TSTP Solution File: KLE041+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE041+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n009.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 01:36:50 EDT 2022
% Result : Theorem 18.91s 19.28s
% Output : Refutation 18.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : KLE041+1 : TPTP v8.1.0. Released v4.0.0.
% 0.15/0.14 % Command : bliksem %s
% 0.15/0.36 % Computer : n009.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % DateTime : Thu Jun 16 14:09:53 EDT 2022
% 0.22/0.36 % CPUTime :
% 18.47/18.84 *** allocated 10000 integers for termspace/termends
% 18.47/18.84 *** allocated 10000 integers for clauses
% 18.47/18.84 *** allocated 10000 integers for justifications
% 18.47/18.84 Bliksem 1.12
% 18.47/18.84
% 18.47/18.84
% 18.47/18.84 Automatic Strategy Selection
% 18.47/18.84
% 18.47/18.84
% 18.47/18.84 Clauses:
% 18.47/18.84
% 18.47/18.84 { addition( X, Y ) = addition( Y, X ) }.
% 18.47/18.84 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 18.47/18.84 { addition( X, zero ) = X }.
% 18.47/18.84 { addition( X, X ) = X }.
% 18.47/18.84 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 18.47/18.84 multiplication( X, Y ), Z ) }.
% 18.47/18.84 { multiplication( X, one ) = X }.
% 18.47/18.84 { multiplication( one, X ) = X }.
% 18.47/18.84 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 18.47/18.84 , multiplication( X, Z ) ) }.
% 18.47/18.84 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 18.47/18.84 , multiplication( Y, Z ) ) }.
% 18.47/18.84 { multiplication( X, zero ) = zero }.
% 18.47/18.84 { multiplication( zero, X ) = zero }.
% 18.47/18.84 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 18.47/18.84 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 18.47/18.84 { leq( addition( one, multiplication( X, star( X ) ) ), star( X ) ) }.
% 18.47/18.84 { leq( addition( one, multiplication( star( X ), X ) ), star( X ) ) }.
% 18.47/18.84 { ! leq( addition( multiplication( X, Y ), Z ), Y ), leq( multiplication(
% 18.47/18.84 star( X ), Z ), Y ) }.
% 18.47/18.84 { ! leq( addition( multiplication( X, Y ), Z ), X ), leq( multiplication( Z
% 18.47/18.84 , star( Y ) ), X ) }.
% 18.47/18.84 { leq( skol1, skol2 ) }.
% 18.47/18.84 { ! leq( star( skol1 ), star( skol2 ) ) }.
% 18.47/18.84
% 18.47/18.84 percentage equality = 0.565217, percentage horn = 1.000000
% 18.47/18.84 This is a problem with some equality
% 18.47/18.84
% 18.47/18.84
% 18.47/18.84
% 18.47/18.84 Options Used:
% 18.47/18.84
% 18.47/18.84 useres = 1
% 18.47/18.84 useparamod = 1
% 18.47/18.84 useeqrefl = 1
% 18.47/18.84 useeqfact = 1
% 18.47/18.84 usefactor = 1
% 18.47/18.84 usesimpsplitting = 0
% 18.47/18.84 usesimpdemod = 5
% 18.47/18.84 usesimpres = 3
% 18.47/18.84
% 18.47/18.84 resimpinuse = 1000
% 18.47/18.84 resimpclauses = 20000
% 18.47/18.84 substype = eqrewr
% 18.47/18.84 backwardsubs = 1
% 18.47/18.84 selectoldest = 5
% 18.47/18.84
% 18.47/18.84 litorderings [0] = split
% 18.47/18.84 litorderings [1] = extend the termordering, first sorting on arguments
% 18.47/18.84
% 18.47/18.84 termordering = kbo
% 18.47/18.84
% 18.47/18.84 litapriori = 0
% 18.47/18.84 termapriori = 1
% 18.47/18.84 litaposteriori = 0
% 18.47/18.84 termaposteriori = 0
% 18.47/18.84 demodaposteriori = 0
% 18.47/18.84 ordereqreflfact = 0
% 18.47/18.84
% 18.47/18.84 litselect = negord
% 18.47/18.84
% 18.47/18.84 maxweight = 15
% 18.47/18.84 maxdepth = 30000
% 18.47/18.84 maxlength = 115
% 18.47/18.84 maxnrvars = 195
% 18.47/18.84 excuselevel = 1
% 18.47/18.84 increasemaxweight = 1
% 18.47/18.84
% 18.47/18.84 maxselected = 10000000
% 18.47/18.84 maxnrclauses = 10000000
% 18.47/18.84
% 18.47/18.84 showgenerated = 0
% 18.47/18.84 showkept = 0
% 18.47/18.84 showselected = 0
% 18.47/18.84 showdeleted = 0
% 18.47/18.84 showresimp = 1
% 18.47/18.84 showstatus = 2000
% 18.47/18.84
% 18.47/18.84 prologoutput = 0
% 18.47/18.84 nrgoals = 5000000
% 18.47/18.84 totalproof = 1
% 18.47/18.84
% 18.47/18.84 Symbols occurring in the translation:
% 18.47/18.84
% 18.47/18.84 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 18.47/18.84 . [1, 2] (w:1, o:21, a:1, s:1, b:0),
% 18.47/18.84 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 18.47/18.84 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 18.47/18.84 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 18.47/18.84 addition [37, 2] (w:1, o:45, a:1, s:1, b:0),
% 18.47/18.84 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 18.47/18.84 multiplication [40, 2] (w:1, o:47, a:1, s:1, b:0),
% 18.47/18.84 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 18.47/18.84 leq [42, 2] (w:1, o:46, a:1, s:1, b:0),
% 18.47/18.84 star [43, 1] (w:1, o:20, a:1, s:1, b:0),
% 18.47/18.84 skol1 [46, 0] (w:1, o:13, a:1, s:1, b:1),
% 18.47/18.84 skol2 [47, 0] (w:1, o:14, a:1, s:1, b:1).
% 18.47/18.84
% 18.47/18.84
% 18.47/18.84 Starting Search:
% 18.47/18.84
% 18.47/18.84 *** allocated 15000 integers for clauses
% 18.47/18.84 *** allocated 22500 integers for clauses
% 18.47/18.84 *** allocated 33750 integers for clauses
% 18.47/18.84 *** allocated 50625 integers for clauses
% 18.47/18.84 *** allocated 15000 integers for termspace/termends
% 18.47/18.84 *** allocated 75937 integers for clauses
% 18.47/18.84 Resimplifying inuse:
% 18.47/18.84 Done
% 18.47/18.84
% 18.47/18.84 *** allocated 113905 integers for clauses
% 18.47/18.84 *** allocated 22500 integers for termspace/termends
% 18.47/18.84 *** allocated 170857 integers for clauses
% 18.47/18.84 *** allocated 33750 integers for termspace/termends
% 18.47/18.84
% 18.47/18.84 Intermediate Status:
% 18.47/18.84 Generated: 14394
% 18.47/18.84 Kept: 2118
% 18.47/18.84 Inuse: 283
% 18.47/18.84 Deleted: 43
% 18.47/18.84 Deletedinuse: 20
% 18.47/18.84
% 18.47/18.84 Resimplifying inuse:
% 18.47/18.84 Done
% 18.47/18.84
% 18.47/18.84 *** allocated 50625 integers for termspace/termends
% 18.47/18.84 Resimplifying inuse:
% 18.47/18.84 Done
% 18.47/18.84
% 18.47/18.84 *** allocated 256285 integers for clauses
% 18.47/18.84 *** allocated 75937 integers for termspace/termends
% 18.47/18.84
% 18.47/18.84 Intermediate Status:
% 18.47/18.84 Generated: 32770
% 18.47/18.84 Kept: 4128
% 18.47/18.84 Inuse: 399
% 18.47/18.84 Deleted: 92
% 18.47/18.84 Deletedinuse: 50
% 18.47/18.84
% 18.47/18.84 Resimplifying inuse:
% 18.47/18.84 Done
% 18.47/18.84
% 18.47/18.84 *** allocated 384427 integers for clauses
% 18.47/18.84 Resimplifying inuse:
% 18.47/18.84 Done
% 18.47/18.84
% 18.47/18.84 *** allocated 113905 integers for termspace/termends
% 18.91/19.28
% 18.91/19.28 Intermediate Status:
% 18.91/19.28 Generated: 57654
% 18.91/19.28 Kept: 6147
% 18.91/19.28 Inuse: 611
% 18.91/19.28 Deleted: 143
% 18.91/19.28 Deletedinuse: 89
% 18.91/19.28
% 18.91/19.28 Resimplifying inuse:
% 18.91/19.28 Done
% 18.91/19.28
% 18.91/19.28 Resimplifying inuse:
% 18.91/19.28 Done
% 18.91/19.28
% 18.91/19.28 *** allocated 576640 integers for clauses
% 18.91/19.28
% 18.91/19.28 Intermediate Status:
% 18.91/19.28 Generated: 74810
% 18.91/19.28 Kept: 8397
% 18.91/19.28 Inuse: 721
% 18.91/19.28 Deleted: 167
% 18.91/19.28 Deletedinuse: 97
% 18.91/19.28
% 18.91/19.28 Resimplifying inuse:
% 18.91/19.28 Done
% 18.91/19.28
% 18.91/19.28 *** allocated 170857 integers for termspace/termends
% 18.91/19.28 Resimplifying inuse:
% 18.91/19.28 Done
% 18.91/19.28
% 18.91/19.28
% 18.91/19.28 Intermediate Status:
% 18.91/19.28 Generated: 105092
% 18.91/19.28 Kept: 10402
% 18.91/19.28 Inuse: 838
% 18.91/19.28 Deleted: 178
% 18.91/19.28 Deletedinuse: 100
% 18.91/19.28
% 18.91/19.28 Resimplifying inuse:
% 18.91/19.28 Done
% 18.91/19.28
% 18.91/19.28 *** allocated 864960 integers for clauses
% 18.91/19.28 Resimplifying inuse:
% 18.91/19.28 Done
% 18.91/19.28
% 18.91/19.28
% 18.91/19.28 Intermediate Status:
% 18.91/19.28 Generated: 139835
% 18.91/19.28 Kept: 12408
% 18.91/19.28 Inuse: 1029
% 18.91/19.28 Deleted: 209
% 18.91/19.28 Deletedinuse: 100
% 18.91/19.28
% 18.91/19.28 Resimplifying inuse:
% 18.91/19.28 Done
% 18.91/19.28
% 18.91/19.28 *** allocated 256285 integers for termspace/termends
% 18.91/19.28 Resimplifying inuse:
% 18.91/19.28 Done
% 18.91/19.28
% 18.91/19.28
% 18.91/19.28 Intermediate Status:
% 18.91/19.28 Generated: 155015
% 18.91/19.28 Kept: 14558
% 18.91/19.28 Inuse: 1102
% 18.91/19.28 Deleted: 253
% 18.91/19.28 Deletedinuse: 104
% 18.91/19.28
% 18.91/19.28 Resimplifying inuse:
