TSTP Solution File: SET804+4 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : SET804+4 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n020.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 0s
% DateTime : Mon Jul 18 22:52:08 EDT 2022

% Result   : Theorem 1.41s 1.78s
% Output   : Refutation 1.41s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET804+4 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13  % Command  : bliksem %s
% 0.13/0.34  % Computer : n020.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 10 12:54:28 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.71/1.07  *** allocated 10000 integers for termspace/termends
% 0.71/1.07  *** allocated 10000 integers for clauses
% 0.71/1.07  *** allocated 10000 integers for justifications
% 0.71/1.07  Bliksem 1.12
% 0.71/1.07  
% 0.71/1.07  
% 0.71/1.07  Automatic Strategy Selection
% 0.71/1.07  
% 0.71/1.07  
% 0.71/1.07  Clauses:
% 0.71/1.07  
% 0.71/1.07  { ! order( X, Y ), alpha1( X, Y ) }.
% 0.71/1.07  { ! order( X, Y ), alpha9( X, Y ) }.
% 0.71/1.07  { ! alpha1( X, Y ), ! alpha9( X, Y ), order( X, Y ) }.
% 0.71/1.07  { ! alpha9( X, Y ), alpha15( X, Y ) }.
% 0.71/1.07  { ! alpha9( X, Y ), alpha19( X, Y ) }.
% 0.71/1.07  { ! alpha15( X, Y ), ! alpha19( X, Y ), alpha9( X, Y ) }.
% 0.71/1.07  { ! alpha19( X, Y ), ! alpha23( Y, Z, T, U ), alpha25( X, Z, T, U ) }.
% 0.71/1.07  { alpha23( Y, skol1( X, Y ), skol14( X, Y ), skol18( X, Y ) ), alpha19( X, 
% 0.71/1.07    Y ) }.
% 0.71/1.07  { ! alpha25( X, skol1( X, Y ), skol14( X, Y ), skol18( X, Y ) ), alpha19( X
% 0.71/1.07    , Y ) }.
% 0.71/1.07  { ! alpha25( X, Y, Z, T ), ! alpha26( X, Y, Z, T ), apply( X, Y, T ) }.
% 0.71/1.07  { alpha26( X, Y, Z, T ), alpha25( X, Y, Z, T ) }.
% 0.71/1.07  { ! apply( X, Y, T ), alpha25( X, Y, Z, T ) }.
% 0.71/1.07  { ! alpha26( X, Y, Z, T ), apply( X, Y, Z ) }.
% 0.71/1.07  { ! alpha26( X, Y, Z, T ), apply( X, Z, T ) }.
% 0.71/1.07  { ! apply( X, Y, Z ), ! apply( X, Z, T ), alpha26( X, Y, Z, T ) }.
% 0.71/1.07  { ! alpha23( X, Y, Z, T ), member( Y, X ) }.
% 0.71/1.07  { ! alpha23( X, Y, Z, T ), alpha21( X, Z, T ) }.
% 0.71/1.07  { ! member( Y, X ), ! alpha21( X, Z, T ), alpha23( X, Y, Z, T ) }.
% 0.71/1.07  { ! alpha21( X, Y, Z ), member( Y, X ) }.
% 0.71/1.07  { ! alpha21( X, Y, Z ), member( Z, X ) }.
% 0.71/1.07  { ! member( Y, X ), ! member( Z, X ), alpha21( X, Y, Z ) }.
% 0.71/1.07  { ! alpha15( X, Y ), ! alpha20( Y, Z, T ), alpha22( X, Z, T ) }.
% 0.71/1.07  { alpha20( Y, skol2( X, Y ), skol15( X, Y ) ), alpha15( X, Y ) }.
% 0.71/1.07  { ! alpha22( X, skol2( X, Y ), skol15( X, Y ) ), alpha15( X, Y ) }.
% 0.71/1.07  { ! alpha22( X, Y, Z ), ! alpha24( X, Y, Z ), Y = Z }.
% 0.71/1.07  { alpha24( X, Y, Z ), alpha22( X, Y, Z ) }.
% 0.71/1.07  { ! Y = Z, alpha22( X, Y, Z ) }.
% 0.71/1.07  { ! alpha24( X, Y, Z ), apply( X, Y, Z ) }.
% 0.71/1.07  { ! alpha24( X, Y, Z ), apply( X, Z, Y ) }.
% 0.71/1.07  { ! apply( X, Y, Z ), ! apply( X, Z, Y ), alpha24( X, Y, Z ) }.
% 0.71/1.07  { ! alpha20( X, Y, Z ), member( Y, X ) }.
% 0.71/1.07  { ! alpha20( X, Y, Z ), member( Z, X ) }.
% 0.71/1.07  { ! member( Y, X ), ! member( Z, X ), alpha20( X, Y, Z ) }.
% 0.71/1.07  { ! alpha1( X, Y ), ! member( Z, Y ), apply( X, Z, Z ) }.
% 0.71/1.07  { member( skol3( Z, Y ), Y ), alpha1( X, Y ) }.
% 0.71/1.07  { ! apply( X, skol3( X, Y ), skol3( X, Y ) ), alpha1( X, Y ) }.
% 0.71/1.07  { ! total_order( X, Y ), order( X, Y ) }.
% 0.71/1.07  { ! total_order( X, Y ), alpha2( X, Y ) }.
% 0.71/1.07  { ! order( X, Y ), ! alpha2( X, Y ), total_order( X, Y ) }.
% 0.71/1.07  { ! alpha2( X, Y ), ! alpha10( Y, Z, T ), alpha16( X, Z, T ) }.
% 0.71/1.07  { alpha10( Y, skol4( X, Y ), skol16( X, Y ) ), alpha2( X, Y ) }.
% 0.71/1.07  { ! alpha16( X, skol4( X, Y ), skol16( X, Y ) ), alpha2( X, Y ) }.
% 0.71/1.07  { ! alpha16( X, Y, Z ), apply( X, Y, Z ), apply( X, Z, Y ) }.
% 0.71/1.07  { ! apply( X, Y, Z ), alpha16( X, Y, Z ) }.
% 0.71/1.07  { ! apply( X, Z, Y ), alpha16( X, Y, Z ) }.
% 0.71/1.07  { ! alpha10( X, Y, Z ), member( Y, X ) }.
% 0.71/1.07  { ! alpha10( X, Y, Z ), member( Z, X ) }.
% 0.71/1.07  { ! member( Y, X ), ! member( Z, X ), alpha10( X, Y, Z ) }.
% 0.71/1.07  { ! upper_bound( Z, X, Y ), ! member( T, Y ), apply( X, T, Z ) }.
% 0.71/1.07  { member( skol5( T, Y, U ), Y ), upper_bound( Z, X, Y ) }.
% 0.71/1.07  { ! apply( X, skol5( X, Y, Z ), Z ), upper_bound( Z, X, Y ) }.
% 0.71/1.07  { ! lower_bound( Z, X, Y ), ! member( T, Y ), apply( X, Z, T ) }.
% 0.71/1.07  { member( skol6( T, Y, U ), Y ), lower_bound( Z, X, Y ) }.
% 0.71/1.07  { ! apply( X, Z, skol6( X, Y, Z ) ), lower_bound( Z, X, Y ) }.
% 0.71/1.07  { ! greatest( Z, X, Y ), member( Z, Y ) }.
% 0.71/1.07  { ! greatest( Z, X, Y ), alpha3( X, Y, Z ) }.
% 0.71/1.07  { ! member( Z, Y ), ! alpha3( X, Y, Z ), greatest( Z, X, Y ) }.
% 0.71/1.07  { ! alpha3( X, Y, Z ), ! member( T, Y ), apply( X, T, Z ) }.
% 0.71/1.07  { member( skol7( T, Y, U ), Y ), alpha3( X, Y, Z ) }.
% 0.71/1.07  { ! apply( X, skol7( X, Y, Z ), Z ), alpha3( X, Y, Z ) }.
% 0.71/1.07  { ! least( Z, X, Y ), member( Z, Y ) }.
% 0.71/1.07  { ! least( Z, X, Y ), alpha4( X, Y, Z ) }.
% 0.71/1.07  { ! member( Z, Y ), ! alpha4( X, Y, Z ), least( Z, X, Y ) }.
% 0.71/1.07  { ! alpha4( X, Y, Z ), ! member( T, Y ), apply( X, Z, T ) }.
% 0.71/1.07  { member( skol8( T, Y, U ), Y ), alpha4( X, Y, Z ) }.
% 0.71/1.07  { ! apply( X, Z, skol8( X, Y, Z ) ), alpha4( X, Y, Z ) }.
% 0.71/1.07  { ! max( Z, X, Y ), member( Z, Y ) }.
% 0.71/1.07  { ! max( Z, X, Y ), alpha5( X, Y, Z ) }.
% 0.71/1.07  { ! member( Z, Y ), ! alpha5( X, Y, Z ), max( Z, X, Y ) }.
% 0.71/1.07  { ! alpha5( X, Y, Z ), ! alpha11( X, Y, Z, T ), Z = T }.
% 0.71/1.07  { ! Z = skol9( T, U, Z ), alpha5( X, Y, Z ) }.
% 0.71/1.07  { alpha11( X, Y, Z, skol9( X, Y, Z ) ), alpha5( X, Y, Z ) }.
% 0.71/1.07  { ! alpha11( X, Y, Z, T ), member( T, Y ) }.
% 1.17/1.61  { ! alpha11( X, Y, Z, T ), apply( X, Z, T ) }.
% 1.17/1.61  { ! member( T, Y ), ! apply( X, Z, T ), alpha11( X, Y, Z, T ) }.
% 1.17/1.61  { ! min( Z, X, Y ), member( Z, Y ) }.
% 1.17/1.61  { ! min( Z, X, Y ), alpha6( X, Y, Z ) }.
% 1.17/1.61  { ! member( Z, Y ), ! alpha6( X, Y, Z ), min( Z, X, Y ) }.
% 1.17/1.61  { ! alpha6( X, Y, Z ), ! alpha12( X, Y, Z, T ), Z = T }.
% 1.17/1.61  { ! Z = skol10( T, U, Z ), alpha6( X, Y, Z ) }.
% 1.17/1.61  { alpha12( X, Y, Z, skol10( X, Y, Z ) ), alpha6( X, Y, Z ) }.
% 1.17/1.61  { ! alpha12( X, Y, Z, T ), member( T, Y ) }.
% 1.17/1.61  { ! alpha12( X, Y, Z, T ), apply( X, T, Z ) }.
% 1.17/1.61  { ! member( T, Y ), ! apply( X, T, Z ), alpha12( X, Y, Z, T ) }.
% 1.17/1.61  { ! least_upper_bound( X, Y, Z, T ), member( X, Y ) }.
% 1.17/1.61  { ! least_upper_bound( X, Y, Z, T ), alpha7( X, Y, Z, T ) }.
% 1.17/1.61  { ! member( X, Y ), ! alpha7( X, Y, Z, T ), least_upper_bound( X, Y, Z, T )
% 1.17/1.61     }.
