TSTP Solution File: SEU252+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SEU252+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Tue Jul 19 07:11:53 EDT 2022
% Result : Theorem 3.60s 3.96s
% Output : Refutation 3.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU252+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : bliksem %s
% 0.13/0.33 % Computer : n004.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % DateTime : Sat Jun 18 22:09:23 EDT 2022
% 0.13/0.33 % CPUTime :
% 2.39/2.79 *** allocated 10000 integers for termspace/termends
% 2.39/2.79 *** allocated 10000 integers for clauses
% 2.39/2.79 *** allocated 10000 integers for justifications
% 2.39/2.79 Bliksem 1.12
% 2.39/2.79
% 2.39/2.79
% 2.39/2.79 Automatic Strategy Selection
% 2.39/2.79
% 2.39/2.79
% 2.39/2.79 Clauses:
% 2.39/2.79
% 2.39/2.79 { ! in( X, Y ), ! in( Y, X ) }.
% 2.39/2.79 { ! empty( X ), function( X ) }.
% 2.39/2.79 { ! relation( X ), ! empty( X ), ! function( X ), relation( X ) }.
% 2.39/2.79 { ! relation( X ), ! empty( X ), ! function( X ), function( X ) }.
% 2.39/2.79 { ! relation( X ), ! empty( X ), ! function( X ), one_to_one( X ) }.
% 2.39/2.79 { unordered_pair( X, Y ) = unordered_pair( Y, X ) }.
% 2.39/2.79 { set_union2( X, Y ) = set_union2( Y, X ) }.
% 2.39/2.79 { set_intersection2( X, Y ) = set_intersection2( Y, X ) }.
% 2.39/2.79 { ordered_pair( X, Y ) = unordered_pair( unordered_pair( X, Y ), singleton
% 2.39/2.79 ( X ) ) }.
% 2.39/2.79 { ! relation( X ), relation_field( X ) = set_union2( relation_dom( X ),
% 2.39/2.79 relation_rng( X ) ) }.
% 2.39/2.79 { ! relation( X ), relation_restriction( X, Y ) = set_intersection2( X,
% 2.39/2.79 cartesian_product2( Y, Y ) ) }.
% 2.39/2.79 { && }.
% 2.39/2.79 { && }.
% 2.39/2.79 { && }.
% 2.39/2.79 { && }.
% 2.39/2.79 { && }.
% 2.39/2.79 { ! relation( X ), relation( relation_restriction( X, Y ) ) }.
% 2.39/2.79 { && }.
% 2.39/2.79 { && }.
% 2.39/2.79 { && }.
% 2.39/2.79 { && }.
% 2.39/2.79 { && }.
% 2.39/2.79 { && }.
% 2.39/2.79 { element( skol1( X ), X ) }.
% 2.39/2.79 { empty( empty_set ) }.
% 2.39/2.79 { ! empty( ordered_pair( X, Y ) ) }.
% 2.39/2.79 { empty( X ), ! empty( set_union2( X, Y ) ) }.
% 2.39/2.79 { empty( X ), ! empty( set_union2( Y, X ) ) }.
% 2.39/2.79 { set_union2( X, X ) = X }.
% 2.39/2.79 { set_intersection2( X, X ) = X }.
% 2.39/2.79 { ! relation( X ), ! reflexive( X ), ! in( Y, relation_field( X ) ), in(
% 2.39/2.79 ordered_pair( Y, Y ), X ) }.
% 2.39/2.79 { ! relation( X ), in( skol2( X ), relation_field( X ) ), reflexive( X ) }
% 2.39/2.79 .
% 2.39/2.79 { ! relation( X ), ! in( ordered_pair( skol2( X ), skol2( X ) ), X ),
% 2.39/2.79 reflexive( X ) }.
% 2.39/2.79 { relation( skol3 ) }.
% 2.39/2.79 { function( skol3 ) }.
% 2.39/2.79 { empty( skol4 ) }.
% 2.39/2.79 { relation( skol5 ) }.
% 2.39/2.79 { empty( skol5 ) }.
% 2.39/2.79 { function( skol5 ) }.
% 2.39/2.79 { ! empty( skol6 ) }.
% 2.39/2.79 { relation( skol7 ) }.
% 2.39/2.79 { function( skol7 ) }.
% 2.39/2.79 { one_to_one( skol7 ) }.
% 2.39/2.79 { ! in( ordered_pair( X, Y ), cartesian_product2( Z, T ) ), in( X, Z ) }.
% 2.39/2.79 { ! in( ordered_pair( X, Y ), cartesian_product2( Z, T ) ), in( Y, T ) }.
% 2.39/2.79 { ! in( X, Z ), ! in( Y, T ), in( ordered_pair( X, Y ), cartesian_product2
% 2.39/2.79 ( Z, T ) ) }.
% 2.39/2.79 { ! relation( X ), ! in( Y, relation_restriction( X, Z ) ), in( Y, X ) }.
% 2.39/2.79 { ! relation( X ), ! in( Y, relation_restriction( X, Z ) ), in( Y,
% 2.39/2.79 cartesian_product2( Z, Z ) ) }.
% 2.39/2.79 { ! relation( X ), ! in( Y, X ), ! in( Y, cartesian_product2( Z, Z ) ), in
% 2.39/2.79 ( Y, relation_restriction( X, Z ) ) }.
% 2.39/2.79 { ! relation( X ), ! in( Y, relation_field( relation_restriction( X, Z ) )
% 2.39/2.79 ), in( Y, relation_field( X ) ) }.
% 2.39/2.79 { ! relation( X ), ! in( Y, relation_field( relation_restriction( X, Z ) )
% 2.39/2.79 ), in( Y, Z ) }.
% 2.39/2.79 { set_union2( X, empty_set ) = X }.
% 2.39/2.79 { ! in( X, Y ), element( X, Y ) }.
% 2.39/2.79 { relation( skol8 ) }.
% 2.39/2.79 { reflexive( skol8 ) }.
% 2.39/2.79 { ! reflexive( relation_restriction( skol8, skol9 ) ) }.
% 2.39/2.79 { set_intersection2( X, empty_set ) = empty_set }.
% 2.39/2.79 { ! element( X, Y ), empty( Y ), in( X, Y ) }.
% 2.39/2.79 { ! empty( X ), X = empty_set }.
% 2.39/2.79 { ! in( X, Y ), ! empty( Y ) }.
% 2.39/2.79 { ! empty( X ), X = Y, ! empty( Y ) }.
