TSTP Solution File: SEU107+1 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : SEU107+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n025.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 : Tue Jul 19 07:10:39 EDT 2022

% Result   : Theorem 0.71s 1.09s
% Output   : Refutation 0.71s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : SEU107+1 : TPTP v8.1.0. Released v3.2.0.
% 0.00/0.12  % Command  : bliksem %s
% 0.11/0.33  % Computer : n025.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % DateTime : Sun Jun 19 19:33:59 EDT 2022
% 0.11/0.33  % CPUTime  : 
% 0.71/1.09  *** allocated 10000 integers for termspace/termends
% 0.71/1.09  *** allocated 10000 integers for clauses
% 0.71/1.09  *** allocated 10000 integers for justifications
% 0.71/1.09  Bliksem 1.12
% 0.71/1.09  
% 0.71/1.09  
% 0.71/1.09  Automatic Strategy Selection
% 0.71/1.09  
% 0.71/1.09  
% 0.71/1.09  Clauses:
% 0.71/1.09  
% 0.71/1.09  { ! in( X, Y ), ! in( Y, X ) }.
% 0.71/1.09  { ! empty( X ), finite( X ) }.
% 0.71/1.09  { ! preboolean( X ), cup_closed( X ) }.
% 0.71/1.09  { ! preboolean( X ), diff_closed( X ) }.
% 0.71/1.09  { ! finite( X ), ! element( Y, powerset( X ) ), finite( Y ) }.
% 0.71/1.09  { ! cup_closed( X ), ! diff_closed( X ), preboolean( X ) }.
% 0.71/1.09  { empty( X ), ! preboolean( X ), ! element( Y, X ), ! element( Z, X ), 
% 0.71/1.09    element( prebool_difference( X, Y, Z ), X ) }.
% 0.71/1.09  { element( skol1( X ), X ) }.
% 0.71/1.09  { ! finite( X ), finite( set_difference( X, Y ) ) }.
% 0.71/1.09  { ! empty( powerset( X ) ) }.
% 0.71/1.09  { empty( empty_set ) }.
% 0.71/1.09  { ! empty( skol2 ) }.
% 0.71/1.09  { finite( skol2 ) }.
% 0.71/1.09  { ! empty( skol3 ) }.
% 0.71/1.09  { cup_closed( skol3 ) }.
% 0.71/1.09  { cap_closed( skol3 ) }.
% 0.71/1.09  { diff_closed( skol3 ) }.
% 0.71/1.09  { preboolean( skol3 ) }.
% 0.71/1.09  { empty( X ), ! empty( skol4( Y ) ) }.
% 0.71/1.09  { empty( X ), element( skol4( X ), powerset( X ) ) }.
% 0.71/1.09  { empty( skol5 ) }.
% 0.71/1.09  { empty( skol6( Y ) ) }.
% 0.71/1.09  { relation( skol6( Y ) ) }.
% 0.71/1.09  { function( skol6( Y ) ) }.
% 0.71/1.09  { one_to_one( skol6( Y ) ) }.
% 0.71/1.09  { epsilon_transitive( skol6( Y ) ) }.
% 0.71/1.09  { epsilon_connected( skol6( Y ) ) }.
% 0.71/1.09  { ordinal( skol6( Y ) ) }.
% 0.71/1.09  { natural( skol6( Y ) ) }.
% 0.71/1.09  { finite( skol6( Y ) ) }.
% 0.71/1.09  { element( skol6( X ), powerset( X ) ) }.
% 0.71/1.09  { empty( skol7( Y ) ) }.
% 0.71/1.09  { element( skol7( X ), powerset( X ) ) }.
% 0.71/1.09  { ! empty( skol8 ) }.
% 0.71/1.09  { empty( X ), ! empty( skol9( Y ) ) }.
% 0.71/1.09  { empty( X ), finite( skol9( Y ) ) }.
% 0.71/1.09  { empty( X ), element( skol9( X ), powerset( X ) ) }.
% 0.71/1.09  { empty( X ), ! empty( skol10( Y ) ) }.
% 0.71/1.09  { empty( X ), finite( skol10( Y ) ) }.
% 0.71/1.09  { empty( X ), element( skol10( X ), powerset( X ) ) }.
% 0.71/1.09  { empty( X ), ! preboolean( X ), ! element( Y, X ), ! element( Z, X ), 
% 0.71/1.09    prebool_difference( X, Y, Z ) = set_difference( Y, Z ) }.
% 0.71/1.09  { subset( X, X ) }.
% 0.71/1.09  { ! empty( skol11 ) }.
% 0.71/1.09  { preboolean( skol11 ) }.
% 0.71/1.09  { ! in( empty_set, skol11 ) }.
% 0.71/1.09  { ! in( X, Y ), element( X, Y ) }.
% 0.71/1.09  { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.71/1.09  { ! set_difference( X, Y ) = empty_set, subset( X, Y ) }.
% 0.71/1.09  { ! subset( X, Y ), set_difference( X, Y ) = empty_set }.
% 0.71/1.09  { set_difference( X, empty_set ) = X }.
% 0.71/1.09  { ! element( X, powerset( Y ) ), subset( X, Y ) }.
% 0.71/1.09  { ! subset( X, Y ), element( X, powerset( Y ) ) }.
% 0.71/1.09  { set_difference( empty_set, X ) = empty_set }.
% 0.71/1.09  { ! in( X, Z ), ! element( Z, powerset( Y ) ), element( X, Y ) }.
% 0.71/1.09  { ! in( X, Y ), ! element( Y, powerset( Z ) ), ! empty( Z ) }.
% 0.71/1.09  { ! empty( X ), X = empty_set }.
% 0.71/1.09  { ! in( X, Y ), ! empty( Y ) }.
% 0.71/1.09  { ! empty( X ), X = Y, ! empty( Y ) }.
