TSTP Solution File: SEU009+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SEU009+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n028.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 07:10:15 EDT 2022
% Result : Theorem 114.82s 115.23s
% Output : Refutation 114.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SEU009+1 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Sun Jun 19 05:54:15 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.26/1.65 *** allocated 10000 integers for termspace/termends
% 1.26/1.65 *** allocated 10000 integers for clauses
% 1.26/1.65 *** allocated 10000 integers for justifications
% 1.26/1.65 Bliksem 1.12
% 1.26/1.65
% 1.26/1.65
% 1.26/1.65 Automatic Strategy Selection
% 1.26/1.65
% 1.26/1.65
% 1.26/1.65 Clauses:
% 1.26/1.65
% 1.26/1.65 { ! in( X, Y ), ! in( Y, X ) }.
% 1.26/1.65 { ! empty( X ), function( X ) }.
% 1.26/1.65 { ! empty( X ), relation( X ) }.
% 1.26/1.65 { ! relation( X ), ! relation( Y ), relation( relation_composition( X, Y )
% 1.26/1.65 ) }.
% 1.26/1.65 { relation( identity_relation( X ) ) }.
% 1.26/1.65 { element( skol1( X ), X ) }.
% 1.26/1.65 { ! empty( X ), ! relation( Y ), empty( relation_composition( Y, X ) ) }.
% 1.26/1.65 { ! empty( X ), ! relation( Y ), relation( relation_composition( Y, X ) ) }
% 1.26/1.65 .
% 1.26/1.65 { empty( empty_set ) }.
% 1.26/1.65 { relation( empty_set ) }.
% 1.26/1.65 { relation_empty_yielding( empty_set ) }.
% 1.26/1.65 { ! relation( X ), ! function( X ), ! relation( Y ), ! function( Y ),
% 1.26/1.65 relation( relation_composition( X, Y ) ) }.
% 1.26/1.65 { ! relation( X ), ! function( X ), ! relation( Y ), ! function( Y ),
% 1.26/1.65 function( relation_composition( X, Y ) ) }.
% 1.26/1.65 { ! empty( powerset( X ) ) }.
% 1.26/1.65 { empty( empty_set ) }.
% 1.26/1.65 { relation( identity_relation( X ) ) }.
% 1.26/1.65 { function( identity_relation( X ) ) }.
% 1.26/1.65 { empty( empty_set ) }.
% 1.26/1.65 { relation( empty_set ) }.
% 1.26/1.65 { empty( X ), ! relation( X ), ! empty( relation_dom( X ) ) }.
% 1.26/1.65 { ! empty( X ), empty( relation_dom( X ) ) }.
% 1.26/1.65 { ! empty( X ), relation( relation_dom( X ) ) }.
% 1.26/1.65 { ! empty( X ), ! relation( Y ), empty( relation_composition( X, Y ) ) }.
% 1.26/1.65 { ! empty( X ), ! relation( Y ), relation( relation_composition( X, Y ) ) }
% 1.26/1.65 .
% 1.26/1.65 { relation( skol2 ) }.
% 1.26/1.65 { function( skol2 ) }.
% 1.26/1.65 { empty( skol3 ) }.
% 1.26/1.65 { relation( skol3 ) }.
% 1.26/1.65 { empty( X ), ! empty( skol4( Y ) ) }.
% 1.26/1.65 { empty( X ), element( skol4( X ), powerset( X ) ) }.
% 1.26/1.65 { empty( skol5 ) }.
% 1.26/1.65 { ! empty( skol6 ) }.
% 1.26/1.65 { relation( skol6 ) }.
% 1.26/1.65 { empty( skol7( Y ) ) }.
% 1.26/1.65 { element( skol7( X ), powerset( X ) ) }.
% 1.26/1.65 { ! empty( skol8 ) }.
% 1.26/1.65 { relation( skol9 ) }.
% 1.26/1.65 { relation_empty_yielding( skol9 ) }.
% 1.26/1.65 { subset( X, X ) }.
% 1.26/1.65 { ! in( X, Y ), element( X, Y ) }.
% 1.26/1.65 { ! relation( X ), ! function( X ), ! relation( Y ), ! function( Y ), ! in
% 1.26/1.65 ( Z, relation_dom( relation_composition( Y, X ) ) ), in( Z, relation_dom
% 1.26/1.65 ( Y ) ) }.
% 1.26/1.65 { ! relation( X ), ! function( X ), ! relation( Y ), ! function( Y ), ! in
% 1.26/1.65 ( Z, relation_dom( relation_composition( Y, X ) ) ), in( apply( Y, Z ),
% 1.26/1.65 relation_dom( X ) ) }.
% 1.26/1.65 { ! relation( X ), ! function( X ), ! relation( Y ), ! function( Y ), ! in
% 1.26/1.65 ( Z, relation_dom( Y ) ), ! in( apply( Y, Z ), relation_dom( X ) ), in( Z
% 1.26/1.65 , relation_dom( relation_composition( Y, X ) ) ) }.
% 1.26/1.65 { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 1.26/1.65 { ! relation( X ), ! function( X ), ! X = identity_relation( Y ),
% 1.26/1.65 relation_dom( X ) = Y }.
% 1.26/1.65 { ! relation( X ), ! function( X ), ! X = identity_relation( Y ), alpha1( X
% 1.26/1.65 , Y ) }.
% 1.26/1.65 { ! relation( X ), ! function( X ), ! relation_dom( X ) = Y, ! alpha1( X, Y
% 1.26/1.65 ), X = identity_relation( Y ) }.
% 1.26/1.65 { ! alpha1( X, Y ), ! in( Z, Y ), apply( X, Z ) = Z }.
% 1.26/1.65 { in( skol10( Z, Y ), Y ), alpha1( X, Y ) }.
% 1.26/1.65 { ! apply( X, skol10( X, Y ) ) = skol10( X, Y ), alpha1( X, Y ) }.
% 1.26/1.65 { ! element( X, powerset( Y ) ), subset( X, Y ) }.
% 1.26/1.65 { ! subset( X, Y ), element( X, powerset( Y ) ) }.
% 1.26/1.65 { relation( skol11 ) }.
% 1.26/1.65 { function( skol11 ) }.
% 1.26/1.65 { alpha2( skol11, skol12, skol13 ), in( skol13, relation_dom( skol11 ) ) }
% 1.26/1.65 .
% 1.26/1.65 { alpha2( skol11, skol12, skol13 ), in( apply( skol11, skol13 ), skol12 ) }
% 1.26/1.65 .
% 1.26/1.65 { alpha2( skol11, skol12, skol13 ), ! in( skol13, relation_dom(
% 1.26/1.65 relation_composition( skol11, identity_relation( skol12 ) ) ) ) }.
% 1.26/1.65 { ! alpha2( X, Y, Z ), in( Z, relation_dom( relation_composition( X,
% 1.26/1.65 identity_relation( Y ) ) ) ) }.
% 1.26/1.65 { ! alpha2( X, Y, Z ), ! in( Z, relation_dom( X ) ), ! in( apply( X, Z ), Y
% 1.26/1.65 ) }.
% 1.26/1.65 { ! in( Z, relation_dom( relation_composition( X, identity_relation( Y ) )
% 1.26/1.65 ) ), in( Z, relation_dom( X ) ), alpha2( X, Y, Z ) }.
% 1.26/1.65 { ! in( Z, relation_dom( relation_composition( X, identity_relation( Y ) )
% 1.26/1.65 ) ), in( apply( X, Z ), Y ), alpha2( X, Y, Z ) }.
% 1.26/1.65 { ! in( X, Z ), ! element( Z, powerset( Y ) ), element( X, Y ) }.
% 1.26/1.65 { ! in( X, Y ), ! element( Y, powerset( Z ) ), ! empty( Z ) }.
% 1.26/1.65 { ! empty( X ), X = empty_set }.
% 1.26/1.65 { ! in( X, Y ), ! empty( Y ) }.
% 1.26/1.65 { ! empty( X ), X = Y, ! empty( Y ) }.
% 1.26/1.65
% 1.26/1.65 percentage equality = 0.065693, percentage horn = 0.885246
% 95.75/96.23 This is a problem with some equality
% 95.75/96.23
% 95.75/96.23
% 95.75/96.23
% 95.75/96.23 Options Used:
% 95.75/96.23
% 95.75/96.23 useres = 1
% 95.75/96.23 useparamod = 1
% 95.75/96.23 useeqrefl = 1
% 95.75/96.23 useeqfact = 1
% 95.75/96.23 usefactor = 1
% 95.75/96.23 usesimpsplitting = 0
% 95.75/96.23 usesimpdemod = 5
% 95.75/96.23 usesimpres = 3
% 95.75/96.23
% 95.75/96.23 resimpinuse = 1000
% 95.75/96.23 resimpclauses = 20000
% 95.75/96.23 substype = eqrewr
% 95.75/96.23 backwardsubs = 1
% 95.75/96.23 selectoldest = 5
% 95.75/96.23
% 95.75/96.23 litorderings [0] = split
% 95.75/96.23 litorderings [1] = extend the termordering, first sorting on arguments
% 95.75/96.23
% 95.75/96.23 termordering = kbo
% 95.75/96.23
% 95.75/96.23 litapriori = 0
% 95.75/96.23 termapriori = 1
% 95.75/96.23 litaposteriori = 0
% 95.75/96.23 termaposteriori = 0
% 95.75/96.23 demodaposteriori = 0
% 95.75/96.23 ordereqreflfact = 0
% 95.75/96.23
% 95.75/96.23 litselect = negord
% 95.75/96.23
% 95.75/96.23 maxweight = 15
% 95.75/96.23 maxdepth = 30000
% 95.75/96.23 maxlength = 115
% 95.75/96.23 maxnrvars = 195
% 95.75/96.23 excuselevel = 1
% 95.75/96.23 increasemaxweight = 1
% 95.75/96.23
% 95.75/96.23 maxselected = 10000000
% 95.75/96.23 maxnrclauses = 10000000
% 95.75/96.23
% 95.75/96.23 showgenerated = 0
% 95.75/96.23 showkept = 0
% 95.75/96.23 showselected = 0
% 95.75/96.23 showdeleted = 0
% 95.75/96.23 showresimp = 1
% 95.75/96.23 showstatus = 2000
% 95.75/96.23
% 95.75/96.23 prologoutput = 0
% 95.75/96.23 nrgoals = 5000000
% 95.75/96.23 totalproof = 1
% 95.75/96.23
% 95.75/96.23 Symbols occurring in the translation:
% 95.75/96.23
% 95.75/96.23 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 95.75/96.23 . [1, 2] (w:1, o:34, a:1, s:1, b:0),
% 95.75/96.23 ! [4, 1] (w:0, o:19, a:1, s:1, b:0),
% 95.75/96.23 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 95.75/96.23 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 95.75/96.23 in [37, 2] (w:1, o:58, a:1, s:1, b:0),
% 95.75/96.23 empty [38, 1] (w:1, o:24, a:1, s:1, b:0),
% 95.75/96.23 function [39, 1] (w:1, o:25, a:1, s:1, b:0),
% 95.75/96.23 relation [40, 1] (w:1, o:26, a:1, s:1, b:0),
% 95.75/96.23 relation_composition [41, 2] (w:1, o:59, a:1, s:1, b:0),
% 95.75/96.23 identity_relation [42, 1] (w:1, o:27, a:1, s:1, b:0),
% 95.75/96.23 element [43, 2] (w:1, o:60, a:1, s:1, b:0),
% 95.75/96.23 empty_set [44, 0] (w:1, o:8, a:1, s:1, b:0),
% 95.75/96.23 relation_empty_yielding [45, 1] (w:1, o:29, a:1, s:1, b:0),
% 95.75/96.23 powerset [46, 1] (w:1, o:30, a:1, s:1, b:0),
% 95.75/96.23 relation_dom [47, 1] (w:1, o:28, a:1, s:1, b:0),
% 95.75/96.23 subset [48, 2] (w:1, o:61, a:1, s:1, b:0),
% 95.75/96.23 apply [50, 2] (w:1, o:62, a:1, s:1, b:0),
% 95.75/96.23 alpha1 [51, 2] (w:1, o:63, a:1, s:1, b:1),
% 95.75/96.23 alpha2 [52, 3] (w:1, o:65, a:1, s:1, b:1),
% 95.75/96.23 skol1 [53, 1] (w:1, o:31, a:1, s:1, b:1),
% 95.75/96.23 skol2 [54, 0] (w:1, o:13, a:1, s:1, b:1),
% 95.75/96.23 skol3 [55, 0] (w:1, o:14, a:1, s:1, b:1),
% 95.75/96.23 skol4 [56, 1] (w:1, o:32, a:1, s:1, b:1),
% 95.75/96.23 skol5 [57, 0] (w:1, o:15, a:1, s:1, b:1),
% 95.75/96.23 skol6 [58, 0] (w:1, o:16, a:1, s:1, b:1),
% 95.75/96.23 skol7 [59, 1] (w:1, o:33, a:1, s:1, b:1),
% 95.75/96.23 skol8 [60, 0] (w:1, o:17, a:1, s:1, b:1),
% 95.75/96.23 skol9 [61, 0] (w:1, o:18, a:1, s:1, b:1),
% 95.75/96.23 skol10 [62, 2] (w:1, o:64, a:1, s:1, b:1),
% 95.75/96.23 skol11 [63, 0] (w:1, o:10, a:1, s:1, b:1),
% 95.75/96.23 skol12 [64, 0] (w:1, o:11, a:1, s:1, b:1),
% 95.75/96.23 skol13 [65, 0] (w:1, o:12, a:1, s:1, b:1).
