TSTP Solution File: SEU056+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SEU056+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n004.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 07:10:27 EDT 2022
% Result : Theorem 1.09s 1.45s
% Output : Refutation 1.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU056+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n004.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 Jun 19 20:18:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.09/1.45 *** allocated 10000 integers for termspace/termends
% 1.09/1.45 *** allocated 10000 integers for clauses
% 1.09/1.45 *** allocated 10000 integers for justifications
% 1.09/1.45 Bliksem 1.12
% 1.09/1.45
% 1.09/1.45
% 1.09/1.45 Automatic Strategy Selection
% 1.09/1.45
% 1.09/1.45
% 1.09/1.45 Clauses:
% 1.09/1.45
% 1.09/1.45 { ! in( X, Y ), ! in( Y, X ) }.
% 1.09/1.45 { ! empty( X ), function( X ) }.
% 1.09/1.45 { ! empty( X ), relation( X ) }.
% 1.09/1.45 { ! relation( X ), ! empty( X ), ! function( X ), relation( X ) }.
% 1.09/1.45 { ! relation( X ), ! empty( X ), ! function( X ), function( X ) }.
% 1.09/1.45 { ! relation( X ), ! empty( X ), ! function( X ), one_to_one( X ) }.
% 1.09/1.45 { set_intersection2( X, Y ) = set_intersection2( Y, X ) }.
% 1.09/1.45 { ! disjoint( X, Y ), set_intersection2( X, Y ) = empty_set }.
% 1.09/1.45 { ! set_intersection2( X, Y ) = empty_set, disjoint( X, Y ) }.
% 1.09/1.45 { element( skol1( X ), X ) }.
% 1.09/1.45 { empty( empty_set ) }.
% 1.09/1.45 { relation( empty_set ) }.
% 1.09/1.45 { relation_empty_yielding( empty_set ) }.
% 1.09/1.45 { ! relation( X ), ! relation( Y ), relation( set_intersection2( X, Y ) ) }
% 1.09/1.45 .
% 1.09/1.45 { ! empty( powerset( X ) ) }.
% 1.09/1.45 { empty( empty_set ) }.
% 1.09/1.45 { empty( empty_set ) }.
% 1.09/1.45 { relation( empty_set ) }.
% 1.09/1.45 { set_intersection2( X, X ) = X }.
% 1.09/1.45 { relation( skol2 ) }.
% 1.09/1.45 { function( skol2 ) }.
% 1.09/1.45 { empty( skol3 ) }.
% 1.09/1.45 { relation( skol3 ) }.
% 1.09/1.45 { empty( X ), ! empty( skol4( Y ) ) }.
% 1.09/1.45 { empty( X ), element( skol4( X ), powerset( X ) ) }.
% 1.09/1.45 { empty( skol5 ) }.
% 1.09/1.45 { relation( skol6 ) }.
% 1.09/1.45 { empty( skol6 ) }.
% 1.09/1.45 { function( skol6 ) }.
% 1.09/1.45 { ! empty( skol7 ) }.
% 1.09/1.45 { relation( skol7 ) }.
% 1.09/1.45 { empty( skol8( Y ) ) }.
% 1.09/1.45 { element( skol8( X ), powerset( X ) ) }.
% 1.09/1.45 { ! empty( skol9 ) }.
% 1.09/1.45 { relation( skol10 ) }.
% 1.09/1.45 { function( skol10 ) }.
% 1.09/1.45 { one_to_one( skol10 ) }.
% 1.09/1.45 { relation( skol11 ) }.
% 1.09/1.45 { relation_empty_yielding( skol11 ) }.
% 1.09/1.45 { subset( X, X ) }.
% 1.09/1.45 { ! disjoint( X, Y ), disjoint( Y, X ) }.
% 1.09/1.45 { ! relation( X ), ! function( X ), ! one_to_one( X ), relation_image( X,
% 1.09/1.45 set_intersection2( Y, Z ) ) = set_intersection2( relation_image( X, Y ),
% 1.09/1.45 relation_image( X, Z ) ) }.
% 1.09/1.45 { relation( skol12 ) }.
% 1.09/1.45 { function( skol12 ) }.
% 1.09/1.45 { disjoint( skol13, skol14 ) }.
% 1.09/1.45 { one_to_one( skol12 ) }.
% 1.09/1.45 { ! disjoint( relation_image( skol12, skol13 ), relation_image( skol12,
% 1.09/1.45 skol14 ) ) }.
% 1.09/1.45 { ! relation( X ), relation_image( X, empty_set ) = empty_set }.
% 1.09/1.45 { ! in( X, Y ), element( X, Y ) }.
% 1.09/1.45 { set_intersection2( X, empty_set ) = empty_set }.
% 1.09/1.45 { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 1.09/1.45 { ! element( X, powerset( Y ) ), subset( X, Y ) }.
% 1.09/1.45 { ! subset( X, Y ), element( X, powerset( Y ) ) }.
% 1.09/1.45 { ! in( X, Z ), ! element( Z, powerset( Y ) ), element( X, Y ) }.
% 1.09/1.45 { ! in( X, Y ), ! element( Y, powerset( Z ) ), ! empty( Z ) }.
% 1.09/1.45 { ! empty( X ), X = empty_set }.
% 1.09/1.45 { ! in( X, Y ), ! empty( Y ) }.
% 1.09/1.45 { ! empty( X ), X = Y, ! empty( Y ) }.
