TSTP Solution File: SEU160+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SEU160+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n010.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 0.78s 1.16s
% Output : Refutation 0.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : SEU160+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.15 % Command : bliksem %s
% 0.15/0.36 % Computer : n010.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % DateTime : Mon Jun 20 03:20:52 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.78/1.16 *** allocated 10000 integers for termspace/termends
% 0.78/1.16 *** allocated 10000 integers for clauses
% 0.78/1.16 *** allocated 10000 integers for justifications
% 0.78/1.16 Bliksem 1.12
% 0.78/1.16
% 0.78/1.16
% 0.78/1.16 Automatic Strategy Selection
% 0.78/1.16
% 0.78/1.16
% 0.78/1.16 Clauses:
% 0.78/1.16
% 0.78/1.16 { empty( skol1 ) }.
% 0.78/1.16 { ! empty( skol2 ) }.
% 0.78/1.16 { subset( X, X ) }.
% 0.78/1.16 { && }.
% 0.78/1.16 { && }.
% 0.78/1.16 { empty( empty_set ) }.
% 0.78/1.16 { alpha1( skol3, skol4 ), skol3 = empty_set, skol3 = singleton( skol4 ) }.
% 0.78/1.16 { alpha1( skol3, skol4 ), ! subset( skol3, singleton( skol4 ) ) }.
% 0.78/1.16 { ! alpha1( X, Y ), subset( X, singleton( Y ) ) }.
% 0.78/1.16 { ! alpha1( X, Y ), ! X = empty_set }.
% 0.78/1.16 { ! alpha1( X, Y ), ! X = singleton( Y ) }.
% 0.78/1.16 { ! subset( X, singleton( Y ) ), X = empty_set, X = singleton( Y ), alpha1
% 0.78/1.16 ( X, Y ) }.
% 0.78/1.16 { ! subset( X, singleton( Y ) ), X = empty_set, X = singleton( Y ) }.
% 0.78/1.16 { ! X = empty_set, subset( X, singleton( Y ) ) }.
% 0.78/1.16 { ! X = singleton( Y ), subset( X, singleton( Y ) ) }.
% 0.78/1.16
% 0.78/1.16 percentage equality = 0.370370, percentage horn = 0.785714
% 0.78/1.16 This is a problem with some equality
% 0.78/1.16
% 0.78/1.16
% 0.78/1.16
% 0.78/1.16 Options Used:
% 0.78/1.16
% 0.78/1.16 useres = 1
% 0.78/1.16 useparamod = 1
% 0.78/1.16 useeqrefl = 1
% 0.78/1.16 useeqfact = 1
% 0.78/1.16 usefactor = 1
% 0.78/1.16 usesimpsplitting = 0
% 0.78/1.16 usesimpdemod = 5
% 0.78/1.16 usesimpres = 3
% 0.78/1.16
% 0.78/1.16 resimpinuse = 1000
% 0.78/1.16 resimpclauses = 20000
% 0.78/1.16 substype = eqrewr
% 0.78/1.16 backwardsubs = 1
% 0.78/1.16 selectoldest = 5
% 0.78/1.16
% 0.78/1.16 litorderings [0] = split
% 0.78/1.16 litorderings [1] = extend the termordering, first sorting on arguments
% 0.78/1.16
% 0.78/1.16 termordering = kbo
% 0.78/1.16
% 0.78/1.16 litapriori = 0
% 0.78/1.16 termapriori = 1
% 0.78/1.16 litaposteriori = 0
% 0.78/1.16 termaposteriori = 0
% 0.78/1.16 demodaposteriori = 0
% 0.78/1.16 ordereqreflfact = 0
% 0.78/1.16
% 0.78/1.16 litselect = negord
% 0.78/1.16
% 0.78/1.16 maxweight = 15
% 0.78/1.16 maxdepth = 30000
% 0.78/1.16 maxlength = 115
% 0.78/1.16 maxnrvars = 195
% 0.78/1.16 excuselevel = 1
% 0.78/1.16 increasemaxweight = 1
% 0.78/1.16
% 0.78/1.16 maxselected = 10000000
% 0.78/1.16 maxnrclauses = 10000000
% 0.78/1.16
% 0.78/1.16 showgenerated = 0
% 0.78/1.16 showkept = 0
% 0.78/1.16 showselected = 0
% 0.78/1.16 showdeleted = 0
% 0.78/1.16 showresimp = 1
% 0.78/1.16 showstatus = 2000
% 0.78/1.16
% 0.78/1.16 prologoutput = 0
% 0.78/1.16 nrgoals = 5000000
% 0.78/1.16 totalproof = 1
% 0.78/1.16
% 0.78/1.16 Symbols occurring in the translation:
% 0.78/1.16
% 0.78/1.16 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.78/1.16 . [1, 2] (w:1, o:20, a:1, s:1, b:0),
% 0.78/1.16 && [3, 0] (w:1, o:4, a:1, s:1, b:0),
% 0.78/1.16 ! [4, 1] (w:0, o:13, a:1, s:1, b:0),
% 0.78/1.16 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.78/1.16 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.78/1.16 empty [36, 1] (w:1, o:18, a:1, s:1, b:0),
% 0.78/1.16 subset [38, 2] (w:1, o:44, a:1, s:1, b:0),
% 0.78/1.16 empty_set [39, 0] (w:1, o:8, a:1, s:1, b:0),
% 0.78/1.16 singleton [40, 1] (w:1, o:19, a:1, s:1, b:0),
% 0.78/1.16 alpha1 [41, 2] (w:1, o:45, a:1, s:1, b:1),
% 0.78/1.16 skol1 [42, 0] (w:1, o:9, a:1, s:1, b:1),
% 0.78/1.16 skol2 [43, 0] (w:1, o:10, a:1, s:1, b:1),
% 0.78/1.16 skol3 [44, 0] (w:1, o:11, a:1, s:1, b:1),
% 0.78/1.16 skol4 [45, 0] (w:1, o:12, a:1, s:1, b:1).
