TSTP Solution File: KLE148+2 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE148+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n006.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 01:37:29 EDT 2022
% Result : Theorem 52.91s 53.37s
% Output : Refutation 52.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE148+2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Thu Jun 16 13:38:56 EDT 2022
% 0.12/0.33 % CPUTime :
% 21.75/22.13 *** allocated 10000 integers for termspace/termends
% 21.75/22.13 *** allocated 10000 integers for clauses
% 21.75/22.13 *** allocated 10000 integers for justifications
% 21.75/22.13 Bliksem 1.12
% 21.75/22.13
% 21.75/22.13
% 21.75/22.13 Automatic Strategy Selection
% 21.75/22.13
% 21.75/22.13
% 21.75/22.13 Clauses:
% 21.75/22.13
% 21.75/22.13 { addition( X, Y ) = addition( Y, X ) }.
% 21.75/22.13 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 21.75/22.13 { addition( X, zero ) = X }.
% 21.75/22.13 { addition( X, X ) = X }.
% 21.75/22.13 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 21.75/22.13 multiplication( X, Y ), Z ) }.
% 21.75/22.13 { multiplication( X, one ) = X }.
% 21.75/22.13 { multiplication( one, X ) = X }.
% 21.75/22.13 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 21.75/22.13 , multiplication( X, Z ) ) }.
% 21.75/22.13 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 21.75/22.13 , multiplication( Y, Z ) ) }.
% 21.75/22.13 { multiplication( zero, X ) = zero }.
% 21.75/22.13 { addition( one, multiplication( X, star( X ) ) ) = star( X ) }.
% 21.75/22.13 { addition( one, multiplication( star( X ), X ) ) = star( X ) }.
% 21.75/22.13 { ! leq( addition( multiplication( X, Z ), Y ), Z ), leq( multiplication(
% 21.75/22.13 star( X ), Y ), Z ) }.
% 21.75/22.13 { ! leq( addition( multiplication( Z, X ), Y ), Z ), leq( multiplication( Y
% 21.75/22.13 , star( X ) ), Z ) }.
% 21.75/22.13 { strong_iteration( X ) = addition( multiplication( X, strong_iteration( X
% 21.75/22.13 ) ), one ) }.
% 21.75/22.13 { ! leq( Z, addition( multiplication( X, Z ), Y ) ), leq( Z, multiplication
% 21.75/22.13 ( strong_iteration( X ), Y ) ) }.
% 21.75/22.13 { strong_iteration( X ) = addition( star( X ), multiplication(
% 21.75/22.13 strong_iteration( X ), zero ) ) }.
% 21.75/22.13 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 21.75/22.13 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 21.75/22.13 { multiplication( skol1, skol2 ) = zero, ! leq( skol1, multiplication(
% 21.75/22.13 skol1, strong_iteration( skol2 ) ) ) }.
% 21.75/22.13 { ! leq( multiplication( skol1, strong_iteration( skol2 ) ), skol1 ), ! leq
% 21.75/22.13 ( skol1, multiplication( skol1, strong_iteration( skol2 ) ) ) }.
% 21.75/22.13
% 21.75/22.13 percentage equality = 0.607143, percentage horn = 1.000000
% 21.75/22.13 This is a problem with some equality
% 21.75/22.13
% 21.75/22.13
% 21.75/22.13
% 21.75/22.13 Options Used:
% 21.75/22.13
% 21.75/22.13 useres = 1
% 21.75/22.13 useparamod = 1
% 21.75/22.13 useeqrefl = 1
% 21.75/22.13 useeqfact = 1
% 21.75/22.13 usefactor = 1
% 21.75/22.13 usesimpsplitting = 0
% 21.75/22.13 usesimpdemod = 5
% 21.75/22.13 usesimpres = 3
% 21.75/22.13
% 21.75/22.13 resimpinuse = 1000
% 21.75/22.13 resimpclauses = 20000
% 21.75/22.13 substype = eqrewr
% 21.75/22.13 backwardsubs = 1
% 21.75/22.13 selectoldest = 5
% 21.75/22.13
% 21.75/22.13 litorderings [0] = split
% 21.75/22.13 litorderings [1] = extend the termordering, first sorting on arguments
% 21.75/22.13
% 21.75/22.13 termordering = kbo
% 21.75/22.13
% 21.75/22.13 litapriori = 0
% 21.75/22.13 termapriori = 1
% 21.75/22.13 litaposteriori = 0
% 21.75/22.13 termaposteriori = 0
% 21.75/22.13 demodaposteriori = 0
% 21.75/22.13 ordereqreflfact = 0
% 21.75/22.13
% 21.75/22.13 litselect = negord
% 21.75/22.13
% 21.75/22.13 maxweight = 15
% 21.75/22.13 maxdepth = 30000
% 21.75/22.13 maxlength = 115
% 21.75/22.13 maxnrvars = 195
% 21.75/22.13 excuselevel = 1
% 21.75/22.13 increasemaxweight = 1
% 21.75/22.13
% 21.75/22.13 maxselected = 10000000
% 21.75/22.13 maxnrclauses = 10000000
% 21.75/22.13
% 21.75/22.13 showgenerated = 0
% 21.75/22.13 showkept = 0
% 21.75/22.13 showselected = 0
% 21.75/22.13 showdeleted = 0
% 21.75/22.13 showresimp = 1
% 21.75/22.13 showstatus = 2000
% 21.75/22.13
% 21.75/22.13 prologoutput = 0
% 21.75/22.13 nrgoals = 5000000
% 21.75/22.13 totalproof = 1
% 21.75/22.13
% 21.75/22.13 Symbols occurring in the translation:
% 21.75/22.13
% 21.75/22.13 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 21.75/22.13 . [1, 2] (w:1, o:22, a:1, s:1, b:0),
% 21.75/22.13 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 21.75/22.13 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 21.75/22.13 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 21.75/22.13 addition [37, 2] (w:1, o:46, a:1, s:1, b:0),
% 21.75/22.13 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 21.75/22.13 multiplication [40, 2] (w:1, o:48, a:1, s:1, b:0),
% 21.75/22.13 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 21.75/22.13 star [42, 1] (w:1, o:20, a:1, s:1, b:0),
% 21.75/22.13 leq [43, 2] (w:1, o:47, a:1, s:1, b:0),
% 21.75/22.13 strong_iteration [44, 1] (w:1, o:21, a:1, s:1, b:0),
% 21.75/22.13 skol1 [47, 0] (w:1, o:13, a:1, s:1, b:1),
% 21.75/22.13 skol2 [48, 0] (w:1, o:14, a:1, s:1, b:1).
% 21.75/22.13
% 21.75/22.13
% 21.75/22.13 Starting Search:
% 21.75/22.13
% 21.75/22.13 *** allocated 15000 integers for clauses
% 21.75/22.13 *** allocated 22500 integers for clauses
% 21.75/22.13 *** allocated 33750 integers for clauses
% 21.75/22.13 *** allocated 50625 integers for clauses
% 21.75/22.13 *** allocated 15000 integers for termspace/termends
% 21.75/22.13 *** allocated 75937 integers for clauses
% 21.75/22.13 Resimplifying inuse:
% 21.75/22.13 Done
% 21.75/22.13
% 21.75/22.13 *** allocated 22500 integers for termspace/termends
% 21.75/22.13 *** allocated 113905 integers for clauses
% 21.75/22.13 *** allocated 33750 integers for termspace/termends
% 21.75/22.13 *** allocated 170857 integers for clauses
% 21.75/22.13
% 21.75/22.13 Intermediate Status:
% 21.75/22.13 Generated: 22428
% 52.91/53.37 Kept: 2000
% 52.91/53.37 Inuse: 263
% 52.91/53.37 Deleted: 82
% 52.91/53.37 Deletedinuse: 37
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37 *** allocated 50625 integers for termspace/termends
% 52.91/53.37 *** allocated 256285 integers for clauses
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37 *** allocated 75937 integers for termspace/termends
% 52.91/53.37
% 52.91/53.37 Intermediate Status:
% 52.91/53.37 Generated: 45795
% 52.91/53.37 Kept: 4043
% 52.91/53.37 Inuse: 417
% 52.91/53.37 Deleted: 92
% 52.91/53.37 Deletedinuse: 41
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37 *** allocated 384427 integers for clauses
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37 *** allocated 113905 integers for termspace/termends
% 52.91/53.37
% 52.91/53.37 Intermediate Status:
% 52.91/53.37 Generated: 71470
% 52.91/53.37 Kept: 6046
% 52.91/53.37 Inuse: 556
% 52.91/53.37 Deleted: 121
% 52.91/53.37 Deletedinuse: 43
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37 *** allocated 576640 integers for clauses
% 52.91/53.37
% 52.91/53.37 Intermediate Status:
% 52.91/53.37 Generated: 94208
% 52.91/53.37 Kept: 8054
% 52.91/53.37 Inuse: 686
% 52.91/53.37 Deleted: 151
% 52.91/53.37 Deletedinuse: 51
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37 *** allocated 170857 integers for termspace/termends
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37
% 52.91/53.37 Intermediate Status:
% 52.91/53.37 Generated: 141443
% 52.91/53.37 Kept: 10054
% 52.91/53.37 Inuse: 878
% 52.91/53.37 Deleted: 173
% 52.91/53.37 Deletedinuse: 57
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37 *** allocated 864960 integers for clauses
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37
% 52.91/53.37 Intermediate Status:
% 52.91/53.37 Generated: 183353
% 52.91/53.37 Kept: 13100
% 52.91/53.37 Inuse: 1035
% 52.91/53.37 Deleted: 363
% 52.91/53.37 Deletedinuse: 142
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37 *** allocated 256285 integers for termspace/termends
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37
% 52.91/53.37 Intermediate Status:
% 52.91/53.37 Generated: 208658
% 52.91/53.37 Kept: 15147
% 52.91/53.37 Inuse: 1116
% 52.91/53.37 Deleted: 441
% 52.91/53.37 Deletedinuse: 170
