TSTP Solution File: LCL469+1 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : LCL469+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n005.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 07:54:01 EDT 2022

% Result   : Theorem 1.45s 1.86s
% Output   : Refutation 1.45s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : LCL469+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.11  % Command  : bliksem %s
% 0.11/0.32  % Computer : n005.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % DateTime : Mon Jul  4 02:05:52 EDT 2022
% 0.11/0.32  % CPUTime  : 
% 0.68/1.07  *** allocated 10000 integers for termspace/termends
% 0.68/1.07  *** allocated 10000 integers for clauses
% 0.68/1.07  *** allocated 10000 integers for justifications
% 0.68/1.07  Bliksem 1.12
% 0.68/1.07  
% 0.68/1.07  
% 0.68/1.07  Automatic Strategy Selection
% 0.68/1.07  
% 0.68/1.07  
% 0.68/1.07  Clauses:
% 0.68/1.07  
% 0.68/1.07  { ! modus_ponens, ! alpha1( X ), is_a_theorem( X ) }.
% 0.68/1.07  { alpha1( skol1 ), modus_ponens }.
% 0.68/1.07  { ! is_a_theorem( skol1 ), modus_ponens }.
% 0.68/1.07  { ! alpha1( X ), is_a_theorem( skol2( Y ) ) }.
% 0.68/1.07  { ! alpha1( X ), is_a_theorem( implies( skol2( X ), X ) ) }.
% 0.68/1.07  { ! is_a_theorem( Y ), ! is_a_theorem( implies( Y, X ) ), alpha1( X ) }.
% 0.68/1.07  { ! substitution_of_equivalents, ! is_a_theorem( equiv( X, Y ) ), X = Y }.
% 0.68/1.07  { is_a_theorem( equiv( skol3, skol28 ) ), substitution_of_equivalents }.
% 0.68/1.07  { ! skol3 = skol28, substitution_of_equivalents }.
% 0.68/1.07  { ! modus_tollens, is_a_theorem( implies( implies( not( Y ), not( X ) ), 
% 0.68/1.07    implies( X, Y ) ) ) }.
% 0.68/1.07  { ! is_a_theorem( implies( implies( not( skol29 ), not( skol4 ) ), implies
% 0.68/1.07    ( skol4, skol29 ) ) ), modus_tollens }.
% 0.68/1.07  { ! implies_1, is_a_theorem( implies( X, implies( Y, X ) ) ) }.
% 0.68/1.07  { ! is_a_theorem( implies( skol5, implies( skol30, skol5 ) ) ), implies_1 }
% 0.68/1.07    .
% 0.68/1.07  { ! implies_2, is_a_theorem( implies( implies( X, implies( X, Y ) ), 
% 0.68/1.07    implies( X, Y ) ) ) }.
% 0.68/1.07  { ! is_a_theorem( implies( implies( skol6, implies( skol6, skol31 ) ), 
% 0.68/1.07    implies( skol6, skol31 ) ) ), implies_2 }.
% 0.68/1.07  { ! implies_3, is_a_theorem( implies( implies( X, Y ), implies( implies( Y
% 0.68/1.07    , Z ), implies( X, Z ) ) ) ) }.
% 0.68/1.07  { ! is_a_theorem( implies( implies( skol7, skol32 ), implies( implies( 
% 0.68/1.07    skol32, skol50 ), implies( skol7, skol50 ) ) ) ), implies_3 }.
% 0.68/1.07  { ! and_1, is_a_theorem( implies( and( X, Y ), X ) ) }.
% 0.68/1.07  { ! is_a_theorem( implies( and( skol8, skol33 ), skol8 ) ), and_1 }.
% 0.68/1.07  { ! and_2, is_a_theorem( implies( and( X, Y ), Y ) ) }.
% 0.68/1.07  { ! is_a_theorem( implies( and( skol9, skol34 ), skol34 ) ), and_2 }.
% 0.68/1.07  { ! and_3, is_a_theorem( implies( X, implies( Y, and( X, Y ) ) ) ) }.
% 0.68/1.07  { ! is_a_theorem( implies( skol10, implies( skol35, and( skol10, skol35 ) )
% 0.68/1.07     ) ), and_3 }.
% 0.68/1.07  { ! or_1, is_a_theorem( implies( X, or( X, Y ) ) ) }.
% 0.68/1.07  { ! is_a_theorem( implies( skol11, or( skol11, skol36 ) ) ), or_1 }.
% 0.68/1.07  { ! or_2, is_a_theorem( implies( Y, or( X, Y ) ) ) }.
% 0.68/1.07  { ! is_a_theorem( implies( skol37, or( skol12, skol37 ) ) ), or_2 }.
% 0.68/1.07  { ! or_3, is_a_theorem( implies( implies( X, Z ), implies( implies( Y, Z )
% 0.68/1.07    , implies( or( X, Y ), Z ) ) ) ) }.
% 0.68/1.07  { ! is_a_theorem( implies( implies( skol13, skol51 ), implies( implies( 
% 0.68/1.07    skol38, skol51 ), implies( or( skol13, skol38 ), skol51 ) ) ) ), or_3 }.
% 0.68/1.07  { ! equivalence_1, is_a_theorem( implies( equiv( X, Y ), implies( X, Y ) )
% 0.68/1.07     ) }.
% 0.68/1.07  { ! is_a_theorem( implies( equiv( skol14, skol39 ), implies( skol14, skol39
% 0.68/1.07     ) ) ), equivalence_1 }.
% 0.68/1.07  { ! equivalence_2, is_a_theorem( implies( equiv( X, Y ), implies( Y, X ) )
% 0.68/1.07     ) }.
% 0.68/1.07  { ! is_a_theorem( implies( equiv( skol15, skol40 ), implies( skol40, skol15
% 0.68/1.07     ) ) ), equivalence_2 }.
% 0.68/1.07  { ! equivalence_3, is_a_theorem( implies( implies( X, Y ), implies( implies
% 0.68/1.07    ( Y, X ), equiv( X, Y ) ) ) ) }.
% 0.68/1.07  { ! is_a_theorem( implies( implies( skol16, skol41 ), implies( implies( 
% 0.68/1.07    skol41, skol16 ), equiv( skol16, skol41 ) ) ) ), equivalence_3 }.
% 0.68/1.07  { ! kn1, is_a_theorem( implies( X, and( X, X ) ) ) }.
% 0.68/1.07  { ! is_a_theorem( implies( skol17, and( skol17, skol17 ) ) ), kn1 }.
% 0.68/1.07  { ! kn2, is_a_theorem( implies( and( X, Y ), X ) ) }.
% 0.68/1.07  { ! is_a_theorem( implies( and( skol18, skol42 ), skol18 ) ), kn2 }.
% 0.68/1.07  { ! kn3, is_a_theorem( implies( implies( X, Y ), implies( not( and( Y, Z )
% 0.68/1.07     ), not( and( Z, X ) ) ) ) ) }.
% 0.68/1.07  { ! is_a_theorem( implies( implies( skol19, skol43 ), implies( not( and( 
% 0.68/1.07    skol43, skol52 ) ), not( and( skol52, skol19 ) ) ) ) ), kn3 }.
% 0.68/1.07  { ! cn1, is_a_theorem( implies( implies( X, Y ), implies( implies( Y, Z ), 
% 0.68/1.07    implies( X, Z ) ) ) ) }.
% 0.68/1.07  { ! is_a_theorem( implies( implies( skol20, skol44 ), implies( implies( 
% 0.68/1.07    skol44, skol53 ), implies( skol20, skol53 ) ) ) ), cn1 }.
% 0.68/1.07  { ! cn2, is_a_theorem( implies( X, implies( not( X ), Y ) ) ) }.
% 0.68/1.07  { ! is_a_theorem( implies( skol21, implies( not( skol21 ), skol45 ) ) ), 
% 0.68/1.07    cn2 }.
% 0.68/1.07  { ! cn3, is_a_theorem( implies( implies( not( X ), X ), X ) ) }.
% 0.68/1.07  { ! is_a_theorem( implies( implies( not( skol22 ), skol22 ), skol22 ) ), 
% 0.68/1.07    cn3 }.
% 0.79/1.19  { ! r1, is_a_theorem( implies( or( X, X ), X ) ) }.
% 0.79/1.19  { ! is_a_theorem( implies( or( skol23, skol23 ), skol23 ) ), r1 }.