% 2.39/2.79
% 2.39/2.79 percentage equality = 0.136364, percentage horn = 0.959184
% 2.39/2.79 This is a problem with some equality
% 2.39/2.79
% 2.39/2.79
% 2.39/2.79
% 2.39/2.79 Options Used:
% 2.39/2.79
% 2.39/2.79 useres = 1
% 2.39/2.79 useparamod = 1
% 2.39/2.79 useeqrefl = 1
% 2.39/2.79 useeqfact = 1
% 2.39/2.79 usefactor = 1
% 2.39/2.79 usesimpsplitting = 0
% 2.39/2.79 usesimpdemod = 5
% 2.39/2.79 usesimpres = 3
% 2.39/2.79
% 2.39/2.79 resimpinuse = 1000
% 2.39/2.79 resimpclauses = 20000
% 2.39/2.79 substype = eqrewr
% 2.39/2.79 backwardsubs = 1
% 2.39/2.79 selectoldest = 5
% 2.39/2.79
% 2.39/2.79 litorderings [0] = split
% 2.39/2.79 litorderings [1] = extend the termordering, first sorting on arguments
% 2.39/2.79
% 2.39/2.79 termordering = kbo
% 2.39/2.79
% 2.39/2.79 litapriori = 0
% 2.39/2.79 termapriori = 1
% 2.39/2.79 litaposteriori = 0
% 2.39/2.79 termaposteriori = 0
% 2.39/2.79 demodaposteriori = 0
% 2.39/2.79 ordereqreflfact = 0
% 2.39/2.79
% 2.39/2.79 litselect = negord
% 2.39/2.79
% 2.39/2.79 maxweight = 15
% 2.39/2.79 maxdepth = 30000
% 2.39/2.79 maxlength = 115
% 2.39/2.79 maxnrvars = 195
% 2.39/2.79 excuselevel = 1
% 2.39/2.79 increasemaxweight = 1
% 2.39/2.79
% 2.39/2.79 maxselected = 10000000
% 2.39/2.79 maxnrclauses = 10000000
% 2.39/2.79
% 2.39/2.79 showgenerated = 0
% 2.39/2.79 showkept = 0
% 2.39/2.79 showselected = 0
% 2.39/2.79 showdeleted = 0
% 2.39/2.79 showresimp = 1
% 2.39/2.79 showstatus = 2000
% 2.39/2.79
% 2.39/2.79 prologoutput = 0
% 2.39/2.79 nrgoals = 5000000
% 2.39/2.79 totalproof = 1
% 2.39/2.79
% 2.39/2.79 Symbols occurring in the translation:
% 2.39/2.79
% 2.39/2.79 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 3.60/3.96 . [1, 2] (w:1, o:34, a:1, s:1, b:0),
% 3.60/3.96 && [3, 0] (w:1, o:4, a:1, s:1, b:0),
% 3.60/3.96 ! [4, 1] (w:0, o:18, a:1, s:1, b:0),
% 3.60/3.96 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 3.60/3.96 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 3.60/3.96 in [37, 2] (w:1, o:58, a:1, s:1, b:0),
% 3.60/3.96 empty [38, 1] (w:1, o:23, a:1, s:1, b:0),
% 3.60/3.96 function [39, 1] (w:1, o:24, a:1, s:1, b:0),
% 3.60/3.96 relation [40, 1] (w:1, o:25, a:1, s:1, b:0),
% 3.60/3.96 one_to_one [41, 1] (w:1, o:26, a:1, s:1, b:0),
% 3.60/3.96 unordered_pair [42, 2] (w:1, o:59, a:1, s:1, b:0),
% 3.60/3.96 set_union2 [43, 2] (w:1, o:61, a:1, s:1, b:0),
% 3.60/3.96 set_intersection2 [44, 2] (w:1, o:62, a:1, s:1, b:0),
% 3.60/3.96 ordered_pair [45, 2] (w:1, o:63, a:1, s:1, b:0),
% 3.60/3.96 singleton [46, 1] (w:1, o:31, a:1, s:1, b:0),
% 3.60/3.96 relation_field [47, 1] (w:1, o:27, a:1, s:1, b:0),
% 3.60/3.96 relation_dom [48, 1] (w:1, o:28, a:1, s:1, b:0),
% 3.60/3.96 relation_rng [49, 1] (w:1, o:29, a:1, s:1, b:0),
% 3.60/3.96 relation_restriction [50, 2] (w:1, o:60, a:1, s:1, b:0),
% 3.60/3.96 cartesian_product2 [51, 2] (w:1, o:64, a:1, s:1, b:0),
% 3.60/3.96 element [52, 2] (w:1, o:65, a:1, s:1, b:0),
% 3.60/3.96 empty_set [53, 0] (w:1, o:8, a:1, s:1, b:0),
% 3.60/3.96 reflexive [54, 1] (w:1, o:30, a:1, s:1, b:0),
% 3.60/3.96 skol1 [57, 1] (w:1, o:32, a:1, s:1, b:1),
% 3.60/3.96 skol2 [58, 1] (w:1, o:33, a:1, s:1, b:1),
% 3.60/3.96 skol3 [59, 0] (w:1, o:11, a:1, s:1, b:1),
% 3.60/3.96 skol4 [60, 0] (w:1, o:12, a:1, s:1, b:1),
% 3.60/3.96 skol5 [61, 0] (w:1, o:13, a:1, s:1, b:1),
% 3.60/3.96 skol6 [62, 0] (w:1, o:14, a:1, s:1, b:1),
% 3.60/3.96 skol7 [63, 0] (w:1, o:15, a:1, s:1, b:1),
% 3.60/3.96 skol8 [64, 0] (w:1, o:16, a:1, s:1, b:1),
% 3.60/3.96 skol9 [65, 0] (w:1, o:17, a:1, s:1, b:1).
% 3.60/3.96
% 3.60/3.96
% 3.60/3.96 Starting Search:
% 3.60/3.96
% 3.60/3.96 *** allocated 15000 integers for clauses
% 3.60/3.96 *** allocated 22500 integers for clauses
% 3.60/3.96 *** allocated 33750 integers for clauses
% 3.60/3.96 *** allocated 50625 integers for clauses
% 3.60/3.96 *** allocated 15000 integers for termspace/termends
% 3.60/3.96 *** allocated 75937 integers for clauses
% 3.60/3.96 Resimplifying inuse:
% 3.60/3.96 Done
% 3.60/3.96
% 3.60/3.96 *** allocated 22500 integers for termspace/termends
% 3.60/3.96 *** allocated 113905 integers for clauses
% 3.60/3.96 *** allocated 33750 integers for termspace/termends
% 3.60/3.96
% 3.60/3.96 Intermediate Status:
% 3.60/3.96 Generated: 6499
% 3.60/3.96 Kept: 2013
% 3.60/3.96 Inuse: 274
% 3.60/3.96 Deleted: 51
% 3.60/3.96 Deletedinuse: 22
% 3.60/3.96
% 3.60/3.96 Resimplifying inuse:
% 3.60/3.96 Done
% 3.60/3.96
% 3.60/3.96 *** allocated 170857 integers for clauses
% 3.60/3.96 *** allocated 50625 integers for termspace/termends
% 3.60/3.96 Resimplifying inuse:
% 3.60/3.96 Done
% 3.60/3.96
% 3.60/3.96 *** allocated 256285 integers for clauses
% 3.60/3.96
% 3.60/3.96 Intermediate Status:
% 3.60/3.96 Generated: 16020
% 3.60/3.96 Kept: 4025
% 3.60/3.96 Inuse: 388
% 3.60/3.96 Deleted: 165
% 3.60/3.96 Deletedinuse: 119
% 3.60/3.96
% 3.60/3.96 Resimplifying inuse:
% 3.60/3.96 Done
% 3.60/3.96
% 3.60/3.96 *** allocated 75937 integers for termspace/termends
% 3.60/3.96 Resimplifying inuse:
% 3.60/3.96 Done
% 3.60/3.96
% 3.60/3.96 *** allocated 384427 integers for clauses
% 3.60/3.96
% 3.60/3.96 Intermediate Status:
% 3.60/3.96 Generated: 27620
% 3.60/3.96 Kept: 6028
% 3.60/3.96 Inuse: 527
% 3.60/3.96 Deleted: 290
% 3.60/3.96 Deletedinuse: 132
% 3.60/3.96
% 3.60/3.96 Resimplifying inuse:
% 3.60/3.96 Done
% 3.60/3.96
% 3.60/3.96 *** allocated 113905 integers for termspace/termends
% 3.60/3.96 Resimplifying inuse:
% 3.60/3.96 Done
% 3.60/3.96
% 3.60/3.96 *** allocated 576640 integers for clauses
% 3.60/3.96
% 3.60/3.96 Intermediate Status:
% 3.60/3.96 Generated: 39086
% 3.60/3.96 Kept: 8038
% 3.60/3.96 Inuse: 622
% 3.60/3.96 Deleted: 397
% 3.60/3.96 Deletedinuse: 190
% 3.60/3.96
% 3.60/3.96 Resimplifying inuse:
% 3.60/3.96 Done
% 3.60/3.96
% 3.60/3.96 *** allocated 170857 integers for termspace/termends
% 3.60/3.96 Resimplifying inuse:
% 3.60/3.96 Done
% 3.60/3.96
% 3.60/3.96
% 3.60/3.96 Intermediate Status:
% 3.60/3.96 Generated: 58840
% 3.60/3.96 Kept: 10227
% 3.60/3.96 Inuse: 707
% 3.60/3.96 Deleted: 430
% 3.60/3.96 Deletedinuse: 190
% 3.60/3.96
% 3.60/3.96 Resimplifying inuse:
% 3.60/3.96 Done
% 3.60/3.96
% 3.60/3.96 Resimplifying inuse:
% 3.60/3.96 Done
% 3.60/3.96
% 3.60/3.96 *** allocated 864960 integers for clauses
% 3.60/3.96
% 3.60/3.96 Intermediate Status:
% 3.60/3.96 Generated: 69297
% 3.60/3.96 Kept: 12239
% 3.60/3.96 Inuse: 793
% 3.60/3.96 Deleted: 447
% 3.60/3.96 Deletedinuse: 206
% 3.60/3.96
% 3.60/3.96 Resimplifying inuse:
% 3.60/3.96 Done
% 3.60/3.96
% 3.60/3.96 Resimplifying inuse:
% 3.60/3.96 Done
% 3.60/3.96
% 3.60/3.96 *** allocated 256285 integers for termspace/termends
% 3.60/3.96
% 3.60/3.96 Intermediate Status:
% 3.60/3.96 Generated: 79075
% 3.60/3.96 Kept: 14255
% 3.60/3.96 Inuse: 862
% 3.60/3.96 Deleted: 449
% 3.60/3.96 Deletedinuse: 208
% 3.60/3.96
% 3.60/3.96 Resimplifying inuse:
% 3.60/3.96 Done
% 3.60/3.96
% 3.60/3.96 Resimplifying inuse:
% 3.60/3.96 Done
% 3.60/3.96
% 3.60/3.96
% 3.60/3.96 Intermediate Status:
% 3.60/3.96 Generated: 99855
% 3.60/3.96 Kept: 16265
% 3.60/3.96 Inuse: 916
% 3.60/3.96 Deleted: 455
% 3.60/3.96 Deletedinuse: 208
% 3.60/3.96
% 3.60/3.96 Resimplifying inuse:
% 3.60/3.96 Done
% 3.60/3.96
% 3.60/3.96 *** allocated 1297440 integers for clauses
% 3.60/3.96 Resimplifying inuse:
% 3.60/3.96 Done
% 3.60/3.96
% 3.60/3.96
% 3.60/3.96 Intermediate Status:
% 3.60/3.96 Generated: 116586
% 3.60/3.96 Kept: 18298
% 3.60/3.96 Inuse: 1011
% 3.60/3.96 Deleted: 461
% 3.60/3.96 Deletedinuse: 208
% 3.60/3.96
% 3.60/3.96 Resimplifying inuse:
% 3.60/3.96 Done
% 3.60/3.96
% 3.60/3.96 Resimplifying inuse:
% 3.60/3.96 Done
% 3.60/3.96
% 3.60/3.96 Resimplifying clauses:
% 3.60/3.96
% 3.60/3.96 Bliksems!, er is een bewijs:
% 3.60/3.96 % SZS status Theorem
% 3.60/3.96 % SZS output start Refutation
% 3.60/3.96
% 3.60/3.96 (10) {G0,W6,D3,L2,V2,M2} I { ! relation( X ), relation(
% 3.60/3.96 relation_restriction( X, Y ) ) }.
