TSTP Solution File: SEU303+3 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SEU303+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n009.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 07:12:17 EDT 2022
% Result : Theorem 0.73s 1.24s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU303+3 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Sun Jun 19 06:37:07 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.69/1.10 *** allocated 10000 integers for termspace/termends
% 0.69/1.10 *** allocated 10000 integers for clauses
% 0.69/1.10 *** allocated 10000 integers for justifications
% 0.69/1.10 Bliksem 1.12
% 0.69/1.10
% 0.69/1.10
% 0.69/1.10 Automatic Strategy Selection
% 0.69/1.10
% 0.69/1.10
% 0.69/1.10 Clauses:
% 0.69/1.10
% 0.69/1.10 { ! in( X, Y ), ! in( Y, X ) }.
% 0.69/1.10 { ! ordinal( X ), ! element( Y, X ), epsilon_transitive( Y ) }.
% 0.69/1.10 { ! ordinal( X ), ! element( Y, X ), epsilon_connected( Y ) }.
% 0.69/1.10 { ! ordinal( X ), ! element( Y, X ), ordinal( Y ) }.
% 0.69/1.10 { ! empty( X ), finite( X ) }.
% 0.69/1.10 { ! empty( X ), function( X ) }.
% 0.69/1.10 { ! ordinal( X ), epsilon_transitive( X ) }.
% 0.69/1.10 { ! ordinal( X ), epsilon_connected( X ) }.
% 0.69/1.10 { ! empty( X ), relation( X ) }.
% 0.69/1.10 { ! empty( X ), ! ordinal( X ), alpha1( X ) }.
% 0.69/1.10 { ! empty( X ), ! ordinal( X ), natural( X ) }.
% 0.69/1.10 { ! alpha1( X ), epsilon_transitive( X ) }.
% 0.69/1.10 { ! alpha1( X ), epsilon_connected( X ) }.
% 0.69/1.10 { ! alpha1( X ), ordinal( X ) }.
% 0.69/1.10 { ! epsilon_transitive( X ), ! epsilon_connected( X ), ! ordinal( X ),
% 0.69/1.10 alpha1( X ) }.
% 0.69/1.10 { ! finite( X ), ! element( Y, powerset( X ) ), finite( Y ) }.
% 0.69/1.10 { ! relation( X ), ! empty( X ), ! function( X ), relation( X ) }.
% 0.69/1.10 { ! relation( X ), ! empty( X ), ! function( X ), function( X ) }.
% 0.69/1.10 { ! relation( X ), ! empty( X ), ! function( X ), one_to_one( X ) }.
% 0.69/1.10 { ! epsilon_transitive( X ), ! epsilon_connected( X ), ordinal( X ) }.
% 0.69/1.10 { ! empty( X ), epsilon_transitive( X ) }.
% 0.69/1.10 { ! empty( X ), epsilon_connected( X ) }.
% 0.69/1.10 { ! empty( X ), ordinal( X ) }.
% 0.69/1.10 { ! element( X, positive_rationals ), ! ordinal( X ), alpha2( X ) }.
% 0.69/1.10 { ! element( X, positive_rationals ), ! ordinal( X ), natural( X ) }.
% 0.69/1.10 { ! alpha2( X ), epsilon_transitive( X ) }.
% 0.69/1.10 { ! alpha2( X ), epsilon_connected( X ) }.
% 0.69/1.10 { ! alpha2( X ), ordinal( X ) }.
% 0.69/1.10 { ! epsilon_transitive( X ), ! epsilon_connected( X ), ! ordinal( X ),
% 0.69/1.10 alpha2( X ) }.
% 0.69/1.10 { element( skol1( X ), X ) }.
% 0.69/1.10 { empty( empty_set ) }.
% 0.69/1.10 { relation( empty_set ) }.
% 0.69/1.10 { relation_empty_yielding( empty_set ) }.
% 0.69/1.10 { ! relation( X ), ! function( X ), ! finite( Y ), finite( relation_image(
% 0.69/1.10 X, Y ) ) }.
% 0.69/1.10 { ! empty( powerset( X ) ) }.
% 0.69/1.10 { empty( empty_set ) }.
% 0.69/1.10 { relation( empty_set ) }.
% 0.69/1.10 { relation_empty_yielding( empty_set ) }.
% 0.69/1.10 { function( empty_set ) }.
% 0.69/1.10 { one_to_one( empty_set ) }.
% 0.69/1.10 { empty( empty_set ) }.
% 0.69/1.10 { epsilon_transitive( empty_set ) }.
% 0.69/1.10 { epsilon_connected( empty_set ) }.
% 0.69/1.10 { ordinal( empty_set ) }.
% 0.69/1.10 { empty( empty_set ) }.
% 0.69/1.10 { relation( empty_set ) }.
% 0.69/1.10 { ! relation( X ), ! function( X ), ! transfinite_sequence( X ),
% 0.69/1.10 epsilon_transitive( relation_dom( X ) ) }.
% 0.69/1.10 { ! relation( X ), ! function( X ), ! transfinite_sequence( X ),
% 0.69/1.10 epsilon_connected( relation_dom( X ) ) }.
% 0.69/1.10 { ! relation( X ), ! function( X ), ! transfinite_sequence( X ), ordinal(
% 0.69/1.10 relation_dom( X ) ) }.
% 0.69/1.10 { empty( X ), ! relation( X ), ! empty( relation_dom( X ) ) }.
% 0.69/1.10 { ! relation( X ), ! relation_non_empty( X ), ! function( X ),
% 0.69/1.10 with_non_empty_elements( relation_rng( X ) ) }.
% 0.69/1.10 { empty( X ), ! relation( X ), ! empty( relation_rng( X ) ) }.
% 0.69/1.10 { ! empty( X ), empty( relation_dom( X ) ) }.
% 0.69/1.10 { ! empty( X ), relation( relation_dom( X ) ) }.
% 0.69/1.10 { ! empty( positive_rationals ) }.
% 0.69/1.10 { ! empty( X ), empty( relation_rng( X ) ) }.
% 0.69/1.10 { ! empty( X ), relation( relation_rng( X ) ) }.
% 0.69/1.10 { ! empty( skol2 ) }.
% 0.69/1.10 { epsilon_transitive( skol2 ) }.
% 0.69/1.10 { epsilon_connected( skol2 ) }.
% 0.69/1.10 { ordinal( skol2 ) }.
% 0.69/1.10 { natural( skol2 ) }.
% 0.69/1.10 { ! empty( skol3 ) }.
% 0.69/1.10 { finite( skol3 ) }.
% 0.69/1.10 { relation( skol4 ) }.
% 0.69/1.10 { function( skol4 ) }.
% 0.69/1.10 { function_yielding( skol4 ) }.
% 0.69/1.10 { relation( skol5 ) }.
% 0.69/1.10 { function( skol5 ) }.
% 0.69/1.10 { epsilon_transitive( skol6 ) }.
% 0.69/1.10 { epsilon_connected( skol6 ) }.
% 0.69/1.10 { ordinal( skol6 ) }.
% 0.69/1.10 { epsilon_transitive( skol7 ) }.
