TSTP Solution File: SEU215+3 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SEU215+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n026.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 07:11:29 EDT 2022
% Result : Theorem 75.70s 76.09s
% Output : Refutation 75.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU215+3 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n026.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 10:51:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 4.48/4.86 *** allocated 10000 integers for termspace/termends
% 4.48/4.86 *** allocated 10000 integers for clauses
% 4.48/4.86 *** allocated 10000 integers for justifications
% 4.48/4.86 Bliksem 1.12
% 4.48/4.86
% 4.48/4.86
% 4.48/4.86 Automatic Strategy Selection
% 4.48/4.86
% 4.48/4.86
% 4.48/4.86 Clauses:
% 4.48/4.86
% 4.48/4.86 { ! in( X, Y ), ! in( Y, X ) }.
% 4.48/4.86 { ! empty( X ), function( X ) }.
% 4.48/4.86 { ! empty( X ), relation( X ) }.
% 4.48/4.86 { unordered_pair( X, Y ) = unordered_pair( Y, X ) }.
% 4.48/4.86 { ! relation( X ), ! function( X ), ! in( Y, relation_dom( X ) ), ! Z =
% 4.48/4.86 apply( X, Y ), in( ordered_pair( Y, Z ), X ) }.
% 4.48/4.86 { ! relation( X ), ! function( X ), ! in( Y, relation_dom( X ) ), ! in(
% 4.48/4.86 ordered_pair( Y, Z ), X ), Z = apply( X, Y ) }.
% 4.48/4.86 { ! relation( X ), ! function( X ), in( Y, relation_dom( X ) ), ! Z = apply
% 4.48/4.86 ( X, Y ), Z = empty_set }.
% 4.48/4.86 { ! relation( X ), ! function( X ), in( Y, relation_dom( X ) ), ! Z =
% 4.48/4.86 empty_set, Z = apply( X, Y ) }.
% 4.48/4.86 { ordered_pair( X, Y ) = unordered_pair( unordered_pair( X, Y ), singleton
% 4.48/4.86 ( X ) ) }.
% 4.48/4.86 { ! relation( X ), ! relation( Y ), relation( relation_composition( X, Y )
% 4.48/4.86 ) }.
% 4.48/4.86 { element( skol1( X ), X ) }.
% 4.48/4.86 { ! empty( X ), ! relation( Y ), empty( relation_composition( Y, X ) ) }.
% 4.48/4.86 { ! empty( X ), ! relation( Y ), relation( relation_composition( Y, X ) ) }
% 4.48/4.86 .
% 4.48/4.86 { empty( empty_set ) }.
% 4.48/4.86 { relation( empty_set ) }.
% 4.48/4.86 { relation_empty_yielding( empty_set ) }.
% 4.48/4.86 { ! relation( X ), ! function( X ), ! relation( Y ), ! function( Y ),
% 4.48/4.86 relation( relation_composition( X, Y ) ) }.
% 4.48/4.86 { ! relation( X ), ! function( X ), ! relation( Y ), ! function( Y ),
% 4.48/4.86 function( relation_composition( X, Y ) ) }.
% 4.48/4.86 { ! empty( powerset( X ) ) }.
% 4.48/4.86 { empty( empty_set ) }.
% 4.48/4.86 { ! empty( ordered_pair( X, Y ) ) }.
% 4.48/4.86 { ! empty( singleton( X ) ) }.
% 4.48/4.86 { ! empty( unordered_pair( X, Y ) ) }.
% 4.48/4.86 { empty( empty_set ) }.
% 4.48/4.86 { relation( empty_set ) }.
% 4.48/4.86 { empty( X ), ! relation( X ), ! empty( relation_dom( X ) ) }.
% 4.48/4.86 { ! empty( X ), empty( relation_dom( X ) ) }.
% 4.48/4.86 { ! empty( X ), relation( relation_dom( X ) ) }.
% 4.48/4.86 { ! empty( X ), ! relation( Y ), empty( relation_composition( X, Y ) ) }.
% 4.48/4.86 { ! empty( X ), ! relation( Y ), relation( relation_composition( X, Y ) ) }
% 4.48/4.86 .
% 4.48/4.86 { relation( skol2 ) }.
% 4.48/4.86 { function( skol2 ) }.
% 4.48/4.86 { empty( skol3 ) }.
% 4.48/4.86 { relation( skol3 ) }.
% 4.48/4.86 { empty( X ), ! empty( skol4( Y ) ) }.
% 4.48/4.86 { empty( X ), element( skol4( X ), powerset( X ) ) }.
% 4.48/4.86 { empty( skol5 ) }.
% 4.48/4.86 { ! empty( skol6 ) }.
% 4.48/4.86 { relation( skol6 ) }.
% 4.48/4.86 { empty( skol7( Y ) ) }.
% 4.48/4.86 { element( skol7( X ), powerset( X ) ) }.
% 4.48/4.86 { ! empty( skol8 ) }.
% 4.48/4.86 { relation( skol9 ) }.
% 4.48/4.86 { relation_empty_yielding( skol9 ) }.
% 4.48/4.86 { subset( X, X ) }.
% 4.48/4.86 { ! in( X, Y ), element( X, Y ) }.
% 4.48/4.86 { ! relation( X ), ! function( X ), ! relation( Y ), ! function( Y ), ! in
% 4.48/4.86 ( Z, relation_dom( relation_composition( Y, X ) ) ), in( Z, relation_dom
% 4.48/4.86 ( Y ) ) }.
% 4.48/4.86 { ! relation( X ), ! function( X ), ! relation( Y ), ! function( Y ), ! in
% 4.48/4.86 ( Z, relation_dom( relation_composition( Y, X ) ) ), in( apply( Y, Z ),
% 4.48/4.86 relation_dom( X ) ) }.
% 4.48/4.86 { ! relation( X ), ! function( X ), ! relation( Y ), ! function( Y ), ! in
% 4.48/4.86 ( Z, relation_dom( Y ) ), ! in( apply( Y, Z ), relation_dom( X ) ), in( Z
% 4.48/4.86 , relation_dom( relation_composition( Y, X ) ) ) }.
% 4.48/4.86 { ! relation( X ), ! function( X ), ! relation( Y ), ! function( Y ), ! in
% 4.48/4.86 ( Z, relation_dom( relation_composition( Y, X ) ) ), apply(
% 4.48/4.86 relation_composition( Y, X ), Z ) = apply( X, apply( Y, Z ) ) }.
% 4.48/4.86 { relation( skol10 ) }.
% 4.48/4.86 { function( skol10 ) }.
% 4.48/4.86 { relation( skol11 ) }.
% 4.48/4.86 { function( skol11 ) }.
% 4.48/4.86 { in( skol12, relation_dom( skol10 ) ) }.
% 4.48/4.86 { ! apply( relation_composition( skol10, skol11 ), skol12 ) = apply( skol11
% 4.48/4.86 , apply( skol10, skol12 ) ) }.
% 4.48/4.86 { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 4.48/4.86 { ! element( X, powerset( Y ) ), subset( X, Y ) }.
% 4.48/4.86 { ! subset( X, Y ), element( X, powerset( Y ) ) }.
% 4.48/4.86 { ! in( X, Z ), ! element( Z, powerset( Y ) ), element( X, Y ) }.
% 4.48/4.86 { ! in( X, Y ), ! element( Y, powerset( Z ) ), ! empty( Z ) }.
% 4.48/4.86 { ! empty( X ), X = empty_set }.
% 4.48/4.86 { ! in( X, Y ), ! empty( Y ) }.
% 4.48/4.86 { ! empty( X ), X = Y, ! empty( Y ) }.
% 4.48/4.86
% 4.48/4.86 percentage equality = 0.090226, percentage horn = 0.933333
% 4.48/4.86 This is a problem with some equality
% 4.48/4.86
% 4.48/4.86
% 4.48/4.86
% 4.48/4.86 Options Used:
% 4.48/4.86
% 4.48/4.86 useres = 1
% 4.48/4.86 useparamod = 1
% 4.48/4.86 useeqrefl = 1
% 4.48/4.86 useeqfact = 1
% 4.48/4.86 usefactor = 1
% 4.48/4.86 usesimpsplitting = 0
% 4.48/4.86 usesimpdemod = 5
% 75.70/76.09 usesimpres = 3
% 75.70/76.09
% 75.70/76.09 resimpinuse = 1000
% 75.70/76.09 resimpclauses = 20000
% 75.70/76.09 substype = eqrewr
% 75.70/76.09 backwardsubs = 1
% 75.70/76.09 selectoldest = 5
% 75.70/76.09
% 75.70/76.09 litorderings [0] = split
% 75.70/76.09 litorderings [1] = extend the termordering, first sorting on arguments
% 75.70/76.09
% 75.70/76.09 termordering = kbo
% 75.70/76.09
% 75.70/76.09 litapriori = 0
% 75.70/76.09 termapriori = 1
% 75.70/76.09 litaposteriori = 0
% 75.70/76.09 termaposteriori = 0
% 75.70/76.09 demodaposteriori = 0
% 75.70/76.09 ordereqreflfact = 0
% 75.70/76.09
% 75.70/76.09 litselect = negord
% 75.70/76.09
% 75.70/76.09 maxweight = 15
% 75.70/76.09 maxdepth = 30000
% 75.70/76.09 maxlength = 115
% 75.70/76.09 maxnrvars = 195
% 75.70/76.09 excuselevel = 1
% 75.70/76.09 increasemaxweight = 1
% 75.70/76.09
% 75.70/76.09 maxselected = 10000000
% 75.70/76.09 maxnrclauses = 10000000
% 75.70/76.09
% 75.70/76.09 showgenerated = 0
% 75.70/76.09 showkept = 0
% 75.70/76.09 showselected = 0
% 75.70/76.09 showdeleted = 0
% 75.70/76.09 showresimp = 1
% 75.70/76.09 showstatus = 2000
% 75.70/76.09
% 75.70/76.09 prologoutput = 0
% 75.70/76.09 nrgoals = 5000000
% 75.70/76.09 totalproof = 1
% 75.70/76.09
% 75.70/76.09 Symbols occurring in the translation:
% 75.70/76.09
% 75.70/76.09 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 75.70/76.09 . [1, 2] (w:1, o:34, a:1, s:1, b:0),
% 75.70/76.09 ! [4, 1] (w:0, o:19, a:1, s:1, b:0),
% 75.70/76.09 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 75.70/76.09 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 75.70/76.09 in [37, 2] (w:1, o:58, a:1, s:1, b:0),
% 75.70/76.09 empty [38, 1] (w:1, o:24, a:1, s:1, b:0),
% 75.70/76.09 function [39, 1] (w:1, o:25, a:1, s:1, b:0),
% 75.70/76.09 relation [40, 1] (w:1, o:26, a:1, s:1, b:0),
% 75.70/76.09 unordered_pair [41, 2] (w:1, o:59, a:1, s:1, b:0),
% 75.70/76.09 relation_dom [43, 1] (w:1, o:27, a:1, s:1, b:0),
% 75.70/76.09 apply [44, 2] (w:1, o:60, a:1, s:1, b:0),
% 75.70/76.09 ordered_pair [45, 2] (w:1, o:61, a:1, s:1, b:0),
% 75.70/76.09 empty_set [46, 0] (w:1, o:9, a:1, s:1, b:0),
% 75.70/76.09 singleton [47, 1] (w:1, o:29, a:1, s:1, b:0),
% 75.70/76.09 relation_composition [48, 2] (w:1, o:62, a:1, s:1, b:0),
% 75.70/76.09 element [49, 2] (w:1, o:63, a:1, s:1, b:0),
% 75.70/76.09 relation_empty_yielding [50, 1] (w:1, o:28, a:1, s:1, b:0),
% 75.70/76.09 powerset [51, 1] (w:1, o:30, a:1, s:1, b:0),
% 75.70/76.09 subset [52, 2] (w:1, o:64, a:1, s:1, b:0),
% 75.70/76.09 skol1 [53, 1] (w:1, o:31, a:1, s:1, b:1),
% 75.70/76.09 skol2 [54, 0] (w:1, o:13, a:1, s:1, b:1),
% 75.70/76.09 skol3 [55, 0] (w:1, o:14, a:1, s:1, b:1),
% 75.70/76.09 skol4 [56, 1] (w:1, o:32, a:1, s:1, b:1),
% 75.70/76.09 skol5 [57, 0] (w:1, o:15, a:1, s:1, b:1),
% 75.70/76.09 skol6 [58, 0] (w:1, o:16, a:1, s:1, b:1),
% 75.70/76.09 skol7 [59, 1] (w:1, o:33, a:1, s:1, b:1),
% 75.70/76.09 skol8 [60, 0] (w:1, o:17, a:1, s:1, b:1),
% 75.70/76.09 skol9 [61, 0] (w:1, o:18, a:1, s:1, b:1),
% 75.70/76.09 skol10 [62, 0] (w:1, o:10, a:1, s:1, b:1),
% 75.70/76.09 skol11 [63, 0] (w:1, o:11, a:1, s:1, b:1),
% 75.70/76.09 skol12 [64, 0] (w:1, o:12, a:1, s:1, b:1).
