TSTP Solution File: SEU096+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SEU096+1 : 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 07:10:36 EDT 2022
% Result : Theorem 1.32s 1.76s
% Output : Refutation 1.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SEU096+1 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.11 % Command : bliksem %s
% 0.11/0.32 % Computer : n016.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % DateTime : Sun Jun 19 19:10:39 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.69/1.09 *** allocated 10000 integers for termspace/termends
% 0.69/1.09 *** allocated 10000 integers for clauses
% 0.69/1.09 *** allocated 10000 integers for justifications
% 0.69/1.09 Bliksem 1.12
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 Automatic Strategy Selection
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 Clauses:
% 0.69/1.09
% 0.69/1.09 { ! in( X, Y ), ! in( Y, X ) }.
% 0.69/1.09 { ! ordinal( X ), ! element( Y, X ), epsilon_transitive( Y ) }.
% 0.69/1.09 { ! ordinal( X ), ! element( Y, X ), epsilon_connected( Y ) }.
% 0.69/1.09 { ! ordinal( X ), ! element( Y, X ), ordinal( Y ) }.
% 0.69/1.09 { ! empty( X ), finite( X ) }.
% 0.69/1.09 { ! empty( X ), function( X ) }.
% 0.69/1.09 { ! ordinal( X ), epsilon_transitive( X ) }.
% 0.69/1.09 { ! ordinal( X ), epsilon_connected( X ) }.
% 0.69/1.09 { ! empty( X ), relation( X ) }.
% 0.69/1.09 { ! empty( X ), ! ordinal( X ), alpha1( X ) }.
% 0.69/1.09 { ! empty( X ), ! ordinal( X ), natural( X ) }.
% 0.69/1.09 { ! alpha1( X ), epsilon_transitive( X ) }.
% 0.69/1.09 { ! alpha1( X ), epsilon_connected( X ) }.
% 0.69/1.09 { ! alpha1( X ), ordinal( X ) }.
% 0.69/1.09 { ! epsilon_transitive( X ), ! epsilon_connected( X ), ! ordinal( X ),
% 0.69/1.09 alpha1( X ) }.
% 0.69/1.09 { ! finite( X ), ! element( Y, powerset( X ) ), finite( Y ) }.
% 0.69/1.09 { ! relation( X ), ! empty( X ), ! function( X ), relation( X ) }.
% 0.69/1.09 { ! relation( X ), ! empty( X ), ! function( X ), function( X ) }.
% 0.69/1.09 { ! relation( X ), ! empty( X ), ! function( X ), one_to_one( X ) }.
% 0.69/1.09 { ! epsilon_transitive( X ), ! epsilon_connected( X ), ordinal( X ) }.
% 0.69/1.09 { ! empty( X ), epsilon_transitive( X ) }.
% 0.69/1.09 { ! empty( X ), epsilon_connected( X ) }.
% 0.69/1.09 { ! empty( X ), ordinal( X ) }.
% 0.69/1.09 { ! element( X, positive_rationals ), ! ordinal( X ), alpha2( X ) }.
% 0.69/1.09 { ! element( X, positive_rationals ), ! ordinal( X ), natural( X ) }.
% 0.69/1.09 { ! alpha2( X ), epsilon_transitive( X ) }.
% 0.69/1.09 { ! alpha2( X ), epsilon_connected( X ) }.
% 0.69/1.09 { ! alpha2( X ), ordinal( X ) }.
% 0.69/1.09 { ! epsilon_transitive( X ), ! epsilon_connected( X ), ! ordinal( X ),
% 0.69/1.09 alpha2( X ) }.
% 0.69/1.09 { element( skol1( X ), X ) }.
% 0.69/1.09 { empty( empty_set ) }.
% 0.69/1.09 { relation( empty_set ) }.
% 0.69/1.09 { relation_empty_yielding( empty_set ) }.
% 0.69/1.09 { ! relation( X ), ! function( X ), ! finite( Y ), finite( relation_image(
% 0.69/1.09 X, Y ) ) }.
% 0.69/1.09 { ! empty( powerset( X ) ) }.
% 0.69/1.09 { empty( empty_set ) }.
% 0.69/1.09 { relation( empty_set ) }.
% 0.69/1.09 { relation_empty_yielding( empty_set ) }.
% 0.69/1.09 { function( empty_set ) }.
% 0.69/1.09 { one_to_one( empty_set ) }.
% 0.69/1.09 { empty( empty_set ) }.
% 0.69/1.09 { epsilon_transitive( empty_set ) }.
% 0.69/1.09 { epsilon_connected( empty_set ) }.
% 0.69/1.09 { ordinal( empty_set ) }.
% 0.69/1.09 { empty( empty_set ) }.
% 0.69/1.09 { relation( empty_set ) }.
% 0.69/1.09 { ! relation( X ), ! relation_non_empty( X ), ! function( X ),
% 0.69/1.09 with_non_empty_elements( relation_rng( X ) ) }.
% 0.69/1.09 { empty( X ), ! relation( X ), ! empty( relation_rng( X ) ) }.
% 0.69/1.09 { ! empty( positive_rationals ) }.
% 0.69/1.09 { ! empty( X ), empty( relation_rng( X ) ) }.
% 0.69/1.09 { ! empty( X ), relation( relation_rng( X ) ) }.
% 0.69/1.09 { ! empty( skol2 ) }.
% 0.69/1.09 { epsilon_transitive( skol2 ) }.
% 0.69/1.09 { epsilon_connected( skol2 ) }.
% 0.69/1.09 { ordinal( skol2 ) }.
% 0.69/1.09 { natural( skol2 ) }.
% 0.69/1.09 { ! empty( skol3 ) }.
% 0.69/1.09 { finite( skol3 ) }.
% 0.69/1.09 { relation( skol4 ) }.
% 0.69/1.09 { function( skol4 ) }.
% 0.69/1.09 { function_yielding( skol4 ) }.
% 0.69/1.09 { relation( skol5 ) }.
% 0.69/1.09 { function( skol5 ) }.
% 0.69/1.09 { epsilon_transitive( skol6 ) }.
% 0.69/1.09 { epsilon_connected( skol6 ) }.
% 0.69/1.09 { ordinal( skol6 ) }.
% 0.69/1.09 { epsilon_transitive( skol7 ) }.
% 0.69/1.09 { epsilon_connected( skol7 ) }.
% 0.69/1.09 { ordinal( skol7 ) }.
% 0.69/1.09 { being_limit_ordinal( skol7 ) }.
% 0.69/1.09 { empty( skol8 ) }.
% 0.69/1.09 { relation( skol8 ) }.
% 0.69/1.09 { empty( X ), ! empty( skol9( Y ) ) }.
% 0.69/1.09 { empty( X ), element( skol9( X ), powerset( X ) ) }.
% 0.69/1.09 { empty( skol10 ) }.
% 0.69/1.09 { element( skol11, positive_rationals ) }.
% 0.69/1.09 { ! empty( skol11 ) }.
% 0.69/1.09 { epsilon_transitive( skol11 ) }.
% 0.69/1.09 { epsilon_connected( skol11 ) }.
% 0.69/1.09 { ordinal( skol11 ) }.
% 0.69/1.09 { empty( skol12( Y ) ) }.
% 0.69/1.09 { relation( skol12( Y ) ) }.
% 0.69/1.09 { function( skol12( Y ) ) }.
% 0.69/1.09 { one_to_one( skol12( Y ) ) }.
% 0.69/1.09 { epsilon_transitive( skol12( Y ) ) }.
% 0.69/1.09 { epsilon_connected( skol12( Y ) ) }.
% 0.69/1.09 { ordinal( skol12( Y ) ) }.
% 0.69/1.09 { natural( skol12( Y ) ) }.
% 0.69/1.09 { finite( skol12( Y ) ) }.
% 0.69/1.09 { element( skol12( X ), powerset( X ) ) }.
% 0.69/1.09 { relation( skol13 ) }.
% 0.69/1.09 { empty( skol13 ) }.
% 0.69/1.09 { function( skol13 ) }.
% 0.69/1.09 { relation( skol14 ) }.
% 0.69/1.09 { function( skol14 ) }.
