TSTP Solution File: SEU225+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SEU225+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n029.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 07:11:38 EDT 2022
% Result : Theorem 25.21s 25.58s
% Output : Refutation 25.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU225+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n029.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 : Mon Jun 20 03:57:15 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.87/2.25 *** allocated 10000 integers for termspace/termends
% 1.87/2.25 *** allocated 10000 integers for clauses
% 1.87/2.25 *** allocated 10000 integers for justifications
% 1.87/2.25 Bliksem 1.12
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 Automatic Strategy Selection
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 Clauses:
% 1.87/2.25
% 1.87/2.25 { ! in( X, Y ), ! in( Y, X ) }.
% 1.87/2.25 { ! empty( X ), function( X ) }.
% 1.87/2.25 { ! empty( X ), relation( X ) }.
% 1.87/2.25 { ! relation( X ), ! empty( X ), ! function( X ), relation( X ) }.
% 1.87/2.25 { ! relation( X ), ! empty( X ), ! function( X ), function( X ) }.
% 1.87/2.25 { ! relation( X ), ! empty( X ), ! function( X ), one_to_one( X ) }.
% 1.87/2.25 { unordered_pair( X, Y ) = unordered_pair( Y, X ) }.
% 1.87/2.25 { set_intersection2( X, Y ) = set_intersection2( Y, X ) }.
% 1.87/2.25 { ! relation( X ), ! function( X ), ! in( Y, relation_dom( X ) ), ! Z =
% 1.87/2.25 apply( X, Y ), in( ordered_pair( Y, Z ), X ) }.
% 1.87/2.25 { ! relation( X ), ! function( X ), ! in( Y, relation_dom( X ) ), ! in(
% 1.87/2.25 ordered_pair( Y, Z ), X ), Z = apply( X, Y ) }.
% 1.87/2.25 { ! relation( X ), ! function( X ), in( Y, relation_dom( X ) ), ! Z = apply
% 1.87/2.25 ( X, Y ), Z = empty_set }.
% 1.87/2.25 { ! relation( X ), ! function( X ), in( Y, relation_dom( X ) ), ! Z =
% 1.87/2.25 empty_set, Z = apply( X, Y ) }.
% 1.87/2.25 { ordered_pair( X, Y ) = unordered_pair( unordered_pair( X, Y ), singleton
% 1.87/2.25 ( X ) ) }.
% 1.87/2.25 { && }.
% 1.87/2.25 { && }.
% 1.87/2.25 { && }.
% 1.87/2.25 { && }.
% 1.87/2.25 { && }.
% 1.87/2.25 { && }.
% 1.87/2.25 { && }.
% 1.87/2.25 { ! relation( X ), relation( relation_dom_restriction( X, Y ) ) }.
% 1.87/2.25 { && }.
% 1.87/2.25 { element( skol1( X ), X ) }.
% 1.87/2.25 { empty( empty_set ) }.
% 1.87/2.25 { relation( empty_set ) }.
% 1.87/2.25 { relation_empty_yielding( empty_set ) }.
% 1.87/2.25 { ! relation( X ), ! relation_empty_yielding( X ), relation(
% 1.87/2.25 relation_dom_restriction( X, Y ) ) }.
% 1.87/2.25 { ! relation( X ), ! relation_empty_yielding( X ), relation_empty_yielding
% 1.87/2.25 ( relation_dom_restriction( X, Y ) ) }.
% 1.87/2.25 { ! relation( X ), ! relation( Y ), relation( set_intersection2( X, Y ) ) }
% 1.87/2.25 .
% 1.87/2.25 { empty( empty_set ) }.
% 1.87/2.25 { ! empty( ordered_pair( X, Y ) ) }.
% 1.87/2.25 { ! empty( singleton( X ) ) }.
% 1.87/2.25 { ! empty( unordered_pair( X, Y ) ) }.
% 1.87/2.25 { ! relation( X ), ! function( X ), relation( relation_dom_restriction( X,
% 1.87/2.25 Y ) ) }.
% 1.87/2.25 { ! relation( X ), ! function( X ), function( relation_dom_restriction( X,
% 1.87/2.25 Y ) ) }.
% 1.87/2.25 { empty( empty_set ) }.
% 1.87/2.25 { relation( empty_set ) }.
% 1.87/2.25 { empty( X ), ! relation( X ), ! empty( relation_dom( X ) ) }.
% 1.87/2.25 { ! empty( X ), empty( relation_dom( X ) ) }.
% 1.87/2.25 { ! empty( X ), relation( relation_dom( X ) ) }.
% 1.87/2.25 { set_intersection2( X, X ) = X }.
% 1.87/2.25 { ! relation( X ), ! function( X ), ! in( Z, relation_dom(
% 1.87/2.25 relation_dom_restriction( X, Y ) ) ), in( Z, relation_dom( X ) ) }.
% 1.87/2.25 { ! relation( X ), ! function( X ), ! in( Z, relation_dom(
% 1.87/2.25 relation_dom_restriction( X, Y ) ) ), in( Z, Y ) }.
% 1.87/2.25 { ! relation( X ), ! function( X ), ! in( Z, relation_dom( X ) ), ! in( Z,
% 1.87/2.25 Y ), in( Z, relation_dom( relation_dom_restriction( X, Y ) ) ) }.
% 1.87/2.25 { relation( skol2 ) }.
% 1.87/2.25 { function( skol2 ) }.
% 1.87/2.25 { empty( skol3 ) }.
% 1.87/2.25 { relation( skol3 ) }.
% 1.87/2.25 { empty( skol4 ) }.
% 1.87/2.25 { relation( skol5 ) }.
% 1.87/2.25 { empty( skol5 ) }.
% 1.87/2.25 { function( skol5 ) }.
% 1.87/2.25 { ! empty( skol6 ) }.
% 1.87/2.25 { relation( skol6 ) }.
% 1.87/2.25 { ! empty( skol7 ) }.
% 1.87/2.25 { relation( skol8 ) }.
% 1.87/2.25 { function( skol8 ) }.
% 1.87/2.25 { one_to_one( skol8 ) }.
% 1.87/2.25 { relation( skol9 ) }.
% 1.87/2.25 { relation_empty_yielding( skol9 ) }.
% 1.87/2.25 { ! in( X, Y ), element( X, Y ) }.
% 1.87/2.25 { set_intersection2( X, empty_set ) = empty_set }.
% 1.87/2.25 { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 1.87/2.25 { ! relation( X ), ! function( X ), ! relation( Y ), ! function( Y ), ! X =
% 1.87/2.25 relation_dom_restriction( Y, Z ), relation_dom( X ) = set_intersection2
% 1.87/2.25 ( relation_dom( Y ), Z ) }.
% 1.87/2.25 { ! relation( X ), ! function( X ), ! relation( Y ), ! function( Y ), ! X =
% 1.87/2.25 relation_dom_restriction( Y, Z ), alpha1( X, Y ) }.
% 1.87/2.25 { ! relation( X ), ! function( X ), ! relation( Y ), ! function( Y ), !
% 1.87/2.25 relation_dom( X ) = set_intersection2( relation_dom( Y ), Z ), ! alpha1(
% 1.87/2.25 X, Y ), X = relation_dom_restriction( Y, Z ) }.
% 1.87/2.25 { ! alpha1( X, Y ), ! in( Z, relation_dom( X ) ), apply( X, Z ) = apply( Y
% 1.87/2.25 , Z ) }.
% 1.87/2.25 { in( skol10( X, Z ), relation_dom( X ) ), alpha1( X, Y ) }.
% 1.87/2.25 { ! apply( X, skol10( X, Y ) ) = apply( Y, skol10( X, Y ) ), alpha1( X, Y )
% 1.87/2.25 }.
% 1.87/2.25 { ! empty( X ), X = empty_set }.
% 1.87/2.25 { relation( skol11 ) }.
% 1.87/2.25 { function( skol11 ) }.
% 1.87/2.25 { in( skol13, skol12 ) }.
% 1.87/2.25 { ! apply( relation_dom_restriction( skol11, skol12 ), skol13 ) = apply(
% 1.87/2.25 skol11, skol13 ) }.
% 1.87/2.25 { ! in( X, Y ), ! empty( Y ) }.
% 22.25/22.64 { ! empty( X ), X = Y, ! empty( Y ) }.