% 0.69/1.10 { epsilon_connected( skol7 ) }.
% 0.69/1.10 { ordinal( skol7 ) }.
% 0.69/1.10 { being_limit_ordinal( skol7 ) }.
% 0.69/1.10 { empty( skol8 ) }.
% 0.69/1.10 { relation( skol8 ) }.
% 0.69/1.10 { empty( X ), ! empty( skol9( Y ) ) }.
% 0.69/1.10 { empty( X ), element( skol9( X ), powerset( X ) ) }.
% 0.69/1.10 { empty( skol10 ) }.
% 0.69/1.10 { element( skol11, positive_rationals ) }.
% 0.69/1.10 { ! empty( skol11 ) }.
% 0.69/1.10 { epsilon_transitive( skol11 ) }.
% 0.69/1.10 { epsilon_connected( skol11 ) }.
% 0.69/1.10 { ordinal( skol11 ) }.
% 0.69/1.10 { empty( skol12( Y ) ) }.
% 0.69/1.10 { relation( skol12( Y ) ) }.
% 0.69/1.10 { function( skol12( Y ) ) }.
% 0.69/1.10 { one_to_one( skol12( Y ) ) }.
% 0.69/1.10 { epsilon_transitive( skol12( Y ) ) }.
% 0.69/1.10 { epsilon_connected( skol12( Y ) ) }.
% 0.69/1.10 { ordinal( skol12( Y ) ) }.
% 0.69/1.10 { natural( skol12( Y ) ) }.
% 0.73/1.24 { finite( skol12( Y ) ) }.
% 0.73/1.24 { element( skol12( X ), powerset( X ) ) }.
% 0.73/1.24 { relation( skol13 ) }.
% 0.73/1.24 { empty( skol13 ) }.
% 0.73/1.24 { function( skol13 ) }.
% 0.73/1.24 { relation( skol14 ) }.
% 0.73/1.24 { function( skol14 ) }.
% 0.73/1.24 { one_to_one( skol14 ) }.
% 0.73/1.24 { empty( skol14 ) }.
% 0.73/1.24 { epsilon_transitive( skol14 ) }.
% 0.73/1.24 { epsilon_connected( skol14 ) }.
% 0.73/1.24 { ordinal( skol14 ) }.
% 0.73/1.24 { relation( skol15 ) }.
% 0.73/1.24 { function( skol15 ) }.
% 0.73/1.24 { transfinite_sequence( skol15 ) }.
% 0.73/1.24 { ordinal_yielding( skol15 ) }.
% 0.73/1.24 { ! empty( skol16 ) }.
% 0.73/1.24 { relation( skol16 ) }.
% 0.73/1.24 { empty( skol17( Y ) ) }.
% 0.73/1.24 { element( skol17( X ), powerset( X ) ) }.
% 0.73/1.24 { ! empty( skol18 ) }.
% 0.73/1.24 { element( skol19, positive_rationals ) }.
% 0.73/1.24 { empty( skol19 ) }.
% 0.73/1.24 { epsilon_transitive( skol19 ) }.
% 0.73/1.24 { epsilon_connected( skol19 ) }.
% 0.73/1.24 { ordinal( skol19 ) }.
% 0.73/1.24 { natural( skol19 ) }.
% 0.73/1.24 { empty( X ), ! empty( skol20( Y ) ) }.
% 0.73/1.24 { empty( X ), finite( skol20( Y ) ) }.
% 0.73/1.24 { empty( X ), element( skol20( X ), powerset( X ) ) }.
% 0.73/1.24 { relation( skol21 ) }.
% 0.73/1.24 { function( skol21 ) }.
% 0.73/1.24 { one_to_one( skol21 ) }.
% 0.73/1.24 { ! empty( skol22 ) }.
% 0.73/1.24 { epsilon_transitive( skol22 ) }.
% 0.73/1.24 { epsilon_connected( skol22 ) }.
% 0.73/1.24 { ordinal( skol22 ) }.
% 0.73/1.24 { relation( skol23 ) }.
% 0.73/1.24 { relation_empty_yielding( skol23 ) }.
% 0.73/1.24 { relation( skol24 ) }.
% 0.73/1.24 { relation_empty_yielding( skol24 ) }.
% 0.73/1.24 { function( skol24 ) }.
% 0.73/1.24 { relation( skol25 ) }.
% 0.73/1.24 { function( skol25 ) }.
% 0.73/1.24 { transfinite_sequence( skol25 ) }.
% 0.73/1.24 { relation( skol26 ) }.
% 0.73/1.24 { relation_non_empty( skol26 ) }.
% 0.73/1.24 { function( skol26 ) }.
% 0.73/1.24 { subset( X, X ) }.
% 0.73/1.24 { ! relation( X ), relation_image( X, relation_dom( X ) ) = relation_rng( X
% 0.73/1.24 ) }.
% 0.73/1.24 { ! relation( X ), ! function( X ), ! finite( Y ), finite( relation_image(
% 0.73/1.24 X, Y ) ) }.
% 0.73/1.24 { ! in( X, Y ), element( X, Y ) }.
% 0.73/1.24 { relation( skol27 ) }.
% 0.73/1.24 { function( skol27 ) }.
% 0.73/1.24 { finite( relation_dom( skol27 ) ) }.
% 0.73/1.24 { ! finite( relation_rng( skol27 ) ) }.
% 0.73/1.24 { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.73/1.24 { ! element( X, powerset( Y ) ), subset( X, Y ) }.
% 0.73/1.24 { ! subset( X, Y ), element( X, powerset( Y ) ) }.
% 0.73/1.24 { ! in( X, Z ), ! element( Z, powerset( Y ) ), element( X, Y ) }.
% 0.73/1.24 { ! in( X, Y ), ! element( Y, powerset( Z ) ), ! empty( Z ) }.
% 0.73/1.24 { ! empty( X ), X = empty_set }.
% 0.73/1.24 { ! in( X, Y ), ! empty( Y ) }.
% 0.73/1.24 { ! empty( X ), X = Y, ! empty( Y ) }.
