TSTP Solution File: SWV389+1 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : SWV389+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n007.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 16:24:42 EDT 2022

% Result   : Theorem 0.83s 1.19s
% Output   : Refutation 0.83s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWV389+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13  % Command  : bliksem %s
% 0.12/0.34  % Computer : n007.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % DateTime : Wed Jun 15 12:57:40 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.45/1.10  *** allocated 10000 integers for termspace/termends
% 0.45/1.10  *** allocated 10000 integers for clauses
% 0.45/1.10  *** allocated 10000 integers for justifications
% 0.45/1.10  Bliksem 1.12
% 0.45/1.10  
% 0.45/1.10  
% 0.45/1.10  Automatic Strategy Selection
% 0.45/1.10  
% 0.45/1.10  
% 0.45/1.10  Clauses:
% 0.45/1.10  
% 0.45/1.10  { ! less_than( X, Z ), ! less_than( Z, Y ), less_than( X, Y ) }.
% 0.45/1.10  { less_than( X, Y ), less_than( Y, X ) }.
% 0.45/1.10  { less_than( X, X ) }.
% 0.45/1.10  { ! strictly_less_than( X, Y ), less_than( X, Y ) }.
% 0.45/1.10  { ! strictly_less_than( X, Y ), ! less_than( Y, X ) }.
% 0.45/1.10  { ! less_than( X, Y ), less_than( Y, X ), strictly_less_than( X, Y ) }.
% 0.45/1.10  { less_than( bottom, X ) }.
% 0.45/1.10  { ! isnonempty_slb( create_slb ) }.
% 0.45/1.10  { isnonempty_slb( insert_slb( X, pair( Y, Z ) ) ) }.
% 0.45/1.10  { ! contains_slb( create_slb, X ) }.
% 0.45/1.10  { ! contains_slb( insert_slb( X, pair( Y, T ) ), Z ), contains_slb( X, Z )
% 0.45/1.10    , Y = Z }.
% 0.45/1.10  { ! contains_slb( X, Z ), contains_slb( insert_slb( X, pair( Y, T ) ), Z )
% 0.45/1.10     }.
% 0.45/1.10  { ! Y = Z, contains_slb( insert_slb( X, pair( Y, T ) ), Z ) }.
% 0.45/1.10  { ! pair_in_list( create_slb, X, Y ) }.
% 0.45/1.10  { ! pair_in_list( insert_slb( X, pair( Y, T ) ), Z, U ), pair_in_list( X, Z
% 0.45/1.10    , U ), alpha1( Y, Z, T, U ) }.
% 0.45/1.10  { ! pair_in_list( X, Z, U ), pair_in_list( insert_slb( X, pair( Y, T ) ), Z
% 0.45/1.10    , U ) }.
% 0.45/1.10  { ! alpha1( Y, Z, T, U ), pair_in_list( insert_slb( X, pair( Y, T ) ), Z, U
% 0.45/1.10     ) }.
% 0.45/1.10  { ! alpha1( X, Y, Z, T ), X = Y }.
% 0.45/1.10  { ! alpha1( X, Y, Z, T ), Z = T }.
% 0.45/1.10  { ! X = Y, ! Z = T, alpha1( X, Y, Z, T ) }.
% 0.45/1.10  { remove_slb( insert_slb( X, pair( Y, Z ) ), Y ) = X }.
% 0.45/1.10  { Y = Z, ! contains_slb( X, Z ), remove_slb( insert_slb( X, pair( Y, T ) )
% 0.45/1.10    , Z ) = insert_slb( remove_slb( X, Z ), pair( Y, T ) ) }.
% 0.45/1.10  { lookup_slb( insert_slb( X, pair( Y, Z ) ), Y ) = Z }.
% 0.45/1.10  { Y = Z, ! contains_slb( X, Z ), lookup_slb( insert_slb( X, pair( Y, T ) )
% 0.45/1.10    , Z ) = lookup_slb( X, Z ) }.
% 0.45/1.10  { update_slb( create_slb, X ) = create_slb }.
% 0.45/1.10  { ! strictly_less_than( Y, X ), update_slb( insert_slb( Z, pair( T, Y ) ), 
% 0.45/1.10    X ) = insert_slb( update_slb( Z, X ), pair( T, X ) ) }.
% 0.45/1.10  { ! less_than( X, Y ), update_slb( insert_slb( Z, pair( T, Y ) ), X ) = 
% 0.45/1.10    insert_slb( update_slb( Z, X ), pair( T, Y ) ) }.
% 0.45/1.10  { succ_cpq( X, X ) }.
% 0.45/1.10  { ! succ_cpq( X, Y ), succ_cpq( X, insert_cpq( Y, Z ) ) }.
% 0.45/1.10  { ! succ_cpq( X, Y ), succ_cpq( X, remove_cpq( Y, Z ) ) }.
% 0.45/1.10  { ! succ_cpq( X, Y ), succ_cpq( X, findmin_cpq_eff( Y ) ) }.
% 0.45/1.10  { ! succ_cpq( X, Y ), succ_cpq( X, removemin_cpq_eff( Y ) ) }.
% 0.45/1.10  { check_cpq( triple( X, create_slb, Y ) ) }.
% 0.45/1.10  { ! less_than( Y, X ), ! check_cpq( triple( Z, insert_slb( T, pair( X, Y )
% 0.45/1.10     ), U ) ), check_cpq( triple( Z, T, U ) ) }.
