TSTP Solution File: SET929+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET929+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n027.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 22:53:27 EDT 2022
% Result : Theorem 0.72s 1.11s
% Output : Refutation 0.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET929+1 : TPTP v8.1.0. Released v3.2.0.
% 0.13/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n027.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 : Sat Jul 9 22:00:47 EDT 2022
% 0.21/0.34 % CPUTime :
% 0.72/1.11 *** allocated 10000 integers for termspace/termends
% 0.72/1.11 *** allocated 10000 integers for clauses
% 0.72/1.11 *** allocated 10000 integers for justifications
% 0.72/1.11 Bliksem 1.12
% 0.72/1.11
% 0.72/1.11
% 0.72/1.11 Automatic Strategy Selection
% 0.72/1.11
% 0.72/1.11
% 0.72/1.11 Clauses:
% 0.72/1.11
% 0.72/1.11 { ! in( X, Y ), ! in( Y, X ) }.
% 0.72/1.11 { unordered_pair( X, Y ) = unordered_pair( Y, X ) }.
% 0.72/1.11 { empty( empty_set ) }.
% 0.72/1.11 { empty( skol1 ) }.
% 0.72/1.11 { ! empty( skol2 ) }.
% 0.72/1.11 { subset( X, X ) }.
% 0.72/1.11 { ! set_difference( X, Y ) = empty_set, subset( X, Y ) }.
% 0.72/1.11 { ! subset( X, Y ), set_difference( X, Y ) = empty_set }.
% 0.72/1.11 { ! subset( unordered_pair( X, Y ), Z ), in( X, Z ) }.
% 0.72/1.11 { ! subset( unordered_pair( X, Y ), Z ), in( Y, Z ) }.
% 0.72/1.11 { ! in( X, Z ), ! in( Y, Z ), subset( unordered_pair( X, Y ), Z ) }.
% 0.72/1.11 { alpha1( skol3, skol4, skol5 ), in( skol3, skol5 ) }.
% 0.72/1.11 { alpha1( skol3, skol4, skol5 ), in( skol4, skol5 ) }.
% 0.72/1.11 { alpha1( skol3, skol4, skol5 ), ! set_difference( unordered_pair( skol3,
% 0.72/1.11 skol4 ), skol5 ) = empty_set }.
% 0.72/1.11 { ! alpha1( X, Y, Z ), set_difference( unordered_pair( X, Y ), Z ) =
% 0.72/1.11 empty_set }.
% 0.72/1.11 { ! alpha1( X, Y, Z ), ! in( X, Z ), ! in( Y, Z ) }.
% 0.72/1.11 { ! set_difference( unordered_pair( X, Y ), Z ) = empty_set, in( X, Z ),
% 0.72/1.11 alpha1( X, Y, Z ) }.
% 0.72/1.11 { ! set_difference( unordered_pair( X, Y ), Z ) = empty_set, in( Y, Z ),
% 0.72/1.11 alpha1( X, Y, Z ) }.
% 0.72/1.11
% 0.72/1.11 percentage equality = 0.200000, percentage horn = 0.777778
% 0.72/1.11 This is a problem with some equality
% 0.72/1.11
% 0.72/1.11
% 0.72/1.11
% 0.72/1.11 Options Used:
% 0.72/1.11
% 0.72/1.11 useres = 1
% 0.72/1.11 useparamod = 1
% 0.72/1.11 useeqrefl = 1
% 0.72/1.11 useeqfact = 1
% 0.72/1.11 usefactor = 1
% 0.72/1.11 usesimpsplitting = 0
% 0.72/1.11 usesimpdemod = 5
% 0.72/1.11 usesimpres = 3
% 0.72/1.11
% 0.72/1.11 resimpinuse = 1000
% 0.72/1.11 resimpclauses = 20000
% 0.72/1.11 substype = eqrewr
% 0.72/1.11 backwardsubs = 1
% 0.72/1.11 selectoldest = 5
% 0.72/1.11
% 0.72/1.11 litorderings [0] = split
% 0.72/1.11 litorderings [1] = extend the termordering, first sorting on arguments
% 0.72/1.11
% 0.72/1.11 termordering = kbo
% 0.72/1.11
% 0.72/1.11 litapriori = 0
% 0.72/1.11 termapriori = 1
% 0.72/1.11 litaposteriori = 0
% 0.72/1.11 termaposteriori = 0
% 0.72/1.11 demodaposteriori = 0
% 0.72/1.11 ordereqreflfact = 0
% 0.72/1.11
% 0.72/1.11 litselect = negord
% 0.72/1.11
% 0.72/1.11 maxweight = 15
% 0.72/1.11 maxdepth = 30000
% 0.72/1.11 maxlength = 115
% 0.72/1.11 maxnrvars = 195
% 0.72/1.11 excuselevel = 1
% 0.72/1.11 increasemaxweight = 1
% 0.72/1.11
% 0.72/1.11 maxselected = 10000000
