TSTP Solution File: SEU295+3 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SEU295+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n016.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 07:12:13 EDT 2022
% Result : Theorem 0.47s 1.11s
% Output : Refutation 0.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU295+3 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.14 % Command : bliksem %s
% 0.14/0.35 % Computer : n016.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % DateTime : Sun Jun 19 20:55:24 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.47/1.10 *** allocated 10000 integers for termspace/termends
% 0.47/1.10 *** allocated 10000 integers for clauses
% 0.47/1.10 *** allocated 10000 integers for justifications
% 0.47/1.10 Bliksem 1.12
% 0.47/1.10
% 0.47/1.10
% 0.47/1.10 Automatic Strategy Selection
% 0.47/1.10
% 0.47/1.10
% 0.47/1.10 Clauses:
% 0.47/1.10
% 0.47/1.10 { ! in( X, Y ), ! in( Y, X ) }.
% 0.47/1.10 { ! ordinal( X ), ! element( Y, X ), epsilon_transitive( Y ) }.
% 0.47/1.10 { ! ordinal( X ), ! element( Y, X ), epsilon_connected( Y ) }.
% 0.47/1.10 { ! ordinal( X ), ! element( Y, X ), ordinal( Y ) }.
% 0.47/1.10 { ! empty( X ), finite( X ) }.
% 0.47/1.10 { ! empty( X ), function( X ) }.
% 0.47/1.10 { ! ordinal( X ), epsilon_transitive( X ) }.
% 0.47/1.10 { ! ordinal( X ), epsilon_connected( X ) }.
% 0.47/1.10 { ! empty( X ), relation( X ) }.
% 0.47/1.10 { ! empty( X ), ! ordinal( X ), alpha1( X ) }.
% 0.47/1.10 { ! empty( X ), ! ordinal( X ), natural( X ) }.
% 0.47/1.10 { ! alpha1( X ), epsilon_transitive( X ) }.
% 0.47/1.10 { ! alpha1( X ), epsilon_connected( X ) }.
% 0.47/1.10 { ! alpha1( X ), ordinal( X ) }.
% 0.47/1.10 { ! epsilon_transitive( X ), ! epsilon_connected( X ), ! ordinal( X ),
% 0.47/1.10 alpha1( X ) }.
% 0.47/1.10 { ! finite( X ), ! element( Y, powerset( X ) ), finite( Y ) }.
% 0.47/1.10 { ! relation( X ), ! empty( X ), ! function( X ), relation( X ) }.
% 0.47/1.10 { ! relation( X ), ! empty( X ), ! function( X ), function( X ) }.
% 0.47/1.10 { ! relation( X ), ! empty( X ), ! function( X ), one_to_one( X ) }.
% 0.47/1.10 { ! epsilon_transitive( X ), ! epsilon_connected( X ), ordinal( X ) }.
% 0.47/1.10 { ! empty( X ), epsilon_transitive( X ) }.
% 0.47/1.10 { ! empty( X ), epsilon_connected( X ) }.
% 0.47/1.10 { ! empty( X ), ordinal( X ) }.
% 0.47/1.10 { ! element( X, positive_rationals ), ! ordinal( X ), alpha2( X ) }.
% 0.47/1.10 { ! element( X, positive_rationals ), ! ordinal( X ), natural( X ) }.
% 0.47/1.10 { ! alpha2( X ), epsilon_transitive( X ) }.
% 0.47/1.10 { ! alpha2( X ), epsilon_connected( X ) }.
% 0.47/1.10 { ! alpha2( X ), ordinal( X ) }.
% 0.47/1.10 { ! epsilon_transitive( X ), ! epsilon_connected( X ), ! ordinal( X ),
% 0.47/1.10 alpha2( X ) }.
% 0.47/1.10 { set_intersection2( X, Y ) = set_intersection2( Y, X ) }.
% 0.47/1.10 { element( skol1( X ), X ) }.
% 0.47/1.10 { ! finite( X ), finite( set_intersection2( Y, X ) ) }.
% 0.47/1.10 { ! finite( X ), finite( set_intersection2( X, Y ) ) }.
% 0.47/1.10 { empty( empty_set ) }.
% 0.47/1.10 { relation( empty_set ) }.
% 0.47/1.10 { relation_empty_yielding( empty_set ) }.
% 0.47/1.10 { ! relation( X ), ! relation( Y ), relation( set_intersection2( X, Y ) ) }
% 0.47/1.10 .
% 0.47/1.10 { ! empty( powerset( X ) ) }.
% 0.47/1.10 { empty( empty_set ) }.
% 0.47/1.10 { relation( empty_set ) }.
% 0.47/1.10 { relation_empty_yielding( empty_set ) }.
% 0.47/1.10 { function( empty_set ) }.
% 0.47/1.10 { one_to_one( empty_set ) }.
% 0.47/1.10 { empty( empty_set ) }.
% 0.47/1.10 { epsilon_transitive( empty_set ) }.
% 0.47/1.10 { epsilon_connected( empty_set ) }.
% 0.47/1.10 { ordinal( empty_set ) }.
% 0.47/1.10 { empty( empty_set ) }.
% 0.47/1.10 { relation( empty_set ) }.
% 0.47/1.10 { ! empty( positive_rationals ) }.
% 0.47/1.10 { set_intersection2( X, X ) = X }.
% 0.47/1.10 { ! empty( skol2 ) }.
% 0.47/1.10 { epsilon_transitive( skol2 ) }.
% 0.47/1.10 { epsilon_connected( skol2 ) }.
% 0.47/1.10 { ordinal( skol2 ) }.
% 0.47/1.10 { natural( skol2 ) }.
% 0.47/1.10 { ! empty( skol3 ) }.
