TSTP Solution File: KLE069+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE069+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n022.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 : Sun Jul 17 01:37:00 EDT 2022
% Result : Theorem 36.34s 36.71s
% Output : Refutation 36.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : KLE069+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : bliksem %s
% 0.14/0.35 % Computer : n022.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % DateTime : Thu Jun 16 10:45:32 EDT 2022
% 0.14/0.35 % CPUTime :
% 24.96/25.37 *** allocated 10000 integers for termspace/termends
% 24.96/25.37 *** allocated 10000 integers for clauses
% 24.96/25.37 *** allocated 10000 integers for justifications
% 24.96/25.37 Bliksem 1.12
% 24.96/25.37
% 24.96/25.37
% 24.96/25.37 Automatic Strategy Selection
% 24.96/25.37
% 24.96/25.37
% 24.96/25.37 Clauses:
% 24.96/25.37
% 24.96/25.37 { addition( X, Y ) = addition( Y, X ) }.
% 24.96/25.37 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 24.96/25.37 { addition( X, zero ) = X }.
% 24.96/25.37 { addition( X, X ) = X }.
% 24.96/25.37 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 24.96/25.37 multiplication( X, Y ), Z ) }.
% 24.96/25.37 { multiplication( X, one ) = X }.
% 24.96/25.37 { multiplication( one, X ) = X }.
% 24.96/25.37 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 24.96/25.37 , multiplication( X, Z ) ) }.
% 24.96/25.37 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 24.96/25.37 , multiplication( Y, Z ) ) }.
% 24.96/25.37 { multiplication( X, zero ) = zero }.
% 24.96/25.37 { multiplication( zero, X ) = zero }.
% 24.96/25.37 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 24.96/25.37 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 24.96/25.37 { addition( X, multiplication( domain( X ), X ) ) = multiplication( domain
% 24.96/25.37 ( X ), X ) }.
% 24.96/25.37 { domain( multiplication( X, Y ) ) = domain( multiplication( X, domain( Y )
% 24.96/25.37 ) ) }.
% 24.96/25.37 { addition( domain( X ), one ) = one }.
% 24.96/25.37 { domain( zero ) = zero }.
% 24.96/25.37 { domain( addition( X, Y ) ) = addition( domain( X ), domain( Y ) ) }.
% 24.96/25.37 { ! multiplication( domain( skol1 ), addition( domain( skol1 ), domain(
% 24.96/25.37 skol2 ) ) ) = domain( skol1 ) }.
% 24.96/25.37
% 24.96/25.37 percentage equality = 0.904762, percentage horn = 1.000000
% 24.96/25.37 This is a pure equality problem
% 24.96/25.37
% 24.96/25.37
% 24.96/25.37
% 24.96/25.37 Options Used:
% 24.96/25.37
% 24.96/25.37 useres = 1
% 24.96/25.37 useparamod = 1
% 24.96/25.37 useeqrefl = 1
% 24.96/25.37 useeqfact = 1
% 24.96/25.37 usefactor = 1
% 24.96/25.37 usesimpsplitting = 0
% 24.96/25.37 usesimpdemod = 5
% 24.96/25.37 usesimpres = 3
% 24.96/25.37
% 24.96/25.37 resimpinuse = 1000
% 24.96/25.37 resimpclauses = 20000
% 24.96/25.37 substype = eqrewr
% 24.96/25.37 backwardsubs = 1
% 24.96/25.37 selectoldest = 5
% 24.96/25.37
% 24.96/25.37 litorderings [0] = split
% 24.96/25.37 litorderings [1] = extend the termordering, first sorting on arguments
% 24.96/25.37
% 24.96/25.37 termordering = kbo
% 24.96/25.37
% 24.96/25.37 litapriori = 0
% 24.96/25.37 termapriori = 1
% 24.96/25.37 litaposteriori = 0
% 24.96/25.37 termaposteriori = 0
% 24.96/25.37 demodaposteriori = 0
% 24.96/25.37 ordereqreflfact = 0
% 24.96/25.37
% 24.96/25.37 litselect = negord
% 24.96/25.37
% 24.96/25.37 maxweight = 15
% 24.96/25.37 maxdepth = 30000
% 24.96/25.37 maxlength = 115
% 24.96/25.37 maxnrvars = 195
% 24.96/25.37 excuselevel = 1
% 24.96/25.37 increasemaxweight = 1
% 24.96/25.37
% 24.96/25.37 maxselected = 10000000
% 24.96/25.37 maxnrclauses = 10000000
% 24.96/25.37
% 24.96/25.37 showgenerated = 0
% 24.96/25.37 showkept = 0
% 24.96/25.37 showselected = 0
% 24.96/25.37 showdeleted = 0
% 24.96/25.37 showresimp = 1
% 24.96/25.37 showstatus = 2000
% 24.96/25.37
% 24.96/25.37 prologoutput = 0
% 24.96/25.37 nrgoals = 5000000
% 24.96/25.37 totalproof = 1
% 24.96/25.37
% 24.96/25.37 Symbols occurring in the translation:
% 24.96/25.37
% 24.96/25.37 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 24.96/25.37 . [1, 2] (w:1, o:21, a:1, s:1, b:0),
% 24.96/25.37 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 24.96/25.37 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 24.96/25.37 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 24.96/25.37 addition [37, 2] (w:1, o:45, a:1, s:1, b:0),
% 24.96/25.37 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 24.96/25.37 multiplication [40, 2] (w:1, o:47, a:1, s:1, b:0),
% 24.96/25.37 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 24.96/25.37 leq [42, 2] (w:1, o:46, a:1, s:1, b:0),
% 24.96/25.37 domain [44, 1] (w:1, o:20, a:1, s:1, b:0),
% 24.96/25.37 skol1 [46, 0] (w:1, o:13, a:1, s:1, b:1),
% 24.96/25.37 skol2 [47, 0] (w:1, o:14, a:1, s:1, b:1).
% 24.96/25.37
% 24.96/25.37
% 24.96/25.37 Starting Search:
% 24.96/25.37
% 24.96/25.37 *** allocated 15000 integers for clauses
% 24.96/25.37 *** allocated 22500 integers for clauses
% 24.96/25.37 *** allocated 33750 integers for clauses
% 24.96/25.37 *** allocated 50625 integers for clauses
% 24.96/25.37 *** allocated 15000 integers for termspace/termends
% 24.96/25.37 *** allocated 75937 integers for clauses
% 24.96/25.37 Resimplifying inuse:
% 24.96/25.37 Done
% 24.96/25.37
% 24.96/25.37 *** allocated 22500 integers for termspace/termends
% 24.96/25.37 *** allocated 113905 integers for clauses
% 24.96/25.37 *** allocated 33750 integers for termspace/termends
% 24.96/25.37
% 24.96/25.37 Intermediate Status:
% 24.96/25.37 Generated: 16508
% 24.96/25.37 Kept: 2002
% 24.96/25.37 Inuse: 234
% 24.96/25.37 Deleted: 22
% 24.96/25.37 Deletedinuse: 9
% 24.96/25.37
% 24.96/25.37 Resimplifying inuse:
% 24.96/25.37 Done
% 24.96/25.37
% 24.96/25.37 *** allocated 170857 integers for clauses
% 24.96/25.37 *** allocated 50625 integers for termspace/termends
% 24.96/25.37 Resimplifying inuse:
% 24.96/25.37 Done
% 24.96/25.37
% 24.96/25.37 *** allocated 256285 integers for clauses
% 24.96/25.37 *** allocated 75937 integers for termspace/termends
% 24.96/25.37
% 24.96/25.37 Intermediate Status:
% 24.96/25.37 Generated: 37304
% 24.96/25.37 Kept: 4011
% 24.96/25.37 Inuse: 367
% 24.96/25.37 Deleted: 58
% 24.96/25.37 Deletedinuse: 18
% 24.96/25.37
% 24.96/25.37 Resimplifying inuse:
% 24.96/25.37 Done
% 24.96/25.37
% 24.96/25.37 Resimplifying inuse:
% 24.96/25.37 Done
% 24.96/25.37
% 24.96/25.37 *** allocated 384427 integers for clauses
% 24.96/25.37 *** allocated 113905 integers for termspace/termends
% 36.34/36.71
% 36.34/36.71 Intermediate Status:
% 36.34/36.71 Generated: 69324
% 36.34/36.71 Kept: 6022
% 36.34/36.71 Inuse: 565
% 36.34/36.71 Deleted: 100
% 36.34/36.71 Deletedinuse: 24
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71
% 36.34/36.71 Intermediate Status:
% 36.34/36.71 Generated: 119859
% 36.34/36.71 Kept: 8215
% 36.34/36.71 Inuse: 647
% 36.34/36.71 Deleted: 124
% 36.34/36.71 Deletedinuse: 36
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71 *** allocated 576640 integers for clauses
% 36.34/36.71 *** allocated 170857 integers for termspace/termends
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71
% 36.34/36.71 Intermediate Status:
% 36.34/36.71 Generated: 149165
% 36.34/36.71 Kept: 10225
% 36.34/36.71 Inuse: 671
% 36.34/36.71 Deleted: 128
% 36.34/36.71 Deletedinuse: 36
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71 *** allocated 256285 integers for termspace/termends
% 36.34/36.71
% 36.34/36.71 Intermediate Status:
% 36.34/36.71 Generated: 180466
% 36.34/36.71 Kept: 12265
% 36.34/36.71 Inuse: 784
% 36.34/36.71 Deleted: 145
% 36.34/36.71 Deletedinuse: 38
% 36.34/36.71
% 36.34/36.71 *** allocated 864960 integers for clauses
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71
% 36.34/36.71 Intermediate Status:
% 36.34/36.71 Generated: 206944
% 36.34/36.71 Kept: 14266
