TSTP Solution File: LCL164-1 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : LCL164-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n013.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 0s
% DateTime : Sun Jul 17 07:51:08 EDT 2022

% Result   : Unsatisfiable 0.69s 1.09s
% Output   : Refutation 0.69s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : LCL164-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12  % Command  : bliksem %s
% 0.12/0.34  % Computer : n013.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % DateTime : Sun Jul  3 07:20:14 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.69/1.09  *** allocated 10000 integers for termspace/termends
% 0.69/1.09  *** allocated 10000 integers for clauses
% 0.69/1.09  *** allocated 10000 integers for justifications
% 0.69/1.09  Bliksem 1.12
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  Automatic Strategy Selection
% 0.69/1.09  
% 0.69/1.09  Clauses:
% 0.69/1.09  [
% 0.69/1.09     [ =( not( X ), xor( X, truth ) ) ],
% 0.69/1.09     [ =( xor( X, falsehood ), X ) ],
% 0.69/1.09     [ =( xor( X, X ), falsehood ) ],
% 0.69/1.09     [ =( 'and_star'( X, truth ), X ) ],
% 0.69/1.09     [ =( 'and_star'( X, falsehood ), falsehood ) ],
% 0.69/1.09     [ =( 'and_star'( xor( truth, X ), X ), falsehood ) ],
% 0.69/1.09     [ =( xor( X, xor( truth, Y ) ), xor( xor( X, truth ), Y ) ) ],
% 0.69/1.09     [ =( 'and_star'( xor( 'and_star'( xor( truth, X ), Y ), truth ), Y ), 
% 0.69/1.09    'and_star'( xor( 'and_star'( xor( truth, Y ), X ), truth ), X ) ) ],
% 0.69/1.09     [ =( xor( X, Y ), xor( Y, X ) ) ],
% 0.69/1.09     [ =( 'and_star'( 'and_star'( X, Y ), Z ), 'and_star'( X, 'and_star'( Y, 
% 0.69/1.09    Z ) ) ) ],
% 0.69/1.09     [ =( 'and_star'( X, Y ), 'and_star'( Y, X ) ) ],
% 0.69/1.09     [ =( not( truth ), falsehood ) ],
% 0.69/1.09     [ =( implies( X, Y ), xor( truth, 'and_star'( X, xor( truth, Y ) ) ) ) ]
% 0.69/1.09    ,
% 0.69/1.09     [ ~( =( implies( implies( not( x ), not( y ) ), implies( y, x ) ), truth
% 0.69/1.09     ) ) ]
% 0.69/1.09  ] .
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  percentage equality = 1.000000, percentage horn = 1.000000
% 0.69/1.09  This is a pure equality problem
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  Options Used:
% 0.69/1.09  
% 0.69/1.09  useres =            1
% 0.69/1.09  useparamod =        1
% 0.69/1.09  useeqrefl =         1
% 0.69/1.09  useeqfact =         1
% 0.69/1.09  usefactor =         1
% 0.69/1.09  usesimpsplitting =  0
% 0.69/1.09  usesimpdemod =      5
% 0.69/1.09  usesimpres =        3
% 0.69/1.09  
% 0.69/1.09  resimpinuse      =  1000
% 0.69/1.09  resimpclauses =     20000
% 0.69/1.09  substype =          eqrewr
% 0.69/1.09  backwardsubs =      1
% 0.69/1.09  selectoldest =      5
% 0.69/1.09  
% 0.69/1.09  litorderings [0] =  split
% 0.69/1.09  litorderings [1] =  extend the termordering, first sorting on arguments
% 0.69/1.09  
% 0.69/1.09  termordering =      kbo
% 0.69/1.09  
% 0.69/1.09  litapriori =        0
% 0.69/1.09  termapriori =       1
% 0.69/1.09  litaposteriori =    0
% 0.69/1.09  termaposteriori =   0
% 0.69/1.09  demodaposteriori =  0
% 0.69/1.09  ordereqreflfact =   0
