TSTP Solution File: NUM383+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : NUM383+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n023.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 : Mon Jul 18 06:21:51 EDT 2022
% Result : Theorem 0.47s 1.12s
% Output : Refutation 0.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM383+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : bliksem %s
% 0.14/0.34 % Computer : n023.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % DateTime : Thu Jul 7 00:58:56 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.47/1.12 *** allocated 10000 integers for termspace/termends
% 0.47/1.12 *** allocated 10000 integers for clauses
% 0.47/1.12 *** allocated 10000 integers for justifications
% 0.47/1.12 Bliksem 1.12
% 0.47/1.12
% 0.47/1.12
% 0.47/1.12 Automatic Strategy Selection
% 0.47/1.12
% 0.47/1.12
% 0.47/1.12 Clauses:
% 0.47/1.12
% 0.47/1.12 { ! in( X, Y ), ! in( Y, X ) }.
% 0.47/1.12 { ! empty( X ), function( X ) }.
% 0.47/1.12 { ! empty( X ), relation( X ) }.
% 0.47/1.12 { ! relation( X ), ! empty( X ), ! function( X ), relation( X ) }.
% 0.47/1.12 { ! relation( X ), ! empty( X ), ! function( X ), function( X ) }.
% 0.47/1.12 { ! relation( X ), ! empty( X ), ! function( X ), one_to_one( X ) }.
% 0.47/1.12 { element( skol1( X ), X ) }.
% 0.47/1.12 { empty( empty_set ) }.
% 0.47/1.12 { relation( empty_set ) }.
% 0.47/1.12 { relation_empty_yielding( empty_set ) }.
% 0.47/1.12 { empty( empty_set ) }.
% 0.47/1.12 { empty( empty_set ) }.
% 0.47/1.12 { relation( empty_set ) }.
% 0.47/1.12 { relation( skol2 ) }.
% 0.47/1.12 { function( skol2 ) }.
% 0.47/1.12 { empty( skol3 ) }.
% 0.47/1.12 { relation( skol3 ) }.
% 0.47/1.12 { empty( skol4 ) }.
% 0.47/1.12 { relation( skol5 ) }.
% 0.47/1.12 { empty( skol5 ) }.
% 0.47/1.12 { function( skol5 ) }.
% 0.47/1.12 { ! empty( skol6 ) }.
% 0.47/1.12 { relation( skol6 ) }.
% 0.47/1.12 { ! empty( skol7 ) }.
% 0.47/1.12 { relation( skol8 ) }.
% 0.47/1.12 { function( skol8 ) }.
% 0.47/1.12 { one_to_one( skol8 ) }.
% 0.47/1.12 { relation( skol9 ) }.
% 0.47/1.12 { relation_empty_yielding( skol9 ) }.
% 0.47/1.12 { relation( skol10 ) }.
% 0.47/1.12 { relation_empty_yielding( skol10 ) }.
% 0.47/1.12 { function( skol10 ) }.
% 0.47/1.12 { relation( skol11 ) }.
% 0.47/1.12 { relation_non_empty( skol11 ) }.
% 0.47/1.12 { function( skol11 ) }.
% 0.47/1.12 { subset( X, X ) }.
% 0.47/1.12 { ! in( X, Y ), element( X, Y ) }.
% 0.47/1.12 { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.47/1.12 { ! element( X, powerset( Y ) ), subset( X, Y ) }.
% 0.47/1.12 { ! subset( X, Y ), element( X, powerset( Y ) ) }.
% 0.47/1.12 { ! in( X, Z ), ! element( Z, powerset( Y ) ), element( X, Y ) }.
% 0.47/1.12 { ! in( X, Y ), ! element( Y, powerset( Z ) ), ! empty( Z ) }.
% 0.47/1.12 { ! empty( X ), X = empty_set }.
% 0.47/1.12 { ! in( X, Y ), ! empty( Y ) }.
% 0.47/1.12 { in( skol12, skol13 ) }.
% 0.47/1.12 { subset( skol13, skol12 ) }.
% 0.47/1.12 { ! empty( X ), X = Y, ! empty( Y ) }.