% 0.73/1.24
% 0.73/1.24 percentage equality = 0.012876, percentage horn = 0.973154
% 0.73/1.24 This is a problem with some equality
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 Options Used:
% 0.73/1.24
% 0.73/1.24 useres = 1
% 0.73/1.24 useparamod = 1
% 0.73/1.24 useeqrefl = 1
% 0.73/1.24 useeqfact = 1
% 0.73/1.24 usefactor = 1
% 0.73/1.24 usesimpsplitting = 0
% 0.73/1.24 usesimpdemod = 5
% 0.73/1.24 usesimpres = 3
% 0.73/1.24
% 0.73/1.24 resimpinuse = 1000
% 0.73/1.24 resimpclauses = 20000
% 0.73/1.24 substype = eqrewr
% 0.73/1.24 backwardsubs = 1
% 0.73/1.24 selectoldest = 5
% 0.73/1.24
% 0.73/1.24 litorderings [0] = split
% 0.73/1.24 litorderings [1] = extend the termordering, first sorting on arguments
% 0.73/1.24
% 0.73/1.24 termordering = kbo
% 0.73/1.24
% 0.73/1.24 litapriori = 0
% 0.73/1.24 termapriori = 1
% 0.73/1.24 litaposteriori = 0
% 0.73/1.24 termaposteriori = 0
% 0.73/1.24 demodaposteriori = 0
% 0.73/1.24 ordereqreflfact = 0
% 0.73/1.24
% 0.73/1.24 litselect = negord
% 0.73/1.24
% 0.73/1.24 maxweight = 15
% 0.73/1.24 maxdepth = 30000
% 0.73/1.24 maxlength = 115
% 0.73/1.24 maxnrvars = 195
% 0.73/1.24 excuselevel = 1
% 0.73/1.24 increasemaxweight = 1
% 0.73/1.24
% 0.73/1.24 maxselected = 10000000
% 0.73/1.24 maxnrclauses = 10000000
% 0.73/1.24
% 0.73/1.24 showgenerated = 0
% 0.73/1.24 showkept = 0
% 0.73/1.24 showselected = 0
% 0.73/1.24 showdeleted = 0
% 0.73/1.24 showresimp = 1
% 0.73/1.24 showstatus = 2000
% 0.73/1.24
% 0.73/1.24 prologoutput = 0
% 0.73/1.24 nrgoals = 5000000
% 0.73/1.24 totalproof = 1
% 0.73/1.24
% 0.73/1.24 Symbols occurring in the translation:
% 0.73/1.24
% 0.73/1.24 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.73/1.24 . [1, 2] (w:1, o:64, a:1, s:1, b:0),
% 0.73/1.24 ! [4, 1] (w:0, o:33, a:1, s:1, b:0),
% 0.73/1.24 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.73/1.24 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.73/1.24 in [37, 2] (w:1, o:88, a:1, s:1, b:0),
% 0.73/1.24 ordinal [38, 1] (w:1, o:39, a:1, s:1, b:0),
% 0.73/1.24 element [39, 2] (w:1, o:89, a:1, s:1, b:0),
% 0.73/1.24 epsilon_transitive [40, 1] (w:1, o:40, a:1, s:1, b:0),
% 0.73/1.24 epsilon_connected [41, 1] (w:1, o:41, a:1, s:1, b:0),
% 0.73/1.24 empty [42, 1] (w:1, o:42, a:1, s:1, b:0),
% 0.73/1.24 finite [43, 1] (w:1, o:43, a:1, s:1, b:0),
% 0.73/1.24 function [44, 1] (w:1, o:44, a:1, s:1, b:0),
% 0.73/1.24 relation [45, 1] (w:1, o:45, a:1, s:1, b:0),
% 0.73/1.24 natural [46, 1] (w:1, o:38, a:1, s:1, b:0),
% 0.73/1.24 powerset [47, 1] (w:1, o:48, a:1, s:1, b:0),
% 0.73/1.24 one_to_one [48, 1] (w:1, o:46, a:1, s:1, b:0),
% 0.73/1.24 positive_rationals [49, 0] (w:1, o:8, a:1, s:1, b:0),
% 0.73/1.24 empty_set [50, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.73/1.24 relation_empty_yielding [51, 1] (w:1, o:50, a:1, s:1, b:0),
% 0.73/1.24 relation_image [52, 2] (w:1, o:90, a:1, s:1, b:0),
% 0.73/1.24 transfinite_sequence [53, 1] (w:1, o:56, a:1, s:1, b:0),
% 0.73/1.24 relation_dom [54, 1] (w:1, o:49, a:1, s:1, b:0),
% 0.73/1.24 relation_non_empty [55, 1] (w:1, o:57, a:1, s:1, b:0),
% 0.73/1.24 relation_rng [56, 1] (w:1, o:58, a:1, s:1, b:0),
% 0.73/1.24 with_non_empty_elements [57, 1] (w:1, o:59, a:1, s:1, b:0),
% 0.73/1.24 function_yielding [58, 1] (w:1, o:60, a:1, s:1, b:0),
% 0.73/1.24 being_limit_ordinal [59, 1] (w:1, o:63, a:1, s:1, b:0),
% 0.73/1.24 ordinal_yielding [60, 1] (w:1, o:47, a:1, s:1, b:0),
% 0.73/1.24 subset [61, 2] (w:1, o:91, a:1, s:1, b:0),
% 0.73/1.24 alpha1 [63, 1] (w:1, o:61, a:1, s:1, b:1),
% 0.73/1.24 alpha2 [64, 1] (w:1, o:62, a:1, s:1, b:1),
% 0.73/1.24 skol1 [65, 1] (w:1, o:51, a:1, s:1, b:1),
% 0.73/1.24 skol2 [66, 0] (w:1, o:19, a:1, s:1, b:1),
% 0.73/1.24 skol3 [67, 0] (w:1, o:27, a:1, s:1, b:1),
% 0.73/1.24 skol4 [68, 0] (w:1, o:28, a:1, s:1, b:1),
% 0.73/1.24 skol5 [69, 0] (w:1, o:29, a:1, s:1, b:1),
% 0.73/1.24 skol6 [70, 0] (w:1, o:30, a:1, s:1, b:1),
% 0.73/1.24 skol7 [71, 0] (w:1, o:31, a:1, s:1, b:1),
% 0.73/1.24 skol8 [72, 0] (w:1, o:32, a:1, s:1, b:1),
% 0.73/1.24 skol9 [73, 1] (w:1, o:52, a:1, s:1, b:1),
% 0.73/1.24 skol10 [74, 0] (w:1, o:11, a:1, s:1, b:1),
% 0.73/1.24 skol11 [75, 0] (w:1, o:12, a:1, s:1, b:1),
% 0.73/1.24 skol12 [76, 1] (w:1, o:53, a:1, s:1, b:1),
% 0.73/1.24 skol13 [77, 0] (w:1, o:13, a:1, s:1, b:1),
% 0.73/1.24 skol14 [78, 0] (w:1, o:14, a:1, s:1, b:1),
% 0.73/1.24 skol15 [79, 0] (w:1, o:15, a:1, s:1, b:1),
% 0.73/1.24 skol16 [80, 0] (w:1, o:16, a:1, s:1, b:1),
% 0.73/1.24 skol17 [81, 1] (w:1, o:54, a:1, s:1, b:1),
% 0.73/1.24 skol18 [82, 0] (w:1, o:17, a:1, s:1, b:1),
% 0.73/1.24 skol19 [83, 0] (w:1, o:18, a:1, s:1, b:1),
% 0.73/1.24 skol20 [84, 1] (w:1, o:55, a:1, s:1, b:1),
% 0.73/1.24 skol21 [85, 0] (w:1, o:20, a:1, s:1, b:1),
% 0.73/1.24 skol22 [86, 0] (w:1, o:21, a:1, s:1, b:1),
% 0.73/1.24 skol23 [87, 0] (w:1, o:22, a:1, s:1, b:1),
% 0.73/1.24 skol24 [88, 0] (w:1, o:23, a:1, s:1, b:1),
% 0.73/1.24 skol25 [89, 0] (w:1, o:24, a:1, s:1, b:1),
% 0.73/1.24 skol26 [90, 0] (w:1, o:25, a:1, s:1, b:1),
% 0.73/1.24 skol27 [91, 0] (w:1, o:26, a:1, s:1, b:1).
