TSTP Solution File: SET366+4 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET366+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n020.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 22:49:06 EDT 2022
% Result : Theorem 0.66s 1.06s
% Output : Refutation 0.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SET366+4 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Mon Jul 11 02:14:28 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.66/1.06 *** allocated 10000 integers for termspace/termends
% 0.66/1.06 *** allocated 10000 integers for clauses
% 0.66/1.06 *** allocated 10000 integers for justifications
% 0.66/1.06 Bliksem 1.12
% 0.66/1.06
% 0.66/1.06
% 0.66/1.06 Automatic Strategy Selection
% 0.66/1.06
% 0.66/1.06
% 0.66/1.06 Clauses:
% 0.66/1.06
% 0.66/1.06 { ! subset( X, Y ), ! member( Z, X ), member( Z, Y ) }.
% 0.66/1.06 { ! member( skol1( Z, Y ), Y ), subset( X, Y ) }.
% 0.66/1.06 { member( skol1( X, Y ), X ), subset( X, Y ) }.
% 0.66/1.06 { ! equal_set( X, Y ), subset( X, Y ) }.
% 0.66/1.06 { ! equal_set( X, Y ), subset( Y, X ) }.
% 0.66/1.06 { ! subset( X, Y ), ! subset( Y, X ), equal_set( X, Y ) }.
% 0.66/1.06 { ! member( X, power_set( Y ) ), subset( X, Y ) }.
% 0.66/1.06 { ! subset( X, Y ), member( X, power_set( Y ) ) }.
% 0.66/1.06 { ! member( X, intersection( Y, Z ) ), member( X, Y ) }.
% 0.66/1.06 { ! member( X, intersection( Y, Z ) ), member( X, Z ) }.
% 0.66/1.06 { ! member( X, Y ), ! member( X, Z ), member( X, intersection( Y, Z ) ) }.
% 0.66/1.06 { ! member( X, union( Y, Z ) ), member( X, Y ), member( X, Z ) }.
% 0.66/1.06 { ! member( X, Y ), member( X, union( Y, Z ) ) }.
% 0.66/1.06 { ! member( X, Z ), member( X, union( Y, Z ) ) }.
% 0.66/1.06 { ! member( X, empty_set ) }.
% 0.66/1.06 { ! member( X, difference( Z, Y ) ), member( X, Z ) }.
% 0.66/1.06 { ! member( X, difference( Z, Y ) ), ! member( X, Y ) }.
% 0.66/1.06 { ! member( X, Z ), member( X, Y ), member( X, difference( Z, Y ) ) }.
% 0.66/1.06 { ! member( X, singleton( Y ) ), X = Y }.
% 0.66/1.06 { ! X = Y, member( X, singleton( Y ) ) }.
% 0.66/1.06 { ! member( X, unordered_pair( Y, Z ) ), X = Y, X = Z }.
% 0.66/1.06 { ! X = Y, member( X, unordered_pair( Y, Z ) ) }.
% 0.66/1.06 { ! X = Z, member( X, unordered_pair( Y, Z ) ) }.
% 0.66/1.06 { ! member( X, sum( Y ) ), member( skol2( Z, Y ), Y ) }.
% 0.66/1.06 { ! member( X, sum( Y ) ), member( X, skol2( X, Y ) ) }.
% 0.66/1.06 { ! member( Z, Y ), ! member( X, Z ), member( X, sum( Y ) ) }.
% 0.66/1.06 { ! member( X, product( Y ) ), ! member( Z, Y ), member( X, Z ) }.
% 0.66/1.06 { member( skol3( Z, Y ), Y ), member( X, product( Y ) ) }.
% 0.66/1.06 { ! member( X, skol3( X, Y ) ), member( X, product( Y ) ) }.
% 0.66/1.06 { ! member( empty_set, power_set( skol4 ) ) }.
