TSTP Solution File: GRP039-5 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GRP039-5 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n011.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 : Sat Jul 16 07:34:31 EDT 2022
% Result : Unsatisfiable 246.44s 246.82s
% Output : Refutation 246.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP039-5 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.12 % Command : bliksem %s
% 0.13/0.33 % Computer : n011.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % DateTime : Mon Jun 13 22:31:04 EDT 2022
% 0.13/0.33 % CPUTime :
% 116.20/116.55 *** allocated 10000 integers for termspace/termends
% 116.20/116.55 *** allocated 10000 integers for clauses
% 116.20/116.55 *** allocated 10000 integers for justifications
% 116.20/116.55 Bliksem 1.12
% 116.20/116.55
% 116.20/116.55
% 116.20/116.55 Automatic Strategy Selection
% 116.20/116.55
% 116.20/116.55 Clauses:
% 116.20/116.55 [
% 116.20/116.55 [ =( multiply( identity, X ), X ) ],
% 116.20/116.55 [ =( multiply( inverse( X ), X ), identity ) ],
% 116.20/116.55 [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply( Y, Z ) ) )
% 116.20/116.55 ],
% 116.20/116.55 [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( inverse( X ) ) ],
% 116.20/116.55 [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( Y ) ), ~( =(
% 116.20/116.55 multiply( X, Y ), Z ) ), 'subgroup_member'( Z ) ],
% 116.20/116.55 [ =( multiply( X, identity ), X ) ],
% 116.20/116.55 [ =( multiply( X, inverse( X ) ), identity ) ],
% 116.20/116.55 [ 'subgroup_member'( identity ) ],
% 116.20/116.55 [ 'subgroup_member'( X ), 'subgroup_member'( Y ), 'subgroup_member'(
% 116.20/116.55 'element_in_O2'( X, Y ) ) ],
% 116.20/116.55 [ 'subgroup_member'( X ), 'subgroup_member'( Y ), =( multiply( X,
% 116.20/116.55 'element_in_O2'( X, Y ) ), Y ) ],
% 116.20/116.55 [ 'subgroup_member'( b ) ],
% 116.20/116.55 [ =( multiply( b, inverse( a ) ), c ) ],
% 116.20/116.55 [ =( multiply( a, c ), d ) ],
% 116.20/116.55 [ ~( 'subgroup_member'( d ) ) ]
% 116.20/116.55 ] .
% 116.20/116.55
% 116.20/116.55
% 116.20/116.55 percentage equality = 0.409091, percentage horn = 0.857143
% 116.20/116.55 This is a problem with some equality
% 116.20/116.55
% 116.20/116.55
% 116.20/116.55
% 116.20/116.55 Options Used:
% 116.20/116.55
% 116.20/116.55 useres = 1
% 116.20/116.55 useparamod = 1
% 116.20/116.55 useeqrefl = 1
% 116.20/116.55 useeqfact = 1
% 116.20/116.55 usefactor = 1
% 116.20/116.55 usesimpsplitting = 0
% 116.20/116.55 usesimpdemod = 5
% 116.20/116.55 usesimpres = 3
% 116.20/116.55
% 116.20/116.55 resimpinuse = 1000
% 116.20/116.55 resimpclauses = 20000
% 116.20/116.55 substype = eqrewr
% 116.20/116.55 backwardsubs = 1
% 116.20/116.55 selectoldest = 5
% 116.20/116.55
% 116.20/116.55 litorderings [0] = split
% 116.20/116.55 litorderings [1] = extend the termordering, first sorting on arguments
% 116.20/116.55
% 116.20/116.55 termordering = kbo
% 116.20/116.55
% 116.20/116.55 litapriori = 0
% 116.20/116.55 termapriori = 1
% 116.20/116.55 litaposteriori = 0
% 116.20/116.55 termaposteriori = 0
% 116.20/116.55 demodaposteriori = 0
% 116.20/116.55 ordereqreflfact = 0
% 116.20/116.55
% 116.20/116.55 litselect = negord
% 116.20/116.55
% 116.20/116.55 maxweight = 15
% 116.20/116.55 maxdepth = 30000
% 116.20/116.55 maxlength = 115
% 116.20/116.55 maxnrvars = 195
% 116.20/116.55 excuselevel = 1
% 116.20/116.55 increasemaxweight = 1
% 116.20/116.55
% 116.20/116.55 maxselected = 10000000
% 116.20/116.55 maxnrclauses = 10000000
% 116.20/116.55
% 116.20/116.55 showgenerated = 0
% 116.20/116.55 showkept = 0
% 116.20/116.55 showselected = 0
% 116.20/116.55 showdeleted = 0
% 116.20/116.55 showresimp = 1
