TSTP Solution File: SEU275+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SEU275+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n013.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 07:12:03 EDT 2022
% Result : Theorem 0.69s 1.09s
% Output : Refutation 0.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU275+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Sun Jun 19 03:06:44 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.69/1.09 *** allocated 10000 integers for termspace/termends
% 0.69/1.09 *** allocated 10000 integers for clauses
% 0.69/1.09 *** allocated 10000 integers for justifications
% 0.69/1.09 Bliksem 1.12
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 Automatic Strategy Selection
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 Clauses:
% 0.69/1.09
% 0.69/1.09 { ! ordinal( X ), epsilon_transitive( X ) }.
% 0.69/1.09 { ! ordinal( X ), epsilon_connected( X ) }.
% 0.69/1.09 { ! epsilon_transitive( X ), ! epsilon_connected( X ), ordinal( X ) }.
% 0.69/1.09 { ! relation( X ), ! well_ordering( X ), reflexive( X ) }.
% 0.69/1.09 { ! relation( X ), ! well_ordering( X ), alpha1( X ) }.
% 0.69/1.09 { ! relation( X ), ! reflexive( X ), ! alpha1( X ), well_ordering( X ) }.
% 0.69/1.09 { ! alpha1( X ), transitive( X ) }.
% 0.69/1.09 { ! alpha1( X ), alpha2( X ) }.
% 0.69/1.09 { ! transitive( X ), ! alpha2( X ), alpha1( X ) }.
% 0.69/1.09 { ! alpha2( X ), antisymmetric( X ) }.
% 0.69/1.09 { ! alpha2( X ), alpha3( X ) }.
% 0.69/1.09 { ! antisymmetric( X ), ! alpha3( X ), alpha2( X ) }.
% 0.69/1.09 { ! alpha3( X ), connected( X ) }.
% 0.69/1.09 { ! alpha3( X ), well_founded_relation( X ) }.
% 0.69/1.09 { ! connected( X ), ! well_founded_relation( X ), alpha3( X ) }.
% 0.69/1.09 { relation( inclusion_relation( X ) ) }.
% 0.69/1.09 { epsilon_transitive( skol1 ) }.
% 0.69/1.09 { epsilon_connected( skol1 ) }.
% 0.69/1.09 { ordinal( skol1 ) }.
% 0.69/1.09 { reflexive( inclusion_relation( X ) ) }.
% 0.69/1.09 { transitive( inclusion_relation( X ) ) }.
% 0.69/1.09 { ! ordinal( X ), connected( inclusion_relation( X ) ) }.
% 0.69/1.09 { antisymmetric( inclusion_relation( X ) ) }.
% 0.69/1.09 { ! ordinal( X ), well_founded_relation( inclusion_relation( X ) ) }.
% 0.69/1.09 { ordinal( skol2 ) }.
% 0.69/1.09 { ! well_ordering( inclusion_relation( skol2 ) ) }.
% 0.69/1.09
% 0.69/1.09 percentage equality = 0.000000, percentage horn = 1.000000
% 0.69/1.09 This is a near-Horn, non-equality problem
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 Options Used:
% 0.69/1.09
% 0.69/1.09 useres = 1
% 0.69/1.09 useparamod = 0
% 0.69/1.09 useeqrefl = 0
% 0.69/1.09 useeqfact = 0
% 0.69/1.09 usefactor = 1
% 0.69/1.09 usesimpsplitting = 0
% 0.69/1.09 usesimpdemod = 0
% 0.69/1.09 usesimpres = 4
% 0.69/1.09
% 0.69/1.09 resimpinuse = 1000
% 0.69/1.09 resimpclauses = 20000
% 0.69/1.09 substype = standard
% 0.69/1.09 backwardsubs = 1
% 0.69/1.09 selectoldest = 5
% 0.69/1.09
% 0.69/1.09 litorderings [0] = split
% 0.69/1.09 litorderings [1] = liftord
% 0.69/1.09
% 0.69/1.09 termordering = none
% 0.69/1.09
% 0.69/1.09 litapriori = 1
% 0.69/1.09 termapriori = 0
% 0.69/1.09 litaposteriori = 0
% 0.69/1.09 termaposteriori = 0
% 0.69/1.09 demodaposteriori = 0
% 0.69/1.09 ordereqreflfact = 0
% 0.69/1.09
% 0.69/1.09 litselect = negative
% 0.69/1.09
% 0.69/1.09 maxweight = 30000
% 0.69/1.09 maxdepth = 30000
% 0.69/1.09 maxlength = 115
