TSTP Solution File: SEU292+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SEU292+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n005.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 07:12:11 EDT 2022
% Result : Theorem 59.78s 60.14s
% Output : Refutation 59.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU292+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n005.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 01:39:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.44/1.00 *** allocated 10000 integers for termspace/termends
% 0.44/1.00 *** allocated 10000 integers for clauses
% 0.44/1.00 *** allocated 10000 integers for justifications
% 0.44/1.00 Bliksem 1.12
% 0.44/1.00
% 0.44/1.00
% 0.44/1.00 Automatic Strategy Selection
% 0.44/1.00
% 0.44/1.00
% 0.44/1.00 Clauses:
% 0.44/1.00
% 0.44/1.00 { ! in( X, Y ), ! in( Y, X ) }.
% 0.44/1.00 { ! empty( X ), function( X ) }.
% 0.44/1.00 { ! empty( X ), relation( X ) }.
% 0.44/1.00 { ! element( X, powerset( cartesian_product2( Y, Z ) ) ), relation( X ) }.
% 0.44/1.00 { ! relation( X ), ! empty( X ), ! function( X ), relation( X ) }.
% 0.44/1.00 { ! relation( X ), ! empty( X ), ! function( X ), function( X ) }.
% 0.44/1.00 { ! relation( X ), ! empty( X ), ! function( X ), one_to_one( X ) }.
% 0.44/1.00 { ! relation_of2_as_subset( Z, X, Y ), alpha1( X, Y ), ! quasi_total( Z, X
% 0.44/1.00 , Y ), X = relation_dom_as_subset( X, Y, Z ) }.
% 0.44/1.00 { ! relation_of2_as_subset( Z, X, Y ), alpha1( X, Y ), ! X =
% 0.44/1.00 relation_dom_as_subset( X, Y, Z ), quasi_total( Z, X, Y ) }.
% 0.44/1.00 { ! relation_of2_as_subset( Z, X, Y ), ! Y = empty_set, X = empty_set, !
% 0.44/1.00 quasi_total( Z, X, Y ), Z = empty_set }.
% 0.44/1.00 { ! relation_of2_as_subset( Z, X, Y ), ! Y = empty_set, X = empty_set, ! Z
% 0.44/1.00 = empty_set, quasi_total( Z, X, Y ) }.
% 0.44/1.00 { ! alpha1( X, Y ), Y = empty_set }.
% 0.44/1.00 { ! alpha1( X, Y ), ! X = empty_set }.
% 0.44/1.00 { ! Y = empty_set, X = empty_set, alpha1( X, Y ) }.
% 0.44/1.00 { && }.
% 0.44/1.00 { && }.
% 0.44/1.00 { && }.
% 0.44/1.00 { && }.
% 0.44/1.00 { && }.
% 0.44/1.00 { ! relation_of2( Z, X, Y ), element( relation_dom_as_subset( X, Y, Z ),
% 0.44/1.00 powerset( X ) ) }.
% 0.44/1.00 { ! relation( X ), ! relation( Y ), relation( relation_composition( X, Y )
% 0.44/1.00 ) }.
% 0.44/1.00 { && }.
% 0.44/1.00 { && }.
% 0.44/1.00 { ! relation_of2_as_subset( Z, X, Y ), element( Z, powerset(
% 0.44/1.00 cartesian_product2( X, Y ) ) ) }.
% 0.44/1.00 { relation_of2( skol1( X, Y ), X, Y ) }.
% 0.44/1.00 { element( skol2( X ), X ) }.
% 0.44/1.00 { relation_of2_as_subset( skol3( X, Y ), X, Y ) }.
% 0.44/1.00 { ! empty( X ), ! relation( Y ), empty( relation_composition( Y, X ) ) }.
% 0.44/1.00 { ! empty( X ), ! relation( Y ), relation( relation_composition( Y, X ) ) }
% 0.44/1.00 .
% 0.44/1.00 { empty( empty_set ) }.
% 0.44/1.00 { relation( empty_set ) }.
% 0.44/1.00 { relation_empty_yielding( empty_set ) }.
% 0.44/1.00 { ! relation( X ), ! function( X ), ! relation( Y ), ! function( Y ),
% 0.44/1.00 relation( relation_composition( X, Y ) ) }.
% 0.44/1.00 { ! relation( X ), ! function( X ), ! relation( Y ), ! function( Y ),
% 0.44/1.00 function( relation_composition( X, Y ) ) }.
% 0.44/1.00 { ! empty( powerset( X ) ) }.
% 0.44/1.00 { empty( empty_set ) }.
% 0.44/1.00 { empty( empty_set ) }.
% 0.44/1.00 { relation( empty_set ) }.
% 0.44/1.00 { empty( X ), empty( Y ), ! empty( cartesian_product2( X, Y ) ) }.
% 0.44/1.00 { empty( X ), ! relation( X ), ! empty( relation_dom( X ) ) }.
% 0.44/1.00 { ! empty( X ), empty( relation_dom( X ) ) }.
% 0.44/1.00 { ! empty( X ), relation( relation_dom( X ) ) }.
% 0.44/1.00 { ! empty( X ), ! relation( Y ), empty( relation_composition( X, Y ) ) }.
% 0.44/1.00 { ! empty( X ), ! relation( Y ), relation( relation_composition( X, Y ) ) }
% 0.44/1.00 .
% 0.44/1.00 { relation( skol4 ) }.
% 0.44/1.00 { function( skol4 ) }.
% 0.44/1.00 { relation( skol5( Z, T ) ) }.
% 0.44/1.00 { function( skol5( Z, T ) ) }.
% 0.44/1.00 { relation_of2( skol5( X, Y ), X, Y ) }.
% 0.44/1.00 { quasi_total( skol5( X, Y ), X, Y ) }.
% 0.44/1.00 { relation( skol6 ) }.
% 0.44/1.00 { function( skol6 ) }.
% 0.44/1.00 { one_to_one( skol6 ) }.
% 0.44/1.00 { empty( skol6 ) }.
% 0.44/1.00 { empty( skol7 ) }.
% 0.44/1.00 { relation( skol7 ) }.
% 0.44/1.00 { empty( X ), ! empty( skol8( Y ) ) }.
% 0.44/1.00 { empty( X ), element( skol8( X ), powerset( X ) ) }.
% 0.44/1.00 { empty( skol9 ) }.
% 0.44/1.00 { relation( skol10 ) }.
% 0.44/1.00 { empty( skol10 ) }.
% 0.44/1.00 { function( skol10 ) }.
% 0.44/1.00 { relation( skol11( Z, T ) ) }.
% 0.44/1.00 { function( skol11( Z, T ) ) }.
% 0.44/1.00 { relation_of2( skol11( X, Y ), X, Y ) }.
% 0.44/1.00 { ! empty( skol12 ) }.
% 0.44/1.00 { relation( skol12 ) }.
% 0.44/1.00 { empty( skol13( Y ) ) }.
% 0.44/1.00 { element( skol13( X ), powerset( X ) ) }.
% 0.44/1.00 { ! empty( skol14 ) }.
% 0.44/1.00 { relation( skol15 ) }.
% 0.44/1.00 { function( skol15 ) }.
% 0.44/1.00 { one_to_one( skol15 ) }.
% 0.44/1.00 { relation( skol16 ) }.
% 0.44/1.00 { relation_empty_yielding( skol16 ) }.
% 0.44/1.00 { relation( skol17 ) }.
% 0.44/1.00 { relation_empty_yielding( skol17 ) }.
% 0.44/1.00 { function( skol17 ) }.
% 0.44/1.00 { ! relation_of2( Z, X, Y ), relation_dom_as_subset( X, Y, Z ) =
% 0.44/1.00 relation_dom( Z ) }.
% 0.44/1.00 { ! relation_of2_as_subset( Z, X, Y ), relation_of2( Z, X, Y ) }.
% 0.44/1.00 { ! relation_of2( Z, X, Y ), relation_of2_as_subset( Z, X, Y ) }.
% 0.44/1.00 { subset( X, X ) }.
% 0.44/1.00 { ! in( X, Y ), element( X, Y ) }.
% 0.44/1.00 { function( skol20 ) }.
% 0.44/1.00 { quasi_total( skol20, skol18, skol19 ) }.
% 0.44/1.00 { relation_of2_as_subset( skol20, skol18, skol19 ) }.
% 0.44/1.00 { relation( skol21 ) }.
% 0.44/1.00 { function( skol21 ) }.
% 0.44/1.00 { in( skol22, skol18 ) }.
% 0.44/1.00 { ! skol19 = empty_set }.
% 0.44/1.00 { ! apply( relation_composition( skol20, skol21 ), skol22 ) = apply( skol21
% 45.22/45.59 , apply( skol20, skol22 ) ) }.
% 45.22/45.59 { ! relation( X ), ! function( X ), ! relation( Y ), ! function( Y ), ! in
% 45.22/45.59 ( Z, relation_dom( X ) ), apply( relation_composition( X, Y ), Z ) =
% 45.22/45.59 apply( Y, apply( X, Z ) ) }.
% 45.22/45.59 { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 45.22/45.59 { ! element( X, powerset( Y ) ), subset( X, Y ) }.
% 45.22/45.59 { ! subset( X, Y ), element( X, powerset( Y ) ) }.
% 45.22/45.59 { ! in( X, Z ), ! element( Z, powerset( Y ) ), element( X, Y ) }.
% 45.22/45.59 { ! in( X, Y ), ! element( Y, powerset( Z ) ), ! empty( Z ) }.
% 45.22/45.59 { ! empty( X ), X = empty_set }.
% 45.22/45.59 { ! in( X, Y ), ! empty( Y ) }.
% 45.22/45.59 { ! empty( X ), X = Y, ! empty( Y ) }.
