TSTP Solution File: KLE139+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE139+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n003.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 01:37:23 EDT 2022
% Result : Theorem 45.54s 45.97s
% Output : Refutation 45.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE139+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : bliksem %s
% 0.13/0.35 % Computer : n003.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % DateTime : Thu Jun 16 09:00:56 EDT 2022
% 0.13/0.35 % CPUTime :
% 18.84/19.25 *** allocated 10000 integers for termspace/termends
% 18.84/19.25 *** allocated 10000 integers for clauses
% 18.84/19.25 *** allocated 10000 integers for justifications
% 18.84/19.25 Bliksem 1.12
% 18.84/19.25
% 18.84/19.25
% 18.84/19.25 Automatic Strategy Selection
% 18.84/19.25
% 18.84/19.25
% 18.84/19.25 Clauses:
% 18.84/19.25
% 18.84/19.25 { addition( X, Y ) = addition( Y, X ) }.
% 18.84/19.25 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 18.84/19.25 { addition( X, zero ) = X }.
% 18.84/19.25 { addition( X, X ) = X }.
% 18.84/19.25 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 18.84/19.25 multiplication( X, Y ), Z ) }.
% 18.84/19.25 { multiplication( X, one ) = X }.
% 18.84/19.25 { multiplication( one, X ) = X }.
% 18.84/19.25 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 18.84/19.25 , multiplication( X, Z ) ) }.
% 18.84/19.25 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 18.84/19.25 , multiplication( Y, Z ) ) }.
% 18.84/19.25 { multiplication( zero, X ) = zero }.
% 18.84/19.25 { addition( one, multiplication( X, star( X ) ) ) = star( X ) }.
% 18.84/19.25 { addition( one, multiplication( star( X ), X ) ) = star( X ) }.
% 18.84/19.25 { ! leq( addition( multiplication( X, Z ), Y ), Z ), leq( multiplication(
% 18.84/19.25 star( X ), Y ), Z ) }.
% 18.84/19.25 { ! leq( addition( multiplication( Z, X ), Y ), Z ), leq( multiplication( Y
% 18.84/19.25 , star( X ) ), Z ) }.
% 18.84/19.25 { strong_iteration( X ) = addition( multiplication( X, strong_iteration( X
% 18.84/19.25 ) ), one ) }.
% 18.84/19.25 { ! leq( Z, addition( multiplication( X, Z ), Y ) ), leq( Z, multiplication
% 18.84/19.25 ( strong_iteration( X ), Y ) ) }.
% 18.84/19.25 { strong_iteration( X ) = addition( star( X ), multiplication(
% 18.84/19.25 strong_iteration( X ), zero ) ) }.
% 18.84/19.25 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 18.84/19.25 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 18.84/19.25 { ! strong_iteration( skol1 ) = addition( multiplication( strong_iteration
% 18.84/19.25 ( skol1 ), skol1 ), one ) }.
% 18.84/19.25
% 18.84/19.25 percentage equality = 0.680000, percentage horn = 1.000000
% 18.84/19.25 This is a problem with some equality
% 18.84/19.25
% 18.84/19.25
% 18.84/19.25
% 18.84/19.25 Options Used:
% 18.84/19.25
% 18.84/19.25 useres = 1
% 18.84/19.25 useparamod = 1
% 18.84/19.25 useeqrefl = 1
% 18.84/19.25 useeqfact = 1
% 18.84/19.25 usefactor = 1
% 18.84/19.25 usesimpsplitting = 0
% 18.84/19.25 usesimpdemod = 5
% 18.84/19.25 usesimpres = 3
% 18.84/19.25
% 18.84/19.25 resimpinuse = 1000
% 18.84/19.25 resimpclauses = 20000
% 18.84/19.25 substype = eqrewr
% 18.84/19.25 backwardsubs = 1
% 18.84/19.25 selectoldest = 5
% 18.84/19.25
% 18.84/19.25 litorderings [0] = split
% 18.84/19.25 litorderings [1] = extend the termordering, first sorting on arguments
% 18.84/19.25
% 18.84/19.25 termordering = kbo
% 18.84/19.25
% 18.84/19.25 litapriori = 0
% 18.84/19.25 termapriori = 1
% 18.84/19.25 litaposteriori = 0
% 18.84/19.25 termaposteriori = 0
% 18.84/19.25 demodaposteriori = 0
% 18.84/19.25 ordereqreflfact = 0
% 18.84/19.25
% 18.84/19.25 litselect = negord
% 18.84/19.25
% 18.84/19.25 maxweight = 15
% 18.84/19.25 maxdepth = 30000
% 18.84/19.25 maxlength = 115
% 18.84/19.25 maxnrvars = 195
% 18.84/19.25 excuselevel = 1
% 18.84/19.25 increasemaxweight = 1
% 18.84/19.25
% 18.84/19.25 maxselected = 10000000
% 18.84/19.25 maxnrclauses = 10000000
% 18.84/19.25
% 18.84/19.25 showgenerated = 0
% 18.84/19.25 showkept = 0
% 18.84/19.25 showselected = 0
% 18.84/19.25 showdeleted = 0
% 18.84/19.25 showresimp = 1
% 18.84/19.25 showstatus = 2000
% 18.84/19.25
% 18.84/19.25 prologoutput = 0
% 18.84/19.25 nrgoals = 5000000
% 18.84/19.25 totalproof = 1
% 18.84/19.25
% 18.84/19.25 Symbols occurring in the translation:
% 18.84/19.25
% 18.84/19.25 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 18.84/19.25 . [1, 2] (w:1, o:20, a:1, s:1, b:0),
% 18.84/19.25 ! [4, 1] (w:0, o:13, a:1, s:1, b:0),
% 18.84/19.25 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 18.84/19.25 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 18.84/19.25 addition [37, 2] (w:1, o:44, a:1, s:1, b:0),
% 18.84/19.25 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 18.84/19.25 multiplication [40, 2] (w:1, o:46, a:1, s:1, b:0),
% 18.84/19.25 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 18.84/19.25 star [42, 1] (w:1, o:18, a:1, s:1, b:0),
% 18.84/19.25 leq [43, 2] (w:1, o:45, a:1, s:1, b:0),
% 18.84/19.25 strong_iteration [44, 1] (w:1, o:19, a:1, s:1, b:0),
% 18.84/19.25 skol1 [46, 0] (w:1, o:12, a:1, s:1, b:1).
% 18.84/19.25
% 18.84/19.25
% 18.84/19.25 Starting Search:
% 18.84/19.25
% 18.84/19.25 *** allocated 15000 integers for clauses
% 18.84/19.25 *** allocated 22500 integers for clauses
% 18.84/19.25 *** allocated 33750 integers for clauses
% 18.84/19.25 *** allocated 50625 integers for clauses
% 18.84/19.25 *** allocated 15000 integers for termspace/termends
% 18.84/19.25 *** allocated 75937 integers for clauses
% 18.84/19.25 Resimplifying inuse:
% 18.84/19.25 Done
% 18.84/19.25
% 18.84/19.25 *** allocated 22500 integers for termspace/termends
% 18.84/19.25 *** allocated 113905 integers for clauses
% 18.84/19.25 *** allocated 33750 integers for termspace/termends
% 18.84/19.25
% 18.84/19.25 Intermediate Status:
% 18.84/19.25 Generated: 21458
% 18.84/19.25 Kept: 2061
% 18.84/19.25 Inuse: 232
% 18.84/19.25 Deleted: 54
% 18.84/19.25 Deletedinuse: 30
% 18.84/19.25
% 18.84/19.25 Resimplifying inuse:
% 18.84/19.25 Done
% 18.84/19.25
% 18.84/19.25 *** allocated 170857 integers for clauses
% 18.84/19.25 *** allocated 50625 integers for termspace/termends
% 18.84/19.25 Resimplifying inuse:
% 18.84/19.25 Done
% 18.84/19.25
% 18.84/19.25 *** allocated 256285 integers for clauses
% 45.54/45.97 *** allocated 75937 integers for termspace/termends
% 45.54/45.97
% 45.54/45.97 Intermediate Status:
% 45.54/45.97 Generated: 48073
% 45.54/45.97 Kept: 4072
% 45.54/45.97 Inuse: 389
% 45.54/45.97 Deleted: 88
% 45.54/45.97 Deletedinuse: 31
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97 *** allocated 384427 integers for clauses
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97
% 45.54/45.97 Intermediate Status:
% 45.54/45.97 Generated: 63940
% 45.54/45.97 Kept: 6079
% 45.54/45.97 Inuse: 485
% 45.54/45.97 Deleted: 105
% 45.54/45.97 Deletedinuse: 33
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97 *** allocated 113905 integers for termspace/termends
% 45.54/45.97 *** allocated 576640 integers for clauses
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97
% 45.54/45.97 Intermediate Status:
% 45.54/45.97 Generated: 98335
% 45.54/45.97 Kept: 8087
% 45.54/45.97 Inuse: 656
% 45.54/45.97 Deleted: 197
% 45.54/45.97 Deletedinuse: 82
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97 *** allocated 170857 integers for termspace/termends
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97
% 45.54/45.97 Intermediate Status:
% 45.54/45.97 Generated: 135094
% 45.54/45.97 Kept: 10087
% 45.54/45.97 Inuse: 792
% 45.54/45.97 Deleted: 273
% 45.54/45.97 Deletedinuse: 150
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97 *** allocated 864960 integers for clauses
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97
% 45.54/45.97 Intermediate Status:
% 45.54/45.97 Generated: 172608
% 45.54/45.97 Kept: 12089
% 45.54/45.97 Inuse: 918
% 45.54/45.97 Deleted: 314
% 45.54/45.97 Deletedinuse: 160
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97 *** allocated 256285 integers for termspace/termends
% 45.54/45.97
% 45.54/45.97 Intermediate Status:
% 45.54/45.97 Generated: 199096
% 45.54/45.97 Kept: 14106
% 45.54/45.97 Inuse: 1027
% 45.54/45.97 Deleted: 366
% 45.54/45.97 Deletedinuse: 170
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97 *** allocated 1297440 integers for clauses
% 45.54/45.97
% 45.54/45.97 Intermediate Status:
% 45.54/45.97 Generated: 225908
% 45.54/45.97 Kept: 16172
% 45.54/45.97 Inuse: 1098
% 45.54/45.97 Deleted: 419
% 45.54/45.97 Deletedinuse: 209
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97
% 45.54/45.97 Intermediate Status:
% 45.54/45.97 Generated: 248307
% 45.54/45.97 Kept: 18221
% 45.54/45.97 Inuse: 1152
% 45.54/45.97 Deleted: 427
% 45.54/45.97 Deletedinuse: 213
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97 Resimplifying clauses:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97 *** allocated 384427 integers for termspace/termends
% 45.54/45.97
% 45.54/45.97 Intermediate Status:
% 45.54/45.97 Generated: 292508
% 45.54/45.97 Kept: 20222
% 45.54/45.97 Inuse: 1266
% 45.54/45.97 Deleted: 3931
% 45.54/45.97 Deletedinuse: 213
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97
% 45.54/45.97 Intermediate Status:
% 45.54/45.97 Generated: 325544
% 45.54/45.97 Kept: 22225
% 45.54/45.97 Inuse: 1371
% 45.54/45.97 Deleted: 3944
% 45.54/45.97 Deletedinuse: 220
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97
% 45.54/45.97 Intermediate Status:
% 45.54/45.97 Generated: 375609
% 45.54/45.97 Kept: 24236
% 45.54/45.97 Inuse: 1432
% 45.54/45.97 Deleted: 3949
% 45.54/45.97 Deletedinuse: 221
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97 *** allocated 1946160 integers for clauses
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97 *** allocated 576640 integers for termspace/termends
% 45.54/45.97
% 45.54/45.97 Intermediate Status:
% 45.54/45.97 Generated: 411006
% 45.54/45.97 Kept: 28410
% 45.54/45.97 Inuse: 1437
% 45.54/45.97 Deleted: 3949
% 45.54/45.97 Deletedinuse: 221
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97
% 45.54/45.97 Intermediate Status:
% 45.54/45.97 Generated: 428618
% 45.54/45.97 Kept: 30434
% 45.54/45.97 Inuse: 1470
% 45.54/45.97 Deleted: 3950
% 45.54/45.97 Deletedinuse: 221
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97
% 45.54/45.97 Intermediate Status:
% 45.54/45.97 Generated: 451119
% 45.54/45.97 Kept: 32460
% 45.54/45.97 Inuse: 1512
% 45.54/45.97 Deleted: 3951
% 45.54/45.97 Deletedinuse: 221
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97
% 45.54/45.97 Intermediate Status:
% 45.54/45.97 Generated: 472254
% 45.54/45.97 Kept: 34603
% 45.54/45.97 Inuse: 1546
% 45.54/45.97 Deleted: 3951
% 45.54/45.97 Deletedinuse: 221
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97
% 45.54/45.97 Intermediate Status:
% 45.54/45.97 Generated: 491397
% 45.54/45.97 Kept: 36656
% 45.54/45.97 Inuse: 1577
% 45.54/45.97 Deleted: 3951
% 45.54/45.97 Deletedinuse: 221
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97
% 45.54/45.97 Intermediate Status:
% 45.54/45.97 Generated: 506766
% 45.54/45.97 Kept: 38698
% 45.54/45.97 Inuse: 1598
% 45.54/45.97 Deleted: 3954
% 45.54/45.97 Deletedinuse: 224
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97 *** allocated 2919240 integers for clauses
% 45.54/45.97 Resimplifying clauses:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97
% 45.54/45.97 Intermediate Status:
% 45.54/45.97 Generated: 543098
% 45.54/45.97 Kept: 40751
% 45.54/45.97 Inuse: 1639
% 45.54/45.97 Deleted: 6373
% 45.54/45.97 Deletedinuse: 224
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97 *** allocated 864960 integers for termspace/termends
% 45.54/45.97
% 45.54/45.97 Intermediate Status:
% 45.54/45.97 Generated: 575486
% 45.54/45.97 Kept: 42760
% 45.54/45.97 Inuse: 1700
% 45.54/45.97 Deleted: 6373
% 45.54/45.97 Deletedinuse: 224
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97
% 45.54/45.97 Intermediate Status:
% 45.54/45.97 Generated: 614079
% 45.54/45.97 Kept: 44761
% 45.54/45.97 Inuse: 1791
% 45.54/45.97 Deleted: 6381
% 45.54/45.97 Deletedinuse: 227
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97
% 45.54/45.97 Intermediate Status:
% 45.54/45.97 Generated: 689620
% 45.54/45.97 Kept: 46765
% 45.54/45.97 Inuse: 1832
% 45.54/45.97 Deleted: 6381
% 45.54/45.97 Deletedinuse: 227
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97
% 45.54/45.97 Intermediate Status:
% 45.54/45.97 Generated: 773019
% 45.54/45.97 Kept: 49110
% 45.54/45.97 Inuse: 1889
% 45.54/45.97 Deleted: 6384
% 45.54/45.97 Deletedinuse: 228
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97
% 45.54/45.97 Intermediate Status:
% 45.54/45.97 Generated: 802644
% 45.54/45.97 Kept: 51148
% 45.54/45.97 Inuse: 1947
% 45.54/45.97 Deleted: 6387
% 45.54/45.97 Deletedinuse: 231
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97
% 45.54/45.97 Intermediate Status:
% 45.54/45.97 Generated: 839510
% 45.54/45.97 Kept: 53229
% 45.54/45.97 Inuse: 2000
% 45.54/45.97 Deleted: 6389
% 45.54/45.97 Deletedinuse: 231
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97
% 45.54/45.97 Intermediate Status:
% 45.54/45.97 Generated: 866983
% 45.54/45.97 Kept: 55519
% 45.54/45.97 Inuse: 2047
% 45.54/45.97 Deleted: 6389
% 45.54/45.97 Deletedinuse: 231
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97
% 45.54/45.97 Intermediate Status:
% 45.54/45.97 Generated: 908948
% 45.54/45.97 Kept: 57523
% 45.54/45.97 Inuse: 2117
% 45.54/45.97 Deleted: 6390
% 45.54/45.97 Deletedinuse: 231
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97
% 45.54/45.97 Intermediate Status:
% 45.54/45.97 Generated: 966254
% 45.54/45.97 Kept: 59577
% 45.54/45.97 Inuse: 2212
% 45.54/45.97 Deleted: 6460
% 45.54/45.97 Deletedinuse: 278
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97 Resimplifying clauses:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97 *** allocated 4378860 integers for clauses
% 45.54/45.97
% 45.54/45.97 Intermediate Status:
% 45.54/45.97 Generated: 977705
% 45.54/45.97 Kept: 61743
% 45.54/45.97 Inuse: 2225
% 45.54/45.97 Deleted: 9890
% 45.54/45.97 Deletedinuse: 278
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97 *** allocated 1297440 integers for termspace/termends
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97
% 45.54/45.97 Intermediate Status:
% 45.54/45.97 Generated: 1006127
% 45.54/45.97 Kept: 63768
% 45.54/45.97 Inuse: 2270
% 45.54/45.97 Deleted: 9890
% 45.54/45.97 Deletedinuse: 278
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97 Done
% 45.54/45.97
% 45.54/45.97 Resimplifying inuse:
% 45.54/45.97
% 45.54/45.97 Bliksems!, er is een bewijs:
% 45.54/45.97 % SZS status Theorem
% 45.54/45.97 % SZS output start Refutation
% 45.54/45.97
% 45.54/45.97 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 45.54/45.97 (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) ==> addition(
% 45.54/45.97 addition( Z, Y ), X ) }.