% 0.69/1.09 { one_to_one( skol14 ) }.
% 0.69/1.09 { empty( skol14 ) }.
% 0.69/1.09 { epsilon_transitive( skol14 ) }.
% 0.69/1.09 { epsilon_connected( skol14 ) }.
% 0.69/1.09 { ordinal( skol14 ) }.
% 0.69/1.09 { relation( skol15 ) }.
% 0.69/1.09 { function( skol15 ) }.
% 0.69/1.09 { transfinite_sequence( skol15 ) }.
% 0.69/1.09 { ordinal_yielding( skol15 ) }.
% 0.69/1.09 { ! empty( skol16 ) }.
% 1.32/1.76 { relation( skol16 ) }.
% 1.32/1.76 { empty( skol17( Y ) ) }.
% 1.32/1.76 { element( skol17( X ), powerset( X ) ) }.
% 1.32/1.76 { ! empty( skol18 ) }.
% 1.32/1.76 { element( skol19, positive_rationals ) }.
% 1.32/1.76 { empty( skol19 ) }.
% 1.32/1.76 { epsilon_transitive( skol19 ) }.
% 1.32/1.76 { epsilon_connected( skol19 ) }.
% 1.32/1.76 { ordinal( skol19 ) }.
% 1.32/1.76 { natural( skol19 ) }.
% 1.32/1.76 { empty( X ), ! empty( skol20( Y ) ) }.
% 1.32/1.76 { empty( X ), finite( skol20( Y ) ) }.
% 1.32/1.76 { empty( X ), element( skol20( X ), powerset( X ) ) }.
% 1.32/1.76 { relation( skol21 ) }.
% 1.32/1.76 { function( skol21 ) }.
% 1.32/1.76 { one_to_one( skol21 ) }.
% 1.32/1.76 { ! empty( skol22 ) }.
% 1.32/1.76 { epsilon_transitive( skol22 ) }.
% 1.32/1.76 { epsilon_connected( skol22 ) }.
% 1.32/1.76 { ordinal( skol22 ) }.
% 1.32/1.76 { relation( skol23 ) }.
% 1.32/1.76 { relation_empty_yielding( skol23 ) }.
% 1.32/1.76 { relation( skol24 ) }.
% 1.32/1.76 { relation_empty_yielding( skol24 ) }.
% 1.32/1.76 { function( skol24 ) }.
% 1.32/1.76 { relation( skol25 ) }.
% 1.32/1.76 { function( skol25 ) }.
% 1.32/1.76 { transfinite_sequence( skol25 ) }.
% 1.32/1.76 { relation( skol26 ) }.
% 1.32/1.76 { relation_non_empty( skol26 ) }.
% 1.32/1.76 { function( skol26 ) }.
% 1.32/1.76 { subset( X, X ) }.
% 1.32/1.76 { ! relation( X ), ! function( X ), ! subset( Y, relation_rng( X ) ),
% 1.32/1.76 relation_image( X, relation_inverse_image( X, Y ) ) = Y }.
% 1.32/1.76 { ! relation( X ), ! function( X ), ! finite( Y ), finite( relation_image(
% 1.32/1.76 X, Y ) ) }.
% 1.32/1.76 { ! in( X, Y ), element( X, Y ) }.
% 1.32/1.76 { relation( skol27 ) }.
% 1.32/1.76 { function( skol27 ) }.
% 1.32/1.76 { subset( skol28, relation_rng( skol27 ) ) }.
% 1.32/1.76 { finite( relation_inverse_image( skol27, skol28 ) ) }.
% 1.32/1.76 { ! finite( skol28 ) }.
% 1.32/1.76 { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 1.32/1.76 { ! element( X, powerset( Y ) ), subset( X, Y ) }.
% 1.32/1.76 { ! subset( X, Y ), element( X, powerset( Y ) ) }.
% 1.32/1.76 { ! in( X, Z ), ! element( Z, powerset( Y ) ), element( X, Y ) }.
% 1.32/1.76 { ! in( X, Y ), ! element( Y, powerset( Z ) ), ! empty( Z ) }.
% 1.32/1.76 { ! empty( X ), X = empty_set }.
% 1.32/1.76 { ! in( X, Y ), ! empty( Y ) }.
% 1.32/1.76 { ! empty( X ), X = Y, ! empty( Y ) }.
% 1.32/1.76
% 1.32/1.76 percentage equality = 0.013825, percentage horn = 0.972222
% 1.32/1.76 This is a problem with some equality
% 1.32/1.76
% 1.32/1.76
% 1.32/1.76
% 1.32/1.76 Options Used:
% 1.32/1.76
% 1.32/1.76 useres = 1
% 1.32/1.76 useparamod = 1
% 1.32/1.76 useeqrefl = 1
% 1.32/1.76 useeqfact = 1
% 1.32/1.76 usefactor = 1
% 1.32/1.76 usesimpsplitting = 0
% 1.32/1.76 usesimpdemod = 5
% 1.32/1.76 usesimpres = 3
% 1.32/1.76
% 1.32/1.76 resimpinuse = 1000
% 1.32/1.76 resimpclauses = 20000
% 1.32/1.76 substype = eqrewr
% 1.32/1.76 backwardsubs = 1
% 1.32/1.76 selectoldest = 5
% 1.32/1.76
% 1.32/1.76 litorderings [0] = split
% 1.32/1.76 litorderings [1] = extend the termordering, first sorting on arguments
% 1.32/1.76
% 1.32/1.76 termordering = kbo
% 1.32/1.76
% 1.32/1.76 litapriori = 0
% 1.32/1.76 termapriori = 1
% 1.32/1.76 litaposteriori = 0
% 1.32/1.76 termaposteriori = 0
% 1.32/1.76 demodaposteriori = 0
% 1.32/1.76 ordereqreflfact = 0
% 1.32/1.76
% 1.32/1.76 litselect = negord
% 1.32/1.76
% 1.32/1.76 maxweight = 15
% 1.32/1.76 maxdepth = 30000
% 1.32/1.76 maxlength = 115
% 1.32/1.76 maxnrvars = 195
% 1.32/1.76 excuselevel = 1
% 1.32/1.76 increasemaxweight = 1
% 1.32/1.76
% 1.32/1.76 maxselected = 10000000
% 1.32/1.76 maxnrclauses = 10000000
% 1.32/1.76
% 1.32/1.76 showgenerated = 0
% 1.32/1.76 showkept = 0
% 1.32/1.76 showselected = 0
% 1.32/1.76 showdeleted = 0
% 1.32/1.76 showresimp = 1
% 1.32/1.76 showstatus = 2000
% 1.32/1.76
% 1.32/1.76 prologoutput = 0
% 1.32/1.76 nrgoals = 5000000
% 1.32/1.76 totalproof = 1
% 1.32/1.76
% 1.32/1.76 Symbols occurring in the translation:
% 1.32/1.76
% 1.32/1.76 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.32/1.76 . [1, 2] (w:1, o:64, a:1, s:1, b:0),
% 1.32/1.76 ! [4, 1] (w:0, o:34, a:1, s:1, b:0),
% 1.32/1.76 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.32/1.76 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.32/1.76 in [37, 2] (w:1, o:88, a:1, s:1, b:0),
% 1.32/1.76 ordinal [38, 1] (w:1, o:40, a:1, s:1, b:0),
% 1.32/1.76 element [39, 2] (w:1, o:89, a:1, s:1, b:0),
% 1.32/1.76 epsilon_transitive [40, 1] (w:1, o:41, a:1, s:1, b:0),
% 1.32/1.76 epsilon_connected [41, 1] (w:1, o:42, a:1, s:1, b:0),
% 1.32/1.76 empty [42, 1] (w:1, o:43, a:1, s:1, b:0),
% 1.32/1.76 finite [43, 1] (w:1, o:44, a:1, s:1, b:0),
% 1.32/1.76 function [44, 1] (w:1, o:45, a:1, s:1, b:0),
% 1.32/1.76 relation [45, 1] (w:1, o:46, a:1, s:1, b:0),
% 1.32/1.76 natural [46, 1] (w:1, o:39, a:1, s:1, b:0),
% 1.32/1.76 powerset [47, 1] (w:1, o:49, a:1, s:1, b:0),
% 1.32/1.76 one_to_one [48, 1] (w:1, o:47, a:1, s:1, b:0),