% 1.17/1.61  { ! alpha7( X, Y, Z, T ), upper_bound( X, Z, Y ) }.
% 1.17/1.61  { ! alpha7( X, Y, Z, T ), alpha13( X, Y, Z, T ) }.
% 1.17/1.61  { ! upper_bound( X, Z, Y ), ! alpha13( X, Y, Z, T ), alpha7( X, Y, Z, T ) }
% 1.17/1.61    .
% 1.17/1.61  { ! alpha13( X, Y, Z, T ), ! alpha17( Y, Z, T, U ), apply( Z, X, U ) }.
% 1.17/1.61  { ! apply( Z, X, skol11( X, U, Z, W ) ), alpha13( X, Y, Z, T ) }.
% 1.17/1.61  { alpha17( Y, Z, T, skol11( X, Y, Z, T ) ), alpha13( X, Y, Z, T ) }.
% 1.17/1.61  { ! alpha17( X, Y, Z, T ), member( T, Z ) }.
% 1.17/1.61  { ! alpha17( X, Y, Z, T ), upper_bound( T, Y, X ) }.
% 1.17/1.61  { ! member( T, Z ), ! upper_bound( T, Y, X ), alpha17( X, Y, Z, T ) }.
% 1.17/1.61  { ! greatest_lower_bound( X, Y, Z, T ), member( X, Y ) }.
% 1.17/1.61  { ! greatest_lower_bound( X, Y, Z, T ), alpha8( X, Y, Z, T ) }.
% 1.17/1.61  { ! member( X, Y ), ! alpha8( X, Y, Z, T ), greatest_lower_bound( X, Y, Z, 
% 1.17/1.61    T ) }.
% 1.17/1.61  { ! alpha8( X, Y, Z, T ), lower_bound( X, Z, Y ) }.
% 1.17/1.61  { ! alpha8( X, Y, Z, T ), alpha14( X, Y, Z, T ) }.
% 1.17/1.61  { ! lower_bound( X, Z, Y ), ! alpha14( X, Y, Z, T ), alpha8( X, Y, Z, T ) }
% 1.17/1.61    .
% 1.17/1.61  { ! alpha14( X, Y, Z, T ), ! alpha18( Y, Z, T, U ), apply( Z, U, X ) }.
% 1.17/1.61  { ! apply( Z, skol12( X, U, Z, W ), X ), alpha14( X, Y, Z, T ) }.
% 1.17/1.61  { alpha18( Y, Z, T, skol12( X, Y, Z, T ) ), alpha14( X, Y, Z, T ) }.
% 1.17/1.61  { ! alpha18( X, Y, Z, T ), member( T, Z ) }.
% 1.17/1.61  { ! alpha18( X, Y, Z, T ), lower_bound( T, Y, X ) }.
% 1.17/1.61  { ! member( T, Z ), ! lower_bound( T, Y, X ), alpha18( X, Y, Z, T ) }.
% 1.17/1.61  { order( skol13, skol17 ) }.
% 1.17/1.61  { min( skol19, skol13, skol17 ) }.
% 1.17/1.61  { min( skol20, skol13, skol17 ) }.
% 1.17/1.61  { ! skol19 = skol20 }.
% 1.17/1.61  { least( skol21, skol13, skol17 ) }.
% 1.17/1.61  
% 1.17/1.61  percentage equality = 0.027237, percentage horn = 0.867257
% 1.17/1.61  This is a problem with some equality
% 1.17/1.61  
% 1.17/1.61  
% 1.17/1.61  
% 1.17/1.61  Options Used:
% 1.17/1.61  
% 1.17/1.61  useres =            1
% 1.17/1.61  useparamod =        1
% 1.17/1.61  useeqrefl =         1
% 1.17/1.61  useeqfact =         1
% 1.17/1.61  usefactor =         1
% 1.17/1.61  usesimpsplitting =  0
% 1.17/1.61  usesimpdemod =      5
% 1.17/1.61  usesimpres =        3
% 1.17/1.61  
% 1.17/1.61  resimpinuse      =  1000
% 1.17/1.61  resimpclauses =     20000
% 1.17/1.61  substype =          eqrewr
% 1.17/1.61  backwardsubs =      1
% 1.17/1.61  selectoldest =      5
% 1.17/1.61  
% 1.17/1.61  litorderings [0] =  split
% 1.17/1.61  litorderings [1] =  extend the termordering, first sorting on arguments
% 1.17/1.61  
% 1.17/1.61  termordering =      kbo
% 1.17/1.61  
% 1.17/1.61  litapriori =        0
% 1.17/1.61  termapriori =       1
% 1.17/1.61  litaposteriori =    0
% 1.17/1.61  termaposteriori =   0
% 1.17/1.61  demodaposteriori =  0
% 1.17/1.61  ordereqreflfact =   0
% 1.17/1.61  
% 1.17/1.61  litselect =         negord
% 1.17/1.61  
% 1.17/1.61  maxweight =         15
% 1.17/1.61  maxdepth =          30000
% 1.17/1.61  maxlength =         115
% 1.17/1.61  maxnrvars =         195
% 1.17/1.61  excuselevel =       1
% 1.17/1.61  increasemaxweight = 1
% 1.17/1.61  
% 1.17/1.61  maxselected =       10000000
% 1.17/1.61  maxnrclauses =      10000000
% 1.17/1.61  
% 1.17/1.61  showgenerated =    0
% 1.17/1.61  showkept =         0
% 1.17/1.61  showselected =     0
% 1.17/1.61  showdeleted =      0
% 1.17/1.61  showresimp =       1
% 1.17/1.61  showstatus =       2000
% 1.17/1.61  
% 1.17/1.61  prologoutput =     0
% 1.17/1.61  nrgoals =          5000000
% 1.17/1.61  totalproof =       1
% 1.17/1.61  
% 1.17/1.61  Symbols occurring in the translation:
% 1.17/1.61  
% 1.17/1.61  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 1.17/1.61  .  [1, 2]      (w:1, o:25, a:1, s:1, b:0), 
% 1.17/1.61  !  [4, 1]      (w:0, o:20, a:1, s:1, b:0), 
% 1.17/1.61  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 1.17/1.61  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 1.17/1.61  order  [37, 2]      (w:1, o:49, a:1, s:1, b:0), 
% 1.17/1.61  member  [39, 2]      (w:1, o:50, a:1, s:1, b:0), 
% 1.17/1.61  apply  [40, 3]      (w:1, o:65, a:1, s:1, b:0), 
% 1.17/1.61  total_order  [43, 2]      (w:1, o:59, a:1, s:1, b:0), 
% 1.17/1.61  upper_bound  [45, 3]      (w:1, o:66, a:1, s:1, b:0), 
% 1.17/1.61  lower_bound  [46, 3]      (w:1, o:67, a:1, s:1, b:0), 
% 1.17/1.61  greatest  [47, 3]      (w:1, o:68, a:1, s:1, b:0), 
% 1.17/1.61  least  [48, 3]      (w:1, o:69, a:1, s:1, b:0), 
% 1.17/1.61  max  [49, 3]      (w:1, o:70, a:1, s:1, b:0), 
% 1.41/1.78  min  [50, 3]      (w:1, o:71, a:1, s:1, b:0), 
% 1.41/1.78  least_upper_bound  [52, 4]      (w:1, o:88, a:1, s:1, b:0), 
% 1.41/1.78  greatest_lower_bound  [53, 4]      (w:1, o:89, a:1, s:1, b:0), 
% 1.41/1.78  alpha1  [56, 2]      (w:1, o:60, a:1, s:1, b:1), 
% 1.41/1.78  alpha2  [57, 2]      (w:1, o:63, a:1, s:1, b:1), 
% 1.41/1.78  alpha3  [58, 3]      (w:1, o:76, a:1, s:1, b:1), 
% 1.41/1.78  alpha4  [59, 3]      (w:1, o:77, a:1, s:1, b:1), 
% 1.41/1.78  alpha5  [60, 3]      (w:1, o:78, a:1, s:1, b:1), 
% 1.41/1.78  alpha6  [61, 3]      (w:1, o:79, a:1, s:1, b:1), 
% 1.41/1.78  alpha7  [62, 4]      (w:1, o:90, a:1, s:1, b:1), 
% 1.41/1.78  alpha8  [63, 4]      (w:1, o:91, a:1, s:1, b:1), 
% 1.41/1.78  alpha9  [64, 2]      (w:1, o:64, a:1, s:1, b:1), 
% 1.41/1.78  alpha10  [65, 3]      (w:1, o:80, a:1, s:1, b:1), 
% 1.41/1.78  alpha11  [66, 4]      (w:1, o:92, a:1, s:1, b:1), 
% 1.41/1.78  alpha12  [67, 4]      (w:1, o:93, a:1, s:1, b:1), 
% 1.41/1.78  alpha13  [68, 4]      (w:1, o:94, a:1, s:1, b:1), 
% 1.41/1.78  alpha14  [69, 4]      (w:1, o:95, a:1, s:1, b:1), 
% 1.41/1.78  alpha15  [70, 2]      (w:1, o:61, a:1, s:1, b:1), 
% 1.41/1.78  alpha16  [71, 3]      (w:1, o:81, a:1, s:1, b:1), 
% 1.41/1.78  alpha17  [72, 4]      (w:1, o:96, a:1, s:1, b:1), 
% 1.41/1.78  alpha18  [73, 4]      (w:1, o:97, a:1, s:1, b:1), 
% 1.41/1.78  alpha19  [74, 2]      (w:1, o:62, a:1, s:1, b:1), 
% 1.41/1.78  alpha20  [75, 3]      (w:1, o:72, a:1, s:1, b:1), 
% 1.41/1.78  alpha21  [76, 3]      (w:1, o:73, a:1, s:1, b:1), 
% 1.41/1.78  alpha22  [77, 3]      (w:1, o:74, a:1, s:1, b:1), 
% 1.41/1.78  alpha23  [78, 4]      (w:1, o:98, a:1, s:1, b:1), 
% 1.41/1.78  alpha24  [79, 3]      (w:1, o:75, a:1, s:1, b:1), 
% 1.41/1.78  alpha25  [80, 4]      (w:1, o:99, a:1, s:1, b:1), 
% 1.41/1.78  alpha26  [81, 4]      (w:1, o:100, a:1, s:1, b:1), 
% 1.41/1.78  skol1  [82, 2]      (w:1, o:51, a:1, s:1, b:1), 
% 1.41/1.78  skol2  [83, 2]      (w:1, o:56, a:1, s:1, b:1), 
% 1.41/1.78  skol3  [84, 2]      (w:1, o:57, a:1, s:1, b:1), 
% 1.41/1.78  skol4  [85, 2]      (w:1, o:58, a:1, s:1, b:1), 
% 1.41/1.78  skol5  [86, 3]      (w:1, o:82, a:1, s:1, b:1), 
% 1.41/1.78  skol6  [87, 3]      (w:1, o:83, a:1, s:1, b:1), 
% 1.41/1.78  skol7  [88, 3]      (w:1, o:84, a:1, s:1, b:1), 
% 1.41/1.78  skol8  [89, 3]      (w:1, o:85, a:1, s:1, b:1), 
% 1.41/1.78  skol9  [90, 3]      (w:1, o:86, a:1, s:1, b:1), 
% 1.41/1.78  skol10  [91, 3]      (w:1, o:87, a:1, s:1, b:1), 
% 1.41/1.78  skol11  [92, 4]      (w:1, o:101, a:1, s:1, b:1), 
% 1.41/1.78  skol12  [93, 4]      (w:1, o:102, a:1, s:1, b:1), 
% 1.41/1.78  skol13  [94, 0]      (w:1, o:15, a:1, s:1, b:1), 
% 1.41/1.78  skol14  [95, 2]      (w:1, o:52, a:1, s:1, b:1), 
% 1.41/1.78  skol15  [96, 2]      (w:1, o:53, a:1, s:1, b:1), 
% 1.41/1.78  skol16  [97, 2]      (w:1, o:54, a:1, s:1, b:1), 
% 1.41/1.78  skol17  [98, 0]      (w:1, o:16, a:1, s:1, b:1), 
% 1.41/1.78  skol18  [99, 2]      (w:1, o:55, a:1, s:1, b:1), 
% 1.41/1.78  skol19  [100, 0]      (w:1, o:17, a:1, s:1, b:1), 
% 1.41/1.78  skol20  [101, 0]      (w:1, o:18, a:1, s:1, b:1), 
% 1.41/1.78  skol21  [102, 0]      (w:1, o:19, a:1, s:1, b:1).