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 Starting Search:
% 0.73/1.24
% 0.73/1.24 *** allocated 15000 integers for clauses
% 0.73/1.24 *** allocated 22500 integers for clauses
% 0.73/1.24 *** allocated 33750 integers for clauses
% 0.73/1.24 *** allocated 50625 integers for clauses
% 0.73/1.24 Resimplifying inuse:
% 0.73/1.24 Done
% 0.73/1.24
% 0.73/1.24 *** allocated 75937 integers for clauses
% 0.73/1.24 *** allocated 15000 integers for termspace/termends
% 0.73/1.24 *** allocated 113905 integers for clauses
% 0.73/1.24 *** allocated 22500 integers for termspace/termends
% 0.73/1.24
% 0.73/1.24 Intermediate Status:
% 0.73/1.24 Generated: 5970
% 0.73/1.24 Kept: 2000
% 0.73/1.24 Inuse: 514
% 0.73/1.24 Deleted: 249
% 0.73/1.24 Deletedinuse: 140
% 0.73/1.24
% 0.73/1.24 Resimplifying inuse:
% 0.73/1.24 Done
% 0.73/1.24
% 0.73/1.24 *** allocated 33750 integers for termspace/termends
% 0.73/1.24 *** allocated 170857 integers for clauses
% 0.73/1.24 Resimplifying inuse:
% 0.73/1.24 Done
% 0.73/1.24
% 0.73/1.24 *** allocated 50625 integers for termspace/termends
% 0.73/1.24 *** allocated 256285 integers for clauses
% 0.73/1.24
% 0.73/1.24 Bliksems!, er is een bewijs:
% 0.73/1.24 % SZS status Theorem
% 0.73/1.24 % SZS output start Refutation
% 0.73/1.24
% 0.73/1.24 (31) {G0,W10,D3,L4,V2,M4} I { ! relation( X ), ! function( X ), ! finite( Y
% 0.73/1.24 ), finite( relation_image( X, Y ) ) }.
% 0.73/1.24 (135) {G0,W9,D4,L2,V1,M2} I { ! relation( X ), relation_image( X,
% 0.73/1.24 relation_dom( X ) ) ==> relation_rng( X ) }.
% 0.73/1.24 (137) {G0,W2,D2,L1,V0,M1} I { relation( skol27 ) }.
% 0.73/1.24 (138) {G0,W2,D2,L1,V0,M1} I { function( skol27 ) }.
% 0.73/1.24 (139) {G0,W3,D3,L1,V0,M1} I { finite( relation_dom( skol27 ) ) }.
% 0.73/1.24 (140) {G0,W3,D3,L1,V0,M1} I { ! finite( relation_rng( skol27 ) ) }.
% 0.73/1.24 (317) {G1,W6,D3,L2,V1,M2} R(31,137);r(138) { ! finite( X ), finite(
% 0.73/1.24 relation_image( skol27, X ) ) }.
% 0.73/1.24 (806) {G1,W7,D4,L1,V0,M1} R(135,137) { relation_image( skol27, relation_dom
% 0.73/1.24 ( skol27 ) ) ==> relation_rng( skol27 ) }.
% 0.73/1.24 (3904) {G2,W0,D0,L0,V0,M0} R(317,139);d(806);r(140) { }.
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 % SZS output end Refutation
% 0.73/1.24 found a proof!
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 Unprocessed initial clauses:
% 0.73/1.24
% 0.73/1.24 (3906) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), ! in( Y, X ) }.
% 0.73/1.24 (3907) {G0,W7,D2,L3,V2,M3} { ! ordinal( X ), ! element( Y, X ),
% 0.73/1.24 epsilon_transitive( Y ) }.
% 0.73/1.24 (3908) {G0,W7,D2,L3,V2,M3} { ! ordinal( X ), ! element( Y, X ),
% 0.73/1.24 epsilon_connected( Y ) }.
% 0.73/1.24 (3909) {G0,W7,D2,L3,V2,M3} { ! ordinal( X ), ! element( Y, X ), ordinal( Y
% 0.73/1.24 ) }.
% 0.73/1.24 (3910) {G0,W4,D2,L2,V1,M2} { ! empty( X ), finite( X ) }.
% 0.73/1.24 (3911) {G0,W4,D2,L2,V1,M2} { ! empty( X ), function( X ) }.
% 0.73/1.24 (3912) {G0,W4,D2,L2,V1,M2} { ! ordinal( X ), epsilon_transitive( X ) }.
% 0.73/1.24 (3913) {G0,W4,D2,L2,V1,M2} { ! ordinal( X ), epsilon_connected( X ) }.
% 0.73/1.24 (3914) {G0,W4,D2,L2,V1,M2} { ! empty( X ), relation( X ) }.
% 0.73/1.24 (3915) {G0,W6,D2,L3,V1,M3} { ! empty( X ), ! ordinal( X ), alpha1( X ) }.
% 0.73/1.24 (3916) {G0,W6,D2,L3,V1,M3} { ! empty( X ), ! ordinal( X ), natural( X )
% 0.73/1.24 }.
% 0.73/1.24 (3917) {G0,W4,D2,L2,V1,M2} { ! alpha1( X ), epsilon_transitive( X ) }.
% 0.73/1.24 (3918) {G0,W4,D2,L2,V1,M2} { ! alpha1( X ), epsilon_connected( X ) }.
% 0.73/1.24 (3919) {G0,W4,D2,L2,V1,M2} { ! alpha1( X ), ordinal( X ) }.
% 0.73/1.24 (3920) {G0,W8,D2,L4,V1,M4} { ! epsilon_transitive( X ), !
% 0.73/1.24 epsilon_connected( X ), ! ordinal( X ), alpha1( X ) }.
% 0.73/1.24 (3921) {G0,W8,D3,L3,V2,M3} { ! finite( X ), ! element( Y, powerset( X ) )
% 0.73/1.24 , finite( Y ) }.
% 0.73/1.24 (3922) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 0.73/1.24 ), relation( X ) }.
% 0.73/1.24 (3923) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 0.73/1.24 ), function( X ) }.
% 0.73/1.24 (3924) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 0.73/1.24 ), one_to_one( X ) }.
% 0.73/1.24 (3925) {G0,W6,D2,L3,V1,M3} { ! epsilon_transitive( X ), !
% 0.73/1.24 epsilon_connected( X ), ordinal( X ) }.
% 0.73/1.24 (3926) {G0,W4,D2,L2,V1,M2} { ! empty( X ), epsilon_transitive( X ) }.
% 0.73/1.24 (3927) {G0,W4,D2,L2,V1,M2} { ! empty( X ), epsilon_connected( X ) }.
% 0.73/1.24 (3928) {G0,W4,D2,L2,V1,M2} { ! empty( X ), ordinal( X ) }.