% 0.78/1.16
% 0.78/1.16
% 0.78/1.16 Starting Search:
% 0.78/1.16
% 0.78/1.16
% 0.78/1.16 Bliksems!, er is een bewijs:
% 0.78/1.16 % SZS status Theorem
% 0.78/1.16 % SZS output start Refutation
% 0.78/1.16
% 0.78/1.16 (2) {G0,W3,D2,L1,V1,M1} I { subset( X, X ) }.
% 0.78/1.16 (5) {G0,W10,D3,L3,V0,M3} I { alpha1( skol3, skol4 ), skol3 ==> empty_set,
% 0.78/1.16 singleton( skol4 ) ==> skol3 }.
% 0.78/1.16 (6) {G0,W7,D3,L2,V0,M2} I { alpha1( skol3, skol4 ), ! subset( skol3,
% 0.78/1.16 singleton( skol4 ) ) }.
% 0.78/1.16 (7) {G0,W7,D3,L2,V2,M2} I { ! alpha1( X, Y ), subset( X, singleton( Y ) )
% 0.78/1.16 }.
% 0.78/1.16 (8) {G0,W6,D2,L2,V2,M2} I { ! alpha1( X, Y ), ! X = empty_set }.
% 0.78/1.16 (9) {G0,W7,D3,L2,V2,M2} I { ! alpha1( X, Y ), ! X = singleton( Y ) }.
% 0.78/1.16 (11) {G0,W11,D3,L3,V2,M3} I { ! subset( X, singleton( Y ) ), X = empty_set
% 0.78/1.16 , X = singleton( Y ) }.
% 0.78/1.16 (12) {G0,W7,D3,L2,V2,M2} I { ! X = empty_set, subset( X, singleton( Y ) )
% 0.78/1.16 }.
% 0.78/1.16 (14) {G1,W3,D2,L1,V1,M1} Q(8) { ! alpha1( empty_set, X ) }.
% 0.78/1.16 (26) {G1,W7,D3,L2,V0,M2} R(7,5);r(11) { skol3 ==> empty_set, singleton(
% 0.78/1.16 skol4 ) ==> skol3 }.
% 0.78/1.16 (29) {G2,W9,D2,L3,V1,M3} P(26,9) { ! alpha1( X, skol4 ), ! X = skol3, skol3
% 0.78/1.16 ==> empty_set }.
% 0.78/1.16 (32) {G3,W6,D2,L2,V0,M2} Q(29) { ! alpha1( skol3, skol4 ), skol3 ==>
% 0.78/1.16 empty_set }.
% 0.78/1.16 (33) {G4,W3,D2,L1,V0,M1} R(6,32);d(26);r(2) { skol3 ==> empty_set }.
% 0.78/1.16 (35) {G5,W0,D0,L0,V0,M0} R(6,12);d(33);d(33);q;r(14) { }.
% 0.78/1.16
% 0.78/1.16
% 0.78/1.16 % SZS output end Refutation
% 0.78/1.16 found a proof!
% 0.78/1.16
% 0.78/1.16
% 0.78/1.16 Unprocessed initial clauses:
% 0.78/1.16
% 0.78/1.16 (37) {G0,W2,D2,L1,V0,M1} { empty( skol1 ) }.
% 0.78/1.16 (38) {G0,W2,D2,L1,V0,M1} { ! empty( skol2 ) }.
% 0.78/1.16 (39) {G0,W3,D2,L1,V1,M1} { subset( X, X ) }.
% 0.78/1.16 (40) {G0,W1,D1,L1,V0,M1} { && }.
% 0.78/1.16 (41) {G0,W1,D1,L1,V0,M1} { && }.
% 0.78/1.16 (42) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.78/1.16 (43) {G0,W10,D3,L3,V0,M3} { alpha1( skol3, skol4 ), skol3 = empty_set,
% 0.78/1.16 skol3 = singleton( skol4 ) }.
