TSTP Solution File: KLE139+1 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : KLE139+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n003.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 : Sun Jul 17 01:37:23 EDT 2022

% Result   : Theorem 45.54s 45.97s
% Output   : Refutation 45.54s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : KLE139+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : bliksem %s
% 0.13/0.35  % Computer : n003.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % DateTime : Thu Jun 16 09:00:56 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 18.84/19.25  *** allocated 10000 integers for termspace/termends
% 18.84/19.25  *** allocated 10000 integers for clauses
% 18.84/19.25  *** allocated 10000 integers for justifications
% 18.84/19.25  Bliksem 1.12
% 18.84/19.25  
% 18.84/19.25  
% 18.84/19.25  Automatic Strategy Selection
% 18.84/19.25  
% 18.84/19.25  
% 18.84/19.25  Clauses:
% 18.84/19.25  
% 18.84/19.25  { addition( X, Y ) = addition( Y, X ) }.
% 18.84/19.25  { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 18.84/19.25  { addition( X, zero ) = X }.
% 18.84/19.25  { addition( X, X ) = X }.
% 18.84/19.25  { multiplication( X, multiplication( Y, Z ) ) = multiplication( 
% 18.84/19.25    multiplication( X, Y ), Z ) }.
% 18.84/19.25  { multiplication( X, one ) = X }.
% 18.84/19.25  { multiplication( one, X ) = X }.
% 18.84/19.25  { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 18.84/19.25    , multiplication( X, Z ) ) }.
% 18.84/19.25  { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 18.84/19.25    , multiplication( Y, Z ) ) }.
% 18.84/19.25  { multiplication( zero, X ) = zero }.
% 18.84/19.25  { addition( one, multiplication( X, star( X ) ) ) = star( X ) }.
% 18.84/19.25  { addition( one, multiplication( star( X ), X ) ) = star( X ) }.
% 18.84/19.25  { ! leq( addition( multiplication( X, Z ), Y ), Z ), leq( multiplication( 
% 18.84/19.25    star( X ), Y ), Z ) }.
% 18.84/19.25  { ! leq( addition( multiplication( Z, X ), Y ), Z ), leq( multiplication( Y
% 18.84/19.25    , star( X ) ), Z ) }.
% 18.84/19.25  { strong_iteration( X ) = addition( multiplication( X, strong_iteration( X
% 18.84/19.25     ) ), one ) }.
% 18.84/19.25  { ! leq( Z, addition( multiplication( X, Z ), Y ) ), leq( Z, multiplication
% 18.84/19.25    ( strong_iteration( X ), Y ) ) }.
% 18.84/19.25  { strong_iteration( X ) = addition( star( X ), multiplication( 
% 18.84/19.25    strong_iteration( X ), zero ) ) }.
% 18.84/19.25  { ! leq( X, Y ), addition( X, Y ) = Y }.
% 18.84/19.25  { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 18.84/19.25  { ! strong_iteration( skol1 ) = addition( multiplication( strong_iteration
% 18.84/19.25    ( skol1 ), skol1 ), one ) }.
% 18.84/19.25  
% 18.84/19.25  percentage equality = 0.680000, percentage horn = 1.000000
% 18.84/19.25  This is a problem with some equality
% 18.84/19.25  
% 18.84/19.25  
% 18.84/19.25  
% 18.84/19.25  Options Used:
% 18.84/19.25  
% 18.84/19.25  useres =            1
% 18.84/19.25  useparamod =        1
% 18.84/19.25  useeqrefl =         1
% 18.84/19.25  useeqfact =         1
% 18.84/19.25  usefactor =         1
% 18.84/19.25  usesimpsplitting =  0
% 18.84/19.25  usesimpdemod =      5
% 18.84/19.25  usesimpres =        3
% 18.84/19.25  
% 18.84/19.25  resimpinuse      =  1000
% 18.84/19.25  resimpclauses =     20000
% 18.84/19.25  substype =          eqrewr
% 18.84/19.25  backwardsubs =      1
% 18.84/19.25  selectoldest =      5
% 18.84/19.25  
% 18.84/19.25  litorderings [0] =  split
% 18.84/19.25  litorderings [1] =  extend the termordering, first sorting on arguments
% 18.84/19.25  
% 18.84/19.25  termordering =      kbo
% 18.84/19.25  
% 18.84/19.25  litapriori =        0
% 18.84/19.25  termapriori =       1
% 18.84/19.25  litaposteriori =    0
% 18.84/19.25  termaposteriori =   0
% 18.84/19.25  demodaposteriori =  0
% 18.84/19.25  ordereqreflfact =   0
% 18.84/19.25  
% 18.84/19.25  litselect =         negord
% 18.84/19.25  
% 18.84/19.25  maxweight =         15
% 18.84/19.25  maxdepth =          30000
% 18.84/19.25  maxlength =         115
% 18.84/19.25  maxnrvars =         195
% 18.84/19.25  excuselevel =       1
% 18.84/19.25  increasemaxweight = 1
% 18.84/19.25  
% 18.84/19.25  maxselected =       10000000
% 18.84/19.25  maxnrclauses =      10000000
% 18.84/19.25  
% 18.84/19.25  showgenerated =    0
% 18.84/19.25  showkept =         0
% 18.84/19.25  showselected =     0
% 18.84/19.25  showdeleted =      0
% 18.84/19.25  showresimp =       1
% 18.84/19.25  showstatus =       2000
% 18.84/19.25  
% 18.84/19.25  prologoutput =     0
% 18.84/19.25  nrgoals =          5000000
% 18.84/19.25  totalproof =       1
% 18.84/19.25  
% 18.84/19.25  Symbols occurring in the translation:
% 18.84/19.25  
% 18.84/19.25  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 18.84/19.25  .  [1, 2]      (w:1, o:20, a:1, s:1, b:0), 
% 18.84/19.25  !  [4, 1]      (w:0, o:13, a:1, s:1, b:0), 
% 18.84/19.25  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 18.84/19.25  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 18.84/19.25  addition  [37, 2]      (w:1, o:44, a:1, s:1, b:0), 
% 18.84/19.25  zero  [39, 0]      (w:1, o:9, a:1, s:1, b:0), 
% 18.84/19.25  multiplication  [40, 2]      (w:1, o:46, a:1, s:1, b:0), 
% 18.84/19.25  one  [41, 0]      (w:1, o:10, a:1, s:1, b:0), 
% 18.84/19.25  star  [42, 1]      (w:1, o:18, a:1, s:1, b:0), 
% 18.84/19.25  leq  [43, 2]      (w:1, o:45, a:1, s:1, b:0), 
% 18.84/19.25  strong_iteration  [44, 1]      (w:1, o:19, a:1, s:1, b:0), 
% 18.84/19.25  skol1  [46, 0]      (w:1, o:12, a:1, s:1, b:1).
% 18.84/19.25  
% 18.84/19.25  
% 18.84/19.25  Starting Search:
% 18.84/19.25  
% 18.84/19.25  *** allocated 15000 integers for clauses
% 18.84/19.25  *** allocated 22500 integers for clauses
% 18.84/19.25  *** allocated 33750 integers for clauses
% 18.84/19.25  *** allocated 50625 integers for clauses
% 18.84/19.25  *** allocated 15000 integers for termspace/termends
% 18.84/19.25  *** allocated 75937 integers for clauses
% 18.84/19.25  Resimplifying inuse:
% 18.84/19.25  Done
% 18.84/19.25  
% 18.84/19.25  *** allocated 22500 integers for termspace/termends
% 18.84/19.25  *** allocated 113905 integers for clauses
% 18.84/19.25  *** allocated 33750 integers for termspace/termends
% 18.84/19.25  
% 18.84/19.25  Intermediate Status:
% 18.84/19.25  Generated:    21458
% 18.84/19.25  Kept:         2061
% 18.84/19.25  Inuse:        232
% 18.84/19.25  Deleted:      54
% 18.84/19.25  Deletedinuse: 30
% 18.84/19.25  
% 18.84/19.25  Resimplifying inuse:
% 18.84/19.25  Done
% 18.84/19.25  
% 18.84/19.25  *** allocated 170857 integers for clauses
% 18.84/19.25  *** allocated 50625 integers for termspace/termends
% 18.84/19.25  Resimplifying inuse:
% 18.84/19.25  Done
% 18.84/19.25  
% 18.84/19.25  *** allocated 256285 integers for clauses
% 45.54/45.97  *** allocated 75937 integers for termspace/termends
% 45.54/45.97  
% 45.54/45.97  Intermediate Status:
% 45.54/45.97  Generated:    48073
% 45.54/45.97  Kept:         4072
% 45.54/45.97  Inuse:        389
% 45.54/45.97  Deleted:      88
% 45.54/45.97  Deletedinuse: 31
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  *** allocated 384427 integers for clauses
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  
% 45.54/45.97  Intermediate Status:
% 45.54/45.97  Generated:    63940
% 45.54/45.97  Kept:         6079
% 45.54/45.97  Inuse:        485
% 45.54/45.97  Deleted:      105
% 45.54/45.97  Deletedinuse: 33
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  *** allocated 113905 integers for termspace/termends
% 45.54/45.97  *** allocated 576640 integers for clauses
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  
% 45.54/45.97  Intermediate Status:
% 45.54/45.97  Generated:    98335
% 45.54/45.97  Kept:         8087
% 45.54/45.97  Inuse:        656
% 45.54/45.97  Deleted:      197
% 45.54/45.97  Deletedinuse: 82
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  *** allocated 170857 integers for termspace/termends
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  
% 45.54/45.97  Intermediate Status:
% 45.54/45.97  Generated:    135094
% 45.54/45.97  Kept:         10087
% 45.54/45.97  Inuse:        792
% 45.54/45.97  Deleted:      273
% 45.54/45.97  Deletedinuse: 150
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  *** allocated 864960 integers for clauses
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  
% 45.54/45.97  Intermediate Status:
% 45.54/45.97  Generated:    172608
% 45.54/45.97  Kept:         12089
% 45.54/45.97  Inuse:        918
% 45.54/45.97  Deleted:      314
% 45.54/45.97  Deletedinuse: 160
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  *** allocated 256285 integers for termspace/termends
% 45.54/45.97  
% 45.54/45.97  Intermediate Status:
% 45.54/45.97  Generated:    199096
% 45.54/45.97  Kept:         14106
% 45.54/45.97  Inuse:        1027
% 45.54/45.97  Deleted:      366
% 45.54/45.97  Deletedinuse: 170
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  *** allocated 1297440 integers for clauses
% 45.54/45.97  
% 45.54/45.97  Intermediate Status:
% 45.54/45.97  Generated:    225908
% 45.54/45.97  Kept:         16172
% 45.54/45.97  Inuse:        1098
% 45.54/45.97  Deleted:      419
% 45.54/45.97  Deletedinuse: 209
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  
% 45.54/45.97  Intermediate Status:
% 45.54/45.97  Generated:    248307
% 45.54/45.97  Kept:         18221
% 45.54/45.97  Inuse:        1152
% 45.54/45.97  Deleted:      427
% 45.54/45.97  Deletedinuse: 213
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  Resimplifying clauses:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  *** allocated 384427 integers for termspace/termends
% 45.54/45.97  
% 45.54/45.97  Intermediate Status:
% 45.54/45.97  Generated:    292508
% 45.54/45.97  Kept:         20222
% 45.54/45.97  Inuse:        1266
% 45.54/45.97  Deleted:      3931
% 45.54/45.97  Deletedinuse: 213
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  
% 45.54/45.97  Intermediate Status:
% 45.54/45.97  Generated:    325544
% 45.54/45.97  Kept:         22225
% 45.54/45.97  Inuse:        1371
% 45.54/45.97  Deleted:      3944
% 45.54/45.97  Deletedinuse: 220
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  
% 45.54/45.97  Intermediate Status:
% 45.54/45.97  Generated:    375609
% 45.54/45.97  Kept:         24236
% 45.54/45.97  Inuse:        1432
% 45.54/45.97  Deleted:      3949
% 45.54/45.97  Deletedinuse: 221
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  *** allocated 1946160 integers for clauses
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  *** allocated 576640 integers for termspace/termends
% 45.54/45.97  
% 45.54/45.97  Intermediate Status:
% 45.54/45.97  Generated:    411006
% 45.54/45.97  Kept:         28410
% 45.54/45.97  Inuse:        1437
% 45.54/45.97  Deleted:      3949
% 45.54/45.97  Deletedinuse: 221
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  
% 45.54/45.97  Intermediate Status:
% 45.54/45.97  Generated:    428618
% 45.54/45.97  Kept:         30434
% 45.54/45.97  Inuse:        1470
% 45.54/45.97  Deleted:      3950
% 45.54/45.97  Deletedinuse: 221
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  
% 45.54/45.97  Intermediate Status:
% 45.54/45.97  Generated:    451119
% 45.54/45.97  Kept:         32460
% 45.54/45.97  Inuse:        1512
% 45.54/45.97  Deleted:      3951
% 45.54/45.97  Deletedinuse: 221
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  
% 45.54/45.97  Intermediate Status:
% 45.54/45.97  Generated:    472254
% 45.54/45.97  Kept:         34603
% 45.54/45.97  Inuse:        1546
% 45.54/45.97  Deleted:      3951
% 45.54/45.97  Deletedinuse: 221
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  
% 45.54/45.97  Intermediate Status:
% 45.54/45.97  Generated:    491397
% 45.54/45.97  Kept:         36656
% 45.54/45.97  Inuse:        1577
% 45.54/45.97  Deleted:      3951
% 45.54/45.97  Deletedinuse: 221
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  
% 45.54/45.97  Intermediate Status:
% 45.54/45.97  Generated:    506766
% 45.54/45.97  Kept:         38698
% 45.54/45.97  Inuse:        1598
% 45.54/45.97  Deleted:      3954
% 45.54/45.97  Deletedinuse: 224
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  *** allocated 2919240 integers for clauses
% 45.54/45.97  Resimplifying clauses:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  
% 45.54/45.97  Intermediate Status:
% 45.54/45.97  Generated:    543098
% 45.54/45.97  Kept:         40751
% 45.54/45.97  Inuse:        1639
% 45.54/45.97  Deleted:      6373
% 45.54/45.97  Deletedinuse: 224
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  *** allocated 864960 integers for termspace/termends
% 45.54/45.97  
% 45.54/45.97  Intermediate Status:
% 45.54/45.97  Generated:    575486
% 45.54/45.97  Kept:         42760
% 45.54/45.97  Inuse:        1700
% 45.54/45.97  Deleted:      6373
% 45.54/45.97  Deletedinuse: 224
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  
% 45.54/45.97  Intermediate Status:
% 45.54/45.97  Generated:    614079
% 45.54/45.97  Kept:         44761
% 45.54/45.97  Inuse:        1791
% 45.54/45.97  Deleted:      6381
% 45.54/45.97  Deletedinuse: 227
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  
% 45.54/45.97  Intermediate Status:
% 45.54/45.97  Generated:    689620
% 45.54/45.97  Kept:         46765
% 45.54/45.97  Inuse:        1832
% 45.54/45.97  Deleted:      6381
% 45.54/45.97  Deletedinuse: 227
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  
% 45.54/45.97  Intermediate Status:
% 45.54/45.97  Generated:    773019
% 45.54/45.97  Kept:         49110
% 45.54/45.97  Inuse:        1889
% 45.54/45.97  Deleted:      6384
% 45.54/45.97  Deletedinuse: 228
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  
% 45.54/45.97  Intermediate Status:
% 45.54/45.97  Generated:    802644
% 45.54/45.97  Kept:         51148
% 45.54/45.97  Inuse:        1947
% 45.54/45.97  Deleted:      6387
% 45.54/45.97  Deletedinuse: 231
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  
% 45.54/45.97  Intermediate Status:
% 45.54/45.97  Generated:    839510
% 45.54/45.97  Kept:         53229
% 45.54/45.97  Inuse:        2000
% 45.54/45.97  Deleted:      6389
% 45.54/45.97  Deletedinuse: 231
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  
% 45.54/45.97  Intermediate Status:
% 45.54/45.97  Generated:    866983
% 45.54/45.97  Kept:         55519
% 45.54/45.97  Inuse:        2047
% 45.54/45.97  Deleted:      6389
% 45.54/45.97  Deletedinuse: 231
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  
% 45.54/45.97  Intermediate Status:
% 45.54/45.97  Generated:    908948
% 45.54/45.97  Kept:         57523
% 45.54/45.97  Inuse:        2117
% 45.54/45.97  Deleted:      6390
% 45.54/45.97  Deletedinuse: 231
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  
% 45.54/45.97  Intermediate Status:
% 45.54/45.97  Generated:    966254
% 45.54/45.97  Kept:         59577
% 45.54/45.97  Inuse:        2212
% 45.54/45.97  Deleted:      6460
% 45.54/45.97  Deletedinuse: 278
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  Resimplifying clauses:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  *** allocated 4378860 integers for clauses
% 45.54/45.97  
% 45.54/45.97  Intermediate Status:
% 45.54/45.97  Generated:    977705
% 45.54/45.97  Kept:         61743
% 45.54/45.97  Inuse:        2225
% 45.54/45.97  Deleted:      9890
% 45.54/45.97  Deletedinuse: 278
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  *** allocated 1297440 integers for termspace/termends
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  
% 45.54/45.97  Intermediate Status:
% 45.54/45.97  Generated:    1006127
% 45.54/45.97  Kept:         63768
% 45.54/45.97  Inuse:        2270
% 45.54/45.97  Deleted:      9890
% 45.54/45.97  Deletedinuse: 278
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  Done
% 45.54/45.97  
% 45.54/45.97  Resimplifying inuse:
% 45.54/45.97  
% 45.54/45.97  Bliksems!, er is een bewijs:
% 45.54/45.97  % SZS status Theorem
% 45.54/45.97  % SZS output start Refutation
% 45.54/45.97  
% 45.54/45.97  (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 45.54/45.97  (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) ==> addition( 
% 45.54/45.97    addition( Z, Y ), X ) }.