% 18.91/19.28 Done
% 18.91/19.28
% 18.91/19.28 Resimplifying inuse:
% 18.91/19.28 Done
% 18.91/19.28
% 18.91/19.28
% 18.91/19.28 Intermediate Status:
% 18.91/19.28 Generated: 198557
% 18.91/19.28 Kept: 16576
% 18.91/19.28 Inuse: 1141
% 18.91/19.28 Deleted: 254
% 18.91/19.28 Deletedinuse: 104
% 18.91/19.28
% 18.91/19.28 Resimplifying inuse:
% 18.91/19.28 Done
% 18.91/19.28
% 18.91/19.28 *** allocated 1297440 integers for clauses
% 18.91/19.28 Resimplifying inuse:
% 18.91/19.28 Done
% 18.91/19.28
% 18.91/19.28 *** allocated 384427 integers for termspace/termends
% 18.91/19.28
% 18.91/19.28 Intermediate Status:
% 18.91/19.28 Generated: 254673
% 18.91/19.28 Kept: 20144
% 18.91/19.28 Inuse: 1165
% 18.91/19.28 Deleted: 256
% 18.91/19.28 Deletedinuse: 106
% 18.91/19.28
% 18.91/19.28 Resimplifying inuse:
% 18.91/19.28 Done
% 18.91/19.28
% 18.91/19.28 Resimplifying clauses:
% 18.91/19.28 Done
% 18.91/19.28
% 18.91/19.28 Resimplifying inuse:
% 18.91/19.28 Done
% 18.91/19.28
% 18.91/19.28
% 18.91/19.28 Intermediate Status:
% 18.91/19.28 Generated: 278032
% 18.91/19.28 Kept: 22171
% 18.91/19.28 Inuse: 1224
% 18.91/19.28 Deleted: 1909
% 18.91/19.28 Deletedinuse: 107
% 18.91/19.28
% 18.91/19.28 Resimplifying inuse:
% 18.91/19.28 Done
% 18.91/19.28
% 18.91/19.28 Resimplifying inuse:
% 18.91/19.28 Done
% 18.91/19.28
% 18.91/19.28
% 18.91/19.28 Intermediate Status:
% 18.91/19.28 Generated: 305347
% 18.91/19.28 Kept: 24196
% 18.91/19.28 Inuse: 1286
% 18.91/19.28 Deleted: 1910
% 18.91/19.28 Deletedinuse: 108
% 18.91/19.28
% 18.91/19.28 Resimplifying inuse:
% 18.91/19.28 Done
% 18.91/19.28
% 18.91/19.28 Resimplifying inuse:
% 18.91/19.28 Done
% 18.91/19.28
% 18.91/19.28
% 18.91/19.28 Intermediate Status:
% 18.91/19.28 Generated: 332744
% 18.91/19.28 Kept: 26196
% 18.91/19.28 Inuse: 1332
% 18.91/19.28 Deleted: 1911
% 18.91/19.28 Deletedinuse: 108
% 18.91/19.28
% 18.91/19.28 Resimplifying inuse:
% 18.91/19.28 Done
% 18.91/19.28
% 18.91/19.28 *** allocated 576640 integers for termspace/termends
% 18.91/19.28 Resimplifying inuse:
% 18.91/19.28 Done
% 18.91/19.28
% 18.91/19.28 *** allocated 1946160 integers for clauses
% 18.91/19.28
% 18.91/19.28 Intermediate Status:
% 18.91/19.28 Generated: 359649
% 18.91/19.28 Kept: 28206
% 18.91/19.28 Inuse: 1382
% 18.91/19.28 Deleted: 1914
% 18.91/19.28 Deletedinuse: 108
% 18.91/19.28
% 18.91/19.28 Resimplifying inuse:
% 18.91/19.28 Done
% 18.91/19.28
% 18.91/19.28 Resimplifying inuse:
% 18.91/19.28 Done
% 18.91/19.28
% 18.91/19.28
% 18.91/19.28 Intermediate Status:
% 18.91/19.28 Generated: 392533
% 18.91/19.28 Kept: 30253
% 18.91/19.28 Inuse: 1443
% 18.91/19.28 Deleted: 1914
% 18.91/19.28 Deletedinuse: 108
% 18.91/19.28
% 18.91/19.28 Resimplifying inuse:
% 18.91/19.28 Done
% 18.91/19.28
% 18.91/19.28 Resimplifying inuse:
% 18.91/19.28 Done
% 18.91/19.28
% 18.91/19.28
% 18.91/19.28 Intermediate Status:
% 18.91/19.28 Generated: 404192
% 18.91/19.28 Kept: 32304
% 18.91/19.28 Inuse: 1466
% 18.91/19.28 Deleted: 1916
% 18.91/19.28 Deletedinuse: 109
% 18.91/19.28
% 18.91/19.28 Resimplifying inuse:
% 18.91/19.28 Done
% 18.91/19.28
% 18.91/19.28 Resimplifying inuse:
% 18.91/19.28 Done
% 18.91/19.28
% 18.91/19.28
% 18.91/19.28 Intermediate Status:
% 18.91/19.28 Generated: 435494
% 18.91/19.28 Kept: 34304
% 18.91/19.28 Inuse: 1543
% 18.91/19.28 Deleted: 1918
% 18.91/19.28 Deletedinuse: 109
% 18.91/19.28
% 18.91/19.28 Resimplifying inuse:
% 18.91/19.28 Done
% 18.91/19.28
% 18.91/19.28 Resimplifying inuse:
% 18.91/19.28 Done
% 18.91/19.28
% 18.91/19.28
% 18.91/19.28 Intermediate Status:
% 18.91/19.28 Generated: 462430
% 18.91/19.28 Kept: 36424
% 18.91/19.28 Inuse: 1611
% 18.91/19.28 Deleted: 1920
% 18.91/19.28 Deletedinuse: 109
% 18.91/19.28
% 18.91/19.28 Resimplifying inuse:
% 18.91/19.28 Done
% 18.91/19.28
% 18.91/19.28 Resimplifying inuse:
% 18.91/19.28 Done
% 18.91/19.28
% 18.91/19.28
% 18.91/19.28 Intermediate Status:
% 18.91/19.28 Generated: 472171
% 18.91/19.28 Kept: 38566
% 18.91/19.28 Inuse: 1631
% 18.91/19.28 Deleted: 1921
% 18.91/19.28 Deletedinuse: 110
% 18.91/19.28
% 18.91/19.28 Resimplifying inuse:
% 18.91/19.28 Done
% 18.91/19.28
% 18.91/19.28 Resimplifying inuse:
% 18.91/19.28 Done
% 18.91/19.28
% 18.91/19.28 Resimplifying clauses:
% 18.91/19.28 Done
% 18.91/19.28
% 18.91/19.28
% 18.91/19.28 Intermediate Status:
% 18.91/19.28 Generated: 496450
% 18.91/19.28 Kept: 40582
% 18.91/19.28 Inuse: 1696
% 18.91/19.28 Deleted: 4736
% 18.91/19.28 Deletedinuse: 129
% 18.91/19.28
% 18.91/19.28 *** allocated 864960 integers for termspace/termends
% 18.91/19.28 Resimplifying inuse:
% 18.91/19.28 Done
% 18.91/19.28
% 18.91/19.28 *** allocated 2919240 integers for clauses
% 18.91/19.28 Resimplifying inuse:
% 18.91/19.28 Done
% 18.91/19.28
% 18.91/19.28
% 18.91/19.28 Intermediate Status:
% 18.91/19.28 Generated: 526470
% 18.91/19.28 Kept: 42599
% 18.91/19.28 Inuse: 1751
% 18.91/19.28 Deleted: 4849
% 18.91/19.28 Deletedinuse: 241
% 18.91/19.28
% 18.91/19.28 Resimplifying inuse:
% 18.91/19.28 Done
% 18.91/19.28
% 18.91/19.28 Resimplifying inuse:
% 18.91/19.28 Done
% 18.91/19.28
% 18.91/19.28
% 18.91/19.28 Intermediate Status:
% 18.91/19.28 Generated: 561069
% 18.91/19.28 Kept: 44618
% 18.91/19.28 Inuse: 1805
% 18.91/19.28 Deleted: 4882
% 18.91/19.28 Deletedinuse: 241
% 18.91/19.28
% 18.91/19.28 Resimplifying inuse:
% 18.91/19.28 Done
% 18.91/19.28
% 18.91/19.28 Resimplifying inuse:
% 18.91/19.28 Done
% 18.91/19.28
% 18.91/19.28
% 18.91/19.28 Intermediate Status:
% 18.91/19.28 Generated: 579459
% 18.91/19.28 Kept: 46820
% 18.91/19.28 Inuse: 1836
% 18.91/19.28 Deleted: 4883
% 18.91/19.28 Deletedinuse: 241
% 18.91/19.28
% 18.91/19.28 Resimplifying inuse:
% 18.91/19.28 Done
% 18.91/19.28
% 18.91/19.28 Resimplifying inuse:
% 18.91/19.28 Done
% 18.91/19.28
% 18.91/19.28
% 18.91/19.28 Intermediate Status:
% 18.91/19.28 Generated: 598049
% 18.91/19.28 Kept: 48825
% 18.91/19.28 Inuse: 1868
% 18.91/19.28 Deleted: 4883
% 18.91/19.28 Deletedinuse: 241
% 18.91/19.28
% 18.91/19.28
% 18.91/19.28 Bliksems!, er is een bewijs:
% 18.91/19.28 % SZS status Theorem
% 18.91/19.28 % SZS output start Refutation
% 18.91/19.28
% 18.91/19.28 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 18.91/19.28 (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) ==> addition(
% 18.91/19.28 addition( Z, Y ), X ) }.
% 18.91/19.28 (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 18.91/19.28 (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 18.91/19.28 (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 18.91/19.28 (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 18.91/19.28 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 18.91/19.28 (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 18.91/19.28 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 18.91/19.28 (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) ==> Y }.
% 18.91/19.28 (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, Y ) }.
% 18.91/19.28 (13) {G0,W9,D5,L1,V1,M1} I { leq( addition( one, multiplication( X, star( X
% 18.91/19.28 ) ) ), star( X ) ) }.
% 18.91/19.28 (14) {G0,W9,D5,L1,V1,M1} I { leq( addition( one, multiplication( star( X )
% 18.91/19.28 , X ) ), star( X ) ) }.
% 18.91/19.28 (15) {G0,W13,D4,L2,V3,M2} I { ! leq( addition( multiplication( X, Y ), Z )
% 18.91/19.28 , Y ), leq( multiplication( star( X ), Z ), Y ) }.
% 18.91/19.28 (17) {G0,W3,D2,L1,V0,M1} I { leq( skol1, skol2 ) }.
% 18.91/19.28 (18) {G0,W5,D3,L1,V0,M1} I { ! leq( star( skol1 ), star( skol2 ) ) }.
% 18.91/19.28 (21) {G1,W9,D4,L1,V2,M1} P(3,1) { addition( addition( Y, X ), X ) ==>
% 18.91/19.28 addition( Y, X ) }.
% 18.91/19.28 (22) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y ), Z ) =
% 18.91/19.28 addition( addition( Y, Z ), X ) }.
% 18.91/19.28 (26) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 18.91/19.28 (27) {G1,W14,D4,L2,V3,M2} P(1,12) { ! addition( addition( X, Y ), Z ) ==>
% 18.91/19.28 addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 18.91/19.28 (29) {G1,W8,D3,L2,V2,M2} P(0,12) { ! addition( Y, X ) ==> Y, leq( X, Y )
% 18.91/19.28 }.
% 18.91/19.28 (34) {G1,W5,D3,L1,V0,M1} R(11,17) { addition( skol1, skol2 ) ==> skol2 }.
% 18.91/19.28 (39) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, ! leq( X, Y )
% 18.91/19.28 }.
% 18.91/19.28 (42) {G2,W5,D3,L1,V0,M1} P(34,0) { addition( skol2, skol1 ) ==> skol2 }.
