TSTP Solution File: KLE038+1 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : KLE038+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n014.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 01:36:49 EDT 2022

% Result   : Theorem 0.83s 1.21s
% Output   : Refutation 0.83s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : KLE038+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : bliksem %s
% 0.13/0.34  % Computer : n014.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % DateTime : Thu Jun 16 09:15:05 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.83/1.21  *** allocated 10000 integers for termspace/termends
% 0.83/1.21  *** allocated 10000 integers for clauses
% 0.83/1.21  *** allocated 10000 integers for justifications
% 0.83/1.21  Bliksem 1.12
% 0.83/1.21  
% 0.83/1.21  
% 0.83/1.21  Automatic Strategy Selection
% 0.83/1.21  
% 0.83/1.21  
% 0.83/1.21  Clauses:
% 0.83/1.21  
% 0.83/1.21  { addition( X, Y ) = addition( Y, X ) }.
% 0.83/1.21  { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 0.83/1.21  { addition( X, zero ) = X }.
% 0.83/1.21  { addition( X, X ) = X }.
% 0.83/1.21  { multiplication( X, multiplication( Y, Z ) ) = multiplication( 
% 0.83/1.21    multiplication( X, Y ), Z ) }.
% 0.83/1.21  { multiplication( X, one ) = X }.
% 0.83/1.21  { multiplication( one, X ) = X }.
% 0.83/1.21  { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 0.83/1.21    , multiplication( X, Z ) ) }.
% 0.83/1.21  { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 0.83/1.21    , multiplication( Y, Z ) ) }.
% 0.83/1.21  { multiplication( X, zero ) = zero }.
% 0.83/1.21  { multiplication( zero, X ) = zero }.
% 0.83/1.21  { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.83/1.21  { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.83/1.21  { leq( addition( one, multiplication( X, star( X ) ) ), star( X ) ) }.
% 0.83/1.21  { leq( addition( one, multiplication( star( X ), X ) ), star( X ) ) }.
% 0.83/1.21  { ! leq( addition( multiplication( X, Y ), Z ), Y ), leq( multiplication( 
% 0.83/1.21    star( X ), Z ), Y ) }.
% 0.83/1.21  { ! leq( addition( multiplication( X, Y ), Z ), X ), leq( multiplication( Z
% 0.83/1.21    , star( Y ) ), X ) }.
% 0.83/1.21  { ! leq( skol1, star( skol1 ) ) }.
% 0.83/1.21  
% 0.83/1.21  percentage equality = 0.590909, percentage horn = 1.000000
% 0.83/1.21  This is a problem with some equality
% 0.83/1.21  
% 0.83/1.21  
% 0.83/1.21  
% 0.83/1.21  Options Used:
% 0.83/1.21  
% 0.83/1.21  useres =            1
% 0.83/1.21  useparamod =        1
% 0.83/1.21  useeqrefl =         1
% 0.83/1.21  useeqfact =         1
% 0.83/1.21  usefactor =         1
% 0.83/1.21  usesimpsplitting =  0
% 0.83/1.21  usesimpdemod =      5
% 0.83/1.21  usesimpres =        3
% 0.83/1.21  
% 0.83/1.21  resimpinuse      =  1000
% 0.83/1.21  resimpclauses =     20000
% 0.83/1.21  substype =          eqrewr
% 0.83/1.21  backwardsubs =      1
% 0.83/1.21  selectoldest =      5
% 0.83/1.21  
% 0.83/1.21  litorderings [0] =  split
% 0.83/1.21  litorderings [1] =  extend the termordering, first sorting on arguments
% 0.83/1.21  
% 0.83/1.21  termordering =      kbo
% 0.83/1.21  
% 0.83/1.21  litapriori =        0
% 0.83/1.21  termapriori =       1
% 0.83/1.21  litaposteriori =    0
% 0.83/1.21  termaposteriori =   0
% 0.83/1.21  demodaposteriori =  0
% 0.83/1.21  ordereqreflfact =   0
% 0.83/1.21  
% 0.83/1.21  litselect =         negord
% 0.83/1.21  
% 0.83/1.21  maxweight =         15
% 0.83/1.21  maxdepth =          30000
% 0.83/1.21  maxlength =         115
% 0.83/1.21  maxnrvars =         195
% 0.83/1.21  excuselevel =       1
% 0.83/1.21  increasemaxweight = 1
% 0.83/1.21  
% 0.83/1.21  maxselected =       10000000
% 0.83/1.21  maxnrclauses =      10000000
% 0.83/1.21  
% 0.83/1.21  showgenerated =    0
% 0.83/1.21  showkept =         0
% 0.83/1.21  showselected =     0
% 0.83/1.21  showdeleted =      0
% 0.83/1.21  showresimp =       1
% 0.83/1.21  showstatus =       2000
% 0.83/1.21  
% 0.83/1.21  prologoutput =     0
% 0.83/1.21  nrgoals =          5000000
% 0.83/1.21  totalproof =       1
% 0.83/1.21  
% 0.83/1.21  Symbols occurring in the translation:
% 0.83/1.21  
% 0.83/1.21  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 0.83/1.21  .  [1, 2]      (w:1, o:19, a:1, s:1, b:0), 
% 0.83/1.21  !  [4, 1]      (w:0, o:13, a:1, s:1, b:0), 
% 0.83/1.21  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.83/1.21  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.83/1.21  addition  [37, 2]      (w:1, o:43, a:1, s:1, b:0), 
% 0.83/1.21  zero  [39, 0]      (w:1, o:9, a:1, s:1, b:0), 
% 0.83/1.21  multiplication  [40, 2]      (w:1, o:45, a:1, s:1, b:0), 
% 0.83/1.21  one  [41, 0]      (w:1, o:10, a:1, s:1, b:0), 
% 0.83/1.21  leq  [42, 2]      (w:1, o:44, a:1, s:1, b:0), 
% 0.83/1.21  star  [43, 1]      (w:1, o:18, a:1, s:1, b:0), 
% 0.83/1.21  skol1  [45, 0]      (w:1, o:12, a:1, s:1, b:1).
