TSTP Solution File: SWV236+1 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : SWV236+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n032.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 : Wed Jul 20 16:23:03 EDT 2022

% Result   : Theorem 0.88s 1.32s
% Output   : Refutation 0.88s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : SWV236+1 : TPTP v8.1.0. Released v3.2.0.
% 0.00/0.10  % Command  : bliksem %s
% 0.10/0.29  % Computer : n032.cluster.edu
% 0.10/0.29  % Model    : x86_64 x86_64
% 0.10/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29  % Memory   : 8042.1875MB
% 0.10/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29  % CPULimit : 300
% 0.10/0.29  % DateTime : Tue Jun 14 22:16:58 EDT 2022
% 0.10/0.30  % CPUTime  : 
% 0.88/1.32  *** allocated 10000 integers for termspace/termends
% 0.88/1.32  *** allocated 10000 integers for clauses
% 0.88/1.32  *** allocated 10000 integers for justifications
% 0.88/1.32  Bliksem 1.12
% 0.88/1.32  
% 0.88/1.32  
% 0.88/1.32  Automatic Strategy Selection
% 0.88/1.32  
% 0.88/1.32  
% 0.88/1.32  Clauses:
% 0.88/1.32  
% 0.88/1.32  { xor( X, Y ) = xor( Y, X ) }.
% 0.88/1.32  { xor( X, xor( Y, Z ) ) = xor( xor( X, Y ), Z ) }.
% 0.88/1.32  { decrypt( X, crypt( X, Y ) ) = Y }.
% 0.88/1.32  { xor( X, id ) = X }.
% 0.88/1.32  { xor( X, X ) = id }.
% 0.88/1.32  { ! p( crypt( xor( X, Y ), Z ) ), ! p( T ), ! p( crypt( xor( km, imp ), U )
% 0.88/1.32     ), p( crypt( xor( km, T ), decrypt( xor( U, T ), crypt( xor( X, Y ), Z )
% 0.88/1.32     ) ) ) }.
% 0.88/1.32  { ! p( crypt( xor( km, X ), Y ) ), ! p( X ), ! p( crypt( xor( km, exp ), Z
% 0.88/1.32     ) ), p( crypt( xor( Z, X ), Y ) ) }.
% 0.88/1.32  { ! p( X ), ! p( Y ), p( crypt( xor( km, xor( kp, Y ) ), X ) ) }.
% 0.88/1.32  { ! p( X ), ! p( crypt( xor( km, xor( kp, Y ) ), Z ) ), ! p( Y ), p( crypt
% 0.88/1.32    ( xor( km, xor( Y, kp ) ), xor( X, Z ) ) ) }.
% 0.88/1.32  { ! p( X ), ! p( crypt( xor( km, xor( Y, kp ) ), Z ) ), ! p( Y ), p( crypt
% 0.88/1.32    ( xor( km, Y ), xor( Z, X ) ) ) }.
% 0.88/1.32  { ! p( X ), ! p( crypt( xor( km, data ), Y ) ), p( crypt( Y, X ) ) }.
% 0.88/1.32  { ! p( X ), ! p( crypt( xor( km, data ), Y ) ), p( decrypt( Y, X ) ) }.
% 0.88/1.32  { ! p( crypt( X, Y ) ), ! p( Z ), ! p( crypt( xor( km, imp ), T ) ), ! p( 
% 0.88/1.32    crypt( xor( km, exp ), U ) ), p( crypt( xor( U, W ), decrypt( xor( Z, T )
% 0.88/1.32    , crypt( X, Y ) ) ) ) }.
% 0.88/1.32  { ! p( X ), ! p( Y ), p( xor( X, Y ) ) }.
% 0.88/1.32  { ! p( crypt( Y, X ) ), ! p( Y ), p( X ) }.
% 0.88/1.32  { ! p( Y ), ! p( X ), p( crypt( X, Y ) ) }.
% 0.88/1.32  { ! p( crypt( xor( X, data ), Y ) ), p( crypt( X, Y ) ) }.
% 0.88/1.32  { p( kp ) }.
% 0.88/1.32  { p( imp ) }.
% 0.88/1.32  { p( data ) }.
% 0.88/1.32  { p( id ) }.
% 0.88/1.32  { p( pin ) }.
% 0.88/1.32  { p( crypt( xor( km, pin ), pp ) ) }.
% 0.88/1.32  { p( crypt( xor( km, exp ), eurk ) ) }.
% 0.88/1.32  { p( crypt( xor( km, data ), eurk ) ) }.
% 0.88/1.32  { p( exp ) }.
% 0.88/1.32  { p( a ) }.
% 0.88/1.32  { ! p( crypt( xor( km, exp ), X ) ), ! p( X ) }.
