TSTP Solution File: SEU217+3 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SEU217+3 : TPTP v8.1.0. Released v3.2.0.
% 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 07:11:30 EDT 2022
% Result : Theorem 9.93s 10.28s
% Output : Refutation 9.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU217+3 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : bliksem %s
% 0.13/0.33 % Computer : n013.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 : Sun Jun 19 20:37:29 EDT 2022
% 0.13/0.33 % CPUTime :
% 9.93/10.28 *** allocated 10000 integers for termspace/termends
% 9.93/10.28 *** allocated 10000 integers for clauses
% 9.93/10.28 *** allocated 10000 integers for justifications
% 9.93/10.28 Bliksem 1.12
% 9.93/10.28
% 9.93/10.28
% 9.93/10.28 Automatic Strategy Selection
% 9.93/10.28
% 9.93/10.28
% 9.93/10.28 Clauses:
% 9.93/10.28
% 9.93/10.28 { subset( X, X ) }.
% 9.93/10.28 { empty( empty_set ) }.
% 9.93/10.28 { relation( empty_set ) }.
% 9.93/10.28 { empty( empty_set ) }.
% 9.93/10.28 { relation( empty_set ) }.
% 9.93/10.28 { relation_empty_yielding( empty_set ) }.
% 9.93/10.28 { empty( empty_set ) }.
% 9.93/10.28 { element( skol1( X ), X ) }.
% 9.93/10.28 { ! empty( X ), function( X ) }.
% 9.93/10.28 { ! empty( powerset( X ) ) }.
% 9.93/10.28 { empty( X ), ! relation( X ), ! empty( relation_dom( X ) ) }.
% 9.93/10.28 { ! empty( X ), empty( relation_dom( X ) ) }.
% 9.93/10.28 { ! empty( X ), relation( relation_dom( X ) ) }.
% 9.93/10.28 { ! empty( X ), relation( X ) }.
% 9.93/10.28 { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 9.93/10.28 { ! element( X, powerset( Y ) ), subset( X, Y ) }.
% 9.93/10.28 { ! subset( X, Y ), element( X, powerset( Y ) ) }.
% 9.93/10.28 { ! in( X, Z ), ! element( Z, powerset( Y ) ), element( X, Y ) }.
% 9.93/10.28 { ! in( X, Y ), ! element( Y, powerset( Z ) ), ! empty( Z ) }.
% 9.93/10.28 { ! empty( X ), X = empty_set }.
% 9.93/10.28 { ! empty( X ), X = Y, ! empty( Y ) }.
% 9.93/10.28 { ! in( X, Y ), ! in( Y, X ) }.
% 9.93/10.28 { relation( identity_relation( X ) ) }.
% 9.93/10.28 { relation( identity_relation( X ) ) }.
% 9.93/10.28 { function( identity_relation( X ) ) }.
% 9.93/10.28 { relation( skol2 ) }.
% 9.93/10.28 { function( skol2 ) }.
% 9.93/10.28 { empty( X ), ! empty( skol3( Y ) ) }.
% 9.93/10.28 { empty( X ), element( skol3( X ), powerset( X ) ) }.
% 9.93/10.28 { empty( skol4( Y ) ) }.
% 9.93/10.28 { element( skol4( X ), powerset( X ) ) }.
% 9.93/10.28 { empty( skol5 ) }.
% 9.93/10.28 { relation( skol5 ) }.
% 9.93/10.28 { ! empty( skol6 ) }.
% 9.93/10.28 { relation( skol6 ) }.
% 9.93/10.28 { relation( skol7 ) }.
% 9.93/10.28 { relation_empty_yielding( skol7 ) }.
% 9.93/10.28 { empty( skol8 ) }.
% 9.93/10.28 { ! empty( skol9 ) }.
% 9.93/10.28 { ! in( X, Y ), element( X, Y ) }.
% 9.93/10.28 { ! in( X, Y ), ! empty( Y ) }.
% 9.93/10.28 { in( skol12, skol10 ) }.
% 9.93/10.28 { ! apply( identity_relation( skol10 ), skol12 ) = skol12 }.
% 9.93/10.28 { ! relation( X ), ! function( X ), ! X = identity_relation( Y ),
% 9.93/10.28 relation_dom( X ) = Y }.
% 9.93/10.28 { ! relation( X ), ! function( X ), ! X = identity_relation( Y ), alpha1( X
% 9.93/10.28 , Y ) }.
% 9.93/10.28 { ! relation( X ), ! function( X ), ! relation_dom( X ) = Y, ! alpha1( X, Y
% 9.93/10.28 ), X = identity_relation( Y ) }.
% 9.93/10.28 { ! alpha1( X, Y ), ! in( Z, Y ), apply( X, Z ) = Z }.
% 9.93/10.28 { in( skol11( Z, Y ), Y ), alpha1( X, Y ) }.
% 9.93/10.28 { ! apply( X, skol11( X, Y ) ) = skol11( X, Y ), alpha1( X, Y ) }.