% 18.91/19.28 (44) {G3,W9,D4,L1,V1,M1} P(42,1) { addition( addition( X, skol2 ), skol1 )
% 18.91/19.28 ==> addition( X, skol2 ) }.
% 18.91/19.28 (52) {G1,W11,D4,L1,V2,M1} P(5,7) { addition( multiplication( X, Y ), X ) =
% 18.91/19.28 multiplication( X, addition( Y, one ) ) }.
% 18.91/19.28 (77) {G1,W16,D4,L2,V3,M2} P(8,12) { ! multiplication( addition( X, Z ), Y )
% 18.91/19.28 ==> multiplication( Z, Y ), leq( multiplication( X, Y ), multiplication
% 18.91/19.28 ( Z, Y ) ) }.
% 18.91/19.28 (151) {G1,W14,D4,L3,V3,M3} P(11,15) { ! leq( Z, Y ), leq( multiplication(
% 18.91/19.28 star( X ), Z ), Y ), ! leq( multiplication( X, Y ), Z ) }.
% 18.91/19.28 (204) {G2,W5,D3,L1,V2,M1} R(21,29) { leq( X, addition( Y, X ) ) }.
% 18.91/19.28 (215) {G3,W9,D4,L1,V3,M1} P(8,204) { leq( multiplication( Z, Y ),
% 18.91/19.28 multiplication( addition( X, Z ), Y ) ) }.
% 18.91/19.28 (219) {G3,W5,D3,L1,V2,M1} P(0,204) { leq( Y, addition( Y, X ) ) }.
% 18.91/19.28 (229) {G4,W7,D4,L1,V3,M1} P(1,219) { leq( X, addition( addition( X, Y ), Z
% 18.91/19.28 ) ) }.
% 18.91/19.28 (239) {G3,W7,D4,L1,V3,M1} P(22,204) { leq( Z, addition( addition( Y, Z ), X
% 18.91/19.28 ) ) }.
% 18.91/19.28 (304) {G2,W8,D3,L2,V3,M2} P(11,27);q { leq( X, addition( Y, Z ) ), ! leq( X
% 18.91/19.28 , Y ) }.
% 18.91/19.28 (342) {G4,W8,D3,L2,V3,M2} P(11,239) { leq( Y, Z ), ! leq( addition( X, Y )
% 18.91/19.28 , Z ) }.
% 18.91/19.28 (352) {G5,W8,D3,L2,V3,M2} P(11,229) { leq( X, Z ), ! leq( addition( X, Y )
% 18.91/19.28 , Z ) }.
% 18.91/19.28 (526) {G2,W9,D2,L3,V2,M3} P(39,11) { ! leq( X, Y ), X = Y, ! leq( Y, X )
% 18.91/19.28 }.
% 18.91/19.28 (784) {G6,W4,D3,L1,V1,M1} R(352,14) { leq( one, star( X ) ) }.
% 18.91/19.28 (787) {G6,W7,D4,L1,V1,M1} R(352,18) { ! leq( addition( star( skol1 ), X ),
% 18.91/19.28 star( skol2 ) ) }.
% 18.91/19.28 (799) {G7,W7,D4,L1,V1,M1} R(784,39) { addition( star( X ), one ) ==> star(
% 18.91/19.28 X ) }.
% 18.91/19.28 (802) {G7,W7,D4,L1,V1,M1} R(784,11) { addition( one, star( X ) ) ==> star(
% 18.91/19.28 X ) }.
% 18.91/19.28 (1021) {G3,W7,D4,L1,V2,M1} P(52,204) { leq( X, multiplication( X, addition
% 18.91/19.28 ( Y, one ) ) ) }.
% 18.91/19.28 (1212) {G8,W6,D4,L1,V2,M1} P(799,1021) { leq( Y, multiplication( Y, star( X
% 18.91/19.28 ) ) ) }.
% 18.91/19.28 (1508) {G8,W6,D4,L1,V2,M1} P(802,77);q;d(6) { leq( Y, multiplication( star
% 18.91/19.28 ( X ), Y ) ) }.
% 18.91/19.28 (1520) {G9,W11,D5,L1,V2,M1} R(1508,11) { addition( X, multiplication( star
% 18.91/19.28 ( Y ), X ) ) ==> multiplication( star( Y ), X ) }.
% 18.91/19.28 (1756) {G7,W8,D3,L2,V1,M2} P(11,787) { ! leq( X, star( skol2 ) ), ! leq(
% 18.91/19.28 star( skol1 ), X ) }.
% 18.91/19.28 (1882) {G5,W7,D4,L1,V1,M1} R(342,13) { leq( multiplication( X, star( X ) )
% 18.91/19.28 , star( X ) ) }.
% 18.91/19.28 (1918) {G9,W8,D5,L1,V3,M1} R(304,1212) { leq( X, addition( multiplication(
% 18.91/19.28 X, star( Y ) ), Z ) ) }.
% 18.91/19.28 (3739) {G9,W8,D4,L1,V1,M1} R(1756,1212) { ! leq( multiplication( star(
% 18.91/19.28 skol1 ), star( X ) ), star( skol2 ) ) }.
% 18.91/19.28 (4797) {G6,W8,D4,L1,V1,M1} R(151,1882);r(26) { leq( multiplication( star( X
% 18.91/19.28 ), star( X ) ), star( X ) ) }.
% 18.91/19.28 (7345) {G4,W9,D4,L1,V2,M1} P(44,215) { leq( multiplication( skol1, Y ),
% 18.91/19.28 multiplication( addition( X, skol2 ), Y ) ) }.
% 18.91/19.28 (8839) {G10,W8,D4,L1,V1,M1} R(4797,39);d(1520) { multiplication( star( X )
% 18.91/19.28 , star( X ) ) ==> star( X ) }.
% 18.91/19.28 (9301) {G10,W12,D4,L2,V1,M2} R(3739,151) { ! leq( star( X ), star( skol2 )
% 18.91/19.28 ), ! leq( multiplication( skol1, star( skol2 ) ), star( X ) ) }.
% 18.91/19.28 (10565) {G10,W9,D4,L2,V3,M2} P(11,1918) { leq( X, Z ), ! leq(
% 18.91/19.28 multiplication( X, star( Y ) ), Z ) }.
% 18.91/19.28 (38223) {G11,W4,D3,L1,V1,M1} R(10565,1882) { leq( X, star( X ) ) }.
% 18.91/19.28 (38315) {G12,W7,D4,L1,V1,M1} R(38223,39) { addition( star( X ), X ) ==>
% 18.91/19.28 star( X ) }.
% 18.91/19.28 (41824) {G13,W8,D4,L1,V1,M1} P(38315,7345) { leq( multiplication( skol1, X
% 18.91/19.28 ), multiplication( star( skol2 ), X ) ) }.
% 18.91/19.28 (49512) {G14,W7,D4,L1,V0,M1} P(8839,41824) { leq( multiplication( skol1,
% 18.91/19.28 star( skol2 ) ), star( skol2 ) ) }.
% 18.91/19.28 (49556) {G15,W13,D3,L3,V1,M3} P(526,49512) { leq( multiplication( skol1, X
% 18.91/19.28 ), X ), ! leq( star( skol2 ), X ), ! leq( X, star( skol2 ) ) }.
% 18.91/19.28 (49558) {G16,W5,D3,L1,V0,M1} F(49556);r(9301) { ! leq( star( skol2 ), star
% 18.91/19.28 ( skol2 ) ) }.
% 18.91/19.28 (49559) {G17,W0,D0,L0,V0,M0} S(49558);r(26) { }.
% 18.91/19.28
% 18.91/19.28
% 18.91/19.28 % SZS output end Refutation
% 18.91/19.28 found a proof!
% 18.91/19.28
% 18.91/19.28
% 18.91/19.28 Unprocessed initial clauses:
% 18.91/19.28
% 18.91/19.28 (49561) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 18.91/19.28 (49562) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition
% 18.91/19.28 ( addition( Z, Y ), X ) }.
% 18.91/19.28 (49563) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 18.91/19.28 (49564) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 18.91/19.28 (49565) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) )
% 18.91/19.28 = multiplication( multiplication( X, Y ), Z ) }.
% 18.91/19.28 (49566) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 18.91/19.28 (49567) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 18.91/19.28 (49568) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 18.91/19.28 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 18.91/19.28 (49569) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 18.91/19.28 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 18.91/19.28 (49570) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero }.
% 18.91/19.28 (49571) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 18.91/19.28 (49572) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 18.91/19.28 (49573) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 18.91/19.28 (49574) {G0,W9,D5,L1,V1,M1} { leq( addition( one, multiplication( X, star
% 18.91/19.28 ( X ) ) ), star( X ) ) }.
% 18.91/19.28 (49575) {G0,W9,D5,L1,V1,M1} { leq( addition( one, multiplication( star( X
% 18.91/19.28 ), X ) ), star( X ) ) }.
% 18.91/19.28 (49576) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( X, Y ), Z
% 18.91/19.28 ), Y ), leq( multiplication( star( X ), Z ), Y ) }.
% 18.91/19.28 (49577) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( X, Y ), Z
% 18.91/19.28 ), X ), leq( multiplication( Z, star( Y ) ), X ) }.
% 18.91/19.28 (49578) {G0,W3,D2,L1,V0,M1} { leq( skol1, skol2 ) }.
% 18.91/19.28 (49579) {G0,W5,D3,L1,V0,M1} { ! leq( star( skol1 ), star( skol2 ) ) }.
% 18.91/19.28
% 18.91/19.28
% 18.91/19.28 Total Proof:
% 18.91/19.28
% 18.91/19.28 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 18.91/19.28 ) }.
% 18.91/19.28 parent0: (49561) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 18.91/19.28 }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 18.91/19.28 ==> addition( addition( Z, Y ), X ) }.
% 18.91/19.28 parent0: (49562) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) =
% 18.91/19.28 addition( addition( Z, Y ), X ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 Z := Z
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 18.91/19.28 parent0: (49564) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 18.91/19.28 parent0: (49566) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 18.91/19.28 parent0: (49567) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 eqswap: (49601) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 18.91/19.28 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 18.91/19.28 parent0[0]: (49568) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y
% 18.91/19.28 , Z ) ) = addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 Z := Z
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y )
% 18.91/19.28 , multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 18.91/19.28 parent0: (49601) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 18.91/19.28 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 Z := Z
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 eqswap: (49609) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 18.91/19.28 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 18.91/19.28 parent0[0]: (49569) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y
% 18.91/19.28 ), Z ) = addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 Z := Z
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z )
% 18.91/19.28 , multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 18.91/19.28 parent0: (49609) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 18.91/19.28 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 Z := Z
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 18.91/19.28 ==> Y }.
% 18.91/19.28 parent0: (49572) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y
% 18.91/19.28 }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 1 ==> 1
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X
% 18.91/19.28 , Y ) }.
% 18.91/19.28 parent0: (49573) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y )
% 18.91/19.28 }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 1 ==> 1
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (13) {G0,W9,D5,L1,V1,M1} I { leq( addition( one,
% 18.91/19.28 multiplication( X, star( X ) ) ), star( X ) ) }.
% 18.91/19.28 parent0: (49574) {G0,W9,D5,L1,V1,M1} { leq( addition( one, multiplication
% 18.91/19.28 ( X, star( X ) ) ), star( X ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (14) {G0,W9,D5,L1,V1,M1} I { leq( addition( one,
% 18.91/19.28 multiplication( star( X ), X ) ), star( X ) ) }.