% 75.70/76.09
% 75.70/76.09
% 75.70/76.09 Starting Search:
% 75.70/76.09
% 75.70/76.09 *** allocated 15000 integers for clauses
% 75.70/76.09 *** allocated 22500 integers for clauses
% 75.70/76.09 *** allocated 33750 integers for clauses
% 75.70/76.09 *** allocated 15000 integers for termspace/termends
% 75.70/76.09 *** allocated 50625 integers for clauses
% 75.70/76.09 *** allocated 22500 integers for termspace/termends
% 75.70/76.09 *** allocated 75937 integers for clauses
% 75.70/76.09 Resimplifying inuse:
% 75.70/76.09 Done
% 75.70/76.09
% 75.70/76.09 *** allocated 113905 integers for clauses
% 75.70/76.09 *** allocated 33750 integers for termspace/termends
% 75.70/76.09
% 75.70/76.09 Intermediate Status:
% 75.70/76.09 Generated: 16217
% 75.70/76.09 Kept: 2002
% 75.70/76.09 Inuse: 265
% 75.70/76.09 Deleted: 140
% 75.70/76.09 Deletedinuse: 32
% 75.70/76.09
% 75.70/76.09 Resimplifying inuse:
% 75.70/76.09 Done
% 75.70/76.09
% 75.70/76.09 *** allocated 170857 integers for clauses
% 75.70/76.09 *** allocated 50625 integers for termspace/termends
% 75.70/76.09 Resimplifying inuse:
% 75.70/76.09 Done
% 75.70/76.09
% 75.70/76.09 *** allocated 256285 integers for clauses
% 75.70/76.09
% 75.70/76.09 Intermediate Status:
% 75.70/76.09 Generated: 36196
% 75.70/76.09 Kept: 4013
% 75.70/76.09 Inuse: 402
% 75.70/76.09 Deleted: 159
% 75.70/76.09 Deletedinuse: 42
% 75.70/76.09
% 75.70/76.09 Resimplifying inuse:
% 75.70/76.09 Done
% 75.70/76.09
% 75.70/76.09 *** allocated 75937 integers for termspace/termends
% 75.70/76.09 *** allocated 384427 integers for clauses
% 75.70/76.09 Resimplifying inuse:
% 75.70/76.09 Done
% 75.70/76.09
% 75.70/76.09 *** allocated 113905 integers for termspace/termends
% 75.70/76.09
% 75.70/76.09 Intermediate Status:
% 75.70/76.09 Generated: 46948
% 75.70/76.09 Kept: 6904
% 75.70/76.09 Inuse: 455
% 75.70/76.09 Deleted: 163
% 75.70/76.09 Deletedinuse: 42
% 75.70/76.09
% 75.70/76.09 Resimplifying inuse:
% 75.70/76.09 Done
% 75.70/76.09
% 75.70/76.09 *** allocated 576640 integers for clauses
% 75.70/76.09 Resimplifying inuse:
% 75.70/76.09 Done
% 75.70/76.09
% 75.70/76.09
% 75.70/76.09 Intermediate Status:
% 75.70/76.09 Generated: 64715
% 75.70/76.09 Kept: 8912
% 75.70/76.09 Inuse: 521
% 75.70/76.09 Deleted: 165
% 75.70/76.09 Deletedinuse: 42
% 75.70/76.09
% 75.70/76.09 Resimplifying inuse:
% 75.70/76.09 Done
% 75.70/76.09
% 75.70/76.09 *** allocated 170857 integers for termspace/termends
% 75.70/76.09 Resimplifying inuse:
% 75.70/76.09 Done
% 75.70/76.09
% 75.70/76.09
% 75.70/76.09 Intermediate Status:
% 75.70/76.09 Generated: 89131
% 75.70/76.09 Kept: 10914
% 75.70/76.09 Inuse: 594
% 75.70/76.09 Deleted: 176
% 75.70/76.09 Deletedinuse: 42
% 75.70/76.09
% 75.70/76.09 Resimplifying inuse:
% 75.70/76.09 Done
% 75.70/76.09
% 75.70/76.09 *** allocated 864960 integers for clauses
% 75.70/76.09 Resimplifying inuse:
% 75.70/76.09 Done
% 75.70/76.09
% 75.70/76.09
% 75.70/76.09 Intermediate Status:
% 75.70/76.09 Generated: 100009
% 75.70/76.09 Kept: 13199
% 75.70/76.09 Inuse: 640
% 75.70/76.09 Deleted: 183
% 75.70/76.09 Deletedinuse: 47
% 75.70/76.09
% 75.70/76.09 Resimplifying inuse:
% 75.70/76.09 Done
% 75.70/76.09
% 75.70/76.09 *** allocated 256285 integers for termspace/termends
% 75.70/76.09 Resimplifying inuse:
% 75.70/76.09 Done
% 75.70/76.09
% 75.70/76.09
% 75.70/76.09 Intermediate Status:
% 75.70/76.09 Generated: 120068
% 75.70/76.09 Kept: 15234
% 75.70/76.09 Inuse: 705
% 75.70/76.09 Deleted: 191
% 75.70/76.09 Deletedinuse: 47
% 75.70/76.09
% 75.70/76.09 Resimplifying inuse:
% 75.70/76.09 Done
% 75.70/76.09
% 75.70/76.09 *** allocated 1297440 integers for clauses
% 75.70/76.09
% 75.70/76.09 Intermediate Status:
% 75.70/76.09 Generated: 136955
% 75.70/76.09 Kept: 17247
% 75.70/76.09 Inuse: 802
% 75.70/76.09 Deleted: 290
% 75.70/76.09 Deletedinuse: 61
% 75.70/76.09
% 75.70/76.09 Resimplifying inuse:
% 75.70/76.09 Done
% 75.70/76.09
% 75.70/76.09 Resimplifying inuse:
% 75.70/76.09 Done
% 75.70/76.09
% 75.70/76.09
% 75.70/76.09 Intermediate Status:
% 75.70/76.09 Generated: 157743
% 75.70/76.09 Kept: 19540
% 75.70/76.09 Inuse: 884
% 75.70/76.09 Deleted: 383
% 75.70/76.09 Deletedinuse: 68
% 75.70/76.09
% 75.70/76.09 Resimplifying inuse:
% 75.70/76.09 Done
% 75.70/76.09
% 75.70/76.09 Resimplifying clauses:
% 75.70/76.09 Done
% 75.70/76.09
% 75.70/76.09 Resimplifying inuse:
% 75.70/76.09 Done
% 75.70/76.09
% 75.70/76.09 *** allocated 384427 integers for termspace/termends
% 75.70/76.09
% 75.70/76.09 Intermediate Status:
% 75.70/76.09 Generated: 229341
% 75.70/76.09 Kept: 21552
% 75.70/76.09 Inuse: 1068
% 75.70/76.09 Deleted: 3064
% 75.70/76.09 Deletedinuse: 69
% 75.70/76.09
% 75.70/76.09 Resimplifying inuse:
% 75.70/76.09 Done
% 75.70/76.09
% 75.70/76.09 Resimplifying inuse:
% 75.70/76.09 Done
% 75.70/76.09
% 75.70/76.09
% 75.70/76.09 Intermediate Status:
% 75.70/76.09 Generated: 347030
% 75.70/76.09 Kept: 23555
% 75.70/76.09 Inuse: 1303
% 75.70/76.09 Deleted: 3090
% 75.70/76.09 Deletedinuse: 73
% 75.70/76.09
% 75.70/76.09 Resimplifying inuse:
% 75.70/76.09 Done
% 75.70/76.09
% 75.70/76.09 Resimplifying inuse:
% 75.70/76.09 Done
% 75.70/76.09
% 75.70/76.09
% 75.70/76.09 Intermediate Status:
% 75.70/76.09 Generated: 403264
% 75.70/76.09 Kept: 25646
% 75.70/76.09 Inuse: 1356
% 75.70/76.09 Deleted: 3097
% 75.70/76.09 Deletedinuse: 78
% 75.70/76.09
% 75.70/76.09 Resimplifying inuse:
% 75.70/76.09 Done
% 75.70/76.09
% 75.70/76.09 *** allocated 1946160 integers for clauses
% 75.70/76.09 Resimplifying inuse:
% 75.70/76.09 Done
% 75.70/76.09
% 75.70/76.09
% 75.70/76.09 Intermediate Status:
% 75.70/76.09 Generated: 470533
% 75.70/76.09 Kept: 27801
% 75.70/76.09 Inuse: 1476
% 75.70/76.09 Deleted: 3097
% 75.70/76.09 Deletedinuse: 78
% 75.70/76.09
% 75.70/76.09 Resimplifying inuse:
% 75.70/76.09 Done
% 75.70/76.09
% 75.70/76.09 Resimplifying inuse:
% 75.70/76.09 Done
% 75.70/76.09
% 75.70/76.09
% 75.70/76.09 Intermediate Status:
% 75.70/76.09 Generated: 552960
% 75.70/76.09 Kept: 30181
% 75.70/76.09 Inuse: 1628
% 75.70/76.09 Deleted: 3098
% 75.70/76.09 Deletedinuse: 78
% 75.70/76.09
% 75.70/76.09 Resimplifying inuse:
% 75.70/76.09 Done
% 75.70/76.09
% 75.70/76.09 *** allocated 576640 integers for termspace/termends
% 75.70/76.09 Resimplifying inuse:
% 75.70/76.09 Done
% 75.70/76.09
% 75.70/76.09
% 75.70/76.09 Intermediate Status:
% 75.70/76.09 Generated: 595996
% 75.70/76.09 Kept: 32185
% 75.70/76.09 Inuse: 1695