% 0.83/1.21  
% 0.83/1.21  
% 0.83/1.21  Starting Search:
% 0.83/1.21  
% 0.83/1.21  *** allocated 15000 integers for clauses
% 0.83/1.21  *** allocated 22500 integers for clauses
% 0.83/1.21  *** allocated 33750 integers for clauses
% 0.83/1.21  *** allocated 50625 integers for clauses
% 0.83/1.21  *** allocated 15000 integers for termspace/termends
% 0.83/1.21  *** allocated 75937 integers for clauses
% 0.83/1.21  Resimplifying inuse:
% 0.83/1.21  Done
% 0.83/1.21  
% 0.83/1.21  *** allocated 22500 integers for termspace/termends
% 0.83/1.21  
% 0.83/1.21  Bliksems!, er is een bewijs:
% 0.83/1.21  % SZS status Theorem
% 0.83/1.21  % SZS output start Refutation
% 0.83/1.21  
% 0.83/1.21  (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 0.83/1.21  (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) ==> addition( 
% 0.83/1.21    addition( Z, Y ), X ) }.
% 0.83/1.21  (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.83/1.21  (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.83/1.21  (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ), 
% 0.83/1.21    multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.83/1.21  (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) ==> Y }.
% 0.83/1.21  (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, Y ) }.
% 0.83/1.21  (13) {G0,W9,D5,L1,V1,M1} I { leq( addition( one, multiplication( X, star( X
% 0.83/1.21     ) ) ), star( X ) ) }.
% 0.83/1.21  (14) {G0,W9,D5,L1,V1,M1} I { leq( addition( one, multiplication( star( X )
% 0.83/1.21    , X ) ), star( X ) ) }.
% 0.83/1.21  (17) {G0,W4,D3,L1,V0,M1} I { ! leq( skol1, star( skol1 ) ) }.
% 0.83/1.21  (24) {G1,W14,D4,L2,V3,M2} P(1,12) { ! addition( addition( X, Y ), Z ) ==> 
% 0.83/1.21    addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 0.83/1.21  (27) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y ), Z ) = 
% 0.83/1.21    addition( addition( Y, Z ), X ) }.
% 0.83/1.21  (62) {G1,W16,D4,L2,V3,M2} P(7,12) { ! multiplication( X, addition( Y, Z ) )
% 0.83/1.21     ==> multiplication( X, Z ), leq( multiplication( X, Y ), multiplication
% 0.83/1.21    ( X, Z ) ) }.
% 0.83/1.21  (198) {G2,W5,D3,L1,V2,M1} P(3,24);q { leq( X, addition( X, Y ) ) }.
% 0.83/1.21  (212) {G3,W7,D4,L1,V3,M1} P(1,198) { leq( X, addition( addition( X, Y ), Z
% 0.83/1.21     ) ) }.
% 0.83/1.21  (213) {G3,W5,D3,L1,V2,M1} P(0,198) { leq( X, addition( Y, X ) ) }.
% 0.83/1.21  (259) {G4,W7,D4,L1,V3,M1} P(27,213) { leq( Z, addition( addition( Y, Z ), X
% 0.83/1.21     ) ) }.
% 0.83/1.21  (297) {G5,W8,D3,L2,V3,M2} P(11,259) { leq( Y, Z ), ! leq( addition( X, Y )
% 0.83/1.21    , Z ) }.
% 0.83/1.21  (307) {G4,W8,D3,L2,V3,M2} P(11,212) { leq( X, Z ), ! leq( addition( X, Y )
% 0.83/1.21    , Z ) }.
% 0.83/1.21  (594) {G5,W4,D3,L1,V1,M1} R(307,14) { leq( one, star( X ) ) }.
% 0.83/1.21  (597) {G5,W6,D3,L1,V1,M1} R(307,17) { ! leq( addition( skol1, X ), star( 
% 0.83/1.21    skol1 ) ) }.
% 0.83/1.21  (611) {G6,W7,D4,L1,V1,M1} R(594,11) { addition( one, star( X ) ) ==> star( 
% 0.83/1.21    X ) }.
% 0.83/1.21  (617) {G6,W7,D3,L2,V1,M2} P(11,597) { ! leq( X, star( skol1 ) ), ! leq( 
% 0.83/1.21    skol1, X ) }.
% 0.83/1.21  (826) {G6,W7,D4,L1,V1,M1} R(297,13) { leq( multiplication( X, star( X ) ), 
% 0.83/1.21    star( X ) ) }.
% 0.83/1.21  (853) {G7,W6,D4,L1,V0,M1} R(826,617) { ! leq( skol1, multiplication( skol1
% 0.83/1.21    , star( skol1 ) ) ) }.
% 0.83/1.21  (1382) {G7,W6,D4,L1,V2,M1} P(611,62);q;d(5) { leq( Y, multiplication( Y, 
% 0.83/1.21    star( X ) ) ) }.
% 0.83/1.21  (1399) {G8,W0,D0,L0,V0,M0} R(1382,853) {  }.
% 0.83/1.21  
% 0.83/1.21  
% 0.83/1.21  % SZS output end Refutation
% 0.83/1.21  found a proof!
% 0.83/1.21  
% 0.83/1.21  
% 0.83/1.21  Unprocessed initial clauses:
% 0.83/1.21  
% 0.83/1.21  (1401) {G0,W7,D3,L1,V2,M1}  { addition( X, Y ) = addition( Y, X ) }.
% 0.83/1.21  (1402) {G0,W11,D4,L1,V3,M1}  { addition( Z, addition( Y, X ) ) = addition( 
% 0.83/1.21    addition( Z, Y ), X ) }.
% 0.83/1.21  (1403) {G0,W5,D3,L1,V1,M1}  { addition( X, zero ) = X }.
% 0.83/1.21  (1404) {G0,W5,D3,L1,V1,M1}  { addition( X, X ) = X }.