% 0.66/1.06
% 0.66/1.06 percentage equality = 0.090909, percentage horn = 0.833333
% 0.66/1.06 This is a problem with some equality
% 0.66/1.06
% 0.66/1.06
% 0.66/1.06
% 0.66/1.06 Options Used:
% 0.66/1.06
% 0.66/1.06 useres = 1
% 0.66/1.06 useparamod = 1
% 0.66/1.06 useeqrefl = 1
% 0.66/1.06 useeqfact = 1
% 0.66/1.06 usefactor = 1
% 0.66/1.06 usesimpsplitting = 0
% 0.66/1.06 usesimpdemod = 5
% 0.66/1.06 usesimpres = 3
% 0.66/1.06
% 0.66/1.06 resimpinuse = 1000
% 0.66/1.06 resimpclauses = 20000
% 0.66/1.06 substype = eqrewr
% 0.66/1.06 backwardsubs = 1
% 0.66/1.06 selectoldest = 5
% 0.66/1.06
% 0.66/1.06 litorderings [0] = split
% 0.66/1.06 litorderings [1] = extend the termordering, first sorting on arguments
% 0.66/1.06
% 0.66/1.06 termordering = kbo
% 0.66/1.06
% 0.66/1.06 litapriori = 0
% 0.66/1.06 termapriori = 1
% 0.66/1.06 litaposteriori = 0
% 0.66/1.06 termaposteriori = 0
% 0.66/1.06 demodaposteriori = 0
% 0.66/1.06 ordereqreflfact = 0
% 0.66/1.06
% 0.66/1.06 litselect = negord
% 0.66/1.06
% 0.66/1.06 maxweight = 15
% 0.66/1.06 maxdepth = 30000
% 0.66/1.06 maxlength = 115
% 0.66/1.06 maxnrvars = 195
% 0.66/1.06 excuselevel = 1
% 0.66/1.06 increasemaxweight = 1
% 0.66/1.06
% 0.66/1.06 maxselected = 10000000
% 0.66/1.06 maxnrclauses = 10000000
% 0.66/1.06
% 0.66/1.06 showgenerated = 0
% 0.66/1.06 showkept = 0
% 0.66/1.06 showselected = 0
% 0.66/1.06 showdeleted = 0
% 0.66/1.06 showresimp = 1
% 0.66/1.06 showstatus = 2000
% 0.66/1.06
% 0.66/1.06 prologoutput = 0
% 0.66/1.06 nrgoals = 5000000
% 0.66/1.06 totalproof = 1
% 0.66/1.06
% 0.66/1.06 Symbols occurring in the translation:
% 0.66/1.06
% 0.66/1.06 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.66/1.06 . [1, 2] (w:1, o:22, a:1, s:1, b:0),
% 0.66/1.06 ! [4, 1] (w:0, o:13, a:1, s:1, b:0),
% 0.66/1.06 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.66/1.06 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.66/1.06 subset [37, 2] (w:1, o:46, a:1, s:1, b:0),
% 0.66/1.06 member [39, 2] (w:1, o:47, a:1, s:1, b:0),
% 0.66/1.06 equal_set [40, 2] (w:1, o:49, a:1, s:1, b:0),
% 0.66/1.06 power_set [41, 1] (w:1, o:18, a:1, s:1, b:0),
% 0.66/1.06 intersection [42, 2] (w:1, o:50, a:1, s:1, b:0),
% 0.66/1.06 union [43, 2] (w:1, o:51, a:1, s:1, b:0),
% 0.66/1.06 empty_set [44, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.66/1.06 difference [46, 2] (w:1, o:48, a:1, s:1, b:0),
% 0.66/1.06 singleton [47, 1] (w:1, o:19, a:1, s:1, b:0),
% 0.66/1.06 unordered_pair [48, 2] (w:1, o:52, a:1, s:1, b:0),
% 0.66/1.06 sum [49, 1] (w:1, o:20, a:1, s:1, b:0),
% 0.66/1.06 product [51, 1] (w:1, o:21, a:1, s:1, b:0),
% 0.66/1.06 skol1 [52, 2] (w:1, o:53, a:1, s:1, b:1),
% 0.66/1.06 skol2 [53, 2] (w:1, o:54, a:1, s:1, b:1),
% 0.66/1.06 skol3 [54, 2] (w:1, o:55, a:1, s:1, b:1),
% 0.66/1.06 skol4 [55, 0] (w:1, o:12, a:1, s:1, b:1).