% 45.54/45.97 (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 45.54/45.97 (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 45.54/45.97 (4) {G0,W11,D4,L1,V3,M1} I { multiplication( X, multiplication( Y, Z ) )
% 45.54/45.97 ==> multiplication( multiplication( X, Y ), Z ) }.
% 45.54/45.97 (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 45.54/45.97 (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 45.54/45.97 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 45.54/45.97 (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 45.54/45.97 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 45.54/45.97 (9) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==> zero }.
% 45.54/45.97 (11) {G0,W9,D5,L1,V1,M1} I { addition( one, multiplication( star( X ), X )
% 45.54/45.97 ) ==> star( X ) }.
% 45.54/45.97 (12) {G0,W13,D4,L2,V3,M2} I { ! leq( addition( multiplication( X, Z ), Y )
% 45.54/45.97 , Z ), leq( multiplication( star( X ), Y ), Z ) }.
% 45.54/45.97 (14) {G0,W9,D5,L1,V1,M1} I { addition( multiplication( X, strong_iteration
% 45.54/45.97 ( X ) ), one ) ==> strong_iteration( X ) }.
% 45.54/45.97 (16) {G0,W10,D5,L1,V1,M1} I { addition( star( X ), multiplication(
% 45.54/45.97 strong_iteration( X ), zero ) ) ==> strong_iteration( X ) }.
% 45.54/45.97 (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) ==> Y }.
% 45.54/45.97 (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, Y ) }.
% 45.54/45.97 (19) {G0,W9,D5,L1,V0,M1} I { ! addition( multiplication( strong_iteration(
% 45.54/45.97 skol1 ), skol1 ), one ) ==> strong_iteration( skol1 ) }.
% 45.54/45.97 (20) {G1,W5,D3,L1,V1,M1} P(0,2) { addition( zero, X ) ==> X }.
% 45.54/45.97 (22) {G1,W3,D2,L1,V1,M1} R(18,3) { leq( X, X ) }.
% 45.54/45.97 (25) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y ), Z ) ==>
% 45.54/45.97 addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 45.54/45.97 (27) {G1,W11,D4,L1,V3,M1} P(0,1);d(1) { addition( addition( Z, Y ), X ) =
% 45.54/45.97 addition( addition( Z, X ), Y ) }.
% 45.54/45.97 (35) {G1,W12,D4,L2,V3,M2} P(17,1) { addition( addition( Z, X ), Y ) ==>
% 45.54/45.97 addition( Z, Y ), ! leq( X, Y ) }.
% 45.54/45.97 (36) {G1,W8,D3,L2,V2,M2} P(17,0) { addition( Y, X ) ==> Y, ! leq( X, Y )
% 45.54/45.97 }.
% 45.54/45.97 (50) {G1,W9,D4,L1,V2,M1} P(9,4) { multiplication( multiplication( Y, zero )
% 45.54/45.97 , X ) ==> multiplication( Y, zero ) }.
% 45.54/45.97 (67) {G1,W16,D4,L2,V3,M2} P(7,18) { ! multiplication( X, addition( Y, Z ) )
% 45.54/45.97 ==> multiplication( X, Z ), leq( multiplication( X, Y ), multiplication
% 45.54/45.97 ( X, Z ) ) }.
% 45.54/45.97 (69) {G1,W11,D4,L1,V2,M1} P(5,7) { addition( X, multiplication( X, Y ) ) =
% 45.54/45.97 multiplication( X, addition( one, Y ) ) }.
% 45.54/45.97 (99) {G1,W16,D4,L2,V3,M2} P(8,18) { ! multiplication( addition( X, Z ), Y )
% 45.54/45.97 ==> multiplication( Z, Y ), leq( multiplication( X, Y ), multiplication
% 45.54/45.97 ( Z, Y ) ) }.
% 45.54/45.97 (100) {G1,W11,D4,L1,V3,M1} P(8,0);d(8) { multiplication( addition( X, Z ),
% 45.54/45.97 Y ) = multiplication( addition( Z, X ), Y ) }.
% 45.54/45.97 (213) {G2,W5,D3,L1,V1,M1} P(14,12);d(5);r(22) { leq( star( X ),
% 45.54/45.97 strong_iteration( X ) ) }.
% 45.54/45.97 (226) {G3,W8,D4,L1,V1,M1} R(213,17) { addition( star( X ), strong_iteration
% 45.54/45.97 ( X ) ) ==> strong_iteration( X ) }.
% 45.54/45.97 (285) {G1,W10,D5,L1,V1,M1} P(16,0) { addition( multiplication(
% 45.54/45.97 strong_iteration( X ), zero ), star( X ) ) ==> strong_iteration( X ) }.
% 45.54/45.97 (312) {G1,W9,D5,L1,V0,M1} P(0,19) { ! addition( one, multiplication(
% 45.54/45.97 strong_iteration( skol1 ), skol1 ) ) ==> strong_iteration( skol1 ) }.
% 45.54/45.97 (328) {G2,W8,D3,L2,V3,M2} P(17,25);q { leq( X, addition( Y, Z ) ), ! leq( X
% 45.54/45.97 , Y ) }.
% 45.54/45.97 (332) {G2,W5,D3,L1,V2,M1} P(3,25);q { leq( X, addition( X, Y ) ) }.
% 45.54/45.97 (371) {G3,W5,D3,L1,V2,M1} P(0,332) { leq( X, addition( Y, X ) ) }.
% 45.54/45.97 (377) {G4,W7,D4,L1,V1,M1} P(11,371) { leq( multiplication( star( X ), X ),
% 45.54/45.97 star( X ) ) }.
% 45.54/45.97 (389) {G2,W14,D5,L1,V2,M1} P(16,27) { addition( addition( star( X ), Y ),
% 45.54/45.97 multiplication( strong_iteration( X ), zero ) ) ==> addition(
% 45.54/45.97 strong_iteration( X ), Y ) }.
% 45.54/45.97 (571) {G2,W15,D4,L2,V2,M2} P(16,35) { addition( strong_iteration( X ), Y )
% 45.54/45.97 ==> addition( star( X ), Y ), ! leq( multiplication( strong_iteration( X
% 45.54/45.97 ), zero ), Y ) }.
% 45.54/45.97 (574) {G2,W14,D4,L2,V2,M2} P(11,35) { addition( star( X ), Y ) ==> addition
% 45.54/45.97 ( one, Y ), ! leq( multiplication( star( X ), X ), Y ) }.
% 45.54/45.97 (812) {G2,W15,D5,L1,V3,M1} P(50,8) { multiplication( addition( Z,
% 45.54/45.97 multiplication( X, zero ) ), Y ) ==> addition( multiplication( Z, Y ),
% 45.54/45.97 multiplication( X, zero ) ) }.
% 45.54/45.97 (1101) {G3,W8,D3,L2,V2,M2} P(16,328) { leq( Y, strong_iteration( X ) ), !
% 45.54/45.97 leq( Y, star( X ) ) }.
% 45.54/45.97 (1111) {G5,W7,D4,L1,V1,M1} R(1101,377) { leq( multiplication( star( X ), X
% 45.54/45.97 ), strong_iteration( X ) ) }.
% 45.54/45.97 (1128) {G6,W10,D5,L1,V1,M1} R(1111,36) { addition( strong_iteration( X ),
% 45.54/45.97 multiplication( star( X ), X ) ) ==> strong_iteration( X ) }.
% 45.54/45.97 (1632) {G2,W7,D3,L1,V2,M1} P(20,67);q { leq( multiplication( Y, zero ),
% 45.54/45.97 multiplication( Y, X ) ) }.
% 45.54/45.97 (5228) {G4,W9,D4,L1,V2,M1} P(226,99);q { leq( multiplication( star( X ), Y
% 45.54/45.97 ), multiplication( strong_iteration( X ), Y ) ) }.
% 45.54/45.97 (12374) {G3,W14,D5,L1,V2,M1} P(285,100);d(812) { addition( multiplication(
% 45.54/45.97 star( X ), Y ), multiplication( strong_iteration( X ), zero ) ) ==>
% 45.54/45.97 multiplication( strong_iteration( X ), Y ) }.
% 45.54/45.97 (18940) {G4,W14,D5,L1,V2,M1} P(69,389);d(12374) { addition(
% 45.54/45.97 strong_iteration( X ), multiplication( star( X ), Y ) ) ==>
% 45.54/45.97 multiplication( strong_iteration( X ), addition( one, Y ) ) }.
% 45.54/45.97 (20024) {G7,W9,D4,L1,V1,M1} S(1128);d(18940) { multiplication(
% 45.54/45.97 strong_iteration( X ), addition( one, X ) ) ==> strong_iteration( X ) }.
% 45.54/45.97 (35715) {G3,W14,D5,L1,V2,M1} P(571,69);r(1632) { addition( star( X ),
% 45.54/45.97 multiplication( strong_iteration( X ), Y ) ) ==> multiplication(
% 45.54/45.97 strong_iteration( X ), addition( one, Y ) ) }.
% 45.54/45.97 (64568) {G8,W9,D5,L1,V1,M1} R(5228,574);d(35715);d(20024) { addition( one,
% 45.54/45.97 multiplication( strong_iteration( X ), X ) ) ==> strong_iteration( X )
% 45.54/45.97 }.
% 45.54/45.97 (64826) {G9,W0,D0,L0,V0,M0} S(312);d(64568);q { }.
% 45.54/45.97
% 45.54/45.97
% 45.54/45.97 % SZS output end Refutation
% 45.54/45.97 found a proof!
% 45.54/45.97
% 45.54/45.97
% 45.54/45.97 Unprocessed initial clauses:
% 45.54/45.97
% 45.54/45.97 (64828) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 45.54/45.97 (64829) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition
% 45.54/45.97 ( addition( Z, Y ), X ) }.
% 45.54/45.97 (64830) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 45.54/45.97 (64831) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 45.54/45.97 (64832) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) )
% 45.54/45.97 = multiplication( multiplication( X, Y ), Z ) }.
% 45.54/45.97 (64833) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 45.54/45.97 (64834) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 45.54/45.97 (64835) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 45.54/45.97 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 45.54/45.97 (64836) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 45.54/45.97 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 45.54/45.97 (64837) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 45.54/45.97 (64838) {G0,W9,D5,L1,V1,M1} { addition( one, multiplication( X, star( X )
% 45.54/45.97 ) ) = star( X ) }.
