TSTP Solution File: SET907+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET907+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n003.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 22:53:15 EDT 2022
% Result : Theorem 0.43s 1.07s
% Output : Refutation 0.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET907+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : bliksem %s
% 0.13/0.33 % Computer : n003.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % DateTime : Sat Jul 9 21:47:44 EDT 2022
% 0.19/0.34 % CPUTime :
% 0.43/1.07 *** allocated 10000 integers for termspace/termends
% 0.43/1.07 *** allocated 10000 integers for clauses
% 0.43/1.07 *** allocated 10000 integers for justifications
% 0.43/1.07 Bliksem 1.12
% 0.43/1.07
% 0.43/1.07
% 0.43/1.07 Automatic Strategy Selection
% 0.43/1.07
% 0.43/1.07
% 0.43/1.07 Clauses:
% 0.43/1.07
% 0.43/1.07 { ! in( X, Y ), ! in( Y, X ) }.
% 0.43/1.07 { unordered_pair( X, Y ) = unordered_pair( Y, X ) }.
% 0.43/1.07 { set_union2( X, Y ) = set_union2( Y, X ) }.
% 0.43/1.07 { empty( X ), ! empty( set_union2( X, Y ) ) }.
% 0.43/1.07 { empty( X ), ! empty( set_union2( Y, X ) ) }.
% 0.43/1.07 { set_union2( X, X ) = X }.
% 0.43/1.07 { empty( skol1 ) }.
% 0.43/1.07 { ! empty( skol2 ) }.
% 0.43/1.07 { subset( X, X ) }.
% 0.43/1.07 { ! subset( X, Y ), set_union2( X, Y ) = Y }.
% 0.43/1.07 { ! subset( unordered_pair( X, Y ), Z ), in( X, Z ) }.
% 0.43/1.07 { ! subset( unordered_pair( X, Y ), Z ), in( Y, Z ) }.
% 0.43/1.07 { ! in( X, Z ), ! in( Y, Z ), subset( unordered_pair( X, Y ), Z ) }.
% 0.43/1.07 { in( skol3, skol4 ) }.
% 0.43/1.07 { in( skol5, skol4 ) }.
% 0.43/1.07 { ! set_union2( unordered_pair( skol3, skol5 ), skol4 ) = skol4 }.
% 0.43/1.07
% 0.43/1.07 percentage equality = 0.208333, percentage horn = 1.000000
% 0.43/1.07 This is a problem with some equality
% 0.43/1.07
% 0.43/1.07
% 0.43/1.07
% 0.43/1.07 Options Used:
% 0.43/1.07
% 0.43/1.07 useres = 1
% 0.43/1.07 useparamod = 1
% 0.43/1.07 useeqrefl = 1
% 0.43/1.07 useeqfact = 1
% 0.43/1.07 usefactor = 1
% 0.43/1.07 usesimpsplitting = 0
% 0.43/1.07 usesimpdemod = 5
% 0.43/1.07 usesimpres = 3
% 0.43/1.07
% 0.43/1.07 resimpinuse = 1000
% 0.43/1.07 resimpclauses = 20000
% 0.43/1.07 substype = eqrewr
% 0.43/1.07 backwardsubs = 1
% 0.43/1.07 selectoldest = 5
% 0.43/1.07
% 0.43/1.07 litorderings [0] = split
% 0.43/1.07 litorderings [1] = extend the termordering, first sorting on arguments
% 0.43/1.07
% 0.43/1.07 termordering = kbo
% 0.43/1.07
% 0.43/1.07 litapriori = 0
% 0.43/1.07 termapriori = 1
% 0.43/1.07 litaposteriori = 0
% 0.43/1.07 termaposteriori = 0
% 0.43/1.07 demodaposteriori = 0
% 0.43/1.07 ordereqreflfact = 0