% 1.09/1.45
% 1.09/1.45 percentage equality = 0.108434, percentage horn = 0.962264
% 1.09/1.45 This is a problem with some equality
% 1.09/1.45
% 1.09/1.45
% 1.09/1.45
% 1.09/1.45 Options Used:
% 1.09/1.45
% 1.09/1.45 useres = 1
% 1.09/1.45 useparamod = 1
% 1.09/1.45 useeqrefl = 1
% 1.09/1.45 useeqfact = 1
% 1.09/1.45 usefactor = 1
% 1.09/1.45 usesimpsplitting = 0
% 1.09/1.45 usesimpdemod = 5
% 1.09/1.45 usesimpres = 3
% 1.09/1.45
% 1.09/1.45 resimpinuse = 1000
% 1.09/1.45 resimpclauses = 20000
% 1.09/1.45 substype = eqrewr
% 1.09/1.45 backwardsubs = 1
% 1.09/1.45 selectoldest = 5
% 1.09/1.45
% 1.09/1.45 litorderings [0] = split
% 1.09/1.45 litorderings [1] = extend the termordering, first sorting on arguments
% 1.09/1.45
% 1.09/1.45 termordering = kbo
% 1.09/1.45
% 1.09/1.45 litapriori = 0
% 1.09/1.45 termapriori = 1
% 1.09/1.45 litaposteriori = 0
% 1.09/1.45 termaposteriori = 0
% 1.09/1.45 demodaposteriori = 0
% 1.09/1.45 ordereqreflfact = 0
% 1.09/1.45
% 1.09/1.45 litselect = negord
% 1.09/1.45
% 1.09/1.45 maxweight = 15
% 1.09/1.45 maxdepth = 30000
% 1.09/1.45 maxlength = 115
% 1.09/1.45 maxnrvars = 195
% 1.09/1.45 excuselevel = 1
% 1.09/1.45 increasemaxweight = 1
% 1.09/1.45
% 1.09/1.45 maxselected = 10000000
% 1.09/1.45 maxnrclauses = 10000000
% 1.09/1.45
% 1.09/1.45 showgenerated = 0
% 1.09/1.45 showkept = 0
% 1.09/1.45 showselected = 0
% 1.09/1.45 showdeleted = 0
% 1.09/1.45 showresimp = 1
% 1.09/1.45 showstatus = 2000
% 1.09/1.45
% 1.09/1.45 prologoutput = 0
% 1.09/1.45 nrgoals = 5000000
% 1.09/1.45 totalproof = 1
% 1.09/1.45
% 1.09/1.45 Symbols occurring in the translation:
% 1.09/1.45
% 1.09/1.45 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.09/1.45 . [1, 2] (w:1, o:35, a:1, s:1, b:0),
% 1.09/1.45 ! [4, 1] (w:0, o:21, a:1, s:1, b:0),
% 1.09/1.45 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.09/1.45 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.09/1.45 in [37, 2] (w:1, o:59, a:1, s:1, b:0),
% 1.09/1.45 empty [38, 1] (w:1, o:26, a:1, s:1, b:0),
% 1.09/1.45 function [39, 1] (w:1, o:27, a:1, s:1, b:0),
% 1.09/1.45 relation [40, 1] (w:1, o:28, a:1, s:1, b:0),
% 1.09/1.45 one_to_one [41, 1] (w:1, o:29, a:1, s:1, b:0),
% 1.09/1.45 set_intersection2 [42, 2] (w:1, o:61, a:1, s:1, b:0),
% 1.09/1.45 disjoint [43, 2] (w:1, o:62, a:1, s:1, b:0),
% 1.09/1.45 empty_set [44, 0] (w:1, o:8, a:1, s:1, b:0),
% 1.09/1.45 element [45, 2] (w:1, o:63, a:1, s:1, b:0),
% 1.09/1.45 relation_empty_yielding [46, 1] (w:1, o:30, a:1, s:1, b:0),
% 1.09/1.45 powerset [47, 1] (w:1, o:31, a:1, s:1, b:0),
% 1.09/1.45 subset [48, 2] (w:1, o:64, a:1, s:1, b:0),
% 1.09/1.45 relation_image [50, 2] (w:1, o:60, a:1, s:1, b:0),
% 1.09/1.45 skol1 [51, 1] (w:1, o:32, a:1, s:1, b:1),
% 1.09/1.45 skol2 [52, 0] (w:1, o:15, a:1, s:1, b:1),
% 1.09/1.45 skol3 [53, 0] (w:1, o:16, a:1, s:1, b:1),
% 1.09/1.45 skol4 [54, 1] (w:1, o:33, a:1, s:1, b:1),
% 1.09/1.45 skol5 [55, 0] (w:1, o:17, a:1, s:1, b:1),
% 1.09/1.45 skol6 [56, 0] (w:1, o:18, a:1, s:1, b:1),
% 1.09/1.45 skol7 [57, 0] (w:1, o:19, a:1, s:1, b:1),
% 1.09/1.45 skol8 [58, 1] (w:1, o:34, a:1, s:1, b:1),
% 1.09/1.45 skol9 [59, 0] (w:1, o:20, a:1, s:1, b:1),
% 1.09/1.45 skol10 [60, 0] (w:1, o:10, a:1, s:1, b:1),
% 1.09/1.45 skol11 [61, 0] (w:1, o:11, a:1, s:1, b:1),
% 1.09/1.45 skol12 [62, 0] (w:1, o:12, a:1, s:1, b:1),
% 1.09/1.45 skol13 [63, 0] (w:1, o:13, a:1, s:1, b:1),
% 1.09/1.45 skol14 [64, 0] (w:1, o:14, a:1, s:1, b:1).
