TSTP Solution File: KLE148+1 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE148+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n018.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 01:37:28 EDT 2022
% Result : Theorem 68.63s 69.08s
% Output : Refutation 68.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE148+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Thu Jun 16 16:27:01 EDT 2022
% 0.12/0.33 % CPUTime :
% 16.43/16.88 *** allocated 10000 integers for termspace/termends
% 16.43/16.88 *** allocated 10000 integers for clauses
% 16.43/16.88 *** allocated 10000 integers for justifications
% 16.43/16.88 Bliksem 1.12
% 16.43/16.88
% 16.43/16.88
% 16.43/16.88 Automatic Strategy Selection
% 16.43/16.88
% 16.43/16.88
% 16.43/16.88 Clauses:
% 16.43/16.88
% 16.43/16.88 { addition( X, Y ) = addition( Y, X ) }.
% 16.43/16.88 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 16.43/16.88 { addition( X, zero ) = X }.
% 16.43/16.88 { addition( X, X ) = X }.
% 16.43/16.88 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 16.43/16.88 multiplication( X, Y ), Z ) }.
% 16.43/16.88 { multiplication( X, one ) = X }.
% 16.43/16.88 { multiplication( one, X ) = X }.
% 16.43/16.88 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 16.43/16.88 , multiplication( X, Z ) ) }.
% 16.43/16.88 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 16.43/16.88 , multiplication( Y, Z ) ) }.
% 16.43/16.88 { multiplication( zero, X ) = zero }.
% 16.43/16.88 { addition( one, multiplication( X, star( X ) ) ) = star( X ) }.
% 16.43/16.88 { addition( one, multiplication( star( X ), X ) ) = star( X ) }.
% 16.43/16.88 { ! leq( addition( multiplication( X, Z ), Y ), Z ), leq( multiplication(
% 16.43/16.88 star( X ), Y ), Z ) }.
% 16.43/16.88 { ! leq( addition( multiplication( Z, X ), Y ), Z ), leq( multiplication( Y
% 16.43/16.88 , star( X ) ), Z ) }.
% 16.43/16.88 { strong_iteration( X ) = addition( multiplication( X, strong_iteration( X
% 16.43/16.88 ) ), one ) }.
% 16.43/16.88 { ! leq( Z, addition( multiplication( X, Z ), Y ) ), leq( Z, multiplication
% 16.43/16.88 ( strong_iteration( X ), Y ) ) }.
% 16.43/16.88 { strong_iteration( X ) = addition( star( X ), multiplication(
% 16.43/16.88 strong_iteration( X ), zero ) ) }.
% 16.43/16.88 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 16.43/16.88 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 16.43/16.88 { multiplication( skol1, skol2 ) = zero }.
% 16.43/16.88 { ! multiplication( skol1, strong_iteration( skol2 ) ) = skol1 }.
% 16.43/16.88
% 16.43/16.88 percentage equality = 0.692308, percentage horn = 1.000000
% 16.43/16.88 This is a problem with some equality
% 16.43/16.88
% 16.43/16.88
% 16.43/16.88
% 16.43/16.88 Options Used:
% 16.43/16.88
% 16.43/16.88 useres = 1
% 16.43/16.88 useparamod = 1
% 16.43/16.88 useeqrefl = 1
% 16.43/16.88 useeqfact = 1
% 16.43/16.88 usefactor = 1
% 16.43/16.88 usesimpsplitting = 0
% 16.43/16.88 usesimpdemod = 5
% 16.43/16.88 usesimpres = 3
% 16.43/16.88
% 16.43/16.88 resimpinuse = 1000
% 16.43/16.88 resimpclauses = 20000
% 16.43/16.88 substype = eqrewr
% 16.43/16.88 backwardsubs = 1
% 16.43/16.88 selectoldest = 5
% 16.43/16.88
% 16.43/16.88 litorderings [0] = split
% 16.43/16.88 litorderings [1] = extend the termordering, first sorting on arguments
% 16.43/16.88
% 16.43/16.88 termordering = kbo
% 16.43/16.88
% 16.43/16.88 litapriori = 0
% 16.43/16.88 termapriori = 1
% 16.43/16.88 litaposteriori = 0
% 16.43/16.88 termaposteriori = 0
% 16.43/16.88 demodaposteriori = 0
% 16.43/16.88 ordereqreflfact = 0
% 16.43/16.88
% 16.43/16.88 litselect = negord
% 16.43/16.88
% 16.43/16.88 maxweight = 15
% 16.43/16.88 maxdepth = 30000
% 16.43/16.88 maxlength = 115
% 16.43/16.88 maxnrvars = 195
% 16.43/16.88 excuselevel = 1
% 16.43/16.88 increasemaxweight = 1
% 16.43/16.88
% 16.43/16.88 maxselected = 10000000
% 16.43/16.88 maxnrclauses = 10000000
% 16.43/16.88
% 16.43/16.88 showgenerated = 0
% 16.43/16.88 showkept = 0
% 16.43/16.88 showselected = 0
% 16.43/16.88 showdeleted = 0
% 16.43/16.88 showresimp = 1
% 16.43/16.88 showstatus = 2000
% 16.43/16.88
% 16.43/16.88 prologoutput = 0
% 16.43/16.88 nrgoals = 5000000
% 16.43/16.88 totalproof = 1
% 16.43/16.88
% 16.43/16.88 Symbols occurring in the translation:
% 16.43/16.88
% 16.43/16.88 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 16.43/16.88 . [1, 2] (w:1, o:22, a:1, s:1, b:0),
% 16.43/16.88 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 16.43/16.88 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 16.43/16.88 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 16.43/16.88 addition [37, 2] (w:1, o:46, a:1, s:1, b:0),
% 16.43/16.88 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 16.43/16.88 multiplication [40, 2] (w:1, o:48, a:1, s:1, b:0),
% 16.43/16.88 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 16.43/16.88 star [42, 1] (w:1, o:20, a:1, s:1, b:0),
% 16.43/16.88 leq [43, 2] (w:1, o:47, a:1, s:1, b:0),
% 16.43/16.88 strong_iteration [44, 1] (w:1, o:21, a:1, s:1, b:0),
% 16.43/16.88 skol1 [47, 0] (w:1, o:13, a:1, s:1, b:1),
% 16.43/16.88 skol2 [48, 0] (w:1, o:14, a:1, s:1, b:1).
% 16.43/16.88
% 16.43/16.88
% 16.43/16.88 Starting Search:
% 16.43/16.88
% 16.43/16.88 *** allocated 15000 integers for clauses
% 16.43/16.88 *** allocated 22500 integers for clauses
% 16.43/16.88 *** allocated 33750 integers for clauses
% 16.43/16.88 *** allocated 50625 integers for clauses
% 16.43/16.88 *** allocated 75937 integers for clauses
% 16.43/16.88 *** allocated 15000 integers for termspace/termends
% 16.43/16.88 Resimplifying inuse:
% 16.43/16.88 Done
% 16.43/16.88
% 16.43/16.88 *** allocated 22500 integers for termspace/termends
% 16.43/16.88 *** allocated 113905 integers for clauses
% 16.43/16.88 *** allocated 33750 integers for termspace/termends
% 16.43/16.88
% 16.43/16.88 Intermediate Status:
% 16.43/16.88 Generated: 13856
% 16.43/16.88 Kept: 2003
% 16.43/16.88 Inuse: 229
% 16.43/16.88 Deleted: 19
% 16.43/16.88 Deletedinuse: 7
% 16.43/16.88
% 16.43/16.88 Resimplifying inuse:
% 16.43/16.88 Done
% 16.43/16.88
% 16.43/16.88 *** allocated 170857 integers for clauses
% 16.43/16.88 *** allocated 50625 integers for termspace/termends
% 68.63/69.07 Resimplifying inuse:
% 68.63/69.07 Done
% 68.63/69.07
% 68.63/69.07 *** allocated 256285 integers for clauses
% 68.63/69.07 *** allocated 75937 integers for termspace/termends
% 68.63/69.07
% 68.63/69.07 Intermediate Status:
% 68.63/69.07 Generated: 33389
% 68.63/69.07 Kept: 4054
% 68.63/69.07 Inuse: 382
% 68.63/69.07 Deleted: 37
% 68.63/69.07 Deletedinuse: 8
% 68.63/69.07
% 68.63/69.07 Resimplifying inuse:
% 68.63/69.07 Done
% 68.63/69.07
% 68.63/69.07 *** allocated 384427 integers for clauses
% 68.63/69.07 Resimplifying inuse:
% 68.63/69.07 Done
% 68.63/69.07
% 68.63/69.07 *** allocated 113905 integers for termspace/termends
% 68.63/69.07
% 68.63/69.07 Intermediate Status:
% 68.63/69.07 Generated: 55931
% 68.63/69.07 Kept: 6062
% 68.63/69.07 Inuse: 586
% 68.63/69.07 Deleted: 60
% 68.63/69.07 Deletedinuse: 11
% 68.63/69.07
% 68.63/69.07 Resimplifying inuse:
% 68.63/69.07 Done
% 68.63/69.07
% 68.63/69.07 Resimplifying inuse:
% 68.63/69.07 Done
% 68.63/69.07
% 68.63/69.07 *** allocated 576640 integers for clauses
% 68.63/69.07
% 68.63/69.07 Intermediate Status:
% 68.63/69.07 Generated: 70680
% 68.63/69.07 Kept: 8101
% 68.63/69.07 Inuse: 681
% 68.63/69.07 Deleted: 69
% 68.63/69.07 Deletedinuse: 13
% 68.63/69.07
% 68.63/69.07 Resimplifying inuse:
% 68.63/69.07 Done
% 68.63/69.07
% 68.63/69.07 *** allocated 170857 integers for termspace/termends
% 68.63/69.07 Resimplifying inuse:
% 68.63/69.07 Done
% 68.63/69.07
% 68.63/69.07
% 68.63/69.07 Intermediate Status:
% 68.63/69.07 Generated: 103831
% 68.63/69.07 Kept: 10120
% 68.63/69.07 Inuse: 900
% 68.63/69.07 Deleted: 92
% 68.63/69.07 Deletedinuse: 14
% 68.63/69.07
% 68.63/69.07 Resimplifying inuse:
% 68.63/69.07 Done
% 68.63/69.07
% 68.63/69.07 *** allocated 864960 integers for clauses
% 68.63/69.07 Resimplifying inuse:
% 68.63/69.07 Done
% 68.63/69.07
% 68.63/69.07
% 68.63/69.07 Intermediate Status:
% 68.63/69.07 Generated: 130740
% 68.63/69.07 Kept: 12128
% 68.63/69.07 Inuse: 1064
% 68.63/69.07 Deleted: 212
% 68.63/69.07 Deletedinuse: 105
% 68.63/69.07
% 68.63/69.07 Resimplifying inuse:
% 68.63/69.07 Done
% 68.63/69.07
% 68.63/69.07 Resimplifying inuse:
% 68.63/69.07 Done
% 68.63/69.07
% 68.63/69.07 *** allocated 256285 integers for termspace/termends
% 68.63/69.07
% 68.63/69.07 Intermediate Status:
% 68.63/69.07 Generated: 156287
% 68.63/69.07 Kept: 14181
% 68.63/69.07 Inuse: 1167
% 68.63/69.07 Deleted: 324
% 68.63/69.07 Deletedinuse: 167
% 68.63/69.07
% 68.63/69.07 Resimplifying inuse:
% 68.63/69.07 Done
% 68.63/69.07
% 68.63/69.07 Resimplifying inuse:
% 68.63/69.07 Done
% 68.63/69.07
% 68.63/69.07 *** allocated 1297440 integers for clauses
% 68.63/69.07
% 68.63/69.07 Intermediate Status:
% 68.63/69.07 Generated: 183779
% 68.63/69.07 Kept: 16185
% 68.63/69.07 Inuse: 1247
% 68.63/69.07 Deleted: 383
% 68.63/69.07 Deletedinuse: 204
% 68.63/69.07
% 68.63/69.07 Resimplifying inuse:
% 68.63/69.07 Done
