TSTP Solution File: KLE061+1 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : KLE061+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n013.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 01:36:58 EDT 2022

% Result   : Theorem 0.94s 1.37s
% Output   : Refutation 0.94s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : KLE061+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : bliksem %s
% 0.13/0.34  % Computer : n013.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 11:57:14 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.94/1.37  *** allocated 10000 integers for termspace/termends
% 0.94/1.37  *** allocated 10000 integers for clauses
% 0.94/1.37  *** allocated 10000 integers for justifications
% 0.94/1.37  Bliksem 1.12
% 0.94/1.37  
% 0.94/1.37  
% 0.94/1.37  Automatic Strategy Selection
% 0.94/1.37  
% 0.94/1.37  
% 0.94/1.37  Clauses:
% 0.94/1.37  
% 0.94/1.37  { addition( X, Y ) = addition( Y, X ) }.
% 0.94/1.37  { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 0.94/1.37  { addition( X, zero ) = X }.
% 0.94/1.37  { addition( X, X ) = X }.
% 0.94/1.37  { multiplication( X, multiplication( Y, Z ) ) = multiplication( 
% 0.94/1.37    multiplication( X, Y ), Z ) }.
% 0.94/1.37  { multiplication( X, one ) = X }.
% 0.94/1.37  { multiplication( one, X ) = X }.
% 0.94/1.37  { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 0.94/1.37    , multiplication( X, Z ) ) }.
% 0.94/1.37  { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 0.94/1.37    , multiplication( Y, Z ) ) }.
% 0.94/1.37  { multiplication( X, zero ) = zero }.
% 0.94/1.37  { multiplication( zero, X ) = zero }.
% 0.94/1.37  { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.94/1.37  { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.94/1.37  { addition( X, multiplication( domain( X ), X ) ) = multiplication( domain
% 0.94/1.37    ( X ), X ) }.
% 0.94/1.37  { domain( multiplication( X, Y ) ) = domain( multiplication( X, domain( Y )
% 0.94/1.37     ) ) }.
% 0.94/1.37  { addition( domain( X ), one ) = one }.
% 0.94/1.37  { domain( zero ) = zero }.
% 0.94/1.37  { domain( addition( X, Y ) ) = addition( domain( X ), domain( Y ) ) }.
% 0.94/1.37  { ! multiplication( domain( skol1 ), domain( skol1 ) ) = domain( skol1 ) }
% 0.94/1.37    .
% 0.94/1.37  
% 0.94/1.37  percentage equality = 0.904762, percentage horn = 1.000000
% 0.94/1.37  This is a pure equality problem
% 0.94/1.37  
% 0.94/1.37  
% 0.94/1.37  
% 0.94/1.37  Options Used:
% 0.94/1.37  
% 0.94/1.37  useres =            1
% 0.94/1.37  useparamod =        1
% 0.94/1.37  useeqrefl =         1
% 0.94/1.37  useeqfact =         1
% 0.94/1.37  usefactor =         1
% 0.94/1.37  usesimpsplitting =  0
% 0.94/1.37  usesimpdemod =      5
% 0.94/1.37  usesimpres =        3
% 0.94/1.37  
% 0.94/1.37  resimpinuse      =  1000
% 0.94/1.37  resimpclauses =     20000
% 0.94/1.37  substype =          eqrewr
% 0.94/1.37  backwardsubs =      1
% 0.94/1.37  selectoldest =      5
% 0.94/1.37  
% 0.94/1.37  litorderings [0] =  split
% 0.94/1.37  litorderings [1] =  extend the termordering, first sorting on arguments
% 0.94/1.37  
% 0.94/1.37  termordering =      kbo
% 0.94/1.37  
% 0.94/1.37  litapriori =        0
% 0.94/1.37  termapriori =       1
% 0.94/1.37  litaposteriori =    0
% 0.94/1.37  termaposteriori =   0
% 0.94/1.37  demodaposteriori =  0
% 0.94/1.37  ordereqreflfact =   0
% 0.94/1.37  
% 0.94/1.37  litselect =         negord
% 0.94/1.37  
% 0.94/1.37  maxweight =         15
% 0.94/1.37  maxdepth =          30000
% 0.94/1.37  maxlength =         115
% 0.94/1.37  maxnrvars =         195
