TSTP Solution File: SEU083+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SEU083+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Tue Jul 19 07:10:33 EDT 2022
% Result : Theorem 0.45s 1.10s
% Output : Refutation 0.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU083+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Sun Jun 19 08:25:44 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.45/1.09 *** allocated 10000 integers for termspace/termends
% 0.45/1.09 *** allocated 10000 integers for clauses
% 0.45/1.09 *** allocated 10000 integers for justifications
% 0.45/1.09 Bliksem 1.12
% 0.45/1.09
% 0.45/1.09
% 0.45/1.09 Automatic Strategy Selection
% 0.45/1.09
% 0.45/1.09
% 0.45/1.09 Clauses:
% 0.45/1.09
% 0.45/1.09 { subset( X, X ) }.
% 0.45/1.09 { ! in( X, Y ), ! in( Y, X ) }.
% 0.45/1.09 { empty( empty_set ) }.
% 0.45/1.09 { relation( empty_set ) }.
% 0.45/1.09 { empty( empty_set ) }.
% 0.45/1.09 { relation( empty_set ) }.
% 0.45/1.09 { relation_empty_yielding( empty_set ) }.
% 0.45/1.09 { relation( empty_set ) }.
% 0.45/1.09 { relation_empty_yielding( empty_set ) }.
% 0.45/1.09 { function( empty_set ) }.
% 0.45/1.09 { one_to_one( empty_set ) }.
% 0.45/1.09 { empty( empty_set ) }.
% 0.45/1.09 { epsilon_transitive( empty_set ) }.
% 0.45/1.09 { epsilon_connected( empty_set ) }.
% 0.45/1.09 { ordinal( empty_set ) }.
% 0.45/1.09 { empty( empty_set ) }.
% 0.45/1.09 { set_union2( X, empty_set ) = X }.
% 0.45/1.09 { ! in( X, Y ), element( X, Y ) }.
% 0.45/1.09 { ! in( X, Z ), ! element( Z, powerset( Y ) ), element( X, Y ) }.
% 0.45/1.09 { ! in( X, Y ), ! element( Y, powerset( Z ) ), ! empty( Z ) }.
% 0.45/1.09 { element( skol1( X ), X ) }.
% 0.45/1.09 { ! empty( X ), finite( X ) }.
% 0.45/1.09 { ! finite( X ), ! element( Y, powerset( X ) ), finite( Y ) }.
% 0.45/1.09 { ! empty( X ), function( X ) }.
% 0.45/1.09 { ! relation( X ), ! empty( X ), ! function( X ), relation( X ) }.
% 0.45/1.09 { ! relation( X ), ! empty( X ), ! function( X ), function( X ) }.
% 0.45/1.09 { ! relation( X ), ! empty( X ), ! function( X ), one_to_one( X ) }.
% 0.45/1.09 { ! relation( X ), ! relation( Y ), relation( set_union2( X, Y ) ) }.
% 0.45/1.09 { ! empty( X ), relation( X ) }.
% 0.45/1.09 { ! empty( positive_rationals ) }.
% 0.45/1.09 { ! ordinal( X ), ! element( Y, X ), epsilon_transitive( Y ) }.
% 0.45/1.09 { ! ordinal( X ), ! element( Y, X ), epsilon_connected( Y ) }.
% 0.45/1.09 { ! ordinal( X ), ! element( Y, X ), ordinal( Y ) }.
% 0.45/1.09 { ! empty( X ), ! ordinal( X ), alpha1( X ) }.
% 0.45/1.09 { ! empty( X ), ! ordinal( X ), natural( X ) }.
% 0.45/1.09 { ! alpha1( X ), epsilon_transitive( X ) }.
% 0.45/1.09 { ! alpha1( X ), epsilon_connected( X ) }.
% 0.45/1.09 { ! alpha1( X ), ordinal( X ) }.
% 0.45/1.09 { ! epsilon_transitive( X ), ! epsilon_connected( X ), ! ordinal( X ),
% 0.45/1.09 alpha1( X ) }.
% 0.45/1.09 { ! element( X, positive_rationals ), ! ordinal( X ), alpha2( X ) }.
% 0.45/1.09 { ! element( X, positive_rationals ), ! ordinal( X ), natural( X ) }.
% 0.45/1.09 { ! alpha2( X ), epsilon_transitive( X ) }.
% 0.45/1.09 { ! alpha2( X ), epsilon_connected( X ) }.
% 0.45/1.09 { ! alpha2( X ), ordinal( X ) }.
% 0.45/1.09 { ! epsilon_transitive( X ), ! epsilon_connected( X ), ! ordinal( X ),
% 0.45/1.09 alpha2( X ) }.
% 0.45/1.09 { ! ordinal( X ), epsilon_transitive( X ) }.
% 0.45/1.09 { ! ordinal( X ), epsilon_connected( X ) }.
% 0.45/1.09 { ! epsilon_transitive( X ), ! epsilon_connected( X ), ordinal( X ) }.
% 0.45/1.09 { ! empty( X ), epsilon_transitive( X ) }.
% 0.45/1.09 { ! empty( X ), epsilon_connected( X ) }.
% 0.45/1.09 { ! empty( X ), ordinal( X ) }.
% 0.45/1.09 { ! empty( powerset( X ) ) }.
% 0.45/1.09 { empty( X ), ! empty( set_union2( X, Y ) ) }.
% 0.45/1.09 { empty( X ), ! empty( set_union2( Y, X ) ) }.
% 0.45/1.09 { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.45/1.09 { ! element( X, powerset( Y ) ), subset( X, Y ) }.
% 0.45/1.09 { ! subset( X, Y ), element( X, powerset( Y ) ) }.
% 0.45/1.09 { ! empty( X ), X = empty_set }.
% 0.45/1.09 { ! in( X, Y ), ! empty( Y ) }.
