TSTP Solution File: SWV371+1 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : SWV371+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n010.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 0s
% DateTime : Wed Jul 20 16:24:37 EDT 2022

% Result   : Theorem 1.63s 2.00s
% Output   : Refutation 1.63s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SWV371+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13  % Command  : bliksem %s
% 0.14/0.34  % Computer : n010.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % DateTime : Tue Jun 14 15:28:24 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.74/1.13  *** allocated 10000 integers for termspace/termends
% 0.74/1.13  *** allocated 10000 integers for clauses
% 0.74/1.13  *** allocated 10000 integers for justifications
% 0.74/1.13  Bliksem 1.12
% 0.74/1.13  
% 0.74/1.13  
% 0.74/1.13  Automatic Strategy Selection
% 0.74/1.13  
% 0.74/1.13  
% 0.74/1.13  Clauses:
% 0.74/1.13  
% 0.74/1.13  { ! less_than( X, Z ), ! less_than( Z, Y ), less_than( X, Y ) }.
% 0.74/1.13  { less_than( X, Y ), less_than( Y, X ) }.
% 0.74/1.13  { less_than( X, X ) }.
% 0.74/1.13  { ! strictly_less_than( X, Y ), less_than( X, Y ) }.
% 0.74/1.13  { ! strictly_less_than( X, Y ), ! less_than( Y, X ) }.
% 0.74/1.13  { ! less_than( X, Y ), less_than( Y, X ), strictly_less_than( X, Y ) }.
% 0.74/1.13  { less_than( bottom, X ) }.
% 0.74/1.13  { ! isnonempty_pq( create_pq ) }.
% 0.74/1.13  { isnonempty_pq( insert_pq( X, Y ) ) }.
% 0.74/1.13  { ! contains_pq( create_pq, X ) }.
% 0.74/1.13  { ! contains_pq( insert_pq( X, Y ), Z ), contains_pq( X, Z ), Y = Z }.
% 0.74/1.13  { ! contains_pq( X, Z ), contains_pq( insert_pq( X, Y ), Z ) }.
% 0.74/1.13  { ! Y = Z, contains_pq( insert_pq( X, Y ), Z ) }.
% 0.74/1.13  { ! issmallestelement_pq( X, Y ), ! contains_pq( X, Z ), less_than( Y, Z )
% 0.74/1.13     }.
% 0.74/1.13  { ! less_than( Y, skol1( Z, Y ) ), issmallestelement_pq( X, Y ) }.
% 0.74/1.13  { contains_pq( X, skol1( X, Y ) ), issmallestelement_pq( X, Y ) }.
% 0.74/1.13  { remove_pq( insert_pq( X, Y ), Y ) = X }.
% 0.74/1.13  { ! contains_pq( X, Z ), Y = Z, remove_pq( insert_pq( X, Y ), Z ) = 
% 0.74/1.13    insert_pq( remove_pq( X, Z ), Y ) }.
% 0.74/1.13  { ! contains_pq( X, Y ), ! issmallestelement_pq( X, Y ), findmin_pq_eff( X
% 0.74/1.13    , Y ) = X }.
% 0.74/1.13  { ! contains_pq( X, Y ), ! issmallestelement_pq( X, Y ), findmin_pq_res( X
% 0.74/1.13    , Y ) = Y }.
% 0.74/1.13  { ! contains_pq( X, Y ), ! issmallestelement_pq( X, Y ), removemin_pq_eff( 
% 0.74/1.13    X, Y ) = remove_pq( X, Y ) }.
% 0.74/1.13  { ! contains_pq( X, Y ), ! issmallestelement_pq( X, Y ), removemin_pq_res( 
% 0.74/1.13    X, Y ) = Y }.
% 0.74/1.13  { insert_pq( insert_pq( X, Y ), Z ) = insert_pq( insert_pq( X, Z ), Y ) }.
% 0.74/1.13  { ! isnonempty_slb( create_slb ) }.
% 0.74/1.13  { isnonempty_slb( insert_slb( X, pair( Y, Z ) ) ) }.
% 0.74/1.13  { ! contains_slb( create_slb, X ) }.
% 0.74/1.13  { ! contains_slb( insert_slb( X, pair( Y, T ) ), Z ), contains_slb( X, Z )
% 0.74/1.13    , Y = Z }.
% 0.74/1.13  { ! contains_slb( X, Z ), contains_slb( insert_slb( X, pair( Y, T ) ), Z )
% 0.74/1.13     }.
% 0.74/1.13  { ! Y = Z, contains_slb( insert_slb( X, pair( Y, T ) ), Z ) }.
% 0.74/1.13  { ! pair_in_list( create_slb, X, Y ) }.
% 0.74/1.13  { ! pair_in_list( insert_slb( X, pair( Y, T ) ), Z, U ), pair_in_list( X, Z
% 0.74/1.13    , U ), alpha1( Y, Z, T, U ) }.
% 0.74/1.13  { ! pair_in_list( X, Z, U ), pair_in_list( insert_slb( X, pair( Y, T ) ), Z
% 0.74/1.13    , U ) }.
% 0.74/1.13  { ! alpha1( Y, Z, T, U ), pair_in_list( insert_slb( X, pair( Y, T ) ), Z, U
% 0.74/1.13     ) }.
% 0.74/1.13  { ! alpha1( X, Y, Z, T ), X = Y }.
% 0.74/1.13  { ! alpha1( X, Y, Z, T ), Z = T }.
% 0.74/1.13  { ! X = Y, ! Z = T, alpha1( X, Y, Z, T ) }.
% 0.74/1.13  { remove_slb( insert_slb( X, pair( Y, Z ) ), Y ) = X }.
% 0.74/1.13  { Y = Z, ! contains_slb( X, Z ), remove_slb( insert_slb( X, pair( Y, T ) )
% 0.74/1.13    , Z ) = insert_slb( remove_slb( X, Z ), pair( Y, T ) ) }.
% 0.74/1.13  { lookup_slb( insert_slb( X, pair( Y, Z ) ), Y ) = Z }.
% 0.74/1.13  { Y = Z, ! contains_slb( X, Z ), lookup_slb( insert_slb( X, pair( Y, T ) )
% 0.74/1.13    , Z ) = lookup_slb( X, Z ) }.
% 0.74/1.13  { update_slb( create_slb, X ) = create_slb }.
% 0.74/1.13  { ! strictly_less_than( Y, X ), update_slb( insert_slb( Z, pair( T, Y ) ), 
% 0.74/1.13    X ) = insert_slb( update_slb( Z, X ), pair( T, X ) ) }.
% 0.74/1.13  { ! less_than( X, Y ), update_slb( insert_slb( Z, pair( T, Y ) ), X ) = 
% 0.74/1.13    insert_slb( update_slb( Z, X ), pair( T, Y ) ) }.
% 0.74/1.13  { succ_cpq( X, X ) }.
% 0.74/1.13  { ! succ_cpq( X, Y ), succ_cpq( X, insert_cpq( Y, Z ) ) }.
% 0.74/1.13  { ! succ_cpq( X, Y ), succ_cpq( X, remove_cpq( Y, Z ) ) }.
% 0.74/1.13  { ! succ_cpq( X, Y ), succ_cpq( X, findmin_cpq_eff( Y ) ) }.
% 0.74/1.13  { ! succ_cpq( X, Y ), succ_cpq( X, removemin_cpq_eff( Y ) ) }.
% 0.74/1.13  { check_cpq( triple( X, create_slb, Y ) ) }.
% 0.74/1.13  { ! less_than( Y, X ), ! check_cpq( triple( Z, insert_slb( T, pair( X, Y )
% 0.74/1.13     ), U ) ), check_cpq( triple( Z, T, U ) ) }.
% 0.74/1.13  { ! less_than( Y, X ), ! check_cpq( triple( Z, T, U ) ), check_cpq( triple
% 0.74/1.13    ( Z, insert_slb( T, pair( X, Y ) ), U ) ) }.
% 0.74/1.13  { ! strictly_less_than( X, Y ), ! check_cpq( triple( Z, insert_slb( T, pair
% 0.74/1.13    ( X, Y ) ), U ) ) }.
% 0.74/1.13  { ! strictly_less_than( X, Y ), ! ||, check_cpq( triple( Z, insert_slb( T, 
% 0.74/1.13    pair( X, Y ) ), U ) ) }.
% 0.74/1.13  { ! contains_cpq( triple( X, Y, Z ), T ), contains_slb( Y, T ) }.
% 0.74/1.13  { ! contains_slb( Y, T ), contains_cpq( triple( X, Y, Z ), T ) }.
% 0.74/1.13  { ! ok( triple( X, Y, bad ) ) }.
% 0.74/1.13  { ! ||, ok( triple( X, Y, bad ) ) }.