% 45.54/45.97 (64839) {G0,W9,D5,L1,V1,M1} { addition( one, multiplication( star( X ), X
% 45.54/45.97 ) ) = star( X ) }.
% 45.54/45.97 (64840) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( X, Z ), Y
% 45.54/45.97 ), Z ), leq( multiplication( star( X ), Y ), Z ) }.
% 45.54/45.97 (64841) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( Z, X ), Y
% 45.54/45.97 ), Z ), leq( multiplication( Y, star( X ) ), Z ) }.
% 45.54/45.97 (64842) {G0,W9,D5,L1,V1,M1} { strong_iteration( X ) = addition(
% 45.54/45.97 multiplication( X, strong_iteration( X ) ), one ) }.
% 45.54/45.97 (64843) {G0,W13,D4,L2,V3,M2} { ! leq( Z, addition( multiplication( X, Z )
% 45.54/45.97 , Y ) ), leq( Z, multiplication( strong_iteration( X ), Y ) ) }.
% 45.54/45.97 (64844) {G0,W10,D5,L1,V1,M1} { strong_iteration( X ) = addition( star( X )
% 45.54/45.97 , multiplication( strong_iteration( X ), zero ) ) }.
% 45.54/45.97 (64845) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 45.54/45.97 (64846) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 45.54/45.97 (64847) {G0,W9,D5,L1,V0,M1} { ! strong_iteration( skol1 ) = addition(
% 45.54/45.97 multiplication( strong_iteration( skol1 ), skol1 ), one ) }.
% 45.54/45.97
% 45.54/45.97
% 45.54/45.97 Total Proof:
% 45.54/45.97
% 45.54/45.97 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 45.54/45.97 ) }.
% 45.54/45.97 parent0: (64828) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 45.54/45.97 }.
% 45.54/45.97 substitution0:
% 45.54/45.97 X := X
% 45.54/45.97 Y := Y
% 45.54/45.97 end
% 45.54/45.97 permutation0:
% 45.54/45.97 0 ==> 0
% 45.54/45.97 end
% 45.54/45.97
% 45.54/45.97 subsumption: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 45.54/45.97 ==> addition( addition( Z, Y ), X ) }.
% 45.54/45.97 parent0: (64829) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) =
% 45.54/45.97 addition( addition( Z, Y ), X ) }.
% 45.54/45.97 substitution0:
% 45.54/45.97 X := X
% 45.54/45.97 Y := Y
% 45.54/45.97 Z := Z
% 45.54/45.97 end
% 45.54/45.97 permutation0:
% 45.54/45.97 0 ==> 0
% 45.54/45.97 end
% 45.54/45.97
% 45.54/45.97 subsumption: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 45.54/45.97 parent0: (64830) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 45.54/45.97 substitution0:
% 45.54/45.97 X := X
% 45.54/45.97 end
% 45.54/45.97 permutation0:
% 45.54/45.97 0 ==> 0
% 45.54/45.97 end
% 45.54/45.97
% 45.54/45.97 subsumption: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 45.54/45.97 parent0: (64831) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 45.54/45.97 substitution0:
% 45.54/45.97 X := X
% 45.54/45.97 end
% 45.54/45.97 permutation0:
% 45.54/45.97 0 ==> 0
% 45.54/45.97 end
% 45.54/45.97
% 45.54/45.97 subsumption: (4) {G0,W11,D4,L1,V3,M1} I { multiplication( X, multiplication
% 45.54/45.97 ( Y, Z ) ) ==> multiplication( multiplication( X, Y ), Z ) }.
% 45.54/45.97 parent0: (64832) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication
% 45.54/45.97 ( Y, Z ) ) = multiplication( multiplication( X, Y ), Z ) }.
% 45.54/45.97 substitution0:
% 45.54/45.97 X := X
% 45.54/45.97 Y := Y
% 45.54/45.97 Z := Z
% 45.54/45.97 end
% 45.54/45.97 permutation0:
% 45.54/45.97 0 ==> 0
% 45.54/45.97 end
% 45.54/45.97
% 45.54/45.97 subsumption: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 45.54/45.97 parent0: (64833) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 45.54/45.97 substitution0:
% 45.54/45.97 X := X
% 45.54/45.97 end
% 45.54/45.97 permutation0:
% 45.54/45.97 0 ==> 0
% 45.54/45.97 end
% 45.54/45.97
% 45.54/45.97 eqswap: (64869) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 45.54/45.97 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 45.54/45.97 parent0[0]: (64835) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y
% 45.54/45.97 , Z ) ) = addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 45.54/45.97 substitution0:
% 45.54/45.97 X := X
% 45.54/45.97 Y := Y
% 45.54/45.97 Z := Z
% 45.54/45.97 end
% 45.54/45.97
% 45.54/45.97 subsumption: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y )
% 45.54/45.97 , multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 45.54/45.97 parent0: (64869) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 45.54/45.97 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 45.54/45.97 substitution0:
% 45.54/45.97 X := X
% 45.54/45.97 Y := Y
% 45.54/45.97 Z := Z
% 45.54/45.97 end
% 45.54/45.97 permutation0:
% 45.54/45.97 0 ==> 0
% 45.54/45.97 end
% 45.54/45.97
% 45.54/45.97 eqswap: (64877) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 45.54/45.97 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 45.54/45.97 parent0[0]: (64836) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y
% 45.54/45.97 ), Z ) = addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 45.54/45.97 substitution0:
% 45.54/45.97 X := X
% 45.54/45.97 Y := Y
% 45.54/45.97 Z := Z
% 45.54/45.97 end
% 45.54/45.97
% 45.54/45.97 subsumption: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z )
% 45.54/45.97 , multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 45.54/45.97 parent0: (64877) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 45.54/45.97 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 45.54/45.97 substitution0:
% 45.54/45.97 X := X
% 45.54/45.97 Y := Y
% 45.54/45.97 Z := Z
% 45.54/45.97 end
% 45.54/45.97 permutation0:
% 45.54/45.97 0 ==> 0
% 45.54/45.97 end
% 45.54/45.97
% 45.54/45.97 subsumption: (9) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==> zero
% 45.54/45.97 }.
% 45.54/45.97 parent0: (64837) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero
% 45.54/45.97 }.
% 45.54/45.97 substitution0:
% 45.54/45.97 X := X
% 45.54/45.97 end
% 45.54/45.97 permutation0:
% 45.54/45.97 0 ==> 0
% 45.54/45.97 end
% 45.54/45.97
% 45.54/45.97 subsumption: (11) {G0,W9,D5,L1,V1,M1} I { addition( one, multiplication(
% 45.54/45.97 star( X ), X ) ) ==> star( X ) }.
% 45.54/45.97 parent0: (64839) {G0,W9,D5,L1,V1,M1} { addition( one, multiplication( star
% 45.54/45.97 ( X ), X ) ) = star( X ) }.
% 45.54/45.97 substitution0:
% 45.54/45.97 X := X
% 45.54/45.97 end
% 45.54/45.97 permutation0:
% 45.54/45.97 0 ==> 0
% 45.54/45.97 end
% 45.54/45.97
% 45.54/45.97 subsumption: (12) {G0,W13,D4,L2,V3,M2} I { ! leq( addition( multiplication
% 45.54/45.97 ( X, Z ), Y ), Z ), leq( multiplication( star( X ), Y ), Z ) }.
% 45.54/45.97 parent0: (64840) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( X
% 45.54/45.97 , Z ), Y ), Z ), leq( multiplication( star( X ), Y ), Z ) }.
% 45.54/45.97 substitution0:
% 45.54/45.97 X := X
% 45.54/45.97 Y := Y
% 45.54/45.97 Z := Z
% 45.54/45.97 end
% 45.54/45.97 permutation0:
% 45.54/45.97 0 ==> 0
% 45.54/45.97 1 ==> 1
% 45.54/45.97 end
% 45.54/45.97
% 45.54/45.97 eqswap: (64920) {G0,W9,D5,L1,V1,M1} { addition( multiplication( X,
% 45.54/45.97 strong_iteration( X ) ), one ) = strong_iteration( X ) }.
% 45.54/45.97 parent0[0]: (64842) {G0,W9,D5,L1,V1,M1} { strong_iteration( X ) = addition
% 45.54/45.97 ( multiplication( X, strong_iteration( X ) ), one ) }.
% 45.54/45.97 substitution0:
% 45.54/45.97 X := X
% 45.54/45.97 end
% 45.54/45.97
% 45.54/45.97 subsumption: (14) {G0,W9,D5,L1,V1,M1} I { addition( multiplication( X,
% 45.54/45.97 strong_iteration( X ) ), one ) ==> strong_iteration( X ) }.
% 45.54/45.97 parent0: (64920) {G0,W9,D5,L1,V1,M1} { addition( multiplication( X,
% 45.54/45.97 strong_iteration( X ) ), one ) = strong_iteration( X ) }.
% 45.54/45.97 substitution0:
% 45.54/45.97 X := X
% 45.54/45.97 end
% 45.54/45.97 permutation0:
% 45.54/45.97 0 ==> 0
% 45.54/45.97 end
% 45.54/45.97
% 45.54/45.97 eqswap: (64933) {G0,W10,D5,L1,V1,M1} { addition( star( X ), multiplication
% 45.54/45.97 ( strong_iteration( X ), zero ) ) = strong_iteration( X ) }.
% 45.54/45.97 parent0[0]: (64844) {G0,W10,D5,L1,V1,M1} { strong_iteration( X ) =
% 45.54/45.97 addition( star( X ), multiplication( strong_iteration( X ), zero ) ) }.
% 45.54/45.97 substitution0:
% 45.54/45.97 X := X
% 45.54/45.97 end
% 45.54/45.97
% 45.54/45.97 subsumption: (16) {G0,W10,D5,L1,V1,M1} I { addition( star( X ),
% 45.54/45.97 multiplication( strong_iteration( X ), zero ) ) ==> strong_iteration( X )
% 45.54/45.97 }.
% 45.54/45.97 parent0: (64933) {G0,W10,D5,L1,V1,M1} { addition( star( X ),
% 45.54/45.97 multiplication( strong_iteration( X ), zero ) ) = strong_iteration( X )
% 45.54/45.97 }.
% 45.54/45.97 substitution0:
% 45.54/45.97 X := X
% 45.54/45.97 end
% 45.54/45.97 permutation0:
% 45.54/45.97 0 ==> 0
% 45.54/45.97 end
% 45.54/45.97
% 45.54/45.97 subsumption: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 45.54/45.97 ==> Y }.
% 45.54/45.97 parent0: (64845) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y
% 45.54/45.97 }.
% 45.54/45.97 substitution0:
% 45.54/45.97 X := X
% 45.54/45.97 Y := Y
% 45.54/45.97 end
% 45.54/45.97 permutation0:
% 45.54/45.97 0 ==> 0
% 45.54/45.97 1 ==> 1
% 45.54/45.97 end
% 45.54/45.97
% 45.54/45.97 subsumption: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X
% 45.54/45.97 , Y ) }.
% 45.54/45.97 parent0: (64846) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y )
% 45.54/45.97 }.
% 45.54/45.97 substitution0:
% 45.54/45.97 X := X
% 45.54/45.97 Y := Y
% 45.54/45.97 end
% 45.54/45.97 permutation0:
% 45.54/45.97 0 ==> 0
% 45.54/45.97 1 ==> 1
% 45.54/45.97 end
% 45.54/45.97
% 45.54/45.97 eqswap: (64978) {G0,W9,D5,L1,V0,M1} { ! addition( multiplication(
% 45.54/45.97 strong_iteration( skol1 ), skol1 ), one ) = strong_iteration( skol1 ) }.
% 45.54/45.97 parent0[0]: (64847) {G0,W9,D5,L1,V0,M1} { ! strong_iteration( skol1 ) =
% 45.54/45.97 addition( multiplication( strong_iteration( skol1 ), skol1 ), one ) }.
% 45.54/45.97 substitution0:
% 45.54/45.97 end
% 45.54/45.97
% 45.54/45.97 subsumption: (19) {G0,W9,D5,L1,V0,M1} I { ! addition( multiplication(
% 45.54/45.97 strong_iteration( skol1 ), skol1 ), one ) ==> strong_iteration( skol1 )
% 45.54/45.97 }.
% 45.54/45.97 parent0: (64978) {G0,W9,D5,L1,V0,M1} { ! addition( multiplication(
% 45.54/45.97 strong_iteration( skol1 ), skol1 ), one ) = strong_iteration( skol1 ) }.
% 45.54/45.97 substitution0:
% 45.54/45.97 end
% 45.54/45.97 permutation0:
% 45.54/45.97 0 ==> 0
% 45.54/45.97 end
% 45.54/45.97
% 45.54/45.97 eqswap: (64979) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, zero ) }.
% 45.54/45.97 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 45.54/45.97 substitution0:
% 45.54/45.97 X := X
% 45.54/45.97 end
% 45.54/45.97
% 45.54/45.97 paramod: (64980) {G1,W5,D3,L1,V1,M1} { X ==> addition( zero, X ) }.
% 45.54/45.97 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 45.54/45.97 }.
% 45.54/45.97 parent1[0; 2]: (64979) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, zero ) }.
% 45.54/45.97 substitution0:
% 45.54/45.97 X := X
% 45.54/45.97 Y := zero
% 45.54/45.97 end
% 45.54/45.97 substitution1:
% 45.54/45.97 X := X
% 45.54/45.97 end
% 45.54/45.97
% 45.54/45.97 eqswap: (64983) {G1,W5,D3,L1,V1,M1} { addition( zero, X ) ==> X }.
% 45.54/45.97 parent0[0]: (64980) {G1,W5,D3,L1,V1,M1} { X ==> addition( zero, X ) }.