% 0.78/1.16 (44) {G0,W7,D3,L2,V0,M2} { alpha1( skol3, skol4 ), ! subset( skol3,
% 0.78/1.16 singleton( skol4 ) ) }.
% 0.78/1.16 (45) {G0,W7,D3,L2,V2,M2} { ! alpha1( X, Y ), subset( X, singleton( Y ) )
% 0.78/1.16 }.
% 0.78/1.16 (46) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), ! X = empty_set }.
% 0.78/1.16 (47) {G0,W7,D3,L2,V2,M2} { ! alpha1( X, Y ), ! X = singleton( Y ) }.
% 0.78/1.16 (48) {G0,W14,D3,L4,V2,M4} { ! subset( X, singleton( Y ) ), X = empty_set,
% 0.78/1.16 X = singleton( Y ), alpha1( X, Y ) }.
% 0.78/1.16 (49) {G0,W11,D3,L3,V2,M3} { ! subset( X, singleton( Y ) ), X = empty_set,
% 0.78/1.16 X = singleton( Y ) }.
% 0.78/1.16 (50) {G0,W7,D3,L2,V2,M2} { ! X = empty_set, subset( X, singleton( Y ) )
% 0.78/1.16 }.
% 0.78/1.16 (51) {G0,W8,D3,L2,V2,M2} { ! X = singleton( Y ), subset( X, singleton( Y )
% 0.78/1.16 ) }.
% 0.78/1.16
% 0.78/1.16
% 0.78/1.16 Total Proof:
% 0.78/1.16
% 0.78/1.16 subsumption: (2) {G0,W3,D2,L1,V1,M1} I { subset( X, X ) }.
% 0.78/1.16 parent0: (39) {G0,W3,D2,L1,V1,M1} { subset( X, X ) }.
% 0.78/1.16 substitution0:
% 0.78/1.16 X := X
% 0.78/1.16 end
% 0.78/1.16 permutation0:
% 0.78/1.16 0 ==> 0
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 eqswap: (53) {G0,W10,D3,L3,V0,M3} { singleton( skol4 ) = skol3, alpha1(
% 0.78/1.16 skol3, skol4 ), skol3 = empty_set }.
% 0.78/1.16 parent0[2]: (43) {G0,W10,D3,L3,V0,M3} { alpha1( skol3, skol4 ), skol3 =
% 0.78/1.16 empty_set, skol3 = singleton( skol4 ) }.
% 0.78/1.16 substitution0:
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 subsumption: (5) {G0,W10,D3,L3,V0,M3} I { alpha1( skol3, skol4 ), skol3 ==>
% 0.78/1.16 empty_set, singleton( skol4 ) ==> skol3 }.
% 0.78/1.16 parent0: (53) {G0,W10,D3,L3,V0,M3} { singleton( skol4 ) = skol3, alpha1(
% 0.78/1.16 skol3, skol4 ), skol3 = empty_set }.
% 0.78/1.16 substitution0:
% 0.78/1.16 end
% 0.78/1.16 permutation0:
% 0.78/1.16 0 ==> 2
% 0.78/1.16 1 ==> 0
% 0.78/1.16 2 ==> 1
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 subsumption: (6) {G0,W7,D3,L2,V0,M2} I { alpha1( skol3, skol4 ), ! subset(
% 0.78/1.16 skol3, singleton( skol4 ) ) }.
% 0.78/1.16 parent0: (44) {G0,W7,D3,L2,V0,M2} { alpha1( skol3, skol4 ), ! subset(
% 0.78/1.16 skol3, singleton( skol4 ) ) }.
% 0.78/1.16 substitution0:
% 0.78/1.16 end
% 0.78/1.16 permutation0:
% 0.78/1.16 0 ==> 0
% 0.78/1.16 1 ==> 1
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 subsumption: (7) {G0,W7,D3,L2,V2,M2} I { ! alpha1( X, Y ), subset( X,
% 0.78/1.16 singleton( Y ) ) }.
% 0.78/1.16 parent0: (45) {G0,W7,D3,L2,V2,M2} { ! alpha1( X, Y ), subset( X, singleton
% 0.78/1.16 ( Y ) ) }.
% 0.78/1.16 substitution0:
% 0.78/1.16 X := X
% 0.78/1.16 Y := Y
% 0.78/1.16 end
% 0.78/1.16 permutation0:
% 0.78/1.16 0 ==> 0
% 0.78/1.16 1 ==> 1
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 subsumption: (8) {G0,W6,D2,L2,V2,M2} I { ! alpha1( X, Y ), ! X = empty_set
% 0.78/1.16 }.
% 0.78/1.16 parent0: (46) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), ! X = empty_set }.
% 0.78/1.16 substitution0:
% 0.78/1.16 X := X
% 0.78/1.16 Y := Y
% 0.78/1.16 end
% 0.78/1.16 permutation0:
% 0.78/1.16 0 ==> 0
% 0.78/1.16 1 ==> 1
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 subsumption: (9) {G0,W7,D3,L2,V2,M2} I { ! alpha1( X, Y ), ! X = singleton
% 0.78/1.16 ( Y ) }.
