TSTP Solution File: NUM835+2 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : NUM835+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n021.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 : Mon Jul 18 06:26:53 EDT 2022

% Result   : Theorem 0.73s 1.10s
% Output   : Refutation 0.73s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : NUM835+2 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12  % Command  : bliksem %s
% 0.13/0.33  % Computer : n021.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % DateTime : Wed Jul  6 07:44:48 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.73/1.10  *** allocated 10000 integers for termspace/termends
% 0.73/1.10  *** allocated 10000 integers for clauses
% 0.73/1.10  *** allocated 10000 integers for justifications
% 0.73/1.10  Bliksem 1.12
% 0.73/1.10  
% 0.73/1.10  
% 0.73/1.10  Automatic Strategy Selection
% 0.73/1.10  
% 0.73/1.10  
% 0.73/1.10  Clauses:
% 0.73/1.10  
% 0.73/1.10  { ! vd165 = vplus( vd151, X ) }.
% 0.73/1.10  { ! vd151 = vplus( vd165, X ) }.
% 0.73/1.10  { ! vd151 = vd165 }.
% 0.73/1.10  { ! vd165 = vplus( vd151, X ), m( vsucc( vd165 ) ) }.
% 0.73/1.10  { ! vd165 = vplus( vd151, X ), vsucc( vplus( vd151, X ) ) = vplus( vd151, 
% 0.73/1.10    vsucc( X ) ) }.
% 0.73/1.10  { ! vd165 = vplus( vd151, X ), vsucc( vd165 ) = vsucc( vplus( vd151, X ) )
% 0.73/1.10     }.
% 0.73/1.10  { ! vd151 = vplus( vd165, X ), X = v1, m( vsucc( vd165 ) ) }.
% 0.73/1.10  { ! vd151 = vplus( vd165, X ), X = v1, vplus( vplus( vd165, v1 ), vskolem3
% 0.73/1.10     ) = vplus( vsucc( vd165 ), vskolem3 ) }.
% 0.73/1.10  { ! vd151 = vplus( vd165, X ), X = v1, vplus( vd165, vplus( v1, vskolem3 )
% 0.73/1.10     ) = vplus( vplus( vd165, v1 ), vskolem3 ) }.
% 0.73/1.10  { ! vd151 = vplus( vd165, X ), X = v1, vd151 = vplus( vd165, vplus( v1, 
% 0.73/1.10    vskolem3 ) ) }.
% 0.73/1.10  { ! vd151 = vplus( vd165, X ), X = v1, vsucc( vskolem3 ) = vplus( v1, 
% 0.73/1.10    vskolem3 ) }.
% 0.73/1.10  { ! vd151 = vplus( vd165, X ), X = v1, X = vsucc( vskolem3 ) }.
% 0.73/1.10  { ! vd151 = vplus( vd165, X ), ! X = v1, m( vsucc( vd165 ) ) }.
% 0.73/1.10  { ! vd151 = vplus( vd165, X ), ! X = v1, vplus( vd165, v1 ) = vsucc( vd165
% 0.73/1.10     ) }.
% 0.73/1.10  { ! vd151 = vplus( vd165, X ), ! X = v1, vd151 = vplus( vd165, v1 ) }.
% 0.73/1.10  { ! vd151 = vd165, m( vsucc( vd165 ) ) }.
% 0.73/1.10  { ! vd151 = vd165, vplus( vd165, v1 ) = vplus( vd151, v1 ) }.
% 0.73/1.10  { ! vd151 = vd165, vsucc( vd165 ) = vplus( vd165, v1 ) }.
% 0.73/1.10  { ! m( Y ), X = Y, alpha1( X, Y ) }.
% 0.73/1.10  { ! X = Y, m( Y ) }.
% 0.73/1.10  { ! alpha1( X, Y ), m( Y ) }.
% 0.73/1.10  { ! alpha1( X, Y ), X = vplus( Y, skol1( X, Y ) ), Y = vplus( X, skol2( X, 
% 0.73/1.10    Y ) ) }.
% 0.73/1.10  { ! X = vplus( Y, Z ), alpha1( X, Y ) }.
% 0.73/1.10  { ! Y = vplus( X, Z ), alpha1( X, Y ) }.
% 0.73/1.10  { vplus( Y, X ) = vplus( X, Y ) }.
% 0.73/1.10  { vplus( vsucc( X ), Y ) = vsucc( vplus( X, Y ) ) }.
% 0.73/1.10  { vplus( v1, X ) = vsucc( X ) }.
% 0.73/1.10  { vplus( vplus( X, Y ), Z ) = vplus( X, vplus( Y, Z ) ) }.
% 0.73/1.10  { vplus( X, vsucc( Y ) ) = vsucc( vplus( X, Y ) ) }.
% 0.73/1.10  { vplus( X, v1 ) = vsucc( X ) }.
% 0.73/1.10  { X = v1, X = vsucc( vskolem2( X ) ) }.