% 3.60/3.96 (18) {G0,W13,D3,L4,V2,M4} I { ! relation( X ), ! reflexive( X ), ! in( Y,
% 3.60/3.96 relation_field( X ) ), in( ordered_pair( Y, Y ), X ) }.
% 3.60/3.96 (19) {G0,W9,D3,L3,V1,M3} I { ! relation( X ), in( skol2( X ),
% 3.60/3.96 relation_field( X ) ), reflexive( X ) }.
% 3.60/3.96 (20) {G0,W11,D4,L3,V1,M3} I { ! relation( X ), ! in( ordered_pair( skol2( X
% 3.60/3.96 ), skol2( X ) ), X ), reflexive( X ) }.
% 3.60/3.96 (33) {G0,W13,D3,L3,V4,M3} I { ! in( X, Z ), ! in( Y, T ), in( ordered_pair
% 3.60/3.96 ( X, Y ), cartesian_product2( Z, T ) ) }.
% 3.60/3.96 (36) {G0,W15,D3,L4,V3,M4} I { ! relation( X ), ! in( Y, X ), ! in( Y,
% 3.60/3.96 cartesian_product2( Z, Z ) ), in( Y, relation_restriction( X, Z ) ) }.
% 3.60/3.96 (37) {G0,W12,D4,L3,V3,M3} I { ! relation( X ), ! in( Y, relation_field(
% 3.60/3.96 relation_restriction( X, Z ) ) ), in( Y, relation_field( X ) ) }.
% 3.60/3.96 (38) {G0,W11,D4,L3,V3,M3} I { ! relation( X ), ! in( Y, relation_field(
% 3.60/3.96 relation_restriction( X, Z ) ) ), in( Y, Z ) }.
% 3.60/3.96 (41) {G0,W2,D2,L1,V0,M1} I { relation( skol8 ) }.
% 3.60/3.96 (42) {G0,W2,D2,L1,V0,M1} I { reflexive( skol8 ) }.
% 3.60/3.96 (43) {G0,W4,D3,L1,V0,M1} I { ! reflexive( relation_restriction( skol8,
% 3.60/3.96 skol9 ) ) }.
% 3.60/3.96 (50) {G1,W10,D3,L2,V2,M2} F(33) { ! in( X, Y ), in( ordered_pair( X, X ),
% 3.60/3.96 cartesian_product2( Y, Y ) ) }.
% 3.60/3.96 (109) {G1,W4,D3,L1,V1,M1} R(10,41) { relation( relation_restriction( skol8
% 3.60/3.96 , X ) ) }.
% 3.60/3.96 (164) {G1,W9,D3,L2,V1,M2} R(18,41);r(42) { ! in( X, relation_field( skol8 )
% 3.60/3.96 ), in( ordered_pair( X, X ), skol8 ) }.
% 3.60/3.96 (187) {G2,W9,D4,L1,V0,M1} R(19,43);r(109) { in( skol2( relation_restriction
% 3.60/3.96 ( skol8, skol9 ) ), relation_field( relation_restriction( skol8, skol9 )
% 3.60/3.96 ) ) }.
% 3.60/3.96 (210) {G2,W13,D5,L1,V0,M1} R(20,43);r(109) { ! in( ordered_pair( skol2(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ), skol2( relation_restriction(
% 3.60/3.96 skol8, skol9 ) ) ), relation_restriction( skol8, skol9 ) ) }.
% 3.60/3.96 (377) {G1,W13,D3,L3,V2,M3} R(36,41) { ! in( X, skol8 ), ! in( X,
% 3.60/3.96 cartesian_product2( Y, Y ) ), in( X, relation_restriction( skol8, Y ) )
% 3.60/3.96 }.
% 3.60/3.96 (4907) {G3,W6,D4,L1,V0,M1} R(187,38);r(41) { in( skol2(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ), skol9 ) }.
% 3.60/3.96 (4908) {G3,W7,D4,L1,V0,M1} R(187,37);r(41) { in( skol2(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ), relation_field( skol8 ) ) }.
% 3.60/3.96 (4982) {G4,W13,D5,L1,V0,M1} R(4907,50) { in( ordered_pair( skol2(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ), skol2( relation_restriction(
% 3.60/3.96 skol8, skol9 ) ) ), cartesian_product2( skol9, skol9 ) ) }.
% 3.60/3.96 (6125) {G4,W11,D5,L1,V0,M1} R(4908,164) { in( ordered_pair( skol2(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ), skol2( relation_restriction(
% 3.60/3.96 skol8, skol9 ) ) ), skol8 ) }.
% 3.60/3.96 (19660) {G5,W13,D5,L1,V0,M1} R(377,210);r(6125) { ! in( ordered_pair( skol2
% 3.60/3.96 ( relation_restriction( skol8, skol9 ) ), skol2( relation_restriction(
% 3.60/3.96 skol8, skol9 ) ) ), cartesian_product2( skol9, skol9 ) ) }.
% 3.60/3.96 (20130) {G6,W0,D0,L0,V0,M0} S(19660);r(4982) { }.
% 3.60/3.96
% 3.60/3.96
% 3.60/3.96 % SZS output end Refutation
% 3.60/3.96 found a proof!
% 3.60/3.96
% 3.60/3.96
% 3.60/3.96 Unprocessed initial clauses:
% 3.60/3.96
% 3.60/3.96 (20132) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), ! in( Y, X ) }.
% 3.60/3.96 (20133) {G0,W4,D2,L2,V1,M2} { ! empty( X ), function( X ) }.
% 3.60/3.96 (20134) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 3.60/3.96 ), relation( X ) }.
% 3.60/3.96 (20135) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 3.60/3.96 ), function( X ) }.
% 3.60/3.96 (20136) {G0,W8,D2,L4,V1,M4} { ! relation( X ), ! empty( X ), ! function( X
% 3.60/3.96 ), one_to_one( X ) }.
% 3.60/3.96 (20137) {G0,W7,D3,L1,V2,M1} { unordered_pair( X, Y ) = unordered_pair( Y,
% 3.60/3.96 X ) }.
% 3.60/3.96 (20138) {G0,W7,D3,L1,V2,M1} { set_union2( X, Y ) = set_union2( Y, X ) }.
% 3.60/3.96 (20139) {G0,W7,D3,L1,V2,M1} { set_intersection2( X, Y ) =
% 3.60/3.96 set_intersection2( Y, X ) }.
% 3.60/3.96 (20140) {G0,W10,D4,L1,V2,M1} { ordered_pair( X, Y ) = unordered_pair(
% 3.60/3.96 unordered_pair( X, Y ), singleton( X ) ) }.
% 3.60/3.96 (20141) {G0,W10,D4,L2,V1,M2} { ! relation( X ), relation_field( X ) =
% 3.60/3.96 set_union2( relation_dom( X ), relation_rng( X ) ) }.