% 45.54/45.97  (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 45.54/45.97  (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 45.54/45.97  (4) {G0,W11,D4,L1,V3,M1} I { multiplication( X, multiplication( Y, Z ) ) 
% 45.54/45.97    ==> multiplication( multiplication( X, Y ), Z ) }.
% 45.54/45.97  (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 45.54/45.97  (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ), 
% 45.54/45.97    multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 45.54/45.97  (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ), 
% 45.54/45.97    multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 45.54/45.97  (9) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==> zero }.
% 45.54/45.97  (11) {G0,W9,D5,L1,V1,M1} I { addition( one, multiplication( star( X ), X )
% 45.54/45.97     ) ==> star( X ) }.
% 45.54/45.97  (12) {G0,W13,D4,L2,V3,M2} I { ! leq( addition( multiplication( X, Z ), Y )
% 45.54/45.97    , Z ), leq( multiplication( star( X ), Y ), Z ) }.
% 45.54/45.97  (14) {G0,W9,D5,L1,V1,M1} I { addition( multiplication( X, strong_iteration
% 45.54/45.97    ( X ) ), one ) ==> strong_iteration( X ) }.
% 45.54/45.97  (16) {G0,W10,D5,L1,V1,M1} I { addition( star( X ), multiplication( 
% 45.54/45.97    strong_iteration( X ), zero ) ) ==> strong_iteration( X ) }.
% 45.54/45.97  (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) ==> Y }.
% 45.54/45.97  (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, Y ) }.
% 45.54/45.97  (19) {G0,W9,D5,L1,V0,M1} I { ! addition( multiplication( strong_iteration( 
% 45.54/45.97    skol1 ), skol1 ), one ) ==> strong_iteration( skol1 ) }.
% 45.54/45.97  (20) {G1,W5,D3,L1,V1,M1} P(0,2) { addition( zero, X ) ==> X }.
% 45.54/45.97  (22) {G1,W3,D2,L1,V1,M1} R(18,3) { leq( X, X ) }.
% 45.54/45.97  (25) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y ), Z ) ==> 
% 45.54/45.97    addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 45.54/45.97  (27) {G1,W11,D4,L1,V3,M1} P(0,1);d(1) { addition( addition( Z, Y ), X ) = 
% 45.54/45.97    addition( addition( Z, X ), Y ) }.
% 45.54/45.97  (35) {G1,W12,D4,L2,V3,M2} P(17,1) { addition( addition( Z, X ), Y ) ==> 
% 45.54/45.97    addition( Z, Y ), ! leq( X, Y ) }.
% 45.54/45.97  (36) {G1,W8,D3,L2,V2,M2} P(17,0) { addition( Y, X ) ==> Y, ! leq( X, Y )
% 45.54/45.97     }.
% 45.54/45.97  (50) {G1,W9,D4,L1,V2,M1} P(9,4) { multiplication( multiplication( Y, zero )
% 45.54/45.97    , X ) ==> multiplication( Y, zero ) }.
% 45.54/45.97  (67) {G1,W16,D4,L2,V3,M2} P(7,18) { ! multiplication( X, addition( Y, Z ) )
% 45.54/45.97     ==> multiplication( X, Z ), leq( multiplication( X, Y ), multiplication
% 45.54/45.97    ( X, Z ) ) }.
% 45.54/45.97  (69) {G1,W11,D4,L1,V2,M1} P(5,7) { addition( X, multiplication( X, Y ) ) = 
% 45.54/45.97    multiplication( X, addition( one, Y ) ) }.
% 45.54/45.97  (99) {G1,W16,D4,L2,V3,M2} P(8,18) { ! multiplication( addition( X, Z ), Y )
% 45.54/45.97     ==> multiplication( Z, Y ), leq( multiplication( X, Y ), multiplication
% 45.54/45.97    ( Z, Y ) ) }.
% 45.54/45.97  (100) {G1,W11,D4,L1,V3,M1} P(8,0);d(8) { multiplication( addition( X, Z ), 
% 45.54/45.97    Y ) = multiplication( addition( Z, X ), Y ) }.
% 45.54/45.97  (213) {G2,W5,D3,L1,V1,M1} P(14,12);d(5);r(22) { leq( star( X ), 
% 45.54/45.97    strong_iteration( X ) ) }.
% 45.54/45.97  (226) {G3,W8,D4,L1,V1,M1} R(213,17) { addition( star( X ), strong_iteration
% 45.54/45.97    ( X ) ) ==> strong_iteration( X ) }.
% 45.54/45.97  (285) {G1,W10,D5,L1,V1,M1} P(16,0) { addition( multiplication( 
% 45.54/45.97    strong_iteration( X ), zero ), star( X ) ) ==> strong_iteration( X ) }.
% 45.54/45.97  (312) {G1,W9,D5,L1,V0,M1} P(0,19) { ! addition( one, multiplication( 
% 45.54/45.97    strong_iteration( skol1 ), skol1 ) ) ==> strong_iteration( skol1 ) }.
% 45.54/45.97  (328) {G2,W8,D3,L2,V3,M2} P(17,25);q { leq( X, addition( Y, Z ) ), ! leq( X
% 45.54/45.97    , Y ) }.
% 45.54/45.97  (332) {G2,W5,D3,L1,V2,M1} P(3,25);q { leq( X, addition( X, Y ) ) }.
% 45.54/45.97  (371) {G3,W5,D3,L1,V2,M1} P(0,332) { leq( X, addition( Y, X ) ) }.
% 45.54/45.97  (377) {G4,W7,D4,L1,V1,M1} P(11,371) { leq( multiplication( star( X ), X ), 
% 45.54/45.97    star( X ) ) }.
% 45.54/45.97  (389) {G2,W14,D5,L1,V2,M1} P(16,27) { addition( addition( star( X ), Y ), 
% 45.54/45.97    multiplication( strong_iteration( X ), zero ) ) ==> addition( 
% 45.54/45.97    strong_iteration( X ), Y ) }.
% 45.54/45.97  (571) {G2,W15,D4,L2,V2,M2} P(16,35) { addition( strong_iteration( X ), Y ) 
% 45.54/45.97    ==> addition( star( X ), Y ), ! leq( multiplication( strong_iteration( X
% 45.54/45.97     ), zero ), Y ) }.
% 45.54/45.97  (574) {G2,W14,D4,L2,V2,M2} P(11,35) { addition( star( X ), Y ) ==> addition
% 45.54/45.97    ( one, Y ), ! leq( multiplication( star( X ), X ), Y ) }.
% 45.54/45.97  (812) {G2,W15,D5,L1,V3,M1} P(50,8) { multiplication( addition( Z, 
% 45.54/45.97    multiplication( X, zero ) ), Y ) ==> addition( multiplication( Z, Y ), 
% 45.54/45.97    multiplication( X, zero ) ) }.
% 45.54/45.97  (1101) {G3,W8,D3,L2,V2,M2} P(16,328) { leq( Y, strong_iteration( X ) ), ! 
% 45.54/45.97    leq( Y, star( X ) ) }.
% 45.54/45.97  (1111) {G5,W7,D4,L1,V1,M1} R(1101,377) { leq( multiplication( star( X ), X
% 45.54/45.97     ), strong_iteration( X ) ) }.
% 45.54/45.97  (1128) {G6,W10,D5,L1,V1,M1} R(1111,36) { addition( strong_iteration( X ), 
% 45.54/45.97    multiplication( star( X ), X ) ) ==> strong_iteration( X ) }.
% 45.54/45.97  (1632) {G2,W7,D3,L1,V2,M1} P(20,67);q { leq( multiplication( Y, zero ), 
% 45.54/45.97    multiplication( Y, X ) ) }.
% 45.54/45.97  (5228) {G4,W9,D4,L1,V2,M1} P(226,99);q { leq( multiplication( star( X ), Y
% 45.54/45.97     ), multiplication( strong_iteration( X ), Y ) ) }.
% 45.54/45.97  (12374) {G3,W14,D5,L1,V2,M1} P(285,100);d(812) { addition( multiplication( 
% 45.54/45.97    star( X ), Y ), multiplication( strong_iteration( X ), zero ) ) ==> 
% 45.54/45.97    multiplication( strong_iteration( X ), Y ) }.
% 45.54/45.97  (18940) {G4,W14,D5,L1,V2,M1} P(69,389);d(12374) { addition( 
% 45.54/45.97    strong_iteration( X ), multiplication( star( X ), Y ) ) ==> 
% 45.54/45.97    multiplication( strong_iteration( X ), addition( one, Y ) ) }.
% 45.54/45.97  (20024) {G7,W9,D4,L1,V1,M1} S(1128);d(18940) { multiplication( 
% 45.54/45.97    strong_iteration( X ), addition( one, X ) ) ==> strong_iteration( X ) }.
% 45.54/45.97  (35715) {G3,W14,D5,L1,V2,M1} P(571,69);r(1632) { addition( star( X ), 
% 45.54/45.97    multiplication( strong_iteration( X ), Y ) ) ==> multiplication( 
% 45.54/45.97    strong_iteration( X ), addition( one, Y ) ) }.
% 45.54/45.97  (64568) {G8,W9,D5,L1,V1,M1} R(5228,574);d(35715);d(20024) { addition( one, 
% 45.54/45.97    multiplication( strong_iteration( X ), X ) ) ==> strong_iteration( X )
% 45.54/45.97     }.
% 45.54/45.97  (64826) {G9,W0,D0,L0,V0,M0} S(312);d(64568);q {  }.
% 45.54/45.97  
% 45.54/45.97  
% 45.54/45.97  % SZS output end Refutation
% 45.54/45.97  found a proof!
% 45.54/45.97  
% 45.54/45.97  
% 45.54/45.97  Unprocessed initial clauses:
% 45.54/45.97  
% 45.54/45.97  (64828) {G0,W7,D3,L1,V2,M1}  { addition( X, Y ) = addition( Y, X ) }.
% 45.54/45.97  (64829) {G0,W11,D4,L1,V3,M1}  { addition( Z, addition( Y, X ) ) = addition
% 45.54/45.97    ( addition( Z, Y ), X ) }.
% 45.54/45.97  (64830) {G0,W5,D3,L1,V1,M1}  { addition( X, zero ) = X }.
% 45.54/45.97  (64831) {G0,W5,D3,L1,V1,M1}  { addition( X, X ) = X }.
% 45.54/45.97  (64832) {G0,W11,D4,L1,V3,M1}  { multiplication( X, multiplication( Y, Z ) )
% 45.54/45.97     = multiplication( multiplication( X, Y ), Z ) }.
% 45.54/45.97  (64833) {G0,W5,D3,L1,V1,M1}  { multiplication( X, one ) = X }.
% 45.54/45.97  (64834) {G0,W5,D3,L1,V1,M1}  { multiplication( one, X ) = X }.
% 45.54/45.97  (64835) {G0,W13,D4,L1,V3,M1}  { multiplication( X, addition( Y, Z ) ) = 
% 45.54/45.97    addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 45.54/45.97  (64836) {G0,W13,D4,L1,V3,M1}  { multiplication( addition( X, Y ), Z ) = 
% 45.54/45.97    addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 45.54/45.97  (64837) {G0,W5,D3,L1,V1,M1}  { multiplication( zero, X ) = zero }.
% 45.54/45.97  (64838) {G0,W9,D5,L1,V1,M1}  { addition( one, multiplication( X, star( X )
% 45.54/45.97     ) ) = star( X ) }.
% 45.54/45.97  (64839) {G0,W9,D5,L1,V1,M1}  { addition( one, multiplication( star( X ), X
% 45.54/45.97     ) ) = star( X ) }.
% 45.54/45.97  (64840) {G0,W13,D4,L2,V3,M2}  { ! leq( addition( multiplication( X, Z ), Y
% 45.54/45.97     ), Z ), leq( multiplication( star( X ), Y ), Z ) }.
% 45.54/45.97  (64841) {G0,W13,D4,L2,V3,M2}  { ! leq( addition( multiplication( Z, X ), Y
% 45.54/45.97     ), Z ), leq( multiplication( Y, star( X ) ), Z ) }.