% 45.54/45.97 substitution0:
% 45.54/45.97 X := X
% 45.54/45.97 end
% 45.54/45.97
% 45.54/45.97 subsumption: (20) {G1,W5,D3,L1,V1,M1} P(0,2) { addition( zero, X ) ==> X
% 45.54/45.97 }.
% 45.54/45.97 parent0: (64983) {G1,W5,D3,L1,V1,M1} { addition( zero, X ) ==> X }.
% 45.54/45.97 substitution0:
% 45.54/45.97 X := X
% 45.54/45.97 end
% 45.54/45.97 permutation0:
% 45.54/45.97 0 ==> 0
% 45.54/45.97 end
% 45.54/45.97
% 45.54/45.97 eqswap: (64984) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 45.54/45.97 ) }.
% 45.54/45.97 parent0[0]: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 45.54/45.97 Y ) }.
% 45.54/45.97 substitution0:
% 45.54/45.97 X := X
% 45.54/45.97 Y := Y
% 45.54/45.97 end
% 45.54/45.97
% 45.54/45.97 eqswap: (64985) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 45.54/45.97 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 45.54/45.97 substitution0:
% 45.54/45.97 X := X
% 45.54/45.97 end
% 45.54/45.97
% 45.54/45.97 resolution: (64986) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 45.54/45.97 parent0[0]: (64984) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X
% 45.54/45.97 , Y ) }.
% 45.54/45.97 parent1[0]: (64985) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 45.54/45.97 substitution0:
% 45.54/45.97 X := X
% 45.54/45.97 Y := X
% 45.54/45.97 end
% 45.54/45.97 substitution1:
% 45.54/45.97 X := X
% 45.54/45.97 end
% 45.54/45.97
% 45.54/45.97 subsumption: (22) {G1,W3,D2,L1,V1,M1} R(18,3) { leq( X, X ) }.
% 45.54/45.97 parent0: (64986) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 45.54/45.97 substitution0:
% 45.54/45.97 X := X
% 45.54/45.97 end
% 45.54/45.97 permutation0:
% 45.54/45.97 0 ==> 0
% 45.54/45.97 end
% 45.54/45.97
% 45.54/45.97 eqswap: (64988) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 45.54/45.97 ) }.
% 45.54/45.97 parent0[0]: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 45.54/45.97 Y ) }.
% 45.54/45.97 substitution0:
% 45.54/45.97 X := X
% 45.54/45.97 Y := Y
% 45.54/45.97 end
% 45.54/45.97
% 45.54/45.97 paramod: (64989) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition(
% 45.54/45.97 addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 45.54/45.97 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 45.54/45.97 ==> addition( addition( Z, Y ), X ) }.
% 45.54/45.97 parent1[0; 5]: (64988) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 45.54/45.97 ( X, Y ) }.
% 45.54/45.97 substitution0:
% 45.54/45.97 X := Y
% 45.54/45.97 Y := X
% 45.54/45.97 Z := Z
% 45.54/45.97 end
% 45.54/45.97 substitution1:
% 45.54/45.97 X := Z
% 45.54/45.97 Y := addition( X, Y )
% 45.54/45.97 end
% 45.54/45.97
% 45.54/45.97 eqswap: (64990) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 45.54/45.97 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 45.54/45.97 parent0[0]: (64989) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition
% 45.54/45.97 ( addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 45.54/45.97 substitution0:
% 45.54/45.97 X := X
% 45.54/45.97 Y := Y
% 45.54/45.97 Z := Z
% 45.54/45.97 end
% 45.54/45.97
% 45.54/45.97 subsumption: (25) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y
% 45.54/45.97 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 45.54/45.97 parent0: (64990) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 45.54/45.97 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 45.54/45.97 substitution0:
% 45.54/45.97 X := Y
% 45.54/45.97 Y := Z
% 45.54/45.97 Z := X
% 45.54/45.97 end
% 45.54/45.97 permutation0:
% 45.54/45.97 0 ==> 0
% 45.54/45.97 1 ==> 1
% 45.54/45.97 end
% 45.54/45.97
% 45.54/45.97 eqswap: (64991) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 45.54/45.97 addition( X, addition( Y, Z ) ) }.
% 45.54/45.97 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 45.54/45.97 ==> addition( addition( Z, Y ), X ) }.
% 45.54/45.97 substitution0:
% 45.54/45.97 X := Z
% 45.54/45.97 Y := Y
% 45.54/45.97 Z := X
% 45.54/45.97 end
% 45.54/45.97
% 45.54/45.97 paramod: (64996) {G1,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z )
% 45.54/45.97 ==> addition( X, addition( Z, Y ) ) }.
% 45.54/45.97 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 45.54/45.97 }.
% 45.54/45.97 parent1[0; 8]: (64991) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ),
% 45.54/45.97 Z ) ==> addition( X, addition( Y, Z ) ) }.
% 45.54/45.97 substitution0:
% 45.54/45.97 X := Y
% 45.54/45.97 Y := Z
% 45.54/45.97 end
% 45.54/45.97 substitution1:
% 45.54/45.97 X := X
% 45.54/45.97 Y := Y
% 45.54/45.97 Z := Z
% 45.54/45.97 end
% 45.54/45.97
% 45.54/45.97 paramod: (65009) {G1,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z )
% 45.54/45.97 ==> addition( addition( X, Z ), Y ) }.
% 45.54/45.97 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 45.54/45.97 ==> addition( addition( Z, Y ), X ) }.
% 45.54/45.97 parent1[0; 6]: (64996) {G1,W11,D4,L1,V3,M1} { addition( addition( X, Y ),
% 45.54/45.97 Z ) ==> addition( X, addition( Z, Y ) ) }.
% 45.54/45.97 substitution0:
% 45.54/45.97 X := Y
% 45.54/45.97 Y := Z
% 45.54/45.97 Z := X
% 45.54/45.97 end
% 45.54/45.97 substitution1:
% 45.54/45.97 X := X
% 45.54/45.97 Y := Y
% 45.54/45.97 Z := Z
% 45.54/45.97 end
% 45.54/45.97
% 45.54/45.97 subsumption: (27) {G1,W11,D4,L1,V3,M1} P(0,1);d(1) { addition( addition( Z
% 45.54/45.97 , Y ), X ) = addition( addition( Z, X ), Y ) }.
% 45.54/45.97 parent0: (65009) {G1,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z )
% 45.54/45.97 ==> addition( addition( X, Z ), Y ) }.
% 45.54/45.97 substitution0:
% 45.54/45.97 X := Z
% 45.54/45.97 Y := Y
% 45.54/45.97 Z := X
% 45.54/45.97 end
% 45.54/45.97 permutation0:
% 45.54/45.97 0 ==> 0
% 45.54/45.97 end
% 45.54/45.97
% 45.54/45.97 eqswap: (65011) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 45.54/45.97 addition( X, addition( Y, Z ) ) }.
% 45.54/45.97 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 45.54/45.98 ==> addition( addition( Z, Y ), X ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := Z
% 45.54/45.98 Y := Y
% 45.54/45.98 Z := X
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 paramod: (65017) {G1,W12,D4,L2,V3,M2} { addition( addition( X, Y ), Z )
% 45.54/45.98 ==> addition( X, Z ), ! leq( Y, Z ) }.
% 45.54/45.98 parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 45.54/45.98 ==> Y }.
% 45.54/45.98 parent1[0; 8]: (65011) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ),
% 45.54/45.98 Z ) ==> addition( X, addition( Y, Z ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := Y
% 45.54/45.98 Y := Z
% 45.54/45.98 end
% 45.54/45.98 substitution1:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Y
% 45.54/45.98 Z := Z
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 subsumption: (35) {G1,W12,D4,L2,V3,M2} P(17,1) { addition( addition( Z, X )
% 45.54/45.98 , Y ) ==> addition( Z, Y ), ! leq( X, Y ) }.
% 45.54/45.98 parent0: (65017) {G1,W12,D4,L2,V3,M2} { addition( addition( X, Y ), Z )
% 45.54/45.98 ==> addition( X, Z ), ! leq( Y, Z ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := Z
% 45.54/45.98 Y := X
% 45.54/45.98 Z := Y
% 45.54/45.98 end
% 45.54/45.98 permutation0:
% 45.54/45.98 0 ==> 0
% 45.54/45.98 1 ==> 1
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 eqswap: (65064) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 45.54/45.98 ) }.
% 45.54/45.98 parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 45.54/45.98 ==> Y }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Y
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 paramod: (65065) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X
% 45.54/45.98 ) }.
% 45.54/45.98 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 45.54/45.98 }.
% 45.54/45.98 parent1[0; 2]: (65064) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq
% 45.54/45.98 ( X, Y ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := Y
% 45.54/45.98 Y := X
% 45.54/45.98 end
% 45.54/45.98 substitution1:
% 45.54/45.98 X := Y
% 45.54/45.98 Y := X
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 eqswap: (65068) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> X, ! leq( Y, X
% 45.54/45.98 ) }.
% 45.54/45.98 parent0[0]: (65065) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y
% 45.54/45.98 , X ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Y
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 subsumption: (36) {G1,W8,D3,L2,V2,M2} P(17,0) { addition( Y, X ) ==> Y, !
% 45.54/45.98 leq( X, Y ) }.
% 45.54/45.98 parent0: (65068) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> X, ! leq( Y, X
% 45.54/45.98 ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := Y
% 45.54/45.98 Y := X
% 45.54/45.98 end
% 45.54/45.98 permutation0:
% 45.54/45.98 0 ==> 0
% 45.54/45.98 1 ==> 1
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 eqswap: (65070) {G0,W11,D4,L1,V3,M1} { multiplication( multiplication( X,
% 45.54/45.98 Y ), Z ) ==> multiplication( X, multiplication( Y, Z ) ) }.
% 45.54/45.98 parent0[0]: (4) {G0,W11,D4,L1,V3,M1} I { multiplication( X, multiplication
% 45.54/45.98 ( Y, Z ) ) ==> multiplication( multiplication( X, Y ), Z ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Y
% 45.54/45.98 Z := Z
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 paramod: (65075) {G1,W9,D4,L1,V2,M1} { multiplication( multiplication( X,
% 45.54/45.98 zero ), Y ) ==> multiplication( X, zero ) }.
% 45.54/45.98 parent0[0]: (9) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==> zero
% 45.54/45.98 }.
% 45.54/45.98 parent1[0; 8]: (65070) {G0,W11,D4,L1,V3,M1} { multiplication(
% 45.54/45.98 multiplication( X, Y ), Z ) ==> multiplication( X, multiplication( Y, Z )
% 45.54/45.98 ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := Y
% 45.54/45.98 end
% 45.54/45.98 substitution1:
% 45.54/45.98 X := X
% 45.54/45.98 Y := zero
% 45.54/45.98 Z := Y
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 subsumption: (50) {G1,W9,D4,L1,V2,M1} P(9,4) { multiplication(
% 45.54/45.98 multiplication( Y, zero ), X ) ==> multiplication( Y, zero ) }.
% 45.54/45.98 parent0: (65075) {G1,W9,D4,L1,V2,M1} { multiplication( multiplication( X,
% 45.54/45.98 zero ), Y ) ==> multiplication( X, zero ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := Y
% 45.54/45.98 Y := X
% 45.54/45.98 end
% 45.54/45.98 permutation0:
% 45.54/45.98 0 ==> 0
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 eqswap: (65084) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 45.54/45.98 ) }.
% 45.54/45.98 parent0[0]: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 45.54/45.98 Y ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Y
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 paramod: (65085) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 45.54/45.98 multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ),
% 45.54/45.98 multiplication( X, Y ) ) }.
% 45.54/45.98 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 45.54/45.98 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 45.54/45.98 parent1[0; 5]: (65084) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 45.54/45.98 ( X, Y ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Z
% 45.54/45.98 Z := Y
% 45.54/45.98 end
% 45.54/45.98 substitution1:
% 45.54/45.98 X := multiplication( X, Z )
% 45.54/45.98 Y := multiplication( X, Y )
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 eqswap: (65086) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, addition( Z, Y
% 45.54/45.98 ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ),
% 45.54/45.98 multiplication( X, Y ) ) }.
% 45.54/45.98 parent0[0]: (65085) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 45.54/45.98 multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ),
% 45.54/45.98 multiplication( X, Y ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Y
% 45.54/45.98 Z := Z
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 subsumption: (67) {G1,W16,D4,L2,V3,M2} P(7,18) { ! multiplication( X,
% 45.54/45.98 addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 45.54/45.98 ), multiplication( X, Z ) ) }.
% 45.54/45.98 parent0: (65086) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, addition( Z,
% 45.54/45.98 Y ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ),
% 45.54/45.98 multiplication( X, Y ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Z
% 45.54/45.98 Z := Y
% 45.54/45.98 end
% 45.54/45.98 permutation0:
% 45.54/45.98 0 ==> 0
% 45.54/45.98 1 ==> 1
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 eqswap: (65088) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z )
% 45.54/45.98 ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 45.54/45.98 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 45.54/45.98 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Y
% 45.54/45.98 Z := Z
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 paramod: (65089) {G1,W11,D4,L1,V2,M1} { multiplication( X, addition( one,
% 45.54/45.98 Y ) ) ==> addition( X, multiplication( X, Y ) ) }.
% 45.54/45.98 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 45.54/45.98 parent1[0; 7]: (65088) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition
% 45.54/45.98 ( Y, Z ) ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) )
% 45.54/45.98 }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 end
% 45.54/45.98 substitution1:
% 45.54/45.98 X := X
% 45.54/45.98 Y := one
% 45.54/45.98 Z := Y
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 eqswap: (65091) {G1,W11,D4,L1,V2,M1} { addition( X, multiplication( X, Y )
% 45.54/45.98 ) ==> multiplication( X, addition( one, Y ) ) }.