% 0.74/1.13  { ok( triple( Y, Z, X ) ), X = bad }.
% 0.74/1.17  { insert_cpq( triple( X, Y, Z ), T ) = triple( insert_pqp( X, T ), 
% 0.74/1.17    insert_slb( Y, pair( T, bottom ) ), Z ) }.
% 0.74/1.17  { contains_slb( X, Y ), remove_cpq( triple( Z, X, T ), Y ) = triple( Z, X, 
% 0.74/1.17    bad ) }.
% 0.74/1.17  { ! contains_slb( X, Y ), ! less_than( lookup_slb( X, Y ), Y ), remove_cpq
% 0.74/1.17    ( triple( Z, X, T ), Y ) = triple( remove_pqp( Z, Y ), remove_slb( X, Y )
% 0.74/1.17    , T ) }.
% 0.74/1.17  { ! contains_slb( X, Y ), ! strictly_less_than( Y, lookup_slb( X, Y ) ), 
% 0.74/1.17    remove_cpq( triple( Z, X, T ), Y ) = triple( remove_pqp( Z, Y ), 
% 0.74/1.17    remove_slb( X, Y ), bad ) }.
% 0.74/1.17  { findmin_cpq_eff( triple( X, create_slb, Y ) ) = triple( X, create_slb, 
% 0.74/1.17    bad ) }.
% 0.74/1.17  { Y = create_slb, contains_slb( Y, findmin_pqp_res( X ) ), findmin_cpq_eff
% 0.74/1.17    ( triple( X, Y, Z ) ) = triple( X, update_slb( Y, findmin_pqp_res( X ) )
% 0.74/1.17    , bad ) }.
% 0.74/1.17  { Y = create_slb, ! contains_slb( Y, findmin_pqp_res( X ) ), ! 
% 0.74/1.17    strictly_less_than( findmin_pqp_res( X ), lookup_slb( Y, findmin_pqp_res
% 0.74/1.17    ( X ) ) ), findmin_cpq_eff( triple( X, Y, Z ) ) = triple( X, update_slb( 
% 0.74/1.17    Y, findmin_pqp_res( X ) ), bad ) }.
% 0.74/1.17  { Y = create_slb, ! contains_slb( Y, findmin_pqp_res( X ) ), ! less_than( 
% 0.74/1.17    lookup_slb( Y, findmin_pqp_res( X ) ), findmin_pqp_res( X ) ), 
% 0.74/1.17    findmin_cpq_eff( triple( X, Y, Z ) ) = triple( X, update_slb( Y, 
% 0.74/1.17    findmin_pqp_res( X ) ), Z ) }.
% 0.74/1.17  { findmin_cpq_res( triple( X, create_slb, Y ) ) = bottom }.
% 0.74/1.17  { X = create_slb, findmin_cpq_res( triple( Y, X, Z ) ) = findmin_pqp_res( Y
% 0.74/1.17     ) }.
% 0.74/1.17  { removemin_cpq_eff( X ) = remove_cpq( findmin_cpq_eff( X ), 
% 0.74/1.17    findmin_cpq_res( X ) ) }.
% 0.74/1.17  { removemin_cpq_res( X ) = findmin_cpq_res( X ) }.
% 0.74/1.17  { i( triple( X, create_slb, Y ) ) = create_pq }.
% 0.74/1.17  { i( triple( X, insert_slb( Y, pair( T, U ) ), Z ) ) = insert_pq( i( triple
% 0.74/1.17    ( X, Y, Z ) ), T ) }.
% 0.74/1.17  { ! pi_sharp_remove( X, Y ), contains_pq( X, Y ) }.
% 0.74/1.17  { ! contains_pq( X, Y ), pi_sharp_remove( X, Y ) }.
% 0.74/1.17  { ! pi_remove( X, Y ), pi_sharp_remove( i( X ), Y ) }.
% 0.74/1.17  { ! pi_sharp_remove( i( X ), Y ), pi_remove( X, Y ) }.
% 0.74/1.17  { ! pi_sharp_find_min( X, Y ), contains_pq( X, Y ) }.
% 0.74/1.17  { ! pi_sharp_find_min( X, Y ), issmallestelement_pq( X, Y ) }.
% 0.74/1.17  { ! contains_pq( X, Y ), ! issmallestelement_pq( X, Y ), pi_sharp_find_min
% 0.74/1.17    ( X, Y ) }.
% 0.74/1.17  { ! pi_find_min( X ), pi_sharp_find_min( i( X ), skol2( X ) ) }.
% 0.74/1.17  { ! pi_sharp_find_min( i( X ), Y ), pi_find_min( X ) }.
% 0.74/1.17  { ! pi_sharp_removemin( X, Y ), contains_pq( X, Y ) }.
% 0.74/1.17  { ! pi_sharp_removemin( X, Y ), issmallestelement_pq( X, Y ) }.
% 0.74/1.17  { ! contains_pq( X, Y ), ! issmallestelement_pq( X, Y ), pi_sharp_removemin
% 0.74/1.17    ( X, Y ) }.
% 0.74/1.17  { ! pi_removemin( X ), pi_sharp_find_min( i( X ), skol3( X ) ) }.
% 0.74/1.17  { ! pi_sharp_find_min( i( X ), Y ), pi_removemin( X ) }.
% 0.74/1.17  { ! phi( X ), alpha2( skol4( Y ) ) }.
% 0.74/1.17  { ! phi( X ), succ_cpq( X, skol4( X ) ) }.
% 0.74/1.17  { ! succ_cpq( X, Y ), ! alpha2( Y ), phi( X ) }.
% 0.74/1.17  { ! alpha2( X ), ok( X ) }.
% 0.74/1.17  { ! alpha2( X ), check_cpq( X ) }.
% 0.74/1.17  { ! ok( X ), ! check_cpq( X ), alpha2( X ) }.
% 0.74/1.17  { ! phi( findmin_cpq_eff( triple( X, Y, Z ) ) ), contains_pq( i( triple( X
% 0.74/1.17    , Y, Z ) ), findmin_cpq_res( triple( X, Y, Z ) ) ) }.
% 0.74/1.17  { ! phi( findmin_cpq_eff( triple( X, Y, Z ) ) ), issmallestelement_pq( i( 
% 0.74/1.17    triple( X, Y, Z ) ), findmin_cpq_res( triple( X, Y, Z ) ) ) }.
% 0.74/1.17  { phi( findmin_cpq_eff( triple( skol5, skol6, skol7 ) ) ) }.
% 0.74/1.17  { ! pi_sharp_find_min( i( triple( skol5, skol6, skol7 ) ), findmin_cpq_res
% 0.74/1.17    ( triple( skol5, skol6, skol7 ) ) ) }.