% 45.54/45.97  (64842) {G0,W9,D5,L1,V1,M1}  { strong_iteration( X ) = addition( 
% 45.54/45.97    multiplication( X, strong_iteration( X ) ), one ) }.
% 45.54/45.97  (64843) {G0,W13,D4,L2,V3,M2}  { ! leq( Z, addition( multiplication( X, Z )
% 45.54/45.97    , Y ) ), leq( Z, multiplication( strong_iteration( X ), Y ) ) }.
% 45.54/45.97  (64844) {G0,W10,D5,L1,V1,M1}  { strong_iteration( X ) = addition( star( X )
% 45.54/45.97    , multiplication( strong_iteration( X ), zero ) ) }.
% 45.54/45.97  (64845) {G0,W8,D3,L2,V2,M2}  { ! leq( X, Y ), addition( X, Y ) = Y }.
% 45.54/45.97  (64846) {G0,W8,D3,L2,V2,M2}  { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 45.54/45.97  (64847) {G0,W9,D5,L1,V0,M1}  { ! strong_iteration( skol1 ) = addition( 
% 45.54/45.97    multiplication( strong_iteration( skol1 ), skol1 ), one ) }.
% 45.54/45.97  
% 45.54/45.97  
% 45.54/45.97  Total Proof:
% 45.54/45.97  
% 45.54/45.97  subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 45.54/45.97     ) }.
% 45.54/45.97  parent0: (64828) {G0,W7,D3,L1,V2,M1}  { addition( X, Y ) = addition( Y, X )
% 45.54/45.97     }.
% 45.54/45.97  substitution0:
% 45.54/45.97     X := X
% 45.54/45.97     Y := Y
% 45.54/45.97  end
% 45.54/45.97  permutation0:
% 45.54/45.97     0 ==> 0
% 45.54/45.97  end
% 45.54/45.97  
% 45.54/45.97  subsumption: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) 
% 45.54/45.97    ==> addition( addition( Z, Y ), X ) }.
% 45.54/45.97  parent0: (64829) {G0,W11,D4,L1,V3,M1}  { addition( Z, addition( Y, X ) ) = 
% 45.54/45.97    addition( addition( Z, Y ), X ) }.
% 45.54/45.97  substitution0:
% 45.54/45.97     X := X
% 45.54/45.97     Y := Y
% 45.54/45.97     Z := Z
% 45.54/45.97  end
% 45.54/45.97  permutation0:
% 45.54/45.97     0 ==> 0
% 45.54/45.97  end
% 45.54/45.97  
% 45.54/45.97  subsumption: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 45.54/45.97  parent0: (64830) {G0,W5,D3,L1,V1,M1}  { addition( X, zero ) = X }.
% 45.54/45.97  substitution0:
% 45.54/45.97     X := X
% 45.54/45.97  end
% 45.54/45.97  permutation0:
% 45.54/45.97     0 ==> 0
% 45.54/45.97  end
% 45.54/45.97  
% 45.54/45.97  subsumption: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 45.54/45.97  parent0: (64831) {G0,W5,D3,L1,V1,M1}  { addition( X, X ) = X }.
% 45.54/45.97  substitution0:
% 45.54/45.97     X := X
% 45.54/45.97  end
% 45.54/45.97  permutation0:
% 45.54/45.97     0 ==> 0
% 45.54/45.97  end
% 45.54/45.97  
% 45.54/45.97  subsumption: (4) {G0,W11,D4,L1,V3,M1} I { multiplication( X, multiplication
% 45.54/45.97    ( Y, Z ) ) ==> multiplication( multiplication( X, Y ), Z ) }.
% 45.54/45.97  parent0: (64832) {G0,W11,D4,L1,V3,M1}  { multiplication( X, multiplication
% 45.54/45.97    ( Y, Z ) ) = multiplication( multiplication( X, Y ), Z ) }.
% 45.54/45.97  substitution0:
% 45.54/45.97     X := X
% 45.54/45.97     Y := Y
% 45.54/45.97     Z := Z
% 45.54/45.97  end
% 45.54/45.97  permutation0:
% 45.54/45.97     0 ==> 0
% 45.54/45.97  end
% 45.54/45.97  
% 45.54/45.97  subsumption: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 45.54/45.97  parent0: (64833) {G0,W5,D3,L1,V1,M1}  { multiplication( X, one ) = X }.
% 45.54/45.97  substitution0:
% 45.54/45.97     X := X
% 45.54/45.97  end
% 45.54/45.97  permutation0:
% 45.54/45.97     0 ==> 0
% 45.54/45.97  end
% 45.54/45.97  
% 45.54/45.97  eqswap: (64869) {G0,W13,D4,L1,V3,M1}  { addition( multiplication( X, Y ), 
% 45.54/45.97    multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 45.54/45.97  parent0[0]: (64835) {G0,W13,D4,L1,V3,M1}  { multiplication( X, addition( Y
% 45.54/45.97    , Z ) ) = addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 45.54/45.97  substitution0:
% 45.54/45.97     X := X
% 45.54/45.97     Y := Y
% 45.54/45.97     Z := Z
% 45.54/45.97  end
% 45.54/45.97  
% 45.54/45.97  subsumption: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y )
% 45.54/45.97    , multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 45.54/45.97  parent0: (64869) {G0,W13,D4,L1,V3,M1}  { addition( multiplication( X, Y ), 
% 45.54/45.97    multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 45.54/45.97  substitution0:
% 45.54/45.97     X := X
% 45.54/45.97     Y := Y
% 45.54/45.97     Z := Z
% 45.54/45.97  end
% 45.54/45.97  permutation0:
% 45.54/45.97     0 ==> 0
% 45.54/45.97  end
% 45.54/45.97  
% 45.54/45.97  eqswap: (64877) {G0,W13,D4,L1,V3,M1}  { addition( multiplication( X, Z ), 
% 45.54/45.97    multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 45.54/45.97  parent0[0]: (64836) {G0,W13,D4,L1,V3,M1}  { multiplication( addition( X, Y
% 45.54/45.97     ), Z ) = addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 45.54/45.97  substitution0:
% 45.54/45.97     X := X
% 45.54/45.97     Y := Y
% 45.54/45.97     Z := Z
% 45.54/45.97  end
% 45.54/45.97  
% 45.54/45.97  subsumption: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z )
% 45.54/45.97    , multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 45.54/45.97  parent0: (64877) {G0,W13,D4,L1,V3,M1}  { addition( multiplication( X, Z ), 
% 45.54/45.97    multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 45.54/45.97  substitution0:
% 45.54/45.97     X := X
% 45.54/45.97     Y := Y
% 45.54/45.97     Z := Z
% 45.54/45.97  end
% 45.54/45.97  permutation0:
% 45.54/45.97     0 ==> 0
% 45.54/45.97  end
% 45.54/45.97  
% 45.54/45.97  subsumption: (9) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==> zero
% 45.54/45.97     }.
% 45.54/45.97  parent0: (64837) {G0,W5,D3,L1,V1,M1}  { multiplication( zero, X ) = zero
% 45.54/45.97     }.
% 45.54/45.97  substitution0:
% 45.54/45.97     X := X
% 45.54/45.97  end
% 45.54/45.97  permutation0:
% 45.54/45.97     0 ==> 0
% 45.54/45.97  end
% 45.54/45.97  
% 45.54/45.97  subsumption: (11) {G0,W9,D5,L1,V1,M1} I { addition( one, multiplication( 
% 45.54/45.97    star( X ), X ) ) ==> star( X ) }.
% 45.54/45.97  parent0: (64839) {G0,W9,D5,L1,V1,M1}  { addition( one, multiplication( star
% 45.54/45.97    ( X ), X ) ) = star( X ) }.
% 45.54/45.97  substitution0:
% 45.54/45.97     X := X
% 45.54/45.97  end
% 45.54/45.97  permutation0:
% 45.54/45.97     0 ==> 0
% 45.54/45.97  end
% 45.54/45.97  
% 45.54/45.97  subsumption: (12) {G0,W13,D4,L2,V3,M2} I { ! leq( addition( multiplication
% 45.54/45.97    ( X, Z ), Y ), Z ), leq( multiplication( star( X ), Y ), Z ) }.
% 45.54/45.97  parent0: (64840) {G0,W13,D4,L2,V3,M2}  { ! leq( addition( multiplication( X
% 45.54/45.97    , Z ), Y ), Z ), leq( multiplication( star( X ), Y ), Z ) }.
% 45.54/45.97  substitution0:
% 45.54/45.97     X := X
% 45.54/45.97     Y := Y
% 45.54/45.97     Z := Z
% 45.54/45.97  end
% 45.54/45.97  permutation0:
% 45.54/45.97     0 ==> 0
% 45.54/45.97     1 ==> 1
% 45.54/45.97  end
% 45.54/45.97  
% 45.54/45.97  eqswap: (64920) {G0,W9,D5,L1,V1,M1}  { addition( multiplication( X, 
% 45.54/45.97    strong_iteration( X ) ), one ) = strong_iteration( X ) }.
% 45.54/45.97  parent0[0]: (64842) {G0,W9,D5,L1,V1,M1}  { strong_iteration( X ) = addition
% 45.54/45.97    ( multiplication( X, strong_iteration( X ) ), one ) }.
% 45.54/45.97  substitution0:
% 45.54/45.97     X := X
% 45.54/45.97  end
% 45.54/45.97  
% 45.54/45.97  subsumption: (14) {G0,W9,D5,L1,V1,M1} I { addition( multiplication( X, 
% 45.54/45.97    strong_iteration( X ) ), one ) ==> strong_iteration( X ) }.
% 45.54/45.97  parent0: (64920) {G0,W9,D5,L1,V1,M1}  { addition( multiplication( X, 
% 45.54/45.97    strong_iteration( X ) ), one ) = strong_iteration( X ) }.
% 45.54/45.97  substitution0:
% 45.54/45.97     X := X
% 45.54/45.97  end
% 45.54/45.97  permutation0:
% 45.54/45.97     0 ==> 0
% 45.54/45.97  end
% 45.54/45.97  
% 45.54/45.97  eqswap: (64933) {G0,W10,D5,L1,V1,M1}  { addition( star( X ), multiplication
% 45.54/45.97    ( strong_iteration( X ), zero ) ) = strong_iteration( X ) }.
% 45.54/45.97  parent0[0]: (64844) {G0,W10,D5,L1,V1,M1}  { strong_iteration( X ) = 
% 45.54/45.97    addition( star( X ), multiplication( strong_iteration( X ), zero ) ) }.
% 45.54/45.97  substitution0:
% 45.54/45.97     X := X
% 45.54/45.97  end
% 45.54/45.97  
% 45.54/45.97  subsumption: (16) {G0,W10,D5,L1,V1,M1} I { addition( star( X ), 
% 45.54/45.97    multiplication( strong_iteration( X ), zero ) ) ==> strong_iteration( X )
% 45.54/45.97     }.
% 45.54/45.97  parent0: (64933) {G0,W10,D5,L1,V1,M1}  { addition( star( X ), 
% 45.54/45.97    multiplication( strong_iteration( X ), zero ) ) = strong_iteration( X )
% 45.54/45.97     }.
% 45.54/45.97  substitution0:
% 45.54/45.97     X := X
% 45.54/45.97  end
% 45.54/45.97  permutation0:
% 45.54/45.97     0 ==> 0
% 45.54/45.97  end
% 45.54/45.97  
% 45.54/45.97  subsumption: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) 
% 45.54/45.97    ==> Y }.
% 45.54/45.97  parent0: (64845) {G0,W8,D3,L2,V2,M2}  { ! leq( X, Y ), addition( X, Y ) = Y
% 45.54/45.97     }.
% 45.54/45.97  substitution0:
% 45.54/45.97     X := X
% 45.54/45.97     Y := Y
% 45.54/45.97  end
% 45.54/45.97  permutation0:
% 45.54/45.97     0 ==> 0
% 45.54/45.97     1 ==> 1
% 45.54/45.97  end
% 45.54/45.97  
% 45.54/45.97  subsumption: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X
% 45.54/45.97    , Y ) }.
% 45.54/45.97  parent0: (64846) {G0,W8,D3,L2,V2,M2}  { ! addition( X, Y ) = Y, leq( X, Y )
% 45.54/45.97     }.
% 45.54/45.97  substitution0:
% 45.54/45.97     X := X
% 45.54/45.97     Y := Y
% 45.54/45.97  end
% 45.54/45.97  permutation0:
% 45.54/45.97     0 ==> 0
% 45.54/45.97     1 ==> 1
% 45.54/45.97  end
% 45.54/45.97  
% 45.54/45.97  eqswap: (64978) {G0,W9,D5,L1,V0,M1}  { ! addition( multiplication( 
% 45.54/45.97    strong_iteration( skol1 ), skol1 ), one ) = strong_iteration( skol1 ) }.
% 45.54/45.97  parent0[0]: (64847) {G0,W9,D5,L1,V0,M1}  { ! strong_iteration( skol1 ) = 
% 45.54/45.97    addition( multiplication( strong_iteration( skol1 ), skol1 ), one ) }.
% 45.54/45.97  substitution0:
% 45.54/45.97  end
% 45.54/45.97  
% 45.54/45.97  subsumption: (19) {G0,W9,D5,L1,V0,M1} I { ! addition( multiplication( 
% 45.54/45.97    strong_iteration( skol1 ), skol1 ), one ) ==> strong_iteration( skol1 )
% 45.54/45.97     }.
% 45.54/45.97  parent0: (64978) {G0,W9,D5,L1,V0,M1}  { ! addition( multiplication( 
% 45.54/45.97    strong_iteration( skol1 ), skol1 ), one ) = strong_iteration( skol1 ) }.
% 45.54/45.97  substitution0:
% 45.54/45.97  end
% 45.54/45.97  permutation0:
% 45.54/45.97     0 ==> 0
% 45.54/45.97  end
% 45.54/45.97  
% 45.54/45.97  eqswap: (64979) {G0,W5,D3,L1,V1,M1}  { X ==> addition( X, zero ) }.
% 45.54/45.97  parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 45.54/45.97  substitution0:
% 45.54/45.97     X := X
% 45.54/45.97  end
% 45.54/45.97  
% 45.54/45.97  paramod: (64980) {G1,W5,D3,L1,V1,M1}  { X ==> addition( zero, X ) }.
% 45.54/45.97  parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 45.54/45.97     }.
% 45.54/45.97  parent1[0; 2]: (64979) {G0,W5,D3,L1,V1,M1}  { X ==> addition( X, zero ) }.
% 45.54/45.97  substitution0:
% 45.54/45.97     X := X
% 45.54/45.97     Y := zero
% 45.54/45.97  end
% 45.54/45.97  substitution1:
% 45.54/45.97     X := X
% 45.54/45.97  end
% 45.54/45.97  
% 45.54/45.97  eqswap: (64983) {G1,W5,D3,L1,V1,M1}  { addition( zero, X ) ==> X }.
% 45.54/45.97  parent0[0]: (64980) {G1,W5,D3,L1,V1,M1}  { X ==> addition( zero, X ) }.