% 0.79/1.19  { ! r2, is_a_theorem( implies( Y, or( X, Y ) ) ) }.
% 0.79/1.19  { ! is_a_theorem( implies( skol46, or( skol24, skol46 ) ) ), r2 }.
% 0.79/1.19  { ! r3, is_a_theorem( implies( or( X, Y ), or( Y, X ) ) ) }.
% 0.79/1.19  { ! is_a_theorem( implies( or( skol25, skol47 ), or( skol47, skol25 ) ) ), 
% 0.79/1.19    r3 }.
% 0.79/1.19  { ! r4, is_a_theorem( implies( or( X, or( Y, Z ) ), or( Y, or( X, Z ) ) ) )
% 0.79/1.19     }.
% 0.79/1.19  { ! is_a_theorem( implies( or( skol26, or( skol48, skol54 ) ), or( skol48, 
% 0.79/1.19    or( skol26, skol54 ) ) ) ), r4 }.
% 0.79/1.19  { ! r5, is_a_theorem( implies( implies( Y, Z ), implies( or( X, Y ), or( X
% 0.79/1.19    , Z ) ) ) ) }.
% 0.79/1.19  { ! is_a_theorem( implies( implies( skol49, skol55 ), implies( or( skol27, 
% 0.79/1.19    skol49 ), or( skol27, skol55 ) ) ) ), r5 }.
% 0.79/1.19  { ! op_or, or( X, Y ) = not( and( not( X ), not( Y ) ) ) }.
% 0.79/1.19  { ! op_and, and( X, Y ) = not( or( not( X ), not( Y ) ) ) }.
% 0.79/1.19  { ! op_implies_and, implies( X, Y ) = not( and( X, not( Y ) ) ) }.
% 0.79/1.19  { ! op_implies_or, implies( X, Y ) = or( not( X ), Y ) }.
% 0.79/1.19  { ! op_equiv, equiv( X, Y ) = and( implies( X, Y ), implies( Y, X ) ) }.
% 0.79/1.19  { op_or }.
% 0.79/1.19  { op_implies }.
% 0.79/1.19  { op_equiv }.
% 0.79/1.19  { modus_ponens }.
% 0.79/1.19  { cn1 }.
% 0.79/1.19  { cn2 }.
% 0.79/1.19  { cn3 }.
% 0.79/1.19  { substitution_of_equivalents }.
% 0.79/1.19  { op_or }.
% 0.79/1.19  { op_implies_and }.
% 0.79/1.19  { op_equiv }.
% 0.79/1.19  { ! or_1 }.
% 0.79/1.19  
% 0.79/1.19  percentage equality = 0.051095, percentage horn = 0.972222
% 0.79/1.19  This is a problem with some equality
% 0.79/1.19  
% 0.79/1.19  
% 0.79/1.19  
% 0.79/1.19  Options Used:
% 0.79/1.19  
% 0.79/1.19  useres =            1
% 0.79/1.19  useparamod =        1
% 0.79/1.19  useeqrefl =         1
% 0.79/1.19  useeqfact =         1
% 0.79/1.19  usefactor =         1
% 0.79/1.19  usesimpsplitting =  0
% 0.79/1.19  usesimpdemod =      5
% 0.79/1.19  usesimpres =        3
% 0.79/1.19  
% 0.79/1.19  resimpinuse      =  1000
% 0.79/1.19  resimpclauses =     20000
% 0.79/1.19  substype =          eqrewr
% 0.79/1.19  backwardsubs =      1
% 0.79/1.19  selectoldest =      5
% 0.79/1.19  
% 0.79/1.19  litorderings [0] =  split
% 0.79/1.19  litorderings [1] =  extend the termordering, first sorting on arguments
% 0.79/1.19  
% 0.79/1.19  termordering =      kbo
% 0.79/1.19  
% 0.79/1.19  litapriori =        0
% 0.79/1.19  termapriori =       1
% 0.79/1.19  litaposteriori =    0
% 0.79/1.19  termaposteriori =   0
% 0.79/1.19  demodaposteriori =  0
% 0.79/1.19  ordereqreflfact =   0
% 0.79/1.19  
% 0.79/1.19  litselect =         negord
% 0.79/1.19  
% 0.79/1.19  maxweight =         15
% 0.79/1.19  maxdepth =          30000
% 0.79/1.19  maxlength =         115
% 0.79/1.19  maxnrvars =         195
% 0.79/1.19  excuselevel =       1
% 0.79/1.19  increasemaxweight = 1
% 0.79/1.19  
% 0.79/1.19  maxselected =       10000000
% 0.79/1.19  maxnrclauses =      10000000
% 0.79/1.19  
% 0.79/1.19  showgenerated =    0
% 0.79/1.19  showkept =         0
% 0.79/1.19  showselected =     0
% 0.79/1.19  showdeleted =      0
% 0.79/1.19  showresimp =       1
% 0.79/1.19  showstatus =       2000
% 0.79/1.19  
% 0.79/1.19  prologoutput =     0
% 0.79/1.19  nrgoals =          5000000
% 0.79/1.19  totalproof =       1
% 0.79/1.19  
% 0.79/1.19  Symbols occurring in the translation:
% 0.79/1.19  
% 0.79/1.19  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 0.79/1.19  .  [1, 2]      (w:1, o:107, a:1, s:1, b:0), 
% 0.79/1.19  !  [4, 1]      (w:0, o:98, a:1, s:1, b:0), 
% 0.79/1.19  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.79/1.19  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.79/1.19  modus_ponens  [35, 0]      (w:1, o:6, a:1, s:1, b:0), 
% 0.79/1.19  is_a_theorem  [38, 1]      (w:1, o:103, a:1, s:1, b:0), 
% 0.79/1.19  implies  [39, 2]      (w:1, o:131, a:1, s:1, b:0), 
% 0.79/1.19  substitution_of_equivalents  [40, 0]      (w:1, o:14, a:1, s:1, b:0), 
% 0.79/1.19  equiv  [41, 2]      (w:1, o:132, a:1, s:1, b:0), 
% 0.79/1.19  modus_tollens  [42, 0]      (w:1, o:15, a:1, s:1, b:0), 
% 0.79/1.19  not  [43, 1]      (w:1, o:104, a:1, s:1, b:0), 
% 0.79/1.19  implies_1  [44, 0]      (w:1, o:16, a:1, s:1, b:0), 
% 0.79/1.19  implies_2  [45, 0]      (w:1, o:17, a:1, s:1, b:0), 
% 0.79/1.19  implies_3  [46, 0]      (w:1, o:18, a:1, s:1, b:0), 
% 0.79/1.19  and_1  [48, 0]      (w:1, o:20, a:1, s:1, b:0), 
% 0.79/1.19  and  [49, 2]      (w:1, o:133, a:1, s:1, b:0), 
% 0.79/1.19  and_2  [50, 0]      (w:1, o:21, a:1, s:1, b:0), 
% 0.79/1.19  and_3  [51, 0]      (w:1, o:22, a:1, s:1, b:0), 
% 0.79/1.19  or_1  [52, 0]      (w:1, o:23, a:1, s:1, b:0), 
% 0.79/1.19  or  [53, 2]      (w:1, o:134, a:1, s:1, b:0), 
% 0.79/1.19  or_2  [54, 0]      (w:1, o:24, a:1, s:1, b:0), 
