TSTP Solution File: SEU160+3 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SEU160+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n009.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 07:11:02 EDT 2022
% Result : Theorem 0.70s 1.07s
% Output : Refutation 0.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU160+3 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n009.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Sun Jun 19 07:47:52 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.70/1.07 *** allocated 10000 integers for termspace/termends
% 0.70/1.07 *** allocated 10000 integers for clauses
% 0.70/1.07 *** allocated 10000 integers for justifications
% 0.70/1.07 Bliksem 1.12
% 0.70/1.07
% 0.70/1.07
% 0.70/1.07 Automatic Strategy Selection
% 0.70/1.07
% 0.70/1.07
% 0.70/1.07 Clauses:
% 0.70/1.07
% 0.70/1.07 { subset( X, X ) }.
% 0.70/1.07 { empty( empty_set ) }.
% 0.70/1.07 { empty( skol1 ) }.
% 0.70/1.07 { ! empty( skol2 ) }.
% 0.70/1.07 { alpha1( skol3, skol4 ), skol3 = empty_set, skol3 = singleton( skol4 ) }.
% 0.70/1.07 { alpha1( skol3, skol4 ), ! subset( skol3, singleton( skol4 ) ) }.
% 0.70/1.07 { ! alpha1( X, Y ), subset( X, singleton( Y ) ) }.
% 0.70/1.07 { ! alpha1( X, Y ), ! X = empty_set }.
% 0.70/1.07 { ! alpha1( X, Y ), ! X = singleton( Y ) }.
% 0.70/1.07 { ! subset( X, singleton( Y ) ), X = empty_set, X = singleton( Y ), alpha1
% 0.70/1.07 ( X, Y ) }.
% 0.70/1.07 { ! subset( X, singleton( Y ) ), X = empty_set, X = singleton( Y ) }.
% 0.70/1.07 { ! X = empty_set, subset( X, singleton( Y ) ) }.
% 0.70/1.07 { ! X = singleton( Y ), subset( X, singleton( Y ) ) }.
% 0.70/1.07
% 0.70/1.07 percentage equality = 0.384615, percentage horn = 0.769231
% 0.70/1.07 This is a problem with some equality
% 0.70/1.07
% 0.70/1.07
% 0.70/1.07
% 0.70/1.07 Options Used:
% 0.70/1.07
% 0.70/1.07 useres = 1
% 0.70/1.07 useparamod = 1
% 0.70/1.07 useeqrefl = 1
% 0.70/1.07 useeqfact = 1
% 0.70/1.07 usefactor = 1
% 0.70/1.07 usesimpsplitting = 0
% 0.70/1.07 usesimpdemod = 5
% 0.70/1.07 usesimpres = 3
% 0.70/1.07
% 0.70/1.07 resimpinuse = 1000
% 0.70/1.07 resimpclauses = 20000
% 0.70/1.07 substype = eqrewr
% 0.70/1.07 backwardsubs = 1
% 0.70/1.07 selectoldest = 5
% 0.70/1.07
% 0.70/1.07 litorderings [0] = split
% 0.70/1.07 litorderings [1] = extend the termordering, first sorting on arguments
% 0.70/1.07
% 0.70/1.07 termordering = kbo
% 0.70/1.07
% 0.70/1.07 litapriori = 0
% 0.70/1.07 termapriori = 1
% 0.70/1.07 litaposteriori = 0
% 0.70/1.07 termaposteriori = 0
% 0.70/1.07 demodaposteriori = 0
% 0.70/1.07 ordereqreflfact = 0
% 0.70/1.07
% 0.70/1.07 litselect = negord
% 0.70/1.07
% 0.70/1.07 maxweight = 15
% 0.70/1.07 maxdepth = 30000
% 0.70/1.07 maxlength = 115
% 0.70/1.07 maxnrvars = 195
% 0.70/1.07 excuselevel = 1
% 0.70/1.07 increasemaxweight = 1
% 0.70/1.07
% 0.70/1.07 maxselected = 10000000
% 0.70/1.07 maxnrclauses = 10000000
% 0.70/1.07
% 0.70/1.07 showgenerated = 0
% 0.70/1.07 showkept = 0
% 0.70/1.07 showselected = 0
% 0.70/1.07 showdeleted = 0
% 0.70/1.07 showresimp = 1
% 0.70/1.07 showstatus = 2000
% 0.70/1.07
% 0.70/1.07 prologoutput = 0
% 0.70/1.07 nrgoals = 5000000
% 0.70/1.07 totalproof = 1
% 0.70/1.07
% 0.70/1.07 Symbols occurring in the translation:
% 0.70/1.07
% 0.70/1.07 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.70/1.07 . [1, 2] (w:1, o:20, a:1, s:1, b:0),
% 0.70/1.07 ! [4, 1] (w:0, o:13, a:1, s:1, b:0),
% 0.70/1.07 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.70/1.07 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.70/1.07 subset [37, 2] (w:1, o:44, a:1, s:1, b:0),
% 0.70/1.07 empty_set [38, 0] (w:1, o:8, a:1, s:1, b:0),
% 0.70/1.07 empty [39, 1] (w:1, o:18, a:1, s:1, b:0),
% 0.70/1.07 singleton [40, 1] (w:1, o:19, a:1, s:1, b:0),
% 0.70/1.07 alpha1 [41, 2] (w:1, o:45, a:1, s:1, b:1),
% 0.70/1.07 skol1 [42, 0] (w:1, o:9, a:1, s:1, b:1),
% 0.70/1.07 skol2 [43, 0] (w:1, o:10, a:1, s:1, b:1),
% 0.70/1.07 skol3 [44, 0] (w:1, o:11, a:1, s:1, b:1),
% 0.70/1.07 skol4 [45, 0] (w:1, o:12, a:1, s:1, b:1).