% 0.94/1.37  excuselevel =       1
% 0.94/1.37  increasemaxweight = 1
% 0.94/1.37  
% 0.94/1.37  maxselected =       10000000
% 0.94/1.37  maxnrclauses =      10000000
% 0.94/1.37  
% 0.94/1.37  showgenerated =    0
% 0.94/1.37  showkept =         0
% 0.94/1.37  showselected =     0
% 0.94/1.37  showdeleted =      0
% 0.94/1.37  showresimp =       1
% 0.94/1.37  showstatus =       2000
% 0.94/1.37  
% 0.94/1.37  prologoutput =     0
% 0.94/1.37  nrgoals =          5000000
% 0.94/1.37  totalproof =       1
% 0.94/1.37  
% 0.94/1.37  Symbols occurring in the translation:
% 0.94/1.37  
% 0.94/1.37  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 0.94/1.37  .  [1, 2]      (w:1, o:20, a:1, s:1, b:0), 
% 0.94/1.37  !  [4, 1]      (w:0, o:14, a:1, s:1, b:0), 
% 0.94/1.37  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.94/1.37  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.94/1.37  addition  [37, 2]      (w:1, o:44, a:1, s:1, b:0), 
% 0.94/1.37  zero  [39, 0]      (w:1, o:9, a:1, s:1, b:0), 
% 0.94/1.37  multiplication  [40, 2]      (w:1, o:46, a:1, s:1, b:0), 
% 0.94/1.37  one  [41, 0]      (w:1, o:10, a:1, s:1, b:0), 
% 0.94/1.37  leq  [42, 2]      (w:1, o:45, a:1, s:1, b:0), 
% 0.94/1.37  domain  [44, 1]      (w:1, o:19, a:1, s:1, b:0), 
% 0.94/1.37  skol1  [46, 0]      (w:1, o:13, a:1, s:1, b:1).
% 0.94/1.37  
% 0.94/1.37  
% 0.94/1.37  Starting Search:
% 0.94/1.37  
% 0.94/1.37  *** allocated 15000 integers for clauses
% 0.94/1.37  *** allocated 22500 integers for clauses
% 0.94/1.37  *** allocated 33750 integers for clauses
% 0.94/1.37  *** allocated 50625 integers for clauses
% 0.94/1.37  *** allocated 15000 integers for termspace/termends
% 0.94/1.37  *** allocated 75937 integers for clauses
% 0.94/1.37  Resimplifying inuse:
% 0.94/1.37  Done
% 0.94/1.37  
% 0.94/1.37  *** allocated 22500 integers for termspace/termends
% 0.94/1.37  *** allocated 113905 integers for clauses
% 0.94/1.37  *** allocated 33750 integers for termspace/termends
% 0.94/1.37  
% 0.94/1.37  Intermediate Status:
% 0.94/1.37  Generated:    16058
% 0.94/1.37  Kept:         2003
% 0.94/1.37  Inuse:        226
% 0.94/1.37  Deleted:      19
% 0.94/1.37  Deletedinuse: 10
% 0.94/1.37  
% 0.94/1.37  Resimplifying inuse:
% 0.94/1.37  Done
% 0.94/1.37  
% 0.94/1.37  *** allocated 170857 integers for clauses
% 0.94/1.37  *** allocated 50625 integers for termspace/termends
% 0.94/1.37  Resimplifying inuse:
% 0.94/1.37  
% 0.94/1.37  Bliksems!, er is een bewijs:
% 0.94/1.37  % SZS status Theorem
% 0.94/1.37  % SZS output start Refutation
% 0.94/1.37  
% 0.94/1.37  (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 0.94/1.37  (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.94/1.37  (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ), 
% 0.94/1.37    multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 0.94/1.37  (13) {G0,W11,D5,L1,V1,M1} I { addition( X, multiplication( domain( X ), X )
% 0.94/1.37     ) ==> multiplication( domain( X ), X ) }.
% 0.94/1.37  (14) {G0,W10,D5,L1,V2,M1} I { domain( multiplication( X, domain( Y ) ) ) 
% 0.94/1.37    ==> domain( multiplication( X, Y ) ) }.
% 0.94/1.37  (15) {G0,W6,D4,L1,V1,M1} I { addition( domain( X ), one ) ==> one }.
% 0.94/1.37  (18) {G0,W8,D4,L1,V0,M1} I { ! multiplication( domain( skol1 ), domain( 
% 0.94/1.37    skol1 ) ) ==> domain( skol1 ) }.
% 0.94/1.37  (20) {G1,W6,D4,L1,V1,M1} P(15,0) { addition( one, domain( X ) ) ==> one }.
% 0.94/1.37  (85) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( X, multiplication( Y, X ) ) = 
% 0.94/1.37    multiplication( addition( one, Y ), X ) }.