% 36.34/36.71 Inuse: 858
% 36.34/36.71 Deleted: 154
% 36.34/36.71 Deletedinuse: 41
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71
% 36.34/36.71 Intermediate Status:
% 36.34/36.71 Generated: 235900
% 36.34/36.71 Kept: 16266
% 36.34/36.71 Inuse: 926
% 36.34/36.71 Deleted: 157
% 36.34/36.71 Deletedinuse: 43
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71 *** allocated 384427 integers for termspace/termends
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71
% 36.34/36.71 Intermediate Status:
% 36.34/36.71 Generated: 269637
% 36.34/36.71 Kept: 18314
% 36.34/36.71 Inuse: 999
% 36.34/36.71 Deleted: 157
% 36.34/36.71 Deletedinuse: 43
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71 *** allocated 1297440 integers for clauses
% 36.34/36.71 Resimplifying clauses:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71
% 36.34/36.71 Intermediate Status:
% 36.34/36.71 Generated: 304347
% 36.34/36.71 Kept: 20380
% 36.34/36.71 Inuse: 1062
% 36.34/36.71 Deleted: 2136
% 36.34/36.71 Deletedinuse: 46
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71
% 36.34/36.71 Intermediate Status:
% 36.34/36.71 Generated: 347900
% 36.34/36.71 Kept: 22393
% 36.34/36.71 Inuse: 1159
% 36.34/36.71 Deleted: 2139
% 36.34/36.71 Deletedinuse: 46
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71
% 36.34/36.71 Intermediate Status:
% 36.34/36.71 Generated: 365599
% 36.34/36.71 Kept: 24477
% 36.34/36.71 Inuse: 1204
% 36.34/36.71 Deleted: 2139
% 36.34/36.71 Deletedinuse: 46
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71 *** allocated 576640 integers for termspace/termends
% 36.34/36.71
% 36.34/36.71 Intermediate Status:
% 36.34/36.71 Generated: 384384
% 36.34/36.71 Kept: 26576
% 36.34/36.71 Inuse: 1233
% 36.34/36.71 Deleted: 2139
% 36.34/36.71 Deletedinuse: 46
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71
% 36.34/36.71 Intermediate Status:
% 36.34/36.71 Generated: 433024
% 36.34/36.71 Kept: 28596
% 36.34/36.71 Inuse: 1312
% 36.34/36.71 Deleted: 2139
% 36.34/36.71 Deletedinuse: 46
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71 *** allocated 1946160 integers for clauses
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71
% 36.34/36.71 Intermediate Status:
% 36.34/36.71 Generated: 473874
% 36.34/36.71 Kept: 30604
% 36.34/36.71 Inuse: 1408
% 36.34/36.71 Deleted: 2139
% 36.34/36.71 Deletedinuse: 46
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71
% 36.34/36.71 Intermediate Status:
% 36.34/36.71 Generated: 500207
% 36.34/36.71 Kept: 32656
% 36.34/36.71 Inuse: 1441
% 36.34/36.71 Deleted: 2139
% 36.34/36.71 Deletedinuse: 46
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71
% 36.34/36.71 Intermediate Status:
% 36.34/36.71 Generated: 558909
% 36.34/36.71 Kept: 35060
% 36.34/36.71 Inuse: 1478
% 36.34/36.71 Deleted: 2139
% 36.34/36.71 Deletedinuse: 46
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71
% 36.34/36.71 Intermediate Status:
% 36.34/36.71 Generated: 592061
% 36.34/36.71 Kept: 37066
% 36.34/36.71 Inuse: 1511
% 36.34/36.71 Deleted: 2139
% 36.34/36.71 Deletedinuse: 46
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71 *** allocated 864960 integers for termspace/termends
% 36.34/36.71
% 36.34/36.71 Intermediate Status:
% 36.34/36.71 Generated: 637721
% 36.34/36.71 Kept: 39141
% 36.34/36.71 Inuse: 1566
% 36.34/36.71 Deleted: 2139
% 36.34/36.71 Deletedinuse: 46
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71 Resimplifying clauses:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71
% 36.34/36.71 Intermediate Status:
% 36.34/36.71 Generated: 695592
% 36.34/36.71 Kept: 41344
% 36.34/36.71 Inuse: 1596
% 36.34/36.71 Deleted: 4159
% 36.34/36.71 Deletedinuse: 46
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71
% 36.34/36.71 Intermediate Status:
% 36.34/36.71 Generated: 748359
% 36.34/36.71 Kept: 43351
% 36.34/36.71 Inuse: 1633
% 36.34/36.71 Deleted: 4159
% 36.34/36.71 Deletedinuse: 46
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71 *** allocated 2919240 integers for clauses
% 36.34/36.71
% 36.34/36.71 Intermediate Status:
% 36.34/36.71 Generated: 805794
% 36.34/36.71 Kept: 45401
% 36.34/36.71 Inuse: 1715
% 36.34/36.71 Deleted: 4161
% 36.34/36.71 Deletedinuse: 48
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71
% 36.34/36.71 Intermediate Status:
% 36.34/36.71 Generated: 893640
% 36.34/36.71 Kept: 47498
% 36.34/36.71 Inuse: 1782
% 36.34/36.71 Deleted: 4163
% 36.34/36.71 Deletedinuse: 50
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71
% 36.34/36.71 Intermediate Status:
% 36.34/36.71 Generated: 943732
% 36.34/36.71 Kept: 49671
% 36.34/36.71 Inuse: 1809
% 36.34/36.71 Deleted: 4163
% 36.34/36.71 Deletedinuse: 50
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71
% 36.34/36.71 Intermediate Status:
% 36.34/36.71 Generated: 977782
% 36.34/36.71 Kept: 51686
% 36.34/36.71 Inuse: 1846
% 36.34/36.71 Deleted: 4163
% 36.34/36.71 Deletedinuse: 50
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71
% 36.34/36.71 Intermediate Status:
% 36.34/36.71 Generated: 1072041
% 36.34/36.71 Kept: 53725
% 36.34/36.71 Inuse: 1890
% 36.34/36.71 Deleted: 4163
% 36.34/36.71 Deletedinuse: 50
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71
% 36.34/36.71 Intermediate Status:
% 36.34/36.71 Generated: 1114826
% 36.34/36.71 Kept: 55903
% 36.34/36.71 Inuse: 1933
% 36.34/36.71 Deleted: 4164
% 36.34/36.71 Deletedinuse: 51
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71 *** allocated 1297440 integers for termspace/termends
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71
% 36.34/36.71 Intermediate Status:
% 36.34/36.71 Generated: 1149367
% 36.34/36.71 Kept: 57918
% 36.34/36.71 Inuse: 1977
% 36.34/36.71 Deleted: 4164
% 36.34/36.71 Deletedinuse: 51
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71 Resimplifying inuse:
% 36.34/36.71 Done
% 36.34/36.71
% 36.34/36.71
% 36.34/36.71 Intermediate Status:
% 36.34/36.71 Generated: 1181490
% 36.34/36.71 Kept: 59946
% 36.34/36.71 Inuse: 2021
% 36.34/36.71 Deleted: 4164
% 36.34/36.71 Deletedinuse: 51
% 36.34/36.71
% 36.34/36.71 Resimplifying clauses:
% 36.34/36.71
% 36.34/36.71 Bliksems!, er is een bewijs:
% 36.34/36.71 % SZS status Theorem
% 36.34/36.71 % SZS output start Refutation
% 36.34/36.71
% 36.34/36.71 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 36.34/36.71 (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) ==> addition(
% 36.34/36.71 addition( Z, Y ), X ) }.
% 36.34/36.71 (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 36.34/36.71 (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 36.34/36.71 (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 36.34/36.71 (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 36.34/36.71 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 36.34/36.71 (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 36.34/36.71 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 36.34/36.71 (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) ==> Y }.
% 36.34/36.71 (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, Y ) }.
% 36.34/36.71 (13) {G0,W11,D5,L1,V1,M1} I { addition( X, multiplication( domain( X ), X )
% 36.34/36.71 ) ==> multiplication( domain( X ), X ) }.
% 36.34/36.71 (14) {G0,W10,D5,L1,V2,M1} I { domain( multiplication( X, domain( Y ) ) )
% 36.34/36.71 ==> domain( multiplication( X, Y ) ) }.
% 36.34/36.71 (15) {G0,W6,D4,L1,V1,M1} I { addition( domain( X ), one ) ==> one }.
% 36.34/36.71 (17) {G0,W10,D4,L1,V2,M1} I { addition( domain( X ), domain( Y ) ) ==>
% 36.34/36.71 domain( addition( X, Y ) ) }.
% 36.34/36.71 (18) {G1,W10,D5,L1,V0,M1} I;d(17) { ! multiplication( domain( skol1 ),
% 36.34/36.71 domain( addition( skol1, skol2 ) ) ) ==> domain( skol1 ) }.
% 36.34/36.71 (20) {G1,W6,D4,L1,V1,M1} P(15,0) { addition( one, domain( X ) ) ==> one }.
% 36.34/36.71 (23) {G1,W9,D4,L1,V2,M1} P(3,1) { addition( addition( Y, X ), X ) ==>
% 36.34/36.71 addition( Y, X ) }.
