TSTP Solution File: KLE088+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : KLE088+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n014.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 01:37:06 EDT 2022
% Result : Theorem 270.80s 271.20s
% Output : Refutation 270.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : KLE088+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.12 % Command : bliksem %s
% 0.12/0.32 % Computer : n014.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % DateTime : Thu Jun 16 08:30:50 EDT 2022
% 0.12/0.32 % CPUTime :
% 17.93/18.31 *** allocated 10000 integers for termspace/termends
% 17.93/18.31 *** allocated 10000 integers for clauses
% 17.93/18.31 *** allocated 10000 integers for justifications
% 17.93/18.31 Bliksem 1.12
% 17.93/18.31
% 17.93/18.31
% 17.93/18.31 Automatic Strategy Selection
% 17.93/18.31
% 17.93/18.31
% 17.93/18.31 Clauses:
% 17.93/18.31
% 17.93/18.31 { addition( X, Y ) = addition( Y, X ) }.
% 17.93/18.31 { addition( Z, addition( Y, X ) ) = addition( addition( Z, Y ), X ) }.
% 17.93/18.31 { addition( X, zero ) = X }.
% 17.93/18.31 { addition( X, X ) = X }.
% 17.93/18.31 { multiplication( X, multiplication( Y, Z ) ) = multiplication(
% 17.93/18.31 multiplication( X, Y ), Z ) }.
% 17.93/18.31 { multiplication( X, one ) = X }.
% 17.93/18.31 { multiplication( one, X ) = X }.
% 17.93/18.31 { multiplication( X, addition( Y, Z ) ) = addition( multiplication( X, Y )
% 17.93/18.31 , multiplication( X, Z ) ) }.
% 17.93/18.31 { multiplication( addition( X, Y ), Z ) = addition( multiplication( X, Z )
% 17.93/18.31 , multiplication( Y, Z ) ) }.
% 17.93/18.31 { multiplication( X, zero ) = zero }.
% 17.93/18.31 { multiplication( zero, X ) = zero }.
% 17.93/18.31 { ! leq( X, Y ), addition( X, Y ) = Y }.
% 17.93/18.31 { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 17.93/18.31 { multiplication( antidomain( X ), X ) = zero }.
% 17.93/18.31 { addition( antidomain( multiplication( X, Y ) ), antidomain(
% 17.93/18.31 multiplication( X, antidomain( antidomain( Y ) ) ) ) ) = antidomain(
% 17.93/18.31 multiplication( X, antidomain( antidomain( Y ) ) ) ) }.
% 17.93/18.31 { addition( antidomain( antidomain( X ) ), antidomain( X ) ) = one }.
% 17.93/18.31 { domain( X ) = antidomain( antidomain( X ) ) }.
% 17.93/18.31 { multiplication( X, coantidomain( X ) ) = zero }.
% 17.93/18.31 { addition( coantidomain( multiplication( X, Y ) ), coantidomain(
% 17.93/18.31 multiplication( coantidomain( coantidomain( X ) ), Y ) ) ) = coantidomain
% 17.93/18.31 ( multiplication( coantidomain( coantidomain( X ) ), Y ) ) }.
% 17.93/18.31 { addition( coantidomain( coantidomain( X ) ), coantidomain( X ) ) = one }
% 17.93/18.31 .
% 17.93/18.31 { codomain( X ) = coantidomain( coantidomain( X ) ) }.
% 17.93/18.31 { multiplication( domain( skol1 ), skol2 ) = zero }.
% 17.93/18.31 { ! addition( domain( skol1 ), antidomain( skol2 ) ) = antidomain( skol2 )
% 17.93/18.31 }.
% 17.93/18.31
% 17.93/18.31 percentage equality = 0.920000, percentage horn = 1.000000
% 17.93/18.31 This is a pure equality problem
% 17.93/18.31
% 17.93/18.31
% 17.93/18.31
% 17.93/18.31 Options Used:
% 17.93/18.31
% 17.93/18.31 useres = 1
% 17.93/18.31 useparamod = 1
% 17.93/18.31 useeqrefl = 1
% 17.93/18.31 useeqfact = 1
% 17.93/18.31 usefactor = 1
% 17.93/18.31 usesimpsplitting = 0
% 17.93/18.31 usesimpdemod = 5
% 17.93/18.31 usesimpres = 3
% 17.93/18.31
% 17.93/18.31 resimpinuse = 1000
% 17.93/18.31 resimpclauses = 20000
% 17.93/18.31 substype = eqrewr
% 17.93/18.31 backwardsubs = 1
% 17.93/18.31 selectoldest = 5
% 17.93/18.31
% 17.93/18.31 litorderings [0] = split
% 17.93/18.31 litorderings [1] = extend the termordering, first sorting on arguments
% 17.93/18.31
% 17.93/18.31 termordering = kbo
% 17.93/18.31
% 17.93/18.31 litapriori = 0
% 17.93/18.31 termapriori = 1
% 17.93/18.31 litaposteriori = 0
% 17.93/18.31 termaposteriori = 0
% 17.93/18.31 demodaposteriori = 0
% 17.93/18.31 ordereqreflfact = 0
% 17.93/18.31
% 17.93/18.31 litselect = negord
% 17.93/18.31
% 17.93/18.31 maxweight = 15
% 17.93/18.31 maxdepth = 30000
% 17.93/18.31 maxlength = 115
% 17.93/18.31 maxnrvars = 195
% 17.93/18.31 excuselevel = 1
% 17.93/18.31 increasemaxweight = 1
% 17.93/18.31
% 17.93/18.31 maxselected = 10000000
% 17.93/18.31 maxnrclauses = 10000000
% 17.93/18.31
% 17.93/18.31 showgenerated = 0
% 17.93/18.31 showkept = 0
% 17.93/18.31 showselected = 0
% 17.93/18.31 showdeleted = 0
% 17.93/18.31 showresimp = 1
% 17.93/18.31 showstatus = 2000
% 17.93/18.31
% 17.93/18.31 prologoutput = 0
% 17.93/18.31 nrgoals = 5000000
% 17.93/18.31 totalproof = 1
% 17.93/18.31
% 17.93/18.31 Symbols occurring in the translation:
% 17.93/18.31
% 17.93/18.31 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 17.93/18.31 . [1, 2] (w:1, o:24, a:1, s:1, b:0),
% 17.93/18.31 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 17.93/18.31 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 17.93/18.31 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 17.93/18.31 addition [37, 2] (w:1, o:48, a:1, s:1, b:0),
% 17.93/18.31 zero [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 17.93/18.31 multiplication [40, 2] (w:1, o:50, a:1, s:1, b:0),
% 17.93/18.31 one [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 17.93/18.31 leq [42, 2] (w:1, o:49, a:1, s:1, b:0),
% 17.93/18.31 antidomain [44, 1] (w:1, o:20, a:1, s:1, b:0),
% 17.93/18.31 domain [46, 1] (w:1, o:23, a:1, s:1, b:0),
% 17.93/18.31 coantidomain [47, 1] (w:1, o:21, a:1, s:1, b:0),
% 17.93/18.31 codomain [48, 1] (w:1, o:22, a:1, s:1, b:0),
% 17.93/18.31 skol1 [49, 0] (w:1, o:13, a:1, s:1, b:1),
% 17.93/18.31 skol2 [50, 0] (w:1, o:14, a:1, s:1, b:1).
% 17.93/18.31
% 17.93/18.31
% 17.93/18.31 Starting Search:
% 17.93/18.31
% 17.93/18.31 *** allocated 15000 integers for clauses
% 17.93/18.31 *** allocated 22500 integers for clauses
% 17.93/18.31 *** allocated 33750 integers for clauses
% 17.93/18.31 *** allocated 50625 integers for clauses
% 17.93/18.31 *** allocated 75937 integers for clauses
% 17.93/18.31 *** allocated 15000 integers for termspace/termends
% 17.93/18.31 Resimplifying inuse:
% 17.93/18.31 Done
% 17.93/18.31
% 17.93/18.31 *** allocated 113905 integers for clauses
% 17.93/18.31 *** allocated 22500 integers for termspace/termends
% 99.82/100.23 *** allocated 170857 integers for clauses
% 99.82/100.23 *** allocated 33750 integers for termspace/termends
% 99.82/100.23
% 99.82/100.23 Intermediate Status:
% 99.82/100.23 Generated: 17328
% 99.82/100.23 Kept: 2118
% 99.82/100.23 Inuse: 306
% 99.82/100.23 Deleted: 27
% 99.82/100.23 Deletedinuse: 8
% 99.82/100.23
% 99.82/100.23 Resimplifying inuse:
% 99.82/100.23 Done
% 99.82/100.23
% 99.82/100.23 *** allocated 256285 integers for clauses
% 99.82/100.23 *** allocated 50625 integers for termspace/termends
% 99.82/100.23 Resimplifying inuse:
% 99.82/100.23 Done
% 99.82/100.23
% 99.82/100.23
% 99.82/100.23 Intermediate Status:
% 99.82/100.23 Generated: 39708
% 99.82/100.23 Kept: 4197
% 99.82/100.23 Inuse: 487
% 99.82/100.23 Deleted: 91
% 99.82/100.23 Deletedinuse: 29
% 99.82/100.23
% 99.82/100.23 Resimplifying inuse:
% 99.82/100.23 Done
% 99.82/100.23
% 99.82/100.23 *** allocated 75937 integers for termspace/termends
% 99.82/100.23 *** allocated 384427 integers for clauses
% 99.82/100.23 Resimplifying inuse:
% 99.82/100.23 Done
% 99.82/100.23
% 99.82/100.23
% 99.82/100.23 Intermediate Status:
% 99.82/100.23 Generated: 60791
% 99.82/100.23 Kept: 6241
% 99.82/100.23 Inuse: 592
% 99.82/100.23 Deleted: 99
% 99.82/100.23 Deletedinuse: 29
% 99.82/100.23
% 99.82/100.23 Resimplifying inuse:
% 99.82/100.23 Done
% 99.82/100.23
% 99.82/100.23 *** allocated 113905 integers for termspace/termends
% 99.82/100.23 *** allocated 576640 integers for clauses
% 99.82/100.23 Resimplifying inuse:
% 99.82/100.23 Done
% 99.82/100.23
% 99.82/100.23
% 99.82/100.23 Intermediate Status:
% 99.82/100.23 Generated: 80429
% 99.82/100.23 Kept: 8372
% 99.82/100.23 Inuse: 668
% 99.82/100.23 Deleted: 106
% 99.82/100.23 Deletedinuse: 30
% 99.82/100.23
% 99.82/100.23 Resimplifying inuse:
% 99.82/100.23 Done
% 99.82/100.23
% 99.82/100.23 *** allocated 170857 integers for termspace/termends
% 99.82/100.23 Resimplifying inuse:
% 99.82/100.23 Done
% 99.82/100.23
% 99.82/100.23
% 99.82/100.23 Intermediate Status:
% 99.82/100.23 Generated: 115839
% 99.82/100.23 Kept: 10409
% 99.82/100.23 Inuse: 813
% 99.82/100.23 Deleted: 108
% 99.82/100.23 Deletedinuse: 30
% 99.82/100.23
% 99.82/100.23 Resimplifying inuse:
% 99.82/100.23 Done
% 99.82/100.23
% 99.82/100.23 *** allocated 864960 integers for clauses
% 99.82/100.23 Resimplifying inuse:
% 99.82/100.23 Done
% 99.82/100.23
% 99.82/100.23
% 99.82/100.23 Intermediate Status:
% 99.82/100.23 Generated: 147697
% 99.82/100.23 Kept: 12621
% 99.82/100.23 Inuse: 922
% 99.82/100.23 Deleted: 110
% 99.82/100.23 Deletedinuse: 31
% 99.82/100.23
% 99.82/100.23 Resimplifying inuse:
% 99.82/100.23 Done
% 99.82/100.23
% 99.82/100.23 *** allocated 256285 integers for termspace/termends
% 99.82/100.23 Resimplifying inuse:
% 99.82/100.23 Done
% 99.82/100.23
% 99.82/100.23
% 99.82/100.23 Intermediate Status:
% 99.82/100.23 Generated: 168430
% 99.82/100.23 Kept: 14622
% 99.82/100.23 Inuse: 1018
% 99.82/100.23 Deleted: 118
% 99.82/100.23 Deletedinuse: 31
% 99.82/100.23
% 99.82/100.23 Resimplifying inuse:
% 99.82/100.23 Done
% 99.82/100.23
% 99.82/100.23 Resimplifying inuse:
% 99.82/100.23 Done
% 99.82/100.23
% 99.82/100.23
% 99.82/100.23 Intermediate Status:
% 99.82/100.23 Generated: 209749
% 99.82/100.23 Kept: 16623
% 99.82/100.23 Inuse: 1182
% 99.82/100.23 Deleted: 125
% 99.82/100.23 Deletedinuse: 31
% 99.82/100.23
% 99.82/100.23 Resimplifying inuse:
% 99.82/100.23 Done
% 99.82/100.23
% 99.82/100.23 *** allocated 1297440 integers for clauses
% 99.82/100.23 Resimplifying inuse:
% 99.82/100.23 Done
% 99.82/100.23
% 99.82/100.23
% 99.82/100.23 Intermediate Status:
% 99.82/100.23 Generated: 237883
% 99.82/100.23 Kept: 18624
% 99.82/100.23 Inuse: 1254
% 99.82/100.23 Deleted: 138
% 99.82/100.23 Deletedinuse: 39
% 99.82/100.23
% 99.82/100.23 Resimplifying inuse:
% 99.82/100.23 Done
% 99.82/100.23
% 99.82/100.23 *** allocated 384427 integers for termspace/termends
% 99.82/100.23 Resimplifying inuse:
% 99.82/100.23 Done
% 99.82/100.23
% 99.82/100.23 Resimplifying clauses:
% 99.82/100.23 Done
% 99.82/100.23
% 99.82/100.23
% 99.82/100.23 Intermediate Status:
% 99.82/100.23 Generated: 271982
% 99.82/100.23 Kept: 20630
% 99.82/100.23 Inuse: 1399
% 99.82/100.23 Deleted: 2179
% 99.82/100.23 Deletedinuse: 45
% 99.82/100.23
% 99.82/100.23 Resimplifying inuse:
% 99.82/100.23 Done
% 99.82/100.23
% 99.82/100.23 Resimplifying inuse:
% 99.82/100.23 Done
% 99.82/100.23
% 99.82/100.23
% 99.82/100.23 Intermediate Status:
% 99.82/100.23 Generated: 301800
% 99.82/100.23 Kept: 22696
% 99.82/100.23 Inuse: 1498
% 99.82/100.23 Deleted: 2179
% 99.82/100.23 Deletedinuse: 45
% 99.82/100.23
% 99.82/100.23 Resimplifying inuse:
% 99.82/100.23 Done
% 99.82/100.23
% 99.82/100.23 Resimplifying inuse:
% 99.82/100.23 Done
% 99.82/100.23
% 99.82/100.23
% 99.82/100.23 Intermediate Status:
% 99.82/100.23 Generated: 337865
% 99.82/100.23 Kept: 24700
% 99.82/100.23 Inuse: 1644
% 99.82/100.23 Deleted: 2184
% 99.82/100.23 Deletedinuse: 45
% 99.82/100.23
% 99.82/100.23 Resimplifying inuse:
% 99.82/100.23 Done
% 99.82/100.23
% 99.82/100.23 *** allocated 1946160 integers for clauses
% 99.82/100.23 Resimplifying inuse:
% 99.82/100.23 Done
% 99.82/100.23
% 99.82/100.23
% 99.82/100.23 Intermediate Status:
% 99.82/100.23 Generated: 367817
% 99.82/100.23 Kept: 26707
% 99.82/100.23 Inuse: 1736
% 99.82/100.23 Deleted: 2191
% 99.82/100.23 Deletedinuse: 52
% 99.82/100.23
% 99.82/100.23 Resimplifying inuse:
% 99.82/100.23 Done
% 99.82/100.23
% 99.82/100.23 Resimplifying inuse:
% 99.82/100.23 Done
% 99.82/100.23
% 99.82/100.23
% 99.82/100.23 Intermediate Status:
% 99.82/100.23 Generated: 414337
% 99.82/100.23 Kept: 28714
% 99.82/100.23 Inuse: 1847
% 99.82/100.23 Deleted: 2204
% 99.82/100.23 Deletedinuse: 64
% 99.82/100.23
% 99.82/100.23 *** allocated 576640 integers for termspace/termends
% 99.82/100.23 Resimplifying inuse:
% 99.82/100.23 Done
% 99.82/100.23
% 99.82/100.23 Resimplifying inuse:
% 99.82/100.23 Done
% 99.82/100.23
% 99.82/100.23
% 99.82/100.23 Intermediate Status:
% 99.82/100.23 Generated: 443429
% 99.82/100.23 Kept: 31115
% 99.82/100.23 Inuse: 1890
% 99.82/100.23 Deleted: 2206
% 99.82/100.23 Deletedinuse: 66
% 99.82/100.23
% 99.82/100.23 Resimplifying inuse:
% 99.82/100.23 Done
% 99.82/100.23
% 99.82/100.23 Resimplifying inuse:
% 99.82/100.23 Done
% 99.82/100.23
% 99.82/100.23
% 99.82/100.23 Intermediate Status:
% 99.82/100.23 Generated: 483101
% 99.82/100.23 Kept: 33140
% 99.82/100.23 Inuse: 1956
% 99.82/100.23 Deleted: 2206
% 99.82/100.23 Deletedinuse: 66
% 99.82/100.23
% 99.82/100.23 Resimplifying inuse:
% 99.82/100.23 Done
% 99.82/100.23
% 99.82/100.23 Resimplifying inuse:
% 99.82/100.23 Done
% 99.82/100.23
% 99.82/100.23
% 99.82/100.23 Intermediate Status:
% 99.82/100.23 Generated: 513592
% 99.82/100.23 Kept: 35317
% 99.82/100.23 Inuse: 2012
% 99.82/100.23 Deleted: 2206
% 99.82/100.23 Deletedinuse: 66
% 99.82/100.23
% 99.82/100.23 Resimplifying inuse:
% 99.82/100.23 Done
% 99.82/100.23
% 99.82/100.23 Resimplifying inuse:
% 99.82/100.23 Done
% 99.82/100.23
% 99.82/100.23
% 99.82/100.23 Intermediate Status:
% 99.82/100.23 Generated: 545877
% 99.82/100.23 Kept: 37421
% 99.82/100.23 Inuse: 2030
% 99.82/100.23 Deleted: 2206
% 99.82/100.23 Deletedinuse: 66
% 99.82/100.23
% 99.82/100.23 Resimplifying inuse:
% 99.82/100.23 Done
% 99.82/100.23
% 99.82/100.23 *** allocated 2919240 integers for clauses
% 99.82/100.23 Resimplifying inuse:
% 99.82/100.23 Done
% 99.82/100.23
% 99.82/100.23
% 99.82/100.23 Intermediate Status:
% 99.82/100.23 Generated: 579782
% 99.82/100.23 Kept: 39431
% 99.82/100.23 Inuse: 2080
% 99.82/100.23 Deleted: 2209
% 99.82/100.23 Deletedinuse: 68
% 99.82/100.23
% 99.82/100.23 Resimplifying clauses:
% 99.82/100.23 Done
% 99.82/100.23
% 99.82/100.23 Resimplifying inuse:
% 99.82/100.23 Done
% 99.82/100.23
% 99.82/100.23 Resimplifying inuse:
% 99.82/100.23 Done
% 99.82/100.23
% 99.82/100.23
% 99.82/100.23 Intermediate Status:
% 270.80/271.20 Generated: 607030
% 270.80/271.20 Kept: 41447
% 270.80/271.20 Inuse: 2142
% 270.80/271.20 Deleted: 3611
% 270.80/271.20 Deletedinuse: 68
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 *** allocated 864960 integers for termspace/termends
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 Intermediate Status:
% 270.80/271.20 Generated: 637931
% 270.80/271.20 Kept: 43448
% 270.80/271.20 Inuse: 2194
% 270.80/271.20 Deleted: 3611
% 270.80/271.20 Deletedinuse: 68
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 Intermediate Status:
% 270.80/271.20 Generated: 715699
% 270.80/271.20 Kept: 45461
% 270.80/271.20 Inuse: 2314
% 270.80/271.20 Deleted: 3614
% 270.80/271.20 Deletedinuse: 70
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 Intermediate Status:
% 270.80/271.20 Generated: 767738
% 270.80/271.20 Kept: 47471
% 270.80/271.20 Inuse: 2424
% 270.80/271.20 Deleted: 3618
% 270.80/271.20 Deletedinuse: 74
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 Intermediate Status:
% 270.80/271.20 Generated: 806400
% 270.80/271.20 Kept: 49491
% 270.80/271.20 Inuse: 2501
% 270.80/271.20 Deleted: 3625
% 270.80/271.20 Deletedinuse: 79
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 Intermediate Status:
% 270.80/271.20 Generated: 847664
% 270.80/271.20 Kept: 51506
% 270.80/271.20 Inuse: 2589
% 270.80/271.20 Deleted: 3628
% 270.80/271.20 Deletedinuse: 80
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 Intermediate Status:
% 270.80/271.20 Generated: 928697
% 270.80/271.20 Kept: 53512
% 270.80/271.20 Inuse: 2626
% 270.80/271.20 Deleted: 3628
% 270.80/271.20 Deletedinuse: 80
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 Intermediate Status:
% 270.80/271.20 Generated: 991107
% 270.80/271.20 Kept: 55526
% 270.80/271.20 Inuse: 2747
% 270.80/271.20 Deleted: 3642
% 270.80/271.20 Deletedinuse: 80
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 Intermediate Status:
% 270.80/271.20 Generated: 1025598
% 270.80/271.20 Kept: 57539
% 270.80/271.20 Inuse: 2825
% 270.80/271.20 Deleted: 3649
% 270.80/271.20 Deletedinuse: 80
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 *** allocated 4378860 integers for clauses
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 Intermediate Status:
% 270.80/271.20 Generated: 1084330
% 270.80/271.20 Kept: 60016
% 270.80/271.20 Inuse: 2931
% 270.80/271.20 Deleted: 3660
% 270.80/271.20 Deletedinuse: 82
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 Resimplifying clauses:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 Intermediate Status:
% 270.80/271.20 Generated: 1141419
% 270.80/271.20 Kept: 62039
% 270.80/271.20 Inuse: 3060
% 270.80/271.20 Deleted: 5002
% 270.80/271.20 Deletedinuse: 84
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 *** allocated 1297440 integers for termspace/termends
% 270.80/271.20
% 270.80/271.20 Intermediate Status:
% 270.80/271.20 Generated: 1214572
% 270.80/271.20 Kept: 64758
% 270.80/271.20 Inuse: 3162
% 270.80/271.20 Deleted: 5004
% 270.80/271.20 Deletedinuse: 84
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 Intermediate Status:
% 270.80/271.20 Generated: 1261443
% 270.80/271.20 Kept: 66788
% 270.80/271.20 Inuse: 3239
% 270.80/271.20 Deleted: 5014
% 270.80/271.20 Deletedinuse: 92
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 Intermediate Status:
% 270.80/271.20 Generated: 1305525
% 270.80/271.20 Kept: 68808
% 270.80/271.20 Inuse: 3334
% 270.80/271.20 Deleted: 5014
% 270.80/271.20 Deletedinuse: 92
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 Intermediate Status:
% 270.80/271.20 Generated: 1344121
% 270.80/271.20 Kept: 70922
% 270.80/271.20 Inuse: 3374
% 270.80/271.20 Deleted: 5016
% 270.80/271.20 Deletedinuse: 94
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 Intermediate Status:
% 270.80/271.20 Generated: 1402154
% 270.80/271.20 Kept: 72934
% 270.80/271.20 Inuse: 3423
% 270.80/271.20 Deleted: 5016
% 270.80/271.20 Deletedinuse: 94
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 Intermediate Status:
% 270.80/271.20 Generated: 1439672
% 270.80/271.20 Kept: 75026
% 270.80/271.20 Inuse: 3484
% 270.80/271.20 Deleted: 5016
% 270.80/271.20 Deletedinuse: 94
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 Intermediate Status:
% 270.80/271.20 Generated: 1510634
% 270.80/271.20 Kept: 77026
% 270.80/271.20 Inuse: 3502
% 270.80/271.20 Deleted: 5016
% 270.80/271.20 Deletedinuse: 94
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 Intermediate Status:
% 270.80/271.20 Generated: 1571675
% 270.80/271.20 Kept: 79653
% 270.80/271.20 Inuse: 3523
% 270.80/271.20 Deleted: 5020
% 270.80/271.20 Deletedinuse: 97
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 Resimplifying clauses:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 Intermediate Status:
% 270.80/271.20 Generated: 1623030
% 270.80/271.20 Kept: 81704
% 270.80/271.20 Inuse: 3599
% 270.80/271.20 Deleted: 6094
% 270.80/271.20 Deletedinuse: 97
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 Intermediate Status:
% 270.80/271.20 Generated: 1665642
% 270.80/271.20 Kept: 83721
% 270.80/271.20 Inuse: 3680
% 270.80/271.20 Deleted: 6110
% 270.80/271.20 Deletedinuse: 111
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 Intermediate Status:
% 270.80/271.20 Generated: 1697300
% 270.80/271.20 Kept: 85804
% 270.80/271.20 Inuse: 3707
% 270.80/271.20 Deleted: 6110
% 270.80/271.20 Deletedinuse: 111
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 Intermediate Status:
% 270.80/271.20 Generated: 1751065
% 270.80/271.20 Kept: 87817
% 270.80/271.20 Inuse: 3775
% 270.80/271.20 Deleted: 6110
% 270.80/271.20 Deletedinuse: 111
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 *** allocated 6568290 integers for clauses
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 Intermediate Status:
% 270.80/271.20 Generated: 1869573
% 270.80/271.20 Kept: 90474
% 270.80/271.20 Inuse: 3802
% 270.80/271.20 Deleted: 6110
% 270.80/271.20 Deletedinuse: 111
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 Intermediate Status:
% 270.80/271.20 Generated: 1935104
% 270.80/271.20 Kept: 93139
% 270.80/271.20 Inuse: 3876
% 270.80/271.20 Deleted: 6111
% 270.80/271.20 Deletedinuse: 111
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 *** allocated 1946160 integers for termspace/termends
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 Intermediate Status:
% 270.80/271.20 Generated: 1976785
% 270.80/271.20 Kept: 95150
% 270.80/271.20 Inuse: 3936
% 270.80/271.20 Deleted: 6113
% 270.80/271.20 Deletedinuse: 113
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 Intermediate Status:
% 270.80/271.20 Generated: 2006503
% 270.80/271.20 Kept: 97181
% 270.80/271.20 Inuse: 3989
% 270.80/271.20 Deleted: 6115
% 270.80/271.20 Deletedinuse: 113
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 Intermediate Status:
% 270.80/271.20 Generated: 2038411
% 270.80/271.20 Kept: 99610
% 270.80/271.20 Inuse: 4029
% 270.80/271.20 Deleted: 6116
% 270.80/271.20 Deletedinuse: 114
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 Resimplifying clauses:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 Intermediate Status:
% 270.80/271.20 Generated: 2088098
% 270.80/271.20 Kept: 102667
% 270.80/271.20 Inuse: 4073
% 270.80/271.20 Deleted: 7010
% 270.80/271.20 Deletedinuse: 114
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 Intermediate Status:
% 270.80/271.20 Generated: 2141069
% 270.80/271.20 Kept: 104976
% 270.80/271.20 Inuse: 4159
% 270.80/271.20 Deleted: 7011
% 270.80/271.20 Deletedinuse: 115
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 Intermediate Status:
% 270.80/271.20 Generated: 2194745
% 270.80/271.20 Kept: 107000
% 270.80/271.20 Inuse: 4217
% 270.80/271.20 Deleted: 7012
% 270.80/271.20 Deletedinuse: 116
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 Intermediate Status:
% 270.80/271.20 Generated: 2233028
% 270.80/271.20 Kept: 109076
% 270.80/271.20 Inuse: 4257
% 270.80/271.20 Deleted: 7012
% 270.80/271.20 Deletedinuse: 116
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 Intermediate Status:
% 270.80/271.20 Generated: 2288825
% 270.80/271.20 Kept: 112019
% 270.80/271.20 Inuse: 4286
% 270.80/271.20 Deleted: 7013
% 270.80/271.20 Deletedinuse: 116
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 Intermediate Status:
% 270.80/271.20 Generated: 2337116
% 270.80/271.20 Kept: 114053
% 270.80/271.20 Inuse: 4323
% 270.80/271.20 Deleted: 7013
% 270.80/271.20 Deletedinuse: 116
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 Intermediate Status:
% 270.80/271.20 Generated: 2410229
% 270.80/271.20 Kept: 116063
% 270.80/271.20 Inuse: 4389
% 270.80/271.20 Deleted: 7013
% 270.80/271.20 Deletedinuse: 116
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 Intermediate Status:
% 270.80/271.20 Generated: 2487686
% 270.80/271.20 Kept: 118193
% 270.80/271.20 Inuse: 4448
% 270.80/271.20 Deleted: 7013
% 270.80/271.20 Deletedinuse: 116
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 Intermediate Status:
% 270.80/271.20 Generated: 2512568
% 270.80/271.20 Kept: 120724
% 270.80/271.20 Inuse: 4473
% 270.80/271.20 Deleted: 7013
% 270.80/271.20 Deletedinuse: 116
% 270.80/271.20
% 270.80/271.20 Resimplifying clauses:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 Intermediate Status:
% 270.80/271.20 Generated: 2543304
% 270.80/271.20 Kept: 123019
% 270.80/271.20 Inuse: 4503
% 270.80/271.20 Deleted: 7719
% 270.80/271.20 Deletedinuse: 117
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 Intermediate Status:
% 270.80/271.20 Generated: 2643117
% 270.80/271.20 Kept: 125036
% 270.80/271.20 Inuse: 4527
% 270.80/271.20 Deleted: 7719
% 270.80/271.20 Deletedinuse: 117
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 Intermediate Status:
% 270.80/271.20 Generated: 2691320
% 270.80/271.20 Kept: 127054
% 270.80/271.20 Inuse: 4594
% 270.80/271.20 Deleted: 7723
% 270.80/271.20 Deletedinuse: 117
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 Intermediate Status:
% 270.80/271.20 Generated: 2729200
% 270.80/271.20 Kept: 129070
% 270.80/271.20 Inuse: 4644
% 270.80/271.20 Deleted: 7723
% 270.80/271.20 Deletedinuse: 117
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 *** allocated 9852435 integers for clauses
% 270.80/271.20 *** allocated 2919240 integers for termspace/termends
% 270.80/271.20
% 270.80/271.20 Intermediate Status:
% 270.80/271.20 Generated: 2808580
% 270.80/271.20 Kept: 144629
% 270.80/271.20 Inuse: 4674
% 270.80/271.20 Deleted: 7723
% 270.80/271.20 Deletedinuse: 117
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 Resimplifying clauses:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 Intermediate Status:
% 270.80/271.20 Generated: 2843009
% 270.80/271.20 Kept: 146640
% 270.80/271.20 Inuse: 4721
% 270.80/271.20 Deleted: 8116
% 270.80/271.20 Deletedinuse: 117
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 Intermediate Status:
% 270.80/271.20 Generated: 2884532
% 270.80/271.20 Kept: 148654
% 270.80/271.20 Inuse: 4779
% 270.80/271.20 Deleted: 9050
% 270.80/271.20 Deletedinuse: 1040
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20 Done
% 270.80/271.20
% 270.80/271.20 Resimplifying inuse:
% 270.80/271.20
% 270.80/271.20 Bliksems!, er is een bewijs:
% 270.80/271.20 % SZS status Theorem
% 270.80/271.20 % SZS output start Refutation
% 270.80/271.20
% 270.80/271.20 (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X ) }.
% 270.80/271.20 (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) ) ==> addition(
% 270.80/271.20 addition( Z, Y ), X ) }.
% 270.80/271.20 (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 270.80/271.20 (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 270.80/271.20 (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 270.80/271.20 (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 270.80/271.20 (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 270.80/271.20 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 270.80/271.20 (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 270.80/271.20 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 270.80/271.20 (9) {G0,W5,D3,L1,V1,M1} I { multiplication( X, zero ) ==> zero }.
