TSTP Solution File: SEU080+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SEU080+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n024.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 07:10:32 EDT 2022
% Result : Theorem 0.78s 1.56s
% Output : Refutation 0.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU080+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : bliksem %s
% 0.14/0.34 % Computer : n024.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % DateTime : Mon Jun 20 02:02:02 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.78/1.56 *** allocated 10000 integers for termspace/termends
% 0.78/1.56 *** allocated 10000 integers for clauses
% 0.78/1.56 *** allocated 10000 integers for justifications
% 0.78/1.56 Bliksem 1.12
% 0.78/1.56
% 0.78/1.56
% 0.78/1.56 Automatic Strategy Selection
% 0.78/1.56
% 0.78/1.56
% 0.78/1.56 Clauses:
% 0.78/1.56
% 0.78/1.56 { ! in( X, Y ), ! in( Y, X ) }.
% 0.78/1.56 { ! empty( X ), function( X ) }.
% 0.78/1.56 { ! empty( X ), relation( X ) }.
% 0.78/1.56 { ! relation( X ), ! empty( X ), ! function( X ), relation( X ) }.
% 0.78/1.56 { ! relation( X ), ! empty( X ), ! function( X ), function( X ) }.
% 0.78/1.56 { ! relation( X ), ! empty( X ), ! function( X ), one_to_one( X ) }.
% 0.78/1.56 { ! X = Y, subset( X, Y ) }.
% 0.78/1.56 { ! X = Y, subset( Y, X ) }.
% 0.78/1.56 { ! subset( X, Y ), ! subset( Y, X ), X = Y }.
% 0.78/1.56 { element( skol1( X ), X ) }.
% 0.78/1.56 { empty( empty_set ) }.
% 0.78/1.56 { relation( empty_set ) }.
% 0.78/1.56 { relation_empty_yielding( empty_set ) }.
% 0.78/1.56 { ! empty( powerset( X ) ) }.
% 0.78/1.56 { empty( empty_set ) }.
% 0.78/1.56 { empty( empty_set ) }.
% 0.78/1.56 { relation( empty_set ) }.
% 0.78/1.56 { empty( X ), ! relation( X ), ! empty( relation_rng( X ) ) }.
% 0.78/1.56 { ! empty( X ), empty( relation_rng( X ) ) }.
% 0.78/1.56 { ! empty( X ), relation( relation_rng( X ) ) }.
% 0.78/1.56 { relation( skol2 ) }.
% 0.78/1.56 { function( skol2 ) }.
% 0.78/1.56 { empty( skol3 ) }.
% 0.78/1.56 { relation( skol3 ) }.
% 0.78/1.56 { empty( X ), ! empty( skol4( Y ) ) }.
% 0.78/1.56 { empty( X ), element( skol4( X ), powerset( X ) ) }.
% 0.78/1.56 { empty( skol5 ) }.
% 0.78/1.56 { relation( skol6 ) }.
% 0.78/1.56 { empty( skol6 ) }.
% 0.78/1.56 { function( skol6 ) }.
% 0.78/1.56 { ! empty( skol7 ) }.
% 0.78/1.56 { relation( skol7 ) }.
% 0.78/1.56 { empty( skol8( Y ) ) }.
% 0.78/1.56 { element( skol8( X ), powerset( X ) ) }.
% 0.78/1.56 { ! empty( skol9 ) }.
% 0.78/1.56 { relation( skol10 ) }.
% 0.78/1.56 { function( skol10 ) }.
% 0.78/1.56 { one_to_one( skol10 ) }.
% 0.78/1.56 { relation( skol11 ) }.
% 0.78/1.56 { relation_empty_yielding( skol11 ) }.
% 0.78/1.56 { subset( X, X ) }.
% 0.78/1.56 { ! relation( X ), ! function( X ), ! subset( relation_inverse_image( X, Y
% 0.78/1.56 ), relation_inverse_image( X, Z ) ), ! subset( Y, relation_rng( X ) ),
% 0.78/1.56 subset( Y, Z ) }.
% 0.78/1.56 { relation( skol12 ) }.
% 0.78/1.56 { function( skol12 ) }.
% 0.78/1.56 { relation_inverse_image( skol12, skol13 ) = relation_inverse_image( skol12
% 0.78/1.56 , skol14 ) }.
% 0.78/1.56 { subset( skol13, relation_rng( skol12 ) ) }.
% 0.78/1.56 { subset( skol14, relation_rng( skol12 ) ) }.