% 116.20/116.55 showstatus = 2000
% 116.20/116.55
% 116.20/116.55 prologoutput = 1
% 116.20/116.55 nrgoals = 5000000
% 116.20/116.55 totalproof = 1
% 116.20/116.55
% 116.20/116.55 Symbols occurring in the translation:
% 116.20/116.55
% 116.20/116.55 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 116.20/116.55 . [1, 2] (w:1, o:24, a:1, s:1, b:0),
% 116.20/116.55 ! [4, 1] (w:0, o:17, a:1, s:1, b:0),
% 116.20/116.55 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 116.20/116.55 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 116.20/116.55 identity [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 116.20/116.55 multiply [41, 2] (w:1, o:49, a:1, s:1, b:0),
% 116.20/116.55 inverse [42, 1] (w:1, o:22, a:1, s:1, b:0),
% 116.20/116.55 'subgroup_member' [45, 1] (w:1, o:23, a:1, s:1, b:0),
% 116.20/116.55 'element_in_O2' [46, 2] (w:1, o:50, a:1, s:1, b:0),
% 116.20/116.55 b [47, 0] (w:1, o:14, a:1, s:1, b:0),
% 116.20/116.55 a [48, 0] (w:1, o:13, a:1, s:1, b:0),
% 116.20/116.55 c [49, 0] (w:1, o:15, a:1, s:1, b:0),
% 116.20/116.55 d [50, 0] (w:1, o:16, a:1, s:1, b:0).
% 116.20/116.55
% 116.20/116.55
% 116.20/116.55 Starting Search:
% 116.20/116.55
% 116.20/116.55 Resimplifying inuse:
% 116.20/116.55 Done
% 116.20/116.55
% 116.20/116.55
% 116.20/116.55 Intermediate Status:
% 116.20/116.55 Generated: 3946
% 116.20/116.55 Kept: 2115
% 116.20/116.55 Inuse: 110
% 116.20/116.55 Deleted: 21
% 116.20/116.55 Deletedinuse: 15
% 116.20/116.55
% 116.20/116.55 Resimplifying inuse:
% 116.20/116.55 Done
% 116.20/116.55
% 116.20/116.55 Resimplifying inuse:
% 116.20/116.55 Done
% 116.20/116.55
% 116.20/116.55
% 116.20/116.55 Intermediate Status:
% 116.20/116.55 Generated: 7788
% 116.20/116.55 Kept: 4383
% 116.20/116.55 Inuse: 161
% 116.20/116.55 Deleted: 25
% 116.20/116.55 Deletedinuse: 15
% 116.20/116.55
% 116.20/116.55 Resimplifying inuse:
% 116.20/116.55 Done
% 116.20/116.55
% 116.20/116.55 Resimplifying inuse:
% 116.20/116.55 Done
% 116.20/116.55
% 116.20/116.55
% 116.20/116.55 Intermediate Status:
% 116.20/116.55 Generated: 13355
% 116.20/116.55 Kept: 6395
% 116.20/116.55 Inuse: 247
% 116.20/116.55 Deleted: 27
% 116.20/116.55 Deletedinuse: 15
% 116.20/116.55
% 116.20/116.55 Resimplifying inuse:
% 116.20/116.55 Done
% 116.20/116.55
% 116.20/116.55 Resimplifying inuse:
% 116.20/116.55 Done
% 116.20/116.55
% 116.20/116.55
% 116.20/116.55 Intermediate Status:
% 116.20/116.55 Generated: 18891
% 116.20/116.55 Kept: 8427
% 116.20/116.55 Inuse: 298
% 116.20/116.55 Deleted: 31
% 116.20/116.55 Deletedinuse: 15
% 116.20/116.55
% 116.20/116.55 Resimplifying inuse:
% 116.20/116.55 Done
% 116.20/116.55
% 116.20/116.55 Resimplifying inuse:
% 116.20/116.55 Done
% 116.20/116.55
% 116.20/116.55
% 116.20/116.55 Intermediate Status:
% 116.20/116.55 Generated: 24807
% 116.20/116.55 Kept: 10489
% 116.20/116.55 Inuse: 327
% 116.20/116.55 Deleted: 31
% 116.20/116.55 Deletedinuse: 15
% 116.20/116.55
% 116.20/116.55 Resimplifying inuse:
% 116.20/116.55 Done
% 116.20/116.55
% 116.20/116.55 Resimplifying inuse:
% 116.20/116.55 Done
% 116.20/116.55
% 116.20/116.55
% 116.20/116.55 Intermediate Status:
% 116.20/116.55 Generated: 29666
% 116.20/116.55 Kept: 12517
% 116.20/116.55 Inuse: 340
% 116.20/116.55 Deleted: 31
% 116.20/116.55 Deletedinuse: 15
% 116.20/116.55
% 116.20/116.55 Resimplifying inuse:
% 116.20/116.55 Done
% 116.20/116.55
% 116.20/116.55 Resimplifying inuse:
% 116.20/116.55 Done
% 116.20/116.55
% 116.20/116.55
% 116.20/116.55 Intermediate Status:
% 116.20/116.55 Generated: 39871
% 116.20/116.55 Kept: 14785
% 116.20/116.55 Inuse: 441
% 116.20/116.55 Deleted: 45
% 116.20/116.55 Deletedinuse: 15
% 116.20/116.55
% 116.20/116.55 Resimplifying inuse:
% 116.20/116.55 Done
% 116.20/116.55