% 3.60/3.96 (20142) {G0,W11,D4,L2,V2,M2} { ! relation( X ), relation_restriction( X, Y
% 3.60/3.96 ) = set_intersection2( X, cartesian_product2( Y, Y ) ) }.
% 3.60/3.96 (20143) {G0,W1,D1,L1,V0,M1} { && }.
% 3.60/3.96 (20144) {G0,W1,D1,L1,V0,M1} { && }.
% 3.60/3.96 (20145) {G0,W1,D1,L1,V0,M1} { && }.
% 3.60/3.96 (20146) {G0,W1,D1,L1,V0,M1} { && }.
% 3.60/3.96 (20147) {G0,W1,D1,L1,V0,M1} { && }.
% 3.60/3.96 (20148) {G0,W6,D3,L2,V2,M2} { ! relation( X ), relation(
% 3.60/3.96 relation_restriction( X, Y ) ) }.
% 3.60/3.96 (20149) {G0,W1,D1,L1,V0,M1} { && }.
% 3.60/3.96 (20150) {G0,W1,D1,L1,V0,M1} { && }.
% 3.60/3.96 (20151) {G0,W1,D1,L1,V0,M1} { && }.
% 3.60/3.96 (20152) {G0,W1,D1,L1,V0,M1} { && }.
% 3.60/3.96 (20153) {G0,W1,D1,L1,V0,M1} { && }.
% 3.60/3.96 (20154) {G0,W1,D1,L1,V0,M1} { && }.
% 3.60/3.96 (20155) {G0,W4,D3,L1,V1,M1} { element( skol1( X ), X ) }.
% 3.60/3.96 (20156) {G0,W2,D2,L1,V0,M1} { empty( empty_set ) }.
% 3.60/3.96 (20157) {G0,W4,D3,L1,V2,M1} { ! empty( ordered_pair( X, Y ) ) }.
% 3.60/3.96 (20158) {G0,W6,D3,L2,V2,M2} { empty( X ), ! empty( set_union2( X, Y ) )
% 3.60/3.96 }.
% 3.60/3.96 (20159) {G0,W6,D3,L2,V2,M2} { empty( X ), ! empty( set_union2( Y, X ) )
% 3.60/3.96 }.
% 3.60/3.96 (20160) {G0,W5,D3,L1,V1,M1} { set_union2( X, X ) = X }.
% 3.60/3.96 (20161) {G0,W5,D3,L1,V1,M1} { set_intersection2( X, X ) = X }.
% 3.60/3.96 (20162) {G0,W13,D3,L4,V2,M4} { ! relation( X ), ! reflexive( X ), ! in( Y
% 3.60/3.96 , relation_field( X ) ), in( ordered_pair( Y, Y ), X ) }.
% 3.60/3.96 (20163) {G0,W9,D3,L3,V1,M3} { ! relation( X ), in( skol2( X ),
% 3.60/3.96 relation_field( X ) ), reflexive( X ) }.
% 3.60/3.96 (20164) {G0,W11,D4,L3,V1,M3} { ! relation( X ), ! in( ordered_pair( skol2
% 3.60/3.96 ( X ), skol2( X ) ), X ), reflexive( X ) }.
% 3.60/3.96 (20165) {G0,W2,D2,L1,V0,M1} { relation( skol3 ) }.
% 3.60/3.96 (20166) {G0,W2,D2,L1,V0,M1} { function( skol3 ) }.
% 3.60/3.96 (20167) {G0,W2,D2,L1,V0,M1} { empty( skol4 ) }.
% 3.60/3.96 (20168) {G0,W2,D2,L1,V0,M1} { relation( skol5 ) }.
% 3.60/3.96 (20169) {G0,W2,D2,L1,V0,M1} { empty( skol5 ) }.
% 3.60/3.96 (20170) {G0,W2,D2,L1,V0,M1} { function( skol5 ) }.
% 3.60/3.96 (20171) {G0,W2,D2,L1,V0,M1} { ! empty( skol6 ) }.
% 3.60/3.96 (20172) {G0,W2,D2,L1,V0,M1} { relation( skol7 ) }.
% 3.60/3.96 (20173) {G0,W2,D2,L1,V0,M1} { function( skol7 ) }.
% 3.60/3.96 (20174) {G0,W2,D2,L1,V0,M1} { one_to_one( skol7 ) }.
% 3.60/3.96 (20175) {G0,W10,D3,L2,V4,M2} { ! in( ordered_pair( X, Y ),
% 3.60/3.96 cartesian_product2( Z, T ) ), in( X, Z ) }.
% 3.60/3.96 (20176) {G0,W10,D3,L2,V4,M2} { ! in( ordered_pair( X, Y ),
% 3.60/3.96 cartesian_product2( Z, T ) ), in( Y, T ) }.
% 3.60/3.96 (20177) {G0,W13,D3,L3,V4,M3} { ! in( X, Z ), ! in( Y, T ), in(
% 3.60/3.96 ordered_pair( X, Y ), cartesian_product2( Z, T ) ) }.
% 3.60/3.96 (20178) {G0,W10,D3,L3,V3,M3} { ! relation( X ), ! in( Y,
% 3.60/3.96 relation_restriction( X, Z ) ), in( Y, X ) }.
% 3.60/3.96 (20179) {G0,W12,D3,L3,V3,M3} { ! relation( X ), ! in( Y,
% 3.60/3.96 relation_restriction( X, Z ) ), in( Y, cartesian_product2( Z, Z ) ) }.
% 3.60/3.96 (20180) {G0,W15,D3,L4,V3,M4} { ! relation( X ), ! in( Y, X ), ! in( Y,
% 3.60/3.96 cartesian_product2( Z, Z ) ), in( Y, relation_restriction( X, Z ) ) }.
% 3.60/3.96 (20181) {G0,W12,D4,L3,V3,M3} { ! relation( X ), ! in( Y, relation_field(
% 3.60/3.96 relation_restriction( X, Z ) ) ), in( Y, relation_field( X ) ) }.
% 3.60/3.96 (20182) {G0,W11,D4,L3,V3,M3} { ! relation( X ), ! in( Y, relation_field(
% 3.60/3.96 relation_restriction( X, Z ) ) ), in( Y, Z ) }.
% 3.60/3.96 (20183) {G0,W5,D3,L1,V1,M1} { set_union2( X, empty_set ) = X }.
% 3.60/3.96 (20184) {G0,W6,D2,L2,V2,M2} { ! in( X, Y ), element( X, Y ) }.
% 3.60/3.96 (20185) {G0,W2,D2,L1,V0,M1} { relation( skol8 ) }.
% 3.60/3.96 (20186) {G0,W2,D2,L1,V0,M1} { reflexive( skol8 ) }.
% 3.60/3.96 (20187) {G0,W4,D3,L1,V0,M1} { ! reflexive( relation_restriction( skol8,
% 3.60/3.96 skol9 ) ) }.
% 3.60/3.96 (20188) {G0,W5,D3,L1,V1,M1} { set_intersection2( X, empty_set ) =
% 3.60/3.96 empty_set }.
% 3.60/3.96 (20189) {G0,W8,D2,L3,V2,M3} { ! element( X, Y ), empty( Y ), in( X, Y )
% 3.60/3.96 }.
% 3.60/3.96 (20190) {G0,W5,D2,L2,V1,M2} { ! empty( X ), X = empty_set }.
% 3.60/3.96 (20191) {G0,W5,D2,L2,V2,M2} { ! in( X, Y ), ! empty( Y ) }.
% 3.60/3.96 (20192) {G0,W7,D2,L3,V2,M3} { ! empty( X ), X = Y, ! empty( Y ) }.
% 3.60/3.96
% 3.60/3.96
% 3.60/3.96 Total Proof:
% 3.60/3.96
% 3.60/3.96 subsumption: (10) {G0,W6,D3,L2,V2,M2} I { ! relation( X ), relation(
% 3.60/3.96 relation_restriction( X, Y ) ) }.
% 3.60/3.96 parent0: (20148) {G0,W6,D3,L2,V2,M2} { ! relation( X ), relation(
% 3.60/3.96 relation_restriction( X, Y ) ) }.
% 3.60/3.96 substitution0:
% 3.60/3.96 X := X
% 3.60/3.96 Y := Y
% 3.60/3.96 end
% 3.60/3.96 permutation0:
% 3.60/3.96 0 ==> 0
% 3.60/3.96 1 ==> 1
% 3.60/3.96 end
% 3.60/3.96
% 3.60/3.96 subsumption: (18) {G0,W13,D3,L4,V2,M4} I { ! relation( X ), ! reflexive( X
% 3.60/3.96 ), ! in( Y, relation_field( X ) ), in( ordered_pair( Y, Y ), X ) }.