% 0.88/1.32  
% 0.88/1.32  percentage equality = 0.086207, percentage horn = 1.000000
% 0.88/1.32  This is a problem with some equality
% 0.88/1.32  
% 0.88/1.32  
% 0.88/1.32  
% 0.88/1.32  Options Used:
% 0.88/1.32  
% 0.88/1.32  useres =            1
% 0.88/1.32  useparamod =        1
% 0.88/1.32  useeqrefl =         1
% 0.88/1.32  useeqfact =         1
% 0.88/1.32  usefactor =         1
% 0.88/1.32  usesimpsplitting =  0
% 0.88/1.32  usesimpdemod =      5
% 0.88/1.32  usesimpres =        3
% 0.88/1.32  
% 0.88/1.32  resimpinuse      =  1000
% 0.88/1.32  resimpclauses =     20000
% 0.88/1.32  substype =          eqrewr
% 0.88/1.32  backwardsubs =      1
% 0.88/1.32  selectoldest =      5
% 0.88/1.32  
% 0.88/1.32  litorderings [0] =  split
% 0.88/1.32  litorderings [1] =  extend the termordering, first sorting on arguments
% 0.88/1.32  
% 0.88/1.32  termordering =      kbo
% 0.88/1.32  
% 0.88/1.32  litapriori =        0
% 0.88/1.32  termapriori =       1
% 0.88/1.32  litaposteriori =    0
% 0.88/1.32  termaposteriori =   0
% 0.88/1.32  demodaposteriori =  0
% 0.88/1.32  ordereqreflfact =   0
% 0.88/1.32  
% 0.88/1.32  litselect =         negord
% 0.88/1.32  
% 0.88/1.32  maxweight =         15
% 0.88/1.32  maxdepth =          30000
% 0.88/1.32  maxlength =         115
% 0.88/1.32  maxnrvars =         195
% 0.88/1.32  excuselevel =       1
% 0.88/1.32  increasemaxweight = 1
% 0.88/1.32  
% 0.88/1.32  maxselected =       10000000
% 0.88/1.32  maxnrclauses =      10000000
% 0.88/1.32  
% 0.88/1.32  showgenerated =    0
% 0.88/1.32  showkept =         0
% 0.88/1.32  showselected =     0
% 0.88/1.32  showdeleted =      0
% 0.88/1.32  showresimp =       1
% 0.88/1.32  showstatus =       2000
% 0.88/1.32  
% 0.88/1.32  prologoutput =     0
% 0.88/1.32  nrgoals =          5000000
% 0.88/1.32  totalproof =       1
% 0.88/1.32  
% 0.88/1.32  Symbols occurring in the translation:
% 0.88/1.32  
% 0.88/1.32  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 0.88/1.32  .  [1, 2]      (w:1, o:34, a:1, s:1, b:0), 
% 0.88/1.32  !  [4, 1]      (w:0, o:28, a:1, s:1, b:0), 
% 0.88/1.32  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.88/1.32  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.88/1.32  xor  [37, 2]      (w:1, o:58, a:1, s:1, b:0), 
% 0.88/1.32  crypt  [39, 2]      (w:1, o:59, a:1, s:1, b:0), 
% 0.88/1.32  decrypt  [40, 2]      (w:1, o:60, a:1, s:1, b:0), 
% 0.88/1.32  id  [41, 0]      (w:1, o:9, a:1, s:1, b:0), 
% 0.88/1.32  p  [47, 1]      (w:1, o:33, a:1, s:1, b:0), 
% 0.88/1.32  km  [48, 0]      (w:1, o:15, a:1, s:1, b:0), 
% 0.88/1.32  imp  [49, 0]      (w:1, o:16, a:1, s:1, b:0), 
% 0.88/1.32  exp  [51, 0]      (w:1, o:19, a:1, s:1, b:0), 
% 0.88/1.32  kp  [53, 0]      (w:1, o:21, a:1, s:1, b:0), 
% 0.88/1.32  data  [55, 0]      (w:1, o:18, a:1, s:1, b:0), 
% 0.88/1.32  pin  [56, 0]      (w:1, o:23, a:1, s:1, b:0), 
% 0.88/1.32  pp  [57, 0]      (w:1, o:24, a:1, s:1, b:0), 
% 0.88/1.32  eurk  [58, 0]      (w:1, o:25, a:1, s:1, b:0), 
% 0.88/1.32  a  [59, 0]      (w:1, o:26, a:1, s:1, b:0).