% 0.83/1.21  (1405) {G0,W11,D4,L1,V3,M1}  { multiplication( X, multiplication( Y, Z ) ) 
% 0.83/1.21    = multiplication( multiplication( X, Y ), Z ) }.
% 0.83/1.21  (1406) {G0,W5,D3,L1,V1,M1}  { multiplication( X, one ) = X }.
% 0.83/1.21  (1407) {G0,W5,D3,L1,V1,M1}  { multiplication( one, X ) = X }.
% 0.83/1.21  (1408) {G0,W13,D4,L1,V3,M1}  { multiplication( X, addition( Y, Z ) ) = 
% 0.83/1.21    addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.83/1.21  (1409) {G0,W13,D4,L1,V3,M1}  { multiplication( addition( X, Y ), Z ) = 
% 0.83/1.21    addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.83/1.21  (1410) {G0,W5,D3,L1,V1,M1}  { multiplication( X, zero ) = zero }.
% 0.83/1.21  (1411) {G0,W5,D3,L1,V1,M1}  { multiplication( zero, X ) = zero }.
% 0.83/1.21  (1412) {G0,W8,D3,L2,V2,M2}  { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.83/1.21  (1413) {G0,W8,D3,L2,V2,M2}  { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.83/1.21  (1414) {G0,W9,D5,L1,V1,M1}  { leq( addition( one, multiplication( X, star( 
% 0.83/1.21    X ) ) ), star( X ) ) }.
% 0.83/1.21  (1415) {G0,W9,D5,L1,V1,M1}  { leq( addition( one, multiplication( star( X )
% 0.83/1.21    , X ) ), star( X ) ) }.
% 0.83/1.21  (1416) {G0,W13,D4,L2,V3,M2}  { ! leq( addition( multiplication( X, Y ), Z )
% 0.83/1.21    , Y ), leq( multiplication( star( X ), Z ), Y ) }.
% 0.83/1.21  (1417) {G0,W13,D4,L2,V3,M2}  { ! leq( addition( multiplication( X, Y ), Z )
% 0.83/1.21    , X ), leq( multiplication( Z, star( Y ) ), X ) }.
% 0.83/1.21  (1418) {G0,W4,D3,L1,V0,M1}  { ! leq( skol1, star( skol1 ) ) }.
% 0.83/1.21  
% 0.83/1.21  
% 0.83/1.21  Total Proof:
% 0.83/1.21  
% 0.83/1.21  subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 0.83/1.21     ) }.
% 0.83/1.21  parent0: (1401) {G0,W7,D3,L1,V2,M1}  { addition( X, Y ) = addition( Y, X )
% 0.83/1.21     }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := X
% 0.83/1.21     Y := Y
% 0.83/1.21  end
% 0.83/1.21  permutation0:
% 0.83/1.21     0 ==> 0
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  subsumption: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) 
% 0.83/1.21    ==> addition( addition( Z, Y ), X ) }.
% 0.83/1.21  parent0: (1402) {G0,W11,D4,L1,V3,M1}  { addition( Z, addition( Y, X ) ) = 
% 0.83/1.21    addition( addition( Z, Y ), X ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := X
% 0.83/1.21     Y := Y
% 0.83/1.21     Z := Z
% 0.83/1.21  end
% 0.83/1.21  permutation0:
% 0.83/1.21     0 ==> 0
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  subsumption: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.83/1.21  parent0: (1404) {G0,W5,D3,L1,V1,M1}  { addition( X, X ) = X }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := X
% 0.83/1.21  end
% 0.83/1.21  permutation0:
% 0.83/1.21     0 ==> 0
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  subsumption: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.83/1.21  parent0: (1406) {G0,W5,D3,L1,V1,M1}  { multiplication( X, one ) = X }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := X
% 0.83/1.21  end
% 0.83/1.21  permutation0:
% 0.83/1.21     0 ==> 0
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  eqswap: (1434) {G0,W13,D4,L1,V3,M1}  { addition( multiplication( X, Y ), 
% 0.83/1.21    multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 0.83/1.21  parent0[0]: (1408) {G0,W13,D4,L1,V3,M1}  { multiplication( X, addition( Y, 
% 0.83/1.21    Z ) ) = addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := X
% 0.83/1.21     Y := Y
% 0.83/1.21     Z := Z
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  subsumption: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y )
% 0.83/1.21    , multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.83/1.21  parent0: (1434) {G0,W13,D4,L1,V3,M1}  { addition( multiplication( X, Y ), 
% 0.83/1.21    multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := X
% 0.83/1.21     Y := Y
% 0.83/1.21     Z := Z
% 0.83/1.21  end
% 0.83/1.21  permutation0:
% 0.83/1.21     0 ==> 0
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  subsumption: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) 
% 0.83/1.21    ==> Y }.
% 0.83/1.21  parent0: (1412) {G0,W8,D3,L2,V2,M2}  { ! leq( X, Y ), addition( X, Y ) = Y
% 0.83/1.21     }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := X
% 0.83/1.21     Y := Y
% 0.83/1.21  end
% 0.83/1.21  permutation0:
% 0.83/1.21     0 ==> 0
% 0.83/1.21     1 ==> 1
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  subsumption: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X
% 0.83/1.21    , Y ) }.
% 0.83/1.21  parent0: (1413) {G0,W8,D3,L2,V2,M2}  { ! addition( X, Y ) = Y, leq( X, Y )
% 0.83/1.21     }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := X
% 0.83/1.21     Y := Y
% 0.83/1.21  end
% 0.83/1.21  permutation0:
% 0.83/1.21     0 ==> 0
% 0.83/1.21     1 ==> 1
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  subsumption: (13) {G0,W9,D5,L1,V1,M1} I { leq( addition( one, 
% 0.83/1.21    multiplication( X, star( X ) ) ), star( X ) ) }.
