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