TSTP Solution File: KLE139+2 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE139+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Sun Jul 17 01:37:23 EDT 2022
% Result : Theorem 50.75s 51.12s
% Output : Refutation 50.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE139+2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n005.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 12:02:38 EDT 2022
% 0.12/0.34 % CPUTime :
% 20.13/20.50 *** allocated 10000 integers for termspace/termends
% 20.13/20.50 *** allocated 10000 integers for clauses
% 20.13/20.50 *** allocated 10000 integers for justifications
% 20.13/20.50 Bliksem 1.12
% 20.13/20.50
% 20.13/20.50
% 20.13/20.50 Automatic Strategy Selection
% 20.13/20.50
% 20.13/20.50
% 20.13/20.50 Clauses:
% 20.13/20.50
% 20.13/20.50 { addition( X, Y ) = addition( Y, X ) }.
% 20.13/20.50 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 20.13/20.50 { addition( X, zero ) = X }.
% 20.13/20.50 { addition( X, X ) = X }.
% 20.13/20.50 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 20.13/20.50 multiplication( X, Y ), Z ) }.
% 20.13/20.50 { multiplication( X, one ) = X }.
% 20.13/20.50 { multiplication( one, X ) = X }.
% 20.13/20.50 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 20.13/20.50 , multiplication( X, Z ) ) }.
% 20.13/20.50 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 20.13/20.50 , multiplication( Y, Z ) ) }.
% 20.13/20.50 { multiplication( zero, X ) = zero }.
% 20.13/20.50 { addition( one, multiplication( X, star( X ) ) ) = star( X ) }.
% 20.13/20.50 { addition( one, multiplication( star( X ), X ) ) = star( X ) }.
% 20.13/20.50 { ! leq( addition( multiplication( X, Z ), Y ), Z ), leq( multiplication(
% 20.13/20.50 star( X ), Y ), Z ) }.
% 20.13/20.50 { ! leq( addition( multiplication( Z, X ), Y ), Z ), leq( multiplication( Y
% 20.13/20.50 , star( X ) ), Z ) }.
% 20.13/20.50 { strong_iteration( X ) = addition( multiplication( X, strong_iteration( X
% 20.13/20.50 ) ), one ) }.
% 20.13/20.50 { ! leq( Z, addition( multiplication( X, Z ), Y ) ), leq( Z, multiplication
% 20.13/20.50 ( strong_iteration( X ), Y ) ) }.
% 20.13/20.50 { strong_iteration( X ) = addition( star( X ), multiplication(
% 20.13/20.50 strong_iteration( X ), zero ) ) }.
% 20.13/20.50 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 20.13/20.50 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 20.13/20.50 { ! leq( strong_iteration( skol1 ), addition( multiplication(
% 20.13/20.50 strong_iteration( skol1 ), skol1 ), one ) ), ! leq( addition(
% 20.13/20.50 multiplication( strong_iteration( skol1 ), skol1 ), one ),
% 20.13/20.50 strong_iteration( skol1 ) ) }.
% 20.13/20.50
% 20.13/20.50 percentage equality = 0.615385, percentage horn = 1.000000
% 20.13/20.50 This is a problem with some equality
% 20.13/20.50
% 20.13/20.50
% 20.13/20.50
% 20.13/20.50 Options Used:
% 20.13/20.50
% 20.13/20.50 useres = 1
% 20.13/20.50 useparamod = 1
% 20.13/20.50 useeqrefl = 1
% 20.13/20.50 useeqfact = 1
% 20.13/20.50 usefactor = 1
% 20.13/20.50 usesimpsplitting = 0
% 20.13/20.50 usesimpdemod = 5
% 20.13/20.50 usesimpres = 3
% 20.13/20.50
% 20.13/20.50 resimpinuse = 1000
% 20.13/20.50 resimpclauses = 20000
% 20.13/20.50 substype = eqrewr
% 20.13/20.50 backwardsubs = 1
% 20.13/20.50 selectoldest = 5
% 20.13/20.50
% 20.13/20.50 litorderings [0] = split
% 20.13/20.50 litorderings [1] = extend the termordering, first sorting on arguments
% 20.13/20.50
% 20.13/20.50 termordering = kbo
% 20.13/20.50
% 20.13/20.50 litapriori = 0
% 20.13/20.50 termapriori = 1
% 20.13/20.50 litaposteriori = 0
% 20.13/20.50 termaposteriori = 0
% 20.13/20.50 demodaposteriori = 0
% 20.13/20.50 ordereqreflfact = 0
% 20.13/20.50
% 20.13/20.50 litselect = negord
% 20.13/20.50
% 20.13/20.50 maxweight = 15
% 20.13/20.50 maxdepth = 30000
% 20.13/20.50 maxlength = 115
% 20.13/20.50 maxnrvars = 195
% 20.13/20.50 excuselevel = 1
% 20.13/20.50 increasemaxweight = 1
% 20.13/20.50
% 20.13/20.50 maxselected = 10000000
% 20.13/20.50 maxnrclauses = 10000000
% 20.13/20.50
% 20.13/20.50 showgenerated = 0
% 20.13/20.50 showkept = 0
% 20.13/20.50 showselected = 0
% 20.13/20.50 showdeleted = 0
% 20.13/20.50 showresimp = 1
% 20.13/20.50 showstatus = 2000
% 20.13/20.50
% 20.13/20.50 prologoutput = 0
% 20.13/20.50 nrgoals = 5000000
% 20.13/20.50 totalproof = 1
% 20.13/20.50
% 20.13/20.50 Symbols occurring in the translation:
% 20.13/20.50
% 20.13/20.50 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 20.13/20.50 . [1, 2] (w:1, o:20, a:1, s:1, b:0),
% 20.13/20.50 ! [4, 1] (w:0, o:13, a:1, s:1, b:0),
% 20.13/20.50 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 20.13/20.50 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 20.13/20.50 addition [37, 2] (w:1, o:44, a:1, s:1, b:0),
% 20.13/20.50 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 20.13/20.50 multiplication [40, 2] (w:1, o:46, a:1, s:1, b:0),
% 20.13/20.50 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 20.13/20.50 star [42, 1] (w:1, o:18, a:1, s:1, b:0),
% 20.13/20.50 leq [43, 2] (w:1, o:45, a:1, s:1, b:0),
% 20.13/20.50 strong_iteration [44, 1] (w:1, o:19, a:1, s:1, b:0),
% 20.13/20.50 skol1 [46, 0] (w:1, o:12, a:1, s:1, b:1).
% 20.13/20.50
% 20.13/20.50
% 20.13/20.50 Starting Search:
% 20.13/20.50
% 20.13/20.50 *** allocated 15000 integers for clauses
% 20.13/20.50 *** allocated 22500 integers for clauses
% 20.13/20.50 *** allocated 33750 integers for clauses
% 20.13/20.50 *** allocated 50625 integers for clauses
% 20.13/20.50 *** allocated 15000 integers for termspace/termends
% 20.13/20.50 *** allocated 75937 integers for clauses
% 20.13/20.50 Resimplifying inuse:
% 20.13/20.50 Done
% 20.13/20.50
% 20.13/20.50 *** allocated 22500 integers for termspace/termends
% 20.13/20.50 *** allocated 113905 integers for clauses
% 20.13/20.50 *** allocated 33750 integers for termspace/termends
% 20.13/20.50
% 20.13/20.50 Intermediate Status:
% 20.13/20.50 Generated: 21864
% 20.13/20.50 Kept: 2052
% 20.13/20.50 Inuse: 233
% 20.13/20.50 Deleted: 53
% 20.13/20.50 Deletedinuse: 30
% 20.13/20.50
% 20.13/20.50 Resimplifying inuse:
% 20.13/20.50 Done
% 20.13/20.50
% 20.13/20.50 *** allocated 170857 integers for clauses
% 50.75/51.12 *** allocated 50625 integers for termspace/termends
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12 *** allocated 256285 integers for clauses
% 50.75/51.12 *** allocated 75937 integers for termspace/termends
% 50.75/51.12
% 50.75/51.12 Intermediate Status:
% 50.75/51.12 Generated: 48365
% 50.75/51.12 Kept: 4106
% 50.75/51.12 Inuse: 389
% 50.75/51.12 Deleted: 82
% 50.75/51.12 Deletedinuse: 31
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12 *** allocated 384427 integers for clauses
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12 *** allocated 113905 integers for termspace/termends
% 50.75/51.12
% 50.75/51.12 Intermediate Status:
% 50.75/51.12 Generated: 64665
% 50.75/51.12 Kept: 6107
% 50.75/51.12 Inuse: 488
% 50.75/51.12 Deleted: 99
% 50.75/51.12 Deletedinuse: 33
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12 *** allocated 576640 integers for clauses
% 50.75/51.12
% 50.75/51.12 Intermediate Status:
% 50.75/51.12 Generated: 95784
% 50.75/51.12 Kept: 8109
% 50.75/51.12 Inuse: 672
% 50.75/51.12 Deleted: 185
% 50.75/51.12 Deletedinuse: 78
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12 *** allocated 170857 integers for termspace/termends
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12
% 50.75/51.12 Intermediate Status:
% 50.75/51.12 Generated: 141188
% 50.75/51.12 Kept: 10110
% 50.75/51.12 Inuse: 804
% 50.75/51.12 Deleted: 278
% 50.75/51.12 Deletedinuse: 160
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12 *** allocated 864960 integers for clauses
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12
% 50.75/51.12 Intermediate Status:
% 50.75/51.12 Generated: 175919
% 50.75/51.12 Kept: 12121
% 50.75/51.12 Inuse: 925
% 50.75/51.12 Deleted: 319
% 50.75/51.12 Deletedinuse: 167
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12 *** allocated 256285 integers for termspace/termends
% 50.75/51.12
% 50.75/51.12 Intermediate Status:
% 50.75/51.12 Generated: 202796
% 50.75/51.12 Kept: 14210
% 50.75/51.12 Inuse: 1028
% 50.75/51.12 Deleted: 366
% 50.75/51.12 Deletedinuse: 177
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12 *** allocated 1297440 integers for clauses
% 50.75/51.12
% 50.75/51.12 Intermediate Status:
% 50.75/51.12 Generated: 230767
% 50.75/51.12 Kept: 16339
% 50.75/51.12 Inuse: 1102
% 50.75/51.12 Deleted: 420
% 50.75/51.12 Deletedinuse: 216
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12
% 50.75/51.12 Intermediate Status:
% 50.75/51.12 Generated: 250801
% 50.75/51.12 Kept: 18344
% 50.75/51.12 Inuse: 1156
% 50.75/51.12 Deleted: 426
% 50.75/51.12 Deletedinuse: 220
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12 Resimplifying clauses:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12 *** allocated 384427 integers for termspace/termends
% 50.75/51.12
% 50.75/51.12 Intermediate Status:
% 50.75/51.12 Generated: 300282
% 50.75/51.12 Kept: 20352
% 50.75/51.12 Inuse: 1291
% 50.75/51.12 Deleted: 3965
% 50.75/51.12 Deletedinuse: 220
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12
% 50.75/51.12 Intermediate Status:
% 50.75/51.12 Generated: 331702
% 50.75/51.12 Kept: 22376
% 50.75/51.12 Inuse: 1381
% 50.75/51.12 Deleted: 3979
% 50.75/51.12 Deletedinuse: 228
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12
% 50.75/51.12 Intermediate Status:
% 50.75/51.12 Generated: 386487
% 50.75/51.12 Kept: 24637
% 50.75/51.12 Inuse: 1442
% 50.75/51.12 Deleted: 3983
% 50.75/51.12 Deletedinuse: 228
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12 *** allocated 1946160 integers for clauses
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12 *** allocated 576640 integers for termspace/termends
% 50.75/51.12
% 50.75/51.12 Intermediate Status:
% 50.75/51.12 Generated: 415706
% 50.75/51.12 Kept: 28491
% 50.75/51.12 Inuse: 1445
% 50.75/51.12 Deleted: 3983
% 50.75/51.12 Deletedinuse: 228
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12
% 50.75/51.12 Intermediate Status:
% 50.75/51.12 Generated: 433164
% 50.75/51.12 Kept: 30530
% 50.75/51.12 Inuse: 1478
% 50.75/51.12 Deleted: 3984
% 50.75/51.12 Deletedinuse: 228
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12
% 50.75/51.12 Intermediate Status:
% 50.75/51.12 Generated: 455793
% 50.75/51.12 Kept: 32553
% 50.75/51.12 Inuse: 1520
% 50.75/51.12 Deleted: 3985
% 50.75/51.12 Deletedinuse: 228
