TSTP Solution File: SEU026+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SEU026+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Tue Jul 19 07:10:19 EDT 2022
% Result : Theorem 13.71s 14.12s
% Output : Refutation 13.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU026+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n029.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 : Mon Jun 20 09:51:45 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.06/2.46 *** allocated 10000 integers for termspace/termends
% 2.06/2.46 *** allocated 10000 integers for clauses
% 2.06/2.46 *** allocated 10000 integers for justifications
% 2.06/2.46 Bliksem 1.12
% 2.06/2.46
% 2.06/2.46
% 2.06/2.46 Automatic Strategy Selection
% 2.06/2.46
% 2.06/2.46
% 2.06/2.46 Clauses:
% 2.06/2.46
% 2.06/2.46 { ! in( X, Y ), ! in( Y, X ) }.
% 2.06/2.46 { ! empty( X ), function( X ) }.
% 2.06/2.46 { ! empty( X ), relation( X ) }.
% 2.06/2.46 { ! relation( X ), ! empty( X ), ! function( X ), relation( X ) }.
% 2.06/2.46 { ! relation( X ), ! empty( X ), ! function( X ), function( X ) }.
% 2.06/2.46 { ! relation( X ), ! empty( X ), ! function( X ), one_to_one( X ) }.
% 2.06/2.46 { ! relation( X ), ! function( X ), relation( function_inverse( X ) ) }.
% 2.06/2.46 { ! relation( X ), ! function( X ), function( function_inverse( X ) ) }.
% 2.06/2.46 { ! relation( X ), ! relation( Y ), relation( relation_composition( X, Y )
% 2.06/2.46 ) }.
% 2.06/2.46 { element( skol1( X ), X ) }.
% 2.06/2.46 { ! empty( X ), ! relation( Y ), empty( relation_composition( Y, X ) ) }.
% 2.06/2.46 { ! empty( X ), ! relation( Y ), relation( relation_composition( Y, X ) ) }
% 2.06/2.46 .
% 2.06/2.46 { empty( empty_set ) }.
% 2.06/2.46 { relation( empty_set ) }.
% 2.06/2.46 { relation_empty_yielding( empty_set ) }.
% 2.06/2.46 { ! relation( X ), ! function( X ), ! relation( Y ), ! function( Y ),
% 2.06/2.46 relation( relation_composition( X, Y ) ) }.
% 2.06/2.46 { ! relation( X ), ! function( X ), ! relation( Y ), ! function( Y ),
% 2.06/2.46 function( relation_composition( X, Y ) ) }.
% 2.06/2.46 { ! empty( powerset( X ) ) }.
% 2.06/2.46 { empty( empty_set ) }.
% 2.06/2.46 { empty( empty_set ) }.
% 2.06/2.46 { relation( empty_set ) }.
% 2.06/2.46 { empty( X ), ! relation( X ), ! empty( relation_dom( X ) ) }.
% 2.06/2.46 { empty( X ), ! relation( X ), ! empty( relation_rng( X ) ) }.
% 2.06/2.46 { ! empty( X ), empty( relation_dom( X ) ) }.
% 2.06/2.46 { ! empty( X ), relation( relation_dom( X ) ) }.
% 2.06/2.46 { ! empty( X ), empty( relation_rng( X ) ) }.
% 2.06/2.46 { ! empty( X ), relation( relation_rng( X ) ) }.
% 2.06/2.46 { ! empty( X ), ! relation( Y ), empty( relation_composition( X, Y ) ) }.
% 2.06/2.46 { ! empty( X ), ! relation( Y ), relation( relation_composition( X, Y ) ) }
% 2.06/2.46 .
% 2.06/2.46 { relation( skol2 ) }.
% 2.06/2.46 { function( skol2 ) }.
% 2.06/2.46 { empty( skol3 ) }.
% 2.06/2.46 { relation( skol3 ) }.
% 2.06/2.46 { empty( X ), ! empty( skol4( Y ) ) }.
% 2.06/2.46 { empty( X ), element( skol4( X ), powerset( X ) ) }.
% 2.06/2.46 { empty( skol5 ) }.
% 2.06/2.46 { relation( skol6 ) }.
% 2.06/2.46 { empty( skol6 ) }.
% 2.06/2.46 { function( skol6 ) }.
% 2.06/2.46 { ! empty( skol7 ) }.
% 2.06/2.46 { relation( skol7 ) }.
% 2.06/2.46 { empty( skol8( Y ) ) }.
% 2.06/2.46 { element( skol8( X ), powerset( X ) ) }.
% 2.06/2.46 { ! empty( skol9 ) }.
% 2.06/2.46 { relation( skol10 ) }.
% 2.06/2.46 { function( skol10 ) }.
% 2.06/2.46 { one_to_one( skol10 ) }.
% 2.06/2.46 { relation( skol11 ) }.
% 2.06/2.46 { relation_empty_yielding( skol11 ) }.
% 2.06/2.46 { subset( X, X ) }.
% 2.06/2.46 { ! in( X, Y ), element( X, Y ) }.
% 2.06/2.46 { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 2.06/2.46 { ! element( X, powerset( Y ) ), subset( X, Y ) }.
% 2.06/2.46 { ! subset( X, Y ), element( X, powerset( Y ) ) }.
% 2.06/2.46 { ! relation( X ), ! relation( Y ), ! subset( relation_rng( X ),
% 2.06/2.46 relation_dom( Y ) ), relation_dom( relation_composition( X, Y ) ) =
% 2.06/2.46 relation_dom( X ) }.
% 2.06/2.46 { ! relation( X ), ! relation( Y ), ! subset( relation_dom( X ),
% 2.06/2.46 relation_rng( Y ) ), relation_rng( relation_composition( Y, X ) ) =
% 2.06/2.46 relation_rng( X ) }.
% 2.06/2.46 { ! in( X, Z ), ! element( Z, powerset( Y ) ), element( X, Y ) }.
% 2.06/2.46 { ! relation( X ), ! function( X ), ! one_to_one( X ), relation_rng( X ) =
% 2.06/2.46 relation_dom( function_inverse( X ) ) }.
% 2.06/2.46 { ! relation( X ), ! function( X ), ! one_to_one( X ), relation_dom( X ) =
% 2.06/2.46 relation_rng( function_inverse( X ) ) }.
% 2.06/2.46 { relation( skol12 ) }.
% 2.06/2.46 { function( skol12 ) }.
% 2.06/2.46 { one_to_one( skol12 ) }.
% 2.06/2.46 { ! relation_dom( relation_composition( function_inverse( skol12 ), skol12
% 2.06/2.46 ) ) = relation_rng( skol12 ), ! relation_rng( relation_composition(
% 2.06/2.46 function_inverse( skol12 ), skol12 ) ) = relation_rng( skol12 ) }.
% 2.06/2.46 { ! in( X, Y ), ! element( Y, powerset( Z ) ), ! empty( Z ) }.
% 2.06/2.46 { ! empty( X ), X = empty_set }.
% 2.06/2.46 { ! in( X, Y ), ! empty( Y ) }.
% 2.06/2.46 { ! empty( X ), X = Y, ! empty( Y ) }.
% 2.06/2.46
% 2.06/2.46 percentage equality = 0.066116, percentage horn = 0.967213
% 2.06/2.46 This is a problem with some equality
% 2.06/2.46
% 2.06/2.46
% 2.06/2.46
% 2.06/2.46 Options Used:
% 2.06/2.46
% 2.06/2.46 useres = 1
% 2.06/2.46 useparamod = 1
% 2.06/2.46 useeqrefl = 1
% 2.06/2.46 useeqfact = 1
% 2.06/2.46 usefactor = 1
% 2.06/2.46 usesimpsplitting = 0
% 2.06/2.46 usesimpdemod = 5
% 2.06/2.46 usesimpres = 3
% 2.06/2.46
% 2.06/2.46 resimpinuse = 1000
% 2.06/2.46 resimpclauses = 20000
% 2.06/2.46 substype = eqrewr
% 2.06/2.46 backwardsubs = 1
% 2.06/2.46 selectoldest = 5
% 2.06/2.46
% 2.06/2.46 litorderings [0] = split
% 2.06/2.46 litorderings [1] = extend the termordering, first sorting on arguments
% 13.71/14.12
% 13.71/14.12 termordering = kbo
% 13.71/14.12
% 13.71/14.12 litapriori = 0
% 13.71/14.12 termapriori = 1
% 13.71/14.12 litaposteriori = 0
% 13.71/14.12 termaposteriori = 0
% 13.71/14.12 demodaposteriori = 0
% 13.71/14.12 ordereqreflfact = 0
% 13.71/14.12
% 13.71/14.12 litselect = negord
% 13.71/14.12
% 13.71/14.12 maxweight = 15
% 13.71/14.12 maxdepth = 30000
% 13.71/14.12 maxlength = 115
% 13.71/14.12 maxnrvars = 195
% 13.71/14.12 excuselevel = 1
% 13.71/14.12 increasemaxweight = 1
% 13.71/14.12
% 13.71/14.12 maxselected = 10000000
% 13.71/14.12 maxnrclauses = 10000000
% 13.71/14.12
% 13.71/14.12 showgenerated = 0
% 13.71/14.12 showkept = 0
% 13.71/14.12 showselected = 0
% 13.71/14.12 showdeleted = 0
% 13.71/14.12 showresimp = 1
% 13.71/14.12 showstatus = 2000
% 13.71/14.12
% 13.71/14.12 prologoutput = 0
% 13.71/14.12 nrgoals = 5000000
% 13.71/14.12 totalproof = 1
% 13.71/14.12
% 13.71/14.12 Symbols occurring in the translation:
% 13.71/14.12
% 13.71/14.12 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 13.71/14.12 . [1, 2] (w:1, o:36, a:1, s:1, b:0),
% 13.71/14.12 ! [4, 1] (w:0, o:19, a:1, s:1, b:0),
% 13.71/14.12 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 13.71/14.12 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 13.71/14.12 in [37, 2] (w:1, o:60, a:1, s:1, b:0),
% 13.71/14.12 empty [38, 1] (w:1, o:24, a:1, s:1, b:0),
% 13.71/14.12 function [39, 1] (w:1, o:25, a:1, s:1, b:0),
% 13.71/14.12 relation [40, 1] (w:1, o:26, a:1, s:1, b:0),
% 13.71/14.12 one_to_one [41, 1] (w:1, o:27, a:1, s:1, b:0),
% 13.71/14.12 function_inverse [42, 1] (w:1, o:28, a:1, s:1, b:0),
% 13.71/14.12 relation_composition [43, 2] (w:1, o:61, a:1, s:1, b:0),
% 13.71/14.12 element [44, 2] (w:1, o:62, a:1, s:1, b:0),
% 13.71/14.12 empty_set [45, 0] (w:1, o:8, a:1, s:1, b:0),
% 13.71/14.12 relation_empty_yielding [46, 1] (w:1, o:30, a:1, s:1, b:0),
% 13.71/14.12 powerset [47, 1] (w:1, o:31, a:1, s:1, b:0),
% 13.71/14.12 relation_dom [48, 1] (w:1, o:29, a:1, s:1, b:0),
% 13.71/14.12 relation_rng [49, 1] (w:1, o:32, a:1, s:1, b:0),
% 13.71/14.12 subset [50, 2] (w:1, o:63, a:1, s:1, b:0),
% 13.71/14.12 skol1 [52, 1] (w:1, o:33, a:1, s:1, b:1),
% 13.71/14.12 skol2 [53, 0] (w:1, o:13, a:1, s:1, b:1),
% 13.71/14.12 skol3 [54, 0] (w:1, o:14, a:1, s:1, b:1),
% 13.71/14.12 skol4 [55, 1] (w:1, o:34, a:1, s:1, b:1),
% 13.71/14.12 skol5 [56, 0] (w:1, o:15, a:1, s:1, b:1),
% 13.71/14.12 skol6 [57, 0] (w:1, o:16, a:1, s:1, b:1),
% 13.71/14.12 skol7 [58, 0] (w:1, o:17, a:1, s:1, b:1),
% 13.71/14.12 skol8 [59, 1] (w:1, o:35, a:1, s:1, b:1),
% 13.71/14.12 skol9 [60, 0] (w:1, o:18, a:1, s:1, b:1),
% 13.71/14.12 skol10 [61, 0] (w:1, o:10, a:1, s:1, b:1),
% 13.71/14.12 skol11 [62, 0] (w:1, o:11, a:1, s:1, b:1),
% 13.71/14.12 skol12 [63, 0] (w:1, o:12, a:1, s:1, b:1).