% 0.73/1.10  { ! vsucc( X ) = X }.
% 0.73/1.10  
% 0.73/1.10  percentage equality = 0.692308, percentage horn = 0.823529
% 0.73/1.10  This is a problem with some equality
% 0.73/1.10  
% 0.73/1.10  
% 0.73/1.10  
% 0.73/1.10  Options Used:
% 0.73/1.10  
% 0.73/1.10  useres =            1
% 0.73/1.10  useparamod =        1
% 0.73/1.10  useeqrefl =         1
% 0.73/1.10  useeqfact =         1
% 0.73/1.10  usefactor =         1
% 0.73/1.10  usesimpsplitting =  0
% 0.73/1.10  usesimpdemod =      5
% 0.73/1.10  usesimpres =        3
% 0.73/1.10  
% 0.73/1.10  resimpinuse      =  1000
% 0.73/1.10  resimpclauses =     20000
% 0.73/1.10  substype =          eqrewr
% 0.73/1.10  backwardsubs =      1
% 0.73/1.10  selectoldest =      5
% 0.73/1.10  
% 0.73/1.10  litorderings [0] =  split
% 0.73/1.10  litorderings [1] =  extend the termordering, first sorting on arguments
% 0.73/1.10  
% 0.73/1.10  termordering =      kbo
% 0.73/1.10  
% 0.73/1.10  litapriori =        0
% 0.73/1.10  termapriori =       1
% 0.73/1.10  litaposteriori =    0
% 0.73/1.10  termaposteriori =   0
% 0.73/1.10  demodaposteriori =  0
% 0.73/1.10  ordereqreflfact =   0
% 0.73/1.10  
% 0.73/1.10  litselect =         negord
% 0.73/1.10  
% 0.73/1.10  maxweight =         15
% 0.73/1.10  maxdepth =          30000
% 0.73/1.10  maxlength =         115
% 0.73/1.10  maxnrvars =         195
% 0.73/1.10  excuselevel =       1
% 0.73/1.10  increasemaxweight = 1
% 0.73/1.10  
% 0.73/1.10  maxselected =       10000000
% 0.73/1.10  maxnrclauses =      10000000
% 0.73/1.10  
% 0.73/1.10  showgenerated =    0
% 0.73/1.10  showkept =         0
% 0.73/1.10  showselected =     0
% 0.73/1.10  showdeleted =      0
% 0.73/1.10  showresimp =       1
% 0.73/1.10  showstatus =       2000
% 0.73/1.10  
% 0.73/1.10  prologoutput =     0
% 0.73/1.10  nrgoals =          5000000
% 0.73/1.10  totalproof =       1
% 0.73/1.10  
% 0.73/1.10  Symbols occurring in the translation:
% 0.73/1.10  
% 0.73/1.10  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 0.73/1.10  .  [1, 2]      (w:1, o:36, a:1, s:1, b:0), 
% 0.73/1.10  !  [4, 1]      (w:0, o:28, a:1, s:1, b:0), 
% 0.73/1.10  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.73/1.10  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.73/1.10  vd165  [36, 0]      (w:1, o:10, a:1, s:1, b:0), 
% 0.73/1.10  vd151  [37, 0]      (w:1, o:9, a:1, s:1, b:0), 
% 0.73/1.10  vplus  [38, 2]      (w:1, o:60, a:1, s:1, b:0), 
% 0.73/1.10  vsucc  [40, 1]      (w:1, o:33, a:1, s:1, b:0), 
% 0.73/1.10  m  [41, 1]      (w:1, o:34, a:1, s:1, b:0), 
% 0.73/1.10  v1  [42, 0]      (w:1, o:11, a:1, s:1, b:0), 
% 0.73/1.10  vskolem3  [43, 0]      (w:1, o:12, a:1, s:1, b:0), 
% 0.73/1.10  vskolem2  [59, 1]      (w:1, o:35, a:1, s:1, b:0), 
% 0.73/1.10  alpha1  [61, 2]      (w:1, o:61, a:1, s:1, b:1), 
% 0.73/1.10  skol1  [62, 2]      (w:1, o:62, a:1, s:1, b:1), 
% 0.73/1.10  skol2  [63, 2]      (w:1, o:63, a:1, s:1, b:1).
% 0.73/1.10  
% 0.73/1.10  
% 0.73/1.10  Starting Search:
% 0.73/1.10  
% 0.73/1.10  *** allocated 15000 integers for clauses
% 0.73/1.10  *** allocated 22500 integers for clauses
% 0.73/1.10  *** allocated 33750 integers for clauses
% 0.73/1.10  *** allocated 50625 integers for clauses
% 0.73/1.10  
% 0.73/1.10  Bliksems!, er is een bewijs:
% 0.73/1.10  % SZS status Theorem
% 0.73/1.10  % SZS output start Refutation
% 0.73/1.10  
% 0.73/1.10  (0) {G0,W5,D3,L1,V1,M1} I { ! vplus( vd151, X ) ==> vd165 }.