% 0.70/1.07
% 0.70/1.07
% 0.70/1.07 Starting Search:
% 0.70/1.07
% 0.70/1.07
% 0.70/1.07 Bliksems!, er is een bewijs:
% 0.70/1.07 % SZS status Theorem
% 0.70/1.07 % SZS output start Refutation
% 0.70/1.07
% 0.70/1.07 (0) {G0,W3,D2,L1,V1,M1} I { subset( X, X ) }.
% 0.70/1.07 (4) {G0,W10,D3,L3,V0,M3} I { alpha1( skol3, skol4 ), skol3 ==> empty_set,
% 0.70/1.07 singleton( skol4 ) ==> skol3 }.
% 0.70/1.07 (5) {G0,W7,D3,L2,V0,M2} I { alpha1( skol3, skol4 ), ! subset( skol3,
% 0.70/1.07 singleton( skol4 ) ) }.
% 0.70/1.07 (6) {G0,W7,D3,L2,V2,M2} I { ! alpha1( X, Y ), subset( X, singleton( Y ) )
% 0.70/1.07 }.
% 0.70/1.07 (7) {G0,W6,D2,L2,V2,M2} I { ! alpha1( X, Y ), ! X = empty_set }.
% 0.70/1.07 (8) {G0,W7,D3,L2,V2,M2} I { ! alpha1( X, Y ), ! X = singleton( Y ) }.
% 0.70/1.07 (10) {G0,W11,D3,L3,V2,M3} I { ! subset( X, singleton( Y ) ), X = empty_set
% 0.70/1.07 , X = singleton( Y ) }.
% 0.70/1.07 (11) {G0,W7,D3,L2,V2,M2} I { ! X = empty_set, subset( X, singleton( Y ) )
% 0.70/1.07 }.
% 0.70/1.07 (23) {G1,W3,D2,L1,V0,M1} R(5,11);r(7) { ! skol3 ==> empty_set }.
% 0.70/1.07 (25) {G1,W6,D2,L2,V0,M2} P(4,5);f;r(0) { alpha1( skol3, skol4 ), skol3 ==>
% 0.70/1.07 empty_set }.
% 0.70/1.07 (27) {G2,W3,D2,L1,V0,M1} S(25);r(23) { alpha1( skol3, skol4 ) }.
% 0.70/1.07 (28) {G3,W4,D3,L1,V0,M1} R(8,27) { ! singleton( skol4 ) ==> skol3 }.
% 0.70/1.07 (30) {G1,W7,D3,L2,V0,M2} R(6,4);r(10) { skol3 ==> empty_set, singleton(
% 0.70/1.07 skol4 ) ==> skol3 }.
% 0.70/1.07 (31) {G4,W0,D0,L0,V0,M0} S(30);r(23);r(28) { }.
% 0.70/1.07
% 0.70/1.07
% 0.70/1.07 % SZS output end Refutation
% 0.70/1.07 found a proof!
% 0.70/1.07
% 0.70/1.07
% 0.70/1.07 Unprocessed initial clauses:
% 0.70/1.07
% 0.70/1.07 (33) {G0,W3,D2,L1,V1,M1} { subset( X, X ) }.
% 0.70/1.07 (34) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.70/1.07 (35) {G0,W2,D2,L1,V0,M1} { empty( skol1 ) }.
% 0.70/1.07 (36) {G0,W2,D2,L1,V0,M1} { ! empty( skol2 ) }.