% 0.47/1.10 { finite( skol3 ) }.
% 0.47/1.10 { relation( skol4 ) }.
% 0.47/1.10 { function( skol4 ) }.
% 0.47/1.10 { function_yielding( skol4 ) }.
% 0.47/1.10 { relation( skol5 ) }.
% 0.47/1.10 { function( skol5 ) }.
% 0.47/1.10 { epsilon_transitive( skol6 ) }.
% 0.47/1.10 { epsilon_connected( skol6 ) }.
% 0.47/1.10 { ordinal( skol6 ) }.
% 0.47/1.10 { epsilon_transitive( skol7 ) }.
% 0.47/1.10 { epsilon_connected( skol7 ) }.
% 0.47/1.10 { ordinal( skol7 ) }.
% 0.47/1.10 { being_limit_ordinal( skol7 ) }.
% 0.47/1.10 { empty( skol8 ) }.
% 0.47/1.10 { relation( skol8 ) }.
% 0.47/1.10 { empty( X ), ! empty( skol9( Y ) ) }.
% 0.47/1.10 { empty( X ), element( skol9( X ), powerset( X ) ) }.
% 0.47/1.10 { empty( skol10 ) }.
% 0.47/1.10 { element( skol11, positive_rationals ) }.
% 0.47/1.10 { ! empty( skol11 ) }.
% 0.47/1.10 { epsilon_transitive( skol11 ) }.
% 0.47/1.10 { epsilon_connected( skol11 ) }.
% 0.47/1.10 { ordinal( skol11 ) }.
% 0.47/1.10 { empty( skol12( Y ) ) }.
% 0.47/1.10 { relation( skol12( Y ) ) }.
% 0.47/1.10 { function( skol12( Y ) ) }.
% 0.47/1.10 { one_to_one( skol12( Y ) ) }.
% 0.47/1.10 { epsilon_transitive( skol12( Y ) ) }.
% 0.47/1.10 { epsilon_connected( skol12( Y ) ) }.
% 0.47/1.10 { ordinal( skol12( Y ) ) }.
% 0.47/1.10 { natural( skol12( Y ) ) }.
% 0.47/1.10 { finite( skol12( Y ) ) }.
% 0.47/1.10 { element( skol12( X ), powerset( X ) ) }.
% 0.47/1.10 { relation( skol13 ) }.
% 0.47/1.10 { empty( skol13 ) }.
% 0.47/1.10 { function( skol13 ) }.
% 0.47/1.10 { relation( skol14 ) }.
% 0.47/1.10 { function( skol14 ) }.
% 0.47/1.10 { one_to_one( skol14 ) }.
% 0.47/1.10 { empty( skol14 ) }.
% 0.47/1.10 { epsilon_transitive( skol14 ) }.
% 0.47/1.10 { epsilon_connected( skol14 ) }.
% 0.47/1.10 { ordinal( skol14 ) }.
% 0.47/1.10 { relation( skol15 ) }.
% 0.47/1.10 { function( skol15 ) }.
% 0.47/1.10 { transfinite_sequence( skol15 ) }.
% 0.47/1.10 { ordinal_yielding( skol15 ) }.
% 0.47/1.10 { ! empty( skol16 ) }.
% 0.47/1.10 { relation( skol16 ) }.
% 0.47/1.10 { empty( skol17( Y ) ) }.
% 0.47/1.10 { element( skol17( X ), powerset( X ) ) }.
% 0.47/1.11 { ! empty( skol18 ) }.
% 0.47/1.11 { element( skol19, positive_rationals ) }.
% 0.47/1.11 { empty( skol19 ) }.
% 0.47/1.11 { epsilon_transitive( skol19 ) }.
% 0.47/1.11 { epsilon_connected( skol19 ) }.
% 0.47/1.11 { ordinal( skol19 ) }.
% 0.47/1.11 { natural( skol19 ) }.
% 0.47/1.11 { empty( X ), ! empty( skol20( Y ) ) }.
% 0.47/1.11 { empty( X ), finite( skol20( Y ) ) }.
% 0.47/1.11 { empty( X ), element( skol20( X ), powerset( X ) ) }.
% 0.47/1.11 { relation( skol21 ) }.
% 0.47/1.11 { function( skol21 ) }.
% 0.47/1.11 { one_to_one( skol21 ) }.
% 0.47/1.11 { ! empty( skol22 ) }.
% 0.47/1.11 { epsilon_transitive( skol22 ) }.
% 0.47/1.11 { epsilon_connected( skol22 ) }.
% 0.47/1.11 { ordinal( skol22 ) }.
% 0.47/1.11 { relation( skol23 ) }.
% 0.47/1.11 { relation_empty_yielding( skol23 ) }.
% 0.47/1.11 { relation( skol24 ) }.
% 0.47/1.11 { relation_empty_yielding( skol24 ) }.
% 0.47/1.11 { function( skol24 ) }.
% 0.47/1.11 { relation( skol25 ) }.
% 0.47/1.11 { function( skol25 ) }.
% 0.47/1.11 { transfinite_sequence( skol25 ) }.
% 0.47/1.11 { relation( skol26 ) }.
% 0.47/1.11 { relation_non_empty( skol26 ) }.
% 0.47/1.11 { function( skol26 ) }.
% 0.47/1.11 { subset( X, X ) }.
% 0.47/1.11 { ! subset( X, Y ), ! finite( Y ), finite( X ) }.
% 0.47/1.11 { finite( skol27 ) }.
% 0.47/1.11 { ! finite( set_intersection2( skol27, skol28 ) ) }.
% 0.47/1.11 { subset( set_intersection2( X, Y ), X ) }.