% 270.80/271.20 (10) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==> zero }.
% 270.80/271.20 (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y ) ==> Y }.
% 270.80/271.20 (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X, Y ) }.
% 270.80/271.20 (13) {G0,W6,D4,L1,V1,M1} I { multiplication( antidomain( X ), X ) ==> zero
% 270.80/271.20 }.
% 270.80/271.20 (14) {G0,W18,D7,L1,V2,M1} I { addition( antidomain( multiplication( X, Y )
% 270.80/271.20 ), antidomain( multiplication( X, antidomain( antidomain( Y ) ) ) ) )
% 270.80/271.20 ==> antidomain( multiplication( X, antidomain( antidomain( Y ) ) ) ) }.
% 270.80/271.20 (15) {G0,W8,D5,L1,V1,M1} I { addition( antidomain( antidomain( X ) ),
% 270.80/271.20 antidomain( X ) ) ==> one }.
% 270.80/271.20 (16) {G0,W6,D4,L1,V1,M1} I { antidomain( antidomain( X ) ) ==> domain( X )
% 270.80/271.20 }.
% 270.80/271.20 (17) {G0,W6,D4,L1,V1,M1} I { multiplication( X, coantidomain( X ) ) ==>
% 270.80/271.20 zero }.
% 270.80/271.20 (18) {G0,W18,D7,L1,V2,M1} I { addition( coantidomain( multiplication( X, Y
% 270.80/271.20 ) ), coantidomain( multiplication( coantidomain( coantidomain( X ) ), Y
% 270.80/271.20 ) ) ) ==> coantidomain( multiplication( coantidomain( coantidomain( X )
% 270.80/271.20 ), Y ) ) }.
% 270.80/271.20 (19) {G0,W8,D5,L1,V1,M1} I { addition( coantidomain( coantidomain( X ) ),
% 270.80/271.20 coantidomain( X ) ) ==> one }.
% 270.80/271.20 (20) {G0,W6,D4,L1,V1,M1} I { coantidomain( coantidomain( X ) ) ==> codomain
% 270.80/271.20 ( X ) }.
% 270.80/271.20 (21) {G0,W6,D4,L1,V0,M1} I { multiplication( domain( skol1 ), skol2 ) ==>
% 270.80/271.20 zero }.
% 270.80/271.20 (22) {G0,W8,D4,L1,V0,M1} I { ! addition( domain( skol1 ), antidomain( skol2
% 270.80/271.20 ) ) ==> antidomain( skol2 ) }.
% 270.80/271.20 (23) {G1,W5,D3,L1,V1,M1} P(2,0) { addition( zero, X ) ==> X }.
% 270.80/271.20 (24) {G1,W7,D4,L1,V1,M1} P(20,20) { codomain( coantidomain( X ) ) ==>
% 270.80/271.20 coantidomain( codomain( X ) ) }.
% 270.80/271.20 (25) {G1,W7,D4,L1,V1,M1} P(20,17) { multiplication( coantidomain( X ),
% 270.80/271.20 codomain( X ) ) ==> zero }.
% 270.80/271.20 (26) {G1,W4,D3,L1,V0,M1} P(17,6) { coantidomain( one ) ==> zero }.
% 270.80/271.20 (27) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y ), Z ) =
% 270.80/271.20 addition( addition( Y, Z ), X ) }.
% 270.80/271.20 (30) {G1,W9,D4,L1,V2,M1} P(3,1) { addition( addition( Y, X ), X ) ==>
% 270.80/271.20 addition( Y, X ) }.
% 270.80/271.20 (31) {G2,W5,D3,L1,V0,M1} P(26,20) { codomain( one ) ==> coantidomain( zero
% 270.80/271.20 ) }.
% 270.80/271.20 (32) {G1,W7,D4,L1,V1,M1} P(16,16) { domain( antidomain( X ) ) ==>
% 270.80/271.20 antidomain( domain( X ) ) }.
% 270.80/271.20 (34) {G1,W4,D3,L1,V0,M1} P(13,5) { antidomain( one ) ==> zero }.
% 270.80/271.20 (38) {G2,W5,D3,L1,V0,M1} P(34,16) { domain( one ) ==> antidomain( zero )
% 270.80/271.20 }.
% 270.80/271.20 (47) {G2,W11,D4,L1,V2,M1} P(13,7);d(23) { multiplication( antidomain( X ),
% 270.80/271.20 addition( X, Y ) ) ==> multiplication( antidomain( X ), Y ) }.
% 270.80/271.20 (51) {G1,W10,D5,L1,V2,M1} P(17,7);d(2) { multiplication( X, addition( Y,
% 270.80/271.20 coantidomain( X ) ) ) ==> multiplication( X, Y ) }.
% 270.80/271.20 (54) {G1,W11,D4,L1,V2,M1} P(5,7) { addition( multiplication( X, Y ), X ) =
% 270.80/271.20 multiplication( X, addition( Y, one ) ) }.
% 270.80/271.20 (55) {G2,W12,D5,L1,V2,M1} P(25,7);d(23) { multiplication( coantidomain( X )
% 270.80/271.20 , addition( codomain( X ), Y ) ) ==> multiplication( coantidomain( X ), Y
% 270.80/271.20 ) }.
% 270.80/271.20 (58) {G2,W3,D2,L1,V1,M1} R(12,23) { leq( zero, X ) }.
% 270.80/271.20 (59) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 270.80/271.20 (60) {G1,W16,D4,L2,V3,M2} P(7,12) { ! multiplication( X, addition( Y, Z ) )
% 270.80/271.20 ==> multiplication( X, Z ), leq( multiplication( X, Y ), multiplication
% 270.80/271.20 ( X, Z ) ) }.
% 270.80/271.20 (63) {G1,W8,D3,L2,V2,M2} P(0,12) { ! addition( Y, X ) ==> Y, leq( X, Y )
% 270.80/271.20 }.
% 270.80/271.20 (64) {G1,W16,D4,L2,V3,M2} P(8,12) { ! multiplication( addition( X, Z ), Y )
% 270.80/271.20 ==> multiplication( Z, Y ), leq( multiplication( X, Y ), multiplication
% 270.80/271.20 ( Z, Y ) ) }.
% 270.80/271.20 (72) {G1,W10,D5,L1,V2,M1} P(13,8);d(2) { multiplication( addition( Y,
% 270.80/271.20 antidomain( X ) ), X ) ==> multiplication( Y, X ) }.
% 270.80/271.20 (74) {G2,W11,D4,L1,V2,M1} P(17,8);d(23) { multiplication( addition( X, Y )
% 270.80/271.20 , coantidomain( X ) ) ==> multiplication( Y, coantidomain( X ) ) }.
% 270.80/271.20 (75) {G1,W11,D4,L1,V2,M1} P(17,8);d(2) { multiplication( addition( Y, X ),
% 270.80/271.20 coantidomain( X ) ) ==> multiplication( Y, coantidomain( X ) ) }.
% 270.80/271.20 (78) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( multiplication( Y, X ), X ) =
% 270.80/271.20 multiplication( addition( Y, one ), X ) }.
% 270.80/271.20 (80) {G2,W10,D3,L2,V2,M2} R(11,63) { addition( X, Y ) ==> Y, ! addition( Y
% 270.80/271.20 , X ) ==> Y }.
% 270.80/271.20 (82) {G2,W9,D2,L3,V2,M3} P(11,63) { ! Y = X, leq( Y, X ), ! leq( X, Y ) }.
% 270.80/271.20 (83) {G1,W16,D4,L2,V3,M2} P(11,8) { multiplication( addition( X, Z ), Y )
% 270.80/271.20 ==> multiplication( Z, Y ), ! leq( multiplication( X, Y ), multiplication
% 270.80/271.20 ( Z, Y ) ) }.
% 270.80/271.20 (87) {G1,W6,D2,L2,V1,M2} P(11,2) { zero = X, ! leq( X, zero ) }.
% 270.80/271.20 (88) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, ! leq( X, Y )
% 270.80/271.20 }.
% 270.80/271.20 (127) {G1,W16,D6,L1,V2,M1} S(14);d(16) { addition( antidomain(
% 270.80/271.20 multiplication( X, Y ) ), antidomain( multiplication( X, domain( Y ) ) )
% 270.80/271.20 ) ==> antidomain( multiplication( X, domain( Y ) ) ) }.
% 270.80/271.20 (156) {G1,W7,D4,L1,V1,M1} S(15);d(16) { addition( domain( X ), antidomain(
% 270.80/271.20 X ) ) ==> one }.
% 270.80/271.20 (167) {G3,W4,D3,L1,V0,M1} P(38,156);d(34);d(2) { antidomain( zero ) ==> one
% 270.80/271.20 }.
% 270.80/271.20 (170) {G1,W16,D6,L1,V2,M1} S(18);d(20) { addition( coantidomain(
% 270.80/271.20 multiplication( X, Y ) ), coantidomain( multiplication( codomain( X ), Y
% 270.80/271.20 ) ) ) ==> coantidomain( multiplication( codomain( X ), Y ) ) }.
% 270.80/271.20 (178) {G1,W7,D4,L1,V1,M1} S(19);d(20) { addition( codomain( X ),
% 270.80/271.20 coantidomain( X ) ) ==> one }.
% 270.80/271.20 (187) {G1,W5,D3,L1,V0,M1} R(22,11) { ! leq( domain( skol1 ), antidomain(
% 270.80/271.20 skol2 ) ) }.
% 270.80/271.20 (211) {G2,W11,D5,L1,V2,M1} P(156,27) { addition( addition( antidomain( X )
% 270.80/271.20 , Y ), domain( X ) ) ==> addition( one, Y ) }.
% 270.80/271.20 (265) {G2,W5,D3,L1,V2,M1} R(30,63) { leq( X, addition( Y, X ) ) }.
% 270.80/271.20 (268) {G2,W6,D4,L1,V1,M1} P(156,30) { addition( one, antidomain( X ) ) ==>
% 270.80/271.20 one }.
% 270.80/271.20 (279) {G3,W7,D4,L1,V3,M1} P(27,265) { leq( Z, addition( addition( Z, X ), Y
% 270.80/271.20 ) ) }.
% 270.80/271.20 (280) {G3,W4,D3,L1,V1,M1} P(156,265) { leq( antidomain( X ), one ) }.
% 270.80/271.20 (286) {G3,W5,D3,L1,V2,M1} P(0,265) { leq( Y, addition( Y, X ) ) }.
% 270.80/271.20 (287) {G4,W6,D4,L1,V1,M1} R(280,11) { addition( antidomain( X ), one ) ==>
% 270.80/271.20 one }.
% 270.80/271.20 (288) {G4,W4,D3,L1,V1,M1} P(16,280) { leq( domain( X ), one ) }.
% 270.80/271.20 (289) {G5,W6,D4,L1,V1,M1} R(288,11) { addition( domain( X ), one ) ==> one
% 270.80/271.20 }.
% 270.80/271.20 (462) {G4,W8,D3,L2,V3,M2} P(11,279) { leq( X, Z ), ! leq( addition( X, Y )
% 270.80/271.20 , Z ) }.
% 270.80/271.20 (463) {G4,W8,D3,L2,V3,M2} P(11,279) { leq( X, addition( Y, Z ) ), ! leq( X
% 270.80/271.20 , Y ) }.
% 270.80/271.20 (472) {G3,W10,D5,L1,V1,M1} P(156,47);d(5) { multiplication( antidomain(
% 270.80/271.20 domain( X ) ), antidomain( X ) ) ==> antidomain( domain( X ) ) }.
% 270.80/271.20 (519) {G4,W4,D3,L1,V1,M1} P(178,286) { leq( codomain( X ), one ) }.
% 270.80/271.20 (520) {G3,W4,D3,L1,V1,M1} P(178,265) { leq( coantidomain( X ), one ) }.
% 270.80/271.20 (521) {G2,W6,D4,L1,V1,M1} P(178,30) { addition( one, coantidomain( X ) )
% 270.80/271.20 ==> one }.
% 270.80/271.20 (533) {G3,W4,D3,L1,V0,M1} P(31,178);d(26);d(2) { coantidomain( zero ) ==>
% 270.80/271.20 one }.
% 270.80/271.20 (540) {G5,W6,D4,L1,V1,M1} R(519,11) { addition( codomain( X ), one ) ==>
% 270.80/271.20 one }.
% 270.80/271.20 (541) {G4,W6,D4,L1,V1,M1} R(520,11) { addition( coantidomain( X ), one )
% 270.80/271.20 ==> one }.
% 270.80/271.20 (548) {G2,W6,D4,L1,V1,M1} P(178,51);d(5) { multiplication( X, codomain( X )
% 270.80/271.20 ) ==> X }.
% 270.80/271.20 (578) {G3,W7,D3,L2,V1,M2} P(87,548);d(9) { ! leq( codomain( X ), zero ),
% 270.80/271.20 zero = X }.
% 270.80/271.20 (582) {G3,W9,D5,L1,V1,M1} P(24,548) { multiplication( coantidomain( X ),
% 270.80/271.20 coantidomain( codomain( X ) ) ) ==> coantidomain( X ) }.
% 270.80/271.20 (593) {G6,W6,D4,L1,V1,M1} P(540,0) { addition( one, codomain( X ) ) ==> one
% 270.80/271.20 }.
% 270.80/271.20 (674) {G3,W7,D4,L1,V2,M1} P(54,265) { leq( X, multiplication( X, addition(
% 270.80/271.20 Y, one ) ) ) }.
% 270.80/271.20 (690) {G2,W12,D4,L2,V2,M2} P(54,12) { ! multiplication( X, addition( Y, one
% 270.80/271.20 ) ) ==> X, leq( multiplication( X, Y ), X ) }.
% 270.80/271.20 (888) {G6,W6,D4,L1,V2,M1} P(289,60);q;d(5) { leq( multiplication( Y, domain
% 270.80/271.20 ( X ) ), Y ) }.
% 270.80/271.20 (922) {G5,W6,D4,L1,V2,M1} P(287,64);q;d(6) { leq( multiplication(
% 270.80/271.20 antidomain( X ), Y ), Y ) }.
% 270.80/271.20 (927) {G2,W14,D4,L2,V2,M2} P(6,64) { ! multiplication( addition( one, Y ),
% 270.80/271.20 X ) ==> multiplication( Y, X ), leq( X, multiplication( Y, X ) ) }.
% 270.80/271.20 (948) {G6,W6,D4,L1,V1,M1} P(548,922) { leq( antidomain( X ), codomain(
% 270.80/271.20 antidomain( X ) ) ) }.
% 270.80/271.20 (977) {G7,W10,D5,L1,V1,M1} R(948,11) { addition( antidomain( X ), codomain
% 270.80/271.20 ( antidomain( X ) ) ) ==> codomain( antidomain( X ) ) }.
% 270.80/271.20 (1116) {G2,W6,D4,L1,V1,M1} P(156,72);d(6) { multiplication( domain( X ), X
% 270.80/271.20 ) ==> X }.
% 270.80/271.20 (1133) {G3,W7,D3,L2,V1,M2} P(87,1116);d(10) { ! leq( domain( X ), zero ),
% 270.80/271.20 zero = X }.
% 270.80/271.20 (1137) {G4,W6,D4,L1,V1,M1} P(32,1116);d(472) { antidomain( domain( X ) )
% 270.80/271.20 ==> antidomain( X ) }.
% 270.80/271.20 (1187) {G4,W6,D4,L1,V1,M1} P(178,74);d(6);d(582) { coantidomain( codomain(
% 270.80/271.20 X ) ) ==> coantidomain( X ) }.
% 270.80/271.20 (1217) {G2,W9,D4,L2,V2,M2} P(11,75);d(17) { ! leq( X, Y ), multiplication(
% 270.80/271.20 X, coantidomain( Y ) ) ==> zero }.
% 270.80/271.20 (1518) {G3,W7,D4,L1,V2,M1} P(78,265) { leq( Y, multiplication( addition( X
% 270.80/271.20 , one ), Y ) ) }.
% 270.80/271.20 (1608) {G5,W8,D3,L2,V1,M2} P(80,521);d(541) { coantidomain( X ) ==> one, !
% 270.80/271.20 coantidomain( X ) ==> one }.
% 270.80/271.20 (1639) {G5,W8,D3,L2,V1,M2} P(80,268);d(287) { antidomain( X ) ==> one, !
% 270.80/271.20 antidomain( X ) ==> one }.
% 270.80/271.20 (1717) {G2,W15,D4,L2,V2,M2} P(178,83);d(6) { ! leq( multiplication(
% 270.80/271.20 codomain( X ), Y ), multiplication( coantidomain( X ), Y ) ),
% 270.80/271.20 multiplication( coantidomain( X ), Y ) ==> Y }.
% 270.80/271.20 (1720) {G2,W15,D4,L2,V2,M2} P(156,83);d(6) { ! leq( multiplication( domain
% 270.80/271.20 ( X ), Y ), multiplication( antidomain( X ), Y ) ), multiplication(
% 270.80/271.20 antidomain( X ), Y ) ==> Y }.
% 270.80/271.20 (2621) {G4,W8,D3,L2,V2,M2} P(88,1518) { leq( Y, multiplication( X, Y ) ), !
% 270.80/271.20 leq( one, X ) }.
% 270.80/271.20 (2651) {G4,W8,D3,L2,V2,M2} P(88,674) { leq( Y, multiplication( Y, X ) ), !
% 270.80/271.20 leq( one, X ) }.
% 270.80/271.20 (3255) {G4,W8,D5,L1,V0,M1} P(21,127);d(167);d(268) { antidomain(
% 270.80/271.20 multiplication( domain( skol1 ), domain( skol2 ) ) ) ==> one }.
% 270.80/271.20 (4595) {G5,W7,D4,L1,V1,M1} R(462,187) { ! leq( addition( domain( skol1 ), X
% 270.80/271.20 ), antidomain( skol2 ) ) }.
% 270.80/271.20 (4913) {G6,W8,D3,L2,V1,M2} P(11,4595) { ! leq( X, antidomain( skol2 ) ), !
% 270.80/271.20 leq( domain( skol1 ), X ) }.
% 270.80/271.20 (5946) {G4,W8,D6,L1,V1,M1} P(13,170);d(533);d(521) { coantidomain(
% 270.80/271.20 multiplication( codomain( antidomain( X ) ), X ) ) ==> one }.
% 270.80/271.20 (6808) {G5,W7,D3,L2,V1,M2} P(17,2651) { leq( X, zero ), ! leq( one,
% 270.80/271.20 coantidomain( X ) ) }.
% 270.80/271.20 (7181) {G6,W7,D3,L2,V2,M2} R(6808,463);d(23) { ! leq( one, coantidomain( X
% 270.80/271.20 ) ), leq( X, Y ) }.
% 270.80/271.20 (7459) {G7,W7,D3,L2,V2,M2} R(7181,82);d(1608);r(59) { leq( X, Y ), !
% 270.80/271.20 coantidomain( X ) ==> one }.
% 270.80/271.20 (7560) {G8,W7,D3,L2,V1,M2} R(7459,578);d(1187) { zero = X, ! coantidomain(
% 270.80/271.20 X ) ==> one }.
% 270.80/271.20 (10029) {G5,W7,D3,L2,V1,M2} P(13,2621) { leq( X, zero ), ! leq( one,
% 270.80/271.20 antidomain( X ) ) }.
% 270.80/271.20 (10135) {G6,W7,D3,L2,V2,M2} R(10029,463);d(23) { ! leq( one, antidomain( X
% 270.80/271.20 ) ), leq( X, Y ) }.
% 270.80/271.20 (10572) {G7,W7,D3,L2,V2,M2} R(10135,82);d(1639);r(59) { leq( X, Y ), !
% 270.80/271.20 antidomain( X ) ==> one }.
% 270.80/271.20 (10680) {G8,W7,D3,L2,V1,M2} R(10572,1133);d(1137) { zero = X, ! antidomain
% 270.80/271.20 ( X ) ==> one }.
% 270.80/271.20 (15619) {G7,W8,D4,L1,V1,M1} R(4913,888) { ! leq( domain( skol1 ),
% 270.80/271.20 multiplication( antidomain( skol2 ), domain( X ) ) ) }.
% 270.80/271.20 (49354) {G9,W7,D4,L1,V0,M1} R(3255,10680) { multiplication( domain( skol1 )
% 270.80/271.20 , domain( skol2 ) ) ==> zero }.
% 270.80/271.20 (56929) {G8,W8,D4,L1,V0,M1} R(927,15619);d(268);d(6) { ! multiplication(
% 270.80/271.20 antidomain( skol2 ), domain( skol1 ) ) ==> domain( skol1 ) }.
% 270.80/271.20 (58463) {G8,W8,D5,L1,V1,M1} P(977,211);d(593) { addition( codomain(
% 270.80/271.20 antidomain( X ) ), domain( X ) ) ==> one }.
% 270.80/271.20 (58938) {G9,W10,D5,L1,V1,M1} P(58463,55);d(5) { multiplication(
% 270.80/271.20 coantidomain( antidomain( X ) ), domain( X ) ) ==> coantidomain(
% 270.80/271.20 antidomain( X ) ) }.
% 270.80/271.20 (65418) {G9,W7,D5,L1,V1,M1} R(5946,7560) { multiplication( codomain(
% 270.80/271.20 antidomain( X ) ), X ) ==> zero }.
% 270.80/271.20 (65554) {G10,W8,D5,L1,V1,M1} P(1137,65418) { multiplication( codomain(
% 270.80/271.20 antidomain( X ) ), domain( X ) ) ==> zero }.
% 270.80/271.20 (147688) {G11,W6,D4,L1,V1,M1} P(65554,1717);d(58938);d(58938);r(58) {
% 270.80/271.20 coantidomain( antidomain( X ) ) ==> domain( X ) }.
% 270.80/271.20 (148025) {G10,W8,D4,L1,V0,M1} P(49354,1720);r(58) { multiplication(
% 270.80/271.20 antidomain( skol1 ), domain( skol2 ) ) ==> domain( skol2 ) }.
% 270.80/271.20 (148464) {G11,W5,D3,L1,V0,M1} P(148025,690);d(289);d(5);q { leq( domain(
% 270.80/271.20 skol2 ), antidomain( skol1 ) ) }.
% 270.80/271.20 (148522) {G12,W7,D4,L1,V0,M1} R(148464,1217);d(147688) { multiplication(
% 270.80/271.20 domain( skol2 ), domain( skol1 ) ) ==> zero }.
% 270.80/271.20 (149605) {G13,W8,D4,L1,V0,M1} P(148522,1720);r(58) { multiplication(
% 270.80/271.20 antidomain( skol2 ), domain( skol1 ) ) ==> domain( skol1 ) }.
% 270.80/271.20 (149766) {G14,W0,D0,L0,V0,M0} S(56929);d(149605);q { }.
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 % SZS output end Refutation
% 270.80/271.20 found a proof!
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 Unprocessed initial clauses:
% 270.80/271.20
% 270.80/271.20 (149768) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X ) }.
% 270.80/271.20 (149769) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) = addition
% 270.80/271.20 ( addition( Z, Y ), X ) }.
% 270.80/271.20 (149770) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 270.80/271.20 (149771) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 270.80/271.20 (149772) {G0,W11,D4,L1,V3,M1} { multiplication( X, multiplication( Y, Z )
% 270.80/271.20 ) = multiplication( multiplication( X, Y ), Z ) }.
% 270.80/271.20 (149773) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 270.80/271.20 (149774) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 270.80/271.20 (149775) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z ) ) =
% 270.80/271.20 addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 270.80/271.20 (149776) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y ), Z ) =
% 270.80/271.20 addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 270.80/271.20 (149777) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero }.
% 270.80/271.20 (149778) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero }.
% 270.80/271.20 (149779) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) = Y }.
% 270.80/271.20 (149780) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y ) }.
% 270.80/271.20 (149781) {G0,W6,D4,L1,V1,M1} { multiplication( antidomain( X ), X ) = zero
% 270.80/271.20 }.
% 270.80/271.20 (149782) {G0,W18,D7,L1,V2,M1} { addition( antidomain( multiplication( X, Y
% 270.80/271.20 ) ), antidomain( multiplication( X, antidomain( antidomain( Y ) ) ) ) )
% 270.80/271.20 = antidomain( multiplication( X, antidomain( antidomain( Y ) ) ) ) }.
% 270.80/271.20 (149783) {G0,W8,D5,L1,V1,M1} { addition( antidomain( antidomain( X ) ),
% 270.80/271.20 antidomain( X ) ) = one }.
% 270.80/271.20 (149784) {G0,W6,D4,L1,V1,M1} { domain( X ) = antidomain( antidomain( X ) )
% 270.80/271.20 }.
% 270.80/271.20 (149785) {G0,W6,D4,L1,V1,M1} { multiplication( X, coantidomain( X ) ) =
% 270.80/271.20 zero }.
% 270.80/271.20 (149786) {G0,W18,D7,L1,V2,M1} { addition( coantidomain( multiplication( X
% 270.80/271.20 , Y ) ), coantidomain( multiplication( coantidomain( coantidomain( X ) )
% 270.80/271.20 , Y ) ) ) = coantidomain( multiplication( coantidomain( coantidomain( X )
% 270.80/271.20 ), Y ) ) }.
% 270.80/271.20 (149787) {G0,W8,D5,L1,V1,M1} { addition( coantidomain( coantidomain( X ) )
% 270.80/271.20 , coantidomain( X ) ) = one }.
% 270.80/271.20 (149788) {G0,W6,D4,L1,V1,M1} { codomain( X ) = coantidomain( coantidomain
% 270.80/271.20 ( X ) ) }.
% 270.80/271.20 (149789) {G0,W6,D4,L1,V0,M1} { multiplication( domain( skol1 ), skol2 ) =
% 270.80/271.20 zero }.
% 270.80/271.20 (149790) {G0,W8,D4,L1,V0,M1} { ! addition( domain( skol1 ), antidomain(
% 270.80/271.20 skol2 ) ) = antidomain( skol2 ) }.
% 270.80/271.20
% 270.80/271.20
% 270.80/271.20 Total Proof:
% 270.80/271.20
% 270.80/271.20 subsumption: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X
% 270.80/271.20 ) }.
% 270.80/271.20 parent0: (149768) {G0,W7,D3,L1,V2,M1} { addition( X, Y ) = addition( Y, X
% 270.80/271.20 ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 270.80/271.20 ==> addition( addition( Z, Y ), X ) }.
% 270.80/271.20 parent0: (149769) {G0,W11,D4,L1,V3,M1} { addition( Z, addition( Y, X ) ) =
% 270.80/271.20 addition( addition( Z, Y ), X ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 Z := Z
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 270.80/271.20 parent0: (149770) {G0,W5,D3,L1,V1,M1} { addition( X, zero ) = X }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 270.80/271.20 parent0: (149771) {G0,W5,D3,L1,V1,M1} { addition( X, X ) = X }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 270.80/271.20 parent0: (149773) {G0,W5,D3,L1,V1,M1} { multiplication( X, one ) = X }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 270.80/271.20 parent0: (149774) {G0,W5,D3,L1,V1,M1} { multiplication( one, X ) = X }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (149814) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y ),
% 270.80/271.20 multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 270.80/271.20 parent0[0]: (149775) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y
% 270.80/271.20 , Z ) ) = addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 Z := Z
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y )
% 270.80/271.20 , multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 270.80/271.20 parent0: (149814) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Y )
% 270.80/271.20 , multiplication( X, Z ) ) = multiplication( X, addition( Y, Z ) ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 Z := Z
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (149822) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z ),
% 270.80/271.20 multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 270.80/271.20 parent0[0]: (149776) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Y
% 270.80/271.20 ), Z ) = addition( multiplication( X, Z ), multiplication( Y, Z ) ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 Z := Z
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z )
% 270.80/271.20 , multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 270.80/271.20 parent0: (149822) {G0,W13,D4,L1,V3,M1} { addition( multiplication( X, Z )
% 270.80/271.20 , multiplication( Y, Z ) ) = multiplication( addition( X, Y ), Z ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 Z := Z
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (9) {G0,W5,D3,L1,V1,M1} I { multiplication( X, zero ) ==> zero
% 270.80/271.20 }.
% 270.80/271.20 parent0: (149777) {G0,W5,D3,L1,V1,M1} { multiplication( X, zero ) = zero
% 270.80/271.20 }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (10) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==>
% 270.80/271.20 zero }.
% 270.80/271.20 parent0: (149778) {G0,W5,D3,L1,V1,M1} { multiplication( zero, X ) = zero
% 270.80/271.20 }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 270.80/271.20 ==> Y }.
% 270.80/271.20 parent0: (149779) {G0,W8,D3,L2,V2,M2} { ! leq( X, Y ), addition( X, Y ) =
% 270.80/271.20 Y }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 1 ==> 1
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X
% 270.80/271.20 , Y ) }.
% 270.80/271.20 parent0: (149780) {G0,W8,D3,L2,V2,M2} { ! addition( X, Y ) = Y, leq( X, Y
% 270.80/271.20 ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 1 ==> 1
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (13) {G0,W6,D4,L1,V1,M1} I { multiplication( antidomain( X ),
% 270.80/271.20 X ) ==> zero }.
% 270.80/271.20 parent0: (149781) {G0,W6,D4,L1,V1,M1} { multiplication( antidomain( X ), X
% 270.80/271.20 ) = zero }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (14) {G0,W18,D7,L1,V2,M1} I { addition( antidomain(
% 270.80/271.20 multiplication( X, Y ) ), antidomain( multiplication( X, antidomain(
% 270.80/271.20 antidomain( Y ) ) ) ) ) ==> antidomain( multiplication( X, antidomain(
% 270.80/271.20 antidomain( Y ) ) ) ) }.
% 270.80/271.20 parent0: (149782) {G0,W18,D7,L1,V2,M1} { addition( antidomain(
% 270.80/271.20 multiplication( X, Y ) ), antidomain( multiplication( X, antidomain(
% 270.80/271.20 antidomain( Y ) ) ) ) ) = antidomain( multiplication( X, antidomain(
% 270.80/271.20 antidomain( Y ) ) ) ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (15) {G0,W8,D5,L1,V1,M1} I { addition( antidomain( antidomain
% 270.80/271.20 ( X ) ), antidomain( X ) ) ==> one }.
% 270.80/271.20 parent0: (149783) {G0,W8,D5,L1,V1,M1} { addition( antidomain( antidomain(
% 270.80/271.20 X ) ), antidomain( X ) ) = one }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (149922) {G0,W6,D4,L1,V1,M1} { antidomain( antidomain( X ) ) =
% 270.80/271.20 domain( X ) }.
% 270.80/271.20 parent0[0]: (149784) {G0,W6,D4,L1,V1,M1} { domain( X ) = antidomain(
% 270.80/271.20 antidomain( X ) ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (16) {G0,W6,D4,L1,V1,M1} I { antidomain( antidomain( X ) ) ==>
% 270.80/271.20 domain( X ) }.
% 270.80/271.20 parent0: (149922) {G0,W6,D4,L1,V1,M1} { antidomain( antidomain( X ) ) =
% 270.80/271.20 domain( X ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (17) {G0,W6,D4,L1,V1,M1} I { multiplication( X, coantidomain(
% 270.80/271.20 X ) ) ==> zero }.
% 270.80/271.20 parent0: (149785) {G0,W6,D4,L1,V1,M1} { multiplication( X, coantidomain( X
% 270.80/271.20 ) ) = zero }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (18) {G0,W18,D7,L1,V2,M1} I { addition( coantidomain(
% 270.80/271.20 multiplication( X, Y ) ), coantidomain( multiplication( coantidomain(
% 270.80/271.20 coantidomain( X ) ), Y ) ) ) ==> coantidomain( multiplication(
% 270.80/271.20 coantidomain( coantidomain( X ) ), Y ) ) }.
% 270.80/271.20 parent0: (149786) {G0,W18,D7,L1,V2,M1} { addition( coantidomain(
% 270.80/271.20 multiplication( X, Y ) ), coantidomain( multiplication( coantidomain(
% 270.80/271.20 coantidomain( X ) ), Y ) ) ) = coantidomain( multiplication( coantidomain
% 270.80/271.20 ( coantidomain( X ) ), Y ) ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (19) {G0,W8,D5,L1,V1,M1} I { addition( coantidomain(
% 270.80/271.20 coantidomain( X ) ), coantidomain( X ) ) ==> one }.