% 0.73/1.10  (1) {G0,W5,D3,L1,V1,M1} I { ! vplus( vd165, X ) ==> vd151 }.
% 0.73/1.10  (2) {G0,W3,D2,L1,V0,M1} I { ! vd165 ==> vd151 }.
% 0.73/1.10  (3) {G0,W8,D2,L3,V2,M3} I { ! m( Y ), X = Y, alpha1( X, Y ) }.
% 0.73/1.10  (4) {G0,W5,D2,L2,V2,M2} I { ! X = Y, m( Y ) }.
% 0.73/1.10  (6) {G0,W17,D4,L3,V2,M3} I { ! alpha1( X, Y ), vplus( Y, skol1( X, Y ) ) 
% 0.73/1.10    ==> X, vplus( X, skol2( X, Y ) ) ==> Y }.
% 0.73/1.10  (17) {G1,W2,D2,L1,V1,M1} Q(4) { m( X ) }.
% 0.73/1.10  (22) {G2,W6,D2,L2,V2,M2} S(3);r(17) { X = Y, alpha1( X, Y ) }.
% 0.73/1.10  (43) {G3,W6,D2,L2,V1,M2} P(22,2) { ! X = vd151, alpha1( vd165, X ) }.
% 0.73/1.10  (46) {G4,W3,D2,L1,V0,M1} Q(43) { alpha1( vd165, vd151 ) }.
% 0.73/1.10  (57) {G5,W7,D4,L1,V0,M1} R(6,46);r(0) { vplus( vd165, skol2( vd165, vd151 )
% 0.73/1.10     ) ==> vd151 }.
% 0.73/1.10  (800) {G6,W0,D0,L0,V0,M0} S(57);r(1) {  }.
% 0.73/1.10  
% 0.73/1.10  
% 0.73/1.10  % SZS output end Refutation
% 0.73/1.10  found a proof!
% 0.73/1.10  
% 0.73/1.10  
% 0.73/1.10  Unprocessed initial clauses:
% 0.73/1.10  
% 0.73/1.10  (802) {G0,W5,D3,L1,V1,M1}  { ! vd165 = vplus( vd151, X ) }.
% 0.73/1.10  (803) {G0,W5,D3,L1,V1,M1}  { ! vd151 = vplus( vd165, X ) }.
% 0.73/1.10  (804) {G0,W3,D2,L1,V0,M1}  { ! vd151 = vd165 }.
% 0.73/1.10  (805) {G0,W8,D3,L2,V1,M2}  { ! vd165 = vplus( vd151, X ), m( vsucc( vd165 )
% 0.73/1.10     ) }.
% 0.73/1.10  (806) {G0,W14,D4,L2,V1,M2}  { ! vd165 = vplus( vd151, X ), vsucc( vplus( 
% 0.73/1.10    vd151, X ) ) = vplus( vd151, vsucc( X ) ) }.
% 0.73/1.10  (807) {G0,W12,D4,L2,V1,M2}  { ! vd165 = vplus( vd151, X ), vsucc( vd165 ) =
% 0.73/1.10     vsucc( vplus( vd151, X ) ) }.
% 0.73/1.10  (808) {G0,W11,D3,L3,V1,M3}  { ! vd151 = vplus( vd165, X ), X = v1, m( vsucc
% 0.73/1.10    ( vd165 ) ) }.
% 0.73/1.10  (809) {G0,W18,D4,L3,V1,M3}  { ! vd151 = vplus( vd165, X ), X = v1, vplus( 
% 0.73/1.10    vplus( vd165, v1 ), vskolem3 ) = vplus( vsucc( vd165 ), vskolem3 ) }.
% 0.73/1.10  (810) {G0,W19,D4,L3,V1,M3}  { ! vd151 = vplus( vd165, X ), X = v1, vplus( 
% 0.73/1.10    vd165, vplus( v1, vskolem3 ) ) = vplus( vplus( vd165, v1 ), vskolem3 )
% 0.73/1.10     }.
% 0.73/1.10  (811) {G0,W15,D4,L3,V1,M3}  { ! vd151 = vplus( vd165, X ), X = v1, vd151 = 
% 0.73/1.10    vplus( vd165, vplus( v1, vskolem3 ) ) }.
% 0.73/1.10  (812) {G0,W14,D3,L3,V1,M3}  { ! vd151 = vplus( vd165, X ), X = v1, vsucc( 
% 0.73/1.10    vskolem3 ) = vplus( v1, vskolem3 ) }.
% 0.73/1.10  (813) {G0,W12,D3,L3,V1,M3}  { ! vd151 = vplus( vd165, X ), X = v1, X = 
% 0.73/1.10    vsucc( vskolem3 ) }.
