%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SET691+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n007.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 22:51:26 EDT 2022
% Result : Theorem 0.41s 1.07s
% Output : Refutation 0.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET691+4 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n007.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 : Sun Jul 10 06:12:16 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.41/1.07 *** allocated 10000 integers for termspace/termends
% 0.41/1.07 *** allocated 10000 integers for clauses
% 0.41/1.07 *** allocated 10000 integers for justifications
% 0.41/1.07 Bliksem 1.12
% 0.41/1.07
% 0.41/1.07
% 0.41/1.07 Automatic Strategy Selection
% 0.41/1.07
% 0.41/1.07
% 0.41/1.07 Clauses:
% 0.41/1.07
% 0.41/1.07 { ! subset( X, Y ), ! member( Z, X ), member( Z, Y ) }.
% 0.41/1.07 { ! member( skol1( Z, Y ), Y ), subset( X, Y ) }.
% 0.41/1.07 { member( skol1( X, Y ), X ), subset( X, Y ) }.
% 0.41/1.07 { ! equal_set( X, Y ), subset( X, Y ) }.
% 0.41/1.07 { ! equal_set( X, Y ), subset( Y, X ) }.
% 0.41/1.07 { ! subset( X, Y ), ! subset( Y, X ), equal_set( X, Y ) }.
% 0.41/1.07 { ! member( X, power_set( Y ) ), subset( X, Y ) }.
% 0.41/1.07 { ! subset( X, Y ), member( X, power_set( Y ) ) }.
% 0.41/1.07 { ! member( X, intersection( Y, Z ) ), member( X, Y ) }.
% 0.41/1.07 { ! member( X, intersection( Y, Z ) ), member( X, Z ) }.
% 0.41/1.07 { ! member( X, Y ), ! member( X, Z ), member( X, intersection( Y, Z ) ) }.
% 0.41/1.07 { ! member( X, union( Y, Z ) ), member( X, Y ), member( X, Z ) }.
% 0.41/1.07 { ! member( X, Y ), member( X, union( Y, Z ) ) }.
% 0.41/1.07 { ! member( X, Z ), member( X, union( Y, Z ) ) }.
% 0.41/1.07 { ! member( X, empty_set ) }.
% 0.41/1.07 { ! member( X, difference( Z, Y ) ), member( X, Z ) }.
% 0.41/1.07 { ! member( X, difference( Z, Y ) ), ! member( X, Y ) }.
% 0.41/1.07 { ! member( X, Z ), member( X, Y ), member( X, difference( Z, Y ) ) }.
% 0.41/1.07 { ! member( X, singleton( Y ) ), X = Y }.
% 0.41/1.07 { ! X = Y, member( X, singleton( Y ) ) }.
% 0.41/1.07 { ! member( X, unordered_pair( Y, Z ) ), X = Y, X = Z }.
% 0.41/1.07 { ! X = Y, member( X, unordered_pair( Y, Z ) ) }.
% 0.41/1.07 { ! X = Z, member( X, unordered_pair( Y, Z ) ) }.
% 0.41/1.07 { ! member( X, sum( Y ) ), member( skol2( Z, Y ), Y ) }.
% 0.41/1.07 { ! member( X, sum( Y ) ), member( X, skol2( X, Y ) ) }.
% 0.41/1.07 { ! member( Z, Y ), ! member( X, Z ), member( X, sum( Y ) ) }.
% 0.41/1.07 { ! member( X, product( Y ) ), ! member( Z, Y ), member( X, Z ) }.
% 0.41/1.07 { member( skol3( Z, Y ), Y ), member( X, product( Y ) ) }.
% 0.41/1.07 { ! member( X, skol3( X, Y ) ), member( X, product( Y ) ) }.
% 0.41/1.07 { alpha1( skol4 ), equal_set( skol4, empty_set ) }.
% 0.41/1.07 { alpha1( skol4 ), ! subset( skol4, empty_set ) }.
% 0.41/1.07 { ! alpha1( X ), subset( X, empty_set ) }.
% 0.41/1.07 { ! alpha1( X ), ! equal_set( X, empty_set ) }.
% 0.41/1.07 { ! subset( X, empty_set ), equal_set( X, empty_set ), alpha1( X ) }.