% 0.47/1.12
% 0.47/1.12 percentage equality = 0.032787, percentage horn = 0.976190
% 0.47/1.12 This is a problem with some equality
% 0.47/1.12
% 0.47/1.12
% 0.47/1.12
% 0.47/1.12 Options Used:
% 0.47/1.12
% 0.47/1.12 useres = 1
% 0.47/1.12 useparamod = 1
% 0.47/1.12 useeqrefl = 1
% 0.47/1.12 useeqfact = 1
% 0.47/1.12 usefactor = 1
% 0.47/1.12 usesimpsplitting = 0
% 0.47/1.12 usesimpdemod = 5
% 0.47/1.12 usesimpres = 3
% 0.47/1.12
% 0.47/1.12 resimpinuse = 1000
% 0.47/1.12 resimpclauses = 20000
% 0.47/1.12 substype = eqrewr
% 0.47/1.12 backwardsubs = 1
% 0.47/1.12 selectoldest = 5
% 0.47/1.12
% 0.47/1.12 litorderings [0] = split
% 0.47/1.12 litorderings [1] = extend the termordering, first sorting on arguments
% 0.47/1.12
% 0.47/1.12 termordering = kbo
% 0.47/1.12
% 0.47/1.12 litapriori = 0
% 0.47/1.12 termapriori = 1
% 0.47/1.12 litaposteriori = 0
% 0.47/1.12 termaposteriori = 0
% 0.47/1.12 demodaposteriori = 0
% 0.47/1.12 ordereqreflfact = 0
% 0.47/1.12
% 0.47/1.12 litselect = negord
% 0.47/1.12
% 0.47/1.12 maxweight = 15
% 0.47/1.12 maxdepth = 30000
% 0.47/1.12 maxlength = 115
% 0.47/1.12 maxnrvars = 195
% 0.47/1.12 excuselevel = 1
% 0.47/1.12 increasemaxweight = 1
% 0.47/1.12
% 0.47/1.12 maxselected = 10000000
% 0.47/1.12 maxnrclauses = 10000000
% 0.47/1.12
% 0.47/1.12 showgenerated = 0
% 0.47/1.12 showkept = 0
% 0.47/1.12 showselected = 0
% 0.47/1.12 showdeleted = 0
% 0.47/1.12 showresimp = 1
% 0.47/1.12 showstatus = 2000
% 0.47/1.12
% 0.47/1.12 prologoutput = 0
% 0.47/1.12 nrgoals = 5000000
% 0.47/1.12 totalproof = 1
% 0.47/1.12
% 0.47/1.12 Symbols occurring in the translation:
% 0.47/1.12
% 0.47/1.12 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.47/1.12 . [1, 2] (w:1, o:35, a:1, s:1, b:0),
% 0.47/1.12 ! [4, 1] (w:0, o:22, a:1, s:1, b:0),
% 0.47/1.12 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.47/1.12 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.47/1.12 in [37, 2] (w:1, o:59, a:1, s:1, b:0),
% 0.47/1.12 empty [38, 1] (w:1, o:27, a:1, s:1, b:0),
% 0.47/1.12 function [39, 1] (w:1, o:28, a:1, s:1, b:0),
% 0.47/1.12 relation [40, 1] (w:1, o:29, a:1, s:1, b:0),
% 0.47/1.12 one_to_one [41, 1] (w:1, o:30, a:1, s:1, b:0),
% 0.47/1.12 element [42, 2] (w:1, o:60, a:1, s:1, b:0),
% 0.47/1.12 empty_set [43, 0] (w:1, o:8, a:1, s:1, b:0),
% 0.47/1.12 relation_empty_yielding [44, 1] (w:1, o:31, a:1, s:1, b:0),
% 0.47/1.12 relation_non_empty [45, 1] (w:1, o:32, a:1, s:1, b:0),
% 0.47/1.12 subset [46, 2] (w:1, o:61, a:1, s:1, b:0),
% 0.47/1.12 powerset [47, 1] (w:1, o:33, a:1, s:1, b:0),
% 0.47/1.12 skol1 [49, 1] (w:1, o:34, a:1, s:1, b:1),
% 0.47/1.12 skol2 [50, 0] (w:1, o:14, a:1, s:1, b:1),
% 0.47/1.12 skol3 [51, 0] (w:1, o:15, a:1, s:1, b:1),
% 0.47/1.12 skol4 [52, 0] (w:1, o:16, a:1, s:1, b:1),
% 0.47/1.12 skol5 [53, 0] (w:1, o:17, a:1, s:1, b:1),
% 0.47/1.12 skol6 [54, 0] (w:1, o:18, a:1, s:1, b:1),
% 0.47/1.12 skol7 [55, 0] (w:1, o:19, a:1, s:1, b:1),
% 0.47/1.12 skol8 [56, 0] (w:1, o:20, a:1, s:1, b:1),
% 0.47/1.12 skol9 [57, 0] (w:1, o:21, a:1, s:1, b:1),
% 0.47/1.12 skol10 [58, 0] (w:1, o:10, a:1, s:1, b:1),
% 0.47/1.12 skol11 [59, 0] (w:1, o:11, a:1, s:1, b:1),
% 0.47/1.12 skol12 [60, 0] (w:1, o:12, a:1, s:1, b:1),
% 0.47/1.12 skol13 [61, 0] (w:1, o:13, a:1, s:1, b:1).
% 0.47/1.12
% 0.47/1.12
% 0.47/1.12 Starting Search:
% 0.47/1.12
% 0.47/1.12 *** allocated 15000 integers for clauses
% 0.47/1.12
% 0.47/1.12 Bliksems!, er is een bewijs:
% 0.47/1.12 % SZS status Theorem
% 0.47/1.12 % SZS output start Refutation
% 0.47/1.12
% 0.47/1.12 (0) {G0,W6,D2,L2,V2,M2} I { ! in( X, Y ), ! in( Y, X ) }.
% 0.47/1.12 (4) {G0,W4,D3,L1,V1,M1} I { element( skol1( X ), X ) }.
% 0.47/1.12 (5) {G0,W2,D2,L1,V0,M1} I { empty( empty_set ) }.
% 0.47/1.12 (32) {G0,W8,D2,L3,V2,M3} I { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.47/1.12 (34) {G0,W7,D3,L2,V2,M2} I { ! subset( X, Y ), element( X, powerset( Y ) )
% 0.47/1.12 }.
% 0.47/1.12 (35) {G0,W10,D3,L3,V3,M3} I { ! in( X, Z ), ! element( Z, powerset( Y ) ),
% 0.47/1.12 element( X, Y ) }.
% 0.47/1.12 (36) {G0,W9,D3,L3,V3,M3} I { ! in( X, Y ), ! element( Y, powerset( Z ) ), !
% 0.47/1.12 empty( Z ) }.
% 0.47/1.12 (37) {G0,W5,D2,L2,V1,M2} I { ! empty( X ), X = empty_set }.
% 0.47/1.12 (38) {G0,W5,D2,L2,V2,M2} I { ! in( X, Y ), ! empty( Y ) }.
% 0.47/1.12 (39) {G0,W3,D2,L1,V0,M1} I { in( skol12, skol13 ) }.