% 270.80/271.20 parent0: (149787) {G0,W8,D5,L1,V1,M1} { addition( coantidomain(
% 270.80/271.20 coantidomain( X ) ), coantidomain( X ) ) = one }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (149996) {G0,W6,D4,L1,V1,M1} { coantidomain( coantidomain( X ) ) =
% 270.80/271.20 codomain( X ) }.
% 270.80/271.20 parent0[0]: (149788) {G0,W6,D4,L1,V1,M1} { codomain( X ) = coantidomain(
% 270.80/271.20 coantidomain( X ) ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (20) {G0,W6,D4,L1,V1,M1} I { coantidomain( coantidomain( X ) )
% 270.80/271.20 ==> codomain( X ) }.
% 270.80/271.20 parent0: (149996) {G0,W6,D4,L1,V1,M1} { coantidomain( coantidomain( X ) )
% 270.80/271.20 = codomain( X ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (21) {G0,W6,D4,L1,V0,M1} I { multiplication( domain( skol1 ),
% 270.80/271.20 skol2 ) ==> zero }.
% 270.80/271.20 parent0: (149789) {G0,W6,D4,L1,V0,M1} { multiplication( domain( skol1 ),
% 270.80/271.20 skol2 ) = zero }.
% 270.80/271.20 substitution0:
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (22) {G0,W8,D4,L1,V0,M1} I { ! addition( domain( skol1 ),
% 270.80/271.20 antidomain( skol2 ) ) ==> antidomain( skol2 ) }.
% 270.80/271.20 parent0: (149790) {G0,W8,D4,L1,V0,M1} { ! addition( domain( skol1 ),
% 270.80/271.20 antidomain( skol2 ) ) = antidomain( skol2 ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (150040) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, zero ) }.
% 270.80/271.20 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 paramod: (150041) {G1,W5,D3,L1,V1,M1} { X ==> addition( zero, X ) }.
% 270.80/271.20 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 270.80/271.20 }.
% 270.80/271.20 parent1[0; 2]: (150040) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, zero )
% 270.80/271.20 }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := zero
% 270.80/271.20 end
% 270.80/271.20 substitution1:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (150044) {G1,W5,D3,L1,V1,M1} { addition( zero, X ) ==> X }.
% 270.80/271.20 parent0[0]: (150041) {G1,W5,D3,L1,V1,M1} { X ==> addition( zero, X ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (23) {G1,W5,D3,L1,V1,M1} P(2,0) { addition( zero, X ) ==> X
% 270.80/271.20 }.
% 270.80/271.20 parent0: (150044) {G1,W5,D3,L1,V1,M1} { addition( zero, X ) ==> X }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (150045) {G0,W6,D4,L1,V1,M1} { codomain( X ) ==> coantidomain(
% 270.80/271.20 coantidomain( X ) ) }.
% 270.80/271.20 parent0[0]: (20) {G0,W6,D4,L1,V1,M1} I { coantidomain( coantidomain( X ) )
% 270.80/271.20 ==> codomain( X ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 paramod: (150048) {G1,W7,D4,L1,V1,M1} { codomain( coantidomain( X ) ) ==>
% 270.80/271.20 coantidomain( codomain( X ) ) }.
% 270.80/271.20 parent0[0]: (20) {G0,W6,D4,L1,V1,M1} I { coantidomain( coantidomain( X ) )
% 270.80/271.20 ==> codomain( X ) }.
% 270.80/271.20 parent1[0; 5]: (150045) {G0,W6,D4,L1,V1,M1} { codomain( X ) ==>
% 270.80/271.20 coantidomain( coantidomain( X ) ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20 substitution1:
% 270.80/271.20 X := coantidomain( X )
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (24) {G1,W7,D4,L1,V1,M1} P(20,20) { codomain( coantidomain( X
% 270.80/271.20 ) ) ==> coantidomain( codomain( X ) ) }.
% 270.80/271.20 parent0: (150048) {G1,W7,D4,L1,V1,M1} { codomain( coantidomain( X ) ) ==>
% 270.80/271.20 coantidomain( codomain( X ) ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (150051) {G0,W6,D4,L1,V1,M1} { zero ==> multiplication( X,
% 270.80/271.20 coantidomain( X ) ) }.
% 270.80/271.20 parent0[0]: (17) {G0,W6,D4,L1,V1,M1} I { multiplication( X, coantidomain( X
% 270.80/271.20 ) ) ==> zero }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 paramod: (150052) {G1,W7,D4,L1,V1,M1} { zero ==> multiplication(
% 270.80/271.20 coantidomain( X ), codomain( X ) ) }.
% 270.80/271.20 parent0[0]: (20) {G0,W6,D4,L1,V1,M1} I { coantidomain( coantidomain( X ) )
% 270.80/271.20 ==> codomain( X ) }.
% 270.80/271.20 parent1[0; 5]: (150051) {G0,W6,D4,L1,V1,M1} { zero ==> multiplication( X,
% 270.80/271.20 coantidomain( X ) ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20 substitution1:
% 270.80/271.20 X := coantidomain( X )
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (150053) {G1,W7,D4,L1,V1,M1} { multiplication( coantidomain( X ),
% 270.80/271.20 codomain( X ) ) ==> zero }.
% 270.80/271.20 parent0[0]: (150052) {G1,W7,D4,L1,V1,M1} { zero ==> multiplication(
% 270.80/271.20 coantidomain( X ), codomain( X ) ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (25) {G1,W7,D4,L1,V1,M1} P(20,17) { multiplication(
% 270.80/271.20 coantidomain( X ), codomain( X ) ) ==> zero }.
% 270.80/271.20 parent0: (150053) {G1,W7,D4,L1,V1,M1} { multiplication( coantidomain( X )
% 270.80/271.20 , codomain( X ) ) ==> zero }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (150054) {G0,W6,D4,L1,V1,M1} { zero ==> multiplication( X,
% 270.80/271.20 coantidomain( X ) ) }.
% 270.80/271.20 parent0[0]: (17) {G0,W6,D4,L1,V1,M1} I { multiplication( X, coantidomain( X
% 270.80/271.20 ) ) ==> zero }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 paramod: (150056) {G1,W4,D3,L1,V0,M1} { zero ==> coantidomain( one ) }.
% 270.80/271.20 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 270.80/271.20 parent1[0; 2]: (150054) {G0,W6,D4,L1,V1,M1} { zero ==> multiplication( X,
% 270.80/271.20 coantidomain( X ) ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := coantidomain( one )
% 270.80/271.20 end
% 270.80/271.20 substitution1:
% 270.80/271.20 X := one
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (150057) {G1,W4,D3,L1,V0,M1} { coantidomain( one ) ==> zero }.
% 270.80/271.20 parent0[0]: (150056) {G1,W4,D3,L1,V0,M1} { zero ==> coantidomain( one )
% 270.80/271.20 }.
% 270.80/271.20 substitution0:
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (26) {G1,W4,D3,L1,V0,M1} P(17,6) { coantidomain( one ) ==>
% 270.80/271.20 zero }.
% 270.80/271.20 parent0: (150057) {G1,W4,D3,L1,V0,M1} { coantidomain( one ) ==> zero }.
% 270.80/271.20 substitution0:
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (150058) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z )
% 270.80/271.20 ==> addition( X, addition( Y, Z ) ) }.
% 270.80/271.20 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 270.80/271.20 ==> addition( addition( Z, Y ), X ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := Z
% 270.80/271.20 Y := Y
% 270.80/271.20 Z := X
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 paramod: (150061) {G1,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z )
% 270.80/271.20 ==> addition( addition( Y, Z ), X ) }.
% 270.80/271.20 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 270.80/271.20 }.
% 270.80/271.20 parent1[0; 6]: (150058) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y )
% 270.80/271.20 , Z ) ==> addition( X, addition( Y, Z ) ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := addition( Y, Z )
% 270.80/271.20 end
% 270.80/271.20 substitution1:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 Z := Z
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (27) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y )
% 270.80/271.20 , Z ) = addition( addition( Y, Z ), X ) }.
% 270.80/271.20 parent0: (150061) {G1,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z )
% 270.80/271.20 ==> addition( addition( Y, Z ), X ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 Z := Z
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (150076) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y ), Z )
% 270.80/271.20 ==> addition( X, addition( Y, Z ) ) }.
% 270.80/271.20 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { addition( Z, addition( Y, X ) )
% 270.80/271.20 ==> addition( addition( Z, Y ), X ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := Z
% 270.80/271.20 Y := Y
% 270.80/271.20 Z := X
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 paramod: (150082) {G1,W9,D4,L1,V2,M1} { addition( addition( X, Y ), Y )
% 270.80/271.20 ==> addition( X, Y ) }.
% 270.80/271.20 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 270.80/271.20 parent1[0; 8]: (150076) {G0,W11,D4,L1,V3,M1} { addition( addition( X, Y )
% 270.80/271.20 , Z ) ==> addition( X, addition( Y, Z ) ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := Y
% 270.80/271.20 end
% 270.80/271.20 substitution1:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 Z := Y
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (30) {G1,W9,D4,L1,V2,M1} P(3,1) { addition( addition( Y, X ),
% 270.80/271.20 X ) ==> addition( Y, X ) }.
% 270.80/271.20 parent0: (150082) {G1,W9,D4,L1,V2,M1} { addition( addition( X, Y ), Y )
% 270.80/271.20 ==> addition( X, Y ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := Y
% 270.80/271.20 Y := X
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (150088) {G0,W6,D4,L1,V1,M1} { codomain( X ) ==> coantidomain(
% 270.80/271.20 coantidomain( X ) ) }.
% 270.80/271.20 parent0[0]: (20) {G0,W6,D4,L1,V1,M1} I { coantidomain( coantidomain( X ) )
% 270.80/271.20 ==> codomain( X ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 paramod: (150089) {G1,W5,D3,L1,V0,M1} { codomain( one ) ==> coantidomain(
% 270.80/271.20 zero ) }.
% 270.80/271.20 parent0[0]: (26) {G1,W4,D3,L1,V0,M1} P(17,6) { coantidomain( one ) ==> zero
% 270.80/271.20 }.
% 270.80/271.20 parent1[0; 4]: (150088) {G0,W6,D4,L1,V1,M1} { codomain( X ) ==>
% 270.80/271.20 coantidomain( coantidomain( X ) ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 end
% 270.80/271.20 substitution1:
% 270.80/271.20 X := one
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (31) {G2,W5,D3,L1,V0,M1} P(26,20) { codomain( one ) ==>
% 270.80/271.20 coantidomain( zero ) }.
% 270.80/271.20 parent0: (150089) {G1,W5,D3,L1,V0,M1} { codomain( one ) ==> coantidomain(
% 270.80/271.20 zero ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (150091) {G0,W6,D4,L1,V1,M1} { domain( X ) ==> antidomain(
% 270.80/271.20 antidomain( X ) ) }.
% 270.80/271.20 parent0[0]: (16) {G0,W6,D4,L1,V1,M1} I { antidomain( antidomain( X ) ) ==>
% 270.80/271.20 domain( X ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 paramod: (150094) {G1,W7,D4,L1,V1,M1} { domain( antidomain( X ) ) ==>
% 270.80/271.20 antidomain( domain( X ) ) }.
% 270.80/271.20 parent0[0]: (16) {G0,W6,D4,L1,V1,M1} I { antidomain( antidomain( X ) ) ==>
% 270.80/271.20 domain( X ) }.
% 270.80/271.20 parent1[0; 5]: (150091) {G0,W6,D4,L1,V1,M1} { domain( X ) ==> antidomain(
% 270.80/271.20 antidomain( X ) ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20 substitution1:
% 270.80/271.20 X := antidomain( X )
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (32) {G1,W7,D4,L1,V1,M1} P(16,16) { domain( antidomain( X ) )
% 270.80/271.20 ==> antidomain( domain( X ) ) }.
% 270.80/271.20 parent0: (150094) {G1,W7,D4,L1,V1,M1} { domain( antidomain( X ) ) ==>
% 270.80/271.20 antidomain( domain( X ) ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (150096) {G0,W6,D4,L1,V1,M1} { zero ==> multiplication( antidomain
% 270.80/271.20 ( X ), X ) }.
% 270.80/271.20 parent0[0]: (13) {G0,W6,D4,L1,V1,M1} I { multiplication( antidomain( X ), X
% 270.80/271.20 ) ==> zero }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 paramod: (150098) {G1,W4,D3,L1,V0,M1} { zero ==> antidomain( one ) }.
% 270.80/271.20 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 270.80/271.20 parent1[0; 2]: (150096) {G0,W6,D4,L1,V1,M1} { zero ==> multiplication(
% 270.80/271.20 antidomain( X ), X ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := antidomain( one )
% 270.80/271.20 end
% 270.80/271.20 substitution1:
% 270.80/271.20 X := one
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (150099) {G1,W4,D3,L1,V0,M1} { antidomain( one ) ==> zero }.
% 270.80/271.20 parent0[0]: (150098) {G1,W4,D3,L1,V0,M1} { zero ==> antidomain( one ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (34) {G1,W4,D3,L1,V0,M1} P(13,5) { antidomain( one ) ==> zero
% 270.80/271.20 }.
% 270.80/271.20 parent0: (150099) {G1,W4,D3,L1,V0,M1} { antidomain( one ) ==> zero }.
% 270.80/271.20 substitution0:
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (150101) {G0,W6,D4,L1,V1,M1} { domain( X ) ==> antidomain(
% 270.80/271.20 antidomain( X ) ) }.
% 270.80/271.20 parent0[0]: (16) {G0,W6,D4,L1,V1,M1} I { antidomain( antidomain( X ) ) ==>
% 270.80/271.20 domain( X ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 paramod: (150102) {G1,W5,D3,L1,V0,M1} { domain( one ) ==> antidomain( zero
% 270.80/271.20 ) }.
% 270.80/271.20 parent0[0]: (34) {G1,W4,D3,L1,V0,M1} P(13,5) { antidomain( one ) ==> zero
% 270.80/271.20 }.
% 270.80/271.20 parent1[0; 4]: (150101) {G0,W6,D4,L1,V1,M1} { domain( X ) ==> antidomain(
% 270.80/271.20 antidomain( X ) ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 end
% 270.80/271.20 substitution1:
% 270.80/271.20 X := one
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (38) {G2,W5,D3,L1,V0,M1} P(34,16) { domain( one ) ==>
% 270.80/271.20 antidomain( zero ) }.
% 270.80/271.20 parent0: (150102) {G1,W5,D3,L1,V0,M1} { domain( one ) ==> antidomain( zero
% 270.80/271.20 ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (150105) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z
% 270.80/271.20 ) ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 270.80/271.20 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 270.80/271.20 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 Z := Z
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 paramod: (150108) {G1,W13,D5,L1,V2,M1} { multiplication( antidomain( X ),
% 270.80/271.20 addition( X, Y ) ) ==> addition( zero, multiplication( antidomain( X ), Y
% 270.80/271.20 ) ) }.
% 270.80/271.20 parent0[0]: (13) {G0,W6,D4,L1,V1,M1} I { multiplication( antidomain( X ), X
% 270.80/271.20 ) ==> zero }.
% 270.80/271.20 parent1[0; 8]: (150105) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition
% 270.80/271.20 ( Y, Z ) ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) )
% 270.80/271.20 }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20 substitution1:
% 270.80/271.20 X := antidomain( X )
% 270.80/271.20 Y := X
% 270.80/271.20 Z := Y
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 paramod: (150110) {G2,W11,D4,L1,V2,M1} { multiplication( antidomain( X ),
% 270.80/271.20 addition( X, Y ) ) ==> multiplication( antidomain( X ), Y ) }.
% 270.80/271.20 parent0[0]: (23) {G1,W5,D3,L1,V1,M1} P(2,0) { addition( zero, X ) ==> X }.
% 270.80/271.20 parent1[0; 7]: (150108) {G1,W13,D5,L1,V2,M1} { multiplication( antidomain
% 270.80/271.20 ( X ), addition( X, Y ) ) ==> addition( zero, multiplication( antidomain
% 270.80/271.20 ( X ), Y ) ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := multiplication( antidomain( X ), Y )
% 270.80/271.20 end
% 270.80/271.20 substitution1:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (47) {G2,W11,D4,L1,V2,M1} P(13,7);d(23) { multiplication(
% 270.80/271.20 antidomain( X ), addition( X, Y ) ) ==> multiplication( antidomain( X ),
% 270.80/271.20 Y ) }.
% 270.80/271.20 parent0: (150110) {G2,W11,D4,L1,V2,M1} { multiplication( antidomain( X ),
% 270.80/271.20 addition( X, Y ) ) ==> multiplication( antidomain( X ), Y ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (150113) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z
% 270.80/271.20 ) ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 270.80/271.20 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 270.80/271.20 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 Z := Z
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 paramod: (150116) {G1,W12,D5,L1,V2,M1} { multiplication( X, addition( Y,
% 270.80/271.20 coantidomain( X ) ) ) ==> addition( multiplication( X, Y ), zero ) }.
% 270.80/271.20 parent0[0]: (17) {G0,W6,D4,L1,V1,M1} I { multiplication( X, coantidomain( X
% 270.80/271.20 ) ) ==> zero }.
% 270.80/271.20 parent1[0; 11]: (150113) {G0,W13,D4,L1,V3,M1} { multiplication( X,
% 270.80/271.20 addition( Y, Z ) ) ==> addition( multiplication( X, Y ), multiplication(
% 270.80/271.20 X, Z ) ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20 substitution1:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 Z := coantidomain( X )
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 paramod: (150117) {G1,W10,D5,L1,V2,M1} { multiplication( X, addition( Y,
% 270.80/271.20 coantidomain( X ) ) ) ==> multiplication( X, Y ) }.
% 270.80/271.20 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 270.80/271.20 parent1[0; 7]: (150116) {G1,W12,D5,L1,V2,M1} { multiplication( X, addition
% 270.80/271.20 ( Y, coantidomain( X ) ) ) ==> addition( multiplication( X, Y ), zero )
% 270.80/271.20 }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := multiplication( X, Y )
% 270.80/271.20 end
% 270.80/271.20 substitution1:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (51) {G1,W10,D5,L1,V2,M1} P(17,7);d(2) { multiplication( X,
% 270.80/271.20 addition( Y, coantidomain( X ) ) ) ==> multiplication( X, Y ) }.
% 270.80/271.20 parent0: (150117) {G1,W10,D5,L1,V2,M1} { multiplication( X, addition( Y,
% 270.80/271.20 coantidomain( X ) ) ) ==> multiplication( X, Y ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (150120) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z
% 270.80/271.20 ) ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 270.80/271.20 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 270.80/271.20 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 Z := Z
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 paramod: (150122) {G1,W11,D4,L1,V2,M1} { multiplication( X, addition( Y,
% 270.80/271.20 one ) ) ==> addition( multiplication( X, Y ), X ) }.
% 270.80/271.20 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 270.80/271.20 parent1[0; 10]: (150120) {G0,W13,D4,L1,V3,M1} { multiplication( X,
% 270.80/271.20 addition( Y, Z ) ) ==> addition( multiplication( X, Y ), multiplication(
% 270.80/271.20 X, Z ) ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20 substitution1:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 Z := one
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (150124) {G1,W11,D4,L1,V2,M1} { addition( multiplication( X, Y ),
% 270.80/271.20 X ) ==> multiplication( X, addition( Y, one ) ) }.
% 270.80/271.20 parent0[0]: (150122) {G1,W11,D4,L1,V2,M1} { multiplication( X, addition( Y
% 270.80/271.20 , one ) ) ==> addition( multiplication( X, Y ), X ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (54) {G1,W11,D4,L1,V2,M1} P(5,7) { addition( multiplication( X
% 270.80/271.20 , Y ), X ) = multiplication( X, addition( Y, one ) ) }.
% 270.80/271.20 parent0: (150124) {G1,W11,D4,L1,V2,M1} { addition( multiplication( X, Y )
% 270.80/271.20 , X ) ==> multiplication( X, addition( Y, one ) ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (150126) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition( Y, Z
% 270.80/271.20 ) ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) ) }.
% 270.80/271.20 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 270.80/271.20 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 Z := Z
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 paramod: (150128) {G1,W14,D5,L1,V2,M1} { multiplication( coantidomain( X )
% 270.80/271.20 , addition( codomain( X ), Y ) ) ==> addition( zero, multiplication(
% 270.80/271.20 coantidomain( X ), Y ) ) }.
% 270.80/271.20 parent0[0]: (25) {G1,W7,D4,L1,V1,M1} P(20,17) { multiplication(
% 270.80/271.20 coantidomain( X ), codomain( X ) ) ==> zero }.
% 270.80/271.20 parent1[0; 9]: (150126) {G0,W13,D4,L1,V3,M1} { multiplication( X, addition
% 270.80/271.20 ( Y, Z ) ) ==> addition( multiplication( X, Y ), multiplication( X, Z ) )
% 270.80/271.20 }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20 substitution1:
% 270.80/271.20 X := coantidomain( X )
% 270.80/271.20 Y := codomain( X )
% 270.80/271.20 Z := Y
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 paramod: (150130) {G2,W12,D5,L1,V2,M1} { multiplication( coantidomain( X )
% 270.80/271.20 , addition( codomain( X ), Y ) ) ==> multiplication( coantidomain( X ), Y
% 270.80/271.20 ) }.
% 270.80/271.20 parent0[0]: (23) {G1,W5,D3,L1,V1,M1} P(2,0) { addition( zero, X ) ==> X }.
% 270.80/271.20 parent1[0; 8]: (150128) {G1,W14,D5,L1,V2,M1} { multiplication(
% 270.80/271.20 coantidomain( X ), addition( codomain( X ), Y ) ) ==> addition( zero,
% 270.80/271.20 multiplication( coantidomain( X ), Y ) ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := multiplication( coantidomain( X ), Y )
% 270.80/271.20 end
% 270.80/271.20 substitution1:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (55) {G2,W12,D5,L1,V2,M1} P(25,7);d(23) { multiplication(
% 270.80/271.20 coantidomain( X ), addition( codomain( X ), Y ) ) ==> multiplication(
% 270.80/271.20 coantidomain( X ), Y ) }.
% 270.80/271.20 parent0: (150130) {G2,W12,D5,L1,V2,M1} { multiplication( coantidomain( X )
% 270.80/271.20 , addition( codomain( X ), Y ) ) ==> multiplication( coantidomain( X ), Y
% 270.80/271.20 ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (150132) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 270.80/271.20 ) }.
% 270.80/271.20 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 270.80/271.20 Y ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (150133) {G1,W5,D3,L1,V1,M1} { X ==> addition( zero, X ) }.
% 270.80/271.20 parent0[0]: (23) {G1,W5,D3,L1,V1,M1} P(2,0) { addition( zero, X ) ==> X }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 resolution: (150134) {G1,W3,D2,L1,V1,M1} { leq( zero, X ) }.
% 270.80/271.20 parent0[0]: (150132) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq(
% 270.80/271.20 X, Y ) }.
% 270.80/271.20 parent1[0]: (150133) {G1,W5,D3,L1,V1,M1} { X ==> addition( zero, X ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := zero
% 270.80/271.20 Y := X
% 270.80/271.20 end
% 270.80/271.20 substitution1:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (58) {G2,W3,D2,L1,V1,M1} R(12,23) { leq( zero, X ) }.
% 270.80/271.20 parent0: (150134) {G1,W3,D2,L1,V1,M1} { leq( zero, X ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (150135) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 270.80/271.20 ) }.
% 270.80/271.20 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 270.80/271.20 Y ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (150136) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 270.80/271.20 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { addition( X, X ) ==> X }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 resolution: (150137) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 270.80/271.20 parent0[0]: (150135) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq(
% 270.80/271.20 X, Y ) }.
% 270.80/271.20 parent1[0]: (150136) {G0,W5,D3,L1,V1,M1} { X ==> addition( X, X ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := X
% 270.80/271.20 end
% 270.80/271.20 substitution1:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (59) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 270.80/271.20 parent0: (150137) {G1,W3,D2,L1,V1,M1} { leq( X, X ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (150139) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 270.80/271.20 ) }.
% 270.80/271.20 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 270.80/271.20 Y ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 paramod: (150140) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 270.80/271.20 multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ),
% 270.80/271.20 multiplication( X, Y ) ) }.
% 270.80/271.20 parent0[0]: (7) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Y ),
% 270.80/271.20 multiplication( X, Z ) ) ==> multiplication( X, addition( Y, Z ) ) }.
% 270.80/271.20 parent1[0; 5]: (150139) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ),
% 270.80/271.20 leq( X, Y ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Z
% 270.80/271.20 Z := Y
% 270.80/271.20 end
% 270.80/271.20 substitution1:
% 270.80/271.20 X := multiplication( X, Z )
% 270.80/271.20 Y := multiplication( X, Y )
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (150141) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, addition( Z,
% 270.80/271.20 Y ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ),
% 270.80/271.20 multiplication( X, Y ) ) }.
% 270.80/271.20 parent0[0]: (150140) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 270.80/271.20 multiplication( X, addition( Z, Y ) ), leq( multiplication( X, Z ),
% 270.80/271.20 multiplication( X, Y ) ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 Z := Z
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (60) {G1,W16,D4,L2,V3,M2} P(7,12) { ! multiplication( X,
% 270.80/271.20 addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 270.80/271.20 ), multiplication( X, Z ) ) }.
% 270.80/271.20 parent0: (150141) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, addition( Z
% 270.80/271.20 , Y ) ) ==> multiplication( X, Y ), leq( multiplication( X, Z ),
% 270.80/271.20 multiplication( X, Y ) ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Z
% 270.80/271.20 Z := Y
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 1 ==> 1
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (150142) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 270.80/271.20 ) }.
% 270.80/271.20 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 270.80/271.20 Y ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 paramod: (150143) {G1,W8,D3,L2,V2,M2} { ! X ==> addition( X, Y ), leq( Y,
% 270.80/271.20 X ) }.
% 270.80/271.20 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 270.80/271.20 }.
% 270.80/271.20 parent1[0; 3]: (150142) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ),
% 270.80/271.20 leq( X, Y ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := Y
% 270.80/271.20 Y := X
% 270.80/271.20 end
% 270.80/271.20 substitution1:
% 270.80/271.20 X := Y
% 270.80/271.20 Y := X
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (150146) {G1,W8,D3,L2,V2,M2} { ! addition( X, Y ) ==> X, leq( Y, X
% 270.80/271.20 ) }.
% 270.80/271.20 parent0[0]: (150143) {G1,W8,D3,L2,V2,M2} { ! X ==> addition( X, Y ), leq(
% 270.80/271.20 Y, X ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (63) {G1,W8,D3,L2,V2,M2} P(0,12) { ! addition( Y, X ) ==> Y,
% 270.80/271.20 leq( X, Y ) }.
% 270.80/271.20 parent0: (150146) {G1,W8,D3,L2,V2,M2} { ! addition( X, Y ) ==> X, leq( Y,
% 270.80/271.20 X ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := Y
% 270.80/271.20 Y := X
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 1 ==> 1
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (150148) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 270.80/271.20 ) }.
% 270.80/271.20 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 270.80/271.20 Y ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 paramod: (150149) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 270.80/271.20 multiplication( addition( Z, X ), Y ), leq( multiplication( Z, Y ),
% 270.80/271.20 multiplication( X, Y ) ) }.
% 270.80/271.20 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 270.80/271.20 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 270.80/271.20 parent1[0; 5]: (150148) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ),
% 270.80/271.20 leq( X, Y ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := Z
% 270.80/271.20 Y := X
% 270.80/271.20 Z := Y
% 270.80/271.20 end
% 270.80/271.20 substitution1:
% 270.80/271.20 X := multiplication( Z, Y )
% 270.80/271.20 Y := multiplication( X, Y )
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (150150) {G1,W16,D4,L2,V3,M2} { ! multiplication( addition( Z, X )
% 270.80/271.20 , Y ) ==> multiplication( X, Y ), leq( multiplication( Z, Y ),
% 270.80/271.20 multiplication( X, Y ) ) }.
% 270.80/271.20 parent0[0]: (150149) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Y ) ==>
% 270.80/271.20 multiplication( addition( Z, X ), Y ), leq( multiplication( Z, Y ),
% 270.80/271.20 multiplication( X, Y ) ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 Z := Z
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (64) {G1,W16,D4,L2,V3,M2} P(8,12) { ! multiplication( addition
% 270.80/271.20 ( X, Z ), Y ) ==> multiplication( Z, Y ), leq( multiplication( X, Y ),
% 270.80/271.20 multiplication( Z, Y ) ) }.
% 270.80/271.20 parent0: (150150) {G1,W16,D4,L2,V3,M2} { ! multiplication( addition( Z, X
% 270.80/271.20 ), Y ) ==> multiplication( X, Y ), leq( multiplication( Z, Y ),
% 270.80/271.20 multiplication( X, Y ) ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := Z
% 270.80/271.20 Y := Y
% 270.80/271.20 Z := X
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 1 ==> 1
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (150152) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Z ),
% 270.80/271.20 Y ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) ) }.
% 270.80/271.20 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 270.80/271.20 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Z
% 270.80/271.20 Z := Y
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 paramod: (150155) {G1,W12,D5,L1,V2,M1} { multiplication( addition( X,
% 270.80/271.20 antidomain( Y ) ), Y ) ==> addition( multiplication( X, Y ), zero ) }.
% 270.80/271.20 parent0[0]: (13) {G0,W6,D4,L1,V1,M1} I { multiplication( antidomain( X ), X
% 270.80/271.20 ) ==> zero }.
% 270.80/271.20 parent1[0; 11]: (150152) {G0,W13,D4,L1,V3,M1} { multiplication( addition(
% 270.80/271.20 X, Z ), Y ) ==> addition( multiplication( X, Y ), multiplication( Z, Y )
% 270.80/271.20 ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := Y
% 270.80/271.20 end
% 270.80/271.20 substitution1:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 Z := antidomain( Y )
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 paramod: (150156) {G1,W10,D5,L1,V2,M1} { multiplication( addition( X,
% 270.80/271.20 antidomain( Y ) ), Y ) ==> multiplication( X, Y ) }.
% 270.80/271.20 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 270.80/271.20 parent1[0; 7]: (150155) {G1,W12,D5,L1,V2,M1} { multiplication( addition( X
% 270.80/271.20 , antidomain( Y ) ), Y ) ==> addition( multiplication( X, Y ), zero ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := multiplication( X, Y )
% 270.80/271.20 end
% 270.80/271.20 substitution1:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (72) {G1,W10,D5,L1,V2,M1} P(13,8);d(2) { multiplication(
% 270.80/271.20 addition( Y, antidomain( X ) ), X ) ==> multiplication( Y, X ) }.
% 270.80/271.20 parent0: (150156) {G1,W10,D5,L1,V2,M1} { multiplication( addition( X,
% 270.80/271.20 antidomain( Y ) ), Y ) ==> multiplication( X, Y ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := Y
% 270.80/271.20 Y := X
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (150159) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Z ),
% 270.80/271.20 Y ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) ) }.
% 270.80/271.20 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 270.80/271.20 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Z
% 270.80/271.20 Z := Y
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 paramod: (150162) {G1,W13,D5,L1,V2,M1} { multiplication( addition( X, Y )
% 270.80/271.20 , coantidomain( X ) ) ==> addition( zero, multiplication( Y, coantidomain
% 270.80/271.20 ( X ) ) ) }.
% 270.80/271.20 parent0[0]: (17) {G0,W6,D4,L1,V1,M1} I { multiplication( X, coantidomain( X
% 270.80/271.20 ) ) ==> zero }.
% 270.80/271.20 parent1[0; 8]: (150159) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X
% 270.80/271.20 , Z ), Y ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) )
% 270.80/271.20 }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20 substitution1:
% 270.80/271.20 X := X
% 270.80/271.20 Y := coantidomain( X )
% 270.80/271.20 Z := Y
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 paramod: (150164) {G2,W11,D4,L1,V2,M1} { multiplication( addition( X, Y )
% 270.80/271.20 , coantidomain( X ) ) ==> multiplication( Y, coantidomain( X ) ) }.
% 270.80/271.20 parent0[0]: (23) {G1,W5,D3,L1,V1,M1} P(2,0) { addition( zero, X ) ==> X }.