% 0.78/1.16 parent0: (47) {G0,W7,D3,L2,V2,M2} { ! alpha1( X, Y ), ! X = singleton( Y )
% 0.78/1.16 }.
% 0.78/1.16 substitution0:
% 0.78/1.16 X := X
% 0.78/1.16 Y := Y
% 0.78/1.16 end
% 0.78/1.16 permutation0:
% 0.78/1.16 0 ==> 0
% 0.78/1.16 1 ==> 1
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 subsumption: (11) {G0,W11,D3,L3,V2,M3} I { ! subset( X, singleton( Y ) ), X
% 0.78/1.16 = empty_set, X = singleton( Y ) }.
% 0.78/1.16 parent0: (49) {G0,W11,D3,L3,V2,M3} { ! subset( X, singleton( Y ) ), X =
% 0.78/1.16 empty_set, X = singleton( Y ) }.
% 0.78/1.16 substitution0:
% 0.78/1.16 X := X
% 0.78/1.16 Y := Y
% 0.78/1.16 end
% 0.78/1.16 permutation0:
% 0.78/1.16 0 ==> 0
% 0.78/1.16 1 ==> 1
% 0.78/1.16 2 ==> 2
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 subsumption: (12) {G0,W7,D3,L2,V2,M2} I { ! X = empty_set, subset( X,
% 0.78/1.16 singleton( Y ) ) }.
% 0.78/1.16 parent0: (50) {G0,W7,D3,L2,V2,M2} { ! X = empty_set, subset( X, singleton
% 0.78/1.16 ( Y ) ) }.
% 0.78/1.16 substitution0:
% 0.78/1.16 X := X
% 0.78/1.16 Y := Y
% 0.78/1.16 end
% 0.78/1.16 permutation0:
% 0.78/1.16 0 ==> 0
% 0.78/1.16 1 ==> 1
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 eqswap: (93) {G0,W6,D2,L2,V2,M2} { ! empty_set = X, ! alpha1( X, Y ) }.
% 0.78/1.16 parent0[1]: (8) {G0,W6,D2,L2,V2,M2} I { ! alpha1( X, Y ), ! X = empty_set
% 0.78/1.16 }.
% 0.78/1.16 substitution0:
% 0.78/1.16 X := X
% 0.78/1.16 Y := Y
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 eqrefl: (94) {G0,W3,D2,L1,V1,M1} { ! alpha1( empty_set, X ) }.
% 0.78/1.16 parent0[0]: (93) {G0,W6,D2,L2,V2,M2} { ! empty_set = X, ! alpha1( X, Y )
% 0.78/1.16 }.
% 0.78/1.16 substitution0:
% 0.78/1.16 X := empty_set
% 0.78/1.16 Y := X
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 subsumption: (14) {G1,W3,D2,L1,V1,M1} Q(8) { ! alpha1( empty_set, X ) }.
% 0.78/1.16 parent0: (94) {G0,W3,D2,L1,V1,M1} { ! alpha1( empty_set, X ) }.
% 0.78/1.16 substitution0:
% 0.78/1.16 X := X
% 0.78/1.16 end
% 0.78/1.16 permutation0:
% 0.78/1.16 0 ==> 0
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 eqswap: (95) {G0,W10,D3,L3,V0,M3} { empty_set ==> skol3, alpha1( skol3,
% 0.78/1.16 skol4 ), singleton( skol4 ) ==> skol3 }.
% 0.78/1.16 parent0[1]: (5) {G0,W10,D3,L3,V0,M3} I { alpha1( skol3, skol4 ), skol3 ==>
% 0.78/1.16 empty_set, singleton( skol4 ) ==> skol3 }.
% 0.78/1.16 substitution0:
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 eqswap: (98) {G0,W11,D3,L3,V2,M3} { empty_set = X, ! subset( X, singleton
% 0.78/1.16 ( Y ) ), X = singleton( Y ) }.
% 0.78/1.16 parent0[1]: (11) {G0,W11,D3,L3,V2,M3} I { ! subset( X, singleton( Y ) ), X
% 0.78/1.16 = empty_set, X = singleton( Y ) }.
% 0.78/1.16 substitution0:
% 0.78/1.16 X := X
% 0.78/1.16 Y := Y
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 resolution: (101) {G1,W11,D3,L3,V0,M3} { subset( skol3, singleton( skol4 )
% 0.78/1.16 ), empty_set ==> skol3, singleton( skol4 ) ==> skol3 }.
% 0.78/1.16 parent0[0]: (7) {G0,W7,D3,L2,V2,M2} I { ! alpha1( X, Y ), subset( X,
% 0.78/1.16 singleton( Y ) ) }.