% 0.69/1.09  
% 0.69/1.09  litselect =         negord
% 0.69/1.09  
% 0.69/1.09  maxweight =         15
% 0.69/1.09  maxdepth =          30000
% 0.69/1.09  maxlength =         115
% 0.69/1.09  maxnrvars =         195
% 0.69/1.09  excuselevel =       1
% 0.69/1.09  increasemaxweight = 1
% 0.69/1.09  
% 0.69/1.09  maxselected =       10000000
% 0.69/1.09  maxnrclauses =      10000000
% 0.69/1.09  
% 0.69/1.09  showgenerated =    0
% 0.69/1.09  showkept =         0
% 0.69/1.09  showselected =     0
% 0.69/1.09  showdeleted =      0
% 0.69/1.09  showresimp =       1
% 0.69/1.09  showstatus =       2000
% 0.69/1.09  
% 0.69/1.09  prologoutput =     1
% 0.69/1.09  nrgoals =          5000000
% 0.69/1.09  totalproof =       1
% 0.69/1.09  
% 0.69/1.09  Symbols occurring in the translation:
% 0.69/1.09  
% 0.69/1.09  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 0.69/1.09  .  [1, 2]      (w:1, o:22, a:1, s:1, b:0), 
% 0.69/1.09  !  [4, 1]      (w:0, o:16, a:1, s:1, b:0), 
% 0.69/1.09  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.69/1.09  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.69/1.09  not  [40, 1]      (w:1, o:21, a:1, s:1, b:0), 
% 0.69/1.09  truth  [41, 0]      (w:1, o:10, a:1, s:1, b:0), 
% 0.69/1.09  xor  [42, 2]      (w:1, o:47, a:1, s:1, b:0), 
% 0.69/1.09  falsehood  [43, 0]      (w:1, o:11, a:1, s:1, b:0), 
% 0.69/1.09  'and_star'  [44, 2]      (w:1, o:48, a:1, s:1, b:0), 
% 0.69/1.09  implies  [47, 2]      (w:1, o:49, a:1, s:1, b:0), 
% 0.69/1.09  x  [48, 0]      (w:1, o:14, a:1, s:1, b:0), 
% 0.69/1.09  y  [49, 0]      (w:1, o:15, a:1, s:1, b:0).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  Starting Search:
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  Bliksems!, er is een bewijs:
% 0.69/1.09  % SZS status Unsatisfiable
% 0.69/1.09  % SZS output start Refutation
% 0.69/1.09  
% 0.69/1.09  clause( 0, [ =( xor( X, truth ), not( X ) ) ] )
% 0.69/1.09  .
% 0.69/1.09  clause( 1, [ =( xor( X, falsehood ), X ) ] )
% 0.69/1.09  .
% 0.69/1.09  clause( 5, [ =( 'and_star'( xor( truth, X ), X ), falsehood ) ] )
% 0.69/1.09  .
% 0.69/1.09  clause( 6, [ =( xor( X, xor( truth, Y ) ), xor( not( X ), Y ) ) ] )
% 0.69/1.09  .
% 0.69/1.09  clause( 8, [ =( xor( X, Y ), xor( Y, X ) ) ] )
% 0.69/1.09  .
% 0.69/1.09  clause( 10, [ =( 'and_star'( X, Y ), 'and_star'( Y, X ) ) ] )
% 0.69/1.09  .
% 0.69/1.09  clause( 11, [ =( not( truth ), falsehood ) ] )
% 0.69/1.09  .
% 0.69/1.09  clause( 12, [ =( xor( truth, 'and_star'( X, xor( truth, Y ) ) ), implies( X
% 0.69/1.09    , Y ) ) ] )
% 0.69/1.09  .
% 0.69/1.09  clause( 13, [ ~( =( implies( implies( not( x ), not( y ) ), implies( y, x )
% 0.69/1.09     ), truth ) ) ] )
% 0.69/1.09  .
% 0.69/1.09  clause( 16, [ =( xor( truth, X ), not( X ) ) ] )
% 0.69/1.09  .
% 0.69/1.09  clause( 17, [ =( xor( falsehood, X ), X ) ] )
% 0.69/1.09  .
% 0.69/1.09  clause( 18, [ =( 'and_star'( not( X ), X ), falsehood ) ] )
% 0.69/1.09  .
% 0.69/1.09  clause( 19, [ =( not( falsehood ), truth ) ] )
% 0.69/1.09  .
% 0.69/1.09  clause( 20, [ =( 'and_star'( X, not( X ) ), falsehood ) ] )
% 0.69/1.09  .
% 0.69/1.09  clause( 21, [ =( xor( X, not( Y ) ), xor( not( X ), Y ) ) ] )
% 0.69/1.09  .