% 0.47/1.11 { ! in( X, Y ), element( X, Y ) }.
% 0.47/1.11 { set_intersection2( X, empty_set ) = empty_set }.
% 0.47/1.11 { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.47/1.11 { ! element( X, powerset( Y ) ), subset( X, Y ) }.
% 0.47/1.11 { ! subset( X, Y ), element( X, powerset( Y ) ) }.
% 0.47/1.11 { ! in( X, Z ), ! element( Z, powerset( Y ) ), element( X, Y ) }.
% 0.47/1.11 { ! in( X, Y ), ! element( Y, powerset( Z ) ), ! empty( Z ) }.
% 0.47/1.11 { ! empty( X ), X = empty_set }.
% 0.47/1.11 { ! in( X, Y ), ! empty( Y ) }.
% 0.47/1.11 { ! empty( X ), X = Y, ! empty( Y ) }.
% 0.47/1.11
% 0.47/1.11 percentage equality = 0.023923, percentage horn = 0.972028
% 0.47/1.11 This is a problem with some equality
% 0.47/1.11
% 0.47/1.11
% 0.47/1.11
% 0.47/1.11 Options Used:
% 0.47/1.11
% 0.47/1.11 useres = 1
% 0.47/1.11 useparamod = 1
% 0.47/1.11 useeqrefl = 1
% 0.47/1.11 useeqfact = 1
% 0.47/1.11 usefactor = 1
% 0.47/1.11 usesimpsplitting = 0
% 0.47/1.11 usesimpdemod = 5
% 0.47/1.11 usesimpres = 3
% 0.47/1.11
% 0.47/1.11 resimpinuse = 1000
% 0.47/1.11 resimpclauses = 20000
% 0.47/1.11 substype = eqrewr
% 0.47/1.11 backwardsubs = 1
% 0.47/1.11 selectoldest = 5
% 0.47/1.11
% 0.47/1.11 litorderings [0] = split
% 0.47/1.11 litorderings [1] = extend the termordering, first sorting on arguments
% 0.47/1.11
% 0.47/1.11 termordering = kbo
% 0.47/1.11
% 0.47/1.11 litapriori = 0
% 0.47/1.11 termapriori = 1
% 0.47/1.11 litaposteriori = 0
% 0.47/1.11 termaposteriori = 0
% 0.47/1.11 demodaposteriori = 0
% 0.47/1.11 ordereqreflfact = 0
% 0.47/1.11
% 0.47/1.11 litselect = negord
% 0.47/1.11
% 0.47/1.11 maxweight = 15
% 0.47/1.11 maxdepth = 30000
% 0.47/1.11 maxlength = 115
% 0.47/1.11 maxnrvars = 195
% 0.47/1.11 excuselevel = 1
% 0.47/1.11 increasemaxweight = 1
% 0.47/1.11
% 0.47/1.11 maxselected = 10000000
% 0.47/1.11 maxnrclauses = 10000000
% 0.47/1.11
% 0.47/1.11 showgenerated = 0
% 0.47/1.11 showkept = 0
% 0.47/1.11 showselected = 0
% 0.47/1.11 showdeleted = 0
% 0.47/1.11 showresimp = 1
% 0.47/1.11 showstatus = 2000
% 0.47/1.11
% 0.47/1.11 prologoutput = 0
% 0.47/1.11 nrgoals = 5000000
% 0.47/1.11 totalproof = 1
% 0.47/1.11
% 0.47/1.11 Symbols occurring in the translation:
% 0.47/1.11
% 0.47/1.11 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.47/1.11 . [1, 2] (w:1, o:62, a:1, s:1, b:0),
% 0.47/1.11 ! [4, 1] (w:0, o:34, a:1, s:1, b:0),
% 0.47/1.11 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.47/1.11 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.47/1.11 in [37, 2] (w:1, o:86, a:1, s:1, b:0),
% 0.47/1.11 ordinal [38, 1] (w:1, o:40, a:1, s:1, b:0),
% 0.47/1.11 element [39, 2] (w:1, o:87, a:1, s:1, b:0),
% 0.47/1.11 epsilon_transitive [40, 1] (w:1, o:41, a:1, s:1, b:0),
% 0.47/1.11 epsilon_connected [41, 1] (w:1, o:42, a:1, s:1, b:0),
% 0.47/1.11 empty [42, 1] (w:1, o:43, a:1, s:1, b:0),
% 0.47/1.11 finite [43, 1] (w:1, o:44, a:1, s:1, b:0),
% 0.47/1.11 function [44, 1] (w:1, o:45, a:1, s:1, b:0),
% 0.47/1.11 relation [45, 1] (w:1, o:46, a:1, s:1, b:0),
% 0.47/1.11 natural [46, 1] (w:1, o:39, a:1, s:1, b:0),
% 0.47/1.11 powerset [47, 1] (w:1, o:49, a:1, s:1, b:0),
% 0.47/1.11 one_to_one [48, 1] (w:1, o:47, a:1, s:1, b:0),
% 0.47/1.11 positive_rationals [49, 0] (w:1, o:8, a:1, s:1, b:0),
% 0.47/1.11 set_intersection2 [50, 2] (w:1, o:88, a:1, s:1, b:0),
% 0.47/1.11 empty_set [51, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.47/1.11 relation_empty_yielding [52, 1] (w:1, o:50, a:1, s:1, b:0),