% 0.78/1.16 parent1[1]: (95) {G0,W10,D3,L3,V0,M3} { empty_set ==> skol3, alpha1( skol3
% 0.78/1.16 , skol4 ), singleton( skol4 ) ==> skol3 }.
% 0.78/1.16 substitution0:
% 0.78/1.16 X := skol3
% 0.78/1.16 Y := skol4
% 0.78/1.16 end
% 0.78/1.16 substitution1:
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 resolution: (102) {G1,W14,D3,L4,V0,M4} { empty_set = skol3, skol3 =
% 0.78/1.16 singleton( skol4 ), empty_set ==> skol3, singleton( skol4 ) ==> skol3 }.
% 0.78/1.16 parent0[1]: (98) {G0,W11,D3,L3,V2,M3} { empty_set = X, ! subset( X,
% 0.78/1.16 singleton( Y ) ), X = singleton( Y ) }.
% 0.78/1.16 parent1[0]: (101) {G1,W11,D3,L3,V0,M3} { subset( skol3, singleton( skol4 )
% 0.78/1.16 ), empty_set ==> skol3, singleton( skol4 ) ==> skol3 }.
% 0.78/1.16 substitution0:
% 0.78/1.16 X := skol3
% 0.78/1.16 Y := skol4
% 0.78/1.16 end
% 0.78/1.16 substitution1:
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 eqswap: (106) {G1,W14,D3,L4,V0,M4} { skol3 ==> singleton( skol4 ),
% 0.78/1.16 empty_set = skol3, skol3 = singleton( skol4 ), empty_set ==> skol3 }.
% 0.78/1.16 parent0[3]: (102) {G1,W14,D3,L4,V0,M4} { empty_set = skol3, skol3 =
% 0.78/1.16 singleton( skol4 ), empty_set ==> skol3, singleton( skol4 ) ==> skol3 }.
% 0.78/1.16 substitution0:
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 eqswap: (109) {G1,W14,D3,L4,V0,M4} { skol3 ==> empty_set, skol3 ==>
% 0.78/1.16 singleton( skol4 ), empty_set = skol3, skol3 = singleton( skol4 ) }.
% 0.78/1.16 parent0[3]: (106) {G1,W14,D3,L4,V0,M4} { skol3 ==> singleton( skol4 ),
% 0.78/1.16 empty_set = skol3, skol3 = singleton( skol4 ), empty_set ==> skol3 }.
% 0.78/1.16 substitution0:
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 eqswap: (111) {G1,W14,D3,L4,V0,M4} { singleton( skol4 ) = skol3, skol3 ==>
% 0.78/1.16 empty_set, skol3 ==> singleton( skol4 ), empty_set = skol3 }.
% 0.78/1.16 parent0[3]: (109) {G1,W14,D3,L4,V0,M4} { skol3 ==> empty_set, skol3 ==>
% 0.78/1.16 singleton( skol4 ), empty_set = skol3, skol3 = singleton( skol4 ) }.
% 0.78/1.16 substitution0:
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 eqswap: (113) {G1,W14,D3,L4,V0,M4} { skol3 = empty_set, singleton( skol4 )
% 0.78/1.16 = skol3, skol3 ==> empty_set, skol3 ==> singleton( skol4 ) }.
% 0.78/1.16 parent0[3]: (111) {G1,W14,D3,L4,V0,M4} { singleton( skol4 ) = skol3, skol3
% 0.78/1.16 ==> empty_set, skol3 ==> singleton( skol4 ), empty_set = skol3 }.
% 0.78/1.16 substitution0:
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 eqswap: (115) {G1,W14,D3,L4,V0,M4} { singleton( skol4 ) ==> skol3, skol3 =
% 0.78/1.16 empty_set, singleton( skol4 ) = skol3, skol3 ==> empty_set }.
% 0.78/1.16 parent0[3]: (113) {G1,W14,D3,L4,V0,M4} { skol3 = empty_set, singleton(
% 0.78/1.16 skol4 ) = skol3, skol3 ==> empty_set, skol3 ==> singleton( skol4 ) }.
% 0.78/1.16 substitution0:
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 factor: (130) {G1,W11,D3,L3,V0,M3} { singleton( skol4 ) ==> skol3, skol3 =
% 0.78/1.16 empty_set, singleton( skol4 ) = skol3 }.
% 0.78/1.16 parent0[1, 3]: (115) {G1,W14,D3,L4,V0,M4} { singleton( skol4 ) ==> skol3,
% 0.78/1.16 skol3 = empty_set, singleton( skol4 ) = skol3, skol3 ==> empty_set }.
% 0.78/1.16 substitution0:
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 factor: (131) {G1,W7,D3,L2,V0,M2} { singleton( skol4 ) ==> skol3, skol3 =
% 0.78/1.16 empty_set }.
% 0.78/1.16 parent0[0, 2]: (130) {G1,W11,D3,L3,V0,M3} { singleton( skol4 ) ==> skol3,
% 0.78/1.16 skol3 = empty_set, singleton( skol4 ) = skol3 }.