% 95.75/96.23
% 95.75/96.23
% 95.75/96.23 Starting Search:
% 95.75/96.23
% 95.75/96.23 *** allocated 15000 integers for clauses
% 95.75/96.23 *** allocated 22500 integers for clauses
% 95.75/96.23 *** allocated 33750 integers for clauses
% 95.75/96.23 *** allocated 15000 integers for termspace/termends
% 95.75/96.23 *** allocated 50625 integers for clauses
% 95.75/96.23 *** allocated 22500 integers for termspace/termends
% 95.75/96.23 Resimplifying inuse:
% 95.75/96.23 Done
% 95.75/96.23
% 95.75/96.23 *** allocated 75937 integers for clauses
% 95.75/96.23 *** allocated 33750 integers for termspace/termends
% 95.75/96.23 *** allocated 113905 integers for clauses
% 95.75/96.23
% 95.75/96.23 Intermediate Status:
% 95.75/96.23 Generated: 6180
% 95.75/96.23 Kept: 2006
% 95.75/96.23 Inuse: 205
% 95.75/96.23 Deleted: 73
% 95.75/96.23 Deletedinuse: 29
% 95.75/96.23
% 95.75/96.23 Resimplifying inuse:
% 95.75/96.23 Done
% 95.75/96.23
% 95.75/96.23 *** allocated 170857 integers for clauses
% 95.75/96.23 *** allocated 50625 integers for termspace/termends
% 95.75/96.23 Resimplifying inuse:
% 95.75/96.23 Done
% 95.75/96.23
% 95.75/96.23 *** allocated 256285 integers for clauses
% 95.75/96.23 *** allocated 75937 integers for termspace/termends
% 95.75/96.23
% 95.75/96.23 Intermediate Status:
% 95.75/96.23 Generated: 11125
% 95.75/96.23 Kept: 4006
% 95.75/96.23 Inuse: 285
% 95.75/96.23 Deleted: 91
% 95.75/96.23 Deletedinuse: 34
% 95.75/96.23
% 95.75/96.23 Resimplifying inuse:
% 95.75/96.23 Done
% 95.75/96.23
% 95.75/96.23 Resimplifying inuse:
% 95.75/96.23 Done
% 95.75/96.23
% 95.75/96.23 *** allocated 384427 integers for clauses
% 95.75/96.23 *** allocated 113905 integers for termspace/termends
% 95.75/96.23
% 95.75/96.23 Intermediate Status:
% 95.75/96.23 Generated: 18697
% 95.75/96.23 Kept: 6051
% 95.75/96.23 Inuse: 369
% 95.75/96.23 Deleted: 201
% 95.75/96.23 Deletedinuse: 54
% 95.75/96.23
% 95.75/96.23 Resimplifying inuse:
% 95.75/96.23 Done
% 95.75/96.23
% 95.75/96.23 Resimplifying inuse:
% 95.75/96.23 Done
% 95.75/96.23
% 95.75/96.23 *** allocated 576640 integers for clauses
% 95.75/96.23
% 95.75/96.23 Intermediate Status:
% 95.75/96.23 Generated: 27423
% 95.75/96.23 Kept: 8054
% 114.82/115.23 Inuse: 444
% 114.82/115.23 Deleted: 253
% 114.82/115.23 Deletedinuse: 67
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23 *** allocated 170857 integers for termspace/termends
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23
% 114.82/115.23 Intermediate Status:
% 114.82/115.23 Generated: 34940
% 114.82/115.23 Kept: 10068
% 114.82/115.23 Inuse: 496
% 114.82/115.23 Deleted: 288
% 114.82/115.23 Deletedinuse: 72
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23 *** allocated 864960 integers for clauses
% 114.82/115.23
% 114.82/115.23 Intermediate Status:
% 114.82/115.23 Generated: 41951
% 114.82/115.23 Kept: 12092
% 114.82/115.23 Inuse: 539
% 114.82/115.23 Deleted: 311
% 114.82/115.23 Deletedinuse: 72
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23 *** allocated 256285 integers for termspace/termends
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23
% 114.82/115.23 Intermediate Status:
% 114.82/115.23 Generated: 55800
% 114.82/115.23 Kept: 14171
% 114.82/115.23 Inuse: 650
% 114.82/115.23 Deleted: 384
% 114.82/115.23 Deletedinuse: 73
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23
% 114.82/115.23 Intermediate Status:
% 114.82/115.23 Generated: 71032
% 114.82/115.23 Kept: 16198
% 114.82/115.23 Inuse: 744
% 114.82/115.23 Deleted: 422
% 114.82/115.23 Deletedinuse: 80
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23 *** allocated 1297440 integers for clauses
% 114.82/115.23
% 114.82/115.23 Intermediate Status:
% 114.82/115.23 Generated: 95638
% 114.82/115.23 Kept: 18278
% 114.82/115.23 Inuse: 880
% 114.82/115.23 Deleted: 453
% 114.82/115.23 Deletedinuse: 99
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23 *** allocated 384427 integers for termspace/termends
% 114.82/115.23 Resimplifying clauses:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23
% 114.82/115.23 Intermediate Status:
% 114.82/115.23 Generated: 135859
% 114.82/115.23 Kept: 20579
% 114.82/115.23 Inuse: 1009
% 114.82/115.23 Deleted: 4319
% 114.82/115.23 Deletedinuse: 99
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23
% 114.82/115.23 Intermediate Status:
% 114.82/115.23 Generated: 148216
% 114.82/115.23 Kept: 22688
% 114.82/115.23 Inuse: 1081
% 114.82/115.23 Deleted: 4329
% 114.82/115.23 Deletedinuse: 108
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23
% 114.82/115.23 Intermediate Status:
% 114.82/115.23 Generated: 167765
% 114.82/115.23 Kept: 25411
% 114.82/115.23 Inuse: 1115
% 114.82/115.23 Deleted: 4341
% 114.82/115.23 Deletedinuse: 109
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23 *** allocated 1946160 integers for clauses
% 114.82/115.23
% 114.82/115.23 Intermediate Status:
% 114.82/115.23 Generated: 179956
% 114.82/115.23 Kept: 27597
% 114.82/115.23 Inuse: 1130
% 114.82/115.23 Deleted: 4343
% 114.82/115.23 Deletedinuse: 111
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23 *** allocated 576640 integers for termspace/termends
% 114.82/115.23
% 114.82/115.23 Intermediate Status:
% 114.82/115.23 Generated: 188282
% 114.82/115.23 Kept: 30835
% 114.82/115.23 Inuse: 1140
% 114.82/115.23 Deleted: 4343
% 114.82/115.23 Deletedinuse: 111
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23
% 114.82/115.23 Intermediate Status:
% 114.82/115.23 Generated: 210121
% 114.82/115.23 Kept: 32855
% 114.82/115.23 Inuse: 1164
% 114.82/115.23 Deleted: 4343
% 114.82/115.23 Deletedinuse: 111
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23
% 114.82/115.23 Intermediate Status:
% 114.82/115.23 Generated: 256747
% 114.82/115.23 Kept: 34874
% 114.82/115.23 Inuse: 1253
% 114.82/115.23 Deleted: 4344
% 114.82/115.23 Deletedinuse: 112
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23
% 114.82/115.23 Intermediate Status:
% 114.82/115.23 Generated: 278654
% 114.82/115.23 Kept: 36931
% 114.82/115.23 Inuse: 1334
% 114.82/115.23 Deleted: 4352
% 114.82/115.23 Deletedinuse: 114
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23
% 114.82/115.23 Intermediate Status:
% 114.82/115.23 Generated: 303918
% 114.82/115.23 Kept: 38962
% 114.82/115.23 Inuse: 1403
% 114.82/115.23 Deleted: 4361
% 114.82/115.23 Deletedinuse: 114
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23 Resimplifying clauses:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23
% 114.82/115.23 Intermediate Status:
% 114.82/115.23 Generated: 332753
% 114.82/115.23 Kept: 40993
% 114.82/115.23 Inuse: 1469
% 114.82/115.23 Deleted: 6133
% 114.82/115.23 Deletedinuse: 114
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23 *** allocated 864960 integers for termspace/termends
% 114.82/115.23 *** allocated 2919240 integers for clauses
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23
% 114.82/115.23 Intermediate Status:
% 114.82/115.23 Generated: 357466
% 114.82/115.23 Kept: 43201
% 114.82/115.23 Inuse: 1513
% 114.82/115.23 Deleted: 6139
% 114.82/115.23 Deletedinuse: 119
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23
% 114.82/115.23 Intermediate Status:
% 114.82/115.23 Generated: 437407
% 114.82/115.23 Kept: 45244
% 114.82/115.23 Inuse: 1595
% 114.82/115.23 Deleted: 6155
% 114.82/115.23 Deletedinuse: 119
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23
% 114.82/115.23 Intermediate Status:
% 114.82/115.23 Generated: 467218
% 114.82/115.23 Kept: 47272
% 114.82/115.23 Inuse: 1662
% 114.82/115.23 Deleted: 6155
% 114.82/115.23 Deletedinuse: 119
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23
% 114.82/115.23 Intermediate Status:
% 114.82/115.23 Generated: 518982
% 114.82/115.23 Kept: 49370
% 114.82/115.23 Inuse: 1727
% 114.82/115.23 Deleted: 6158
% 114.82/115.23 Deletedinuse: 120
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23
% 114.82/115.23 Intermediate Status:
% 114.82/115.23 Generated: 542868
% 114.82/115.23 Kept: 51406
% 114.82/115.23 Inuse: 1776
% 114.82/115.23 Deleted: 6163
% 114.82/115.23 Deletedinuse: 123
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23
% 114.82/115.23 Intermediate Status:
% 114.82/115.23 Generated: 578871
% 114.82/115.23 Kept: 53427
% 114.82/115.23 Inuse: 1827
% 114.82/115.23 Deleted: 6163
% 114.82/115.23 Deletedinuse: 123
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23
% 114.82/115.23 Intermediate Status:
% 114.82/115.23 Generated: 607962
% 114.82/115.23 Kept: 55452
% 114.82/115.23 Inuse: 1868
% 114.82/115.23 Deleted: 6163
% 114.82/115.23 Deletedinuse: 123
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23
% 114.82/115.23 Intermediate Status:
% 114.82/115.23 Generated: 638291
% 114.82/115.23 Kept: 57473
% 114.82/115.23 Inuse: 1926
% 114.82/115.23 Deleted: 6163
% 114.82/115.23 Deletedinuse: 123
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23
% 114.82/115.23 Intermediate Status:
% 114.82/115.23 Generated: 675818
% 114.82/115.23 Kept: 59624
% 114.82/115.23 Inuse: 1961
% 114.82/115.23 Deleted: 6163
% 114.82/115.23 Deletedinuse: 123
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23 Resimplifying inuse:
% 114.82/115.23 Done
% 114.82/115.23
% 114.82/115.23 Resimplifying clauses:
% 114.82/115.23
% 114.82/115.23 Bliksems!, er is een bewijs:
% 114.82/115.23 % SZS status Theorem
% 114.82/115.23 % SZS output start Refutation
% 114.82/115.23
% 114.82/115.23 (4) {G0,W3,D3,L1,V1,M1} I { relation( identity_relation( X ) ) }.