% 0.88/1.32  
% 0.88/1.32  
% 0.88/1.32  Starting Search:
% 0.88/1.32  
% 0.88/1.32  *** allocated 15000 integers for clauses
% 0.88/1.32  *** allocated 22500 integers for clauses
% 0.88/1.32  *** allocated 33750 integers for clauses
% 0.88/1.32  *** allocated 15000 integers for termspace/termends
% 0.88/1.32  *** allocated 50625 integers for clauses
% 0.88/1.32  *** allocated 75937 integers for clauses
% 0.88/1.32  *** allocated 22500 integers for termspace/termends
% 0.88/1.32  Resimplifying inuse:
% 0.88/1.32  Done
% 0.88/1.32  
% 0.88/1.32  *** allocated 113905 integers for clauses
% 0.88/1.32  *** allocated 33750 integers for termspace/termends
% 0.88/1.32  
% 0.88/1.32  Intermediate Status:
% 0.88/1.32  Generated:    4699
% 0.88/1.32  Kept:         2000
% 0.88/1.32  Inuse:        121
% 0.88/1.32  Deleted:      1
% 0.88/1.32  Deletedinuse: 1
% 0.88/1.32  
% 0.88/1.32  Resimplifying inuse:
% 0.88/1.32  Done
% 0.88/1.32  
% 0.88/1.32  *** allocated 170857 integers for clauses
% 0.88/1.32  *** allocated 50625 integers for termspace/termends
% 0.88/1.32  Resimplifying inuse:
% 0.88/1.32  Done
% 0.88/1.32  
% 0.88/1.32  *** allocated 256285 integers for clauses
% 0.88/1.32  
% 0.88/1.32  Intermediate Status:
% 0.88/1.32  Generated:    9091
% 0.88/1.32  Kept:         4000
% 0.88/1.32  Inuse:        169
% 0.88/1.32  Deleted:      3
% 0.88/1.32  Deletedinuse: 2
% 0.88/1.32  
% 0.88/1.32  Resimplifying inuse:
% 0.88/1.32  Done
% 0.88/1.32  
% 0.88/1.32  *** allocated 75937 integers for termspace/termends
% 0.88/1.32  
% 0.88/1.32  Bliksems!, er is een bewijs:
% 0.88/1.32  % SZS status Theorem
% 0.88/1.32  % SZS output start Refutation
% 0.88/1.32  
% 0.88/1.32  (1) {G0,W11,D4,L1,V3,M1} I { xor( X, xor( Y, Z ) ) ==> xor( xor( X, Y ), Z
% 0.88/1.32     ) }.
% 0.88/1.32  (3) {G0,W5,D3,L1,V1,M1} I { xor( X, id ) ==> X }.
% 0.88/1.32  (4) {G0,W5,D3,L1,V1,M1} I { xor( X, X ) ==> id }.
% 0.88/1.32  (7) {G1,W12,D5,L3,V2,M3} I;d(1) { ! p( X ), ! p( Y ), p( crypt( xor( xor( 
% 0.88/1.32    km, kp ), Y ), X ) ) }.
% 0.88/1.32  (13) {G0,W8,D3,L3,V2,M3} I { ! p( X ), ! p( Y ), p( xor( X, Y ) ) }.
% 0.88/1.32  (17) {G0,W2,D2,L1,V0,M1} I { p( kp ) }.
% 0.88/1.32  (25) {G0,W2,D2,L1,V0,M1} I { p( exp ) }.
% 0.88/1.32  (27) {G0,W8,D4,L2,V1,M2} I { ! p( crypt( xor( km, exp ), X ) ), ! p( X )
% 0.88/1.32     }.
% 0.88/1.32  (33) {G2,W10,D5,L2,V1,M2} F(7) { ! p( X ), p( crypt( xor( xor( km, kp ), X
% 0.88/1.32     ), X ) ) }.
% 0.88/1.32  (44) {G1,W7,D4,L1,V2,M1} P(4,1);d(3) { xor( xor( Y, X ), X ) ==> Y }.
% 0.88/1.32  (679) {G1,W6,D3,L2,V1,M2} R(13,17) { ! p( X ), p( xor( kp, X ) ) }.
% 0.88/1.32  (4731) {G2,W4,D3,L1,V0,M1} R(679,25) { p( xor( kp, exp ) ) }.
% 0.88/1.32  (4988) {G3,W8,D4,L1,V0,M1} R(4731,33);d(1);d(44) { p( crypt( xor( km, exp )
% 0.88/1.32    , xor( kp, exp ) ) ) }.
% 0.88/1.32  (4991) {G4,W0,D0,L0,V0,M0} R(4731,27);r(4988) {  }.
% 0.88/1.32  
% 0.88/1.32  
% 0.88/1.32  % SZS output end Refutation
% 0.88/1.32  found a proof!
% 0.88/1.32  
% 0.88/1.32  
% 0.88/1.32  Unprocessed initial clauses:
% 0.88/1.32  
% 0.88/1.32  (4993) {G0,W7,D3,L1,V2,M1}  { xor( X, Y ) = xor( Y, X ) }.
% 0.88/1.32  (4994) {G0,W11,D4,L1,V3,M1}  { xor( X, xor( Y, Z ) ) = xor( xor( X, Y ), Z
% 0.88/1.32     ) }.
% 0.88/1.32  (4995) {G0,W7,D4,L1,V2,M1}  { decrypt( X, crypt( X, Y ) ) = Y }.