% 0.83/1.21  parent0: (1414) {G0,W9,D5,L1,V1,M1}  { leq( addition( one, multiplication( 
% 0.83/1.21    X, star( X ) ) ), star( X ) ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := X
% 0.83/1.21  end
% 0.83/1.21  permutation0:
% 0.83/1.21     0 ==> 0
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  subsumption: (14) {G0,W9,D5,L1,V1,M1} I { leq( addition( one, 
% 0.83/1.21    multiplication( star( X ), X ) ), star( X ) ) }.
% 0.83/1.21  parent0: (1415) {G0,W9,D5,L1,V1,M1}  { leq( addition( one, multiplication( 
% 0.83/1.21    star( X ), X ) ), star( X ) ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := X
% 0.83/1.21  end
% 0.83/1.21  permutation0:
% 0.83/1.21     0 ==> 0
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  subsumption: (17) {G0,W4,D3,L1,V0,M1} I { ! leq( skol1, star( skol1 ) ) }.
% 0.83/1.21  parent0: (1418) {G0,W4,D3,L1,V0,M1}  { ! leq( skol1, star( skol1 ) ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21  end
% 0.83/1.21  permutation0:
% 0.83/1.21     0 ==> 0
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  eqswap: (1495) {G0,W8,D3,L2,V2,M2}  { ! Y ==> addition( X, Y ), leq( X, Y )
% 0.83/1.21     }.
% 0.83/1.21  parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, 
% 0.83/1.21    Y ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := X
% 0.83/1.21     Y := Y
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  paramod: (1496) {G1,W14,D4,L2,V3,M2}  { ! addition( X, Y ) ==> addition( 
% 0.83/1.21    addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 0.83/1.21  parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) 
% 0.83/1.21    ==> addition( addition( Z, Y ), X ) }.
% 0.83/1.21  parent1[0; 5]: (1495) {G0,W8,D3,L2,V2,M2}  { ! Y ==> addition( X, Y ), leq
% 0.83/1.21    ( X, Y ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := Y
% 0.83/1.21     Y := X
% 0.83/1.21     Z := Z
% 0.83/1.21  end
% 0.83/1.21  substitution1:
% 0.83/1.21     X := Z
% 0.83/1.21     Y := addition( X, Y )
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  eqswap: (1497) {G1,W14,D4,L2,V3,M2}  { ! addition( addition( Z, X ), Y ) 
% 0.83/1.21    ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 0.83/1.21  parent0[0]: (1496) {G1,W14,D4,L2,V3,M2}  { ! addition( X, Y ) ==> addition
% 0.83/1.21    ( addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := X
% 0.83/1.21     Y := Y
% 0.83/1.21     Z := Z
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  subsumption: (24) {G1,W14,D4,L2,V3,M2} P(1,12) { ! addition( addition( X, Y
% 0.83/1.21     ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 0.83/1.21  parent0: (1497) {G1,W14,D4,L2,V3,M2}  { ! addition( addition( Z, X ), Y ) 
% 0.83/1.21    ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := Y
% 0.83/1.21     Y := Z
% 0.83/1.21     Z := X
% 0.83/1.21  end
% 0.83/1.21  permutation0:
% 0.83/1.21     0 ==> 0
% 0.83/1.21     1 ==> 1
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  eqswap: (1498) {G0,W11,D4,L1,V3,M1}  { addition( addition( X, Y ), Z ) ==> 
% 0.83/1.21    addition( X, addition( Y, Z ) ) }.
% 0.83/1.21  parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) 
% 0.83/1.21    ==> addition( addition( Z, Y ), X ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := Z
% 0.83/1.21     Y := Y
% 0.83/1.21     Z := X
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  paramod: (1501) {G1,W11,D4,L1,V3,M1}  { addition( addition( X, Y ), Z ) ==>
% 0.83/1.21     addition( addition( Y, Z ), X ) }.
% 0.83/1.21  parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.83/1.21     }.
% 0.83/1.21  parent1[0; 6]: (1498) {G0,W11,D4,L1,V3,M1}  { addition( addition( X, Y ), Z
% 0.83/1.21     ) ==> addition( X, addition( Y, Z ) ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := X
% 0.83/1.21     Y := addition( Y, Z )
% 0.83/1.21  end
% 0.83/1.21  substitution1:
% 0.83/1.21     X := X
% 0.83/1.21     Y := Y
% 0.83/1.21     Z := Z
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  subsumption: (27) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y )
% 0.83/1.21    , Z ) = addition( addition( Y, Z ), X ) }.
% 0.83/1.21  parent0: (1501) {G1,W11,D4,L1,V3,M1}  { addition( addition( X, Y ), Z ) ==>
% 0.83/1.21     addition( addition( Y, Z ), X ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := X
% 0.83/1.21     Y := Y
% 0.83/1.21     Z := Z
% 0.83/1.21  end
% 0.83/1.21  permutation0:
% 0.83/1.21     0 ==> 0
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  eqswap: (1516) {G0,W8,D3,L2,V2,M2}  { ! Y ==> addition( X, Y ), leq( X, Y )
% 0.83/1.21     }.
% 0.83/1.21  parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, 
% 0.83/1.21    Y ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := X
% 0.83/1.21     Y := Y
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  paramod: (1517) {G1,W16,D4,L2,V3,M2}  { ! multiplication( X, Y ) ==> 
% 0.83/1.21    multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ), 
% 0.83/1.21    multiplication( X, Y ) ) }.
% 0.83/1.21  parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ), 
% 0.83/1.21    multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.83/1.21  parent1[0; 5]: (1516) {G0,W8,D3,L2,V2,M2}  { ! Y ==> addition( X, Y ), leq
% 0.83/1.21    ( X, Y ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := X
% 0.83/1.21     Y := Z
% 0.83/1.21     Z := Y
% 0.83/1.21  end
% 0.83/1.21  substitution1:
% 0.83/1.21     X := multiplication( X, Z )
% 0.83/1.21     Y := multiplication( X, Y )
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  eqswap: (1518) {G1,W16,D4,L2,V3,M2}  { ! multiplication( X, addition( Z, Y
% 0.83/1.21     ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ), 
% 0.83/1.21    multiplication( X, Y ) ) }.