% 0.47/1.11 function_yielding [53, 1] (w:1, o:51, a:1, s:1, b:0),
% 0.47/1.11 being_limit_ordinal [54, 1] (w:1, o:54, a:1, s:1, b:0),
% 0.47/1.11 transfinite_sequence [55, 1] (w:1, o:60, a:1, s:1, b:0),
% 0.47/1.11 ordinal_yielding [56, 1] (w:1, o:48, a:1, s:1, b:0),
% 0.47/1.11 relation_non_empty [57, 1] (w:1, o:61, a:1, s:1, b:0),
% 0.47/1.11 subset [58, 2] (w:1, o:89, a:1, s:1, b:0),
% 0.47/1.11 alpha1 [60, 1] (w:1, o:52, a:1, s:1, b:1),
% 0.47/1.11 alpha2 [61, 1] (w:1, o:53, a:1, s:1, b:1),
% 0.47/1.11 skol1 [62, 1] (w:1, o:55, a:1, s:1, b:1),
% 0.47/1.11 skol2 [63, 0] (w:1, o:19, a:1, s:1, b:1),
% 0.47/1.11 skol3 [64, 0] (w:1, o:28, a:1, s:1, b:1),
% 0.47/1.11 skol4 [65, 0] (w:1, o:29, a:1, s:1, b:1),
% 0.47/1.11 skol5 [66, 0] (w:1, o:30, a:1, s:1, b:1),
% 0.47/1.11 skol6 [67, 0] (w:1, o:31, a:1, s:1, b:1),
% 0.47/1.11 skol7 [68, 0] (w:1, o:32, a:1, s:1, b:1),
% 0.47/1.11 skol8 [69, 0] (w:1, o:33, a:1, s:1, b:1),
% 0.47/1.11 skol9 [70, 1] (w:1, o:56, a:1, s:1, b:1),
% 0.47/1.11 skol10 [71, 0] (w:1, o:11, a:1, s:1, b:1),
% 0.47/1.11 skol11 [72, 0] (w:1, o:12, a:1, s:1, b:1),
% 0.47/1.11 skol12 [73, 1] (w:1, o:57, a:1, s:1, b:1),
% 0.47/1.11 skol13 [74, 0] (w:1, o:13, a:1, s:1, b:1),
% 0.47/1.11 skol14 [75, 0] (w:1, o:14, a:1, s:1, b:1),
% 0.47/1.11 skol15 [76, 0] (w:1, o:15, a:1, s:1, b:1),
% 0.47/1.11 skol16 [77, 0] (w:1, o:16, a:1, s:1, b:1),
% 0.47/1.11 skol17 [78, 1] (w:1, o:58, a:1, s:1, b:1),
% 0.47/1.11 skol18 [79, 0] (w:1, o:17, a:1, s:1, b:1),
% 0.47/1.11 skol19 [80, 0] (w:1, o:18, a:1, s:1, b:1),
% 0.47/1.11 skol20 [81, 1] (w:1, o:59, a:1, s:1, b:1),
% 0.47/1.11 skol21 [82, 0] (w:1, o:20, a:1, s:1, b:1),
% 0.47/1.11 skol22 [83, 0] (w:1, o:21, a:1, s:1, b:1),
% 0.47/1.11 skol23 [84, 0] (w:1, o:22, a:1, s:1, b:1),
% 0.47/1.11 skol24 [85, 0] (w:1, o:23, a:1, s:1, b:1),
% 0.47/1.11 skol25 [86, 0] (w:1, o:24, a:1, s:1, b:1),
% 0.47/1.11 skol26 [87, 0] (w:1, o:25, a:1, s:1, b:1),
% 0.47/1.11 skol27 [88, 0] (w:1, o:26, a:1, s:1, b:1),
% 0.47/1.11 skol28 [89, 0] (w:1, o:27, a:1, s:1, b:1).
% 0.47/1.11
% 0.47/1.11
% 0.47/1.11 Starting Search:
% 0.47/1.11
% 0.47/1.11 *** allocated 15000 integers for clauses
% 0.47/1.11 *** allocated 22500 integers for clauses
% 0.47/1.11
% 0.47/1.11 Bliksems!, er is een bewijs:
% 0.47/1.11 % SZS status Theorem
% 0.47/1.11 % SZS output start Refutation
% 0.47/1.11
% 0.47/1.11 (30) {G0,W6,D3,L2,V2,M2} I { ! finite( X ), finite( set_intersection2( X, Y
% 0.47/1.11 ) ) }.
% 0.47/1.11 (130) {G0,W2,D2,L1,V0,M1} I { finite( skol27 ) }.
% 0.47/1.11 (131) {G0,W4,D3,L1,V0,M1} I { ! finite( set_intersection2( skol27, skol28 )
% 0.47/1.11 ) }.
% 0.47/1.11 (325) {G1,W4,D3,L1,V1,M1} R(30,130) { finite( set_intersection2( skol27, X
% 0.47/1.11 ) ) }.
% 0.47/1.11 (472) {G2,W0,D0,L0,V0,M0} S(131);r(325) { }.
% 0.47/1.11
% 0.47/1.11
% 0.47/1.11 % SZS output end Refutation
% 0.47/1.11 found a proof!
% 0.47/1.11
% 0.47/1.11 *** allocated 33750 integers for clauses
% 0.47/1.11
% 0.47/1.11 Unprocessed initial clauses:
% 0.47/1.11
% 0.47/1.11 (474) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), ! in( Y, X ) }.
% 0.47/1.11 (475) {G0,W7,D2,L3,V2,M3} { ! ordinal( X ), ! element( Y, X ),
% 0.47/1.11 epsilon_transitive( Y ) }.
% 0.47/1.11 (476) {G0,W7,D2,L3,V2,M3} { ! ordinal( X ), ! element( Y, X ),
% 0.47/1.11 epsilon_connected( Y ) }.
% 0.47/1.11 (477) {G0,W7,D2,L3,V2,M3} { ! ordinal( X ), ! element( Y, X ), ordinal( Y
% 0.47/1.11 ) }.