% 0.71/1.09  
% 0.71/1.09  percentage equality = 0.071429, percentage horn = 0.862069
% 0.71/1.09  This is a problem with some equality
% 0.71/1.09  
% 0.71/1.09  
% 0.71/1.09  
% 0.71/1.09  Options Used:
% 0.71/1.09  
% 0.71/1.09  useres =            1
% 0.71/1.09  useparamod =        1
% 0.71/1.09  useeqrefl =         1
% 0.71/1.09  useeqfact =         1
% 0.71/1.09  usefactor =         1
% 0.71/1.09  usesimpsplitting =  0
% 0.71/1.09  usesimpdemod =      5
% 0.71/1.09  usesimpres =        3
% 0.71/1.09  
% 0.71/1.09  resimpinuse      =  1000
% 0.71/1.09  resimpclauses =     20000
% 0.71/1.09  substype =          eqrewr
% 0.71/1.09  backwardsubs =      1
% 0.71/1.09  selectoldest =      5
% 0.71/1.09  
% 0.71/1.09  litorderings [0] =  split
% 0.71/1.09  litorderings [1] =  extend the termordering, first sorting on arguments
% 0.71/1.09  
% 0.71/1.09  termordering =      kbo
% 0.71/1.09  
% 0.71/1.09  litapriori =        0
% 0.71/1.09  termapriori =       1
% 0.71/1.09  litaposteriori =    0
% 0.71/1.09  termaposteriori =   0
% 0.71/1.09  demodaposteriori =  0
% 0.71/1.09  ordereqreflfact =   0
% 0.71/1.09  
% 0.71/1.09  litselect =         negord
% 0.71/1.09  
% 0.71/1.09  maxweight =         15
% 0.71/1.09  maxdepth =          30000
% 0.71/1.09  maxlength =         115
% 0.71/1.09  maxnrvars =         195
% 0.71/1.09  excuselevel =       1
% 0.71/1.09  increasemaxweight = 1
% 0.71/1.09  
% 0.71/1.09  maxselected =       10000000
% 0.71/1.09  maxnrclauses =      10000000
% 0.71/1.09  
% 0.71/1.09  showgenerated =    0
% 0.71/1.09  showkept =         0
% 0.71/1.09  showselected =     0
% 0.71/1.09  showdeleted =      0
% 0.71/1.09  showresimp =       1
% 0.71/1.09  showstatus =       2000
% 0.71/1.09  
% 0.71/1.09  prologoutput =     0
% 0.71/1.09  nrgoals =          5000000
% 0.71/1.09  totalproof =       1
% 0.71/1.09  
% 0.71/1.09  Symbols occurring in the translation:
% 0.71/1.09  
% 0.71/1.09  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 0.71/1.09  .  [1, 2]      (w:1, o:40, a:1, s:1, b:0), 
% 0.71/1.09  !  [4, 1]      (w:0, o:15, a:1, s:1, b:0), 
% 0.71/1.09  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.71/1.09  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 0.71/1.09  in  [37, 2]      (w:1, o:64, a:1, s:1, b:0), 
% 0.71/1.09  empty  [38, 1]      (w:1, o:22, a:1, s:1, b:0), 
% 0.71/1.09  finite  [39, 1]      (w:1, o:25, a:1, s:1, b:0), 
% 0.71/1.09  preboolean  [40, 1]      (w:1, o:29, a:1, s:1, b:0), 
% 0.71/1.09  cup_closed  [41, 1]      (w:1, o:30, a:1, s:1, b:0), 
% 0.71/1.09  diff_closed  [42, 1]      (w:1, o:21, a:1, s:1, b:0), 
% 0.71/1.09  powerset  [43, 1]      (w:1, o:31, a:1, s:1, b:0), 
% 0.71/1.09  element  [44, 2]      (w:1, o:65, a:1, s:1, b:0), 
% 0.71/1.09  prebool_difference  [46, 3]      (w:1, o:68, a:1, s:1, b:0), 
% 0.71/1.09  set_difference  [47, 2]      (w:1, o:66, a:1, s:1, b:0), 
% 0.71/1.09  empty_set  [48, 0]      (w:1, o:9, a:1, s:1, b:0), 
% 0.71/1.09  cap_closed  [49, 1]      (w:1, o:20, a:1, s:1, b:0), 
% 0.71/1.09  relation  [50, 1]      (w:1, o:32, a:1, s:1, b:0), 
% 0.71/1.09  function  [51, 1]      (w:1, o:33, a:1, s:1, b:0), 
% 0.71/1.09  one_to_one  [52, 1]      (w:1, o:27, a:1, s:1, b:0), 
% 0.71/1.09  epsilon_transitive  [53, 1]      (w:1, o:23, a:1, s:1, b:0), 
% 0.71/1.09  epsilon_connected  [54, 1]      (w:1, o:24, a:1, s:1, b:0), 
% 0.71/1.09  ordinal  [55, 1]      (w:1, o:28, a:1, s:1, b:0), 
% 0.71/1.09  natural  [56, 1]      (w:1, o:26, a:1, s:1, b:0), 
% 0.71/1.09  subset  [57, 2]      (w:1, o:67, a:1, s:1, b:0), 
% 0.71/1.09  skol1  [58, 1]      (w:1, o:34, a:1, s:1, b:1), 
% 0.71/1.09  skol2  [59, 0]      (w:1, o:11, a:1, s:1, b:1), 
% 0.71/1.09  skol3  [60, 0]      (w:1, o:12, a:1, s:1, b:1), 
% 0.71/1.09  skol4  [61, 1]      (w:1, o:35, a:1, s:1, b:1), 
% 0.71/1.09  skol5  [62, 0]      (w:1, o:13, a:1, s:1, b:1), 
% 0.71/1.09  skol6  [63, 1]      (w:1, o:36, a:1, s:1, b:1), 
% 0.71/1.09  skol7  [64, 1]      (w:1, o:37, a:1, s:1, b:1), 
% 0.71/1.09  skol8  [65, 0]      (w:1, o:14, a:1, s:1, b:1), 
% 0.71/1.09  skol9  [66, 1]      (w:1, o:38, a:1, s:1, b:1), 
% 0.71/1.09  skol10  [67, 1]      (w:1, o:39, a:1, s:1, b:1), 
% 0.71/1.09  skol11  [68, 0]      (w:1, o:10, a:1, s:1, b:1).