% 9.93/10.28
% 9.93/10.28 percentage equality = 0.123457, percentage horn = 0.933333
% 9.93/10.28 This is a problem with some equality
% 9.93/10.28
% 9.93/10.28
% 9.93/10.28
% 9.93/10.28 Options Used:
% 9.93/10.28
% 9.93/10.28 useres = 1
% 9.93/10.28 useparamod = 1
% 9.93/10.28 useeqrefl = 1
% 9.93/10.28 useeqfact = 1
% 9.93/10.28 usefactor = 1
% 9.93/10.28 usesimpsplitting = 0
% 9.93/10.28 usesimpdemod = 5
% 9.93/10.28 usesimpres = 3
% 9.93/10.28
% 9.93/10.28 resimpinuse = 1000
% 9.93/10.28 resimpclauses = 20000
% 9.93/10.28 substype = eqrewr
% 9.93/10.28 backwardsubs = 1
% 9.93/10.28 selectoldest = 5
% 9.93/10.28
% 9.93/10.28 litorderings [0] = split
% 9.93/10.28 litorderings [1] = extend the termordering, first sorting on arguments
% 9.93/10.28
% 9.93/10.28 termordering = kbo
% 9.93/10.28
% 9.93/10.28 litapriori = 0
% 9.93/10.28 termapriori = 1
% 9.93/10.28 litaposteriori = 0
% 9.93/10.28 termaposteriori = 0
% 9.93/10.28 demodaposteriori = 0
% 9.93/10.28 ordereqreflfact = 0
% 9.93/10.28
% 9.93/10.28 litselect = negord
% 9.93/10.28
% 9.93/10.28 maxweight = 15
% 9.93/10.28 maxdepth = 30000
% 9.93/10.28 maxlength = 115
% 9.93/10.28 maxnrvars = 195
% 9.93/10.28 excuselevel = 1
% 9.93/10.28 increasemaxweight = 1
% 9.93/10.28
% 9.93/10.28 maxselected = 10000000
% 9.93/10.28 maxnrclauses = 10000000
% 9.93/10.28
% 9.93/10.28 showgenerated = 0
% 9.93/10.28 showkept = 0
% 9.93/10.28 showselected = 0
% 9.93/10.28 showdeleted = 0
% 9.93/10.28 showresimp = 1
% 9.93/10.28 showstatus = 2000
% 9.93/10.28
% 9.93/10.28 prologoutput = 0
% 9.93/10.28 nrgoals = 5000000
% 9.93/10.28 totalproof = 1
% 9.93/10.28
% 9.93/10.28 Symbols occurring in the translation:
% 9.93/10.28
% 9.93/10.28 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 9.93/10.28 . [1, 2] (w:1, o:33, a:1, s:1, b:0),
% 9.93/10.28 ! [4, 1] (w:0, o:18, a:1, s:1, b:0),
% 9.93/10.28 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 9.93/10.28 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 9.93/10.28 subset [37, 2] (w:1, o:57, a:1, s:1, b:0),
% 9.93/10.28 empty_set [38, 0] (w:1, o:8, a:1, s:1, b:0),
% 9.93/10.28 empty [39, 1] (w:1, o:23, a:1, s:1, b:0),
% 9.93/10.28 relation [40, 1] (w:1, o:24, a:1, s:1, b:0),
% 9.93/10.28 relation_empty_yielding [41, 1] (w:1, o:26, a:1, s:1, b:0),
% 9.93/10.28 element [42, 2] (w:1, o:58, a:1, s:1, b:0),
% 9.93/10.28 function [43, 1] (w:1, o:27, a:1, s:1, b:0),
% 9.93/10.28 powerset [44, 1] (w:1, o:28, a:1, s:1, b:0),
% 9.93/10.28 relation_dom [45, 1] (w:1, o:25, a:1, s:1, b:0),
% 9.93/10.28 in [46, 2] (w:1, o:59, a:1, s:1, b:0),
% 9.93/10.28 identity_relation [48, 1] (w:1, o:29, a:1, s:1, b:0),
% 9.93/10.28 apply [49, 2] (w:1, o:60, a:1, s:1, b:0),
% 9.93/10.28 alpha1 [50, 2] (w:1, o:61, a:1, s:1, b:1),
% 9.93/10.28 skol1 [51, 1] (w:1, o:30, a:1, s:1, b:1),
% 9.93/10.28 skol2 [52, 0] (w:1, o:12, a:1, s:1, b:1),
% 9.93/10.28 skol3 [53, 1] (w:1, o:31, a:1, s:1, b:1),
% 9.93/10.28 skol4 [54, 1] (w:1, o:32, a:1, s:1, b:1),
% 9.93/10.28 skol5 [55, 0] (w:1, o:13, a:1, s:1, b:1),
% 9.93/10.28 skol6 [56, 0] (w:1, o:14, a:1, s:1, b:1),
% 9.93/10.28 skol7 [57, 0] (w:1, o:15, a:1, s:1, b:1),
% 9.93/10.28 skol8 [58, 0] (w:1, o:16, a:1, s:1, b:1),
% 9.93/10.28 skol9 [59, 0] (w:1, o:17, a:1, s:1, b:1),
% 9.93/10.28 skol10 [60, 0] (w:1, o:10, a:1, s:1, b:1),
% 9.93/10.28 skol11 [61, 2] (w:1, o:62, a:1, s:1, b:1),
% 9.93/10.28 skol12 [62, 0] (w:1, o:11, a:1, s:1, b:1).