% 75.70/76.09 Deleted: 3098
% 75.70/76.09 Deletedinuse: 78
% 75.70/76.09
% 75.70/76.09 Resimplifying inuse:
% 75.70/76.09 Done
% 75.70/76.09
% 75.70/76.09 Resimplifying inuse:
% 75.70/76.09 Done
% 75.70/76.09
% 75.70/76.09
% 75.70/76.09 Intermediate Status:
% 75.70/76.09 Generated: 614028
% 75.70/76.09 Kept: 34205
% 75.70/76.09 Inuse: 1725
% 75.70/76.09 Deleted: 3098
% 75.70/76.09 Deletedinuse: 78
% 75.70/76.09
% 75.70/76.09 Resimplifying inuse:
% 75.70/76.09 Done
% 75.70/76.09
% 75.70/76.09 Resimplifying inuse:
% 75.70/76.09 Done
% 75.70/76.09
% 75.70/76.09
% 75.70/76.09 Intermediate Status:
% 75.70/76.09 Generated: 628969
% 75.70/76.09 Kept: 36392
% 75.70/76.09 Inuse: 1758
% 75.70/76.09 Deleted: 3155
% 75.70/76.09 Deletedinuse: 135
% 75.70/76.09
% 75.70/76.09 Resimplifying inuse:
% 75.70/76.09 Done
% 75.70/76.09
% 75.70/76.09
% 75.70/76.09 Intermediate Status:
% 75.70/76.09 Generated: 666612
% 75.70/76.09 Kept: 38432
% 75.70/76.09 Inuse: 1872
% 75.70/76.09 Deleted: 3160
% 75.70/76.09 Deletedinuse: 135
% 75.70/76.09
% 75.70/76.09 Resimplifying inuse:
% 75.70/76.09 Done
% 75.70/76.09
% 75.70/76.09 Resimplifying inuse:
% 75.70/76.09 Done
% 75.70/76.09
% 75.70/76.09 Resimplifying clauses:
% 75.70/76.09
% 75.70/76.09 Bliksems!, er is een bewijs:
% 75.70/76.09 % SZS status Theorem
% 75.70/76.09 % SZS output start Refutation
% 75.70/76.09
% 75.70/76.09 (6) {G0,W16,D3,L5,V3,M5} I { ! relation( X ), ! function( X ), in( Y,
% 75.70/76.09 relation_dom( X ) ), ! Z = apply( X, Y ), Z = empty_set }.
% 75.70/76.09 (9) {G0,W8,D3,L3,V2,M3} I { ! relation( X ), ! relation( Y ), relation(
% 75.70/76.09 relation_composition( X, Y ) ) }.
% 75.70/76.09 (16) {G0,W12,D3,L5,V2,M5} I { ! relation( X ), ! function( X ), ! relation
% 75.70/76.09 ( Y ), ! function( Y ), function( relation_composition( X, Y ) ) }.
% 75.70/76.09 (44) {G0,W24,D4,L7,V3,M7} I { ! relation( X ), ! function( X ), ! relation
% 75.70/76.09 ( Y ), ! function( Y ), ! in( Z, relation_dom( Y ) ), ! in( apply( Y, Z )
% 75.70/76.09 , relation_dom( X ) ), in( Z, relation_dom( relation_composition( Y, X )
% 75.70/76.09 ) ) }.
% 75.70/76.09 (45) {G0,W25,D4,L6,V3,M6} I { ! relation( X ), ! function( X ), ! relation
% 75.70/76.09 ( Y ), ! function( Y ), ! in( Z, relation_dom( relation_composition( Y, X
% 75.70/76.09 ) ) ), apply( X, apply( Y, Z ) ) ==> apply( relation_composition( Y, X )
% 75.70/76.09 , Z ) }.
% 75.70/76.09 (46) {G0,W2,D2,L1,V0,M1} I { relation( skol10 ) }.
% 75.70/76.09 (47) {G0,W2,D2,L1,V0,M1} I { function( skol10 ) }.
% 75.70/76.09 (48) {G0,W2,D2,L1,V0,M1} I { relation( skol11 ) }.
% 75.70/76.09 (49) {G0,W2,D2,L1,V0,M1} I { function( skol11 ) }.
% 75.70/76.09 (50) {G0,W4,D3,L1,V0,M1} I { in( skol12, relation_dom( skol10 ) ) }.
% 75.70/76.09 (51) {G0,W11,D4,L1,V0,M1} I { ! apply( skol11, apply( skol10, skol12 ) )
% 75.70/76.09 ==> apply( relation_composition( skol10, skol11 ), skol12 ) }.
% 75.70/76.09 (62) {G1,W13,D3,L4,V2,M4} Q(6) { ! relation( X ), ! function( X ), in( Y,
% 75.70/76.09 relation_dom( X ) ), apply( X, Y ) ==> empty_set }.
% 75.70/76.09 (180) {G1,W6,D3,L2,V1,M2} R(9,46) { ! relation( X ), relation(
% 75.70/76.09 relation_composition( skol10, X ) ) }.
% 75.70/76.09 (238) {G1,W8,D3,L3,V1,M3} R(16,46);r(47) { ! relation( X ), ! function( X )
% 75.70/76.09 , function( relation_composition( skol10, X ) ) }.
% 75.70/76.09 (505) {G1,W20,D4,L5,V2,M5} R(44,48);r(49) { ! relation( X ), ! function( X
% 75.70/76.09 ), ! in( Y, relation_dom( X ) ), ! in( apply( X, Y ), relation_dom(
% 75.70/76.09 skol11 ) ), in( Y, relation_dom( relation_composition( X, skol11 ) ) )
% 75.70/76.09 }.
% 75.70/76.09 (562) {G1,W12,D4,L4,V0,M4} R(51,45);r(48) { ! function( skol11 ), !
% 75.70/76.09 relation( skol10 ), ! function( skol10 ), ! in( skol12, relation_dom(
% 75.70/76.09 relation_composition( skol10, skol11 ) ) ) }.
% 75.70/76.09 (767) {G2,W15,D4,L3,V0,M3} P(62,51);r(48) { ! apply( relation_composition(
% 75.70/76.09 skol10, skol11 ), skol12 ) ==> empty_set, ! function( skol11 ), in( apply
% 75.70/76.09 ( skol10, skol12 ), relation_dom( skol11 ) ) }.
% 75.70/76.09 (2370) {G2,W4,D3,L1,V0,M1} R(180,48) { relation( relation_composition(
% 75.70/76.09 skol10, skol11 ) ) }.
% 75.70/76.09 (12451) {G2,W4,D3,L1,V0,M1} R(238,48);r(49) { function(
% 75.70/76.09 relation_composition( skol10, skol11 ) ) }.
% 75.70/76.09 (20259) {G3,W13,D4,L2,V0,M2} S(767);r(49) { ! apply( relation_composition(
% 75.70/76.09 skol10, skol11 ), skol12 ) ==> empty_set, in( apply( skol10, skol12 ),
% 75.70/76.09 relation_dom( skol11 ) ) }.
% 75.70/76.09 (20261) {G2,W6,D4,L1,V0,M1} S(562);r(49);r(46);r(47) { ! in( skol12,
% 75.70/76.09 relation_dom( relation_composition( skol10, skol11 ) ) ) }.
% 75.70/76.09 (20578) {G3,W11,D4,L2,V0,M2} R(20261,62);r(2370) { ! function(
% 75.70/76.09 relation_composition( skol10, skol11 ) ), apply( relation_composition(
% 75.70/76.09 skol10, skol11 ), skol12 ) ==> empty_set }.
% 75.70/76.09 (25033) {G3,W12,D3,L3,V0,M3} R(505,20261);r(46) { ! function( skol10 ), !
% 75.70/76.09 in( skol12, relation_dom( skol10 ) ), ! in( apply( skol10, skol12 ),
% 75.70/76.09 relation_dom( skol11 ) ) }.
% 75.70/76.09 (40296) {G4,W6,D3,L1,V0,M1} S(25033);r(47);r(50) { ! in( apply( skol10,
% 75.70/76.09 skol12 ), relation_dom( skol11 ) ) }.
% 75.70/76.09 (40364) {G4,W7,D4,L1,V0,M1} S(20578);r(12451) { apply( relation_composition
% 75.70/76.09 ( skol10, skol11 ), skol12 ) ==> empty_set }.
% 75.70/76.09 (40394) {G5,W0,D0,L0,V0,M0} S(20259);d(40364);q;r(40296) { }.
% 75.70/76.09
% 75.70/76.09
% 75.70/76.09 % SZS output end Refutation
% 75.70/76.09 found a proof!
% 75.70/76.09
% 75.70/76.09
% 75.70/76.09 Unprocessed initial clauses:
% 75.70/76.09
% 75.70/76.09 (40396) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), ! in( Y, X ) }.
% 75.70/76.09 (40397) {G0,W4,D2,L2,V1,M2} { ! empty( X ), function( X ) }.
% 75.70/76.09 (40398) {G0,W4,D2,L2,V1,M2} { ! empty( X ), relation( X ) }.
% 75.70/76.09 (40399) {G0,W7,D3,L1,V2,M1} { unordered_pair( X, Y ) = unordered_pair( Y,
% 75.70/76.09 X ) }.
% 75.70/76.09 (40400) {G0,W18,D3,L5,V3,M5} { ! relation( X ), ! function( X ), ! in( Y,
% 75.70/76.09 relation_dom( X ) ), ! Z = apply( X, Y ), in( ordered_pair( Y, Z ), X )
% 75.70/76.09 }.
% 75.70/76.09 (40401) {G0,W18,D3,L5,V3,M5} { ! relation( X ), ! function( X ), ! in( Y,
% 75.70/76.09 relation_dom( X ) ), ! in( ordered_pair( Y, Z ), X ), Z = apply( X, Y )
% 75.70/76.09 }.