% 0.69/1.09 maxnrvars = 195
% 0.69/1.09 excuselevel = 0
% 0.69/1.09 increasemaxweight = 0
% 0.69/1.09
% 0.69/1.09 maxselected = 10000000
% 0.69/1.09 maxnrclauses = 10000000
% 0.69/1.09
% 0.69/1.09 showgenerated = 0
% 0.69/1.09 showkept = 0
% 0.69/1.09 showselected = 0
% 0.69/1.09 showdeleted = 0
% 0.69/1.09 showresimp = 1
% 0.69/1.09 showstatus = 2000
% 0.69/1.09
% 0.69/1.09 prologoutput = 0
% 0.69/1.09 nrgoals = 5000000
% 0.69/1.09 totalproof = 1
% 0.69/1.09
% 0.69/1.09 Symbols occurring in the translation:
% 0.69/1.09
% 0.69/1.09 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.69/1.09 . [1, 2] (w:1, o:28, a:1, s:1, b:0),
% 0.69/1.09 ! [4, 1] (w:1, o:9, a:1, s:1, b:0),
% 0.69/1.09 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.69/1.09 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.69/1.09 ordinal [36, 1] (w:1, o:14, a:1, s:1, b:0),
% 0.69/1.09 epsilon_transitive [37, 1] (w:1, o:15, a:1, s:1, b:0),
% 0.69/1.09 epsilon_connected [38, 1] (w:1, o:16, a:1, s:1, b:0),
% 0.69/1.09 relation [39, 1] (w:1, o:17, a:1, s:1, b:0),
% 0.69/1.09 well_ordering [40, 1] (w:1, o:18, a:1, s:1, b:0),
% 0.69/1.09 reflexive [41, 1] (w:1, o:19, a:1, s:1, b:0),
% 0.69/1.09 transitive [42, 1] (w:1, o:20, a:1, s:1, b:0),
% 0.69/1.09 antisymmetric [43, 1] (w:1, o:21, a:1, s:1, b:0),
% 0.69/1.09 connected [44, 1] (w:1, o:22, a:1, s:1, b:0),
% 0.69/1.09 well_founded_relation [45, 1] (w:1, o:23, a:1, s:1, b:0),
% 0.69/1.09 inclusion_relation [46, 1] (w:1, o:24, a:1, s:1, b:0),
% 0.69/1.09 alpha1 [47, 1] (w:1, o:25, a:1, s:1, b:0),
% 0.69/1.09 alpha2 [48, 1] (w:1, o:26, a:1, s:1, b:0),
% 0.69/1.09 alpha3 [49, 1] (w:1, o:27, a:1, s:1, b:0),
% 0.69/1.09 skol1 [50, 0] (w:1, o:7, a:1, s:1, b:0),
% 0.69/1.09 skol2 [51, 0] (w:1, o:8, a:1, s:1, b:0).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 Starting Search:
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 Bliksems!, er is een bewijs:
% 0.69/1.09 % SZS status Theorem
% 0.69/1.09 % SZS output start Refutation
% 0.69/1.09
% 0.69/1.09 (5) {G0,W11,D2,L4,V1,M1} I { ! alpha1( X ), ! reflexive( X ), well_ordering
% 0.69/1.09 ( X ), ! relation( X ) }.
% 0.69/1.09 (8) {G0,W8,D2,L3,V1,M1} I { ! alpha2( X ), alpha1( X ), ! transitive( X )
% 0.69/1.09 }.
% 0.69/1.09 (11) {G0,W8,D2,L3,V1,M1} I { ! alpha3( X ), alpha2( X ), ! antisymmetric( X
% 0.69/1.09 ) }.
% 0.69/1.09 (14) {G0,W8,D2,L3,V1,M1} I { alpha3( X ), ! well_founded_relation( X ), !
% 0.69/1.09 connected( X ) }.
% 0.69/1.09 (15) {G0,W3,D3,L1,V1,M1} I { relation( inclusion_relation( X ) ) }.
% 0.69/1.09 (19) {G0,W3,D3,L1,V1,M1} I { reflexive( inclusion_relation( X ) ) }.
% 0.69/1.09 (20) {G0,W3,D3,L1,V1,M1} I { transitive( inclusion_relation( X ) ) }.
% 0.69/1.09 (21) {G0,W6,D3,L2,V1,M1} I { connected( inclusion_relation( X ) ), !
% 0.69/1.09 ordinal( X ) }.
% 0.69/1.09 (22) {G0,W3,D3,L1,V1,M1} I { antisymmetric( inclusion_relation( X ) ) }.
% 0.69/1.09 (23) {G0,W6,D3,L2,V1,M1} I { well_founded_relation( inclusion_relation( X )
% 0.69/1.09 ), ! ordinal( X ) }.
% 0.69/1.09 (24) {G0,W2,D2,L1,V0,M1} I { ordinal( skol2 ) }.
% 0.69/1.09 (25) {G0,W4,D3,L1,V0,M1} I { ! well_ordering( inclusion_relation( skol2 ) )
% 0.69/1.09 }.
% 0.69/1.09 (29) {G1,W3,D3,L1,V0,M1} R(23,24) { well_founded_relation(
% 0.69/1.09 inclusion_relation( skol2 ) ) }.
% 0.69/1.09 (31) {G1,W3,D3,L1,V0,M1} R(21,24) { connected( inclusion_relation( skol2 )
% 0.69/1.09 ) }.