% 36.34/36.71 (33) {G1,W8,D3,L2,V2,M2} P(0,12) { ! addition( Y, X ) ==> Y, leq( X, Y )
% 36.34/36.71 }.
% 36.34/36.71 (43) {G1,W16,D4,L2,V3,M2} P(7,11) { ! leq( multiplication( X, Y ),
% 36.34/36.71 multiplication( X, Z ) ), multiplication( X, addition( Y, Z ) ) ==>
% 36.34/36.71 multiplication( X, Z ) }.
% 36.34/36.71 (46) {G1,W16,D4,L2,V3,M2} P(7,12) { ! multiplication( X, addition( Y, Z ) )
% 36.34/36.71 ==> multiplication( X, Z ), leq( multiplication( X, Y ), multiplication
% 36.34/36.71 ( X, Z ) ) }.
% 36.34/36.71 (85) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( X, multiplication( Y, X ) ) =
% 36.34/36.71 multiplication( addition( one, Y ), X ) }.
% 36.34/36.71 (139) {G1,W6,D4,L1,V1,M1} P(6,14);d(6) { domain( domain( X ) ) ==> domain(
% 36.34/36.71 X ) }.
% 36.34/36.71 (216) {G2,W10,D5,L1,V0,M1} P(0,18) { ! multiplication( domain( skol1 ),
% 36.34/36.71 domain( addition( skol2, skol1 ) ) ) ==> domain( skol1 ) }.
% 36.34/36.71 (258) {G2,W5,D3,L1,V2,M1} R(23,33) { leq( X, addition( Y, X ) ) }.
% 36.34/36.71 (266) {G3,W7,D4,L1,V2,M1} P(17,258) { leq( domain( Y ), domain( addition( X
% 36.34/36.71 , Y ) ) ) }.
% 36.34/36.71 (651) {G2,W12,D4,L2,V2,M2} P(20,43);d(5);d(5) { ! leq( Y, multiplication( Y
% 36.34/36.71 , domain( X ) ) ), multiplication( Y, domain( X ) ) ==> Y }.
% 36.34/36.71 (726) {G2,W10,D3,L2,V3,M2} P(11,46);q { leq( multiplication( Z, X ),
% 36.34/36.71 multiplication( Z, Y ) ), ! leq( X, Y ) }.
% 36.34/36.71 (2746) {G2,W6,D4,L1,V1,M1} P(85,13);d(20);d(6) { multiplication( domain( X
% 36.34/36.71 ), X ) ==> X }.
% 36.34/36.71 (51790) {G3,W10,D5,L1,V0,M1} R(651,216) { ! leq( domain( skol1 ),
% 36.34/36.71 multiplication( domain( skol1 ), domain( addition( skol2, skol1 ) ) ) )
% 36.34/36.71 }.
% 36.34/36.71 (59070) {G3,W9,D4,L2,V2,M2} P(2746,726) { leq( X, multiplication( domain( X
% 36.34/36.71 ), Y ) ), ! leq( X, Y ) }.
% 36.34/36.71 (59423) {G4,W10,D5,L1,V2,M1} R(59070,266);d(139) { leq( domain( X ),
% 36.34/36.71 multiplication( domain( X ), domain( addition( Y, X ) ) ) ) }.
% 36.34/36.71 (60063) {G5,W0,D0,L0,V0,M0} S(51790);r(59423) { }.
% 36.34/36.71
% 36.34/36.71
% 36.34/36.71 % SZS output end Refutation
% 36.34/36.71 found a proof!
% 36.34/36.71
% 36.34/36.71
% 36.34/36.71 Unprocessed initial clauses:
% 36.34/36.71
% 36.34/36.71 (60065) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 36.34/36.71 (60066) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition
% 36.34/36.71 ( addition( Z, Y ), X ) }.
% 36.34/36.71 (60067) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 36.34/36.71 (60068) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 36.34/36.71 (60069) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) )
% 36.34/36.71 = multiplication( multiplication( X, Y ), Z ) }.
% 36.34/36.71 (60070) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 36.34/36.71 (60071) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 36.34/36.71 (60072) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 36.34/36.71 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 36.34/36.71 (60073) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 36.34/36.71 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 36.34/36.71 (60074) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero }.
% 36.34/36.71 (60075) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 36.34/36.71 (60076) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 36.34/36.71 (60077) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 36.34/36.71 (60078) {G0,W11,D5,L1,V1,M1} { addition( X, multiplication( domain( X ), X
% 36.34/36.71 ) ) = multiplication( domain( X ), X ) }.
% 36.34/36.71 (60079) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, Y ) ) = domain(
% 36.34/36.71 multiplication( X, domain( Y ) ) ) }.
% 36.34/36.71 (60080) {G0,W6,D4,L1,V1,M1} { addition( domain( X ), one ) = one }.
% 36.34/36.71 (60081) {G0,W4,D3,L1,V0,M1} { domain( zero ) = zero }.
% 36.34/36.71 (60082) {G0,W10,D4,L1,V2,M1} { domain( addition( X, Y ) ) = addition(
% 36.34/36.71 domain( X ), domain( Y ) ) }.
% 36.34/36.71 (60083) {G0,W11,D5,L1,V0,M1} { ! multiplication( domain( skol1 ), addition
% 36.34/36.71 ( domain( skol1 ), domain( skol2 ) ) ) = domain( skol1 ) }.
% 36.34/36.71
% 36.34/36.71
% 36.34/36.71 Total Proof:
% 36.34/36.71
% 36.34/36.71 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 36.34/36.71 ) }.
% 36.34/36.71 parent0: (60065) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 36.34/36.71 }.
% 36.34/36.71 substitution0:
% 36.34/36.71 X := X
% 36.34/36.71 Y := Y
% 36.34/36.71 end
% 36.34/36.71 permutation0:
% 36.34/36.71 0 ==> 0
% 36.34/36.71 end
% 36.34/36.71
% 36.34/36.71 subsumption: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 36.34/36.71 ==> addition( addition( Z, Y ), X ) }.
% 36.34/36.71 parent0: (60066) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) =
% 36.34/36.71 addition( addition( Z, Y ), X ) }.
% 36.34/36.71 substitution0:
% 36.34/36.71 X := X
% 36.34/36.71 Y := Y
% 36.34/36.71 Z := Z
% 36.34/36.71 end
% 36.34/36.71 permutation0:
% 36.34/36.71 0 ==> 0
% 36.34/36.71 end
% 36.34/36.71
% 36.34/36.71 subsumption: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 36.34/36.71 parent0: (60068) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 36.34/36.71 substitution0:
% 36.34/36.71 X := X
% 36.34/36.71 end
% 36.34/36.71 permutation0:
% 36.34/36.71 0 ==> 0
% 36.34/36.71 end
% 36.34/36.71
% 36.34/36.71 subsumption: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 36.34/36.71 parent0: (60070) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 36.34/36.71 substitution0:
% 36.34/36.71 X := X
% 36.34/36.71 end
% 36.34/36.71 permutation0:
% 36.34/36.71 0 ==> 0
% 36.34/36.71 end
% 36.34/36.71
% 36.34/36.71 subsumption: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 36.34/36.71 parent0: (60071) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 36.34/36.71 substitution0:
% 36.34/36.71 X := X
% 36.34/36.71 end
% 36.34/36.71 permutation0:
% 36.34/36.71 0 ==> 0
% 36.34/36.71 end
% 36.34/36.71
% 36.34/36.71 eqswap: (60105) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 36.34/36.71 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 36.34/36.71 parent0[0]: (60072) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y
% 36.34/36.71 , Z ) ) = addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 36.34/36.71 substitution0:
% 36.34/36.71 X := X
% 36.34/36.71 Y := Y
% 36.34/36.71 Z := Z
% 36.34/36.71 end
% 36.34/36.71
% 36.34/36.71 subsumption: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y )
% 36.34/36.71 , multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 36.34/36.71 parent0: (60105) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 36.34/36.71 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 36.34/36.71 substitution0:
% 36.34/36.71 X := X
% 36.34/36.71 Y := Y
% 36.34/36.71 Z := Z
% 36.34/36.71 end
% 36.34/36.71 permutation0:
% 36.34/36.71 0 ==> 0
% 36.34/36.71 end
% 36.34/36.71
% 36.34/36.71 eqswap: (60113) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 36.34/36.71 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 36.34/36.71 parent0[0]: (60073) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y
% 36.34/36.71 ), Z ) = addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 36.34/36.71 substitution0:
% 36.34/36.71 X := X
% 36.34/36.71 Y := Y
% 36.34/36.71 Z := Z
% 36.34/36.71 end
% 36.34/36.71
% 36.34/36.71 subsumption: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z )
% 36.34/36.71 , multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 36.34/36.71 parent0: (60113) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 36.34/36.71 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 36.34/36.71 substitution0:
% 36.34/36.71 X := X
% 36.34/36.71 Y := Y
% 36.34/36.71 Z := Z
% 36.34/36.71 end
% 36.34/36.71 permutation0:
% 36.34/36.71 0 ==> 0
% 36.34/36.71 end
% 36.34/36.71
% 36.34/36.71 subsumption: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 36.34/36.71 ==> Y }.
% 36.34/36.71 parent0: (60076) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y
% 36.34/36.71 }.
% 36.34/36.71 substitution0:
% 36.34/36.71 X := X
% 36.34/36.71 Y := Y
% 36.34/36.71 end
% 36.34/36.71 permutation0:
% 36.34/36.71 0 ==> 0
% 36.34/36.71 1 ==> 1
% 36.34/36.71 end
% 36.34/36.71
% 36.34/36.71 subsumption: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X
% 36.34/36.71 , Y ) }.
