TSTP Solution File: SEU215+3 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : SEU215+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n026.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 0s
% DateTime : Tue Jul 19 07:11:29 EDT 2022

% Result   : Theorem 75.70s 76.09s
% Output   : Refutation 75.70s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU215+3 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13  % Command  : bliksem %s
% 0.13/0.34  % Computer : n026.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % DateTime : Sun Jun 19 10:51:40 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 4.48/4.86  *** allocated 10000 integers for termspace/termends
% 4.48/4.86  *** allocated 10000 integers for clauses
% 4.48/4.86  *** allocated 10000 integers for justifications
% 4.48/4.86  Bliksem 1.12
% 4.48/4.86  
% 4.48/4.86  
% 4.48/4.86  Automatic Strategy Selection
% 4.48/4.86  
% 4.48/4.86  
% 4.48/4.86  Clauses:
% 4.48/4.86  
% 4.48/4.86  { ! in( X, Y ), ! in( Y, X ) }.
% 4.48/4.86  { ! empty( X ), function( X ) }.
% 4.48/4.86  { ! empty( X ), relation( X ) }.
% 4.48/4.86  { unordered_pair( X, Y ) = unordered_pair( Y, X ) }.
% 4.48/4.86  { ! relation( X ), ! function( X ), ! in( Y, relation_dom( X ) ), ! Z = 
% 4.48/4.86    apply( X, Y ), in( ordered_pair( Y, Z ), X ) }.
% 4.48/4.86  { ! relation( X ), ! function( X ), ! in( Y, relation_dom( X ) ), ! in( 
% 4.48/4.86    ordered_pair( Y, Z ), X ), Z = apply( X, Y ) }.
% 4.48/4.86  { ! relation( X ), ! function( X ), in( Y, relation_dom( X ) ), ! Z = apply
% 4.48/4.86    ( X, Y ), Z = empty_set }.
% 4.48/4.86  { ! relation( X ), ! function( X ), in( Y, relation_dom( X ) ), ! Z = 
% 4.48/4.86    empty_set, Z = apply( X, Y ) }.
% 4.48/4.86  { ordered_pair( X, Y ) = unordered_pair( unordered_pair( X, Y ), singleton
% 4.48/4.86    ( X ) ) }.
% 4.48/4.86  { ! relation( X ), ! relation( Y ), relation( relation_composition( X, Y )
% 4.48/4.86     ) }.
% 4.48/4.86  { element( skol1( X ), X ) }.
% 4.48/4.86  { ! empty( X ), ! relation( Y ), empty( relation_composition( Y, X ) ) }.
% 4.48/4.86  { ! empty( X ), ! relation( Y ), relation( relation_composition( Y, X ) ) }
% 4.48/4.86    .
% 4.48/4.86  { empty( empty_set ) }.
% 4.48/4.86  { relation( empty_set ) }.
% 4.48/4.86  { relation_empty_yielding( empty_set ) }.
% 4.48/4.86  { ! relation( X ), ! function( X ), ! relation( Y ), ! function( Y ), 
% 4.48/4.86    relation( relation_composition( X, Y ) ) }.
% 4.48/4.86  { ! relation( X ), ! function( X ), ! relation( Y ), ! function( Y ), 
% 4.48/4.86    function( relation_composition( X, Y ) ) }.
% 4.48/4.86  { ! empty( powerset( X ) ) }.
% 4.48/4.86  { empty( empty_set ) }.
% 4.48/4.86  { ! empty( ordered_pair( X, Y ) ) }.
% 4.48/4.86  { ! empty( singleton( X ) ) }.
% 4.48/4.86  { ! empty( unordered_pair( X, Y ) ) }.
% 4.48/4.86  { empty( empty_set ) }.
% 4.48/4.86  { relation( empty_set ) }.
% 4.48/4.86  { empty( X ), ! relation( X ), ! empty( relation_dom( X ) ) }.
% 4.48/4.86  { ! empty( X ), empty( relation_dom( X ) ) }.
% 4.48/4.86  { ! empty( X ), relation( relation_dom( X ) ) }.
% 4.48/4.86  { ! empty( X ), ! relation( Y ), empty( relation_composition( X, Y ) ) }.
% 4.48/4.86  { ! empty( X ), ! relation( Y ), relation( relation_composition( X, Y ) ) }
% 4.48/4.86    .
% 4.48/4.86  { relation( skol2 ) }.
% 4.48/4.86  { function( skol2 ) }.
% 4.48/4.86  { empty( skol3 ) }.
% 4.48/4.86  { relation( skol3 ) }.
% 4.48/4.86  { empty( X ), ! empty( skol4( Y ) ) }.
% 4.48/4.86  { empty( X ), element( skol4( X ), powerset( X ) ) }.
% 4.48/4.86  { empty( skol5 ) }.
% 4.48/4.86  { ! empty( skol6 ) }.
% 4.48/4.86  { relation( skol6 ) }.
% 4.48/4.86  { empty( skol7( Y ) ) }.
% 4.48/4.86  { element( skol7( X ), powerset( X ) ) }.
% 4.48/4.86  { ! empty( skol8 ) }.
% 4.48/4.86  { relation( skol9 ) }.
% 4.48/4.86  { relation_empty_yielding( skol9 ) }.
% 4.48/4.86  { subset( X, X ) }.
% 4.48/4.86  { ! in( X, Y ), element( X, Y ) }.
% 4.48/4.86  { ! relation( X ), ! function( X ), ! relation( Y ), ! function( Y ), ! in
% 4.48/4.86    ( Z, relation_dom( relation_composition( Y, X ) ) ), in( Z, relation_dom
% 4.48/4.86    ( Y ) ) }.
% 4.48/4.86  { ! relation( X ), ! function( X ), ! relation( Y ), ! function( Y ), ! in
% 4.48/4.86    ( Z, relation_dom( relation_composition( Y, X ) ) ), in( apply( Y, Z ), 
% 4.48/4.86    relation_dom( X ) ) }.
% 4.48/4.86  { ! relation( X ), ! function( X ), ! relation( Y ), ! function( Y ), ! in
% 4.48/4.86    ( Z, relation_dom( Y ) ), ! in( apply( Y, Z ), relation_dom( X ) ), in( Z
% 4.48/4.86    , relation_dom( relation_composition( Y, X ) ) ) }.
% 4.48/4.86  { ! relation( X ), ! function( X ), ! relation( Y ), ! function( Y ), ! in
% 4.48/4.86    ( Z, relation_dom( relation_composition( Y, X ) ) ), apply( 
% 4.48/4.86    relation_composition( Y, X ), Z ) = apply( X, apply( Y, Z ) ) }.
% 4.48/4.86  { relation( skol10 ) }.
% 4.48/4.86  { function( skol10 ) }.
% 4.48/4.86  { relation( skol11 ) }.
% 4.48/4.86  { function( skol11 ) }.
% 4.48/4.86  { in( skol12, relation_dom( skol10 ) ) }.
% 4.48/4.86  { ! apply( relation_composition( skol10, skol11 ), skol12 ) = apply( skol11
% 4.48/4.86    , apply( skol10, skol12 ) ) }.
% 4.48/4.86  { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 4.48/4.86  { ! element( X, powerset( Y ) ), subset( X, Y ) }.
% 4.48/4.86  { ! subset( X, Y ), element( X, powerset( Y ) ) }.
% 4.48/4.86  { ! in( X, Z ), ! element( Z, powerset( Y ) ), element( X, Y ) }.
% 4.48/4.86  { ! in( X, Y ), ! element( Y, powerset( Z ) ), ! empty( Z ) }.
% 4.48/4.86  { ! empty( X ), X = empty_set }.
% 4.48/4.86  { ! in( X, Y ), ! empty( Y ) }.
% 4.48/4.86  { ! empty( X ), X = Y, ! empty( Y ) }.
% 4.48/4.86  
% 4.48/4.86  percentage equality = 0.090226, percentage horn = 0.933333
% 4.48/4.86  This is a problem with some equality
% 4.48/4.86  
% 4.48/4.86  
% 4.48/4.86  
% 4.48/4.86  Options Used:
% 4.48/4.86  
% 4.48/4.86  useres =            1
% 4.48/4.86  useparamod =        1
% 4.48/4.86  useeqrefl =         1
% 4.48/4.86  useeqfact =         1
% 4.48/4.86  usefactor =         1
% 4.48/4.86  usesimpsplitting =  0
% 4.48/4.86  usesimpdemod =      5
% 75.70/76.09  usesimpres =        3
% 75.70/76.09  
% 75.70/76.09  resimpinuse      =  1000
% 75.70/76.09  resimpclauses =     20000
% 75.70/76.09  substype =          eqrewr
% 75.70/76.09  backwardsubs =      1
% 75.70/76.09  selectoldest =      5
% 75.70/76.09  
% 75.70/76.09  litorderings [0] =  split
% 75.70/76.09  litorderings [1] =  extend the termordering, first sorting on arguments
% 75.70/76.09  
% 75.70/76.09  termordering =      kbo
% 75.70/76.09  
% 75.70/76.09  litapriori =        0
% 75.70/76.09  termapriori =       1
% 75.70/76.09  litaposteriori =    0
% 75.70/76.09  termaposteriori =   0
% 75.70/76.09  demodaposteriori =  0
% 75.70/76.09  ordereqreflfact =   0
% 75.70/76.09  
% 75.70/76.09  litselect =         negord
% 75.70/76.09  
% 75.70/76.09  maxweight =         15
% 75.70/76.09  maxdepth =          30000
% 75.70/76.09  maxlength =         115
% 75.70/76.09  maxnrvars =         195
% 75.70/76.09  excuselevel =       1
% 75.70/76.09  increasemaxweight = 1
% 75.70/76.09  
% 75.70/76.09  maxselected =       10000000
% 75.70/76.09  maxnrclauses =      10000000
% 75.70/76.09  
% 75.70/76.09  showgenerated =    0
% 75.70/76.09  showkept =         0
% 75.70/76.09  showselected =     0
% 75.70/76.09  showdeleted =      0
% 75.70/76.09  showresimp =       1
% 75.70/76.09  showstatus =       2000
% 75.70/76.09  
% 75.70/76.09  prologoutput =     0
% 75.70/76.09  nrgoals =          5000000
% 75.70/76.09  totalproof =       1
% 75.70/76.09  
% 75.70/76.09  Symbols occurring in the translation:
% 75.70/76.09  
% 75.70/76.09  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 75.70/76.09  .  [1, 2]      (w:1, o:34, a:1, s:1, b:0), 
% 75.70/76.09  !  [4, 1]      (w:0, o:19, a:1, s:1, b:0), 
% 75.70/76.09  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 75.70/76.09  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 75.70/76.09  in  [37, 2]      (w:1, o:58, a:1, s:1, b:0), 
% 75.70/76.09  empty  [38, 1]      (w:1, o:24, a:1, s:1, b:0), 
% 75.70/76.09  function  [39, 1]      (w:1, o:25, a:1, s:1, b:0), 
% 75.70/76.09  relation  [40, 1]      (w:1, o:26, a:1, s:1, b:0), 
% 75.70/76.09  unordered_pair  [41, 2]      (w:1, o:59, a:1, s:1, b:0), 
% 75.70/76.09  relation_dom  [43, 1]      (w:1, o:27, a:1, s:1, b:0), 
% 75.70/76.09  apply  [44, 2]      (w:1, o:60, a:1, s:1, b:0), 
% 75.70/76.09  ordered_pair  [45, 2]      (w:1, o:61, a:1, s:1, b:0), 
% 75.70/76.09  empty_set  [46, 0]      (w:1, o:9, a:1, s:1, b:0), 
% 75.70/76.09  singleton  [47, 1]      (w:1, o:29, a:1, s:1, b:0), 
% 75.70/76.09  relation_composition  [48, 2]      (w:1, o:62, a:1, s:1, b:0), 
% 75.70/76.09  element  [49, 2]      (w:1, o:63, a:1, s:1, b:0), 
% 75.70/76.09  relation_empty_yielding  [50, 1]      (w:1, o:28, a:1, s:1, b:0), 
% 75.70/76.09  powerset  [51, 1]      (w:1, o:30, a:1, s:1, b:0), 
% 75.70/76.09  subset  [52, 2]      (w:1, o:64, a:1, s:1, b:0), 
% 75.70/76.09  skol1  [53, 1]      (w:1, o:31, a:1, s:1, b:1), 
% 75.70/76.09  skol2  [54, 0]      (w:1, o:13, a:1, s:1, b:1), 
% 75.70/76.09  skol3  [55, 0]      (w:1, o:14, a:1, s:1, b:1), 
% 75.70/76.09  skol4  [56, 1]      (w:1, o:32, a:1, s:1, b:1), 
% 75.70/76.09  skol5  [57, 0]      (w:1, o:15, a:1, s:1, b:1), 
% 75.70/76.09  skol6  [58, 0]      (w:1, o:16, a:1, s:1, b:1), 
% 75.70/76.09  skol7  [59, 1]      (w:1, o:33, a:1, s:1, b:1), 
% 75.70/76.09  skol8  [60, 0]      (w:1, o:17, a:1, s:1, b:1), 
% 75.70/76.09  skol9  [61, 0]      (w:1, o:18, a:1, s:1, b:1), 
% 75.70/76.09  skol10  [62, 0]      (w:1, o:10, a:1, s:1, b:1), 
% 75.70/76.09  skol11  [63, 0]      (w:1, o:11, a:1, s:1, b:1), 
% 75.70/76.09  skol12  [64, 0]      (w:1, o:12, a:1, s:1, b:1).