% 0.41/1.07
% 0.41/1.07 percentage equality = 0.078947, percentage horn = 0.794118
% 0.41/1.07 This is a problem with some equality
% 0.41/1.07
% 0.41/1.07
% 0.41/1.07
% 0.41/1.07 Options Used:
% 0.41/1.07
% 0.41/1.07 useres = 1
% 0.41/1.07 useparamod = 1
% 0.41/1.07 useeqrefl = 1
% 0.41/1.07 useeqfact = 1
% 0.41/1.07 usefactor = 1
% 0.41/1.07 usesimpsplitting = 0
% 0.41/1.07 usesimpdemod = 5
% 0.41/1.07 usesimpres = 3
% 0.41/1.07
% 0.41/1.07 resimpinuse = 1000
% 0.41/1.07 resimpclauses = 20000
% 0.41/1.07 substype = eqrewr
% 0.41/1.07 backwardsubs = 1
% 0.41/1.07 selectoldest = 5
% 0.41/1.07
% 0.41/1.07 litorderings [0] = split
% 0.41/1.07 litorderings [1] = extend the termordering, first sorting on arguments
% 0.41/1.07
% 0.41/1.07 termordering = kbo
% 0.41/1.07
% 0.41/1.07 litapriori = 0
% 0.41/1.07 termapriori = 1
% 0.41/1.07 litaposteriori = 0
% 0.41/1.07 termaposteriori = 0
% 0.41/1.07 demodaposteriori = 0
% 0.41/1.07 ordereqreflfact = 0
% 0.41/1.07
% 0.41/1.07 litselect = negord
% 0.41/1.07
% 0.41/1.07 maxweight = 15
% 0.41/1.07 maxdepth = 30000
% 0.41/1.07 maxlength = 115
% 0.41/1.07 maxnrvars = 195
% 0.41/1.07 excuselevel = 1
% 0.41/1.07 increasemaxweight = 1
% 0.41/1.07
% 0.41/1.07 maxselected = 10000000
% 0.41/1.07 maxnrclauses = 10000000
% 0.41/1.07
% 0.41/1.07 showgenerated = 0
% 0.41/1.07 showkept = 0
% 0.41/1.07 showselected = 0
% 0.41/1.07 showdeleted = 0
% 0.41/1.07 showresimp = 1
% 0.41/1.07 showstatus = 2000
% 0.41/1.07
% 0.41/1.07 prologoutput = 0
% 0.41/1.07 nrgoals = 5000000
% 0.41/1.07 totalproof = 1
% 0.41/1.07
% 0.41/1.07 Symbols occurring in the translation:
% 0.41/1.07
% 0.41/1.07 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.41/1.07 . [1, 2] (w:1, o:23, a:1, s:1, b:0),
% 0.41/1.07 ! [4, 1] (w:0, o:13, a:1, s:1, b:0),
% 0.41/1.07 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.41/1.07 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.41/1.07 subset [37, 2] (w:1, o:47, a:1, s:1, b:0),
% 0.41/1.07 member [39, 2] (w:1, o:48, a:1, s:1, b:0),
% 0.41/1.07 equal_set [40, 2] (w:1, o:50, a:1, s:1, b:0),
% 0.41/1.07 power_set [41, 1] (w:1, o:18, a:1, s:1, b:0),
% 0.41/1.07 intersection [42, 2] (w:1, o:51, a:1, s:1, b:0),
% 0.41/1.07 union [43, 2] (w:1, o:52, a:1, s:1, b:0),
% 0.41/1.07 empty_set [44, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.41/1.07 difference [46, 2] (w:1, o:49, a:1, s:1, b:0),
% 0.41/1.07 singleton [47, 1] (w:1, o:19, a:1, s:1, b:0),
% 0.41/1.07 unordered_pair [48, 2] (w:1, o:53, a:1, s:1, b:0),
% 0.41/1.07 sum [49, 1] (w:1, o:20, a:1, s:1, b:0),
% 0.41/1.07 product [51, 1] (w:1, o:21, a:1, s:1, b:0),
% 0.41/1.07 alpha1 [52, 1] (w:1, o:22, a:1, s:1, b:1),
% 0.41/1.07 skol1 [53, 2] (w:1, o:54, a:1, s:1, b:1),
% 0.41/1.07 skol2 [54, 2] (w:1, o:55, a:1, s:1, b:1),
% 0.41/1.07 skol3 [55, 2] (w:1, o:56, a:1, s:1, b:1),
% 0.41/1.07 skol4 [56, 0] (w:1, o:12, a:1, s:1, b:1).
