%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE170+1.004 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n021.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 01:37:39 EDT 2022
% Result : Theorem 173.66s 174.07s
% Output : Refutation 173.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : KLE170+1.004 : TPTP v8.1.0. Released v5.2.0.
% 0.08/0.15 % Command : bliksem %s
% 0.16/0.37 % Computer : n021.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % DateTime : Thu Jun 16 14:03:00 EDT 2022
% 0.16/0.37 % CPUTime :
% 20.56/20.94 *** allocated 10000 integers for termspace/termends
% 20.56/20.94 *** allocated 10000 integers for clauses
% 20.56/20.94 *** allocated 10000 integers for justifications
% 20.56/20.94 Bliksem 1.12
% 20.56/20.94
% 20.56/20.94
% 20.56/20.94 Automatic Strategy Selection
% 20.56/20.94
% 20.56/20.94
% 20.56/20.94 Clauses:
% 20.56/20.94
% 20.56/20.94 { addition( X, Y ) = addition( Y, X ) }.
% 20.56/20.94 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 20.56/20.94 { addition( X, zero ) = X }.
% 20.56/20.94 { addition( X, X ) = X }.
% 20.56/20.94 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 20.56/20.94 multiplication( X, Y ), Z ) }.
% 20.56/20.94 { multiplication( X, one ) = X }.
% 20.56/20.94 { multiplication( one, X ) = X }.
% 20.56/20.94 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 20.56/20.94 , multiplication( X, Z ) ) }.
% 20.56/20.94 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 20.56/20.94 , multiplication( Y, Z ) ) }.
% 20.56/20.94 { multiplication( X, zero ) = zero }.
% 20.56/20.94 { multiplication( zero, X ) = zero }.
% 20.56/20.94 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 20.56/20.94 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 20.56/20.94 { leq( addition( one, multiplication( X, star( X ) ) ), star( X ) ) }.
% 20.56/20.94 { leq( addition( one, multiplication( star( X ), X ) ), star( X ) ) }.
% 20.56/20.95 { ! leq( addition( multiplication( X, Y ), Z ), Y ), leq( multiplication(
% 20.56/20.95 star( X ), Z ), Y ) }.
% 20.56/20.95 { ! leq( addition( multiplication( X, Y ), Z ), X ), leq( multiplication( Z
% 20.56/20.95 , star( Y ) ), X ) }.
% 20.56/20.95 { ! leq( multiplication( a, multiplication( a, multiplication( a, a ) ) ),
% 20.56/20.95 star( a ) ) }.
% 20.56/20.95
% 20.56/20.95 percentage equality = 0.590909, percentage horn = 1.000000
% 20.56/20.95 This is a problem with some equality
% 20.56/20.95
% 20.56/20.95
% 20.56/20.95
% 20.56/20.95 Options Used:
% 20.56/20.95
% 20.56/20.95 useres = 1
% 20.56/20.95 useparamod = 1
% 20.56/20.95 useeqrefl = 1
% 20.56/20.95 useeqfact = 1
% 20.56/20.95 usefactor = 1
% 20.56/20.95 usesimpsplitting = 0
% 20.56/20.95 usesimpdemod = 5
% 20.56/20.95 usesimpres = 3
% 20.56/20.95
% 20.56/20.95 resimpinuse = 1000
% 20.56/20.95 resimpclauses = 20000
% 20.56/20.95 substype = eqrewr
% 20.56/20.95 backwardsubs = 1
% 20.56/20.95 selectoldest = 5
% 20.56/20.95
% 20.56/20.95 litorderings [0] = split
% 20.56/20.95 litorderings [1] = extend the termordering, first sorting on arguments
% 20.56/20.95
% 20.56/20.95 termordering = kbo
% 20.56/20.95
% 20.56/20.95 litapriori = 0
% 20.56/20.95 termapriori = 1
% 20.56/20.95 litaposteriori = 0
% 20.56/20.95 termaposteriori = 0
% 20.56/20.95 demodaposteriori = 0
% 20.56/20.95 ordereqreflfact = 0
% 20.56/20.95
% 20.56/20.95 litselect = negord
% 20.56/20.95
% 20.56/20.95 maxweight = 15
% 20.56/20.95 maxdepth = 30000
% 20.56/20.95 maxlength = 115
% 20.56/20.95 maxnrvars = 195
% 20.56/20.95 excuselevel = 1
% 20.56/20.95 increasemaxweight = 1
% 20.56/20.95
% 20.56/20.95 maxselected = 10000000
% 20.56/20.95 maxnrclauses = 10000000
% 20.56/20.95
% 20.56/20.95 showgenerated = 0
% 20.56/20.95 showkept = 0
% 20.56/20.95 showselected = 0
% 20.56/20.95 showdeleted = 0
% 20.56/20.95 showresimp = 1
% 20.56/20.95 showstatus = 2000
% 20.56/20.95
% 20.56/20.95 prologoutput = 0
% 20.56/20.95 nrgoals = 5000000
% 20.56/20.95 totalproof = 1
% 20.56/20.95
% 20.56/20.95 Symbols occurring in the translation:
% 20.56/20.95
% 20.56/20.95 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 20.56/20.95 . [1, 2] (w:1, o:18, a:1, s:1, b:0),
% 20.56/20.95 ! [4, 1] (w:0, o:12, a:1, s:1, b:0),
% 20.56/20.95 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 20.56/20.95 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 20.56/20.95 addition [37, 2] (w:1, o:42, a:1, s:1, b:0),
% 20.56/20.95 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 20.56/20.95 multiplication [40, 2] (w:1, o:44, a:1, s:1, b:0),
% 20.56/20.95 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 20.56/20.95 leq [42, 2] (w:1, o:43, a:1, s:1, b:0),
% 20.56/20.95 star [43, 1] (w:1, o:17, a:1, s:1, b:0),
% 20.56/20.95 a [44, 0] (w:1, o:11, a:1, s:1, b:0).
% 20.56/20.95
% 20.56/20.95
% 20.56/20.95 Starting Search:
% 20.56/20.95
% 20.56/20.95 *** allocated 15000 integers for clauses
% 20.56/20.95 *** allocated 22500 integers for clauses
% 20.56/20.95 *** allocated 33750 integers for clauses
% 20.56/20.95 *** allocated 50625 integers for clauses
% 20.56/20.95 *** allocated 15000 integers for termspace/termends
% 20.56/20.95 *** allocated 75937 integers for clauses
% 20.56/20.95 Resimplifying inuse:
% 20.56/20.95 Done
% 20.56/20.95
% 20.56/20.95 *** allocated 22500 integers for termspace/termends
% 20.56/20.95 *** allocated 113905 integers for clauses
% 20.56/20.95 *** allocated 33750 integers for termspace/termends
% 20.56/20.95
% 20.56/20.95 Intermediate Status:
% 20.56/20.95 Generated: 21498
% 20.56/20.95 Kept: 2012
% 20.56/20.95 Inuse: 225
% 20.56/20.95 Deleted: 56
% 20.56/20.95 Deletedinuse: 34
% 20.56/20.95
% 20.56/20.95 Resimplifying inuse:
% 20.56/20.95 Done
% 20.56/20.95
% 20.56/20.95 *** allocated 170857 integers for clauses
% 20.56/20.95 *** allocated 50625 integers for termspace/termends
% 20.56/20.95 Resimplifying inuse:
% 20.56/20.95 Done
% 20.56/20.95
% 20.56/20.95 *** allocated 256285 integers for clauses
% 20.56/20.95 *** allocated 75937 integers for termspace/termends
% 20.56/20.95
% 20.56/20.95 Intermediate Status:
% 20.56/20.95 Generated: 41764
% 20.56/20.95 Kept: 4147
% 20.56/20.95 Inuse: 335
% 20.56/20.95 Deleted: 85
% 20.56/20.95 Deletedinuse: 36
% 20.56/20.95
% 20.56/20.95 Resimplifying inuse:
% 20.56/20.95 Done
% 20.56/20.95
% 20.56/20.95 Resimplifying inuse:
% 20.56/20.95 Done
% 20.56/20.95
% 20.56/20.95 *** allocated 384427 integers for clauses
% 20.56/20.95 *** allocated 113905 integers for termspace/termends
% 68.25/68.67
% 68.25/68.67 Intermediate Status:
% 68.25/68.67 Generated: 70441
% 68.25/68.67 Kept: 6163
% 68.25/68.67 Inuse: 385
% 68.25/68.67 Deleted: 94
% 68.25/68.67 Deletedinuse: 36
% 68.25/68.67
% 68.25/68.67 Resimplifying inuse:
% 68.25/68.67 Done
% 68.25/68.67
% 68.25/68.67 Resimplifying inuse:
% 68.25/68.67 Done
% 68.25/68.67
% 68.25/68.67 *** allocated 170857 integers for termspace/termends
% 68.25/68.67 *** allocated 576640 integers for clauses
% 68.25/68.67
% 68.25/68.67 Intermediate Status:
% 68.25/68.67 Generated: 90701
% 68.25/68.67 Kept: 8170
% 68.25/68.67 Inuse: 454
% 68.25/68.67 Deleted: 118
% 68.25/68.67 Deletedinuse: 36
% 68.25/68.67
% 68.25/68.67 Resimplifying inuse:
% 68.25/68.67 Done
% 68.25/68.67
% 68.25/68.67 Resimplifying inuse:
% 68.25/68.67 Done
% 68.25/68.67
% 68.25/68.67
% 68.25/68.67 Intermediate Status:
% 68.25/68.67 Generated: 115937
% 68.25/68.67 Kept: 10180
% 68.25/68.67 Inuse: 542
% 68.25/68.67 Deleted: 137
% 68.25/68.67 Deletedinuse: 42
% 68.25/68.67
% 68.25/68.67 Resimplifying inuse:
% 68.25/68.67 Done
% 68.25/68.67
% 68.25/68.67 Resimplifying inuse:
% 68.25/68.67 Done
% 68.25/68.67
% 68.25/68.67 *** allocated 864960 integers for clauses
% 68.25/68.67
% 68.25/68.67 Intermediate Status:
% 68.25/68.67 Generated: 138590
% 68.25/68.67 Kept: 12184
% 68.25/68.67 Inuse: 609
% 68.25/68.67 Deleted: 169
% 68.25/68.67 Deletedinuse: 56
% 68.25/68.67
% 68.25/68.67 Resimplifying inuse:
% 68.25/68.67 Done
% 68.25/68.67
% 68.25/68.67 *** allocated 256285 integers for termspace/termends
% 68.25/68.67 Resimplifying inuse:
% 68.25/68.67 Done
% 68.25/68.67
% 68.25/68.67
% 68.25/68.67 Intermediate Status:
% 68.25/68.67 Generated: 171154
% 68.25/68.67 Kept: 14185
% 68.25/68.67 Inuse: 722
% 68.25/68.67 Deleted: 180
% 68.25/68.67 Deletedinuse: 56
% 68.25/68.67
% 68.25/68.67 Resimplifying inuse:
% 68.25/68.67 Done
% 68.25/68.67
% 68.25/68.67 Resimplifying inuse:
% 68.25/68.67 Done
% 68.25/68.67
% 68.25/68.67
% 68.25/68.67 Intermediate Status:
% 68.25/68.67 Generated: 197802
% 68.25/68.67 Kept: 16186
% 68.25/68.67 Inuse: 784
% 68.25/68.67 Deleted: 187
% 68.25/68.67 Deletedinuse: 56
% 68.25/68.67
% 68.25/68.67 Resimplifying inuse:
% 68.25/68.67 Done
% 68.25/68.67
% 68.25/68.67 Resimplifying inuse:
% 68.25/68.67 Done
% 68.25/68.67
% 68.25/68.67 *** allocated 1297440 integers for clauses
% 68.25/68.67
% 68.25/68.67 Intermediate Status:
% 68.25/68.67 Generated: 225201
% 68.25/68.67 Kept: 18248
% 68.25/68.67 Inuse: 845
% 68.25/68.67 Deleted: 205
% 68.25/68.67 Deletedinuse: 57
% 68.25/68.67
% 68.25/68.67 *** allocated 384427 integers for termspace/termends
% 68.25/68.67 Resimplifying inuse:
% 68.25/68.67 Done
% 68.25/68.67
% 68.25/68.67 Resimplifying inuse:
% 68.25/68.67 Done
% 68.25/68.67
% 68.25/68.67 Resimplifying clauses:
% 68.25/68.67 Done
% 68.25/68.67
% 68.25/68.67
% 68.25/68.67 Intermediate Status:
% 68.25/68.67 Generated: 238735
% 68.25/68.67 Kept: 20253
% 68.25/68.67 Inuse: 868
% 68.25/68.67 Deleted: 2151
% 68.25/68.67 Deletedinuse: 57
% 68.25/68.67
% 68.25/68.67 Resimplifying inuse:
% 68.25/68.67 Done
% 68.25/68.67
% 68.25/68.67 Resimplifying inuse:
% 68.25/68.67 Done
% 68.25/68.67
% 68.25/68.67
% 68.25/68.67 Intermediate Status:
% 68.25/68.67 Generated: 256872
% 68.25/68.67 Kept: 22263
% 68.25/68.67 Inuse: 906
% 68.25/68.67 Deleted: 2153
% 68.25/68.67 Deletedinuse: 59
% 68.25/68.67
% 68.25/68.67 Resimplifying inuse:
% 68.25/68.67 Done
% 68.25/68.67
% 68.25/68.67 Resimplifying inuse:
% 68.25/68.67 Done
% 68.25/68.67
% 68.25/68.67
% 68.25/68.67 Intermediate Status:
% 68.25/68.67 Generated: 286439
% 68.25/68.67 Kept: 24501
% 68.25/68.67 Inuse: 938
% 68.25/68.67 Deleted: 2153
% 68.25/68.67 Deletedinuse: 59
% 68.25/68.67
% 68.25/68.67 Resimplifying inuse:
% 68.25/68.67 Done
% 68.25/68.67
% 68.25/68.67 Resimplifying inuse:
% 68.25/68.67 Done
% 68.25/68.67
% 68.25/68.67
% 68.25/68.67 Intermediate Status:
% 68.25/68.67 Generated: 316279
% 68.25/68.67 Kept: 26508
% 68.25/68.67 Inuse: 998
% 68.25/68.67 Deleted: 2153
% 68.25/68.67 Deletedinuse: 59
% 68.25/68.67
% 68.25/68.67 *** allocated 576640 integers for termspace/termends
% 68.25/68.67 Resimplifying inuse:
% 68.25/68.67 Done
% 68.25/68.67
% 68.25/68.67 *** allocated 1946160 integers for clauses
% 68.25/68.67
% 68.25/68.67 Intermediate Status:
% 68.25/68.67 Generated: 333463
% 68.25/68.67 Kept: 28526
% 68.25/68.67 Inuse: 1028
% 68.25/68.67 Deleted: 2153
% 68.25/68.67 Deletedinuse: 59
% 68.25/68.67
% 68.25/68.67 Resimplifying inuse:
% 68.25/68.67 Done
% 68.25/68.67
% 68.25/68.67 Resimplifying inuse:
% 68.25/68.67 Done
% 68.25/68.67
% 68.25/68.67
% 68.25/68.67 Intermediate Status:
% 68.25/68.67 Generated: 357409
% 68.25/68.67 Kept: 30549
% 68.25/68.67 Inuse: 1062
% 68.25/68.67 Deleted: 2153
% 68.25/68.67 Deletedinuse: 59
% 68.25/68.67
% 68.25/68.67 Resimplifying inuse:
% 68.25/68.67 Done
% 68.25/68.67
% 68.25/68.67 Resimplifying inuse:
% 68.25/68.67 Done
% 68.25/68.67
% 68.25/68.67
% 68.25/68.67 Intermediate Status:
% 68.25/68.67 Generated: 384796
% 68.25/68.67 Kept: 32565
% 68.25/68.67 Inuse: 1119
% 68.25/68.67 Deleted: 2153
% 68.25/68.67 Deletedinuse: 59
% 68.25/68.67
% 68.25/68.67 Resimplifying inuse:
% 68.25/68.67 Done
% 68.25/68.67
% 68.25/68.67 Resimplifying inuse:
% 68.25/68.67 Done
% 68.25/68.67
% 68.25/68.67
% 68.25/68.67 Intermediate Status:
% 68.25/68.67 Generated: 416216
% 68.25/68.67 Kept: 34599
% 68.25/68.67 Inuse: 1181
% 68.25/68.67 Deleted: 2157
% 68.25/68.67 Deletedinuse: 63
% 68.25/68.67
% 68.25/68.67 Resimplifying inuse:
% 68.25/68.67 Done
% 68.25/68.67
% 68.25/68.67 Resimplifying inuse:
% 68.25/68.67 Done
% 68.25/68.67
% 68.25/68.67
% 68.25/68.67 Intermediate Status:
% 68.25/68.67 Generated: 495273
% 68.25/68.67 Kept: 36653
% 68.25/68.67 Inuse: 1261
% 68.25/68.67 Deleted: 2157
% 68.25/68.67 Deletedinuse: 63
% 68.25/68.67
% 68.25/68.67 Resimplifying inuse:
% 68.25/68.67 Done
% 68.25/68.67
% 68.25/68.67 Resimplifying inuse:
% 68.25/68.67 Done
% 68.25/68.67
% 68.25/68.67
% 68.25/68.67 Intermediate Status:
% 68.25/68.67 Generated: 524989
% 68.25/68.67 Kept: 38663
% 68.25/68.67 Inuse: 1322
% 68.25/68.67 Deleted: 2218
% 68.25/68.67 Deletedinuse: 120
% 68.25/68.67
% 68.25/68.67 Resimplifying inuse:
% 68.25/68.67 Done
% 68.25/68.67
% 68.25/68.67 Resimplifying inuse:
% 68.25/68.67 Done
% 68.25/68.67
% 68.25/68.67 Resimplifying clauses:
% 68.25/68.67 Done
% 68.25/68.67
% 68.25/68.67 *** allocated 864960 integers for termspace/termends
% 68.25/68.67
% 68.25/68.67 Intermediate Status:
% 68.25/68.67 Generated: 545062
% 68.25/68.67 Kept: 40677