% 22.25/22.64
% 22.25/22.64 percentage equality = 0.159091, percentage horn = 0.935484
% 22.25/22.64 This is a problem with some equality
% 22.25/22.64
% 22.25/22.64
% 22.25/22.64
% 22.25/22.64 Options Used:
% 22.25/22.64
% 22.25/22.64 useres = 1
% 22.25/22.64 useparamod = 1
% 22.25/22.64 useeqrefl = 1
% 22.25/22.64 useeqfact = 1
% 22.25/22.64 usefactor = 1
% 22.25/22.64 usesimpsplitting = 0
% 22.25/22.64 usesimpdemod = 5
% 22.25/22.64 usesimpres = 3
% 22.25/22.64
% 22.25/22.64 resimpinuse = 1000
% 22.25/22.64 resimpclauses = 20000
% 22.25/22.64 substype = eqrewr
% 22.25/22.64 backwardsubs = 1
% 22.25/22.64 selectoldest = 5
% 22.25/22.64
% 22.25/22.64 litorderings [0] = split
% 22.25/22.64 litorderings [1] = extend the termordering, first sorting on arguments
% 22.25/22.64
% 22.25/22.64 termordering = kbo
% 22.25/22.64
% 22.25/22.64 litapriori = 0
% 22.25/22.64 termapriori = 1
% 22.25/22.64 litaposteriori = 0
% 22.25/22.64 termaposteriori = 0
% 22.25/22.64 demodaposteriori = 0
% 22.25/22.64 ordereqreflfact = 0
% 22.25/22.64
% 22.25/22.64 litselect = negord
% 22.25/22.64
% 22.25/22.64 maxweight = 15
% 22.25/22.64 maxdepth = 30000
% 22.25/22.64 maxlength = 115
% 22.25/22.64 maxnrvars = 195
% 22.25/22.64 excuselevel = 1
% 22.25/22.64 increasemaxweight = 1
% 22.25/22.64
% 22.25/22.64 maxselected = 10000000
% 22.25/22.64 maxnrclauses = 10000000
% 22.25/22.64
% 22.25/22.64 showgenerated = 0
% 22.25/22.64 showkept = 0
% 22.25/22.64 showselected = 0
% 22.25/22.64 showdeleted = 0
% 22.25/22.64 showresimp = 1
% 22.25/22.64 showstatus = 2000
% 22.25/22.64
% 22.25/22.64 prologoutput = 0
% 22.25/22.64 nrgoals = 5000000
% 22.25/22.64 totalproof = 1
% 22.25/22.64
% 22.25/22.64 Symbols occurring in the translation:
% 22.25/22.64
% 22.25/22.64 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 22.25/22.64 . [1, 2] (w:1, o:35, a:1, s:1, b:0),
% 22.25/22.64 && [3, 0] (w:1, o:4, a:1, s:1, b:0),
% 22.25/22.64 ! [4, 1] (w:0, o:22, a:1, s:1, b:0),
% 22.25/22.64 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 22.25/22.64 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 22.25/22.64 in [37, 2] (w:1, o:59, a:1, s:1, b:0),
% 22.25/22.64 empty [38, 1] (w:1, o:27, a:1, s:1, b:0),
% 22.25/22.64 function [39, 1] (w:1, o:28, a:1, s:1, b:0),
% 22.25/22.64 relation [40, 1] (w:1, o:29, a:1, s:1, b:0),
% 22.25/22.64 one_to_one [41, 1] (w:1, o:30, a:1, s:1, b:0),
% 22.25/22.64 unordered_pair [42, 2] (w:1, o:60, a:1, s:1, b:0),
% 22.25/22.64 set_intersection2 [43, 2] (w:1, o:62, a:1, s:1, b:0),
% 22.25/22.64 relation_dom [45, 1] (w:1, o:31, a:1, s:1, b:0),
% 22.25/22.64 apply [46, 2] (w:1, o:63, a:1, s:1, b:0),
% 22.25/22.64 ordered_pair [47, 2] (w:1, o:64, a:1, s:1, b:0),
% 22.25/22.64 empty_set [48, 0] (w:1, o:9, a:1, s:1, b:0),
% 22.25/22.64 singleton [49, 1] (w:1, o:33, a:1, s:1, b:0),
% 22.25/22.64 relation_dom_restriction [50, 2] (w:1, o:61, a:1, s:1, b:0),
% 22.25/22.64 element [51, 2] (w:1, o:65, a:1, s:1, b:0),
% 22.25/22.64 relation_empty_yielding [52, 1] (w:1, o:32, a:1, s:1, b:0),
% 22.25/22.64 alpha1 [54, 2] (w:1, o:66, a:1, s:1, b:1),
% 22.25/22.64 skol1 [55, 1] (w:1, o:34, a:1, s:1, b:1),
% 22.25/22.64 skol2 [56, 0] (w:1, o:14, a:1, s:1, b:1),
% 22.25/22.64 skol3 [57, 0] (w:1, o:15, a:1, s:1, b:1),
% 22.25/22.64 skol4 [58, 0] (w:1, o:16, a:1, s:1, b:1),
% 22.25/22.64 skol5 [59, 0] (w:1, o:17, a:1, s:1, b:1),
% 22.25/22.64 skol6 [60, 0] (w:1, o:18, a:1, s:1, b:1),
% 22.25/22.64 skol7 [61, 0] (w:1, o:19, a:1, s:1, b:1),
% 22.25/22.64 skol8 [62, 0] (w:1, o:20, a:1, s:1, b:1),
% 22.25/22.64 skol9 [63, 0] (w:1, o:21, a:1, s:1, b:1),
% 22.25/22.64 skol10 [64, 2] (w:1, o:67, a:1, s:1, b:1),
% 22.25/22.64 skol11 [65, 0] (w:1, o:11, a:1, s:1, b:1),
% 22.25/22.64 skol12 [66, 0] (w:1, o:12, a:1, s:1, b:1),
% 22.25/22.64 skol13 [67, 0] (w:1, o:13, a:1, s:1, b:1).