% 0.71/1.09  
% 0.71/1.09  
% 0.71/1.09  Starting Search:
% 0.71/1.09  
% 0.71/1.09  *** allocated 15000 integers for clauses
% 0.71/1.09  *** allocated 22500 integers for clauses
% 0.71/1.09  *** allocated 33750 integers for clauses
% 0.71/1.09  
% 0.71/1.09  Bliksems!, er is een bewijs:
% 0.71/1.09  % SZS status Theorem
% 0.71/1.09  % SZS output start Refutation
% 0.71/1.09  
% 0.71/1.09  (6) {G0,W16,D3,L5,V3,M5} I { empty( X ), ! preboolean( X ), ! element( Y, X
% 0.71/1.09     ), ! element( Z, X ), element( prebool_difference( X, Y, Z ), X ) }.
% 0.71/1.09  (7) {G0,W4,D3,L1,V1,M1} I { element( skol1( X ), X ) }.
% 0.71/1.09  (40) {G0,W18,D3,L5,V3,M5} I { empty( X ), ! preboolean( X ), ! element( Y, 
% 0.71/1.09    X ), ! element( Z, X ), prebool_difference( X, Y, Z ) ==> set_difference
% 0.71/1.09    ( Y, Z ) }.
% 0.71/1.09  (41) {G0,W3,D2,L1,V1,M1} I { subset( X, X ) }.
% 0.71/1.09  (42) {G0,W2,D2,L1,V0,M1} I { ! empty( skol11 ) }.
% 0.71/1.09  (43) {G0,W2,D2,L1,V0,M1} I { preboolean( skol11 ) }.
% 0.71/1.09  (44) {G0,W3,D2,L1,V0,M1} I { ! in( empty_set, skol11 ) }.
% 0.71/1.09  (46) {G0,W8,D2,L3,V2,M3} I { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.71/1.09  (48) {G0,W8,D3,L2,V2,M2} I { ! subset( X, Y ), set_difference( X, Y ) ==> 
% 0.71/1.09    empty_set }.
% 0.71/1.09  (73) {G1,W15,D3,L5,V3,M5} S(6);d(40) { empty( X ), ! preboolean( X ), ! 
% 0.71/1.09    element( Y, X ), ! element( Z, X ), element( set_difference( Y, Z ), X )
% 0.71/1.09     }.
% 0.71/1.09  (270) {G1,W3,D2,L1,V0,M1} R(46,44);r(42) { ! element( empty_set, skol11 )
% 0.71/1.09     }.
% 0.71/1.09  (318) {G1,W5,D3,L1,V1,M1} R(48,41) { set_difference( X, X ) ==> empty_set
% 0.71/1.09     }.
% 0.71/1.09  (569) {G2,W11,D3,L3,V2,M3} R(73,42);r(43) { ! element( X, skol11 ), ! 
% 0.71/1.09    element( Y, skol11 ), element( set_difference( X, Y ), skol11 ) }.
% 0.71/1.09  (570) {G3,W3,D2,L1,V1,M1} F(569);d(318);r(270) { ! element( X, skol11 ) }.
% 0.71/1.09  (585) {G4,W0,D0,L0,V0,M0} R(570,7) {  }.
% 0.71/1.09  
% 0.71/1.09  
% 0.71/1.09  % SZS output end Refutation
% 0.71/1.09  found a proof!
% 0.71/1.09  
% 0.71/1.09  
% 0.71/1.09  Unprocessed initial clauses:
% 0.71/1.09  
% 0.71/1.09  (587) {G0,W6,D2,L2,V2,M2}  { ! in( X, Y ), ! in( Y, X ) }.
% 0.71/1.09  (588) {G0,W4,D2,L2,V1,M2}  { ! empty( X ), finite( X ) }.
% 0.71/1.09  (589) {G0,W4,D2,L2,V1,M2}  { ! preboolean( X ), cup_closed( X ) }.
% 0.71/1.09  (590) {G0,W4,D2,L2,V1,M2}  { ! preboolean( X ), diff_closed( X ) }.
% 0.71/1.09  (591) {G0,W8,D3,L3,V2,M3}  { ! finite( X ), ! element( Y, powerset( X ) ), 
% 0.71/1.09    finite( Y ) }.
% 0.71/1.09  (592) {G0,W6,D2,L3,V1,M3}  { ! cup_closed( X ), ! diff_closed( X ), 
% 0.71/1.09    preboolean( X ) }.
% 0.71/1.09  (593) {G0,W16,D3,L5,V3,M5}  { empty( X ), ! preboolean( X ), ! element( Y, 
% 0.71/1.09    X ), ! element( Z, X ), element( prebool_difference( X, Y, Z ), X ) }.
% 0.71/1.09  (594) {G0,W4,D3,L1,V1,M1}  { element( skol1( X ), X ) }.
% 0.71/1.09  (595) {G0,W6,D3,L2,V2,M2}  { ! finite( X ), finite( set_difference( X, Y )
% 0.71/1.09     ) }.
% 0.71/1.09  (596) {G0,W3,D3,L1,V1,M1}  { ! empty( powerset( X ) ) }.
% 0.71/1.09  (597) {G0,W2,D2,L1,V0,M1}  { empty( empty_set ) }.
% 0.71/1.09  (598) {G0,W2,D2,L1,V0,M1}  { ! empty( skol2 ) }.
% 0.71/1.09  (599) {G0,W2,D2,L1,V0,M1}  { finite( skol2 ) }.
% 0.71/1.09  (600) {G0,W2,D2,L1,V0,M1}  { ! empty( skol3 ) }.
% 0.71/1.09  (601) {G0,W2,D2,L1,V0,M1}  { cup_closed( skol3 ) }.
% 0.71/1.09  (602) {G0,W2,D2,L1,V0,M1}  { cap_closed( skol3 ) }.
% 0.71/1.09  (603) {G0,W2,D2,L1,V0,M1}  { diff_closed( skol3 ) }.
% 0.71/1.09  (604) {G0,W2,D2,L1,V0,M1}  { preboolean( skol3 ) }.
% 0.71/1.09  (605) {G0,W5,D3,L2,V2,M2}  { empty( X ), ! empty( skol4( Y ) ) }.