% 0.47/1.12 (40) {G0,W3,D2,L1,V0,M1} I { subset( skol13, skol12 ) }.
% 0.47/1.12 (42) {G1,W3,D2,L1,V1,M1} F(0) { ! in( X, X ) }.
% 0.47/1.12 (50) {G2,W5,D2,L2,V1,M2} R(32,42) { ! element( X, X ), empty( X ) }.
% 0.47/1.12 (51) {G1,W6,D3,L2,V1,M2} R(32,4) { empty( X ), in( skol1( X ), X ) }.
% 0.47/1.12 (67) {G1,W3,D2,L1,V1,M1} R(38,5) { ! in( X, empty_set ) }.
% 0.47/1.12 (73) {G1,W4,D3,L1,V0,M1} R(34,40) { element( skol13, powerset( skol12 ) )
% 0.47/1.12 }.
% 0.47/1.12 (84) {G2,W6,D2,L2,V1,M2} R(73,35) { ! in( X, skol13 ), element( X, skol12 )
% 0.47/1.12 }.
% 0.47/1.12 (97) {G2,W5,D2,L2,V1,M2} R(36,73) { ! in( X, skol13 ), ! empty( skol12 )
% 0.47/1.12 }.
% 0.47/1.12 (114) {G3,W2,D2,L1,V0,M1} R(97,39) { ! empty( skol12 ) }.
% 0.47/1.12 (117) {G3,W6,D2,L2,V1,M2} R(37,50) { X = empty_set, ! element( X, X ) }.
% 0.47/1.12 (153) {G4,W4,D3,L1,V0,M1} R(51,114) { in( skol1( skol12 ), skol12 ) }.
% 0.47/1.12 (313) {G4,W3,D2,L1,V0,M1} R(84,117);r(39) { skol12 ==> empty_set }.
% 0.47/1.12 (324) {G5,W0,D0,L0,V0,M0} P(313,153);r(67) { }.
% 0.47/1.12
% 0.47/1.12
% 0.47/1.12 % SZS output end Refutation
% 0.47/1.12 found a proof!
% 0.47/1.12
% 0.47/1.12 *** allocated 22500 integers for clauses
% 0.47/1.12
% 0.47/1.12 Unprocessed initial clauses:
% 0.47/1.12
% 0.47/1.12 (326) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), ! in( Y, X ) }.
% 0.47/1.12 (327) {G0,W4,D2,L2,V1,M2} { ! empty( X ), function( X ) }.
% 0.47/1.12 (328) {G0,W4,D2,L2,V1,M2} { ! empty( X ), relation( X ) }.
% 0.47/1.12 (329) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X )
% 0.47/1.12 , relation( X ) }.
% 0.47/1.12 (330) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X )
% 0.47/1.12 , function( X ) }.
% 0.47/1.12 (331) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X )
% 0.47/1.12 , one_to_one( X ) }.
% 0.47/1.12 (332) {G0,W4,D3,L1,V1,M1} { element( skol1( X ), X ) }.
% 0.47/1.12 (333) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.47/1.12 (334) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 0.47/1.12 (335) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( empty_set ) }.
% 0.47/1.12 (336) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.47/1.12 (337) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.47/1.12 (338) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 0.47/1.12 (339) {G0,W2,D2,L1,V0,M1} { relation( skol2 ) }.
% 0.47/1.12 (340) {G0,W2,D2,L1,V0,M1} { function( skol2 ) }.
% 0.47/1.12 (341) {G0,W2,D2,L1,V0,M1} { empty( skol3 ) }.
% 0.47/1.12 (342) {G0,W2,D2,L1,V0,M1} { relation( skol3 ) }.
% 0.47/1.12 (343) {G0,W2,D2,L1,V0,M1} { empty( skol4 ) }.
% 0.47/1.12 (344) {G0,W2,D2,L1,V0,M1} { relation( skol5 ) }.
% 0.47/1.12 (345) {G0,W2,D2,L1,V0,M1} { empty( skol5 ) }.
% 0.47/1.12 (346) {G0,W2,D2,L1,V0,M1} { function( skol5 ) }.
% 0.47/1.12 (347) {G0,W2,D2,L1,V0,M1} { ! empty( skol6 ) }.
% 0.47/1.12 (348) {G0,W2,D2,L1,V0,M1} { relation( skol6 ) }.
% 0.47/1.12 (349) {G0,W2,D2,L1,V0,M1} { ! empty( skol7 ) }.
% 0.47/1.12 (350) {G0,W2,D2,L1,V0,M1} { relation( skol8 ) }.
% 0.47/1.12 (351) {G0,W2,D2,L1,V0,M1} { function( skol8 ) }.
% 0.47/1.12 (352) {G0,W2,D2,L1,V0,M1} { one_to_one( skol8 ) }.
% 0.47/1.12 (353) {G0,W2,D2,L1,V0,M1} { relation( skol9 ) }.
% 0.47/1.12 (354) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( skol9 ) }.
% 0.47/1.12 (355) {G0,W2,D2,L1,V0,M1} { relation( skol10 ) }.
% 0.47/1.12 (356) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( skol10 ) }.
% 0.47/1.12 (357) {G0,W2,D2,L1,V0,M1} { function( skol10 ) }.
% 0.47/1.12 (358) {G0,W2,D2,L1,V0,M1} { relation( skol11 ) }.
% 0.47/1.12 (359) {G0,W2,D2,L1,V0,M1} { relation_non_empty( skol11 ) }.
% 0.47/1.12 (360) {G0,W2,D2,L1,V0,M1} { function( skol11 ) }.