% 13.71/14.12
% 13.71/14.12
% 13.71/14.12 Starting Search:
% 13.71/14.12
% 13.71/14.12 *** allocated 15000 integers for clauses
% 13.71/14.12 *** allocated 22500 integers for clauses
% 13.71/14.12 *** allocated 33750 integers for clauses
% 13.71/14.12 *** allocated 50625 integers for clauses
% 13.71/14.12 *** allocated 15000 integers for termspace/termends
% 13.71/14.12 *** allocated 75937 integers for clauses
% 13.71/14.12 Resimplifying inuse:
% 13.71/14.12 Done
% 13.71/14.12
% 13.71/14.12 *** allocated 22500 integers for termspace/termends
% 13.71/14.12 *** allocated 113905 integers for clauses
% 13.71/14.12 *** allocated 33750 integers for termspace/termends
% 13.71/14.12
% 13.71/14.12 Intermediate Status:
% 13.71/14.12 Generated: 5240
% 13.71/14.12 Kept: 2054
% 13.71/14.12 Inuse: 217
% 13.71/14.12 Deleted: 40
% 13.71/14.12 Deletedinuse: 1
% 13.71/14.12
% 13.71/14.12 Resimplifying inuse:
% 13.71/14.12 Done
% 13.71/14.12
% 13.71/14.12 *** allocated 170857 integers for clauses
% 13.71/14.12 *** allocated 50625 integers for termspace/termends
% 13.71/14.12 Resimplifying inuse:
% 13.71/14.12 Done
% 13.71/14.12
% 13.71/14.12 *** allocated 256285 integers for clauses
% 13.71/14.12
% 13.71/14.12 Intermediate Status:
% 13.71/14.12 Generated: 8993
% 13.71/14.12 Kept: 4086
% 13.71/14.12 Inuse: 287
% 13.71/14.12 Deleted: 168
% 13.71/14.12 Deletedinuse: 110
% 13.71/14.12
% 13.71/14.12 Resimplifying inuse:
% 13.71/14.12 Done
% 13.71/14.12
% 13.71/14.12 *** allocated 75937 integers for termspace/termends
% 13.71/14.12 *** allocated 384427 integers for clauses
% 13.71/14.12 Resimplifying inuse:
% 13.71/14.12 Done
% 13.71/14.12
% 13.71/14.12
% 13.71/14.12 Intermediate Status:
% 13.71/14.12 Generated: 12431
% 13.71/14.12 Kept: 6105
% 13.71/14.12 Inuse: 326
% 13.71/14.12 Deleted: 176
% 13.71/14.12 Deletedinuse: 118
% 13.71/14.12
% 13.71/14.12 Resimplifying inuse:
% 13.71/14.12 Done
% 13.71/14.12
% 13.71/14.12 *** allocated 113905 integers for termspace/termends
% 13.71/14.12 *** allocated 576640 integers for clauses
% 13.71/14.12 Resimplifying inuse:
% 13.71/14.12 Done
% 13.71/14.12
% 13.71/14.12
% 13.71/14.12 Intermediate Status:
% 13.71/14.12 Generated: 16834
% 13.71/14.12 Kept: 8110
% 13.71/14.12 Inuse: 362
% 13.71/14.12 Deleted: 182
% 13.71/14.12 Deletedinuse: 118
% 13.71/14.12
% 13.71/14.12 Resimplifying inuse:
% 13.71/14.12 Done
% 13.71/14.12
% 13.71/14.12 Resimplifying inuse:
% 13.71/14.12 Done
% 13.71/14.12
% 13.71/14.12 *** allocated 170857 integers for termspace/termends
% 13.71/14.12
% 13.71/14.12 Intermediate Status:
% 13.71/14.12 Generated: 21816
% 13.71/14.12 Kept: 10121
% 13.71/14.12 Inuse: 445
% 13.71/14.12 Deleted: 368
% 13.71/14.12 Deletedinuse: 150
% 13.71/14.12
% 13.71/14.12 Resimplifying inuse:
% 13.71/14.12 Done
% 13.71/14.12
% 13.71/14.12 *** allocated 864960 integers for clauses
% 13.71/14.12 Resimplifying inuse:
% 13.71/14.12 Done
% 13.71/14.12
% 13.71/14.12
% 13.71/14.12 Intermediate Status:
% 13.71/14.12 Generated: 27146
% 13.71/14.12 Kept: 12124
% 13.71/14.12 Inuse: 522
% 13.71/14.12 Deleted: 494
% 13.71/14.12 Deletedinuse: 186
% 13.71/14.12
% 13.71/14.12 Resimplifying inuse:
% 13.71/14.12 Done
% 13.71/14.12
% 13.71/14.12 Resimplifying inuse:
% 13.71/14.12 Done
% 13.71/14.12
% 13.71/14.12
% 13.71/14.12 Intermediate Status:
% 13.71/14.12 Generated: 33227
% 13.71/14.12 Kept: 14147
% 13.71/14.12 Inuse: 587
% 13.71/14.12 Deleted: 525
% 13.71/14.12 Deletedinuse: 186
% 13.71/14.12
% 13.71/14.12 *** allocated 256285 integers for termspace/termends
% 13.71/14.12 Resimplifying inuse:
% 13.71/14.12 Done
% 13.71/14.12
% 13.71/14.12 Resimplifying inuse:
% 13.71/14.12 Done
% 13.71/14.12
% 13.71/14.12
% 13.71/14.12 Intermediate Status:
% 13.71/14.12 Generated: 38144
% 13.71/14.12 Kept: 16212
% 13.71/14.12 Inuse: 630
% 13.71/14.12 Deleted: 542
% 13.71/14.12 Deletedinuse: 186
% 13.71/14.12
% 13.71/14.12 *** allocated 1297440 integers for clauses
% 13.71/14.12 Resimplifying inuse:
% 13.71/14.12 Done
% 13.71/14.12
% 13.71/14.12 Resimplifying inuse:
% 13.71/14.12 Done
% 13.71/14.12
% 13.71/14.12
% 13.71/14.12 Intermediate Status:
% 13.71/14.12 Generated: 42135
% 13.71/14.12 Kept: 18239
% 13.71/14.12 Inuse: 658
% 13.71/14.12 Deleted: 546
% 13.71/14.12 Deletedinuse: 186
% 13.71/14.12
% 13.71/14.12 Resimplifying inuse:
% 13.71/14.12 Done
% 13.71/14.12
% 13.71/14.12 Resimplifying clauses:
% 13.71/14.12 Done
% 13.71/14.12
% 13.71/14.12
% 13.71/14.12 Intermediate Status:
% 13.71/14.12 Generated: 49303
% 13.71/14.12 Kept: 20296
% 13.71/14.12 Inuse: 688
% 13.71/14.12 Deleted: 4208
% 13.71/14.12 Deletedinuse: 186
% 13.71/14.12
% 13.71/14.12 Resimplifying inuse:
% 13.71/14.12 Done
% 13.71/14.12
% 13.71/14.12 Resimplifying inuse:
% 13.71/14.12 Done
% 13.71/14.12
% 13.71/14.12 *** allocated 384427 integers for termspace/termends
% 13.71/14.12
% 13.71/14.12 Intermediate Status:
% 13.71/14.12 Generated: 55821
% 13.71/14.12 Kept: 22305
% 13.71/14.12 Inuse: 725
% 13.71/14.12 Deleted: 4267
% 13.71/14.12 Deletedinuse: 224
% 13.71/14.12
% 13.71/14.12 Resimplifying inuse:
% 13.71/14.12 Done
% 13.71/14.12
% 13.71/14.12 Resimplifying inuse:
% 13.71/14.12 Done
% 13.71/14.12
% 13.71/14.12
% 13.71/14.12 Intermediate Status:
% 13.71/14.12 Generated: 61299
% 13.71/14.12 Kept: 24440
% 13.71/14.12 Inuse: 783
% 13.71/14.12 Deleted: 4321
% 13.71/14.12 Deletedinuse: 249
% 13.71/14.12
% 13.71/14.12 Resimplifying inuse:
% 13.71/14.12 Done
% 13.71/14.12
% 13.71/14.12 *** allocated 1946160 integers for clauses
% 13.71/14.12 Resimplifying inuse:
% 13.71/14.12 Done
% 13.71/14.12
% 13.71/14.12
% 13.71/14.12 Intermediate Status:
% 13.71/14.12 Generated: 66247
% 13.71/14.12 Kept: 26486
% 13.71/14.12 Inuse: 819
% 13.71/14.12 Deleted: 4384
% 13.71/14.12 Deletedinuse: 284
% 13.71/14.12
% 13.71/14.12 Resimplifying inuse:
% 13.71/14.12 Done
% 13.71/14.12
% 13.71/14.12 Resimplifying inuse:
% 13.71/14.12 Done
% 13.71/14.12
% 13.71/14.12
% 13.71/14.12 Intermediate Status:
% 13.71/14.12 Generated: 71727
% 13.71/14.12 Kept: 28493
% 13.71/14.12 Inuse: 850
% 13.71/14.12 Deleted: 4394
% 13.71/14.12 Deletedinuse: 288
% 13.71/14.12
% 13.71/14.12 Resimplifying inuse:
% 13.71/14.12 Done
% 13.71/14.12
% 13.71/14.12 Resimplifying inuse:
% 13.71/14.12 Done
% 13.71/14.12
% 13.71/14.12
% 13.71/14.12 Intermediate Status:
% 13.71/14.12 Generated: 77610
% 13.71/14.12 Kept: 30531
% 13.71/14.12 Inuse: 888
% 13.71/14.12 Deleted: 4396
% 13.71/14.12 Deletedinuse: 288
% 13.71/14.12
% 13.71/14.12 Resimplifying inuse:
% 13.71/14.12 Done
% 13.71/14.12
% 13.71/14.12 Resimplifying inuse:
% 13.71/14.12 Done
% 13.71/14.12
% 13.71/14.12 *** allocated 576640 integers for termspace/termends
% 13.71/14.12
% 13.71/14.12 Intermediate Status:
% 13.71/14.12 Generated: 83167
% 13.71/14.12 Kept: 32566
% 13.71/14.12 Inuse: 921
% 13.71/14.12 Deleted: 4400
% 13.71/14.12 Deletedinuse: 290
% 13.71/14.12
% 13.71/14.12 Resimplifying inuse:
% 13.71/14.12 Done
% 13.71/14.12
% 13.71/14.12 Resimplifying inuse:
% 13.71/14.12 Done
% 13.71/14.12
% 13.71/14.12
% 13.71/14.12 Intermediate Status:
% 13.71/14.12 Generated: 88388
% 13.71/14.12 Kept: 34566
% 13.71/14.12 Inuse: 951
% 13.71/14.12 Deleted: 4402
% 13.71/14.12 Deletedinuse: 292
% 13.71/14.12
% 13.71/14.12 Resimplifying inuse:
% 13.71/14.12 Done
% 13.71/14.12
% 13.71/14.12 Resimplifying inuse:
% 13.71/14.12 Done
% 13.71/14.12
% 13.71/14.12
% 13.71/14.12 Intermediate Status:
% 13.71/14.12 Generated: 94968
% 13.71/14.12 Kept: 36587
% 13.71/14.12 Inuse: 988
% 13.71/14.12 Deleted: 4406
% 13.71/14.12 Deletedinuse: 292
% 13.71/14.12
% 13.71/14.12 Resimplifying inuse:
% 13.71/14.12 Done
% 13.71/14.12
% 13.71/14.12 Resimplifying inuse:
% 13.71/14.12 Done
% 13.71/14.12
% 13.71/14.12 *** allocated 2919240 integers for clauses
% 13.71/14.12
% 13.71/14.12 Intermediate Status:
% 13.71/14.12 Generated: 101356
% 13.71/14.12 Kept: 38607
% 13.71/14.12 Inuse: 1023
% 13.71/14.12 Deleted: 4410
% 13.71/14.12 Deletedinuse: 292
% 13.71/14.12
% 13.71/14.12 Resimplifying inuse:
% 13.71/14.12 Done
% 13.71/14.12
% 13.71/14.12 Resimplifying inuse:
% 13.71/14.12 Done
% 13.71/14.12
% 13.71/14.12 Resimplifying clauses:
% 13.71/14.12
% 13.71/14.12 Bliksems!, er is een bewijs:
% 13.71/14.12 % SZS status Theorem
% 13.71/14.12 % SZS output start Refutation
% 13.71/14.12
% 13.71/14.12 (4) {G0,W7,D3,L3,V1,M3} I { ! relation( X ), ! function( X ), relation(
% 13.71/14.12 function_inverse( X ) ) }.
% 13.71/14.12 (43) {G0,W3,D2,L1,V1,M1} I { subset( X, X ) }.
% 13.71/14.12 (48) {G0,W16,D4,L4,V2,M4} I { ! relation( X ), ! relation( Y ), ! subset(
% 13.71/14.12 relation_rng( X ), relation_dom( Y ) ), relation_dom(
% 13.71/14.12 relation_composition( X, Y ) ) ==> relation_dom( X ) }.
% 13.71/14.12 (49) {G0,W16,D4,L4,V2,M4} I { ! relation( X ), ! relation( Y ), ! subset(
% 13.71/14.12 relation_dom( X ), relation_rng( Y ) ), relation_rng(
% 13.71/14.12 relation_composition( Y, X ) ) ==> relation_rng( X ) }.
% 13.71/14.12 (51) {G0,W12,D4,L4,V1,M4} I { ! relation( X ), ! function( X ), !
% 13.71/14.12 one_to_one( X ), relation_dom( function_inverse( X ) ) ==> relation_rng(
% 13.71/14.12 X ) }.
% 13.71/14.12 (52) {G0,W12,D4,L4,V1,M4} I { ! relation( X ), ! function( X ), !
% 13.71/14.12 one_to_one( X ), relation_rng( function_inverse( X ) ) ==> relation_dom(
% 13.71/14.12 X ) }.
% 13.71/14.12 (53) {G0,W2,D2,L1,V0,M1} I { relation( skol12 ) }.
% 13.71/14.12 (54) {G0,W2,D2,L1,V0,M1} I { function( skol12 ) }.
% 13.71/14.12 (55) {G0,W2,D2,L1,V0,M1} I { one_to_one( skol12 ) }.
% 13.71/14.12 (56) {G0,W16,D5,L2,V0,M2} I { ! relation_dom( relation_composition(
% 13.71/14.12 function_inverse( skol12 ), skol12 ) ) ==> relation_rng( skol12 ), !
% 13.71/14.12 relation_rng( relation_composition( function_inverse( skol12 ), skol12 )
% 13.71/14.12 ) ==> relation_rng( skol12 ) }.
% 13.71/14.12 (79) {G1,W3,D3,L1,V0,M1} R(4,53);r(54) { relation( function_inverse( skol12
% 13.71/14.12 ) ) }.
% 13.71/14.12 (853) {G1,W21,D5,L5,V2,M5} R(48,4) { ! relation( X ), ! subset(
% 13.71/14.12 relation_rng( function_inverse( Y ) ), relation_dom( X ) ), relation_dom
% 13.71/14.12 ( relation_composition( function_inverse( Y ), X ) ) ==> relation_dom(
% 13.71/14.12 function_inverse( Y ) ), ! relation( Y ), ! function( Y ) }.
% 13.71/14.12 (1055) {G1,W8,D4,L2,V0,M2} R(51,53);r(54) { ! one_to_one( skol12 ),
% 13.71/14.12 relation_dom( function_inverse( skol12 ) ) ==> relation_rng( skol12 ) }.
% 13.71/14.12 (1150) {G1,W8,D4,L2,V0,M2} R(52,53);r(54) { ! one_to_one( skol12 ),
% 13.71/14.12 relation_rng( function_inverse( skol12 ) ) ==> relation_dom( skol12 ) }.
% 13.71/14.12 (20109) {G2,W6,D4,L1,V0,M1} S(1150);r(55) { relation_rng( function_inverse
% 13.71/14.12 ( skol12 ) ) ==> relation_dom( skol12 ) }.
% 13.71/14.12 (20118) {G2,W6,D4,L1,V0,M1} S(1055);r(55) { relation_dom( function_inverse
% 13.71/14.12 ( skol12 ) ) ==> relation_rng( skol12 ) }.
% 13.71/14.12 (21020) {G3,W15,D5,L3,V1,M3} P(20109,49);r(79) { ! relation( X ), ! subset
% 13.71/14.12 ( relation_dom( X ), relation_dom( skol12 ) ), relation_rng(
% 13.71/14.12 relation_composition( function_inverse( skol12 ), X ) ) ==> relation_rng
% 13.71/14.12 ( X ) }.
% 13.71/14.12 (39409) {G4,W7,D3,L2,V0,M2} P(853,56);f;d(20118);d(20109);d(21020);q;q;r(53
% 13.71/14.12 ) { ! function( skol12 ), ! subset( relation_dom( skol12 ), relation_dom
% 13.71/14.12 ( skol12 ) ) }.
% 13.71/14.12 (40151) {G5,W0,D0,L0,V0,M0} S(39409);r(54);r(43) { }.
% 13.71/14.12
% 13.71/14.12
% 13.71/14.12 % SZS output end Refutation
% 13.71/14.12 found a proof!
% 13.71/14.12
% 13.71/14.12
% 13.71/14.12 Unprocessed initial clauses:
% 13.71/14.12
% 13.71/14.12 (40153) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), ! in( Y, X ) }.
% 13.71/14.12 (40154) {G0,W4,D2,L2,V1,M2} { ! empty( X ), function( X ) }.
% 13.71/14.12 (40155) {G0,W4,D2,L2,V1,M2} { ! empty( X ), relation( X ) }.
% 13.71/14.12 (40156) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 13.71/14.12 ), relation( X ) }.
% 13.71/14.12 (40157) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 13.71/14.12 ), function( X ) }.
% 13.71/14.12 (40158) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 13.71/14.12 ), one_to_one( X ) }.
% 13.71/14.12 (40159) {G0,W7,D3,L3,V1,M3} { ! relation( X ), ! function( X ), relation(
% 13.71/14.12 function_inverse( X ) ) }.
% 13.71/14.12 (40160) {G0,W7,D3,L3,V1,M3} { ! relation( X ), ! function( X ), function(
% 13.71/14.12 function_inverse( X ) ) }.