% 0.69/1.09 (33) {G2,W3,D3,L1,V0,M1} R(14,31);r(29) { alpha3( inclusion_relation( skol2
% 0.69/1.09 ) ) }.
% 0.69/1.09 (35) {G1,W7,D3,L2,V1,M1} R(5,15);r(19) { well_ordering( inclusion_relation
% 0.69/1.09 ( X ) ), ! alpha1( inclusion_relation( X ) ) }.
% 0.69/1.09 (36) {G1,W7,D3,L2,V1,M1} R(11,22) { alpha2( inclusion_relation( X ) ), !
% 0.69/1.09 alpha3( inclusion_relation( X ) ) }.
% 0.69/1.09 (37) {G1,W7,D3,L2,V1,M1} R(8,20) { alpha1( inclusion_relation( X ) ), !
% 0.69/1.09 alpha2( inclusion_relation( X ) ) }.
% 0.69/1.09 (39) {G3,W3,D3,L1,V0,M1} R(36,33) { alpha2( inclusion_relation( skol2 ) )
% 0.69/1.09 }.
% 0.69/1.09 (42) {G4,W3,D3,L1,V0,M1} R(39,37) { alpha1( inclusion_relation( skol2 ) )
% 0.69/1.09 }.
% 0.69/1.09 (43) {G5,W0,D0,L0,V0,M0} R(42,35);r(25) { }.
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 % SZS output end Refutation
% 0.69/1.09 found a proof!
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 Unprocessed initial clauses:
% 0.69/1.09
% 0.69/1.09 (45) {G0,W5,D2,L2,V1,M2} { ! ordinal( X ), epsilon_transitive( X ) }.
% 0.69/1.09 (46) {G0,W5,D2,L2,V1,M2} { ! ordinal( X ), epsilon_connected( X ) }.
% 0.69/1.09 (47) {G0,W8,D2,L3,V1,M3} { ! epsilon_transitive( X ), ! epsilon_connected
% 0.69/1.09 ( X ), ordinal( X ) }.
% 0.69/1.09 (48) {G0,W8,D2,L3,V1,M3} { ! relation( X ), ! well_ordering( X ),
% 0.69/1.09 reflexive( X ) }.
% 0.69/1.09 (49) {G0,W8,D2,L3,V1,M3} { ! relation( X ), ! well_ordering( X ), alpha1(
% 0.69/1.09 X ) }.
% 0.69/1.09 (50) {G0,W11,D2,L4,V1,M4} { ! relation( X ), ! reflexive( X ), ! alpha1( X
% 0.69/1.09 ), well_ordering( X ) }.
% 0.69/1.09 (51) {G0,W5,D2,L2,V1,M2} { ! alpha1( X ), transitive( X ) }.
% 0.69/1.09 (52) {G0,W5,D2,L2,V1,M2} { ! alpha1( X ), alpha2( X ) }.
% 0.69/1.09 (53) {G0,W8,D2,L3,V1,M3} { ! transitive( X ), ! alpha2( X ), alpha1( X )
% 0.69/1.09 }.
% 0.69/1.09 (54) {G0,W5,D2,L2,V1,M2} { ! alpha2( X ), antisymmetric( X ) }.
% 0.69/1.09 (55) {G0,W5,D2,L2,V1,M2} { ! alpha2( X ), alpha3( X ) }.
% 0.69/1.09 (56) {G0,W8,D2,L3,V1,M3} { ! antisymmetric( X ), ! alpha3( X ), alpha2( X
% 0.69/1.09 ) }.
% 0.69/1.09 (57) {G0,W5,D2,L2,V1,M2} { ! alpha3( X ), connected( X ) }.
% 0.69/1.09 (58) {G0,W5,D2,L2,V1,M2} { ! alpha3( X ), well_founded_relation( X ) }.
% 0.69/1.09 (59) {G0,W8,D2,L3,V1,M3} { ! connected( X ), ! well_founded_relation( X )
% 0.69/1.09 , alpha3( X ) }.
% 0.69/1.09 (60) {G0,W3,D3,L1,V1,M1} { relation( inclusion_relation( X ) ) }.
% 0.69/1.09 (61) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol1 ) }.
% 0.69/1.09 (62) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol1 ) }.
% 0.69/1.09 (63) {G0,W2,D2,L1,V0,M1} { ordinal( skol1 ) }.
% 0.69/1.09 (64) {G0,W3,D3,L1,V1,M1} { reflexive( inclusion_relation( X ) ) }.
% 0.69/1.09 (65) {G0,W3,D3,L1,V1,M1} { transitive( inclusion_relation( X ) ) }.
% 0.69/1.09 (66) {G0,W6,D3,L2,V1,M2} { ! ordinal( X ), connected( inclusion_relation(
% 0.69/1.09 X ) ) }.
% 0.69/1.09 (67) {G0,W3,D3,L1,V1,M1} { antisymmetric( inclusion_relation( X ) ) }.