% 75.70/76.09  
% 75.70/76.09  
% 75.70/76.09  Starting Search:
% 75.70/76.09  
% 75.70/76.09  *** allocated 15000 integers for clauses
% 75.70/76.09  *** allocated 22500 integers for clauses
% 75.70/76.09  *** allocated 33750 integers for clauses
% 75.70/76.09  *** allocated 15000 integers for termspace/termends
% 75.70/76.09  *** allocated 50625 integers for clauses
% 75.70/76.09  *** allocated 22500 integers for termspace/termends
% 75.70/76.09  *** allocated 75937 integers for clauses
% 75.70/76.09  Resimplifying inuse:
% 75.70/76.09  Done
% 75.70/76.09  
% 75.70/76.09  *** allocated 113905 integers for clauses
% 75.70/76.09  *** allocated 33750 integers for termspace/termends
% 75.70/76.09  
% 75.70/76.09  Intermediate Status:
% 75.70/76.09  Generated:    16217
% 75.70/76.09  Kept:         2002
% 75.70/76.09  Inuse:        265
% 75.70/76.09  Deleted:      140
% 75.70/76.09  Deletedinuse: 32
% 75.70/76.09  
% 75.70/76.09  Resimplifying inuse:
% 75.70/76.09  Done
% 75.70/76.09  
% 75.70/76.09  *** allocated 170857 integers for clauses
% 75.70/76.09  *** allocated 50625 integers for termspace/termends
% 75.70/76.09  Resimplifying inuse:
% 75.70/76.09  Done
% 75.70/76.09  
% 75.70/76.09  *** allocated 256285 integers for clauses
% 75.70/76.09  
% 75.70/76.09  Intermediate Status:
% 75.70/76.09  Generated:    36196
% 75.70/76.09  Kept:         4013
% 75.70/76.09  Inuse:        402
% 75.70/76.09  Deleted:      159
% 75.70/76.09  Deletedinuse: 42
% 75.70/76.09  
% 75.70/76.09  Resimplifying inuse:
% 75.70/76.09  Done
% 75.70/76.09  
% 75.70/76.09  *** allocated 75937 integers for termspace/termends
% 75.70/76.09  *** allocated 384427 integers for clauses
% 75.70/76.09  Resimplifying inuse:
% 75.70/76.09  Done
% 75.70/76.09  
% 75.70/76.09  *** allocated 113905 integers for termspace/termends
% 75.70/76.09  
% 75.70/76.09  Intermediate Status:
% 75.70/76.09  Generated:    46948
% 75.70/76.09  Kept:         6904
% 75.70/76.09  Inuse:        455
% 75.70/76.09  Deleted:      163
% 75.70/76.09  Deletedinuse: 42
% 75.70/76.09  
% 75.70/76.09  Resimplifying inuse:
% 75.70/76.09  Done
% 75.70/76.09  
% 75.70/76.09  *** allocated 576640 integers for clauses
% 75.70/76.09  Resimplifying inuse:
% 75.70/76.09  Done
% 75.70/76.09  
% 75.70/76.09  
% 75.70/76.09  Intermediate Status:
% 75.70/76.09  Generated:    64715
% 75.70/76.09  Kept:         8912
% 75.70/76.09  Inuse:        521
% 75.70/76.09  Deleted:      165
% 75.70/76.09  Deletedinuse: 42
% 75.70/76.09  
% 75.70/76.09  Resimplifying inuse:
% 75.70/76.09  Done
% 75.70/76.09  
% 75.70/76.09  *** allocated 170857 integers for termspace/termends
% 75.70/76.09  Resimplifying inuse:
% 75.70/76.09  Done
% 75.70/76.09  
% 75.70/76.09  
% 75.70/76.09  Intermediate Status:
% 75.70/76.09  Generated:    89131
% 75.70/76.09  Kept:         10914
% 75.70/76.09  Inuse:        594
% 75.70/76.09  Deleted:      176
% 75.70/76.09  Deletedinuse: 42
% 75.70/76.09  
% 75.70/76.09  Resimplifying inuse:
% 75.70/76.09  Done
% 75.70/76.09  
% 75.70/76.09  *** allocated 864960 integers for clauses
% 75.70/76.09  Resimplifying inuse:
% 75.70/76.09  Done
% 75.70/76.09  
% 75.70/76.09  
% 75.70/76.09  Intermediate Status:
% 75.70/76.09  Generated:    100009
% 75.70/76.09  Kept:         13199
% 75.70/76.09  Inuse:        640
% 75.70/76.09  Deleted:      183
% 75.70/76.09  Deletedinuse: 47
% 75.70/76.09  
% 75.70/76.09  Resimplifying inuse:
% 75.70/76.09  Done
% 75.70/76.09  
% 75.70/76.09  *** allocated 256285 integers for termspace/termends
% 75.70/76.09  Resimplifying inuse:
% 75.70/76.09  Done
% 75.70/76.09  
% 75.70/76.09  
% 75.70/76.09  Intermediate Status:
% 75.70/76.09  Generated:    120068
% 75.70/76.09  Kept:         15234
% 75.70/76.09  Inuse:        705
% 75.70/76.09  Deleted:      191
% 75.70/76.09  Deletedinuse: 47
% 75.70/76.09  
% 75.70/76.09  Resimplifying inuse:
% 75.70/76.09  Done
% 75.70/76.09  
% 75.70/76.09  *** allocated 1297440 integers for clauses
% 75.70/76.09  
% 75.70/76.09  Intermediate Status:
% 75.70/76.09  Generated:    136955
% 75.70/76.09  Kept:         17247
% 75.70/76.09  Inuse:        802
% 75.70/76.09  Deleted:      290
% 75.70/76.09  Deletedinuse: 61
% 75.70/76.09  
% 75.70/76.09  Resimplifying inuse:
% 75.70/76.09  Done
% 75.70/76.09  
% 75.70/76.09  Resimplifying inuse:
% 75.70/76.09  Done
% 75.70/76.09  
% 75.70/76.09  
% 75.70/76.09  Intermediate Status:
% 75.70/76.09  Generated:    157743
% 75.70/76.09  Kept:         19540
% 75.70/76.09  Inuse:        884
% 75.70/76.09  Deleted:      383
% 75.70/76.09  Deletedinuse: 68
% 75.70/76.09  
% 75.70/76.09  Resimplifying inuse:
% 75.70/76.09  Done
% 75.70/76.09  
% 75.70/76.09  Resimplifying clauses:
% 75.70/76.09  Done
% 75.70/76.09  
% 75.70/76.09  Resimplifying inuse:
% 75.70/76.09  Done
% 75.70/76.09  
% 75.70/76.09  *** allocated 384427 integers for termspace/termends
% 75.70/76.09  
% 75.70/76.09  Intermediate Status:
% 75.70/76.09  Generated:    229341
% 75.70/76.09  Kept:         21552
% 75.70/76.09  Inuse:        1068
% 75.70/76.09  Deleted:      3064
% 75.70/76.09  Deletedinuse: 69
% 75.70/76.09  
% 75.70/76.09  Resimplifying inuse:
% 75.70/76.09  Done
% 75.70/76.09  
% 75.70/76.09  Resimplifying inuse:
% 75.70/76.09  Done
% 75.70/76.09  
% 75.70/76.09  
% 75.70/76.09  Intermediate Status:
% 75.70/76.09  Generated:    347030
% 75.70/76.09  Kept:         23555
% 75.70/76.09  Inuse:        1303
% 75.70/76.09  Deleted:      3090
% 75.70/76.09  Deletedinuse: 73
% 75.70/76.09  
% 75.70/76.09  Resimplifying inuse:
% 75.70/76.09  Done
% 75.70/76.09  
% 75.70/76.09  Resimplifying inuse:
% 75.70/76.09  Done
% 75.70/76.09  
% 75.70/76.09  
% 75.70/76.09  Intermediate Status:
% 75.70/76.09  Generated:    403264
% 75.70/76.09  Kept:         25646
% 75.70/76.09  Inuse:        1356
% 75.70/76.09  Deleted:      3097
% 75.70/76.09  Deletedinuse: 78
% 75.70/76.09  
% 75.70/76.09  Resimplifying inuse:
% 75.70/76.09  Done
% 75.70/76.09  
% 75.70/76.09  *** allocated 1946160 integers for clauses
% 75.70/76.09  Resimplifying inuse:
% 75.70/76.09  Done
% 75.70/76.09  
% 75.70/76.09  
% 75.70/76.09  Intermediate Status:
% 75.70/76.09  Generated:    470533
% 75.70/76.09  Kept:         27801
% 75.70/76.09  Inuse:        1476
% 75.70/76.09  Deleted:      3097
% 75.70/76.09  Deletedinuse: 78
% 75.70/76.09  
% 75.70/76.09  Resimplifying inuse:
% 75.70/76.09  Done
% 75.70/76.09  
% 75.70/76.09  Resimplifying inuse:
% 75.70/76.09  Done
% 75.70/76.09  
% 75.70/76.09  
% 75.70/76.09  Intermediate Status:
% 75.70/76.09  Generated:    552960
% 75.70/76.09  Kept:         30181
% 75.70/76.09  Inuse:        1628
% 75.70/76.09  Deleted:      3098
% 75.70/76.09  Deletedinuse: 78
% 75.70/76.09  
% 75.70/76.09  Resimplifying inuse:
% 75.70/76.09  Done
% 75.70/76.09  
% 75.70/76.09  *** allocated 576640 integers for termspace/termends
% 75.70/76.09  Resimplifying inuse:
% 75.70/76.09  Done
% 75.70/76.09  
% 75.70/76.09  
% 75.70/76.09  Intermediate Status:
% 75.70/76.09  Generated:    595996
