TSTP Solution File: LCL006-1 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : LCL006-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n023.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 07:49:06 EDT 2022

% Result   : Unsatisfiable 0.80s 1.18s
% Output   : Refutation 0.80s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : LCL006-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13  % Command  : bliksem %s
% 0.13/0.34  % Computer : n023.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % DateTime : Sun Jul  3 22:33:28 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.80/1.18  *** allocated 10000 integers for termspace/termends
% 0.80/1.18  *** allocated 10000 integers for clauses
% 0.80/1.18  *** allocated 10000 integers for justifications
% 0.80/1.18  Bliksem 1.12
% 0.80/1.18  
% 0.80/1.18  
% 0.80/1.18  Automatic Strategy Selection
% 0.80/1.18  
% 0.80/1.18  Clauses:
% 0.80/1.18  [
% 0.80/1.18     [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), ~( 'is_a_theorem'( X ) ), 
% 0.80/1.18    'is_a_theorem'( Y ) ],
% 0.80/1.18     [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent( Y, X ) ) )
% 0.80/1.18     ],
% 0.80/1.18     [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ), Z ), 
% 0.80/1.18    equivalent( X, equivalent( Y, Z ) ) ) ) ],
% 0.80/1.18     [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( a, b ), 
% 0.80/1.18    equivalent( c, a ) ), equivalent( b, c ) ) ) ) ]
% 0.80/1.18  ] .
% 0.80/1.18  
% 0.80/1.18  
% 0.80/1.18  percentage equality = 0.000000, percentage horn = 1.000000
% 0.80/1.18  This is a near-Horn, non-equality  problem
% 0.80/1.18  
% 0.80/1.18  
% 0.80/1.18  Options Used:
% 0.80/1.18  
% 0.80/1.18  useres =            1
% 0.80/1.18  useparamod =        0
% 0.80/1.18  useeqrefl =         0
% 0.80/1.18  useeqfact =         0
% 0.80/1.18  usefactor =         1
% 0.80/1.18  usesimpsplitting =  0
% 0.80/1.18  usesimpdemod =      0
% 0.80/1.18  usesimpres =        4
% 0.80/1.18  
% 0.80/1.18  resimpinuse      =  1000
% 0.80/1.18  resimpclauses =     20000
% 0.80/1.18  substype =          standard
% 0.80/1.18  backwardsubs =      1
% 0.80/1.18  selectoldest =      5
% 0.80/1.18  
% 0.80/1.18  litorderings [0] =  split
% 0.80/1.18  litorderings [1] =  liftord
% 0.80/1.18  
% 0.80/1.18  termordering =      none
% 0.80/1.18  
% 0.80/1.18  litapriori =        1
% 0.80/1.18  termapriori =       0
% 0.80/1.18  litaposteriori =    0
% 0.80/1.18  termaposteriori =   0
% 0.80/1.18  demodaposteriori =  0
% 0.80/1.18  ordereqreflfact =   0
% 0.80/1.18  
% 0.80/1.18  litselect =         negative
% 0.80/1.18  
% 0.80/1.18  maxweight =         30000
% 0.80/1.18  maxdepth =          30000
% 0.80/1.18  maxlength =         115
% 0.80/1.18  maxnrvars =         195
% 0.80/1.18  excuselevel =       0
% 0.80/1.18  increasemaxweight = 0
% 0.80/1.18  
% 0.80/1.18  maxselected =       10000000
% 0.80/1.18  maxnrclauses =      10000000
% 0.80/1.18  
% 0.80/1.18  showgenerated =    0
% 0.80/1.18  showkept =         0
% 0.80/1.18  showselected =     0
% 0.80/1.18  showdeleted =      0
% 0.80/1.18  showresimp =       1
% 0.80/1.18  showstatus =       2000
% 0.80/1.18  
% 0.80/1.18  prologoutput =     1
% 0.80/1.18  nrgoals =          5000000
% 0.80/1.18  totalproof =       1
% 0.80/1.18  
% 0.80/1.18  Symbols occurring in the translation:
% 0.80/1.18  
% 0.80/1.18  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 0.80/1.18  .  [1, 2]      (w:1, o:21, a:1, s:1, b:0), 
% 0.80/1.18  !  [4, 1]      (w:1, o:15, a:1, s:1, b:0), 
% 0.80/1.18  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.80/1.18  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.80/1.18  equivalent  [41, 2]      (w:1, o:46, a:1, s:1, b:0), 
% 0.80/1.18  'is_a_theorem'  [42, 1]      (w:1, o:20, a:1, s:1, b:0), 
% 0.80/1.18  a  [44, 0]      (w:1, o:12, a:1, s:1, b:0), 
% 0.80/1.18  b  [45, 0]      (w:1, o:13, a:1, s:1, b:0), 
% 0.80/1.18  c  [46, 0]      (w:1, o:14, a:1, s:1, b:0).