% 45.22/45.59
% 45.22/45.59 percentage equality = 0.113924, percentage horn = 0.909091
% 45.22/45.59 This is a problem with some equality
% 45.22/45.59
% 45.22/45.59
% 45.22/45.59
% 45.22/45.59 Options Used:
% 45.22/45.59
% 45.22/45.59 useres = 1
% 45.22/45.59 useparamod = 1
% 45.22/45.59 useeqrefl = 1
% 45.22/45.59 useeqfact = 1
% 45.22/45.59 usefactor = 1
% 45.22/45.59 usesimpsplitting = 0
% 45.22/45.59 usesimpdemod = 5
% 45.22/45.59 usesimpres = 3
% 45.22/45.59
% 45.22/45.59 resimpinuse = 1000
% 45.22/45.59 resimpclauses = 20000
% 45.22/45.59 substype = eqrewr
% 45.22/45.59 backwardsubs = 1
% 45.22/45.59 selectoldest = 5
% 45.22/45.59
% 45.22/45.59 litorderings [0] = split
% 45.22/45.59 litorderings [1] = extend the termordering, first sorting on arguments
% 45.22/45.59
% 45.22/45.59 termordering = kbo
% 45.22/45.59
% 45.22/45.59 litapriori = 0
% 45.22/45.59 termapriori = 1
% 45.22/45.59 litaposteriori = 0
% 45.22/45.59 termaposteriori = 0
% 45.22/45.59 demodaposteriori = 0
% 45.22/45.59 ordereqreflfact = 0
% 45.22/45.59
% 45.22/45.59 litselect = negord
% 45.22/45.59
% 45.22/45.59 maxweight = 15
% 45.22/45.59 maxdepth = 30000
% 45.22/45.59 maxlength = 115
% 45.22/45.59 maxnrvars = 195
% 45.22/45.59 excuselevel = 1
% 45.22/45.59 increasemaxweight = 1
% 45.22/45.59
% 45.22/45.59 maxselected = 10000000
% 45.22/45.59 maxnrclauses = 10000000
% 45.22/45.59
% 45.22/45.59 showgenerated = 0
% 45.22/45.59 showkept = 0
% 45.22/45.59 showselected = 0
% 45.22/45.59 showdeleted = 0
% 45.22/45.59 showresimp = 1
% 45.22/45.59 showstatus = 2000
% 45.22/45.59
% 45.22/45.59 prologoutput = 0
% 45.22/45.59 nrgoals = 5000000
% 45.22/45.59 totalproof = 1
% 45.22/45.59
% 45.22/45.59 Symbols occurring in the translation:
% 45.22/45.59
% 45.22/45.59 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 45.22/45.59 . [1, 2] (w:1, o:42, a:1, s:1, b:0),
% 45.22/45.59 && [3, 0] (w:1, o:4, a:1, s:1, b:0),
% 45.22/45.59 ! [4, 1] (w:0, o:27, a:1, s:1, b:0),
% 45.22/45.59 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 45.22/45.59 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 45.22/45.59 in [37, 2] (w:1, o:66, a:1, s:1, b:0),
% 45.22/45.59 empty [38, 1] (w:1, o:32, a:1, s:1, b:0),
% 45.22/45.59 function [39, 1] (w:1, o:33, a:1, s:1, b:0),
% 45.22/45.59 relation [40, 1] (w:1, o:34, a:1, s:1, b:0),
% 45.22/45.59 cartesian_product2 [42, 2] (w:1, o:67, a:1, s:1, b:0),
% 45.22/45.59 powerset [43, 1] (w:1, o:36, a:1, s:1, b:0),
% 45.22/45.59 element [44, 2] (w:1, o:68, a:1, s:1, b:0),
% 45.22/45.59 one_to_one [45, 1] (w:1, o:35, a:1, s:1, b:0),
% 45.22/45.59 relation_of2_as_subset [46, 3] (w:1, o:78, a:1, s:1, b:0),
% 45.22/45.59 empty_set [47, 0] (w:1, o:9, a:1, s:1, b:0),
% 45.22/45.59 quasi_total [48, 3] (w:1, o:77, a:1, s:1, b:0),
% 45.22/45.59 relation_dom_as_subset [49, 3] (w:1, o:79, a:1, s:1, b:0),
% 45.22/45.59 relation_of2 [50, 3] (w:1, o:80, a:1, s:1, b:0),
% 45.22/45.59 relation_composition [51, 2] (w:1, o:69, a:1, s:1, b:0),
% 45.22/45.59 relation_empty_yielding [52, 1] (w:1, o:38, a:1, s:1, b:0),
% 45.22/45.59 relation_dom [53, 1] (w:1, o:37, a:1, s:1, b:0),
% 45.22/45.59 subset [54, 2] (w:1, o:70, a:1, s:1, b:0),
% 45.22/45.59 apply [57, 2] (w:1, o:71, a:1, s:1, b:0),
% 45.22/45.59 alpha1 [58, 2] (w:1, o:72, a:1, s:1, b:1),
% 45.22/45.59 skol1 [59, 2] (w:1, o:73, a:1, s:1, b:1),
% 45.22/45.59 skol2 [60, 1] (w:1, o:40, a:1, s:1, b:1),
% 45.22/45.59 skol3 [61, 2] (w:1, o:74, a:1, s:1, b:1),
% 45.22/45.59 skol4 [62, 0] (w:1, o:12, a:1, s:1, b:1),
% 45.22/45.59 skol5 [63, 2] (w:1, o:75, a:1, s:1, b:1),
% 45.22/45.59 skol6 [64, 0] (w:1, o:13, a:1, s:1, b:1),
% 45.22/45.59 skol7 [65, 0] (w:1, o:14, a:1, s:1, b:1),
% 45.22/45.59 skol8 [66, 1] (w:1, o:41, a:1, s:1, b:1),
% 45.22/45.59 skol9 [67, 0] (w:1, o:15, a:1, s:1, b:1),
% 45.22/45.59 skol10 [68, 0] (w:1, o:16, a:1, s:1, b:1),
% 45.22/45.59 skol11 [69, 2] (w:1, o:76, a:1, s:1, b:1),
% 45.22/45.59 skol12 [70, 0] (w:1, o:17, a:1, s:1, b:1),
% 45.22/45.59 skol13 [71, 1] (w:1, o:39, a:1, s:1, b:1),
% 45.22/45.59 skol14 [72, 0] (w:1, o:18, a:1, s:1, b:1),
% 45.22/45.59 skol15 [73, 0] (w:1, o:19, a:1, s:1, b:1),
% 45.22/45.59 skol16 [74, 0] (w:1, o:20, a:1, s:1, b:1),
% 45.22/45.59 skol17 [75, 0] (w:1, o:21, a:1, s:1, b:1),
% 45.22/45.59 skol18 [76, 0] (w:1, o:22, a:1, s:1, b:1),
% 45.22/45.59 skol19 [77, 0] (w:1, o:23, a:1, s:1, b:1),
% 45.22/45.59 skol20 [78, 0] (w:1, o:24, a:1, s:1, b:1),
% 45.22/45.59 skol21 [79, 0] (w:1, o:25, a:1, s:1, b:1),
% 59.78/60.14 skol22 [80, 0] (w:1, o:26, a:1, s:1, b:1).
% 59.78/60.14
% 59.78/60.14
% 59.78/60.14 Starting Search:
% 59.78/60.14
% 59.78/60.14 *** allocated 15000 integers for clauses
% 59.78/60.14 *** allocated 22500 integers for clauses
% 59.78/60.14 *** allocated 33750 integers for clauses
% 59.78/60.14 *** allocated 15000 integers for termspace/termends
% 59.78/60.14 *** allocated 50625 integers for clauses
% 59.78/60.14 Resimplifying inuse:
% 59.78/60.14 Done
% 59.78/60.14
% 59.78/60.14 *** allocated 75937 integers for clauses
% 59.78/60.14 *** allocated 22500 integers for termspace/termends
% 59.78/60.14 *** allocated 113905 integers for clauses
% 59.78/60.14 *** allocated 33750 integers for termspace/termends
% 59.78/60.14
% 59.78/60.14 Intermediate Status:
% 59.78/60.14 Generated: 12436
% 59.78/60.14 Kept: 2021
% 59.78/60.14 Inuse: 265
% 59.78/60.14 Deleted: 17
% 59.78/60.14 Deletedinuse: 1
% 59.78/60.14
% 59.78/60.14 Resimplifying inuse:
% 59.78/60.14 Done
% 59.78/60.14
% 59.78/60.14 *** allocated 170857 integers for clauses
% 59.78/60.14 *** allocated 50625 integers for termspace/termends
% 59.78/60.14 Resimplifying inuse:
% 59.78/60.14 Done
% 59.78/60.14
% 59.78/60.14 *** allocated 256285 integers for clauses
% 59.78/60.14 *** allocated 75937 integers for termspace/termends
% 59.78/60.14
% 59.78/60.14 Intermediate Status:
% 59.78/60.14 Generated: 53965
% 59.78/60.14 Kept: 4021
% 59.78/60.14 Inuse: 433
% 59.78/60.14 Deleted: 158
% 59.78/60.14 Deletedinuse: 92
% 59.78/60.14
% 59.78/60.14 Resimplifying inuse:
% 59.78/60.14 Done
% 59.78/60.14
% 59.78/60.14 Resimplifying inuse:
% 59.78/60.14 Done
% 59.78/60.14
% 59.78/60.14 *** allocated 113905 integers for termspace/termends
% 59.78/60.14 *** allocated 384427 integers for clauses
% 59.78/60.14
% 59.78/60.14 Intermediate Status:
% 59.78/60.14 Generated: 112402
% 59.78/60.14 Kept: 6037
% 59.78/60.14 Inuse: 569
% 59.78/60.14 Deleted: 196
% 59.78/60.14 Deletedinuse: 93
% 59.78/60.14
% 59.78/60.14 Resimplifying inuse:
% 59.78/60.14 Done
% 59.78/60.14
% 59.78/60.14 Resimplifying inuse:
% 59.78/60.14 Done
% 59.78/60.14
% 59.78/60.14
% 59.78/60.14 Intermediate Status:
% 59.78/60.14 Generated: 142394
% 59.78/60.14 Kept: 8076
% 59.78/60.14 Inuse: 665
% 59.78/60.14 Deleted: 212
% 59.78/60.14 Deletedinuse: 93
% 59.78/60.14
% 59.78/60.14 Resimplifying inuse:
% 59.78/60.14 Done
% 59.78/60.14
% 59.78/60.14 *** allocated 576640 integers for clauses
% 59.78/60.14 *** allocated 170857 integers for termspace/termends
% 59.78/60.14 Resimplifying inuse:
% 59.78/60.14 Done
% 59.78/60.14
% 59.78/60.14
% 59.78/60.14 Intermediate Status:
% 59.78/60.14 Generated: 207508
% 59.78/60.14 Kept: 10094
% 59.78/60.14 Inuse: 727
% 59.78/60.14 Deleted: 370
% 59.78/60.14 Deletedinuse: 107
% 59.78/60.14
