TSTP Solution File: KLE007+1 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : KLE007+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n009.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 01:36:32 EDT 2022

% Result   : Theorem 0.87s 1.25s
% Output   : Refutation 0.87s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : KLE007+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12  % Command  : bliksem %s
% 0.12/0.33  % Computer : n009.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 09:09:08 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.87/1.25  *** allocated 10000 integers for termspace/termends
% 0.87/1.25  *** allocated 10000 integers for clauses
% 0.87/1.25  *** allocated 10000 integers for justifications
% 0.87/1.25  Bliksem 1.12
% 0.87/1.25  
% 0.87/1.25  
% 0.87/1.25  Automatic Strategy Selection
% 0.87/1.25  
% 0.87/1.25  
% 0.87/1.25  Clauses:
% 0.87/1.25  
% 0.87/1.25  { addition( X, Y ) = addition( Y, X ) }.
% 0.87/1.25  { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 0.87/1.25  { addition( X, zero ) = X }.
% 0.87/1.25  { addition( X, X ) = X }.
% 0.87/1.25  { multiplication( X, multiplication( Y, Z ) ) = multiplication( 
% 0.87/1.25    multiplication( X, Y ), Z ) }.
% 0.87/1.25  { multiplication( X, one ) = X }.
% 0.87/1.25  { multiplication( one, X ) = X }.
% 0.87/1.25  { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 0.87/1.25    , multiplication( X, Z ) ) }.
% 0.87/1.25  { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 0.87/1.25    , multiplication( Y, Z ) ) }.
% 0.87/1.25  { multiplication( X, zero ) = zero }.
% 0.87/1.25  { multiplication( zero, X ) = zero }.
% 0.87/1.25  { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.87/1.25  { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.87/1.25  { ! test( X ), complement( skol1( X ), X ) }.
% 0.87/1.25  { ! complement( Y, X ), test( X ) }.
% 0.87/1.25  { ! complement( Y, X ), multiplication( X, Y ) = zero }.
% 0.87/1.25  { ! complement( Y, X ), alpha1( X, Y ) }.
% 0.87/1.25  { ! multiplication( X, Y ) = zero, ! alpha1( X, Y ), complement( Y, X ) }.
% 0.87/1.25  { ! alpha1( X, Y ), multiplication( Y, X ) = zero }.
% 0.87/1.25  { ! alpha1( X, Y ), addition( X, Y ) = one }.
% 0.87/1.25  { ! multiplication( Y, X ) = zero, ! addition( X, Y ) = one, alpha1( X, Y )
% 0.87/1.25     }.
% 0.87/1.25  { ! test( X ), ! c( X ) = Y, complement( X, Y ) }.
% 0.87/1.25  { ! test( X ), ! complement( X, Y ), c( X ) = Y }.
% 0.87/1.25  { test( X ), c( X ) = zero }.
% 0.87/1.25  { test( skol3 ) }.
% 0.87/1.25  { test( skol2 ) }.
% 0.87/1.25  { ! one = addition( multiplication( addition( skol2, c( skol2 ) ), skol3 )
% 0.87/1.25    , multiplication( addition( skol2, c( skol2 ) ), c( skol3 ) ) ) }.
% 0.87/1.25  
% 0.87/1.25  percentage equality = 0.522727, percentage horn = 0.962963
% 0.87/1.25  This is a problem with some equality
% 0.87/1.25  
% 0.87/1.25  
% 0.87/1.25  
% 0.87/1.25  Options Used:
% 0.87/1.25  
% 0.87/1.25  useres =            1
% 0.87/1.25  useparamod =        1
% 0.87/1.25  useeqrefl =         1
% 0.87/1.25  useeqfact =         1
% 0.87/1.25  usefactor =         1
% 0.87/1.25  usesimpsplitting =  0
% 0.87/1.25  usesimpdemod =      5
% 0.87/1.25  usesimpres =        3
% 0.87/1.25  
% 0.87/1.25  resimpinuse      =  1000
% 0.87/1.25  resimpclauses =     20000
% 0.87/1.25  substype =          eqrewr
% 0.87/1.25  backwardsubs =      1
% 0.87/1.25  selectoldest =      5
% 0.87/1.25  
% 0.87/1.25  litorderings [0] =  split
% 0.87/1.25  litorderings [1] =  extend the termordering, first sorting on arguments
% 0.87/1.25  
% 0.87/1.25  termordering =      kbo
% 0.87/1.25  
% 0.87/1.25  litapriori =        0
% 0.87/1.25  termapriori =       1
% 0.87/1.25  litaposteriori =    0
% 0.87/1.25  termaposteriori =   0
% 0.87/1.25  demodaposteriori =  0
% 0.87/1.25  ordereqreflfact =   0
% 0.87/1.25  
% 0.87/1.25  litselect =         negord
% 0.87/1.25  
% 0.87/1.25  maxweight =         15
% 0.87/1.25  maxdepth =          30000
% 0.87/1.25  maxlength =         115
% 0.87/1.25  maxnrvars =         195
% 0.87/1.25  excuselevel =       1