% 0.45/1.10  { ! less_than( Y, X ), ! check_cpq( triple( Z, T, U ) ), check_cpq( triple
% 0.45/1.10    ( Z, insert_slb( T, pair( X, Y ) ), U ) ) }.
% 0.45/1.10  { ! strictly_less_than( X, Y ), ! check_cpq( triple( Z, insert_slb( T, pair
% 0.45/1.10    ( X, Y ) ), U ) ) }.
% 0.45/1.10  { ! strictly_less_than( X, Y ), ! ||, check_cpq( triple( Z, insert_slb( T, 
% 0.45/1.10    pair( X, Y ) ), U ) ) }.
% 0.45/1.10  { ! contains_cpq( triple( X, Y, Z ), T ), contains_slb( Y, T ) }.
% 0.45/1.10  { ! contains_slb( Y, T ), contains_cpq( triple( X, Y, Z ), T ) }.
% 0.45/1.10  { ! ok( triple( X, Y, bad ) ) }.
% 0.45/1.10  { ! ||, ok( triple( X, Y, bad ) ) }.
% 0.45/1.10  { ok( triple( Y, Z, X ) ), X = bad }.
% 0.45/1.10  { insert_cpq( triple( X, Y, Z ), T ) = triple( insert_pqp( X, T ), 
% 0.45/1.10    insert_slb( Y, pair( T, bottom ) ), Z ) }.
% 0.45/1.10  { contains_slb( X, Y ), remove_cpq( triple( Z, X, T ), Y ) = triple( Z, X, 
% 0.45/1.10    bad ) }.
% 0.45/1.10  { ! contains_slb( X, Y ), ! less_than( lookup_slb( X, Y ), Y ), remove_cpq
% 0.45/1.10    ( triple( Z, X, T ), Y ) = triple( remove_pqp( Z, Y ), remove_slb( X, Y )
% 0.45/1.10    , T ) }.
% 0.45/1.10  { ! contains_slb( X, Y ), ! strictly_less_than( Y, lookup_slb( X, Y ) ), 
% 0.45/1.10    remove_cpq( triple( Z, X, T ), Y ) = triple( remove_pqp( Z, Y ), 
% 0.45/1.10    remove_slb( X, Y ), bad ) }.
% 0.45/1.10  { findmin_cpq_eff( triple( X, create_slb, Y ) ) = triple( X, create_slb, 
% 0.45/1.10    bad ) }.
% 0.45/1.10  { Y = create_slb, contains_slb( Y, findmin_pqp_res( X ) ), findmin_cpq_eff
% 0.45/1.10    ( triple( X, Y, Z ) ) = triple( X, update_slb( Y, findmin_pqp_res( X ) )
% 0.45/1.10    , bad ) }.
% 0.45/1.10  { Y = create_slb, ! contains_slb( Y, findmin_pqp_res( X ) ), ! 
% 0.45/1.10    strictly_less_than( findmin_pqp_res( X ), lookup_slb( Y, findmin_pqp_res
% 0.45/1.10    ( X ) ) ), findmin_cpq_eff( triple( X, Y, Z ) ) = triple( X, update_slb( 
% 0.45/1.10    Y, findmin_pqp_res( X ) ), bad ) }.
% 0.45/1.10  { Y = create_slb, ! contains_slb( Y, findmin_pqp_res( X ) ), ! less_than( 
% 0.45/1.10    lookup_slb( Y, findmin_pqp_res( X ) ), findmin_pqp_res( X ) ), 
% 0.83/1.19    findmin_cpq_eff( triple( X, Y, Z ) ) = triple( X, update_slb( Y, 
% 0.83/1.19    findmin_pqp_res( X ) ), Z ) }.
% 0.83/1.19  { findmin_cpq_res( triple( X, create_slb, Y ) ) = bottom }.
% 0.83/1.19  { X = create_slb, findmin_cpq_res( triple( Y, X, Z ) ) = findmin_pqp_res( Y
% 0.83/1.19     ) }.
% 0.83/1.19  { removemin_cpq_eff( X ) = remove_cpq( findmin_cpq_eff( X ), 
% 0.83/1.19    findmin_cpq_res( X ) ) }.
% 0.83/1.19  { removemin_cpq_res( X ) = findmin_cpq_res( X ) }.
% 0.83/1.19  { ! check_cpq( removemin_cpq_eff( triple( X, Y, Z ) ) ), ! ok( 
% 0.83/1.19    removemin_cpq_eff( triple( X, Y, Z ) ) ), check_cpq( triple( X, Y, Z ) )
% 0.83/1.19     }.
% 0.83/1.19  { ! check_cpq( triple( skol1, skol2, skol3 ) ) }.
% 0.83/1.19  { check_cpq( removemin_cpq_eff( triple( skol1, skol2, skol3 ) ) ) }.
% 0.83/1.19  { ok( removemin_cpq_eff( triple( skol1, skol2, skol3 ) ) ) }.