% 18.91/19.28 parent0: (49575) {G0,W9,D5,L1,V1,M1} { leq( addition( one, multiplication
% 18.91/19.28 ( star( X ), X ) ), star( X ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (15) {G0,W13,D4,L2,V3,M2} I { ! leq( addition( multiplication
% 18.91/19.28 ( X, Y ), Z ), Y ), leq( multiplication( star( X ), Z ), Y ) }.
% 18.91/19.28 parent0: (49576) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( X
% 18.91/19.28 , Y ), Z ), Y ), leq( multiplication( star( X ), Z ), Y ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 Z := Z
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 1 ==> 1
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (17) {G0,W3,D2,L1,V0,M1} I { leq( skol1, skol2 ) }.
% 18.91/19.28 parent0: (49578) {G0,W3,D2,L1,V0,M1} { leq( skol1, skol2 ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (18) {G0,W5,D3,L1,V0,M1} I { ! leq( star( skol1 ), star( skol2
% 18.91/19.28 ) ) }.
% 18.91/19.28 parent0: (49579) {G0,W5,D3,L1,V0,M1} { ! leq( star( skol1 ), star( skol2 )
% 18.91/19.28 ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 eqswap: (49694) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 18.91/19.28 addition( X, addition( Y, Z ) ) }.
% 18.91/19.28 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 18.91/19.28 ==> addition( addition( Z, Y ), X ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := Z
% 18.91/19.28 Y := Y
% 18.91/19.28 Z := X
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 paramod: (49700) {G1,W9,D4,L1,V2,M1} { addition( addition( X, Y ), Y ) ==>
% 18.91/19.28 addition( X, Y ) }.
% 18.91/19.28 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 18.91/19.28 parent1[0; 8]: (49694) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ),
% 18.91/19.28 Z ) ==> addition( X, addition( Y, Z ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := Y
% 18.91/19.28 end
% 18.91/19.28 substitution1:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 Z := Y
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (21) {G1,W9,D4,L1,V2,M1} P(3,1) { addition( addition( Y, X ),
% 18.91/19.28 X ) ==> addition( Y, X ) }.
% 18.91/19.28 parent0: (49700) {G1,W9,D4,L1,V2,M1} { addition( addition( X, Y ), Y ) ==>
% 18.91/19.28 addition( X, Y ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := Y
% 18.91/19.28 Y := X
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 eqswap: (49705) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 18.91/19.28 addition( X, addition( Y, Z ) ) }.
% 18.91/19.28 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 18.91/19.28 ==> addition( addition( Z, Y ), X ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := Z
% 18.91/19.28 Y := Y
% 18.91/19.28 Z := X
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 paramod: (49708) {G1,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z )
% 18.91/19.28 ==> addition( addition( Y, Z ), X ) }.
% 18.91/19.28 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 18.91/19.28 }.
% 18.91/19.28 parent1[0; 6]: (49705) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ),
% 18.91/19.28 Z ) ==> addition( X, addition( Y, Z ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := addition( Y, Z )
% 18.91/19.28 end
% 18.91/19.28 substitution1:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 Z := Z
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (22) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y )
% 18.91/19.28 , Z ) = addition( addition( Y, Z ), X ) }.
% 18.91/19.28 parent0: (49708) {G1,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z )
% 18.91/19.28 ==> addition( addition( Y, Z ), X ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 Z := Z
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 eqswap: (49722) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 18.91/19.28 ) }.
% 18.91/19.28 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 18.91/19.28 Y ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 eqswap: (49723) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 18.91/19.28 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 resolution: (49724) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 18.91/19.28 parent0[0]: (49722) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X
% 18.91/19.28 , Y ) }.
% 18.91/19.28 parent1[0]: (49723) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := X
% 18.91/19.28 end
% 18.91/19.28 substitution1:
% 18.91/19.28 X := X
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (26) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 18.91/19.28 parent0: (49724) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 eqswap: (49726) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 18.91/19.28 ) }.
% 18.91/19.28 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 18.91/19.28 Y ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 paramod: (49727) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition(
% 18.91/19.28 addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 18.91/19.28 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 18.91/19.28 ==> addition( addition( Z, Y ), X ) }.
% 18.91/19.28 parent1[0; 5]: (49726) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 18.91/19.28 ( X, Y ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := Y
% 18.91/19.28 Y := X
% 18.91/19.28 Z := Z
% 18.91/19.28 end
% 18.91/19.28 substitution1:
% 18.91/19.28 X := Z
% 18.91/19.28 Y := addition( X, Y )
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 eqswap: (49728) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 18.91/19.28 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 18.91/19.28 parent0[0]: (49727) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition
% 18.91/19.28 ( addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 Z := Z
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (27) {G1,W14,D4,L2,V3,M2} P(1,12) { ! addition( addition( X, Y
% 18.91/19.28 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 18.91/19.28 parent0: (49728) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 18.91/19.28 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := Y
% 18.91/19.28 Y := Z
% 18.91/19.28 Z := X
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 1 ==> 1
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 eqswap: (49729) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 18.91/19.28 ) }.
% 18.91/19.28 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 18.91/19.28 Y ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 paramod: (49730) {G1,W8,D3,L2,V2,M2} { ! X ==> addition( X, Y ), leq( Y, X
% 18.91/19.28 ) }.
% 18.91/19.28 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 18.91/19.28 }.
% 18.91/19.28 parent1[0; 3]: (49729) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 18.91/19.28 ( X, Y ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := Y
% 18.91/19.28 Y := X
% 18.91/19.28 end
% 18.91/19.28 substitution1:
% 18.91/19.28 X := Y
% 18.91/19.28 Y := X
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 eqswap: (49733) {G1,W8,D3,L2,V2,M2} { ! addition( X, Y ) ==> X, leq( Y, X
% 18.91/19.28 ) }.
% 18.91/19.28 parent0[0]: (49730) {G1,W8,D3,L2,V2,M2} { ! X ==> addition( X, Y ), leq( Y
% 18.91/19.28 , X ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (29) {G1,W8,D3,L2,V2,M2} P(0,12) { ! addition( Y, X ) ==> Y,
% 18.91/19.28 leq( X, Y ) }.
% 18.91/19.28 parent0: (49733) {G1,W8,D3,L2,V2,M2} { ! addition( X, Y ) ==> X, leq( Y, X
% 18.91/19.28 ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := Y
% 18.91/19.28 Y := X
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 1 ==> 1
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 eqswap: (49734) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 18.91/19.28 ) }.
% 18.91/19.28 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 18.91/19.28 ==> Y }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 resolution: (49735) {G1,W5,D3,L1,V0,M1} { skol2 ==> addition( skol1, skol2
% 18.91/19.28 ) }.
% 18.91/19.28 parent0[1]: (49734) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X
% 18.91/19.28 , Y ) }.
% 18.91/19.28 parent1[0]: (17) {G0,W3,D2,L1,V0,M1} I { leq( skol1, skol2 ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := skol1
% 18.91/19.28 Y := skol2
% 18.91/19.28 end
% 18.91/19.28 substitution1:
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 eqswap: (49736) {G1,W5,D3,L1,V0,M1} { addition( skol1, skol2 ) ==> skol2
% 18.91/19.28 }.
% 18.91/19.28 parent0[0]: (49735) {G1,W5,D3,L1,V0,M1} { skol2 ==> addition( skol1, skol2
% 18.91/19.28 ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (34) {G1,W5,D3,L1,V0,M1} R(11,17) { addition( skol1, skol2 )
% 18.91/19.28 ==> skol2 }.
% 18.91/19.28 parent0: (49736) {G1,W5,D3,L1,V0,M1} { addition( skol1, skol2 ) ==> skol2
% 18.91/19.28 }.
% 18.91/19.28 substitution0:
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 eqswap: (49737) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 18.91/19.28 ) }.
% 18.91/19.28 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 18.91/19.28 ==> Y }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 paramod: (49738) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X
% 18.91/19.28 ) }.
% 18.91/19.28 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 18.91/19.28 }.
% 18.91/19.28 parent1[0; 2]: (49737) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq
% 18.91/19.28 ( X, Y ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := Y
% 18.91/19.28 Y := X
% 18.91/19.28 end
% 18.91/19.28 substitution1:
% 18.91/19.28 X := Y
% 18.91/19.28 Y := X
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 eqswap: (49741) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> X, ! leq( Y, X
% 18.91/19.28 ) }.
% 18.91/19.28 parent0[0]: (49738) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y
% 18.91/19.28 , X ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (39) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, !
% 18.91/19.28 leq( X, Y ) }.
% 18.91/19.28 parent0: (49741) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> X, ! leq( Y, X
% 18.91/19.28 ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := Y
% 18.91/19.28 Y := X
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 1 ==> 1
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 eqswap: (49742) {G1,W5,D3,L1,V0,M1} { skol2 ==> addition( skol1, skol2 )
% 18.91/19.28 }.
% 18.91/19.28 parent0[0]: (34) {G1,W5,D3,L1,V0,M1} R(11,17) { addition( skol1, skol2 )
% 18.91/19.28 ==> skol2 }.
% 18.91/19.28 substitution0:
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 paramod: (49743) {G1,W5,D3,L1,V0,M1} { skol2 ==> addition( skol2, skol1 )
% 18.91/19.28 }.
% 18.91/19.28 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 18.91/19.28 }.
% 18.91/19.28 parent1[0; 2]: (49742) {G1,W5,D3,L1,V0,M1} { skol2 ==> addition( skol1,
% 18.91/19.28 skol2 ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := skol1
% 18.91/19.28 Y := skol2
% 18.91/19.28 end
% 18.91/19.28 substitution1:
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 eqswap: (49746) {G1,W5,D3,L1,V0,M1} { addition( skol2, skol1 ) ==> skol2
% 18.91/19.28 }.
% 18.91/19.28 parent0[0]: (49743) {G1,W5,D3,L1,V0,M1} { skol2 ==> addition( skol2, skol1
% 18.91/19.28 ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (42) {G2,W5,D3,L1,V0,M1} P(34,0) { addition( skol2, skol1 )
% 18.91/19.28 ==> skol2 }.
% 18.91/19.28 parent0: (49746) {G1,W5,D3,L1,V0,M1} { addition( skol2, skol1 ) ==> skol2
% 18.91/19.28 }.
% 18.91/19.28 substitution0:
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 eqswap: (49748) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z ) ==>
% 18.91/19.28 addition( X, addition( Y, Z ) ) }.
% 18.91/19.28 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 18.91/19.28 ==> addition( addition( Z, Y ), X ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := Z
% 18.91/19.28 Y := Y
% 18.91/19.28 Z := X
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 paramod: (49750) {G1,W9,D4,L1,V1,M1} { addition( addition( X, skol2 ),
% 18.91/19.28 skol1 ) ==> addition( X, skol2 ) }.
% 18.91/19.28 parent0[0]: (42) {G2,W5,D3,L1,V0,M1} P(34,0) { addition( skol2, skol1 ) ==>
% 18.91/19.28 skol2 }.
% 18.91/19.28 parent1[0; 8]: (49748) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ),
% 18.91/19.28 Z ) ==> addition( X, addition( Y, Z ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 end
% 18.91/19.28 substitution1:
% 18.91/19.28 X := X
% 18.91/19.28 Y := skol2
% 18.91/19.28 Z := skol1
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (44) {G3,W9,D4,L1,V1,M1} P(42,1) { addition( addition( X,
% 18.91/19.28 skol2 ), skol1 ) ==> addition( X, skol2 ) }.
