TSTP Solution File: SEU062+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SEU062+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n011.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 07:10:28 EDT 2022
% Result : Theorem 0.75s 1.23s
% Output : Refutation 0.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU062+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n011.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 : Mon Jun 20 01:24:39 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.75/1.23 *** allocated 10000 integers for termspace/termends
% 0.75/1.23 *** allocated 10000 integers for clauses
% 0.75/1.23 *** allocated 10000 integers for justifications
% 0.75/1.23 Bliksem 1.12
% 0.75/1.23
% 0.75/1.23
% 0.75/1.23 Automatic Strategy Selection
% 0.75/1.23
% 0.75/1.23
% 0.75/1.23 Clauses:
% 0.75/1.23
% 0.75/1.23 { ! in( X, Y ), ! in( Y, X ) }.
% 0.75/1.23 { ! empty( X ), function( X ) }.
% 0.75/1.23 { ! empty( X ), relation( X ) }.
% 0.75/1.23 { ! relation( X ), ! empty( X ), ! function( X ), relation( X ) }.
% 0.75/1.23 { ! relation( X ), ! empty( X ), ! function( X ), function( X ) }.
% 0.75/1.23 { ! relation( X ), ! empty( X ), ! function( X ), one_to_one( X ) }.
% 0.75/1.23 { ! subset( X, Y ), ! in( Z, X ), in( Z, Y ) }.
% 0.75/1.23 { ! in( skol1( Z, Y ), Y ), subset( X, Y ) }.
% 0.75/1.23 { in( skol1( X, Y ), X ), subset( X, Y ) }.
% 0.75/1.23 { element( skol2( X ), X ) }.
% 0.75/1.23 { empty( empty_set ) }.
% 0.75/1.23 { relation( empty_set ) }.
% 0.75/1.23 { relation_empty_yielding( empty_set ) }.
% 0.75/1.23 { ! empty( powerset( X ) ) }.
% 0.75/1.23 { empty( empty_set ) }.
% 0.75/1.23 { ! empty( singleton( X ) ) }.
% 0.75/1.23 { empty( empty_set ) }.
% 0.75/1.23 { relation( empty_set ) }.
% 0.75/1.23 { empty( X ), ! relation( X ), ! empty( relation_rng( X ) ) }.
% 0.75/1.23 { ! empty( X ), empty( relation_rng( X ) ) }.
% 0.75/1.23 { ! empty( X ), relation( relation_rng( X ) ) }.
% 0.75/1.23 { relation( skol3 ) }.
% 0.75/1.23 { function( skol3 ) }.
% 0.75/1.23 { empty( skol4 ) }.
% 0.75/1.23 { relation( skol4 ) }.
% 0.75/1.23 { empty( X ), ! empty( skol5( Y ) ) }.
% 0.75/1.23 { empty( X ), element( skol5( X ), powerset( X ) ) }.
% 0.75/1.23 { empty( skol6 ) }.
% 0.75/1.23 { relation( skol7 ) }.
% 0.75/1.23 { empty( skol7 ) }.
% 0.75/1.23 { function( skol7 ) }.
% 0.75/1.23 { ! empty( skol8 ) }.
% 0.75/1.23 { relation( skol8 ) }.
% 0.75/1.23 { empty( skol9( Y ) ) }.
% 0.75/1.23 { element( skol9( X ), powerset( X ) ) }.
% 0.75/1.23 { ! empty( skol10 ) }.
% 0.75/1.23 { relation( skol11 ) }.
% 0.75/1.23 { function( skol11 ) }.
% 0.75/1.23 { one_to_one( skol11 ) }.
% 0.75/1.23 { relation( skol12 ) }.
% 0.75/1.23 { relation_empty_yielding( skol12 ) }.
% 0.75/1.23 { subset( X, X ) }.
% 0.75/1.23 { ! relation( X ), ! in( Y, relation_rng( X ) ), ! relation_inverse_image(
% 0.75/1.23 X, singleton( Y ) ) = empty_set }.
% 0.75/1.23 { ! relation( X ), relation_inverse_image( X, singleton( Y ) ) = empty_set
% 0.75/1.23 , in( Y, relation_rng( X ) ) }.
% 0.75/1.23 { relation( skol13 ) }.
% 0.75/1.23 { ! in( X, skol14 ), ! relation_inverse_image( skol13, singleton( X ) ) =
% 0.75/1.23 empty_set }.
% 0.75/1.23 { ! subset( skol14, relation_rng( skol13 ) ) }.
% 0.75/1.23 { ! in( X, Y ), element( X, Y ) }.
% 0.75/1.23 { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.75/1.23 { ! element( X, powerset( Y ) ), subset( X, Y ) }.
% 0.75/1.23 { ! subset( X, Y ), element( X, powerset( Y ) ) }.
% 0.75/1.23 { ! in( X, Z ), ! element( Z, powerset( Y ) ), element( X, Y ) }.
% 0.75/1.23 { ! in( X, Y ), ! element( Y, powerset( Z ) ), ! empty( Z ) }.
% 0.75/1.23 { ! empty( X ), X = empty_set }.
% 0.75/1.23 { ! in( X, Y ), ! empty( Y ) }.
% 0.75/1.23 { ! empty( X ), X = Y, ! empty( Y ) }.