% 3.60/3.96 parent0: (20162) {G0,W13,D3,L4,V2,M4} { ! relation( X ), ! reflexive( X )
% 3.60/3.96 , ! in( Y, relation_field( X ) ), in( ordered_pair( Y, Y ), X ) }.
% 3.60/3.96 substitution0:
% 3.60/3.96 X := X
% 3.60/3.96 Y := Y
% 3.60/3.96 end
% 3.60/3.96 permutation0:
% 3.60/3.96 0 ==> 0
% 3.60/3.96 1 ==> 1
% 3.60/3.96 2 ==> 2
% 3.60/3.96 3 ==> 3
% 3.60/3.96 end
% 3.60/3.96
% 3.60/3.96 subsumption: (19) {G0,W9,D3,L3,V1,M3} I { ! relation( X ), in( skol2( X ),
% 3.60/3.96 relation_field( X ) ), reflexive( X ) }.
% 3.60/3.96 parent0: (20163) {G0,W9,D3,L3,V1,M3} { ! relation( X ), in( skol2( X ),
% 3.60/3.96 relation_field( X ) ), reflexive( X ) }.
% 3.60/3.96 substitution0:
% 3.60/3.96 X := X
% 3.60/3.96 end
% 3.60/3.96 permutation0:
% 3.60/3.96 0 ==> 0
% 3.60/3.96 1 ==> 1
% 3.60/3.96 2 ==> 2
% 3.60/3.96 end
% 3.60/3.96
% 3.60/3.96 subsumption: (20) {G0,W11,D4,L3,V1,M3} I { ! relation( X ), ! in(
% 3.60/3.96 ordered_pair( skol2( X ), skol2( X ) ), X ), reflexive( X ) }.
% 3.60/3.96 parent0: (20164) {G0,W11,D4,L3,V1,M3} { ! relation( X ), ! in(
% 3.60/3.96 ordered_pair( skol2( X ), skol2( X ) ), X ), reflexive( X ) }.
% 3.60/3.96 substitution0:
% 3.60/3.96 X := X
% 3.60/3.96 end
% 3.60/3.96 permutation0:
% 3.60/3.96 0 ==> 0
% 3.60/3.96 1 ==> 1
% 3.60/3.96 2 ==> 2
% 3.60/3.96 end
% 3.60/3.96
% 3.60/3.96 subsumption: (33) {G0,W13,D3,L3,V4,M3} I { ! in( X, Z ), ! in( Y, T ), in(
% 3.60/3.96 ordered_pair( X, Y ), cartesian_product2( Z, T ) ) }.
% 3.60/3.96 parent0: (20177) {G0,W13,D3,L3,V4,M3} { ! in( X, Z ), ! in( Y, T ), in(
% 3.60/3.96 ordered_pair( X, Y ), cartesian_product2( Z, T ) ) }.
% 3.60/3.96 substitution0:
% 3.60/3.96 X := X
% 3.60/3.96 Y := Y
% 3.60/3.96 Z := Z
% 3.60/3.96 T := T
% 3.60/3.96 end
% 3.60/3.96 permutation0:
% 3.60/3.96 0 ==> 0
% 3.60/3.96 1 ==> 1
% 3.60/3.96 2 ==> 2
% 3.60/3.96 end
% 3.60/3.96
% 3.60/3.96 subsumption: (36) {G0,W15,D3,L4,V3,M4} I { ! relation( X ), ! in( Y, X ), !
% 3.60/3.96 in( Y, cartesian_product2( Z, Z ) ), in( Y, relation_restriction( X, Z )
% 3.60/3.96 ) }.
% 3.60/3.96 parent0: (20180) {G0,W15,D3,L4,V3,M4} { ! relation( X ), ! in( Y, X ), !
% 3.60/3.96 in( Y, cartesian_product2( Z, Z ) ), in( Y, relation_restriction( X, Z )
% 3.60/3.96 ) }.
% 3.60/3.96 substitution0:
% 3.60/3.96 X := X
% 3.60/3.96 Y := Y
% 3.60/3.96 Z := Z
% 3.60/3.96 end
% 3.60/3.96 permutation0:
% 3.60/3.96 0 ==> 0
% 3.60/3.96 1 ==> 1
% 3.60/3.96 2 ==> 2
% 3.60/3.96 3 ==> 3
% 3.60/3.96 end
% 3.60/3.96
% 3.60/3.96 subsumption: (37) {G0,W12,D4,L3,V3,M3} I { ! relation( X ), ! in( Y,
% 3.60/3.96 relation_field( relation_restriction( X, Z ) ) ), in( Y, relation_field(
% 3.60/3.96 X ) ) }.
% 3.60/3.96 parent0: (20181) {G0,W12,D4,L3,V3,M3} { ! relation( X ), ! in( Y,
% 3.60/3.96 relation_field( relation_restriction( X, Z ) ) ), in( Y, relation_field(
% 3.60/3.96 X ) ) }.
% 3.60/3.96 substitution0:
% 3.60/3.96 X := X
% 3.60/3.96 Y := Y
% 3.60/3.96 Z := Z
% 3.60/3.96 end
% 3.60/3.96 permutation0:
% 3.60/3.96 0 ==> 0
% 3.60/3.96 1 ==> 1
% 3.60/3.96 2 ==> 2
% 3.60/3.96 end
% 3.60/3.96
% 3.60/3.96 subsumption: (38) {G0,W11,D4,L3,V3,M3} I { ! relation( X ), ! in( Y,
% 3.60/3.96 relation_field( relation_restriction( X, Z ) ) ), in( Y, Z ) }.
% 3.60/3.96 parent0: (20182) {G0,W11,D4,L3,V3,M3} { ! relation( X ), ! in( Y,
% 3.60/3.96 relation_field( relation_restriction( X, Z ) ) ), in( Y, Z ) }.
% 3.60/3.96 substitution0:
% 3.60/3.96 X := X
% 3.60/3.96 Y := Y
% 3.60/3.96 Z := Z
% 3.60/3.96 end
% 3.60/3.96 permutation0:
% 3.60/3.96 0 ==> 0
% 3.60/3.96 1 ==> 1
% 3.60/3.96 2 ==> 2
% 3.60/3.96 end
% 3.60/3.96
% 3.60/3.96 subsumption: (41) {G0,W2,D2,L1,V0,M1} I { relation( skol8 ) }.
% 3.60/3.96 parent0: (20185) {G0,W2,D2,L1,V0,M1} { relation( skol8 ) }.
% 3.60/3.96 substitution0:
% 3.60/3.96 end
% 3.60/3.96 permutation0:
% 3.60/3.96 0 ==> 0
% 3.60/3.96 end
% 3.60/3.96
% 3.60/3.96 subsumption: (42) {G0,W2,D2,L1,V0,M1} I { reflexive( skol8 ) }.
% 3.60/3.96 parent0: (20186) {G0,W2,D2,L1,V0,M1} { reflexive( skol8 ) }.
% 3.60/3.96 substitution0:
% 3.60/3.96 end
% 3.60/3.96 permutation0:
% 3.60/3.96 0 ==> 0
% 3.60/3.96 end
% 3.60/3.96
% 3.60/3.96 subsumption: (43) {G0,W4,D3,L1,V0,M1} I { ! reflexive( relation_restriction
% 3.60/3.96 ( skol8, skol9 ) ) }.
% 3.60/3.96 parent0: (20187) {G0,W4,D3,L1,V0,M1} { ! reflexive( relation_restriction(
% 3.60/3.96 skol8, skol9 ) ) }.
% 3.60/3.96 substitution0:
% 3.60/3.96 end
% 3.60/3.96 permutation0:
% 3.60/3.96 0 ==> 0
% 3.60/3.96 end
% 3.60/3.96
% 3.60/3.96 factor: (20273) {G0,W10,D3,L2,V2,M2} { ! in( X, Y ), in( ordered_pair( X,
% 3.60/3.96 X ), cartesian_product2( Y, Y ) ) }.
% 3.60/3.96 parent0[0, 1]: (33) {G0,W13,D3,L3,V4,M3} I { ! in( X, Z ), ! in( Y, T ), in
% 3.60/3.96 ( ordered_pair( X, Y ), cartesian_product2( Z, T ) ) }.