% 0.83/1.19  
% 0.83/1.19  percentage equality = 0.280702, percentage horn = 0.793103
% 0.83/1.19  This is a problem with some equality
% 0.83/1.19  
% 0.83/1.19  
% 0.83/1.19  
% 0.83/1.19  Options Used:
% 0.83/1.19  
% 0.83/1.19  useres =            1
% 0.83/1.19  useparamod =        1
% 0.83/1.19  useeqrefl =         1
% 0.83/1.19  useeqfact =         1
% 0.83/1.19  usefactor =         1
% 0.83/1.19  usesimpsplitting =  0
% 0.83/1.19  usesimpdemod =      5
% 0.83/1.19  usesimpres =        3
% 0.83/1.19  
% 0.83/1.19  resimpinuse      =  1000
% 0.83/1.19  resimpclauses =     20000
% 0.83/1.19  substype =          eqrewr
% 0.83/1.19  backwardsubs =      1
% 0.83/1.19  selectoldest =      5
% 0.83/1.19  
% 0.83/1.19  litorderings [0] =  split
% 0.83/1.19  litorderings [1] =  extend the termordering, first sorting on arguments
% 0.83/1.19  
% 0.83/1.19  termordering =      kbo
% 0.83/1.19  
% 0.83/1.19  litapriori =        0
% 0.83/1.19  termapriori =       1
% 0.83/1.19  litaposteriori =    0
% 0.83/1.19  termaposteriori =   0
% 0.83/1.19  demodaposteriori =  0
% 0.83/1.19  ordereqreflfact =   0
% 0.83/1.19  
% 0.83/1.19  litselect =         negord
% 0.83/1.19  
% 0.83/1.19  maxweight =         15
% 0.83/1.19  maxdepth =          30000
% 0.83/1.19  maxlength =         115
% 0.83/1.19  maxnrvars =         195
% 0.83/1.19  excuselevel =       1
% 0.83/1.19  increasemaxweight = 1
% 0.83/1.19  
% 0.83/1.19  maxselected =       10000000
% 0.83/1.19  maxnrclauses =      10000000
% 0.83/1.19  
% 0.83/1.19  showgenerated =    0
% 0.83/1.19  showkept =         0
% 0.83/1.19  showselected =     0
% 0.83/1.19  showdeleted =      0
% 0.83/1.19  showresimp =       1
% 0.83/1.19  showstatus =       2000
% 0.83/1.19  
% 0.83/1.19  prologoutput =     0
% 0.83/1.19  nrgoals =          5000000
% 0.83/1.19  totalproof =       1
% 0.83/1.19  
% 0.83/1.19  Symbols occurring in the translation:
% 0.83/1.19  
% 0.83/1.19  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 0.83/1.19  .  [1, 2]      (w:1, o:30, a:1, s:1, b:0), 
% 0.83/1.19  ||  [2, 0]      (w:1, o:3, a:1, s:1, b:0), 
% 0.83/1.19  !  [4, 1]      (w:0, o:17, a:1, s:1, b:0), 
% 0.83/1.19  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.83/1.19  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.83/1.19  less_than  [38, 2]      (w:1, o:54, a:1, s:1, b:0), 
% 0.83/1.19  strictly_less_than  [39, 2]      (w:1, o:58, a:1, s:1, b:0), 
% 0.83/1.19  bottom  [40, 0]      (w:1, o:9, a:1, s:1, b:0), 
% 0.83/1.19  create_slb  [41, 0]      (w:1, o:11, a:1, s:1, b:0), 
% 0.83/1.19  isnonempty_slb  [42, 1]      (w:1, o:22, a:1, s:1, b:0), 
% 0.83/1.19  pair  [43, 2]      (w:1, o:59, a:1, s:1, b:0), 
% 0.83/1.19  insert_slb  [44, 2]      (w:1, o:60, a:1, s:1, b:0), 
% 0.83/1.19  contains_slb  [45, 2]      (w:1, o:61, a:1, s:1, b:0), 
% 0.83/1.19  pair_in_list  [47, 3]      (w:1, o:68, a:1, s:1, b:0), 
% 0.83/1.19  remove_slb  [49, 2]      (w:1, o:55, a:1, s:1, b:0), 
% 0.83/1.19  lookup_slb  [50, 2]      (w:1, o:62, a:1, s:1, b:0), 
% 0.83/1.19  update_slb  [51, 2]      (w:1, o:63, a:1, s:1, b:0), 
% 0.83/1.19  succ_cpq  [52, 2]      (w:1, o:64, a:1, s:1, b:0), 
% 0.83/1.19  insert_cpq  [53, 2]      (w:1, o:65, a:1, s:1, b:0), 
% 0.83/1.19  remove_cpq  [54, 2]      (w:1, o:56, a:1, s:1, b:0), 
% 0.83/1.19  findmin_cpq_eff  [55, 1]      (w:1, o:23, a:1, s:1, b:0), 
% 0.83/1.19  removemin_cpq_eff  [56, 1]      (w:1, o:24, a:1, s:1, b:0), 
% 0.83/1.19  triple  [57, 3]      (w:1, o:69, a:1, s:1, b:0), 
% 0.83/1.19  check_cpq  [58, 1]      (w:1, o:25, a:1, s:1, b:0), 
% 0.83/1.19  contains_cpq  [59, 2]      (w:1, o:66, a:1, s:1, b:0), 
% 0.83/1.19  bad  [60, 0]      (w:1, o:10, a:1, s:1, b:0), 
% 0.83/1.19  ok  [61, 1]      (w:1, o:26, a:1, s:1, b:0), 
% 0.83/1.19  insert_pqp  [62, 2]      (w:1, o:67, a:1, s:1, b:0), 
% 0.83/1.19  remove_pqp  [63, 2]      (w:1, o:57, a:1, s:1, b:0), 
% 0.83/1.19  findmin_pqp_res  [64, 1]      (w:1, o:27, a:1, s:1, b:0), 
% 0.83/1.19  findmin_cpq_res  [65, 1]      (w:1, o:28, a:1, s:1, b:0), 
% 0.83/1.19  removemin_cpq_res  [66, 1]      (w:1, o:29, a:1, s:1, b:0), 
% 0.83/1.19  alpha1  [67, 4]      (w:1, o:70, a:1, s:1, b:1), 
% 0.83/1.19  skol1  [68, 0]      (w:1, o:14, a:1, s:1, b:1), 
% 0.83/1.19  skol2  [69, 0]      (w:1, o:15, a:1, s:1, b:1), 
% 0.83/1.19  skol3  [70, 0]      (w:1, o:16, a:1, s:1, b:1).