% 0.83/1.21  parent0[0]: (1517) {G1,W16,D4,L2,V3,M2}  { ! multiplication( X, Y ) ==> 
% 0.83/1.21    multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ), 
% 0.83/1.21    multiplication( X, Y ) ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := X
% 0.83/1.21     Y := Y
% 0.83/1.21     Z := Z
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  subsumption: (62) {G1,W16,D4,L2,V3,M2} P(7,12) { ! multiplication( X, 
% 0.83/1.21    addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 0.83/1.21     ), multiplication( X, Z ) ) }.
% 0.83/1.21  parent0: (1518) {G1,W16,D4,L2,V3,M2}  { ! multiplication( X, addition( Z, Y
% 0.83/1.21     ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ), 
% 0.83/1.21    multiplication( X, Y ) ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := X
% 0.83/1.21     Y := Z
% 0.83/1.21     Z := Y
% 0.83/1.21  end
% 0.83/1.21  permutation0:
% 0.83/1.21     0 ==> 0
% 0.83/1.21     1 ==> 1
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  eqswap: (1520) {G1,W14,D4,L2,V3,M2}  { ! addition( Y, Z ) ==> addition( 
% 0.83/1.21    addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 0.83/1.21  parent0[0]: (24) {G1,W14,D4,L2,V3,M2} P(1,12) { ! addition( addition( X, Y
% 0.83/1.21     ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := X
% 0.83/1.21     Y := Y
% 0.83/1.21     Z := Z
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  paramod: (1523) {G1,W12,D3,L2,V2,M2}  { ! addition( X, Y ) ==> addition( X
% 0.83/1.21    , Y ), leq( X, addition( X, Y ) ) }.
% 0.83/1.21  parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 0.83/1.21  parent1[0; 6]: (1520) {G1,W14,D4,L2,V3,M2}  { ! addition( Y, Z ) ==> 
% 0.83/1.21    addition( addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := X
% 0.83/1.21  end
% 0.83/1.21  substitution1:
% 0.83/1.21     X := X
% 0.83/1.21     Y := X
% 0.83/1.21     Z := Y
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  eqrefl: (1526) {G0,W5,D3,L1,V2,M1}  { leq( X, addition( X, Y ) ) }.
% 0.83/1.21  parent0[0]: (1523) {G1,W12,D3,L2,V2,M2}  { ! addition( X, Y ) ==> addition
% 0.83/1.21    ( X, Y ), leq( X, addition( X, Y ) ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := X
% 0.83/1.21     Y := Y
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  subsumption: (198) {G2,W5,D3,L1,V2,M1} P(3,24);q { leq( X, addition( X, Y )
% 0.83/1.21     ) }.
% 0.83/1.21  parent0: (1526) {G0,W5,D3,L1,V2,M1}  { leq( X, addition( X, Y ) ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := X
% 0.83/1.21     Y := Y
% 0.83/1.21  end
% 0.83/1.21  permutation0:
% 0.83/1.21     0 ==> 0
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  paramod: (1528) {G1,W7,D4,L1,V3,M1}  { leq( X, addition( addition( X, Y ), 
% 0.83/1.21    Z ) ) }.
% 0.83/1.21  parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) 
% 0.83/1.21    ==> addition( addition( Z, Y ), X ) }.
% 0.83/1.21  parent1[0; 2]: (198) {G2,W5,D3,L1,V2,M1} P(3,24);q { leq( X, addition( X, Y
% 0.83/1.21     ) ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := Z
% 0.83/1.21     Y := Y
% 0.83/1.21     Z := X
% 0.83/1.21  end
% 0.83/1.21  substitution1:
% 0.83/1.21     X := X
% 0.83/1.21     Y := addition( Y, Z )
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  subsumption: (212) {G3,W7,D4,L1,V3,M1} P(1,198) { leq( X, addition( 
% 0.83/1.21    addition( X, Y ), Z ) ) }.
% 0.83/1.21  parent0: (1528) {G1,W7,D4,L1,V3,M1}  { leq( X, addition( addition( X, Y ), 
% 0.83/1.21    Z ) ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := X
% 0.83/1.21     Y := Y
% 0.83/1.21     Z := Z
% 0.83/1.21  end
% 0.83/1.21  permutation0:
% 0.83/1.21     0 ==> 0
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  paramod: (1529) {G1,W5,D3,L1,V2,M1}  { leq( X, addition( Y, X ) ) }.
% 0.83/1.21  parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.83/1.21     }.
% 0.83/1.21  parent1[0; 2]: (198) {G2,W5,D3,L1,V2,M1} P(3,24);q { leq( X, addition( X, Y
% 0.83/1.21     ) ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := X
% 0.83/1.21     Y := Y
% 0.83/1.21  end
% 0.83/1.21  substitution1:
% 0.83/1.21     X := X
% 0.83/1.21     Y := Y
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  subsumption: (213) {G3,W5,D3,L1,V2,M1} P(0,198) { leq( X, addition( Y, X )
% 0.83/1.21     ) }.
% 0.83/1.21  parent0: (1529) {G1,W5,D3,L1,V2,M1}  { leq( X, addition( Y, X ) ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := X
% 0.83/1.21     Y := Y
% 0.83/1.21  end
% 0.83/1.21  permutation0:
% 0.83/1.21     0 ==> 0
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  eqswap: (1531) {G1,W11,D4,L1,V3,M1}  { addition( addition( Y, Z ), X ) = 
% 0.83/1.21    addition( addition( X, Y ), Z ) }.
% 0.83/1.21  parent0[0]: (27) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y ), 
% 0.83/1.21    Z ) = addition( addition( Y, Z ), X ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := X
% 0.83/1.21     Y := Y
% 0.83/1.21     Z := Z
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  paramod: (1532) {G2,W7,D4,L1,V3,M1}  { leq( X, addition( addition( X, Y ), 
% 0.83/1.21    Z ) ) }.
% 0.83/1.21  parent0[0]: (1531) {G1,W11,D4,L1,V3,M1}  { addition( addition( Y, Z ), X ) 
% 0.83/1.21    = addition( addition( X, Y ), Z ) }.