% 22.25/22.64
% 22.25/22.64
% 22.25/22.64 Starting Search:
% 22.25/22.64
% 22.25/22.64 *** allocated 15000 integers for clauses
% 22.25/22.64 *** allocated 22500 integers for clauses
% 22.25/22.64 *** allocated 33750 integers for clauses
% 22.25/22.64 *** allocated 15000 integers for termspace/termends
% 22.25/22.64 *** allocated 50625 integers for clauses
% 22.25/22.64 *** allocated 75937 integers for clauses
% 22.25/22.64 *** allocated 22500 integers for termspace/termends
% 22.25/22.64 Resimplifying inuse:
% 22.25/22.64 Done
% 22.25/22.64
% 22.25/22.64 *** allocated 113905 integers for clauses
% 22.25/22.64 *** allocated 33750 integers for termspace/termends
% 22.25/22.64
% 22.25/22.64 Intermediate Status:
% 22.25/22.64 Generated: 7848
% 22.25/22.64 Kept: 2008
% 22.25/22.64 Inuse: 248
% 22.25/22.64 Deleted: 69
% 22.25/22.64 Deletedinuse: 30
% 22.25/22.64
% 22.25/22.64 Resimplifying inuse:
% 22.25/22.64 Done
% 22.25/22.64
% 22.25/22.64 *** allocated 170857 integers for clauses
% 22.25/22.64 *** allocated 50625 integers for termspace/termends
% 22.25/22.64 Resimplifying inuse:
% 22.25/22.64 Done
% 22.25/22.64
% 22.25/22.64 *** allocated 256285 integers for clauses
% 22.25/22.64
% 22.25/22.64 Intermediate Status:
% 22.25/22.64 Generated: 30598
% 22.25/22.64 Kept: 4019
% 22.25/22.64 Inuse: 368
% 22.25/22.64 Deleted: 76
% 22.25/22.64 Deletedinuse: 30
% 22.25/22.64
% 22.25/22.64 Resimplifying inuse:
% 22.25/22.64 Done
% 22.25/22.64
% 22.25/22.64 *** allocated 75937 integers for termspace/termends
% 22.25/22.64 Resimplifying inuse:
% 22.25/22.64 Done
% 22.25/22.64
% 22.25/22.64 *** allocated 384427 integers for clauses
% 22.25/22.64
% 22.25/22.64 Intermediate Status:
% 22.25/22.64 Generated: 55551
% 22.25/22.64 Kept: 6034
% 22.25/22.64 Inuse: 507
% 22.25/22.64 Deleted: 89
% 25.21/25.58 Deletedinuse: 31
% 25.21/25.58
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58 *** allocated 113905 integers for termspace/termends
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58 *** allocated 576640 integers for clauses
% 25.21/25.58
% 25.21/25.58 Intermediate Status:
% 25.21/25.58 Generated: 79484
% 25.21/25.58 Kept: 9066
% 25.21/25.58 Inuse: 590
% 25.21/25.58 Deleted: 102
% 25.21/25.58 Deletedinuse: 31
% 25.21/25.58
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58 *** allocated 170857 integers for termspace/termends
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58
% 25.21/25.58 Intermediate Status:
% 25.21/25.58 Generated: 82953
% 25.21/25.58 Kept: 11201
% 25.21/25.58 Inuse: 599
% 25.21/25.58 Deleted: 103
% 25.21/25.58 Deletedinuse: 31
% 25.21/25.58
% 25.21/25.58 *** allocated 864960 integers for clauses
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58
% 25.21/25.58 Intermediate Status:
% 25.21/25.58 Generated: 93507
% 25.21/25.58 Kept: 13261
% 25.21/25.58 Inuse: 632
% 25.21/25.58 Deleted: 118
% 25.21/25.58 Deletedinuse: 34
% 25.21/25.58
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58 *** allocated 256285 integers for termspace/termends
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58
% 25.21/25.58 Intermediate Status:
% 25.21/25.58 Generated: 98914
% 25.21/25.58 Kept: 15963
% 25.21/25.58 Inuse: 657
% 25.21/25.58 Deleted: 118
% 25.21/25.58 Deletedinuse: 34
% 25.21/25.58
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58 *** allocated 1297440 integers for clauses
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58
% 25.21/25.58 Intermediate Status:
% 25.21/25.58 Generated: 116412
% 25.21/25.58 Kept: 18223
% 25.21/25.58 Inuse: 696
% 25.21/25.58 Deleted: 144
% 25.21/25.58 Deletedinuse: 34
% 25.21/25.58
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58
% 25.21/25.58 Intermediate Status:
% 25.21/25.58 Generated: 124068
% 25.21/25.58 Kept: 20381
% 25.21/25.58 Inuse: 717
% 25.21/25.58 Deleted: 144
% 25.21/25.58 Deletedinuse: 34
% 25.21/25.58
% 25.21/25.58 Resimplifying clauses:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58 *** allocated 384427 integers for termspace/termends
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58
% 25.21/25.58 Intermediate Status:
% 25.21/25.58 Generated: 151571
% 25.21/25.58 Kept: 22400
% 25.21/25.58 Inuse: 806
% 25.21/25.58 Deleted: 2189
% 25.21/25.58 Deletedinuse: 82
% 25.21/25.58
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58
% 25.21/25.58 Intermediate Status:
% 25.21/25.58 Generated: 183475
% 25.21/25.58 Kept: 24425
% 25.21/25.58 Inuse: 881
% 25.21/25.58 Deleted: 2198
% 25.21/25.58 Deletedinuse: 87
% 25.21/25.58
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58 *** allocated 1946160 integers for clauses
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58
% 25.21/25.58 Intermediate Status:
% 25.21/25.58 Generated: 211115
% 25.21/25.58 Kept: 26454
% 25.21/25.58 Inuse: 946
% 25.21/25.58 Deleted: 2199
% 25.21/25.58 Deletedinuse: 87
% 25.21/25.58
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58
% 25.21/25.58 Intermediate Status:
% 25.21/25.58 Generated: 260536
% 25.21/25.58 Kept: 28475
% 25.21/25.58 Inuse: 1035
% 25.21/25.58 Deleted: 2246
% 25.21/25.58 Deletedinuse: 88
% 25.21/25.58
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58
% 25.21/25.58 Intermediate Status:
% 25.21/25.58 Generated: 299424
% 25.21/25.58 Kept: 30503
% 25.21/25.58 Inuse: 1100
% 25.21/25.58 Deleted: 2255
% 25.21/25.58 Deletedinuse: 97
% 25.21/25.58
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58 *** allocated 576640 integers for termspace/termends
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58
% 25.21/25.58 Intermediate Status:
% 25.21/25.58 Generated: 323776
% 25.21/25.58 Kept: 32787
% 25.21/25.58 Inuse: 1145
% 25.21/25.58 Deleted: 2265
% 25.21/25.58 Deletedinuse: 98
% 25.21/25.58
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58
% 25.21/25.58 Intermediate Status:
% 25.21/25.58 Generated: 328480
% 25.21/25.58 Kept: 35163
% 25.21/25.58 Inuse: 1151
% 25.21/25.58 Deleted: 2267
% 25.21/25.58 Deletedinuse: 98
% 25.21/25.58
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58 *** allocated 2919240 integers for clauses
% 25.21/25.58
% 25.21/25.58 Intermediate Status:
% 25.21/25.58 Generated: 333085
% 25.21/25.58 Kept: 37538
% 25.21/25.58 Inuse: 1156
% 25.21/25.58 Deleted: 2270
% 25.21/25.58 Deletedinuse: 99
% 25.21/25.58
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58
% 25.21/25.58 Intermediate Status:
% 25.21/25.58 Generated: 337760
% 25.21/25.58 Kept: 39939
% 25.21/25.58 Inuse: 1161
% 25.21/25.58 Deleted: 2273
% 25.21/25.58 Deletedinuse: 99
% 25.21/25.58
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58 Resimplifying clauses:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58
% 25.21/25.58 Intermediate Status:
% 25.21/25.58 Generated: 356735
% 25.21/25.58 Kept: 42075
% 25.21/25.58 Inuse: 1213
% 25.21/25.58 Deleted: 4499
% 25.21/25.58 Deletedinuse: 99
% 25.21/25.58
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58
% 25.21/25.58 Intermediate Status:
% 25.21/25.58 Generated: 361322
% 25.21/25.58 Kept: 44587
% 25.21/25.58 Inuse: 1220
% 25.21/25.58 Deleted: 4502
% 25.21/25.58 Deletedinuse: 102
% 25.21/25.58
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58
% 25.21/25.58 Intermediate Status:
% 25.21/25.58 Generated: 368459
% 25.21/25.58 Kept: 46805
% 25.21/25.58 Inuse: 1237
% 25.21/25.58 Deleted: 4504
% 25.21/25.58 Deletedinuse: 104
% 25.21/25.58
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58 *** allocated 864960 integers for termspace/termends
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58
% 25.21/25.58 Intermediate Status:
% 25.21/25.58 Generated: 376710
% 25.21/25.58 Kept: 48815
% 25.21/25.58 Inuse: 1241
% 25.21/25.58 Deleted: 4504
% 25.21/25.58 Deletedinuse: 104
% 25.21/25.58
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58
% 25.21/25.58 Intermediate Status:
% 25.21/25.58 Generated: 380774
% 25.21/25.58 Kept: 51351
% 25.21/25.58 Inuse: 1245
% 25.21/25.58 Deleted: 4504
% 25.21/25.58 Deletedinuse: 104
% 25.21/25.58
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58
% 25.21/25.58 Intermediate Status:
% 25.21/25.58 Generated: 385415
% 25.21/25.58 Kept: 53936
% 25.21/25.58 Inuse: 1250
% 25.21/25.58 Deleted: 4504
% 25.21/25.58 Deletedinuse: 104
% 25.21/25.58
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58 *** allocated 4378860 integers for clauses
% 25.21/25.58
% 25.21/25.58 Intermediate Status:
% 25.21/25.58 Generated: 389721
% 25.21/25.58 Kept: 56528
% 25.21/25.58 Inuse: 1255
% 25.21/25.58 Deleted: 4504
% 25.21/25.58 Deletedinuse: 104
% 25.21/25.58
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58
% 25.21/25.58 Intermediate Status:
% 25.21/25.58 Generated: 393991
% 25.21/25.58 Kept: 58630
% 25.21/25.58 Inuse: 1260
% 25.21/25.58 Deleted: 4504
% 25.21/25.58 Deletedinuse: 104
% 25.21/25.58
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58
% 25.21/25.58 Intermediate Status:
% 25.21/25.58 Generated: 404144
% 25.21/25.58 Kept: 61288
% 25.21/25.58 Inuse: 1265
% 25.21/25.58 Deleted: 4504
% 25.21/25.58 Deletedinuse: 104
% 25.21/25.58
% 25.21/25.58 Resimplifying inuse:
% 25.21/25.58 Done
% 25.21/25.58
% 25.21/25.58 Resimplifying clauses:
% 25.21/25.58
% 25.21/25.58 Bliksems!, er is een bewijs:
% 25.21/25.58 % SZS status Theorem
% 25.21/25.58 % SZS output start Refutation
% 25.21/25.58
% 25.21/25.58 (8) {G0,W16,D3,L5,V3,M5} I { ! relation( X ), ! function( X ), in( Y,
% 25.21/25.58 relation_dom( X ) ), ! Z = apply( X, Y ), Z = empty_set }.