% 0.70/1.07 (37) {G0,W10,D3,L3,V0,M3} { alpha1( skol3, skol4 ), skol3 = empty_set,
% 0.70/1.07 skol3 = singleton( skol4 ) }.
% 0.70/1.07 (38) {G0,W7,D3,L2,V0,M2} { alpha1( skol3, skol4 ), ! subset( skol3,
% 0.70/1.07 singleton( skol4 ) ) }.
% 0.70/1.07 (39) {G0,W7,D3,L2,V2,M2} { ! alpha1( X, Y ), subset( X, singleton( Y ) )
% 0.70/1.07 }.
% 0.70/1.07 (40) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), ! X = empty_set }.
% 0.70/1.07 (41) {G0,W7,D3,L2,V2,M2} { ! alpha1( X, Y ), ! X = singleton( Y ) }.
% 0.70/1.07 (42) {G0,W14,D3,L4,V2,M4} { ! subset( X, singleton( Y ) ), X = empty_set,
% 0.70/1.07 X = singleton( Y ), alpha1( X, Y ) }.
% 0.70/1.07 (43) {G0,W11,D3,L3,V2,M3} { ! subset( X, singleton( Y ) ), X = empty_set,
% 0.70/1.07 X = singleton( Y ) }.
% 0.70/1.07 (44) {G0,W7,D3,L2,V2,M2} { ! X = empty_set, subset( X, singleton( Y ) )
% 0.70/1.07 }.
% 0.70/1.07 (45) {G0,W8,D3,L2,V2,M2} { ! X = singleton( Y ), subset( X, singleton( Y )
% 0.70/1.07 ) }.
% 0.70/1.07
% 0.70/1.07
% 0.70/1.07 Total Proof:
% 0.70/1.07
% 0.70/1.07 subsumption: (0) {G0,W3,D2,L1,V1,M1} I { subset( X, X ) }.
% 0.70/1.07 parent0: (33) {G0,W3,D2,L1,V1,M1} { subset( X, X ) }.
% 0.70/1.07 substitution0:
% 0.70/1.07 X := X
% 0.70/1.07 end
% 0.70/1.07 permutation0:
% 0.70/1.07 0 ==> 0
% 0.70/1.07 end
% 0.70/1.07
% 0.70/1.07 eqswap: (47) {G0,W10,D3,L3,V0,M3} { singleton( skol4 ) = skol3, alpha1(
% 0.70/1.07 skol3, skol4 ), skol3 = empty_set }.
% 0.70/1.07 parent0[2]: (37) {G0,W10,D3,L3,V0,M3} { alpha1( skol3, skol4 ), skol3 =
% 0.70/1.07 empty_set, skol3 = singleton( skol4 ) }.
% 0.70/1.07 substitution0:
% 0.70/1.07 end
% 0.70/1.07
% 0.70/1.07 subsumption: (4) {G0,W10,D3,L3,V0,M3} I { alpha1( skol3, skol4 ), skol3 ==>
% 0.70/1.07 empty_set, singleton( skol4 ) ==> skol3 }.
% 0.70/1.07 parent0: (47) {G0,W10,D3,L3,V0,M3} { singleton( skol4 ) = skol3, alpha1(
% 0.70/1.07 skol3, skol4 ), skol3 = empty_set }.
% 0.70/1.07 substitution0:
% 0.70/1.07 end
% 0.70/1.07 permutation0:
% 0.70/1.07 0 ==> 2
% 0.70/1.07 1 ==> 0
% 0.70/1.07 2 ==> 1
% 0.70/1.07 end
% 0.70/1.07
% 0.70/1.07 subsumption: (5) {G0,W7,D3,L2,V0,M2} I { alpha1( skol3, skol4 ), ! subset(
% 0.70/1.07 skol3, singleton( skol4 ) ) }.
% 0.70/1.07 parent0: (38) {G0,W7,D3,L2,V0,M2} { alpha1( skol3, skol4 ), ! subset(
% 0.70/1.07 skol3, singleton( skol4 ) ) }.
% 0.70/1.07 substitution0:
% 0.70/1.07 end
% 0.70/1.07 permutation0:
% 0.70/1.07 0 ==> 0
% 0.70/1.07 1 ==> 1
% 0.70/1.07 end
% 0.70/1.07
% 0.70/1.07 subsumption: (6) {G0,W7,D3,L2,V2,M2} I { ! alpha1( X, Y ), subset( X,
% 0.70/1.07 singleton( Y ) ) }.
% 0.70/1.07 parent0: (39) {G0,W7,D3,L2,V2,M2} { ! alpha1( X, Y ), subset( X, singleton
% 0.70/1.07 ( Y ) ) }.