% 0.45/1.09 { ! empty( X ), X = Y, ! empty( Y ) }.
% 0.45/1.09 { set_union2( X, Y ) = set_union2( Y, X ) }.
% 0.45/1.09 { set_union2( X, X ) = X }.
% 0.45/1.09 { ! finite( X ), ! finite( Y ), finite( set_union2( X, Y ) ) }.
% 0.45/1.09 { ! empty( skol2 ) }.
% 0.45/1.09 { finite( skol2 ) }.
% 0.45/1.09 { empty( skol3( Y ) ) }.
% 0.45/1.09 { relation( skol3( Y ) ) }.
% 0.45/1.09 { function( skol3( Y ) ) }.
% 0.45/1.09 { one_to_one( skol3( Y ) ) }.
% 0.45/1.09 { epsilon_transitive( skol3( Y ) ) }.
% 0.45/1.09 { epsilon_connected( skol3( Y ) ) }.
% 0.45/1.09 { ordinal( skol3( Y ) ) }.
% 0.45/1.09 { natural( skol3( Y ) ) }.
% 0.45/1.09 { finite( skol3( Y ) ) }.
% 0.45/1.09 { element( skol3( X ), powerset( X ) ) }.
% 0.45/1.09 { empty( X ), ! empty( skol4( Y ) ) }.
% 0.45/1.09 { empty( X ), finite( skol4( Y ) ) }.
% 0.45/1.09 { empty( X ), element( skol4( X ), powerset( X ) ) }.
% 0.45/1.09 { relation( skol5 ) }.
% 0.45/1.09 { function( skol5 ) }.
% 0.45/1.09 { relation( skol6 ) }.
% 0.45/1.09 { empty( skol6 ) }.
% 0.45/1.09 { function( skol6 ) }.
% 0.45/1.09 { relation( skol7 ) }.
% 0.45/1.09 { function( skol7 ) }.
% 0.45/1.09 { one_to_one( skol7 ) }.
% 0.45/1.09 { relation( skol8 ) }.
% 0.45/1.09 { relation_empty_yielding( skol8 ) }.
% 0.45/1.09 { function( skol8 ) }.
% 0.45/1.09 { relation( skol9 ) }.
% 0.45/1.09 { relation_non_empty( skol9 ) }.
% 0.45/1.09 { function( skol9 ) }.
% 0.45/1.09 { epsilon_transitive( skol10 ) }.
% 0.45/1.09 { epsilon_connected( skol10 ) }.
% 0.45/1.09 { ordinal( skol10 ) }.
% 0.45/1.09 { being_limit_ordinal( skol10 ) }.
% 0.45/1.09 { relation( skol11 ) }.
% 0.45/1.09 { function( skol11 ) }.
% 0.45/1.09 { transfinite_sequence( skol11 ) }.
% 0.45/1.09 { ordinal_yielding( skol11 ) }.
% 0.45/1.09 { empty( skol12 ) }.
% 0.45/1.09 { relation( skol12 ) }.
% 0.45/1.10 { ! empty( skol13 ) }.
% 0.45/1.10 { relation( skol13 ) }.
% 0.45/1.10 { relation( skol14 ) }.
% 0.45/1.10 { relation_empty_yielding( skol14 ) }.
% 0.45/1.10 { ! empty( skol15 ) }.
% 0.45/1.10 { epsilon_transitive( skol15 ) }.
% 0.45/1.10 { epsilon_connected( skol15 ) }.
% 0.45/1.10 { ordinal( skol15 ) }.
% 0.45/1.10 { natural( skol15 ) }.
% 0.45/1.10 { element( skol16, positive_rationals ) }.
% 0.45/1.10 { ! empty( skol16 ) }.
% 0.45/1.10 { epsilon_transitive( skol16 ) }.
% 0.45/1.10 { epsilon_connected( skol16 ) }.
% 0.45/1.10 { ordinal( skol16 ) }.
% 0.45/1.10 { element( skol17, positive_rationals ) }.
% 0.45/1.10 { empty( skol17 ) }.
% 0.45/1.10 { epsilon_transitive( skol17 ) }.
% 0.45/1.10 { epsilon_connected( skol17 ) }.
% 0.45/1.10 { ordinal( skol17 ) }.
% 0.45/1.10 { natural( skol17 ) }.
% 0.45/1.10 { epsilon_transitive( skol18 ) }.
% 0.45/1.10 { epsilon_connected( skol18 ) }.
% 0.45/1.10 { ordinal( skol18 ) }.
% 0.45/1.10 { relation( skol19 ) }.
% 0.45/1.10 { function( skol19 ) }.
% 0.45/1.10 { one_to_one( skol19 ) }.
% 0.45/1.10 { empty( skol19 ) }.
% 0.45/1.10 { epsilon_transitive( skol19 ) }.
% 0.45/1.10 { epsilon_connected( skol19 ) }.
% 0.45/1.10 { ordinal( skol19 ) }.
% 0.45/1.10 { ! empty( skol20 ) }.
% 0.45/1.10 { epsilon_transitive( skol20 ) }.
% 0.45/1.10 { epsilon_connected( skol20 ) }.
% 0.45/1.10 { ordinal( skol20 ) }.
% 0.45/1.10 { relation( skol21 ) }.
% 0.45/1.10 { function( skol21 ) }.
% 0.45/1.10 { transfinite_sequence( skol21 ) }.
% 0.45/1.10 { empty( X ), ! empty( skol22( Y ) ) }.
% 0.45/1.10 { empty( X ), element( skol22( X ), powerset( X ) ) }.
% 0.45/1.10 { empty( skol23( Y ) ) }.
% 0.45/1.10 { element( skol23( X ), powerset( X ) ) }.
% 0.45/1.10 { empty( skol24 ) }.
