TSTP Solution File: SEU089+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SEU089+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Tue Jul 19 07:10:34 EDT 2022
% Result : Theorem 0.87s 1.24s
% Output : Refutation 0.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU089+1 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.11 % Command : bliksem %s
% 0.10/0.32 % Computer : n025.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % DateTime : Sun Jun 19 04:22:13 EDT 2022
% 0.10/0.32 % CPUTime :
% 0.67/1.08 *** allocated 10000 integers for termspace/termends
% 0.67/1.08 *** allocated 10000 integers for clauses
% 0.67/1.08 *** allocated 10000 integers for justifications
% 0.67/1.08 Bliksem 1.12
% 0.67/1.08
% 0.67/1.08
% 0.67/1.08 Automatic Strategy Selection
% 0.67/1.08
% 0.67/1.08
% 0.67/1.08 Clauses:
% 0.67/1.08
% 0.67/1.08 { ! in( X, Y ), ! in( Y, X ) }.
% 0.67/1.08 { ! ordinal( X ), ! element( Y, X ), epsilon_transitive( Y ) }.
% 0.67/1.08 { ! ordinal( X ), ! element( Y, X ), epsilon_connected( Y ) }.
% 0.67/1.08 { ! ordinal( X ), ! element( Y, X ), ordinal( Y ) }.
% 0.67/1.08 { ! empty( X ), finite( X ) }.
% 0.67/1.08 { ! empty( X ), function( X ) }.
% 0.67/1.08 { ! ordinal( X ), epsilon_transitive( X ) }.
% 0.67/1.08 { ! ordinal( X ), epsilon_connected( X ) }.
% 0.67/1.08 { ! empty( X ), relation( X ) }.
% 0.67/1.08 { ! element( X, powerset( cartesian_product2( Y, Z ) ) ), relation( X ) }.
% 0.67/1.08 { ! empty( X ), ! ordinal( X ), alpha1( X ) }.
% 0.67/1.08 { ! empty( X ), ! ordinal( X ), natural( X ) }.
% 0.67/1.08 { ! alpha1( X ), epsilon_transitive( X ) }.
% 0.67/1.08 { ! alpha1( X ), epsilon_connected( X ) }.
% 0.67/1.08 { ! alpha1( X ), ordinal( X ) }.
% 0.67/1.08 { ! epsilon_transitive( X ), ! epsilon_connected( X ), ! ordinal( X ),
% 0.67/1.08 alpha1( X ) }.
% 0.67/1.08 { ! finite( X ), ! element( Y, powerset( X ) ), finite( Y ) }.
% 0.67/1.08 { ! relation( X ), ! empty( X ), ! function( X ), relation( X ) }.
% 0.67/1.08 { ! relation( X ), ! empty( X ), ! function( X ), function( X ) }.
% 0.67/1.08 { ! relation( X ), ! empty( X ), ! function( X ), one_to_one( X ) }.
% 0.67/1.08 { ! epsilon_transitive( X ), ! epsilon_connected( X ), ordinal( X ) }.
% 0.67/1.08 { ! empty( X ), epsilon_transitive( X ) }.
% 0.67/1.08 { ! empty( X ), epsilon_connected( X ) }.
% 0.67/1.08 { ! empty( X ), ordinal( X ) }.
% 0.67/1.08 { ! element( X, positive_rationals ), ! ordinal( X ), alpha2( X ) }.
% 0.67/1.08 { ! element( X, positive_rationals ), ! ordinal( X ), natural( X ) }.
% 0.67/1.08 { ! alpha2( X ), epsilon_transitive( X ) }.
% 0.67/1.08 { ! alpha2( X ), epsilon_connected( X ) }.
% 0.67/1.08 { ! alpha2( X ), ordinal( X ) }.
% 0.67/1.08 { ! epsilon_transitive( X ), ! epsilon_connected( X ), ! ordinal( X ),
% 0.67/1.08 alpha2( X ) }.
% 0.67/1.08 { cartesian_product3( X, Y, Z ) = cartesian_product2( cartesian_product2( X
% 0.67/1.08 , Y ), Z ) }.
% 0.67/1.08 { element( skol1( X ), X ) }.
% 0.67/1.08 { empty( empty_set ) }.
% 0.67/1.08 { relation( empty_set ) }.
% 0.67/1.08 { relation_empty_yielding( empty_set ) }.
% 0.67/1.08 { ! finite( X ), ! finite( Y ), finite( cartesian_product2( X, Y ) ) }.
% 0.67/1.08 { ! empty( powerset( X ) ) }.
% 0.67/1.08 { empty( empty_set ) }.
% 0.67/1.08 { relation( empty_set ) }.
% 0.67/1.08 { relation_empty_yielding( empty_set ) }.
% 0.67/1.08 { function( empty_set ) }.
% 0.67/1.08 { one_to_one( empty_set ) }.
% 0.67/1.08 { empty( empty_set ) }.
% 0.67/1.08 { epsilon_transitive( empty_set ) }.
% 0.67/1.08 { epsilon_connected( empty_set ) }.
% 0.67/1.08 { ordinal( empty_set ) }.
% 0.67/1.08 { empty( empty_set ) }.
% 0.67/1.08 { relation( empty_set ) }.
% 0.67/1.08 { empty( X ), empty( Y ), ! empty( cartesian_product2( X, Y ) ) }.
% 0.67/1.08 { empty( X ), empty( Y ), empty( Z ), ! empty( cartesian_product3( X, Y, Z
% 0.67/1.08 ) ) }.
% 0.67/1.08 { ! empty( positive_rationals ) }.
% 0.67/1.08 { ! empty( skol2 ) }.
% 0.67/1.08 { epsilon_transitive( skol2 ) }.
% 0.67/1.08 { epsilon_connected( skol2 ) }.
% 0.67/1.08 { ordinal( skol2 ) }.
% 0.67/1.08 { natural( skol2 ) }.
% 0.67/1.08 { ! empty( skol3 ) }.
% 0.67/1.08 { finite( skol3 ) }.
% 0.67/1.08 { relation( skol4 ) }.
% 0.67/1.08 { function( skol4 ) }.
% 0.67/1.08 { function_yielding( skol4 ) }.
% 0.67/1.08 { relation( skol5 ) }.
% 0.67/1.08 { function( skol5 ) }.
% 0.67/1.08 { epsilon_transitive( skol6 ) }.
% 0.67/1.08 { epsilon_connected( skol6 ) }.
% 0.67/1.08 { ordinal( skol6 ) }.
% 0.67/1.08 { epsilon_transitive( skol7 ) }.
% 0.67/1.08 { epsilon_connected( skol7 ) }.
% 0.67/1.08 { ordinal( skol7 ) }.
% 0.67/1.08 { being_limit_ordinal( skol7 ) }.
% 0.67/1.08 { empty( skol8 ) }.
% 0.67/1.08 { relation( skol8 ) }.
% 0.67/1.08 { empty( X ), ! empty( skol9( Y ) ) }.