% 0.83/1.21  parent1[0; 2]: (213) {G3,W5,D3,L1,V2,M1} P(0,198) { leq( X, addition( Y, X
% 0.83/1.21     ) ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := X
% 0.83/1.21     Y := Y
% 0.83/1.21     Z := Z
% 0.83/1.21  end
% 0.83/1.21  substitution1:
% 0.83/1.21     X := X
% 0.83/1.21     Y := addition( Y, Z )
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  paramod: (1533) {G2,W7,D4,L1,V3,M1}  { leq( X, addition( addition( Z, X ), 
% 0.83/1.21    Y ) ) }.
% 0.83/1.21  parent0[0]: (1531) {G1,W11,D4,L1,V3,M1}  { addition( addition( Y, Z ), X ) 
% 0.83/1.21    = addition( addition( X, Y ), Z ) }.
% 0.83/1.21  parent1[0; 2]: (1532) {G2,W7,D4,L1,V3,M1}  { leq( X, addition( addition( X
% 0.83/1.21    , Y ), Z ) ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := Z
% 0.83/1.21     Y := X
% 0.83/1.21     Z := Y
% 0.83/1.21  end
% 0.83/1.21  substitution1:
% 0.83/1.21     X := X
% 0.83/1.21     Y := Y
% 0.83/1.21     Z := Z
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  subsumption: (259) {G4,W7,D4,L1,V3,M1} P(27,213) { leq( Z, addition( 
% 0.83/1.21    addition( Y, Z ), X ) ) }.
% 0.83/1.21  parent0: (1533) {G2,W7,D4,L1,V3,M1}  { leq( X, addition( addition( Z, X ), 
% 0.83/1.21    Y ) ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := Z
% 0.83/1.21     Y := X
% 0.83/1.21     Z := Y
% 0.83/1.21  end
% 0.83/1.21  permutation0:
% 0.83/1.21     0 ==> 0
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  paramod: (1536) {G1,W8,D3,L2,V3,M2}  { leq( X, Z ), ! leq( addition( Y, X )
% 0.83/1.21    , Z ) }.
% 0.83/1.21  parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) 
% 0.83/1.21    ==> Y }.
% 0.83/1.21  parent1[0; 2]: (259) {G4,W7,D4,L1,V3,M1} P(27,213) { leq( Z, addition( 
% 0.83/1.21    addition( Y, Z ), X ) ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := addition( Y, X )
% 0.83/1.21     Y := Z
% 0.83/1.21  end
% 0.83/1.21  substitution1:
% 0.83/1.21     X := Z
% 0.83/1.21     Y := Y
% 0.83/1.21     Z := X
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  subsumption: (297) {G5,W8,D3,L2,V3,M2} P(11,259) { leq( Y, Z ), ! leq( 
% 0.83/1.21    addition( X, Y ), Z ) }.
% 0.83/1.21  parent0: (1536) {G1,W8,D3,L2,V3,M2}  { leq( X, Z ), ! leq( addition( Y, X )
% 0.83/1.21    , Z ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := Y
% 0.83/1.21     Y := X
% 0.83/1.21     Z := Z
% 0.83/1.21  end
% 0.83/1.21  permutation0:
% 0.83/1.21     0 ==> 0
% 0.83/1.21     1 ==> 1
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  paramod: (1541) {G1,W8,D3,L2,V3,M2}  { leq( X, Z ), ! leq( addition( X, Y )
% 0.83/1.21    , Z ) }.
% 0.83/1.21  parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) 
% 0.83/1.21    ==> Y }.
% 0.83/1.21  parent1[0; 2]: (212) {G3,W7,D4,L1,V3,M1} P(1,198) { leq( X, addition( 
% 0.83/1.21    addition( X, Y ), Z ) ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := addition( X, Y )
% 0.83/1.21     Y := Z
% 0.83/1.21  end
% 0.83/1.21  substitution1:
% 0.83/1.21     X := X
% 0.83/1.21     Y := Y
% 0.83/1.21     Z := Z
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  subsumption: (307) {G4,W8,D3,L2,V3,M2} P(11,212) { leq( X, Z ), ! leq( 
% 0.83/1.21    addition( X, Y ), Z ) }.
% 0.83/1.21  parent0: (1541) {G1,W8,D3,L2,V3,M2}  { leq( X, Z ), ! leq( addition( X, Y )
% 0.83/1.21    , Z ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := X
% 0.83/1.21     Y := Y
% 0.83/1.21     Z := Z
% 0.83/1.21  end
% 0.83/1.21  permutation0:
% 0.83/1.21     0 ==> 0
% 0.83/1.21     1 ==> 1
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  resolution: (1545) {G1,W4,D3,L1,V1,M1}  { leq( one, star( X ) ) }.
% 0.83/1.21  parent0[1]: (307) {G4,W8,D3,L2,V3,M2} P(11,212) { leq( X, Z ), ! leq( 
% 0.83/1.21    addition( X, Y ), Z ) }.
% 0.83/1.21  parent1[0]: (14) {G0,W9,D5,L1,V1,M1} I { leq( addition( one, multiplication
% 0.83/1.21    ( star( X ), X ) ), star( X ) ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := one
% 0.83/1.21     Y := multiplication( star( X ), X )
% 0.83/1.21     Z := star( X )
% 0.83/1.21  end
% 0.83/1.21  substitution1:
% 0.83/1.21     X := X
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  subsumption: (594) {G5,W4,D3,L1,V1,M1} R(307,14) { leq( one, star( X ) )
% 0.83/1.21     }.
% 0.83/1.21  parent0: (1545) {G1,W4,D3,L1,V1,M1}  { leq( one, star( X ) ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := X
% 0.83/1.21  end
% 0.83/1.21  permutation0:
% 0.83/1.21     0 ==> 0
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  resolution: (1546) {G1,W6,D3,L1,V1,M1}  { ! leq( addition( skol1, X ), star
% 0.83/1.21    ( skol1 ) ) }.