% 0.74/1.17  
% 0.74/1.17  percentage equality = 0.226804, percentage horn = 0.843750
% 0.74/1.17  This is a problem with some equality
% 0.74/1.17  
% 0.74/1.17  
% 0.74/1.17  
% 0.74/1.17  Options Used:
% 0.74/1.17  
% 0.74/1.17  useres =            1
% 0.74/1.17  useparamod =        1
% 0.74/1.17  useeqrefl =         1
% 0.74/1.17  useeqfact =         1
% 0.74/1.17  usefactor =         1
% 0.74/1.17  usesimpsplitting =  0
% 0.74/1.17  usesimpdemod =      5
% 0.74/1.17  usesimpres =        3
% 0.74/1.17  
% 0.74/1.17  resimpinuse      =  1000
% 0.74/1.17  resimpclauses =     20000
% 0.74/1.17  substype =          eqrewr
% 0.74/1.17  backwardsubs =      1
% 0.74/1.17  selectoldest =      5
% 0.74/1.17  
% 0.74/1.17  litorderings [0] =  split
% 0.74/1.17  litorderings [1] =  extend the termordering, first sorting on arguments
% 0.74/1.17  
% 0.74/1.17  termordering =      kbo
% 0.74/1.17  
% 0.74/1.17  litapriori =        0
% 0.74/1.17  termapriori =       1
% 0.74/1.17  litaposteriori =    0
% 0.74/1.17  termaposteriori =   0
% 0.74/1.17  demodaposteriori =  0
% 0.74/1.17  ordereqreflfact =   0
% 0.74/1.17  
% 0.74/1.17  litselect =         negord
% 0.74/1.17  
% 0.74/1.17  maxweight =         15
% 0.74/1.17  maxdepth =          30000
% 0.74/1.17  maxlength =         115
% 0.74/1.17  maxnrvars =         195
% 0.74/1.17  excuselevel =       1
% 0.74/1.17  increasemaxweight = 1
% 1.63/2.00  
% 1.63/2.00  maxselected =       10000000
% 1.63/2.00  maxnrclauses =      10000000
% 1.63/2.00  
% 1.63/2.00  showgenerated =    0
% 1.63/2.00  showkept =         0
% 1.63/2.00  showselected =     0
% 1.63/2.00  showdeleted =      0
% 1.63/2.00  showresimp =       1
% 1.63/2.00  showstatus =       2000
% 1.63/2.00  
% 1.63/2.00  prologoutput =     0
% 1.63/2.00  nrgoals =          5000000
% 1.63/2.00  totalproof =       1
% 1.63/2.00  
% 1.63/2.00  Symbols occurring in the translation:
% 1.63/2.00  
% 1.63/2.00  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 1.63/2.00  .  [1, 2]      (w:1, o:40, a:1, s:1, b:0), 
% 1.63/2.00  ||  [2, 0]      (w:1, o:3, a:1, s:1, b:0), 
% 1.63/2.00  !  [4, 1]      (w:0, o:18, a:1, s:1, b:0), 
% 1.63/2.00  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 1.63/2.00  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 1.63/2.00  less_than  [38, 2]      (w:1, o:64, a:1, s:1, b:0), 
% 1.63/2.00  strictly_less_than  [39, 2]      (w:1, o:71, a:1, s:1, b:0), 
% 1.63/2.00  bottom  [40, 0]      (w:1, o:9, a:1, s:1, b:0), 
% 1.63/2.00  create_pq  [41, 0]      (w:1, o:11, a:1, s:1, b:0), 
% 1.63/2.00  isnonempty_pq  [42, 1]      (w:1, o:23, a:1, s:1, b:0), 
% 1.63/2.00  insert_pq  [43, 2]      (w:1, o:72, a:1, s:1, b:0), 
% 1.63/2.00  contains_pq  [44, 2]      (w:1, o:73, a:1, s:1, b:0), 
% 1.63/2.00  issmallestelement_pq  [45, 2]      (w:1, o:74, a:1, s:1, b:0), 
% 1.63/2.00  remove_pq  [46, 2]      (w:1, o:65, a:1, s:1, b:0), 
% 1.63/2.00  findmin_pq_eff  [47, 2]      (w:1, o:75, a:1, s:1, b:0), 
% 1.63/2.00  findmin_pq_res  [48, 2]      (w:1, o:76, a:1, s:1, b:0), 
% 1.63/2.00  removemin_pq_eff  [49, 2]      (w:1, o:66, a:1, s:1, b:0), 
% 1.63/2.00  removemin_pq_res  [50, 2]      (w:1, o:67, a:1, s:1, b:0), 
% 1.63/2.00  create_slb  [51, 0]      (w:1, o:12, a:1, s:1, b:0), 
% 1.63/2.00  isnonempty_slb  [52, 1]      (w:1, o:24, a:1, s:1, b:0), 
% 1.63/2.00  pair  [53, 2]      (w:1, o:77, a:1, s:1, b:0), 
% 1.63/2.00  insert_slb  [54, 2]      (w:1, o:78, a:1, s:1, b:0), 
% 1.63/2.00  contains_slb  [55, 2]      (w:1, o:79, a:1, s:1, b:0), 
% 1.63/2.00  pair_in_list  [57, 3]      (w:1, o:91, a:1, s:1, b:0), 
% 1.63/2.00  remove_slb  [59, 2]      (w:1, o:68, a:1, s:1, b:0), 
% 1.63/2.00  lookup_slb  [60, 2]      (w:1, o:80, a:1, s:1, b:0), 
% 1.63/2.00  update_slb  [61, 2]      (w:1, o:81, a:1, s:1, b:0), 
% 1.63/2.00  succ_cpq  [62, 2]      (w:1, o:82, a:1, s:1, b:0), 
% 1.63/2.00  insert_cpq  [63, 2]      (w:1, o:83, a:1, s:1, b:0), 
% 1.63/2.00  remove_cpq  [64, 2]      (w:1, o:69, a:1, s:1, b:0), 
% 1.63/2.00  findmin_cpq_eff  [65, 1]      (w:1, o:25, a:1, s:1, b:0), 
% 1.63/2.00  removemin_cpq_eff  [66, 1]      (w:1, o:26, a:1, s:1, b:0), 
% 1.63/2.00  triple  [67, 3]      (w:1, o:92, a:1, s:1, b:0), 
% 1.63/2.00  check_cpq  [68, 1]      (w:1, o:27, a:1, s:1, b:0), 
% 1.63/2.00  contains_cpq  [69, 2]      (w:1, o:84, a:1, s:1, b:0), 
% 1.63/2.00  bad  [70, 0]      (w:1, o:10, a:1, s:1, b:0), 
% 1.63/2.00  ok  [71, 1]      (w:1, o:28, a:1, s:1, b:0), 
% 1.63/2.00  insert_pqp  [72, 2]      (w:1, o:85, a:1, s:1, b:0), 
% 1.63/2.00  remove_pqp  [73, 2]      (w:1, o:70, a:1, s:1, b:0), 
% 1.63/2.00  findmin_pqp_res  [74, 1]      (w:1, o:29, a:1, s:1, b:0), 
% 1.63/2.00  findmin_cpq_res  [75, 1]      (w:1, o:30, a:1, s:1, b:0), 
% 1.63/2.00  removemin_cpq_res  [76, 1]      (w:1, o:31, a:1, s:1, b:0), 
% 1.63/2.00  i  [77, 1]      (w:1, o:32, a:1, s:1, b:0), 
% 1.63/2.00  pi_sharp_remove  [78, 2]      (w:1, o:87, a:1, s:1, b:0), 
% 1.63/2.00  pi_remove  [79, 2]      (w:1, o:86, a:1, s:1, b:0), 
% 1.63/2.00  pi_sharp_find_min  [80, 2]      (w:1, o:88, a:1, s:1, b:0), 
% 1.63/2.00  pi_find_min  [81, 1]      (w:1, o:34, a:1, s:1, b:0), 
% 1.63/2.00  pi_sharp_removemin  [82, 2]      (w:1, o:89, a:1, s:1, b:0), 
% 1.63/2.00  pi_removemin  [83, 1]      (w:1, o:35, a:1, s:1, b:0), 
% 1.63/2.00  phi  [84, 1]      (w:1, o:33, a:1, s:1, b:0), 
% 1.63/2.00  alpha1  [85, 4]      (w:1, o:93, a:1, s:1, b:1), 
% 1.63/2.00  alpha2  [86, 1]      (w:1, o:36, a:1, s:1, b:1), 
% 1.63/2.00  skol1  [87, 2]      (w:1, o:90, a:1, s:1, b:1), 
% 1.63/2.00  skol2  [88, 1]      (w:1, o:37, a:1, s:1, b:1), 
% 1.63/2.00  skol3  [89, 1]      (w:1, o:38, a:1, s:1, b:1), 
% 1.63/2.00  skol4  [90, 1]      (w:1, o:39, a:1, s:1, b:1), 
% 1.63/2.00  skol5  [91, 0]      (w:1, o:15, a:1, s:1, b:1), 
% 1.63/2.00  skol6  [92, 0]      (w:1, o:16, a:1, s:1, b:1), 
% 1.63/2.00  skol7  [93, 0]      (w:1, o:17, a:1, s:1, b:1).