% 0.66/1.06
% 0.66/1.06
% 0.66/1.06 Starting Search:
% 0.66/1.06
% 0.66/1.06
% 0.66/1.06 Bliksems!, er is een bewijs:
% 0.66/1.06 % SZS status Theorem
% 0.66/1.06 % SZS output start Refutation
% 0.66/1.06
% 0.66/1.06 (2) {G0,W8,D3,L2,V2,M2} I { member( skol1( X, Y ), X ), subset( X, Y ) }.
% 0.66/1.06 (7) {G0,W7,D3,L2,V2,M2} I { ! subset( X, Y ), member( X, power_set( Y ) )
% 0.66/1.06 }.
% 0.66/1.06 (14) {G0,W3,D2,L1,V1,M1} I { ! member( X, empty_set ) }.
% 0.66/1.06 (29) {G0,W4,D3,L1,V0,M1} I { ! member( empty_set, power_set( skol4 ) ) }.
% 0.66/1.06 (68) {G1,W3,D2,L1,V1,M1} R(2,14) { subset( empty_set, X ) }.
% 0.66/1.06 (113) {G2,W0,D0,L0,V0,M0} R(7,29);r(68) { }.
% 0.66/1.06
% 0.66/1.06
% 0.66/1.06 % SZS output end Refutation
% 0.66/1.06 found a proof!
% 0.66/1.06
% 0.66/1.06
% 0.66/1.06 Unprocessed initial clauses:
% 0.66/1.06
% 0.66/1.06 (115) {G0,W9,D2,L3,V3,M3} { ! subset( X, Y ), ! member( Z, X ), member( Z
% 0.66/1.06 , Y ) }.
% 0.66/1.06 (116) {G0,W8,D3,L2,V3,M2} { ! member( skol1( Z, Y ), Y ), subset( X, Y )
% 0.66/1.06 }.
% 0.66/1.06 (117) {G0,W8,D3,L2,V2,M2} { member( skol1( X, Y ), X ), subset( X, Y ) }.
% 0.66/1.06 (118) {G0,W6,D2,L2,V2,M2} { ! equal_set( X, Y ), subset( X, Y ) }.
% 0.66/1.06 (119) {G0,W6,D2,L2,V2,M2} { ! equal_set( X, Y ), subset( Y, X ) }.
% 0.66/1.06 (120) {G0,W9,D2,L3,V2,M3} { ! subset( X, Y ), ! subset( Y, X ), equal_set
% 0.66/1.06 ( X, Y ) }.
% 0.66/1.06 (121) {G0,W7,D3,L2,V2,M2} { ! member( X, power_set( Y ) ), subset( X, Y )
% 0.66/1.06 }.
% 0.66/1.06 (122) {G0,W7,D3,L2,V2,M2} { ! subset( X, Y ), member( X, power_set( Y ) )
% 0.66/1.06 }.
% 0.66/1.06 (123) {G0,W8,D3,L2,V3,M2} { ! member( X, intersection( Y, Z ) ), member( X
% 0.66/1.06 , Y ) }.
% 0.66/1.06 (124) {G0,W8,D3,L2,V3,M2} { ! member( X, intersection( Y, Z ) ), member( X
% 0.66/1.06 , Z ) }.
% 0.66/1.06 (125) {G0,W11,D3,L3,V3,M3} { ! member( X, Y ), ! member( X, Z ), member( X
% 0.66/1.06 , intersection( Y, Z ) ) }.
% 0.66/1.06 (126) {G0,W11,D3,L3,V3,M3} { ! member( X, union( Y, Z ) ), member( X, Y )
% 0.66/1.06 , member( X, Z ) }.
% 0.66/1.06 (127) {G0,W8,D3,L2,V3,M2} { ! member( X, Y ), member( X, union( Y, Z ) )
% 0.66/1.06 }.
% 0.66/1.06 (128) {G0,W8,D3,L2,V3,M2} { ! member( X, Z ), member( X, union( Y, Z ) )
% 0.66/1.06 }.
% 0.66/1.06 (129) {G0,W3,D2,L1,V1,M1} { ! member( X, empty_set ) }.