% 0.80/1.18  
% 0.80/1.18  
% 0.80/1.18  Starting Search:
% 0.80/1.18  
% 0.80/1.18  Resimplifying inuse:
% 0.80/1.18  Done
% 0.80/1.18  
% 0.80/1.18  
% 0.80/1.18  Intermediate Status:
% 0.80/1.18  Generated:    4220
% 0.80/1.18  Kept:         2042
% 0.80/1.18  Inuse:        276
% 0.80/1.18  Deleted:      0
% 0.80/1.18  Deletedinuse: 0
% 0.80/1.18  
% 0.80/1.18  Resimplifying inuse:
% 0.80/1.18  Done
% 0.80/1.18  
% 0.80/1.18  Resimplifying inuse:
% 0.80/1.18  Done
% 0.80/1.18  
% 0.80/1.18  
% 0.80/1.18  Intermediate Status:
% 0.80/1.18  Generated:    7773
% 0.80/1.18  Kept:         4049
% 0.80/1.18  Inuse:        422
% 0.80/1.18  Deleted:      0
% 0.80/1.18  Deletedinuse: 0
% 0.80/1.18  
% 0.80/1.18  Resimplifying inuse:
% 0.80/1.18  Done
% 0.80/1.18  
% 0.80/1.18  
% 0.80/1.18  Bliksems!, er is een bewijs:
% 0.80/1.18  % SZS status Unsatisfiable
% 0.80/1.18  % SZS output start Refutation
% 0.80/1.18  
% 0.80/1.18  clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y )
% 0.80/1.18    , ~( 'is_a_theorem'( X ) ) ] )
% 0.80/1.18  .
% 0.80/1.18  clause( 1, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent( Y
% 0.80/1.18    , X ) ) ) ] )
% 0.80/1.18  .
% 0.80/1.18  clause( 2, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ), Z
% 0.80/1.18     ), equivalent( X, equivalent( Y, Z ) ) ) ) ] )
% 0.80/1.18  .
% 0.80/1.18  clause( 3, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( a, b )
% 0.80/1.18    , equivalent( c, a ) ), equivalent( b, c ) ) ) ) ] )
% 0.80/1.18  .
% 0.80/1.18  clause( 5, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent( equivalent( 
% 0.80/1.18    equivalent( equivalent( X, Y ), Z ), equivalent( X, equivalent( Y, Z ) )
% 0.80/1.18     ), T ) ) ) ] )
% 0.80/1.18  .
% 0.80/1.18  clause( 7, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent( Z
% 0.80/1.18    , equivalent( X, equivalent( Y, Z ) ) ) ) ) ] )
% 0.80/1.18  .
% 0.80/1.18  clause( 8, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y, Z )
% 0.80/1.18     ), equivalent( equivalent( X, Y ), Z ) ) ) ] )
% 0.80/1.18  .
% 0.80/1.18  clause( 12, [ 'is_a_theorem'( equivalent( equivalent( equivalent( 
% 0.80/1.18    equivalent( X, Y ), Z ), X ), equivalent( Y, Z ) ) ) ] )
% 0.80/1.18  .
% 0.80/1.18  clause( 16, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent( 
% 0.80/1.18    equivalent( equivalent( equivalent( equivalent( X, Y ), Z ), X ), 
% 0.80/1.18    equivalent( Y, Z ) ), T ) ) ) ] )
% 0.80/1.18  .
% 0.80/1.18  clause( 17, [ 'is_a_theorem'( equivalent( X, equivalent( equivalent( 
% 0.80/1.18    equivalent( Y, Z ), T ), equivalent( equivalent( Y, equivalent( Z, T ) )
% 0.80/1.18    , X ) ) ) ) ] )
% 0.80/1.18  .
% 0.80/1.18  clause( 103, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent( 
% 0.80/1.18    equivalent( equivalent( Z, X ), Y ), Z ) ) ) ] )
% 0.80/1.18  .