% 0.73/1.10  (814) {G0,W11,D3,L3,V1,M3}  { ! vd151 = vplus( vd165, X ), ! X = v1, m( 
% 0.73/1.10    vsucc( vd165 ) ) }.
% 0.73/1.10  (815) {G0,W14,D3,L3,V1,M3}  { ! vd151 = vplus( vd165, X ), ! X = v1, vplus
% 0.73/1.10    ( vd165, v1 ) = vsucc( vd165 ) }.
% 0.73/1.10  (816) {G0,W13,D3,L3,V1,M3}  { ! vd151 = vplus( vd165, X ), ! X = v1, vd151 
% 0.73/1.10    = vplus( vd165, v1 ) }.
% 0.73/1.10  (817) {G0,W6,D3,L2,V0,M2}  { ! vd151 = vd165, m( vsucc( vd165 ) ) }.
% 0.73/1.10  (818) {G0,W10,D3,L2,V0,M2}  { ! vd151 = vd165, vplus( vd165, v1 ) = vplus( 
% 0.73/1.10    vd151, v1 ) }.
% 0.73/1.10  (819) {G0,W9,D3,L2,V0,M2}  { ! vd151 = vd165, vsucc( vd165 ) = vplus( vd165
% 0.73/1.10    , v1 ) }.
% 0.73/1.10  (820) {G0,W8,D2,L3,V2,M3}  { ! m( Y ), X = Y, alpha1( X, Y ) }.
% 0.73/1.10  (821) {G0,W5,D2,L2,V2,M2}  { ! X = Y, m( Y ) }.
% 0.73/1.10  (822) {G0,W5,D2,L2,V2,M2}  { ! alpha1( X, Y ), m( Y ) }.
% 0.73/1.10  (823) {G0,W17,D4,L3,V2,M3}  { ! alpha1( X, Y ), X = vplus( Y, skol1( X, Y )
% 0.73/1.10     ), Y = vplus( X, skol2( X, Y ) ) }.
% 0.73/1.10  (824) {G0,W8,D3,L2,V3,M2}  { ! X = vplus( Y, Z ), alpha1( X, Y ) }.
% 0.73/1.10  (825) {G0,W8,D3,L2,V3,M2}  { ! Y = vplus( X, Z ), alpha1( X, Y ) }.
% 0.73/1.10  (826) {G0,W7,D3,L1,V2,M1}  { vplus( Y, X ) = vplus( X, Y ) }.
% 0.73/1.10  (827) {G0,W9,D4,L1,V2,M1}  { vplus( vsucc( X ), Y ) = vsucc( vplus( X, Y )
% 0.73/1.10     ) }.
% 0.73/1.10  (828) {G0,W6,D3,L1,V1,M1}  { vplus( v1, X ) = vsucc( X ) }.
% 0.73/1.10  (829) {G0,W11,D4,L1,V3,M1}  { vplus( vplus( X, Y ), Z ) = vplus( X, vplus( 
% 0.73/1.10    Y, Z ) ) }.
% 0.73/1.10  (830) {G0,W9,D4,L1,V2,M1}  { vplus( X, vsucc( Y ) ) = vsucc( vplus( X, Y )
% 0.73/1.10     ) }.
% 0.73/1.10  (831) {G0,W6,D3,L1,V1,M1}  { vplus( X, v1 ) = vsucc( X ) }.
% 0.73/1.10  (832) {G0,W8,D4,L2,V1,M2}  { X = v1, X = vsucc( vskolem2( X ) ) }.
% 0.73/1.10  (833) {G0,W4,D3,L1,V1,M1}  { ! vsucc( X ) = X }.
% 0.73/1.10  
% 0.73/1.10  
% 0.73/1.10  Total Proof:
% 0.73/1.10  
% 0.73/1.10  eqswap: (834) {G0,W5,D3,L1,V1,M1}  { ! vplus( vd151, X ) = vd165 }.
% 0.73/1.10  parent0[0]: (802) {G0,W5,D3,L1,V1,M1}  { ! vd165 = vplus( vd151, X ) }.
% 0.73/1.10  substitution0:
% 0.73/1.10     X := X
% 0.73/1.10  end
% 0.73/1.10  
% 0.73/1.10  subsumption: (0) {G0,W5,D3,L1,V1,M1} I { ! vplus( vd151, X ) ==> vd165 }.
% 0.73/1.10  parent0: (834) {G0,W5,D3,L1,V1,M1}  { ! vplus( vd151, X ) = vd165 }.
% 0.73/1.10  substitution0:
% 0.73/1.10     X := X
% 0.73/1.10  end
% 0.73/1.10  permutation0:
% 0.73/1.10     0 ==> 0
% 0.73/1.10  end
% 0.73/1.10  
% 0.73/1.10  eqswap: (836) {G0,W5,D3,L1,V1,M1}  { ! vplus( vd165, X ) = vd151 }.