% 0.83/1.19  
% 0.83/1.19  
% 0.83/1.19  Starting Search:
% 0.83/1.19  
% 0.83/1.19  *** allocated 15000 integers for clauses
% 0.83/1.19  *** allocated 22500 integers for clauses
% 0.83/1.19  *** allocated 33750 integers for clauses
% 0.83/1.19  *** allocated 15000 integers for termspace/termends
% 0.83/1.19  *** allocated 50625 integers for clauses
% 0.83/1.19  *** allocated 22500 integers for termspace/termends
% 0.83/1.19  *** allocated 75937 integers for clauses
% 0.83/1.19  Resimplifying inuse:
% 0.83/1.19  Done
% 0.83/1.19  
% 0.83/1.19  *** allocated 33750 integers for termspace/termends
% 0.83/1.19  *** allocated 113905 integers for clauses
% 0.83/1.19  *** allocated 50625 integers for termspace/termends
% 0.83/1.19  *** allocated 170857 integers for clauses
% 0.83/1.19  
% 0.83/1.19  Intermediate Status:
% 0.83/1.19  Generated:    4126
% 0.83/1.19  Kept:         2231
% 0.83/1.19  Inuse:        138
% 0.83/1.19  Deleted:      4
% 0.83/1.19  Deletedinuse: 1
% 0.83/1.19  
% 0.83/1.19  Resimplifying inuse:
% 0.83/1.19  Done
% 0.83/1.19  
% 0.83/1.19  *** allocated 75937 integers for termspace/termends
% 0.83/1.19  *** allocated 256285 integers for clauses
% 0.83/1.19  Resimplifying inuse:
% 0.83/1.19  Done
% 0.83/1.19  
% 0.83/1.19  *** allocated 113905 integers for termspace/termends
% 0.83/1.19  
% 0.83/1.19  Intermediate Status:
% 0.83/1.19  Generated:    9478
% 0.83/1.19  Kept:         4346
% 0.83/1.19  Inuse:        183
% 0.83/1.19  Deleted:      5
% 0.83/1.19  Deletedinuse: 2
% 0.83/1.19  
% 0.83/1.19  
% 0.83/1.19  Bliksems!, er is een bewijs:
% 0.83/1.19  % SZS status Theorem
% 0.83/1.19  % SZS output start Refutation
% 0.83/1.19  
% 0.83/1.19  (54) {G0,W17,D4,L3,V3,M3} I { ! check_cpq( removemin_cpq_eff( triple( X, Y
% 0.83/1.19    , Z ) ) ), ! ok( removemin_cpq_eff( triple( X, Y, Z ) ) ), check_cpq( 
% 0.83/1.19    triple( X, Y, Z ) ) }.
% 0.83/1.19  (55) {G0,W5,D3,L1,V0,M1} I { ! check_cpq( triple( skol1, skol2, skol3 ) )
% 0.83/1.19     }.
% 0.83/1.19  (56) {G0,W6,D4,L1,V0,M1} I { check_cpq( removemin_cpq_eff( triple( skol1, 
% 0.83/1.19    skol2, skol3 ) ) ) }.
% 0.83/1.19  (57) {G0,W6,D4,L1,V0,M1} I { ok( removemin_cpq_eff( triple( skol1, skol2, 
% 0.83/1.19    skol3 ) ) ) }.
% 0.83/1.19  (4404) {G1,W5,D3,L1,V0,M1} R(54,56);r(57) { check_cpq( triple( skol1, skol2
% 0.83/1.19    , skol3 ) ) }.
% 0.83/1.19  (4437) {G2,W0,D0,L0,V0,M0} S(4404);r(55) {  }.
% 0.83/1.19  
% 0.83/1.19  
% 0.83/1.19  % SZS output end Refutation
% 0.83/1.19  found a proof!
% 0.83/1.19  
% 0.83/1.19  
% 0.83/1.19  Unprocessed initial clauses:
% 0.83/1.19  
% 0.83/1.19  (4439) {G0,W9,D2,L3,V3,M3}  { ! less_than( X, Z ), ! less_than( Z, Y ), 
% 0.83/1.19    less_than( X, Y ) }.
% 0.83/1.19  (4440) {G0,W6,D2,L2,V2,M2}  { less_than( X, Y ), less_than( Y, X ) }.
% 0.83/1.19  (4441) {G0,W3,D2,L1,V1,M1}  { less_than( X, X ) }.