% 59.78/60.14 Resimplifying inuse:
% 59.78/60.14 Done
% 59.78/60.14
% 59.78/60.14 Resimplifying inuse:
% 59.78/60.14 Done
% 59.78/60.14
% 59.78/60.14
% 59.78/60.14 Intermediate Status:
% 59.78/60.14 Generated: 253274
% 59.78/60.14 Kept: 12099
% 59.78/60.14 Inuse: 803
% 59.78/60.14 Deleted: 431
% 59.78/60.14 Deletedinuse: 121
% 59.78/60.14
% 59.78/60.14 Resimplifying inuse:
% 59.78/60.14 Done
% 59.78/60.14
% 59.78/60.14 *** allocated 864960 integers for clauses
% 59.78/60.14 Resimplifying inuse:
% 59.78/60.14 Done
% 59.78/60.14
% 59.78/60.14 *** allocated 256285 integers for termspace/termends
% 59.78/60.14
% 59.78/60.14 Intermediate Status:
% 59.78/60.14 Generated: 278763
% 59.78/60.14 Kept: 14099
% 59.78/60.14 Inuse: 867
% 59.78/60.14 Deleted: 450
% 59.78/60.14 Deletedinuse: 128
% 59.78/60.14
% 59.78/60.14 Resimplifying inuse:
% 59.78/60.14 Done
% 59.78/60.14
% 59.78/60.14 Resimplifying inuse:
% 59.78/60.14 Done
% 59.78/60.14
% 59.78/60.14
% 59.78/60.14 Intermediate Status:
% 59.78/60.14 Generated: 318801
% 59.78/60.14 Kept: 16275
% 59.78/60.14 Inuse: 936
% 59.78/60.14 Deleted: 465
% 59.78/60.14 Deletedinuse: 128
% 59.78/60.14
% 59.78/60.14 Resimplifying inuse:
% 59.78/60.14 Done
% 59.78/60.14
% 59.78/60.14 Resimplifying inuse:
% 59.78/60.14 Done
% 59.78/60.14
% 59.78/60.14
% 59.78/60.14 Intermediate Status:
% 59.78/60.14 Generated: 351594
% 59.78/60.14 Kept: 18289
% 59.78/60.14 Inuse: 958
% 59.78/60.14 Deleted: 469
% 59.78/60.14 Deletedinuse: 129
% 59.78/60.14
% 59.78/60.14 *** allocated 1297440 integers for clauses
% 59.78/60.14 Resimplifying inuse:
% 59.78/60.14 Done
% 59.78/60.14
% 59.78/60.14 Resimplifying clauses:
% 59.78/60.14 Done
% 59.78/60.14
% 59.78/60.14
% 59.78/60.14 Intermediate Status:
% 59.78/60.14 Generated: 391338
% 59.78/60.14 Kept: 20305
% 59.78/60.14 Inuse: 990
% 59.78/60.14 Deleted: 3961
% 59.78/60.14 Deletedinuse: 134
% 59.78/60.14
% 59.78/60.14 Resimplifying inuse:
% 59.78/60.14 Done
% 59.78/60.14
% 59.78/60.14 *** allocated 384427 integers for termspace/termends
% 59.78/60.14 Resimplifying inuse:
% 59.78/60.14 Done
% 59.78/60.14
% 59.78/60.14
% 59.78/60.14 Intermediate Status:
% 59.78/60.14 Generated: 457117
% 59.78/60.14 Kept: 22383
% 59.78/60.14 Inuse: 1050
% 59.78/60.14 Deleted: 3996
% 59.78/60.14 Deletedinuse: 153
% 59.78/60.14
% 59.78/60.14 Resimplifying inuse:
% 59.78/60.14 Done
% 59.78/60.14
% 59.78/60.14 Resimplifying inuse:
% 59.78/60.14 Done
% 59.78/60.14
% 59.78/60.14
% 59.78/60.14 Intermediate Status:
% 59.78/60.14 Generated: 465351
% 59.78/60.14 Kept: 24456
% 59.78/60.14 Inuse: 1062
% 59.78/60.14 Deleted: 3996
% 59.78/60.14 Deletedinuse: 153
% 59.78/60.14
% 59.78/60.14 Resimplifying inuse:
% 59.78/60.14 Done
% 59.78/60.14
% 59.78/60.14 Resimplifying inuse:
% 59.78/60.14 Done
% 59.78/60.14
% 59.78/60.14
% 59.78/60.14 Intermediate Status:
% 59.78/60.14 Generated: 484838
% 59.78/60.14 Kept: 26488
% 59.78/60.14 Inuse: 1097
% 59.78/60.14 Deleted: 3996
% 59.78/60.14 Deletedinuse: 153
% 59.78/60.14
% 59.78/60.14 Resimplifying inuse:
% 59.78/60.14 Done
% 59.78/60.14
% 59.78/60.14 Resimplifying inuse:
% 59.78/60.14 Done
% 59.78/60.14
% 59.78/60.14
% 59.78/60.14 Intermediate Status:
% 59.78/60.14 Generated: 503847
% 59.78/60.14 Kept: 28504
% 59.78/60.14 Inuse: 1129
% 59.78/60.14 Deleted: 3996
% 59.78/60.14 Deletedinuse: 153
% 59.78/60.14
% 59.78/60.14 Resimplifying inuse:
% 59.78/60.14 Done
% 59.78/60.14
% 59.78/60.14 *** allocated 1946160 integers for clauses
% 59.78/60.14 Resimplifying inuse:
% 59.78/60.14 Done
% 59.78/60.14
% 59.78/60.14
% 59.78/60.14 Intermediate Status:
% 59.78/60.14 Generated: 545710
% 59.78/60.14 Kept: 30515
% 59.78/60.14 Inuse: 1186
% 59.78/60.14 Deleted: 4001
% 59.78/60.14 Deletedinuse: 153
% 59.78/60.14
% 59.78/60.14 Resimplifying inuse:
% 59.78/60.14 Done
% 59.78/60.14
% 59.78/60.14 *** allocated 576640 integers for termspace/termends
% 59.78/60.14 Resimplifying inuse:
% 59.78/60.14 Done
% 59.78/60.14
% 59.78/60.14
% 59.78/60.14 Intermediate Status:
% 59.78/60.14 Generated: 615094
% 59.78/60.14 Kept: 32579
% 59.78/60.14 Inuse: 1292
% 59.78/60.14 Deleted: 4019
% 59.78/60.14 Deletedinuse: 166
% 59.78/60.14
% 59.78/60.14 Resimplifying inuse:
% 59.78/60.14 Done
% 59.78/60.14
% 59.78/60.14 Resimplifying inuse:
% 59.78/60.14 Done
% 59.78/60.14
% 59.78/60.14
% 59.78/60.14 Intermediate Status:
% 59.78/60.14 Generated: 641635
% 59.78/60.14 Kept: 34649
% 59.78/60.14 Inuse: 1336
% 59.78/60.14 Deleted: 4024
% 59.78/60.14 Deletedinuse: 170
% 59.78/60.14
% 59.78/60.14 Resimplifying inuse:
% 59.78/60.14 Done
% 59.78/60.14
% 59.78/60.14 Resimplifying inuse:
% 59.78/60.14 Done
% 59.78/60.14
% 59.78/60.14
% 59.78/60.14 Intermediate Status:
% 59.78/60.14 Generated: 678205
% 59.78/60.14 Kept: 36693
% 59.78/60.14 Inuse: 1363
% 59.78/60.14 Deleted: 4024
% 59.78/60.14 Deletedinuse: 170
% 59.78/60.14
% 59.78/60.14 Resimplifying inuse:
% 59.78/60.14 Done
% 59.78/60.14
% 59.78/60.14 Resimplifying inuse:
% 59.78/60.14 Done
% 59.78/60.14
% 59.78/60.14
% 59.78/60.14 Intermediate Status:
% 59.78/60.14 Generated: 706181
% 59.78/60.14 Kept: 38701
% 59.78/60.14 Inuse: 1391
% 59.78/60.14 Deleted: 4028
% 59.78/60.14 Deletedinuse: 170
% 59.78/60.14
% 59.78/60.14 Resimplifying inuse:
% 59.78/60.14 Done
% 59.78/60.14
% 59.78/60.14 Resimplifying inuse:
% 59.78/60.14 Done
% 59.78/60.14
% 59.78/60.14 Resimplifying clauses:
% 59.78/60.14
% 59.78/60.14 Bliksems!, er is een bewijs:
% 59.78/60.14 % SZS status Theorem
% 59.78/60.14 % SZS output start Refutation
% 59.78/60.14
% 59.78/60.14 (3) {G0,W8,D4,L2,V3,M2} I { ! element( X, powerset( cartesian_product2( Y,
% 59.78/60.14 Z ) ) ), relation( X ) }.
% 59.78/60.14 (5) {G0,W17,D3,L4,V3,M4} I { ! relation_of2_as_subset( Z, X, Y ), alpha1( X
% 59.78/60.14 , Y ), ! quasi_total( Z, X, Y ), relation_dom_as_subset( X, Y, Z ) ==> X
% 59.78/60.14 }.
% 59.78/60.14 (9) {G0,W6,D2,L2,V2,M2} I { ! alpha1( X, Y ), Y = empty_set }.
% 59.78/60.14 (15) {G0,W10,D4,L2,V3,M2} I { ! relation_of2_as_subset( Z, X, Y ), element
% 59.78/60.14 ( Z, powerset( cartesian_product2( X, Y ) ) ) }.
% 59.78/60.14 (66) {G0,W11,D3,L2,V3,M2} I { ! relation_of2( Z, X, Y ),
% 59.78/60.14 relation_dom_as_subset( X, Y, Z ) ==> relation_dom( Z ) }.
% 59.78/60.14 (67) {G0,W8,D2,L2,V3,M2} I { ! relation_of2_as_subset( Z, X, Y ),
% 59.78/60.14 relation_of2( Z, X, Y ) }.
% 59.78/60.14 (71) {G0,W2,D2,L1,V0,M1} I { function( skol20 ) }.
% 59.78/60.14 (72) {G0,W4,D2,L1,V0,M1} I { quasi_total( skol20, skol18, skol19 ) }.
% 59.78/60.14 (73) {G0,W4,D2,L1,V0,M1} I { relation_of2_as_subset( skol20, skol18, skol19
% 59.78/60.14 ) }.
% 59.78/60.14 (74) {G0,W2,D2,L1,V0,M1} I { relation( skol21 ) }.
% 59.78/60.14 (75) {G0,W2,D2,L1,V0,M1} I { function( skol21 ) }.
% 59.78/60.14 (76) {G0,W3,D2,L1,V0,M1} I { in( skol22, skol18 ) }.
% 59.78/60.14 (77) {G0,W3,D2,L1,V0,M1} I { ! skol19 ==> empty_set }.
% 59.78/60.14 (78) {G0,W11,D4,L1,V0,M1} I { ! apply( skol21, apply( skol20, skol22 ) )
% 59.78/60.14 ==> apply( relation_composition( skol20, skol21 ), skol22 ) }.
% 59.78/60.14 (79) {G0,W23,D4,L6,V3,M6} I { ! relation( X ), ! function( X ), ! relation
% 59.78/60.14 ( Y ), ! function( Y ), ! in( Z, relation_dom( X ) ), apply( Y, apply( X
% 59.78/60.14 , Z ) ) ==> apply( relation_composition( X, Y ), Z ) }.
