TSTP Solution File: SEU115+1 by Bliksem---1.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : SEU115+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n003.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 07:10:41 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
% 0.03/0.12  % Problem  : SEU115+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13  % Command  : bliksem %s
% 0.13/0.34  % Computer : n003.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % DateTime : Sun Jun 19 08:52:58 EDT 2022
% 0.13/0.34  % 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  { subset( X, X ) }.
% 0.71/1.09  { ! in( X, Y ), ! in( Y, X ) }.
% 0.71/1.09  { ! in( X, Y ), element( X, Y ) }.
% 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  { element( skol1( X ), X ) }.
% 0.71/1.09  { ! preboolean( X ), cup_closed( X ) }.
% 0.71/1.09  { ! preboolean( X ), diff_closed( X ) }.
% 0.71/1.09  { ! cup_closed( X ), ! diff_closed( X ), preboolean( X ) }.
% 0.71/1.09  { ! element( X, finite_subsets( Y ) ), finite( X ) }.
% 0.71/1.09  { ! empty( X ), finite( X ) }.
% 0.71/1.09  { ! finite( X ), ! element( Y, powerset( X ) ), finite( Y ) }.
% 0.71/1.09  { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 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  { ! in( X, Y ), ! empty( Y ) }.
% 0.71/1.09  { ! empty( X ), X = Y, ! empty( Y ) }.
% 0.71/1.09  { preboolean( finite_subsets( X ) ) }.
% 0.71/1.09  { ! empty( powerset( X ) ) }.
% 0.71/1.09  { cup_closed( powerset( X ) ) }.
% 0.71/1.09  { diff_closed( powerset( X ) ) }.
% 0.71/1.09  { preboolean( powerset( X ) ) }.
% 0.71/1.09  { ! empty( finite_subsets( X ) ) }.
% 0.71/1.09  { cup_closed( finite_subsets( X ) ) }.
% 0.71/1.09  { diff_closed( finite_subsets( X ) ) }.
% 0.71/1.09  { preboolean( finite_subsets( X ) ) }.
% 0.71/1.09  { ! empty( skol2 ) }.
% 0.71/1.09  { cup_closed( skol2 ) }.
% 0.71/1.09  { cap_closed( skol2 ) }.
% 0.71/1.09  { diff_closed( skol2 ) }.
% 0.71/1.09  { preboolean( skol2 ) }.
% 0.71/1.09  { ! empty( singleton( X ) ) }.
% 0.71/1.09  { finite( singleton( X ) ) }.
% 0.71/1.09  { ! empty( skol3 ) }.
% 0.71/1.09  { finite( skol3 ) }.
% 0.71/1.09  { empty( skol4( Y ) ) }.
% 0.71/1.09  { relation( skol4( Y ) ) }.
% 0.71/1.09  { function( skol4( Y ) ) }.
% 0.71/1.09  { one_to_one( skol4( Y ) ) }.
% 0.71/1.09  { epsilon_transitive( skol4( Y ) ) }.
% 0.71/1.09  { epsilon_connected( skol4( Y ) ) }.
% 0.71/1.09  { ordinal( skol4( Y ) ) }.
% 0.71/1.09  { natural( skol4( Y ) ) }.
% 0.71/1.09  { finite( skol4( Y ) ) }.
% 0.71/1.09  { element( skol4( X ), powerset( X ) ) }.
% 0.71/1.09  { empty( X ), ! empty( skol5( Y ) ) }.
% 0.71/1.09  { empty( X ), finite( skol5( Y ) ) }.
% 0.71/1.09  { empty( X ), element( skol5( X ), powerset( X ) ) }.
% 0.71/1.09  { empty( X ), ! empty( skol6( Y ) ) }.
% 0.71/1.09  { empty( X ), finite( skol6( Y ) ) }.
% 0.71/1.09  { empty( X ), element( skol6( X ), powerset( X ) ) }.
% 0.71/1.09  { ! empty( powerset( X ) ) }.
% 0.71/1.09  { ! empty( singleton( X ) ) }.
% 0.71/1.09  { empty( X ), ! empty( skol7( Y ) ) }.
% 0.71/1.09  { empty( X ), element( skol7( X ), powerset( X ) ) }.
% 0.71/1.09  { empty( skol8( Y ) ) }.
% 0.71/1.09  { element( skol8( X ), powerset( X ) ) }.
% 0.71/1.09  { empty( empty_set ) }.