% 0.80/1.18  clause( 110, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent( 
% 0.80/1.18    equivalent( equivalent( X, Y ), equivalent( equivalent( equivalent( Z, X
% 0.80/1.18     ), Y ), Z ) ), T ) ) ) ] )
% 0.80/1.18  .
% 0.80/1.18  clause( 121, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent( 
% 0.80/1.18    equivalent( X, equivalent( equivalent( equivalent( Y, Z ), T ), 
% 0.80/1.18    equivalent( equivalent( Y, equivalent( Z, T ) ), X ) ) ), U ) ) ) ] )
% 0.80/1.18  .
% 0.80/1.18  clause( 3298, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( 
% 0.80/1.18    equivalent( Y, Z ), T ) ), equivalent( equivalent( Y, equivalent( Z, T )
% 0.80/1.18     ), X ) ) ) ] )
% 0.80/1.18  .
% 0.80/1.18  clause( 4485, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y )
% 0.80/1.18    , equivalent( Z, X ) ), equivalent( Y, Z ) ) ) ] )
% 0.80/1.18  .
% 0.80/1.18  clause( 4496, [] )
% 0.80/1.18  .
% 0.80/1.18  
% 0.80/1.18  
% 0.80/1.18  % SZS output end Refutation
% 0.80/1.18  found a proof!
% 0.80/1.18  
% 0.80/1.18  % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.80/1.18  
% 0.80/1.18  initialclauses(
% 0.80/1.18  [ clause( 4498, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), ~( 
% 0.80/1.18    'is_a_theorem'( X ) ), 'is_a_theorem'( Y ) ] )
% 0.80/1.18  , clause( 4499, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), 
% 0.80/1.18    equivalent( Y, X ) ) ) ] )
% 0.81/1.18  , clause( 4500, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.81/1.18     ), Z ), equivalent( X, equivalent( Y, Z ) ) ) ) ] )
% 0.81/1.18  , clause( 4501, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( a
% 0.81/1.18    , b ), equivalent( c, a ) ), equivalent( b, c ) ) ) ) ] )
% 0.81/1.18  ] ).
% 0.81/1.18  
% 0.81/1.18  
% 0.81/1.18  
% 0.81/1.18  subsumption(
% 0.81/1.18  clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y )
% 0.81/1.18    , ~( 'is_a_theorem'( X ) ) ] )
% 0.81/1.18  , clause( 4498, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), ~( 
% 0.81/1.18    'is_a_theorem'( X ) ), 'is_a_theorem'( Y ) ] )
% 0.81/1.18  , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.81/1.18     ), ==>( 1, 2 ), ==>( 2, 1 )] ) ).
% 0.81/1.18  
% 0.81/1.18  
% 0.81/1.18  subsumption(
% 0.81/1.18  clause( 1, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent( Y
% 0.81/1.18    , X ) ) ) ] )
% 0.81/1.18  , clause( 4499, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), 
% 0.81/1.18    equivalent( Y, X ) ) ) ] )
% 0.81/1.18  , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.81/1.18     )] ) ).