% 202.02/202.44  parent0[0]: (803) {G0,W5,D3,L1,V1,M1}  { ! vd151 = vplus( vd165, X ) }.
% 202.02/202.44  substitution0:
% 202.02/202.44     X := X
% 202.02/202.44  end
% 202.02/202.44  
% 202.02/202.44  subsumption: (1) {G0,W5,D3,L1,V1,M1} I { ! vplus( vd165, X ) ==> vd151 }.
% 202.02/202.44  parent0: (836) {G0,W5,D3,L1,V1,M1}  { ! vplus( vd165, X ) = vd151 }.
% 202.02/202.44  substitution0:
% 202.02/202.44     X := X
% 202.02/202.44  end
% 202.02/202.44  permutation0:
% 202.02/202.44     0 ==> 0
% 202.02/202.44  end
% 202.02/202.44  
% 202.02/202.44  eqswap: (839) {G0,W3,D2,L1,V0,M1}  { ! vd165 = vd151 }.
% 202.02/202.44  parent0[0]: (804) {G0,W3,D2,L1,V0,M1}  { ! vd151 = vd165 }.
% 202.02/202.44  substitution0:
% 202.02/202.44  end
% 202.02/202.44  
% 202.02/202.44  subsumption: (2) {G0,W3,D2,L1,V0,M1} I { ! vd165 ==> vd151 }.
% 202.02/202.44  parent0: (839) {G0,W3,D2,L1,V0,M1}  { ! vd165 = vd151 }.
% 202.02/202.44  substitution0:
% 202.02/202.44  end
% 202.02/202.44  permutation0:
% 202.02/202.44     0 ==> 0
% 202.02/202.44  end
% 202.02/202.44  
% 202.02/202.44  *** allocated 15000 integers for termspace/termends
% 202.02/202.44  subsumption: (3) {G0,W8,D2,L3,V2,M3} I { ! m( Y ), X = Y, alpha1( X, Y )
% 202.02/202.44     }.
% 202.02/202.44  parent0: (820) {G0,W8,D2,L3,V2,M3}  { ! m( Y ), X = Y, alpha1( X, Y ) }.
% 202.02/202.44  substitution0:
% 202.02/202.44     X := X
% 202.02/202.44     Y := Y
% 202.02/202.44  end
% 202.02/202.44  permutation0:
% 202.02/202.44     0 ==> 0
% 202.02/202.44     1 ==> 1
% 202.02/202.44     2 ==> 2
% 202.02/202.44  end
% 202.02/202.44  
% 202.02/202.44  subsumption: (4) {G0,W5,D2,L2,V2,M2} I { ! X = Y, m( Y ) }.
% 202.02/202.44  parent0: (821) {G0,W5,D2,L2,V2,M2}  { ! X = Y, m( Y ) }.
% 202.02/202.45  substitution0:
% 202.02/202.45     X := X
% 202.02/202.45     Y := Y
% 202.02/202.45  end
% 202.02/202.45  permutation0:
% 202.02/202.45     0 ==> 0
% 202.02/202.45     1 ==> 1
% 202.02/202.45  end
% 202.02/202.45  
% 202.02/202.45  eqswap: (1062) {G0,W17,D4,L3,V2,M3}  { vplus( Y, skol2( Y, X ) ) = X, ! 
% 202.02/202.45    alpha1( Y, X ), Y = vplus( X, skol1( Y, X ) ) }.
% 202.02/202.45  parent0[2]: (823) {G0,W17,D4,L3,V2,M3}  { ! alpha1( X, Y ), X = vplus( Y, 
% 202.02/202.45    skol1( X, Y ) ), Y = vplus( X, skol2( X, Y ) ) }.
% 202.02/202.45  substitution0:
% 202.02/202.45     X := Y
% 202.02/202.45     Y := X
% 202.02/202.45  end
% 202.02/202.45  
% 202.02/202.45  eqswap: (1063) {G0,W17,D4,L3,V2,M3}  { vplus( Y, skol1( X, Y ) ) = X, vplus
% 202.02/202.45    ( X, skol2( X, Y ) ) = Y, ! alpha1( X, Y ) }.
% 202.02/202.45  parent0[2]: (1062) {G0,W17,D4,L3,V2,M3}  { vplus( Y, skol2( Y, X ) ) = X, !
% 202.02/202.45     alpha1( Y, X ), Y = vplus( X, skol1( Y, X ) ) }.
% 202.02/202.45  substitution0:
% 202.02/202.45     X := Y
% 202.02/202.45     Y := X
% 202.02/202.45  end
% 202.02/202.45  
% 202.02/202.45  subsumption: (6) {G0,W17,D4,L3,V2,M3} I { ! alpha1( X, Y ), vplus( Y, skol1
% 202.02/202.45    ( X, Y ) ) ==> X, vplus( X, skol2( X, Y ) ) ==> Y }.