% 45.54/45.98 parent0[0]: (65089) {G1,W11,D4,L1,V2,M1} { multiplication( X, addition(
% 45.54/45.98 one, Y ) ) ==> addition( X, multiplication( X, Y ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Y
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 subsumption: (69) {G1,W11,D4,L1,V2,M1} P(5,7) { addition( X, multiplication
% 45.54/45.98 ( X, Y ) ) = multiplication( X, addition( one, Y ) ) }.
% 45.54/45.98 parent0: (65091) {G1,W11,D4,L1,V2,M1} { addition( X, multiplication( X, Y
% 45.54/45.98 ) ) ==> multiplication( X, addition( one, Y ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Y
% 45.54/45.98 end
% 45.54/45.98 permutation0:
% 45.54/45.98 0 ==> 0
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 eqswap: (65094) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 45.54/45.98 ) }.
% 45.54/45.98 parent0[0]: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 45.54/45.98 Y ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Y
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 paramod: (65095) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 45.54/45.98 multiplication( addition( Z, X ), Y ), leq( multiplication( Z, Y ),
% 45.54/45.98 multiplication( X, Y ) ) }.
% 45.54/45.98 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 45.54/45.98 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 45.54/45.98 parent1[0; 5]: (65094) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 45.54/45.98 ( X, Y ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := Z
% 45.54/45.98 Y := X
% 45.54/45.98 Z := Y
% 45.54/45.98 end
% 45.54/45.98 substitution1:
% 45.54/45.98 X := multiplication( Z, Y )
% 45.54/45.98 Y := multiplication( X, Y )
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 eqswap: (65096) {G1,W16,D4,L2,V3,M2} { ! multiplication( addition( Z, X )
% 45.54/45.98 , Y ) ==> multiplication( X, Y ), leq( multiplication( Z, Y ),
% 45.54/45.98 multiplication( X, Y ) ) }.
% 45.54/45.98 parent0[0]: (65095) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 45.54/45.98 multiplication( addition( Z, X ), Y ), leq( multiplication( Z, Y ),
% 45.54/45.98 multiplication( X, Y ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Y
% 45.54/45.98 Z := Z
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 subsumption: (99) {G1,W16,D4,L2,V3,M2} P(8,18) { ! multiplication( addition
% 45.54/45.98 ( X, Z ), Y ) ==> multiplication( Z, Y ), leq( multiplication( X, Y ),
% 45.54/45.98 multiplication( Z, Y ) ) }.
% 45.54/45.98 parent0: (65096) {G1,W16,D4,L2,V3,M2} { ! multiplication( addition( Z, X )
% 45.54/45.98 , Y ) ==> multiplication( X, Y ), leq( multiplication( Z, Y ),
% 45.54/45.98 multiplication( X, Y ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := Z
% 45.54/45.98 Y := Y
% 45.54/45.98 Z := X
% 45.54/45.98 end
% 45.54/45.98 permutation0:
% 45.54/45.98 0 ==> 0
% 45.54/45.98 1 ==> 1
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 eqswap: (65097) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Z ), Y
% 45.54/45.98 ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) ) }.
% 45.54/45.98 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 45.54/45.98 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Z
% 45.54/45.98 Z := Y
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 paramod: (65099) {G1,W13,D4,L1,V3,M1} { multiplication( addition( Y, X ),
% 45.54/45.98 Z ) ==> addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 45.54/45.98 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 45.54/45.98 }.
% 45.54/45.98 parent1[0; 2]: (65097) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X
% 45.54/45.98 , Z ), Y ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) )
% 45.54/45.98 }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Y
% 45.54/45.98 end
% 45.54/45.98 substitution1:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Z
% 45.54/45.98 Z := Y
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 paramod: (65101) {G1,W11,D4,L1,V3,M1} { multiplication( addition( X, Y ),
% 45.54/45.98 Z ) ==> multiplication( addition( Y, X ), Z ) }.
% 45.54/45.98 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 45.54/45.98 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 45.54/45.98 parent1[0; 6]: (65099) {G1,W13,D4,L1,V3,M1} { multiplication( addition( Y
% 45.54/45.98 , X ), Z ) ==> addition( multiplication( X, Z ), multiplication( Y, Z ) )
% 45.54/45.98 }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := Y
% 45.54/45.98 Y := X
% 45.54/45.98 Z := Z
% 45.54/45.98 end
% 45.54/45.98 substitution1:
% 45.54/45.98 X := Y
% 45.54/45.98 Y := X
% 45.54/45.98 Z := Z
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 subsumption: (100) {G1,W11,D4,L1,V3,M1} P(8,0);d(8) { multiplication(
% 45.54/45.98 addition( X, Z ), Y ) = multiplication( addition( Z, X ), Y ) }.
% 45.54/45.98 parent0: (65101) {G1,W11,D4,L1,V3,M1} { multiplication( addition( X, Y ),
% 45.54/45.98 Z ) ==> multiplication( addition( Y, X ), Z ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Z
% 45.54/45.98 Z := Y
% 45.54/45.98 end
% 45.54/45.98 permutation0:
% 45.54/45.98 0 ==> 0
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 paramod: (65104) {G1,W12,D4,L2,V1,M2} { ! leq( strong_iteration( X ),
% 45.54/45.98 strong_iteration( X ) ), leq( multiplication( star( X ), one ),
% 45.54/45.98 strong_iteration( X ) ) }.
% 45.54/45.98 parent0[0]: (14) {G0,W9,D5,L1,V1,M1} I { addition( multiplication( X,
% 45.54/45.98 strong_iteration( X ) ), one ) ==> strong_iteration( X ) }.
% 45.54/45.98 parent1[0; 2]: (12) {G0,W13,D4,L2,V3,M2} I { ! leq( addition(
% 45.54/45.98 multiplication( X, Z ), Y ), Z ), leq( multiplication( star( X ), Y ), Z
% 45.54/45.98 ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 end
% 45.54/45.98 substitution1:
% 45.54/45.98 X := X
% 45.54/45.98 Y := one
% 45.54/45.98 Z := strong_iteration( X )
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 paramod: (65105) {G1,W10,D3,L2,V1,M2} { leq( star( X ), strong_iteration(
% 45.54/45.98 X ) ), ! leq( strong_iteration( X ), strong_iteration( X ) ) }.
% 45.54/45.98 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 45.54/45.98 parent1[1; 1]: (65104) {G1,W12,D4,L2,V1,M2} { ! leq( strong_iteration( X )
% 45.54/45.98 , strong_iteration( X ) ), leq( multiplication( star( X ), one ),
% 45.54/45.98 strong_iteration( X ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := star( X )
% 45.54/45.98 end
% 45.54/45.98 substitution1:
% 45.54/45.98 X := X
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 resolution: (65106) {G2,W5,D3,L1,V1,M1} { leq( star( X ), strong_iteration
% 45.54/45.98 ( X ) ) }.
% 45.54/45.98 parent0[1]: (65105) {G1,W10,D3,L2,V1,M2} { leq( star( X ),
% 45.54/45.98 strong_iteration( X ) ), ! leq( strong_iteration( X ), strong_iteration(
% 45.54/45.98 X ) ) }.
% 45.54/45.98 parent1[0]: (22) {G1,W3,D2,L1,V1,M1} R(18,3) { leq( X, X ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 end
% 45.54/45.98 substitution1:
% 45.54/45.98 X := strong_iteration( X )
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 subsumption: (213) {G2,W5,D3,L1,V1,M1} P(14,12);d(5);r(22) { leq( star( X )
% 45.54/45.98 , strong_iteration( X ) ) }.
% 45.54/45.98 parent0: (65106) {G2,W5,D3,L1,V1,M1} { leq( star( X ), strong_iteration( X
% 45.54/45.98 ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 end
% 45.54/45.98 permutation0:
% 45.54/45.98 0 ==> 0
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 eqswap: (65107) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 45.54/45.98 ) }.
% 45.54/45.98 parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 45.54/45.98 ==> Y }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Y
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 resolution: (65108) {G1,W8,D4,L1,V1,M1} { strong_iteration( X ) ==>
% 45.54/45.98 addition( star( X ), strong_iteration( X ) ) }.
% 45.54/45.98 parent0[1]: (65107) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X
% 45.54/45.98 , Y ) }.
% 45.54/45.98 parent1[0]: (213) {G2,W5,D3,L1,V1,M1} P(14,12);d(5);r(22) { leq( star( X )
% 45.54/45.98 , strong_iteration( X ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := star( X )
% 45.54/45.98 Y := strong_iteration( X )
% 45.54/45.98 end
% 45.54/45.98 substitution1:
% 45.54/45.98 X := X
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 eqswap: (65109) {G1,W8,D4,L1,V1,M1} { addition( star( X ),
% 45.54/45.98 strong_iteration( X ) ) ==> strong_iteration( X ) }.
% 45.54/45.98 parent0[0]: (65108) {G1,W8,D4,L1,V1,M1} { strong_iteration( X ) ==>
% 45.54/45.98 addition( star( X ), strong_iteration( X ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 subsumption: (226) {G3,W8,D4,L1,V1,M1} R(213,17) { addition( star( X ),
% 45.54/45.98 strong_iteration( X ) ) ==> strong_iteration( X ) }.
% 45.54/45.98 parent0: (65109) {G1,W8,D4,L1,V1,M1} { addition( star( X ),
% 45.54/45.98 strong_iteration( X ) ) ==> strong_iteration( X ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 end
% 45.54/45.98 permutation0:
% 45.54/45.98 0 ==> 0
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 eqswap: (65110) {G0,W10,D5,L1,V1,M1} { strong_iteration( X ) ==> addition
% 45.54/45.98 ( star( X ), multiplication( strong_iteration( X ), zero ) ) }.
% 45.54/45.98 parent0[0]: (16) {G0,W10,D5,L1,V1,M1} I { addition( star( X ),
% 45.54/45.98 multiplication( strong_iteration( X ), zero ) ) ==> strong_iteration( X )
% 45.54/45.98 }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 paramod: (65111) {G1,W10,D5,L1,V1,M1} { strong_iteration( X ) ==> addition
% 45.54/45.98 ( multiplication( strong_iteration( X ), zero ), star( X ) ) }.
% 45.54/45.98 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 45.54/45.98 }.
% 45.54/45.98 parent1[0; 3]: (65110) {G0,W10,D5,L1,V1,M1} { strong_iteration( X ) ==>
% 45.54/45.98 addition( star( X ), multiplication( strong_iteration( X ), zero ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := star( X )
% 45.54/45.98 Y := multiplication( strong_iteration( X ), zero )
% 45.54/45.98 end
% 45.54/45.98 substitution1:
% 45.54/45.98 X := X
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 eqswap: (65114) {G1,W10,D5,L1,V1,M1} { addition( multiplication(
% 45.54/45.98 strong_iteration( X ), zero ), star( X ) ) ==> strong_iteration( X ) }.
% 45.54/45.98 parent0[0]: (65111) {G1,W10,D5,L1,V1,M1} { strong_iteration( X ) ==>
% 45.54/45.98 addition( multiplication( strong_iteration( X ), zero ), star( X ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 subsumption: (285) {G1,W10,D5,L1,V1,M1} P(16,0) { addition( multiplication
% 45.54/45.98 ( strong_iteration( X ), zero ), star( X ) ) ==> strong_iteration( X )
% 45.54/45.98 }.
% 45.54/45.98 parent0: (65114) {G1,W10,D5,L1,V1,M1} { addition( multiplication(
% 45.54/45.98 strong_iteration( X ), zero ), star( X ) ) ==> strong_iteration( X ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 end
% 45.54/45.98 permutation0:
% 45.54/45.98 0 ==> 0
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 eqswap: (65115) {G0,W9,D5,L1,V0,M1} { ! strong_iteration( skol1 ) ==>
% 45.54/45.98 addition( multiplication( strong_iteration( skol1 ), skol1 ), one ) }.
% 45.54/45.98 parent0[0]: (19) {G0,W9,D5,L1,V0,M1} I { ! addition( multiplication(
% 45.54/45.98 strong_iteration( skol1 ), skol1 ), one ) ==> strong_iteration( skol1 )
% 45.54/45.98 }.
% 45.54/45.98 substitution0:
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 paramod: (65116) {G1,W9,D5,L1,V0,M1} { ! strong_iteration( skol1 ) ==>
% 45.54/45.98 addition( one, multiplication( strong_iteration( skol1 ), skol1 ) ) }.
% 45.54/45.98 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 45.54/45.98 }.
% 45.54/45.98 parent1[0; 4]: (65115) {G0,W9,D5,L1,V0,M1} { ! strong_iteration( skol1 )
% 45.54/45.98 ==> addition( multiplication( strong_iteration( skol1 ), skol1 ), one )
% 45.54/45.98 }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := multiplication( strong_iteration( skol1 ), skol1 )
% 45.54/45.98 Y := one
% 45.54/45.98 end
% 45.54/45.98 substitution1:
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 eqswap: (65119) {G1,W9,D5,L1,V0,M1} { ! addition( one, multiplication(
% 45.54/45.98 strong_iteration( skol1 ), skol1 ) ) ==> strong_iteration( skol1 ) }.
% 45.54/45.98 parent0[0]: (65116) {G1,W9,D5,L1,V0,M1} { ! strong_iteration( skol1 ) ==>
% 45.54/45.98 addition( one, multiplication( strong_iteration( skol1 ), skol1 ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 subsumption: (312) {G1,W9,D5,L1,V0,M1} P(0,19) { ! addition( one,
% 45.54/45.98 multiplication( strong_iteration( skol1 ), skol1 ) ) ==> strong_iteration
% 45.54/45.98 ( skol1 ) }.
% 45.54/45.98 parent0: (65119) {G1,W9,D5,L1,V0,M1} { ! addition( one, multiplication(
% 45.54/45.98 strong_iteration( skol1 ), skol1 ) ) ==> strong_iteration( skol1 ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 end
% 45.54/45.98 permutation0:
% 45.54/45.98 0 ==> 0
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 eqswap: (65121) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==> addition(
% 45.54/45.98 addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 45.54/45.98 parent0[0]: (25) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y
% 45.54/45.98 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Y
% 45.54/45.98 Z := Z
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 paramod: (65124) {G1,W15,D3,L3,V3,M3} { ! addition( X, Y ) ==> addition( X
% 45.54/45.98 , Y ), ! leq( Z, X ), leq( Z, addition( X, Y ) ) }.