% 0.73/1.24 (3929) {G0,W7,D2,L3,V1,M3} { ! element( X, positive_rationals ), ! ordinal
% 0.73/1.24 ( X ), alpha2( X ) }.
% 0.73/1.24 (3930) {G0,W7,D2,L3,V1,M3} { ! element( X, positive_rationals ), ! ordinal
% 0.73/1.24 ( X ), natural( X ) }.
% 0.73/1.24 (3931) {G0,W4,D2,L2,V1,M2} { ! alpha2( X ), epsilon_transitive( X ) }.
% 0.73/1.24 (3932) {G0,W4,D2,L2,V1,M2} { ! alpha2( X ), epsilon_connected( X ) }.
% 0.73/1.24 (3933) {G0,W4,D2,L2,V1,M2} { ! alpha2( X ), ordinal( X ) }.
% 0.73/1.24 (3934) {G0,W8,D2,L4,V1,M4} { ! epsilon_transitive( X ), !
% 0.73/1.24 epsilon_connected( X ), ! ordinal( X ), alpha2( X ) }.
% 0.73/1.24 (3935) {G0,W4,D3,L1,V1,M1} { element( skol1( X ), X ) }.
% 0.73/1.24 (3936) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.73/1.24 (3937) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 0.73/1.24 (3938) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( empty_set ) }.
% 0.73/1.24 (3939) {G0,W10,D3,L4,V2,M4} { ! relation( X ), ! function( X ), ! finite(
% 0.73/1.24 Y ), finite( relation_image( X, Y ) ) }.
% 0.73/1.24 (3940) {G0,W3,D3,L1,V1,M1} { ! empty( powerset( X ) ) }.
% 0.73/1.24 (3941) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.73/1.24 (3942) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 0.73/1.24 (3943) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( empty_set ) }.
% 0.73/1.24 (3944) {G0,W2,D2,L1,V0,M1} { function( empty_set ) }.
% 0.73/1.24 (3945) {G0,W2,D2,L1,V0,M1} { one_to_one( empty_set ) }.
% 0.73/1.24 (3946) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.73/1.24 (3947) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( empty_set ) }.
% 0.73/1.24 (3948) {G0,W2,D2,L1,V0,M1} { epsilon_connected( empty_set ) }.
% 0.73/1.24 (3949) {G0,W2,D2,L1,V0,M1} { ordinal( empty_set ) }.
% 0.73/1.24 (3950) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.73/1.24 (3951) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 0.73/1.24 (3952) {G0,W9,D3,L4,V1,M4} { ! relation( X ), ! function( X ), !
% 0.73/1.24 transfinite_sequence( X ), epsilon_transitive( relation_dom( X ) ) }.
% 0.73/1.24 (3953) {G0,W9,D3,L4,V1,M4} { ! relation( X ), ! function( X ), !
% 0.73/1.24 transfinite_sequence( X ), epsilon_connected( relation_dom( X ) ) }.
% 0.73/1.24 (3954) {G0,W9,D3,L4,V1,M4} { ! relation( X ), ! function( X ), !
% 0.73/1.24 transfinite_sequence( X ), ordinal( relation_dom( X ) ) }.
% 0.73/1.24 (3955) {G0,W7,D3,L3,V1,M3} { empty( X ), ! relation( X ), ! empty(
% 0.73/1.24 relation_dom( X ) ) }.
% 0.73/1.24 (3956) {G0,W9,D3,L4,V1,M4} { ! relation( X ), ! relation_non_empty( X ), !
% 0.73/1.24 function( X ), with_non_empty_elements( relation_rng( X ) ) }.
% 0.73/1.24 (3957) {G0,W7,D3,L3,V1,M3} { empty( X ), ! relation( X ), ! empty(
% 0.73/1.24 relation_rng( X ) ) }.
% 0.73/1.24 (3958) {G0,W5,D3,L2,V1,M2} { ! empty( X ), empty( relation_dom( X ) ) }.
% 0.73/1.24 (3959) {G0,W5,D3,L2,V1,M2} { ! empty( X ), relation( relation_dom( X ) )
% 0.73/1.24 }.
% 0.73/1.24 (3960) {G0,W2,D2,L1,V0,M1} { ! empty( positive_rationals ) }.
% 0.73/1.24 (3961) {G0,W5,D3,L2,V1,M2} { ! empty( X ), empty( relation_rng( X ) ) }.
% 0.73/1.24 (3962) {G0,W5,D3,L2,V1,M2} { ! empty( X ), relation( relation_rng( X ) )
% 0.73/1.24 }.
% 0.73/1.24 (3963) {G0,W2,D2,L1,V0,M1} { ! empty( skol2 ) }.
% 0.73/1.24 (3964) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol2 ) }.
% 0.73/1.24 (3965) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol2 ) }.
% 0.73/1.24 (3966) {G0,W2,D2,L1,V0,M1} { ordinal( skol2 ) }.
% 0.73/1.24 (3967) {G0,W2,D2,L1,V0,M1} { natural( skol2 ) }.
% 0.73/1.24 (3968) {G0,W2,D2,L1,V0,M1} { ! empty( skol3 ) }.
% 0.73/1.24 (3969) {G0,W2,D2,L1,V0,M1} { finite( skol3 ) }.
% 0.73/1.24 (3970) {G0,W2,D2,L1,V0,M1} { relation( skol4 ) }.
% 0.73/1.24 (3971) {G0,W2,D2,L1,V0,M1} { function( skol4 ) }.
% 0.73/1.24 (3972) {G0,W2,D2,L1,V0,M1} { function_yielding( skol4 ) }.
% 0.73/1.24 (3973) {G0,W2,D2,L1,V0,M1} { relation( skol5 ) }.
% 0.73/1.24 (3974) {G0,W2,D2,L1,V0,M1} { function( skol5 ) }.
% 0.73/1.24 (3975) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol6 ) }.
% 0.73/1.24 (3976) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol6 ) }.
% 0.73/1.24 (3977) {G0,W2,D2,L1,V0,M1} { ordinal( skol6 ) }.
% 0.73/1.24 (3978) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol7 ) }.
% 0.73/1.24 (3979) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol7 ) }.
% 0.73/1.24 (3980) {G0,W2,D2,L1,V0,M1} { ordinal( skol7 ) }.
% 0.73/1.24 (3981) {G0,W2,D2,L1,V0,M1} { being_limit_ordinal( skol7 ) }.
% 0.73/1.24 (3982) {G0,W2,D2,L1,V0,M1} { empty( skol8 ) }.
% 0.73/1.24 (3983) {G0,W2,D2,L1,V0,M1} { relation( skol8 ) }.
% 0.73/1.24 (3984) {G0,W5,D3,L2,V2,M2} { empty( X ), ! empty( skol9( Y ) ) }.
% 0.73/1.24 (3985) {G0,W7,D3,L2,V1,M2} { empty( X ), element( skol9( X ), powerset( X
% 0.73/1.24 ) ) }.
% 0.73/1.24 (3986) {G0,W2,D2,L1,V0,M1} { empty( skol10 ) }.