% 1.32/1.76 positive_rationals [49, 0] (w:1, o:8, a:1, s:1, b:0),
% 1.32/1.76 empty_set [50, 0] (w:1, o:9, a:1, s:1, b:0),
% 1.32/1.76 relation_empty_yielding [51, 1] (w:1, o:50, a:1, s:1, b:0),
% 1.32/1.76 relation_image [52, 2] (w:1, o:90, a:1, s:1, b:0),
% 1.32/1.76 relation_non_empty [53, 1] (w:1, o:51, a:1, s:1, b:0),
% 1.32/1.76 relation_rng [54, 1] (w:1, o:52, a:1, s:1, b:0),
% 1.32/1.76 with_non_empty_elements [55, 1] (w:1, o:53, a:1, s:1, b:0),
% 1.32/1.76 function_yielding [56, 1] (w:1, o:54, a:1, s:1, b:0),
% 1.32/1.76 being_limit_ordinal [57, 1] (w:1, o:57, a:1, s:1, b:0),
% 1.32/1.76 transfinite_sequence [58, 1] (w:1, o:63, a:1, s:1, b:0),
% 1.32/1.76 ordinal_yielding [59, 1] (w:1, o:48, a:1, s:1, b:0),
% 1.32/1.76 subset [60, 2] (w:1, o:92, a:1, s:1, b:0),
% 1.32/1.76 relation_inverse_image [61, 2] (w:1, o:91, a:1, s:1, b:0),
% 1.32/1.76 alpha1 [63, 1] (w:1, o:55, a:1, s:1, b:1),
% 1.32/1.76 alpha2 [64, 1] (w:1, o:56, a:1, s:1, b:1),
% 1.32/1.76 skol1 [65, 1] (w:1, o:58, a:1, s:1, b:1),
% 1.32/1.76 skol2 [66, 0] (w:1, o:19, a:1, s:1, b:1),
% 1.32/1.76 skol3 [67, 0] (w:1, o:28, a:1, s:1, b:1),
% 1.32/1.76 skol4 [68, 0] (w:1, o:29, a:1, s:1, b:1),
% 1.32/1.76 skol5 [69, 0] (w:1, o:30, a:1, s:1, b:1),
% 1.32/1.76 skol6 [70, 0] (w:1, o:31, a:1, s:1, b:1),
% 1.32/1.76 skol7 [71, 0] (w:1, o:32, a:1, s:1, b:1),
% 1.32/1.76 skol8 [72, 0] (w:1, o:33, a:1, s:1, b:1),
% 1.32/1.76 skol9 [73, 1] (w:1, o:59, a:1, s:1, b:1),
% 1.32/1.76 skol10 [74, 0] (w:1, o:11, a:1, s:1, b:1),
% 1.32/1.76 skol11 [75, 0] (w:1, o:12, a:1, s:1, b:1),
% 1.32/1.76 skol12 [76, 1] (w:1, o:60, a:1, s:1, b:1),
% 1.32/1.76 skol13 [77, 0] (w:1, o:13, a:1, s:1, b:1),
% 1.32/1.76 skol14 [78, 0] (w:1, o:14, a:1, s:1, b:1),
% 1.32/1.76 skol15 [79, 0] (w:1, o:15, a:1, s:1, b:1),
% 1.32/1.76 skol16 [80, 0] (w:1, o:16, a:1, s:1, b:1),
% 1.32/1.76 skol17 [81, 1] (w:1, o:61, a:1, s:1, b:1),
% 1.32/1.76 skol18 [82, 0] (w:1, o:17, a:1, s:1, b:1),
% 1.32/1.76 skol19 [83, 0] (w:1, o:18, a:1, s:1, b:1),
% 1.32/1.76 skol20 [84, 1] (w:1, o:62, a:1, s:1, b:1),
% 1.32/1.76 skol21 [85, 0] (w:1, o:20, a:1, s:1, b:1),
% 1.32/1.76 skol22 [86, 0] (w:1, o:21, a:1, s:1, b:1),
% 1.32/1.76 skol23 [87, 0] (w:1, o:22, a:1, s:1, b:1),
% 1.32/1.76 skol24 [88, 0] (w:1, o:23, a:1, s:1, b:1),
% 1.32/1.76 skol25 [89, 0] (w:1, o:24, a:1, s:1, b:1),
% 1.32/1.76 skol26 [90, 0] (w:1, o:25, a:1, s:1, b:1),
% 1.32/1.76 skol27 [91, 0] (w:1, o:26, a:1, s:1, b:1),
% 1.32/1.76 skol28 [92, 0] (w:1, o:27, a:1, s:1, b:1).
% 1.32/1.76
% 1.32/1.76
% 1.32/1.76 Starting Search:
% 1.32/1.76
% 1.32/1.76 *** allocated 15000 integers for clauses
% 1.32/1.76 *** allocated 22500 integers for clauses
% 1.32/1.76 *** allocated 33750 integers for clauses
% 1.32/1.76 *** allocated 50625 integers for clauses
% 1.32/1.76 Resimplifying inuse:
% 1.32/1.76 Done
% 1.32/1.76
% 1.32/1.76 *** allocated 75937 integers for clauses
% 1.32/1.76 *** allocated 15000 integers for termspace/termends
% 1.32/1.76 *** allocated 22500 integers for termspace/termends
% 1.32/1.76 *** allocated 113905 integers for clauses
% 1.32/1.76
% 1.32/1.76 Intermediate Status:
% 1.32/1.76 Generated: 6872
% 1.32/1.76 Kept: 2010
% 1.32/1.76 Inuse: 539
% 1.32/1.76 Deleted: 212
% 1.32/1.76 Deletedinuse: 130
% 1.32/1.76
% 1.32/1.76 Resimplifying inuse:
% 1.32/1.76 Done
% 1.32/1.76
% 1.32/1.76 *** allocated 33750 integers for termspace/termends
% 1.32/1.76 *** allocated 170857 integers for clauses
% 1.32/1.76 Resimplifying inuse:
% 1.32/1.76 Done
% 1.32/1.76
% 1.32/1.76 *** allocated 50625 integers for termspace/termends
% 1.32/1.76 *** allocated 256285 integers for clauses
% 1.32/1.76
% 1.32/1.76 Intermediate Status:
% 1.32/1.76 Generated: 11970
% 1.32/1.76 Kept: 4017
% 1.32/1.76 Inuse: 715
% 1.32/1.76 Deleted: 257
% 1.32/1.76 Deletedinuse: 130
% 1.32/1.76
% 1.32/1.76 Resimplifying inuse:
% 1.32/1.76 Done
% 1.32/1.76
% 1.32/1.76 Resimplifying inuse:
% 1.32/1.76 Done
% 1.32/1.76
% 1.32/1.76 *** allocated 75937 integers for termspace/termends
% 1.32/1.76 *** allocated 384427 integers for clauses
% 1.32/1.76
% 1.32/1.76 Intermediate Status:
% 1.32/1.76 Generated: 18819
% 1.32/1.76 Kept: 6018
% 1.32/1.76 Inuse: 926
% 1.32/1.76 Deleted: 312
% 1.32/1.76 Deletedinuse: 139
% 1.32/1.76
% 1.32/1.76 Resimplifying inuse:
% 1.32/1.76 Done
% 1.32/1.76
% 1.32/1.76 Resimplifying inuse:
% 1.32/1.76 Done
% 1.32/1.76
% 1.32/1.76 *** allocated 113905 integers for termspace/termends
% 1.32/1.76
% 1.32/1.76 Intermediate Status:
% 1.32/1.76 Generated: 25247
% 1.32/1.76 Kept: 8018
% 1.32/1.76 Inuse: 1119
% 1.32/1.76 Deleted: 361
% 1.32/1.76 Deletedinuse: 143
% 1.32/1.76
% 1.32/1.76 Resimplifying inuse:
% 1.32/1.76 Done
% 1.32/1.76
% 1.32/1.76 *** allocated 576640 integers for clauses
% 1.32/1.76 Resimplifying inuse:
% 1.32/1.76 Done
% 1.32/1.76
% 1.32/1.76
% 1.32/1.76 Intermediate Status:
% 1.32/1.76 Generated: 31276
% 1.32/1.76 Kept: 10102
% 1.32/1.76 Inuse: 1265
% 1.32/1.76 Deleted: 379
% 1.32/1.76 Deletedinuse: 143
% 1.32/1.76
% 1.32/1.76 Resimplifying inuse:
% 1.32/1.76 Done
% 1.32/1.76
% 1.32/1.76
% 1.32/1.76 Bliksems!, er is een bewijs:
% 1.32/1.76 % SZS status Theorem
% 1.32/1.76 % SZS output start Refutation
% 1.32/1.76
% 1.32/1.76 (31) {G0,W10,D3,L4,V2,M4} I { ! relation( X ), ! function( X ), ! finite( Y
% 1.32/1.76 ), finite( relation_image( X, Y ) ) }.
