TSTP Solution File: KLE021+1 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : KLE021+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n027.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 01:36:40 EDT 2022

% Result   : Theorem 0.44s 1.08s
% Output   : Refutation 0.44s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : KLE021+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12  % Command  : bliksem %s
% 0.12/0.33  % Computer : n027.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % DateTime : Thu Jun 16 15:26:50 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.44/1.08  *** allocated 10000 integers for termspace/termends
% 0.44/1.08  *** allocated 10000 integers for clauses
% 0.44/1.08  *** allocated 10000 integers for justifications
% 0.44/1.08  Bliksem 1.12
% 0.44/1.08  
% 0.44/1.08  
% 0.44/1.08  Automatic Strategy Selection
% 0.44/1.08  
% 0.44/1.08  
% 0.44/1.08  Clauses:
% 0.44/1.08  
% 0.44/1.08  { addition( X, Y ) = addition( Y, X ) }.
% 0.44/1.08  { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 0.44/1.08  { addition( X, zero ) = X }.
% 0.44/1.08  { addition( X, X ) = X }.
% 0.44/1.08  { multiplication( X, multiplication( Y, Z ) ) = multiplication( 
% 0.44/1.08    multiplication( X, Y ), Z ) }.
% 0.44/1.08  { multiplication( X, one ) = X }.
% 0.44/1.08  { multiplication( one, X ) = X }.
% 0.44/1.08  { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 0.44/1.08    , multiplication( X, Z ) ) }.
% 0.44/1.08  { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 0.44/1.08    , multiplication( Y, Z ) ) }.
% 0.44/1.08  { multiplication( X, zero ) = zero }.
% 0.44/1.08  { multiplication( zero, X ) = zero }.
% 0.44/1.08  { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.44/1.08  { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.44/1.08  { ! test( X ), complement( skol1( X ), X ) }.
% 0.44/1.08  { ! complement( Y, X ), test( X ) }.
% 0.44/1.08  { ! complement( Y, X ), multiplication( X, Y ) = zero }.
% 0.44/1.08  { ! complement( Y, X ), alpha1( X, Y ) }.
% 0.44/1.08  { ! multiplication( X, Y ) = zero, ! alpha1( X, Y ), complement( Y, X ) }.
% 0.44/1.08  { ! alpha1( X, Y ), multiplication( Y, X ) = zero }.
% 0.44/1.08  { ! alpha1( X, Y ), addition( X, Y ) = one }.
% 0.44/1.08  { ! multiplication( Y, X ) = zero, ! addition( X, Y ) = one, alpha1( X, Y )
% 0.44/1.08     }.
% 0.44/1.08  { ! test( X ), ! c( X ) = Y, complement( X, Y ) }.
% 0.44/1.08  { ! test( X ), ! complement( X, Y ), c( X ) = Y }.
% 0.44/1.08  { test( X ), c( X ) = zero }.
% 0.44/1.08  { test( skol2 ) }.
% 0.44/1.08  { ! skol3 = addition( multiplication( skol2, skol3 ), multiplication( c( 
% 0.44/1.08    skol2 ), skol3 ) ) }.