% 0.94/1.37  (139) {G1,W6,D4,L1,V1,M1} P(6,14);d(6) { domain( domain( X ) ) ==> domain( 
% 0.94/1.37    X ) }.
% 0.94/1.37  (2688) {G2,W6,D4,L1,V1,M1} P(85,13);d(20);d(6) { multiplication( domain( X
% 0.94/1.37     ), X ) ==> X }.
% 0.94/1.37  (2708) {G3,W8,D4,L1,V1,M1} P(139,2688) { multiplication( domain( X ), 
% 0.94/1.37    domain( X ) ) ==> domain( X ) }.
% 0.94/1.37  (3028) {G4,W0,D0,L0,V0,M0} S(18);d(2708);q {  }.
% 0.94/1.37  
% 0.94/1.37  
% 0.94/1.37  % SZS output end Refutation
% 0.94/1.37  found a proof!
% 0.94/1.37  
% 0.94/1.37  
% 0.94/1.37  Unprocessed initial clauses:
% 0.94/1.37  
% 0.94/1.37  (3030) {G0,W7,D3,L1,V2,M1}  { addition( X, Y ) = addition( Y, X ) }.
% 0.94/1.37  (3031) {G0,W11,D4,L1,V3,M1}  { addition( Z, addition( Y, X ) ) = addition( 
% 0.94/1.37    addition( Z, Y ), X ) }.
% 0.94/1.37  (3032) {G0,W5,D3,L1,V1,M1}  { addition( X, zero ) = X }.
% 0.94/1.37  (3033) {G0,W5,D3,L1,V1,M1}  { addition( X, X ) = X }.
% 0.94/1.37  (3034) {G0,W11,D4,L1,V3,M1}  { multiplication( X, multiplication( Y, Z ) ) 
% 0.94/1.37    = multiplication( multiplication( X, Y ), Z ) }.
% 0.94/1.37  (3035) {G0,W5,D3,L1,V1,M1}  { multiplication( X, one ) = X }.
% 0.94/1.37  (3036) {G0,W5,D3,L1,V1,M1}  { multiplication( one, X ) = X }.
% 0.94/1.37  (3037) {G0,W13,D4,L1,V3,M1}  { multiplication( X, addition( Y, Z ) ) = 
% 0.94/1.37    addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.94/1.37  (3038) {G0,W13,D4,L1,V3,M1}  { multiplication( addition( X, Y ), Z ) = 
% 0.94/1.37    addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.94/1.37  (3039) {G0,W5,D3,L1,V1,M1}  { multiplication( X, zero ) = zero }.
% 0.94/1.37  (3040) {G0,W5,D3,L1,V1,M1}  { multiplication( zero, X ) = zero }.
% 0.94/1.37  (3041) {G0,W8,D3,L2,V2,M2}  { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.94/1.37  (3042) {G0,W8,D3,L2,V2,M2}  { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.94/1.37  (3043) {G0,W11,D5,L1,V1,M1}  { addition( X, multiplication( domain( X ), X
% 0.94/1.37     ) ) = multiplication( domain( X ), X ) }.
% 0.94/1.37  (3044) {G0,W10,D5,L1,V2,M1}  { domain( multiplication( X, Y ) ) = domain( 
% 0.94/1.37    multiplication( X, domain( Y ) ) ) }.
% 0.94/1.37  (3045) {G0,W6,D4,L1,V1,M1}  { addition( domain( X ), one ) = one }.
% 0.94/1.37  (3046) {G0,W4,D3,L1,V0,M1}  { domain( zero ) = zero }.
% 0.94/1.37  (3047) {G0,W10,D4,L1,V2,M1}  { domain( addition( X, Y ) ) = addition( 
% 0.94/1.37    domain( X ), domain( Y ) ) }.
% 0.94/1.37  (3048) {G0,W8,D4,L1,V0,M1}  { ! multiplication( domain( skol1 ), domain( 
% 0.94/1.37    skol1 ) ) = domain( skol1 ) }.
% 0.94/1.37  
% 0.94/1.37  
% 0.94/1.37  Total Proof:
% 0.94/1.37  
% 0.94/1.37  subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 0.94/1.37     ) }.
% 0.94/1.37  parent0: (3030) {G0,W7,D3,L1,V2,M1}  { addition( X, Y ) = addition( Y, X )
% 0.94/1.37     }.