% 0.75/1.23
% 0.75/1.23 percentage equality = 0.058824, percentage horn = 0.921569
% 0.75/1.23 This is a problem with some equality
% 0.75/1.23
% 0.75/1.23
% 0.75/1.23
% 0.75/1.23 Options Used:
% 0.75/1.23
% 0.75/1.23 useres = 1
% 0.75/1.23 useparamod = 1
% 0.75/1.23 useeqrefl = 1
% 0.75/1.23 useeqfact = 1
% 0.75/1.23 usefactor = 1
% 0.75/1.23 usesimpsplitting = 0
% 0.75/1.23 usesimpdemod = 5
% 0.75/1.23 usesimpres = 3
% 0.75/1.23
% 0.75/1.23 resimpinuse = 1000
% 0.75/1.23 resimpclauses = 20000
% 0.75/1.23 substype = eqrewr
% 0.75/1.23 backwardsubs = 1
% 0.75/1.23 selectoldest = 5
% 0.75/1.23
% 0.75/1.23 litorderings [0] = split
% 0.75/1.23 litorderings [1] = extend the termordering, first sorting on arguments
% 0.75/1.23
% 0.75/1.23 termordering = kbo
% 0.75/1.23
% 0.75/1.23 litapriori = 0
% 0.75/1.23 termapriori = 1
% 0.75/1.23 litaposteriori = 0
% 0.75/1.23 termaposteriori = 0
% 0.75/1.23 demodaposteriori = 0
% 0.75/1.23 ordereqreflfact = 0
% 0.75/1.23
% 0.75/1.23 litselect = negord
% 0.75/1.23
% 0.75/1.23 maxweight = 15
% 0.75/1.23 maxdepth = 30000
% 0.75/1.23 maxlength = 115
% 0.75/1.23 maxnrvars = 195
% 0.75/1.23 excuselevel = 1
% 0.75/1.23 increasemaxweight = 1
% 0.75/1.23
% 0.75/1.23 maxselected = 10000000
% 0.75/1.23 maxnrclauses = 10000000
% 0.75/1.23
% 0.75/1.23 showgenerated = 0
% 0.75/1.23 showkept = 0
% 0.75/1.23 showselected = 0
% 0.75/1.23 showdeleted = 0
% 0.75/1.23 showresimp = 1
% 0.75/1.23 showstatus = 2000
% 0.75/1.23
% 0.75/1.23 prologoutput = 0
% 0.75/1.23 nrgoals = 5000000
% 0.75/1.23 totalproof = 1
% 0.75/1.23
% 0.75/1.23 Symbols occurring in the translation:
% 0.75/1.23
% 0.75/1.23 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.75/1.23 . [1, 2] (w:1, o:36, a:1, s:1, b:0),
% 0.75/1.23 ! [4, 1] (w:0, o:20, a:1, s:1, b:0),
% 0.75/1.23 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.75/1.23 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.75/1.23 in [37, 2] (w:1, o:60, a:1, s:1, b:0),
% 0.75/1.23 empty [38, 1] (w:1, o:25, a:1, s:1, b:0),
% 0.75/1.23 function [39, 1] (w:1, o:26, a:1, s:1, b:0),
% 0.75/1.23 relation [40, 1] (w:1, o:27, a:1, s:1, b:0),
% 0.75/1.23 one_to_one [41, 1] (w:1, o:28, a:1, s:1, b:0),
% 0.75/1.23 subset [42, 2] (w:1, o:62, a:1, s:1, b:0),
% 0.75/1.23 element [44, 2] (w:1, o:63, a:1, s:1, b:0),
% 0.75/1.23 empty_set [45, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.75/1.23 relation_empty_yielding [46, 1] (w:1, o:29, a:1, s:1, b:0),
% 0.75/1.23 powerset [47, 1] (w:1, o:30, a:1, s:1, b:0),
% 0.75/1.23 singleton [48, 1] (w:1, o:32, a:1, s:1, b:0),
% 0.75/1.23 relation_rng [49, 1] (w:1, o:31, a:1, s:1, b:0),
% 0.75/1.23 relation_inverse_image [50, 2] (w:1, o:61, a:1, s:1, b:0),
% 0.75/1.23 skol1 [51, 2] (w:1, o:64, a:1, s:1, b:1),
% 0.75/1.23 skol2 [52, 1] (w:1, o:33, a:1, s:1, b:1),
% 0.75/1.23 skol3 [53, 0] (w:1, o:10, a:1, s:1, b:1),
% 0.75/1.23 skol4 [54, 0] (w:1, o:11, a:1, s:1, b:1),
% 0.75/1.23 skol5 [55, 1] (w:1, o:34, a:1, s:1, b:1),
% 0.75/1.23 skol6 [56, 0] (w:1, o:12, a:1, s:1, b:1),
% 0.75/1.23 skol7 [57, 0] (w:1, o:13, a:1, s:1, b:1),
% 0.75/1.23 skol8 [58, 0] (w:1, o:14, a:1, s:1, b:1),
% 0.75/1.23 skol9 [59, 1] (w:1, o:35, a:1, s:1, b:1),
% 0.75/1.23 skol10 [60, 0] (w:1, o:15, a:1, s:1, b:1),
% 0.75/1.23 skol11 [61, 0] (w:1, o:16, a:1, s:1, b:1),
% 0.75/1.23 skol12 [62, 0] (w:1, o:17, a:1, s:1, b:1),
% 0.75/1.23 skol13 [63, 0] (w:1, o:18, a:1, s:1, b:1),
% 0.75/1.23 skol14 [64, 0] (w:1, o:19, a:1, s:1, b:1).