% 0.44/1.08  
% 0.44/1.08  percentage equality = 0.534884, percentage horn = 0.961538
% 0.44/1.08  This is a problem with some equality
% 0.44/1.08  
% 0.44/1.08  
% 0.44/1.08  
% 0.44/1.08  Options Used:
% 0.44/1.08  
% 0.44/1.08  useres =            1
% 0.44/1.08  useparamod =        1
% 0.44/1.08  useeqrefl =         1
% 0.44/1.08  useeqfact =         1
% 0.44/1.08  usefactor =         1
% 0.44/1.08  usesimpsplitting =  0
% 0.44/1.08  usesimpdemod =      5
% 0.44/1.08  usesimpres =        3
% 0.44/1.08  
% 0.44/1.08  resimpinuse      =  1000
% 0.44/1.08  resimpclauses =     20000
% 0.44/1.08  substype =          eqrewr
% 0.44/1.08  backwardsubs =      1
% 0.44/1.08  selectoldest =      5
% 0.44/1.08  
% 0.44/1.08  litorderings [0] =  split
% 0.44/1.08  litorderings [1] =  extend the termordering, first sorting on arguments
% 0.44/1.08  
% 0.44/1.08  termordering =      kbo
% 0.44/1.08  
% 0.44/1.08  litapriori =        0
% 0.44/1.08  termapriori =       1
% 0.44/1.08  litaposteriori =    0
% 0.44/1.08  termaposteriori =   0
% 0.44/1.08  demodaposteriori =  0
% 0.44/1.08  ordereqreflfact =   0
% 0.44/1.08  
% 0.44/1.08  litselect =         negord
% 0.44/1.08  
% 0.44/1.08  maxweight =         15
% 0.44/1.08  maxdepth =          30000
% 0.44/1.08  maxlength =         115
% 0.44/1.08  maxnrvars =         195
% 0.44/1.08  excuselevel =       1
% 0.44/1.08  increasemaxweight = 1
% 0.44/1.08  
% 0.44/1.08  maxselected =       10000000
% 0.44/1.08  maxnrclauses =      10000000
% 0.44/1.08  
% 0.44/1.08  showgenerated =    0
% 0.44/1.08  showkept =         0
% 0.44/1.08  showselected =     0
% 0.44/1.08  showdeleted =      0
% 0.44/1.08  showresimp =       1
% 0.44/1.08  showstatus =       2000
% 0.44/1.08  
% 0.44/1.08  prologoutput =     0
% 0.44/1.08  nrgoals =          5000000
% 0.44/1.08  totalproof =       1
% 0.44/1.08  
% 0.44/1.08  Symbols occurring in the translation:
% 0.44/1.08  
% 0.44/1.08  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 0.44/1.08  .  [1, 2]      (w:1, o:23, a:1, s:1, b:0), 
% 0.44/1.08  !  [4, 1]      (w:0, o:15, a:1, s:1, b:0), 
% 0.44/1.08  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.44/1.08  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.44/1.08  addition  [37, 2]      (w:1, o:47, a:1, s:1, b:0), 
% 0.44/1.08  zero  [39, 0]      (w:1, o:9, a:1, s:1, b:0), 
% 0.44/1.08  multiplication  [40, 2]      (w:1, o:49, a:1, s:1, b:0), 
% 0.44/1.08  one  [41, 0]      (w:1, o:10, a:1, s:1, b:0), 
% 0.44/1.08  leq  [42, 2]      (w:1, o:48, a:1, s:1, b:0), 
% 0.44/1.08  test  [44, 1]      (w:1, o:21, a:1, s:1, b:0), 
% 0.44/1.08  complement  [46, 2]      (w:1, o:50, a:1, s:1, b:0), 
% 0.44/1.08  c  [47, 1]      (w:1, o:22, a:1, s:1, b:0), 
% 0.44/1.08  alpha1  [48, 2]      (w:1, o:51, a:1, s:1, b:1), 
% 0.44/1.08  skol1  [49, 1]      (w:1, o:20, a:1, s:1, b:1), 
% 0.44/1.08  skol2  [50, 0]      (w:1, o:13, a:1, s:1, b:1), 
% 0.44/1.08  skol3  [51, 0]      (w:1, o:14, a:1, s:1, b:1).
% 0.44/1.08  
% 0.44/1.08  
% 0.44/1.08  Starting Search:
% 0.44/1.08  
% 0.44/1.08  *** allocated 15000 integers for clauses
% 0.44/1.08  *** allocated 22500 integers for clauses
% 0.44/1.08  *** allocated 33750 integers for clauses
% 0.44/1.08  
% 0.44/1.08  Bliksems!, er is een bewijs:
% 0.44/1.08  % SZS status Theorem
% 0.44/1.08  % SZS output start Refutation
% 0.44/1.08  
% 0.44/1.08  (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 0.44/1.08  (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.44/1.08  (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ), 
% 0.44/1.08    multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 0.44/1.08  (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X, Y ) }.