% 18.91/19.28 parent0: (49750) {G1,W9,D4,L1,V1,M1} { addition( addition( X, skol2 ),
% 18.91/19.28 skol1 ) ==> addition( X, skol2 ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 eqswap: (49754) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z )
% 18.91/19.28 ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 18.91/19.28 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 18.91/19.28 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 Z := Z
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 paramod: (49756) {G1,W11,D4,L1,V2,M1} { multiplication( X, addition( Y,
% 18.91/19.28 one ) ) ==> addition( multiplication( X, Y ), X ) }.
% 18.91/19.28 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 18.91/19.28 parent1[0; 10]: (49754) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition
% 18.91/19.28 ( Y, Z ) ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) )
% 18.91/19.28 }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 end
% 18.91/19.28 substitution1:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 Z := one
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 eqswap: (49758) {G1,W11,D4,L1,V2,M1} { addition( multiplication( X, Y ), X
% 18.91/19.28 ) ==> multiplication( X, addition( Y, one ) ) }.
% 18.91/19.28 parent0[0]: (49756) {G1,W11,D4,L1,V2,M1} { multiplication( X, addition( Y
% 18.91/19.28 , one ) ) ==> addition( multiplication( X, Y ), X ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (52) {G1,W11,D4,L1,V2,M1} P(5,7) { addition( multiplication( X
% 18.91/19.28 , Y ), X ) = multiplication( X, addition( Y, one ) ) }.
% 18.91/19.28 parent0: (49758) {G1,W11,D4,L1,V2,M1} { addition( multiplication( X, Y ),
% 18.91/19.28 X ) ==> multiplication( X, addition( Y, one ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 eqswap: (49760) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 18.91/19.28 ) }.
% 18.91/19.28 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 18.91/19.28 Y ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 paramod: (49761) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 18.91/19.28 multiplication( addition( Z, X ), Y ), leq( multiplication( Z, Y ),
% 18.91/19.28 multiplication( X, Y ) ) }.
% 18.91/19.28 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 18.91/19.28 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 18.91/19.28 parent1[0; 5]: (49760) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 18.91/19.28 ( X, Y ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := Z
% 18.91/19.28 Y := X
% 18.91/19.28 Z := Y
% 18.91/19.28 end
% 18.91/19.28 substitution1:
% 18.91/19.28 X := multiplication( Z, Y )
% 18.91/19.28 Y := multiplication( X, Y )
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 eqswap: (49762) {G1,W16,D4,L2,V3,M2} { ! multiplication( addition( Z, X )
% 18.91/19.28 , Y ) ==> multiplication( X, Y ), leq( multiplication( Z, Y ),
% 18.91/19.28 multiplication( X, Y ) ) }.
% 18.91/19.28 parent0[0]: (49761) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 18.91/19.28 multiplication( addition( Z, X ), Y ), leq( multiplication( Z, Y ),
% 18.91/19.28 multiplication( X, Y ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 Z := Z
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (77) {G1,W16,D4,L2,V3,M2} P(8,12) { ! multiplication( addition
% 18.91/19.28 ( X, Z ), Y ) ==> multiplication( Z, Y ), leq( multiplication( X, Y ),
% 18.91/19.28 multiplication( Z, Y ) ) }.
% 18.91/19.28 parent0: (49762) {G1,W16,D4,L2,V3,M2} { ! multiplication( addition( Z, X )
% 18.91/19.28 , Y ) ==> multiplication( X, Y ), leq( multiplication( Z, Y ),
% 18.91/19.28 multiplication( X, Y ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := Z
% 18.91/19.28 Y := Y
% 18.91/19.28 Z := X
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 1 ==> 1
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 paramod: (49764) {G1,W14,D4,L3,V3,M3} { ! leq( Z, Y ), ! leq(
% 18.91/19.28 multiplication( X, Y ), Z ), leq( multiplication( star( X ), Z ), Y ) }.
% 18.91/19.28 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 18.91/19.28 ==> Y }.
% 18.91/19.28 parent1[0; 2]: (15) {G0,W13,D4,L2,V3,M2} I { ! leq( addition(
% 18.91/19.28 multiplication( X, Y ), Z ), Y ), leq( multiplication( star( X ), Z ), Y
% 18.91/19.28 ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := multiplication( X, Y )
% 18.91/19.28 Y := Z
% 18.91/19.28 end
% 18.91/19.28 substitution1:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 Z := Z
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (151) {G1,W14,D4,L3,V3,M3} P(11,15) { ! leq( Z, Y ), leq(
% 18.91/19.28 multiplication( star( X ), Z ), Y ), ! leq( multiplication( X, Y ), Z )
% 18.91/19.28 }.
% 18.91/19.28 parent0: (49764) {G1,W14,D4,L3,V3,M3} { ! leq( Z, Y ), ! leq(
% 18.91/19.28 multiplication( X, Y ), Z ), leq( multiplication( star( X ), Z ), Y ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 Z := Z
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 1 ==> 2
% 18.91/19.28 2 ==> 1
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 eqswap: (49765) {G1,W9,D4,L1,V2,M1} { addition( X, Y ) ==> addition(
% 18.91/19.28 addition( X, Y ), Y ) }.
% 18.91/19.28 parent0[0]: (21) {G1,W9,D4,L1,V2,M1} P(3,1) { addition( addition( Y, X ), X
% 18.91/19.28 ) ==> addition( Y, X ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := Y
% 18.91/19.28 Y := X
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 eqswap: (49766) {G1,W8,D3,L2,V2,M2} { ! X ==> addition( X, Y ), leq( Y, X
% 18.91/19.28 ) }.
% 18.91/19.28 parent0[0]: (29) {G1,W8,D3,L2,V2,M2} P(0,12) { ! addition( Y, X ) ==> Y,
% 18.91/19.28 leq( X, Y ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := Y
% 18.91/19.28 Y := X
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 resolution: (49767) {G2,W5,D3,L1,V2,M1} { leq( Y, addition( X, Y ) ) }.
% 18.91/19.28 parent0[0]: (49766) {G1,W8,D3,L2,V2,M2} { ! X ==> addition( X, Y ), leq( Y
% 18.91/19.28 , X ) }.
% 18.91/19.28 parent1[0]: (49765) {G1,W9,D4,L1,V2,M1} { addition( X, Y ) ==> addition(
% 18.91/19.28 addition( X, Y ), Y ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := addition( X, Y )
% 18.91/19.28 Y := Y
% 18.91/19.28 end
% 18.91/19.28 substitution1:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (204) {G2,W5,D3,L1,V2,M1} R(21,29) { leq( X, addition( Y, X )
% 18.91/19.28 ) }.
% 18.91/19.28 parent0: (49767) {G2,W5,D3,L1,V2,M1} { leq( Y, addition( X, Y ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := Y
% 18.91/19.28 Y := X
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 paramod: (49769) {G1,W9,D4,L1,V3,M1} { leq( multiplication( X, Y ),
% 18.91/19.28 multiplication( addition( Z, X ), Y ) ) }.
% 18.91/19.28 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 18.91/19.28 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 18.91/19.28 parent1[0; 4]: (204) {G2,W5,D3,L1,V2,M1} R(21,29) { leq( X, addition( Y, X
% 18.91/19.28 ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := Z
% 18.91/19.28 Y := X
% 18.91/19.28 Z := Y
% 18.91/19.28 end
% 18.91/19.28 substitution1:
% 18.91/19.28 X := multiplication( X, Y )
% 18.91/19.28 Y := multiplication( Z, Y )
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (215) {G3,W9,D4,L1,V3,M1} P(8,204) { leq( multiplication( Z, Y
% 18.91/19.28 ), multiplication( addition( X, Z ), Y ) ) }.
% 18.91/19.28 parent0: (49769) {G1,W9,D4,L1,V3,M1} { leq( multiplication( X, Y ),
% 18.91/19.28 multiplication( addition( Z, X ), Y ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := Z
% 18.91/19.28 Y := Y
% 18.91/19.28 Z := X
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 paramod: (49770) {G1,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 18.91/19.28 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 18.91/19.28 }.
% 18.91/19.28 parent1[0; 2]: (204) {G2,W5,D3,L1,V2,M1} R(21,29) { leq( X, addition( Y, X
% 18.91/19.28 ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := Y
% 18.91/19.28 Y := X
% 18.91/19.28 end
% 18.91/19.28 substitution1:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (219) {G3,W5,D3,L1,V2,M1} P(0,204) { leq( Y, addition( Y, X )
% 18.91/19.28 ) }.
% 18.91/19.28 parent0: (49770) {G1,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := Y
% 18.91/19.28 Y := X
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 paramod: (49773) {G1,W7,D4,L1,V3,M1} { leq( X, addition( addition( X, Y )
% 18.91/19.28 , Z ) ) }.
% 18.91/19.28 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 18.91/19.28 ==> addition( addition( Z, Y ), X ) }.
% 18.91/19.28 parent1[0; 2]: (219) {G3,W5,D3,L1,V2,M1} P(0,204) { leq( Y, addition( Y, X
% 18.91/19.28 ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := Z
% 18.91/19.28 Y := Y
% 18.91/19.28 Z := X
% 18.91/19.28 end
% 18.91/19.28 substitution1:
% 18.91/19.28 X := addition( Y, Z )
% 18.91/19.28 Y := X
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (229) {G4,W7,D4,L1,V3,M1} P(1,219) { leq( X, addition(
% 18.91/19.28 addition( X, Y ), Z ) ) }.
% 18.91/19.28 parent0: (49773) {G1,W7,D4,L1,V3,M1} { leq( X, addition( addition( X, Y )
% 18.91/19.28 , Z ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 Z := Z
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 eqswap: (49774) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X ) =
% 18.91/19.28 addition( addition( X, Y ), Z ) }.
% 18.91/19.28 parent0[0]: (22) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y ),
% 18.91/19.28 Z ) = addition( addition( Y, Z ), X ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 Z := Z
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 paramod: (49775) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( X, Y )
% 18.91/19.28 , Z ) ) }.
% 18.91/19.28 parent0[0]: (49774) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X )
% 18.91/19.28 = addition( addition( X, Y ), Z ) }.
% 18.91/19.28 parent1[0; 2]: (204) {G2,W5,D3,L1,V2,M1} R(21,29) { leq( X, addition( Y, X
% 18.91/19.28 ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 Z := Z
% 18.91/19.28 end
% 18.91/19.28 substitution1:
% 18.91/19.28 X := X
% 18.91/19.28 Y := addition( Y, Z )
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 paramod: (49776) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( Z, X )
% 18.91/19.28 , Y ) ) }.
% 18.91/19.28 parent0[0]: (49774) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X )
% 18.91/19.28 = addition( addition( X, Y ), Z ) }.
% 18.91/19.28 parent1[0; 2]: (49775) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( X
% 18.91/19.28 , Y ), Z ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := Z
% 18.91/19.28 Y := X
% 18.91/19.28 Z := Y
% 18.91/19.28 end
% 18.91/19.28 substitution1:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 Z := Z
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (239) {G3,W7,D4,L1,V3,M1} P(22,204) { leq( Z, addition(
% 18.91/19.28 addition( Y, Z ), X ) ) }.
% 18.91/19.28 parent0: (49776) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( Z, X )
% 18.91/19.28 , Y ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := Z
% 18.91/19.28 Y := X
% 18.91/19.28 Z := Y
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 eqswap: (49779) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==> addition(
% 18.91/19.28 addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 18.91/19.28 parent0[0]: (27) {G1,W14,D4,L2,V3,M2} P(1,12) { ! addition( addition( X, Y
% 18.91/19.28 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 Z := Z
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 paramod: (49782) {G1,W15,D3,L3,V3,M3} { ! addition( X, Y ) ==> addition( X
% 18.91/19.28 , Y ), ! leq( Z, X ), leq( Z, addition( X, Y ) ) }.