% 36.34/36.71 parent0: (60077) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y )
% 36.34/36.71 }.
% 36.34/36.71 substitution0:
% 36.34/36.71 X := X
% 36.34/36.71 Y := Y
% 36.34/36.71 end
% 36.34/36.71 permutation0:
% 36.34/36.71 0 ==> 0
% 36.34/36.71 1 ==> 1
% 36.34/36.71 end
% 36.34/36.71
% 36.34/36.71 subsumption: (13) {G0,W11,D5,L1,V1,M1} I { addition( X, multiplication(
% 36.34/36.71 domain( X ), X ) ) ==> multiplication( domain( X ), X ) }.
% 36.34/36.71 parent0: (60078) {G0,W11,D5,L1,V1,M1} { addition( X, multiplication(
% 36.34/36.71 domain( X ), X ) ) = multiplication( domain( X ), X ) }.
% 36.34/36.71 substitution0:
% 36.34/36.71 X := X
% 36.34/36.71 end
% 36.34/36.71 permutation0:
% 36.34/36.71 0 ==> 0
% 36.34/36.71 end
% 36.34/36.71
% 36.34/36.71 eqswap: (60163) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, domain(
% 36.34/36.71 Y ) ) ) = domain( multiplication( X, Y ) ) }.
% 36.34/36.71 parent0[0]: (60079) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, Y )
% 36.34/36.71 ) = domain( multiplication( X, domain( Y ) ) ) }.
% 36.34/36.71 substitution0:
% 36.34/36.71 X := X
% 36.34/36.71 Y := Y
% 36.34/36.71 end
% 36.34/36.71
% 36.34/36.71 subsumption: (14) {G0,W10,D5,L1,V2,M1} I { domain( multiplication( X,
% 36.34/36.71 domain( Y ) ) ) ==> domain( multiplication( X, Y ) ) }.
% 36.34/36.71 parent0: (60163) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, domain
% 36.34/36.71 ( Y ) ) ) = domain( multiplication( X, Y ) ) }.
% 36.34/36.71 substitution0:
% 36.34/36.71 X := X
% 36.34/36.71 Y := Y
% 36.34/36.71 end
% 36.34/36.71 permutation0:
% 36.34/36.71 0 ==> 0
% 36.34/36.71 end
% 36.34/36.71
% 36.34/36.71 subsumption: (15) {G0,W6,D4,L1,V1,M1} I { addition( domain( X ), one ) ==>
% 36.34/36.71 one }.
% 36.34/36.71 parent0: (60080) {G0,W6,D4,L1,V1,M1} { addition( domain( X ), one ) = one
% 36.34/36.71 }.
% 36.34/36.71 substitution0:
% 36.34/36.71 X := X
% 36.34/36.71 end
% 36.34/36.71 permutation0:
% 36.34/36.71 0 ==> 0
% 36.34/36.71 end
% 36.34/36.71
% 36.34/36.71 eqswap: (60195) {G0,W10,D4,L1,V2,M1} { addition( domain( X ), domain( Y )
% 36.34/36.71 ) = domain( addition( X, Y ) ) }.
% 36.34/36.71 parent0[0]: (60082) {G0,W10,D4,L1,V2,M1} { domain( addition( X, Y ) ) =
% 36.34/36.71 addition( domain( X ), domain( Y ) ) }.
% 36.34/36.71 substitution0:
% 36.34/36.71 X := X
% 36.34/36.71 Y := Y
% 36.34/36.71 end
% 36.34/36.71
% 36.34/36.71 subsumption: (17) {G0,W10,D4,L1,V2,M1} I { addition( domain( X ), domain( Y
% 36.34/36.71 ) ) ==> domain( addition( X, Y ) ) }.
% 36.34/36.71 parent0: (60195) {G0,W10,D4,L1,V2,M1} { addition( domain( X ), domain( Y )
% 36.34/36.71 ) = domain( addition( X, Y ) ) }.
% 36.34/36.71 substitution0:
% 36.34/36.71 X := X
% 36.34/36.71 Y := Y
% 36.34/36.71 end
% 36.34/36.71 permutation0:
% 36.34/36.71 0 ==> 0
% 36.34/36.71 end
% 36.34/36.71
% 36.34/36.71 paramod: (60235) {G1,W10,D5,L1,V0,M1} { ! multiplication( domain( skol1 )
% 36.34/36.71 , domain( addition( skol1, skol2 ) ) ) = domain( skol1 ) }.
% 36.34/36.71 parent0[0]: (17) {G0,W10,D4,L1,V2,M1} I { addition( domain( X ), domain( Y
% 36.34/36.71 ) ) ==> domain( addition( X, Y ) ) }.
% 36.34/36.71 parent1[0; 5]: (60083) {G0,W11,D5,L1,V0,M1} { ! multiplication( domain(
% 36.34/36.71 skol1 ), addition( domain( skol1 ), domain( skol2 ) ) ) = domain( skol1 )
% 36.34/36.71 }.
% 36.34/36.71 substitution0:
% 36.34/36.71 X := skol1
% 36.34/36.71 Y := skol2
% 36.34/36.71 end
% 36.34/36.71 substitution1:
% 36.34/36.71 end
% 36.34/36.71
% 36.34/36.71 subsumption: (18) {G1,W10,D5,L1,V0,M1} I;d(17) { ! multiplication( domain(
% 36.34/36.71 skol1 ), domain( addition( skol1, skol2 ) ) ) ==> domain( skol1 ) }.
% 36.34/36.71 parent0: (60235) {G1,W10,D5,L1,V0,M1} { ! multiplication( domain( skol1 )
% 36.34/36.71 , domain( addition( skol1, skol2 ) ) ) = domain( skol1 ) }.
% 36.34/36.71 substitution0:
% 36.34/36.71 end
% 36.34/36.71 permutation0:
% 36.34/36.71 0 ==> 0
% 36.34/36.71 end
% 36.34/36.71
% 36.34/36.71 eqswap: (60237) {G0,W6,D4,L1,V1,M1} { one ==> addition( domain( X ), one )
% 36.34/36.71 }.
% 36.34/36.71 parent0[0]: (15) {G0,W6,D4,L1,V1,M1} I { addition( domain( X ), one ) ==>
% 36.34/36.71 one }.
% 36.34/36.71 substitution0:
% 36.34/36.71 X := X
% 36.34/36.71 end
% 36.34/36.71
% 36.34/36.71 paramod: (60238) {G1,W6,D4,L1,V1,M1} { one ==> addition( one, domain( X )
% 36.34/36.71 ) }.
% 36.34/36.71 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 36.34/36.71 }.
% 36.34/36.71 parent1[0; 2]: (60237) {G0,W6,D4,L1,V1,M1} { one ==> addition( domain( X )
% 36.34/36.71 , one ) }.
% 36.34/36.71 substitution0:
% 36.34/36.71 X := domain( X )
% 36.34/36.71 Y := one
% 36.34/36.71 end
% 36.34/36.71 substitution1:
% 36.34/36.71 X := X
% 36.34/36.71 end
% 36.34/36.71
% 36.34/36.71 eqswap: (60241) {G1,W6,D4,L1,V1,M1} { addition( one, domain( X ) ) ==> one
% 36.34/36.71 }.
% 36.34/36.71 parent0[0]: (60238) {G1,W6,D4,L1,V1,M1} { one ==> addition( one, domain( X
% 36.34/36.71 ) ) }.
% 36.34/36.71 substitution0:
% 36.34/36.71 X := X
% 36.34/36.71 end
% 36.34/36.71
% 36.34/36.71 subsumption: (20) {G1,W6,D4,L1,V1,M1} P(15,0) { addition( one, domain( X )
% 36.34/36.71 ) ==> one }.
% 36.34/36.71 parent0: (60241) {G1,W6,D4,L1,V1,M1} { addition( one, domain( X ) ) ==>
% 36.34/36.71 one }.
% 36.34/36.71 substitution0:
% 36.34/36.71 X := X
% 36.34/36.71 end
% 36.34/36.71 permutation0:
% 36.34/36.71 0 ==> 0
% 36.34/36.71 end
% 36.34/36.71
% 36.34/36.71 eqswap: (60243) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 36.34/36.71 addition( X, addition( Y, Z ) ) }.
% 36.34/36.71 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 36.34/36.71 ==> addition( addition( Z, Y ), X ) }.
% 36.34/36.71 substitution0:
% 36.34/36.71 X := Z
% 36.34/36.71 Y := Y
% 36.34/36.71 Z := X
% 36.34/36.71 end
% 36.34/36.71
% 36.34/36.71 paramod: (60249) {G1,W9,D4,L1,V2,M1} { addition( addition( X, Y ), Y ) ==>
% 36.34/36.71 addition( X, Y ) }.
% 36.34/36.71 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 36.34/36.71 parent1[0; 8]: (60243) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ),
% 36.34/36.71 Z ) ==> addition( X, addition( Y, Z ) ) }.
% 36.34/36.71 substitution0:
% 36.34/36.71 X := Y
% 36.34/36.71 end
% 36.34/36.71 substitution1:
% 36.34/36.71 X := X
% 36.34/36.71 Y := Y
% 36.34/36.71 Z := Y
% 36.34/36.71 end
% 36.34/36.71
% 36.34/36.71 subsumption: (23) {G1,W9,D4,L1,V2,M1} P(3,1) { addition( addition( Y, X ),
% 36.34/36.71 X ) ==> addition( Y, X ) }.