% 0.43/1.07
% 0.43/1.07 litselect = negord
% 0.43/1.07
% 0.43/1.07 maxweight = 15
% 0.43/1.07 maxdepth = 30000
% 0.43/1.07 maxlength = 115
% 0.43/1.07 maxnrvars = 195
% 0.43/1.07 excuselevel = 1
% 0.43/1.07 increasemaxweight = 1
% 0.43/1.07
% 0.43/1.07 maxselected = 10000000
% 0.43/1.07 maxnrclauses = 10000000
% 0.43/1.07
% 0.43/1.07 showgenerated = 0
% 0.43/1.07 showkept = 0
% 0.43/1.07 showselected = 0
% 0.43/1.07 showdeleted = 0
% 0.43/1.07 showresimp = 1
% 0.43/1.07 showstatus = 2000
% 0.43/1.07
% 0.43/1.07 prologoutput = 0
% 0.43/1.07 nrgoals = 5000000
% 0.43/1.07 totalproof = 1
% 0.43/1.07
% 0.43/1.07 Symbols occurring in the translation:
% 0.43/1.07
% 0.43/1.07 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.43/1.07 . [1, 2] (w:1, o:20, a:1, s:1, b:0),
% 0.43/1.07 ! [4, 1] (w:0, o:14, a:1, s:1, b:0),
% 0.43/1.07 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.43/1.07 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.43/1.07 in [37, 2] (w:1, o:44, a:1, s:1, b:0),
% 0.43/1.07 unordered_pair [38, 2] (w:1, o:45, a:1, s:1, b:0),
% 0.43/1.07 set_union2 [39, 2] (w:1, o:46, a:1, s:1, b:0),
% 0.43/1.07 empty [40, 1] (w:1, o:19, a:1, s:1, b:0),
% 0.43/1.07 subset [41, 2] (w:1, o:47, a:1, s:1, b:0),
% 0.43/1.07 skol1 [43, 0] (w:1, o:9, a:1, s:1, b:1),
% 0.43/1.07 skol2 [44, 0] (w:1, o:10, a:1, s:1, b:1),
% 0.43/1.07 skol3 [45, 0] (w:1, o:11, a:1, s:1, b:1),
% 0.43/1.07 skol4 [46, 0] (w:1, o:12, a:1, s:1, b:1),
% 0.43/1.07 skol5 [47, 0] (w:1, o:13, a:1, s:1, b:1).
% 0.43/1.07
% 0.43/1.07
% 0.43/1.07 Starting Search:
% 0.43/1.07
% 0.43/1.07
% 0.43/1.07 Bliksems!, er is een bewijs:
% 0.43/1.07 % SZS status Theorem
% 0.43/1.07 % SZS output start Refutation
% 0.43/1.07
% 0.43/1.07 (9) {G0,W8,D3,L2,V2,M2} I { ! subset( X, Y ), set_union2( X, Y ) ==> Y }.
% 0.43/1.07 (12) {G0,W11,D3,L3,V3,M3} I { ! in( X, Z ), ! in( Y, Z ), subset(
% 0.43/1.07 unordered_pair( X, Y ), Z ) }.
% 0.43/1.07 (13) {G0,W3,D2,L1,V0,M1} I { in( skol3, skol4 ) }.
% 0.43/1.07 (14) {G0,W3,D2,L1,V0,M1} I { in( skol5, skol4 ) }.
% 0.43/1.07 (15) {G0,W7,D4,L1,V0,M1} I { ! set_union2( unordered_pair( skol3, skol5 ),
% 0.43/1.07 skol4 ) ==> skol4 }.
% 0.43/1.07 (101) {G1,W5,D3,L1,V0,M1} R(15,9) { ! subset( unordered_pair( skol3, skol5
% 0.43/1.07 ), skol4 ) }.
% 0.43/1.07 (104) {G2,W3,D2,L1,V0,M1} R(101,12);r(13) { ! in( skol5, skol4 ) }.
% 0.43/1.07 (106) {G3,W0,D0,L0,V0,M0} S(104);r(14) { }.
% 0.43/1.07
% 0.43/1.07
% 0.43/1.07 % SZS output end Refutation
% 0.43/1.07 found a proof!
% 0.43/1.07
% 0.43/1.07
% 0.43/1.07 Unprocessed initial clauses:
% 0.43/1.07
% 0.43/1.07 (108) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), ! in( Y, X ) }.