% 270.80/271.20 parent1[0; 7]: (150162) {G1,W13,D5,L1,V2,M1} { multiplication( addition( X
% 270.80/271.20 , Y ), coantidomain( X ) ) ==> addition( zero, multiplication( Y,
% 270.80/271.20 coantidomain( X ) ) ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := multiplication( Y, coantidomain( X ) )
% 270.80/271.20 end
% 270.80/271.20 substitution1:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (74) {G2,W11,D4,L1,V2,M1} P(17,8);d(23) { multiplication(
% 270.80/271.20 addition( X, Y ), coantidomain( X ) ) ==> multiplication( Y, coantidomain
% 270.80/271.20 ( X ) ) }.
% 270.80/271.20 parent0: (150164) {G2,W11,D4,L1,V2,M1} { multiplication( addition( X, Y )
% 270.80/271.20 , coantidomain( X ) ) ==> multiplication( Y, coantidomain( X ) ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (150167) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Z ),
% 270.80/271.20 Y ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) ) }.
% 270.80/271.20 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 270.80/271.20 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Z
% 270.80/271.20 Z := Y
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 paramod: (150171) {G1,W13,D5,L1,V2,M1} { multiplication( addition( X, Y )
% 270.80/271.20 , coantidomain( Y ) ) ==> addition( multiplication( X, coantidomain( Y )
% 270.80/271.20 ), zero ) }.
% 270.80/271.20 parent0[0]: (17) {G0,W6,D4,L1,V1,M1} I { multiplication( X, coantidomain( X
% 270.80/271.20 ) ) ==> zero }.
% 270.80/271.20 parent1[0; 12]: (150167) {G0,W13,D4,L1,V3,M1} { multiplication( addition(
% 270.80/271.20 X, Z ), Y ) ==> addition( multiplication( X, Y ), multiplication( Z, Y )
% 270.80/271.20 ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := Y
% 270.80/271.20 end
% 270.80/271.20 substitution1:
% 270.80/271.20 X := X
% 270.80/271.20 Y := coantidomain( Y )
% 270.80/271.20 Z := Y
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 paramod: (150172) {G1,W11,D4,L1,V2,M1} { multiplication( addition( X, Y )
% 270.80/271.20 , coantidomain( Y ) ) ==> multiplication( X, coantidomain( Y ) ) }.
% 270.80/271.20 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 270.80/271.20 parent1[0; 7]: (150171) {G1,W13,D5,L1,V2,M1} { multiplication( addition( X
% 270.80/271.20 , Y ), coantidomain( Y ) ) ==> addition( multiplication( X, coantidomain
% 270.80/271.20 ( Y ) ), zero ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := multiplication( X, coantidomain( Y ) )
% 270.80/271.20 end
% 270.80/271.20 substitution1:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (75) {G1,W11,D4,L1,V2,M1} P(17,8);d(2) { multiplication(
% 270.80/271.20 addition( Y, X ), coantidomain( X ) ) ==> multiplication( Y, coantidomain
% 270.80/271.20 ( X ) ) }.
% 270.80/271.20 parent0: (150172) {G1,W11,D4,L1,V2,M1} { multiplication( addition( X, Y )
% 270.80/271.20 , coantidomain( Y ) ) ==> multiplication( X, coantidomain( Y ) ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := Y
% 270.80/271.20 Y := X
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (150175) {G0,W13,D4,L1,V3,M1} { multiplication( addition( X, Z ),
% 270.80/271.20 Y ) ==> addition( multiplication( X, Y ), multiplication( Z, Y ) ) }.
% 270.80/271.20 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 270.80/271.20 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Z
% 270.80/271.20 Z := Y
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 paramod: (150177) {G1,W11,D4,L1,V2,M1} { multiplication( addition( X, one
% 270.80/271.20 ), Y ) ==> addition( multiplication( X, Y ), Y ) }.
% 270.80/271.20 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 270.80/271.20 parent1[0; 10]: (150175) {G0,W13,D4,L1,V3,M1} { multiplication( addition(
% 270.80/271.20 X, Z ), Y ) ==> addition( multiplication( X, Y ), multiplication( Z, Y )
% 270.80/271.20 ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := Y
% 270.80/271.20 end
% 270.80/271.20 substitution1:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 Z := one
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (150179) {G1,W11,D4,L1,V2,M1} { addition( multiplication( X, Y ),
% 270.80/271.20 Y ) ==> multiplication( addition( X, one ), Y ) }.
% 270.80/271.20 parent0[0]: (150177) {G1,W11,D4,L1,V2,M1} { multiplication( addition( X,
% 270.80/271.20 one ), Y ) ==> addition( multiplication( X, Y ), Y ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (78) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( multiplication( Y
% 270.80/271.20 , X ), X ) = multiplication( addition( Y, one ), X ) }.
% 270.80/271.20 parent0: (150179) {G1,W11,D4,L1,V2,M1} { addition( multiplication( X, Y )
% 270.80/271.20 , Y ) ==> multiplication( addition( X, one ), Y ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := Y
% 270.80/271.20 Y := X
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (150180) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 270.80/271.20 ) }.
% 270.80/271.20 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 270.80/271.20 ==> Y }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (150181) {G1,W8,D3,L2,V2,M2} { ! X ==> addition( X, Y ), leq( Y, X
% 270.80/271.20 ) }.
% 270.80/271.20 parent0[0]: (63) {G1,W8,D3,L2,V2,M2} P(0,12) { ! addition( Y, X ) ==> Y,
% 270.80/271.20 leq( X, Y ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := Y
% 270.80/271.20 Y := X
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 resolution: (150182) {G1,W10,D3,L2,V2,M2} { X ==> addition( Y, X ), ! X
% 270.80/271.20 ==> addition( X, Y ) }.
% 270.80/271.20 parent0[1]: (150180) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq(
% 270.80/271.20 X, Y ) }.
% 270.80/271.20 parent1[1]: (150181) {G1,W8,D3,L2,V2,M2} { ! X ==> addition( X, Y ), leq(
% 270.80/271.20 Y, X ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := Y
% 270.80/271.20 Y := X
% 270.80/271.20 end
% 270.80/271.20 substitution1:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (150184) {G1,W10,D3,L2,V2,M2} { ! addition( X, Y ) ==> X, X ==>
% 270.80/271.20 addition( Y, X ) }.
% 270.80/271.20 parent0[1]: (150182) {G1,W10,D3,L2,V2,M2} { X ==> addition( Y, X ), ! X
% 270.80/271.20 ==> addition( X, Y ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (150185) {G1,W10,D3,L2,V2,M2} { addition( Y, X ) ==> X, ! addition
% 270.80/271.20 ( X, Y ) ==> X }.
% 270.80/271.20 parent0[1]: (150184) {G1,W10,D3,L2,V2,M2} { ! addition( X, Y ) ==> X, X
% 270.80/271.20 ==> addition( Y, X ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (80) {G2,W10,D3,L2,V2,M2} R(11,63) { addition( X, Y ) ==> Y, !
% 270.80/271.20 addition( Y, X ) ==> Y }.
% 270.80/271.20 parent0: (150185) {G1,W10,D3,L2,V2,M2} { addition( Y, X ) ==> X, !
% 270.80/271.20 addition( X, Y ) ==> X }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := Y
% 270.80/271.20 Y := X
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 1 ==> 1
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (150187) {G1,W8,D3,L2,V2,M2} { ! X ==> addition( X, Y ), leq( Y, X
% 270.80/271.20 ) }.
% 270.80/271.20 parent0[0]: (63) {G1,W8,D3,L2,V2,M2} P(0,12) { ! addition( Y, X ) ==> Y,
% 270.80/271.20 leq( X, Y ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := Y
% 270.80/271.20 Y := X
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 paramod: (150188) {G1,W9,D2,L3,V2,M3} { ! X ==> Y, ! leq( X, Y ), leq( Y,
% 270.80/271.20 X ) }.
% 270.80/271.20 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 270.80/271.20 ==> Y }.
% 270.80/271.20 parent1[0; 3]: (150187) {G1,W8,D3,L2,V2,M2} { ! X ==> addition( X, Y ),
% 270.80/271.20 leq( Y, X ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 end
% 270.80/271.20 substitution1:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (150189) {G1,W9,D2,L3,V2,M3} { ! Y ==> X, ! leq( X, Y ), leq( Y, X
% 270.80/271.20 ) }.
% 270.80/271.20 parent0[0]: (150188) {G1,W9,D2,L3,V2,M3} { ! X ==> Y, ! leq( X, Y ), leq(
% 270.80/271.20 Y, X ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (82) {G2,W9,D2,L3,V2,M3} P(11,63) { ! Y = X, leq( Y, X ), !
% 270.80/271.20 leq( X, Y ) }.
% 270.80/271.20 parent0: (150189) {G1,W9,D2,L3,V2,M3} { ! Y ==> X, ! leq( X, Y ), leq( Y,
% 270.80/271.20 X ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 1 ==> 2
% 270.80/271.20 2 ==> 1
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (150190) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 270.80/271.20 ) }.
% 270.80/271.20 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 270.80/271.20 ==> Y }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 paramod: (150192) {G1,W16,D4,L2,V3,M2} { multiplication( X, Y ) ==>
% 270.80/271.20 multiplication( addition( Z, X ), Y ), ! leq( multiplication( Z, Y ),
% 270.80/271.20 multiplication( X, Y ) ) }.
% 270.80/271.20 parent0[0]: (8) {G0,W13,D4,L1,V3,M1} I { addition( multiplication( X, Z ),
% 270.80/271.20 multiplication( Y, Z ) ) ==> multiplication( addition( X, Y ), Z ) }.
% 270.80/271.20 parent1[0; 4]: (150190) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), !
% 270.80/271.20 leq( X, Y ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := Z
% 270.80/271.20 Y := X
% 270.80/271.20 Z := Y
% 270.80/271.20 end
% 270.80/271.20 substitution1:
% 270.80/271.20 X := multiplication( Z, Y )
% 270.80/271.20 Y := multiplication( X, Y )
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (150193) {G1,W16,D4,L2,V3,M2} { multiplication( addition( Z, X ),
% 270.80/271.20 Y ) ==> multiplication( X, Y ), ! leq( multiplication( Z, Y ),
% 270.80/271.20 multiplication( X, Y ) ) }.
% 270.80/271.20 parent0[0]: (150192) {G1,W16,D4,L2,V3,M2} { multiplication( X, Y ) ==>
% 270.80/271.20 multiplication( addition( Z, X ), Y ), ! leq( multiplication( Z, Y ),
% 270.80/271.20 multiplication( X, Y ) ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 Z := Z
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (83) {G1,W16,D4,L2,V3,M2} P(11,8) { multiplication( addition(
% 270.80/271.20 X, Z ), Y ) ==> multiplication( Z, Y ), ! leq( multiplication( X, Y ),
% 270.80/271.20 multiplication( Z, Y ) ) }.
% 270.80/271.20 parent0: (150193) {G1,W16,D4,L2,V3,M2} { multiplication( addition( Z, X )
% 270.80/271.20 , Y ) ==> multiplication( X, Y ), ! leq( multiplication( Z, Y ),
% 270.80/271.20 multiplication( X, Y ) ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := Z
% 270.80/271.20 Y := Y
% 270.80/271.20 Z := X
% 270.80/271.20 end
% 270.80/271.20 permutation0:
% 270.80/271.20 0 ==> 0
% 270.80/271.20 1 ==> 1
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 eqswap: (150194) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 270.80/271.20 ) }.
% 270.80/271.20 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 270.80/271.20 ==> Y }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 Y := Y
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 paramod: (150196) {G1,W6,D2,L2,V1,M2} { zero ==> X, ! leq( X, zero ) }.
% 270.80/271.20 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 270.80/271.20 parent1[0; 2]: (150194) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), !
% 270.80/271.20 leq( X, Y ) }.
% 270.80/271.20 substitution0:
% 270.80/271.20 X := X
% 270.80/271.20 end
% 270.80/271.20 substitution1:
% 270.80/271.20 X := X
% 270.80/271.20 Y := zero
% 270.80/271.20 end
% 270.80/271.20
% 270.80/271.20 subsumption: (87) {G1,W6,D2,L2,V1,M2} P(11,2) { zero = X, ! leq( X, zero )
% 270.80/271.20 }.
% 270.80/271.20 parent0: (150196) {G1,W6,D2,L2,V1,M2} { zero ==> X, ! leq( X, zero ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 1 ==> 1
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150198) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 270.80/271.21 ) }.
% 270.80/271.21 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 270.80/271.21 ==> Y }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150199) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq( Y,
% 270.80/271.21 X ) }.
% 270.80/271.21 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 270.80/271.21 }.
% 270.80/271.21 parent1[0; 2]: (150198) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), !
% 270.80/271.21 leq( X, Y ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := Y
% 270.80/271.21 Y := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := Y
% 270.80/271.21 Y := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150202) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> X, ! leq( Y, X
% 270.80/271.21 ) }.
% 270.80/271.21 parent0[0]: (150199) {G1,W8,D3,L2,V2,M2} { X ==> addition( X, Y ), ! leq(
% 270.80/271.21 Y, X ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (88) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, !
% 270.80/271.21 leq( X, Y ) }.
% 270.80/271.21 parent0: (150202) {G1,W8,D3,L2,V2,M2} { addition( X, Y ) ==> X, ! leq( Y,
% 270.80/271.21 X ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := Y
% 270.80/271.21 Y := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 1 ==> 1
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150206) {G1,W17,D7,L1,V2,M1} { addition( antidomain(
% 270.80/271.21 multiplication( X, Y ) ), antidomain( multiplication( X, antidomain(
% 270.80/271.21 antidomain( Y ) ) ) ) ) ==> antidomain( multiplication( X, domain( Y ) )
% 270.80/271.21 ) }.
% 270.80/271.21 parent0[0]: (16) {G0,W6,D4,L1,V1,M1} I { antidomain( antidomain( X ) ) ==>
% 270.80/271.21 domain( X ) }.
% 270.80/271.21 parent1[0; 15]: (14) {G0,W18,D7,L1,V2,M1} I { addition( antidomain(
% 270.80/271.21 multiplication( X, Y ) ), antidomain( multiplication( X, antidomain(
% 270.80/271.21 antidomain( Y ) ) ) ) ) ==> antidomain( multiplication( X, antidomain(
% 270.80/271.21 antidomain( Y ) ) ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := Y
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150207) {G1,W16,D6,L1,V2,M1} { addition( antidomain(
% 270.80/271.21 multiplication( X, Y ) ), antidomain( multiplication( X, domain( Y ) ) )
% 270.80/271.21 ) ==> antidomain( multiplication( X, domain( Y ) ) ) }.
% 270.80/271.21 parent0[0]: (16) {G0,W6,D4,L1,V1,M1} I { antidomain( antidomain( X ) ) ==>
% 270.80/271.21 domain( X ) }.
% 270.80/271.21 parent1[0; 9]: (150206) {G1,W17,D7,L1,V2,M1} { addition( antidomain(
% 270.80/271.21 multiplication( X, Y ) ), antidomain( multiplication( X, antidomain(
% 270.80/271.21 antidomain( Y ) ) ) ) ) ==> antidomain( multiplication( X, domain( Y ) )
% 270.80/271.21 ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := Y
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (127) {G1,W16,D6,L1,V2,M1} S(14);d(16) { addition( antidomain
% 270.80/271.21 ( multiplication( X, Y ) ), antidomain( multiplication( X, domain( Y ) )
% 270.80/271.21 ) ) ==> antidomain( multiplication( X, domain( Y ) ) ) }.
% 270.80/271.21 parent0: (150207) {G1,W16,D6,L1,V2,M1} { addition( antidomain(
% 270.80/271.21 multiplication( X, Y ) ), antidomain( multiplication( X, domain( Y ) ) )
% 270.80/271.21 ) ==> antidomain( multiplication( X, domain( Y ) ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150213) {G1,W7,D4,L1,V1,M1} { addition( domain( X ), antidomain
% 270.80/271.21 ( X ) ) ==> one }.
% 270.80/271.21 parent0[0]: (16) {G0,W6,D4,L1,V1,M1} I { antidomain( antidomain( X ) ) ==>
% 270.80/271.21 domain( X ) }.
% 270.80/271.21 parent1[0; 2]: (15) {G0,W8,D5,L1,V1,M1} I { addition( antidomain(
% 270.80/271.21 antidomain( X ) ), antidomain( X ) ) ==> one }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (156) {G1,W7,D4,L1,V1,M1} S(15);d(16) { addition( domain( X )
% 270.80/271.21 , antidomain( X ) ) ==> one }.
% 270.80/271.21 parent0: (150213) {G1,W7,D4,L1,V1,M1} { addition( domain( X ), antidomain
% 270.80/271.21 ( X ) ) ==> one }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150216) {G1,W7,D4,L1,V1,M1} { one ==> addition( domain( X ),
% 270.80/271.21 antidomain( X ) ) }.
% 270.80/271.21 parent0[0]: (156) {G1,W7,D4,L1,V1,M1} S(15);d(16) { addition( domain( X ),
% 270.80/271.21 antidomain( X ) ) ==> one }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150219) {G2,W7,D4,L1,V0,M1} { one ==> addition( antidomain( zero
% 270.80/271.21 ), antidomain( one ) ) }.
% 270.80/271.21 parent0[0]: (38) {G2,W5,D3,L1,V0,M1} P(34,16) { domain( one ) ==>
% 270.80/271.21 antidomain( zero ) }.
% 270.80/271.21 parent1[0; 3]: (150216) {G1,W7,D4,L1,V1,M1} { one ==> addition( domain( X
% 270.80/271.21 ), antidomain( X ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := one
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150220) {G2,W6,D4,L1,V0,M1} { one ==> addition( antidomain( zero
% 270.80/271.21 ), zero ) }.
% 270.80/271.21 parent0[0]: (34) {G1,W4,D3,L1,V0,M1} P(13,5) { antidomain( one ) ==> zero
% 270.80/271.21 }.
% 270.80/271.21 parent1[0; 5]: (150219) {G2,W7,D4,L1,V0,M1} { one ==> addition( antidomain
% 270.80/271.21 ( zero ), antidomain( one ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150221) {G1,W4,D3,L1,V0,M1} { one ==> antidomain( zero ) }.
% 270.80/271.21 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 270.80/271.21 parent1[0; 2]: (150220) {G2,W6,D4,L1,V0,M1} { one ==> addition( antidomain
% 270.80/271.21 ( zero ), zero ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := antidomain( zero )
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150222) {G1,W4,D3,L1,V0,M1} { antidomain( zero ) ==> one }.
% 270.80/271.21 parent0[0]: (150221) {G1,W4,D3,L1,V0,M1} { one ==> antidomain( zero ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (167) {G3,W4,D3,L1,V0,M1} P(38,156);d(34);d(2) { antidomain(
% 270.80/271.21 zero ) ==> one }.
% 270.80/271.21 parent0: (150222) {G1,W4,D3,L1,V0,M1} { antidomain( zero ) ==> one }.
% 270.80/271.21 substitution0:
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150226) {G1,W17,D7,L1,V2,M1} { addition( coantidomain(
% 270.80/271.21 multiplication( X, Y ) ), coantidomain( multiplication( coantidomain(
% 270.80/271.21 coantidomain( X ) ), Y ) ) ) ==> coantidomain( multiplication( codomain(
% 270.80/271.21 X ), Y ) ) }.
% 270.80/271.21 parent0[0]: (20) {G0,W6,D4,L1,V1,M1} I { coantidomain( coantidomain( X ) )
% 270.80/271.21 ==> codomain( X ) }.
% 270.80/271.21 parent1[0; 14]: (18) {G0,W18,D7,L1,V2,M1} I { addition( coantidomain(
% 270.80/271.21 multiplication( X, Y ) ), coantidomain( multiplication( coantidomain(
% 270.80/271.21 coantidomain( X ) ), Y ) ) ) ==> coantidomain( multiplication(
% 270.80/271.21 coantidomain( coantidomain( X ) ), Y ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150227) {G1,W16,D6,L1,V2,M1} { addition( coantidomain(
% 270.80/271.21 multiplication( X, Y ) ), coantidomain( multiplication( codomain( X ), Y
% 270.80/271.21 ) ) ) ==> coantidomain( multiplication( codomain( X ), Y ) ) }.
% 270.80/271.21 parent0[0]: (20) {G0,W6,D4,L1,V1,M1} I { coantidomain( coantidomain( X ) )
% 270.80/271.21 ==> codomain( X ) }.
% 270.80/271.21 parent1[0; 8]: (150226) {G1,W17,D7,L1,V2,M1} { addition( coantidomain(
% 270.80/271.21 multiplication( X, Y ) ), coantidomain( multiplication( coantidomain(
% 270.80/271.21 coantidomain( X ) ), Y ) ) ) ==> coantidomain( multiplication( codomain(
% 270.80/271.21 X ), Y ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (170) {G1,W16,D6,L1,V2,M1} S(18);d(20) { addition(
% 270.80/271.21 coantidomain( multiplication( X, Y ) ), coantidomain( multiplication(
% 270.80/271.21 codomain( X ), Y ) ) ) ==> coantidomain( multiplication( codomain( X ), Y
% 270.80/271.21 ) ) }.
% 270.80/271.21 parent0: (150227) {G1,W16,D6,L1,V2,M1} { addition( coantidomain(
% 270.80/271.21 multiplication( X, Y ) ), coantidomain( multiplication( codomain( X ), Y
% 270.80/271.21 ) ) ) ==> coantidomain( multiplication( codomain( X ), Y ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150233) {G1,W7,D4,L1,V1,M1} { addition( codomain( X ),
% 270.80/271.21 coantidomain( X ) ) ==> one }.
% 270.80/271.21 parent0[0]: (20) {G0,W6,D4,L1,V1,M1} I { coantidomain( coantidomain( X ) )
% 270.80/271.21 ==> codomain( X ) }.
% 270.80/271.21 parent1[0; 2]: (19) {G0,W8,D5,L1,V1,M1} I { addition( coantidomain(
% 270.80/271.21 coantidomain( X ) ), coantidomain( X ) ) ==> one }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (178) {G1,W7,D4,L1,V1,M1} S(19);d(20) { addition( codomain( X
% 270.80/271.21 ), coantidomain( X ) ) ==> one }.
% 270.80/271.21 parent0: (150233) {G1,W7,D4,L1,V1,M1} { addition( codomain( X ),
% 270.80/271.21 coantidomain( X ) ) ==> one }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150235) {G0,W8,D4,L1,V0,M1} { ! antidomain( skol2 ) ==> addition
% 270.80/271.21 ( domain( skol1 ), antidomain( skol2 ) ) }.
% 270.80/271.21 parent0[0]: (22) {G0,W8,D4,L1,V0,M1} I { ! addition( domain( skol1 ),
% 270.80/271.21 antidomain( skol2 ) ) ==> antidomain( skol2 ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150236) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 270.80/271.21 ) }.
% 270.80/271.21 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 270.80/271.21 ==> Y }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 resolution: (150237) {G1,W5,D3,L1,V0,M1} { ! leq( domain( skol1 ),
% 270.80/271.21 antidomain( skol2 ) ) }.
% 270.80/271.21 parent0[0]: (150235) {G0,W8,D4,L1,V0,M1} { ! antidomain( skol2 ) ==>
% 270.80/271.21 addition( domain( skol1 ), antidomain( skol2 ) ) }.
% 270.80/271.21 parent1[0]: (150236) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq(
% 270.80/271.21 X, Y ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := domain( skol1 )
% 270.80/271.21 Y := antidomain( skol2 )
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (187) {G1,W5,D3,L1,V0,M1} R(22,11) { ! leq( domain( skol1 ),
% 270.80/271.21 antidomain( skol2 ) ) }.
% 270.80/271.21 parent0: (150237) {G1,W5,D3,L1,V0,M1} { ! leq( domain( skol1 ), antidomain
% 270.80/271.21 ( skol2 ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150239) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X ) =
% 270.80/271.21 addition( addition( X, Y ), Z ) }.
% 270.80/271.21 parent0[0]: (27) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y ),
% 270.80/271.21 Z ) = addition( addition( Y, Z ), X ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 Z := Z
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150241) {G2,W11,D5,L1,V2,M1} { addition( addition( antidomain( X
% 270.80/271.21 ), Y ), domain( X ) ) = addition( one, Y ) }.
% 270.80/271.21 parent0[0]: (156) {G1,W7,D4,L1,V1,M1} S(15);d(16) { addition( domain( X ),
% 270.80/271.21 antidomain( X ) ) ==> one }.
% 270.80/271.21 parent1[0; 9]: (150239) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z )
% 270.80/271.21 , X ) = addition( addition( X, Y ), Z ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := domain( X )
% 270.80/271.21 Y := antidomain( X )
% 270.80/271.21 Z := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (211) {G2,W11,D5,L1,V2,M1} P(156,27) { addition( addition(
% 270.80/271.21 antidomain( X ), Y ), domain( X ) ) ==> addition( one, Y ) }.
% 270.80/271.21 parent0: (150241) {G2,W11,D5,L1,V2,M1} { addition( addition( antidomain( X
% 270.80/271.21 ), Y ), domain( X ) ) = addition( one, Y ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150244) {G1,W9,D4,L1,V2,M1} { addition( X, Y ) ==> addition(
% 270.80/271.21 addition( X, Y ), Y ) }.
% 270.80/271.21 parent0[0]: (30) {G1,W9,D4,L1,V2,M1} P(3,1) { addition( addition( Y, X ), X
% 270.80/271.21 ) ==> addition( Y, X ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := Y
% 270.80/271.21 Y := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150245) {G1,W8,D3,L2,V2,M2} { ! X ==> addition( X, Y ), leq( Y, X
% 270.80/271.21 ) }.
% 270.80/271.21 parent0[0]: (63) {G1,W8,D3,L2,V2,M2} P(0,12) { ! addition( Y, X ) ==> Y,
% 270.80/271.21 leq( X, Y ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := Y
% 270.80/271.21 Y := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 resolution: (150246) {G2,W5,D3,L1,V2,M1} { leq( Y, addition( X, Y ) ) }.
% 270.80/271.21 parent0[0]: (150245) {G1,W8,D3,L2,V2,M2} { ! X ==> addition( X, Y ), leq(
% 270.80/271.21 Y, X ) }.
% 270.80/271.21 parent1[0]: (150244) {G1,W9,D4,L1,V2,M1} { addition( X, Y ) ==> addition(
% 270.80/271.21 addition( X, Y ), Y ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := addition( X, Y )
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (265) {G2,W5,D3,L1,V2,M1} R(30,63) { leq( X, addition( Y, X )
% 270.80/271.21 ) }.
% 270.80/271.21 parent0: (150246) {G2,W5,D3,L1,V2,M1} { leq( Y, addition( X, Y ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := Y
% 270.80/271.21 Y := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150248) {G1,W9,D4,L1,V2,M1} { addition( X, Y ) ==> addition(
% 270.80/271.21 addition( X, Y ), Y ) }.
% 270.80/271.21 parent0[0]: (30) {G1,W9,D4,L1,V2,M1} P(3,1) { addition( addition( Y, X ), X
% 270.80/271.21 ) ==> addition( Y, X ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := Y
% 270.80/271.21 Y := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150250) {G2,W10,D4,L1,V1,M1} { addition( domain( X ), antidomain
% 270.80/271.21 ( X ) ) ==> addition( one, antidomain( X ) ) }.
% 270.80/271.21 parent0[0]: (156) {G1,W7,D4,L1,V1,M1} S(15);d(16) { addition( domain( X ),
% 270.80/271.21 antidomain( X ) ) ==> one }.
% 270.80/271.21 parent1[0; 7]: (150248) {G1,W9,D4,L1,V2,M1} { addition( X, Y ) ==>
% 270.80/271.21 addition( addition( X, Y ), Y ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := domain( X )
% 270.80/271.21 Y := antidomain( X )
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150251) {G2,W6,D4,L1,V1,M1} { one ==> addition( one, antidomain
% 270.80/271.21 ( X ) ) }.
% 270.80/271.21 parent0[0]: (156) {G1,W7,D4,L1,V1,M1} S(15);d(16) { addition( domain( X ),
% 270.80/271.21 antidomain( X ) ) ==> one }.
% 270.80/271.21 parent1[0; 1]: (150250) {G2,W10,D4,L1,V1,M1} { addition( domain( X ),
% 270.80/271.21 antidomain( X ) ) ==> addition( one, antidomain( X ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150253) {G2,W6,D4,L1,V1,M1} { addition( one, antidomain( X ) )
% 270.80/271.21 ==> one }.
% 270.80/271.21 parent0[0]: (150251) {G2,W6,D4,L1,V1,M1} { one ==> addition( one,
% 270.80/271.21 antidomain( X ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (268) {G2,W6,D4,L1,V1,M1} P(156,30) { addition( one,
% 270.80/271.21 antidomain( X ) ) ==> one }.
% 270.80/271.21 parent0: (150253) {G2,W6,D4,L1,V1,M1} { addition( one, antidomain( X ) )
% 270.80/271.21 ==> one }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150255) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X ) =
% 270.80/271.21 addition( addition( X, Y ), Z ) }.
% 270.80/271.21 parent0[0]: (27) {G1,W11,D4,L1,V3,M1} P(1,0) { addition( addition( X, Y ),
% 270.80/271.21 Z ) = addition( addition( Y, Z ), X ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 Z := Z
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150256) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( X, Y )
% 270.80/271.21 , Z ) ) }.
% 270.80/271.21 parent0[0]: (150255) {G1,W11,D4,L1,V3,M1} { addition( addition( Y, Z ), X
% 270.80/271.21 ) = addition( addition( X, Y ), Z ) }.
% 270.80/271.21 parent1[0; 2]: (265) {G2,W5,D3,L1,V2,M1} R(30,63) { leq( X, addition( Y, X
% 270.80/271.21 ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 Z := Z
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 Y := addition( Y, Z )
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (279) {G3,W7,D4,L1,V3,M1} P(27,265) { leq( Z, addition(
% 270.80/271.21 addition( Z, X ), Y ) ) }.
% 270.80/271.21 parent0: (150256) {G2,W7,D4,L1,V3,M1} { leq( X, addition( addition( X, Y )
% 270.80/271.21 , Z ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := Z
% 270.80/271.21 Y := X
% 270.80/271.21 Z := Y
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150260) {G2,W4,D3,L1,V1,M1} { leq( antidomain( X ), one ) }.
% 270.80/271.21 parent0[0]: (156) {G1,W7,D4,L1,V1,M1} S(15);d(16) { addition( domain( X ),
% 270.80/271.21 antidomain( X ) ) ==> one }.
% 270.80/271.21 parent1[0; 3]: (265) {G2,W5,D3,L1,V2,M1} R(30,63) { leq( X, addition( Y, X
% 270.80/271.21 ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := antidomain( X )
% 270.80/271.21 Y := domain( X )
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (280) {G3,W4,D3,L1,V1,M1} P(156,265) { leq( antidomain( X ),
% 270.80/271.21 one ) }.
% 270.80/271.21 parent0: (150260) {G2,W4,D3,L1,V1,M1} { leq( antidomain( X ), one ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150261) {G1,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 270.80/271.21 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 270.80/271.21 }.
% 270.80/271.21 parent1[0; 2]: (265) {G2,W5,D3,L1,V2,M1} R(30,63) { leq( X, addition( Y, X
% 270.80/271.21 ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := Y
% 270.80/271.21 Y := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (286) {G3,W5,D3,L1,V2,M1} P(0,265) { leq( Y, addition( Y, X )
% 270.80/271.21 ) }.
% 270.80/271.21 parent0: (150261) {G1,W5,D3,L1,V2,M1} { leq( X, addition( X, Y ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := Y
% 270.80/271.21 Y := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150263) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 270.80/271.21 ) }.
% 270.80/271.21 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 270.80/271.21 ==> Y }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 resolution: (150264) {G1,W6,D4,L1,V1,M1} { one ==> addition( antidomain( X
% 270.80/271.21 ), one ) }.
% 270.80/271.21 parent0[1]: (150263) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq(
% 270.80/271.21 X, Y ) }.
% 270.80/271.21 parent1[0]: (280) {G3,W4,D3,L1,V1,M1} P(156,265) { leq( antidomain( X ),
% 270.80/271.21 one ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := antidomain( X )
% 270.80/271.21 Y := one
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150265) {G1,W6,D4,L1,V1,M1} { addition( antidomain( X ), one )
% 270.80/271.21 ==> one }.