% 114.82/115.23 (13) {G0,W3,D3,L1,V1,M1} I { function( identity_relation( X ) ) }.
% 114.82/115.23 (35) {G0,W18,D4,L6,V3,M6} I { ! relation( X ), ! function( X ), ! relation
% 114.82/115.23 ( Y ), ! function( Y ), ! in( Z, relation_dom( relation_composition( Y, X
% 114.82/115.23 ) ) ), in( Z, relation_dom( Y ) ) }.
% 114.82/115.23 (36) {G0,W20,D4,L6,V3,M6} I { ! relation( X ), ! function( X ), ! relation
% 114.82/115.23 ( Y ), ! function( Y ), ! in( Z, relation_dom( relation_composition( Y, X
% 114.82/115.23 ) ) ), in( apply( Y, Z ), relation_dom( X ) ) }.
% 114.82/115.23 (37) {G0,W24,D4,L7,V3,M7} I { ! relation( X ), ! function( X ), ! relation
% 114.82/115.23 ( Y ), ! function( Y ), ! in( Z, relation_dom( Y ) ), ! in( apply( Y, Z )
% 114.82/115.23 , relation_dom( X ) ), in( Z, relation_dom( relation_composition( Y, X )
% 114.82/115.23 ) ) }.
% 114.82/115.23 (39) {G0,W12,D3,L4,V2,M4} I { ! relation( X ), ! function( X ), ! X =
% 114.82/115.23 identity_relation( Y ), relation_dom( X ) = Y }.
% 114.82/115.23 (47) {G0,W2,D2,L1,V0,M1} I { relation( skol11 ) }.
% 114.82/115.23 (48) {G0,W2,D2,L1,V0,M1} I { function( skol11 ) }.
% 114.82/115.23 (49) {G0,W8,D3,L2,V0,M2} I { alpha2( skol11, skol12, skol13 ), in( skol13,
% 114.82/115.23 relation_dom( skol11 ) ) }.
% 114.82/115.23 (50) {G0,W9,D3,L2,V0,M2} I { alpha2( skol11, skol12, skol13 ), in( apply(
% 114.82/115.23 skol11, skol13 ), skol12 ) }.
% 114.82/115.23 (51) {G0,W11,D5,L2,V0,M2} I { alpha2( skol11, skol12, skol13 ), ! in(
% 114.82/115.23 skol13, relation_dom( relation_composition( skol11, identity_relation(
% 114.82/115.23 skol12 ) ) ) ) }.
% 114.82/115.23 (52) {G0,W11,D5,L2,V3,M2} I { ! alpha2( X, Y, Z ), in( Z, relation_dom(
% 114.82/115.23 relation_composition( X, identity_relation( Y ) ) ) ) }.
% 114.82/115.23 (53) {G0,W13,D3,L3,V3,M3} I { ! alpha2( X, Y, Z ), ! in( Z, relation_dom( X
% 114.82/115.23 ) ), ! in( apply( X, Z ), Y ) }.
% 114.82/115.23 (269) {G1,W15,D5,L4,V3,M4} R(35,13);r(4) { ! relation( Y ), ! function( Y )
% 114.82/115.23 , ! in( Z, relation_dom( relation_composition( Y, identity_relation( X )
% 114.82/115.23 ) ) ), in( Z, relation_dom( Y ) ) }.
% 114.82/115.23 (331) {G1,W16,D4,L4,V2,M4} R(36,47);r(48) { ! relation( X ), ! function( X
% 114.82/115.23 ), ! in( Y, relation_dom( relation_composition( skol11, X ) ) ), in(
% 114.82/115.23 apply( skol11, Y ), relation_dom( X ) ) }.
% 114.82/115.23 (357) {G1,W20,D4,L5,V2,M5} R(37,47);r(48) { ! relation( X ), ! function( X
% 114.82/115.23 ), ! in( Y, relation_dom( skol11 ) ), ! in( apply( skol11, Y ),
% 114.82/115.23 relation_dom( X ) ), in( Y, relation_dom( relation_composition( skol11, X
% 114.82/115.23 ) ) ) }.
% 114.82/115.23 (430) {G1,W10,D4,L2,V2,M2} R(39,13);r(4) { ! identity_relation( X ) =
% 114.82/115.23 identity_relation( Y ), relation_dom( identity_relation( X ) ) = Y }.
% 114.82/115.23 (549) {G2,W5,D4,L1,V1,M1} Q(430) { relation_dom( identity_relation( X ) )
% 114.82/115.23 ==> X }.
% 114.82/115.23 (909) {G1,W12,D5,L2,V0,M2} R(52,50) { in( skol13, relation_dom(
% 114.82/115.23 relation_composition( skol11, identity_relation( skol12 ) ) ) ), in(
% 114.82/115.23 apply( skol11, skol13 ), skol12 ) }.
% 114.82/115.23 (910) {G1,W11,D5,L2,V0,M2} R(52,49) { in( skol13, relation_dom(
% 114.82/115.23 relation_composition( skol11, identity_relation( skol12 ) ) ) ), in(
% 114.82/115.23 skol13, relation_dom( skol11 ) ) }.
% 114.82/115.23 (13975) {G2,W11,D5,L2,V2,M2} R(269,47);r(48) { ! in( X, relation_dom(
% 114.82/115.23 relation_composition( skol11, identity_relation( Y ) ) ) ), in( X,
% 114.82/115.23 relation_dom( skol11 ) ) }.
% 114.82/115.23 (17811) {G3,W12,D3,L3,V2,M3} R(331,52);d(549);r(4) { ! function(
% 114.82/115.23 identity_relation( X ) ), ! alpha2( skol11, X, Y ), in( apply( skol11, Y
% 114.82/115.23 ), X ) }.
% 114.82/115.23 (17812) {G3,W12,D5,L2,V2,M2} R(331,13);d(549);r(4) { ! in( Y, relation_dom
% 114.82/115.23 ( relation_composition( skol11, identity_relation( X ) ) ) ), in( apply(
% 114.82/115.23 skol11, Y ), X ) }.
% 114.82/115.23 (20058) {G4,W9,D3,L2,V2,M2} S(17811);r(13) { ! alpha2( skol11, X, Y ), in(
% 114.82/115.23 apply( skol11, Y ), X ) }.
% 114.82/115.23 (20508) {G4,W5,D3,L1,V0,M1} S(909);r(17812) { in( apply( skol11, skol13 ),
% 114.82/115.23 skol12 ) }.
% 114.82/115.23 (20509) {G3,W4,D3,L1,V0,M1} S(910);r(13975) { in( skol13, relation_dom(
% 114.82/115.23 skol11 ) ) }.
% 114.82/115.23 (20586) {G5,W4,D2,L1,V1,M1} R(20509,53);r(20058) { ! alpha2( skol11, X,
% 114.82/115.23 skol13 ) }.
% 114.82/115.23 (20708) {G6,W7,D5,L1,V0,M1} R(20586,51) { ! in( skol13, relation_dom(
% 114.82/115.23 relation_composition( skol11, identity_relation( skol12 ) ) ) ) }.
% 114.82/115.23 (56366) {G7,W12,D3,L3,V0,M3} R(20708,357);d(549);r(4) { ! function(
% 114.82/115.23 identity_relation( skol12 ) ), ! in( skol13, relation_dom( skol11 ) ), !
% 114.82/115.23 in( apply( skol11, skol13 ), skol12 ) }.
% 114.82/115.23 (60867) {G8,W0,D0,L0,V0,M0} S(56366);r(13);r(20509);r(20508) { }.
% 114.82/115.23
% 114.82/115.23
% 114.82/115.23 % SZS output end Refutation
% 114.82/115.23 found a proof!
% 114.82/115.23
% 114.82/115.23
% 114.82/115.23 Unprocessed initial clauses:
% 114.82/115.23
% 114.82/115.23 (60869) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), ! in( Y, X ) }.
% 114.82/115.23 (60870) {G0,W4,D2,L2,V1,M2} { ! empty( X ), function( X ) }.
% 114.82/115.23 (60871) {G0,W4,D2,L2,V1,M2} { ! empty( X ), relation( X ) }.
% 114.82/115.23 (60872) {G0,W8,D3,L3,V2,M3} { ! relation( X ), ! relation( Y ), relation(
% 114.82/115.23 relation_composition( X, Y ) ) }.
% 114.82/115.23 (60873) {G0,W3,D3,L1,V1,M1} { relation( identity_relation( X ) ) }.
% 114.82/115.23 (60874) {G0,W4,D3,L1,V1,M1} { element( skol1( X ), X ) }.
% 114.82/115.23 (60875) {G0,W8,D3,L3,V2,M3} { ! empty( X ), ! relation( Y ), empty(
% 114.82/115.23 relation_composition( Y, X ) ) }.
% 114.82/115.23 (60876) {G0,W8,D3,L3,V2,M3} { ! empty( X ), ! relation( Y ), relation(
% 114.82/115.23 relation_composition( Y, X ) ) }.
% 114.82/115.23 (60877) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 114.82/115.23 (60878) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 114.82/115.23 (60879) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( empty_set ) }.
% 114.82/115.23 (60880) {G0,W12,D3,L5,V2,M5} { ! relation( X ), ! function( X ), !
% 114.82/115.23 relation( Y ), ! function( Y ), relation( relation_composition( X, Y ) )
% 114.82/115.23 }.
% 114.82/115.23 (60881) {G0,W12,D3,L5,V2,M5} { ! relation( X ), ! function( X ), !
% 114.82/115.23 relation( Y ), ! function( Y ), function( relation_composition( X, Y ) )
% 114.82/115.23 }.
% 114.82/115.23 (60882) {G0,W3,D3,L1,V1,M1} { ! empty( powerset( X ) ) }.
% 114.82/115.23 (60883) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 114.82/115.23 (60884) {G0,W3,D3,L1,V1,M1} { relation( identity_relation( X ) ) }.
% 114.82/115.23 (60885) {G0,W3,D3,L1,V1,M1} { function( identity_relation( X ) ) }.
% 114.82/115.23 (60886) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 114.82/115.23 (60887) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 114.82/115.23 (60888) {G0,W7,D3,L3,V1,M3} { empty( X ), ! relation( X ), ! empty(
% 114.82/115.23 relation_dom( X ) ) }.
% 114.82/115.23 (60889) {G0,W5,D3,L2,V1,M2} { ! empty( X ), empty( relation_dom( X ) ) }.
% 114.82/115.23 (60890) {G0,W5,D3,L2,V1,M2} { ! empty( X ), relation( relation_dom( X ) )
% 114.82/115.23 }.
% 114.82/115.23 (60891) {G0,W8,D3,L3,V2,M3} { ! empty( X ), ! relation( Y ), empty(
% 114.82/115.23 relation_composition( X, Y ) ) }.
% 114.82/115.23 (60892) {G0,W8,D3,L3,V2,M3} { ! empty( X ), ! relation( Y ), relation(
% 114.82/115.23 relation_composition( X, Y ) ) }.
% 114.82/115.23 (60893) {G0,W2,D2,L1,V0,M1} { relation( skol2 ) }.
% 114.82/115.23 (60894) {G0,W2,D2,L1,V0,M1} { function( skol2 ) }.
% 114.82/115.23 (60895) {G0,W2,D2,L1,V0,M1} { empty( skol3 ) }.
% 114.82/115.23 (60896) {G0,W2,D2,L1,V0,M1} { relation( skol3 ) }.
% 114.82/115.23 (60897) {G0,W5,D3,L2,V2,M2} { empty( X ), ! empty( skol4( Y ) ) }.