% 0.78/1.56 { ! skol13 = skol14 }.
% 0.78/1.56 { ! in( X, Y ), element( X, Y ) }.
% 0.78/1.56 { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.78/1.56 { ! element( X, powerset( Y ) ), subset( X, Y ) }.
% 0.78/1.56 { ! subset( X, Y ), element( X, powerset( Y ) ) }.
% 0.78/1.56 { ! in( X, Z ), ! element( Z, powerset( Y ) ), element( X, Y ) }.
% 0.78/1.56 { ! in( X, Y ), ! element( Y, powerset( Z ) ), ! empty( Z ) }.
% 0.78/1.56 { ! empty( X ), X = empty_set }.
% 0.78/1.56 { ! in( X, Y ), ! empty( Y ) }.
% 0.78/1.56 { ! empty( X ), X = Y, ! empty( Y ) }.
% 0.78/1.56
% 0.78/1.56 percentage equality = 0.082353, percentage horn = 0.961538
% 0.78/1.56 This is a problem with some equality
% 0.78/1.56
% 0.78/1.56
% 0.78/1.56
% 0.78/1.56 Options Used:
% 0.78/1.56
% 0.78/1.56 useres = 1
% 0.78/1.56 useparamod = 1
% 0.78/1.56 useeqrefl = 1
% 0.78/1.56 useeqfact = 1
% 0.78/1.56 usefactor = 1
% 0.78/1.56 usesimpsplitting = 0
% 0.78/1.56 usesimpdemod = 5
% 0.78/1.56 usesimpres = 3
% 0.78/1.56
% 0.78/1.56 resimpinuse = 1000
% 0.78/1.56 resimpclauses = 20000
% 0.78/1.56 substype = eqrewr
% 0.78/1.56 backwardsubs = 1
% 0.78/1.56 selectoldest = 5
% 0.78/1.56
% 0.78/1.56 litorderings [0] = split
% 0.78/1.56 litorderings [1] = extend the termordering, first sorting on arguments
% 0.78/1.56
% 0.78/1.56 termordering = kbo
% 0.78/1.56
% 0.78/1.56 litapriori = 0
% 0.78/1.56 termapriori = 1
% 0.78/1.56 litaposteriori = 0
% 0.78/1.56 termaposteriori = 0
% 0.78/1.56 demodaposteriori = 0
% 0.78/1.56 ordereqreflfact = 0
% 0.78/1.56
% 0.78/1.56 litselect = negord
% 0.78/1.56
% 0.78/1.56 maxweight = 15
% 0.78/1.56 maxdepth = 30000
% 0.78/1.56 maxlength = 115
% 0.78/1.56 maxnrvars = 195
% 0.78/1.56 excuselevel = 1
% 0.78/1.56 increasemaxweight = 1
% 0.78/1.56
% 0.78/1.56 maxselected = 10000000
% 0.78/1.56 maxnrclauses = 10000000
% 0.78/1.56
% 0.78/1.56 showgenerated = 0
% 0.78/1.56 showkept = 0
% 0.78/1.56 showselected = 0
% 0.78/1.56 showdeleted = 0
% 0.78/1.56 showresimp = 1
% 0.78/1.56 showstatus = 2000
% 0.78/1.56
% 0.78/1.56 prologoutput = 0
% 0.78/1.56 nrgoals = 5000000
% 0.78/1.56 totalproof = 1
% 0.78/1.56
% 0.78/1.56 Symbols occurring in the translation:
% 0.78/1.56
% 0.78/1.56 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.78/1.56 . [1, 2] (w:1, o:36, a:1, s:1, b:0),
% 0.78/1.56 ! [4, 1] (w:0, o:21, a:1, s:1, b:0),
% 0.78/1.56 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.78/1.56 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.78/1.56 in [37, 2] (w:1, o:60, a:1, s:1, b:0),
% 0.78/1.56 empty [38, 1] (w:1, o:26, a:1, s:1, b:0),
% 0.78/1.56 function [39, 1] (w:1, o:27, a:1, s:1, b:0),
% 0.78/1.56 relation [40, 1] (w:1, o:28, a:1, s:1, b:0),
% 0.78/1.56 one_to_one [41, 1] (w:1, o:29, a:1, s:1, b:0),
% 0.78/1.56 subset [42, 2] (w:1, o:62, a:1, s:1, b:0),