% 1.32/1.76 (129) {G0,W15,D4,L4,V2,M4} I { ! relation( X ), ! function( X ), ! subset(
% 1.32/1.76 Y, relation_rng( X ) ), relation_image( X, relation_inverse_image( X, Y )
% 1.32/1.76 ) ==> Y }.
% 1.32/1.76 (131) {G0,W2,D2,L1,V0,M1} I { relation( skol27 ) }.
% 1.32/1.76 (132) {G0,W2,D2,L1,V0,M1} I { function( skol27 ) }.
% 1.32/1.76 (133) {G0,W4,D3,L1,V0,M1} I { subset( skol28, relation_rng( skol27 ) ) }.
% 1.32/1.76 (134) {G0,W4,D3,L1,V0,M1} I { finite( relation_inverse_image( skol27,
% 1.32/1.76 skol28 ) ) }.
% 1.32/1.76 (135) {G0,W2,D2,L1,V0,M1} I { ! finite( skol28 ) }.
% 1.32/1.76 (554) {G1,W11,D4,L2,V1,M2} R(129,131);r(132) { ! subset( X, relation_rng(
% 1.32/1.76 skol27 ) ), relation_image( skol27, relation_inverse_image( skol27, X ) )
% 1.32/1.76 ==> X }.
% 1.32/1.76 (595) {G1,W10,D4,L3,V1,M3} R(134,31) { ! relation( X ), ! function( X ),
% 1.32/1.76 finite( relation_image( X, relation_inverse_image( skol27, skol28 ) ) )
% 1.32/1.76 }.
% 1.32/1.76 (9067) {G2,W7,D4,L1,V0,M1} R(554,133) { relation_image( skol27,
% 1.32/1.76 relation_inverse_image( skol27, skol28 ) ) ==> skol28 }.
% 1.32/1.76 (10556) {G3,W2,D2,L1,V0,M1} R(595,131);d(9067);r(132) { finite( skol28 )
% 1.32/1.76 }.
% 1.32/1.76 (10559) {G4,W0,D0,L0,V0,M0} S(10556);r(135) { }.
% 1.32/1.76
% 1.32/1.76
% 1.32/1.76 % SZS output end Refutation
% 1.32/1.76 found a proof!
% 1.32/1.76
% 1.32/1.76
% 1.32/1.76 Unprocessed initial clauses:
% 1.32/1.76
% 1.32/1.76 (10561) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), ! in( Y, X ) }.
% 1.32/1.76 (10562) {G0,W7,D2,L3,V2,M3} { ! ordinal( X ), ! element( Y, X ),
% 1.32/1.76 epsilon_transitive( Y ) }.
% 1.32/1.76 (10563) {G0,W7,D2,L3,V2,M3} { ! ordinal( X ), ! element( Y, X ),
% 1.32/1.76 epsilon_connected( Y ) }.
% 1.32/1.76 (10564) {G0,W7,D2,L3,V2,M3} { ! ordinal( X ), ! element( Y, X ), ordinal(
% 1.32/1.76 Y ) }.
% 1.32/1.76 (10565) {G0,W4,D2,L2,V1,M2} { ! empty( X ), finite( X ) }.
% 1.32/1.76 (10566) {G0,W4,D2,L2,V1,M2} { ! empty( X ), function( X ) }.
% 1.32/1.76 (10567) {G0,W4,D2,L2,V1,M2} { ! ordinal( X ), epsilon_transitive( X ) }.
% 1.32/1.76 (10568) {G0,W4,D2,L2,V1,M2} { ! ordinal( X ), epsilon_connected( X ) }.
% 1.32/1.76 (10569) {G0,W4,D2,L2,V1,M2} { ! empty( X ), relation( X ) }.
% 1.32/1.76 (10570) {G0,W6,D2,L3,V1,M3} { ! empty( X ), ! ordinal( X ), alpha1( X )
% 1.32/1.76 }.
% 1.32/1.76 (10571) {G0,W6,D2,L3,V1,M3} { ! empty( X ), ! ordinal( X ), natural( X )
% 1.32/1.76 }.
% 1.32/1.76 (10572) {G0,W4,D2,L2,V1,M2} { ! alpha1( X ), epsilon_transitive( X ) }.
% 1.32/1.76 (10573) {G0,W4,D2,L2,V1,M2} { ! alpha1( X ), epsilon_connected( X ) }.
% 1.32/1.76 (10574) {G0,W4,D2,L2,V1,M2} { ! alpha1( X ), ordinal( X ) }.
% 1.32/1.76 (10575) {G0,W8,D2,L4,V1,M4} { ! epsilon_transitive( X ), !
% 1.32/1.76 epsilon_connected( X ), ! ordinal( X ), alpha1( X ) }.
% 1.32/1.76 (10576) {G0,W8,D3,L3,V2,M3} { ! finite( X ), ! element( Y, powerset( X ) )
% 1.32/1.76 , finite( Y ) }.
% 1.32/1.76 (10577) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 1.32/1.76 ), relation( X ) }.
% 1.32/1.76 (10578) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 1.32/1.76 ), function( X ) }.
% 1.32/1.76 (10579) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 1.32/1.76 ), one_to_one( X ) }.
% 1.32/1.76 (10580) {G0,W6,D2,L3,V1,M3} { ! epsilon_transitive( X ), !
% 1.32/1.76 epsilon_connected( X ), ordinal( X ) }.
% 1.32/1.76 (10581) {G0,W4,D2,L2,V1,M2} { ! empty( X ), epsilon_transitive( X ) }.
% 1.32/1.76 (10582) {G0,W4,D2,L2,V1,M2} { ! empty( X ), epsilon_connected( X ) }.
% 1.32/1.76 (10583) {G0,W4,D2,L2,V1,M2} { ! empty( X ), ordinal( X ) }.
% 1.32/1.76 (10584) {G0,W7,D2,L3,V1,M3} { ! element( X, positive_rationals ), !
% 1.32/1.76 ordinal( X ), alpha2( X ) }.
% 1.32/1.76 (10585) {G0,W7,D2,L3,V1,M3} { ! element( X, positive_rationals ), !
% 1.32/1.76 ordinal( X ), natural( X ) }.
% 1.32/1.76 (10586) {G0,W4,D2,L2,V1,M2} { ! alpha2( X ), epsilon_transitive( X ) }.
% 1.32/1.76 (10587) {G0,W4,D2,L2,V1,M2} { ! alpha2( X ), epsilon_connected( X ) }.
% 1.32/1.76 (10588) {G0,W4,D2,L2,V1,M2} { ! alpha2( X ), ordinal( X ) }.
% 1.32/1.76 (10589) {G0,W8,D2,L4,V1,M4} { ! epsilon_transitive( X ), !
% 1.32/1.76 epsilon_connected( X ), ! ordinal( X ), alpha2( X ) }.
% 1.32/1.76 (10590) {G0,W4,D3,L1,V1,M1} { element( skol1( X ), X ) }.
% 1.32/1.76 (10591) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 1.32/1.76 (10592) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 1.32/1.76 (10593) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( empty_set ) }.