% 1.63/2.00  
% 1.63/2.00  
% 1.63/2.00  Starting Search:
% 1.63/2.00  
% 1.63/2.00  *** allocated 15000 integers for clauses
% 1.63/2.00  *** allocated 22500 integers for clauses
% 1.63/2.00  *** allocated 33750 integers for clauses
% 1.63/2.00  *** allocated 15000 integers for termspace/termends
% 1.63/2.00  *** allocated 50625 integers for clauses
% 1.63/2.00  *** allocated 22500 integers for termspace/termends
% 1.63/2.00  *** allocated 75937 integers for clauses
% 1.63/2.00  Resimplifying inuse:
% 1.63/2.00  Done
% 1.63/2.00  
% 1.63/2.00  *** allocated 33750 integers for termspace/termends
% 1.63/2.00  *** allocated 113905 integers for clauses
% 1.63/2.00  *** allocated 50625 integers for termspace/termends
% 1.63/2.00  
% 1.63/2.00  Intermediate Status:
% 1.63/2.00  Generated:    3989
% 1.63/2.00  Kept:         2056
% 1.63/2.00  Inuse:        160
% 1.63/2.00  Deleted:      4
% 1.63/2.00  Deletedinuse: 3
% 1.63/2.00  
% 1.63/2.00  *** allocated 170857 integers for clauses
% 1.63/2.00  Resimplifying inuse:
% 1.63/2.00  Done
% 1.63/2.00  
% 1.63/2.00  *** allocated 75937 integers for termspace/termends
% 1.63/2.00  Resimplifying inuse:
% 1.63/2.00  Done
% 1.63/2.00  
% 1.63/2.00  *** allocated 256285 integers for clauses
% 1.63/2.00  *** allocated 113905 integers for termspace/termends
% 1.63/2.00  
% 1.63/2.00  Intermediate Status:
% 1.63/2.00  Generated:    8173
% 1.63/2.00  Kept:         4192
% 1.63/2.00  Inuse:        235
% 1.63/2.00  Deleted:      4
% 1.63/2.00  Deletedinuse: 3
% 1.63/2.00  
% 1.63/2.00  Resimplifying inuse:
% 1.63/2.00  Done
% 1.63/2.00  
% 1.63/2.00  *** allocated 384427 integers for clauses
% 1.63/2.00  Resimplifying inuse:
% 1.63/2.00  Done
% 1.63/2.00  
% 1.63/2.00  *** allocated 170857 integers for termspace/termends
% 1.63/2.00  
% 1.63/2.00  Intermediate Status:
% 1.63/2.00  Generated:    13220
% 1.63/2.00  Kept:         6194
% 1.63/2.00  Inuse:        291
% 1.63/2.00  Deleted:      6
% 1.63/2.00  Deletedinuse: 5
% 1.63/2.00  
% 1.63/2.00  Resimplifying inuse:
% 1.63/2.00  Done
% 1.63/2.00  
% 1.63/2.00  *** allocated 576640 integers for clauses
% 1.63/2.00  Resimplifying inuse:
% 1.63/2.00  Done
% 1.63/2.00  
% 1.63/2.00  
% 1.63/2.00  Intermediate Status:
% 1.63/2.00  Generated:    21439
% 1.63/2.00  Kept:         8610
% 1.63/2.00  Inuse:        345
% 1.63/2.00  Deleted:      6
% 1.63/2.00  Deletedinuse: 5
% 1.63/2.00  
% 1.63/2.00  Resimplifying inuse:
% 1.63/2.00  Done
% 1.63/2.00  
% 1.63/2.00  *** allocated 256285 integers for termspace/termends
% 1.63/2.00  Resimplifying inuse:
% 1.63/2.00  Done
% 1.63/2.00  
% 1.63/2.00  
% 1.63/2.00  Intermediate Status:
% 1.63/2.00  Generated:    34985
% 1.63/2.00  Kept:         10627
% 1.63/2.00  Inuse:        484
% 1.63/2.00  Deleted:      13
% 1.63/2.00  Deletedinuse: 5
% 1.63/2.00  
% 1.63/2.00  Resimplifying inuse:
% 1.63/2.00  Done
% 1.63/2.00  
% 1.63/2.00  Resimplifying inuse:
% 1.63/2.00  Done
% 1.63/2.00  
% 1.63/2.00  *** allocated 864960 integers for clauses
% 1.63/2.00  
% 1.63/2.00  Intermediate Status:
% 1.63/2.00  Generated:    46305
% 1.63/2.00  Kept:         12633
% 1.63/2.00  Inuse:        563
% 1.63/2.00  Deleted:      15
% 1.63/2.00  Deletedinuse: 5
% 1.63/2.00  
% 1.63/2.00  Resimplifying inuse:
% 1.63/2.00  Done
% 1.63/2.00  
% 1.63/2.00  
% 1.63/2.00  Intermediate Status:
% 1.63/2.00  Generated:    53313
% 1.63/2.00  Kept:         14683
% 1.63/2.00  Inuse:        580
% 1.63/2.00  Deleted:      15
% 1.63/2.00  Deletedinuse: 5
% 1.63/2.00  
% 1.63/2.00  Resimplifying inuse:
% 1.63/2.00  Done
% 1.63/2.00  
% 1.63/2.00  *** allocated 384427 integers for termspace/termends
% 1.63/2.00  Resimplifying inuse:
% 1.63/2.00  Done
% 1.63/2.00  
% 1.63/2.00  
% 1.63/2.00  Intermediate Status:
% 1.63/2.00  Generated:    65256
% 1.63/2.00  Kept:         18287
% 1.63/2.00  Inuse:        623
% 1.63/2.00  Deleted:      15
% 1.63/2.00  Deletedinuse: 5
% 1.63/2.00  
% 1.63/2.00  Resimplifying inuse:
% 1.63/2.00  Done
% 1.63/2.00  
% 1.63/2.00  *** allocated 1297440 integers for clauses
% 1.63/2.00  Resimplifying inuse:
% 1.63/2.00  Done
% 1.63/2.00  
% 1.63/2.00  Resimplifying clauses:
% 1.63/2.00  
% 1.63/2.00  Bliksems!, er is een bewijs:
% 1.63/2.00  % SZS status Theorem
% 1.63/2.00  % SZS output start Refutation
% 1.63/2.00  
% 1.63/2.00  (78) {G0,W9,D2,L3,V2,M3} I { ! contains_pq( X, Y ), ! issmallestelement_pq
% 1.63/2.00    ( X, Y ), pi_sharp_find_min( X, Y ) }.
% 1.63/2.00  (92) {G0,W17,D4,L2,V3,M2} I { ! phi( findmin_cpq_eff( triple( X, Y, Z ) ) )
% 1.63/2.00    , contains_pq( i( triple( X, Y, Z ) ), findmin_cpq_res( triple( X, Y, Z )
% 1.63/2.00     ) ) }.
% 1.63/2.00  (93) {G0,W17,D4,L2,V3,M2} I { ! phi( findmin_cpq_eff( triple( X, Y, Z ) ) )
% 1.63/2.00    , issmallestelement_pq( i( triple( X, Y, Z ) ), findmin_cpq_res( triple( 
% 1.63/2.00    X, Y, Z ) ) ) }.
% 1.63/2.00  (94) {G0,W6,D4,L1,V0,M1} I { phi( findmin_cpq_eff( triple( skol5, skol6, 
% 1.63/2.00    skol7 ) ) ) }.
% 1.63/2.00  (95) {G0,W11,D4,L1,V0,M1} I { ! pi_sharp_find_min( i( triple( skol5, skol6
% 1.63/2.00    , skol7 ) ), findmin_cpq_res( triple( skol5, skol6, skol7 ) ) ) }.
% 1.63/2.00  (5678) {G1,W11,D4,L1,V0,M1} R(92,94) { contains_pq( i( triple( skol5, skol6
% 1.63/2.00    , skol7 ) ), findmin_cpq_res( triple( skol5, skol6, skol7 ) ) ) }.
% 1.63/2.00  (5843) {G1,W11,D4,L1,V0,M1} R(93,94) { issmallestelement_pq( i( triple( 
% 1.63/2.00    skol5, skol6, skol7 ) ), findmin_cpq_res( triple( skol5, skol6, skol7 ) )
% 1.63/2.00     ) }.
% 1.63/2.00  (5994) {G2,W11,D4,L1,V0,M1} R(95,78);r(5678) { ! issmallestelement_pq( i( 
% 1.63/2.00    triple( skol5, skol6, skol7 ) ), findmin_cpq_res( triple( skol5, skol6, 
% 1.63/2.00    skol7 ) ) ) }.
% 1.63/2.00  (20006) {G3,W0,D0,L0,V0,M0} S(5994);r(5843) {  }.
% 1.63/2.00  
% 1.63/2.00  
% 1.63/2.00  % SZS output end Refutation
% 1.63/2.00  found a proof!
% 1.63/2.00  
% 1.63/2.00  
% 1.63/2.00  Unprocessed initial clauses:
% 1.63/2.00  
% 1.63/2.00  (20008) {G0,W9,D2,L3,V3,M3}  { ! less_than( X, Z ), ! less_than( Z, Y ), 
% 1.63/2.00    less_than( X, Y ) }.
% 1.63/2.00  (20009) {G0,W6,D2,L2,V2,M2}  { less_than( X, Y ), less_than( Y, X ) }.
% 1.63/2.00  (20010) {G0,W3,D2,L1,V1,M1}  { less_than( X, X ) }.
% 1.63/2.00  (20011) {G0,W6,D2,L2,V2,M2}  { ! strictly_less_than( X, Y ), less_than( X, 
% 1.63/2.00    Y ) }.
% 1.63/2.00  (20012) {G0,W6,D2,L2,V2,M2}  { ! strictly_less_than( X, Y ), ! less_than( Y
% 1.63/2.00    , X ) }.
% 1.63/2.00  (20013) {G0,W9,D2,L3,V2,M3}  { ! less_than( X, Y ), less_than( Y, X ), 
% 1.63/2.00    strictly_less_than( X, Y ) }.
% 1.63/2.00  (20014) {G0,W3,D2,L1,V1,M1}  { less_than( bottom, X ) }.
% 1.63/2.00  (20015) {G0,W2,D2,L1,V0,M1}  { ! isnonempty_pq( create_pq ) }.