% 0.47/1.11 (478) {G0,W4,D2,L2,V1,M2} { ! empty( X ), finite( X ) }.
% 0.47/1.11 (479) {G0,W4,D2,L2,V1,M2} { ! empty( X ), function( X ) }.
% 0.47/1.11 (480) {G0,W4,D2,L2,V1,M2} { ! ordinal( X ), epsilon_transitive( X ) }.
% 0.47/1.11 (481) {G0,W4,D2,L2,V1,M2} { ! ordinal( X ), epsilon_connected( X ) }.
% 0.47/1.11 (482) {G0,W4,D2,L2,V1,M2} { ! empty( X ), relation( X ) }.
% 0.47/1.11 (483) {G0,W6,D2,L3,V1,M3} { ! empty( X ), ! ordinal( X ), alpha1( X ) }.
% 0.47/1.11 (484) {G0,W6,D2,L3,V1,M3} { ! empty( X ), ! ordinal( X ), natural( X ) }.
% 0.47/1.11 (485) {G0,W4,D2,L2,V1,M2} { ! alpha1( X ), epsilon_transitive( X ) }.
% 0.47/1.11 (486) {G0,W4,D2,L2,V1,M2} { ! alpha1( X ), epsilon_connected( X ) }.
% 0.47/1.11 (487) {G0,W4,D2,L2,V1,M2} { ! alpha1( X ), ordinal( X ) }.
% 0.47/1.11 (488) {G0,W8,D2,L4,V1,M4} { ! epsilon_transitive( X ), ! epsilon_connected
% 0.47/1.11 ( X ), ! ordinal( X ), alpha1( X ) }.
% 0.47/1.11 (489) {G0,W8,D3,L3,V2,M3} { ! finite( X ), ! element( Y, powerset( X ) ),
% 0.47/1.11 finite( Y ) }.
% 0.47/1.11 (490) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X )
% 0.47/1.11 , relation( X ) }.
% 0.47/1.11 (491) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X )
% 0.47/1.11 , function( X ) }.
% 0.47/1.11 (492) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X )
% 0.47/1.11 , one_to_one( X ) }.
% 0.47/1.11 (493) {G0,W6,D2,L3,V1,M3} { ! epsilon_transitive( X ), ! epsilon_connected
% 0.47/1.11 ( X ), ordinal( X ) }.
% 0.47/1.11 (494) {G0,W4,D2,L2,V1,M2} { ! empty( X ), epsilon_transitive( X ) }.
% 0.47/1.11 (495) {G0,W4,D2,L2,V1,M2} { ! empty( X ), epsilon_connected( X ) }.
% 0.47/1.11 (496) {G0,W4,D2,L2,V1,M2} { ! empty( X ), ordinal( X ) }.
% 0.47/1.11 (497) {G0,W7,D2,L3,V1,M3} { ! element( X, positive_rationals ), ! ordinal
% 0.47/1.11 ( X ), alpha2( X ) }.
% 0.47/1.11 (498) {G0,W7,D2,L3,V1,M3} { ! element( X, positive_rationals ), ! ordinal
% 0.47/1.11 ( X ), natural( X ) }.
% 0.47/1.11 (499) {G0,W4,D2,L2,V1,M2} { ! alpha2( X ), epsilon_transitive( X ) }.
% 0.47/1.11 (500) {G0,W4,D2,L2,V1,M2} { ! alpha2( X ), epsilon_connected( X ) }.
% 0.47/1.11 (501) {G0,W4,D2,L2,V1,M2} { ! alpha2( X ), ordinal( X ) }.
% 0.47/1.11 (502) {G0,W8,D2,L4,V1,M4} { ! epsilon_transitive( X ), ! epsilon_connected
% 0.47/1.11 ( X ), ! ordinal( X ), alpha2( X ) }.
% 0.47/1.11 (503) {G0,W7,D3,L1,V2,M1} { set_intersection2( X, Y ) = set_intersection2
% 0.47/1.11 ( Y, X ) }.
% 0.47/1.11 (504) {G0,W4,D3,L1,V1,M1} { element( skol1( X ), X ) }.
% 0.47/1.11 (505) {G0,W6,D3,L2,V2,M2} { ! finite( X ), finite( set_intersection2( Y, X
% 0.47/1.11 ) ) }.
% 0.47/1.11 (506) {G0,W6,D3,L2,V2,M2} { ! finite( X ), finite( set_intersection2( X, Y
% 0.47/1.11 ) ) }.
% 0.47/1.11 (507) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.47/1.11 (508) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 0.47/1.11 (509) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( empty_set ) }.
% 0.47/1.11 (510) {G0,W8,D3,L3,V2,M3} { ! relation( X ), ! relation( Y ), relation(
% 0.47/1.11 set_intersection2( X, Y ) ) }.
% 0.47/1.11 (511) {G0,W3,D3,L1,V1,M1} { ! empty( powerset( X ) ) }.
% 0.47/1.11 (512) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.47/1.11 (513) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 0.47/1.11 (514) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( empty_set ) }.
% 0.47/1.11 (515) {G0,W2,D2,L1,V0,M1} { function( empty_set ) }.
% 0.47/1.11 (516) {G0,W2,D2,L1,V0,M1} { one_to_one( empty_set ) }.
% 0.47/1.11 (517) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.47/1.11 (518) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( empty_set ) }.
% 0.47/1.11 (519) {G0,W2,D2,L1,V0,M1} { epsilon_connected( empty_set ) }.
% 0.47/1.11 (520) {G0,W2,D2,L1,V0,M1} { ordinal( empty_set ) }.