% 0.47/1.12 (361) {G0,W3,D2,L1,V1,M1} { subset( X, X ) }.
% 0.47/1.12 (362) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), element( X, Y ) }.
% 0.47/1.12 (363) {G0,W8,D2,L3,V2,M3} { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.47/1.12 (364) {G0,W7,D3,L2,V2,M2} { ! element( X, powerset( Y ) ), subset( X, Y )
% 0.47/1.12 }.
% 0.47/1.12 (365) {G0,W7,D3,L2,V2,M2} { ! subset( X, Y ), element( X, powerset( Y ) )
% 0.47/1.12 }.
% 0.47/1.12 (366) {G0,W10,D3,L3,V3,M3} { ! in( X, Z ), ! element( Z, powerset( Y ) ),
% 0.47/1.12 element( X, Y ) }.
% 0.47/1.12 (367) {G0,W9,D3,L3,V3,M3} { ! in( X, Y ), ! element( Y, powerset( Z ) ), !
% 0.47/1.12 empty( Z ) }.
% 0.47/1.12 (368) {G0,W5,D2,L2,V1,M2} { ! empty( X ), X = empty_set }.
% 0.47/1.12 (369) {G0,W5,D2,L2,V2,M2} { ! in( X, Y ), ! empty( Y ) }.
% 0.47/1.12 (370) {G0,W3,D2,L1,V0,M1} { in( skol12, skol13 ) }.
% 0.47/1.12 (371) {G0,W3,D2,L1,V0,M1} { subset( skol13, skol12 ) }.
% 0.47/1.12 (372) {G0,W7,D2,L3,V2,M3} { ! empty( X ), X = Y, ! empty( Y ) }.
% 0.47/1.12
% 0.47/1.12
% 0.47/1.12 Total Proof:
% 0.47/1.12
% 0.47/1.12 subsumption: (0) {G0,W6,D2,L2,V2,M2} I { ! in( X, Y ), ! in( Y, X ) }.
% 0.47/1.12 parent0: (326) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), ! in( Y, X ) }.
% 0.47/1.12 substitution0:
% 0.47/1.12 X := X
% 0.47/1.12 Y := Y
% 0.47/1.12 end
% 0.47/1.12 permutation0:
% 0.47/1.12 0 ==> 0
% 0.47/1.12 1 ==> 1
% 0.47/1.12 end
% 0.47/1.12
% 0.47/1.12 subsumption: (4) {G0,W4,D3,L1,V1,M1} I { element( skol1( X ), X ) }.
% 0.47/1.12 parent0: (332) {G0,W4,D3,L1,V1,M1} { element( skol1( X ), X ) }.
% 0.47/1.12 substitution0:
% 0.47/1.12 X := X
% 0.47/1.12 end
% 0.47/1.12 permutation0:
% 0.47/1.12 0 ==> 0
% 0.47/1.12 end
% 0.47/1.12
% 0.47/1.12 subsumption: (5) {G0,W2,D2,L1,V0,M1} I { empty( empty_set ) }.
% 0.47/1.12 parent0: (333) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.47/1.12 substitution0:
% 0.47/1.12 end
% 0.47/1.12 permutation0:
% 0.47/1.12 0 ==> 0
% 0.47/1.12 end
% 0.47/1.12
% 0.47/1.12 subsumption: (32) {G0,W8,D2,L3,V2,M3} I { ! element( X, Y ), empty( Y ), in
% 0.47/1.12 ( X, Y ) }.
% 0.47/1.12 parent0: (363) {G0,W8,D2,L3,V2,M3} { ! element( X, Y ), empty( Y ), in( X
% 0.47/1.12 , Y ) }.
% 0.47/1.12 substitution0:
% 0.47/1.12 X := X
% 0.47/1.12 Y := Y
% 0.47/1.12 end
% 0.47/1.12 permutation0:
% 0.47/1.12 0 ==> 0
% 0.47/1.12 1 ==> 1
% 0.47/1.12 2 ==> 2
% 0.47/1.12 end
% 0.47/1.12
% 0.47/1.12 subsumption: (34) {G0,W7,D3,L2,V2,M2} I { ! subset( X, Y ), element( X,
% 0.47/1.12 powerset( Y ) ) }.
% 0.47/1.12 parent0: (365) {G0,W7,D3,L2,V2,M2} { ! subset( X, Y ), element( X,
% 0.47/1.12 powerset( Y ) ) }.
% 0.47/1.12 substitution0:
% 0.47/1.12 X := X
% 0.47/1.12 Y := Y
% 0.47/1.12 end
% 0.47/1.12 permutation0:
% 0.47/1.12 0 ==> 0
% 0.47/1.12 1 ==> 1
% 0.47/1.12 end
% 0.47/1.12
% 0.47/1.12 subsumption: (35) {G0,W10,D3,L3,V3,M3} I { ! in( X, Z ), ! element( Z,
% 0.47/1.12 powerset( Y ) ), element( X, Y ) }.
% 0.47/1.12 parent0: (366) {G0,W10,D3,L3,V3,M3} { ! in( X, Z ), ! element( Z, powerset
% 0.47/1.12 ( Y ) ), element( X, Y ) }.
% 0.47/1.12 substitution0:
% 0.47/1.12 X := X
% 0.47/1.12 Y := Y
% 0.47/1.12 Z := Z
% 0.47/1.12 end
% 0.47/1.12 permutation0:
% 0.47/1.12 0 ==> 0
% 0.47/1.12 1 ==> 1
% 0.47/1.12 2 ==> 2
% 0.47/1.12 end
% 0.47/1.12
% 0.47/1.12 subsumption: (36) {G0,W9,D3,L3,V3,M3} I { ! in( X, Y ), ! element( Y,
% 0.47/1.12 powerset( Z ) ), ! empty( Z ) }.