% 0.88/1.32  (4996) {G0,W5,D3,L1,V1,M1}  { xor( X, id ) = X }.
% 0.88/1.32  (4997) {G0,W5,D3,L1,V1,M1}  { xor( X, X ) = id }.
% 0.88/1.32  (4998) {G0,W28,D6,L4,V5,M4}  { ! p( crypt( xor( X, Y ), Z ) ), ! p( T ), ! 
% 0.88/1.32    p( crypt( xor( km, imp ), U ) ), p( crypt( xor( km, T ), decrypt( xor( U
% 0.88/1.32    , T ), crypt( xor( X, Y ), Z ) ) ) ) }.
% 0.88/1.32  (4999) {G0,W20,D4,L4,V3,M4}  { ! p( crypt( xor( km, X ), Y ) ), ! p( X ), !
% 0.88/1.32     p( crypt( xor( km, exp ), Z ) ), p( crypt( xor( Z, X ), Y ) ) }.
% 0.88/1.32  (5000) {G0,W12,D5,L3,V2,M3}  { ! p( X ), ! p( Y ), p( crypt( xor( km, xor( 
% 0.88/1.32    kp, Y ) ), X ) ) }.
% 0.88/1.32  (5001) {G0,W22,D5,L4,V3,M4}  { ! p( X ), ! p( crypt( xor( km, xor( kp, Y )
% 0.88/1.32     ), Z ) ), ! p( Y ), p( crypt( xor( km, xor( Y, kp ) ), xor( X, Z ) ) )
% 0.88/1.32     }.
% 0.88/1.32  (5002) {G0,W20,D5,L4,V3,M4}  { ! p( X ), ! p( crypt( xor( km, xor( Y, kp )
% 0.88/1.32     ), Z ) ), ! p( Y ), p( crypt( xor( km, Y ), xor( Z, X ) ) ) }.
% 0.88/1.32  (5003) {G0,W12,D4,L3,V2,M3}  { ! p( X ), ! p( crypt( xor( km, data ), Y ) )
% 0.88/1.32    , p( crypt( Y, X ) ) }.
% 0.88/1.32  (5004) {G0,W12,D4,L3,V2,M3}  { ! p( X ), ! p( crypt( xor( km, data ), Y ) )
% 0.88/1.32    , p( decrypt( Y, X ) ) }.
% 0.88/1.32  (5005) {G0,W30,D5,L5,V6,M5}  { ! p( crypt( X, Y ) ), ! p( Z ), ! p( crypt( 
% 0.88/1.32    xor( km, imp ), T ) ), ! p( crypt( xor( km, exp ), U ) ), p( crypt( xor( 
% 0.88/1.32    U, W ), decrypt( xor( Z, T ), crypt( X, Y ) ) ) ) }.
% 0.88/1.32  (5006) {G0,W8,D3,L3,V2,M3}  { ! p( X ), ! p( Y ), p( xor( X, Y ) ) }.
% 0.88/1.32  (5007) {G0,W8,D3,L3,V2,M3}  { ! p( crypt( Y, X ) ), ! p( Y ), p( X ) }.
% 0.88/1.32  (5008) {G0,W8,D3,L3,V2,M3}  { ! p( Y ), ! p( X ), p( crypt( X, Y ) ) }.
% 0.88/1.32  (5009) {G0,W10,D4,L2,V2,M2}  { ! p( crypt( xor( X, data ), Y ) ), p( crypt
% 0.88/1.32    ( X, Y ) ) }.
% 0.88/1.32  (5010) {G0,W2,D2,L1,V0,M1}  { p( kp ) }.
% 0.88/1.32  (5011) {G0,W2,D2,L1,V0,M1}  { p( imp ) }.
% 0.88/1.32  (5012) {G0,W2,D2,L1,V0,M1}  { p( data ) }.
% 0.88/1.32  (5013) {G0,W2,D2,L1,V0,M1}  { p( id ) }.
% 0.88/1.32  (5014) {G0,W2,D2,L1,V0,M1}  { p( pin ) }.
% 0.88/1.32  (5015) {G0,W6,D4,L1,V0,M1}  { p( crypt( xor( km, pin ), pp ) ) }.
% 0.88/1.32  (5016) {G0,W6,D4,L1,V0,M1}  { p( crypt( xor( km, exp ), eurk ) ) }.
% 0.88/1.32  (5017) {G0,W6,D4,L1,V0,M1}  { p( crypt( xor( km, data ), eurk ) ) }.
% 0.88/1.32  (5018) {G0,W2,D2,L1,V0,M1}  { p( exp ) }.
% 0.88/1.32  (5019) {G0,W2,D2,L1,V0,M1}  { p( a ) }.
% 0.88/1.32  (5020) {G0,W8,D4,L2,V1,M2}  { ! p( crypt( xor( km, exp ), X ) ), ! p( X )
% 0.88/1.32     }.