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37 *** allocated 1297440 integers for clauses
% 52.91/53.37
% 52.91/53.37 Intermediate Status:
% 52.91/53.37 Generated: 250804
% 52.91/53.37 Kept: 17271
% 52.91/53.37 Inuse: 1195
% 52.91/53.37 Deleted: 541
% 52.91/53.37 Deletedinuse: 250
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37
% 52.91/53.37 Intermediate Status:
% 52.91/53.37 Generated: 284885
% 52.91/53.37 Kept: 19281
% 52.91/53.37 Inuse: 1272
% 52.91/53.37 Deleted: 595
% 52.91/53.37 Deletedinuse: 278
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37 *** allocated 384427 integers for termspace/termends
% 52.91/53.37 Resimplifying clauses:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37
% 52.91/53.37 Intermediate Status:
% 52.91/53.37 Generated: 301056
% 52.91/53.37 Kept: 21293
% 52.91/53.37 Inuse: 1313
% 52.91/53.37 Deleted: 4424
% 52.91/53.37 Deletedinuse: 278
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37
% 52.91/53.37 Intermediate Status:
% 52.91/53.37 Generated: 337044
% 52.91/53.37 Kept: 23343
% 52.91/53.37 Inuse: 1422
% 52.91/53.37 Deleted: 4426
% 52.91/53.37 Deletedinuse: 280
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37 *** allocated 1946160 integers for clauses
% 52.91/53.37
% 52.91/53.37 Intermediate Status:
% 52.91/53.37 Generated: 355025
% 52.91/53.37 Kept: 25347
% 52.91/53.37 Inuse: 1453
% 52.91/53.37 Deleted: 4426
% 52.91/53.37 Deletedinuse: 280
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37 *** allocated 576640 integers for termspace/termends
% 52.91/53.37
% 52.91/53.37 Intermediate Status:
% 52.91/53.37 Generated: 371701
% 52.91/53.37 Kept: 28535
% 52.91/53.37 Inuse: 1464
% 52.91/53.37 Deleted: 4426
% 52.91/53.37 Deletedinuse: 280
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37
% 52.91/53.37 Intermediate Status:
% 52.91/53.37 Generated: 412144
% 52.91/53.37 Kept: 30539
% 52.91/53.37 Inuse: 1530
% 52.91/53.37 Deleted: 4426
% 52.91/53.37 Deletedinuse: 280
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37
% 52.91/53.37 Intermediate Status:
% 52.91/53.37 Generated: 455121
% 52.91/53.37 Kept: 32567
% 52.91/53.37 Inuse: 1624
% 52.91/53.37 Deleted: 4426
% 52.91/53.37 Deletedinuse: 280
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37
% 52.91/53.37 Intermediate Status:
% 52.91/53.37 Generated: 481838
% 52.91/53.37 Kept: 34616
% 52.91/53.37 Inuse: 1669
% 52.91/53.37 Deleted: 4426
% 52.91/53.37 Deletedinuse: 280
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37
% 52.91/53.37 Intermediate Status:
% 52.91/53.37 Generated: 547158
% 52.91/53.37 Kept: 36626
% 52.91/53.37 Inuse: 1749
% 52.91/53.37 Deleted: 4438
% 52.91/53.37 Deletedinuse: 283
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37
% 52.91/53.37 Intermediate Status:
% 52.91/53.37 Generated: 615064
% 52.91/53.37 Kept: 38633
% 52.91/53.37 Inuse: 1827
% 52.91/53.37 Deleted: 4441
% 52.91/53.37 Deletedinuse: 284
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37 *** allocated 2919240 integers for clauses
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37 Resimplifying clauses:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37
% 52.91/53.37 Intermediate Status:
% 52.91/53.37 Generated: 669198
% 52.91/53.37 Kept: 40898
% 52.91/53.37 Inuse: 1880
% 52.91/53.37 Deleted: 6414
% 52.91/53.37 Deletedinuse: 284
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37 *** allocated 864960 integers for termspace/termends
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37
% 52.91/53.37 Intermediate Status:
% 52.91/53.37 Generated: 697052
% 52.91/53.37 Kept: 43036
% 52.91/53.37 Inuse: 1915
% 52.91/53.37 Deleted: 6414
% 52.91/53.37 Deletedinuse: 284
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37
% 52.91/53.37 Intermediate Status:
% 52.91/53.37 Generated: 720868
% 52.91/53.37 Kept: 45071
% 52.91/53.37 Inuse: 1955
% 52.91/53.37 Deleted: 6414
% 52.91/53.37 Deletedinuse: 284
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37
% 52.91/53.37 Intermediate Status:
% 52.91/53.37 Generated: 742975
% 52.91/53.37 Kept: 47076
% 52.91/53.37 Inuse: 1989
% 52.91/53.37 Deleted: 6417
% 52.91/53.37 Deletedinuse: 284
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37
% 52.91/53.37 Intermediate Status:
% 52.91/53.37 Generated: 764911
% 52.91/53.37 Kept: 49172
% 52.91/53.37 Inuse: 2033
% 52.91/53.37 Deleted: 6417
% 52.91/53.37 Deletedinuse: 284
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37
% 52.91/53.37 Intermediate Status:
% 52.91/53.37 Generated: 787196
% 52.91/53.37 Kept: 51218
% 52.91/53.37 Inuse: 2063
% 52.91/53.37 Deleted: 6417
% 52.91/53.37 Deletedinuse: 284
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37
% 52.91/53.37 Intermediate Status:
% 52.91/53.37 Generated: 832120
% 52.91/53.37 Kept: 53249
% 52.91/53.37 Inuse: 2105
% 52.91/53.37 Deleted: 6417
% 52.91/53.37 Deletedinuse: 284
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37
% 52.91/53.37 Intermediate Status:
% 52.91/53.37 Generated: 862298
% 52.91/53.37 Kept: 55349
% 52.91/53.37 Inuse: 2134
% 52.91/53.37 Deleted: 6417
% 52.91/53.37 Deletedinuse: 284
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37
% 52.91/53.37 Intermediate Status:
% 52.91/53.37 Generated: 890608
% 52.91/53.37 Kept: 57349
% 52.91/53.37 Inuse: 2170
% 52.91/53.37 Deleted: 6420
% 52.91/53.37 Deletedinuse: 287
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37
% 52.91/53.37 Intermediate Status:
% 52.91/53.37 Generated: 935584
% 52.91/53.37 Kept: 59732
% 52.91/53.37 Inuse: 2229
% 52.91/53.37 Deleted: 6420
% 52.91/53.37 Deletedinuse: 287
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37 Resimplifying clauses:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37 *** allocated 1297440 integers for termspace/termends
% 52.91/53.37
% 52.91/53.37 Intermediate Status:
% 52.91/53.37 Generated: 963221
% 52.91/53.37 Kept: 61733
% 52.91/53.37 Inuse: 2268
% 52.91/53.37 Deleted: 9682
% 52.91/53.37 Deletedinuse: 287
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37 *** allocated 4378860 integers for clauses
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37
% 52.91/53.37 Intermediate Status:
% 52.91/53.37 Generated: 995592
% 52.91/53.37 Kept: 63781
% 52.91/53.37 Inuse: 2323
% 52.91/53.37 Deleted: 9682
% 52.91/53.37 Deletedinuse: 287
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37
% 52.91/53.37 Intermediate Status:
% 52.91/53.37 Generated: 1035183
% 52.91/53.37 Kept: 65799
% 52.91/53.37 Inuse: 2395
% 52.91/53.37 Deleted: 9682
% 52.91/53.37 Deletedinuse: 287
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37
% 52.91/53.37 Intermediate Status:
% 52.91/53.37 Generated: 1081251
% 52.91/53.37 Kept: 67800
% 52.91/53.37 Inuse: 2485
% 52.91/53.37 Deleted: 9682
% 52.91/53.37 Deletedinuse: 287
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37
% 52.91/53.37 Intermediate Status:
% 52.91/53.37 Generated: 1119277
% 52.91/53.37 Kept: 69990
% 52.91/53.37 Inuse: 2541
% 52.91/53.37 Deleted: 9682
% 52.91/53.37 Deletedinuse: 287
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37
% 52.91/53.37 Intermediate Status:
% 52.91/53.37 Generated: 1130706
% 52.91/53.37 Kept: 71997
% 52.91/53.37 Inuse: 2557
% 52.91/53.37 Deleted: 9682
% 52.91/53.37 Deletedinuse: 287
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37
% 52.91/53.37 Intermediate Status:
% 52.91/53.37 Generated: 1165963
% 52.91/53.37 Kept: 74013
% 52.91/53.37 Inuse: 2604
% 52.91/53.37 Deleted: 9684
% 52.91/53.37 Deletedinuse: 287
% 52.91/53.37
% 52.91/53.37 Resimplifying inuse:
% 52.91/53.37 Done
% 52.91/53.37
% 52.91/53.37
% 52.91/53.37 Bliksems!, er is een bewijs:
% 52.91/53.37 % SZS status Theorem
% 52.91/53.37 % SZS output start Refutation
% 52.91/53.37
% 52.91/53.37 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 52.91/53.37 (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) ==> addition(
% 52.91/53.37 addition( Z, Y ), X ) }.
% 52.91/53.37 (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 52.91/53.37 (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 52.91/53.37 (4) {G0,W11,D4,L1,V3,M1} I { multiplication( X, multiplication( Y, Z ) )
% 52.91/53.37 ==> multiplication( multiplication( X, Y ), Z ) }.
% 52.91/53.37 (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 52.91/53.37 (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 52.91/53.37 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 52.91/53.37 (9) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==> zero }.