% 0.69/1.09 (68) {G0,W6,D3,L2,V1,M2} { ! ordinal( X ), well_founded_relation(
% 0.69/1.09 inclusion_relation( X ) ) }.
% 0.69/1.09 (69) {G0,W2,D2,L1,V0,M1} { ordinal( skol2 ) }.
% 0.69/1.09 (70) {G0,W4,D3,L1,V0,M1} { ! well_ordering( inclusion_relation( skol2 ) )
% 0.69/1.09 }.
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 Total Proof:
% 0.69/1.09
% 0.69/1.09 subsumption: (5) {G0,W11,D2,L4,V1,M1} I { ! alpha1( X ), ! reflexive( X ),
% 0.69/1.09 well_ordering( X ), ! relation( X ) }.
% 0.69/1.09 parent0: (50) {G0,W11,D2,L4,V1,M4} { ! relation( X ), ! reflexive( X ), !
% 0.69/1.09 alpha1( X ), well_ordering( X ) }.
% 0.69/1.09 substitution0:
% 0.69/1.09 X := X
% 0.69/1.09 end
% 0.69/1.09 permutation0:
% 0.69/1.09 0 ==> 3
% 0.69/1.09 1 ==> 1
% 0.69/1.09 2 ==> 0
% 0.69/1.09 3 ==> 2
% 0.69/1.09 end
% 0.69/1.09
% 0.69/1.09 subsumption: (8) {G0,W8,D2,L3,V1,M1} I { ! alpha2( X ), alpha1( X ), !
% 0.69/1.09 transitive( X ) }.
% 0.69/1.09 parent0: (53) {G0,W8,D2,L3,V1,M3} { ! transitive( X ), ! alpha2( X ),
% 0.69/1.09 alpha1( X ) }.
% 0.69/1.09 substitution0:
% 0.69/1.09 X := X
% 0.69/1.09 end
% 0.69/1.09 permutation0:
% 0.69/1.09 0 ==> 2
% 0.69/1.09 1 ==> 0
% 0.69/1.09 2 ==> 1
% 0.69/1.09 end
% 0.69/1.09
% 0.69/1.09 subsumption: (11) {G0,W8,D2,L3,V1,M1} I { ! alpha3( X ), alpha2( X ), !
% 0.69/1.09 antisymmetric( X ) }.
% 0.69/1.09 parent0: (56) {G0,W8,D2,L3,V1,M3} { ! antisymmetric( X ), ! alpha3( X ),
% 0.69/1.09 alpha2( X ) }.
% 0.69/1.09 substitution0:
% 0.69/1.09 X := X
% 0.69/1.09 end
% 0.69/1.09 permutation0:
% 0.69/1.09 0 ==> 2
% 0.69/1.09 1 ==> 0
% 0.69/1.09 2 ==> 1
% 0.69/1.09 end
% 0.69/1.09
% 0.69/1.09 subsumption: (14) {G0,W8,D2,L3,V1,M1} I { alpha3( X ), !
% 0.69/1.09 well_founded_relation( X ), ! connected( X ) }.
% 0.69/1.09 parent0: (59) {G0,W8,D2,L3,V1,M3} { ! connected( X ), !
% 0.69/1.09 well_founded_relation( X ), alpha3( X ) }.
% 0.69/1.09 substitution0:
% 0.69/1.09 X := X
% 0.69/1.09 end
% 0.69/1.09 permutation0:
% 0.69/1.09 0 ==> 2
% 0.69/1.09 1 ==> 1
% 0.69/1.09 2 ==> 0
% 0.69/1.09 end
% 0.69/1.09
% 0.69/1.09 subsumption: (15) {G0,W3,D3,L1,V1,M1} I { relation( inclusion_relation( X )
% 0.69/1.09 ) }.
% 0.69/1.09 parent0: (60) {G0,W3,D3,L1,V1,M1} { relation( inclusion_relation( X ) )
% 0.69/1.09 }.
% 0.69/1.09 substitution0:
% 0.69/1.09 X := X
% 0.69/1.09 end
% 0.69/1.09 permutation0:
% 0.69/1.09 0 ==> 0
% 0.69/1.09 end
% 0.69/1.09
% 0.69/1.09 subsumption: (19) {G0,W3,D3,L1,V1,M1} I { reflexive( inclusion_relation( X
% 0.69/1.09 ) ) }.
% 0.69/1.09 parent0: (64) {G0,W3,D3,L1,V1,M1} { reflexive( inclusion_relation( X ) )
% 0.69/1.09 }.
% 0.69/1.09 substitution0:
% 0.69/1.09 X := X
% 0.69/1.09 end
% 0.69/1.09 permutation0:
% 0.69/1.09 0 ==> 0
% 0.69/1.09 end
% 0.69/1.09
% 0.69/1.09 subsumption: (20) {G0,W3,D3,L1,V1,M1} I { transitive( inclusion_relation( X
% 0.69/1.09 ) ) }.