% 0.69/1.09  clause( 22, [ =( not( not( X ) ), X ) ] )
% 0.69/1.09  .
% 0.69/1.09  clause( 38, [ =( not( 'and_star'( X, not( Y ) ) ), implies( X, Y ) ) ] )
% 0.69/1.09  .
% 0.69/1.09  clause( 49, [ =( implies( Y, not( X ) ), not( 'and_star'( Y, X ) ) ) ] )
% 0.69/1.09  .
% 0.69/1.09  clause( 50, [ =( implies( X, X ), truth ) ] )
% 0.69/1.09  .
% 0.69/1.09  clause( 55, [ =( not( 'and_star'( not( Y ), X ) ), implies( X, Y ) ) ] )
% 0.69/1.09  .
% 0.69/1.09  clause( 57, [] )
% 0.69/1.09  .
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  % SZS output end Refutation
% 0.69/1.09  found a proof!
% 0.69/1.09  
% 0.69/1.09  % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.69/1.09  
% 0.69/1.09  initialclauses(
% 0.69/1.09  [ clause( 59, [ =( not( X ), xor( X, truth ) ) ] )
% 0.69/1.09  , clause( 60, [ =( xor( X, falsehood ), X ) ] )
% 0.69/1.09  , clause( 61, [ =( xor( X, X ), falsehood ) ] )
% 0.69/1.09  , clause( 62, [ =( 'and_star'( X, truth ), X ) ] )
% 0.69/1.09  , clause( 63, [ =( 'and_star'( X, falsehood ), falsehood ) ] )
% 0.69/1.09  , clause( 64, [ =( 'and_star'( xor( truth, X ), X ), falsehood ) ] )
% 0.69/1.09  , clause( 65, [ =( xor( X, xor( truth, Y ) ), xor( xor( X, truth ), Y ) ) ]
% 0.69/1.09     )
% 0.69/1.09  , clause( 66, [ =( 'and_star'( xor( 'and_star'( xor( truth, X ), Y ), truth
% 0.69/1.09     ), Y ), 'and_star'( xor( 'and_star'( xor( truth, Y ), X ), truth ), X )
% 0.69/1.09     ) ] )
% 0.69/1.09  , clause( 67, [ =( xor( X, Y ), xor( Y, X ) ) ] )
% 0.69/1.09  , clause( 68, [ =( 'and_star'( 'and_star'( X, Y ), Z ), 'and_star'( X, 
% 0.69/1.09    'and_star'( Y, Z ) ) ) ] )
% 0.69/1.09  , clause( 69, [ =( 'and_star'( X, Y ), 'and_star'( Y, X ) ) ] )
% 0.69/1.09  , clause( 70, [ =( not( truth ), falsehood ) ] )
% 0.69/1.09  , clause( 71, [ =( implies( X, Y ), xor( truth, 'and_star'( X, xor( truth, 
% 0.69/1.09    Y ) ) ) ) ] )
% 0.69/1.09  , clause( 72, [ ~( =( implies( implies( not( x ), not( y ) ), implies( y, x
% 0.69/1.09     ) ), truth ) ) ] )
% 0.69/1.09  ] ).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  eqswap(
% 0.69/1.09  clause( 73, [ =( xor( X, truth ), not( X ) ) ] )
% 0.69/1.09  , clause( 59, [ =( not( X ), xor( X, truth ) ) ] )
% 0.69/1.09  , 0, substitution( 0, [ :=( X, X )] )).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  subsumption(
% 0.69/1.09  clause( 0, [ =( xor( X, truth ), not( X ) ) ] )
% 0.69/1.09  , clause( 73, [ =( xor( X, truth ), not( X ) ) ] )
% 0.69/1.09  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  subsumption(
% 0.69/1.09  clause( 1, [ =( xor( X, falsehood ), X ) ] )
% 0.69/1.09  , clause( 60, [ =( xor( X, falsehood ), X ) ] )
% 0.69/1.09  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  subsumption(
% 0.69/1.09  clause( 5, [ =( 'and_star'( xor( truth, X ), X ), falsehood ) ] )
% 0.69/1.09  , clause( 64, [ =( 'and_star'( xor( truth, X ), X ), falsehood ) ] )
% 0.69/1.09  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  paramod(
% 0.69/1.09  clause( 98, [ =( xor( X, xor( truth, Y ) ), xor( not( X ), Y ) ) ] )
% 0.69/1.09  , clause( 0, [ =( xor( X, truth ), not( X ) ) ] )
% 0.69/1.09  , 0, clause( 65, [ =( xor( X, xor( truth, Y ) ), xor( xor( X, truth ), Y )
% 0.69/1.09     ) ] )
% 0.69/1.09  , 0, 7, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ), 
% 0.69/1.09    :=( Y, Y )] )).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  subsumption(