% 0.78/1.56 element [43, 2] (w:1, o:63, a:1, s:1, b:0),
% 0.78/1.56 empty_set [44, 0] (w:1, o:8, a:1, s:1, b:0),
% 0.78/1.56 relation_empty_yielding [45, 1] (w:1, o:30, a:1, s:1, b:0),
% 0.78/1.56 powerset [46, 1] (w:1, o:31, a:1, s:1, b:0),
% 0.78/1.56 relation_rng [47, 1] (w:1, o:32, a:1, s:1, b:0),
% 0.78/1.56 relation_inverse_image [49, 2] (w:1, o:61, a:1, s:1, b:0),
% 0.78/1.56 skol1 [50, 1] (w:1, o:33, a:1, s:1, b:1),
% 0.78/1.56 skol2 [51, 0] (w:1, o:15, a:1, s:1, b:1),
% 0.78/1.56 skol3 [52, 0] (w:1, o:16, a:1, s:1, b:1),
% 0.78/1.56 skol4 [53, 1] (w:1, o:34, a:1, s:1, b:1),
% 0.78/1.56 skol5 [54, 0] (w:1, o:17, a:1, s:1, b:1),
% 0.78/1.56 skol6 [55, 0] (w:1, o:18, a:1, s:1, b:1),
% 0.78/1.56 skol7 [56, 0] (w:1, o:19, a:1, s:1, b:1),
% 0.78/1.56 skol8 [57, 1] (w:1, o:35, a:1, s:1, b:1),
% 0.78/1.56 skol9 [58, 0] (w:1, o:20, a:1, s:1, b:1),
% 0.78/1.56 skol10 [59, 0] (w:1, o:10, a:1, s:1, b:1),
% 0.78/1.56 skol11 [60, 0] (w:1, o:11, a:1, s:1, b:1),
% 0.78/1.56 skol12 [61, 0] (w:1, o:12, a:1, s:1, b:1),
% 0.78/1.56 skol13 [62, 0] (w:1, o:13, a:1, s:1, b:1),
% 0.78/1.56 skol14 [63, 0] (w:1, o:14, a:1, s:1, b:1).
% 0.78/1.56
% 0.78/1.56
% 0.78/1.56 Starting Search:
% 0.78/1.56
% 0.78/1.56 *** allocated 15000 integers for clauses
% 0.78/1.56 *** allocated 22500 integers for clauses
% 0.78/1.56 *** allocated 33750 integers for clauses
% 0.78/1.56 *** allocated 50625 integers for clauses
% 0.78/1.56 *** allocated 15000 integers for termspace/termends
% 0.78/1.56 Resimplifying inuse:
% 0.78/1.56 Done
% 0.78/1.56
% 0.78/1.56 *** allocated 75937 integers for clauses
% 0.78/1.56 *** allocated 22500 integers for termspace/termends
% 0.78/1.56 *** allocated 113905 integers for clauses
% 0.78/1.56
% 0.78/1.56 Intermediate Status:
% 0.78/1.56 Generated: 9973
% 0.78/1.56 Kept: 2020
% 0.78/1.56 Inuse: 337
% 0.78/1.56 Deleted: 179
% 0.78/1.56 Deletedinuse: 64
% 0.78/1.56
% 0.78/1.56 Resimplifying inuse:
% 0.78/1.56 Done
% 0.78/1.56
% 0.78/1.56 *** allocated 33750 integers for termspace/termends
% 0.78/1.56 *** allocated 170857 integers for clauses
% 0.78/1.56 Resimplifying inuse:
% 0.78/1.56 Done
% 0.78/1.56
% 0.78/1.56 *** allocated 50625 integers for termspace/termends
% 0.78/1.56 *** allocated 256285 integers for clauses
% 0.78/1.56
% 0.78/1.56 Intermediate Status:
% 0.78/1.56 Generated: 19825
% 0.78/1.56 Kept: 4023
% 0.78/1.56 Inuse: 490
% 0.78/1.56 Deleted: 240
% 0.78/1.56 Deletedinuse: 76
% 0.78/1.56
% 0.78/1.56 Resimplifying inuse:
% 0.78/1.56 Done
% 0.78/1.56
% 0.78/1.56 *** allocated 75937 integers for termspace/termends
% 0.78/1.56
% 0.78/1.56 Bliksems!, er is een bewijs:
% 0.78/1.56 % SZS status Theorem
% 0.78/1.56 % SZS output start Refutation
% 0.78/1.56
% 0.78/1.56 (4) {G0,W6,D2,L2,V2,M2} I { ! X = Y, subset( X, Y ) }.