% 0.67/1.08 { empty( X ), element( skol9( X ), powerset( X ) ) }.
% 0.67/1.08 { empty( skol10 ) }.
% 0.67/1.08 { element( skol11, positive_rationals ) }.
% 0.67/1.08 { ! empty( skol11 ) }.
% 0.67/1.08 { epsilon_transitive( skol11 ) }.
% 0.67/1.08 { epsilon_connected( skol11 ) }.
% 0.67/1.08 { ordinal( skol11 ) }.
% 0.67/1.08 { empty( skol12( Y ) ) }.
% 0.67/1.08 { relation( skol12( Y ) ) }.
% 0.67/1.08 { function( skol12( Y ) ) }.
% 0.67/1.08 { one_to_one( skol12( Y ) ) }.
% 0.67/1.08 { epsilon_transitive( skol12( Y ) ) }.
% 0.67/1.08 { epsilon_connected( skol12( Y ) ) }.
% 0.67/1.08 { ordinal( skol12( Y ) ) }.
% 0.67/1.08 { natural( skol12( Y ) ) }.
% 0.67/1.08 { finite( skol12( Y ) ) }.
% 0.67/1.08 { element( skol12( X ), powerset( X ) ) }.
% 0.67/1.08 { relation( skol13 ) }.
% 0.67/1.08 { empty( skol13 ) }.
% 0.67/1.08 { function( skol13 ) }.
% 0.67/1.08 { relation( skol14 ) }.
% 0.67/1.08 { function( skol14 ) }.
% 0.67/1.08 { one_to_one( skol14 ) }.
% 0.67/1.08 { empty( skol14 ) }.
% 0.67/1.08 { epsilon_transitive( skol14 ) }.
% 0.67/1.08 { epsilon_connected( skol14 ) }.
% 0.67/1.08 { ordinal( skol14 ) }.
% 0.67/1.08 { relation( skol15 ) }.
% 0.67/1.08 { function( skol15 ) }.
% 0.67/1.08 { transfinite_sequence( skol15 ) }.
% 0.67/1.08 { ordinal_yielding( skol15 ) }.
% 0.87/1.24 { ! empty( skol16 ) }.
% 0.87/1.24 { relation( skol16 ) }.
% 0.87/1.24 { empty( skol17( Y ) ) }.
% 0.87/1.24 { element( skol17( X ), powerset( X ) ) }.
% 0.87/1.24 { ! empty( skol18 ) }.
% 0.87/1.24 { element( skol19, positive_rationals ) }.
% 0.87/1.24 { empty( skol19 ) }.
% 0.87/1.24 { epsilon_transitive( skol19 ) }.
% 0.87/1.24 { epsilon_connected( skol19 ) }.
% 0.87/1.24 { ordinal( skol19 ) }.
% 0.87/1.24 { natural( skol19 ) }.
% 0.87/1.24 { empty( X ), ! empty( skol20( Y ) ) }.
% 0.87/1.24 { empty( X ), finite( skol20( Y ) ) }.
% 0.87/1.24 { empty( X ), element( skol20( X ), powerset( X ) ) }.
% 0.87/1.24 { relation( skol21 ) }.
% 0.87/1.24 { function( skol21 ) }.
% 0.87/1.24 { one_to_one( skol21 ) }.
% 0.87/1.24 { ! empty( skol22 ) }.
% 0.87/1.24 { epsilon_transitive( skol22 ) }.
% 0.87/1.24 { epsilon_connected( skol22 ) }.
% 0.87/1.24 { ordinal( skol22 ) }.
% 0.87/1.24 { relation( skol23 ) }.
% 0.87/1.24 { relation_empty_yielding( skol23 ) }.
% 0.87/1.24 { relation( skol24 ) }.
% 0.87/1.24 { relation_empty_yielding( skol24 ) }.
% 0.87/1.24 { function( skol24 ) }.
% 0.87/1.24 { relation( skol25 ) }.
% 0.87/1.24 { function( skol25 ) }.
% 0.87/1.24 { transfinite_sequence( skol25 ) }.
% 0.87/1.24 { relation( skol26 ) }.
% 0.87/1.24 { relation_non_empty( skol26 ) }.
% 0.87/1.24 { function( skol26 ) }.
% 0.87/1.24 { subset( X, X ) }.
% 0.87/1.24 { ! finite( X ), ! finite( Y ), finite( cartesian_product2( X, Y ) ) }.
% 0.87/1.24 { ! in( X, Y ), element( X, Y ) }.
% 0.87/1.24 { finite( skol27 ) }.
% 0.87/1.24 { finite( skol28 ) }.
% 0.87/1.24 { finite( skol29 ) }.
% 0.87/1.24 { ! finite( cartesian_product3( skol27, skol28, skol29 ) ) }.
% 0.87/1.24 { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.87/1.24 { ! element( X, powerset( Y ) ), subset( X, Y ) }.
% 0.87/1.24 { ! subset( X, Y ), element( X, powerset( Y ) ) }.
% 0.87/1.24 { ! in( X, Z ), ! element( Z, powerset( Y ) ), element( X, Y ) }.
% 0.87/1.24 { ! in( X, Y ), ! element( Y, powerset( Z ) ), ! empty( Z ) }.
% 0.87/1.24 { ! empty( X ), X = empty_set }.
% 0.87/1.24 { ! in( X, Y ), ! empty( Y ) }.
% 0.87/1.24 { ! empty( X ), X = Y, ! empty( Y ) }.