% 1.63/2.00  (20016) {G0,W4,D3,L1,V2,M1}  { isnonempty_pq( insert_pq( X, Y ) ) }.
% 1.63/2.00  (20017) {G0,W3,D2,L1,V1,M1}  { ! contains_pq( create_pq, X ) }.
% 1.63/2.00  (20018) {G0,W11,D3,L3,V3,M3}  { ! contains_pq( insert_pq( X, Y ), Z ), 
% 1.63/2.00    contains_pq( X, Z ), Y = Z }.
% 1.63/2.00  (20019) {G0,W8,D3,L2,V3,M2}  { ! contains_pq( X, Z ), contains_pq( 
% 1.63/2.00    insert_pq( X, Y ), Z ) }.
% 1.63/2.00  (20020) {G0,W8,D3,L2,V3,M2}  { ! Y = Z, contains_pq( insert_pq( X, Y ), Z )
% 1.63/2.00     }.
% 1.63/2.00  (20021) {G0,W9,D2,L3,V3,M3}  { ! issmallestelement_pq( X, Y ), ! 
% 1.63/2.00    contains_pq( X, Z ), less_than( Y, Z ) }.
% 1.63/2.00  (20022) {G0,W8,D3,L2,V3,M2}  { ! less_than( Y, skol1( Z, Y ) ), 
% 1.63/2.00    issmallestelement_pq( X, Y ) }.
% 1.63/2.00  (20023) {G0,W8,D3,L2,V2,M2}  { contains_pq( X, skol1( X, Y ) ), 
% 1.63/2.00    issmallestelement_pq( X, Y ) }.
% 1.63/2.00  (20024) {G0,W7,D4,L1,V2,M1}  { remove_pq( insert_pq( X, Y ), Y ) = X }.
% 1.63/2.00  (20025) {G0,W17,D4,L3,V3,M3}  { ! contains_pq( X, Z ), Y = Z, remove_pq( 
% 1.63/2.00    insert_pq( X, Y ), Z ) = insert_pq( remove_pq( X, Z ), Y ) }.
% 1.63/2.00  (20026) {G0,W11,D3,L3,V2,M3}  { ! contains_pq( X, Y ), ! 
% 1.63/2.00    issmallestelement_pq( X, Y ), findmin_pq_eff( X, Y ) = X }.
% 1.63/2.00  (20027) {G0,W11,D3,L3,V2,M3}  { ! contains_pq( X, Y ), ! 
% 1.63/2.00    issmallestelement_pq( X, Y ), findmin_pq_res( X, Y ) = Y }.
% 1.63/2.00  (20028) {G0,W13,D3,L3,V2,M3}  { ! contains_pq( X, Y ), ! 
% 1.63/2.00    issmallestelement_pq( X, Y ), removemin_pq_eff( X, Y ) = remove_pq( X, Y
% 1.63/2.00     ) }.
% 1.63/2.00  (20029) {G0,W11,D3,L3,V2,M3}  { ! contains_pq( X, Y ), ! 
% 1.63/2.00    issmallestelement_pq( X, Y ), removemin_pq_res( X, Y ) = Y }.
% 1.63/2.00  (20030) {G0,W11,D4,L1,V3,M1}  { insert_pq( insert_pq( X, Y ), Z ) = 
% 1.63/2.00    insert_pq( insert_pq( X, Z ), Y ) }.
% 1.63/2.00  (20031) {G0,W2,D2,L1,V0,M1}  { ! isnonempty_slb( create_slb ) }.
% 1.63/2.00  (20032) {G0,W6,D4,L1,V3,M1}  { isnonempty_slb( insert_slb( X, pair( Y, Z )
% 1.63/2.00     ) ) }.
% 1.63/2.00  (20033) {G0,W3,D2,L1,V1,M1}  { ! contains_slb( create_slb, X ) }.
% 1.63/2.00  (20034) {G0,W13,D4,L3,V4,M3}  { ! contains_slb( insert_slb( X, pair( Y, T )
% 1.63/2.00     ), Z ), contains_slb( X, Z ), Y = Z }.
% 1.63/2.00  (20035) {G0,W10,D4,L2,V4,M2}  { ! contains_slb( X, Z ), contains_slb( 
% 1.63/2.00    insert_slb( X, pair( Y, T ) ), Z ) }.
% 1.63/2.00  (20036) {G0,W10,D4,L2,V4,M2}  { ! Y = Z, contains_slb( insert_slb( X, pair
% 1.63/2.00    ( Y, T ) ), Z ) }.
% 1.63/2.00  (20037) {G0,W4,D2,L1,V2,M1}  { ! pair_in_list( create_slb, X, Y ) }.
% 1.63/2.00  (20038) {G0,W17,D4,L3,V5,M3}  { ! pair_in_list( insert_slb( X, pair( Y, T )
% 1.63/2.00     ), Z, U ), pair_in_list( X, Z, U ), alpha1( Y, Z, T, U ) }.
% 1.63/2.00  (20039) {G0,W12,D4,L2,V5,M2}  { ! pair_in_list( X, Z, U ), pair_in_list( 
% 1.63/2.00    insert_slb( X, pair( Y, T ) ), Z, U ) }.
% 1.63/2.00  (20040) {G0,W13,D4,L2,V5,M2}  { ! alpha1( Y, Z, T, U ), pair_in_list( 
% 1.63/2.00    insert_slb( X, pair( Y, T ) ), Z, U ) }.
% 1.63/2.00  (20041) {G0,W8,D2,L2,V4,M2}  { ! alpha1( X, Y, Z, T ), X = Y }.
% 1.63/2.00  (20042) {G0,W8,D2,L2,V4,M2}  { ! alpha1( X, Y, Z, T ), Z = T }.
% 1.63/2.00  (20043) {G0,W11,D2,L3,V4,M3}  { ! X = Y, ! Z = T, alpha1( X, Y, Z, T ) }.
% 1.63/2.00  (20044) {G0,W9,D5,L1,V3,M1}  { remove_slb( insert_slb( X, pair( Y, Z ) ), Y
% 1.63/2.00     ) = X }.
% 1.63/2.00  (20045) {G0,W21,D5,L3,V4,M3}  { Y = Z, ! contains_slb( X, Z ), remove_slb( 
% 1.63/2.00    insert_slb( X, pair( Y, T ) ), Z ) = insert_slb( remove_slb( X, Z ), pair
% 1.63/2.00    ( Y, T ) ) }.
% 1.63/2.00  (20046) {G0,W9,D5,L1,V3,M1}  { lookup_slb( insert_slb( X, pair( Y, Z ) ), Y
% 1.63/2.00     ) = Z }.
% 1.63/2.00  (20047) {G0,W17,D5,L3,V4,M3}  { Y = Z, ! contains_slb( X, Z ), lookup_slb( 
% 1.63/2.00    insert_slb( X, pair( Y, T ) ), Z ) = lookup_slb( X, Z ) }.
% 1.63/2.00  (20048) {G0,W5,D3,L1,V1,M1}  { update_slb( create_slb, X ) = create_slb }.
% 1.63/2.00  (20049) {G0,W18,D5,L2,V4,M2}  { ! strictly_less_than( Y, X ), update_slb( 
% 1.63/2.00    insert_slb( Z, pair( T, Y ) ), X ) = insert_slb( update_slb( Z, X ), pair
% 1.63/2.00    ( T, X ) ) }.
% 1.63/2.00  (20050) {G0,W18,D5,L2,V4,M2}  { ! less_than( X, Y ), update_slb( insert_slb
% 1.63/2.00    ( Z, pair( T, Y ) ), X ) = insert_slb( update_slb( Z, X ), pair( T, Y ) )
% 1.63/2.00     }.
% 1.63/2.00  (20051) {G0,W3,D2,L1,V1,M1}  { succ_cpq( X, X ) }.
% 1.63/2.00  (20052) {G0,W8,D3,L2,V3,M2}  { ! succ_cpq( X, Y ), succ_cpq( X, insert_cpq
% 1.63/2.00    ( Y, Z ) ) }.
% 1.63/2.00  (20053) {G0,W8,D3,L2,V3,M2}  { ! succ_cpq( X, Y ), succ_cpq( X, remove_cpq
% 1.63/2.00    ( Y, Z ) ) }.
% 1.63/2.00  (20054) {G0,W7,D3,L2,V2,M2}  { ! succ_cpq( X, Y ), succ_cpq( X, 
% 1.63/2.00    findmin_cpq_eff( Y ) ) }.
% 1.63/2.00  (20055) {G0,W7,D3,L2,V2,M2}  { ! succ_cpq( X, Y ), succ_cpq( X, 
% 1.63/2.00    removemin_cpq_eff( Y ) ) }.