% 36.34/36.71 parent0: (60249) {G1,W9,D4,L1,V2,M1} { addition( addition( X, Y ), Y ) ==>
% 36.34/36.71 addition( X, Y ) }.
% 36.34/36.71 substitution0:
% 36.34/36.71 X := Y
% 36.34/36.71 Y := X
% 36.34/36.71 end
% 36.34/36.71 permutation0:
% 36.34/36.71 0 ==> 0
% 36.34/36.71 end
% 36.34/36.71
% 36.34/36.71 eqswap: (60254) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 36.34/36.71 ) }.
% 36.34/36.71 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 36.34/36.71 Y ) }.
% 36.34/36.71 substitution0:
% 36.34/36.71 X := X
% 36.34/36.71 Y := Y
% 36.34/36.71 end
% 36.34/36.71
% 36.34/36.71 paramod: (60255) {G1,W8,D3,L2,V2,M2} { ! X ==> addition( X, Y ), leq( Y, X
% 36.34/36.71 ) }.
% 36.34/36.71 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 36.34/36.71 }.
% 36.34/36.71 parent1[0; 3]: (60254) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 36.34/36.71 ( X, Y ) }.
% 36.34/36.71 substitution0:
% 36.34/36.71 X := Y
% 36.34/36.71 Y := X
% 36.34/36.71 end
% 36.34/36.71 substitution1:
% 36.34/36.71 X := Y
% 36.34/36.71 Y := X
% 36.34/36.71 end
% 36.34/36.71
% 36.34/36.71 eqswap: (60258) {G1,W8,D3,L2,V2,M2} { ! addition( X, Y ) ==> X, leq( Y, X
% 36.34/36.71 ) }.
% 36.34/36.71 parent0[0]: (60255) {G1,W8,D3,L2,V2,M2} { ! X ==> addition( X, Y ), leq( Y
% 36.34/36.71 , X ) }.
% 36.34/36.71 substitution0:
% 36.34/36.71 X := X
% 36.34/36.71 Y := Y
% 36.34/36.71 end
% 36.34/36.71
% 36.34/36.71 subsumption: (33) {G1,W8,D3,L2,V2,M2} P(0,12) { ! addition( Y, X ) ==> Y,
% 36.34/36.71 leq( X, Y ) }.
% 36.34/36.71 parent0: (60258) {G1,W8,D3,L2,V2,M2} { ! addition( X, Y ) ==> X, leq( Y, X
% 36.34/36.71 ) }.
% 36.34/36.71 substitution0:
% 36.34/36.71 X := Y
% 36.34/36.71 Y := X
% 36.34/36.71 end
% 36.34/36.71 permutation0:
% 36.34/36.71 0 ==> 0
% 36.34/36.71 1 ==> 1
% 36.34/36.71 end
% 36.34/36.71
% 36.34/36.71 eqswap: (60259) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z )
% 36.34/36.71 ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 36.34/36.71 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 36.34/36.71 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 36.34/36.71 substitution0:
% 36.34/36.71 X := X
% 36.34/36.71 Y := Y
% 36.34/36.71 Z := Z
% 36.34/36.71 end
% 36.34/36.71
% 36.34/36.71 paramod: (60262) {G1,W16,D4,L2,V3,M2} { multiplication( X, addition( Y, Z
% 36.34/36.71 ) ) ==> multiplication( X, Z ), ! leq( multiplication( X, Y ),
% 36.34/36.71 multiplication( X, Z ) ) }.
% 36.34/36.71 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 36.34/36.71 ==> Y }.
% 36.34/36.71 parent1[0; 6]: (60259) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition
% 36.34/36.71 ( Y, Z ) ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) )
% 36.34/36.71 }.
% 36.34/36.71 substitution0:
% 36.34/36.71 X := multiplication( X, Y )
% 36.34/36.71 Y := multiplication( X, Z )
% 36.34/36.71 end
% 36.34/36.71 substitution1:
% 36.34/36.71 X := X
% 36.34/36.71 Y := Y
% 36.34/36.71 Z := Z
% 36.34/36.71 end
% 36.34/36.71
% 36.34/36.71 subsumption: (43) {G1,W16,D4,L2,V3,M2} P(7,11) { ! leq( multiplication( X,
% 36.34/36.71 Y ), multiplication( X, Z ) ), multiplication( X, addition( Y, Z ) ) ==>
% 36.34/36.71 multiplication( X, Z ) }.
% 36.34/36.71 parent0: (60262) {G1,W16,D4,L2,V3,M2} { multiplication( X, addition( Y, Z
% 36.34/36.71 ) ) ==> multiplication( X, Z ), ! leq( multiplication( X, Y ),
% 36.34/36.71 multiplication( X, Z ) ) }.
% 36.34/36.71 substitution0:
% 36.34/36.71 X := X
% 36.34/36.71 Y := Y
% 36.34/36.71 Z := Z
% 36.34/36.71 end
% 36.34/36.71 permutation0:
% 36.34/36.71 0 ==> 1
% 36.34/36.71 1 ==> 0
% 36.34/36.71 end
% 36.34/36.71
% 36.34/36.71 eqswap: (60267) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 36.34/36.71 ) }.
% 36.34/36.71 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 36.34/36.71 Y ) }.
% 36.34/36.71 substitution0:
% 36.34/36.71 X := X
% 36.34/36.71 Y := Y
% 36.34/36.71 end
% 36.34/36.71
% 36.34/36.71 paramod: (60268) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 36.34/36.71 multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ),
% 36.34/36.71 multiplication( X, Y ) ) }.
% 36.34/36.72 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 36.34/36.72 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 36.34/36.72 parent1[0; 5]: (60267) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 36.34/36.72 ( X, Y ) }.
% 36.34/36.72 substitution0:
% 36.34/36.72 X := X
% 36.34/36.72 Y := Z
% 36.34/36.72 Z := Y
% 36.34/36.72 end
% 36.34/36.72 substitution1:
% 36.34/36.72 X := multiplication( X, Z )
% 36.34/36.72 Y := multiplication( X, Y )
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 eqswap: (60269) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, addition( Z, Y
% 36.34/36.72 ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ),
% 36.34/36.72 multiplication( X, Y ) ) }.
% 36.34/36.72 parent0[0]: (60268) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 36.34/36.72 multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ),
% 36.34/36.72 multiplication( X, Y ) ) }.
% 36.34/36.72 substitution0:
% 36.34/36.72 X := X
% 36.34/36.72 Y := Y
% 36.34/36.72 Z := Z
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 subsumption: (46) {G1,W16,D4,L2,V3,M2} P(7,12) { ! multiplication( X,
% 36.34/36.72 addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 36.34/36.72 ), multiplication( X, Z ) ) }.
% 36.34/36.72 parent0: (60269) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, addition( Z,
% 36.34/36.72 Y ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ),
% 36.34/36.72 multiplication( X, Y ) ) }.
% 36.34/36.72 substitution0:
% 36.34/36.72 X := X
% 36.34/36.72 Y := Z
% 36.34/36.72 Z := Y
% 36.34/36.72 end
% 36.34/36.72 permutation0:
% 36.34/36.72 0 ==> 0
% 36.34/36.72 1 ==> 1
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 eqswap: (60271) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Z ), Y
% 36.34/36.72 ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) ) }.
% 36.34/36.72 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 36.34/36.72 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 36.34/36.72 substitution0:
% 36.34/36.72 X := X
% 36.34/36.72 Y := Z
% 36.34/36.72 Z := Y
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 paramod: (60272) {G1,W11,D4,L1,V2,M1} { multiplication( addition( one, X )
% 36.34/36.72 , Y ) ==> addition( Y, multiplication( X, Y ) ) }.
% 36.34/36.72 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 36.34/36.72 parent1[0; 7]: (60271) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X
% 36.34/36.72 , Z ), Y ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) )
% 36.34/36.72 }.
% 36.34/36.72 substitution0:
% 36.34/36.72 X := Y
% 36.34/36.72 end
% 36.34/36.72 substitution1:
% 36.34/36.72 X := one
% 36.34/36.72 Y := Y
% 36.34/36.72 Z := X
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 eqswap: (60274) {G1,W11,D4,L1,V2,M1} { addition( Y, multiplication( X, Y )
% 36.34/36.72 ) ==> multiplication( addition( one, X ), Y ) }.
% 36.34/36.72 parent0[0]: (60272) {G1,W11,D4,L1,V2,M1} { multiplication( addition( one,
% 36.34/36.72 X ), Y ) ==> addition( Y, multiplication( X, Y ) ) }.
% 36.34/36.72 substitution0:
% 36.34/36.72 X := X
% 36.34/36.72 Y := Y
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 subsumption: (85) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( X, multiplication
% 36.34/36.72 ( Y, X ) ) = multiplication( addition( one, Y ), X ) }.
% 36.34/36.72 parent0: (60274) {G1,W11,D4,L1,V2,M1} { addition( Y, multiplication( X, Y
% 36.34/36.72 ) ) ==> multiplication( addition( one, X ), Y ) }.
% 36.34/36.72 substitution0:
% 36.34/36.72 X := Y
% 36.34/36.72 Y := X
% 36.34/36.72 end
% 36.34/36.72 permutation0:
% 36.34/36.72 0 ==> 0
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 eqswap: (60277) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, Y ) )
% 36.34/36.72 ==> domain( multiplication( X, domain( Y ) ) ) }.
% 36.34/36.72 parent0[0]: (14) {G0,W10,D5,L1,V2,M1} I { domain( multiplication( X, domain
% 36.34/36.72 ( Y ) ) ) ==> domain( multiplication( X, Y ) ) }.