% 0.87/1.24
% 0.87/1.24 percentage equality = 0.014286, percentage horn = 0.957746
% 0.87/1.24 This is a problem with some equality
% 0.87/1.24
% 0.87/1.24
% 0.87/1.24
% 0.87/1.24 Options Used:
% 0.87/1.24
% 0.87/1.24 useres = 1
% 0.87/1.24 useparamod = 1
% 0.87/1.24 useeqrefl = 1
% 0.87/1.24 useeqfact = 1
% 0.87/1.24 usefactor = 1
% 0.87/1.24 usesimpsplitting = 0
% 0.87/1.24 usesimpdemod = 5
% 0.87/1.24 usesimpres = 3
% 0.87/1.24
% 0.87/1.24 resimpinuse = 1000
% 0.87/1.24 resimpclauses = 20000
% 0.87/1.24 substype = eqrewr
% 0.87/1.24 backwardsubs = 1
% 0.87/1.24 selectoldest = 5
% 0.87/1.24
% 0.87/1.24 litorderings [0] = split
% 0.87/1.24 litorderings [1] = extend the termordering, first sorting on arguments
% 0.87/1.24
% 0.87/1.24 termordering = kbo
% 0.87/1.24
% 0.87/1.24 litapriori = 0
% 0.87/1.24 termapriori = 1
% 0.87/1.24 litaposteriori = 0
% 0.87/1.24 termaposteriori = 0
% 0.87/1.24 demodaposteriori = 0
% 0.87/1.24 ordereqreflfact = 0
% 0.87/1.24
% 0.87/1.24 litselect = negord
% 0.87/1.24
% 0.87/1.24 maxweight = 15
% 0.87/1.24 maxdepth = 30000
% 0.87/1.24 maxlength = 115
% 0.87/1.24 maxnrvars = 195
% 0.87/1.24 excuselevel = 1
% 0.87/1.24 increasemaxweight = 1
% 0.87/1.24
% 0.87/1.24 maxselected = 10000000
% 0.87/1.24 maxnrclauses = 10000000
% 0.87/1.24
% 0.87/1.24 showgenerated = 0
% 0.87/1.24 showkept = 0
% 0.87/1.24 showselected = 0
% 0.87/1.24 showdeleted = 0
% 0.87/1.24 showresimp = 1
% 0.87/1.24 showstatus = 2000
% 0.87/1.24
% 0.87/1.24 prologoutput = 0
% 0.87/1.24 nrgoals = 5000000
% 0.87/1.24 totalproof = 1
% 0.87/1.24
% 0.87/1.24 Symbols occurring in the translation:
% 0.87/1.24
% 0.87/1.24 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.87/1.24 . [1, 2] (w:1, o:63, a:1, s:1, b:0),
% 0.87/1.24 ! [4, 1] (w:0, o:35, a:1, s:1, b:0),
% 0.87/1.24 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.87/1.24 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.87/1.24 in [37, 2] (w:1, o:87, a:1, s:1, b:0),
% 0.87/1.24 ordinal [38, 1] (w:1, o:41, a:1, s:1, b:0),
% 0.87/1.24 element [39, 2] (w:1, o:88, a:1, s:1, b:0),
% 0.87/1.24 epsilon_transitive [40, 1] (w:1, o:42, a:1, s:1, b:0),
% 0.87/1.24 epsilon_connected [41, 1] (w:1, o:43, a:1, s:1, b:0),
% 0.87/1.24 empty [42, 1] (w:1, o:44, a:1, s:1, b:0),
% 0.87/1.24 finite [43, 1] (w:1, o:45, a:1, s:1, b:0),
% 0.87/1.24 function [44, 1] (w:1, o:46, a:1, s:1, b:0),
% 0.87/1.24 relation [45, 1] (w:1, o:47, a:1, s:1, b:0),
% 0.87/1.24 cartesian_product2 [47, 2] (w:1, o:89, a:1, s:1, b:0),
% 0.87/1.24 powerset [48, 1] (w:1, o:50, a:1, s:1, b:0),
% 0.87/1.24 natural [49, 1] (w:1, o:40, a:1, s:1, b:0),
% 0.87/1.24 one_to_one [50, 1] (w:1, o:48, a:1, s:1, b:0),
% 0.87/1.24 positive_rationals [51, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.87/1.24 cartesian_product3 [52, 3] (w:1, o:91, a:1, s:1, b:0),
% 0.87/1.24 empty_set [53, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.87/1.24 relation_empty_yielding [54, 1] (w:1, o:51, a:1, s:1, b:0),
% 0.87/1.24 function_yielding [55, 1] (w:1, o:52, a:1, s:1, b:0),
% 0.87/1.24 being_limit_ordinal [56, 1] (w:1, o:55, a:1, s:1, b:0),
% 0.87/1.24 transfinite_sequence [57, 1] (w:1, o:61, a:1, s:1, b:0),
% 0.87/1.24 ordinal_yielding [58, 1] (w:1, o:49, a:1, s:1, b:0),
% 0.87/1.24 relation_non_empty [59, 1] (w:1, o:62, a:1, s:1, b:0),
% 0.87/1.24 subset [60, 2] (w:1, o:90, a:1, s:1, b:0),
% 0.87/1.24 alpha1 [61, 1] (w:1, o:53, a:1, s:1, b:1),
% 0.87/1.24 alpha2 [62, 1] (w:1, o:54, a:1, s:1, b:1),
% 0.87/1.24 skol1 [63, 1] (w:1, o:56, a:1, s:1, b:1),
% 0.87/1.24 skol2 [64, 0] (w:1, o:19, a:1, s:1, b:1),
% 0.87/1.24 skol3 [65, 0] (w:1, o:29, a:1, s:1, b:1),
% 0.87/1.24 skol4 [66, 0] (w:1, o:30, a:1, s:1, b:1),
% 0.87/1.24 skol5 [67, 0] (w:1, o:31, a:1, s:1, b:1),
% 0.87/1.24 skol6 [68, 0] (w:1, o:32, a:1, s:1, b:1),
% 0.87/1.24 skol7 [69, 0] (w:1, o:33, a:1, s:1, b:1),
% 0.87/1.24 skol8 [70, 0] (w:1, o:34, a:1, s:1, b:1),
% 0.87/1.24 skol9 [71, 1] (w:1, o:57, a:1, s:1, b:1),
% 0.87/1.24 skol10 [72, 0] (w:1, o:11, a:1, s:1, b:1),
% 0.87/1.24 skol11 [73, 0] (w:1, o:12, a:1, s:1, b:1),
% 0.87/1.24 skol12 [74, 1] (w:1, o:58, a:1, s:1, b:1),
% 0.87/1.24 skol13 [75, 0] (w:1, o:13, a:1, s:1, b:1),
% 0.87/1.24 skol14 [76, 0] (w:1, o:14, a:1, s:1, b:1),
% 0.87/1.24 skol15 [77, 0] (w:1, o:15, a:1, s:1, b:1),
% 0.87/1.24 skol16 [78, 0] (w:1, o:16, a:1, s:1, b:1),
% 0.87/1.24 skol17 [79, 1] (w:1, o:59, a:1, s:1, b:1),
% 0.87/1.24 skol18 [80, 0] (w:1, o:17, a:1, s:1, b:1),
% 0.87/1.24 skol19 [81, 0] (w:1, o:18, a:1, s:1, b:1),
% 0.87/1.24 skol20 [82, 1] (w:1, o:60, a:1, s:1, b:1),
% 0.87/1.24 skol21 [83, 0] (w:1, o:20, a:1, s:1, b:1),
% 0.87/1.24 skol22 [84, 0] (w:1, o:21, a:1, s:1, b:1),
% 0.87/1.24 skol23 [85, 0] (w:1, o:22, a:1, s:1, b:1),
% 0.87/1.24 skol24 [86, 0] (w:1, o:23, a:1, s:1, b:1),
% 0.87/1.24 skol25 [87, 0] (w:1, o:24, a:1, s:1, b:1),
% 0.87/1.24 skol26 [88, 0] (w:1, o:25, a:1, s:1, b:1),
% 0.87/1.24 skol27 [89, 0] (w:1, o:26, a:1, s:1, b:1),
% 0.87/1.24 skol28 [90, 0] (w:1, o:27, a:1, s:1, b:1),
% 0.87/1.24 skol29 [91, 0] (w:1, o:28, a:1, s:1, b:1).