% 0.41/1.07
% 0.41/1.07
% 0.41/1.07 Starting Search:
% 0.41/1.07
% 0.41/1.07
% 0.41/1.07 Bliksems!, er is een bewijs:
% 0.41/1.07 % SZS status Theorem
% 0.41/1.07 % SZS output start Refutation
% 0.41/1.07
% 0.41/1.07 (2) {G0,W8,D3,L2,V2,M2} I { member( skol1( X, Y ), X ), subset( X, Y ) }.
% 0.41/1.07 (3) {G0,W6,D2,L2,V2,M2} I { ! equal_set( X, Y ), subset( X, Y ) }.
% 0.41/1.07 (5) {G0,W9,D2,L3,V2,M3} I { ! subset( X, Y ), ! subset( Y, X ), equal_set(
% 0.41/1.07 X, Y ) }.
% 0.41/1.07 (14) {G0,W3,D2,L1,V1,M1} I { ! member( X, empty_set ) }.
% 0.41/1.07 (29) {G0,W5,D2,L2,V0,M2} I { alpha1( skol4 ), equal_set( skol4, empty_set )
% 0.41/1.07 }.
% 0.41/1.07 (30) {G0,W5,D2,L2,V0,M2} I { alpha1( skol4 ), ! subset( skol4, empty_set )
% 0.41/1.07 }.
% 0.41/1.07 (31) {G0,W5,D2,L2,V1,M2} I { ! alpha1( X ), subset( X, empty_set ) }.
% 0.41/1.07 (32) {G0,W5,D2,L2,V1,M2} I { ! alpha1( X ), ! equal_set( X, empty_set ) }.
% 0.41/1.07 (44) {G1,W3,D2,L1,V0,M1} R(30,32);r(3) { ! equal_set( skol4, empty_set )
% 0.41/1.07 }.
% 0.41/1.07 (51) {G2,W2,D2,L1,V0,M1} S(29);r(44) { alpha1( skol4 ) }.
% 0.41/1.07 (55) {G3,W3,D2,L1,V0,M1} R(51,31) { subset( skol4, empty_set ) }.
% 0.41/1.07 (64) {G1,W3,D2,L1,V1,M1} R(2,14) { subset( empty_set, X ) }.
% 0.41/1.07 (92) {G4,W3,D2,L1,V0,M1} R(5,55);r(64) { equal_set( skol4, empty_set ) }.
% 0.41/1.07 (101) {G5,W0,D0,L0,V0,M0} S(92);r(44) { }.
% 0.41/1.07
% 0.41/1.07
% 0.41/1.07 % SZS output end Refutation
% 0.41/1.07 found a proof!
% 0.41/1.07
% 0.41/1.07
% 0.41/1.07 Unprocessed initial clauses:
% 0.41/1.07
% 0.41/1.07 (103) {G0,W9,D2,L3,V3,M3} { ! subset( X, Y ), ! member( Z, X ), member( Z
% 0.41/1.07 , Y ) }.
% 0.41/1.07 (104) {G0,W8,D3,L2,V3,M2} { ! member( skol1( Z, Y ), Y ), subset( X, Y )
% 0.41/1.07 }.
% 0.41/1.07 (105) {G0,W8,D3,L2,V2,M2} { member( skol1( X, Y ), X ), subset( X, Y ) }.
% 0.41/1.07 (106) {G0,W6,D2,L2,V2,M2} { ! equal_set( X, Y ), subset( X, Y ) }.
% 0.41/1.07 (107) {G0,W6,D2,L2,V2,M2} { ! equal_set( X, Y ), subset( Y, X ) }.
% 0.41/1.07 (108) {G0,W9,D2,L3,V2,M3} { ! subset( X, Y ), ! subset( Y, X ), equal_set
% 0.41/1.07 ( X, Y ) }.