% 68.25/68.67 Inuse: 1361
% 68.25/68.67 Deleted: 5744
% 68.25/68.67 Deletedinuse: 121
% 68.25/68.67
% 68.25/68.67 Resimplifying inuse:
% 68.25/68.67 Done
% 68.25/68.67
% 68.25/68.67 *** allocated 2919240 integers for clauses
% 68.25/68.67 Resimplifying inuse:
% 68.25/68.67 Done
% 68.25/68.67
% 68.25/68.67
% 68.25/68.67 Intermediate Status:
% 68.25/68.67 Generated: 599374
% 68.25/68.67 Kept: 42734
% 68.25/68.67 Inuse: 1435
% 68.25/68.67 Deleted: 5744
% 68.25/68.67 Deletedinuse: 121
% 68.25/68.67
% 68.25/68.67 Resimplifying inuse:
% 68.25/68.67 Done
% 68.25/68.67
% 68.25/68.67 Resimplifying inuse:
% 68.25/68.67 Done
% 68.25/68.67
% 68.25/68.67
% 68.25/68.67 Intermediate Status:
% 68.25/68.67 Generated: 631623
% 68.25/68.67 Kept: 44736
% 68.25/68.67 Inuse: 1499
% 68.25/68.67 Deleted: 5744
% 68.25/68.67 Deletedinuse: 121
% 68.25/68.67
% 68.25/68.67 Resimplifying inuse:
% 68.25/68.67 Done
% 68.25/68.67
% 68.25/68.67 Resimplifying inuse:
% 68.25/68.67 Done
% 68.25/68.67
% 68.25/68.67
% 68.25/68.67 Intermediate Status:
% 68.25/68.67 Generated: 657575
% 68.25/68.67 Kept: 46746
% 68.25/68.67 Inuse: 1537
% 68.25/68.67 Deleted: 5745
% 68.25/68.67 Deletedinuse: 122
% 68.25/68.67
% 68.25/68.67 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07
% 173.66/174.07 Intermediate Status:
% 173.66/174.07 Generated: 686120
% 173.66/174.07 Kept: 48760
% 173.66/174.07 Inuse: 1581
% 173.66/174.07 Deleted: 5750
% 173.66/174.07 Deletedinuse: 125
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07
% 173.66/174.07 Intermediate Status:
% 173.66/174.07 Generated: 718841
% 173.66/174.07 Kept: 50770
% 173.66/174.07 Inuse: 1634
% 173.66/174.07 Deleted: 5751
% 173.66/174.07 Deletedinuse: 126
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07
% 173.66/174.07 Intermediate Status:
% 173.66/174.07 Generated: 744706
% 173.66/174.07 Kept: 52779
% 173.66/174.07 Inuse: 1678
% 173.66/174.07 Deleted: 5751
% 173.66/174.07 Deletedinuse: 126
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07
% 173.66/174.07 Intermediate Status:
% 173.66/174.07 Generated: 798936
% 173.66/174.07 Kept: 54978
% 173.66/174.07 Inuse: 1767
% 173.66/174.07 Deleted: 5755
% 173.66/174.07 Deletedinuse: 127
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07
% 173.66/174.07 Intermediate Status:
% 173.66/174.07 Generated: 850115
% 173.66/174.07 Kept: 57122
% 173.66/174.07 Inuse: 1852
% 173.66/174.07 Deleted: 5755
% 173.66/174.07 Deletedinuse: 127
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07
% 173.66/174.07 Intermediate Status:
% 173.66/174.07 Generated: 885351
% 173.66/174.07 Kept: 59228
% 173.66/174.07 Inuse: 1913
% 173.66/174.07 Deleted: 5755
% 173.66/174.07 Deletedinuse: 127
% 173.66/174.07
% 173.66/174.07 *** allocated 1297440 integers for termspace/termends
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07 Resimplifying clauses:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07
% 173.66/174.07 Intermediate Status:
% 173.66/174.07 Generated: 897000
% 173.66/174.07 Kept: 61349
% 173.66/174.07 Inuse: 1925
% 173.66/174.07 Deleted: 8385
% 173.66/174.07 Deletedinuse: 127
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07 *** allocated 4378860 integers for clauses
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07
% 173.66/174.07 Intermediate Status:
% 173.66/174.07 Generated: 935089
% 173.66/174.07 Kept: 63350
% 173.66/174.07 Inuse: 1977
% 173.66/174.07 Deleted: 8385
% 173.66/174.07 Deletedinuse: 127
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07
% 173.66/174.07 Intermediate Status:
% 173.66/174.07 Generated: 958735
% 173.66/174.07 Kept: 65599
% 173.66/174.07 Inuse: 2000
% 173.66/174.07 Deleted: 8385
% 173.66/174.07 Deletedinuse: 127
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07
% 173.66/174.07 Intermediate Status:
% 173.66/174.07 Generated: 985629
% 173.66/174.07 Kept: 67867
% 173.66/174.07 Inuse: 2020
% 173.66/174.07 Deleted: 8385
% 173.66/174.07 Deletedinuse: 127
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07
% 173.66/174.07 Intermediate Status:
% 173.66/174.07 Generated: 1037317
% 173.66/174.07 Kept: 69867
% 173.66/174.07 Inuse: 2069
% 173.66/174.07 Deleted: 8385
% 173.66/174.07 Deletedinuse: 127
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07
% 173.66/174.07 Intermediate Status:
% 173.66/174.07 Generated: 1065225
% 173.66/174.07 Kept: 71904
% 173.66/174.07 Inuse: 2094
% 173.66/174.07 Deleted: 8386
% 173.66/174.07 Deletedinuse: 128
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07
% 173.66/174.07 Intermediate Status:
% 173.66/174.07 Generated: 1089058
% 173.66/174.07 Kept: 73944
% 173.66/174.07 Inuse: 2122
% 173.66/174.07 Deleted: 8386
% 173.66/174.07 Deletedinuse: 128
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07
% 173.66/174.07 Intermediate Status:
% 173.66/174.07 Generated: 1112217
% 173.66/174.07 Kept: 75975
% 173.66/174.07 Inuse: 2159
% 173.66/174.07 Deleted: 8388
% 173.66/174.07 Deletedinuse: 129
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07
% 173.66/174.07 Intermediate Status:
% 173.66/174.07 Generated: 1142371
% 173.66/174.07 Kept: 77987
% 173.66/174.07 Inuse: 2208
% 173.66/174.07 Deleted: 8402
% 173.66/174.07 Deletedinuse: 140
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07
% 173.66/174.07 Intermediate Status:
% 173.66/174.07 Generated: 1160544
% 173.66/174.07 Kept: 79988
% 173.66/174.07 Inuse: 2234
% 173.66/174.07 Deleted: 8402
% 173.66/174.07 Deletedinuse: 140
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07 Resimplifying clauses:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07
% 173.66/174.07 Intermediate Status:
% 173.66/174.07 Generated: 1188363
% 173.66/174.07 Kept: 82027
% 173.66/174.07 Inuse: 2294
% 173.66/174.07 Deleted: 10344
% 173.66/174.07 Deletedinuse: 173
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07
% 173.66/174.07 Intermediate Status:
% 173.66/174.07 Generated: 1211981
% 173.66/174.07 Kept: 84096
% 173.66/174.07 Inuse: 2332
% 173.66/174.07 Deleted: 10344
% 173.66/174.07 Deletedinuse: 173
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07
% 173.66/174.07 Intermediate Status:
% 173.66/174.07 Generated: 1241901
% 173.66/174.07 Kept: 86104
% 173.66/174.07 Inuse: 2379
% 173.66/174.07 Deleted: 10344
% 173.66/174.07 Deletedinuse: 173
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07
% 173.66/174.07 Intermediate Status:
% 173.66/174.07 Generated: 1329034
% 173.66/174.07 Kept: 88114
% 173.66/174.07 Inuse: 2477
% 173.66/174.07 Deleted: 10349
% 173.66/174.07 Deletedinuse: 177
% 173.66/174.07
% 173.66/174.07 *** allocated 1946160 integers for termspace/termends
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07
% 173.66/174.07 Intermediate Status:
% 173.66/174.07 Generated: 1374275
% 173.66/174.07 Kept: 90121
% 173.66/174.07 Inuse: 2536
% 173.66/174.07 Deleted: 10349
% 173.66/174.07 Deletedinuse: 177
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07
% 173.66/174.07 Intermediate Status:
% 173.66/174.07 Generated: 1424117
% 173.66/174.07 Kept: 92154
% 173.66/174.07 Inuse: 2572
% 173.66/174.07 Deleted: 10349
% 173.66/174.07 Deletedinuse: 177
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07
% 173.66/174.07 Intermediate Status:
% 173.66/174.07 Generated: 1479239
% 173.66/174.07 Kept: 94189
% 173.66/174.07 Inuse: 2611
% 173.66/174.07 Deleted: 10349
% 173.66/174.07 Deletedinuse: 177
% 173.66/174.07
% 173.66/174.07 *** allocated 6568290 integers for clauses
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07
% 173.66/174.07 Intermediate Status:
% 173.66/174.07 Generated: 1519423
% 173.66/174.07 Kept: 96214
% 173.66/174.07 Inuse: 2648
% 173.66/174.07 Deleted: 10349
% 173.66/174.07 Deletedinuse: 177
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07
% 173.66/174.07 Intermediate Status:
% 173.66/174.07 Generated: 1540531
% 173.66/174.07 Kept: 98327
% 173.66/174.07 Inuse: 2666
% 173.66/174.07 Deleted: 10349
% 173.66/174.07 Deletedinuse: 177
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07
% 173.66/174.07 Intermediate Status:
% 173.66/174.07 Generated: 1607591
% 173.66/174.07 Kept: 100344
% 173.66/174.07 Inuse: 2707
% 173.66/174.07 Deleted: 10349
% 173.66/174.07 Deletedinuse: 177
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07 Resimplifying clauses:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07
% 173.66/174.07 Intermediate Status:
% 173.66/174.07 Generated: 1889658
% 173.66/174.07 Kept: 102390
% 173.66/174.07 Inuse: 2749
% 173.66/174.07 Deleted: 11660
% 173.66/174.07 Deletedinuse: 177
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07
% 173.66/174.07 Intermediate Status:
% 173.66/174.07 Generated: 2206567
% 173.66/174.07 Kept: 104569
% 173.66/174.07 Inuse: 2838
% 173.66/174.07 Deleted: 11661
% 173.66/174.07 Deletedinuse: 178
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07
% 173.66/174.07 Intermediate Status:
% 173.66/174.07 Generated: 2238707
% 173.66/174.07 Kept: 106764
% 173.66/174.07 Inuse: 2849
% 173.66/174.07 Deleted: 11661
% 173.66/174.07 Deletedinuse: 178
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07
% 173.66/174.07 Intermediate Status:
% 173.66/174.07 Generated: 2275948
% 173.66/174.07 Kept: 108918
% 173.66/174.07 Inuse: 2866
% 173.66/174.07 Deleted: 11661
% 173.66/174.07 Deletedinuse: 178
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07
% 173.66/174.07 Intermediate Status:
% 173.66/174.07 Generated: 2294373
% 173.66/174.07 Kept: 110941
% 173.66/174.07 Inuse: 2881
% 173.66/174.07 Deleted: 11661
% 173.66/174.07 Deletedinuse: 178
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07
% 173.66/174.07 Intermediate Status:
% 173.66/174.07 Generated: 2313163
% 173.66/174.07 Kept: 113069
% 173.66/174.07 Inuse: 2896
% 173.66/174.07 Deleted: 11661
% 173.66/174.07 Deletedinuse: 178
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07
% 173.66/174.07 Intermediate Status:
% 173.66/174.07 Generated: 2328147
% 173.66/174.07 Kept: 115252
% 173.66/174.07 Inuse: 2908
% 173.66/174.07 Deleted: 11661
% 173.66/174.07 Deletedinuse: 178
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07
% 173.66/174.07 Intermediate Status:
% 173.66/174.07 Generated: 2402156
% 173.66/174.07 Kept: 117258
% 173.66/174.07 Inuse: 2925
% 173.66/174.07 Deleted: 11661
% 173.66/174.07 Deletedinuse: 178
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07
% 173.66/174.07 Intermediate Status:
% 173.66/174.07 Generated: 2538584
% 173.66/174.07 Kept: 119343
% 173.66/174.07 Inuse: 2956
% 173.66/174.07 Deleted: 11662
% 173.66/174.07 Deletedinuse: 178
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07 Resimplifying clauses:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07 Done
% 173.66/174.07
% 173.66/174.07
% 173.66/174.07 Intermediate Status:
% 173.66/174.07 Generated: 2646274
% 173.66/174.07 Kept: 121397
% 173.66/174.07 Inuse: 2987
% 173.66/174.07 Deleted: 12873
% 173.66/174.07 Deletedinuse: 178
% 173.66/174.07
% 173.66/174.07 Resimplifying inuse:
% 173.66/174.07
% 173.66/174.07 Bliksems!, er is een bewijs:
% 173.66/174.07 % SZS status Theorem
% 173.66/174.07 % SZS output start Refutation
% 173.66/174.07
% 173.66/174.07 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 173.66/174.07 (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) ==> addition(
% 173.66/174.07 addition( Z, Y ), X ) }.
% 173.66/174.07 (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 173.66/174.07 (4) {G0,W11,D4,L1,V3,M1} I { multiplication( X, multiplication( Y, Z ) )
% 173.66/174.07 ==> multiplication( multiplication( X, Y ), Z ) }.
% 173.66/174.07 (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 173.66/174.07 (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 173.66/174.07 (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 173.66/174.07 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 173.66/174.07 (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 173.66/174.07 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 173.66/174.07 (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) ==> Y }.
% 173.66/174.07 (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, Y ) }.
% 173.66/174.07 (13) {G0,W9,D5,L1,V1,M1} I { leq( addition( one, multiplication( X, star( X
% 173.66/174.07 ) ) ), star( X ) ) }.
% 173.66/174.07 (14) {G0,W9,D5,L1,V1,M1} I { leq( addition( one, multiplication( star( X )
% 173.66/174.07 , X ) ), star( X ) ) }.
% 173.66/174.07 (15) {G0,W13,D4,L2,V3,M2} I { ! leq( addition( multiplication( X, Y ), Z )
% 173.66/174.07 , Y ), leq( multiplication( star( X ), Z ), Y ) }.
% 173.66/174.07 (17) {G1,W10,D5,L1,V0,M1} I;d(4);d(4) { ! leq( multiplication(
% 173.66/174.07 multiplication( multiplication( a, a ), a ), a ), star( a ) ) }.
% 173.66/174.07 (20) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 173.66/174.07 (23) {G1,W14,D4,L2,V3,M2} P(1,12) { ! addition( addition( X, Y ), Z ) ==>
% 173.66/174.07 addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 173.66/174.07 (24) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y ), Z ) =
% 173.66/174.07 addition( addition( Y, Z ), X ) }.