% 0.69/1.09 parent0: (65) {G0,W3,D3,L1,V1,M1} { transitive( inclusion_relation( X ) )
% 0.69/1.09 }.
% 0.69/1.09 substitution0:
% 0.69/1.09 X := X
% 0.69/1.09 end
% 0.69/1.09 permutation0:
% 0.69/1.09 0 ==> 0
% 0.69/1.09 end
% 0.69/1.09
% 0.69/1.09 subsumption: (21) {G0,W6,D3,L2,V1,M1} I { connected( inclusion_relation( X
% 0.69/1.09 ) ), ! ordinal( X ) }.
% 0.69/1.09 parent0: (66) {G0,W6,D3,L2,V1,M2} { ! ordinal( X ), connected(
% 0.69/1.09 inclusion_relation( X ) ) }.
% 0.69/1.09 substitution0:
% 0.69/1.09 X := X
% 0.69/1.09 end
% 0.69/1.09 permutation0:
% 0.69/1.09 0 ==> 1
% 0.69/1.09 1 ==> 0
% 0.69/1.09 end
% 0.69/1.09
% 0.69/1.09 subsumption: (22) {G0,W3,D3,L1,V1,M1} I { antisymmetric( inclusion_relation
% 0.69/1.09 ( X ) ) }.
% 0.69/1.09 parent0: (67) {G0,W3,D3,L1,V1,M1} { antisymmetric( inclusion_relation( X )
% 0.69/1.09 ) }.
% 0.69/1.09 substitution0:
% 0.69/1.09 X := X
% 0.69/1.09 end
% 0.69/1.09 permutation0:
% 0.69/1.09 0 ==> 0
% 0.69/1.09 end
% 0.69/1.09
% 0.69/1.09 subsumption: (23) {G0,W6,D3,L2,V1,M1} I { well_founded_relation(
% 0.69/1.09 inclusion_relation( X ) ), ! ordinal( X ) }.
% 0.69/1.09 parent0: (68) {G0,W6,D3,L2,V1,M2} { ! ordinal( X ), well_founded_relation
% 0.69/1.09 ( inclusion_relation( X ) ) }.
% 0.69/1.09 substitution0:
% 0.69/1.09 X := X
% 0.69/1.09 end
% 0.69/1.09 permutation0:
% 0.69/1.09 0 ==> 1
% 0.69/1.09 1 ==> 0
% 0.69/1.09 end
% 0.69/1.09
% 0.69/1.09 subsumption: (24) {G0,W2,D2,L1,V0,M1} I { ordinal( skol2 ) }.
% 0.69/1.09 parent0: (69) {G0,W2,D2,L1,V0,M1} { ordinal( skol2 ) }.
% 0.69/1.09 substitution0:
% 0.69/1.09 end
% 0.69/1.09 permutation0:
% 0.69/1.09 0 ==> 0
% 0.69/1.09 end
% 0.69/1.09
% 0.69/1.09 subsumption: (25) {G0,W4,D3,L1,V0,M1} I { ! well_ordering(
% 0.69/1.09 inclusion_relation( skol2 ) ) }.
% 0.69/1.09 parent0: (70) {G0,W4,D3,L1,V0,M1} { ! well_ordering( inclusion_relation(
% 0.69/1.09 skol2 ) ) }.
% 0.69/1.09 substitution0:
% 0.69/1.09 end
% 0.69/1.09 permutation0:
% 0.69/1.09 0 ==> 0
% 0.69/1.09 end
% 0.69/1.09
% 0.69/1.09 resolution: (71) {G1,W3,D3,L1,V0,M1} { well_founded_relation(
% 0.69/1.09 inclusion_relation( skol2 ) ) }.
% 0.69/1.09 parent0[1]: (23) {G0,W6,D3,L2,V1,M1} I { well_founded_relation(
% 0.69/1.09 inclusion_relation( X ) ), ! ordinal( X ) }.
% 0.69/1.09 parent1[0]: (24) {G0,W2,D2,L1,V0,M1} I { ordinal( skol2 ) }.
% 0.69/1.09 substitution0:
% 0.69/1.09 X := skol2
% 0.69/1.09 end
% 0.69/1.09 substitution1:
% 0.69/1.09 end
% 0.69/1.09
% 0.69/1.09 subsumption: (29) {G1,W3,D3,L1,V0,M1} R(23,24) { well_founded_relation(
% 0.69/1.09 inclusion_relation( skol2 ) ) }.
% 0.69/1.09 parent0: (71) {G1,W3,D3,L1,V0,M1} { well_founded_relation(
% 0.69/1.09 inclusion_relation( skol2 ) ) }.
% 0.69/1.09 substitution0:
% 0.69/1.09 end
% 0.69/1.09 permutation0:
% 0.69/1.09 0 ==> 0
% 0.69/1.09 end
% 0.69/1.09
% 0.69/1.09 resolution: (72) {G1,W3,D3,L1,V0,M1} { connected( inclusion_relation(
% 0.69/1.09 skol2 ) ) }.