% 0.87/1.24
% 0.87/1.24
% 0.87/1.24 Starting Search:
% 0.87/1.24
% 0.87/1.24 *** allocated 15000 integers for clauses
% 0.87/1.24 *** allocated 22500 integers for clauses
% 0.87/1.24 *** allocated 33750 integers for clauses
% 0.87/1.24 *** allocated 50625 integers for clauses
% 0.87/1.24 Resimplifying inuse:
% 0.87/1.24 Done
% 0.87/1.24
% 0.87/1.24 *** allocated 15000 integers for termspace/termends
% 0.87/1.24 *** allocated 75937 integers for clauses
% 0.87/1.24 *** allocated 22500 integers for termspace/termends
% 0.87/1.24 *** allocated 113905 integers for clauses
% 0.87/1.24
% 0.87/1.24 Intermediate Status:
% 0.87/1.24 Generated: 5314
% 0.87/1.24 Kept: 2008
% 0.87/1.24 Inuse: 418
% 0.87/1.24 Deleted: 138
% 0.87/1.24 Deletedinuse: 94
% 0.87/1.24
% 0.87/1.24 Resimplifying inuse:
% 0.87/1.24 Done
% 0.87/1.24
% 0.87/1.24 *** allocated 33750 integers for termspace/termends
% 0.87/1.24 *** allocated 170857 integers for clauses
% 0.87/1.24 Resimplifying inuse:
% 0.87/1.24 Done
% 0.87/1.24
% 0.87/1.24 *** allocated 50625 integers for termspace/termends
% 0.87/1.24 *** allocated 256285 integers for clauses
% 0.87/1.24
% 0.87/1.24 Bliksems!, er is een bewijs:
% 0.87/1.24 % SZS status Theorem
% 0.87/1.24 % SZS output start Refutation
% 0.87/1.24
% 0.87/1.24 (28) {G0,W10,D4,L1,V3,M1} I { cartesian_product2( cartesian_product2( X, Y
% 0.87/1.24 ), Z ) ==> cartesian_product3( X, Y, Z ) }.
% 0.87/1.24 (33) {G0,W8,D3,L3,V2,M3} I { ! finite( X ), ! finite( Y ), finite(
% 0.87/1.24 cartesian_product2( X, Y ) ) }.
% 0.87/1.24 (130) {G0,W2,D2,L1,V0,M1} I { finite( skol27 ) }.
% 0.87/1.24 (131) {G0,W2,D2,L1,V0,M1} I { finite( skol28 ) }.
% 0.87/1.24 (132) {G0,W2,D2,L1,V0,M1} I { finite( skol29 ) }.
% 0.87/1.24 (133) {G0,W5,D3,L1,V0,M1} I { ! finite( cartesian_product3( skol27, skol28
% 0.87/1.24 , skol29 ) ) }.
% 0.87/1.24 (307) {G1,W11,D3,L4,V3,M4} R(33,33);d(28) { ! finite( X ), ! finite( Y ), !
% 0.87/1.24 finite( Z ), finite( cartesian_product3( Y, Z, X ) ) }.
% 0.87/1.24 (3490) {G2,W4,D2,L2,V0,M2} R(307,133);r(132) { ! finite( skol27 ), ! finite
% 0.87/1.24 ( skol28 ) }.
% 0.87/1.24 (3758) {G3,W0,D0,L0,V0,M0} S(3490);r(130);r(131) { }.
% 0.87/1.24
% 0.87/1.24
% 0.87/1.24 % SZS output end Refutation
% 0.87/1.24 found a proof!
% 0.87/1.24
% 0.87/1.24
% 0.87/1.24 Unprocessed initial clauses:
% 0.87/1.24
% 0.87/1.24 (3760) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), ! in( Y, X ) }.
% 0.87/1.24 (3761) {G0,W7,D2,L3,V2,M3} { ! ordinal( X ), ! element( Y, X ),
% 0.87/1.24 epsilon_transitive( Y ) }.
% 0.87/1.24 (3762) {G0,W7,D2,L3,V2,M3} { ! ordinal( X ), ! element( Y, X ),
% 0.87/1.24 epsilon_connected( Y ) }.
% 0.87/1.24 (3763) {G0,W7,D2,L3,V2,M3} { ! ordinal( X ), ! element( Y, X ), ordinal( Y
% 0.87/1.24 ) }.
% 0.87/1.24 (3764) {G0,W4,D2,L2,V1,M2} { ! empty( X ), finite( X ) }.
% 0.87/1.24 (3765) {G0,W4,D2,L2,V1,M2} { ! empty( X ), function( X ) }.
% 0.87/1.24 (3766) {G0,W4,D2,L2,V1,M2} { ! ordinal( X ), epsilon_transitive( X ) }.
% 0.87/1.24 (3767) {G0,W4,D2,L2,V1,M2} { ! ordinal( X ), epsilon_connected( X ) }.
% 0.87/1.24 (3768) {G0,W4,D2,L2,V1,M2} { ! empty( X ), relation( X ) }.
% 0.87/1.24 (3769) {G0,W8,D4,L2,V3,M2} { ! element( X, powerset( cartesian_product2( Y
% 0.87/1.24 , Z ) ) ), relation( X ) }.
% 0.87/1.24 (3770) {G0,W6,D2,L3,V1,M3} { ! empty( X ), ! ordinal( X ), alpha1( X ) }.
% 0.87/1.24 (3771) {G0,W6,D2,L3,V1,M3} { ! empty( X ), ! ordinal( X ), natural( X )
% 0.87/1.24 }.
% 0.87/1.24 (3772) {G0,W4,D2,L2,V1,M2} { ! alpha1( X ), epsilon_transitive( X ) }.
% 0.87/1.24 (3773) {G0,W4,D2,L2,V1,M2} { ! alpha1( X ), epsilon_connected( X ) }.
% 0.87/1.24 (3774) {G0,W4,D2,L2,V1,M2} { ! alpha1( X ), ordinal( X ) }.
% 0.87/1.24 (3775) {G0,W8,D2,L4,V1,M4} { ! epsilon_transitive( X ), !
% 0.87/1.24 epsilon_connected( X ), ! ordinal( X ), alpha1( X ) }.
% 0.87/1.24 (3776) {G0,W8,D3,L3,V2,M3} { ! finite( X ), ! element( Y, powerset( X ) )
% 0.87/1.24 , finite( Y ) }.
% 0.87/1.24 (3777) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 0.87/1.24 ), relation( X ) }.
% 0.87/1.24 (3778) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 0.87/1.24 ), function( X ) }.
% 0.87/1.24 (3779) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 0.87/1.24 ), one_to_one( X ) }.
% 0.87/1.24 (3780) {G0,W6,D2,L3,V1,M3} { ! epsilon_transitive( X ), !
% 0.87/1.24 epsilon_connected( X ), ordinal( X ) }.
% 0.87/1.24 (3781) {G0,W4,D2,L2,V1,M2} { ! empty( X ), epsilon_transitive( X ) }.
% 0.87/1.24 (3782) {G0,W4,D2,L2,V1,M2} { ! empty( X ), epsilon_connected( X ) }.