% 0.72/1.11 maxnrclauses = 10000000
% 0.72/1.11
% 0.72/1.11 showgenerated = 0
% 0.72/1.11 showkept = 0
% 0.72/1.11 showselected = 0
% 0.72/1.11 showdeleted = 0
% 0.72/1.11 showresimp = 1
% 0.72/1.11 showstatus = 2000
% 0.72/1.11
% 0.72/1.11 prologoutput = 0
% 0.72/1.11 nrgoals = 5000000
% 0.72/1.11 totalproof = 1
% 0.72/1.11
% 0.72/1.11 Symbols occurring in the translation:
% 0.72/1.11
% 0.72/1.11 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.72/1.11 . [1, 2] (w:1, o:21, a:1, s:1, b:0),
% 0.72/1.11 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 0.72/1.11 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.72/1.11 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.72/1.11 in [37, 2] (w:1, o:45, a:1, s:1, b:0),
% 0.72/1.11 unordered_pair [38, 2] (w:1, o:46, a:1, s:1, b:0),
% 0.72/1.11 empty_set [39, 0] (w:1, o:8, a:1, s:1, b:0),
% 0.72/1.11 empty [40, 1] (w:1, o:20, a:1, s:1, b:0),
% 0.72/1.11 subset [41, 2] (w:1, o:47, a:1, s:1, b:0),
% 0.72/1.11 set_difference [42, 2] (w:1, o:48, a:1, s:1, b:0),
% 0.72/1.11 alpha1 [44, 3] (w:1, o:49, a:1, s:1, b:1),
% 0.72/1.11 skol1 [45, 0] (w:1, o:10, a:1, s:1, b:1),
% 0.72/1.11 skol2 [46, 0] (w:1, o:11, a:1, s:1, b:1),
% 0.72/1.11 skol3 [47, 0] (w:1, o:12, a:1, s:1, b:1),
% 0.72/1.11 skol4 [48, 0] (w:1, o:13, a:1, s:1, b:1),
% 0.72/1.11 skol5 [49, 0] (w:1, o:14, a:1, s:1, b:1).
% 0.72/1.11
% 0.72/1.11
% 0.72/1.11 Starting Search:
% 0.72/1.11
% 0.72/1.11
% 0.72/1.11 Bliksems!, er is een bewijs:
% 0.72/1.11 % SZS status Theorem
% 0.72/1.11 % SZS output start Refutation
% 0.72/1.11
% 0.72/1.11 (6) {G0,W8,D3,L2,V2,M2} I { ! set_difference( X, Y ) ==> empty_set, subset
% 0.72/1.11 ( X, Y ) }.
% 0.72/1.11 (7) {G0,W8,D3,L2,V2,M2} I { ! subset( X, Y ), set_difference( X, Y ) ==>
% 0.72/1.11 empty_set }.
% 0.72/1.11 (8) {G0,W8,D3,L2,V3,M2} I { ! subset( unordered_pair( X, Y ), Z ), in( X, Z
% 0.72/1.11 ) }.
% 0.72/1.11 (9) {G0,W8,D3,L2,V3,M2} I { ! subset( unordered_pair( X, Y ), Z ), in( Y, Z
% 0.72/1.11 ) }.
% 0.72/1.11 (10) {G0,W11,D3,L3,V3,M3} I { ! in( X, Z ), ! in( Y, Z ), subset(
% 0.72/1.11 unordered_pair( X, Y ), Z ) }.
% 0.72/1.11 (11) {G0,W7,D2,L2,V0,M2} I { alpha1( skol3, skol4, skol5 ), in( skol3,
% 0.72/1.11 skol5 ) }.
% 0.72/1.11 (12) {G0,W7,D2,L2,V0,M2} I { alpha1( skol3, skol4, skol5 ), in( skol4,
% 0.72/1.11 skol5 ) }.
% 0.72/1.11 (13) {G0,W11,D4,L2,V0,M2} I { alpha1( skol3, skol4, skol5 ), !
% 0.72/1.11 set_difference( unordered_pair( skol3, skol4 ), skol5 ) ==> empty_set }.
% 0.72/1.11 (14) {G0,W11,D4,L2,V3,M2} I { ! alpha1( X, Y, Z ), set_difference(
% 0.72/1.11 unordered_pair( X, Y ), Z ) ==> empty_set }.
% 0.72/1.11 (15) {G0,W10,D2,L3,V3,M3} I { ! alpha1( X, Y, Z ), ! in( X, Z ), ! in( Y, Z
% 0.72/1.11 ) }.
% 0.72/1.11 (31) {G1,W10,D4,L2,V3,M2} R(6,9) { ! set_difference( unordered_pair( X, Y )
% 0.72/1.11 , Z ) ==> empty_set, in( Y, Z ) }.
% 0.72/1.11 (45) {G1,W10,D4,L2,V3,M2} R(8,6) { in( X, Y ), ! set_difference(
% 0.72/1.11 unordered_pair( X, Z ), Y ) ==> empty_set }.
% 0.72/1.11 (57) {G1,W13,D4,L3,V3,M3} R(10,7) { ! in( X, Y ), ! in( Z, Y ),
% 0.72/1.11 set_difference( unordered_pair( X, Z ), Y ) ==> empty_set }.
% 0.72/1.11 (89) {G2,W3,D2,L1,V0,M1} R(14,11);r(45) { in( skol3, skol5 ) }.
% 0.72/1.11 (91) {G2,W3,D2,L1,V0,M1} R(14,12);r(31) { in( skol4, skol5 ) }.
% 0.72/1.11 (109) {G3,W3,D2,L1,V0,M1} R(15,13);d(57);q;r(89) { ! in( skol4, skol5 ) }.