% 45.54/45.97  substitution0:
% 45.54/45.97     X := X
% 45.54/45.97  end
% 45.54/45.97  
% 45.54/45.97  subsumption: (20) {G1,W5,D3,L1,V1,M1} P(0,2) { addition( zero, X ) ==> X
% 45.54/45.97     }.
% 45.54/45.97  parent0: (64983) {G1,W5,D3,L1,V1,M1}  { addition( zero, X ) ==> X }.
% 45.54/45.97  substitution0:
% 45.54/45.97     X := X
% 45.54/45.97  end
% 45.54/45.97  permutation0:
% 45.54/45.97     0 ==> 0
% 45.54/45.97  end
% 45.54/45.97  
% 45.54/45.97  eqswap: (64984) {G0,W8,D3,L2,V2,M2}  { ! Y ==> addition( X, Y ), leq( X, Y
% 45.54/45.97     ) }.
% 45.54/45.97  parent0[0]: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, 
% 45.54/45.97    Y ) }.
% 45.54/45.97  substitution0:
% 45.54/45.97     X := X
% 45.54/45.97     Y := Y
% 45.54/45.97  end
% 45.54/45.97  
% 45.54/45.97  eqswap: (64985) {G0,W5,D3,L1,V1,M1}  { X ==> addition( X, X ) }.
% 45.54/45.97  parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 45.54/45.97  substitution0:
% 45.54/45.97     X := X
% 45.54/45.97  end
% 45.54/45.97  
% 45.54/45.97  resolution: (64986) {G1,W3,D2,L1,V1,M1}  { leq( X, X ) }.
% 45.54/45.97  parent0[0]: (64984) {G0,W8,D3,L2,V2,M2}  { ! Y ==> addition( X, Y ), leq( X
% 45.54/45.97    , Y ) }.
% 45.54/45.97  parent1[0]: (64985) {G0,W5,D3,L1,V1,M1}  { X ==> addition( X, X ) }.
% 45.54/45.97  substitution0:
% 45.54/45.97     X := X
% 45.54/45.97     Y := X
% 45.54/45.97  end
% 45.54/45.97  substitution1:
% 45.54/45.97     X := X
% 45.54/45.97  end
% 45.54/45.97  
% 45.54/45.97  subsumption: (22) {G1,W3,D2,L1,V1,M1} R(18,3) { leq( X, X ) }.
% 45.54/45.97  parent0: (64986) {G1,W3,D2,L1,V1,M1}  { leq( X, X ) }.
% 45.54/45.97  substitution0:
% 45.54/45.97     X := X
% 45.54/45.97  end
% 45.54/45.97  permutation0:
% 45.54/45.97     0 ==> 0
% 45.54/45.97  end
% 45.54/45.97  
% 45.54/45.97  eqswap: (64988) {G0,W8,D3,L2,V2,M2}  { ! Y ==> addition( X, Y ), leq( X, Y
% 45.54/45.97     ) }.
% 45.54/45.97  parent0[0]: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, 
% 45.54/45.97    Y ) }.
% 45.54/45.97  substitution0:
% 45.54/45.97     X := X
% 45.54/45.97     Y := Y
% 45.54/45.97  end
% 45.54/45.97  
% 45.54/45.97  paramod: (64989) {G1,W14,D4,L2,V3,M2}  { ! addition( X, Y ) ==> addition( 
% 45.54/45.97    addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 45.54/45.97  parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) 
% 45.54/45.97    ==> addition( addition( Z, Y ), X ) }.
% 45.54/45.97  parent1[0; 5]: (64988) {G0,W8,D3,L2,V2,M2}  { ! Y ==> addition( X, Y ), leq
% 45.54/45.97    ( X, Y ) }.
% 45.54/45.97  substitution0:
% 45.54/45.97     X := Y
% 45.54/45.97     Y := X
% 45.54/45.97     Z := Z
% 45.54/45.97  end
% 45.54/45.97  substitution1:
% 45.54/45.97     X := Z
% 45.54/45.97     Y := addition( X, Y )
% 45.54/45.97  end
% 45.54/45.97  
% 45.54/45.97  eqswap: (64990) {G1,W14,D4,L2,V3,M2}  { ! addition( addition( Z, X ), Y ) 
% 45.54/45.97    ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 45.54/45.97  parent0[0]: (64989) {G1,W14,D4,L2,V3,M2}  { ! addition( X, Y ) ==> addition
% 45.54/45.97    ( addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 45.54/45.97  substitution0:
% 45.54/45.97     X := X
% 45.54/45.97     Y := Y
% 45.54/45.97     Z := Z
% 45.54/45.97  end
% 45.54/45.97  
% 45.54/45.97  subsumption: (25) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y
% 45.54/45.97     ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 45.54/45.97  parent0: (64990) {G1,W14,D4,L2,V3,M2}  { ! addition( addition( Z, X ), Y ) 
% 45.54/45.97    ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 45.54/45.97  substitution0:
% 45.54/45.97     X := Y
% 45.54/45.97     Y := Z
% 45.54/45.97     Z := X
% 45.54/45.97  end
% 45.54/45.97  permutation0:
% 45.54/45.97     0 ==> 0
% 45.54/45.97     1 ==> 1
% 45.54/45.97  end
% 45.54/45.97  
% 45.54/45.97  eqswap: (64991) {G0,W11,D4,L1,V3,M1}  { addition( addition( X, Y ), Z ) ==>
% 45.54/45.97     addition( X, addition( Y, Z ) ) }.
% 45.54/45.97  parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) 
% 45.54/45.97    ==> addition( addition( Z, Y ), X ) }.
% 45.54/45.97  substitution0:
% 45.54/45.97     X := Z
% 45.54/45.97     Y := Y
% 45.54/45.97     Z := X
% 45.54/45.97  end
% 45.54/45.97  
% 45.54/45.97  paramod: (64996) {G1,W11,D4,L1,V3,M1}  { addition( addition( X, Y ), Z ) 
% 45.54/45.97    ==> addition( X, addition( Z, Y ) ) }.
% 45.54/45.97  parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 45.54/45.97     }.
% 45.54/45.97  parent1[0; 8]: (64991) {G0,W11,D4,L1,V3,M1}  { addition( addition( X, Y ), 
% 45.54/45.97    Z ) ==> addition( X, addition( Y, Z ) ) }.
% 45.54/45.97  substitution0:
% 45.54/45.97     X := Y
% 45.54/45.97     Y := Z
% 45.54/45.97  end
% 45.54/45.97  substitution1:
% 45.54/45.97     X := X
% 45.54/45.97     Y := Y
% 45.54/45.97     Z := Z
% 45.54/45.97  end
% 45.54/45.97  
% 45.54/45.97  paramod: (65009) {G1,W11,D4,L1,V3,M1}  { addition( addition( X, Y ), Z ) 
% 45.54/45.97    ==> addition( addition( X, Z ), Y ) }.
% 45.54/45.97  parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) 
% 45.54/45.97    ==> addition( addition( Z, Y ), X ) }.
% 45.54/45.97  parent1[0; 6]: (64996) {G1,W11,D4,L1,V3,M1}  { addition( addition( X, Y ), 
% 45.54/45.97    Z ) ==> addition( X, addition( Z, Y ) ) }.
% 45.54/45.97  substitution0:
% 45.54/45.97     X := Y
% 45.54/45.97     Y := Z
% 45.54/45.97     Z := X
% 45.54/45.97  end
% 45.54/45.97  substitution1:
% 45.54/45.97     X := X
% 45.54/45.97     Y := Y
% 45.54/45.97     Z := Z
% 45.54/45.97  end
% 45.54/45.97  
% 45.54/45.97  subsumption: (27) {G1,W11,D4,L1,V3,M1} P(0,1);d(1) { addition( addition( Z
% 45.54/45.97    , Y ), X ) = addition( addition( Z, X ), Y ) }.
% 45.54/45.97  parent0: (65009) {G1,W11,D4,L1,V3,M1}  { addition( addition( X, Y ), Z ) 
% 45.54/45.97    ==> addition( addition( X, Z ), Y ) }.
% 45.54/45.97  substitution0:
% 45.54/45.97     X := Z
% 45.54/45.97     Y := Y
% 45.54/45.97     Z := X
% 45.54/45.97  end
% 45.54/45.97  permutation0:
% 45.54/45.97     0 ==> 0
% 45.54/45.97  end
% 45.54/45.97  
% 45.54/45.97  eqswap: (65011) {G0,W11,D4,L1,V3,M1}  { addition( addition( X, Y ), Z ) ==>
% 45.54/45.97     addition( X, addition( Y, Z ) ) }.
% 45.54/45.97  parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) 
% 45.54/45.98    ==> addition( addition( Z, Y ), X ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := Z
% 45.54/45.98     Y := Y
% 45.54/45.98     Z := X
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  paramod: (65017) {G1,W12,D4,L2,V3,M2}  { addition( addition( X, Y ), Z ) 
% 45.54/45.98    ==> addition( X, Z ), ! leq( Y, Z ) }.
% 45.54/45.98  parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) 
% 45.54/45.98    ==> Y }.
% 45.54/45.98  parent1[0; 8]: (65011) {G0,W11,D4,L1,V3,M1}  { addition( addition( X, Y ), 
% 45.54/45.98    Z ) ==> addition( X, addition( Y, Z ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := Y
% 45.54/45.98     Y := Z
% 45.54/45.98  end
% 45.54/45.98  substitution1:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Y
% 45.54/45.98     Z := Z
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  subsumption: (35) {G1,W12,D4,L2,V3,M2} P(17,1) { addition( addition( Z, X )
% 45.54/45.98    , Y ) ==> addition( Z, Y ), ! leq( X, Y ) }.
% 45.54/45.98  parent0: (65017) {G1,W12,D4,L2,V3,M2}  { addition( addition( X, Y ), Z ) 
% 45.54/45.98    ==> addition( X, Z ), ! leq( Y, Z ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := Z
% 45.54/45.98     Y := X
% 45.54/45.98     Z := Y
% 45.54/45.98  end
% 45.54/45.98  permutation0:
% 45.54/45.98     0 ==> 0
% 45.54/45.98     1 ==> 1
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  eqswap: (65064) {G0,W8,D3,L2,V2,M2}  { Y ==> addition( X, Y ), ! leq( X, Y
% 45.54/45.98     ) }.
% 45.54/45.98  parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) 
% 45.54/45.98    ==> Y }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Y
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  paramod: (65065) {G1,W8,D3,L2,V2,M2}  { X ==> addition( X, Y ), ! leq( Y, X
% 45.54/45.98     ) }.
% 45.54/45.98  parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 45.54/45.98     }.
% 45.54/45.98  parent1[0; 2]: (65064) {G0,W8,D3,L2,V2,M2}  { Y ==> addition( X, Y ), ! leq
% 45.54/45.98    ( X, Y ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := Y
% 45.54/45.98     Y := X
% 45.54/45.98  end
% 45.54/45.98  substitution1:
% 45.54/45.98     X := Y
% 45.54/45.98     Y := X
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  eqswap: (65068) {G1,W8,D3,L2,V2,M2}  { addition( X, Y ) ==> X, ! leq( Y, X
% 45.54/45.98     ) }.
% 45.54/45.98  parent0[0]: (65065) {G1,W8,D3,L2,V2,M2}  { X ==> addition( X, Y ), ! leq( Y
% 45.54/45.98    , X ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Y
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  subsumption: (36) {G1,W8,D3,L2,V2,M2} P(17,0) { addition( Y, X ) ==> Y, ! 
% 45.54/45.98    leq( X, Y ) }.
% 45.54/45.98  parent0: (65068) {G1,W8,D3,L2,V2,M2}  { addition( X, Y ) ==> X, ! leq( Y, X
% 45.54/45.98     ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := Y
% 45.54/45.98     Y := X
% 45.54/45.98  end
% 45.54/45.98  permutation0:
% 45.54/45.98     0 ==> 0
% 45.54/45.98     1 ==> 1
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  eqswap: (65070) {G0,W11,D4,L1,V3,M1}  { multiplication( multiplication( X, 
% 45.54/45.98    Y ), Z ) ==> multiplication( X, multiplication( Y, Z ) ) }.
% 45.54/45.98  parent0[0]: (4) {G0,W11,D4,L1,V3,M1} I { multiplication( X, multiplication
% 45.54/45.98    ( Y, Z ) ) ==> multiplication( multiplication( X, Y ), Z ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Y
% 45.54/45.98     Z := Z
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  paramod: (65075) {G1,W9,D4,L1,V2,M1}  { multiplication( multiplication( X, 
% 45.54/45.98    zero ), Y ) ==> multiplication( X, zero ) }.
% 45.54/45.98  parent0[0]: (9) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==> zero
% 45.54/45.98     }.
% 45.54/45.98  parent1[0; 8]: (65070) {G0,W11,D4,L1,V3,M1}  { multiplication( 
% 45.54/45.98    multiplication( X, Y ), Z ) ==> multiplication( X, multiplication( Y, Z )
% 45.54/45.98     ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := Y
% 45.54/45.98  end
% 45.54/45.98  substitution1:
% 45.54/45.98     X := X
% 45.54/45.98     Y := zero
% 45.54/45.98     Z := Y
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  subsumption: (50) {G1,W9,D4,L1,V2,M1} P(9,4) { multiplication( 
% 45.54/45.98    multiplication( Y, zero ), X ) ==> multiplication( Y, zero ) }.
% 45.54/45.98  parent0: (65075) {G1,W9,D4,L1,V2,M1}  { multiplication( multiplication( X, 
% 45.54/45.98    zero ), Y ) ==> multiplication( X, zero ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := Y
% 45.54/45.98     Y := X
% 45.54/45.98  end
% 45.54/45.98  permutation0:
% 45.54/45.98     0 ==> 0
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  eqswap: (65084) {G0,W8,D3,L2,V2,M2}  { ! Y ==> addition( X, Y ), leq( X, Y
% 45.54/45.98     ) }.
% 45.54/45.98  parent0[0]: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, 
% 45.54/45.98    Y ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Y
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  paramod: (65085) {G1,W16,D4,L2,V3,M2}  { ! multiplication( X, Y ) ==> 
% 45.54/45.98    multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ), 
% 45.54/45.98    multiplication( X, Y ) ) }.
% 45.54/45.98  parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ), 
% 45.54/45.98    multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 45.54/45.98  parent1[0; 5]: (65084) {G0,W8,D3,L2,V2,M2}  { ! Y ==> addition( X, Y ), leq
% 45.54/45.98    ( X, Y ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Z
% 45.54/45.98     Z := Y
% 45.54/45.98  end
% 45.54/45.98  substitution1:
% 45.54/45.98     X := multiplication( X, Z )
% 45.54/45.98     Y := multiplication( X, Y )
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  eqswap: (65086) {G1,W16,D4,L2,V3,M2}  { ! multiplication( X, addition( Z, Y
% 45.54/45.98     ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ), 
% 45.54/45.98    multiplication( X, Y ) ) }.