% 25.21/25.58 (12) {G0,W6,D3,L2,V2,M2} I { ! relation( X ), relation(
% 25.21/25.58 relation_dom_restriction( X, Y ) ) }.
% 25.21/25.58 (22) {G0,W8,D3,L3,V2,M3} I { ! relation( X ), ! function( X ), function(
% 25.21/25.58 relation_dom_restriction( X, Y ) ) }.
% 25.21/25.58 (27) {G0,W14,D4,L4,V3,M4} I { ! relation( X ), ! function( X ), ! in( Z,
% 25.21/25.58 relation_dom( relation_dom_restriction( X, Y ) ) ), in( Z, relation_dom(
% 25.21/25.58 X ) ) }.
% 25.21/25.58 (29) {G0,W17,D4,L5,V3,M5} I { ! relation( X ), ! function( X ), ! in( Z,
% 25.21/25.58 relation_dom( X ) ), ! in( Z, Y ), in( Z, relation_dom(
% 25.21/25.58 relation_dom_restriction( X, Y ) ) ) }.
% 25.21/25.58 (50) {G0,W16,D3,L6,V3,M6} I { ! relation( X ), ! function( X ), ! relation
% 25.21/25.58 ( Y ), ! function( Y ), ! X = relation_dom_restriction( Y, Z ), alpha1( X
% 25.21/25.58 , Y ) }.
% 25.21/25.58 (52) {G0,W14,D3,L3,V3,M3} I { ! alpha1( X, Y ), ! in( Z, relation_dom( X )
% 25.21/25.58 ), apply( X, Z ) = apply( Y, Z ) }.
% 25.21/25.58 (56) {G0,W2,D2,L1,V0,M1} I { relation( skol11 ) }.
% 25.21/25.58 (57) {G0,W2,D2,L1,V0,M1} I { function( skol11 ) }.
% 25.21/25.58 (58) {G0,W3,D2,L1,V0,M1} I { in( skol13, skol12 ) }.
% 25.21/25.58 (59) {G0,W9,D4,L1,V0,M1} I { ! apply( relation_dom_restriction( skol11,
% 25.21/25.58 skol12 ), skol13 ) ==> apply( skol11, skol13 ) }.
% 25.21/25.58 (64) {G1,W13,D3,L4,V2,M4} Q(8) { ! relation( X ), ! function( X ), in( Y,
% 25.21/25.58 relation_dom( X ) ), apply( X, Y ) ==> empty_set }.
% 25.21/25.58 (182) {G1,W4,D3,L1,V1,M1} R(12,56) { relation( relation_dom_restriction(
% 25.21/25.58 skol11, X ) ) }.
% 25.21/25.58 (296) {G1,W4,D3,L1,V1,M1} R(22,56);r(57) { function(
% 25.21/25.58 relation_dom_restriction( skol11, X ) ) }.
% 25.21/25.58 (367) {G1,W10,D4,L2,V2,M2} R(27,56);r(57) { ! in( X, relation_dom(
% 25.21/25.58 relation_dom_restriction( skol11, Y ) ) ), in( X, relation_dom( skol11 )
% 25.21/25.58 ) }.
% 25.21/25.58 (438) {G1,W13,D4,L3,V2,M3} R(29,56);r(57) { ! in( X, relation_dom( skol11 )
% 25.21/25.58 ), ! in( X, Y ), in( X, relation_dom( relation_dom_restriction( skol11,
% 25.21/25.58 Y ) ) ) }.
% 25.21/25.58 (602) {G1,W12,D3,L4,V2,M4} R(50,56);r(57) { ! relation( X ), ! function( X
% 25.21/25.58 ), ! X = relation_dom_restriction( skol11, Y ), alpha1( X, skol11 ) }.
% 25.21/25.58 (606) {G2,W9,D3,L2,V1,M2} Q(602);r(182) { ! function(
% 25.21/25.58 relation_dom_restriction( skol11, X ) ), alpha1( relation_dom_restriction
% 25.21/25.58 ( skol11, X ), skol11 ) }.
% 25.21/25.58 (721) {G1,W18,D4,L3,V1,M3} P(52,59) { ! apply( X, skol13 ) = apply( skol11
% 25.21/25.58 , skol13 ), ! alpha1( relation_dom_restriction( skol11, skol12 ), X ), !
% 25.21/25.58 in( skol13, relation_dom( relation_dom_restriction( skol11, skol12 ) ) )
% 25.21/25.58 }.
% 25.21/25.58 (737) {G2,W11,D4,L2,V0,M2} Q(721) { ! alpha1( relation_dom_restriction(
% 25.21/25.58 skol11, skol12 ), skol11 ), ! in( skol13, relation_dom(
% 25.21/25.58 relation_dom_restriction( skol11, skol12 ) ) ) }.
% 25.21/25.58 (20455) {G3,W5,D3,L1,V1,M1} S(606);r(296) { alpha1(
% 25.21/25.58 relation_dom_restriction( skol11, X ), skol11 ) }.
% 25.21/25.58 (40677) {G4,W6,D4,L1,V0,M1} S(737);r(20455) { ! in( skol13, relation_dom(
% 25.21/25.58 relation_dom_restriction( skol11, skol12 ) ) ) }.
% 25.21/25.58 (40680) {G5,W4,D3,L1,V0,M1} R(40677,438);r(58) { ! in( skol13, relation_dom
% 25.21/25.58 ( skol11 ) ) }.
% 25.21/25.58 (40803) {G6,W6,D4,L1,V1,M1} R(40680,367) { ! in( skol13, relation_dom(
% 25.21/25.58 relation_dom_restriction( skol11, X ) ) ) }.
% 25.21/25.58 (40805) {G6,W7,D3,L2,V0,M2} R(40680,64);r(56) { ! function( skol11 ), apply
% 25.21/25.58 ( skol11, skol13 ) ==> empty_set }.
% 25.21/25.58 (41041) {G7,W5,D3,L1,V0,M1} S(40805);r(57) { apply( skol11, skol13 ) ==>
% 25.21/25.58 empty_set }.
% 25.21/25.58 (42075) {G8,W7,D4,L1,V0,M1} S(59);d(41041) { ! apply(
% 25.21/25.58 relation_dom_restriction( skol11, skol12 ), skol13 ) ==> empty_set }.
% 25.21/25.58 (42076) {G9,W10,D4,L2,V0,M2} R(42075,64);r(182) { ! function(
% 25.21/25.58 relation_dom_restriction( skol11, skol12 ) ), in( skol13, relation_dom(
% 25.21/25.58 relation_dom_restriction( skol11, skol12 ) ) ) }.
% 25.21/25.58 (61302) {G10,W0,D0,L0,V0,M0} S(42076);r(296);r(40803) { }.
% 25.21/25.58
% 25.21/25.58
% 25.21/25.58 % SZS output end Refutation
% 25.21/25.58 found a proof!
% 25.21/25.58
% 25.21/25.58
% 25.21/25.58 Unprocessed initial clauses:
% 25.21/25.58
% 25.21/25.58 (61304) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), ! in( Y, X ) }.
% 25.21/25.58 (61305) {G0,W4,D2,L2,V1,M2} { ! empty( X ), function( X ) }.
% 25.21/25.58 (61306) {G0,W4,D2,L2,V1,M2} { ! empty( X ), relation( X ) }.
% 25.21/25.58 (61307) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 25.21/25.58 ), relation( X ) }.
% 25.21/25.58 (61308) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 25.21/25.58 ), function( X ) }.
% 25.21/25.58 (61309) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 25.21/25.58 ), one_to_one( X ) }.
% 25.21/25.58 (61310) {G0,W7,D3,L1,V2,M1} { unordered_pair( X, Y ) = unordered_pair( Y,
% 25.21/25.58 X ) }.