% 0.69/1.09  clause( 6, [ =( xor( X, xor( truth, Y ) ), xor( not( X ), Y ) ) ] )
% 0.69/1.09  , clause( 98, [ =( xor( X, xor( truth, Y ) ), xor( not( X ), Y ) ) ] )
% 0.69/1.09  , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.69/1.09     )] ) ).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  subsumption(
% 0.69/1.09  clause( 8, [ =( xor( X, Y ), xor( Y, X ) ) ] )
% 0.69/1.09  , clause( 67, [ =( xor( X, Y ), xor( Y, X ) ) ] )
% 0.69/1.09  , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.69/1.09     )] ) ).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  subsumption(
% 0.69/1.09  clause( 10, [ =( 'and_star'( X, Y ), 'and_star'( Y, X ) ) ] )
% 0.69/1.09  , clause( 69, [ =( 'and_star'( X, Y ), 'and_star'( Y, X ) ) ] )
% 0.69/1.09  , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.69/1.09     )] ) ).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  subsumption(
% 0.69/1.09  clause( 11, [ =( not( truth ), falsehood ) ] )
% 0.69/1.09  , clause( 70, [ =( not( truth ), falsehood ) ] )
% 0.69/1.09  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  eqswap(
% 0.69/1.09  clause( 133, [ =( xor( truth, 'and_star'( X, xor( truth, Y ) ) ), implies( 
% 0.69/1.09    X, Y ) ) ] )
% 0.69/1.09  , clause( 71, [ =( implies( X, Y ), xor( truth, 'and_star'( X, xor( truth, 
% 0.69/1.09    Y ) ) ) ) ] )
% 0.69/1.09  , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  subsumption(
% 0.69/1.09  clause( 12, [ =( xor( truth, 'and_star'( X, xor( truth, Y ) ) ), implies( X
% 0.69/1.09    , Y ) ) ] )
% 0.69/1.09  , clause( 133, [ =( xor( truth, 'and_star'( X, xor( truth, Y ) ) ), implies( 
% 0.69/1.09    X, Y ) ) ] )
% 0.69/1.09  , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.69/1.09     )] ) ).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  subsumption(
% 0.69/1.09  clause( 13, [ ~( =( implies( implies( not( x ), not( y ) ), implies( y, x )
% 0.69/1.09     ), truth ) ) ] )
% 0.69/1.09  , clause( 72, [ ~( =( implies( implies( not( x ), not( y ) ), implies( y, x
% 0.69/1.09     ) ), truth ) ) ] )
% 0.69/1.09  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  eqswap(
% 0.69/1.09  clause( 145, [ =( not( X ), xor( X, truth ) ) ] )
% 0.69/1.09  , clause( 0, [ =( xor( X, truth ), not( X ) ) ] )
% 0.69/1.09  , 0, substitution( 0, [ :=( X, X )] )).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  paramod(
% 0.69/1.09  clause( 146, [ =( not( X ), xor( truth, X ) ) ] )
% 0.69/1.09  , clause( 8, [ =( xor( X, Y ), xor( Y, X ) ) ] )
% 0.69/1.09  , 0, clause( 145, [ =( not( X ), xor( X, truth ) ) ] )
% 0.69/1.09  , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, truth )] ), substitution( 1
% 0.69/1.09    , [ :=( X, X )] )).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  eqswap(
% 0.69/1.09  clause( 149, [ =( xor( truth, X ), not( X ) ) ] )
% 0.69/1.09  , clause( 146, [ =( not( X ), xor( truth, X ) ) ] )
% 0.69/1.09  , 0, substitution( 0, [ :=( X, X )] )).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  subsumption(
% 0.69/1.09  clause( 16, [ =( xor( truth, X ), not( X ) ) ] )
% 0.69/1.09  , clause( 149, [ =( xor( truth, X ), not( X ) ) ] )
% 0.69/1.09  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  eqswap(
% 0.69/1.09  clause( 150, [ =( X, xor( X, falsehood ) ) ] )
% 0.69/1.09  , clause( 1, [ =( xor( X, falsehood ), X ) ] )