% 1.41/1.78  
% 1.41/1.78  
% 1.41/1.78  Starting Search:
% 1.41/1.78  
% 1.41/1.78  *** allocated 15000 integers for clauses
% 1.41/1.78  *** allocated 22500 integers for clauses
% 1.41/1.78  *** allocated 33750 integers for clauses
% 1.41/1.78  *** allocated 50625 integers for clauses
% 1.41/1.78  *** allocated 15000 integers for termspace/termends
% 1.41/1.78  Resimplifying inuse:
% 1.41/1.78  Done
% 1.41/1.78  
% 1.41/1.78  *** allocated 75937 integers for clauses
% 1.41/1.78  *** allocated 22500 integers for termspace/termends
% 1.41/1.78  *** allocated 113905 integers for clauses
% 1.41/1.78  *** allocated 33750 integers for termspace/termends
% 1.41/1.78  
% 1.41/1.78  Intermediate Status:
% 1.41/1.78  Generated:    3314
% 1.41/1.78  Kept:         2027
% 1.41/1.78  Inuse:        278
% 1.41/1.78  Deleted:      0
% 1.41/1.78  Deletedinuse: 0
% 1.41/1.78  
% 1.41/1.78  Resimplifying inuse:
% 1.41/1.78  Done
% 1.41/1.78  
% 1.41/1.78  *** allocated 50625 integers for termspace/termends
% 1.41/1.78  *** allocated 170857 integers for clauses
% 1.41/1.78  Resimplifying inuse:
% 1.41/1.78  Done
% 1.41/1.78  
% 1.41/1.78  *** allocated 256285 integers for clauses
% 1.41/1.78  *** allocated 75937 integers for termspace/termends
% 1.41/1.78  
% 1.41/1.78  Intermediate Status:
% 1.41/1.78  Generated:    15798
% 1.41/1.78  Kept:         4027
% 1.41/1.78  Inuse:        640
% 1.41/1.78  Deleted:      2
% 1.41/1.78  Deletedinuse: 0
% 1.41/1.78  
% 1.41/1.78  Resimplifying inuse:
% 1.41/1.78  Done
% 1.41/1.78  
% 1.41/1.78  Resimplifying inuse:
% 1.41/1.78  Done
% 1.41/1.78  
% 1.41/1.78  *** allocated 384427 integers for clauses
% 1.41/1.78  *** allocated 113905 integers for termspace/termends
% 1.41/1.78  
% 1.41/1.78  Intermediate Status:
% 1.41/1.78  Generated:    29414
% 1.41/1.78  Kept:         6042
% 1.41/1.78  Inuse:        824
% 1.41/1.78  Deleted:      5
% 1.41/1.78  Deletedinuse: 3
% 1.41/1.78  
% 1.41/1.78  Resimplifying inuse:
% 1.41/1.78  Done
% 1.41/1.78  
% 1.41/1.78  Resimplifying inuse:
% 1.41/1.78  Done
% 1.41/1.78  
% 1.41/1.78  
% 1.41/1.78  Intermediate Status:
% 1.41/1.78  Generated:    38108
% 1.41/1.78  Kept:         8042
% 1.41/1.78  Inuse:        953
% 1.41/1.78  Deleted:      9
% 1.41/1.78  Deletedinuse: 7
% 1.41/1.78  
% 1.41/1.78  Resimplifying inuse:
% 1.41/1.78  Done
% 1.41/1.78  
% 1.41/1.78  *** allocated 170857 integers for termspace/termends
% 1.41/1.78  *** allocated 576640 integers for clauses
% 1.41/1.78  Resimplifying inuse:
% 1.41/1.78  Done
% 1.41/1.78  
% 1.41/1.78  
% 1.41/1.78  Intermediate Status:
% 1.41/1.78  Generated:    51151
% 1.41/1.78  Kept:         10053
% 1.41/1.78  Inuse:        1082
% 1.41/1.78  Deleted:      9
% 1.41/1.78  Deletedinuse: 7
% 1.41/1.78  
% 1.41/1.78  Resimplifying inuse:
% 1.41/1.78  Done
% 1.41/1.78  
% 1.41/1.78  Resimplifying inuse:
% 1.41/1.78  Done
% 1.41/1.78  
% 1.41/1.78  
% 1.41/1.78  Intermediate Status:
% 1.41/1.78  Generated:    60468
% 1.41/1.78  Kept:         12053
% 1.41/1.78  Inuse:        1269
% 1.41/1.78  Deleted:      432
% 1.41/1.78  Deletedinuse: 400
% 1.41/1.78  
% 1.41/1.78  Resimplifying inuse:
% 1.41/1.78  Done
% 1.41/1.78  
% 1.41/1.78  *** allocated 256285 integers for termspace/termends
% 1.41/1.78  
% 1.41/1.78  Bliksems!, er is een bewijs:
% 1.41/1.78  % SZS status Theorem
% 1.41/1.78  % SZS output start Refutation
% 1.41/1.78  
% 1.41/1.78  (60) {G0,W7,D2,L2,V3,M2} I { ! least( Z, X, Y ), member( Z, Y ) }.
% 1.41/1.78  (61) {G0,W8,D2,L2,V3,M2} I { ! least( Z, X, Y ), alpha4( X, Y, Z ) }.
% 1.41/1.78  (63) {G0,W11,D2,L3,V4,M3} I { ! alpha4( X, Y, Z ), ! member( T, Y ), apply
% 1.41/1.78    ( X, Z, T ) }.
% 1.41/1.78  (75) {G0,W7,D2,L2,V3,M2} I { ! min( Z, X, Y ), member( Z, Y ) }.
% 1.41/1.78  (76) {G0,W8,D2,L2,V3,M2} I { ! min( Z, X, Y ), alpha6( X, Y, Z ) }.
% 1.41/1.78  (78) {G0,W12,D2,L3,V4,M3} I { ! alpha6( X, Y, Z ), ! alpha12( X, Y, Z, T )
% 1.41/1.78    , Z = T }.
% 1.41/1.78  (83) {G0,W12,D2,L3,V4,M3} I { ! member( T, Y ), ! apply( X, T, Z ), alpha12
% 1.41/1.78    ( X, Y, Z, T ) }.
% 1.41/1.78  (109) {G0,W4,D2,L1,V0,M1} I { min( skol19, skol13, skol17 ) }.
% 1.41/1.78  (110) {G0,W4,D2,L1,V0,M1} I { min( skol20, skol13, skol17 ) }.
% 1.41/1.78  (111) {G0,W3,D2,L1,V0,M1} I { ! skol20 ==> skol19 }.
% 1.41/1.78  (112) {G0,W4,D2,L1,V0,M1} I { least( skol21, skol13, skol17 ) }.
% 1.41/1.78  (131) {G1,W3,D2,L1,V0,M1} R(75,109) { member( skol19, skol17 ) }.
% 1.41/1.78  (132) {G1,W3,D2,L1,V0,M1} R(75,110) { member( skol20, skol17 ) }.
% 1.41/1.78  (137) {G1,W3,D2,L1,V0,M1} R(60,112) { member( skol21, skol17 ) }.
% 1.41/1.78  (1570) {G1,W4,D2,L1,V0,M1} R(61,112) { alpha4( skol13, skol17, skol21 ) }.
% 1.41/1.78  (1620) {G2,W7,D2,L2,V1,M2} R(63,1570) { ! member( X, skol17 ), apply( 
% 1.41/1.78    skol13, skol21, X ) }.
% 1.41/1.78  (1689) {G3,W4,D2,L1,V0,M1} R(1620,132) { apply( skol13, skol21, skol20 )
% 1.41/1.78     }.
% 1.41/1.78  (1690) {G3,W4,D2,L1,V0,M1} R(1620,131) { apply( skol13, skol21, skol19 )
% 1.41/1.78     }.
% 1.41/1.78  (2253) {G1,W4,D2,L1,V0,M1} R(76,109) { alpha6( skol13, skol17, skol19 ) }.
% 1.41/1.78  (2254) {G1,W4,D2,L1,V0,M1} R(76,110) { alpha6( skol13, skol17, skol20 ) }.
% 1.41/1.78  (2437) {G4,W8,D2,L2,V1,M2} R(83,1690) { ! member( skol21, X ), alpha12( 
% 1.41/1.78    skol13, X, skol19, skol21 ) }.
% 1.41/1.78  (10854) {G5,W5,D2,L1,V0,M1} R(2437,137) { alpha12( skol13, skol17, skol19, 
% 1.41/1.78    skol21 ) }.
% 1.41/1.78  (10889) {G6,W3,D2,L1,V0,M1} R(10854,78);r(2253) { skol21 ==> skol19 }.
% 1.41/1.78  (10925) {G7,W4,D2,L1,V0,M1} P(10889,1689) { apply( skol13, skol19, skol20 )
% 1.41/1.78     }.
% 1.41/1.78  (10996) {G8,W8,D2,L2,V1,M2} R(10925,83) { ! member( skol19, X ), alpha12( 
% 1.41/1.78    skol13, X, skol20, skol19 ) }.
% 1.41/1.78  (12851) {G9,W5,D2,L1,V0,M1} R(10996,131) { alpha12( skol13, skol17, skol20
% 1.41/1.78    , skol19 ) }.
% 1.41/1.78  (12853) {G10,W3,D2,L1,V0,M1} R(12851,78);r(2254) { skol20 ==> skol19 }.