% 0.83/1.19  (4442) {G0,W6,D2,L2,V2,M2}  { ! strictly_less_than( X, Y ), less_than( X, Y
% 0.83/1.19     ) }.
% 0.83/1.19  (4443) {G0,W6,D2,L2,V2,M2}  { ! strictly_less_than( X, Y ), ! less_than( Y
% 0.83/1.19    , X ) }.
% 0.83/1.19  (4444) {G0,W9,D2,L3,V2,M3}  { ! less_than( X, Y ), less_than( Y, X ), 
% 0.83/1.19    strictly_less_than( X, Y ) }.
% 0.83/1.19  (4445) {G0,W3,D2,L1,V1,M1}  { less_than( bottom, X ) }.
% 0.83/1.19  (4446) {G0,W2,D2,L1,V0,M1}  { ! isnonempty_slb( create_slb ) }.
% 0.83/1.19  (4447) {G0,W6,D4,L1,V3,M1}  { isnonempty_slb( insert_slb( X, pair( Y, Z ) )
% 0.83/1.19     ) }.
% 0.83/1.19  (4448) {G0,W3,D2,L1,V1,M1}  { ! contains_slb( create_slb, X ) }.
% 0.83/1.19  (4449) {G0,W13,D4,L3,V4,M3}  { ! contains_slb( insert_slb( X, pair( Y, T )
% 0.83/1.19     ), Z ), contains_slb( X, Z ), Y = Z }.
% 0.83/1.19  (4450) {G0,W10,D4,L2,V4,M2}  { ! contains_slb( X, Z ), contains_slb( 
% 0.83/1.19    insert_slb( X, pair( Y, T ) ), Z ) }.
% 0.83/1.19  (4451) {G0,W10,D4,L2,V4,M2}  { ! Y = Z, contains_slb( insert_slb( X, pair( 
% 0.83/1.19    Y, T ) ), Z ) }.
% 0.83/1.19  (4452) {G0,W4,D2,L1,V2,M1}  { ! pair_in_list( create_slb, X, Y ) }.
% 0.83/1.19  (4453) {G0,W17,D4,L3,V5,M3}  { ! pair_in_list( insert_slb( X, pair( Y, T )
% 0.83/1.19     ), Z, U ), pair_in_list( X, Z, U ), alpha1( Y, Z, T, U ) }.
% 0.83/1.19  (4454) {G0,W12,D4,L2,V5,M2}  { ! pair_in_list( X, Z, U ), pair_in_list( 
% 0.83/1.19    insert_slb( X, pair( Y, T ) ), Z, U ) }.
% 0.83/1.19  (4455) {G0,W13,D4,L2,V5,M2}  { ! alpha1( Y, Z, T, U ), pair_in_list( 
% 0.83/1.19    insert_slb( X, pair( Y, T ) ), Z, U ) }.
% 0.83/1.19  (4456) {G0,W8,D2,L2,V4,M2}  { ! alpha1( X, Y, Z, T ), X = Y }.
% 0.83/1.19  (4457) {G0,W8,D2,L2,V4,M2}  { ! alpha1( X, Y, Z, T ), Z = T }.
% 0.83/1.19  (4458) {G0,W11,D2,L3,V4,M3}  { ! X = Y, ! Z = T, alpha1( X, Y, Z, T ) }.
% 0.83/1.19  (4459) {G0,W9,D5,L1,V3,M1}  { remove_slb( insert_slb( X, pair( Y, Z ) ), Y
% 0.83/1.19     ) = X }.
% 0.83/1.19  (4460) {G0,W21,D5,L3,V4,M3}  { Y = Z, ! contains_slb( X, Z ), remove_slb( 
% 0.83/1.19    insert_slb( X, pair( Y, T ) ), Z ) = insert_slb( remove_slb( X, Z ), pair
% 0.83/1.19    ( Y, T ) ) }.
% 0.83/1.19  (4461) {G0,W9,D5,L1,V3,M1}  { lookup_slb( insert_slb( X, pair( Y, Z ) ), Y
% 0.83/1.19     ) = Z }.
% 0.83/1.19  (4462) {G0,W17,D5,L3,V4,M3}  { Y = Z, ! contains_slb( X, Z ), lookup_slb( 
% 0.83/1.19    insert_slb( X, pair( Y, T ) ), Z ) = lookup_slb( X, Z ) }.
% 0.83/1.19  (4463) {G0,W5,D3,L1,V1,M1}  { update_slb( create_slb, X ) = create_slb }.
% 0.83/1.19  (4464) {G0,W18,D5,L2,V4,M2}  { ! strictly_less_than( Y, X ), update_slb( 
% 0.83/1.19    insert_slb( Z, pair( T, Y ) ), X ) = insert_slb( update_slb( Z, X ), pair
% 0.83/1.19    ( T, X ) ) }.
% 0.83/1.19  (4465) {G0,W18,D5,L2,V4,M2}  { ! less_than( X, Y ), update_slb( insert_slb
% 0.83/1.19    ( Z, pair( T, Y ) ), X ) = insert_slb( update_slb( Z, X ), pair( T, Y ) )
% 0.83/1.19     }.
% 0.83/1.19  (4466) {G0,W3,D2,L1,V1,M1}  { succ_cpq( X, X ) }.