% 25.21/25.58 (61311) {G0,W7,D3,L1,V2,M1} { set_intersection2( X, Y ) =
% 25.21/25.58 set_intersection2( Y, X ) }.
% 25.21/25.58 (61312) {G0,W18,D3,L5,V3,M5} { ! relation( X ), ! function( X ), ! in( Y,
% 25.21/25.58 relation_dom( X ) ), ! Z = apply( X, Y ), in( ordered_pair( Y, Z ), X )
% 25.21/25.58 }.
% 25.21/25.58 (61313) {G0,W18,D3,L5,V3,M5} { ! relation( X ), ! function( X ), ! in( Y,
% 25.21/25.58 relation_dom( X ) ), ! in( ordered_pair( Y, Z ), X ), Z = apply( X, Y )
% 25.21/25.58 }.
% 25.21/25.58 (61314) {G0,W16,D3,L5,V3,M5} { ! relation( X ), ! function( X ), in( Y,
% 25.21/25.58 relation_dom( X ) ), ! Z = apply( X, Y ), Z = empty_set }.
% 25.21/25.58 (61315) {G0,W16,D3,L5,V3,M5} { ! relation( X ), ! function( X ), in( Y,
% 25.21/25.58 relation_dom( X ) ), ! Z = empty_set, Z = apply( X, Y ) }.
% 25.21/25.58 (61316) {G0,W10,D4,L1,V2,M1} { ordered_pair( X, Y ) = unordered_pair(
% 25.21/25.58 unordered_pair( X, Y ), singleton( X ) ) }.
% 25.21/25.58 (61317) {G0,W1,D1,L1,V0,M1} { && }.
% 25.21/25.58 (61318) {G0,W1,D1,L1,V0,M1} { && }.
% 25.21/25.58 (61319) {G0,W1,D1,L1,V0,M1} { && }.
% 25.21/25.58 (61320) {G0,W1,D1,L1,V0,M1} { && }.
% 25.21/25.58 (61321) {G0,W1,D1,L1,V0,M1} { && }.
% 25.21/25.58 (61322) {G0,W1,D1,L1,V0,M1} { && }.
% 25.21/25.58 (61323) {G0,W1,D1,L1,V0,M1} { && }.
% 25.21/25.58 (61324) {G0,W6,D3,L2,V2,M2} { ! relation( X ), relation(
% 25.21/25.58 relation_dom_restriction( X, Y ) ) }.
% 25.21/25.58 (61325) {G0,W1,D1,L1,V0,M1} { && }.
% 25.21/25.58 (61326) {G0,W4,D3,L1,V1,M1} { element( skol1( X ), X ) }.
% 25.21/25.58 (61327) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 25.21/25.58 (61328) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 25.21/25.58 (61329) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( empty_set ) }.
% 25.21/25.58 (61330) {G0,W8,D3,L3,V2,M3} { ! relation( X ), ! relation_empty_yielding(
% 25.21/25.58 X ), relation( relation_dom_restriction( X, Y ) ) }.
% 25.21/25.58 (61331) {G0,W8,D3,L3,V2,M3} { ! relation( X ), ! relation_empty_yielding(
% 25.21/25.58 X ), relation_empty_yielding( relation_dom_restriction( X, Y ) ) }.
% 25.21/25.58 (61332) {G0,W8,D3,L3,V2,M3} { ! relation( X ), ! relation( Y ), relation(
% 25.21/25.58 set_intersection2( X, Y ) ) }.
% 25.21/25.58 (61333) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 25.21/25.58 (61334) {G0,W4,D3,L1,V2,M1} { ! empty( ordered_pair( X, Y ) ) }.
% 25.21/25.58 (61335) {G0,W3,D3,L1,V1,M1} { ! empty( singleton( X ) ) }.
% 25.21/25.58 (61336) {G0,W4,D3,L1,V2,M1} { ! empty( unordered_pair( X, Y ) ) }.
% 25.21/25.58 (61337) {G0,W8,D3,L3,V2,M3} { ! relation( X ), ! function( X ), relation(
% 25.21/25.58 relation_dom_restriction( X, Y ) ) }.
% 25.21/25.58 (61338) {G0,W8,D3,L3,V2,M3} { ! relation( X ), ! function( X ), function(
% 25.21/25.58 relation_dom_restriction( X, Y ) ) }.
% 25.21/25.58 (61339) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 25.21/25.58 (61340) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 25.21/25.58 (61341) {G0,W7,D3,L3,V1,M3} { empty( X ), ! relation( X ), ! empty(
% 25.21/25.58 relation_dom( X ) ) }.
% 25.21/25.58 (61342) {G0,W5,D3,L2,V1,M2} { ! empty( X ), empty( relation_dom( X ) ) }.
% 25.21/25.58 (61343) {G0,W5,D3,L2,V1,M2} { ! empty( X ), relation( relation_dom( X ) )
% 25.21/25.58 }.
% 25.21/25.58 (61344) {G0,W5,D3,L1,V1,M1} { set_intersection2( X, X ) = X }.
% 25.21/25.58 (61345) {G0,W14,D4,L4,V3,M4} { ! relation( X ), ! function( X ), ! in( Z,
% 25.21/25.58 relation_dom( relation_dom_restriction( X, Y ) ) ), in( Z, relation_dom(
% 25.21/25.58 X ) ) }.
% 25.21/25.58 (61346) {G0,W13,D4,L4,V3,M4} { ! relation( X ), ! function( X ), ! in( Z,
% 25.21/25.58 relation_dom( relation_dom_restriction( X, Y ) ) ), in( Z, Y ) }.
% 25.21/25.58 (61347) {G0,W17,D4,L5,V3,M5} { ! relation( X ), ! function( X ), ! in( Z,
% 25.21/25.58 relation_dom( X ) ), ! in( Z, Y ), in( Z, relation_dom(
% 25.21/25.58 relation_dom_restriction( X, Y ) ) ) }.
% 25.21/25.58 (61348) {G0,W2,D2,L1,V0,M1} { relation( skol2 ) }.
% 25.21/25.58 (61349) {G0,W2,D2,L1,V0,M1} { function( skol2 ) }.
% 25.21/25.58 (61350) {G0,W2,D2,L1,V0,M1} { empty( skol3 ) }.
% 25.21/25.58 (61351) {G0,W2,D2,L1,V0,M1} { relation( skol3 ) }.
% 25.21/25.58 (61352) {G0,W2,D2,L1,V0,M1} { empty( skol4 ) }.
% 25.21/25.58 (61353) {G0,W2,D2,L1,V0,M1} { relation( skol5 ) }.
% 25.21/25.58 (61354) {G0,W2,D2,L1,V0,M1} { empty( skol5 ) }.
% 25.21/25.58 (61355) {G0,W2,D2,L1,V0,M1} { function( skol5 ) }.
% 25.21/25.58 (61356) {G0,W2,D2,L1,V0,M1} { ! empty( skol6 ) }.
% 25.21/25.58 (61357) {G0,W2,D2,L1,V0,M1} { relation( skol6 ) }.
% 25.21/25.58 (61358) {G0,W2,D2,L1,V0,M1} { ! empty( skol7 ) }.
% 25.21/25.58 (61359) {G0,W2,D2,L1,V0,M1} { relation( skol8 ) }.
% 25.21/25.58 (61360) {G0,W2,D2,L1,V0,M1} { function( skol8 ) }.
% 25.21/25.58 (61361) {G0,W2,D2,L1,V0,M1} { one_to_one( skol8 ) }.
% 25.21/25.58 (61362) {G0,W2,D2,L1,V0,M1} { relation( skol9 ) }.
% 25.21/25.58 (61363) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( skol9 ) }.
% 25.21/25.58 (61364) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), element( X, Y ) }.
% 25.21/25.58 (61365) {G0,W5,D3,L1,V1,M1} { set_intersection2( X, empty_set ) =
% 25.21/25.58 empty_set }.
% 25.21/25.58 (61366) {G0,W8,D2,L3,V2,M3} { ! element( X, Y ), empty( Y ), in( X, Y )
% 25.21/25.58 }.
% 25.21/25.58 (61367) {G0,W20,D4,L6,V3,M6} { ! relation( X ), ! function( X ), !