% 0.87/1.25  increasemaxweight = 1
% 0.87/1.25  
% 0.87/1.25  maxselected =       10000000
% 0.87/1.25  maxnrclauses =      10000000
% 0.87/1.25  
% 0.87/1.25  showgenerated =    0
% 0.87/1.25  showkept =         0
% 0.87/1.25  showselected =     0
% 0.87/1.25  showdeleted =      0
% 0.87/1.25  showresimp =       1
% 0.87/1.25  showstatus =       2000
% 0.87/1.25  
% 0.87/1.25  prologoutput =     0
% 0.87/1.25  nrgoals =          5000000
% 0.87/1.25  totalproof =       1
% 0.87/1.25  
% 0.87/1.25  Symbols occurring in the translation:
% 0.87/1.25  
% 0.87/1.25  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 0.87/1.25  .  [1, 2]      (w:1, o:23, a:1, s:1, b:0), 
% 0.87/1.25  !  [4, 1]      (w:0, o:15, a:1, s:1, b:0), 
% 0.87/1.25  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.87/1.25  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.87/1.25  addition  [37, 2]      (w:1, o:47, a:1, s:1, b:0), 
% 0.87/1.25  zero  [39, 0]      (w:1, o:9, a:1, s:1, b:0), 
% 0.87/1.25  multiplication  [40, 2]      (w:1, o:49, a:1, s:1, b:0), 
% 0.87/1.25  one  [41, 0]      (w:1, o:10, a:1, s:1, b:0), 
% 0.87/1.25  leq  [42, 2]      (w:1, o:48, a:1, s:1, b:0), 
% 0.87/1.25  test  [44, 1]      (w:1, o:21, a:1, s:1, b:0), 
% 0.87/1.25  complement  [46, 2]      (w:1, o:50, a:1, s:1, b:0), 
% 0.87/1.25  c  [47, 1]      (w:1, o:22, a:1, s:1, b:0), 
% 0.87/1.25  alpha1  [48, 2]      (w:1, o:51, a:1, s:1, b:1), 
% 0.87/1.25  skol1  [49, 1]      (w:1, o:20, a:1, s:1, b:1), 
% 0.87/1.25  skol2  [50, 0]      (w:1, o:13, a:1, s:1, b:1), 
% 0.87/1.25  skol3  [51, 0]      (w:1, o:14, a:1, s:1, b:1).
% 0.87/1.25  
% 0.87/1.25  
% 0.87/1.25  Starting Search:
% 0.87/1.25  
% 0.87/1.25  *** allocated 15000 integers for clauses
% 0.87/1.25  *** allocated 22500 integers for clauses
% 0.87/1.25  *** allocated 33750 integers for clauses
% 0.87/1.25  *** allocated 50625 integers for clauses
% 0.87/1.25  *** allocated 15000 integers for termspace/termends
% 0.87/1.25  *** allocated 75937 integers for clauses
% 0.87/1.25  Resimplifying inuse:
% 0.87/1.25  Done
% 0.87/1.25  
% 0.87/1.25  *** allocated 22500 integers for termspace/termends
% 0.87/1.25  *** allocated 113905 integers for clauses
% 0.87/1.25  *** allocated 33750 integers for termspace/termends
% 0.87/1.25  
% 0.87/1.25  Intermediate Status:
% 0.87/1.25  Generated:    13715
% 0.87/1.25  Kept:         2003
% 0.87/1.25  Inuse:        229
% 0.87/1.25  Deleted:      52
% 0.87/1.25  Deletedinuse: 22
% 0.87/1.25  
% 0.87/1.25  Resimplifying inuse:
% 0.87/1.25  Done
% 0.87/1.25  
% 0.87/1.25  *** allocated 170857 integers for clauses
% 0.87/1.25  
% 0.87/1.25  Bliksems!, er is een bewijs:
% 0.87/1.25  % SZS status Theorem
% 0.87/1.25  % SZS output start Refutation
% 0.87/1.25  
% 0.87/1.25  (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 0.87/1.25  (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.87/1.25  (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ), 
% 0.87/1.25    multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.87/1.25  (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X, Y ) }.
% 0.87/1.25  (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y ) ==> one }.
% 0.87/1.25  (21) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! c( X ) = Y, complement( X, Y )
% 0.87/1.25     }.
% 0.87/1.25  (24) {G0,W2,D2,L1,V0,M1} I { test( skol3 ) }.
% 0.87/1.25  (25) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 0.87/1.25  (26) {G1,W11,D5,L1,V0,M1} I;d(7) { ! multiplication( addition( skol2, c( 
% 0.87/1.25    skol2 ) ), addition( skol3, c( skol3 ) ) ) ==> one }.
% 0.87/1.25  (27) {G1,W6,D3,L2,V1,M2} Q(21) { ! test( X ), complement( X, c( X ) ) }.
% 0.87/1.25  (37) {G2,W4,D3,L1,V0,M1} R(27,24) { complement( skol3, c( skol3 ) ) }.
% 0.87/1.25  (38) {G2,W4,D3,L1,V0,M1} R(27,25) { complement( skol2, c( skol2 ) ) }.
% 0.87/1.25  (39) {G3,W4,D3,L1,V0,M1} R(37,16) { alpha1( c( skol3 ), skol3 ) }.
% 0.87/1.25  (42) {G3,W4,D3,L1,V0,M1} R(38,16) { alpha1( c( skol2 ), skol2 ) }.
% 0.87/1.25  (261) {G4,W6,D4,L1,V0,M1} R(19,42) { addition( c( skol2 ), skol2 ) ==> one
% 0.87/1.25     }.