% 114.82/115.23 (60898) {G0,W7,D3,L2,V1,M2} { empty( X ), element( skol4( X ), powerset( X
% 114.82/115.23 ) ) }.
% 114.82/115.23 (60899) {G0,W2,D2,L1,V0,M1} { empty( skol5 ) }.
% 114.82/115.23 (60900) {G0,W2,D2,L1,V0,M1} { ! empty( skol6 ) }.
% 114.82/115.23 (60901) {G0,W2,D2,L1,V0,M1} { relation( skol6 ) }.
% 114.82/115.23 (60902) {G0,W3,D3,L1,V1,M1} { empty( skol7( Y ) ) }.
% 114.82/115.23 (60903) {G0,W5,D3,L1,V1,M1} { element( skol7( X ), powerset( X ) ) }.
% 114.82/115.23 (60904) {G0,W2,D2,L1,V0,M1} { ! empty( skol8 ) }.
% 114.82/115.23 (60905) {G0,W2,D2,L1,V0,M1} { relation( skol9 ) }.
% 114.82/115.23 (60906) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( skol9 ) }.
% 114.82/115.23 (60907) {G0,W3,D2,L1,V1,M1} { subset( X, X ) }.
% 114.82/115.23 (60908) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), element( X, Y ) }.
% 114.82/115.23 (60909) {G0,W18,D4,L6,V3,M6} { ! relation( X ), ! function( X ), !
% 114.82/115.23 relation( Y ), ! function( Y ), ! in( Z, relation_dom(
% 114.82/115.23 relation_composition( Y, X ) ) ), in( Z, relation_dom( Y ) ) }.
% 114.82/115.23 (60910) {G0,W20,D4,L6,V3,M6} { ! relation( X ), ! function( X ), !
% 114.82/115.23 relation( Y ), ! function( Y ), ! in( Z, relation_dom(
% 114.82/115.23 relation_composition( Y, X ) ) ), in( apply( Y, Z ), relation_dom( X ) )
% 114.82/115.23 }.
% 114.82/115.23 (60911) {G0,W24,D4,L7,V3,M7} { ! relation( X ), ! function( X ), !
% 114.82/115.23 relation( Y ), ! function( Y ), ! in( Z, relation_dom( Y ) ), ! in( apply
% 114.82/115.23 ( Y, Z ), relation_dom( X ) ), in( Z, relation_dom( relation_composition
% 114.82/115.23 ( Y, X ) ) ) }.
% 114.82/115.23 (60912) {G0,W8,D2,L3,V2,M3} { ! element( X, Y ), empty( Y ), in( X, Y )
% 114.82/115.23 }.
% 114.82/115.23 (60913) {G0,W12,D3,L4,V2,M4} { ! relation( X ), ! function( X ), ! X =
% 114.82/115.23 identity_relation( Y ), relation_dom( X ) = Y }.
% 114.82/115.23 (60914) {G0,W11,D3,L4,V2,M4} { ! relation( X ), ! function( X ), ! X =
% 114.82/115.23 identity_relation( Y ), alpha1( X, Y ) }.
% 114.82/115.23 (60915) {G0,W15,D3,L5,V2,M5} { ! relation( X ), ! function( X ), !
% 114.82/115.23 relation_dom( X ) = Y, ! alpha1( X, Y ), X = identity_relation( Y ) }.
% 114.82/115.23 (60916) {G0,W11,D3,L3,V3,M3} { ! alpha1( X, Y ), ! in( Z, Y ), apply( X, Z
% 114.82/115.23 ) = Z }.
% 114.82/115.23 (60917) {G0,W8,D3,L2,V3,M2} { in( skol10( Z, Y ), Y ), alpha1( X, Y ) }.
% 114.82/115.23 (60918) {G0,W12,D4,L2,V2,M2} { ! apply( X, skol10( X, Y ) ) = skol10( X, Y
% 114.82/115.23 ), alpha1( X, Y ) }.
% 114.82/115.23 (60919) {G0,W7,D3,L2,V2,M2} { ! element( X, powerset( Y ) ), subset( X, Y
% 114.82/115.23 ) }.
% 114.82/115.23 (60920) {G0,W7,D3,L2,V2,M2} { ! subset( X, Y ), element( X, powerset( Y )
% 114.82/115.24 ) }.
% 114.82/115.24 (60921) {G0,W2,D2,L1,V0,M1} { relation( skol11 ) }.
% 114.82/115.24 (60922) {G0,W2,D2,L1,V0,M1} { function( skol11 ) }.
% 114.82/115.24 (60923) {G0,W8,D3,L2,V0,M2} { alpha2( skol11, skol12, skol13 ), in( skol13
% 114.82/115.24 , relation_dom( skol11 ) ) }.
% 114.82/115.24 (60924) {G0,W9,D3,L2,V0,M2} { alpha2( skol11, skol12, skol13 ), in( apply
% 114.82/115.24 ( skol11, skol13 ), skol12 ) }.
% 114.82/115.24 (60925) {G0,W11,D5,L2,V0,M2} { alpha2( skol11, skol12, skol13 ), ! in(
% 114.82/115.24 skol13, relation_dom( relation_composition( skol11, identity_relation(
% 114.82/115.24 skol12 ) ) ) ) }.
% 114.82/115.24 (60926) {G0,W11,D5,L2,V3,M2} { ! alpha2( X, Y, Z ), in( Z, relation_dom(
% 114.82/115.24 relation_composition( X, identity_relation( Y ) ) ) ) }.
% 114.82/115.24 (60927) {G0,W13,D3,L3,V3,M3} { ! alpha2( X, Y, Z ), ! in( Z, relation_dom
% 114.82/115.24 ( X ) ), ! in( apply( X, Z ), Y ) }.
% 114.82/115.24 (60928) {G0,W15,D5,L3,V3,M3} { ! in( Z, relation_dom( relation_composition
% 114.82/115.24 ( X, identity_relation( Y ) ) ) ), in( Z, relation_dom( X ) ), alpha2( X
% 114.82/115.24 , Y, Z ) }.
% 114.82/115.24 (60929) {G0,W16,D5,L3,V3,M3} { ! in( Z, relation_dom( relation_composition
% 114.82/115.24 ( X, identity_relation( Y ) ) ) ), in( apply( X, Z ), Y ), alpha2( X, Y,
% 114.82/115.24 Z ) }.
% 114.82/115.24 (60930) {G0,W10,D3,L3,V3,M3} { ! in( X, Z ), ! element( Z, powerset( Y ) )
% 114.82/115.24 , element( X, Y ) }.
% 114.82/115.24 (60931) {G0,W9,D3,L3,V3,M3} { ! in( X, Y ), ! element( Y, powerset( Z ) )
% 114.82/115.24 , ! empty( Z ) }.
% 114.82/115.24 (60932) {G0,W5,D2,L2,V1,M2} { ! empty( X ), X = empty_set }.
% 114.82/115.24 (60933) {G0,W5,D2,L2,V2,M2} { ! in( X, Y ), ! empty( Y ) }.
% 114.82/115.24 (60934) {G0,W7,D2,L3,V2,M3} { ! empty( X ), X = Y, ! empty( Y ) }.
% 114.82/115.24
% 114.82/115.24
% 114.82/115.24 Total Proof:
% 114.82/115.24
% 114.82/115.24 subsumption: (4) {G0,W3,D3,L1,V1,M1} I { relation( identity_relation( X ) )
% 114.82/115.24 }.
% 114.82/115.24 parent0: (60873) {G0,W3,D3,L1,V1,M1} { relation( identity_relation( X ) )
% 114.82/115.24 }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := X
% 114.82/115.24 end
% 114.82/115.24 permutation0:
% 114.82/115.24 0 ==> 0
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 subsumption: (13) {G0,W3,D3,L1,V1,M1} I { function( identity_relation( X )
% 114.82/115.24 ) }.
% 114.82/115.24 parent0: (60885) {G0,W3,D3,L1,V1,M1} { function( identity_relation( X ) )
% 114.82/115.24 }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := X
% 114.82/115.24 end
% 114.82/115.24 permutation0:
% 114.82/115.24 0 ==> 0
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 subsumption: (35) {G0,W18,D4,L6,V3,M6} I { ! relation( X ), ! function( X )
% 114.82/115.24 , ! relation( Y ), ! function( Y ), ! in( Z, relation_dom(
% 114.82/115.24 relation_composition( Y, X ) ) ), in( Z, relation_dom( Y ) ) }.
% 114.82/115.24 parent0: (60909) {G0,W18,D4,L6,V3,M6} { ! relation( X ), ! function( X ),
% 114.82/115.24 ! relation( Y ), ! function( Y ), ! in( Z, relation_dom(
% 114.82/115.24 relation_composition( Y, X ) ) ), in( Z, relation_dom( Y ) ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := X
% 114.82/115.24 Y := Y
% 114.82/115.24 Z := Z
% 114.82/115.24 end
% 114.82/115.24 permutation0:
% 114.82/115.24 0 ==> 0
% 114.82/115.24 1 ==> 1
% 114.82/115.24 2 ==> 2
% 114.82/115.24 3 ==> 3
% 114.82/115.24 4 ==> 4
% 114.82/115.24 5 ==> 5
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 subsumption: (36) {G0,W20,D4,L6,V3,M6} I { ! relation( X ), ! function( X )
% 114.82/115.24 , ! relation( Y ), ! function( Y ), ! in( Z, relation_dom(
% 114.82/115.24 relation_composition( Y, X ) ) ), in( apply( Y, Z ), relation_dom( X ) )
% 114.82/115.24 }.
% 114.82/115.24 parent0: (60910) {G0,W20,D4,L6,V3,M6} { ! relation( X ), ! function( X ),
% 114.82/115.24 ! relation( Y ), ! function( Y ), ! in( Z, relation_dom(
% 114.82/115.24 relation_composition( Y, X ) ) ), in( apply( Y, Z ), relation_dom( X ) )
% 114.82/115.24 }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := X
% 114.82/115.24 Y := Y
% 114.82/115.24 Z := Z
% 114.82/115.24 end
% 114.82/115.24 permutation0:
% 114.82/115.24 0 ==> 0
% 114.82/115.24 1 ==> 1
% 114.82/115.24 2 ==> 2
% 114.82/115.24 3 ==> 3
% 114.82/115.24 4 ==> 4
% 114.82/115.24 5 ==> 5
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 subsumption: (37) {G0,W24,D4,L7,V3,M7} I { ! relation( X ), ! function( X )
% 114.82/115.24 , ! relation( Y ), ! function( Y ), ! in( Z, relation_dom( Y ) ), ! in(
% 114.82/115.24 apply( Y, Z ), relation_dom( X ) ), in( Z, relation_dom(
% 114.82/115.24 relation_composition( Y, X ) ) ) }.
% 114.82/115.24 parent0: (60911) {G0,W24,D4,L7,V3,M7} { ! relation( X ), ! function( X ),
% 114.82/115.24 ! relation( Y ), ! function( Y ), ! in( Z, relation_dom( Y ) ), ! in(
% 114.82/115.24 apply( Y, Z ), relation_dom( X ) ), in( Z, relation_dom(
% 114.82/115.24 relation_composition( Y, X ) ) ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := X
% 114.82/115.24 Y := Y
% 114.82/115.24 Z := Z
% 114.82/115.24 end
% 114.82/115.24 permutation0:
% 114.82/115.24 0 ==> 0
% 114.82/115.24 1 ==> 1
% 114.82/115.24 2 ==> 2
% 114.82/115.24 3 ==> 3
% 114.82/115.24 4 ==> 4
% 114.82/115.24 5 ==> 5
% 114.82/115.24 6 ==> 6
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 subsumption: (39) {G0,W12,D3,L4,V2,M4} I { ! relation( X ), ! function( X )
% 114.82/115.24 , ! X = identity_relation( Y ), relation_dom( X ) = Y }.