% 52.91/53.37 (14) {G0,W9,D5,L1,V1,M1} I { addition( multiplication( X, strong_iteration
% 52.91/53.37 ( X ) ), one ) ==> strong_iteration( X ) }.
% 52.91/53.37 (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) ==> Y }.
% 52.91/53.37 (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, Y ) }.
% 52.91/53.37 (19) {G0,W11,D4,L2,V0,M2} I { multiplication( skol1, skol2 ) ==> zero, !
% 52.91/53.37 leq( skol1, multiplication( skol1, strong_iteration( skol2 ) ) ) }.
% 52.91/53.37 (20) {G0,W12,D4,L2,V0,M2} I { ! leq( multiplication( skol1,
% 52.91/53.37 strong_iteration( skol2 ) ), skol1 ), ! leq( skol1, multiplication( skol1
% 52.91/53.37 , strong_iteration( skol2 ) ) ) }.
% 52.91/53.37 (21) {G1,W5,D3,L1,V1,M1} P(0,2) { addition( zero, X ) ==> X }.
% 52.91/53.37 (24) {G1,W8,D3,L2,V2,M2} P(0,18) { ! addition( Y, X ) ==> Y, leq( X, Y )
% 52.91/53.37 }.
% 52.91/53.37 (25) {G1,W6,D2,L2,V1,M2} P(2,18) { ! X = zero, leq( X, zero ) }.
% 52.91/53.37 (26) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y ), Z ) ==>
% 52.91/53.37 addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 52.91/53.37 (33) {G2,W6,D2,L2,V1,M2} R(17,25);d(2) { ! X = zero, X = zero }.
% 52.91/53.37 (34) {G2,W9,D2,L3,V2,M3} P(17,24) { ! Y = X, leq( Y, X ), ! leq( X, Y ) }.
% 52.91/53.37 (64) {G3,W14,D4,L2,V3,M2} P(33,7);d(21) { ! multiplication( X, Y ) ==> zero
% 52.91/53.37 , multiplication( X, addition( Y, Z ) ) ==> multiplication( X, Z ) }.
% 52.91/53.37 (68) {G1,W16,D4,L2,V3,M2} P(7,18) { ! multiplication( X, addition( Y, Z ) )
% 52.91/53.37 ==> multiplication( X, Z ), leq( multiplication( X, Y ), multiplication
% 52.91/53.37 ( X, Z ) ) }.
% 52.91/53.37 (364) {G2,W5,D3,L1,V2,M1} P(3,26);q { leq( X, addition( X, Y ) ) }.
% 52.91/53.37 (423) {G3,W5,D3,L1,V2,M1} P(0,364) { leq( X, addition( Y, X ) ) }.
% 52.91/53.37 (429) {G4,W4,D3,L1,V1,M1} P(14,423) { leq( one, strong_iteration( X ) ) }.
% 52.91/53.37 (437) {G5,W7,D4,L1,V1,M1} R(429,17) { addition( one, strong_iteration( X )
% 52.91/53.37 ) ==> strong_iteration( X ) }.
% 52.91/53.37 (969) {G4,W14,D4,L2,V2,M2} P(14,64);d(4);d(5) { ! multiplication(
% 52.91/53.37 multiplication( Y, X ), strong_iteration( X ) ) ==> zero, multiplication
% 52.91/53.37 ( Y, strong_iteration( X ) ) ==> Y }.
% 52.91/53.37 (1237) {G6,W6,D4,L1,V2,M1} P(437,68);q;d(5) { leq( Y, multiplication( Y,
% 52.91/53.37 strong_iteration( X ) ) ) }.
% 52.91/53.37 (1275) {G7,W6,D4,L1,V0,M1} R(1237,20) { ! leq( multiplication( skol1,
% 52.91/53.37 strong_iteration( skol2 ) ), skol1 ) }.
% 52.91/53.37 (1277) {G7,W5,D3,L1,V0,M1} R(1237,19) { multiplication( skol1, skol2 ) ==>
% 52.91/53.37 zero }.
% 52.91/53.37 (1393) {G8,W6,D4,L1,V0,M1} R(1275,34);r(1237) { ! multiplication( skol1,
% 52.91/53.37 strong_iteration( skol2 ) ) ==> skol1 }.
% 52.91/53.37 (74623) {G9,W0,D0,L0,V0,M0} R(969,1393);d(1277);d(9);q { }.
% 52.91/53.37
% 52.91/53.37
% 52.91/53.37 % SZS output end Refutation
% 52.91/53.37 found a proof!
% 52.91/53.37
% 52.91/53.37
% 52.91/53.37 Unprocessed initial clauses:
% 52.91/53.37
% 52.91/53.37 (74625) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 52.91/53.37 (74626) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition
% 52.91/53.37 ( addition( Z, Y ), X ) }.
% 52.91/53.37 (74627) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 52.91/53.37 (74628) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 52.91/53.37 (74629) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z ) )
% 52.91/53.37 = multiplication( multiplication( X, Y ), Z ) }.
% 52.91/53.37 (74630) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 52.91/53.37 (74631) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 52.91/53.37 (74632) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 52.91/53.37 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 52.91/53.37 (74633) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 52.91/53.37 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 52.91/53.37 (74634) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 52.91/53.37 (74635) {G0,W9,D5,L1,V1,M1} { addition( one, multiplication( X, star( X )
% 52.91/53.37 ) ) = star( X ) }.
% 52.91/53.37 (74636) {G0,W9,D5,L1,V1,M1} { addition( one, multiplication( star( X ), X
% 52.91/53.37 ) ) = star( X ) }.
% 52.91/53.37 (74637) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( X, Z ), Y
% 52.91/53.37 ), Z ), leq( multiplication( star( X ), Y ), Z ) }.
% 52.91/53.37 (74638) {G0,W13,D4,L2,V3,M2} { ! leq( addition( multiplication( Z, X ), Y
% 52.91/53.37 ), Z ), leq( multiplication( Y, star( X ) ), Z ) }.
% 52.91/53.37 (74639) {G0,W9,D5,L1,V1,M1} { strong_iteration( X ) = addition(
% 52.91/53.37 multiplication( X, strong_iteration( X ) ), one ) }.
% 52.91/53.37 (74640) {G0,W13,D4,L2,V3,M2} { ! leq( Z, addition( multiplication( X, Z )
% 52.91/53.37 , Y ) ), leq( Z, multiplication( strong_iteration( X ), Y ) ) }.
% 52.91/53.37 (74641) {G0,W10,D5,L1,V1,M1} { strong_iteration( X ) = addition( star( X )
% 52.91/53.37 , multiplication( strong_iteration( X ), zero ) ) }.
% 52.91/53.37 (74642) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 52.91/53.37 (74643) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 52.91/53.37 (74644) {G0,W11,D4,L2,V0,M2} { multiplication( skol1, skol2 ) = zero, !
% 52.91/53.37 leq( skol1, multiplication( skol1, strong_iteration( skol2 ) ) ) }.
% 52.91/53.37 (74645) {G0,W12,D4,L2,V0,M2} { ! leq( multiplication( skol1,
% 52.91/53.37 strong_iteration( skol2 ) ), skol1 ), ! leq( skol1, multiplication( skol1
% 52.91/53.37 , strong_iteration( skol2 ) ) ) }.
% 52.91/53.37
% 52.91/53.37
% 52.91/53.37 Total Proof:
% 52.91/53.37
% 52.91/53.37 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 52.91/53.37 ) }.
% 52.91/53.37 parent0: (74625) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X )
% 52.91/53.37 }.
% 52.91/53.37 substitution0:
% 52.91/53.37 X := X
% 52.91/53.37 Y := Y
% 52.91/53.37 end
% 52.91/53.37 permutation0:
% 52.91/53.37 0 ==> 0
% 52.91/53.37 end
% 52.91/53.37
% 52.91/53.37 subsumption: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 52.91/53.37 ==> addition( addition( Z, Y ), X ) }.
% 52.91/53.37 parent0: (74626) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) =
% 52.91/53.37 addition( addition( Z, Y ), X ) }.
% 52.91/53.37 substitution0:
% 52.91/53.37 X := X
% 52.91/53.37 Y := Y
% 52.91/53.37 Z := Z
% 52.91/53.37 end
% 52.91/53.37 permutation0:
% 52.91/53.37 0 ==> 0
% 52.91/53.37 end
% 52.91/53.37
% 52.91/53.37 subsumption: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 52.91/53.37 parent0: (74627) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 52.91/53.37 substitution0:
% 52.91/53.37 X := X
% 52.91/53.37 end
% 52.91/53.37 permutation0:
% 52.91/53.37 0 ==> 0
% 52.91/53.37 end
% 52.91/53.37
% 52.91/53.37 subsumption: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 52.91/53.37 parent0: (74628) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 52.91/53.37 substitution0:
% 52.91/53.37 X := X
% 52.91/53.37 end
% 52.91/53.37 permutation0:
% 52.91/53.37 0 ==> 0
% 52.91/53.37 end
% 52.91/53.37
% 52.91/53.37 subsumption: (4) {G0,W11,D4,L1,V3,M1} I { multiplication( X, multiplication
% 52.91/53.37 ( Y, Z ) ) ==> multiplication( multiplication( X, Y ), Z ) }.
% 52.91/53.37 parent0: (74629) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication
% 52.91/53.37 ( Y, Z ) ) = multiplication( multiplication( X, Y ), Z ) }.