% 1.09/1.45
% 1.09/1.45
% 1.09/1.45 Starting Search:
% 1.09/1.45
% 1.09/1.45 *** allocated 15000 integers for clauses
% 1.09/1.45 *** allocated 22500 integers for clauses
% 1.09/1.45 *** allocated 33750 integers for clauses
% 1.09/1.45 *** allocated 50625 integers for clauses
% 1.09/1.45 *** allocated 15000 integers for termspace/termends
% 1.09/1.45 *** allocated 75937 integers for clauses
% 1.09/1.45 Resimplifying inuse:
% 1.09/1.45 Done
% 1.09/1.45
% 1.09/1.45 *** allocated 22500 integers for termspace/termends
% 1.09/1.45 *** allocated 113905 integers for clauses
% 1.09/1.45
% 1.09/1.45 Intermediate Status:
% 1.09/1.45 Generated: 8180
% 1.09/1.45 Kept: 2010
% 1.09/1.45 Inuse: 296
% 1.09/1.45 Deleted: 49
% 1.09/1.45 Deletedinuse: 28
% 1.09/1.45
% 1.09/1.45 Resimplifying inuse:
% 1.09/1.45 Done
% 1.09/1.45
% 1.09/1.45 *** allocated 33750 integers for termspace/termends
% 1.09/1.45 *** allocated 170857 integers for clauses
% 1.09/1.45 Resimplifying inuse:
% 1.09/1.45 Done
% 1.09/1.45
% 1.09/1.45 *** allocated 50625 integers for termspace/termends
% 1.09/1.45 *** allocated 256285 integers for clauses
% 1.09/1.45
% 1.09/1.45 Intermediate Status:
% 1.09/1.45 Generated: 15988
% 1.09/1.45 Kept: 4031
% 1.09/1.45 Inuse: 406
% 1.09/1.45 Deleted: 69
% 1.09/1.45 Deletedinuse: 28
% 1.09/1.45
% 1.09/1.45 Resimplifying inuse:
% 1.09/1.45 Done
% 1.09/1.45
% 1.09/1.45
% 1.09/1.45 Bliksems!, er is een bewijs:
% 1.09/1.45 % SZS status Theorem
% 1.09/1.45 % SZS output start Refutation
% 1.09/1.45
% 1.09/1.45 (5) {G0,W8,D3,L2,V2,M2} I { ! disjoint( X, Y ), set_intersection2( X, Y )
% 1.09/1.45 ==> empty_set }.
% 1.09/1.45 (6) {G0,W8,D3,L2,V2,M2} I { ! set_intersection2( X, Y ) ==> empty_set,
% 1.09/1.45 disjoint( X, Y ) }.
% 1.09/1.45 (36) {G0,W19,D4,L4,V3,M4} I { ! relation( X ), ! function( X ), !
% 1.09/1.45 one_to_one( X ), set_intersection2( relation_image( X, Y ),
% 1.09/1.45 relation_image( X, Z ) ) ==> relation_image( X, set_intersection2( Y, Z )
% 1.09/1.45 ) }.
% 1.09/1.45 (37) {G0,W2,D2,L1,V0,M1} I { relation( skol12 ) }.
% 1.09/1.45 (38) {G0,W2,D2,L1,V0,M1} I { function( skol12 ) }.
% 1.09/1.45 (39) {G0,W3,D2,L1,V0,M1} I { disjoint( skol13, skol14 ) }.
% 1.09/1.45 (40) {G0,W2,D2,L1,V0,M1} I { one_to_one( skol12 ) }.
% 1.09/1.45 (41) {G0,W7,D3,L1,V0,M1} I { ! disjoint( relation_image( skol12, skol13 ),
% 1.09/1.45 relation_image( skol12, skol14 ) ) }.
% 1.09/1.45 (42) {G0,W7,D3,L2,V1,M2} I { ! relation( X ), relation_image( X, empty_set
% 1.09/1.45 ) ==> empty_set }.
% 1.09/1.45 (60) {G1,W5,D3,L1,V0,M1} R(39,5) { set_intersection2( skol13, skol14 ) ==>
% 1.09/1.45 empty_set }.
% 1.09/1.45 (161) {G1,W20,D4,L5,V3,M5} P(36,6) { ! relation_image( X, set_intersection2
% 1.09/1.45 ( Y, Z ) ) ==> empty_set, disjoint( relation_image( X, Y ),
% 1.09/1.45 relation_image( X, Z ) ), ! relation( X ), ! function( X ), ! one_to_one
% 1.09/1.45 ( X ) }.
% 1.09/1.45 (4192) {G2,W4,D2,L2,V0,M2} R(161,41);d(60);d(42);q;r(37) { ! function(
% 1.09/1.45 skol12 ), ! one_to_one( skol12 ) }.
% 1.09/1.45 (4195) {G3,W0,D0,L0,V0,M0} S(4192);r(38);r(40) { }.
% 1.09/1.45
% 1.09/1.45
% 1.09/1.45 % SZS output end Refutation
% 1.09/1.45 found a proof!
% 1.09/1.45
% 1.09/1.45
% 1.09/1.45 Unprocessed initial clauses:
% 1.09/1.45
% 1.09/1.45 (4197) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), ! in( Y, X ) }.
% 1.09/1.45 (4198) {G0,W4,D2,L2,V1,M2} { ! empty( X ), function( X ) }.
% 1.09/1.45 (4199) {G0,W4,D2,L2,V1,M2} { ! empty( X ), relation( X ) }.
% 1.09/1.45 (4200) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 1.09/1.45 ), relation( X ) }.
% 1.09/1.45 (4201) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 1.09/1.45 ), function( X ) }.
% 1.09/1.45 (4202) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 1.09/1.45 ), one_to_one( X ) }.
% 1.09/1.45 (4203) {G0,W7,D3,L1,V2,M1} { set_intersection2( X, Y ) = set_intersection2
% 1.09/1.45 ( Y, X ) }.
% 1.09/1.45 (4204) {G0,W8,D3,L2,V2,M2} { ! disjoint( X, Y ), set_intersection2( X, Y )
% 1.09/1.45 = empty_set }.
% 1.09/1.45 (4205) {G0,W8,D3,L2,V2,M2} { ! set_intersection2( X, Y ) = empty_set,
% 1.09/1.45 disjoint( X, Y ) }.
% 1.09/1.45 (4206) {G0,W4,D3,L1,V1,M1} { element( skol1( X ), X ) }.
% 1.09/1.45 (4207) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 1.09/1.45 (4208) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 1.09/1.45 (4209) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( empty_set ) }.