% 1.63/2.00  (20056) {G0,W5,D3,L1,V2,M1}  { check_cpq( triple( X, create_slb, Y ) ) }.
% 1.63/2.00  (20057) {G0,W17,D5,L3,V5,M3}  { ! less_than( Y, X ), ! check_cpq( triple( Z
% 1.63/2.00    , insert_slb( T, pair( X, Y ) ), U ) ), check_cpq( triple( Z, T, U ) )
% 1.63/2.00     }.
% 1.63/2.00  (20058) {G0,W17,D5,L3,V5,M3}  { ! less_than( Y, X ), ! check_cpq( triple( Z
% 1.63/2.00    , T, U ) ), check_cpq( triple( Z, insert_slb( T, pair( X, Y ) ), U ) )
% 1.63/2.00     }.
% 1.63/2.00  (20059) {G0,W12,D5,L2,V5,M2}  { ! strictly_less_than( X, Y ), ! check_cpq( 
% 1.63/2.00    triple( Z, insert_slb( T, pair( X, Y ) ), U ) ) }.
% 1.63/2.00  (20060) {G0,W13,D5,L3,V5,M3}  { ! strictly_less_than( X, Y ), ! ||, 
% 1.63/2.00    check_cpq( triple( Z, insert_slb( T, pair( X, Y ) ), U ) ) }.
% 1.63/2.00  (20061) {G0,W9,D3,L2,V4,M2}  { ! contains_cpq( triple( X, Y, Z ), T ), 
% 1.63/2.00    contains_slb( Y, T ) }.
% 1.63/2.00  (20062) {G0,W9,D3,L2,V4,M2}  { ! contains_slb( Y, T ), contains_cpq( triple
% 1.63/2.00    ( X, Y, Z ), T ) }.
% 1.63/2.00  (20063) {G0,W5,D3,L1,V2,M1}  { ! ok( triple( X, Y, bad ) ) }.
% 1.63/2.00  (20064) {G0,W6,D3,L2,V2,M2}  { ! ||, ok( triple( X, Y, bad ) ) }.
% 1.63/2.00  (20065) {G0,W8,D3,L2,V3,M2}  { ok( triple( Y, Z, X ) ), X = bad }.
% 1.63/2.00  (20066) {G0,W17,D5,L1,V4,M1}  { insert_cpq( triple( X, Y, Z ), T ) = triple
% 1.63/2.00    ( insert_pqp( X, T ), insert_slb( Y, pair( T, bottom ) ), Z ) }.
% 1.63/2.00  (20067) {G0,W14,D4,L2,V4,M2}  { contains_slb( X, Y ), remove_cpq( triple( Z
% 1.63/2.00    , X, T ), Y ) = triple( Z, X, bad ) }.
% 1.63/2.00  (20068) {G0,W23,D4,L3,V4,M3}  { ! contains_slb( X, Y ), ! less_than( 
% 1.63/2.00    lookup_slb( X, Y ), Y ), remove_cpq( triple( Z, X, T ), Y ) = triple( 
% 1.63/2.00    remove_pqp( Z, Y ), remove_slb( X, Y ), T ) }.
% 1.63/2.00  (20069) {G0,W23,D4,L3,V4,M3}  { ! contains_slb( X, Y ), ! 
% 1.63/2.00    strictly_less_than( Y, lookup_slb( X, Y ) ), remove_cpq( triple( Z, X, T
% 1.63/2.00     ), Y ) = triple( remove_pqp( Z, Y ), remove_slb( X, Y ), bad ) }.
% 1.63/2.00  (20070) {G0,W10,D4,L1,V2,M1}  { findmin_cpq_eff( triple( X, create_slb, Y )
% 1.63/2.00     ) = triple( X, create_slb, bad ) }.
% 1.63/2.00  (20071) {G0,W20,D5,L3,V3,M3}  { Y = create_slb, contains_slb( Y, 
% 1.63/2.00    findmin_pqp_res( X ) ), findmin_cpq_eff( triple( X, Y, Z ) ) = triple( X
% 1.63/2.00    , update_slb( Y, findmin_pqp_res( X ) ), bad ) }.
% 1.63/2.00  (20072) {G0,W27,D5,L4,V3,M4}  { Y = create_slb, ! contains_slb( Y, 
% 1.63/2.00    findmin_pqp_res( X ) ), ! strictly_less_than( findmin_pqp_res( X ), 
% 1.63/2.00    lookup_slb( Y, findmin_pqp_res( X ) ) ), findmin_cpq_eff( triple( X, Y, Z
% 1.63/2.00     ) ) = triple( X, update_slb( Y, findmin_pqp_res( X ) ), bad ) }.
% 1.63/2.00  (20073) {G0,W27,D5,L4,V3,M4}  { Y = create_slb, ! contains_slb( Y, 
% 1.63/2.00    findmin_pqp_res( X ) ), ! less_than( lookup_slb( Y, findmin_pqp_res( X )
% 1.63/2.00     ), findmin_pqp_res( X ) ), findmin_cpq_eff( triple( X, Y, Z ) ) = triple
% 1.63/2.00    ( X, update_slb( Y, findmin_pqp_res( X ) ), Z ) }.
% 1.63/2.00  (20074) {G0,W7,D4,L1,V2,M1}  { findmin_cpq_res( triple( X, create_slb, Y )
% 1.63/2.00     ) = bottom }.
% 1.63/2.00  (20075) {G0,W11,D4,L2,V3,M2}  { X = create_slb, findmin_cpq_res( triple( Y
% 1.63/2.00    , X, Z ) ) = findmin_pqp_res( Y ) }.
% 1.63/2.00  (20076) {G0,W8,D4,L1,V1,M1}  { removemin_cpq_eff( X ) = remove_cpq( 
% 1.63/2.00    findmin_cpq_eff( X ), findmin_cpq_res( X ) ) }.
% 1.63/2.00  (20077) {G0,W5,D3,L1,V1,M1}  { removemin_cpq_res( X ) = findmin_cpq_res( X
% 1.63/2.00     ) }.
% 1.63/2.00  (20078) {G0,W7,D4,L1,V2,M1}  { i( triple( X, create_slb, Y ) ) = create_pq
% 1.63/2.00     }.
% 1.63/2.00  (20079) {G0,W17,D6,L1,V5,M1}  { i( triple( X, insert_slb( Y, pair( T, U ) )
% 1.63/2.00    , Z ) ) = insert_pq( i( triple( X, Y, Z ) ), T ) }.
% 1.63/2.00  (20080) {G0,W6,D2,L2,V2,M2}  { ! pi_sharp_remove( X, Y ), contains_pq( X, Y
% 1.63/2.00     ) }.
% 1.63/2.00  (20081) {G0,W6,D2,L2,V2,M2}  { ! contains_pq( X, Y ), pi_sharp_remove( X, Y
% 1.63/2.00     ) }.
% 1.63/2.00  (20082) {G0,W7,D3,L2,V2,M2}  { ! pi_remove( X, Y ), pi_sharp_remove( i( X )
% 1.63/2.00    , Y ) }.
% 1.63/2.00  (20083) {G0,W7,D3,L2,V2,M2}  { ! pi_sharp_remove( i( X ), Y ), pi_remove( X
% 1.63/2.00    , Y ) }.
% 1.63/2.00  (20084) {G0,W6,D2,L2,V2,M2}  { ! pi_sharp_find_min( X, Y ), contains_pq( X
% 1.63/2.00    , Y ) }.
% 1.63/2.00  (20085) {G0,W6,D2,L2,V2,M2}  { ! pi_sharp_find_min( X, Y ), 
% 1.63/2.00    issmallestelement_pq( X, Y ) }.
% 1.63/2.00  (20086) {G0,W9,D2,L3,V2,M3}  { ! contains_pq( X, Y ), ! 
% 1.63/2.00    issmallestelement_pq( X, Y ), pi_sharp_find_min( X, Y ) }.
% 1.63/2.00  (20087) {G0,W7,D3,L2,V1,M2}  { ! pi_find_min( X ), pi_sharp_find_min( i( X
% 1.63/2.00     ), skol2( X ) ) }.
% 1.63/2.00  (20088) {G0,W6,D3,L2,V2,M2}  { ! pi_sharp_find_min( i( X ), Y ), 
% 1.63/2.00    pi_find_min( X ) }.
% 1.63/2.00  (20089) {G0,W6,D2,L2,V2,M2}  { ! pi_sharp_removemin( X, Y ), contains_pq( X
% 1.63/2.00    , Y ) }.
% 1.63/2.00  (20090) {G0,W6,D2,L2,V2,M2}  { ! pi_sharp_removemin( X, Y ), 
% 1.63/2.00    issmallestelement_pq( X, Y ) }.