% 13.71/14.12 (40161) {G0,W8,D3,L3,V2,M3} { ! relation( X ), ! relation( Y ), relation(
% 13.71/14.12 relation_composition( X, Y ) ) }.
% 13.71/14.12 (40162) {G0,W4,D3,L1,V1,M1} { element( skol1( X ), X ) }.
% 13.71/14.12 (40163) {G0,W8,D3,L3,V2,M3} { ! empty( X ), ! relation( Y ), empty(
% 13.71/14.12 relation_composition( Y, X ) ) }.
% 13.71/14.12 (40164) {G0,W8,D3,L3,V2,M3} { ! empty( X ), ! relation( Y ), relation(
% 13.71/14.12 relation_composition( Y, X ) ) }.
% 13.71/14.12 (40165) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 13.71/14.12 (40166) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 13.71/14.12 (40167) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( empty_set ) }.
% 13.71/14.12 (40168) {G0,W12,D3,L5,V2,M5} { ! relation( X ), ! function( X ), !
% 13.71/14.12 relation( Y ), ! function( Y ), relation( relation_composition( X, Y ) )
% 13.71/14.12 }.
% 13.71/14.12 (40169) {G0,W12,D3,L5,V2,M5} { ! relation( X ), ! function( X ), !
% 13.71/14.12 relation( Y ), ! function( Y ), function( relation_composition( X, Y ) )
% 13.71/14.12 }.
% 13.71/14.12 (40170) {G0,W3,D3,L1,V1,M1} { ! empty( powerset( X ) ) }.
% 13.71/14.12 (40171) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 13.71/14.12 (40172) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 13.71/14.12 (40173) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 13.71/14.12 (40174) {G0,W7,D3,L3,V1,M3} { empty( X ), ! relation( X ), ! empty(
% 13.71/14.12 relation_dom( X ) ) }.
% 13.71/14.12 (40175) {G0,W7,D3,L3,V1,M3} { empty( X ), ! relation( X ), ! empty(
% 13.71/14.12 relation_rng( X ) ) }.
% 13.71/14.12 (40176) {G0,W5,D3,L2,V1,M2} { ! empty( X ), empty( relation_dom( X ) ) }.
% 13.71/14.12 (40177) {G0,W5,D3,L2,V1,M2} { ! empty( X ), relation( relation_dom( X ) )
% 13.71/14.12 }.
% 13.71/14.12 (40178) {G0,W5,D3,L2,V1,M2} { ! empty( X ), empty( relation_rng( X ) ) }.
% 13.71/14.12 (40179) {G0,W5,D3,L2,V1,M2} { ! empty( X ), relation( relation_rng( X ) )
% 13.71/14.12 }.
% 13.71/14.12 (40180) {G0,W8,D3,L3,V2,M3} { ! empty( X ), ! relation( Y ), empty(
% 13.71/14.12 relation_composition( X, Y ) ) }.
% 13.71/14.12 (40181) {G0,W8,D3,L3,V2,M3} { ! empty( X ), ! relation( Y ), relation(
% 13.71/14.12 relation_composition( X, Y ) ) }.
% 13.71/14.12 (40182) {G0,W2,D2,L1,V0,M1} { relation( skol2 ) }.
% 13.71/14.12 (40183) {G0,W2,D2,L1,V0,M1} { function( skol2 ) }.
% 13.71/14.12 (40184) {G0,W2,D2,L1,V0,M1} { empty( skol3 ) }.
% 13.71/14.12 (40185) {G0,W2,D2,L1,V0,M1} { relation( skol3 ) }.
% 13.71/14.12 (40186) {G0,W5,D3,L2,V2,M2} { empty( X ), ! empty( skol4( Y ) ) }.
% 13.71/14.12 (40187) {G0,W7,D3,L2,V1,M2} { empty( X ), element( skol4( X ), powerset( X
% 13.71/14.12 ) ) }.
% 13.71/14.12 (40188) {G0,W2,D2,L1,V0,M1} { empty( skol5 ) }.
% 13.71/14.12 (40189) {G0,W2,D2,L1,V0,M1} { relation( skol6 ) }.
% 13.71/14.12 (40190) {G0,W2,D2,L1,V0,M1} { empty( skol6 ) }.
% 13.71/14.12 (40191) {G0,W2,D2,L1,V0,M1} { function( skol6 ) }.
% 13.71/14.12 (40192) {G0,W2,D2,L1,V0,M1} { ! empty( skol7 ) }.
% 13.71/14.12 (40193) {G0,W2,D2,L1,V0,M1} { relation( skol7 ) }.
% 13.71/14.12 (40194) {G0,W3,D3,L1,V1,M1} { empty( skol8( Y ) ) }.
% 13.71/14.12 (40195) {G0,W5,D3,L1,V1,M1} { element( skol8( X ), powerset( X ) ) }.
% 13.71/14.12 (40196) {G0,W2,D2,L1,V0,M1} { ! empty( skol9 ) }.
% 13.71/14.12 (40197) {G0,W2,D2,L1,V0,M1} { relation( skol10 ) }.
% 13.71/14.12 (40198) {G0,W2,D2,L1,V0,M1} { function( skol10 ) }.
% 13.71/14.12 (40199) {G0,W2,D2,L1,V0,M1} { one_to_one( skol10 ) }.
% 13.71/14.12 (40200) {G0,W2,D2,L1,V0,M1} { relation( skol11 ) }.
% 13.71/14.12 (40201) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( skol11 ) }.
% 13.71/14.12 (40202) {G0,W3,D2,L1,V1,M1} { subset( X, X ) }.
% 13.71/14.12 (40203) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), element( X, Y ) }.
% 13.71/14.12 (40204) {G0,W8,D2,L3,V2,M3} { ! element( X, Y ), empty( Y ), in( X, Y )
% 13.71/14.12 }.
% 13.71/14.12 (40205) {G0,W7,D3,L2,V2,M2} { ! element( X, powerset( Y ) ), subset( X, Y
% 13.71/14.12 ) }.
% 13.71/14.12 (40206) {G0,W7,D3,L2,V2,M2} { ! subset( X, Y ), element( X, powerset( Y )
% 13.71/14.12 ) }.
% 13.71/14.12 (40207) {G0,W16,D4,L4,V2,M4} { ! relation( X ), ! relation( Y ), ! subset
% 13.71/14.12 ( relation_rng( X ), relation_dom( Y ) ), relation_dom(
% 13.71/14.12 relation_composition( X, Y ) ) = relation_dom( X ) }.
% 13.71/14.12 (40208) {G0,W16,D4,L4,V2,M4} { ! relation( X ), ! relation( Y ), ! subset
% 13.71/14.12 ( relation_dom( X ), relation_rng( Y ) ), relation_rng(
% 13.71/14.12 relation_composition( Y, X ) ) = relation_rng( X ) }.
% 13.71/14.12 (40209) {G0,W10,D3,L3,V3,M3} { ! in( X, Z ), ! element( Z, powerset( Y ) )
% 13.71/14.12 , element( X, Y ) }.
% 13.71/14.12 (40210) {G0,W12,D4,L4,V1,M4} { ! relation( X ), ! function( X ), !
% 13.71/14.12 one_to_one( X ), relation_rng( X ) = relation_dom( function_inverse( X )
% 13.71/14.12 ) }.
% 13.71/14.12 (40211) {G0,W12,D4,L4,V1,M4} { ! relation( X ), ! function( X ), !
% 13.71/14.12 one_to_one( X ), relation_dom( X ) = relation_rng( function_inverse( X )
% 13.71/14.12 ) }.
% 13.71/14.12 (40212) {G0,W2,D2,L1,V0,M1} { relation( skol12 ) }.
% 13.71/14.12 (40213) {G0,W2,D2,L1,V0,M1} { function( skol12 ) }.
% 13.71/14.12 (40214) {G0,W2,D2,L1,V0,M1} { one_to_one( skol12 ) }.
% 13.71/14.12 (40215) {G0,W16,D5,L2,V0,M2} { ! relation_dom( relation_composition(
% 13.71/14.12 function_inverse( skol12 ), skol12 ) ) = relation_rng( skol12 ), !
% 13.71/14.12 relation_rng( relation_composition( function_inverse( skol12 ), skol12 )
% 13.71/14.12 ) = relation_rng( skol12 ) }.
% 13.71/14.12 (40216) {G0,W9,D3,L3,V3,M3} { ! in( X, Y ), ! element( Y, powerset( Z ) )
% 13.71/14.12 , ! empty( Z ) }.
% 13.71/14.12 (40217) {G0,W5,D2,L2,V1,M2} { ! empty( X ), X = empty_set }.
% 13.71/14.12 (40218) {G0,W5,D2,L2,V2,M2} { ! in( X, Y ), ! empty( Y ) }.
% 13.71/14.12 (40219) {G0,W7,D2,L3,V2,M3} { ! empty( X ), X = Y, ! empty( Y ) }.
% 13.71/14.12
% 13.71/14.12
% 13.71/14.12 Total Proof:
% 13.71/14.12
% 13.71/14.12 subsumption: (4) {G0,W7,D3,L3,V1,M3} I { ! relation( X ), ! function( X ),
% 13.71/14.12 relation( function_inverse( X ) ) }.
% 13.71/14.12 parent0: (40159) {G0,W7,D3,L3,V1,M3} { ! relation( X ), ! function( X ),
% 13.71/14.12 relation( function_inverse( X ) ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 X := X
% 13.71/14.12 end
% 13.71/14.12 permutation0:
% 13.71/14.12 0 ==> 0
% 13.71/14.12 1 ==> 1
% 13.71/14.12 2 ==> 2
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 subsumption: (43) {G0,W3,D2,L1,V1,M1} I { subset( X, X ) }.
% 13.71/14.12 parent0: (40202) {G0,W3,D2,L1,V1,M1} { subset( X, X ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 X := X
% 13.71/14.12 end
% 13.71/14.12 permutation0:
% 13.71/14.12 0 ==> 0
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 subsumption: (48) {G0,W16,D4,L4,V2,M4} I { ! relation( X ), ! relation( Y )
% 13.71/14.12 , ! subset( relation_rng( X ), relation_dom( Y ) ), relation_dom(
% 13.71/14.12 relation_composition( X, Y ) ) ==> relation_dom( X ) }.