% 173.66/174.07 (35) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, ! leq( X, Y )
% 173.66/174.07 }.
% 173.66/174.07 (63) {G1,W16,D4,L2,V3,M2} P(7,12) { ! multiplication( X, addition( Y, Z ) )
% 173.66/174.07 ==> multiplication( X, Z ), leq( multiplication( X, Y ), multiplication
% 173.66/174.07 ( X, Z ) ) }.
% 173.66/174.07 (65) {G1,W11,D4,L1,V2,M1} P(5,7) { addition( X, multiplication( X, Y ) ) =
% 173.66/174.07 multiplication( X, addition( one, Y ) ) }.
% 173.66/174.07 (94) {G1,W16,D4,L2,V3,M2} P(8,12) { ! multiplication( addition( X, Z ), Y )
% 173.66/174.07 ==> multiplication( Z, Y ), leq( multiplication( X, Y ), multiplication
% 173.66/174.07 ( Z, Y ) ) }.
% 173.66/174.07 (96) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( X, multiplication( Y, X ) ) =
% 173.66/174.07 multiplication( addition( one, Y ), X ) }.
% 173.66/174.07 (162) {G1,W14,D4,L3,V3,M3} P(11,15) { ! leq( Z, Y ), leq( multiplication(
% 173.66/174.07 star( X ), Z ), Y ), ! leq( multiplication( X, Y ), Z ) }.
% 173.66/174.07 (167) {G1,W11,D4,L2,V2,M2} P(5,15) { ! leq( addition( multiplication( X, Y
% 173.66/174.07 ), one ), Y ), leq( star( X ), Y ) }.
% 173.66/174.07 (226) {G2,W8,D3,L2,V3,M2} P(11,23);q { leq( X, addition( Y, Z ) ), ! leq( X
% 173.66/174.07 , Y ) }.
% 173.66/174.07 (230) {G2,W5,D3,L1,V2,M1} P(3,23);q { leq( X, addition( X, Y ) ) }.
% 173.66/174.07 (237) {G3,W7,D4,L1,V3,M1} P(1,230) { leq( X, addition( addition( X, Y ), Z
% 173.66/174.07 ) ) }.
% 173.66/174.07 (238) {G3,W5,D3,L1,V2,M1} P(0,230) { leq( X, addition( Y, X ) ) }.
% 173.66/174.07 (240) {G4,W9,D4,L1,V3,M1} P(8,238) { leq( multiplication( Z, Y ),
% 173.66/174.07 multiplication( addition( X, Z ), Y ) ) }.
% 173.66/174.07 (249) {G4,W7,D4,L1,V3,M1} P(24,238) { leq( Z, addition( addition( Y, Z ), X
% 173.66/174.07 ) ) }.
% 173.66/174.07 (477) {G2,W9,D2,L3,V2,M3} P(35,11) { ! leq( X, Y ), X = Y, ! leq( Y, X )
% 173.66/174.07 }.
% 173.66/174.07 (511) {G5,W8,D3,L2,V3,M2} P(11,249) { leq( Y, Z ), ! leq( addition( X, Y )
% 173.66/174.07 , Z ) }.
% 173.66/174.07 (524) {G4,W8,D3,L2,V3,M2} P(11,237) { leq( X, Z ), ! leq( addition( X, Y )
% 173.66/174.07 , Z ) }.
% 173.66/174.07 (718) {G5,W4,D3,L1,V1,M1} R(524,14) { leq( one, star( X ) ) }.
% 173.66/174.07 (730) {G5,W9,D2,L3,V3,M3} P(11,524) { leq( X, Z ), ! leq( Y, Z ), ! leq( X
% 173.66/174.07 , Y ) }.
% 173.66/174.07 (732) {G6,W7,D4,L1,V1,M1} R(718,35) { addition( star( X ), one ) ==> star(
% 173.66/174.07 X ) }.
% 173.66/174.07 (735) {G6,W7,D4,L1,V1,M1} R(718,11) { addition( one, star( X ) ) ==> star(
% 173.66/174.07 X ) }.
% 173.66/174.07 (881) {G6,W7,D4,L1,V1,M1} R(511,14) { leq( multiplication( star( X ), X ),
% 173.66/174.07 star( X ) ) }.
% 173.66/174.07 (882) {G6,W7,D4,L1,V1,M1} R(511,13) { leq( multiplication( X, star( X ) ),
% 173.66/174.07 star( X ) ) }.
% 173.66/174.07 (885) {G6,W12,D4,L2,V4,M2} P(8,511) { leq( multiplication( Z, Y ), T ), !
% 173.66/174.07 leq( multiplication( addition( X, Z ), Y ), T ) }.
% 173.66/174.07 (886) {G6,W12,D4,L2,V4,M2} P(7,511) { leq( multiplication( X, Z ), T ), !
% 173.66/174.07 leq( multiplication( X, addition( Y, Z ) ), T ) }.
% 173.66/174.07 (888) {G7,W10,D5,L1,V1,M1} R(881,35) { addition( star( X ), multiplication
% 173.66/174.07 ( star( X ), X ) ) ==> star( X ) }.
% 173.66/174.07 (1585) {G7,W6,D4,L1,V2,M1} P(735,63);q;d(5) { leq( Y, multiplication( Y,
% 173.66/174.07 star( X ) ) ) }.
% 173.66/174.07 (2870) {G7,W6,D4,L1,V2,M1} P(735,94);q;d(6) { leq( Y, multiplication( star
% 173.66/174.07 ( X ), Y ) ) }.
% 173.66/174.07 (2878) {G8,W8,D5,L1,V3,M1} R(2870,226) { leq( X, addition( multiplication(
% 173.66/174.07 star( Y ), X ), Z ) ) }.
% 173.66/174.07 (3022) {G9,W9,D4,L2,V3,M2} P(11,2878) { leq( Y, Z ), ! leq( multiplication
% 173.66/174.07 ( star( X ), Y ), Z ) }.
% 173.66/174.07 (3177) {G2,W11,D4,L1,V1,M1} P(96,65) { multiplication( X, addition( one, X
% 173.66/174.07 ) ) ==> multiplication( addition( one, X ), X ) }.
% 173.66/174.07 (8634) {G10,W4,D3,L1,V1,M1} R(3022,881) { leq( X, star( X ) ) }.
% 173.66/174.07 (8649) {G11,W8,D3,L2,V1,M2} R(8634,477) { star( X ) ==> X, ! leq( star( X )
% 173.66/174.07 , X ) }.
% 173.66/174.07 (8650) {G11,W7,D3,L2,V2,M2} R(8634,730) { leq( X, star( Y ) ), ! leq( X, Y
% 173.66/174.07 ) }.
% 173.66/174.07 (8654) {G11,W7,D4,L1,V1,M1} R(8634,35) { addition( star( X ), X ) ==> star
% 173.66/174.07 ( X ) }.
% 173.66/174.07 (8966) {G12,W8,D4,L1,V2,M1} P(8654,240) { leq( multiplication( X, Y ),
% 173.66/174.07 multiplication( star( X ), Y ) ) }.
% 173.66/174.07 (9455) {G7,W8,D4,L1,V1,M1} R(162,882);r(20) { leq( multiplication( star( X
% 173.66/174.07 ), star( X ) ), star( X ) ) }.
% 173.66/174.07 (9871) {G13,W9,D5,L1,V2,M1} R(8966,8650) { leq( multiplication( X, Y ),
% 173.66/174.07 star( multiplication( star( X ), Y ) ) ) }.
% 173.66/174.07 (10034) {G8,W8,D4,L1,V1,M1} R(9455,477);r(1585) { multiplication( star( X )
% 173.66/174.07 , star( X ) ) ==> star( X ) }.
% 173.66/174.07 (10038) {G9,W6,D4,L1,V1,M1} P(10034,167);d(732);r(20) { leq( star( star( X
% 173.66/174.07 ) ), star( X ) ) }.
% 173.66/174.07 (10055) {G12,W6,D4,L1,V1,M1} R(10038,8649) { star( star( X ) ) ==> star( X
% 173.66/174.07 ) }.
% 173.66/174.07 (74412) {G8,W9,D4,L1,V1,M1} P(888,65) { multiplication( star( X ), addition
% 173.66/174.07 ( one, X ) ) ==> star( X ) }.
% 173.66/174.07 (74420) {G14,W8,D4,L1,V1,M1} P(74412,9871);d(3177);d(10055) { leq(
% 173.66/174.07 multiplication( addition( one, X ), X ), star( X ) ) }.
% 173.66/174.07 (74588) {G15,W6,D3,L1,V1,M1} R(74420,885) { leq( multiplication( X, X ),
% 173.66/174.07 star( X ) ) }.
% 173.66/174.07 (74687) {G16,W10,D4,L1,V2,M1} R(74588,886) { leq( multiplication( addition
% 173.66/174.07 ( X, Y ), Y ), star( addition( X, Y ) ) ) }.
% 173.66/174.07 (74730) {G16,W9,D4,L1,V1,M1} R(74588,35) { addition( star( X ),
% 173.66/174.07 multiplication( X, X ) ) ==> star( X ) }.
% 173.66/174.07 (121790) {G17,W8,D4,L1,V2,M1} R(74687,885) { leq( multiplication( X, X ),
% 173.66/174.07 star( addition( Y, X ) ) ) }.
% 173.66/174.07 (121855) {G18,W10,D5,L1,V1,M1} P(74730,121790);d(4);d(10055) { leq(
% 173.66/174.07 multiplication( multiplication( multiplication( X, X ), X ), X ), star( X
% 173.66/174.07 ) ) }.
% 173.66/174.07 (122078) {G19,W0,D0,L0,V0,M0} S(17);r(121855) { }.
% 173.66/174.07
% 173.66/174.07
% 173.66/174.07 % SZS output end Refutation
% 173.66/174.07 found a proof!
% 173.66/174.07
% 173.66/174.07
% 173.66/174.07 Unprocessed initial clauses:
% 173.66/174.07
% 173.66/174.07 (122080) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 173.66/174.07 (122081) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition
% 173.66/174.07 ( addition( Z, Y ), X ) }.
% 173.66/174.07 (122082) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 173.66/174.07 (122083) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 173.66/174.07 (122084) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z )
% 173.66/174.07 ) = multiplication( multiplication( X, Y ), Z ) }.
% 173.66/174.07 (122085) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 173.66/174.07 (122086) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 173.66/174.07 (122087) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 173.66/174.07 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 173.66/174.07 (122088) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 173.66/174.07 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 173.66/174.07 (122089) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero }.
% 173.66/174.07 (122090) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 173.66/174.07 (122091) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 173.66/174.07 (122092) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 173.66/174.07 (122093) {G0,W9,D5,L1,V1,M1} { leq( addition( one, multiplication( X, star
% 173.66/174.07 ( X ) ) ), star( X ) ) }.
% 173.66/174.07 (122094) {G0,W9,D5,L1,V1,M1} { leq( addition( one, multiplication( star( X
% 173.66/174.07 ), X ) ), star( X ) ) }.
% 173.66/174.07 (122095) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( X, Y ), Z
% 173.66/174.07 ), Y ), leq( multiplication( star( X ), Z ), Y ) }.
% 173.66/174.07 (122096) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( X, Y ), Z
% 173.66/174.07 ), X ), leq( multiplication( Z, star( Y ) ), X ) }.
% 173.66/174.07 (122097) {G0,W10,D5,L1,V0,M1} { ! leq( multiplication( a, multiplication(
% 173.66/174.07 a, multiplication( a, a ) ) ), star( a ) ) }.
% 173.66/174.07
% 173.66/174.07
% 173.66/174.07 Total Proof:
% 173.66/174.07
% 173.66/174.07 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 173.66/174.07 ) }.
% 173.66/174.07 parent0: (122080) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X
% 173.66/174.07 ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 end
% 173.66/174.07 permutation0:
% 173.66/174.07 0 ==> 0
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 subsumption: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 173.66/174.07 ==> addition( addition( Z, Y ), X ) }.
% 173.66/174.07 parent0: (122081) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) =
% 173.66/174.07 addition( addition( Z, Y ), X ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 Z := Z
% 173.66/174.07 end
% 173.66/174.07 permutation0:
% 173.66/174.07 0 ==> 0
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 subsumption: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 173.66/174.07 parent0: (122083) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 end
% 173.66/174.07 permutation0:
% 173.66/174.07 0 ==> 0
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 subsumption: (4) {G0,W11,D4,L1,V3,M1} I { multiplication( X, multiplication
% 173.66/174.07 ( Y, Z ) ) ==> multiplication( multiplication( X, Y ), Z ) }.
% 173.66/174.07 parent0: (122084) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication
% 173.66/174.07 ( Y, Z ) ) = multiplication( multiplication( X, Y ), Z ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 Z := Z
% 173.66/174.07 end
% 173.66/174.07 permutation0:
% 173.66/174.07 0 ==> 0
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 subsumption: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 173.66/174.07 parent0: (122085) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 end
% 173.66/174.07 permutation0:
% 173.66/174.07 0 ==> 0
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 subsumption: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 173.66/174.07 parent0: (122086) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 end
% 173.66/174.07 permutation0:
% 173.66/174.07 0 ==> 0
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 eqswap: (122123) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 173.66/174.07 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 173.66/174.07 parent0[0]: (122087) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y
% 173.66/174.07 , Z ) ) = addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 Z := Z
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 subsumption: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y )
% 173.66/174.07 , multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 173.66/174.07 parent0: (122123) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y )
% 173.66/174.07 , multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 Z := Z
% 173.66/174.07 end
% 173.66/174.07 permutation0:
% 173.66/174.07 0 ==> 0
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 eqswap: (122131) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 173.66/174.07 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 173.66/174.07 parent0[0]: (122088) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y
% 173.66/174.07 ), Z ) = addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 Z := Z
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 subsumption: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z )
% 173.66/174.07 , multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 173.66/174.07 parent0: (122131) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z )
% 173.66/174.07 , multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 Z := Z
% 173.66/174.07 end
% 173.66/174.07 permutation0:
% 173.66/174.07 0 ==> 0
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 subsumption: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 173.66/174.07 ==> Y }.
% 173.66/174.07 parent0: (122091) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) =
% 173.66/174.07 Y }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 end
% 173.66/174.07 permutation0:
% 173.66/174.07 0 ==> 0
% 173.66/174.07 1 ==> 1
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 subsumption: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X
% 173.66/174.07 , Y ) }.
% 173.66/174.07 parent0: (122092) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y
% 173.66/174.07 ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 end
% 173.66/174.07 permutation0:
% 173.66/174.07 0 ==> 0
% 173.66/174.07 1 ==> 1
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 subsumption: (13) {G0,W9,D5,L1,V1,M1} I { leq( addition( one,
% 173.66/174.07 multiplication( X, star( X ) ) ), star( X ) ) }.
% 173.66/174.07 parent0: (122093) {G0,W9,D5,L1,V1,M1} { leq( addition( one, multiplication
% 173.66/174.07 ( X, star( X ) ) ), star( X ) ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 end
% 173.66/174.07 permutation0:
% 173.66/174.07 0 ==> 0
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 subsumption: (14) {G0,W9,D5,L1,V1,M1} I { leq( addition( one,
% 173.66/174.07 multiplication( star( X ), X ) ), star( X ) ) }.
% 173.66/174.07 parent0: (122094) {G0,W9,D5,L1,V1,M1} { leq( addition( one, multiplication
% 173.66/174.07 ( star( X ), X ) ), star( X ) ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 end
% 173.66/174.07 permutation0:
% 173.66/174.07 0 ==> 0
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 subsumption: (15) {G0,W13,D4,L2,V3,M2} I { ! leq( addition( multiplication
% 173.66/174.07 ( X, Y ), Z ), Y ), leq( multiplication( star( X ), Z ), Y ) }.
% 173.66/174.07 parent0: (122095) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication(
% 173.66/174.07 X, Y ), Z ), Y ), leq( multiplication( star( X ), Z ), Y ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 Z := Z
% 173.66/174.07 end
% 173.66/174.07 permutation0:
% 173.66/174.07 0 ==> 0
% 173.66/174.07 1 ==> 1
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 paramod: (122242) {G1,W10,D5,L1,V0,M1} { ! leq( multiplication( a,
% 173.66/174.07 multiplication( multiplication( a, a ), a ) ), star( a ) ) }.