% 18.91/19.28 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 18.91/19.28 ==> Y }.
% 18.91/19.28 parent1[0; 6]: (49779) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==>
% 18.91/19.28 addition( addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := Z
% 18.91/19.28 Y := X
% 18.91/19.28 end
% 18.91/19.28 substitution1:
% 18.91/19.28 X := Z
% 18.91/19.28 Y := X
% 18.91/19.28 Z := Y
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 eqrefl: (49831) {G0,W8,D3,L2,V3,M2} { ! leq( Z, X ), leq( Z, addition( X,
% 18.91/19.28 Y ) ) }.
% 18.91/19.28 parent0[0]: (49782) {G1,W15,D3,L3,V3,M3} { ! addition( X, Y ) ==> addition
% 18.91/19.28 ( X, Y ), ! leq( Z, X ), leq( Z, addition( X, Y ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 Z := Z
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (304) {G2,W8,D3,L2,V3,M2} P(11,27);q { leq( X, addition( Y, Z
% 18.91/19.28 ) ), ! leq( X, Y ) }.
% 18.91/19.28 parent0: (49831) {G0,W8,D3,L2,V3,M2} { ! leq( Z, X ), leq( Z, addition( X
% 18.91/19.28 , Y ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := Y
% 18.91/19.28 Y := Z
% 18.91/19.28 Z := X
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 1
% 18.91/19.28 1 ==> 0
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 paramod: (49833) {G1,W8,D3,L2,V3,M2} { leq( X, Z ), ! leq( addition( Y, X
% 18.91/19.28 ), Z ) }.
% 18.91/19.28 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 18.91/19.28 ==> Y }.
% 18.91/19.28 parent1[0; 2]: (239) {G3,W7,D4,L1,V3,M1} P(22,204) { leq( Z, addition(
% 18.91/19.28 addition( Y, Z ), X ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := addition( Y, X )
% 18.91/19.28 Y := Z
% 18.91/19.28 end
% 18.91/19.28 substitution1:
% 18.91/19.28 X := Z
% 18.91/19.28 Y := Y
% 18.91/19.28 Z := X
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (342) {G4,W8,D3,L2,V3,M2} P(11,239) { leq( Y, Z ), ! leq(
% 18.91/19.28 addition( X, Y ), Z ) }.
% 18.91/19.28 parent0: (49833) {G1,W8,D3,L2,V3,M2} { leq( X, Z ), ! leq( addition( Y, X
% 18.91/19.28 ), Z ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := Y
% 18.91/19.28 Y := X
% 18.91/19.28 Z := Z
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 1 ==> 1
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 paramod: (49838) {G1,W8,D3,L2,V3,M2} { leq( X, Z ), ! leq( addition( X, Y
% 18.91/19.28 ), Z ) }.
% 18.91/19.28 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 18.91/19.28 ==> Y }.
% 18.91/19.28 parent1[0; 2]: (229) {G4,W7,D4,L1,V3,M1} P(1,219) { leq( X, addition(
% 18.91/19.28 addition( X, Y ), Z ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := addition( X, Y )
% 18.91/19.28 Y := Z
% 18.91/19.28 end
% 18.91/19.28 substitution1:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 Z := Z
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (352) {G5,W8,D3,L2,V3,M2} P(11,229) { leq( X, Z ), ! leq(
% 18.91/19.28 addition( X, Y ), Z ) }.
% 18.91/19.28 parent0: (49838) {G1,W8,D3,L2,V3,M2} { leq( X, Z ), ! leq( addition( X, Y
% 18.91/19.28 ), Z ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 Z := Z
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 1 ==> 1
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 eqswap: (49842) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X
% 18.91/19.28 ) }.
% 18.91/19.28 parent0[0]: (39) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, !
% 18.91/19.28 leq( X, Y ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := Y
% 18.91/19.28 Y := X
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 paramod: (49844) {G1,W9,D2,L3,V2,M3} { X ==> Y, ! leq( X, Y ), ! leq( Y, X
% 18.91/19.28 ) }.
% 18.91/19.28 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 18.91/19.28 ==> Y }.
% 18.91/19.28 parent1[0; 2]: (49842) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq
% 18.91/19.28 ( Y, X ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 end
% 18.91/19.28 substitution1:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (526) {G2,W9,D2,L3,V2,M3} P(39,11) { ! leq( X, Y ), X = Y, !
% 18.91/19.28 leq( Y, X ) }.
% 18.91/19.28 parent0: (49844) {G1,W9,D2,L3,V2,M3} { X ==> Y, ! leq( X, Y ), ! leq( Y, X
% 18.91/19.28 ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 1
% 18.91/19.28 1 ==> 0
% 18.91/19.28 2 ==> 2
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 resolution: (49846) {G1,W4,D3,L1,V1,M1} { leq( one, star( X ) ) }.
% 18.91/19.28 parent0[1]: (352) {G5,W8,D3,L2,V3,M2} P(11,229) { leq( X, Z ), ! leq(
% 18.91/19.28 addition( X, Y ), Z ) }.
% 18.91/19.28 parent1[0]: (14) {G0,W9,D5,L1,V1,M1} I { leq( addition( one, multiplication
% 18.91/19.28 ( star( X ), X ) ), star( X ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := one
% 18.91/19.28 Y := multiplication( star( X ), X )
% 18.91/19.28 Z := star( X )
% 18.91/19.28 end
% 18.91/19.28 substitution1:
% 18.91/19.28 X := X
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (784) {G6,W4,D3,L1,V1,M1} R(352,14) { leq( one, star( X ) )
% 18.91/19.28 }.
% 18.91/19.28 parent0: (49846) {G1,W4,D3,L1,V1,M1} { leq( one, star( X ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 resolution: (49847) {G1,W7,D4,L1,V1,M1} { ! leq( addition( star( skol1 ),
% 18.91/19.28 X ), star( skol2 ) ) }.
% 18.91/19.28 parent0[0]: (18) {G0,W5,D3,L1,V0,M1} I { ! leq( star( skol1 ), star( skol2
% 18.91/19.28 ) ) }.
% 18.91/19.28 parent1[0]: (352) {G5,W8,D3,L2,V3,M2} P(11,229) { leq( X, Z ), ! leq(
% 18.91/19.28 addition( X, Y ), Z ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 end
% 18.91/19.28 substitution1:
% 18.91/19.28 X := star( skol1 )
% 18.91/19.28 Y := X
% 18.91/19.28 Z := star( skol2 )
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (787) {G6,W7,D4,L1,V1,M1} R(352,18) { ! leq( addition( star(
% 18.91/19.28 skol1 ), X ), star( skol2 ) ) }.
% 18.91/19.28 parent0: (49847) {G1,W7,D4,L1,V1,M1} { ! leq( addition( star( skol1 ), X )
% 18.91/19.28 , star( skol2 ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 eqswap: (49848) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X
% 18.91/19.28 ) }.
% 18.91/19.28 parent0[0]: (39) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, !
% 18.91/19.28 leq( X, Y ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := Y
% 18.91/19.28 Y := X
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 resolution: (49849) {G2,W7,D4,L1,V1,M1} { star( X ) ==> addition( star( X
% 18.91/19.28 ), one ) }.
% 18.91/19.28 parent0[1]: (49848) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y
% 18.91/19.28 , X ) }.
% 18.91/19.28 parent1[0]: (784) {G6,W4,D3,L1,V1,M1} R(352,14) { leq( one, star( X ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := star( X )
% 18.91/19.28 Y := one
% 18.91/19.28 end
% 18.91/19.28 substitution1:
% 18.91/19.28 X := X
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 eqswap: (49850) {G2,W7,D4,L1,V1,M1} { addition( star( X ), one ) ==> star
% 18.91/19.28 ( X ) }.
% 18.91/19.28 parent0[0]: (49849) {G2,W7,D4,L1,V1,M1} { star( X ) ==> addition( star( X
% 18.91/19.28 ), one ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (799) {G7,W7,D4,L1,V1,M1} R(784,39) { addition( star( X ), one
% 18.91/19.28 ) ==> star( X ) }.
% 18.91/19.28 parent0: (49850) {G2,W7,D4,L1,V1,M1} { addition( star( X ), one ) ==> star
% 18.91/19.28 ( X ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 eqswap: (49851) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 18.91/19.28 ) }.
% 18.91/19.28 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 18.91/19.28 ==> Y }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 resolution: (49852) {G1,W7,D4,L1,V1,M1} { star( X ) ==> addition( one,
% 18.91/19.28 star( X ) ) }.
% 18.91/19.28 parent0[1]: (49851) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X
% 18.91/19.28 , Y ) }.
% 18.91/19.28 parent1[0]: (784) {G6,W4,D3,L1,V1,M1} R(352,14) { leq( one, star( X ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := one
% 18.91/19.28 Y := star( X )
% 18.91/19.28 end
% 18.91/19.28 substitution1:
% 18.91/19.28 X := X
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 eqswap: (49853) {G1,W7,D4,L1,V1,M1} { addition( one, star( X ) ) ==> star
% 18.91/19.28 ( X ) }.
% 18.91/19.28 parent0[0]: (49852) {G1,W7,D4,L1,V1,M1} { star( X ) ==> addition( one,
% 18.91/19.28 star( X ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (802) {G7,W7,D4,L1,V1,M1} R(784,11) { addition( one, star( X )
% 18.91/19.28 ) ==> star( X ) }.
% 18.91/19.28 parent0: (49853) {G1,W7,D4,L1,V1,M1} { addition( one, star( X ) ) ==> star
% 18.91/19.28 ( X ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 paramod: (49855) {G2,W7,D4,L1,V2,M1} { leq( X, multiplication( X, addition
% 18.91/19.28 ( Y, one ) ) ) }.
% 18.91/19.28 parent0[0]: (52) {G1,W11,D4,L1,V2,M1} P(5,7) { addition( multiplication( X
% 18.91/19.28 , Y ), X ) = multiplication( X, addition( Y, one ) ) }.
% 18.91/19.28 parent1[0; 2]: (204) {G2,W5,D3,L1,V2,M1} R(21,29) { leq( X, addition( Y, X
% 18.91/19.28 ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 end
% 18.91/19.28 substitution1:
% 18.91/19.28 X := X
% 18.91/19.28 Y := multiplication( X, Y )
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (1021) {G3,W7,D4,L1,V2,M1} P(52,204) { leq( X, multiplication
% 18.91/19.28 ( X, addition( Y, one ) ) ) }.
% 18.91/19.28 parent0: (49855) {G2,W7,D4,L1,V2,M1} { leq( X, multiplication( X, addition
% 18.91/19.28 ( Y, one ) ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 paramod: (49857) {G4,W6,D4,L1,V2,M1} { leq( X, multiplication( X, star( Y
% 18.91/19.28 ) ) ) }.
% 18.91/19.28 parent0[0]: (799) {G7,W7,D4,L1,V1,M1} R(784,39) { addition( star( X ), one
% 18.91/19.28 ) ==> star( X ) }.
% 18.91/19.28 parent1[0; 4]: (1021) {G3,W7,D4,L1,V2,M1} P(52,204) { leq( X,
% 18.91/19.28 multiplication( X, addition( Y, one ) ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := Y
% 18.91/19.28 end
% 18.91/19.28 substitution1:
% 18.91/19.28 X := X
% 18.91/19.28 Y := star( Y )
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (1212) {G8,W6,D4,L1,V2,M1} P(799,1021) { leq( Y,
% 18.91/19.28 multiplication( Y, star( X ) ) ) }.