% 52.91/53.37 substitution0:
% 52.91/53.37 X := X
% 52.91/53.37 Y := Y
% 52.91/53.37 Z := Z
% 52.91/53.37 end
% 52.91/53.37 permutation0:
% 52.91/53.37 0 ==> 0
% 52.91/53.37 end
% 52.91/53.37
% 52.91/53.37 subsumption: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 52.91/53.37 parent0: (74630) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 52.91/53.37 substitution0:
% 52.91/53.37 X := X
% 52.91/53.37 end
% 52.91/53.37 permutation0:
% 52.91/53.37 0 ==> 0
% 52.91/53.37 end
% 52.91/53.37
% 52.91/53.37 eqswap: (74667) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 52.91/53.37 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 52.91/53.37 parent0[0]: (74632) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y
% 52.91/53.37 , Z ) ) = addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 52.91/53.37 substitution0:
% 52.91/53.37 X := X
% 52.91/53.37 Y := Y
% 52.91/53.37 Z := Z
% 52.91/53.37 end
% 52.91/53.37
% 52.91/53.37 subsumption: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y )
% 52.91/53.37 , multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 52.91/53.37 parent0: (74667) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 52.91/53.37 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 52.91/53.37 substitution0:
% 52.91/53.37 X := X
% 52.91/53.37 Y := Y
% 52.91/53.37 Z := Z
% 52.91/53.37 end
% 52.91/53.37 permutation0:
% 52.91/53.37 0 ==> 0
% 52.91/53.37 end
% 52.91/53.37
% 52.91/53.37 subsumption: (9) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==> zero
% 52.91/53.37 }.
% 52.91/53.37 parent0: (74634) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero
% 52.91/53.37 }.
% 52.91/53.37 substitution0:
% 52.91/53.37 X := X
% 52.91/53.37 end
% 52.91/53.37 permutation0:
% 52.91/53.37 0 ==> 0
% 52.91/53.37 end
% 52.91/53.37
% 52.91/53.37 eqswap: (74688) {G0,W9,D5,L1,V1,M1} { addition( multiplication( X,
% 52.91/53.37 strong_iteration( X ) ), one ) = strong_iteration( X ) }.
% 52.91/53.37 parent0[0]: (74639) {G0,W9,D5,L1,V1,M1} { strong_iteration( X ) = addition
% 52.91/53.37 ( multiplication( X, strong_iteration( X ) ), one ) }.
% 52.91/53.37 substitution0:
% 52.91/53.37 X := X
% 52.91/53.37 end
% 52.91/53.37
% 52.91/53.37 subsumption: (14) {G0,W9,D5,L1,V1,M1} I { addition( multiplication( X,
% 52.91/53.37 strong_iteration( X ) ), one ) ==> strong_iteration( X ) }.
% 52.91/53.37 parent0: (74688) {G0,W9,D5,L1,V1,M1} { addition( multiplication( X,
% 52.91/53.37 strong_iteration( X ) ), one ) = strong_iteration( X ) }.
% 52.91/53.37 substitution0:
% 52.91/53.37 X := X
% 52.91/53.37 end
% 52.91/53.37 permutation0:
% 52.91/53.37 0 ==> 0
% 52.91/53.37 end
% 52.91/53.37
% 52.91/53.37 subsumption: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 52.91/53.37 ==> Y }.
% 52.91/53.37 parent0: (74642) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y
% 52.91/53.37 }.
% 52.91/53.37 substitution0:
% 52.91/53.37 X := X
% 52.91/53.37 Y := Y
% 52.91/53.37 end
% 52.91/53.37 permutation0:
% 52.91/53.37 0 ==> 0
% 52.91/53.37 1 ==> 1
% 52.91/53.37 end
% 52.91/53.37
% 52.91/53.37 subsumption: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X
% 52.91/53.37 , Y ) }.
% 52.91/53.37 parent0: (74643) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y )
% 52.91/53.37 }.
% 52.91/53.37 substitution0:
% 52.91/53.37 X := X
% 52.91/53.37 Y := Y
% 52.91/53.37 end
% 52.91/53.37 permutation0:
% 52.91/53.37 0 ==> 0
% 52.91/53.37 1 ==> 1
% 52.91/53.37 end
% 52.91/53.37
% 52.91/53.37 subsumption: (19) {G0,W11,D4,L2,V0,M2} I { multiplication( skol1, skol2 )
% 52.91/53.37 ==> zero, ! leq( skol1, multiplication( skol1, strong_iteration( skol2 )
% 52.91/53.37 ) ) }.
% 52.91/53.37 parent0: (74644) {G0,W11,D4,L2,V0,M2} { multiplication( skol1, skol2 ) =
% 52.91/53.37 zero, ! leq( skol1, multiplication( skol1, strong_iteration( skol2 ) ) )
% 52.91/53.37 }.
% 52.91/53.37 substitution0:
% 52.91/53.37 end
% 52.91/53.37 permutation0:
% 52.91/53.37 0 ==> 0
% 52.91/53.37 1 ==> 1
% 52.91/53.37 end
% 52.91/53.37
% 52.91/53.37 subsumption: (20) {G0,W12,D4,L2,V0,M2} I { ! leq( multiplication( skol1,
% 52.91/53.37 strong_iteration( skol2 ) ), skol1 ), ! leq( skol1, multiplication( skol1
% 52.91/53.37 , strong_iteration( skol2 ) ) ) }.
% 52.91/53.37 parent0: (74645) {G0,W12,D4,L2,V0,M2} { ! leq( multiplication( skol1,
% 52.91/53.37 strong_iteration( skol2 ) ), skol1 ), ! leq( skol1, multiplication( skol1
% 52.91/53.37 , strong_iteration( skol2 ) ) ) }.
% 52.91/53.37 substitution0:
% 52.91/53.37 end
% 52.91/53.37 permutation0:
% 52.91/53.37 0 ==> 0
% 52.91/53.37 1 ==> 1
% 52.91/53.37 end
% 52.91/53.37
% 52.91/53.37 eqswap: (74750) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, zero ) }.
% 52.91/53.37 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 52.91/53.37 substitution0:
% 52.91/53.37 X := X
% 52.91/53.37 end
% 52.91/53.37
% 52.91/53.37 paramod: (74751) {G1,W5,D3,L1,V1,M1} { X ==> addition( zero, X ) }.
% 52.91/53.37 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 52.91/53.37 }.
% 52.91/53.37 parent1[0; 2]: (74750) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, zero ) }.
% 52.91/53.37 substitution0:
% 52.91/53.37 X := X
% 52.91/53.37 Y := zero
% 52.91/53.37 end
% 52.91/53.37 substitution1:
% 52.91/53.37 X := X
% 52.91/53.37 end
% 52.91/53.37
% 52.91/53.37 eqswap: (74754) {G1,W5,D3,L1,V1,M1} { addition( zero, X ) ==> X }.
% 52.91/53.37 parent0[0]: (74751) {G1,W5,D3,L1,V1,M1} { X ==> addition( zero, X ) }.
% 52.91/53.37 substitution0:
% 52.91/53.37 X := X
% 52.91/53.37 end
% 52.91/53.37
% 52.91/53.37 subsumption: (21) {G1,W5,D3,L1,V1,M1} P(0,2) { addition( zero, X ) ==> X
% 52.91/53.37 }.
% 52.91/53.37 parent0: (74754) {G1,W5,D3,L1,V1,M1} { addition( zero, X ) ==> X }.
% 52.91/53.37 substitution0:
% 52.91/53.37 X := X
% 52.91/53.37 end
% 52.91/53.37 permutation0:
% 52.91/53.37 0 ==> 0
% 52.91/53.37 end
% 52.91/53.37
% 52.91/53.37 eqswap: (74755) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 52.91/53.37 ) }.
% 52.91/53.37 parent0[0]: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 52.91/53.37 Y ) }.
% 52.91/53.37 substitution0:
% 52.91/53.37 X := X
% 52.91/53.37 Y := Y
% 52.91/53.37 end
% 52.91/53.37
% 52.91/53.37 paramod: (74756) {G1,W8,D3,L2,V2,M2} { ! X ==> addition( X, Y ), leq( Y, X
% 52.91/53.37 ) }.
% 52.91/53.37 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 52.91/53.37 }.
% 52.91/53.37 parent1[0; 3]: (74755) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 52.91/53.37 ( X, Y ) }.
% 52.91/53.37 substitution0:
% 52.91/53.37 X := Y
% 52.91/53.37 Y := X
% 52.91/53.37 end
% 52.91/53.37 substitution1:
% 52.91/53.37 X := Y
% 52.91/53.37 Y := X
% 52.91/53.37 end
% 52.91/53.37
% 52.91/53.37 eqswap: (74759) {G1,W8,D3,L2,V2,M2} { ! addition( X, Y ) ==> X, leq( Y, X
% 52.91/53.37 ) }.
% 52.91/53.37 parent0[0]: (74756) {G1,W8,D3,L2,V2,M2} { ! X ==> addition( X, Y ), leq( Y
% 52.91/53.37 , X ) }.
% 52.91/53.37 substitution0:
% 52.91/53.37 X := X
% 52.91/53.37 Y := Y
% 52.91/53.37 end
% 52.91/53.37
% 52.91/53.37 subsumption: (24) {G1,W8,D3,L2,V2,M2} P(0,18) { ! addition( Y, X ) ==> Y,
% 52.91/53.37 leq( X, Y ) }.
% 52.91/53.37 parent0: (74759) {G1,W8,D3,L2,V2,M2} { ! addition( X, Y ) ==> X, leq( Y, X
% 52.91/53.37 ) }.
% 52.91/53.37 substitution0:
% 52.91/53.37 X := Y
% 52.91/53.37 Y := X
% 52.91/53.37 end
% 52.91/53.37 permutation0:
% 52.91/53.37 0 ==> 0
% 52.91/53.37 1 ==> 1
% 52.91/53.37 end
% 52.91/53.37
% 52.91/53.37 eqswap: (74761) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 52.91/53.37 ) }.
% 52.91/53.37 parent0[0]: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 52.91/53.37 Y ) }.