% 0.78/1.56 (5) {G0,W9,D2,L3,V2,M3} I { ! subset( X, Y ), ! subset( Y, X ), X = Y }.
% 0.78/1.56 (34) {G0,W3,D2,L1,V1,M1} I { subset( X, X ) }.
% 0.78/1.56 (35) {G0,W18,D3,L5,V3,M5} I { ! relation( X ), ! function( X ), ! subset(
% 0.78/1.56 relation_inverse_image( X, Y ), relation_inverse_image( X, Z ) ), !
% 0.78/1.56 subset( Y, relation_rng( X ) ), subset( Y, Z ) }.
% 0.78/1.56 (36) {G0,W2,D2,L1,V0,M1} I { relation( skol12 ) }.
% 0.78/1.56 (37) {G0,W2,D2,L1,V0,M1} I { function( skol12 ) }.
% 0.78/1.56 (38) {G0,W7,D3,L1,V0,M1} I { relation_inverse_image( skol12, skol14 ) ==>
% 0.78/1.56 relation_inverse_image( skol12, skol13 ) }.
% 0.78/1.56 (39) {G0,W4,D3,L1,V0,M1} I { subset( skol13, relation_rng( skol12 ) ) }.
% 0.78/1.56 (40) {G0,W4,D3,L1,V0,M1} I { subset( skol14, relation_rng( skol12 ) ) }.
% 0.78/1.56 (41) {G0,W3,D2,L1,V0,M1} I { ! skol14 ==> skol13 }.
% 0.78/1.56 (57) {G1,W6,D2,L2,V2,M2} R(5,4);r(4) { X = Y, ! Y = X }.
% 0.78/1.56 (83) {G1,W9,D2,L3,V1,M3} P(5,41) { ! X = skol13, ! subset( skol14, X ), !
% 0.78/1.56 subset( X, skol14 ) }.
% 0.78/1.56 (84) {G2,W6,D2,L2,V0,M2} Q(83) { ! subset( skol14, skol13 ), ! subset(
% 0.78/1.56 skol13, skol14 ) }.
% 0.78/1.56 (212) {G1,W18,D3,L5,V3,M5} R(35,4) { ! relation( X ), ! function( X ), !
% 0.78/1.56 subset( Y, relation_rng( X ) ), subset( Y, Z ), ! relation_inverse_image
% 0.78/1.56 ( X, Y ) = relation_inverse_image( X, Z ) }.
% 0.78/1.56 (222) {G1,W14,D3,L3,V2,M3} R(35,36);r(37) { ! subset(
% 0.78/1.56 relation_inverse_image( skol12, X ), relation_inverse_image( skol12, Y )
% 0.78/1.56 ), ! subset( X, relation_rng( skol12 ) ), subset( X, Y ) }.
% 0.78/1.56 (504) {G2,W7,D3,L2,V1,M2} P(57,39) { subset( X, relation_rng( skol12 ) ), !
% 0.78/1.56 X = skol13 }.
% 0.78/1.56 (4082) {G2,W12,D3,L3,V1,M3} R(212,40);d(38);r(36) { ! function( skol12 ),
% 0.78/1.56 subset( skol14, X ), ! relation_inverse_image( skol12, skol13 ) =
% 0.78/1.56 relation_inverse_image( skol12, X ) }.
% 0.78/1.56 (4086) {G3,W3,D2,L1,V0,M1} Q(4082);r(37) { subset( skol14, skol13 ) }.
% 0.78/1.56 (4092) {G4,W3,D2,L1,V0,M1} R(4086,84) { ! subset( skol13, skol14 ) }.
% 0.78/1.56 (4135) {G5,W6,D2,L2,V1,M2} P(57,4092) { ! subset( X, skol14 ), ! X = skol13
% 0.78/1.56 }.
% 0.78/1.56 (4625) {G6,W10,D3,L2,V1,M2} R(222,4135);d(38);r(504) { ! X = skol13, !
% 0.78/1.56 subset( relation_inverse_image( skol12, X ), relation_inverse_image(
% 0.78/1.56 skol12, skol13 ) ) }.
% 0.78/1.56 (4704) {G7,W0,D0,L0,V0,M0} Q(4625);r(34) { }.
% 0.78/1.56
% 0.78/1.56
% 0.78/1.56 % SZS output end Refutation
% 0.78/1.56 found a proof!
% 0.78/1.56
% 0.78/1.56
% 0.78/1.56 Unprocessed initial clauses:
% 0.78/1.56
% 0.78/1.56 (4706) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), ! in( Y, X ) }.