% 45.54/45.98 parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 45.54/45.98 ==> Y }.
% 45.54/45.98 parent1[0; 6]: (65121) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==>
% 45.54/45.98 addition( addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := Z
% 45.54/45.98 Y := X
% 45.54/45.98 end
% 45.54/45.98 substitution1:
% 45.54/45.98 X := Z
% 45.54/45.98 Y := X
% 45.54/45.98 Z := Y
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 eqrefl: (65173) {G0,W8,D3,L2,V3,M2} { ! leq( Z, X ), leq( Z, addition( X,
% 45.54/45.98 Y ) ) }.
% 45.54/45.98 parent0[0]: (65124) {G1,W15,D3,L3,V3,M3} { ! addition( X, Y ) ==> addition
% 45.54/45.98 ( X, Y ), ! leq( Z, X ), leq( Z, addition( X, Y ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Y
% 45.54/45.98 Z := Z
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 subsumption: (328) {G2,W8,D3,L2,V3,M2} P(17,25);q { leq( X, addition( Y, Z
% 45.54/45.98 ) ), ! leq( X, Y ) }.
% 45.54/45.98 parent0: (65173) {G0,W8,D3,L2,V3,M2} { ! leq( Z, X ), leq( Z, addition( X
% 45.54/45.98 , Y ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := Y
% 45.54/45.98 Y := Z
% 45.54/45.98 Z := X
% 45.54/45.98 end
% 45.54/45.98 permutation0:
% 45.54/45.98 0 ==> 1
% 45.54/45.98 1 ==> 0
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 eqswap: (65175) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==> addition(
% 45.54/45.98 addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 45.54/45.98 parent0[0]: (25) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y
% 45.54/45.98 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Y
% 45.54/45.98 Z := Z
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 paramod: (65178) {G1,W12,D3,L2,V2,M2} { ! addition( X, Y ) ==> addition( X
% 45.54/45.98 , Y ), leq( X, addition( X, Y ) ) }.
% 45.54/45.98 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 45.54/45.98 parent1[0; 6]: (65175) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==>
% 45.54/45.98 addition( addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 end
% 45.54/45.98 substitution1:
% 45.54/45.98 X := X
% 45.54/45.98 Y := X
% 45.54/45.98 Z := Y
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 eqrefl: (65181) {G0,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 45.54/45.98 parent0[0]: (65178) {G1,W12,D3,L2,V2,M2} { ! addition( X, Y ) ==> addition
% 45.54/45.98 ( X, Y ), leq( X, addition( X, Y ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Y
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 subsumption: (332) {G2,W5,D3,L1,V2,M1} P(3,25);q { leq( X, addition( X, Y )
% 45.54/45.98 ) }.
% 45.54/45.98 parent0: (65181) {G0,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Y
% 45.54/45.98 end
% 45.54/45.98 permutation0:
% 45.54/45.98 0 ==> 0
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 paramod: (65182) {G1,W5,D3,L1,V2,M1} { leq( X, addition( Y, X ) ) }.
% 45.54/45.98 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 45.54/45.98 }.
% 45.54/45.98 parent1[0; 2]: (332) {G2,W5,D3,L1,V2,M1} P(3,25);q { leq( X, addition( X, Y
% 45.54/45.98 ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Y
% 45.54/45.98 end
% 45.54/45.98 substitution1:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Y
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 subsumption: (371) {G3,W5,D3,L1,V2,M1} P(0,332) { leq( X, addition( Y, X )
% 45.54/45.98 ) }.
% 45.54/45.98 parent0: (65182) {G1,W5,D3,L1,V2,M1} { leq( X, addition( Y, X ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Y
% 45.54/45.98 end
% 45.54/45.98 permutation0:
% 45.54/45.98 0 ==> 0
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 paramod: (65185) {G1,W7,D4,L1,V1,M1} { leq( multiplication( star( X ), X )
% 45.54/45.98 , star( X ) ) }.
% 45.54/45.98 parent0[0]: (11) {G0,W9,D5,L1,V1,M1} I { addition( one, multiplication(
% 45.54/45.98 star( X ), X ) ) ==> star( X ) }.
% 45.54/45.98 parent1[0; 5]: (371) {G3,W5,D3,L1,V2,M1} P(0,332) { leq( X, addition( Y, X
% 45.54/45.98 ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 end
% 45.54/45.98 substitution1:
% 45.54/45.98 X := multiplication( star( X ), X )
% 45.54/45.98 Y := one
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 subsumption: (377) {G4,W7,D4,L1,V1,M1} P(11,371) { leq( multiplication(
% 45.54/45.98 star( X ), X ), star( X ) ) }.
% 45.54/45.98 parent0: (65185) {G1,W7,D4,L1,V1,M1} { leq( multiplication( star( X ), X )
% 45.54/45.98 , star( X ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 end
% 45.54/45.98 permutation0:
% 45.54/45.98 0 ==> 0
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 paramod: (65188) {G1,W14,D5,L1,V2,M1} { addition( addition( star( X ), Y )
% 45.54/45.98 , multiplication( strong_iteration( X ), zero ) ) = addition(
% 45.54/45.98 strong_iteration( X ), Y ) }.
% 45.54/45.98 parent0[0]: (16) {G0,W10,D5,L1,V1,M1} I { addition( star( X ),
% 45.54/45.98 multiplication( strong_iteration( X ), zero ) ) ==> strong_iteration( X )
% 45.54/45.98 }.
% 45.54/45.98 parent1[0; 11]: (27) {G1,W11,D4,L1,V3,M1} P(0,1);d(1) { addition( addition
% 45.54/45.98 ( Z, Y ), X ) = addition( addition( Z, X ), Y ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 end
% 45.54/45.98 substitution1:
% 45.54/45.98 X := multiplication( strong_iteration( X ), zero )
% 45.54/45.98 Y := Y
% 45.54/45.98 Z := star( X )
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 subsumption: (389) {G2,W14,D5,L1,V2,M1} P(16,27) { addition( addition( star
% 45.54/45.98 ( X ), Y ), multiplication( strong_iteration( X ), zero ) ) ==> addition
% 45.54/45.98 ( strong_iteration( X ), Y ) }.
% 45.54/45.98 parent0: (65188) {G1,W14,D5,L1,V2,M1} { addition( addition( star( X ), Y )
% 45.54/45.98 , multiplication( strong_iteration( X ), zero ) ) = addition(
% 45.54/45.98 strong_iteration( X ), Y ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Y
% 45.54/45.98 end
% 45.54/45.98 permutation0:
% 45.54/45.98 0 ==> 0
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 eqswap: (65190) {G1,W12,D4,L2,V3,M2} { addition( X, Z ) ==> addition(
% 45.54/45.98 addition( X, Y ), Z ), ! leq( Y, Z ) }.
% 45.54/45.98 parent0[0]: (35) {G1,W12,D4,L2,V3,M2} P(17,1) { addition( addition( Z, X )
% 45.54/45.98 , Y ) ==> addition( Z, Y ), ! leq( X, Y ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := Y
% 45.54/45.98 Y := Z
% 45.54/45.98 Z := X
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 paramod: (65192) {G1,W15,D4,L2,V2,M2} { addition( star( X ), Y ) ==>
% 45.54/45.98 addition( strong_iteration( X ), Y ), ! leq( multiplication(
% 45.54/45.98 strong_iteration( X ), zero ), Y ) }.
% 45.54/45.98 parent0[0]: (16) {G0,W10,D5,L1,V1,M1} I { addition( star( X ),
% 45.54/45.98 multiplication( strong_iteration( X ), zero ) ) ==> strong_iteration( X )
% 45.54/45.98 }.
% 45.54/45.98 parent1[0; 6]: (65190) {G1,W12,D4,L2,V3,M2} { addition( X, Z ) ==>
% 45.54/45.98 addition( addition( X, Y ), Z ), ! leq( Y, Z ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 end
% 45.54/45.98 substitution1:
% 45.54/45.98 X := star( X )
% 45.54/45.98 Y := multiplication( strong_iteration( X ), zero )
% 45.54/45.98 Z := Y
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 eqswap: (65194) {G1,W15,D4,L2,V2,M2} { addition( strong_iteration( X ), Y
% 45.54/45.98 ) ==> addition( star( X ), Y ), ! leq( multiplication( strong_iteration
% 45.54/45.98 ( X ), zero ), Y ) }.
% 45.54/45.98 parent0[0]: (65192) {G1,W15,D4,L2,V2,M2} { addition( star( X ), Y ) ==>
% 45.54/45.98 addition( strong_iteration( X ), Y ), ! leq( multiplication(
% 45.54/45.98 strong_iteration( X ), zero ), Y ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Y
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 subsumption: (571) {G2,W15,D4,L2,V2,M2} P(16,35) { addition(
% 45.54/45.98 strong_iteration( X ), Y ) ==> addition( star( X ), Y ), ! leq(
% 45.54/45.98 multiplication( strong_iteration( X ), zero ), Y ) }.
% 45.54/45.98 parent0: (65194) {G1,W15,D4,L2,V2,M2} { addition( strong_iteration( X ), Y
% 45.54/45.98 ) ==> addition( star( X ), Y ), ! leq( multiplication( strong_iteration
% 45.54/45.98 ( X ), zero ), Y ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Y
% 45.54/45.98 end
% 45.54/45.98 permutation0:
% 45.54/45.98 0 ==> 0
% 45.54/45.98 1 ==> 1
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 eqswap: (65196) {G1,W12,D4,L2,V3,M2} { addition( X, Z ) ==> addition(
% 45.54/45.98 addition( X, Y ), Z ), ! leq( Y, Z ) }.
% 45.54/45.98 parent0[0]: (35) {G1,W12,D4,L2,V3,M2} P(17,1) { addition( addition( Z, X )
% 45.54/45.98 , Y ) ==> addition( Z, Y ), ! leq( X, Y ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := Y
% 45.54/45.98 Y := Z
% 45.54/45.98 Z := X
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 paramod: (65198) {G1,W14,D4,L2,V2,M2} { addition( one, X ) ==> addition(
% 45.54/45.98 star( Y ), X ), ! leq( multiplication( star( Y ), Y ), X ) }.
% 45.54/45.98 parent0[0]: (11) {G0,W9,D5,L1,V1,M1} I { addition( one, multiplication(
% 45.54/45.98 star( X ), X ) ) ==> star( X ) }.
% 45.54/45.98 parent1[0; 5]: (65196) {G1,W12,D4,L2,V3,M2} { addition( X, Z ) ==>
% 45.54/45.98 addition( addition( X, Y ), Z ), ! leq( Y, Z ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := Y
% 45.54/45.98 end
% 45.54/45.98 substitution1:
% 45.54/45.98 X := one
% 45.54/45.98 Y := multiplication( star( Y ), Y )
% 45.54/45.98 Z := X
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 eqswap: (65200) {G1,W14,D4,L2,V2,M2} { addition( star( Y ), X ) ==>
% 45.54/45.98 addition( one, X ), ! leq( multiplication( star( Y ), Y ), X ) }.
% 45.54/45.98 parent0[0]: (65198) {G1,W14,D4,L2,V2,M2} { addition( one, X ) ==> addition
% 45.54/45.98 ( star( Y ), X ), ! leq( multiplication( star( Y ), Y ), X ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Y
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 subsumption: (574) {G2,W14,D4,L2,V2,M2} P(11,35) { addition( star( X ), Y )
% 45.54/45.98 ==> addition( one, Y ), ! leq( multiplication( star( X ), X ), Y ) }.
% 45.54/45.98 parent0: (65200) {G1,W14,D4,L2,V2,M2} { addition( star( Y ), X ) ==>
% 45.54/45.98 addition( one, X ), ! leq( multiplication( star( Y ), Y ), X ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := Y
% 45.54/45.98 Y := X
% 45.54/45.98 end
% 45.54/45.98 permutation0:
% 45.54/45.98 0 ==> 0
% 45.54/45.98 1 ==> 1
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 eqswap: (65202) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Z ), Y
% 45.54/45.98 ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) ) }.
% 45.54/45.98 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 45.54/45.98 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Z
% 45.54/45.98 Z := Y
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 paramod: (65204) {G1,W15,D5,L1,V3,M1} { multiplication( addition( X,
% 45.54/45.98 multiplication( Y, zero ) ), Z ) ==> addition( multiplication( X, Z ),
% 45.54/45.98 multiplication( Y, zero ) ) }.
% 45.54/45.98 parent0[0]: (50) {G1,W9,D4,L1,V2,M1} P(9,4) { multiplication(
% 45.54/45.98 multiplication( Y, zero ), X ) ==> multiplication( Y, zero ) }.
% 45.54/45.98 parent1[0; 12]: (65202) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X
% 45.54/45.98 , Z ), Y ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) )
% 45.54/45.98 }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := Z
% 45.54/45.98 Y := Y
% 45.54/45.98 end
% 45.54/45.98 substitution1:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Z
% 45.54/45.98 Z := multiplication( Y, zero )
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 subsumption: (812) {G2,W15,D5,L1,V3,M1} P(50,8) { multiplication( addition
% 45.54/45.98 ( Z, multiplication( X, zero ) ), Y ) ==> addition( multiplication( Z, Y
% 45.54/45.98 ), multiplication( X, zero ) ) }.
% 45.54/45.98 parent0: (65204) {G1,W15,D5,L1,V3,M1} { multiplication( addition( X,
% 45.54/45.98 multiplication( Y, zero ) ), Z ) ==> addition( multiplication( X, Z ),
% 45.54/45.98 multiplication( Y, zero ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := Z
% 45.54/45.98 Y := X
% 45.54/45.98 Z := Y
% 45.54/45.98 end
% 45.54/45.98 permutation0:
% 45.54/45.98 0 ==> 0
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 paramod: (65208) {G1,W8,D3,L2,V2,M2} { leq( X, strong_iteration( Y ) ), !