% 270.80/271.21 parent0[0]: (150264) {G1,W6,D4,L1,V1,M1} { one ==> addition( antidomain( X
% 270.80/271.21 ), one ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (287) {G4,W6,D4,L1,V1,M1} R(280,11) { addition( antidomain( X
% 270.80/271.21 ), one ) ==> one }.
% 270.80/271.21 parent0: (150265) {G1,W6,D4,L1,V1,M1} { addition( antidomain( X ), one )
% 270.80/271.21 ==> one }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150267) {G1,W4,D3,L1,V1,M1} { leq( domain( X ), one ) }.
% 270.80/271.21 parent0[0]: (16) {G0,W6,D4,L1,V1,M1} I { antidomain( antidomain( X ) ) ==>
% 270.80/271.21 domain( X ) }.
% 270.80/271.21 parent1[0; 1]: (280) {G3,W4,D3,L1,V1,M1} P(156,265) { leq( antidomain( X )
% 270.80/271.21 , one ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := antidomain( X )
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (288) {G4,W4,D3,L1,V1,M1} P(16,280) { leq( domain( X ), one )
% 270.80/271.21 }.
% 270.80/271.21 parent0: (150267) {G1,W4,D3,L1,V1,M1} { leq( domain( X ), one ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150268) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 270.80/271.21 ) }.
% 270.80/271.21 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 270.80/271.21 ==> Y }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 resolution: (150269) {G1,W6,D4,L1,V1,M1} { one ==> addition( domain( X ),
% 270.80/271.21 one ) }.
% 270.80/271.21 parent0[1]: (150268) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq(
% 270.80/271.21 X, Y ) }.
% 270.80/271.21 parent1[0]: (288) {G4,W4,D3,L1,V1,M1} P(16,280) { leq( domain( X ), one )
% 270.80/271.21 }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := domain( X )
% 270.80/271.21 Y := one
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150270) {G1,W6,D4,L1,V1,M1} { addition( domain( X ), one ) ==>
% 270.80/271.21 one }.
% 270.80/271.21 parent0[0]: (150269) {G1,W6,D4,L1,V1,M1} { one ==> addition( domain( X ),
% 270.80/271.21 one ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (289) {G5,W6,D4,L1,V1,M1} R(288,11) { addition( domain( X ),
% 270.80/271.21 one ) ==> one }.
% 270.80/271.21 parent0: (150270) {G1,W6,D4,L1,V1,M1} { addition( domain( X ), one ) ==>
% 270.80/271.21 one }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150272) {G1,W8,D3,L2,V3,M2} { leq( X, Z ), ! leq( addition( X, Y
% 270.80/271.21 ), Z ) }.
% 270.80/271.21 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 270.80/271.21 ==> Y }.
% 270.80/271.21 parent1[0; 2]: (279) {G3,W7,D4,L1,V3,M1} P(27,265) { leq( Z, addition(
% 270.80/271.21 addition( Z, X ), Y ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := addition( X, Y )
% 270.80/271.21 Y := Z
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := Y
% 270.80/271.21 Y := Z
% 270.80/271.21 Z := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (462) {G4,W8,D3,L2,V3,M2} P(11,279) { leq( X, Z ), ! leq(
% 270.80/271.21 addition( X, Y ), Z ) }.
% 270.80/271.21 parent0: (150272) {G1,W8,D3,L2,V3,M2} { leq( X, Z ), ! leq( addition( X, Y
% 270.80/271.21 ), Z ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 Z := Z
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 1 ==> 1
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150278) {G1,W8,D3,L2,V3,M2} { leq( X, addition( Y, Z ) ), ! leq
% 270.80/271.21 ( X, Y ) }.
% 270.80/271.21 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 270.80/271.21 ==> Y }.
% 270.80/271.21 parent1[0; 3]: (279) {G3,W7,D4,L1,V3,M1} P(27,265) { leq( Z, addition(
% 270.80/271.21 addition( Z, X ), Y ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := Y
% 270.80/271.21 Y := Z
% 270.80/271.21 Z := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (463) {G4,W8,D3,L2,V3,M2} P(11,279) { leq( X, addition( Y, Z )
% 270.80/271.21 ), ! leq( X, Y ) }.
% 270.80/271.21 parent0: (150278) {G1,W8,D3,L2,V3,M2} { leq( X, addition( Y, Z ) ), ! leq
% 270.80/271.21 ( X, Y ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 Z := Z
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 1 ==> 1
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150282) {G2,W11,D4,L1,V2,M1} { multiplication( antidomain( X ), Y
% 270.80/271.21 ) ==> multiplication( antidomain( X ), addition( X, Y ) ) }.
% 270.80/271.21 parent0[0]: (47) {G2,W11,D4,L1,V2,M1} P(13,7);d(23) { multiplication(
% 270.80/271.21 antidomain( X ), addition( X, Y ) ) ==> multiplication( antidomain( X ),
% 270.80/271.21 Y ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150284) {G2,W12,D5,L1,V1,M1} { multiplication( antidomain(
% 270.80/271.21 domain( X ) ), antidomain( X ) ) ==> multiplication( antidomain( domain(
% 270.80/271.21 X ) ), one ) }.
% 270.80/271.21 parent0[0]: (156) {G1,W7,D4,L1,V1,M1} S(15);d(16) { addition( domain( X ),
% 270.80/271.21 antidomain( X ) ) ==> one }.
% 270.80/271.21 parent1[0; 11]: (150282) {G2,W11,D4,L1,V2,M1} { multiplication( antidomain
% 270.80/271.21 ( X ), Y ) ==> multiplication( antidomain( X ), addition( X, Y ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := domain( X )
% 270.80/271.21 Y := antidomain( X )
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150285) {G1,W10,D5,L1,V1,M1} { multiplication( antidomain(
% 270.80/271.21 domain( X ) ), antidomain( X ) ) ==> antidomain( domain( X ) ) }.
% 270.80/271.21 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 270.80/271.21 parent1[0; 7]: (150284) {G2,W12,D5,L1,V1,M1} { multiplication( antidomain
% 270.80/271.21 ( domain( X ) ), antidomain( X ) ) ==> multiplication( antidomain( domain
% 270.80/271.21 ( X ) ), one ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := antidomain( domain( X ) )
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (472) {G3,W10,D5,L1,V1,M1} P(156,47);d(5) { multiplication(
% 270.80/271.21 antidomain( domain( X ) ), antidomain( X ) ) ==> antidomain( domain( X )
% 270.80/271.21 ) }.
% 270.80/271.21 parent0: (150285) {G1,W10,D5,L1,V1,M1} { multiplication( antidomain(
% 270.80/271.21 domain( X ) ), antidomain( X ) ) ==> antidomain( domain( X ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150288) {G2,W4,D3,L1,V1,M1} { leq( codomain( X ), one ) }.
% 270.80/271.21 parent0[0]: (178) {G1,W7,D4,L1,V1,M1} S(19);d(20) { addition( codomain( X )
% 270.80/271.21 , coantidomain( X ) ) ==> one }.
% 270.80/271.21 parent1[0; 3]: (286) {G3,W5,D3,L1,V2,M1} P(0,265) { leq( Y, addition( Y, X
% 270.80/271.21 ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := coantidomain( X )
% 270.80/271.21 Y := codomain( X )
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (519) {G4,W4,D3,L1,V1,M1} P(178,286) { leq( codomain( X ), one
% 270.80/271.21 ) }.
% 270.80/271.21 parent0: (150288) {G2,W4,D3,L1,V1,M1} { leq( codomain( X ), one ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150290) {G2,W4,D3,L1,V1,M1} { leq( coantidomain( X ), one ) }.
% 270.80/271.21 parent0[0]: (178) {G1,W7,D4,L1,V1,M1} S(19);d(20) { addition( codomain( X )
% 270.80/271.21 , coantidomain( X ) ) ==> one }.
% 270.80/271.21 parent1[0; 3]: (265) {G2,W5,D3,L1,V2,M1} R(30,63) { leq( X, addition( Y, X
% 270.80/271.21 ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := coantidomain( X )
% 270.80/271.21 Y := codomain( X )
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (520) {G3,W4,D3,L1,V1,M1} P(178,265) { leq( coantidomain( X )
% 270.80/271.21 , one ) }.
% 270.80/271.21 parent0: (150290) {G2,W4,D3,L1,V1,M1} { leq( coantidomain( X ), one ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150292) {G1,W9,D4,L1,V2,M1} { addition( X, Y ) ==> addition(
% 270.80/271.21 addition( X, Y ), Y ) }.
% 270.80/271.21 parent0[0]: (30) {G1,W9,D4,L1,V2,M1} P(3,1) { addition( addition( Y, X ), X
% 270.80/271.21 ) ==> addition( Y, X ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := Y
% 270.80/271.21 Y := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150294) {G2,W10,D4,L1,V1,M1} { addition( codomain( X ),
% 270.80/271.21 coantidomain( X ) ) ==> addition( one, coantidomain( X ) ) }.
% 270.80/271.21 parent0[0]: (178) {G1,W7,D4,L1,V1,M1} S(19);d(20) { addition( codomain( X )
% 270.80/271.21 , coantidomain( X ) ) ==> one }.
% 270.80/271.21 parent1[0; 7]: (150292) {G1,W9,D4,L1,V2,M1} { addition( X, Y ) ==>
% 270.80/271.21 addition( addition( X, Y ), Y ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := codomain( X )
% 270.80/271.21 Y := coantidomain( X )
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150295) {G2,W6,D4,L1,V1,M1} { one ==> addition( one,
% 270.80/271.21 coantidomain( X ) ) }.
% 270.80/271.21 parent0[0]: (178) {G1,W7,D4,L1,V1,M1} S(19);d(20) { addition( codomain( X )
% 270.80/271.21 , coantidomain( X ) ) ==> one }.
% 270.80/271.21 parent1[0; 1]: (150294) {G2,W10,D4,L1,V1,M1} { addition( codomain( X ),
% 270.80/271.21 coantidomain( X ) ) ==> addition( one, coantidomain( X ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150297) {G2,W6,D4,L1,V1,M1} { addition( one, coantidomain( X ) )
% 270.80/271.21 ==> one }.
% 270.80/271.21 parent0[0]: (150295) {G2,W6,D4,L1,V1,M1} { one ==> addition( one,
% 270.80/271.21 coantidomain( X ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (521) {G2,W6,D4,L1,V1,M1} P(178,30) { addition( one,
% 270.80/271.21 coantidomain( X ) ) ==> one }.
% 270.80/271.21 parent0: (150297) {G2,W6,D4,L1,V1,M1} { addition( one, coantidomain( X ) )
% 270.80/271.21 ==> one }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150300) {G1,W7,D4,L1,V1,M1} { one ==> addition( codomain( X ),
% 270.80/271.21 coantidomain( X ) ) }.
% 270.80/271.21 parent0[0]: (178) {G1,W7,D4,L1,V1,M1} S(19);d(20) { addition( codomain( X )
% 270.80/271.21 , coantidomain( X ) ) ==> one }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150303) {G2,W7,D4,L1,V0,M1} { one ==> addition( coantidomain(
% 270.80/271.21 zero ), coantidomain( one ) ) }.
% 270.80/271.21 parent0[0]: (31) {G2,W5,D3,L1,V0,M1} P(26,20) { codomain( one ) ==>
% 270.80/271.21 coantidomain( zero ) }.
% 270.80/271.21 parent1[0; 3]: (150300) {G1,W7,D4,L1,V1,M1} { one ==> addition( codomain(
% 270.80/271.21 X ), coantidomain( X ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := one
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150304) {G2,W6,D4,L1,V0,M1} { one ==> addition( coantidomain(
% 270.80/271.21 zero ), zero ) }.
% 270.80/271.21 parent0[0]: (26) {G1,W4,D3,L1,V0,M1} P(17,6) { coantidomain( one ) ==> zero
% 270.80/271.21 }.
% 270.80/271.21 parent1[0; 5]: (150303) {G2,W7,D4,L1,V0,M1} { one ==> addition(
% 270.80/271.21 coantidomain( zero ), coantidomain( one ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150305) {G1,W4,D3,L1,V0,M1} { one ==> coantidomain( zero ) }.
% 270.80/271.21 parent0[0]: (2) {G0,W5,D3,L1,V1,M1} I { addition( X, zero ) ==> X }.
% 270.80/271.21 parent1[0; 2]: (150304) {G2,W6,D4,L1,V0,M1} { one ==> addition(
% 270.80/271.21 coantidomain( zero ), zero ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := coantidomain( zero )
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150306) {G1,W4,D3,L1,V0,M1} { coantidomain( zero ) ==> one }.
% 270.80/271.21 parent0[0]: (150305) {G1,W4,D3,L1,V0,M1} { one ==> coantidomain( zero )
% 270.80/271.21 }.
% 270.80/271.21 substitution0:
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (533) {G3,W4,D3,L1,V0,M1} P(31,178);d(26);d(2) { coantidomain
% 270.80/271.21 ( zero ) ==> one }.
% 270.80/271.21 parent0: (150306) {G1,W4,D3,L1,V0,M1} { coantidomain( zero ) ==> one }.
% 270.80/271.21 substitution0:
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150307) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 270.80/271.21 ) }.
% 270.80/271.21 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 270.80/271.21 ==> Y }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 resolution: (150308) {G1,W6,D4,L1,V1,M1} { one ==> addition( codomain( X )
% 270.80/271.21 , one ) }.
% 270.80/271.21 parent0[1]: (150307) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq(
% 270.80/271.21 X, Y ) }.
% 270.80/271.21 parent1[0]: (519) {G4,W4,D3,L1,V1,M1} P(178,286) { leq( codomain( X ), one
% 270.80/271.21 ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := codomain( X )
% 270.80/271.21 Y := one
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150309) {G1,W6,D4,L1,V1,M1} { addition( codomain( X ), one ) ==>
% 270.80/271.21 one }.
% 270.80/271.21 parent0[0]: (150308) {G1,W6,D4,L1,V1,M1} { one ==> addition( codomain( X )
% 270.80/271.21 , one ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (540) {G5,W6,D4,L1,V1,M1} R(519,11) { addition( codomain( X )
% 270.80/271.21 , one ) ==> one }.
% 270.80/271.21 parent0: (150309) {G1,W6,D4,L1,V1,M1} { addition( codomain( X ), one ) ==>
% 270.80/271.21 one }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150310) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 270.80/271.21 ) }.
% 270.80/271.21 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 270.80/271.21 ==> Y }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 resolution: (150311) {G1,W6,D4,L1,V1,M1} { one ==> addition( coantidomain
% 270.80/271.21 ( X ), one ) }.
% 270.80/271.21 parent0[1]: (150310) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq(
% 270.80/271.21 X, Y ) }.
% 270.80/271.21 parent1[0]: (520) {G3,W4,D3,L1,V1,M1} P(178,265) { leq( coantidomain( X ),
% 270.80/271.21 one ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := coantidomain( X )
% 270.80/271.21 Y := one
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150312) {G1,W6,D4,L1,V1,M1} { addition( coantidomain( X ), one )
% 270.80/271.21 ==> one }.
% 270.80/271.21 parent0[0]: (150311) {G1,W6,D4,L1,V1,M1} { one ==> addition( coantidomain
% 270.80/271.21 ( X ), one ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (541) {G4,W6,D4,L1,V1,M1} R(520,11) { addition( coantidomain(
% 270.80/271.21 X ), one ) ==> one }.
% 270.80/271.21 parent0: (150312) {G1,W6,D4,L1,V1,M1} { addition( coantidomain( X ), one )
% 270.80/271.21 ==> one }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150314) {G1,W10,D5,L1,V2,M1} { multiplication( X, Y ) ==>
% 270.80/271.21 multiplication( X, addition( Y, coantidomain( X ) ) ) }.
% 270.80/271.21 parent0[0]: (51) {G1,W10,D5,L1,V2,M1} P(17,7);d(2) { multiplication( X,
% 270.80/271.21 addition( Y, coantidomain( X ) ) ) ==> multiplication( X, Y ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150316) {G2,W8,D4,L1,V1,M1} { multiplication( X, codomain( X ) )
% 270.80/271.21 ==> multiplication( X, one ) }.
% 270.80/271.21 parent0[0]: (178) {G1,W7,D4,L1,V1,M1} S(19);d(20) { addition( codomain( X )
% 270.80/271.21 , coantidomain( X ) ) ==> one }.
% 270.80/271.21 parent1[0; 7]: (150314) {G1,W10,D5,L1,V2,M1} { multiplication( X, Y ) ==>
% 270.80/271.21 multiplication( X, addition( Y, coantidomain( X ) ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 Y := codomain( X )
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150317) {G1,W6,D4,L1,V1,M1} { multiplication( X, codomain( X ) )
% 270.80/271.21 ==> X }.
% 270.80/271.21 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 270.80/271.21 parent1[0; 5]: (150316) {G2,W8,D4,L1,V1,M1} { multiplication( X, codomain
% 270.80/271.21 ( X ) ) ==> multiplication( X, one ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (548) {G2,W6,D4,L1,V1,M1} P(178,51);d(5) { multiplication( X,
% 270.80/271.21 codomain( X ) ) ==> X }.
% 270.80/271.21 parent0: (150317) {G1,W6,D4,L1,V1,M1} { multiplication( X, codomain( X ) )
% 270.80/271.21 ==> X }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150319) {G1,W6,D2,L2,V1,M2} { X = zero, ! leq( X, zero ) }.
% 270.80/271.21 parent0[0]: (87) {G1,W6,D2,L2,V1,M2} P(11,2) { zero = X, ! leq( X, zero )
% 270.80/271.21 }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150320) {G2,W6,D4,L1,V1,M1} { X ==> multiplication( X, codomain(
% 270.80/271.21 X ) ) }.
% 270.80/271.21 parent0[0]: (548) {G2,W6,D4,L1,V1,M1} P(178,51);d(5) { multiplication( X,
% 270.80/271.21 codomain( X ) ) ==> X }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150323) {G2,W9,D3,L2,V1,M2} { X ==> multiplication( X, zero ), !
% 270.80/271.21 leq( codomain( X ), zero ) }.
% 270.80/271.21 parent0[0]: (150319) {G1,W6,D2,L2,V1,M2} { X = zero, ! leq( X, zero ) }.
% 270.80/271.21 parent1[0; 4]: (150320) {G2,W6,D4,L1,V1,M1} { X ==> multiplication( X,
% 270.80/271.21 codomain( X ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := codomain( X )
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150344) {G1,W7,D3,L2,V1,M2} { X ==> zero, ! leq( codomain( X ),
% 270.80/271.21 zero ) }.
% 270.80/271.21 parent0[0]: (9) {G0,W5,D3,L1,V1,M1} I { multiplication( X, zero ) ==> zero
% 270.80/271.21 }.
% 270.80/271.21 parent1[0; 2]: (150323) {G2,W9,D3,L2,V1,M2} { X ==> multiplication( X,
% 270.80/271.21 zero ), ! leq( codomain( X ), zero ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150345) {G1,W7,D3,L2,V1,M2} { zero ==> X, ! leq( codomain( X ),
% 270.80/271.21 zero ) }.
% 270.80/271.21 parent0[0]: (150344) {G1,W7,D3,L2,V1,M2} { X ==> zero, ! leq( codomain( X
% 270.80/271.21 ), zero ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (578) {G3,W7,D3,L2,V1,M2} P(87,548);d(9) { ! leq( codomain( X
% 270.80/271.21 ), zero ), zero = X }.
% 270.80/271.21 parent0: (150345) {G1,W7,D3,L2,V1,M2} { zero ==> X, ! leq( codomain( X ),
% 270.80/271.21 zero ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 1
% 270.80/271.21 1 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150347) {G2,W6,D4,L1,V1,M1} { X ==> multiplication( X, codomain(
% 270.80/271.21 X ) ) }.
% 270.80/271.21 parent0[0]: (548) {G2,W6,D4,L1,V1,M1} P(178,51);d(5) { multiplication( X,
% 270.80/271.21 codomain( X ) ) ==> X }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150348) {G2,W9,D5,L1,V1,M1} { coantidomain( X ) ==>
% 270.80/271.21 multiplication( coantidomain( X ), coantidomain( codomain( X ) ) ) }.
% 270.80/271.21 parent0[0]: (24) {G1,W7,D4,L1,V1,M1} P(20,20) { codomain( coantidomain( X )
% 270.80/271.21 ) ==> coantidomain( codomain( X ) ) }.
% 270.80/271.21 parent1[0; 6]: (150347) {G2,W6,D4,L1,V1,M1} { X ==> multiplication( X,
% 270.80/271.21 codomain( X ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := coantidomain( X )
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150349) {G2,W9,D5,L1,V1,M1} { multiplication( coantidomain( X ),
% 270.80/271.21 coantidomain( codomain( X ) ) ) ==> coantidomain( X ) }.
% 270.80/271.21 parent0[0]: (150348) {G2,W9,D5,L1,V1,M1} { coantidomain( X ) ==>
% 270.80/271.21 multiplication( coantidomain( X ), coantidomain( codomain( X ) ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (582) {G3,W9,D5,L1,V1,M1} P(24,548) { multiplication(
% 270.80/271.21 coantidomain( X ), coantidomain( codomain( X ) ) ) ==> coantidomain( X )
% 270.80/271.21 }.
% 270.80/271.21 parent0: (150349) {G2,W9,D5,L1,V1,M1} { multiplication( coantidomain( X )
% 270.80/271.21 , coantidomain( codomain( X ) ) ) ==> coantidomain( X ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150350) {G5,W6,D4,L1,V1,M1} { one ==> addition( codomain( X ),
% 270.80/271.21 one ) }.
% 270.80/271.21 parent0[0]: (540) {G5,W6,D4,L1,V1,M1} R(519,11) { addition( codomain( X ),
% 270.80/271.21 one ) ==> one }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150351) {G1,W6,D4,L1,V1,M1} { one ==> addition( one, codomain( X
% 270.80/271.21 ) ) }.
% 270.80/271.21 parent0[0]: (0) {G0,W7,D3,L1,V2,M1} I { addition( X, Y ) = addition( Y, X )
% 270.80/271.21 }.
% 270.80/271.21 parent1[0; 2]: (150350) {G5,W6,D4,L1,V1,M1} { one ==> addition( codomain(
% 270.80/271.21 X ), one ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := codomain( X )
% 270.80/271.21 Y := one
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150354) {G1,W6,D4,L1,V1,M1} { addition( one, codomain( X ) ) ==>
% 270.80/271.21 one }.
% 270.80/271.21 parent0[0]: (150351) {G1,W6,D4,L1,V1,M1} { one ==> addition( one, codomain
% 270.80/271.21 ( X ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (593) {G6,W6,D4,L1,V1,M1} P(540,0) { addition( one, codomain(
% 270.80/271.21 X ) ) ==> one }.
% 270.80/271.21 parent0: (150354) {G1,W6,D4,L1,V1,M1} { addition( one, codomain( X ) ) ==>
% 270.80/271.21 one }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150356) {G2,W7,D4,L1,V2,M1} { leq( X, multiplication( X,
% 270.80/271.21 addition( Y, one ) ) ) }.
% 270.80/271.21 parent0[0]: (54) {G1,W11,D4,L1,V2,M1} P(5,7) { addition( multiplication( X
% 270.80/271.21 , Y ), X ) = multiplication( X, addition( Y, one ) ) }.
% 270.80/271.21 parent1[0; 2]: (265) {G2,W5,D3,L1,V2,M1} R(30,63) { leq( X, addition( Y, X
% 270.80/271.21 ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 Y := multiplication( X, Y )
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (674) {G3,W7,D4,L1,V2,M1} P(54,265) { leq( X, multiplication(
% 270.80/271.21 X, addition( Y, one ) ) ) }.
% 270.80/271.21 parent0: (150356) {G2,W7,D4,L1,V2,M1} { leq( X, multiplication( X,
% 270.80/271.21 addition( Y, one ) ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150358) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ), leq( X, Y
% 270.80/271.21 ) }.
% 270.80/271.21 parent0[0]: (12) {G0,W8,D3,L2,V2,M2} I { ! addition( X, Y ) ==> Y, leq( X,
% 270.80/271.21 Y ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150359) {G1,W12,D4,L2,V2,M2} { ! X ==> multiplication( X,
% 270.80/271.21 addition( Y, one ) ), leq( multiplication( X, Y ), X ) }.
% 270.80/271.21 parent0[0]: (54) {G1,W11,D4,L1,V2,M1} P(5,7) { addition( multiplication( X
% 270.80/271.21 , Y ), X ) = multiplication( X, addition( Y, one ) ) }.
% 270.80/271.21 parent1[0; 3]: (150358) {G0,W8,D3,L2,V2,M2} { ! Y ==> addition( X, Y ),
% 270.80/271.21 leq( X, Y ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := multiplication( X, Y )
% 270.80/271.21 Y := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150360) {G1,W12,D4,L2,V2,M2} { ! multiplication( X, addition( Y,
% 270.80/271.21 one ) ) ==> X, leq( multiplication( X, Y ), X ) }.
% 270.80/271.21 parent0[0]: (150359) {G1,W12,D4,L2,V2,M2} { ! X ==> multiplication( X,
% 270.80/271.21 addition( Y, one ) ), leq( multiplication( X, Y ), X ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (690) {G2,W12,D4,L2,V2,M2} P(54,12) { ! multiplication( X,
% 270.80/271.21 addition( Y, one ) ) ==> X, leq( multiplication( X, Y ), X ) }.
% 270.80/271.21 parent0: (150360) {G1,W12,D4,L2,V2,M2} { ! multiplication( X, addition( Y
% 270.80/271.21 , one ) ) ==> X, leq( multiplication( X, Y ), X ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 1 ==> 1
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150362) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Z ) ==>
% 270.80/271.21 multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ),
% 270.80/271.21 multiplication( X, Z ) ) }.
% 270.80/271.21 parent0[0]: (60) {G1,W16,D4,L2,V3,M2} P(7,12) { ! multiplication( X,
% 270.80/271.21 addition( Y, Z ) ) ==> multiplication( X, Z ), leq( multiplication( X, Y
% 270.80/271.21 ), multiplication( X, Z ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 Z := Z
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150364) {G2,W15,D4,L2,V2,M2} { ! multiplication( X, one ) ==>
% 270.80/271.21 multiplication( X, one ), leq( multiplication( X, domain( Y ) ),
% 270.80/271.21 multiplication( X, one ) ) }.
% 270.80/271.21 parent0[0]: (289) {G5,W6,D4,L1,V1,M1} R(288,11) { addition( domain( X ),
% 270.80/271.21 one ) ==> one }.
% 270.80/271.21 parent1[0; 7]: (150362) {G1,W16,D4,L2,V3,M2} { ! multiplication( X, Z )
% 270.80/271.21 ==> multiplication( X, addition( Y, Z ) ), leq( multiplication( X, Y ),
% 270.80/271.21 multiplication( X, Z ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := Y
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 Y := domain( Y )
% 270.80/271.21 Z := one
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqrefl: (150365) {G0,W8,D4,L1,V2,M1} { leq( multiplication( X, domain( Y )
% 270.80/271.21 ), multiplication( X, one ) ) }.
% 270.80/271.21 parent0[0]: (150364) {G2,W15,D4,L2,V2,M2} { ! multiplication( X, one ) ==>
% 270.80/271.21 multiplication( X, one ), leq( multiplication( X, domain( Y ) ),
% 270.80/271.21 multiplication( X, one ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150366) {G1,W6,D4,L1,V2,M1} { leq( multiplication( X, domain( Y
% 270.80/271.21 ) ), X ) }.
% 270.80/271.21 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 270.80/271.21 parent1[0; 5]: (150365) {G0,W8,D4,L1,V2,M1} { leq( multiplication( X,
% 270.80/271.21 domain( Y ) ), multiplication( X, one ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (888) {G6,W6,D4,L1,V2,M1} P(289,60);q;d(5) { leq(
% 270.80/271.21 multiplication( Y, domain( X ) ), Y ) }.
% 270.80/271.21 parent0: (150366) {G1,W6,D4,L1,V2,M1} { leq( multiplication( X, domain( Y
% 270.80/271.21 ) ), X ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := Y
% 270.80/271.21 Y := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150368) {G1,W16,D4,L2,V3,M2} { ! multiplication( Y, Z ) ==>
% 270.80/271.21 multiplication( addition( X, Y ), Z ), leq( multiplication( X, Z ),
% 270.80/271.21 multiplication( Y, Z ) ) }.
% 270.80/271.21 parent0[0]: (64) {G1,W16,D4,L2,V3,M2} P(8,12) { ! multiplication( addition
% 270.80/271.21 ( X, Z ), Y ) ==> multiplication( Z, Y ), leq( multiplication( X, Y ),
% 270.80/271.21 multiplication( Z, Y ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Z
% 270.80/271.21 Z := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150370) {G2,W15,D4,L2,V2,M2} { ! multiplication( one, X ) ==>
% 270.80/271.21 multiplication( one, X ), leq( multiplication( antidomain( Y ), X ),
% 270.80/271.21 multiplication( one, X ) ) }.
% 270.80/271.21 parent0[0]: (287) {G4,W6,D4,L1,V1,M1} R(280,11) { addition( antidomain( X )
% 270.80/271.21 , one ) ==> one }.
% 270.80/271.21 parent1[0; 6]: (150368) {G1,W16,D4,L2,V3,M2} { ! multiplication( Y, Z )
% 270.80/271.21 ==> multiplication( addition( X, Y ), Z ), leq( multiplication( X, Z ),
% 270.80/271.21 multiplication( Y, Z ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := Y
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := antidomain( Y )
% 270.80/271.21 Y := one
% 270.80/271.21 Z := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqrefl: (150371) {G0,W8,D4,L1,V2,M1} { leq( multiplication( antidomain( Y
% 270.80/271.21 ), X ), multiplication( one, X ) ) }.
% 270.80/271.21 parent0[0]: (150370) {G2,W15,D4,L2,V2,M2} { ! multiplication( one, X ) ==>
% 270.80/271.21 multiplication( one, X ), leq( multiplication( antidomain( Y ), X ),
% 270.80/271.21 multiplication( one, X ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150372) {G1,W6,D4,L1,V2,M1} { leq( multiplication( antidomain( X
% 270.80/271.21 ), Y ), Y ) }.
% 270.80/271.21 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 270.80/271.21 parent1[0; 5]: (150371) {G0,W8,D4,L1,V2,M1} { leq( multiplication(
% 270.80/271.21 antidomain( Y ), X ), multiplication( one, X ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := Y
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := Y
% 270.80/271.21 Y := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (922) {G5,W6,D4,L1,V2,M1} P(287,64);q;d(6) { leq(
% 270.80/271.21 multiplication( antidomain( X ), Y ), Y ) }.
% 270.80/271.21 parent0: (150372) {G1,W6,D4,L1,V2,M1} { leq( multiplication( antidomain( X
% 270.80/271.21 ), Y ), Y ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150374) {G1,W16,D4,L2,V3,M2} { ! multiplication( Y, Z ) ==>
% 270.80/271.21 multiplication( addition( X, Y ), Z ), leq( multiplication( X, Z ),
% 270.80/271.21 multiplication( Y, Z ) ) }.
% 270.80/271.21 parent0[0]: (64) {G1,W16,D4,L2,V3,M2} P(8,12) { ! multiplication( addition
% 270.80/271.21 ( X, Z ), Y ) ==> multiplication( Z, Y ), leq( multiplication( X, Y ),
% 270.80/271.21 multiplication( Z, Y ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Z
% 270.80/271.21 Z := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150376) {G1,W14,D4,L2,V2,M2} { leq( X, multiplication( Y, X ) )
% 270.80/271.21 , ! multiplication( Y, X ) ==> multiplication( addition( one, Y ), X )
% 270.80/271.21 }.
% 270.80/271.21 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 270.80/271.21 parent1[1; 1]: (150374) {G1,W16,D4,L2,V3,M2} { ! multiplication( Y, Z )
% 270.80/271.21 ==> multiplication( addition( X, Y ), Z ), leq( multiplication( X, Z ),
% 270.80/271.21 multiplication( Y, Z ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := one
% 270.80/271.21 Y := Y
% 270.80/271.21 Z := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150380) {G1,W14,D4,L2,V2,M2} { ! multiplication( addition( one, X
% 270.80/271.21 ), Y ) ==> multiplication( X, Y ), leq( Y, multiplication( X, Y ) ) }.