% 0.66/1.06 (130) {G0,W8,D3,L2,V3,M2} { ! member( X, difference( Z, Y ) ), member( X,
% 0.66/1.06 Z ) }.
% 0.66/1.06 (131) {G0,W8,D3,L2,V3,M2} { ! member( X, difference( Z, Y ) ), ! member( X
% 0.66/1.06 , Y ) }.
% 0.66/1.06 (132) {G0,W11,D3,L3,V3,M3} { ! member( X, Z ), member( X, Y ), member( X,
% 0.66/1.06 difference( Z, Y ) ) }.
% 0.66/1.06 (133) {G0,W7,D3,L2,V2,M2} { ! member( X, singleton( Y ) ), X = Y }.
% 0.66/1.06 (134) {G0,W7,D3,L2,V2,M2} { ! X = Y, member( X, singleton( Y ) ) }.
% 0.66/1.06 (135) {G0,W11,D3,L3,V3,M3} { ! member( X, unordered_pair( Y, Z ) ), X = Y
% 0.66/1.06 , X = Z }.
% 0.66/1.06 (136) {G0,W8,D3,L2,V3,M2} { ! X = Y, member( X, unordered_pair( Y, Z ) )
% 0.66/1.06 }.
% 0.66/1.06 (137) {G0,W8,D3,L2,V3,M2} { ! X = Z, member( X, unordered_pair( Y, Z ) )
% 0.66/1.06 }.
% 0.66/1.06 (138) {G0,W9,D3,L2,V3,M2} { ! member( X, sum( Y ) ), member( skol2( Z, Y )
% 0.66/1.06 , Y ) }.
% 0.66/1.06 (139) {G0,W9,D3,L2,V2,M2} { ! member( X, sum( Y ) ), member( X, skol2( X,
% 0.66/1.06 Y ) ) }.
% 0.66/1.06 (140) {G0,W10,D3,L3,V3,M3} { ! member( Z, Y ), ! member( X, Z ), member( X
% 0.66/1.06 , sum( Y ) ) }.
% 0.66/1.06 (141) {G0,W10,D3,L3,V3,M3} { ! member( X, product( Y ) ), ! member( Z, Y )
% 0.66/1.06 , member( X, Z ) }.
% 0.66/1.06 (142) {G0,W9,D3,L2,V3,M2} { member( skol3( Z, Y ), Y ), member( X, product
% 0.66/1.06 ( Y ) ) }.
% 0.66/1.06 (143) {G0,W9,D3,L2,V2,M2} { ! member( X, skol3( X, Y ) ), member( X,
% 0.66/1.06 product( Y ) ) }.
% 0.66/1.06 (144) {G0,W4,D3,L1,V0,M1} { ! member( empty_set, power_set( skol4 ) ) }.
% 0.66/1.06
% 0.66/1.06
% 0.66/1.06 Total Proof:
% 0.66/1.06
% 0.66/1.06 subsumption: (2) {G0,W8,D3,L2,V2,M2} I { member( skol1( X, Y ), X ), subset
% 0.66/1.06 ( X, Y ) }.
% 0.66/1.06 parent0: (117) {G0,W8,D3,L2,V2,M2} { member( skol1( X, Y ), X ), subset( X
% 0.66/1.06 , Y ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 X := X
% 0.66/1.06 Y := Y
% 0.66/1.06 end
% 0.66/1.06 permutation0:
% 0.66/1.06 0 ==> 0
% 0.66/1.06 1 ==> 1
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 subsumption: (7) {G0,W7,D3,L2,V2,M2} I { ! subset( X, Y ), member( X,
% 0.66/1.06 power_set( Y ) ) }.
% 0.66/1.06 parent0: (122) {G0,W7,D3,L2,V2,M2} { ! subset( X, Y ), member( X,
% 0.66/1.06 power_set( Y ) ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 X := X
% 0.66/1.06 Y := Y
% 0.66/1.06 end
% 0.66/1.06 permutation0:
% 0.66/1.06 0 ==> 0
% 0.66/1.06 1 ==> 1
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 subsumption: (14) {G0,W3,D2,L1,V1,M1} I { ! member( X, empty_set ) }.