% 0.41/1.07 (109) {G0,W7,D3,L2,V2,M2} { ! member( X, power_set( Y ) ), subset( X, Y )
% 0.41/1.07 }.
% 0.41/1.07 (110) {G0,W7,D3,L2,V2,M2} { ! subset( X, Y ), member( X, power_set( Y ) )
% 0.41/1.07 }.
% 0.41/1.07 (111) {G0,W8,D3,L2,V3,M2} { ! member( X, intersection( Y, Z ) ), member( X
% 0.41/1.07 , Y ) }.
% 0.41/1.07 (112) {G0,W8,D3,L2,V3,M2} { ! member( X, intersection( Y, Z ) ), member( X
% 0.41/1.07 , Z ) }.
% 0.41/1.07 (113) {G0,W11,D3,L3,V3,M3} { ! member( X, Y ), ! member( X, Z ), member( X
% 0.41/1.07 , intersection( Y, Z ) ) }.
% 0.41/1.07 (114) {G0,W11,D3,L3,V3,M3} { ! member( X, union( Y, Z ) ), member( X, Y )
% 0.41/1.07 , member( X, Z ) }.
% 0.41/1.07 (115) {G0,W8,D3,L2,V3,M2} { ! member( X, Y ), member( X, union( Y, Z ) )
% 0.41/1.07 }.
% 0.41/1.07 (116) {G0,W8,D3,L2,V3,M2} { ! member( X, Z ), member( X, union( Y, Z ) )
% 0.41/1.07 }.
% 0.41/1.07 (117) {G0,W3,D2,L1,V1,M1} { ! member( X, empty_set ) }.
% 0.41/1.07 (118) {G0,W8,D3,L2,V3,M2} { ! member( X, difference( Z, Y ) ), member( X,
% 0.41/1.07 Z ) }.
% 0.41/1.07 (119) {G0,W8,D3,L2,V3,M2} { ! member( X, difference( Z, Y ) ), ! member( X
% 0.41/1.07 , Y ) }.
% 0.41/1.07 (120) {G0,W11,D3,L3,V3,M3} { ! member( X, Z ), member( X, Y ), member( X,
% 0.41/1.07 difference( Z, Y ) ) }.
% 0.41/1.07 (121) {G0,W7,D3,L2,V2,M2} { ! member( X, singleton( Y ) ), X = Y }.
% 0.41/1.07 (122) {G0,W7,D3,L2,V2,M2} { ! X = Y, member( X, singleton( Y ) ) }.
% 0.41/1.07 (123) {G0,W11,D3,L3,V3,M3} { ! member( X, unordered_pair( Y, Z ) ), X = Y
% 0.41/1.07 , X = Z }.
% 0.41/1.07 (124) {G0,W8,D3,L2,V3,M2} { ! X = Y, member( X, unordered_pair( Y, Z ) )
% 0.41/1.07 }.
% 0.41/1.07 (125) {G0,W8,D3,L2,V3,M2} { ! X = Z, member( X, unordered_pair( Y, Z ) )
% 0.41/1.07 }.
% 0.41/1.07 (126) {G0,W9,D3,L2,V3,M2} { ! member( X, sum( Y ) ), member( skol2( Z, Y )
% 0.41/1.07 , Y ) }.
% 0.41/1.07 (127) {G0,W9,D3,L2,V2,M2} { ! member( X, sum( Y ) ), member( X, skol2( X,
% 0.41/1.07 Y ) ) }.
% 0.41/1.07 (128) {G0,W10,D3,L3,V3,M3} { ! member( Z, Y ), ! member( X, Z ), member( X
% 0.41/1.07 , sum( Y ) ) }.
% 0.41/1.07 (129) {G0,W10,D3,L3,V3,M3} { ! member( X, product( Y ) ), ! member( Z, Y )
% 0.41/1.07 , member( X, Z ) }.
% 0.41/1.07 (130) {G0,W9,D3,L2,V3,M2} { member( skol3( Z, Y ), Y ), member( X, product
% 0.41/1.07 ( Y ) ) }.
% 0.41/1.07 (131) {G0,W9,D3,L2,V2,M2} { ! member( X, skol3( X, Y ) ), member( X,
% 0.41/1.07 product( Y ) ) }.