% 0.81/1.18  
% 0.81/1.18  
% 0.81/1.18  subsumption(
% 0.81/1.18  clause( 2, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y ), Z
% 0.81/1.18     ), equivalent( X, equivalent( Y, Z ) ) ) ) ] )
% 0.81/1.18  , clause( 4500, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.81/1.18     ), Z ), equivalent( X, equivalent( Y, Z ) ) ) ) ] )
% 0.81/1.18  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ), 
% 0.81/1.18    permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.81/1.18  
% 0.81/1.18  
% 0.81/1.18  subsumption(
% 0.81/1.18  clause( 3, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( a, b )
% 0.81/1.18    , equivalent( c, a ) ), equivalent( b, c ) ) ) ) ] )
% 0.81/1.18  , clause( 4501, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( a
% 0.81/1.18    , b ), equivalent( c, a ) ), equivalent( b, c ) ) ) ) ] )
% 0.81/1.18  , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.81/1.18  
% 0.81/1.18  
% 0.81/1.18  resolution(
% 0.81/1.18  clause( 4503, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( 
% 0.81/1.18    equivalent( X, Y ), Z ), equivalent( X, equivalent( Y, Z ) ) ), T ) ) ), 
% 0.81/1.18    'is_a_theorem'( T ) ] )
% 0.81/1.18  , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.81/1.18     ), ~( 'is_a_theorem'( X ) ) ] )
% 0.81/1.18  , 2, clause( 2, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.81/1.18     ), Z ), equivalent( X, equivalent( Y, Z ) ) ) ) ] )
% 0.81/1.18  , 0, substitution( 0, [ :=( X, equivalent( equivalent( equivalent( X, Y ), 
% 0.81/1.18    Z ), equivalent( X, equivalent( Y, Z ) ) ) ), :=( Y, T )] ), 
% 0.81/1.18    substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.81/1.18  
% 0.81/1.18  
% 0.81/1.18  subsumption(
% 0.81/1.18  clause( 5, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent( equivalent( 
% 0.81/1.18    equivalent( equivalent( X, Y ), Z ), equivalent( X, equivalent( Y, Z ) )
% 0.81/1.18     ), T ) ) ) ] )
% 0.81/1.18  , clause( 4503, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( 
% 0.81/1.18    equivalent( X, Y ), Z ), equivalent( X, equivalent( Y, Z ) ) ), T ) ) ), 
% 0.81/1.18    'is_a_theorem'( T ) ] )
% 0.81/1.18  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ), 
% 0.81/1.18    permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.81/1.18  
% 0.81/1.18  
% 0.81/1.18  resolution(
% 0.81/1.18  clause( 4504, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent( 
% 0.81/1.18    Z, equivalent( X, equivalent( Y, Z ) ) ) ) ) ] )
% 0.81/1.18  , clause( 5, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent( 
% 0.81/1.18    equivalent( equivalent( equivalent( X, Y ), Z ), equivalent( X, 
% 0.81/1.18    equivalent( Y, Z ) ) ), T ) ) ) ] )
% 0.81/1.18  , 1, clause( 2, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.81/1.18     ), Z ), equivalent( X, equivalent( Y, Z ) ) ) ) ] )
% 0.81/1.18  , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, 
% 0.81/1.18    equivalent( equivalent( X, Y ), equivalent( Z, equivalent( X, equivalent( 
% 0.81/1.18    Y, Z ) ) ) ) )] ), substitution( 1, [ :=( X, equivalent( X, Y ) ), :=( Y
% 0.81/1.18    , Z ), :=( Z, equivalent( X, equivalent( Y, Z ) ) )] )).
% 0.81/1.18  
% 0.81/1.18  
% 0.81/1.18  subsumption(
% 0.81/1.18  clause( 7, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent( Z
% 0.81/1.18    , equivalent( X, equivalent( Y, Z ) ) ) ) ) ] )
% 0.81/1.18  , clause( 4504, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), 
% 0.81/1.18    equivalent( Z, equivalent( X, equivalent( Y, Z ) ) ) ) ) ] )
% 0.81/1.18  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ), 
% 0.81/1.18    permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.81/1.18  
% 0.81/1.18  
% 0.81/1.18  resolution(
% 0.81/1.18  clause( 4505, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y, Z
% 0.81/1.18     ) ), equivalent( equivalent( X, Y ), Z ) ) ) ] )
% 0.81/1.18  , clause( 5, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent( 
% 0.81/1.18    equivalent( equivalent( equivalent( X, Y ), Z ), equivalent( X, 
% 0.81/1.18    equivalent( Y, Z ) ) ), T ) ) ) ] )
% 0.81/1.18  , 1, clause( 1, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), 
% 0.81/1.18    equivalent( Y, X ) ) ) ] )
% 0.81/1.18  , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, 
% 0.81/1.18    equivalent( equivalent( X, equivalent( Y, Z ) ), equivalent( equivalent( 
% 0.81/1.18    X, Y ), Z ) ) )] ), substitution( 1, [ :=( X, equivalent( equivalent( X, 
% 0.81/1.18    Y ), Z ) ), :=( Y, equivalent( X, equivalent( Y, Z ) ) )] )).