% 1.09/1.45 (4210) {G0,W8,D3,L3,V2,M3} { ! relation( X ), ! relation( Y ), relation(
% 1.09/1.45 set_intersection2( X, Y ) ) }.
% 1.09/1.45 (4211) {G0,W3,D3,L1,V1,M1} { ! empty( powerset( X ) ) }.
% 1.09/1.45 (4212) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 1.09/1.45 (4213) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 1.09/1.45 (4214) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 1.09/1.45 (4215) {G0,W5,D3,L1,V1,M1} { set_intersection2( X, X ) = X }.
% 1.09/1.45 (4216) {G0,W2,D2,L1,V0,M1} { relation( skol2 ) }.
% 1.09/1.45 (4217) {G0,W2,D2,L1,V0,M1} { function( skol2 ) }.
% 1.09/1.45 (4218) {G0,W2,D2,L1,V0,M1} { empty( skol3 ) }.
% 1.09/1.45 (4219) {G0,W2,D2,L1,V0,M1} { relation( skol3 ) }.
% 1.09/1.45 (4220) {G0,W5,D3,L2,V2,M2} { empty( X ), ! empty( skol4( Y ) ) }.
% 1.09/1.45 (4221) {G0,W7,D3,L2,V1,M2} { empty( X ), element( skol4( X ), powerset( X
% 1.09/1.45 ) ) }.
% 1.09/1.45 (4222) {G0,W2,D2,L1,V0,M1} { empty( skol5 ) }.
% 1.09/1.45 (4223) {G0,W2,D2,L1,V0,M1} { relation( skol6 ) }.
% 1.09/1.45 (4224) {G0,W2,D2,L1,V0,M1} { empty( skol6 ) }.
% 1.09/1.45 (4225) {G0,W2,D2,L1,V0,M1} { function( skol6 ) }.
% 1.09/1.45 (4226) {G0,W2,D2,L1,V0,M1} { ! empty( skol7 ) }.
% 1.09/1.45 (4227) {G0,W2,D2,L1,V0,M1} { relation( skol7 ) }.
% 1.09/1.45 (4228) {G0,W3,D3,L1,V1,M1} { empty( skol8( Y ) ) }.
% 1.09/1.45 (4229) {G0,W5,D3,L1,V1,M1} { element( skol8( X ), powerset( X ) ) }.
% 1.09/1.45 (4230) {G0,W2,D2,L1,V0,M1} { ! empty( skol9 ) }.
% 1.09/1.45 (4231) {G0,W2,D2,L1,V0,M1} { relation( skol10 ) }.
% 1.09/1.45 (4232) {G0,W2,D2,L1,V0,M1} { function( skol10 ) }.
% 1.09/1.45 (4233) {G0,W2,D2,L1,V0,M1} { one_to_one( skol10 ) }.
% 1.09/1.45 (4234) {G0,W2,D2,L1,V0,M1} { relation( skol11 ) }.
% 1.09/1.45 (4235) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( skol11 ) }.
% 1.09/1.45 (4236) {G0,W3,D2,L1,V1,M1} { subset( X, X ) }.
% 1.09/1.45 (4237) {G0,W6,D2,L2,V2,M2} { ! disjoint( X, Y ), disjoint( Y, X ) }.
% 1.09/1.45 (4238) {G0,W19,D4,L4,V3,M4} { ! relation( X ), ! function( X ), !
% 1.09/1.45 one_to_one( X ), relation_image( X, set_intersection2( Y, Z ) ) =
% 1.09/1.45 set_intersection2( relation_image( X, Y ), relation_image( X, Z ) ) }.
% 1.09/1.45 (4239) {G0,W2,D2,L1,V0,M1} { relation( skol12 ) }.
% 1.09/1.45 (4240) {G0,W2,D2,L1,V0,M1} { function( skol12 ) }.
% 1.09/1.45 (4241) {G0,W3,D2,L1,V0,M1} { disjoint( skol13, skol14 ) }.
% 1.09/1.45 (4242) {G0,W2,D2,L1,V0,M1} { one_to_one( skol12 ) }.
% 1.09/1.45 (4243) {G0,W7,D3,L1,V0,M1} { ! disjoint( relation_image( skol12, skol13 )
% 1.09/1.45 , relation_image( skol12, skol14 ) ) }.
% 1.09/1.45 (4244) {G0,W7,D3,L2,V1,M2} { ! relation( X ), relation_image( X, empty_set
% 1.09/1.45 ) = empty_set }.
% 1.09/1.45 (4245) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), element( X, Y ) }.
% 1.09/1.45 (4246) {G0,W5,D3,L1,V1,M1} { set_intersection2( X, empty_set ) = empty_set
% 1.09/1.45 }.
% 1.09/1.45 (4247) {G0,W8,D2,L3,V2,M3} { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 1.09/1.45 (4248) {G0,W7,D3,L2,V2,M2} { ! element( X, powerset( Y ) ), subset( X, Y )
% 1.09/1.45 }.
% 1.09/1.45 (4249) {G0,W7,D3,L2,V2,M2} { ! subset( X, Y ), element( X, powerset( Y ) )
% 1.09/1.45 }.
% 1.09/1.45 (4250) {G0,W10,D3,L3,V3,M3} { ! in( X, Z ), ! element( Z, powerset( Y ) )
% 1.09/1.45 , element( X, Y ) }.
% 1.09/1.45 (4251) {G0,W9,D3,L3,V3,M3} { ! in( X, Y ), ! element( Y, powerset( Z ) ),
% 1.09/1.45 ! empty( Z ) }.
% 1.09/1.45 (4252) {G0,W5,D2,L2,V1,M2} { ! empty( X ), X = empty_set }.
% 1.09/1.45 (4253) {G0,W5,D2,L2,V2,M2} { ! in( X, Y ), ! empty( Y ) }.
% 1.09/1.45 (4254) {G0,W7,D2,L3,V2,M3} { ! empty( X ), X = Y, ! empty( Y ) }.