% 0.79/1.19  or_3  [55, 0]      (w:1, o:25, a:1, s:1, b:0), 
% 0.79/1.19  equivalence_1  [56, 0]      (w:1, o:26, a:1, s:1, b:0), 
% 0.79/1.19  equivalence_2  [57, 0]      (w:1, o:27, a:1, s:1, b:0), 
% 0.79/1.19  equivalence_3  [58, 0]      (w:1, o:28, a:1, s:1, b:0), 
% 0.79/1.19  kn1  [59, 0]      (w:1, o:29, a:1, s:1, b:0), 
% 0.79/1.19  kn2  [61, 0]      (w:1, o:31, a:1, s:1, b:0), 
% 0.79/1.19  kn3  [63, 0]      (w:1, o:33, a:1, s:1, b:0), 
% 0.79/1.19  cn1  [65, 0]      (w:1, o:35, a:1, s:1, b:0), 
% 0.79/1.19  cn2  [66, 0]      (w:1, o:36, a:1, s:1, b:0), 
% 0.79/1.19  cn3  [67, 0]      (w:1, o:37, a:1, s:1, b:0), 
% 0.79/1.19  r1  [68, 0]      (w:1, o:9, a:1, s:1, b:0), 
% 0.79/1.19  r2  [69, 0]      (w:1, o:10, a:1, s:1, b:0), 
% 1.45/1.86  r3  [70, 0]      (w:1, o:11, a:1, s:1, b:0), 
% 1.45/1.86  r4  [71, 0]      (w:1, o:12, a:1, s:1, b:0), 
% 1.45/1.86  r5  [72, 0]      (w:1, o:13, a:1, s:1, b:0), 
% 1.45/1.86  op_or  [73, 0]      (w:1, o:38, a:1, s:1, b:0), 
% 1.45/1.86  op_and  [74, 0]      (w:1, o:39, a:1, s:1, b:0), 
% 1.45/1.86  op_implies_and  [75, 0]      (w:1, o:40, a:1, s:1, b:0), 
% 1.45/1.86  op_implies_or  [76, 0]      (w:1, o:41, a:1, s:1, b:0), 
% 1.45/1.86  op_equiv  [77, 0]      (w:1, o:42, a:1, s:1, b:0), 
% 1.45/1.86  op_implies  [78, 0]      (w:1, o:43, a:1, s:1, b:0), 
% 1.45/1.86  alpha1  [79, 1]      (w:1, o:105, a:1, s:1, b:1), 
% 1.45/1.86  skol1  [80, 0]      (w:1, o:44, a:1, s:1, b:1), 
% 1.45/1.86  skol2  [81, 1]      (w:1, o:106, a:1, s:1, b:1), 
% 1.45/1.86  skol3  [82, 0]      (w:1, o:55, a:1, s:1, b:1), 
% 1.45/1.86  skol4  [83, 0]      (w:1, o:66, a:1, s:1, b:1), 
% 1.45/1.86  skol5  [84, 0]      (w:1, o:77, a:1, s:1, b:1), 
% 1.45/1.86  skol6  [85, 0]      (w:1, o:84, a:1, s:1, b:1), 
% 1.45/1.86  skol7  [86, 0]      (w:1, o:85, a:1, s:1, b:1), 
% 1.45/1.86  skol8  [87, 0]      (w:1, o:86, a:1, s:1, b:1), 
% 1.45/1.86  skol9  [88, 0]      (w:1, o:87, a:1, s:1, b:1), 
% 1.45/1.86  skol10  [89, 0]      (w:1, o:88, a:1, s:1, b:1), 
% 1.45/1.86  skol11  [90, 0]      (w:1, o:89, a:1, s:1, b:1), 
% 1.45/1.86  skol12  [91, 0]      (w:1, o:90, a:1, s:1, b:1), 
% 1.45/1.86  skol13  [92, 0]      (w:1, o:91, a:1, s:1, b:1), 
% 1.45/1.86  skol14  [93, 0]      (w:1, o:92, a:1, s:1, b:1), 
% 1.45/1.86  skol15  [94, 0]      (w:1, o:93, a:1, s:1, b:1), 
% 1.45/1.86  skol16  [95, 0]      (w:1, o:94, a:1, s:1, b:1), 
% 1.45/1.86  skol17  [96, 0]      (w:1, o:95, a:1, s:1, b:1), 
% 1.45/1.86  skol18  [97, 0]      (w:1, o:96, a:1, s:1, b:1), 
% 1.45/1.86  skol19  [98, 0]      (w:1, o:97, a:1, s:1, b:1), 
% 1.45/1.86  skol20  [99, 0]      (w:1, o:45, a:1, s:1, b:1), 
% 1.45/1.86  skol21  [100, 0]      (w:1, o:46, a:1, s:1, b:1), 
% 1.45/1.86  skol22  [101, 0]      (w:1, o:47, a:1, s:1, b:1), 
% 1.45/1.86  skol23  [102, 0]      (w:1, o:48, a:1, s:1, b:1), 
% 1.45/1.86  skol24  [103, 0]      (w:1, o:49, a:1, s:1, b:1), 
% 1.45/1.86  skol25  [104, 0]      (w:1, o:50, a:1, s:1, b:1), 
% 1.45/1.86  skol26  [105, 0]      (w:1, o:51, a:1, s:1, b:1), 
% 1.45/1.86  skol27  [106, 0]      (w:1, o:52, a:1, s:1, b:1), 
% 1.45/1.86  skol28  [107, 0]      (w:1, o:53, a:1, s:1, b:1), 
% 1.45/1.86  skol29  [108, 0]      (w:1, o:54, a:1, s:1, b:1), 
% 1.45/1.86  skol30  [109, 0]      (w:1, o:56, a:1, s:1, b:1), 
% 1.45/1.86  skol31  [110, 0]      (w:1, o:57, a:1, s:1, b:1), 
% 1.45/1.86  skol32  [111, 0]      (w:1, o:58, a:1, s:1, b:1), 
% 1.45/1.86  skol33  [112, 0]      (w:1, o:59, a:1, s:1, b:1), 
% 1.45/1.86  skol34  [113, 0]      (w:1, o:60, a:1, s:1, b:1), 
% 1.45/1.86  skol35  [114, 0]      (w:1, o:61, a:1, s:1, b:1), 
% 1.45/1.86  skol36  [115, 0]      (w:1, o:62, a:1, s:1, b:1), 
% 1.45/1.86  skol37  [116, 0]      (w:1, o:63, a:1, s:1, b:1), 
% 1.45/1.86  skol38  [117, 0]      (w:1, o:64, a:1, s:1, b:1), 
% 1.45/1.86  skol39  [118, 0]      (w:1, o:65, a:1, s:1, b:1), 
% 1.45/1.86  skol40  [119, 0]      (w:1, o:67, a:1, s:1, b:1), 
% 1.45/1.86  skol41  [120, 0]      (w:1, o:68, a:1, s:1, b:1), 
% 1.45/1.86  skol42  [121, 0]      (w:1, o:69, a:1, s:1, b:1), 
% 1.45/1.86  skol43  [122, 0]      (w:1, o:70, a:1, s:1, b:1), 
% 1.45/1.86  skol44  [123, 0]      (w:1, o:71, a:1, s:1, b:1), 
% 1.45/1.86  skol45  [124, 0]      (w:1, o:72, a:1, s:1, b:1), 
% 1.45/1.86  skol46  [125, 0]      (w:1, o:73, a:1, s:1, b:1), 
% 1.45/1.86  skol47  [126, 0]      (w:1, o:74, a:1, s:1, b:1), 
% 1.45/1.86  skol48  [127, 0]      (w:1, o:75, a:1, s:1, b:1), 
% 1.45/1.86  skol49  [128, 0]      (w:1, o:76, a:1, s:1, b:1), 
% 1.45/1.86  skol50  [129, 0]      (w:1, o:78, a:1, s:1, b:1), 
% 1.45/1.86  skol51  [130, 0]      (w:1, o:79, a:1, s:1, b:1), 
% 1.45/1.86  skol52  [131, 0]      (w:1, o:80, a:1, s:1, b:1), 
% 1.45/1.86  skol53  [132, 0]      (w:1, o:81, a:1, s:1, b:1), 
% 1.45/1.86  skol54  [133, 0]      (w:1, o:82, a:1, s:1, b:1), 
% 1.45/1.86  skol55  [134, 0]      (w:1, o:83, a:1, s:1, b:1).