% 68.63/69.07
% 68.63/69.07 Resimplifying inuse:
% 68.63/69.07 Done
% 68.63/69.07
% 68.63/69.07
% 68.63/69.07 Intermediate Status:
% 68.63/69.07 Generated: 207005
% 68.63/69.07 Kept: 18190
% 68.63/69.07 Inuse: 1318
% 68.63/69.07 Deleted: 499
% 68.63/69.07 Deletedinuse: 230
% 68.63/69.07
% 68.63/69.07 Resimplifying inuse:
% 68.63/69.07 Done
% 68.63/69.07
% 68.63/69.07 Resimplifying inuse:
% 68.63/69.07 Done
% 68.63/69.07
% 68.63/69.07 Resimplifying clauses:
% 68.63/69.07 Done
% 68.63/69.07
% 68.63/69.07 *** allocated 384427 integers for termspace/termends
% 68.63/69.07
% 68.63/69.07 Intermediate Status:
% 68.63/69.07 Generated: 249671
% 68.63/69.07 Kept: 20264
% 68.63/69.07 Inuse: 1405
% 68.63/69.07 Deleted: 4158
% 68.63/69.07 Deletedinuse: 301
% 68.63/69.07
% 68.63/69.07 Resimplifying inuse:
% 68.63/69.07 Done
% 68.63/69.07
% 68.63/69.07 Resimplifying inuse:
% 68.63/69.07 Done
% 68.63/69.07
% 68.63/69.07
% 68.63/69.07 Intermediate Status:
% 68.63/69.07 Generated: 275745
% 68.63/69.07 Kept: 22287
% 68.63/69.07 Inuse: 1493
% 68.63/69.07 Deleted: 4161
% 68.63/69.07 Deletedinuse: 304
% 68.63/69.07
% 68.63/69.07 Resimplifying inuse:
% 68.63/69.07 Done
% 68.63/69.07
% 68.63/69.07 Resimplifying inuse:
% 68.63/69.07 Done
% 68.63/69.07
% 68.63/69.07
% 68.63/69.07 Intermediate Status:
% 68.63/69.07 Generated: 293443
% 68.63/69.07 Kept: 24334
% 68.63/69.07 Inuse: 1528
% 68.63/69.07 Deleted: 4161
% 68.63/69.07 Deletedinuse: 304
% 68.63/69.07
% 68.63/69.07 *** allocated 1946160 integers for clauses
% 68.63/69.07 Resimplifying inuse:
% 68.63/69.07 Done
% 68.63/69.07
% 68.63/69.07 Resimplifying inuse:
% 68.63/69.07 Done
% 68.63/69.07
% 68.63/69.07
% 68.63/69.07 Intermediate Status:
% 68.63/69.07 Generated: 326914
% 68.63/69.07 Kept: 28601
% 68.63/69.07 Inuse: 1563
% 68.63/69.07 Deleted: 4162
% 68.63/69.07 Deletedinuse: 304
% 68.63/69.07
% 68.63/69.07 Resimplifying inuse:
% 68.63/69.07 Done
% 68.63/69.07
% 68.63/69.07 *** allocated 576640 integers for termspace/termends
% 68.63/69.07 Resimplifying inuse:
% 68.63/69.07 Done
% 68.63/69.07
% 68.63/69.07
% 68.63/69.07 Intermediate Status:
% 68.63/69.07 Generated: 353313
% 68.63/69.07 Kept: 30656
% 68.63/69.07 Inuse: 1637
% 68.63/69.07 Deleted: 4163
% 68.63/69.07 Deletedinuse: 304
% 68.63/69.07
% 68.63/69.07 Resimplifying inuse:
% 68.63/69.07 Done
% 68.63/69.07
% 68.63/69.07 Resimplifying inuse:
% 68.63/69.07 Done
% 68.63/69.07
% 68.63/69.07
% 68.63/69.07 Intermediate Status:
% 68.63/69.07 Generated: 386287
% 68.63/69.07 Kept: 32664
% 68.63/69.07 Inuse: 1747
% 68.63/69.07 Deleted: 4166
% 68.63/69.07 Deletedinuse: 306
% 68.63/69.07
% 68.63/69.07 Resimplifying inuse:
% 68.63/69.07 Done
% 68.63/69.07
% 68.63/69.07 Resimplifying inuse:
% 68.63/69.07 Done
% 68.63/69.07
% 68.63/69.07
% 68.63/69.07 Intermediate Status:
% 68.63/69.07 Generated: 412590
% 68.63/69.07 Kept: 34703
% 68.63/69.07 Inuse: 1811
% 68.63/69.07 Deleted: 4166
% 68.63/69.07 Deletedinuse: 306
% 68.63/69.07
% 68.63/69.07 Resimplifying inuse:
% 68.63/69.07 Done
% 68.63/69.07
% 68.63/69.07 Resimplifying inuse:
% 68.63/69.07 Done
% 68.63/69.07
% 68.63/69.07
% 68.63/69.07 Intermediate Status:
% 68.63/69.07 Generated: 434265
% 68.63/69.07 Kept: 36720
% 68.63/69.07 Inuse: 1859
% 68.63/69.07 Deleted: 4175
% 68.63/69.07 Deletedinuse: 307
% 68.63/69.07
% 68.63/69.07 Resimplifying inuse:
% 68.63/69.07 Done
% 68.63/69.07
% 68.63/69.07 Resimplifying inuse:
% 68.63/69.07 Done
% 68.63/69.07
% 68.63/69.07 *** allocated 2919240 integers for clauses
% 68.63/69.07
% 68.63/69.07 Intermediate Status:
% 68.63/69.07 Generated: 466217
% 68.63/69.07 Kept: 38744
% 68.63/69.07 Inuse: 1966
% 68.63/69.07 Deleted: 4193
% 68.63/69.07 Deletedinuse: 319
% 68.63/69.07
% 68.63/69.07 Resimplifying inuse:
% 68.63/69.07 Done
% 68.63/69.07
% 68.63/69.07 Resimplifying clauses:
% 68.63/69.07 Done
% 68.63/69.07
% 68.63/69.07
% 68.63/69.07 Intermediate Status:
% 68.63/69.07 Generated: 511558
% 68.63/69.07 Kept: 41500
% 68.63/69.07 Inuse: 2023
% 68.63/69.07 Deleted: 6573
% 68.63/69.07 Deletedinuse: 335
% 68.63/69.07
% 68.63/69.07 Resimplifying inuse:
% 68.63/69.07 Done
% 68.63/69.07
% 68.63/69.07 *** allocated 864960 integers for termspace/termends
% 68.63/69.07 Resimplifying inuse:
% 68.63/69.07 Done
% 68.63/69.07
% 68.63/69.07
% 68.63/69.07 Intermediate Status:
% 68.63/69.07 Generated: 542352
% 68.63/69.07 Kept: 43538
% 68.63/69.07 Inuse: 2133
% 68.63/69.07 Deleted: 6581
% 68.63/69.07 Deletedinuse: 338
% 68.63/69.07
% 68.63/69.07 Resimplifying inuse:
% 68.63/69.07 Done
% 68.63/69.07
% 68.63/69.07 Resimplifying inuse:
% 68.63/69.07 Done
% 68.63/69.07
% 68.63/69.07
% 68.63/69.07 Intermediate Status:
% 68.63/69.07 Generated: 599942
% 68.63/69.07 Kept: 45726
% 68.63/69.07 Inuse: 2191
% 68.63/69.08 Deleted: 6581
% 68.63/69.08 Deletedinuse: 338
% 68.63/69.08
% 68.63/69.08 Resimplifying inuse:
% 68.63/69.08 Done
% 68.63/69.08
% 68.63/69.08 Resimplifying inuse:
% 68.63/69.08 Done
% 68.63/69.08
% 68.63/69.08
% 68.63/69.08 Intermediate Status:
% 68.63/69.08 Generated: 669305
% 68.63/69.08 Kept: 47751
% 68.63/69.08 Inuse: 2217
% 68.63/69.08 Deleted: 6586
% 68.63/69.08 Deletedinuse: 343
% 68.63/69.08
% 68.63/69.08 Resimplifying inuse:
% 68.63/69.08 Done
% 68.63/69.08
% 68.63/69.08 Resimplifying inuse:
% 68.63/69.08 Done
% 68.63/69.08
% 68.63/69.08
% 68.63/69.08 Intermediate Status:
% 68.63/69.08 Generated: 714109
% 68.63/69.08 Kept: 49841
% 68.63/69.08 Inuse: 2241
% 68.63/69.08 Deleted: 6586
% 68.63/69.08 Deletedinuse: 343
% 68.63/69.08
% 68.63/69.08 Resimplifying inuse:
% 68.63/69.08 Done
% 68.63/69.08
% 68.63/69.08 Resimplifying inuse:
% 68.63/69.08 Done
% 68.63/69.08
% 68.63/69.08
% 68.63/69.08 Intermediate Status:
% 68.63/69.08 Generated: 793695
% 68.63/69.08 Kept: 51854
% 68.63/69.08 Inuse: 2310
% 68.63/69.08 Deleted: 6587
% 68.63/69.08 Deletedinuse: 344
% 68.63/69.08
% 68.63/69.08 Resimplifying inuse:
% 68.63/69.08 Done
% 68.63/69.08
% 68.63/69.08 Resimplifying inuse:
% 68.63/69.08 Done
% 68.63/69.08
% 68.63/69.08
% 68.63/69.08 Intermediate Status:
% 68.63/69.08 Generated: 817541
% 68.63/69.08 Kept: 53861
% 68.63/69.08 Inuse: 2349
% 68.63/69.08 Deleted: 6587
% 68.63/69.08 Deletedinuse: 344
% 68.63/69.08
% 68.63/69.08 Resimplifying inuse:
% 68.63/69.08 Done
% 68.63/69.08
% 68.63/69.08 Resimplifying inuse:
% 68.63/69.08 Done
% 68.63/69.08
% 68.63/69.08
% 68.63/69.08 Intermediate Status:
% 68.63/69.08 Generated: 841271
% 68.63/69.08 Kept: 55889
% 68.63/69.08 Inuse: 2398
% 68.63/69.08 Deleted: 6590
% 68.63/69.08 Deletedinuse: 344
% 68.63/69.08
% 68.63/69.08 Resimplifying inuse:
% 68.63/69.08 Done
% 68.63/69.08
% 68.63/69.08 Resimplifying inuse:
% 68.63/69.08 Done
% 68.63/69.08
% 68.63/69.08
% 68.63/69.08 Intermediate Status:
% 68.63/69.08 Generated: 855845
% 68.63/69.08 Kept: 58039
% 68.63/69.08 Inuse: 2420
% 68.63/69.08 Deleted: 6590
% 68.63/69.08 Deletedinuse: 344
% 68.63/69.08
% 68.63/69.08 Resimplifying inuse:
% 68.63/69.08 Done
% 68.63/69.08
% 68.63/69.08 Resimplifying inuse:
% 68.63/69.08 Done
% 68.63/69.08
% 68.63/69.08
% 68.63/69.08 Intermediate Status:
% 68.63/69.08 Generated: 878906
% 68.63/69.08 Kept: 60099
% 68.63/69.08 Inuse: 2467
% 68.63/69.08 Deleted: 6590
% 68.63/69.08 Deletedinuse: 344
% 68.63/69.08
% 68.63/69.08 Resimplifying clauses:
% 68.63/69.08 Done
% 68.63/69.08
% 68.63/69.08 *** allocated 4378860 integers for clauses
% 68.63/69.08 Resimplifying inuse:
% 68.63/69.08 Done
% 68.63/69.08
% 68.63/69.08 Resimplifying inuse:
% 68.63/69.08 Done
% 68.63/69.08
% 68.63/69.08 *** allocated 1297440 integers for termspace/termends
% 68.63/69.08
% 68.63/69.08 Intermediate Status:
% 68.63/69.08 Generated: 895093
% 68.63/69.08 Kept: 62143
% 68.63/69.08 Inuse: 2496
% 68.63/69.08 Deleted: 9123
% 68.63/69.08 Deletedinuse: 344
% 68.63/69.08
% 68.63/69.08 Resimplifying inuse:
% 68.63/69.08 Done
% 68.63/69.08
% 68.63/69.08 Resimplifying inuse:
% 68.63/69.08 Done
% 68.63/69.08
% 68.63/69.08
% 68.63/69.08 Intermediate Status:
% 68.63/69.08 Generated: 940297
% 68.63/69.08 Kept: 64149
% 68.63/69.08 Inuse: 2537
% 68.63/69.08 Deleted: 9123
% 68.63/69.08 Deletedinuse: 344
% 68.63/69.08
% 68.63/69.08 Resimplifying inuse:
% 68.63/69.08 Done
% 68.63/69.08
% 68.63/69.08 Resimplifying inuse:
% 68.63/69.08 Done
% 68.63/69.08
% 68.63/69.08
% 68.63/69.08 Intermediate Status:
% 68.63/69.08 Generated: 959767
% 68.63/69.08 Kept: 66188
% 68.63/69.08 Inuse: 2558
% 68.63/69.08 Deleted: 9123
% 68.63/69.08 Deletedinuse: 344
% 68.63/69.08
% 68.63/69.08 Resimplifying inuse:
% 68.63/69.08 Done
% 68.63/69.08
% 68.63/69.08 Resimplifying inuse:
% 68.63/69.08 Done
% 68.63/69.08
% 68.63/69.08
% 68.63/69.08 Intermediate Status:
% 68.63/69.08 Generated: 994865
% 68.63/69.08 Kept: 68204
% 68.63/69.08 Inuse: 2594
% 68.63/69.08 Deleted: 9123
% 68.63/69.08 Deletedinuse: 344
% 68.63/69.08
% 68.63/69.08 Resimplifying inuse:
% 68.63/69.08 Done
% 68.63/69.08
% 68.63/69.08 Resimplifying inuse:
% 68.63/69.08 Done
% 68.63/69.08
% 68.63/69.08
% 68.63/69.08 Intermediate Status:
% 68.63/69.08 Generated: 1030965
% 68.63/69.08 Kept: 70286
% 68.63/69.08 Inuse: 2624
% 68.63/69.08 Deleted: 9123
% 68.63/69.08 Deletedinuse: 344
% 68.63/69.08