% 1.09/1.45
% 1.09/1.45
% 1.09/1.45 Total Proof:
% 1.09/1.45
% 1.09/1.45 subsumption: (5) {G0,W8,D3,L2,V2,M2} I { ! disjoint( X, Y ),
% 1.09/1.45 set_intersection2( X, Y ) ==> empty_set }.
% 1.09/1.45 parent0: (4204) {G0,W8,D3,L2,V2,M2} { ! disjoint( X, Y ),
% 1.09/1.45 set_intersection2( X, Y ) = empty_set }.
% 1.09/1.45 substitution0:
% 1.09/1.45 X := X
% 1.09/1.45 Y := Y
% 1.09/1.45 end
% 1.09/1.45 permutation0:
% 1.09/1.45 0 ==> 0
% 1.09/1.45 1 ==> 1
% 1.09/1.45 end
% 1.09/1.45
% 1.09/1.45 subsumption: (6) {G0,W8,D3,L2,V2,M2} I { ! set_intersection2( X, Y ) ==>
% 1.09/1.45 empty_set, disjoint( X, Y ) }.
% 1.09/1.45 parent0: (4205) {G0,W8,D3,L2,V2,M2} { ! set_intersection2( X, Y ) =
% 1.09/1.45 empty_set, disjoint( X, Y ) }.
% 1.09/1.45 substitution0:
% 1.09/1.45 X := X
% 1.09/1.45 Y := Y
% 1.09/1.45 end
% 1.09/1.45 permutation0:
% 1.09/1.45 0 ==> 0
% 1.09/1.45 1 ==> 1
% 1.09/1.45 end
% 1.09/1.45
% 1.09/1.45 eqswap: (4265) {G0,W19,D4,L4,V3,M4} { set_intersection2( relation_image( X
% 1.09/1.45 , Y ), relation_image( X, Z ) ) = relation_image( X, set_intersection2( Y
% 1.09/1.45 , Z ) ), ! relation( X ), ! function( X ), ! one_to_one( X ) }.
% 1.09/1.45 parent0[3]: (4238) {G0,W19,D4,L4,V3,M4} { ! relation( X ), ! function( X )
% 1.09/1.45 , ! one_to_one( X ), relation_image( X, set_intersection2( Y, Z ) ) =
% 1.09/1.45 set_intersection2( relation_image( X, Y ), relation_image( X, Z ) ) }.
% 1.09/1.45 substitution0:
% 1.09/1.45 X := X
% 1.09/1.45 Y := Y
% 1.09/1.45 Z := Z
% 1.09/1.45 end
% 1.09/1.45
% 1.09/1.45 subsumption: (36) {G0,W19,D4,L4,V3,M4} I { ! relation( X ), ! function( X )
% 1.09/1.45 , ! one_to_one( X ), set_intersection2( relation_image( X, Y ),
% 1.09/1.45 relation_image( X, Z ) ) ==> relation_image( X, set_intersection2( Y, Z )
% 1.09/1.45 ) }.
% 1.09/1.45 parent0: (4265) {G0,W19,D4,L4,V3,M4} { set_intersection2( relation_image(
% 1.09/1.45 X, Y ), relation_image( X, Z ) ) = relation_image( X, set_intersection2(
% 1.09/1.45 Y, Z ) ), ! relation( X ), ! function( X ), ! one_to_one( X ) }.
% 1.09/1.45 substitution0:
% 1.09/1.45 X := X
% 1.09/1.45 Y := Y
% 1.09/1.45 Z := Z
% 1.09/1.45 end
% 1.09/1.45 permutation0:
% 1.09/1.45 0 ==> 3
% 1.09/1.45 1 ==> 0
% 1.09/1.45 2 ==> 1
% 1.09/1.45 3 ==> 2
% 1.09/1.45 end
% 1.09/1.45
% 1.09/1.45 subsumption: (37) {G0,W2,D2,L1,V0,M1} I { relation( skol12 ) }.
% 1.09/1.45 parent0: (4239) {G0,W2,D2,L1,V0,M1} { relation( skol12 ) }.
% 1.09/1.45 substitution0:
% 1.09/1.45 end
% 1.09/1.45 permutation0:
% 1.09/1.45 0 ==> 0
% 1.09/1.45 end
% 1.09/1.45
% 1.09/1.45 subsumption: (38) {G0,W2,D2,L1,V0,M1} I { function( skol12 ) }.
% 1.09/1.45 parent0: (4240) {G0,W2,D2,L1,V0,M1} { function( skol12 ) }.
% 1.09/1.45 substitution0:
% 1.09/1.45 end
% 1.09/1.45 permutation0:
% 1.09/1.45 0 ==> 0
% 1.09/1.45 end
% 1.09/1.45
% 1.09/1.45 subsumption: (39) {G0,W3,D2,L1,V0,M1} I { disjoint( skol13, skol14 ) }.
% 1.09/1.45 parent0: (4241) {G0,W3,D2,L1,V0,M1} { disjoint( skol13, skol14 ) }.
% 1.09/1.45 substitution0:
% 1.09/1.45 end
% 1.09/1.45 permutation0:
% 1.09/1.45 0 ==> 0
% 1.09/1.45 end
% 1.09/1.45
% 1.09/1.45 subsumption: (40) {G0,W2,D2,L1,V0,M1} I { one_to_one( skol12 ) }.
% 1.09/1.45 parent0: (4242) {G0,W2,D2,L1,V0,M1} { one_to_one( skol12 ) }.
% 1.09/1.45 substitution0:
% 1.09/1.45 end
% 1.09/1.45 permutation0:
% 1.09/1.45 0 ==> 0
% 1.09/1.45 end
% 1.09/1.45
% 1.09/1.45 subsumption: (41) {G0,W7,D3,L1,V0,M1} I { ! disjoint( relation_image(
% 1.09/1.45 skol12, skol13 ), relation_image( skol12, skol14 ) ) }.