% 202.02/202.45  parent0: (1063) {G0,W17,D4,L3,V2,M3}  { vplus( Y, skol1( X, Y ) ) = X, 
% 202.02/202.45    vplus( X, skol2( X, Y ) ) = Y, ! alpha1( X, Y ) }.
% 202.02/202.45  substitution0:
% 202.02/202.45     X := X
% 202.02/202.45     Y := Y
% 202.02/202.45  end
% 202.02/202.45  permutation0:
% 202.02/202.45     0 ==> 1
% 202.02/202.45     1 ==> 2
% 202.02/202.45     2 ==> 0
% 202.02/202.45  end
% 202.02/202.45  
% 202.02/202.45  eqswap: (1064) {G0,W5,D2,L2,V2,M2}  { ! Y = X, m( Y ) }.
% 202.02/202.45  parent0[0]: (4) {G0,W5,D2,L2,V2,M2} I { ! X = Y, m( Y ) }.
% 202.02/202.45  substitution0:
% 202.02/202.45     X := X
% 202.02/202.45     Y := Y
% 202.02/202.45  end
% 202.02/202.45  
% 202.02/202.45  eqrefl: (1065) {G0,W2,D2,L1,V1,M1}  { m( X ) }.
% 202.02/202.45  parent0[0]: (1064) {G0,W5,D2,L2,V2,M2}  { ! Y = X, m( Y ) }.
% 202.02/202.45  substitution0:
% 202.02/202.45     X := X
% 202.02/202.45     Y := X
% 202.02/202.45  end
% 202.02/202.45  
% 202.02/202.45  subsumption: (17) {G1,W2,D2,L1,V1,M1} Q(4) { m( X ) }.
% 202.02/202.45  parent0: (1065) {G0,W2,D2,L1,V1,M1}  { m( X ) }.
% 202.02/202.45  substitution0:
% 202.02/202.45     X := X
% 202.02/202.45  end
% 202.02/202.45  permutation0:
% 202.02/202.45     0 ==> 0
% 202.02/202.45  end
% 202.02/202.45  
% 202.02/202.45  resolution: (1067) {G1,W6,D2,L2,V2,M2}  { Y = X, alpha1( Y, X ) }.
% 202.02/202.45  parent0[0]: (3) {G0,W8,D2,L3,V2,M3} I { ! m( Y ), X = Y, alpha1( X, Y ) }.
% 202.02/202.45  parent1[0]: (17) {G1,W2,D2,L1,V1,M1} Q(4) { m( X ) }.
% 202.02/202.45  substitution0:
% 202.02/202.45     X := Y
% 202.02/202.45     Y := X
% 202.02/202.45  end
% 202.02/202.45  substitution1:
% 202.02/202.45     X := X
% 202.02/202.45  end
% 202.02/202.45  
% 202.02/202.45  subsumption: (22) {G2,W6,D2,L2,V2,M2} S(3);r(17) { X = Y, alpha1( X, Y )
% 202.02/202.45     }.
% 202.02/202.45  parent0: (1067) {G1,W6,D2,L2,V2,M2}  { Y = X, alpha1( Y, X ) }.
% 202.02/202.45  substitution0:
% 202.02/202.45     X := Y
% 202.02/202.45     Y := X
% 202.02/202.45  end
% 202.02/202.45  permutation0:
% 202.02/202.45     0 ==> 0
% 202.02/202.45     1 ==> 1
% 202.02/202.45  end
% 202.02/202.45  
% 202.02/202.45  *** allocated 22500 integers for termspace/termends
% 202.02/202.45  *** allocated 75937 integers for clauses
% 202.02/202.45  *** allocated 15000 integers for justifications
% 202.02/202.45  *** allocated 33750 integers for termspace/termends
% 202.02/202.45  *** allocated 22500 integers for justifications
% 202.02/202.45  *** allocated 33750 integers for justifications
% 202.02/202.45  *** allocated 50625 integers for termspace/termends
% 202.02/202.45  *** allocated 50625 integers for justifications
% 202.02/202.45  *** allocated 113905 integers for clauses
% 202.02/202.45  *** allocated 75937 integers for justifications
% 202.02/202.45  *** allocated 75937 integers for termspace/termends
% 202.02/202.45  *** allocated 113905 integers for justifications
% 202.02/202.45  *** allocated 170857 integers for clauses
% 202.02/202.45  *** allocated 113905 integers for termspace/termends
% 202.02/202.45  *** allocated 170857 integers for justifications
% 202.02/202.45  *** allocated 170857 integers for termspace/termends
% 202.02/202.45  *** allocated 256285 integers for clauses
% 202.02/202.45  *** allocated 256285 integers for justifications
% 202.02/202.45  *** allocated 256285 integers for termspace/termends
% 202.02/202.45  *** allocated 384427 integers for justifications
% 202.02/202.45  *** allocated 384427 integers for clauses
% 202.02/202.45  *** allocated 384427 integers for termspace/termends
% 202.02/202.45  *** allocated 576640 integers for justifications
% 202.02/202.45  eqswap: (1070) {G0,W3,D2,L1,V0,M1}  { ! vd151 ==> vd165 }.