% 68.63/69.08 Resimplifying inuse:
% 68.63/69.08 Done
% 68.63/69.08
% 68.63/69.08 Resimplifying inuse:
% 68.63/69.08 Done
% 68.63/69.08
% 68.63/69.08
% 68.63/69.08 Intermediate Status:
% 68.63/69.08 Generated: 1063951
% 68.63/69.08 Kept: 72287
% 68.63/69.08 Inuse: 2666
% 68.63/69.08 Deleted: 9124
% 68.63/69.08 Deletedinuse: 345
% 68.63/69.08
% 68.63/69.08 Resimplifying inuse:
% 68.63/69.08 Done
% 68.63/69.08
% 68.63/69.08 Resimplifying inuse:
% 68.63/69.08 Done
% 68.63/69.08
% 68.63/69.08
% 68.63/69.08 Intermediate Status:
% 68.63/69.08 Generated: 1135133
% 68.63/69.08 Kept: 74328
% 68.63/69.08 Inuse: 2709
% 68.63/69.08 Deleted: 9126
% 68.63/69.08 Deletedinuse: 347
% 68.63/69.08
% 68.63/69.08 Resimplifying inuse:
% 68.63/69.08 Done
% 68.63/69.08
% 68.63/69.08 Resimplifying inuse:
% 68.63/69.08 Done
% 68.63/69.08
% 68.63/69.08
% 68.63/69.08 Intermediate Status:
% 68.63/69.08 Generated: 1158511
% 68.63/69.08 Kept: 76328
% 68.63/69.08 Inuse: 2744
% 68.63/69.08 Deleted: 9126
% 68.63/69.08 Deletedinuse: 347
% 68.63/69.08
% 68.63/69.08 Resimplifying inuse:
% 68.63/69.08 Done
% 68.63/69.08
% 68.63/69.08 Resimplifying inuse:
% 68.63/69.08 Done
% 68.63/69.08
% 68.63/69.08
% 68.63/69.08 Intermediate Status:
% 68.63/69.08 Generated: 1175389
% 68.63/69.08 Kept: 78330
% 68.63/69.08 Inuse: 2767
% 68.63/69.08 Deleted: 9126
% 68.63/69.08 Deletedinuse: 347
% 68.63/69.08
% 68.63/69.08 Resimplifying inuse:
% 68.63/69.08 Done
% 68.63/69.08
% 68.63/69.08 Resimplifying inuse:
% 68.63/69.08 Done
% 68.63/69.08
% 68.63/69.08 Resimplifying clauses:
% 68.63/69.08 Done
% 68.63/69.08
% 68.63/69.08
% 68.63/69.08 Intermediate Status:
% 68.63/69.08 Generated: 1203117
% 68.63/69.08 Kept: 80801
% 68.63/69.08 Inuse: 2805
% 68.63/69.08 Deleted: 10911
% 68.63/69.08 Deletedinuse: 347
% 68.63/69.08
% 68.63/69.08 Resimplifying inuse:
% 68.63/69.08 Done
% 68.63/69.08
% 68.63/69.08 Resimplifying inuse:
% 68.63/69.08 Done
% 68.63/69.08
% 68.63/69.08
% 68.63/69.08 Intermediate Status:
% 68.63/69.08 Generated: 1218829
% 68.63/69.08 Kept: 83002
% 68.63/69.08 Inuse: 2825
% 68.63/69.08 Deleted: 10911
% 68.63/69.08 Deletedinuse: 347
% 68.63/69.08
% 68.63/69.08 Resimplifying inuse:
% 68.63/69.08 Done
% 68.63/69.08
% 68.63/69.08 Resimplifying inuse:
% 68.63/69.08 Done
% 68.63/69.08
% 68.63/69.08
% 68.63/69.08 Intermediate Status:
% 68.63/69.08 Generated: 1233038
% 68.63/69.08 Kept: 85023
% 68.63/69.08 Inuse: 2843
% 68.63/69.08 Deleted: 10911
% 68.63/69.08 Deletedinuse: 347
% 68.63/69.08
% 68.63/69.08 Resimplifying inuse:
% 68.63/69.08 Done
% 68.63/69.08
% 68.63/69.08 Resimplifying inuse:
% 68.63/69.08 Done
% 68.63/69.08
% 68.63/69.08
% 68.63/69.08 Intermediate Status:
% 68.63/69.08 Generated: 1253181
% 68.63/69.08 Kept: 87051
% 68.63/69.08 Inuse: 2875
% 68.63/69.08 Deleted: 10919
% 68.63/69.08 Deletedinuse: 355
% 68.63/69.08
% 68.63/69.08 Resimplifying inuse:
% 68.63/69.08 Done
% 68.63/69.08
% 68.63/69.08
% 68.63/69.08 Bliksems!, er is een bewijs:
% 68.63/69.08 % SZS status Theorem
% 68.63/69.08 % SZS output start Refutation
% 68.63/69.08
% 68.63/69.08 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 68.63/69.08 (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) ==> addition(
% 68.63/69.08 addition( Z, Y ), X ) }.
% 68.63/69.08 (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 68.63/69.08 (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 68.63/69.08 (4) {G0,W11,D4,L1,V3,M1} I { multiplication( X, multiplication( Y, Z ) )
% 68.63/69.08 ==> multiplication( multiplication( X, Y ), Z ) }.
% 68.63/69.08 (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 68.63/69.08 (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 68.63/69.08 (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 68.63/69.08 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 68.63/69.08 (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 68.63/69.08 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 68.63/69.08 (9) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==> zero }.
% 68.63/69.08 (10) {G0,W9,D5,L1,V1,M1} I { addition( one, multiplication( X, star( X ) )
% 68.63/69.08 ) ==> star( X ) }.
% 68.63/69.08 (11) {G0,W9,D5,L1,V1,M1} I { addition( one, multiplication( star( X ), X )
% 68.63/69.08 ) ==> star( X ) }.
% 68.63/69.08 (13) {G0,W13,D4,L2,V3,M2} I { ! leq( addition( multiplication( Z, X ), Y )
% 68.63/69.08 , Z ), leq( multiplication( Y, star( X ) ), Z ) }.
% 68.63/69.08 (14) {G0,W9,D5,L1,V1,M1} I { addition( multiplication( X, strong_iteration
% 68.63/69.08 ( X ) ), one ) ==> strong_iteration( X ) }.
% 68.63/69.08 (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) ==> Y }.
% 68.63/69.08 (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, Y ) }.
% 68.63/69.08 (19) {G0,W5,D3,L1,V0,M1} I { multiplication( skol1, skol2 ) ==> zero }.
% 68.63/69.08 (20) {G0,W6,D4,L1,V0,M1} I { ! multiplication( skol1, strong_iteration(
% 68.63/69.08 skol2 ) ) ==> skol1 }.
% 68.63/69.08 (21) {G1,W5,D3,L1,V1,M1} P(0,2) { addition( zero, X ) ==> X }.
% 68.63/69.08 (23) {G1,W3,D2,L1,V1,M1} R(18,3) { leq( X, X ) }.
% 68.63/69.08 (24) {G1,W8,D3,L2,V2,M2} P(0,18) { ! addition( Y, X ) ==> Y, leq( X, Y )
% 68.63/69.08 }.
% 68.63/69.08 (26) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y ), Z ) ==>
% 68.63/69.08 addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 68.63/69.08 (27) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y ), Z ) =
% 68.63/69.08 addition( addition( Y, Z ), X ) }.
% 68.63/69.08 (30) {G1,W9,D4,L1,V2,M1} P(3,1) { addition( addition( Y, X ), X ) ==>
% 68.63/69.08 addition( Y, X ) }.
% 68.63/69.08 (36) {G2,W9,D2,L3,V2,M3} P(17,24) { ! Y = X, leq( Y, X ), ! leq( X, Y ) }.
% 68.63/69.08 (39) {G1,W8,D3,L2,V2,M2} P(17,0) { addition( Y, X ) ==> Y, ! leq( X, Y )
% 68.63/69.08 }.
% 68.63/69.08 (61) {G1,W16,D4,L2,V3,M2} P(7,17) { ! leq( multiplication( X, Y ),
% 68.63/69.08 multiplication( X, Z ) ), multiplication( X, addition( Y, Z ) ) ==>
% 68.63/69.08 multiplication( X, Z ) }.
% 68.63/69.08 (65) {G1,W16,D4,L2,V3,M2} P(7,18) { ! multiplication( X, addition( Y, Z ) )
% 68.63/69.08 ==> multiplication( X, Z ), leq( multiplication( X, Y ), multiplication
% 68.63/69.08 ( X, Z ) ) }.
% 68.63/69.08 (105) {G2,W9,D4,L1,V1,M1} P(19,8);d(21) { multiplication( addition( skol1,
% 68.63/69.08 X ), skol2 ) ==> multiplication( X, skol2 ) }.
% 68.63/69.08 (109) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( multiplication( Y, X ), X ) =
% 68.63/69.08 multiplication( addition( Y, one ), X ) }.
% 68.63/69.08 (126) {G1,W13,D5,L1,V2,M1} P(10,1) { addition( addition( Y, one ),
% 68.63/69.08 multiplication( X, star( X ) ) ) ==> addition( Y, star( X ) ) }.
% 68.63/69.08 (149) {G1,W9,D5,L1,V1,M1} P(11,0) { addition( multiplication( star( X ), X
% 68.63/69.08 ), one ) ==> star( X ) }.
% 68.63/69.08 (204) {G1,W17,D5,L2,V4,M2} P(4,13) { ! leq( addition( multiplication(
% 68.63/69.08 multiplication( X, Y ), Z ), T ), X ), leq( multiplication( T, star(
% 68.63/69.08 multiplication( Y, Z ) ) ), X ) }.
% 68.63/69.08 (306) {G2,W5,D3,L1,V2,M1} P(3,26);q { leq( X, addition( X, Y ) ) }.
% 68.63/69.08 (316) {G3,W4,D3,L1,V1,M1} P(11,306) { leq( one, star( X ) ) }.
% 68.63/69.08 (322) {G3,W5,D3,L1,V2,M1} P(0,306) { leq( X, addition( Y, X ) ) }.
% 68.63/69.08 (323) {G4,W7,D4,L1,V1,M1} R(316,17) { addition( one, star( X ) ) ==> star(
% 68.63/69.08 X ) }.
% 68.63/69.08 (348) {G4,W7,D4,L1,V3,M1} P(27,322) { leq( Z, addition( addition( Y, Z ), X
% 68.63/69.08 ) ) }.
% 68.63/69.08 (353) {G2,W13,D6,L1,V2,M1} P(11,27) { addition( addition( multiplication(
% 68.63/69.08 star( X ), X ), Y ), one ) ==> addition( star( X ), Y ) }.
% 68.63/69.08 (417) {G2,W7,D4,L1,V1,M1} P(14,30) { addition( strong_iteration( X ), one )
% 68.63/69.08 ==> strong_iteration( X ) }.
% 68.63/69.08 (531) {G3,W9,D2,L3,V2,M3} R(36,17);d(39) { ! X = Y, ! leq( Y, X ), X = Y
% 68.63/69.08 }.
% 68.63/69.08 (550) {G5,W8,D3,L2,V3,M2} P(17,348) { leq( Y, Z ), ! leq( addition( X, Y )
% 68.63/69.08 , Z ) }.
% 68.63/69.08 (660) {G4,W7,D4,L1,V1,M1} R(39,316) { addition( star( X ), one ) ==> star(
% 68.63/69.08 X ) }.
% 68.63/69.08 (1535) {G3,W12,D4,L2,V2,M2} P(417,61);d(5);d(5) { ! leq( multiplication( Y
% 68.63/69.08 , strong_iteration( X ) ), Y ), multiplication( Y, strong_iteration( X )
% 68.63/69.08 ) ==> Y }.
% 68.63/69.08 (1908) {G5,W6,D4,L1,V2,M1} P(323,65);q;d(5) { leq( Y, multiplication( Y,
% 68.63/69.08 star( X ) ) ) }.
% 68.63/69.08 (1947) {G6,W11,D5,L1,V2,M1} R(1908,17) { addition( X, multiplication( X,
% 68.63/69.08 star( Y ) ) ) ==> multiplication( X, star( Y ) ) }.
% 68.63/69.08 (3711) {G3,W8,D3,L2,V1,M2} P(39,105);d(19) { ! leq( X, skol1 ),
% 68.63/69.08 multiplication( X, skol2 ) ==> zero }.
% 68.63/69.08 (4723) {G3,W8,D4,L1,V2,M1} P(126,306) { leq( addition( X, one ), addition(
% 68.63/69.08 X, star( Y ) ) ) }.
% 68.63/69.08 (8116) {G4,W8,D4,L1,V2,M1} P(0,4723) { leq( addition( X, one ), addition(
% 68.63/69.08 star( Y ), X ) ) }.
% 68.63/69.08 (8688) {G4,W14,D5,L3,V3,M3} P(3711,204);d(9);d(21) { leq( multiplication( Z
% 68.63/69.08 , star( multiplication( skol2, Y ) ) ), X ), ! leq( X, skol1 ), ! leq( Z
% 68.63/69.08 , X ) }.