% 13.71/14.12 parent0: (40207) {G0,W16,D4,L4,V2,M4} { ! relation( X ), ! relation( Y ),
% 13.71/14.12 ! subset( relation_rng( X ), relation_dom( Y ) ), relation_dom(
% 13.71/14.12 relation_composition( X, Y ) ) = relation_dom( X ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 X := X
% 13.71/14.12 Y := Y
% 13.71/14.12 end
% 13.71/14.12 permutation0:
% 13.71/14.12 0 ==> 0
% 13.71/14.12 1 ==> 1
% 13.71/14.12 2 ==> 2
% 13.71/14.12 3 ==> 3
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 subsumption: (49) {G0,W16,D4,L4,V2,M4} I { ! relation( X ), ! relation( Y )
% 13.71/14.12 , ! subset( relation_dom( X ), relation_rng( Y ) ), relation_rng(
% 13.71/14.12 relation_composition( Y, X ) ) ==> relation_rng( X ) }.
% 13.71/14.12 parent0: (40208) {G0,W16,D4,L4,V2,M4} { ! relation( X ), ! relation( Y ),
% 13.71/14.12 ! subset( relation_dom( X ), relation_rng( Y ) ), relation_rng(
% 13.71/14.12 relation_composition( Y, X ) ) = relation_rng( X ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 X := X
% 13.71/14.12 Y := Y
% 13.71/14.12 end
% 13.71/14.12 permutation0:
% 13.71/14.12 0 ==> 0
% 13.71/14.12 1 ==> 1
% 13.71/14.12 2 ==> 2
% 13.71/14.12 3 ==> 3
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 eqswap: (40260) {G0,W12,D4,L4,V1,M4} { relation_dom( function_inverse( X )
% 13.71/14.12 ) = relation_rng( X ), ! relation( X ), ! function( X ), ! one_to_one( X
% 13.71/14.12 ) }.
% 13.71/14.12 parent0[3]: (40210) {G0,W12,D4,L4,V1,M4} { ! relation( X ), ! function( X
% 13.71/14.12 ), ! one_to_one( X ), relation_rng( X ) = relation_dom( function_inverse
% 13.71/14.12 ( X ) ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 X := X
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 subsumption: (51) {G0,W12,D4,L4,V1,M4} I { ! relation( X ), ! function( X )
% 13.71/14.12 , ! one_to_one( X ), relation_dom( function_inverse( X ) ) ==>
% 13.71/14.12 relation_rng( X ) }.
% 13.71/14.12 parent0: (40260) {G0,W12,D4,L4,V1,M4} { relation_dom( function_inverse( X
% 13.71/14.12 ) ) = relation_rng( X ), ! relation( X ), ! function( X ), ! one_to_one
% 13.71/14.12 ( X ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 X := X
% 13.71/14.12 end
% 13.71/14.12 permutation0:
% 13.71/14.12 0 ==> 3
% 13.71/14.12 1 ==> 0
% 13.71/14.12 2 ==> 1
% 13.71/14.12 3 ==> 2
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 eqswap: (40274) {G0,W12,D4,L4,V1,M4} { relation_rng( function_inverse( X )
% 13.71/14.12 ) = relation_dom( X ), ! relation( X ), ! function( X ), ! one_to_one( X
% 13.71/14.12 ) }.
% 13.71/14.12 parent0[3]: (40211) {G0,W12,D4,L4,V1,M4} { ! relation( X ), ! function( X
% 13.71/14.12 ), ! one_to_one( X ), relation_dom( X ) = relation_rng( function_inverse
% 13.71/14.12 ( X ) ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 X := X
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 subsumption: (52) {G0,W12,D4,L4,V1,M4} I { ! relation( X ), ! function( X )
% 13.71/14.12 , ! one_to_one( X ), relation_rng( function_inverse( X ) ) ==>
% 13.71/14.12 relation_dom( X ) }.
% 13.71/14.12 parent0: (40274) {G0,W12,D4,L4,V1,M4} { relation_rng( function_inverse( X
% 13.71/14.12 ) ) = relation_dom( X ), ! relation( X ), ! function( X ), ! one_to_one
% 13.71/14.12 ( X ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 X := X
% 13.71/14.12 end
% 13.71/14.12 permutation0:
% 13.71/14.12 0 ==> 3
% 13.71/14.12 1 ==> 0
% 13.71/14.12 2 ==> 1
% 13.71/14.12 3 ==> 2
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 subsumption: (53) {G0,W2,D2,L1,V0,M1} I { relation( skol12 ) }.
% 13.71/14.12 parent0: (40212) {G0,W2,D2,L1,V0,M1} { relation( skol12 ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 end
% 13.71/14.12 permutation0:
% 13.71/14.12 0 ==> 0
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 subsumption: (54) {G0,W2,D2,L1,V0,M1} I { function( skol12 ) }.
% 13.71/14.12 parent0: (40213) {G0,W2,D2,L1,V0,M1} { function( skol12 ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 end
% 13.71/14.12 permutation0:
% 13.71/14.12 0 ==> 0
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 subsumption: (55) {G0,W2,D2,L1,V0,M1} I { one_to_one( skol12 ) }.
% 13.71/14.12 parent0: (40214) {G0,W2,D2,L1,V0,M1} { one_to_one( skol12 ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 end
% 13.71/14.12 permutation0:
% 13.71/14.12 0 ==> 0
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 subsumption: (56) {G0,W16,D5,L2,V0,M2} I { ! relation_dom(
% 13.71/14.12 relation_composition( function_inverse( skol12 ), skol12 ) ) ==>
% 13.71/14.12 relation_rng( skol12 ), ! relation_rng( relation_composition(
% 13.71/14.12 function_inverse( skol12 ), skol12 ) ) ==> relation_rng( skol12 ) }.
% 13.71/14.12 parent0: (40215) {G0,W16,D5,L2,V0,M2} { ! relation_dom(
% 13.71/14.12 relation_composition( function_inverse( skol12 ), skol12 ) ) =
% 13.71/14.12 relation_rng( skol12 ), ! relation_rng( relation_composition(
% 13.71/14.12 function_inverse( skol12 ), skol12 ) ) = relation_rng( skol12 ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 end
% 13.71/14.12 permutation0:
% 13.71/14.12 0 ==> 0
% 13.71/14.12 1 ==> 1
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 resolution: (40334) {G1,W5,D3,L2,V0,M2} { ! function( skol12 ), relation(
% 13.71/14.12 function_inverse( skol12 ) ) }.
% 13.71/14.12 parent0[0]: (4) {G0,W7,D3,L3,V1,M3} I { ! relation( X ), ! function( X ),
% 13.71/14.12 relation( function_inverse( X ) ) }.
% 13.71/14.12 parent1[0]: (53) {G0,W2,D2,L1,V0,M1} I { relation( skol12 ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 X := skol12
% 13.71/14.12 end
% 13.71/14.12 substitution1:
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 resolution: (40335) {G1,W3,D3,L1,V0,M1} { relation( function_inverse(
% 13.71/14.12 skol12 ) ) }.
% 13.71/14.12 parent0[0]: (40334) {G1,W5,D3,L2,V0,M2} { ! function( skol12 ), relation(
% 13.71/14.12 function_inverse( skol12 ) ) }.
% 13.71/14.12 parent1[0]: (54) {G0,W2,D2,L1,V0,M1} I { function( skol12 ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 end
% 13.71/14.12 substitution1:
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 subsumption: (79) {G1,W3,D3,L1,V0,M1} R(4,53);r(54) { relation(
% 13.71/14.12 function_inverse( skol12 ) ) }.
% 13.71/14.12 parent0: (40335) {G1,W3,D3,L1,V0,M1} { relation( function_inverse( skol12
% 13.71/14.12 ) ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 end
% 13.71/14.12 permutation0:
% 13.71/14.12 0 ==> 0
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 eqswap: (40336) {G0,W16,D4,L4,V2,M4} { relation_dom( X ) ==> relation_dom
% 13.71/14.12 ( relation_composition( X, Y ) ), ! relation( X ), ! relation( Y ), !
% 13.71/14.12 subset( relation_rng( X ), relation_dom( Y ) ) }.
% 13.71/14.12 parent0[3]: (48) {G0,W16,D4,L4,V2,M4} I { ! relation( X ), ! relation( Y )
% 13.71/14.12 , ! subset( relation_rng( X ), relation_dom( Y ) ), relation_dom(
% 13.71/14.12 relation_composition( X, Y ) ) ==> relation_dom( X ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 X := X
% 13.71/14.12 Y := Y
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 resolution: (40337) {G1,W21,D5,L5,V2,M5} { relation_dom( function_inverse
% 13.71/14.12 ( X ) ) ==> relation_dom( relation_composition( function_inverse( X ), Y
% 13.71/14.12 ) ), ! relation( Y ), ! subset( relation_rng( function_inverse( X ) ),
% 13.71/14.12 relation_dom( Y ) ), ! relation( X ), ! function( X ) }.
% 13.71/14.12 parent0[1]: (40336) {G0,W16,D4,L4,V2,M4} { relation_dom( X ) ==>
% 13.71/14.12 relation_dom( relation_composition( X, Y ) ), ! relation( X ), ! relation
% 13.71/14.12 ( Y ), ! subset( relation_rng( X ), relation_dom( Y ) ) }.
% 13.71/14.12 parent1[2]: (4) {G0,W7,D3,L3,V1,M3} I { ! relation( X ), ! function( X ),
% 13.71/14.12 relation( function_inverse( X ) ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 X := function_inverse( X )
% 13.71/14.12 Y := Y
% 13.71/14.12 end
% 13.71/14.12 substitution1:
% 13.71/14.12 X := X
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 eqswap: (40340) {G1,W21,D5,L5,V2,M5} { relation_dom( relation_composition
% 13.71/14.12 ( function_inverse( X ), Y ) ) ==> relation_dom( function_inverse( X ) )
% 13.71/14.12 , ! relation( Y ), ! subset( relation_rng( function_inverse( X ) ),
% 13.71/14.12 relation_dom( Y ) ), ! relation( X ), ! function( X ) }.