% 0.43/1.07 (109) {G0,W7,D3,L1,V2,M1} { unordered_pair( X, Y ) = unordered_pair( Y, X
% 0.43/1.07 ) }.
% 0.43/1.07 (110) {G0,W7,D3,L1,V2,M1} { set_union2( X, Y ) = set_union2( Y, X ) }.
% 0.43/1.07 (111) {G0,W6,D3,L2,V2,M2} { empty( X ), ! empty( set_union2( X, Y ) ) }.
% 0.43/1.07 (112) {G0,W6,D3,L2,V2,M2} { empty( X ), ! empty( set_union2( Y, X ) ) }.
% 0.43/1.07 (113) {G0,W5,D3,L1,V1,M1} { set_union2( X, X ) = X }.
% 0.43/1.07 (114) {G0,W2,D2,L1,V0,M1} { empty( skol1 ) }.
% 0.43/1.07 (115) {G0,W2,D2,L1,V0,M1} { ! empty( skol2 ) }.
% 0.43/1.07 (116) {G0,W3,D2,L1,V1,M1} { subset( X, X ) }.
% 0.43/1.07 (117) {G0,W8,D3,L2,V2,M2} { ! subset( X, Y ), set_union2( X, Y ) = Y }.
% 0.43/1.07 (118) {G0,W8,D3,L2,V3,M2} { ! subset( unordered_pair( X, Y ), Z ), in( X,
% 0.43/1.07 Z ) }.
% 0.43/1.07 (119) {G0,W8,D3,L2,V3,M2} { ! subset( unordered_pair( X, Y ), Z ), in( Y,
% 0.43/1.07 Z ) }.
% 0.43/1.07 (120) {G0,W11,D3,L3,V3,M3} { ! in( X, Z ), ! in( Y, Z ), subset(
% 0.43/1.07 unordered_pair( X, Y ), Z ) }.
% 0.43/1.07 (121) {G0,W3,D2,L1,V0,M1} { in( skol3, skol4 ) }.
% 0.43/1.07 (122) {G0,W3,D2,L1,V0,M1} { in( skol5, skol4 ) }.
% 0.43/1.07 (123) {G0,W7,D4,L1,V0,M1} { ! set_union2( unordered_pair( skol3, skol5 ),
% 0.43/1.07 skol4 ) = skol4 }.
% 0.43/1.07
% 0.43/1.07
% 0.43/1.07 Total Proof:
% 0.43/1.07
% 0.43/1.07 subsumption: (9) {G0,W8,D3,L2,V2,M2} I { ! subset( X, Y ), set_union2( X, Y
% 0.43/1.07 ) ==> Y }.
% 0.43/1.07 parent0: (117) {G0,W8,D3,L2,V2,M2} { ! subset( X, Y ), set_union2( X, Y )
% 0.43/1.07 = Y }.
% 0.43/1.07 substitution0:
% 0.43/1.07 X := X
% 0.43/1.07 Y := Y
% 0.43/1.07 end
% 0.43/1.07 permutation0:
% 0.43/1.07 0 ==> 0
% 0.43/1.07 1 ==> 1
% 0.43/1.07 end
% 0.43/1.07
% 0.43/1.07 subsumption: (12) {G0,W11,D3,L3,V3,M3} I { ! in( X, Z ), ! in( Y, Z ),
% 0.43/1.07 subset( unordered_pair( X, Y ), Z ) }.
% 0.43/1.07 parent0: (120) {G0,W11,D3,L3,V3,M3} { ! in( X, Z ), ! in( Y, Z ), subset(
% 0.43/1.07 unordered_pair( X, Y ), Z ) }.
% 0.43/1.07 substitution0:
% 0.43/1.07 X := X
% 0.43/1.07 Y := Y
% 0.43/1.07 Z := Z
% 0.43/1.07 end
% 0.43/1.07 permutation0:
% 0.43/1.07 0 ==> 0
% 0.43/1.07 1 ==> 1
% 0.43/1.07 2 ==> 2
% 0.43/1.07 end
% 0.43/1.07
% 0.43/1.07 subsumption: (13) {G0,W3,D2,L1,V0,M1} I { in( skol3, skol4 ) }.