% 173.66/174.07 parent0[0]: (4) {G0,W11,D4,L1,V3,M1} I { multiplication( X, multiplication
% 173.66/174.07 ( Y, Z ) ) ==> multiplication( multiplication( X, Y ), Z ) }.
% 173.66/174.07 parent1[0; 4]: (122097) {G0,W10,D5,L1,V0,M1} { ! leq( multiplication( a,
% 173.66/174.07 multiplication( a, multiplication( a, a ) ) ), star( a ) ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := a
% 173.66/174.07 Y := a
% 173.66/174.07 Z := a
% 173.66/174.07 end
% 173.66/174.07 substitution1:
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 paramod: (122245) {G1,W10,D5,L1,V0,M1} { ! leq( multiplication(
% 173.66/174.07 multiplication( a, multiplication( a, a ) ), a ), star( a ) ) }.
% 173.66/174.07 parent0[0]: (4) {G0,W11,D4,L1,V3,M1} I { multiplication( X, multiplication
% 173.66/174.07 ( Y, Z ) ) ==> multiplication( multiplication( X, Y ), Z ) }.
% 173.66/174.07 parent1[0; 2]: (122242) {G1,W10,D5,L1,V0,M1} { ! leq( multiplication( a,
% 173.66/174.07 multiplication( multiplication( a, a ), a ) ), star( a ) ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := a
% 173.66/174.07 Y := multiplication( a, a )
% 173.66/174.07 Z := a
% 173.66/174.07 end
% 173.66/174.07 substitution1:
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 paramod: (122246) {G1,W10,D5,L1,V0,M1} { ! leq( multiplication(
% 173.66/174.07 multiplication( multiplication( a, a ), a ), a ), star( a ) ) }.
% 173.66/174.07 parent0[0]: (4) {G0,W11,D4,L1,V3,M1} I { multiplication( X, multiplication
% 173.66/174.07 ( Y, Z ) ) ==> multiplication( multiplication( X, Y ), Z ) }.
% 173.66/174.07 parent1[0; 3]: (122245) {G1,W10,D5,L1,V0,M1} { ! leq( multiplication(
% 173.66/174.07 multiplication( a, multiplication( a, a ) ), a ), star( a ) ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := a
% 173.66/174.07 Y := a
% 173.66/174.07 Z := a
% 173.66/174.07 end
% 173.66/174.07 substitution1:
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 subsumption: (17) {G1,W10,D5,L1,V0,M1} I;d(4);d(4) { ! leq( multiplication
% 173.66/174.07 ( multiplication( multiplication( a, a ), a ), a ), star( a ) ) }.
% 173.66/174.07 parent0: (122246) {G1,W10,D5,L1,V0,M1} { ! leq( multiplication(
% 173.66/174.07 multiplication( multiplication( a, a ), a ), a ), star( a ) ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 end
% 173.66/174.07 permutation0:
% 173.66/174.07 0 ==> 0
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 eqswap: (122247) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 173.66/174.07 ) }.
% 173.66/174.07 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 173.66/174.07 Y ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 eqswap: (122248) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 173.66/174.07 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 resolution: (122249) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 173.66/174.07 parent0[0]: (122247) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq(
% 173.66/174.07 X, Y ) }.
% 173.66/174.07 parent1[0]: (122248) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := X
% 173.66/174.07 end
% 173.66/174.07 substitution1:
% 173.66/174.07 X := X
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 subsumption: (20) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 173.66/174.07 parent0: (122249) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 end
% 173.66/174.07 permutation0:
% 173.66/174.07 0 ==> 0
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 eqswap: (122251) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 173.66/174.07 ) }.
% 173.66/174.07 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 173.66/174.07 Y ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 paramod: (122252) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition(
% 173.66/174.07 addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 173.66/174.07 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 173.66/174.07 ==> addition( addition( Z, Y ), X ) }.
% 173.66/174.07 parent1[0; 5]: (122251) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ),
% 173.66/174.07 leq( X, Y ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := Y
% 173.66/174.07 Y := X
% 173.66/174.07 Z := Z
% 173.66/174.07 end
% 173.66/174.07 substitution1:
% 173.66/174.07 X := Z
% 173.66/174.07 Y := addition( X, Y )
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 eqswap: (122253) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 173.66/174.07 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 173.66/174.07 parent0[0]: (122252) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==>
% 173.66/174.07 addition( addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 Z := Z
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 subsumption: (23) {G1,W14,D4,L2,V3,M2} P(1,12) { ! addition( addition( X, Y
% 173.66/174.07 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 173.66/174.07 parent0: (122253) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 173.66/174.07 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := Y
% 173.66/174.07 Y := Z
% 173.66/174.07 Z := X
% 173.66/174.07 end
% 173.66/174.07 permutation0:
% 173.66/174.07 0 ==> 0
% 173.66/174.07 1 ==> 1
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 eqswap: (122254) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z )
% 173.66/174.07 ==> addition( X, addition( Y, Z ) ) }.
% 173.66/174.07 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 173.66/174.07 ==> addition( addition( Z, Y ), X ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := Z
% 173.66/174.07 Y := Y
% 173.66/174.07 Z := X
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 paramod: (122257) {G1,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z )
% 173.66/174.07 ==> addition( addition( Y, Z ), X ) }.
% 173.66/174.07 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 173.66/174.07 }.
% 173.66/174.07 parent1[0; 6]: (122254) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y )
% 173.66/174.07 , Z ) ==> addition( X, addition( Y, Z ) ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := addition( Y, Z )
% 173.66/174.07 end
% 173.66/174.07 substitution1:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 Z := Z
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 subsumption: (24) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y )
% 173.66/174.07 , Z ) = addition( addition( Y, Z ), X ) }.
% 173.66/174.07 parent0: (122257) {G1,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z )
% 173.66/174.07 ==> addition( addition( Y, Z ), X ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 Z := Z
% 173.66/174.07 end
% 173.66/174.07 permutation0:
% 173.66/174.07 0 ==> 0
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 eqswap: (122271) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 173.66/174.07 ) }.
% 173.66/174.07 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 173.66/174.07 ==> Y }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 paramod: (122272) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y,
% 173.66/174.07 X ) }.
% 173.66/174.07 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 173.66/174.07 }.
% 173.66/174.07 parent1[0; 2]: (122271) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), !
% 173.66/174.07 leq( X, Y ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := Y
% 173.66/174.07 Y := X
% 173.66/174.07 end
% 173.66/174.07 substitution1:
% 173.66/174.07 X := Y
% 173.66/174.07 Y := X
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 eqswap: (122275) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> X, ! leq( Y, X
% 173.66/174.07 ) }.
% 173.66/174.07 parent0[0]: (122272) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq(
% 173.66/174.07 Y, X ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 subsumption: (35) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, !
% 173.66/174.07 leq( X, Y ) }.
% 173.66/174.07 parent0: (122275) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> X, ! leq( Y,
% 173.66/174.07 X ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := Y
% 173.66/174.07 Y := X
% 173.66/174.07 end
% 173.66/174.07 permutation0:
% 173.66/174.07 0 ==> 0
% 173.66/174.07 1 ==> 1
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 eqswap: (122277) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 173.66/174.07 ) }.
% 173.66/174.07 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 173.66/174.07 Y ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 paramod: (122278) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 173.66/174.07 multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ),
% 173.66/174.07 multiplication( X, Y ) ) }.
% 173.66/174.07 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 173.66/174.07 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 173.66/174.07 parent1[0; 5]: (122277) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ),
% 173.66/174.07 leq( X, Y ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Z
% 173.66/174.07 Z := Y
% 173.66/174.07 end
% 173.66/174.07 substitution1:
% 173.66/174.07 X := multiplication( X, Z )
% 173.66/174.07 Y := multiplication( X, Y )
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 eqswap: (122279) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, addition( Z,
% 173.66/174.07 Y ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ),
% 173.66/174.07 multiplication( X, Y ) ) }.
% 173.66/174.07 parent0[0]: (122278) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 173.66/174.07 multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ),
% 173.66/174.07 multiplication( X, Y ) ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 Z := Z
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 subsumption: (63) {G1,W16,D4,L2,V3,M2} P(7,12) { ! multiplication( X,
% 173.66/174.07 addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 173.66/174.07 ), multiplication( X, Z ) ) }.
% 173.66/174.07 parent0: (122279) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, addition( Z
% 173.66/174.07 , Y ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ),
% 173.66/174.07 multiplication( X, Y ) ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Z
% 173.66/174.07 Z := Y
% 173.66/174.07 end
% 173.66/174.07 permutation0:
% 173.66/174.07 0 ==> 0
% 173.66/174.07 1 ==> 1
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 eqswap: (122281) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z
% 173.66/174.07 ) ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 173.66/174.07 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 173.66/174.07 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 Z := Z
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 paramod: (122282) {G1,W11,D4,L1,V2,M1} { multiplication( X, addition( one
% 173.66/174.07 , Y ) ) ==> addition( X, multiplication( X, Y ) ) }.
% 173.66/174.07 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 173.66/174.07 parent1[0; 7]: (122281) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition
% 173.66/174.07 ( Y, Z ) ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) )
% 173.66/174.07 }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 end
% 173.66/174.07 substitution1:
% 173.66/174.07 X := X
% 173.66/174.07 Y := one
% 173.66/174.07 Z := Y
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 eqswap: (122284) {G1,W11,D4,L1,V2,M1} { addition( X, multiplication( X, Y
% 173.66/174.07 ) ) ==> multiplication( X, addition( one, Y ) ) }.
% 173.66/174.07 parent0[0]: (122282) {G1,W11,D4,L1,V2,M1} { multiplication( X, addition(
% 173.66/174.07 one, Y ) ) ==> addition( X, multiplication( X, Y ) ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 subsumption: (65) {G1,W11,D4,L1,V2,M1} P(5,7) { addition( X, multiplication
% 173.66/174.07 ( X, Y ) ) = multiplication( X, addition( one, Y ) ) }.
% 173.66/174.07 parent0: (122284) {G1,W11,D4,L1,V2,M1} { addition( X, multiplication( X, Y
% 173.66/174.07 ) ) ==> multiplication( X, addition( one, Y ) ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 end
% 173.66/174.07 permutation0:
% 173.66/174.07 0 ==> 0
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 eqswap: (122287) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 173.66/174.07 ) }.
% 173.66/174.07 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 173.66/174.07 Y ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 paramod: (122288) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 173.66/174.07 multiplication( addition( Z, X ), Y ), leq( multiplication( Z, Y ),
% 173.66/174.07 multiplication( X, Y ) ) }.
% 173.66/174.07 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 173.66/174.07 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 173.66/174.07 parent1[0; 5]: (122287) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ),
% 173.66/174.07 leq( X, Y ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := Z
% 173.66/174.07 Y := X
% 173.66/174.07 Z := Y
% 173.66/174.07 end
% 173.66/174.07 substitution1:
% 173.66/174.07 X := multiplication( Z, Y )
% 173.66/174.07 Y := multiplication( X, Y )
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 eqswap: (122289) {G1,W16,D4,L2,V3,M2} { ! multiplication( addition( Z, X )
% 173.66/174.07 , Y ) ==> multiplication( X, Y ), leq( multiplication( Z, Y ),
% 173.66/174.07 multiplication( X, Y ) ) }.
% 173.66/174.07 parent0[0]: (122288) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 173.66/174.07 multiplication( addition( Z, X ), Y ), leq( multiplication( Z, Y ),
% 173.66/174.07 multiplication( X, Y ) ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 Z := Z
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 subsumption: (94) {G1,W16,D4,L2,V3,M2} P(8,12) { ! multiplication( addition
% 173.66/174.07 ( X, Z ), Y ) ==> multiplication( Z, Y ), leq( multiplication( X, Y ),
% 173.66/174.07 multiplication( Z, Y ) ) }.
% 173.66/174.07 parent0: (122289) {G1,W16,D4,L2,V3,M2} { ! multiplication( addition( Z, X
% 173.66/174.07 ), Y ) ==> multiplication( X, Y ), leq( multiplication( Z, Y ),
% 173.66/174.07 multiplication( X, Y ) ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := Z
% 173.66/174.07 Y := Y
% 173.66/174.07 Z := X
% 173.66/174.07 end
% 173.66/174.07 permutation0:
% 173.66/174.07 0 ==> 0
% 173.66/174.07 1 ==> 1
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 eqswap: (122291) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Z ),
% 173.66/174.07 Y ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) ) }.
% 173.66/174.07 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 173.66/174.07 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Z
% 173.66/174.07 Z := Y
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 paramod: (122292) {G1,W11,D4,L1,V2,M1} { multiplication( addition( one, X
% 173.66/174.07 ), Y ) ==> addition( Y, multiplication( X, Y ) ) }.
% 173.66/174.07 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 173.66/174.07 parent1[0; 7]: (122291) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X
% 173.66/174.07 , Z ), Y ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) )
% 173.66/174.07 }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := Y
% 173.66/174.07 end
% 173.66/174.07 substitution1:
% 173.66/174.07 X := one
% 173.66/174.07 Y := Y
% 173.66/174.07 Z := X
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 eqswap: (122294) {G1,W11,D4,L1,V2,M1} { addition( Y, multiplication( X, Y
% 173.66/174.07 ) ) ==> multiplication( addition( one, X ), Y ) }.
% 173.66/174.07 parent0[0]: (122292) {G1,W11,D4,L1,V2,M1} { multiplication( addition( one
% 173.66/174.07 , X ), Y ) ==> addition( Y, multiplication( X, Y ) ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 subsumption: (96) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( X, multiplication
% 173.66/174.07 ( Y, X ) ) = multiplication( addition( one, Y ), X ) }.
% 173.66/174.07 parent0: (122294) {G1,W11,D4,L1,V2,M1} { addition( Y, multiplication( X, Y
% 173.66/174.07 ) ) ==> multiplication( addition( one, X ), Y ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := Y
% 173.66/174.07 Y := X
% 173.66/174.07 end
% 173.66/174.07 permutation0:
% 173.66/174.07 0 ==> 0
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 paramod: (122297) {G1,W14,D4,L3,V3,M3} { ! leq( Z, Y ), ! leq(
% 173.66/174.07 multiplication( X, Y ), Z ), leq( multiplication( star( X ), Z ), Y ) }.
% 173.66/174.07 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 173.66/174.07 ==> Y }.
% 173.66/174.07 parent1[0; 2]: (15) {G0,W13,D4,L2,V3,M2} I { ! leq( addition(
% 173.66/174.07 multiplication( X, Y ), Z ), Y ), leq( multiplication( star( X ), Z ), Y
% 173.66/174.07 ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := multiplication( X, Y )
% 173.66/174.07 Y := Z
% 173.66/174.07 end
% 173.66/174.07 substitution1:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 Z := Z
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 subsumption: (162) {G1,W14,D4,L3,V3,M3} P(11,15) { ! leq( Z, Y ), leq(
% 173.66/174.07 multiplication( star( X ), Z ), Y ), ! leq( multiplication( X, Y ), Z )
% 173.66/174.07 }.
% 173.66/174.07 parent0: (122297) {G1,W14,D4,L3,V3,M3} { ! leq( Z, Y ), ! leq(
% 173.66/174.07 multiplication( X, Y ), Z ), leq( multiplication( star( X ), Z ), Y ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 Z := Z
% 173.66/174.07 end
% 173.66/174.07 permutation0:
% 173.66/174.07 0 ==> 0
% 173.66/174.07 1 ==> 2
% 173.66/174.07 2 ==> 1
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 paramod: (122300) {G1,W11,D4,L2,V2,M2} { leq( star( X ), Y ), ! leq(
% 173.66/174.07 addition( multiplication( X, Y ), one ), Y ) }.
% 173.66/174.07 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 173.66/174.07 parent1[1; 1]: (15) {G0,W13,D4,L2,V3,M2} I { ! leq( addition(
% 173.66/174.07 multiplication( X, Y ), Z ), Y ), leq( multiplication( star( X ), Z ), Y
% 173.66/174.07 ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := star( X )
% 173.66/174.07 end
% 173.66/174.07 substitution1:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 Z := one
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 subsumption: (167) {G1,W11,D4,L2,V2,M2} P(5,15) { ! leq( addition(
% 173.66/174.07 multiplication( X, Y ), one ), Y ), leq( star( X ), Y ) }.