% 0.72/1.11 (118) {G4,W0,D0,L0,V0,M0} S(109);r(91) { }.
% 0.72/1.11
% 0.72/1.11
% 0.72/1.11 % SZS output end Refutation
% 0.72/1.11 found a proof!
% 0.72/1.11
% 0.72/1.11
% 0.72/1.11 Unprocessed initial clauses:
% 0.72/1.11
% 0.72/1.11 (120) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), ! in( Y, X ) }.
% 0.72/1.11 (121) {G0,W7,D3,L1,V2,M1} { unordered_pair( X, Y ) = unordered_pair( Y, X
% 0.72/1.11 ) }.
% 0.72/1.11 (122) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.72/1.11 (123) {G0,W2,D2,L1,V0,M1} { empty( skol1 ) }.
% 0.72/1.11 (124) {G0,W2,D2,L1,V0,M1} { ! empty( skol2 ) }.
% 0.72/1.11 (125) {G0,W3,D2,L1,V1,M1} { subset( X, X ) }.
% 0.72/1.11 (126) {G0,W8,D3,L2,V2,M2} { ! set_difference( X, Y ) = empty_set, subset(
% 0.72/1.11 X, Y ) }.
% 0.72/1.11 (127) {G0,W8,D3,L2,V2,M2} { ! subset( X, Y ), set_difference( X, Y ) =
% 0.72/1.11 empty_set }.
% 0.72/1.11 (128) {G0,W8,D3,L2,V3,M2} { ! subset( unordered_pair( X, Y ), Z ), in( X,
% 0.72/1.11 Z ) }.
% 0.72/1.11 (129) {G0,W8,D3,L2,V3,M2} { ! subset( unordered_pair( X, Y ), Z ), in( Y,
% 0.72/1.11 Z ) }.
% 0.72/1.11 (130) {G0,W11,D3,L3,V3,M3} { ! in( X, Z ), ! in( Y, Z ), subset(
% 0.72/1.11 unordered_pair( X, Y ), Z ) }.
% 0.72/1.11 (131) {G0,W7,D2,L2,V0,M2} { alpha1( skol3, skol4, skol5 ), in( skol3,
% 0.72/1.11 skol5 ) }.
% 0.72/1.11 (132) {G0,W7,D2,L2,V0,M2} { alpha1( skol3, skol4, skol5 ), in( skol4,
% 0.72/1.11 skol5 ) }.
% 0.72/1.11 (133) {G0,W11,D4,L2,V0,M2} { alpha1( skol3, skol4, skol5 ), !
% 0.72/1.11 set_difference( unordered_pair( skol3, skol4 ), skol5 ) = empty_set }.
% 0.72/1.11 (134) {G0,W11,D4,L2,V3,M2} { ! alpha1( X, Y, Z ), set_difference(
% 0.72/1.11 unordered_pair( X, Y ), Z ) = empty_set }.
% 0.72/1.11 (135) {G0,W10,D2,L3,V3,M3} { ! alpha1( X, Y, Z ), ! in( X, Z ), ! in( Y, Z
% 0.72/1.11 ) }.
% 0.72/1.11 (136) {G0,W14,D4,L3,V3,M3} { ! set_difference( unordered_pair( X, Y ), Z )
% 0.72/1.11 = empty_set, in( X, Z ), alpha1( X, Y, Z ) }.
% 0.72/1.11 (137) {G0,W14,D4,L3,V3,M3} { ! set_difference( unordered_pair( X, Y ), Z )
% 0.72/1.11 = empty_set, in( Y, Z ), alpha1( X, Y, Z ) }.
% 0.72/1.11
% 0.72/1.11
% 0.72/1.11 Total Proof:
% 0.72/1.11
% 0.72/1.11 subsumption: (6) {G0,W8,D3,L2,V2,M2} I { ! set_difference( X, Y ) ==>
% 0.72/1.11 empty_set, subset( X, Y ) }.
% 0.72/1.11 parent0: (126) {G0,W8,D3,L2,V2,M2} { ! set_difference( X, Y ) = empty_set
% 0.72/1.11 , subset( X, Y ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := X
% 0.72/1.11 Y := Y
% 0.72/1.11 end
% 0.72/1.11 permutation0:
% 0.72/1.11 0 ==> 0
% 0.72/1.11 1 ==> 1
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 subsumption: (7) {G0,W8,D3,L2,V2,M2} I { ! subset( X, Y ), set_difference(
% 0.72/1.11 X, Y ) ==> empty_set }.
% 0.72/1.11 parent0: (127) {G0,W8,D3,L2,V2,M2} { ! subset( X, Y ), set_difference( X,
% 0.72/1.11 Y ) = empty_set }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := X
% 0.72/1.11 Y := Y
% 0.72/1.11 end
% 0.72/1.11 permutation0:
% 0.72/1.11 0 ==> 0
% 0.72/1.11 1 ==> 1
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 subsumption: (8) {G0,W8,D3,L2,V3,M2} I { ! subset( unordered_pair( X, Y ),
% 0.72/1.11 Z ), in( X, Z ) }.