% 75.70/76.09  Kept:         32185
% 75.70/76.09  Inuse:        1695
% 75.70/76.09  Deleted:      3098
% 75.70/76.09  Deletedinuse: 78
% 75.70/76.09  
% 75.70/76.09  Resimplifying inuse:
% 75.70/76.09  Done
% 75.70/76.09  
% 75.70/76.09  Resimplifying inuse:
% 75.70/76.09  Done
% 75.70/76.09  
% 75.70/76.09  
% 75.70/76.09  Intermediate Status:
% 75.70/76.09  Generated:    614028
% 75.70/76.09  Kept:         34205
% 75.70/76.09  Inuse:        1725
% 75.70/76.09  Deleted:      3098
% 75.70/76.09  Deletedinuse: 78
% 75.70/76.09  
% 75.70/76.09  Resimplifying inuse:
% 75.70/76.09  Done
% 75.70/76.09  
% 75.70/76.09  Resimplifying inuse:
% 75.70/76.09  Done
% 75.70/76.09  
% 75.70/76.09  
% 75.70/76.09  Intermediate Status:
% 75.70/76.09  Generated:    628969
% 75.70/76.09  Kept:         36392
% 75.70/76.09  Inuse:        1758
% 75.70/76.09  Deleted:      3155
% 75.70/76.09  Deletedinuse: 135
% 75.70/76.09  
% 75.70/76.09  Resimplifying inuse:
% 75.70/76.09  Done
% 75.70/76.09  
% 75.70/76.09  
% 75.70/76.09  Intermediate Status:
% 75.70/76.09  Generated:    666612
% 75.70/76.09  Kept:         38432
% 75.70/76.09  Inuse:        1872
% 75.70/76.09  Deleted:      3160
% 75.70/76.09  Deletedinuse: 135
% 75.70/76.09  
% 75.70/76.09  Resimplifying inuse:
% 75.70/76.09  Done
% 75.70/76.09  
% 75.70/76.09  Resimplifying inuse:
% 75.70/76.09  Done
% 75.70/76.09  
% 75.70/76.09  Resimplifying clauses:
% 75.70/76.09  
% 75.70/76.09  Bliksems!, er is een bewijs:
% 75.70/76.09  % SZS status Theorem
% 75.70/76.09  % SZS output start Refutation
% 75.70/76.09  
% 75.70/76.09  (6) {G0,W16,D3,L5,V3,M5} I { ! relation( X ), ! function( X ), in( Y, 
% 75.70/76.09    relation_dom( X ) ), ! Z = apply( X, Y ), Z = empty_set }.
% 75.70/76.09  (9) {G0,W8,D3,L3,V2,M3} I { ! relation( X ), ! relation( Y ), relation( 
% 75.70/76.09    relation_composition( X, Y ) ) }.
% 75.70/76.09  (16) {G0,W12,D3,L5,V2,M5} I { ! relation( X ), ! function( X ), ! relation
% 75.70/76.09    ( Y ), ! function( Y ), function( relation_composition( X, Y ) ) }.
% 75.70/76.09  (44) {G0,W24,D4,L7,V3,M7} I { ! relation( X ), ! function( X ), ! relation
% 75.70/76.09    ( Y ), ! function( Y ), ! in( Z, relation_dom( Y ) ), ! in( apply( Y, Z )
% 75.70/76.09    , relation_dom( X ) ), in( Z, relation_dom( relation_composition( Y, X )
% 75.70/76.09     ) ) }.
% 75.70/76.09  (45) {G0,W25,D4,L6,V3,M6} I { ! relation( X ), ! function( X ), ! relation
% 75.70/76.09    ( Y ), ! function( Y ), ! in( Z, relation_dom( relation_composition( Y, X
% 75.70/76.09     ) ) ), apply( X, apply( Y, Z ) ) ==> apply( relation_composition( Y, X )
% 75.70/76.09    , Z ) }.
% 75.70/76.09  (46) {G0,W2,D2,L1,V0,M1} I { relation( skol10 ) }.
% 75.70/76.09  (47) {G0,W2,D2,L1,V0,M1} I { function( skol10 ) }.
% 75.70/76.09  (48) {G0,W2,D2,L1,V0,M1} I { relation( skol11 ) }.
% 75.70/76.09  (49) {G0,W2,D2,L1,V0,M1} I { function( skol11 ) }.
% 75.70/76.09  (50) {G0,W4,D3,L1,V0,M1} I { in( skol12, relation_dom( skol10 ) ) }.
% 75.70/76.09  (51) {G0,W11,D4,L1,V0,M1} I { ! apply( skol11, apply( skol10, skol12 ) ) 
% 75.70/76.09    ==> apply( relation_composition( skol10, skol11 ), skol12 ) }.
% 75.70/76.09  (62) {G1,W13,D3,L4,V2,M4} Q(6) { ! relation( X ), ! function( X ), in( Y, 
% 75.70/76.09    relation_dom( X ) ), apply( X, Y ) ==> empty_set }.
% 75.70/76.09  (180) {G1,W6,D3,L2,V1,M2} R(9,46) { ! relation( X ), relation( 
% 75.70/76.09    relation_composition( skol10, X ) ) }.
% 75.70/76.09  (238) {G1,W8,D3,L3,V1,M3} R(16,46);r(47) { ! relation( X ), ! function( X )
% 75.70/76.09    , function( relation_composition( skol10, X ) ) }.
% 75.70/76.09  (505) {G1,W20,D4,L5,V2,M5} R(44,48);r(49) { ! relation( X ), ! function( X
% 75.70/76.09     ), ! in( Y, relation_dom( X ) ), ! in( apply( X, Y ), relation_dom( 
% 75.70/76.09    skol11 ) ), in( Y, relation_dom( relation_composition( X, skol11 ) ) )
% 75.70/76.09     }.
% 75.70/76.09  (562) {G1,W12,D4,L4,V0,M4} R(51,45);r(48) { ! function( skol11 ), ! 
% 75.70/76.09    relation( skol10 ), ! function( skol10 ), ! in( skol12, relation_dom( 
% 75.70/76.09    relation_composition( skol10, skol11 ) ) ) }.
% 75.70/76.09  (767) {G2,W15,D4,L3,V0,M3} P(62,51);r(48) { ! apply( relation_composition( 
% 75.70/76.09    skol10, skol11 ), skol12 ) ==> empty_set, ! function( skol11 ), in( apply
% 75.70/76.09    ( skol10, skol12 ), relation_dom( skol11 ) ) }.
% 75.70/76.09  (2370) {G2,W4,D3,L1,V0,M1} R(180,48) { relation( relation_composition( 
% 75.70/76.09    skol10, skol11 ) ) }.
% 75.70/76.09  (12451) {G2,W4,D3,L1,V0,M1} R(238,48);r(49) { function( 
% 75.70/76.09    relation_composition( skol10, skol11 ) ) }.
% 75.70/76.09  (20259) {G3,W13,D4,L2,V0,M2} S(767);r(49) { ! apply( relation_composition( 
% 75.70/76.09    skol10, skol11 ), skol12 ) ==> empty_set, in( apply( skol10, skol12 ), 
% 75.70/76.09    relation_dom( skol11 ) ) }.
% 75.70/76.09  (20261) {G2,W6,D4,L1,V0,M1} S(562);r(49);r(46);r(47) { ! in( skol12, 
% 75.70/76.09    relation_dom( relation_composition( skol10, skol11 ) ) ) }.
% 75.70/76.09  (20578) {G3,W11,D4,L2,V0,M2} R(20261,62);r(2370) { ! function( 
% 75.70/76.09    relation_composition( skol10, skol11 ) ), apply( relation_composition( 
% 75.70/76.09    skol10, skol11 ), skol12 ) ==> empty_set }.
% 75.70/76.09  (25033) {G3,W12,D3,L3,V0,M3} R(505,20261);r(46) { ! function( skol10 ), ! 
% 75.70/76.09    in( skol12, relation_dom( skol10 ) ), ! in( apply( skol10, skol12 ), 
% 75.70/76.09    relation_dom( skol11 ) ) }.
% 75.70/76.09  (40296) {G4,W6,D3,L1,V0,M1} S(25033);r(47);r(50) { ! in( apply( skol10, 
% 75.70/76.09    skol12 ), relation_dom( skol11 ) ) }.
% 75.70/76.09  (40364) {G4,W7,D4,L1,V0,M1} S(20578);r(12451) { apply( relation_composition
% 75.70/76.09    ( skol10, skol11 ), skol12 ) ==> empty_set }.
% 75.70/76.09  (40394) {G5,W0,D0,L0,V0,M0} S(20259);d(40364);q;r(40296) {  }.
% 75.70/76.09  
% 75.70/76.09  
% 75.70/76.09  % SZS output end Refutation
% 75.70/76.09  found a proof!
% 75.70/76.09  
% 75.70/76.09  
% 75.70/76.09  Unprocessed initial clauses:
% 75.70/76.09  
% 75.70/76.09  (40396) {G0,W6,D2,L2,V2,M2}  { ! in( X, Y ), ! in( Y, X ) }.
% 75.70/76.09  (40397) {G0,W4,D2,L2,V1,M2}  { ! empty( X ), function( X ) }.
% 75.70/76.09  (40398) {G0,W4,D2,L2,V1,M2}  { ! empty( X ), relation( X ) }.
% 75.70/76.09  (40399) {G0,W7,D3,L1,V2,M1}  { unordered_pair( X, Y ) = unordered_pair( Y, 
% 75.70/76.09    X ) }.
% 75.70/76.09  (40400) {G0,W18,D3,L5,V3,M5}  { ! relation( X ), ! function( X ), ! in( Y, 
% 75.70/76.09    relation_dom( X ) ), ! Z = apply( X, Y ), in( ordered_pair( Y, Z ), X )
% 75.70/76.09     }.
% 75.70/76.09  (40401) {G0,W18,D3,L5,V3,M5}  { ! relation( X ), ! function( X ), ! in( Y, 
% 75.70/76.09    relation_dom( X ) ), ! in( ordered_pair( Y, Z ), X ), Z = apply( X, Y )
% 75.70/76.09     }.
% 75.70/76.09  (40402) {G0,W16,D3,L5,V3,M5}  { ! relation( X ), ! function( X ), in( Y, 
% 75.70/76.09    relation_dom( X ) ), ! Z = apply( X, Y ), Z = empty_set }.