% 0.71/1.09  { empty( skol9 ) }.
% 0.71/1.09  { ! empty( skol10 ) }.
% 0.71/1.09  { ! empty( X ), X = empty_set }.
% 0.71/1.09  { ! finite_subsets( empty_set ) = singleton( empty_set ) }.
% 0.71/1.09  { ! finite( X ), finite_subsets( X ) = powerset( X ) }.
% 0.71/1.09  { powerset( empty_set ) = singleton( empty_set ) }.
% 0.71/1.09  
% 0.71/1.09  percentage equality = 0.054348, percentage horn = 0.901639
% 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:41, a:1, s:1, b:0), 
% 0.71/1.09  !  [4, 1]      (w:0, o:14, 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  subset  [37, 2]      (w:1, o:65, a:1, s:1, b:0), 
% 0.71/1.09  in  [38, 2]      (w:1, o:66, a:1, s:1, b:0), 
% 0.71/1.09  element  [39, 2]      (w:1, o:67, a:1, s:1, b:0), 
% 0.71/1.09  powerset  [41, 1]      (w:1, o:22, a:1, s:1, b:0), 
% 0.71/1.09  empty  [42, 1]      (w:1, o:25, a:1, s:1, b:0), 
% 0.71/1.09  preboolean  [43, 1]      (w:1, o:26, a:1, s:1, b:0), 
% 0.71/1.09  cup_closed  [44, 1]      (w:1, o:27, a:1, s:1, b:0), 
% 0.71/1.09  diff_closed  [45, 1]      (w:1, o:24, a:1, s:1, b:0), 
% 0.71/1.09  finite_subsets  [46, 1]      (w:1, o:30, a:1, s:1, b:0), 
% 0.71/1.09  finite  [47, 1]      (w:1, o:31, a:1, s:1, b:0), 
% 0.71/1.09  cap_closed  [48, 1]      (w:1, o:23, a:1, s:1, b:0), 
% 0.71/1.09  singleton  [49, 1]      (w:1, o:33, 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:34, a:1, s:1, b:0), 
% 0.71/1.09  one_to_one  [52, 1]      (w:1, o:20, a:1, s:1, b:0), 
% 0.71/1.09  epsilon_transitive  [53, 1]      (w:1, o:28, a:1, s:1, b:0), 
% 0.71/1.09  epsilon_connected  [54, 1]      (w:1, o:29, a:1, s:1, b:0), 
% 0.71/1.09  ordinal  [55, 1]      (w:1, o:21, a:1, s:1, b:0), 
% 0.71/1.09  natural  [56, 1]      (w:1, o:19, a:1, s:1, b:0), 
% 0.71/1.09  empty_set  [57, 0]      (w:1, o:9, a:1, s:1, b:0), 
% 0.71/1.09  skol1  [58, 1]      (w:1, o:35, 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:36, a:1, s:1, b:1), 
% 0.71/1.09  skol5  [62, 1]      (w:1, o:37, a:1, s:1, b:1), 
% 0.71/1.09  skol6  [63, 1]      (w:1, o:38, a:1, s:1, b:1), 
% 0.71/1.09  skol7  [64, 1]      (w:1, o:39, a:1, s:1, b:1), 
% 0.71/1.09  skol8  [65, 1]      (w:1, o:40, a:1, s:1, b:1), 
% 0.71/1.09  skol9  [66, 0]      (w:1, o:13, a:1, s:1, b:1), 
% 0.71/1.09  skol10  [67, 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  
% 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  (10) {G0,W4,D2,L2,V1,M2} I { ! empty( X ), finite( X ) }.
% 0.71/1.09  (54) {G0,W2,D2,L1,V0,M1} I { empty( empty_set ) }.
% 0.71/1.09  (58) {G0,W5,D3,L1,V0,M1} I { ! singleton( empty_set ) ==> finite_subsets( 
% 0.71/1.09    empty_set ) }.
% 0.71/1.09  (59) {G0,W7,D3,L2,V1,M2} I { ! finite( X ), finite_subsets( X ) ==> 
% 0.71/1.09    powerset( X ) }.
% 0.71/1.09  (60) {G0,W5,D3,L1,V0,M1} I { singleton( empty_set ) ==> powerset( empty_set
% 0.71/1.09     ) }.
% 0.71/1.09  (73) {G1,W2,D2,L1,V0,M1} R(10,54) { finite( empty_set ) }.