% 202.02/202.45  parent0[0]: (2) {G0,W3,D2,L1,V0,M1} I { ! vd165 ==> vd151 }.
% 202.02/202.45  substitution0:
% 202.02/202.45  end
% 202.02/202.45  
% 202.02/202.45  paramod: (24792) {G1,W6,D2,L2,V1,M2}  { ! vd151 ==> X, alpha1( vd165, X )
% 202.02/202.45     }.
% 202.02/202.45  parent0[0]: (22) {G2,W6,D2,L2,V2,M2} S(3);r(17) { X = Y, alpha1( X, Y ) }.
% 202.02/202.45  parent1[0; 3]: (1070) {G0,W3,D2,L1,V0,M1}  { ! vd151 ==> vd165 }.
% 202.02/202.45  substitution0:
% 202.02/202.45     X := vd165
% 202.02/202.45     Y := X
% 202.02/202.45  end
% 202.02/202.45  substitution1:
% 202.02/202.45  end
% 202.02/202.45  
% 202.02/202.45  eqswap: (24834) {G1,W6,D2,L2,V1,M2}  { ! X ==> vd151, alpha1( vd165, X )
% 202.02/202.45     }.
% 202.02/202.45  parent0[0]: (24792) {G1,W6,D2,L2,V1,M2}  { ! vd151 ==> X, alpha1( vd165, X
% 202.02/202.45     ) }.
% 202.02/202.45  substitution0:
% 202.02/202.45     X := X
% 202.02/202.45  end
% 202.02/202.45  
% 202.02/202.45  subsumption: (43) {G3,W6,D2,L2,V1,M2} P(22,2) { ! X = vd151, alpha1( vd165
% 202.02/202.45    , X ) }.
% 202.02/202.45  parent0: (24834) {G1,W6,D2,L2,V1,M2}  { ! X ==> vd151, alpha1( vd165, X )
% 202.02/202.45     }.
% 202.02/202.45  substitution0:
% 202.02/202.45     X := X
% 202.02/202.45  end
% 202.02/202.45  permutation0:
% 202.02/202.45     0 ==> 0
% 202.02/202.45     1 ==> 1
% 202.02/202.45  end
% 202.02/202.45  
% 202.02/202.45  eqswap: (36651) {G3,W6,D2,L2,V1,M2}  { ! vd151 = X, alpha1( vd165, X ) }.
% 202.02/202.45  parent0[0]: (43) {G3,W6,D2,L2,V1,M2} P(22,2) { ! X = vd151, alpha1( vd165, 
% 202.02/202.45    X ) }.
% 202.02/202.45  substitution0:
% 202.02/202.45     X := X
% 202.02/202.45  end
% 202.02/202.45  
% 202.02/202.45  eqrefl: (36652) {G0,W3,D2,L1,V0,M1}  { alpha1( vd165, vd151 ) }.
% 202.02/202.45  parent0[0]: (36651) {G3,W6,D2,L2,V1,M2}  { ! vd151 = X, alpha1( vd165, X )
% 202.02/202.45     }.
% 202.02/202.45  substitution0:
% 202.02/202.45     X := vd151
% 202.02/202.45  end
% 202.02/202.45  
% 202.02/202.45  subsumption: (46) {G4,W3,D2,L1,V0,M1} Q(43) { alpha1( vd165, vd151 ) }.
% 202.02/202.45  parent0: (36652) {G0,W3,D2,L1,V0,M1}  { alpha1( vd165, vd151 ) }.
% 202.02/202.45  substitution0:
% 202.02/202.45  end
% 202.02/202.45  permutation0:
% 202.02/202.45     0 ==> 0
% 202.02/202.45  end
% 202.02/202.45  
% 202.02/202.45  eqswap: (36653) {G0,W17,D4,L3,V2,M3}  { Y ==> vplus( X, skol1( Y, X ) ), ! 
% 202.02/202.45    alpha1( Y, X ), vplus( Y, skol2( Y, X ) ) ==> X }.
% 202.02/202.45  parent0[1]: (6) {G0,W17,D4,L3,V2,M3} I { ! alpha1( X, Y ), vplus( Y, skol1
% 202.02/202.45    ( X, Y ) ) ==> X, vplus( X, skol2( X, Y ) ) ==> Y }.
% 202.02/202.45  substitution0:
% 202.02/202.45     X := Y
% 202.02/202.45     Y := X
% 202.02/202.45  end
% 202.02/202.45  
% 202.02/202.45  eqswap: (36656) {G0,W5,D3,L1,V1,M1}  { ! vd165 ==> vplus( vd151, X ) }.
% 202.02/202.45  parent0[0]: (0) {G0,W5,D3,L1,V1,M1} I { ! vplus( vd151, X ) ==> vd165 }.