% 0.75/1.23
% 0.75/1.23
% 0.75/1.23 Starting Search:
% 0.75/1.23
% 0.75/1.23 *** allocated 15000 integers for clauses
% 0.75/1.23 *** allocated 22500 integers for clauses
% 0.75/1.23 *** allocated 33750 integers for clauses
% 0.75/1.23 *** allocated 50625 integers for clauses
% 0.75/1.23 *** allocated 15000 integers for termspace/termends
% 0.75/1.23 Resimplifying inuse:
% 0.75/1.23 Done
% 0.75/1.23
% 0.75/1.23 *** allocated 75937 integers for clauses
% 0.75/1.23 *** allocated 22500 integers for termspace/termends
% 0.75/1.23 *** allocated 113905 integers for clauses
% 0.75/1.23
% 0.75/1.23 Intermediate Status:
% 0.75/1.23 Generated: 8020
% 0.75/1.23 Kept: 2040
% 0.75/1.23 Inuse: 379
% 0.75/1.23 Deleted: 152
% 0.75/1.23 Deletedinuse: 77
% 0.75/1.23
% 0.75/1.23 Resimplifying inuse:
% 0.75/1.23 Done
% 0.75/1.23
% 0.75/1.23 *** allocated 33750 integers for termspace/termends
% 0.75/1.23 *** allocated 170857 integers for clauses
% 0.75/1.23
% 0.75/1.23 Bliksems!, er is een bewijs:
% 0.75/1.23 % SZS status Theorem
% 0.75/1.23 % SZS output start Refutation
% 0.75/1.23
% 0.75/1.23 (0) {G0,W6,D2,L2,V2,M2} I { ! in( X, Y ), ! in( Y, X ) }.
% 0.75/1.23 (5) {G0,W8,D3,L2,V3,M2} I { ! in( skol1( Z, Y ), Y ), subset( X, Y ) }.
% 0.75/1.23 (6) {G0,W8,D3,L2,V2,M2} I { in( skol1( X, Y ), X ), subset( X, Y ) }.
% 0.75/1.23 (11) {G0,W3,D3,L1,V1,M1} I { ! empty( powerset( X ) ) }.
% 0.75/1.23 (38) {G0,W12,D4,L3,V2,M3} I { ! relation( X ), relation_inverse_image( X,
% 0.75/1.23 singleton( Y ) ) ==> empty_set, in( Y, relation_rng( X ) ) }.
% 0.75/1.23 (39) {G0,W2,D2,L1,V0,M1} I { relation( skol13 ) }.
% 0.75/1.23 (40) {G0,W9,D4,L2,V1,M2} I { ! in( X, skol14 ), ! relation_inverse_image(
% 0.75/1.23 skol13, singleton( X ) ) ==> empty_set }.
% 0.75/1.23 (41) {G0,W4,D3,L1,V0,M1} I { ! subset( skol14, relation_rng( skol13 ) ) }.
% 0.75/1.23 (43) {G0,W8,D2,L3,V2,M3} I { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.75/1.23 (45) {G0,W7,D3,L2,V2,M2} I { ! subset( X, Y ), element( X, powerset( Y ) )
% 0.75/1.23 }.
% 0.75/1.23 (51) {G1,W3,D2,L1,V1,M1} F(0) { ! in( X, X ) }.
% 0.75/1.23 (84) {G1,W6,D4,L1,V0,M1} R(41,6) { in( skol1( skol14, relation_rng( skol13
% 0.75/1.23 ) ), skol14 ) }.
% 0.75/1.23 (194) {G1,W7,D3,L2,V1,M2} R(40,38);r(39) { ! in( X, skol14 ), in( X,
% 0.75/1.23 relation_rng( skol13 ) ) }.
% 0.75/1.23 (227) {G2,W5,D2,L2,V1,M2} R(43,51) { ! element( X, X ), empty( X ) }.
% 0.75/1.23 (444) {G3,W4,D3,L1,V1,M1} R(227,45);r(11) { ! subset( powerset( X ), X )
% 0.75/1.23 }.
% 0.75/1.23 (474) {G4,W5,D3,L1,V2,M1} R(444,5) { ! in( skol1( X, Y ), Y ) }.
% 0.75/1.23 (2862) {G5,W0,D0,L0,V0,M0} R(194,84);r(474) { }.
% 0.75/1.23
% 0.75/1.23
% 0.75/1.23 % SZS output end Refutation
% 0.75/1.23 found a proof!
% 0.75/1.23
% 0.75/1.23
% 0.75/1.23 Unprocessed initial clauses:
% 0.75/1.23
% 0.75/1.23 (2864) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), ! in( Y, X ) }.
% 0.75/1.23 (2865) {G0,W4,D2,L2,V1,M2} { ! empty( X ), function( X ) }.
% 0.75/1.23 (2866) {G0,W4,D2,L2,V1,M2} { ! empty( X ), relation( X ) }.
% 0.75/1.23 (2867) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 0.75/1.23 ), relation( X ) }.
% 0.75/1.23 (2868) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 0.75/1.23 ), function( X ) }.
% 0.75/1.23 (2869) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 0.75/1.23 ), one_to_one( X ) }.
% 0.75/1.23 (2870) {G0,W9,D2,L3,V3,M3} { ! subset( X, Y ), ! in( Z, X ), in( Z, Y )
% 0.75/1.23 }.
% 0.75/1.23 (2871) {G0,W8,D3,L2,V3,M2} { ! in( skol1( Z, Y ), Y ), subset( X, Y ) }.
% 0.75/1.23 (2872) {G0,W8,D3,L2,V2,M2} { in( skol1( X, Y ), X ), subset( X, Y ) }.