% 173.66/174.07 parent0: (122300) {G1,W11,D4,L2,V2,M2} { leq( star( X ), Y ), ! leq(
% 173.66/174.07 addition( multiplication( X, Y ), one ), Y ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 end
% 173.66/174.07 permutation0:
% 173.66/174.07 0 ==> 1
% 173.66/174.07 1 ==> 0
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 eqswap: (122302) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==> addition(
% 173.66/174.07 addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 173.66/174.07 parent0[0]: (23) {G1,W14,D4,L2,V3,M2} P(1,12) { ! addition( addition( X, Y
% 173.66/174.07 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 Z := Z
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 paramod: (122305) {G1,W15,D3,L3,V3,M3} { ! addition( X, Y ) ==> addition(
% 173.66/174.07 X, Y ), ! leq( Z, X ), leq( Z, addition( X, Y ) ) }.
% 173.66/174.07 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 173.66/174.07 ==> Y }.
% 173.66/174.07 parent1[0; 6]: (122302) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==>
% 173.66/174.07 addition( addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := Z
% 173.66/174.07 Y := X
% 173.66/174.07 end
% 173.66/174.07 substitution1:
% 173.66/174.07 X := Z
% 173.66/174.07 Y := X
% 173.66/174.07 Z := Y
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 eqrefl: (122354) {G0,W8,D3,L2,V3,M2} { ! leq( Z, X ), leq( Z, addition( X
% 173.66/174.07 , Y ) ) }.
% 173.66/174.07 parent0[0]: (122305) {G1,W15,D3,L3,V3,M3} { ! addition( X, Y ) ==>
% 173.66/174.07 addition( X, Y ), ! leq( Z, X ), leq( Z, addition( X, Y ) ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 Z := Z
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 subsumption: (226) {G2,W8,D3,L2,V3,M2} P(11,23);q { leq( X, addition( Y, Z
% 173.66/174.07 ) ), ! leq( X, Y ) }.
% 173.66/174.07 parent0: (122354) {G0,W8,D3,L2,V3,M2} { ! leq( Z, X ), leq( Z, addition( X
% 173.66/174.07 , Y ) ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := Y
% 173.66/174.07 Y := Z
% 173.66/174.07 Z := X
% 173.66/174.07 end
% 173.66/174.07 permutation0:
% 173.66/174.07 0 ==> 1
% 173.66/174.07 1 ==> 0
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 eqswap: (122356) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==> addition(
% 173.66/174.07 addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 173.66/174.07 parent0[0]: (23) {G1,W14,D4,L2,V3,M2} P(1,12) { ! addition( addition( X, Y
% 173.66/174.07 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 Z := Z
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 paramod: (122359) {G1,W12,D3,L2,V2,M2} { ! addition( X, Y ) ==> addition(
% 173.66/174.07 X, Y ), leq( X, addition( X, Y ) ) }.
% 173.66/174.07 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 173.66/174.07 parent1[0; 6]: (122356) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==>
% 173.66/174.07 addition( addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 end
% 173.66/174.07 substitution1:
% 173.66/174.07 X := X
% 173.66/174.07 Y := X
% 173.66/174.07 Z := Y
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 eqrefl: (122362) {G0,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 173.66/174.07 parent0[0]: (122359) {G1,W12,D3,L2,V2,M2} { ! addition( X, Y ) ==>
% 173.66/174.07 addition( X, Y ), leq( X, addition( X, Y ) ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 subsumption: (230) {G2,W5,D3,L1,V2,M1} P(3,23);q { leq( X, addition( X, Y )
% 173.66/174.07 ) }.
% 173.66/174.07 parent0: (122362) {G0,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 end
% 173.66/174.07 permutation0:
% 173.66/174.07 0 ==> 0
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 paramod: (122364) {G1,W7,D4,L1,V3,M1} { leq( X, addition( addition( X, Y )
% 173.66/174.07 , Z ) ) }.
% 173.66/174.07 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 173.66/174.07 ==> addition( addition( Z, Y ), X ) }.
% 173.66/174.07 parent1[0; 2]: (230) {G2,W5,D3,L1,V2,M1} P(3,23);q { leq( X, addition( X, Y
% 173.66/174.07 ) ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := Z
% 173.66/174.07 Y := Y
% 173.66/174.07 Z := X
% 173.66/174.07 end
% 173.66/174.07 substitution1:
% 173.66/174.07 X := X
% 173.66/174.07 Y := addition( Y, Z )
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 subsumption: (237) {G3,W7,D4,L1,V3,M1} P(1,230) { leq( X, addition(
% 173.66/174.07 addition( X, Y ), Z ) ) }.
% 173.66/174.07 parent0: (122364) {G1,W7,D4,L1,V3,M1} { leq( X, addition( addition( X, Y )
% 173.66/174.07 , Z ) ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 Z := Z
% 173.66/174.07 end
% 173.66/174.07 permutation0:
% 173.66/174.07 0 ==> 0
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 paramod: (122365) {G1,W5,D3,L1,V2,M1} { leq( X, addition( Y, X ) ) }.
% 173.66/174.07 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 173.66/174.07 }.
% 173.66/174.07 parent1[0; 2]: (230) {G2,W5,D3,L1,V2,M1} P(3,23);q { leq( X, addition( X, Y
% 173.66/174.07 ) ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 end
% 173.66/174.07 substitution1:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 subsumption: (238) {G3,W5,D3,L1,V2,M1} P(0,230) { leq( X, addition( Y, X )
% 173.66/174.07 ) }.
% 173.66/174.07 parent0: (122365) {G1,W5,D3,L1,V2,M1} { leq( X, addition( Y, X ) ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 end
% 173.66/174.07 permutation0:
% 173.66/174.07 0 ==> 0
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 paramod: (122368) {G1,W9,D4,L1,V3,M1} { leq( multiplication( X, Y ),
% 173.66/174.07 multiplication( addition( Z, X ), Y ) ) }.
% 173.66/174.07 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 173.66/174.07 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 173.66/174.07 parent1[0; 4]: (238) {G3,W5,D3,L1,V2,M1} P(0,230) { leq( X, addition( Y, X
% 173.66/174.07 ) ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := Z
% 173.66/174.07 Y := X
% 173.66/174.07 Z := Y
% 173.66/174.07 end
% 173.66/174.07 substitution1:
% 173.66/174.07 X := multiplication( X, Y )
% 173.66/174.07 Y := multiplication( Z, Y )
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 subsumption: (240) {G4,W9,D4,L1,V3,M1} P(8,238) { leq( multiplication( Z, Y
% 173.66/174.07 ), multiplication( addition( X, Z ), Y ) ) }.
% 173.66/174.07 parent0: (122368) {G1,W9,D4,L1,V3,M1} { leq( multiplication( X, Y ),
% 173.66/174.07 multiplication( addition( Z, X ), Y ) ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := Z
% 173.66/174.07 Y := Y
% 173.66/174.07 Z := X
% 173.66/174.07 end
% 173.66/174.07 permutation0:
% 173.66/174.07 0 ==> 0
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 eqswap: (122369) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X ) =
% 173.66/174.07 addition( addition( X, Y ), Z ) }.
% 173.66/174.07 parent0[0]: (24) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y ),
% 173.66/174.07 Z ) = addition( addition( Y, Z ), X ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 Z := Z
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 paramod: (122370) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( X, Y )
% 173.66/174.07 , Z ) ) }.
% 173.66/174.07 parent0[0]: (122369) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X
% 173.66/174.07 ) = addition( addition( X, Y ), Z ) }.
% 173.66/174.07 parent1[0; 2]: (238) {G3,W5,D3,L1,V2,M1} P(0,230) { leq( X, addition( Y, X
% 173.66/174.07 ) ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 Z := Z
% 173.66/174.07 end
% 173.66/174.07 substitution1:
% 173.66/174.07 X := X
% 173.66/174.07 Y := addition( Y, Z )
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 paramod: (122371) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( Z, X )
% 173.66/174.07 , Y ) ) }.
% 173.66/174.07 parent0[0]: (122369) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X
% 173.66/174.07 ) = addition( addition( X, Y ), Z ) }.
% 173.66/174.07 parent1[0; 2]: (122370) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition(
% 173.66/174.07 X, Y ), Z ) ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := Z
% 173.66/174.07 Y := X
% 173.66/174.07 Z := Y
% 173.66/174.07 end
% 173.66/174.07 substitution1:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 Z := Z
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 subsumption: (249) {G4,W7,D4,L1,V3,M1} P(24,238) { leq( Z, addition(
% 173.66/174.07 addition( Y, Z ), X ) ) }.
% 173.66/174.07 parent0: (122371) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( Z, X )
% 173.66/174.07 , Y ) ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := Z
% 173.66/174.07 Y := X
% 173.66/174.07 Z := Y
% 173.66/174.07 end
% 173.66/174.07 permutation0:
% 173.66/174.07 0 ==> 0
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 eqswap: (122373) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X
% 173.66/174.07 ) }.
% 173.66/174.07 parent0[0]: (35) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, !
% 173.66/174.07 leq( X, Y ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := Y
% 173.66/174.07 Y := X
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 paramod: (122375) {G1,W9,D2,L3,V2,M3} { X ==> Y, ! leq( X, Y ), ! leq( Y,
% 173.66/174.07 X ) }.
% 173.66/174.07 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 173.66/174.07 ==> Y }.
% 173.66/174.07 parent1[0; 2]: (122373) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), !
% 173.66/174.07 leq( Y, X ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 end
% 173.66/174.07 substitution1:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 subsumption: (477) {G2,W9,D2,L3,V2,M3} P(35,11) { ! leq( X, Y ), X = Y, !
% 173.66/174.07 leq( Y, X ) }.
% 173.66/174.07 parent0: (122375) {G1,W9,D2,L3,V2,M3} { X ==> Y, ! leq( X, Y ), ! leq( Y,
% 173.66/174.07 X ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 end
% 173.66/174.07 permutation0:
% 173.66/174.07 0 ==> 1
% 173.66/174.07 1 ==> 0
% 173.66/174.07 2 ==> 2
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 paramod: (122378) {G1,W8,D3,L2,V3,M2} { leq( X, Z ), ! leq( addition( Y, X
% 173.66/174.07 ), Z ) }.
% 173.66/174.07 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 173.66/174.07 ==> Y }.
% 173.66/174.07 parent1[0; 2]: (249) {G4,W7,D4,L1,V3,M1} P(24,238) { leq( Z, addition(
% 173.66/174.07 addition( Y, Z ), X ) ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := addition( Y, X )
% 173.66/174.07 Y := Z
% 173.66/174.07 end
% 173.66/174.07 substitution1:
% 173.66/174.07 X := Z
% 173.66/174.07 Y := Y
% 173.66/174.07 Z := X
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 subsumption: (511) {G5,W8,D3,L2,V3,M2} P(11,249) { leq( Y, Z ), ! leq(
% 173.66/174.07 addition( X, Y ), Z ) }.
% 173.66/174.07 parent0: (122378) {G1,W8,D3,L2,V3,M2} { leq( X, Z ), ! leq( addition( Y, X
% 173.66/174.07 ), Z ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := Y
% 173.66/174.07 Y := X
% 173.66/174.07 Z := Z
% 173.66/174.07 end
% 173.66/174.07 permutation0:
% 173.66/174.07 0 ==> 0
% 173.66/174.07 1 ==> 1
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 paramod: (122383) {G1,W8,D3,L2,V3,M2} { leq( X, Z ), ! leq( addition( X, Y
% 173.66/174.07 ), Z ) }.
% 173.66/174.07 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 173.66/174.07 ==> Y }.
% 173.66/174.07 parent1[0; 2]: (237) {G3,W7,D4,L1,V3,M1} P(1,230) { leq( X, addition(
% 173.66/174.07 addition( X, Y ), Z ) ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := addition( X, Y )
% 173.66/174.07 Y := Z
% 173.66/174.07 end
% 173.66/174.07 substitution1:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 Z := Z
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 subsumption: (524) {G4,W8,D3,L2,V3,M2} P(11,237) { leq( X, Z ), ! leq(
% 173.66/174.07 addition( X, Y ), Z ) }.
% 173.66/174.07 parent0: (122383) {G1,W8,D3,L2,V3,M2} { leq( X, Z ), ! leq( addition( X, Y
% 173.66/174.07 ), Z ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 Z := Z
% 173.66/174.07 end
% 173.66/174.07 permutation0:
% 173.66/174.07 0 ==> 0
% 173.66/174.07 1 ==> 1
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 resolution: (122387) {G1,W4,D3,L1,V1,M1} { leq( one, star( X ) ) }.
% 173.66/174.07 parent0[1]: (524) {G4,W8,D3,L2,V3,M2} P(11,237) { leq( X, Z ), ! leq(
% 173.66/174.07 addition( X, Y ), Z ) }.
% 173.66/174.07 parent1[0]: (14) {G0,W9,D5,L1,V1,M1} I { leq( addition( one, multiplication
% 173.66/174.07 ( star( X ), X ) ), star( X ) ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := one
% 173.66/174.07 Y := multiplication( star( X ), X )
% 173.66/174.07 Z := star( X )
% 173.66/174.07 end
% 173.66/174.07 substitution1:
% 173.66/174.07 X := X
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 subsumption: (718) {G5,W4,D3,L1,V1,M1} R(524,14) { leq( one, star( X ) )
% 173.66/174.07 }.
% 173.66/174.07 parent0: (122387) {G1,W4,D3,L1,V1,M1} { leq( one, star( X ) ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 end
% 173.66/174.07 permutation0:
% 173.66/174.07 0 ==> 0
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 paramod: (122389) {G1,W9,D2,L3,V3,M3} { ! leq( Y, Z ), ! leq( X, Y ), leq
% 173.66/174.07 ( X, Z ) }.
% 173.66/174.07 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 173.66/174.07 ==> Y }.
% 173.66/174.07 parent1[1; 2]: (524) {G4,W8,D3,L2,V3,M2} P(11,237) { leq( X, Z ), ! leq(
% 173.66/174.07 addition( X, Y ), Z ) }.
% 173.66/174.07 substitution0:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 end
% 173.66/174.07 substitution1:
% 173.66/174.07 X := X
% 173.66/174.07 Y := Y
% 173.66/174.07 Z := Z
% 173.66/174.07 end
% 173.66/174.07
% 173.66/174.07 subsumption: (730) {G5,W9,D2,L3,V3,M3} P(11,524) { leq( X, Z ), ! leq( Y, Z
% 173.66/174.07 ), ! leq( X, Y ) }.
% 173.66/174.08 parent0: (122389) {G1,W9,D2,L3,V3,M3} { ! leq( Y, Z ), ! leq( X, Y ), leq
% 173.66/174.08 ( X, Z ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 Y := Y
% 173.66/174.08 Z := Z
% 173.66/174.08 end
% 173.66/174.08 permutation0:
% 173.66/174.08 0 ==> 1
% 173.66/174.08 1 ==> 2
% 173.66/174.08 2 ==> 0
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 eqswap: (122391) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X
% 173.66/174.08 ) }.
% 173.66/174.08 parent0[0]: (35) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, !
% 173.66/174.08 leq( X, Y ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := Y
% 173.66/174.08 Y := X
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 resolution: (122392) {G2,W7,D4,L1,V1,M1} { star( X ) ==> addition( star( X
% 173.66/174.08 ), one ) }.
% 173.66/174.08 parent0[1]: (122391) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq(
% 173.66/174.08 Y, X ) }.
% 173.66/174.08 parent1[0]: (718) {G5,W4,D3,L1,V1,M1} R(524,14) { leq( one, star( X ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := star( X )
% 173.66/174.08 Y := one
% 173.66/174.08 end
% 173.66/174.08 substitution1:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 eqswap: (122393) {G2,W7,D4,L1,V1,M1} { addition( star( X ), one ) ==> star
% 173.66/174.08 ( X ) }.
% 173.66/174.08 parent0[0]: (122392) {G2,W7,D4,L1,V1,M1} { star( X ) ==> addition( star( X
% 173.66/174.08 ), one ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 subsumption: (732) {G6,W7,D4,L1,V1,M1} R(718,35) { addition( star( X ), one
% 173.66/174.08 ) ==> star( X ) }.
% 173.66/174.08 parent0: (122393) {G2,W7,D4,L1,V1,M1} { addition( star( X ), one ) ==>
% 173.66/174.08 star( X ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08 permutation0:
% 173.66/174.08 0 ==> 0
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 eqswap: (122394) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 173.66/174.08 ) }.
% 173.66/174.08 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 173.66/174.08 ==> Y }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 Y := Y
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 resolution: (122395) {G1,W7,D4,L1,V1,M1} { star( X ) ==> addition( one,
% 173.66/174.08 star( X ) ) }.