% 36.34/36.72 substitution0:
% 36.34/36.72 X := X
% 36.34/36.72 Y := Y
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 paramod: (60280) {G1,W8,D4,L1,V1,M1} { domain( multiplication( one, X ) )
% 36.34/36.72 ==> domain( domain( X ) ) }.
% 36.34/36.72 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 36.34/36.72 parent1[0; 6]: (60277) {G0,W10,D5,L1,V2,M1} { domain( multiplication( X, Y
% 36.34/36.72 ) ) ==> domain( multiplication( X, domain( Y ) ) ) }.
% 36.34/36.72 substitution0:
% 36.34/36.72 X := domain( X )
% 36.34/36.72 end
% 36.34/36.72 substitution1:
% 36.34/36.72 X := one
% 36.34/36.72 Y := X
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 paramod: (60282) {G1,W6,D4,L1,V1,M1} { domain( X ) ==> domain( domain( X )
% 36.34/36.72 ) }.
% 36.34/36.72 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 36.34/36.72 parent1[0; 2]: (60280) {G1,W8,D4,L1,V1,M1} { domain( multiplication( one,
% 36.34/36.72 X ) ) ==> domain( domain( X ) ) }.
% 36.34/36.72 substitution0:
% 36.34/36.72 X := X
% 36.34/36.72 end
% 36.34/36.72 substitution1:
% 36.34/36.72 X := X
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 eqswap: (60283) {G1,W6,D4,L1,V1,M1} { domain( domain( X ) ) ==> domain( X
% 36.34/36.72 ) }.
% 36.34/36.72 parent0[0]: (60282) {G1,W6,D4,L1,V1,M1} { domain( X ) ==> domain( domain(
% 36.34/36.72 X ) ) }.
% 36.34/36.72 substitution0:
% 36.34/36.72 X := X
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 subsumption: (139) {G1,W6,D4,L1,V1,M1} P(6,14);d(6) { domain( domain( X ) )
% 36.34/36.72 ==> domain( X ) }.
% 36.34/36.72 parent0: (60283) {G1,W6,D4,L1,V1,M1} { domain( domain( X ) ) ==> domain( X
% 36.34/36.72 ) }.
% 36.34/36.72 substitution0:
% 36.34/36.72 X := X
% 36.34/36.72 end
% 36.34/36.72 permutation0:
% 36.34/36.72 0 ==> 0
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 eqswap: (60284) {G1,W10,D5,L1,V0,M1} { ! domain( skol1 ) ==>
% 36.34/36.72 multiplication( domain( skol1 ), domain( addition( skol1, skol2 ) ) ) }.
% 36.34/36.72 parent0[0]: (18) {G1,W10,D5,L1,V0,M1} I;d(17) { ! multiplication( domain(
% 36.34/36.72 skol1 ), domain( addition( skol1, skol2 ) ) ) ==> domain( skol1 ) }.
% 36.34/36.72 substitution0:
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 paramod: (60285) {G1,W10,D5,L1,V0,M1} { ! domain( skol1 ) ==>
% 36.34/36.72 multiplication( domain( skol1 ), domain( addition( skol2, skol1 ) ) ) }.
% 36.34/36.72 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 36.34/36.72 }.
% 36.34/36.72 parent1[0; 8]: (60284) {G1,W10,D5,L1,V0,M1} { ! domain( skol1 ) ==>
% 36.34/36.72 multiplication( domain( skol1 ), domain( addition( skol1, skol2 ) ) ) }.
% 36.34/36.72 substitution0:
% 36.34/36.72 X := skol1
% 36.34/36.72 Y := skol2
% 36.34/36.72 end
% 36.34/36.72 substitution1:
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 eqswap: (60288) {G1,W10,D5,L1,V0,M1} { ! multiplication( domain( skol1 ),
% 36.34/36.72 domain( addition( skol2, skol1 ) ) ) ==> domain( skol1 ) }.
% 36.34/36.72 parent0[0]: (60285) {G1,W10,D5,L1,V0,M1} { ! domain( skol1 ) ==>
% 36.34/36.72 multiplication( domain( skol1 ), domain( addition( skol2, skol1 ) ) ) }.
% 36.34/36.72 substitution0:
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 subsumption: (216) {G2,W10,D5,L1,V0,M1} P(0,18) { ! multiplication( domain
% 36.34/36.72 ( skol1 ), domain( addition( skol2, skol1 ) ) ) ==> domain( skol1 ) }.
% 36.34/36.72 parent0: (60288) {G1,W10,D5,L1,V0,M1} { ! multiplication( domain( skol1 )
% 36.34/36.72 , domain( addition( skol2, skol1 ) ) ) ==> domain( skol1 ) }.
% 36.34/36.72 substitution0:
% 36.34/36.72 end
% 36.34/36.72 permutation0:
% 36.34/36.72 0 ==> 0
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 eqswap: (60289) {G1,W9,D4,L1,V2,M1} { addition( X, Y ) ==> addition(
% 36.34/36.72 addition( X, Y ), Y ) }.
% 36.34/36.72 parent0[0]: (23) {G1,W9,D4,L1,V2,M1} P(3,1) { addition( addition( Y, X ), X
% 36.34/36.72 ) ==> addition( Y, X ) }.
% 36.34/36.72 substitution0:
% 36.34/36.72 X := Y
% 36.34/36.72 Y := X
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 eqswap: (60290) {G1,W8,D3,L2,V2,M2} { ! X ==> addition( X, Y ), leq( Y, X
% 36.34/36.72 ) }.
% 36.34/36.72 parent0[0]: (33) {G1,W8,D3,L2,V2,M2} P(0,12) { ! addition( Y, X ) ==> Y,
% 36.34/36.72 leq( X, Y ) }.
% 36.34/36.72 substitution0:
% 36.34/36.72 X := Y
% 36.34/36.72 Y := X
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 resolution: (60291) {G2,W5,D3,L1,V2,M1} { leq( Y, addition( X, Y ) ) }.
% 36.34/36.72 parent0[0]: (60290) {G1,W8,D3,L2,V2,M2} { ! X ==> addition( X, Y ), leq( Y
% 36.34/36.72 , X ) }.
% 36.34/36.72 parent1[0]: (60289) {G1,W9,D4,L1,V2,M1} { addition( X, Y ) ==> addition(
% 36.34/36.72 addition( X, Y ), Y ) }.
% 36.34/36.72 substitution0:
% 36.34/36.72 X := addition( X, Y )
% 36.34/36.72 Y := Y
% 36.34/36.72 end
% 36.34/36.72 substitution1:
% 36.34/36.72 X := X
% 36.34/36.72 Y := Y
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 subsumption: (258) {G2,W5,D3,L1,V2,M1} R(23,33) { leq( X, addition( Y, X )
% 36.34/36.72 ) }.
% 36.34/36.72 parent0: (60291) {G2,W5,D3,L1,V2,M1} { leq( Y, addition( X, Y ) ) }.
% 36.34/36.72 substitution0:
% 36.34/36.72 X := Y
% 36.34/36.72 Y := X
% 36.34/36.72 end
% 36.34/36.72 permutation0:
% 36.34/36.72 0 ==> 0
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 paramod: (60293) {G1,W7,D4,L1,V2,M1} { leq( domain( X ), domain( addition
% 36.34/36.72 ( Y, X ) ) ) }.
% 36.34/36.72 parent0[0]: (17) {G0,W10,D4,L1,V2,M1} I { addition( domain( X ), domain( Y
% 36.34/36.72 ) ) ==> domain( addition( X, Y ) ) }.
% 36.34/36.72 parent1[0; 3]: (258) {G2,W5,D3,L1,V2,M1} R(23,33) { leq( X, addition( Y, X
% 36.34/36.72 ) ) }.
% 36.34/36.72 substitution0:
% 36.34/36.72 X := Y
% 36.34/36.72 Y := X
% 36.34/36.72 end
% 36.34/36.72 substitution1:
% 36.34/36.72 X := domain( X )
% 36.34/36.72 Y := domain( Y )
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 subsumption: (266) {G3,W7,D4,L1,V2,M1} P(17,258) { leq( domain( Y ), domain
% 36.34/36.72 ( addition( X, Y ) ) ) }.
% 36.34/36.72 parent0: (60293) {G1,W7,D4,L1,V2,M1} { leq( domain( X ), domain( addition
% 36.34/36.72 ( Y, X ) ) ) }.
% 36.34/36.72 substitution0:
% 36.34/36.72 X := Y
% 36.34/36.72 Y := X
% 36.34/36.72 end
% 36.34/36.72 permutation0:
% 36.34/36.72 0 ==> 0
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 eqswap: (60295) {G1,W16,D4,L2,V3,M2} { multiplication( X, Z ) ==>
% 36.34/36.72 multiplication( X, addition( Y, Z ) ), ! leq( multiplication( X, Y ),
% 36.34/36.72 multiplication( X, Z ) ) }.
% 36.34/36.72 parent0[1]: (43) {G1,W16,D4,L2,V3,M2} P(7,11) { ! leq( multiplication( X, Y
% 36.34/36.72 ), multiplication( X, Z ) ), multiplication( X, addition( Y, Z ) ) ==>
% 36.34/36.72 multiplication( X, Z ) }.
% 36.34/36.72 substitution0:
% 36.34/36.72 X := X
% 36.34/36.72 Y := Y
% 36.34/36.72 Z := Z
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 paramod: (60298) {G2,W16,D4,L2,V2,M2} { multiplication( X, domain( Y ) )
% 36.34/36.72 ==> multiplication( X, one ), ! leq( multiplication( X, one ),
% 36.34/36.72 multiplication( X, domain( Y ) ) ) }.