% 0.69/1.09 parent0[1]: (21) {G0,W6,D3,L2,V1,M1} I { connected( inclusion_relation( X )
% 0.69/1.09 ), ! ordinal( X ) }.
% 0.69/1.09 parent1[0]: (24) {G0,W2,D2,L1,V0,M1} I { ordinal( skol2 ) }.
% 0.69/1.09 substitution0:
% 0.69/1.09 X := skol2
% 0.69/1.09 end
% 0.69/1.09 substitution1:
% 0.69/1.09 end
% 0.69/1.09
% 0.69/1.09 subsumption: (31) {G1,W3,D3,L1,V0,M1} R(21,24) { connected(
% 0.69/1.09 inclusion_relation( skol2 ) ) }.
% 0.69/1.09 parent0: (72) {G1,W3,D3,L1,V0,M1} { connected( inclusion_relation( skol2 )
% 0.69/1.09 ) }.
% 0.69/1.09 substitution0:
% 0.69/1.09 end
% 0.69/1.09 permutation0:
% 0.69/1.09 0 ==> 0
% 0.69/1.09 end
% 0.69/1.09
% 0.69/1.09 resolution: (73) {G1,W7,D3,L2,V0,M2} { alpha3( inclusion_relation( skol2 )
% 0.69/1.09 ), ! well_founded_relation( inclusion_relation( skol2 ) ) }.
% 0.69/1.09 parent0[2]: (14) {G0,W8,D2,L3,V1,M1} I { alpha3( X ), !
% 0.69/1.09 well_founded_relation( X ), ! connected( X ) }.
% 0.69/1.09 parent1[0]: (31) {G1,W3,D3,L1,V0,M1} R(21,24) { connected(
% 0.69/1.09 inclusion_relation( skol2 ) ) }.
% 0.69/1.09 substitution0:
% 0.69/1.09 X := inclusion_relation( skol2 )
% 0.69/1.09 end
% 0.69/1.09 substitution1:
% 0.69/1.09 end
% 0.69/1.09
% 0.69/1.09 resolution: (74) {G2,W3,D3,L1,V0,M1} { alpha3( inclusion_relation( skol2 )
% 0.69/1.09 ) }.
% 0.69/1.09 parent0[1]: (73) {G1,W7,D3,L2,V0,M2} { alpha3( inclusion_relation( skol2 )
% 0.69/1.09 ), ! well_founded_relation( inclusion_relation( skol2 ) ) }.
% 0.69/1.09 parent1[0]: (29) {G1,W3,D3,L1,V0,M1} R(23,24) { well_founded_relation(
% 0.69/1.09 inclusion_relation( skol2 ) ) }.
% 0.69/1.09 substitution0:
% 0.69/1.09 end
% 0.69/1.09 substitution1:
% 0.69/1.09 end
% 0.69/1.09
% 0.69/1.09 subsumption: (33) {G2,W3,D3,L1,V0,M1} R(14,31);r(29) { alpha3(
% 0.69/1.09 inclusion_relation( skol2 ) ) }.
% 0.69/1.09 parent0: (74) {G2,W3,D3,L1,V0,M1} { alpha3( inclusion_relation( skol2 ) )
% 0.69/1.09 }.
% 0.69/1.09 substitution0:
% 0.69/1.09 end
% 0.69/1.09 permutation0:
% 0.69/1.09 0 ==> 0
% 0.69/1.09 end
% 0.69/1.09
% 0.69/1.09 resolution: (75) {G1,W11,D3,L3,V1,M3} { ! alpha1( inclusion_relation( X )
% 0.69/1.09 ), ! reflexive( inclusion_relation( X ) ), well_ordering(
% 0.69/1.09 inclusion_relation( X ) ) }.
% 0.69/1.09 parent0[3]: (5) {G0,W11,D2,L4,V1,M1} I { ! alpha1( X ), ! reflexive( X ),
% 0.69/1.09 well_ordering( X ), ! relation( X ) }.
% 0.69/1.09 parent1[0]: (15) {G0,W3,D3,L1,V1,M1} I { relation( inclusion_relation( X )
% 0.69/1.09 ) }.
% 0.69/1.09 substitution0:
% 0.69/1.09 X := inclusion_relation( X )
% 0.69/1.09 end
% 0.69/1.09 substitution1:
% 0.69/1.09 X := X
% 0.69/1.09 end
% 0.69/1.09
% 0.69/1.09 resolution: (76) {G1,W7,D3,L2,V1,M2} { ! alpha1( inclusion_relation( X ) )
% 0.69/1.09 , well_ordering( inclusion_relation( X ) ) }.
% 0.69/1.09 parent0[1]: (75) {G1,W11,D3,L3,V1,M3} { ! alpha1( inclusion_relation( X )
% 0.69/1.09 ), ! reflexive( inclusion_relation( X ) ), well_ordering(
% 0.69/1.09 inclusion_relation( X ) ) }.
% 0.69/1.09 parent1[0]: (19) {G0,W3,D3,L1,V1,M1} I { reflexive( inclusion_relation( X )
% 0.69/1.09 ) }.