% 0.88/1.32  
% 0.88/1.32  
% 0.88/1.32  Total Proof:
% 0.88/1.32  
% 0.88/1.32  subsumption: (1) {G0,W11,D4,L1,V3,M1} I { xor( X, xor( Y, Z ) ) ==> xor( 
% 0.88/1.32    xor( X, Y ), Z ) }.
% 0.88/1.32  parent0: (4994) {G0,W11,D4,L1,V3,M1}  { xor( X, xor( Y, Z ) ) = xor( xor( X
% 0.88/1.32    , Y ), Z ) }.
% 0.88/1.32  substitution0:
% 0.88/1.32     X := X
% 0.88/1.32     Y := Y
% 0.88/1.32     Z := Z
% 0.88/1.32  end
% 0.88/1.32  permutation0:
% 0.88/1.32     0 ==> 0
% 0.88/1.32  end
% 0.88/1.32  
% 0.88/1.32  subsumption: (3) {G0,W5,D3,L1,V1,M1} I { xor( X, id ) ==> X }.
% 0.88/1.32  parent0: (4996) {G0,W5,D3,L1,V1,M1}  { xor( X, id ) = X }.
% 0.88/1.32  substitution0:
% 0.88/1.32     X := X
% 0.88/1.32  end
% 0.88/1.32  permutation0:
% 0.88/1.32     0 ==> 0
% 0.88/1.32  end
% 0.88/1.32  
% 0.88/1.32  subsumption: (4) {G0,W5,D3,L1,V1,M1} I { xor( X, X ) ==> id }.
% 0.88/1.32  parent0: (4997) {G0,W5,D3,L1,V1,M1}  { xor( X, X ) = id }.
% 0.88/1.32  substitution0:
% 0.88/1.32     X := X
% 0.88/1.32  end
% 0.88/1.32  permutation0:
% 0.88/1.32     0 ==> 0
% 0.88/1.32  end
% 0.88/1.32  
% 0.88/1.32  paramod: (5051) {G1,W12,D5,L3,V2,M3}  { p( crypt( xor( xor( km, kp ), X ), 
% 0.88/1.32    Y ) ), ! p( Y ), ! p( X ) }.
% 0.88/1.32  parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { xor( X, xor( Y, Z ) ) ==> xor( xor
% 0.88/1.32    ( X, Y ), Z ) }.
% 0.88/1.32  parent1[2; 2]: (5000) {G0,W12,D5,L3,V2,M3}  { ! p( X ), ! p( Y ), p( crypt
% 0.88/1.32    ( xor( km, xor( kp, Y ) ), X ) ) }.
% 0.88/1.32  substitution0:
% 0.88/1.32     X := km
% 0.88/1.32     Y := kp
% 0.88/1.32     Z := X
% 0.88/1.32  end
% 0.88/1.32  substitution1:
% 0.88/1.32     X := Y
% 0.88/1.32     Y := X
% 0.88/1.32  end
% 0.88/1.32  
% 0.88/1.32  subsumption: (7) {G1,W12,D5,L3,V2,M3} I;d(1) { ! p( X ), ! p( Y ), p( crypt
% 0.88/1.32    ( xor( xor( km, kp ), Y ), X ) ) }.
% 0.88/1.32  parent0: (5051) {G1,W12,D5,L3,V2,M3}  { p( crypt( xor( xor( km, kp ), X ), 
% 0.88/1.32    Y ) ), ! p( Y ), ! p( X ) }.
% 0.88/1.32  substitution0:
% 0.88/1.32     X := Y
% 0.88/1.32     Y := X
% 0.88/1.32  end
% 0.88/1.32  permutation0:
% 0.88/1.32     0 ==> 2
% 0.88/1.32     1 ==> 0
% 0.88/1.32     2 ==> 1
% 0.88/1.32  end
% 0.88/1.32  
% 0.88/1.32  subsumption: (13) {G0,W8,D3,L3,V2,M3} I { ! p( X ), ! p( Y ), p( xor( X, Y
% 0.88/1.32     ) ) }.
% 0.88/1.32  parent0: (5006) {G0,W8,D3,L3,V2,M3}  { ! p( X ), ! p( Y ), p( xor( X, Y ) )
% 0.88/1.32     }.
% 0.88/1.32  substitution0:
% 0.88/1.32     X := X
% 0.88/1.32     Y := Y
% 0.88/1.32  end
% 0.88/1.32  permutation0:
% 0.88/1.32     0 ==> 0
% 0.88/1.32     1 ==> 1
% 0.88/1.32     2 ==> 2
% 0.88/1.32  end
% 0.88/1.32  
% 0.88/1.32  subsumption: (17) {G0,W2,D2,L1,V0,M1} I { p( kp ) }.
% 0.88/1.32  parent0: (5010) {G0,W2,D2,L1,V0,M1}  { p( kp ) }.