% 114.82/115.24 parent0: (60913) {G0,W12,D3,L4,V2,M4} { ! relation( X ), ! function( X ),
% 114.82/115.24 ! X = identity_relation( Y ), relation_dom( X ) = Y }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := X
% 114.82/115.24 Y := Y
% 114.82/115.24 end
% 114.82/115.24 permutation0:
% 114.82/115.24 0 ==> 0
% 114.82/115.24 1 ==> 1
% 114.82/115.24 2 ==> 2
% 114.82/115.24 3 ==> 3
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 subsumption: (47) {G0,W2,D2,L1,V0,M1} I { relation( skol11 ) }.
% 114.82/115.24 parent0: (60921) {G0,W2,D2,L1,V0,M1} { relation( skol11 ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 end
% 114.82/115.24 permutation0:
% 114.82/115.24 0 ==> 0
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 subsumption: (48) {G0,W2,D2,L1,V0,M1} I { function( skol11 ) }.
% 114.82/115.24 parent0: (60922) {G0,W2,D2,L1,V0,M1} { function( skol11 ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 end
% 114.82/115.24 permutation0:
% 114.82/115.24 0 ==> 0
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 subsumption: (49) {G0,W8,D3,L2,V0,M2} I { alpha2( skol11, skol12, skol13 )
% 114.82/115.24 , in( skol13, relation_dom( skol11 ) ) }.
% 114.82/115.24 parent0: (60923) {G0,W8,D3,L2,V0,M2} { alpha2( skol11, skol12, skol13 ),
% 114.82/115.24 in( skol13, relation_dom( skol11 ) ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 end
% 114.82/115.24 permutation0:
% 114.82/115.24 0 ==> 0
% 114.82/115.24 1 ==> 1
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 subsumption: (50) {G0,W9,D3,L2,V0,M2} I { alpha2( skol11, skol12, skol13 )
% 114.82/115.24 , in( apply( skol11, skol13 ), skol12 ) }.
% 114.82/115.24 parent0: (60924) {G0,W9,D3,L2,V0,M2} { alpha2( skol11, skol12, skol13 ),
% 114.82/115.24 in( apply( skol11, skol13 ), skol12 ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 end
% 114.82/115.24 permutation0:
% 114.82/115.24 0 ==> 0
% 114.82/115.24 1 ==> 1
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 subsumption: (51) {G0,W11,D5,L2,V0,M2} I { alpha2( skol11, skol12, skol13 )
% 114.82/115.24 , ! in( skol13, relation_dom( relation_composition( skol11,
% 114.82/115.24 identity_relation( skol12 ) ) ) ) }.
% 114.82/115.24 parent0: (60925) {G0,W11,D5,L2,V0,M2} { alpha2( skol11, skol12, skol13 ),
% 114.82/115.24 ! in( skol13, relation_dom( relation_composition( skol11,
% 114.82/115.24 identity_relation( skol12 ) ) ) ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 end
% 114.82/115.24 permutation0:
% 114.82/115.24 0 ==> 0
% 114.82/115.24 1 ==> 1
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 subsumption: (52) {G0,W11,D5,L2,V3,M2} I { ! alpha2( X, Y, Z ), in( Z,
% 114.82/115.24 relation_dom( relation_composition( X, identity_relation( Y ) ) ) ) }.
% 114.82/115.24 parent0: (60926) {G0,W11,D5,L2,V3,M2} { ! alpha2( X, Y, Z ), in( Z,
% 114.82/115.24 relation_dom( relation_composition( X, identity_relation( Y ) ) ) ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := X
% 114.82/115.24 Y := Y
% 114.82/115.24 Z := Z
% 114.82/115.24 end
% 114.82/115.24 permutation0:
% 114.82/115.24 0 ==> 0
% 114.82/115.24 1 ==> 1
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 subsumption: (53) {G0,W13,D3,L3,V3,M3} I { ! alpha2( X, Y, Z ), ! in( Z,
% 114.82/115.24 relation_dom( X ) ), ! in( apply( X, Z ), Y ) }.
% 114.82/115.24 parent0: (60927) {G0,W13,D3,L3,V3,M3} { ! alpha2( X, Y, Z ), ! in( Z,
% 114.82/115.24 relation_dom( X ) ), ! in( apply( X, Z ), Y ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := X
% 114.82/115.24 Y := Y
% 114.82/115.24 Z := Z
% 114.82/115.24 end
% 114.82/115.24 permutation0:
% 114.82/115.24 0 ==> 0
% 114.82/115.24 1 ==> 1
% 114.82/115.24 2 ==> 2
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 resolution: (61135) {G1,W18,D5,L5,V3,M5} { ! relation( identity_relation(
% 114.82/115.24 X ) ), ! relation( Y ), ! function( Y ), ! in( Z, relation_dom(
% 114.82/115.24 relation_composition( Y, identity_relation( X ) ) ) ), in( Z,
% 114.82/115.24 relation_dom( Y ) ) }.
% 114.82/115.24 parent0[1]: (35) {G0,W18,D4,L6,V3,M6} I { ! relation( X ), ! function( X )
% 114.82/115.24 , ! relation( Y ), ! function( Y ), ! in( Z, relation_dom(
% 114.82/115.24 relation_composition( Y, X ) ) ), in( Z, relation_dom( Y ) ) }.
% 114.82/115.24 parent1[0]: (13) {G0,W3,D3,L1,V1,M1} I { function( identity_relation( X ) )
% 114.82/115.24 }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := identity_relation( X )
% 114.82/115.24 Y := Y
% 114.82/115.24 Z := Z
% 114.82/115.24 end
% 114.82/115.24 substitution1:
% 114.82/115.24 X := X
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 resolution: (61138) {G1,W15,D5,L4,V3,M4} { ! relation( Y ), ! function( Y
% 114.82/115.24 ), ! in( Z, relation_dom( relation_composition( Y, identity_relation( X
% 114.82/115.24 ) ) ) ), in( Z, relation_dom( Y ) ) }.
% 114.82/115.24 parent0[0]: (61135) {G1,W18,D5,L5,V3,M5} { ! relation( identity_relation(
% 114.82/115.24 X ) ), ! relation( Y ), ! function( Y ), ! in( Z, relation_dom(
% 114.82/115.24 relation_composition( Y, identity_relation( X ) ) ) ), in( Z,
% 114.82/115.24 relation_dom( Y ) ) }.
% 114.82/115.24 parent1[0]: (4) {G0,W3,D3,L1,V1,M1} I { relation( identity_relation( X ) )
% 114.82/115.24 }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := X
% 114.82/115.24 Y := Y
% 114.82/115.24 Z := Z
% 114.82/115.24 end
% 114.82/115.24 substitution1:
% 114.82/115.24 X := X
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 subsumption: (269) {G1,W15,D5,L4,V3,M4} R(35,13);r(4) { ! relation( Y ), !
% 114.82/115.24 function( Y ), ! in( Z, relation_dom( relation_composition( Y,
% 114.82/115.24 identity_relation( X ) ) ) ), in( Z, relation_dom( Y ) ) }.
% 114.82/115.24 parent0: (61138) {G1,W15,D5,L4,V3,M4} { ! relation( Y ), ! function( Y ),
% 114.82/115.24 ! in( Z, relation_dom( relation_composition( Y, identity_relation( X ) )
% 114.82/115.24 ) ), in( Z, relation_dom( Y ) ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := X
% 114.82/115.24 Y := Y
% 114.82/115.24 Z := Z
% 114.82/115.24 end
% 114.82/115.24 permutation0:
% 114.82/115.24 0 ==> 0
% 114.82/115.24 1 ==> 1
% 114.82/115.24 2 ==> 2
% 114.82/115.24 3 ==> 3
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 resolution: (61140) {G1,W18,D4,L5,V2,M5} { ! relation( X ), ! function( X
% 114.82/115.24 ), ! function( skol11 ), ! in( Y, relation_dom( relation_composition(
% 114.82/115.24 skol11, X ) ) ), in( apply( skol11, Y ), relation_dom( X ) ) }.
% 114.82/115.24 parent0[2]: (36) {G0,W20,D4,L6,V3,M6} I { ! relation( X ), ! function( X )
% 114.82/115.24 , ! relation( Y ), ! function( Y ), ! in( Z, relation_dom(
% 114.82/115.24 relation_composition( Y, X ) ) ), in( apply( Y, Z ), relation_dom( X ) )
% 114.82/115.24 }.
% 114.82/115.24 parent1[0]: (47) {G0,W2,D2,L1,V0,M1} I { relation( skol11 ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := X
% 114.82/115.24 Y := skol11
% 114.82/115.24 Z := Y
% 114.82/115.24 end
% 114.82/115.24 substitution1:
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 resolution: (61144) {G1,W16,D4,L4,V2,M4} { ! relation( X ), ! function( X
% 114.82/115.24 ), ! in( Y, relation_dom( relation_composition( skol11, X ) ) ), in(
% 114.82/115.24 apply( skol11, Y ), relation_dom( X ) ) }.
% 114.82/115.24 parent0[2]: (61140) {G1,W18,D4,L5,V2,M5} { ! relation( X ), ! function( X
% 114.82/115.24 ), ! function( skol11 ), ! in( Y, relation_dom( relation_composition(
% 114.82/115.24 skol11, X ) ) ), in( apply( skol11, Y ), relation_dom( X ) ) }.
% 114.82/115.24 parent1[0]: (48) {G0,W2,D2,L1,V0,M1} I { function( skol11 ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := X
% 114.82/115.24 Y := Y
% 114.82/115.24 end
% 114.82/115.24 substitution1:
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 subsumption: (331) {G1,W16,D4,L4,V2,M4} R(36,47);r(48) { ! relation( X ), !
% 114.82/115.24 function( X ), ! in( Y, relation_dom( relation_composition( skol11, X )
% 114.82/115.24 ) ), in( apply( skol11, Y ), relation_dom( X ) ) }.
% 114.82/115.24 parent0: (61144) {G1,W16,D4,L4,V2,M4} { ! relation( X ), ! function( X ),
% 114.82/115.24 ! in( Y, relation_dom( relation_composition( skol11, X ) ) ), in( apply(
% 114.82/115.24 skol11, Y ), relation_dom( X ) ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := X
% 114.82/115.24 Y := Y
% 114.82/115.24 end
% 114.82/115.24 permutation0:
% 114.82/115.24 0 ==> 0
% 114.82/115.24 1 ==> 1
% 114.82/115.24 2 ==> 2
% 114.82/115.24 3 ==> 3
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 resolution: (61146) {G1,W22,D4,L6,V2,M6} { ! relation( X ), ! function( X
% 114.82/115.24 ), ! function( skol11 ), ! in( Y, relation_dom( skol11 ) ), ! in( apply
% 114.82/115.24 ( skol11, Y ), relation_dom( X ) ), in( Y, relation_dom(
% 114.82/115.24 relation_composition( skol11, X ) ) ) }.
% 114.82/115.24 parent0[2]: (37) {G0,W24,D4,L7,V3,M7} I { ! relation( X ), ! function( X )
% 114.82/115.24 , ! relation( Y ), ! function( Y ), ! in( Z, relation_dom( Y ) ), ! in(
% 114.82/115.24 apply( Y, Z ), relation_dom( X ) ), in( Z, relation_dom(
% 114.82/115.24 relation_composition( Y, X ) ) ) }.
% 114.82/115.24 parent1[0]: (47) {G0,W2,D2,L1,V0,M1} I { relation( skol11 ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := X
% 114.82/115.24 Y := skol11
% 114.82/115.24 Z := Y
% 114.82/115.24 end
% 114.82/115.24 substitution1:
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 resolution: (61150) {G1,W20,D4,L5,V2,M5} { ! relation( X ), ! function( X
% 114.82/115.24 ), ! in( Y, relation_dom( skol11 ) ), ! in( apply( skol11, Y ),
% 114.82/115.24 relation_dom( X ) ), in( Y, relation_dom( relation_composition( skol11, X
% 114.82/115.24 ) ) ) }.
% 114.82/115.24 parent0[2]: (61146) {G1,W22,D4,L6,V2,M6} { ! relation( X ), ! function( X
% 114.82/115.24 ), ! function( skol11 ), ! in( Y, relation_dom( skol11 ) ), ! in( apply
% 114.82/115.24 ( skol11, Y ), relation_dom( X ) ), in( Y, relation_dom(
% 114.82/115.24 relation_composition( skol11, X ) ) ) }.