% 0.75/1.23 (2873) {G0,W4,D3,L1,V1,M1} { element( skol2( X ), X ) }.
% 0.75/1.23 (2874) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.75/1.23 (2875) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 0.75/1.23 (2876) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( empty_set ) }.
% 0.75/1.23 (2877) {G0,W3,D3,L1,V1,M1} { ! empty( powerset( X ) ) }.
% 0.75/1.23 (2878) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.75/1.23 (2879) {G0,W3,D3,L1,V1,M1} { ! empty( singleton( X ) ) }.
% 0.75/1.23 (2880) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.75/1.23 (2881) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 0.75/1.23 (2882) {G0,W7,D3,L3,V1,M3} { empty( X ), ! relation( X ), ! empty(
% 0.75/1.23 relation_rng( X ) ) }.
% 0.75/1.23 (2883) {G0,W5,D3,L2,V1,M2} { ! empty( X ), empty( relation_rng( X ) ) }.
% 0.75/1.23 (2884) {G0,W5,D3,L2,V1,M2} { ! empty( X ), relation( relation_rng( X ) )
% 0.75/1.23 }.
% 0.75/1.23 (2885) {G0,W2,D2,L1,V0,M1} { relation( skol3 ) }.
% 0.75/1.23 (2886) {G0,W2,D2,L1,V0,M1} { function( skol3 ) }.
% 0.75/1.23 (2887) {G0,W2,D2,L1,V0,M1} { empty( skol4 ) }.
% 0.75/1.23 (2888) {G0,W2,D2,L1,V0,M1} { relation( skol4 ) }.
% 0.75/1.23 (2889) {G0,W5,D3,L2,V2,M2} { empty( X ), ! empty( skol5( Y ) ) }.
% 0.75/1.23 (2890) {G0,W7,D3,L2,V1,M2} { empty( X ), element( skol5( X ), powerset( X
% 0.75/1.23 ) ) }.
% 0.75/1.23 (2891) {G0,W2,D2,L1,V0,M1} { empty( skol6 ) }.
% 0.75/1.23 (2892) {G0,W2,D2,L1,V0,M1} { relation( skol7 ) }.
% 0.75/1.23 (2893) {G0,W2,D2,L1,V0,M1} { empty( skol7 ) }.
% 0.75/1.23 (2894) {G0,W2,D2,L1,V0,M1} { function( skol7 ) }.
% 0.75/1.23 (2895) {G0,W2,D2,L1,V0,M1} { ! empty( skol8 ) }.
% 0.75/1.23 (2896) {G0,W2,D2,L1,V0,M1} { relation( skol8 ) }.
% 0.75/1.23 (2897) {G0,W3,D3,L1,V1,M1} { empty( skol9( Y ) ) }.
% 0.75/1.23 (2898) {G0,W5,D3,L1,V1,M1} { element( skol9( X ), powerset( X ) ) }.
% 0.75/1.23 (2899) {G0,W2,D2,L1,V0,M1} { ! empty( skol10 ) }.
% 0.75/1.23 (2900) {G0,W2,D2,L1,V0,M1} { relation( skol11 ) }.
% 0.75/1.23 (2901) {G0,W2,D2,L1,V0,M1} { function( skol11 ) }.
% 0.75/1.23 (2902) {G0,W2,D2,L1,V0,M1} { one_to_one( skol11 ) }.
% 0.75/1.23 (2903) {G0,W2,D2,L1,V0,M1} { relation( skol12 ) }.
% 0.75/1.23 (2904) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( skol12 ) }.
% 0.75/1.23 (2905) {G0,W3,D2,L1,V1,M1} { subset( X, X ) }.
% 0.75/1.23 (2906) {G0,W12,D4,L3,V2,M3} { ! relation( X ), ! in( Y, relation_rng( X )
% 0.75/1.23 ), ! relation_inverse_image( X, singleton( Y ) ) = empty_set }.
% 0.75/1.23 (2907) {G0,W12,D4,L3,V2,M3} { ! relation( X ), relation_inverse_image( X,
% 0.75/1.23 singleton( Y ) ) = empty_set, in( Y, relation_rng( X ) ) }.
% 0.75/1.23 (2908) {G0,W2,D2,L1,V0,M1} { relation( skol13 ) }.
% 0.75/1.23 (2909) {G0,W9,D4,L2,V1,M2} { ! in( X, skol14 ), ! relation_inverse_image(
% 0.75/1.23 skol13, singleton( X ) ) = empty_set }.
% 0.75/1.23 (2910) {G0,W4,D3,L1,V0,M1} { ! subset( skol14, relation_rng( skol13 ) )
% 0.75/1.23 }.
% 0.75/1.23 (2911) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), element( X, Y ) }.
% 0.75/1.23 (2912) {G0,W8,D2,L3,V2,M3} { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.75/1.23 (2913) {G0,W7,D3,L2,V2,M2} { ! element( X, powerset( Y ) ), subset( X, Y )
% 0.75/1.23 }.
% 0.75/1.23 (2914) {G0,W7,D3,L2,V2,M2} { ! subset( X, Y ), element( X, powerset( Y ) )
% 0.75/1.23 }.
% 0.75/1.23 (2915) {G0,W10,D3,L3,V3,M3} { ! in( X, Z ), ! element( Z, powerset( Y ) )
% 0.75/1.23 , element( X, Y ) }.
% 0.75/1.23 (2916) {G0,W9,D3,L3,V3,M3} { ! in( X, Y ), ! element( Y, powerset( Z ) ),
% 0.75/1.23 ! empty( Z ) }.