% 1.32/1.76 (10594) {G0,W10,D3,L4,V2,M4} { ! relation( X ), ! function( X ), ! finite
% 1.32/1.76 ( Y ), finite( relation_image( X, Y ) ) }.
% 1.32/1.76 (10595) {G0,W3,D3,L1,V1,M1} { ! empty( powerset( X ) ) }.
% 1.32/1.76 (10596) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 1.32/1.76 (10597) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 1.32/1.76 (10598) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( empty_set ) }.
% 1.32/1.76 (10599) {G0,W2,D2,L1,V0,M1} { function( empty_set ) }.
% 1.32/1.76 (10600) {G0,W2,D2,L1,V0,M1} { one_to_one( empty_set ) }.
% 1.32/1.76 (10601) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 1.32/1.76 (10602) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( empty_set ) }.
% 1.32/1.76 (10603) {G0,W2,D2,L1,V0,M1} { epsilon_connected( empty_set ) }.
% 1.32/1.76 (10604) {G0,W2,D2,L1,V0,M1} { ordinal( empty_set ) }.
% 1.32/1.76 (10605) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 1.32/1.76 (10606) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 1.32/1.76 (10607) {G0,W9,D3,L4,V1,M4} { ! relation( X ), ! relation_non_empty( X ),
% 1.32/1.76 ! function( X ), with_non_empty_elements( relation_rng( X ) ) }.
% 1.32/1.76 (10608) {G0,W7,D3,L3,V1,M3} { empty( X ), ! relation( X ), ! empty(
% 1.32/1.76 relation_rng( X ) ) }.
% 1.32/1.76 (10609) {G0,W2,D2,L1,V0,M1} { ! empty( positive_rationals ) }.
% 1.32/1.76 (10610) {G0,W5,D3,L2,V1,M2} { ! empty( X ), empty( relation_rng( X ) ) }.
% 1.32/1.76 (10611) {G0,W5,D3,L2,V1,M2} { ! empty( X ), relation( relation_rng( X ) )
% 1.32/1.76 }.
% 1.32/1.76 (10612) {G0,W2,D2,L1,V0,M1} { ! empty( skol2 ) }.
% 1.32/1.76 (10613) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol2 ) }.
% 1.32/1.76 (10614) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol2 ) }.
% 1.32/1.76 (10615) {G0,W2,D2,L1,V0,M1} { ordinal( skol2 ) }.
% 1.32/1.76 (10616) {G0,W2,D2,L1,V0,M1} { natural( skol2 ) }.
% 1.32/1.76 (10617) {G0,W2,D2,L1,V0,M1} { ! empty( skol3 ) }.
% 1.32/1.76 (10618) {G0,W2,D2,L1,V0,M1} { finite( skol3 ) }.
% 1.32/1.76 (10619) {G0,W2,D2,L1,V0,M1} { relation( skol4 ) }.
% 1.32/1.76 (10620) {G0,W2,D2,L1,V0,M1} { function( skol4 ) }.
% 1.32/1.76 (10621) {G0,W2,D2,L1,V0,M1} { function_yielding( skol4 ) }.
% 1.32/1.76 (10622) {G0,W2,D2,L1,V0,M1} { relation( skol5 ) }.
% 1.32/1.76 (10623) {G0,W2,D2,L1,V0,M1} { function( skol5 ) }.
% 1.32/1.76 (10624) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol6 ) }.
% 1.32/1.76 (10625) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol6 ) }.
% 1.32/1.76 (10626) {G0,W2,D2,L1,V0,M1} { ordinal( skol6 ) }.
% 1.32/1.76 (10627) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol7 ) }.
% 1.32/1.76 (10628) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol7 ) }.
% 1.32/1.76 (10629) {G0,W2,D2,L1,V0,M1} { ordinal( skol7 ) }.
% 1.32/1.76 (10630) {G0,W2,D2,L1,V0,M1} { being_limit_ordinal( skol7 ) }.
% 1.32/1.76 (10631) {G0,W2,D2,L1,V0,M1} { empty( skol8 ) }.
% 1.32/1.76 (10632) {G0,W2,D2,L1,V0,M1} { relation( skol8 ) }.
% 1.32/1.76 (10633) {G0,W5,D3,L2,V2,M2} { empty( X ), ! empty( skol9( Y ) ) }.
% 1.32/1.76 (10634) {G0,W7,D3,L2,V1,M2} { empty( X ), element( skol9( X ), powerset( X
% 1.32/1.76 ) ) }.
% 1.32/1.76 (10635) {G0,W2,D2,L1,V0,M1} { empty( skol10 ) }.
% 1.32/1.76 (10636) {G0,W3,D2,L1,V0,M1} { element( skol11, positive_rationals ) }.
% 1.32/1.76 (10637) {G0,W2,D2,L1,V0,M1} { ! empty( skol11 ) }.
% 1.32/1.76 (10638) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol11 ) }.
% 1.32/1.76 (10639) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol11 ) }.
% 1.32/1.76 (10640) {G0,W2,D2,L1,V0,M1} { ordinal( skol11 ) }.
% 1.32/1.76 (10641) {G0,W3,D3,L1,V1,M1} { empty( skol12( Y ) ) }.
% 1.32/1.76 (10642) {G0,W3,D3,L1,V1,M1} { relation( skol12( Y ) ) }.
% 1.32/1.76 (10643) {G0,W3,D3,L1,V1,M1} { function( skol12( Y ) ) }.
% 1.32/1.76 (10644) {G0,W3,D3,L1,V1,M1} { one_to_one( skol12( Y ) ) }.
% 1.32/1.76 (10645) {G0,W3,D3,L1,V1,M1} { epsilon_transitive( skol12( Y ) ) }.
% 1.32/1.76 (10646) {G0,W3,D3,L1,V1,M1} { epsilon_connected( skol12( Y ) ) }.
% 1.32/1.76 (10647) {G0,W3,D3,L1,V1,M1} { ordinal( skol12( Y ) ) }.
% 1.32/1.76 (10648) {G0,W3,D3,L1,V1,M1} { natural( skol12( Y ) ) }.
% 1.32/1.76 (10649) {G0,W3,D3,L1,V1,M1} { finite( skol12( Y ) ) }.
% 1.32/1.76 (10650) {G0,W5,D3,L1,V1,M1} { element( skol12( X ), powerset( X ) ) }.
% 1.32/1.76 (10651) {G0,W2,D2,L1,V0,M1} { relation( skol13 ) }.
% 1.32/1.76 (10652) {G0,W2,D2,L1,V0,M1} { empty( skol13 ) }.
% 1.32/1.76 (10653) {G0,W2,D2,L1,V0,M1} { function( skol13 ) }.
% 1.32/1.76 (10654) {G0,W2,D2,L1,V0,M1} { relation( skol14 ) }.
% 1.32/1.76 (10655) {G0,W2,D2,L1,V0,M1} { function( skol14 ) }.
% 1.32/1.76 (10656) {G0,W2,D2,L1,V0,M1} { one_to_one( skol14 ) }.
% 1.32/1.76 (10657) {G0,W2,D2,L1,V0,M1} { empty( skol14 ) }.
% 1.32/1.76 (10658) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol14 ) }.
% 1.32/1.76 (10659) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol14 ) }.
% 1.32/1.76 (10660) {G0,W2,D2,L1,V0,M1} { ordinal( skol14 ) }.
% 1.32/1.76 (10661) {G0,W2,D2,L1,V0,M1} { relation( skol15 ) }.
% 1.32/1.76 (10662) {G0,W2,D2,L1,V0,M1} { function( skol15 ) }.
% 1.32/1.76 (10663) {G0,W2,D2,L1,V0,M1} { transfinite_sequence( skol15 ) }.
% 1.32/1.76 (10664) {G0,W2,D2,L1,V0,M1} { ordinal_yielding( skol15 ) }.
% 1.32/1.76 (10665) {G0,W2,D2,L1,V0,M1} { ! empty( skol16 ) }.
% 1.32/1.76 (10666) {G0,W2,D2,L1,V0,M1} { relation( skol16 ) }.
% 1.32/1.76 (10667) {G0,W3,D3,L1,V1,M1} { empty( skol17( Y ) ) }.