% 0.47/1.12 parent0: (367) {G0,W9,D3,L3,V3,M3} { ! in( X, Y ), ! element( Y, powerset
% 0.47/1.12 ( Z ) ), ! empty( Z ) }.
% 0.47/1.12 substitution0:
% 0.47/1.12 X := X
% 0.47/1.12 Y := Y
% 0.47/1.12 Z := Z
% 0.47/1.12 end
% 0.47/1.12 permutation0:
% 0.47/1.12 0 ==> 0
% 0.47/1.12 1 ==> 1
% 0.47/1.12 2 ==> 2
% 0.47/1.12 end
% 0.47/1.12
% 0.47/1.12 subsumption: (37) {G0,W5,D2,L2,V1,M2} I { ! empty( X ), X = empty_set }.
% 0.47/1.12 parent0: (368) {G0,W5,D2,L2,V1,M2} { ! empty( X ), X = empty_set }.
% 0.47/1.12 substitution0:
% 0.47/1.12 X := X
% 0.47/1.12 end
% 0.47/1.12 permutation0:
% 0.47/1.12 0 ==> 0
% 0.47/1.12 1 ==> 1
% 0.47/1.12 end
% 0.47/1.12
% 0.47/1.12 subsumption: (38) {G0,W5,D2,L2,V2,M2} I { ! in( X, Y ), ! empty( Y ) }.
% 0.47/1.12 parent0: (369) {G0,W5,D2,L2,V2,M2} { ! in( X, Y ), ! empty( Y ) }.
% 0.47/1.12 substitution0:
% 0.47/1.12 X := X
% 0.47/1.12 Y := Y
% 0.47/1.12 end
% 0.47/1.12 permutation0:
% 0.47/1.12 0 ==> 0
% 0.47/1.12 1 ==> 1
% 0.47/1.12 end
% 0.47/1.12
% 0.47/1.12 subsumption: (39) {G0,W3,D2,L1,V0,M1} I { in( skol12, skol13 ) }.
% 0.47/1.12 parent0: (370) {G0,W3,D2,L1,V0,M1} { in( skol12, skol13 ) }.
% 0.47/1.12 substitution0:
% 0.47/1.12 end
% 0.47/1.12 permutation0:
% 0.47/1.12 0 ==> 0
% 0.47/1.12 end
% 0.47/1.12
% 0.47/1.12 subsumption: (40) {G0,W3,D2,L1,V0,M1} I { subset( skol13, skol12 ) }.
% 0.47/1.12 parent0: (371) {G0,W3,D2,L1,V0,M1} { subset( skol13, skol12 ) }.
% 0.47/1.12 substitution0:
% 0.47/1.12 end
% 0.47/1.12 permutation0:
% 0.47/1.12 0 ==> 0
% 0.47/1.12 end
% 0.47/1.12
% 0.47/1.12 factor: (388) {G0,W3,D2,L1,V1,M1} { ! in( X, X ) }.
% 0.47/1.12 parent0[0, 1]: (0) {G0,W6,D2,L2,V2,M2} I { ! in( X, Y ), ! in( Y, X ) }.
% 0.47/1.12 substitution0:
% 0.47/1.12 X := X
% 0.47/1.12 Y := X
% 0.47/1.12 end
% 0.47/1.12
% 0.47/1.12 subsumption: (42) {G1,W3,D2,L1,V1,M1} F(0) { ! in( X, X ) }.
% 0.47/1.12 parent0: (388) {G0,W3,D2,L1,V1,M1} { ! in( X, X ) }.
% 0.47/1.12 substitution0:
% 0.47/1.12 X := X
% 0.47/1.12 end
% 0.47/1.12 permutation0:
% 0.47/1.12 0 ==> 0
% 0.47/1.12 end
% 0.47/1.12
% 0.47/1.12 resolution: (389) {G1,W5,D2,L2,V1,M2} { ! element( X, X ), empty( X ) }.
% 0.47/1.12 parent0[0]: (42) {G1,W3,D2,L1,V1,M1} F(0) { ! in( X, X ) }.
% 0.47/1.12 parent1[2]: (32) {G0,W8,D2,L3,V2,M3} I { ! element( X, Y ), empty( Y ), in
% 0.47/1.12 ( X, Y ) }.
% 0.47/1.12 substitution0:
% 0.47/1.12 X := X
% 0.47/1.12 end
% 0.47/1.12 substitution1:
% 0.47/1.12 X := X
% 0.47/1.12 Y := X
% 0.47/1.12 end
% 0.47/1.12
% 0.47/1.12 subsumption: (50) {G2,W5,D2,L2,V1,M2} R(32,42) { ! element( X, X ), empty(
% 0.47/1.12 X ) }.
% 0.47/1.12 parent0: (389) {G1,W5,D2,L2,V1,M2} { ! element( X, X ), empty( X ) }.
% 0.47/1.12 substitution0:
% 0.47/1.12 X := X
% 0.47/1.12 end
% 0.47/1.12 permutation0:
% 0.47/1.12 0 ==> 0
% 0.47/1.12 1 ==> 1
% 0.47/1.12 end
% 0.47/1.12
% 0.47/1.12 resolution: (390) {G1,W6,D3,L2,V1,M2} { empty( X ), in( skol1( X ), X )
% 0.47/1.12 }.
% 0.47/1.12 parent0[0]: (32) {G0,W8,D2,L3,V2,M3} I { ! element( X, Y ), empty( Y ), in
% 0.47/1.12 ( X, Y ) }.