% 68.63/69.08 (8692) {G5,W8,D5,L1,V1,M1} F(8688);r(23) { leq( multiplication( skol1, star
% 68.63/69.08 ( multiplication( skol2, X ) ) ), skol1 ) }.
% 68.63/69.08 (13567) {G5,W7,D4,L1,V1,M1} P(109,353);d(660);d(149) { addition( star( X )
% 68.63/69.08 , X ) ==> star( X ) }.
% 68.63/69.08 (13613) {G6,W6,D3,L1,V1,M1} P(13567,8116) { leq( addition( X, one ), star(
% 68.63/69.08 X ) ) }.
% 68.63/69.08 (13710) {G7,W8,D5,L1,V1,M1} P(14,13613) { leq( strong_iteration( X ), star
% 68.63/69.08 ( multiplication( X, strong_iteration( X ) ) ) ) }.
% 68.63/69.08 (28571) {G4,W15,D4,L3,V1,M3} P(531,20) { ! X = skol1, ! X = multiplication
% 68.63/69.08 ( skol1, strong_iteration( skol2 ) ), ! leq( multiplication( skol1,
% 68.63/69.08 strong_iteration( skol2 ) ), X ) }.
% 68.63/69.08 (28584) {G5,W6,D4,L1,V0,M1} Q(28571);d(1535);q { ! leq( multiplication(
% 68.63/69.08 skol1, strong_iteration( skol2 ) ), skol1 ) }.
% 68.63/69.08 (28601) {G6,W8,D5,L1,V1,M1} R(28584,550) { ! leq( addition( X,
% 68.63/69.08 multiplication( skol1, strong_iteration( skol2 ) ) ), skol1 ) }.
% 68.63/69.08 (33004) {G7,W8,D5,L1,V1,M1} P(7,28601) { ! leq( multiplication( skol1,
% 68.63/69.08 addition( X, strong_iteration( skol2 ) ) ), skol1 ) }.
% 68.63/69.08 (33078) {G8,W9,D3,L2,V1,M2} P(39,33004) { ! leq( multiplication( skol1, X )
% 68.63/69.08 , skol1 ), ! leq( strong_iteration( skol2 ), X ) }.
% 68.63/69.08 (38029) {G7,W8,D5,L1,V1,M1} R(8692,39);d(1947) { multiplication( skol1,
% 68.63/69.08 star( multiplication( skol2, X ) ) ) ==> skol1 }.
% 68.63/69.08 (87935) {G9,W0,D0,L0,V0,M0} R(33078,13710);d(38029);r(23) { }.
% 68.63/69.08
% 68.63/69.08
% 68.63/69.08 % SZS output end Refutation
% 68.63/69.08 found a proof!
% 68.63/69.08
% 68.63/69.08
% 68.63/69.08 Unprocessed initial clauses:
% 68.63/69.08
% 68.63/69.08 (87937) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 68.63/69.08 (87938) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition
% 68.63/69.08 ( addition( Z, Y ), X ) }.
% 68.63/69.08 (87939) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 68.63/69.08 (87940) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 68.63/69.08 (87941) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) )
% 68.63/69.08 = multiplication( multiplication( X, Y ), Z ) }.
% 68.63/69.08 (87942) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 68.63/69.08 (87943) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 68.63/69.08 (87944) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 68.63/69.08 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 68.63/69.08 (87945) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 68.63/69.08 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 68.63/69.08 (87946) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 68.63/69.08 (87947) {G0,W9,D5,L1,V1,M1} { addition( one, multiplication( X, star( X )
% 68.63/69.08 ) ) = star( X ) }.
% 68.63/69.08 (87948) {G0,W9,D5,L1,V1,M1} { addition( one, multiplication( star( X ), X
% 68.63/69.08 ) ) = star( X ) }.
% 68.63/69.08 (87949) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( X, Z ), Y
% 68.63/69.08 ), Z ), leq( multiplication( star( X ), Y ), Z ) }.
% 68.63/69.08 (87950) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( Z, X ), Y
% 68.63/69.08 ), Z ), leq( multiplication( Y, star( X ) ), Z ) }.
% 68.63/69.08 (87951) {G0,W9,D5,L1,V1,M1} { strong_iteration( X ) = addition(
% 68.63/69.08 multiplication( X, strong_iteration( X ) ), one ) }.
% 68.63/69.08 (87952) {G0,W13,D4,L2,V3,M2} { ! leq( Z, addition( multiplication( X, Z )
% 68.63/69.08 , Y ) ), leq( Z, multiplication( strong_iteration( X ), Y ) ) }.
% 68.63/69.08 (87953) {G0,W10,D5,L1,V1,M1} { strong_iteration( X ) = addition( star( X )
% 68.63/69.08 , multiplication( strong_iteration( X ), zero ) ) }.
% 68.63/69.08 (87954) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 68.63/69.08 (87955) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 68.63/69.08 (87956) {G0,W5,D3,L1,V0,M1} { multiplication( skol1, skol2 ) = zero }.
% 68.63/69.08 (87957) {G0,W6,D4,L1,V0,M1} { ! multiplication( skol1, strong_iteration(
% 68.63/69.08 skol2 ) ) = skol1 }.
% 68.63/69.08
% 68.63/69.08
% 68.63/69.08 Total Proof:
% 68.63/69.08
% 68.63/69.08 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 68.63/69.08 ) }.
% 68.63/69.08 parent0: (87937) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 68.63/69.08 }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 68.63/69.08 ==> addition( addition( Z, Y ), X ) }.
% 68.63/69.08 parent0: (87938) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) =
% 68.63/69.08 addition( addition( Z, Y ), X ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 Z := Z
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 68.63/69.08 parent0: (87939) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 68.63/69.08 parent0: (87940) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (4) {G0,W11,D4,L1,V3,M1} I { multiplication( X, multiplication
% 68.63/69.08 ( Y, Z ) ) ==> multiplication( multiplication( X, Y ), Z ) }.
% 68.63/69.08 parent0: (87941) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication
% 68.63/69.08 ( Y, Z ) ) = multiplication( multiplication( X, Y ), Z ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 Z := Z
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 68.63/69.08 parent0: (87942) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 68.63/69.08 parent0: (87943) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (87985) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 68.63/69.08 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 68.63/69.08 parent0[0]: (87944) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y
% 68.63/69.08 , Z ) ) = addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 Z := Z
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y )
% 68.63/69.08 , multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 68.63/69.08 parent0: (87985) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 68.63/69.08 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 Z := Z
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (87993) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 68.63/69.08 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 68.63/69.08 parent0[0]: (87945) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y
% 68.63/69.08 ), Z ) = addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 Z := Z
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z )
% 68.63/69.08 , multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 68.63/69.08 parent0: (87993) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 68.63/69.08 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 Z := Z
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (9) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==> zero
% 68.63/69.08 }.
% 68.63/69.08 parent0: (87946) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero
% 68.63/69.08 }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (10) {G0,W9,D5,L1,V1,M1} I { addition( one, multiplication( X
% 68.63/69.08 , star( X ) ) ) ==> star( X ) }.
% 68.63/69.08 parent0: (87947) {G0,W9,D5,L1,V1,M1} { addition( one, multiplication( X,
% 68.63/69.08 star( X ) ) ) = star( X ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (11) {G0,W9,D5,L1,V1,M1} I { addition( one, multiplication(
% 68.63/69.08 star( X ), X ) ) ==> star( X ) }.
% 68.63/69.08 parent0: (87948) {G0,W9,D5,L1,V1,M1} { addition( one, multiplication( star
% 68.63/69.08 ( X ), X ) ) = star( X ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (13) {G0,W13,D4,L2,V3,M2} I { ! leq( addition( multiplication
% 68.63/69.08 ( Z, X ), Y ), Z ), leq( multiplication( Y, star( X ) ), Z ) }.
% 68.63/69.08 parent0: (87950) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( Z
% 68.63/69.08 , X ), Y ), Z ), leq( multiplication( Y, star( X ) ), Z ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 Z := Z
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 1 ==> 1
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88046) {G0,W9,D5,L1,V1,M1} { addition( multiplication( X,
% 68.63/69.08 strong_iteration( X ) ), one ) = strong_iteration( X ) }.
% 68.63/69.08 parent0[0]: (87951) {G0,W9,D5,L1,V1,M1} { strong_iteration( X ) = addition
% 68.63/69.08 ( multiplication( X, strong_iteration( X ) ), one ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (14) {G0,W9,D5,L1,V1,M1} I { addition( multiplication( X,
% 68.63/69.08 strong_iteration( X ) ), one ) ==> strong_iteration( X ) }.
% 68.63/69.08 parent0: (88046) {G0,W9,D5,L1,V1,M1} { addition( multiplication( X,
% 68.63/69.08 strong_iteration( X ) ), one ) = strong_iteration( X ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 68.63/69.08 ==> Y }.
% 68.63/69.08 parent0: (87954) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y
% 68.63/69.08 }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 1 ==> 1
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X
% 68.63/69.08 , Y ) }.
% 68.63/69.08 parent0: (87955) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y )
% 68.63/69.08 }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 1 ==> 1
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (19) {G0,W5,D3,L1,V0,M1} I { multiplication( skol1, skol2 )
% 68.63/69.08 ==> zero }.
% 68.63/69.08 parent0: (87956) {G0,W5,D3,L1,V0,M1} { multiplication( skol1, skol2 ) =
% 68.63/69.08 zero }.
% 68.63/69.08 substitution0:
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (20) {G0,W6,D4,L1,V0,M1} I { ! multiplication( skol1,
% 68.63/69.08 strong_iteration( skol2 ) ) ==> skol1 }.
% 68.63/69.08 parent0: (87957) {G0,W6,D4,L1,V0,M1} { ! multiplication( skol1,
% 68.63/69.08 strong_iteration( skol2 ) ) = skol1 }.
% 68.63/69.08 substitution0:
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88109) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, zero ) }.
% 68.63/69.08 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 paramod: (88110) {G1,W5,D3,L1,V1,M1} { X ==> addition( zero, X ) }.
% 68.63/69.08 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 68.63/69.08 }.
% 68.63/69.08 parent1[0; 2]: (88109) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, zero ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := zero
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88113) {G1,W5,D3,L1,V1,M1} { addition( zero, X ) ==> X }.
% 68.63/69.08 parent0[0]: (88110) {G1,W5,D3,L1,V1,M1} { X ==> addition( zero, X ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (21) {G1,W5,D3,L1,V1,M1} P(0,2) { addition( zero, X ) ==> X
% 68.63/69.08 }.
% 68.63/69.08 parent0: (88113) {G1,W5,D3,L1,V1,M1} { addition( zero, X ) ==> X }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88114) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 68.63/69.08 ) }.
% 68.63/69.08 parent0[0]: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 68.63/69.08 Y ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88115) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 68.63/69.08 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 resolution: (88116) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 68.63/69.08 parent0[0]: (88114) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X
% 68.63/69.08 , Y ) }.
% 68.63/69.08 parent1[0]: (88115) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := X
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (23) {G1,W3,D2,L1,V1,M1} R(18,3) { leq( X, X ) }.
% 68.63/69.08 parent0: (88116) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88117) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 68.63/69.08 ) }.
% 68.63/69.08 parent0[0]: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 68.63/69.08 Y ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 paramod: (88118) {G1,W8,D3,L2,V2,M2} { ! X ==> addition( X, Y ), leq( Y, X
% 68.63/69.08 ) }.
% 68.63/69.08 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 68.63/69.08 }.
% 68.63/69.08 parent1[0; 3]: (88117) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 68.63/69.08 ( X, Y ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := Y
% 68.63/69.08 Y := X
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := Y
% 68.63/69.08 Y := X
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88121) {G1,W8,D3,L2,V2,M2} { ! addition( X, Y ) ==> X, leq( Y, X
% 68.63/69.08 ) }.
% 68.63/69.08 parent0[0]: (88118) {G1,W8,D3,L2,V2,M2} { ! X ==> addition( X, Y ), leq( Y
% 68.63/69.08 , X ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (24) {G1,W8,D3,L2,V2,M2} P(0,18) { ! addition( Y, X ) ==> Y,
% 68.63/69.08 leq( X, Y ) }.
% 68.63/69.08 parent0: (88121) {G1,W8,D3,L2,V2,M2} { ! addition( X, Y ) ==> X, leq( Y, X
% 68.63/69.08 ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := Y
% 68.63/69.08 Y := X
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 1 ==> 1
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88123) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 68.63/69.08 ) }.
% 68.63/69.08 parent0[0]: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 68.63/69.08 Y ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 paramod: (88124) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition(
% 68.63/69.08 addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 68.63/69.08 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 68.63/69.08 ==> addition( addition( Z, Y ), X ) }.