% 1.32/1.76 (10668) {G0,W5,D3,L1,V1,M1} { element( skol17( X ), powerset( X ) ) }.
% 1.32/1.76 (10669) {G0,W2,D2,L1,V0,M1} { ! empty( skol18 ) }.
% 1.32/1.76 (10670) {G0,W3,D2,L1,V0,M1} { element( skol19, positive_rationals ) }.
% 1.32/1.76 (10671) {G0,W2,D2,L1,V0,M1} { empty( skol19 ) }.
% 1.32/1.76 (10672) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol19 ) }.
% 1.32/1.76 (10673) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol19 ) }.
% 1.32/1.76 (10674) {G0,W2,D2,L1,V0,M1} { ordinal( skol19 ) }.
% 1.32/1.76 (10675) {G0,W2,D2,L1,V0,M1} { natural( skol19 ) }.
% 1.32/1.76 (10676) {G0,W5,D3,L2,V2,M2} { empty( X ), ! empty( skol20( Y ) ) }.
% 1.32/1.76 (10677) {G0,W5,D3,L2,V2,M2} { empty( X ), finite( skol20( Y ) ) }.
% 1.32/1.76 (10678) {G0,W7,D3,L2,V1,M2} { empty( X ), element( skol20( X ), powerset(
% 1.32/1.76 X ) ) }.
% 1.32/1.76 (10679) {G0,W2,D2,L1,V0,M1} { relation( skol21 ) }.
% 1.32/1.76 (10680) {G0,W2,D2,L1,V0,M1} { function( skol21 ) }.
% 1.32/1.76 (10681) {G0,W2,D2,L1,V0,M1} { one_to_one( skol21 ) }.
% 1.32/1.76 (10682) {G0,W2,D2,L1,V0,M1} { ! empty( skol22 ) }.
% 1.32/1.76 (10683) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol22 ) }.
% 1.32/1.76 (10684) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol22 ) }.
% 1.32/1.76 (10685) {G0,W2,D2,L1,V0,M1} { ordinal( skol22 ) }.
% 1.32/1.76 (10686) {G0,W2,D2,L1,V0,M1} { relation( skol23 ) }.
% 1.32/1.76 (10687) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( skol23 ) }.
% 1.32/1.76 (10688) {G0,W2,D2,L1,V0,M1} { relation( skol24 ) }.
% 1.32/1.76 (10689) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( skol24 ) }.
% 1.32/1.76 (10690) {G0,W2,D2,L1,V0,M1} { function( skol24 ) }.
% 1.32/1.76 (10691) {G0,W2,D2,L1,V0,M1} { relation( skol25 ) }.
% 1.32/1.76 (10692) {G0,W2,D2,L1,V0,M1} { function( skol25 ) }.
% 1.32/1.76 (10693) {G0,W2,D2,L1,V0,M1} { transfinite_sequence( skol25 ) }.
% 1.32/1.76 (10694) {G0,W2,D2,L1,V0,M1} { relation( skol26 ) }.
% 1.32/1.76 (10695) {G0,W2,D2,L1,V0,M1} { relation_non_empty( skol26 ) }.
% 1.32/1.76 (10696) {G0,W2,D2,L1,V0,M1} { function( skol26 ) }.
% 1.32/1.76 (10697) {G0,W3,D2,L1,V1,M1} { subset( X, X ) }.
% 1.32/1.76 (10698) {G0,W15,D4,L4,V2,M4} { ! relation( X ), ! function( X ), ! subset
% 1.32/1.76 ( Y, relation_rng( X ) ), relation_image( X, relation_inverse_image( X, Y
% 1.32/1.76 ) ) = Y }.
% 1.32/1.76 (10699) {G0,W10,D3,L4,V2,M4} { ! relation( X ), ! function( X ), ! finite
% 1.32/1.76 ( Y ), finite( relation_image( X, Y ) ) }.
% 1.32/1.76 (10700) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), element( X, Y ) }.
% 1.32/1.76 (10701) {G0,W2,D2,L1,V0,M1} { relation( skol27 ) }.
% 1.32/1.76 (10702) {G0,W2,D2,L1,V0,M1} { function( skol27 ) }.
% 1.32/1.76 (10703) {G0,W4,D3,L1,V0,M1} { subset( skol28, relation_rng( skol27 ) ) }.
% 1.32/1.76 (10704) {G0,W4,D3,L1,V0,M1} { finite( relation_inverse_image( skol27,
% 1.32/1.76 skol28 ) ) }.
% 1.32/1.76 (10705) {G0,W2,D2,L1,V0,M1} { ! finite( skol28 ) }.
% 1.32/1.76 (10706) {G0,W8,D2,L3,V2,M3} { ! element( X, Y ), empty( Y ), in( X, Y )
% 1.32/1.76 }.
% 1.32/1.76 (10707) {G0,W7,D3,L2,V2,M2} { ! element( X, powerset( Y ) ), subset( X, Y
% 1.32/1.76 ) }.
% 1.32/1.76 (10708) {G0,W7,D3,L2,V2,M2} { ! subset( X, Y ), element( X, powerset( Y )
% 1.32/1.76 ) }.
% 1.32/1.76 (10709) {G0,W10,D3,L3,V3,M3} { ! in( X, Z ), ! element( Z, powerset( Y ) )
% 1.32/1.76 , element( X, Y ) }.
% 1.32/1.76 (10710) {G0,W9,D3,L3,V3,M3} { ! in( X, Y ), ! element( Y, powerset( Z ) )
% 1.32/1.76 , ! empty( Z ) }.
% 1.32/1.76 (10711) {G0,W5,D2,L2,V1,M2} { ! empty( X ), X = empty_set }.
% 1.32/1.76 (10712) {G0,W5,D2,L2,V2,M2} { ! in( X, Y ), ! empty( Y ) }.
% 1.32/1.76 (10713) {G0,W7,D2,L3,V2,M3} { ! empty( X ), X = Y, ! empty( Y ) }.
% 1.32/1.76
% 1.32/1.76
% 1.32/1.76 Total Proof:
% 1.32/1.76
% 1.32/1.76 subsumption: (31) {G0,W10,D3,L4,V2,M4} I { ! relation( X ), ! function( X )
% 1.32/1.76 , ! finite( Y ), finite( relation_image( X, Y ) ) }.
% 1.32/1.76 parent0: (10594) {G0,W10,D3,L4,V2,M4} { ! relation( X ), ! function( X ),
% 1.32/1.76 ! finite( Y ), finite( relation_image( X, Y ) ) }.
% 1.32/1.76 substitution0:
% 1.32/1.76 X := X
% 1.32/1.76 Y := Y
% 1.32/1.76 end
% 1.32/1.76 permutation0:
% 1.32/1.76 0 ==> 0
% 1.32/1.76 1 ==> 1
% 1.32/1.76 2 ==> 2
% 1.32/1.76 3 ==> 3
% 1.32/1.76 end
% 1.32/1.76
% 1.32/1.76 subsumption: (129) {G0,W15,D4,L4,V2,M4} I { ! relation( X ), ! function( X
% 1.32/1.76 ), ! subset( Y, relation_rng( X ) ), relation_image( X,
% 1.32/1.76 relation_inverse_image( X, Y ) ) ==> Y }.
% 1.32/1.76 parent0: (10698) {G0,W15,D4,L4,V2,M4} { ! relation( X ), ! function( X ),
% 1.32/1.76 ! subset( Y, relation_rng( X ) ), relation_image( X,
% 1.32/1.76 relation_inverse_image( X, Y ) ) = Y }.
% 1.32/1.76 substitution0:
% 1.32/1.76 X := X
% 1.32/1.76 Y := Y
% 1.32/1.76 end
% 1.32/1.76 permutation0:
% 1.32/1.76 0 ==> 0
% 1.32/1.76 1 ==> 1
% 1.32/1.76 2 ==> 2
% 1.32/1.76 3 ==> 3
% 1.32/1.76 end
% 1.32/1.76
% 1.32/1.76 subsumption: (131) {G0,W2,D2,L1,V0,M1} I { relation( skol27 ) }.