% 1.41/1.78  (12854) {G11,W0,D0,L0,V0,M0} S(12853);r(111) {  }.
% 1.41/1.78  
% 1.41/1.78  
% 1.41/1.78  % SZS output end Refutation
% 1.41/1.78  found a proof!
% 1.41/1.78  
% 1.41/1.78  
% 1.41/1.78  Unprocessed initial clauses:
% 1.41/1.78  
% 1.41/1.78  (12856) {G0,W6,D2,L2,V2,M2}  { ! order( X, Y ), alpha1( X, Y ) }.
% 1.41/1.78  (12857) {G0,W6,D2,L2,V2,M2}  { ! order( X, Y ), alpha9( X, Y ) }.
% 1.41/1.78  (12858) {G0,W9,D2,L3,V2,M3}  { ! alpha1( X, Y ), ! alpha9( X, Y ), order( X
% 1.41/1.78    , Y ) }.
% 1.41/1.78  (12859) {G0,W6,D2,L2,V2,M2}  { ! alpha9( X, Y ), alpha15( X, Y ) }.
% 1.41/1.78  (12860) {G0,W6,D2,L2,V2,M2}  { ! alpha9( X, Y ), alpha19( X, Y ) }.
% 1.41/1.78  (12861) {G0,W9,D2,L3,V2,M3}  { ! alpha15( X, Y ), ! alpha19( X, Y ), alpha9
% 1.41/1.78    ( X, Y ) }.
% 1.41/1.78  (12862) {G0,W13,D2,L3,V5,M3}  { ! alpha19( X, Y ), ! alpha23( Y, Z, T, U )
% 1.41/1.78    , alpha25( X, Z, T, U ) }.
% 1.41/1.78  (12863) {G0,W14,D3,L2,V2,M2}  { alpha23( Y, skol1( X, Y ), skol14( X, Y ), 
% 1.41/1.78    skol18( X, Y ) ), alpha19( X, Y ) }.
% 1.41/1.78  (12864) {G0,W14,D3,L2,V2,M2}  { ! alpha25( X, skol1( X, Y ), skol14( X, Y )
% 1.41/1.78    , skol18( X, Y ) ), alpha19( X, Y ) }.
% 1.41/1.78  (12865) {G0,W14,D2,L3,V4,M3}  { ! alpha25( X, Y, Z, T ), ! alpha26( X, Y, Z
% 1.41/1.78    , T ), apply( X, Y, T ) }.
% 1.41/1.78  (12866) {G0,W10,D2,L2,V4,M2}  { alpha26( X, Y, Z, T ), alpha25( X, Y, Z, T
% 1.41/1.78     ) }.
% 1.41/1.78  (12867) {G0,W9,D2,L2,V4,M2}  { ! apply( X, Y, T ), alpha25( X, Y, Z, T )
% 1.41/1.78     }.
% 1.41/1.78  (12868) {G0,W9,D2,L2,V4,M2}  { ! alpha26( X, Y, Z, T ), apply( X, Y, Z )
% 1.41/1.78     }.
% 1.41/1.78  (12869) {G0,W9,D2,L2,V4,M2}  { ! alpha26( X, Y, Z, T ), apply( X, Z, T )
% 1.41/1.78     }.
% 1.41/1.78  (12870) {G0,W13,D2,L3,V4,M3}  { ! apply( X, Y, Z ), ! apply( X, Z, T ), 
% 1.41/1.78    alpha26( X, Y, Z, T ) }.
% 1.41/1.78  (12871) {G0,W8,D2,L2,V4,M2}  { ! alpha23( X, Y, Z, T ), member( Y, X ) }.
% 1.41/1.78  (12872) {G0,W9,D2,L2,V4,M2}  { ! alpha23( X, Y, Z, T ), alpha21( X, Z, T )
% 1.41/1.78     }.
% 1.41/1.78  (12873) {G0,W12,D2,L3,V4,M3}  { ! member( Y, X ), ! alpha21( X, Z, T ), 
% 1.41/1.78    alpha23( X, Y, Z, T ) }.
% 1.41/1.78  (12874) {G0,W7,D2,L2,V3,M2}  { ! alpha21( X, Y, Z ), member( Y, X ) }.
% 1.41/1.78  (12875) {G0,W7,D2,L2,V3,M2}  { ! alpha21( X, Y, Z ), member( Z, X ) }.
% 1.41/1.78  (12876) {G0,W10,D2,L3,V3,M3}  { ! member( Y, X ), ! member( Z, X ), alpha21
% 1.41/1.78    ( X, Y, Z ) }.
% 1.41/1.78  (12877) {G0,W11,D2,L3,V4,M3}  { ! alpha15( X, Y ), ! alpha20( Y, Z, T ), 
% 1.41/1.78    alpha22( X, Z, T ) }.
% 1.41/1.78  (12878) {G0,W11,D3,L2,V2,M2}  { alpha20( Y, skol2( X, Y ), skol15( X, Y ) )
% 1.41/1.78    , alpha15( X, Y ) }.
% 1.41/1.78  (12879) {G0,W11,D3,L2,V2,M2}  { ! alpha22( X, skol2( X, Y ), skol15( X, Y )
% 1.41/1.78     ), alpha15( X, Y ) }.
% 1.41/1.78  (12880) {G0,W11,D2,L3,V3,M3}  { ! alpha22( X, Y, Z ), ! alpha24( X, Y, Z )
% 1.41/1.78    , Y = Z }.
% 1.41/1.78  (12881) {G0,W8,D2,L2,V3,M2}  { alpha24( X, Y, Z ), alpha22( X, Y, Z ) }.
% 1.41/1.78  (12882) {G0,W7,D2,L2,V3,M2}  { ! Y = Z, alpha22( X, Y, Z ) }.
% 1.41/1.78  (12883) {G0,W8,D2,L2,V3,M2}  { ! alpha24( X, Y, Z ), apply( X, Y, Z ) }.
% 1.41/1.78  (12884) {G0,W8,D2,L2,V3,M2}  { ! alpha24( X, Y, Z ), apply( X, Z, Y ) }.
% 1.41/1.78  (12885) {G0,W12,D2,L3,V3,M3}  { ! apply( X, Y, Z ), ! apply( X, Z, Y ), 
% 1.41/1.78    alpha24( X, Y, Z ) }.
% 1.41/1.78  (12886) {G0,W7,D2,L2,V3,M2}  { ! alpha20( X, Y, Z ), member( Y, X ) }.
% 1.41/1.78  (12887) {G0,W7,D2,L2,V3,M2}  { ! alpha20( X, Y, Z ), member( Z, X ) }.
% 1.41/1.78  (12888) {G0,W10,D2,L3,V3,M3}  { ! member( Y, X ), ! member( Z, X ), alpha20
% 1.41/1.78    ( X, Y, Z ) }.
% 1.41/1.78  (12889) {G0,W10,D2,L3,V3,M3}  { ! alpha1( X, Y ), ! member( Z, Y ), apply( 
% 1.41/1.78    X, Z, Z ) }.
% 1.41/1.78  (12890) {G0,W8,D3,L2,V3,M2}  { member( skol3( Z, Y ), Y ), alpha1( X, Y )
% 1.41/1.78     }.
% 1.41/1.78  (12891) {G0,W11,D3,L2,V2,M2}  { ! apply( X, skol3( X, Y ), skol3( X, Y ) )
% 1.41/1.78    , alpha1( X, Y ) }.
% 1.41/1.78  (12892) {G0,W6,D2,L2,V2,M2}  { ! total_order( X, Y ), order( X, Y ) }.
% 1.41/1.78  (12893) {G0,W6,D2,L2,V2,M2}  { ! total_order( X, Y ), alpha2( X, Y ) }.
% 1.41/1.78  (12894) {G0,W9,D2,L3,V2,M3}  { ! order( X, Y ), ! alpha2( X, Y ), 
% 1.41/1.78    total_order( X, Y ) }.
% 1.41/1.78  (12895) {G0,W11,D2,L3,V4,M3}  { ! alpha2( X, Y ), ! alpha10( Y, Z, T ), 
% 1.41/1.78    alpha16( X, Z, T ) }.
% 1.41/1.78  (12896) {G0,W11,D3,L2,V2,M2}  { alpha10( Y, skol4( X, Y ), skol16( X, Y ) )
% 1.41/1.78    , alpha2( X, Y ) }.
% 1.41/1.78  (12897) {G0,W11,D3,L2,V2,M2}  { ! alpha16( X, skol4( X, Y ), skol16( X, Y )
% 1.41/1.78     ), alpha2( X, Y ) }.
% 1.41/1.78  (12898) {G0,W12,D2,L3,V3,M3}  { ! alpha16( X, Y, Z ), apply( X, Y, Z ), 
% 1.41/1.78    apply( X, Z, Y ) }.
% 1.41/1.78  (12899) {G0,W8,D2,L2,V3,M2}  { ! apply( X, Y, Z ), alpha16( X, Y, Z ) }.
% 1.41/1.78  (12900) {G0,W8,D2,L2,V3,M2}  { ! apply( X, Z, Y ), alpha16( X, Y, Z ) }.
% 1.41/1.78  (12901) {G0,W7,D2,L2,V3,M2}  { ! alpha10( X, Y, Z ), member( Y, X ) }.
% 1.41/1.78  (12902) {G0,W7,D2,L2,V3,M2}  { ! alpha10( X, Y, Z ), member( Z, X ) }.
% 1.41/1.78  (12903) {G0,W10,D2,L3,V3,M3}  { ! member( Y, X ), ! member( Z, X ), alpha10
% 1.41/1.78    ( X, Y, Z ) }.
% 1.41/1.78  (12904) {G0,W11,D2,L3,V4,M3}  { ! upper_bound( Z, X, Y ), ! member( T, Y )
% 1.41/1.78    , apply( X, T, Z ) }.
% 1.41/1.78  (12905) {G0,W10,D3,L2,V5,M2}  { member( skol5( T, Y, U ), Y ), upper_bound
% 1.41/1.78    ( Z, X, Y ) }.
% 1.41/1.78  (12906) {G0,W11,D3,L2,V3,M2}  { ! apply( X, skol5( X, Y, Z ), Z ), 
% 1.41/1.78    upper_bound( Z, X, Y ) }.
% 1.41/1.78  (12907) {G0,W11,D2,L3,V4,M3}  { ! lower_bound( Z, X, Y ), ! member( T, Y )
% 1.41/1.78    , apply( X, Z, T ) }.
% 1.41/1.78  (12908) {G0,W10,D3,L2,V5,M2}  { member( skol6( T, Y, U ), Y ), lower_bound
% 1.41/1.78    ( Z, X, Y ) }.
% 1.41/1.78  (12909) {G0,W11,D3,L2,V3,M2}  { ! apply( X, Z, skol6( X, Y, Z ) ), 
% 1.41/1.78    lower_bound( Z, X, Y ) }.