% 0.87/1.25  (262) {G4,W6,D4,L1,V0,M1} R(19,39) { addition( c( skol3 ), skol3 ) ==> one
% 0.87/1.25     }.
% 0.87/1.25  (446) {G5,W6,D4,L1,V0,M1} P(0,26);d(261);d(6) { ! addition( skol3, c( skol3
% 0.87/1.25     ) ) ==> one }.
% 0.87/1.25  (2218) {G6,W0,D0,L0,V0,M0} P(0,446);d(262);q {  }.
% 0.87/1.25  
% 0.87/1.25  
% 0.87/1.25  % SZS output end Refutation
% 0.87/1.25  found a proof!
% 0.87/1.25  
% 0.87/1.25  
% 0.87/1.25  Unprocessed initial clauses:
% 0.87/1.25  
% 0.87/1.25  (2220) {G0,W7,D3,L1,V2,M1}  { addition( X, Y ) = addition( Y, X ) }.
% 0.87/1.25  (2221) {G0,W11,D4,L1,V3,M1}  { addition( Z, addition( Y, X ) ) = addition( 
% 0.87/1.25    addition( Z, Y ), X ) }.
% 0.87/1.25  (2222) {G0,W5,D3,L1,V1,M1}  { addition( X, zero ) = X }.
% 0.87/1.25  (2223) {G0,W5,D3,L1,V1,M1}  { addition( X, X ) = X }.
% 0.87/1.25  (2224) {G0,W11,D4,L1,V3,M1}  { multiplication( X, multiplication( Y, Z ) ) 
% 0.87/1.25    = multiplication( multiplication( X, Y ), Z ) }.
% 0.87/1.25  (2225) {G0,W5,D3,L1,V1,M1}  { multiplication( X, one ) = X }.
% 0.87/1.25  (2226) {G0,W5,D3,L1,V1,M1}  { multiplication( one, X ) = X }.
% 0.87/1.25  (2227) {G0,W13,D4,L1,V3,M1}  { multiplication( X, addition( Y, Z ) ) = 
% 0.87/1.25    addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.87/1.25  (2228) {G0,W13,D4,L1,V3,M1}  { multiplication( addition( X, Y ), Z ) = 
% 0.87/1.25    addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 0.87/1.25  (2229) {G0,W5,D3,L1,V1,M1}  { multiplication( X, zero ) = zero }.
% 0.87/1.25  (2230) {G0,W5,D3,L1,V1,M1}  { multiplication( zero, X ) = zero }.
% 0.87/1.25  (2231) {G0,W8,D3,L2,V2,M2}  { ! leq( X, Y ), addition( X, Y ) = Y }.
% 0.87/1.25  (2232) {G0,W8,D3,L2,V2,M2}  { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 0.87/1.25  (2233) {G0,W6,D3,L2,V1,M2}  { ! test( X ), complement( skol1( X ), X ) }.
% 0.87/1.25  (2234) {G0,W5,D2,L2,V2,M2}  { ! complement( Y, X ), test( X ) }.
% 0.87/1.25  (2235) {G0,W8,D3,L2,V2,M2}  { ! complement( Y, X ), multiplication( X, Y ) 
% 0.87/1.25    = zero }.
% 0.87/1.25  (2236) {G0,W6,D2,L2,V2,M2}  { ! complement( Y, X ), alpha1( X, Y ) }.
% 0.87/1.25  (2237) {G0,W11,D3,L3,V2,M3}  { ! multiplication( X, Y ) = zero, ! alpha1( X
% 0.87/1.25    , Y ), complement( Y, X ) }.
% 0.87/1.25  (2238) {G0,W8,D3,L2,V2,M2}  { ! alpha1( X, Y ), multiplication( Y, X ) = 
% 0.87/1.25    zero }.
% 0.87/1.25  (2239) {G0,W8,D3,L2,V2,M2}  { ! alpha1( X, Y ), addition( X, Y ) = one }.
% 0.87/1.25  (2240) {G0,W13,D3,L3,V2,M3}  { ! multiplication( Y, X ) = zero, ! addition
% 0.87/1.25    ( X, Y ) = one, alpha1( X, Y ) }.
% 0.87/1.25  (2241) {G0,W9,D3,L3,V2,M3}  { ! test( X ), ! c( X ) = Y, complement( X, Y )
% 0.87/1.25     }.
% 0.87/1.25  (2242) {G0,W9,D3,L3,V2,M3}  { ! test( X ), ! complement( X, Y ), c( X ) = Y
% 0.87/1.25     }.
% 0.87/1.25  (2243) {G0,W6,D3,L2,V1,M2}  { test( X ), c( X ) = zero }.
% 0.87/1.25  (2244) {G0,W2,D2,L1,V0,M1}  { test( skol3 ) }.
% 0.87/1.25  (2245) {G0,W2,D2,L1,V0,M1}  { test( skol2 ) }.
% 0.87/1.25  (2246) {G0,W16,D6,L1,V0,M1}  { ! one = addition( multiplication( addition( 
% 0.87/1.25    skol2, c( skol2 ) ), skol3 ), multiplication( addition( skol2, c( skol2 )
% 0.87/1.25     ), c( skol3 ) ) ) }.
% 0.87/1.25  
% 0.87/1.25  
% 0.87/1.25  Total Proof:
% 0.87/1.25  
% 0.87/1.25  subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 0.87/1.25     ) }.