% 0.45/1.10 { ! empty( skol25 ) }.
% 0.45/1.10 { relation( skol26 ) }.
% 0.45/1.10 { function( skol26 ) }.
% 0.45/1.10 { function_yielding( skol26 ) }.
% 0.45/1.10 { finite( skol27 ) }.
% 0.45/1.10 { finite( skol28 ) }.
% 0.45/1.10 { ! finite( set_union2( skol27, skol28 ) ) }.
% 0.45/1.10 { ! finite( X ), ! finite( Y ), finite( set_union2( X, Y ) ) }.
% 0.45/1.10
% 0.45/1.10 percentage equality = 0.023923, percentage horn = 0.972028
% 0.45/1.10 This is a problem with some equality
% 0.45/1.10
% 0.45/1.10
% 0.45/1.10
% 0.45/1.10 Options Used:
% 0.45/1.10
% 0.45/1.10 useres = 1
% 0.45/1.10 useparamod = 1
% 0.45/1.10 useeqrefl = 1
% 0.45/1.10 useeqfact = 1
% 0.45/1.10 usefactor = 1
% 0.45/1.10 usesimpsplitting = 0
% 0.45/1.10 usesimpdemod = 5
% 0.45/1.10 usesimpres = 3
% 0.45/1.10
% 0.45/1.10 resimpinuse = 1000
% 0.45/1.10 resimpclauses = 20000
% 0.45/1.10 substype = eqrewr
% 0.45/1.10 backwardsubs = 1
% 0.45/1.10 selectoldest = 5
% 0.45/1.10
% 0.45/1.10 litorderings [0] = split
% 0.45/1.10 litorderings [1] = extend the termordering, first sorting on arguments
% 0.45/1.10
% 0.45/1.10 termordering = kbo
% 0.45/1.10
% 0.45/1.10 litapriori = 0
% 0.45/1.10 termapriori = 1
% 0.45/1.10 litaposteriori = 0
% 0.45/1.10 termaposteriori = 0
% 0.45/1.10 demodaposteriori = 0
% 0.45/1.10 ordereqreflfact = 0
% 0.45/1.10
% 0.45/1.10 litselect = negord
% 0.45/1.10
% 0.45/1.10 maxweight = 15
% 0.45/1.10 maxdepth = 30000
% 0.45/1.10 maxlength = 115
% 0.45/1.10 maxnrvars = 195
% 0.45/1.10 excuselevel = 1
% 0.45/1.10 increasemaxweight = 1
% 0.45/1.10
% 0.45/1.10 maxselected = 10000000
% 0.45/1.10 maxnrclauses = 10000000
% 0.45/1.10
% 0.45/1.10 showgenerated = 0
% 0.45/1.10 showkept = 0
% 0.45/1.10 showselected = 0
% 0.45/1.10 showdeleted = 0
% 0.45/1.10 showresimp = 1
% 0.45/1.10 showstatus = 2000
% 0.45/1.10
% 0.45/1.10 prologoutput = 0
% 0.45/1.10 nrgoals = 5000000
% 0.45/1.10 totalproof = 1
% 0.45/1.10
% 0.45/1.10 Symbols occurring in the translation:
% 0.45/1.10
% 0.45/1.10 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.45/1.10 . [1, 2] (w:1, o:62, a:1, s:1, b:0),
% 0.45/1.10 ! [4, 1] (w:0, o:34, a:1, s:1, b:0),
% 0.45/1.10 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.45/1.10 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.45/1.10 subset [37, 2] (w:1, o:86, a:1, s:1, b:0),
% 0.45/1.10 in [38, 2] (w:1, o:87, a:1, s:1, b:0),
% 0.45/1.10 empty_set [39, 0] (w:1, o:8, a:1, s:1, b:0),
% 0.45/1.10 empty [40, 1] (w:1, o:39, a:1, s:1, b:0),
% 0.45/1.10 relation [41, 1] (w:1, o:40, a:1, s:1, b:0),
% 0.45/1.10 relation_empty_yielding [42, 1] (w:1, o:41, a:1, s:1, b:0),
% 0.45/1.10 function [43, 1] (w:1, o:44, a:1, s:1, b:0),
% 0.45/1.10 one_to_one [44, 1] (w:1, o:46, a:1, s:1, b:0),
% 0.45/1.10 epsilon_transitive [45, 1] (w:1, o:42, a:1, s:1, b:0),
% 0.45/1.10 epsilon_connected [46, 1] (w:1, o:43, a:1, s:1, b:0),
% 0.45/1.10 ordinal [47, 1] (w:1, o:47, a:1, s:1, b:0),
% 0.45/1.10 set_union2 [48, 2] (w:1, o:88, a:1, s:1, b:0),
% 0.45/1.10 element [49, 2] (w:1, o:89, a:1, s:1, b:0),
% 0.45/1.10 powerset [51, 1] (w:1, o:49, a:1, s:1, b:0),
% 0.45/1.10 finite [52, 1] (w:1, o:50, a:1, s:1, b:0),
% 0.45/1.10 positive_rationals [53, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.45/1.10 natural [54, 1] (w:1, o:45, a:1, s:1, b:0),
% 0.45/1.10 relation_non_empty [55, 1] (w:1, o:51, a:1, s:1, b:0),
% 0.45/1.10 being_limit_ordinal [56, 1] (w:1, o:54, a:1, s:1, b:0),
% 0.45/1.10 transfinite_sequence [57, 1] (w:1, o:60, a:1, s:1, b:0),
% 0.45/1.10 ordinal_yielding [58, 1] (w:1, o:48, a:1, s:1, b:0),
% 0.45/1.10 function_yielding [59, 1] (w:1, o:61, a:1, s:1, b:0),
% 0.45/1.10 alpha1 [60, 1] (w:1, o:52, a:1, s:1, b:1),
% 0.45/1.10 alpha2 [61, 1] (w:1, o:53, a:1, s:1, b:1),