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12
% 50.75/51.12 Intermediate Status:
% 50.75/51.12 Generated: 476042
% 50.75/51.12 Kept: 34632
% 50.75/51.12 Inuse: 1553
% 50.75/51.12 Deleted: 3985
% 50.75/51.12 Deletedinuse: 228
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12
% 50.75/51.12 Intermediate Status:
% 50.75/51.12 Generated: 497472
% 50.75/51.12 Kept: 37249
% 50.75/51.12 Inuse: 1584
% 50.75/51.12 Deleted: 3988
% 50.75/51.12 Deletedinuse: 231
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12
% 50.75/51.12 Intermediate Status:
% 50.75/51.12 Generated: 517742
% 50.75/51.12 Kept: 39266
% 50.75/51.12 Inuse: 1616
% 50.75/51.12 Deleted: 3988
% 50.75/51.12 Deletedinuse: 231
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12 *** allocated 2919240 integers for clauses
% 50.75/51.12 Resimplifying clauses:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12
% 50.75/51.12 Intermediate Status:
% 50.75/51.12 Generated: 558004
% 50.75/51.12 Kept: 41268
% 50.75/51.12 Inuse: 1656
% 50.75/51.12 Deleted: 6407
% 50.75/51.12 Deletedinuse: 231
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12 *** allocated 864960 integers for termspace/termends
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12
% 50.75/51.12 Intermediate Status:
% 50.75/51.12 Generated: 589636
% 50.75/51.12 Kept: 43268
% 50.75/51.12 Inuse: 1737
% 50.75/51.12 Deleted: 6408
% 50.75/51.12 Deletedinuse: 231
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12
% 50.75/51.12 Intermediate Status:
% 50.75/51.12 Generated: 658003
% 50.75/51.12 Kept: 45308
% 50.75/51.12 Inuse: 1805
% 50.75/51.12 Deleted: 6415
% 50.75/51.12 Deletedinuse: 234
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12
% 50.75/51.12 Intermediate Status:
% 50.75/51.12 Generated: 716478
% 50.75/51.12 Kept: 47377
% 50.75/51.12 Inuse: 1855
% 50.75/51.12 Deleted: 6417
% 50.75/51.12 Deletedinuse: 235
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12
% 50.75/51.12 Intermediate Status:
% 50.75/51.12 Generated: 780104
% 50.75/51.12 Kept: 49391
% 50.75/51.12 Inuse: 1901
% 50.75/51.12 Deleted: 6419
% 50.75/51.12 Deletedinuse: 236
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12
% 50.75/51.12 Intermediate Status:
% 50.75/51.12 Generated: 815669
% 50.75/51.12 Kept: 51476
% 50.75/51.12 Inuse: 1956
% 50.75/51.12 Deleted: 6422
% 50.75/51.12 Deletedinuse: 238
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12
% 50.75/51.12 Intermediate Status:
% 50.75/51.12 Generated: 848892
% 50.75/51.12 Kept: 53522
% 50.75/51.12 Inuse: 2015
% 50.75/51.12 Deleted: 6423
% 50.75/51.12 Deletedinuse: 238
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12
% 50.75/51.12 Intermediate Status:
% 50.75/51.12 Generated: 869016
% 50.75/51.12 Kept: 55537
% 50.75/51.12 Inuse: 2050
% 50.75/51.12 Deleted: 6423
% 50.75/51.12 Deletedinuse: 238
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12
% 50.75/51.12 Intermediate Status:
% 50.75/51.12 Generated: 912804
% 50.75/51.12 Kept: 57537
% 50.75/51.12 Inuse: 2122
% 50.75/51.12 Deleted: 6469
% 50.75/51.12 Deletedinuse: 283
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12
% 50.75/51.12 Intermediate Status:
% 50.75/51.12 Generated: 968425
% 50.75/51.12 Kept: 59550
% 50.75/51.12 Inuse: 2216
% 50.75/51.12 Deleted: 6494
% 50.75/51.12 Deletedinuse: 285
% 50.75/51.12
% 50.75/51.12 Resimplifying clauses:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12 *** allocated 4378860 integers for clauses
% 50.75/51.12
% 50.75/51.12 Intermediate Status:
% 50.75/51.12 Generated: 981935
% 50.75/51.12 Kept: 61644
% 50.75/51.12 Inuse: 2232
% 50.75/51.12 Deleted: 9962
% 50.75/51.12 Deletedinuse: 285
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12 *** allocated 1297440 integers for termspace/termends
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12
% 50.75/51.12 Intermediate Status:
% 50.75/51.12 Generated: 1009319
% 50.75/51.12 Kept: 63678
% 50.75/51.12 Inuse: 2275
% 50.75/51.12 Deleted: 9962
% 50.75/51.12 Deletedinuse: 285
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12 Done
% 50.75/51.12
% 50.75/51.12
% 50.75/51.12 Intermediate Status:
% 50.75/51.12 Generated: 1050375
% 50.75/51.12 Kept: 65682
% 50.75/51.12 Inuse: 2344
% 50.75/51.12 Deleted: 9968
% 50.75/51.12 Deletedinuse: 285
% 50.75/51.12
% 50.75/51.12 Resimplifying inuse:
% 50.75/51.12
% 50.75/51.12 Bliksems!, er is een bewijs:
% 50.75/51.12 % SZS status Theorem
% 50.75/51.12 % SZS output start Refutation
% 50.75/51.12
% 50.75/51.12 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 50.75/51.12 (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) ==> addition(
% 50.75/51.12 addition( Z, Y ), X ) }.
% 50.75/51.12 (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 50.75/51.12 (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 50.75/51.12 (4) {G0,W11,D4,L1,V3,M1} I { multiplication( X, multiplication( Y, Z ) )
% 50.75/51.12 ==> multiplication( multiplication( X, Y ), Z ) }.
% 50.75/51.12 (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 50.75/51.12 (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 50.75/51.12 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 50.75/51.12 (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 50.75/51.12 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 50.75/51.12 (9) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==> zero }.
% 50.75/51.12 (11) {G0,W9,D5,L1,V1,M1} I { addition( one, multiplication( star( X ), X )
% 50.75/51.12 ) ==> star( X ) }.
% 50.75/51.12 (12) {G0,W13,D4,L2,V3,M2} I { ! leq( addition( multiplication( X, Z ), Y )
% 50.75/51.12 , Z ), leq( multiplication( star( X ), Y ), Z ) }.
% 50.75/51.12 (14) {G0,W9,D5,L1,V1,M1} I { addition( multiplication( X, strong_iteration
% 50.75/51.12 ( X ) ), one ) ==> strong_iteration( X ) }.
% 50.75/51.12 (16) {G0,W10,D5,L1,V1,M1} I { addition( star( X ), multiplication(
% 50.75/51.12 strong_iteration( X ), zero ) ) ==> strong_iteration( X ) }.
% 50.75/51.12 (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) ==> Y }.
% 50.75/51.12 (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, Y ) }.
% 50.75/51.12 (19) {G0,W18,D5,L2,V0,M2} I { ! leq( strong_iteration( skol1 ), addition(
% 50.75/51.12 multiplication( strong_iteration( skol1 ), skol1 ), one ) ), ! leq(
% 50.75/51.12 addition( multiplication( strong_iteration( skol1 ), skol1 ), one ),
% 50.75/51.12 strong_iteration( skol1 ) ) }.
% 50.75/51.12 (20) {G1,W5,D3,L1,V1,M1} P(0,2) { addition( zero, X ) ==> X }.
% 50.75/51.12 (22) {G1,W3,D2,L1,V1,M1} R(18,3) { leq( X, X ) }.
% 50.75/51.12 (25) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y ), Z ) ==>
% 50.75/51.12 addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 50.75/51.12 (27) {G1,W11,D4,L1,V3,M1} P(0,1);d(1) { addition( addition( Z, Y ), X ) =
% 50.75/51.12 addition( addition( Z, X ), Y ) }.
% 50.75/51.12 (35) {G1,W12,D4,L2,V3,M2} P(17,1) { addition( addition( Z, X ), Y ) ==>
% 50.75/51.12 addition( Z, Y ), ! leq( X, Y ) }.
% 50.75/51.12 (36) {G1,W8,D3,L2,V2,M2} P(17,0) { addition( Y, X ) ==> Y, ! leq( X, Y )
% 50.75/51.12 }.
% 50.75/51.12 (50) {G1,W9,D4,L1,V2,M1} P(9,4) { multiplication( multiplication( Y, zero )
% 50.75/51.12 , X ) ==> multiplication( Y, zero ) }.
% 50.75/51.12 (67) {G1,W16,D4,L2,V3,M2} P(7,18) { ! multiplication( X, addition( Y, Z ) )
% 50.75/51.12 ==> multiplication( X, Z ), leq( multiplication( X, Y ), multiplication
% 50.75/51.12 ( X, Z ) ) }.
% 50.75/51.12 (69) {G1,W11,D4,L1,V2,M1} P(5,7) { addition( X, multiplication( X, Y ) ) =
% 50.75/51.12 multiplication( X, addition( one, Y ) ) }.
% 50.75/51.12 (99) {G1,W16,D4,L2,V3,M2} P(8,18) { ! multiplication( addition( X, Z ), Y )
% 50.75/51.12 ==> multiplication( Z, Y ), leq( multiplication( X, Y ), multiplication
% 50.75/51.12 ( Z, Y ) ) }.
% 50.75/51.12 (100) {G1,W11,D4,L1,V3,M1} P(8,0);d(8) { multiplication( addition( X, Z ),
% 50.75/51.12 Y ) = multiplication( addition( Z, X ), Y ) }.
% 50.75/51.12 (213) {G2,W5,D3,L1,V1,M1} P(14,12);d(5);r(22) { leq( star( X ),
% 50.75/51.12 strong_iteration( X ) ) }.
% 50.75/51.12 (226) {G3,W8,D4,L1,V1,M1} R(213,17) { addition( star( X ), strong_iteration
% 50.75/51.12 ( X ) ) ==> strong_iteration( X ) }.
% 50.75/51.12 (285) {G1,W10,D5,L1,V1,M1} P(16,0) { addition( multiplication(
% 50.75/51.12 strong_iteration( X ), zero ), star( X ) ) ==> strong_iteration( X ) }.
% 50.75/51.12 (306) {G1,W18,D5,L2,V0,M2} P(0,19) { ! leq( strong_iteration( skol1 ),
% 50.75/51.12 addition( one, multiplication( strong_iteration( skol1 ), skol1 ) ) ), !
% 50.75/51.12 leq( addition( one, multiplication( strong_iteration( skol1 ), skol1 ) )
% 50.75/51.12 , strong_iteration( skol1 ) ) }.
% 50.75/51.12 (319) {G2,W8,D3,L2,V3,M2} P(17,25);q { leq( X, addition( Y, Z ) ), ! leq( X
% 50.75/51.12 , Y ) }.
% 50.75/51.12 (323) {G2,W5,D3,L1,V2,M1} P(3,25);q { leq( X, addition( X, Y ) ) }.
% 50.75/51.12 (362) {G3,W5,D3,L1,V2,M1} P(0,323) { leq( X, addition( Y, X ) ) }.
% 50.75/51.12 (368) {G4,W7,D4,L1,V1,M1} P(11,362) { leq( multiplication( star( X ), X ),
% 50.75/51.12 star( X ) ) }.
% 50.75/51.12 (380) {G2,W14,D5,L1,V2,M1} P(16,27) { addition( addition( star( X ), Y ),
% 50.75/51.12 multiplication( strong_iteration( X ), zero ) ) ==> addition(
% 50.75/51.12 strong_iteration( X ), Y ) }.
% 50.75/51.12 (562) {G2,W15,D4,L2,V2,M2} P(16,35) { addition( strong_iteration( X ), Y )
% 50.75/51.12 ==> addition( star( X ), Y ), ! leq( multiplication( strong_iteration( X
% 50.75/51.12 ), zero ), Y ) }.
% 50.75/51.12 (565) {G2,W14,D4,L2,V2,M2} P(11,35) { addition( star( X ), Y ) ==> addition
% 50.75/51.12 ( one, Y ), ! leq( multiplication( star( X ), X ), Y ) }.
% 50.75/51.12 (809) {G2,W15,D5,L1,V3,M1} P(50,8) { multiplication( addition( Z,
% 50.75/51.12 multiplication( X, zero ) ), Y ) ==> addition( multiplication( Z, Y ),
% 50.75/51.12 multiplication( X, zero ) ) }.
% 50.75/51.12 (1092) {G3,W8,D3,L2,V2,M2} P(16,319) { leq( Y, strong_iteration( X ) ), !
% 50.75/51.12 leq( Y, star( X ) ) }.
% 50.75/51.12 (1102) {G5,W7,D4,L1,V1,M1} R(1092,368) { leq( multiplication( star( X ), X
% 50.75/51.12 ), strong_iteration( X ) ) }.
% 50.75/51.12 (1119) {G6,W10,D5,L1,V1,M1} R(1102,36) { addition( strong_iteration( X ),
% 50.75/51.12 multiplication( star( X ), X ) ) ==> strong_iteration( X ) }.
% 50.75/51.12 (1628) {G2,W7,D3,L1,V2,M1} P(20,67);q { leq( multiplication( Y, zero ),
% 50.75/51.12 multiplication( Y, X ) ) }.
% 50.75/51.12 (5199) {G4,W9,D4,L1,V2,M1} P(226,99);q { leq( multiplication( star( X ), Y
% 50.75/51.12 ), multiplication( strong_iteration( X ), Y ) ) }.