% 0.94/1.37  substitution0:
% 0.94/1.37     X := X
% 0.94/1.37     Y := Y
% 0.94/1.37  end
% 0.94/1.37  permutation0:
% 0.94/1.37     0 ==> 0
% 0.94/1.37  end
% 0.94/1.37  
% 0.94/1.37  subsumption: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.94/1.37  parent0: (3036) {G0,W5,D3,L1,V1,M1}  { multiplication( one, X ) = X }.
% 0.94/1.37  substitution0:
% 0.94/1.37     X := X
% 0.94/1.37  end
% 0.94/1.37  permutation0:
% 0.94/1.37     0 ==> 0
% 0.94/1.37  end
% 0.94/1.37  
% 0.94/1.37  eqswap: (3062) {G0,W13,D4,L1,V3,M1}  { addition( multiplication( X, Z ), 
% 0.94/1.37    multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 0.94/1.37  parent0[0]: (3038) {G0,W13,D4,L1,V3,M1}  { multiplication( addition( X, Y )
% 0.94/1.37    , Z ) = addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.94/1.37  substitution0:
% 0.94/1.37     X := X
% 0.94/1.37     Y := Y
% 0.94/1.37     Z := Z
% 0.94/1.37  end
% 0.94/1.37  
% 0.94/1.37  subsumption: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z )
% 0.94/1.37    , multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 0.94/1.37  parent0: (3062) {G0,W13,D4,L1,V3,M1}  { addition( multiplication( X, Z ), 
% 0.94/1.37    multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 0.94/1.37  substitution0:
% 0.94/1.37     X := X
% 0.94/1.37     Y := Y
% 0.94/1.37     Z := Z
% 0.94/1.37  end
% 0.94/1.37  permutation0:
% 0.94/1.37     0 ==> 0
% 0.94/1.37  end
% 0.94/1.37  
% 0.94/1.37  subsumption: (13) {G0,W11,D5,L1,V1,M1} I { addition( X, multiplication( 
% 0.94/1.37    domain( X ), X ) ) ==> multiplication( domain( X ), X ) }.
% 0.94/1.37  parent0: (3043) {G0,W11,D5,L1,V1,M1}  { addition( X, multiplication( domain
% 0.94/1.37    ( X ), X ) ) = multiplication( domain( X ), X ) }.
% 0.94/1.37  substitution0:
% 0.94/1.37     X := X
% 0.94/1.37  end
% 0.94/1.37  permutation0:
% 0.94/1.37     0 ==> 0
% 0.94/1.37  end
% 0.94/1.37  
% 0.94/1.37  eqswap: (3089) {G0,W10,D5,L1,V2,M1}  { domain( multiplication( X, domain( Y
% 0.94/1.37     ) ) ) = domain( multiplication( X, Y ) ) }.
% 0.94/1.37  parent0[0]: (3044) {G0,W10,D5,L1,V2,M1}  { domain( multiplication( X, Y ) )
% 0.94/1.37     = domain( multiplication( X, domain( Y ) ) ) }.
% 0.94/1.37  substitution0:
% 0.94/1.37     X := X
% 0.94/1.37     Y := Y
% 0.94/1.37  end
% 0.94/1.37  
% 0.94/1.37  subsumption: (14) {G0,W10,D5,L1,V2,M1} I { domain( multiplication( X, 
% 0.94/1.37    domain( Y ) ) ) ==> domain( multiplication( X, Y ) ) }.
% 0.94/1.37  parent0: (3089) {G0,W10,D5,L1,V2,M1}  { domain( multiplication( X, domain( 
% 0.94/1.37    Y ) ) ) = domain( multiplication( X, Y ) ) }.
% 0.94/1.37  substitution0:
% 0.94/1.37     X := X
% 0.94/1.37     Y := Y
% 0.94/1.37  end
% 0.94/1.37  permutation0:
% 0.94/1.37     0 ==> 0
% 0.94/1.37  end
% 0.94/1.37  
% 0.94/1.37  subsumption: (15) {G0,W6,D4,L1,V1,M1} I { addition( domain( X ), one ) ==> 
% 0.94/1.37    one }.
% 0.94/1.37  parent0: (3045) {G0,W6,D4,L1,V1,M1}  { addition( domain( X ), one ) = one
% 0.94/1.37     }.
% 0.94/1.37  substitution0:
% 0.94/1.37     X := X
% 0.94/1.37  end
% 0.94/1.37  permutation0:
% 0.94/1.37     0 ==> 0
% 0.94/1.37  end
% 0.94/1.37  
% 0.94/1.37  subsumption: (18) {G0,W8,D4,L1,V0,M1} I { ! multiplication( domain( skol1 )
% 0.94/1.37    , domain( skol1 ) ) ==> domain( skol1 ) }.