% 0.72/1.11 parent0: (128) {G0,W8,D3,L2,V3,M2} { ! subset( unordered_pair( X, Y ), Z )
% 0.72/1.11 , in( X, Z ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := X
% 0.72/1.11 Y := Y
% 0.72/1.11 Z := Z
% 0.72/1.11 end
% 0.72/1.11 permutation0:
% 0.72/1.11 0 ==> 0
% 0.72/1.11 1 ==> 1
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 subsumption: (9) {G0,W8,D3,L2,V3,M2} I { ! subset( unordered_pair( X, Y ),
% 0.72/1.11 Z ), in( Y, Z ) }.
% 0.72/1.11 parent0: (129) {G0,W8,D3,L2,V3,M2} { ! subset( unordered_pair( X, Y ), Z )
% 0.72/1.11 , in( Y, Z ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := X
% 0.72/1.11 Y := Y
% 0.72/1.11 Z := Z
% 0.72/1.11 end
% 0.72/1.11 permutation0:
% 0.72/1.11 0 ==> 0
% 0.72/1.11 1 ==> 1
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 subsumption: (10) {G0,W11,D3,L3,V3,M3} I { ! in( X, Z ), ! in( Y, Z ),
% 0.72/1.11 subset( unordered_pair( X, Y ), Z ) }.
% 0.72/1.11 parent0: (130) {G0,W11,D3,L3,V3,M3} { ! in( X, Z ), ! in( Y, Z ), subset(
% 0.72/1.11 unordered_pair( X, Y ), Z ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := X
% 0.72/1.11 Y := Y
% 0.72/1.11 Z := Z
% 0.72/1.11 end
% 0.72/1.11 permutation0:
% 0.72/1.11 0 ==> 0
% 0.72/1.11 1 ==> 1
% 0.72/1.11 2 ==> 2
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 subsumption: (11) {G0,W7,D2,L2,V0,M2} I { alpha1( skol3, skol4, skol5 ), in
% 0.72/1.11 ( skol3, skol5 ) }.
% 0.72/1.11 parent0: (131) {G0,W7,D2,L2,V0,M2} { alpha1( skol3, skol4, skol5 ), in(
% 0.72/1.11 skol3, skol5 ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 end
% 0.72/1.11 permutation0:
% 0.72/1.11 0 ==> 0
% 0.72/1.11 1 ==> 1
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 subsumption: (12) {G0,W7,D2,L2,V0,M2} I { alpha1( skol3, skol4, skol5 ), in
% 0.72/1.11 ( skol4, skol5 ) }.
% 0.72/1.11 parent0: (132) {G0,W7,D2,L2,V0,M2} { alpha1( skol3, skol4, skol5 ), in(
% 0.72/1.11 skol4, skol5 ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 end
% 0.72/1.11 permutation0:
% 0.72/1.11 0 ==> 0
% 0.72/1.11 1 ==> 1
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 subsumption: (13) {G0,W11,D4,L2,V0,M2} I { alpha1( skol3, skol4, skol5 ), !
% 0.72/1.11 set_difference( unordered_pair( skol3, skol4 ), skol5 ) ==> empty_set
% 0.72/1.11 }.
% 0.72/1.11 parent0: (133) {G0,W11,D4,L2,V0,M2} { alpha1( skol3, skol4, skol5 ), !
% 0.72/1.11 set_difference( unordered_pair( skol3, skol4 ), skol5 ) = empty_set }.
% 0.72/1.11 substitution0:
% 0.72/1.11 end
% 0.72/1.11 permutation0:
% 0.72/1.11 0 ==> 0
% 0.72/1.11 1 ==> 1
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 subsumption: (14) {G0,W11,D4,L2,V3,M2} I { ! alpha1( X, Y, Z ),
% 0.72/1.11 set_difference( unordered_pair( X, Y ), Z ) ==> empty_set }.
% 0.72/1.11 parent0: (134) {G0,W11,D4,L2,V3,M2} { ! alpha1( X, Y, Z ), set_difference
% 0.72/1.11 ( unordered_pair( X, Y ), Z ) = empty_set }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := X
% 0.72/1.11 Y := Y
% 0.72/1.11 Z := Z
% 0.72/1.11 end
% 0.72/1.11 permutation0:
% 0.72/1.11 0 ==> 0
% 0.72/1.11 1 ==> 1
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 subsumption: (15) {G0,W10,D2,L3,V3,M3} I { ! alpha1( X, Y, Z ), ! in( X, Z
% 0.72/1.11 ), ! in( Y, Z ) }.
% 0.72/1.11 parent0: (135) {G0,W10,D2,L3,V3,M3} { ! alpha1( X, Y, Z ), ! in( X, Z ), !
% 0.72/1.11 in( Y, Z ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := X
% 0.72/1.11 Y := Y
% 0.72/1.11 Z := Z
% 0.72/1.11 end
% 0.72/1.11 permutation0:
% 0.72/1.11 0 ==> 0
% 0.72/1.11 1 ==> 1
% 0.72/1.11 2 ==> 2
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 eqswap: (179) {G0,W8,D3,L2,V2,M2} { ! empty_set ==> set_difference( X, Y )
% 0.72/1.11 , subset( X, Y ) }.
% 0.72/1.11 parent0[0]: (6) {G0,W8,D3,L2,V2,M2} I { ! set_difference( X, Y ) ==>
% 0.72/1.11 empty_set, subset( X, Y ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := X
% 0.72/1.11 Y := Y
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 resolution: (180) {G1,W10,D4,L2,V3,M2} { in( Y, Z ), ! empty_set ==>
% 0.72/1.11 set_difference( unordered_pair( X, Y ), Z ) }.