% 0.70/1.07 substitution0:
% 0.70/1.07 X := X
% 0.70/1.07 Y := Y
% 0.70/1.07 end
% 0.70/1.07 permutation0:
% 0.70/1.07 0 ==> 0
% 0.70/1.07 1 ==> 1
% 0.70/1.07 end
% 0.70/1.07
% 0.70/1.07 subsumption: (7) {G0,W6,D2,L2,V2,M2} I { ! alpha1( X, Y ), ! X = empty_set
% 0.70/1.07 }.
% 0.70/1.07 parent0: (40) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), ! X = empty_set }.
% 0.70/1.07 substitution0:
% 0.70/1.07 X := X
% 0.70/1.07 Y := Y
% 0.70/1.07 end
% 0.70/1.07 permutation0:
% 0.70/1.07 0 ==> 0
% 0.70/1.07 1 ==> 1
% 0.70/1.07 end
% 0.70/1.07
% 0.70/1.07 subsumption: (8) {G0,W7,D3,L2,V2,M2} I { ! alpha1( X, Y ), ! X = singleton
% 0.70/1.07 ( Y ) }.
% 0.70/1.07 parent0: (41) {G0,W7,D3,L2,V2,M2} { ! alpha1( X, Y ), ! X = singleton( Y )
% 0.70/1.07 }.
% 0.70/1.07 substitution0:
% 0.70/1.07 X := X
% 0.70/1.07 Y := Y
% 0.70/1.07 end
% 0.70/1.07 permutation0:
% 0.70/1.07 0 ==> 0
% 0.70/1.07 1 ==> 1
% 0.70/1.07 end
% 0.70/1.07
% 0.70/1.07 subsumption: (10) {G0,W11,D3,L3,V2,M3} I { ! subset( X, singleton( Y ) ), X
% 0.70/1.07 = empty_set, X = singleton( Y ) }.
% 0.70/1.07 parent0: (43) {G0,W11,D3,L3,V2,M3} { ! subset( X, singleton( Y ) ), X =
% 0.70/1.07 empty_set, X = singleton( Y ) }.
% 0.70/1.07 substitution0:
% 0.70/1.07 X := X
% 0.70/1.07 Y := Y
% 0.70/1.07 end
% 0.70/1.07 permutation0:
% 0.70/1.07 0 ==> 0
% 0.70/1.07 1 ==> 1
% 0.70/1.07 2 ==> 2
% 0.70/1.07 end
% 0.70/1.07
% 0.70/1.07 subsumption: (11) {G0,W7,D3,L2,V2,M2} I { ! X = empty_set, subset( X,
% 0.70/1.07 singleton( Y ) ) }.
% 0.70/1.07 parent0: (44) {G0,W7,D3,L2,V2,M2} { ! X = empty_set, subset( X, singleton
% 0.70/1.07 ( Y ) ) }.
% 0.70/1.07 substitution0:
% 0.70/1.07 X := X
% 0.70/1.07 Y := Y
% 0.70/1.07 end
% 0.70/1.07 permutation0:
% 0.70/1.07 0 ==> 0
% 0.70/1.07 1 ==> 1
% 0.70/1.07 end
% 0.70/1.07
% 0.70/1.07 eqswap: (87) {G0,W7,D3,L2,V2,M2} { ! empty_set = X, subset( X, singleton(
% 0.70/1.07 Y ) ) }.
% 0.70/1.07 parent0[0]: (11) {G0,W7,D3,L2,V2,M2} I { ! X = empty_set, subset( X,
% 0.70/1.07 singleton( Y ) ) }.
% 0.70/1.07 substitution0:
% 0.70/1.07 X := X
% 0.70/1.07 Y := Y
% 0.70/1.07 end
% 0.70/1.07
% 0.70/1.07 resolution: (89) {G1,W6,D2,L2,V0,M2} { alpha1( skol3, skol4 ), ! empty_set
% 0.70/1.07 = skol3 }.
% 0.70/1.07 parent0[1]: (5) {G0,W7,D3,L2,V0,M2} I { alpha1( skol3, skol4 ), ! subset(
% 0.70/1.07 skol3, singleton( skol4 ) ) }.
% 0.70/1.07 parent1[1]: (87) {G0,W7,D3,L2,V2,M2} { ! empty_set = X, subset( X,
% 0.70/1.07 singleton( Y ) ) }.
% 0.70/1.07 substitution0:
% 0.70/1.07 end
% 0.70/1.07 substitution1:
% 0.70/1.07 X := skol3
% 0.70/1.07 Y := skol4
% 0.70/1.07 end
% 0.70/1.07
% 0.70/1.07 resolution: (92) {G1,W6,D2,L2,V0,M2} { ! skol3 = empty_set, ! empty_set =
% 0.70/1.07 skol3 }.