% 0.44/1.08  (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y ) ==> one }.
% 0.44/1.08  (21) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! c( X ) = Y, complement( X, Y )
% 0.44/1.08     }.
% 0.44/1.08  (24) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 0.44/1.08  (25) {G1,W8,D5,L1,V0,M1} I;d(8) { ! multiplication( addition( skol2, c( 
% 0.44/1.08    skol2 ) ), skol3 ) ==> skol3 }.
% 0.44/1.08  (26) {G1,W6,D3,L2,V1,M2} Q(21) { ! test( X ), complement( X, c( X ) ) }.
% 0.44/1.08  (36) {G2,W4,D3,L1,V0,M1} R(26,24) { complement( skol2, c( skol2 ) ) }.
% 0.44/1.08  (37) {G3,W4,D3,L1,V0,M1} R(36,16) { alpha1( c( skol2 ), skol2 ) }.
% 0.44/1.08  (267) {G4,W6,D4,L1,V0,M1} R(19,37) { addition( c( skol2 ), skol2 ) ==> one
% 0.44/1.08     }.
% 0.44/1.08  (451) {G5,W0,D0,L0,V0,M0} P(0,25);d(267);d(6);q {  }.
% 0.44/1.08  
% 0.44/1.08  
% 0.44/1.08  % SZS output end Refutation
% 0.44/1.08  found a proof!
% 0.44/1.08  
% 0.44/1.08  
% 0.44/1.08  Unprocessed initial clauses:
% 0.44/1.08  
% 0.44/1.08  (453) {G0,W7,D3,L1,V2,M1}  { addition( X, Y ) = addition( Y, X ) }.
% 0.44/1.08  (454) {G0,W11,D4,L1,V3,M1}  { addition( Z, addition( Y, X ) ) = addition( 
% 0.44/1.08    addition( Z, Y ), X ) }.
% 0.44/1.08  (455) {G0,W5,D3,L1,V1,M1}  { addition( X, zero ) = X }.
% 0.44/1.08  (456) {G0,W5,D3,L1,V1,M1}  { addition( X, X ) = X }.
% 0.44/1.08  (457) {G0,W11,D4,L1,V3,M1}  { multiplication( X, multiplication( Y, Z ) ) =
% 0.44/1.08     multiplication( multiplication( X, Y ), Z ) }.
% 0.44/1.08  (458) {G0,W5,D3,L1,V1,M1}  { multiplication( X, one ) = X }.
% 0.44/1.08  (459) {G0,W5,D3,L1,V1,M1}  { multiplication( one, X ) = X }.
% 0.44/1.08  (460) {G0,W13,D4,L1,V3,M1}  { multiplication( X, addition( Y, Z ) ) = 
% 0.44/1.08    addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.44/1.08  (461) {G0,W13,D4,L1,V3,M1}  { multiplication( addition( X, Y ), Z ) = 
% 0.44/1.08    addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.44/1.08  (462) {G0,W5,D3,L1,V1,M1}  { multiplication( X, zero ) = zero }.
% 0.44/1.08  (463) {G0,W5,D3,L1,V1,M1}  { multiplication( zero, X ) = zero }.
% 0.44/1.08  (464) {G0,W8,D3,L2,V2,M2}  { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.44/1.08  (465) {G0,W8,D3,L2,V2,M2}  { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.44/1.08  (466) {G0,W6,D3,L2,V1,M2}  { ! test( X ), complement( skol1( X ), X ) }.
% 0.44/1.08  (467) {G0,W5,D2,L2,V2,M2}  { ! complement( Y, X ), test( X ) }.
% 0.44/1.08  (468) {G0,W8,D3,L2,V2,M2}  { ! complement( Y, X ), multiplication( X, Y ) =
% 0.44/1.08     zero }.