% 173.66/174.08 parent0[1]: (122394) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq(
% 173.66/174.08 X, Y ) }.
% 173.66/174.08 parent1[0]: (718) {G5,W4,D3,L1,V1,M1} R(524,14) { leq( one, star( X ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := one
% 173.66/174.08 Y := star( X )
% 173.66/174.08 end
% 173.66/174.08 substitution1:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 eqswap: (122396) {G1,W7,D4,L1,V1,M1} { addition( one, star( X ) ) ==> star
% 173.66/174.08 ( X ) }.
% 173.66/174.08 parent0[0]: (122395) {G1,W7,D4,L1,V1,M1} { star( X ) ==> addition( one,
% 173.66/174.08 star( X ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 subsumption: (735) {G6,W7,D4,L1,V1,M1} R(718,11) { addition( one, star( X )
% 173.66/174.08 ) ==> star( X ) }.
% 173.66/174.08 parent0: (122396) {G1,W7,D4,L1,V1,M1} { addition( one, star( X ) ) ==>
% 173.66/174.08 star( X ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08 permutation0:
% 173.66/174.08 0 ==> 0
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 resolution: (122397) {G1,W7,D4,L1,V1,M1} { leq( multiplication( star( X )
% 173.66/174.08 , X ), star( X ) ) }.
% 173.66/174.08 parent0[1]: (511) {G5,W8,D3,L2,V3,M2} P(11,249) { leq( Y, Z ), ! leq(
% 173.66/174.08 addition( X, Y ), Z ) }.
% 173.66/174.08 parent1[0]: (14) {G0,W9,D5,L1,V1,M1} I { leq( addition( one, multiplication
% 173.66/174.08 ( star( X ), X ) ), star( X ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := one
% 173.66/174.08 Y := multiplication( star( X ), X )
% 173.66/174.08 Z := star( X )
% 173.66/174.08 end
% 173.66/174.08 substitution1:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 subsumption: (881) {G6,W7,D4,L1,V1,M1} R(511,14) { leq( multiplication(
% 173.66/174.08 star( X ), X ), star( X ) ) }.
% 173.66/174.08 parent0: (122397) {G1,W7,D4,L1,V1,M1} { leq( multiplication( star( X ), X
% 173.66/174.08 ), star( X ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08 permutation0:
% 173.66/174.08 0 ==> 0
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 resolution: (122398) {G1,W7,D4,L1,V1,M1} { leq( multiplication( X, star( X
% 173.66/174.08 ) ), star( X ) ) }.
% 173.66/174.08 parent0[1]: (511) {G5,W8,D3,L2,V3,M2} P(11,249) { leq( Y, Z ), ! leq(
% 173.66/174.08 addition( X, Y ), Z ) }.
% 173.66/174.08 parent1[0]: (13) {G0,W9,D5,L1,V1,M1} I { leq( addition( one, multiplication
% 173.66/174.08 ( X, star( X ) ) ), star( X ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := one
% 173.66/174.08 Y := multiplication( X, star( X ) )
% 173.66/174.08 Z := star( X )
% 173.66/174.08 end
% 173.66/174.08 substitution1:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 subsumption: (882) {G6,W7,D4,L1,V1,M1} R(511,13) { leq( multiplication( X,
% 173.66/174.08 star( X ) ), star( X ) ) }.
% 173.66/174.08 parent0: (122398) {G1,W7,D4,L1,V1,M1} { leq( multiplication( X, star( X )
% 173.66/174.08 ), star( X ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08 permutation0:
% 173.66/174.08 0 ==> 0
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 paramod: (122400) {G1,W12,D4,L2,V4,M2} { ! leq( multiplication( addition(
% 173.66/174.08 X, Z ), Y ), T ), leq( multiplication( Z, Y ), T ) }.
% 173.66/174.08 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 173.66/174.08 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 173.66/174.08 parent1[1; 2]: (511) {G5,W8,D3,L2,V3,M2} P(11,249) { leq( Y, Z ), ! leq(
% 173.66/174.08 addition( X, Y ), Z ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 Y := Z
% 173.66/174.08 Z := Y
% 173.66/174.08 end
% 173.66/174.08 substitution1:
% 173.66/174.08 X := multiplication( X, Y )
% 173.66/174.08 Y := multiplication( Z, Y )
% 173.66/174.08 Z := T
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 subsumption: (885) {G6,W12,D4,L2,V4,M2} P(8,511) { leq( multiplication( Z,
% 173.66/174.08 Y ), T ), ! leq( multiplication( addition( X, Z ), Y ), T ) }.
% 173.66/174.08 parent0: (122400) {G1,W12,D4,L2,V4,M2} { ! leq( multiplication( addition(
% 173.66/174.08 X, Z ), Y ), T ), leq( multiplication( Z, Y ), T ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 Y := Y
% 173.66/174.08 Z := Z
% 173.66/174.08 T := T
% 173.66/174.08 end
% 173.66/174.08 permutation0:
% 173.66/174.08 0 ==> 1
% 173.66/174.08 1 ==> 0
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 paramod: (122402) {G1,W12,D4,L2,V4,M2} { ! leq( multiplication( X,
% 173.66/174.08 addition( Y, Z ) ), T ), leq( multiplication( X, Z ), T ) }.
% 173.66/174.08 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 173.66/174.08 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 173.66/174.08 parent1[1; 2]: (511) {G5,W8,D3,L2,V3,M2} P(11,249) { leq( Y, Z ), ! leq(
% 173.66/174.08 addition( X, Y ), Z ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 Y := Y
% 173.66/174.08 Z := Z
% 173.66/174.08 end
% 173.66/174.08 substitution1:
% 173.66/174.08 X := multiplication( X, Y )
% 173.66/174.08 Y := multiplication( X, Z )
% 173.66/174.08 Z := T
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 subsumption: (886) {G6,W12,D4,L2,V4,M2} P(7,511) { leq( multiplication( X,
% 173.66/174.08 Z ), T ), ! leq( multiplication( X, addition( Y, Z ) ), T ) }.
% 173.66/174.08 parent0: (122402) {G1,W12,D4,L2,V4,M2} { ! leq( multiplication( X,
% 173.66/174.08 addition( Y, Z ) ), T ), leq( multiplication( X, Z ), T ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 Y := Y
% 173.66/174.08 Z := Z
% 173.66/174.08 T := T
% 173.66/174.08 end
% 173.66/174.08 permutation0:
% 173.66/174.08 0 ==> 1
% 173.66/174.08 1 ==> 0
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 eqswap: (122403) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X
% 173.66/174.08 ) }.
% 173.66/174.08 parent0[0]: (35) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, !
% 173.66/174.08 leq( X, Y ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := Y
% 173.66/174.08 Y := X
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 resolution: (122404) {G2,W10,D5,L1,V1,M1} { star( X ) ==> addition( star(
% 173.66/174.08 X ), multiplication( star( X ), X ) ) }.
% 173.66/174.08 parent0[1]: (122403) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq(
% 173.66/174.08 Y, X ) }.
% 173.66/174.08 parent1[0]: (881) {G6,W7,D4,L1,V1,M1} R(511,14) { leq( multiplication( star
% 173.66/174.08 ( X ), X ), star( X ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := star( X )
% 173.66/174.08 Y := multiplication( star( X ), X )
% 173.66/174.08 end
% 173.66/174.08 substitution1:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 eqswap: (122405) {G2,W10,D5,L1,V1,M1} { addition( star( X ),
% 173.66/174.08 multiplication( star( X ), X ) ) ==> star( X ) }.
% 173.66/174.08 parent0[0]: (122404) {G2,W10,D5,L1,V1,M1} { star( X ) ==> addition( star(
% 173.66/174.08 X ), multiplication( star( X ), X ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 subsumption: (888) {G7,W10,D5,L1,V1,M1} R(881,35) { addition( star( X ),
% 173.66/174.08 multiplication( star( X ), X ) ) ==> star( X ) }.
% 173.66/174.08 parent0: (122405) {G2,W10,D5,L1,V1,M1} { addition( star( X ),
% 173.66/174.08 multiplication( star( X ), X ) ) ==> star( X ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08 permutation0:
% 173.66/174.08 0 ==> 0
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 eqswap: (122407) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Z ) ==>
% 173.66/174.08 multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ),
% 173.66/174.08 multiplication( X, Z ) ) }.
% 173.66/174.08 parent0[0]: (63) {G1,W16,D4,L2,V3,M2} P(7,12) { ! multiplication( X,
% 173.66/174.08 addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 173.66/174.08 ), multiplication( X, Z ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 Y := Y
% 173.66/174.08 Z := Z
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 paramod: (122409) {G2,W17,D4,L2,V2,M2} { ! multiplication( X, star( Y ) )
% 173.66/174.08 ==> multiplication( X, star( Y ) ), leq( multiplication( X, one ),
% 173.66/174.08 multiplication( X, star( Y ) ) ) }.
% 173.66/174.08 parent0[0]: (735) {G6,W7,D4,L1,V1,M1} R(718,11) { addition( one, star( X )
% 173.66/174.08 ) ==> star( X ) }.
% 173.66/174.08 parent1[0; 8]: (122407) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Z )
% 173.66/174.08 ==> multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ),
% 173.66/174.08 multiplication( X, Z ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := Y
% 173.66/174.08 end
% 173.66/174.08 substitution1:
% 173.66/174.08 X := X
% 173.66/174.08 Y := one
% 173.66/174.08 Z := star( Y )
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 eqrefl: (122410) {G0,W8,D4,L1,V2,M1} { leq( multiplication( X, one ),
% 173.66/174.08 multiplication( X, star( Y ) ) ) }.
% 173.66/174.08 parent0[0]: (122409) {G2,W17,D4,L2,V2,M2} { ! multiplication( X, star( Y )
% 173.66/174.08 ) ==> multiplication( X, star( Y ) ), leq( multiplication( X, one ),
% 173.66/174.08 multiplication( X, star( Y ) ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 Y := Y
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 paramod: (122411) {G1,W6,D4,L1,V2,M1} { leq( X, multiplication( X, star( Y
% 173.66/174.08 ) ) ) }.
% 173.66/174.08 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 173.66/174.08 parent1[0; 1]: (122410) {G0,W8,D4,L1,V2,M1} { leq( multiplication( X, one
% 173.66/174.08 ), multiplication( X, star( Y ) ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08 substitution1:
% 173.66/174.08 X := X
% 173.66/174.08 Y := Y
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 subsumption: (1585) {G7,W6,D4,L1,V2,M1} P(735,63);q;d(5) { leq( Y,
% 173.66/174.08 multiplication( Y, star( X ) ) ) }.
% 173.66/174.08 parent0: (122411) {G1,W6,D4,L1,V2,M1} { leq( X, multiplication( X, star( Y
% 173.66/174.08 ) ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := Y
% 173.66/174.08 Y := X
% 173.66/174.08 end
% 173.66/174.08 permutation0:
% 173.66/174.08 0 ==> 0
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 eqswap: (122413) {G1,W16,D4,L2,V3,M2} { ! multiplication( Y, Z ) ==>
% 173.66/174.08 multiplication( addition( X, Y ), Z ), leq( multiplication( X, Z ),
% 173.66/174.08 multiplication( Y, Z ) ) }.
% 173.66/174.08 parent0[0]: (94) {G1,W16,D4,L2,V3,M2} P(8,12) { ! multiplication( addition
% 173.66/174.08 ( X, Z ), Y ) ==> multiplication( Z, Y ), leq( multiplication( X, Y ),
% 173.66/174.08 multiplication( Z, Y ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 Y := Z
% 173.66/174.08 Z := Y
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 paramod: (122415) {G2,W17,D4,L2,V2,M2} { ! multiplication( star( X ), Y )
% 173.66/174.08 ==> multiplication( star( X ), Y ), leq( multiplication( one, Y ),
% 173.66/174.08 multiplication( star( X ), Y ) ) }.
% 173.66/174.08 parent0[0]: (735) {G6,W7,D4,L1,V1,M1} R(718,11) { addition( one, star( X )
% 173.66/174.08 ) ==> star( X ) }.
% 173.66/174.08 parent1[0; 7]: (122413) {G1,W16,D4,L2,V3,M2} { ! multiplication( Y, Z )
% 173.66/174.08 ==> multiplication( addition( X, Y ), Z ), leq( multiplication( X, Z ),
% 173.66/174.08 multiplication( Y, Z ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08 substitution1:
% 173.66/174.08 X := one
% 173.66/174.08 Y := star( X )
% 173.66/174.08 Z := Y
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 eqrefl: (122416) {G0,W8,D4,L1,V2,M1} { leq( multiplication( one, Y ),
% 173.66/174.08 multiplication( star( X ), Y ) ) }.
% 173.66/174.08 parent0[0]: (122415) {G2,W17,D4,L2,V2,M2} { ! multiplication( star( X ), Y
% 173.66/174.08 ) ==> multiplication( star( X ), Y ), leq( multiplication( one, Y ),
% 173.66/174.08 multiplication( star( X ), Y ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 Y := Y
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 paramod: (122417) {G1,W6,D4,L1,V2,M1} { leq( X, multiplication( star( Y )
% 173.66/174.08 , X ) ) }.
% 173.66/174.08 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 173.66/174.08 parent1[0; 1]: (122416) {G0,W8,D4,L1,V2,M1} { leq( multiplication( one, Y
% 173.66/174.08 ), multiplication( star( X ), Y ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08 substitution1:
% 173.66/174.08 X := Y
% 173.66/174.08 Y := X
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 subsumption: (2870) {G7,W6,D4,L1,V2,M1} P(735,94);q;d(6) { leq( Y,
% 173.66/174.08 multiplication( star( X ), Y ) ) }.
% 173.66/174.08 parent0: (122417) {G1,W6,D4,L1,V2,M1} { leq( X, multiplication( star( Y )
% 173.66/174.08 , X ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := Y
% 173.66/174.08 Y := X
% 173.66/174.08 end
% 173.66/174.08 permutation0:
% 173.66/174.08 0 ==> 0
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 resolution: (122418) {G3,W8,D5,L1,V3,M1} { leq( X, addition(
% 173.66/174.08 multiplication( star( Y ), X ), Z ) ) }.
% 173.66/174.08 parent0[1]: (226) {G2,W8,D3,L2,V3,M2} P(11,23);q { leq( X, addition( Y, Z )
% 173.66/174.08 ), ! leq( X, Y ) }.
% 173.66/174.08 parent1[0]: (2870) {G7,W6,D4,L1,V2,M1} P(735,94);q;d(6) { leq( Y,
% 173.66/174.08 multiplication( star( X ), Y ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 Y := multiplication( star( Y ), X )
% 173.66/174.08 Z := Z
% 173.66/174.08 end
% 173.66/174.08 substitution1:
% 173.66/174.08 X := Y
% 173.66/174.08 Y := X
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 subsumption: (2878) {G8,W8,D5,L1,V3,M1} R(2870,226) { leq( X, addition(
% 173.66/174.08 multiplication( star( Y ), X ), Z ) ) }.
% 173.66/174.08 parent0: (122418) {G3,W8,D5,L1,V3,M1} { leq( X, addition( multiplication(
% 173.66/174.08 star( Y ), X ), Z ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 Y := Y
% 173.66/174.08 Z := Z
% 173.66/174.08 end
% 173.66/174.08 permutation0:
% 173.66/174.08 0 ==> 0
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 paramod: (122420) {G1,W9,D4,L2,V3,M2} { leq( X, Z ), ! leq( multiplication
% 173.66/174.08 ( star( Y ), X ), Z ) }.
% 173.66/174.08 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 173.66/174.08 ==> Y }.
% 173.66/174.08 parent1[0; 2]: (2878) {G8,W8,D5,L1,V3,M1} R(2870,226) { leq( X, addition(
% 173.66/174.08 multiplication( star( Y ), X ), Z ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := multiplication( star( Y ), X )
% 173.66/174.08 Y := Z
% 173.66/174.08 end
% 173.66/174.08 substitution1:
% 173.66/174.08 X := X
% 173.66/174.08 Y := Y
% 173.66/174.08 Z := Z
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 subsumption: (3022) {G9,W9,D4,L2,V3,M2} P(11,2878) { leq( Y, Z ), ! leq(
% 173.66/174.08 multiplication( star( X ), Y ), Z ) }.