% 0.45/1.10 skol1 [62, 1] (w:1, o:55, a:1, s:1, b:1),
% 0.45/1.10 skol2 [63, 0] (w:1, o:21, a:1, s:1, b:1),
% 0.45/1.10 skol3 [64, 1] (w:1, o:58, a:1, s:1, b:1),
% 0.45/1.10 skol4 [65, 1] (w:1, o:59, a:1, s:1, b:1),
% 0.45/1.10 skol5 [66, 0] (w:1, o:22, a:1, s:1, b:1),
% 0.45/1.10 skol6 [67, 0] (w:1, o:23, a:1, s:1, b:1),
% 0.45/1.10 skol7 [68, 0] (w:1, o:24, a:1, s:1, b:1),
% 0.45/1.10 skol8 [69, 0] (w:1, o:25, a:1, s:1, b:1),
% 0.45/1.10 skol9 [70, 0] (w:1, o:26, a:1, s:1, b:1),
% 0.45/1.10 skol10 [71, 0] (w:1, o:11, a:1, s:1, b:1),
% 0.45/1.10 skol11 [72, 0] (w:1, o:12, a:1, s:1, b:1),
% 0.45/1.10 skol12 [73, 0] (w:1, o:13, a:1, s:1, b:1),
% 0.45/1.10 skol13 [74, 0] (w:1, o:14, a:1, s:1, b:1),
% 0.45/1.10 skol14 [75, 0] (w:1, o:15, a:1, s:1, b:1),
% 0.45/1.10 skol15 [76, 0] (w:1, o:16, a:1, s:1, b:1),
% 0.45/1.10 skol16 [77, 0] (w:1, o:17, a:1, s:1, b:1),
% 0.45/1.10 skol17 [78, 0] (w:1, o:18, a:1, s:1, b:1),
% 0.45/1.10 skol18 [79, 0] (w:1, o:19, a:1, s:1, b:1),
% 0.45/1.10 skol19 [80, 0] (w:1, o:20, a:1, s:1, b:1),
% 0.45/1.10 skol20 [81, 0] (w:1, o:27, a:1, s:1, b:1),
% 0.45/1.10 skol21 [82, 0] (w:1, o:28, a:1, s:1, b:1),
% 0.45/1.10 skol22 [83, 1] (w:1, o:56, a:1, s:1, b:1),
% 0.45/1.10 skol23 [84, 1] (w:1, o:57, a:1, s:1, b:1),
% 0.45/1.10 skol24 [85, 0] (w:1, o:29, a:1, s:1, b:1),
% 0.45/1.10 skol25 [86, 0] (w:1, o:30, a:1, s:1, b:1),
% 0.45/1.10 skol26 [87, 0] (w:1, o:31, a:1, s:1, b:1),
% 0.45/1.10 skol27 [88, 0] (w:1, o:32, a:1, s:1, b:1),
% 0.45/1.10 skol28 [89, 0] (w:1, o:33, a:1, s:1, b:1).
% 0.45/1.10
% 0.45/1.10
% 0.45/1.10 Starting Search:
% 0.45/1.10
% 0.45/1.10 *** allocated 15000 integers for clauses
% 0.45/1.10 *** allocated 22500 integers for clauses
% 0.45/1.10 *** allocated 33750 integers for clauses
% 0.45/1.10
% 0.45/1.10 Bliksems!, er is een bewijs:
% 0.45/1.10 % SZS status Theorem
% 0.45/1.10 % SZS output start Refutation
% 0.45/1.10
% 0.45/1.10 (54) {G0,W8,D3,L3,V2,M3} I { ! finite( X ), ! finite( Y ), finite(
% 0.45/1.10 set_union2( X, Y ) ) }.
% 0.45/1.10 (140) {G0,W2,D2,L1,V0,M1} I { finite( skol27 ) }.
% 0.45/1.10 (141) {G0,W2,D2,L1,V0,M1} I { finite( skol28 ) }.
% 0.45/1.10 (142) {G0,W4,D3,L1,V0,M1} I { ! finite( set_union2( skol27, skol28 ) ) }.
% 0.45/1.10 (613) {G1,W2,D2,L1,V0,M1} R(142,54);r(140) { ! finite( skol28 ) }.
% 0.45/1.10 (621) {G2,W0,D0,L0,V0,M0} S(613);r(141) { }.
% 0.45/1.10
% 0.45/1.10
% 0.45/1.10 % SZS output end Refutation
% 0.45/1.10 found a proof!
% 0.45/1.10
% 0.45/1.10
% 0.45/1.10 Unprocessed initial clauses:
% 0.45/1.10
% 0.45/1.10 (623) {G0,W3,D2,L1,V1,M1} { subset( X, X ) }.
% 0.45/1.10 (624) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), ! in( Y, X ) }.
% 0.45/1.10 (625) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.45/1.10 (626) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 0.45/1.10 (627) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.45/1.10 (628) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 0.45/1.10 (629) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( empty_set ) }.
% 0.45/1.10 (630) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 0.45/1.10 (631) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( empty_set ) }.
% 0.45/1.10 (632) {G0,W2,D2,L1,V0,M1} { function( empty_set ) }.
% 0.45/1.10 (633) {G0,W2,D2,L1,V0,M1} { one_to_one( empty_set ) }.
% 0.45/1.10 (634) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.45/1.10 (635) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( empty_set ) }.
% 0.45/1.10 (636) {G0,W2,D2,L1,V0,M1} { epsilon_connected( empty_set ) }.
% 0.45/1.10 (637) {G0,W2,D2,L1,V0,M1} { ordinal( empty_set ) }.
% 0.45/1.10 (638) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.45/1.10 (639) {G0,W5,D3,L1,V1,M1} { set_union2( X, empty_set ) = X }.