% 1.45/1.86  
% 1.45/1.86  
% 1.45/1.86  Starting Search:
% 1.45/1.86  
% 1.45/1.86  *** allocated 15000 integers for clauses
% 1.45/1.86  *** allocated 22500 integers for clauses
% 1.45/1.86  *** allocated 33750 integers for clauses
% 1.45/1.86  *** allocated 50625 integers for clauses
% 1.45/1.86  *** allocated 15000 integers for termspace/termends
% 1.45/1.86  *** allocated 75937 integers for clauses
% 1.45/1.86  Resimplifying inuse:
% 1.45/1.86  Done
% 1.45/1.86  
% 1.45/1.86  *** allocated 22500 integers for termspace/termends
% 1.45/1.86  *** allocated 113905 integers for clauses
% 1.45/1.86  *** allocated 33750 integers for termspace/termends
% 1.45/1.86  
% 1.45/1.86  Intermediate Status:
% 1.45/1.86  Generated:    3829
% 1.45/1.86  Kept:         2045
% 1.45/1.86  Inuse:        165
% 1.45/1.86  Deleted:      35
% 1.45/1.86  Deletedinuse: 3
% 1.45/1.86  
% 1.45/1.86  Resimplifying inuse:
% 1.45/1.86  Done
% 1.45/1.86  
% 1.45/1.86  *** allocated 170857 integers for clauses
% 1.45/1.86  *** allocated 50625 integers for termspace/termends
% 1.45/1.86  Resimplifying inuse:
% 1.45/1.86  Done
% 1.45/1.86  
% 1.45/1.86  *** allocated 75937 integers for termspace/termends
% 1.45/1.86  *** allocated 256285 integers for clauses
% 1.45/1.86  
% 1.45/1.86  Intermediate Status:
% 1.45/1.86  Generated:    7770
% 1.45/1.86  Kept:         4061
% 1.45/1.86  Inuse:        256
% 1.45/1.86  Deleted:      41
% 1.45/1.86  Deletedinuse: 6
% 1.45/1.86  
% 1.45/1.86  Resimplifying inuse:
% 1.45/1.86  Done
% 1.45/1.86  
% 1.45/1.86  Resimplifying inuse:
% 1.45/1.86  Done
% 1.45/1.86  
% 1.45/1.86  *** allocated 113905 integers for termspace/termends
% 1.45/1.86  
% 1.45/1.86  Intermediate Status:
% 1.45/1.86  Generated:    11625
% 1.45/1.86  Kept:         6074
% 1.45/1.86  Inuse:        323
% 1.45/1.86  Deleted:      53
% 1.45/1.86  Deletedinuse: 7
% 1.45/1.86  
% 1.45/1.86  Resimplifying inuse:
% 1.45/1.86  Done
% 1.45/1.86  
% 1.45/1.86  *** allocated 384427 integers for clauses
% 1.45/1.86  Resimplifying inuse:
% 1.45/1.86  Done
% 1.45/1.86  
% 1.45/1.86  *** allocated 170857 integers for termspace/termends
% 1.45/1.86  
% 1.45/1.86  Intermediate Status:
% 1.45/1.86  Generated:    15647
% 1.45/1.86  Kept:         8710
% 1.45/1.86  Inuse:        356
% 1.45/1.86  Deleted:      57
% 1.45/1.86  Deletedinuse: 7
% 1.45/1.86  
% 1.45/1.86  Resimplifying inuse:
% 1.45/1.86  Done
% 1.45/1.86  
% 1.45/1.86  *** allocated 576640 integers for clauses
% 1.45/1.86  Resimplifying inuse:
% 1.45/1.86  Done
% 1.45/1.86  
% 1.45/1.86  
% 1.45/1.86  Intermediate Status:
% 1.45/1.86  Generated:    18766
% 1.45/1.86  Kept:         10714
% 1.45/1.86  Inuse:        371
% 1.45/1.86  Deleted:      57
% 1.45/1.86  Deletedinuse: 7
% 1.45/1.86  
% 1.45/1.86  Resimplifying inuse:
% 1.45/1.86  Done
% 1.45/1.86  
% 1.45/1.86  *** allocated 256285 integers for termspace/termends
% 1.45/1.86  Resimplifying inuse:
% 1.45/1.86  Done
% 1.45/1.86  
% 1.45/1.86  
% 1.45/1.86  Intermediate Status:
% 1.45/1.86  Generated:    21481
% 1.45/1.86  Kept:         12741
% 1.45/1.86  Inuse:        396
% 1.45/1.86  Deleted:      59
% 1.45/1.86  Deletedinuse: 7
% 1.45/1.86  
% 1.45/1.86  Resimplifying inuse:
% 1.45/1.86  Done
% 1.45/1.86  
% 1.45/1.86  *** allocated 864960 integers for clauses
% 1.45/1.86  Resimplifying inuse:
% 1.45/1.86  Done
% 1.45/1.86  
% 1.45/1.86  
% 1.45/1.86  Intermediate Status:
% 1.45/1.86  Generated:    24462
% 1.45/1.86  Kept:         14746
% 1.45/1.86  Inuse:        424
% 1.45/1.86  Deleted:      59
% 1.45/1.86  Deletedinuse: 7
% 1.45/1.86  
% 1.45/1.86  Resimplifying inuse:
% 1.45/1.86  Done
% 1.45/1.86  
% 1.45/1.86  Resimplifying inuse:
% 1.45/1.86  Done
% 1.45/1.86  
% 1.45/1.86  *** allocated 384427 integers for termspace/termends
% 1.45/1.86  
% 1.45/1.86  Intermediate Status:
% 1.45/1.86  Generated:    27957
% 1.45/1.86  Kept:         16771
% 1.45/1.86  Inuse:        462
% 1.45/1.86  Deleted:      59
% 1.45/1.86  Deletedinuse: 7
% 1.45/1.86  
% 1.45/1.86  Resimplifying inuse:
% 1.45/1.86  Done
% 1.45/1.86  
% 1.45/1.86  Resimplifying inuse:
% 1.45/1.86  Done
% 1.45/1.86  
% 1.45/1.86  
% 1.45/1.86  Intermediate Status:
% 1.45/1.86  Generated:    31982
% 1.45/1.86  Kept:         18798
% 1.45/1.86  Inuse:        484
% 1.45/1.86  Deleted:      97
% 1.45/1.86  Deletedinuse: 20
% 1.45/1.86  
% 1.45/1.86  Resimplifying inuse:
% 1.45/1.86  Done
% 1.45/1.86  
% 1.45/1.86  Resimplifying clauses:
% 1.45/1.86  Done
% 1.45/1.86  
% 1.45/1.86  Resimplifying inuse:
% 1.45/1.86  
% 1.45/1.86  Bliksems!, er is een bewijs:
% 1.45/1.86  % SZS status Theorem
% 1.45/1.86  % SZS output start Refutation
% 1.45/1.86  
% 1.45/1.86  (24) {G0,W7,D4,L2,V0,M2} I { ! is_a_theorem( implies( skol11, or( skol11, 
% 1.45/1.86    skol36 ) ) ), or_1 }.
% 1.45/1.86  (43) {G0,W8,D5,L2,V2,M2} I { ! cn2, is_a_theorem( implies( X, implies( not
% 1.45/1.86    ( X ), Y ) ) ) }.
% 1.45/1.86  (57) {G0,W11,D5,L2,V2,M2} I { ! op_or, not( and( not( X ), not( Y ) ) ) ==>
% 1.45/1.86     or( X, Y ) }.
% 1.45/1.86  (59) {G0,W10,D5,L2,V2,M2} I { ! op_implies_and, not( and( X, not( Y ) ) ) 
% 1.45/1.86    ==> implies( X, Y ) }.
% 1.45/1.86  (62) {G0,W1,D1,L1,V0,M1} I { op_or }.
% 1.45/1.86  (67) {G0,W1,D1,L1,V0,M1} I { cn2 }.
% 1.45/1.86  (70) {G0,W1,D1,L1,V0,M1} I { op_implies_and }.
% 1.45/1.86  (71) {G0,W1,D1,L1,V0,M1} I { ! or_1 }.
% 1.45/1.86  (811) {G1,W6,D4,L1,V0,M1} S(24);r(71) { ! is_a_theorem( implies( skol11, or
% 1.45/1.86    ( skol11, skol36 ) ) ) }.
% 1.45/1.86  (1776) {G1,W7,D5,L1,V2,M1} S(43);r(67) { is_a_theorem( implies( X, implies
% 1.45/1.86    ( not( X ), Y ) ) ) }.
% 1.45/1.86  (2725) {G1,W10,D5,L1,V2,M1} S(57);r(62) { not( and( not( X ), not( Y ) ) ) 
% 1.45/1.86    ==> or( X, Y ) }.
% 1.45/1.86  (2877) {G1,W9,D5,L1,V2,M1} S(59);r(70) { not( and( X, not( Y ) ) ) ==> 
% 1.45/1.86    implies( X, Y ) }.
% 1.45/1.86  (20113) {G2,W8,D4,L1,V2,M1} S(2725);d(2877) { implies( not( X ), Y ) ==> or
% 1.45/1.86    ( X, Y ) }.
% 1.45/1.86  (20651) {G3,W6,D4,L1,V2,M1} S(1776);d(20113) { is_a_theorem( implies( X, or
% 1.45/1.86    ( X, Y ) ) ) }.