% 116.20/116.55 Resimplifying inuse:
% 116.20/116.55 Done
% 116.20/116.55
% 116.20/116.55
% 116.20/116.55 Intermediate Status:
% 246.44/246.81 Generated: 44225
% 246.44/246.81 Kept: 16907
% 246.44/246.81 Inuse: 463
% 246.44/246.81 Deleted: 98
% 246.44/246.81 Deletedinuse: 64
% 246.44/246.81
% 246.44/246.81 Resimplifying inuse:
% 246.44/246.81 Done
% 246.44/246.81
% 246.44/246.81 Resimplifying inuse:
% 246.44/246.81 Done
% 246.44/246.81
% 246.44/246.81
% 246.44/246.81 Intermediate Status:
% 246.44/246.81 Generated: 49092
% 246.44/246.81 Kept: 18960
% 246.44/246.81 Inuse: 482
% 246.44/246.81 Deleted: 98
% 246.44/246.81 Deletedinuse: 64
% 246.44/246.81
% 246.44/246.81 Resimplifying inuse:
% 246.44/246.81 Done
% 246.44/246.81
% 246.44/246.81 Resimplifying clauses:
% 246.44/246.81 Done
% 246.44/246.81
% 246.44/246.81 Resimplifying inuse:
% 246.44/246.81 Done
% 246.44/246.81
% 246.44/246.81
% 246.44/246.81 Intermediate Status:
% 246.44/246.81 Generated: 55632
% 246.44/246.81 Kept: 21026
% 246.44/246.81 Inuse: 497
% 246.44/246.81 Deleted: 2475
% 246.44/246.81 Deletedinuse: 64
% 246.44/246.81
% 246.44/246.81 Resimplifying inuse:
% 246.44/246.81 Done
% 246.44/246.81
% 246.44/246.81 Resimplifying inuse:
% 246.44/246.81 Done
% 246.44/246.81
% 246.44/246.81
% 246.44/246.81 Intermediate Status:
% 246.44/246.81 Generated: 60669
% 246.44/246.81 Kept: 23219
% 246.44/246.81 Inuse: 525
% 246.44/246.81 Deleted: 2475
% 246.44/246.81 Deletedinuse: 64
% 246.44/246.81
% 246.44/246.81 Resimplifying inuse:
% 246.44/246.81 Done
% 246.44/246.81
% 246.44/246.81 Resimplifying inuse:
% 246.44/246.81 Done
% 246.44/246.81
% 246.44/246.81
% 246.44/246.81 Intermediate Status:
% 246.44/246.81 Generated: 65889
% 246.44/246.81 Kept: 25277
% 246.44/246.81 Inuse: 545
% 246.44/246.81 Deleted: 2475
% 246.44/246.81 Deletedinuse: 64
% 246.44/246.81
% 246.44/246.81 Resimplifying inuse:
% 246.44/246.81 Done
% 246.44/246.81
% 246.44/246.81 Resimplifying inuse:
% 246.44/246.81 Done
% 246.44/246.81
% 246.44/246.81
% 246.44/246.81 Intermediate Status:
% 246.44/246.81 Generated: 70310
% 246.44/246.81 Kept: 27341
% 246.44/246.81 Inuse: 568
% 246.44/246.81 Deleted: 2477
% 246.44/246.81 Deletedinuse: 66
% 246.44/246.81
% 246.44/246.81 Resimplifying inuse:
% 246.44/246.81 Done
% 246.44/246.81
% 246.44/246.81
% 246.44/246.81 Intermediate Status:
% 246.44/246.82 Generated: 75652
% 246.44/246.82 Kept: 29478
% 246.44/246.82 Inuse: 592
% 246.44/246.82 Deleted: 2477
% 246.44/246.82 Deletedinuse: 66
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 Intermediate Status:
% 246.44/246.82 Generated: 81601
% 246.44/246.82 Kept: 31641
% 246.44/246.82 Inuse: 617
% 246.44/246.82 Deleted: 2477
% 246.44/246.82 Deletedinuse: 66
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 Intermediate Status:
% 246.44/246.82 Generated: 88278
% 246.44/246.82 Kept: 33659
% 246.44/246.82 Inuse: 657
% 246.44/246.82 Deleted: 2477
% 246.44/246.82 Deletedinuse: 66
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 Intermediate Status:
% 246.44/246.82 Generated: 95360
% 246.44/246.82 Kept: 35690
% 246.44/246.82 Inuse: 685
% 246.44/246.82 Deleted: 2477
% 246.44/246.82 Deletedinuse: 66
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 Intermediate Status:
% 246.44/246.82 Generated: 102831
% 246.44/246.82 Kept: 37818
% 246.44/246.82 Inuse: 702
% 246.44/246.82 Deleted: 2477
% 246.44/246.82 Deletedinuse: 66
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 Intermediate Status:
% 246.44/246.82 Generated: 107338
% 246.44/246.82 Kept: 39868
% 246.44/246.82 Inuse: 714
% 246.44/246.82 Deleted: 2477
% 246.44/246.82 Deletedinuse: 66
% 246.44/246.82
% 246.44/246.82 Resimplifying clauses:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 Intermediate Status:
% 246.44/246.82 Generated: 117395
% 246.44/246.82 Kept: 41927
% 246.44/246.82 Inuse: 750
% 246.44/246.82 Deleted: 2570
% 246.44/246.82 Deletedinuse: 66
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 Intermediate Status:
% 246.44/246.82 Generated: 124898
% 246.44/246.82 Kept: 43947
% 246.44/246.82 Inuse: 780
% 246.44/246.82 Deleted: 2570
% 246.44/246.82 Deletedinuse: 66
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 Intermediate Status:
% 246.44/246.82 Generated: 134925
% 246.44/246.82 Kept: 46118
% 246.44/246.82 Inuse: 812
% 246.44/246.82 Deleted: 2570
% 246.44/246.82 Deletedinuse: 66
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 Intermediate Status:
% 246.44/246.82 Generated: 145515
% 246.44/246.82 Kept: 48227
% 246.44/246.82 Inuse: 844
% 246.44/246.82 Deleted: 2570
% 246.44/246.82 Deletedinuse: 66
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 Intermediate Status:
% 246.44/246.82 Generated: 151350
% 246.44/246.82 Kept: 50281
% 246.44/246.82 Inuse: 856
% 246.44/246.82 Deleted: 2570
% 246.44/246.82 Deletedinuse: 66
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 Intermediate Status:
% 246.44/246.82 Generated: 159986
% 246.44/246.82 Kept: 52311
% 246.44/246.82 Inuse: 875
% 246.44/246.82 Deleted: 2570
% 246.44/246.82 Deletedinuse: 66
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 Intermediate Status:
% 246.44/246.82 Generated: 167101
% 246.44/246.82 Kept: 54491
% 246.44/246.82 Inuse: 887
% 246.44/246.82 Deleted: 2570
% 246.44/246.82 Deletedinuse: 66
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 Intermediate Status:
% 246.44/246.82 Generated: 174834
% 246.44/246.82 Kept: 56563
% 246.44/246.82 Inuse: 910
% 246.44/246.82 Deleted: 2570
% 246.44/246.82 Deletedinuse: 66
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 Intermediate Status:
% 246.44/246.82 Generated: 183181
% 246.44/246.82 Kept: 59509
% 246.44/246.82 Inuse: 925
% 246.44/246.82 Deleted: 2570
% 246.44/246.82 Deletedinuse: 66
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82 Resimplifying clauses:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 Intermediate Status:
% 246.44/246.82 Generated: 187014
% 246.44/246.82 Kept: 61540
% 246.44/246.82 Inuse: 932
% 246.44/246.82 Deleted: 2570
% 246.44/246.82 Deletedinuse: 66
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 Intermediate Status:
% 246.44/246.82 Generated: 192291
% 246.44/246.82 Kept: 63991
% 246.44/246.82 Inuse: 943
% 246.44/246.82 Deleted: 2570
% 246.44/246.82 Deletedinuse: 66
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 Intermediate Status:
% 246.44/246.82 Generated: 197102
% 246.44/246.82 Kept: 66237
% 246.44/246.82 Inuse: 949
% 246.44/246.82 Deleted: 2570
% 246.44/246.82 Deletedinuse: 66
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 Intermediate Status:
% 246.44/246.82 Generated: 203304
% 246.44/246.82 Kept: 68250
% 246.44/246.82 Inuse: 962
% 246.44/246.82 Deleted: 2570
% 246.44/246.82 Deletedinuse: 66
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 Intermediate Status:
% 246.44/246.82 Generated: 209169
% 246.44/246.82 Kept: 70717
% 246.44/246.82 Inuse: 977
% 246.44/246.82 Deleted: 2570
% 246.44/246.82 Deletedinuse: 66
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 Intermediate Status:
% 246.44/246.82 Generated: 215103
% 246.44/246.82 Kept: 72796
% 246.44/246.82 Inuse: 989
% 246.44/246.82 Deleted: 2570
% 246.44/246.82 Deletedinuse: 66
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 Intermediate Status:
% 246.44/246.82 Generated: 220817
% 246.44/246.82 Kept: 74893
% 246.44/246.82 Inuse: 996
% 246.44/246.82 Deleted: 2570
% 246.44/246.82 Deletedinuse: 66
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 Intermediate Status:
% 246.44/246.82 Generated: 225950
% 246.44/246.82 Kept: 76910
% 246.44/246.82 Inuse: 1002
% 246.44/246.82 Deleted: 2570
% 246.44/246.82 Deletedinuse: 66
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 Intermediate Status:
% 246.44/246.82 Generated: 231926
% 246.44/246.82 Kept: 79130
% 246.44/246.82 Inuse: 1017
% 246.44/246.82 Deleted: 2570
% 246.44/246.82 Deletedinuse: 66
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82 Resimplifying clauses:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 Intermediate Status:
% 246.44/246.82 Generated: 239790
% 246.44/246.82 Kept: 81227
% 246.44/246.82 Inuse: 1042
% 246.44/246.82 Deleted: 2570
% 246.44/246.82 Deletedinuse: 66
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 Intermediate Status:
% 246.44/246.82 Generated: 247576
% 246.44/246.82 Kept: 83518
% 246.44/246.82 Inuse: 1072
% 246.44/246.82 Deleted: 2570
% 246.44/246.82 Deletedinuse: 66
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 Intermediate Status:
% 246.44/246.82 Generated: 271812
% 246.44/246.82 Kept: 85575
% 246.44/246.82 Inuse: 1168
% 246.44/246.82 Deleted: 2739
% 246.44/246.82 Deletedinuse: 232
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 Intermediate Status:
% 246.44/246.82 Generated: 282708
% 246.44/246.82 Kept: 87783
% 246.44/246.82 Inuse: 1206
% 246.44/246.82 Deleted: 2740
% 246.44/246.82 Deletedinuse: 232
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 Intermediate Status:
% 246.44/246.82 Generated: 287067
% 246.44/246.82 Kept: 89847
% 246.44/246.82 Inuse: 1240
% 246.44/246.82 Deleted: 2763
% 246.44/246.82 Deletedinuse: 249
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 Intermediate Status:
% 246.44/246.82 Generated: 291349
% 246.44/246.82 Kept: 92062
% 246.44/246.82 Inuse: 1249
% 246.44/246.82 Deleted: 2764
% 246.44/246.82 Deletedinuse: 249
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 Intermediate Status:
% 246.44/246.82 Generated: 296285
% 246.44/246.82 Kept: 94122
% 246.44/246.82 Inuse: 1270
% 246.44/246.82 Deleted: 2765
% 246.44/246.82 Deletedinuse: 249
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 Intermediate Status:
% 246.44/246.82 Generated: 300096
% 246.44/246.82 Kept: 96179
% 246.44/246.82 Inuse: 1281
% 246.44/246.82 Deleted: 2766
% 246.44/246.82 Deletedinuse: 249
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 Intermediate Status:
% 246.44/246.82 Generated: 304509
% 246.44/246.82 Kept: 98297
% 246.44/246.82 Inuse: 1290
% 246.44/246.82 Deleted: 2766
% 246.44/246.82 Deletedinuse: 249
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82 Resimplifying inuse:
% 246.44/246.82 Done
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 Intermediate Status:
% 246.44/246.82 Generated: 309289
% 246.44/246.82 Kept: 100568
% 246.44/246.82 Inuse: 1315
% 246.44/246.82 Deleted: 2772
% 246.44/246.82 Deletedinuse: 249
% 246.44/246.82
% 246.44/246.82 Resimplifying clauses:
% 246.44/246.82
% 246.44/246.82 Bliksems!, er is een bewijs:
% 246.44/246.82 % SZS status Unsatisfiable
% 246.44/246.82 % SZS output start Refutation
% 246.44/246.82
% 246.44/246.82 clause( 0, [ =( multiply( identity, X ), X ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y )
% 246.44/246.82 , Z ) ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 3, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( inverse( X ) )
% 246.44/246.82 ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 4, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( Y ) ), ~(
% 246.44/246.82 =( multiply( X, Y ), Z ) ), 'subgroup_member'( Z ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 5, [ =( multiply( X, identity ), X ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 6, [ =( multiply( X, inverse( X ) ), identity ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 8, [ 'subgroup_member'( X ), 'subgroup_member'( Y ),