% 0.71/1.09  (606) {G0,W7,D3,L2,V1,M2}  { empty( X ), element( skol4( X ), powerset( X )
% 0.71/1.09     ) }.
% 0.71/1.09  (607) {G0,W2,D2,L1,V0,M1}  { empty( skol5 ) }.
% 0.71/1.09  (608) {G0,W3,D3,L1,V1,M1}  { empty( skol6( Y ) ) }.
% 0.71/1.09  (609) {G0,W3,D3,L1,V1,M1}  { relation( skol6( Y ) ) }.
% 0.71/1.09  (610) {G0,W3,D3,L1,V1,M1}  { function( skol6( Y ) ) }.
% 0.71/1.09  (611) {G0,W3,D3,L1,V1,M1}  { one_to_one( skol6( Y ) ) }.
% 0.71/1.09  (612) {G0,W3,D3,L1,V1,M1}  { epsilon_transitive( skol6( Y ) ) }.
% 0.71/1.09  (613) {G0,W3,D3,L1,V1,M1}  { epsilon_connected( skol6( Y ) ) }.
% 0.71/1.09  (614) {G0,W3,D3,L1,V1,M1}  { ordinal( skol6( Y ) ) }.
% 0.71/1.09  (615) {G0,W3,D3,L1,V1,M1}  { natural( skol6( Y ) ) }.
% 0.71/1.09  (616) {G0,W3,D3,L1,V1,M1}  { finite( skol6( Y ) ) }.
% 0.71/1.09  (617) {G0,W5,D3,L1,V1,M1}  { element( skol6( X ), powerset( X ) ) }.
% 0.71/1.09  (618) {G0,W3,D3,L1,V1,M1}  { empty( skol7( Y ) ) }.
% 0.71/1.09  (619) {G0,W5,D3,L1,V1,M1}  { element( skol7( X ), powerset( X ) ) }.
% 0.71/1.09  (620) {G0,W2,D2,L1,V0,M1}  { ! empty( skol8 ) }.
% 0.71/1.09  (621) {G0,W5,D3,L2,V2,M2}  { empty( X ), ! empty( skol9( Y ) ) }.
% 0.71/1.09  (622) {G0,W5,D3,L2,V2,M2}  { empty( X ), finite( skol9( Y ) ) }.
% 0.71/1.09  (623) {G0,W7,D3,L2,V1,M2}  { empty( X ), element( skol9( X ), powerset( X )
% 0.71/1.09     ) }.
% 0.71/1.09  (624) {G0,W5,D3,L2,V2,M2}  { empty( X ), ! empty( skol10( Y ) ) }.
% 0.71/1.09  (625) {G0,W5,D3,L2,V2,M2}  { empty( X ), finite( skol10( Y ) ) }.
% 0.71/1.09  (626) {G0,W7,D3,L2,V1,M2}  { empty( X ), element( skol10( X ), powerset( X
% 0.71/1.09     ) ) }.
% 0.71/1.09  (627) {G0,W18,D3,L5,V3,M5}  { empty( X ), ! preboolean( X ), ! element( Y, 
% 0.71/1.09    X ), ! element( Z, X ), prebool_difference( X, Y, Z ) = set_difference( Y
% 0.71/1.09    , Z ) }.
% 0.71/1.09  (628) {G0,W3,D2,L1,V1,M1}  { subset( X, X ) }.
% 0.71/1.09  (629) {G0,W2,D2,L1,V0,M1}  { ! empty( skol11 ) }.
% 0.71/1.09  (630) {G0,W2,D2,L1,V0,M1}  { preboolean( skol11 ) }.
% 0.71/1.09  (631) {G0,W3,D2,L1,V0,M1}  { ! in( empty_set, skol11 ) }.
% 0.71/1.09  (632) {G0,W6,D2,L2,V2,M2}  { ! in( X, Y ), element( X, Y ) }.
% 0.71/1.09  (633) {G0,W8,D2,L3,V2,M3}  { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.71/1.09  (634) {G0,W8,D3,L2,V2,M2}  { ! set_difference( X, Y ) = empty_set, subset( 
% 0.71/1.09    X, Y ) }.
% 0.71/1.09  (635) {G0,W8,D3,L2,V2,M2}  { ! subset( X, Y ), set_difference( X, Y ) = 
% 0.71/1.09    empty_set }.
% 0.71/1.09  (636) {G0,W5,D3,L1,V1,M1}  { set_difference( X, empty_set ) = X }.
% 0.71/1.09  (637) {G0,W7,D3,L2,V2,M2}  { ! element( X, powerset( Y ) ), subset( X, Y )
% 0.71/1.09     }.
% 0.71/1.09  (638) {G0,W7,D3,L2,V2,M2}  { ! subset( X, Y ), element( X, powerset( Y ) )
% 0.71/1.09     }.
% 0.71/1.09  (639) {G0,W5,D3,L1,V1,M1}  { set_difference( empty_set, X ) = empty_set }.
% 0.71/1.09  (640) {G0,W10,D3,L3,V3,M3}  { ! in( X, Z ), ! element( Z, powerset( Y ) ), 
% 0.71/1.09    element( X, Y ) }.
% 0.71/1.09  (641) {G0,W9,D3,L3,V3,M3}  { ! in( X, Y ), ! element( Y, powerset( Z ) ), !
% 0.71/1.09     empty( Z ) }.
% 0.71/1.09  (642) {G0,W5,D2,L2,V1,M2}  { ! empty( X ), X = empty_set }.
% 0.71/1.09  (643) {G0,W5,D2,L2,V2,M2}  { ! in( X, Y ), ! empty( Y ) }.
% 0.71/1.09  (644) {G0,W7,D2,L3,V2,M3}  { ! empty( X ), X = Y, ! empty( Y ) }.
% 0.71/1.09  
% 0.71/1.09  
% 0.71/1.09  Total Proof:
% 0.71/1.09  
% 0.71/1.09  subsumption: (6) {G0,W16,D3,L5,V3,M5} I { empty( X ), ! preboolean( X ), ! 