% 1.45/1.86  (20654) {G4,W0,D0,L0,V0,M0} S(811);r(20651) {  }.
% 1.45/1.86  
% 1.45/1.86  
% 1.45/1.86  % SZS output end Refutation
% 1.45/1.86  found a proof!
% 1.45/1.86  
% 1.45/1.86  
% 1.45/1.86  Unprocessed initial clauses:
% 1.45/1.86  
% 1.45/1.86  (20656) {G0,W5,D2,L3,V1,M3}  { ! modus_ponens, ! alpha1( X ), is_a_theorem
% 1.45/1.86    ( X ) }.
% 1.45/1.86  (20657) {G0,W3,D2,L2,V0,M2}  { alpha1( skol1 ), modus_ponens }.
% 1.45/1.86  (20658) {G0,W3,D2,L2,V0,M2}  { ! is_a_theorem( skol1 ), modus_ponens }.
% 1.45/1.86  (20659) {G0,W5,D3,L2,V2,M2}  { ! alpha1( X ), is_a_theorem( skol2( Y ) )
% 1.45/1.86     }.
% 1.45/1.86  (20660) {G0,W7,D4,L2,V1,M2}  { ! alpha1( X ), is_a_theorem( implies( skol2
% 1.45/1.86    ( X ), X ) ) }.
% 1.45/1.86  (20661) {G0,W8,D3,L3,V2,M3}  { ! is_a_theorem( Y ), ! is_a_theorem( implies
% 1.45/1.86    ( Y, X ) ), alpha1( X ) }.
% 1.45/1.86  (20662) {G0,W8,D3,L3,V2,M3}  { ! substitution_of_equivalents, ! 
% 1.45/1.86    is_a_theorem( equiv( X, Y ) ), X = Y }.
% 1.45/1.86  (20663) {G0,W5,D3,L2,V0,M2}  { is_a_theorem( equiv( skol3, skol28 ) ), 
% 1.45/1.86    substitution_of_equivalents }.
% 1.45/1.86  (20664) {G0,W4,D2,L2,V0,M2}  { ! skol3 = skol28, 
% 1.45/1.86    substitution_of_equivalents }.
% 1.45/1.86  (20665) {G0,W11,D5,L2,V2,M2}  { ! modus_tollens, is_a_theorem( implies( 
% 1.45/1.86    implies( not( Y ), not( X ) ), implies( X, Y ) ) ) }.
% 1.45/1.86  (20666) {G0,W11,D5,L2,V0,M2}  { ! is_a_theorem( implies( implies( not( 
% 1.45/1.86    skol29 ), not( skol4 ) ), implies( skol4, skol29 ) ) ), modus_tollens }.
% 1.45/1.86  (20667) {G0,W7,D4,L2,V2,M2}  { ! implies_1, is_a_theorem( implies( X, 
% 1.45/1.86    implies( Y, X ) ) ) }.
% 1.45/1.86  (20668) {G0,W7,D4,L2,V0,M2}  { ! is_a_theorem( implies( skol5, implies( 
% 1.45/1.86    skol30, skol5 ) ) ), implies_1 }.
% 1.45/1.86  (20669) {G0,W11,D5,L2,V2,M2}  { ! implies_2, is_a_theorem( implies( implies
% 1.45/1.86    ( X, implies( X, Y ) ), implies( X, Y ) ) ) }.
% 1.45/1.86  (20670) {G0,W11,D5,L2,V0,M2}  { ! is_a_theorem( implies( implies( skol6, 
% 1.45/1.86    implies( skol6, skol31 ) ), implies( skol6, skol31 ) ) ), implies_2 }.
% 1.45/1.86  (20671) {G0,W13,D5,L2,V3,M2}  { ! implies_3, is_a_theorem( implies( implies
% 1.45/1.86    ( X, Y ), implies( implies( Y, Z ), implies( X, Z ) ) ) ) }.
% 1.45/1.86  (20672) {G0,W13,D5,L2,V0,M2}  { ! is_a_theorem( implies( implies( skol7, 
% 1.45/1.86    skol32 ), implies( implies( skol32, skol50 ), implies( skol7, skol50 ) )
% 1.45/1.86     ) ), implies_3 }.
% 1.45/1.86  (20673) {G0,W7,D4,L2,V2,M2}  { ! and_1, is_a_theorem( implies( and( X, Y )
% 1.45/1.86    , X ) ) }.
% 1.45/1.86  (20674) {G0,W7,D4,L2,V0,M2}  { ! is_a_theorem( implies( and( skol8, skol33
% 1.45/1.86     ), skol8 ) ), and_1 }.
% 1.45/1.86  (20675) {G0,W7,D4,L2,V2,M2}  { ! and_2, is_a_theorem( implies( and( X, Y )
% 1.45/1.86    , Y ) ) }.
% 1.45/1.86  (20676) {G0,W7,D4,L2,V0,M2}  { ! is_a_theorem( implies( and( skol9, skol34
% 1.45/1.86     ), skol34 ) ), and_2 }.
% 1.45/1.86  (20677) {G0,W9,D5,L2,V2,M2}  { ! and_3, is_a_theorem( implies( X, implies( 
% 1.45/1.86    Y, and( X, Y ) ) ) ) }.
% 1.45/1.86  (20678) {G0,W9,D5,L2,V0,M2}  { ! is_a_theorem( implies( skol10, implies( 
% 1.45/1.86    skol35, and( skol10, skol35 ) ) ) ), and_3 }.
% 1.45/1.86  (20679) {G0,W7,D4,L2,V2,M2}  { ! or_1, is_a_theorem( implies( X, or( X, Y )
% 1.45/1.86     ) ) }.
% 1.45/1.86  (20680) {G0,W7,D4,L2,V0,M2}  { ! is_a_theorem( implies( skol11, or( skol11
% 1.45/1.86    , skol36 ) ) ), or_1 }.
% 1.45/1.86  (20681) {G0,W7,D4,L2,V2,M2}  { ! or_2, is_a_theorem( implies( Y, or( X, Y )
% 1.45/1.86     ) ) }.
% 1.45/1.86  (20682) {G0,W7,D4,L2,V0,M2}  { ! is_a_theorem( implies( skol37, or( skol12
% 1.45/1.86    , skol37 ) ) ), or_2 }.
% 1.45/1.86  (20683) {G0,W15,D6,L2,V3,M2}  { ! or_3, is_a_theorem( implies( implies( X, 
% 1.45/1.86    Z ), implies( implies( Y, Z ), implies( or( X, Y ), Z ) ) ) ) }.
% 1.45/1.86  (20684) {G0,W15,D6,L2,V0,M2}  { ! is_a_theorem( implies( implies( skol13, 
% 1.45/1.86    skol51 ), implies( implies( skol38, skol51 ), implies( or( skol13, skol38
% 1.45/1.86     ), skol51 ) ) ) ), or_3 }.
% 1.45/1.86  (20685) {G0,W9,D4,L2,V2,M2}  { ! equivalence_1, is_a_theorem( implies( 
% 1.45/1.86    equiv( X, Y ), implies( X, Y ) ) ) }.
% 1.45/1.86  (20686) {G0,W9,D4,L2,V0,M2}  { ! is_a_theorem( implies( equiv( skol14, 
% 1.45/1.86    skol39 ), implies( skol14, skol39 ) ) ), equivalence_1 }.
% 1.45/1.86  (20687) {G0,W9,D4,L2,V2,M2}  { ! equivalence_2, is_a_theorem( implies( 
% 1.45/1.86    equiv( X, Y ), implies( Y, X ) ) ) }.
% 1.45/1.86  (20688) {G0,W9,D4,L2,V0,M2}  { ! is_a_theorem( implies( equiv( skol15, 
% 1.45/1.86    skol40 ), implies( skol40, skol15 ) ) ), equivalence_2 }.
% 1.45/1.86  (20689) {G0,W13,D5,L2,V2,M2}  { ! equivalence_3, is_a_theorem( implies( 
% 1.45/1.86    implies( X, Y ), implies( implies( Y, X ), equiv( X, Y ) ) ) ) }.
% 1.45/1.86  (20690) {G0,W13,D5,L2,V0,M2}  { ! is_a_theorem( implies( implies( skol16, 
% 1.45/1.86    skol41 ), implies( implies( skol41, skol16 ), equiv( skol16, skol41 ) ) )
% 1.45/1.86     ), equivalence_3 }.