% 0.44/1.08  (469) {G0,W6,D2,L2,V2,M2}  { ! complement( Y, X ), alpha1( X, Y ) }.
% 0.44/1.08  (470) {G0,W11,D3,L3,V2,M3}  { ! multiplication( X, Y ) = zero, ! alpha1( X
% 0.44/1.08    , Y ), complement( Y, X ) }.
% 0.44/1.08  (471) {G0,W8,D3,L2,V2,M2}  { ! alpha1( X, Y ), multiplication( Y, X ) = 
% 0.44/1.08    zero }.
% 0.44/1.08  (472) {G0,W8,D3,L2,V2,M2}  { ! alpha1( X, Y ), addition( X, Y ) = one }.
% 0.44/1.08  (473) {G0,W13,D3,L3,V2,M3}  { ! multiplication( Y, X ) = zero, ! addition( 
% 0.44/1.08    X, Y ) = one, alpha1( X, Y ) }.
% 0.44/1.08  (474) {G0,W9,D3,L3,V2,M3}  { ! test( X ), ! c( X ) = Y, complement( X, Y )
% 0.44/1.08     }.
% 0.44/1.08  (475) {G0,W9,D3,L3,V2,M3}  { ! test( X ), ! complement( X, Y ), c( X ) = Y
% 0.44/1.08     }.
% 0.44/1.08  (476) {G0,W6,D3,L2,V1,M2}  { test( X ), c( X ) = zero }.
% 0.44/1.08  (477) {G0,W2,D2,L1,V0,M1}  { test( skol2 ) }.
% 0.44/1.08  (478) {G0,W10,D5,L1,V0,M1}  { ! skol3 = addition( multiplication( skol2, 
% 0.44/1.08    skol3 ), multiplication( c( skol2 ), skol3 ) ) }.
% 0.44/1.08  
% 0.44/1.08  
% 0.44/1.08  Total Proof:
% 0.44/1.08  
% 0.44/1.08  subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 0.44/1.08     ) }.
% 0.44/1.08  parent0: (453) {G0,W7,D3,L1,V2,M1}  { addition( X, Y ) = addition( Y, X )
% 0.44/1.08     }.
% 0.44/1.08  substitution0:
% 0.44/1.08     X := X
% 0.44/1.08     Y := Y
% 0.44/1.08  end
% 0.44/1.08  permutation0:
% 0.44/1.08     0 ==> 0
% 0.44/1.08  end
% 0.44/1.08  
% 0.44/1.08  subsumption: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.44/1.08  parent0: (459) {G0,W5,D3,L1,V1,M1}  { multiplication( one, X ) = X }.
% 0.44/1.08  substitution0:
% 0.44/1.08     X := X
% 0.44/1.08  end
% 0.44/1.08  permutation0:
% 0.44/1.08     0 ==> 0
% 0.44/1.08  end
% 0.44/1.08  
% 0.44/1.08  eqswap: (492) {G0,W13,D4,L1,V3,M1}  { addition( multiplication( X, Z ), 
% 0.44/1.08    multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 0.44/1.08  parent0[0]: (461) {G0,W13,D4,L1,V3,M1}  { multiplication( addition( X, Y )
% 0.44/1.08    , Z ) = addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.44/1.08  substitution0:
% 0.44/1.08     X := X
% 0.44/1.08     Y := Y
% 0.44/1.08     Z := Z
% 0.44/1.08  end
% 0.44/1.08  
% 0.44/1.08  subsumption: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z )
% 0.44/1.08    , multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 0.44/1.08  parent0: (492) {G0,W13,D4,L1,V3,M1}  { addition( multiplication( X, Z ), 
% 0.44/1.08    multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 0.44/1.08  substitution0:
% 0.44/1.08     X := X
% 0.44/1.08     Y := Y
% 0.44/1.08     Z := Z
% 0.44/1.08  end
% 0.44/1.08  permutation0:
% 0.44/1.08     0 ==> 0
% 0.44/1.08  end
% 0.44/1.08  
% 0.44/1.08  subsumption: (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X, 
% 0.72/1.08    Y ) }.