% 52.91/53.37 substitution0:
% 52.91/53.37 X := X
% 52.91/53.37 Y := Y
% 52.91/53.37 end
% 52.91/53.37
% 52.91/53.37 paramod: (74762) {G1,W6,D2,L2,V1,M2} { ! zero ==> X, leq( X, zero ) }.
% 52.91/53.37 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 52.91/53.37 parent1[0; 3]: (74761) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 52.91/53.37 ( X, Y ) }.
% 52.91/53.37 substitution0:
% 52.91/53.37 X := X
% 52.91/53.37 end
% 52.91/53.37 substitution1:
% 52.91/53.37 X := X
% 52.91/53.37 Y := zero
% 52.91/53.37 end
% 52.91/53.37
% 52.91/53.37 eqswap: (74763) {G1,W6,D2,L2,V1,M2} { ! X ==> zero, leq( X, zero ) }.
% 52.91/53.37 parent0[0]: (74762) {G1,W6,D2,L2,V1,M2} { ! zero ==> X, leq( X, zero ) }.
% 52.91/53.37 substitution0:
% 52.91/53.37 X := X
% 52.91/53.37 end
% 52.91/53.37
% 52.91/53.37 subsumption: (25) {G1,W6,D2,L2,V1,M2} P(2,18) { ! X = zero, leq( X, zero )
% 52.91/53.37 }.
% 52.91/53.37 parent0: (74763) {G1,W6,D2,L2,V1,M2} { ! X ==> zero, leq( X, zero ) }.
% 52.91/53.37 substitution0:
% 52.91/53.37 X := X
% 52.91/53.37 end
% 52.91/53.37 permutation0:
% 52.91/53.37 0 ==> 0
% 52.91/53.37 1 ==> 1
% 52.91/53.37 end
% 52.91/53.37
% 52.91/53.37 eqswap: (74765) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 52.91/53.37 ) }.
% 52.91/53.37 parent0[0]: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 52.91/53.37 Y ) }.
% 52.91/53.37 substitution0:
% 52.91/53.37 X := X
% 52.91/53.37 Y := Y
% 52.91/53.37 end
% 52.91/53.37
% 52.91/53.37 paramod: (74766) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition(
% 52.91/53.37 addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 52.91/53.37 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 52.91/53.37 ==> addition( addition( Z, Y ), X ) }.
% 52.91/53.37 parent1[0; 5]: (74765) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 52.91/53.37 ( X, Y ) }.
% 52.91/53.37 substitution0:
% 52.91/53.37 X := Y
% 52.91/53.37 Y := X
% 52.91/53.37 Z := Z
% 52.91/53.37 end
% 52.91/53.37 substitution1:
% 52.91/53.37 X := Z
% 52.91/53.37 Y := addition( X, Y )
% 52.91/53.37 end
% 52.91/53.37
% 52.91/53.37 eqswap: (74767) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 52.91/53.37 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 52.91/53.37 parent0[0]: (74766) {G1,W14,D4,L2,V3,M2} { ! addition( X, Y ) ==> addition
% 52.91/53.37 ( addition( Z, X ), Y ), leq( Z, addition( X, Y ) ) }.
% 52.91/53.37 substitution0:
% 52.91/53.37 X := X
% 52.91/53.37 Y := Y
% 52.91/53.37 Z := Z
% 52.91/53.37 end
% 52.91/53.37
% 52.91/53.37 subsumption: (26) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y
% 52.91/53.37 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 52.91/53.37 parent0: (74767) {G1,W14,D4,L2,V3,M2} { ! addition( addition( Z, X ), Y )
% 53.01/53.38 ==> addition( X, Y ), leq( Z, addition( X, Y ) ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := Y
% 53.01/53.38 Y := Z
% 53.01/53.38 Z := X
% 53.01/53.38 end
% 53.01/53.38 permutation0:
% 53.01/53.38 0 ==> 0
% 53.01/53.38 1 ==> 1
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 eqswap: (74768) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 53.01/53.38 ) }.
% 53.01/53.38 parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 53.01/53.38 ==> Y }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := X
% 53.01/53.38 Y := Y
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 eqswap: (74769) {G1,W6,D2,L2,V1,M2} { ! zero = X, leq( X, zero ) }.
% 53.01/53.38 parent0[0]: (25) {G1,W6,D2,L2,V1,M2} P(2,18) { ! X = zero, leq( X, zero )
% 53.01/53.38 }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := X
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 resolution: (74771) {G1,W8,D3,L2,V1,M2} { zero ==> addition( X, zero ), !
% 53.01/53.38 zero = X }.
% 53.01/53.38 parent0[1]: (74768) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X
% 53.01/53.38 , Y ) }.
% 53.01/53.38 parent1[1]: (74769) {G1,W6,D2,L2,V1,M2} { ! zero = X, leq( X, zero ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := X
% 53.01/53.38 Y := zero
% 53.01/53.38 end
% 53.01/53.38 substitution1:
% 53.01/53.38 X := X
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 paramod: (74772) {G1,W6,D2,L2,V1,M2} { zero ==> X, ! zero = X }.
% 53.01/53.38 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 53.01/53.38 parent1[0; 2]: (74771) {G1,W8,D3,L2,V1,M2} { zero ==> addition( X, zero )
% 53.01/53.38 , ! zero = X }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := X
% 53.01/53.38 end
% 53.01/53.38 substitution1:
% 53.01/53.38 X := X
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 eqswap: (74774) {G1,W6,D2,L2,V1,M2} { ! X = zero, zero ==> X }.
% 53.01/53.38 parent0[1]: (74772) {G1,W6,D2,L2,V1,M2} { zero ==> X, ! zero = X }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := X
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 eqswap: (74775) {G1,W6,D2,L2,V1,M2} { X ==> zero, ! X = zero }.
% 53.01/53.38 parent0[1]: (74774) {G1,W6,D2,L2,V1,M2} { ! X = zero, zero ==> X }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := X
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 subsumption: (33) {G2,W6,D2,L2,V1,M2} R(17,25);d(2) { ! X = zero, X = zero
% 53.01/53.38 }.
% 53.01/53.38 parent0: (74775) {G1,W6,D2,L2,V1,M2} { X ==> zero, ! X = zero }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := X
% 53.01/53.38 end
% 53.01/53.38 permutation0:
% 53.01/53.38 0 ==> 1
% 53.01/53.38 1 ==> 0
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 eqswap: (74777) {G1,W8,D3,L2,V2,M2} { ! X ==> addition( X, Y ), leq( Y, X
% 53.01/53.38 ) }.
% 53.01/53.38 parent0[0]: (24) {G1,W8,D3,L2,V2,M2} P(0,18) { ! addition( Y, X ) ==> Y,
% 53.01/53.38 leq( X, Y ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := Y
% 53.01/53.38 Y := X
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 paramod: (74778) {G1,W9,D2,L3,V2,M3} { ! X ==> Y, ! leq( X, Y ), leq( Y, X
% 53.01/53.38 ) }.
% 53.01/53.38 parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 53.01/53.38 ==> Y }.
% 53.01/53.38 parent1[0; 3]: (74777) {G1,W8,D3,L2,V2,M2} { ! X ==> addition( X, Y ), leq
% 53.01/53.38 ( Y, X ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := X
% 53.01/53.38 Y := Y
% 53.01/53.38 end
% 53.01/53.38 substitution1:
% 53.01/53.38 X := X
% 53.01/53.38 Y := Y
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 eqswap: (74779) {G1,W9,D2,L3,V2,M3} { ! Y ==> X, ! leq( X, Y ), leq( Y, X
% 53.01/53.38 ) }.
% 53.01/53.38 parent0[0]: (74778) {G1,W9,D2,L3,V2,M3} { ! X ==> Y, ! leq( X, Y ), leq( Y
% 53.01/53.38 , X ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := X
% 53.01/53.38 Y := Y
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 subsumption: (34) {G2,W9,D2,L3,V2,M3} P(17,24) { ! Y = X, leq( Y, X ), !
% 53.01/53.38 leq( X, Y ) }.
% 53.01/53.38 parent0: (74779) {G1,W9,D2,L3,V2,M3} { ! Y ==> X, ! leq( X, Y ), leq( Y, X
% 53.01/53.38 ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := X
% 53.01/53.38 Y := Y
% 53.01/53.38 end
% 53.01/53.38 permutation0:
% 53.01/53.38 0 ==> 0
% 53.01/53.38 1 ==> 2
% 53.01/53.38 2 ==> 1
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 eqswap: (74780) {G2,W6,D2,L2,V1,M2} { ! zero = X, X = zero }.
% 53.01/53.38 parent0[0]: (33) {G2,W6,D2,L2,V1,M2} R(17,25);d(2) { ! X = zero, X = zero
% 53.01/53.38 }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := X
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 eqswap: (74783) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z )
% 53.01/53.38 ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 53.01/53.38 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 53.01/53.38 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := X
% 53.01/53.38 Y := Y
% 53.01/53.38 Z := Z
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 paramod: (74788) {G1,W16,D4,L2,V3,M2} { multiplication( X, addition( Y, Z
% 53.01/53.38 ) ) ==> addition( zero, multiplication( X, Z ) ), ! zero =
% 53.01/53.38 multiplication( X, Y ) }.
% 53.01/53.38 parent0[1]: (74780) {G2,W6,D2,L2,V1,M2} { ! zero = X, X = zero }.
% 53.01/53.38 parent1[0; 7]: (74783) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition
% 53.01/53.38 ( Y, Z ) ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) )
% 53.01/53.38 }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := multiplication( X, Y )
% 53.01/53.38 end
% 53.01/53.38 substitution1:
% 53.01/53.38 X := X
% 53.01/53.38 Y := Y
% 53.01/53.38 Z := Z
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 paramod: (75586) {G2,W14,D4,L2,V3,M2} { multiplication( X, addition( Y, Z
% 53.01/53.38 ) ) ==> multiplication( X, Z ), ! zero = multiplication( X, Y ) }.