% 1.45/1.86  (20691) {G0,W7,D4,L2,V1,M2}  { ! kn1, is_a_theorem( implies( X, and( X, X )
% 1.45/1.86     ) ) }.
% 1.45/1.86  (20692) {G0,W7,D4,L2,V0,M2}  { ! is_a_theorem( implies( skol17, and( skol17
% 1.45/1.86    , skol17 ) ) ), kn1 }.
% 1.45/1.86  (20693) {G0,W7,D4,L2,V2,M2}  { ! kn2, is_a_theorem( implies( and( X, Y ), X
% 1.45/1.86     ) ) }.
% 1.45/1.86  (20694) {G0,W7,D4,L2,V0,M2}  { ! is_a_theorem( implies( and( skol18, skol42
% 1.45/1.86     ), skol18 ) ), kn2 }.
% 1.45/1.86  (20695) {G0,W15,D6,L2,V3,M2}  { ! kn3, is_a_theorem( implies( implies( X, Y
% 1.45/1.86     ), implies( not( and( Y, Z ) ), not( and( Z, X ) ) ) ) ) }.
% 1.45/1.86  (20696) {G0,W15,D6,L2,V0,M2}  { ! is_a_theorem( implies( implies( skol19, 
% 1.45/1.86    skol43 ), implies( not( and( skol43, skol52 ) ), not( and( skol52, skol19
% 1.45/1.86     ) ) ) ) ), kn3 }.
% 1.45/1.86  (20697) {G0,W13,D5,L2,V3,M2}  { ! cn1, is_a_theorem( implies( implies( X, Y
% 1.45/1.86     ), implies( implies( Y, Z ), implies( X, Z ) ) ) ) }.
% 1.45/1.86  (20698) {G0,W13,D5,L2,V0,M2}  { ! is_a_theorem( implies( implies( skol20, 
% 1.45/1.86    skol44 ), implies( implies( skol44, skol53 ), implies( skol20, skol53 ) )
% 1.45/1.86     ) ), cn1 }.
% 1.45/1.86  (20699) {G0,W8,D5,L2,V2,M2}  { ! cn2, is_a_theorem( implies( X, implies( 
% 1.45/1.86    not( X ), Y ) ) ) }.
% 1.45/1.86  (20700) {G0,W8,D5,L2,V0,M2}  { ! is_a_theorem( implies( skol21, implies( 
% 1.45/1.86    not( skol21 ), skol45 ) ) ), cn2 }.
% 1.45/1.86  (20701) {G0,W8,D5,L2,V1,M2}  { ! cn3, is_a_theorem( implies( implies( not( 
% 1.45/1.86    X ), X ), X ) ) }.
% 1.45/1.86  (20702) {G0,W8,D5,L2,V0,M2}  { ! is_a_theorem( implies( implies( not( 
% 1.45/1.86    skol22 ), skol22 ), skol22 ) ), cn3 }.
% 1.45/1.86  (20703) {G0,W7,D4,L2,V1,M2}  { ! r1, is_a_theorem( implies( or( X, X ), X )
% 1.45/1.86     ) }.
% 1.45/1.86  (20704) {G0,W7,D4,L2,V0,M2}  { ! is_a_theorem( implies( or( skol23, skol23
% 1.45/1.86     ), skol23 ) ), r1 }.
% 1.45/1.86  (20705) {G0,W7,D4,L2,V2,M2}  { ! r2, is_a_theorem( implies( Y, or( X, Y ) )
% 1.45/1.86     ) }.
% 1.45/1.86  (20706) {G0,W7,D4,L2,V0,M2}  { ! is_a_theorem( implies( skol46, or( skol24
% 1.45/1.86    , skol46 ) ) ), r2 }.
% 1.45/1.86  (20707) {G0,W9,D4,L2,V2,M2}  { ! r3, is_a_theorem( implies( or( X, Y ), or
% 1.45/1.86    ( Y, X ) ) ) }.
% 1.45/1.86  (20708) {G0,W9,D4,L2,V0,M2}  { ! is_a_theorem( implies( or( skol25, skol47
% 1.45/1.86     ), or( skol47, skol25 ) ) ), r3 }.
% 1.45/1.86  (20709) {G0,W13,D5,L2,V3,M2}  { ! r4, is_a_theorem( implies( or( X, or( Y, 
% 1.45/1.86    Z ) ), or( Y, or( X, Z ) ) ) ) }.
% 1.45/1.86  (20710) {G0,W13,D5,L2,V0,M2}  { ! is_a_theorem( implies( or( skol26, or( 
% 1.45/1.86    skol48, skol54 ) ), or( skol48, or( skol26, skol54 ) ) ) ), r4 }.
% 1.45/1.86  (20711) {G0,W13,D5,L2,V3,M2}  { ! r5, is_a_theorem( implies( implies( Y, Z
% 1.45/1.86     ), implies( or( X, Y ), or( X, Z ) ) ) ) }.
% 1.45/1.86  (20712) {G0,W13,D5,L2,V0,M2}  { ! is_a_theorem( implies( implies( skol49, 
% 1.45/1.86    skol55 ), implies( or( skol27, skol49 ), or( skol27, skol55 ) ) ) ), r5
% 1.45/1.86     }.
% 1.45/1.86  (20713) {G0,W11,D5,L2,V2,M2}  { ! op_or, or( X, Y ) = not( and( not( X ), 
% 1.45/1.86    not( Y ) ) ) }.
% 1.45/1.86  (20714) {G0,W11,D5,L2,V2,M2}  { ! op_and, and( X, Y ) = not( or( not( X ), 
% 1.45/1.86    not( Y ) ) ) }.
% 1.45/1.86  (20715) {G0,W10,D5,L2,V2,M2}  { ! op_implies_and, implies( X, Y ) = not( 
% 1.45/1.86    and( X, not( Y ) ) ) }.
% 1.45/1.86  (20716) {G0,W9,D4,L2,V2,M2}  { ! op_implies_or, implies( X, Y ) = or( not( 
% 1.45/1.86    X ), Y ) }.
% 1.45/1.86  (20717) {G0,W12,D4,L2,V2,M2}  { ! op_equiv, equiv( X, Y ) = and( implies( X
% 1.45/1.86    , Y ), implies( Y, X ) ) }.
% 1.45/1.86  (20718) {G0,W1,D1,L1,V0,M1}  { op_or }.
% 1.45/1.86  (20719) {G0,W1,D1,L1,V0,M1}  { op_implies }.
% 1.45/1.86  (20720) {G0,W1,D1,L1,V0,M1}  { op_equiv }.
% 1.45/1.86  (20721) {G0,W1,D1,L1,V0,M1}  { modus_ponens }.
% 1.45/1.86  (20722) {G0,W1,D1,L1,V0,M1}  { cn1 }.
% 1.45/1.86  (20723) {G0,W1,D1,L1,V0,M1}  { cn2 }.
% 1.45/1.86  (20724) {G0,W1,D1,L1,V0,M1}  { cn3 }.
% 1.45/1.86  (20725) {G0,W1,D1,L1,V0,M1}  { substitution_of_equivalents }.
% 1.45/1.86  (20726) {G0,W1,D1,L1,V0,M1}  { op_or }.
% 1.45/1.86  (20727) {G0,W1,D1,L1,V0,M1}  { op_implies_and }.
% 1.45/1.86  (20728) {G0,W1,D1,L1,V0,M1}  { op_equiv }.
% 1.45/1.86  (20729) {G0,W1,D1,L1,V0,M1}  { ! or_1 }.
% 1.45/1.86  
% 1.45/1.86  
% 1.45/1.86  Total Proof:
% 1.45/1.86  
% 1.45/1.86  subsumption: (24) {G0,W7,D4,L2,V0,M2} I { ! is_a_theorem( implies( skol11, 
% 1.45/1.86    or( skol11, skol36 ) ) ), or_1 }.
% 1.45/1.86  parent0: (20680) {G0,W7,D4,L2,V0,M2}  { ! is_a_theorem( implies( skol11, or
% 1.45/1.86    ( skol11, skol36 ) ) ), or_1 }.
% 1.45/1.86  substitution0:
% 1.45/1.86  end
% 1.45/1.86  permutation0:
% 1.45/1.86     0 ==> 0
% 1.45/1.86     1 ==> 1
% 1.45/1.86  end
% 1.45/1.86  
% 1.45/1.86  subsumption: (43) {G0,W8,D5,L2,V2,M2} I { ! cn2, is_a_theorem( implies( X, 
% 1.45/1.86    implies( not( X ), Y ) ) ) }.