% 59.78/60.14 (242) {G1,W3,D2,L1,V1,M1} P(9,77);q { ! alpha1( X, skol19 ) }.
% 59.78/60.14 (299) {G2,W10,D3,L2,V0,M2} R(73,5);r(242) { ! quasi_total( skol20, skol18,
% 59.78/60.14 skol19 ), relation_dom_as_subset( skol18, skol19, skol20 ) ==> skol18 }.
% 59.78/60.14 (458) {G1,W6,D2,L2,V3,M2} R(15,3) { ! relation_of2_as_subset( X, Y, Z ),
% 59.78/60.14 relation( X ) }.
% 59.78/60.14 (1134) {G1,W4,D2,L1,V0,M1} R(67,73) { relation_of2( skol20, skol18, skol19
% 59.78/60.14 ) }.
% 59.78/60.14 (1135) {G2,W7,D3,L1,V0,M1} R(1134,66) { relation_dom_as_subset( skol18,
% 59.78/60.14 skol19, skol20 ) ==> relation_dom( skol20 ) }.
% 59.78/60.14 (1285) {G1,W10,D3,L4,V0,M4} R(79,78);r(71) { ! relation( skol20 ), !
% 59.78/60.14 relation( skol21 ), ! function( skol21 ), ! in( skol22, relation_dom(
% 59.78/60.14 skol20 ) ) }.
% 59.78/60.14 (2572) {G2,W2,D2,L1,V0,M1} R(458,73) { relation( skol20 ) }.
% 59.78/60.14 (13374) {G3,W4,D3,L1,V0,M1} S(299);d(1135);r(72) { relation_dom( skol20 )
% 59.78/60.14 ==> skol18 }.
% 59.78/60.14 (20097) {G4,W7,D2,L3,V0,M3} S(1285);d(13374);r(2572) { ! relation( skol21 )
% 59.78/60.14 , ! function( skol21 ), ! in( skol22, skol18 ) }.
% 59.78/60.14 (40153) {G5,W0,D0,L0,V0,M0} S(20097);r(74);r(75);r(76) { }.
% 59.78/60.14
% 59.78/60.14
% 59.78/60.14 % SZS output end Refutation
% 59.78/60.14 found a proof!
% 59.78/60.14
% 59.78/60.14
% 59.78/60.14 Unprocessed initial clauses:
% 59.78/60.14
% 59.78/60.14 (40155) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), ! in( Y, X ) }.
% 59.78/60.14 (40156) {G0,W4,D2,L2,V1,M2} { ! empty( X ), function( X ) }.
% 59.78/60.14 (40157) {G0,W4,D2,L2,V1,M2} { ! empty( X ), relation( X ) }.
% 59.78/60.14 (40158) {G0,W8,D4,L2,V3,M2} { ! element( X, powerset( cartesian_product2(
% 59.78/60.14 Y, Z ) ) ), relation( X ) }.
% 59.78/60.14 (40159) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 59.78/60.14 ), relation( X ) }.
% 59.78/60.14 (40160) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 59.78/60.14 ), function( X ) }.
% 59.78/60.14 (40161) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 59.78/60.14 ), one_to_one( X ) }.
% 59.78/60.14 (40162) {G0,W17,D3,L4,V3,M4} { ! relation_of2_as_subset( Z, X, Y ), alpha1
% 59.78/60.14 ( X, Y ), ! quasi_total( Z, X, Y ), X = relation_dom_as_subset( X, Y, Z )
% 59.78/60.14 }.
% 59.78/60.14 (40163) {G0,W17,D3,L4,V3,M4} { ! relation_of2_as_subset( Z, X, Y ), alpha1
% 59.78/60.14 ( X, Y ), ! X = relation_dom_as_subset( X, Y, Z ), quasi_total( Z, X, Y )
% 59.78/60.14 }.
% 59.78/60.14 (40164) {G0,W17,D2,L5,V3,M5} { ! relation_of2_as_subset( Z, X, Y ), ! Y =
% 59.78/60.14 empty_set, X = empty_set, ! quasi_total( Z, X, Y ), Z = empty_set }.
% 59.78/60.14 (40165) {G0,W17,D2,L5,V3,M5} { ! relation_of2_as_subset( Z, X, Y ), ! Y =
% 59.78/60.14 empty_set, X = empty_set, ! Z = empty_set, quasi_total( Z, X, Y ) }.
% 59.78/60.14 (40166) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), Y = empty_set }.
% 59.78/60.14 (40167) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), ! X = empty_set }.
% 59.78/60.14 (40168) {G0,W9,D2,L3,V2,M3} { ! Y = empty_set, X = empty_set, alpha1( X, Y
% 59.78/60.14 ) }.
% 59.78/60.14 (40169) {G0,W1,D1,L1,V0,M1} { && }.
% 59.78/60.14 (40170) {G0,W1,D1,L1,V0,M1} { && }.
% 59.78/60.14 (40171) {G0,W1,D1,L1,V0,M1} { && }.
% 59.78/60.14 (40172) {G0,W1,D1,L1,V0,M1} { && }.
% 59.78/60.14 (40173) {G0,W1,D1,L1,V0,M1} { && }.
% 59.78/60.14 (40174) {G0,W11,D3,L2,V3,M2} { ! relation_of2( Z, X, Y ), element(
% 59.78/60.14 relation_dom_as_subset( X, Y, Z ), powerset( X ) ) }.
% 59.78/60.14 (40175) {G0,W8,D3,L3,V2,M3} { ! relation( X ), ! relation( Y ), relation(
% 59.78/60.14 relation_composition( X, Y ) ) }.
% 59.78/60.14 (40176) {G0,W1,D1,L1,V0,M1} { && }.
% 59.78/60.14 (40177) {G0,W1,D1,L1,V0,M1} { && }.
% 59.78/60.14 (40178) {G0,W10,D4,L2,V3,M2} { ! relation_of2_as_subset( Z, X, Y ),
% 59.78/60.14 element( Z, powerset( cartesian_product2( X, Y ) ) ) }.
% 59.78/60.14 (40179) {G0,W6,D3,L1,V2,M1} { relation_of2( skol1( X, Y ), X, Y ) }.
% 59.78/60.14 (40180) {G0,W4,D3,L1,V1,M1} { element( skol2( X ), X ) }.
% 59.78/60.14 (40181) {G0,W6,D3,L1,V2,M1} { relation_of2_as_subset( skol3( X, Y ), X, Y
% 59.78/60.14 ) }.
% 59.78/60.14 (40182) {G0,W8,D3,L3,V2,M3} { ! empty( X ), ! relation( Y ), empty(
% 59.78/60.14 relation_composition( Y, X ) ) }.
% 59.78/60.14 (40183) {G0,W8,D3,L3,V2,M3} { ! empty( X ), ! relation( Y ), relation(
% 59.78/60.14 relation_composition( Y, X ) ) }.
% 59.78/60.14 (40184) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 59.78/60.14 (40185) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 59.78/60.14 (40186) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( empty_set ) }.
% 59.78/60.14 (40187) {G0,W12,D3,L5,V2,M5} { ! relation( X ), ! function( X ), !
% 59.78/60.14 relation( Y ), ! function( Y ), relation( relation_composition( X, Y ) )
% 59.78/60.14 }.
% 59.78/60.14 (40188) {G0,W12,D3,L5,V2,M5} { ! relation( X ), ! function( X ), !
% 59.78/60.14 relation( Y ), ! function( Y ), function( relation_composition( X, Y ) )
% 59.78/60.14 }.
% 59.78/60.14 (40189) {G0,W3,D3,L1,V1,M1} { ! empty( powerset( X ) ) }.
% 59.78/60.14 (40190) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 59.78/60.14 (40191) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 59.78/60.14 (40192) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 59.78/60.14 (40193) {G0,W8,D3,L3,V2,M3} { empty( X ), empty( Y ), ! empty(
% 59.78/60.14 cartesian_product2( X, Y ) ) }.
% 59.78/60.14 (40194) {G0,W7,D3,L3,V1,M3} { empty( X ), ! relation( X ), ! empty(
% 59.78/60.14 relation_dom( X ) ) }.
% 59.78/60.14 (40195) {G0,W5,D3,L2,V1,M2} { ! empty( X ), empty( relation_dom( X ) ) }.
% 59.78/60.14 (40196) {G0,W5,D3,L2,V1,M2} { ! empty( X ), relation( relation_dom( X ) )
% 59.78/60.14 }.
% 59.78/60.14 (40197) {G0,W8,D3,L3,V2,M3} { ! empty( X ), ! relation( Y ), empty(
% 59.78/60.14 relation_composition( X, Y ) ) }.
% 59.78/60.14 (40198) {G0,W8,D3,L3,V2,M3} { ! empty( X ), ! relation( Y ), relation(
% 59.78/60.14 relation_composition( X, Y ) ) }.
% 59.78/60.14 (40199) {G0,W2,D2,L1,V0,M1} { relation( skol4 ) }.
% 59.78/60.14 (40200) {G0,W2,D2,L1,V0,M1} { function( skol4 ) }.
% 59.78/60.14 (40201) {G0,W4,D3,L1,V2,M1} { relation( skol5( Z, T ) ) }.
% 59.78/60.14 (40202) {G0,W4,D3,L1,V2,M1} { function( skol5( Z, T ) ) }.
% 59.78/60.14 (40203) {G0,W6,D3,L1,V2,M1} { relation_of2( skol5( X, Y ), X, Y ) }.
% 59.78/60.14 (40204) {G0,W6,D3,L1,V2,M1} { quasi_total( skol5( X, Y ), X, Y ) }.
% 59.78/60.14 (40205) {G0,W2,D2,L1,V0,M1} { relation( skol6 ) }.
% 59.78/60.14 (40206) {G0,W2,D2,L1,V0,M1} { function( skol6 ) }.
% 59.78/60.14 (40207) {G0,W2,D2,L1,V0,M1} { one_to_one( skol6 ) }.
% 59.78/60.14 (40208) {G0,W2,D2,L1,V0,M1} { empty( skol6 ) }.
% 59.78/60.14 (40209) {G0,W2,D2,L1,V0,M1} { empty( skol7 ) }.
% 59.78/60.14 (40210) {G0,W2,D2,L1,V0,M1} { relation( skol7 ) }.
% 59.78/60.14 (40211) {G0,W5,D3,L2,V2,M2} { empty( X ), ! empty( skol8( Y ) ) }.
% 59.78/60.14 (40212) {G0,W7,D3,L2,V1,M2} { empty( X ), element( skol8( X ), powerset( X
% 59.78/60.14 ) ) }.