% 0.87/1.25  parent0: (2220) {G0,W7,D3,L1,V2,M1}  { addition( X, Y ) = addition( Y, X )
% 0.87/1.25     }.
% 0.87/1.25  substitution0:
% 0.87/1.25     X := X
% 0.87/1.25     Y := Y
% 0.87/1.25  end
% 0.87/1.25  permutation0:
% 0.87/1.25     0 ==> 0
% 0.87/1.25  end
% 0.87/1.25  
% 0.87/1.25  subsumption: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.87/1.25  parent0: (2226) {G0,W5,D3,L1,V1,M1}  { multiplication( one, X ) = X }.
% 0.87/1.25  substitution0:
% 0.87/1.25     X := X
% 0.87/1.25  end
% 0.87/1.25  permutation0:
% 0.87/1.25     0 ==> 0
% 0.87/1.25  end
% 0.87/1.25  
% 0.87/1.25  eqswap: (2259) {G0,W13,D4,L1,V3,M1}  { addition( multiplication( X, Y ), 
% 0.87/1.25    multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 0.87/1.25  parent0[0]: (2227) {G0,W13,D4,L1,V3,M1}  { multiplication( X, addition( Y, 
% 0.87/1.25    Z ) ) = addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 0.87/1.25  substitution0:
% 0.87/1.25     X := X
% 0.87/1.25     Y := Y
% 0.87/1.25     Z := Z
% 0.87/1.25  end
% 0.87/1.25  
% 0.87/1.25  subsumption: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y )
% 0.87/1.25    , multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.87/1.25  parent0: (2259) {G0,W13,D4,L1,V3,M1}  { addition( multiplication( X, Y ), 
% 0.87/1.25    multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 0.87/1.25  substitution0:
% 0.87/1.25     X := X
% 0.87/1.25     Y := Y
% 0.87/1.25     Z := Z
% 0.87/1.25  end
% 0.87/1.25  permutation0:
% 0.87/1.25     0 ==> 0
% 0.87/1.25  end
% 0.87/1.25  
% 0.87/1.25  subsumption: (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X, 
% 0.87/1.25    Y ) }.
% 0.87/1.25  parent0: (2236) {G0,W6,D2,L2,V2,M2}  { ! complement( Y, X ), alpha1( X, Y )
% 0.87/1.25     }.
% 0.87/1.25  substitution0:
% 0.87/1.25     X := X
% 0.87/1.25     Y := Y
% 0.87/1.25  end
% 0.87/1.25  permutation0:
% 0.87/1.25     0 ==> 0
% 0.87/1.25     1 ==> 1
% 0.87/1.25  end
% 0.87/1.25  
% 0.87/1.25  subsumption: (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y
% 0.87/1.25     ) ==> one }.
% 0.87/1.25  parent0: (2239) {G0,W8,D3,L2,V2,M2}  { ! alpha1( X, Y ), addition( X, Y ) =
% 0.87/1.25     one }.
% 0.87/1.25  substitution0:
% 0.87/1.25     X := X
% 0.87/1.25     Y := Y
% 0.87/1.25  end
% 0.87/1.25  permutation0:
% 0.87/1.25     0 ==> 0
% 0.87/1.25     1 ==> 1
% 0.87/1.25  end
% 0.87/1.25  
% 0.87/1.25  subsumption: (21) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! c( X ) = Y, 
% 0.87/1.25    complement( X, Y ) }.
% 0.87/1.25  parent0: (2241) {G0,W9,D3,L3,V2,M3}  { ! test( X ), ! c( X ) = Y, 
% 0.87/1.25    complement( X, Y ) }.
% 0.87/1.25  substitution0:
% 0.87/1.25     X := X
% 0.87/1.25     Y := Y
% 0.87/1.25  end
% 0.87/1.25  permutation0:
% 0.87/1.25     0 ==> 0
% 0.87/1.25     1 ==> 1
% 0.87/1.25     2 ==> 2
% 0.87/1.25  end
% 0.87/1.25  
% 0.87/1.25  subsumption: (24) {G0,W2,D2,L1,V0,M1} I { test( skol3 ) }.
% 0.87/1.25  parent0: (2244) {G0,W2,D2,L1,V0,M1}  { test( skol3 ) }.
% 0.87/1.25  substitution0:
% 0.87/1.25  end
% 0.87/1.25  permutation0:
% 0.87/1.25     0 ==> 0
% 0.87/1.25  end
% 0.87/1.25  
% 0.87/1.25  subsumption: (25) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 0.87/1.25  parent0: (2245) {G0,W2,D2,L1,V0,M1}  { test( skol2 ) }.
% 0.87/1.25  substitution0:
% 0.87/1.26  end
% 0.87/1.26  permutation0:
% 0.87/1.26     0 ==> 0
% 0.87/1.26  end
% 0.87/1.26  
% 0.87/1.26  paramod: (2405) {G1,W11,D5,L1,V0,M1}  { ! one = multiplication( addition( 
% 0.87/1.26    skol2, c( skol2 ) ), addition( skol3, c( skol3 ) ) ) }.
% 0.87/1.26  parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ), 
% 0.87/1.26    multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 0.87/1.26  parent1[0; 3]: (2246) {G0,W16,D6,L1,V0,M1}  { ! one = addition( 
% 0.87/1.26    multiplication( addition( skol2, c( skol2 ) ), skol3 ), multiplication( 
% 0.87/1.26    addition( skol2, c( skol2 ) ), c( skol3 ) ) ) }.