% 1.45/1.86  parent0: (20699) {G0,W8,D5,L2,V2,M2}  { ! cn2, is_a_theorem( implies( X, 
% 1.45/1.86    implies( not( X ), Y ) ) ) }.
% 1.45/1.86  substitution0:
% 1.45/1.86     X := X
% 1.45/1.86     Y := Y
% 1.45/1.86  end
% 1.45/1.86  permutation0:
% 1.45/1.86     0 ==> 0
% 1.45/1.86     1 ==> 1
% 1.45/1.86  end
% 1.45/1.86  
% 1.45/1.86  eqswap: (20736) {G0,W11,D5,L2,V2,M2}  { not( and( not( X ), not( Y ) ) ) = 
% 1.45/1.86    or( X, Y ), ! op_or }.
% 1.45/1.86  parent0[1]: (20713) {G0,W11,D5,L2,V2,M2}  { ! op_or, or( X, Y ) = not( and
% 1.45/1.86    ( not( X ), not( Y ) ) ) }.
% 1.45/1.86  substitution0:
% 1.45/1.86     X := X
% 1.45/1.86     Y := Y
% 1.45/1.86  end
% 1.45/1.86  
% 1.45/1.86  subsumption: (57) {G0,W11,D5,L2,V2,M2} I { ! op_or, not( and( not( X ), not
% 1.45/1.86    ( Y ) ) ) ==> or( X, Y ) }.
% 1.45/1.86  parent0: (20736) {G0,W11,D5,L2,V2,M2}  { not( and( not( X ), not( Y ) ) ) =
% 1.45/1.86     or( X, Y ), ! op_or }.
% 1.45/1.86  substitution0:
% 1.45/1.86     X := X
% 1.45/1.86     Y := Y
% 1.45/1.86  end
% 1.45/1.86  permutation0:
% 1.45/1.86     0 ==> 1
% 1.45/1.86     1 ==> 0
% 1.45/1.86  end
% 1.45/1.86  
% 1.45/1.86  eqswap: (20741) {G0,W10,D5,L2,V2,M2}  { not( and( X, not( Y ) ) ) = implies
% 1.45/1.86    ( X, Y ), ! op_implies_and }.
% 1.45/1.86  parent0[1]: (20715) {G0,W10,D5,L2,V2,M2}  { ! op_implies_and, implies( X, Y
% 1.45/1.86     ) = not( and( X, not( Y ) ) ) }.
% 1.45/1.86  substitution0:
% 1.45/1.86     X := X
% 1.45/1.86     Y := Y
% 1.45/1.86  end
% 1.45/1.86  
% 1.45/1.86  subsumption: (59) {G0,W10,D5,L2,V2,M2} I { ! op_implies_and, not( and( X, 
% 1.45/1.86    not( Y ) ) ) ==> implies( X, Y ) }.
% 1.45/1.86  parent0: (20741) {G0,W10,D5,L2,V2,M2}  { not( and( X, not( Y ) ) ) = 
% 1.45/1.86    implies( X, Y ), ! op_implies_and }.
% 1.45/1.86  substitution0:
% 1.45/1.86     X := X
% 1.45/1.86     Y := Y
% 1.45/1.86  end
% 1.45/1.86  permutation0:
% 1.45/1.86     0 ==> 1
% 1.45/1.86     1 ==> 0
% 1.45/1.86  end
% 1.45/1.86  
% 1.45/1.86  subsumption: (62) {G0,W1,D1,L1,V0,M1} I { op_or }.
% 1.45/1.86  parent0: (20718) {G0,W1,D1,L1,V0,M1}  { op_or }.
% 1.45/1.86  substitution0:
% 1.45/1.86  end
% 1.45/1.86  permutation0:
% 1.45/1.86     0 ==> 0
% 1.45/1.86  end
% 1.45/1.86  
% 1.45/1.86  subsumption: (67) {G0,W1,D1,L1,V0,M1} I { cn2 }.
% 1.45/1.86  parent0: (20723) {G0,W1,D1,L1,V0,M1}  { cn2 }.
% 1.45/1.86  substitution0:
% 1.45/1.86  end
% 1.45/1.86  permutation0:
% 1.45/1.86     0 ==> 0
% 1.45/1.86  end
% 1.45/1.86  
% 1.45/1.86  subsumption: (70) {G0,W1,D1,L1,V0,M1} I { op_implies_and }.
% 1.45/1.86  parent0: (20727) {G0,W1,D1,L1,V0,M1}  { op_implies_and }.
% 1.45/1.86  substitution0:
% 1.45/1.86  end
% 1.45/1.86  permutation0:
% 1.45/1.86     0 ==> 0
% 1.45/1.86  end
% 1.45/1.86  
% 1.45/1.86  subsumption: (71) {G0,W1,D1,L1,V0,M1} I { ! or_1 }.
% 1.45/1.86  parent0: (20729) {G0,W1,D1,L1,V0,M1}  { ! or_1 }.
% 1.45/1.86  substitution0:
% 1.45/1.86  end
% 1.45/1.86  permutation0:
% 1.45/1.86     0 ==> 0
% 1.45/1.86  end
% 1.45/1.86  
% 1.45/1.86  resolution: (20770) {G1,W6,D4,L1,V0,M1}  { ! is_a_theorem( implies( skol11
% 1.45/1.86    , or( skol11, skol36 ) ) ) }.
% 1.45/1.86  parent0[0]: (71) {G0,W1,D1,L1,V0,M1} I { ! or_1 }.
% 1.45/1.86  parent1[1]: (24) {G0,W7,D4,L2,V0,M2} I { ! is_a_theorem( implies( skol11, 
% 1.45/1.86    or( skol11, skol36 ) ) ), or_1 }.
% 1.45/1.86  substitution0:
% 1.45/1.86  end
% 1.45/1.86  substitution1:
% 1.45/1.86  end
% 1.45/1.86  
% 1.45/1.86  subsumption: (811) {G1,W6,D4,L1,V0,M1} S(24);r(71) { ! is_a_theorem( 
% 1.45/1.86    implies( skol11, or( skol11, skol36 ) ) ) }.
% 1.45/1.86  parent0: (20770) {G1,W6,D4,L1,V0,M1}  { ! is_a_theorem( implies( skol11, or
% 1.45/1.86    ( skol11, skol36 ) ) ) }.
% 1.45/1.86  substitution0:
% 1.45/1.86  end
% 1.45/1.86  permutation0:
% 1.45/1.86     0 ==> 0
% 1.45/1.86  end
% 1.45/1.86  
% 1.45/1.86  resolution: (20771) {G1,W7,D5,L1,V2,M1}  { is_a_theorem( implies( X, 
% 1.45/1.86    implies( not( X ), Y ) ) ) }.
% 1.45/1.86  parent0[0]: (43) {G0,W8,D5,L2,V2,M2} I { ! cn2, is_a_theorem( implies( X, 
% 1.45/1.86    implies( not( X ), Y ) ) ) }.
% 1.45/1.86  parent1[0]: (67) {G0,W1,D1,L1,V0,M1} I { cn2 }.
% 1.45/1.86  substitution0:
% 1.45/1.86     X := X
% 1.45/1.86     Y := Y
% 1.45/1.86  end
% 1.45/1.86  substitution1:
% 1.45/1.86  end
% 1.45/1.86  
% 1.45/1.86  subsumption: (1776) {G1,W7,D5,L1,V2,M1} S(43);r(67) { is_a_theorem( implies
% 1.45/1.86    ( X, implies( not( X ), Y ) ) ) }.
% 1.45/1.86  parent0: (20771) {G1,W7,D5,L1,V2,M1}  { is_a_theorem( implies( X, implies( 
% 1.45/1.86    not( X ), Y ) ) ) }.
% 1.45/1.86  substitution0:
% 1.45/1.86     X := X
% 1.45/1.86     Y := Y
% 1.45/1.86  end
% 1.45/1.86  permutation0:
% 1.45/1.86     0 ==> 0
% 1.45/1.86  end
% 1.45/1.86  
% 1.45/1.86  resolution: (20773) {G1,W10,D5,L1,V2,M1}  { not( and( not( X ), not( Y ) )
% 1.45/1.86     ) ==> or( X, Y ) }.