% 0.71/1.09    element( Y, X ), ! element( Z, X ), element( prebool_difference( X, Y, Z
% 0.71/1.09     ), X ) }.
% 0.71/1.09  parent0: (593) {G0,W16,D3,L5,V3,M5}  { empty( X ), ! preboolean( X ), ! 
% 0.71/1.09    element( Y, X ), ! element( Z, X ), element( prebool_difference( X, Y, Z
% 0.71/1.09     ), X ) }.
% 0.71/1.09  substitution0:
% 0.71/1.09     X := X
% 0.71/1.09     Y := Y
% 0.71/1.09     Z := Z
% 0.71/1.09  end
% 0.71/1.09  permutation0:
% 0.71/1.09     0 ==> 0
% 0.71/1.09     1 ==> 1
% 0.71/1.09     2 ==> 2
% 0.71/1.09     3 ==> 3
% 0.71/1.09     4 ==> 4
% 0.71/1.09  end
% 0.71/1.09  
% 0.71/1.09  subsumption: (7) {G0,W4,D3,L1,V1,M1} I { element( skol1( X ), X ) }.
% 0.71/1.09  parent0: (594) {G0,W4,D3,L1,V1,M1}  { element( skol1( X ), X ) }.
% 0.71/1.09  substitution0:
% 0.71/1.09     X := X
% 0.71/1.09  end
% 0.71/1.09  permutation0:
% 0.71/1.09     0 ==> 0
% 0.71/1.09  end
% 0.71/1.09  
% 0.71/1.09  subsumption: (40) {G0,W18,D3,L5,V3,M5} I { empty( X ), ! preboolean( X ), !
% 0.71/1.09     element( Y, X ), ! element( Z, X ), prebool_difference( X, Y, Z ) ==> 
% 0.71/1.09    set_difference( Y, Z ) }.
% 0.71/1.09  parent0: (627) {G0,W18,D3,L5,V3,M5}  { empty( X ), ! preboolean( X ), ! 
% 0.71/1.09    element( Y, X ), ! element( Z, X ), prebool_difference( X, Y, Z ) = 
% 0.71/1.09    set_difference( Y, Z ) }.
% 0.71/1.09  substitution0:
% 0.71/1.09     X := X
% 0.71/1.09     Y := Y
% 0.71/1.09     Z := Z
% 0.71/1.09  end
% 0.71/1.09  permutation0:
% 0.71/1.09     0 ==> 0
% 0.71/1.09     1 ==> 1
% 0.71/1.09     2 ==> 2
% 0.71/1.09     3 ==> 3
% 0.71/1.09     4 ==> 4
% 0.71/1.09  end
% 0.71/1.09  
% 0.71/1.09  subsumption: (41) {G0,W3,D2,L1,V1,M1} I { subset( X, X ) }.
% 0.71/1.09  parent0: (628) {G0,W3,D2,L1,V1,M1}  { subset( X, X ) }.
% 0.71/1.09  substitution0:
% 0.71/1.09     X := X
% 0.71/1.09  end
% 0.71/1.09  permutation0:
% 0.71/1.09     0 ==> 0
% 0.71/1.09  end
% 0.71/1.09  
% 0.71/1.09  subsumption: (42) {G0,W2,D2,L1,V0,M1} I { ! empty( skol11 ) }.
% 0.71/1.09  parent0: (629) {G0,W2,D2,L1,V0,M1}  { ! empty( skol11 ) }.
% 0.71/1.09  substitution0:
% 0.71/1.09  end
% 0.71/1.09  permutation0:
% 0.71/1.09     0 ==> 0
% 0.71/1.09  end
% 0.71/1.09  
% 0.71/1.09  subsumption: (43) {G0,W2,D2,L1,V0,M1} I { preboolean( skol11 ) }.
% 0.71/1.09  parent0: (630) {G0,W2,D2,L1,V0,M1}  { preboolean( skol11 ) }.
% 0.71/1.09  substitution0:
% 0.71/1.09  end
% 0.71/1.09  permutation0:
% 0.71/1.09     0 ==> 0
% 0.71/1.09  end
% 0.71/1.09  
% 0.71/1.09  subsumption: (44) {G0,W3,D2,L1,V0,M1} I { ! in( empty_set, skol11 ) }.
% 0.71/1.09  parent0: (631) {G0,W3,D2,L1,V0,M1}  { ! in( empty_set, skol11 ) }.
% 0.71/1.09  substitution0:
% 0.71/1.09  end
% 0.71/1.09  permutation0:
% 0.71/1.09     0 ==> 0
% 0.71/1.09  end
% 0.71/1.09  
% 0.71/1.09  subsumption: (46) {G0,W8,D2,L3,V2,M3} I { ! element( X, Y ), empty( Y ), in
% 0.71/1.09    ( X, Y ) }.
% 0.71/1.09  parent0: (633) {G0,W8,D2,L3,V2,M3}  { ! element( X, Y ), empty( Y ), in( X
% 0.71/1.09    , Y ) }.
% 0.71/1.09  substitution0:
% 0.71/1.09     X := X
% 0.71/1.09     Y := Y
% 0.71/1.09  end
% 0.71/1.09  permutation0:
% 0.71/1.09     0 ==> 0
% 0.71/1.09     1 ==> 1
% 0.71/1.09     2 ==> 2
% 0.71/1.09  end
% 0.71/1.09  
% 0.71/1.09  subsumption: (48) {G0,W8,D3,L2,V2,M2} I { ! subset( X, Y ), set_difference
% 0.71/1.09    ( X, Y ) ==> empty_set }.
% 0.71/1.09  parent0: (635) {G0,W8,D3,L2,V2,M2}  { ! subset( X, Y ), set_difference( X, 
% 0.71/1.09    Y ) = empty_set }.
% 0.71/1.09  substitution0:
% 0.71/1.09     X := X
% 0.71/1.09     Y := Y
% 0.71/1.09  end
% 0.71/1.09  permutation0:
% 0.71/1.09     0 ==> 0
% 0.71/1.09     1 ==> 1
% 0.71/1.09  end
% 0.71/1.09  
% 0.71/1.09  paramod: (695) {G1,W25,D3,L9,V3,M9}  { element( set_difference( Y, Z ), X )
% 0.71/1.09    , empty( X ), ! preboolean( X ), ! element( Y, X ), ! element( Z, X ), 
% 0.71/1.09    empty( X ), ! preboolean( X ), ! element( Y, X ), ! element( Z, X ) }.