% 75.70/76.09 (40402) {G0,W16,D3,L5,V3,M5} { ! relation( X ), ! function( X ), in( Y,
% 75.70/76.09 relation_dom( X ) ), ! Z = apply( X, Y ), Z = empty_set }.
% 75.70/76.09 (40403) {G0,W16,D3,L5,V3,M5} { ! relation( X ), ! function( X ), in( Y,
% 75.70/76.09 relation_dom( X ) ), ! Z = empty_set, Z = apply( X, Y ) }.
% 75.70/76.09 (40404) {G0,W10,D4,L1,V2,M1} { ordered_pair( X, Y ) = unordered_pair(
% 75.70/76.09 unordered_pair( X, Y ), singleton( X ) ) }.
% 75.70/76.09 (40405) {G0,W8,D3,L3,V2,M3} { ! relation( X ), ! relation( Y ), relation(
% 75.70/76.09 relation_composition( X, Y ) ) }.
% 75.70/76.09 (40406) {G0,W4,D3,L1,V1,M1} { element( skol1( X ), X ) }.
% 75.70/76.09 (40407) {G0,W8,D3,L3,V2,M3} { ! empty( X ), ! relation( Y ), empty(
% 75.70/76.09 relation_composition( Y, X ) ) }.
% 75.70/76.09 (40408) {G0,W8,D3,L3,V2,M3} { ! empty( X ), ! relation( Y ), relation(
% 75.70/76.09 relation_composition( Y, X ) ) }.
% 75.70/76.09 (40409) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 75.70/76.09 (40410) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 75.70/76.09 (40411) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( empty_set ) }.
% 75.70/76.09 (40412) {G0,W12,D3,L5,V2,M5} { ! relation( X ), ! function( X ), !
% 75.70/76.09 relation( Y ), ! function( Y ), relation( relation_composition( X, Y ) )
% 75.70/76.09 }.
% 75.70/76.09 (40413) {G0,W12,D3,L5,V2,M5} { ! relation( X ), ! function( X ), !
% 75.70/76.09 relation( Y ), ! function( Y ), function( relation_composition( X, Y ) )
% 75.70/76.09 }.
% 75.70/76.09 (40414) {G0,W3,D3,L1,V1,M1} { ! empty( powerset( X ) ) }.
% 75.70/76.09 (40415) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 75.70/76.09 (40416) {G0,W4,D3,L1,V2,M1} { ! empty( ordered_pair( X, Y ) ) }.
% 75.70/76.09 (40417) {G0,W3,D3,L1,V1,M1} { ! empty( singleton( X ) ) }.
% 75.70/76.09 (40418) {G0,W4,D3,L1,V2,M1} { ! empty( unordered_pair( X, Y ) ) }.
% 75.70/76.09 (40419) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 75.70/76.09 (40420) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 75.70/76.09 (40421) {G0,W7,D3,L3,V1,M3} { empty( X ), ! relation( X ), ! empty(
% 75.70/76.09 relation_dom( X ) ) }.
% 75.70/76.09 (40422) {G0,W5,D3,L2,V1,M2} { ! empty( X ), empty( relation_dom( X ) ) }.
% 75.70/76.09 (40423) {G0,W5,D3,L2,V1,M2} { ! empty( X ), relation( relation_dom( X ) )
% 75.70/76.09 }.
% 75.70/76.09 (40424) {G0,W8,D3,L3,V2,M3} { ! empty( X ), ! relation( Y ), empty(
% 75.70/76.09 relation_composition( X, Y ) ) }.
% 75.70/76.09 (40425) {G0,W8,D3,L3,V2,M3} { ! empty( X ), ! relation( Y ), relation(
% 75.70/76.09 relation_composition( X, Y ) ) }.
% 75.70/76.09 (40426) {G0,W2,D2,L1,V0,M1} { relation( skol2 ) }.
% 75.70/76.09 (40427) {G0,W2,D2,L1,V0,M1} { function( skol2 ) }.
% 75.70/76.09 (40428) {G0,W2,D2,L1,V0,M1} { empty( skol3 ) }.
% 75.70/76.09 (40429) {G0,W2,D2,L1,V0,M1} { relation( skol3 ) }.
% 75.70/76.09 (40430) {G0,W5,D3,L2,V2,M2} { empty( X ), ! empty( skol4( Y ) ) }.
% 75.70/76.09 (40431) {G0,W7,D3,L2,V1,M2} { empty( X ), element( skol4( X ), powerset( X
% 75.70/76.09 ) ) }.
% 75.70/76.09 (40432) {G0,W2,D2,L1,V0,M1} { empty( skol5 ) }.
% 75.70/76.09 (40433) {G0,W2,D2,L1,V0,M1} { ! empty( skol6 ) }.
% 75.70/76.09 (40434) {G0,W2,D2,L1,V0,M1} { relation( skol6 ) }.
% 75.70/76.09 (40435) {G0,W3,D3,L1,V1,M1} { empty( skol7( Y ) ) }.
% 75.70/76.09 (40436) {G0,W5,D3,L1,V1,M1} { element( skol7( X ), powerset( X ) ) }.
% 75.70/76.09 (40437) {G0,W2,D2,L1,V0,M1} { ! empty( skol8 ) }.
% 75.70/76.09 (40438) {G0,W2,D2,L1,V0,M1} { relation( skol9 ) }.
% 75.70/76.09 (40439) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( skol9 ) }.
% 75.70/76.09 (40440) {G0,W3,D2,L1,V1,M1} { subset( X, X ) }.
% 75.70/76.09 (40441) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), element( X, Y ) }.
% 75.70/76.09 (40442) {G0,W18,D4,L6,V3,M6} { ! relation( X ), ! function( X ), !
% 75.70/76.09 relation( Y ), ! function( Y ), ! in( Z, relation_dom(
% 75.70/76.09 relation_composition( Y, X ) ) ), in( Z, relation_dom( Y ) ) }.
% 75.70/76.09 (40443) {G0,W20,D4,L6,V3,M6} { ! relation( X ), ! function( X ), !
% 75.70/76.09 relation( Y ), ! function( Y ), ! in( Z, relation_dom(
% 75.70/76.09 relation_composition( Y, X ) ) ), in( apply( Y, Z ), relation_dom( X ) )
% 75.70/76.09 }.
% 75.70/76.09 (40444) {G0,W24,D4,L7,V3,M7} { ! relation( X ), ! function( X ), !
% 75.70/76.09 relation( Y ), ! function( Y ), ! in( Z, relation_dom( Y ) ), ! in( apply
% 75.70/76.09 ( Y, Z ), relation_dom( X ) ), in( Z, relation_dom( relation_composition
% 75.70/76.09 ( Y, X ) ) ) }.
% 75.70/76.09 (40445) {G0,W25,D4,L6,V3,M6} { ! relation( X ), ! function( X ), !
% 75.70/76.09 relation( Y ), ! function( Y ), ! in( Z, relation_dom(
% 75.70/76.09 relation_composition( Y, X ) ) ), apply( relation_composition( Y, X ), Z
% 75.70/76.09 ) = apply( X, apply( Y, Z ) ) }.
% 75.70/76.09 (40446) {G0,W2,D2,L1,V0,M1} { relation( skol10 ) }.
% 75.70/76.09 (40447) {G0,W2,D2,L1,V0,M1} { function( skol10 ) }.
% 75.70/76.09 (40448) {G0,W2,D2,L1,V0,M1} { relation( skol11 ) }.
% 75.70/76.09 (40449) {G0,W2,D2,L1,V0,M1} { function( skol11 ) }.
% 75.70/76.09 (40450) {G0,W4,D3,L1,V0,M1} { in( skol12, relation_dom( skol10 ) ) }.
% 75.70/76.09 (40451) {G0,W11,D4,L1,V0,M1} { ! apply( relation_composition( skol10,
% 75.70/76.09 skol11 ), skol12 ) = apply( skol11, apply( skol10, skol12 ) ) }.
% 75.70/76.09 (40452) {G0,W8,D2,L3,V2,M3} { ! element( X, Y ), empty( Y ), in( X, Y )
% 75.70/76.09 }.
% 75.70/76.09 (40453) {G0,W7,D3,L2,V2,M2} { ! element( X, powerset( Y ) ), subset( X, Y
% 75.70/76.09 ) }.
% 75.70/76.09 (40454) {G0,W7,D3,L2,V2,M2} { ! subset( X, Y ), element( X, powerset( Y )
% 75.70/76.09 ) }.
% 75.70/76.09 (40455) {G0,W10,D3,L3,V3,M3} { ! in( X, Z ), ! element( Z, powerset( Y ) )
% 75.70/76.09 , element( X, Y ) }.
% 75.70/76.09 (40456) {G0,W9,D3,L3,V3,M3} { ! in( X, Y ), ! element( Y, powerset( Z ) )
% 75.70/76.09 , ! empty( Z ) }.
% 75.70/76.09 (40457) {G0,W5,D2,L2,V1,M2} { ! empty( X ), X = empty_set }.
% 75.70/76.09 (40458) {G0,W5,D2,L2,V2,M2} { ! in( X, Y ), ! empty( Y ) }.
% 75.70/76.09 (40459) {G0,W7,D2,L3,V2,M3} { ! empty( X ), X = Y, ! empty( Y ) }.
% 75.70/76.09
% 75.70/76.09
% 75.70/76.09 Total Proof:
% 75.70/76.09
% 75.70/76.09 subsumption: (6) {G0,W16,D3,L5,V3,M5} I { ! relation( X ), ! function( X )
% 75.70/76.09 , in( Y, relation_dom( X ) ), ! Z = apply( X, Y ), Z = empty_set }.
% 75.70/76.09 parent0: (40402) {G0,W16,D3,L5,V3,M5} { ! relation( X ), ! function( X ),
% 75.70/76.09 in( Y, relation_dom( X ) ), ! Z = apply( X, Y ), Z = empty_set }.
% 75.70/76.09 substitution0:
% 75.70/76.09 X := X
% 75.70/76.09 Y := Y
% 75.70/76.09 Z := Z
% 75.70/76.09 end
% 75.70/76.09 permutation0:
% 75.70/76.09 0 ==> 0
% 75.70/76.09 1 ==> 1
% 75.70/76.09 2 ==> 2
% 75.70/76.09 3 ==> 3
% 75.70/76.09 4 ==> 4
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 subsumption: (9) {G0,W8,D3,L3,V2,M3} I { ! relation( X ), ! relation( Y ),
% 75.70/76.09 relation( relation_composition( X, Y ) ) }.
% 75.70/76.09 parent0: (40405) {G0,W8,D3,L3,V2,M3} { ! relation( X ), ! relation( Y ),
% 75.70/76.09 relation( relation_composition( X, Y ) ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 X := X
% 75.70/76.09 Y := Y
% 75.70/76.09 end
% 75.70/76.09 permutation0:
% 75.70/76.09 0 ==> 0
% 75.70/76.09 1 ==> 1
% 75.70/76.09 2 ==> 2
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 subsumption: (16) {G0,W12,D3,L5,V2,M5} I { ! relation( X ), ! function( X )
% 75.70/76.09 , ! relation( Y ), ! function( Y ), function( relation_composition( X, Y
% 75.70/76.09 ) ) }.