% 1.09/1.45 parent0: (4243) {G0,W7,D3,L1,V0,M1} { ! disjoint( relation_image( skol12,
% 1.09/1.45 skol13 ), relation_image( skol12, skol14 ) ) }.
% 1.09/1.45 substitution0:
% 1.09/1.45 end
% 1.09/1.45 permutation0:
% 1.09/1.45 0 ==> 0
% 1.09/1.45 end
% 1.09/1.45
% 1.09/1.45 subsumption: (42) {G0,W7,D3,L2,V1,M2} I { ! relation( X ), relation_image(
% 1.09/1.45 X, empty_set ) ==> empty_set }.
% 1.09/1.45 parent0: (4244) {G0,W7,D3,L2,V1,M2} { ! relation( X ), relation_image( X,
% 1.09/1.45 empty_set ) = empty_set }.
% 1.09/1.45 substitution0:
% 1.09/1.45 X := X
% 1.09/1.45 end
% 1.09/1.45 permutation0:
% 1.09/1.45 0 ==> 0
% 1.09/1.45 1 ==> 1
% 1.09/1.45 end
% 1.09/1.45
% 1.09/1.45 eqswap: (4303) {G0,W8,D3,L2,V2,M2} { empty_set ==> set_intersection2( X, Y
% 1.09/1.45 ), ! disjoint( X, Y ) }.
% 1.09/1.45 parent0[1]: (5) {G0,W8,D3,L2,V2,M2} I { ! disjoint( X, Y ),
% 1.09/1.45 set_intersection2( X, Y ) ==> empty_set }.
% 1.09/1.45 substitution0:
% 1.09/1.45 X := X
% 1.09/1.45 Y := Y
% 1.09/1.45 end
% 1.09/1.45
% 1.09/1.45 resolution: (4304) {G1,W5,D3,L1,V0,M1} { empty_set ==> set_intersection2(
% 1.09/1.45 skol13, skol14 ) }.
% 1.09/1.45 parent0[1]: (4303) {G0,W8,D3,L2,V2,M2} { empty_set ==> set_intersection2(
% 1.09/1.45 X, Y ), ! disjoint( X, Y ) }.
% 1.09/1.45 parent1[0]: (39) {G0,W3,D2,L1,V0,M1} I { disjoint( skol13, skol14 ) }.
% 1.09/1.45 substitution0:
% 1.09/1.45 X := skol13
% 1.09/1.45 Y := skol14
% 1.09/1.45 end
% 1.09/1.45 substitution1:
% 1.09/1.45 end
% 1.09/1.45
% 1.09/1.45 eqswap: (4305) {G1,W5,D3,L1,V0,M1} { set_intersection2( skol13, skol14 )
% 1.09/1.45 ==> empty_set }.
% 1.09/1.45 parent0[0]: (4304) {G1,W5,D3,L1,V0,M1} { empty_set ==> set_intersection2(
% 1.09/1.45 skol13, skol14 ) }.
% 1.09/1.45 substitution0:
% 1.09/1.45 end
% 1.09/1.45
% 1.09/1.45 subsumption: (60) {G1,W5,D3,L1,V0,M1} R(39,5) { set_intersection2( skol13,
% 1.09/1.45 skol14 ) ==> empty_set }.
% 1.09/1.45 parent0: (4305) {G1,W5,D3,L1,V0,M1} { set_intersection2( skol13, skol14 )
% 1.09/1.45 ==> empty_set }.
% 1.09/1.45 substitution0:
% 1.09/1.45 end
% 1.09/1.45 permutation0:
% 1.09/1.45 0 ==> 0
% 1.09/1.45 end
% 1.09/1.45
% 1.09/1.45 eqswap: (4307) {G0,W8,D3,L2,V2,M2} { ! empty_set ==> set_intersection2( X
% 1.09/1.45 , Y ), disjoint( X, Y ) }.
% 1.09/1.45 parent0[0]: (6) {G0,W8,D3,L2,V2,M2} I { ! set_intersection2( X, Y ) ==>
% 1.09/1.45 empty_set, disjoint( X, Y ) }.
% 1.09/1.45 substitution0:
% 1.09/1.45 X := X
% 1.09/1.45 Y := Y
% 1.09/1.45 end
% 1.09/1.45
% 1.09/1.45 paramod: (4308) {G1,W20,D4,L5,V3,M5} { ! empty_set ==> relation_image( X,
% 1.09/1.45 set_intersection2( Y, Z ) ), ! relation( X ), ! function( X ), !
% 1.09/1.45 one_to_one( X ), disjoint( relation_image( X, Y ), relation_image( X, Z )
% 1.09/1.45 ) }.
% 1.09/1.45 parent0[3]: (36) {G0,W19,D4,L4,V3,M4} I { ! relation( X ), ! function( X )
% 1.09/1.45 , ! one_to_one( X ), set_intersection2( relation_image( X, Y ),
% 1.09/1.45 relation_image( X, Z ) ) ==> relation_image( X, set_intersection2( Y, Z )
% 1.09/1.45 ) }.
% 1.09/1.45 parent1[0; 3]: (4307) {G0,W8,D3,L2,V2,M2} { ! empty_set ==>
% 1.09/1.45 set_intersection2( X, Y ), disjoint( X, Y ) }.
% 1.09/1.45 substitution0:
% 1.09/1.45 X := X
% 1.09/1.45 Y := Y
% 1.09/1.45 Z := Z
% 1.09/1.45 end
% 1.09/1.45 substitution1:
% 1.09/1.45 X := relation_image( X, Y )
% 1.09/1.45 Y := relation_image( X, Z )
% 1.09/1.45 end
% 1.09/1.45
% 1.09/1.45 eqswap: (4309) {G1,W20,D4,L5,V3,M5} { ! relation_image( X,
% 1.09/1.45 set_intersection2( Y, Z ) ) ==> empty_set, ! relation( X ), ! function( X
% 1.09/1.45 ), ! one_to_one( X ), disjoint( relation_image( X, Y ), relation_image(
% 1.09/1.45 X, Z ) ) }.