% 50.75/51.12 (12403) {G3,W14,D5,L1,V2,M1} P(285,100);d(809) { addition( multiplication(
% 50.75/51.12 star( X ), Y ), multiplication( strong_iteration( X ), zero ) ) ==>
% 50.75/51.12 multiplication( strong_iteration( X ), Y ) }.
% 50.75/51.12 (18716) {G4,W14,D5,L1,V2,M1} P(69,380);d(12403) { addition(
% 50.75/51.12 strong_iteration( X ), multiplication( star( X ), Y ) ) ==>
% 50.75/51.12 multiplication( strong_iteration( X ), addition( one, Y ) ) }.
% 50.75/51.12 (20029) {G7,W9,D4,L1,V1,M1} S(1119);d(18716) { multiplication(
% 50.75/51.12 strong_iteration( X ), addition( one, X ) ) ==> strong_iteration( X ) }.
% 50.75/51.12 (35640) {G3,W14,D5,L1,V2,M1} P(562,69);r(1628) { addition( star( X ),
% 50.75/51.12 multiplication( strong_iteration( X ), Y ) ) ==> multiplication(
% 50.75/51.12 strong_iteration( X ), addition( one, Y ) ) }.
% 50.75/51.12 (64713) {G8,W9,D5,L1,V1,M1} R(5199,565);d(35640);d(20029) { addition( one,
% 50.75/51.12 multiplication( strong_iteration( X ), X ) ) ==> strong_iteration( X )
% 50.75/51.12 }.
% 50.75/51.12 (65698) {G9,W0,D0,L0,V0,M0} S(306);d(64713);d(64713);f;r(22) { }.
% 50.75/51.12
% 50.75/51.12
% 50.75/51.12 % SZS output end Refutation
% 50.75/51.12 found a proof!
% 50.75/51.12
% 50.75/51.12
% 50.75/51.12 Unprocessed initial clauses:
% 50.75/51.12
% 50.75/51.12 (65700) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 50.75/51.12 (65701) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition
% 50.75/51.12 ( addition( Z, Y ), X ) }.
% 50.75/51.12 (65702) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 50.75/51.12 (65703) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 50.75/51.12 (65704) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) )
% 50.75/51.12 = multiplication( multiplication( X, Y ), Z ) }.
% 50.75/51.12 (65705) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 50.75/51.12 (65706) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 50.75/51.12 (65707) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 50.75/51.12 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 50.75/51.12 (65708) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 50.75/51.12 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 50.75/51.12 (65709) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 50.75/51.12 (65710) {G0,W9,D5,L1,V1,M1} { addition( one, multiplication( X, star( X )
% 50.75/51.12 ) ) = star( X ) }.
% 50.75/51.12 (65711) {G0,W9,D5,L1,V1,M1} { addition( one, multiplication( star( X ), X
% 50.75/51.12 ) ) = star( X ) }.
% 50.75/51.12 (65712) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( X, Z ), Y
% 50.75/51.12 ), Z ), leq( multiplication( star( X ), Y ), Z ) }.
% 50.75/51.12 (65713) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( Z, X ), Y
% 50.75/51.12 ), Z ), leq( multiplication( Y, star( X ) ), Z ) }.
% 50.75/51.12 (65714) {G0,W9,D5,L1,V1,M1} { strong_iteration( X ) = addition(
% 50.75/51.12 multiplication( X, strong_iteration( X ) ), one ) }.
% 50.75/51.12 (65715) {G0,W13,D4,L2,V3,M2} { ! leq( Z, addition( multiplication( X, Z )
% 50.75/51.12 , Y ) ), leq( Z, multiplication( strong_iteration( X ), Y ) ) }.
% 50.75/51.12 (65716) {G0,W10,D5,L1,V1,M1} { strong_iteration( X ) = addition( star( X )
% 50.75/51.12 , multiplication( strong_iteration( X ), zero ) ) }.
% 50.75/51.12 (65717) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 50.75/51.12 (65718) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 50.75/51.12 (65719) {G0,W18,D5,L2,V0,M2} { ! leq( strong_iteration( skol1 ), addition
% 50.75/51.12 ( multiplication( strong_iteration( skol1 ), skol1 ), one ) ), ! leq(
% 50.75/51.12 addition( multiplication( strong_iteration( skol1 ), skol1 ), one ),
% 50.75/51.12 strong_iteration( skol1 ) ) }.
% 50.75/51.12
% 50.75/51.12
% 50.75/51.12 Total Proof:
% 50.75/51.12
% 50.75/51.12 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 50.75/51.12 ) }.
% 50.75/51.12 parent0: (65700) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 50.75/51.12 }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 50.75/51.12 ==> addition( addition( Z, Y ), X ) }.
% 50.75/51.12 parent0: (65701) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) =
% 50.75/51.12 addition( addition( Z, Y ), X ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 Z := Z
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 50.75/51.12 parent0: (65702) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 50.75/51.12 parent0: (65703) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (4) {G0,W11,D4,L1,V3,M1} I { multiplication( X, multiplication
% 50.75/51.12 ( Y, Z ) ) ==> multiplication( multiplication( X, Y ), Z ) }.
% 50.75/51.12 parent0: (65704) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication
% 50.75/51.12 ( Y, Z ) ) = multiplication( multiplication( X, Y ), Z ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 Z := Z
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 50.75/51.12 parent0: (65705) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 eqswap: (65741) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 50.75/51.12 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 50.75/51.12 parent0[0]: (65707) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y
% 50.75/51.12 , Z ) ) = addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 Z := Z
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y )
% 50.75/51.12 , multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 50.75/51.12 parent0: (65741) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 50.75/51.12 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 Z := Z
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 eqswap: (65749) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 50.75/51.12 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 50.75/51.12 parent0[0]: (65708) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y
% 50.75/51.12 ), Z ) = addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 Z := Z
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z )
% 50.75/51.12 , multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 50.75/51.12 parent0: (65749) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 50.75/51.12 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 Z := Z
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (9) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==> zero
% 50.75/51.12 }.
% 50.75/51.12 parent0: (65709) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero
% 50.75/51.12 }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (11) {G0,W9,D5,L1,V1,M1} I { addition( one, multiplication(
% 50.75/51.12 star( X ), X ) ) ==> star( X ) }.
% 50.75/51.12 parent0: (65711) {G0,W9,D5,L1,V1,M1} { addition( one, multiplication( star
% 50.75/51.12 ( X ), X ) ) = star( X ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (12) {G0,W13,D4,L2,V3,M2} I { ! leq( addition( multiplication
% 50.75/51.12 ( X, Z ), Y ), Z ), leq( multiplication( star( X ), Y ), Z ) }.
% 50.75/51.12 parent0: (65712) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( X
% 50.75/51.12 , Z ), Y ), Z ), leq( multiplication( star( X ), Y ), Z ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 Z := Z
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 1 ==> 1
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 eqswap: (65792) {G0,W9,D5,L1,V1,M1} { addition( multiplication( X,
% 50.75/51.12 strong_iteration( X ) ), one ) = strong_iteration( X ) }.
% 50.75/51.12 parent0[0]: (65714) {G0,W9,D5,L1,V1,M1} { strong_iteration( X ) = addition
% 50.75/51.12 ( multiplication( X, strong_iteration( X ) ), one ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (14) {G0,W9,D5,L1,V1,M1} I { addition( multiplication( X,
% 50.75/51.12 strong_iteration( X ) ), one ) ==> strong_iteration( X ) }.
% 50.75/51.12 parent0: (65792) {G0,W9,D5,L1,V1,M1} { addition( multiplication( X,
% 50.75/51.12 strong_iteration( X ) ), one ) = strong_iteration( X ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 eqswap: (65805) {G0,W10,D5,L1,V1,M1} { addition( star( X ), multiplication
% 50.75/51.12 ( strong_iteration( X ), zero ) ) = strong_iteration( X ) }.
% 50.75/51.12 parent0[0]: (65716) {G0,W10,D5,L1,V1,M1} { strong_iteration( X ) =
% 50.75/51.12 addition( star( X ), multiplication( strong_iteration( X ), zero ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (16) {G0,W10,D5,L1,V1,M1} I { addition( star( X ),
% 50.75/51.12 multiplication( strong_iteration( X ), zero ) ) ==> strong_iteration( X )
% 50.75/51.12 }.
% 50.75/51.12 parent0: (65805) {G0,W10,D5,L1,V1,M1} { addition( star( X ),
% 50.75/51.12 multiplication( strong_iteration( X ), zero ) ) = strong_iteration( X )
% 50.75/51.12 }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 50.75/51.12 ==> Y }.
% 50.75/51.12 parent0: (65717) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y
% 50.75/51.12 }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 1 ==> 1
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X
% 50.75/51.12 , Y ) }.
% 50.75/51.12 parent0: (65718) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y )
% 50.75/51.12 }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 1 ==> 1
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (19) {G0,W18,D5,L2,V0,M2} I { ! leq( strong_iteration( skol1 )
% 50.75/51.12 , addition( multiplication( strong_iteration( skol1 ), skol1 ), one ) ),
% 50.75/51.12 ! leq( addition( multiplication( strong_iteration( skol1 ), skol1 ), one
% 50.75/51.12 ), strong_iteration( skol1 ) ) }.
% 50.75/51.12 parent0: (65719) {G0,W18,D5,L2,V0,M2} { ! leq( strong_iteration( skol1 ),
% 50.75/51.12 addition( multiplication( strong_iteration( skol1 ), skol1 ), one ) ), !
% 50.75/51.12 leq( addition( multiplication( strong_iteration( skol1 ), skol1 ), one )
% 50.75/51.12 , strong_iteration( skol1 ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 1 ==> 1
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 eqswap: (65850) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, zero ) }.
% 50.75/51.12 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 paramod: (65851) {G1,W5,D3,L1,V1,M1} { X ==> addition( zero, X ) }.
% 50.75/51.12 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 50.75/51.12 }.
% 50.75/51.12 parent1[0; 2]: (65850) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, zero ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := zero
% 50.75/51.12 end
% 50.75/51.12 substitution1:
% 50.75/51.12 X := X
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 eqswap: (65854) {G1,W5,D3,L1,V1,M1} { addition( zero, X ) ==> X }.
% 50.75/51.12 parent0[0]: (65851) {G1,W5,D3,L1,V1,M1} { X ==> addition( zero, X ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (20) {G1,W5,D3,L1,V1,M1} P(0,2) { addition( zero, X ) ==> X
% 50.75/51.12 }.
% 50.75/51.12 parent0: (65854) {G1,W5,D3,L1,V1,M1} { addition( zero, X ) ==> X }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 eqswap: (65855) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 50.75/51.12 ) }.
% 50.75/51.12 parent0[0]: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 50.75/51.12 Y ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 eqswap: (65856) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 50.75/51.12 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 resolution: (65857) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 50.75/51.12 parent0[0]: (65855) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X
% 50.75/51.12 , Y ) }.
% 50.75/51.12 parent1[0]: (65856) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := X
% 50.75/51.12 end
% 50.75/51.12 substitution1:
% 50.75/51.12 X := X
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (22) {G1,W3,D2,L1,V1,M1} R(18,3) { leq( X, X ) }.
% 50.75/51.12 parent0: (65857) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 eqswap: (65859) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 50.75/51.12 ) }.
% 50.75/51.12 parent0[0]: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 50.75/51.12 Y ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 paramod: (65860) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition(
% 50.75/51.12 addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 50.75/51.12 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 50.75/51.12 ==> addition( addition( Z, Y ), X ) }.
% 50.75/51.12 parent1[0; 5]: (65859) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 50.75/51.12 ( X, Y ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := Y
% 50.75/51.12 Y := X
% 50.75/51.12 Z := Z
% 50.75/51.12 end
% 50.75/51.12 substitution1:
% 50.75/51.12 X := Z
% 50.75/51.12 Y := addition( X, Y )
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 eqswap: (65861) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 50.75/51.12 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 50.75/51.12 parent0[0]: (65860) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition
% 50.75/51.12 ( addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 Z := Z
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (25) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y
% 50.75/51.12 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 50.75/51.12 parent0: (65861) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 50.75/51.12 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := Y
% 50.75/51.12 Y := Z
% 50.75/51.12 Z := X
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 1 ==> 1
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 eqswap: (65862) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 50.75/51.12 addition( X, addition( Y, Z ) ) }.
% 50.75/51.12 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 50.75/51.12 ==> addition( addition( Z, Y ), X ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := Z
% 50.75/51.12 Y := Y
% 50.75/51.12 Z := X
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 paramod: (65867) {G1,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z )
% 50.75/51.12 ==> addition( X, addition( Z, Y ) ) }.
% 50.75/51.12 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 50.75/51.12 }.
% 50.75/51.12 parent1[0; 8]: (65862) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ),
% 50.75/51.12 Z ) ==> addition( X, addition( Y, Z ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := Y
% 50.75/51.12 Y := Z
% 50.75/51.12 end
% 50.75/51.12 substitution1:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 Z := Z
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 paramod: (65880) {G1,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z )
% 50.75/51.12 ==> addition( addition( X, Z ), Y ) }.