% 3.60/3.96 substitution0:
% 3.60/3.96 X := X
% 3.60/3.96 Y := X
% 3.60/3.96 Z := Y
% 3.60/3.96 T := Y
% 3.60/3.96 end
% 3.60/3.96
% 3.60/3.96 subsumption: (50) {G1,W10,D3,L2,V2,M2} F(33) { ! in( X, Y ), in(
% 3.60/3.96 ordered_pair( X, X ), cartesian_product2( Y, Y ) ) }.
% 3.60/3.96 parent0: (20273) {G0,W10,D3,L2,V2,M2} { ! in( X, Y ), in( ordered_pair( X
% 3.60/3.96 , X ), cartesian_product2( Y, Y ) ) }.
% 3.60/3.96 substitution0:
% 3.60/3.96 X := X
% 3.60/3.96 Y := Y
% 3.60/3.96 end
% 3.60/3.96 permutation0:
% 3.60/3.96 0 ==> 0
% 3.60/3.96 1 ==> 1
% 3.60/3.96 end
% 3.60/3.96
% 3.60/3.96 resolution: (20274) {G1,W4,D3,L1,V1,M1} { relation( relation_restriction(
% 3.60/3.96 skol8, X ) ) }.
% 3.60/3.96 parent0[0]: (10) {G0,W6,D3,L2,V2,M2} I { ! relation( X ), relation(
% 3.60/3.96 relation_restriction( X, Y ) ) }.
% 3.60/3.96 parent1[0]: (41) {G0,W2,D2,L1,V0,M1} I { relation( skol8 ) }.
% 3.60/3.96 substitution0:
% 3.60/3.96 X := skol8
% 3.60/3.96 Y := X
% 3.60/3.96 end
% 3.60/3.96 substitution1:
% 3.60/3.96 end
% 3.60/3.96
% 3.60/3.96 subsumption: (109) {G1,W4,D3,L1,V1,M1} R(10,41) { relation(
% 3.60/3.96 relation_restriction( skol8, X ) ) }.
% 3.60/3.96 parent0: (20274) {G1,W4,D3,L1,V1,M1} { relation( relation_restriction(
% 3.60/3.96 skol8, X ) ) }.
% 3.60/3.96 substitution0:
% 3.60/3.96 X := X
% 3.60/3.96 end
% 3.60/3.96 permutation0:
% 3.60/3.96 0 ==> 0
% 3.60/3.96 end
% 3.60/3.96
% 3.60/3.96 resolution: (20275) {G1,W11,D3,L3,V1,M3} { ! reflexive( skol8 ), ! in( X,
% 3.60/3.96 relation_field( skol8 ) ), in( ordered_pair( X, X ), skol8 ) }.
% 3.60/3.96 parent0[0]: (18) {G0,W13,D3,L4,V2,M4} I { ! relation( X ), ! reflexive( X )
% 3.60/3.96 , ! in( Y, relation_field( X ) ), in( ordered_pair( Y, Y ), X ) }.
% 3.60/3.96 parent1[0]: (41) {G0,W2,D2,L1,V0,M1} I { relation( skol8 ) }.
% 3.60/3.96 substitution0:
% 3.60/3.96 X := skol8
% 3.60/3.96 Y := X
% 3.60/3.96 end
% 3.60/3.96 substitution1:
% 3.60/3.96 end
% 3.60/3.96
% 3.60/3.96 resolution: (20276) {G1,W9,D3,L2,V1,M2} { ! in( X, relation_field( skol8 )
% 3.60/3.96 ), in( ordered_pair( X, X ), skol8 ) }.
% 3.60/3.96 parent0[0]: (20275) {G1,W11,D3,L3,V1,M3} { ! reflexive( skol8 ), ! in( X,
% 3.60/3.96 relation_field( skol8 ) ), in( ordered_pair( X, X ), skol8 ) }.
% 3.60/3.96 parent1[0]: (42) {G0,W2,D2,L1,V0,M1} I { reflexive( skol8 ) }.
% 3.60/3.96 substitution0:
% 3.60/3.96 X := X
% 3.60/3.96 end
% 3.60/3.96 substitution1:
% 3.60/3.96 end
% 3.60/3.96
% 3.60/3.96 subsumption: (164) {G1,W9,D3,L2,V1,M2} R(18,41);r(42) { ! in( X,
% 3.60/3.96 relation_field( skol8 ) ), in( ordered_pair( X, X ), skol8 ) }.
% 3.60/3.96 parent0: (20276) {G1,W9,D3,L2,V1,M2} { ! in( X, relation_field( skol8 ) )
% 3.60/3.96 , in( ordered_pair( X, X ), skol8 ) }.
% 3.60/3.96 substitution0:
% 3.60/3.96 X := X
% 3.60/3.96 end
% 3.60/3.96 permutation0:
% 3.60/3.96 0 ==> 0
% 3.60/3.96 1 ==> 1
% 3.60/3.96 end
% 3.60/3.96
% 3.60/3.96 resolution: (20277) {G1,W13,D4,L2,V0,M2} { ! relation(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ), in( skol2( relation_restriction(
% 3.60/3.96 skol8, skol9 ) ), relation_field( relation_restriction( skol8, skol9 ) )
% 3.60/3.96 ) }.
% 3.60/3.96 parent0[0]: (43) {G0,W4,D3,L1,V0,M1} I { ! reflexive( relation_restriction
% 3.60/3.96 ( skol8, skol9 ) ) }.
% 3.60/3.96 parent1[2]: (19) {G0,W9,D3,L3,V1,M3} I { ! relation( X ), in( skol2( X ),
% 3.60/3.96 relation_field( X ) ), reflexive( X ) }.
% 3.60/3.96 substitution0:
% 3.60/3.96 end
% 3.60/3.96 substitution1:
% 3.60/3.96 X := relation_restriction( skol8, skol9 )
% 3.60/3.96 end
% 3.60/3.96
% 3.60/3.96 resolution: (20278) {G2,W9,D4,L1,V0,M1} { in( skol2( relation_restriction
% 3.60/3.96 ( skol8, skol9 ) ), relation_field( relation_restriction( skol8, skol9 )
% 3.60/3.96 ) ) }.
% 3.60/3.96 parent0[0]: (20277) {G1,W13,D4,L2,V0,M2} { ! relation(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ), in( skol2( relation_restriction(
% 3.60/3.96 skol8, skol9 ) ), relation_field( relation_restriction( skol8, skol9 ) )
% 3.60/3.96 ) }.
% 3.60/3.96 parent1[0]: (109) {G1,W4,D3,L1,V1,M1} R(10,41) { relation(
% 3.60/3.96 relation_restriction( skol8, X ) ) }.
% 3.60/3.96 substitution0:
% 3.60/3.96 end
% 3.60/3.96 substitution1:
% 3.60/3.96 X := skol9
% 3.60/3.96 end
% 3.60/3.96
% 3.60/3.96 subsumption: (187) {G2,W9,D4,L1,V0,M1} R(19,43);r(109) { in( skol2(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ), relation_field(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ) ) }.
% 3.60/3.96 parent0: (20278) {G2,W9,D4,L1,V0,M1} { in( skol2( relation_restriction(
% 3.60/3.96 skol8, skol9 ) ), relation_field( relation_restriction( skol8, skol9 ) )
% 3.60/3.96 ) }.
% 3.60/3.96 substitution0:
% 3.60/3.96 end
% 3.60/3.96 permutation0:
% 3.60/3.96 0 ==> 0
% 3.60/3.96 end
% 3.60/3.96
% 3.60/3.96 resolution: (20279) {G1,W17,D5,L2,V0,M2} { ! relation(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ), ! in( ordered_pair( skol2(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ), skol2( relation_restriction(
% 3.60/3.96 skol8, skol9 ) ) ), relation_restriction( skol8, skol9 ) ) }.
% 3.60/3.96 parent0[0]: (43) {G0,W4,D3,L1,V0,M1} I { ! reflexive( relation_restriction
% 3.60/3.96 ( skol8, skol9 ) ) }.
% 3.60/3.96 parent1[2]: (20) {G0,W11,D4,L3,V1,M3} I { ! relation( X ), ! in(
% 3.60/3.96 ordered_pair( skol2( X ), skol2( X ) ), X ), reflexive( X ) }.
% 3.60/3.96 substitution0:
% 3.60/3.96 end
% 3.60/3.96 substitution1:
% 3.60/3.96 X := relation_restriction( skol8, skol9 )
% 3.60/3.96 end
% 3.60/3.96
% 3.60/3.96 resolution: (20280) {G2,W13,D5,L1,V0,M1} { ! in( ordered_pair( skol2(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ), skol2( relation_restriction(
% 3.60/3.96 skol8, skol9 ) ) ), relation_restriction( skol8, skol9 ) ) }.