% 0.73/1.24 (3987) {G0,W3,D2,L1,V0,M1} { element( skol11, positive_rationals ) }.
% 0.73/1.24 (3988) {G0,W2,D2,L1,V0,M1} { ! empty( skol11 ) }.
% 0.73/1.24 (3989) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol11 ) }.
% 0.73/1.24 (3990) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol11 ) }.
% 0.73/1.24 (3991) {G0,W2,D2,L1,V0,M1} { ordinal( skol11 ) }.
% 0.73/1.24 (3992) {G0,W3,D3,L1,V1,M1} { empty( skol12( Y ) ) }.
% 0.73/1.24 (3993) {G0,W3,D3,L1,V1,M1} { relation( skol12( Y ) ) }.
% 0.73/1.24 (3994) {G0,W3,D3,L1,V1,M1} { function( skol12( Y ) ) }.
% 0.73/1.24 (3995) {G0,W3,D3,L1,V1,M1} { one_to_one( skol12( Y ) ) }.
% 0.73/1.24 (3996) {G0,W3,D3,L1,V1,M1} { epsilon_transitive( skol12( Y ) ) }.
% 0.73/1.24 (3997) {G0,W3,D3,L1,V1,M1} { epsilon_connected( skol12( Y ) ) }.
% 0.73/1.24 (3998) {G0,W3,D3,L1,V1,M1} { ordinal( skol12( Y ) ) }.
% 0.73/1.24 (3999) {G0,W3,D3,L1,V1,M1} { natural( skol12( Y ) ) }.
% 0.73/1.24 (4000) {G0,W3,D3,L1,V1,M1} { finite( skol12( Y ) ) }.
% 0.73/1.24 (4001) {G0,W5,D3,L1,V1,M1} { element( skol12( X ), powerset( X ) ) }.
% 0.73/1.24 (4002) {G0,W2,D2,L1,V0,M1} { relation( skol13 ) }.
% 0.73/1.24 (4003) {G0,W2,D2,L1,V0,M1} { empty( skol13 ) }.
% 0.73/1.24 (4004) {G0,W2,D2,L1,V0,M1} { function( skol13 ) }.
% 0.73/1.24 (4005) {G0,W2,D2,L1,V0,M1} { relation( skol14 ) }.
% 0.73/1.24 (4006) {G0,W2,D2,L1,V0,M1} { function( skol14 ) }.
% 0.73/1.24 (4007) {G0,W2,D2,L1,V0,M1} { one_to_one( skol14 ) }.
% 0.73/1.24 (4008) {G0,W2,D2,L1,V0,M1} { empty( skol14 ) }.
% 0.73/1.24 (4009) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol14 ) }.
% 0.73/1.24 (4010) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol14 ) }.
% 0.73/1.24 (4011) {G0,W2,D2,L1,V0,M1} { ordinal( skol14 ) }.
% 0.73/1.24 (4012) {G0,W2,D2,L1,V0,M1} { relation( skol15 ) }.
% 0.73/1.24 (4013) {G0,W2,D2,L1,V0,M1} { function( skol15 ) }.
% 0.73/1.24 (4014) {G0,W2,D2,L1,V0,M1} { transfinite_sequence( skol15 ) }.
% 0.73/1.24 (4015) {G0,W2,D2,L1,V0,M1} { ordinal_yielding( skol15 ) }.
% 0.73/1.24 (4016) {G0,W2,D2,L1,V0,M1} { ! empty( skol16 ) }.
% 0.73/1.24 (4017) {G0,W2,D2,L1,V0,M1} { relation( skol16 ) }.
% 0.73/1.24 (4018) {G0,W3,D3,L1,V1,M1} { empty( skol17( Y ) ) }.
% 0.73/1.24 (4019) {G0,W5,D3,L1,V1,M1} { element( skol17( X ), powerset( X ) ) }.
% 0.73/1.24 (4020) {G0,W2,D2,L1,V0,M1} { ! empty( skol18 ) }.
% 0.73/1.24 (4021) {G0,W3,D2,L1,V0,M1} { element( skol19, positive_rationals ) }.
% 0.73/1.24 (4022) {G0,W2,D2,L1,V0,M1} { empty( skol19 ) }.
% 0.73/1.24 (4023) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol19 ) }.
% 0.73/1.24 (4024) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol19 ) }.
% 0.73/1.24 (4025) {G0,W2,D2,L1,V0,M1} { ordinal( skol19 ) }.
% 0.73/1.24 (4026) {G0,W2,D2,L1,V0,M1} { natural( skol19 ) }.
% 0.73/1.24 (4027) {G0,W5,D3,L2,V2,M2} { empty( X ), ! empty( skol20( Y ) ) }.
% 0.73/1.24 (4028) {G0,W5,D3,L2,V2,M2} { empty( X ), finite( skol20( Y ) ) }.
% 0.73/1.24 (4029) {G0,W7,D3,L2,V1,M2} { empty( X ), element( skol20( X ), powerset( X
% 0.73/1.24 ) ) }.
% 0.73/1.24 (4030) {G0,W2,D2,L1,V0,M1} { relation( skol21 ) }.
% 0.73/1.24 (4031) {G0,W2,D2,L1,V0,M1} { function( skol21 ) }.
% 0.73/1.24 (4032) {G0,W2,D2,L1,V0,M1} { one_to_one( skol21 ) }.
% 0.73/1.24 (4033) {G0,W2,D2,L1,V0,M1} { ! empty( skol22 ) }.
% 0.73/1.24 (4034) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol22 ) }.
% 0.73/1.24 (4035) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol22 ) }.
% 0.73/1.24 (4036) {G0,W2,D2,L1,V0,M1} { ordinal( skol22 ) }.
% 0.73/1.24 (4037) {G0,W2,D2,L1,V0,M1} { relation( skol23 ) }.
% 0.73/1.24 (4038) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( skol23 ) }.
% 0.73/1.24 (4039) {G0,W2,D2,L1,V0,M1} { relation( skol24 ) }.
% 0.73/1.24 (4040) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( skol24 ) }.
% 0.73/1.24 (4041) {G0,W2,D2,L1,V0,M1} { function( skol24 ) }.
% 0.73/1.24 (4042) {G0,W2,D2,L1,V0,M1} { relation( skol25 ) }.
% 0.73/1.24 (4043) {G0,W2,D2,L1,V0,M1} { function( skol25 ) }.
% 0.73/1.24 (4044) {G0,W2,D2,L1,V0,M1} { transfinite_sequence( skol25 ) }.
% 0.73/1.24 (4045) {G0,W2,D2,L1,V0,M1} { relation( skol26 ) }.
% 0.73/1.24 (4046) {G0,W2,D2,L1,V0,M1} { relation_non_empty( skol26 ) }.
% 0.73/1.24 (4047) {G0,W2,D2,L1,V0,M1} { function( skol26 ) }.
% 0.73/1.24 (4048) {G0,W3,D2,L1,V1,M1} { subset( X, X ) }.
% 0.73/1.24 (4049) {G0,W9,D4,L2,V1,M2} { ! relation( X ), relation_image( X,
% 0.73/1.24 relation_dom( X ) ) = relation_rng( X ) }.