% 18.91/19.28 parent0: (49857) {G4,W6,D4,L1,V2,M1} { leq( X, multiplication( X, star( Y
% 18.91/19.28 ) ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := Y
% 18.91/19.28 Y := X
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 eqswap: (49859) {G1,W16,D4,L2,V3,M2} { ! multiplication( Y, Z ) ==>
% 18.91/19.28 multiplication( addition( X, Y ), Z ), leq( multiplication( X, Z ),
% 18.91/19.28 multiplication( Y, Z ) ) }.
% 18.91/19.28 parent0[0]: (77) {G1,W16,D4,L2,V3,M2} P(8,12) { ! multiplication( addition
% 18.91/19.28 ( X, Z ), Y ) ==> multiplication( Z, Y ), leq( multiplication( X, Y ),
% 18.91/19.28 multiplication( Z, Y ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Z
% 18.91/19.28 Z := Y
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 paramod: (49861) {G2,W17,D4,L2,V2,M2} { ! multiplication( star( X ), Y )
% 18.91/19.28 ==> multiplication( star( X ), Y ), leq( multiplication( one, Y ),
% 18.91/19.28 multiplication( star( X ), Y ) ) }.
% 18.91/19.28 parent0[0]: (802) {G7,W7,D4,L1,V1,M1} R(784,11) { addition( one, star( X )
% 18.91/19.28 ) ==> star( X ) }.
% 18.91/19.28 parent1[0; 7]: (49859) {G1,W16,D4,L2,V3,M2} { ! multiplication( Y, Z ) ==>
% 18.91/19.28 multiplication( addition( X, Y ), Z ), leq( multiplication( X, Z ),
% 18.91/19.28 multiplication( Y, Z ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 end
% 18.91/19.28 substitution1:
% 18.91/19.28 X := one
% 18.91/19.28 Y := star( X )
% 18.91/19.28 Z := Y
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 eqrefl: (49862) {G0,W8,D4,L1,V2,M1} { leq( multiplication( one, Y ),
% 18.91/19.28 multiplication( star( X ), Y ) ) }.
% 18.91/19.28 parent0[0]: (49861) {G2,W17,D4,L2,V2,M2} { ! multiplication( star( X ), Y
% 18.91/19.28 ) ==> multiplication( star( X ), Y ), leq( multiplication( one, Y ),
% 18.91/19.28 multiplication( star( X ), Y ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 paramod: (49863) {G1,W6,D4,L1,V2,M1} { leq( X, multiplication( star( Y ),
% 18.91/19.28 X ) ) }.
% 18.91/19.28 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 18.91/19.28 parent1[0; 1]: (49862) {G0,W8,D4,L1,V2,M1} { leq( multiplication( one, Y )
% 18.91/19.28 , multiplication( star( X ), Y ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 end
% 18.91/19.28 substitution1:
% 18.91/19.28 X := Y
% 18.91/19.28 Y := X
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (1508) {G8,W6,D4,L1,V2,M1} P(802,77);q;d(6) { leq( Y,
% 18.91/19.28 multiplication( star( X ), Y ) ) }.
% 18.91/19.28 parent0: (49863) {G1,W6,D4,L1,V2,M1} { leq( X, multiplication( star( Y ),
% 18.91/19.28 X ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := Y
% 18.91/19.28 Y := X
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 eqswap: (49864) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 18.91/19.28 ) }.
% 18.91/19.28 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 18.91/19.28 ==> Y }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 resolution: (49865) {G1,W11,D5,L1,V2,M1} { multiplication( star( X ), Y )
% 18.91/19.28 ==> addition( Y, multiplication( star( X ), Y ) ) }.
% 18.91/19.28 parent0[1]: (49864) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X
% 18.91/19.28 , Y ) }.
% 18.91/19.28 parent1[0]: (1508) {G8,W6,D4,L1,V2,M1} P(802,77);q;d(6) { leq( Y,
% 18.91/19.28 multiplication( star( X ), Y ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := Y
% 18.91/19.28 Y := multiplication( star( X ), Y )
% 18.91/19.28 end
% 18.91/19.28 substitution1:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 eqswap: (49866) {G1,W11,D5,L1,V2,M1} { addition( Y, multiplication( star(
% 18.91/19.28 X ), Y ) ) ==> multiplication( star( X ), Y ) }.
% 18.91/19.28 parent0[0]: (49865) {G1,W11,D5,L1,V2,M1} { multiplication( star( X ), Y )
% 18.91/19.28 ==> addition( Y, multiplication( star( X ), Y ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (1520) {G9,W11,D5,L1,V2,M1} R(1508,11) { addition( X,
% 18.91/19.28 multiplication( star( Y ), X ) ) ==> multiplication( star( Y ), X ) }.
% 18.91/19.28 parent0: (49866) {G1,W11,D5,L1,V2,M1} { addition( Y, multiplication( star
% 18.91/19.28 ( X ), Y ) ) ==> multiplication( star( X ), Y ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := Y
% 18.91/19.28 Y := X
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 paramod: (49868) {G1,W8,D3,L2,V1,M2} { ! leq( X, star( skol2 ) ), ! leq(
% 18.91/19.28 star( skol1 ), X ) }.
% 18.91/19.28 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 18.91/19.28 ==> Y }.
% 18.91/19.28 parent1[0; 2]: (787) {G6,W7,D4,L1,V1,M1} R(352,18) { ! leq( addition( star
% 18.91/19.28 ( skol1 ), X ), star( skol2 ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := star( skol1 )
% 18.91/19.28 Y := X
% 18.91/19.28 end
% 18.91/19.28 substitution1:
% 18.91/19.28 X := X
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (1756) {G7,W8,D3,L2,V1,M2} P(11,787) { ! leq( X, star( skol2 )
% 18.91/19.28 ), ! leq( star( skol1 ), X ) }.
% 18.91/19.28 parent0: (49868) {G1,W8,D3,L2,V1,M2} { ! leq( X, star( skol2 ) ), ! leq(
% 18.91/19.28 star( skol1 ), X ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 1 ==> 1
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 resolution: (49869) {G1,W7,D4,L1,V1,M1} { leq( multiplication( X, star( X
% 18.91/19.28 ) ), star( X ) ) }.
% 18.91/19.28 parent0[1]: (342) {G4,W8,D3,L2,V3,M2} P(11,239) { leq( Y, Z ), ! leq(
% 18.91/19.28 addition( X, Y ), Z ) }.
% 18.91/19.28 parent1[0]: (13) {G0,W9,D5,L1,V1,M1} I { leq( addition( one, multiplication
% 18.91/19.28 ( X, star( X ) ) ), star( X ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := one
% 18.91/19.28 Y := multiplication( X, star( X ) )
% 18.91/19.28 Z := star( X )
% 18.91/19.28 end
% 18.91/19.28 substitution1:
% 18.91/19.28 X := X
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (1882) {G5,W7,D4,L1,V1,M1} R(342,13) { leq( multiplication( X
% 18.91/19.28 , star( X ) ), star( X ) ) }.
% 18.91/19.28 parent0: (49869) {G1,W7,D4,L1,V1,M1} { leq( multiplication( X, star( X ) )
% 18.91/19.28 , star( X ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 resolution: (49870) {G3,W8,D5,L1,V3,M1} { leq( X, addition( multiplication
% 18.91/19.28 ( X, star( Y ) ), Z ) ) }.
% 18.91/19.28 parent0[1]: (304) {G2,W8,D3,L2,V3,M2} P(11,27);q { leq( X, addition( Y, Z )
% 18.91/19.28 ), ! leq( X, Y ) }.
% 18.91/19.28 parent1[0]: (1212) {G8,W6,D4,L1,V2,M1} P(799,1021) { leq( Y, multiplication
% 18.91/19.28 ( Y, star( X ) ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := multiplication( X, star( Y ) )
% 18.91/19.28 Z := Z
% 18.91/19.28 end
% 18.91/19.28 substitution1:
% 18.91/19.28 X := Y
% 18.91/19.28 Y := X
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (1918) {G9,W8,D5,L1,V3,M1} R(304,1212) { leq( X, addition(
% 18.91/19.28 multiplication( X, star( Y ) ), Z ) ) }.
% 18.91/19.28 parent0: (49870) {G3,W8,D5,L1,V3,M1} { leq( X, addition( multiplication( X
% 18.91/19.28 , star( Y ) ), Z ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := Y
% 18.91/19.28 Z := Z
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 resolution: (49871) {G8,W8,D4,L1,V1,M1} { ! leq( multiplication( star(
% 18.91/19.28 skol1 ), star( X ) ), star( skol2 ) ) }.
% 18.91/19.28 parent0[1]: (1756) {G7,W8,D3,L2,V1,M2} P(11,787) { ! leq( X, star( skol2 )
% 18.91/19.28 ), ! leq( star( skol1 ), X ) }.
% 18.91/19.28 parent1[0]: (1212) {G8,W6,D4,L1,V2,M1} P(799,1021) { leq( Y, multiplication
% 18.91/19.28 ( Y, star( X ) ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := multiplication( star( skol1 ), star( X ) )
% 18.91/19.28 end
% 18.91/19.28 substitution1:
% 18.91/19.28 X := X
% 18.91/19.28 Y := star( skol1 )
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (3739) {G9,W8,D4,L1,V1,M1} R(1756,1212) { ! leq(
% 18.91/19.28 multiplication( star( skol1 ), star( X ) ), star( skol2 ) ) }.
% 18.91/19.28 parent0: (49871) {G8,W8,D4,L1,V1,M1} { ! leq( multiplication( star( skol1
% 18.91/19.28 ), star( X ) ), star( skol2 ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 end
% 18.91/19.28 permutation0:
% 18.91/19.28 0 ==> 0
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 resolution: (49873) {G2,W13,D4,L2,V1,M2} { ! leq( star( X ), star( X ) ),
% 18.91/19.28 leq( multiplication( star( X ), star( X ) ), star( X ) ) }.
% 18.91/19.28 parent0[2]: (151) {G1,W14,D4,L3,V3,M3} P(11,15) { ! leq( Z, Y ), leq(
% 18.91/19.28 multiplication( star( X ), Z ), Y ), ! leq( multiplication( X, Y ), Z )
% 18.91/19.28 }.
% 18.91/19.28 parent1[0]: (1882) {G5,W7,D4,L1,V1,M1} R(342,13) { leq( multiplication( X,
% 18.91/19.28 star( X ) ), star( X ) ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 Y := star( X )
% 18.91/19.28 Z := star( X )
% 18.91/19.28 end
% 18.91/19.28 substitution1:
% 18.91/19.28 X := X
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 resolution: (49874) {G2,W8,D4,L1,V1,M1} { leq( multiplication( star( X ),
% 18.91/19.28 star( X ) ), star( X ) ) }.
% 18.91/19.28 parent0[0]: (49873) {G2,W13,D4,L2,V1,M2} { ! leq( star( X ), star( X ) ),
% 18.91/19.28 leq( multiplication( star( X ), star( X ) ), star( X ) ) }.
% 18.91/19.28 parent1[0]: (26) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 18.91/19.28 substitution0:
% 18.91/19.28 X := X
% 18.91/19.28 end
% 18.91/19.28 substitution1:
% 18.91/19.28 X := star( X )
% 18.91/19.28 end
% 18.91/19.28
% 18.91/19.28 subsumption: (4797) {G6,W8,D4,L1,V1,M1} R(151,1882);r(26) { leq(
% 18.91/19.28 multiplication( star( X ), star( X ) ), star( X ) ) }.