% 50.75/51.12 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 50.75/51.12 ==> addition( addition( Z, Y ), X ) }.
% 50.75/51.12 parent1[0; 6]: (65867) {G1,W11,D4,L1,V3,M1} { addition( addition( X, Y ),
% 50.75/51.12 Z ) ==> addition( X, addition( Z, Y ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := Y
% 50.75/51.12 Y := Z
% 50.75/51.12 Z := X
% 50.75/51.12 end
% 50.75/51.12 substitution1:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 Z := Z
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (27) {G1,W11,D4,L1,V3,M1} P(0,1);d(1) { addition( addition( Z
% 50.75/51.12 , Y ), X ) = addition( addition( Z, X ), Y ) }.
% 50.75/51.12 parent0: (65880) {G1,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z )
% 50.75/51.12 ==> addition( addition( X, Z ), Y ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := Z
% 50.75/51.12 Y := Y
% 50.75/51.12 Z := X
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 eqswap: (65882) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 50.75/51.12 addition( X, addition( Y, Z ) ) }.
% 50.75/51.12 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 50.75/51.12 ==> addition( addition( Z, Y ), X ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := Z
% 50.75/51.12 Y := Y
% 50.75/51.12 Z := X
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 paramod: (65888) {G1,W12,D4,L2,V3,M2} { addition( addition( X, Y ), Z )
% 50.75/51.12 ==> addition( X, Z ), ! leq( Y, Z ) }.
% 50.75/51.12 parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 50.75/51.12 ==> Y }.
% 50.75/51.12 parent1[0; 8]: (65882) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ),
% 50.75/51.12 Z ) ==> addition( X, addition( Y, Z ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := Y
% 50.75/51.12 Y := Z
% 50.75/51.12 end
% 50.75/51.12 substitution1:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 Z := Z
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (35) {G1,W12,D4,L2,V3,M2} P(17,1) { addition( addition( Z, X )
% 50.75/51.12 , Y ) ==> addition( Z, Y ), ! leq( X, Y ) }.
% 50.75/51.12 parent0: (65888) {G1,W12,D4,L2,V3,M2} { addition( addition( X, Y ), Z )
% 50.75/51.12 ==> addition( X, Z ), ! leq( Y, Z ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := Z
% 50.75/51.12 Y := X
% 50.75/51.12 Z := Y
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 1 ==> 1
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 eqswap: (65935) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 50.75/51.12 ) }.
% 50.75/51.12 parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 50.75/51.12 ==> Y }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 paramod: (65936) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X
% 50.75/51.12 ) }.
% 50.75/51.12 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 50.75/51.12 }.
% 50.75/51.12 parent1[0; 2]: (65935) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq
% 50.75/51.12 ( X, Y ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := Y
% 50.75/51.12 Y := X
% 50.75/51.12 end
% 50.75/51.12 substitution1:
% 50.75/51.12 X := Y
% 50.75/51.12 Y := X
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 eqswap: (65939) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> X, ! leq( Y, X
% 50.75/51.12 ) }.
% 50.75/51.12 parent0[0]: (65936) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y
% 50.75/51.12 , X ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (36) {G1,W8,D3,L2,V2,M2} P(17,0) { addition( Y, X ) ==> Y, !
% 50.75/51.12 leq( X, Y ) }.
% 50.75/51.12 parent0: (65939) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> X, ! leq( Y, X
% 50.75/51.12 ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := Y
% 50.75/51.12 Y := X
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 1 ==> 1
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 eqswap: (65941) {G0,W11,D4,L1,V3,M1} { multiplication( multiplication( X,
% 50.75/51.12 Y ), Z ) ==> multiplication( X, multiplication( Y, Z ) ) }.
% 50.75/51.12 parent0[0]: (4) {G0,W11,D4,L1,V3,M1} I { multiplication( X, multiplication
% 50.75/51.12 ( Y, Z ) ) ==> multiplication( multiplication( X, Y ), Z ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 Z := Z
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 paramod: (65946) {G1,W9,D4,L1,V2,M1} { multiplication( multiplication( X,
% 50.75/51.12 zero ), Y ) ==> multiplication( X, zero ) }.
% 50.75/51.12 parent0[0]: (9) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==> zero
% 50.75/51.12 }.
% 50.75/51.12 parent1[0; 8]: (65941) {G0,W11,D4,L1,V3,M1} { multiplication(
% 50.75/51.12 multiplication( X, Y ), Z ) ==> multiplication( X, multiplication( Y, Z )
% 50.75/51.12 ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := Y
% 50.75/51.12 end
% 50.75/51.12 substitution1:
% 50.75/51.12 X := X
% 50.75/51.12 Y := zero
% 50.75/51.12 Z := Y
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (50) {G1,W9,D4,L1,V2,M1} P(9,4) { multiplication(
% 50.75/51.12 multiplication( Y, zero ), X ) ==> multiplication( Y, zero ) }.
% 50.75/51.12 parent0: (65946) {G1,W9,D4,L1,V2,M1} { multiplication( multiplication( X,
% 50.75/51.12 zero ), Y ) ==> multiplication( X, zero ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := Y
% 50.75/51.12 Y := X
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 eqswap: (65955) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 50.75/51.12 ) }.
% 50.75/51.12 parent0[0]: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 50.75/51.12 Y ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 paramod: (65956) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 50.75/51.12 multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ),
% 50.75/51.12 multiplication( X, Y ) ) }.
% 50.75/51.12 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 50.75/51.12 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 50.75/51.12 parent1[0; 5]: (65955) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 50.75/51.12 ( X, Y ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Z
% 50.75/51.12 Z := Y
% 50.75/51.12 end
% 50.75/51.12 substitution1:
% 50.75/51.12 X := multiplication( X, Z )
% 50.75/51.12 Y := multiplication( X, Y )
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 eqswap: (65957) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, addition( Z, Y
% 50.75/51.12 ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ),
% 50.75/51.12 multiplication( X, Y ) ) }.
% 50.75/51.12 parent0[0]: (65956) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 50.75/51.12 multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ),
% 50.75/51.12 multiplication( X, Y ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 Z := Z
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (67) {G1,W16,D4,L2,V3,M2} P(7,18) { ! multiplication( X,
% 50.75/51.12 addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 50.75/51.12 ), multiplication( X, Z ) ) }.
% 50.75/51.12 parent0: (65957) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, addition( Z,
% 50.75/51.12 Y ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ),
% 50.75/51.12 multiplication( X, Y ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Z
% 50.75/51.12 Z := Y
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 1 ==> 1
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 eqswap: (65959) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z )
% 50.75/51.12 ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 50.75/51.12 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 50.75/51.12 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 Z := Z
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 paramod: (65960) {G1,W11,D4,L1,V2,M1} { multiplication( X, addition( one,
% 50.75/51.12 Y ) ) ==> addition( X, multiplication( X, Y ) ) }.
% 50.75/51.12 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 50.75/51.12 parent1[0; 7]: (65959) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition
% 50.75/51.12 ( Y, Z ) ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) )
% 50.75/51.12 }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 end
% 50.75/51.12 substitution1:
% 50.75/51.12 X := X
% 50.75/51.12 Y := one
% 50.75/51.12 Z := Y
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 eqswap: (65962) {G1,W11,D4,L1,V2,M1} { addition( X, multiplication( X, Y )
% 50.75/51.12 ) ==> multiplication( X, addition( one, Y ) ) }.
% 50.75/51.12 parent0[0]: (65960) {G1,W11,D4,L1,V2,M1} { multiplication( X, addition(
% 50.75/51.12 one, Y ) ) ==> addition( X, multiplication( X, Y ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (69) {G1,W11,D4,L1,V2,M1} P(5,7) { addition( X, multiplication
% 50.75/51.12 ( X, Y ) ) = multiplication( X, addition( one, Y ) ) }.
% 50.75/51.12 parent0: (65962) {G1,W11,D4,L1,V2,M1} { addition( X, multiplication( X, Y
% 50.75/51.12 ) ) ==> multiplication( X, addition( one, Y ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 eqswap: (65965) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 50.75/51.12 ) }.
% 50.75/51.12 parent0[0]: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 50.75/51.12 Y ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 paramod: (65966) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 50.75/51.12 multiplication( addition( Z, X ), Y ), leq( multiplication( Z, Y ),
% 50.75/51.12 multiplication( X, Y ) ) }.
% 50.75/51.12 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 50.75/51.12 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 50.75/51.12 parent1[0; 5]: (65965) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 50.75/51.12 ( X, Y ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := Z
% 50.75/51.12 Y := X
% 50.75/51.12 Z := Y
% 50.75/51.12 end
% 50.75/51.12 substitution1:
% 50.75/51.12 X := multiplication( Z, Y )
% 50.75/51.12 Y := multiplication( X, Y )
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 eqswap: (65967) {G1,W16,D4,L2,V3,M2} { ! multiplication( addition( Z, X )
% 50.75/51.12 , Y ) ==> multiplication( X, Y ), leq( multiplication( Z, Y ),
% 50.75/51.12 multiplication( X, Y ) ) }.
% 50.75/51.12 parent0[0]: (65966) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 50.75/51.12 multiplication( addition( Z, X ), Y ), leq( multiplication( Z, Y ),
% 50.75/51.12 multiplication( X, Y ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 Z := Z
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (99) {G1,W16,D4,L2,V3,M2} P(8,18) { ! multiplication( addition
% 50.75/51.12 ( X, Z ), Y ) ==> multiplication( Z, Y ), leq( multiplication( X, Y ),
% 50.75/51.12 multiplication( Z, Y ) ) }.
% 50.75/51.12 parent0: (65967) {G1,W16,D4,L2,V3,M2} { ! multiplication( addition( Z, X )
% 50.75/51.12 , Y ) ==> multiplication( X, Y ), leq( multiplication( Z, Y ),
% 50.75/51.12 multiplication( X, Y ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := Z
% 50.75/51.12 Y := Y
% 50.75/51.12 Z := X
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 1 ==> 1
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 eqswap: (65968) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Z ), Y
% 50.75/51.12 ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) ) }.
% 50.75/51.12 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 50.75/51.12 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Z
% 50.75/51.12 Z := Y
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 paramod: (65970) {G1,W13,D4,L1,V3,M1} { multiplication( addition( Y, X ),
% 50.75/51.12 Z ) ==> addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 50.75/51.12 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 50.75/51.12 }.
% 50.75/51.12 parent1[0; 2]: (65968) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X
% 50.75/51.12 , Z ), Y ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) )
% 50.75/51.12 }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 end
% 50.75/51.12 substitution1:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Z
% 50.75/51.12 Z := Y
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 paramod: (65972) {G1,W11,D4,L1,V3,M1} { multiplication( addition( X, Y ),
% 50.75/51.12 Z ) ==> multiplication( addition( Y, X ), Z ) }.
% 50.75/51.12 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 50.75/51.12 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 50.75/51.12 parent1[0; 6]: (65970) {G1,W13,D4,L1,V3,M1} { multiplication( addition( Y
% 50.75/51.12 , X ), Z ) ==> addition( multiplication( X, Z ), multiplication( Y, Z ) )
% 50.75/51.12 }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := Y
% 50.75/51.12 Y := X
% 50.75/51.12 Z := Z
% 50.75/51.12 end
% 50.75/51.12 substitution1:
% 50.75/51.12 X := Y
% 50.75/51.12 Y := X
% 50.75/51.12 Z := Z
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (100) {G1,W11,D4,L1,V3,M1} P(8,0);d(8) { multiplication(
% 50.75/51.12 addition( X, Z ), Y ) = multiplication( addition( Z, X ), Y ) }.
% 50.75/51.12 parent0: (65972) {G1,W11,D4,L1,V3,M1} { multiplication( addition( X, Y ),
% 50.75/51.12 Z ) ==> multiplication( addition( Y, X ), Z ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Z
% 50.75/51.12 Z := Y
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 paramod: (65975) {G1,W12,D4,L2,V1,M2} { ! leq( strong_iteration( X ),
% 50.75/51.12 strong_iteration( X ) ), leq( multiplication( star( X ), one ),
% 50.75/51.12 strong_iteration( X ) ) }.
% 50.75/51.12 parent0[0]: (14) {G0,W9,D5,L1,V1,M1} I { addition( multiplication( X,
% 50.75/51.12 strong_iteration( X ) ), one ) ==> strong_iteration( X ) }.
% 50.75/51.12 parent1[0; 2]: (12) {G0,W13,D4,L2,V3,M2} I { ! leq( addition(
% 50.75/51.12 multiplication( X, Z ), Y ), Z ), leq( multiplication( star( X ), Y ), Z
% 50.75/51.12 ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 end
% 50.75/51.12 substitution1:
% 50.75/51.12 X := X
% 50.75/51.12 Y := one
% 50.75/51.12 Z := strong_iteration( X )
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 paramod: (65976) {G1,W10,D3,L2,V1,M2} { leq( star( X ), strong_iteration(
% 50.75/51.12 X ) ), ! leq( strong_iteration( X ), strong_iteration( X ) ) }.