% 75.70/76.09  (40403) {G0,W16,D3,L5,V3,M5}  { ! relation( X ), ! function( X ), in( Y, 
% 75.70/76.09    relation_dom( X ) ), ! Z = empty_set, Z = apply( X, Y ) }.
% 75.70/76.09  (40404) {G0,W10,D4,L1,V2,M1}  { ordered_pair( X, Y ) = unordered_pair( 
% 75.70/76.09    unordered_pair( X, Y ), singleton( X ) ) }.
% 75.70/76.09  (40405) {G0,W8,D3,L3,V2,M3}  { ! relation( X ), ! relation( Y ), relation( 
% 75.70/76.09    relation_composition( X, Y ) ) }.
% 75.70/76.09  (40406) {G0,W4,D3,L1,V1,M1}  { element( skol1( X ), X ) }.
% 75.70/76.09  (40407) {G0,W8,D3,L3,V2,M3}  { ! empty( X ), ! relation( Y ), empty( 
% 75.70/76.09    relation_composition( Y, X ) ) }.
% 75.70/76.09  (40408) {G0,W8,D3,L3,V2,M3}  { ! empty( X ), ! relation( Y ), relation( 
% 75.70/76.09    relation_composition( Y, X ) ) }.
% 75.70/76.09  (40409) {G0,W2,D2,L1,V0,M1}  { empty( empty_set ) }.
% 75.70/76.09  (40410) {G0,W2,D2,L1,V0,M1}  { relation( empty_set ) }.
% 75.70/76.09  (40411) {G0,W2,D2,L1,V0,M1}  { relation_empty_yielding( empty_set ) }.
% 75.70/76.09  (40412) {G0,W12,D3,L5,V2,M5}  { ! relation( X ), ! function( X ), ! 
% 75.70/76.09    relation( Y ), ! function( Y ), relation( relation_composition( X, Y ) )
% 75.70/76.09     }.
% 75.70/76.09  (40413) {G0,W12,D3,L5,V2,M5}  { ! relation( X ), ! function( X ), ! 
% 75.70/76.09    relation( Y ), ! function( Y ), function( relation_composition( X, Y ) )
% 75.70/76.09     }.
% 75.70/76.09  (40414) {G0,W3,D3,L1,V1,M1}  { ! empty( powerset( X ) ) }.
% 75.70/76.09  (40415) {G0,W2,D2,L1,V0,M1}  { empty( empty_set ) }.
% 75.70/76.09  (40416) {G0,W4,D3,L1,V2,M1}  { ! empty( ordered_pair( X, Y ) ) }.
% 75.70/76.09  (40417) {G0,W3,D3,L1,V1,M1}  { ! empty( singleton( X ) ) }.
% 75.70/76.09  (40418) {G0,W4,D3,L1,V2,M1}  { ! empty( unordered_pair( X, Y ) ) }.
% 75.70/76.09  (40419) {G0,W2,D2,L1,V0,M1}  { empty( empty_set ) }.
% 75.70/76.09  (40420) {G0,W2,D2,L1,V0,M1}  { relation( empty_set ) }.
% 75.70/76.09  (40421) {G0,W7,D3,L3,V1,M3}  { empty( X ), ! relation( X ), ! empty( 
% 75.70/76.09    relation_dom( X ) ) }.
% 75.70/76.09  (40422) {G0,W5,D3,L2,V1,M2}  { ! empty( X ), empty( relation_dom( X ) ) }.
% 75.70/76.09  (40423) {G0,W5,D3,L2,V1,M2}  { ! empty( X ), relation( relation_dom( X ) )
% 75.70/76.09     }.
% 75.70/76.09  (40424) {G0,W8,D3,L3,V2,M3}  { ! empty( X ), ! relation( Y ), empty( 
% 75.70/76.09    relation_composition( X, Y ) ) }.
% 75.70/76.09  (40425) {G0,W8,D3,L3,V2,M3}  { ! empty( X ), ! relation( Y ), relation( 
% 75.70/76.09    relation_composition( X, Y ) ) }.
% 75.70/76.09  (40426) {G0,W2,D2,L1,V0,M1}  { relation( skol2 ) }.
% 75.70/76.09  (40427) {G0,W2,D2,L1,V0,M1}  { function( skol2 ) }.
% 75.70/76.09  (40428) {G0,W2,D2,L1,V0,M1}  { empty( skol3 ) }.
% 75.70/76.09  (40429) {G0,W2,D2,L1,V0,M1}  { relation( skol3 ) }.
% 75.70/76.09  (40430) {G0,W5,D3,L2,V2,M2}  { empty( X ), ! empty( skol4( Y ) ) }.
% 75.70/76.09  (40431) {G0,W7,D3,L2,V1,M2}  { empty( X ), element( skol4( X ), powerset( X
% 75.70/76.09     ) ) }.
% 75.70/76.09  (40432) {G0,W2,D2,L1,V0,M1}  { empty( skol5 ) }.
% 75.70/76.09  (40433) {G0,W2,D2,L1,V0,M1}  { ! empty( skol6 ) }.
% 75.70/76.09  (40434) {G0,W2,D2,L1,V0,M1}  { relation( skol6 ) }.
% 75.70/76.09  (40435) {G0,W3,D3,L1,V1,M1}  { empty( skol7( Y ) ) }.
% 75.70/76.09  (40436) {G0,W5,D3,L1,V1,M1}  { element( skol7( X ), powerset( X ) ) }.
% 75.70/76.09  (40437) {G0,W2,D2,L1,V0,M1}  { ! empty( skol8 ) }.
% 75.70/76.09  (40438) {G0,W2,D2,L1,V0,M1}  { relation( skol9 ) }.
% 75.70/76.09  (40439) {G0,W2,D2,L1,V0,M1}  { relation_empty_yielding( skol9 ) }.
% 75.70/76.09  (40440) {G0,W3,D2,L1,V1,M1}  { subset( X, X ) }.
% 75.70/76.09  (40441) {G0,W6,D2,L2,V2,M2}  { ! in( X, Y ), element( X, Y ) }.
% 75.70/76.09  (40442) {G0,W18,D4,L6,V3,M6}  { ! relation( X ), ! function( X ), ! 
% 75.70/76.09    relation( Y ), ! function( Y ), ! in( Z, relation_dom( 
% 75.70/76.09    relation_composition( Y, X ) ) ), in( Z, relation_dom( Y ) ) }.
% 75.70/76.09  (40443) {G0,W20,D4,L6,V3,M6}  { ! relation( X ), ! function( X ), ! 
% 75.70/76.09    relation( Y ), ! function( Y ), ! in( Z, relation_dom( 
% 75.70/76.09    relation_composition( Y, X ) ) ), in( apply( Y, Z ), relation_dom( X ) )
% 75.70/76.09     }.
% 75.70/76.09  (40444) {G0,W24,D4,L7,V3,M7}  { ! relation( X ), ! function( X ), ! 
% 75.70/76.09    relation( Y ), ! function( Y ), ! in( Z, relation_dom( Y ) ), ! in( apply
% 75.70/76.09    ( Y, Z ), relation_dom( X ) ), in( Z, relation_dom( relation_composition
% 75.70/76.09    ( Y, X ) ) ) }.
% 75.70/76.09  (40445) {G0,W25,D4,L6,V3,M6}  { ! relation( X ), ! function( X ), ! 
% 75.70/76.09    relation( Y ), ! function( Y ), ! in( Z, relation_dom( 
% 75.70/76.09    relation_composition( Y, X ) ) ), apply( relation_composition( Y, X ), Z
% 75.70/76.09     ) = apply( X, apply( Y, Z ) ) }.
% 75.70/76.09  (40446) {G0,W2,D2,L1,V0,M1}  { relation( skol10 ) }.
% 75.70/76.09  (40447) {G0,W2,D2,L1,V0,M1}  { function( skol10 ) }.
% 75.70/76.09  (40448) {G0,W2,D2,L1,V0,M1}  { relation( skol11 ) }.
% 75.70/76.09  (40449) {G0,W2,D2,L1,V0,M1}  { function( skol11 ) }.
% 75.70/76.09  (40450) {G0,W4,D3,L1,V0,M1}  { in( skol12, relation_dom( skol10 ) ) }.
% 75.70/76.09  (40451) {G0,W11,D4,L1,V0,M1}  { ! apply( relation_composition( skol10, 
% 75.70/76.09    skol11 ), skol12 ) = apply( skol11, apply( skol10, skol12 ) ) }.
% 75.70/76.09  (40452) {G0,W8,D2,L3,V2,M3}  { ! element( X, Y ), empty( Y ), in( X, Y )
% 75.70/76.09     }.
% 75.70/76.09  (40453) {G0,W7,D3,L2,V2,M2}  { ! element( X, powerset( Y ) ), subset( X, Y
% 75.70/76.09     ) }.
% 75.70/76.09  (40454) {G0,W7,D3,L2,V2,M2}  { ! subset( X, Y ), element( X, powerset( Y )
% 75.70/76.09     ) }.
% 75.70/76.09  (40455) {G0,W10,D3,L3,V3,M3}  { ! in( X, Z ), ! element( Z, powerset( Y ) )
% 75.70/76.09    , element( X, Y ) }.
% 75.70/76.09  (40456) {G0,W9,D3,L3,V3,M3}  { ! in( X, Y ), ! element( Y, powerset( Z ) )
% 75.70/76.09    , ! empty( Z ) }.
% 75.70/76.09  (40457) {G0,W5,D2,L2,V1,M2}  { ! empty( X ), X = empty_set }.
% 75.70/76.09  (40458) {G0,W5,D2,L2,V2,M2}  { ! in( X, Y ), ! empty( Y ) }.
% 75.70/76.09  (40459) {G0,W7,D2,L3,V2,M3}  { ! empty( X ), X = Y, ! empty( Y ) }.
% 75.70/76.09  
% 75.70/76.09  
% 75.70/76.09  Total Proof:
% 75.70/76.09  
% 75.70/76.09  subsumption: (6) {G0,W16,D3,L5,V3,M5} I { ! relation( X ), ! function( X )
% 75.70/76.09    , in( Y, relation_dom( X ) ), ! Z = apply( X, Y ), Z = empty_set }.
% 75.70/76.09  parent0: (40402) {G0,W16,D3,L5,V3,M5}  { ! relation( X ), ! function( X ), 
% 75.70/76.09    in( Y, relation_dom( X ) ), ! Z = apply( X, Y ), Z = empty_set }.
% 75.70/76.09  substitution0:
% 75.70/76.09     X := X
% 75.70/76.09     Y := Y
% 75.70/76.09     Z := Z
% 75.70/76.09  end
% 75.70/76.09  permutation0:
% 75.70/76.09     0 ==> 0
% 75.70/76.09     1 ==> 1
% 75.70/76.09     2 ==> 2
% 75.70/76.09     3 ==> 3
% 75.70/76.09     4 ==> 4
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  subsumption: (9) {G0,W8,D3,L3,V2,M3} I { ! relation( X ), ! relation( Y ), 
% 75.70/76.09    relation( relation_composition( X, Y ) ) }.