% 0.87/1.26  substitution0:
% 0.87/1.26     X := addition( skol2, c( skol2 ) )
% 0.87/1.26     Y := skol3
% 0.87/1.26     Z := c( skol3 )
% 0.87/1.26  end
% 0.87/1.26  substitution1:
% 0.87/1.26  end
% 0.87/1.26  
% 0.87/1.26  eqswap: (2406) {G1,W11,D5,L1,V0,M1}  { ! multiplication( addition( skol2, c
% 0.87/1.26    ( skol2 ) ), addition( skol3, c( skol3 ) ) ) = one }.
% 0.87/1.26  parent0[0]: (2405) {G1,W11,D5,L1,V0,M1}  { ! one = multiplication( addition
% 0.87/1.26    ( skol2, c( skol2 ) ), addition( skol3, c( skol3 ) ) ) }.
% 0.87/1.26  substitution0:
% 0.87/1.26  end
% 0.87/1.26  
% 0.87/1.26  subsumption: (26) {G1,W11,D5,L1,V0,M1} I;d(7) { ! multiplication( addition
% 0.87/1.26    ( skol2, c( skol2 ) ), addition( skol3, c( skol3 ) ) ) ==> one }.
% 0.87/1.26  parent0: (2406) {G1,W11,D5,L1,V0,M1}  { ! multiplication( addition( skol2, 
% 0.87/1.26    c( skol2 ) ), addition( skol3, c( skol3 ) ) ) = one }.
% 0.87/1.26  substitution0:
% 0.87/1.26  end
% 0.87/1.26  permutation0:
% 0.87/1.26     0 ==> 0
% 0.87/1.26  end
% 0.87/1.26  
% 0.87/1.26  eqswap: (2407) {G0,W9,D3,L3,V2,M3}  { ! Y = c( X ), ! test( X ), complement
% 0.87/1.26    ( X, Y ) }.
% 0.87/1.26  parent0[1]: (21) {G0,W9,D3,L3,V2,M3} I { ! test( X ), ! c( X ) = Y, 
% 0.87/1.26    complement( X, Y ) }.
% 0.87/1.26  substitution0:
% 0.87/1.26     X := X
% 0.87/1.26     Y := Y
% 0.87/1.26  end
% 0.87/1.26  
% 0.87/1.26  eqrefl: (2408) {G0,W6,D3,L2,V1,M2}  { ! test( X ), complement( X, c( X ) )
% 0.87/1.26     }.
% 0.87/1.26  parent0[0]: (2407) {G0,W9,D3,L3,V2,M3}  { ! Y = c( X ), ! test( X ), 
% 0.87/1.26    complement( X, Y ) }.
% 0.87/1.26  substitution0:
% 0.87/1.26     X := X
% 0.87/1.26     Y := c( X )
% 0.87/1.26  end
% 0.87/1.26  
% 0.87/1.26  subsumption: (27) {G1,W6,D3,L2,V1,M2} Q(21) { ! test( X ), complement( X, c
% 0.87/1.26    ( X ) ) }.
% 0.87/1.26  parent0: (2408) {G0,W6,D3,L2,V1,M2}  { ! test( X ), complement( X, c( X ) )
% 0.87/1.26     }.
% 0.87/1.26  substitution0:
% 0.87/1.26     X := X
% 0.87/1.26  end
% 0.87/1.26  permutation0:
% 0.87/1.26     0 ==> 0
% 0.87/1.26     1 ==> 1
% 0.87/1.26  end
% 0.87/1.26  
% 0.87/1.26  resolution: (2409) {G1,W4,D3,L1,V0,M1}  { complement( skol3, c( skol3 ) )
% 0.87/1.26     }.
% 0.87/1.26  parent0[0]: (27) {G1,W6,D3,L2,V1,M2} Q(21) { ! test( X ), complement( X, c
% 0.87/1.26    ( X ) ) }.
% 0.87/1.26  parent1[0]: (24) {G0,W2,D2,L1,V0,M1} I { test( skol3 ) }.
% 0.87/1.26  substitution0:
% 0.87/1.26     X := skol3
% 0.87/1.26  end
% 0.87/1.26  substitution1:
% 0.87/1.26  end
% 0.87/1.26  
% 0.87/1.26  subsumption: (37) {G2,W4,D3,L1,V0,M1} R(27,24) { complement( skol3, c( 
% 0.87/1.26    skol3 ) ) }.
% 0.87/1.26  parent0: (2409) {G1,W4,D3,L1,V0,M1}  { complement( skol3, c( skol3 ) ) }.
% 0.87/1.26  substitution0:
% 0.87/1.26  end
% 0.87/1.26  permutation0:
% 0.87/1.26     0 ==> 0
% 0.87/1.26  end
% 0.87/1.26  
% 0.87/1.26  resolution: (2410) {G1,W4,D3,L1,V0,M1}  { complement( skol2, c( skol2 ) )
% 0.87/1.26     }.
% 0.87/1.26  parent0[0]: (27) {G1,W6,D3,L2,V1,M2} Q(21) { ! test( X ), complement( X, c
% 0.87/1.26    ( X ) ) }.
% 0.87/1.26  parent1[0]: (25) {G0,W2,D2,L1,V0,M1} I { test( skol2 ) }.