% 0.71/1.09  (326) {G1,W5,D3,L1,V0,M1} S(58);d(60) { ! finite_subsets( empty_set ) ==> 
% 0.71/1.09    powerset( empty_set ) }.
% 0.71/1.09  (334) {G2,W0,D0,L0,V0,M0} R(59,326);r(73) {  }.
% 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  (336) {G0,W3,D2,L1,V1,M1}  { subset( X, X ) }.
% 0.71/1.09  (337) {G0,W6,D2,L2,V2,M2}  { ! in( X, Y ), ! in( Y, X ) }.
% 0.71/1.09  (338) {G0,W6,D2,L2,V2,M2}  { ! in( X, Y ), element( X, Y ) }.
% 0.71/1.09  (339) {G0,W10,D3,L3,V3,M3}  { ! in( X, Z ), ! element( Z, powerset( Y ) ), 
% 0.71/1.09    element( X, Y ) }.
% 0.71/1.09  (340) {G0,W9,D3,L3,V3,M3}  { ! in( X, Y ), ! element( Y, powerset( Z ) ), !
% 0.71/1.09     empty( Z ) }.
% 0.71/1.09  (341) {G0,W4,D3,L1,V1,M1}  { element( skol1( X ), X ) }.
% 0.71/1.09  (342) {G0,W4,D2,L2,V1,M2}  { ! preboolean( X ), cup_closed( X ) }.
% 0.71/1.09  (343) {G0,W4,D2,L2,V1,M2}  { ! preboolean( X ), diff_closed( X ) }.
% 0.71/1.09  (344) {G0,W6,D2,L3,V1,M3}  { ! cup_closed( X ), ! diff_closed( X ), 
% 0.71/1.09    preboolean( X ) }.
% 0.71/1.09  (345) {G0,W6,D3,L2,V2,M2}  { ! element( X, finite_subsets( Y ) ), finite( X
% 0.71/1.09     ) }.
% 0.71/1.09  (346) {G0,W4,D2,L2,V1,M2}  { ! empty( X ), finite( X ) }.
% 0.71/1.09  (347) {G0,W8,D3,L3,V2,M3}  { ! finite( X ), ! element( Y, powerset( X ) ), 
% 0.71/1.09    finite( Y ) }.
% 0.71/1.09  (348) {G0,W8,D2,L3,V2,M3}  { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.71/1.09  (349) {G0,W7,D3,L2,V2,M2}  { ! element( X, powerset( Y ) ), subset( X, Y )
% 0.71/1.09     }.
% 0.71/1.09  (350) {G0,W7,D3,L2,V2,M2}  { ! subset( X, Y ), element( X, powerset( Y ) )
% 0.71/1.09     }.
% 0.71/1.09  (351) {G0,W5,D2,L2,V2,M2}  { ! in( X, Y ), ! empty( Y ) }.
% 0.71/1.09  (352) {G0,W7,D2,L3,V2,M3}  { ! empty( X ), X = Y, ! empty( Y ) }.
% 0.71/1.09  (353) {G0,W3,D3,L1,V1,M1}  { preboolean( finite_subsets( X ) ) }.
% 0.71/1.09  (354) {G0,W3,D3,L1,V1,M1}  { ! empty( powerset( X ) ) }.
% 0.71/1.09  (355) {G0,W3,D3,L1,V1,M1}  { cup_closed( powerset( X ) ) }.
% 0.71/1.09  (356) {G0,W3,D3,L1,V1,M1}  { diff_closed( powerset( X ) ) }.
% 0.71/1.09  (357) {G0,W3,D3,L1,V1,M1}  { preboolean( powerset( X ) ) }.
% 0.71/1.09  (358) {G0,W3,D3,L1,V1,M1}  { ! empty( finite_subsets( X ) ) }.
% 0.71/1.09  (359) {G0,W3,D3,L1,V1,M1}  { cup_closed( finite_subsets( X ) ) }.
% 0.71/1.09  (360) {G0,W3,D3,L1,V1,M1}  { diff_closed( finite_subsets( X ) ) }.
% 0.71/1.09  (361) {G0,W3,D3,L1,V1,M1}  { preboolean( finite_subsets( X ) ) }.
% 0.71/1.09  (362) {G0,W2,D2,L1,V0,M1}  { ! empty( skol2 ) }.
% 0.71/1.09  (363) {G0,W2,D2,L1,V0,M1}  { cup_closed( skol2 ) }.