% 53.01/53.38 parent0[0]: (21) {G1,W5,D3,L1,V1,M1} P(0,2) { addition( zero, X ) ==> X }.
% 53.01/53.38 parent1[0; 6]: (74788) {G1,W16,D4,L2,V3,M2} { multiplication( X, addition
% 53.01/53.38 ( Y, Z ) ) ==> addition( zero, multiplication( X, Z ) ), ! zero =
% 53.01/53.38 multiplication( X, Y ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := multiplication( X, Z )
% 53.01/53.38 end
% 53.01/53.38 substitution1:
% 53.01/53.38 X := X
% 53.01/53.38 Y := Y
% 53.01/53.38 Z := Z
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 eqswap: (75588) {G2,W14,D4,L2,V3,M2} { ! multiplication( X, Y ) = zero,
% 53.01/53.38 multiplication( X, addition( Y, Z ) ) ==> multiplication( X, Z ) }.
% 53.01/53.38 parent0[1]: (75586) {G2,W14,D4,L2,V3,M2} { multiplication( X, addition( Y
% 53.01/53.38 , Z ) ) ==> multiplication( X, Z ), ! zero = multiplication( X, Y ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := X
% 53.01/53.38 Y := Y
% 53.01/53.38 Z := Z
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 subsumption: (64) {G3,W14,D4,L2,V3,M2} P(33,7);d(21) { ! multiplication( X
% 53.01/53.38 , Y ) ==> zero, multiplication( X, addition( Y, Z ) ) ==> multiplication
% 53.01/53.38 ( X, Z ) }.
% 53.01/53.38 parent0: (75588) {G2,W14,D4,L2,V3,M2} { ! multiplication( X, Y ) = zero,
% 53.01/53.38 multiplication( X, addition( Y, Z ) ) ==> multiplication( X, Z ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := X
% 53.01/53.38 Y := Y
% 53.01/53.38 Z := Z
% 53.01/53.38 end
% 53.01/53.38 permutation0:
% 53.01/53.38 0 ==> 0
% 53.01/53.38 1 ==> 1
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 eqswap: (75591) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 53.01/53.38 ) }.
% 53.01/53.38 parent0[0]: (18) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 53.01/53.38 Y ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := X
% 53.01/53.38 Y := Y
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 paramod: (75592) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 53.01/53.38 multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ),
% 53.01/53.38 multiplication( X, Y ) ) }.
% 53.01/53.38 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 53.01/53.38 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 53.01/53.38 parent1[0; 5]: (75591) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq
% 53.01/53.38 ( X, Y ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := X
% 53.01/53.38 Y := Z
% 53.01/53.38 Z := Y
% 53.01/53.38 end
% 53.01/53.38 substitution1:
% 53.01/53.38 X := multiplication( X, Z )
% 53.01/53.38 Y := multiplication( X, Y )
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 eqswap: (75593) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, addition( Z, Y
% 53.01/53.38 ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ),
% 53.01/53.38 multiplication( X, Y ) ) }.
% 53.01/53.38 parent0[0]: (75592) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 53.01/53.38 multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ),
% 53.01/53.38 multiplication( X, Y ) ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := X
% 53.01/53.38 Y := Y
% 53.01/53.38 Z := Z
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 subsumption: (68) {G1,W16,D4,L2,V3,M2} P(7,18) { ! multiplication( X,
% 53.01/53.38 addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 53.01/53.38 ), multiplication( X, Z ) ) }.
% 53.01/53.38 parent0: (75593) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, addition( Z,
% 53.01/53.38 Y ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ),
% 53.01/53.38 multiplication( X, Y ) ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := X
% 53.01/53.38 Y := Z
% 53.01/53.38 Z := Y
% 53.01/53.38 end
% 53.01/53.38 permutation0:
% 53.01/53.38 0 ==> 0
% 53.01/53.38 1 ==> 1
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 eqswap: (75595) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==> addition(
% 53.01/53.38 addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 53.01/53.38 parent0[0]: (26) {G1,W14,D4,L2,V3,M2} P(1,18) { ! addition( addition( X, Y
% 53.01/53.38 ), Z ) ==> addition( Y, Z ), leq( X, addition( Y, Z ) ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := X
% 53.01/53.38 Y := Y
% 53.01/53.38 Z := Z
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 paramod: (75598) {G1,W12,D3,L2,V2,M2} { ! addition( X, Y ) ==> addition( X
% 53.01/53.38 , Y ), leq( X, addition( X, Y ) ) }.
% 53.01/53.38 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 53.01/53.38 parent1[0; 6]: (75595) {G1,W14,D4,L2,V3,M2} { ! addition( Y, Z ) ==>
% 53.01/53.38 addition( addition( X, Y ), Z ), leq( X, addition( Y, Z ) ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := X
% 53.01/53.38 end
% 53.01/53.38 substitution1:
% 53.01/53.38 X := X
% 53.01/53.38 Y := X
% 53.01/53.38 Z := Y
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 eqrefl: (75601) {G0,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 53.01/53.38 parent0[0]: (75598) {G1,W12,D3,L2,V2,M2} { ! addition( X, Y ) ==> addition
% 53.01/53.38 ( X, Y ), leq( X, addition( X, Y ) ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := X
% 53.01/53.38 Y := Y
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 subsumption: (364) {G2,W5,D3,L1,V2,M1} P(3,26);q { leq( X, addition( X, Y )
% 53.01/53.38 ) }.
% 53.01/53.38 parent0: (75601) {G0,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := X
% 53.01/53.38 Y := Y
% 53.01/53.38 end
% 53.01/53.38 permutation0:
% 53.01/53.38 0 ==> 0
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 paramod: (75602) {G1,W5,D3,L1,V2,M1} { leq( X, addition( Y, X ) ) }.
% 53.01/53.38 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 53.01/53.38 }.
% 53.01/53.38 parent1[0; 2]: (364) {G2,W5,D3,L1,V2,M1} P(3,26);q { leq( X, addition( X, Y
% 53.01/53.38 ) ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := X
% 53.01/53.38 Y := Y
% 53.01/53.38 end
% 53.01/53.38 substitution1:
% 53.01/53.38 X := X
% 53.01/53.38 Y := Y
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 subsumption: (423) {G3,W5,D3,L1,V2,M1} P(0,364) { leq( X, addition( Y, X )
% 53.01/53.38 ) }.
% 53.01/53.38 parent0: (75602) {G1,W5,D3,L1,V2,M1} { leq( X, addition( Y, X ) ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := X
% 53.01/53.38 Y := Y
% 53.01/53.38 end
% 53.01/53.38 permutation0:
% 53.01/53.38 0 ==> 0
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 paramod: (75605) {G1,W4,D3,L1,V1,M1} { leq( one, strong_iteration( X ) )
% 53.01/53.38 }.
% 53.01/53.38 parent0[0]: (14) {G0,W9,D5,L1,V1,M1} I { addition( multiplication( X,
% 53.01/53.38 strong_iteration( X ) ), one ) ==> strong_iteration( X ) }.
% 53.01/53.38 parent1[0; 2]: (423) {G3,W5,D3,L1,V2,M1} P(0,364) { leq( X, addition( Y, X
% 53.01/53.38 ) ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := X
% 53.01/53.38 end
% 53.01/53.38 substitution1:
% 53.01/53.38 X := one
% 53.01/53.38 Y := multiplication( X, strong_iteration( X ) )
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 subsumption: (429) {G4,W4,D3,L1,V1,M1} P(14,423) { leq( one,
% 53.01/53.38 strong_iteration( X ) ) }.
% 53.01/53.38 parent0: (75605) {G1,W4,D3,L1,V1,M1} { leq( one, strong_iteration( X ) )
% 53.01/53.38 }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := X
% 53.01/53.38 end
% 53.01/53.38 permutation0:
% 53.01/53.38 0 ==> 0
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 eqswap: (75606) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 53.01/53.38 ) }.
% 53.01/53.38 parent0[1]: (17) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 53.01/53.38 ==> Y }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := X
% 53.01/53.38 Y := Y
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 resolution: (75607) {G1,W7,D4,L1,V1,M1} { strong_iteration( X ) ==>
% 53.01/53.38 addition( one, strong_iteration( X ) ) }.
% 53.01/53.38 parent0[1]: (75606) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X
% 53.01/53.38 , Y ) }.
% 53.01/53.38 parent1[0]: (429) {G4,W4,D3,L1,V1,M1} P(14,423) { leq( one,
% 53.01/53.38 strong_iteration( X ) ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := one
% 53.01/53.38 Y := strong_iteration( X )
% 53.01/53.38 end
% 53.01/53.38 substitution1:
% 53.01/53.38 X := X
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 eqswap: (75608) {G1,W7,D4,L1,V1,M1} { addition( one, strong_iteration( X )
% 53.01/53.38 ) ==> strong_iteration( X ) }.
% 53.01/53.38 parent0[0]: (75607) {G1,W7,D4,L1,V1,M1} { strong_iteration( X ) ==>
% 53.01/53.38 addition( one, strong_iteration( X ) ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := X
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 subsumption: (437) {G5,W7,D4,L1,V1,M1} R(429,17) { addition( one,
% 53.01/53.38 strong_iteration( X ) ) ==> strong_iteration( X ) }.
% 53.01/53.38 parent0: (75608) {G1,W7,D4,L1,V1,M1} { addition( one, strong_iteration( X
% 53.01/53.38 ) ) ==> strong_iteration( X ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := X
% 53.01/53.38 end
% 53.01/53.38 permutation0:
% 53.01/53.38 0 ==> 0
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 eqswap: (75610) {G3,W14,D4,L2,V3,M2} { ! zero ==> multiplication( X, Y ),
% 53.01/53.38 multiplication( X, addition( Y, Z ) ) ==> multiplication( X, Z ) }.