% 45.54/45.98  parent0[0]: (65085) {G1,W16,D4,L2,V3,M2}  { ! multiplication( X, Y ) ==> 
% 45.54/45.98    multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ), 
% 45.54/45.98    multiplication( X, Y ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Y
% 45.54/45.98     Z := Z
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  subsumption: (67) {G1,W16,D4,L2,V3,M2} P(7,18) { ! multiplication( X, 
% 45.54/45.98    addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 45.54/45.98     ), multiplication( X, Z ) ) }.
% 45.54/45.98  parent0: (65086) {G1,W16,D4,L2,V3,M2}  { ! multiplication( X, addition( Z, 
% 45.54/45.98    Y ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ), 
% 45.54/45.98    multiplication( X, Y ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Z
% 45.54/45.98     Z := Y
% 45.54/45.98  end
% 45.54/45.98  permutation0:
% 45.54/45.98     0 ==> 0
% 45.54/45.98     1 ==> 1
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  eqswap: (65088) {G0,W13,D4,L1,V3,M1}  { multiplication( X, addition( Y, Z )
% 45.54/45.98     ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 45.54/45.98  parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ), 
% 45.54/45.98    multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Y
% 45.54/45.98     Z := Z
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  paramod: (65089) {G1,W11,D4,L1,V2,M1}  { multiplication( X, addition( one, 
% 45.54/45.98    Y ) ) ==> addition( X, multiplication( X, Y ) ) }.
% 45.54/45.98  parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 45.54/45.98  parent1[0; 7]: (65088) {G0,W13,D4,L1,V3,M1}  { multiplication( X, addition
% 45.54/45.98    ( Y, Z ) ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) )
% 45.54/45.98     }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98  end
% 45.54/45.98  substitution1:
% 45.54/45.98     X := X
% 45.54/45.98     Y := one
% 45.54/45.98     Z := Y
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  eqswap: (65091) {G1,W11,D4,L1,V2,M1}  { addition( X, multiplication( X, Y )
% 45.54/45.98     ) ==> multiplication( X, addition( one, Y ) ) }.
% 45.54/45.98  parent0[0]: (65089) {G1,W11,D4,L1,V2,M1}  { multiplication( X, addition( 
% 45.54/45.98    one, Y ) ) ==> addition( X, multiplication( X, Y ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Y
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  subsumption: (69) {G1,W11,D4,L1,V2,M1} P(5,7) { addition( X, multiplication
% 45.54/45.98    ( X, Y ) ) = multiplication( X, addition( one, Y ) ) }.
% 45.54/45.98  parent0: (65091) {G1,W11,D4,L1,V2,M1}  { addition( X, multiplication( X, Y
% 45.54/45.98     ) ) ==> multiplication( X, addition( one, Y ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Y
% 45.54/45.98  end
% 45.54/45.98  permutation0:
% 45.54/45.98     0 ==> 0
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  eqswap: (65094) {G0,W8,D3,L2,V2,M2}  { ! Y ==> addition( X, Y ), leq( X, Y
% 45.54/45.98     ) }.
% 45.54/45.98  parent0[0]: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, 
% 45.54/45.98    Y ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Y
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  paramod: (65095) {G1,W16,D4,L2,V3,M2}  { ! multiplication( X, Y ) ==> 
% 45.54/45.98    multiplication( addition( Z, X ), Y ), leq( multiplication( Z, Y ), 
% 45.54/45.98    multiplication( X, Y ) ) }.
% 45.54/45.98  parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ), 
% 45.54/45.98    multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 45.54/45.98  parent1[0; 5]: (65094) {G0,W8,D3,L2,V2,M2}  { ! Y ==> addition( X, Y ), leq
% 45.54/45.98    ( X, Y ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := Z
% 45.54/45.98     Y := X
% 45.54/45.98     Z := Y
% 45.54/45.98  end
% 45.54/45.98  substitution1:
% 45.54/45.98     X := multiplication( Z, Y )
% 45.54/45.98     Y := multiplication( X, Y )
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  eqswap: (65096) {G1,W16,D4,L2,V3,M2}  { ! multiplication( addition( Z, X )
% 45.54/45.98    , Y ) ==> multiplication( X, Y ), leq( multiplication( Z, Y ), 
% 45.54/45.98    multiplication( X, Y ) ) }.
% 45.54/45.98  parent0[0]: (65095) {G1,W16,D4,L2,V3,M2}  { ! multiplication( X, Y ) ==> 
% 45.54/45.98    multiplication( addition( Z, X ), Y ), leq( multiplication( Z, Y ), 
% 45.54/45.98    multiplication( X, Y ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Y
% 45.54/45.98     Z := Z
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  subsumption: (99) {G1,W16,D4,L2,V3,M2} P(8,18) { ! multiplication( addition
% 45.54/45.98    ( X, Z ), Y ) ==> multiplication( Z, Y ), leq( multiplication( X, Y ), 
% 45.54/45.98    multiplication( Z, Y ) ) }.
% 45.54/45.98  parent0: (65096) {G1,W16,D4,L2,V3,M2}  { ! multiplication( addition( Z, X )
% 45.54/45.98    , Y ) ==> multiplication( X, Y ), leq( multiplication( Z, Y ), 
% 45.54/45.98    multiplication( X, Y ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := Z
% 45.54/45.98     Y := Y
% 45.54/45.98     Z := X
% 45.54/45.98  end
% 45.54/45.98  permutation0:
% 45.54/45.98     0 ==> 0
% 45.54/45.98     1 ==> 1
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  eqswap: (65097) {G0,W13,D4,L1,V3,M1}  { multiplication( addition( X, Z ), Y
% 45.54/45.98     ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) ) }.
% 45.54/45.98  parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ), 
% 45.54/45.98    multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Z
% 45.54/45.98     Z := Y
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  paramod: (65099) {G1,W13,D4,L1,V3,M1}  { multiplication( addition( Y, X ), 
% 45.54/45.98    Z ) ==> addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 45.54/45.98  parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 45.54/45.98     }.
% 45.54/45.98  parent1[0; 2]: (65097) {G0,W13,D4,L1,V3,M1}  { multiplication( addition( X
% 45.54/45.98    , Z ), Y ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) )
% 45.54/45.98     }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Y
% 45.54/45.98  end
% 45.54/45.98  substitution1:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Z
% 45.54/45.98     Z := Y
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  paramod: (65101) {G1,W11,D4,L1,V3,M1}  { multiplication( addition( X, Y ), 
% 45.54/45.98    Z ) ==> multiplication( addition( Y, X ), Z ) }.
% 45.54/45.98  parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ), 
% 45.54/45.98    multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 45.54/45.98  parent1[0; 6]: (65099) {G1,W13,D4,L1,V3,M1}  { multiplication( addition( Y
% 45.54/45.98    , X ), Z ) ==> addition( multiplication( X, Z ), multiplication( Y, Z ) )
% 45.54/45.98     }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := Y
% 45.54/45.98     Y := X
% 45.54/45.98     Z := Z
% 45.54/45.98  end
% 45.54/45.98  substitution1:
% 45.54/45.98     X := Y
% 45.54/45.98     Y := X
% 45.54/45.98     Z := Z
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  subsumption: (100) {G1,W11,D4,L1,V3,M1} P(8,0);d(8) { multiplication( 
% 45.54/45.98    addition( X, Z ), Y ) = multiplication( addition( Z, X ), Y ) }.
% 45.54/45.98  parent0: (65101) {G1,W11,D4,L1,V3,M1}  { multiplication( addition( X, Y ), 
% 45.54/45.98    Z ) ==> multiplication( addition( Y, X ), Z ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Z
% 45.54/45.98     Z := Y
% 45.54/45.98  end
% 45.54/45.98  permutation0:
% 45.54/45.98     0 ==> 0
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  paramod: (65104) {G1,W12,D4,L2,V1,M2}  { ! leq( strong_iteration( X ), 
% 45.54/45.98    strong_iteration( X ) ), leq( multiplication( star( X ), one ), 
% 45.54/45.98    strong_iteration( X ) ) }.
% 45.54/45.98  parent0[0]: (14) {G0,W9,D5,L1,V1,M1} I { addition( multiplication( X, 
% 45.54/45.98    strong_iteration( X ) ), one ) ==> strong_iteration( X ) }.
% 45.54/45.98  parent1[0; 2]: (12) {G0,W13,D4,L2,V3,M2} I { ! leq( addition( 
% 45.54/45.98    multiplication( X, Z ), Y ), Z ), leq( multiplication( star( X ), Y ), Z
% 45.54/45.98     ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98  end
% 45.54/45.98  substitution1:
% 45.54/45.98     X := X
% 45.54/45.98     Y := one
% 45.54/45.98     Z := strong_iteration( X )
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  paramod: (65105) {G1,W10,D3,L2,V1,M2}  { leq( star( X ), strong_iteration( 
% 45.54/45.98    X ) ), ! leq( strong_iteration( X ), strong_iteration( X ) ) }.
% 45.54/45.98  parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 45.54/45.98  parent1[1; 1]: (65104) {G1,W12,D4,L2,V1,M2}  { ! leq( strong_iteration( X )
% 45.54/45.98    , strong_iteration( X ) ), leq( multiplication( star( X ), one ), 
% 45.54/45.98    strong_iteration( X ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := star( X )
% 45.54/45.98  end
% 45.54/45.98  substitution1:
% 45.54/45.98     X := X
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  resolution: (65106) {G2,W5,D3,L1,V1,M1}  { leq( star( X ), strong_iteration
% 45.54/45.98    ( X ) ) }.
% 45.54/45.98  parent0[1]: (65105) {G1,W10,D3,L2,V1,M2}  { leq( star( X ), 
% 45.54/45.98    strong_iteration( X ) ), ! leq( strong_iteration( X ), strong_iteration( 
% 45.54/45.98    X ) ) }.
% 45.54/45.98  parent1[0]: (22) {G1,W3,D2,L1,V1,M1} R(18,3) { leq( X, X ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98  end
% 45.54/45.98  substitution1:
% 45.54/45.98     X := strong_iteration( X )
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  subsumption: (213) {G2,W5,D3,L1,V1,M1} P(14,12);d(5);r(22) { leq( star( X )
% 45.54/45.98    , strong_iteration( X ) ) }.
% 45.54/45.98  parent0: (65106) {G2,W5,D3,L1,V1,M1}  { leq( star( X ), strong_iteration( X
% 45.54/45.98     ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98  end
% 45.54/45.98  permutation0:
% 45.54/45.98     0 ==> 0
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  eqswap: (65107) {G0,W8,D3,L2,V2,M2}  { Y ==> addition( X, Y ), ! leq( X, Y
% 45.54/45.98     ) }.
% 45.54/45.98  parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) 
% 45.54/45.98    ==> Y }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Y
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  resolution: (65108) {G1,W8,D4,L1,V1,M1}  { strong_iteration( X ) ==> 
% 45.54/45.98    addition( star( X ), strong_iteration( X ) ) }.
% 45.54/45.98  parent0[1]: (65107) {G0,W8,D3,L2,V2,M2}  { Y ==> addition( X, Y ), ! leq( X
% 45.54/45.98    , Y ) }.
% 45.54/45.98  parent1[0]: (213) {G2,W5,D3,L1,V1,M1} P(14,12);d(5);r(22) { leq( star( X )
% 45.54/45.98    , strong_iteration( X ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := star( X )
% 45.54/45.98     Y := strong_iteration( X )
% 45.54/45.98  end
% 45.54/45.98  substitution1:
% 45.54/45.98     X := X
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  eqswap: (65109) {G1,W8,D4,L1,V1,M1}  { addition( star( X ), 
% 45.54/45.98    strong_iteration( X ) ) ==> strong_iteration( X ) }.
% 45.54/45.98  parent0[0]: (65108) {G1,W8,D4,L1,V1,M1}  { strong_iteration( X ) ==> 
% 45.54/45.98    addition( star( X ), strong_iteration( X ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  subsumption: (226) {G3,W8,D4,L1,V1,M1} R(213,17) { addition( star( X ), 
% 45.54/45.98    strong_iteration( X ) ) ==> strong_iteration( X ) }.
% 45.54/45.98  parent0: (65109) {G1,W8,D4,L1,V1,M1}  { addition( star( X ), 
% 45.54/45.98    strong_iteration( X ) ) ==> strong_iteration( X ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98  end
% 45.54/45.98  permutation0:
% 45.54/45.98     0 ==> 0
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  eqswap: (65110) {G0,W10,D5,L1,V1,M1}  { strong_iteration( X ) ==> addition
% 45.54/45.98    ( star( X ), multiplication( strong_iteration( X ), zero ) ) }.
% 45.54/45.98  parent0[0]: (16) {G0,W10,D5,L1,V1,M1} I { addition( star( X ), 
% 45.54/45.98    multiplication( strong_iteration( X ), zero ) ) ==> strong_iteration( X )
% 45.54/45.98     }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  paramod: (65111) {G1,W10,D5,L1,V1,M1}  { strong_iteration( X ) ==> addition
% 45.54/45.98    ( multiplication( strong_iteration( X ), zero ), star( X ) ) }.
% 45.54/45.98  parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 45.54/45.98     }.
% 45.54/45.98  parent1[0; 3]: (65110) {G0,W10,D5,L1,V1,M1}  { strong_iteration( X ) ==> 
% 45.54/45.98    addition( star( X ), multiplication( strong_iteration( X ), zero ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := star( X )
% 45.54/45.98     Y := multiplication( strong_iteration( X ), zero )
% 45.54/45.98  end
% 45.54/45.98  substitution1:
% 45.54/45.98     X := X
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  eqswap: (65114) {G1,W10,D5,L1,V1,M1}  { addition( multiplication( 
% 45.54/45.98    strong_iteration( X ), zero ), star( X ) ) ==> strong_iteration( X ) }.
% 45.54/45.98  parent0[0]: (65111) {G1,W10,D5,L1,V1,M1}  { strong_iteration( X ) ==> 
% 45.54/45.98    addition( multiplication( strong_iteration( X ), zero ), star( X ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  subsumption: (285) {G1,W10,D5,L1,V1,M1} P(16,0) { addition( multiplication
% 45.54/45.98    ( strong_iteration( X ), zero ), star( X ) ) ==> strong_iteration( X )
% 45.54/45.98     }.
% 45.54/45.98  parent0: (65114) {G1,W10,D5,L1,V1,M1}  { addition( multiplication( 
% 45.54/45.98    strong_iteration( X ), zero ), star( X ) ) ==> strong_iteration( X ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98  end
% 45.54/45.98  permutation0:
% 45.54/45.98     0 ==> 0
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  eqswap: (65115) {G0,W9,D5,L1,V0,M1}  { ! strong_iteration( skol1 ) ==> 
% 45.54/45.98    addition( multiplication( strong_iteration( skol1 ), skol1 ), one ) }.
% 45.54/45.98  parent0[0]: (19) {G0,W9,D5,L1,V0,M1} I { ! addition( multiplication( 
% 45.54/45.98    strong_iteration( skol1 ), skol1 ), one ) ==> strong_iteration( skol1 )
% 45.54/45.98     }.