% 0.75/1.23 (2917) {G0,W5,D2,L2,V1,M2} { ! empty( X ), X = empty_set }.
% 0.75/1.23 (2918) {G0,W5,D2,L2,V2,M2} { ! in( X, Y ), ! empty( Y ) }.
% 0.75/1.23 (2919) {G0,W7,D2,L3,V2,M3} { ! empty( X ), X = Y, ! empty( Y ) }.
% 0.75/1.23
% 0.75/1.23
% 0.75/1.23 Total Proof:
% 0.75/1.23
% 0.75/1.23 subsumption: (0) {G0,W6,D2,L2,V2,M2} I { ! in( X, Y ), ! in( Y, X ) }.
% 0.75/1.23 parent0: (2864) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), ! in( Y, X ) }.
% 0.75/1.23 substitution0:
% 0.75/1.23 X := X
% 0.75/1.23 Y := Y
% 0.75/1.23 end
% 0.75/1.23 permutation0:
% 0.75/1.23 0 ==> 0
% 0.75/1.23 1 ==> 1
% 0.75/1.23 end
% 0.75/1.23
% 0.75/1.23 subsumption: (5) {G0,W8,D3,L2,V3,M2} I { ! in( skol1( Z, Y ), Y ), subset(
% 0.75/1.23 X, Y ) }.
% 0.75/1.23 parent0: (2871) {G0,W8,D3,L2,V3,M2} { ! in( skol1( Z, Y ), Y ), subset( X
% 0.75/1.23 , Y ) }.
% 0.75/1.23 substitution0:
% 0.75/1.23 X := X
% 0.75/1.23 Y := Y
% 0.75/1.23 Z := Z
% 0.75/1.23 end
% 0.75/1.23 permutation0:
% 0.75/1.23 0 ==> 0
% 0.75/1.23 1 ==> 1
% 0.75/1.23 end
% 0.75/1.23
% 0.75/1.23 subsumption: (6) {G0,W8,D3,L2,V2,M2} I { in( skol1( X, Y ), X ), subset( X
% 0.75/1.23 , Y ) }.
% 0.75/1.23 parent0: (2872) {G0,W8,D3,L2,V2,M2} { in( skol1( X, Y ), X ), subset( X, Y
% 0.75/1.23 ) }.
% 0.75/1.23 substitution0:
% 0.75/1.23 X := X
% 0.75/1.23 Y := Y
% 0.75/1.23 end
% 0.75/1.23 permutation0:
% 0.75/1.23 0 ==> 0
% 0.75/1.23 1 ==> 1
% 0.75/1.23 end
% 0.75/1.23
% 0.75/1.23 subsumption: (11) {G0,W3,D3,L1,V1,M1} I { ! empty( powerset( X ) ) }.
% 0.75/1.23 parent0: (2877) {G0,W3,D3,L1,V1,M1} { ! empty( powerset( X ) ) }.
% 0.75/1.23 substitution0:
% 0.75/1.23 X := X
% 0.75/1.23 end
% 0.75/1.23 permutation0:
% 0.75/1.23 0 ==> 0
% 0.75/1.23 end
% 0.75/1.23
% 0.75/1.23 subsumption: (38) {G0,W12,D4,L3,V2,M3} I { ! relation( X ),
% 0.75/1.23 relation_inverse_image( X, singleton( Y ) ) ==> empty_set, in( Y,
% 0.75/1.23 relation_rng( X ) ) }.
% 0.75/1.23 parent0: (2907) {G0,W12,D4,L3,V2,M3} { ! relation( X ),
% 0.75/1.23 relation_inverse_image( X, singleton( Y ) ) = empty_set, in( Y,
% 0.75/1.23 relation_rng( X ) ) }.
% 0.75/1.23 substitution0:
% 0.75/1.23 X := X
% 0.75/1.23 Y := Y
% 0.75/1.23 end
% 0.75/1.23 permutation0:
% 0.75/1.23 0 ==> 0
% 0.75/1.23 1 ==> 1
% 0.75/1.23 2 ==> 2
% 0.75/1.23 end
% 0.75/1.23
% 0.75/1.23 subsumption: (39) {G0,W2,D2,L1,V0,M1} I { relation( skol13 ) }.
% 0.75/1.23 parent0: (2908) {G0,W2,D2,L1,V0,M1} { relation( skol13 ) }.
% 0.75/1.23 substitution0:
% 0.75/1.23 end
% 0.75/1.23 permutation0:
% 0.75/1.23 0 ==> 0
% 0.75/1.23 end
% 0.75/1.23
% 0.75/1.23 subsumption: (40) {G0,W9,D4,L2,V1,M2} I { ! in( X, skol14 ), !
% 0.75/1.23 relation_inverse_image( skol13, singleton( X ) ) ==> empty_set }.
% 0.75/1.23 parent0: (2909) {G0,W9,D4,L2,V1,M2} { ! in( X, skol14 ), !
% 0.75/1.23 relation_inverse_image( skol13, singleton( X ) ) = empty_set }.
% 0.75/1.23 substitution0:
% 0.75/1.23 X := X
% 0.75/1.23 end
% 0.75/1.23 permutation0:
% 0.75/1.23 0 ==> 0
% 0.75/1.23 1 ==> 1
% 0.75/1.23 end
% 0.75/1.23
% 0.75/1.23 subsumption: (41) {G0,W4,D3,L1,V0,M1} I { ! subset( skol14, relation_rng(
% 0.75/1.23 skol13 ) ) }.
