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