% 1.41/1.78  (12910) {G0,W7,D2,L2,V3,M2}  { ! greatest( Z, X, Y ), member( Z, Y ) }.
% 1.41/1.78  (12911) {G0,W8,D2,L2,V3,M2}  { ! greatest( Z, X, Y ), alpha3( X, Y, Z ) }.
% 1.41/1.78  (12912) {G0,W11,D2,L3,V3,M3}  { ! member( Z, Y ), ! alpha3( X, Y, Z ), 
% 1.41/1.78    greatest( Z, X, Y ) }.
% 1.41/1.78  (12913) {G0,W11,D2,L3,V4,M3}  { ! alpha3( X, Y, Z ), ! member( T, Y ), 
% 1.41/1.78    apply( X, T, Z ) }.
% 1.41/1.78  (12914) {G0,W10,D3,L2,V5,M2}  { member( skol7( T, Y, U ), Y ), alpha3( X, Y
% 1.41/1.78    , Z ) }.
% 1.41/1.78  (12915) {G0,W11,D3,L2,V3,M2}  { ! apply( X, skol7( X, Y, Z ), Z ), alpha3( 
% 1.41/1.78    X, Y, Z ) }.
% 1.41/1.78  (12916) {G0,W7,D2,L2,V3,M2}  { ! least( Z, X, Y ), member( Z, Y ) }.
% 1.41/1.78  (12917) {G0,W8,D2,L2,V3,M2}  { ! least( Z, X, Y ), alpha4( X, Y, Z ) }.
% 1.41/1.78  (12918) {G0,W11,D2,L3,V3,M3}  { ! member( Z, Y ), ! alpha4( X, Y, Z ), 
% 1.41/1.78    least( Z, X, Y ) }.
% 1.41/1.78  (12919) {G0,W11,D2,L3,V4,M3}  { ! alpha4( X, Y, Z ), ! member( T, Y ), 
% 1.41/1.78    apply( X, Z, T ) }.
% 1.41/1.78  (12920) {G0,W10,D3,L2,V5,M2}  { member( skol8( T, Y, U ), Y ), alpha4( X, Y
% 1.41/1.78    , Z ) }.
% 1.41/1.78  (12921) {G0,W11,D3,L2,V3,M2}  { ! apply( X, Z, skol8( X, Y, Z ) ), alpha4( 
% 1.41/1.78    X, Y, Z ) }.
% 1.41/1.78  (12922) {G0,W7,D2,L2,V3,M2}  { ! max( Z, X, Y ), member( Z, Y ) }.
% 1.41/1.78  (12923) {G0,W8,D2,L2,V3,M2}  { ! max( Z, X, Y ), alpha5( X, Y, Z ) }.
% 1.41/1.78  (12924) {G0,W11,D2,L3,V3,M3}  { ! member( Z, Y ), ! alpha5( X, Y, Z ), max
% 1.41/1.78    ( Z, X, Y ) }.
% 1.41/1.78  (12925) {G0,W12,D2,L3,V4,M3}  { ! alpha5( X, Y, Z ), ! alpha11( X, Y, Z, T
% 1.41/1.78     ), Z = T }.
% 1.41/1.78  (12926) {G0,W10,D3,L2,V5,M2}  { ! Z = skol9( T, U, Z ), alpha5( X, Y, Z )
% 1.41/1.78     }.
% 1.41/1.78  (12927) {G0,W12,D3,L2,V3,M2}  { alpha11( X, Y, Z, skol9( X, Y, Z ) ), 
% 1.41/1.78    alpha5( X, Y, Z ) }.
% 1.41/1.78  (12928) {G0,W8,D2,L2,V4,M2}  { ! alpha11( X, Y, Z, T ), member( T, Y ) }.
% 1.41/1.78  (12929) {G0,W9,D2,L2,V4,M2}  { ! alpha11( X, Y, Z, T ), apply( X, Z, T )
% 1.41/1.78     }.
% 1.41/1.78  (12930) {G0,W12,D2,L3,V4,M3}  { ! member( T, Y ), ! apply( X, Z, T ), 
% 1.41/1.78    alpha11( X, Y, Z, T ) }.
% 1.41/1.78  (12931) {G0,W7,D2,L2,V3,M2}  { ! min( Z, X, Y ), member( Z, Y ) }.
% 1.41/1.78  (12932) {G0,W8,D2,L2,V3,M2}  { ! min( Z, X, Y ), alpha6( X, Y, Z ) }.
% 1.41/1.78  (12933) {G0,W11,D2,L3,V3,M3}  { ! member( Z, Y ), ! alpha6( X, Y, Z ), min
% 1.41/1.78    ( Z, X, Y ) }.
% 1.41/1.78  (12934) {G0,W12,D2,L3,V4,M3}  { ! alpha6( X, Y, Z ), ! alpha12( X, Y, Z, T
% 1.41/1.78     ), Z = T }.
% 1.41/1.78  (12935) {G0,W10,D3,L2,V5,M2}  { ! Z = skol10( T, U, Z ), alpha6( X, Y, Z )
% 1.41/1.78     }.
% 1.41/1.78  (12936) {G0,W12,D3,L2,V3,M2}  { alpha12( X, Y, Z, skol10( X, Y, Z ) ), 
% 1.41/1.78    alpha6( X, Y, Z ) }.
% 1.41/1.78  (12937) {G0,W8,D2,L2,V4,M2}  { ! alpha12( X, Y, Z, T ), member( T, Y ) }.
% 1.41/1.78  (12938) {G0,W9,D2,L2,V4,M2}  { ! alpha12( X, Y, Z, T ), apply( X, T, Z )
% 1.41/1.78     }.
% 1.41/1.78  (12939) {G0,W12,D2,L3,V4,M3}  { ! member( T, Y ), ! apply( X, T, Z ), 
% 1.41/1.78    alpha12( X, Y, Z, T ) }.
% 1.41/1.78  (12940) {G0,W8,D2,L2,V4,M2}  { ! least_upper_bound( X, Y, Z, T ), member( X
% 1.41/1.78    , Y ) }.
% 1.41/1.78  (12941) {G0,W10,D2,L2,V4,M2}  { ! least_upper_bound( X, Y, Z, T ), alpha7( 
% 1.41/1.78    X, Y, Z, T ) }.
% 1.41/1.78  (12942) {G0,W13,D2,L3,V4,M3}  { ! member( X, Y ), ! alpha7( X, Y, Z, T ), 
% 1.41/1.78    least_upper_bound( X, Y, Z, T ) }.
% 1.41/1.78  (12943) {G0,W9,D2,L2,V4,M2}  { ! alpha7( X, Y, Z, T ), upper_bound( X, Z, Y
% 1.41/1.78     ) }.
% 1.41/1.78  (12944) {G0,W10,D2,L2,V4,M2}  { ! alpha7( X, Y, Z, T ), alpha13( X, Y, Z, T
% 1.41/1.78     ) }.
% 1.41/1.78  (12945) {G0,W14,D2,L3,V4,M3}  { ! upper_bound( X, Z, Y ), ! alpha13( X, Y, 
% 1.41/1.78    Z, T ), alpha7( X, Y, Z, T ) }.
% 1.41/1.78  (12946) {G0,W14,D2,L3,V5,M3}  { ! alpha13( X, Y, Z, T ), ! alpha17( Y, Z, T
% 1.41/1.78    , U ), apply( Z, X, U ) }.
% 1.41/1.78  (12947) {G0,W13,D3,L2,V6,M2}  { ! apply( Z, X, skol11( X, U, Z, W ) ), 
% 1.41/1.78    alpha13( X, Y, Z, T ) }.
% 1.41/1.78  (12948) {G0,W14,D3,L2,V4,M2}  { alpha17( Y, Z, T, skol11( X, Y, Z, T ) ), 
% 1.41/1.78    alpha13( X, Y, Z, T ) }.
% 1.41/1.78  (12949) {G0,W8,D2,L2,V4,M2}  { ! alpha17( X, Y, Z, T ), member( T, Z ) }.
% 1.41/1.78  (12950) {G0,W9,D2,L2,V4,M2}  { ! alpha17( X, Y, Z, T ), upper_bound( T, Y, 
% 1.41/1.78    X ) }.
% 1.41/1.78  (12951) {G0,W12,D2,L3,V4,M3}  { ! member( T, Z ), ! upper_bound( T, Y, X )
% 1.41/1.78    , alpha17( X, Y, Z, T ) }.
% 1.41/1.78  (12952) {G0,W8,D2,L2,V4,M2}  { ! greatest_lower_bound( X, Y, Z, T ), member
% 1.41/1.78    ( X, Y ) }.
% 1.41/1.78  (12953) {G0,W10,D2,L2,V4,M2}  { ! greatest_lower_bound( X, Y, Z, T ), 
% 1.41/1.78    alpha8( X, Y, Z, T ) }.
% 1.41/1.78  (12954) {G0,W13,D2,L3,V4,M3}  { ! member( X, Y ), ! alpha8( X, Y, Z, T ), 
% 1.41/1.78    greatest_lower_bound( X, Y, Z, T ) }.
% 1.41/1.78  (12955) {G0,W9,D2,L2,V4,M2}  { ! alpha8( X, Y, Z, T ), lower_bound( X, Z, Y
% 1.41/1.78     ) }.
% 1.41/1.78  (12956) {G0,W10,D2,L2,V4,M2}  { ! alpha8( X, Y, Z, T ), alpha14( X, Y, Z, T
% 1.41/1.78     ) }.
% 1.41/1.78  (12957) {G0,W14,D2,L3,V4,M3}  { ! lower_bound( X, Z, Y ), ! alpha14( X, Y, 
% 1.41/1.78    Z, T ), alpha8( X, Y, Z, T ) }.
% 1.41/1.78  (12958) {G0,W14,D2,L3,V5,M3}  { ! alpha14( X, Y, Z, T ), ! alpha18( Y, Z, T
% 1.41/1.78    , U ), apply( Z, U, X ) }.
% 1.41/1.78  (12959) {G0,W13,D3,L2,V6,M2}  { ! apply( Z, skol12( X, U, Z, W ), X ), 
% 1.41/1.78    alpha14( X, Y, Z, T ) }.
% 1.41/1.78  (12960) {G0,W14,D3,L2,V4,M2}  { alpha18( Y, Z, T, skol12( X, Y, Z, T ) ), 
% 1.41/1.78    alpha14( X, Y, Z, T ) }.
% 1.41/1.78  (12961) {G0,W8,D2,L2,V4,M2}  { ! alpha18( X, Y, Z, T ), member( T, Z ) }.
% 1.41/1.78  (12962) {G0,W9,D2,L2,V4,M2}  { ! alpha18( X, Y, Z, T ), lower_bound( T, Y, 
% 1.41/1.78    X ) }.
% 1.41/1.78  (12963) {G0,W12,D2,L3,V4,M3}  { ! member( T, Z ), ! lower_bound( T, Y, X )
% 1.41/1.78    , alpha18( X, Y, Z, T ) }.
% 1.41/1.78  (12964) {G0,W3,D2,L1,V0,M1}  { order( skol13, skol17 ) }.