% 0.87/1.26  substitution0:
% 0.87/1.26     X := skol2
% 0.87/1.26  end
% 0.87/1.26  substitution1:
% 0.87/1.26  end
% 0.87/1.26  
% 0.87/1.26  subsumption: (38) {G2,W4,D3,L1,V0,M1} R(27,25) { complement( skol2, c( 
% 0.87/1.26    skol2 ) ) }.
% 0.87/1.26  parent0: (2410) {G1,W4,D3,L1,V0,M1}  { complement( skol2, c( skol2 ) ) }.
% 0.87/1.26  substitution0:
% 0.87/1.26  end
% 0.87/1.26  permutation0:
% 0.87/1.26     0 ==> 0
% 0.87/1.26  end
% 0.87/1.26  
% 0.87/1.26  resolution: (2411) {G1,W4,D3,L1,V0,M1}  { alpha1( c( skol3 ), skol3 ) }.
% 0.87/1.26  parent0[0]: (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X, Y
% 0.87/1.26     ) }.
% 0.87/1.26  parent1[0]: (37) {G2,W4,D3,L1,V0,M1} R(27,24) { complement( skol3, c( skol3
% 0.87/1.26     ) ) }.
% 0.87/1.26  substitution0:
% 0.87/1.26     X := c( skol3 )
% 0.87/1.26     Y := skol3
% 0.87/1.26  end
% 0.87/1.26  substitution1:
% 0.87/1.26  end
% 0.87/1.26  
% 0.87/1.26  subsumption: (39) {G3,W4,D3,L1,V0,M1} R(37,16) { alpha1( c( skol3 ), skol3
% 0.87/1.26     ) }.
% 0.87/1.26  parent0: (2411) {G1,W4,D3,L1,V0,M1}  { alpha1( c( skol3 ), skol3 ) }.
% 0.87/1.26  substitution0:
% 0.87/1.26  end
% 0.87/1.26  permutation0:
% 0.87/1.26     0 ==> 0
% 0.87/1.26  end
% 0.87/1.26  
% 0.87/1.26  resolution: (2412) {G1,W4,D3,L1,V0,M1}  { alpha1( c( skol2 ), skol2 ) }.
% 0.87/1.26  parent0[0]: (16) {G0,W6,D2,L2,V2,M2} I { ! complement( Y, X ), alpha1( X, Y
% 0.87/1.26     ) }.
% 0.87/1.26  parent1[0]: (38) {G2,W4,D3,L1,V0,M1} R(27,25) { complement( skol2, c( skol2
% 0.87/1.26     ) ) }.
% 0.87/1.26  substitution0:
% 0.87/1.26     X := c( skol2 )
% 0.87/1.26     Y := skol2
% 0.87/1.26  end
% 0.87/1.26  substitution1:
% 0.87/1.26  end
% 0.87/1.26  
% 0.87/1.26  subsumption: (42) {G3,W4,D3,L1,V0,M1} R(38,16) { alpha1( c( skol2 ), skol2
% 0.87/1.26     ) }.
% 0.87/1.26  parent0: (2412) {G1,W4,D3,L1,V0,M1}  { alpha1( c( skol2 ), skol2 ) }.
% 0.87/1.26  substitution0:
% 0.87/1.26  end
% 0.87/1.26  permutation0:
% 0.87/1.26     0 ==> 0
% 0.87/1.26  end
% 0.87/1.26  
% 0.87/1.26  eqswap: (2413) {G0,W8,D3,L2,V2,M2}  { one ==> addition( X, Y ), ! alpha1( X
% 0.87/1.26    , Y ) }.
% 0.87/1.26  parent0[1]: (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y )
% 0.87/1.26     ==> one }.
% 0.87/1.26  substitution0:
% 0.87/1.26     X := X
% 0.87/1.26     Y := Y
% 0.87/1.26  end
% 0.87/1.26  
% 0.87/1.26  resolution: (2414) {G1,W6,D4,L1,V0,M1}  { one ==> addition( c( skol2 ), 
% 0.87/1.26    skol2 ) }.
% 0.87/1.26  parent0[1]: (2413) {G0,W8,D3,L2,V2,M2}  { one ==> addition( X, Y ), ! 
% 0.87/1.26    alpha1( X, Y ) }.
% 0.87/1.26  parent1[0]: (42) {G3,W4,D3,L1,V0,M1} R(38,16) { alpha1( c( skol2 ), skol2 )
% 0.87/1.26     }.
% 0.87/1.26  substitution0:
% 0.87/1.26     X := c( skol2 )
% 0.87/1.26     Y := skol2
% 0.87/1.26  end
% 0.87/1.26  substitution1:
% 0.87/1.26  end
% 0.87/1.26  
% 0.87/1.26  eqswap: (2415) {G1,W6,D4,L1,V0,M1}  { addition( c( skol2 ), skol2 ) ==> one
% 0.87/1.26     }.
% 0.87/1.26  parent0[0]: (2414) {G1,W6,D4,L1,V0,M1}  { one ==> addition( c( skol2 ), 
% 0.87/1.26    skol2 ) }.
% 0.87/1.26  substitution0:
% 0.87/1.26  end
% 0.87/1.26  
% 0.87/1.26  subsumption: (261) {G4,W6,D4,L1,V0,M1} R(19,42) { addition( c( skol2 ), 
% 0.87/1.26    skol2 ) ==> one }.