% 0.72/1.11 parent0[0]: (9) {G0,W8,D3,L2,V3,M2} I { ! subset( unordered_pair( X, Y ), Z
% 0.72/1.11 ), in( Y, Z ) }.
% 0.72/1.11 parent1[1]: (179) {G0,W8,D3,L2,V2,M2} { ! empty_set ==> set_difference( X
% 0.72/1.11 , Y ), subset( X, Y ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := X
% 0.72/1.11 Y := Y
% 0.72/1.11 Z := Z
% 0.72/1.11 end
% 0.72/1.11 substitution1:
% 0.72/1.11 X := unordered_pair( X, Y )
% 0.72/1.11 Y := Z
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 eqswap: (181) {G1,W10,D4,L2,V3,M2} { ! set_difference( unordered_pair( X,
% 0.72/1.11 Y ), Z ) ==> empty_set, in( Y, Z ) }.
% 0.72/1.11 parent0[1]: (180) {G1,W10,D4,L2,V3,M2} { in( Y, Z ), ! empty_set ==>
% 0.72/1.11 set_difference( unordered_pair( X, Y ), Z ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := X
% 0.72/1.11 Y := Y
% 0.72/1.11 Z := Z
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 subsumption: (31) {G1,W10,D4,L2,V3,M2} R(6,9) { ! set_difference(
% 0.72/1.11 unordered_pair( X, Y ), Z ) ==> empty_set, in( Y, Z ) }.
% 0.72/1.11 parent0: (181) {G1,W10,D4,L2,V3,M2} { ! set_difference( unordered_pair( X
% 0.72/1.11 , Y ), Z ) ==> empty_set, in( Y, Z ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := X
% 0.72/1.11 Y := Y
% 0.72/1.11 Z := Z
% 0.72/1.11 end
% 0.72/1.11 permutation0:
% 0.72/1.11 0 ==> 0
% 0.72/1.11 1 ==> 1
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 eqswap: (182) {G0,W8,D3,L2,V2,M2} { ! empty_set ==> set_difference( X, Y )
% 0.72/1.11 , subset( X, Y ) }.
% 0.72/1.11 parent0[0]: (6) {G0,W8,D3,L2,V2,M2} I { ! set_difference( X, Y ) ==>
% 0.72/1.11 empty_set, subset( X, Y ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := X
% 0.72/1.11 Y := Y
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 resolution: (183) {G1,W10,D4,L2,V3,M2} { in( X, Z ), ! empty_set ==>
% 0.72/1.11 set_difference( unordered_pair( X, Y ), Z ) }.
% 0.72/1.11 parent0[0]: (8) {G0,W8,D3,L2,V3,M2} I { ! subset( unordered_pair( X, Y ), Z
% 0.72/1.11 ), in( X, Z ) }.
% 0.72/1.11 parent1[1]: (182) {G0,W8,D3,L2,V2,M2} { ! empty_set ==> set_difference( X
% 0.72/1.11 , Y ), subset( X, Y ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := X
% 0.72/1.11 Y := Y
% 0.72/1.11 Z := Z
% 0.72/1.11 end
% 0.72/1.11 substitution1:
% 0.72/1.11 X := unordered_pair( X, Y )
% 0.72/1.11 Y := Z
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 eqswap: (184) {G1,W10,D4,L2,V3,M2} { ! set_difference( unordered_pair( X,
% 0.72/1.11 Y ), Z ) ==> empty_set, in( X, Z ) }.
% 0.72/1.11 parent0[1]: (183) {G1,W10,D4,L2,V3,M2} { in( X, Z ), ! empty_set ==>
% 0.72/1.11 set_difference( unordered_pair( X, Y ), Z ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := X
% 0.72/1.11 Y := Y
% 0.72/1.11 Z := Z
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 subsumption: (45) {G1,W10,D4,L2,V3,M2} R(8,6) { in( X, Y ), !
% 0.72/1.11 set_difference( unordered_pair( X, Z ), Y ) ==> empty_set }.
% 0.72/1.11 parent0: (184) {G1,W10,D4,L2,V3,M2} { ! set_difference( unordered_pair( X
% 0.72/1.11 , Y ), Z ) ==> empty_set, in( X, Z ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := X
% 0.72/1.11 Y := Z
% 0.72/1.11 Z := Y
% 0.72/1.11 end
% 0.72/1.11 permutation0:
% 0.72/1.11 0 ==> 1
% 0.72/1.11 1 ==> 0
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 eqswap: (185) {G0,W8,D3,L2,V2,M2} { empty_set ==> set_difference( X, Y ),
% 0.72/1.11 ! subset( X, Y ) }.
% 0.72/1.11 parent0[1]: (7) {G0,W8,D3,L2,V2,M2} I { ! subset( X, Y ), set_difference( X
% 0.72/1.11 , Y ) ==> empty_set }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := X
% 0.72/1.11 Y := Y
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 resolution: (186) {G1,W13,D4,L3,V3,M3} { empty_set ==> set_difference(
% 0.72/1.11 unordered_pair( X, Y ), Z ), ! in( X, Z ), ! in( Y, Z ) }.
% 0.72/1.11 parent0[1]: (185) {G0,W8,D3,L2,V2,M2} { empty_set ==> set_difference( X, Y
% 0.72/1.11 ), ! subset( X, Y ) }.