% 0.73/1.24 (4050) {G0,W10,D3,L4,V2,M4} { ! relation( X ), ! function( X ), ! finite(
% 0.73/1.24 Y ), finite( relation_image( X, Y ) ) }.
% 0.73/1.24 (4051) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), element( X, Y ) }.
% 0.73/1.24 (4052) {G0,W2,D2,L1,V0,M1} { relation( skol27 ) }.
% 0.73/1.24 (4053) {G0,W2,D2,L1,V0,M1} { function( skol27 ) }.
% 0.73/1.24 (4054) {G0,W3,D3,L1,V0,M1} { finite( relation_dom( skol27 ) ) }.
% 0.73/1.24 (4055) {G0,W3,D3,L1,V0,M1} { ! finite( relation_rng( skol27 ) ) }.
% 0.73/1.24 (4056) {G0,W8,D2,L3,V2,M3} { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.73/1.24 (4057) {G0,W7,D3,L2,V2,M2} { ! element( X, powerset( Y ) ), subset( X, Y )
% 0.73/1.24 }.
% 0.73/1.24 (4058) {G0,W7,D3,L2,V2,M2} { ! subset( X, Y ), element( X, powerset( Y ) )
% 0.73/1.24 }.
% 0.73/1.24 (4059) {G0,W10,D3,L3,V3,M3} { ! in( X, Z ), ! element( Z, powerset( Y ) )
% 0.73/1.24 , element( X, Y ) }.
% 0.73/1.24 (4060) {G0,W9,D3,L3,V3,M3} { ! in( X, Y ), ! element( Y, powerset( Z ) ),
% 0.73/1.24 ! empty( Z ) }.
% 0.73/1.24 (4061) {G0,W5,D2,L2,V1,M2} { ! empty( X ), X = empty_set }.
% 0.73/1.24 (4062) {G0,W5,D2,L2,V2,M2} { ! in( X, Y ), ! empty( Y ) }.
% 0.73/1.24 (4063) {G0,W7,D2,L3,V2,M3} { ! empty( X ), X = Y, ! empty( Y ) }.
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 Total Proof:
% 0.73/1.24
% 0.73/1.24 subsumption: (31) {G0,W10,D3,L4,V2,M4} I { ! relation( X ), ! function( X )
% 0.73/1.24 , ! finite( Y ), finite( relation_image( X, Y ) ) }.
% 0.73/1.24 parent0: (3939) {G0,W10,D3,L4,V2,M4} { ! relation( X ), ! function( X ), !
% 0.73/1.24 finite( Y ), finite( relation_image( X, Y ) ) }.
% 0.73/1.24 substitution0:
% 0.73/1.24 X := X
% 0.73/1.24 Y := Y
% 0.73/1.24 end
% 0.73/1.24 permutation0:
% 0.73/1.24 0 ==> 0
% 0.73/1.24 1 ==> 1
% 0.73/1.24 2 ==> 2
% 0.73/1.24 3 ==> 3
% 0.73/1.24 end
% 0.73/1.24
% 0.73/1.24 subsumption: (135) {G0,W9,D4,L2,V1,M2} I { ! relation( X ), relation_image
% 0.73/1.24 ( X, relation_dom( X ) ) ==> relation_rng( X ) }.
% 0.73/1.24 parent0: (4049) {G0,W9,D4,L2,V1,M2} { ! relation( X ), relation_image( X,
% 0.73/1.24 relation_dom( X ) ) = relation_rng( X ) }.
% 0.73/1.24 substitution0:
% 0.73/1.24 X := X
% 0.73/1.24 end
% 0.73/1.24 permutation0:
% 0.73/1.24 0 ==> 0
% 0.73/1.24 1 ==> 1
% 0.73/1.24 end
% 0.73/1.24
% 0.73/1.24 subsumption: (137) {G0,W2,D2,L1,V0,M1} I { relation( skol27 ) }.
% 0.73/1.24 parent0: (4052) {G0,W2,D2,L1,V0,M1} { relation( skol27 ) }.
% 0.73/1.24 substitution0:
% 0.73/1.24 end
% 0.73/1.24 permutation0:
% 0.73/1.24 0 ==> 0
% 0.73/1.24 end
% 0.73/1.24
% 0.73/1.24 subsumption: (138) {G0,W2,D2,L1,V0,M1} I { function( skol27 ) }.
% 0.73/1.24 parent0: (4053) {G0,W2,D2,L1,V0,M1} { function( skol27 ) }.
% 0.73/1.24 substitution0:
% 0.73/1.24 end
% 0.73/1.24 permutation0:
% 0.73/1.24 0 ==> 0
% 0.73/1.24 end
% 0.73/1.24
% 0.73/1.24 subsumption: (139) {G0,W3,D3,L1,V0,M1} I { finite( relation_dom( skol27 ) )
% 0.73/1.24 }.
% 0.73/1.24 parent0: (4054) {G0,W3,D3,L1,V0,M1} { finite( relation_dom( skol27 ) ) }.
% 0.73/1.24 substitution0:
% 0.73/1.24 end
% 0.73/1.24 permutation0:
% 0.73/1.24 0 ==> 0
% 0.73/1.24 end
% 0.73/1.24
% 0.73/1.24 subsumption: (140) {G0,W3,D3,L1,V0,M1} I { ! finite( relation_rng( skol27 )
% 0.73/1.24 ) }.
% 0.73/1.24 parent0: (4055) {G0,W3,D3,L1,V0,M1} { ! finite( relation_rng( skol27 ) )
% 0.73/1.24 }.
% 0.73/1.24 substitution0:
% 0.73/1.24 end
% 0.73/1.24 permutation0:
% 0.73/1.24 0 ==> 0
% 0.73/1.24 end
% 0.73/1.24
% 0.73/1.24 resolution: (4075) {G1,W8,D3,L3,V1,M3} { ! function( skol27 ), ! finite( X
% 0.73/1.24 ), finite( relation_image( skol27, X ) ) }.
% 0.73/1.24 parent0[0]: (31) {G0,W10,D3,L4,V2,M4} I { ! relation( X ), ! function( X )
% 0.73/1.24 , ! finite( Y ), finite( relation_image( X, Y ) ) }.
% 0.73/1.24 parent1[0]: (137) {G0,W2,D2,L1,V0,M1} I { relation( skol27 ) }.
% 0.73/1.24 substitution0:
% 0.73/1.24 X := skol27
% 0.73/1.24 Y := X
% 0.73/1.24 end
% 0.73/1.24 substitution1:
% 0.73/1.24 end
% 0.73/1.24
% 0.73/1.24 resolution: (4076) {G1,W6,D3,L2,V1,M2} { ! finite( X ), finite(
% 0.73/1.24 relation_image( skol27, X ) ) }.
% 0.73/1.24 parent0[0]: (4075) {G1,W8,D3,L3,V1,M3} { ! function( skol27 ), ! finite( X
% 0.73/1.24 ), finite( relation_image( skol27, X ) ) }.
% 0.73/1.24 parent1[0]: (138) {G0,W2,D2,L1,V0,M1} I { function( skol27 ) }.