% 0.83/1.21  parent0[0]: (17) {G0,W4,D3,L1,V0,M1} I { ! leq( skol1, star( skol1 ) ) }.
% 0.83/1.21  parent1[0]: (307) {G4,W8,D3,L2,V3,M2} P(11,212) { leq( X, Z ), ! leq( 
% 0.83/1.21    addition( X, Y ), Z ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21  end
% 0.83/1.21  substitution1:
% 0.83/1.21     X := skol1
% 0.83/1.21     Y := X
% 0.83/1.21     Z := star( skol1 )
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  subsumption: (597) {G5,W6,D3,L1,V1,M1} R(307,17) { ! leq( addition( skol1, 
% 0.83/1.21    X ), star( skol1 ) ) }.
% 0.83/1.21  parent0: (1546) {G1,W6,D3,L1,V1,M1}  { ! leq( addition( skol1, X ), star( 
% 0.83/1.21    skol1 ) ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := X
% 0.83/1.21  end
% 0.83/1.21  permutation0:
% 0.83/1.21     0 ==> 0
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  eqswap: (1547) {G0,W8,D3,L2,V2,M2}  { Y ==> addition( X, Y ), ! leq( X, Y )
% 0.83/1.21     }.
% 0.83/1.21  parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) 
% 0.83/1.21    ==> Y }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := X
% 0.83/1.21     Y := Y
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  resolution: (1548) {G1,W7,D4,L1,V1,M1}  { star( X ) ==> addition( one, star
% 0.83/1.21    ( X ) ) }.
% 0.83/1.21  parent0[1]: (1547) {G0,W8,D3,L2,V2,M2}  { Y ==> addition( X, Y ), ! leq( X
% 0.83/1.21    , Y ) }.
% 0.83/1.21  parent1[0]: (594) {G5,W4,D3,L1,V1,M1} R(307,14) { leq( one, star( X ) ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := one
% 0.83/1.21     Y := star( X )
% 0.83/1.21  end
% 0.83/1.21  substitution1:
% 0.83/1.21     X := X
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  eqswap: (1549) {G1,W7,D4,L1,V1,M1}  { addition( one, star( X ) ) ==> star( 
% 0.83/1.21    X ) }.
% 0.83/1.21  parent0[0]: (1548) {G1,W7,D4,L1,V1,M1}  { star( X ) ==> addition( one, star
% 0.83/1.21    ( X ) ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := X
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  subsumption: (611) {G6,W7,D4,L1,V1,M1} R(594,11) { addition( one, star( X )
% 0.83/1.21     ) ==> star( X ) }.
% 0.83/1.21  parent0: (1549) {G1,W7,D4,L1,V1,M1}  { addition( one, star( X ) ) ==> star
% 0.83/1.21    ( X ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := X
% 0.83/1.21  end
% 0.83/1.21  permutation0:
% 0.83/1.21     0 ==> 0
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  paramod: (1551) {G1,W7,D3,L2,V1,M2}  { ! leq( X, star( skol1 ) ), ! leq( 
% 0.83/1.21    skol1, X ) }.
% 0.83/1.21  parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) 
% 0.83/1.21    ==> Y }.
% 0.83/1.21  parent1[0; 2]: (597) {G5,W6,D3,L1,V1,M1} R(307,17) { ! leq( addition( skol1
% 0.83/1.21    , X ), star( skol1 ) ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := skol1
% 0.83/1.21     Y := X
% 0.83/1.21  end
% 0.83/1.21  substitution1:
% 0.83/1.21     X := X
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  subsumption: (617) {G6,W7,D3,L2,V1,M2} P(11,597) { ! leq( X, star( skol1 )
% 0.83/1.21     ), ! leq( skol1, X ) }.
% 0.83/1.21  parent0: (1551) {G1,W7,D3,L2,V1,M2}  { ! leq( X, star( skol1 ) ), ! leq( 
% 0.83/1.21    skol1, X ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := X
% 0.83/1.21  end
% 0.83/1.21  permutation0:
% 0.83/1.21     0 ==> 0
% 0.83/1.21     1 ==> 1
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  resolution: (1552) {G1,W7,D4,L1,V1,M1}  { leq( multiplication( X, star( X )
% 0.83/1.21     ), star( X ) ) }.
% 0.83/1.21  parent0[1]: (297) {G5,W8,D3,L2,V3,M2} P(11,259) { leq( Y, Z ), ! leq( 
% 0.83/1.21    addition( X, Y ), Z ) }.
% 0.83/1.21  parent1[0]: (13) {G0,W9,D5,L1,V1,M1} I { leq( addition( one, multiplication
% 0.83/1.21    ( X, star( X ) ) ), star( X ) ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := one
% 0.83/1.21     Y := multiplication( X, star( X ) )
% 0.83/1.21     Z := star( X )
% 0.83/1.21  end
% 0.83/1.21  substitution1:
% 0.83/1.21     X := X
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  subsumption: (826) {G6,W7,D4,L1,V1,M1} R(297,13) { leq( multiplication( X, 
% 0.83/1.21    star( X ) ), star( X ) ) }.
% 0.83/1.21  parent0: (1552) {G1,W7,D4,L1,V1,M1}  { leq( multiplication( X, star( X ) )
% 0.83/1.21    , star( X ) ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := X
% 0.83/1.21  end
% 0.83/1.21  permutation0:
% 0.83/1.21     0 ==> 0
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  resolution: (1553) {G7,W6,D4,L1,V0,M1}  { ! leq( skol1, multiplication( 
% 0.83/1.21    skol1, star( skol1 ) ) ) }.
% 0.83/1.21  parent0[0]: (617) {G6,W7,D3,L2,V1,M2} P(11,597) { ! leq( X, star( skol1 ) )
% 0.83/1.21    , ! leq( skol1, X ) }.