% 9.93/10.28
% 9.93/10.28
% 9.93/10.28 Starting Search:
% 9.93/10.28
% 9.93/10.28 *** allocated 15000 integers for clauses
% 9.93/10.28 *** allocated 22500 integers for clauses
% 9.93/10.28 *** allocated 33750 integers for clauses
% 9.93/10.28 *** allocated 50625 integers for clauses
% 9.93/10.28 *** allocated 15000 integers for termspace/termends
% 9.93/10.28 Resimplifying inuse:
% 9.93/10.28 Done
% 9.93/10.28
% 9.93/10.28 *** allocated 75937 integers for clauses
% 9.93/10.28 *** allocated 22500 integers for termspace/termends
% 9.93/10.28 *** allocated 113905 integers for clauses
% 9.93/10.28 *** allocated 33750 integers for termspace/termends
% 9.93/10.28
% 9.93/10.28 Intermediate Status:
% 9.93/10.28 Generated: 6781
% 9.93/10.28 Kept: 2003
% 9.93/10.28 Inuse: 247
% 9.93/10.28 Deleted: 87
% 9.93/10.28 Deletedinuse: 44
% 9.93/10.28
% 9.93/10.28 Resimplifying inuse:
% 9.93/10.28 Done
% 9.93/10.28
% 9.93/10.28 *** allocated 170857 integers for clauses
% 9.93/10.28 *** allocated 50625 integers for termspace/termends
% 9.93/10.28 Resimplifying inuse:
% 9.93/10.28 Done
% 9.93/10.28
% 9.93/10.28 *** allocated 256285 integers for clauses
% 9.93/10.28 *** allocated 75937 integers for termspace/termends
% 9.93/10.28
% 9.93/10.28 Intermediate Status:
% 9.93/10.28 Generated: 18061
% 9.93/10.28 Kept: 4044
% 9.93/10.28 Inuse: 374
% 9.93/10.28 Deleted: 131
% 9.93/10.28 Deletedinuse: 55
% 9.93/10.28
% 9.93/10.28 Resimplifying inuse:
% 9.93/10.28 Done
% 9.93/10.28
% 9.93/10.28 Resimplifying inuse:
% 9.93/10.28 Done
% 9.93/10.28
% 9.93/10.28 *** allocated 384427 integers for clauses
% 9.93/10.28 *** allocated 113905 integers for termspace/termends
% 9.93/10.28
% 9.93/10.28 Intermediate Status:
% 9.93/10.28 Generated: 30511
% 9.93/10.28 Kept: 6050
% 9.93/10.28 Inuse: 493
% 9.93/10.28 Deleted: 178
% 9.93/10.28 Deletedinuse: 73
% 9.93/10.28
% 9.93/10.28 Resimplifying inuse:
% 9.93/10.28 Done
% 9.93/10.28
% 9.93/10.28 Resimplifying inuse:
% 9.93/10.28 Done
% 9.93/10.28
% 9.93/10.28
% 9.93/10.28 Intermediate Status:
% 9.93/10.28 Generated: 42624
% 9.93/10.28 Kept: 8055
% 9.93/10.28 Inuse: 614
% 9.93/10.28 Deleted: 193
% 9.93/10.28 Deletedinuse: 78
% 9.93/10.28
% 9.93/10.28 Resimplifying inuse:
% 9.93/10.28 Done
% 9.93/10.28
% 9.93/10.28 *** allocated 576640 integers for clauses
% 9.93/10.28 *** allocated 170857 integers for termspace/termends
% 9.93/10.28 Resimplifying inuse:
% 9.93/10.28 Done
% 9.93/10.28
% 9.93/10.28
% 9.93/10.28 Intermediate Status:
% 9.93/10.28 Generated: 54339
% 9.93/10.28 Kept: 10150
% 9.93/10.28 Inuse: 666
% 9.93/10.28 Deleted: 203
% 9.93/10.28 Deletedinuse: 83
% 9.93/10.28
% 9.93/10.28 Resimplifying inuse:
% 9.93/10.28 Done
% 9.93/10.28
% 9.93/10.28 Resimplifying inuse:
% 9.93/10.28 Done
% 9.93/10.28
% 9.93/10.28
% 9.93/10.28 Intermediate Status:
% 9.93/10.28 Generated: 60546
% 9.93/10.28 Kept: 12741
% 9.93/10.28 Inuse: 685
% 9.93/10.28 Deleted: 204
% 9.93/10.28 Deletedinuse: 83
% 9.93/10.28
% 9.93/10.28 Resimplifying inuse:
% 9.93/10.28 Done
% 9.93/10.28
% 9.93/10.28 *** allocated 256285 integers for termspace/termends
% 9.93/10.28 *** allocated 864960 integers for clauses
% 9.93/10.28 Resimplifying inuse:
% 9.93/10.28 Done
% 9.93/10.28
% 9.93/10.28
% 9.93/10.28 Intermediate Status:
% 9.93/10.28 Generated: 80902
% 9.93/10.28 Kept: 14760
% 9.93/10.28 Inuse: 771
% 9.93/10.28 Deleted: 223
% 9.93/10.28 Deletedinuse: 87
% 9.93/10.28
% 9.93/10.28 Resimplifying inuse:
% 9.93/10.28 Done
% 9.93/10.28
% 9.93/10.28 Resimplifying inuse:
% 9.93/10.28 Done
% 9.93/10.28
% 9.93/10.28
% 9.93/10.28 Intermediate Status:
% 9.93/10.28 Generated: 96832