% 50.75/51.12 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 50.75/51.12 parent1[1; 1]: (65975) {G1,W12,D4,L2,V1,M2} { ! leq( strong_iteration( X )
% 50.75/51.12 , strong_iteration( X ) ), leq( multiplication( star( X ), one ),
% 50.75/51.12 strong_iteration( X ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := star( X )
% 50.75/51.12 end
% 50.75/51.12 substitution1:
% 50.75/51.12 X := X
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 resolution: (65977) {G2,W5,D3,L1,V1,M1} { leq( star( X ), strong_iteration
% 50.75/51.12 ( X ) ) }.
% 50.75/51.12 parent0[1]: (65976) {G1,W10,D3,L2,V1,M2} { leq( star( X ),
% 50.75/51.12 strong_iteration( X ) ), ! leq( strong_iteration( X ), strong_iteration(
% 50.75/51.12 X ) ) }.
% 50.75/51.12 parent1[0]: (22) {G1,W3,D2,L1,V1,M1} R(18,3) { leq( X, X ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 end
% 50.75/51.12 substitution1:
% 50.75/51.12 X := strong_iteration( X )
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (213) {G2,W5,D3,L1,V1,M1} P(14,12);d(5);r(22) { leq( star( X )
% 50.75/51.12 , strong_iteration( X ) ) }.
% 50.75/51.12 parent0: (65977) {G2,W5,D3,L1,V1,M1} { leq( star( X ), strong_iteration( X
% 50.75/51.12 ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 eqswap: (65978) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 50.75/51.12 ) }.
% 50.75/51.12 parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 50.75/51.12 ==> Y }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 resolution: (65979) {G1,W8,D4,L1,V1,M1} { strong_iteration( X ) ==>
% 50.75/51.12 addition( star( X ), strong_iteration( X ) ) }.
% 50.75/51.12 parent0[1]: (65978) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X
% 50.75/51.12 , Y ) }.
% 50.75/51.12 parent1[0]: (213) {G2,W5,D3,L1,V1,M1} P(14,12);d(5);r(22) { leq( star( X )
% 50.75/51.12 , strong_iteration( X ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := star( X )
% 50.75/51.12 Y := strong_iteration( X )
% 50.75/51.12 end
% 50.75/51.12 substitution1:
% 50.75/51.12 X := X
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 eqswap: (65980) {G1,W8,D4,L1,V1,M1} { addition( star( X ),
% 50.75/51.12 strong_iteration( X ) ) ==> strong_iteration( X ) }.
% 50.75/51.12 parent0[0]: (65979) {G1,W8,D4,L1,V1,M1} { strong_iteration( X ) ==>
% 50.75/51.12 addition( star( X ), strong_iteration( X ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (226) {G3,W8,D4,L1,V1,M1} R(213,17) { addition( star( X ),
% 50.75/51.12 strong_iteration( X ) ) ==> strong_iteration( X ) }.
% 50.75/51.12 parent0: (65980) {G1,W8,D4,L1,V1,M1} { addition( star( X ),
% 50.75/51.12 strong_iteration( X ) ) ==> strong_iteration( X ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 eqswap: (65981) {G0,W10,D5,L1,V1,M1} { strong_iteration( X ) ==> addition
% 50.75/51.12 ( star( X ), multiplication( strong_iteration( X ), zero ) ) }.
% 50.75/51.12 parent0[0]: (16) {G0,W10,D5,L1,V1,M1} I { addition( star( X ),
% 50.75/51.12 multiplication( strong_iteration( X ), zero ) ) ==> strong_iteration( X )
% 50.75/51.12 }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 paramod: (65982) {G1,W10,D5,L1,V1,M1} { strong_iteration( X ) ==> addition
% 50.75/51.12 ( multiplication( strong_iteration( X ), zero ), star( X ) ) }.
% 50.75/51.12 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 50.75/51.12 }.
% 50.75/51.12 parent1[0; 3]: (65981) {G0,W10,D5,L1,V1,M1} { strong_iteration( X ) ==>
% 50.75/51.12 addition( star( X ), multiplication( strong_iteration( X ), zero ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := star( X )
% 50.75/51.12 Y := multiplication( strong_iteration( X ), zero )
% 50.75/51.12 end
% 50.75/51.12 substitution1:
% 50.75/51.12 X := X
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 eqswap: (65985) {G1,W10,D5,L1,V1,M1} { addition( multiplication(
% 50.75/51.12 strong_iteration( X ), zero ), star( X ) ) ==> strong_iteration( X ) }.
% 50.75/51.12 parent0[0]: (65982) {G1,W10,D5,L1,V1,M1} { strong_iteration( X ) ==>
% 50.75/51.12 addition( multiplication( strong_iteration( X ), zero ), star( X ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (285) {G1,W10,D5,L1,V1,M1} P(16,0) { addition( multiplication
% 50.75/51.12 ( strong_iteration( X ), zero ), star( X ) ) ==> strong_iteration( X )
% 50.75/51.12 }.
% 50.75/51.12 parent0: (65985) {G1,W10,D5,L1,V1,M1} { addition( multiplication(
% 50.75/51.12 strong_iteration( X ), zero ), star( X ) ) ==> strong_iteration( X ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 paramod: (65987) {G1,W18,D5,L2,V0,M2} { ! leq( addition( one,
% 50.75/51.12 multiplication( strong_iteration( skol1 ), skol1 ) ), strong_iteration(
% 50.75/51.12 skol1 ) ), ! leq( strong_iteration( skol1 ), addition( multiplication(
% 50.75/51.12 strong_iteration( skol1 ), skol1 ), one ) ) }.
% 50.75/51.12 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 50.75/51.12 }.
% 50.75/51.12 parent1[1; 2]: (19) {G0,W18,D5,L2,V0,M2} I { ! leq( strong_iteration( skol1
% 50.75/51.12 ), addition( multiplication( strong_iteration( skol1 ), skol1 ), one ) )
% 50.75/51.12 , ! leq( addition( multiplication( strong_iteration( skol1 ), skol1 ),
% 50.75/51.12 one ), strong_iteration( skol1 ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := multiplication( strong_iteration( skol1 ), skol1 )
% 50.75/51.12 Y := one
% 50.75/51.12 end
% 50.75/51.12 substitution1:
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 paramod: (65989) {G1,W18,D5,L2,V0,M2} { ! leq( strong_iteration( skol1 ),
% 50.75/51.12 addition( one, multiplication( strong_iteration( skol1 ), skol1 ) ) ), !
% 50.75/51.12 leq( addition( one, multiplication( strong_iteration( skol1 ), skol1 ) )
% 50.75/51.12 , strong_iteration( skol1 ) ) }.
% 50.75/51.12 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 50.75/51.12 }.
% 50.75/51.12 parent1[1; 4]: (65987) {G1,W18,D5,L2,V0,M2} { ! leq( addition( one,
% 50.75/51.12 multiplication( strong_iteration( skol1 ), skol1 ) ), strong_iteration(
% 50.75/51.12 skol1 ) ), ! leq( strong_iteration( skol1 ), addition( multiplication(
% 50.75/51.12 strong_iteration( skol1 ), skol1 ), one ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := multiplication( strong_iteration( skol1 ), skol1 )
% 50.75/51.12 Y := one
% 50.75/51.12 end
% 50.75/51.12 substitution1:
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (306) {G1,W18,D5,L2,V0,M2} P(0,19) { ! leq( strong_iteration(
% 50.75/51.12 skol1 ), addition( one, multiplication( strong_iteration( skol1 ), skol1
% 50.75/51.12 ) ) ), ! leq( addition( one, multiplication( strong_iteration( skol1 ),
% 50.75/51.12 skol1 ) ), strong_iteration( skol1 ) ) }.
% 50.75/51.12 parent0: (65989) {G1,W18,D5,L2,V0,M2} { ! leq( strong_iteration( skol1 ),
% 50.75/51.12 addition( one, multiplication( strong_iteration( skol1 ), skol1 ) ) ), !
% 50.75/51.12 leq( addition( one, multiplication( strong_iteration( skol1 ), skol1 ) )
% 50.75/51.12 , strong_iteration( skol1 ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 1 ==> 1
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 eqswap: (65991) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==> addition(
% 50.75/51.12 addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 50.75/51.12 parent0[0]: (25) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y
% 50.75/51.12 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 Z := Z
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 paramod: (65994) {G1,W15,D3,L3,V3,M3} { ! addition( X, Y ) ==> addition( X
% 50.75/51.12 , Y ), ! leq( Z, X ), leq( Z, addition( X, Y ) ) }.
% 50.75/51.12 parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 50.75/51.12 ==> Y }.
% 50.75/51.12 parent1[0; 6]: (65991) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==>
% 50.75/51.12 addition( addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := Z
% 50.75/51.12 Y := X
% 50.75/51.12 end
% 50.75/51.12 substitution1:
% 50.75/51.12 X := Z
% 50.75/51.12 Y := X
% 50.75/51.12 Z := Y
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 eqrefl: (66043) {G0,W8,D3,L2,V3,M2} { ! leq( Z, X ), leq( Z, addition( X,
% 50.75/51.12 Y ) ) }.
% 50.75/51.12 parent0[0]: (65994) {G1,W15,D3,L3,V3,M3} { ! addition( X, Y ) ==> addition
% 50.75/51.12 ( X, Y ), ! leq( Z, X ), leq( Z, addition( X, Y ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 Z := Z
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (319) {G2,W8,D3,L2,V3,M2} P(17,25);q { leq( X, addition( Y, Z
% 50.75/51.12 ) ), ! leq( X, Y ) }.
% 50.75/51.12 parent0: (66043) {G0,W8,D3,L2,V3,M2} { ! leq( Z, X ), leq( Z, addition( X
% 50.75/51.12 , Y ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := Y
% 50.75/51.12 Y := Z
% 50.75/51.12 Z := X
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 1
% 50.75/51.12 1 ==> 0
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 eqswap: (66045) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==> addition(
% 50.75/51.12 addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 50.75/51.12 parent0[0]: (25) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y
% 50.75/51.12 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 Z := Z
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 paramod: (66048) {G1,W12,D3,L2,V2,M2} { ! addition( X, Y ) ==> addition( X
% 50.75/51.12 , Y ), leq( X, addition( X, Y ) ) }.
% 50.75/51.12 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 50.75/51.12 parent1[0; 6]: (66045) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==>
% 50.75/51.12 addition( addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 end
% 50.75/51.12 substitution1:
% 50.75/51.12 X := X
% 50.75/51.12 Y := X
% 50.75/51.12 Z := Y
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 eqrefl: (66051) {G0,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 50.75/51.12 parent0[0]: (66048) {G1,W12,D3,L2,V2,M2} { ! addition( X, Y ) ==> addition
% 50.75/51.12 ( X, Y ), leq( X, addition( X, Y ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (323) {G2,W5,D3,L1,V2,M1} P(3,25);q { leq( X, addition( X, Y )
% 50.75/51.12 ) }.
% 50.75/51.12 parent0: (66051) {G0,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 paramod: (66052) {G1,W5,D3,L1,V2,M1} { leq( X, addition( Y, X ) ) }.
% 50.75/51.12 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 50.75/51.12 }.
% 50.75/51.12 parent1[0; 2]: (323) {G2,W5,D3,L1,V2,M1} P(3,25);q { leq( X, addition( X, Y
% 50.75/51.12 ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 end
% 50.75/51.12 substitution1:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (362) {G3,W5,D3,L1,V2,M1} P(0,323) { leq( X, addition( Y, X )
% 50.75/51.12 ) }.
% 50.75/51.12 parent0: (66052) {G1,W5,D3,L1,V2,M1} { leq( X, addition( Y, X ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 paramod: (66055) {G1,W7,D4,L1,V1,M1} { leq( multiplication( star( X ), X )
% 50.75/51.12 , star( X ) ) }.
% 50.75/51.12 parent0[0]: (11) {G0,W9,D5,L1,V1,M1} I { addition( one, multiplication(
% 50.75/51.12 star( X ), X ) ) ==> star( X ) }.
% 50.75/51.12 parent1[0; 5]: (362) {G3,W5,D3,L1,V2,M1} P(0,323) { leq( X, addition( Y, X
% 50.75/51.12 ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 end
% 50.75/51.12 substitution1:
% 50.75/51.12 X := multiplication( star( X ), X )
% 50.75/51.12 Y := one
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (368) {G4,W7,D4,L1,V1,M1} P(11,362) { leq( multiplication(
% 50.75/51.12 star( X ), X ), star( X ) ) }.
% 50.75/51.12 parent0: (66055) {G1,W7,D4,L1,V1,M1} { leq( multiplication( star( X ), X )
% 50.75/51.12 , star( X ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 paramod: (66058) {G1,W14,D5,L1,V2,M1} { addition( addition( star( X ), Y )
% 50.75/51.12 , multiplication( strong_iteration( X ), zero ) ) = addition(
% 50.75/51.12 strong_iteration( X ), Y ) }.