% 0.83/1.19  (4467) {G0,W8,D3,L2,V3,M2}  { ! succ_cpq( X, Y ), succ_cpq( X, insert_cpq( 
% 0.83/1.19    Y, Z ) ) }.
% 0.83/1.19  (4468) {G0,W8,D3,L2,V3,M2}  { ! succ_cpq( X, Y ), succ_cpq( X, remove_cpq( 
% 0.83/1.19    Y, Z ) ) }.
% 0.83/1.19  (4469) {G0,W7,D3,L2,V2,M2}  { ! succ_cpq( X, Y ), succ_cpq( X, 
% 0.83/1.19    findmin_cpq_eff( Y ) ) }.
% 0.83/1.19  (4470) {G0,W7,D3,L2,V2,M2}  { ! succ_cpq( X, Y ), succ_cpq( X, 
% 0.83/1.19    removemin_cpq_eff( Y ) ) }.
% 0.83/1.19  (4471) {G0,W5,D3,L1,V2,M1}  { check_cpq( triple( X, create_slb, Y ) ) }.
% 0.83/1.19  (4472) {G0,W17,D5,L3,V5,M3}  { ! less_than( Y, X ), ! check_cpq( triple( Z
% 0.83/1.19    , insert_slb( T, pair( X, Y ) ), U ) ), check_cpq( triple( Z, T, U ) )
% 0.83/1.19     }.
% 0.83/1.19  (4473) {G0,W17,D5,L3,V5,M3}  { ! less_than( Y, X ), ! check_cpq( triple( Z
% 0.83/1.19    , T, U ) ), check_cpq( triple( Z, insert_slb( T, pair( X, Y ) ), U ) )
% 0.83/1.19     }.
% 0.83/1.19  (4474) {G0,W12,D5,L2,V5,M2}  { ! strictly_less_than( X, Y ), ! check_cpq( 
% 0.83/1.19    triple( Z, insert_slb( T, pair( X, Y ) ), U ) ) }.
% 0.83/1.19  (4475) {G0,W13,D5,L3,V5,M3}  { ! strictly_less_than( X, Y ), ! ||, 
% 0.83/1.19    check_cpq( triple( Z, insert_slb( T, pair( X, Y ) ), U ) ) }.
% 0.83/1.19  (4476) {G0,W9,D3,L2,V4,M2}  { ! contains_cpq( triple( X, Y, Z ), T ), 
% 0.83/1.19    contains_slb( Y, T ) }.
% 0.83/1.19  (4477) {G0,W9,D3,L2,V4,M2}  { ! contains_slb( Y, T ), contains_cpq( triple
% 0.83/1.19    ( X, Y, Z ), T ) }.
% 0.83/1.19  (4478) {G0,W5,D3,L1,V2,M1}  { ! ok( triple( X, Y, bad ) ) }.
% 0.83/1.19  (4479) {G0,W6,D3,L2,V2,M2}  { ! ||, ok( triple( X, Y, bad ) ) }.
% 0.83/1.19  (4480) {G0,W8,D3,L2,V3,M2}  { ok( triple( Y, Z, X ) ), X = bad }.
% 0.83/1.19  (4481) {G0,W17,D5,L1,V4,M1}  { insert_cpq( triple( X, Y, Z ), T ) = triple
% 0.83/1.19    ( insert_pqp( X, T ), insert_slb( Y, pair( T, bottom ) ), Z ) }.
% 0.83/1.19  (4482) {G0,W14,D4,L2,V4,M2}  { contains_slb( X, Y ), remove_cpq( triple( Z
% 0.83/1.19    , X, T ), Y ) = triple( Z, X, bad ) }.
% 0.83/1.19  (4483) {G0,W23,D4,L3,V4,M3}  { ! contains_slb( X, Y ), ! less_than( 
% 0.83/1.19    lookup_slb( X, Y ), Y ), remove_cpq( triple( Z, X, T ), Y ) = triple( 
% 0.83/1.19    remove_pqp( Z, Y ), remove_slb( X, Y ), T ) }.
% 0.83/1.19  (4484) {G0,W23,D4,L3,V4,M3}  { ! contains_slb( X, Y ), ! strictly_less_than
% 0.83/1.19    ( Y, lookup_slb( X, Y ) ), remove_cpq( triple( Z, X, T ), Y ) = triple( 
% 0.83/1.19    remove_pqp( Z, Y ), remove_slb( X, Y ), bad ) }.
% 0.83/1.19  (4485) {G0,W10,D4,L1,V2,M1}  { findmin_cpq_eff( triple( X, create_slb, Y )
% 0.83/1.19     ) = triple( X, create_slb, bad ) }.
% 0.83/1.19  (4486) {G0,W20,D5,L3,V3,M3}  { Y = create_slb, contains_slb( Y, 
% 0.83/1.19    findmin_pqp_res( X ) ), findmin_cpq_eff( triple( X, Y, Z ) ) = triple( X
% 0.83/1.19    , update_slb( Y, findmin_pqp_res( X ) ), bad ) }.
% 0.83/1.19  (4487) {G0,W27,D5,L4,V3,M4}  { Y = create_slb, ! contains_slb( Y, 
% 0.83/1.19    findmin_pqp_res( X ) ), ! strictly_less_than( findmin_pqp_res( X ), 
% 0.83/1.19    lookup_slb( Y, findmin_pqp_res( X ) ) ), findmin_cpq_eff( triple( X, Y, Z
% 0.83/1.19     ) ) = triple( X, update_slb( Y, findmin_pqp_res( X ) ), bad ) }.