% 75.70/76.09 parent0: (40413) {G0,W12,D3,L5,V2,M5} { ! relation( X ), ! function( X ),
% 75.70/76.09 ! relation( Y ), ! function( Y ), function( relation_composition( X, Y )
% 75.70/76.09 ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 X := X
% 75.70/76.09 Y := Y
% 75.70/76.09 end
% 75.70/76.09 permutation0:
% 75.70/76.09 0 ==> 0
% 75.70/76.09 1 ==> 1
% 75.70/76.09 2 ==> 2
% 75.70/76.09 3 ==> 3
% 75.70/76.09 4 ==> 4
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 subsumption: (44) {G0,W24,D4,L7,V3,M7} I { ! relation( X ), ! function( X )
% 75.70/76.09 , ! relation( Y ), ! function( Y ), ! in( Z, relation_dom( Y ) ), ! in(
% 75.70/76.09 apply( Y, Z ), relation_dom( X ) ), in( Z, relation_dom(
% 75.70/76.09 relation_composition( Y, X ) ) ) }.
% 75.70/76.09 parent0: (40444) {G0,W24,D4,L7,V3,M7} { ! relation( X ), ! function( X ),
% 75.70/76.09 ! relation( Y ), ! function( Y ), ! in( Z, relation_dom( Y ) ), ! in(
% 75.70/76.09 apply( Y, Z ), relation_dom( X ) ), in( Z, relation_dom(
% 75.70/76.09 relation_composition( Y, X ) ) ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 X := X
% 75.70/76.09 Y := Y
% 75.70/76.09 Z := Z
% 75.70/76.09 end
% 75.70/76.09 permutation0:
% 75.70/76.09 0 ==> 0
% 75.70/76.09 1 ==> 1
% 75.70/76.09 2 ==> 2
% 75.70/76.09 3 ==> 3
% 75.70/76.09 4 ==> 4
% 75.70/76.09 5 ==> 5
% 75.70/76.09 6 ==> 6
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 eqswap: (40534) {G0,W25,D4,L6,V3,M6} { apply( Y, apply( X, Z ) ) = apply(
% 75.70/76.09 relation_composition( X, Y ), Z ), ! relation( Y ), ! function( Y ), !
% 75.70/76.09 relation( X ), ! function( X ), ! in( Z, relation_dom(
% 75.70/76.09 relation_composition( X, Y ) ) ) }.
% 75.70/76.09 parent0[5]: (40445) {G0,W25,D4,L6,V3,M6} { ! relation( X ), ! function( X
% 75.70/76.09 ), ! relation( Y ), ! function( Y ), ! in( Z, relation_dom(
% 75.70/76.09 relation_composition( Y, X ) ) ), apply( relation_composition( Y, X ), Z
% 75.70/76.09 ) = apply( X, apply( Y, Z ) ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 X := Y
% 75.70/76.09 Y := X
% 75.70/76.09 Z := Z
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 subsumption: (45) {G0,W25,D4,L6,V3,M6} I { ! relation( X ), ! function( X )
% 75.70/76.09 , ! relation( Y ), ! function( Y ), ! in( Z, relation_dom(
% 75.70/76.09 relation_composition( Y, X ) ) ), apply( X, apply( Y, Z ) ) ==> apply(
% 75.70/76.09 relation_composition( Y, X ), Z ) }.
% 75.70/76.09 parent0: (40534) {G0,W25,D4,L6,V3,M6} { apply( Y, apply( X, Z ) ) = apply
% 75.70/76.09 ( relation_composition( X, Y ), Z ), ! relation( Y ), ! function( Y ), !
% 75.70/76.09 relation( X ), ! function( X ), ! in( Z, relation_dom(
% 75.70/76.09 relation_composition( X, Y ) ) ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 X := Y
% 75.70/76.09 Y := X
% 75.70/76.09 Z := Z
% 75.70/76.09 end
% 75.70/76.09 permutation0:
% 75.70/76.09 0 ==> 5
% 75.70/76.09 1 ==> 0
% 75.70/76.09 2 ==> 1
% 75.70/76.09 3 ==> 2
% 75.70/76.09 4 ==> 3
% 75.70/76.09 5 ==> 4
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 subsumption: (46) {G0,W2,D2,L1,V0,M1} I { relation( skol10 ) }.
% 75.70/76.09 parent0: (40446) {G0,W2,D2,L1,V0,M1} { relation( skol10 ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 end
% 75.70/76.09 permutation0:
% 75.70/76.09 0 ==> 0
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 subsumption: (47) {G0,W2,D2,L1,V0,M1} I { function( skol10 ) }.
% 75.70/76.09 parent0: (40447) {G0,W2,D2,L1,V0,M1} { function( skol10 ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 end
% 75.70/76.09 permutation0:
% 75.70/76.09 0 ==> 0
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 subsumption: (48) {G0,W2,D2,L1,V0,M1} I { relation( skol11 ) }.
% 75.70/76.09 parent0: (40448) {G0,W2,D2,L1,V0,M1} { relation( skol11 ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 end
% 75.70/76.09 permutation0:
% 75.70/76.09 0 ==> 0
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 subsumption: (49) {G0,W2,D2,L1,V0,M1} I { function( skol11 ) }.
% 75.70/76.09 parent0: (40449) {G0,W2,D2,L1,V0,M1} { function( skol11 ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 end
% 75.70/76.09 permutation0:
% 75.70/76.09 0 ==> 0
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 subsumption: (50) {G0,W4,D3,L1,V0,M1} I { in( skol12, relation_dom( skol10
% 75.70/76.09 ) ) }.
% 75.70/76.09 parent0: (40450) {G0,W4,D3,L1,V0,M1} { in( skol12, relation_dom( skol10 )
% 75.70/76.09 ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 end
% 75.70/76.09 permutation0:
% 75.70/76.09 0 ==> 0
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 eqswap: (40695) {G0,W11,D4,L1,V0,M1} { ! apply( skol11, apply( skol10,
% 75.70/76.09 skol12 ) ) = apply( relation_composition( skol10, skol11 ), skol12 ) }.
% 75.70/76.09 parent0[0]: (40451) {G0,W11,D4,L1,V0,M1} { ! apply( relation_composition(
% 75.70/76.09 skol10, skol11 ), skol12 ) = apply( skol11, apply( skol10, skol12 ) ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 subsumption: (51) {G0,W11,D4,L1,V0,M1} I { ! apply( skol11, apply( skol10,
% 75.70/76.09 skol12 ) ) ==> apply( relation_composition( skol10, skol11 ), skol12 )
% 75.70/76.09 }.
% 75.70/76.09 parent0: (40695) {G0,W11,D4,L1,V0,M1} { ! apply( skol11, apply( skol10,
% 75.70/76.09 skol12 ) ) = apply( relation_composition( skol10, skol11 ), skol12 ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 end
% 75.70/76.09 permutation0:
% 75.70/76.09 0 ==> 0
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 eqswap: (40696) {G0,W16,D3,L5,V3,M5} { ! apply( Y, Z ) = X, ! relation( Y
% 75.70/76.09 ), ! function( Y ), in( Z, relation_dom( Y ) ), X = empty_set }.
% 75.70/76.09 parent0[3]: (6) {G0,W16,D3,L5,V3,M5} I { ! relation( X ), ! function( X ),
% 75.70/76.09 in( Y, relation_dom( X ) ), ! Z = apply( X, Y ), Z = empty_set }.
% 75.70/76.09 substitution0:
% 75.70/76.09 X := Y
% 75.70/76.09 Y := Z
% 75.70/76.09 Z := X
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 eqrefl: (40699) {G0,W13,D3,L4,V2,M4} { ! relation( X ), ! function( X ),
% 75.70/76.09 in( Y, relation_dom( X ) ), apply( X, Y ) = empty_set }.
% 75.70/76.09 parent0[0]: (40696) {G0,W16,D3,L5,V3,M5} { ! apply( Y, Z ) = X, ! relation
% 75.70/76.09 ( Y ), ! function( Y ), in( Z, relation_dom( Y ) ), X = empty_set }.
% 75.70/76.09 substitution0:
% 75.70/76.09 X := apply( X, Y )
% 75.70/76.09 Y := X
% 75.70/76.09 Z := Y
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 subsumption: (62) {G1,W13,D3,L4,V2,M4} Q(6) { ! relation( X ), ! function(
% 75.70/76.09 X ), in( Y, relation_dom( X ) ), apply( X, Y ) ==> empty_set }.
% 75.70/76.09 parent0: (40699) {G0,W13,D3,L4,V2,M4} { ! relation( X ), ! function( X ),
% 75.70/76.09 in( Y, relation_dom( X ) ), apply( X, Y ) = empty_set }.
% 75.70/76.09 substitution0:
% 75.70/76.09 X := X
% 75.70/76.09 Y := Y
% 75.70/76.09 end
% 75.70/76.09 permutation0:
% 75.70/76.09 0 ==> 0
% 75.70/76.09 1 ==> 1
% 75.70/76.09 2 ==> 2
% 75.70/76.09 3 ==> 3
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 resolution: (40701) {G1,W6,D3,L2,V1,M2} { ! relation( X ), relation(
% 75.70/76.09 relation_composition( skol10, X ) ) }.
% 75.70/76.09 parent0[0]: (9) {G0,W8,D3,L3,V2,M3} I { ! relation( X ), ! relation( Y ),
% 75.70/76.09 relation( relation_composition( X, Y ) ) }.
% 75.70/76.09 parent1[0]: (46) {G0,W2,D2,L1,V0,M1} I { relation( skol10 ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 X := skol10
% 75.70/76.09 Y := X
% 75.70/76.09 end
% 75.70/76.09 substitution1:
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 subsumption: (180) {G1,W6,D3,L2,V1,M2} R(9,46) { ! relation( X ), relation
% 75.70/76.09 ( relation_composition( skol10, X ) ) }.
% 75.70/76.09 parent0: (40701) {G1,W6,D3,L2,V1,M2} { ! relation( X ), relation(
% 75.70/76.09 relation_composition( skol10, X ) ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 X := X
% 75.70/76.09 end
% 75.70/76.09 permutation0:
% 75.70/76.09 0 ==> 0
% 75.70/76.09 1 ==> 1
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 resolution: (40703) {G1,W10,D3,L4,V1,M4} { ! function( skol10 ), !
% 75.70/76.09 relation( X ), ! function( X ), function( relation_composition( skol10, X
% 75.70/76.09 ) ) }.
% 75.70/76.09 parent0[0]: (16) {G0,W12,D3,L5,V2,M5} I { ! relation( X ), ! function( X )
% 75.70/76.09 , ! relation( Y ), ! function( Y ), function( relation_composition( X, Y
% 75.70/76.09 ) ) }.