% 75.70/76.09  parent0: (40405) {G0,W8,D3,L3,V2,M3}  { ! relation( X ), ! relation( Y ), 
% 75.70/76.09    relation( relation_composition( X, Y ) ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09     X := X
% 75.70/76.09     Y := Y
% 75.70/76.09  end
% 75.70/76.09  permutation0:
% 75.70/76.09     0 ==> 0
% 75.70/76.09     1 ==> 1
% 75.70/76.09     2 ==> 2
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  subsumption: (16) {G0,W12,D3,L5,V2,M5} I { ! relation( X ), ! function( X )
% 75.70/76.09    , ! relation( Y ), ! function( Y ), function( relation_composition( X, Y
% 75.70/76.09     ) ) }.
% 75.70/76.09  parent0: (40413) {G0,W12,D3,L5,V2,M5}  { ! relation( X ), ! function( X ), 
% 75.70/76.09    ! relation( Y ), ! function( Y ), function( relation_composition( X, Y )
% 75.70/76.09     ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09     X := X
% 75.70/76.09     Y := Y
% 75.70/76.09  end
% 75.70/76.09  permutation0:
% 75.70/76.09     0 ==> 0
% 75.70/76.09     1 ==> 1
% 75.70/76.09     2 ==> 2
% 75.70/76.09     3 ==> 3
% 75.70/76.09     4 ==> 4
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  subsumption: (44) {G0,W24,D4,L7,V3,M7} I { ! relation( X ), ! function( X )
% 75.70/76.09    , ! relation( Y ), ! function( Y ), ! in( Z, relation_dom( Y ) ), ! in( 
% 75.70/76.09    apply( Y, Z ), relation_dom( X ) ), in( Z, relation_dom( 
% 75.70/76.09    relation_composition( Y, X ) ) ) }.
% 75.70/76.09  parent0: (40444) {G0,W24,D4,L7,V3,M7}  { ! relation( X ), ! function( X ), 
% 75.70/76.09    ! relation( Y ), ! function( Y ), ! in( Z, relation_dom( Y ) ), ! in( 
% 75.70/76.09    apply( Y, Z ), relation_dom( X ) ), in( Z, relation_dom( 
% 75.70/76.09    relation_composition( Y, X ) ) ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09     X := X
% 75.70/76.09     Y := Y
% 75.70/76.09     Z := Z
% 75.70/76.09  end
% 75.70/76.09  permutation0:
% 75.70/76.09     0 ==> 0
% 75.70/76.09     1 ==> 1
% 75.70/76.09     2 ==> 2
% 75.70/76.09     3 ==> 3
% 75.70/76.09     4 ==> 4
% 75.70/76.09     5 ==> 5
% 75.70/76.09     6 ==> 6
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  eqswap: (40534) {G0,W25,D4,L6,V3,M6}  { apply( Y, apply( X, Z ) ) = apply( 
% 75.70/76.09    relation_composition( X, Y ), Z ), ! relation( Y ), ! function( Y ), ! 
% 75.70/76.09    relation( X ), ! function( X ), ! in( Z, relation_dom( 
% 75.70/76.09    relation_composition( X, Y ) ) ) }.
% 75.70/76.09  parent0[5]: (40445) {G0,W25,D4,L6,V3,M6}  { ! relation( X ), ! function( X
% 75.70/76.09     ), ! relation( Y ), ! function( Y ), ! in( Z, relation_dom( 
% 75.70/76.09    relation_composition( Y, X ) ) ), apply( relation_composition( Y, X ), Z
% 75.70/76.09     ) = apply( X, apply( Y, Z ) ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09     X := Y
% 75.70/76.09     Y := X
% 75.70/76.09     Z := Z
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  subsumption: (45) {G0,W25,D4,L6,V3,M6} I { ! relation( X ), ! function( X )
% 75.70/76.09    , ! relation( Y ), ! function( Y ), ! in( Z, relation_dom( 
% 75.70/76.09    relation_composition( Y, X ) ) ), apply( X, apply( Y, Z ) ) ==> apply( 
% 75.70/76.09    relation_composition( Y, X ), Z ) }.
% 75.70/76.09  parent0: (40534) {G0,W25,D4,L6,V3,M6}  { apply( Y, apply( X, Z ) ) = apply
% 75.70/76.09    ( relation_composition( X, Y ), Z ), ! relation( Y ), ! function( Y ), ! 
% 75.70/76.09    relation( X ), ! function( X ), ! in( Z, relation_dom( 
% 75.70/76.09    relation_composition( X, Y ) ) ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09     X := Y
% 75.70/76.09     Y := X
% 75.70/76.09     Z := Z
% 75.70/76.09  end
% 75.70/76.09  permutation0:
% 75.70/76.09     0 ==> 5
% 75.70/76.09     1 ==> 0
% 75.70/76.09     2 ==> 1
% 75.70/76.09     3 ==> 2
% 75.70/76.09     4 ==> 3
% 75.70/76.09     5 ==> 4
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  subsumption: (46) {G0,W2,D2,L1,V0,M1} I { relation( skol10 ) }.
% 75.70/76.09  parent0: (40446) {G0,W2,D2,L1,V0,M1}  { relation( skol10 ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09  end
% 75.70/76.09  permutation0:
% 75.70/76.09     0 ==> 0
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  subsumption: (47) {G0,W2,D2,L1,V0,M1} I { function( skol10 ) }.
% 75.70/76.09  parent0: (40447) {G0,W2,D2,L1,V0,M1}  { function( skol10 ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09  end
% 75.70/76.09  permutation0:
% 75.70/76.09     0 ==> 0
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  subsumption: (48) {G0,W2,D2,L1,V0,M1} I { relation( skol11 ) }.
% 75.70/76.09  parent0: (40448) {G0,W2,D2,L1,V0,M1}  { relation( skol11 ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09  end
% 75.70/76.09  permutation0:
% 75.70/76.09     0 ==> 0
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  subsumption: (49) {G0,W2,D2,L1,V0,M1} I { function( skol11 ) }.
% 75.70/76.09  parent0: (40449) {G0,W2,D2,L1,V0,M1}  { function( skol11 ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09  end
% 75.70/76.09  permutation0:
% 75.70/76.09     0 ==> 0
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  subsumption: (50) {G0,W4,D3,L1,V0,M1} I { in( skol12, relation_dom( skol10
% 75.70/76.09     ) ) }.
% 75.70/76.09  parent0: (40450) {G0,W4,D3,L1,V0,M1}  { in( skol12, relation_dom( skol10 )
% 75.70/76.09     ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09  end
% 75.70/76.09  permutation0:
% 75.70/76.09     0 ==> 0
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  eqswap: (40695) {G0,W11,D4,L1,V0,M1}  { ! apply( skol11, apply( skol10, 
% 75.70/76.09    skol12 ) ) = apply( relation_composition( skol10, skol11 ), skol12 ) }.
% 75.70/76.09  parent0[0]: (40451) {G0,W11,D4,L1,V0,M1}  { ! apply( relation_composition( 
% 75.70/76.09    skol10, skol11 ), skol12 ) = apply( skol11, apply( skol10, skol12 ) ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  subsumption: (51) {G0,W11,D4,L1,V0,M1} I { ! apply( skol11, apply( skol10, 
% 75.70/76.09    skol12 ) ) ==> apply( relation_composition( skol10, skol11 ), skol12 )
% 75.70/76.09     }.
% 75.70/76.09  parent0: (40695) {G0,W11,D4,L1,V0,M1}  { ! apply( skol11, apply( skol10, 
% 75.70/76.09    skol12 ) ) = apply( relation_composition( skol10, skol11 ), skol12 ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09  end
% 75.70/76.09  permutation0:
% 75.70/76.09     0 ==> 0
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  eqswap: (40696) {G0,W16,D3,L5,V3,M5}  { ! apply( Y, Z ) = X, ! relation( Y
% 75.70/76.09     ), ! function( Y ), in( Z, relation_dom( Y ) ), X = empty_set }.
% 75.70/76.09  parent0[3]: (6) {G0,W16,D3,L5,V3,M5} I { ! relation( X ), ! function( X ), 
% 75.70/76.09    in( Y, relation_dom( X ) ), ! Z = apply( X, Y ), Z = empty_set }.
% 75.70/76.09  substitution0:
% 75.70/76.09     X := Y
% 75.70/76.09     Y := Z
% 75.70/76.09     Z := X
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  eqrefl: (40699) {G0,W13,D3,L4,V2,M4}  { ! relation( X ), ! function( X ), 
% 75.70/76.09    in( Y, relation_dom( X ) ), apply( X, Y ) = empty_set }.
% 75.70/76.09  parent0[0]: (40696) {G0,W16,D3,L5,V3,M5}  { ! apply( Y, Z ) = X, ! relation
% 75.70/76.09    ( Y ), ! function( Y ), in( Z, relation_dom( Y ) ), X = empty_set }.
% 75.70/76.09  substitution0:
% 75.70/76.09     X := apply( X, Y )
% 75.70/76.09     Y := X
% 75.70/76.09     Z := Y
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  subsumption: (62) {G1,W13,D3,L4,V2,M4} Q(6) { ! relation( X ), ! function( 
% 75.70/76.09    X ), in( Y, relation_dom( X ) ), apply( X, Y ) ==> empty_set }.
% 75.70/76.09  parent0: (40699) {G0,W13,D3,L4,V2,M4}  { ! relation( X ), ! function( X ), 
% 75.70/76.09    in( Y, relation_dom( X ) ), apply( X, Y ) = empty_set }.
% 75.70/76.09  substitution0:
% 75.70/76.09     X := X
% 75.70/76.09     Y := Y
% 75.70/76.09  end
% 75.70/76.09  permutation0:
% 75.70/76.09     0 ==> 0
% 75.70/76.09     1 ==> 1
% 75.70/76.09     2 ==> 2
% 75.70/76.09     3 ==> 3
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  resolution: (40701) {G1,W6,D3,L2,V1,M2}  { ! relation( X ), relation( 
% 75.70/76.09    relation_composition( skol10, X ) ) }.
% 75.70/76.09  parent0[0]: (9) {G0,W8,D3,L3,V2,M3} I { ! relation( X ), ! relation( Y ), 
% 75.70/76.09    relation( relation_composition( X, Y ) ) }.
% 75.70/76.09  parent1[0]: (46) {G0,W2,D2,L1,V0,M1} I { relation( skol10 ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09     X := skol10
% 75.70/76.09     Y := X
% 75.70/76.09  end
% 75.70/76.09  substitution1:
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  subsumption: (180) {G1,W6,D3,L2,V1,M2} R(9,46) { ! relation( X ), relation
% 75.70/76.09    ( relation_composition( skol10, X ) ) }.
% 75.70/76.09  parent0: (40701) {G1,W6,D3,L2,V1,M2}  { ! relation( X ), relation( 
% 75.70/76.09    relation_composition( skol10, X ) ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09     X := X
% 75.70/76.09  end
% 75.70/76.09  permutation0:
% 75.70/76.09     0 ==> 0
% 75.70/76.09     1 ==> 1
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  resolution: (40703) {G1,W10,D3,L4,V1,M4}  { ! function( skol10 ), ! 