% 9.93/10.28 Kept: 16904
% 9.93/10.28 Inuse: 851
% 9.93/10.28 Deleted: 238
% 9.93/10.28 Deletedinuse: 87
% 9.93/10.28
% 9.93/10.28 Resimplifying inuse:
% 9.93/10.28 Done
% 9.93/10.28
% 9.93/10.28 Resimplifying inuse:
% 9.93/10.28 Done
% 9.93/10.28
% 9.93/10.28
% 9.93/10.28 Intermediate Status:
% 9.93/10.28 Generated: 121665
% 9.93/10.28 Kept: 19011
% 9.93/10.28 Inuse: 896
% 9.93/10.28 Deleted: 243
% 9.93/10.28 Deletedinuse: 87
% 9.93/10.28
% 9.93/10.28 Resimplifying inuse:
% 9.93/10.28 Done
% 9.93/10.28
% 9.93/10.28 *** allocated 384427 integers for termspace/termends
% 9.93/10.28 Resimplifying inuse:
% 9.93/10.28 Done
% 9.93/10.28
% 9.93/10.28 Resimplifying clauses:
% 9.93/10.28 *** allocated 1297440 integers for clauses
% 9.93/10.28 Done
% 9.93/10.28
% 9.93/10.28
% 9.93/10.28 Intermediate Status:
% 9.93/10.28 Generated: 139936
% 9.93/10.28 Kept: 21016
% 9.93/10.28 Inuse: 958
% 9.93/10.28 Deleted: 2578
% 9.93/10.28 Deletedinuse: 87
% 9.93/10.28
% 9.93/10.28 Resimplifying inuse:
% 9.93/10.28 Done
% 9.93/10.28
% 9.93/10.28 Resimplifying inuse:
% 9.93/10.28 Done
% 9.93/10.28
% 9.93/10.28
% 9.93/10.28 Intermediate Status:
% 9.93/10.28 Generated: 161340
% 9.93/10.28 Kept: 23047
% 9.93/10.28 Inuse: 1039
% 9.93/10.28 Deleted: 2587
% 9.93/10.28 Deletedinuse: 96
% 9.93/10.28
% 9.93/10.28 Resimplifying inuse:
% 9.93/10.28 Done
% 9.93/10.28
% 9.93/10.28 Resimplifying inuse:
% 9.93/10.28 Done
% 9.93/10.28
% 9.93/10.28
% 9.93/10.28 Bliksems!, er is een bewijs:
% 9.93/10.28 % SZS status Theorem
% 9.93/10.28 % SZS output start Refutation
% 9.93/10.28
% 9.93/10.28 (19) {G0,W3,D3,L1,V1,M1} I { relation( identity_relation( X ) ) }.
% 9.93/10.28 (20) {G0,W3,D3,L1,V1,M1} I { function( identity_relation( X ) ) }.
% 9.93/10.28 (37) {G0,W3,D2,L1,V0,M1} I { in( skol12, skol10 ) }.
% 9.93/10.28 (38) {G0,W6,D4,L1,V0,M1} I { ! apply( identity_relation( skol10 ), skol12 )
% 9.93/10.28 ==> skol12 }.
% 9.93/10.28 (40) {G0,W11,D3,L4,V2,M4} I { ! relation( X ), ! function( X ), ! X =
% 9.93/10.28 identity_relation( Y ), alpha1( X, Y ) }.
% 9.93/10.29 (42) {G0,W11,D3,L3,V3,M3} I { ! alpha1( X, Y ), ! in( Z, Y ), apply( X, Z )
% 9.93/10.29 ==> Z }.
% 9.93/10.29 (410) {G1,W9,D3,L2,V2,M2} R(40,19);r(20) { ! identity_relation( X ) =
% 9.93/10.29 identity_relation( Y ), alpha1( identity_relation( X ), Y ) }.
% 9.93/10.29 (418) {G2,W4,D3,L1,V1,M1} Q(410) { alpha1( identity_relation( X ), X ) }.
% 9.93/10.29 (513) {G1,W7,D3,L2,V1,M2} R(42,38) { ! alpha1( identity_relation( skol10 )
% 9.93/10.29 , X ), ! in( skol12, X ) }.
% 9.93/10.29 (24967) {G3,W0,D0,L0,V0,M0} R(513,418);r(37) { }.
% 9.93/10.29
% 9.93/10.29
% 9.93/10.29 % SZS output end Refutation
% 9.93/10.29 found a proof!
% 9.93/10.29
% 9.93/10.29
% 9.93/10.29 Unprocessed initial clauses:
% 9.93/10.29
% 9.93/10.29 (24969) {G0,W3,D2,L1,V1,M1} { subset( X, X ) }.
% 9.93/10.29 (24970) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 9.93/10.29 (24971) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 9.93/10.29 (24972) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 9.93/10.29 (24973) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 9.93/10.29 (24974) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( empty_set ) }.
% 9.93/10.29 (24975) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 9.93/10.29 (24976) {G0,W4,D3,L1,V1,M1} { element( skol1( X ), X ) }.
% 9.93/10.29 (24977) {G0,W4,D2,L2,V1,M2} { ! empty( X ), function( X ) }.
% 9.93/10.29 (24978) {G0,W3,D3,L1,V1,M1} { ! empty( powerset( X ) ) }.
% 9.93/10.29 (24979) {G0,W7,D3,L3,V1,M3} { empty( X ), ! relation( X ), ! empty(
% 9.93/10.29 relation_dom( X ) ) }.