% 0.81/1.18  
% 0.81/1.18  
% 0.81/1.18  subsumption(
% 0.81/1.18  clause( 8, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y, Z )
% 0.81/1.18     ), equivalent( equivalent( X, Y ), Z ) ) ) ] )
% 0.81/1.18  , clause( 4505, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y
% 0.81/1.18    , Z ) ), equivalent( equivalent( X, Y ), Z ) ) ) ] )
% 0.81/1.18  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ), 
% 0.81/1.18    permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.81/1.18  
% 0.81/1.18  
% 0.81/1.18  resolution(
% 0.81/1.18  clause( 4506, [ 'is_a_theorem'( equivalent( equivalent( equivalent( 
% 0.81/1.18    equivalent( X, Y ), Z ), X ), equivalent( Y, Z ) ) ) ] )
% 0.81/1.18  , clause( 5, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent( 
% 0.81/1.18    equivalent( equivalent( equivalent( X, Y ), Z ), equivalent( X, 
% 0.81/1.18    equivalent( Y, Z ) ) ), T ) ) ) ] )
% 0.81/1.18  , 1, clause( 8, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y
% 0.81/1.18    , Z ) ), equivalent( equivalent( X, Y ), Z ) ) ) ] )
% 0.81/1.18  , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, 
% 0.81/1.18    equivalent( equivalent( equivalent( equivalent( X, Y ), Z ), X ), 
% 0.81/1.18    equivalent( Y, Z ) ) )] ), substitution( 1, [ :=( X, equivalent( 
% 0.81/1.18    equivalent( X, Y ), Z ) ), :=( Y, X ), :=( Z, equivalent( Y, Z ) )] )
% 0.81/1.18    ).
% 0.81/1.18  
% 0.81/1.18  
% 0.81/1.18  subsumption(
% 0.81/1.18  clause( 12, [ 'is_a_theorem'( equivalent( equivalent( equivalent( 
% 0.81/1.18    equivalent( X, Y ), Z ), X ), equivalent( Y, Z ) ) ) ] )
% 0.81/1.18  , clause( 4506, [ 'is_a_theorem'( equivalent( equivalent( equivalent( 
% 0.81/1.18    equivalent( X, Y ), Z ), X ), equivalent( Y, Z ) ) ) ] )
% 0.81/1.18  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ), 
% 0.81/1.18    permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.81/1.18  
% 0.81/1.18  
% 0.81/1.18  resolution(
% 0.81/1.18  clause( 4508, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( 
% 0.81/1.18    equivalent( equivalent( X, Y ), Z ), X ), equivalent( Y, Z ) ), T ) ) ), 
% 0.81/1.18    'is_a_theorem'( T ) ] )
% 0.81/1.18  , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.81/1.18     ), ~( 'is_a_theorem'( X ) ) ] )
% 0.81/1.18  , 2, clause( 12, [ 'is_a_theorem'( equivalent( equivalent( equivalent( 
% 0.81/1.18    equivalent( X, Y ), Z ), X ), equivalent( Y, Z ) ) ) ] )
% 0.81/1.18  , 0, substitution( 0, [ :=( X, equivalent( equivalent( equivalent( 
% 0.81/1.18    equivalent( X, Y ), Z ), X ), equivalent( Y, Z ) ) ), :=( Y, T )] ), 
% 0.81/1.18    substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.81/1.18  
% 0.81/1.18  
% 0.81/1.18  subsumption(
% 0.81/1.18  clause( 16, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent( 
% 0.81/1.18    equivalent( equivalent( equivalent( equivalent( X, Y ), Z ), X ), 
% 0.81/1.18    equivalent( Y, Z ) ), T ) ) ) ] )
% 0.81/1.18  , clause( 4508, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( 
% 0.81/1.18    equivalent( equivalent( X, Y ), Z ), X ), equivalent( Y, Z ) ), T ) ) ), 
% 0.81/1.18    'is_a_theorem'( T ) ] )
% 0.81/1.18  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ), 
% 0.81/1.18    permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.81/1.18  
% 0.81/1.18  
% 0.81/1.18  resolution(
% 0.81/1.18  clause( 4509, [ 'is_a_theorem'( equivalent( X, equivalent( equivalent( 
% 0.81/1.18    equivalent( Y, Z ), T ), equivalent( equivalent( Y, equivalent( Z, T ) )
% 0.81/1.18    , X ) ) ) ) ] )
% 0.81/1.18  , clause( 5, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent( 
% 0.81/1.18    equivalent( equivalent( equivalent( X, Y ), Z ), equivalent( X, 
% 0.81/1.18    equivalent( Y, Z ) ) ), T ) ) ) ] )
% 0.81/1.18  , 1, clause( 7, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), 
% 0.81/1.18    equivalent( Z, equivalent( X, equivalent( Y, Z ) ) ) ) ) ] )
% 0.81/1.18  , 0, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, T ), :=( T, 
% 0.81/1.18    equivalent( X, equivalent( equivalent( equivalent( Y, Z ), T ), 
% 0.81/1.18    equivalent( equivalent( Y, equivalent( Z, T ) ), X ) ) ) )] ), 
% 0.81/1.18    substitution( 1, [ :=( X, equivalent( equivalent( Y, Z ), T ) ), :=( Y, 
% 0.81/1.18    equivalent( Y, equivalent( Z, T ) ) ), :=( Z, X )] )).