% 0.66/1.06 parent0: (129) {G0,W3,D2,L1,V1,M1} { ! member( X, empty_set ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 X := X
% 0.66/1.06 end
% 0.66/1.06 permutation0:
% 0.66/1.06 0 ==> 0
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 subsumption: (29) {G0,W4,D3,L1,V0,M1} I { ! member( empty_set, power_set(
% 0.66/1.06 skol4 ) ) }.
% 0.66/1.06 parent0: (144) {G0,W4,D3,L1,V0,M1} { ! member( empty_set, power_set( skol4
% 0.66/1.06 ) ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 end
% 0.66/1.06 permutation0:
% 0.66/1.06 0 ==> 0
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 resolution: (162) {G1,W3,D2,L1,V1,M1} { subset( empty_set, X ) }.
% 0.66/1.06 parent0[0]: (14) {G0,W3,D2,L1,V1,M1} I { ! member( X, empty_set ) }.
% 0.66/1.06 parent1[0]: (2) {G0,W8,D3,L2,V2,M2} I { member( skol1( X, Y ), X ), subset
% 0.66/1.06 ( X, Y ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 X := skol1( empty_set, X )
% 0.66/1.06 end
% 0.66/1.06 substitution1:
% 0.66/1.06 X := empty_set
% 0.66/1.06 Y := X
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 subsumption: (68) {G1,W3,D2,L1,V1,M1} R(2,14) { subset( empty_set, X ) }.
% 0.66/1.06 parent0: (162) {G1,W3,D2,L1,V1,M1} { subset( empty_set, X ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 X := X
% 0.66/1.06 end
% 0.66/1.06 permutation0:
% 0.66/1.06 0 ==> 0
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 resolution: (163) {G1,W3,D2,L1,V0,M1} { ! subset( empty_set, skol4 ) }.
% 0.66/1.06 parent0[0]: (29) {G0,W4,D3,L1,V0,M1} I { ! member( empty_set, power_set(
% 0.66/1.06 skol4 ) ) }.
% 0.66/1.06 parent1[1]: (7) {G0,W7,D3,L2,V2,M2} I { ! subset( X, Y ), member( X,
% 0.66/1.06 power_set( Y ) ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 end
% 0.66/1.06 substitution1:
% 0.66/1.06 X := empty_set
% 0.66/1.06 Y := skol4
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 resolution: (164) {G2,W0,D0,L0,V0,M0} { }.
% 0.66/1.06 parent0[0]: (163) {G1,W3,D2,L1,V0,M1} { ! subset( empty_set, skol4 ) }.
% 0.66/1.06 parent1[0]: (68) {G1,W3,D2,L1,V1,M1} R(2,14) { subset( empty_set, X ) }.
% 0.66/1.06 substitution0:
% 0.66/1.06 end
% 0.66/1.06 substitution1:
% 0.66/1.06 X := skol4
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 subsumption: (113) {G2,W0,D0,L0,V0,M0} R(7,29);r(68) { }.
% 0.66/1.06 parent0: (164) {G2,W0,D0,L0,V0,M0} { }.
% 0.66/1.06 substitution0:
% 0.66/1.06 end
% 0.66/1.06 permutation0:
% 0.66/1.06 end
% 0.66/1.06
% 0.66/1.06 Proof check complete!
% 0.66/1.06
% 0.66/1.06 Memory use:
% 0.66/1.06
% 0.66/1.06 space for terms: 1565
% 0.66/1.06 space for clauses: 5707
% 0.66/1.06
% 0.66/1.06
% 0.66/1.06 clauses generated: 194
% 0.66/1.06 clauses kept: 114
% 0.66/1.06 clauses selected: 30
% 0.66/1.06 clauses deleted: 1
% 0.66/1.06 clauses inuse deleted: 0
% 0.66/1.06
% 0.66/1.06 subsentry: 221
% 0.66/1.06 literals s-matched: 200
% 0.66/1.06 literals matched: 200
% 0.66/1.06 full subsumption: 52
% 0.66/1.06
% 0.66/1.06 checksum: 1034861691
% 0.66/1.06
% 0.66/1.06
% 0.66/1.06 Bliksem ended
%------------------------------------------------------------------------------