% 0.47/1.11 (521) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.47/1.11 (522) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 0.47/1.11 (523) {G0,W2,D2,L1,V0,M1} { ! empty( positive_rationals ) }.
% 0.47/1.11 (524) {G0,W5,D3,L1,V1,M1} { set_intersection2( X, X ) = X }.
% 0.47/1.11 (525) {G0,W2,D2,L1,V0,M1} { ! empty( skol2 ) }.
% 0.47/1.11 (526) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol2 ) }.
% 0.47/1.11 (527) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol2 ) }.
% 0.47/1.11 (528) {G0,W2,D2,L1,V0,M1} { ordinal( skol2 ) }.
% 0.47/1.11 (529) {G0,W2,D2,L1,V0,M1} { natural( skol2 ) }.
% 0.47/1.11 (530) {G0,W2,D2,L1,V0,M1} { ! empty( skol3 ) }.
% 0.47/1.11 (531) {G0,W2,D2,L1,V0,M1} { finite( skol3 ) }.
% 0.47/1.11 (532) {G0,W2,D2,L1,V0,M1} { relation( skol4 ) }.
% 0.47/1.11 (533) {G0,W2,D2,L1,V0,M1} { function( skol4 ) }.
% 0.47/1.11 (534) {G0,W2,D2,L1,V0,M1} { function_yielding( skol4 ) }.
% 0.47/1.11 (535) {G0,W2,D2,L1,V0,M1} { relation( skol5 ) }.
% 0.47/1.11 (536) {G0,W2,D2,L1,V0,M1} { function( skol5 ) }.
% 0.47/1.11 (537) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol6 ) }.
% 0.47/1.11 (538) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol6 ) }.
% 0.47/1.11 (539) {G0,W2,D2,L1,V0,M1} { ordinal( skol6 ) }.
% 0.47/1.11 (540) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol7 ) }.
% 0.47/1.11 (541) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol7 ) }.
% 0.47/1.11 (542) {G0,W2,D2,L1,V0,M1} { ordinal( skol7 ) }.
% 0.47/1.11 (543) {G0,W2,D2,L1,V0,M1} { being_limit_ordinal( skol7 ) }.
% 0.47/1.11 (544) {G0,W2,D2,L1,V0,M1} { empty( skol8 ) }.
% 0.47/1.11 (545) {G0,W2,D2,L1,V0,M1} { relation( skol8 ) }.
% 0.47/1.11 (546) {G0,W5,D3,L2,V2,M2} { empty( X ), ! empty( skol9( Y ) ) }.
% 0.47/1.11 (547) {G0,W7,D3,L2,V1,M2} { empty( X ), element( skol9( X ), powerset( X )
% 0.47/1.11 ) }.
% 0.47/1.11 (548) {G0,W2,D2,L1,V0,M1} { empty( skol10 ) }.
% 0.47/1.11 (549) {G0,W3,D2,L1,V0,M1} { element( skol11, positive_rationals ) }.
% 0.47/1.11 (550) {G0,W2,D2,L1,V0,M1} { ! empty( skol11 ) }.
% 0.47/1.11 (551) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol11 ) }.
% 0.47/1.11 (552) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol11 ) }.
% 0.47/1.11 (553) {G0,W2,D2,L1,V0,M1} { ordinal( skol11 ) }.
% 0.47/1.11 (554) {G0,W3,D3,L1,V1,M1} { empty( skol12( Y ) ) }.
% 0.47/1.11 (555) {G0,W3,D3,L1,V1,M1} { relation( skol12( Y ) ) }.
% 0.47/1.11 (556) {G0,W3,D3,L1,V1,M1} { function( skol12( Y ) ) }.
% 0.47/1.11 (557) {G0,W3,D3,L1,V1,M1} { one_to_one( skol12( Y ) ) }.
% 0.47/1.11 (558) {G0,W3,D3,L1,V1,M1} { epsilon_transitive( skol12( Y ) ) }.
% 0.47/1.11 (559) {G0,W3,D3,L1,V1,M1} { epsilon_connected( skol12( Y ) ) }.
% 0.47/1.11 (560) {G0,W3,D3,L1,V1,M1} { ordinal( skol12( Y ) ) }.
% 0.47/1.11 (561) {G0,W3,D3,L1,V1,M1} { natural( skol12( Y ) ) }.
% 0.47/1.11 (562) {G0,W3,D3,L1,V1,M1} { finite( skol12( Y ) ) }.
% 0.47/1.11 (563) {G0,W5,D3,L1,V1,M1} { element( skol12( X ), powerset( X ) ) }.
% 0.47/1.11 (564) {G0,W2,D2,L1,V0,M1} { relation( skol13 ) }.
% 0.47/1.11 (565) {G0,W2,D2,L1,V0,M1} { empty( skol13 ) }.
% 0.47/1.11 (566) {G0,W2,D2,L1,V0,M1} { function( skol13 ) }.
% 0.47/1.11 (567) {G0,W2,D2,L1,V0,M1} { relation( skol14 ) }.
% 0.47/1.11 (568) {G0,W2,D2,L1,V0,M1} { function( skol14 ) }.
% 0.47/1.11 (569) {G0,W2,D2,L1,V0,M1} { one_to_one( skol14 ) }.
% 0.47/1.11 (570) {G0,W2,D2,L1,V0,M1} { empty( skol14 ) }.
% 0.47/1.11 (571) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol14 ) }.
% 0.47/1.11 (572) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol14 ) }.
% 0.47/1.11 (573) {G0,W2,D2,L1,V0,M1} { ordinal( skol14 ) }.
% 0.47/1.11 (574) {G0,W2,D2,L1,V0,M1} { relation( skol15 ) }.