% 270.80/271.21 parent0[1]: (150376) {G1,W14,D4,L2,V2,M2} { leq( X, multiplication( Y, X )
% 270.80/271.21 ), ! multiplication( Y, X ) ==> multiplication( addition( one, Y ), X )
% 270.80/271.21 }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := Y
% 270.80/271.21 Y := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (927) {G2,W14,D4,L2,V2,M2} P(6,64) { ! multiplication(
% 270.80/271.21 addition( one, Y ), X ) ==> multiplication( Y, X ), leq( X,
% 270.80/271.21 multiplication( Y, X ) ) }.
% 270.80/271.21 parent0: (150380) {G1,W14,D4,L2,V2,M2} { ! multiplication( addition( one,
% 270.80/271.21 X ), Y ) ==> multiplication( X, Y ), leq( Y, multiplication( X, Y ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := Y
% 270.80/271.21 Y := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 1 ==> 1
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150384) {G3,W6,D4,L1,V1,M1} { leq( antidomain( X ), codomain(
% 270.80/271.21 antidomain( X ) ) ) }.
% 270.80/271.21 parent0[0]: (548) {G2,W6,D4,L1,V1,M1} P(178,51);d(5) { multiplication( X,
% 270.80/271.21 codomain( X ) ) ==> X }.
% 270.80/271.21 parent1[0; 1]: (922) {G5,W6,D4,L1,V2,M1} P(287,64);q;d(6) { leq(
% 270.80/271.21 multiplication( antidomain( X ), Y ), Y ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := antidomain( X )
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 Y := codomain( antidomain( X ) )
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (948) {G6,W6,D4,L1,V1,M1} P(548,922) { leq( antidomain( X ),
% 270.80/271.21 codomain( antidomain( X ) ) ) }.
% 270.80/271.21 parent0: (150384) {G3,W6,D4,L1,V1,M1} { leq( antidomain( X ), codomain(
% 270.80/271.21 antidomain( X ) ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150385) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq( X, Y
% 270.80/271.21 ) }.
% 270.80/271.21 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 270.80/271.21 ==> Y }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 resolution: (150386) {G1,W10,D5,L1,V1,M1} { codomain( antidomain( X ) )
% 270.80/271.21 ==> addition( antidomain( X ), codomain( antidomain( X ) ) ) }.
% 270.80/271.21 parent0[1]: (150385) {G0,W8,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! leq(
% 270.80/271.21 X, Y ) }.
% 270.80/271.21 parent1[0]: (948) {G6,W6,D4,L1,V1,M1} P(548,922) { leq( antidomain( X ),
% 270.80/271.21 codomain( antidomain( X ) ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := antidomain( X )
% 270.80/271.21 Y := codomain( antidomain( X ) )
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150387) {G1,W10,D5,L1,V1,M1} { addition( antidomain( X ),
% 270.80/271.21 codomain( antidomain( X ) ) ) ==> codomain( antidomain( X ) ) }.
% 270.80/271.21 parent0[0]: (150386) {G1,W10,D5,L1,V1,M1} { codomain( antidomain( X ) )
% 270.80/271.21 ==> addition( antidomain( X ), codomain( antidomain( X ) ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (977) {G7,W10,D5,L1,V1,M1} R(948,11) { addition( antidomain( X
% 270.80/271.21 ), codomain( antidomain( X ) ) ) ==> codomain( antidomain( X ) ) }.
% 270.80/271.21 parent0: (150387) {G1,W10,D5,L1,V1,M1} { addition( antidomain( X ),
% 270.80/271.21 codomain( antidomain( X ) ) ) ==> codomain( antidomain( X ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150389) {G1,W10,D5,L1,V2,M1} { multiplication( X, Y ) ==>
% 270.80/271.21 multiplication( addition( X, antidomain( Y ) ), Y ) }.
% 270.80/271.21 parent0[0]: (72) {G1,W10,D5,L1,V2,M1} P(13,8);d(2) { multiplication(
% 270.80/271.21 addition( Y, antidomain( X ) ), X ) ==> multiplication( Y, X ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := Y
% 270.80/271.21 Y := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150391) {G2,W8,D4,L1,V1,M1} { multiplication( domain( X ), X )
% 270.80/271.21 ==> multiplication( one, X ) }.
% 270.80/271.21 parent0[0]: (156) {G1,W7,D4,L1,V1,M1} S(15);d(16) { addition( domain( X ),
% 270.80/271.21 antidomain( X ) ) ==> one }.
% 270.80/271.21 parent1[0; 6]: (150389) {G1,W10,D5,L1,V2,M1} { multiplication( X, Y ) ==>
% 270.80/271.21 multiplication( addition( X, antidomain( Y ) ), Y ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := domain( X )
% 270.80/271.21 Y := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150392) {G1,W6,D4,L1,V1,M1} { multiplication( domain( X ), X )
% 270.80/271.21 ==> X }.
% 270.80/271.21 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 270.80/271.21 parent1[0; 5]: (150391) {G2,W8,D4,L1,V1,M1} { multiplication( domain( X )
% 270.80/271.21 , X ) ==> multiplication( one, X ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (1116) {G2,W6,D4,L1,V1,M1} P(156,72);d(6) { multiplication(
% 270.80/271.21 domain( X ), X ) ==> X }.
% 270.80/271.21 parent0: (150392) {G1,W6,D4,L1,V1,M1} { multiplication( domain( X ), X )
% 270.80/271.21 ==> X }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150394) {G1,W6,D2,L2,V1,M2} { X = zero, ! leq( X, zero ) }.
% 270.80/271.21 parent0[0]: (87) {G1,W6,D2,L2,V1,M2} P(11,2) { zero = X, ! leq( X, zero )
% 270.80/271.21 }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150395) {G2,W6,D4,L1,V1,M1} { X ==> multiplication( domain( X ),
% 270.80/271.21 X ) }.
% 270.80/271.21 parent0[0]: (1116) {G2,W6,D4,L1,V1,M1} P(156,72);d(6) { multiplication(
% 270.80/271.21 domain( X ), X ) ==> X }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150398) {G2,W9,D3,L2,V1,M2} { X ==> multiplication( zero, X ), !
% 270.80/271.21 leq( domain( X ), zero ) }.
% 270.80/271.21 parent0[0]: (150394) {G1,W6,D2,L2,V1,M2} { X = zero, ! leq( X, zero ) }.
% 270.80/271.21 parent1[0; 3]: (150395) {G2,W6,D4,L1,V1,M1} { X ==> multiplication( domain
% 270.80/271.21 ( X ), X ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := domain( X )
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150419) {G1,W7,D3,L2,V1,M2} { X ==> zero, ! leq( domain( X ),
% 270.80/271.21 zero ) }.
% 270.80/271.21 parent0[0]: (10) {G0,W5,D3,L1,V1,M1} I { multiplication( zero, X ) ==> zero
% 270.80/271.21 }.
% 270.80/271.21 parent1[0; 2]: (150398) {G2,W9,D3,L2,V1,M2} { X ==> multiplication( zero,
% 270.80/271.21 X ), ! leq( domain( X ), zero ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150420) {G1,W7,D3,L2,V1,M2} { zero ==> X, ! leq( domain( X ),
% 270.80/271.21 zero ) }.
% 270.80/271.21 parent0[0]: (150419) {G1,W7,D3,L2,V1,M2} { X ==> zero, ! leq( domain( X )
% 270.80/271.21 , zero ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (1133) {G3,W7,D3,L2,V1,M2} P(87,1116);d(10) { ! leq( domain( X
% 270.80/271.21 ), zero ), zero = X }.
% 270.80/271.21 parent0: (150420) {G1,W7,D3,L2,V1,M2} { zero ==> X, ! leq( domain( X ),
% 270.80/271.21 zero ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 1
% 270.80/271.21 1 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150422) {G2,W6,D4,L1,V1,M1} { X ==> multiplication( domain( X ),
% 270.80/271.21 X ) }.
% 270.80/271.21 parent0[0]: (1116) {G2,W6,D4,L1,V1,M1} P(156,72);d(6) { multiplication(
% 270.80/271.21 domain( X ), X ) ==> X }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150424) {G2,W9,D5,L1,V1,M1} { antidomain( X ) ==> multiplication
% 270.80/271.21 ( antidomain( domain( X ) ), antidomain( X ) ) }.
% 270.80/271.21 parent0[0]: (32) {G1,W7,D4,L1,V1,M1} P(16,16) { domain( antidomain( X ) )
% 270.80/271.21 ==> antidomain( domain( X ) ) }.
% 270.80/271.21 parent1[0; 4]: (150422) {G2,W6,D4,L1,V1,M1} { X ==> multiplication( domain
% 270.80/271.21 ( X ), X ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := antidomain( X )
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150425) {G3,W6,D4,L1,V1,M1} { antidomain( X ) ==> antidomain(
% 270.80/271.21 domain( X ) ) }.
% 270.80/271.21 parent0[0]: (472) {G3,W10,D5,L1,V1,M1} P(156,47);d(5) { multiplication(
% 270.80/271.21 antidomain( domain( X ) ), antidomain( X ) ) ==> antidomain( domain( X )
% 270.80/271.21 ) }.
% 270.80/271.21 parent1[0; 3]: (150424) {G2,W9,D5,L1,V1,M1} { antidomain( X ) ==>
% 270.80/271.21 multiplication( antidomain( domain( X ) ), antidomain( X ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150426) {G3,W6,D4,L1,V1,M1} { antidomain( domain( X ) ) ==>
% 270.80/271.21 antidomain( X ) }.
% 270.80/271.21 parent0[0]: (150425) {G3,W6,D4,L1,V1,M1} { antidomain( X ) ==> antidomain
% 270.80/271.21 ( domain( X ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (1137) {G4,W6,D4,L1,V1,M1} P(32,1116);d(472) { antidomain(
% 270.80/271.21 domain( X ) ) ==> antidomain( X ) }.
% 270.80/271.21 parent0: (150426) {G3,W6,D4,L1,V1,M1} { antidomain( domain( X ) ) ==>
% 270.80/271.21 antidomain( X ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150428) {G2,W11,D4,L1,V2,M1} { multiplication( Y, coantidomain( X
% 270.80/271.21 ) ) ==> multiplication( addition( X, Y ), coantidomain( X ) ) }.
% 270.80/271.21 parent0[0]: (74) {G2,W11,D4,L1,V2,M1} P(17,8);d(23) { multiplication(
% 270.80/271.21 addition( X, Y ), coantidomain( X ) ) ==> multiplication( Y, coantidomain
% 270.80/271.21 ( X ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150431) {G2,W12,D5,L1,V1,M1} { multiplication( coantidomain( X )
% 270.80/271.21 , coantidomain( codomain( X ) ) ) ==> multiplication( one, coantidomain(
% 270.80/271.21 codomain( X ) ) ) }.
% 270.80/271.21 parent0[0]: (178) {G1,W7,D4,L1,V1,M1} S(19);d(20) { addition( codomain( X )
% 270.80/271.21 , coantidomain( X ) ) ==> one }.
% 270.80/271.21 parent1[0; 8]: (150428) {G2,W11,D4,L1,V2,M1} { multiplication( Y,
% 270.80/271.21 coantidomain( X ) ) ==> multiplication( addition( X, Y ), coantidomain( X
% 270.80/271.21 ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := codomain( X )
% 270.80/271.21 Y := coantidomain( X )
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150432) {G1,W10,D5,L1,V1,M1} { multiplication( coantidomain( X )
% 270.80/271.21 , coantidomain( codomain( X ) ) ) ==> coantidomain( codomain( X ) ) }.
% 270.80/271.21 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 270.80/271.21 parent1[0; 7]: (150431) {G2,W12,D5,L1,V1,M1} { multiplication(
% 270.80/271.21 coantidomain( X ), coantidomain( codomain( X ) ) ) ==> multiplication(
% 270.80/271.21 one, coantidomain( codomain( X ) ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := coantidomain( codomain( X ) )
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150433) {G2,W6,D4,L1,V1,M1} { coantidomain( X ) ==> coantidomain
% 270.80/271.21 ( codomain( X ) ) }.
% 270.80/271.21 parent0[0]: (582) {G3,W9,D5,L1,V1,M1} P(24,548) { multiplication(
% 270.80/271.21 coantidomain( X ), coantidomain( codomain( X ) ) ) ==> coantidomain( X )
% 270.80/271.21 }.
% 270.80/271.21 parent1[0; 1]: (150432) {G1,W10,D5,L1,V1,M1} { multiplication(
% 270.80/271.21 coantidomain( X ), coantidomain( codomain( X ) ) ) ==> coantidomain(
% 270.80/271.21 codomain( X ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150434) {G2,W6,D4,L1,V1,M1} { coantidomain( codomain( X ) ) ==>
% 270.80/271.21 coantidomain( X ) }.
% 270.80/271.21 parent0[0]: (150433) {G2,W6,D4,L1,V1,M1} { coantidomain( X ) ==>
% 270.80/271.21 coantidomain( codomain( X ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (1187) {G4,W6,D4,L1,V1,M1} P(178,74);d(6);d(582) {
% 270.80/271.21 coantidomain( codomain( X ) ) ==> coantidomain( X ) }.
% 270.80/271.21 parent0: (150434) {G2,W6,D4,L1,V1,M1} { coantidomain( codomain( X ) ) ==>
% 270.80/271.21 coantidomain( X ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150436) {G1,W11,D4,L1,V2,M1} { multiplication( X, coantidomain( Y
% 270.80/271.21 ) ) ==> multiplication( addition( X, Y ), coantidomain( Y ) ) }.
% 270.80/271.21 parent0[0]: (75) {G1,W11,D4,L1,V2,M1} P(17,8);d(2) { multiplication(
% 270.80/271.21 addition( Y, X ), coantidomain( X ) ) ==> multiplication( Y, coantidomain
% 270.80/271.21 ( X ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := Y
% 270.80/271.21 Y := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150438) {G1,W12,D4,L2,V2,M2} { multiplication( X, coantidomain(
% 270.80/271.21 Y ) ) ==> multiplication( Y, coantidomain( Y ) ), ! leq( X, Y ) }.
% 270.80/271.21 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 270.80/271.21 ==> Y }.
% 270.80/271.21 parent1[0; 6]: (150436) {G1,W11,D4,L1,V2,M1} { multiplication( X,
% 270.80/271.21 coantidomain( Y ) ) ==> multiplication( addition( X, Y ), coantidomain( Y
% 270.80/271.21 ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150439) {G1,W9,D4,L2,V2,M2} { multiplication( X, coantidomain( Y
% 270.80/271.21 ) ) ==> zero, ! leq( X, Y ) }.
% 270.80/271.21 parent0[0]: (17) {G0,W6,D4,L1,V1,M1} I { multiplication( X, coantidomain( X
% 270.80/271.21 ) ) ==> zero }.
% 270.80/271.21 parent1[0; 5]: (150438) {G1,W12,D4,L2,V2,M2} { multiplication( X,
% 270.80/271.21 coantidomain( Y ) ) ==> multiplication( Y, coantidomain( Y ) ), ! leq( X
% 270.80/271.21 , Y ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := Y
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (1217) {G2,W9,D4,L2,V2,M2} P(11,75);d(17) { ! leq( X, Y ),
% 270.80/271.21 multiplication( X, coantidomain( Y ) ) ==> zero }.
% 270.80/271.21 parent0: (150439) {G1,W9,D4,L2,V2,M2} { multiplication( X, coantidomain( Y
% 270.80/271.21 ) ) ==> zero, ! leq( X, Y ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 1
% 270.80/271.21 1 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150442) {G2,W7,D4,L1,V2,M1} { leq( X, multiplication( addition(
% 270.80/271.21 Y, one ), X ) ) }.
% 270.80/271.21 parent0[0]: (78) {G1,W11,D4,L1,V2,M1} P(6,8) { addition( multiplication( Y
% 270.80/271.21 , X ), X ) = multiplication( addition( Y, one ), X ) }.
% 270.80/271.21 parent1[0; 2]: (265) {G2,W5,D3,L1,V2,M1} R(30,63) { leq( X, addition( Y, X
% 270.80/271.21 ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 Y := multiplication( Y, X )
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (1518) {G3,W7,D4,L1,V2,M1} P(78,265) { leq( Y, multiplication
% 270.80/271.21 ( addition( X, one ), Y ) ) }.
% 270.80/271.21 parent0: (150442) {G2,W7,D4,L1,V2,M1} { leq( X, multiplication( addition(
% 270.80/271.21 Y, one ), X ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := Y
% 270.80/271.21 Y := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150443) {G2,W10,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! addition
% 270.80/271.21 ( Y, X ) ==> Y }.
% 270.80/271.21 parent0[0]: (80) {G2,W10,D3,L2,V2,M2} R(11,63) { addition( X, Y ) ==> Y, !
% 270.80/271.21 addition( Y, X ) ==> Y }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150448) {G3,W11,D4,L2,V1,M2} { coantidomain( X ) ==> one, !
% 270.80/271.21 addition( coantidomain( X ), one ) ==> coantidomain( X ) }.
% 270.80/271.21 parent0[0]: (521) {G2,W6,D4,L1,V1,M1} P(178,30) { addition( one,
% 270.80/271.21 coantidomain( X ) ) ==> one }.
% 270.80/271.21 parent1[0; 3]: (150443) {G2,W10,D3,L2,V2,M2} { Y ==> addition( X, Y ), !
% 270.80/271.21 addition( Y, X ) ==> Y }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := one
% 270.80/271.21 Y := coantidomain( X )
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150451) {G4,W8,D3,L2,V1,M2} { ! one ==> coantidomain( X ),
% 270.80/271.21 coantidomain( X ) ==> one }.
% 270.80/271.21 parent0[0]: (541) {G4,W6,D4,L1,V1,M1} R(520,11) { addition( coantidomain( X
% 270.80/271.21 ), one ) ==> one }.
% 270.80/271.21 parent1[1; 2]: (150448) {G3,W11,D4,L2,V1,M2} { coantidomain( X ) ==> one,
% 270.80/271.21 ! addition( coantidomain( X ), one ) ==> coantidomain( X ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150452) {G4,W8,D3,L2,V1,M2} { ! coantidomain( X ) ==> one,
% 270.80/271.21 coantidomain( X ) ==> one }.
% 270.80/271.21 parent0[0]: (150451) {G4,W8,D3,L2,V1,M2} { ! one ==> coantidomain( X ),
% 270.80/271.21 coantidomain( X ) ==> one }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (1608) {G5,W8,D3,L2,V1,M2} P(80,521);d(541) { coantidomain( X
% 270.80/271.21 ) ==> one, ! coantidomain( X ) ==> one }.
% 270.80/271.21 parent0: (150452) {G4,W8,D3,L2,V1,M2} { ! coantidomain( X ) ==> one,
% 270.80/271.21 coantidomain( X ) ==> one }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 1
% 270.80/271.21 1 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150455) {G2,W10,D3,L2,V2,M2} { Y ==> addition( X, Y ), ! addition
% 270.80/271.21 ( Y, X ) ==> Y }.
% 270.80/271.21 parent0[0]: (80) {G2,W10,D3,L2,V2,M2} R(11,63) { addition( X, Y ) ==> Y, !
% 270.80/271.21 addition( Y, X ) ==> Y }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150460) {G3,W11,D4,L2,V1,M2} { antidomain( X ) ==> one, !
% 270.80/271.21 addition( antidomain( X ), one ) ==> antidomain( X ) }.
% 270.80/271.21 parent0[0]: (268) {G2,W6,D4,L1,V1,M1} P(156,30) { addition( one, antidomain
% 270.80/271.21 ( X ) ) ==> one }.
% 270.80/271.21 parent1[0; 3]: (150455) {G2,W10,D3,L2,V2,M2} { Y ==> addition( X, Y ), !
% 270.80/271.21 addition( Y, X ) ==> Y }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := one
% 270.80/271.21 Y := antidomain( X )
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150463) {G4,W8,D3,L2,V1,M2} { ! one ==> antidomain( X ),
% 270.80/271.21 antidomain( X ) ==> one }.
% 270.80/271.21 parent0[0]: (287) {G4,W6,D4,L1,V1,M1} R(280,11) { addition( antidomain( X )
% 270.80/271.21 , one ) ==> one }.
% 270.80/271.21 parent1[1; 2]: (150460) {G3,W11,D4,L2,V1,M2} { antidomain( X ) ==> one, !
% 270.80/271.21 addition( antidomain( X ), one ) ==> antidomain( X ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150464) {G4,W8,D3,L2,V1,M2} { ! antidomain( X ) ==> one,
% 270.80/271.21 antidomain( X ) ==> one }.
% 270.80/271.21 parent0[0]: (150463) {G4,W8,D3,L2,V1,M2} { ! one ==> antidomain( X ),
% 270.80/271.21 antidomain( X ) ==> one }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (1639) {G5,W8,D3,L2,V1,M2} P(80,268);d(287) { antidomain( X )
% 270.80/271.21 ==> one, ! antidomain( X ) ==> one }.
% 270.80/271.21 parent0: (150464) {G4,W8,D3,L2,V1,M2} { ! antidomain( X ) ==> one,
% 270.80/271.21 antidomain( X ) ==> one }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 1
% 270.80/271.21 1 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150468) {G1,W16,D4,L2,V3,M2} { multiplication( Y, Z ) ==>
% 270.80/271.21 multiplication( addition( X, Y ), Z ), ! leq( multiplication( X, Z ),
% 270.80/271.21 multiplication( Y, Z ) ) }.
% 270.80/271.21 parent0[0]: (83) {G1,W16,D4,L2,V3,M2} P(11,8) { multiplication( addition( X
% 270.80/271.21 , Z ), Y ) ==> multiplication( Z, Y ), ! leq( multiplication( X, Y ),
% 270.80/271.21 multiplication( Z, Y ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Z
% 270.80/271.21 Z := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150470) {G2,W17,D4,L2,V2,M2} { multiplication( coantidomain( X )
% 270.80/271.21 , Y ) ==> multiplication( one, Y ), ! leq( multiplication( codomain( X )
% 270.80/271.21 , Y ), multiplication( coantidomain( X ), Y ) ) }.
% 270.80/271.21 parent0[0]: (178) {G1,W7,D4,L1,V1,M1} S(19);d(20) { addition( codomain( X )
% 270.80/271.21 , coantidomain( X ) ) ==> one }.
% 270.80/271.21 parent1[0; 6]: (150468) {G1,W16,D4,L2,V3,M2} { multiplication( Y, Z ) ==>
% 270.80/271.21 multiplication( addition( X, Y ), Z ), ! leq( multiplication( X, Z ),
% 270.80/271.21 multiplication( Y, Z ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := codomain( X )
% 270.80/271.21 Y := coantidomain( X )
% 270.80/271.21 Z := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150471) {G1,W15,D4,L2,V2,M2} { multiplication( coantidomain( X )
% 270.80/271.21 , Y ) ==> Y, ! leq( multiplication( codomain( X ), Y ), multiplication(
% 270.80/271.21 coantidomain( X ), Y ) ) }.
% 270.80/271.21 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 270.80/271.21 parent1[0; 5]: (150470) {G2,W17,D4,L2,V2,M2} { multiplication(
% 270.80/271.21 coantidomain( X ), Y ) ==> multiplication( one, Y ), ! leq(
% 270.80/271.21 multiplication( codomain( X ), Y ), multiplication( coantidomain( X ), Y
% 270.80/271.21 ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := Y
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (1717) {G2,W15,D4,L2,V2,M2} P(178,83);d(6) { ! leq(
% 270.80/271.21 multiplication( codomain( X ), Y ), multiplication( coantidomain( X ), Y
% 270.80/271.21 ) ), multiplication( coantidomain( X ), Y ) ==> Y }.
% 270.80/271.21 parent0: (150471) {G1,W15,D4,L2,V2,M2} { multiplication( coantidomain( X )
% 270.80/271.21 , Y ) ==> Y, ! leq( multiplication( codomain( X ), Y ), multiplication(
% 270.80/271.21 coantidomain( X ), Y ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 1
% 270.80/271.21 1 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150474) {G1,W16,D4,L2,V3,M2} { multiplication( Y, Z ) ==>
% 270.80/271.21 multiplication( addition( X, Y ), Z ), ! leq( multiplication( X, Z ),
% 270.80/271.21 multiplication( Y, Z ) ) }.
% 270.80/271.21 parent0[0]: (83) {G1,W16,D4,L2,V3,M2} P(11,8) { multiplication( addition( X
% 270.80/271.21 , Z ), Y ) ==> multiplication( Z, Y ), ! leq( multiplication( X, Y ),
% 270.80/271.21 multiplication( Z, Y ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Z
% 270.80/271.21 Z := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150476) {G2,W17,D4,L2,V2,M2} { multiplication( antidomain( X ),
% 270.80/271.21 Y ) ==> multiplication( one, Y ), ! leq( multiplication( domain( X ), Y )
% 270.80/271.21 , multiplication( antidomain( X ), Y ) ) }.
% 270.80/271.21 parent0[0]: (156) {G1,W7,D4,L1,V1,M1} S(15);d(16) { addition( domain( X ),
% 270.80/271.21 antidomain( X ) ) ==> one }.
% 270.80/271.21 parent1[0; 6]: (150474) {G1,W16,D4,L2,V3,M2} { multiplication( Y, Z ) ==>
% 270.80/271.21 multiplication( addition( X, Y ), Z ), ! leq( multiplication( X, Z ),
% 270.80/271.21 multiplication( Y, Z ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := domain( X )
% 270.80/271.21 Y := antidomain( X )
% 270.80/271.21 Z := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150477) {G1,W15,D4,L2,V2,M2} { multiplication( antidomain( X ),
% 270.80/271.21 Y ) ==> Y, ! leq( multiplication( domain( X ), Y ), multiplication(
% 270.80/271.21 antidomain( X ), Y ) ) }.
% 270.80/271.21 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 270.80/271.21 parent1[0; 5]: (150476) {G2,W17,D4,L2,V2,M2} { multiplication( antidomain
% 270.80/271.21 ( X ), Y ) ==> multiplication( one, Y ), ! leq( multiplication( domain( X
% 270.80/271.21 ), Y ), multiplication( antidomain( X ), Y ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := Y
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (1720) {G2,W15,D4,L2,V2,M2} P(156,83);d(6) { ! leq(
% 270.80/271.21 multiplication( domain( X ), Y ), multiplication( antidomain( X ), Y ) )
% 270.80/271.21 , multiplication( antidomain( X ), Y ) ==> Y }.
% 270.80/271.21 parent0: (150477) {G1,W15,D4,L2,V2,M2} { multiplication( antidomain( X ),
% 270.80/271.21 Y ) ==> Y, ! leq( multiplication( domain( X ), Y ), multiplication(
% 270.80/271.21 antidomain( X ), Y ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 1
% 270.80/271.21 1 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150480) {G2,W8,D3,L2,V2,M2} { leq( X, multiplication( Y, X ) ),
% 270.80/271.21 ! leq( one, Y ) }.
% 270.80/271.21 parent0[0]: (88) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, !
% 270.80/271.21 leq( X, Y ) }.
% 270.80/271.21 parent1[0; 3]: (1518) {G3,W7,D4,L1,V2,M1} P(78,265) { leq( Y,
% 270.80/271.21 multiplication( addition( X, one ), Y ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := one
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := Y
% 270.80/271.21 Y := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (2621) {G4,W8,D3,L2,V2,M2} P(88,1518) { leq( Y, multiplication
% 270.80/271.21 ( X, Y ) ), ! leq( one, X ) }.
% 270.80/271.21 parent0: (150480) {G2,W8,D3,L2,V2,M2} { leq( X, multiplication( Y, X ) ),
% 270.80/271.21 ! leq( one, Y ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := Y
% 270.80/271.21 Y := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 1 ==> 1
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150482) {G2,W8,D3,L2,V2,M2} { leq( X, multiplication( X, Y ) ),
% 270.80/271.21 ! leq( one, Y ) }.
% 270.80/271.21 parent0[0]: (88) {G1,W8,D3,L2,V2,M2} P(11,0) { addition( Y, X ) ==> Y, !
% 270.80/271.21 leq( X, Y ) }.
% 270.80/271.21 parent1[0; 4]: (674) {G3,W7,D4,L1,V2,M1} P(54,265) { leq( X, multiplication
% 270.80/271.21 ( X, addition( Y, one ) ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := one
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (2651) {G4,W8,D3,L2,V2,M2} P(88,674) { leq( Y, multiplication
% 270.80/271.21 ( Y, X ) ), ! leq( one, X ) }.
% 270.80/271.21 parent0: (150482) {G2,W8,D3,L2,V2,M2} { leq( X, multiplication( X, Y ) ),
% 270.80/271.21 ! leq( one, Y ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := Y
% 270.80/271.21 Y := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 1 ==> 1
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150484) {G1,W16,D6,L1,V2,M1} { antidomain( multiplication( X,
% 270.80/271.21 domain( Y ) ) ) ==> addition( antidomain( multiplication( X, Y ) ),
% 270.80/271.21 antidomain( multiplication( X, domain( Y ) ) ) ) }.
% 270.80/271.21 parent0[0]: (127) {G1,W16,D6,L1,V2,M1} S(14);d(16) { addition( antidomain(
% 270.80/271.21 multiplication( X, Y ) ), antidomain( multiplication( X, domain( Y ) ) )
% 270.80/271.21 ) ==> antidomain( multiplication( X, domain( Y ) ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150487) {G1,W16,D6,L1,V0,M1} { antidomain( multiplication(
% 270.80/271.21 domain( skol1 ), domain( skol2 ) ) ) ==> addition( antidomain( zero ),
% 270.80/271.21 antidomain( multiplication( domain( skol1 ), domain( skol2 ) ) ) ) }.
% 270.80/271.21 parent0[0]: (21) {G0,W6,D4,L1,V0,M1} I { multiplication( domain( skol1 ),
% 270.80/271.21 skol2 ) ==> zero }.
% 270.80/271.21 parent1[0; 9]: (150484) {G1,W16,D6,L1,V2,M1} { antidomain( multiplication
% 270.80/271.21 ( X, domain( Y ) ) ) ==> addition( antidomain( multiplication( X, Y ) ),
% 270.80/271.21 antidomain( multiplication( X, domain( Y ) ) ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := domain( skol1 )
% 270.80/271.21 Y := skol2
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150488) {G2,W15,D6,L1,V0,M1} { antidomain( multiplication(
% 270.80/271.21 domain( skol1 ), domain( skol2 ) ) ) ==> addition( one, antidomain(
% 270.80/271.21 multiplication( domain( skol1 ), domain( skol2 ) ) ) ) }.
% 270.80/271.21 parent0[0]: (167) {G3,W4,D3,L1,V0,M1} P(38,156);d(34);d(2) { antidomain(
% 270.80/271.21 zero ) ==> one }.
% 270.80/271.21 parent1[0; 8]: (150487) {G1,W16,D6,L1,V0,M1} { antidomain( multiplication
% 270.80/271.21 ( domain( skol1 ), domain( skol2 ) ) ) ==> addition( antidomain( zero ),
% 270.80/271.21 antidomain( multiplication( domain( skol1 ), domain( skol2 ) ) ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150489) {G3,W8,D5,L1,V0,M1} { antidomain( multiplication( domain
% 270.80/271.21 ( skol1 ), domain( skol2 ) ) ) ==> one }.
% 270.80/271.21 parent0[0]: (268) {G2,W6,D4,L1,V1,M1} P(156,30) { addition( one, antidomain
% 270.80/271.21 ( X ) ) ==> one }.
% 270.80/271.21 parent1[0; 7]: (150488) {G2,W15,D6,L1,V0,M1} { antidomain( multiplication
% 270.80/271.21 ( domain( skol1 ), domain( skol2 ) ) ) ==> addition( one, antidomain(
% 270.80/271.21 multiplication( domain( skol1 ), domain( skol2 ) ) ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := multiplication( domain( skol1 ), domain( skol2 ) )
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (3255) {G4,W8,D5,L1,V0,M1} P(21,127);d(167);d(268) {
% 270.80/271.21 antidomain( multiplication( domain( skol1 ), domain( skol2 ) ) ) ==> one
% 270.80/271.21 }.