% 0.94/1.37  parent0: (3048) {G0,W8,D4,L1,V0,M1}  { ! multiplication( domain( skol1 ), 
% 0.94/1.37    domain( skol1 ) ) = domain( skol1 ) }.
% 0.94/1.37  substitution0:
% 0.94/1.37  end
% 0.94/1.37  permutation0:
% 0.94/1.37     0 ==> 0
% 0.94/1.37  end
% 0.94/1.37  
% 0.94/1.37  eqswap: (3123) {G0,W6,D4,L1,V1,M1}  { one ==> addition( domain( X ), one )
% 0.94/1.37     }.
% 0.94/1.37  parent0[0]: (15) {G0,W6,D4,L1,V1,M1} I { addition( domain( X ), one ) ==> 
% 0.94/1.37    one }.
% 0.94/1.37  substitution0:
% 0.94/1.37     X := X
% 0.94/1.37  end
% 0.94/1.37  
% 0.94/1.37  paramod: (3124) {G1,W6,D4,L1,V1,M1}  { one ==> addition( one, domain( X ) )
% 0.94/1.37     }.
% 0.94/1.37  parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.94/1.37     }.
% 0.94/1.37  parent1[0; 2]: (3123) {G0,W6,D4,L1,V1,M1}  { one ==> addition( domain( X )
% 0.94/1.37    , one ) }.
% 0.94/1.37  substitution0:
% 0.94/1.37     X := domain( X )
% 0.94/1.37     Y := one
% 0.94/1.37  end
% 0.94/1.37  substitution1:
% 0.94/1.37     X := X
% 0.94/1.37  end
% 0.94/1.37  
% 0.94/1.37  eqswap: (3127) {G1,W6,D4,L1,V1,M1}  { addition( one, domain( X ) ) ==> one
% 0.94/1.37     }.
% 0.94/1.37  parent0[0]: (3124) {G1,W6,D4,L1,V1,M1}  { one ==> addition( one, domain( X
% 0.94/1.37     ) ) }.
% 0.94/1.37  substitution0:
% 0.94/1.37     X := X
% 0.94/1.37  end
% 0.94/1.37  
% 0.94/1.37  subsumption: (20) {G1,W6,D4,L1,V1,M1} P(15,0) { addition( one, domain( X )
% 0.94/1.37     ) ==> one }.
% 0.94/1.37  parent0: (3127) {G1,W6,D4,L1,V1,M1}  { addition( one, domain( X ) ) ==> one
% 0.94/1.37     }.
% 0.94/1.37  substitution0:
% 0.94/1.37     X := X
% 0.94/1.37  end
% 0.94/1.37  permutation0:
% 0.94/1.37     0 ==> 0
% 0.94/1.37  end
% 0.94/1.37  
% 0.94/1.37  eqswap: (3129) {G0,W13,D4,L1,V3,M1}  { multiplication( addition( X, Z ), Y
% 0.94/1.37     ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) ) }.
% 0.94/1.37  parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ), 
% 0.94/1.37    multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 0.94/1.37  substitution0:
% 0.94/1.37     X := X
% 0.94/1.37     Y := Z
% 0.94/1.37     Z := Y
% 0.94/1.37  end
% 0.94/1.37  
% 0.94/1.37  paramod: (3130) {G1,W11,D4,L1,V2,M1}  { multiplication( addition( one, X )
% 0.94/1.37    , Y ) ==> addition( Y, multiplication( X, Y ) ) }.
% 0.94/1.37  parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.94/1.37  parent1[0; 7]: (3129) {G0,W13,D4,L1,V3,M1}  { multiplication( addition( X, 
% 0.94/1.37    Z ), Y ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) )
% 0.94/1.37     }.
% 0.94/1.37  substitution0:
% 0.94/1.37     X := Y
% 0.94/1.37  end
% 0.94/1.37  substitution1:
% 0.94/1.37     X := one
% 0.94/1.37     Y := Y
% 0.94/1.37     Z := X
% 0.94/1.37  end
% 0.94/1.37  
% 0.94/1.37  eqswap: (3132) {G1,W11,D4,L1,V2,M1}  { addition( Y, multiplication( X, Y )
% 0.94/1.37     ) ==> multiplication( addition( one, X ), Y ) }.
% 0.94/1.37  parent0[0]: (3130) {G1,W11,D4,L1,V2,M1}  { multiplication( addition( one, X
% 0.94/1.37     ), Y ) ==> addition( Y, multiplication( X, Y ) ) }.