% 0.71/1.09  (364) {G0,W2,D2,L1,V0,M1}  { cap_closed( skol2 ) }.
% 0.71/1.09  (365) {G0,W2,D2,L1,V0,M1}  { diff_closed( skol2 ) }.
% 0.71/1.09  (366) {G0,W2,D2,L1,V0,M1}  { preboolean( skol2 ) }.
% 0.71/1.09  (367) {G0,W3,D3,L1,V1,M1}  { ! empty( singleton( X ) ) }.
% 0.71/1.09  (368) {G0,W3,D3,L1,V1,M1}  { finite( singleton( X ) ) }.
% 0.71/1.09  (369) {G0,W2,D2,L1,V0,M1}  { ! empty( skol3 ) }.
% 0.71/1.09  (370) {G0,W2,D2,L1,V0,M1}  { finite( skol3 ) }.
% 0.71/1.09  (371) {G0,W3,D3,L1,V1,M1}  { empty( skol4( Y ) ) }.
% 0.71/1.09  (372) {G0,W3,D3,L1,V1,M1}  { relation( skol4( Y ) ) }.
% 0.71/1.09  (373) {G0,W3,D3,L1,V1,M1}  { function( skol4( Y ) ) }.
% 0.71/1.09  (374) {G0,W3,D3,L1,V1,M1}  { one_to_one( skol4( Y ) ) }.
% 0.71/1.09  (375) {G0,W3,D3,L1,V1,M1}  { epsilon_transitive( skol4( Y ) ) }.
% 0.71/1.09  (376) {G0,W3,D3,L1,V1,M1}  { epsilon_connected( skol4( Y ) ) }.
% 0.71/1.09  (377) {G0,W3,D3,L1,V1,M1}  { ordinal( skol4( Y ) ) }.
% 0.71/1.09  (378) {G0,W3,D3,L1,V1,M1}  { natural( skol4( Y ) ) }.
% 0.71/1.09  (379) {G0,W3,D3,L1,V1,M1}  { finite( skol4( Y ) ) }.
% 0.71/1.09  (380) {G0,W5,D3,L1,V1,M1}  { element( skol4( X ), powerset( X ) ) }.
% 0.71/1.09  (381) {G0,W5,D3,L2,V2,M2}  { empty( X ), ! empty( skol5( Y ) ) }.
% 0.71/1.09  (382) {G0,W5,D3,L2,V2,M2}  { empty( X ), finite( skol5( Y ) ) }.
% 0.71/1.09  (383) {G0,W7,D3,L2,V1,M2}  { empty( X ), element( skol5( X ), powerset( X )
% 0.71/1.09     ) }.
% 0.71/1.09  (384) {G0,W5,D3,L2,V2,M2}  { empty( X ), ! empty( skol6( Y ) ) }.
% 0.71/1.09  (385) {G0,W5,D3,L2,V2,M2}  { empty( X ), finite( skol6( Y ) ) }.
% 0.71/1.09  (386) {G0,W7,D3,L2,V1,M2}  { empty( X ), element( skol6( X ), powerset( X )
% 0.71/1.09     ) }.
% 0.71/1.09  (387) {G0,W3,D3,L1,V1,M1}  { ! empty( powerset( X ) ) }.
% 0.71/1.09  (388) {G0,W3,D3,L1,V1,M1}  { ! empty( singleton( X ) ) }.
% 0.71/1.09  (389) {G0,W5,D3,L2,V2,M2}  { empty( X ), ! empty( skol7( Y ) ) }.
% 0.71/1.09  (390) {G0,W7,D3,L2,V1,M2}  { empty( X ), element( skol7( X ), powerset( X )
% 0.71/1.09     ) }.
% 0.71/1.09  (391) {G0,W3,D3,L1,V1,M1}  { empty( skol8( Y ) ) }.
% 0.71/1.09  (392) {G0,W5,D3,L1,V1,M1}  { element( skol8( X ), powerset( X ) ) }.
% 0.71/1.09  (393) {G0,W2,D2,L1,V0,M1}  { empty( empty_set ) }.
% 0.71/1.09  (394) {G0,W2,D2,L1,V0,M1}  { empty( skol9 ) }.
% 0.71/1.09  (395) {G0,W2,D2,L1,V0,M1}  { ! empty( skol10 ) }.
% 0.71/1.09  (396) {G0,W5,D2,L2,V1,M2}  { ! empty( X ), X = empty_set }.