% 0.45/1.10 (640) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), element( X, Y ) }.
% 0.45/1.10 (641) {G0,W10,D3,L3,V3,M3} { ! in( X, Z ), ! element( Z, powerset( Y ) ),
% 0.45/1.10 element( X, Y ) }.
% 0.45/1.10 (642) {G0,W9,D3,L3,V3,M3} { ! in( X, Y ), ! element( Y, powerset( Z ) ), !
% 0.45/1.10 empty( Z ) }.
% 0.45/1.10 (643) {G0,W4,D3,L1,V1,M1} { element( skol1( X ), X ) }.
% 0.45/1.10 (644) {G0,W4,D2,L2,V1,M2} { ! empty( X ), finite( X ) }.
% 0.45/1.10 (645) {G0,W8,D3,L3,V2,M3} { ! finite( X ), ! element( Y, powerset( X ) ),
% 0.45/1.10 finite( Y ) }.
% 0.45/1.10 (646) {G0,W4,D2,L2,V1,M2} { ! empty( X ), function( X ) }.
% 0.45/1.10 (647) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X )
% 0.45/1.10 , relation( X ) }.
% 0.45/1.10 (648) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X )
% 0.45/1.10 , function( X ) }.
% 0.45/1.10 (649) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X )
% 0.45/1.10 , one_to_one( X ) }.
% 0.45/1.10 (650) {G0,W8,D3,L3,V2,M3} { ! relation( X ), ! relation( Y ), relation(
% 0.45/1.10 set_union2( X, Y ) ) }.
% 0.45/1.10 (651) {G0,W4,D2,L2,V1,M2} { ! empty( X ), relation( X ) }.
% 0.45/1.10 (652) {G0,W2,D2,L1,V0,M1} { ! empty( positive_rationals ) }.
% 0.45/1.10 (653) {G0,W7,D2,L3,V2,M3} { ! ordinal( X ), ! element( Y, X ),
% 0.45/1.10 epsilon_transitive( Y ) }.
% 0.45/1.10 (654) {G0,W7,D2,L3,V2,M3} { ! ordinal( X ), ! element( Y, X ),
% 0.45/1.10 epsilon_connected( Y ) }.
% 0.45/1.10 (655) {G0,W7,D2,L3,V2,M3} { ! ordinal( X ), ! element( Y, X ), ordinal( Y
% 0.45/1.10 ) }.
% 0.45/1.10 (656) {G0,W6,D2,L3,V1,M3} { ! empty( X ), ! ordinal( X ), alpha1( X ) }.
% 0.45/1.10 (657) {G0,W6,D2,L3,V1,M3} { ! empty( X ), ! ordinal( X ), natural( X ) }.
% 0.45/1.10 (658) {G0,W4,D2,L2,V1,M2} { ! alpha1( X ), epsilon_transitive( X ) }.
% 0.45/1.10 (659) {G0,W4,D2,L2,V1,M2} { ! alpha1( X ), epsilon_connected( X ) }.
% 0.45/1.10 (660) {G0,W4,D2,L2,V1,M2} { ! alpha1( X ), ordinal( X ) }.
% 0.45/1.10 (661) {G0,W8,D2,L4,V1,M4} { ! epsilon_transitive( X ), ! epsilon_connected
% 0.45/1.10 ( X ), ! ordinal( X ), alpha1( X ) }.
% 0.45/1.10 (662) {G0,W7,D2,L3,V1,M3} { ! element( X, positive_rationals ), ! ordinal
% 0.45/1.10 ( X ), alpha2( X ) }.
% 0.45/1.10 (663) {G0,W7,D2,L3,V1,M3} { ! element( X, positive_rationals ), ! ordinal
% 0.45/1.10 ( X ), natural( X ) }.
% 0.45/1.10 (664) {G0,W4,D2,L2,V1,M2} { ! alpha2( X ), epsilon_transitive( X ) }.
% 0.45/1.10 (665) {G0,W4,D2,L2,V1,M2} { ! alpha2( X ), epsilon_connected( X ) }.
% 0.45/1.10 (666) {G0,W4,D2,L2,V1,M2} { ! alpha2( X ), ordinal( X ) }.
% 0.45/1.10 (667) {G0,W8,D2,L4,V1,M4} { ! epsilon_transitive( X ), ! epsilon_connected
% 0.45/1.10 ( X ), ! ordinal( X ), alpha2( X ) }.
% 0.45/1.10 (668) {G0,W4,D2,L2,V1,M2} { ! ordinal( X ), epsilon_transitive( X ) }.
% 0.45/1.10 (669) {G0,W4,D2,L2,V1,M2} { ! ordinal( X ), epsilon_connected( X ) }.
% 0.45/1.10 (670) {G0,W6,D2,L3,V1,M3} { ! epsilon_transitive( X ), ! epsilon_connected
% 0.45/1.10 ( X ), ordinal( X ) }.
% 0.45/1.10 (671) {G0,W4,D2,L2,V1,M2} { ! empty( X ), epsilon_transitive( X ) }.
% 0.45/1.10 (672) {G0,W4,D2,L2,V1,M2} { ! empty( X ), epsilon_connected( X ) }.
% 0.45/1.10 (673) {G0,W4,D2,L2,V1,M2} { ! empty( X ), ordinal( X ) }.
% 0.45/1.10 (674) {G0,W3,D3,L1,V1,M1} { ! empty( powerset( X ) ) }.
% 0.45/1.10 (675) {G0,W6,D3,L2,V2,M2} { empty( X ), ! empty( set_union2( X, Y ) ) }.
% 0.45/1.10 (676) {G0,W6,D3,L2,V2,M2} { empty( X ), ! empty( set_union2( Y, X ) ) }.