% 3.60/3.96 parent0[0]: (20279) {G1,W17,D5,L2,V0,M2} { ! relation(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ), ! in( ordered_pair( skol2(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ), skol2( relation_restriction(
% 3.60/3.96 skol8, skol9 ) ) ), relation_restriction( skol8, skol9 ) ) }.
% 3.60/3.96 parent1[0]: (109) {G1,W4,D3,L1,V1,M1} R(10,41) { relation(
% 3.60/3.96 relation_restriction( skol8, X ) ) }.
% 3.60/3.96 substitution0:
% 3.60/3.96 end
% 3.60/3.96 substitution1:
% 3.60/3.96 X := skol9
% 3.60/3.96 end
% 3.60/3.96
% 3.60/3.96 subsumption: (210) {G2,W13,D5,L1,V0,M1} R(20,43);r(109) { ! in(
% 3.60/3.96 ordered_pair( skol2( relation_restriction( skol8, skol9 ) ), skol2(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ) ), relation_restriction( skol8,
% 3.60/3.96 skol9 ) ) }.
% 3.60/3.96 parent0: (20280) {G2,W13,D5,L1,V0,M1} { ! in( ordered_pair( skol2(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ), skol2( relation_restriction(
% 3.60/3.96 skol8, skol9 ) ) ), relation_restriction( skol8, skol9 ) ) }.
% 3.60/3.96 substitution0:
% 3.60/3.96 end
% 3.60/3.96 permutation0:
% 3.60/3.96 0 ==> 0
% 3.60/3.96 end
% 3.60/3.96
% 3.60/3.96 resolution: (20281) {G1,W13,D3,L3,V2,M3} { ! in( X, skol8 ), ! in( X,
% 3.60/3.96 cartesian_product2( Y, Y ) ), in( X, relation_restriction( skol8, Y ) )
% 3.60/3.96 }.
% 3.60/3.96 parent0[0]: (36) {G0,W15,D3,L4,V3,M4} I { ! relation( X ), ! in( Y, X ), !
% 3.60/3.96 in( Y, cartesian_product2( Z, Z ) ), in( Y, relation_restriction( X, Z )
% 3.60/3.96 ) }.
% 3.60/3.96 parent1[0]: (41) {G0,W2,D2,L1,V0,M1} I { relation( skol8 ) }.
% 3.60/3.96 substitution0:
% 3.60/3.96 X := skol8
% 3.60/3.96 Y := X
% 3.60/3.96 Z := Y
% 3.60/3.96 end
% 3.60/3.96 substitution1:
% 3.60/3.96 end
% 3.60/3.96
% 3.60/3.96 subsumption: (377) {G1,W13,D3,L3,V2,M3} R(36,41) { ! in( X, skol8 ), ! in(
% 3.60/3.96 X, cartesian_product2( Y, Y ) ), in( X, relation_restriction( skol8, Y )
% 3.60/3.96 ) }.
% 3.60/3.96 parent0: (20281) {G1,W13,D3,L3,V2,M3} { ! in( X, skol8 ), ! in( X,
% 3.60/3.96 cartesian_product2( Y, Y ) ), in( X, relation_restriction( skol8, Y ) )
% 3.60/3.96 }.
% 3.60/3.96 substitution0:
% 3.60/3.96 X := X
% 3.60/3.96 Y := Y
% 3.60/3.96 end
% 3.60/3.96 permutation0:
% 3.60/3.96 0 ==> 0
% 3.60/3.96 1 ==> 1
% 3.60/3.96 2 ==> 2
% 3.60/3.96 end
% 3.60/3.96
% 3.60/3.96 resolution: (20282) {G1,W8,D4,L2,V0,M2} { ! relation( skol8 ), in( skol2(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ), skol9 ) }.
% 3.60/3.96 parent0[1]: (38) {G0,W11,D4,L3,V3,M3} I { ! relation( X ), ! in( Y,
% 3.60/3.96 relation_field( relation_restriction( X, Z ) ) ), in( Y, Z ) }.
% 3.60/3.96 parent1[0]: (187) {G2,W9,D4,L1,V0,M1} R(19,43);r(109) { in( skol2(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ), relation_field(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ) ) }.
% 3.60/3.96 substitution0:
% 3.60/3.96 X := skol8
% 3.60/3.96 Y := skol2( relation_restriction( skol8, skol9 ) )
% 3.60/3.96 Z := skol9
% 3.60/3.96 end
% 3.60/3.96 substitution1:
% 3.60/3.96 end
% 3.60/3.96
% 3.60/3.96 resolution: (20283) {G1,W6,D4,L1,V0,M1} { in( skol2( relation_restriction
% 3.60/3.96 ( skol8, skol9 ) ), skol9 ) }.
% 3.60/3.96 parent0[0]: (20282) {G1,W8,D4,L2,V0,M2} { ! relation( skol8 ), in( skol2(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ), skol9 ) }.
% 3.60/3.96 parent1[0]: (41) {G0,W2,D2,L1,V0,M1} I { relation( skol8 ) }.
% 3.60/3.96 substitution0:
% 3.60/3.96 end
% 3.60/3.96 substitution1:
% 3.60/3.96 end
% 3.60/3.96
% 3.60/3.96 subsumption: (4907) {G3,W6,D4,L1,V0,M1} R(187,38);r(41) { in( skol2(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ), skol9 ) }.
% 3.60/3.96 parent0: (20283) {G1,W6,D4,L1,V0,M1} { in( skol2( relation_restriction(
% 3.60/3.96 skol8, skol9 ) ), skol9 ) }.
% 3.60/3.96 substitution0:
% 3.60/3.96 end
% 3.60/3.96 permutation0:
% 3.60/3.96 0 ==> 0
% 3.60/3.96 end
% 3.60/3.96
% 3.60/3.96 resolution: (20284) {G1,W9,D4,L2,V0,M2} { ! relation( skol8 ), in( skol2(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ), relation_field( skol8 ) ) }.
% 3.60/3.96 parent0[1]: (37) {G0,W12,D4,L3,V3,M3} I { ! relation( X ), ! in( Y,
% 3.60/3.96 relation_field( relation_restriction( X, Z ) ) ), in( Y, relation_field(
% 3.60/3.96 X ) ) }.
% 3.60/3.96 parent1[0]: (187) {G2,W9,D4,L1,V0,M1} R(19,43);r(109) { in( skol2(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ), relation_field(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ) ) }.
% 3.60/3.96 substitution0:
% 3.60/3.96 X := skol8
% 3.60/3.96 Y := skol2( relation_restriction( skol8, skol9 ) )
% 3.60/3.96 Z := skol9
% 3.60/3.96 end
% 3.60/3.96 substitution1:
% 3.60/3.96 end
% 3.60/3.96
% 3.60/3.96 resolution: (20285) {G1,W7,D4,L1,V0,M1} { in( skol2( relation_restriction
% 3.60/3.96 ( skol8, skol9 ) ), relation_field( skol8 ) ) }.
% 3.60/3.96 parent0[0]: (20284) {G1,W9,D4,L2,V0,M2} { ! relation( skol8 ), in( skol2(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ), relation_field( skol8 ) ) }.
% 3.60/3.96 parent1[0]: (41) {G0,W2,D2,L1,V0,M1} I { relation( skol8 ) }.
% 3.60/3.96 substitution0:
% 3.60/3.96 end
% 3.60/3.96 substitution1:
% 3.60/3.96 end
% 3.60/3.96
% 3.60/3.96 subsumption: (4908) {G3,W7,D4,L1,V0,M1} R(187,37);r(41) { in( skol2(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ), relation_field( skol8 ) ) }.
% 3.60/3.96 parent0: (20285) {G1,W7,D4,L1,V0,M1} { in( skol2( relation_restriction(
% 3.60/3.96 skol8, skol9 ) ), relation_field( skol8 ) ) }.
% 3.60/3.96 substitution0:
% 3.60/3.96 end
% 3.60/3.96 permutation0:
% 3.60/3.96 0 ==> 0
% 3.60/3.96 end
% 3.60/3.96
% 3.60/3.96 resolution: (20286) {G2,W13,D5,L1,V0,M1} { in( ordered_pair( skol2(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ), skol2( relation_restriction(
% 3.60/3.96 skol8, skol9 ) ) ), cartesian_product2( skol9, skol9 ) ) }.
% 3.60/3.96 parent0[0]: (50) {G1,W10,D3,L2,V2,M2} F(33) { ! in( X, Y ), in(
% 3.60/3.96 ordered_pair( X, X ), cartesian_product2( Y, Y ) ) }.
% 3.60/3.96 parent1[0]: (4907) {G3,W6,D4,L1,V0,M1} R(187,38);r(41) { in( skol2(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ), skol9 ) }.