% 1.63/2.00  (20091) {G0,W9,D2,L3,V2,M3}  { ! contains_pq( X, Y ), ! 
% 1.63/2.00    issmallestelement_pq( X, Y ), pi_sharp_removemin( X, Y ) }.
% 1.63/2.00  (20092) {G0,W7,D3,L2,V1,M2}  { ! pi_removemin( X ), pi_sharp_find_min( i( X
% 1.63/2.00     ), skol3( X ) ) }.
% 1.63/2.00  (20093) {G0,W6,D3,L2,V2,M2}  { ! pi_sharp_find_min( i( X ), Y ), 
% 1.63/2.00    pi_removemin( X ) }.
% 1.63/2.00  (20094) {G0,W5,D3,L2,V2,M2}  { ! phi( X ), alpha2( skol4( Y ) ) }.
% 1.63/2.00  (20095) {G0,W6,D3,L2,V1,M2}  { ! phi( X ), succ_cpq( X, skol4( X ) ) }.
% 1.63/2.00  (20096) {G0,W7,D2,L3,V2,M3}  { ! succ_cpq( X, Y ), ! alpha2( Y ), phi( X )
% 1.63/2.00     }.
% 1.63/2.00  (20097) {G0,W4,D2,L2,V1,M2}  { ! alpha2( X ), ok( X ) }.
% 1.63/2.00  (20098) {G0,W4,D2,L2,V1,M2}  { ! alpha2( X ), check_cpq( X ) }.
% 1.63/2.00  (20099) {G0,W6,D2,L3,V1,M3}  { ! ok( X ), ! check_cpq( X ), alpha2( X ) }.
% 1.63/2.00  (20100) {G0,W17,D4,L2,V3,M2}  { ! phi( findmin_cpq_eff( triple( X, Y, Z ) )
% 1.63/2.00     ), contains_pq( i( triple( X, Y, Z ) ), findmin_cpq_res( triple( X, Y, Z
% 1.63/2.00     ) ) ) }.
% 1.63/2.00  (20101) {G0,W17,D4,L2,V3,M2}  { ! phi( findmin_cpq_eff( triple( X, Y, Z ) )
% 1.63/2.00     ), issmallestelement_pq( i( triple( X, Y, Z ) ), findmin_cpq_res( triple
% 1.63/2.00    ( X, Y, Z ) ) ) }.
% 1.63/2.00  (20102) {G0,W6,D4,L1,V0,M1}  { phi( findmin_cpq_eff( triple( skol5, skol6, 
% 1.63/2.00    skol7 ) ) ) }.
% 1.63/2.00  (20103) {G0,W11,D4,L1,V0,M1}  { ! pi_sharp_find_min( i( triple( skol5, 
% 1.63/2.00    skol6, skol7 ) ), findmin_cpq_res( triple( skol5, skol6, skol7 ) ) ) }.
% 1.63/2.00  
% 1.63/2.00  
% 1.63/2.00  Total Proof:
% 1.63/2.00  
% 1.63/2.00  subsumption: (78) {G0,W9,D2,L3,V2,M3} I { ! contains_pq( X, Y ), ! 
% 1.63/2.00    issmallestelement_pq( X, Y ), pi_sharp_find_min( X, Y ) }.
% 1.63/2.00  parent0: (20086) {G0,W9,D2,L3,V2,M3}  { ! contains_pq( X, Y ), ! 
% 1.63/2.00    issmallestelement_pq( X, Y ), pi_sharp_find_min( X, Y ) }.
% 1.63/2.00  substitution0:
% 1.63/2.00     X := X
% 1.63/2.00     Y := Y
% 1.63/2.00  end
% 1.63/2.00  permutation0:
% 1.63/2.00     0 ==> 0
% 1.63/2.00     1 ==> 1
% 1.63/2.00     2 ==> 2
% 1.63/2.00  end
% 1.63/2.00  
% 1.63/2.00  subsumption: (92) {G0,W17,D4,L2,V3,M2} I { ! phi( findmin_cpq_eff( triple( 
% 1.63/2.00    X, Y, Z ) ) ), contains_pq( i( triple( X, Y, Z ) ), findmin_cpq_res( 
% 1.63/2.00    triple( X, Y, Z ) ) ) }.
% 1.63/2.00  parent0: (20100) {G0,W17,D4,L2,V3,M2}  { ! phi( findmin_cpq_eff( triple( X
% 1.63/2.00    , Y, Z ) ) ), contains_pq( i( triple( X, Y, Z ) ), findmin_cpq_res( 
% 1.63/2.00    triple( X, Y, Z ) ) ) }.
% 1.63/2.00  substitution0:
% 1.63/2.00     X := X
% 1.63/2.00     Y := Y
% 1.63/2.00     Z := Z
% 1.63/2.00  end
% 1.63/2.00  permutation0:
% 1.63/2.00     0 ==> 0
% 1.63/2.00     1 ==> 1
% 1.63/2.00  end
% 1.63/2.00  
% 1.63/2.00  subsumption: (93) {G0,W17,D4,L2,V3,M2} I { ! phi( findmin_cpq_eff( triple( 
% 1.63/2.00    X, Y, Z ) ) ), issmallestelement_pq( i( triple( X, Y, Z ) ), 
% 1.63/2.00    findmin_cpq_res( triple( X, Y, Z ) ) ) }.
% 1.63/2.00  parent0: (20101) {G0,W17,D4,L2,V3,M2}  { ! phi( findmin_cpq_eff( triple( X
% 1.63/2.00    , Y, Z ) ) ), issmallestelement_pq( i( triple( X, Y, Z ) ), 
% 1.63/2.00    findmin_cpq_res( triple( X, Y, Z ) ) ) }.
% 1.63/2.00  substitution0:
% 1.63/2.00     X := X
% 1.63/2.00     Y := Y
% 1.63/2.00     Z := Z
% 1.63/2.00  end
% 1.63/2.00  permutation0:
% 1.63/2.00     0 ==> 0
% 1.63/2.00     1 ==> 1
% 1.63/2.00  end
% 1.63/2.00  
% 1.63/2.00  subsumption: (94) {G0,W6,D4,L1,V0,M1} I { phi( findmin_cpq_eff( triple( 
% 1.63/2.00    skol5, skol6, skol7 ) ) ) }.
% 1.63/2.00  parent0: (20102) {G0,W6,D4,L1,V0,M1}  { phi( findmin_cpq_eff( triple( skol5
% 1.63/2.00    , skol6, skol7 ) ) ) }.
% 1.63/2.00  substitution0:
% 1.63/2.00  end
% 1.63/2.00  permutation0:
% 1.63/2.00     0 ==> 0
% 1.63/2.00  end
% 1.63/2.00  
% 1.63/2.00  subsumption: (95) {G0,W11,D4,L1,V0,M1} I { ! pi_sharp_find_min( i( triple( 
% 1.63/2.00    skol5, skol6, skol7 ) ), findmin_cpq_res( triple( skol5, skol6, skol7 ) )
% 1.63/2.00     ) }.
% 1.63/2.00  parent0: (20103) {G0,W11,D4,L1,V0,M1}  { ! pi_sharp_find_min( i( triple( 
% 1.63/2.00    skol5, skol6, skol7 ) ), findmin_cpq_res( triple( skol5, skol6, skol7 ) )
% 1.63/2.00     ) }.
% 1.63/2.00  substitution0:
% 1.63/2.00  end
% 1.63/2.00  permutation0:
% 1.63/2.00     0 ==> 0
% 1.63/2.00  end
% 1.63/2.00  
% 1.63/2.00  resolution: (20389) {G1,W11,D4,L1,V0,M1}  { contains_pq( i( triple( skol5, 
% 1.63/2.00    skol6, skol7 ) ), findmin_cpq_res( triple( skol5, skol6, skol7 ) ) ) }.
% 1.63/2.00  parent0[0]: (92) {G0,W17,D4,L2,V3,M2} I { ! phi( findmin_cpq_eff( triple( X
% 1.63/2.00    , Y, Z ) ) ), contains_pq( i( triple( X, Y, Z ) ), findmin_cpq_res( 
% 1.63/2.00    triple( X, Y, Z ) ) ) }.
% 1.63/2.00  parent1[0]: (94) {G0,W6,D4,L1,V0,M1} I { phi( findmin_cpq_eff( triple( 
% 1.63/2.00    skol5, skol6, skol7 ) ) ) }.
% 1.63/2.00  substitution0:
% 1.63/2.00     X := skol5
% 1.63/2.00     Y := skol6
% 1.63/2.00     Z := skol7
% 1.63/2.00  end
% 1.63/2.00  substitution1:
% 1.63/2.00  end
% 1.63/2.00  
% 1.63/2.00  subsumption: (5678) {G1,W11,D4,L1,V0,M1} R(92,94) { contains_pq( i( triple
% 1.63/2.00    ( skol5, skol6, skol7 ) ), findmin_cpq_res( triple( skol5, skol6, skol7 )
% 1.63/2.00     ) ) }.