% 0.45/1.10 (677) {G0,W8,D2,L3,V2,M3} { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.45/1.10 (678) {G0,W7,D3,L2,V2,M2} { ! element( X, powerset( Y ) ), subset( X, Y )
% 0.45/1.10 }.
% 0.45/1.10 (679) {G0,W7,D3,L2,V2,M2} { ! subset( X, Y ), element( X, powerset( Y ) )
% 0.45/1.10 }.
% 0.45/1.10 (680) {G0,W5,D2,L2,V1,M2} { ! empty( X ), X = empty_set }.
% 0.45/1.10 (681) {G0,W5,D2,L2,V2,M2} { ! in( X, Y ), ! empty( Y ) }.
% 0.45/1.10 (682) {G0,W7,D2,L3,V2,M3} { ! empty( X ), X = Y, ! empty( Y ) }.
% 0.45/1.10 (683) {G0,W7,D3,L1,V2,M1} { set_union2( X, Y ) = set_union2( Y, X ) }.
% 0.45/1.10 (684) {G0,W5,D3,L1,V1,M1} { set_union2( X, X ) = X }.
% 0.45/1.10 (685) {G0,W8,D3,L3,V2,M3} { ! finite( X ), ! finite( Y ), finite(
% 0.45/1.10 set_union2( X, Y ) ) }.
% 0.45/1.10 (686) {G0,W2,D2,L1,V0,M1} { ! empty( skol2 ) }.
% 0.45/1.10 (687) {G0,W2,D2,L1,V0,M1} { finite( skol2 ) }.
% 0.45/1.10 (688) {G0,W3,D3,L1,V1,M1} { empty( skol3( Y ) ) }.
% 0.45/1.10 (689) {G0,W3,D3,L1,V1,M1} { relation( skol3( Y ) ) }.
% 0.45/1.10 (690) {G0,W3,D3,L1,V1,M1} { function( skol3( Y ) ) }.
% 0.45/1.10 (691) {G0,W3,D3,L1,V1,M1} { one_to_one( skol3( Y ) ) }.
% 0.45/1.10 (692) {G0,W3,D3,L1,V1,M1} { epsilon_transitive( skol3( Y ) ) }.
% 0.45/1.10 (693) {G0,W3,D3,L1,V1,M1} { epsilon_connected( skol3( Y ) ) }.
% 0.45/1.10 (694) {G0,W3,D3,L1,V1,M1} { ordinal( skol3( Y ) ) }.
% 0.45/1.10 (695) {G0,W3,D3,L1,V1,M1} { natural( skol3( Y ) ) }.
% 0.45/1.10 (696) {G0,W3,D3,L1,V1,M1} { finite( skol3( Y ) ) }.
% 0.45/1.10 (697) {G0,W5,D3,L1,V1,M1} { element( skol3( X ), powerset( X ) ) }.
% 0.45/1.10 (698) {G0,W5,D3,L2,V2,M2} { empty( X ), ! empty( skol4( Y ) ) }.
% 0.45/1.10 (699) {G0,W5,D3,L2,V2,M2} { empty( X ), finite( skol4( Y ) ) }.
% 0.45/1.10 (700) {G0,W7,D3,L2,V1,M2} { empty( X ), element( skol4( X ), powerset( X )
% 0.45/1.10 ) }.
% 0.45/1.10 (701) {G0,W2,D2,L1,V0,M1} { relation( skol5 ) }.
% 0.45/1.10 (702) {G0,W2,D2,L1,V0,M1} { function( skol5 ) }.
% 0.45/1.10 (703) {G0,W2,D2,L1,V0,M1} { relation( skol6 ) }.
% 0.45/1.10 (704) {G0,W2,D2,L1,V0,M1} { empty( skol6 ) }.
% 0.45/1.10 (705) {G0,W2,D2,L1,V0,M1} { function( skol6 ) }.
% 0.45/1.10 (706) {G0,W2,D2,L1,V0,M1} { relation( skol7 ) }.
% 0.45/1.10 (707) {G0,W2,D2,L1,V0,M1} { function( skol7 ) }.
% 0.45/1.10 (708) {G0,W2,D2,L1,V0,M1} { one_to_one( skol7 ) }.
% 0.45/1.10 (709) {G0,W2,D2,L1,V0,M1} { relation( skol8 ) }.
% 0.45/1.10 (710) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( skol8 ) }.
% 0.45/1.10 (711) {G0,W2,D2,L1,V0,M1} { function( skol8 ) }.
% 0.45/1.10 (712) {G0,W2,D2,L1,V0,M1} { relation( skol9 ) }.
% 0.45/1.10 (713) {G0,W2,D2,L1,V0,M1} { relation_non_empty( skol9 ) }.
% 0.45/1.10 (714) {G0,W2,D2,L1,V0,M1} { function( skol9 ) }.
% 0.45/1.10 (715) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol10 ) }.
% 0.45/1.10 (716) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol10 ) }.
% 0.45/1.10 (717) {G0,W2,D2,L1,V0,M1} { ordinal( skol10 ) }.
% 0.45/1.10 (718) {G0,W2,D2,L1,V0,M1} { being_limit_ordinal( skol10 ) }.
% 0.45/1.10 (719) {G0,W2,D2,L1,V0,M1} { relation( skol11 ) }.
% 0.45/1.10 (720) {G0,W2,D2,L1,V0,M1} { function( skol11 ) }.
% 0.45/1.10 (721) {G0,W2,D2,L1,V0,M1} { transfinite_sequence( skol11 ) }.
% 0.45/1.10 (722) {G0,W2,D2,L1,V0,M1} { ordinal_yielding( skol11 ) }.
% 0.45/1.10 (723) {G0,W2,D2,L1,V0,M1} { empty( skol12 ) }.
% 0.45/1.10 (724) {G0,W2,D2,L1,V0,M1} { relation( skol12 ) }.