% 36.34/36.72 parent0[0]: (20) {G1,W6,D4,L1,V1,M1} P(15,0) { addition( one, domain( X ) )
% 36.34/36.72 ==> one }.
% 36.34/36.72 parent1[0; 7]: (60295) {G1,W16,D4,L2,V3,M2} { multiplication( X, Z ) ==>
% 36.34/36.72 multiplication( X, addition( Y, Z ) ), ! leq( multiplication( X, Y ),
% 36.34/36.72 multiplication( X, Z ) ) }.
% 36.34/36.72 substitution0:
% 36.34/36.72 X := Y
% 36.34/36.72 end
% 36.34/36.72 substitution1:
% 36.34/36.72 X := X
% 36.34/36.72 Y := one
% 36.34/36.72 Z := domain( Y )
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 paramod: (60300) {G1,W14,D4,L2,V2,M2} { ! leq( X, multiplication( X,
% 36.34/36.72 domain( Y ) ) ), multiplication( X, domain( Y ) ) ==> multiplication( X,
% 36.34/36.72 one ) }.
% 36.34/36.72 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 36.34/36.72 parent1[1; 2]: (60298) {G2,W16,D4,L2,V2,M2} { multiplication( X, domain( Y
% 36.34/36.72 ) ) ==> multiplication( X, one ), ! leq( multiplication( X, one ),
% 36.34/36.72 multiplication( X, domain( Y ) ) ) }.
% 36.34/36.72 substitution0:
% 36.34/36.72 X := X
% 36.34/36.72 end
% 36.34/36.72 substitution1:
% 36.34/36.72 X := X
% 36.34/36.72 Y := Y
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 paramod: (60302) {G1,W12,D4,L2,V2,M2} { multiplication( X, domain( Y ) )
% 36.34/36.72 ==> X, ! leq( X, multiplication( X, domain( Y ) ) ) }.
% 36.34/36.72 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 36.34/36.72 parent1[1; 5]: (60300) {G1,W14,D4,L2,V2,M2} { ! leq( X, multiplication( X
% 36.34/36.72 , domain( Y ) ) ), multiplication( X, domain( Y ) ) ==> multiplication( X
% 36.34/36.72 , one ) }.
% 36.34/36.72 substitution0:
% 36.34/36.72 X := X
% 36.34/36.72 end
% 36.34/36.72 substitution1:
% 36.34/36.72 X := X
% 36.34/36.72 Y := Y
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 subsumption: (651) {G2,W12,D4,L2,V2,M2} P(20,43);d(5);d(5) { ! leq( Y,
% 36.34/36.72 multiplication( Y, domain( X ) ) ), multiplication( Y, domain( X ) ) ==>
% 36.34/36.72 Y }.
% 36.34/36.72 parent0: (60302) {G1,W12,D4,L2,V2,M2} { multiplication( X, domain( Y ) )
% 36.34/36.72 ==> X, ! leq( X, multiplication( X, domain( Y ) ) ) }.
% 36.34/36.72 substitution0:
% 36.34/36.72 X := Y
% 36.34/36.72 Y := X
% 36.34/36.72 end
% 36.34/36.72 permutation0:
% 36.34/36.72 0 ==> 1
% 36.34/36.72 1 ==> 0
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 eqswap: (60305) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Z ) ==>
% 36.34/36.72 multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ),
% 36.34/36.72 multiplication( X, Z ) ) }.
% 36.34/36.72 parent0[0]: (46) {G1,W16,D4,L2,V3,M2} P(7,12) { ! multiplication( X,
% 36.34/36.72 addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 36.34/36.72 ), multiplication( X, Z ) ) }.
% 36.34/36.72 substitution0:
% 36.34/36.72 X := X
% 36.34/36.72 Y := Y
% 36.34/36.72 Z := Z
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 paramod: (60306) {G1,W17,D3,L3,V3,M3} { ! multiplication( X, Y ) ==>
% 36.34/36.72 multiplication( X, Y ), ! leq( Z, Y ), leq( multiplication( X, Z ),
% 36.34/36.72 multiplication( X, Y ) ) }.
% 36.34/36.72 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 36.34/36.72 ==> Y }.
% 36.34/36.72 parent1[0; 7]: (60305) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Z ) ==>
% 36.34/36.72 multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ),
% 36.34/36.72 multiplication( X, Z ) ) }.
% 36.34/36.72 substitution0:
% 36.34/36.72 X := Z
% 36.34/36.72 Y := Y
% 36.34/36.72 end
% 36.34/36.72 substitution1:
% 36.34/36.72 X := X
% 36.34/36.72 Y := Z
% 36.34/36.72 Z := Y
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 eqrefl: (60307) {G0,W10,D3,L2,V3,M2} { ! leq( Z, Y ), leq( multiplication
% 36.34/36.72 ( X, Z ), multiplication( X, Y ) ) }.
% 36.34/36.72 parent0[0]: (60306) {G1,W17,D3,L3,V3,M3} { ! multiplication( X, Y ) ==>
% 36.34/36.72 multiplication( X, Y ), ! leq( Z, Y ), leq( multiplication( X, Z ),
% 36.34/36.72 multiplication( X, Y ) ) }.
% 36.34/36.72 substitution0:
% 36.34/36.72 X := X
% 36.34/36.72 Y := Y
% 36.34/36.72 Z := Z
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 subsumption: (726) {G2,W10,D3,L2,V3,M2} P(11,46);q { leq( multiplication( Z
% 36.34/36.72 , X ), multiplication( Z, Y ) ), ! leq( X, Y ) }.
% 36.34/36.72 parent0: (60307) {G0,W10,D3,L2,V3,M2} { ! leq( Z, Y ), leq( multiplication
% 36.34/36.72 ( X, Z ), multiplication( X, Y ) ) }.
% 36.34/36.72 substitution0:
% 36.34/36.72 X := Z
% 36.34/36.72 Y := Y
% 36.34/36.72 Z := X
% 36.34/36.72 end
% 36.34/36.72 permutation0:
% 36.34/36.72 0 ==> 1
% 36.34/36.72 1 ==> 0
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 eqswap: (60308) {G1,W11,D4,L1,V2,M1} { multiplication( addition( one, Y )
% 36.34/36.72 , X ) = addition( X, multiplication( Y, X ) ) }.
% 36.34/36.72 parent0[0]: (85) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( X, multiplication
% 36.34/36.72 ( Y, X ) ) = multiplication( addition( one, Y ), X ) }.
% 36.34/36.72 substitution0:
% 36.34/36.72 X := X
% 36.34/36.72 Y := Y
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 paramod: (60313) {G1,W11,D5,L1,V1,M1} { multiplication( addition( one,
% 36.34/36.72 domain( X ) ), X ) = multiplication( domain( X ), X ) }.
% 36.34/36.72 parent0[0]: (13) {G0,W11,D5,L1,V1,M1} I { addition( X, multiplication(
% 36.34/36.72 domain( X ), X ) ) ==> multiplication( domain( X ), X ) }.
% 36.34/36.72 parent1[0; 7]: (60308) {G1,W11,D4,L1,V2,M1} { multiplication( addition(
% 36.34/36.72 one, Y ), X ) = addition( X, multiplication( Y, X ) ) }.
% 36.34/36.72 substitution0:
% 36.34/36.72 X := X
% 36.34/36.72 end
% 36.34/36.72 substitution1:
% 36.34/36.72 X := X
% 36.34/36.72 Y := domain( X )
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 paramod: (60314) {G2,W8,D4,L1,V1,M1} { multiplication( one, X ) =
% 36.34/36.72 multiplication( domain( X ), X ) }.
% 36.34/36.72 parent0[0]: (20) {G1,W6,D4,L1,V1,M1} P(15,0) { addition( one, domain( X ) )
% 36.34/36.72 ==> one }.
% 36.34/36.72 parent1[0; 2]: (60313) {G1,W11,D5,L1,V1,M1} { multiplication( addition(
% 36.34/36.72 one, domain( X ) ), X ) = multiplication( domain( X ), X ) }.
% 36.34/36.72 substitution0:
% 36.34/36.72 X := X
% 36.34/36.72 end
% 36.34/36.72 substitution1:
% 36.34/36.72 X := X
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 paramod: (60315) {G1,W6,D4,L1,V1,M1} { X = multiplication( domain( X ), X
% 36.34/36.72 ) }.
% 36.34/36.72 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 36.34/36.72 parent1[0; 1]: (60314) {G2,W8,D4,L1,V1,M1} { multiplication( one, X ) =
% 36.34/36.72 multiplication( domain( X ), X ) }.
% 36.34/36.72 substitution0:
% 36.34/36.72 X := X
% 36.34/36.72 end
% 36.34/36.72 substitution1:
% 36.34/36.72 X := X
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 eqswap: (60316) {G1,W6,D4,L1,V1,M1} { multiplication( domain( X ), X ) = X
% 36.34/36.72 }.
% 36.34/36.72 parent0[0]: (60315) {G1,W6,D4,L1,V1,M1} { X = multiplication( domain( X )
% 36.34/36.72 , X ) }.
% 36.34/36.72 substitution0:
% 36.34/36.72 X := X
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 subsumption: (2746) {G2,W6,D4,L1,V1,M1} P(85,13);d(20);d(6) {
% 36.34/36.72 multiplication( domain( X ), X ) ==> X }.