% 68.63/69.08 parent1[0; 5]: (88123) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 68.63/69.08 ( X, Y ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := Y
% 68.63/69.08 Y := X
% 68.63/69.08 Z := Z
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := Z
% 68.63/69.08 Y := addition( X, Y )
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88125) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 68.63/69.08 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 68.63/69.08 parent0[0]: (88124) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition
% 68.63/69.08 ( addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 Z := Z
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (26) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y
% 68.63/69.08 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 68.63/69.08 parent0: (88125) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 68.63/69.08 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := Y
% 68.63/69.08 Y := Z
% 68.63/69.08 Z := X
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 1 ==> 1
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88126) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 68.63/69.08 addition( X, addition( Y, Z ) ) }.
% 68.63/69.08 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 68.63/69.08 ==> addition( addition( Z, Y ), X ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := Z
% 68.63/69.08 Y := Y
% 68.63/69.08 Z := X
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 paramod: (88129) {G1,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z )
% 68.63/69.08 ==> addition( addition( Y, Z ), X ) }.
% 68.63/69.08 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 68.63/69.08 }.
% 68.63/69.08 parent1[0; 6]: (88126) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ),
% 68.63/69.08 Z ) ==> addition( X, addition( Y, Z ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := addition( Y, Z )
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 Z := Z
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (27) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y )
% 68.63/69.08 , Z ) = addition( addition( Y, Z ), X ) }.
% 68.63/69.08 parent0: (88129) {G1,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z )
% 68.63/69.08 ==> addition( addition( Y, Z ), X ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 Z := Z
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88144) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 68.63/69.08 addition( X, addition( Y, Z ) ) }.
% 68.63/69.08 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 68.63/69.08 ==> addition( addition( Z, Y ), X ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := Z
% 68.63/69.08 Y := Y
% 68.63/69.08 Z := X
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 paramod: (88150) {G1,W9,D4,L1,V2,M1} { addition( addition( X, Y ), Y ) ==>
% 68.63/69.08 addition( X, Y ) }.
% 68.63/69.08 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 68.63/69.08 parent1[0; 8]: (88144) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ),
% 68.63/69.08 Z ) ==> addition( X, addition( Y, Z ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := Y
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 Z := Y
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (30) {G1,W9,D4,L1,V2,M1} P(3,1) { addition( addition( Y, X ),
% 68.63/69.08 X ) ==> addition( Y, X ) }.
% 68.63/69.08 parent0: (88150) {G1,W9,D4,L1,V2,M1} { addition( addition( X, Y ), Y ) ==>
% 68.63/69.08 addition( X, Y ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := Y
% 68.63/69.08 Y := X
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88156) {G1,W8,D3,L2,V2,M2} { ! X ==> addition( X, Y ), leq( Y, X
% 68.63/69.08 ) }.
% 68.63/69.08 parent0[0]: (24) {G1,W8,D3,L2,V2,M2} P(0,18) { ! addition( Y, X ) ==> Y,
% 68.63/69.08 leq( X, Y ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := Y
% 68.63/69.08 Y := X
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 paramod: (88157) {G1,W9,D2,L3,V2,M3} { ! X ==> Y, ! leq( X, Y ), leq( Y, X
% 68.63/69.08 ) }.
% 68.63/69.08 parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 68.63/69.08 ==> Y }.
% 68.63/69.08 parent1[0; 3]: (88156) {G1,W8,D3,L2,V2,M2} { ! X ==> addition( X, Y ), leq
% 68.63/69.08 ( Y, X ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88158) {G1,W9,D2,L3,V2,M3} { ! Y ==> X, ! leq( X, Y ), leq( Y, X
% 68.63/69.08 ) }.
% 68.63/69.08 parent0[0]: (88157) {G1,W9,D2,L3,V2,M3} { ! X ==> Y, ! leq( X, Y ), leq( Y
% 68.63/69.08 , X ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (36) {G2,W9,D2,L3,V2,M3} P(17,24) { ! Y = X, leq( Y, X ), !
% 68.63/69.08 leq( X, Y ) }.
% 68.63/69.08 parent0: (88158) {G1,W9,D2,L3,V2,M3} { ! Y ==> X, ! leq( X, Y ), leq( Y, X
% 68.63/69.08 ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 1 ==> 2
% 68.63/69.08 2 ==> 1
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88159) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 68.63/69.08 ) }.
% 68.63/69.08 parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 68.63/69.08 ==> Y }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 paramod: (88160) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X
% 68.63/69.08 ) }.
% 68.63/69.08 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 68.63/69.08 }.
% 68.63/69.08 parent1[0; 2]: (88159) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq
% 68.63/69.08 ( X, Y ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := Y
% 68.63/69.08 Y := X
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := Y
% 68.63/69.08 Y := X
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88163) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> X, ! leq( Y, X
% 68.63/69.08 ) }.
% 68.63/69.08 parent0[0]: (88160) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y
% 68.63/69.08 , X ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (39) {G1,W8,D3,L2,V2,M2} P(17,0) { addition( Y, X ) ==> Y, !
% 68.63/69.08 leq( X, Y ) }.
% 68.63/69.08 parent0: (88163) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> X, ! leq( Y, X
% 68.63/69.08 ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := Y
% 68.63/69.08 Y := X
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 1 ==> 1
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88164) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z )
% 68.63/69.08 ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 68.63/69.08 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 68.63/69.08 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 Z := Z
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 paramod: (88167) {G1,W16,D4,L2,V3,M2} { multiplication( X, addition( Y, Z
% 68.63/69.08 ) ) ==> multiplication( X, Z ), ! leq( multiplication( X, Y ),
% 68.63/69.08 multiplication( X, Z ) ) }.
% 68.63/69.08 parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 68.63/69.08 ==> Y }.
% 68.63/69.08 parent1[0; 6]: (88164) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition
% 68.63/69.08 ( Y, Z ) ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) )
% 68.63/69.08 }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := multiplication( X, Y )
% 68.63/69.08 Y := multiplication( X, Z )
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 Z := Z
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (61) {G1,W16,D4,L2,V3,M2} P(7,17) { ! leq( multiplication( X,
% 68.63/69.08 Y ), multiplication( X, Z ) ), multiplication( X, addition( Y, Z ) ) ==>
% 68.63/69.08 multiplication( X, Z ) }.
% 68.63/69.08 parent0: (88167) {G1,W16,D4,L2,V3,M2} { multiplication( X, addition( Y, Z
% 68.63/69.08 ) ) ==> multiplication( X, Z ), ! leq( multiplication( X, Y ),
% 68.63/69.08 multiplication( X, Z ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 Z := Z
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 1
% 68.63/69.08 1 ==> 0
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88172) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 68.63/69.08 ) }.
% 68.63/69.08 parent0[0]: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 68.63/69.08 Y ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 paramod: (88173) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 68.63/69.08 multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ),
% 68.63/69.08 multiplication( X, Y ) ) }.
% 68.63/69.08 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 68.63/69.08 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 68.63/69.08 parent1[0; 5]: (88172) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 68.63/69.08 ( X, Y ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Z
% 68.63/69.08 Z := Y
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := multiplication( X, Z )
% 68.63/69.08 Y := multiplication( X, Y )
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88174) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, addition( Z, Y
% 68.63/69.08 ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ),
% 68.63/69.08 multiplication( X, Y ) ) }.
% 68.63/69.08 parent0[0]: (88173) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 68.63/69.08 multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ),
% 68.63/69.08 multiplication( X, Y ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 Z := Z
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (65) {G1,W16,D4,L2,V3,M2} P(7,18) { ! multiplication( X,
% 68.63/69.08 addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 68.63/69.08 ), multiplication( X, Z ) ) }.
% 68.63/69.08 parent0: (88174) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, addition( Z,
% 68.63/69.08 Y ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ),
% 68.63/69.08 multiplication( X, Y ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Z
% 68.63/69.08 Z := Y
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 1 ==> 1
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88176) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Z ), Y
% 68.63/69.08 ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) ) }.
% 68.63/69.08 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 68.63/69.08 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Z
% 68.63/69.08 Z := Y
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 paramod: (88178) {G1,W11,D4,L1,V1,M1} { multiplication( addition( skol1, X
% 68.63/69.08 ), skol2 ) ==> addition( zero, multiplication( X, skol2 ) ) }.
% 68.63/69.08 parent0[0]: (19) {G0,W5,D3,L1,V0,M1} I { multiplication( skol1, skol2 ) ==>
% 68.63/69.08 zero }.
% 68.63/69.08 parent1[0; 7]: (88176) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X
% 68.63/69.08 , Z ), Y ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) )
% 68.63/69.08 }.
% 68.63/69.08 substitution0:
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := skol1
% 68.63/69.08 Y := skol2
% 68.63/69.08 Z := X
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 paramod: (88180) {G2,W9,D4,L1,V1,M1} { multiplication( addition( skol1, X
% 68.63/69.08 ), skol2 ) ==> multiplication( X, skol2 ) }.
% 68.63/69.08 parent0[0]: (21) {G1,W5,D3,L1,V1,M1} P(0,2) { addition( zero, X ) ==> X }.
% 68.63/69.08 parent1[0; 6]: (88178) {G1,W11,D4,L1,V1,M1} { multiplication( addition(
% 68.63/69.08 skol1, X ), skol2 ) ==> addition( zero, multiplication( X, skol2 ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := multiplication( X, skol2 )
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (105) {G2,W9,D4,L1,V1,M1} P(19,8);d(21) { multiplication(
% 68.63/69.08 addition( skol1, X ), skol2 ) ==> multiplication( X, skol2 ) }.
% 68.63/69.08 parent0: (88180) {G2,W9,D4,L1,V1,M1} { multiplication( addition( skol1, X
% 68.63/69.08 ), skol2 ) ==> multiplication( X, skol2 ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88183) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Z ), Y
% 68.63/69.08 ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) ) }.
% 68.63/69.08 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 68.63/69.08 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Z
% 68.63/69.08 Z := Y
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 paramod: (88185) {G1,W11,D4,L1,V2,M1} { multiplication( addition( X, one )
% 68.63/69.08 , Y ) ==> addition( multiplication( X, Y ), Y ) }.
% 68.63/69.08 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 68.63/69.08 parent1[0; 10]: (88183) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X
% 68.63/69.08 , Z ), Y ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) )
% 68.63/69.08 }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := Y
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 Z := one
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88187) {G1,W11,D4,L1,V2,M1} { addition( multiplication( X, Y ), Y
% 68.63/69.08 ) ==> multiplication( addition( X, one ), Y ) }.
% 68.63/69.08 parent0[0]: (88185) {G1,W11,D4,L1,V2,M1} { multiplication( addition( X,
% 68.63/69.08 one ), Y ) ==> addition( multiplication( X, Y ), Y ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (109) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( multiplication(
% 68.63/69.08 Y, X ), X ) = multiplication( addition( Y, one ), X ) }.
% 68.63/69.08 parent0: (88187) {G1,W11,D4,L1,V2,M1} { addition( multiplication( X, Y ),
% 68.63/69.08 Y ) ==> multiplication( addition( X, one ), Y ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := Y
% 68.63/69.08 Y := X
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88189) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 68.63/69.08 addition( X, addition( Y, Z ) ) }.
% 68.63/69.08 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 68.63/69.08 ==> addition( addition( Z, Y ), X ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := Z
% 68.63/69.08 Y := Y
% 68.63/69.08 Z := X
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 paramod: (88191) {G1,W13,D5,L1,V2,M1} { addition( addition( X, one ),
% 68.63/69.08 multiplication( Y, star( Y ) ) ) ==> addition( X, star( Y ) ) }.
% 68.63/69.08 parent0[0]: (10) {G0,W9,D5,L1,V1,M1} I { addition( one, multiplication( X,
% 68.63/69.08 star( X ) ) ) ==> star( X ) }.
% 68.63/69.08 parent1[0; 11]: (88189) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y )
% 68.63/69.08 , Z ) ==> addition( X, addition( Y, Z ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := Y
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := X
% 68.63/69.08 Y := one
% 68.63/69.08 Z := multiplication( Y, star( Y ) )
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (126) {G1,W13,D5,L1,V2,M1} P(10,1) { addition( addition( Y,
% 68.63/69.08 one ), multiplication( X, star( X ) ) ) ==> addition( Y, star( X ) ) }.
% 68.63/69.08 parent0: (88191) {G1,W13,D5,L1,V2,M1} { addition( addition( X, one ),
% 68.63/69.08 multiplication( Y, star( Y ) ) ) ==> addition( X, star( Y ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := Y
% 68.63/69.08 Y := X
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88194) {G0,W9,D5,L1,V1,M1} { star( X ) ==> addition( one,
% 68.63/69.08 multiplication( star( X ), X ) ) }.
% 68.63/69.08 parent0[0]: (11) {G0,W9,D5,L1,V1,M1} I { addition( one, multiplication(
% 68.63/69.08 star( X ), X ) ) ==> star( X ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 paramod: (88195) {G1,W9,D5,L1,V1,M1} { star( X ) ==> addition(
% 68.63/69.08 multiplication( star( X ), X ), one ) }.
% 68.63/69.08 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 68.63/69.08 }.