% 0.83/1.21  parent1[0]: (826) {G6,W7,D4,L1,V1,M1} R(297,13) { leq( multiplication( X, 
% 0.83/1.21    star( X ) ), star( X ) ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := multiplication( skol1, star( skol1 ) )
% 0.83/1.21  end
% 0.83/1.21  substitution1:
% 0.83/1.21     X := skol1
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  subsumption: (853) {G7,W6,D4,L1,V0,M1} R(826,617) { ! leq( skol1, 
% 0.83/1.21    multiplication( skol1, star( skol1 ) ) ) }.
% 0.83/1.21  parent0: (1553) {G7,W6,D4,L1,V0,M1}  { ! leq( skol1, multiplication( skol1
% 0.83/1.21    , star( skol1 ) ) ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21  end
% 0.83/1.21  permutation0:
% 0.83/1.21     0 ==> 0
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  eqswap: (1555) {G1,W16,D4,L2,V3,M2}  { ! multiplication( X, Z ) ==> 
% 0.83/1.21    multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ), 
% 0.83/1.21    multiplication( X, Z ) ) }.
% 0.83/1.21  parent0[0]: (62) {G1,W16,D4,L2,V3,M2} P(7,12) { ! multiplication( X, 
% 0.83/1.21    addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 0.83/1.21     ), multiplication( X, Z ) ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := X
% 0.83/1.21     Y := Y
% 0.83/1.21     Z := Z
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  paramod: (1557) {G2,W17,D4,L2,V2,M2}  { ! multiplication( X, star( Y ) ) 
% 0.83/1.21    ==> multiplication( X, star( Y ) ), leq( multiplication( X, one ), 
% 0.83/1.21    multiplication( X, star( Y ) ) ) }.
% 0.83/1.21  parent0[0]: (611) {G6,W7,D4,L1,V1,M1} R(594,11) { addition( one, star( X )
% 0.83/1.21     ) ==> star( X ) }.
% 0.83/1.21  parent1[0; 8]: (1555) {G1,W16,D4,L2,V3,M2}  { ! multiplication( X, Z ) ==> 
% 0.83/1.21    multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ), 
% 0.83/1.21    multiplication( X, Z ) ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := Y
% 0.83/1.21  end
% 0.83/1.21  substitution1:
% 0.83/1.21     X := X
% 0.83/1.21     Y := one
% 0.83/1.21     Z := star( Y )
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  eqrefl: (1558) {G0,W8,D4,L1,V2,M1}  { leq( multiplication( X, one ), 
% 0.83/1.21    multiplication( X, star( Y ) ) ) }.
% 0.83/1.21  parent0[0]: (1557) {G2,W17,D4,L2,V2,M2}  { ! multiplication( X, star( Y ) )
% 0.83/1.21     ==> multiplication( X, star( Y ) ), leq( multiplication( X, one ), 
% 0.83/1.21    multiplication( X, star( Y ) ) ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := X
% 0.83/1.21     Y := Y
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  paramod: (1559) {G1,W6,D4,L1,V2,M1}  { leq( X, multiplication( X, star( Y )
% 0.83/1.21     ) ) }.
% 0.83/1.21  parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 0.83/1.21  parent1[0; 1]: (1558) {G0,W8,D4,L1,V2,M1}  { leq( multiplication( X, one )
% 0.83/1.21    , multiplication( X, star( Y ) ) ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := X
% 0.83/1.21  end
% 0.83/1.21  substitution1:
% 0.83/1.21     X := X
% 0.83/1.21     Y := Y
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  subsumption: (1382) {G7,W6,D4,L1,V2,M1} P(611,62);q;d(5) { leq( Y, 
% 0.83/1.21    multiplication( Y, star( X ) ) ) }.
% 0.83/1.21  parent0: (1559) {G1,W6,D4,L1,V2,M1}  { leq( X, multiplication( X, star( Y )
% 0.83/1.21     ) ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21     X := Y
% 0.83/1.21     Y := X
% 0.83/1.21  end
% 0.83/1.21  permutation0:
% 0.83/1.21     0 ==> 0
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  resolution: (1560) {G8,W0,D0,L0,V0,M0}  {  }.
% 0.83/1.21  parent0[0]: (853) {G7,W6,D4,L1,V0,M1} R(826,617) { ! leq( skol1, 
% 0.83/1.21    multiplication( skol1, star( skol1 ) ) ) }.
% 0.83/1.21  parent1[0]: (1382) {G7,W6,D4,L1,V2,M1} P(611,62);q;d(5) { leq( Y, 
% 0.83/1.21    multiplication( Y, star( X ) ) ) }.
% 0.83/1.21  substitution0:
% 0.83/1.21  end
% 0.83/1.21  substitution1:
% 0.83/1.21     X := skol1
% 0.83/1.21     Y := skol1
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  subsumption: (1399) {G8,W0,D0,L0,V0,M0} R(1382,853) {  }.
% 0.83/1.21  parent0: (1560) {G8,W0,D0,L0,V0,M0}  {  }.
% 0.83/1.21  substitution0:
% 0.83/1.21  end
% 0.83/1.21  permutation0:
% 0.83/1.21  end
% 0.83/1.21  
% 0.83/1.21  Proof check complete!
% 0.83/1.21  
% 0.83/1.21  Memory use:
% 0.83/1.21  
% 0.83/1.21  space for terms:        17847
% 0.83/1.21  space for clauses:      71131
% 0.83/1.21  
% 0.83/1.21  
% 0.83/1.21  clauses generated:      10504
% 0.83/1.21  clauses kept:           1400
% 0.83/1.21  clauses selected:       193
% 0.83/1.21  clauses deleted:        32
% 0.83/1.21  clauses inuse deleted:  23
% 0.83/1.21  
% 0.83/1.21  subsentry:          22684
% 0.83/1.21  literals s-matched: 16208
% 0.83/1.21  literals matched:   15447
% 0.83/1.21  full subsumption:   2026
% 0.83/1.21  
% 0.83/1.21  checksum:           612699136
% 0.83/1.21  
% 0.83/1.21  
% 0.83/1.21  Bliksem ended
%------------------------------------------------------------------------------