% 0.71/1.09  parent0[4]: (40) {G0,W18,D3,L5,V3,M5} I { empty( X ), ! preboolean( X ), ! 
% 0.71/1.09    element( Y, X ), ! element( Z, X ), prebool_difference( X, Y, Z ) ==> 
% 0.71/1.09    set_difference( Y, Z ) }.
% 0.71/1.09  parent1[4; 1]: (6) {G0,W16,D3,L5,V3,M5} I { empty( X ), ! preboolean( X ), 
% 0.71/1.09    ! element( Y, X ), ! element( Z, X ), element( prebool_difference( X, Y, 
% 0.71/1.09    Z ), X ) }.
% 0.71/1.09  substitution0:
% 0.71/1.09     X := X
% 0.71/1.09     Y := Y
% 0.71/1.09     Z := Z
% 0.71/1.09  end
% 0.71/1.09  substitution1:
% 0.71/1.09     X := X
% 0.71/1.09     Y := Y
% 0.71/1.09     Z := Z
% 0.71/1.09  end
% 0.71/1.09  
% 0.71/1.09  factor: (698) {G1,W22,D3,L8,V3,M8}  { element( set_difference( X, Y ), Z )
% 0.71/1.09    , empty( Z ), ! preboolean( Z ), ! element( X, Z ), ! element( Y, Z ), 
% 0.71/1.09    empty( Z ), ! preboolean( Z ), ! element( Y, Z ) }.
% 0.71/1.09  parent0[3, 7]: (695) {G1,W25,D3,L9,V3,M9}  { element( set_difference( Y, Z
% 0.71/1.09     ), X ), empty( X ), ! preboolean( X ), ! element( Y, X ), ! element( Z, 
% 0.71/1.09    X ), empty( X ), ! preboolean( X ), ! element( Y, X ), ! element( Z, X )
% 0.71/1.09     }.
% 0.71/1.09  substitution0:
% 0.71/1.09     X := Z
% 0.71/1.09     Y := X
% 0.71/1.09     Z := Y
% 0.71/1.09  end
% 0.71/1.09  
% 0.71/1.09  factor: (701) {G1,W19,D3,L7,V3,M7}  { element( set_difference( X, Y ), Z )
% 0.71/1.09    , empty( Z ), ! preboolean( Z ), ! element( X, Z ), ! element( Y, Z ), 
% 0.71/1.09    empty( Z ), ! preboolean( Z ) }.
% 0.71/1.09  parent0[4, 7]: (698) {G1,W22,D3,L8,V3,M8}  { element( set_difference( X, Y
% 0.71/1.09     ), Z ), empty( Z ), ! preboolean( Z ), ! element( X, Z ), ! element( Y, 
% 0.71/1.09    Z ), empty( Z ), ! preboolean( Z ), ! element( Y, Z ) }.
% 0.71/1.09  substitution0:
% 0.71/1.09     X := X
% 0.71/1.09     Y := Y
% 0.71/1.09     Z := Z
% 0.71/1.09  end
% 0.71/1.09  
% 0.71/1.09  factor: (702) {G1,W17,D3,L6,V3,M6}  { element( set_difference( X, Y ), Z )
% 0.71/1.09    , empty( Z ), ! preboolean( Z ), ! element( X, Z ), ! element( Y, Z ), ! 
% 0.71/1.09    preboolean( Z ) }.
% 0.71/1.09  parent0[1, 5]: (701) {G1,W19,D3,L7,V3,M7}  { element( set_difference( X, Y
% 0.71/1.09     ), Z ), empty( Z ), ! preboolean( Z ), ! element( X, Z ), ! element( Y, 
% 0.71/1.09    Z ), empty( Z ), ! preboolean( Z ) }.
% 0.71/1.09  substitution0:
% 0.71/1.09     X := X
% 0.71/1.09     Y := Y
% 0.71/1.09     Z := Z
% 0.71/1.09  end
% 0.71/1.09  
% 0.71/1.09  factor: (706) {G1,W15,D3,L5,V3,M5}  { element( set_difference( X, Y ), Z )
% 0.71/1.09    , empty( Z ), ! preboolean( Z ), ! element( X, Z ), ! element( Y, Z ) }.
% 0.71/1.09  parent0[2, 5]: (702) {G1,W17,D3,L6,V3,M6}  { element( set_difference( X, Y
% 0.71/1.09     ), Z ), empty( Z ), ! preboolean( Z ), ! element( X, Z ), ! element( Y, 
% 0.71/1.09    Z ), ! preboolean( Z ) }.
% 0.71/1.09  substitution0:
% 0.71/1.09     X := X
% 0.71/1.09     Y := Y
% 0.71/1.09     Z := Z
% 0.71/1.09  end
% 0.71/1.09  
% 0.71/1.09  subsumption: (73) {G1,W15,D3,L5,V3,M5} S(6);d(40) { empty( X ), ! 
% 0.71/1.09    preboolean( X ), ! element( Y, X ), ! element( Z, X ), element( 
% 0.71/1.09    set_difference( Y, Z ), X ) }.
% 0.71/1.09  parent0: (706) {G1,W15,D3,L5,V3,M5}  { element( set_difference( X, Y ), Z )
% 0.71/1.09    , empty( Z ), ! preboolean( Z ), ! element( X, Z ), ! element( Y, Z ) }.
% 0.71/1.09  substitution0:
% 0.71/1.09     X := Y
% 0.71/1.09     Y := Z
% 0.71/1.09     Z := X
% 0.71/1.09  end
% 0.71/1.09  permutation0:
% 0.71/1.09     0 ==> 4
% 0.71/1.09     1 ==> 0
% 0.71/1.09     2 ==> 1
% 0.71/1.09     3 ==> 2
% 0.71/1.09     4 ==> 3
% 0.71/1.09  end
% 0.71/1.09  
% 0.71/1.09  resolution: (707) {G1,W5,D2,L2,V0,M2}  { ! element( empty_set, skol11 ), 
% 0.71/1.09    empty( skol11 ) }.