% 36.34/36.72 parent0: (60316) {G1,W6,D4,L1,V1,M1} { multiplication( domain( X ), X ) =
% 36.34/36.72 X }.
% 36.34/36.72 substitution0:
% 36.34/36.72 X := X
% 36.34/36.72 end
% 36.34/36.72 permutation0:
% 36.34/36.72 0 ==> 0
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 eqswap: (60317) {G2,W12,D4,L2,V2,M2} { X ==> multiplication( X, domain( Y
% 36.34/36.72 ) ), ! leq( X, multiplication( X, domain( Y ) ) ) }.
% 36.34/36.72 parent0[1]: (651) {G2,W12,D4,L2,V2,M2} P(20,43);d(5);d(5) { ! leq( Y,
% 36.34/36.72 multiplication( Y, domain( X ) ) ), multiplication( Y, domain( X ) ) ==>
% 36.34/36.72 Y }.
% 36.34/36.72 substitution0:
% 36.34/36.72 X := Y
% 36.34/36.72 Y := X
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 eqswap: (60318) {G2,W10,D5,L1,V0,M1} { ! domain( skol1 ) ==>
% 36.34/36.72 multiplication( domain( skol1 ), domain( addition( skol2, skol1 ) ) ) }.
% 36.34/36.72 parent0[0]: (216) {G2,W10,D5,L1,V0,M1} P(0,18) { ! multiplication( domain(
% 36.34/36.72 skol1 ), domain( addition( skol2, skol1 ) ) ) ==> domain( skol1 ) }.
% 36.34/36.72 substitution0:
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 resolution: (60319) {G3,W10,D5,L1,V0,M1} { ! leq( domain( skol1 ),
% 36.34/36.72 multiplication( domain( skol1 ), domain( addition( skol2, skol1 ) ) ) )
% 36.34/36.72 }.
% 36.34/36.72 parent0[0]: (60318) {G2,W10,D5,L1,V0,M1} { ! domain( skol1 ) ==>
% 36.34/36.72 multiplication( domain( skol1 ), domain( addition( skol2, skol1 ) ) ) }.
% 36.34/36.72 parent1[0]: (60317) {G2,W12,D4,L2,V2,M2} { X ==> multiplication( X, domain
% 36.34/36.72 ( Y ) ), ! leq( X, multiplication( X, domain( Y ) ) ) }.
% 36.34/36.72 substitution0:
% 36.34/36.72 end
% 36.34/36.72 substitution1:
% 36.34/36.72 X := domain( skol1 )
% 36.34/36.72 Y := addition( skol2, skol1 )
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 subsumption: (51790) {G3,W10,D5,L1,V0,M1} R(651,216) { ! leq( domain( skol1
% 36.34/36.72 ), multiplication( domain( skol1 ), domain( addition( skol2, skol1 ) ) )
% 36.34/36.72 ) }.
% 36.34/36.72 parent0: (60319) {G3,W10,D5,L1,V0,M1} { ! leq( domain( skol1 ),
% 36.34/36.72 multiplication( domain( skol1 ), domain( addition( skol2, skol1 ) ) ) )
% 36.34/36.72 }.
% 36.34/36.72 substitution0:
% 36.34/36.72 end
% 36.34/36.72 permutation0:
% 36.34/36.72 0 ==> 0
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 paramod: (60321) {G3,W9,D4,L2,V2,M2} { leq( X, multiplication( domain( X )
% 36.34/36.72 , Y ) ), ! leq( X, Y ) }.
% 36.34/36.72 parent0[0]: (2746) {G2,W6,D4,L1,V1,M1} P(85,13);d(20);d(6) { multiplication
% 36.34/36.72 ( domain( X ), X ) ==> X }.
% 36.34/36.72 parent1[0; 1]: (726) {G2,W10,D3,L2,V3,M2} P(11,46);q { leq( multiplication
% 36.34/36.72 ( Z, X ), multiplication( Z, Y ) ), ! leq( X, Y ) }.
% 36.34/36.72 substitution0:
% 36.34/36.72 X := X
% 36.34/36.72 end
% 36.34/36.72 substitution1:
% 36.34/36.72 X := X
% 36.34/36.72 Y := Y
% 36.34/36.72 Z := domain( X )
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 subsumption: (59070) {G3,W9,D4,L2,V2,M2} P(2746,726) { leq( X,
% 36.34/36.72 multiplication( domain( X ), Y ) ), ! leq( X, Y ) }.
% 36.34/36.72 parent0: (60321) {G3,W9,D4,L2,V2,M2} { leq( X, multiplication( domain( X )
% 36.34/36.72 , Y ) ), ! leq( X, Y ) }.
% 36.34/36.72 substitution0:
% 36.34/36.72 X := X
% 36.34/36.72 Y := Y
% 36.34/36.72 end
% 36.34/36.72 permutation0:
% 36.34/36.72 0 ==> 0
% 36.34/36.72 1 ==> 1
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 resolution: (60324) {G4,W11,D5,L1,V2,M1} { leq( domain( X ),
% 36.34/36.72 multiplication( domain( domain( X ) ), domain( addition( Y, X ) ) ) ) }.
% 36.34/36.72 parent0[1]: (59070) {G3,W9,D4,L2,V2,M2} P(2746,726) { leq( X,
% 36.34/36.72 multiplication( domain( X ), Y ) ), ! leq( X, Y ) }.
% 36.34/36.72 parent1[0]: (266) {G3,W7,D4,L1,V2,M1} P(17,258) { leq( domain( Y ), domain
% 36.34/36.72 ( addition( X, Y ) ) ) }.
% 36.34/36.72 substitution0:
% 36.34/36.72 X := domain( X )
% 36.34/36.72 Y := domain( addition( Y, X ) )
% 36.34/36.72 end
% 36.34/36.72 substitution1:
% 36.34/36.72 X := Y
% 36.34/36.72 Y := X
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 paramod: (60325) {G2,W10,D5,L1,V2,M1} { leq( domain( X ), multiplication(
% 36.34/36.72 domain( X ), domain( addition( Y, X ) ) ) ) }.
% 36.34/36.72 parent0[0]: (139) {G1,W6,D4,L1,V1,M1} P(6,14);d(6) { domain( domain( X ) )
% 36.34/36.72 ==> domain( X ) }.
% 36.34/36.72 parent1[0; 4]: (60324) {G4,W11,D5,L1,V2,M1} { leq( domain( X ),
% 36.34/36.72 multiplication( domain( domain( X ) ), domain( addition( Y, X ) ) ) ) }.
% 36.34/36.72 substitution0:
% 36.34/36.72 X := X
% 36.34/36.72 end
% 36.34/36.72 substitution1:
% 36.34/36.72 X := X
% 36.34/36.72 Y := Y
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 subsumption: (59423) {G4,W10,D5,L1,V2,M1} R(59070,266);d(139) { leq( domain
% 36.34/36.72 ( X ), multiplication( domain( X ), domain( addition( Y, X ) ) ) ) }.
% 36.34/36.72 parent0: (60325) {G2,W10,D5,L1,V2,M1} { leq( domain( X ), multiplication(
% 36.34/36.72 domain( X ), domain( addition( Y, X ) ) ) ) }.
% 36.34/36.72 substitution0:
% 36.34/36.72 X := X
% 36.34/36.72 Y := Y
% 36.34/36.72 end
% 36.34/36.72 permutation0:
% 36.34/36.72 0 ==> 0
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 resolution: (60326) {G4,W0,D0,L0,V0,M0} { }.
% 36.34/36.72 parent0[0]: (51790) {G3,W10,D5,L1,V0,M1} R(651,216) { ! leq( domain( skol1
% 36.34/36.72 ), multiplication( domain( skol1 ), domain( addition( skol2, skol1 ) ) )
% 36.34/36.72 ) }.
% 36.34/36.72 parent1[0]: (59423) {G4,W10,D5,L1,V2,M1} R(59070,266);d(139) { leq( domain
% 36.34/36.72 ( X ), multiplication( domain( X ), domain( addition( Y, X ) ) ) ) }.
% 36.34/36.72 substitution0:
% 36.34/36.72 end
% 36.34/36.72 substitution1:
% 36.34/36.72 X := skol1
% 36.34/36.72 Y := skol2
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 subsumption: (60063) {G5,W0,D0,L0,V0,M0} S(51790);r(59423) { }.
% 36.34/36.72 parent0: (60326) {G4,W0,D0,L0,V0,M0} { }.
% 36.34/36.72 substitution0:
% 36.34/36.72 end
% 36.34/36.72 permutation0:
% 36.34/36.72 end
% 36.34/36.72
% 36.34/36.72 Proof check complete!
% 36.34/36.72
% 36.34/36.72 Memory use:
% 36.34/36.72
% 36.34/36.72 space for terms: 906151
% 36.34/36.72 space for clauses: 2652557
% 36.34/36.72
% 36.34/36.72
% 36.34/36.72 clauses generated: 1184212
% 36.34/36.72 clauses kept: 60064
% 36.34/36.72 clauses selected: 2023
% 36.34/36.72 clauses deleted: 4531
% 36.34/36.72 clauses inuse deleted: 51
% 36.34/36.72
% 36.34/36.72 subsentry: 13252850
% 36.34/36.72 literals s-matched: 5109304
% 36.34/36.72 literals matched: 4883414
% 36.34/36.72 full subsumption: 1932605
% 36.34/36.72
% 36.34/36.72 checksum: -244092727
% 36.34/36.72
% 36.34/36.72
% 36.34/36.72 Bliksem ended
%------------------------------------------------------------------------------