% 50.75/51.12 parent0[0]: (16) {G0,W10,D5,L1,V1,M1} I { addition( star( X ),
% 50.75/51.12 multiplication( strong_iteration( X ), zero ) ) ==> strong_iteration( X )
% 50.75/51.12 }.
% 50.75/51.12 parent1[0; 11]: (27) {G1,W11,D4,L1,V3,M1} P(0,1);d(1) { addition( addition
% 50.75/51.12 ( Z, Y ), X ) = addition( addition( Z, X ), Y ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 end
% 50.75/51.12 substitution1:
% 50.75/51.12 X := multiplication( strong_iteration( X ), zero )
% 50.75/51.12 Y := Y
% 50.75/51.12 Z := star( X )
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (380) {G2,W14,D5,L1,V2,M1} P(16,27) { addition( addition( star
% 50.75/51.12 ( X ), Y ), multiplication( strong_iteration( X ), zero ) ) ==> addition
% 50.75/51.12 ( strong_iteration( X ), Y ) }.
% 50.75/51.12 parent0: (66058) {G1,W14,D5,L1,V2,M1} { addition( addition( star( X ), Y )
% 50.75/51.12 , multiplication( strong_iteration( X ), zero ) ) = addition(
% 50.75/51.12 strong_iteration( X ), Y ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 eqswap: (66060) {G1,W12,D4,L2,V3,M2} { addition( X, Z ) ==> addition(
% 50.75/51.12 addition( X, Y ), Z ), ! leq( Y, Z ) }.
% 50.75/51.12 parent0[0]: (35) {G1,W12,D4,L2,V3,M2} P(17,1) { addition( addition( Z, X )
% 50.75/51.12 , Y ) ==> addition( Z, Y ), ! leq( X, Y ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := Y
% 50.75/51.12 Y := Z
% 50.75/51.12 Z := X
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 paramod: (66062) {G1,W15,D4,L2,V2,M2} { addition( star( X ), Y ) ==>
% 50.75/51.12 addition( strong_iteration( X ), Y ), ! leq( multiplication(
% 50.75/51.12 strong_iteration( X ), zero ), Y ) }.
% 50.75/51.12 parent0[0]: (16) {G0,W10,D5,L1,V1,M1} I { addition( star( X ),
% 50.75/51.12 multiplication( strong_iteration( X ), zero ) ) ==> strong_iteration( X )
% 50.75/51.12 }.
% 50.75/51.12 parent1[0; 6]: (66060) {G1,W12,D4,L2,V3,M2} { addition( X, Z ) ==>
% 50.75/51.12 addition( addition( X, Y ), Z ), ! leq( Y, Z ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 end
% 50.75/51.12 substitution1:
% 50.75/51.12 X := star( X )
% 50.75/51.12 Y := multiplication( strong_iteration( X ), zero )
% 50.75/51.12 Z := Y
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 eqswap: (66064) {G1,W15,D4,L2,V2,M2} { addition( strong_iteration( X ), Y
% 50.75/51.12 ) ==> addition( star( X ), Y ), ! leq( multiplication( strong_iteration
% 50.75/51.12 ( X ), zero ), Y ) }.
% 50.75/51.12 parent0[0]: (66062) {G1,W15,D4,L2,V2,M2} { addition( star( X ), Y ) ==>
% 50.75/51.12 addition( strong_iteration( X ), Y ), ! leq( multiplication(
% 50.75/51.12 strong_iteration( X ), zero ), Y ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (562) {G2,W15,D4,L2,V2,M2} P(16,35) { addition(
% 50.75/51.12 strong_iteration( X ), Y ) ==> addition( star( X ), Y ), ! leq(
% 50.75/51.12 multiplication( strong_iteration( X ), zero ), Y ) }.
% 50.75/51.12 parent0: (66064) {G1,W15,D4,L2,V2,M2} { addition( strong_iteration( X ), Y
% 50.75/51.12 ) ==> addition( star( X ), Y ), ! leq( multiplication( strong_iteration
% 50.75/51.12 ( X ), zero ), Y ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 1 ==> 1
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 eqswap: (66066) {G1,W12,D4,L2,V3,M2} { addition( X, Z ) ==> addition(
% 50.75/51.12 addition( X, Y ), Z ), ! leq( Y, Z ) }.
% 50.75/51.12 parent0[0]: (35) {G1,W12,D4,L2,V3,M2} P(17,1) { addition( addition( Z, X )
% 50.75/51.12 , Y ) ==> addition( Z, Y ), ! leq( X, Y ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := Y
% 50.75/51.12 Y := Z
% 50.75/51.12 Z := X
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 paramod: (66068) {G1,W14,D4,L2,V2,M2} { addition( one, X ) ==> addition(
% 50.75/51.12 star( Y ), X ), ! leq( multiplication( star( Y ), Y ), X ) }.
% 50.75/51.12 parent0[0]: (11) {G0,W9,D5,L1,V1,M1} I { addition( one, multiplication(
% 50.75/51.12 star( X ), X ) ) ==> star( X ) }.
% 50.75/51.12 parent1[0; 5]: (66066) {G1,W12,D4,L2,V3,M2} { addition( X, Z ) ==>
% 50.75/51.12 addition( addition( X, Y ), Z ), ! leq( Y, Z ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := Y
% 50.75/51.12 end
% 50.75/51.12 substitution1:
% 50.75/51.12 X := one
% 50.75/51.12 Y := multiplication( star( Y ), Y )
% 50.75/51.12 Z := X
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 eqswap: (66070) {G1,W14,D4,L2,V2,M2} { addition( star( Y ), X ) ==>
% 50.75/51.12 addition( one, X ), ! leq( multiplication( star( Y ), Y ), X ) }.
% 50.75/51.12 parent0[0]: (66068) {G1,W14,D4,L2,V2,M2} { addition( one, X ) ==> addition
% 50.75/51.12 ( star( Y ), X ), ! leq( multiplication( star( Y ), Y ), X ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (565) {G2,W14,D4,L2,V2,M2} P(11,35) { addition( star( X ), Y )
% 50.75/51.12 ==> addition( one, Y ), ! leq( multiplication( star( X ), X ), Y ) }.
% 50.75/51.12 parent0: (66070) {G1,W14,D4,L2,V2,M2} { addition( star( Y ), X ) ==>
% 50.75/51.12 addition( one, X ), ! leq( multiplication( star( Y ), Y ), X ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := Y
% 50.75/51.12 Y := X
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 1 ==> 1
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 eqswap: (66072) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Z ), Y
% 50.75/51.12 ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) ) }.
% 50.75/51.12 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 50.75/51.12 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Z
% 50.75/51.12 Z := Y
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 paramod: (66074) {G1,W15,D5,L1,V3,M1} { multiplication( addition( X,
% 50.75/51.12 multiplication( Y, zero ) ), Z ) ==> addition( multiplication( X, Z ),
% 50.75/51.12 multiplication( Y, zero ) ) }.
% 50.75/51.12 parent0[0]: (50) {G1,W9,D4,L1,V2,M1} P(9,4) { multiplication(
% 50.75/51.12 multiplication( Y, zero ), X ) ==> multiplication( Y, zero ) }.
% 50.75/51.12 parent1[0; 12]: (66072) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X
% 50.75/51.12 , Z ), Y ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) )
% 50.75/51.12 }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := Z
% 50.75/51.12 Y := Y
% 50.75/51.12 end
% 50.75/51.12 substitution1:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Z
% 50.75/51.12 Z := multiplication( Y, zero )
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (809) {G2,W15,D5,L1,V3,M1} P(50,8) { multiplication( addition
% 50.75/51.12 ( Z, multiplication( X, zero ) ), Y ) ==> addition( multiplication( Z, Y
% 50.75/51.12 ), multiplication( X, zero ) ) }.
% 50.75/51.12 parent0: (66074) {G1,W15,D5,L1,V3,M1} { multiplication( addition( X,
% 50.75/51.12 multiplication( Y, zero ) ), Z ) ==> addition( multiplication( X, Z ),
% 50.75/51.12 multiplication( Y, zero ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := Z
% 50.75/51.12 Y := X
% 50.75/51.12 Z := Y
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 paramod: (66078) {G1,W8,D3,L2,V2,M2} { leq( X, strong_iteration( Y ) ), !
% 50.75/51.12 leq( X, star( Y ) ) }.
% 50.75/51.12 parent0[0]: (16) {G0,W10,D5,L1,V1,M1} I { addition( star( X ),
% 50.75/51.12 multiplication( strong_iteration( X ), zero ) ) ==> strong_iteration( X )
% 50.75/51.12 }.
% 50.75/51.12 parent1[0; 2]: (319) {G2,W8,D3,L2,V3,M2} P(17,25);q { leq( X, addition( Y,
% 50.75/51.12 Z ) ), ! leq( X, Y ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := Y
% 50.75/51.12 end
% 50.75/51.12 substitution1:
% 50.75/51.12 X := X
% 50.75/51.12 Y := star( Y )
% 50.75/51.12 Z := multiplication( strong_iteration( Y ), zero )
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (1092) {G3,W8,D3,L2,V2,M2} P(16,319) { leq( Y,
% 50.75/51.12 strong_iteration( X ) ), ! leq( Y, star( X ) ) }.
% 50.75/51.12 parent0: (66078) {G1,W8,D3,L2,V2,M2} { leq( X, strong_iteration( Y ) ), !
% 50.75/51.12 leq( X, star( Y ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := Y
% 50.75/51.12 Y := X
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 1 ==> 1
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 resolution: (66079) {G4,W7,D4,L1,V1,M1} { leq( multiplication( star( X ),
% 50.75/51.12 X ), strong_iteration( X ) ) }.
% 50.75/51.12 parent0[1]: (1092) {G3,W8,D3,L2,V2,M2} P(16,319) { leq( Y, strong_iteration
% 50.75/51.12 ( X ) ), ! leq( Y, star( X ) ) }.
% 50.75/51.12 parent1[0]: (368) {G4,W7,D4,L1,V1,M1} P(11,362) { leq( multiplication( star
% 50.75/51.12 ( X ), X ), star( X ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := multiplication( star( X ), X )
% 50.75/51.12 end
% 50.75/51.12 substitution1:
% 50.75/51.12 X := X
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (1102) {G5,W7,D4,L1,V1,M1} R(1092,368) { leq( multiplication(
% 50.75/51.12 star( X ), X ), strong_iteration( X ) ) }.
% 50.75/51.12 parent0: (66079) {G4,W7,D4,L1,V1,M1} { leq( multiplication( star( X ), X )
% 50.75/51.12 , strong_iteration( X ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 eqswap: (66080) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X
% 50.75/51.12 ) }.
% 50.75/51.12 parent0[0]: (36) {G1,W8,D3,L2,V2,M2} P(17,0) { addition( Y, X ) ==> Y, !
% 50.75/51.12 leq( X, Y ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := Y
% 50.75/51.12 Y := X
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 resolution: (66081) {G2,W10,D5,L1,V1,M1} { strong_iteration( X ) ==>
% 50.75/51.12 addition( strong_iteration( X ), multiplication( star( X ), X ) ) }.
% 50.75/51.12 parent0[1]: (66080) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y
% 50.75/51.12 , X ) }.
% 50.75/51.12 parent1[0]: (1102) {G5,W7,D4,L1,V1,M1} R(1092,368) { leq( multiplication(
% 50.75/51.12 star( X ), X ), strong_iteration( X ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := strong_iteration( X )
% 50.75/51.12 Y := multiplication( star( X ), X )
% 50.75/51.12 end
% 50.75/51.12 substitution1:
% 50.75/51.12 X := X
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 eqswap: (66082) {G2,W10,D5,L1,V1,M1} { addition( strong_iteration( X ),
% 50.75/51.12 multiplication( star( X ), X ) ) ==> strong_iteration( X ) }.
% 50.75/51.12 parent0[0]: (66081) {G2,W10,D5,L1,V1,M1} { strong_iteration( X ) ==>
% 50.75/51.12 addition( strong_iteration( X ), multiplication( star( X ), X ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (1119) {G6,W10,D5,L1,V1,M1} R(1102,36) { addition(
% 50.75/51.12 strong_iteration( X ), multiplication( star( X ), X ) ) ==>
% 50.75/51.12 strong_iteration( X ) }.
% 50.75/51.12 parent0: (66082) {G2,W10,D5,L1,V1,M1} { addition( strong_iteration( X ),
% 50.75/51.12 multiplication( star( X ), X ) ) ==> strong_iteration( X ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 eqswap: (66084) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Z ) ==>
% 50.75/51.12 multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ),
% 50.75/51.12 multiplication( X, Z ) ) }.
% 50.75/51.12 parent0[0]: (67) {G1,W16,D4,L2,V3,M2} P(7,18) { ! multiplication( X,
% 50.75/51.12 addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 50.75/51.12 ), multiplication( X, Z ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 Z := Z
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 paramod: (66085) {G2,W14,D3,L2,V2,M2} { ! multiplication( X, Y ) ==>
% 50.75/51.12 multiplication( X, Y ), leq( multiplication( X, zero ), multiplication( X
% 50.75/51.12 , Y ) ) }.