% 25.21/25.58 relation( Y ), ! function( Y ), ! X = relation_dom_restriction( Y, Z ),
% 25.21/25.58 relation_dom( X ) = set_intersection2( relation_dom( Y ), Z ) }.
% 25.21/25.58 (61368) {G0,W16,D3,L6,V3,M6} { ! relation( X ), ! function( X ), !
% 25.21/25.58 relation( Y ), ! function( Y ), ! X = relation_dom_restriction( Y, Z ),
% 25.21/25.58 alpha1( X, Y ) }.
% 25.21/25.58 (61369) {G0,W23,D4,L7,V3,M7} { ! relation( X ), ! function( X ), !
% 25.21/25.58 relation( Y ), ! function( Y ), ! relation_dom( X ) = set_intersection2(
% 25.21/25.58 relation_dom( Y ), Z ), ! alpha1( X, Y ), X = relation_dom_restriction( Y
% 25.21/25.58 , Z ) }.
% 25.21/25.58 (61370) {G0,W14,D3,L3,V3,M3} { ! alpha1( X, Y ), ! in( Z, relation_dom( X
% 25.21/25.58 ) ), apply( X, Z ) = apply( Y, Z ) }.
% 25.21/25.58 (61371) {G0,W9,D3,L2,V3,M2} { in( skol10( X, Z ), relation_dom( X ) ),
% 25.21/25.58 alpha1( X, Y ) }.
% 25.21/25.58 (61372) {G0,W14,D4,L2,V2,M2} { ! apply( X, skol10( X, Y ) ) = apply( Y,
% 25.21/25.58 skol10( X, Y ) ), alpha1( X, Y ) }.
% 25.21/25.58 (61373) {G0,W5,D2,L2,V1,M2} { ! empty( X ), X = empty_set }.
% 25.21/25.58 (61374) {G0,W2,D2,L1,V0,M1} { relation( skol11 ) }.
% 25.21/25.58 (61375) {G0,W2,D2,L1,V0,M1} { function( skol11 ) }.
% 25.21/25.58 (61376) {G0,W3,D2,L1,V0,M1} { in( skol13, skol12 ) }.
% 25.21/25.58 (61377) {G0,W9,D4,L1,V0,M1} { ! apply( relation_dom_restriction( skol11,
% 25.21/25.58 skol12 ), skol13 ) = apply( skol11, skol13 ) }.
% 25.21/25.58 (61378) {G0,W5,D2,L2,V2,M2} { ! in( X, Y ), ! empty( Y ) }.
% 25.21/25.58 (61379) {G0,W7,D2,L3,V2,M3} { ! empty( X ), X = Y, ! empty( Y ) }.
% 25.21/25.58
% 25.21/25.58
% 25.21/25.58 Total Proof:
% 25.21/25.58
% 25.21/25.58 subsumption: (8) {G0,W16,D3,L5,V3,M5} I { ! relation( X ), ! function( X )
% 25.21/25.58 , in( Y, relation_dom( X ) ), ! Z = apply( X, Y ), Z = empty_set }.
% 25.21/25.58 parent0: (61314) {G0,W16,D3,L5,V3,M5} { ! relation( X ), ! function( X ),
% 25.21/25.58 in( Y, relation_dom( X ) ), ! Z = apply( X, Y ), Z = empty_set }.
% 25.21/25.58 substitution0:
% 25.21/25.58 X := X
% 25.21/25.58 Y := Y
% 25.21/25.58 Z := Z
% 25.21/25.58 end
% 25.21/25.58 permutation0:
% 25.21/25.58 0 ==> 0
% 25.21/25.58 1 ==> 1
% 25.21/25.58 2 ==> 2
% 25.21/25.58 3 ==> 3
% 25.21/25.58 4 ==> 4
% 25.21/25.58 end
% 25.21/25.58
% 25.21/25.58 subsumption: (12) {G0,W6,D3,L2,V2,M2} I { ! relation( X ), relation(
% 25.21/25.58 relation_dom_restriction( X, Y ) ) }.
% 25.21/25.58 parent0: (61324) {G0,W6,D3,L2,V2,M2} { ! relation( X ), relation(
% 25.21/25.58 relation_dom_restriction( X, Y ) ) }.
% 25.21/25.58 substitution0:
% 25.21/25.58 X := X
% 25.21/25.58 Y := Y
% 25.21/25.58 end
% 25.21/25.58 permutation0:
% 25.21/25.58 0 ==> 0
% 25.21/25.58 1 ==> 1
% 25.21/25.58 end
% 25.21/25.58
% 25.21/25.58 subsumption: (22) {G0,W8,D3,L3,V2,M3} I { ! relation( X ), ! function( X )
% 25.21/25.58 , function( relation_dom_restriction( X, Y ) ) }.
% 25.21/25.58 parent0: (61338) {G0,W8,D3,L3,V2,M3} { ! relation( X ), ! function( X ),
% 25.21/25.58 function( relation_dom_restriction( X, Y ) ) }.
% 25.21/25.58 substitution0:
% 25.21/25.58 X := X
% 25.21/25.58 Y := Y
% 25.21/25.58 end
% 25.21/25.58 permutation0:
% 25.21/25.58 0 ==> 0
% 25.21/25.58 1 ==> 1
% 25.21/25.58 2 ==> 2
% 25.21/25.58 end
% 25.21/25.58
% 25.21/25.58 subsumption: (27) {G0,W14,D4,L4,V3,M4} I { ! relation( X ), ! function( X )
% 25.21/25.58 , ! in( Z, relation_dom( relation_dom_restriction( X, Y ) ) ), in( Z,
% 25.21/25.58 relation_dom( X ) ) }.
% 25.21/25.58 parent0: (61345) {G0,W14,D4,L4,V3,M4} { ! relation( X ), ! function( X ),
% 25.21/25.58 ! in( Z, relation_dom( relation_dom_restriction( X, Y ) ) ), in( Z,
% 25.21/25.58 relation_dom( X ) ) }.
% 25.21/25.58 substitution0:
% 25.21/25.58 X := X
% 25.21/25.58 Y := Y
% 25.21/25.58 Z := Z
% 25.21/25.58 end
% 25.21/25.58 permutation0:
% 25.21/25.58 0 ==> 0
% 25.21/25.58 1 ==> 1
% 25.21/25.58 2 ==> 2
% 25.21/25.58 3 ==> 3
% 25.21/25.58 end
% 25.21/25.58
% 25.21/25.58 subsumption: (29) {G0,W17,D4,L5,V3,M5} I { ! relation( X ), ! function( X )
% 25.21/25.58 , ! in( Z, relation_dom( X ) ), ! in( Z, Y ), in( Z, relation_dom(
% 25.21/25.58 relation_dom_restriction( X, Y ) ) ) }.
% 25.21/25.58 parent0: (61347) {G0,W17,D4,L5,V3,M5} { ! relation( X ), ! function( X ),
% 25.21/25.58 ! in( Z, relation_dom( X ) ), ! in( Z, Y ), in( Z, relation_dom(
% 25.21/25.58 relation_dom_restriction( X, Y ) ) ) }.
% 25.21/25.58 substitution0:
% 25.21/25.58 X := X
% 25.21/25.58 Y := Y
% 25.21/25.58 Z := Z
% 25.21/25.58 end
% 25.21/25.58 permutation0:
% 25.21/25.58 0 ==> 0
% 25.21/25.58 1 ==> 1
% 25.21/25.58 2 ==> 2
% 25.21/25.58 3 ==> 3
% 25.21/25.58 4 ==> 4
% 25.21/25.58 end
% 25.21/25.58
% 25.21/25.58 subsumption: (50) {G0,W16,D3,L6,V3,M6} I { ! relation( X ), ! function( X )
% 25.21/25.58 , ! relation( Y ), ! function( Y ), ! X = relation_dom_restriction( Y, Z
% 25.21/25.58 ), alpha1( X, Y ) }.
% 25.21/25.58 parent0: (61368) {G0,W16,D3,L6,V3,M6} { ! relation( X ), ! function( X ),
% 25.21/25.58 ! relation( Y ), ! function( Y ), ! X = relation_dom_restriction( Y, Z )
% 25.21/25.58 , alpha1( X, Y ) }.