% 0.47/1.12 parent1[0]: (4) {G0,W4,D3,L1,V1,M1} I { element( skol1( X ), X ) }.
% 0.47/1.12 substitution0:
% 0.47/1.12 X := skol1( X )
% 0.47/1.12 Y := X
% 0.47/1.12 end
% 0.47/1.12 substitution1:
% 0.47/1.12 X := X
% 0.47/1.12 end
% 0.47/1.12
% 0.47/1.12 subsumption: (51) {G1,W6,D3,L2,V1,M2} R(32,4) { empty( X ), in( skol1( X )
% 0.47/1.12 , X ) }.
% 0.47/1.12 parent0: (390) {G1,W6,D3,L2,V1,M2} { empty( X ), in( skol1( X ), X ) }.
% 0.47/1.12 substitution0:
% 0.47/1.12 X := X
% 0.47/1.12 end
% 0.47/1.12 permutation0:
% 0.47/1.12 0 ==> 0
% 0.47/1.12 1 ==> 1
% 0.47/1.12 end
% 0.47/1.12
% 0.47/1.12 resolution: (391) {G1,W3,D2,L1,V1,M1} { ! in( X, empty_set ) }.
% 0.47/1.12 parent0[1]: (38) {G0,W5,D2,L2,V2,M2} I { ! in( X, Y ), ! empty( Y ) }.
% 0.47/1.12 parent1[0]: (5) {G0,W2,D2,L1,V0,M1} I { empty( empty_set ) }.
% 0.47/1.12 substitution0:
% 0.47/1.12 X := X
% 0.47/1.12 Y := empty_set
% 0.47/1.12 end
% 0.47/1.12 substitution1:
% 0.47/1.12 end
% 0.47/1.12
% 0.47/1.12 subsumption: (67) {G1,W3,D2,L1,V1,M1} R(38,5) { ! in( X, empty_set ) }.
% 0.47/1.12 parent0: (391) {G1,W3,D2,L1,V1,M1} { ! in( X, empty_set ) }.
% 0.47/1.12 substitution0:
% 0.47/1.12 X := X
% 0.47/1.12 end
% 0.47/1.12 permutation0:
% 0.47/1.12 0 ==> 0
% 0.47/1.12 end
% 0.47/1.12
% 0.47/1.12 resolution: (392) {G1,W4,D3,L1,V0,M1} { element( skol13, powerset( skol12
% 0.47/1.12 ) ) }.
% 0.47/1.12 parent0[0]: (34) {G0,W7,D3,L2,V2,M2} I { ! subset( X, Y ), element( X,
% 0.47/1.12 powerset( Y ) ) }.
% 0.47/1.12 parent1[0]: (40) {G0,W3,D2,L1,V0,M1} I { subset( skol13, skol12 ) }.
% 0.47/1.12 substitution0:
% 0.47/1.12 X := skol13
% 0.47/1.12 Y := skol12
% 0.47/1.12 end
% 0.47/1.12 substitution1:
% 0.47/1.12 end
% 0.47/1.12
% 0.47/1.12 subsumption: (73) {G1,W4,D3,L1,V0,M1} R(34,40) { element( skol13, powerset
% 0.47/1.12 ( skol12 ) ) }.
% 0.47/1.12 parent0: (392) {G1,W4,D3,L1,V0,M1} { element( skol13, powerset( skol12 ) )
% 0.47/1.12 }.
% 0.47/1.12 substitution0:
% 0.47/1.12 end
% 0.47/1.12 permutation0:
% 0.47/1.12 0 ==> 0
% 0.47/1.12 end
% 0.47/1.12
% 0.47/1.12 resolution: (393) {G1,W6,D2,L2,V1,M2} { ! in( X, skol13 ), element( X,
% 0.47/1.12 skol12 ) }.
% 0.47/1.12 parent0[1]: (35) {G0,W10,D3,L3,V3,M3} I { ! in( X, Z ), ! element( Z,
% 0.47/1.12 powerset( Y ) ), element( X, Y ) }.
% 0.47/1.12 parent1[0]: (73) {G1,W4,D3,L1,V0,M1} R(34,40) { element( skol13, powerset(
% 0.47/1.12 skol12 ) ) }.
% 0.47/1.12 substitution0:
% 0.47/1.12 X := X
% 0.47/1.12 Y := skol12
% 0.47/1.12 Z := skol13
% 0.47/1.12 end
% 0.47/1.12 substitution1:
% 0.47/1.12 end
% 0.47/1.12
% 0.47/1.12 subsumption: (84) {G2,W6,D2,L2,V1,M2} R(73,35) { ! in( X, skol13 ), element
% 0.47/1.12 ( X, skol12 ) }.
% 0.47/1.12 parent0: (393) {G1,W6,D2,L2,V1,M2} { ! in( X, skol13 ), element( X, skol12
% 0.47/1.12 ) }.
% 0.47/1.12 substitution0:
% 0.47/1.12 X := X
% 0.47/1.12 end
% 0.47/1.12 permutation0:
% 0.47/1.12 0 ==> 0
% 0.47/1.12 1 ==> 1
% 0.47/1.12 end
% 0.47/1.12
% 0.47/1.12 resolution: (394) {G1,W5,D2,L2,V1,M2} { ! in( X, skol13 ), ! empty( skol12
% 0.47/1.12 ) }.
% 0.47/1.12 parent0[1]: (36) {G0,W9,D3,L3,V3,M3} I { ! in( X, Y ), ! element( Y,
% 0.47/1.12 powerset( Z ) ), ! empty( Z ) }.