% 45.54/45.98 leq( X, star( Y ) ) }.
% 45.54/45.98 parent0[0]: (16) {G0,W10,D5,L1,V1,M1} I { addition( star( X ),
% 45.54/45.98 multiplication( strong_iteration( X ), zero ) ) ==> strong_iteration( X )
% 45.54/45.98 }.
% 45.54/45.98 parent1[0; 2]: (328) {G2,W8,D3,L2,V3,M2} P(17,25);q { leq( X, addition( Y,
% 45.54/45.98 Z ) ), ! leq( X, Y ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := Y
% 45.54/45.98 end
% 45.54/45.98 substitution1:
% 45.54/45.98 X := X
% 45.54/45.98 Y := star( Y )
% 45.54/45.98 Z := multiplication( strong_iteration( Y ), zero )
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 subsumption: (1101) {G3,W8,D3,L2,V2,M2} P(16,328) { leq( Y,
% 45.54/45.98 strong_iteration( X ) ), ! leq( Y, star( X ) ) }.
% 45.54/45.98 parent0: (65208) {G1,W8,D3,L2,V2,M2} { leq( X, strong_iteration( Y ) ), !
% 45.54/45.98 leq( X, star( Y ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := Y
% 45.54/45.98 Y := X
% 45.54/45.98 end
% 45.54/45.98 permutation0:
% 45.54/45.98 0 ==> 0
% 45.54/45.98 1 ==> 1
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 resolution: (65209) {G4,W7,D4,L1,V1,M1} { leq( multiplication( star( X ),
% 45.54/45.98 X ), strong_iteration( X ) ) }.
% 45.54/45.98 parent0[1]: (1101) {G3,W8,D3,L2,V2,M2} P(16,328) { leq( Y, strong_iteration
% 45.54/45.98 ( X ) ), ! leq( Y, star( X ) ) }.
% 45.54/45.98 parent1[0]: (377) {G4,W7,D4,L1,V1,M1} P(11,371) { leq( multiplication( star
% 45.54/45.98 ( X ), X ), star( X ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := multiplication( star( X ), X )
% 45.54/45.98 end
% 45.54/45.98 substitution1:
% 45.54/45.98 X := X
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 subsumption: (1111) {G5,W7,D4,L1,V1,M1} R(1101,377) { leq( multiplication(
% 45.54/45.98 star( X ), X ), strong_iteration( X ) ) }.
% 45.54/45.98 parent0: (65209) {G4,W7,D4,L1,V1,M1} { leq( multiplication( star( X ), X )
% 45.54/45.98 , strong_iteration( X ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 end
% 45.54/45.98 permutation0:
% 45.54/45.98 0 ==> 0
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 eqswap: (65210) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X
% 45.54/45.98 ) }.
% 45.54/45.98 parent0[0]: (36) {G1,W8,D3,L2,V2,M2} P(17,0) { addition( Y, X ) ==> Y, !
% 45.54/45.98 leq( X, Y ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := Y
% 45.54/45.98 Y := X
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 resolution: (65211) {G2,W10,D5,L1,V1,M1} { strong_iteration( X ) ==>
% 45.54/45.98 addition( strong_iteration( X ), multiplication( star( X ), X ) ) }.
% 45.54/45.98 parent0[1]: (65210) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y
% 45.54/45.98 , X ) }.
% 45.54/45.98 parent1[0]: (1111) {G5,W7,D4,L1,V1,M1} R(1101,377) { leq( multiplication(
% 45.54/45.98 star( X ), X ), strong_iteration( X ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := strong_iteration( X )
% 45.54/45.98 Y := multiplication( star( X ), X )
% 45.54/45.98 end
% 45.54/45.98 substitution1:
% 45.54/45.98 X := X
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 eqswap: (65212) {G2,W10,D5,L1,V1,M1} { addition( strong_iteration( X ),
% 45.54/45.98 multiplication( star( X ), X ) ) ==> strong_iteration( X ) }.
% 45.54/45.98 parent0[0]: (65211) {G2,W10,D5,L1,V1,M1} { strong_iteration( X ) ==>
% 45.54/45.98 addition( strong_iteration( X ), multiplication( star( X ), X ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 subsumption: (1128) {G6,W10,D5,L1,V1,M1} R(1111,36) { addition(
% 45.54/45.98 strong_iteration( X ), multiplication( star( X ), X ) ) ==>
% 45.54/45.98 strong_iteration( X ) }.
% 45.54/45.98 parent0: (65212) {G2,W10,D5,L1,V1,M1} { addition( strong_iteration( X ),
% 45.54/45.98 multiplication( star( X ), X ) ) ==> strong_iteration( X ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 end
% 45.54/45.98 permutation0:
% 45.54/45.98 0 ==> 0
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 eqswap: (65214) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Z ) ==>
% 45.54/45.98 multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ),
% 45.54/45.98 multiplication( X, Z ) ) }.
% 45.54/45.98 parent0[0]: (67) {G1,W16,D4,L2,V3,M2} P(7,18) { ! multiplication( X,
% 45.54/45.98 addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 45.54/45.98 ), multiplication( X, Z ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Y
% 45.54/45.98 Z := Z
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 paramod: (65215) {G2,W14,D3,L2,V2,M2} { ! multiplication( X, Y ) ==>
% 45.54/45.98 multiplication( X, Y ), leq( multiplication( X, zero ), multiplication( X
% 45.54/45.98 , Y ) ) }.
% 45.54/45.98 parent0[0]: (20) {G1,W5,D3,L1,V1,M1} P(0,2) { addition( zero, X ) ==> X }.
% 45.54/45.98 parent1[0; 7]: (65214) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Z ) ==>
% 45.54/45.98 multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ),
% 45.54/45.98 multiplication( X, Z ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := Y
% 45.54/45.98 end
% 45.54/45.98 substitution1:
% 45.54/45.98 X := X
% 45.54/45.98 Y := zero
% 45.54/45.98 Z := Y
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 eqrefl: (65216) {G0,W7,D3,L1,V2,M1} { leq( multiplication( X, zero ),
% 45.54/45.98 multiplication( X, Y ) ) }.
% 45.54/45.98 parent0[0]: (65215) {G2,W14,D3,L2,V2,M2} { ! multiplication( X, Y ) ==>
% 45.54/45.98 multiplication( X, Y ), leq( multiplication( X, zero ), multiplication( X
% 45.54/45.98 , Y ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Y
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 subsumption: (1632) {G2,W7,D3,L1,V2,M1} P(20,67);q { leq( multiplication( Y
% 45.54/45.98 , zero ), multiplication( Y, X ) ) }.
% 45.54/45.98 parent0: (65216) {G0,W7,D3,L1,V2,M1} { leq( multiplication( X, zero ),
% 45.54/45.98 multiplication( X, Y ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := Y
% 45.54/45.98 Y := X
% 45.54/45.98 end
% 45.54/45.98 permutation0:
% 45.54/45.98 0 ==> 0
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 eqswap: (65218) {G1,W16,D4,L2,V3,M2} { ! multiplication( Y, Z ) ==>
% 45.54/45.98 multiplication( addition( X, Y ), Z ), leq( multiplication( X, Z ),
% 45.54/45.98 multiplication( Y, Z ) ) }.
% 45.54/45.98 parent0[0]: (99) {G1,W16,D4,L2,V3,M2} P(8,18) { ! multiplication( addition
% 45.54/45.98 ( X, Z ), Y ) ==> multiplication( Z, Y ), leq( multiplication( X, Y ),
% 45.54/45.98 multiplication( Z, Y ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Z
% 45.54/45.98 Z := Y
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 paramod: (65219) {G2,W18,D4,L2,V2,M2} { ! multiplication( strong_iteration
% 45.54/45.98 ( X ), Y ) ==> multiplication( strong_iteration( X ), Y ), leq(
% 45.54/45.98 multiplication( star( X ), Y ), multiplication( strong_iteration( X ), Y
% 45.54/45.98 ) ) }.
% 45.54/45.98 parent0[0]: (226) {G3,W8,D4,L1,V1,M1} R(213,17) { addition( star( X ),
% 45.54/45.98 strong_iteration( X ) ) ==> strong_iteration( X ) }.
% 45.54/45.98 parent1[0; 7]: (65218) {G1,W16,D4,L2,V3,M2} { ! multiplication( Y, Z ) ==>
% 45.54/45.98 multiplication( addition( X, Y ), Z ), leq( multiplication( X, Z ),
% 45.54/45.98 multiplication( Y, Z ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 end
% 45.54/45.98 substitution1:
% 45.54/45.98 X := star( X )
% 45.54/45.98 Y := strong_iteration( X )
% 45.54/45.98 Z := Y
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 eqrefl: (65220) {G0,W9,D4,L1,V2,M1} { leq( multiplication( star( X ), Y )
% 45.54/45.98 , multiplication( strong_iteration( X ), Y ) ) }.
% 45.54/45.98 parent0[0]: (65219) {G2,W18,D4,L2,V2,M2} { ! multiplication(
% 45.54/45.98 strong_iteration( X ), Y ) ==> multiplication( strong_iteration( X ), Y )
% 45.54/45.98 , leq( multiplication( star( X ), Y ), multiplication( strong_iteration(
% 45.54/45.98 X ), Y ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Y
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 subsumption: (5228) {G4,W9,D4,L1,V2,M1} P(226,99);q { leq( multiplication(
% 45.54/45.98 star( X ), Y ), multiplication( strong_iteration( X ), Y ) ) }.
% 45.54/45.98 parent0: (65220) {G0,W9,D4,L1,V2,M1} { leq( multiplication( star( X ), Y )
% 45.54/45.98 , multiplication( strong_iteration( X ), Y ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Y
% 45.54/45.98 end
% 45.54/45.98 permutation0:
% 45.54/45.98 0 ==> 0
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 paramod: (65224) {G2,W14,D6,L1,V2,M1} { multiplication( addition( star( X
% 45.54/45.98 ), multiplication( strong_iteration( X ), zero ) ), Y ) = multiplication
% 45.54/45.98 ( strong_iteration( X ), Y ) }.
% 45.54/45.98 parent0[0]: (285) {G1,W10,D5,L1,V1,M1} P(16,0) { addition( multiplication(
% 45.54/45.98 strong_iteration( X ), zero ), star( X ) ) ==> strong_iteration( X ) }.
% 45.54/45.98 parent1[0; 11]: (100) {G1,W11,D4,L1,V3,M1} P(8,0);d(8) { multiplication(
% 45.54/45.98 addition( X, Z ), Y ) = multiplication( addition( Z, X ), Y ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 end
% 45.54/45.98 substitution1:
% 45.54/45.98 X := star( X )
% 45.54/45.98 Y := Y
% 45.54/45.98 Z := multiplication( strong_iteration( X ), zero )
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 paramod: (65225) {G3,W14,D5,L1,V2,M1} { addition( multiplication( star( X
% 45.54/45.98 ), Y ), multiplication( strong_iteration( X ), zero ) ) = multiplication
% 45.54/45.98 ( strong_iteration( X ), Y ) }.
% 45.54/45.98 parent0[0]: (812) {G2,W15,D5,L1,V3,M1} P(50,8) { multiplication( addition(
% 45.54/45.98 Z, multiplication( X, zero ) ), Y ) ==> addition( multiplication( Z, Y )
% 45.54/45.98 , multiplication( X, zero ) ) }.
% 45.54/45.98 parent1[0; 1]: (65224) {G2,W14,D6,L1,V2,M1} { multiplication( addition(
% 45.54/45.98 star( X ), multiplication( strong_iteration( X ), zero ) ), Y ) =
% 45.54/45.98 multiplication( strong_iteration( X ), Y ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := strong_iteration( X )
% 45.54/45.98 Y := Y
% 45.54/45.98 Z := star( X )
% 45.54/45.98 end
% 45.54/45.98 substitution1:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Y
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 subsumption: (12374) {G3,W14,D5,L1,V2,M1} P(285,100);d(812) { addition(
% 45.54/45.98 multiplication( star( X ), Y ), multiplication( strong_iteration( X ),
% 45.54/45.98 zero ) ) ==> multiplication( strong_iteration( X ), Y ) }.
% 45.54/45.98 parent0: (65225) {G3,W14,D5,L1,V2,M1} { addition( multiplication( star( X
% 45.54/45.98 ), Y ), multiplication( strong_iteration( X ), zero ) ) = multiplication
% 45.54/45.98 ( strong_iteration( X ), Y ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Y
% 45.54/45.98 end
% 45.54/45.98 permutation0:
% 45.54/45.98 0 ==> 0
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 eqswap: (65228) {G2,W14,D5,L1,V2,M1} { addition( strong_iteration( X ), Y
% 45.54/45.98 ) ==> addition( addition( star( X ), Y ), multiplication(
% 45.54/45.98 strong_iteration( X ), zero ) ) }.
% 45.54/45.98 parent0[0]: (389) {G2,W14,D5,L1,V2,M1} P(16,27) { addition( addition( star
% 45.54/45.98 ( X ), Y ), multiplication( strong_iteration( X ), zero ) ) ==> addition
% 45.54/45.98 ( strong_iteration( X ), Y ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Y
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 paramod: (65231) {G2,W19,D5,L1,V2,M1} { addition( strong_iteration( X ),
% 45.54/45.98 multiplication( star( X ), Y ) ) ==> addition( multiplication( star( X )
% 45.54/45.98 , addition( one, Y ) ), multiplication( strong_iteration( X ), zero ) )
% 45.54/45.98 }.
% 45.54/45.98 parent0[0]: (69) {G1,W11,D4,L1,V2,M1} P(5,7) { addition( X, multiplication
% 45.54/45.98 ( X, Y ) ) = multiplication( X, addition( one, Y ) ) }.