% 0.88/1.32  substitution0:
% 0.88/1.32  end
% 0.88/1.32  permutation0:
% 0.88/1.32     0 ==> 0
% 0.88/1.32  end
% 0.88/1.32  
% 0.88/1.32  subsumption: (25) {G0,W2,D2,L1,V0,M1} I { p( exp ) }.
% 0.88/1.32  parent0: (5018) {G0,W2,D2,L1,V0,M1}  { p( exp ) }.
% 0.88/1.32  substitution0:
% 0.88/1.32  end
% 0.88/1.32  permutation0:
% 0.88/1.32     0 ==> 0
% 0.88/1.32  end
% 0.88/1.32  
% 0.88/1.32  subsumption: (27) {G0,W8,D4,L2,V1,M2} I { ! p( crypt( xor( km, exp ), X ) )
% 0.88/1.32    , ! p( X ) }.
% 0.88/1.32  parent0: (5020) {G0,W8,D4,L2,V1,M2}  { ! p( crypt( xor( km, exp ), X ) ), !
% 0.88/1.32     p( X ) }.
% 0.88/1.32  substitution0:
% 0.88/1.32     X := X
% 0.88/1.32  end
% 0.88/1.32  permutation0:
% 0.88/1.32     0 ==> 0
% 0.88/1.32     1 ==> 1
% 0.88/1.32  end
% 0.88/1.32  
% 0.88/1.32  factor: (5164) {G1,W10,D5,L2,V1,M2}  { ! p( X ), p( crypt( xor( xor( km, kp
% 0.88/1.32     ), X ), X ) ) }.
% 0.88/1.32  parent0[0, 1]: (7) {G1,W12,D5,L3,V2,M3} I;d(1) { ! p( X ), ! p( Y ), p( 
% 0.88/1.32    crypt( xor( xor( km, kp ), Y ), X ) ) }.
% 0.88/1.32  substitution0:
% 0.88/1.32     X := X
% 0.88/1.32     Y := X
% 0.88/1.32  end
% 0.88/1.32  
% 0.88/1.32  subsumption: (33) {G2,W10,D5,L2,V1,M2} F(7) { ! p( X ), p( crypt( xor( xor
% 0.88/1.32    ( km, kp ), X ), X ) ) }.
% 0.88/1.32  parent0: (5164) {G1,W10,D5,L2,V1,M2}  { ! p( X ), p( crypt( xor( xor( km, 
% 0.88/1.32    kp ), X ), X ) ) }.
% 0.88/1.32  substitution0:
% 0.88/1.32     X := X
% 0.88/1.32  end
% 0.88/1.32  permutation0:
% 0.88/1.32     0 ==> 0
% 0.88/1.32     1 ==> 1
% 0.88/1.32  end
% 0.88/1.32  
% 0.88/1.32  eqswap: (5166) {G0,W11,D4,L1,V3,M1}  { xor( xor( X, Y ), Z ) ==> xor( X, 
% 0.88/1.32    xor( Y, Z ) ) }.
% 0.88/1.32  parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { xor( X, xor( Y, Z ) ) ==> xor( xor
% 0.88/1.32    ( X, Y ), Z ) }.
% 0.88/1.32  substitution0:
% 0.88/1.32     X := X
% 0.88/1.32     Y := Y
% 0.88/1.32     Z := Z
% 0.88/1.32  end
% 0.88/1.32  
% 0.88/1.32  paramod: (5172) {G1,W9,D4,L1,V2,M1}  { xor( xor( X, Y ), Y ) ==> xor( X, id
% 0.88/1.32     ) }.
% 0.88/1.32  parent0[0]: (4) {G0,W5,D3,L1,V1,M1} I { xor( X, X ) ==> id }.
% 0.88/1.32  parent1[0; 8]: (5166) {G0,W11,D4,L1,V3,M1}  { xor( xor( X, Y ), Z ) ==> xor
% 0.88/1.32    ( X, xor( Y, Z ) ) }.
% 0.88/1.32  substitution0:
% 0.88/1.32     X := Y
% 0.88/1.32  end
% 0.88/1.32  substitution1:
% 0.88/1.32     X := X
% 0.88/1.32     Y := Y
% 0.88/1.32     Z := Y
% 0.88/1.32  end
% 0.88/1.32  
% 0.88/1.32  paramod: (5173) {G1,W7,D4,L1,V2,M1}  { xor( xor( X, Y ), Y ) ==> X }.
% 0.88/1.32  parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { xor( X, id ) ==> X }.
% 0.88/1.32  parent1[0; 6]: (5172) {G1,W9,D4,L1,V2,M1}  { xor( xor( X, Y ), Y ) ==> xor
% 0.88/1.32    ( X, id ) }.