% 1.09/1.45 parent0[0]: (4308) {G1,W20,D4,L5,V3,M5} { ! empty_set ==> relation_image(
% 1.09/1.45 X, set_intersection2( Y, Z ) ), ! relation( X ), ! function( X ), !
% 1.09/1.45 one_to_one( X ), disjoint( relation_image( X, Y ), relation_image( X, Z )
% 1.09/1.45 ) }.
% 1.09/1.45 substitution0:
% 1.09/1.45 X := X
% 1.09/1.45 Y := Y
% 1.09/1.45 Z := Z
% 1.09/1.45 end
% 1.09/1.45
% 1.09/1.45 subsumption: (161) {G1,W20,D4,L5,V3,M5} P(36,6) { ! relation_image( X,
% 1.09/1.45 set_intersection2( Y, Z ) ) ==> empty_set, disjoint( relation_image( X, Y
% 1.09/1.45 ), relation_image( X, Z ) ), ! relation( X ), ! function( X ), !
% 1.09/1.45 one_to_one( X ) }.
% 1.09/1.45 parent0: (4309) {G1,W20,D4,L5,V3,M5} { ! relation_image( X,
% 1.09/1.45 set_intersection2( Y, Z ) ) ==> empty_set, ! relation( X ), ! function( X
% 1.09/1.45 ), ! one_to_one( X ), disjoint( relation_image( X, Y ), relation_image(
% 1.09/1.45 X, Z ) ) }.
% 1.09/1.45 substitution0:
% 1.09/1.45 X := X
% 1.09/1.45 Y := Y
% 1.09/1.45 Z := Z
% 1.09/1.45 end
% 1.09/1.45 permutation0:
% 1.09/1.45 0 ==> 0
% 1.09/1.45 1 ==> 2
% 1.09/1.45 2 ==> 3
% 1.09/1.45 3 ==> 4
% 1.09/1.45 4 ==> 1
% 1.09/1.45 end
% 1.09/1.45
% 1.09/1.45 eqswap: (4310) {G1,W20,D4,L5,V3,M5} { ! empty_set ==> relation_image( X,
% 1.09/1.45 set_intersection2( Y, Z ) ), disjoint( relation_image( X, Y ),
% 1.09/1.45 relation_image( X, Z ) ), ! relation( X ), ! function( X ), ! one_to_one
% 1.09/1.45 ( X ) }.
% 1.09/1.45 parent0[0]: (161) {G1,W20,D4,L5,V3,M5} P(36,6) { ! relation_image( X,
% 1.09/1.45 set_intersection2( Y, Z ) ) ==> empty_set, disjoint( relation_image( X, Y
% 1.09/1.45 ), relation_image( X, Z ) ), ! relation( X ), ! function( X ), !
% 1.09/1.45 one_to_one( X ) }.
% 1.09/1.45 substitution0:
% 1.09/1.45 X := X
% 1.09/1.45 Y := Y
% 1.09/1.45 Z := Z
% 1.09/1.45 end
% 1.09/1.45
% 1.09/1.45 resolution: (4313) {G1,W13,D4,L4,V0,M4} { ! empty_set ==> relation_image(
% 1.09/1.45 skol12, set_intersection2( skol13, skol14 ) ), ! relation( skol12 ), !
% 1.09/1.45 function( skol12 ), ! one_to_one( skol12 ) }.
% 1.09/1.45 parent0[0]: (41) {G0,W7,D3,L1,V0,M1} I { ! disjoint( relation_image( skol12
% 1.09/1.45 , skol13 ), relation_image( skol12, skol14 ) ) }.
% 1.09/1.45 parent1[1]: (4310) {G1,W20,D4,L5,V3,M5} { ! empty_set ==> relation_image(
% 1.09/1.45 X, set_intersection2( Y, Z ) ), disjoint( relation_image( X, Y ),
% 1.09/1.45 relation_image( X, Z ) ), ! relation( X ), ! function( X ), ! one_to_one
% 1.09/1.45 ( X ) }.
% 1.09/1.45 substitution0:
% 1.09/1.45 end
% 1.09/1.45 substitution1:
% 1.09/1.45 X := skol12
% 1.09/1.45 Y := skol13
% 1.09/1.45 Z := skol14
% 1.09/1.45 end
% 1.09/1.45
% 1.09/1.45 paramod: (4314) {G2,W11,D3,L4,V0,M4} { ! empty_set ==> relation_image(
% 1.09/1.45 skol12, empty_set ), ! relation( skol12 ), ! function( skol12 ), !
% 1.09/1.45 one_to_one( skol12 ) }.
% 1.09/1.45 parent0[0]: (60) {G1,W5,D3,L1,V0,M1} R(39,5) { set_intersection2( skol13,
% 1.09/1.45 skol14 ) ==> empty_set }.
% 1.09/1.45 parent1[0; 5]: (4313) {G1,W13,D4,L4,V0,M4} { ! empty_set ==>
% 1.09/1.45 relation_image( skol12, set_intersection2( skol13, skol14 ) ), ! relation
% 1.09/1.45 ( skol12 ), ! function( skol12 ), ! one_to_one( skol12 ) }.
% 1.09/1.45 substitution0:
% 1.09/1.45 end
% 1.09/1.45 substitution1:
% 1.09/1.45 end
% 1.09/1.45
% 1.09/1.45 paramod: (4315) {G1,W11,D2,L5,V0,M5} { ! empty_set ==> empty_set, !
% 1.09/1.45 relation( skol12 ), ! relation( skol12 ), ! function( skol12 ), !
% 1.09/1.45 one_to_one( skol12 ) }.