% 0.45/1.10 (725) {G0,W2,D2,L1,V0,M1} { ! empty( skol13 ) }.
% 0.45/1.10 (726) {G0,W2,D2,L1,V0,M1} { relation( skol13 ) }.
% 0.45/1.10 (727) {G0,W2,D2,L1,V0,M1} { relation( skol14 ) }.
% 0.45/1.10 (728) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( skol14 ) }.
% 0.45/1.10 (729) {G0,W2,D2,L1,V0,M1} { ! empty( skol15 ) }.
% 0.45/1.10 (730) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol15 ) }.
% 0.45/1.10 (731) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol15 ) }.
% 0.45/1.10 (732) {G0,W2,D2,L1,V0,M1} { ordinal( skol15 ) }.
% 0.45/1.10 (733) {G0,W2,D2,L1,V0,M1} { natural( skol15 ) }.
% 0.45/1.10 (734) {G0,W3,D2,L1,V0,M1} { element( skol16, positive_rationals ) }.
% 0.45/1.10 (735) {G0,W2,D2,L1,V0,M1} { ! empty( skol16 ) }.
% 0.45/1.10 (736) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol16 ) }.
% 0.45/1.10 (737) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol16 ) }.
% 0.45/1.10 (738) {G0,W2,D2,L1,V0,M1} { ordinal( skol16 ) }.
% 0.45/1.10 (739) {G0,W3,D2,L1,V0,M1} { element( skol17, positive_rationals ) }.
% 0.45/1.10 (740) {G0,W2,D2,L1,V0,M1} { empty( skol17 ) }.
% 0.45/1.10 (741) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol17 ) }.
% 0.45/1.10 (742) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol17 ) }.
% 0.45/1.10 (743) {G0,W2,D2,L1,V0,M1} { ordinal( skol17 ) }.
% 0.45/1.10 (744) {G0,W2,D2,L1,V0,M1} { natural( skol17 ) }.
% 0.45/1.10 (745) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol18 ) }.
% 0.45/1.10 (746) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol18 ) }.
% 0.45/1.10 (747) {G0,W2,D2,L1,V0,M1} { ordinal( skol18 ) }.
% 0.45/1.10 (748) {G0,W2,D2,L1,V0,M1} { relation( skol19 ) }.
% 0.45/1.10 (749) {G0,W2,D2,L1,V0,M1} { function( skol19 ) }.
% 0.45/1.10 (750) {G0,W2,D2,L1,V0,M1} { one_to_one( skol19 ) }.
% 0.45/1.10 (751) {G0,W2,D2,L1,V0,M1} { empty( skol19 ) }.
% 0.45/1.10 (752) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol19 ) }.
% 0.45/1.10 (753) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol19 ) }.
% 0.45/1.10 (754) {G0,W2,D2,L1,V0,M1} { ordinal( skol19 ) }.
% 0.45/1.10 (755) {G0,W2,D2,L1,V0,M1} { ! empty( skol20 ) }.
% 0.45/1.10 (756) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol20 ) }.
% 0.45/1.10 (757) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol20 ) }.
% 0.45/1.10 (758) {G0,W2,D2,L1,V0,M1} { ordinal( skol20 ) }.
% 0.45/1.10 (759) {G0,W2,D2,L1,V0,M1} { relation( skol21 ) }.
% 0.45/1.10 (760) {G0,W2,D2,L1,V0,M1} { function( skol21 ) }.
% 0.45/1.10 (761) {G0,W2,D2,L1,V0,M1} { transfinite_sequence( skol21 ) }.
% 0.45/1.10 (762) {G0,W5,D3,L2,V2,M2} { empty( X ), ! empty( skol22( Y ) ) }.
% 0.45/1.10 (763) {G0,W7,D3,L2,V1,M2} { empty( X ), element( skol22( X ), powerset( X
% 0.45/1.10 ) ) }.
% 0.45/1.10 (764) {G0,W3,D3,L1,V1,M1} { empty( skol23( Y ) ) }.
% 0.45/1.10 (765) {G0,W5,D3,L1,V1,M1} { element( skol23( X ), powerset( X ) ) }.
% 0.45/1.10 (766) {G0,W2,D2,L1,V0,M1} { empty( skol24 ) }.
% 0.45/1.10 (767) {G0,W2,D2,L1,V0,M1} { ! empty( skol25 ) }.
% 0.45/1.10 (768) {G0,W2,D2,L1,V0,M1} { relation( skol26 ) }.
% 0.45/1.10 (769) {G0,W2,D2,L1,V0,M1} { function( skol26 ) }.
% 0.45/1.10 (770) {G0,W2,D2,L1,V0,M1} { function_yielding( skol26 ) }.
% 0.45/1.10 (771) {G0,W2,D2,L1,V0,M1} { finite( skol27 ) }.
% 0.45/1.10 (772) {G0,W2,D2,L1,V0,M1} { finite( skol28 ) }.
% 0.45/1.10 (773) {G0,W4,D3,L1,V0,M1} { ! finite( set_union2( skol27, skol28 ) ) }.
% 0.45/1.10 (774) {G0,W8,D3,L3,V2,M3} { ! finite( X ), ! finite( Y ), finite(
% 0.45/1.10 set_union2( X, Y ) ) }.
% 0.45/1.10
% 0.45/1.10
% 0.45/1.10 Total Proof:
% 0.45/1.10
% 0.45/1.10 subsumption: (54) {G0,W8,D3,L3,V2,M3} I { ! finite( X ), ! finite( Y ),
% 0.45/1.10 finite( set_union2( X, Y ) ) }.
% 0.45/1.10 parent0: (685) {G0,W8,D3,L3,V2,M3} { ! finite( X ), ! finite( Y ), finite
% 0.45/1.10 ( set_union2( X, Y ) ) }.