% 0.72/1.08  parent0: (469) {G0,W6,D2,L2,V2,M2}  { ! complement( Y, X ), alpha1( X, Y )
% 0.72/1.08     }.
% 0.72/1.08  substitution0:
% 0.72/1.08     X := X
% 0.72/1.08     Y := Y
% 0.72/1.08  end
% 0.72/1.08  permutation0:
% 0.72/1.08     0 ==> 0
% 0.72/1.08     1 ==> 1
% 0.72/1.08  end
% 0.72/1.08  
% 0.72/1.08  subsumption: (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y
% 0.72/1.08     ) ==> one }.
% 0.72/1.08  parent0: (472) {G0,W8,D3,L2,V2,M2}  { ! alpha1( X, Y ), addition( X, Y ) = 
% 0.72/1.08    one }.
% 0.72/1.08  substitution0:
% 0.72/1.08     X := X
% 0.72/1.08     Y := Y
% 0.72/1.08  end
% 0.72/1.08  permutation0:
% 0.72/1.08     0 ==> 0
% 0.72/1.08     1 ==> 1
% 0.72/1.08  end
% 0.72/1.08  
% 0.72/1.08  subsumption: (21) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! c( X ) = Y, 
% 0.72/1.08    complement( X, Y ) }.
% 0.72/1.08  parent0: (474) {G0,W9,D3,L3,V2,M3}  { ! test( X ), ! c( X ) = Y, complement
% 0.72/1.08    ( X, Y ) }.
% 0.72/1.08  substitution0:
% 0.72/1.08     X := X
% 0.72/1.08     Y := Y
% 0.72/1.08  end
% 0.72/1.08  permutation0:
% 0.72/1.08     0 ==> 0
% 0.72/1.08     1 ==> 1
% 0.72/1.08     2 ==> 2
% 0.72/1.08  end
% 0.72/1.08  
% 0.72/1.08  subsumption: (24) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 0.72/1.08  parent0: (477) {G0,W2,D2,L1,V0,M1}  { test( skol2 ) }.
% 0.72/1.08  substitution0:
% 0.72/1.08  end
% 0.72/1.08  permutation0:
% 0.72/1.08     0 ==> 0
% 0.72/1.08  end
% 0.72/1.08  
% 0.72/1.08  paramod: (615) {G1,W8,D5,L1,V0,M1}  { ! skol3 = multiplication( addition( 
% 0.72/1.08    skol2, c( skol2 ) ), skol3 ) }.
% 0.72/1.08  parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ), 
% 0.72/1.08    multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 0.72/1.08  parent1[0; 3]: (478) {G0,W10,D5,L1,V0,M1}  { ! skol3 = addition( 
% 0.72/1.08    multiplication( skol2, skol3 ), multiplication( c( skol2 ), skol3 ) ) }.
% 0.72/1.08  substitution0:
% 0.72/1.08     X := skol2
% 0.72/1.08     Y := c( skol2 )
% 0.72/1.08     Z := skol3
% 0.72/1.08  end
% 0.72/1.08  substitution1:
% 0.72/1.08  end
% 0.72/1.08  
% 0.72/1.08  eqswap: (616) {G1,W8,D5,L1,V0,M1}  { ! multiplication( addition( skol2, c( 
% 0.72/1.08    skol2 ) ), skol3 ) = skol3 }.
% 0.72/1.08  parent0[0]: (615) {G1,W8,D5,L1,V0,M1}  { ! skol3 = multiplication( addition
% 0.72/1.08    ( skol2, c( skol2 ) ), skol3 ) }.