% 0.69/1.09  , 0, substitution( 0, [ :=( X, X )] )).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  paramod(
% 0.69/1.09  clause( 151, [ =( X, xor( falsehood, X ) ) ] )
% 0.69/1.09  , clause( 8, [ =( xor( X, Y ), xor( Y, X ) ) ] )
% 0.69/1.09  , 0, clause( 150, [ =( X, xor( X, falsehood ) ) ] )
% 0.69/1.09  , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, falsehood )] ), 
% 0.69/1.09    substitution( 1, [ :=( X, X )] )).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  eqswap(
% 0.69/1.09  clause( 154, [ =( xor( falsehood, X ), X ) ] )
% 0.69/1.09  , clause( 151, [ =( X, xor( falsehood, X ) ) ] )
% 0.69/1.09  , 0, substitution( 0, [ :=( X, X )] )).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  subsumption(
% 0.69/1.09  clause( 17, [ =( xor( falsehood, X ), X ) ] )
% 0.69/1.09  , clause( 154, [ =( xor( falsehood, X ), X ) ] )
% 0.69/1.09  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  paramod(
% 0.69/1.09  clause( 157, [ =( 'and_star'( not( X ), X ), falsehood ) ] )
% 0.69/1.09  , clause( 16, [ =( xor( truth, X ), not( X ) ) ] )
% 0.69/1.09  , 0, clause( 5, [ =( 'and_star'( xor( truth, X ), X ), falsehood ) ] )
% 0.69/1.09  , 0, 2, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 0.69/1.09    ).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  subsumption(
% 0.69/1.09  clause( 18, [ =( 'and_star'( not( X ), X ), falsehood ) ] )
% 0.69/1.09  , clause( 157, [ =( 'and_star'( not( X ), X ), falsehood ) ] )
% 0.69/1.09  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  eqswap(
% 0.69/1.09  clause( 159, [ =( X, xor( falsehood, X ) ) ] )
% 0.69/1.09  , clause( 17, [ =( xor( falsehood, X ), X ) ] )
% 0.69/1.09  , 0, substitution( 0, [ :=( X, X )] )).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  paramod(
% 0.69/1.09  clause( 161, [ =( truth, not( falsehood ) ) ] )
% 0.69/1.09  , clause( 0, [ =( xor( X, truth ), not( X ) ) ] )
% 0.69/1.09  , 0, clause( 159, [ =( X, xor( falsehood, X ) ) ] )
% 0.69/1.09  , 0, 2, substitution( 0, [ :=( X, falsehood )] ), substitution( 1, [ :=( X
% 0.69/1.09    , truth )] )).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  eqswap(
% 0.69/1.09  clause( 162, [ =( not( falsehood ), truth ) ] )
% 0.69/1.09  , clause( 161, [ =( truth, not( falsehood ) ) ] )
% 0.69/1.09  , 0, substitution( 0, [] )).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  subsumption(
% 0.69/1.09  clause( 19, [ =( not( falsehood ), truth ) ] )
% 0.69/1.09  , clause( 162, [ =( not( falsehood ), truth ) ] )
% 0.69/1.09  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  eqswap(
% 0.69/1.09  clause( 163, [ =( falsehood, 'and_star'( not( X ), X ) ) ] )
% 0.69/1.09  , clause( 18, [ =( 'and_star'( not( X ), X ), falsehood ) ] )
% 0.69/1.09  , 0, substitution( 0, [ :=( X, X )] )).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  paramod(
% 0.69/1.09  clause( 164, [ =( falsehood, 'and_star'( X, not( X ) ) ) ] )
% 0.69/1.09  , clause( 10, [ =( 'and_star'( X, Y ), 'and_star'( Y, X ) ) ] )
% 0.69/1.09  , 0, clause( 163, [ =( falsehood, 'and_star'( not( X ), X ) ) ] )
% 0.69/1.09  , 0, 2, substitution( 0, [ :=( X, not( X ) ), :=( Y, X )] ), substitution( 
% 0.69/1.09    1, [ :=( X, X )] )).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  eqswap(
% 0.69/1.09  clause( 167, [ =( 'and_star'( X, not( X ) ), falsehood ) ] )
% 0.69/1.09  , clause( 164, [ =( falsehood, 'and_star'( X, not( X ) ) ) ] )