% 0.69/1.09 substitution0:
% 0.69/1.09 X := X
% 0.69/1.09 end
% 0.69/1.09 substitution1:
% 0.69/1.09 X := X
% 0.69/1.09 end
% 0.69/1.09
% 0.69/1.09 subsumption: (35) {G1,W7,D3,L2,V1,M1} R(5,15);r(19) { well_ordering(
% 0.69/1.09 inclusion_relation( X ) ), ! alpha1( inclusion_relation( X ) ) }.
% 0.69/1.09 parent0: (76) {G1,W7,D3,L2,V1,M2} { ! alpha1( inclusion_relation( X ) ),
% 0.69/1.09 well_ordering( inclusion_relation( X ) ) }.
% 0.69/1.09 substitution0:
% 0.69/1.09 X := X
% 0.69/1.09 end
% 0.69/1.09 permutation0:
% 0.69/1.09 0 ==> 1
% 0.69/1.09 1 ==> 0
% 0.69/1.09 end
% 0.69/1.09
% 0.69/1.09 resolution: (77) {G1,W7,D3,L2,V1,M2} { ! alpha3( inclusion_relation( X ) )
% 0.69/1.09 , alpha2( inclusion_relation( X ) ) }.
% 0.69/1.09 parent0[2]: (11) {G0,W8,D2,L3,V1,M1} I { ! alpha3( X ), alpha2( X ), !
% 0.69/1.09 antisymmetric( X ) }.
% 0.69/1.09 parent1[0]: (22) {G0,W3,D3,L1,V1,M1} I { antisymmetric( inclusion_relation
% 0.69/1.09 ( X ) ) }.
% 0.69/1.09 substitution0:
% 0.69/1.09 X := inclusion_relation( X )
% 0.69/1.09 end
% 0.69/1.09 substitution1:
% 0.69/1.09 X := X
% 0.69/1.09 end
% 0.69/1.09
% 0.69/1.09 subsumption: (36) {G1,W7,D3,L2,V1,M1} R(11,22) { alpha2( inclusion_relation
% 0.69/1.09 ( X ) ), ! alpha3( inclusion_relation( X ) ) }.
% 0.69/1.09 parent0: (77) {G1,W7,D3,L2,V1,M2} { ! alpha3( inclusion_relation( X ) ),
% 0.69/1.09 alpha2( inclusion_relation( X ) ) }.
% 0.69/1.09 substitution0:
% 0.69/1.09 X := X
% 0.69/1.09 end
% 0.69/1.09 permutation0:
% 0.69/1.09 0 ==> 1
% 0.69/1.09 1 ==> 0
% 0.69/1.09 end
% 0.69/1.09
% 0.69/1.09 resolution: (78) {G1,W7,D3,L2,V1,M2} { ! alpha2( inclusion_relation( X ) )
% 0.69/1.09 , alpha1( inclusion_relation( X ) ) }.
% 0.69/1.09 parent0[2]: (8) {G0,W8,D2,L3,V1,M1} I { ! alpha2( X ), alpha1( X ), !
% 0.69/1.09 transitive( X ) }.
% 0.69/1.09 parent1[0]: (20) {G0,W3,D3,L1,V1,M1} I { transitive( inclusion_relation( X
% 0.69/1.09 ) ) }.
% 0.69/1.09 substitution0:
% 0.69/1.09 X := inclusion_relation( X )
% 0.69/1.09 end
% 0.69/1.09 substitution1:
% 0.69/1.09 X := X
% 0.69/1.09 end
% 0.69/1.09
% 0.69/1.09 subsumption: (37) {G1,W7,D3,L2,V1,M1} R(8,20) { alpha1( inclusion_relation
% 0.69/1.09 ( X ) ), ! alpha2( inclusion_relation( X ) ) }.
% 0.69/1.09 parent0: (78) {G1,W7,D3,L2,V1,M2} { ! alpha2( inclusion_relation( X ) ),
% 0.69/1.09 alpha1( inclusion_relation( X ) ) }.
% 0.69/1.09 substitution0:
% 0.69/1.09 X := X
% 0.69/1.09 end
% 0.69/1.09 permutation0:
% 0.69/1.09 0 ==> 1
% 0.69/1.09 1 ==> 0
% 0.69/1.09 end
% 0.69/1.09
% 0.69/1.09 resolution: (79) {G2,W3,D3,L1,V0,M1} { alpha2( inclusion_relation( skol2 )
% 0.69/1.09 ) }.
% 0.69/1.09 parent0[1]: (36) {G1,W7,D3,L2,V1,M1} R(11,22) { alpha2( inclusion_relation
% 0.69/1.09 ( X ) ), ! alpha3( inclusion_relation( X ) ) }.
% 0.69/1.09 parent1[0]: (33) {G2,W3,D3,L1,V0,M1} R(14,31);r(29) { alpha3(
% 0.69/1.09 inclusion_relation( skol2 ) ) }.