% 0.94/1.37  substitution0:
% 0.94/1.37     X := X
% 0.94/1.37     Y := Y
% 0.94/1.37  end
% 0.94/1.37  
% 0.94/1.37  subsumption: (85) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( X, multiplication
% 0.94/1.37    ( Y, X ) ) = multiplication( addition( one, Y ), X ) }.
% 0.94/1.37  parent0: (3132) {G1,W11,D4,L1,V2,M1}  { addition( Y, multiplication( X, Y )
% 0.94/1.37     ) ==> multiplication( addition( one, X ), Y ) }.
% 0.94/1.37  substitution0:
% 0.94/1.37     X := Y
% 0.94/1.37     Y := X
% 0.94/1.37  end
% 0.94/1.37  permutation0:
% 0.94/1.37     0 ==> 0
% 0.94/1.37  end
% 0.94/1.37  
% 0.94/1.37  eqswap: (3135) {G0,W10,D5,L1,V2,M1}  { domain( multiplication( X, Y ) ) ==>
% 0.94/1.37     domain( multiplication( X, domain( Y ) ) ) }.
% 0.94/1.37  parent0[0]: (14) {G0,W10,D5,L1,V2,M1} I { domain( multiplication( X, domain
% 0.94/1.37    ( Y ) ) ) ==> domain( multiplication( X, Y ) ) }.
% 0.94/1.37  substitution0:
% 0.94/1.37     X := X
% 0.94/1.37     Y := Y
% 0.94/1.37  end
% 0.94/1.37  
% 0.94/1.37  paramod: (3138) {G1,W8,D4,L1,V1,M1}  { domain( multiplication( one, X ) ) 
% 0.94/1.37    ==> domain( domain( X ) ) }.
% 0.94/1.37  parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.94/1.37  parent1[0; 6]: (3135) {G0,W10,D5,L1,V2,M1}  { domain( multiplication( X, Y
% 0.94/1.37     ) ) ==> domain( multiplication( X, domain( Y ) ) ) }.
% 0.94/1.37  substitution0:
% 0.94/1.37     X := domain( X )
% 0.94/1.37  end
% 0.94/1.37  substitution1:
% 0.94/1.37     X := one
% 0.94/1.37     Y := X
% 0.94/1.37  end
% 0.94/1.37  
% 0.94/1.37  paramod: (3140) {G1,W6,D4,L1,V1,M1}  { domain( X ) ==> domain( domain( X )
% 0.94/1.37     ) }.
% 0.94/1.37  parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.94/1.37  parent1[0; 2]: (3138) {G1,W8,D4,L1,V1,M1}  { domain( multiplication( one, X
% 0.94/1.37     ) ) ==> domain( domain( X ) ) }.
% 0.94/1.37  substitution0:
% 0.94/1.37     X := X
% 0.94/1.37  end
% 0.94/1.37  substitution1:
% 0.94/1.37     X := X
% 0.94/1.37  end
% 0.94/1.37  
% 0.94/1.37  eqswap: (3141) {G1,W6,D4,L1,V1,M1}  { domain( domain( X ) ) ==> domain( X )
% 0.94/1.37     }.
% 0.94/1.37  parent0[0]: (3140) {G1,W6,D4,L1,V1,M1}  { domain( X ) ==> domain( domain( X
% 0.94/1.37     ) ) }.
% 0.94/1.37  substitution0:
% 0.94/1.37     X := X
% 0.94/1.37  end
% 0.94/1.37  
% 0.94/1.37  subsumption: (139) {G1,W6,D4,L1,V1,M1} P(6,14);d(6) { domain( domain( X ) )
% 0.94/1.37     ==> domain( X ) }.
% 0.94/1.37  parent0: (3141) {G1,W6,D4,L1,V1,M1}  { domain( domain( X ) ) ==> domain( X
% 0.94/1.37     ) }.
% 0.94/1.37  substitution0:
% 0.94/1.37     X := X
% 0.94/1.37  end
% 0.94/1.37  permutation0:
% 0.94/1.37     0 ==> 0
% 0.94/1.37  end
% 0.94/1.37  
% 0.94/1.37  eqswap: (3142) {G1,W11,D4,L1,V2,M1}  { multiplication( addition( one, Y ), 
% 0.94/1.37    X ) = addition( X, multiplication( Y, X ) ) }.
% 0.94/1.37  parent0[0]: (85) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( X, multiplication
% 0.94/1.37    ( Y, X ) ) = multiplication( addition( one, Y ), X ) }.