% 0.70/1.07 parent0[0]: (7) {G0,W6,D2,L2,V2,M2} I { ! alpha1( X, Y ), ! X = empty_set
% 0.70/1.07 }.
% 0.70/1.07 parent1[0]: (89) {G1,W6,D2,L2,V0,M2} { alpha1( skol3, skol4 ), ! empty_set
% 0.70/1.07 = skol3 }.
% 0.70/1.07 substitution0:
% 0.70/1.07 X := skol3
% 0.70/1.07 Y := skol4
% 0.70/1.07 end
% 0.70/1.07 substitution1:
% 0.70/1.07 end
% 0.70/1.07
% 0.70/1.07 eqswap: (94) {G1,W6,D2,L2,V0,M2} { ! skol3 = empty_set, ! skol3 =
% 0.70/1.07 empty_set }.
% 0.70/1.07 parent0[1]: (92) {G1,W6,D2,L2,V0,M2} { ! skol3 = empty_set, ! empty_set =
% 0.70/1.07 skol3 }.
% 0.70/1.07 substitution0:
% 0.70/1.07 end
% 0.70/1.07
% 0.70/1.07 factor: (96) {G1,W3,D2,L1,V0,M1} { ! skol3 = empty_set }.
% 0.70/1.07 parent0[0, 1]: (94) {G1,W6,D2,L2,V0,M2} { ! skol3 = empty_set, ! skol3 =
% 0.70/1.07 empty_set }.
% 0.70/1.07 substitution0:
% 0.70/1.07 end
% 0.70/1.07
% 0.70/1.07 subsumption: (23) {G1,W3,D2,L1,V0,M1} R(5,11);r(7) { ! skol3 ==> empty_set
% 0.70/1.07 }.
% 0.70/1.07 parent0: (96) {G1,W3,D2,L1,V0,M1} { ! skol3 = empty_set }.
% 0.70/1.07 substitution0:
% 0.70/1.07 end
% 0.70/1.07 permutation0:
% 0.70/1.07 0 ==> 0
% 0.70/1.07 end
% 0.70/1.07
% 0.70/1.07 eqswap: (97) {G0,W10,D3,L3,V0,M3} { empty_set ==> skol3, alpha1( skol3,
% 0.70/1.07 skol4 ), singleton( skol4 ) ==> skol3 }.
% 0.70/1.07 parent0[1]: (4) {G0,W10,D3,L3,V0,M3} I { alpha1( skol3, skol4 ), skol3 ==>
% 0.70/1.07 empty_set, singleton( skol4 ) ==> skol3 }.
% 0.70/1.07 substitution0:
% 0.70/1.07 end
% 0.70/1.07
% 0.70/1.07 paramod: (100) {G1,W12,D2,L4,V0,M4} { ! subset( skol3, skol3 ), empty_set
% 0.70/1.07 ==> skol3, alpha1( skol3, skol4 ), alpha1( skol3, skol4 ) }.
% 0.70/1.07 parent0[2]: (97) {G0,W10,D3,L3,V0,M3} { empty_set ==> skol3, alpha1( skol3
% 0.70/1.07 , skol4 ), singleton( skol4 ) ==> skol3 }.
% 0.70/1.07 parent1[1; 3]: (5) {G0,W7,D3,L2,V0,M2} I { alpha1( skol3, skol4 ), ! subset
% 0.70/1.07 ( skol3, singleton( skol4 ) ) }.
% 0.70/1.07 substitution0:
% 0.70/1.07 end
% 0.70/1.07 substitution1:
% 0.70/1.07 end
% 0.70/1.07
% 0.70/1.07 resolution: (102) {G1,W9,D2,L3,V0,M3} { empty_set ==> skol3, alpha1( skol3
% 0.70/1.07 , skol4 ), alpha1( skol3, skol4 ) }.
% 0.70/1.07 parent0[0]: (100) {G1,W12,D2,L4,V0,M4} { ! subset( skol3, skol3 ),
% 0.70/1.07 empty_set ==> skol3, alpha1( skol3, skol4 ), alpha1( skol3, skol4 ) }.
% 0.70/1.07 parent1[0]: (0) {G0,W3,D2,L1,V1,M1} I { subset( X, X ) }.
% 0.70/1.07 substitution0:
% 0.70/1.07 end
% 0.70/1.07 substitution1:
% 0.70/1.07 X := skol3
% 0.70/1.07 end
% 0.70/1.07
% 0.70/1.07 eqswap: (103) {G1,W9,D2,L3,V0,M3} { skol3 ==> empty_set, alpha1( skol3,
% 0.70/1.07 skol4 ), alpha1( skol3, skol4 ) }.