% 53.01/53.38 parent0[0]: (64) {G3,W14,D4,L2,V3,M2} P(33,7);d(21) { ! multiplication( X,
% 53.01/53.38 Y ) ==> zero, multiplication( X, addition( Y, Z ) ) ==> multiplication( X
% 53.01/53.38 , Z ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := X
% 53.01/53.38 Y := Y
% 53.01/53.38 Z := Z
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 paramod: (75615) {G1,W16,D5,L2,V2,M2} { multiplication( X,
% 53.01/53.38 strong_iteration( Y ) ) ==> multiplication( X, one ), ! zero ==>
% 53.01/53.38 multiplication( X, multiplication( Y, strong_iteration( Y ) ) ) }.
% 53.01/53.38 parent0[0]: (14) {G0,W9,D5,L1,V1,M1} I { addition( multiplication( X,
% 53.01/53.38 strong_iteration( X ) ), one ) ==> strong_iteration( X ) }.
% 53.01/53.38 parent1[1; 3]: (75610) {G3,W14,D4,L2,V3,M2} { ! zero ==> multiplication( X
% 53.01/53.38 , Y ), multiplication( X, addition( Y, Z ) ) ==> multiplication( X, Z )
% 53.01/53.38 }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := Y
% 53.01/53.38 end
% 53.01/53.38 substitution1:
% 53.01/53.38 X := X
% 53.01/53.38 Y := multiplication( Y, strong_iteration( Y ) )
% 53.01/53.38 Z := one
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 paramod: (75616) {G1,W16,D4,L2,V2,M2} { ! zero ==> multiplication(
% 53.01/53.38 multiplication( X, Y ), strong_iteration( Y ) ), multiplication( X,
% 53.01/53.38 strong_iteration( Y ) ) ==> multiplication( X, one ) }.
% 53.01/53.38 parent0[0]: (4) {G0,W11,D4,L1,V3,M1} I { multiplication( X, multiplication
% 53.01/53.38 ( Y, Z ) ) ==> multiplication( multiplication( X, Y ), Z ) }.
% 53.01/53.38 parent1[1; 3]: (75615) {G1,W16,D5,L2,V2,M2} { multiplication( X,
% 53.01/53.38 strong_iteration( Y ) ) ==> multiplication( X, one ), ! zero ==>
% 53.01/53.38 multiplication( X, multiplication( Y, strong_iteration( Y ) ) ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := X
% 53.01/53.38 Y := Y
% 53.01/53.38 Z := strong_iteration( Y )
% 53.01/53.38 end
% 53.01/53.38 substitution1:
% 53.01/53.38 X := X
% 53.01/53.38 Y := Y
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 paramod: (75617) {G1,W14,D4,L2,V2,M2} { multiplication( X,
% 53.01/53.38 strong_iteration( Y ) ) ==> X, ! zero ==> multiplication( multiplication
% 53.01/53.38 ( X, Y ), strong_iteration( Y ) ) }.
% 53.01/53.38 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 53.01/53.38 parent1[1; 5]: (75616) {G1,W16,D4,L2,V2,M2} { ! zero ==> multiplication(
% 53.01/53.38 multiplication( X, Y ), strong_iteration( Y ) ), multiplication( X,
% 53.01/53.38 strong_iteration( Y ) ) ==> multiplication( X, one ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := X
% 53.01/53.38 end
% 53.01/53.38 substitution1:
% 53.01/53.38 X := X
% 53.01/53.38 Y := Y
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 eqswap: (75619) {G1,W14,D4,L2,V2,M2} { ! multiplication( multiplication( X
% 53.01/53.38 , Y ), strong_iteration( Y ) ) ==> zero, multiplication( X,
% 53.01/53.38 strong_iteration( Y ) ) ==> X }.
% 53.01/53.38 parent0[1]: (75617) {G1,W14,D4,L2,V2,M2} { multiplication( X,
% 53.01/53.38 strong_iteration( Y ) ) ==> X, ! zero ==> multiplication( multiplication
% 53.01/53.38 ( X, Y ), strong_iteration( Y ) ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := X
% 53.01/53.38 Y := Y
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 subsumption: (969) {G4,W14,D4,L2,V2,M2} P(14,64);d(4);d(5) { !
% 53.01/53.38 multiplication( multiplication( Y, X ), strong_iteration( X ) ) ==> zero
% 53.01/53.38 , multiplication( Y, strong_iteration( X ) ) ==> Y }.
% 53.01/53.38 parent0: (75619) {G1,W14,D4,L2,V2,M2} { ! multiplication( multiplication(
% 53.01/53.38 X, Y ), strong_iteration( Y ) ) ==> zero, multiplication( X,
% 53.01/53.38 strong_iteration( Y ) ) ==> X }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := Y
% 53.01/53.38 Y := X
% 53.01/53.38 end
% 53.01/53.38 permutation0:
% 53.01/53.38 0 ==> 0
% 53.01/53.38 1 ==> 1
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 eqswap: (75622) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Z ) ==>
% 53.01/53.38 multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ),
% 53.01/53.38 multiplication( X, Z ) ) }.
% 53.01/53.38 parent0[0]: (68) {G1,W16,D4,L2,V3,M2} P(7,18) { ! multiplication( X,
% 53.01/53.38 addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 53.01/53.38 ), multiplication( X, Z ) ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := X
% 53.01/53.38 Y := Y
% 53.01/53.38 Z := Z
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 paramod: (75624) {G2,W17,D4,L2,V2,M2} { ! multiplication( X,
% 53.01/53.38 strong_iteration( Y ) ) ==> multiplication( X, strong_iteration( Y ) ),
% 53.01/53.38 leq( multiplication( X, one ), multiplication( X, strong_iteration( Y ) )
% 53.01/53.38 ) }.
% 53.01/53.38 parent0[0]: (437) {G5,W7,D4,L1,V1,M1} R(429,17) { addition( one,
% 53.01/53.38 strong_iteration( X ) ) ==> strong_iteration( X ) }.
% 53.01/53.38 parent1[0; 8]: (75622) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Z ) ==>
% 53.01/53.38 multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ),
% 53.01/53.38 multiplication( X, Z ) ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := Y
% 53.01/53.38 end
% 53.01/53.38 substitution1:
% 53.01/53.38 X := X
% 53.01/53.38 Y := one
% 53.01/53.38 Z := strong_iteration( Y )
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 eqrefl: (75625) {G0,W8,D4,L1,V2,M1} { leq( multiplication( X, one ),
% 53.01/53.38 multiplication( X, strong_iteration( Y ) ) ) }.
% 53.01/53.38 parent0[0]: (75624) {G2,W17,D4,L2,V2,M2} { ! multiplication( X,
% 53.01/53.38 strong_iteration( Y ) ) ==> multiplication( X, strong_iteration( Y ) ),
% 53.01/53.38 leq( multiplication( X, one ), multiplication( X, strong_iteration( Y ) )
% 53.01/53.38 ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := X
% 53.01/53.38 Y := Y
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 paramod: (75626) {G1,W6,D4,L1,V2,M1} { leq( X, multiplication( X,
% 53.01/53.38 strong_iteration( Y ) ) ) }.
% 53.01/53.38 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 53.01/53.38 parent1[0; 1]: (75625) {G0,W8,D4,L1,V2,M1} { leq( multiplication( X, one )
% 53.01/53.38 , multiplication( X, strong_iteration( Y ) ) ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := X
% 53.01/53.38 end
% 53.01/53.38 substitution1:
% 53.01/53.38 X := X
% 53.01/53.38 Y := Y
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 subsumption: (1237) {G6,W6,D4,L1,V2,M1} P(437,68);q;d(5) { leq( Y,
% 53.01/53.38 multiplication( Y, strong_iteration( X ) ) ) }.
% 53.01/53.38 parent0: (75626) {G1,W6,D4,L1,V2,M1} { leq( X, multiplication( X,
% 53.01/53.38 strong_iteration( Y ) ) ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := Y
% 53.01/53.38 Y := X
% 53.01/53.38 end
% 53.01/53.38 permutation0:
% 53.01/53.38 0 ==> 0
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 resolution: (75627) {G1,W6,D4,L1,V0,M1} { ! leq( multiplication( skol1,
% 53.01/53.38 strong_iteration( skol2 ) ), skol1 ) }.
% 53.01/53.38 parent0[1]: (20) {G0,W12,D4,L2,V0,M2} I { ! leq( multiplication( skol1,
% 53.01/53.38 strong_iteration( skol2 ) ), skol1 ), ! leq( skol1, multiplication( skol1
% 53.01/53.38 , strong_iteration( skol2 ) ) ) }.
% 53.01/53.38 parent1[0]: (1237) {G6,W6,D4,L1,V2,M1} P(437,68);q;d(5) { leq( Y,
% 53.01/53.38 multiplication( Y, strong_iteration( X ) ) ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 end
% 53.01/53.38 substitution1:
% 53.01/53.38 X := skol2
% 53.01/53.38 Y := skol1
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 subsumption: (1275) {G7,W6,D4,L1,V0,M1} R(1237,20) { ! leq( multiplication
% 53.01/53.38 ( skol1, strong_iteration( skol2 ) ), skol1 ) }.
% 53.01/53.38 parent0: (75627) {G1,W6,D4,L1,V0,M1} { ! leq( multiplication( skol1,
% 53.01/53.38 strong_iteration( skol2 ) ), skol1 ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 end
% 53.01/53.38 permutation0:
% 53.01/53.38 0 ==> 0
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 eqswap: (75628) {G0,W11,D4,L2,V0,M2} { zero ==> multiplication( skol1,
% 53.01/53.38 skol2 ), ! leq( skol1, multiplication( skol1, strong_iteration( skol2 ) )
% 53.01/53.38 ) }.