% 13.71/14.12 parent0[0]: (40337) {G1,W21,D5,L5,V2,M5} { relation_dom( function_inverse
% 13.71/14.12 ( X ) ) ==> relation_dom( relation_composition( function_inverse( X ), Y
% 13.71/14.12 ) ), ! relation( Y ), ! subset( relation_rng( function_inverse( X ) ),
% 13.71/14.12 relation_dom( Y ) ), ! relation( X ), ! function( X ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 X := X
% 13.71/14.12 Y := Y
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 subsumption: (853) {G1,W21,D5,L5,V2,M5} R(48,4) { ! relation( X ), ! subset
% 13.71/14.12 ( relation_rng( function_inverse( Y ) ), relation_dom( X ) ),
% 13.71/14.12 relation_dom( relation_composition( function_inverse( Y ), X ) ) ==>
% 13.71/14.12 relation_dom( function_inverse( Y ) ), ! relation( Y ), ! function( Y )
% 13.71/14.12 }.
% 13.71/14.12 parent0: (40340) {G1,W21,D5,L5,V2,M5} { relation_dom( relation_composition
% 13.71/14.12 ( function_inverse( X ), Y ) ) ==> relation_dom( function_inverse( X ) )
% 13.71/14.12 , ! relation( Y ), ! subset( relation_rng( function_inverse( X ) ),
% 13.71/14.12 relation_dom( Y ) ), ! relation( X ), ! function( X ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 X := Y
% 13.71/14.12 Y := X
% 13.71/14.12 end
% 13.71/14.12 permutation0:
% 13.71/14.12 0 ==> 2
% 13.71/14.12 1 ==> 0
% 13.71/14.12 2 ==> 1
% 13.71/14.12 3 ==> 3
% 13.71/14.12 4 ==> 4
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 eqswap: (40345) {G0,W12,D4,L4,V1,M4} { relation_rng( X ) ==> relation_dom
% 13.71/14.12 ( function_inverse( X ) ), ! relation( X ), ! function( X ), ! one_to_one
% 13.71/14.12 ( X ) }.
% 13.71/14.12 parent0[3]: (51) {G0,W12,D4,L4,V1,M4} I { ! relation( X ), ! function( X )
% 13.71/14.12 , ! one_to_one( X ), relation_dom( function_inverse( X ) ) ==>
% 13.71/14.12 relation_rng( X ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 X := X
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 resolution: (40346) {G1,W10,D4,L3,V0,M3} { relation_rng( skol12 ) ==>
% 13.71/14.12 relation_dom( function_inverse( skol12 ) ), ! function( skol12 ), !
% 13.71/14.12 one_to_one( skol12 ) }.
% 13.71/14.12 parent0[1]: (40345) {G0,W12,D4,L4,V1,M4} { relation_rng( X ) ==>
% 13.71/14.12 relation_dom( function_inverse( X ) ), ! relation( X ), ! function( X ),
% 13.71/14.12 ! one_to_one( X ) }.
% 13.71/14.12 parent1[0]: (53) {G0,W2,D2,L1,V0,M1} I { relation( skol12 ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 X := skol12
% 13.71/14.12 end
% 13.71/14.12 substitution1:
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 resolution: (40347) {G1,W8,D4,L2,V0,M2} { relation_rng( skol12 ) ==>
% 13.71/14.12 relation_dom( function_inverse( skol12 ) ), ! one_to_one( skol12 ) }.
% 13.71/14.12 parent0[1]: (40346) {G1,W10,D4,L3,V0,M3} { relation_rng( skol12 ) ==>
% 13.71/14.12 relation_dom( function_inverse( skol12 ) ), ! function( skol12 ), !
% 13.71/14.12 one_to_one( skol12 ) }.
% 13.71/14.12 parent1[0]: (54) {G0,W2,D2,L1,V0,M1} I { function( skol12 ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 end
% 13.71/14.12 substitution1:
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 eqswap: (40348) {G1,W8,D4,L2,V0,M2} { relation_dom( function_inverse(
% 13.71/14.12 skol12 ) ) ==> relation_rng( skol12 ), ! one_to_one( skol12 ) }.
% 13.71/14.12 parent0[0]: (40347) {G1,W8,D4,L2,V0,M2} { relation_rng( skol12 ) ==>
% 13.71/14.12 relation_dom( function_inverse( skol12 ) ), ! one_to_one( skol12 ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 subsumption: (1055) {G1,W8,D4,L2,V0,M2} R(51,53);r(54) { ! one_to_one(
% 13.71/14.12 skol12 ), relation_dom( function_inverse( skol12 ) ) ==> relation_rng(
% 13.71/14.12 skol12 ) }.
% 13.71/14.12 parent0: (40348) {G1,W8,D4,L2,V0,M2} { relation_dom( function_inverse(
% 13.71/14.12 skol12 ) ) ==> relation_rng( skol12 ), ! one_to_one( skol12 ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 end
% 13.71/14.12 permutation0:
% 13.71/14.12 0 ==> 1
% 13.71/14.12 1 ==> 0
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 eqswap: (40349) {G0,W12,D4,L4,V1,M4} { relation_dom( X ) ==> relation_rng
% 13.71/14.12 ( function_inverse( X ) ), ! relation( X ), ! function( X ), ! one_to_one
% 13.71/14.12 ( X ) }.
% 13.71/14.12 parent0[3]: (52) {G0,W12,D4,L4,V1,M4} I { ! relation( X ), ! function( X )
% 13.71/14.12 , ! one_to_one( X ), relation_rng( function_inverse( X ) ) ==>
% 13.71/14.12 relation_dom( X ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 X := X
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 resolution: (40350) {G1,W10,D4,L3,V0,M3} { relation_dom( skol12 ) ==>
% 13.71/14.12 relation_rng( function_inverse( skol12 ) ), ! function( skol12 ), !
% 13.71/14.12 one_to_one( skol12 ) }.
% 13.71/14.12 parent0[1]: (40349) {G0,W12,D4,L4,V1,M4} { relation_dom( X ) ==>
% 13.71/14.12 relation_rng( function_inverse( X ) ), ! relation( X ), ! function( X ),
% 13.71/14.12 ! one_to_one( X ) }.
% 13.71/14.12 parent1[0]: (53) {G0,W2,D2,L1,V0,M1} I { relation( skol12 ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 X := skol12
% 13.71/14.12 end
% 13.71/14.12 substitution1:
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 resolution: (40351) {G1,W8,D4,L2,V0,M2} { relation_dom( skol12 ) ==>
% 13.71/14.12 relation_rng( function_inverse( skol12 ) ), ! one_to_one( skol12 ) }.
% 13.71/14.12 parent0[1]: (40350) {G1,W10,D4,L3,V0,M3} { relation_dom( skol12 ) ==>
% 13.71/14.12 relation_rng( function_inverse( skol12 ) ), ! function( skol12 ), !
% 13.71/14.12 one_to_one( skol12 ) }.
% 13.71/14.12 parent1[0]: (54) {G0,W2,D2,L1,V0,M1} I { function( skol12 ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 end
% 13.71/14.12 substitution1:
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 eqswap: (40352) {G1,W8,D4,L2,V0,M2} { relation_rng( function_inverse(
% 13.71/14.12 skol12 ) ) ==> relation_dom( skol12 ), ! one_to_one( skol12 ) }.
% 13.71/14.12 parent0[0]: (40351) {G1,W8,D4,L2,V0,M2} { relation_dom( skol12 ) ==>
% 13.71/14.12 relation_rng( function_inverse( skol12 ) ), ! one_to_one( skol12 ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 subsumption: (1150) {G1,W8,D4,L2,V0,M2} R(52,53);r(54) { ! one_to_one(
% 13.71/14.12 skol12 ), relation_rng( function_inverse( skol12 ) ) ==> relation_dom(
% 13.71/14.12 skol12 ) }.
% 13.71/14.12 parent0: (40352) {G1,W8,D4,L2,V0,M2} { relation_rng( function_inverse(
% 13.71/14.12 skol12 ) ) ==> relation_dom( skol12 ), ! one_to_one( skol12 ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 end
% 13.71/14.12 permutation0:
% 13.71/14.12 0 ==> 1
% 13.71/14.12 1 ==> 0
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 resolution: (40354) {G1,W6,D4,L1,V0,M1} { relation_rng( function_inverse(
% 13.71/14.12 skol12 ) ) ==> relation_dom( skol12 ) }.
% 13.71/14.12 parent0[0]: (1150) {G1,W8,D4,L2,V0,M2} R(52,53);r(54) { ! one_to_one(
% 13.71/14.12 skol12 ), relation_rng( function_inverse( skol12 ) ) ==> relation_dom(
% 13.71/14.12 skol12 ) }.
% 13.71/14.12 parent1[0]: (55) {G0,W2,D2,L1,V0,M1} I { one_to_one( skol12 ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 end
% 13.71/14.12 substitution1:
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 subsumption: (20109) {G2,W6,D4,L1,V0,M1} S(1150);r(55) { relation_rng(
% 13.71/14.12 function_inverse( skol12 ) ) ==> relation_dom( skol12 ) }.
% 13.71/14.12 parent0: (40354) {G1,W6,D4,L1,V0,M1} { relation_rng( function_inverse(
% 13.71/14.12 skol12 ) ) ==> relation_dom( skol12 ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 end
% 13.71/14.12 permutation0:
% 13.71/14.12 0 ==> 0
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 resolution: (40357) {G1,W6,D4,L1,V0,M1} { relation_dom( function_inverse(
% 13.71/14.12 skol12 ) ) ==> relation_rng( skol12 ) }.
% 13.71/14.12 parent0[0]: (1055) {G1,W8,D4,L2,V0,M2} R(51,53);r(54) { ! one_to_one(
% 13.71/14.12 skol12 ), relation_dom( function_inverse( skol12 ) ) ==> relation_rng(
% 13.71/14.12 skol12 ) }.
% 13.71/14.12 parent1[0]: (55) {G0,W2,D2,L1,V0,M1} I { one_to_one( skol12 ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 end
% 13.71/14.12 substitution1:
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 subsumption: (20118) {G2,W6,D4,L1,V0,M1} S(1055);r(55) { relation_dom(
% 13.71/14.12 function_inverse( skol12 ) ) ==> relation_rng( skol12 ) }.
% 13.71/14.12 parent0: (40357) {G1,W6,D4,L1,V0,M1} { relation_dom( function_inverse(
% 13.71/14.12 skol12 ) ) ==> relation_rng( skol12 ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 end
% 13.71/14.12 permutation0:
% 13.71/14.12 0 ==> 0
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 eqswap: (40360) {G0,W16,D4,L4,V2,M4} { relation_rng( Y ) ==> relation_rng
% 13.71/14.12 ( relation_composition( X, Y ) ), ! relation( Y ), ! relation( X ), !