% 0.78/1.16 substitution0:
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 subsumption: (26) {G1,W7,D3,L2,V0,M2} R(7,5);r(11) { skol3 ==> empty_set,
% 0.78/1.16 singleton( skol4 ) ==> skol3 }.
% 0.78/1.16 parent0: (131) {G1,W7,D3,L2,V0,M2} { singleton( skol4 ) ==> skol3, skol3 =
% 0.78/1.16 empty_set }.
% 0.78/1.16 substitution0:
% 0.78/1.16 end
% 0.78/1.16 permutation0:
% 0.78/1.16 0 ==> 1
% 0.78/1.16 1 ==> 0
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 eqswap: (138) {G1,W7,D3,L2,V0,M2} { empty_set ==> skol3, singleton( skol4
% 0.78/1.16 ) ==> skol3 }.
% 0.78/1.16 parent0[0]: (26) {G1,W7,D3,L2,V0,M2} R(7,5);r(11) { skol3 ==> empty_set,
% 0.78/1.16 singleton( skol4 ) ==> skol3 }.
% 0.78/1.16 substitution0:
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 eqswap: (141) {G0,W7,D3,L2,V2,M2} { ! singleton( Y ) = X, ! alpha1( X, Y )
% 0.78/1.16 }.
% 0.78/1.16 parent0[1]: (9) {G0,W7,D3,L2,V2,M2} I { ! alpha1( X, Y ), ! X = singleton(
% 0.78/1.16 Y ) }.
% 0.78/1.16 substitution0:
% 0.78/1.16 X := X
% 0.78/1.16 Y := Y
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 paramod: (142) {G1,W9,D2,L3,V1,M3} { ! skol3 = X, empty_set ==> skol3, !
% 0.78/1.16 alpha1( X, skol4 ) }.
% 0.78/1.16 parent0[1]: (138) {G1,W7,D3,L2,V0,M2} { empty_set ==> skol3, singleton(
% 0.78/1.16 skol4 ) ==> skol3 }.
% 0.78/1.16 parent1[0; 2]: (141) {G0,W7,D3,L2,V2,M2} { ! singleton( Y ) = X, ! alpha1
% 0.78/1.16 ( X, Y ) }.
% 0.78/1.16 substitution0:
% 0.78/1.16 end
% 0.78/1.16 substitution1:
% 0.78/1.16 X := X
% 0.78/1.16 Y := skol4
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 eqswap: (144) {G1,W9,D2,L3,V1,M3} { skol3 ==> empty_set, ! skol3 = X, !
% 0.78/1.16 alpha1( X, skol4 ) }.
% 0.78/1.16 parent0[1]: (142) {G1,W9,D2,L3,V1,M3} { ! skol3 = X, empty_set ==> skol3,
% 0.78/1.16 ! alpha1( X, skol4 ) }.
% 0.78/1.16 substitution0:
% 0.78/1.16 X := X
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 eqswap: (145) {G1,W9,D2,L3,V1,M3} { ! X = skol3, skol3 ==> empty_set, !
% 0.78/1.16 alpha1( X, skol4 ) }.
% 0.78/1.16 parent0[1]: (144) {G1,W9,D2,L3,V1,M3} { skol3 ==> empty_set, ! skol3 = X,
% 0.78/1.16 ! alpha1( X, skol4 ) }.
% 0.78/1.16 substitution0:
% 0.78/1.16 X := X
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 subsumption: (29) {G2,W9,D2,L3,V1,M3} P(26,9) { ! alpha1( X, skol4 ), ! X =
% 0.78/1.16 skol3, skol3 ==> empty_set }.
% 0.78/1.16 parent0: (145) {G1,W9,D2,L3,V1,M3} { ! X = skol3, skol3 ==> empty_set, !
% 0.78/1.16 alpha1( X, skol4 ) }.
% 0.78/1.16 substitution0:
% 0.78/1.16 X := X
% 0.78/1.16 end
% 0.78/1.16 permutation0:
% 0.78/1.16 0 ==> 1
% 0.78/1.16 1 ==> 2
% 0.78/1.16 2 ==> 0
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 eqswap: (146) {G2,W9,D2,L3,V1,M3} { ! skol3 = X, ! alpha1( X, skol4 ),
% 0.78/1.16 skol3 ==> empty_set }.
% 0.78/1.16 parent0[1]: (29) {G2,W9,D2,L3,V1,M3} P(26,9) { ! alpha1( X, skol4 ), ! X =
% 0.78/1.16 skol3, skol3 ==> empty_set }.
% 0.78/1.16 substitution0:
% 0.78/1.16 X := X
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 eqrefl: (149) {G0,W6,D2,L2,V0,M2} { ! alpha1( skol3, skol4 ), skol3 ==>
% 0.78/1.16 empty_set }.