% 9.93/10.29 (24980) {G0,W5,D3,L2,V1,M2} { ! empty( X ), empty( relation_dom( X ) ) }.
% 9.93/10.29 (24981) {G0,W5,D3,L2,V1,M2} { ! empty( X ), relation( relation_dom( X ) )
% 9.93/10.29 }.
% 9.93/10.29 (24982) {G0,W4,D2,L2,V1,M2} { ! empty( X ), relation( X ) }.
% 9.93/10.29 (24983) {G0,W8,D2,L3,V2,M3} { ! element( X, Y ), empty( Y ), in( X, Y )
% 9.93/10.29 }.
% 9.93/10.29 (24984) {G0,W7,D3,L2,V2,M2} { ! element( X, powerset( Y ) ), subset( X, Y
% 9.93/10.29 ) }.
% 9.93/10.29 (24985) {G0,W7,D3,L2,V2,M2} { ! subset( X, Y ), element( X, powerset( Y )
% 9.93/10.29 ) }.
% 9.93/10.29 (24986) {G0,W10,D3,L3,V3,M3} { ! in( X, Z ), ! element( Z, powerset( Y ) )
% 9.93/10.29 , element( X, Y ) }.
% 9.93/10.29 (24987) {G0,W9,D3,L3,V3,M3} { ! in( X, Y ), ! element( Y, powerset( Z ) )
% 9.93/10.29 , ! empty( Z ) }.
% 9.93/10.29 (24988) {G0,W5,D2,L2,V1,M2} { ! empty( X ), X = empty_set }.
% 9.93/10.29 (24989) {G0,W7,D2,L3,V2,M3} { ! empty( X ), X = Y, ! empty( Y ) }.
% 9.93/10.29 (24990) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), ! in( Y, X ) }.
% 9.93/10.29 (24991) {G0,W3,D3,L1,V1,M1} { relation( identity_relation( X ) ) }.
% 9.93/10.29 (24992) {G0,W3,D3,L1,V1,M1} { relation( identity_relation( X ) ) }.
% 9.93/10.29 (24993) {G0,W3,D3,L1,V1,M1} { function( identity_relation( X ) ) }.
% 9.93/10.29 (24994) {G0,W2,D2,L1,V0,M1} { relation( skol2 ) }.
% 9.93/10.29 (24995) {G0,W2,D2,L1,V0,M1} { function( skol2 ) }.
% 9.93/10.29 (24996) {G0,W5,D3,L2,V2,M2} { empty( X ), ! empty( skol3( Y ) ) }.
% 9.93/10.29 (24997) {G0,W7,D3,L2,V1,M2} { empty( X ), element( skol3( X ), powerset( X
% 9.93/10.29 ) ) }.
% 9.93/10.29 (24998) {G0,W3,D3,L1,V1,M1} { empty( skol4( Y ) ) }.
% 9.93/10.29 (24999) {G0,W5,D3,L1,V1,M1} { element( skol4( X ), powerset( X ) ) }.
% 9.93/10.29 (25000) {G0,W2,D2,L1,V0,M1} { empty( skol5 ) }.
% 9.93/10.29 (25001) {G0,W2,D2,L1,V0,M1} { relation( skol5 ) }.
% 9.93/10.29 (25002) {G0,W2,D2,L1,V0,M1} { ! empty( skol6 ) }.
% 9.93/10.29 (25003) {G0,W2,D2,L1,V0,M1} { relation( skol6 ) }.
% 9.93/10.29 (25004) {G0,W2,D2,L1,V0,M1} { relation( skol7 ) }.
% 9.93/10.29 (25005) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( skol7 ) }.
% 9.93/10.29 (25006) {G0,W2,D2,L1,V0,M1} { empty( skol8 ) }.
% 9.93/10.29 (25007) {G0,W2,D2,L1,V0,M1} { ! empty( skol9 ) }.
% 9.93/10.29 (25008) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), element( X, Y ) }.
% 9.93/10.29 (25009) {G0,W5,D2,L2,V2,M2} { ! in( X, Y ), ! empty( Y ) }.
% 9.93/10.29 (25010) {G0,W3,D2,L1,V0,M1} { in( skol12, skol10 ) }.
% 9.93/10.29 (25011) {G0,W6,D4,L1,V0,M1} { ! apply( identity_relation( skol10 ), skol12
% 9.93/10.29 ) = skol12 }.
% 9.93/10.29 (25012) {G0,W12,D3,L4,V2,M4} { ! relation( X ), ! function( X ), ! X =
% 9.93/10.29 identity_relation( Y ), relation_dom( X ) = Y }.
% 9.93/10.29 (25013) {G0,W11,D3,L4,V2,M4} { ! relation( X ), ! function( X ), ! X =
% 9.93/10.29 identity_relation( Y ), alpha1( X, Y ) }.
% 9.93/10.29 (25014) {G0,W15,D3,L5,V2,M5} { ! relation( X ), ! function( X ), !
% 9.93/10.29 relation_dom( X ) = Y, ! alpha1( X, Y ), X = identity_relation( Y ) }.
% 9.93/10.29 (25015) {G0,W11,D3,L3,V3,M3} { ! alpha1( X, Y ), ! in( Z, Y ), apply( X, Z
% 9.93/10.29 ) = Z }.