% 173.66/174.08 parent0: (122420) {G1,W9,D4,L2,V3,M2} { leq( X, Z ), ! leq( multiplication
% 173.66/174.08 ( star( Y ), X ), Z ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := Y
% 173.66/174.08 Y := X
% 173.66/174.08 Z := Z
% 173.66/174.08 end
% 173.66/174.08 permutation0:
% 173.66/174.08 0 ==> 0
% 173.66/174.08 1 ==> 1
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 eqswap: (122421) {G1,W11,D4,L1,V2,M1} { multiplication( addition( one, Y )
% 173.66/174.08 , X ) = addition( X, multiplication( Y, X ) ) }.
% 173.66/174.08 parent0[0]: (96) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( X, multiplication
% 173.66/174.08 ( Y, X ) ) = multiplication( addition( one, Y ), X ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 Y := Y
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 paramod: (122442) {G2,W11,D4,L1,V1,M1} { multiplication( addition( one, X
% 173.66/174.08 ), X ) = multiplication( X, addition( one, X ) ) }.
% 173.66/174.08 parent0[0]: (65) {G1,W11,D4,L1,V2,M1} P(5,7) { addition( X, multiplication
% 173.66/174.08 ( X, Y ) ) = multiplication( X, addition( one, Y ) ) }.
% 173.66/174.08 parent1[0; 6]: (122421) {G1,W11,D4,L1,V2,M1} { multiplication( addition(
% 173.66/174.08 one, Y ), X ) = addition( X, multiplication( Y, X ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 Y := X
% 173.66/174.08 end
% 173.66/174.08 substitution1:
% 173.66/174.08 X := X
% 173.66/174.08 Y := X
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 eqswap: (122444) {G2,W11,D4,L1,V1,M1} { multiplication( X, addition( one,
% 173.66/174.08 X ) ) = multiplication( addition( one, X ), X ) }.
% 173.66/174.08 parent0[0]: (122442) {G2,W11,D4,L1,V1,M1} { multiplication( addition( one
% 173.66/174.08 , X ), X ) = multiplication( X, addition( one, X ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 subsumption: (3177) {G2,W11,D4,L1,V1,M1} P(96,65) { multiplication( X,
% 173.66/174.08 addition( one, X ) ) ==> multiplication( addition( one, X ), X ) }.
% 173.66/174.08 parent0: (122444) {G2,W11,D4,L1,V1,M1} { multiplication( X, addition( one
% 173.66/174.08 , X ) ) = multiplication( addition( one, X ), X ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08 permutation0:
% 173.66/174.08 0 ==> 0
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 resolution: (122445) {G7,W4,D3,L1,V1,M1} { leq( X, star( X ) ) }.
% 173.66/174.08 parent0[1]: (3022) {G9,W9,D4,L2,V3,M2} P(11,2878) { leq( Y, Z ), ! leq(
% 173.66/174.08 multiplication( star( X ), Y ), Z ) }.
% 173.66/174.08 parent1[0]: (881) {G6,W7,D4,L1,V1,M1} R(511,14) { leq( multiplication( star
% 173.66/174.08 ( X ), X ), star( X ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 Y := X
% 173.66/174.08 Z := star( X )
% 173.66/174.08 end
% 173.66/174.08 substitution1:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 subsumption: (8634) {G10,W4,D3,L1,V1,M1} R(3022,881) { leq( X, star( X ) )
% 173.66/174.08 }.
% 173.66/174.08 parent0: (122445) {G7,W4,D3,L1,V1,M1} { leq( X, star( X ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08 permutation0:
% 173.66/174.08 0 ==> 0
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 resolution: (122447) {G3,W8,D3,L2,V1,M2} { ! leq( star( X ), X ), star( X
% 173.66/174.08 ) = X }.
% 173.66/174.08 parent0[2]: (477) {G2,W9,D2,L3,V2,M3} P(35,11) { ! leq( X, Y ), X = Y, !
% 173.66/174.08 leq( Y, X ) }.
% 173.66/174.08 parent1[0]: (8634) {G10,W4,D3,L1,V1,M1} R(3022,881) { leq( X, star( X ) )
% 173.66/174.08 }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := star( X )
% 173.66/174.08 Y := X
% 173.66/174.08 end
% 173.66/174.08 substitution1:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 subsumption: (8649) {G11,W8,D3,L2,V1,M2} R(8634,477) { star( X ) ==> X, !
% 173.66/174.08 leq( star( X ), X ) }.
% 173.66/174.08 parent0: (122447) {G3,W8,D3,L2,V1,M2} { ! leq( star( X ), X ), star( X ) =
% 173.66/174.08 X }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08 permutation0:
% 173.66/174.08 0 ==> 1
% 173.66/174.08 1 ==> 0
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 resolution: (122448) {G6,W7,D3,L2,V2,M2} { leq( X, star( Y ) ), ! leq( X,
% 173.66/174.08 Y ) }.
% 173.66/174.08 parent0[1]: (730) {G5,W9,D2,L3,V3,M3} P(11,524) { leq( X, Z ), ! leq( Y, Z
% 173.66/174.08 ), ! leq( X, Y ) }.
% 173.66/174.08 parent1[0]: (8634) {G10,W4,D3,L1,V1,M1} R(3022,881) { leq( X, star( X ) )
% 173.66/174.08 }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 Y := Y
% 173.66/174.08 Z := star( Y )
% 173.66/174.08 end
% 173.66/174.08 substitution1:
% 173.66/174.08 X := Y
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 subsumption: (8650) {G11,W7,D3,L2,V2,M2} R(8634,730) { leq( X, star( Y ) )
% 173.66/174.08 , ! leq( X, Y ) }.
% 173.66/174.08 parent0: (122448) {G6,W7,D3,L2,V2,M2} { leq( X, star( Y ) ), ! leq( X, Y )
% 173.66/174.08 }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 Y := Y
% 173.66/174.08 end
% 173.66/174.08 permutation0:
% 173.66/174.08 0 ==> 0
% 173.66/174.08 1 ==> 1
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 eqswap: (122450) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X
% 173.66/174.08 ) }.
% 173.66/174.08 parent0[0]: (35) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, !
% 173.66/174.08 leq( X, Y ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := Y
% 173.66/174.08 Y := X
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 resolution: (122451) {G2,W7,D4,L1,V1,M1} { star( X ) ==> addition( star( X
% 173.66/174.08 ), X ) }.
% 173.66/174.08 parent0[1]: (122450) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq(
% 173.66/174.08 Y, X ) }.
% 173.66/174.08 parent1[0]: (8634) {G10,W4,D3,L1,V1,M1} R(3022,881) { leq( X, star( X ) )
% 173.66/174.08 }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := star( X )
% 173.66/174.08 Y := X
% 173.66/174.08 end
% 173.66/174.08 substitution1:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 eqswap: (122452) {G2,W7,D4,L1,V1,M1} { addition( star( X ), X ) ==> star(
% 173.66/174.08 X ) }.
% 173.66/174.08 parent0[0]: (122451) {G2,W7,D4,L1,V1,M1} { star( X ) ==> addition( star( X
% 173.66/174.08 ), X ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 subsumption: (8654) {G11,W7,D4,L1,V1,M1} R(8634,35) { addition( star( X ),
% 173.66/174.08 X ) ==> star( X ) }.
% 173.66/174.08 parent0: (122452) {G2,W7,D4,L1,V1,M1} { addition( star( X ), X ) ==> star
% 173.66/174.08 ( X ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08 permutation0:
% 173.66/174.08 0 ==> 0
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 paramod: (122454) {G5,W8,D4,L1,V2,M1} { leq( multiplication( X, Y ),
% 173.66/174.08 multiplication( star( X ), Y ) ) }.
% 173.66/174.08 parent0[0]: (8654) {G11,W7,D4,L1,V1,M1} R(8634,35) { addition( star( X ), X
% 173.66/174.08 ) ==> star( X ) }.
% 173.66/174.08 parent1[0; 5]: (240) {G4,W9,D4,L1,V3,M1} P(8,238) { leq( multiplication( Z
% 173.66/174.08 , Y ), multiplication( addition( X, Z ), Y ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08 substitution1:
% 173.66/174.08 X := star( X )
% 173.66/174.08 Y := Y
% 173.66/174.08 Z := X
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 subsumption: (8966) {G12,W8,D4,L1,V2,M1} P(8654,240) { leq( multiplication
% 173.66/174.08 ( X, Y ), multiplication( star( X ), Y ) ) }.
% 173.66/174.08 parent0: (122454) {G5,W8,D4,L1,V2,M1} { leq( multiplication( X, Y ),
% 173.66/174.08 multiplication( star( X ), Y ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 Y := Y
% 173.66/174.08 end
% 173.66/174.08 permutation0:
% 173.66/174.08 0 ==> 0
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 resolution: (122456) {G2,W13,D4,L2,V1,M2} { ! leq( star( X ), star( X ) )
% 173.66/174.08 , leq( multiplication( star( X ), star( X ) ), star( X ) ) }.
% 173.66/174.08 parent0[2]: (162) {G1,W14,D4,L3,V3,M3} P(11,15) { ! leq( Z, Y ), leq(
% 173.66/174.08 multiplication( star( X ), Z ), Y ), ! leq( multiplication( X, Y ), Z )
% 173.66/174.08 }.
% 173.66/174.08 parent1[0]: (882) {G6,W7,D4,L1,V1,M1} R(511,13) { leq( multiplication( X,
% 173.66/174.08 star( X ) ), star( X ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 Y := star( X )
% 173.66/174.08 Z := star( X )
% 173.66/174.08 end
% 173.66/174.08 substitution1:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 resolution: (122457) {G2,W8,D4,L1,V1,M1} { leq( multiplication( star( X )
% 173.66/174.08 , star( X ) ), star( X ) ) }.
% 173.66/174.08 parent0[0]: (122456) {G2,W13,D4,L2,V1,M2} { ! leq( star( X ), star( X ) )
% 173.66/174.08 , leq( multiplication( star( X ), star( X ) ), star( X ) ) }.
% 173.66/174.08 parent1[0]: (20) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08 substitution1:
% 173.66/174.08 X := star( X )
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 subsumption: (9455) {G7,W8,D4,L1,V1,M1} R(162,882);r(20) { leq(
% 173.66/174.08 multiplication( star( X ), star( X ) ), star( X ) ) }.
% 173.66/174.08 parent0: (122457) {G2,W8,D4,L1,V1,M1} { leq( multiplication( star( X ),
% 173.66/174.08 star( X ) ), star( X ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08 permutation0:
% 173.66/174.08 0 ==> 0
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 resolution: (122458) {G12,W9,D5,L1,V2,M1} { leq( multiplication( X, Y ),
% 173.66/174.08 star( multiplication( star( X ), Y ) ) ) }.
% 173.66/174.08 parent0[1]: (8650) {G11,W7,D3,L2,V2,M2} R(8634,730) { leq( X, star( Y ) ),
% 173.66/174.08 ! leq( X, Y ) }.
% 173.66/174.08 parent1[0]: (8966) {G12,W8,D4,L1,V2,M1} P(8654,240) { leq( multiplication(
% 173.66/174.08 X, Y ), multiplication( star( X ), Y ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := multiplication( X, Y )
% 173.66/174.08 Y := multiplication( star( X ), Y )
% 173.66/174.08 end
% 173.66/174.08 substitution1:
% 173.66/174.08 X := X
% 173.66/174.08 Y := Y
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 subsumption: (9871) {G13,W9,D5,L1,V2,M1} R(8966,8650) { leq( multiplication
% 173.66/174.08 ( X, Y ), star( multiplication( star( X ), Y ) ) ) }.
% 173.66/174.08 parent0: (122458) {G12,W9,D5,L1,V2,M1} { leq( multiplication( X, Y ), star
% 173.66/174.08 ( multiplication( star( X ), Y ) ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 Y := Y
% 173.66/174.08 end
% 173.66/174.08 permutation0:
% 173.66/174.08 0 ==> 0
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 resolution: (122459) {G3,W16,D4,L2,V1,M2} { multiplication( star( X ),
% 173.66/174.08 star( X ) ) = star( X ), ! leq( star( X ), multiplication( star( X ),
% 173.66/174.08 star( X ) ) ) }.
% 173.66/174.08 parent0[0]: (477) {G2,W9,D2,L3,V2,M3} P(35,11) { ! leq( X, Y ), X = Y, !
% 173.66/174.08 leq( Y, X ) }.
% 173.66/174.08 parent1[0]: (9455) {G7,W8,D4,L1,V1,M1} R(162,882);r(20) { leq(
% 173.66/174.08 multiplication( star( X ), star( X ) ), star( X ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := multiplication( star( X ), star( X ) )
% 173.66/174.08 Y := star( X )
% 173.66/174.08 end
% 173.66/174.08 substitution1:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 resolution: (122461) {G4,W8,D4,L1,V1,M1} { multiplication( star( X ), star
% 173.66/174.08 ( X ) ) = star( X ) }.
% 173.66/174.08 parent0[1]: (122459) {G3,W16,D4,L2,V1,M2} { multiplication( star( X ),
% 173.66/174.08 star( X ) ) = star( X ), ! leq( star( X ), multiplication( star( X ),
% 173.66/174.08 star( X ) ) ) }.
% 173.66/174.08 parent1[0]: (1585) {G7,W6,D4,L1,V2,M1} P(735,63);q;d(5) { leq( Y,
% 173.66/174.08 multiplication( Y, star( X ) ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08 substitution1:
% 173.66/174.08 X := X
% 173.66/174.08 Y := star( X )
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 subsumption: (10034) {G8,W8,D4,L1,V1,M1} R(9455,477);r(1585) {
% 173.66/174.08 multiplication( star( X ), star( X ) ) ==> star( X ) }.
% 173.66/174.08 parent0: (122461) {G4,W8,D4,L1,V1,M1} { multiplication( star( X ), star( X
% 173.66/174.08 ) ) = star( X ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08 permutation0:
% 173.66/174.08 0 ==> 0
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 paramod: (122465) {G2,W13,D4,L2,V1,M2} { ! leq( addition( star( X ), one )
% 173.66/174.08 , star( X ) ), leq( star( star( X ) ), star( X ) ) }.
% 173.66/174.08 parent0[0]: (10034) {G8,W8,D4,L1,V1,M1} R(9455,477);r(1585) {
% 173.66/174.08 multiplication( star( X ), star( X ) ) ==> star( X ) }.
% 173.66/174.08 parent1[0; 3]: (167) {G1,W11,D4,L2,V2,M2} P(5,15) { ! leq( addition(
% 173.66/174.08 multiplication( X, Y ), one ), Y ), leq( star( X ), Y ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08 substitution1:
% 173.66/174.08 X := star( X )
% 173.66/174.08 Y := star( X )
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 paramod: (122466) {G3,W11,D4,L2,V1,M2} { ! leq( star( X ), star( X ) ),
% 173.66/174.08 leq( star( star( X ) ), star( X ) ) }.
% 173.66/174.08 parent0[0]: (732) {G6,W7,D4,L1,V1,M1} R(718,35) { addition( star( X ), one
% 173.66/174.08 ) ==> star( X ) }.
% 173.66/174.08 parent1[0; 2]: (122465) {G2,W13,D4,L2,V1,M2} { ! leq( addition( star( X )
% 173.66/174.08 , one ), star( X ) ), leq( star( star( X ) ), star( X ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08 substitution1:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 resolution: (122467) {G2,W6,D4,L1,V1,M1} { leq( star( star( X ) ), star( X
% 173.66/174.08 ) ) }.
% 173.66/174.08 parent0[0]: (122466) {G3,W11,D4,L2,V1,M2} { ! leq( star( X ), star( X ) )
% 173.66/174.08 , leq( star( star( X ) ), star( X ) ) }.
% 173.66/174.08 parent1[0]: (20) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08 substitution1:
% 173.66/174.08 X := star( X )
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 subsumption: (10038) {G9,W6,D4,L1,V1,M1} P(10034,167);d(732);r(20) { leq(
% 173.66/174.08 star( star( X ) ), star( X ) ) }.
% 173.66/174.08 parent0: (122467) {G2,W6,D4,L1,V1,M1} { leq( star( star( X ) ), star( X )
% 173.66/174.08 ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08 permutation0:
% 173.66/174.08 0 ==> 0
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 eqswap: (122468) {G11,W8,D3,L2,V1,M2} { X ==> star( X ), ! leq( star( X )
% 173.66/174.08 , X ) }.
% 173.66/174.08 parent0[0]: (8649) {G11,W8,D3,L2,V1,M2} R(8634,477) { star( X ) ==> X, !