% 45.54/45.98  substitution0:
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  paramod: (65116) {G1,W9,D5,L1,V0,M1}  { ! strong_iteration( skol1 ) ==> 
% 45.54/45.98    addition( one, multiplication( strong_iteration( skol1 ), skol1 ) ) }.
% 45.54/45.98  parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 45.54/45.98     }.
% 45.54/45.98  parent1[0; 4]: (65115) {G0,W9,D5,L1,V0,M1}  { ! strong_iteration( skol1 ) 
% 45.54/45.98    ==> addition( multiplication( strong_iteration( skol1 ), skol1 ), one )
% 45.54/45.98     }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := multiplication( strong_iteration( skol1 ), skol1 )
% 45.54/45.98     Y := one
% 45.54/45.98  end
% 45.54/45.98  substitution1:
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  eqswap: (65119) {G1,W9,D5,L1,V0,M1}  { ! addition( one, multiplication( 
% 45.54/45.98    strong_iteration( skol1 ), skol1 ) ) ==> strong_iteration( skol1 ) }.
% 45.54/45.98  parent0[0]: (65116) {G1,W9,D5,L1,V0,M1}  { ! strong_iteration( skol1 ) ==> 
% 45.54/45.98    addition( one, multiplication( strong_iteration( skol1 ), skol1 ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  subsumption: (312) {G1,W9,D5,L1,V0,M1} P(0,19) { ! addition( one, 
% 45.54/45.98    multiplication( strong_iteration( skol1 ), skol1 ) ) ==> strong_iteration
% 45.54/45.98    ( skol1 ) }.
% 45.54/45.98  parent0: (65119) {G1,W9,D5,L1,V0,M1}  { ! addition( one, multiplication( 
% 45.54/45.98    strong_iteration( skol1 ), skol1 ) ) ==> strong_iteration( skol1 ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98  end
% 45.54/45.98  permutation0:
% 45.54/45.98     0 ==> 0
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  eqswap: (65121) {G1,W14,D4,L2,V3,M2}  { ! addition( Y, Z ) ==> addition( 
% 45.54/45.98    addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 45.54/45.98  parent0[0]: (25) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y
% 45.54/45.98     ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Y
% 45.54/45.98     Z := Z
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  paramod: (65124) {G1,W15,D3,L3,V3,M3}  { ! addition( X, Y ) ==> addition( X
% 45.54/45.98    , Y ), ! leq( Z, X ), leq( Z, addition( X, Y ) ) }.
% 45.54/45.98  parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) 
% 45.54/45.98    ==> Y }.
% 45.54/45.98  parent1[0; 6]: (65121) {G1,W14,D4,L2,V3,M2}  { ! addition( Y, Z ) ==> 
% 45.54/45.98    addition( addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := Z
% 45.54/45.98     Y := X
% 45.54/45.98  end
% 45.54/45.98  substitution1:
% 45.54/45.98     X := Z
% 45.54/45.98     Y := X
% 45.54/45.98     Z := Y
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  eqrefl: (65173) {G0,W8,D3,L2,V3,M2}  { ! leq( Z, X ), leq( Z, addition( X, 
% 45.54/45.98    Y ) ) }.
% 45.54/45.98  parent0[0]: (65124) {G1,W15,D3,L3,V3,M3}  { ! addition( X, Y ) ==> addition
% 45.54/45.98    ( X, Y ), ! leq( Z, X ), leq( Z, addition( X, Y ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Y
% 45.54/45.98     Z := Z
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  subsumption: (328) {G2,W8,D3,L2,V3,M2} P(17,25);q { leq( X, addition( Y, Z
% 45.54/45.98     ) ), ! leq( X, Y ) }.
% 45.54/45.98  parent0: (65173) {G0,W8,D3,L2,V3,M2}  { ! leq( Z, X ), leq( Z, addition( X
% 45.54/45.98    , Y ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := Y
% 45.54/45.98     Y := Z
% 45.54/45.98     Z := X
% 45.54/45.98  end
% 45.54/45.98  permutation0:
% 45.54/45.98     0 ==> 1
% 45.54/45.98     1 ==> 0
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  eqswap: (65175) {G1,W14,D4,L2,V3,M2}  { ! addition( Y, Z ) ==> addition( 
% 45.54/45.98    addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 45.54/45.98  parent0[0]: (25) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y
% 45.54/45.98     ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Y
% 45.54/45.98     Z := Z
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  paramod: (65178) {G1,W12,D3,L2,V2,M2}  { ! addition( X, Y ) ==> addition( X
% 45.54/45.98    , Y ), leq( X, addition( X, Y ) ) }.
% 45.54/45.98  parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 45.54/45.98  parent1[0; 6]: (65175) {G1,W14,D4,L2,V3,M2}  { ! addition( Y, Z ) ==> 
% 45.54/45.98    addition( addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98  end
% 45.54/45.98  substitution1:
% 45.54/45.98     X := X
% 45.54/45.98     Y := X
% 45.54/45.98     Z := Y
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  eqrefl: (65181) {G0,W5,D3,L1,V2,M1}  { leq( X, addition( X, Y ) ) }.
% 45.54/45.98  parent0[0]: (65178) {G1,W12,D3,L2,V2,M2}  { ! addition( X, Y ) ==> addition
% 45.54/45.98    ( X, Y ), leq( X, addition( X, Y ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Y
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  subsumption: (332) {G2,W5,D3,L1,V2,M1} P(3,25);q { leq( X, addition( X, Y )
% 45.54/45.98     ) }.
% 45.54/45.98  parent0: (65181) {G0,W5,D3,L1,V2,M1}  { leq( X, addition( X, Y ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Y
% 45.54/45.98  end
% 45.54/45.98  permutation0:
% 45.54/45.98     0 ==> 0
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  paramod: (65182) {G1,W5,D3,L1,V2,M1}  { leq( X, addition( Y, X ) ) }.
% 45.54/45.98  parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 45.54/45.98     }.
% 45.54/45.98  parent1[0; 2]: (332) {G2,W5,D3,L1,V2,M1} P(3,25);q { leq( X, addition( X, Y
% 45.54/45.98     ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Y
% 45.54/45.98  end
% 45.54/45.98  substitution1:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Y
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  subsumption: (371) {G3,W5,D3,L1,V2,M1} P(0,332) { leq( X, addition( Y, X )
% 45.54/45.98     ) }.
% 45.54/45.98  parent0: (65182) {G1,W5,D3,L1,V2,M1}  { leq( X, addition( Y, X ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Y
% 45.54/45.98  end
% 45.54/45.98  permutation0:
% 45.54/45.98     0 ==> 0
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  paramod: (65185) {G1,W7,D4,L1,V1,M1}  { leq( multiplication( star( X ), X )
% 45.54/45.98    , star( X ) ) }.
% 45.54/45.98  parent0[0]: (11) {G0,W9,D5,L1,V1,M1} I { addition( one, multiplication( 
% 45.54/45.98    star( X ), X ) ) ==> star( X ) }.
% 45.54/45.98  parent1[0; 5]: (371) {G3,W5,D3,L1,V2,M1} P(0,332) { leq( X, addition( Y, X
% 45.54/45.98     ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98  end
% 45.54/45.98  substitution1:
% 45.54/45.98     X := multiplication( star( X ), X )
% 45.54/45.98     Y := one
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  subsumption: (377) {G4,W7,D4,L1,V1,M1} P(11,371) { leq( multiplication( 
% 45.54/45.98    star( X ), X ), star( X ) ) }.
% 45.54/45.98  parent0: (65185) {G1,W7,D4,L1,V1,M1}  { leq( multiplication( star( X ), X )
% 45.54/45.98    , star( X ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98  end
% 45.54/45.98  permutation0:
% 45.54/45.98     0 ==> 0
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  paramod: (65188) {G1,W14,D5,L1,V2,M1}  { addition( addition( star( X ), Y )
% 45.54/45.98    , multiplication( strong_iteration( X ), zero ) ) = addition( 
% 45.54/45.98    strong_iteration( X ), Y ) }.
% 45.54/45.98  parent0[0]: (16) {G0,W10,D5,L1,V1,M1} I { addition( star( X ), 
% 45.54/45.98    multiplication( strong_iteration( X ), zero ) ) ==> strong_iteration( X )
% 45.54/45.98     }.
% 45.54/45.98  parent1[0; 11]: (27) {G1,W11,D4,L1,V3,M1} P(0,1);d(1) { addition( addition
% 45.54/45.98    ( Z, Y ), X ) = addition( addition( Z, X ), Y ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98  end
% 45.54/45.98  substitution1:
% 45.54/45.98     X := multiplication( strong_iteration( X ), zero )
% 45.54/45.98     Y := Y
% 45.54/45.98     Z := star( X )
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  subsumption: (389) {G2,W14,D5,L1,V2,M1} P(16,27) { addition( addition( star
% 45.54/45.98    ( X ), Y ), multiplication( strong_iteration( X ), zero ) ) ==> addition
% 45.54/45.98    ( strong_iteration( X ), Y ) }.
% 45.54/45.98  parent0: (65188) {G1,W14,D5,L1,V2,M1}  { addition( addition( star( X ), Y )
% 45.54/45.98    , multiplication( strong_iteration( X ), zero ) ) = addition( 
% 45.54/45.98    strong_iteration( X ), Y ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Y
% 45.54/45.98  end
% 45.54/45.98  permutation0:
% 45.54/45.98     0 ==> 0
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  eqswap: (65190) {G1,W12,D4,L2,V3,M2}  { addition( X, Z ) ==> addition( 
% 45.54/45.98    addition( X, Y ), Z ), ! leq( Y, Z ) }.
% 45.54/45.98  parent0[0]: (35) {G1,W12,D4,L2,V3,M2} P(17,1) { addition( addition( Z, X )
% 45.54/45.98    , Y ) ==> addition( Z, Y ), ! leq( X, Y ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := Y
% 45.54/45.98     Y := Z
% 45.54/45.98     Z := X
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  paramod: (65192) {G1,W15,D4,L2,V2,M2}  { addition( star( X ), Y ) ==> 
% 45.54/45.98    addition( strong_iteration( X ), Y ), ! leq( multiplication( 
% 45.54/45.98    strong_iteration( X ), zero ), Y ) }.
% 45.54/45.98  parent0[0]: (16) {G0,W10,D5,L1,V1,M1} I { addition( star( X ), 
% 45.54/45.98    multiplication( strong_iteration( X ), zero ) ) ==> strong_iteration( X )
% 45.54/45.98     }.
% 45.54/45.98  parent1[0; 6]: (65190) {G1,W12,D4,L2,V3,M2}  { addition( X, Z ) ==> 
% 45.54/45.98    addition( addition( X, Y ), Z ), ! leq( Y, Z ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98  end
% 45.54/45.98  substitution1:
% 45.54/45.98     X := star( X )
% 45.54/45.98     Y := multiplication( strong_iteration( X ), zero )
% 45.54/45.98     Z := Y
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  eqswap: (65194) {G1,W15,D4,L2,V2,M2}  { addition( strong_iteration( X ), Y
% 45.54/45.98     ) ==> addition( star( X ), Y ), ! leq( multiplication( strong_iteration
% 45.54/45.98    ( X ), zero ), Y ) }.
% 45.54/45.98  parent0[0]: (65192) {G1,W15,D4,L2,V2,M2}  { addition( star( X ), Y ) ==> 
% 45.54/45.98    addition( strong_iteration( X ), Y ), ! leq( multiplication( 
% 45.54/45.98    strong_iteration( X ), zero ), Y ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Y
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  subsumption: (571) {G2,W15,D4,L2,V2,M2} P(16,35) { addition( 
% 45.54/45.98    strong_iteration( X ), Y ) ==> addition( star( X ), Y ), ! leq( 
% 45.54/45.98    multiplication( strong_iteration( X ), zero ), Y ) }.
% 45.54/45.98  parent0: (65194) {G1,W15,D4,L2,V2,M2}  { addition( strong_iteration( X ), Y
% 45.54/45.98     ) ==> addition( star( X ), Y ), ! leq( multiplication( strong_iteration
% 45.54/45.98    ( X ), zero ), Y ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Y
% 45.54/45.98  end
% 45.54/45.98  permutation0:
% 45.54/45.98     0 ==> 0
% 45.54/45.98     1 ==> 1
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  eqswap: (65196) {G1,W12,D4,L2,V3,M2}  { addition( X, Z ) ==> addition( 
% 45.54/45.98    addition( X, Y ), Z ), ! leq( Y, Z ) }.
% 45.54/45.98  parent0[0]: (35) {G1,W12,D4,L2,V3,M2} P(17,1) { addition( addition( Z, X )
% 45.54/45.98    , Y ) ==> addition( Z, Y ), ! leq( X, Y ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := Y
% 45.54/45.98     Y := Z
% 45.54/45.98     Z := X
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  paramod: (65198) {G1,W14,D4,L2,V2,M2}  { addition( one, X ) ==> addition( 
% 45.54/45.98    star( Y ), X ), ! leq( multiplication( star( Y ), Y ), X ) }.
% 45.54/45.98  parent0[0]: (11) {G0,W9,D5,L1,V1,M1} I { addition( one, multiplication( 
% 45.54/45.98    star( X ), X ) ) ==> star( X ) }.
% 45.54/45.98  parent1[0; 5]: (65196) {G1,W12,D4,L2,V3,M2}  { addition( X, Z ) ==> 
% 45.54/45.98    addition( addition( X, Y ), Z ), ! leq( Y, Z ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := Y
% 45.54/45.98  end
% 45.54/45.98  substitution1:
% 45.54/45.98     X := one
% 45.54/45.98     Y := multiplication( star( Y ), Y )
% 45.54/45.98     Z := X
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  eqswap: (65200) {G1,W14,D4,L2,V2,M2}  { addition( star( Y ), X ) ==> 
% 45.54/45.98    addition( one, X ), ! leq( multiplication( star( Y ), Y ), X ) }.
% 45.54/45.98  parent0[0]: (65198) {G1,W14,D4,L2,V2,M2}  { addition( one, X ) ==> addition
% 45.54/45.98    ( star( Y ), X ), ! leq( multiplication( star( Y ), Y ), X ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Y
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  subsumption: (574) {G2,W14,D4,L2,V2,M2} P(11,35) { addition( star( X ), Y )
% 45.54/45.98     ==> addition( one, Y ), ! leq( multiplication( star( X ), X ), Y ) }.
% 45.54/45.98  parent0: (65200) {G1,W14,D4,L2,V2,M2}  { addition( star( Y ), X ) ==> 
% 45.54/45.98    addition( one, X ), ! leq( multiplication( star( Y ), Y ), X ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := Y
% 45.54/45.98     Y := X
% 45.54/45.98  end
% 45.54/45.98  permutation0:
% 45.54/45.98     0 ==> 0
% 45.54/45.98     1 ==> 1
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  eqswap: (65202) {G0,W13,D4,L1,V3,M1}  { multiplication( addition( X, Z ), Y
% 45.54/45.98     ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) ) }.