% 9.93/10.29 (25016) {G0,W8,D3,L2,V3,M2} { in( skol11( Z, Y ), Y ), alpha1( X, Y ) }.
% 9.93/10.29 (25017) {G0,W12,D4,L2,V2,M2} { ! apply( X, skol11( X, Y ) ) = skol11( X, Y
% 9.93/10.29 ), alpha1( X, Y ) }.
% 9.93/10.29
% 9.93/10.29
% 9.93/10.29 Total Proof:
% 9.93/10.29
% 9.93/10.29 subsumption: (19) {G0,W3,D3,L1,V1,M1} I { relation( identity_relation( X )
% 9.93/10.29 ) }.
% 9.93/10.29 parent0: (24991) {G0,W3,D3,L1,V1,M1} { relation( identity_relation( X ) )
% 9.93/10.29 }.
% 9.93/10.29 substitution0:
% 9.93/10.29 X := X
% 9.93/10.29 end
% 9.93/10.29 permutation0:
% 9.93/10.29 0 ==> 0
% 9.93/10.29 end
% 9.93/10.29
% 9.93/10.29 subsumption: (20) {G0,W3,D3,L1,V1,M1} I { function( identity_relation( X )
% 9.93/10.29 ) }.
% 9.93/10.29 parent0: (24993) {G0,W3,D3,L1,V1,M1} { function( identity_relation( X ) )
% 9.93/10.29 }.
% 9.93/10.29 substitution0:
% 9.93/10.29 X := X
% 9.93/10.29 end
% 9.93/10.29 permutation0:
% 9.93/10.29 0 ==> 0
% 9.93/10.29 end
% 9.93/10.29
% 9.93/10.29 subsumption: (37) {G0,W3,D2,L1,V0,M1} I { in( skol12, skol10 ) }.
% 9.93/10.29 parent0: (25010) {G0,W3,D2,L1,V0,M1} { in( skol12, skol10 ) }.
% 9.93/10.29 substitution0:
% 9.93/10.29 end
% 9.93/10.29 permutation0:
% 9.93/10.29 0 ==> 0
% 9.93/10.29 end
% 9.93/10.29
% 9.93/10.29 subsumption: (38) {G0,W6,D4,L1,V0,M1} I { ! apply( identity_relation(
% 9.93/10.29 skol10 ), skol12 ) ==> skol12 }.
% 9.93/10.29 parent0: (25011) {G0,W6,D4,L1,V0,M1} { ! apply( identity_relation( skol10
% 9.93/10.29 ), skol12 ) = skol12 }.
% 9.93/10.29 substitution0:
% 9.93/10.29 end
% 9.93/10.29 permutation0:
% 9.93/10.29 0 ==> 0
% 9.93/10.29 end
% 9.93/10.29
% 9.93/10.29 subsumption: (40) {G0,W11,D3,L4,V2,M4} I { ! relation( X ), ! function( X )
% 9.93/10.29 , ! X = identity_relation( Y ), alpha1( X, Y ) }.
% 9.93/10.29 parent0: (25013) {G0,W11,D3,L4,V2,M4} { ! relation( X ), ! function( X ),
% 9.93/10.29 ! X = identity_relation( Y ), alpha1( X, Y ) }.
% 9.93/10.29 substitution0:
% 9.93/10.29 X := X
% 9.93/10.29 Y := Y
% 9.93/10.29 end
% 9.93/10.29 permutation0:
% 9.93/10.29 0 ==> 0
% 9.93/10.29 1 ==> 1
% 9.93/10.29 2 ==> 2
% 9.93/10.29 3 ==> 3
% 9.93/10.29 end
% 9.93/10.29
% 9.93/10.29 subsumption: (42) {G0,W11,D3,L3,V3,M3} I { ! alpha1( X, Y ), ! in( Z, Y ),
% 9.93/10.29 apply( X, Z ) ==> Z }.
% 9.93/10.29 parent0: (25015) {G0,W11,D3,L3,V3,M3} { ! alpha1( X, Y ), ! in( Z, Y ),
% 9.93/10.29 apply( X, Z ) = Z }.
% 9.93/10.29 substitution0:
% 9.93/10.29 X := X
% 9.93/10.29 Y := Y
% 9.93/10.29 Z := Z
% 9.93/10.29 end
% 9.93/10.29 permutation0:
% 9.93/10.29 0 ==> 0
% 9.93/10.29 1 ==> 1
% 9.93/10.29 2 ==> 2
% 9.93/10.29 end
% 9.93/10.29
% 9.93/10.29 eqswap: (25051) {G0,W11,D3,L4,V2,M4} { ! identity_relation( Y ) = X, !
% 9.93/10.29 relation( X ), ! function( X ), alpha1( X, Y ) }.
% 9.93/10.29 parent0[2]: (40) {G0,W11,D3,L4,V2,M4} I { ! relation( X ), ! function( X )
% 9.93/10.29 , ! X = identity_relation( Y ), alpha1( X, Y ) }.
% 9.93/10.29 substitution0:
% 9.93/10.29 X := X
% 9.93/10.29 Y := Y
% 9.93/10.29 end
% 9.93/10.29
% 9.93/10.29 resolution: (25052) {G1,W12,D3,L3,V2,M3} { ! identity_relation( X ) =
% 9.93/10.29 identity_relation( Y ), ! function( identity_relation( Y ) ), alpha1(
% 9.93/10.29 identity_relation( Y ), X ) }.