% 18.91/19.28 parent0: (49874) {G2,W8,D4,L1,V1,M1} { leq( multiplication( star( X ),
% 18.91/19.29 star( X ) ), star( X ) ) }.
% 18.91/19.29 substitution0:
% 18.91/19.29 X := X
% 18.91/19.29 end
% 18.91/19.29 permutation0:
% 18.91/19.29 0 ==> 0
% 18.91/19.29 end
% 18.91/19.29
% 18.91/19.29 paramod: (49876) {G4,W9,D4,L1,V2,M1} { leq( multiplication( skol1, X ),
% 18.91/19.29 multiplication( addition( Y, skol2 ), X ) ) }.
% 18.91/19.29 parent0[0]: (44) {G3,W9,D4,L1,V1,M1} P(42,1) { addition( addition( X, skol2
% 18.91/19.29 ), skol1 ) ==> addition( X, skol2 ) }.
% 18.91/19.29 parent1[0; 5]: (215) {G3,W9,D4,L1,V3,M1} P(8,204) { leq( multiplication( Z
% 18.91/19.29 , Y ), multiplication( addition( X, Z ), Y ) ) }.
% 18.91/19.29 substitution0:
% 18.91/19.29 X := Y
% 18.91/19.29 end
% 18.91/19.29 substitution1:
% 18.91/19.29 X := addition( Y, skol2 )
% 18.91/19.29 Y := X
% 18.91/19.29 Z := skol1
% 18.91/19.29 end
% 18.91/19.29
% 18.91/19.29 subsumption: (7345) {G4,W9,D4,L1,V2,M1} P(44,215) { leq( multiplication(
% 18.91/19.29 skol1, Y ), multiplication( addition( X, skol2 ), Y ) ) }.
% 18.91/19.29 parent0: (49876) {G4,W9,D4,L1,V2,M1} { leq( multiplication( skol1, X ),
% 18.91/19.29 multiplication( addition( Y, skol2 ), X ) ) }.
% 18.91/19.29 substitution0:
% 18.91/19.29 X := Y
% 18.91/19.29 Y := X
% 18.91/19.29 end
% 18.91/19.29 permutation0:
% 18.91/19.29 0 ==> 0
% 18.91/19.29 end
% 18.91/19.29
% 18.91/19.29 eqswap: (49877) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X
% 18.91/19.29 ) }.
% 18.91/19.29 parent0[0]: (39) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, !
% 18.91/19.29 leq( X, Y ) }.
% 18.91/19.29 substitution0:
% 18.91/19.29 X := Y
% 18.91/19.29 Y := X
% 18.91/19.29 end
% 18.91/19.29
% 18.91/19.29 resolution: (49879) {G2,W11,D5,L1,V1,M1} { star( X ) ==> addition( star( X
% 18.91/19.29 ), multiplication( star( X ), star( X ) ) ) }.
% 18.91/19.29 parent0[1]: (49877) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y
% 18.91/19.29 , X ) }.
% 18.91/19.29 parent1[0]: (4797) {G6,W8,D4,L1,V1,M1} R(151,1882);r(26) { leq(
% 18.91/19.29 multiplication( star( X ), star( X ) ), star( X ) ) }.
% 18.91/19.29 substitution0:
% 18.91/19.29 X := star( X )
% 18.91/19.29 Y := multiplication( star( X ), star( X ) )
% 18.91/19.29 end
% 18.91/19.29 substitution1:
% 18.91/19.29 X := X
% 18.91/19.29 end
% 18.91/19.29
% 18.91/19.29 paramod: (49880) {G3,W8,D4,L1,V1,M1} { star( X ) ==> multiplication( star
% 18.91/19.29 ( X ), star( X ) ) }.
% 18.91/19.29 parent0[0]: (1520) {G9,W11,D5,L1,V2,M1} R(1508,11) { addition( X,
% 18.91/19.29 multiplication( star( Y ), X ) ) ==> multiplication( star( Y ), X ) }.
% 18.91/19.29 parent1[0; 3]: (49879) {G2,W11,D5,L1,V1,M1} { star( X ) ==> addition( star
% 18.91/19.29 ( X ), multiplication( star( X ), star( X ) ) ) }.
% 18.91/19.29 substitution0:
% 18.91/19.29 X := star( X )
% 18.91/19.29 Y := X
% 18.91/19.29 end
% 18.91/19.29 substitution1:
% 18.91/19.29 X := X
% 18.91/19.29 end
% 18.91/19.29
% 18.91/19.29 eqswap: (49881) {G3,W8,D4,L1,V1,M1} { multiplication( star( X ), star( X )
% 18.91/19.29 ) ==> star( X ) }.
% 18.91/19.29 parent0[0]: (49880) {G3,W8,D4,L1,V1,M1} { star( X ) ==> multiplication(
% 18.91/19.29 star( X ), star( X ) ) }.
% 18.91/19.29 substitution0:
% 18.91/19.29 X := X
% 18.91/19.29 end
% 18.91/19.29
% 18.91/19.29 subsumption: (8839) {G10,W8,D4,L1,V1,M1} R(4797,39);d(1520) {
% 18.91/19.29 multiplication( star( X ), star( X ) ) ==> star( X ) }.
% 18.91/19.29 parent0: (49881) {G3,W8,D4,L1,V1,M1} { multiplication( star( X ), star( X
% 18.91/19.29 ) ) ==> star( X ) }.
% 18.91/19.29 substitution0:
% 18.91/19.29 X := X
% 18.91/19.29 end
% 18.91/19.29 permutation0:
% 18.91/19.29 0 ==> 0
% 18.91/19.29 end
% 18.91/19.29
% 18.91/19.29 resolution: (49882) {G2,W12,D4,L2,V1,M2} { ! leq( star( X ), star( skol2 )
% 18.91/19.29 ), ! leq( multiplication( skol1, star( skol2 ) ), star( X ) ) }.
% 18.91/19.29 parent0[0]: (3739) {G9,W8,D4,L1,V1,M1} R(1756,1212) { ! leq( multiplication
% 18.91/19.29 ( star( skol1 ), star( X ) ), star( skol2 ) ) }.
% 18.91/19.29 parent1[1]: (151) {G1,W14,D4,L3,V3,M3} P(11,15) { ! leq( Z, Y ), leq(
% 18.91/19.29 multiplication( star( X ), Z ), Y ), ! leq( multiplication( X, Y ), Z )
% 18.91/19.29 }.
% 18.91/19.29 substitution0:
% 18.91/19.29 X := X
% 18.91/19.29 end
% 18.91/19.29 substitution1:
% 18.91/19.29 X := skol1
% 18.91/19.29 Y := star( skol2 )
% 18.91/19.29 Z := star( X )
% 18.91/19.29 end
% 18.91/19.29
% 18.91/19.29 subsumption: (9301) {G10,W12,D4,L2,V1,M2} R(3739,151) { ! leq( star( X ),
% 18.91/19.29 star( skol2 ) ), ! leq( multiplication( skol1, star( skol2 ) ), star( X )
% 18.91/19.29 ) }.
% 18.91/19.29 parent0: (49882) {G2,W12,D4,L2,V1,M2} { ! leq( star( X ), star( skol2 ) )
% 18.91/19.29 , ! leq( multiplication( skol1, star( skol2 ) ), star( X ) ) }.
% 18.91/19.29 substitution0:
% 18.91/19.29 X := X
% 18.91/19.29 end
% 18.91/19.29 permutation0:
% 18.91/19.29 0 ==> 0
% 18.91/19.29 1 ==> 1
% 18.91/19.29 end
% 18.91/19.29
% 18.91/19.29 paramod: (49884) {G1,W9,D4,L2,V3,M2} { leq( X, Z ), ! leq( multiplication
% 18.91/19.29 ( X, star( Y ) ), Z ) }.
% 18.91/19.29 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 18.91/19.29 ==> Y }.
% 18.91/19.29 parent1[0; 2]: (1918) {G9,W8,D5,L1,V3,M1} R(304,1212) { leq( X, addition(
% 18.91/19.29 multiplication( X, star( Y ) ), Z ) ) }.
% 18.91/19.29 substitution0:
% 18.91/19.29 X := multiplication( X, star( Y ) )
% 18.91/19.29 Y := Z
% 18.91/19.29 end
% 18.91/19.29 substitution1:
% 18.91/19.29 X := X
% 18.91/19.29 Y := Y
% 18.91/19.29 Z := Z
% 18.91/19.29 end
% 18.91/19.29
% 18.91/19.29 subsumption: (10565) {G10,W9,D4,L2,V3,M2} P(11,1918) { leq( X, Z ), ! leq(
% 18.91/19.29 multiplication( X, star( Y ) ), Z ) }.
% 18.91/19.29 parent0: (49884) {G1,W9,D4,L2,V3,M2} { leq( X, Z ), ! leq( multiplication
% 18.91/19.29 ( X, star( Y ) ), Z ) }.
% 18.91/19.29 substitution0:
% 18.91/19.29 X := X
% 18.91/19.29 Y := Y
% 18.91/19.29 Z := Z
% 18.91/19.29 end
% 18.91/19.29 permutation0:
% 18.91/19.29 0 ==> 0
% 18.91/19.29 1 ==> 1
% 18.91/19.29 end
% 18.91/19.29
% 18.91/19.29 resolution: (49885) {G6,W4,D3,L1,V1,M1} { leq( X, star( X ) ) }.
% 18.91/19.29 parent0[1]: (10565) {G10,W9,D4,L2,V3,M2} P(11,1918) { leq( X, Z ), ! leq(
% 18.91/19.29 multiplication( X, star( Y ) ), Z ) }.
% 18.91/19.29 parent1[0]: (1882) {G5,W7,D4,L1,V1,M1} R(342,13) { leq( multiplication( X,
% 18.91/19.29 star( X ) ), star( X ) ) }.
% 18.91/19.29 substitution0:
% 18.91/19.29 X := X
% 18.91/19.29 Y := X
% 18.91/19.29 Z := star( X )
% 18.91/19.29 end
% 18.91/19.29 substitution1:
% 18.91/19.29 X := X
% 18.91/19.29 end
% 18.91/19.29
% 18.91/19.29 subsumption: (38223) {G11,W4,D3,L1,V1,M1} R(10565,1882) { leq( X, star( X )
% 18.91/19.29 ) }.
% 18.91/19.29 parent0: (49885) {G6,W4,D3,L1,V1,M1} { leq( X, star( X ) ) }.
% 18.91/19.29 substitution0:
% 18.91/19.29 X := X
% 18.91/19.29 end
% 18.91/19.29 permutation0:
% 18.91/19.29 0 ==> 0
% 18.91/19.29 end
% 18.91/19.29
% 18.91/19.29 eqswap: (49886) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X
% 18.91/19.29 ) }.
% 18.91/19.29 parent0[0]: (39) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, !
% 18.91/19.29 leq( X, Y ) }.
% 18.91/19.29 substitution0:
% 18.91/19.29 X := Y
% 18.91/19.29 Y := X
% 18.91/19.29 end
% 18.91/19.29
% 18.91/19.29 resolution: (49887) {G2,W7,D4,L1,V1,M1} { star( X ) ==> addition( star( X
% 18.91/19.29 ), X ) }.
% 18.91/19.29 parent0[1]: (49886) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y
% 18.91/19.29 , X Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------