% 0.47/1.12 parent1[0]: (73) {G1,W4,D3,L1,V0,M1} R(34,40) { element( skol13, powerset(
% 0.47/1.12 skol12 ) ) }.
% 0.47/1.12 substitution0:
% 0.47/1.12 X := X
% 0.47/1.12 Y := skol13
% 0.47/1.12 Z := skol12
% 0.47/1.12 end
% 0.47/1.12 substitution1:
% 0.47/1.12 end
% 0.47/1.12
% 0.47/1.12 subsumption: (97) {G2,W5,D2,L2,V1,M2} R(36,73) { ! in( X, skol13 ), ! empty
% 0.47/1.12 ( skol12 ) }.
% 0.47/1.12 parent0: (394) {G1,W5,D2,L2,V1,M2} { ! in( X, skol13 ), ! empty( skol12 )
% 0.47/1.12 }.
% 0.47/1.12 substitution0:
% 0.47/1.12 X := X
% 0.47/1.12 end
% 0.47/1.12 permutation0:
% 0.47/1.12 0 ==> 0
% 0.47/1.12 1 ==> 1
% 0.47/1.12 end
% 0.47/1.12
% 0.47/1.12 resolution: (395) {G1,W2,D2,L1,V0,M1} { ! empty( skol12 ) }.
% 0.47/1.12 parent0[0]: (97) {G2,W5,D2,L2,V1,M2} R(36,73) { ! in( X, skol13 ), ! empty
% 0.47/1.12 ( skol12 ) }.
% 0.47/1.12 parent1[0]: (39) {G0,W3,D2,L1,V0,M1} I { in( skol12, skol13 ) }.
% 0.47/1.12 substitution0:
% 0.47/1.12 X := skol12
% 0.47/1.12 end
% 0.47/1.12 substitution1:
% 0.47/1.12 end
% 0.47/1.12
% 0.47/1.12 subsumption: (114) {G3,W2,D2,L1,V0,M1} R(97,39) { ! empty( skol12 ) }.
% 0.47/1.12 parent0: (395) {G1,W2,D2,L1,V0,M1} { ! empty( skol12 ) }.
% 0.47/1.12 substitution0:
% 0.47/1.12 end
% 0.47/1.12 permutation0:
% 0.47/1.12 0 ==> 0
% 0.47/1.12 end
% 0.47/1.12
% 0.47/1.12 eqswap: (396) {G0,W5,D2,L2,V1,M2} { empty_set = X, ! empty( X ) }.
% 0.47/1.12 parent0[1]: (37) {G0,W5,D2,L2,V1,M2} I { ! empty( X ), X = empty_set }.
% 0.47/1.12 substitution0:
% 0.47/1.12 X := X
% 0.47/1.12 end
% 0.47/1.12
% 0.47/1.12 resolution: (397) {G1,W6,D2,L2,V1,M2} { empty_set = X, ! element( X, X )
% 0.47/1.12 }.
% 0.47/1.12 parent0[1]: (396) {G0,W5,D2,L2,V1,M2} { empty_set = X, ! empty( X ) }.
% 0.47/1.12 parent1[1]: (50) {G2,W5,D2,L2,V1,M2} R(32,42) { ! element( X, X ), empty( X
% 0.47/1.12 ) }.
% 0.47/1.12 substitution0:
% 0.47/1.12 X := X
% 0.47/1.12 end
% 0.47/1.12 substitution1:
% 0.47/1.12 X := X
% 0.47/1.12 end
% 0.47/1.12
% 0.47/1.12 eqswap: (398) {G1,W6,D2,L2,V1,M2} { X = empty_set, ! element( X, X ) }.
% 0.47/1.12 parent0[0]: (397) {G1,W6,D2,L2,V1,M2} { empty_set = X, ! element( X, X )
% 0.47/1.12 }.
% 0.47/1.12 substitution0:
% 0.47/1.12 X := X
% 0.47/1.12 end
% 0.47/1.12
% 0.47/1.12 subsumption: (117) {G3,W6,D2,L2,V1,M2} R(37,50) { X = empty_set, ! element
% 0.47/1.12 ( X, X ) }.
% 0.47/1.12 parent0: (398) {G1,W6,D2,L2,V1,M2} { X = empty_set, ! element( X, X ) }.
% 0.47/1.12 substitution0:
% 0.47/1.12 X := X
% 0.47/1.12 end
% 0.47/1.12 permutation0:
% 0.47/1.12 0 ==> 0
% 0.47/1.12 1 ==> 1
% 0.47/1.12 end
% 0.47/1.12
% 0.47/1.12 resolution: (399) {G2,W4,D3,L1,V0,M1} { in( skol1( skol12 ), skol12 ) }.
% 0.47/1.12 parent0[0]: (114) {G3,W2,D2,L1,V0,M1} R(97,39) { ! empty( skol12 ) }.
% 0.47/1.12 parent1[0]: (51) {G1,W6,D3,L2,V1,M2} R(32,4) { empty( X ), in( skol1( X ),
% 0.47/1.12 X ) }.
% 0.47/1.12 substitution0:
% 0.47/1.12 end
% 0.47/1.12 substitution1:
% 0.47/1.12 X := skol12
% 0.47/1.12 end
% 0.47/1.12
% 0.47/1.12 subsumption: (153) {G4,W4,D3,L1,V0,M1} R(51,114) { in( skol1( skol12 ),
% 0.47/1.12 skol12 ) }.
% 0.47/1.12 parent0: (399) {G2,W4,D3,L1,V0,M1} { in( skol1( skol12 ), skol12 ) }.