% 0.83/1.19  (4488) {G0,W27,D5,L4,V3,M4}  { Y = create_slb, ! contains_slb( Y, 
% 0.83/1.19    findmin_pqp_res( X ) ), ! less_than( lookup_slb( Y, findmin_pqp_res( X )
% 0.83/1.19     ), findmin_pqp_res( X ) ), findmin_cpq_eff( triple( X, Y, Z ) ) = triple
% 0.83/1.19    ( X, update_slb( Y, findmin_pqp_res( X ) ), Z ) }.
% 0.83/1.19  (4489) {G0,W7,D4,L1,V2,M1}  { findmin_cpq_res( triple( X, create_slb, Y ) )
% 0.83/1.19     = bottom }.
% 0.83/1.19  (4490) {G0,W11,D4,L2,V3,M2}  { X = create_slb, findmin_cpq_res( triple( Y, 
% 0.83/1.19    X, Z ) ) = findmin_pqp_res( Y ) }.
% 0.83/1.19  (4491) {G0,W8,D4,L1,V1,M1}  { removemin_cpq_eff( X ) = remove_cpq( 
% 0.83/1.19    findmin_cpq_eff( X ), findmin_cpq_res( X ) ) }.
% 0.83/1.19  (4492) {G0,W5,D3,L1,V1,M1}  { removemin_cpq_res( X ) = findmin_cpq_res( X )
% 0.83/1.19     }.
% 0.83/1.19  (4493) {G0,W17,D4,L3,V3,M3}  { ! check_cpq( removemin_cpq_eff( triple( X, Y
% 0.83/1.19    , Z ) ) ), ! ok( removemin_cpq_eff( triple( X, Y, Z ) ) ), check_cpq( 
% 0.83/1.19    triple( X, Y, Z ) ) }.
% 0.83/1.19  (4494) {G0,W5,D3,L1,V0,M1}  { ! check_cpq( triple( skol1, skol2, skol3 ) )
% 0.83/1.19     }.
% 0.83/1.19  (4495) {G0,W6,D4,L1,V0,M1}  { check_cpq( removemin_cpq_eff( triple( skol1, 
% 0.83/1.19    skol2, skol3 ) ) ) }.
% 0.83/1.19  (4496) {G0,W6,D4,L1,V0,M1}  { ok( removemin_cpq_eff( triple( skol1, skol2, 
% 0.83/1.19    skol3 ) ) ) }.
% 0.83/1.19  
% 0.83/1.19  
% 0.83/1.19  Total Proof:
% 0.83/1.19  
% 0.83/1.19  subsumption: (54) {G0,W17,D4,L3,V3,M3} I { ! check_cpq( removemin_cpq_eff( 
% 0.83/1.19    triple( X, Y, Z ) ) ), ! ok( removemin_cpq_eff( triple( X, Y, Z ) ) ), 
% 0.83/1.19    check_cpq( triple( X, Y, Z ) ) }.
% 0.83/1.19  parent0: (4493) {G0,W17,D4,L3,V3,M3}  { ! check_cpq( removemin_cpq_eff( 
% 0.83/1.19    triple( X, Y, Z ) ) ), ! ok( removemin_cpq_eff( triple( X, Y, Z ) ) ), 
% 0.83/1.19    check_cpq( triple( X, Y, Z ) ) }.
% 0.83/1.19  substitution0:
% 0.83/1.19     X := X
% 0.83/1.19     Y := Y
% 0.83/1.19     Z := Z
% 0.83/1.19  end
% 0.83/1.19  permutation0:
% 0.83/1.19     0 ==> 0
% 0.83/1.19     1 ==> 1
% 0.83/1.19     2 ==> 2
% 0.83/1.19  end
% 0.83/1.19  
% 0.83/1.19  subsumption: (55) {G0,W5,D3,L1,V0,M1} I { ! check_cpq( triple( skol1, skol2
% 0.83/1.19    , skol3 ) ) }.
% 0.83/1.19  parent0: (4494) {G0,W5,D3,L1,V0,M1}  { ! check_cpq( triple( skol1, skol2, 
% 0.83/1.19    skol3 ) ) }.
% 0.83/1.19  substitution0:
% 0.83/1.19  end
% 0.83/1.19  permutation0:
% 0.83/1.19     0 ==> 0
% 0.83/1.19  end
% 0.83/1.19  
% 0.83/1.19  subsumption: (56) {G0,W6,D4,L1,V0,M1} I { check_cpq( removemin_cpq_eff( 
% 0.83/1.19    triple( skol1, skol2, skol3 ) ) ) }.
% 0.83/1.19  parent0: (4495) {G0,W6,D4,L1,V0,M1}  { check_cpq( removemin_cpq_eff( triple
% 0.83/1.19    ( skol1, skol2, skol3 ) ) ) }.
% 0.83/1.19  substitution0:
% 0.83/1.19  end
% 0.83/1.19  permutation0:
% 0.83/1.19     0 ==> 0
% 0.83/1.19  end
% 0.83/1.19  
% 0.83/1.19  subsumption: (57) {G0,W6,D4,L1,V0,M1} I { ok( removemin_cpq_eff( triple( 
% 0.83/1.19    skol1, skol2, skol3 ) ) ) }.