% 59.78/60.14 (40213) {G0,W2,D2,L1,V0,M1} { empty( skol9 ) }.
% 59.78/60.14 (40214) {G0,W2,D2,L1,V0,M1} { relation( skol10 ) }.
% 59.78/60.14 (40215) {G0,W2,D2,L1,V0,M1} { empty( skol10 ) }.
% 59.78/60.14 (40216) {G0,W2,D2,L1,V0,M1} { function( skol10 ) }.
% 59.78/60.14 (40217) {G0,W4,D3,L1,V2,M1} { relation( skol11( Z, T ) ) }.
% 59.78/60.14 (40218) {G0,W4,D3,L1,V2,M1} { function( skol11( Z, T ) ) }.
% 59.78/60.14 (40219) {G0,W6,D3,L1,V2,M1} { relation_of2( skol11( X, Y ), X, Y ) }.
% 59.78/60.14 (40220) {G0,W2,D2,L1,V0,M1} { ! empty( skol12 ) }.
% 59.78/60.14 (40221) {G0,W2,D2,L1,V0,M1} { relation( skol12 ) }.
% 59.78/60.14 (40222) {G0,W3,D3,L1,V1,M1} { empty( skol13( Y ) ) }.
% 59.78/60.14 (40223) {G0,W5,D3,L1,V1,M1} { element( skol13( X ), powerset( X ) ) }.
% 59.78/60.14 (40224) {G0,W2,D2,L1,V0,M1} { ! empty( skol14 ) }.
% 59.78/60.14 (40225) {G0,W2,D2,L1,V0,M1} { relation( skol15 ) }.
% 59.78/60.14 (40226) {G0,W2,D2,L1,V0,M1} { function( skol15 ) }.
% 59.78/60.14 (40227) {G0,W2,D2,L1,V0,M1} { one_to_one( skol15 ) }.
% 59.78/60.14 (40228) {G0,W2,D2,L1,V0,M1} { relation( skol16 ) }.
% 59.78/60.14 (40229) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( skol16 ) }.
% 59.78/60.14 (40230) {G0,W2,D2,L1,V0,M1} { relation( skol17 ) }.
% 59.78/60.14 (40231) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( skol17 ) }.
% 59.78/60.14 (40232) {G0,W2,D2,L1,V0,M1} { function( skol17 ) }.
% 59.78/60.14 (40233) {G0,W11,D3,L2,V3,M2} { ! relation_of2( Z, X, Y ),
% 59.78/60.14 relation_dom_as_subset( X, Y, Z ) = relation_dom( Z ) }.
% 59.78/60.14 (40234) {G0,W8,D2,L2,V3,M2} { ! relation_of2_as_subset( Z, X, Y ),
% 59.78/60.14 relation_of2( Z, X, Y ) }.
% 59.78/60.14 (40235) {G0,W8,D2,L2,V3,M2} { ! relation_of2( Z, X, Y ),
% 59.78/60.14 relation_of2_as_subset( Z, X, Y ) }.
% 59.78/60.14 (40236) {G0,W3,D2,L1,V1,M1} { subset( X, X ) }.
% 59.78/60.14 (40237) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), element( X, Y ) }.
% 59.78/60.14 (40238) {G0,W2,D2,L1,V0,M1} { function( skol20 ) }.
% 59.78/60.14 (40239) {G0,W4,D2,L1,V0,M1} { quasi_total( skol20, skol18, skol19 ) }.
% 59.78/60.14 (40240) {G0,W4,D2,L1,V0,M1} { relation_of2_as_subset( skol20, skol18,
% 59.78/60.14 skol19 ) }.
% 59.78/60.14 (40241) {G0,W2,D2,L1,V0,M1} { relation( skol21 ) }.
% 59.78/60.14 (40242) {G0,W2,D2,L1,V0,M1} { function( skol21 ) }.
% 59.78/60.14 (40243) {G0,W3,D2,L1,V0,M1} { in( skol22, skol18 ) }.
% 59.78/60.14 (40244) {G0,W3,D2,L1,V0,M1} { ! skol19 = empty_set }.
% 59.78/60.14 (40245) {G0,W11,D4,L1,V0,M1} { ! apply( relation_composition( skol20,
% 59.78/60.14 skol21 ), skol22 ) = apply( skol21, apply( skol20, skol22 ) ) }.
% 59.78/60.14 (40246) {G0,W23,D4,L6,V3,M6} { ! relation( X ), ! function( X ), !
% 59.78/60.14 relation( Y ), ! function( Y ), ! in( Z, relation_dom( X ) ), apply(
% 59.78/60.14 relation_composition( X, Y ), Z ) = apply( Y, apply( X, Z ) ) }.
% 59.78/60.14 (40247) {G0,W8,D2,L3,V2,M3} { ! element( X, Y ), empty( Y ), in( X, Y )
% 59.78/60.14 }.
% 59.78/60.14 (40248) {G0,W7,D3,L2,V2,M2} { ! element( X, powerset( Y ) ), subset( X, Y
% 59.78/60.14 ) }.
% 59.78/60.14 (40249) {G0,W7,D3,L2,V2,M2} { ! subset( X, Y ), element( X, powerset( Y )
% 59.78/60.14 ) }.
% 59.78/60.14 (40250) {G0,W10,D3,L3,V3,M3} { ! in( X, Z ), ! element( Z, powerset( Y ) )
% 59.78/60.14 , element( X, Y ) }.
% 59.78/60.14 (40251) {G0,W9,D3,L3,V3,M3} { ! in( X, Y ), ! element( Y, powerset( Z ) )
% 59.78/60.14 , ! empty( Z ) }.
% 59.78/60.14 (40252) {G0,W5,D2,L2,V1,M2} { ! empty( X ), X = empty_set }.
% 59.78/60.14 (40253) {G0,W5,D2,L2,V2,M2} { ! in( X, Y ), ! empty( Y ) }.
% 59.78/60.14 (40254) {G0,W7,D2,L3,V2,M3} { ! empty( X ), X = Y, ! empty( Y ) }.
% 59.78/60.14
% 59.78/60.14
% 59.78/60.14 Total Proof:
% 59.78/60.14
% 59.78/60.14 subsumption: (3) {G0,W8,D4,L2,V3,M2} I { ! element( X, powerset(
% 59.78/60.14 cartesian_product2( Y, Z ) ) ), relation( X ) }.
% 59.78/60.14 parent0: (40158) {G0,W8,D4,L2,V3,M2} { ! element( X, powerset(
% 59.78/60.14 cartesian_product2( Y, Z ) ) ), relation( X ) }.
% 59.78/60.14 substitution0:
% 59.78/60.14 X := X
% 59.78/60.14 Y := Y
% 59.78/60.14 Z := Z
% 59.78/60.14 end
% 59.78/60.14 permutation0:
% 59.78/60.14 0 ==> 0
% 59.78/60.14 1 ==> 1
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 eqswap: (40257) {G0,W17,D3,L4,V3,M4} { relation_dom_as_subset( X, Y, Z ) =
% 59.78/60.14 X, ! relation_of2_as_subset( Z, X, Y ), alpha1( X, Y ), ! quasi_total( Z
% 59.78/60.14 , X, Y ) }.
% 59.78/60.14 parent0[3]: (40162) {G0,W17,D3,L4,V3,M4} { ! relation_of2_as_subset( Z, X
% 59.78/60.14 , Y ), alpha1( X, Y ), ! quasi_total( Z, X, Y ), X =
% 59.78/60.14 relation_dom_as_subset( X, Y, Z ) }.
% 59.78/60.14 substitution0:
% 59.78/60.14 X := X
% 59.78/60.14 Y := Y
% 59.78/60.14 Z := Z
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 subsumption: (5) {G0,W17,D3,L4,V3,M4} I { ! relation_of2_as_subset( Z, X, Y
% 59.78/60.14 ), alpha1( X, Y ), ! quasi_total( Z, X, Y ), relation_dom_as_subset( X,
% 59.78/60.14 Y, Z ) ==> X }.
% 59.78/60.14 parent0: (40257) {G0,W17,D3,L4,V3,M4} { relation_dom_as_subset( X, Y, Z )
% 59.78/60.14 = X, ! relation_of2_as_subset( Z, X, Y ), alpha1( X, Y ), ! quasi_total(
% 59.78/60.14 Z, X, Y ) }.
% 59.78/60.14 substitution0:
% 59.78/60.14 X := X
% 59.78/60.14 Y := Y
% 59.78/60.14 Z := Z
% 59.78/60.14 end
% 59.78/60.14 permutation0:
% 59.78/60.14 0 ==> 3
% 59.78/60.14 1 ==> 0
% 59.78/60.14 2 ==> 1
% 59.78/60.14 3 ==> 2
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 subsumption: (9) {G0,W6,D2,L2,V2,M2} I { ! alpha1( X, Y ), Y = empty_set
% 59.78/60.14 }.
% 59.78/60.14 parent0: (40166) {G0,W6,D2,L2,V2,M2} { ! alpha1( X, Y ), Y = empty_set }.
% 59.78/60.14 substitution0:
% 59.78/60.14 X := X
% 59.78/60.14 Y := Y
% 59.78/60.14 end
% 59.78/60.14 permutation0:
% 59.78/60.14 0 ==> 0
% 59.78/60.14 1 ==> 1
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 subsumption: (15) {G0,W10,D4,L2,V3,M2} I { ! relation_of2_as_subset( Z, X,
% 59.78/60.14 Y ), element( Z, powerset( cartesian_product2( X, Y ) ) ) }.
% 59.78/60.14 parent0: (40178) {G0,W10,D4,L2,V3,M2} { ! relation_of2_as_subset( Z, X, Y
% 59.78/60.14 ), element( Z, powerset( cartesian_product2( X, Y ) ) ) }.
% 59.78/60.14 substitution0:
% 59.78/60.14 X := X
% 59.78/60.14 Y := Y
% 59.78/60.14 Z := Z
% 59.78/60.14 end
% 59.78/60.14 permutation0:
% 59.78/60.14 0 ==> 0
% 59.78/60.14 1 ==> 1
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 subsumption: (66) {G0,W11,D3,L2,V3,M2} I { ! relation_of2( Z, X, Y ),
% 59.78/60.14 relation_dom_as_subset( X, Y, Z ) ==> relation_dom( Z ) }.
% 59.78/60.14 parent0: (40233) {G0,W11,D3,L2,V3,M2} { ! relation_of2( Z, X, Y ),
% 59.78/60.14 relation_dom_as_subset( X, Y, Z ) = relation_dom( Z ) }.