% 270.80/271.21 parent0: (150489) {G3,W8,D5,L1,V0,M1} { antidomain( multiplication( domain
% 270.80/271.21 ( skol1 ), domain( skol2 ) ) ) ==> one }.
% 270.80/271.21 substitution0:
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 resolution: (150491) {G2,W7,D4,L1,V1,M1} { ! leq( addition( domain( skol1
% 270.80/271.21 ), X ), antidomain( skol2 ) ) }.
% 270.80/271.21 parent0[0]: (187) {G1,W5,D3,L1,V0,M1} R(22,11) { ! leq( domain( skol1 ),
% 270.80/271.21 antidomain( skol2 ) ) }.
% 270.80/271.21 parent1[0]: (462) {G4,W8,D3,L2,V3,M2} P(11,279) { leq( X, Z ), ! leq(
% 270.80/271.21 addition( X, Y ), Z ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := domain( skol1 )
% 270.80/271.21 Y := X
% 270.80/271.21 Z := antidomain( skol2 )
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (4595) {G5,W7,D4,L1,V1,M1} R(462,187) { ! leq( addition(
% 270.80/271.21 domain( skol1 ), X ), antidomain( skol2 ) ) }.
% 270.80/271.21 parent0: (150491) {G2,W7,D4,L1,V1,M1} { ! leq( addition( domain( skol1 ),
% 270.80/271.21 X ), antidomain( skol2 ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150493) {G1,W8,D3,L2,V1,M2} { ! leq( X, antidomain( skol2 ) ), !
% 270.80/271.21 leq( domain( skol1 ), X ) }.
% 270.80/271.21 parent0[1]: (11) {G0,W8,D3,L2,V2,M2} I { ! leq( X, Y ), addition( X, Y )
% 270.80/271.21 ==> Y }.
% 270.80/271.21 parent1[0; 2]: (4595) {G5,W7,D4,L1,V1,M1} R(462,187) { ! leq( addition(
% 270.80/271.21 domain( skol1 ), X ), antidomain( skol2 ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := domain( skol1 )
% 270.80/271.21 Y := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (4913) {G6,W8,D3,L2,V1,M2} P(11,4595) { ! leq( X, antidomain(
% 270.80/271.21 skol2 ) ), ! leq( domain( skol1 ), X ) }.
% 270.80/271.21 parent0: (150493) {G1,W8,D3,L2,V1,M2} { ! leq( X, antidomain( skol2 ) ), !
% 270.80/271.21 leq( domain( skol1 ), X ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 1 ==> 1
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150495) {G1,W16,D6,L1,V2,M1} { coantidomain( multiplication(
% 270.80/271.21 codomain( X ), Y ) ) ==> addition( coantidomain( multiplication( X, Y ) )
% 270.80/271.21 , coantidomain( multiplication( codomain( X ), Y ) ) ) }.
% 270.80/271.21 parent0[0]: (170) {G1,W16,D6,L1,V2,M1} S(18);d(20) { addition( coantidomain
% 270.80/271.21 ( multiplication( X, Y ) ), coantidomain( multiplication( codomain( X ),
% 270.80/271.21 Y ) ) ) ==> coantidomain( multiplication( codomain( X ), Y ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150498) {G1,W16,D7,L1,V1,M1} { coantidomain( multiplication(
% 270.80/271.21 codomain( antidomain( X ) ), X ) ) ==> addition( coantidomain( zero ),
% 270.80/271.21 coantidomain( multiplication( codomain( antidomain( X ) ), X ) ) ) }.
% 270.80/271.21 parent0[0]: (13) {G0,W6,D4,L1,V1,M1} I { multiplication( antidomain( X ), X
% 270.80/271.21 ) ==> zero }.
% 270.80/271.21 parent1[0; 9]: (150495) {G1,W16,D6,L1,V2,M1} { coantidomain(
% 270.80/271.21 multiplication( codomain( X ), Y ) ) ==> addition( coantidomain(
% 270.80/271.21 multiplication( X, Y ) ), coantidomain( multiplication( codomain( X ), Y
% 270.80/271.21 ) ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := antidomain( X )
% 270.80/271.21 Y := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150499) {G2,W15,D7,L1,V1,M1} { coantidomain( multiplication(
% 270.80/271.21 codomain( antidomain( X ) ), X ) ) ==> addition( one, coantidomain(
% 270.80/271.21 multiplication( codomain( antidomain( X ) ), X ) ) ) }.
% 270.80/271.21 parent0[0]: (533) {G3,W4,D3,L1,V0,M1} P(31,178);d(26);d(2) { coantidomain(
% 270.80/271.21 zero ) ==> one }.
% 270.80/271.21 parent1[0; 8]: (150498) {G1,W16,D7,L1,V1,M1} { coantidomain(
% 270.80/271.21 multiplication( codomain( antidomain( X ) ), X ) ) ==> addition(
% 270.80/271.21 coantidomain( zero ), coantidomain( multiplication( codomain( antidomain
% 270.80/271.21 ( X ) ), X ) ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150500) {G3,W8,D6,L1,V1,M1} { coantidomain( multiplication(
% 270.80/271.21 codomain( antidomain( X ) ), X ) ) ==> one }.
% 270.80/271.21 parent0[0]: (521) {G2,W6,D4,L1,V1,M1} P(178,30) { addition( one,
% 270.80/271.21 coantidomain( X ) ) ==> one }.
% 270.80/271.21 parent1[0; 7]: (150499) {G2,W15,D7,L1,V1,M1} { coantidomain(
% 270.80/271.21 multiplication( codomain( antidomain( X ) ), X ) ) ==> addition( one,
% 270.80/271.21 coantidomain( multiplication( codomain( antidomain( X ) ), X ) ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := multiplication( codomain( antidomain( X ) ), X )
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (5946) {G4,W8,D6,L1,V1,M1} P(13,170);d(533);d(521) {
% 270.80/271.21 coantidomain( multiplication( codomain( antidomain( X ) ), X ) ) ==> one
% 270.80/271.21 }.
% 270.80/271.21 parent0: (150500) {G3,W8,D6,L1,V1,M1} { coantidomain( multiplication(
% 270.80/271.21 codomain( antidomain( X ) ), X ) ) ==> one }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150503) {G1,W7,D3,L2,V1,M2} { leq( X, zero ), ! leq( one,
% 270.80/271.21 coantidomain( X ) ) }.
% 270.80/271.21 parent0[0]: (17) {G0,W6,D4,L1,V1,M1} I { multiplication( X, coantidomain( X
% 270.80/271.21 ) ) ==> zero }.
% 270.80/271.21 parent1[0; 2]: (2651) {G4,W8,D3,L2,V2,M2} P(88,674) { leq( Y,
% 270.80/271.21 multiplication( Y, X ) ), ! leq( one, X ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := coantidomain( X )
% 270.80/271.21 Y := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (6808) {G5,W7,D3,L2,V1,M2} P(17,2651) { leq( X, zero ), ! leq
% 270.80/271.21 ( one, coantidomain( X ) ) }.
% 270.80/271.21 parent0: (150503) {G1,W7,D3,L2,V1,M2} { leq( X, zero ), ! leq( one,
% 270.80/271.21 coantidomain( X ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 1 ==> 1
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 resolution: (150505) {G5,W9,D3,L2,V2,M2} { leq( X, addition( zero, Y ) ),
% 270.80/271.21 ! leq( one, coantidomain( X ) ) }.
% 270.80/271.21 parent0[1]: (463) {G4,W8,D3,L2,V3,M2} P(11,279) { leq( X, addition( Y, Z )
% 270.80/271.21 ), ! leq( X, Y ) }.
% 270.80/271.21 parent1[0]: (6808) {G5,W7,D3,L2,V1,M2} P(17,2651) { leq( X, zero ), ! leq(
% 270.80/271.21 one, coantidomain( X ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := zero
% 270.80/271.21 Z := Y
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150506) {G2,W7,D3,L2,V2,M2} { leq( X, Y ), ! leq( one,
% 270.80/271.21 coantidomain( X ) ) }.
% 270.80/271.21 parent0[0]: (23) {G1,W5,D3,L1,V1,M1} P(2,0) { addition( zero, X ) ==> X }.
% 270.80/271.21 parent1[0; 2]: (150505) {G5,W9,D3,L2,V2,M2} { leq( X, addition( zero, Y )
% 270.80/271.21 ), ! leq( one, coantidomain( X ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := Y
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (7181) {G6,W7,D3,L2,V2,M2} R(6808,463);d(23) { ! leq( one,
% 270.80/271.21 coantidomain( X ) ), leq( X, Y ) }.
% 270.80/271.21 parent0: (150506) {G2,W7,D3,L2,V2,M2} { leq( X, Y ), ! leq( one,
% 270.80/271.21 coantidomain( X ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 1
% 270.80/271.21 1 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150507) {G2,W9,D2,L3,V2,M3} { ! Y = X, leq( X, Y ), ! leq( Y, X )
% 270.80/271.21 }.
% 270.80/271.21 parent0[0]: (82) {G2,W9,D2,L3,V2,M3} P(11,63) { ! Y = X, leq( Y, X ), ! leq
% 270.80/271.21 ( X, Y ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := Y
% 270.80/271.21 Y := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150509) {G5,W8,D3,L2,V1,M2} { ! one ==> coantidomain( X ),
% 270.80/271.21 coantidomain( X ) ==> one }.
% 270.80/271.21 parent0[1]: (1608) {G5,W8,D3,L2,V1,M2} P(80,521);d(541) { coantidomain( X )
% 270.80/271.21 ==> one, ! coantidomain( X ) ==> one }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 resolution: (150511) {G3,W11,D3,L3,V2,M3} { leq( X, Y ), ! coantidomain( X
% 270.80/271.21 ) = one, ! leq( coantidomain( X ), one ) }.
% 270.80/271.21 parent0[0]: (7181) {G6,W7,D3,L2,V2,M2} R(6808,463);d(23) { ! leq( one,
% 270.80/271.21 coantidomain( X ) ), leq( X, Y ) }.
% 270.80/271.21 parent1[1]: (150507) {G2,W9,D2,L3,V2,M3} { ! Y = X, leq( X, Y ), ! leq( Y
% 270.80/271.21 , X ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := one
% 270.80/271.21 Y := coantidomain( X )
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150513) {G4,W14,D3,L4,V2,M4} { ! leq( one, one ), ! one ==>
% 270.80/271.21 coantidomain( X ), leq( X, Y ), ! coantidomain( X ) = one }.
% 270.80/271.21 parent0[1]: (150509) {G5,W8,D3,L2,V1,M2} { ! one ==> coantidomain( X ),
% 270.80/271.21 coantidomain( X ) ==> one }.
% 270.80/271.21 parent1[2; 2]: (150511) {G3,W11,D3,L3,V2,M3} { leq( X, Y ), ! coantidomain
% 270.80/271.21 ( X ) = one, ! leq( coantidomain( X ), one ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 resolution: (150538) {G2,W11,D3,L3,V2,M3} { ! one ==> coantidomain( X ),
% 270.80/271.21 leq( X, Y ), ! coantidomain( X ) = one }.
% 270.80/271.21 parent0[0]: (150513) {G4,W14,D3,L4,V2,M4} { ! leq( one, one ), ! one ==>
% 270.80/271.21 coantidomain( X ), leq( X, Y ), ! coantidomain( X ) = one }.
% 270.80/271.21 parent1[0]: (59) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := one
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150539) {G2,W11,D3,L3,V2,M3} { ! coantidomain( X ) ==> one, leq(
% 270.80/271.21 X, Y ), ! coantidomain( X ) = one }.
% 270.80/271.21 parent0[0]: (150538) {G2,W11,D3,L3,V2,M3} { ! one ==> coantidomain( X ),
% 270.80/271.21 leq( X, Y ), ! coantidomain( X ) = one }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 factor: (150542) {G2,W7,D3,L2,V2,M2} { ! coantidomain( X ) ==> one, leq( X
% 270.80/271.21 , Y ) }.
% 270.80/271.21 parent0[0, 2]: (150539) {G2,W11,D3,L3,V2,M3} { ! coantidomain( X ) ==> one
% 270.80/271.21 , leq( X, Y ), ! coantidomain( X ) = one }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (7459) {G7,W7,D3,L2,V2,M2} R(7181,82);d(1608);r(59) { leq( X,
% 270.80/271.21 Y ), ! coantidomain( X ) ==> one }.
% 270.80/271.21 parent0: (150542) {G2,W7,D3,L2,V2,M2} { ! coantidomain( X ) ==> one, leq(
% 270.80/271.21 X, Y ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 1
% 270.80/271.21 1 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150544) {G7,W7,D3,L2,V2,M2} { ! one ==> coantidomain( X ), leq( X
% 270.80/271.21 , Y ) }.
% 270.80/271.21 parent0[1]: (7459) {G7,W7,D3,L2,V2,M2} R(7181,82);d(1608);r(59) { leq( X, Y
% 270.80/271.21 ), ! coantidomain( X ) ==> one }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150545) {G3,W7,D3,L2,V1,M2} { X = zero, ! leq( codomain( X ),
% 270.80/271.21 zero ) }.
% 270.80/271.21 parent0[1]: (578) {G3,W7,D3,L2,V1,M2} P(87,548);d(9) { ! leq( codomain( X )
% 270.80/271.21 , zero ), zero = X }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 resolution: (150547) {G4,W8,D4,L2,V1,M2} { X = zero, ! one ==>
% 270.80/271.21 coantidomain( codomain( X ) ) }.
% 270.80/271.21 parent0[1]: (150545) {G3,W7,D3,L2,V1,M2} { X = zero, ! leq( codomain( X )
% 270.80/271.21 , zero ) }.
% 270.80/271.21 parent1[1]: (150544) {G7,W7,D3,L2,V2,M2} { ! one ==> coantidomain( X ),
% 270.80/271.21 leq( X, Y ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := codomain( X )
% 270.80/271.21 Y := zero
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150548) {G5,W7,D3,L2,V1,M2} { ! one ==> coantidomain( X ), X =
% 270.80/271.21 zero }.
% 270.80/271.21 parent0[0]: (1187) {G4,W6,D4,L1,V1,M1} P(178,74);d(6);d(582) { coantidomain
% 270.80/271.21 ( codomain( X ) ) ==> coantidomain( X ) }.
% 270.80/271.21 parent1[1; 3]: (150547) {G4,W8,D4,L2,V1,M2} { X = zero, ! one ==>
% 270.80/271.21 coantidomain( codomain( X ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150550) {G5,W7,D3,L2,V1,M2} { zero = X, ! one ==> coantidomain( X
% 270.80/271.21 ) }.
% 270.80/271.21 parent0[1]: (150548) {G5,W7,D3,L2,V1,M2} { ! one ==> coantidomain( X ), X
% 270.80/271.21 = zero }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150551) {G5,W7,D3,L2,V1,M2} { ! coantidomain( X ) ==> one, zero =
% 270.80/271.21 X }.
% 270.80/271.21 parent0[1]: (150550) {G5,W7,D3,L2,V1,M2} { zero = X, ! one ==>
% 270.80/271.21 coantidomain( X ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (7560) {G8,W7,D3,L2,V1,M2} R(7459,578);d(1187) { zero = X, !
% 270.80/271.21 coantidomain( X ) ==> one }.
% 270.80/271.21 parent0: (150551) {G5,W7,D3,L2,V1,M2} { ! coantidomain( X ) ==> one, zero
% 270.80/271.21 = X }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 1
% 270.80/271.21 1 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150553) {G1,W7,D3,L2,V1,M2} { leq( X, zero ), ! leq( one,
% 270.80/271.21 antidomain( X ) ) }.
% 270.80/271.21 parent0[0]: (13) {G0,W6,D4,L1,V1,M1} I { multiplication( antidomain( X ), X
% 270.80/271.21 ) ==> zero }.
% 270.80/271.21 parent1[0; 2]: (2621) {G4,W8,D3,L2,V2,M2} P(88,1518) { leq( Y,
% 270.80/271.21 multiplication( X, Y ) ), ! leq( one, X ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := antidomain( X )
% 270.80/271.21 Y := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (10029) {G5,W7,D3,L2,V1,M2} P(13,2621) { leq( X, zero ), ! leq
% 270.80/271.21 ( one, antidomain( X ) ) }.
% 270.80/271.21 parent0: (150553) {G1,W7,D3,L2,V1,M2} { leq( X, zero ), ! leq( one,
% 270.80/271.21 antidomain( X ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 1 ==> 1
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 resolution: (150555) {G5,W9,D3,L2,V2,M2} { leq( X, addition( zero, Y ) ),
% 270.80/271.21 ! leq( one, antidomain( X ) ) }.
% 270.80/271.21 parent0[1]: (463) {G4,W8,D3,L2,V3,M2} P(11,279) { leq( X, addition( Y, Z )
% 270.80/271.21 ), ! leq( X, Y ) }.
% 270.80/271.21 parent1[0]: (10029) {G5,W7,D3,L2,V1,M2} P(13,2621) { leq( X, zero ), ! leq
% 270.80/271.21 ( one, antidomain( X ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := zero
% 270.80/271.21 Z := Y
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150556) {G2,W7,D3,L2,V2,M2} { leq( X, Y ), ! leq( one,
% 270.80/271.21 antidomain( X ) ) }.
% 270.80/271.21 parent0[0]: (23) {G1,W5,D3,L1,V1,M1} P(2,0) { addition( zero, X ) ==> X }.
% 270.80/271.21 parent1[0; 2]: (150555) {G5,W9,D3,L2,V2,M2} { leq( X, addition( zero, Y )
% 270.80/271.21 ), ! leq( one, antidomain( X ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := Y
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (10135) {G6,W7,D3,L2,V2,M2} R(10029,463);d(23) { ! leq( one,
% 270.80/271.21 antidomain( X ) ), leq( X, Y ) }.
% 270.80/271.21 parent0: (150556) {G2,W7,D3,L2,V2,M2} { leq( X, Y ), ! leq( one,
% 270.80/271.21 antidomain( X ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 1
% 270.80/271.21 1 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150557) {G2,W9,D2,L3,V2,M3} { ! Y = X, leq( X, Y ), ! leq( Y, X )
% 270.80/271.21 }.
% 270.80/271.21 parent0[0]: (82) {G2,W9,D2,L3,V2,M3} P(11,63) { ! Y = X, leq( Y, X ), ! leq
% 270.80/271.21 ( X, Y ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := Y
% 270.80/271.21 Y := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150559) {G5,W8,D3,L2,V1,M2} { ! one ==> antidomain( X ),
% 270.80/271.21 antidomain( X ) ==> one }.
% 270.80/271.21 parent0[1]: (1639) {G5,W8,D3,L2,V1,M2} P(80,268);d(287) { antidomain( X )
% 270.80/271.21 ==> one, ! antidomain( X ) ==> one }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 resolution: (150561) {G3,W11,D3,L3,V2,M3} { leq( X, Y ), ! antidomain( X )
% 270.80/271.21 = one, ! leq( antidomain( X ), one ) }.
% 270.80/271.21 parent0[0]: (10135) {G6,W7,D3,L2,V2,M2} R(10029,463);d(23) { ! leq( one,
% 270.80/271.21 antidomain( X ) ), leq( X, Y ) }.
% 270.80/271.21 parent1[1]: (150557) {G2,W9,D2,L3,V2,M3} { ! Y = X, leq( X, Y ), ! leq( Y
% 270.80/271.21 , X ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := one
% 270.80/271.21 Y := antidomain( X )
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150563) {G4,W14,D3,L4,V2,M4} { ! leq( one, one ), ! one ==>
% 270.80/271.21 antidomain( X ), leq( X, Y ), ! antidomain( X ) = one }.
% 270.80/271.21 parent0[1]: (150559) {G5,W8,D3,L2,V1,M2} { ! one ==> antidomain( X ),
% 270.80/271.21 antidomain( X ) ==> one }.
% 270.80/271.21 parent1[2; 2]: (150561) {G3,W11,D3,L3,V2,M3} { leq( X, Y ), ! antidomain(
% 270.80/271.21 X ) = one, ! leq( antidomain( X ), one ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 resolution: (150588) {G2,W11,D3,L3,V2,M3} { ! one ==> antidomain( X ), leq
% 270.80/271.21 ( X, Y ), ! antidomain( X ) = one }.
% 270.80/271.21 parent0[0]: (150563) {G4,W14,D3,L4,V2,M4} { ! leq( one, one ), ! one ==>
% 270.80/271.21 antidomain( X ), leq( X, Y ), ! antidomain( X ) = one }.
% 270.80/271.21 parent1[0]: (59) {G1,W3,D2,L1,V1,M1} R(12,3) { leq( X, X ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := one
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150589) {G2,W11,D3,L3,V2,M3} { ! antidomain( X ) ==> one, leq( X
% 270.80/271.21 , Y ), ! antidomain( X ) = one }.
% 270.80/271.21 parent0[0]: (150588) {G2,W11,D3,L3,V2,M3} { ! one ==> antidomain( X ), leq
% 270.80/271.21 ( X, Y ), ! antidomain( X ) = one }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 factor: (150592) {G2,W7,D3,L2,V2,M2} { ! antidomain( X ) ==> one, leq( X,
% 270.80/271.21 Y ) }.
% 270.80/271.21 parent0[0, 2]: (150589) {G2,W11,D3,L3,V2,M3} { ! antidomain( X ) ==> one,
% 270.80/271.21 leq( X, Y ), ! antidomain( X ) = one }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (10572) {G7,W7,D3,L2,V2,M2} R(10135,82);d(1639);r(59) { leq( X
% 270.80/271.21 , Y ), ! antidomain( X ) ==> one }.
% 270.80/271.21 parent0: (150592) {G2,W7,D3,L2,V2,M2} { ! antidomain( X ) ==> one, leq( X
% 270.80/271.21 , Y ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 1
% 270.80/271.21 1 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150594) {G7,W7,D3,L2,V2,M2} { ! one ==> antidomain( X ), leq( X,
% 270.80/271.21 Y ) }.
% 270.80/271.21 parent0[1]: (10572) {G7,W7,D3,L2,V2,M2} R(10135,82);d(1639);r(59) { leq( X
% 270.80/271.21 , Y ), ! antidomain( X ) ==> one }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150595) {G3,W7,D3,L2,V1,M2} { X = zero, ! leq( domain( X ), zero
% 270.80/271.21 ) }.
% 270.80/271.21 parent0[1]: (1133) {G3,W7,D3,L2,V1,M2} P(87,1116);d(10) { ! leq( domain( X
% 270.80/271.21 ), zero ), zero = X }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 resolution: (150597) {G4,W8,D4,L2,V1,M2} { X = zero, ! one ==> antidomain
% 270.80/271.21 ( domain( X ) ) }.
% 270.80/271.21 parent0[1]: (150595) {G3,W7,D3,L2,V1,M2} { X = zero, ! leq( domain( X ),
% 270.80/271.21 zero ) }.
% 270.80/271.21 parent1[1]: (150594) {G7,W7,D3,L2,V2,M2} { ! one ==> antidomain( X ), leq
% 270.80/271.21 ( X, Y ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := domain( X )
% 270.80/271.21 Y := zero
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150598) {G5,W7,D3,L2,V1,M2} { ! one ==> antidomain( X ), X =
% 270.80/271.21 zero }.
% 270.80/271.21 parent0[0]: (1137) {G4,W6,D4,L1,V1,M1} P(32,1116);d(472) { antidomain(
% 270.80/271.21 domain( X ) ) ==> antidomain( X ) }.
% 270.80/271.21 parent1[1; 3]: (150597) {G4,W8,D4,L2,V1,M2} { X = zero, ! one ==>
% 270.80/271.21 antidomain( domain( X ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150600) {G5,W7,D3,L2,V1,M2} { zero = X, ! one ==> antidomain( X )
% 270.80/271.21 }.
% 270.80/271.21 parent0[1]: (150598) {G5,W7,D3,L2,V1,M2} { ! one ==> antidomain( X ), X =
% 270.80/271.21 zero }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150601) {G5,W7,D3,L2,V1,M2} { ! antidomain( X ) ==> one, zero = X
% 270.80/271.21 }.
% 270.80/271.21 parent0[1]: (150600) {G5,W7,D3,L2,V1,M2} { zero = X, ! one ==> antidomain
% 270.80/271.21 ( X ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (10680) {G8,W7,D3,L2,V1,M2} R(10572,1133);d(1137) { zero = X,
% 270.80/271.21 ! antidomain( X ) ==> one }.
% 270.80/271.21 parent0: (150601) {G5,W7,D3,L2,V1,M2} { ! antidomain( X ) ==> one, zero =
% 270.80/271.21 X }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 1
% 270.80/271.21 1 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 resolution: (150602) {G7,W8,D4,L1,V1,M1} { ! leq( domain( skol1 ),
% 270.80/271.21 multiplication( antidomain( skol2 ), domain( X ) ) ) }.
% 270.80/271.21 parent0[0]: (4913) {G6,W8,D3,L2,V1,M2} P(11,4595) { ! leq( X, antidomain(
% 270.80/271.21 skol2 ) ), ! leq( domain( skol1 ), X ) }.
% 270.80/271.21 parent1[0]: (888) {G6,W6,D4,L1,V2,M1} P(289,60);q;d(5) { leq(
% 270.80/271.21 multiplication( Y, domain( X ) ), Y ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := multiplication( antidomain( skol2 ), domain( X ) )
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 Y := antidomain( skol2 )
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (15619) {G7,W8,D4,L1,V1,M1} R(4913,888) { ! leq( domain( skol1
% 270.80/271.21 ), multiplication( antidomain( skol2 ), domain( X ) ) ) }.
% 270.80/271.21 parent0: (150602) {G7,W8,D4,L1,V1,M1} { ! leq( domain( skol1 ),
% 270.80/271.21 multiplication( antidomain( skol2 ), domain( X ) ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150603) {G4,W8,D5,L1,V0,M1} { one ==> antidomain( multiplication
% 270.80/271.21 ( domain( skol1 ), domain( skol2 ) ) ) }.
% 270.80/271.21 parent0[0]: (3255) {G4,W8,D5,L1,V0,M1} P(21,127);d(167);d(268) { antidomain
% 270.80/271.21 ( multiplication( domain( skol1 ), domain( skol2 ) ) ) ==> one }.
% 270.80/271.21 substitution0:
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150605) {G8,W7,D3,L2,V1,M2} { ! one ==> antidomain( X ), zero = X
% 270.80/271.21 }.
% 270.80/271.21 parent0[1]: (10680) {G8,W7,D3,L2,V1,M2} R(10572,1133);d(1137) { zero = X, !
% 270.80/271.21 antidomain( X ) ==> one }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150606) {G8,W7,D3,L2,V1,M2} { X = zero, ! one ==> antidomain( X )
% 270.80/271.21 }.
% 270.80/271.21 parent0[1]: (150605) {G8,W7,D3,L2,V1,M2} { ! one ==> antidomain( X ), zero
% 270.80/271.21 = X }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 resolution: (150607) {G5,W7,D4,L1,V0,M1} { multiplication( domain( skol1 )
% 270.80/271.21 , domain( skol2 ) ) = zero }.
% 270.80/271.21 parent0[1]: (150606) {G8,W7,D3,L2,V1,M2} { X = zero, ! one ==> antidomain
% 270.80/271.21 ( X ) }.
% 270.80/271.21 parent1[0]: (150603) {G4,W8,D5,L1,V0,M1} { one ==> antidomain(
% 270.80/271.21 multiplication( domain( skol1 ), domain( skol2 ) ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := multiplication( domain( skol1 ), domain( skol2 ) )
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (49354) {G9,W7,D4,L1,V0,M1} R(3255,10680) { multiplication(
% 270.80/271.21 domain( skol1 ), domain( skol2 ) ) ==> zero }.
% 270.80/271.21 parent0: (150607) {G5,W7,D4,L1,V0,M1} { multiplication( domain( skol1 ),
% 270.80/271.21 domain( skol2 ) ) = zero }.
% 270.80/271.21 substitution0:
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150609) {G2,W14,D4,L2,V2,M2} { ! multiplication( X, Y ) ==>
% 270.80/271.21 multiplication( addition( one, X ), Y ), leq( Y, multiplication( X, Y ) )
% 270.80/271.21 }.
% 270.80/271.21 parent0[0]: (927) {G2,W14,D4,L2,V2,M2} P(6,64) { ! multiplication( addition
% 270.80/271.21 ( one, Y ), X ) ==> multiplication( Y, X ), leq( X, multiplication( Y, X
% 270.80/271.21 ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := Y
% 270.80/271.21 Y := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 resolution: (150612) {G3,W13,D5,L1,V0,M1} { ! multiplication( antidomain(
% 270.80/271.21 skol2 ), domain( skol1 ) ) ==> multiplication( addition( one, antidomain
% 270.80/271.21 ( skol2 ) ), domain( skol1 ) ) }.
% 270.80/271.21 parent0[0]: (15619) {G7,W8,D4,L1,V1,M1} R(4913,888) { ! leq( domain( skol1
% 270.80/271.21 ), multiplication( antidomain( skol2 ), domain( X ) ) ) }.
% 270.80/271.21 parent1[1]: (150609) {G2,W14,D4,L2,V2,M2} { ! multiplication( X, Y ) ==>
% 270.80/271.21 multiplication( addition( one, X ), Y ), leq( Y, multiplication( X, Y ) )
% 270.80/271.21 }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := skol1
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := antidomain( skol2 )
% 270.80/271.21 Y := domain( skol1 )
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150613) {G3,W10,D4,L1,V0,M1} { ! multiplication( antidomain(
% 270.80/271.21 skol2 ), domain( skol1 ) ) ==> multiplication( one, domain( skol1 ) ) }.
% 270.80/271.21 parent0[0]: (268) {G2,W6,D4,L1,V1,M1} P(156,30) { addition( one, antidomain
% 270.80/271.21 ( X ) ) ==> one }.
% 270.80/271.21 parent1[0; 8]: (150612) {G3,W13,D5,L1,V0,M1} { ! multiplication(
% 270.80/271.21 antidomain( skol2 ), domain( skol1 ) ) ==> multiplication( addition( one
% 270.80/271.21 , antidomain( skol2 ) ), domain( skol1 ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := skol2
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150614) {G1,W8,D4,L1,V0,M1} { ! multiplication( antidomain(
% 270.80/271.21 skol2 ), domain( skol1 ) ) ==> domain( skol1 ) }.
% 270.80/271.21 parent0[0]: (6) {G0,W5,D3,L1,V1,M1} I { multiplication( one, X ) ==> X }.
% 270.80/271.21 parent1[0; 7]: (150613) {G3,W10,D4,L1,V0,M1} { ! multiplication(
% 270.80/271.21 antidomain( skol2 ), domain( skol1 ) ) ==> multiplication( one, domain(
% 270.80/271.21 skol1 ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := domain( skol1 )
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (56929) {G8,W8,D4,L1,V0,M1} R(927,15619);d(268);d(6) { !
% 270.80/271.21 multiplication( antidomain( skol2 ), domain( skol1 ) ) ==> domain( skol1
% 270.80/271.21 ) }.
% 270.80/271.21 parent0: (150614) {G1,W8,D4,L1,V0,M1} { ! multiplication( antidomain(
% 270.80/271.21 skol2 ), domain( skol1 ) ) ==> domain( skol1 ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150617) {G2,W11,D5,L1,V2,M1} { addition( one, Y ) ==> addition(
% 270.80/271.21 addition( antidomain( X ), Y ), domain( X ) ) }.
% 270.80/271.21 parent0[0]: (211) {G2,W11,D5,L1,V2,M1} P(156,27) { addition( addition(
% 270.80/271.21 antidomain( X ), Y ), domain( X ) ) ==> addition( one, Y ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150619) {G3,W12,D5,L1,V1,M1} { addition( one, codomain(
% 270.80/271.21 antidomain( X ) ) ) ==> addition( codomain( antidomain( X ) ), domain( X
% 270.80/271.21 ) ) }.
% 270.80/271.21 parent0[0]: (977) {G7,W10,D5,L1,V1,M1} R(948,11) { addition( antidomain( X
% 270.80/271.21 ), codomain( antidomain( X ) ) ) ==> codomain( antidomain( X ) ) }.