% 0.71/1.09  (397) {G0,W5,D3,L1,V0,M1}  { ! finite_subsets( empty_set ) = singleton( 
% 0.71/1.09    empty_set ) }.
% 0.71/1.09  (398) {G0,W7,D3,L2,V1,M2}  { ! finite( X ), finite_subsets( X ) = powerset
% 0.71/1.09    ( X ) }.
% 0.71/1.09  (399) {G0,W5,D3,L1,V0,M1}  { powerset( empty_set ) = singleton( empty_set )
% 0.71/1.09     }.
% 0.71/1.09  
% 0.71/1.09  
% 0.71/1.09  Total Proof:
% 0.71/1.09  
% 0.71/1.09  subsumption: (10) {G0,W4,D2,L2,V1,M2} I { ! empty( X ), finite( X ) }.
% 0.71/1.09  parent0: (346) {G0,W4,D2,L2,V1,M2}  { ! empty( X ), finite( 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     1 ==> 1
% 0.71/1.09  end
% 0.71/1.09  
% 0.71/1.09  subsumption: (54) {G0,W2,D2,L1,V0,M1} I { empty( empty_set ) }.
% 0.71/1.09  parent0: (393) {G0,W2,D2,L1,V0,M1}  { empty( empty_set ) }.
% 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: (406) {G0,W5,D3,L1,V0,M1}  { ! singleton( empty_set ) = 
% 0.71/1.09    finite_subsets( empty_set ) }.
% 0.71/1.09  parent0[0]: (397) {G0,W5,D3,L1,V0,M1}  { ! finite_subsets( empty_set ) = 
% 0.71/1.09    singleton( empty_set ) }.
% 0.71/1.09  substitution0:
% 0.71/1.09  end
% 0.71/1.09  
% 0.71/1.09  subsumption: (58) {G0,W5,D3,L1,V0,M1} I { ! singleton( empty_set ) ==> 
% 0.71/1.09    finite_subsets( empty_set ) }.
% 0.71/1.09  parent0: (406) {G0,W5,D3,L1,V0,M1}  { ! singleton( empty_set ) = 
% 0.71/1.09    finite_subsets( empty_set ) }.
% 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: (59) {G0,W7,D3,L2,V1,M2} I { ! finite( X ), finite_subsets( X
% 0.71/1.09     ) ==> powerset( X ) }.
% 0.71/1.09  parent0: (398) {G0,W7,D3,L2,V1,M2}  { ! finite( X ), finite_subsets( X ) = 
% 0.71/1.09    powerset( 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     1 ==> 1
% 0.71/1.09  end
% 0.71/1.09  
% 0.71/1.09  eqswap: (417) {G0,W5,D3,L1,V0,M1}  { singleton( empty_set ) = powerset( 
% 0.71/1.09    empty_set ) }.
% 0.71/1.09  parent0[0]: (399) {G0,W5,D3,L1,V0,M1}  { powerset( empty_set ) = singleton
% 0.71/1.09    ( empty_set ) }.
% 0.71/1.09  substitution0:
% 0.71/1.09  end
% 0.71/1.09  
% 0.71/1.09  subsumption: (60) {G0,W5,D3,L1,V0,M1} I { singleton( empty_set ) ==> 
% 0.71/1.09    powerset( empty_set ) }.
% 0.71/1.09  parent0: (417) {G0,W5,D3,L1,V0,M1}  { singleton( empty_set ) = powerset( 
% 0.71/1.09    empty_set ) }.
% 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  resolution: (418) {G1,W2,D2,L1,V0,M1}  { finite( empty_set ) }.
% 0.71/1.09  parent0[0]: (10) {G0,W4,D2,L2,V1,M2} I { ! empty( X ), finite( X ) }.
% 0.71/1.09  parent1[0]: (54) {G0,W2,D2,L1,V0,M1} I { empty( empty_set ) }.
% 0.71/1.09  substitution0:
% 0.71/1.09     X := empty_set
% 0.71/1.09  end
% 0.71/1.09  substitution1:
% 0.71/1.09  end
% 0.71/1.09  
% 0.71/1.09  subsumption: (73) {G1,W2,D2,L1,V0,M1} R(10,54) { finite( empty_set ) }.
% 0.71/1.09  parent0: (418) {G1,W2,D2,L1,V0,M1}  { finite( empty_set ) }.
% 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  paramod: (421) {G1,W5,D3,L1,V0,M1}  { ! powerset( empty_set ) ==> 
% 0.71/1.09    finite_subsets( empty_set ) }.