% 0.87/1.24 (3783) {G0,W4,D2,L2,V1,M2} { ! empty( X ), ordinal( X ) }.
% 0.87/1.24 (3784) {G0,W7,D2,L3,V1,M3} { ! element( X, positive_rationals ), ! ordinal
% 0.87/1.24 ( X ), alpha2( X ) }.
% 0.87/1.24 (3785) {G0,W7,D2,L3,V1,M3} { ! element( X, positive_rationals ), ! ordinal
% 0.87/1.24 ( X ), natural( X ) }.
% 0.87/1.24 (3786) {G0,W4,D2,L2,V1,M2} { ! alpha2( X ), epsilon_transitive( X ) }.
% 0.87/1.24 (3787) {G0,W4,D2,L2,V1,M2} { ! alpha2( X ), epsilon_connected( X ) }.
% 0.87/1.24 (3788) {G0,W4,D2,L2,V1,M2} { ! alpha2( X ), ordinal( X ) }.
% 0.87/1.24 (3789) {G0,W8,D2,L4,V1,M4} { ! epsilon_transitive( X ), !
% 0.87/1.24 epsilon_connected( X ), ! ordinal( X ), alpha2( X ) }.
% 0.87/1.24 (3790) {G0,W10,D4,L1,V3,M1} { cartesian_product3( X, Y, Z ) =
% 0.87/1.24 cartesian_product2( cartesian_product2( X, Y ), Z ) }.
% 0.87/1.24 (3791) {G0,W4,D3,L1,V1,M1} { element( skol1( X ), X ) }.
% 0.87/1.24 (3792) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.87/1.24 (3793) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 0.87/1.24 (3794) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( empty_set ) }.
% 0.87/1.24 (3795) {G0,W8,D3,L3,V2,M3} { ! finite( X ), ! finite( Y ), finite(
% 0.87/1.24 cartesian_product2( X, Y ) ) }.
% 0.87/1.24 (3796) {G0,W3,D3,L1,V1,M1} { ! empty( powerset( X ) ) }.
% 0.87/1.24 (3797) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.87/1.24 (3798) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 0.87/1.24 (3799) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( empty_set ) }.
% 0.87/1.24 (3800) {G0,W2,D2,L1,V0,M1} { function( empty_set ) }.
% 0.87/1.24 (3801) {G0,W2,D2,L1,V0,M1} { one_to_one( empty_set ) }.
% 0.87/1.24 (3802) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.87/1.24 (3803) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( empty_set ) }.
% 0.87/1.24 (3804) {G0,W2,D2,L1,V0,M1} { epsilon_connected( empty_set ) }.
% 0.87/1.24 (3805) {G0,W2,D2,L1,V0,M1} { ordinal( empty_set ) }.
% 0.87/1.24 (3806) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 0.87/1.24 (3807) {G0,W2,D2,L1,V0,M1} { relation( empty_set ) }.
% 0.87/1.24 (3808) {G0,W8,D3,L3,V2,M3} { empty( X ), empty( Y ), ! empty(
% 0.87/1.24 cartesian_product2( X, Y ) ) }.
% 0.87/1.24 (3809) {G0,W11,D3,L4,V3,M4} { empty( X ), empty( Y ), empty( Z ), ! empty
% 0.87/1.24 ( cartesian_product3( X, Y, Z ) ) }.
% 0.87/1.24 (3810) {G0,W2,D2,L1,V0,M1} { ! empty( positive_rationals ) }.
% 0.87/1.24 (3811) {G0,W2,D2,L1,V0,M1} { ! empty( skol2 ) }.
% 0.87/1.24 (3812) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol2 ) }.
% 0.87/1.24 (3813) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol2 ) }.
% 0.87/1.24 (3814) {G0,W2,D2,L1,V0,M1} { ordinal( skol2 ) }.
% 0.87/1.24 (3815) {G0,W2,D2,L1,V0,M1} { natural( skol2 ) }.
% 0.87/1.24 (3816) {G0,W2,D2,L1,V0,M1} { ! empty( skol3 ) }.
% 0.87/1.24 (3817) {G0,W2,D2,L1,V0,M1} { finite( skol3 ) }.
% 0.87/1.24 (3818) {G0,W2,D2,L1,V0,M1} { relation( skol4 ) }.
% 0.87/1.24 (3819) {G0,W2,D2,L1,V0,M1} { function( skol4 ) }.
% 0.87/1.24 (3820) {G0,W2,D2,L1,V0,M1} { function_yielding( skol4 ) }.
% 0.87/1.24 (3821) {G0,W2,D2,L1,V0,M1} { relation( skol5 ) }.
% 0.87/1.24 (3822) {G0,W2,D2,L1,V0,M1} { function( skol5 ) }.
% 0.87/1.24 (3823) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol6 ) }.
% 0.87/1.24 (3824) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol6 ) }.
% 0.87/1.24 (3825) {G0,W2,D2,L1,V0,M1} { ordinal( skol6 ) }.
% 0.87/1.24 (3826) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol7 ) }.
% 0.87/1.24 (3827) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol7 ) }.
% 0.87/1.24 (3828) {G0,W2,D2,L1,V0,M1} { ordinal( skol7 ) }.
% 0.87/1.24 (3829) {G0,W2,D2,L1,V0,M1} { being_limit_ordinal( skol7 ) }.
% 0.87/1.24 (3830) {G0,W2,D2,L1,V0,M1} { empty( skol8 ) }.
% 0.87/1.24 (3831) {G0,W2,D2,L1,V0,M1} { relation( skol8 ) }.
% 0.87/1.24 (3832) {G0,W5,D3,L2,V2,M2} { empty( X ), ! empty( skol9( Y ) ) }.
% 0.87/1.24 (3833) {G0,W7,D3,L2,V1,M2} { empty( X ), element( skol9( X ), powerset( X
% 0.87/1.24 ) ) }.
% 0.87/1.24 (3834) {G0,W2,D2,L1,V0,M1} { empty( skol10 ) }.
% 0.87/1.24 (3835) {G0,W3,D2,L1,V0,M1} { element( skol11, positive_rationals ) }.
% 0.87/1.24 (3836) {G0,W2,D2,L1,V0,M1} { ! empty( skol11 ) }.
% 0.87/1.24 (3837) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol11 ) }.
% 0.87/1.24 (3838) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol11 ) }.
% 0.87/1.24 (3839) {G0,W2,D2,L1,V0,M1} { ordinal( skol11 ) }.
% 0.87/1.24 (3840) {G0,W3,D3,L1,V1,M1} { empty( skol12( Y ) ) }.
% 0.87/1.24 (3841) {G0,W3,D3,L1,V1,M1} { relation( skol12( Y ) ) }.
% 0.87/1.24 (3842) {G0,W3,D3,L1,V1,M1} { function( skol12( Y ) ) }.
% 0.87/1.24 (3843) {G0,W3,D3,L1,V1,M1} { one_to_one( skol12( Y ) ) }.