% 0.70/1.07 parent0[0]: (102) {G1,W9,D2,L3,V0,M3} { empty_set ==> skol3, alpha1( skol3
% 0.70/1.07 , skol4 ), alpha1( skol3, skol4 ) }.
% 0.70/1.07 substitution0:
% 0.70/1.07 end
% 0.70/1.07
% 0.70/1.07 factor: (104) {G1,W6,D2,L2,V0,M2} { skol3 ==> empty_set, alpha1( skol3,
% 0.70/1.07 skol4 ) }.
% 0.70/1.07 parent0[1, 2]: (103) {G1,W9,D2,L3,V0,M3} { skol3 ==> empty_set, alpha1(
% 0.70/1.07 skol3, skol4 ), alpha1( skol3, skol4 ) }.
% 0.70/1.07 substitution0:
% 0.70/1.07 end
% 0.70/1.07
% 0.70/1.07 subsumption: (25) {G1,W6,D2,L2,V0,M2} P(4,5);f;r(0) { alpha1( skol3, skol4
% 0.70/1.08 ), skol3 ==> empty_set }.
% 0.70/1.08 parent0: (104) {G1,W6,D2,L2,V0,M2} { skol3 ==> empty_set, alpha1( skol3,
% 0.70/1.08 skol4 ) }.
% 0.70/1.08 substitution0:
% 0.70/1.08 end
% 0.70/1.08 permutation0:
% 0.70/1.08 0 ==> 1
% 0.70/1.08 1 ==> 0
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 resolution: (108) {G2,W3,D2,L1,V0,M1} { alpha1( skol3, skol4 ) }.
% 0.70/1.08 parent0[0]: (23) {G1,W3,D2,L1,V0,M1} R(5,11);r(7) { ! skol3 ==> empty_set
% 0.70/1.08 }.
% 0.70/1.08 parent1[1]: (25) {G1,W6,D2,L2,V0,M2} P(4,5);f;r(0) { alpha1( skol3, skol4 )
% 0.70/1.08 , skol3 ==> empty_set }.
% 0.70/1.08 substitution0:
% 0.70/1.08 end
% 0.70/1.08 substitution1:
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 subsumption: (27) {G2,W3,D2,L1,V0,M1} S(25);r(23) { alpha1( skol3, skol4 )
% 0.70/1.08 }.
% 0.70/1.08 parent0: (108) {G2,W3,D2,L1,V0,M1} { alpha1( skol3, skol4 ) }.
% 0.70/1.08 substitution0:
% 0.70/1.08 end
% 0.70/1.08 permutation0:
% 0.70/1.08 0 ==> 0
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 eqswap: (109) {G0,W7,D3,L2,V2,M2} { ! singleton( Y ) = X, ! alpha1( X, Y )
% 0.70/1.08 }.
% 0.70/1.08 parent0[1]: (8) {G0,W7,D3,L2,V2,M2} I { ! alpha1( X, Y ), ! X = singleton(
% 0.70/1.08 Y ) }.
% 0.70/1.08 substitution0:
% 0.70/1.08 X := X
% 0.70/1.08 Y := Y
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 resolution: (110) {G1,W4,D3,L1,V0,M1} { ! singleton( skol4 ) = skol3 }.
% 0.70/1.08 parent0[1]: (109) {G0,W7,D3,L2,V2,M2} { ! singleton( Y ) = X, ! alpha1( X
% 0.70/1.08 , Y ) }.
% 0.70/1.08 parent1[0]: (27) {G2,W3,D2,L1,V0,M1} S(25);r(23) { alpha1( skol3, skol4 )
% 0.70/1.08 }.
% 0.70/1.08 substitution0:
% 0.70/1.08 X := skol3
% 0.70/1.08 Y := skol4
% 0.70/1.08 end
% 0.70/1.08 substitution1:
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 subsumption: (28) {G3,W4,D3,L1,V0,M1} R(8,27) { ! singleton( skol4 ) ==>
% 0.70/1.08 skol3 }.
% 0.70/1.08 parent0: (110) {G1,W4,D3,L1,V0,M1} { ! singleton( skol4 ) = skol3 }.
% 0.70/1.08 substitution0:
% 0.70/1.08 end
% 0.70/1.08 permutation0:
% 0.70/1.08 0 ==> 0
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 eqswap: (112) {G0,W10,D3,L3,V0,M3} { empty_set ==> skol3, alpha1( skol3,
% 0.70/1.08 skol4 ), singleton( skol4 ) ==> skol3 }.
% 0.70/1.08 parent0[1]: (4) {G0,W10,D3,L3,V0,M3} I { alpha1( skol3, skol4 ), skol3 ==>
% 0.70/1.08 empty_set, singleton( skol4 ) ==> skol3 }.