% 0.88/1.32  substitution0:
% 0.88/1.32     X := X
% 0.88/1.32  end
% 0.88/1.32  substitution1:
% 0.88/1.32     X := X
% 0.88/1.32     Y := Y
% 0.88/1.32  end
% 0.88/1.32  
% 0.88/1.32  subsumption: (44) {G1,W7,D4,L1,V2,M1} P(4,1);d(3) { xor( xor( Y, X ), X ) 
% 0.88/1.32    ==> Y }.
% 0.88/1.32  parent0: (5173) {G1,W7,D4,L1,V2,M1}  { xor( xor( X, Y ), Y ) ==> X }.
% 0.88/1.32  substitution0:
% 0.88/1.32     X := Y
% 0.88/1.32     Y := X
% 0.88/1.32  end
% 0.88/1.32  permutation0:
% 0.88/1.32     0 ==> 0
% 0.88/1.32  end
% 0.88/1.32  
% 0.88/1.32  resolution: (5175) {G1,W6,D3,L2,V1,M2}  { ! p( X ), p( xor( kp, X ) ) }.
% 0.88/1.32  parent0[0]: (13) {G0,W8,D3,L3,V2,M3} I { ! p( X ), ! p( Y ), p( xor( X, Y )
% 0.88/1.32     ) }.
% 0.88/1.32  parent1[0]: (17) {G0,W2,D2,L1,V0,M1} I { p( kp ) }.
% 0.88/1.32  substitution0:
% 0.88/1.32     X := kp
% 0.88/1.32     Y := X
% 0.88/1.32  end
% 0.88/1.32  substitution1:
% 0.88/1.32  end
% 0.88/1.32  
% 0.88/1.32  subsumption: (679) {G1,W6,D3,L2,V1,M2} R(13,17) { ! p( X ), p( xor( kp, X )
% 0.88/1.32     ) }.
% 0.88/1.32  parent0: (5175) {G1,W6,D3,L2,V1,M2}  { ! p( X ), p( xor( kp, X ) ) }.
% 0.88/1.32  substitution0:
% 0.88/1.32     X := X
% 0.88/1.32  end
% 0.88/1.32  permutation0:
% 0.88/1.32     0 ==> 0
% 0.88/1.32     1 ==> 1
% 0.88/1.32  end
% 0.88/1.32  
% 0.88/1.32  resolution: (5177) {G1,W4,D3,L1,V0,M1}  { p( xor( kp, exp ) ) }.
% 0.88/1.32  parent0[0]: (679) {G1,W6,D3,L2,V1,M2} R(13,17) { ! p( X ), p( xor( kp, X )
% 0.88/1.32     ) }.
% 0.88/1.32  parent1[0]: (25) {G0,W2,D2,L1,V0,M1} I { p( exp ) }.
% 0.88/1.32  substitution0:
% 0.88/1.32     X := exp
% 0.88/1.32  end
% 0.88/1.32  substitution1:
% 0.88/1.32  end
% 0.88/1.32  
% 0.88/1.32  subsumption: (4731) {G2,W4,D3,L1,V0,M1} R(679,25) { p( xor( kp, exp ) ) }.
% 0.88/1.32  parent0: (5177) {G1,W4,D3,L1,V0,M1}  { p( xor( kp, exp ) ) }.
% 0.88/1.32  substitution0:
% 0.88/1.32  end
% 0.88/1.32  permutation0:
% 0.88/1.32     0 ==> 0
% 0.88/1.32  end
% 0.88/1.32  
% 0.88/1.32  resolution: (5180) {G3,W12,D5,L1,V0,M1}  { p( crypt( xor( xor( km, kp ), 
% 0.88/1.32    xor( kp, exp ) ), xor( kp, exp ) ) ) }.
% 0.88/1.32  parent0[0]: (33) {G2,W10,D5,L2,V1,M2} F(7) { ! p( X ), p( crypt( xor( xor( 
% 0.88/1.32    km, kp ), X ), X ) ) }.
% 0.88/1.32  parent1[0]: (4731) {G2,W4,D3,L1,V0,M1} R(679,25) { p( xor( kp, exp ) ) }.
% 0.88/1.32  substitution0:
% 0.88/1.32     X := xor( kp, exp )
% 0.88/1.32  end
% 0.88/1.32  substitution1:
% 0.88/1.32  end
% 0.88/1.32  
% 0.88/1.32  paramod: (5181) {G1,W12,D6,L1,V0,M1}  { p( crypt( xor( xor( xor( km, kp ), 
% 0.88/1.32    kp ), exp ), xor( kp, exp ) ) ) }.
% 0.88/1.32  parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { xor( X, xor( Y, Z ) ) ==> xor( xor
% 0.88/1.32    ( X, Y ), Z ) }.
% 0.88/1.32  parent1[0; 2]: (5180) {G3,W12,D5,L1,V0,M1}  { p( crypt( xor( xor( km, kp )
% 0.88/1.32    , xor( kp, exp ) ), xor( kp, exp ) ) ) }.