% 75.70/76.09    relation( X ), ! function( X ), function( relation_composition( skol10, X
% 75.70/76.09     ) ) }.
% 75.70/76.09  parent0[0]: (16) {G0,W12,D3,L5,V2,M5} I { ! relation( X ), ! function( X )
% 75.70/76.09    , ! relation( Y ), ! function( Y ), function( relation_composition( X, Y
% 75.70/76.09     ) ) }.
% 75.70/76.09  parent1[0]: (46) {G0,W2,D2,L1,V0,M1} I { relation( skol10 ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09     X := skol10
% 75.70/76.09     Y := X
% 75.70/76.09  end
% 75.70/76.09  substitution1:
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  resolution: (40706) {G1,W8,D3,L3,V1,M3}  { ! relation( X ), ! function( X )
% 75.70/76.09    , function( relation_composition( skol10, X ) ) }.
% 75.70/76.09  parent0[0]: (40703) {G1,W10,D3,L4,V1,M4}  { ! function( skol10 ), ! 
% 75.70/76.09    relation( X ), ! function( X ), function( relation_composition( skol10, X
% 75.70/76.09     ) ) }.
% 75.70/76.09  parent1[0]: (47) {G0,W2,D2,L1,V0,M1} I { function( skol10 ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09     X := X
% 75.70/76.09  end
% 75.70/76.09  substitution1:
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  subsumption: (238) {G1,W8,D3,L3,V1,M3} R(16,46);r(47) { ! relation( X ), ! 
% 75.70/76.09    function( X ), function( relation_composition( skol10, X ) ) }.
% 75.70/76.09  parent0: (40706) {G1,W8,D3,L3,V1,M3}  { ! relation( X ), ! function( X ), 
% 75.70/76.09    function( relation_composition( skol10, X ) ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09     X := X
% 75.70/76.09  end
% 75.70/76.09  permutation0:
% 75.70/76.09     0 ==> 0
% 75.70/76.09     1 ==> 1
% 75.70/76.09     2 ==> 2
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  resolution: (40707) {G1,W22,D4,L6,V2,M6}  { ! function( skol11 ), ! 
% 75.70/76.09    relation( X ), ! function( X ), ! in( Y, relation_dom( X ) ), ! in( apply
% 75.70/76.09    ( X, Y ), relation_dom( skol11 ) ), in( Y, relation_dom( 
% 75.70/76.09    relation_composition( X, skol11 ) ) ) }.
% 75.70/76.09  parent0[0]: (44) {G0,W24,D4,L7,V3,M7} I { ! relation( X ), ! function( X )
% 75.70/76.09    , ! relation( Y ), ! function( Y ), ! in( Z, relation_dom( Y ) ), ! in( 
% 75.70/76.09    apply( Y, Z ), relation_dom( X ) ), in( Z, relation_dom( 
% 75.70/76.09    relation_composition( Y, X ) ) ) }.
% 75.70/76.09  parent1[0]: (48) {G0,W2,D2,L1,V0,M1} I { relation( skol11 ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09     X := skol11
% 75.70/76.09     Y := X
% 75.70/76.09     Z := Y
% 75.70/76.09  end
% 75.70/76.09  substitution1:
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  resolution: (40710) {G1,W20,D4,L5,V2,M5}  { ! relation( X ), ! function( X
% 75.70/76.09     ), ! in( Y, relation_dom( X ) ), ! in( apply( X, Y ), relation_dom( 
% 75.70/76.09    skol11 ) ), in( Y, relation_dom( relation_composition( X, skol11 ) ) )
% 75.70/76.09     }.
% 75.70/76.09  parent0[0]: (40707) {G1,W22,D4,L6,V2,M6}  { ! function( skol11 ), ! 
% 75.70/76.09    relation( X ), ! function( X ), ! in( Y, relation_dom( X ) ), ! in( apply
% 75.70/76.09    ( X, Y ), relation_dom( skol11 ) ), in( Y, relation_dom( 
% 75.70/76.09    relation_composition( X, skol11 ) ) ) }.
% 75.70/76.09  parent1[0]: (49) {G0,W2,D2,L1,V0,M1} I { function( skol11 ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09     X := X
% 75.70/76.09     Y := Y
% 75.70/76.09  end
% 75.70/76.09  substitution1:
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  subsumption: (505) {G1,W20,D4,L5,V2,M5} R(44,48);r(49) { ! relation( X ), !
% 75.70/76.09     function( X ), ! in( Y, relation_dom( X ) ), ! in( apply( X, Y ), 
% 75.70/76.09    relation_dom( skol11 ) ), in( Y, relation_dom( relation_composition( X, 
% 75.70/76.09    skol11 ) ) ) }.
% 75.70/76.09  parent0: (40710) {G1,W20,D4,L5,V2,M5}  { ! relation( X ), ! function( X ), 
% 75.70/76.09    ! in( Y, relation_dom( X ) ), ! in( apply( X, Y ), relation_dom( skol11 )
% 75.70/76.09     ), in( Y, relation_dom( relation_composition( X, skol11 ) ) ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09     X := X
% 75.70/76.09     Y := Y
% 75.70/76.09  end
% 75.70/76.09  permutation0:
% 75.70/76.09     0 ==> 0
% 75.70/76.09     1 ==> 1
% 75.70/76.09     2 ==> 2
% 75.70/76.09     3 ==> 3
% 75.70/76.09     4 ==> 4
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  eqswap: (40711) {G0,W11,D4,L1,V0,M1}  { ! apply( relation_composition( 
% 75.70/76.09    skol10, skol11 ), skol12 ) ==> apply( skol11, apply( skol10, skol12 ) )
% 75.70/76.09     }.
% 75.70/76.09  parent0[0]: (51) {G0,W11,D4,L1,V0,M1} I { ! apply( skol11, apply( skol10, 
% 75.70/76.09    skol12 ) ) ==> apply( relation_composition( skol10, skol11 ), skol12 )
% 75.70/76.09     }.
% 75.70/76.09  substitution0:
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  eqswap: (40712) {G0,W25,D4,L6,V3,M6}  { apply( relation_composition( Y, X )
% 75.70/76.09    , Z ) ==> apply( X, apply( Y, Z ) ), ! relation( X ), ! function( X ), ! 
% 75.70/76.09    relation( Y ), ! function( Y ), ! in( Z, relation_dom( 
% 75.70/76.09    relation_composition( Y, X ) ) ) }.
% 75.70/76.09  parent0[5]: (45) {G0,W25,D4,L6,V3,M6} I { ! relation( X ), ! function( X )
% 75.70/76.09    , ! relation( Y ), ! function( Y ), ! in( Z, relation_dom( 
% 75.70/76.09    relation_composition( Y, X ) ) ), apply( X, apply( Y, Z ) ) ==> apply( 
% 75.70/76.09    relation_composition( Y, X ), Z ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09     X := X
% 75.70/76.09     Y := Y
% 75.70/76.09     Z := Z
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  resolution: (40713) {G1,W14,D4,L5,V0,M5}  { ! relation( skol11 ), ! 
% 75.70/76.09    function( skol11 ), ! relation( skol10 ), ! function( skol10 ), ! in( 
% 75.70/76.09    skol12, relation_dom( relation_composition( skol10, skol11 ) ) ) }.
% 75.70/76.09  parent0[0]: (40711) {G0,W11,D4,L1,V0,M1}  { ! apply( relation_composition( 
% 75.70/76.09    skol10, skol11 ), skol12 ) ==> apply( skol11, apply( skol10, skol12 ) )
% 75.70/76.09     }.
% 75.70/76.09  parent1[0]: (40712) {G0,W25,D4,L6,V3,M6}  { apply( relation_composition( Y
% 75.70/76.09    , X ), Z ) ==> apply( X, apply( Y, Z ) ), ! relation( X ), ! function( X
% 75.70/76.09     ), ! relation( Y ), ! function( Y ), ! in( Z, relation_dom( 
% 75.70/76.09    relation_composition( Y, X ) ) ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09  end
% 75.70/76.09  substitution1:
% 75.70/76.09     X := skol11
% 75.70/76.09     Y := skol10
% 75.70/76.09     Z := skol12
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  resolution: (40714) {G1,W12,D4,L4,V0,M4}  { ! function( skol11 ), ! 
% 75.70/76.09    relation( skol10 ), ! function( skol10 ), ! in( skol12, relation_dom( 
% 75.70/76.09    relation_composition( skol10, skol11 ) ) ) }.
% 75.70/76.09  parent0[0]: (40713) {G1,W14,D4,L5,V0,M5}  { ! relation( skol11 ), ! 
% 75.70/76.09    function( skol11 ), ! relation( skol10 ), ! function( skol10 ), ! in( 
% 75.70/76.09    skol12, relation_dom( relation_composition( skol10, skol11 ) ) ) }.
% 75.70/76.09  parent1[0]: (48) {G0,W2,D2,L1,V0,M1} I { relation( skol11 ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09  end
% 75.70/76.09  substitution1:
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  subsumption: (562) {G1,W12,D4,L4,V0,M4} R(51,45);r(48) { ! function( skol11
% 75.70/76.09     ), ! relation( skol10 ), ! function( skol10 ), ! in( skol12, 
% 75.70/76.09    relation_dom( relation_composition( skol10, skol11 ) ) ) }.
% 75.70/76.09  parent0: (40714) {G1,W12,D4,L4,V0,M4}  { ! function( skol11 ), ! relation( 
% 75.70/76.09    skol10 ), ! function( skol10 ), ! in( skol12, relation_dom( 
% 75.70/76.09    relation_composition( skol10, skol11 ) ) ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09  end
% 75.70/76.09  permutation0:
% 75.70/76.09     0 ==> 0
% 75.70/76.09     1 ==> 1
% 75.70/76.09     2 ==> 2
% 75.70/76.09     3 ==> 3
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  eqswap: (40716) {G0,W11,D4,L1,V0,M1}  { ! apply( relation_composition( 
% 75.70/76.09    skol10, skol11 ), skol12 ) ==> apply( skol11, apply( skol10, skol12 ) )
% 75.70/76.09     }.
% 75.70/76.09  parent0[0]: (51) {G0,W11,D4,L1,V0,M1} I { ! apply( skol11, apply( skol10, 
% 75.70/76.09    skol12 ) ) ==> apply( relation_composition( skol10, skol11 ), skol12 )
% 75.70/76.09     }.
% 75.70/76.09  substitution0:
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  paramod: (40718) {G1,W17,D4,L4,V0,M4}  { ! apply( relation_composition( 
% 75.70/76.09    skol10, skol11 ), skol12 ) ==> empty_set, ! relation( skol11 ), ! 
% 75.70/76.09    function( skol11 ), in( apply( skol10, skol12 ), relation_dom( skol11 ) )
% 75.70/76.09     }.
% 75.70/76.09  parent0[3]: (62) {G1,W13,D3,L4,V2,M4} Q(6) { ! relation( X ), ! function( X
% 75.70/76.09     ), in( Y, relation_dom( X ) ), apply( X, Y ) ==> empty_set }.