% 0.78/1.16 parent0[0]: (146) {G2,W9,D2,L3,V1,M3} { ! skol3 = X, ! alpha1( X, skol4 )
% 0.78/1.16 , skol3 ==> empty_set }.
% 0.78/1.16 substitution0:
% 0.78/1.16 X := skol3
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 subsumption: (32) {G3,W6,D2,L2,V0,M2} Q(29) { ! alpha1( skol3, skol4 ),
% 0.78/1.16 skol3 ==> empty_set }.
% 0.78/1.16 parent0: (149) {G0,W6,D2,L2,V0,M2} { ! alpha1( skol3, skol4 ), skol3 ==>
% 0.78/1.16 empty_set }.
% 0.78/1.16 substitution0:
% 0.78/1.16 end
% 0.78/1.16 permutation0:
% 0.78/1.16 0 ==> 0
% 0.78/1.16 1 ==> 1
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 eqswap: (151) {G3,W6,D2,L2,V0,M2} { empty_set ==> skol3, ! alpha1( skol3,
% 0.78/1.16 skol4 ) }.
% 0.78/1.16 parent0[1]: (32) {G3,W6,D2,L2,V0,M2} Q(29) { ! alpha1( skol3, skol4 ),
% 0.78/1.16 skol3 ==> empty_set }.
% 0.78/1.16 substitution0:
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 eqswap: (152) {G1,W7,D3,L2,V0,M2} { empty_set ==> skol3, singleton( skol4
% 0.78/1.16 ) ==> skol3 }.
% 0.78/1.16 parent0[0]: (26) {G1,W7,D3,L2,V0,M2} R(7,5);r(11) { skol3 ==> empty_set,
% 0.78/1.16 singleton( skol4 ) ==> skol3 }.
% 0.78/1.16 substitution0:
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 resolution: (155) {G1,W7,D3,L2,V0,M2} { empty_set ==> skol3, ! subset(
% 0.78/1.16 skol3, singleton( skol4 ) ) }.
% 0.78/1.16 parent0[1]: (151) {G3,W6,D2,L2,V0,M2} { empty_set ==> skol3, ! alpha1(
% 0.78/1.16 skol3, skol4 ) }.
% 0.78/1.16 parent1[0]: (6) {G0,W7,D3,L2,V0,M2} I { alpha1( skol3, skol4 ), ! subset(
% 0.78/1.16 skol3, singleton( skol4 ) ) }.
% 0.78/1.16 substitution0:
% 0.78/1.16 end
% 0.78/1.16 substitution1:
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 paramod: (156) {G2,W9,D2,L3,V0,M3} { ! subset( skol3, skol3 ), empty_set
% 0.78/1.16 ==> skol3, empty_set ==> skol3 }.
% 0.78/1.16 parent0[1]: (152) {G1,W7,D3,L2,V0,M2} { empty_set ==> skol3, singleton(
% 0.78/1.16 skol4 ) ==> skol3 }.
% 0.78/1.16 parent1[1; 3]: (155) {G1,W7,D3,L2,V0,M2} { empty_set ==> skol3, ! subset(
% 0.78/1.16 skol3, singleton( skol4 ) ) }.
% 0.78/1.16 substitution0:
% 0.78/1.16 end
% 0.78/1.16 substitution1:
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 factor: (157) {G2,W6,D2,L2,V0,M2} { ! subset( skol3, skol3 ), empty_set
% 0.78/1.16 ==> skol3 }.
% 0.78/1.16 parent0[1, 2]: (156) {G2,W9,D2,L3,V0,M3} { ! subset( skol3, skol3 ),
% 0.78/1.16 empty_set ==> skol3, empty_set ==> skol3 }.
% 0.78/1.16 substitution0:
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 resolution: (158) {G1,W3,D2,L1,V0,M1} { empty_set ==> skol3 }.
% 0.78/1.16 parent0[0]: (157) {G2,W6,D2,L2,V0,M2} { ! subset( skol3, skol3 ),
% 0.78/1.16 empty_set ==> skol3 }.
% 0.78/1.16 parent1[0]: (2) {G0,W3,D2,L1,V1,M1} I { subset( X, X ) }.
% 0.78/1.16 substitution0:
% 0.78/1.16 end
% 0.78/1.16 substitution1:
% 0.78/1.16 X := skol3
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 eqswap: (159) {G1,W3,D2,L1,V0,M1} { skol3 ==> empty_set }.
% 0.78/1.16 parent0[0]: (158) {G1,W3,D2,L1,V0,M1} { empty_set ==> skol3 }.
% 0.78/1.16 substitution0:
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 subsumption: (33) {G4,W3,D2,L1,V0,M1} R(6,32);d(26);r(2) { skol3 ==>
% 0.78/1.16 empty_set }.
% 0.78/1.16 parent0: (159) {G1,W3,D2,L1,V0,M1} { skol3 ==> empty_set }.