% 202.02/202.45  substitution0:
% 202.02/202.45     X := X
% 202.02/202.45  end
% 202.02/202.45  
% 202.02/202.45  resolution: (36657) {G1,W14,D4,L2,V0,M2}  { vd165 ==> vplus( vd151, skol1( 
% 202.02/202.45    vd165, vd151 ) ), vplus( vd165, skol2( vd165, vd151 ) ) ==> vd151 }.
% 202.02/202.45  parent0[1]: (36653) {G0,W17,D4,L3,V2,M3}  { Y ==> vplus( X, skol1( Y, X ) )
% 202.02/202.45    , ! alpha1( Y, X ), vplus( Y, skol2( Y, X ) ) ==> X }.
% 202.02/202.45  parent1[0]: (46) {G4,W3,D2,L1,V0,M1} Q(43) { alpha1( vd165, vd151 ) }.
% 202.02/202.45  substitution0:
% 202.02/202.45     X := vd151
% 202.02/202.45     Y := vd165
% 202.02/202.45  end
% 202.02/202.45  substitution1:
% 202.02/202.45  end
% 202.02/202.45  
% 202.02/202.45  resolution: (36658) {G1,W7,D4,L1,V0,M1}  { vplus( vd165, skol2( vd165, 
% 202.02/202.45    vd151 ) ) ==> vd151 }.
% 202.02/202.45  parent0[0]: (36656) {G0,W5,D3,L1,V1,M1}  { ! vd165 ==> vplus( vd151, X )
% 202.02/202.45     }.
% 202.02/202.45  parent1[0]: (36657) {G1,W14,D4,L2,V0,M2}  { vd165 ==> vplus( vd151, skol1( 
% 202.02/202.45    vd165, vd151 ) ), vplus( vd165, skol2( vd165, vd151 ) ) ==> vd151 }.
% 202.02/202.45  substitution0:
% 202.02/202.45     X := skol1( vd165, vd151 )
% 202.02/202.45  end
% 202.02/202.45  substitution1:
% 202.02/202.45  end
% 202.02/202.45  
% 202.02/202.45  subsumption: (57) {G5,W7,D4,L1,V0,M1} R(6,46);r(0) { vplus( vd165, skol2( 
% 202.02/202.45    vd165, vd151 ) ) ==> vd151 }.
% 202.02/202.45  parent0: (36658) {G1,W7,D4,L1,V0,M1}  { vplus( vd165, skol2( vd165, vd151 )
% 202.02/202.45     ) ==> vd151 }.
% 202.02/202.45  substitution0:
% 202.02/202.45  end
% 202.02/202.45  permutation0:
% 202.02/202.45     0 ==> 0
% 202.02/202.45  end
% 202.02/202.45  
% 202.02/202.45  resolution: (36662) {G1,W0,D0,L0,V0,M0}  {  }.
% 202.02/202.45  parent0[0]: (1) {G0,W5,D3,L1,V1,M1} I { ! vplus( vd165, X ) ==> vd151 }.
% 202.02/202.45  parent1[0]: (57) {G5,W7,D4,L1,V0,M1} R(6,46);r(0) { vplus( vd165, skol2( 
% 202.02/202.45    vd165, vd151 ) ) ==> vd151 }.
% 202.02/202.45  substitution0:
% 202.02/202.45     X := skol2( vd165, vd151 )
% 202.02/202.45  end
% 202.02/202.45  substitution1:
% 202.02/202.45  end
% 202.02/202.45  
% 202.02/202.45  subsumption: (800) {G6,W0,D0,L0,V0,M0} S(57);r(1) {  }.
% 202.02/202.45  parent0: (36662) {G1,W0,D0,L0,V0,M0}  {  }.
% 202.02/202.45  substitution0:
% 202.02/202.45  end
% 202.02/202.45  permutation0:
% 202.02/202.45  end
% 202.02/202.45  
% 202.02/202.45  Proof check complete!
% 202.02/202.45  
% 202.02/202.45  Memory use:
% 202.02/202.45  
% 202.02/202.45  space for terms:        9182
% 202.02/202.45  space for clauses:      41081
% 202.02/202.45  
% 202.02/202.45  
% 202.02/202.45  clauses generated:      1517
% 202.02/202.45  clauses kept:           801
% 202.02/202.45  clauses selected:       147
% 202.02/202.45  clauses deleted:        4
% 202.02/202.45  clauses inuse deleted:  0
% 202.02/202.45  
% 202.02/202.45  subsentry:          316283656
% 202.02/202.45  literals s-matched: 129405503
% 202.02/202.45  literals matched:   102642527
% 202.02/202.45  full subsumption:   102594032
% 202.02/202.45  
% 202.02/202.45  checksum:           -1915025828
% 202.02/202.45  
% 202.02/202.45  
% 202.02/202.45  Bliksem ended
%------------------------------------------------------------------------------