% 0.78/1.56 (4707) {G0,W4,D2,L2,V1,M2} { ! empty( X ), function( X ) }.
% 0.78/1.56 (4708) {G0,W4,D2,L2,V1,M2} { ! empty( X ), relation( X ) }.
% 0.78/1.56 (4709) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 0.78/1.56 ), relation( X ) }.
% 0.78/1.56 (4710) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 0.78/1.56 ), function( X ) }.
% 0.78/1.56 (4711) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 0.78/1.56 ), one_to_one( X ) }.
% 0.78/1.56 (4712) {G0,W6,D2,L2,V2,M2} { ! X = Y, subset( X, Y ) }.
% 0.78/1.56 (4713) {G0,W6,D2,L2,V2,M2} { ! X = Y, subset( Y, X ) }.
% 0.78/1.56 (4714) {G0,W9,D2,L3,V2,M3} { ! subset( X, Y ), ! subset( Y, X ), X = Y }.
% 0.78/1.56 (4715) {G0,W4,D3,L1,V1,M1} { element( skol1( X ), X ) }.
% 0.78/1.56 (4716) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.78/1.56 (4717) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 0.78/1.56 (4718) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( empty_set ) }.
% 0.78/1.56 (4719) {G0,W3,D3,L1,V1,M1} { ! empty( powerset( X ) ) }.
% 0.78/1.56 (4720) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.78/1.56 (4721) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.78/1.56 (4722) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 0.78/1.56 (4723) {G0,W7,D3,L3,V1,M3} { empty( X ), ! relation( X ), ! empty(
% 0.78/1.56 relation_rng( X ) ) }.
% 0.78/1.56 (4724) {G0,W5,D3,L2,V1,M2} { ! empty( X ), empty( relation_rng( X ) ) }.
% 0.78/1.56 (4725) {G0,W5,D3,L2,V1,M2} { ! empty( X ), relation( relation_rng( X ) )
% 0.78/1.56 }.
% 0.78/1.56 (4726) {G0,W2,D2,L1,V0,M1} { relation( skol2 ) }.
% 0.78/1.56 (4727) {G0,W2,D2,L1,V0,M1} { function( skol2 ) }.
% 0.78/1.56 (4728) {G0,W2,D2,L1,V0,M1} { empty( skol3 ) }.
% 0.78/1.56 (4729) {G0,W2,D2,L1,V0,M1} { relation( skol3 ) }.
% 0.78/1.56 (4730) {G0,W5,D3,L2,V2,M2} { empty( X ), ! empty( skol4( Y ) ) }.
% 0.78/1.56 (4731) {G0,W7,D3,L2,V1,M2} { empty( X ), element( skol4( X ), powerset( X
% 0.78/1.56 ) ) }.
% 0.78/1.56 (4732) {G0,W2,D2,L1,V0,M1} { empty( skol5 ) }.
% 0.78/1.56 (4733) {G0,W2,D2,L1,V0,M1} { relation( skol6 ) }.
% 0.78/1.56 (4734) {G0,W2,D2,L1,V0,M1} { empty( skol6 ) }.
% 0.78/1.56 (4735) {G0,W2,D2,L1,V0,M1} { function( skol6 ) }.
% 0.78/1.56 (4736) {G0,W2,D2,L1,V0,M1} { ! empty( skol7 ) }.
% 0.78/1.56 (4737) {G0,W2,D2,L1,V0,M1} { relation( skol7 ) }.
% 0.78/1.56 (4738) {G0,W3,D3,L1,V1,M1} { empty( skol8( Y ) ) }.
% 0.78/1.56 (4739) {G0,W5,D3,L1,V1,M1} { element( skol8( X ), powerset( X ) ) }.
% 0.78/1.56 (4740) {G0,W2,D2,L1,V0,M1} { ! empty( skol9 ) }.
% 0.78/1.56 (4741) {G0,W2,D2,L1,V0,M1} { relation( skol10 ) }.
% 0.78/1.56 (4742) {G0,W2,D2,L1,V0,M1} { function( skol10 ) }.
% 0.78/1.56 (4743) {G0,W2,D2,L1,V0,M1} { one_to_one( skol10 ) }.
% 0.78/1.56 (4744) {G0,W2,D2,L1,V0,M1} { relation( skol11 ) }.
% 0.78/1.56 (4745) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( skol11 ) }.
% 0.78/1.56 (4746) {G0,W3,D2,L1,V1,M1} { subset( X, X ) }.