% 0.47/1.12 substitution0:
% 0.47/1.12 end
% 0.47/1.12 permutation0:
% 0.47/1.12 0 ==> 0
% 0.47/1.12 end
% 0.47/1.12
% 0.47/1.12 eqswap: (400) {G3,W6,D2,L2,V1,M2} { empty_set = X, ! element( X, X ) }.
% 0.47/1.12 parent0[0]: (117) {G3,W6,D2,L2,V1,M2} R(37,50) { X = empty_set, ! element(
% 0.47/1.12 X, X ) }.
% 0.47/1.12 substitution0:
% 0.47/1.12 X := X
% 0.47/1.12 end
% 0.47/1.12
% 0.47/1.12 resolution: (401) {G3,W6,D2,L2,V0,M2} { empty_set = skol12, ! in( skol12,
% 0.47/1.12 skol13 ) }.
% 0.47/1.12 parent0[1]: (400) {G3,W6,D2,L2,V1,M2} { empty_set = X, ! element( X, X )
% 0.47/1.12 }.
% 0.47/1.12 parent1[1]: (84) {G2,W6,D2,L2,V1,M2} R(73,35) { ! in( X, skol13 ), element
% 0.47/1.12 ( X, skol12 ) }.
% 0.47/1.12 substitution0:
% 0.47/1.12 X := skol12
% 0.47/1.12 end
% 0.47/1.12 substitution1:
% 0.47/1.12 X := skol12
% 0.47/1.12 end
% 0.47/1.12
% 0.47/1.12 resolution: (402) {G1,W3,D2,L1,V0,M1} { empty_set = skol12 }.
% 0.47/1.12 parent0[1]: (401) {G3,W6,D2,L2,V0,M2} { empty_set = skol12, ! in( skol12,
% 0.47/1.12 skol13 ) }.
% 0.47/1.12 parent1[0]: (39) {G0,W3,D2,L1,V0,M1} I { in( skol12, skol13 ) }.
% 0.47/1.12 substitution0:
% 0.47/1.12 end
% 0.47/1.12 substitution1:
% 0.47/1.12 end
% 0.47/1.12
% 0.47/1.12 eqswap: (403) {G1,W3,D2,L1,V0,M1} { skol12 = empty_set }.
% 0.47/1.12 parent0[0]: (402) {G1,W3,D2,L1,V0,M1} { empty_set = skol12 }.
% 0.47/1.12 substitution0:
% 0.47/1.12 end
% 0.47/1.12
% 0.47/1.12 subsumption: (313) {G4,W3,D2,L1,V0,M1} R(84,117);r(39) { skol12 ==>
% 0.47/1.12 empty_set }.
% 0.47/1.12 parent0: (403) {G1,W3,D2,L1,V0,M1} { skol12 = empty_set }.
% 0.47/1.12 substitution0:
% 0.47/1.12 end
% 0.47/1.12 permutation0:
% 0.47/1.12 0 ==> 0
% 0.47/1.12 end
% 0.47/1.12
% 0.47/1.12 paramod: (406) {G5,W4,D3,L1,V0,M1} { in( skol1( skol12 ), empty_set ) }.
% 0.47/1.12 parent0[0]: (313) {G4,W3,D2,L1,V0,M1} R(84,117);r(39) { skol12 ==>
% 0.47/1.12 empty_set }.
% 0.47/1.12 parent1[0; 3]: (153) {G4,W4,D3,L1,V0,M1} R(51,114) { in( skol1( skol12 ),
% 0.47/1.12 skol12 ) }.
% 0.47/1.12 substitution0:
% 0.47/1.12 end
% 0.47/1.12 substitution1:
% 0.47/1.12 end
% 0.47/1.12
% 0.47/1.12 resolution: (408) {G2,W0,D0,L0,V0,M0} { }.
% 0.47/1.12 parent0[0]: (67) {G1,W3,D2,L1,V1,M1} R(38,5) { ! in( X, empty_set ) }.
% 0.47/1.12 parent1[0]: (406) {G5,W4,D3,L1,V0,M1} { in( skol1( skol12 ), empty_set )
% 0.47/1.12 }.
% 0.47/1.12 substitution0:
% 0.47/1.12 X := skol1( skol12 )
% 0.47/1.12 end
% 0.47/1.12 substitution1:
% 0.47/1.12 end
% 0.47/1.12
% 0.47/1.12 subsumption: (324) {G5,W0,D0,L0,V0,M0} P(313,153);r(67) { }.
% 0.47/1.12 parent0: (408) {G2,W0,D0,L0,V0,M0} { }.
% 0.47/1.12 substitution0:
% 0.47/1.12 end
% 0.47/1.12 permutation0:
% 0.47/1.12 end
% 0.47/1.12
% 0.47/1.12 Proof check complete!
% 0.47/1.12
% 0.47/1.12 Memory use:
% 0.47/1.12
% 0.47/1.12 space for terms: 3263
% 0.47/1.12 space for clauses: 14885
% 0.47/1.12
% 0.47/1.12
% 0.47/1.12 clauses generated: 1050
% 0.47/1.12 clauses kept: 325
% 0.47/1.12 clauses selected: 104
% 0.47/1.12 clauses deleted: 4
% 0.47/1.12 clauses inuse deleted: 0
% 0.47/1.12
% 0.47/1.12 subsentry: 1411
% 0.47/1.12 literals s-matched: 1142
% 0.47/1.12 literals matched: 1124
% 0.47/1.12 full subsumption: 155
% 0.47/1.12
% 0.47/1.12 checksum: 1341272587
% 0.47/1.12
% 0.47/1.12
% 0.47/1.12 Bliksem ended
%------------------------------------------------------------------------------