% 114.82/115.24 parent1[0]: (48) {G0,W2,D2,L1,V0,M1} I { function( skol11 ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := X
% 114.82/115.24 Y := Y
% 114.82/115.24 end
% 114.82/115.24 substitution1:
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 subsumption: (357) {G1,W20,D4,L5,V2,M5} R(37,47);r(48) { ! relation( X ), !
% 114.82/115.24 function( X ), ! in( Y, relation_dom( skol11 ) ), ! in( apply( skol11, Y
% 114.82/115.24 ), relation_dom( X ) ), in( Y, relation_dom( relation_composition(
% 114.82/115.24 skol11, X ) ) ) }.
% 114.82/115.24 parent0: (61150) {G1,W20,D4,L5,V2,M5} { ! relation( X ), ! function( X ),
% 114.82/115.24 ! in( Y, relation_dom( skol11 ) ), ! in( apply( skol11, Y ), relation_dom
% 114.82/115.24 ( X ) ), in( Y, relation_dom( relation_composition( skol11, X ) ) ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := X
% 114.82/115.24 Y := Y
% 114.82/115.24 end
% 114.82/115.24 permutation0:
% 114.82/115.24 0 ==> 0
% 114.82/115.24 1 ==> 1
% 114.82/115.24 2 ==> 2
% 114.82/115.24 3 ==> 3
% 114.82/115.24 4 ==> 4
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 eqswap: (61151) {G0,W12,D3,L4,V2,M4} { ! identity_relation( Y ) = X, !
% 114.82/115.24 relation( X ), ! function( X ), relation_dom( X ) = Y }.
% 114.82/115.24 parent0[2]: (39) {G0,W12,D3,L4,V2,M4} I { ! relation( X ), ! function( X )
% 114.82/115.24 , ! X = identity_relation( Y ), relation_dom( X ) = Y }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := X
% 114.82/115.24 Y := Y
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 resolution: (61154) {G1,W13,D4,L3,V2,M3} { ! identity_relation( X ) =
% 114.82/115.24 identity_relation( Y ), ! relation( identity_relation( Y ) ),
% 114.82/115.24 relation_dom( identity_relation( Y ) ) = X }.
% 114.82/115.24 parent0[2]: (61151) {G0,W12,D3,L4,V2,M4} { ! identity_relation( Y ) = X, !
% 114.82/115.24 relation( X ), ! function( X ), relation_dom( X ) = Y }.
% 114.82/115.24 parent1[0]: (13) {G0,W3,D3,L1,V1,M1} I { function( identity_relation( X ) )
% 114.82/115.24 }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := identity_relation( Y )
% 114.82/115.24 Y := X
% 114.82/115.24 end
% 114.82/115.24 substitution1:
% 114.82/115.24 X := Y
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 resolution: (61155) {G1,W10,D4,L2,V2,M2} { ! identity_relation( X ) =
% 114.82/115.24 identity_relation( Y ), relation_dom( identity_relation( Y ) ) = X }.
% 114.82/115.24 parent0[1]: (61154) {G1,W13,D4,L3,V2,M3} { ! identity_relation( X ) =
% 114.82/115.24 identity_relation( Y ), ! relation( identity_relation( Y ) ),
% 114.82/115.24 relation_dom( identity_relation( Y ) ) = X }.
% 114.82/115.24 parent1[0]: (4) {G0,W3,D3,L1,V1,M1} I { relation( identity_relation( X ) )
% 114.82/115.24 }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := X
% 114.82/115.24 Y := Y
% 114.82/115.24 end
% 114.82/115.24 substitution1:
% 114.82/115.24 X := Y
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 eqswap: (61156) {G1,W10,D4,L2,V2,M2} { ! identity_relation( Y ) =
% 114.82/115.24 identity_relation( X ), relation_dom( identity_relation( Y ) ) = X }.
% 114.82/115.24 parent0[0]: (61155) {G1,W10,D4,L2,V2,M2} { ! identity_relation( X ) =
% 114.82/115.24 identity_relation( Y ), relation_dom( identity_relation( Y ) ) = X }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := X
% 114.82/115.24 Y := Y
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 subsumption: (430) {G1,W10,D4,L2,V2,M2} R(39,13);r(4) { ! identity_relation
% 114.82/115.24 ( X ) = identity_relation( Y ), relation_dom( identity_relation( X ) ) =
% 114.82/115.24 Y }.
% 114.82/115.24 parent0: (61156) {G1,W10,D4,L2,V2,M2} { ! identity_relation( Y ) =
% 114.82/115.24 identity_relation( X ), relation_dom( identity_relation( Y ) ) = X }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := Y
% 114.82/115.24 Y := X
% 114.82/115.24 end
% 114.82/115.24 permutation0:
% 114.82/115.24 0 ==> 0
% 114.82/115.24 1 ==> 1
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 eqswap: (61159) {G1,W10,D4,L2,V2,M2} { ! identity_relation( Y ) =
% 114.82/115.24 identity_relation( X ), relation_dom( identity_relation( X ) ) = Y }.
% 114.82/115.24 parent0[0]: (430) {G1,W10,D4,L2,V2,M2} R(39,13);r(4) { ! identity_relation
% 114.82/115.24 ( X ) = identity_relation( Y ), relation_dom( identity_relation( X ) ) =
% 114.82/115.24 Y }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := X
% 114.82/115.24 Y := Y
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 eqrefl: (61162) {G0,W5,D4,L1,V1,M1} { relation_dom( identity_relation( X )
% 114.82/115.24 ) = X }.
% 114.82/115.24 parent0[0]: (61159) {G1,W10,D4,L2,V2,M2} { ! identity_relation( Y ) =
% 114.82/115.24 identity_relation( X ), relation_dom( identity_relation( X ) ) = Y }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := X
% 114.82/115.24 Y := X
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 subsumption: (549) {G2,W5,D4,L1,V1,M1} Q(430) { relation_dom(
% 114.82/115.24 identity_relation( X ) ) ==> X }.
% 114.82/115.24 parent0: (61162) {G0,W5,D4,L1,V1,M1} { relation_dom( identity_relation( X
% 114.82/115.24 ) ) = X }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := X
% 114.82/115.24 end
% 114.82/115.24 permutation0:
% 114.82/115.24 0 ==> 0
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 resolution: (61164) {G1,W12,D5,L2,V0,M2} { in( skol13, relation_dom(
% 114.82/115.24 relation_composition( skol11, identity_relation( skol12 ) ) ) ), in(
% 114.82/115.24 apply( skol11, skol13 ), skol12 ) }.
% 114.82/115.24 parent0[0]: (52) {G0,W11,D5,L2,V3,M2} I { ! alpha2( X, Y, Z ), in( Z,
% 114.82/115.24 relation_dom( relation_composition( X, identity_relation( Y ) ) ) ) }.
% 114.82/115.24 parent1[0]: (50) {G0,W9,D3,L2,V0,M2} I { alpha2( skol11, skol12, skol13 ),
% 114.82/115.24 in( apply( skol11, skol13 ), skol12 ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := skol11
% 114.82/115.24 Y := skol12
% 114.82/115.24 Z := skol13
% 114.82/115.24 end
% 114.82/115.24 substitution1:
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 subsumption: (909) {G1,W12,D5,L2,V0,M2} R(52,50) { in( skol13, relation_dom
% 114.82/115.24 ( relation_composition( skol11, identity_relation( skol12 ) ) ) ), in(
% 114.82/115.24 apply( skol11, skol13 ), skol12 ) }.
% 114.82/115.24 parent0: (61164) {G1,W12,D5,L2,V0,M2} { in( skol13, relation_dom(
% 114.82/115.24 relation_composition( skol11, identity_relation( skol12 ) ) ) ), in(
% 114.82/115.24 apply( skol11, skol13 ), skol12 ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 end
% 114.82/115.24 permutation0:
% 114.82/115.24 0 ==> 0
% 114.82/115.24 1 ==> 1
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 resolution: (61165) {G1,W11,D5,L2,V0,M2} { in( skol13, relation_dom(
% 114.82/115.24 relation_composition( skol11, identity_relation( skol12 ) ) ) ), in(
% 114.82/115.24 skol13, relation_dom( skol11 ) ) }.
% 114.82/115.24 parent0[0]: (52) {G0,W11,D5,L2,V3,M2} I { ! alpha2( X, Y, Z ), in( Z,
% 114.82/115.24 relation_dom( relation_composition( X, identity_relation( Y ) ) ) ) }.
% 114.82/115.24 parent1[0]: (49) {G0,W8,D3,L2,V0,M2} I { alpha2( skol11, skol12, skol13 ),
% 114.82/115.24 in( skol13, relation_dom( skol11 ) ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := skol11
% 114.82/115.24 Y := skol12
% 114.82/115.24 Z := skol13
% 114.82/115.24 end
% 114.82/115.24 substitution1:
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 subsumption: (910) {G1,W11,D5,L2,V0,M2} R(52,49) { in( skol13, relation_dom
% 114.82/115.24 ( relation_composition( skol11, identity_relation( skol12 ) ) ) ), in(
% 114.82/115.24 skol13, relation_dom( skol11 ) ) }.
% 114.82/115.24 parent0: (61165) {G1,W11,D5,L2,V0,M2} { in( skol13, relation_dom(
% 114.82/115.24 relation_composition( skol11, identity_relation( skol12 ) ) ) ), in(
% 114.82/115.24 skol13, relation_dom( skol11 ) ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 end
% 114.82/115.24 permutation0:
% 114.82/115.24 0 ==> 0
% 114.82/115.24 1 ==> 1
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 resolution: (61166) {G1,W13,D5,L3,V2,M3} { ! function( skol11 ), ! in( X,
% 114.82/115.24 relation_dom( relation_composition( skol11, identity_relation( Y ) ) ) )
% 114.82/115.24 , in( X, relation_dom( skol11 ) ) }.
% 114.82/115.24 parent0[0]: (269) {G1,W15,D5,L4,V3,M4} R(35,13);r(4) { ! relation( Y ), !
% 114.82/115.24 function( Y ), ! in( Z, relation_dom( relation_composition( Y,
% 114.82/115.24 identity_relation( X ) ) ) ), in( Z, relation_dom( Y ) ) }.
% 114.82/115.24 parent1[0]: (47) {G0,W2,D2,L1,V0,M1} I { relation( skol11 ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := Y
% 114.82/115.24 Y := skol11
% 114.82/115.24 Z := X
% 114.82/115.24 end
% 114.82/115.24 substitution1:
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 resolution: (61167) {G1,W11,D5,L2,V2,M2} { ! in( X, relation_dom(
% 114.82/115.24 relation_composition( skol11, identity_relation( Y ) ) ) ), in( X,
% 114.82/115.24 relation_dom( skol11 ) ) }.
% 114.82/115.24 parent0[0]: (61166) {G1,W13,D5,L3,V2,M3} { ! function( skol11 ), ! in( X,
% 114.82/115.24 relation_dom( relation_composition( skol11, identity_relation( Y ) ) ) )
% 114.82/115.24 , in( X, relation_dom( skol11 ) ) }.
% 114.82/115.24 parent1[0]: (48) {G0,W2,D2,L1,V0,M1} I { function( skol11 ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := X
% 114.82/115.24 Y := Y
% 114.82/115.24 end
% 114.82/115.24 substitution1:
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 subsumption: (13975) {G2,W11,D5,L2,V2,M2} R(269,47);r(48) { ! in( X,
% 114.82/115.24 relation_dom( relation_composition( skol11, identity_relation( Y ) ) ) )
% 114.82/115.24 , in( X, relation_dom( skol11 ) ) }.
% 114.82/115.24 parent0: (61167) {G1,W11,D5,L2,V2,M2} { ! in( X, relation_dom(
% 114.82/115.24 relation_composition( skol11, identity_relation( Y ) ) ) ), in( X,
% 114.82/115.24 relation_dom( skol11 ) ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := X
% 114.82/115.24 Y := Y
% 114.82/115.24 end
% 114.82/115.24 permutation0:
% 114.82/115.24 0 ==> 0
% 114.82/115.24 1 ==> 1
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 resolution: (61169) {G1,W17,D4,L4,V2,M4} { ! relation( identity_relation(
% 114.82/115.24 X ) ), ! function( identity_relation( X ) ), in( apply( skol11, Y ),
% 114.82/115.24 relation_dom( identity_relation( X ) ) ), ! alpha2( skol11, X, Y ) }.