% 25.21/25.58 substitution0:
% 25.21/25.58 X := X
% 25.21/25.58 Y := Y
% 25.21/25.58 Z := Z
% 25.21/25.58 end
% 25.21/25.58 permutation0:
% 25.21/25.58 0 ==> 0
% 25.21/25.58 1 ==> 1
% 25.21/25.58 2 ==> 2
% 25.21/25.58 3 ==> 3
% 25.21/25.58 4 ==> 4
% 25.21/25.58 5 ==> 5
% 25.21/25.58 end
% 25.21/25.58
% 25.21/25.58 subsumption: (52) {G0,W14,D3,L3,V3,M3} I { ! alpha1( X, Y ), ! in( Z,
% 25.21/25.58 relation_dom( X ) ), apply( X, Z ) = apply( Y, Z ) }.
% 25.21/25.58 parent0: (61370) {G0,W14,D3,L3,V3,M3} { ! alpha1( X, Y ), ! in( Z,
% 25.21/25.58 relation_dom( X ) ), apply( X, Z ) = apply( Y, Z ) }.
% 25.21/25.58 substitution0:
% 25.21/25.58 X := X
% 25.21/25.58 Y := Y
% 25.21/25.58 Z := Z
% 25.21/25.58 end
% 25.21/25.58 permutation0:
% 25.21/25.58 0 ==> 0
% 25.21/25.58 1 ==> 1
% 25.21/25.58 2 ==> 2
% 25.21/25.58 end
% 25.21/25.58
% 25.21/25.58 subsumption: (56) {G0,W2,D2,L1,V0,M1} I { relation( skol11 ) }.
% 25.21/25.58 parent0: (61374) {G0,W2,D2,L1,V0,M1} { relation( skol11 ) }.
% 25.21/25.58 substitution0:
% 25.21/25.58 end
% 25.21/25.58 permutation0:
% 25.21/25.58 0 ==> 0
% 25.21/25.58 end
% 25.21/25.58
% 25.21/25.58 subsumption: (57) {G0,W2,D2,L1,V0,M1} I { function( skol11 ) }.
% 25.21/25.58 parent0: (61375) {G0,W2,D2,L1,V0,M1} { function( skol11 ) }.
% 25.21/25.58 substitution0:
% 25.21/25.58 end
% 25.21/25.58 permutation0:
% 25.21/25.58 0 ==> 0
% 25.21/25.58 end
% 25.21/25.58
% 25.21/25.58 subsumption: (58) {G0,W3,D2,L1,V0,M1} I { in( skol13, skol12 ) }.
% 25.21/25.58 parent0: (61376) {G0,W3,D2,L1,V0,M1} { in( skol13, skol12 ) }.
% 25.21/25.58 substitution0:
% 25.21/25.58 end
% 25.21/25.58 permutation0:
% 25.21/25.58 0 ==> 0
% 25.21/25.58 end
% 25.21/25.58
% 25.21/25.58 subsumption: (59) {G0,W9,D4,L1,V0,M1} I { ! apply( relation_dom_restriction
% 25.21/25.58 ( skol11, skol12 ), skol13 ) ==> apply( skol11, skol13 ) }.
% 25.21/25.58 parent0: (61377) {G0,W9,D4,L1,V0,M1} { ! apply( relation_dom_restriction(
% 25.21/25.58 skol11, skol12 ), skol13 ) = apply( skol11, skol13 ) }.
% 25.21/25.58 substitution0:
% 25.21/25.58 end
% 25.21/25.58 permutation0:
% 25.21/25.58 0 ==> 0
% 25.21/25.58 end
% 25.21/25.58
% 25.21/25.58 eqswap: (61681) {G0,W16,D3,L5,V3,M5} { ! apply( Y, Z ) = X, ! relation( Y
% 25.21/25.58 ), ! function( Y ), in( Z, relation_dom( Y ) ), X = empty_set }.
% 25.21/25.58 parent0[3]: (8) {G0,W16,D3,L5,V3,M5} I { ! relation( X ), ! function( X ),
% 25.21/25.58 in( Y, relation_dom( X ) ), ! Z = apply( X, Y ), Z = empty_set }.
% 25.21/25.58 substitution0:
% 25.21/25.58 X := Y
% 25.21/25.58 Y := Z
% 25.21/25.58 Z := X
% 25.21/25.58 end
% 25.21/25.58
% 25.21/25.58 eqrefl: (61684) {G0,W13,D3,L4,V2,M4} { ! relation( X ), ! function( X ),
% 25.21/25.58 in( Y, relation_dom( X ) ), apply( X, Y ) = empty_set }.
% 25.21/25.58 parent0[0]: (61681) {G0,W16,D3,L5,V3,M5} { ! apply( Y, Z ) = X, ! relation
% 25.21/25.58 ( Y ), ! function( Y ), in( Z, relation_dom( Y ) ), X = empty_set }.
% 25.21/25.58 substitution0:
% 25.21/25.58 X := apply( X, Y )
% 25.21/25.58 Y := X
% 25.21/25.58 Z := Y
% 25.21/25.58 end
% 25.21/25.58
% 25.21/25.58 subsumption: (64) {G1,W13,D3,L4,V2,M4} Q(8) { ! relation( X ), ! function(
% 25.21/25.58 X ), in( Y, relation_dom( X ) ), apply( X, Y ) ==> empty_set }.
% 25.21/25.58 parent0: (61684) {G0,W13,D3,L4,V2,M4} { ! relation( X ), ! function( X ),
% 25.21/25.58 in( Y, relation_dom( X ) ), apply( X, Y ) = empty_set }.
% 25.21/25.58 substitution0:
% 25.21/25.58 X := X
% 25.21/25.58 Y := Y
% 25.21/25.58 end
% 25.21/25.58 permutation0:
% 25.21/25.58 0 ==> 0
% 25.21/25.58 1 ==> 1
% 25.21/25.58 2 ==> 2
% 25.21/25.58 3 ==> 3
% 25.21/25.58 end
% 25.21/25.58
% 25.21/25.58 resolution: (61686) {G1,W4,D3,L1,V1,M1} { relation(
% 25.21/25.58 relation_dom_restriction( skol11, X ) ) }.
% 25.21/25.58 parent0[0]: (12) {G0,W6,D3,L2,V2,M2} I { ! relation( X ), relation(
% 25.21/25.58 relation_dom_restriction( X, Y ) ) }.
% 25.21/25.58 parent1[0]: (56) {G0,W2,D2,L1,V0,M1} I { relation( skol11 ) }.
% 25.21/25.58 substitution0:
% 25.21/25.58 X := skol11
% 25.21/25.58 Y := X
% 25.21/25.58 end
% 25.21/25.58 substitution1:
% 25.21/25.58 end
% 25.21/25.58
% 25.21/25.58 subsumption: (182) {G1,W4,D3,L1,V1,M1} R(12,56) { relation(
% 25.21/25.58 relation_dom_restriction( skol11, X ) ) }.
% 25.21/25.58 parent0: (61686) {G1,W4,D3,L1,V1,M1} { relation( relation_dom_restriction
% 25.21/25.58 ( skol11, X ) ) }.
% 25.21/25.58 substitution0:
% 25.21/25.58 X := X
% 25.21/25.58 end
% 25.21/25.58 permutation0:
% 25.21/25.58 0 ==> 0
% 25.21/25.58 end
% 25.21/25.58
% 25.21/25.58 resolution: (61687) {G1,W6,D3,L2,V1,M2} { ! function( skol11 ), function(
% 25.21/25.58 relation_dom_restriction( skol11, X ) ) }.
% 25.21/25.58 parent0[0]: (22) {G0,W8,D3,L3,V2,M3} I { ! relation( X ), ! function( X ),
% 25.21/25.58 function( relation_dom_restriction( X, Y ) ) }.
% 25.21/25.58 parent1[0]: (56) {G0,W2,D2,L1,V0,M1} I { relation( skol11 ) }.
% 25.21/25.58 substitution0:
% 25.21/25.58 X := skol11
% 25.21/25.58 Y := X
% 25.21/25.58 end
% 25.21/25.58 substitution1:
% 25.21/25.58 end
% 25.21/25.58
% 25.21/25.58 resolution: (61688) {G1,W4,D3,L1,V1,M1} { function(
% 25.21/25.58 relation_dom_restriction( skol11, X ) ) }.
% 25.21/25.58 parent0[0]: (61687) {G1,W6,D3,L2,V1,M2} { ! function( skol11 ), function(
% 25.21/25.58 relation_dom_restriction( skol11, X ) ) }.
% 25.21/25.58 parent1[0]: (57) {G0,W2,D2,L1,V0,M1} I { function( skol11 ) }.