% 0.41/1.07 (132) {G0,W5,D2,L2,V0,M2} { alpha1( skol4 ), equal_set( skol4, empty_set )
% 0.41/1.07 }.
% 0.41/1.07 (133) {G0,W5,D2,L2,V0,M2} { alpha1( skol4 ), ! subset( skol4, empty_set )
% 0.41/1.07 }.
% 0.41/1.07 (134) {G0,W5,D2,L2,V1,M2} { ! alpha1( X ), subset( X, empty_set ) }.
% 0.41/1.07 (135) {G0,W5,D2,L2,V1,M2} { ! alpha1( X ), ! equal_set( X, empty_set ) }.
% 0.41/1.07 (136) {G0,W8,D2,L3,V1,M3} { ! subset( X, empty_set ), equal_set( X,
% 0.41/1.07 empty_set ), alpha1( X ) }.
% 0.41/1.07
% 0.41/1.07
% 0.41/1.07 Total Proof:
% 0.41/1.07
% 0.41/1.07 subsumption: (2) {G0,W8,D3,L2,V2,M2} I { member( skol1( X, Y ), X ), subset
% 0.41/1.07 ( X, Y ) }.
% 0.41/1.07 parent0: (105) {G0,W8,D3,L2,V2,M2} { member( skol1( X, Y ), X ), subset( X
% 0.41/1.07 , Y ) }.
% 0.41/1.07 substitution0:
% 0.41/1.07 X := X
% 0.41/1.07 Y := Y
% 0.41/1.07 end
% 0.41/1.07 permutation0:
% 0.41/1.07 0 ==> 0
% 0.41/1.07 1 ==> 1
% 0.41/1.07 end
% 0.41/1.07
% 0.41/1.07 subsumption: (3) {G0,W6,D2,L2,V2,M2} I { ! equal_set( X, Y ), subset( X, Y
% 0.41/1.07 ) }.
% 0.41/1.07 parent0: (106) {G0,W6,D2,L2,V2,M2} { ! equal_set( X, Y ), subset( X, Y )
% 0.41/1.07 }.
% 0.41/1.07 substitution0:
% 0.41/1.07 X := X
% 0.41/1.07 Y := Y
% 0.41/1.07 end
% 0.41/1.07 permutation0:
% 0.41/1.07 0 ==> 0
% 0.41/1.07 1 ==> 1
% 0.41/1.07 end
% 0.41/1.07
% 0.41/1.07 subsumption: (5) {G0,W9,D2,L3,V2,M3} I { ! subset( X, Y ), ! subset( Y, X )
% 0.41/1.07 , equal_set( X, Y ) }.
% 0.41/1.07 parent0: (108) {G0,W9,D2,L3,V2,M3} { ! subset( X, Y ), ! subset( Y, X ),
% 0.41/1.07 equal_set( X, Y ) }.
% 0.41/1.07 substitution0:
% 0.41/1.07 X := X
% 0.41/1.07 Y := Y
% 0.41/1.07 end
% 0.41/1.07 permutation0:
% 0.41/1.07 0 ==> 0
% 0.41/1.07 1 ==> 1
% 0.41/1.07 2 ==> 2
% 0.41/1.07 end
% 0.41/1.07
% 0.41/1.07 subsumption: (14) {G0,W3,D2,L1,V1,M1} I { ! member( X, empty_set ) }.
% 0.41/1.07 parent0: (117) {G0,W3,D2,L1,V1,M1} { ! member( X, empty_set ) }.
% 0.41/1.07 substitution0:
% 0.41/1.07 X := X
% 0.41/1.07 end
% 0.41/1.07 permutation0:
% 0.41/1.07 0 ==> 0
% 0.41/1.07 end
% 0.41/1.07
% 0.41/1.07 subsumption: (29) {G0,W5,D2,L2,V0,M2} I { alpha1( skol4 ), equal_set( skol4
% 0.41/1.07 , empty_set ) }.
% 0.41/1.07 parent0: (132) {G0,W5,D2,L2,V0,M2} { alpha1( skol4 ), equal_set( skol4,
% 0.41/1.07 empty_set ) }.