% 0.78/1.56 (4747) {G0,W18,D3,L5,V3,M5} { ! relation( X ), ! function( X ), ! subset(
% 0.78/1.56 relation_inverse_image( X, Y ), relation_inverse_image( X, Z ) ), !
% 0.78/1.56 subset( Y, relation_rng( X ) ), subset( Y, Z ) }.
% 0.78/1.56 (4748) {G0,W2,D2,L1,V0,M1} { relation( skol12 ) }.
% 0.78/1.56 (4749) {G0,W2,D2,L1,V0,M1} { function( skol12 ) }.
% 0.78/1.56 (4750) {G0,W7,D3,L1,V0,M1} { relation_inverse_image( skol12, skol13 ) =
% 0.78/1.56 relation_inverse_image( skol12, skol14 ) }.
% 0.78/1.56 (4751) {G0,W4,D3,L1,V0,M1} { subset( skol13, relation_rng( skol12 ) ) }.
% 0.78/1.56 (4752) {G0,W4,D3,L1,V0,M1} { subset( skol14, relation_rng( skol12 ) ) }.
% 0.78/1.56 (4753) {G0,W3,D2,L1,V0,M1} { ! skol13 = skol14 }.
% 0.78/1.56 (4754) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), element( X, Y ) }.
% 0.78/1.56 (4755) {G0,W8,D2,L3,V2,M3} { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.78/1.56 (4756) {G0,W7,D3,L2,V2,M2} { ! element( X, powerset( Y ) ), subset( X, Y )
% 0.78/1.56 }.
% 0.78/1.56 (4757) {G0,W7,D3,L2,V2,M2} { ! subset( X, Y ), element( X, powerset( Y ) )
% 0.78/1.56 }.
% 0.78/1.56 (4758) {G0,W10,D3,L3,V3,M3} { ! in( X, Z ), ! element( Z, powerset( Y ) )
% 0.78/1.56 , element( X, Y ) }.
% 0.78/1.56 (4759) {G0,W9,D3,L3,V3,M3} { ! in( X, Y ), ! element( Y, powerset( Z ) ),
% 0.78/1.56 ! empty( Z ) }.
% 0.78/1.56 (4760) {G0,W5,D2,L2,V1,M2} { ! empty( X ), X = empty_set }.
% 0.78/1.56 (4761) {G0,W5,D2,L2,V2,M2} { ! in( X, Y ), ! empty( Y ) }.
% 0.78/1.56 (4762) {G0,W7,D2,L3,V2,M3} { ! empty( X ), X = Y, ! empty( Y ) }.
% 0.78/1.56
% 0.78/1.56
% 0.78/1.56 Total Proof:
% 0.78/1.56
% 0.78/1.56 subsumption: (4) {G0,W6,D2,L2,V2,M2} I { ! X = Y, subset( X, Y ) }.
% 0.78/1.56 parent0: (4712) {G0,W6,D2,L2,V2,M2} { ! X = Y, subset( X, Y ) }.
% 0.78/1.56 substitution0:
% 0.78/1.56 X := X
% 0.78/1.56 Y := Y
% 0.78/1.56 end
% 0.78/1.56 permutation0:
% 0.78/1.56 0 ==> 0
% 0.78/1.56 1 ==> 1
% 0.78/1.56 end
% 0.78/1.56
% 0.78/1.56 subsumption: (5) {G0,W9,D2,L3,V2,M3} I { ! subset( X, Y ), ! subset( Y, X )
% 0.78/1.56 , X = Y }.
% 0.78/1.56 parent0: (4714) {G0,W9,D2,L3,V2,M3} { ! subset( X, Y ), ! subset( Y, X ),
% 0.78/1.56 X = Y }.
% 0.78/1.56 substitution0:
% 0.78/1.56 X := X
% 0.78/1.56 Y := Y
% 0.78/1.56 end
% 0.78/1.56 permutation0:
% 0.78/1.56 0 ==> 0
% 0.78/1.56 1 ==> 1
% 0.78/1.56 2 ==> 2
% 0.78/1.56 end
% 0.78/1.56
% 0.78/1.56 subsumption: (34) {G0,W3,D2,L1,V1,M1} I { subset( X, X ) }.
% 0.78/1.56 parent0: (4746) {G0,W3,D2,L1,V1,M1} { subset( X, X ) }.