% 0.72/1.11 parent1[2]: (10) {G0,W11,D3,L3,V3,M3} I { ! in( X, Z ), ! in( Y, Z ),
% 0.72/1.11 subset( unordered_pair( X, Y ), Z ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := unordered_pair( X, Y )
% 0.72/1.11 Y := Z
% 0.72/1.11 end
% 0.72/1.11 substitution1:
% 0.72/1.11 X := X
% 0.72/1.11 Y := Y
% 0.72/1.11 Z := Z
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 eqswap: (187) {G1,W13,D4,L3,V3,M3} { set_difference( unordered_pair( X, Y
% 0.72/1.11 ), Z ) ==> empty_set, ! in( X, Z ), ! in( Y, Z ) }.
% 0.72/1.11 parent0[0]: (186) {G1,W13,D4,L3,V3,M3} { empty_set ==> set_difference(
% 0.72/1.11 unordered_pair( X, Y ), Z ), ! in( X, Z ), ! in( Y, Z ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := X
% 0.72/1.11 Y := Y
% 0.72/1.11 Z := Z
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 subsumption: (57) {G1,W13,D4,L3,V3,M3} R(10,7) { ! in( X, Y ), ! in( Z, Y )
% 0.72/1.11 , set_difference( unordered_pair( X, Z ), Y ) ==> empty_set }.
% 0.72/1.11 parent0: (187) {G1,W13,D4,L3,V3,M3} { set_difference( unordered_pair( X, Y
% 0.72/1.11 ), Z ) ==> empty_set, ! in( X, Z ), ! in( Y, Z ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := X
% 0.72/1.11 Y := Z
% 0.72/1.11 Z := Y
% 0.72/1.11 end
% 0.72/1.11 permutation0:
% 0.72/1.11 0 ==> 2
% 0.72/1.11 1 ==> 0
% 0.72/1.11 2 ==> 1
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 eqswap: (190) {G0,W11,D4,L2,V3,M2} { empty_set ==> set_difference(
% 0.72/1.11 unordered_pair( X, Y ), Z ), ! alpha1( X, Y, Z ) }.
% 0.72/1.11 parent0[1]: (14) {G0,W11,D4,L2,V3,M2} I { ! alpha1( X, Y, Z ),
% 0.72/1.11 set_difference( unordered_pair( X, Y ), Z ) ==> empty_set }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := X
% 0.72/1.11 Y := Y
% 0.72/1.11 Z := Z
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 eqswap: (191) {G1,W10,D4,L2,V3,M2} { ! empty_set ==> set_difference(
% 0.72/1.11 unordered_pair( X, Y ), Z ), in( X, Z ) }.
% 0.72/1.11 parent0[1]: (45) {G1,W10,D4,L2,V3,M2} R(8,6) { in( X, Y ), ! set_difference
% 0.72/1.11 ( unordered_pair( X, Z ), Y ) ==> empty_set }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := X
% 0.72/1.11 Y := Z
% 0.72/1.11 Z := Y
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 resolution: (192) {G1,W10,D4,L2,V0,M2} { empty_set ==> set_difference(
% 0.72/1.11 unordered_pair( skol3, skol4 ), skol5 ), in( skol3, skol5 ) }.
% 0.72/1.11 parent0[1]: (190) {G0,W11,D4,L2,V3,M2} { empty_set ==> set_difference(
% 0.72/1.11 unordered_pair( X, Y ), Z ), ! alpha1( X, Y, Z ) }.
% 0.72/1.11 parent1[0]: (11) {G0,W7,D2,L2,V0,M2} I { alpha1( skol3, skol4, skol5 ), in
% 0.72/1.11 ( skol3, skol5 ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := skol3
% 0.72/1.11 Y := skol4
% 0.72/1.11 Z := skol5
% 0.72/1.11 end
% 0.72/1.11 substitution1:
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 resolution: (193) {G2,W6,D2,L2,V0,M2} { in( skol3, skol5 ), in( skol3,
% 0.72/1.11 skol5 ) }.
% 0.72/1.11 parent0[0]: (191) {G1,W10,D4,L2,V3,M2} { ! empty_set ==> set_difference(
% 0.72/1.11 unordered_pair( X, Y ), Z ), in( X, Z ) }.
% 0.72/1.11 parent1[0]: (192) {G1,W10,D4,L2,V0,M2} { empty_set ==> set_difference(
% 0.72/1.11 unordered_pair( skol3, skol4 ), skol5 ), in( skol3, skol5 ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := skol3
% 0.72/1.11 Y := skol4
% 0.72/1.11 Z := skol5
% 0.72/1.11 end
% 0.72/1.11 substitution1:
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 factor: (194) {G2,W3,D2,L1,V0,M1} { in( skol3, skol5 ) }.
% 0.72/1.11 parent0[0, 1]: (193) {G2,W6,D2,L2,V0,M2} { in( skol3, skol5 ), in( skol3,
% 0.72/1.11 skol5 ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 subsumption: (89) {G2,W3,D2,L1,V0,M1} R(14,11);r(45) { in( skol3, skol5 )
% 0.72/1.11 }.