% 0.88/1.32  substitution0:
% 0.88/1.32     X := xor( km, kp )
% 0.88/1.32     Y := kp
% 0.88/1.32     Z := exp
% 0.88/1.32  end
% 0.88/1.32  substitution1:
% 0.88/1.32  end
% 0.88/1.32  
% 0.88/1.32  paramod: (5182) {G2,W8,D4,L1,V0,M1}  { p( crypt( xor( km, exp ), xor( kp, 
% 0.88/1.32    exp ) ) ) }.
% 0.88/1.32  parent0[0]: (44) {G1,W7,D4,L1,V2,M1} P(4,1);d(3) { xor( xor( Y, X ), X ) 
% 0.88/1.32    ==> Y }.
% 0.88/1.32  parent1[0; 3]: (5181) {G1,W12,D6,L1,V0,M1}  { p( crypt( xor( xor( xor( km, 
% 0.88/1.32    kp ), kp ), exp ), xor( kp, exp ) ) ) }.
% 0.88/1.32  substitution0:
% 0.88/1.32     X := kp
% 0.88/1.32     Y := km
% 0.88/1.32  end
% 0.88/1.32  substitution1:
% 0.88/1.32  end
% 0.88/1.32  
% 0.88/1.32  subsumption: (4988) {G3,W8,D4,L1,V0,M1} R(4731,33);d(1);d(44) { p( crypt( 
% 0.88/1.32    xor( km, exp ), xor( kp, exp ) ) ) }.
% 0.88/1.32  parent0: (5182) {G2,W8,D4,L1,V0,M1}  { p( crypt( xor( km, exp ), xor( kp, 
% 0.88/1.32    exp ) ) ) }.
% 0.88/1.32  substitution0:
% 0.88/1.32  end
% 0.88/1.32  permutation0:
% 0.88/1.32     0 ==> 0
% 0.88/1.32  end
% 0.88/1.32  
% 0.88/1.32  resolution: (5183) {G1,W8,D4,L1,V0,M1}  { ! p( crypt( xor( km, exp ), xor( 
% 0.88/1.32    kp, exp ) ) ) }.
% 0.88/1.32  parent0[1]: (27) {G0,W8,D4,L2,V1,M2} I { ! p( crypt( xor( km, exp ), X ) )
% 0.88/1.32    , ! p( X ) }.
% 0.88/1.32  parent1[0]: (4731) {G2,W4,D3,L1,V0,M1} R(679,25) { p( xor( kp, exp ) ) }.
% 0.88/1.32  substitution0:
% 0.88/1.32     X := xor( kp, exp )
% 0.88/1.32  end
% 0.88/1.32  substitution1:
% 0.88/1.32  end
% 0.88/1.32  
% 0.88/1.32  resolution: (5184) {G2,W0,D0,L0,V0,M0}  {  }.
% 0.88/1.32  parent0[0]: (5183) {G1,W8,D4,L1,V0,M1}  { ! p( crypt( xor( km, exp ), xor( 
% 0.88/1.32    kp, exp ) ) ) }.
% 0.88/1.32  parent1[0]: (4988) {G3,W8,D4,L1,V0,M1} R(4731,33);d(1);d(44) { p( crypt( 
% 0.88/1.32    xor( km, exp ), xor( kp, exp ) ) ) }.
% 0.88/1.32  substitution0:
% 0.88/1.32  end
% 0.88/1.32  substitution1:
% 0.88/1.32  end
% 0.88/1.32  
% 0.88/1.32  subsumption: (4991) {G4,W0,D0,L0,V0,M0} R(4731,27);r(4988) {  }.
% 0.88/1.32  parent0: (5184) {G2,W0,D0,L0,V0,M0}  {  }.
% 0.88/1.32  substitution0:
% 0.88/1.32  end
% 0.88/1.32  permutation0:
% 0.88/1.32  end
% 0.88/1.32  
% 0.88/1.32  Proof check complete!
% 0.88/1.32  
% 0.88/1.32  Memory use:
% 0.88/1.32  
% 0.88/1.32  space for terms:        50660
% 0.88/1.32  space for clauses:      242233
% 0.88/1.32  
% 0.88/1.32  
% 0.88/1.32  clauses generated:      10612
% 0.88/1.32  clauses kept:           4992
% 0.88/1.32  clauses selected:       186
% 0.88/1.32  clauses deleted:        3
% 0.88/1.32  clauses inuse deleted:  2
% 0.88/1.32  
% 0.88/1.32  subsentry:          21014
% 0.88/1.32  literals s-matched: 7153
% 0.88/1.32  literals matched:   6602
% 0.88/1.32  full subsumption:   4115
% 0.88/1.32  
% 0.88/1.32  checksum:           -1771058159
% 0.88/1.32  
% 0.88/1.32  
% 0.88/1.32  Bliksem ended
%------------------------------------------------------------------------------