% 0.41/1.07 substitution0:
% 0.41/1.07 end
% 0.41/1.07 permutation0:
% 0.41/1.07 0 ==> 0
% 0.41/1.07 1 ==> 1
% 0.41/1.07 end
% 0.41/1.07
% 0.41/1.07 subsumption: (30) {G0,W5,D2,L2,V0,M2} I { alpha1( skol4 ), ! subset( skol4
% 0.41/1.07 , empty_set ) }.
% 0.41/1.07 parent0: (133) {G0,W5,D2,L2,V0,M2} { alpha1( skol4 ), ! subset( skol4,
% 0.41/1.07 empty_set ) }.
% 0.41/1.07 substitution0:
% 0.41/1.07 end
% 0.41/1.07 permutation0:
% 0.41/1.07 0 ==> 0
% 0.41/1.07 1 ==> 1
% 0.41/1.07 end
% 0.41/1.07
% 0.41/1.07 subsumption: (31) {G0,W5,D2,L2,V1,M2} I { ! alpha1( X ), subset( X,
% 0.41/1.07 empty_set ) }.
% 0.41/1.07 parent0: (134) {G0,W5,D2,L2,V1,M2} { ! alpha1( X ), subset( X, empty_set )
% 0.41/1.07 }.
% 0.41/1.07 substitution0:
% 0.41/1.07 X := X
% 0.41/1.07 end
% 0.41/1.07 permutation0:
% 0.41/1.07 0 ==> 0
% 0.41/1.07 1 ==> 1
% 0.41/1.07 end
% 0.41/1.07
% 0.41/1.07 subsumption: (32) {G0,W5,D2,L2,V1,M2} I { ! alpha1( X ), ! equal_set( X,
% 0.41/1.07 empty_set ) }.
% 0.41/1.07 parent0: (135) {G0,W5,D2,L2,V1,M2} { ! alpha1( X ), ! equal_set( X,
% 0.41/1.07 empty_set ) }.
% 0.41/1.07 substitution0:
% 0.41/1.07 X := X
% 0.41/1.07 end
% 0.41/1.07 permutation0:
% 0.41/1.07 0 ==> 0
% 0.41/1.07 1 ==> 1
% 0.41/1.07 end
% 0.41/1.07
% 0.41/1.07 resolution: (193) {G1,W6,D2,L2,V0,M2} { ! equal_set( skol4, empty_set ), !
% 0.41/1.07 subset( skol4, empty_set ) }.
% 0.41/1.07 parent0[0]: (32) {G0,W5,D2,L2,V1,M2} I { ! alpha1( X ), ! equal_set( X,
% 0.41/1.07 empty_set ) }.
% 0.41/1.07 parent1[0]: (30) {G0,W5,D2,L2,V0,M2} I { alpha1( skol4 ), ! subset( skol4,
% 0.41/1.07 empty_set ) }.
% 0.41/1.07 substitution0:
% 0.41/1.07 X := skol4
% 0.41/1.07 end
% 0.41/1.07 substitution1:
% 0.41/1.07 end
% 0.41/1.07
% 0.41/1.07 resolution: (194) {G1,W6,D2,L2,V0,M2} { ! equal_set( skol4, empty_set ), !
% 0.41/1.07 equal_set( skol4, empty_set ) }.
% 0.41/1.07 parent0[1]: (193) {G1,W6,D2,L2,V0,M2} { ! equal_set( skol4, empty_set ), !
% 0.41/1.07 subset( skol4, empty_set ) }.
% 0.41/1.07 parent1[1]: (3) {G0,W6,D2,L2,V2,M2} I { ! equal_set( X, Y ), subset( X, Y )
% 0.41/1.07 }.
% 0.41/1.07 substitution0:
% 0.41/1.07 end
% 0.41/1.07 substitution1:
% 0.41/1.07 X := skol4
% 0.41/1.07 Y := empty_set
% 0.41/1.07 end
% 0.41/1.07
% 0.41/1.07 factor: (195) {G1,W3,D2,L1,V0,M1} { ! equal_set( skol4, empty_set ) }.
% 0.41/1.07 parent0[0, 1]: (194) {G1,W6,D2,L2,V0,M2} { ! equal_set( skol4, empty_set )
% 0.41/1.07 , ! equal_set( skol4, empty_set ) }.