% 45.54/45.98  parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ), 
% 45.54/45.98    multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Z
% 45.54/45.98     Z := Y
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  paramod: (65204) {G1,W15,D5,L1,V3,M1}  { multiplication( addition( X, 
% 45.54/45.98    multiplication( Y, zero ) ), Z ) ==> addition( multiplication( X, Z ), 
% 45.54/45.98    multiplication( Y, zero ) ) }.
% 45.54/45.98  parent0[0]: (50) {G1,W9,D4,L1,V2,M1} P(9,4) { multiplication( 
% 45.54/45.98    multiplication( Y, zero ), X ) ==> multiplication( Y, zero ) }.
% 45.54/45.98  parent1[0; 12]: (65202) {G0,W13,D4,L1,V3,M1}  { multiplication( addition( X
% 45.54/45.98    , Z ), Y ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) )
% 45.54/45.98     }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := Z
% 45.54/45.98     Y := Y
% 45.54/45.98  end
% 45.54/45.98  substitution1:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Z
% 45.54/45.98     Z := multiplication( Y, zero )
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  subsumption: (812) {G2,W15,D5,L1,V3,M1} P(50,8) { multiplication( addition
% 45.54/45.98    ( Z, multiplication( X, zero ) ), Y ) ==> addition( multiplication( Z, Y
% 45.54/45.98     ), multiplication( X, zero ) ) }.
% 45.54/45.98  parent0: (65204) {G1,W15,D5,L1,V3,M1}  { multiplication( addition( X, 
% 45.54/45.98    multiplication( Y, zero ) ), Z ) ==> addition( multiplication( X, Z ), 
% 45.54/45.98    multiplication( Y, zero ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := Z
% 45.54/45.98     Y := X
% 45.54/45.98     Z := Y
% 45.54/45.98  end
% 45.54/45.98  permutation0:
% 45.54/45.98     0 ==> 0
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  paramod: (65208) {G1,W8,D3,L2,V2,M2}  { leq( X, strong_iteration( Y ) ), ! 
% 45.54/45.98    leq( X, star( Y ) ) }.
% 45.54/45.98  parent0[0]: (16) {G0,W10,D5,L1,V1,M1} I { addition( star( X ), 
% 45.54/45.98    multiplication( strong_iteration( X ), zero ) ) ==> strong_iteration( X )
% 45.54/45.98     }.
% 45.54/45.98  parent1[0; 2]: (328) {G2,W8,D3,L2,V3,M2} P(17,25);q { leq( X, addition( Y, 
% 45.54/45.98    Z ) ), ! leq( X, Y ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := Y
% 45.54/45.98  end
% 45.54/45.98  substitution1:
% 45.54/45.98     X := X
% 45.54/45.98     Y := star( Y )
% 45.54/45.98     Z := multiplication( strong_iteration( Y ), zero )
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  subsumption: (1101) {G3,W8,D3,L2,V2,M2} P(16,328) { leq( Y, 
% 45.54/45.98    strong_iteration( X ) ), ! leq( Y, star( X ) ) }.
% 45.54/45.98  parent0: (65208) {G1,W8,D3,L2,V2,M2}  { leq( X, strong_iteration( Y ) ), ! 
% 45.54/45.98    leq( X, star( Y ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := Y
% 45.54/45.98     Y := X
% 45.54/45.98  end
% 45.54/45.98  permutation0:
% 45.54/45.98     0 ==> 0
% 45.54/45.98     1 ==> 1
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  resolution: (65209) {G4,W7,D4,L1,V1,M1}  { leq( multiplication( star( X ), 
% 45.54/45.98    X ), strong_iteration( X ) ) }.
% 45.54/45.98  parent0[1]: (1101) {G3,W8,D3,L2,V2,M2} P(16,328) { leq( Y, strong_iteration
% 45.54/45.98    ( X ) ), ! leq( Y, star( X ) ) }.
% 45.54/45.98  parent1[0]: (377) {G4,W7,D4,L1,V1,M1} P(11,371) { leq( multiplication( star
% 45.54/45.98    ( X ), X ), star( X ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := multiplication( star( X ), X )
% 45.54/45.98  end
% 45.54/45.98  substitution1:
% 45.54/45.98     X := X
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  subsumption: (1111) {G5,W7,D4,L1,V1,M1} R(1101,377) { leq( multiplication( 
% 45.54/45.98    star( X ), X ), strong_iteration( X ) ) }.
% 45.54/45.98  parent0: (65209) {G4,W7,D4,L1,V1,M1}  { leq( multiplication( star( X ), X )
% 45.54/45.98    , strong_iteration( X ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98  end
% 45.54/45.98  permutation0:
% 45.54/45.98     0 ==> 0
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  eqswap: (65210) {G1,W8,D3,L2,V2,M2}  { X ==> addition( X, Y ), ! leq( Y, X
% 45.54/45.98     ) }.
% 45.54/45.98  parent0[0]: (36) {G1,W8,D3,L2,V2,M2} P(17,0) { addition( Y, X ) ==> Y, ! 
% 45.54/45.98    leq( X, Y ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := Y
% 45.54/45.98     Y := X
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  resolution: (65211) {G2,W10,D5,L1,V1,M1}  { strong_iteration( X ) ==> 
% 45.54/45.98    addition( strong_iteration( X ), multiplication( star( X ), X ) ) }.
% 45.54/45.98  parent0[1]: (65210) {G1,W8,D3,L2,V2,M2}  { X ==> addition( X, Y ), ! leq( Y
% 45.54/45.98    , X ) }.
% 45.54/45.98  parent1[0]: (1111) {G5,W7,D4,L1,V1,M1} R(1101,377) { leq( multiplication( 
% 45.54/45.98    star( X ), X ), strong_iteration( X ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := strong_iteration( X )
% 45.54/45.98     Y := multiplication( star( X ), X )
% 45.54/45.98  end
% 45.54/45.98  substitution1:
% 45.54/45.98     X := X
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  eqswap: (65212) {G2,W10,D5,L1,V1,M1}  { addition( strong_iteration( X ), 
% 45.54/45.98    multiplication( star( X ), X ) ) ==> strong_iteration( X ) }.
% 45.54/45.98  parent0[0]: (65211) {G2,W10,D5,L1,V1,M1}  { strong_iteration( X ) ==> 
% 45.54/45.98    addition( strong_iteration( X ), multiplication( star( X ), X ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  subsumption: (1128) {G6,W10,D5,L1,V1,M1} R(1111,36) { addition( 
% 45.54/45.98    strong_iteration( X ), multiplication( star( X ), X ) ) ==> 
% 45.54/45.98    strong_iteration( X ) }.
% 45.54/45.98  parent0: (65212) {G2,W10,D5,L1,V1,M1}  { addition( strong_iteration( X ), 
% 45.54/45.98    multiplication( star( X ), X ) ) ==> strong_iteration( X ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98  end
% 45.54/45.98  permutation0:
% 45.54/45.98     0 ==> 0
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  eqswap: (65214) {G1,W16,D4,L2,V3,M2}  { ! multiplication( X, Z ) ==> 
% 45.54/45.98    multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ), 
% 45.54/45.98    multiplication( X, Z ) ) }.
% 45.54/45.98  parent0[0]: (67) {G1,W16,D4,L2,V3,M2} P(7,18) { ! multiplication( X, 
% 45.54/45.98    addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 45.54/45.98     ), multiplication( X, Z ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Y
% 45.54/45.98     Z := Z
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  paramod: (65215) {G2,W14,D3,L2,V2,M2}  { ! multiplication( X, Y ) ==> 
% 45.54/45.98    multiplication( X, Y ), leq( multiplication( X, zero ), multiplication( X
% 45.54/45.98    , Y ) ) }.
% 45.54/45.98  parent0[0]: (20) {G1,W5,D3,L1,V1,M1} P(0,2) { addition( zero, X ) ==> X }.
% 45.54/45.98  parent1[0; 7]: (65214) {G1,W16,D4,L2,V3,M2}  { ! multiplication( X, Z ) ==>
% 45.54/45.98     multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ), 
% 45.54/45.98    multiplication( X, Z ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := Y
% 45.54/45.98  end
% 45.54/45.98  substitution1:
% 45.54/45.98     X := X
% 45.54/45.98     Y := zero
% 45.54/45.98     Z := Y
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  eqrefl: (65216) {G0,W7,D3,L1,V2,M1}  { leq( multiplication( X, zero ), 
% 45.54/45.98    multiplication( X, Y ) ) }.
% 45.54/45.98  parent0[0]: (65215) {G2,W14,D3,L2,V2,M2}  { ! multiplication( X, Y ) ==> 
% 45.54/45.98    multiplication( X, Y ), leq( multiplication( X, zero ), multiplication( X
% 45.54/45.98    , Y ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Y
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  subsumption: (1632) {G2,W7,D3,L1,V2,M1} P(20,67);q { leq( multiplication( Y
% 45.54/45.98    , zero ), multiplication( Y, X ) ) }.
% 45.54/45.98  parent0: (65216) {G0,W7,D3,L1,V2,M1}  { leq( multiplication( X, zero ), 
% 45.54/45.98    multiplication( X, Y ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := Y
% 45.54/45.98     Y := X
% 45.54/45.98  end
% 45.54/45.98  permutation0:
% 45.54/45.98     0 ==> 0
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  eqswap: (65218) {G1,W16,D4,L2,V3,M2}  { ! multiplication( Y, Z ) ==> 
% 45.54/45.98    multiplication( addition( X, Y ), Z ), leq( multiplication( X, Z ), 
% 45.54/45.98    multiplication( Y, Z ) ) }.
% 45.54/45.98  parent0[0]: (99) {G1,W16,D4,L2,V3,M2} P(8,18) { ! multiplication( addition
% 45.54/45.98    ( X, Z ), Y ) ==> multiplication( Z, Y ), leq( multiplication( X, Y ), 
% 45.54/45.98    multiplication( Z, Y ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Z
% 45.54/45.98     Z := Y
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  paramod: (65219) {G2,W18,D4,L2,V2,M2}  { ! multiplication( strong_iteration
% 45.54/45.98    ( X ), Y ) ==> multiplication( strong_iteration( X ), Y ), leq( 
% 45.54/45.98    multiplication( star( X ), Y ), multiplication( strong_iteration( X ), Y
% 45.54/45.98     ) ) }.
% 45.54/45.98  parent0[0]: (226) {G3,W8,D4,L1,V1,M1} R(213,17) { addition( star( X ), 
% 45.54/45.98    strong_iteration( X ) ) ==> strong_iteration( X ) }.
% 45.54/45.98  parent1[0; 7]: (65218) {G1,W16,D4,L2,V3,M2}  { ! multiplication( Y, Z ) ==>
% 45.54/45.98     multiplication( addition( X, Y ), Z ), leq( multiplication( X, Z ), 
% 45.54/45.98    multiplication( Y, Z ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98  end
% 45.54/45.98  substitution1:
% 45.54/45.98     X := star( X )
% 45.54/45.98     Y := strong_iteration( X )
% 45.54/45.98     Z := Y
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  eqrefl: (65220) {G0,W9,D4,L1,V2,M1}  { leq( multiplication( star( X ), Y )
% 45.54/45.98    , multiplication( strong_iteration( X ), Y ) ) }.
% 45.54/45.98  parent0[0]: (65219) {G2,W18,D4,L2,V2,M2}  { ! multiplication( 
% 45.54/45.98    strong_iteration( X ), Y ) ==> multiplication( strong_iteration( X ), Y )
% 45.54/45.98    , leq( multiplication( star( X ), Y ), multiplication( strong_iteration( 
% 45.54/45.98    X ), Y ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Y
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  subsumption: (5228) {G4,W9,D4,L1,V2,M1} P(226,99);q { leq( multiplication( 
% 45.54/45.98    star( X ), Y ), multiplication( strong_iteration( X ), Y ) ) }.
% 45.54/45.98  parent0: (65220) {G0,W9,D4,L1,V2,M1}  { leq( multiplication( star( X ), Y )
% 45.54/45.98    , multiplication( strong_iteration( X ), Y ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Y
% 45.54/45.98  end
% 45.54/45.98  permutation0:
% 45.54/45.98     0 ==> 0
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  paramod: (65224) {G2,W14,D6,L1,V2,M1}  { multiplication( addition( star( X
% 45.54/45.98     ), multiplication( strong_iteration( X ), zero ) ), Y ) = multiplication
% 45.54/45.98    ( strong_iteration( X ), Y ) }.
% 45.54/45.98  parent0[0]: (285) {G1,W10,D5,L1,V1,M1} P(16,0) { addition( multiplication( 
% 45.54/45.98    strong_iteration( X ), zero ), star( X ) ) ==> strong_iteration( X ) }.
% 45.54/45.98  parent1[0; 11]: (100) {G1,W11,D4,L1,V3,M1} P(8,0);d(8) { multiplication( 
% 45.54/45.98    addition( X, Z ), Y ) = multiplication( addition( Z, X ), Y ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98  end
% 45.54/45.98  substitution1:
% 45.54/45.98     X := star( X )
% 45.54/45.98     Y := Y
% 45.54/45.98     Z := multiplication( strong_iteration( X ), zero )
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  paramod: (65225) {G3,W14,D5,L1,V2,M1}  { addition( multiplication( star( X
% 45.54/45.98     ), Y ), multiplication( strong_iteration( X ), zero ) ) = multiplication
% 45.54/45.98    ( strong_iteration( X ), Y ) }.
% 45.54/45.98  parent0[0]: (812) {G2,W15,D5,L1,V3,M1} P(50,8) { multiplication( addition( 
% 45.54/45.98    Z, multiplication( X, zero ) ), Y ) ==> addition( multiplication( Z, Y )
% 45.54/45.98    , multiplication( X, zero ) ) }.
% 45.54/45.98  parent1[0; 1]: (65224) {G2,W14,D6,L1,V2,M1}  { multiplication( addition( 
% 45.54/45.98    star( X ), multiplication( strong_iteration( X ), zero ) ), Y ) = 
% 45.54/45.98    multiplication( strong_iteration( X ), Y ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := strong_iteration( X )
% 45.54/45.98     Y := Y
% 45.54/45.98     Z := star( X )
% 45.54/45.98  end
% 45.54/45.98  substitution1:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Y
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  subsumption: (12374) {G3,W14,D5,L1,V2,M1} P(285,100);d(812) { addition( 
% 45.54/45.98    multiplication( star( X ), Y ), multiplication( strong_iteration( X ), 
% 45.54/45.98    zero ) ) ==> multiplication( strong_iteration( X ), Y ) }.
% 45.54/45.98  parent0: (65225) {G3,W14,D5,L1,V2,M1}  { addition( multiplication( star( X
% 45.54/45.98     ), Y ), multiplication( strong_iteration( X ), zero ) ) = multiplication
% 45.54/45.98    ( strong_iteration( X ), Y ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Y
% 45.54/45.98  end
% 45.54/45.98  permutation0:
% 45.54/45.98     0 ==> 0
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  eqswap: (65228) {G2,W14,D5,L1,V2,M1}  { addition( strong_iteration( X ), Y
% 45.54/45.98     ) ==> addition( addition( star( X ), Y ), multiplication( 
% 45.54/45.98    strong_iteration( X ), zero ) ) }.