% 0.72/1.08  substitution0:
% 0.72/1.08  end
% 0.72/1.08  
% 0.72/1.08  subsumption: (25) {G1,W8,D5,L1,V0,M1} I;d(8) { ! multiplication( addition( 
% 0.72/1.08    skol2, c( skol2 ) ), skol3 ) ==> skol3 }.
% 0.72/1.08  parent0: (616) {G1,W8,D5,L1,V0,M1}  { ! multiplication( addition( skol2, c
% 0.72/1.08    ( skol2 ) ), skol3 ) = skol3 }.
% 0.72/1.08  substitution0:
% 0.72/1.08  end
% 0.72/1.08  permutation0:
% 0.72/1.08     0 ==> 0
% 0.72/1.08  end
% 0.72/1.08  
% 0.72/1.08  eqswap: (617) {G0,W9,D3,L3,V2,M3}  { ! Y = c( X ), ! test( X ), complement
% 0.72/1.08    ( X, Y ) }.
% 0.72/1.08  parent0[1]: (21) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! c( X ) = Y, 
% 0.72/1.08    complement( X, Y ) }.
% 0.72/1.08  substitution0:
% 0.72/1.08     X := X
% 0.72/1.08     Y := Y
% 0.72/1.08  end
% 0.72/1.08  
% 0.72/1.08  eqrefl: (618) {G0,W6,D3,L2,V1,M2}  { ! test( X ), complement( X, c( X ) )
% 0.72/1.08     }.
% 0.72/1.08  parent0[0]: (617) {G0,W9,D3,L3,V2,M3}  { ! Y = c( X ), ! test( X ), 
% 0.72/1.08    complement( X, Y ) }.
% 0.72/1.08  substitution0:
% 0.72/1.08     X := X
% 0.72/1.08     Y := c( X )
% 0.72/1.08  end
% 0.72/1.08  
% 0.72/1.08  subsumption: (26) {G1,W6,D3,L2,V1,M2} Q(21) { ! test( X ), complement( X, c
% 0.72/1.08    ( X ) ) }.
% 0.72/1.08  parent0: (618) {G0,W6,D3,L2,V1,M2}  { ! test( X ), complement( X, c( X ) )
% 0.72/1.08     }.
% 0.72/1.08  substitution0:
% 0.72/1.08     X := X
% 0.72/1.08  end
% 0.72/1.08  permutation0:
% 0.72/1.08     0 ==> 0
% 0.72/1.08     1 ==> 1
% 0.72/1.08  end
% 0.72/1.08  
% 0.72/1.08  resolution: (619) {G1,W4,D3,L1,V0,M1}  { complement( skol2, c( skol2 ) )
% 0.72/1.08     }.
% 0.72/1.08  parent0[0]: (26) {G1,W6,D3,L2,V1,M2} Q(21) { ! test( X ), complement( X, c
% 0.72/1.08    ( X ) ) }.
% 0.72/1.08  parent1[0]: (24) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 0.72/1.08  substitution0:
% 0.72/1.08     X := skol2
% 0.72/1.08  end
% 0.72/1.08  substitution1:
% 0.72/1.08  end
% 0.72/1.08  
% 0.72/1.08  subsumption: (36) {G2,W4,D3,L1,V0,M1} R(26,24) { complement( skol2, c( 
% 0.72/1.08    skol2 ) ) }.
% 0.72/1.08  parent0: (619) {G1,W4,D3,L1,V0,M1}  { complement( skol2, c( skol2 ) ) }.
% 0.72/1.08  substitution0:
% 0.72/1.08  end
% 0.72/1.08  permutation0:
% 0.72/1.08     0 ==> 0
% 0.72/1.08  end
% 0.72/1.08  
% 0.72/1.08  resolution: (620) {G1,W4,D3,L1,V0,M1}  { alpha1( c( skol2 ), skol2 ) }.
% 0.72/1.08  parent0[0]: (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X, Y
% 0.72/1.08     ) }.