% 0.72/1.11 parent0: (194) {G2,W3,D2,L1,V0,M1} { in( skol3, skol5 ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 end
% 0.72/1.11 permutation0:
% 0.72/1.11 0 ==> 0
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 eqswap: (195) {G0,W11,D4,L2,V3,M2} { empty_set ==> set_difference(
% 0.72/1.11 unordered_pair( X, Y ), Z ), ! alpha1( X, Y, Z ) }.
% 0.72/1.11 parent0[1]: (14) {G0,W11,D4,L2,V3,M2} I { ! alpha1( X, Y, Z ),
% 0.72/1.11 set_difference( unordered_pair( X, Y ), Z ) ==> empty_set }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := X
% 0.72/1.11 Y := Y
% 0.72/1.11 Z := Z
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 eqswap: (196) {G1,W10,D4,L2,V3,M2} { ! empty_set ==> set_difference(
% 0.72/1.11 unordered_pair( X, Y ), Z ), in( Y, Z ) }.
% 0.72/1.11 parent0[0]: (31) {G1,W10,D4,L2,V3,M2} R(6,9) { ! set_difference(
% 0.72/1.11 unordered_pair( X, Y ), Z ) ==> empty_set, in( Y, Z ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := X
% 0.72/1.11 Y := Y
% 0.72/1.11 Z := Z
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 resolution: (197) {G1,W10,D4,L2,V0,M2} { empty_set ==> set_difference(
% 0.72/1.11 unordered_pair( skol3, skol4 ), skol5 ), in( skol4, skol5 ) }.
% 0.72/1.11 parent0[1]: (195) {G0,W11,D4,L2,V3,M2} { empty_set ==> set_difference(
% 0.72/1.11 unordered_pair( X, Y ), Z ), ! alpha1( X, Y, Z ) }.
% 0.72/1.11 parent1[0]: (12) {G0,W7,D2,L2,V0,M2} I { alpha1( skol3, skol4, skol5 ), in
% 0.72/1.11 ( skol4, skol5 ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := skol3
% 0.72/1.11 Y := skol4
% 0.72/1.11 Z := skol5
% 0.72/1.11 end
% 0.72/1.11 substitution1:
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 resolution: (198) {G2,W6,D2,L2,V0,M2} { in( skol4, skol5 ), in( skol4,
% 0.72/1.11 skol5 ) }.
% 0.72/1.11 parent0[0]: (196) {G1,W10,D4,L2,V3,M2} { ! empty_set ==> set_difference(
% 0.72/1.11 unordered_pair( X, Y ), Z ), in( Y, Z ) }.
% 0.72/1.11 parent1[0]: (197) {G1,W10,D4,L2,V0,M2} { empty_set ==> set_difference(
% 0.72/1.11 unordered_pair( skol3, skol4 ), skol5 ), in( skol4, skol5 ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := skol3
% 0.72/1.11 Y := skol4
% 0.72/1.11 Z := skol5
% 0.72/1.11 end
% 0.72/1.11 substitution1:
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 factor: (199) {G2,W3,D2,L1,V0,M1} { in( skol4, skol5 ) }.
% 0.72/1.11 parent0[0, 1]: (198) {G2,W6,D2,L2,V0,M2} { in( skol4, skol5 ), in( skol4,
% 0.72/1.11 skol5 ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 subsumption: (91) {G2,W3,D2,L1,V0,M1} R(14,12);r(31) { in( skol4, skol5 )
% 0.72/1.11 }.
% 0.72/1.11 parent0: (199) {G2,W3,D2,L1,V0,M1} { in( skol4, skol5 ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 end
% 0.72/1.11 permutation0:
% 0.72/1.11 0 ==> 0
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 eqswap: (200) {G0,W11,D4,L2,V0,M2} { ! empty_set ==> set_difference(
% 0.72/1.11 unordered_pair( skol3, skol4 ), skol5 ), alpha1( skol3, skol4, skol5 )
% 0.72/1.11 }.
% 0.72/1.11 parent0[1]: (13) {G0,W11,D4,L2,V0,M2} I { alpha1( skol3, skol4, skol5 ), !
% 0.72/1.11 set_difference( unordered_pair( skol3, skol4 ), skol5 ) ==> empty_set }.
% 0.72/1.11 substitution0:
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 resolution: (202) {G1,W13,D4,L3,V0,M3} { ! in( skol3, skol5 ), ! in( skol4
% 0.72/1.11 , skol5 ), ! empty_set ==> set_difference( unordered_pair( skol3, skol4 )
% 0.72/1.11 , skol5 ) }.
% 0.72/1.11 parent0[0]: (15) {G0,W10,D2,L3,V3,M3} I { ! alpha1( X, Y, Z ), ! in( X, Z )
% 0.72/1.11 , ! in( Y, Z ) }.
% 0.72/1.11 parent1[1]: (200) {G0,W11,D4,L2,V0,M2} { ! empty_set ==> set_difference(
% 0.72/1.11 unordered_pair( skol3, skol4 ), skol5 ), alpha1( skol3, skol4, skol5 )
% 0.72/1.11 }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := skol3
% 0.72/1.11 Y := skol4
% 0.72/1.11 Z := skol5
% 0.72/1.11 end
% 0.72/1.11 substitution1:
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 paramod: (203) {G2,W15,D2,L5,V0,M5} { ! empty_set ==> empty_set, ! in(
% 0.72/1.11 skol3, skol5 ), ! in( skol4, skol5 ), ! in( skol3, skol5 ), ! in( skol4,
% 0.72/1.11 skol5 ) }.