% 0.71/1.09  parent0[0]: (44) {G0,W3,D2,L1,V0,M1} I { ! in( empty_set, skol11 ) }.
% 0.71/1.09  parent1[2]: (46) {G0,W8,D2,L3,V2,M3} I { ! element( X, Y ), empty( Y ), in
% 0.71/1.09    ( X, Y ) }.
% 0.71/1.09  substitution0:
% 0.71/1.09  end
% 0.71/1.09  substitution1:
% 0.71/1.09     X := empty_set
% 0.71/1.09     Y := skol11
% 0.71/1.09  end
% 0.71/1.09  
% 0.71/1.09  resolution: (708) {G1,W3,D2,L1,V0,M1}  { ! element( empty_set, skol11 ) }.
% 0.71/1.09  parent0[0]: (42) {G0,W2,D2,L1,V0,M1} I { ! empty( skol11 ) }.
% 0.71/1.09  parent1[1]: (707) {G1,W5,D2,L2,V0,M2}  { ! element( empty_set, skol11 ), 
% 0.71/1.09    empty( skol11 ) }.
% 0.71/1.09  substitution0:
% 0.71/1.09  end
% 0.71/1.09  substitution1:
% 0.71/1.09  end
% 0.71/1.09  
% 0.71/1.09  subsumption: (270) {G1,W3,D2,L1,V0,M1} R(46,44);r(42) { ! element( 
% 0.71/1.09    empty_set, skol11 ) }.
% 0.71/1.09  parent0: (708) {G1,W3,D2,L1,V0,M1}  { ! element( empty_set, skol11 ) }.
% 0.71/1.09  substitution0:
% 0.71/1.09  end
% 0.71/1.09  permutation0:
% 0.71/1.09     0 ==> 0
% 0.71/1.09  end
% 0.71/1.09  
% 0.71/1.09  eqswap: (709) {G0,W8,D3,L2,V2,M2}  { empty_set ==> set_difference( X, Y ), 
% 0.71/1.09    ! subset( X, Y ) }.
% 0.71/1.09  parent0[1]: (48) {G0,W8,D3,L2,V2,M2} I { ! subset( X, Y ), set_difference( 
% 0.71/1.09    X, Y ) ==> empty_set }.
% 0.71/1.09  substitution0:
% 0.71/1.09     X := X
% 0.71/1.09     Y := Y
% 0.71/1.09  end
% 0.71/1.09  
% 0.71/1.09  resolution: (710) {G1,W5,D3,L1,V1,M1}  { empty_set ==> set_difference( X, X
% 0.71/1.09     ) }.
% 0.71/1.09  parent0[1]: (709) {G0,W8,D3,L2,V2,M2}  { empty_set ==> set_difference( X, Y
% 0.71/1.09     ), ! subset( X, Y ) }.
% 0.71/1.09  parent1[0]: (41) {G0,W3,D2,L1,V1,M1} I { subset( X, X ) }.
% 0.71/1.09  substitution0:
% 0.71/1.09     X := X
% 0.71/1.09     Y := X
% 0.71/1.09  end
% 0.71/1.09  substitution1:
% 0.71/1.09     X := X
% 0.71/1.09  end
% 0.71/1.09  
% 0.71/1.09  eqswap: (711) {G1,W5,D3,L1,V1,M1}  { set_difference( X, X ) ==> empty_set
% 0.71/1.09     }.
% 0.71/1.09  parent0[0]: (710) {G1,W5,D3,L1,V1,M1}  { empty_set ==> set_difference( X, X
% 0.71/1.09     ) }.
% 0.71/1.09  substitution0:
% 0.71/1.09     X := X
% 0.71/1.09  end
% 0.71/1.09  
% 0.71/1.09  subsumption: (318) {G1,W5,D3,L1,V1,M1} R(48,41) { set_difference( X, X ) 
% 0.71/1.09    ==> empty_set }.
% 0.71/1.09  parent0: (711) {G1,W5,D3,L1,V1,M1}  { set_difference( X, X ) ==> empty_set
% 0.71/1.09     }.
% 0.71/1.09  substitution0:
% 0.71/1.09     X := X
% 0.71/1.09  end
% 0.71/1.09  permutation0:
% 0.71/1.09     0 ==> 0
% 0.71/1.09  end
% 0.71/1.09  
% 0.71/1.09  resolution: (712) {G1,W13,D3,L4,V2,M4}  { ! preboolean( skol11 ), ! element
% 0.71/1.09    ( X, skol11 ), ! element( Y, skol11 ), element( set_difference( X, Y ), 
% 0.71/1.09    skol11 ) }.
% 0.71/1.09  parent0[0]: (42) {G0,W2,D2,L1,V0,M1} I { ! empty( skol11 ) }.
% 0.71/1.09  parent1[0]: (73) {G1,W15,D3,L5,V3,M5} S(6);d(40) { empty( X ), ! preboolean
% 0.71/1.09    ( X ), ! element( Y, X ), ! element( Z, X ), element( set_difference( Y, 
% 0.71/1.09    Z ), X ) }.
% 0.71/1.09  substitution0:
% 0.71/1.09  end
% 0.71/1.09  substitution1:
% 0.71/1.09     X := skol11
% 0.71/1.09     Y := X
% 0.71/1.09     Z := Y
% 0.71/1.09  end
% 0.71/1.09  
% 0.71/1.09  resolution: (715) {G1,W11,D3,L3,V2,M3}  { ! element( X, skol11 ), ! element
% 0.71/1.09    ( Y, skol11 ), element( set_difference( X, Y ), skol11 ) }.
% 0.71/1.09  parent0[0]: (712) {G1,W13,D3,L4,V2,M4}  { ! preboolean( skol11 ), ! element
% 0.71/1.09    ( X, skol11 ), ! element( Y, skol11 ), element( set_difference( X, Y ), 
% 0.71/1.09    skol11 ) }.
% 0.71/1.09  parent1[0]: (43) {G0,W2,D2,L1,V0,M1} I { preboolean( skol11 ) }.