% 1.41/1.78  (12965) {G0,W4,D2,L1,V0,M1}  { min( skol19, skol13, skol17 ) }.
% 1.41/1.78  (12966) {G0,W4,D2,L1,V0,M1}  { min( skol20, skol13, skol17 ) }.
% 1.41/1.78  (12967) {G0,W3,D2,L1,V0,M1}  { ! skol19 = skol20 }.
% 1.41/1.78  (12968) {G0,W4,D2,L1,V0,M1}  { least( skol21, skol13, skol17 ) }.
% 1.41/1.78  
% 1.41/1.78  
% 1.41/1.78  Total Proof:
% 1.41/1.78  
% 1.41/1.78  subsumption: (60) {G0,W7,D2,L2,V3,M2} I { ! least( Z, X, Y ), member( Z, Y
% 1.41/1.78     ) }.
% 1.41/1.78  parent0: (12916) {G0,W7,D2,L2,V3,M2}  { ! least( Z, X, Y ), member( Z, Y )
% 1.41/1.78     }.
% 1.41/1.78  substitution0:
% 1.41/1.78     X := X
% 1.41/1.78     Y := Y
% 1.41/1.78     Z := Z
% 1.41/1.78  end
% 1.41/1.78  permutation0:
% 1.41/1.78     0 ==> 0
% 1.41/1.78     1 ==> 1
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  subsumption: (61) {G0,W8,D2,L2,V3,M2} I { ! least( Z, X, Y ), alpha4( X, Y
% 1.41/1.78    , Z ) }.
% 1.41/1.78  parent0: (12917) {G0,W8,D2,L2,V3,M2}  { ! least( Z, X, Y ), alpha4( X, Y, Z
% 1.41/1.78     ) }.
% 1.41/1.78  substitution0:
% 1.41/1.78     X := X
% 1.41/1.78     Y := Y
% 1.41/1.78     Z := Z
% 1.41/1.78  end
% 1.41/1.78  permutation0:
% 1.41/1.78     0 ==> 0
% 1.41/1.78     1 ==> 1
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  subsumption: (63) {G0,W11,D2,L3,V4,M3} I { ! alpha4( X, Y, Z ), ! member( T
% 1.41/1.78    , Y ), apply( X, Z, T ) }.
% 1.41/1.78  parent0: (12919) {G0,W11,D2,L3,V4,M3}  { ! alpha4( X, Y, Z ), ! member( T, 
% 1.41/1.78    Y ), apply( X, Z, T ) }.
% 1.41/1.78  substitution0:
% 1.41/1.78     X := X
% 1.41/1.78     Y := Y
% 1.41/1.78     Z := Z
% 1.41/1.78     T := T
% 1.41/1.78  end
% 1.41/1.78  permutation0:
% 1.41/1.78     0 ==> 0
% 1.41/1.78     1 ==> 1
% 1.41/1.78     2 ==> 2
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  subsumption: (75) {G0,W7,D2,L2,V3,M2} I { ! min( Z, X, Y ), member( Z, Y )
% 1.41/1.78     }.
% 1.41/1.78  parent0: (12931) {G0,W7,D2,L2,V3,M2}  { ! min( Z, X, Y ), member( Z, Y )
% 1.41/1.78     }.
% 1.41/1.78  substitution0:
% 1.41/1.78     X := X
% 1.41/1.78     Y := Y
% 1.41/1.78     Z := Z
% 1.41/1.78  end
% 1.41/1.78  permutation0:
% 1.41/1.78     0 ==> 0
% 1.41/1.78     1 ==> 1
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  subsumption: (76) {G0,W8,D2,L2,V3,M2} I { ! min( Z, X, Y ), alpha6( X, Y, Z
% 1.41/1.78     ) }.
% 1.41/1.78  parent0: (12932) {G0,W8,D2,L2,V3,M2}  { ! min( Z, X, Y ), alpha6( X, Y, Z )
% 1.41/1.78     }.
% 1.41/1.78  substitution0:
% 1.41/1.78     X := X
% 1.41/1.78     Y := Y
% 1.41/1.78     Z := Z
% 1.41/1.78  end
% 1.41/1.78  permutation0:
% 1.41/1.78     0 ==> 0
% 1.41/1.78     1 ==> 1
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  subsumption: (78) {G0,W12,D2,L3,V4,M3} I { ! alpha6( X, Y, Z ), ! alpha12( 
% 1.41/1.78    X, Y, Z, T ), Z = T }.
% 1.41/1.78  parent0: (12934) {G0,W12,D2,L3,V4,M3}  { ! alpha6( X, Y, Z ), ! alpha12( X
% 1.41/1.78    , Y, Z, T ), Z = T }.
% 1.41/1.78  substitution0:
% 1.41/1.78     X := X
% 1.41/1.78     Y := Y
% 1.41/1.78     Z := Z
% 1.41/1.78     T := T
% 1.41/1.78  end
% 1.41/1.78  permutation0:
% 1.41/1.78     0 ==> 0
% 1.41/1.78     1 ==> 1
% 1.41/1.78     2 ==> 2
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  subsumption: (83) {G0,W12,D2,L3,V4,M3} I { ! member( T, Y ), ! apply( X, T
% 1.41/1.78    , Z ), alpha12( X, Y, Z, T ) }.
% 1.41/1.78  parent0: (12939) {G0,W12,D2,L3,V4,M3}  { ! member( T, Y ), ! apply( X, T, Z
% 1.41/1.78     ), alpha12( X, Y, Z, T ) }.
% 1.41/1.78  substitution0:
% 1.41/1.78     X := X
% 1.41/1.78     Y := Y
% 1.41/1.78     Z := Z
% 1.41/1.78     T := T
% 1.41/1.78  end
% 1.41/1.78  permutation0:
% 1.41/1.78     0 ==> 0
% 1.41/1.78     1 ==> 1
% 1.41/1.78     2 ==> 2
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  subsumption: (109) {G0,W4,D2,L1,V0,M1} I { min( skol19, skol13, skol17 )
% 1.41/1.78     }.
% 1.41/1.78  parent0: (12965) {G0,W4,D2,L1,V0,M1}  { min( skol19, skol13, skol17 ) }.
% 1.41/1.78  substitution0:
% 1.41/1.78  end
% 1.41/1.78  permutation0:
% 1.41/1.78     0 ==> 0
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  subsumption: (110) {G0,W4,D2,L1,V0,M1} I { min( skol20, skol13, skol17 )
% 1.41/1.78     }.
% 1.41/1.78  parent0: (12966) {G0,W4,D2,L1,V0,M1}  { min( skol20, skol13, skol17 ) }.
% 1.41/1.78  substitution0:
% 1.41/1.78  end
% 1.41/1.78  permutation0:
% 1.41/1.78     0 ==> 0
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  eqswap: (13072) {G0,W3,D2,L1,V0,M1}  { ! skol20 = skol19 }.
% 1.41/1.78  parent0[0]: (12967) {G0,W3,D2,L1,V0,M1}  { ! skol19 = skol20 }.
% 1.41/1.78  substitution0:
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  subsumption: (111) {G0,W3,D2,L1,V0,M1} I { ! skol20 ==> skol19 }.
% 1.41/1.78  parent0: (13072) {G0,W3,D2,L1,V0,M1}  { ! skol20 = skol19 }.
% 1.41/1.78  substitution0:
% 1.41/1.78  end
% 1.41/1.78  permutation0:
% 1.41/1.78     0 ==> 0
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  subsumption: (112) {G0,W4,D2,L1,V0,M1} I { least( skol21, skol13, skol17 )
% 1.41/1.78     }.
% 1.41/1.78  parent0: (12968) {G0,W4,D2,L1,V0,M1}  { least( skol21, skol13, skol17 ) }.
% 1.41/1.78  substitution0:
% 1.41/1.78  end
% 1.41/1.78  permutation0:
% 1.41/1.78     0 ==> 0
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  resolution: (13086) {G1,W3,D2,L1,V0,M1}  { member( skol19, skol17 ) }.
% 1.41/1.78  parent0[0]: (75) {G0,W7,D2,L2,V3,M2} I { ! min( Z, X, Y ), member( Z, Y )
% 1.41/1.78     }.
% 1.41/1.78  parent1[0]: (109) {G0,W4,D2,L1,V0,M1} I { min( skol19, skol13, skol17 ) }.
% 1.41/1.78  substitution0:
% 1.41/1.78     X := skol13
% 1.41/1.78     Y := skol17
% 1.41/1.78     Z := skol19
% 1.41/1.78  end
% 1.41/1.78  substitution1:
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  subsumption: (131) {G1,W3,D2,L1,V0,M1} R(75,109) { member( skol19, skol17 )
% 1.41/1.78     }.
% 1.41/1.78  parent0: (13086) {G1,W3,D2,L1,V0,M1}  { member( skol19, skol17 ) }.
% 1.41/1.78  substitution0:
% 1.41/1.78  end
% 1.41/1.78  permutation0:
% 1.41/1.78     0 ==> 0
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  resolution: (13087) {G1,W3,D2,L1,V0,M1}  { member( skol20, skol17 ) }.
% 1.41/1.78  parent0[0]: (75) {G0,W7,D2,L2,V3,M2} I { ! min( Z, X, Y ), member( Z, Y )
% 1.41/1.78     }.
% 1.41/1.78  parent1[0]: (110) {G0,W4,D2,L1,V0,M1} I { min( skol20, skol13, skol17 ) }.
% 1.41/1.78  substitution0:
% 1.41/1.78     X := skol13
% 1.41/1.78     Y := skol17
% 1.41/1.78     Z := skol20
% 1.41/1.78  end
% 1.41/1.78  substitution1:
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  subsumption: (132) {G1,W3,D2,L1,V0,M1} R(75,110) { member( skol20, skol17 )
% 1.41/1.78     }.
% 1.41/1.78  parent0: (13087) {G1,W3,D2,L1,V0,M1}  { member( skol20, skol17 ) }.
% 1.41/1.78  substitution0:
% 1.41/1.78  end
% 1.41/1.78  permutation0:
% 1.41/1.78     0 ==> 0
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  resolution: (13088) {G1,W3,D2,L1,V0,M1}  { member( skol21, skol17 ) }.
% 1.41/1.78  parent0[0]: (60) {G0,W7,D2,L2,V3,M2} I { ! least( Z, X, Y ), member( Z, Y )
% 1.41/1.78     }.
% 1.41/1.78  parent1[0]: (112) {G0,W4,D2,L1,V0,M1} I { least( skol21, skol13, skol17 )
% 1.41/1.78     }.
% 1.41/1.78  substitution0:
% 1.41/1.78     X := skol13
% 1.41/1.78     Y := skol17
% 1.41/1.78     Z := skol21
% 1.41/1.78  end
% 1.41/1.78  substitution1:
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  subsumption: (137) {G1,W3,D2,L1,V0,M1} R(60,112) { member( skol21, skol17 )
% 1.41/1.78     }.