% 114.82/115.24 parent0[2]: (331) {G1,W16,D4,L4,V2,M4} R(36,47);r(48) { ! relation( X ), !
% 114.82/115.24 function( X ), ! in( Y, relation_dom( relation_composition( skol11, X ) )
% 114.82/115.24 ), in( apply( skol11, Y ), relation_dom( X ) ) }.
% 114.82/115.24 parent1[1]: (52) {G0,W11,D5,L2,V3,M2} I { ! alpha2( X, Y, Z ), in( Z,
% 114.82/115.24 relation_dom( relation_composition( X, identity_relation( Y ) ) ) ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := identity_relation( X )
% 114.82/115.24 Y := Y
% 114.82/115.24 end
% 114.82/115.24 substitution1:
% 114.82/115.24 X := skol11
% 114.82/115.24 Y := X
% 114.82/115.24 Z := Y
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 paramod: (61170) {G2,W15,D3,L4,V2,M4} { in( apply( skol11, X ), Y ), !
% 114.82/115.24 relation( identity_relation( Y ) ), ! function( identity_relation( Y ) )
% 114.82/115.24 , ! alpha2( skol11, Y, X ) }.
% 114.82/115.24 parent0[0]: (549) {G2,W5,D4,L1,V1,M1} Q(430) { relation_dom(
% 114.82/115.24 identity_relation( X ) ) ==> X }.
% 114.82/115.24 parent1[2; 4]: (61169) {G1,W17,D4,L4,V2,M4} { ! relation(
% 114.82/115.24 identity_relation( X ) ), ! function( identity_relation( X ) ), in( apply
% 114.82/115.24 ( skol11, Y ), relation_dom( identity_relation( X ) ) ), ! alpha2( skol11
% 114.82/115.24 , X, Y ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := Y
% 114.82/115.24 end
% 114.82/115.24 substitution1:
% 114.82/115.24 X := Y
% 114.82/115.24 Y := X
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 resolution: (61171) {G1,W12,D3,L3,V2,M3} { in( apply( skol11, X ), Y ), !
% 114.82/115.24 function( identity_relation( Y ) ), ! alpha2( skol11, Y, X ) }.
% 114.82/115.24 parent0[1]: (61170) {G2,W15,D3,L4,V2,M4} { in( apply( skol11, X ), Y ), !
% 114.82/115.24 relation( identity_relation( Y ) ), ! function( identity_relation( Y ) )
% 114.82/115.24 , ! alpha2( skol11, Y, X ) }.
% 114.82/115.24 parent1[0]: (4) {G0,W3,D3,L1,V1,M1} I { relation( identity_relation( X ) )
% 114.82/115.24 }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := X
% 114.82/115.24 Y := Y
% 114.82/115.24 end
% 114.82/115.24 substitution1:
% 114.82/115.24 X := Y
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 subsumption: (17811) {G3,W12,D3,L3,V2,M3} R(331,52);d(549);r(4) { !
% 114.82/115.24 function( identity_relation( X ) ), ! alpha2( skol11, X, Y ), in( apply(
% 114.82/115.24 skol11, Y ), X ) }.
% 114.82/115.24 parent0: (61171) {G1,W12,D3,L3,V2,M3} { in( apply( skol11, X ), Y ), !
% 114.82/115.24 function( identity_relation( Y ) ), ! alpha2( skol11, Y, X ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := Y
% 114.82/115.24 Y := X
% 114.82/115.24 end
% 114.82/115.24 permutation0:
% 114.82/115.24 0 ==> 2
% 114.82/115.24 1 ==> 0
% 114.82/115.24 2 ==> 1
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 resolution: (61173) {G1,W17,D5,L3,V2,M3} { ! relation( identity_relation(
% 114.82/115.24 X ) ), ! in( Y, relation_dom( relation_composition( skol11,
% 114.82/115.24 identity_relation( X ) ) ) ), in( apply( skol11, Y ), relation_dom(
% 114.82/115.24 identity_relation( X ) ) ) }.
% 114.82/115.24 parent0[1]: (331) {G1,W16,D4,L4,V2,M4} R(36,47);r(48) { ! relation( X ), !
% 114.82/115.24 function( X ), ! in( Y, relation_dom( relation_composition( skol11, X ) )
% 114.82/115.24 ), in( apply( skol11, Y ), relation_dom( X ) ) }.
% 114.82/115.24 parent1[0]: (13) {G0,W3,D3,L1,V1,M1} I { function( identity_relation( X ) )
% 114.82/115.24 }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := identity_relation( X )
% 114.82/115.24 Y := Y
% 114.82/115.24 end
% 114.82/115.24 substitution1:
% 114.82/115.24 X := X
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 paramod: (61174) {G2,W15,D5,L3,V2,M3} { in( apply( skol11, X ), Y ), !
% 114.82/115.24 relation( identity_relation( Y ) ), ! in( X, relation_dom(
% 114.82/115.24 relation_composition( skol11, identity_relation( Y ) ) ) ) }.
% 114.82/115.24 parent0[0]: (549) {G2,W5,D4,L1,V1,M1} Q(430) { relation_dom(
% 114.82/115.24 identity_relation( X ) ) ==> X }.
% 114.82/115.24 parent1[2; 4]: (61173) {G1,W17,D5,L3,V2,M3} { ! relation(
% 114.82/115.24 identity_relation( X ) ), ! in( Y, relation_dom( relation_composition(
% 114.82/115.24 skol11, identity_relation( X ) ) ) ), in( apply( skol11, Y ),
% 114.82/115.24 relation_dom( identity_relation( X ) ) ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := Y
% 114.82/115.24 end
% 114.82/115.24 substitution1:
% 114.82/115.24 X := Y
% 114.82/115.24 Y := X
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 resolution: (61175) {G1,W12,D5,L2,V2,M2} { in( apply( skol11, X ), Y ), !
% 114.82/115.24 in( X, relation_dom( relation_composition( skol11, identity_relation( Y )
% 114.82/115.24 ) ) ) }.
% 114.82/115.24 parent0[1]: (61174) {G2,W15,D5,L3,V2,M3} { in( apply( skol11, X ), Y ), !
% 114.82/115.24 relation( identity_relation( Y ) ), ! in( X, relation_dom(
% 114.82/115.24 relation_composition( skol11, identity_relation( Y ) ) ) ) }.
% 114.82/115.24 parent1[0]: (4) {G0,W3,D3,L1,V1,M1} I { relation( identity_relation( X ) )
% 114.82/115.24 }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := X
% 114.82/115.24 Y := Y
% 114.82/115.24 end
% 114.82/115.24 substitution1:
% 114.82/115.24 X := Y
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 subsumption: (17812) {G3,W12,D5,L2,V2,M2} R(331,13);d(549);r(4) { ! in( Y,
% 114.82/115.24 relation_dom( relation_composition( skol11, identity_relation( X ) ) ) )
% 114.82/115.24 , in( apply( skol11, Y ), X ) }.
% 114.82/115.24 parent0: (61175) {G1,W12,D5,L2,V2,M2} { in( apply( skol11, X ), Y ), ! in
% 114.82/115.24 ( X, relation_dom( relation_composition( skol11, identity_relation( Y ) )
% 114.82/115.24 ) ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := Y
% 114.82/115.24 Y := X
% 114.82/115.24 end
% 114.82/115.24 permutation0:
% 114.82/115.24 0 ==> 1
% 114.82/115.24 1 ==> 0
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 resolution: (61176) {G1,W9,D3,L2,V2,M2} { ! alpha2( skol11, X, Y ), in(
% 114.82/115.24 apply( skol11, Y ), X ) }.
% 114.82/115.24 parent0[0]: (17811) {G3,W12,D3,L3,V2,M3} R(331,52);d(549);r(4) { ! function
% 114.82/115.24 ( identity_relation( X ) ), ! alpha2( skol11, X, Y ), in( apply( skol11,
% 114.82/115.24 Y ), X ) }.
% 114.82/115.24 parent1[0]: (13) {G0,W3,D3,L1,V1,M1} I { function( identity_relation( X ) )
% 114.82/115.24 }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := X
% 114.82/115.24 Y := Y
% 114.82/115.24 end
% 114.82/115.24 substitution1:
% 114.82/115.24 X := X
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 subsumption: (20058) {G4,W9,D3,L2,V2,M2} S(17811);r(13) { ! alpha2( skol11
% 114.82/115.24 , X, Y ), in( apply( skol11, Y ), X ) }.
% 114.82/115.24 parent0: (61176) {G1,W9,D3,L2,V2,M2} { ! alpha2( skol11, X, Y ), in( apply
% 114.82/115.24 ( skol11, Y ), X ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := X
% 114.82/115.24 Y := Y
% 114.82/115.24 end
% 114.82/115.24 permutation0:
% 114.82/115.24 0 ==> 0
% 114.82/115.24 1 ==> 1
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 resolution: (61177) {G2,W10,D3,L2,V0,M2} { in( apply( skol11, skol13 ),
% 114.82/115.24 skol12 ), in( apply( skol11, skol13 ), skol12 ) }.
% 114.82/115.24 parent0[0]: (17812) {G3,W12,D5,L2,V2,M2} R(331,13);d(549);r(4) { ! in( Y,
% 114.82/115.24 relation_dom( relation_composition( skol11, identity_relation( X ) ) ) )
% 114.82/115.24 , in( apply( skol11, Y ), X ) }.
% 114.82/115.24 parent1[0]: (909) {G1,W12,D5,L2,V0,M2} R(52,50) { in( skol13, relation_dom
% 114.82/115.24 ( relation_composition( skol11, identity_relation( skol12 ) ) ) ), in(
% 114.82/115.24 apply( skol11, skol13 ), skol12 ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := skol12
% 114.82/115.24 Y := skol13
% 114.82/115.24 end
% 114.82/115.24 substitution1:
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 factor: (61178) {G2,W5,D3,L1,V0,M1} { in( apply( skol11, skol13 ), skol12
% 114.82/115.24 ) }.
% 114.82/115.24 parent0[0, 1]: (61177) {G2,W10,D3,L2,V0,M2} { in( apply( skol11, skol13 )
% 114.82/115.24 , skol12 ), in( apply( skol11, skol13 ), skol12 ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 subsumption: (20508) {G4,W5,D3,L1,V0,M1} S(909);r(17812) { in( apply(
% 114.82/115.24 skol11, skol13 ), skol12 ) }.
% 114.82/115.24 parent0: (61178) {G2,W5,D3,L1,V0,M1} { in( apply( skol11, skol13 ), skol12
% 114.82/115.24 ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 end
% 114.82/115.24 permutation0:
% 114.82/115.24 0 ==> 0
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 resolution: (61179) {G2,W8,D3,L2,V0,M2} { in( skol13, relation_dom( skol11
% 114.82/115.24 ) ), in( skol13, relation_dom( skol11 ) ) }.
% 114.82/115.24 parent0[0]: (13975) {G2,W11,D5,L2,V2,M2} R(269,47);r(48) { ! in( X,
% 114.82/115.24 relation_dom( relation_composition( skol11, identity_relation( Y ) ) ) )
% 114.82/115.24 , in( X, relation_dom( skol11 ) ) }.
% 114.82/115.24 parent1[0]: (910) {G1,W11,D5,L2,V0,M2} R(52,49) { in( skol13, relation_dom
% 114.82/115.24 ( relation_composition( skol11, identity_relation( skol12 ) ) ) ), in(
% 114.82/115.24 skol13, relation_dom( skol11 ) ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := skol13
% 114.82/115.24 Y := skol12
% 114.82/115.24 end
% 114.82/115.24 substitution1:
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 factor: (61180) {G2,W4,D3,L1,V0,M1} { in( skol13, relation_dom( skol11 ) )
% 114.82/115.24 }.