% 25.21/25.58 substitution0:
% 25.21/25.58 X := X
% 25.21/25.58 end
% 25.21/25.58 substitution1:
% 25.21/25.58 end
% 25.21/25.58
% 25.21/25.58 subsumption: (296) {G1,W4,D3,L1,V1,M1} R(22,56);r(57) { function(
% 25.21/25.58 relation_dom_restriction( skol11, X ) ) }.
% 25.21/25.58 parent0: (61688) {G1,W4,D3,L1,V1,M1} { function( relation_dom_restriction
% 25.21/25.58 ( skol11, X ) ) }.
% 25.21/25.58 substitution0:
% 25.21/25.58 X := X
% 25.21/25.58 end
% 25.21/25.58 permutation0:
% 25.21/25.58 0 ==> 0
% 25.21/25.58 end
% 25.21/25.58
% 25.21/25.58 resolution: (61689) {G1,W12,D4,L3,V2,M3} { ! function( skol11 ), ! in( X,
% 25.21/25.58 relation_dom( relation_dom_restriction( skol11, Y ) ) ), in( X,
% 25.21/25.58 relation_dom( skol11 ) ) }.
% 25.21/25.58 parent0[0]: (27) {G0,W14,D4,L4,V3,M4} I { ! relation( X ), ! function( X )
% 25.21/25.58 , ! in( Z, relation_dom( relation_dom_restriction( X, Y ) ) ), in( Z,
% 25.21/25.58 relation_dom( X ) ) }.
% 25.21/25.58 parent1[0]: (56) {G0,W2,D2,L1,V0,M1} I { relation( skol11 ) }.
% 25.21/25.58 substitution0:
% 25.21/25.58 X := skol11
% 25.21/25.58 Y := Y
% 25.21/25.58 Z := X
% 25.21/25.58 end
% 25.21/25.58 substitution1:
% 25.21/25.58 end
% 25.21/25.58
% 25.21/25.58 resolution: (61690) {G1,W10,D4,L2,V2,M2} { ! in( X, relation_dom(
% 25.21/25.58 relation_dom_restriction( skol11, Y ) ) ), in( X, relation_dom( skol11 )
% 25.21/25.58 ) }.
% 25.21/25.58 parent0[0]: (61689) {G1,W12,D4,L3,V2,M3} { ! function( skol11 ), ! in( X,
% 25.21/25.58 relation_dom( relation_dom_restriction( skol11, Y ) ) ), in( X,
% 25.21/25.58 relation_dom( skol11 ) ) }.
% 25.21/25.58 parent1[0]: (57) {G0,W2,D2,L1,V0,M1} I { function( skol11 ) }.
% 25.21/25.58 substitution0:
% 25.21/25.58 X := X
% 25.21/25.58 Y := Y
% 25.21/25.58 end
% 25.21/25.58 substitution1:
% 25.21/25.58 end
% 25.21/25.58
% 25.21/25.58 subsumption: (367) {G1,W10,D4,L2,V2,M2} R(27,56);r(57) { ! in( X,
% 25.21/25.58 relation_dom( relation_dom_restriction( skol11, Y ) ) ), in( X,
% 25.21/25.58 relation_dom( skol11 ) ) }.
% 25.21/25.58 parent0: (61690) {G1,W10,D4,L2,V2,M2} { ! in( X, relation_dom(
% 25.21/25.58 relation_dom_restriction( skol11, Y ) ) ), in( X, relation_dom( skol11 )
% 25.21/25.58 ) }.
% 25.21/25.58 substitution0:
% 25.21/25.58 X := X
% 25.21/25.58 Y := Y
% 25.21/25.58 end
% 25.21/25.58 permutation0:
% 25.21/25.58 0 ==> 0
% 25.21/25.58 1 ==> 1
% 25.21/25.58 end
% 25.21/25.58
% 25.21/25.58 resolution: (61691) {G1,W15,D4,L4,V2,M4} { ! function( skol11 ), ! in( X,
% 25.21/25.58 relation_dom( skol11 ) ), ! in( X, Y ), in( X, relation_dom(
% 25.21/25.58 relation_dom_restriction( skol11, Y ) ) ) }.
% 25.21/25.58 parent0[0]: (29) {G0,W17,D4,L5,V3,M5} I { ! relation( X ), ! function( X )
% 25.21/25.58 , ! in( Z, relation_dom( X ) ), ! in( Z, Y ), in( Z, relation_dom(
% 25.21/25.58 relation_dom_restriction( X, Y ) ) ) }.
% 25.21/25.58 parent1[0]: (56) {G0,W2,D2,L1,V0,M1} I { relation( skol11 ) }.
% 25.21/25.58 substitution0:
% 25.21/25.58 X := skol11
% 25.21/25.58 Y := Y
% 25.21/25.58 Z := X
% 25.21/25.58 end
% 25.21/25.58 substitution1:
% 25.21/25.58 end
% 25.21/25.58
% 25.21/25.58 resolution: (61694) {G1,W13,D4,L3,V2,M3} { ! in( X, relation_dom( skol11 )
% 25.21/25.58 ), ! in( X, Y ), in( X, relation_dom( relation_dom_restriction( skol11,
% 25.21/25.58 Y ) ) ) }.
% 25.21/25.58 parent0[0]: (61691) {G1,W15,D4,L4,V2,M4} { ! function( skol11 ), ! in( X,
% 25.21/25.58 relation_dom( skol11 ) ), ! in( X, Y ), in( X, relation_dom(
% 25.21/25.58 relation_dom_restriction( skol11, Y ) ) ) }.
% 25.21/25.58 parent1[0]: (57) {G0,W2,D2,L1,V0,M1} I { function( skol11 ) }.
% 25.21/25.58 substitution0:
% 25.21/25.58 X := X
% 25.21/25.58 Y := Y
% 25.21/25.58 end
% 25.21/25.58 substitution1:
% 25.21/25.58 end
% 25.21/25.58
% 25.21/25.58 subsumption: (438) {G1,W13,D4,L3,V2,M3} R(29,56);r(57) { ! in( X,
% 25.21/25.58 relation_dom( skol11 ) ), ! in( X, Y ), in( X, relation_dom(
% 25.21/25.58 relation_dom_restriction( skol11, Y ) ) ) }.
% 25.21/25.58 parent0: (61694) {G1,W13,D4,L3,V2,M3} { ! in( X, relation_dom( skol11 ) )
% 25.21/25.58 , ! in( X, Y ), in( X, relation_dom( relation_dom_restriction( skol11, Y
% 25.21/25.58 ) ) ) }.
% 25.21/25.58 substitution0:
% 25.21/25.58 X := X
% 25.21/25.58 Y := Y
% 25.21/25.58 end
% 25.21/25.58 permutation0:
% 25.21/25.58 0 ==> 0
% 25.21/25.58 1 ==> 1
% 25.21/25.58 2 ==> 2
% 25.21/25.58 end
% 25.21/25.58
% 25.21/25.58 eqswap: (61696) {G0,W16,D3,L6,V3,M6} { ! relation_dom_restriction( Y, Z )
% 25.21/25.58 = X, ! relation( X ), ! function( X ), ! relation( Y ), ! function( Y ),
% 25.21/25.58 alpha1( X, Y ) }.
% 25.21/25.58 parent0[4]: (50) {G0,W16,D3,L6,V3,M6} I { ! relation( X ), ! function( X )
% 25.21/25.58 , ! relation( Y ), ! function( Y ), ! X = relation_dom_restriction( Y, Z
% 25.21/25.58 ), alpha1( X, Y ) }.
% 25.21/25.58 substitution0:
% 25.21/25.58 X := X
% 25.21/25.58 Y := Y
% 25.21/25.58 Z := Z
% 25.21/25.58 end
% 25.21/25.58
% 25.21/25.58 resolution: (61698) {G1,W14,D3,L5,V2,M5} { ! relation_dom_restriction(
% 25.21/25.58 skol11, X ) = Y, ! relation( Y ), ! function( Y ), ! function( skol11 ),
% 25.21/25.58 alpha1( Y, skol11 ) }.
% 25.21/25.58 parent0[3]: (61696) {G0,W16,D3,L6,V3,M6} { ! relation_dom_restriction( Y,
% 25.21/25.58 Z ) = X, ! relation( X ), ! function( X ), ! relation( Y ), ! function( YCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------