% 1.41/1.78  parent0: (13088) {G1,W3,D2,L1,V0,M1}  { member( skol21, skol17 ) }.
% 1.41/1.78  substitution0:
% 1.41/1.78  end
% 1.41/1.78  permutation0:
% 1.41/1.78     0 ==> 0
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  resolution: (13089) {G1,W4,D2,L1,V0,M1}  { alpha4( skol13, skol17, skol21 )
% 1.41/1.78     }.
% 1.41/1.78  parent0[0]: (61) {G0,W8,D2,L2,V3,M2} I { ! least( Z, X, Y ), alpha4( X, Y, 
% 1.41/1.78    Z ) }.
% 1.41/1.78  parent1[0]: (112) {G0,W4,D2,L1,V0,M1} I { least( skol21, skol13, skol17 )
% 1.41/1.78     }.
% 1.41/1.78  substitution0:
% 1.41/1.78     X := skol13
% 1.41/1.78     Y := skol17
% 1.41/1.78     Z := skol21
% 1.41/1.78  end
% 1.41/1.78  substitution1:
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  subsumption: (1570) {G1,W4,D2,L1,V0,M1} R(61,112) { alpha4( skol13, skol17
% 1.41/1.78    , skol21 ) }.
% 1.41/1.78  parent0: (13089) {G1,W4,D2,L1,V0,M1}  { alpha4( skol13, skol17, skol21 )
% 1.41/1.78     }.
% 1.41/1.78  substitution0:
% 1.41/1.78  end
% 1.41/1.78  permutation0:
% 1.41/1.78     0 ==> 0
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  resolution: (13090) {G1,W7,D2,L2,V1,M2}  { ! member( X, skol17 ), apply( 
% 1.41/1.78    skol13, skol21, X ) }.
% 1.41/1.78  parent0[0]: (63) {G0,W11,D2,L3,V4,M3} I { ! alpha4( X, Y, Z ), ! member( T
% 1.41/1.78    , Y ), apply( X, Z, T ) }.
% 1.41/1.78  parent1[0]: (1570) {G1,W4,D2,L1,V0,M1} R(61,112) { alpha4( skol13, skol17, 
% 1.41/1.78    skol21 ) }.
% 1.41/1.78  substitution0:
% 1.41/1.78     X := skol13
% 1.41/1.78     Y := skol17
% 1.41/1.78     Z := skol21
% 1.41/1.78     T := X
% 1.41/1.78  end
% 1.41/1.78  substitution1:
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  subsumption: (1620) {G2,W7,D2,L2,V1,M2} R(63,1570) { ! member( X, skol17 )
% 1.41/1.78    , apply( skol13, skol21, X ) }.
% 1.41/1.78  parent0: (13090) {G1,W7,D2,L2,V1,M2}  { ! member( X, skol17 ), apply( 
% 1.41/1.78    skol13, skol21, X ) }.
% 1.41/1.78  substitution0:
% 1.41/1.78     X := X
% 1.41/1.78  end
% 1.41/1.78  permutation0:
% 1.41/1.78     0 ==> 0
% 1.41/1.78     1 ==> 1
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  resolution: (13091) {G2,W4,D2,L1,V0,M1}  { apply( skol13, skol21, skol20 )
% 1.41/1.78     }.
% 1.41/1.78  parent0[0]: (1620) {G2,W7,D2,L2,V1,M2} R(63,1570) { ! member( X, skol17 ), 
% 1.41/1.78    apply( skol13, skol21, X ) }.
% 1.41/1.78  parent1[0]: (132) {G1,W3,D2,L1,V0,M1} R(75,110) { member( skol20, skol17 )
% 1.41/1.78     }.
% 1.41/1.78  substitution0:
% 1.41/1.78     X := skol20
% 1.41/1.78  end
% 1.41/1.78  substitution1:
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  subsumption: (1689) {G3,W4,D2,L1,V0,M1} R(1620,132) { apply( skol13, skol21
% 1.41/1.78    , skol20 ) }.
% 1.41/1.78  parent0: (13091) {G2,W4,D2,L1,V0,M1}  { apply( skol13, skol21, skol20 ) }.
% 1.41/1.78  substitution0:
% 1.41/1.78  end
% 1.41/1.78  permutation0:
% 1.41/1.78     0 ==> 0
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  resolution: (13092) {G2,W4,D2,L1,V0,M1}  { apply( skol13, skol21, skol19 )
% 1.41/1.78     }.
% 1.41/1.78  parent0[0]: (1620) {G2,W7,D2,L2,V1,M2} R(63,1570) { ! member( X, skol17 ), 
% 1.41/1.78    apply( skol13, skol21, X ) }.
% 1.41/1.78  parent1[0]: (131) {G1,W3,D2,L1,V0,M1} R(75,109) { member( skol19, skol17 )
% 1.41/1.78     }.
% 1.41/1.78  substitution0:
% 1.41/1.78     X := skol19
% 1.41/1.78  end
% 1.41/1.78  substitution1:
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  subsumption: (1690) {G3,W4,D2,L1,V0,M1} R(1620,131) { apply( skol13, skol21
% 1.41/1.78    , skol19 ) }.
% 1.41/1.78  parent0: (13092) {G2,W4,D2,L1,V0,M1}  { apply( skol13, skol21, skol19 ) }.
% 1.41/1.78  substitution0:
% 1.41/1.78  end
% 1.41/1.78  permutation0:
% 1.41/1.78     0 ==> 0
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  resolution: (13093) {G1,W4,D2,L1,V0,M1}  { alpha6( skol13, skol17, skol19 )
% 1.41/1.78     }.
% 1.41/1.78  parent0[0]: (76) {G0,W8,D2,L2,V3,M2} I { ! min( Z, X, Y ), alpha6( X, Y, Z
% 1.41/1.78     ) }.
% 1.41/1.78  parent1[0]: (109) {G0,W4,D2,L1,V0,M1} I { min( skol19, skol13, skol17 ) }.
% 1.41/1.78  substitution0:
% 1.41/1.78     X := skol13
% 1.41/1.78     Y := skol17
% 1.41/1.78     Z := skol19
% 1.41/1.78  end
% 1.41/1.78  substitution1:
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  subsumption: (2253) {G1,W4,D2,L1,V0,M1} R(76,109) { alpha6( skol13, skol17
% 1.41/1.78    , skol19 ) }.
% 1.41/1.78  parent0: (13093) {G1,W4,D2,L1,V0,M1}  { alpha6( skol13, skol17, skol19 )
% 1.41/1.78     }.
% 1.41/1.78  substitution0:
% 1.41/1.78  end
% 1.41/1.78  permutation0:
% 1.41/1.78     0 ==> 0
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  resolution: (13094) {G1,W4,D2,L1,V0,M1}  { alpha6( skol13, skol17, skol20 )
% 1.41/1.78     }.
% 1.41/1.78  parent0[0]: (76) {G0,W8,D2,L2,V3,M2} I { ! min( Z, X, Y ), alpha6( X, Y, Z
% 1.41/1.78     ) }.
% 1.41/1.78  parent1[0]: (110) {G0,W4,D2,L1,V0,M1} I { min( skol20, skol13, skol17 ) }.
% 1.41/1.78  substitution0:
% 1.41/1.78     X := skol13
% 1.41/1.78     Y := skol17
% 1.41/1.78     Z := skol20
% 1.41/1.78  end
% 1.41/1.78  substitution1:
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  subsumption: (2254) {G1,W4,D2,L1,V0,M1} R(76,110) { alpha6( skol13, skol17
% 1.41/1.78    , skol20 ) }.
% 1.41/1.78  parent0: (13094) {G1,W4,D2,L1,V0,M1}  { alpha6( skol13, skol17, skol20 )
% 1.41/1.78     }.
% 1.41/1.78  substitution0:
% 1.41/1.78  end
% 1.41/1.78  permutation0:
% 1.41/1.78     0 ==> 0
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  resolution: (13095) {G1,W8,D2,L2,V1,M2}  { ! member( skol21, X ), alpha12( 
% 1.41/1.78    skol13, X, skol19, skol21 ) }.
% 1.41/1.78  parent0[1]: (83) {G0,W12,D2,L3,V4,M3} I { ! member( T, Y ), ! apply( X, T, 
% 1.41/1.78    Z ), alpha12( X, Y, Z, T ) }.
% 1.41/1.78  parent1[0]: (1690) {G3,W4,D2,L1,V0,M1} R(1620,131) { apply( skol13, skol21
% 1.41/1.78    , skol19 ) }.
% 1.41/1.78  substitution0:
% 1.41/1.78     X := skol13
% 1.41/1.78     Y := X
% 1.41/1.78     Z := skol19
% 1.41/1.78     T := skol21
% 1.41/1.78  end
% 1.41/1.78  substitution1:
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  subsumption: (2437) {G4,W8,D2,L2,V1,M2} R(83,1690) { ! member( skol21, X )
% 1.41/1.78    , alpha12( skol13, X, skol19, skol21 ) }.
% 1.41/1.78  parent0: (13095) {G1,W8,D2,L2,V1,M2}  { ! member( skol21, X ), alpha12( 
% 1.41/1.78    skol13, X, skol19, skol21 ) }.
% 1.41/1.78  substitution0:
% 1.41/1.78     X := X
% 1.41/1.78  end
% 1.41/1.78  permutation0:
% 1.41/1.78     0 ==> 0
% 1.41/1.78     1 ==> 1
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  resolution: (13096) {G2,W5,D2,L1,V0,M1}  { alpha12( skol13, skol17, skol19
% 1.41/1.78    , skol21 ) }.
% 1.41/1.78  parent0[0]: (2437) {G4,W8,D2,L2,V1,M2} R(83,1690) { ! member( skol21, X ), 
% 1.41/1.78    alpha12( skol13, X, skol19, skol21 ) }.
% 1.41/1.78  parent1[0]: (137) {G1,W3,D2,L1,V0,M1} R(60,112) { member( skol21, skol17 )
% 1.41/1.78     }.
% 1.41/1.78  substitution0:
% 1.41/1.78     X := skol17
% 1.41/1.78  end
% 1.41/1.78  substitution1:
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  subsumption: (10854) {G5,W5,D2,L1,V0,M1} R(2437,137) { alpha12( skol13, 
% 1.41/1.78    skol17, skol19, skol21 ) }.
% 1.41/1.78  parent0: (13096) {G2,W5,D2,L1,V0,M1}  { alpha12( skol13, skol17, skol19, 
% 1.41/1.78    skol21 ) }.
% 1.41/1.78  substitution0:
% 1.41/1.78  end
% 1.41/1.78  permutation0:
% 1.41/1.78     0 ==> 0
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  eqswap: (13097) {G0,W12,D2,L3,V4,M3}  { Y = X, ! alpha6( Z, T, X ), ! 
% 1.41/1.78    alpha12( Z, T, X, Y ) }.