% 270.80/271.21 parent1[0; 7]: (150617) {G2,W11,D5,L1,V2,M1} { addition( one, Y ) ==>
% 270.80/271.21 addition( addition( antidomain( X ), Y ), domain( X ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 Y := codomain( antidomain( X ) )
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150620) {G4,W8,D5,L1,V1,M1} { one ==> addition( codomain(
% 270.80/271.21 antidomain( X ) ), domain( X ) ) }.
% 270.80/271.21 parent0[0]: (593) {G6,W6,D4,L1,V1,M1} P(540,0) { addition( one, codomain( X
% 270.80/271.21 ) ) ==> one }.
% 270.80/271.21 parent1[0; 1]: (150619) {G3,W12,D5,L1,V1,M1} { addition( one, codomain(
% 270.80/271.21 antidomain( X ) ) ) ==> addition( codomain( antidomain( X ) ), domain( X
% 270.80/271.21 ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := antidomain( X )
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150621) {G4,W8,D5,L1,V1,M1} { addition( codomain( antidomain( X )
% 270.80/271.21 ), domain( X ) ) ==> one }.
% 270.80/271.21 parent0[0]: (150620) {G4,W8,D5,L1,V1,M1} { one ==> addition( codomain(
% 270.80/271.21 antidomain( X ) ), domain( X ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (58463) {G8,W8,D5,L1,V1,M1} P(977,211);d(593) { addition(
% 270.80/271.21 codomain( antidomain( X ) ), domain( X ) ) ==> one }.
% 270.80/271.21 parent0: (150621) {G4,W8,D5,L1,V1,M1} { addition( codomain( antidomain( X
% 270.80/271.21 ) ), domain( X ) ) ==> one }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150623) {G2,W12,D5,L1,V2,M1} { multiplication( coantidomain( X )
% 270.80/271.21 , Y ) ==> multiplication( coantidomain( X ), addition( codomain( X ), Y )
% 270.80/271.21 ) }.
% 270.80/271.21 parent0[0]: (55) {G2,W12,D5,L1,V2,M1} P(25,7);d(23) { multiplication(
% 270.80/271.21 coantidomain( X ), addition( codomain( X ), Y ) ) ==> multiplication(
% 270.80/271.21 coantidomain( X ), Y ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150625) {G3,W12,D5,L1,V1,M1} { multiplication( coantidomain(
% 270.80/271.21 antidomain( X ) ), domain( X ) ) ==> multiplication( coantidomain(
% 270.80/271.21 antidomain( X ) ), one ) }.
% 270.80/271.21 parent0[0]: (58463) {G8,W8,D5,L1,V1,M1} P(977,211);d(593) { addition(
% 270.80/271.21 codomain( antidomain( X ) ), domain( X ) ) ==> one }.
% 270.80/271.21 parent1[0; 11]: (150623) {G2,W12,D5,L1,V2,M1} { multiplication(
% 270.80/271.21 coantidomain( X ), Y ) ==> multiplication( coantidomain( X ), addition(
% 270.80/271.21 codomain( X ), Y ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := antidomain( X )
% 270.80/271.21 Y := domain( X )
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150626) {G1,W10,D5,L1,V1,M1} { multiplication( coantidomain(
% 270.80/271.21 antidomain( X ) ), domain( X ) ) ==> coantidomain( antidomain( X ) ) }.
% 270.80/271.21 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 270.80/271.21 parent1[0; 7]: (150625) {G3,W12,D5,L1,V1,M1} { multiplication(
% 270.80/271.21 coantidomain( antidomain( X ) ), domain( X ) ) ==> multiplication(
% 270.80/271.21 coantidomain( antidomain( X ) ), one ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := coantidomain( antidomain( X ) )
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (58938) {G9,W10,D5,L1,V1,M1} P(58463,55);d(5) { multiplication
% 270.80/271.21 ( coantidomain( antidomain( X ) ), domain( X ) ) ==> coantidomain(
% 270.80/271.21 antidomain( X ) ) }.
% 270.80/271.21 parent0: (150626) {G1,W10,D5,L1,V1,M1} { multiplication( coantidomain(
% 270.80/271.21 antidomain( X ) ), domain( X ) ) ==> coantidomain( antidomain( X ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150628) {G4,W8,D6,L1,V1,M1} { one ==> coantidomain(
% 270.80/271.21 multiplication( codomain( antidomain( X ) ), X ) ) }.
% 270.80/271.21 parent0[0]: (5946) {G4,W8,D6,L1,V1,M1} P(13,170);d(533);d(521) {
% 270.80/271.21 coantidomain( multiplication( codomain( antidomain( X ) ), X ) ) ==> one
% 270.80/271.21 }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150630) {G8,W7,D3,L2,V1,M2} { ! one ==> coantidomain( X ), zero =
% 270.80/271.21 X }.
% 270.80/271.21 parent0[1]: (7560) {G8,W7,D3,L2,V1,M2} R(7459,578);d(1187) { zero = X, !
% 270.80/271.21 coantidomain( X ) ==> one }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150631) {G8,W7,D3,L2,V1,M2} { X = zero, ! one ==> coantidomain( X
% 270.80/271.21 ) }.
% 270.80/271.21 parent0[1]: (150630) {G8,W7,D3,L2,V1,M2} { ! one ==> coantidomain( X ),
% 270.80/271.21 zero = X }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 resolution: (150632) {G5,W7,D5,L1,V1,M1} { multiplication( codomain(
% 270.80/271.21 antidomain( X ) ), X ) = zero }.
% 270.80/271.21 parent0[1]: (150631) {G8,W7,D3,L2,V1,M2} { X = zero, ! one ==>
% 270.80/271.21 coantidomain( X ) }.
% 270.80/271.21 parent1[0]: (150628) {G4,W8,D6,L1,V1,M1} { one ==> coantidomain(
% 270.80/271.21 multiplication( codomain( antidomain( X ) ), X ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := multiplication( codomain( antidomain( X ) ), X )
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (65418) {G9,W7,D5,L1,V1,M1} R(5946,7560) { multiplication(
% 270.80/271.21 codomain( antidomain( X ) ), X ) ==> zero }.
% 270.80/271.21 parent0: (150632) {G5,W7,D5,L1,V1,M1} { multiplication( codomain(
% 270.80/271.21 antidomain( X ) ), X ) = zero }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150635) {G9,W7,D5,L1,V1,M1} { zero ==> multiplication( codomain(
% 270.80/271.21 antidomain( X ) ), X ) }.
% 270.80/271.21 parent0[0]: (65418) {G9,W7,D5,L1,V1,M1} R(5946,7560) { multiplication(
% 270.80/271.21 codomain( antidomain( X ) ), X ) ==> zero }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150636) {G5,W8,D5,L1,V1,M1} { zero ==> multiplication( codomain
% 270.80/271.21 ( antidomain( X ) ), domain( X ) ) }.
% 270.80/271.21 parent0[0]: (1137) {G4,W6,D4,L1,V1,M1} P(32,1116);d(472) { antidomain(
% 270.80/271.21 domain( X ) ) ==> antidomain( X ) }.
% 270.80/271.21 parent1[0; 4]: (150635) {G9,W7,D5,L1,V1,M1} { zero ==> multiplication(
% 270.80/271.21 codomain( antidomain( X ) ), X ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := domain( X )
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150637) {G5,W8,D5,L1,V1,M1} { multiplication( codomain(
% 270.80/271.21 antidomain( X ) ), domain( X ) ) ==> zero }.
% 270.80/271.21 parent0[0]: (150636) {G5,W8,D5,L1,V1,M1} { zero ==> multiplication(
% 270.80/271.21 codomain( antidomain( X ) ), domain( X ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (65554) {G10,W8,D5,L1,V1,M1} P(1137,65418) { multiplication(
% 270.80/271.21 codomain( antidomain( X ) ), domain( X ) ) ==> zero }.
% 270.80/271.21 parent0: (150637) {G5,W8,D5,L1,V1,M1} { multiplication( codomain(
% 270.80/271.21 antidomain( X ) ), domain( X ) ) ==> zero }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 permutation0:
% 270.80/271.21 0 ==> 0
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150639) {G2,W15,D4,L2,V2,M2} { Y ==> multiplication( coantidomain
% 270.80/271.21 ( X ), Y ), ! leq( multiplication( codomain( X ), Y ), multiplication(
% 270.80/271.21 coantidomain( X ), Y ) ) }.
% 270.80/271.21 parent0[1]: (1717) {G2,W15,D4,L2,V2,M2} P(178,83);d(6) { ! leq(
% 270.80/271.21 multiplication( codomain( X ), Y ), multiplication( coantidomain( X ), Y
% 270.80/271.21 ) ), multiplication( coantidomain( X ), Y ) ==> Y }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 Y := Y
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150642) {G3,W17,D5,L2,V1,M2} { ! leq( zero, multiplication(
% 270.80/271.21 coantidomain( antidomain( X ) ), domain( X ) ) ), domain( X ) ==>
% 270.80/271.21 multiplication( coantidomain( antidomain( X ) ), domain( X ) ) }.
% 270.80/271.21 parent0[0]: (65554) {G10,W8,D5,L1,V1,M1} P(1137,65418) { multiplication(
% 270.80/271.21 codomain( antidomain( X ) ), domain( X ) ) ==> zero }.
% 270.80/271.21 parent1[1; 2]: (150639) {G2,W15,D4,L2,V2,M2} { Y ==> multiplication(
% 270.80/271.21 coantidomain( X ), Y ), ! leq( multiplication( codomain( X ), Y ),
% 270.80/271.21 multiplication( coantidomain( X ), Y ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := antidomain( X )
% 270.80/271.21 Y := domain( X )
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150644) {G4,W14,D5,L2,V1,M2} { domain( X ) ==> coantidomain(
% 270.80/271.21 antidomain( X ) ), ! leq( zero, multiplication( coantidomain( antidomain
% 270.80/271.21 ( X ) ), domain( X ) ) ) }.
% 270.80/271.21 parent0[0]: (58938) {G9,W10,D5,L1,V1,M1} P(58463,55);d(5) { multiplication
% 270.80/271.21 ( coantidomain( antidomain( X ) ), domain( X ) ) ==> coantidomain(
% 270.80/271.21 antidomain( X ) ) }.
% 270.80/271.21 parent1[1; 3]: (150642) {G3,W17,D5,L2,V1,M2} { ! leq( zero, multiplication
% 270.80/271.21 ( coantidomain( antidomain( X ) ), domain( X ) ) ), domain( X ) ==>
% 270.80/271.21 multiplication( coantidomain( antidomain( X ) ), domain( X ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 paramod: (150646) {G5,W11,D4,L2,V1,M2} { ! leq( zero, coantidomain(
% 270.80/271.21 antidomain( X ) ) ), domain( X ) ==> coantidomain( antidomain( X ) ) }.
% 270.80/271.21 parent0[0]: (58938) {G9,W10,D5,L1,V1,M1} P(58463,55);d(5) { multiplication
% 270.80/271.21 ( coantidomain( antidomain( X ) ), domain( X ) ) ==> coantidomain(
% 270.80/271.21 antidomain( X ) ) }.
% 270.80/271.21 parent1[1; 3]: (150644) {G4,W14,D5,L2,V1,M2} { domain( X ) ==>
% 270.80/271.21 coantidomain( antidomain( X ) ), ! leq( zero, multiplication(
% 270.80/271.21 coantidomain( antidomain( X ) ), domain( X ) ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 resolution: (150647) {G3,W6,D4,L1,V1,M1} { domain( X ) ==> coantidomain(
% 270.80/271.21 antidomain( X ) ) }.
% 270.80/271.21 parent0[0]: (150646) {G5,W11,D4,L2,V1,M2} { ! leq( zero, coantidomain(
% 270.80/271.21 antidomain( X ) ) ), domain( X ) ==> coantidomain( antidomain( X ) ) }.
% 270.80/271.21 parent1[0]: (58) {G2,W3,D2,L1,V1,M1} R(12,23) { leq( zero, X ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21 substitution1:
% 270.80/271.21 X := coantidomain( antidomain( X ) )
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 eqswap: (150648) {G3,W6,D4,L1,V1,M1} { coantidomain( antidomain( X ) ) ==>
% 270.80/271.21 domain( X ) }.
% 270.80/271.21 parent0[0]: (150647) {G3,W6,D4,L1,V1,M1} { domain( X ) ==> coantidomain(
% 270.80/271.21 antidomain( X ) ) }.
% 270.80/271.21 substitution0:
% 270.80/271.21 X := X
% 270.80/271.21 end
% 270.80/271.21
% 270.80/271.21 subsumption: (147688) {G11,W6,D4,L1,V1,M1} P(65554,1717);d(58938);d(58938);
% 270.80/271.21 r(58) { coantidomain( antidomain( X ) ) ==> domain( X ) }.
% 270.80/271.21 parent0: (150648) {G3,W6,D4,L1,V1,M1} { coantidomain( antidomain( X ) )
% 270.80/271.21 ==> domain( X ) }.
% 270.80/271.22 substitution0:
% 270.80/271.22 X := X
% 270.80/271.22 end
% 270.80/271.22 permutation0:
% 270.80/271.22 0 ==> 0
% 270.80/271.22 end
% 270.80/271.22
% 270.80/271.22 eqswap: (150650) {G2,W15,D4,L2,V2,M2} { Y ==> multiplication( antidomain(
% 270.80/271.22 X ), Y ), ! leq( multiplication( domain( X ), Y ), multiplication(
% 270.80/271.22 antidomain( X ), Y ) ) }.
% 270.80/271.22 parent0[1]: (1720) {G2,W15,D4,L2,V2,M2} P(156,83);d(6) { ! leq(
% 270.80/271.22 multiplication( domain( X ), Y ), multiplication( antidomain( X ), Y ) )
% 270.80/271.22 , multiplication( antidomain( X ), Y ) ==> Y }.
% 270.80/271.22 substitution0:
% 270.80/271.22 X := X
% 270.80/271.22 Y := Y
% 270.80/271.22 end
% 270.80/271.22
% 270.80/271.22 paramod: (150651) {G3,W15,D4,L2,V0,M2} { ! leq( zero, multiplication(
% 270.80/271.22 antidomain( skol1 ), domain( skol2 ) ) ), domain( skol2 ) ==>
% 270.80/271.22 multiplication( antidomain( skol1 ), domain( skol2 ) ) }.
% 270.80/271.22 parent0[0]: (49354) {G9,W7,D4,L1,V0,M1} R(3255,10680) { multiplication(
% 270.80/271.22 domain( skol1 ), domain( skol2 ) ) ==> zero }.
% 270.80/271.22 parent1[1; 2]: (150650) {G2,W15,D4,L2,V2,M2} { Y ==> multiplication(
% 270.80/271.22 antidomain( X ), Y ), ! leq( multiplication( domain( X ), Y ),
% 270.80/271.22 multiplication( antidomain( X ), Y ) ) }.
% 270.80/271.22 substitution0:
% 270.80/271.22 end
% 270.80/271.22 substitution1:
% 270.80/271.22 X := skol1
% 270.80/271.22 Y := domain( skol2 )
% 270.80/271.22 end
% 270.80/271.22
% 270.80/271.22 resolution: (150652) {G3,W8,D4,L1,V0,M1} { domain( skol2 ) ==>
% 270.80/271.22 multiplication( antidomain( skol1 ), domain( skol2 ) ) }.
% 270.80/271.22 parent0[0]: (150651) {G3,W15,D4,L2,V0,M2} { ! leq( zero, multiplication(
% 270.80/271.22 antidomain( skol1 ), domain( skol2 ) ) ), domain( skol2 ) ==>
% 270.80/271.22 multiplication( antidomain( skol1 ), domain( skol2 ) ) }.
% 270.80/271.22 parent1[0]: (58) {G2,W3,D2,L1,V1,M1} R(12,23) { leq( zero, X ) }.
% 270.80/271.22 substitution0:
% 270.80/271.22 end
% 270.80/271.22 substitution1:
% 270.80/271.22 X := multiplication( antidomain( skol1 ), domain( skol2 ) )
% 270.80/271.22 end
% 270.80/271.22
% 270.80/271.22 eqswap: (150653) {G3,W8,D4,L1,V0,M1} { multiplication( antidomain( skol1 )
% 270.80/271.22 , domain( skol2 ) ) ==> domain( skol2 ) }.
% 270.80/271.22 parent0[0]: (150652) {G3,W8,D4,L1,V0,M1} { domain( skol2 ) ==>
% 270.80/271.22 multiplication( antidomain( skol1 ), domain( skol2 ) ) }.
% 270.80/271.22 substitution0:
% 270.80/271.22 end
% 270.80/271.22
% 270.80/271.22 subsumption: (148025) {G10,W8,D4,L1,V0,M1} P(49354,1720);r(58) {
% 270.80/271.22 multiplication( antidomain( skol1 ), domain( skol2 ) ) ==> domain( skol2
% 270.80/271.22 ) }.
% 270.80/271.22 parent0: (150653) {G3,W8,D4,L1,V0,M1} { multiplication( antidomain( skol1
% 270.80/271.22 ), domain( skol2 ) ) ==> domain( skol2 ) }.
% 270.80/271.22 substitution0:
% 270.80/271.22 end
% 270.80/271.22 permutation0:
% 270.80/271.22 0 ==> 0
% 270.80/271.22 end
% 270.80/271.22
% 270.80/271.22 eqswap: (150655) {G2,W12,D4,L2,V2,M2} { ! X ==> multiplication( X,
% 270.80/271.22 addition( Y, one ) ), leq( multiplication( X, Y ), X ) }.
% 270.80/271.22 parent0[0]: (690) {G2,W12,D4,L2,V2,M2} P(54,12) { ! multiplication( X,
% 270.80/271.22 addition( Y, one ) ) ==> X, leq( multiplication( X, Y ), X ) }.
% 270.80/271.22 substitution0:
% 270.80/271.22 X := X
% 270.80/271.22 Y := Y
% 270.80/271.22 end
% 270.80/271.22
% 270.80/271.22 paramod: (150658) {G3,W15,D5,L2,V0,M2} { leq( domain( skol2 ), antidomain
% 270.80/271.22 ( skol1 ) ), ! antidomain( skol1 ) ==> multiplication( antidomain( skol1
% 270.80/271.22 ), addition( domain( skol2 ), one ) ) }.
% 270.80/271.22 parent0[0]: (148025) {G10,W8,D4,L1,V0,M1} P(49354,1720);r(58) {
% 270.80/271.22 multiplication( antidomain( skol1 ), domain( skol2 ) ) ==> domain( skol2
% 270.80/271.22 ) }.
% 270.80/271.22 parent1[1; 1]: (150655) {G2,W12,D4,L2,V2,M2} { ! X ==> multiplication( X,
% 270.80/271.22 addition( Y, one ) ), leq( multiplication( X, Y ), X ) }.
% 270.80/271.22 substitution0:
% 270.80/271.22 end
% 270.80/271.22 substitution1:
% 270.80/271.22 X := antidomain( skol1 )
% 270.80/271.22 Y := domain( skol2 )
% 270.80/271.22 end
% 270.80/271.22
% 270.80/271.22 paramod: (150659) {G4,W12,D4,L2,V0,M2} { ! antidomain( skol1 ) ==>
% 270.80/271.22 multiplication( antidomain( skol1 ), one ), leq( domain( skol2 ),
% 270.80/271.22 antidomain( skol1 ) ) }.
% 270.80/271.22 parent0[0]: (289) {G5,W6,D4,L1,V1,M1} R(288,11) { addition( domain( X ),
% 270.80/271.22 one ) ==> one }.
% 270.80/271.22 parent1[1; 7]: (150658) {G3,W15,D5,L2,V0,M2} { leq( domain( skol2 ),
% 270.80/271.22 antidomain( skol1 ) ), ! antidomain( skol1 ) ==> multiplication(
% 270.80/271.22 antidomain( skol1 ), addition( domain( skol2 ), one ) ) }.
% 270.80/271.22 substitution0:
% 270.80/271.22 X := skol2
% 270.80/271.22 end
% 270.80/271.22 substitution1:
% 270.80/271.22 end
% 270.80/271.22
% 270.80/271.22 paramod: (150660) {G1,W10,D3,L2,V0,M2} { ! antidomain( skol1 ) ==>
% 270.80/271.22 antidomain( skol1 ), leq( domain( skol2 ), antidomain( skol1 ) ) }.
% 270.80/271.22 parent0[0]: (5) {G0,W5,D3,L1,V1,M1} I { multiplication( X, one ) ==> X }.
% 270.80/271.22 parent1[0; 4]: (150659) {G4,W12,D4,L2,V0,M2} { ! antidomain( skol1 ) ==>
% 270.80/271.22 multiplication( antidomain( skol1 ), one ), leq( domain( skol2 ),
% 270.80/271.22 antidomain( skol1 ) ) }.
% 270.80/271.22 substitution0:
% 270.80/271.22 X := antidomain( skol1 )
% 270.80/271.22 end
% 270.80/271.22 substitution1:
% 270.80/271.22 end
% 270.80/271.22
% 270.80/271.22 eqrefl: (150661) {G0,W5,D3,L1,V0,M1} { leq( domain( skol2 ), antidomain(
% 270.80/271.22 skol1 ) ) }.
% 270.80/271.22 parent0[0]: (150660) {G1,W10,D3,L2,V0,M2} { ! antidomain( skol1 ) ==>
% 270.80/271.22 antidomain( skol1 ), leq( domain( skol2 ), antidomain( skol1 ) ) }.
% 270.80/271.22 substitution0:
% 270.80/271.22 end
% 270.80/271.22
% 270.80/271.22 subsumption: (148464) {G11,W5,D3,L1,V0,M1} P(148025,690);d(289);d(5);q {
% 270.80/271.22 leq( domain( skol2 ), antidomain( skol1 ) ) }.
% 270.80/271.22 parent0: (150661) {G0,W5,D3,L1,V0,M1} { leq( domain( skol2 ), antidomain(
% 270.80/271.22 skol1 ) ) }.
% 270.80/271.22 substitution0:
% 270.80/271.22 end
% 270.80/271.22 permutation0:
% 270.80/271.22 0 ==> 0
% 270.80/271.22 end
% 270.80/271.22
% 270.80/271.22 eqswap: (150662) {G2,W9,D4,L2,V2,M2} { zero ==> multiplication( X,
% 270.80/271.22 coantidomain( Y ) ), ! leq( X, Y ) }.
% 270.80/271.22 parent0[1]: (1217) {G2,W9,D4,L2,V2,M2} P(11,75);d(17) { ! leq( X, Y ),
% 270.80/271.22 multiplication( X, coantidomain( Y ) ) ==> zero }.
% 270.80/271.22 substitution0:
% 270.80/271.22 X := X
% 270.80/271.22 Y := Y
% 270.80/271.22 end
% 270.80/271.22
% 270.80/271.22 resolution: (150664) {G3,W8,D5,L1,V0,M1} { zero ==> multiplication( domain
% 270.80/271.22 ( skol2 ), coantidomain( antidomain( skol1 ) ) ) }.
% 270.80/271.22 parent0[1]: (150662) {G2,W9,D4,L2,V2,M2} { zero ==> multiplication( X,
% 270.80/271.22 coantidomain( Y ) ), ! leq( X, Y ) }.
% 270.80/271.22 parent1[0]: (148464) {G11,W5,D3,L1,V0,M1} P(148025,690);d(289);d(5);q { leq
% 270.80/271.22 ( domain( skol2 ), antidomain( skol1 ) ) }.
% 270.80/271.22 substitution0:
% 270.80/271.22 X := domain( skol2 )
% 270.80/271.22 Y := antidomain( skol1 )
% 270.80/271.22 end
% 270.80/271.22 substitution1:
% 270.80/271.22 end
% 270.80/271.22
% 270.80/271.22 paramod: (150665) {G4,W7,D4,L1,V0,M1} { zero ==> multiplication( domain(
% 270.80/271.22 skol2 ), domain( skol1 ) ) }.
% 270.80/271.22 parent0[0]: (147688) {G11,W6,D4,L1,V1,M1} P(65554,1717);d(58938);d(58938);r
% 270.80/271.22 (58) { coantidomain( antidomain( X ) ) ==> domain( X ) }.
% 270.80/271.22 parent1[0; 5]: (150664) {G3,W8,D5,L1,V0,M1} { zero ==> multiplication(
% 270.80/271.22 domain( skol2 ), coantidomain( antidomain( skol1 ) ) ) }.
% 270.80/271.22 substitution0:
% 270.80/271.22 X := skol1
% 270.80/271.22 end
% 270.80/271.22 substitution1:
% 270.80/271.22 end
% 270.80/271.22
% 270.80/271.22 eqswap: (150666) {G4,W7,D4,L1,V0,M1} { multiplication( domain( skol2 ),
% 270.80/271.22 domain( skol1 ) ) ==> zero }.
% 270.80/271.22 parent0[0]: (150665) {G4,W7,D4,L1,V0,M1} { zero ==> multiplication( domain
% 270.80/271.22 ( skol2 ), domain( skol1 ) ) }.
% 270.80/271.22 substitution0:
% 270.80/271.22 end
% 270.80/271.22
% 270.80/271.22 subsumption: (148522) {G12,W7,D4,L1,V0,M1} R(148464,1217);d(147688) {
% 270.80/271.22 multiplication( domain( skol2 ), domain( skol1 ) ) ==> zero }.
% 270.80/271.22 parent0: (150666) {G4,W7,D4,L1,V0,M1} { multiplication( domain( skol2 ),
% 270.80/271.22 domain( skol1 ) ) ==> zero }.
% 270.80/271.22 substitution0:
% 270.80/271.22 end
% 270.80/271.22 permutation0:
% 270.80/271.22 0 ==> 0
% 270.80/271.22 end
% 270.80/271.22
% 270.80/271.22 eqswap: (150668) {G2,W15,D4,L2,V2,M2} { Y ==> multiplication( antidomain(
% 270.80/271.22 X ), Y ), ! leq( multiplication( domain( X ), Y ), multiplication(
% 270.80/271.22 antidomain( X ), Y ) ) }.
% 270.80/271.22 parent0[1]: (1720) {G2,W15,D4,L2,V2,M2} P(156,83);d(6) { ! leq(
% 270.80/271.22 multiplication( domain( X ), Y ), multiplication( antidomain( X ), Y ) )
% 270.80/271.22 , multiplication( antidomain( X ), Y ) ==> Y }.
% 270.80/271.22 substitution0:
% 270.80/271.22 X := X
% 270.80/271.22 Y := Y
% 270.80/271.22 end
% 270.80/271.22
% 270.80/271.22 paramod: (150669) {G3,W15,D4,L2,V0,M2} { ! leq( zero, multiplication(
% 270.80/271.22 antidomain( skol2 ), domain( skol1 ) ) ), domain( skol1 ) ==>
% 270.80/271.22 multiplication( antidomain( skol2 ), domain( skol1 ) ) }.
% 270.80/271.22 parent0[0]: (148522) {G12,W7,D4,L1,V0,M1} R(148464,1217);d(147688) {
% 270.80/271.22 multiplication( domain( skol2 ), domain( skol1 ) ) ==> zero }.
% 270.80/271.22 parent1[1; 2]: (150668) {G2,W15,D4,L2,V2,M2} { Y ==> multiplication(
% 270.80/271.22 antidomain( X ), Y ), ! leq( multiplication( domain( X ), Y ),
% 270.80/271.22 multiplication( antidomain( X ), Y ) ) }.
% 270.80/271.22 substitution0:
% 270.80/271.22 end
% 270.80/271.22 substitution1:
% 270.80/271.22 X := skol2
% 270.80/271.22 Y := domain( skol1 )
% 270.80/271.22 end
% 270.80/271.22
% 270.80/271.22 resolution: (150670) {G3,W8,D4,L1,V0,M1} { domain( skol1 ) ==>
% 270.80/271.22 multiplication( antidomain( skol2 ), domain( skol1 ) ) }.
% 270.80/271.22 parent0[0]: (150669) {G3,W15,D4,L2,V0,M2} { ! leq( zero, multiplication(
% 270.80/271.22 antidomain( skol2 ), domain( skol1 ) ) ), domain( skol1 ) ==>
% 270.80/271.22 multiplication( antidomain( skol2 ), domain( skol1 ) ) }.
% 270.80/271.22 parent1[0]: (58) {G2,W3,D2,L1,V1,M1} R(12,23) { leq( zero, X ) }.
% 270.80/271.22 substitution0:
% 270.80/271.22 end
% 270.80/271.22 substitution1:
% 270.80/271.22 X := multiplication( antidomain( skol2 ), domain( skol1 ) )
% 270.80/271.22 end
% 270.80/271.22
% 270.80/271.22 eqswap: (150671) {G3,W8,D4,L1,V0,M1} { multiplication( antidomain( skol2 )
% 270.80/271.22 , domain( skol1 ) ) ==> domain( skol1 ) }.
% 270.80/271.22 parent0[0]: (150670) {G3,W8,D4,L1,V0,M1} { domain( skol1 ) ==>
% 270.80/271.22 multiplication( antidomain( skol2 ), domain( skol1 ) ) }.
% 270.80/271.22 substitution0:
% 270.80/271.22 end
% 270.80/271.22
% 270.80/271.22 subsumption: (149605) {G13,W8,D4,L1,V0,M1} P(148522,1720);r(58) {
% 270.80/271.22 multiplication( antidomain( skol2 ), domain( skol1 ) ) ==> domain( skol1
% 270.80/271.22 ) }.
% 270.80/271.22 parent0: (150671) {G3,W8,D4,L1,V0,M1} { multiplication( antidomain( skol2
% 270.80/271.22 ), domain( skol1 ) ) ==> domain( skol1 ) }.
% 270.80/271.22 substitution0:
% 270.80/271.22 end
% 270.80/271.22 permutation0:
% 270.80/271.22 0 ==> 0
% 270.80/271.22 end
% 270.80/271.22
% 270.80/271.22 paramod: (150674) {G9,W5,D3,L1,V0,M1} { ! domain( skol1 ) ==> domain(
% 270.80/271.22 skol1 ) }.
% 270.80/271.22 parent0[0]: (149605) {G13,W8,D4,L1,V0,M1} P(148522,1720);r(58) {
% 270.80/271.22 multiplication( antidomain( skol2 ), domain( skol1 ) ) ==> domain( skol1
% 270.80/271.22 ) }.
% 270.80/271.22 parent1[0; 2]: (56929) {G8,W8,D4,L1,V0,M1} R(927,15619);d(268);d(6) { !
% 270.80/271.22 multiplication( antidomain( skol2 ), domain( skol1 ) ) ==> domain( skol1
% 270.80/271.22 ) }.
% 270.80/271.22 substitution0:
% 270.80/271.22 end
% 270.80/271.22 substitution1:
% 270.80/271.22 end
% 270.80/271.22
% 270.80/271.22 eqrefl: (150675) {G0,W0,D0,L0,V0,M0} { }.
% 270.80/271.22 parent0[0]: (150674) {G9,W5,D3,L1,V0,M1} { ! domain( skol1 ) ==> domain(
% 270.80/271.22 skol1 ) }.
% 270.80/271.22 substitution0:
% 270.80/271.22 end
% 270.80/271.22
% 270.80/271.22 subsumption: (149766) {G14,W0,D0,L0,V0,M0} S(56929);d(149605);q { }.
% 270.80/271.22 parent0: (150675) {G0,W0,D0,L0,V0,M0} { }.
% 270.80/271.22 substitution0:
% 270.80/271.22 end
% 270.80/271.22 permutation0:
% 270.80/271.22 end
% 270.80/271.22
% 270.80/271.22 Proof check complete!
% 270.80/271.22
% 270.80/271.22 Memory use:
% 270.80/271.22
% 270.80/271.22 space for terms: 2126648
% 270.80/271.22 space for clauses: 7267145
% 270.80/271.22
% 270.80/271.22
% 270.80/271.22 clauses generated: 2908698
% 270.80/271.22 clauses kept: 149767
% 270.80/271.22 clauses selected: 4822
% 270.80/271.22 clauses deleted: 10101
% 270.80/271.22 clauses inuse deleted: 2086
% 270.80/271.22
% 270.80/271.22 subsentry: 30774121
% 270.80/271.22 literals s-matched: 9712914
% 270.80/271.22 literals matched: 9114643
% 270.80/271.22 full subsumption: 3153050
% 270.80/271.22
% 270.80/271.22 checksum: -671381223
% 270.80/271.22
% 270.80/271.22
% 270.80/271.22 Bliksem ended
%------------------------------------------------------------------------------