% 0.87/1.24 (3844) {G0,W3,D3,L1,V1,M1} { epsilon_transitive( skol12( Y ) ) }.
% 0.87/1.24 (3845) {G0,W3,D3,L1,V1,M1} { epsilon_connected( skol12( Y ) ) }.
% 0.87/1.24 (3846) {G0,W3,D3,L1,V1,M1} { ordinal( skol12( Y ) ) }.
% 0.87/1.24 (3847) {G0,W3,D3,L1,V1,M1} { natural( skol12( Y ) ) }.
% 0.87/1.24 (3848) {G0,W3,D3,L1,V1,M1} { finite( skol12( Y ) ) }.
% 0.87/1.24 (3849) {G0,W5,D3,L1,V1,M1} { element( skol12( X ), powerset( X ) ) }.
% 0.87/1.24 (3850) {G0,W2,D2,L1,V0,M1} { relation( skol13 ) }.
% 0.87/1.24 (3851) {G0,W2,D2,L1,V0,M1} { empty( skol13 ) }.
% 0.87/1.24 (3852) {G0,W2,D2,L1,V0,M1} { function( skol13 ) }.
% 0.87/1.24 (3853) {G0,W2,D2,L1,V0,M1} { relation( skol14 ) }.
% 0.87/1.24 (3854) {G0,W2,D2,L1,V0,M1} { function( skol14 ) }.
% 0.87/1.24 (3855) {G0,W2,D2,L1,V0,M1} { one_to_one( skol14 ) }.
% 0.87/1.24 (3856) {G0,W2,D2,L1,V0,M1} { empty( skol14 ) }.
% 0.87/1.24 (3857) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol14 ) }.
% 0.87/1.24 (3858) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol14 ) }.
% 0.87/1.24 (3859) {G0,W2,D2,L1,V0,M1} { ordinal( skol14 ) }.
% 0.87/1.24 (3860) {G0,W2,D2,L1,V0,M1} { relation( skol15 ) }.
% 0.87/1.24 (3861) {G0,W2,D2,L1,V0,M1} { function( skol15 ) }.
% 0.87/1.24 (3862) {G0,W2,D2,L1,V0,M1} { transfinite_sequence( skol15 ) }.
% 0.87/1.24 (3863) {G0,W2,D2,L1,V0,M1} { ordinal_yielding( skol15 ) }.
% 0.87/1.24 (3864) {G0,W2,D2,L1,V0,M1} { ! empty( skol16 ) }.
% 0.87/1.24 (3865) {G0,W2,D2,L1,V0,M1} { relation( skol16 ) }.
% 0.87/1.24 (3866) {G0,W3,D3,L1,V1,M1} { empty( skol17( Y ) ) }.
% 0.87/1.24 (3867) {G0,W5,D3,L1,V1,M1} { element( skol17( X ), powerset( X ) ) }.
% 0.87/1.24 (3868) {G0,W2,D2,L1,V0,M1} { ! empty( skol18 ) }.
% 0.87/1.24 (3869) {G0,W3,D2,L1,V0,M1} { element( skol19, positive_rationals ) }.
% 0.87/1.24 (3870) {G0,W2,D2,L1,V0,M1} { empty( skol19 ) }.
% 0.87/1.24 (3871) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol19 ) }.
% 0.87/1.24 (3872) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol19 ) }.
% 0.87/1.24 (3873) {G0,W2,D2,L1,V0,M1} { ordinal( skol19 ) }.
% 0.87/1.24 (3874) {G0,W2,D2,L1,V0,M1} { natural( skol19 ) }.
% 0.87/1.24 (3875) {G0,W5,D3,L2,V2,M2} { empty( X ), ! empty( skol20( Y ) ) }.
% 0.87/1.24 (3876) {G0,W5,D3,L2,V2,M2} { empty( X ), finite( skol20( Y ) ) }.
% 0.87/1.24 (3877) {G0,W7,D3,L2,V1,M2} { empty( X ), element( skol20( X ), powerset( X
% 0.87/1.24 ) ) }.
% 0.87/1.24 (3878) {G0,W2,D2,L1,V0,M1} { relation( skol21 ) }.
% 0.87/1.24 (3879) {G0,W2,D2,L1,V0,M1} { function( skol21 ) }.
% 0.87/1.24 (3880) {G0,W2,D2,L1,V0,M1} { one_to_one( skol21 ) }.
% 0.87/1.24 (3881) {G0,W2,D2,L1,V0,M1} { ! empty( skol22 ) }.
% 0.87/1.24 (3882) {G0,W2,D2,L1,V0,M1} { epsilon_transitive( skol22 ) }.
% 0.87/1.24 (3883) {G0,W2,D2,L1,V0,M1} { epsilon_connected( skol22 ) }.
% 0.87/1.24 (3884) {G0,W2,D2,L1,V0,M1} { ordinal( skol22 ) }.
% 0.87/1.24 (3885) {G0,W2,D2,L1,V0,M1} { relation( skol23 ) }.
% 0.87/1.24 (3886) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( skol23 ) }.
% 0.87/1.24 (3887) {G0,W2,D2,L1,V0,M1} { relation( skol24 ) }.
% 0.87/1.24 (3888) {G0,W2,D2,L1,V0,M1} { relation_empty_yielding( skol24 ) }.
% 0.87/1.24 (3889) {G0,W2,D2,L1,V0,M1} { function( skol24 ) }.
% 0.87/1.24 (3890) {G0,W2,D2,L1,V0,M1} { relation( skol25 ) }.
% 0.87/1.24 (3891) {G0,W2,D2,L1,V0,M1} { function( skol25 ) }.
% 0.87/1.24 (3892) {G0,W2,D2,L1,V0,M1} { transfinite_sequence( skol25 ) }.
% 0.87/1.24 (3893) {G0,W2,D2,L1,V0,M1} { relation( skol26 ) }.
% 0.87/1.24 (3894) {G0,W2,D2,L1,V0,M1} { relation_non_empty( skol26 ) }.
% 0.87/1.24 (3895) {G0,W2,D2,L1,V0,M1} { function( skol26 ) }.
% 0.87/1.24 (3896) {G0,W3,D2,L1,V1,M1} { subset( X, X ) }.
% 0.87/1.24 (3897) {G0,W8,D3,L3,V2,M3} { ! finite( X ), ! finite( Y ), finite(
% 0.87/1.24 cartesian_product2( X, Y ) ) }.
% 0.87/1.24 (3898) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), element( X, Y ) }.
% 0.87/1.24 (3899) {G0,W2,D2,L1,V0,M1} { finite( skol27 ) }.
% 0.87/1.24 (3900) {G0,W2,D2,L1,V0,M1} { finite( skol28 ) }.
% 0.87/1.24 (3901) {G0,W2,D2,L1,V0,M1} { finite( skol29 ) }.
% 0.87/1.24 (3902) {G0,W5,D3,L1,V0,M1} { ! finite( cartesian_product3( skol27, skol28
% 0.87/1.24 , skol29 ) ) }.