% 1.32/1.76 parent0: (10701) {G0,W2,D2,L1,V0,M1} { relation( skol27 ) }.
% 1.32/1.76 substitution0:
% 1.32/1.76 end
% 1.32/1.76 permutation0:
% 1.32/1.76 0 ==> 0
% 1.32/1.76 end
% 1.32/1.76
% 1.32/1.76 subsumption: (132) {G0,W2,D2,L1,V0,M1} I { function( skol27 ) }.
% 1.32/1.76 parent0: (10702) {G0,W2,D2,L1,V0,M1} { function( skol27 ) }.
% 1.32/1.76 substitution0:
% 1.32/1.76 end
% 1.32/1.76 permutation0:
% 1.32/1.76 0 ==> 0
% 1.32/1.76 end
% 1.32/1.76
% 1.32/1.76 subsumption: (133) {G0,W4,D3,L1,V0,M1} I { subset( skol28, relation_rng(
% 1.32/1.76 skol27 ) ) }.
% 1.32/1.76 parent0: (10703) {G0,W4,D3,L1,V0,M1} { subset( skol28, relation_rng(
% 1.32/1.76 skol27 ) ) }.
% 1.32/1.76 substitution0:
% 1.32/1.76 end
% 1.32/1.76 permutation0:
% 1.32/1.76 0 ==> 0
% 1.32/1.76 end
% 1.32/1.76
% 1.32/1.76 subsumption: (134) {G0,W4,D3,L1,V0,M1} I { finite( relation_inverse_image(
% 1.32/1.76 skol27, skol28 ) ) }.
% 1.32/1.76 parent0: (10704) {G0,W4,D3,L1,V0,M1} { finite( relation_inverse_image(
% 1.32/1.76 skol27, skol28 ) ) }.
% 1.32/1.76 substitution0:
% 1.32/1.76 end
% 1.32/1.76 permutation0:
% 1.32/1.76 0 ==> 0
% 1.32/1.76 end
% 1.32/1.76
% 1.32/1.76 subsumption: (135) {G0,W2,D2,L1,V0,M1} I { ! finite( skol28 ) }.
% 1.32/1.76 parent0: (10705) {G0,W2,D2,L1,V0,M1} { ! finite( skol28 ) }.
% 1.32/1.76 substitution0:
% 1.32/1.76 end
% 1.32/1.76 permutation0:
% 1.32/1.76 0 ==> 0
% 1.32/1.76 end
% 1.32/1.76
% 1.32/1.76 eqswap: (10727) {G0,W15,D4,L4,V2,M4} { Y ==> relation_image( X,
% 1.32/1.76 relation_inverse_image( X, Y ) ), ! relation( X ), ! function( X ), !
% 1.32/1.76 subset( Y, relation_rng( X ) ) }.
% 1.32/1.76 parent0[3]: (129) {G0,W15,D4,L4,V2,M4} I { ! relation( X ), ! function( X )
% 1.32/1.76 , ! subset( Y, relation_rng( X ) ), relation_image( X,
% 1.32/1.76 relation_inverse_image( X, Y ) ) ==> Y }.
% 1.32/1.76 substitution0:
% 1.32/1.76 X := X
% 1.32/1.76 Y := Y
% 1.32/1.76 end
% 1.32/1.76
% 1.32/1.76 resolution: (10728) {G1,W13,D4,L3,V1,M3} { X ==> relation_image( skol27,
% 1.32/1.76 relation_inverse_image( skol27, X ) ), ! function( skol27 ), ! subset( X
% 1.32/1.76 , relation_rng( skol27 ) ) }.
% 1.32/1.76 parent0[1]: (10727) {G0,W15,D4,L4,V2,M4} { Y ==> relation_image( X,
% 1.32/1.76 relation_inverse_image( X, Y ) ), ! relation( X ), ! function( X ), !
% 1.32/1.76 subset( Y, relation_rng( X ) ) }.
% 1.32/1.76 parent1[0]: (131) {G0,W2,D2,L1,V0,M1} I { relation( skol27 ) }.
% 1.32/1.76 substitution0:
% 1.32/1.76 X := skol27
% 1.32/1.76 Y := X
% 1.32/1.76 end
% 1.32/1.76 substitution1:
% 1.32/1.76 end
% 1.32/1.76
% 1.32/1.76 resolution: (10729) {G1,W11,D4,L2,V1,M2} { X ==> relation_image( skol27,
% 1.32/1.76 relation_inverse_image( skol27, X ) ), ! subset( X, relation_rng( skol27
% 1.32/1.76 ) ) }.
% 1.32/1.76 parent0[1]: (10728) {G1,W13,D4,L3,V1,M3} { X ==> relation_image( skol27,
% 1.32/1.76 relation_inverse_image( skol27, X ) ), ! function( skol27 ), ! subset( X
% 1.32/1.76 , relation_rng( skol27 ) ) }.
% 1.32/1.76 parent1[0]: (132) {G0,W2,D2,L1,V0,M1} I { function( skol27 ) }.
% 1.32/1.76 substitution0:
% 1.32/1.76 X := X
% 1.32/1.76 end
% 1.32/1.76 substitution1:
% 1.32/1.76 end
% 1.32/1.76
% 1.32/1.76 eqswap: (10730) {G1,W11,D4,L2,V1,M2} { relation_image( skol27,
% 1.32/1.76 relation_inverse_image( skol27, X ) ) ==> X, ! subset( X, relation_rng(
% 1.32/1.76 skol27 ) ) }.
% 1.32/1.76 parent0[0]: (10729) {G1,W11,D4,L2,V1,M2} { X ==> relation_image( skol27,
% 1.32/1.76 relation_inverse_image( skol27, X ) ), ! subset( X, relation_rng( skol27
% 1.32/1.76 ) ) }.
% 1.32/1.76 substitution0:
% 1.32/1.76 X := X
% 1.32/1.76 end
% 1.32/1.76
% 1.32/1.76 subsumption: (554) {G1,W11,D4,L2,V1,M2} R(129,131);r(132) { ! subset( X,
% 1.32/1.76 relation_rng( skol27 ) ), relation_image( skol27, relation_inverse_image
% 1.32/1.76 ( skol27, X ) ) ==> X }.
% 1.32/1.76 parent0: (10730) {G1,W11,D4,L2,V1,M2} { relation_image( skol27,
% 1.32/1.76 relation_inverse_image( skol27, X ) ) ==> X, ! subset( X, relation_rng(
% 1.32/1.76 skol27 ) ) }.
% 1.32/1.76 substitution0:
% 1.32/1.76 X := X
% 1.32/1.76 end
% 1.32/1.76 permutation0:
% 1.32/1.76 0 ==> 1
% 1.32/1.76 1 ==> 0
% 1.32/1.76 end
% 1.32/1.76
% 1.32/1.76 resolution: (10731) {G1,W10,D4,L3,V1,M3} { ! relation( X ), ! function( X
% 1.32/1.76 ), finite( relation_image( X, relation_inverse_image( skol27, skol28 ) )
% 1.32/1.76 ) }.
% 1.32/1.76 parent0[2]: (31) {G0,W10,D3,L4,V2,M4} I { ! relation( X ), ! function( X )
% 1.32/1.76 , ! finite( Y ), finite( relation_image( X, Y ) ) }.
% 1.32/1.76 parent1[0]: (134) {G0,W4,D3,L1,V0,M1} I { finite( relation_inverse_image(
% 1.32/1.76 skol27, skol28 ) ) }.
% 1.32/1.76 substitution0:
% 1.32/1.76 X := X
% 1.32/1.76 Y := relation_inverse_image( skol27, skol28 )
% 1.32/1.76 end
% 1.32/1.76 substitution1:
% 1.32/1.76 end
% 1.32/1.76
% 1.32/1.76 subsumption: (595) {G1,W10,D4,L3,V1,M3} R(134,31) { ! relation( X ), !
% 1.32/1.76 function( X ), finite( relation_image( X, relation_inverse_image( skol27
% 1.32/1.76 , skol28 ) ) ) }.
% 1.32/1.76 parent0: (10731) {G1,W10,D4,L3,V1,M3} { ! relation( X ), ! function( X ),
% 1.32/1.76 finite( relation_image( X, relation_inverse_image( skol27, skol28 ) ) )
% 1.32/1.76 }.