% 0.43/1.07 parent0: (121) {G0,W3,D2,L1,V0,M1} { in( skol3, skol4 ) }.
% 0.43/1.07 substitution0:
% 0.43/1.07 end
% 0.43/1.07 permutation0:
% 0.43/1.07 0 ==> 0
% 0.43/1.07 end
% 0.43/1.07
% 0.43/1.07 subsumption: (14) {G0,W3,D2,L1,V0,M1} I { in( skol5, skol4 ) }.
% 0.43/1.07 parent0: (122) {G0,W3,D2,L1,V0,M1} { in( skol5, skol4 ) }.
% 0.43/1.07 substitution0:
% 0.43/1.07 end
% 0.43/1.07 permutation0:
% 0.43/1.07 0 ==> 0
% 0.43/1.07 end
% 0.43/1.07
% 0.43/1.07 subsumption: (15) {G0,W7,D4,L1,V0,M1} I { ! set_union2( unordered_pair(
% 0.43/1.07 skol3, skol5 ), skol4 ) ==> skol4 }.
% 0.43/1.07 parent0: (123) {G0,W7,D4,L1,V0,M1} { ! set_union2( unordered_pair( skol3,
% 0.43/1.07 skol5 ), skol4 ) = skol4 }.
% 0.43/1.07 substitution0:
% 0.43/1.07 end
% 0.43/1.07 permutation0:
% 0.43/1.07 0 ==> 0
% 0.43/1.07 end
% 0.43/1.07
% 0.43/1.07 eqswap: (144) {G0,W7,D4,L1,V0,M1} { ! skol4 ==> set_union2( unordered_pair
% 0.43/1.07 ( skol3, skol5 ), skol4 ) }.
% 0.43/1.07 parent0[0]: (15) {G0,W7,D4,L1,V0,M1} I { ! set_union2( unordered_pair(
% 0.43/1.07 skol3, skol5 ), skol4 ) ==> skol4 }.
% 0.43/1.07 substitution0:
% 0.43/1.07 end
% 0.43/1.07
% 0.43/1.07 eqswap: (145) {G0,W8,D3,L2,V2,M2} { Y ==> set_union2( X, Y ), ! subset( X
% 0.43/1.07 , Y ) }.
% 0.43/1.07 parent0[1]: (9) {G0,W8,D3,L2,V2,M2} I { ! subset( X, Y ), set_union2( X, Y
% 0.43/1.07 ) ==> Y }.
% 0.43/1.07 substitution0:
% 0.43/1.07 X := X
% 0.43/1.07 Y := Y
% 0.43/1.07 end
% 0.43/1.07
% 0.43/1.07 resolution: (146) {G1,W5,D3,L1,V0,M1} { ! subset( unordered_pair( skol3,
% 0.43/1.07 skol5 ), skol4 ) }.
% 0.43/1.07 parent0[0]: (144) {G0,W7,D4,L1,V0,M1} { ! skol4 ==> set_union2(
% 0.43/1.07 unordered_pair( skol3, skol5 ), skol4 ) }.
% 0.43/1.07 parent1[0]: (145) {G0,W8,D3,L2,V2,M2} { Y ==> set_union2( X, Y ), ! subset
% 0.43/1.07 ( X, Y ) }.
% 0.43/1.07 substitution0:
% 0.43/1.07 end
% 0.43/1.07 substitution1:
% 0.43/1.07 X := unordered_pair( skol3, skol5 )
% 0.43/1.07 Y := skol4
% 0.43/1.07 end
% 0.43/1.07
% 0.43/1.07 subsumption: (101) {G1,W5,D3,L1,V0,M1} R(15,9) { ! subset( unordered_pair(
% 0.43/1.07 skol3, skol5 ), skol4 ) }.
% 0.43/1.07 parent0: (146) {G1,W5,D3,L1,V0,M1} { ! subset( unordered_pair( skol3,
% 0.43/1.07 skol5 ), skol4 ) }.