% 59.78/60.14 substitution0:
% 59.78/60.14 X := X
% 59.78/60.14 Y := Y
% 59.78/60.14 Z := Z
% 59.78/60.14 end
% 59.78/60.14 permutation0:
% 59.78/60.14 0 ==> 0
% 59.78/60.14 1 ==> 1
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 subsumption: (67) {G0,W8,D2,L2,V3,M2} I { ! relation_of2_as_subset( Z, X, Y
% 59.78/60.14 ), relation_of2( Z, X, Y ) }.
% 59.78/60.14 parent0: (40234) {G0,W8,D2,L2,V3,M2} { ! relation_of2_as_subset( Z, X, Y )
% 59.78/60.14 , relation_of2( Z, X, Y ) }.
% 59.78/60.14 substitution0:
% 59.78/60.14 X := X
% 59.78/60.14 Y := Y
% 59.78/60.14 Z := Z
% 59.78/60.14 end
% 59.78/60.14 permutation0:
% 59.78/60.14 0 ==> 0
% 59.78/60.14 1 ==> 1
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 subsumption: (71) {G0,W2,D2,L1,V0,M1} I { function( skol20 ) }.
% 59.78/60.14 parent0: (40238) {G0,W2,D2,L1,V0,M1} { function( skol20 ) }.
% 59.78/60.14 substitution0:
% 59.78/60.14 end
% 59.78/60.14 permutation0:
% 59.78/60.14 0 ==> 0
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 subsumption: (72) {G0,W4,D2,L1,V0,M1} I { quasi_total( skol20, skol18,
% 59.78/60.14 skol19 ) }.
% 59.78/60.14 parent0: (40239) {G0,W4,D2,L1,V0,M1} { quasi_total( skol20, skol18, skol19
% 59.78/60.14 ) }.
% 59.78/60.14 substitution0:
% 59.78/60.14 end
% 59.78/60.14 permutation0:
% 59.78/60.14 0 ==> 0
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 subsumption: (73) {G0,W4,D2,L1,V0,M1} I { relation_of2_as_subset( skol20,
% 59.78/60.14 skol18, skol19 ) }.
% 59.78/60.14 parent0: (40240) {G0,W4,D2,L1,V0,M1} { relation_of2_as_subset( skol20,
% 59.78/60.14 skol18, skol19 ) }.
% 59.78/60.14 substitution0:
% 59.78/60.14 end
% 59.78/60.14 permutation0:
% 59.78/60.14 0 ==> 0
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 subsumption: (74) {G0,W2,D2,L1,V0,M1} I { relation( skol21 ) }.
% 59.78/60.14 parent0: (40241) {G0,W2,D2,L1,V0,M1} { relation( skol21 ) }.
% 59.78/60.14 substitution0:
% 59.78/60.14 end
% 59.78/60.14 permutation0:
% 59.78/60.14 0 ==> 0
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 subsumption: (75) {G0,W2,D2,L1,V0,M1} I { function( skol21 ) }.
% 59.78/60.14 parent0: (40242) {G0,W2,D2,L1,V0,M1} { function( skol21 ) }.
% 59.78/60.14 substitution0:
% 59.78/60.14 end
% 59.78/60.14 permutation0:
% 59.78/60.14 0 ==> 0
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 subsumption: (76) {G0,W3,D2,L1,V0,M1} I { in( skol22, skol18 ) }.
% 59.78/60.14 parent0: (40243) {G0,W3,D2,L1,V0,M1} { in( skol22, skol18 ) }.
% 59.78/60.14 substitution0:
% 59.78/60.14 end
% 59.78/60.14 permutation0:
% 59.78/60.14 0 ==> 0
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 subsumption: (77) {G0,W3,D2,L1,V0,M1} I { ! skol19 ==> empty_set }.
% 59.78/60.14 parent0: (40244) {G0,W3,D2,L1,V0,M1} { ! skol19 = empty_set }.
% 59.78/60.14 substitution0:
% 59.78/60.14 end
% 59.78/60.14 permutation0:
% 59.78/60.14 0 ==> 0
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 eqswap: (40699) {G0,W11,D4,L1,V0,M1} { ! apply( skol21, apply( skol20,
% 59.78/60.14 skol22 ) ) = apply( relation_composition( skol20, skol21 ), skol22 ) }.
% 59.78/60.14 parent0[0]: (40245) {G0,W11,D4,L1,V0,M1} { ! apply( relation_composition(
% 59.78/60.14 skol20, skol21 ), skol22 ) = apply( skol21, apply( skol20, skol22 ) ) }.
% 59.78/60.14 substitution0:
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 subsumption: (78) {G0,W11,D4,L1,V0,M1} I { ! apply( skol21, apply( skol20,
% 59.78/60.14 skol22 ) ) ==> apply( relation_composition( skol20, skol21 ), skol22 )
% 59.78/60.14 }.
% 59.78/60.14 parent0: (40699) {G0,W11,D4,L1,V0,M1} { ! apply( skol21, apply( skol20,
% 59.78/60.14 skol22 ) ) = apply( relation_composition( skol20, skol21 ), skol22 ) }.
% 59.78/60.14 substitution0:
% 59.78/60.14 end
% 59.78/60.14 permutation0:
% 59.78/60.14 0 ==> 0
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 eqswap: (40740) {G0,W23,D4,L6,V3,M6} { apply( Y, apply( X, Z ) ) = apply(
% 59.78/60.14 relation_composition( X, Y ), Z ), ! relation( X ), ! function( X ), !
% 59.78/60.14 relation( Y ), ! function( Y ), ! in( Z, relation_dom( X ) ) }.
% 59.78/60.14 parent0[5]: (40246) {G0,W23,D4,L6,V3,M6} { ! relation( X ), ! function( X
% 59.78/60.14 ), ! relation( Y ), ! function( Y ), ! in( Z, relation_dom( X ) ), apply
% 59.78/60.14 ( relation_composition( X, Y ), Z ) = apply( Y, apply( X, Z ) ) }.
% 59.78/60.14 substitution0:
% 59.78/60.14 X := X
% 59.78/60.14 Y := Y
% 59.78/60.14 Z := Z
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 subsumption: (79) {G0,W23,D4,L6,V3,M6} I { ! relation( X ), ! function( X )
% 59.78/60.14 , ! relation( Y ), ! function( Y ), ! in( Z, relation_dom( X ) ), apply(
% 59.78/60.14 Y, apply( X, Z ) ) ==> apply( relation_composition( X, Y ), Z ) }.
% 59.78/60.14 parent0: (40740) {G0,W23,D4,L6,V3,M6} { apply( Y, apply( X, Z ) ) = apply
% 59.78/60.14 ( relation_composition( X, Y ), Z ), ! relation( X ), ! function( X ), !
% 59.78/60.14 relation( Y ), ! function( Y ), ! in( Z, relation_dom( X ) ) }.
% 59.78/60.14 substitution0:
% 59.78/60.14 X := X
% 59.78/60.14 Y := Y
% 59.78/60.14 Z := Z
% 59.78/60.14 end
% 59.78/60.14 permutation0:
% 59.78/60.14 0 ==> 5
% 59.78/60.14 1 ==> 0
% 59.78/60.14 2 ==> 1
% 59.78/60.14 3 ==> 2
% 59.78/60.14 4 ==> 3
% 59.78/60.14 5 ==> 4
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 eqswap: (40746) {G0,W3,D2,L1,V0,M1} { ! empty_set ==> skol19 }.
% 59.78/60.14 parent0[0]: (77) {G0,W3,D2,L1,V0,M1} I { ! skol19 ==> empty_set }.
% 59.78/60.14 substitution0:
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 paramod: (40750) {G1,W6,D2,L2,V1,M2} { ! empty_set ==> empty_set, ! alpha1
% 59.78/60.14 ( X, skol19 ) }.
% 59.78/60.14 parent0[1]: (9) {G0,W6,D2,L2,V2,M2} I { ! alpha1( X, Y ), Y = empty_set }.
% 59.78/60.14 parent1[0; 3]: (40746) {G0,W3,D2,L1,V0,M1} { ! empty_set ==> skol19 }.
% 59.78/60.14 substitution0:
% 59.78/60.14 X := X
% 59.78/60.14 Y := skol19
% 59.78/60.14 end
% 59.78/60.14 substitution1:
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 eqrefl: (40761) {G0,W3,D2,L1,V1,M1} { ! alpha1( X, skol19 ) }.
% 59.78/60.14 parent0[0]: (40750) {G1,W6,D2,L2,V1,M2} { ! empty_set ==> empty_set, !
% 59.78/60.14 alpha1( X, skol19 ) }.
% 59.78/60.14 substitution0:
% 59.78/60.14 X := X
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 subsumption: (242) {G1,W3,D2,L1,V1,M1} P(9,77);q { ! alpha1( X, skol19 )
% 59.78/60.14 }.
% 59.78/60.14 parent0: (40761) {G0,W3,D2,L1,V1,M1} { ! alpha1( X, skol19 ) }.
% 59.78/60.14 substitution0:
% 59.78/60.14 X := X
% 59.78/60.14 end
% 59.78/60.14 permutation0:
% 59.78/60.14 0 ==> 0
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 eqswap: (40762) {G0,W17,D3,L4,V3,M4} { X ==> relation_dom_as_subset( X, Y
% 59.78/60.14 , Z ), ! relation_of2_as_subset( Z, X, Y ), alpha1( X, Y ), ! quasi_total
% 59.78/60.14 ( Z, X, Y ) }.
% 59.78/60.14 parent0[3]: (5) {G0,W17,D3,L4,V3,M4} I { ! relation_of2_as_subset( Z, X, Y
% 59.78/60.14 ), alpha1( X, Y ), ! quasi_total( Z, X, Y ), relation_dom_as_subset( X,
% 59.78/60.14 Y, Z ) ==> X }.
% 59.78/60.14 substitution0:
% 59.78/60.14 X := X
% 59.78/60.14 Y := Y
% 59.78/60.14 Z := Z
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 resolution: (40763) {G1,W13,D3,L3,V0,M3} { skol18 ==>
% 59.78/60.14 relation_dom_as_subset( skol18, skol19, skol20 ), alpha1( skol18, skol19
% 59.78/60.14 ), ! quasi_total( skol20, skol18, skol19 ) }.
% 59.78/60.14 parent0[1]: (40762) {G0,W17,D3,L4,V3,M4} { X ==> relation_dom_as_subset( X
% 59.78/60.14 , Y, Z ), ! relation_of2_as_subset( Z, X, Y ), alpha1( X, Y ), !
% 59.78/60.14 quasi_total( Z, X, Y ) }.
% 59.78/60.14 parent1[0]: (73) {G0,W4,D2,L1,V0,M1} I { relation_of2_as_subset( skol20,
% 59.78/60.14 skol18, skol19 ) }.