% 0.69/1.09  , 0, substitution( 0, [ :=( X, X )] )).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  subsumption(
% 0.69/1.09  clause( 20, [ =( 'and_star'( X, not( X ) ), falsehood ) ] )
% 0.69/1.09  , clause( 167, [ =( 'and_star'( X, not( X ) ), falsehood ) ] )
% 0.69/1.09  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  paramod(
% 0.69/1.09  clause( 170, [ =( xor( X, not( Y ) ), xor( not( X ), Y ) ) ] )
% 0.69/1.09  , clause( 16, [ =( xor( truth, X ), not( X ) ) ] )
% 0.69/1.09  , 0, clause( 6, [ =( xor( X, xor( truth, Y ) ), xor( not( X ), Y ) ) ] )
% 0.69/1.09  , 0, 3, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ), 
% 0.69/1.09    :=( Y, Y )] )).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  subsumption(
% 0.69/1.09  clause( 21, [ =( xor( X, not( Y ) ), xor( not( X ), Y ) ) ] )
% 0.69/1.09  , clause( 170, [ =( xor( X, not( Y ) ), xor( not( X ), Y ) ) ] )
% 0.69/1.09  , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.69/1.09     )] ) ).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  eqswap(
% 0.69/1.09  clause( 172, [ =( xor( not( X ), Y ), xor( X, not( Y ) ) ) ] )
% 0.69/1.09  , clause( 21, [ =( xor( X, not( Y ) ), xor( not( X ), Y ) ) ] )
% 0.69/1.09  , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  paramod(
% 0.69/1.09  clause( 176, [ =( xor( not( truth ), X ), not( not( X ) ) ) ] )
% 0.69/1.09  , clause( 16, [ =( xor( truth, X ), not( X ) ) ] )
% 0.69/1.09  , 0, clause( 172, [ =( xor( not( X ), Y ), xor( X, not( Y ) ) ) ] )
% 0.69/1.09  , 0, 5, substitution( 0, [ :=( X, not( X ) )] ), substitution( 1, [ :=( X, 
% 0.69/1.09    truth ), :=( Y, X )] )).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  paramod(
% 0.69/1.09  clause( 177, [ =( xor( falsehood, X ), not( not( X ) ) ) ] )
% 0.69/1.09  , clause( 11, [ =( not( truth ), falsehood ) ] )
% 0.69/1.09  , 0, clause( 176, [ =( xor( not( truth ), X ), not( not( X ) ) ) ] )
% 0.69/1.09  , 0, 2, substitution( 0, [] ), substitution( 1, [ :=( X, X )] )).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  paramod(
% 0.69/1.09  clause( 178, [ =( X, not( not( X ) ) ) ] )
% 0.69/1.09  , clause( 17, [ =( xor( falsehood, X ), X ) ] )
% 0.69/1.09  , 0, clause( 177, [ =( xor( falsehood, X ), not( not( X ) ) ) ] )
% 0.69/1.09  , 0, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 0.69/1.09    ).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  eqswap(
% 0.69/1.09  clause( 179, [ =( not( not( X ) ), X ) ] )
% 0.69/1.09  , clause( 178, [ =( X, not( not( X ) ) ) ] )
% 0.69/1.09  , 0, substitution( 0, [ :=( X, X )] )).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  subsumption(
% 0.69/1.09  clause( 22, [ =( not( not( X ) ), X ) ] )
% 0.69/1.09  , clause( 179, [ =( not( not( X ) ), X ) ] )
% 0.69/1.09  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  paramod(
% 0.69/1.09  clause( 184, [ =( xor( truth, 'and_star'( X, not( Y ) ) ), implies( X, Y )
% 0.69/1.09     ) ] )
% 0.69/1.09  , clause( 16, [ =( xor( truth, X ), not( X ) ) ] )
% 0.69/1.09  , 0, clause( 12, [ =( xor( truth, 'and_star'( X, xor( truth, Y ) ) ), 
% 0.69/1.09    implies( X, Y ) ) ] )
% 0.69/1.09  , 0, 5, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ), 
% 0.69/1.09    :=( Y, Y )] )).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  paramod(
% 0.69/1.09  clause( 186, [ =( not( 'and_star'( X, not( Y ) ) ), implies( X, Y ) ) ] )
% 0.69/1.09  , clause( 16, [ =( xor( truth, X ), not( X ) ) ] )