% 0.41/1.07 substitution0:
% 0.41/1.07 end
% 0.41/1.07
% 0.41/1.07 subsumption: (44) {G1,W3,D2,L1,V0,M1} R(30,32);r(3) { ! equal_set( skol4,
% 0.41/1.07 empty_set ) }.
% 0.41/1.07 parent0: (195) {G1,W3,D2,L1,V0,M1} { ! equal_set( skol4, empty_set ) }.
% 0.41/1.07 substitution0:
% 0.41/1.07 end
% 0.41/1.07 permutation0:
% 0.41/1.07 0 ==> 0
% 0.41/1.07 end
% 0.41/1.07
% 0.41/1.07 resolution: (196) {G1,W2,D2,L1,V0,M1} { alpha1( skol4 ) }.
% 0.41/1.07 parent0[0]: (44) {G1,W3,D2,L1,V0,M1} R(30,32);r(3) { ! equal_set( skol4,
% 0.41/1.07 empty_set ) }.
% 0.41/1.07 parent1[1]: (29) {G0,W5,D2,L2,V0,M2} I { alpha1( skol4 ), equal_set( skol4
% 0.41/1.07 , empty_set ) }.
% 0.41/1.07 substitution0:
% 0.41/1.07 end
% 0.41/1.07 substitution1:
% 0.41/1.07 end
% 0.41/1.07
% 0.41/1.07 subsumption: (51) {G2,W2,D2,L1,V0,M1} S(29);r(44) { alpha1( skol4 ) }.
% 0.41/1.07 parent0: (196) {G1,W2,D2,L1,V0,M1} { alpha1( skol4 ) }.
% 0.41/1.07 substitution0:
% 0.41/1.07 end
% 0.41/1.07 permutation0:
% 0.41/1.07 0 ==> 0
% 0.41/1.07 end
% 0.41/1.07
% 0.41/1.07 resolution: (197) {G1,W3,D2,L1,V0,M1} { subset( skol4, empty_set ) }.
% 0.41/1.07 parent0[0]: (31) {G0,W5,D2,L2,V1,M2} I { ! alpha1( X ), subset( X,
% 0.41/1.07 empty_set ) }.
% 0.41/1.07 parent1[0]: (51) {G2,W2,D2,L1,V0,M1} S(29);r(44) { alpha1( skol4 ) }.
% 0.41/1.07 substitution0:
% 0.41/1.07 X := skol4
% 0.41/1.07 end
% 0.41/1.07 substitution1:
% 0.41/1.07 end
% 0.41/1.07
% 0.41/1.07 subsumption: (55) {G3,W3,D2,L1,V0,M1} R(51,31) { subset( skol4, empty_set )
% 0.41/1.07 }.
% 0.41/1.07 parent0: (197) {G1,W3,D2,L1,V0,M1} { subset( skol4, empty_set ) }.
% 0.41/1.07 substitution0:
% 0.41/1.07 end
% 0.41/1.07 permutation0:
% 0.41/1.07 0 ==> 0
% 0.41/1.07 end
% 0.41/1.07
% 0.41/1.07 resolution: (198) {G1,W3,D2,L1,V1,M1} { subset( empty_set, X ) }.
% 0.41/1.07 parent0[0]: (14) {G0,W3,D2,L1,V1,M1} I { ! member( X, empty_set ) }.
% 0.41/1.07 parent1[0]: (2) {G0,W8,D3,L2,V2,M2} I { member( skol1( X, Y ), X ), subset
% 0.41/1.07 ( X, Y ) }.
% 0.41/1.07 substitution0:
% 0.41/1.07 X := skol1( empty_set, X )
% 0.41/1.07 end
% 0.41/1.07 substitution1:
% 0.41/1.07 X := empty_set
% 0.41/1.07 Y := X
% 0.41/1.07 end
% 0.41/1.07
% 0.41/1.07 subsumption: (64) {G1,W3,D2,L1,V1,M1} R(2,14) { subset( empty_set, X ) }.
% 0.41/1.07 parent0: (198) {G1,W3,D2,L1,V1,M1} { subset( empty_set, X ) }.