% 0.75/1.23 parent0: (2910) {G0,W4,D3,L1,V0,M1} { ! subset( skol14, relation_rng(
% 0.75/1.23 skol13 ) ) }.
% 0.75/1.23 substitution0:
% 0.75/1.23 end
% 0.75/1.23 permutation0:
% 0.75/1.23 0 ==> 0
% 0.75/1.23 end
% 0.75/1.23
% 0.75/1.23 subsumption: (43) {G0,W8,D2,L3,V2,M3} I { ! element( X, Y ), empty( Y ), in
% 0.75/1.23 ( X, Y ) }.
% 0.75/1.23 parent0: (2912) {G0,W8,D2,L3,V2,M3} { ! element( X, Y ), empty( Y ), in( X
% 0.75/1.23 , Y ) }.
% 0.75/1.23 substitution0:
% 0.75/1.23 X := X
% 0.75/1.23 Y := Y
% 0.75/1.23 end
% 0.75/1.23 permutation0:
% 0.75/1.23 0 ==> 0
% 0.75/1.23 1 ==> 1
% 0.75/1.23 2 ==> 2
% 0.75/1.23 end
% 0.75/1.23
% 0.75/1.23 subsumption: (45) {G0,W7,D3,L2,V2,M2} I { ! subset( X, Y ), element( X,
% 0.75/1.23 powerset( Y ) ) }.
% 0.75/1.23 parent0: (2914) {G0,W7,D3,L2,V2,M2} { ! subset( X, Y ), element( X,
% 0.75/1.23 powerset( Y ) ) }.
% 0.75/1.23 substitution0:
% 0.75/1.23 X := X
% 0.75/1.23 Y := Y
% 0.75/1.23 end
% 0.75/1.23 permutation0:
% 0.75/1.23 0 ==> 0
% 0.75/1.23 1 ==> 1
% 0.75/1.23 end
% 0.75/1.23
% 0.75/1.23 factor: (2946) {G0,W3,D2,L1,V1,M1} { ! in( X, X ) }.
% 0.75/1.23 parent0[0, 1]: (0) {G0,W6,D2,L2,V2,M2} I { ! in( X, Y ), ! in( Y, X ) }.
% 0.75/1.23 substitution0:
% 0.75/1.23 X := X
% 0.75/1.23 Y := X
% 0.75/1.23 end
% 0.75/1.23
% 0.75/1.23 subsumption: (51) {G1,W3,D2,L1,V1,M1} F(0) { ! in( X, X ) }.
% 0.75/1.23 parent0: (2946) {G0,W3,D2,L1,V1,M1} { ! in( X, X ) }.
% 0.75/1.23 substitution0:
% 0.75/1.23 X := X
% 0.75/1.23 end
% 0.75/1.23 permutation0:
% 0.75/1.23 0 ==> 0
% 0.75/1.23 end
% 0.75/1.23
% 0.75/1.23 resolution: (2947) {G1,W6,D4,L1,V0,M1} { in( skol1( skol14, relation_rng(
% 0.75/1.23 skol13 ) ), skol14 ) }.
% 0.75/1.23 parent0[0]: (41) {G0,W4,D3,L1,V0,M1} I { ! subset( skol14, relation_rng(
% 0.75/1.23 skol13 ) ) }.
% 0.75/1.23 parent1[1]: (6) {G0,W8,D3,L2,V2,M2} I { in( skol1( X, Y ), X ), subset( X,
% 0.75/1.23 Y ) }.
% 0.75/1.23 substitution0:
% 0.75/1.23 end
% 0.75/1.23 substitution1:
% 0.75/1.23 X := skol14
% 0.75/1.23 Y := relation_rng( skol13 )
% 0.75/1.23 end
% 0.75/1.23
% 0.75/1.23 subsumption: (84) {G1,W6,D4,L1,V0,M1} R(41,6) { in( skol1( skol14,
% 0.75/1.23 relation_rng( skol13 ) ), skol14 ) }.
% 0.75/1.23 parent0: (2947) {G1,W6,D4,L1,V0,M1} { in( skol1( skol14, relation_rng(
% 0.75/1.23 skol13 ) ), skol14 ) }.
% 0.75/1.23 substitution0:
% 0.75/1.23 end
% 0.75/1.23 permutation0:
% 0.75/1.23 0 ==> 0
% 0.75/1.23 end
% 0.75/1.23
% 0.75/1.23 eqswap: (2948) {G0,W9,D4,L2,V1,M2} { ! empty_set ==>
% 0.75/1.23 relation_inverse_image( skol13, singleton( X ) ), ! in( X, skol14 ) }.
% 0.75/1.23 parent0[1]: (40) {G0,W9,D4,L2,V1,M2} I { ! in( X, skol14 ), !
% 0.75/1.23 relation_inverse_image( skol13, singleton( X ) ) ==> empty_set }.
% 0.75/1.23 substitution0:
% 0.75/1.23 X := X
% 0.75/1.23 end
% 0.75/1.23
% 0.75/1.23 eqswap: (2949) {G0,W12,D4,L3,V2,M3} { empty_set ==> relation_inverse_image
% 0.75/1.23 ( X, singleton( Y ) ), ! relation( X ), in( Y, relation_rng( X ) ) }.
% 0.75/1.23 parent0[1]: (38) {G0,W12,D4,L3,V2,M3} I { ! relation( X ),
% 0.75/1.23 relation_inverse_image( X, singleton( Y ) ) ==> empty_set, in( Y,
% 0.75/1.23 relation_rng( X ) ) }.