% 0.70/1.08 substitution0:
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 eqswap: (115) {G0,W11,D3,L3,V2,M3} { empty_set = X, ! subset( X, singleton
% 0.70/1.08 ( Y ) ), X = singleton( Y ) }.
% 0.70/1.08 parent0[1]: (10) {G0,W11,D3,L3,V2,M3} I { ! subset( X, singleton( Y ) ), X
% 0.70/1.08 = empty_set, X = singleton( Y ) }.
% 0.70/1.08 substitution0:
% 0.70/1.08 X := X
% 0.70/1.08 Y := Y
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 resolution: (118) {G1,W11,D3,L3,V0,M3} { subset( skol3, singleton( skol4 )
% 0.70/1.08 ), empty_set ==> skol3, singleton( skol4 ) ==> skol3 }.
% 0.70/1.08 parent0[0]: (6) {G0,W7,D3,L2,V2,M2} I { ! alpha1( X, Y ), subset( X,
% 0.70/1.08 singleton( Y ) ) }.
% 0.70/1.08 parent1[1]: (112) {G0,W10,D3,L3,V0,M3} { empty_set ==> skol3, alpha1(
% 0.70/1.08 skol3, skol4 ), singleton( skol4 ) ==> skol3 }.
% 0.70/1.08 substitution0:
% 0.70/1.08 X := skol3
% 0.70/1.08 Y := skol4
% 0.70/1.08 end
% 0.70/1.08 substitution1:
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 resolution: (119) {G1,W14,D3,L4,V0,M4} { empty_set = skol3, skol3 =
% 0.70/1.08 singleton( skol4 ), empty_set ==> skol3, singleton( skol4 ) ==> skol3 }.
% 0.70/1.08 parent0[1]: (115) {G0,W11,D3,L3,V2,M3} { empty_set = X, ! subset( X,
% 0.70/1.08 singleton( Y ) ), X = singleton( Y ) }.
% 0.70/1.08 parent1[0]: (118) {G1,W11,D3,L3,V0,M3} { subset( skol3, singleton( skol4 )
% 0.70/1.08 ), empty_set ==> skol3, singleton( skol4 ) ==> skol3 }.
% 0.70/1.08 substitution0:
% 0.70/1.08 X := skol3
% 0.70/1.08 Y := skol4
% 0.70/1.08 end
% 0.70/1.08 substitution1:
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 eqswap: (123) {G1,W14,D3,L4,V0,M4} { skol3 ==> singleton( skol4 ),
% 0.70/1.08 empty_set = skol3, skol3 = singleton( skol4 ), empty_set ==> skol3 }.
% 0.70/1.08 parent0[3]: (119) {G1,W14,D3,L4,V0,M4} { empty_set = skol3, skol3 =
% 0.70/1.08 singleton( skol4 ), empty_set ==> skol3, singleton( skol4 ) ==> skol3 }.
% 0.70/1.08 substitution0:
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 eqswap: (126) {G1,W14,D3,L4,V0,M4} { skol3 ==> empty_set, skol3 ==>
% 0.70/1.08 singleton( skol4 ), empty_set = skol3, skol3 = singleton( skol4 ) }.
% 0.70/1.08 parent0[3]: (123) {G1,W14,D3,L4,V0,M4} { skol3 ==> singleton( skol4 ),
% 0.70/1.08 empty_set = skol3, skol3 = singleton( skol4 ), empty_set ==> skol3 }.
% 0.70/1.08 substitution0:
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 eqswap: (128) {G1,W14,D3,L4,V0,M4} { singleton( skol4 ) = skol3, skol3 ==>
% 0.70/1.08 empty_set, skol3 ==> singleton( skol4 ), empty_set = skol3 }.
% 0.70/1.08 parent0[3]: (126) {G1,W14,D3,L4,V0,M4} { skol3 ==> empty_set, skol3 ==>
% 0.70/1.08 singleton( skol4 ), empty_set = skol3, skol3 = singleton( skol4 ) }.
% 0.70/1.08 substitution0:
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 eqswap: (130) {G1,W14,D3,L4,V0,M4} { skol3 = empty_set, singleton( skol4 )
% 0.70/1.08 = skol3, skol3 ==> empty_set, skol3 ==> singleton( skol4 ) }.
% 0.70/1.08 parent0[3]: (128) {G1,W14,D3,L4,V0,M4} { singleton( skol4 ) = skol3, skol3
% 0.70/1.08 ==> empty_set, skol3 ==> singleton( skol4 ), empty_set = skol3 }.