% 0.78/1.16 substitution0:
% 0.78/1.16 end
% 0.78/1.16 permutation0:
% 0.78/1.16 0 ==> 0
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 eqswap: (160) {G0,W7,D3,L2,V2,M2} { ! empty_set = X, subset( X, singleton
% 0.78/1.16 ( Y ) ) }.
% 0.78/1.16 parent0[0]: (12) {G0,W7,D3,L2,V2,M2} I { ! X = empty_set, subset( X,
% 0.78/1.16 singleton( Y ) ) }.
% 0.78/1.16 substitution0:
% 0.78/1.16 X := X
% 0.78/1.16 Y := Y
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 resolution: (163) {G1,W6,D2,L2,V0,M2} { alpha1( skol3, skol4 ), !
% 0.78/1.16 empty_set = skol3 }.
% 0.78/1.16 parent0[1]: (6) {G0,W7,D3,L2,V0,M2} I { alpha1( skol3, skol4 ), ! subset(
% 0.78/1.16 skol3, singleton( skol4 ) ) }.
% 0.78/1.16 parent1[1]: (160) {G0,W7,D3,L2,V2,M2} { ! empty_set = X, subset( X,
% 0.78/1.16 singleton( Y ) ) }.
% 0.78/1.16 substitution0:
% 0.78/1.16 end
% 0.78/1.16 substitution1:
% 0.78/1.16 X := skol3
% 0.78/1.16 Y := skol4
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 paramod: (165) {G2,W6,D2,L2,V0,M2} { ! empty_set = empty_set, alpha1(
% 0.78/1.16 skol3, skol4 ) }.
% 0.78/1.16 parent0[0]: (33) {G4,W3,D2,L1,V0,M1} R(6,32);d(26);r(2) { skol3 ==>
% 0.78/1.16 empty_set }.
% 0.78/1.16 parent1[1; 3]: (163) {G1,W6,D2,L2,V0,M2} { alpha1( skol3, skol4 ), !
% 0.78/1.16 empty_set = skol3 }.
% 0.78/1.16 substitution0:
% 0.78/1.16 end
% 0.78/1.16 substitution1:
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 paramod: (167) {G3,W6,D2,L2,V0,M2} { alpha1( empty_set, skol4 ), !
% 0.78/1.16 empty_set = empty_set }.
% 0.78/1.16 parent0[0]: (33) {G4,W3,D2,L1,V0,M1} R(6,32);d(26);r(2) { skol3 ==>
% 0.78/1.16 empty_set }.
% 0.78/1.16 parent1[1; 1]: (165) {G2,W6,D2,L2,V0,M2} { ! empty_set = empty_set, alpha1
% 0.78/1.16 ( skol3, skol4 ) }.
% 0.78/1.16 substitution0:
% 0.78/1.16 end
% 0.78/1.16 substitution1:
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 eqrefl: (168) {G0,W3,D2,L1,V0,M1} { alpha1( empty_set, skol4 ) }.
% 0.78/1.16 parent0[1]: (167) {G3,W6,D2,L2,V0,M2} { alpha1( empty_set, skol4 ), !
% 0.78/1.16 empty_set = empty_set }.
% 0.78/1.16 substitution0:
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 resolution: (169) {G1,W0,D0,L0,V0,M0} { }.
% 0.78/1.16 parent0[0]: (14) {G1,W3,D2,L1,V1,M1} Q(8) { ! alpha1( empty_set, X ) }.
% 0.78/1.16 parent1[0]: (168) {G0,W3,D2,L1,V0,M1} { alpha1( empty_set, skol4 ) }.
% 0.78/1.16 substitution0:
% 0.78/1.16 X := skol4
% 0.78/1.16 end
% 0.78/1.16 substitution1:
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 subsumption: (35) {G5,W0,D0,L0,V0,M0} R(6,12);d(33);d(33);q;r(14) { }.
% 0.78/1.16 parent0: (169) {G1,W0,D0,L0,V0,M0} { }.
% 0.78/1.16 substitution0:
% 0.78/1.16 end
% 0.78/1.16 permutation0:
% 0.78/1.16 end
% 0.78/1.16
% 0.78/1.16 Proof check complete!
% 0.78/1.16
% 0.78/1.16 Memory use:
% 0.78/1.16
% 0.78/1.16 space for terms: 500
% 0.78/1.16 space for clauses: 1851
% 0.78/1.16
% 0.78/1.16
% 0.78/1.16 clauses generated: 70
% 0.78/1.16 clauses kept: 36
% 0.78/1.16 clauses selected: 16
% 0.78/1.16 clauses deleted: 0
% 0.78/1.16 clauses inuse deleted: 0
% 0.78/1.16
% 0.78/1.16 subsentry: 1260
% 0.78/1.16 literals s-matched: 261
% 0.78/1.16 literals matched: 261
% 0.78/1.16 full subsumption: 0
% 0.78/1.16
% 0.78/1.16 checksum: 537548880
% 0.78/1.16
% 0.78/1.16
% 0.78/1.16 Bliksem ended
%------------------------------------------------------------------------------