% 0.43/1.07 substitution0:
% 0.43/1.07 end
% 0.43/1.07 permutation0:
% 0.43/1.07 0 ==> 0
% 0.43/1.07 end
% 0.43/1.07
% 0.43/1.07 resolution: (147) {G1,W6,D2,L2,V0,M2} { ! in( skol3, skol4 ), ! in( skol5
% 0.43/1.07 , skol4 ) }.
% 0.43/1.07 parent0[0]: (101) {G1,W5,D3,L1,V0,M1} R(15,9) { ! subset( unordered_pair(
% 0.43/1.07 skol3, skol5 ), skol4 ) }.
% 0.43/1.07 parent1[2]: (12) {G0,W11,D3,L3,V3,M3} I { ! in( X, Z ), ! in( Y, Z ),
% 0.43/1.07 subset( unordered_pair( X, Y ), Z ) }.
% 0.43/1.07 substitution0:
% 0.43/1.07 end
% 0.43/1.07 substitution1:
% 0.43/1.07 X := skol3
% 0.43/1.07 Y := skol5
% 0.43/1.07 Z := skol4
% 0.43/1.07 end
% 0.43/1.07
% 0.43/1.07 resolution: (148) {G1,W3,D2,L1,V0,M1} { ! in( skol5, skol4 ) }.
% 0.43/1.07 parent0[0]: (147) {G1,W6,D2,L2,V0,M2} { ! in( skol3, skol4 ), ! in( skol5
% 0.43/1.07 , skol4 ) }.
% 0.43/1.07 parent1[0]: (13) {G0,W3,D2,L1,V0,M1} I { in( skol3, skol4 ) }.
% 0.43/1.07 substitution0:
% 0.43/1.07 end
% 0.43/1.07 substitution1:
% 0.43/1.07 end
% 0.43/1.07
% 0.43/1.07 subsumption: (104) {G2,W3,D2,L1,V0,M1} R(101,12);r(13) { ! in( skol5, skol4
% 0.43/1.07 ) }.
% 0.43/1.07 parent0: (148) {G1,W3,D2,L1,V0,M1} { ! in( skol5, skol4 ) }.
% 0.43/1.07 substitution0:
% 0.43/1.07 end
% 0.43/1.07 permutation0:
% 0.43/1.07 0 ==> 0
% 0.43/1.07 end
% 0.43/1.07
% 0.43/1.07 resolution: (149) {G1,W0,D0,L0,V0,M0} { }.
% 0.43/1.07 parent0[0]: (104) {G2,W3,D2,L1,V0,M1} R(101,12);r(13) { ! in( skol5, skol4
% 0.43/1.07 ) }.
% 0.43/1.07 parent1[0]: (14) {G0,W3,D2,L1,V0,M1} I { in( skol5, skol4 ) }.
% 0.43/1.07 substitution0:
% 0.43/1.07 end
% 0.43/1.07 substitution1:
% 0.43/1.07 end
% 0.43/1.07
% 0.43/1.07 subsumption: (106) {G3,W0,D0,L0,V0,M0} S(104);r(14) { }.
% 0.43/1.07 parent0: (149) {G1,W0,D0,L0,V0,M0} { }.
% 0.43/1.07 substitution0:
% 0.43/1.07 end
% 0.43/1.07 permutation0:
% 0.43/1.07 end
% 0.43/1.07
% 0.43/1.07 Proof check complete!
% 0.43/1.07
% 0.43/1.07 Memory use:
% 0.43/1.07
% 0.43/1.07 space for terms: 1176
% 0.43/1.07 space for clauses: 5907
% 0.43/1.07
% 0.43/1.07
% 0.43/1.07 clauses generated: 246
% 0.43/1.07 clauses kept: 107
% 0.43/1.07 clauses selected: 42
% 0.43/1.07 clauses deleted: 1
% 0.43/1.07 clauses inuse deleted: 0
% 0.43/1.07
% 0.43/1.07 subsentry: 336
% 0.43/1.07 literals s-matched: 261
% 0.43/1.07 literals matched: 261
% 0.43/1.07 full subsumption: 27
% 0.43/1.07
% 0.43/1.07 checksum: 442839729
% 0.43/1.07
% 0.43/1.07
% 0.43/1.07 Bliksem ended
%------------------------------------------------------------------------------