% 75.70/76.09  parent1[0; 7]: (40716) {G0,W11,D4,L1,V0,M1}  { ! apply( 
% 75.70/76.09    relation_composition( skol10, skol11 ), skol12 ) ==> apply( skol11, apply
% 75.70/76.09    ( skol10, skol12 ) ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09     X := skol11
% 75.70/76.09     Y := apply( skol10, skol12 )
% 75.70/76.09  end
% 75.70/76.09  substitution1:
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  resolution: (40727) {G1,W15,D4,L3,V0,M3}  { ! apply( relation_composition( 
% 75.70/76.09    skol10, skol11 ), skol12 ) ==> empty_set, ! function( skol11 ), in( apply
% 75.70/76.09    ( skol10, skol12 ), relation_dom( skol11 ) ) }.
% 75.70/76.09  parent0[1]: (40718) {G1,W17,D4,L4,V0,M4}  { ! apply( relation_composition( 
% 75.70/76.09    skol10, skol11 ), skol12 ) ==> empty_set, ! relation( skol11 ), ! 
% 75.70/76.09    function( skol11 ), in( apply( skol10, skol12 ), relation_dom( skol11 ) )
% 75.70/76.09     }.
% 75.70/76.09  parent1[0]: (48) {G0,W2,D2,L1,V0,M1} I { relation( skol11 ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09  end
% 75.70/76.09  substitution1:
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  subsumption: (767) {G2,W15,D4,L3,V0,M3} P(62,51);r(48) { ! apply( 
% 75.70/76.09    relation_composition( skol10, skol11 ), skol12 ) ==> empty_set, ! 
% 75.70/76.09    function( skol11 ), in( apply( skol10, skol12 ), relation_dom( skol11 ) )
% 75.70/76.09     }.
% 75.70/76.09  parent0: (40727) {G1,W15,D4,L3,V0,M3}  { ! apply( relation_composition( 
% 75.70/76.09    skol10, skol11 ), skol12 ) ==> empty_set, ! function( skol11 ), in( apply
% 75.70/76.09    ( skol10, skol12 ), relation_dom( skol11 ) ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09  end
% 75.70/76.09  permutation0:
% 75.70/76.09     0 ==> 0
% 75.70/76.09     1 ==> 1
% 75.70/76.09     2 ==> 2
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  resolution: (40729) {G1,W4,D3,L1,V0,M1}  { relation( relation_composition( 
% 75.70/76.09    skol10, skol11 ) ) }.
% 75.70/76.09  parent0[0]: (180) {G1,W6,D3,L2,V1,M2} R(9,46) { ! relation( X ), relation( 
% 75.70/76.09    relation_composition( skol10, X ) ) }.
% 75.70/76.09  parent1[0]: (48) {G0,W2,D2,L1,V0,M1} I { relation( skol11 ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09     X := skol11
% 75.70/76.09  end
% 75.70/76.09  substitution1:
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  subsumption: (2370) {G2,W4,D3,L1,V0,M1} R(180,48) { relation( 
% 75.70/76.09    relation_composition( skol10, skol11 ) ) }.
% 75.70/76.09  parent0: (40729) {G1,W4,D3,L1,V0,M1}  { relation( relation_composition( 
% 75.70/76.09    skol10, skol11 ) ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09  end
% 75.70/76.09  permutation0:
% 75.70/76.09     0 ==> 0
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  resolution: (40730) {G1,W6,D3,L2,V0,M2}  { ! function( skol11 ), function( 
% 75.70/76.09    relation_composition( skol10, skol11 ) ) }.
% 75.70/76.09  parent0[0]: (238) {G1,W8,D3,L3,V1,M3} R(16,46);r(47) { ! relation( X ), ! 
% 75.70/76.09    function( X ), function( relation_composition( skol10, X ) ) }.
% 75.70/76.09  parent1[0]: (48) {G0,W2,D2,L1,V0,M1} I { relation( skol11 ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09     X := skol11
% 75.70/76.09  end
% 75.70/76.09  substitution1:
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  resolution: (40731) {G1,W4,D3,L1,V0,M1}  { function( relation_composition( 
% 75.70/76.09    skol10, skol11 ) ) }.
% 75.70/76.09  parent0[0]: (40730) {G1,W6,D3,L2,V0,M2}  { ! function( skol11 ), function( 
% 75.70/76.09    relation_composition( skol10, skol11 ) ) }.
% 75.70/76.09  parent1[0]: (49) {G0,W2,D2,L1,V0,M1} I { function( skol11 ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09  end
% 75.70/76.09  substitution1:
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  subsumption: (12451) {G2,W4,D3,L1,V0,M1} R(238,48);r(49) { function( 
% 75.70/76.09    relation_composition( skol10, skol11 ) ) }.
% 75.70/76.09  parent0: (40731) {G1,W4,D3,L1,V0,M1}  { function( relation_composition( 
% 75.70/76.09    skol10, skol11 ) ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09  end
% 75.70/76.09  permutation0:
% 75.70/76.09     0 ==> 0
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  resolution: (40733) {G1,W13,D4,L2,V0,M2}  { ! apply( relation_composition( 
% 75.70/76.09    skol10, skol11 ), skol12 ) ==> empty_set, in( apply( skol10, skol12 ), 
% 75.70/76.09    relation_dom( skol11 ) ) }.
% 75.70/76.09  parent0[1]: (767) {G2,W15,D4,L3,V0,M3} P(62,51);r(48) { ! apply( 
% 75.70/76.09    relation_composition( skol10, skol11 ), skol12 ) ==> empty_set, ! 
% 75.70/76.09    function( skol11 ), in( apply( skol10, skol12 ), relation_dom( skol11 ) )
% 75.70/76.09     }.
% 75.70/76.09  parent1[0]: (49) {G0,W2,D2,L1,V0,M1} I { function( skol11 ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09  end
% 75.70/76.09  substitution1:
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  subsumption: (20259) {G3,W13,D4,L2,V0,M2} S(767);r(49) { ! apply( 
% 75.70/76.09    relation_composition( skol10, skol11 ), skol12 ) ==> empty_set, in( apply
% 75.70/76.09    ( skol10, skol12 ), relation_dom( skol11 ) ) }.
% 75.70/76.09  parent0: (40733) {G1,W13,D4,L2,V0,M2}  { ! apply( relation_composition( 
% 75.70/76.09    skol10, skol11 ), skol12 ) ==> empty_set, in( apply( skol10, skol12 ), 
% 75.70/76.09    relation_dom( skol11 ) ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09  end
% 75.70/76.09  permutation0:
% 75.70/76.09     0 ==> 0
% 75.70/76.09     1 ==> 1
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  resolution: (40735) {G1,W10,D4,L3,V0,M3}  { ! relation( skol10 ), ! 
% 75.70/76.09    function( skol10 ), ! in( skol12, relation_dom( relation_composition( 
% 75.70/76.09    skol10, skol11 ) ) ) }.
% 75.70/76.09  parent0[0]: (562) {G1,W12,D4,L4,V0,M4} R(51,45);r(48) { ! function( skol11
% 75.70/76.09     ), ! relation( skol10 ), ! function( skol10 ), ! in( skol12, 
% 75.70/76.09    relation_dom( relation_composition( skol10, skol11 ) ) ) }.
% 75.70/76.09  parent1[0]: (49) {G0,W2,D2,L1,V0,M1} I { function( skol11 ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09  end
% 75.70/76.09  substitution1:
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  resolution: (40736) {G1,W8,D4,L2,V0,M2}  { ! function( skol10 ), ! in( 
% 75.70/76.09    skol12, relation_dom( relation_composition( skol10, skol11 ) ) ) }.
% 75.70/76.09  parent0[0]: (40735) {G1,W10,D4,L3,V0,M3}  { ! relation( skol10 ), ! 
% 75.70/76.09    function( skol10 ), ! in( skol12, relation_dom( relation_composition( 
% 75.70/76.09    skol10, skol11 ) ) ) }.
% 75.70/76.09  parent1[0]: (46) {G0,W2,D2,L1,V0,M1} I { relation( skol10 ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09  end
% 75.70/76.09  substitution1:
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  resolution: (40737) {G1,W6,D4,L1,V0,M1}  { ! in( skol12, relation_dom( 
% 75.70/76.09    relation_composition( skol10, skol11 ) ) ) }.
% 75.70/76.09  parent0[0]: (40736) {G1,W8,D4,L2,V0,M2}  { ! function( skol10 ), ! in( 
% 75.70/76.09    skol12, relation_dom( relation_composition( skol10, skol11 ) ) ) }.
% 75.70/76.09  parent1[0]: (47) {G0,W2,D2,L1,V0,M1} I { function( skol10 ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09  end
% 75.70/76.09  substitution1:
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  subsumption: (20261) {G2,W6,D4,L1,V0,M1} S(562);r(49);r(46);r(47) { ! in( 
% 75.70/76.09    skol12, relation_dom( relation_composition( skol10, skol11 ) ) ) }.
% 75.70/76.09  parent0: (40737) {G1,W6,D4,L1,V0,M1}  { ! in( skol12, relation_dom( 
% 75.70/76.09    relation_composition( skol10, skol11 ) ) ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09  end
% 75.70/76.09  permutation0:
% 75.70/76.09     0 ==> 0
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  eqswap: (40738) {G1,W13,D3,L4,V2,M4}  { empty_set ==> apply( X, Y ), ! 
% 75.70/76.09    relation( X ), ! function( X ), in( Y, relation_dom( X ) ) }.
% 75.70/76.09  parent0[3]: (62) {G1,W13,D3,L4,V2,M4} Q(6) { ! relation( X ), ! function( X
% 75.70/76.09     ), in( Y, relation_dom( X ) ), apply( X, Y ) ==> empty_set }.
% 75.70/76.09  substitution0:
% 75.70/76.09     X := X
% 75.70/76.09     Y := Y
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  resolution: (40739) {G2,W15,D4,L3,V0,M3}  { empty_set ==> apply( 
% 75.70/76.09    relation_composition( skol10, skol11 ), skol12 ), ! relation( 
% 75.70/76.09    relation_composition( skol10, skol11 ) ), ! function( 
% 75.70/76.09    relation_composition( skol10, skol11 ) ) }.
% 75.70/76.09  parent0[0]: (20261) {G2,W6,D4,L1,V0,M1} S(562);r(49);r(46);r(47) { ! in( 
% 75.70/76.09    skol12, relation_dom( relation_composition( skol10, skol11 ) ) ) }.
% 75.70/76.09  parent1[3]: (40738) {G1,W13,D3,L4,V2,M4}  { empty_set ==> apply( X, Y ), ! 
% 75.70/76.09    relation( X ), ! function( X ), in( Y, relation_dom( X ) ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09  end
% 75.70/76.09  substitution1:
% 75.70/76.09     X := relation_composition( skol10, skol11 )
% 75.70/76.09     Y := skol12
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  resolution: (40740) {G3,W11,D4,L2,V0,M2}  { empty_set ==> apply( 
% 75.70/76.09    relation_composition( skol10, skol11 ), skol12 ), ! function( 
% 75.70/76.09    relation_composition( skol10, skol11 ) ) }.
% 75.70/76.09  parent0[1]: (40739) {G2,W15,D4,L3,V0,M3}  { empty_set ==> apply( 
% 75.70/76.09    relation_composition( skol10, skol11 ), skol12 ), ! relation( 
% 75.70/76.09    relation_composition( skol10, skol11 ) ), ! function( 
% 75.70/76.09    relation_composition( skol10, skol11 ) ) }.