% 0.72/1.08  parent1[0]: (36) {G2,W4,D3,L1,V0,M1} R(26,24) { complement( skol2, c( skol2
% 0.72/1.08     ) ) }.
% 0.72/1.08  substitution0:
% 0.72/1.08     X := c( skol2 )
% 0.72/1.08     Y := skol2
% 0.72/1.08  end
% 0.72/1.08  substitution1:
% 0.72/1.08  end
% 0.72/1.08  
% 0.72/1.08  subsumption: (37) {G3,W4,D3,L1,V0,M1} R(36,16) { alpha1( c( skol2 ), skol2
% 0.72/1.08     ) }.
% 0.72/1.08  parent0: (620) {G1,W4,D3,L1,V0,M1}  { alpha1( c( skol2 ), skol2 ) }.
% 0.72/1.08  substitution0:
% 0.72/1.08  end
% 0.72/1.08  permutation0:
% 0.72/1.08     0 ==> 0
% 0.72/1.08  end
% 0.72/1.08  
% 0.72/1.08  eqswap: (621) {G0,W8,D3,L2,V2,M2}  { one ==> addition( X, Y ), ! alpha1( X
% 0.72/1.08    , Y ) }.
% 0.72/1.08  parent0[1]: (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y )
% 0.72/1.08     ==> one }.
% 0.72/1.08  substitution0:
% 0.72/1.08     X := X
% 0.72/1.08     Y := Y
% 0.72/1.08  end
% 0.72/1.08  
% 0.72/1.08  resolution: (622) {G1,W6,D4,L1,V0,M1}  { one ==> addition( c( skol2 ), 
% 0.72/1.08    skol2 ) }.
% 0.72/1.08  parent0[1]: (621) {G0,W8,D3,L2,V2,M2}  { one ==> addition( X, Y ), ! alpha1
% 0.72/1.08    ( X, Y ) }.
% 0.72/1.08  parent1[0]: (37) {G3,W4,D3,L1,V0,M1} R(36,16) { alpha1( c( skol2 ), skol2 )
% 0.72/1.08     }.
% 0.72/1.08  substitution0:
% 0.72/1.08     X := c( skol2 )
% 0.72/1.08     Y := skol2
% 0.72/1.08  end
% 0.72/1.08  substitution1:
% 0.72/1.08  end
% 0.72/1.08  
% 0.72/1.08  eqswap: (623) {G1,W6,D4,L1,V0,M1}  { addition( c( skol2 ), skol2 ) ==> one
% 0.72/1.08     }.
% 0.72/1.08  parent0[0]: (622) {G1,W6,D4,L1,V0,M1}  { one ==> addition( c( skol2 ), 
% 0.72/1.08    skol2 ) }.
% 0.72/1.08  substitution0:
% 0.72/1.08  end
% 0.72/1.08  
% 0.72/1.08  subsumption: (267) {G4,W6,D4,L1,V0,M1} R(19,37) { addition( c( skol2 ), 
% 0.72/1.08    skol2 ) ==> one }.
% 0.72/1.08  parent0: (623) {G1,W6,D4,L1,V0,M1}  { addition( c( skol2 ), skol2 ) ==> one
% 0.72/1.08     }.
% 0.72/1.08  substitution0:
% 0.72/1.08  end
% 0.72/1.08  permutation0:
% 0.72/1.08     0 ==> 0
% 0.72/1.08  end
% 0.72/1.08  
% 0.72/1.08  eqswap: (624) {G1,W8,D5,L1,V0,M1}  { ! skol3 ==> multiplication( addition( 
% 0.72/1.08    skol2, c( skol2 ) ), skol3 ) }.
% 0.72/1.08  parent0[0]: (25) {G1,W8,D5,L1,V0,M1} I;d(8) { ! multiplication( addition( 
% 0.72/1.08    skol2, c( skol2 ) ), skol3 ) ==> skol3 }.