% 0.47/1.11 (575) {G0,W2,D2,L1,V0,M1} { function( skol15 ) }.
% 0.47/1.11 (576) {G0,W2,D2,L1,V0,M1} { transfinite_sequence( skol15 ) }.
% 0.47/1.11 (577) {G0,W2,D2,L1,V0,M1} { ordinal_yielding( skol15 ) }.
% 0.47/1.11 (578) {G0,W2,D2,L1,V0,M1} { ! empty( skol16 ) }.
% 0.47/1.11 (579) {G0,W2,D2,L1,V0,M1} { relation( skol16 ) }.
% 0.47/1.11 (580) {G0,W3,D3,L1,V1,M1} { empty( skol17( Y ) ) }.
% 0.47/1.11 (581) {G0,W5,D3,L1,V1,M1} { element( skol17( X ), powerset( X ) ) }.
% 0.47/1.11 (582) {G0,W2,D2,L1,V0,M1} { ! empty( skol18 ) }.
% 0.47/1.11 (583) {G0,W3,D2,L1,V0,M1} { element( skol19, positive_rationals ) }.
% 0.47/1.11 (584) {G0,W2,D2,L1,V0,M1} { empty( skol19 ) }.
% 0.47/1.11 (585) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol19 ) }.
% 0.47/1.11 (586) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol19 ) }.
% 0.47/1.11 (587) {G0,W2,D2,L1,V0,M1} { ordinal( skol19 ) }.
% 0.47/1.11 (588) {G0,W2,D2,L1,V0,M1} { natural( skol19 ) }.
% 0.47/1.11 (589) {G0,W5,D3,L2,V2,M2} { empty( X ), ! empty( skol20( Y ) ) }.
% 0.47/1.11 (590) {G0,W5,D3,L2,V2,M2} { empty( X ), finite( skol20( Y ) ) }.
% 0.47/1.11 (591) {G0,W7,D3,L2,V1,M2} { empty( X ), element( skol20( X ), powerset( X
% 0.47/1.11 ) ) }.
% 0.47/1.11 (592) {G0,W2,D2,L1,V0,M1} { relation( skol21 ) }.
% 0.47/1.11 (593) {G0,W2,D2,L1,V0,M1} { function( skol21 ) }.
% 0.47/1.11 (594) {G0,W2,D2,L1,V0,M1} { one_to_one( skol21 ) }.
% 0.47/1.11 (595) {G0,W2,D2,L1,V0,M1} { ! empty( skol22 ) }.
% 0.47/1.11 (596) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol22 ) }.
% 0.47/1.11 (597) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol22 ) }.
% 0.47/1.11 (598) {G0,W2,D2,L1,V0,M1} { ordinal( skol22 ) }.
% 0.47/1.11 (599) {G0,W2,D2,L1,V0,M1} { relation( skol23 ) }.
% 0.47/1.11 (600) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( skol23 ) }.
% 0.47/1.11 (601) {G0,W2,D2,L1,V0,M1} { relation( skol24 ) }.
% 0.47/1.11 (602) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( skol24 ) }.
% 0.47/1.11 (603) {G0,W2,D2,L1,V0,M1} { function( skol24 ) }.
% 0.47/1.11 (604) {G0,W2,D2,L1,V0,M1} { relation( skol25 ) }.
% 0.47/1.11 (605) {G0,W2,D2,L1,V0,M1} { function( skol25 ) }.
% 0.47/1.11 (606) {G0,W2,D2,L1,V0,M1} { transfinite_sequence( skol25 ) }.
% 0.47/1.11 (607) {G0,W2,D2,L1,V0,M1} { relation( skol26 ) }.
% 0.47/1.11 (608) {G0,W2,D2,L1,V0,M1} { relation_non_empty( skol26 ) }.
% 0.47/1.11 (609) {G0,W2,D2,L1,V0,M1} { function( skol26 ) }.
% 0.47/1.11 (610) {G0,W3,D2,L1,V1,M1} { subset( X, X ) }.
% 0.47/1.11 (611) {G0,W7,D2,L3,V2,M3} { ! subset( X, Y ), ! finite( Y ), finite( X )
% 0.47/1.11 }.
% 0.47/1.11 (612) {G0,W2,D2,L1,V0,M1} { finite( skol27 ) }.
% 0.47/1.11 (613) {G0,W4,D3,L1,V0,M1} { ! finite( set_intersection2( skol27, skol28 )
% 0.47/1.11 ) }.
% 0.47/1.11 (614) {G0,W5,D3,L1,V2,M1} { subset( set_intersection2( X, Y ), X ) }.
% 0.47/1.11 (615) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), element( X, Y ) }.
% 0.47/1.11 (616) {G0,W5,D3,L1,V1,M1} { set_intersection2( X, empty_set ) = empty_set
% 0.47/1.11 }.
% 0.47/1.11 (617) {G0,W8,D2,L3,V2,M3} { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.47/1.11 (618) {G0,W7,D3,L2,V2,M2} { ! element( X, powerset( Y ) ), subset( X, Y )
% 0.47/1.11 }.
% 0.47/1.11 (619) {G0,W7,D3,L2,V2,M2} { ! subset( X, Y ), element( X, powerset( Y ) )
% 0.47/1.11 }.
% 0.47/1.11 (620) {G0,W10,D3,L3,V3,M3} { ! in( X, Z ), ! element( Z, powerset( Y ) ),
% 0.47/1.11 element( X, Y ) }.
% 0.47/1.11 (621) {G0,W9,D3,L3,V3,M3} { ! in( X, Y ), ! element( Y, powerset( Z ) ), !
% 0.47/1.11 empty( Z ) }.