% 0.73/1.24 substitution0:
% 0.73/1.24 X := X
% 0.73/1.24 end
% 0.73/1.24 substitution1:
% 0.73/1.24 end
% 0.73/1.24
% 0.73/1.24 subsumption: (317) {G1,W6,D3,L2,V1,M2} R(31,137);r(138) { ! finite( X ),
% 0.73/1.24 finite( relation_image( skol27, X ) ) }.
% 0.73/1.24 parent0: (4076) {G1,W6,D3,L2,V1,M2} { ! finite( X ), finite(
% 0.73/1.24 relation_image( skol27, X ) ) }.
% 0.73/1.24 substitution0:
% 0.73/1.24 X := X
% 0.73/1.24 end
% 0.73/1.24 permutation0:
% 0.73/1.24 0 ==> 0
% 0.73/1.24 1 ==> 1
% 0.73/1.24 end
% 0.73/1.24
% 0.73/1.24 eqswap: (4077) {G0,W9,D4,L2,V1,M2} { relation_rng( X ) ==> relation_image
% 0.73/1.24 ( X, relation_dom( X ) ), ! relation( X ) }.
% 0.73/1.24 parent0[1]: (135) {G0,W9,D4,L2,V1,M2} I { ! relation( X ), relation_image(
% 0.73/1.24 X, relation_dom( X ) ) ==> relation_rng( X ) }.
% 0.73/1.24 substitution0:
% 0.73/1.24 X := X
% 0.73/1.24 end
% 0.73/1.24
% 0.73/1.24 resolution: (4078) {G1,W7,D4,L1,V0,M1} { relation_rng( skol27 ) ==>
% 0.73/1.24 relation_image( skol27, relation_dom( skol27 ) ) }.
% 0.73/1.24 parent0[1]: (4077) {G0,W9,D4,L2,V1,M2} { relation_rng( X ) ==>
% 0.73/1.24 relation_image( X, relation_dom( X ) ), ! relation( X ) }.
% 0.73/1.24 parent1[0]: (137) {G0,W2,D2,L1,V0,M1} I { relation( skol27 ) }.
% 0.73/1.24 substitution0:
% 0.73/1.24 X := skol27
% 0.73/1.24 end
% 0.73/1.24 substitution1:
% 0.73/1.24 end
% 0.73/1.24
% 0.73/1.24 eqswap: (4079) {G1,W7,D4,L1,V0,M1} { relation_image( skol27, relation_dom
% 0.73/1.24 ( skol27 ) ) ==> relation_rng( skol27 ) }.
% 0.73/1.24 parent0[0]: (4078) {G1,W7,D4,L1,V0,M1} { relation_rng( skol27 ) ==>
% 0.73/1.24 relation_image( skol27, relation_dom( skol27 ) ) }.
% 0.73/1.24 substitution0:
% 0.73/1.24 end
% 0.73/1.24
% 0.73/1.24 subsumption: (806) {G1,W7,D4,L1,V0,M1} R(135,137) { relation_image( skol27
% 0.73/1.24 , relation_dom( skol27 ) ) ==> relation_rng( skol27 ) }.
% 0.73/1.24 parent0: (4079) {G1,W7,D4,L1,V0,M1} { relation_image( skol27, relation_dom
% 0.73/1.24 ( skol27 ) ) ==> relation_rng( skol27 ) }.
% 0.73/1.24 substitution0:
% 0.73/1.24 end
% 0.73/1.24 permutation0:
% 0.73/1.24 0 ==> 0
% 0.73/1.24 end
% 0.73/1.24
% 0.73/1.24 resolution: (4081) {G1,W5,D4,L1,V0,M1} { finite( relation_image( skol27,
% 0.73/1.24 relation_dom( skol27 ) ) ) }.
% 0.73/1.24 parent0[0]: (317) {G1,W6,D3,L2,V1,M2} R(31,137);r(138) { ! finite( X ),
% 0.73/1.24 finite( relation_image( skol27, X ) ) }.
% 0.73/1.24 parent1[0]: (139) {G0,W3,D3,L1,V0,M1} I { finite( relation_dom( skol27 ) )
% 0.73/1.24 }.
% 0.73/1.24 substitution0:
% 0.73/1.24 X := relation_dom( skol27 )
% 0.73/1.24 end
% 0.73/1.24 substitution1:
% 0.73/1.24 end
% 0.73/1.24
% 0.73/1.24 paramod: (4082) {G2,W3,D3,L1,V0,M1} { finite( relation_rng( skol27 ) ) }.
% 0.73/1.24 parent0[0]: (806) {G1,W7,D4,L1,V0,M1} R(135,137) { relation_image( skol27,
% 0.73/1.24 relation_dom( skol27 ) ) ==> relation_rng( skol27 ) }.
% 0.73/1.24 parent1[0; 1]: (4081) {G1,W5,D4,L1,V0,M1} { finite( relation_image( skol27
% 0.73/1.24 , relation_dom( skol27 ) ) ) }.
% 0.73/1.24 substitution0:
% 0.73/1.24 end
% 0.73/1.24 substitution1:
% 0.73/1.24 end
% 0.73/1.24
% 0.73/1.24 resolution: (4083) {G1,W0,D0,L0,V0,M0} { }.
% 0.73/1.24 parent0[0]: (140) {G0,W3,D3,L1,V0,M1} I { ! finite( relation_rng( skol27 )
% 0.73/1.24 ) }.
% 0.73/1.24 parent1[0]: (4082) {G2,W3,D3,L1,V0,M1} { finite( relation_rng( skol27 ) )
% 0.73/1.24 }.
% 0.73/1.24 substitution0:
% 0.73/1.24 end
% 0.73/1.24 substitution1:
% 0.73/1.24 end
% 0.73/1.24
% 0.73/1.24 subsumption: (3904) {G2,W0,D0,L0,V0,M0} R(317,139);d(806);r(140) { }.
% 0.73/1.24 parent0: (4083) {G1,W0,D0,L0,V0,M0} { }.
% 0.73/1.24 substitution0:
% 0.73/1.24 end
% 0.73/1.24 permutation0:
% 0.73/1.24 end
% 0.73/1.24
% 0.73/1.24 Proof check complete!
% 0.73/1.24
% 0.73/1.24 Memory use:
% 0.73/1.24
% 0.73/1.24 space for terms: 36386
% 0.73/1.24 space for clauses: 179533
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 clauses generated: 10611
% 0.73/1.24 clauses kept: 3905
% 0.73/1.24 clauses selected: 681
% 0.73/1.24 clauses deleted: 295
% 0.73/1.24 clauses inuse deleted: 140
% 0.73/1.24
% 0.73/1.24 subsentry: 19146
% 0.73/1.24 literals s-matched: 14074
% 0.73/1.24 literals matched: 13430
% 0.73/1.24 full subsumption: 1470
% 0.73/1.24
% 0.73/1.24 checksum: -1654458809
% 0.73/1.24
% 0.73/1.24
% 0.73/1.24 Bliksem ended
%------------------------------------------------------------------------------