% 0.94/1.37  substitution0:
% 0.94/1.37     X := X
% 0.94/1.37     Y := Y
% 0.94/1.37  end
% 0.94/1.37  
% 0.94/1.37  paramod: (3147) {G1,W11,D5,L1,V1,M1}  { multiplication( addition( one, 
% 0.94/1.37    domain( X ) ), X ) = multiplication( domain( X ), X ) }.
% 0.94/1.37  parent0[0]: (13) {G0,W11,D5,L1,V1,M1} I { addition( X, multiplication( 
% 0.94/1.37    domain( X ), X ) ) ==> multiplication( domain( X ), X ) }.
% 0.94/1.37  parent1[0; 7]: (3142) {G1,W11,D4,L1,V2,M1}  { multiplication( addition( one
% 0.94/1.37    , Y ), X ) = addition( X, multiplication( Y, X ) ) }.
% 0.94/1.37  substitution0:
% 0.94/1.37     X := X
% 0.94/1.37  end
% 0.94/1.37  substitution1:
% 0.94/1.37     X := X
% 0.94/1.37     Y := domain( X )
% 0.94/1.37  end
% 0.94/1.37  
% 0.94/1.37  paramod: (3148) {G2,W8,D4,L1,V1,M1}  { multiplication( one, X ) = 
% 0.94/1.37    multiplication( domain( X ), X ) }.
% 0.94/1.37  parent0[0]: (20) {G1,W6,D4,L1,V1,M1} P(15,0) { addition( one, domain( X ) )
% 0.94/1.37     ==> one }.
% 0.94/1.37  parent1[0; 2]: (3147) {G1,W11,D5,L1,V1,M1}  { multiplication( addition( one
% 0.94/1.37    , domain( X ) ), X ) = multiplication( domain( X ), X ) }.
% 0.94/1.37  substitution0:
% 0.94/1.37     X := X
% 0.94/1.37  end
% 0.94/1.37  substitution1:
% 0.94/1.37     X := X
% 0.94/1.37  end
% 0.94/1.37  
% 0.94/1.37  paramod: (3149) {G1,W6,D4,L1,V1,M1}  { X = multiplication( domain( X ), X )
% 0.94/1.37     }.
% 0.94/1.37  parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.94/1.37  parent1[0; 1]: (3148) {G2,W8,D4,L1,V1,M1}  { multiplication( one, X ) = 
% 0.94/1.37    multiplication( domain( X ), X ) }.
% 0.94/1.37  substitution0:
% 0.94/1.37     X := X
% 0.94/1.37  end
% 0.94/1.37  substitution1:
% 0.94/1.37     X := X
% 0.94/1.37  end
% 0.94/1.37  
% 0.94/1.37  eqswap: (3150) {G1,W6,D4,L1,V1,M1}  { multiplication( domain( X ), X ) = X
% 0.94/1.37     }.
% 0.94/1.37  parent0[0]: (3149) {G1,W6,D4,L1,V1,M1}  { X = multiplication( domain( X ), 
% 0.94/1.37    X ) }.
% 0.94/1.37  substitution0:
% 0.94/1.37     X := X
% 0.94/1.37  end
% 0.94/1.37  
% 0.94/1.37  subsumption: (2688) {G2,W6,D4,L1,V1,M1} P(85,13);d(20);d(6) { 
% 0.94/1.37    multiplication( domain( X ), X ) ==> X }.
% 0.94/1.37  parent0: (3150) {G1,W6,D4,L1,V1,M1}  { multiplication( domain( X ), X ) = X
% 0.94/1.37     }.
% 0.94/1.37  substitution0:
% 0.94/1.37     X := X
% 0.94/1.37  end
% 0.94/1.37  permutation0:
% 0.94/1.37     0 ==> 0
% 0.94/1.37  end
% 0.94/1.37  
% 0.94/1.37  eqswap: (3152) {G2,W6,D4,L1,V1,M1}  { X ==> multiplication( domain( X ), X
% 0.94/1.37     ) }.
% 0.94/1.37  parent0[0]: (2688) {G2,W6,D4,L1,V1,M1} P(85,13);d(20);d(6) { multiplication
% 0.94/1.37    ( domain( X ), X ) ==> X }.
% 0.94/1.37  substitution0:
% 0.94/1.37     X := X
% 0.94/1.37  end
% 0.94/1.37  
% 0.94/1.37  paramod: (3153) {G2,W8,D4,L1,V1,M1}  { domain( X ) ==> multiplication( 
% 0.94/1.37    domain( X ), domain( X ) ) }.