% 50.75/51.12 parent0[0]: (20) {G1,W5,D3,L1,V1,M1} P(0,2) { addition( zero, X ) ==> X }.
% 50.75/51.12 parent1[0; 7]: (66084) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Z ) ==>
% 50.75/51.12 multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ),
% 50.75/51.12 multiplication( X, Z ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := Y
% 50.75/51.12 end
% 50.75/51.12 substitution1:
% 50.75/51.12 X := X
% 50.75/51.12 Y := zero
% 50.75/51.12 Z := Y
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 eqrefl: (66086) {G0,W7,D3,L1,V2,M1} { leq( multiplication( X, zero ),
% 50.75/51.12 multiplication( X, Y ) ) }.
% 50.75/51.12 parent0[0]: (66085) {G2,W14,D3,L2,V2,M2} { ! multiplication( X, Y ) ==>
% 50.75/51.12 multiplication( X, Y ), leq( multiplication( X, zero ), multiplication( X
% 50.75/51.12 , Y ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (1628) {G2,W7,D3,L1,V2,M1} P(20,67);q { leq( multiplication( Y
% 50.75/51.12 , zero ), multiplication( Y, X ) ) }.
% 50.75/51.12 parent0: (66086) {G0,W7,D3,L1,V2,M1} { leq( multiplication( X, zero ),
% 50.75/51.12 multiplication( X, Y ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := Y
% 50.75/51.12 Y := X
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 eqswap: (66088) {G1,W16,D4,L2,V3,M2} { ! multiplication( Y, Z ) ==>
% 50.75/51.12 multiplication( addition( X, Y ), Z ), leq( multiplication( X, Z ),
% 50.75/51.12 multiplication( Y, Z ) ) }.
% 50.75/51.12 parent0[0]: (99) {G1,W16,D4,L2,V3,M2} P(8,18) { ! multiplication( addition
% 50.75/51.12 ( X, Z ), Y ) ==> multiplication( Z, Y ), leq( multiplication( X, Y ),
% 50.75/51.12 multiplication( Z, Y ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Z
% 50.75/51.12 Z := Y
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 paramod: (66089) {G2,W18,D4,L2,V2,M2} { ! multiplication( strong_iteration
% 50.75/51.12 ( X ), Y ) ==> multiplication( strong_iteration( X ), Y ), leq(
% 50.75/51.12 multiplication( star( X ), Y ), multiplication( strong_iteration( X ), Y
% 50.75/51.12 ) ) }.
% 50.75/51.12 parent0[0]: (226) {G3,W8,D4,L1,V1,M1} R(213,17) { addition( star( X ),
% 50.75/51.12 strong_iteration( X ) ) ==> strong_iteration( X ) }.
% 50.75/51.12 parent1[0; 7]: (66088) {G1,W16,D4,L2,V3,M2} { ! multiplication( Y, Z ) ==>
% 50.75/51.12 multiplication( addition( X, Y ), Z ), leq( multiplication( X, Z ),
% 50.75/51.12 multiplication( Y, Z ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 end
% 50.75/51.12 substitution1:
% 50.75/51.12 X := star( X )
% 50.75/51.12 Y := strong_iteration( X )
% 50.75/51.12 Z := Y
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 eqrefl: (66090) {G0,W9,D4,L1,V2,M1} { leq( multiplication( star( X ), Y )
% 50.75/51.12 , multiplication( strong_iteration( X ), Y ) ) }.
% 50.75/51.12 parent0[0]: (66089) {G2,W18,D4,L2,V2,M2} { ! multiplication(
% 50.75/51.12 strong_iteration( X ), Y ) ==> multiplication( strong_iteration( X ), Y )
% 50.75/51.12 , leq( multiplication( star( X ), Y ), multiplication( strong_iteration(
% 50.75/51.12 X ), Y ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (5199) {G4,W9,D4,L1,V2,M1} P(226,99);q { leq( multiplication(
% 50.75/51.12 star( X ), Y ), multiplication( strong_iteration( X ), Y ) ) }.
% 50.75/51.12 parent0: (66090) {G0,W9,D4,L1,V2,M1} { leq( multiplication( star( X ), Y )
% 50.75/51.12 , multiplication( strong_iteration( X ), Y ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 paramod: (66094) {G2,W14,D6,L1,V2,M1} { multiplication( addition( star( X
% 50.75/51.12 ), multiplication( strong_iteration( X ), zero ) ), Y ) = multiplication
% 50.75/51.12 ( strong_iteration( X ), Y ) }.
% 50.75/51.12 parent0[0]: (285) {G1,W10,D5,L1,V1,M1} P(16,0) { addition( multiplication(
% 50.75/51.12 strong_iteration( X ), zero ), star( X ) ) ==> strong_iteration( X ) }.
% 50.75/51.12 parent1[0; 11]: (100) {G1,W11,D4,L1,V3,M1} P(8,0);d(8) { multiplication(
% 50.75/51.12 addition( X, Z ), Y ) = multiplication( addition( Z, X ), Y ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 end
% 50.75/51.12 substitution1:
% 50.75/51.12 X := star( X )
% 50.75/51.12 Y := Y
% 50.75/51.12 Z := multiplication( strong_iteration( X ), zero )
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 paramod: (66095) {G3,W14,D5,L1,V2,M1} { addition( multiplication( star( X
% 50.75/51.12 ), Y ), multiplication( strong_iteration( X ), zero ) ) = multiplication
% 50.75/51.12 ( strong_iteration( X ), Y ) }.
% 50.75/51.12 parent0[0]: (809) {G2,W15,D5,L1,V3,M1} P(50,8) { multiplication( addition(
% 50.75/51.12 Z, multiplication( X, zero ) ), Y ) ==> addition( multiplication( Z, Y )
% 50.75/51.12 , multiplication( X, zero ) ) }.
% 50.75/51.12 parent1[0; 1]: (66094) {G2,W14,D6,L1,V2,M1} { multiplication( addition(
% 50.75/51.12 star( X ), multiplication( strong_iteration( X ), zero ) ), Y ) =
% 50.75/51.12 multiplication( strong_iteration( X ), Y ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := strong_iteration( X )
% 50.75/51.12 Y := Y
% 50.75/51.12 Z := star( X )
% 50.75/51.12 end
% 50.75/51.12 substitution1:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (12403) {G3,W14,D5,L1,V2,M1} P(285,100);d(809) { addition(
% 50.75/51.12 multiplication( star( X ), Y ), multiplication( strong_iteration( X ),
% 50.75/51.12 zero ) ) ==> multiplication( strong_iteration( X ), Y ) }.
% 50.75/51.12 parent0: (66095) {G3,W14,D5,L1,V2,M1} { addition( multiplication( star( X
% 50.75/51.12 ), Y ), multiplication( strong_iteration( X ), zero ) ) = multiplication
% 50.75/51.12 ( strong_iteration( X ), Y ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 eqswap: (66098) {G2,W14,D5,L1,V2,M1} { addition( strong_iteration( X ), Y
% 50.75/51.12 ) ==> addition( addition( star( X ), Y ), multiplication(
% 50.75/51.12 strong_iteration( X ), zero ) ) }.
% 50.75/51.12 parent0[0]: (380) {G2,W14,D5,L1,V2,M1} P(16,27) { addition( addition( star
% 50.75/51.12 ( X ), Y ), multiplication( strong_iteration( X ), zero ) ) ==> addition
% 50.75/51.12 ( strong_iteration( X ), Y ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 paramod: (66101) {G2,W19,D5,L1,V2,M1} { addition( strong_iteration( X ),
% 50.75/51.12 multiplication( star( X ), Y ) ) ==> addition( multiplication( star( X )
% 50.75/51.12 , addition( one, Y ) ), multiplication( strong_iteration( X ), zero ) )
% 50.75/51.12 }.
% 50.75/51.12 parent0[0]: (69) {G1,W11,D4,L1,V2,M1} P(5,7) { addition( X, multiplication
% 50.75/51.12 ( X, Y ) ) = multiplication( X, addition( one, Y ) ) }.
% 50.75/51.12 parent1[0; 9]: (66098) {G2,W14,D5,L1,V2,M1} { addition( strong_iteration(
% 50.75/51.12 X ), Y ) ==> addition( addition( star( X ), Y ), multiplication(
% 50.75/51.12 strong_iteration( X ), zero ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := star( X )
% 50.75/51.12 Y := Y
% 50.75/51.12 end
% 50.75/51.12 substitution1:
% 50.75/51.12 X := X
% 50.75/51.12 Y := multiplication( star( X ), Y )
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 paramod: (66102) {G3,W14,D5,L1,V2,M1} { addition( strong_iteration( X ),
% 50.75/51.12 multiplication( star( X ), Y ) ) ==> multiplication( strong_iteration( X
% 50.75/51.12 ), addition( one, Y ) ) }.
% 50.75/51.12 parent0[0]: (12403) {G3,W14,D5,L1,V2,M1} P(285,100);d(809) { addition(
% 50.75/51.12 multiplication( star( X ), Y ), multiplication( strong_iteration( X ),
% 50.75/51.12 zero ) ) ==> multiplication( strong_iteration( X ), Y ) }.
% 50.75/51.12 parent1[0; 8]: (66101) {G2,W19,D5,L1,V2,M1} { addition( strong_iteration(
% 50.75/51.12 X ), multiplication( star( X ), Y ) ) ==> addition( multiplication( star
% 50.75/51.12 ( X ), addition( one, Y ) ), multiplication( strong_iteration( X ), zero
% 50.75/51.12 ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := addition( one, Y )
% 50.75/51.12 end
% 50.75/51.12 substitution1:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (18716) {G4,W14,D5,L1,V2,M1} P(69,380);d(12403) { addition(
% 50.75/51.12 strong_iteration( X ), multiplication( star( X ), Y ) ) ==>
% 50.75/51.12 multiplication( strong_iteration( X ), addition( one, Y ) ) }.
% 50.75/51.12 parent0: (66102) {G3,W14,D5,L1,V2,M1} { addition( strong_iteration( X ),
% 50.75/51.12 multiplication( star( X ), Y ) ) ==> multiplication( strong_iteration( X
% 50.75/51.12 ), addition( one, Y ) ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 paramod: (66106) {G5,W9,D4,L1,V1,M1} { multiplication( strong_iteration( X
% 50.75/51.12 ), addition( one, X ) ) ==> strong_iteration( X ) }.
% 50.75/51.12 parent0[0]: (18716) {G4,W14,D5,L1,V2,M1} P(69,380);d(12403) { addition(
% 50.75/51.12 strong_iteration( X ), multiplication( star( X ), Y ) ) ==>
% 50.75/51.12 multiplication( strong_iteration( X ), addition( one, Y ) ) }.
% 50.75/51.12 parent1[0; 1]: (1119) {G6,W10,D5,L1,V1,M1} R(1102,36) { addition(
% 50.75/51.12 strong_iteration( X ), multiplication( star( X ), X ) ) ==>
% 50.75/51.12 strong_iteration( X ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := X
% 50.75/51.12 end
% 50.75/51.12 substitution1:
% 50.75/51.12 X := X
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 subsumption: (20029) {G7,W9,D4,L1,V1,M1} S(1119);d(18716) { multiplication
% 50.75/51.12 ( strong_iteration( X ), addition( one, X ) ) ==> strong_iteration( X )
% 50.75/51.12 }.
% 50.75/51.12 parent0: (66106) {G5,W9,D4,L1,V1,M1} { multiplication( strong_iteration( X
% 50.75/51.12 ), addition( one, X ) ) ==> strong_iteration( X ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 end
% 50.75/51.12 permutation0:
% 50.75/51.12 0 ==> 0
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 eqswap: (66108) {G2,W15,D4,L2,V2,M2} { addition( star( X ), Y ) ==>
% 50.75/51.12 addition( strong_iteration( X ), Y ), ! leq( multiplication(
% 50.75/51.12 strong_iteration( X ), zero ), Y ) }.
% 50.75/51.12 parent0[0]: (562) {G2,W15,D4,L2,V2,M2} P(16,35) { addition(
% 50.75/51.12 strong_iteration( X ), Y ) ==> addition( star( X ), Y ), ! leq(
% 50.75/51.12 multiplication( strong_iteration( X ), zero ), Y ) }.
% 50.75/51.12 substitution0:
% 50.75/51.12 X := X
% 50.75/51.12 Y := Y
% 50.75/51.12 end
% 50.75/51.12
% 50.75/51.12 paramod: (66111) {G2,W23,D5,L2,V2,M2} { addition( star( X ),
% 50.75/51.12 multiplication( strong_iteration( X ), Y ) ) ==> multiplication(
% 50.75/51.12 strong_iteration( X ), addition( one, Y ) ), ! leq( multiplication(
% 50.75/51.13 strong_iteration( X ), zero ), multiplication( strong_iteration( X ), Y )
% 50.75/51.13 ) }.