% 0.78/1.56 substitution0:
% 0.78/1.56 X := X
% 0.78/1.56 end
% 0.78/1.56 permutation0:
% 0.78/1.56 0 ==> 0
% 0.78/1.56 end
% 0.78/1.56
% 0.78/1.56 subsumption: (35) {G0,W18,D3,L5,V3,M5} I { ! relation( X ), ! function( X )
% 0.78/1.56 , ! subset( relation_inverse_image( X, Y ), relation_inverse_image( X, Z
% 0.78/1.56 ) ), ! subset( Y, relation_rng( X ) ), subset( Y, Z ) }.
% 0.78/1.56 parent0: (4747) {G0,W18,D3,L5,V3,M5} { ! relation( X ), ! function( X ), !
% 0.78/1.56 subset( relation_inverse_image( X, Y ), relation_inverse_image( X, Z ) )
% 0.78/1.56 , ! subset( Y, relation_rng( X ) ), subset( Y, Z ) }.
% 0.78/1.56 substitution0:
% 0.78/1.56 X := X
% 0.78/1.56 Y := Y
% 0.78/1.56 Z := Z
% 0.78/1.56 end
% 0.78/1.56 permutation0:
% 0.78/1.56 0 ==> 0
% 0.78/1.56 1 ==> 1
% 0.78/1.56 2 ==> 2
% 0.78/1.56 3 ==> 3
% 0.78/1.56 4 ==> 4
% 0.78/1.56 end
% 0.78/1.56
% 0.78/1.56 subsumption: (36) {G0,W2,D2,L1,V0,M1} I { relation( skol12 ) }.
% 0.78/1.56 parent0: (4748) {G0,W2,D2,L1,V0,M1} { relation( skol12 ) }.
% 0.78/1.56 substitution0:
% 0.78/1.56 end
% 0.78/1.56 permutation0:
% 0.78/1.56 0 ==> 0
% 0.78/1.56 end
% 0.78/1.56
% 0.78/1.56 subsumption: (37) {G0,W2,D2,L1,V0,M1} I { function( skol12 ) }.
% 0.78/1.56 parent0: (4749) {G0,W2,D2,L1,V0,M1} { function( skol12 ) }.
% 0.78/1.56 substitution0:
% 0.78/1.56 end
% 0.78/1.56 permutation0:
% 0.78/1.56 0 ==> 0
% 0.78/1.56 end
% 0.78/1.56
% 0.78/1.56 eqswap: (4789) {G0,W7,D3,L1,V0,M1} { relation_inverse_image( skol12,
% 0.78/1.56 skol14 ) = relation_inverse_image( skol12, skol13 ) }.
% 0.78/1.56 parent0[0]: (4750) {G0,W7,D3,L1,V0,M1} { relation_inverse_image( skol12,
% 0.78/1.56 skol13 ) = relation_inverse_image( skol12, skol14 ) }.
% 0.78/1.56 substitution0:
% 0.78/1.56 end
% 0.78/1.56
% 0.78/1.56 subsumption: (38) {G0,W7,D3,L1,V0,M1} I { relation_inverse_image( skol12,
% 0.78/1.56 skol14 ) ==> relation_inverse_image( skol12, skol13 ) }.
% 0.78/1.56 parent0: (4789) {G0,W7,D3,L1,V0,M1} { relation_inverse_image( skol12,
% 0.78/1.56 skol14 ) = relation_inverse_image( skol12, skol13 ) }.
% 0.78/1.56 substitution0:
% 0.78/1.56 end
% 0.78/1.56 permutation0:
% 0.78/1.56 0 ==> 0
% 0.78/1.56 end
% 0.78/1.56
% 0.78/1.56 subsumption: (39) {G0,W4,D3,L1,V0,M1} I { subset( skol13, relation_rng(
% 0.78/1.56 skol12 ) ) }.
% 0.78/1.56 parent0: (4751) {G0,W4,D3,L1,V0,M1} { subset( skol13, relation_rng( skol12
% 0.78/1.56 ) ) }.
% 0.78/1.56 substitution0:
% 0.78/1.56 end
% 0.78/1.56 permutation0:
% 0.78/1.56 0 ==> 0
% 0.78/1.56 end
% 0.78/1.56
% 0.78/1.56 subsumption: (40) {G0,W4,D3,L1,V0,M1} I { subset( skol14, relation_rng(
% 0.78/1.56 skol12 ) ) }.
% 0.78/1.56 parent0: (4752) {G0,W4,D3,L1,V0,M1} { subset( skol14, relation_rng( skol12
% 0.78/1.56 ) ) }.