% 1.09/1.45 parent0[1]: (42) {G0,W7,D3,L2,V1,M2} I { ! relation( X ), relation_image( X
% 1.09/1.45 , empty_set ) ==> empty_set }.
% 1.09/1.45 parent1[0; 3]: (4314) {G2,W11,D3,L4,V0,M4} { ! empty_set ==>
% 1.09/1.45 relation_image( skol12, empty_set ), ! relation( skol12 ), ! function(
% 1.09/1.45 skol12 ), ! one_to_one( skol12 ) }.
% 1.09/1.45 substitution0:
% 1.09/1.45 X := skol12
% 1.09/1.45 end
% 1.09/1.45 substitution1:
% 1.09/1.45 end
% 1.09/1.45
% 1.09/1.45 factor: (4316) {G1,W9,D2,L4,V0,M4} { ! empty_set ==> empty_set, ! relation
% 1.09/1.45 ( skol12 ), ! function( skol12 ), ! one_to_one( skol12 ) }.
% 1.09/1.45 parent0[1, 2]: (4315) {G1,W11,D2,L5,V0,M5} { ! empty_set ==> empty_set, !
% 1.09/1.45 relation( skol12 ), ! relation( skol12 ), ! function( skol12 ), !
% 1.09/1.45 one_to_one( skol12 ) }.
% 1.09/1.45 substitution0:
% 1.09/1.45 end
% 1.09/1.45
% 1.09/1.45 eqrefl: (4317) {G0,W6,D2,L3,V0,M3} { ! relation( skol12 ), ! function(
% 1.09/1.45 skol12 ), ! one_to_one( skol12 ) }.
% 1.09/1.45 parent0[0]: (4316) {G1,W9,D2,L4,V0,M4} { ! empty_set ==> empty_set, !
% 1.09/1.45 relation( skol12 ), ! function( skol12 ), ! one_to_one( skol12 ) }.
% 1.09/1.45 substitution0:
% 1.09/1.45 end
% 1.09/1.45
% 1.09/1.45 resolution: (4318) {G1,W4,D2,L2,V0,M2} { ! function( skol12 ), !
% 1.09/1.45 one_to_one( skol12 ) }.
% 1.09/1.45 parent0[0]: (4317) {G0,W6,D2,L3,V0,M3} { ! relation( skol12 ), ! function
% 1.09/1.45 ( skol12 ), ! one_to_one( skol12 ) }.
% 1.09/1.45 parent1[0]: (37) {G0,W2,D2,L1,V0,M1} I { relation( skol12 ) }.
% 1.09/1.45 substitution0:
% 1.09/1.45 end
% 1.09/1.45 substitution1:
% 1.09/1.45 end
% 1.09/1.45
% 1.09/1.45 subsumption: (4192) {G2,W4,D2,L2,V0,M2} R(161,41);d(60);d(42);q;r(37) { !
% 1.09/1.45 function( skol12 ), ! one_to_one( skol12 ) }.
% 1.09/1.45 parent0: (4318) {G1,W4,D2,L2,V0,M2} { ! function( skol12 ), ! one_to_one(
% 1.09/1.45 skol12 ) }.
% 1.09/1.45 substitution0:
% 1.09/1.45 end
% 1.09/1.45 permutation0:
% 1.09/1.45 0 ==> 0
% 1.09/1.45 1 ==> 1
% 1.09/1.45 end
% 1.09/1.45
% 1.09/1.45 resolution: (4319) {G1,W2,D2,L1,V0,M1} { ! one_to_one( skol12 ) }.
% 1.09/1.45 parent0[0]: (4192) {G2,W4,D2,L2,V0,M2} R(161,41);d(60);d(42);q;r(37) { !
% 1.09/1.45 function( skol12 ), ! one_to_one( skol12 ) }.
% 1.09/1.45 parent1[0]: (38) {G0,W2,D2,L1,V0,M1} I { function( skol12 ) }.
% 1.09/1.45 substitution0:
% 1.09/1.45 end
% 1.09/1.45 substitution1:
% 1.09/1.45 end
% 1.09/1.45
% 1.09/1.45 resolution: (4320) {G1,W0,D0,L0,V0,M0} { }.
% 1.09/1.45 parent0[0]: (4319) {G1,W2,D2,L1,V0,M1} { ! one_to_one( skol12 ) }.
% 1.09/1.45 parent1[0]: (40) {G0,W2,D2,L1,V0,M1} I { one_to_one( skol12 ) }.
% 1.09/1.45 substitution0:
% 1.09/1.45 end
% 1.09/1.45 substitution1:
% 1.09/1.45 end
% 1.09/1.45
% 1.09/1.45 subsumption: (4195) {G3,W0,D0,L0,V0,M0} S(4192);r(38);r(40) { }.
% 1.09/1.45 parent0: (4320) {G1,W0,D0,L0,V0,M0} { }.
% 1.09/1.45 substitution0:
% 1.09/1.45 end
% 1.09/1.45 permutation0:
% 1.09/1.45 end
% 1.09/1.45
% 1.09/1.45 Proof check complete!
% 1.09/1.45
% 1.09/1.45 Memory use:
% 1.09/1.45
% 1.09/1.45 space for terms: 46266
% 1.09/1.45 space for clauses: 212411
% 1.09/1.45
% 1.09/1.45
% 1.09/1.45 clauses generated: 17088
% 1.09/1.45 clauses kept: 4196
% 1.09/1.45 clauses selected: 415
% 1.09/1.45 clauses deleted: 70
% 1.09/1.45 clauses inuse deleted: 28
% 1.09/1.45
% 1.09/1.45 subsentry: 35768
% 1.09/1.45 literals s-matched: 19075
% 1.09/1.45 literals matched: 18862
% 1.09/1.45 full subsumption: 4184
% 1.09/1.45
% 1.09/1.45 checksum: -473558490
% 1.09/1.45
% 1.09/1.45
% 1.09/1.45 Bliksem ended
%------------------------------------------------------------------------------