% 45.54/45.98 parent1[0; 9]: (65228) {G2,W14,D5,L1,V2,M1} { addition( strong_iteration(
% 45.54/45.98 X ), Y ) ==> addition( addition( star( X ), Y ), multiplication(
% 45.54/45.98 strong_iteration( X ), zero ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := star( X )
% 45.54/45.98 Y := Y
% 45.54/45.98 end
% 45.54/45.98 substitution1:
% 45.54/45.98 X := X
% 45.54/45.98 Y := multiplication( star( X ), Y )
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 paramod: (65232) {G3,W14,D5,L1,V2,M1} { addition( strong_iteration( X ),
% 45.54/45.98 multiplication( star( X ), Y ) ) ==> multiplication( strong_iteration( X
% 45.54/45.98 ), addition( one, Y ) ) }.
% 45.54/45.98 parent0[0]: (12374) {G3,W14,D5,L1,V2,M1} P(285,100);d(812) { addition(
% 45.54/45.98 multiplication( star( X ), Y ), multiplication( strong_iteration( X ),
% 45.54/45.98 zero ) ) ==> multiplication( strong_iteration( X ), Y ) }.
% 45.54/45.98 parent1[0; 8]: (65231) {G2,W19,D5,L1,V2,M1} { addition( strong_iteration(
% 45.54/45.98 X ), multiplication( star( X ), Y ) ) ==> addition( multiplication( star
% 45.54/45.98 ( X ), addition( one, Y ) ), multiplication( strong_iteration( X ), zero
% 45.54/45.98 ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := addition( one, Y )
% 45.54/45.98 end
% 45.54/45.98 substitution1:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Y
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 subsumption: (18940) {G4,W14,D5,L1,V2,M1} P(69,389);d(12374) { addition(
% 45.54/45.98 strong_iteration( X ), multiplication( star( X ), Y ) ) ==>
% 45.54/45.98 multiplication( strong_iteration( X ), addition( one, Y ) ) }.
% 45.54/45.98 parent0: (65232) {G3,W14,D5,L1,V2,M1} { addition( strong_iteration( X ),
% 45.54/45.98 multiplication( star( X ), Y ) ) ==> multiplication( strong_iteration( X
% 45.54/45.98 ), addition( one, Y ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Y
% 45.54/45.98 end
% 45.54/45.98 permutation0:
% 45.54/45.98 0 ==> 0
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 paramod: (65236) {G5,W9,D4,L1,V1,M1} { multiplication( strong_iteration( X
% 45.54/45.98 ), addition( one, X ) ) ==> strong_iteration( X ) }.
% 45.54/45.98 parent0[0]: (18940) {G4,W14,D5,L1,V2,M1} P(69,389);d(12374) { addition(
% 45.54/45.98 strong_iteration( X ), multiplication( star( X ), Y ) ) ==>
% 45.54/45.98 multiplication( strong_iteration( X ), addition( one, Y ) ) }.
% 45.54/45.98 parent1[0; 1]: (1128) {G6,W10,D5,L1,V1,M1} R(1111,36) { addition(
% 45.54/45.98 strong_iteration( X ), multiplication( star( X ), X ) ) ==>
% 45.54/45.98 strong_iteration( X ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := X
% 45.54/45.98 end
% 45.54/45.98 substitution1:
% 45.54/45.98 X := X
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 subsumption: (20024) {G7,W9,D4,L1,V1,M1} S(1128);d(18940) { multiplication
% 45.54/45.98 ( strong_iteration( X ), addition( one, X ) ) ==> strong_iteration( X )
% 45.54/45.98 }.
% 45.54/45.98 parent0: (65236) {G5,W9,D4,L1,V1,M1} { multiplication( strong_iteration( X
% 45.54/45.98 ), addition( one, X ) ) ==> strong_iteration( X ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 end
% 45.54/45.98 permutation0:
% 45.54/45.98 0 ==> 0
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 eqswap: (65238) {G2,W15,D4,L2,V2,M2} { addition( star( X ), Y ) ==>
% 45.54/45.98 addition( strong_iteration( X ), Y ), ! leq( multiplication(
% 45.54/45.98 strong_iteration( X ), zero ), Y ) }.
% 45.54/45.98 parent0[0]: (571) {G2,W15,D4,L2,V2,M2} P(16,35) { addition(
% 45.54/45.98 strong_iteration( X ), Y ) ==> addition( star( X ), Y ), ! leq(
% 45.54/45.98 multiplication( strong_iteration( X ), zero ), Y ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Y
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 paramod: (65241) {G2,W23,D5,L2,V2,M2} { addition( star( X ),
% 45.54/45.98 multiplication( strong_iteration( X ), Y ) ) ==> multiplication(
% 45.54/45.98 strong_iteration( X ), addition( one, Y ) ), ! leq( multiplication(
% 45.54/45.98 strong_iteration( X ), zero ), multiplication( strong_iteration( X ), Y )
% 45.54/45.98 ) }.
% 45.54/45.98 parent0[0]: (69) {G1,W11,D4,L1,V2,M1} P(5,7) { addition( X, multiplication
% 45.54/45.98 ( X, Y ) ) = multiplication( X, addition( one, Y ) ) }.
% 45.54/45.98 parent1[0; 8]: (65238) {G2,W15,D4,L2,V2,M2} { addition( star( X ), Y ) ==>
% 45.54/45.98 addition( strong_iteration( X ), Y ), ! leq( multiplication(
% 45.54/45.98 strong_iteration( X ), zero ), Y ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := strong_iteration( X )
% 45.54/45.98 Y := Y
% 45.54/45.98 end
% 45.54/45.98 substitution1:
% 45.54/45.98 X := X
% 45.54/45.98 Y := multiplication( strong_iteration( X ), Y )
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 resolution: (65242) {G3,W14,D5,L1,V2,M1} { addition( star( X ),
% 45.54/45.98 multiplication( strong_iteration( X ), Y ) ) ==> multiplication(
% 45.54/45.98 strong_iteration( X ), addition( one, Y ) ) }.
% 45.54/45.98 parent0[1]: (65241) {G2,W23,D5,L2,V2,M2} { addition( star( X ),
% 45.54/45.98 multiplication( strong_iteration( X ), Y ) ) ==> multiplication(
% 45.54/45.98 strong_iteration( X ), addition( one, Y ) ), ! leq( multiplication(
% 45.54/45.98 strong_iteration( X ), zero ), multiplication( strong_iteration( X ), Y )
% 45.54/45.98 ) }.
% 45.54/45.98 parent1[0]: (1632) {G2,W7,D3,L1,V2,M1} P(20,67);q { leq( multiplication( Y
% 45.54/45.98 , zero ), multiplication( Y, X ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Y
% 45.54/45.98 end
% 45.54/45.98 substitution1:
% 45.54/45.98 X := Y
% 45.54/45.98 Y := strong_iteration( X )
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 subsumption: (35715) {G3,W14,D5,L1,V2,M1} P(571,69);r(1632) { addition(
% 45.54/45.98 star( X ), multiplication( strong_iteration( X ), Y ) ) ==>
% 45.54/45.98 multiplication( strong_iteration( X ), addition( one, Y ) ) }.
% 45.54/45.98 parent0: (65242) {G3,W14,D5,L1,V2,M1} { addition( star( X ),
% 45.54/45.98 multiplication( strong_iteration( X ), Y ) ) ==> multiplication(
% 45.54/45.98 strong_iteration( X ), addition( one, Y ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Y
% 45.54/45.98 end
% 45.54/45.98 permutation0:
% 45.54/45.98 0 ==> 0
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 eqswap: (65244) {G2,W14,D4,L2,V2,M2} { addition( one, Y ) ==> addition(
% 45.54/45.98 star( X ), Y ), ! leq( multiplication( star( X ), X ), Y ) }.
% 45.54/45.98 parent0[0]: (574) {G2,W14,D4,L2,V2,M2} P(11,35) { addition( star( X ), Y )
% 45.54/45.98 ==> addition( one, Y ), ! leq( multiplication( star( X ), X ), Y ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := Y
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 resolution: (65247) {G3,W14,D5,L1,V1,M1} { addition( one, multiplication(
% 45.54/45.98 strong_iteration( X ), X ) ) ==> addition( star( X ), multiplication(
% 45.54/45.98 strong_iteration( X ), X ) ) }.
% 45.54/45.98 parent0[1]: (65244) {G2,W14,D4,L2,V2,M2} { addition( one, Y ) ==> addition
% 45.54/45.98 ( star( X ), Y ), ! leq( multiplication( star( X ), X ), Y ) }.
% 45.54/45.98 parent1[0]: (5228) {G4,W9,D4,L1,V2,M1} P(226,99);q { leq( multiplication(
% 45.54/45.98 star( X ), Y ), multiplication( strong_iteration( X ), Y ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := multiplication( strong_iteration( X ), X )
% 45.54/45.98 end
% 45.54/45.98 substitution1:
% 45.54/45.98 X := X
% 45.54/45.98 Y := X
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 paramod: (65248) {G4,W13,D5,L1,V1,M1} { addition( one, multiplication(
% 45.54/45.98 strong_iteration( X ), X ) ) ==> multiplication( strong_iteration( X ),
% 45.54/45.98 addition( one, X ) ) }.
% 45.54/45.98 parent0[0]: (35715) {G3,W14,D5,L1,V2,M1} P(571,69);r(1632) { addition( star
% 45.54/45.98 ( X ), multiplication( strong_iteration( X ), Y ) ) ==> multiplication(
% 45.54/45.98 strong_iteration( X ), addition( one, Y ) ) }.
% 45.54/45.98 parent1[0; 7]: (65247) {G3,W14,D5,L1,V1,M1} { addition( one,
% 45.54/45.98 multiplication( strong_iteration( X ), X ) ) ==> addition( star( X ),
% 45.54/45.98 multiplication( strong_iteration( X ), X ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 Y := X
% 45.54/45.98 end
% 45.54/45.98 substitution1:
% 45.54/45.98 X := X
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 paramod: (65249) {G5,W9,D5,L1,V1,M1} { addition( one, multiplication(
% 45.54/45.98 strong_iteration( X ), X ) ) ==> strong_iteration( X ) }.
% 45.54/45.98 parent0[0]: (20024) {G7,W9,D4,L1,V1,M1} S(1128);d(18940) { multiplication(
% 45.54/45.98 strong_iteration( X ), addition( one, X ) ) ==> strong_iteration( X ) }.
% 45.54/45.98 parent1[0; 7]: (65248) {G4,W13,D5,L1,V1,M1} { addition( one,
% 45.54/45.98 multiplication( strong_iteration( X ), X ) ) ==> multiplication(
% 45.54/45.98 strong_iteration( X ), addition( one, X ) ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 end
% 45.54/45.98 substitution1:
% 45.54/45.98 X := X
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 subsumption: (64568) {G8,W9,D5,L1,V1,M1} R(5228,574);d(35715);d(20024) {
% 45.54/45.98 addition( one, multiplication( strong_iteration( X ), X ) ) ==>
% 45.54/45.98 strong_iteration( X ) }.
% 45.54/45.98 parent0: (65249) {G5,W9,D5,L1,V1,M1} { addition( one, multiplication(
% 45.54/45.98 strong_iteration( X ), X ) ) ==> strong_iteration( X ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := X
% 45.54/45.98 end
% 45.54/45.98 permutation0:
% 45.54/45.98 0 ==> 0
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 paramod: (65253) {G2,W5,D3,L1,V0,M1} { ! strong_iteration( skol1 ) ==>
% 45.54/45.98 strong_iteration( skol1 ) }.
% 45.54/45.98 parent0[0]: (64568) {G8,W9,D5,L1,V1,M1} R(5228,574);d(35715);d(20024) {
% 45.54/45.98 addition( one, multiplication( strong_iteration( X ), X ) ) ==>
% 45.54/45.98 strong_iteration( X ) }.
% 45.54/45.98 parent1[0; 2]: (312) {G1,W9,D5,L1,V0,M1} P(0,19) { ! addition( one,
% 45.54/45.98 multiplication( strong_iteration( skol1 ), skol1 ) ) ==> strong_iteration
% 45.54/45.98 ( skol1 ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 X := skol1
% 45.54/45.98 end
% 45.54/45.98 substitution1:
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 eqrefl: (65254) {G0,W0,D0,L0,V0,M0} { }.
% 45.54/45.98 parent0[0]: (65253) {G2,W5,D3,L1,V0,M1} { ! strong_iteration( skol1 ) ==>
% 45.54/45.98 strong_iteration( skol1 ) }.
% 45.54/45.98 substitution0:
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 subsumption: (64826) {G9,W0,D0,L0,V0,M0} S(312);d(64568);q { }.
% 45.54/45.98 parent0: (65254) {G0,W0,D0,L0,V0,M0} { }.
% 45.54/45.98 substitution0:
% 45.54/45.98 end
% 45.54/45.98 permutation0:
% 45.54/45.98 end
% 45.54/45.98
% 45.54/45.98 Proof check complete!
% 45.54/45.98
% 45.54/45.98 Memory use:
% 45.54/45.98
% 45.54/45.98 space for terms: 909367
% 45.54/45.98 space for clauses: 3095304
% 45.54/45.98
% 45.54/45.98
% 45.54/45.98 clauses generated: 1024230
% 45.54/45.98 clauses kept: 64827
% 45.54/45.98 clauses selected: 2302
% 45.54/45.98 clauses deleted: 9896
% 45.54/45.98 clauses inuse deleted: 279
% 45.54/45.98
% 45.54/45.98 subsentry: 7771195
% 45.54/45.98 literals s-matched: 3737885
% 45.54/45.98 literals matched: 3436831
% 45.54/45.98 full subsumption: 1203651
% 45.54/45.98
% 45.54/45.98 checksum: -1591008498
% 45.54/45.98
% 45.54/45.98
% 45.54/45.98 Bliksem ended
%------------------------------------------------------------------------------