W2,D2,L1,V0,M1} I { ! finite( skol27 ) }.
% 0.66/1.07 parent0: (811) {G0,W2,D2,L1,V0,M1} { ! finite( skol27 ) }.
% 0.66/1.07 substitution0:
% 0.66/1.07 end
% 0.66/1.07 permutation0:
% 0.66/1.07 0 ==> 0
% 0.66/1.07 end
% 0.66/1.07
% 0.66/1.07 subsumption: (130) {G0,W7,D3,L2,V2,M2} I { ! subset( X, Y ), element( X,
% 0.66/1.07 powerset( Y ) ) }.
% 0.66/1.07 parent0: (815) {G0,W7,D3,L2,V2,M2} { ! subset( X, Y ), element( X,
% 0.66/1.07 powerset( Y ) ) }.
% 0.66/1.07 substitution0:
% 0.66/1.07 X := X
% 0.66/1.07 Y := Y
% 0.66/1.07 end
% 0.66/1.07 permutation0:
% 0.66/1.07 0 ==> 0
% 0.66/1.07 1 ==> 1
% 0.66/1.07 end
% 0.66/1.07
% 0.66/1.07 resolution: (826) {G1,W4,D3,L1,V0,M1} { element( skol27, powerset( skol28
% 0.66/1.07 ) ) }.
% 0.66/1.07 parent0[0]: (130) {G0,W7,D3,L2,V2,M2} I { ! subset( X, Y ), element( X,
% 0.66/1.07 powerset( Y ) ) }.
% 0.66/1.07 parent1[0]: (124) {G0,W3,D2,L1,V0,M1} I { subset( skol27, skol28 ) }.
% 0.66/1.07 substitution0:
% 0.66/1.07 X := skol27
% 0.66/1.07 Y := skol28
% 0.66/1.07 end
% 0.66/1.07 substitution1:
% 0.66/1.07 end
% 0.66/1.07
% 0.66/1.07 subsumption: (409) {G1,W4,D3,L1,V0,M1} R(130,124) { element( skol27,
% 0.66/1.07 powerset( skol28 ) ) }.
% 0.66/1.07 parent0: (826) {G1,W4,D3,L1,V0,M1} { element( skol27, powerset( skol28 ) )
% 0.66/1.07 }.
% 0.66/1.07 substitution0:
% 0.66/1.07 end
% 0.66/1.07 permutation0:
% 0.66/1.07 0 ==> 0
% 0.66/1.07 end
% 0.66/1.07
% 0.66/1.07 resolution: (827) {G1,W4,D2,L2,V0,M2} { ! finite( skol28 ), finite( skol27
% 0.66/1.07 ) }.
% 0.66/1.07 parent0[1]: (15) {G0,W8,D3,L3,V2,M3} I { ! finite( X ), ! element( Y,
% 0.66/1.07 powerset( X ) ), finite( Y ) }.
% 0.66/1.07 parent1[0]: (409) {G1,W4,D3,L1,V0,M1} R(130,124) { element( skol27,
% 0.66/1.07 powerset( skol28 ) ) }.
% 0.66/1.07 substitution0:
% 0.66/1.07 X := skol28
% 0.66/1.07 Y := skol27
% 0.66/1.07 end
% 0.66/1.07 substitution1:
% 0.66/1.07 end
% 0.66/1.07
% 0.66/1.07 resolution: (828) {G1,W2,D2,L1,V0,M1} { finite( skol27 ) }.
% 0.66/1.07 parent0[0]: (827) {G1,W4,D2,L2,V0,M2} { ! finite( skol28 ), finite( skol27
% 0.66/1.07 ) }.
% 0.66/1.07 parent1[0]: (125) {G0,W2,D2,L1,V0,M1} I { finite( skol28 ) }.
% 0.66/1.07 substitution0:
% 0.66/1.07 end
% 0.66/1.07 substitution1:
% 0.66/1.07 end
% 0.66/1.07
% 0.66/1.07 subsumption: (669) {G2,W2,D2,L1,V0,M1} R(409,15);r(125) { finite( skol27 )
% 0.66/1.07 }.
% 0.66/1.07 parent0: (828) {G1,W2,D2,L1,V0,M1} { finite( skol27 ) }.
% 0.66/1.07 substitution0:
% 0.66/1.07 end
% 0.66/1.07 permutation0:
% 0.66/1.07 0 ==> 0
% 0.66/1.07 end
% 0.66/1.07
% 0.66/1.07 resolution: (829) {G1,W0,D0,L0,V0,M0} { }.
% 0.66/1.07 parent0[0]: (126) {G0,W2,D2,L1,V0,M1} I { ! finite( skol27 ) }.
% 0.66/1.07 parent1[0]: (669) {G2,W2,D2,L1,V0,M1} R(409,15);r(125) { finite( skol27 )
% 0.66/1.07 }.
% 0.66/1.07 substitution0:
% 0.66/1.07 end
% 0.66/1.07 substitution1:
% 0.66/1.07 end
% 0.66/1.07
% 0.66/1.07 subsumption: (675) {G3,W0,D0,L0,V0,M0} S(669);r(126) { }.
% 0.66/1.07 parent0: (829) {G1,W0,D0,L0,V0,M0} { }.
% 0.66/1.07 substitution0:
% 0.66/1.07 end
% 0.66/1.07 permutation0:
% 0.66/1.07 end
% 0.66/1.07
% 0.66/1.07 Proof check complete!
% 0.66/1.07
% 0.66/1.07 Memory use:
% 0.66/1.07
% 0.66/1.07 space for terms: 6212
% 0.66/1.07 space for clauses: 30368
% 0.66/1.07
% 0.66/1.07
% 0.66/1.07 clauses generated: 2013
% 0.66/1.07 clauses kept: 676
% 0.66/1.07 clauses selected: 248
% 0.66/1.07 clauses deleted: 12
% 0.66/1.07 clauses inuse deleted: 0
% 0.66/1.07
% 0.66/1.07 subsentry: 2302
% 0.66/1.07 literals s-matched: 1971
% 0.66/1.07 literals matched: 1971
% 0.66/1.07 full subsumption: 269
% 0.66/1.07
% 0.66/1.07 checksum: -536684961
% 0.66/1.07
% 0.66/1.07
% 0.66/1.07 Bliksem ended
%------------------------------------------------------------------------------