% 0.72/1.11 parent0[2]: (57) {G1,W13,D4,L3,V3,M3} R(10,7) { ! in( X, Y ), ! in( Z, Y )
% 0.72/1.11 , set_difference( unordered_pair( X, Z ), Y ) ==> empty_set }.
% 0.72/1.11 parent1[2; 3]: (202) {G1,W13,D4,L3,V0,M3} { ! in( skol3, skol5 ), ! in(
% 0.72/1.11 skol4, skol5 ), ! empty_set ==> set_difference( unordered_pair( skol3,
% 0.72/1.11 skol4 ), skol5 ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 X := skol3
% 0.72/1.11 Y := skol5
% 0.72/1.11 Z := skol4
% 0.72/1.11 end
% 0.72/1.11 substitution1:
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 factor: (204) {G2,W12,D2,L4,V0,M4} { ! empty_set ==> empty_set, ! in(
% 0.72/1.11 skol3, skol5 ), ! in( skol4, skol5 ), ! in( skol4, skol5 ) }.
% 0.72/1.11 parent0[1, 3]: (203) {G2,W15,D2,L5,V0,M5} { ! empty_set ==> empty_set, !
% 0.72/1.11 in( skol3, skol5 ), ! in( skol4, skol5 ), ! in( skol3, skol5 ), ! in(
% 0.72/1.11 skol4, skol5 ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 factor: (205) {G2,W9,D2,L3,V0,M3} { ! empty_set ==> empty_set, ! in( skol3
% 0.72/1.11 , skol5 ), ! in( skol4, skol5 ) }.
% 0.72/1.11 parent0[2, 3]: (204) {G2,W12,D2,L4,V0,M4} { ! empty_set ==> empty_set, !
% 0.72/1.11 in( skol3, skol5 ), ! in( skol4, skol5 ), ! in( skol4, skol5 ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 eqrefl: (206) {G0,W6,D2,L2,V0,M2} { ! in( skol3, skol5 ), ! in( skol4,
% 0.72/1.11 skol5 ) }.
% 0.72/1.11 parent0[0]: (205) {G2,W9,D2,L3,V0,M3} { ! empty_set ==> empty_set, ! in(
% 0.72/1.11 skol3, skol5 ), ! in( skol4, skol5 ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 resolution: (207) {G1,W3,D2,L1,V0,M1} { ! in( skol4, skol5 ) }.
% 0.72/1.11 parent0[0]: (206) {G0,W6,D2,L2,V0,M2} { ! in( skol3, skol5 ), ! in( skol4
% 0.72/1.11 , skol5 ) }.
% 0.72/1.11 parent1[0]: (89) {G2,W3,D2,L1,V0,M1} R(14,11);r(45) { in( skol3, skol5 )
% 0.72/1.11 }.
% 0.72/1.11 substitution0:
% 0.72/1.11 end
% 0.72/1.11 substitution1:
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 subsumption: (109) {G3,W3,D2,L1,V0,M1} R(15,13);d(57);q;r(89) { ! in( skol4
% 0.72/1.11 , skol5 ) }.
% 0.72/1.11 parent0: (207) {G1,W3,D2,L1,V0,M1} { ! in( skol4, skol5 ) }.
% 0.72/1.11 substitution0:
% 0.72/1.11 end
% 0.72/1.11 permutation0:
% 0.72/1.11 0 ==> 0
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 resolution: (208) {G3,W0,D0,L0,V0,M0} { }.
% 0.72/1.11 parent0[0]: (109) {G3,W3,D2,L1,V0,M1} R(15,13);d(57);q;r(89) { ! in( skol4
% 0.72/1.11 , skol5 ) }.
% 0.72/1.11 parent1[0]: (91) {G2,W3,D2,L1,V0,M1} R(14,12);r(31) { in( skol4, skol5 )
% 0.72/1.11 }.
% 0.72/1.11 substitution0:
% 0.72/1.11 end
% 0.72/1.11 substitution1:
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 subsumption: (118) {G4,W0,D0,L0,V0,M0} S(109);r(91) { }.
% 0.72/1.11 parent0: (208) {G3,W0,D0,L0,V0,M0} { }.
% 0.72/1.11 substitution0:
% 0.72/1.11 end
% 0.72/1.11 permutation0:
% 0.72/1.11 end
% 0.72/1.11
% 0.72/1.11 Proof check complete!
% 0.72/1.11
% 0.72/1.11 Memory use:
% 0.72/1.11
% 0.72/1.11 space for terms: 1406
% 0.72/1.11 space for clauses: 6404
% 0.72/1.11
% 0.72/1.11
% 0.72/1.11 clauses generated: 276
% 0.72/1.11 clauses kept: 119
% 0.72/1.11 clauses selected: 46
% 0.72/1.11 clauses deleted: 1
% 0.72/1.11 clauses inuse deleted: 0
% 0.72/1.11
% 0.72/1.11 subsentry: 601
% 0.72/1.11 literals s-matched: 392
% 0.72/1.11 literals matched: 384
% 0.72/1.11 full subsumption: 39
% 0.72/1.11
% 0.72/1.11 checksum: -202018492
% 0.72/1.11
% 0.72/1.11
% 0.72/1.11 Bliksem ended
%------------------------------------------------------------------------------