% 13.71/14.12 subset( relation_dom( Y ), relation_rng( X ) ) }.
% 13.71/14.12 parent0[3]: (49) {G0,W16,D4,L4,V2,M4} I { ! relation( X ), ! relation( Y )
% 13.71/14.12 , ! subset( relation_dom( X ), relation_rng( Y ) ), relation_rng(
% 13.71/14.12 relation_composition( Y, X ) ) ==> relation_rng( X ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 X := Y
% 13.71/14.12 Y := X
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 paramod: (40362) {G1,W18,D5,L4,V1,M4} { ! subset( relation_dom( X ),
% 13.71/14.12 relation_dom( skol12 ) ), relation_rng( X ) ==> relation_rng(
% 13.71/14.12 relation_composition( function_inverse( skol12 ), X ) ), ! relation( X )
% 13.71/14.12 , ! relation( function_inverse( skol12 ) ) }.
% 13.71/14.12 parent0[0]: (20109) {G2,W6,D4,L1,V0,M1} S(1150);r(55) { relation_rng(
% 13.71/14.12 function_inverse( skol12 ) ) ==> relation_dom( skol12 ) }.
% 13.71/14.12 parent1[3; 4]: (40360) {G0,W16,D4,L4,V2,M4} { relation_rng( Y ) ==>
% 13.71/14.12 relation_rng( relation_composition( X, Y ) ), ! relation( Y ), ! relation
% 13.71/14.12 ( X ), ! subset( relation_dom( Y ), relation_rng( X ) ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 end
% 13.71/14.12 substitution1:
% 13.71/14.12 X := function_inverse( skol12 )
% 13.71/14.12 Y := X
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 resolution: (40367) {G2,W15,D5,L3,V1,M3} { ! subset( relation_dom( X ),
% 13.71/14.12 relation_dom( skol12 ) ), relation_rng( X ) ==> relation_rng(
% 13.71/14.12 relation_composition( function_inverse( skol12 ), X ) ), ! relation( X )
% 13.71/14.12 }.
% 13.71/14.12 parent0[3]: (40362) {G1,W18,D5,L4,V1,M4} { ! subset( relation_dom( X ),
% 13.71/14.12 relation_dom( skol12 ) ), relation_rng( X ) ==> relation_rng(
% 13.71/14.12 relation_composition( function_inverse( skol12 ), X ) ), ! relation( X )
% 13.71/14.12 , ! relation( function_inverse( skol12 ) ) }.
% 13.71/14.12 parent1[0]: (79) {G1,W3,D3,L1,V0,M1} R(4,53);r(54) { relation(
% 13.71/14.12 function_inverse( skol12 ) ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 X := X
% 13.71/14.12 end
% 13.71/14.12 substitution1:
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 eqswap: (40368) {G2,W15,D5,L3,V1,M3} { relation_rng( relation_composition
% 13.71/14.12 ( function_inverse( skol12 ), X ) ) ==> relation_rng( X ), ! subset(
% 13.71/14.12 relation_dom( X ), relation_dom( skol12 ) ), ! relation( X ) }.
% 13.71/14.12 parent0[1]: (40367) {G2,W15,D5,L3,V1,M3} { ! subset( relation_dom( X ),
% 13.71/14.12 relation_dom( skol12 ) ), relation_rng( X ) ==> relation_rng(
% 13.71/14.12 relation_composition( function_inverse( skol12 ), X ) ), ! relation( X )
% 13.71/14.12 }.
% 13.71/14.12 substitution0:
% 13.71/14.12 X := X
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 subsumption: (21020) {G3,W15,D5,L3,V1,M3} P(20109,49);r(79) { ! relation( X
% 13.71/14.12 ), ! subset( relation_dom( X ), relation_dom( skol12 ) ), relation_rng(
% 13.71/14.12 relation_composition( function_inverse( skol12 ), X ) ) ==> relation_rng
% 13.71/14.12 ( X ) }.
% 13.71/14.12 parent0: (40368) {G2,W15,D5,L3,V1,M3} { relation_rng( relation_composition
% 13.71/14.12 ( function_inverse( skol12 ), X ) ) ==> relation_rng( X ), ! subset(
% 13.71/14.12 relation_dom( X ), relation_dom( skol12 ) ), ! relation( X ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 X := X
% 13.71/14.12 end
% 13.71/14.12 permutation0:
% 13.71/14.12 0 ==> 2
% 13.71/14.12 1 ==> 1
% 13.71/14.12 2 ==> 0
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 eqswap: (40370) {G0,W16,D5,L2,V0,M2} { ! relation_rng( skol12 ) ==>
% 13.71/14.12 relation_dom( relation_composition( function_inverse( skol12 ), skol12 )
% 13.71/14.12 ), ! relation_rng( relation_composition( function_inverse( skol12 ),
% 13.71/14.12 skol12 ) ) ==> relation_rng( skol12 ) }.
% 13.71/14.12 parent0[0]: (56) {G0,W16,D5,L2,V0,M2} I { ! relation_dom(
% 13.71/14.12 relation_composition( function_inverse( skol12 ), skol12 ) ) ==>
% 13.71/14.12 relation_rng( skol12 ), ! relation_rng( relation_composition(
% 13.71/14.12 function_inverse( skol12 ), skol12 ) ) ==> relation_rng( skol12 ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 paramod: (40376) {G1,W26,D5,L6,V0,M6} { ! relation_rng( skol12 ) ==>
% 13.71/14.12 relation_dom( function_inverse( skol12 ) ), ! relation( skol12 ), !
% 13.71/14.12 subset( relation_rng( function_inverse( skol12 ) ), relation_dom( skol12
% 13.71/14.12 ) ), ! relation( skol12 ), ! function( skol12 ), ! relation_rng(
% 13.71/14.12 relation_composition( function_inverse( skol12 ), skol12 ) ) ==>
% 13.71/14.12 relation_rng( skol12 ) }.
% 13.71/14.12 parent0[2]: (853) {G1,W21,D5,L5,V2,M5} R(48,4) { ! relation( X ), ! subset
% 13.71/14.12 ( relation_rng( function_inverse( Y ) ), relation_dom( X ) ),
% 13.71/14.12 relation_dom( relation_composition( function_inverse( Y ), X ) ) ==>
% 13.71/14.12 relation_dom( function_inverse( Y ) ), ! relation( Y ), ! function( Y )
% 13.71/14.12 }.
% 13.71/14.12 parent1[0; 4]: (40370) {G0,W16,D5,L2,V0,M2} { ! relation_rng( skol12 ) ==>
% 13.71/14.12 relation_dom( relation_composition( function_inverse( skol12 ), skol12 )
% 13.71/14.12 ), ! relation_rng( relation_composition( function_inverse( skol12 ),
% 13.71/14.12 skol12 ) ) ==> relation_rng( skol12 ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 X := skol12
% 13.71/14.12 Y := skol12
% 13.71/14.12 end
% 13.71/14.12 substitution1:
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 paramod: (40378) {G2,W25,D5,L6,V0,M6} { ! relation_rng( skol12 ) ==>
% 13.71/14.12 relation_rng( skol12 ), ! relation( skol12 ), ! subset( relation_rng(
% 13.71/14.12 function_inverse( skol12 ) ), relation_dom( skol12 ) ), ! relation(
% 13.71/14.12 skol12 ), ! function( skol12 ), ! relation_rng( relation_composition(
% 13.71/14.12 function_inverse( skol12 ), skol12 ) ) ==> relation_rng( skol12 ) }.
% 13.71/14.12 parent0[0]: (20118) {G2,W6,D4,L1,V0,M1} S(1055);r(55) { relation_dom(
% 13.71/14.12 function_inverse( skol12 ) ) ==> relation_rng( skol12 ) }.
% 13.71/14.12 parent1[0; 4]: (40376) {G1,W26,D5,L6,V0,M6} { ! relation_rng( skol12 ) ==>
% 13.71/14.12 relation_dom( function_inverse( skol12 ) ), ! relation( skol12 ), !
% 13.71/14.12 subset( relation_rng( function_inverse( skol12 ) ), relation_dom( skol12
% 13.71/14.12 ) ), ! relation( skol12 ), ! function( skol12 ), ! relation_rng(
% 13.71/14.12 relation_composition( function_inverse( skol12 ), skol12 ) ) ==>
% 13.71/14.12 relation_rng( skol12 ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 end
% 13.71/14.12 substitution1:
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 factor: (40379) {G2,W23,D5,L5,V0,M5} { ! relation_rng( skol12 ) ==>
% 13.71/14.12 relation_rng( skol12 ), ! relation( skol12 ), ! subset( relation_rng(
% 13.71/14.12 function_inverse( skol12 ) ), relation_dom( skol12 ) ), ! function(
% 13.71/14.12 skol12 ), ! relation_rng( relation_composition( function_inverse( skol12
% 13.71/14.12 ), skol12 ) ) ==> relation_rng( skol12 ) }.
% 13.71/14.12 parent0[1, 3]: (40378) {G2,W25,D5,L6,V0,M6} { ! relation_rng( skol12 ) ==>
% 13.71/14.12 relation_rng( skol12 ), ! relation( skol12 ), ! subset( relation_rng(
% 13.71/14.12 function_inverse( skol12 ) ), relation_dom( skol12 ) ), ! relation(
% 13.71/14.12 skol12 ), ! function( skol12 ), ! relation_rng( relation_composition(
% 13.71/14.12 function_inverse( skol12 ), skol12 ) ) ==> relation_rng( skol12 ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 paramod: (40380) {G3,W22,D5,L5,V0,M5} { ! subset( relation_dom( skol12 ),
% 13.71/14.12 relation_dom( skol12 ) ), ! relation_rng( skol12 ) ==> relation_rng(
% 13.71/14.12 skol12 ), ! relation( skol12 ), ! function( skol12 ), ! relation_rng(
% 13.71/14.12 relation_composition( function_inverse( skol12 ), skol12 ) ) ==>
% 13.71/14.12 relation_rng( skol12 ) }.
% 13.71/14.12 parent0[0]: (20109) {G2,W6,D4,L1,V0,M1} S(1150);r(55) { relation_rng(
% 13.71/14.12 function_inverse( skol12 ) ) ==> relation_dom( skol12 ) }.