% 0.81/1.18  
% 0.81/1.18  
% 0.81/1.18  subsumption(
% 0.81/1.18  clause( 17, [ 'is_a_theorem'( equivalent( X, equivalent( equivalent( 
% 0.81/1.18    equivalent( Y, Z ), T ), equivalent( equivalent( Y, equivalent( Z, T ) )
% 0.81/1.18    , X ) ) ) ) ] )
% 0.81/1.18  , clause( 4509, [ 'is_a_theorem'( equivalent( X, equivalent( equivalent( 
% 0.81/1.18    equivalent( Y, Z ), T ), equivalent( equivalent( Y, equivalent( Z, T ) )
% 0.81/1.18    , X ) ) ) ) ] )
% 0.81/1.18  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ), 
% 0.81/1.18    permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.81/1.18  
% 0.81/1.18  
% 0.81/1.18  resolution(
% 0.81/1.18  clause( 4510, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent( 
% 0.81/1.18    equivalent( equivalent( Z, X ), Y ), Z ) ) ) ] )
% 0.81/1.18  , clause( 16, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent( 
% 0.81/1.18    equivalent( equivalent( equivalent( equivalent( X, Y ), Z ), X ), 
% 0.81/1.18    equivalent( Y, Z ) ), T ) ) ) ] )
% 0.81/1.18  , 1, clause( 1, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), 
% 0.81/1.18    equivalent( Y, X ) ) ) ] )
% 0.81/1.18  , 0, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y ), :=( T, 
% 0.81/1.18    equivalent( equivalent( X, Y ), equivalent( equivalent( equivalent( Z, X
% 0.81/1.18     ), Y ), Z ) ) )] ), substitution( 1, [ :=( X, equivalent( equivalent( 
% 0.81/1.18    equivalent( Z, X ), Y ), Z ) ), :=( Y, equivalent( X, Y ) )] )).
% 0.81/1.18  
% 0.81/1.18  
% 0.81/1.18  subsumption(
% 0.81/1.18  clause( 103, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), equivalent( 
% 0.81/1.18    equivalent( equivalent( Z, X ), Y ), Z ) ) ) ] )
% 0.81/1.18  , clause( 4510, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), 
% 0.81/1.18    equivalent( equivalent( equivalent( Z, X ), Y ), Z ) ) ) ] )
% 0.81/1.18  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ), 
% 0.81/1.18    permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.81/1.18  
% 0.81/1.18  
% 0.81/1.18  resolution(
% 0.81/1.18  clause( 4512, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.81/1.18     ), equivalent( equivalent( equivalent( Z, X ), Y ), Z ) ), T ) ) ), 
% 0.81/1.18    'is_a_theorem'( T ) ] )
% 0.81/1.18  , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.81/1.18     ), ~( 'is_a_theorem'( X ) ) ] )
% 0.81/1.18  , 2, clause( 103, [ 'is_a_theorem'( equivalent( equivalent( X, Y ), 
% 0.81/1.18    equivalent( equivalent( equivalent( Z, X ), Y ), Z ) ) ) ] )
% 0.81/1.18  , 0, substitution( 0, [ :=( X, equivalent( equivalent( X, Y ), equivalent( 
% 0.81/1.18    equivalent( equivalent( Z, X ), Y ), Z ) ) ), :=( Y, T )] ), 
% 0.81/1.18    substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.81/1.18  
% 0.81/1.18  
% 0.81/1.18  subsumption(
% 0.81/1.18  clause( 110, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent( 
% 0.81/1.18    equivalent( equivalent( X, Y ), equivalent( equivalent( equivalent( Z, X
% 0.81/1.18     ), Y ), Z ) ), T ) ) ) ] )