% 0.71/1.09  parent0[0]: (60) {G0,W5,D3,L1,V0,M1} I { singleton( empty_set ) ==> 
% 0.71/1.09    powerset( empty_set ) }.
% 0.71/1.09  parent1[0; 2]: (58) {G0,W5,D3,L1,V0,M1} I { ! singleton( empty_set ) ==> 
% 0.71/1.09    finite_subsets( empty_set ) }.
% 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  eqswap: (422) {G1,W5,D3,L1,V0,M1}  { ! finite_subsets( empty_set ) ==> 
% 0.71/1.09    powerset( empty_set ) }.
% 0.71/1.09  parent0[0]: (421) {G1,W5,D3,L1,V0,M1}  { ! powerset( empty_set ) ==> 
% 0.71/1.09    finite_subsets( empty_set ) }.
% 0.71/1.09  substitution0:
% 0.71/1.09  end
% 0.71/1.09  
% 0.71/1.09  subsumption: (326) {G1,W5,D3,L1,V0,M1} S(58);d(60) { ! finite_subsets( 
% 0.71/1.09    empty_set ) ==> powerset( empty_set ) }.
% 0.71/1.09  parent0: (422) {G1,W5,D3,L1,V0,M1}  { ! finite_subsets( empty_set ) ==> 
% 0.71/1.09    powerset( empty_set ) }.
% 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: (423) {G0,W7,D3,L2,V1,M2}  { powerset( X ) ==> finite_subsets( X )
% 0.71/1.09    , ! finite( X ) }.
% 0.71/1.09  parent0[1]: (59) {G0,W7,D3,L2,V1,M2} I { ! finite( X ), finite_subsets( X )
% 0.71/1.09     ==> powerset( X ) }.
% 0.71/1.09  substitution0:
% 0.71/1.09     X := X
% 0.71/1.09  end
% 0.71/1.09  
% 0.71/1.09  eqswap: (424) {G1,W5,D3,L1,V0,M1}  { ! powerset( empty_set ) ==> 
% 0.71/1.09    finite_subsets( empty_set ) }.
% 0.71/1.09  parent0[0]: (326) {G1,W5,D3,L1,V0,M1} S(58);d(60) { ! finite_subsets( 
% 0.71/1.09    empty_set ) ==> powerset( empty_set ) }.
% 0.71/1.09  substitution0:
% 0.71/1.09  end
% 0.71/1.09  
% 0.71/1.09  resolution: (425) {G1,W2,D2,L1,V0,M1}  { ! finite( empty_set ) }.
% 0.71/1.09  parent0[0]: (424) {G1,W5,D3,L1,V0,M1}  { ! powerset( empty_set ) ==> 
% 0.71/1.09    finite_subsets( empty_set ) }.
% 0.71/1.09  parent1[0]: (423) {G0,W7,D3,L2,V1,M2}  { powerset( X ) ==> finite_subsets( 
% 0.71/1.09    X ), ! finite( X ) }.
% 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  end
% 0.71/1.09  
% 0.71/1.09  resolution: (426) {G2,W0,D0,L0,V0,M0}  {  }.
% 0.71/1.09  parent0[0]: (425) {G1,W2,D2,L1,V0,M1}  { ! finite( empty_set ) }.
% 0.71/1.09  parent1[0]: (73) {G1,W2,D2,L1,V0,M1} R(10,54) { finite( empty_set ) }.
% 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: (334) {G2,W0,D0,L0,V0,M0} R(59,326);r(73) {  }.
% 0.71/1.09  parent0: (426) {G2,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:        3243
% 0.71/1.09  space for clauses:      16553
% 0.71/1.09  
% 0.71/1.09  
% 0.71/1.09  clauses generated:      1046
% 0.71/1.09  clauses kept:           335
% 0.71/1.09  clauses selected:       128
% 0.71/1.09  clauses deleted:        3
% 0.71/1.09  clauses inuse deleted:  0
% 0.71/1.09  
% 0.71/1.09  subsentry:          1195
% 0.71/1.09  literals s-matched: 1014
% 0.71/1.09  literals matched:   1009
% 0.71/1.09  full subsumption:   101
% 0.71/1.09  
% 0.71/1.09  checksum:           -2144258227
% 0.71/1.09  
% 0.71/1.09  
% 0.71/1.09  Bliksem ended
%------------------------------------------------------------------------------