% 75.70/76.09 parent1[0]: (46) {G0,W2,D2,L1,V0,M1} I { relation( skol10 ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 X := skol10
% 75.70/76.09 Y := X
% 75.70/76.09 end
% 75.70/76.09 substitution1:
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 resolution: (40706) {G1,W8,D3,L3,V1,M3} { ! relation( X ), ! function( X )
% 75.70/76.09 , function( relation_composition( skol10, X ) ) }.
% 75.70/76.09 parent0[0]: (40703) {G1,W10,D3,L4,V1,M4} { ! function( skol10 ), !
% 75.70/76.09 relation( X ), ! function( X ), function( relation_composition( skol10, X
% 75.70/76.09 ) ) }.
% 75.70/76.09 parent1[0]: (47) {G0,W2,D2,L1,V0,M1} I { function( skol10 ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 X := X
% 75.70/76.09 end
% 75.70/76.09 substitution1:
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 subsumption: (238) {G1,W8,D3,L3,V1,M3} R(16,46);r(47) { ! relation( X ), !
% 75.70/76.09 function( X ), function( relation_composition( skol10, X ) ) }.
% 75.70/76.09 parent0: (40706) {G1,W8,D3,L3,V1,M3} { ! relation( X ), ! function( X ),
% 75.70/76.09 function( relation_composition( skol10, X ) ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 X := X
% 75.70/76.09 end
% 75.70/76.09 permutation0:
% 75.70/76.09 0 ==> 0
% 75.70/76.09 1 ==> 1
% 75.70/76.09 2 ==> 2
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 resolution: (40707) {G1,W22,D4,L6,V2,M6} { ! function( skol11 ), !
% 75.70/76.09 relation( X ), ! function( X ), ! in( Y, relation_dom( X ) ), ! in( apply
% 75.70/76.09 ( X, Y ), relation_dom( skol11 ) ), in( Y, relation_dom(
% 75.70/76.09 relation_composition( X, skol11 ) ) ) }.
% 75.70/76.09 parent0[0]: (44) {G0,W24,D4,L7,V3,M7} I { ! relation( X ), ! function( X )
% 75.70/76.09 , ! relation( Y ), ! function( Y ), ! in( Z, relation_dom( Y ) ), ! in(
% 75.70/76.09 apply( Y, Z ), relation_dom( X ) ), in( Z, relation_dom(
% 75.70/76.09 relation_composition( Y, X ) ) ) }.
% 75.70/76.09 parent1[0]: (48) {G0,W2,D2,L1,V0,M1} I { relation( skol11 ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 X := skol11
% 75.70/76.09 Y := X
% 75.70/76.09 Z := Y
% 75.70/76.09 end
% 75.70/76.09 substitution1:
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 resolution: (40710) {G1,W20,D4,L5,V2,M5} { ! relation( X ), ! function( X
% 75.70/76.09 ), ! in( Y, relation_dom( X ) ), ! in( apply( X, Y ), relation_dom(
% 75.70/76.09 skol11 ) ), in( Y, relation_dom( relation_composition( X, skol11 ) ) )
% 75.70/76.09 }.
% 75.70/76.09 parent0[0]: (40707) {G1,W22,D4,L6,V2,M6} { ! function( skol11 ), !
% 75.70/76.09 relation( X ), ! function( X ), ! in( Y, relation_dom( X ) ), ! in( apply
% 75.70/76.09 ( X, Y ), relation_dom( skol11 ) ), in( Y, relation_dom(
% 75.70/76.09 relation_composition( X, skol11 ) ) ) }.
% 75.70/76.09 parent1[0]: (49) {G0,W2,D2,L1,V0,M1} I { function( skol11 ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 X := X
% 75.70/76.09 Y := Y
% 75.70/76.09 end
% 75.70/76.09 substitution1:
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 subsumption: (505) {G1,W20,D4,L5,V2,M5} R(44,48);r(49) { ! relation( X ), !
% 75.70/76.09 function( X ), ! in( Y, relation_dom( X ) ), ! in( apply( X, Y ),
% 75.70/76.09 relation_dom( skol11 ) ), in( Y, relation_dom( relation_composition( X,
% 75.70/76.09 skol11 ) ) ) }.
% 75.70/76.09 parent0: (40710) {G1,W20,D4,L5,V2,M5} { ! relation( X ), ! function( X ),
% 75.70/76.09 ! in( Y, relation_dom( X ) ), ! in( apply( X, Y ), relation_dom( skol11 )
% 75.70/76.09 ), in( Y, relation_dom( relation_composition( X, skol11 ) ) ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 X := X
% 75.70/76.09 Y := Y
% 75.70/76.09 end
% 75.70/76.09 permutation0:
% 75.70/76.09 0 ==> 0
% 75.70/76.09 1 ==> 1
% 75.70/76.09 2 ==> 2
% 75.70/76.09 3 ==> 3
% 75.70/76.09 4 ==> 4
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 eqswap: (40711) {G0,W11,D4,L1,V0,M1} { ! apply( relation_composition(
% 75.70/76.09 skol10, skol11 ), skol12 ) ==> apply( skol11, apply( skol10, skol12 ) )
% 75.70/76.09 }.
% 75.70/76.09 parent0[0]: (51) {G0,W11,D4,L1,V0,M1} I { ! apply( skol11, apply( skol10,
% 75.70/76.09 skol12 ) ) ==> apply( relation_composition( skol10, skol11 ), skol12 )
% 75.70/76.09 }.
% 75.70/76.09 substitution0:
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 eqswap: (40712) {G0,W25,D4,L6,V3,M6} { apply( relation_composition( Y, X )
% 75.70/76.09 , Z ) ==> apply( X, apply( Y, Z ) ), ! relation( X ), ! function( X ), !
% 75.70/76.09 relation( Y ), ! function( Y ), ! in( Z, relation_dom(
% 75.70/76.09 relation_composition( Y, X ) ) ) }.
% 75.70/76.09 parent0[5]: (45) {G0,W25,D4,L6,V3,M6} I { ! relation( X ), ! function( X )
% 75.70/76.09 , ! relation( Y ), ! function( Y ), ! in( Z, relation_dom(
% 75.70/76.09 relation_composition( Y, X ) ) ), apply( X, apply( Y, Z ) ) ==> apply(
% 75.70/76.09 relation_composition( Y, X ), Z ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 X := X
% 75.70/76.09 Y := Y
% 75.70/76.09 Z := Z
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 resolution: (40713) {G1,W14,D4,L5,V0,M5} { ! relation( skol11 ), !
% 75.70/76.09 function( skol11 ), ! relation( skol10 ), ! function( skol10 ), ! in(
% 75.70/76.09 skol12, relation_dom( relation_composition( skol10, skol11 ) ) ) }.
% 75.70/76.09 parent0[0]: (40711) {G0,W11,D4,L1,V0,M1} { ! apply( relation_composition(
% 75.70/76.09 skol10, skol11 ), skol12 ) ==> apply( skol11, apply( skol10, skol12 ) )
% 75.70/76.09 }.
% 75.70/76.09 parent1[0]: (40712) {G0,W25,D4,L6,V3,M6} { apply( relation_composition( Y
% 75.70/76.09 , X ), Z ) ==> apply( X, apply( Y, Z ) ), ! relation( X ), ! function( X
% 75.70/76.09 ), ! relation( Y ), ! function( Y ), ! in( Z, relation_dom(
% 75.70/76.09 relation_composition( Y, X ) ) ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 end
% 75.70/76.09 substitution1:
% 75.70/76.09 X := skol11
% 75.70/76.09 Y := skol10
% 75.70/76.09 Z := skol12
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 resolution: (40714) {G1,W12,D4,L4,V0,M4} { ! function( skol11 ), !
% 75.70/76.09 relation( skol10 ), ! function( skol10 ), ! in( skol12, relation_dom(
% 75.70/76.09 relation_composition( skol10, skol11 ) ) ) }.
% 75.70/76.09 parent0[0]: (40713) {G1,W14,D4,L5,V0,M5} { ! relation( skol11 ), !
% 75.70/76.09 function( skol11 ), ! relation( skol10 ), ! function( skol10 ), ! in(
% 75.70/76.09 skol12, relation_dom( relation_composition( skol10, skol11 ) ) ) }.
% 75.70/76.09 parent1[0]: (48) {G0,W2,D2,L1,V0,M1} I { relation( skol11 ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 end
% 75.70/76.09 substitution1:
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 subsumption: (562) {G1,W12,D4,L4,V0,M4} R(51,45);r(48) { ! function( skol11
% 75.70/76.09 ), ! relation( skol10 ), ! function( skol10 ), ! in( skol12,
% 75.70/76.09 relation_dom( relation_composition( skol10, skol11 ) ) ) }.
% 75.70/76.09 parent0: (40714) {G1,W12,D4,L4,V0,M4} { ! function( skol11 ), ! relation(
% 75.70/76.09 skol10 ), ! function( skol10 ), ! in( skol12, relation_dom(
% 75.70/76.09 relation_composition( skol10, skol11 ) ) ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 end
% 75.70/76.09 permutation0:
% 75.70/76.09 0 ==> 0
% 75.70/76.09 1 ==> 1
% 75.70/76.09 2 ==> 2
% 75.70/76.09 3 ==> 3
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 eqswap: (40716) {G0,W11,D4,L1,V0,M1} { ! apply( relation_composition(
% 75.70/76.09 skol10, skol11 ), skol12 ) ==> apply( skol11, apply( skol10, skol12 ) )
% 75.70/76.09 }.
% 75.70/76.09 parent0[0]: (51) {G0,W11,D4,L1,V0,M1} I { ! apply( skol11, apply( skol10,
% 75.70/76.09 skol12 ) ) ==> apply( relation_composition( skol10, skol11 ), skol12 )
% 75.70/76.09 }.
% 75.70/76.09 substitution0:
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 paramod: (40718) {G1,W17,D4,L4,V0,M4} { ! apply( relation_composition(
% 75.70/76.09 skol10, skol11 ), skol12 ) ==> empty_set, ! relation( skol11 ), !
% 75.70/76.09 function( skol11 ), in( apply( skol10, skol12 ), relation_dom( skol11 ) )
% 75.70/76.09 }.
% 75.70/76.09 parent0[3]: (62) {G1,W13,D3,L4,V2,M4} Q(6) { ! relation( X ), ! function( X
% 75.70/76.09 ), in( Y, relation_dom( X ) ), apply( X, Y ) ==> empty_set }.