% 0.94/1.37  parent0[0]: (139) {G1,W6,D4,L1,V1,M1} P(6,14);d(6) { domain( domain( X ) ) 
% 0.94/1.37    ==> domain( X ) }.
% 0.94/1.37  parent1[0; 4]: (3152) {G2,W6,D4,L1,V1,M1}  { X ==> multiplication( domain( 
% 0.94/1.37    X ), X ) }.
% 0.94/1.37  substitution0:
% 0.94/1.37     X := X
% 0.94/1.37  end
% 0.94/1.37  substitution1:
% 0.94/1.37     X := domain( X )
% 0.94/1.37  end
% 0.94/1.37  
% 0.94/1.37  eqswap: (3154) {G2,W8,D4,L1,V1,M1}  { multiplication( domain( X ), domain( 
% 0.94/1.37    X ) ) ==> domain( X ) }.
% 0.94/1.37  parent0[0]: (3153) {G2,W8,D4,L1,V1,M1}  { domain( X ) ==> multiplication( 
% 0.94/1.37    domain( X ), domain( X ) ) }.
% 0.94/1.37  substitution0:
% 0.94/1.37     X := X
% 0.94/1.37  end
% 0.94/1.37  
% 0.94/1.37  subsumption: (2708) {G3,W8,D4,L1,V1,M1} P(139,2688) { multiplication( 
% 0.94/1.37    domain( X ), domain( X ) ) ==> domain( X ) }.
% 0.94/1.37  parent0: (3154) {G2,W8,D4,L1,V1,M1}  { multiplication( domain( X ), domain
% 0.94/1.37    ( X ) ) ==> domain( X ) }.
% 0.94/1.37  substitution0:
% 0.94/1.37     X := X
% 0.94/1.37  end
% 0.94/1.37  permutation0:
% 0.94/1.37     0 ==> 0
% 0.94/1.37  end
% 0.94/1.37  
% 0.94/1.37  paramod: (3157) {G1,W5,D3,L1,V0,M1}  { ! domain( skol1 ) ==> domain( skol1
% 0.94/1.37     ) }.
% 0.94/1.37  parent0[0]: (2708) {G3,W8,D4,L1,V1,M1} P(139,2688) { multiplication( domain
% 0.94/1.37    ( X ), domain( X ) ) ==> domain( X ) }.
% 0.94/1.37  parent1[0; 2]: (18) {G0,W8,D4,L1,V0,M1} I { ! multiplication( domain( skol1
% 0.94/1.37     ), domain( skol1 ) ) ==> domain( skol1 ) }.
% 0.94/1.37  substitution0:
% 0.94/1.37     X := skol1
% 0.94/1.37  end
% 0.94/1.37  substitution1:
% 0.94/1.37  end
% 0.94/1.37  
% 0.94/1.37  eqrefl: (3158) {G0,W0,D0,L0,V0,M0}  {  }.
% 0.94/1.37  parent0[0]: (3157) {G1,W5,D3,L1,V0,M1}  { ! domain( skol1 ) ==> domain( 
% 0.94/1.37    skol1 ) }.
% 0.94/1.37  substitution0:
% 0.94/1.37  end
% 0.94/1.37  
% 0.94/1.37  subsumption: (3028) {G4,W0,D0,L0,V0,M0} S(18);d(2708);q {  }.
% 0.94/1.37  parent0: (3158) {G0,W0,D0,L0,V0,M0}  {  }.
% 0.94/1.37  substitution0:
% 0.94/1.37  end
% 0.94/1.37  permutation0:
% 0.94/1.37  end
% 0.94/1.37  
% 0.94/1.37  Proof check complete!
% 0.94/1.37  
% 0.94/1.37  Memory use:
% 0.94/1.37  
% 0.94/1.37  space for terms:        38800
% 0.94/1.37  space for clauses:      154571
% 0.94/1.37  
% 0.94/1.37  
% 0.94/1.37  clauses generated:      26522
% 0.94/1.37  clauses kept:           3029
% 0.94/1.37  clauses selected:       289
% 0.94/1.37  clauses deleted:        37
% 0.94/1.37  clauses inuse deleted:  17
% 0.94/1.37  
% 0.94/1.37  subsentry:          66165
% 0.94/1.37  literals s-matched: 44339
% 0.94/1.37  literals matched:   42196
% 0.94/1.37  full subsumption:   7995
% 0.94/1.37  
% 0.94/1.37  checksum:           -827825170
% 0.94/1.37  
% 0.94/1.37  
% 0.94/1.37  Bliksem ended
%------------------------------------------------------------------------------