% 0.81/1.18  , clause( 4512, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 0.81/1.18    , Y ), equivalent( equivalent( equivalent( Z, X ), Y ), Z ) ), T ) ) ), 
% 0.81/1.18    'is_a_theorem'( T ) ] )
% 0.81/1.18  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ), 
% 0.81/1.18    permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.81/1.18  
% 0.81/1.18  
% 0.81/1.18  resolution(
% 0.81/1.18  clause( 4514, [ ~( 'is_a_theorem'( equivalent( equivalent( X, equivalent( 
% 0.81/1.18    equivalent( equivalent( Y, Z ), T ), equivalent( equivalent( Y, 
% 0.81/1.18    equivalent( Z, T ) ), X ) ) ), U ) ) ), 'is_a_theorem'( U ) ] )
% 0.81/1.18  , clause( 0, [ ~( 'is_a_theorem'( equivalent( X, Y ) ) ), 'is_a_theorem'( Y
% 0.81/1.18     ), ~( 'is_a_theorem'( X ) ) ] )
% 0.81/1.18  , 2, clause( 17, [ 'is_a_theorem'( equivalent( X, equivalent( equivalent( 
% 0.81/1.18    equivalent( Y, Z ), T ), equivalent( equivalent( Y, equivalent( Z, T ) )
% 0.81/1.18    , X ) ) ) ) ] )
% 0.81/1.18  , 0, substitution( 0, [ :=( X, equivalent( X, equivalent( equivalent( 
% 0.81/1.18    equivalent( Y, Z ), T ), equivalent( equivalent( Y, equivalent( Z, T ) )
% 0.81/1.18    , X ) ) ) ), :=( Y, U )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), 
% 0.81/1.18    :=( Z, Z ), :=( T, T )] )).
% 0.81/1.18  
% 0.81/1.18  
% 0.81/1.18  subsumption(
% 0.81/1.18  clause( 121, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent( 
% 0.81/1.18    equivalent( X, equivalent( equivalent( equivalent( Y, Z ), T ), 
% 0.81/1.18    equivalent( equivalent( Y, equivalent( Z, T ) ), X ) ) ), U ) ) ) ] )
% 0.81/1.18  , clause( 4514, [ ~( 'is_a_theorem'( equivalent( equivalent( X, equivalent( 
% 0.81/1.18    equivalent( equivalent( Y, Z ), T ), equivalent( equivalent( Y, 
% 0.81/1.18    equivalent( Z, T ) ), X ) ) ), U ) ) ), 'is_a_theorem'( U ) ] )
% 0.81/1.18  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.81/1.18    , U )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.81/1.18  
% 0.81/1.18  
% 0.81/1.18  resolution(
% 0.81/1.18  clause( 4515, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( 
% 0.81/1.18    equivalent( Y, Z ), T ) ), equivalent( equivalent( Y, equivalent( Z, T )
% 0.81/1.18     ), X ) ) ) ] )
% 0.81/1.18  , clause( 121, [ 'is_a_theorem'( U ), ~( 'is_a_theorem'( equivalent( 
% 0.81/1.18    equivalent( X, equivalent( equivalent( equivalent( Y, Z ), T ), 
% 0.81/1.18    equivalent( equivalent( Y, equivalent( Z, T ) ), X ) ) ), U ) ) ) ] )
% 0.81/1.18  , 1, clause( 8, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( Y
% 0.81/1.18    , Z ) ), equivalent( equivalent( X, Y ), Z ) ) ) ] )
% 0.81/1.18  , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), 
% 0.81/1.18    :=( U, equivalent( equivalent( X, equivalent( equivalent( Y, Z ), T ) ), 
% 0.81/1.18    equivalent( equivalent( Y, equivalent( Z, T ) ), X ) ) )] ), 
% 0.81/1.18    substitution( 1, [ :=( X, X ), :=( Y, equivalent( equivalent( Y, Z ), T )
% 0.81/1.18     ), :=( Z, equivalent( equivalent( Y, equivalent( Z, T ) ), X ) )] )).