% 75.70/76.09 parent1[0; 7]: (40716) {G0,W11,D4,L1,V0,M1} { ! apply(
% 75.70/76.09 relation_composition( skol10, skol11 ), skol12 ) ==> apply( skol11, apply
% 75.70/76.09 ( skol10, skol12 ) ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 X := skol11
% 75.70/76.09 Y := apply( skol10, skol12 )
% 75.70/76.09 end
% 75.70/76.09 substitution1:
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 resolution: (40727) {G1,W15,D4,L3,V0,M3} { ! apply( relation_composition(
% 75.70/76.09 skol10, skol11 ), skol12 ) ==> empty_set, ! function( skol11 ), in( apply
% 75.70/76.09 ( skol10, skol12 ), relation_dom( skol11 ) ) }.
% 75.70/76.09 parent0[1]: (40718) {G1,W17,D4,L4,V0,M4} { ! apply( relation_composition(
% 75.70/76.09 skol10, skol11 ), skol12 ) ==> empty_set, ! relation( skol11 ), !
% 75.70/76.09 function( skol11 ), in( apply( skol10, skol12 ), relation_dom( skol11 ) )
% 75.70/76.09 }.
% 75.70/76.09 parent1[0]: (48) {G0,W2,D2,L1,V0,M1} I { relation( skol11 ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 end
% 75.70/76.09 substitution1:
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 subsumption: (767) {G2,W15,D4,L3,V0,M3} P(62,51);r(48) { ! apply(
% 75.70/76.09 relation_composition( skol10, skol11 ), skol12 ) ==> empty_set, !
% 75.70/76.09 function( skol11 ), in( apply( skol10, skol12 ), relation_dom( skol11 ) )
% 75.70/76.09 }.
% 75.70/76.09 parent0: (40727) {G1,W15,D4,L3,V0,M3} { ! apply( relation_composition(
% 75.70/76.09 skol10, skol11 ), skol12 ) ==> empty_set, ! function( skol11 ), in( apply
% 75.70/76.09 ( skol10, skol12 ), relation_dom( skol11 ) ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 end
% 75.70/76.09 permutation0:
% 75.70/76.09 0 ==> 0
% 75.70/76.09 1 ==> 1
% 75.70/76.09 2 ==> 2
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 resolution: (40729) {G1,W4,D3,L1,V0,M1} { relation( relation_composition(
% 75.70/76.09 skol10, skol11 ) ) }.
% 75.70/76.09 parent0[0]: (180) {G1,W6,D3,L2,V1,M2} R(9,46) { ! relation( X ), relation(
% 75.70/76.09 relation_composition( skol10, X ) ) }.
% 75.70/76.09 parent1[0]: (48) {G0,W2,D2,L1,V0,M1} I { relation( skol11 ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 X := skol11
% 75.70/76.09 end
% 75.70/76.09 substitution1:
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 subsumption: (2370) {G2,W4,D3,L1,V0,M1} R(180,48) { relation(
% 75.70/76.09 relation_composition( skol10, skol11 ) ) }.
% 75.70/76.09 parent0: (40729) {G1,W4,D3,L1,V0,M1} { relation( relation_composition(
% 75.70/76.09 skol10, skol11 ) ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 end
% 75.70/76.09 permutation0:
% 75.70/76.09 0 ==> 0
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 resolution: (40730) {G1,W6,D3,L2,V0,M2} { ! function( skol11 ), function(
% 75.70/76.09 relation_composition( skol10, skol11 ) ) }.
% 75.70/76.09 parent0[0]: (238) {G1,W8,D3,L3,V1,M3} R(16,46);r(47) { ! relation( X ), !
% 75.70/76.09 function( X ), function( relation_composition( skol10, X ) ) }.
% 75.70/76.09 parent1[0]: (48) {G0,W2,D2,L1,V0,M1} I { relation( skol11 ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 X := skol11
% 75.70/76.09 end
% 75.70/76.09 substitution1:
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 resolution: (40731) {G1,W4,D3,L1,V0,M1} { function( relation_composition(
% 75.70/76.09 skol10, skol11 ) ) }.
% 75.70/76.09 parent0[0]: (40730) {G1,W6,D3,L2,V0,M2} { ! function( skol11 ), function(
% 75.70/76.09 relation_composition( skol10, skol11 ) ) }.
% 75.70/76.09 parent1[0]: (49) {G0,W2,D2,L1,V0,M1} I { function( skol11 ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 end
% 75.70/76.09 substitution1:
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 subsumption: (12451) {G2,W4,D3,L1,V0,M1} R(238,48);r(49) { function(
% 75.70/76.09 relation_composition( skol10, skol11 ) ) }.
% 75.70/76.09 parent0: (40731) {G1,W4,D3,L1,V0,M1} { function( relation_composition(
% 75.70/76.09 skol10, skol11 ) ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 end
% 75.70/76.09 permutation0:
% 75.70/76.09 0 ==> 0
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 resolution: (40733) {G1,W13,D4,L2,V0,M2} { ! apply( relation_composition(
% 75.70/76.09 skol10, skol11 ), skol12 ) ==> empty_set, in( apply( skol10, skol12 ),
% 75.70/76.09 relation_dom( skol11 ) ) }.
% 75.70/76.09 parent0[1]: (767) {G2,W15,D4,L3,V0,M3} P(62,51);r(48) { ! apply(
% 75.70/76.09 relation_composition( skol10, skol11 ), skol12 ) ==> empty_set, !
% 75.70/76.09 function( skol11 ), in( apply( skol10, skol12 ), relation_dom( skol11 ) )
% 75.70/76.09 }.
% 75.70/76.09 parent1[0]: (49) {G0,W2,D2,L1,V0,M1} I { function( skol11 ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 end
% 75.70/76.09 substitution1:
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 subsumption: (20259) {G3,W13,D4,L2,V0,M2} S(767);r(49) { ! apply(
% 75.70/76.09 relation_composition( skol10, skol11 ), skol12 ) ==> empty_set, in( apply
% 75.70/76.09 ( skol10, skol12 ), relation_dom( skol11 ) ) }.
% 75.70/76.09 parent0: (40733) {G1,W13,D4,L2,V0,M2} { ! apply( relation_composition(
% 75.70/76.09 skol10, skol11 ), skol12 ) ==> empty_set, in( apply( skol10, skol12 ),
% 75.70/76.09 relation_dom( skol11 ) ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 end
% 75.70/76.09 permutation0:
% 75.70/76.09 0 ==> 0
% 75.70/76.09 1 ==> 1
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 resolution: (40735) {G1,W10,D4,L3,V0,M3} { ! relation( skol10 ), !
% 75.70/76.09 function( skol10 ), ! in( skol12, relation_dom( relation_composition(
% 75.70/76.09 skol10, skol11 ) ) ) }.
% 75.70/76.09 parent0[0]: (562) {G1,W12,D4,L4,V0,M4} R(51,45);r(48) { ! function( skol11
% 75.70/76.09 ), ! relation( skol10 ), ! function( skol10 ), ! in( skol12,
% 75.70/76.09 relation_dom( relation_composition( skol10, skol11 ) ) ) }.
% 75.70/76.09 parent1[0]: (49) {G0,W2,D2,L1,V0,M1} I { function( skol11 ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 end
% 75.70/76.09 substitution1:
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 resolution: (40736) {G1,W8,D4,L2,V0,M2} { ! function( skol10 ), ! in(
% 75.70/76.09 skol12, relation_dom( relation_composition( skol10, skol11 ) ) ) }.
% 75.70/76.09 parent0[0]: (40735) {G1,W10,D4,L3,V0,M3} { ! relation( skol10 ), !
% 75.70/76.09 function( skol10 ), ! in( skol12, relation_dom( relation_composition(
% 75.70/76.09 skol10, skol11 ) ) ) }.
% 75.70/76.09 parent1[0]: (46) {G0,W2,D2,L1,V0,M1} I { relation( skol10 ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 end
% 75.70/76.09 substitution1:
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 resolution: (40737) {G1,W6,D4,L1,V0,M1} { ! in( skol12, relation_dom(
% 75.70/76.09 relation_composition( skol10, skol11 ) ) ) }.
% 75.70/76.09 parent0[0]: (40736) {G1,W8,D4,L2,V0,M2} { ! function( skol10 ), ! in(
% 75.70/76.09 skol12, relation_dom( relation_composition( skol10, skol11 ) ) ) }.
% 75.70/76.09 parent1[0]: (47) {G0,W2,D2,L1,V0,M1} I { function( skol10 ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 end
% 75.70/76.09 substitution1:
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 subsumption: (20261) {G2,W6,D4,L1,V0,M1} S(562);r(49);r(46);r(47) { ! in(
% 75.70/76.09 skol12, relation_dom( relation_composition( skol10, skol11 ) ) ) }.
% 75.70/76.09 parent0: (40737) {G1,W6,D4,L1,V0,M1} { ! in( skol12, relation_dom(
% 75.70/76.09 relation_composition( skol10, skol11 ) ) ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 end
% 75.70/76.09 permutation0:
% 75.70/76.09 0 ==> 0
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 eqswap: (40738) {G1,W13,D3,L4,V2,M4} { empty_set ==> apply( X, Y ), !
% 75.70/76.09 relation( X ), ! function( X ), in( Y, relation_dom( X ) ) }.
% 75.70/76.09 parent0[3]: (62) {G1,W13,D3,L4,V2,M4} Q(6) { ! relation( X ), ! function( X
% 75.70/76.09 ), in( Y, relation_dom( X ) ), apply( X, Y ) ==> empty_set }.
% 75.70/76.09 substitution0:
% 75.70/76.09 X := X
% 75.70/76.09 Y := Y
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 resolution: (40739) {G2,W15,D4,L3,V0,M3} { empty_set ==> apply(
% 75.70/76.09 relation_composition( skol10, skol11 ), skol12 ), ! relation(
% 75.70/76.09 relation_composition( skol10, skol11 ) ), ! function(
% 75.70/76.09 relation_composition( skol10, skol11 ) ) }.
% 75.70/76.09 parent0[0]: (20261) {G2,W6,D4,L1,V0,M1} S(562);r(49);r(46);r(47) { ! in(
% 75.70/76.09 skol12, relation_dom( relation_composition( skol10, skol11 ) ) ) }.
% 75.70/76.09 parent1[3]: (40738) {G1,W13,D3,L4,V2,M4} { empty_set ==> apply( X, Y ), !
% 75.70/76.09 relation( X ), ! function( X ), in( Y, relation_dom( X ) ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 end
% 75.70/76.09 substitution1:
% 75.70/76.09 X := relation_composition( skol10, skol11 )
% 75.70/76.09 Y := skol12
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 resolution: (40740) {G3,W11,D4,L2,V0,M2} { empty_set ==> apply(
% 75.70/76.09 relation_composition( skol10, skol11 ), skol12 ), ! function(
% 75.70/76.09 relation_composition( skol10, skol11 ) ) }.
% 75.70/76.09 parent0[1]: (40739) {G2,W15,D4,L3,V0,M3} { empty_set ==> apply(
% 75.70/76.09 relation_composition( skol10, skol11 ), skol12 ), ! relation(
% 75.70/76.09 relation_composition( skol10, skol11 ) ), ! function(
% 75.70/76.09 relation_composition( skol10, skol11 ) ) }.