% 0.70/1.08 substitution0:
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 eqswap: (132) {G1,W14,D3,L4,V0,M4} { singleton( skol4 ) ==> skol3, skol3 =
% 0.70/1.08 empty_set, singleton( skol4 ) = skol3, skol3 ==> empty_set }.
% 0.70/1.08 parent0[3]: (130) {G1,W14,D3,L4,V0,M4} { skol3 = empty_set, singleton(
% 0.70/1.08 skol4 ) = skol3, skol3 ==> empty_set, skol3 ==> singleton( skol4 ) }.
% 0.70/1.08 substitution0:
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 factor: (147) {G1,W11,D3,L3,V0,M3} { singleton( skol4 ) ==> skol3, skol3 =
% 0.70/1.08 empty_set, singleton( skol4 ) = skol3 }.
% 0.70/1.08 parent0[1, 3]: (132) {G1,W14,D3,L4,V0,M4} { singleton( skol4 ) ==> skol3,
% 0.70/1.08 skol3 = empty_set, singleton( skol4 ) = skol3, skol3 ==> empty_set }.
% 0.70/1.08 substitution0:
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 factor: (148) {G1,W7,D3,L2,V0,M2} { singleton( skol4 ) ==> skol3, skol3 =
% 0.70/1.08 empty_set }.
% 0.70/1.08 parent0[0, 2]: (147) {G1,W11,D3,L3,V0,M3} { singleton( skol4 ) ==> skol3,
% 0.70/1.08 skol3 = empty_set, singleton( skol4 ) = skol3 }.
% 0.70/1.08 substitution0:
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 subsumption: (30) {G1,W7,D3,L2,V0,M2} R(6,4);r(10) { skol3 ==> empty_set,
% 0.70/1.08 singleton( skol4 ) ==> skol3 }.
% 0.70/1.08 parent0: (148) {G1,W7,D3,L2,V0,M2} { singleton( skol4 ) ==> skol3, skol3 =
% 0.70/1.08 empty_set }.
% 0.70/1.08 substitution0:
% 0.70/1.08 end
% 0.70/1.08 permutation0:
% 0.70/1.08 0 ==> 1
% 0.70/1.08 1 ==> 0
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 resolution: (160) {G2,W4,D3,L1,V0,M1} { singleton( skol4 ) ==> skol3 }.
% 0.70/1.08 parent0[0]: (23) {G1,W3,D2,L1,V0,M1} R(5,11);r(7) { ! skol3 ==> empty_set
% 0.70/1.08 }.
% 0.70/1.08 parent1[0]: (30) {G1,W7,D3,L2,V0,M2} R(6,4);r(10) { skol3 ==> empty_set,
% 0.70/1.08 singleton( skol4 ) ==> skol3 }.
% 0.70/1.08 substitution0:
% 0.70/1.08 end
% 0.70/1.08 substitution1:
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 resolution: (161) {G3,W0,D0,L0,V0,M0} { }.
% 0.70/1.08 parent0[0]: (28) {G3,W4,D3,L1,V0,M1} R(8,27) { ! singleton( skol4 ) ==>
% 0.70/1.08 skol3 }.
% 0.70/1.08 parent1[0]: (160) {G2,W4,D3,L1,V0,M1} { singleton( skol4 ) ==> skol3 }.
% 0.70/1.08 substitution0:
% 0.70/1.08 end
% 0.70/1.08 substitution1:
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 subsumption: (31) {G4,W0,D0,L0,V0,M0} S(30);r(23);r(28) { }.
% 0.70/1.08 parent0: (161) {G3,W0,D0,L0,V0,M0} { }.
% 0.70/1.08 substitution0:
% 0.70/1.08 end
% 0.70/1.08 permutation0:
% 0.70/1.08 end
% 0.70/1.08
% 0.70/1.08 Proof check complete!
% 0.70/1.08
% 0.70/1.08 Memory use:
% 0.70/1.08
% 0.70/1.08 space for terms: 445
% 0.70/1.08 space for clauses: 1708
% 0.70/1.08
% 0.70/1.08
% 0.70/1.08 clauses generated: 60
% 0.70/1.08 clauses kept: 32
% 0.70/1.08 clauses selected: 17
% 0.70/1.08 clauses deleted: 2
% 0.70/1.08 clauses inuse deleted: 0
% 0.70/1.08
% 0.70/1.08 subsentry: 1242
% 0.70/1.08 literals s-matched: 268
% 0.70/1.08 literals matched: 268
% 0.70/1.08 full subsumption: 0
% 0.70/1.08
% 0.70/1.08 checksum: 1111922463
% 0.70/1.08
% 0.70/1.08
% 0.70/1.08 Bliksem ended
%------------------------------------------------------------------------------