% 68.63/69.08 parent1[0; 3]: (88194) {G0,W9,D5,L1,V1,M1} { star( X ) ==> addition( one,
% 68.63/69.08 multiplication( star( X ), X ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := one
% 68.63/69.08 Y := multiplication( star( X ), X )
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88198) {G1,W9,D5,L1,V1,M1} { addition( multiplication( star( X )
% 68.63/69.08 , X ), one ) ==> star( X ) }.
% 68.63/69.08 parent0[0]: (88195) {G1,W9,D5,L1,V1,M1} { star( X ) ==> addition(
% 68.63/69.08 multiplication( star( X ), X ), one ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (149) {G1,W9,D5,L1,V1,M1} P(11,0) { addition( multiplication(
% 68.63/69.08 star( X ), X ), one ) ==> star( X ) }.
% 68.63/69.08 parent0: (88198) {G1,W9,D5,L1,V1,M1} { addition( multiplication( star( X )
% 68.63/69.08 , X ), one ) ==> star( X ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 paramod: (88200) {G1,W17,D5,L2,V4,M2} { ! leq( addition( multiplication(
% 68.63/69.08 multiplication( X, Y ), Z ), T ), X ), leq( multiplication( T, star(
% 68.63/69.08 multiplication( Y, Z ) ) ), X ) }.
% 68.63/69.08 parent0[0]: (4) {G0,W11,D4,L1,V3,M1} I { multiplication( X, multiplication
% 68.63/69.08 ( Y, Z ) ) ==> multiplication( multiplication( X, Y ), Z ) }.
% 68.63/69.08 parent1[0; 3]: (13) {G0,W13,D4,L2,V3,M2} I { ! leq( addition(
% 68.63/69.08 multiplication( Z, X ), Y ), Z ), leq( multiplication( Y, star( X ) ), Z
% 68.63/69.08 ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 Z := Z
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := multiplication( Y, Z )
% 68.63/69.08 Y := T
% 68.63/69.08 Z := X
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (204) {G1,W17,D5,L2,V4,M2} P(4,13) { ! leq( addition(
% 68.63/69.08 multiplication( multiplication( X, Y ), Z ), T ), X ), leq(
% 68.63/69.08 multiplication( T, star( multiplication( Y, Z ) ) ), X ) }.
% 68.63/69.08 parent0: (88200) {G1,W17,D5,L2,V4,M2} { ! leq( addition( multiplication(
% 68.63/69.08 multiplication( X, Y ), Z ), T ), X ), leq( multiplication( T, star(
% 68.63/69.08 multiplication( Y, Z ) ) ), X ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 Z := Z
% 68.63/69.08 T := T
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 1 ==> 1
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88202) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==> addition(
% 68.63/69.08 addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 68.63/69.08 parent0[0]: (26) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y
% 68.63/69.08 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 Z := Z
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 paramod: (88205) {G1,W12,D3,L2,V2,M2} { ! addition( X, Y ) ==> addition( X
% 68.63/69.08 , Y ), leq( X, addition( X, Y ) ) }.
% 68.63/69.08 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 68.63/69.08 parent1[0; 6]: (88202) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==>
% 68.63/69.08 addition( addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := X
% 68.63/69.08 Y := X
% 68.63/69.08 Z := Y
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqrefl: (88208) {G0,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 68.63/69.08 parent0[0]: (88205) {G1,W12,D3,L2,V2,M2} { ! addition( X, Y ) ==> addition
% 68.63/69.08 ( X, Y ), leq( X, addition( X, Y ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (306) {G2,W5,D3,L1,V2,M1} P(3,26);q { leq( X, addition( X, Y )
% 68.63/69.08 ) }.
% 68.63/69.08 parent0: (88208) {G0,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 paramod: (88210) {G1,W4,D3,L1,V1,M1} { leq( one, star( X ) ) }.
% 68.63/69.08 parent0[0]: (11) {G0,W9,D5,L1,V1,M1} I { addition( one, multiplication(
% 68.63/69.08 star( X ), X ) ) ==> star( X ) }.
% 68.63/69.08 parent1[0; 2]: (306) {G2,W5,D3,L1,V2,M1} P(3,26);q { leq( X, addition( X, Y
% 68.63/69.08 ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := one
% 68.63/69.08 Y := multiplication( star( X ), X )
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (316) {G3,W4,D3,L1,V1,M1} P(11,306) { leq( one, star( X ) )
% 68.63/69.08 }.
% 68.63/69.08 parent0: (88210) {G1,W4,D3,L1,V1,M1} { leq( one, star( X ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 paramod: (88211) {G1,W5,D3,L1,V2,M1} { leq( X, addition( Y, X ) ) }.
% 68.63/69.08 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 68.63/69.08 }.
% 68.63/69.08 parent1[0; 2]: (306) {G2,W5,D3,L1,V2,M1} P(3,26);q { leq( X, addition( X, Y
% 68.63/69.08 ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (322) {G3,W5,D3,L1,V2,M1} P(0,306) { leq( X, addition( Y, X )
% 68.63/69.08 ) }.
% 68.63/69.08 parent0: (88211) {G1,W5,D3,L1,V2,M1} { leq( X, addition( Y, X ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88213) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 68.63/69.08 ) }.
% 68.63/69.08 parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 68.63/69.08 ==> Y }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 resolution: (88214) {G1,W7,D4,L1,V1,M1} { star( X ) ==> addition( one,
% 68.63/69.08 star( X ) ) }.
% 68.63/69.08 parent0[1]: (88213) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X
% 68.63/69.08 , Y ) }.
% 68.63/69.08 parent1[0]: (316) {G3,W4,D3,L1,V1,M1} P(11,306) { leq( one, star( X ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := one
% 68.63/69.08 Y := star( X )
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88215) {G1,W7,D4,L1,V1,M1} { addition( one, star( X ) ) ==> star
% 68.63/69.08 ( X ) }.
% 68.63/69.08 parent0[0]: (88214) {G1,W7,D4,L1,V1,M1} { star( X ) ==> addition( one,
% 68.63/69.08 star( X ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (323) {G4,W7,D4,L1,V1,M1} R(316,17) { addition( one, star( X )
% 68.63/69.08 ) ==> star( X ) }.
% 68.63/69.08 parent0: (88215) {G1,W7,D4,L1,V1,M1} { addition( one, star( X ) ) ==> star
% 68.63/69.08 ( X ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88216) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X ) =
% 68.63/69.08 addition( addition( X, Y ), Z ) }.
% 68.63/69.08 parent0[0]: (27) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y ),
% 68.63/69.08 Z ) = addition( addition( Y, Z ), X ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 Z := Z
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 paramod: (88217) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( X, Y )
% 68.63/69.08 , Z ) ) }.
% 68.63/69.08 parent0[0]: (88216) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X )
% 68.63/69.08 = addition( addition( X, Y ), Z ) }.
% 68.63/69.08 parent1[0; 2]: (322) {G3,W5,D3,L1,V2,M1} P(0,306) { leq( X, addition( Y, X
% 68.63/69.08 ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 Z := Z
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := X
% 68.63/69.08 Y := addition( Y, Z )
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 paramod: (88218) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( Z, X )
% 68.63/69.08 , Y ) ) }.
% 68.63/69.08 parent0[0]: (88216) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X )
% 68.63/69.08 = addition( addition( X, Y ), Z ) }.
% 68.63/69.08 parent1[0; 2]: (88217) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( X
% 68.63/69.08 , Y ), Z ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := Z
% 68.63/69.08 Y := X
% 68.63/69.08 Z := Y
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 Z := Z
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (348) {G4,W7,D4,L1,V3,M1} P(27,322) { leq( Z, addition(
% 68.63/69.08 addition( Y, Z ), X ) ) }.
% 68.63/69.08 parent0: (88218) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( Z, X )
% 68.63/69.08 , Y ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := Z
% 68.63/69.08 Y := X
% 68.63/69.08 Z := Y
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88221) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X ) =
% 68.63/69.08 addition( addition( X, Y ), Z ) }.
% 68.63/69.08 parent0[0]: (27) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y ),
% 68.63/69.08 Z ) = addition( addition( Y, Z ), X ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 Z := Z
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 paramod: (88223) {G1,W13,D6,L1,V2,M1} { addition( addition( multiplication
% 68.63/69.08 ( star( X ), X ), Y ), one ) = addition( star( X ), Y ) }.
% 68.63/69.08 parent0[0]: (11) {G0,W9,D5,L1,V1,M1} I { addition( one, multiplication(
% 68.63/69.08 star( X ), X ) ) ==> star( X ) }.
% 68.63/69.08 parent1[0; 10]: (88221) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z )
% 68.63/69.08 , X ) = addition( addition( X, Y ), Z ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := one
% 68.63/69.08 Y := multiplication( star( X ), X )
% 68.63/69.08 Z := Y
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (353) {G2,W13,D6,L1,V2,M1} P(11,27) { addition( addition(
% 68.63/69.08 multiplication( star( X ), X ), Y ), one ) ==> addition( star( X ), Y )
% 68.63/69.08 }.
% 68.63/69.08 parent0: (88223) {G1,W13,D6,L1,V2,M1} { addition( addition( multiplication
% 68.63/69.08 ( star( X ), X ), Y ), one ) = addition( star( X ), Y ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88227) {G1,W9,D4,L1,V2,M1} { addition( X, Y ) ==> addition(
% 68.63/69.08 addition( X, Y ), Y ) }.
% 68.63/69.08 parent0[0]: (30) {G1,W9,D4,L1,V2,M1} P(3,1) { addition( addition( Y, X ), X
% 68.63/69.08 ) ==> addition( Y, X ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := Y
% 68.63/69.08 Y := X
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 paramod: (88229) {G1,W11,D5,L1,V1,M1} { addition( multiplication( X,
% 68.63/69.08 strong_iteration( X ) ), one ) ==> addition( strong_iteration( X ), one )
% 68.63/69.08 }.
% 68.63/69.08 parent0[0]: (14) {G0,W9,D5,L1,V1,M1} I { addition( multiplication( X,
% 68.63/69.08 strong_iteration( X ) ), one ) ==> strong_iteration( X ) }.
% 68.63/69.08 parent1[0; 8]: (88227) {G1,W9,D4,L1,V2,M1} { addition( X, Y ) ==> addition
% 68.63/69.08 ( addition( X, Y ), Y ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := multiplication( X, strong_iteration( X ) )
% 68.63/69.08 Y := one
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 paramod: (88230) {G1,W7,D4,L1,V1,M1} { strong_iteration( X ) ==> addition
% 68.63/69.08 ( strong_iteration( X ), one ) }.
% 68.63/69.08 parent0[0]: (14) {G0,W9,D5,L1,V1,M1} I { addition( multiplication( X,
% 68.63/69.08 strong_iteration( X ) ), one ) ==> strong_iteration( X ) }.
% 68.63/69.08 parent1[0; 1]: (88229) {G1,W11,D5,L1,V1,M1} { addition( multiplication( X
% 68.63/69.08 , strong_iteration( X ) ), one ) ==> addition( strong_iteration( X ), one
% 68.63/69.08 ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88232) {G1,W7,D4,L1,V1,M1} { addition( strong_iteration( X ), one
% 68.63/69.08 ) ==> strong_iteration( X ) }.
% 68.63/69.08 parent0[0]: (88230) {G1,W7,D4,L1,V1,M1} { strong_iteration( X ) ==>
% 68.63/69.08 addition( strong_iteration( X ), one ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (417) {G2,W7,D4,L1,V1,M1} P(14,30) { addition(
% 68.63/69.08 strong_iteration( X ), one ) ==> strong_iteration( X ) }.
% 68.63/69.08 parent0: (88232) {G1,W7,D4,L1,V1,M1} { addition( strong_iteration( X ),
% 68.63/69.08 one ) ==> strong_iteration( X ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88234) {G2,W9,D2,L3,V2,M3} { ! Y = X, leq( X, Y ), ! leq( Y, X )
% 68.63/69.08 }.
% 68.63/69.08 parent0[0]: (36) {G2,W9,D2,L3,V2,M3} P(17,24) { ! Y = X, leq( Y, X ), ! leq
% 68.63/69.08 ( X, Y ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := Y
% 68.63/69.08 Y := X
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88235) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 68.63/69.08 ) }.
% 68.63/69.08 parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 68.63/69.08 ==> Y }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 resolution: (88246) {G1,W11,D3,L3,V2,M3} { X ==> addition( Y, X ), ! X = Y
% 68.63/69.08 , ! leq( X, Y ) }.
% 68.63/69.08 parent0[1]: (88235) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X
% 68.63/69.08 , Y ) }.
% 68.63/69.08 parent1[1]: (88234) {G2,W9,D2,L3,V2,M3} { ! Y = X, leq( X, Y ), ! leq( Y,
% 68.63/69.08 X ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := Y
% 68.63/69.08 Y := X
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := Y
% 68.63/69.08 Y := X
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 paramod: (88247) {G2,W12,D2,L4,V2,M4} { X ==> Y, ! leq( X, Y ), ! X = Y, !
% 68.63/69.08 leq( X, Y ) }.
% 68.63/69.08 parent0[0]: (39) {G1,W8,D3,L2,V2,M2} P(17,0) { addition( Y, X ) ==> Y, !
% 68.63/69.08 leq( X, Y ) }.