% 0.81/1.18  
% 0.81/1.18  
% 0.81/1.18  subsumption(
% 0.81/1.18  clause( 3298, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( 
% 0.81/1.18    equivalent( Y, Z ), T ) ), equivalent( equivalent( Y, equivalent( Z, T )
% 0.81/1.18     ), X ) ) ) ] )
% 0.81/1.18  , clause( 4515, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( 
% 0.81/1.18    equivalent( Y, Z ), T ) ), equivalent( equivalent( Y, equivalent( Z, T )
% 0.81/1.18     ), X ) ) ) ] )
% 0.81/1.18  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ), 
% 0.81/1.18    permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.81/1.18  
% 0.81/1.18  
% 0.81/1.18  resolution(
% 0.81/1.18  clause( 4516, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y )
% 0.81/1.18    , equivalent( Z, X ) ), equivalent( Y, Z ) ) ) ] )
% 0.81/1.18  , clause( 110, [ 'is_a_theorem'( T ), ~( 'is_a_theorem'( equivalent( 
% 0.81/1.18    equivalent( equivalent( X, Y ), equivalent( equivalent( equivalent( Z, X
% 0.81/1.18     ), Y ), Z ) ), T ) ) ) ] )
% 0.81/1.18  , 1, clause( 3298, [ 'is_a_theorem'( equivalent( equivalent( X, equivalent( 
% 0.81/1.18    equivalent( Y, Z ), T ) ), equivalent( equivalent( Y, equivalent( Z, T )
% 0.81/1.18     ), X ) ) ) ] )
% 0.81/1.18  , 0, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X ), :=( T, 
% 0.81/1.18    equivalent( equivalent( equivalent( X, Y ), equivalent( Z, X ) ), 
% 0.81/1.18    equivalent( Y, Z ) ) )] ), substitution( 1, [ :=( X, equivalent( Y, Z ) )
% 0.81/1.18    , :=( Y, equivalent( X, Y ) ), :=( Z, Z ), :=( T, X )] )).
% 0.81/1.18  
% 0.81/1.18  
% 0.81/1.18  subsumption(
% 0.81/1.18  clause( 4485, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y )
% 0.81/1.18    , equivalent( Z, X ) ), equivalent( Y, Z ) ) ) ] )
% 0.81/1.18  , clause( 4516, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X, Y
% 0.81/1.18     ), equivalent( Z, X ) ), equivalent( Y, Z ) ) ) ] )
% 0.81/1.18  , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ), 
% 0.81/1.18    permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.81/1.18  
% 0.81/1.18  
% 0.81/1.18  resolution(
% 0.81/1.18  clause( 4517, [] )
% 0.81/1.18  , clause( 3, [ ~( 'is_a_theorem'( equivalent( equivalent( equivalent( a, b
% 0.81/1.18     ), equivalent( c, a ) ), equivalent( b, c ) ) ) ) ] )
% 0.81/1.18  , 0, clause( 4485, [ 'is_a_theorem'( equivalent( equivalent( equivalent( X
% 0.81/1.18    , Y ), equivalent( Z, X ) ), equivalent( Y, Z ) ) ) ] )
% 0.81/1.18  , 0, substitution( 0, [] ), substitution( 1, [ :=( X, a ), :=( Y, b ), :=( 
% 0.81/1.18    Z, c )] )).
% 0.81/1.18  
% 0.81/1.18  
% 0.81/1.18  subsumption(
% 0.81/1.18  clause( 4496, [] )
% 0.81/1.18  , clause( 4517, [] )
% 0.81/1.18  , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.81/1.18  
% 0.81/1.18  
% 0.81/1.18  end.
% 0.81/1.18  
% 0.81/1.18  % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.81/1.18  
% 0.81/1.18  Memory use:
% 0.81/1.18  
% 0.81/1.18  space for terms:        83913
% 0.81/1.18  space for clauses:      382493
% 0.81/1.18  
% 0.81/1.18  
% 0.81/1.18  clauses generated:      8866
% 0.81/1.18  clauses kept:           4497
% 0.81/1.18  clauses selected:       478
% 0.81/1.18  clauses deleted:        0
% 0.81/1.18  clauses inuse deleted:  0
% 0.81/1.18  
% 0.81/1.18  subsentry:          4951
% 0.81/1.18  literals s-matched: 4369
% 0.81/1.18  literals matched:   4369
% 0.81/1.18  full subsumption:   0
% 0.81/1.18  
% 0.81/1.18  checksum:           -1986447035
% 0.81/1.18  
% 0.81/1.18  
% 0.81/1.18  Bliksem ended
%------------------------------------------------------------------------------