% 246.44/246.82 'subgroup_member'( 'element_in_O2'( X, Y ) ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 9, [ 'subgroup_member'( X ), 'subgroup_member'( Y ), =( multiply( X
% 246.44/246.82 , 'element_in_O2'( X, Y ) ), Y ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 10, [ 'subgroup_member'( b ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 11, [ =( multiply( b, inverse( a ) ), c ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 12, [ =( multiply( a, c ), d ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 13, [ ~( 'subgroup_member'( d ) ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 15, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( Y ) ),
% 246.44/246.82 'subgroup_member'( multiply( X, Y ) ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 16, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( multiply( X,
% 246.44/246.82 X ) ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 21, [ 'subgroup_member'( inverse( b ) ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 23, [ =( multiply( multiply( X, a ), c ), multiply( X, d ) ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 25, [ =( multiply( multiply( Y, inverse( X ) ), X ), Y ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 44, [ ~( 'subgroup_member'( X ) ), ~( =( multiply( inverse( b ), X
% 246.44/246.82 ), Y ) ), 'subgroup_member'( Y ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 47, [ ~( 'subgroup_member'( X ) ), ~( =( multiply( X, inverse( Y )
% 246.44/246.82 ), Z ) ), 'subgroup_member'( Z ), ~( 'subgroup_member'( Y ) ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 50, [ ~( 'subgroup_member'( X ) ), ~( =( multiply( b, X ), Y ) ),
% 246.44/246.82 'subgroup_member'( Y ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 54, [ ~( 'subgroup_member'( a ) ), ~( 'subgroup_member'( c ) ), ~(
% 246.44/246.82 =( d, X ) ), 'subgroup_member'( X ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 56, [ ~( 'subgroup_member'( a ) ), ~( 'subgroup_member'( c ) ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 62, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( multiply( b,
% 246.44/246.82 X ) ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 69, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( multiply(
% 246.44/246.82 inverse( b ), X ) ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 134, [ ~( 'subgroup_member'( multiply( X, Y ) ) ),
% 246.44/246.82 'subgroup_member'( multiply( multiply( b, X ), Y ) ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 216, [ 'subgroup_member'( X ), 'subgroup_member'( 'element_in_O2'(
% 246.44/246.82 Y, X ) ), ~( 'subgroup_member'( Z ) ), ~( =( multiply( Y, Z ), T ) ),
% 246.44/246.82 'subgroup_member'( T ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 223, [ 'subgroup_member'( X ), 'subgroup_member'( 'element_in_O2'(
% 246.44/246.82 X, Y ) ), 'subgroup_member'( inverse( Y ) ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 225, [ 'subgroup_member'( X ), 'subgroup_member'( 'element_in_O2'(
% 246.44/246.82 d, X ) ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 247, [ 'subgroup_member'( X ), 'subgroup_member'( 'element_in_O2'(
% 246.44/246.82 Y, X ) ), ~( 'subgroup_member'( Z ) ), ~( =( multiply( Y, Z ), X ) ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 366, [ 'subgroup_member'( X ), =( multiply( X, 'element_in_O2'( X,
% 246.44/246.82 Y ) ), Y ), 'subgroup_member'( inverse( Y ) ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 369, [ =( multiply( multiply( Z, X ), 'element_in_O2'( X, Y ) ),