% 114.82/115.24 parent0[0, 1]: (61179) {G2,W8,D3,L2,V0,M2} { in( skol13, relation_dom(
% 114.82/115.24 skol11 ) ), in( skol13, relation_dom( skol11 ) ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 subsumption: (20509) {G3,W4,D3,L1,V0,M1} S(910);r(13975) { in( skol13,
% 114.82/115.24 relation_dom( skol11 ) ) }.
% 114.82/115.24 parent0: (61180) {G2,W4,D3,L1,V0,M1} { in( skol13, relation_dom( skol11 )
% 114.82/115.24 ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 end
% 114.82/115.24 permutation0:
% 114.82/115.24 0 ==> 0
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 resolution: (61181) {G1,W9,D3,L2,V1,M2} { ! alpha2( skol11, X, skol13 ), !
% 114.82/115.24 in( apply( skol11, skol13 ), X ) }.
% 114.82/115.24 parent0[1]: (53) {G0,W13,D3,L3,V3,M3} I { ! alpha2( X, Y, Z ), ! in( Z,
% 114.82/115.24 relation_dom( X ) ), ! in( apply( X, Z ), Y ) }.
% 114.82/115.24 parent1[0]: (20509) {G3,W4,D3,L1,V0,M1} S(910);r(13975) { in( skol13,
% 114.82/115.24 relation_dom( skol11 ) ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := skol11
% 114.82/115.24 Y := X
% 114.82/115.24 Z := skol13
% 114.82/115.24 end
% 114.82/115.24 substitution1:
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 resolution: (61182) {G2,W8,D2,L2,V1,M2} { ! alpha2( skol11, X, skol13 ), !
% 114.82/115.24 alpha2( skol11, X, skol13 ) }.
% 114.82/115.24 parent0[1]: (61181) {G1,W9,D3,L2,V1,M2} { ! alpha2( skol11, X, skol13 ), !
% 114.82/115.24 in( apply( skol11, skol13 ), X ) }.
% 114.82/115.24 parent1[1]: (20058) {G4,W9,D3,L2,V2,M2} S(17811);r(13) { ! alpha2( skol11,
% 114.82/115.24 X, Y ), in( apply( skol11, Y ), X ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := X
% 114.82/115.24 end
% 114.82/115.24 substitution1:
% 114.82/115.24 X := X
% 114.82/115.24 Y := skol13
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 factor: (61183) {G2,W4,D2,L1,V1,M1} { ! alpha2( skol11, X, skol13 ) }.
% 114.82/115.24 parent0[0, 1]: (61182) {G2,W8,D2,L2,V1,M2} { ! alpha2( skol11, X, skol13 )
% 114.82/115.24 , ! alpha2( skol11, X, skol13 ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := X
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 subsumption: (20586) {G5,W4,D2,L1,V1,M1} R(20509,53);r(20058) { ! alpha2(
% 114.82/115.24 skol11, X, skol13 ) }.
% 114.82/115.24 parent0: (61183) {G2,W4,D2,L1,V1,M1} { ! alpha2( skol11, X, skol13 ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := X
% 114.82/115.24 end
% 114.82/115.24 permutation0:
% 114.82/115.24 0 ==> 0
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 resolution: (61184) {G1,W7,D5,L1,V0,M1} { ! in( skol13, relation_dom(
% 114.82/115.24 relation_composition( skol11, identity_relation( skol12 ) ) ) ) }.
% 114.82/115.24 parent0[0]: (20586) {G5,W4,D2,L1,V1,M1} R(20509,53);r(20058) { ! alpha2(
% 114.82/115.24 skol11, X, skol13 ) }.
% 114.82/115.24 parent1[0]: (51) {G0,W11,D5,L2,V0,M2} I { alpha2( skol11, skol12, skol13 )
% 114.82/115.24 , ! in( skol13, relation_dom( relation_composition( skol11,
% 114.82/115.24 identity_relation( skol12 ) ) ) ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := skol12
% 114.82/115.24 end
% 114.82/115.24 substitution1:
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 subsumption: (20708) {G6,W7,D5,L1,V0,M1} R(20586,51) { ! in( skol13,
% 114.82/115.24 relation_dom( relation_composition( skol11, identity_relation( skol12 ) )
% 114.82/115.24 ) ) }.
% 114.82/115.24 parent0: (61184) {G1,W7,D5,L1,V0,M1} { ! in( skol13, relation_dom(
% 114.82/115.24 relation_composition( skol11, identity_relation( skol12 ) ) ) ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 end
% 114.82/115.24 permutation0:
% 114.82/115.24 0 ==> 0
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 resolution: (61186) {G2,W17,D4,L4,V0,M4} { ! relation( identity_relation(
% 114.82/115.24 skol12 ) ), ! function( identity_relation( skol12 ) ), ! in( skol13,
% 114.82/115.24 relation_dom( skol11 ) ), ! in( apply( skol11, skol13 ), relation_dom(
% 114.82/115.24 identity_relation( skol12 ) ) ) }.
% 114.82/115.24 parent0[0]: (20708) {G6,W7,D5,L1,V0,M1} R(20586,51) { ! in( skol13,
% 114.82/115.24 relation_dom( relation_composition( skol11, identity_relation( skol12 ) )
% 114.82/115.24 ) ) }.
% 114.82/115.24 parent1[4]: (357) {G1,W20,D4,L5,V2,M5} R(37,47);r(48) { ! relation( X ), !
% 114.82/115.24 function( X ), ! in( Y, relation_dom( skol11 ) ), ! in( apply( skol11, Y
% 114.82/115.24 ), relation_dom( X ) ), in( Y, relation_dom( relation_composition(
% 114.82/115.24 skol11, X ) ) ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 end
% 114.82/115.24 substitution1:
% 114.82/115.24 X := identity_relation( skol12 )
% 114.82/115.24 Y := skol13
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 paramod: (61187) {G3,W15,D3,L4,V0,M4} { ! in( apply( skol11, skol13 ),
% 114.82/115.24 skol12 ), ! relation( identity_relation( skol12 ) ), ! function(
% 114.82/115.24 identity_relation( skol12 ) ), ! in( skol13, relation_dom( skol11 ) ) }.
% 114.82/115.24 parent0[0]: (549) {G2,W5,D4,L1,V1,M1} Q(430) { relation_dom(
% 114.82/115.24 identity_relation( X ) ) ==> X }.
% 114.82/115.24 parent1[3; 5]: (61186) {G2,W17,D4,L4,V0,M4} { ! relation(
% 114.82/115.24 identity_relation( skol12 ) ), ! function( identity_relation( skol12 ) )
% 114.82/115.24 , ! in( skol13, relation_dom( skol11 ) ), ! in( apply( skol11, skol13 ),
% 114.82/115.24 relation_dom( identity_relation( skol12 ) ) ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 X := skol12
% 114.82/115.24 end
% 114.82/115.24 substitution1:
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 resolution: (61188) {G1,W12,D3,L3,V0,M3} { ! in( apply( skol11, skol13 ),
% 114.82/115.24 skol12 ), ! function( identity_relation( skol12 ) ), ! in( skol13,
% 114.82/115.24 relation_dom( skol11 ) ) }.
% 114.82/115.24 parent0[1]: (61187) {G3,W15,D3,L4,V0,M4} { ! in( apply( skol11, skol13 ),
% 114.82/115.24 skol12 ), ! relation( identity_relation( skol12 ) ), ! function(
% 114.82/115.24 identity_relation( skol12 ) ), ! in( skol13, relation_dom( skol11 ) ) }.
% 114.82/115.24 parent1[0]: (4) {G0,W3,D3,L1,V1,M1} I { relation( identity_relation( X ) )
% 114.82/115.24 }.
% 114.82/115.24 substitution0:
% 114.82/115.24 end
% 114.82/115.24 substitution1:
% 114.82/115.24 X := skol12
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 subsumption: (56366) {G7,W12,D3,L3,V0,M3} R(20708,357);d(549);r(4) { !
% 114.82/115.24 function( identity_relation( skol12 ) ), ! in( skol13, relation_dom(
% 114.82/115.24 skol11 ) ), ! in( apply( skol11, skol13 ), skol12 ) }.
% 114.82/115.24 parent0: (61188) {G1,W12,D3,L3,V0,M3} { ! in( apply( skol11, skol13 ),
% 114.82/115.24 skol12 ), ! function( identity_relation( skol12 ) ), ! in( skol13,
% 114.82/115.24 relation_dom( skol11 ) ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 end
% 114.82/115.24 permutation0:
% 114.82/115.24 0 ==> 2
% 114.82/115.24 1 ==> 0
% 114.82/115.24 2 ==> 1
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 resolution: (61189) {G1,W9,D3,L2,V0,M2} { ! in( skol13, relation_dom(
% 114.82/115.24 skol11 ) ), ! in( apply( skol11, skol13 ), skol12 ) }.
% 114.82/115.24 parent0[0]: (56366) {G7,W12,D3,L3,V0,M3} R(20708,357);d(549);r(4) { !
% 114.82/115.24 function( identity_relation( skol12 ) ), ! in( skol13, relation_dom(
% 114.82/115.24 skol11 ) ), ! in( apply( skol11, skol13 ), skol12 ) }.
% 114.82/115.24 parent1[0]: (13) {G0,W3,D3,L1,V1,M1} I { function( identity_relation( X ) )
% 114.82/115.24 }.
% 114.82/115.24 substitution0:
% 114.82/115.24 end
% 114.82/115.24 substitution1:
% 114.82/115.24 X := skol12
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 resolution: (61190) {G2,W5,D3,L1,V0,M1} { ! in( apply( skol11, skol13 ),
% 114.82/115.24 skol12 ) }.
% 114.82/115.24 parent0[0]: (61189) {G1,W9,D3,L2,V0,M2} { ! in( skol13, relation_dom(
% 114.82/115.24 skol11 ) ), ! in( apply( skol11, skol13 ), skol12 ) }.
% 114.82/115.24 parent1[0]: (20509) {G3,W4,D3,L1,V0,M1} S(910);r(13975) { in( skol13,
% 114.82/115.24 relation_dom( skol11 ) ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 end
% 114.82/115.24 substitution1:
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 resolution: (61191) {G3,W0,D0,L0,V0,M0} { }.
% 114.82/115.24 parent0[0]: (61190) {G2,W5,D3,L1,V0,M1} { ! in( apply( skol11, skol13 ),
% 114.82/115.24 skol12 ) }.
% 114.82/115.24 parent1[0]: (20508) {G4,W5,D3,L1,V0,M1} S(909);r(17812) { in( apply( skol11
% 114.82/115.24 , skol13 ), skol12 ) }.
% 114.82/115.24 substitution0:
% 114.82/115.24 end
% 114.82/115.24 substitution1:
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 subsumption: (60867) {G8,W0,D0,L0,V0,M0} S(56366);r(13);r(20509);r(20508)
% 114.82/115.24 { }.
% 114.82/115.24 parent0: (61191) {G3,W0,D0,L0,V0,M0} { }.
% 114.82/115.24 substitution0:
% 114.82/115.24 end
% 114.82/115.24 permutation0:
% 114.82/115.24 end
% 114.82/115.24
% 114.82/115.24 Proof check complete!
% 114.82/115.24
% 114.82/115.24 Memory use:
% 114.82/115.24
% 114.82/115.24 space for terms: 830676
% 114.82/115.24 space for clauses: 2751982
% 114.82/115.24
% 114.82/115.24
% 114.82/115.24 clauses generated: 682161
% 114.82/115.24 clauses kept: 60868
% 114.82/115.24 clauses selected: 1976
% 114.82/115.24 clauses deleted: 6229
% 114.82/115.24 clauses inuse deleted: 123
% 114.82/115.24
% 114.82/115.24 subsentry: 1258463
% 114.82/115.24 literals s-matched: 786779
% 114.82/115.24 literals matched: 736446
% 114.82/115.24 full subsumption: 127555
% 114.82/115.24
% 114.82/115.24 checksum: -877053333
% 114.82/115.24
% 114.82/115.24
% 114.82/115.24 Bliksem ended
%------------------------------------------------------------------------------