% 53.01/53.38 parent0[0]: (19) {G0,W11,D4,L2,V0,M2} I { multiplication( skol1, skol2 )
% 53.01/53.38 ==> zero, ! leq( skol1, multiplication( skol1, strong_iteration( skol2 )
% 53.01/53.38 ) ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 resolution: (75629) {G1,W5,D3,L1,V0,M1} { zero ==> multiplication( skol1,
% 53.01/53.38 skol2 ) }.
% 53.01/53.38 parent0[1]: (75628) {G0,W11,D4,L2,V0,M2} { zero ==> multiplication( skol1
% 53.01/53.38 , skol2 ), ! leq( skol1, multiplication( skol1, strong_iteration( skol2 )
% 53.01/53.38 ) ) }.
% 53.01/53.38 parent1[0]: (1237) {G6,W6,D4,L1,V2,M1} P(437,68);q;d(5) { leq( Y,
% 53.01/53.38 multiplication( Y, strong_iteration( X ) ) ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 end
% 53.01/53.38 substitution1:
% 53.01/53.38 X := skol2
% 53.01/53.38 Y := skol1
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 eqswap: (75630) {G1,W5,D3,L1,V0,M1} { multiplication( skol1, skol2 ) ==>
% 53.01/53.38 zero }.
% 53.01/53.38 parent0[0]: (75629) {G1,W5,D3,L1,V0,M1} { zero ==> multiplication( skol1,
% 53.01/53.38 skol2 ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 subsumption: (1277) {G7,W5,D3,L1,V0,M1} R(1237,19) { multiplication( skol1
% 53.01/53.38 , skol2 ) ==> zero }.
% 53.01/53.38 parent0: (75630) {G1,W5,D3,L1,V0,M1} { multiplication( skol1, skol2 ) ==>
% 53.01/53.38 zero }.
% 53.01/53.38 substitution0:
% 53.01/53.38 end
% 53.01/53.38 permutation0:
% 53.01/53.38 0 ==> 0
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 eqswap: (75631) {G2,W9,D2,L3,V2,M3} { ! Y = X, leq( X, Y ), ! leq( Y, X )
% 53.01/53.38 }.
% 53.01/53.38 parent0[0]: (34) {G2,W9,D2,L3,V2,M3} P(17,24) { ! Y = X, leq( Y, X ), ! leq
% 53.01/53.38 ( X, Y ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := Y
% 53.01/53.38 Y := X
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 resolution: (75632) {G3,W12,D4,L2,V0,M2} { ! skol1 = multiplication( skol1
% 53.01/53.38 , strong_iteration( skol2 ) ), ! leq( skol1, multiplication( skol1,
% 53.01/53.38 strong_iteration( skol2 ) ) ) }.
% 53.01/53.38 parent0[0]: (1275) {G7,W6,D4,L1,V0,M1} R(1237,20) { ! leq( multiplication(
% 53.01/53.38 skol1, strong_iteration( skol2 ) ), skol1 ) }.
% 53.01/53.38 parent1[1]: (75631) {G2,W9,D2,L3,V2,M3} { ! Y = X, leq( X, Y ), ! leq( Y,
% 53.01/53.38 X ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 end
% 53.01/53.38 substitution1:
% 53.01/53.38 X := multiplication( skol1, strong_iteration( skol2 ) )
% 53.01/53.38 Y := skol1
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 resolution: (75633) {G4,W6,D4,L1,V0,M1} { ! skol1 = multiplication( skol1
% 53.01/53.38 , strong_iteration( skol2 ) ) }.
% 53.01/53.38 parent0[1]: (75632) {G3,W12,D4,L2,V0,M2} { ! skol1 = multiplication( skol1
% 53.01/53.38 , strong_iteration( skol2 ) ), ! leq( skol1, multiplication( skol1,
% 53.01/53.38 strong_iteration( skol2 ) ) ) }.
% 53.01/53.38 parent1[0]: (1237) {G6,W6,D4,L1,V2,M1} P(437,68);q;d(5) { leq( Y,
% 53.01/53.38 multiplication( Y, strong_iteration( X ) ) ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 end
% 53.01/53.38 substitution1:
% 53.01/53.38 X := skol2
% 53.01/53.38 Y := skol1
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 eqswap: (75634) {G4,W6,D4,L1,V0,M1} { ! multiplication( skol1,
% 53.01/53.38 strong_iteration( skol2 ) ) = skol1 }.
% 53.01/53.38 parent0[0]: (75633) {G4,W6,D4,L1,V0,M1} { ! skol1 = multiplication( skol1
% 53.01/53.38 , strong_iteration( skol2 ) ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 subsumption: (1393) {G8,W6,D4,L1,V0,M1} R(1275,34);r(1237) { !
% 53.01/53.38 multiplication( skol1, strong_iteration( skol2 ) ) ==> skol1 }.
% 53.01/53.38 parent0: (75634) {G4,W6,D4,L1,V0,M1} { ! multiplication( skol1,
% 53.01/53.38 strong_iteration( skol2 ) ) = skol1 }.
% 53.01/53.38 substitution0:
% 53.01/53.38 end
% 53.01/53.38 permutation0:
% 53.01/53.38 0 ==> 0
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 eqswap: (75635) {G4,W14,D4,L2,V2,M2} { ! zero ==> multiplication(
% 53.01/53.38 multiplication( X, Y ), strong_iteration( Y ) ), multiplication( X,
% 53.01/53.38 strong_iteration( Y ) ) ==> X }.
% 53.01/53.38 parent0[0]: (969) {G4,W14,D4,L2,V2,M2} P(14,64);d(4);d(5) { !
% 53.01/53.38 multiplication( multiplication( Y, X ), strong_iteration( X ) ) ==> zero
% 53.01/53.38 , multiplication( Y, strong_iteration( X ) ) ==> Y }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := Y
% 53.01/53.38 Y := X
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 resolution: (75641) {G5,W8,D4,L1,V0,M1} { ! zero ==> multiplication(
% 53.01/53.38 multiplication( skol1, skol2 ), strong_iteration( skol2 ) ) }.
% 53.01/53.38 parent0[0]: (1393) {G8,W6,D4,L1,V0,M1} R(1275,34);r(1237) { !
% 53.01/53.38 multiplication( skol1, strong_iteration( skol2 ) ) ==> skol1 }.
% 53.01/53.38 parent1[1]: (75635) {G4,W14,D4,L2,V2,M2} { ! zero ==> multiplication(
% 53.01/53.38 multiplication( X, Y ), strong_iteration( Y ) ), multiplication( X,
% 53.01/53.38 strong_iteration( Y ) ) ==> X }.
% 53.01/53.38 substitution0:
% 53.01/53.38 end
% 53.01/53.38 substitution1:
% 53.01/53.38 X := skol1
% 53.01/53.38 Y := skol2
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 paramod: (75642) {G6,W6,D4,L1,V0,M1} { ! zero ==> multiplication( zero,
% 53.01/53.38 strong_iteration( skol2 ) ) }.
% 53.01/53.38 parent0[0]: (1277) {G7,W5,D3,L1,V0,M1} R(1237,19) { multiplication( skol1,
% 53.01/53.38 skol2 ) ==> zero }.
% 53.01/53.38 parent1[0; 4]: (75641) {G5,W8,D4,L1,V0,M1} { ! zero ==> multiplication(
% 53.01/53.38 multiplication( skol1, skol2 ), strong_iteration( skol2 ) ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 end
% 53.01/53.38 substitution1:
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 paramod: (75643) {G1,W3,D2,L1,V0,M1} { ! zero ==> zero }.
% 53.01/53.38 parent0[0]: (9) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==> zero
% 53.01/53.38 }.
% 53.01/53.38 parent1[0; 3]: (75642) {G6,W6,D4,L1,V0,M1} { ! zero ==> multiplication(
% 53.01/53.38 zero, strong_iteration( skol2 ) ) }.
% 53.01/53.38 substitution0:
% 53.01/53.38 X := strong_iteration( skol2 )
% 53.01/53.38 end
% 53.01/53.38 substitution1:
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 eqrefl: (75644) {G0,W0,D0,L0,V0,M0} { }.
% 53.01/53.38 parent0[0]: (75643) {G1,W3,D2,L1,V0,M1} { ! zero ==> zero }.
% 53.01/53.38 substitution0:
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 subsumption: (74623) {G9,W0,D0,L0,V0,M0} R(969,1393);d(1277);d(9);q { }.
% 53.01/53.38 parent0: (75644) {G0,W0,D0,L0,V0,M0} { }.
% 53.01/53.38 substitution0:
% 53.01/53.38 end
% 53.01/53.38 permutation0:
% 53.01/53.38 end
% 53.01/53.38
% 53.01/53.38 Proof check complete!
% 53.01/53.38
% 53.01/53.38 Memory use:
% 53.01/53.38
% 53.01/53.38 space for terms: 1057655
% 53.01/53.38 space for clauses: 3518909
% 53.01/53.38
% 53.01/53.38
% 53.01/53.38 clauses generated: 1181300
% 53.01/53.38 clauses kept: 74624
% 53.01/53.38 clauses selected: 2625
% 53.01/53.38 clauses deleted: 9686
% 53.01/53.38 clauses inuse deleted: 287
% 53.01/53.38
% 53.01/53.38 subsentry: 8966617
% 53.01/53.38 literals s-matched: 4064940
% 53.01/53.38 literals matched: 3774536
% 53.01/53.38 full subsumption: 1327307
% 53.01/53.38
% 53.01/53.38 checksum: -510282722
% 53.01/53.38
% 53.01/53.38
% 53.01/53.38 Bliksem ended
%------------------------------------------------------------------------------