% 173.66/174.08 leq( star( X ), X ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 resolution: (122469) {G10,W6,D4,L1,V1,M1} { star( X ) ==> star( star( X )
% 173.66/174.08 ) }.
% 173.66/174.08 parent0[1]: (122468) {G11,W8,D3,L2,V1,M2} { X ==> star( X ), ! leq( star(
% 173.66/174.08 X ), X ) }.
% 173.66/174.08 parent1[0]: (10038) {G9,W6,D4,L1,V1,M1} P(10034,167);d(732);r(20) { leq(
% 173.66/174.08 star( star( X ) ), star( X ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := star( X )
% 173.66/174.08 end
% 173.66/174.08 substitution1:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 eqswap: (122470) {G10,W6,D4,L1,V1,M1} { star( star( X ) ) ==> star( X )
% 173.66/174.08 }.
% 173.66/174.08 parent0[0]: (122469) {G10,W6,D4,L1,V1,M1} { star( X ) ==> star( star( X )
% 173.66/174.08 ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 subsumption: (10055) {G12,W6,D4,L1,V1,M1} R(10038,8649) { star( star( X ) )
% 173.66/174.08 ==> star( X ) }.
% 173.66/174.08 parent0: (122470) {G10,W6,D4,L1,V1,M1} { star( star( X ) ) ==> star( X )
% 173.66/174.08 }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08 permutation0:
% 173.66/174.08 0 ==> 0
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 eqswap: (122471) {G7,W10,D5,L1,V1,M1} { star( X ) ==> addition( star( X )
% 173.66/174.08 , multiplication( star( X ), X ) ) }.
% 173.66/174.08 parent0[0]: (888) {G7,W10,D5,L1,V1,M1} R(881,35) { addition( star( X ),
% 173.66/174.08 multiplication( star( X ), X ) ) ==> star( X ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 paramod: (122475) {G2,W9,D4,L1,V1,M1} { star( X ) ==> multiplication( star
% 173.66/174.08 ( X ), addition( one, X ) ) }.
% 173.66/174.08 parent0[0]: (65) {G1,W11,D4,L1,V2,M1} P(5,7) { addition( X, multiplication
% 173.66/174.08 ( X, Y ) ) = multiplication( X, addition( one, Y ) ) }.
% 173.66/174.08 parent1[0; 3]: (122471) {G7,W10,D5,L1,V1,M1} { star( X ) ==> addition(
% 173.66/174.08 star( X ), multiplication( star( X ), X ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := star( X )
% 173.66/174.08 Y := X
% 173.66/174.08 end
% 173.66/174.08 substitution1:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 eqswap: (122476) {G2,W9,D4,L1,V1,M1} { multiplication( star( X ), addition
% 173.66/174.08 ( one, X ) ) ==> star( X ) }.
% 173.66/174.08 parent0[0]: (122475) {G2,W9,D4,L1,V1,M1} { star( X ) ==> multiplication(
% 173.66/174.08 star( X ), addition( one, X ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 subsumption: (74412) {G8,W9,D4,L1,V1,M1} P(888,65) { multiplication( star(
% 173.66/174.08 X ), addition( one, X ) ) ==> star( X ) }.
% 173.66/174.08 parent0: (122476) {G2,W9,D4,L1,V1,M1} { multiplication( star( X ),
% 173.66/174.08 addition( one, X ) ) ==> star( X ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08 permutation0:
% 173.66/174.08 0 ==> 0
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 paramod: (122481) {G9,W9,D4,L1,V1,M1} { leq( multiplication( X, addition(
% 173.66/174.08 one, X ) ), star( star( X ) ) ) }.
% 173.66/174.08 parent0[0]: (74412) {G8,W9,D4,L1,V1,M1} P(888,65) { multiplication( star( X
% 173.66/174.08 ), addition( one, X ) ) ==> star( X ) }.
% 173.66/174.08 parent1[0; 7]: (9871) {G13,W9,D5,L1,V2,M1} R(8966,8650) { leq(
% 173.66/174.08 multiplication( X, Y ), star( multiplication( star( X ), Y ) ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08 substitution1:
% 173.66/174.08 X := X
% 173.66/174.08 Y := addition( one, X )
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 paramod: (122482) {G3,W9,D4,L1,V1,M1} { leq( multiplication( addition( one
% 173.66/174.08 , X ), X ), star( star( X ) ) ) }.
% 173.66/174.08 parent0[0]: (3177) {G2,W11,D4,L1,V1,M1} P(96,65) { multiplication( X,
% 173.66/174.08 addition( one, X ) ) ==> multiplication( addition( one, X ), X ) }.
% 173.66/174.08 parent1[0; 1]: (122481) {G9,W9,D4,L1,V1,M1} { leq( multiplication( X,
% 173.66/174.08 addition( one, X ) ), star( star( X ) ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08 substitution1:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 paramod: (122483) {G4,W8,D4,L1,V1,M1} { leq( multiplication( addition( one
% 173.66/174.08 , X ), X ), star( X ) ) }.
% 173.66/174.08 parent0[0]: (10055) {G12,W6,D4,L1,V1,M1} R(10038,8649) { star( star( X ) )
% 173.66/174.08 ==> star( X ) }.
% 173.66/174.08 parent1[0; 6]: (122482) {G3,W9,D4,L1,V1,M1} { leq( multiplication(
% 173.66/174.08 addition( one, X ), X ), star( star( X ) ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08 substitution1:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 subsumption: (74420) {G14,W8,D4,L1,V1,M1} P(74412,9871);d(3177);d(10055) {
% 173.66/174.08 leq( multiplication( addition( one, X ), X ), star( X ) ) }.
% 173.66/174.08 parent0: (122483) {G4,W8,D4,L1,V1,M1} { leq( multiplication( addition( one
% 173.66/174.08 , X ), X ), star( X ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08 permutation0:
% 173.66/174.08 0 ==> 0
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 resolution: (122484) {G7,W6,D3,L1,V1,M1} { leq( multiplication( X, X ),
% 173.66/174.08 star( X ) ) }.
% 173.66/174.08 parent0[1]: (885) {G6,W12,D4,L2,V4,M2} P(8,511) { leq( multiplication( Z, Y
% 173.66/174.08 ), T ), ! leq( multiplication( addition( X, Z ), Y ), T ) }.
% 173.66/174.08 parent1[0]: (74420) {G14,W8,D4,L1,V1,M1} P(74412,9871);d(3177);d(10055) {
% 173.66/174.08 leq( multiplication( addition( one, X ), X ), star( X ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := one
% 173.66/174.08 Y := X
% 173.66/174.08 Z := X
% 173.66/174.08 T := star( X )
% 173.66/174.08 end
% 173.66/174.08 substitution1:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 subsumption: (74588) {G15,W6,D3,L1,V1,M1} R(74420,885) { leq(
% 173.66/174.08 multiplication( X, X ), star( X ) ) }.
% 173.66/174.08 parent0: (122484) {G7,W6,D3,L1,V1,M1} { leq( multiplication( X, X ), star
% 173.66/174.08 ( X ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08 permutation0:
% 173.66/174.08 0 ==> 0
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 resolution: (122485) {G7,W10,D4,L1,V2,M1} { leq( multiplication( addition
% 173.66/174.08 ( X, Y ), Y ), star( addition( X, Y ) ) ) }.
% 173.66/174.08 parent0[1]: (886) {G6,W12,D4,L2,V4,M2} P(7,511) { leq( multiplication( X, Z
% 173.66/174.08 ), T ), ! leq( multiplication( X, addition( Y, Z ) ), T ) }.
% 173.66/174.08 parent1[0]: (74588) {G15,W6,D3,L1,V1,M1} R(74420,885) { leq( multiplication
% 173.66/174.08 ( X, X ), star( X ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := addition( X, Y )
% 173.66/174.08 Y := X
% 173.66/174.08 Z := Y
% 173.66/174.08 T := star( addition( X, Y ) )
% 173.66/174.08 end
% 173.66/174.08 substitution1:
% 173.66/174.08 X := addition( X, Y )
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 subsumption: (74687) {G16,W10,D4,L1,V2,M1} R(74588,886) { leq(
% 173.66/174.08 multiplication( addition( X, Y ), Y ), star( addition( X, Y ) ) ) }.
% 173.66/174.08 parent0: (122485) {G7,W10,D4,L1,V2,M1} { leq( multiplication( addition( X
% 173.66/174.08 , Y ), Y ), star( addition( X, Y ) ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 Y := Y
% 173.66/174.08 end
% 173.66/174.08 permutation0:
% 173.66/174.08 0 ==> 0
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 eqswap: (122486) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y, X
% 173.66/174.08 ) }.
% 173.66/174.08 parent0[0]: (35) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, !
% 173.66/174.08 leq( X, Y ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := Y
% 173.66/174.08 Y := X
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 resolution: (122487) {G2,W9,D4,L1,V1,M1} { star( X ) ==> addition( star( X
% 173.66/174.08 ), multiplication( X, X ) ) }.
% 173.66/174.08 parent0[1]: (122486) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq(
% 173.66/174.08 Y, X ) }.
% 173.66/174.08 parent1[0]: (74588) {G15,W6,D3,L1,V1,M1} R(74420,885) { leq( multiplication
% 173.66/174.08 ( X, X ), star( X ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := star( X )
% 173.66/174.08 Y := multiplication( X, X )
% 173.66/174.08 end
% 173.66/174.08 substitution1:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 eqswap: (122488) {G2,W9,D4,L1,V1,M1} { addition( star( X ), multiplication
% 173.66/174.08 ( X, X ) ) ==> star( X ) }.
% 173.66/174.08 parent0[0]: (122487) {G2,W9,D4,L1,V1,M1} { star( X ) ==> addition( star( X
% 173.66/174.08 ), multiplication( X, X ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 subsumption: (74730) {G16,W9,D4,L1,V1,M1} R(74588,35) { addition( star( X )
% 173.66/174.08 , multiplication( X, X ) ) ==> star( X ) }.
% 173.66/174.08 parent0: (122488) {G2,W9,D4,L1,V1,M1} { addition( star( X ),
% 173.66/174.08 multiplication( X, X ) ) ==> star( X ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08 permutation0:
% 173.66/174.08 0 ==> 0
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 resolution: (122489) {G7,W8,D4,L1,V2,M1} { leq( multiplication( X, X ),
% 173.66/174.08 star( addition( Y, X ) ) ) }.
% 173.66/174.08 parent0[1]: (885) {G6,W12,D4,L2,V4,M2} P(8,511) { leq( multiplication( Z, Y
% 173.66/174.08 ), T ), ! leq( multiplication( addition( X, Z ), Y ), T ) }.
% 173.66/174.08 parent1[0]: (74687) {G16,W10,D4,L1,V2,M1} R(74588,886) { leq(
% 173.66/174.08 multiplication( addition( X, Y ), Y ), star( addition( X, Y ) ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := Y
% 173.66/174.08 Y := X
% 173.66/174.08 Z := X
% 173.66/174.08 T := star( addition( Y, X ) )
% 173.66/174.08 end
% 173.66/174.08 substitution1:
% 173.66/174.08 X := Y
% 173.66/174.08 Y := X
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 subsumption: (121790) {G17,W8,D4,L1,V2,M1} R(74687,885) { leq(
% 173.66/174.08 multiplication( X, X ), star( addition( Y, X ) ) ) }.
% 173.66/174.08 parent0: (122489) {G7,W8,D4,L1,V2,M1} { leq( multiplication( X, X ), star
% 173.66/174.08 ( addition( Y, X ) ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 Y := Y
% 173.66/174.08 end
% 173.66/174.08 permutation0:
% 173.66/174.08 0 ==> 0
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 paramod: (122493) {G17,W11,D4,L1,V1,M1} { leq( multiplication(
% 173.66/174.08 multiplication( X, X ), multiplication( X, X ) ), star( star( X ) ) ) }.
% 173.66/174.08 parent0[0]: (74730) {G16,W9,D4,L1,V1,M1} R(74588,35) { addition( star( X )
% 173.66/174.08 , multiplication( X, X ) ) ==> star( X ) }.
% 173.66/174.08 parent1[0; 9]: (121790) {G17,W8,D4,L1,V2,M1} R(74687,885) { leq(
% 173.66/174.08 multiplication( X, X ), star( addition( Y, X ) ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08 substitution1:
% 173.66/174.08 X := multiplication( X, X )
% 173.66/174.08 Y := star( X )
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 paramod: (122494) {G1,W11,D5,L1,V1,M1} { leq( multiplication(
% 173.66/174.08 multiplication( multiplication( X, X ), X ), X ), star( star( X ) ) ) }.
% 173.66/174.08 parent0[0]: (4) {G0,W11,D4,L1,V3,M1} I { multiplication( X, multiplication
% 173.66/174.08 ( Y, Z ) ) ==> multiplication( multiplication( X, Y ), Z ) }.
% 173.66/174.08 parent1[0; 1]: (122493) {G17,W11,D4,L1,V1,M1} { leq( multiplication(
% 173.66/174.08 multiplication( X, X ), multiplication( X, X ) ), star( star( X ) ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := multiplication( X, X )
% 173.66/174.08 Y := X
% 173.66/174.08 Z := X
% 173.66/174.08 end
% 173.66/174.08 substitution1:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 paramod: (122495) {G2,W10,D5,L1,V1,M1} { leq( multiplication(
% 173.66/174.08 multiplication( multiplication( X, X ), X ), X ), star( X ) ) }.
% 173.66/174.08 parent0[0]: (10055) {G12,W6,D4,L1,V1,M1} R(10038,8649) { star( star( X ) )
% 173.66/174.08 ==> star( X ) }.
% 173.66/174.08 parent1[0; 8]: (122494) {G1,W11,D5,L1,V1,M1} { leq( multiplication(
% 173.66/174.08 multiplication( multiplication( X, X ), X ), X ), star( star( X ) ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08 substitution1:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 subsumption: (121855) {G18,W10,D5,L1,V1,M1} P(74730,121790);d(4);d(10055)
% 173.66/174.08 { leq( multiplication( multiplication( multiplication( X, X ), X ), X )
% 173.66/174.08 , star( X ) ) }.
% 173.66/174.08 parent0: (122495) {G2,W10,D5,L1,V1,M1} { leq( multiplication(
% 173.66/174.08 multiplication( multiplication( X, X ), X ), X ), star( X ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 X := X
% 173.66/174.08 end
% 173.66/174.08 permutation0:
% 173.66/174.08 0 ==> 0
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 resolution: (122496) {G2,W0,D0,L0,V0,M0} { }.
% 173.66/174.08 parent0[0]: (17) {G1,W10,D5,L1,V0,M1} I;d(4);d(4) { ! leq( multiplication(
% 173.66/174.08 multiplication( multiplication( a, a ), a ), a ), star( a ) ) }.
% 173.66/174.08 parent1[0]: (121855) {G18,W10,D5,L1,V1,M1} P(74730,121790);d(4);d(10055) {
% 173.66/174.08 leq( multiplication( multiplication( multiplication( X, X ), X ), X ),
% 173.66/174.08 star( X ) ) }.
% 173.66/174.08 substitution0:
% 173.66/174.08 end
% 173.66/174.08 substitution1:
% 173.66/174.08 X := a
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 subsumption: (122078) {G19,W0,D0,L0,V0,M0} S(17);r(121855) { }.
% 173.66/174.08 parent0: (122496) {G2,W0,D0,L0,V0,M0} { }.
% 173.66/174.08 substitution0:
% 173.66/174.08 end
% 173.66/174.08 permutation0:
% 173.66/174.08 end
% 173.66/174.08
% 173.66/174.08 Proof check complete!
% 173.66/174.08
% 173.66/174.08 Memory use:
% 173.66/174.08
% 173.66/174.08 space for terms: 1820378
% 173.66/174.08 space for clauses: 5528509
% 173.66/174.08
% 173.66/174.08
% 173.66/174.08 clauses generated: 2707158
% 173.66/174.08 clauses kept: 122079
% 173.66/174.08 clauses selected: 3000
% 173.66/174.08 clauses deleted: 12874
% 173.66/174.08 clauses inuse deleted: 179
% 173.66/174.08
% 173.66/174.08 subsentry: 33942374
% 173.66/174.08 literals s-matched: 12544113
% 173.66/174.08 literals matched: 11293701
% 173.66/174.08 full subsumption: 3916807
% 173.66/174.08
% 173.66/174.08 checksum: 1584329443
% 173.66/174.08
% 173.66/174.08
% 173.66/174.08 Bliksem ended
%------------------------------------------------------------------------------