% 9.93/10.29 parent0[1]: (25051) {G0,W11,D3,L4,V2,M4} { ! identity_relation( Y ) = X, !
% 9.93/10.29 relation( X ), ! function( X ), alpha1( X, Y ) }.
% 9.93/10.29 parent1[0]: (19) {G0,W3,D3,L1,V1,M1} I { relation( identity_relation( X ) )
% 9.93/10.29 }.
% 9.93/10.29 substitution0:
% 9.93/10.29 X := identity_relation( Y )
% 9.93/10.29 Y := X
% 9.93/10.29 end
% 9.93/10.29 substitution1:
% 9.93/10.29 X := Y
% 9.93/10.29 end
% 9.93/10.29
% 9.93/10.29 resolution: (25053) {G1,W9,D3,L2,V2,M2} { ! identity_relation( X ) =
% 9.93/10.29 identity_relation( Y ), alpha1( identity_relation( Y ), X ) }.
% 9.93/10.29 parent0[1]: (25052) {G1,W12,D3,L3,V2,M3} { ! identity_relation( X ) =
% 9.93/10.29 identity_relation( Y ), ! function( identity_relation( Y ) ), alpha1(
% 9.93/10.29 identity_relation( Y ), X ) }.
% 9.93/10.29 parent1[0]: (20) {G0,W3,D3,L1,V1,M1} I { function( identity_relation( X ) )
% 9.93/10.29 }.
% 9.93/10.29 substitution0:
% 9.93/10.29 X := X
% 9.93/10.29 Y := Y
% 9.93/10.29 end
% 9.93/10.29 substitution1:
% 9.93/10.29 X := Y
% 9.93/10.29 end
% 9.93/10.29
% 9.93/10.29 eqswap: (25054) {G1,W9,D3,L2,V2,M2} { ! identity_relation( Y ) =
% 9.93/10.29 identity_relation( X ), alpha1( identity_relation( Y ), X ) }.
% 9.93/10.29 parent0[0]: (25053) {G1,W9,D3,L2,V2,M2} { ! identity_relation( X ) =
% 9.93/10.29 identity_relation( Y ), alpha1( identity_relation( Y ), X ) }.
% 9.93/10.29 substitution0:
% 9.93/10.29 X := X
% 9.93/10.29 Y := Y
% 9.93/10.29 end
% 9.93/10.29
% 9.93/10.29 subsumption: (410) {G1,W9,D3,L2,V2,M2} R(40,19);r(20) { ! identity_relation
% 9.93/10.29 ( X ) = identity_relation( Y ), alpha1( identity_relation( X ), Y ) }.
% 9.93/10.29 parent0: (25054) {G1,W9,D3,L2,V2,M2} { ! identity_relation( Y ) =
% 9.93/10.29 identity_relation( X ), alpha1( identity_relation( Y ), X ) }.
% 9.93/10.29 substitution0:
% 9.93/10.29 X := Y
% 9.93/10.29 Y := X
% 9.93/10.29 end
% 9.93/10.29 permutation0:
% 9.93/10.29 0 ==> 0
% 9.93/10.29 1 ==> 1
% 9.93/10.29 end
% 9.93/10.29
% 9.93/10.29 eqswap: (25055) {G1,W9,D3,L2,V2,M2} { ! identity_relation( Y ) =
% 9.93/10.29 identity_relation( X ), alpha1( identity_relation( X ), Y ) }.
% 9.93/10.29 parent0[0]: (410) {G1,W9,D3,L2,V2,M2} R(40,19);r(20) { ! identity_relation
% 9.93/10.29 ( X ) = identity_relation( Y ), alpha1( identity_relation( X ), Y ) }.
% 9.93/10.29 substitution0:
% 9.93/10.29 X := X
% 9.93/10.29 Y := Y
% 9.93/10.29 end
% 9.93/10.29
% 9.93/10.29 eqrefl: (25056) {G0,W4,D3,L1,V1,M1} { alpha1( identity_relation( X ), X )
% 9.93/10.29 }.
% 9.93/10.29 parent0[0]: (25055) {G1,W9,D3,L2,V2,M2} { ! identity_relation( Y ) =
% 9.93/10.29 identity_relation( X ), alpha1( identity_relation( X ), Y ) }.
% 9.93/10.29 substitution0:
% 9.93/10.29 X := X
% 9.93/10.29 Y := X
% 9.93/10.29 end
% 9.93/10.29
% 9.93/10.29 subsumption: (418) {G2,W4,D3,L1,V1,M1} Q(410) { alpha1( identity_relation(
% 9.93/10.29 X ), X ) }.
% 9.93/10.29 parent0: (25056) {G0,W4,D3,L1,V1,M1} { alpha1( identity_relation( X ), X )
% 9.93/10.29 }.
% 9.93/10.29 substitution0:
% 9.93/10.29 X := X
% 9.93/10.29 end
% 9.93/10.29 permutation0:
% 9.93/10.29 0 ==> 0
% 9.93/10.29 end
% 9.93/10.29
% 9.93/10.29 eqswap: (25057) {G0,W11,D3,L3,V3,M3} { Y ==> apply( X, Y ), ! alpha1( X, Z
% 9.93/10.29 ), ! in( Y, Z ) }.