% 59.78/60.14 substitution0:
% 59.78/60.14 X := skol18
% 59.78/60.14 Y := skol19
% 59.78/60.14 Z := skol20
% 59.78/60.14 end
% 59.78/60.14 substitution1:
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 resolution: (40764) {G2,W10,D3,L2,V0,M2} { skol18 ==>
% 59.78/60.14 relation_dom_as_subset( skol18, skol19, skol20 ), ! quasi_total( skol20,
% 59.78/60.14 skol18, skol19 ) }.
% 59.78/60.14 parent0[0]: (242) {G1,W3,D2,L1,V1,M1} P(9,77);q { ! alpha1( X, skol19 ) }.
% 59.78/60.14 parent1[1]: (40763) {G1,W13,D3,L3,V0,M3} { skol18 ==>
% 59.78/60.14 relation_dom_as_subset( skol18, skol19, skol20 ), alpha1( skol18, skol19
% 59.78/60.14 ), ! quasi_total( skol20, skol18, skol19 ) }.
% 59.78/60.14 substitution0:
% 59.78/60.14 X := skol18
% 59.78/60.14 end
% 59.78/60.14 substitution1:
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 eqswap: (40765) {G2,W10,D3,L2,V0,M2} { relation_dom_as_subset( skol18,
% 59.78/60.14 skol19, skol20 ) ==> skol18, ! quasi_total( skol20, skol18, skol19 ) }.
% 59.78/60.14 parent0[0]: (40764) {G2,W10,D3,L2,V0,M2} { skol18 ==>
% 59.78/60.14 relation_dom_as_subset( skol18, skol19, skol20 ), ! quasi_total( skol20,
% 59.78/60.14 skol18, skol19 ) }.
% 59.78/60.14 substitution0:
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 subsumption: (299) {G2,W10,D3,L2,V0,M2} R(73,5);r(242) { ! quasi_total(
% 59.78/60.14 skol20, skol18, skol19 ), relation_dom_as_subset( skol18, skol19, skol20
% 59.78/60.14 ) ==> skol18 }.
% 59.78/60.14 parent0: (40765) {G2,W10,D3,L2,V0,M2} { relation_dom_as_subset( skol18,
% 59.78/60.14 skol19, skol20 ) ==> skol18, ! quasi_total( skol20, skol18, skol19 ) }.
% 59.78/60.14 substitution0:
% 59.78/60.14 end
% 59.78/60.14 permutation0:
% 59.78/60.14 0 ==> 1
% 59.78/60.14 1 ==> 0
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 resolution: (40766) {G1,W6,D2,L2,V3,M2} { relation( X ), !
% 59.78/60.14 relation_of2_as_subset( X, Y, Z ) }.
% 59.78/60.14 parent0[0]: (3) {G0,W8,D4,L2,V3,M2} I { ! element( X, powerset(
% 59.78/60.14 cartesian_product2( Y, Z ) ) ), relation( X ) }.
% 59.78/60.14 parent1[1]: (15) {G0,W10,D4,L2,V3,M2} I { ! relation_of2_as_subset( Z, X, Y
% 59.78/60.14 ), element( Z, powerset( cartesian_product2( X, Y ) ) ) }.
% 59.78/60.14 substitution0:
% 59.78/60.14 X := X
% 59.78/60.14 Y := Y
% 59.78/60.14 Z := Z
% 59.78/60.14 end
% 59.78/60.14 substitution1:
% 59.78/60.14 X := Y
% 59.78/60.14 Y := Z
% 59.78/60.14 Z := X
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 subsumption: (458) {G1,W6,D2,L2,V3,M2} R(15,3) { ! relation_of2_as_subset(
% 59.78/60.14 X, Y, Z ), relation( X ) }.
% 59.78/60.14 parent0: (40766) {G1,W6,D2,L2,V3,M2} { relation( X ), !
% 59.78/60.14 relation_of2_as_subset( X, Y, Z ) }.
% 59.78/60.14 substitution0:
% 59.78/60.14 X := X
% 59.78/60.14 Y := Y
% 59.78/60.14 Z := Z
% 59.78/60.14 end
% 59.78/60.14 permutation0:
% 59.78/60.14 0 ==> 1
% 59.78/60.14 1 ==> 0
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 resolution: (40767) {G1,W4,D2,L1,V0,M1} { relation_of2( skol20, skol18,
% 59.78/60.14 skol19 ) }.
% 59.78/60.14 parent0[0]: (67) {G0,W8,D2,L2,V3,M2} I { ! relation_of2_as_subset( Z, X, Y
% 59.78/60.14 ), relation_of2( Z, X, Y ) }.
% 59.78/60.14 parent1[0]: (73) {G0,W4,D2,L1,V0,M1} I { relation_of2_as_subset( skol20,
% 59.78/60.14 skol18, skol19 ) }.
% 59.78/60.14 substitution0:
% 59.78/60.14 X := skol18
% 59.78/60.14 Y := skol19
% 59.78/60.14 Z := skol20
% 59.78/60.14 end
% 59.78/60.14 substitution1:
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 subsumption: (1134) {G1,W4,D2,L1,V0,M1} R(67,73) { relation_of2( skol20,
% 59.78/60.14 skol18, skol19 ) }.
% 59.78/60.14 parent0: (40767) {G1,W4,D2,L1,V0,M1} { relation_of2( skol20, skol18,
% 59.78/60.14 skol19 ) }.
% 59.78/60.14 substitution0:
% 59.78/60.14 end
% 59.78/60.14 permutation0:
% 59.78/60.14 0 ==> 0
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 eqswap: (40768) {G0,W11,D3,L2,V3,M2} { relation_dom( Z ) ==>
% 59.78/60.14 relation_dom_as_subset( X, Y, Z ), ! relation_of2( Z, X, Y ) }.
% 59.78/60.14 parent0[1]: (66) {G0,W11,D3,L2,V3,M2} I { ! relation_of2( Z, X, Y ),
% 59.78/60.14 relation_dom_as_subset( X, Y, Z ) ==> relation_dom( Z ) }.
% 59.78/60.14 substitution0:
% 59.78/60.14 X := X
% 59.78/60.14 Y := Y
% 59.78/60.14 Z := Z
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 resolution: (40769) {G1,W7,D3,L1,V0,M1} { relation_dom( skol20 ) ==>
% 59.78/60.14 relation_dom_as_subset( skol18, skol19, skol20 ) }.
% 59.78/60.14 parent0[1]: (40768) {G0,W11,D3,L2,V3,M2} { relation_dom( Z ) ==>
% 59.78/60.14 relation_dom_as_subset( X, Y, Z ), ! relation_of2( Z, X, Y ) }.
% 59.78/60.14 parent1[0]: (1134) {G1,W4,D2,L1,V0,M1} R(67,73) { relation_of2( skol20,
% 59.78/60.14 skol18, skol19 ) }.
% 59.78/60.14 substitution0:
% 59.78/60.14 X := skol18
% 59.78/60.14 Y := skol19
% 59.78/60.14 Z := skol20
% 59.78/60.14 end
% 59.78/60.14 substitution1:
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 eqswap: (40770) {G1,W7,D3,L1,V0,M1} { relation_dom_as_subset( skol18,
% 59.78/60.14 skol19, skol20 ) ==> relation_dom( skol20 ) }.
% 59.78/60.14 parent0[0]: (40769) {G1,W7,D3,L1,V0,M1} { relation_dom( skol20 ) ==>
% 59.78/60.14 relation_dom_as_subset( skol18, skol19, skol20 ) }.
% 59.78/60.14 substitution0:
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 subsumption: (1135) {G2,W7,D3,L1,V0,M1} R(1134,66) { relation_dom_as_subset
% 59.78/60.14 ( skol18, skol19, skol20 ) ==> relation_dom( skol20 ) }.
% 59.78/60.14 parent0: (40770) {G1,W7,D3,L1,V0,M1} { relation_dom_as_subset( skol18,
% 59.78/60.14 skol19, skol20 ) ==> relation_dom( skol20 ) }.
% 59.78/60.14 substitution0:
% 59.78/60.14 end
% 59.78/60.14 permutation0:
% 59.78/60.14 0 ==> 0
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 eqswap: (40771) {G0,W23,D4,L6,V3,M6} { apply( relation_composition( Y, X )
% 59.78/60.14 , Z ) ==> apply( X, apply( Y, Z ) ), ! relation( Y ), ! function( Y ), !
% 59.78/60.14 relation( X ), ! function( X ), ! in( Z, relation_dom( Y ) ) }.
% 59.78/60.14 parent0[5]: (79) {G0,W23,D4,L6,V3,M6} I { ! relation( X ), ! function( X )
% 59.78/60.14 , ! relation( Y ), ! function( Y ), ! in( Z, relation_dom( X ) ), apply(
% 59.78/60.14 Y, apply( X, Z ) ) ==> apply( relation_composition( X, Y ), Z ) }.
% 59.78/60.14 substitution0:
% 59.78/60.14 X := Y
% 59.78/60.14 Y := X
% 59.78/60.14 Z := Z
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 eqswap: (40772) {G0,W11,D4,L1,V0,M1} { ! apply( relation_composition(
% 59.78/60.14 skol20, skol21 ), skol22 ) ==> apply( skol21, apply( skol20, skol22 ) )
% 59.78/60.14 }.
% 59.78/60.14 parent0[0]: (78) {G0,W11,D4,L1,V0,M1} I { ! apply( skol21, apply( skol20,
% 59.78/60.14 skol22 ) ) ==> apply( relation_composition( skol20, skol21 ), skol22 )
% 59.78/60.14 }.
% 59.78/60.14 substitution0:
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 resolution: (40773) {G1,W12,D3,L5,V0,M5} { ! relation( skol20 ), !
% 59.78/60.14 function( skol20 ), ! relation( skol21 ), ! function( skol21 ), ! in(
% 59.78/60.14 skol22, relation_dom( skol20 ) ) }.
% 59.78/60.14 parent0[0]: (40772) {G0,W11,D4,L1,V0,M1} { ! apply( relation_composition(
% 59.78/60.14 skol20, skol21 ), skol22 ) ==> apply( skol21, apply( skol20, skol22 ) )
% 59.78/60.14 }.
% 59.78/60.14 parent1[0]: (40771) {G0,W23,D4,L6,V3,M6} { apply( relation_composition( Y
% 59.78/60.14 , X ), Z ) ==> apply( X, apply( Y, Z ) ), ! relation( Y ), ! function( Y
% 59.78/60.14 ), ! relation( X ), ! function( X ), ! in( Z, relation_dom( Y ) ) }.
% 59.78/60.14 substitution0:
% 59.78/60.14 end
% 59.78/60.14 substitution1:
% 59.78/60.14 X := skol21
% 59.78/60.14 Y := skol20
% 59.78/60.14 Z := skol22
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 resolution: (40774) {G1,W10,D3,L4,V0,M4} { ! relation( skol20 ), !