% 1.63/2.00  parent0: (20389) {G1,W11,D4,L1,V0,M1}  { contains_pq( i( triple( skol5, 
% 1.63/2.00    skol6, skol7 ) ), findmin_cpq_res( triple( skol5, skol6, skol7 ) ) ) }.
% 1.63/2.00  substitution0:
% 1.63/2.00  end
% 1.63/2.00  permutation0:
% 1.63/2.00     0 ==> 0
% 1.63/2.00  end
% 1.63/2.00  
% 1.63/2.00  resolution: (20390) {G1,W11,D4,L1,V0,M1}  { issmallestelement_pq( i( triple
% 1.63/2.00    ( skol5, skol6, skol7 ) ), findmin_cpq_res( triple( skol5, skol6, skol7 )
% 1.63/2.00     ) ) }.
% 1.63/2.00  parent0[0]: (93) {G0,W17,D4,L2,V3,M2} I { ! phi( findmin_cpq_eff( triple( X
% 1.63/2.00    , Y, Z ) ) ), issmallestelement_pq( i( triple( X, Y, Z ) ), 
% 1.63/2.00    findmin_cpq_res( triple( X, Y, Z ) ) ) }.
% 1.63/2.00  parent1[0]: (94) {G0,W6,D4,L1,V0,M1} I { phi( findmin_cpq_eff( triple( 
% 1.63/2.00    skol5, skol6, skol7 ) ) ) }.
% 1.63/2.00  substitution0:
% 1.63/2.00     X := skol5
% 1.63/2.00     Y := skol6
% 1.63/2.00     Z := skol7
% 1.63/2.00  end
% 1.63/2.00  substitution1:
% 1.63/2.00  end
% 1.63/2.00  
% 1.63/2.00  subsumption: (5843) {G1,W11,D4,L1,V0,M1} R(93,94) { issmallestelement_pq( i
% 1.63/2.00    ( triple( skol5, skol6, skol7 ) ), findmin_cpq_res( triple( skol5, skol6
% 1.63/2.00    , skol7 ) ) ) }.
% 1.63/2.00  parent0: (20390) {G1,W11,D4,L1,V0,M1}  { issmallestelement_pq( i( triple( 
% 1.63/2.00    skol5, skol6, skol7 ) ), findmin_cpq_res( triple( skol5, skol6, skol7 ) )
% 1.63/2.00     ) }.
% 1.63/2.00  substitution0:
% 1.63/2.00  end
% 1.63/2.00  permutation0:
% 1.63/2.00     0 ==> 0
% 1.63/2.00  end
% 1.63/2.00  
% 1.63/2.00  resolution: (20391) {G1,W22,D4,L2,V0,M2}  { ! contains_pq( i( triple( skol5
% 1.63/2.00    , skol6, skol7 ) ), findmin_cpq_res( triple( skol5, skol6, skol7 ) ) ), !
% 1.63/2.00     issmallestelement_pq( i( triple( skol5, skol6, skol7 ) ), 
% 1.63/2.00    findmin_cpq_res( triple( skol5, skol6, skol7 ) ) ) }.
% 1.63/2.00  parent0[0]: (95) {G0,W11,D4,L1,V0,M1} I { ! pi_sharp_find_min( i( triple( 
% 1.63/2.00    skol5, skol6, skol7 ) ), findmin_cpq_res( triple( skol5, skol6, skol7 ) )
% 1.63/2.00     ) }.
% 1.63/2.00  parent1[2]: (78) {G0,W9,D2,L3,V2,M3} I { ! contains_pq( X, Y ), ! 
% 1.63/2.00    issmallestelement_pq( X, Y ), pi_sharp_find_min( X, Y ) }.
% 1.63/2.00  substitution0:
% 1.63/2.00  end
% 1.63/2.00  substitution1:
% 1.63/2.00     X := i( triple( skol5, skol6, skol7 ) )
% 1.63/2.00     Y := findmin_cpq_res( triple( skol5, skol6, skol7 ) )
% 1.63/2.00  end
% 1.63/2.00  
% 1.63/2.00  resolution: (20392) {G2,W11,D4,L1,V0,M1}  { ! issmallestelement_pq( i( 
% 1.63/2.00    triple( skol5, skol6, skol7 ) ), findmin_cpq_res( triple( skol5, skol6, 
% 1.63/2.00    skol7 ) ) ) }.
% 1.63/2.00  parent0[0]: (20391) {G1,W22,D4,L2,V0,M2}  { ! contains_pq( i( triple( skol5
% 1.63/2.00    , skol6, skol7 ) ), findmin_cpq_res( triple( skol5, skol6, skol7 ) ) ), !
% 1.63/2.00     issmallestelement_pq( i( triple( skol5, skol6, skol7 ) ), 
% 1.63/2.00    findmin_cpq_res( triple( skol5, skol6, skol7 ) ) ) }.
% 1.63/2.00  parent1[0]: (5678) {G1,W11,D4,L1,V0,M1} R(92,94) { contains_pq( i( triple( 
% 1.63/2.00    skol5, skol6, skol7 ) ), findmin_cpq_res( triple( skol5, skol6, skol7 ) )
% 1.63/2.00     ) }.
% 1.63/2.00  substitution0:
% 1.63/2.00  end
% 1.63/2.00  substitution1:
% 1.63/2.00  end
% 1.63/2.00  
% 1.63/2.00  subsumption: (5994) {G2,W11,D4,L1,V0,M1} R(95,78);r(5678) { ! 
% 1.63/2.00    issmallestelement_pq( i( triple( skol5, skol6, skol7 ) ), findmin_cpq_res
% 1.63/2.00    ( triple( skol5, skol6, skol7 ) ) ) }.
% 1.63/2.00  parent0: (20392) {G2,W11,D4,L1,V0,M1}  { ! issmallestelement_pq( i( triple
% 1.63/2.00    ( skol5, skol6, skol7 ) ), findmin_cpq_res( triple( skol5, skol6, skol7 )
% 1.63/2.00     ) ) }.
% 1.63/2.00  substitution0:
% 1.63/2.00  end
% 1.63/2.00  permutation0:
% 1.63/2.00     0 ==> 0
% 1.63/2.00  end
% 1.63/2.00  
% 1.63/2.00  resolution: (20393) {G2,W0,D0,L0,V0,M0}  {  }.
% 1.63/2.00  parent0[0]: (5994) {G2,W11,D4,L1,V0,M1} R(95,78);r(5678) { ! 
% 1.63/2.00    issmallestelement_pq( i( triple( skol5, skol6, skol7 ) ), findmin_cpq_res
% 1.63/2.00    ( triple( skol5, skol6, skol7 ) ) ) }.
% 1.63/2.00  parent1[0]: (5843) {G1,W11,D4,L1,V0,M1} R(93,94) { issmallestelement_pq( i
% 1.63/2.00    ( triple( skol5, skol6, skol7 ) ), findmin_cpq_res( triple( skol5, skol6
% 1.63/2.00    , skol7 ) ) ) }.
% 1.63/2.00  substitution0:
% 1.63/2.00  end
% 1.63/2.00  substitution1:
% 1.63/2.00  end
% 1.63/2.00  
% 1.63/2.00  subsumption: (20006) {G3,W0,D0,L0,V0,M0} S(5994);r(5843) {  }.
% 1.63/2.00  parent0: (20393) {G2,W0,D0,L0,V0,M0}  {  }.
% 1.63/2.00  substitution0:
% 1.63/2.00  end
% 1.63/2.00  permutation0:
% 1.63/2.00  end
% 1.63/2.00  
% 1.63/2.00  Proof check complete!
% 1.63/2.00  
% 1.63/2.00  Memory use:
% 1.63/2.00  
% 1.63/2.00  space for terms:        325158
% 1.63/2.00  space for clauses:      885375
% 1.63/2.00  
% 1.63/2.00  
% 1.63/2.00  clauses generated:      68128
% 1.63/2.00  clauses kept:           20007
% 1.63/2.00  clauses selected:       625
% 1.63/2.00  clauses deleted:        85
% 1.63/2.00  clauses inuse deleted:  5
% 1.63/2.00  
% 1.63/2.00  subsentry:          173354
% 1.63/2.00  literals s-matched: 103983
% 1.63/2.00  literals matched:   96845
% 1.63/2.00  full subsumption:   19232
% 1.63/2.00  
% 1.63/2.00  checksum:           -515230415
% 1.63/2.00  
% 1.63/2.00  
% 1.63/2.00  Bliksem ended
%------------------------------------------------------------------------------