% 0.83/1.19  parent0: (4496) {G0,W6,D4,L1,V0,M1}  { ok( removemin_cpq_eff( triple( skol1
% 0.83/1.19    , skol2, skol3 ) ) ) }.
% 0.83/1.19  substitution0:
% 0.83/1.19  end
% 0.83/1.19  permutation0:
% 0.83/1.19     0 ==> 0
% 0.83/1.19  end
% 0.83/1.19  
% 0.83/1.19  resolution: (4677) {G1,W11,D4,L2,V0,M2}  { ! ok( removemin_cpq_eff( triple
% 0.83/1.19    ( skol1, skol2, skol3 ) ) ), check_cpq( triple( skol1, skol2, skol3 ) )
% 0.83/1.19     }.
% 0.83/1.19  parent0[0]: (54) {G0,W17,D4,L3,V3,M3} I { ! check_cpq( removemin_cpq_eff( 
% 0.83/1.19    triple( X, Y, Z ) ) ), ! ok( removemin_cpq_eff( triple( X, Y, Z ) ) ), 
% 0.83/1.19    check_cpq( triple( X, Y, Z ) ) }.
% 0.83/1.19  parent1[0]: (56) {G0,W6,D4,L1,V0,M1} I { check_cpq( removemin_cpq_eff( 
% 0.83/1.19    triple( skol1, skol2, skol3 ) ) ) }.
% 0.83/1.19  substitution0:
% 0.83/1.19     X := skol1
% 0.83/1.19     Y := skol2
% 0.83/1.19     Z := skol3
% 0.83/1.19  end
% 0.83/1.19  substitution1:
% 0.83/1.19  end
% 0.83/1.19  
% 0.83/1.19  resolution: (4678) {G1,W5,D3,L1,V0,M1}  { check_cpq( triple( skol1, skol2, 
% 0.83/1.19    skol3 ) ) }.
% 0.83/1.19  parent0[0]: (4677) {G1,W11,D4,L2,V0,M2}  { ! ok( removemin_cpq_eff( triple
% 0.83/1.19    ( skol1, skol2, skol3 ) ) ), check_cpq( triple( skol1, skol2, skol3 ) )
% 0.83/1.19     }.
% 0.83/1.19  parent1[0]: (57) {G0,W6,D4,L1,V0,M1} I { ok( removemin_cpq_eff( triple( 
% 0.83/1.19    skol1, skol2, skol3 ) ) ) }.
% 0.83/1.19  substitution0:
% 0.83/1.19  end
% 0.83/1.19  substitution1:
% 0.83/1.19  end
% 0.83/1.19  
% 0.83/1.19  subsumption: (4404) {G1,W5,D3,L1,V0,M1} R(54,56);r(57) { check_cpq( triple
% 0.83/1.19    ( skol1, skol2, skol3 ) ) }.
% 0.83/1.19  parent0: (4678) {G1,W5,D3,L1,V0,M1}  { check_cpq( triple( skol1, skol2, 
% 0.83/1.19    skol3 ) ) }.
% 0.83/1.19  substitution0:
% 0.83/1.19  end
% 0.83/1.19  permutation0:
% 0.83/1.19     0 ==> 0
% 0.83/1.19  end
% 0.83/1.19  
% 0.83/1.19  resolution: (4679) {G1,W0,D0,L0,V0,M0}  {  }.
% 0.83/1.19  parent0[0]: (55) {G0,W5,D3,L1,V0,M1} I { ! check_cpq( triple( skol1, skol2
% 0.83/1.19    , skol3 ) ) }.
% 0.83/1.19  parent1[0]: (4404) {G1,W5,D3,L1,V0,M1} R(54,56);r(57) { check_cpq( triple( 
% 0.83/1.19    skol1, skol2, skol3 ) ) }.
% 0.83/1.19  substitution0:
% 0.83/1.19  end
% 0.83/1.19  substitution1:
% 0.83/1.19  end
% 0.83/1.19  
% 0.83/1.19  subsumption: (4437) {G2,W0,D0,L0,V0,M0} S(4404);r(55) {  }.
% 0.83/1.19  parent0: (4679) {G1,W0,D0,L0,V0,M0}  {  }.
% 0.83/1.19  substitution0:
% 0.83/1.19  end
% 0.83/1.19  permutation0:
% 0.83/1.19  end
% 0.83/1.19  
% 0.83/1.19  Proof check complete!
% 0.83/1.19  
% 0.83/1.19  Memory use:
% 0.83/1.19  
% 0.83/1.19  space for terms:        88451
% 0.83/1.19  space for clauses:      238169
% 0.83/1.19  
% 0.83/1.19  
% 0.83/1.19  clauses generated:      9764
% 0.83/1.19  clauses kept:           4438
% 0.83/1.19  clauses selected:       188
% 0.83/1.19  clauses deleted:        6
% 0.83/1.19  clauses inuse deleted:  2
% 0.83/1.19  
% 0.83/1.19  subsentry:          10084
% 0.83/1.19  literals s-matched: 7884
% 0.83/1.19  literals matched:   7605
% 0.83/1.19  full subsumption:   2255
% 0.83/1.19  
% 0.83/1.19  checksum:           -855509345
% 0.83/1.19  
% 0.83/1.19  
% 0.83/1.19  Bliksem ended
%------------------------------------------------------------------------------