% 0.87/1.24 (3903) {G0,W8,D2,L3,V2,M3} { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 0.87/1.24 (3904) {G0,W7,D3,L2,V2,M2} { ! element( X, powerset( Y ) ), subset( X, Y )
% 0.87/1.24 }.
% 0.87/1.24 (3905) {G0,W7,D3,L2,V2,M2} { ! subset( X, Y ), element( X, powerset( Y ) )
% 0.87/1.24 }.
% 0.87/1.24 (3906) {G0,W10,D3,L3,V3,M3} { ! in( X, Z ), ! element( Z, powerset( Y ) )
% 0.87/1.24 , element( X, Y ) }.
% 0.87/1.24 (3907) {G0,W9,D3,L3,V3,M3} { ! in( X, Y ), ! element( Y, powerset( Z ) ),
% 0.87/1.24 ! empty( Z ) }.
% 0.87/1.24 (3908) {G0,W5,D2,L2,V1,M2} { ! empty( X ), X = empty_set }.
% 0.87/1.24 (3909) {G0,W5,D2,L2,V2,M2} { ! in( X, Y ), ! empty( Y ) }.
% 0.87/1.24 (3910) {G0,W7,D2,L3,V2,M3} { ! empty( X ), X = Y, ! empty( Y ) }.
% 0.87/1.24
% 0.87/1.24
% 0.87/1.24 Total Proof:
% 0.87/1.24
% 0.87/1.24 eqswap: (3912) {G0,W10,D4,L1,V3,M1} { cartesian_product2(
% 0.87/1.24 cartesian_product2( X, Y ), Z ) = cartesian_product3( X, Y, Z ) }.
% 0.87/1.24 parent0[0]: (3790) {G0,W10,D4,L1,V3,M1} { cartesian_product3( X, Y, Z ) =
% 0.87/1.24 cartesian_product2( cartesian_product2( X, Y ), Z ) }.
% 0.87/1.24 substitution0:
% 0.87/1.24 X := X
% 0.87/1.24 Y := Y
% 0.87/1.24 Z := Z
% 0.87/1.24 end
% 0.87/1.24
% 0.87/1.24 subsumption: (28) {G0,W10,D4,L1,V3,M1} I { cartesian_product2(
% 0.87/1.24 cartesian_product2( X, Y ), Z ) ==> cartesian_product3( X, Y, Z ) }.
% 0.87/1.24 parent0: (3912) {G0,W10,D4,L1,V3,M1} { cartesian_product2(
% 0.87/1.24 cartesian_product2( X, Y ), Z ) = cartesian_product3( X, Y, Z ) }.
% 0.87/1.24 substitution0:
% 0.87/1.24 X := X
% 0.87/1.24 Y := Y
% 0.87/1.24 Z := Z
% 0.87/1.24 end
% 0.87/1.24 permutation0:
% 0.87/1.24 0 ==> 0
% 0.87/1.24 end
% 0.87/1.24
% 0.87/1.24 subsumption: (33) {G0,W8,D3,L3,V2,M3} I { ! finite( X ), ! finite( Y ),
% 0.87/1.24 finite( cartesian_product2( X, Y ) ) }.
% 0.87/1.24 parent0: (3795) {G0,W8,D3,L3,V2,M3} { ! finite( X ), ! finite( Y ), finite
% 0.87/1.24 ( cartesian_product2( X, Y ) ) }.
% 0.87/1.24 substitution0:
% 0.87/1.24 X := X
% 0.87/1.24 Y := Y
% 0.87/1.24 end
% 0.87/1.24 permutation0:
% 0.87/1.24 0 ==> 0
% 0.87/1.24 1 ==> 1
% 0.87/1.24 2 ==> 2
% 0.87/1.24 end
% 0.87/1.24
% 0.87/1.24 subsumption: (130) {G0,W2,D2,L1,V0,M1} I { finite( skol27 ) }.
% 0.87/1.24 parent0: (3899) {G0,W2,D2,L1,V0,M1} { finite( skol27 ) }.
% 0.87/1.24 substitution0:
% 0.87/1.24 end
% 0.87/1.24 permutation0:
% 0.87/1.24 0 ==> 0
% 0.87/1.24 end
% 0.87/1.24
% 0.87/1.24 subsumption: (131) {G0,W2,D2,L1,V0,M1} I { finite( skol28 ) }.
% 0.87/1.24 parent0: (3900) {G0,W2,D2,L1,V0,M1} { finite( skol28 ) }.
% 0.87/1.24 substitution0:
% 0.87/1.24 end
% 0.87/1.24 permutation0:
% 0.87/1.24 0 ==> 0
% 0.87/1.24 end
% 0.87/1.24
% 0.87/1.24 subsumption: (132) {G0,W2,D2,L1,V0,M1} I { finite( skol29 ) }.
% 0.87/1.24 parent0: (3901) {G0,W2,D2,L1,V0,M1} { finite( skol29 ) }.
% 0.87/1.24 substitution0:
% 0.87/1.24 end
% 0.87/1.24 permutation0:
% 0.87/1.24 0 ==> 0
% 0.87/1.24 end
% 0.87/1.24
% 0.87/1.24 subsumption: (133) {G0,W5,D3,L1,V0,M1} I { ! finite( cartesian_product3(
% 0.87/1.24 skol27, skol28, skol29 ) ) }.
% 0.87/1.24 parent0: (3902) {G0,W5,D3,L1,V0,M1} { ! finite( cartesian_product3( skol27
% 0.87/1.24 , skol28, skol29 ) ) }.
% 0.87/1.24 substitution0:
% 0.87/1.24 end
% 0.87/1.24 permutation0:
% 0.87/1.24 0 ==> 0
% 0.87/1.24 end
% 0.87/1.24
% 0.87/1.24 resolution: (3953) {G1,W12,D4,L4,V3,M4} { ! finite( Z ), finite(
% 0.87/1.24 cartesian_product2( cartesian_product2( X, Y ), Z ) ), ! finite( X ), !
% 0.87/1.24 finite( Y ) }.
% 0.87/1.24 parent0[0]: (33) {G0,W8,D3,L3,V2,M3} I { ! finite( X ), ! finite( Y ),
% 0.87/1.24 finite( cartesian_product2( X, Y ) ) }.
% 0.87/1.24 parent1[2]: (33) {G0,W8,D3,L3,V2,M3} I { ! finite( X ), ! finite( Y ),
% 0.87/1.24 finite( cartesian_product2( X, Y ) ) }.
% 0.87/1.24 substitution0:
% 0.87/1.24 X := cartesian_product2( X, Y )
% 0.87/1.24 Y := Z
% 0.87/1.24 end
% 0.87/1.24 substitution1:
% 0.87/1.24 X := X
% 0.87/1.24 Y := Y
% 0.87/1.24 end
% 0.87/1.24
% 0.87/1.24 paramod: (3970) {G1,W11,D3,L4,V3,M4} { finite( cartesian_product3( X, Y, Z
% 0.87/1.24 ) ), ! finite( Z ), ! finite( X ), ! finite( Y ) }.