% 1.45/1.86  parent0[0]: (57) {G0,W11,D5,L2,V2,M2} I { ! op_or, not( and( not( X ), not
% 1.45/1.86    ( Y ) ) ) ==> or( X, Y ) }.
% 1.45/1.86  parent1[0]: (62) {G0,W1,D1,L1,V0,M1} I { op_or }.
% 1.45/1.86  substitution0:
% 1.45/1.86     X := X
% 1.45/1.86     Y := Y
% 1.45/1.86  end
% 1.45/1.86  substitution1:
% 1.45/1.86  end
% 1.45/1.86  
% 1.45/1.86  subsumption: (2725) {G1,W10,D5,L1,V2,M1} S(57);r(62) { not( and( not( X ), 
% 1.45/1.86    not( Y ) ) ) ==> or( X, Y ) }.
% 1.45/1.86  parent0: (20773) {G1,W10,D5,L1,V2,M1}  { not( and( not( X ), not( Y ) ) ) 
% 1.45/1.86    ==> or( X, Y ) }.
% 1.45/1.86  substitution0:
% 1.45/1.86     X := X
% 1.45/1.86     Y := Y
% 1.45/1.86  end
% 1.45/1.86  permutation0:
% 1.45/1.86     0 ==> 0
% 1.45/1.86  end
% 1.45/1.86  
% 1.45/1.86  resolution: (20776) {G1,W9,D5,L1,V2,M1}  { not( and( X, not( Y ) ) ) ==> 
% 1.45/1.86    implies( X, Y ) }.
% 1.45/1.86  parent0[0]: (59) {G0,W10,D5,L2,V2,M2} I { ! op_implies_and, not( and( X, 
% 1.45/1.86    not( Y ) ) ) ==> implies( X, Y ) }.
% 1.45/1.86  parent1[0]: (70) {G0,W1,D1,L1,V0,M1} I { op_implies_and }.
% 1.45/1.86  substitution0:
% 1.45/1.86     X := X
% 1.45/1.86     Y := Y
% 1.45/1.86  end
% 1.45/1.86  substitution1:
% 1.45/1.86  end
% 1.45/1.86  
% 1.45/1.86  subsumption: (2877) {G1,W9,D5,L1,V2,M1} S(59);r(70) { not( and( X, not( Y )
% 1.45/1.86     ) ) ==> implies( X, Y ) }.
% 1.45/1.86  parent0: (20776) {G1,W9,D5,L1,V2,M1}  { not( and( X, not( Y ) ) ) ==> 
% 1.45/1.86    implies( X, Y ) }.
% 1.45/1.86  substitution0:
% 1.45/1.86     X := X
% 1.45/1.86     Y := Y
% 1.45/1.86  end
% 1.45/1.86  permutation0:
% 1.45/1.86     0 ==> 0
% 1.45/1.86  end
% 1.45/1.86  
% 1.45/1.86  paramod: (20780) {G2,W8,D4,L1,V2,M1}  { implies( not( X ), Y ) ==> or( X, Y
% 1.45/1.86     ) }.
% 1.45/1.86  parent0[0]: (2877) {G1,W9,D5,L1,V2,M1} S(59);r(70) { not( and( X, not( Y )
% 1.45/1.86     ) ) ==> implies( X, Y ) }.
% 1.45/1.86  parent1[0; 1]: (2725) {G1,W10,D5,L1,V2,M1} S(57);r(62) { not( and( not( X )
% 1.45/1.86    , not( Y ) ) ) ==> or( X, Y ) }.
% 1.45/1.86  substitution0:
% 1.45/1.86     X := not( X )
% 1.45/1.86     Y := Y
% 1.45/1.86  end
% 1.45/1.86  substitution1:
% 1.45/1.86     X := X
% 1.45/1.86     Y := Y
% 1.45/1.86  end
% 1.45/1.86  
% 1.45/1.86  subsumption: (20113) {G2,W8,D4,L1,V2,M1} S(2725);d(2877) { implies( not( X
% 1.45/1.86     ), Y ) ==> or( X, Y ) }.
% 1.45/1.86  parent0: (20780) {G2,W8,D4,L1,V2,M1}  { implies( not( X ), Y ) ==> or( X, Y
% 1.45/1.86     ) }.
% 1.45/1.86  substitution0:
% 1.45/1.86     X := X
% 1.45/1.86     Y := Y
% 1.45/1.86  end
% 1.45/1.86  permutation0:
% 1.45/1.86     0 ==> 0
% 1.45/1.86  end
% 1.45/1.86  
% 1.45/1.86  paramod: (20783) {G2,W6,D4,L1,V2,M1}  { is_a_theorem( implies( X, or( X, Y
% 1.45/1.86     ) ) ) }.
% 1.45/1.86  parent0[0]: (20113) {G2,W8,D4,L1,V2,M1} S(2725);d(2877) { implies( not( X )
% 1.45/1.86    , Y ) ==> or( X, Y ) }.
% 1.45/1.86  parent1[0; 3]: (1776) {G1,W7,D5,L1,V2,M1} S(43);r(67) { is_a_theorem( 
% 1.45/1.86    implies( X, implies( not( X ), Y ) ) ) }.
% 1.45/1.86  substitution0:
% 1.45/1.86     X := X
% 1.45/1.86     Y := Y
% 1.45/1.86  end
% 1.45/1.86  substitution1:
% 1.45/1.86     X := X
% 1.45/1.86     Y := Y
% 1.45/1.86  end
% 1.45/1.86  
% 1.45/1.86  subsumption: (20651) {G3,W6,D4,L1,V2,M1} S(1776);d(20113) { is_a_theorem( 
% 1.45/1.86    implies( X, or( X, Y ) ) ) }.
% 1.45/1.86  parent0: (20783) {G2,W6,D4,L1,V2,M1}  { is_a_theorem( implies( X, or( X, Y
% 1.45/1.86     ) ) ) }.
% 1.45/1.86  substitution0:
% 1.45/1.86     X := X
% 1.45/1.86     Y := Y
% 1.45/1.86  end
% 1.45/1.86  permutation0:
% 1.45/1.86     0 ==> 0
% 1.45/1.86  end
% 1.45/1.86  
% 1.45/1.86  resolution: (20784) {G2,W0,D0,L0,V0,M0}  {  }.
% 1.45/1.86  parent0[0]: (811) {G1,W6,D4,L1,V0,M1} S(24);r(71) { ! is_a_theorem( implies
% 1.45/1.86    ( skol11, or( skol11, skol36 ) ) ) }.
% 1.45/1.86  parent1[0]: (20651) {G3,W6,D4,L1,V2,M1} S(1776);d(20113) { is_a_theorem( 
% 1.45/1.86    implies( X, or( X, Y ) ) ) }.
% 1.45/1.86  substitution0:
% 1.45/1.86  end
% 1.45/1.86  substitution1:
% 1.45/1.86     X := skol11
% 1.45/1.86     Y := skol36
% 1.45/1.86  end
% 1.45/1.86  
% 1.45/1.86  subsumption: (20654) {G4,W0,D0,L0,V0,M0} S(811);r(20651) {  }.
% 1.45/1.86  parent0: (20784) {G2,W0,D0,L0,V0,M0}  {  }.
% 1.45/1.86  substitution0:
% 1.45/1.86  end
% 1.45/1.86  permutation0:
% 1.45/1.86  end
% 1.45/1.86  
% 1.45/1.86  Proof check complete!
% 1.45/1.86  
% 1.45/1.86  Memory use:
% 1.45/1.86  
% 1.45/1.86  space for terms:        316916
% 1.45/1.86  space for clauses:      841492
% 1.45/1.86  
% 1.45/1.86  
% 1.45/1.86  clauses generated:      36128
% 1.45/1.86  clauses kept:           20655
% 1.45/1.86  clauses selected:       506
% 1.45/1.86  clauses deleted:        1117
% 1.45/1.86  clauses inuse deleted:  85
% 1.45/1.86  
% 1.45/1.86  subsentry:          86326
% 1.45/1.86  literals s-matched: 55675
% 1.45/1.86  literals matched:   55646
% 1.45/1.86  full subsumption:   10848
% 1.45/1.86  
% 1.45/1.86  checksum:           705313960
% 1.45/1.86  
% 1.45/1.86  
% 1.45/1.86  Bliksem ended
%------------------------------------------------------------------------------