% 59.78/60.14 relation( skol21 ), ! function( skol21 ), ! in( skol22, relation_dom(
% 59.78/60.14 skol20 ) ) }.
% 59.78/60.14 parent0[1]: (40773) {G1,W12,D3,L5,V0,M5} { ! relation( skol20 ), !
% 59.78/60.14 function( skol20 ), ! relation( skol21 ), ! function( skol21 ), ! in(
% 59.78/60.14 skol22, relation_dom( skol20 ) ) }.
% 59.78/60.14 parent1[0]: (71) {G0,W2,D2,L1,V0,M1} I { function( skol20 ) }.
% 59.78/60.14 substitution0:
% 59.78/60.14 end
% 59.78/60.14 substitution1:
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 subsumption: (1285) {G1,W10,D3,L4,V0,M4} R(79,78);r(71) { ! relation(
% 59.78/60.14 skol20 ), ! relation( skol21 ), ! function( skol21 ), ! in( skol22,
% 59.78/60.14 relation_dom( skol20 ) ) }.
% 59.78/60.14 parent0: (40774) {G1,W10,D3,L4,V0,M4} { ! relation( skol20 ), ! relation(
% 59.78/60.14 skol21 ), ! function( skol21 ), ! in( skol22, relation_dom( skol20 ) )
% 59.78/60.14 }.
% 59.78/60.14 substitution0:
% 59.78/60.14 end
% 59.78/60.14 permutation0:
% 59.78/60.14 0 ==> 0
% 59.78/60.14 1 ==> 1
% 59.78/60.14 2 ==> 2
% 59.78/60.14 3 ==> 3
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 resolution: (40775) {G1,W2,D2,L1,V0,M1} { relation( skol20 ) }.
% 59.78/60.14 parent0[0]: (458) {G1,W6,D2,L2,V3,M2} R(15,3) { ! relation_of2_as_subset( X
% 59.78/60.14 , Y, Z ), relation( X ) }.
% 59.78/60.14 parent1[0]: (73) {G0,W4,D2,L1,V0,M1} I { relation_of2_as_subset( skol20,
% 59.78/60.14 skol18, skol19 ) }.
% 59.78/60.14 substitution0:
% 59.78/60.14 X := skol20
% 59.78/60.14 Y := skol18
% 59.78/60.14 Z := skol19
% 59.78/60.14 end
% 59.78/60.14 substitution1:
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 subsumption: (2572) {G2,W2,D2,L1,V0,M1} R(458,73) { relation( skol20 ) }.
% 59.78/60.14 parent0: (40775) {G1,W2,D2,L1,V0,M1} { relation( skol20 ) }.
% 59.78/60.14 substitution0:
% 59.78/60.14 end
% 59.78/60.14 permutation0:
% 59.78/60.14 0 ==> 0
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 paramod: (40778) {G3,W8,D3,L2,V0,M2} { relation_dom( skol20 ) ==> skol18,
% 59.78/60.14 ! quasi_total( skol20, skol18, skol19 ) }.
% 59.78/60.14 parent0[0]: (1135) {G2,W7,D3,L1,V0,M1} R(1134,66) { relation_dom_as_subset
% 59.78/60.14 ( skol18, skol19, skol20 ) ==> relation_dom( skol20 ) }.
% 59.78/60.14 parent1[1; 1]: (299) {G2,W10,D3,L2,V0,M2} R(73,5);r(242) { ! quasi_total(
% 59.78/60.14 skol20, skol18, skol19 ), relation_dom_as_subset( skol18, skol19, skol20
% 59.78/60.14 ) ==> skol18 }.
% 59.78/60.14 substitution0:
% 59.78/60.14 end
% 59.78/60.14 substitution1:
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 resolution: (40779) {G1,W4,D3,L1,V0,M1} { relation_dom( skol20 ) ==>
% 59.78/60.14 skol18 }.
% 59.78/60.14 parent0[1]: (40778) {G3,W8,D3,L2,V0,M2} { relation_dom( skol20 ) ==>
% 59.78/60.14 skol18, ! quasi_total( skol20, skol18, skol19 ) }.
% 59.78/60.14 parent1[0]: (72) {G0,W4,D2,L1,V0,M1} I { quasi_total( skol20, skol18,
% 59.78/60.14 skol19 ) }.
% 59.78/60.14 substitution0:
% 59.78/60.14 end
% 59.78/60.14 substitution1:
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 subsumption: (13374) {G3,W4,D3,L1,V0,M1} S(299);d(1135);r(72) {
% 59.78/60.14 relation_dom( skol20 ) ==> skol18 }.
% 59.78/60.14 parent0: (40779) {G1,W4,D3,L1,V0,M1} { relation_dom( skol20 ) ==> skol18
% 59.78/60.14 }.
% 59.78/60.14 substitution0:
% 59.78/60.14 end
% 59.78/60.14 permutation0:
% 59.78/60.14 0 ==> 0
% 59.78/60.14 end
% 59.78/60.14
% 59.78/60.14 paramod: (40782) {G2,W9,D2,L4,V0,M4} { ! in( skol22, skol18 ), ! relation
% 59.78/60.14 ( skol20 ), ! relation( skol21 ), ! function( skol21 ) }.
% 59.78/60.15 parent0[0]: (13374) {G3,W4,D3,L1,V0,M1} S(299);d(1135);r(72) { relation_dom
% 59.78/60.15 ( skol20 ) ==> skol18 }.
% 59.78/60.15 parent1[3; 3]: (1285) {G1,W10,D3,L4,V0,M4} R(79,78);r(71) { ! relation(
% 59.78/60.15 skol20 ), ! relation( skol21 ), ! function( skol21 ), ! in( skol22,
% 59.78/60.15 relation_dom( skol20 ) ) }.
% 59.78/60.15 substitution0:
% 59.78/60.15 end
% 59.78/60.15 substitution1:
% 59.78/60.15 end
% 59.78/60.15
% 59.78/60.15 resolution: (40783) {G3,W7,D2,L3,V0,M3} { ! in( skol22, skol18 ), !
% 59.78/60.15 relation( skol21 ), ! function( skol21 ) }.
% 59.78/60.15 parent0[1]: (40782) {G2,W9,D2,L4,V0,M4} { ! in( skol22, skol18 ), !
% 59.78/60.15 relation( skol20 ), ! relation( skol21 ), ! function( skol21 ) }.
% 59.78/60.15 parent1[0]: (2572) {G2,W2,D2,L1,V0,M1} R(458,73) { relation( skol20 ) }.
% 59.78/60.15 substitution0:
% 59.78/60.15 end
% 59.78/60.15 substitution1:
% 59.78/60.15 end
% 59.78/60.15
% 59.78/60.15 subsumption: (20097) {G4,W7,D2,L3,V0,M3} S(1285);d(13374);r(2572) { !
% 59.78/60.15 relation( skol21 ), ! function( skol21 ), ! in( skol22, skol18 ) }.
% 59.78/60.15 parent0: (40783) {G3,W7,D2,L3,V0,M3} { ! in( skol22, skol18 ), ! relation
% 59.78/60.15 ( skol21 ), ! function( skol21 ) }.
% 59.78/60.15 substitution0:
% 59.78/60.15 end
% 59.78/60.15 permutation0:
% 59.78/60.15 0 ==> 2
% 59.78/60.15 1 ==> 0
% 59.78/60.15 2 ==> 1
% 59.78/60.15 end
% 59.78/60.15
% 59.78/60.15 resolution: (40784) {G1,W5,D2,L2,V0,M2} { ! function( skol21 ), ! in(
% 59.78/60.15 skol22, skol18 ) }.
% 59.78/60.15 parent0[0]: (20097) {G4,W7,D2,L3,V0,M3} S(1285);d(13374);r(2572) { !
% 59.78/60.15 relation( skol21 ), ! function( skol21 ), ! in( skol22, skol18 ) }.
% 59.78/60.15 parent1[0]: (74) {G0,W2,D2,L1,V0,M1} I { relation( skol21 ) }.
% 59.78/60.15 substitution0:
% 59.78/60.15 end
% 59.78/60.15 substitution1:
% 59.78/60.15 end
% 59.78/60.15
% 59.78/60.15 resolution: (40785) {G1,W3,D2,L1,V0,M1} { ! in( skol22, skol18 ) }.
% 59.78/60.15 parent0[0]: (40784) {G1,W5,D2,L2,V0,M2} { ! function( skol21 ), ! in(
% 59.78/60.15 skol22, skol18 ) }.
% 59.78/60.15 parent1[0]: (75) {G0,W2,D2,L1,V0,M1} I { function( skol21 ) }.
% 59.78/60.15 substitution0:
% 59.78/60.15 end
% 59.78/60.15 substitution1:
% 59.78/60.15 end
% 59.78/60.15
% 59.78/60.15 resolution: (40786) {G1,W0,D0,L0,V0,M0} { }.
% 59.78/60.15 parent0[0]: (40785) {G1,W3,D2,L1,V0,M1} { ! in( skol22, skol18 ) }.
% 59.78/60.15 parent1[0]: (76) {G0,W3,D2,L1,V0,M1} I { in( skol22, skol18 ) }.
% 59.78/60.15 substitution0:
% 59.78/60.15 end
% 59.78/60.15 substitution1:
% 59.78/60.15 end
% 59.78/60.15
% 59.78/60.15 subsumption: (40153) {G5,W0,D0,L0,V0,M0} S(20097);r(74);r(75);r(76) { }.
% 59.78/60.15 parent0: (40786) {G1,W0,D0,L0,V0,M0} { }.
% 59.78/60.15 substitution0:
% 59.78/60.15 end
% 59.78/60.15 permutation0:
% 59.78/60.15 end
% 59.78/60.15
% 59.78/60.15 Proof check complete!
% 59.78/60.15
% 59.78/60.15 Memory use:
% 59.78/60.15
% 59.78/60.15 space for terms: 500666
% 59.78/60.15 space for clauses: 1832401
% 59.78/60.15
% 59.78/60.15
% 59.78/60.15 clauses generated: 731738
% 59.78/60.15 clauses kept: 40154
% 59.78/60.15 clauses selected: 1414
% 59.78/60.15 clauses deleted: 6843
% 59.78/60.15 clauses inuse deleted: 171
% 59.78/60.15
% 59.78/60.15 subsentry: 1203457
% 59.78/60.15 literals s-matched: 726186
% 59.78/60.15 literals matched: 706887
% 59.78/60.15 full subsumption: 267517
% 59.78/60.15
% 59.78/60.15 checksum: -671688089
% 59.78/60.15
% 59.78/60.15
% 59.78/60.15 Bliksem ended
%------------------------------------------------------------------------------