% 0.69/1.09 substitution0:
% 0.69/1.09 X := skol2
% 0.69/1.09 end
% 0.69/1.09 substitution1:
% 0.69/1.09 end
% 0.69/1.09
% 0.69/1.09 subsumption: (39) {G3,W3,D3,L1,V0,M1} R(36,33) { alpha2( inclusion_relation
% 0.69/1.09 ( skol2 ) ) }.
% 0.69/1.09 parent0: (79) {G2,W3,D3,L1,V0,M1} { alpha2( inclusion_relation( skol2 ) )
% 0.69/1.09 }.
% 0.69/1.09 substitution0:
% 0.69/1.09 end
% 0.69/1.09 permutation0:
% 0.69/1.09 0 ==> 0
% 0.69/1.09 end
% 0.69/1.09
% 0.69/1.09 resolution: (80) {G2,W3,D3,L1,V0,M1} { alpha1( inclusion_relation( skol2 )
% 0.69/1.09 ) }.
% 0.69/1.09 parent0[1]: (37) {G1,W7,D3,L2,V1,M1} R(8,20) { alpha1( inclusion_relation(
% 0.69/1.09 X ) ), ! alpha2( inclusion_relation( X ) ) }.
% 0.69/1.09 parent1[0]: (39) {G3,W3,D3,L1,V0,M1} R(36,33) { alpha2( inclusion_relation
% 0.69/1.09 ( skol2 ) ) }.
% 0.69/1.09 substitution0:
% 0.69/1.09 X := skol2
% 0.69/1.09 end
% 0.69/1.09 substitution1:
% 0.69/1.09 end
% 0.69/1.09
% 0.69/1.09 subsumption: (42) {G4,W3,D3,L1,V0,M1} R(39,37) { alpha1( inclusion_relation
% 0.69/1.09 ( skol2 ) ) }.
% 0.69/1.09 parent0: (80) {G2,W3,D3,L1,V0,M1} { alpha1( inclusion_relation( skol2 ) )
% 0.69/1.09 }.
% 0.69/1.09 substitution0:
% 0.69/1.09 end
% 0.69/1.09 permutation0:
% 0.69/1.09 0 ==> 0
% 0.69/1.09 end
% 0.69/1.09
% 0.69/1.09 resolution: (81) {G2,W3,D3,L1,V0,M1} { well_ordering( inclusion_relation(
% 0.69/1.09 skol2 ) ) }.
% 0.69/1.09 parent0[1]: (35) {G1,W7,D3,L2,V1,M1} R(5,15);r(19) { well_ordering(
% 0.69/1.09 inclusion_relation( X ) ), ! alpha1( inclusion_relation( X ) ) }.
% 0.69/1.09 parent1[0]: (42) {G4,W3,D3,L1,V0,M1} R(39,37) { alpha1( inclusion_relation
% 0.69/1.09 ( skol2 ) ) }.
% 0.69/1.09 substitution0:
% 0.69/1.09 X := skol2
% 0.69/1.09 end
% 0.69/1.09 substitution1:
% 0.69/1.09 end
% 0.69/1.09
% 0.69/1.09 resolution: (82) {G1,W0,D0,L0,V0,M0} { }.
% 0.69/1.09 parent0[0]: (25) {G0,W4,D3,L1,V0,M1} I { ! well_ordering(
% 0.69/1.09 inclusion_relation( skol2 ) ) }.
% 0.69/1.09 parent1[0]: (81) {G2,W3,D3,L1,V0,M1} { well_ordering( inclusion_relation(
% 0.69/1.09 skol2 ) ) }.
% 0.69/1.09 substitution0:
% 0.69/1.09 end
% 0.69/1.09 substitution1:
% 0.69/1.09 end
% 0.69/1.09
% 0.69/1.09 subsumption: (43) {G5,W0,D0,L0,V0,M0} R(42,35);r(25) { }.
% 0.69/1.09 parent0: (82) {G1,W0,D0,L0,V0,M0} { }.
% 0.69/1.09 substitution0:
% 0.69/1.09 end
% 0.69/1.09 permutation0:
% 0.69/1.09 end
% 0.69/1.09
% 0.69/1.09 Proof check complete!
% 0.69/1.09
% 0.69/1.09 Memory use:
% 0.69/1.09
% 0.69/1.09 space for terms: 510
% 0.69/1.09 space for clauses: 2314
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 clauses generated: 59
% 0.69/1.09 clauses kept: 44
% 0.69/1.09 clauses selected: 42
% 0.69/1.09 clauses deleted: 0
% 0.69/1.09 clauses inuse deleted: 0
% 0.69/1.09
% 0.69/1.09 subsentry: 15
% 0.69/1.09 literals s-matched: 15
% 0.69/1.09 literals matched: 15
% 0.69/1.09 full subsumption: 0
% 0.69/1.09
% 0.69/1.09 checksum: 2110522181
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 Bliksem ended
%------------------------------------------------------------------------------