% 75.70/76.09 parent1[0]: (2370) {G2,W4,D3,L1,V0,M1} R(180,48) { relation(
% 75.70/76.09 relation_composition( skol10, skol11 ) ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 end
% 75.70/76.09 substitution1:
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 eqswap: (40741) {G3,W11,D4,L2,V0,M2} { apply( relation_composition( skol10
% 75.70/76.09 , skol11 ), skol12 ) ==> empty_set, ! function( relation_composition(
% 75.70/76.09 skol10, skol11 ) ) }.
% 75.70/76.09 parent0[0]: (40740) {G3,W11,D4,L2,V0,M2} { empty_set ==> apply(
% 75.70/76.09 relation_composition( skol10, skol11 ), skol12 ), ! function(
% 75.70/76.09 relation_composition( skol10, skol11 ) ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 subsumption: (20578) {G3,W11,D4,L2,V0,M2} R(20261,62);r(2370) { ! function
% 75.70/76.09 ( relation_composition( skol10, skol11 ) ), apply( relation_composition(
% 75.70/76.09 skol10, skol11 ), skol12 ) ==> empty_set }.
% 75.70/76.09 parent0: (40741) {G3,W11,D4,L2,V0,M2} { apply( relation_composition(
% 75.70/76.09 skol10, skol11 ), skol12 ) ==> empty_set, ! function(
% 75.70/76.09 relation_composition( skol10, skol11 ) ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 end
% 75.70/76.09 permutation0:
% 75.70/76.09 0 ==> 1
% 75.70/76.09 1 ==> 0
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 resolution: (40742) {G2,W14,D3,L4,V0,M4} { ! relation( skol10 ), !
% 75.70/76.09 function( skol10 ), ! in( skol12, relation_dom( skol10 ) ), ! in( apply(
% 75.70/76.09 skol10, skol12 ), relation_dom( skol11 ) ) }.
% 75.70/76.09 parent0[0]: (20261) {G2,W6,D4,L1,V0,M1} S(562);r(49);r(46);r(47) { ! in(
% 75.70/76.09 skol12, relation_dom( relation_composition( skol10, skol11 ) ) ) }.
% 75.70/76.09 parent1[4]: (505) {G1,W20,D4,L5,V2,M5} R(44,48);r(49) { ! relation( X ), !
% 75.70/76.09 function( X ), ! in( Y, relation_dom( X ) ), ! in( apply( X, Y ),
% 75.70/76.09 relation_dom( skol11 ) ), in( Y, relation_dom( relation_composition( X,
% 75.70/76.09 skol11 ) ) ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 end
% 75.70/76.09 substitution1:
% 75.70/76.09 X := skol10
% 75.70/76.09 Y := skol12
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 resolution: (40743) {G1,W12,D3,L3,V0,M3} { ! function( skol10 ), ! in(
% 75.70/76.09 skol12, relation_dom( skol10 ) ), ! in( apply( skol10, skol12 ),
% 75.70/76.09 relation_dom( skol11 ) ) }.
% 75.70/76.09 parent0[0]: (40742) {G2,W14,D3,L4,V0,M4} { ! relation( skol10 ), !
% 75.70/76.09 function( skol10 ), ! in( skol12, relation_dom( skol10 ) ), ! in( apply(
% 75.70/76.09 skol10, skol12 ), relation_dom( skol11 ) ) }.
% 75.70/76.09 parent1[0]: (46) {G0,W2,D2,L1,V0,M1} I { relation( skol10 ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 end
% 75.70/76.09 substitution1:
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 subsumption: (25033) {G3,W12,D3,L3,V0,M3} R(505,20261);r(46) { ! function(
% 75.70/76.09 skol10 ), ! in( skol12, relation_dom( skol10 ) ), ! in( apply( skol10,
% 75.70/76.09 skol12 ), relation_dom( skol11 ) ) }.
% 75.70/76.09 parent0: (40743) {G1,W12,D3,L3,V0,M3} { ! function( skol10 ), ! in( skol12
% 75.70/76.09 , relation_dom( skol10 ) ), ! in( apply( skol10, skol12 ), relation_dom(
% 75.70/76.09 skol11 ) ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 end
% 75.70/76.09 permutation0:
% 75.70/76.09 0 ==> 0
% 75.70/76.09 1 ==> 1
% 75.70/76.09 2 ==> 2
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 resolution: (40744) {G1,W10,D3,L2,V0,M2} { ! in( skol12, relation_dom(
% 75.70/76.09 skol10 ) ), ! in( apply( skol10, skol12 ), relation_dom( skol11 ) ) }.
% 75.70/76.09 parent0[0]: (25033) {G3,W12,D3,L3,V0,M3} R(505,20261);r(46) { ! function(
% 75.70/76.09 skol10 ), ! in( skol12, relation_dom( skol10 ) ), ! in( apply( skol10,
% 75.70/76.09 skol12 ), relation_dom( skol11 ) ) }.
% 75.70/76.09 parent1[0]: (47) {G0,W2,D2,L1,V0,M1} I { function( skol10 ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 end
% 75.70/76.09 substitution1:
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 resolution: (40745) {G1,W6,D3,L1,V0,M1} { ! in( apply( skol10, skol12 ),
% 75.70/76.09 relation_dom( skol11 ) ) }.
% 75.70/76.09 parent0[0]: (40744) {G1,W10,D3,L2,V0,M2} { ! in( skol12, relation_dom(
% 75.70/76.09 skol10 ) ), ! in( apply( skol10, skol12 ), relation_dom( skol11 ) ) }.
% 75.70/76.09 parent1[0]: (50) {G0,W4,D3,L1,V0,M1} I { in( skol12, relation_dom( skol10 )
% 75.70/76.09 ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 end
% 75.70/76.09 substitution1:
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 subsumption: (40296) {G4,W6,D3,L1,V0,M1} S(25033);r(47);r(50) { ! in( apply
% 75.70/76.09 ( skol10, skol12 ), relation_dom( skol11 ) ) }.
% 75.70/76.09 parent0: (40745) {G1,W6,D3,L1,V0,M1} { ! in( apply( skol10, skol12 ),
% 75.70/76.09 relation_dom( skol11 ) ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 end
% 75.70/76.09 permutation0:
% 75.70/76.09 0 ==> 0
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 resolution: (40747) {G3,W7,D4,L1,V0,M1} { apply( relation_composition(
% 75.70/76.09 skol10, skol11 ), skol12 ) ==> empty_set }.
% 75.70/76.09 parent0[0]: (20578) {G3,W11,D4,L2,V0,M2} R(20261,62);r(2370) { ! function(
% 75.70/76.09 relation_composition( skol10, skol11 ) ), apply( relation_composition(
% 75.70/76.09 skol10, skol11 ), skol12 ) ==> empty_set }.
% 75.70/76.09 parent1[0]: (12451) {G2,W4,D3,L1,V0,M1} R(238,48);r(49) { function(
% 75.70/76.09 relation_composition( skol10, skol11 ) ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 end
% 75.70/76.09 substitution1:
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 subsumption: (40364) {G4,W7,D4,L1,V0,M1} S(20578);r(12451) { apply(
% 75.70/76.09 relation_composition( skol10, skol11 ), skol12 ) ==> empty_set }.
% 75.70/76.09 parent0: (40747) {G3,W7,D4,L1,V0,M1} { apply( relation_composition( skol10
% 75.70/76.09 , skol11 ), skol12 ) ==> empty_set }.
% 75.70/76.09 substitution0:
% 75.70/76.09 end
% 75.70/76.09 permutation0:
% 75.70/76.09 0 ==> 0
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 paramod: (40751) {G4,W9,D3,L2,V0,M2} { ! empty_set ==> empty_set, in(
% 75.70/76.09 apply( skol10, skol12 ), relation_dom( skol11 ) ) }.
% 75.70/76.09 parent0[0]: (40364) {G4,W7,D4,L1,V0,M1} S(20578);r(12451) { apply(
% 75.70/76.09 relation_composition( skol10, skol11 ), skol12 ) ==> empty_set }.
% 75.70/76.09 parent1[0; 2]: (20259) {G3,W13,D4,L2,V0,M2} S(767);r(49) { ! apply(
% 75.70/76.09 relation_composition( skol10, skol11 ), skol12 ) ==> empty_set, in( apply
% 75.70/76.09 ( skol10, skol12 ), relation_dom( skol11 ) ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 end
% 75.70/76.09 substitution1:
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 eqrefl: (40752) {G0,W6,D3,L1,V0,M1} { in( apply( skol10, skol12 ),
% 75.70/76.09 relation_dom( skol11 ) ) }.
% 75.70/76.09 parent0[0]: (40751) {G4,W9,D3,L2,V0,M2} { ! empty_set ==> empty_set, in(
% 75.70/76.09 apply( skol10, skol12 ), relation_dom( skol11 ) ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 resolution: (40753) {G1,W0,D0,L0,V0,M0} { }.
% 75.70/76.09 parent0[0]: (40296) {G4,W6,D3,L1,V0,M1} S(25033);r(47);r(50) { ! in( apply
% 75.70/76.09 ( skol10, skol12 ), relation_dom( skol11 ) ) }.
% 75.70/76.09 parent1[0]: (40752) {G0,W6,D3,L1,V0,M1} { in( apply( skol10, skol12 ),
% 75.70/76.09 relation_dom( skol11 ) ) }.
% 75.70/76.09 substitution0:
% 75.70/76.09 end
% 75.70/76.09 substitution1:
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 subsumption: (40394) {G5,W0,D0,L0,V0,M0} S(20259);d(40364);q;r(40296) {
% 75.70/76.09 }.
% 75.70/76.09 parent0: (40753) {G1,W0,D0,L0,V0,M0} { }.
% 75.70/76.09 substitution0:
% 75.70/76.09 end
% 75.70/76.09 permutation0:
% 75.70/76.09 end
% 75.70/76.09
% 75.70/76.09 Proof check complete!
% 75.70/76.09
% 75.70/76.09 Memory use:
% 75.70/76.09
% 75.70/76.09 space for terms: 523339
% 75.70/76.09 space for clauses: 1889482
% 75.70/76.09
% 75.70/76.09
% 75.70/76.09 clauses generated: 727331
% 75.70/76.09 clauses kept: 40395
% 75.70/76.09 clauses selected: 1900
% 75.70/76.09 clauses deleted: 5886
% 75.70/76.09 clauses inuse deleted: 135
% 75.70/76.09
% 75.70/76.09 subsentry: 1359399
% 75.70/76.09 literals s-matched: 853875
% 75.70/76.09 literals matched: 776446
% 75.70/76.09 full subsumption: 136309
% 75.70/76.09
% 75.70/76.09 checksum: -954407775
% 75.70/76.09
% 75.70/76.09
% 75.70/76.09 Bliksem ended
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