% 0.75/1.23 substitution0:
% 0.75/1.23 X := X
% 0.75/1.23 Y := Y
% 0.75/1.23 end
% 0.75/1.23
% 0.75/1.23 resolution: (2950) {G1,W9,D3,L3,V1,M3} { ! in( X, skol14 ), ! relation(
% 0.75/1.23 skol13 ), in( X, relation_rng( skol13 ) ) }.
% 0.75/1.23 parent0[0]: (2948) {G0,W9,D4,L2,V1,M2} { ! empty_set ==>
% 0.75/1.23 relation_inverse_image( skol13, singleton( X ) ), ! in( X, skol14 ) }.
% 0.75/1.23 parent1[0]: (2949) {G0,W12,D4,L3,V2,M3} { empty_set ==>
% 0.75/1.23 relation_inverse_image( X, singleton( Y ) ), ! relation( X ), in( Y,
% 0.75/1.23 relation_rng( X ) ) }.
% 0.75/1.23 substitution0:
% 0.75/1.23 X := X
% 0.75/1.23 end
% 0.75/1.23 substitution1:
% 0.75/1.23 X := skol13
% 0.75/1.23 Y := X
% 0.75/1.23 end
% 0.75/1.23
% 0.75/1.23 resolution: (2951) {G1,W7,D3,L2,V1,M2} { ! in( X, skol14 ), in( X,
% 0.75/1.23 relation_rng( skol13 ) ) }.
% 0.75/1.23 parent0[1]: (2950) {G1,W9,D3,L3,V1,M3} { ! in( X, skol14 ), ! relation(
% 0.75/1.23 skol13 ), in( X, relation_rng( skol13 ) ) }.
% 0.75/1.23 parent1[0]: (39) {G0,W2,D2,L1,V0,M1} I { relation( skol13 ) }.
% 0.75/1.23 substitution0:
% 0.75/1.23 X := X
% 0.75/1.23 end
% 0.75/1.23 substitution1:
% 0.75/1.23 end
% 0.75/1.23
% 0.75/1.23 subsumption: (194) {G1,W7,D3,L2,V1,M2} R(40,38);r(39) { ! in( X, skol14 ),
% 0.75/1.23 in( X, relation_rng( skol13 ) ) }.
% 0.75/1.23 parent0: (2951) {G1,W7,D3,L2,V1,M2} { ! in( X, skol14 ), in( X,
% 0.75/1.23 relation_rng( skol13 ) ) }.
% 0.75/1.23 substitution0:
% 0.75/1.23 X := X
% 0.75/1.23 end
% 0.75/1.23 permutation0:
% 0.75/1.23 0 ==> 0
% 0.75/1.23 1 ==> 1
% 0.75/1.23 end
% 0.75/1.23
% 0.75/1.23 resolution: (2952) {G1,W5,D2,L2,V1,M2} { ! element( X, X ), empty( X ) }.
% 0.75/1.23 parent0[0]: (51) {G1,W3,D2,L1,V1,M1} F(0) { ! in( X, X ) }.
% 0.75/1.23 parent1[2]: (43) {G0,W8,D2,L3,V2,M3} I { ! element( X, Y ), empty( Y ), in
% 0.75/1.23 ( X, Y ) }.
% 0.75/1.23 substitution0:
% 0.75/1.23 X := X
% 0.75/1.23 end
% 0.75/1.23 substitution1:
% 0.75/1.23 X := X
% 0.75/1.23 Y := X
% 0.75/1.23 end
% 0.75/1.23
% 0.75/1.23 subsumption: (227) {G2,W5,D2,L2,V1,M2} R(43,51) { ! element( X, X ), empty
% 0.75/1.23 ( X ) }.
% 0.75/1.23 parent0: (2952) {G1,W5,D2,L2,V1,M2} { ! element( X, X ), empty( X ) }.
% 0.75/1.23 substitution0:
% 0.75/1.23 X := X
% 0.75/1.23 end
% 0.75/1.23 permutation0:
% 0.75/1.23 0 ==> 0
% 0.75/1.23 1 ==> 1
% 0.75/1.23 end
% 0.75/1.23
% 0.75/1.23 resolution: (2953) {G1,W7,D3,L2,V1,M2} { empty( powerset( X ) ), ! subset
% 0.75/1.23 ( powerset( X ), X ) }.
% 0.75/1.23 parent0[0]: (227) {G2,W5,D2,L2,V1,M2} R(43,51) { ! element( X, X ), empty(
% 0.75/1.23 X ) }.
% 0.75/1.23 parent1[1]: (45) {G0,W7,D3,L2,V2,M2} I { ! subset( X, Y ), element( X,
% 0.75/1.23 powerset( Y ) ) }.
% 0.75/1.23 substitution0:
% 0.75/1.23 X := powerset( X )
% 0.75/1.23 end
% 0.75/1.23 substitution1:
% 0.75/1.23 X := powerset( X )
% 0.75/1.23 Y := X
% 0.75/1.23 end
% 0.75/1.23
% 0.75/1.23 resolution: (2954) {G1,W4,D3,L1,V1,M1} { ! subset( powerset( X ), X ) }.
% 0.75/1.23 parent0[0]: (11) {G0,W3,D3,L1,V1,M1} I { ! empty( powerset( X ) ) }.
% 0.75/1.23 parent1[0]: (2953) {G1,W7,D3,L2,V1,M2} { empty( powerset( X ) ), ! subset
% 0.75/1.23 ( powerset( X ), X ) }.