% 0.41/1.07 substitution0:
% 0.41/1.07 X := X
% 0.41/1.07 end
% 0.41/1.07 permutation0:
% 0.41/1.07 0 ==> 0
% 0.41/1.07 end
% 0.41/1.07
% 0.41/1.07 resolution: (199) {G1,W6,D2,L2,V0,M2} { ! subset( empty_set, skol4 ),
% 0.41/1.07 equal_set( skol4, empty_set ) }.
% 0.41/1.07 parent0[0]: (5) {G0,W9,D2,L3,V2,M3} I { ! subset( X, Y ), ! subset( Y, X )
% 0.41/1.07 , equal_set( X, Y ) }.
% 0.41/1.07 parent1[0]: (55) {G3,W3,D2,L1,V0,M1} R(51,31) { subset( skol4, empty_set )
% 0.41/1.07 }.
% 0.41/1.07 substitution0:
% 0.41/1.07 X := skol4
% 0.41/1.07 Y := empty_set
% 0.41/1.07 end
% 0.41/1.07 substitution1:
% 0.41/1.07 end
% 0.41/1.07
% 0.41/1.07 resolution: (201) {G2,W3,D2,L1,V0,M1} { equal_set( skol4, empty_set ) }.
% 0.41/1.07 parent0[0]: (199) {G1,W6,D2,L2,V0,M2} { ! subset( empty_set, skol4 ),
% 0.41/1.07 equal_set( skol4, empty_set ) }.
% 0.41/1.07 parent1[0]: (64) {G1,W3,D2,L1,V1,M1} R(2,14) { subset( empty_set, X ) }.
% 0.41/1.07 substitution0:
% 0.41/1.07 end
% 0.41/1.07 substitution1:
% 0.41/1.07 X := skol4
% 0.41/1.07 end
% 0.41/1.07
% 0.41/1.07 subsumption: (92) {G4,W3,D2,L1,V0,M1} R(5,55);r(64) { equal_set( skol4,
% 0.41/1.07 empty_set ) }.
% 0.41/1.07 parent0: (201) {G2,W3,D2,L1,V0,M1} { equal_set( skol4, empty_set ) }.
% 0.41/1.07 substitution0:
% 0.41/1.07 end
% 0.41/1.07 permutation0:
% 0.41/1.07 0 ==> 0
% 0.41/1.07 end
% 0.41/1.07
% 0.41/1.07 resolution: (202) {G2,W0,D0,L0,V0,M0} { }.
% 0.41/1.07 parent0[0]: (44) {G1,W3,D2,L1,V0,M1} R(30,32);r(3) { ! equal_set( skol4,
% 0.41/1.07 empty_set ) }.
% 0.41/1.07 parent1[0]: (92) {G4,W3,D2,L1,V0,M1} R(5,55);r(64) { equal_set( skol4,
% 0.41/1.07 empty_set ) }.
% 0.41/1.07 substitution0:
% 0.41/1.07 end
% 0.41/1.07 substitution1:
% 0.41/1.07 end
% 0.41/1.07
% 0.41/1.07 subsumption: (101) {G5,W0,D0,L0,V0,M0} S(92);r(44) { }.
% 0.41/1.07 parent0: (202) {G2,W0,D0,L0,V0,M0} { }.
% 0.41/1.07 substitution0:
% 0.41/1.07 end
% 0.41/1.07 permutation0:
% 0.41/1.07 end
% 0.41/1.07
% 0.41/1.07 Proof check complete!
% 0.41/1.07
% 0.41/1.07 Memory use:
% 0.41/1.07
% 0.41/1.07 space for terms: 1415
% 0.41/1.07 space for clauses: 5112
% 0.41/1.07
% 0.41/1.07
% 0.41/1.07 clauses generated: 154
% 0.41/1.07 clauses kept: 102
% 0.41/1.07 clauses selected: 31
% 0.41/1.07 clauses deleted: 3
% 0.41/1.07 clauses inuse deleted: 0
% 0.41/1.07
% 0.41/1.07 subsentry: 341
% 0.41/1.07 literals s-matched: 321
% 0.41/1.07 literals matched: 321
% 0.41/1.07 full subsumption: 160
% 0.41/1.07
% 0.41/1.07 checksum: -662711933
% 0.41/1.07
% 0.41/1.07
% 0.41/1.07 Bliksem ended
%------------------------------------------------------------------------------