% 68.63/69.08 parent1[0; 2]: (88246) {G1,W11,D3,L3,V2,M3} { X ==> addition( Y, X ), ! X
% 68.63/69.08 = Y, ! leq( X, Y ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88249) {G2,W12,D2,L4,V2,M4} { ! Y = X, X ==> Y, ! leq( X, Y ), !
% 68.63/69.08 leq( X, Y ) }.
% 68.63/69.08 parent0[2]: (88247) {G2,W12,D2,L4,V2,M4} { X ==> Y, ! leq( X, Y ), ! X = Y
% 68.63/69.08 , ! leq( X, Y ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88250) {G2,W12,D2,L4,V2,M4} { Y ==> X, ! Y = X, ! leq( X, Y ), !
% 68.63/69.08 leq( X, Y ) }.
% 68.63/69.08 parent0[1]: (88249) {G2,W12,D2,L4,V2,M4} { ! Y = X, X ==> Y, ! leq( X, Y )
% 68.63/69.08 , ! leq( X, Y ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 factor: (88252) {G2,W9,D2,L3,V2,M3} { X ==> Y, ! X = Y, ! leq( Y, X ) }.
% 68.63/69.08 parent0[2, 3]: (88250) {G2,W12,D2,L4,V2,M4} { Y ==> X, ! Y = X, ! leq( X,
% 68.63/69.08 Y ), ! leq( X, Y ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := Y
% 68.63/69.08 Y := X
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (531) {G3,W9,D2,L3,V2,M3} R(36,17);d(39) { ! X = Y, ! leq( Y,
% 68.63/69.08 X ), X = Y }.
% 68.63/69.08 parent0: (88252) {G2,W9,D2,L3,V2,M3} { X ==> Y, ! X = Y, ! leq( Y, X ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 2
% 68.63/69.08 1 ==> 0
% 68.63/69.08 2 ==> 1
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 paramod: (88256) {G1,W8,D3,L2,V3,M2} { leq( X, Z ), ! leq( addition( Y, X
% 68.63/69.08 ), Z ) }.
% 68.63/69.08 parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 68.63/69.08 ==> Y }.
% 68.63/69.08 parent1[0; 2]: (348) {G4,W7,D4,L1,V3,M1} P(27,322) { leq( Z, addition(
% 68.63/69.08 addition( Y, Z ), X ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := addition( Y, X )
% 68.63/69.08 Y := Z
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := Z
% 68.63/69.08 Y := Y
% 68.63/69.08 Z := X
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (550) {G5,W8,D3,L2,V3,M2} P(17,348) { leq( Y, Z ), ! leq(
% 68.63/69.08 addition( X, Y ), Z ) }.
% 68.63/69.08 parent0: (88256) {G1,W8,D3,L2,V3,M2} { leq( X, Z ), ! leq( addition( Y, X
% 68.63/69.08 ), Z ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := Y
% 68.63/69.08 Y := X
% 68.63/69.08 Z := Z
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 1 ==> 1
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88260) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X
% 68.63/69.08 ) }.
% 68.63/69.08 parent0[0]: (39) {G1,W8,D3,L2,V2,M2} P(17,0) { addition( Y, X ) ==> Y, !
% 68.63/69.08 leq( X, Y ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := Y
% 68.63/69.08 Y := X
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 resolution: (88261) {G2,W7,D4,L1,V1,M1} { star( X ) ==> addition( star( X
% 68.63/69.08 ), one ) }.
% 68.63/69.08 parent0[1]: (88260) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y
% 68.63/69.08 , X ) }.
% 68.63/69.08 parent1[0]: (316) {G3,W4,D3,L1,V1,M1} P(11,306) { leq( one, star( X ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := star( X )
% 68.63/69.08 Y := one
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88262) {G2,W7,D4,L1,V1,M1} { addition( star( X ), one ) ==> star
% 68.63/69.08 ( X ) }.
% 68.63/69.08 parent0[0]: (88261) {G2,W7,D4,L1,V1,M1} { star( X ) ==> addition( star( X
% 68.63/69.08 ), one ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (660) {G4,W7,D4,L1,V1,M1} R(39,316) { addition( star( X ), one
% 68.63/69.08 ) ==> star( X ) }.
% 68.63/69.08 parent0: (88262) {G2,W7,D4,L1,V1,M1} { addition( star( X ), one ) ==> star
% 68.63/69.08 ( X ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88264) {G1,W16,D4,L2,V3,M2} { multiplication( X, Z ) ==>
% 68.63/69.08 multiplication( X, addition( Y, Z ) ), ! leq( multiplication( X, Y ),
% 68.63/69.08 multiplication( X, Z ) ) }.
% 68.63/69.08 parent0[1]: (61) {G1,W16,D4,L2,V3,M2} P(7,17) { ! leq( multiplication( X, Y
% 68.63/69.08 ), multiplication( X, Z ) ), multiplication( X, addition( Y, Z ) ) ==>
% 68.63/69.08 multiplication( X, Z ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 Z := Z
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 paramod: (88267) {G2,W16,D4,L2,V2,M2} { multiplication( X, one ) ==>
% 68.63/69.08 multiplication( X, strong_iteration( Y ) ), ! leq( multiplication( X,
% 68.63/69.08 strong_iteration( Y ) ), multiplication( X, one ) ) }.
% 68.63/69.08 parent0[0]: (417) {G2,W7,D4,L1,V1,M1} P(14,30) { addition( strong_iteration
% 68.63/69.08 ( X ), one ) ==> strong_iteration( X ) }.
% 68.63/69.08 parent1[0; 6]: (88264) {G1,W16,D4,L2,V3,M2} { multiplication( X, Z ) ==>
% 68.63/69.08 multiplication( X, addition( Y, Z ) ), ! leq( multiplication( X, Y ),
% 68.63/69.08 multiplication( X, Z ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := Y
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := X
% 68.63/69.08 Y := strong_iteration( Y )
% 68.63/69.08 Z := one
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 paramod: (88269) {G1,W14,D4,L2,V2,M2} { ! leq( multiplication( X,
% 68.63/69.08 strong_iteration( Y ) ), X ), multiplication( X, one ) ==> multiplication
% 68.63/69.08 ( X, strong_iteration( Y ) ) }.
% 68.63/69.08 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 68.63/69.08 parent1[1; 6]: (88267) {G2,W16,D4,L2,V2,M2} { multiplication( X, one ) ==>
% 68.63/69.08 multiplication( X, strong_iteration( Y ) ), ! leq( multiplication( X,
% 68.63/69.08 strong_iteration( Y ) ), multiplication( X, one ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 paramod: (88271) {G1,W12,D4,L2,V2,M2} { X ==> multiplication( X,
% 68.63/69.08 strong_iteration( Y ) ), ! leq( multiplication( X, strong_iteration( Y )
% 68.63/69.08 ), X ) }.
% 68.63/69.08 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 68.63/69.08 parent1[1; 1]: (88269) {G1,W14,D4,L2,V2,M2} { ! leq( multiplication( X,
% 68.63/69.08 strong_iteration( Y ) ), X ), multiplication( X, one ) ==> multiplication
% 68.63/69.08 ( X, strong_iteration( Y ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88272) {G1,W12,D4,L2,V2,M2} { multiplication( X, strong_iteration
% 68.63/69.08 ( Y ) ) ==> X, ! leq( multiplication( X, strong_iteration( Y ) ), X ) }.
% 68.63/69.08 parent0[0]: (88271) {G1,W12,D4,L2,V2,M2} { X ==> multiplication( X,
% 68.63/69.08 strong_iteration( Y ) ), ! leq( multiplication( X, strong_iteration( Y )
% 68.63/69.08 ), X ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (1535) {G3,W12,D4,L2,V2,M2} P(417,61);d(5);d(5) { ! leq(
% 68.63/69.08 multiplication( Y, strong_iteration( X ) ), Y ), multiplication( Y,
% 68.63/69.08 strong_iteration( X ) ) ==> Y }.
% 68.63/69.08 parent0: (88272) {G1,W12,D4,L2,V2,M2} { multiplication( X,
% 68.63/69.08 strong_iteration( Y ) ) ==> X, ! leq( multiplication( X, strong_iteration
% 68.63/69.08 ( Y ) ), X ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := Y
% 68.63/69.08 Y := X
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 1
% 68.63/69.08 1 ==> 0
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88274) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Z ) ==>
% 68.63/69.08 multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ),
% 68.63/69.08 multiplication( X, Z ) ) }.
% 68.63/69.08 parent0[0]: (65) {G1,W16,D4,L2,V3,M2} P(7,18) { ! multiplication( X,
% 68.63/69.08 addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 68.63/69.08 ), multiplication( X, Z ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 Z := Z
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 paramod: (88276) {G2,W17,D4,L2,V2,M2} { ! multiplication( X, star( Y ) )
% 68.63/69.08 ==> multiplication( X, star( Y ) ), leq( multiplication( X, one ),
% 68.63/69.08 multiplication( X, star( Y ) ) ) }.
% 68.63/69.08 parent0[0]: (323) {G4,W7,D4,L1,V1,M1} R(316,17) { addition( one, star( X )
% 68.63/69.08 ) ==> star( X ) }.
% 68.63/69.08 parent1[0; 8]: (88274) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Z ) ==>
% 68.63/69.08 multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ),
% 68.63/69.08 multiplication( X, Z ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := Y
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := X
% 68.63/69.08 Y := one
% 68.63/69.08 Z := star( Y )
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqrefl: (88277) {G0,W8,D4,L1,V2,M1} { leq( multiplication( X, one ),
% 68.63/69.08 multiplication( X, star( Y ) ) ) }.
% 68.63/69.08 parent0[0]: (88276) {G2,W17,D4,L2,V2,M2} { ! multiplication( X, star( Y )
% 68.63/69.08 ) ==> multiplication( X, star( Y ) ), leq( multiplication( X, one ),
% 68.63/69.08 multiplication( X, star( Y ) ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 paramod: (88278) {G1,W6,D4,L1,V2,M1} { leq( X, multiplication( X, star( Y
% 68.63/69.08 ) ) ) }.
% 68.63/69.08 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 68.63/69.08 parent1[0; 1]: (88277) {G0,W8,D4,L1,V2,M1} { leq( multiplication( X, one )
% 68.63/69.08 , multiplication( X, star( Y ) ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (1908) {G5,W6,D4,L1,V2,M1} P(323,65);q;d(5) { leq( Y,
% 68.63/69.08 multiplication( Y, star( X ) ) ) }.
% 68.63/69.08 parent0: (88278) {G1,W6,D4,L1,V2,M1} { leq( X, multiplication( X, star( Y
% 68.63/69.08 ) ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := Y
% 68.63/69.08 Y := X
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88279) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 68.63/69.08 ) }.
% 68.63/69.08 parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 68.63/69.08 ==> Y }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 resolution: (88280) {G1,W11,D5,L1,V2,M1} { multiplication( X, star( Y ) )
% 68.63/69.08 ==> addition( X, multiplication( X, star( Y ) ) ) }.
% 68.63/69.08 parent0[1]: (88279) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X
% 68.63/69.08 , Y ) }.
% 68.63/69.08 parent1[0]: (1908) {G5,W6,D4,L1,V2,M1} P(323,65);q;d(5) { leq( Y,
% 68.63/69.08 multiplication( Y, star( X ) ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := multiplication( X, star( Y ) )
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := Y
% 68.63/69.08 Y := X
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88281) {G1,W11,D5,L1,V2,M1} { addition( X, multiplication( X,
% 68.63/69.08 star( Y ) ) ) ==> multiplication( X, star( Y ) ) }.
% 68.63/69.08 parent0[0]: (88280) {G1,W11,D5,L1,V2,M1} { multiplication( X, star( Y ) )
% 68.63/69.08 ==> addition( X, multiplication( X, star( Y ) ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (1947) {G6,W11,D5,L1,V2,M1} R(1908,17) { addition( X,
% 68.63/69.08 multiplication( X, star( Y ) ) ) ==> multiplication( X, star( Y ) ) }.
% 68.63/69.08 parent0: (88281) {G1,W11,D5,L1,V2,M1} { addition( X, multiplication( X,
% 68.63/69.08 star( Y ) ) ) ==> multiplication( X, star( Y ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88283) {G2,W9,D4,L1,V1,M1} { multiplication( X, skol2 ) ==>
% 68.63/69.08 multiplication( addition( skol1, X ), skol2 ) }.
% 68.63/69.08 parent0[0]: (105) {G2,W9,D4,L1,V1,M1} P(19,8);d(21) { multiplication(
% 68.63/69.08 addition( skol1, X ), skol2 ) ==> multiplication( X, skol2 ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 paramod: (88285) {G2,W10,D3,L2,V1,M2} { multiplication( X, skol2 ) ==>
% 68.63/69.08 multiplication( skol1, skol2 ), ! leq( X, skol1 ) }.
% 68.63/69.08 parent0[0]: (39) {G1,W8,D3,L2,V2,M2} P(17,0) { addition( Y, X ) ==> Y, !
% 68.63/69.08 leq( X, Y ) }.