% 0.45/1.10 substitution0:
% 0.45/1.10 X := X
% 0.45/1.10 Y := Y
% 0.45/1.10 end
% 0.45/1.10 permutation0:
% 0.45/1.10 0 ==> 0
% 0.45/1.10 1 ==> 1
% 0.45/1.10 2 ==> 2
% 0.45/1.10 end
% 0.45/1.10
% 0.45/1.10 subsumption: (140) {G0,W2,D2,L1,V0,M1} I { finite( skol27 ) }.
% 0.45/1.10 parent0: (771) {G0,W2,D2,L1,V0,M1} { finite( skol27 ) }.
% 0.45/1.10 substitution0:
% 0.45/1.10 end
% 0.45/1.10 permutation0:
% 0.45/1.10 0 ==> 0
% 0.45/1.10 end
% 0.45/1.10
% 0.45/1.10 subsumption: (141) {G0,W2,D2,L1,V0,M1} I { finite( skol28 ) }.
% 0.45/1.10 parent0: (772) {G0,W2,D2,L1,V0,M1} { finite( skol28 ) }.
% 0.45/1.10 substitution0:
% 0.45/1.10 end
% 0.45/1.10 permutation0:
% 0.45/1.10 0 ==> 0
% 0.45/1.10 end
% 0.45/1.10
% 0.45/1.10 subsumption: (142) {G0,W4,D3,L1,V0,M1} I { ! finite( set_union2( skol27,
% 0.45/1.10 skol28 ) ) }.
% 0.45/1.10 parent0: (773) {G0,W4,D3,L1,V0,M1} { ! finite( set_union2( skol27, skol28
% 0.45/1.10 ) ) }.
% 0.45/1.10 substitution0:
% 0.45/1.10 end
% 0.45/1.10 permutation0:
% 0.45/1.10 0 ==> 0
% 0.45/1.10 end
% 0.45/1.10
% 0.45/1.10 resolution: (803) {G1,W4,D2,L2,V0,M2} { ! finite( skol27 ), ! finite(
% 0.45/1.10 skol28 ) }.
% 0.45/1.10 parent0[0]: (142) {G0,W4,D3,L1,V0,M1} I { ! finite( set_union2( skol27,
% 0.45/1.10 skol28 ) ) }.
% 0.45/1.10 parent1[2]: (54) {G0,W8,D3,L3,V2,M3} I { ! finite( X ), ! finite( Y ),
% 0.45/1.10 finite( set_union2( X, Y ) ) }.
% 0.45/1.10 substitution0:
% 0.45/1.10 end
% 0.45/1.10 substitution1:
% 0.45/1.10 X := skol27
% 0.45/1.10 Y := skol28
% 0.45/1.10 end
% 0.45/1.10
% 0.45/1.10 resolution: (804) {G1,W2,D2,L1,V0,M1} { ! finite( skol28 ) }.
% 0.45/1.10 parent0[0]: (803) {G1,W4,D2,L2,V0,M2} { ! finite( skol27 ), ! finite(
% 0.45/1.10 skol28 ) }.
% 0.45/1.10 parent1[0]: (140) {G0,W2,D2,L1,V0,M1} I { finite( skol27 ) }.
% 0.45/1.10 substitution0:
% 0.45/1.10 end
% 0.45/1.10 substitution1:
% 0.45/1.10 end
% 0.45/1.10
% 0.45/1.10 subsumption: (613) {G1,W2,D2,L1,V0,M1} R(142,54);r(140) { ! finite( skol28
% 0.45/1.10 ) }.
% 0.45/1.10 parent0: (804) {G1,W2,D2,L1,V0,M1} { ! finite( skol28 ) }.
% 0.45/1.10 substitution0:
% 0.45/1.10 end
% 0.45/1.10 permutation0:
% 0.45/1.10 0 ==> 0
% 0.45/1.10 end
% 0.45/1.10
% 0.45/1.10 resolution: (805) {G1,W0,D0,L0,V0,M0} { }.
% 0.45/1.10 parent0[0]: (613) {G1,W2,D2,L1,V0,M1} R(142,54);r(140) { ! finite( skol28 )
% 0.45/1.10 }.
% 0.45/1.10 parent1[0]: (141) {G0,W2,D2,L1,V0,M1} I { finite( skol28 ) }.
% 0.45/1.10 substitution0:
% 0.45/1.10 end
% 0.45/1.10 substitution1:
% 0.45/1.10 end
% 0.45/1.10
% 0.45/1.10 subsumption: (621) {G2,W0,D0,L0,V0,M0} S(613);r(141) { }.
% 0.45/1.10 parent0: (805) {G1,W0,D0,L0,V0,M0} { }.
% 0.45/1.10 substitution0:
% 0.45/1.10 end
% 0.45/1.10 permutation0:
% 0.45/1.10 end
% 0.45/1.10
% 0.45/1.10 Proof check complete!
% 0.45/1.10
% 0.45/1.10 Memory use:
% 0.45/1.10
% 0.45/1.10 space for terms: 5747
% 0.45/1.10 space for clauses: 29007
% 0.45/1.10
% 0.45/1.10
% 0.45/1.10 clauses generated: 1840
% 0.45/1.10 clauses kept: 622
% 0.45/1.10 clauses selected: 243
% 0.45/1.10 clauses deleted: 7
% 0.45/1.10 clauses inuse deleted: 0
% 0.45/1.10
% 0.45/1.10 subsentry: 1650
% 0.45/1.10 literals s-matched: 1455
% 0.45/1.10 literals matched: 1455
% 0.45/1.10 full subsumption: 200
% 0.45/1.10
% 0.45/1.10 checksum: -1834033316
% 0.45/1.10
% 0.45/1.10
% 0.45/1.10 Bliksem ended
%------------------------------------------------------------------------------