% 3.60/3.96 substitution0:
% 3.60/3.96 X := skol2( relation_restriction( skol8, skol9 ) )
% 3.60/3.96 Y := skol9
% 3.60/3.96 end
% 3.60/3.96 substitution1:
% 3.60/3.96 end
% 3.60/3.96
% 3.60/3.96 subsumption: (4982) {G4,W13,D5,L1,V0,M1} R(4907,50) { in( ordered_pair(
% 3.60/3.96 skol2( relation_restriction( skol8, skol9 ) ), skol2(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ) ), cartesian_product2( skol9,
% 3.60/3.96 skol9 ) ) }.
% 3.60/3.96 parent0: (20286) {G2,W13,D5,L1,V0,M1} { in( ordered_pair( skol2(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ), skol2( relation_restriction(
% 3.60/3.96 skol8, skol9 ) ) ), cartesian_product2( skol9, skol9 ) ) }.
% 3.60/3.96 substitution0:
% 3.60/3.96 end
% 3.60/3.96 permutation0:
% 3.60/3.96 0 ==> 0
% 3.60/3.96 end
% 3.60/3.96
% 3.60/3.96 resolution: (20287) {G2,W11,D5,L1,V0,M1} { in( ordered_pair( skol2(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ), skol2( relation_restriction(
% 3.60/3.96 skol8, skol9 ) ) ), skol8 ) }.
% 3.60/3.96 parent0[0]: (164) {G1,W9,D3,L2,V1,M2} R(18,41);r(42) { ! in( X,
% 3.60/3.96 relation_field( skol8 ) ), in( ordered_pair( X, X ), skol8 ) }.
% 3.60/3.96 parent1[0]: (4908) {G3,W7,D4,L1,V0,M1} R(187,37);r(41) { in( skol2(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ), relation_field( skol8 ) ) }.
% 3.60/3.96 substitution0:
% 3.60/3.96 X := skol2( relation_restriction( skol8, skol9 ) )
% 3.60/3.96 end
% 3.60/3.96 substitution1:
% 3.60/3.96 end
% 3.60/3.96
% 3.60/3.96 subsumption: (6125) {G4,W11,D5,L1,V0,M1} R(4908,164) { in( ordered_pair(
% 3.60/3.96 skol2( relation_restriction( skol8, skol9 ) ), skol2(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ) ), skol8 ) }.
% 3.60/3.96 parent0: (20287) {G2,W11,D5,L1,V0,M1} { in( ordered_pair( skol2(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ), skol2( relation_restriction(
% 3.60/3.96 skol8, skol9 ) ) ), skol8 ) }.
% 3.60/3.96 substitution0:
% 3.60/3.96 end
% 3.60/3.96 permutation0:
% 3.60/3.96 0 ==> 0
% 3.60/3.96 end
% 3.60/3.96
% 3.60/3.96 resolution: (20288) {G2,W24,D5,L2,V0,M2} { ! in( ordered_pair( skol2(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ), skol2( relation_restriction(
% 3.60/3.96 skol8, skol9 ) ) ), skol8 ), ! in( ordered_pair( skol2(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ), skol2( relation_restriction(
% 3.60/3.96 skol8, skol9 ) ) ), cartesian_product2( skol9, skol9 ) ) }.
% 3.60/3.96 parent0[0]: (210) {G2,W13,D5,L1,V0,M1} R(20,43);r(109) { ! in( ordered_pair
% 3.60/3.96 ( skol2( relation_restriction( skol8, skol9 ) ), skol2(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ) ), relation_restriction( skol8,
% 3.60/3.96 skol9 ) ) }.
% 3.60/3.96 parent1[2]: (377) {G1,W13,D3,L3,V2,M3} R(36,41) { ! in( X, skol8 ), ! in( X
% 3.60/3.96 , cartesian_product2( Y, Y ) ), in( X, relation_restriction( skol8, Y ) )
% 3.60/3.96 }.
% 3.60/3.96 substitution0:
% 3.60/3.96 end
% 3.60/3.96 substitution1:
% 3.60/3.96 X := ordered_pair( skol2( relation_restriction( skol8, skol9 ) ), skol2
% 3.60/3.96 ( relation_restriction( skol8, skol9 ) ) )
% 3.60/3.96 Y := skol9
% 3.60/3.96 end
% 3.60/3.96
% 3.60/3.96 resolution: (20289) {G3,W13,D5,L1,V0,M1} { ! in( ordered_pair( skol2(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ), skol2( relation_restriction(
% 3.60/3.96 skol8, skol9 ) ) ), cartesian_product2( skol9, skol9 ) ) }.
% 3.60/3.96 parent0[0]: (20288) {G2,W24,D5,L2,V0,M2} { ! in( ordered_pair( skol2(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ), skol2( relation_restriction(
% 3.60/3.96 skol8, skol9 ) ) ), skol8 ), ! in( ordered_pair( skol2(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ), skol2( relation_restriction(
% 3.60/3.96 skol8, skol9 ) ) ), cartesian_product2( skol9, skol9 ) ) }.
% 3.60/3.96 parent1[0]: (6125) {G4,W11,D5,L1,V0,M1} R(4908,164) { in( ordered_pair(
% 3.60/3.96 skol2( relation_restriction( skol8, skol9 ) ), skol2(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ) ), skol8 ) }.
% 3.60/3.96 substitution0:
% 3.60/3.96 end
% 3.60/3.96 substitution1:
% 3.60/3.96 end
% 3.60/3.96
% 3.60/3.96 subsumption: (19660) {G5,W13,D5,L1,V0,M1} R(377,210);r(6125) { ! in(
% 3.60/3.96 ordered_pair( skol2( relation_restriction( skol8, skol9 ) ), skol2(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ) ), cartesian_product2( skol9,
% 3.60/3.96 skol9 ) ) }.
% 3.60/3.96 parent0: (20289) {G3,W13,D5,L1,V0,M1} { ! in( ordered_pair( skol2(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ), skol2( relation_restriction(
% 3.60/3.96 skol8, skol9 ) ) ), cartesian_product2( skol9, skol9 ) ) }.
% 3.60/3.96 substitution0:
% 3.60/3.96 end
% 3.60/3.96 permutation0:
% 3.60/3.96 0 ==> 0
% 3.60/3.96 end
% 3.60/3.96
% 3.60/3.96 resolution: (20290) {G5,W0,D0,L0,V0,M0} { }.
% 3.60/3.96 parent0[0]: (19660) {G5,W13,D5,L1,V0,M1} R(377,210);r(6125) { ! in(
% 3.60/3.96 ordered_pair( skol2( relation_restriction( skol8, skol9 ) ), skol2(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ) ), cartesian_product2( skol9,
% 3.60/3.96 skol9 ) ) }.
% 3.60/3.96 parent1[0]: (4982) {G4,W13,D5,L1,V0,M1} R(4907,50) { in( ordered_pair(
% 3.60/3.96 skol2( relation_restriction( skol8, skol9 ) ), skol2(
% 3.60/3.96 relation_restriction( skol8, skol9 ) ) ), cartesian_product2( skol9,
% 3.60/3.96 skol9 ) ) }.
% 3.60/3.96 substitution0:
% 3.60/3.96 end
% 3.60/3.96 substitution1:
% 3.60/3.96 end
% 3.60/3.96
% 3.60/3.96 subsumption: (20130) {G6,W0,D0,L0,V0,M0} S(19660);r(4982) { }.
% 3.60/3.96 parent0: (20290) {G5,W0,D0,L0,V0,M0} { }.
% 3.60/3.96 substitution0:
% 3.60/3.96 end
% 3.60/3.96 permutation0:
% 3.60/3.96 end
% 3.60/3.96
% 3.60/3.96 Proof check complete!
% 3.60/3.96
% 3.60/3.96 Memory use:
% 3.60/3.96
% 3.60/3.96 space for terms: 252820
% 3.60/3.96 space for clauses: 1008374
% 3.60/3.96
% 3.60/3.96
% 3.60/3.96 clauses generated: 152061
% 3.60/3.96 clauses kept: 20131
% 3.60/3.96 clauses selected: 1099
% 3.60/3.96 clauses deleted: 574
% 3.60/3.96 clauses inuse deleted: 208
% 3.60/3.96
% 3.60/3.96 subsentry: 434276
% 3.60/3.96 literals s-matched: 309533
% 3.60/3.96 literals matched: 299723
% 3.60/3.96 full subsumption: 79377
% 3.60/3.96
% 3.60/3.96 checksum: -964140127
% 3.60/3.96
% 3.60/3.96
% 3.60/3.96 Bliksem ended
%------------------------------------------------------------------------------