% 68.63/69.08 parent1[0; 5]: (88283) {G2,W9,D4,L1,V1,M1} { multiplication( X, skol2 )
% 68.63/69.08 ==> multiplication( addition( skol1, X ), skol2 ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := skol1
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 paramod: (88286) {G1,W8,D3,L2,V1,M2} { multiplication( X, skol2 ) ==> zero
% 68.63/69.08 , ! leq( X, skol1 ) }.
% 68.63/69.08 parent0[0]: (19) {G0,W5,D3,L1,V0,M1} I { multiplication( skol1, skol2 ) ==>
% 68.63/69.08 zero }.
% 68.63/69.08 parent1[0; 4]: (88285) {G2,W10,D3,L2,V1,M2} { multiplication( X, skol2 )
% 68.63/69.08 ==> multiplication( skol1, skol2 ), ! leq( X, skol1 ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (3711) {G3,W8,D3,L2,V1,M2} P(39,105);d(19) { ! leq( X, skol1 )
% 68.63/69.08 , multiplication( X, skol2 ) ==> zero }.
% 68.63/69.08 parent0: (88286) {G1,W8,D3,L2,V1,M2} { multiplication( X, skol2 ) ==> zero
% 68.63/69.08 , ! leq( X, skol1 ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 1
% 68.63/69.08 1 ==> 0
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 paramod: (88289) {G2,W8,D4,L1,V2,M1} { leq( addition( X, one ), addition(
% 68.63/69.08 X, star( Y ) ) ) }.
% 68.63/69.08 parent0[0]: (126) {G1,W13,D5,L1,V2,M1} P(10,1) { addition( addition( Y, one
% 68.63/69.08 ), multiplication( X, star( X ) ) ) ==> addition( Y, star( X ) ) }.
% 68.63/69.08 parent1[0; 4]: (306) {G2,W5,D3,L1,V2,M1} P(3,26);q { leq( X, addition( X, Y
% 68.63/69.08 ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := Y
% 68.63/69.08 Y := X
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := addition( X, one )
% 68.63/69.08 Y := multiplication( Y, star( Y ) )
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (4723) {G3,W8,D4,L1,V2,M1} P(126,306) { leq( addition( X, one
% 68.63/69.08 ), addition( X, star( Y ) ) ) }.
% 68.63/69.08 parent0: (88289) {G2,W8,D4,L1,V2,M1} { leq( addition( X, one ), addition(
% 68.63/69.08 X, star( Y ) ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 paramod: (88291) {G1,W8,D4,L1,V2,M1} { leq( addition( X, one ), addition(
% 68.63/69.08 star( Y ), X ) ) }.
% 68.63/69.08 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 68.63/69.08 }.
% 68.63/69.08 parent1[0; 4]: (4723) {G3,W8,D4,L1,V2,M1} P(126,306) { leq( addition( X,
% 68.63/69.08 one ), addition( X, star( Y ) ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := star( Y )
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (8116) {G4,W8,D4,L1,V2,M1} P(0,4723) { leq( addition( X, one )
% 68.63/69.08 , addition( star( Y ), X ) ) }.
% 68.63/69.08 parent0: (88291) {G1,W8,D4,L1,V2,M1} { leq( addition( X, one ), addition(
% 68.63/69.08 star( Y ), X ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 paramod: (88298) {G2,W18,D5,L3,V3,M3} { ! leq( addition( multiplication(
% 68.63/69.08 zero, Y ), Z ), X ), ! leq( X, skol1 ), leq( multiplication( Z, star(
% 68.63/69.08 multiplication( skol2, Y ) ) ), X ) }.
% 68.63/69.08 parent0[1]: (3711) {G3,W8,D3,L2,V1,M2} P(39,105);d(19) { ! leq( X, skol1 )
% 68.63/69.08 , multiplication( X, skol2 ) ==> zero }.
% 68.63/69.08 parent1[0; 4]: (204) {G1,W17,D5,L2,V4,M2} P(4,13) { ! leq( addition(
% 68.63/69.08 multiplication( multiplication( X, Y ), Z ), T ), X ), leq(
% 68.63/69.08 multiplication( T, star( multiplication( Y, Z ) ) ), X ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := X
% 68.63/69.08 Y := skol2
% 68.63/69.08 Z := Y
% 68.63/69.08 T := Z
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 paramod: (88302) {G1,W16,D5,L3,V3,M3} { ! leq( addition( zero, Y ), Z ), !
% 68.63/69.08 leq( Z, skol1 ), leq( multiplication( Y, star( multiplication( skol2, X
% 68.63/69.08 ) ) ), Z ) }.
% 68.63/69.08 parent0[0]: (9) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==> zero
% 68.63/69.08 }.
% 68.63/69.08 parent1[0; 3]: (88298) {G2,W18,D5,L3,V3,M3} { ! leq( addition(
% 68.63/69.08 multiplication( zero, Y ), Z ), X ), ! leq( X, skol1 ), leq(
% 68.63/69.08 multiplication( Z, star( multiplication( skol2, Y ) ) ), X ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := Z
% 68.63/69.08 Y := X
% 68.63/69.08 Z := Y
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 paramod: (88303) {G2,W14,D5,L3,V3,M3} { ! leq( X, Y ), ! leq( Y, skol1 ),
% 68.63/69.08 leq( multiplication( X, star( multiplication( skol2, Z ) ) ), Y ) }.
% 68.63/69.08 parent0[0]: (21) {G1,W5,D3,L1,V1,M1} P(0,2) { addition( zero, X ) ==> X }.
% 68.63/69.08 parent1[0; 2]: (88302) {G1,W16,D5,L3,V3,M3} { ! leq( addition( zero, Y ),
% 68.63/69.08 Z ), ! leq( Z, skol1 ), leq( multiplication( Y, star( multiplication(
% 68.63/69.08 skol2, X ) ) ), Z ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := Z
% 68.63/69.08 Y := X
% 68.63/69.08 Z := Y
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (8688) {G4,W14,D5,L3,V3,M3} P(3711,204);d(9);d(21) { leq(
% 68.63/69.08 multiplication( Z, star( multiplication( skol2, Y ) ) ), X ), ! leq( X,
% 68.63/69.08 skol1 ), ! leq( Z, X ) }.
% 68.63/69.08 parent0: (88303) {G2,W14,D5,L3,V3,M3} { ! leq( X, Y ), ! leq( Y, skol1 ),
% 68.63/69.08 leq( multiplication( X, star( multiplication( skol2, Z ) ) ), Y ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := Z
% 68.63/69.08 Y := X
% 68.63/69.08 Z := Y
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 2
% 68.63/69.08 1 ==> 1
% 68.63/69.08 2 ==> 0
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 factor: (88305) {G4,W11,D5,L2,V1,M2} { leq( multiplication( skol1, star(
% 68.63/69.08 multiplication( skol2, X ) ) ), skol1 ), ! leq( skol1, skol1 ) }.
% 68.63/69.08 parent0[1, 2]: (8688) {G4,W14,D5,L3,V3,M3} P(3711,204);d(9);d(21) { leq(
% 68.63/69.08 multiplication( Z, star( multiplication( skol2, Y ) ) ), X ), ! leq( X,
% 68.63/69.08 skol1 ), ! leq( Z, X ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := skol1
% 68.63/69.08 Y := X
% 68.63/69.08 Z := skol1
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 resolution: (88306) {G2,W8,D5,L1,V1,M1} { leq( multiplication( skol1, star
% 68.63/69.08 ( multiplication( skol2, X ) ) ), skol1 ) }.
% 68.63/69.08 parent0[1]: (88305) {G4,W11,D5,L2,V1,M2} { leq( multiplication( skol1,
% 68.63/69.08 star( multiplication( skol2, X ) ) ), skol1 ), ! leq( skol1, skol1 ) }.
% 68.63/69.08 parent1[0]: (23) {G1,W3,D2,L1,V1,M1} R(18,3) { leq( X, X ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := skol1
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (8692) {G5,W8,D5,L1,V1,M1} F(8688);r(23) { leq( multiplication
% 68.63/69.08 ( skol1, star( multiplication( skol2, X ) ) ), skol1 ) }.
% 68.63/69.08 parent0: (88306) {G2,W8,D5,L1,V1,M1} { leq( multiplication( skol1, star(
% 68.63/69.08 multiplication( skol2, X ) ) ), skol1 ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 eqswap: (88308) {G2,W13,D6,L1,V2,M1} { addition( star( X ), Y ) ==>
% 68.63/69.08 addition( addition( multiplication( star( X ), X ), Y ), one ) }.
% 68.63/69.08 parent0[0]: (353) {G2,W13,D6,L1,V2,M1} P(11,27) { addition( addition(
% 68.63/69.08 multiplication( star( X ), X ), Y ), one ) ==> addition( star( X ), Y )
% 68.63/69.08 }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := Y
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 paramod: (88312) {G2,W13,D6,L1,V1,M1} { addition( star( X ), X ) ==>
% 68.63/69.08 addition( multiplication( addition( star( X ), one ), X ), one ) }.
% 68.63/69.08 parent0[0]: (109) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( multiplication( Y
% 68.63/69.08 , X ), X ) = multiplication( addition( Y, one ), X ) }.
% 68.63/69.08 parent1[0; 6]: (88308) {G2,W13,D6,L1,V2,M1} { addition( star( X ), Y ) ==>
% 68.63/69.08 addition( addition( multiplication( star( X ), X ), Y ), one ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 Y := star( X )
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := X
% 68.63/69.08 Y := X
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 paramod: (88313) {G3,W11,D5,L1,V1,M1} { addition( star( X ), X ) ==>
% 68.63/69.08 addition( multiplication( star( X ), X ), one ) }.
% 68.63/69.08 parent0[0]: (660) {G4,W7,D4,L1,V1,M1} R(39,316) { addition( star( X ), one
% 68.63/69.08 ) ==> star( X ) }.
% 68.63/69.08 parent1[0; 7]: (88312) {G2,W13,D6,L1,V1,M1} { addition( star( X ), X ) ==>
% 68.63/69.08 addition( multiplication( addition( star( X ), one ), X ), one ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 paramod: (88314) {G2,W7,D4,L1,V1,M1} { addition( star( X ), X ) ==> star(
% 68.63/69.08 X ) }.
% 68.63/69.08 parent0[0]: (149) {G1,W9,D5,L1,V1,M1} P(11,0) { addition( multiplication(
% 68.63/69.08 star( X ), X ), one ) ==> star( X ) }.
% 68.63/69.08 parent1[0; 5]: (88313) {G3,W11,D5,L1,V1,M1} { addition( star( X ), X ) ==>
% 68.63/69.08 addition( multiplication( star( X ), X ), one ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (13567) {G5,W7,D4,L1,V1,M1} P(109,353);d(660);d(149) {
% 68.63/69.08 addition( star( X ), X ) ==> star( X ) }.
% 68.63/69.08 parent0: (88314) {G2,W7,D4,L1,V1,M1} { addition( star( X ), X ) ==> star(
% 68.63/69.08 X ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 paramod: (88318) {G5,W6,D3,L1,V1,M1} { leq( addition( X, one ), star( X )
% 68.63/69.08 ) }.
% 68.63/69.08 parent0[0]: (13567) {G5,W7,D4,L1,V1,M1} P(109,353);d(660);d(149) { addition
% 68.63/69.08 ( star( X ), X ) ==> star( X ) }.
% 68.63/69.08 parent1[0; 4]: (8116) {G4,W8,D4,L1,V2,M1} P(0,4723) { leq( addition( X, one
% 68.63/69.08 ), addition( star( Y ), X ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := X
% 68.63/69.08 Y := X
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (13613) {G6,W6,D3,L1,V1,M1} P(13567,8116) { leq( addition( X,
% 68.63/69.08 one ), star( X ) ) }.
% 68.63/69.08 parent0: (88318) {G5,W6,D3,L1,V1,M1} { leq( addition( X, one ), star( X )
% 68.63/69.08 ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08 permutation0:
% 68.63/69.08 0 ==> 0
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 paramod: (88320) {G1,W8,D5,L1,V1,M1} { leq( strong_iteration( X ), star(
% 68.63/69.08 multiplication( X, strong_iteration( X ) ) ) ) }.
% 68.63/69.08 parent0[0]: (14) {G0,W9,D5,L1,V1,M1} I { addition( multiplication( X,
% 68.63/69.08 strong_iteration( X ) ), one ) ==> strong_iteration( X ) }.
% 68.63/69.08 parent1[0; 1]: (13613) {G6,W6,D3,L1,V1,M1} P(13567,8116) { leq( addition( X
% 68.63/69.08 , one ), star( X ) ) }.
% 68.63/69.08 substitution0:
% 68.63/69.08 X := X
% 68.63/69.08 end
% 68.63/69.08 substitution1:
% 68.63/69.08 X := multiplication( X, strong_iteration( X ) )
% 68.63/69.08 end
% 68.63/69.08
% 68.63/69.08 subsumption: (13710) {G7,W8,D5,L1,V1,M1} P(14,13613) { leq(
% 68.63/69.08 strong_iteration( X ), star( multiplication( X, strong_Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------