% 50.75/51.13 parent0[0]: (69) {G1,W11,D4,L1,V2,M1} P(5,7) { addition( X, multiplication
% 50.75/51.13 ( X, Y ) ) = multiplication( X, addition( one, Y ) ) }.
% 50.75/51.13 parent1[0; 8]: (66108) {G2,W15,D4,L2,V2,M2} { addition( star( X ), Y ) ==>
% 50.75/51.13 addition( strong_iteration( X ), Y ), ! leq( multiplication(
% 50.75/51.13 strong_iteration( X ), zero ), Y ) }.
% 50.75/51.13 substitution0:
% 50.75/51.13 X := strong_iteration( X )
% 50.75/51.13 Y := Y
% 50.75/51.13 end
% 50.75/51.13 substitution1:
% 50.75/51.13 X := X
% 50.75/51.13 Y := multiplication( strong_iteration( X ), Y )
% 50.75/51.13 end
% 50.75/51.13
% 50.75/51.13 resolution: (66112) {G3,W14,D5,L1,V2,M1} { addition( star( X ),
% 50.75/51.13 multiplication( strong_iteration( X ), Y ) ) ==> multiplication(
% 50.75/51.13 strong_iteration( X ), addition( one, Y ) ) }.
% 50.75/51.13 parent0[1]: (66111) {G2,W23,D5,L2,V2,M2} { addition( star( X ),
% 50.75/51.13 multiplication( strong_iteration( X ), Y ) ) ==> multiplication(
% 50.75/51.13 strong_iteration( X ), addition( one, Y ) ), ! leq( multiplication(
% 50.75/51.13 strong_iteration( X ), zero ), multiplication( strong_iteration( X ), Y )
% 50.75/51.13 ) }.
% 50.75/51.13 parent1[0]: (1628) {G2,W7,D3,L1,V2,M1} P(20,67);q { leq( multiplication( Y
% 50.75/51.13 , zero ), multiplication( Y, X ) ) }.
% 50.75/51.13 substitution0:
% 50.75/51.13 X := X
% 50.75/51.13 Y := Y
% 50.75/51.13 end
% 50.75/51.13 substitution1:
% 50.75/51.13 X := Y
% 50.75/51.13 Y := strong_iteration( X )
% 50.75/51.13 end
% 50.75/51.13
% 50.75/51.13 subsumption: (35640) {G3,W14,D5,L1,V2,M1} P(562,69);r(1628) { addition(
% 50.75/51.13 star( X ), multiplication( strong_iteration( X ), Y ) ) ==>
% 50.75/51.13 multiplication( strong_iteration( X ), addition( one, Y ) ) }.
% 50.75/51.13 parent0: (66112) {G3,W14,D5,L1,V2,M1} { addition( star( X ),
% 50.75/51.13 multiplication( strong_iteration( X ), Y ) ) ==> multiplication(
% 50.75/51.13 strong_iteration( X ), addition( one, Y ) ) }.
% 50.75/51.13 substitution0:
% 50.75/51.13 X := X
% 50.75/51.13 Y := Y
% 50.75/51.13 end
% 50.75/51.13 permutation0:
% 50.75/51.13 0 ==> 0
% 50.75/51.13 end
% 50.75/51.13
% 50.75/51.13 eqswap: (66114) {G2,W14,D4,L2,V2,M2} { addition( one, Y ) ==> addition(
% 50.75/51.13 star( X ), Y ), ! leq( multiplication( star( X ), X ), Y ) }.
% 50.75/51.13 parent0[0]: (565) {G2,W14,D4,L2,V2,M2} P(11,35) { addition( star( X ), Y )
% 50.75/51.13 ==> addition( one, Y ), ! leq( multiplication( star( X ), X ), Y ) }.
% 50.75/51.13 substitution0:
% 50.75/51.13 X := X
% 50.75/51.13 Y := Y
% 50.75/51.13 end
% 50.75/51.13
% 50.75/51.13 resolution: (66117) {G3,W14,D5,L1,V1,M1} { addition( one, multiplication(
% 50.75/51.13 strong_iteration( X ), X ) ) ==> addition( star( X ), multiplication(
% 50.75/51.13 strong_iteration( X ), X ) ) }.
% 50.75/51.13 parent0[1]: (66114) {G2,W14,D4,L2,V2,M2} { addition( one, Y ) ==> addition
% 50.75/51.13 ( star( X ), Y ), ! leq( multiplication( star( X ), X ), Y ) }.
% 50.75/51.13 parent1[0]: (5199) {G4,W9,D4,L1,V2,M1} P(226,99);q { leq( multiplication(
% 50.75/51.13 star( X ), Y ), multiplication( strong_iteration( X ), Y ) ) }.
% 50.75/51.13 substitution0:
% 50.75/51.13 X := X
% 50.75/51.13 Y := multiplication( strong_iteration( X ), X )
% 50.75/51.13 end
% 50.75/51.13 substitution1:
% 50.75/51.13 X := X
% 50.75/51.13 Y := X
% 50.75/51.13 end
% 50.75/51.13
% 50.75/51.13 paramod: (66118) {G4,W13,D5,L1,V1,M1} { addition( one, multiplication(
% 50.75/51.13 strong_iteration( X ), X ) ) ==> multiplication( strong_iteration( X ),
% 50.75/51.13 addition( one, X ) ) }.
% 50.75/51.13 parent0[0]: (35640) {G3,W14,D5,L1,V2,M1} P(562,69);r(1628) { addition( star
% 50.75/51.13 ( X ), multiplication( strong_iteration( X ), Y ) ) ==> multiplication(
% 50.75/51.13 strong_iteration( X ), addition( one, Y ) ) }.
% 50.75/51.13 parent1[0; 7]: (66117) {G3,W14,D5,L1,V1,M1} { addition( one,
% 50.75/51.13 multiplication( strong_iteration( X ), X ) ) ==> addition( star( X ),
% 50.75/51.13 multiplication( strong_iteration( X ), X ) ) }.
% 50.75/51.13 substitution0:
% 50.75/51.13 X := X
% 50.75/51.13 Y := X
% 50.75/51.13 end
% 50.75/51.13 substitution1:
% 50.75/51.13 X := X
% 50.75/51.13 end
% 50.75/51.13
% 50.75/51.13 paramod: (66119) {G5,W9,D5,L1,V1,M1} { addition( one, multiplication(
% 50.75/51.13 strong_iteration( X ), X ) ) ==> strong_iteration( X ) }.
% 50.75/51.13 parent0[0]: (20029) {G7,W9,D4,L1,V1,M1} S(1119);d(18716) { multiplication(
% 50.75/51.13 strong_iteration( X ), addition( one, X ) ) ==> strong_iteration( X ) }.
% 50.75/51.13 parent1[0; 7]: (66118) {G4,W13,D5,L1,V1,M1} { addition( one,
% 50.75/51.13 multiplication( strong_iteration( X ), X ) ) ==> multiplication(
% 50.75/51.13 strong_iteration( X ), addition( one, X ) ) }.
% 50.75/51.13 substitution0:
% 50.75/51.13 X := X
% 50.75/51.13 end
% 50.75/51.13 substitution1:
% 50.75/51.13 X := X
% 50.75/51.13 end
% 50.75/51.13
% 50.75/51.13 subsumption: (64713) {G8,W9,D5,L1,V1,M1} R(5199,565);d(35640);d(20029) {
% 50.75/51.13 addition( one, multiplication( strong_iteration( X ), X ) ) ==>
% 50.75/51.13 strong_iteration( X ) }.
% 50.75/51.13 parent0: (66119) {G5,W9,D5,L1,V1,M1} { addition( one, multiplication(
% 50.75/51.13 strong_iteration( X ), X ) ) ==> strong_iteration( X ) }.
% 50.75/51.13 substitution0:
% 50.75/51.13 X := X
% 50.75/51.13 end
% 50.75/51.13 permutation0:
% 50.75/51.13 0 ==> 0
% 50.75/51.13 end
% 50.75/51.13
% 50.75/51.13 paramod: (66124) {G2,W14,D5,L2,V0,M2} { ! leq( strong_iteration( skol1 ),
% 50.75/51.13 strong_iteration( skol1 ) ), ! leq( strong_iteration( skol1 ), addition(
% 50.75/51.13 one, multiplication( strong_iteration( skol1 ), skol1 ) ) ) }.
% 50.75/51.13 parent0[0]: (64713) {G8,W9,D5,L1,V1,M1} R(5199,565);d(35640);d(20029) {
% 50.75/51.13 addition( one, multiplication( strong_iteration( X ), X ) ) ==>
% 50.75/51.13 strong_iteration( X ) }.
% 50.75/51.13 parent1[1; 2]: (306) {G1,W18,D5,L2,V0,M2} P(0,19) { ! leq( strong_iteration
% 50.75/51.13 ( skol1 ), addition( one, multiplication( strong_iteration( skol1 ),
% 50.75/51.13 skol1 ) ) ), ! leq( addition( one, multiplication( strong_iteration(
% 50.75/51.13 skol1 ), skol1 ) ), strong_iteration( skol1 ) ) }.
% 50.75/51.13 substitution0:
% 50.75/51.13 X := skol1
% 50.75/51.13 end
% 50.75/51.13 substitution1:
% 50.75/51.13 end
% 50.75/51.13
% 50.75/51.13 paramod: (66127) {G3,W10,D3,L2,V0,M2} { ! leq( strong_iteration( skol1 ),
% 50.75/51.13 strong_iteration( skol1 ) ), ! leq( strong_iteration( skol1 ),
% 50.75/51.13 strong_iteration( skol1 ) ) }.
% 50.75/51.13 parent0[0]: (64713) {G8,W9,D5,L1,V1,M1} R(5199,565);d(35640);d(20029) {
% 50.75/51.13 addition( one, multiplication( strong_iteration( X ), X ) ) ==>
% 50.75/51.13 strong_iteration( X ) }.
% 50.75/51.13 parent1[1; 4]: (66124) {G2,W14,D5,L2,V0,M2} { ! leq( strong_iteration(
% 50.75/51.13 skol1 ), strong_iteration( skol1 ) ), ! leq( strong_iteration( skol1 ),
% 50.75/51.13 addition( one, multiplication( strong_iteration( skol1 ), skol1 ) ) ) }.
% 50.75/51.13 substitution0:
% 50.75/51.13 X := skol1
% 50.75/51.13 end
% 50.75/51.13 substitution1:
% 50.75/51.13 end
% 50.75/51.13
% 50.75/51.13 factor: (66128) {G3,W5,D3,L1,V0,M1} { ! leq( strong_iteration( skol1 ),
% 50.75/51.13 strong_iteration( skol1 ) ) }.
% 50.75/51.13 parent0[0, 1]: (66127) {G3,W10,D3,L2,V0,M2} { ! leq( strong_iteration(
% 50.75/51.13 skol1 ), strong_iteration( skol1 ) ), ! leq( strong_iteration( skol1 ),
% 50.75/51.13 strong_iteration( skol1 ) ) }.
% 50.75/51.13 substitution0:
% 50.75/51.13 end
% 50.75/51.13
% 50.75/51.13 resolution: (66130) {G2,W0,D0,L0,V0,M0} { }.
% 50.75/51.13 parent0[0]: (66128) {G3,W5,D3,L1,V0,M1} { ! leq( strong_iteration( skol1 )
% 50.75/51.13 , strong_iteration( skol1 ) ) }.
% 50.75/51.13 parent1[0]: (22) {G1,W3,D2,L1,V1,M1} R(18,3) { leq( X, X ) }.
% 50.75/51.13 substitution0:
% 50.75/51.13 end
% 50.75/51.13 substitution1:
% 50.75/51.13 X := strong_iteration( skol1 )
% 50.75/51.13 end
% 50.75/51.13
% 50.75/51.13 subsumption: (65698) {G9,W0,D0,L0,V0,M0} S(306);d(64713);d(64713);f;r(22)
% 50.75/51.13 { }.
% 50.75/51.13 parent0: (66130) {G2,W0,D0,L0,V0,M0} { }.
% 50.75/51.13 substitution0:
% 50.75/51.13 end
% 50.75/51.13 permutation0:
% 50.75/51.13 end
% 50.75/51.13
% 50.75/51.13 Proof check complete!
% 50.75/51.13
% 50.75/51.13 Memory use:
% 50.75/51.13
% 50.75/51.13 space for terms: 922698
% 50.75/51.13 space for clauses: 3134785
% 50.75/51.13
% 50.75/51.13
% 50.75/51.13 clauses generated: 1052627
% 50.75/51.13 clauses kept: 65699
% 50.75/51.13 clauses selected: 2346
% 50.75/51.13 clauses deleted: 9969
% 50.75/51.13 clauses inuse deleted: 286
% 50.75/51.13
% 50.75/51.13 subsentry: 7872321
% 50.75/51.13 literals s-matched: 3787632
% 50.75/51.13 literals matched: 3485254
% 50.75/51.13 full subsumption: 1210716
% 50.75/51.13
% 50.75/51.13 checksum: 1593375906
% 50.75/51.13
% 50.75/51.13
% 50.75/51.13 Bliksem ended
%------------------------------------------------------------------------------