% 0.47/1.11 (622) {G0,W5,D2,L2,V1,M2} { ! empty( X ), X = empty_set }.
% 0.47/1.11 (623) {G0,W5,D2,L2,V2,M2} { ! in( X, Y ), ! empty( Y ) }.
% 0.47/1.11 (624) {G0,W7,D2,L3,V2,M3} { ! empty( X ), X = Y, ! empty( Y ) }.
% 0.47/1.11
% 0.47/1.11
% 0.47/1.11 Total Proof:
% 0.47/1.11
% 0.47/1.11 subsumption: (30) {G0,W6,D3,L2,V2,M2} I { ! finite( X ), finite(
% 0.47/1.11 set_intersection2( X, Y ) ) }.
% 0.47/1.11 parent0: (506) {G0,W6,D3,L2,V2,M2} { ! finite( X ), finite(
% 0.47/1.11 set_intersection2( X, Y ) ) }.
% 0.47/1.11 substitution0:
% 0.47/1.11 X := X
% 0.47/1.11 Y := Y
% 0.47/1.11 end
% 0.47/1.11 permutation0:
% 0.47/1.11 0 ==> 0
% 0.47/1.11 1 ==> 1
% 0.47/1.11 end
% 0.47/1.11
% 0.47/1.11 subsumption: (130) {G0,W2,D2,L1,V0,M1} I { finite( skol27 ) }.
% 0.47/1.11 parent0: (612) {G0,W2,D2,L1,V0,M1} { finite( skol27 ) }.
% 0.47/1.11 substitution0:
% 0.47/1.11 end
% 0.47/1.11 permutation0:
% 0.47/1.11 0 ==> 0
% 0.47/1.11 end
% 0.47/1.11
% 0.47/1.11 subsumption: (131) {G0,W4,D3,L1,V0,M1} I { ! finite( set_intersection2(
% 0.47/1.11 skol27, skol28 ) ) }.
% 0.47/1.11 parent0: (613) {G0,W4,D3,L1,V0,M1} { ! finite( set_intersection2( skol27,
% 0.47/1.11 skol28 ) ) }.
% 0.47/1.11 substitution0:
% 0.47/1.11 end
% 0.47/1.11 permutation0:
% 0.47/1.11 0 ==> 0
% 0.47/1.11 end
% 0.47/1.11
% 0.47/1.11 resolution: (632) {G1,W4,D3,L1,V1,M1} { finite( set_intersection2( skol27
% 0.47/1.11 , X ) ) }.
% 0.47/1.11 parent0[0]: (30) {G0,W6,D3,L2,V2,M2} I { ! finite( X ), finite(
% 0.47/1.11 set_intersection2( X, Y ) ) }.
% 0.47/1.11 parent1[0]: (130) {G0,W2,D2,L1,V0,M1} I { finite( skol27 ) }.
% 0.47/1.11 substitution0:
% 0.47/1.11 X := skol27
% 0.47/1.11 Y := X
% 0.47/1.11 end
% 0.47/1.11 substitution1:
% 0.47/1.11 end
% 0.47/1.11
% 0.47/1.11 subsumption: (325) {G1,W4,D3,L1,V1,M1} R(30,130) { finite(
% 0.47/1.11 set_intersection2( skol27, X ) ) }.
% 0.47/1.11 parent0: (632) {G1,W4,D3,L1,V1,M1} { finite( set_intersection2( skol27, X
% 0.47/1.11 ) ) }.
% 0.47/1.11 substitution0:
% 0.47/1.11 X := X
% 0.47/1.11 end
% 0.47/1.11 permutation0:
% 0.47/1.11 0 ==> 0
% 0.47/1.11 end
% 0.47/1.11
% 0.47/1.11 resolution: (633) {G1,W0,D0,L0,V0,M0} { }.
% 0.47/1.11 parent0[0]: (131) {G0,W4,D3,L1,V0,M1} I { ! finite( set_intersection2(
% 0.47/1.11 skol27, skol28 ) ) }.
% 0.47/1.11 parent1[0]: (325) {G1,W4,D3,L1,V1,M1} R(30,130) { finite( set_intersection2
% 0.47/1.11 ( skol27, X ) ) }.
% 0.47/1.11 substitution0:
% 0.47/1.11 end
% 0.47/1.11 substitution1:
% 0.47/1.11 X := skol28
% 0.47/1.11 end
% 0.47/1.11
% 0.47/1.11 subsumption: (472) {G2,W0,D0,L0,V0,M0} S(131);r(325) { }.
% 0.47/1.11 parent0: (633) {G1,W0,D0,L0,V0,M0} { }.
% 0.47/1.11 substitution0:
% 0.47/1.11 end
% 0.47/1.11 permutation0:
% 0.47/1.11 end
% 0.47/1.11
% 0.47/1.11 Proof check complete!
% 0.47/1.11
% 0.47/1.11 Memory use:
% 0.47/1.11
% 0.47/1.11 space for terms: 4336
% 0.47/1.11 space for clauses: 22053
% 0.47/1.11
% 0.47/1.11
% 0.47/1.11 clauses generated: 868
% 0.47/1.11 clauses kept: 473
% 0.47/1.11 clauses selected: 202
% 0.47/1.11 clauses deleted: 9
% 0.47/1.11 clauses inuse deleted: 0
% 0.47/1.11
% 0.47/1.11 subsentry: 586
% 0.47/1.11 literals s-matched: 513
% 0.47/1.11 literals matched: 513
% 0.47/1.11 full subsumption: 30
% 0.47/1.11
% 0.47/1.11 checksum: 645619391
% 0.47/1.11
% 0.47/1.11
% 0.47/1.11 Bliksem ended
%------------------------------------------------------------------------------