% 13.71/14.12 parent1[2; 2]: (40379) {G2,W23,D5,L5,V0,M5} { ! relation_rng( skol12 ) ==>
% 13.71/14.12 relation_rng( skol12 ), ! relation( skol12 ), ! subset( relation_rng(
% 13.71/14.12 function_inverse( skol12 ) ), relation_dom( skol12 ) ), ! function(
% 13.71/14.12 skol12 ), ! relation_rng( relation_composition( function_inverse( skol12
% 13.71/14.12 ), skol12 ) ) ==> relation_rng( skol12 ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 end
% 13.71/14.12 substitution1:
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 paramod: (40381) {G4,W26,D3,L7,V0,M7} { ! relation_rng( skol12 ) ==>
% 13.71/14.12 relation_rng( skol12 ), ! relation( skol12 ), ! subset( relation_dom(
% 13.71/14.12 skol12 ), relation_dom( skol12 ) ), ! subset( relation_dom( skol12 ),
% 13.71/14.12 relation_dom( skol12 ) ), ! relation_rng( skol12 ) ==> relation_rng(
% 13.71/14.12 skol12 ), ! relation( skol12 ), ! function( skol12 ) }.
% 13.71/14.12 parent0[2]: (21020) {G3,W15,D5,L3,V1,M3} P(20109,49);r(79) { ! relation( X
% 13.71/14.12 ), ! subset( relation_dom( X ), relation_dom( skol12 ) ), relation_rng(
% 13.71/14.12 relation_composition( function_inverse( skol12 ), X ) ) ==> relation_rng
% 13.71/14.12 ( X ) }.
% 13.71/14.12 parent1[4; 2]: (40380) {G3,W22,D5,L5,V0,M5} { ! subset( relation_dom(
% 13.71/14.12 skol12 ), relation_dom( skol12 ) ), ! relation_rng( skol12 ) ==>
% 13.71/14.12 relation_rng( skol12 ), ! relation( skol12 ), ! function( skol12 ), !
% 13.71/14.12 relation_rng( relation_composition( function_inverse( skol12 ), skol12 )
% 13.71/14.12 ) ==> relation_rng( skol12 ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 X := skol12
% 13.71/14.12 end
% 13.71/14.12 substitution1:
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 eqrefl: (40395) {G0,W21,D3,L6,V0,M6} { ! relation( skol12 ), ! subset(
% 13.71/14.12 relation_dom( skol12 ), relation_dom( skol12 ) ), ! subset( relation_dom
% 13.71/14.12 ( skol12 ), relation_dom( skol12 ) ), ! relation_rng( skol12 ) ==>
% 13.71/14.12 relation_rng( skol12 ), ! relation( skol12 ), ! function( skol12 ) }.
% 13.71/14.12 parent0[0]: (40381) {G4,W26,D3,L7,V0,M7} { ! relation_rng( skol12 ) ==>
% 13.71/14.12 relation_rng( skol12 ), ! relation( skol12 ), ! subset( relation_dom(
% 13.71/14.12 skol12 ), relation_dom( skol12 ) ), ! subset( relation_dom( skol12 ),
% 13.71/14.12 relation_dom( skol12 ) ), ! relation_rng( skol12 ) ==> relation_rng(
% 13.71/14.12 skol12 ), ! relation( skol12 ), ! function( skol12 ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 factor: (40396) {G0,W19,D3,L5,V0,M5} { ! relation( skol12 ), ! subset(
% 13.71/14.12 relation_dom( skol12 ), relation_dom( skol12 ) ), ! subset( relation_dom
% 13.71/14.12 ( skol12 ), relation_dom( skol12 ) ), ! relation_rng( skol12 ) ==>
% 13.71/14.12 relation_rng( skol12 ), ! function( skol12 ) }.
% 13.71/14.12 parent0[0, 4]: (40395) {G0,W21,D3,L6,V0,M6} { ! relation( skol12 ), !
% 13.71/14.12 subset( relation_dom( skol12 ), relation_dom( skol12 ) ), ! subset(
% 13.71/14.12 relation_dom( skol12 ), relation_dom( skol12 ) ), ! relation_rng( skol12
% 13.71/14.12 ) ==> relation_rng( skol12 ), ! relation( skol12 ), ! function( skol12 )
% 13.71/14.12 }.
% 13.71/14.12 substitution0:
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 eqrefl: (40399) {G0,W14,D3,L4,V0,M4} { ! relation( skol12 ), ! subset(
% 13.71/14.12 relation_dom( skol12 ), relation_dom( skol12 ) ), ! subset( relation_dom
% 13.71/14.12 ( skol12 ), relation_dom( skol12 ) ), ! function( skol12 ) }.
% 13.71/14.12 parent0[3]: (40396) {G0,W19,D3,L5,V0,M5} { ! relation( skol12 ), ! subset
% 13.71/14.12 ( relation_dom( skol12 ), relation_dom( skol12 ) ), ! subset(
% 13.71/14.12 relation_dom( skol12 ), relation_dom( skol12 ) ), ! relation_rng( skol12
% 13.71/14.12 ) ==> relation_rng( skol12 ), ! function( skol12 ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 factor: (40400) {G0,W9,D3,L3,V0,M3} { ! relation( skol12 ), ! subset(
% 13.71/14.12 relation_dom( skol12 ), relation_dom( skol12 ) ), ! function( skol12 )
% 13.71/14.12 }.
% 13.71/14.12 parent0[1, 2]: (40399) {G0,W14,D3,L4,V0,M4} { ! relation( skol12 ), !
% 13.71/14.12 subset( relation_dom( skol12 ), relation_dom( skol12 ) ), ! subset(
% 13.71/14.12 relation_dom( skol12 ), relation_dom( skol12 ) ), ! function( skol12 )
% 13.71/14.12 }.
% 13.71/14.12 substitution0:
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 resolution: (40401) {G1,W7,D3,L2,V0,M2} { ! subset( relation_dom( skol12 )
% 13.71/14.12 , relation_dom( skol12 ) ), ! function( skol12 ) }.
% 13.71/14.12 parent0[0]: (40400) {G0,W9,D3,L3,V0,M3} { ! relation( skol12 ), ! subset(
% 13.71/14.12 relation_dom( skol12 ), relation_dom( skol12 ) ), ! function( skol12 )
% 13.71/14.12 }.
% 13.71/14.12 parent1[0]: (53) {G0,W2,D2,L1,V0,M1} I { relation( skol12 ) }.
% 13.71/14.12 substitution0:
% 13.71/14.12 end
% 13.71/14.12 substitution1:
% 13.71/14.12 end
% 13.71/14.12
% 13.71/14.12 subsumption: (39409) {G4,W7,D3,L2,V0,M2} P(853,56);f;d(20118);d(20109);d(
% 13.71/14.12 21020);q;q;r(53) { ! function( skol12 ), ! subset( relation_dom( skol12 )
% 13.71/14.13 , relation_dom( skol12 ) ) }.
% 13.71/14.13 parent0: (40401) {G1,W7,D3,L2,V0,M2} { ! subset( relation_dom( skol12 ),
% 13.71/14.13 relation_dom( skol12 ) ), ! function( skol12 ) }.
% 13.71/14.13 substitution0:
% 13.71/14.13 end
% 13.71/14.13 permutation0:
% 13.71/14.13 0 ==> 1
% 13.71/14.13 1 ==> 0
% 13.71/14.13 end
% 13.71/14.13
% 13.71/14.13 resolution: (40402) {G1,W5,D3,L1,V0,M1} { ! subset( relation_dom( skol12 )
% 13.71/14.13 , relation_dom( skol12 ) ) }.
% 13.71/14.13 parent0[0]: (39409) {G4,W7,D3,L2,V0,M2} P(853,56);f;d(20118);d(20109);d(
% 13.71/14.13 21020);q;q;r(53) { ! function( skol12 ), ! subset( relation_dom( skol12 )
% 13.71/14.13 , relation_dom( skol12 ) ) }.
% 13.71/14.13 parent1[0]: (54) {G0,W2,D2,L1,V0,M1} I { function( skol12 ) }.
% 13.71/14.13 substitution0:
% 13.71/14.13 end
% 13.71/14.13 substitution1:
% 13.71/14.13 end
% 13.71/14.13
% 13.71/14.13 resolution: (40403) {G1,W0,D0,L0,V0,M0} { }.
% 13.71/14.13 parent0[0]: (40402) {G1,W5,D3,L1,V0,M1} { ! subset( relation_dom( skol12 )
% 13.71/14.13 , relation_dom( skol12 ) ) }.
% 13.71/14.13 parent1[0]: (43) {G0,W3,D2,L1,V1,M1} I { subset( X, X ) }.
% 13.71/14.13 substitution0:
% 13.71/14.13 end
% 13.71/14.13 substitution1:
% 13.71/14.13 X := relation_dom( skol12 )
% 13.71/14.13 end
% 13.71/14.13
% 13.71/14.13 subsumption: (40151) {G5,W0,D0,L0,V0,M0} S(39409);r(54);r(43) { }.
% 13.71/14.13 parent0: (40403) {G1,W0,D0,L0,V0,M0} { }.
% 13.71/14.13 substitution0:
% 13.71/14.13 end
% 13.71/14.13 permutation0:
% 13.71/14.13 end
% 13.71/14.13
% 13.71/14.13 Proof check complete!
% 13.71/14.13
% 13.71/14.13 Memory use:
% 13.71/14.13
% 13.71/14.13 space for terms: 491610
% 13.71/14.13 space for clauses: 2024872
% 13.71/14.13
% 13.71/14.13
% 13.71/14.13 clauses generated: 110959
% 13.71/14.13 clauses kept: 40152
% 13.71/14.13 clauses selected: 1055
% 13.71/14.13 clauses deleted: 4418
% 13.71/14.13 clauses inuse deleted: 292
% 13.71/14.13
% 13.71/14.13 subsentry: 269422
% 13.71/14.13 literals s-matched: 110179
% 13.71/14.13 literals matched: 106923
% 13.71/14.13 full subsumption: 25326
% 13.71/14.13
% 13.71/14.13 checksum: 737069862
% 13.71/14.13
% 13.71/14.13
% 13.71/14.13 Bliksem ended
%------------------------------------------------------------------------------