% 0.78/1.56 substitution0:
% 0.78/1.56 end
% 0.78/1.56 permutation0:
% 0.78/1.56 0 ==> 0
% 0.78/1.56 end
% 0.78/1.56
% 0.78/1.56 eqswap: (4805) {G0,W3,D2,L1,V0,M1} { ! skol14 = skol13 }.
% 0.78/1.56 parent0[0]: (4753) {G0,W3,D2,L1,V0,M1} { ! skol13 = skol14 }.
% 0.78/1.56 substitution0:
% 0.78/1.56 end
% 0.78/1.56
% 0.78/1.56 subsumption: (41) {G0,W3,D2,L1,V0,M1} I { ! skol14 ==> skol13 }.
% 0.78/1.56 parent0: (4805) {G0,W3,D2,L1,V0,M1} { ! skol14 = skol13 }.
% 0.78/1.56 substitution0:
% 0.78/1.56 end
% 0.78/1.56 permutation0:
% 0.78/1.56 0 ==> 0
% 0.78/1.56 end
% 0.78/1.56
% 0.78/1.56 eqswap: (4806) {G0,W6,D2,L2,V2,M2} { ! Y = X, subset( X, Y ) }.
% 0.78/1.56 parent0[0]: (4) {G0,W6,D2,L2,V2,M2} I { ! X = Y, subset( X, Y ) }.
% 0.78/1.56 substitution0:
% 0.78/1.56 X := X
% 0.78/1.56 Y := Y
% 0.78/1.56 end
% 0.78/1.56
% 0.78/1.56 eqswap: (4807) {G0,W6,D2,L2,V2,M2} { ! Y = X, subset( X, Y ) }.
% 0.78/1.56 parent0[0]: (4) {G0,W6,D2,L2,V2,M2} I { ! X = Y, subset( X, Y ) }.
% 0.78/1.56 substitution0:
% 0.78/1.56 X := X
% 0.78/1.56 Y := Y
% 0.78/1.56 end
% 0.78/1.56
% 0.78/1.56 resolution: (4808) {G1,W9,D2,L3,V2,M3} { ! subset( Y, X ), X = Y, ! Y = X
% 0.78/1.56 }.
% 0.78/1.56 parent0[0]: (5) {G0,W9,D2,L3,V2,M3} I { ! subset( X, Y ), ! subset( Y, X )
% 0.78/1.56 , X = Y }.
% 0.78/1.56 parent1[1]: (4806) {G0,W6,D2,L2,V2,M2} { ! Y = X, subset( X, Y ) }.
% 0.78/1.56 substitution0:
% 0.78/1.56 X := X
% 0.78/1.56 Y := Y
% 0.78/1.56 end
% 0.78/1.56 substitution1:
% 0.78/1.56 X := X
% 0.78/1.56 Y := Y
% 0.78/1.56 end
% 0.78/1.56
% 0.78/1.56 resolution: (4810) {G1,W9,D2,L3,V2,M3} { Y = X, ! X = Y, ! Y = X }.
% 0.78/1.56 parent0[0]: (4808) {G1,W9,D2,L3,V2,M3} { ! subset( Y, X ), X = Y, ! Y = X
% 0.78/1.56 }.
% 0.78/1.56 parent1[1]: (4807) {G0,W6,D2,L2,V2,M2} { ! Y = X, subset( X, Y ) }.
% 0.78/1.56 substitution0:
% 0.78/1.56 X := Y
% 0.78/1.56 Y := X
% 0.78/1.56 end
% 0.78/1.56 substitution1:
% 0.78/1.56 X := X
% 0.78/1.56 Y := Y
% 0.78/1.56 end
% 0.78/1.56
% 0.78/1.56 eqswap: (4812) {G1,W9,D2,L3,V2,M3} { ! Y = X, X = Y, ! Y = X }.
% 0.78/1.56 parent0[2]: (4810) {G1,W9,D2,L3,V2,M3} { Y = X, ! X = Y, ! Y = X }.
% 0.78/1.56 substitution0:
% 0.78/1.56 X := Y
% 0.78/1.56 Y := X
% 0.78/1.56 end
% 0.78/1.56
% 0.78/1.56 factor: (4814) {G1,W6,D2,L2,V2,M2} { ! X = Y, Y = X }.
% 0.78/1.56 parent0[0, 2]: (4812) {G1,W9,D2,L3,V2,M3} { ! Y = X, X = Y, ! Y = X }.
% 0.78/1.56 substitution0:
% 0.78/1.56 X := Y
% 0.78/1.56 Y := X
% 0.78/1.56 enCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------