% 1.32/1.76 substitution0:
% 1.32/1.76 X := X
% 1.32/1.76 end
% 1.32/1.76 permutation0:
% 1.32/1.76 0 ==> 0
% 1.32/1.76 1 ==> 1
% 1.32/1.76 2 ==> 2
% 1.32/1.76 end
% 1.32/1.76
% 1.32/1.76 eqswap: (10732) {G1,W11,D4,L2,V1,M2} { X ==> relation_image( skol27,
% 1.32/1.76 relation_inverse_image( skol27, X ) ), ! subset( X, relation_rng( skol27
% 1.32/1.76 ) ) }.
% 1.32/1.76 parent0[1]: (554) {G1,W11,D4,L2,V1,M2} R(129,131);r(132) { ! subset( X,
% 1.32/1.76 relation_rng( skol27 ) ), relation_image( skol27, relation_inverse_image
% 1.32/1.76 ( skol27, X ) ) ==> X }.
% 1.32/1.76 substitution0:
% 1.32/1.76 X := X
% 1.32/1.76 end
% 1.32/1.76
% 1.32/1.76 resolution: (10733) {G1,W7,D4,L1,V0,M1} { skol28 ==> relation_image(
% 1.32/1.76 skol27, relation_inverse_image( skol27, skol28 ) ) }.
% 1.32/1.76 parent0[1]: (10732) {G1,W11,D4,L2,V1,M2} { X ==> relation_image( skol27,
% 1.32/1.76 relation_inverse_image( skol27, X ) ), ! subset( X, relation_rng( skol27
% 1.32/1.76 ) ) }.
% 1.32/1.76 parent1[0]: (133) {G0,W4,D3,L1,V0,M1} I { subset( skol28, relation_rng(
% 1.32/1.76 skol27 ) ) }.
% 1.32/1.76 substitution0:
% 1.32/1.76 X := skol28
% 1.32/1.76 end
% 1.32/1.76 substitution1:
% 1.32/1.76 end
% 1.32/1.76
% 1.32/1.76 eqswap: (10734) {G1,W7,D4,L1,V0,M1} { relation_image( skol27,
% 1.32/1.76 relation_inverse_image( skol27, skol28 ) ) ==> skol28 }.
% 1.32/1.76 parent0[0]: (10733) {G1,W7,D4,L1,V0,M1} { skol28 ==> relation_image(
% 1.32/1.76 skol27, relation_inverse_image( skol27, skol28 ) ) }.
% 1.32/1.76 substitution0:
% 1.32/1.76 end
% 1.32/1.76
% 1.32/1.76 subsumption: (9067) {G2,W7,D4,L1,V0,M1} R(554,133) { relation_image( skol27
% 1.32/1.76 , relation_inverse_image( skol27, skol28 ) ) ==> skol28 }.
% 1.32/1.76 parent0: (10734) {G1,W7,D4,L1,V0,M1} { relation_image( skol27,
% 1.32/1.76 relation_inverse_image( skol27, skol28 ) ) ==> skol28 }.
% 1.32/1.76 substitution0:
% 1.32/1.76 end
% 1.32/1.76 permutation0:
% 1.32/1.76 0 ==> 0
% 1.32/1.76 end
% 1.32/1.76
% 1.32/1.76 resolution: (10736) {G1,W8,D4,L2,V0,M2} { ! function( skol27 ), finite(
% 1.32/1.76 relation_image( skol27, relation_inverse_image( skol27, skol28 ) ) ) }.
% 1.32/1.76 parent0[0]: (595) {G1,W10,D4,L3,V1,M3} R(134,31) { ! relation( X ), !
% 1.32/1.76 function( X ), finite( relation_image( X, relation_inverse_image( skol27
% 1.32/1.76 , skol28 ) ) ) }.
% 1.32/1.76 parent1[0]: (131) {G0,W2,D2,L1,V0,M1} I { relation( skol27 ) }.
% 1.32/1.76 substitution0:
% 1.32/1.76 X := skol27
% 1.32/1.76 end
% 1.32/1.76 substitution1:
% 1.32/1.76 end
% 1.32/1.76
% 1.32/1.76 paramod: (10737) {G2,W4,D2,L2,V0,M2} { finite( skol28 ), ! function(
% 1.32/1.76 skol27 ) }.
% 1.32/1.76 parent0[0]: (9067) {G2,W7,D4,L1,V0,M1} R(554,133) { relation_image( skol27
% 1.32/1.76 , relation_inverse_image( skol27, skol28 ) ) ==> skol28 }.
% 1.32/1.76 parent1[1; 1]: (10736) {G1,W8,D4,L2,V0,M2} { ! function( skol27 ), finite
% 1.32/1.76 ( relation_image( skol27, relation_inverse_image( skol27, skol28 ) ) )
% 1.32/1.76 }.
% 1.32/1.76 substitution0:
% 1.32/1.76 end
% 1.32/1.76 substitution1:
% 1.32/1.76 end
% 1.32/1.76
% 1.32/1.76 resolution: (10738) {G1,W2,D2,L1,V0,M1} { finite( skol28 ) }.
% 1.32/1.76 parent0[1]: (10737) {G2,W4,D2,L2,V0,M2} { finite( skol28 ), ! function(
% 1.32/1.76 skol27 ) }.
% 1.32/1.76 parent1[0]: (132) {G0,W2,D2,L1,V0,M1} I { function( skol27 ) }.
% 1.32/1.76 substitution0:
% 1.32/1.76 end
% 1.32/1.76 substitution1:
% 1.32/1.76 end
% 1.32/1.76
% 1.32/1.76 subsumption: (10556) {G3,W2,D2,L1,V0,M1} R(595,131);d(9067);r(132) { finite
% 1.32/1.76 ( skol28 ) }.
% 1.32/1.76 parent0: (10738) {G1,W2,D2,L1,V0,M1} { finite( skol28 ) }.
% 1.32/1.76 substitution0:
% 1.32/1.76 end
% 1.32/1.76 permutation0:
% 1.32/1.76 0 ==> 0
% 1.32/1.76 end
% 1.32/1.76
% 1.32/1.76 resolution: (10739) {G1,W0,D0,L0,V0,M0} { }.
% 1.32/1.76 parent0[0]: (135) {G0,W2,D2,L1,V0,M1} I { ! finite( skol28 ) }.
% 1.32/1.76 parent1[0]: (10556) {G3,W2,D2,L1,V0,M1} R(595,131);d(9067);r(132) { finite
% 1.32/1.76 ( skol28 ) }.
% 1.32/1.76 substitution0:
% 1.32/1.76 end
% 1.32/1.76 substitution1:
% 1.32/1.76 end
% 1.32/1.76
% 1.32/1.76 subsumption: (10559) {G4,W0,D0,L0,V0,M0} S(10556);r(135) { }.
% 1.32/1.76 parent0: (10739) {G1,W0,D0,L0,V0,M0} { }.
% 1.32/1.76 substitution0:
% 1.32/1.76 end
% 1.32/1.76 permutation0:
% 1.32/1.76 end
% 1.32/1.76
% 1.32/1.76 Proof check complete!
% 1.32/1.76
% 1.32/1.76 Memory use:
% 1.32/1.76
% 1.32/1.76 space for terms: 109280
% 1.32/1.76 space for clauses: 477952
% 1.32/1.76
% 1.32/1.76
% 1.32/1.76 clauses generated: 33390
% 1.32/1.76 clauses kept: 10560
% 1.32/1.76 clauses selected: 1305
% 1.32/1.76 clauses deleted: 390
% 1.32/1.76 clauses inuse deleted: 143
% 1.32/1.76
% 1.32/1.76 subsentry: 89515
% 1.32/1.76 literals s-matched: 60806
% 1.32/1.76 literals matched: 58362
% 1.32/1.76 full subsumption: 5447
% 1.32/1.76
% 1.32/1.76 checksum: -1691293469
% 1.32/1.76
% 1.32/1.76
% 1.32/1.76 Bliksem ended
%------------------------------------------------------------------------------