% 0.72/1.08  substitution0:
% 0.72/1.08  end
% 0.72/1.08  
% 0.72/1.08  paramod: (627) {G1,W8,D5,L1,V0,M1}  { ! skol3 ==> multiplication( addition
% 0.72/1.08    ( c( skol2 ), skol2 ), skol3 ) }.
% 0.72/1.08  parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.72/1.08     }.
% 0.72/1.08  parent1[0; 4]: (624) {G1,W8,D5,L1,V0,M1}  { ! skol3 ==> multiplication( 
% 0.72/1.08    addition( skol2, c( skol2 ) ), skol3 ) }.
% 0.72/1.08  substitution0:
% 0.72/1.08     X := skol2
% 0.72/1.08     Y := c( skol2 )
% 0.72/1.08  end
% 0.72/1.08  substitution1:
% 0.72/1.08  end
% 0.72/1.08  
% 0.72/1.08  paramod: (629) {G2,W5,D3,L1,V0,M1}  { ! skol3 ==> multiplication( one, 
% 0.72/1.08    skol3 ) }.
% 0.72/1.08  parent0[0]: (267) {G4,W6,D4,L1,V0,M1} R(19,37) { addition( c( skol2 ), 
% 0.72/1.08    skol2 ) ==> one }.
% 0.72/1.08  parent1[0; 4]: (627) {G1,W8,D5,L1,V0,M1}  { ! skol3 ==> multiplication( 
% 0.72/1.08    addition( c( skol2 ), skol2 ), skol3 ) }.
% 0.72/1.08  substitution0:
% 0.72/1.08  end
% 0.72/1.08  substitution1:
% 0.72/1.08  end
% 0.72/1.08  
% 0.72/1.08  paramod: (630) {G1,W3,D2,L1,V0,M1}  { ! skol3 ==> skol3 }.
% 0.72/1.08  parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.72/1.08  parent1[0; 3]: (629) {G2,W5,D3,L1,V0,M1}  { ! skol3 ==> multiplication( one
% 0.72/1.08    , skol3 ) }.
% 0.72/1.08  substitution0:
% 0.72/1.08     X := skol3
% 0.72/1.08  end
% 0.72/1.08  substitution1:
% 0.72/1.08  end
% 0.72/1.08  
% 0.72/1.08  eqrefl: (631) {G0,W0,D0,L0,V0,M0}  {  }.
% 0.72/1.08  parent0[0]: (630) {G1,W3,D2,L1,V0,M1}  { ! skol3 ==> skol3 }.
% 0.72/1.08  substitution0:
% 0.72/1.08  end
% 0.72/1.08  
% 0.72/1.08  subsumption: (451) {G5,W0,D0,L0,V0,M0} P(0,25);d(267);d(6);q {  }.
% 0.72/1.08  parent0: (631) {G0,W0,D0,L0,V0,M0}  {  }.
% 0.72/1.08  substitution0:
% 0.72/1.08  end
% 0.72/1.08  permutation0:
% 0.72/1.08  end
% 0.72/1.08  
% 0.72/1.08  Proof check complete!
% 0.72/1.08  
% 0.72/1.08  Memory use:
% 0.72/1.08  
% 0.72/1.08  space for terms:        5009
% 0.72/1.08  space for clauses:      25933
% 0.72/1.08  
% 0.72/1.08  
% 0.72/1.08  clauses generated:      1618
% 0.72/1.08  clauses kept:           452
% 0.72/1.08  clauses selected:       76
% 0.72/1.08  clauses deleted:        0
% 0.72/1.08  clauses inuse deleted:  0
% 0.72/1.08  
% 0.72/1.08  subsentry:          2592
% 0.72/1.08  literals s-matched: 1628
% 0.72/1.08  literals matched:   1628
% 0.72/1.08  full subsumption:   90
% 0.72/1.08  
% 0.72/1.08  checksum:           1942018401
% 0.72/1.08  
% 0.72/1.08  
% 0.72/1.08  Bliksem ended
%------------------------------------------------------------------------------