% 0.69/1.09  , 0, clause( 184, [ =( xor( truth, 'and_star'( X, not( Y ) ) ), implies( X
% 0.69/1.09    , Y ) ) ] )
% 0.69/1.09  , 0, 1, substitution( 0, [ :=( X, 'and_star'( X, not( Y ) ) )] ), 
% 0.69/1.09    substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  subsumption(
% 0.69/1.09  clause( 38, [ =( not( 'and_star'( X, not( Y ) ) ), implies( X, Y ) ) ] )
% 0.69/1.09  , clause( 186, [ =( not( 'and_star'( X, not( Y ) ) ), implies( X, Y ) ) ]
% 0.69/1.09     )
% 0.69/1.09  , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.69/1.09     )] ) ).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  eqswap(
% 0.69/1.09  clause( 189, [ =( implies( X, Y ), not( 'and_star'( X, not( Y ) ) ) ) ] )
% 0.69/1.09  , clause( 38, [ =( not( 'and_star'( X, not( Y ) ) ), implies( X, Y ) ) ] )
% 0.69/1.09  , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  paramod(
% 0.69/1.09  clause( 192, [ =( implies( X, not( Y ) ), not( 'and_star'( X, Y ) ) ) ] )
% 0.69/1.09  , clause( 22, [ =( not( not( X ) ), X ) ] )
% 0.69/1.09  , 0, clause( 189, [ =( implies( X, Y ), not( 'and_star'( X, not( Y ) ) ) )
% 0.69/1.09     ] )
% 0.69/1.09  , 0, 8, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ), 
% 0.69/1.09    :=( Y, not( Y ) )] )).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  subsumption(
% 0.69/1.09  clause( 49, [ =( implies( Y, not( X ) ), not( 'and_star'( Y, X ) ) ) ] )
% 0.69/1.09  , clause( 192, [ =( implies( X, not( Y ) ), not( 'and_star'( X, Y ) ) ) ]
% 0.69/1.09     )
% 0.69/1.09  , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 0.69/1.09     )] ) ).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  eqswap(
% 0.69/1.09  clause( 195, [ =( implies( X, Y ), not( 'and_star'( X, not( Y ) ) ) ) ] )
% 0.69/1.09  , clause( 38, [ =( not( 'and_star'( X, not( Y ) ) ), implies( X, Y ) ) ] )
% 0.69/1.09  , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  paramod(
% 0.69/1.09  clause( 198, [ =( implies( X, X ), not( falsehood ) ) ] )
% 0.69/1.09  , clause( 20, [ =( 'and_star'( X, not( X ) ), falsehood ) ] )
% 0.69/1.09  , 0, clause( 195, [ =( implies( X, Y ), not( 'and_star'( X, not( Y ) ) ) )
% 0.69/1.09     ] )
% 0.69/1.09  , 0, 5, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ), 
% 0.69/1.09    :=( Y, X )] )).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  paramod(
% 0.69/1.09  clause( 199, [ =( implies( X, X ), truth ) ] )
% 0.69/1.09  , clause( 19, [ =( not( falsehood ), truth ) ] )
% 0.69/1.09  , 0, clause( 198, [ =( implies( X, X ), not( falsehood ) ) ] )
% 0.69/1.09  , 0, 4, substitution( 0, [] ), substitution( 1, [ :=( X, X )] )).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  subsumption(
% 0.69/1.09  clause( 50, [ =( implies( X, X ), truth ) ] )
% 0.69/1.09  , clause( 199, [ =( implies( X, X ), truth ) ] )
% 0.69/1.09  , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  eqswap(
% 0.69/1.09  clause( 201, [ =( implies( X, Y ), not( 'and_star'( X, not( Y ) ) ) ) ] )
% 0.69/1.09  , clause( 38, [ =( not( 'and_star'( X, not( Y ) ) ), implies( X, Y ) ) ] )
% 0.69/1.09  , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  paramod(
% 0.69/1.09  clause( 202, [ =( implies( X, Y ), not( 'and_star'( not( Y ), X ) ) ) ] )
% 0.69/1.09  , clause( 10, [ =( 'and_star'( X, Y ), 'and_star'( Y, X ) ) ] )
% 0.69/1.09  , 0, clause( 201, [ =( implies( X, Y ), not( 'and_star'( X, not( Y ) ) ) )