% 0.87/1.26  parent0: (2415) {G1,W6,D4,L1,V0,M1}  { addition( c( skol2 ), skol2 ) ==> 
% 0.87/1.26    one }.
% 0.87/1.26  substitution0:
% 0.87/1.26  end
% 0.87/1.26  permutation0:
% 0.87/1.26     0 ==> 0
% 0.87/1.26  end
% 0.87/1.26  
% 0.87/1.26  eqswap: (2416) {G0,W8,D3,L2,V2,M2}  { one ==> addition( X, Y ), ! alpha1( X
% 0.87/1.26    , Y ) }.
% 0.87/1.26  parent0[1]: (19) {G0,W8,D3,L2,V2,M2} I { ! alpha1( X, Y ), addition( X, Y )
% 0.87/1.26     ==> one }.
% 0.87/1.26  substitution0:
% 0.87/1.26     X := X
% 0.87/1.26     Y := Y
% 0.87/1.26  end
% 0.87/1.26  
% 0.87/1.26  resolution: (2417) {G1,W6,D4,L1,V0,M1}  { one ==> addition( c( skol3 ), 
% 0.87/1.26    skol3 ) }.
% 0.87/1.26  parent0[1]: (2416) {G0,W8,D3,L2,V2,M2}  { one ==> addition( X, Y ), ! 
% 0.87/1.26    alpha1( X, Y ) }.
% 0.87/1.26  parent1[0]: (39) {G3,W4,D3,L1,V0,M1} R(37,16) { alpha1( c( skol3 ), skol3 )
% 0.87/1.26     }.
% 0.87/1.26  substitution0:
% 0.87/1.26     X := c( skol3 )
% 0.87/1.26     Y := skol3
% 0.87/1.26  end
% 0.87/1.26  substitution1:
% 0.87/1.26  end
% 0.87/1.26  
% 0.87/1.26  eqswap: (2418) {G1,W6,D4,L1,V0,M1}  { addition( c( skol3 ), skol3 ) ==> one
% 0.87/1.26     }.
% 0.87/1.26  parent0[0]: (2417) {G1,W6,D4,L1,V0,M1}  { one ==> addition( c( skol3 ), 
% 0.87/1.26    skol3 ) }.
% 0.87/1.26  substitution0:
% 0.87/1.26  end
% 0.87/1.26  
% 0.87/1.26  subsumption: (262) {G4,W6,D4,L1,V0,M1} R(19,39) { addition( c( skol3 ), 
% 0.87/1.26    skol3 ) ==> one }.
% 0.87/1.26  parent0: (2418) {G1,W6,D4,L1,V0,M1}  { addition( c( skol3 ), skol3 ) ==> 
% 0.87/1.26    one }.
% 0.87/1.26  substitution0:
% 0.87/1.26  end
% 0.87/1.26  permutation0:
% 0.87/1.26     0 ==> 0
% 0.87/1.26  end
% 0.87/1.26  
% 0.87/1.26  eqswap: (2419) {G1,W11,D5,L1,V0,M1}  { ! one ==> multiplication( addition( 
% 0.87/1.26    skol2, c( skol2 ) ), addition( skol3, c( skol3 ) ) ) }.
% 0.87/1.26  parent0[0]: (26) {G1,W11,D5,L1,V0,M1} I;d(7) { ! multiplication( addition( 
% 0.87/1.26    skol2, c( skol2 ) ), addition( skol3, c( skol3 ) ) ) ==> one }.
% 0.87/1.26  substitution0:
% 0.87/1.26  end
% 0.87/1.26  
% 0.87/1.26  paramod: (2422) {G1,W11,D5,L1,V0,M1}  { ! one ==> multiplication( addition
% 0.87/1.26    ( c( skol2 ), skol2 ), addition( skol3, c( skol3 ) ) ) }.
% 0.87/1.26  parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.87/1.26     }.
% 0.87/1.26  parent1[0; 4]: (2419) {G1,W11,D5,L1,V0,M1}  { ! one ==> multiplication( 
% 0.87/1.26    addition( skol2, c( skol2 ) ), addition( skol3, c( skol3 ) ) ) }.
% 0.87/1.26  substitution0:
% 0.87/1.26     X := skol2
% 0.87/1.26     Y := c( skol2 )
% 0.87/1.26  end
% 0.87/1.26  substitution1:
% 0.87/1.26  end
% 0.87/1.26  
% 0.87/1.26  paramod: (2429) {G2,W8,D5,L1,V0,M1}  { ! one ==> multiplication( one, 
% 0.87/1.26    addition( skol3, c( skol3 ) ) ) }.
% 0.87/1.26  parent0[0]: (261) {G4,W6,D4,L1,V0,M1} R(19,42) { addition( c( skol2 ), 
% 0.87/1.26    skol2 ) ==> one }.
% 0.87/1.26  parent1[0; 4]: (2422) {G1,W11,D5,L1,V0,M1}  { ! one ==> multiplication( 
% 0.87/1.26    addition( c( skol2 ), skol2 ), addition( skol3, c( skol3 ) ) ) }.
% 0.87/1.26  substitution0:
% 0.87/1.26  end
% 0.87/1.26  substitution1:
% 0.87/1.26  end
% 0.87/1.26  
% 0.87/1.26  paramod: (2430) {G1,W6,D4,L1,V0,M1}  { ! one ==> addition( skol3, c( skol3
% 0.87/1.26     ) ) }.