% 9.93/10.29 parent0[2]: (42) {G0,W11,D3,L3,V3,M3} I { ! alpha1( X, Y ), ! in( Z, Y ),
% 9.93/10.29 apply( X, Z ) ==> Z }.
% 9.93/10.29 substitution0:
% 9.93/10.29 X := X
% 9.93/10.29 Y := Z
% 9.93/10.29 Z := Y
% 9.93/10.29 end
% 9.93/10.29
% 9.93/10.29 eqswap: (25058) {G0,W6,D4,L1,V0,M1} { ! skol12 ==> apply(
% 9.93/10.29 identity_relation( skol10 ), skol12 ) }.
% 9.93/10.29 parent0[0]: (38) {G0,W6,D4,L1,V0,M1} I { ! apply( identity_relation( skol10
% 9.93/10.29 ), skol12 ) ==> skol12 }.
% 9.93/10.29 substitution0:
% 9.93/10.29 end
% 9.93/10.29
% 9.93/10.29 resolution: (25059) {G1,W7,D3,L2,V1,M2} { ! alpha1( identity_relation(
% 9.93/10.29 skol10 ), X ), ! in( skol12, X ) }.
% 9.93/10.29 parent0[0]: (25058) {G0,W6,D4,L1,V0,M1} { ! skol12 ==> apply(
% 9.93/10.29 identity_relation( skol10 ), skol12 ) }.
% 9.93/10.29 parent1[0]: (25057) {G0,W11,D3,L3,V3,M3} { Y ==> apply( X, Y ), ! alpha1(
% 9.93/10.29 X, Z ), ! in( Y, Z ) }.
% 9.93/10.29 substitution0:
% 9.93/10.29 end
% 9.93/10.29 substitution1:
% 9.93/10.29 X := identity_relation( skol10 )
% 9.93/10.29 Y := skol12
% 9.93/10.29 Z := X
% 9.93/10.29 end
% 9.93/10.29
% 9.93/10.29 subsumption: (513) {G1,W7,D3,L2,V1,M2} R(42,38) { ! alpha1(
% 9.93/10.29 identity_relation( skol10 ), X ), ! in( skol12, X ) }.
% 9.93/10.29 parent0: (25059) {G1,W7,D3,L2,V1,M2} { ! alpha1( identity_relation( skol10
% 9.93/10.29 ), X ), ! in( skol12, X ) }.
% 9.93/10.29 substitution0:
% 9.93/10.29 X := X
% 9.93/10.29 end
% 9.93/10.29 permutation0:
% 9.93/10.29 0 ==> 0
% 9.93/10.29 1 ==> 1
% 9.93/10.29 end
% 9.93/10.29
% 9.93/10.29 resolution: (25060) {G2,W3,D2,L1,V0,M1} { ! in( skol12, skol10 ) }.
% 9.93/10.29 parent0[0]: (513) {G1,W7,D3,L2,V1,M2} R(42,38) { ! alpha1(
% 9.93/10.29 identity_relation( skol10 ), X ), ! in( skol12, X ) }.
% 9.93/10.29 parent1[0]: (418) {G2,W4,D3,L1,V1,M1} Q(410) { alpha1( identity_relation( X
% 9.93/10.29 ), X ) }.
% 9.93/10.29 substitution0:
% 9.93/10.29 X := skol10
% 9.93/10.29 end
% 9.93/10.29 substitution1:
% 9.93/10.29 X := skol10
% 9.93/10.29 end
% 9.93/10.29
% 9.93/10.29 resolution: (25061) {G1,W0,D0,L0,V0,M0} { }.
% 9.93/10.29 parent0[0]: (25060) {G2,W3,D2,L1,V0,M1} { ! in( skol12, skol10 ) }.
% 9.93/10.29 parent1[0]: (37) {G0,W3,D2,L1,V0,M1} I { in( skol12, skol10 ) }.
% 9.93/10.29 substitution0:
% 9.93/10.29 end
% 9.93/10.29 substitution1:
% 9.93/10.29 end
% 9.93/10.29
% 9.93/10.29 subsumption: (24967) {G3,W0,D0,L0,V0,M0} R(513,418);r(37) { }.
% 9.93/10.29 parent0: (25061) {G1,W0,D0,L0,V0,M0} { }.
% 9.93/10.29 substitution0:
% 9.93/10.29 end
% 9.93/10.29 permutation0:
% 9.93/10.29 end
% 9.93/10.29
% 9.93/10.29 Proof check complete!
% 9.93/10.29
% 9.93/10.29 Memory use:
% 9.93/10.29
% 9.93/10.29 space for terms: 339090
% 9.93/10.29 space for clauses: 1055586
% 9.93/10.29
% 9.93/10.29
% 9.93/10.29 clauses generated: 177843
% 9.93/10.29 clauses kept: 24968
% 9.93/10.29 clauses selected: 1094
% 9.93/10.29 clauses deleted: 2587
% 9.93/10.29 clauses inuse deleted: 96
% 9.93/10.29
% 9.93/10.29 subsentry: 763761
% 9.93/10.29 literals s-matched: 493096
% 9.93/10.29 literals matched: 451174
% 9.93/10.29 full subsumption: 65719
% 9.93/10.29
% 9.93/10.29 checksum: 1506872458
% 9.93/10.29
% 9.93/10.29
% 9.93/10.29 Bliksem ended
%------------------------------------------------------------------------------