% 0.71/1.09  substitution0:
% 0.71/1.09     X := X
% 0.71/1.09     Y := Y
% 0.71/1.09  end
% 0.71/1.09  substitution1:
% 0.71/1.09  end
% 0.71/1.09  
% 0.71/1.09  subsumption: (569) {G2,W11,D3,L3,V2,M3} R(73,42);r(43) { ! element( X, 
% 0.71/1.09    skol11 ), ! element( Y, skol11 ), element( set_difference( X, Y ), skol11
% 0.71/1.09     ) }.
% 0.71/1.09  parent0: (715) {G1,W11,D3,L3,V2,M3}  { ! element( X, skol11 ), ! element( Y
% 0.71/1.09    , skol11 ), element( set_difference( X, Y ), skol11 ) }.
% 0.71/1.09  substitution0:
% 0.71/1.09     X := X
% 0.71/1.09     Y := Y
% 0.71/1.09  end
% 0.71/1.09  permutation0:
% 0.71/1.09     0 ==> 0
% 0.71/1.09     1 ==> 1
% 0.71/1.09     2 ==> 2
% 0.71/1.09  end
% 0.71/1.09  
% 0.71/1.09  factor: (718) {G2,W8,D3,L2,V1,M2}  { ! element( X, skol11 ), element( 
% 0.71/1.09    set_difference( X, X ), skol11 ) }.
% 0.71/1.09  parent0[0, 1]: (569) {G2,W11,D3,L3,V2,M3} R(73,42);r(43) { ! element( X, 
% 0.71/1.09    skol11 ), ! element( Y, skol11 ), element( set_difference( X, Y ), skol11
% 0.71/1.09     ) }.
% 0.71/1.09  substitution0:
% 0.71/1.09     X := X
% 0.71/1.09     Y := X
% 0.71/1.09  end
% 0.71/1.09  
% 0.71/1.09  paramod: (719) {G2,W6,D2,L2,V1,M2}  { element( empty_set, skol11 ), ! 
% 0.71/1.09    element( X, skol11 ) }.
% 0.71/1.09  parent0[0]: (318) {G1,W5,D3,L1,V1,M1} R(48,41) { set_difference( X, X ) ==>
% 0.71/1.09     empty_set }.
% 0.71/1.09  parent1[1; 1]: (718) {G2,W8,D3,L2,V1,M2}  { ! element( X, skol11 ), element
% 0.71/1.09    ( set_difference( X, X ), skol11 ) }.
% 0.71/1.09  substitution0:
% 0.71/1.09     X := X
% 0.71/1.09  end
% 0.71/1.09  substitution1:
% 0.71/1.09     X := X
% 0.71/1.09  end
% 0.71/1.09  
% 0.71/1.09  resolution: (720) {G2,W3,D2,L1,V1,M1}  { ! element( X, skol11 ) }.
% 0.71/1.09  parent0[0]: (270) {G1,W3,D2,L1,V0,M1} R(46,44);r(42) { ! element( empty_set
% 0.71/1.09    , skol11 ) }.
% 0.71/1.09  parent1[0]: (719) {G2,W6,D2,L2,V1,M2}  { element( empty_set, skol11 ), ! 
% 0.71/1.09    element( X, skol11 ) }.
% 0.71/1.09  substitution0:
% 0.71/1.09  end
% 0.71/1.09  substitution1:
% 0.71/1.09     X := X
% 0.71/1.09  end
% 0.71/1.09  
% 0.71/1.09  subsumption: (570) {G3,W3,D2,L1,V1,M1} F(569);d(318);r(270) { ! element( X
% 0.71/1.09    , skol11 ) }.
% 0.71/1.09  parent0: (720) {G2,W3,D2,L1,V1,M1}  { ! element( X, skol11 ) }.
% 0.71/1.09  substitution0:
% 0.71/1.09     X := X
% 0.71/1.09  end
% 0.71/1.09  permutation0:
% 0.71/1.09     0 ==> 0
% 0.71/1.09  end
% 0.71/1.09  
% 0.71/1.09  resolution: (721) {G1,W0,D0,L0,V0,M0}  {  }.
% 0.71/1.09  parent0[0]: (570) {G3,W3,D2,L1,V1,M1} F(569);d(318);r(270) { ! element( X, 
% 0.71/1.09    skol11 ) }.
% 0.71/1.09  parent1[0]: (7) {G0,W4,D3,L1,V1,M1} I { element( skol1( X ), X ) }.
% 0.71/1.09  substitution0:
% 0.71/1.09     X := skol1( skol11 )
% 0.71/1.09  end
% 0.71/1.09  substitution1:
% 0.71/1.09     X := skol11
% 0.71/1.09  end
% 0.71/1.09  
% 0.71/1.09  subsumption: (585) {G4,W0,D0,L0,V0,M0} R(570,7) {  }.
% 0.71/1.09  parent0: (721) {G1,W0,D0,L0,V0,M0}  {  }.
% 0.71/1.09  substitution0:
% 0.71/1.09  end
% 0.71/1.09  permutation0:
% 0.71/1.09  end
% 0.71/1.09  
% 0.71/1.09  Proof check complete!
% 0.71/1.09  
% 0.71/1.09  Memory use:
% 0.71/1.09  
% 0.71/1.09  space for terms:        6286
% 0.71/1.09  space for clauses:      29779
% 0.71/1.09  
% 0.71/1.09  
% 0.71/1.09  clauses generated:      2002
% 0.71/1.09  clauses kept:           586
% 0.71/1.09  clauses selected:       178
% 0.71/1.09  clauses deleted:        14
% 0.71/1.09  clauses inuse deleted:  0
% 0.71/1.09  
% 0.71/1.09  subsentry:          2901
% 0.71/1.09  literals s-matched: 2205
% 0.71/1.09  literals matched:   2067
% 0.71/1.09  full subsumption:   271
% 0.71/1.09  
% 0.71/1.09  checksum:           2041367567
% 0.71/1.09  
% 0.71/1.09  
% 0.71/1.09  Bliksem ended
%------------------------------------------------------------------------------