% 0.87/1.26  parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 0.87/1.26  parent1[0; 3]: (2429) {G2,W8,D5,L1,V0,M1}  { ! one ==> multiplication( one
% 0.87/1.26    , addition( skol3, c( skol3 ) ) ) }.
% 0.87/1.26  substitution0:
% 0.87/1.26     X := addition( skol3, c( skol3 ) )
% 0.87/1.26  end
% 0.87/1.26  substitution1:
% 0.87/1.26  end
% 0.87/1.26  
% 0.87/1.26  eqswap: (2431) {G1,W6,D4,L1,V0,M1}  { ! addition( skol3, c( skol3 ) ) ==> 
% 0.87/1.26    one }.
% 0.87/1.26  parent0[0]: (2430) {G1,W6,D4,L1,V0,M1}  { ! one ==> addition( skol3, c( 
% 0.87/1.26    skol3 ) ) }.
% 0.87/1.26  substitution0:
% 0.87/1.26  end
% 0.87/1.26  
% 0.87/1.26  subsumption: (446) {G5,W6,D4,L1,V0,M1} P(0,26);d(261);d(6) { ! addition( 
% 0.87/1.26    skol3, c( skol3 ) ) ==> one }.
% 0.87/1.26  parent0: (2431) {G1,W6,D4,L1,V0,M1}  { ! addition( skol3, c( skol3 ) ) ==> 
% 0.87/1.26    one }.
% 0.87/1.26  substitution0:
% 0.87/1.26  end
% 0.87/1.26  permutation0:
% 0.87/1.26     0 ==> 0
% 0.87/1.26  end
% 0.87/1.26  
% 0.87/1.26  eqswap: (2432) {G5,W6,D4,L1,V0,M1}  { ! one ==> addition( skol3, c( skol3 )
% 0.87/1.26     ) }.
% 0.87/1.26  parent0[0]: (446) {G5,W6,D4,L1,V0,M1} P(0,26);d(261);d(6) { ! addition( 
% 0.87/1.26    skol3, c( skol3 ) ) ==> one }.
% 0.87/1.26  substitution0:
% 0.87/1.26  end
% 0.87/1.26  
% 0.87/1.26  paramod: (2434) {G1,W6,D4,L1,V0,M1}  { ! one ==> addition( c( skol3 ), 
% 0.87/1.26    skol3 ) }.
% 0.87/1.26  parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 0.87/1.26     }.
% 0.87/1.26  parent1[0; 3]: (2432) {G5,W6,D4,L1,V0,M1}  { ! one ==> addition( skol3, c( 
% 0.87/1.26    skol3 ) ) }.
% 0.87/1.26  substitution0:
% 0.87/1.26     X := skol3
% 0.87/1.26     Y := c( skol3 )
% 0.87/1.26  end
% 0.87/1.26  substitution1:
% 0.87/1.26  end
% 0.87/1.26  
% 0.87/1.26  paramod: (2436) {G2,W3,D2,L1,V0,M1}  { ! one ==> one }.
% 0.87/1.26  parent0[0]: (262) {G4,W6,D4,L1,V0,M1} R(19,39) { addition( c( skol3 ), 
% 0.87/1.26    skol3 ) ==> one }.
% 0.87/1.26  parent1[0; 3]: (2434) {G1,W6,D4,L1,V0,M1}  { ! one ==> addition( c( skol3 )
% 0.87/1.26    , skol3 ) }.
% 0.87/1.26  substitution0:
% 0.87/1.26  end
% 0.87/1.26  substitution1:
% 0.87/1.26  end
% 0.87/1.26  
% 0.87/1.26  eqrefl: (2437) {G0,W0,D0,L0,V0,M0}  {  }.
% 0.87/1.26  parent0[0]: (2436) {G2,W3,D2,L1,V0,M1}  { ! one ==> one }.
% 0.87/1.26  substitution0:
% 0.87/1.26  end
% 0.87/1.26  
% 0.87/1.26  subsumption: (2218) {G6,W0,D0,L0,V0,M0} P(0,446);d(262);q {  }.
% 0.87/1.26  parent0: (2437) {G0,W0,D0,L0,V0,M0}  {  }.
% 0.87/1.26  substitution0:
% 0.87/1.26  end
% 0.87/1.26  permutation0:
% 0.87/1.26  end
% 0.87/1.26  
% 0.87/1.26  Proof check complete!
% 0.87/1.26  
% 0.87/1.26  Memory use:
% 0.87/1.26  
% 0.87/1.26  space for terms:        26529
% 0.87/1.26  space for clauses:      116854
% 0.87/1.26  
% 0.87/1.26  
% 0.87/1.26  clauses generated:      14921
% 0.87/1.26  clauses kept:           2219
% 0.87/1.26  clauses selected:       240
% 0.87/1.26  clauses deleted:        80
% 0.87/1.26  clauses inuse deleted:  35
% 0.87/1.26  
% 0.87/1.26  subsentry:          26336
% 0.87/1.26  literals s-matched: 18544
% 0.87/1.26  literals matched:   18091
% 0.87/1.26  full subsumption:   2437
% 0.87/1.26  
% 0.87/1.26  checksum:           -1284641959
% 0.87/1.26  
% 0.87/1.26  
% 0.87/1.26  Bliksem ended
%------------------------------------------------------------------------------