% 1.41/1.78  parent0[2]: (78) {G0,W12,D2,L3,V4,M3} I { ! alpha6( X, Y, Z ), ! alpha12( X
% 1.41/1.78    , Y, Z, T ), Z = T }.
% 1.41/1.78  substitution0:
% 1.41/1.78     X := Z
% 1.41/1.78     Y := T
% 1.41/1.78     Z := X
% 1.41/1.78     T := Y
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  resolution: (13098) {G1,W7,D2,L2,V0,M2}  { skol21 = skol19, ! alpha6( 
% 1.41/1.78    skol13, skol17, skol19 ) }.
% 1.41/1.78  parent0[2]: (13097) {G0,W12,D2,L3,V4,M3}  { Y = X, ! alpha6( Z, T, X ), ! 
% 1.41/1.78    alpha12( Z, T, X, Y ) }.
% 1.41/1.78  parent1[0]: (10854) {G5,W5,D2,L1,V0,M1} R(2437,137) { alpha12( skol13, 
% 1.41/1.78    skol17, skol19, skol21 ) }.
% 1.41/1.78  substitution0:
% 1.41/1.78     X := skol19
% 1.41/1.78     Y := skol21
% 1.41/1.78     Z := skol13
% 1.41/1.78     T := skol17
% 1.41/1.78  end
% 1.41/1.78  substitution1:
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  resolution: (13099) {G2,W3,D2,L1,V0,M1}  { skol21 = skol19 }.
% 1.41/1.78  parent0[1]: (13098) {G1,W7,D2,L2,V0,M2}  { skol21 = skol19, ! alpha6( 
% 1.41/1.78    skol13, skol17, skol19 ) }.
% 1.41/1.78  parent1[0]: (2253) {G1,W4,D2,L1,V0,M1} R(76,109) { alpha6( skol13, skol17, 
% 1.41/1.78    skol19 ) }.
% 1.41/1.78  substitution0:
% 1.41/1.78  end
% 1.41/1.78  substitution1:
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  subsumption: (10889) {G6,W3,D2,L1,V0,M1} R(10854,78);r(2253) { skol21 ==> 
% 1.41/1.78    skol19 }.
% 1.41/1.78  parent0: (13099) {G2,W3,D2,L1,V0,M1}  { skol21 = skol19 }.
% 1.41/1.78  substitution0:
% 1.41/1.78  end
% 1.41/1.78  permutation0:
% 1.41/1.78     0 ==> 0
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  paramod: (13102) {G4,W4,D2,L1,V0,M1}  { apply( skol13, skol19, skol20 ) }.
% 1.41/1.78  parent0[0]: (10889) {G6,W3,D2,L1,V0,M1} R(10854,78);r(2253) { skol21 ==> 
% 1.41/1.78    skol19 }.
% 1.41/1.78  parent1[0; 2]: (1689) {G3,W4,D2,L1,V0,M1} R(1620,132) { apply( skol13, 
% 1.41/1.78    skol21, skol20 ) }.
% 1.41/1.78  substitution0:
% 1.41/1.78  end
% 1.41/1.78  substitution1:
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  subsumption: (10925) {G7,W4,D2,L1,V0,M1} P(10889,1689) { apply( skol13, 
% 1.41/1.78    skol19, skol20 ) }.
% 1.41/1.78  parent0: (13102) {G4,W4,D2,L1,V0,M1}  { apply( skol13, skol19, skol20 ) }.
% 1.41/1.78  substitution0:
% 1.41/1.78  end
% 1.41/1.78  permutation0:
% 1.41/1.78     0 ==> 0
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  resolution: (13103) {G1,W8,D2,L2,V1,M2}  { ! member( skol19, X ), alpha12( 
% 1.41/1.78    skol13, X, skol20, skol19 ) }.
% 1.41/1.78  parent0[1]: (83) {G0,W12,D2,L3,V4,M3} I { ! member( T, Y ), ! apply( X, T, 
% 1.41/1.78    Z ), alpha12( X, Y, Z, T ) }.
% 1.41/1.78  parent1[0]: (10925) {G7,W4,D2,L1,V0,M1} P(10889,1689) { apply( skol13, 
% 1.41/1.78    skol19, skol20 ) }.
% 1.41/1.78  substitution0:
% 1.41/1.78     X := skol13
% 1.41/1.78     Y := X
% 1.41/1.78     Z := skol20
% 1.41/1.78     T := skol19
% 1.41/1.78  end
% 1.41/1.78  substitution1:
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  subsumption: (10996) {G8,W8,D2,L2,V1,M2} R(10925,83) { ! member( skol19, X
% 1.41/1.78     ), alpha12( skol13, X, skol20, skol19 ) }.
% 1.41/1.78  parent0: (13103) {G1,W8,D2,L2,V1,M2}  { ! member( skol19, X ), alpha12( 
% 1.41/1.78    skol13, X, skol20, skol19 ) }.
% 1.41/1.78  substitution0:
% 1.41/1.78     X := X
% 1.41/1.78  end
% 1.41/1.78  permutation0:
% 1.41/1.78     0 ==> 0
% 1.41/1.78     1 ==> 1
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  resolution: (13104) {G2,W5,D2,L1,V0,M1}  { alpha12( skol13, skol17, skol20
% 1.41/1.78    , skol19 ) }.
% 1.41/1.78  parent0[0]: (10996) {G8,W8,D2,L2,V1,M2} R(10925,83) { ! member( skol19, X )
% 1.41/1.78    , alpha12( skol13, X, skol20, skol19 ) }.
% 1.41/1.78  parent1[0]: (131) {G1,W3,D2,L1,V0,M1} R(75,109) { member( skol19, skol17 )
% 1.41/1.78     }.
% 1.41/1.78  substitution0:
% 1.41/1.78     X := skol17
% 1.41/1.78  end
% 1.41/1.78  substitution1:
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  subsumption: (12851) {G9,W5,D2,L1,V0,M1} R(10996,131) { alpha12( skol13, 
% 1.41/1.78    skol17, skol20, skol19 ) }.
% 1.41/1.78  parent0: (13104) {G2,W5,D2,L1,V0,M1}  { alpha12( skol13, skol17, skol20, 
% 1.41/1.78    skol19 ) }.
% 1.41/1.78  substitution0:
% 1.41/1.78  end
% 1.41/1.78  permutation0:
% 1.41/1.78     0 ==> 0
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  eqswap: (13105) {G0,W12,D2,L3,V4,M3}  { Y = X, ! alpha6( Z, T, X ), ! 
% 1.41/1.78    alpha12( Z, T, X, Y ) }.
% 1.41/1.78  parent0[2]: (78) {G0,W12,D2,L3,V4,M3} I { ! alpha6( X, Y, Z ), ! alpha12( X
% 1.41/1.78    , Y, Z, T ), Z = T }.
% 1.41/1.78  substitution0:
% 1.41/1.78     X := Z
% 1.41/1.78     Y := T
% 1.41/1.78     Z := X
% 1.41/1.78     T := Y
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  resolution: (13106) {G1,W7,D2,L2,V0,M2}  { skol19 = skol20, ! alpha6( 
% 1.41/1.78    skol13, skol17, skol20 ) }.
% 1.41/1.78  parent0[2]: (13105) {G0,W12,D2,L3,V4,M3}  { Y = X, ! alpha6( Z, T, X ), ! 
% 1.41/1.78    alpha12( Z, T, X, Y ) }.
% 1.41/1.78  parent1[0]: (12851) {G9,W5,D2,L1,V0,M1} R(10996,131) { alpha12( skol13, 
% 1.41/1.78    skol17, skol20, skol19 ) }.
% 1.41/1.78  substitution0:
% 1.41/1.78     X := skol20
% 1.41/1.78     Y := skol19
% 1.41/1.78     Z := skol13
% 1.41/1.78     T := skol17
% 1.41/1.78  end
% 1.41/1.78  substitution1:
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  resolution: (13107) {G2,W3,D2,L1,V0,M1}  { skol19 = skol20 }.
% 1.41/1.78  parent0[1]: (13106) {G1,W7,D2,L2,V0,M2}  { skol19 = skol20, ! alpha6( 
% 1.41/1.78    skol13, skol17, skol20 ) }.
% 1.41/1.78  parent1[0]: (2254) {G1,W4,D2,L1,V0,M1} R(76,110) { alpha6( skol13, skol17, 
% 1.41/1.78    skol20 ) }.
% 1.41/1.78  substitution0:
% 1.41/1.78  end
% 1.41/1.78  substitution1:
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  eqswap: (13108) {G2,W3,D2,L1,V0,M1}  { skol20 = skol19 }.
% 1.41/1.78  parent0[0]: (13107) {G2,W3,D2,L1,V0,M1}  { skol19 = skol20 }.
% 1.41/1.78  substitution0:
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  subsumption: (12853) {G10,W3,D2,L1,V0,M1} R(12851,78);r(2254) { skol20 ==> 
% 1.41/1.78    skol19 }.
% 1.41/1.78  parent0: (13108) {G2,W3,D2,L1,V0,M1}  { skol20 = skol19 }.
% 1.41/1.78  substitution0:
% 1.41/1.78  end
% 1.41/1.78  permutation0:
% 1.41/1.78     0 ==> 0
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  resolution: (13111) {G1,W0,D0,L0,V0,M0}  {  }.
% 1.41/1.78  parent0[0]: (111) {G0,W3,D2,L1,V0,M1} I { ! skol20 ==> skol19 }.
% 1.41/1.78  parent1[0]: (12853) {G10,W3,D2,L1,V0,M1} R(12851,78);r(2254) { skol20 ==> 
% 1.41/1.78    skol19 }.
% 1.41/1.78  substitution0:
% 1.41/1.78  end
% 1.41/1.78  substitution1:
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  subsumption: (12854) {G11,W0,D0,L0,V0,M0} S(12853);r(111) {  }.
% 1.41/1.78  parent0: (13111) {G1,W0,D0,L0,V0,M0}  {  }.
% 1.41/1.78  substitution0:
% 1.41/1.78  end
% 1.41/1.78  permutation0:
% 1.41/1.78  end
% 1.41/1.78  
% 1.41/1.78  Proof check complete!
% 1.41/1.78  
% 1.41/1.78  Memory use:
% 1.41/1.78  
% 1.41/1.78  space for terms:        171220
% 1.41/1.78  space for clauses:      537977
% 1.41/1.78  
% 1.41/1.78  
% 1.41/1.78  clauses generated:      66221
% 1.41/1.78  clauses kept:           12855
% 1.41/1.78  clauses selected:       1352
% 1.41/1.78  clauses deleted:        443
% 1.41/1.78  clauses inuse deleted:  400
% 1.41/1.78  
% 1.41/1.78  subsentry:          201288
% 1.41/1.78  literals s-matched: 167235
% 1.41/1.78  literals matched:   112805
% 1.41/1.78  full subsumption:   3559
% 1.41/1.78  
% 1.41/1.78  checksum:           -1755166554
% 1.41/1.78  
% 1.41/1.78  
% 1.41/1.78  Bliksem ended
%------------------------------------------------------------------------------