% 75.70/76.09  parent1[0]: (2370) {G2,W4,D3,L1,V0,M1} R(180,48) { relation( 
% 75.70/76.09    relation_composition( skol10, skol11 ) ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09  end
% 75.70/76.09  substitution1:
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  eqswap: (40741) {G3,W11,D4,L2,V0,M2}  { apply( relation_composition( skol10
% 75.70/76.09    , skol11 ), skol12 ) ==> empty_set, ! function( relation_composition( 
% 75.70/76.09    skol10, skol11 ) ) }.
% 75.70/76.09  parent0[0]: (40740) {G3,W11,D4,L2,V0,M2}  { empty_set ==> apply( 
% 75.70/76.09    relation_composition( skol10, skol11 ), skol12 ), ! function( 
% 75.70/76.09    relation_composition( skol10, skol11 ) ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  subsumption: (20578) {G3,W11,D4,L2,V0,M2} R(20261,62);r(2370) { ! function
% 75.70/76.09    ( relation_composition( skol10, skol11 ) ), apply( relation_composition( 
% 75.70/76.09    skol10, skol11 ), skol12 ) ==> empty_set }.
% 75.70/76.09  parent0: (40741) {G3,W11,D4,L2,V0,M2}  { apply( relation_composition( 
% 75.70/76.09    skol10, skol11 ), skol12 ) ==> empty_set, ! function( 
% 75.70/76.09    relation_composition( skol10, skol11 ) ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09  end
% 75.70/76.09  permutation0:
% 75.70/76.09     0 ==> 1
% 75.70/76.09     1 ==> 0
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  resolution: (40742) {G2,W14,D3,L4,V0,M4}  { ! relation( skol10 ), ! 
% 75.70/76.09    function( skol10 ), ! in( skol12, relation_dom( skol10 ) ), ! in( apply( 
% 75.70/76.09    skol10, skol12 ), relation_dom( skol11 ) ) }.
% 75.70/76.09  parent0[0]: (20261) {G2,W6,D4,L1,V0,M1} S(562);r(49);r(46);r(47) { ! in( 
% 75.70/76.09    skol12, relation_dom( relation_composition( skol10, skol11 ) ) ) }.
% 75.70/76.09  parent1[4]: (505) {G1,W20,D4,L5,V2,M5} R(44,48);r(49) { ! relation( X ), ! 
% 75.70/76.09    function( X ), ! in( Y, relation_dom( X ) ), ! in( apply( X, Y ), 
% 75.70/76.09    relation_dom( skol11 ) ), in( Y, relation_dom( relation_composition( X, 
% 75.70/76.09    skol11 ) ) ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09  end
% 75.70/76.09  substitution1:
% 75.70/76.09     X := skol10
% 75.70/76.09     Y := skol12
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  resolution: (40743) {G1,W12,D3,L3,V0,M3}  { ! function( skol10 ), ! in( 
% 75.70/76.09    skol12, relation_dom( skol10 ) ), ! in( apply( skol10, skol12 ), 
% 75.70/76.09    relation_dom( skol11 ) ) }.
% 75.70/76.09  parent0[0]: (40742) {G2,W14,D3,L4,V0,M4}  { ! relation( skol10 ), ! 
% 75.70/76.09    function( skol10 ), ! in( skol12, relation_dom( skol10 ) ), ! in( apply( 
% 75.70/76.09    skol10, skol12 ), relation_dom( skol11 ) ) }.
% 75.70/76.09  parent1[0]: (46) {G0,W2,D2,L1,V0,M1} I { relation( skol10 ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09  end
% 75.70/76.09  substitution1:
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  subsumption: (25033) {G3,W12,D3,L3,V0,M3} R(505,20261);r(46) { ! function( 
% 75.70/76.09    skol10 ), ! in( skol12, relation_dom( skol10 ) ), ! in( apply( skol10, 
% 75.70/76.09    skol12 ), relation_dom( skol11 ) ) }.
% 75.70/76.09  parent0: (40743) {G1,W12,D3,L3,V0,M3}  { ! function( skol10 ), ! in( skol12
% 75.70/76.09    , relation_dom( skol10 ) ), ! in( apply( skol10, skol12 ), relation_dom( 
% 75.70/76.09    skol11 ) ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09  end
% 75.70/76.09  permutation0:
% 75.70/76.09     0 ==> 0
% 75.70/76.09     1 ==> 1
% 75.70/76.09     2 ==> 2
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  resolution: (40744) {G1,W10,D3,L2,V0,M2}  { ! in( skol12, relation_dom( 
% 75.70/76.09    skol10 ) ), ! in( apply( skol10, skol12 ), relation_dom( skol11 ) ) }.
% 75.70/76.09  parent0[0]: (25033) {G3,W12,D3,L3,V0,M3} R(505,20261);r(46) { ! function( 
% 75.70/76.09    skol10 ), ! in( skol12, relation_dom( skol10 ) ), ! in( apply( skol10, 
% 75.70/76.09    skol12 ), relation_dom( skol11 ) ) }.
% 75.70/76.09  parent1[0]: (47) {G0,W2,D2,L1,V0,M1} I { function( skol10 ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09  end
% 75.70/76.09  substitution1:
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  resolution: (40745) {G1,W6,D3,L1,V0,M1}  { ! in( apply( skol10, skol12 ), 
% 75.70/76.09    relation_dom( skol11 ) ) }.
% 75.70/76.09  parent0[0]: (40744) {G1,W10,D3,L2,V0,M2}  { ! in( skol12, relation_dom( 
% 75.70/76.09    skol10 ) ), ! in( apply( skol10, skol12 ), relation_dom( skol11 ) ) }.
% 75.70/76.09  parent1[0]: (50) {G0,W4,D3,L1,V0,M1} I { in( skol12, relation_dom( skol10 )
% 75.70/76.09     ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09  end
% 75.70/76.09  substitution1:
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  subsumption: (40296) {G4,W6,D3,L1,V0,M1} S(25033);r(47);r(50) { ! in( apply
% 75.70/76.09    ( skol10, skol12 ), relation_dom( skol11 ) ) }.
% 75.70/76.09  parent0: (40745) {G1,W6,D3,L1,V0,M1}  { ! in( apply( skol10, skol12 ), 
% 75.70/76.09    relation_dom( skol11 ) ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09  end
% 75.70/76.09  permutation0:
% 75.70/76.09     0 ==> 0
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  resolution: (40747) {G3,W7,D4,L1,V0,M1}  { apply( relation_composition( 
% 75.70/76.09    skol10, skol11 ), skol12 ) ==> empty_set }.
% 75.70/76.09  parent0[0]: (20578) {G3,W11,D4,L2,V0,M2} R(20261,62);r(2370) { ! function( 
% 75.70/76.09    relation_composition( skol10, skol11 ) ), apply( relation_composition( 
% 75.70/76.09    skol10, skol11 ), skol12 ) ==> empty_set }.
% 75.70/76.09  parent1[0]: (12451) {G2,W4,D3,L1,V0,M1} R(238,48);r(49) { function( 
% 75.70/76.09    relation_composition( skol10, skol11 ) ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09  end
% 75.70/76.09  substitution1:
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  subsumption: (40364) {G4,W7,D4,L1,V0,M1} S(20578);r(12451) { apply( 
% 75.70/76.09    relation_composition( skol10, skol11 ), skol12 ) ==> empty_set }.
% 75.70/76.09  parent0: (40747) {G3,W7,D4,L1,V0,M1}  { apply( relation_composition( skol10
% 75.70/76.09    , skol11 ), skol12 ) ==> empty_set }.
% 75.70/76.09  substitution0:
% 75.70/76.09  end
% 75.70/76.09  permutation0:
% 75.70/76.09     0 ==> 0
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  paramod: (40751) {G4,W9,D3,L2,V0,M2}  { ! empty_set ==> empty_set, in( 
% 75.70/76.09    apply( skol10, skol12 ), relation_dom( skol11 ) ) }.
% 75.70/76.09  parent0[0]: (40364) {G4,W7,D4,L1,V0,M1} S(20578);r(12451) { apply( 
% 75.70/76.09    relation_composition( skol10, skol11 ), skol12 ) ==> empty_set }.
% 75.70/76.09  parent1[0; 2]: (20259) {G3,W13,D4,L2,V0,M2} S(767);r(49) { ! apply( 
% 75.70/76.09    relation_composition( skol10, skol11 ), skol12 ) ==> empty_set, in( apply
% 75.70/76.09    ( skol10, skol12 ), relation_dom( skol11 ) ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09  end
% 75.70/76.09  substitution1:
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  eqrefl: (40752) {G0,W6,D3,L1,V0,M1}  { in( apply( skol10, skol12 ), 
% 75.70/76.09    relation_dom( skol11 ) ) }.
% 75.70/76.09  parent0[0]: (40751) {G4,W9,D3,L2,V0,M2}  { ! empty_set ==> empty_set, in( 
% 75.70/76.09    apply( skol10, skol12 ), relation_dom( skol11 ) ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  resolution: (40753) {G1,W0,D0,L0,V0,M0}  {  }.
% 75.70/76.09  parent0[0]: (40296) {G4,W6,D3,L1,V0,M1} S(25033);r(47);r(50) { ! in( apply
% 75.70/76.09    ( skol10, skol12 ), relation_dom( skol11 ) ) }.
% 75.70/76.09  parent1[0]: (40752) {G0,W6,D3,L1,V0,M1}  { in( apply( skol10, skol12 ), 
% 75.70/76.09    relation_dom( skol11 ) ) }.
% 75.70/76.09  substitution0:
% 75.70/76.09  end
% 75.70/76.09  substitution1:
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  subsumption: (40394) {G5,W0,D0,L0,V0,M0} S(20259);d(40364);q;r(40296) { 
% 75.70/76.09     }.
% 75.70/76.09  parent0: (40753) {G1,W0,D0,L0,V0,M0}  {  }.
% 75.70/76.09  substitution0:
% 75.70/76.09  end
% 75.70/76.09  permutation0:
% 75.70/76.09  end
% 75.70/76.09  
% 75.70/76.09  Proof check complete!
% 75.70/76.09  
% 75.70/76.09  Memory use:
% 75.70/76.09  
% 75.70/76.09  space for terms:        523339
% 75.70/76.09  space for clauses:      1889482
% 75.70/76.09  
% 75.70/76.09  
% 75.70/76.09  clauses generated:      727331
% 75.70/76.09  clauses kept:           40395
% 75.70/76.09  clauses selected:       1900
% 75.70/76.09  clauses deleted:        5886
% 75.70/76.09  clauses inuse deleted:  135
% 75.70/76.09  
% 75.70/76.09  subsentry:          1359399
% 75.70/76.09  literals s-matched: 853875
% 75.70/76.09  literals matched:   776446
% 75.70/76.09  full subsumption:   136309
% 75.70/76.09  
% 75.70/76.09  checksum:           -954407775
% 75.70/76.09  
% 75.70/76.09  
% 75.70/76.09  Bliksem ended
%------------------------------------------------------------------------------