% 0.87/1.24 parent0[0]: (28) {G0,W10,D4,L1,V3,M1} I { cartesian_product2(
% 0.87/1.24 cartesian_product2( X, Y ), Z ) ==> cartesian_product3( X, Y, Z ) }.
% 0.87/1.24 parent1[1; 1]: (3953) {G1,W12,D4,L4,V3,M4} { ! finite( Z ), finite(
% 0.87/1.24 cartesian_product2( cartesian_product2( X, Y ), Z ) ), ! finite( X ), !
% 0.87/1.24 finite( Y ) }.
% 0.87/1.24 substitution0:
% 0.87/1.24 X := X
% 0.87/1.24 Y := Y
% 0.87/1.24 Z := Z
% 0.87/1.24 end
% 0.87/1.24 substitution1:
% 0.87/1.24 X := X
% 0.87/1.24 Y := Y
% 0.87/1.24 Z := Z
% 0.87/1.24 end
% 0.87/1.24
% 0.87/1.24 subsumption: (307) {G1,W11,D3,L4,V3,M4} R(33,33);d(28) { ! finite( X ), !
% 0.87/1.24 finite( Y ), ! finite( Z ), finite( cartesian_product3( Y, Z, X ) ) }.
% 0.87/1.24 parent0: (3970) {G1,W11,D3,L4,V3,M4} { finite( cartesian_product3( X, Y, Z
% 0.87/1.24 ) ), ! finite( Z ), ! finite( X ), ! finite( Y ) }.
% 0.87/1.24 substitution0:
% 0.87/1.24 X := Y
% 0.87/1.24 Y := Z
% 0.87/1.24 Z := X
% 0.87/1.24 end
% 0.87/1.24 permutation0:
% 0.87/1.24 0 ==> 3
% 0.87/1.24 1 ==> 0
% 0.87/1.24 2 ==> 1
% 0.87/1.24 3 ==> 2
% 0.87/1.24 end
% 0.87/1.24
% 0.87/1.24 resolution: (3975) {G1,W6,D2,L3,V0,M3} { ! finite( skol29 ), ! finite(
% 0.87/1.24 skol27 ), ! finite( skol28 ) }.
% 0.87/1.24 parent0[0]: (133) {G0,W5,D3,L1,V0,M1} I { ! finite( cartesian_product3(
% 0.87/1.24 skol27, skol28, skol29 ) ) }.
% 0.87/1.24 parent1[3]: (307) {G1,W11,D3,L4,V3,M4} R(33,33);d(28) { ! finite( X ), !
% 0.87/1.24 finite( Y ), ! finite( Z ), finite( cartesian_product3( Y, Z, X ) ) }.
% 0.87/1.24 substitution0:
% 0.87/1.24 end
% 0.87/1.24 substitution1:
% 0.87/1.24 X := skol29
% 0.87/1.24 Y := skol27
% 0.87/1.24 Z := skol28
% 0.87/1.24 end
% 0.87/1.24
% 0.87/1.24 resolution: (3976) {G1,W4,D2,L2,V0,M2} { ! finite( skol27 ), ! finite(
% 0.87/1.24 skol28 ) }.
% 0.87/1.24 parent0[0]: (3975) {G1,W6,D2,L3,V0,M3} { ! finite( skol29 ), ! finite(
% 0.87/1.24 skol27 ), ! finite( skol28 ) }.
% 0.87/1.24 parent1[0]: (132) {G0,W2,D2,L1,V0,M1} I { finite( skol29 ) }.
% 0.87/1.24 substitution0:
% 0.87/1.24 end
% 0.87/1.24 substitution1:
% 0.87/1.24 end
% 0.87/1.24
% 0.87/1.24 subsumption: (3490) {G2,W4,D2,L2,V0,M2} R(307,133);r(132) { ! finite(
% 0.87/1.24 skol27 ), ! finite( skol28 ) }.
% 0.87/1.24 parent0: (3976) {G1,W4,D2,L2,V0,M2} { ! finite( skol27 ), ! finite( skol28
% 0.87/1.24 ) }.
% 0.87/1.24 substitution0:
% 0.87/1.24 end
% 0.87/1.24 permutation0:
% 0.87/1.24 0 ==> 0
% 0.87/1.24 1 ==> 1
% 0.87/1.24 end
% 0.87/1.24
% 0.87/1.24 resolution: (3977) {G1,W2,D2,L1,V0,M1} { ! finite( skol28 ) }.
% 0.87/1.24 parent0[0]: (3490) {G2,W4,D2,L2,V0,M2} R(307,133);r(132) { ! finite( skol27
% 0.87/1.24 ), ! finite( skol28 ) }.
% 0.87/1.24 parent1[0]: (130) {G0,W2,D2,L1,V0,M1} I { finite( skol27 ) }.
% 0.87/1.24 substitution0:
% 0.87/1.24 end
% 0.87/1.24 substitution1:
% 0.87/1.24 end
% 0.87/1.24
% 0.87/1.24 resolution: (3978) {G1,W0,D0,L0,V0,M0} { }.
% 0.87/1.24 parent0[0]: (3977) {G1,W2,D2,L1,V0,M1} { ! finite( skol28 ) }.
% 0.87/1.24 parent1[0]: (131) {G0,W2,D2,L1,V0,M1} I { finite( skol28 ) }.
% 0.87/1.24 substitution0:
% 0.87/1.24 end
% 0.87/1.24 substitution1:
% 0.87/1.24 end
% 0.87/1.24
% 0.87/1.24 subsumption: (3758) {G3,W0,D0,L0,V0,M0} S(3490);r(130);r(131) { }.
% 0.87/1.24 parent0: (3978) {G1,W0,D0,L0,V0,M0} { }.
% 0.87/1.24 substitution0:
% 0.87/1.24 end
% 0.87/1.24 permutation0:
% 0.87/1.24 end
% 0.87/1.24
% 0.87/1.24 Proof check complete!
% 0.87/1.24
% 0.87/1.24 Memory use:
% 0.87/1.24
% 0.87/1.24 space for terms: 38159
% 0.87/1.24 space for clauses: 175094
% 0.87/1.24
% 0.87/1.24
% 0.87/1.24 clauses generated: 10088
% 0.87/1.24 clauses kept: 3759
% 0.87/1.24 clauses selected: 589
% 0.87/1.24 clauses deleted: 157
% 0.87/1.24 clauses inuse deleted: 94
% 0.87/1.24
% 0.87/1.24 subsentry: 25990
% 0.87/1.24 literals s-matched: 15102
% 0.87/1.24 literals matched: 14546
% 0.87/1.24 full subsumption: 2427
% 0.87/1.24
% 0.87/1.24 checksum: 1051623709
% 0.87/1.24
% 0.87/1.24
% 0.87/1.24 Bliksem ended
%------------------------------------------------------------------------------