% 0.75/1.23 substitution0:
% 0.75/1.23 X := X
% 0.75/1.23 end
% 0.75/1.23 substitution1:
% 0.75/1.23 X := X
% 0.75/1.23 end
% 0.75/1.23
% 0.75/1.23 subsumption: (444) {G3,W4,D3,L1,V1,M1} R(227,45);r(11) { ! subset( powerset
% 0.75/1.23 ( X ), X ) }.
% 0.75/1.23 parent0: (2954) {G1,W4,D3,L1,V1,M1} { ! subset( powerset( X ), X ) }.
% 0.75/1.23 substitution0:
% 0.75/1.23 X := X
% 0.75/1.23 end
% 0.75/1.23 permutation0:
% 0.75/1.23 0 ==> 0
% 0.75/1.23 end
% 0.75/1.23
% 0.75/1.23 resolution: (2955) {G1,W5,D3,L1,V2,M1} { ! in( skol1( Y, X ), X ) }.
% 0.75/1.23 parent0[0]: (444) {G3,W4,D3,L1,V1,M1} R(227,45);r(11) { ! subset( powerset
% 0.75/1.23 ( X ), X ) }.
% 0.75/1.23 parent1[1]: (5) {G0,W8,D3,L2,V3,M2} I { ! in( skol1( Z, Y ), Y ), subset( X
% 0.75/1.23 , Y ) }.
% 0.75/1.23 substitution0:
% 0.75/1.23 X := X
% 0.75/1.23 end
% 0.75/1.23 substitution1:
% 0.75/1.23 X := powerset( X )
% 0.75/1.23 Y := X
% 0.75/1.23 Z := Y
% 0.75/1.23 end
% 0.75/1.23
% 0.75/1.23 subsumption: (474) {G4,W5,D3,L1,V2,M1} R(444,5) { ! in( skol1( X, Y ), Y )
% 0.75/1.23 }.
% 0.75/1.23 parent0: (2955) {G1,W5,D3,L1,V2,M1} { ! in( skol1( Y, X ), X ) }.
% 0.75/1.23 substitution0:
% 0.75/1.23 X := Y
% 0.75/1.23 Y := X
% 0.75/1.23 end
% 0.75/1.23 permutation0:
% 0.75/1.23 0 ==> 0
% 0.75/1.23 end
% 0.75/1.23
% 0.75/1.23 resolution: (2956) {G2,W7,D4,L1,V0,M1} { in( skol1( skol14, relation_rng(
% 0.75/1.23 skol13 ) ), relation_rng( skol13 ) ) }.
% 0.75/1.23 parent0[0]: (194) {G1,W7,D3,L2,V1,M2} R(40,38);r(39) { ! in( X, skol14 ),
% 0.75/1.23 in( X, relation_rng( skol13 ) ) }.
% 0.75/1.23 parent1[0]: (84) {G1,W6,D4,L1,V0,M1} R(41,6) { in( skol1( skol14,
% 0.75/1.23 relation_rng( skol13 ) ), skol14 ) }.
% 0.75/1.23 substitution0:
% 0.75/1.23 X := skol1( skol14, relation_rng( skol13 ) )
% 0.75/1.23 end
% 0.75/1.23 substitution1:
% 0.75/1.23 end
% 0.75/1.23
% 0.75/1.23 resolution: (2957) {G3,W0,D0,L0,V0,M0} { }.
% 0.75/1.23 parent0[0]: (474) {G4,W5,D3,L1,V2,M1} R(444,5) { ! in( skol1( X, Y ), Y )
% 0.75/1.23 }.
% 0.75/1.23 parent1[0]: (2956) {G2,W7,D4,L1,V0,M1} { in( skol1( skol14, relation_rng(
% 0.75/1.23 skol13 ) ), relation_rng( skol13 ) ) }.
% 0.75/1.23 substitution0:
% 0.75/1.23 X := skol14
% 0.75/1.23 Y := relation_rng( skol13 )
% 0.75/1.23 end
% 0.75/1.23 substitution1:
% 0.75/1.23 end
% 0.75/1.23
% 0.75/1.23 subsumption: (2862) {G5,W0,D0,L0,V0,M0} R(194,84);r(474) { }.
% 0.75/1.23 parent0: (2957) {G3,W0,D0,L0,V0,M0} { }.
% 0.75/1.23 substitution0:
% 0.75/1.23 end
% 0.75/1.23 permutation0:
% 0.75/1.23 end
% 0.75/1.23
% 0.75/1.23 Proof check complete!
% 0.75/1.23
% 0.75/1.23 Memory use:
% 0.75/1.23
% 0.75/1.23 space for terms: 31202
% 0.75/1.23 space for clauses: 140612
% 0.75/1.23
% 0.75/1.23
% 0.75/1.23 clauses generated: 10653
% 0.75/1.23 clauses kept: 2863
% 0.75/1.23 clauses selected: 449
% 0.75/1.23 clauses deleted: 169
% 0.75/1.23 clauses inuse deleted: 82
% 0.75/1.23
% 0.75/1.23 subsentry: 24325
% 0.75/1.23 literals s-matched: 16251
% 0.75/1.23 literals matched: 15904
% 0.75/1.23 full subsumption: 2514
% 0.75/1.23
% 0.75/1.23 checksum: 1359858303
% 0.75/1.23
% 0.75/1.23
% 0.75/1.23 Bliksem ended
%------------------------------------------------------------------------------