% 45.54/45.98  parent0[0]: (389) {G2,W14,D5,L1,V2,M1} P(16,27) { addition( addition( star
% 45.54/45.98    ( X ), Y ), multiplication( strong_iteration( X ), zero ) ) ==> addition
% 45.54/45.98    ( strong_iteration( X ), Y ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Y
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  paramod: (65231) {G2,W19,D5,L1,V2,M1}  { addition( strong_iteration( X ), 
% 45.54/45.98    multiplication( star( X ), Y ) ) ==> addition( multiplication( star( X )
% 45.54/45.98    , addition( one, Y ) ), multiplication( strong_iteration( X ), zero ) )
% 45.54/45.98     }.
% 45.54/45.98  parent0[0]: (69) {G1,W11,D4,L1,V2,M1} P(5,7) { addition( X, multiplication
% 45.54/45.98    ( X, Y ) ) = multiplication( X, addition( one, Y ) ) }.
% 45.54/45.98  parent1[0; 9]: (65228) {G2,W14,D5,L1,V2,M1}  { addition( strong_iteration( 
% 45.54/45.98    X ), Y ) ==> addition( addition( star( X ), Y ), multiplication( 
% 45.54/45.98    strong_iteration( X ), zero ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := star( X )
% 45.54/45.98     Y := Y
% 45.54/45.98  end
% 45.54/45.98  substitution1:
% 45.54/45.98     X := X
% 45.54/45.98     Y := multiplication( star( X ), Y )
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  paramod: (65232) {G3,W14,D5,L1,V2,M1}  { addition( strong_iteration( X ), 
% 45.54/45.98    multiplication( star( X ), Y ) ) ==> multiplication( strong_iteration( X
% 45.54/45.98     ), addition( one, Y ) ) }.
% 45.54/45.98  parent0[0]: (12374) {G3,W14,D5,L1,V2,M1} P(285,100);d(812) { addition( 
% 45.54/45.98    multiplication( star( X ), Y ), multiplication( strong_iteration( X ), 
% 45.54/45.98    zero ) ) ==> multiplication( strong_iteration( X ), Y ) }.
% 45.54/45.98  parent1[0; 8]: (65231) {G2,W19,D5,L1,V2,M1}  { addition( strong_iteration( 
% 45.54/45.98    X ), multiplication( star( X ), Y ) ) ==> addition( multiplication( star
% 45.54/45.98    ( X ), addition( one, Y ) ), multiplication( strong_iteration( X ), zero
% 45.54/45.98     ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := addition( one, Y )
% 45.54/45.98  end
% 45.54/45.98  substitution1:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Y
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  subsumption: (18940) {G4,W14,D5,L1,V2,M1} P(69,389);d(12374) { addition( 
% 45.54/45.98    strong_iteration( X ), multiplication( star( X ), Y ) ) ==> 
% 45.54/45.98    multiplication( strong_iteration( X ), addition( one, Y ) ) }.
% 45.54/45.98  parent0: (65232) {G3,W14,D5,L1,V2,M1}  { addition( strong_iteration( X ), 
% 45.54/45.98    multiplication( star( X ), Y ) ) ==> multiplication( strong_iteration( X
% 45.54/45.98     ), addition( one, Y ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Y
% 45.54/45.98  end
% 45.54/45.98  permutation0:
% 45.54/45.98     0 ==> 0
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  paramod: (65236) {G5,W9,D4,L1,V1,M1}  { multiplication( strong_iteration( X
% 45.54/45.98     ), addition( one, X ) ) ==> strong_iteration( X ) }.
% 45.54/45.98  parent0[0]: (18940) {G4,W14,D5,L1,V2,M1} P(69,389);d(12374) { addition( 
% 45.54/45.98    strong_iteration( X ), multiplication( star( X ), Y ) ) ==> 
% 45.54/45.98    multiplication( strong_iteration( X ), addition( one, Y ) ) }.
% 45.54/45.98  parent1[0; 1]: (1128) {G6,W10,D5,L1,V1,M1} R(1111,36) { addition( 
% 45.54/45.98    strong_iteration( X ), multiplication( star( X ), X ) ) ==> 
% 45.54/45.98    strong_iteration( X ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := X
% 45.54/45.98  end
% 45.54/45.98  substitution1:
% 45.54/45.98     X := X
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  subsumption: (20024) {G7,W9,D4,L1,V1,M1} S(1128);d(18940) { multiplication
% 45.54/45.98    ( strong_iteration( X ), addition( one, X ) ) ==> strong_iteration( X )
% 45.54/45.98     }.
% 45.54/45.98  parent0: (65236) {G5,W9,D4,L1,V1,M1}  { multiplication( strong_iteration( X
% 45.54/45.98     ), addition( one, X ) ) ==> strong_iteration( X ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98  end
% 45.54/45.98  permutation0:
% 45.54/45.98     0 ==> 0
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  eqswap: (65238) {G2,W15,D4,L2,V2,M2}  { addition( star( X ), Y ) ==> 
% 45.54/45.98    addition( strong_iteration( X ), Y ), ! leq( multiplication( 
% 45.54/45.98    strong_iteration( X ), zero ), Y ) }.
% 45.54/45.98  parent0[0]: (571) {G2,W15,D4,L2,V2,M2} P(16,35) { addition( 
% 45.54/45.98    strong_iteration( X ), Y ) ==> addition( star( X ), Y ), ! leq( 
% 45.54/45.98    multiplication( strong_iteration( X ), zero ), Y ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Y
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  paramod: (65241) {G2,W23,D5,L2,V2,M2}  { addition( star( X ), 
% 45.54/45.98    multiplication( strong_iteration( X ), Y ) ) ==> multiplication( 
% 45.54/45.98    strong_iteration( X ), addition( one, Y ) ), ! leq( multiplication( 
% 45.54/45.98    strong_iteration( X ), zero ), multiplication( strong_iteration( X ), Y )
% 45.54/45.98     ) }.
% 45.54/45.98  parent0[0]: (69) {G1,W11,D4,L1,V2,M1} P(5,7) { addition( X, multiplication
% 45.54/45.98    ( X, Y ) ) = multiplication( X, addition( one, Y ) ) }.
% 45.54/45.98  parent1[0; 8]: (65238) {G2,W15,D4,L2,V2,M2}  { addition( star( X ), Y ) ==>
% 45.54/45.98     addition( strong_iteration( X ), Y ), ! leq( multiplication( 
% 45.54/45.98    strong_iteration( X ), zero ), Y ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := strong_iteration( X )
% 45.54/45.98     Y := Y
% 45.54/45.98  end
% 45.54/45.98  substitution1:
% 45.54/45.98     X := X
% 45.54/45.98     Y := multiplication( strong_iteration( X ), Y )
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  resolution: (65242) {G3,W14,D5,L1,V2,M1}  { addition( star( X ), 
% 45.54/45.98    multiplication( strong_iteration( X ), Y ) ) ==> multiplication( 
% 45.54/45.98    strong_iteration( X ), addition( one, Y ) ) }.
% 45.54/45.98  parent0[1]: (65241) {G2,W23,D5,L2,V2,M2}  { addition( star( X ), 
% 45.54/45.98    multiplication( strong_iteration( X ), Y ) ) ==> multiplication( 
% 45.54/45.98    strong_iteration( X ), addition( one, Y ) ), ! leq( multiplication( 
% 45.54/45.98    strong_iteration( X ), zero ), multiplication( strong_iteration( X ), Y )
% 45.54/45.98     ) }.
% 45.54/45.98  parent1[0]: (1632) {G2,W7,D3,L1,V2,M1} P(20,67);q { leq( multiplication( Y
% 45.54/45.98    , zero ), multiplication( Y, X ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Y
% 45.54/45.98  end
% 45.54/45.98  substitution1:
% 45.54/45.98     X := Y
% 45.54/45.98     Y := strong_iteration( X )
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  subsumption: (35715) {G3,W14,D5,L1,V2,M1} P(571,69);r(1632) { addition( 
% 45.54/45.98    star( X ), multiplication( strong_iteration( X ), Y ) ) ==> 
% 45.54/45.98    multiplication( strong_iteration( X ), addition( one, Y ) ) }.
% 45.54/45.98  parent0: (65242) {G3,W14,D5,L1,V2,M1}  { addition( star( X ), 
% 45.54/45.98    multiplication( strong_iteration( X ), Y ) ) ==> multiplication( 
% 45.54/45.98    strong_iteration( X ), addition( one, Y ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Y
% 45.54/45.98  end
% 45.54/45.98  permutation0:
% 45.54/45.98     0 ==> 0
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  eqswap: (65244) {G2,W14,D4,L2,V2,M2}  { addition( one, Y ) ==> addition( 
% 45.54/45.98    star( X ), Y ), ! leq( multiplication( star( X ), X ), Y ) }.
% 45.54/45.98  parent0[0]: (574) {G2,W14,D4,L2,V2,M2} P(11,35) { addition( star( X ), Y ) 
% 45.54/45.98    ==> addition( one, Y ), ! leq( multiplication( star( X ), X ), Y ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := Y
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  resolution: (65247) {G3,W14,D5,L1,V1,M1}  { addition( one, multiplication( 
% 45.54/45.98    strong_iteration( X ), X ) ) ==> addition( star( X ), multiplication( 
% 45.54/45.98    strong_iteration( X ), X ) ) }.
% 45.54/45.98  parent0[1]: (65244) {G2,W14,D4,L2,V2,M2}  { addition( one, Y ) ==> addition
% 45.54/45.98    ( star( X ), Y ), ! leq( multiplication( star( X ), X ), Y ) }.
% 45.54/45.98  parent1[0]: (5228) {G4,W9,D4,L1,V2,M1} P(226,99);q { leq( multiplication( 
% 45.54/45.98    star( X ), Y ), multiplication( strong_iteration( X ), Y ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := multiplication( strong_iteration( X ), X )
% 45.54/45.98  end
% 45.54/45.98  substitution1:
% 45.54/45.98     X := X
% 45.54/45.98     Y := X
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  paramod: (65248) {G4,W13,D5,L1,V1,M1}  { addition( one, multiplication( 
% 45.54/45.98    strong_iteration( X ), X ) ) ==> multiplication( strong_iteration( X ), 
% 45.54/45.98    addition( one, X ) ) }.
% 45.54/45.98  parent0[0]: (35715) {G3,W14,D5,L1,V2,M1} P(571,69);r(1632) { addition( star
% 45.54/45.98    ( X ), multiplication( strong_iteration( X ), Y ) ) ==> multiplication( 
% 45.54/45.98    strong_iteration( X ), addition( one, Y ) ) }.
% 45.54/45.98  parent1[0; 7]: (65247) {G3,W14,D5,L1,V1,M1}  { addition( one, 
% 45.54/45.98    multiplication( strong_iteration( X ), X ) ) ==> addition( star( X ), 
% 45.54/45.98    multiplication( strong_iteration( X ), X ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98     Y := X
% 45.54/45.98  end
% 45.54/45.98  substitution1:
% 45.54/45.98     X := X
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  paramod: (65249) {G5,W9,D5,L1,V1,M1}  { addition( one, multiplication( 
% 45.54/45.98    strong_iteration( X ), X ) ) ==> strong_iteration( X ) }.
% 45.54/45.98  parent0[0]: (20024) {G7,W9,D4,L1,V1,M1} S(1128);d(18940) { multiplication( 
% 45.54/45.98    strong_iteration( X ), addition( one, X ) ) ==> strong_iteration( X ) }.
% 45.54/45.98  parent1[0; 7]: (65248) {G4,W13,D5,L1,V1,M1}  { addition( one, 
% 45.54/45.98    multiplication( strong_iteration( X ), X ) ) ==> multiplication( 
% 45.54/45.98    strong_iteration( X ), addition( one, X ) ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98  end
% 45.54/45.98  substitution1:
% 45.54/45.98     X := X
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  subsumption: (64568) {G8,W9,D5,L1,V1,M1} R(5228,574);d(35715);d(20024) { 
% 45.54/45.98    addition( one, multiplication( strong_iteration( X ), X ) ) ==> 
% 45.54/45.98    strong_iteration( X ) }.
% 45.54/45.98  parent0: (65249) {G5,W9,D5,L1,V1,M1}  { addition( one, multiplication( 
% 45.54/45.98    strong_iteration( X ), X ) ) ==> strong_iteration( X ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := X
% 45.54/45.98  end
% 45.54/45.98  permutation0:
% 45.54/45.98     0 ==> 0
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  paramod: (65253) {G2,W5,D3,L1,V0,M1}  { ! strong_iteration( skol1 ) ==> 
% 45.54/45.98    strong_iteration( skol1 ) }.
% 45.54/45.98  parent0[0]: (64568) {G8,W9,D5,L1,V1,M1} R(5228,574);d(35715);d(20024) { 
% 45.54/45.98    addition( one, multiplication( strong_iteration( X ), X ) ) ==> 
% 45.54/45.98    strong_iteration( X ) }.
% 45.54/45.98  parent1[0; 2]: (312) {G1,W9,D5,L1,V0,M1} P(0,19) { ! addition( one, 
% 45.54/45.98    multiplication( strong_iteration( skol1 ), skol1 ) ) ==> strong_iteration
% 45.54/45.98    ( skol1 ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98     X := skol1
% 45.54/45.98  end
% 45.54/45.98  substitution1:
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  eqrefl: (65254) {G0,W0,D0,L0,V0,M0}  {  }.
% 45.54/45.98  parent0[0]: (65253) {G2,W5,D3,L1,V0,M1}  { ! strong_iteration( skol1 ) ==> 
% 45.54/45.98    strong_iteration( skol1 ) }.
% 45.54/45.98  substitution0:
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  subsumption: (64826) {G9,W0,D0,L0,V0,M0} S(312);d(64568);q {  }.
% 45.54/45.98  parent0: (65254) {G0,W0,D0,L0,V0,M0}  {  }.
% 45.54/45.98  substitution0:
% 45.54/45.98  end
% 45.54/45.98  permutation0:
% 45.54/45.98  end
% 45.54/45.98  
% 45.54/45.98  Proof check complete!
% 45.54/45.98  
% 45.54/45.98  Memory use:
% 45.54/45.98  
% 45.54/45.98  space for terms:        909367
% 45.54/45.98  space for clauses:      3095304
% 45.54/45.98  
% 45.54/45.98  
% 45.54/45.98  clauses generated:      1024230
% 45.54/45.98  clauses kept:           64827
% 45.54/45.98  clauses selected:       2302
% 45.54/45.98  clauses deleted:        9896
% 45.54/45.98  clauses inuse deleted:  279
% 45.54/45.98  
% 45.54/45.98  subsentry:          7771195
% 45.54/45.98  literals s-matched: 3737885
% 45.54/45.98  literals matched:   3436831
% 45.54/45.98  full subsumption:   1203651
% 45.54/45.98  
% 45.54/45.98  checksum:           -1591008498
% 45.54/45.98  
% 45.54/45.98  
% 45.54/45.98  Bliksem ended
%------------------------------------------------------------------------------