% 0.69/1.09     ] )
% 0.69/1.09  , 0, 5, substitution( 0, [ :=( X, X ), :=( Y, not( Y ) )] ), substitution( 
% 0.69/1.09    1, [ :=( X, X ), :=( Y, Y )] )).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  eqswap(
% 0.69/1.09  clause( 205, [ =( not( 'and_star'( not( Y ), X ) ), implies( X, Y ) ) ] )
% 0.69/1.09  , clause( 202, [ =( implies( X, Y ), not( 'and_star'( not( Y ), X ) ) ) ]
% 0.69/1.09     )
% 0.69/1.09  , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  subsumption(
% 0.69/1.09  clause( 55, [ =( not( 'and_star'( not( Y ), X ) ), implies( X, Y ) ) ] )
% 0.69/1.09  , clause( 205, [ =( not( 'and_star'( not( Y ), X ) ), implies( X, Y ) ) ]
% 0.69/1.09     )
% 0.69/1.09  , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.69/1.09     )] ) ).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  paramod(
% 0.69/1.09  clause( 210, [ ~( =( implies( not( 'and_star'( not( x ), y ) ), implies( y
% 0.69/1.09    , x ) ), truth ) ) ] )
% 0.69/1.09  , clause( 49, [ =( implies( Y, not( X ) ), not( 'and_star'( Y, X ) ) ) ] )
% 0.69/1.09  , 0, clause( 13, [ ~( =( implies( implies( not( x ), not( y ) ), implies( y
% 0.69/1.09    , x ) ), truth ) ) ] )
% 0.69/1.09  , 0, 3, substitution( 0, [ :=( X, y ), :=( Y, not( x ) )] ), substitution( 
% 0.69/1.09    1, [] )).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  paramod(
% 0.69/1.09  clause( 211, [ ~( =( implies( implies( y, x ), implies( y, x ) ), truth ) )
% 0.69/1.09     ] )
% 0.69/1.09  , clause( 55, [ =( not( 'and_star'( not( Y ), X ) ), implies( X, Y ) ) ] )
% 0.69/1.09  , 0, clause( 210, [ ~( =( implies( not( 'and_star'( not( x ), y ) ), 
% 0.69/1.09    implies( y, x ) ), truth ) ) ] )
% 0.69/1.09  , 0, 3, substitution( 0, [ :=( X, y ), :=( Y, x )] ), substitution( 1, [] )
% 0.69/1.09    ).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  paramod(
% 0.69/1.09  clause( 212, [ ~( =( truth, truth ) ) ] )
% 0.69/1.09  , clause( 50, [ =( implies( X, X ), truth ) ] )
% 0.69/1.09  , 0, clause( 211, [ ~( =( implies( implies( y, x ), implies( y, x ) ), 
% 0.69/1.09    truth ) ) ] )
% 0.69/1.09  , 0, 2, substitution( 0, [ :=( X, implies( y, x ) )] ), substitution( 1, [] )
% 0.69/1.09    ).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  eqrefl(
% 0.69/1.09  clause( 213, [] )
% 0.69/1.09  , clause( 212, [ ~( =( truth, truth ) ) ] )
% 0.69/1.09  , 0, substitution( 0, [] )).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  subsumption(
% 0.69/1.09  clause( 57, [] )
% 0.69/1.09  , clause( 213, [] )
% 0.69/1.09  , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  end.
% 0.69/1.09  
% 0.69/1.09  % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.69/1.09  
% 0.69/1.09  Memory use:
% 0.69/1.09  
% 0.69/1.09  space for terms:        780
% 0.69/1.09  space for clauses:      5584
% 0.69/1.09  
% 0.69/1.09  
% 0.69/1.09  clauses generated:      363
% 0.69/1.09  clauses kept:           58
% 0.69/1.09  clauses selected:       26
% 0.69/1.09  clauses deleted:        5
% 0.69/1.09  clauses inuse deleted:  0
% 0.69/1.10  
% 0.69/1.10  subsentry:          576
% 0.69/1.10  literals s-matched: 272
% 0.69/1.10  literals matched:   272
% 0.69/1.10  full subsumption:   0
% 0.69/1.10  
% 0.69/1.10  checksum:           37851670
% 0.69/1.10  
% 0.69/1.10  
% 0.69/1.10  Bliksem ended
%------------------------------------------------------------------------------