% 246.44/246.82 multiply( Z, Y ) ), 'subgroup_member'( X ), 'subgroup_member'( Y ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 371, [ 'subgroup_member'( inverse( X ) ), =( multiply( inverse( X )
% 246.44/246.82 , 'element_in_O2'( inverse( X ), X ) ), X ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 463, [ ~( 'subgroup_member'( inverse( a ) ) ), 'subgroup_member'( c
% 246.44/246.82 ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 465, [ =( multiply( multiply( X, b ), inverse( a ) ), multiply( X,
% 246.44/246.82 c ) ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 478, [ ~( 'subgroup_member'( a ) ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 803, [ =( multiply( inverse( a ), d ), c ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 872, [ =( multiply( X, inverse( inverse( Y ) ) ), multiply( X, Y )
% 246.44/246.82 ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 878, [ =( inverse( inverse( X ) ), X ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 883, [ ~( 'subgroup_member'( inverse( X ) ) ), 'subgroup_member'( X
% 246.44/246.82 ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 891, [ ~( 'subgroup_member'( inverse( a ) ) ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 898, [ ~( 'subgroup_member'( inverse( X ) ) ), 'subgroup_member'(
% 246.44/246.82 multiply( X, X ) ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 3777, [ ~( =( X, Z ) ), 'subgroup_member'( Z ), ~(
% 246.44/246.82 'subgroup_member'( Y ) ), ~( 'subgroup_member'( multiply( X, Y ) ) ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 3778, [ 'subgroup_member'( X ), ~( 'subgroup_member'( Y ) ), ~(
% 246.44/246.82 'subgroup_member'( multiply( X, Y ) ) ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 59229, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'(
% 246.44/246.82 multiply( inverse( a ), X ) ) ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 84265, [ =( multiply( c, 'element_in_O2'( d, X ) ), multiply(
% 246.44/246.82 inverse( a ), X ) ), 'subgroup_member'( X ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 84267, [ 'subgroup_member'( inverse( X ) ), 'subgroup_member'( Y )
% 246.44/246.82 , =( 'element_in_O2'( inverse( X ), Y ), multiply( X, Y ) ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 84709, [ 'subgroup_member'( Y ), ~( =( X, Y ) ), 'subgroup_member'(
% 246.44/246.82 inverse( X ) ), 'subgroup_member'( multiply( X, Y ) ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 84713, [ 'subgroup_member'( inverse( X ) ), 'subgroup_member'(
% 246.44/246.82 multiply( X, X ) ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 84715, [ 'subgroup_member'( multiply( X, X ) ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 84826, [ 'subgroup_member'( multiply( multiply( b, X ), X ) ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 85719, [ 'subgroup_member'( multiply( c, inverse( a ) ) ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 85839, [ 'subgroup_member'( multiply( multiply( inverse( b ), c ),
% 246.44/246.82 inverse( a ) ) ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 89068, [ =( multiply( inverse( b ), c ), inverse( a ) ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 89127, [ ~( 'subgroup_member'( c ) ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 89200, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'(
% 246.44/246.82 multiply( c, X ) ) ) ] )
% 246.44/246.82 .
% 246.44/246.82 clause( 100398, [ ~( 'subgroup_member'( multiply( inverse( a ), X ) ) ) ]
% 246.44/246.82 )
% 246.44/246.82 .
% 246.44/246.82 clause( 100572, [] )
% 246.44/246.82 .
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 % SZS output end Refutation
% 246.44/246.82 found a proof!
% 246.44/246.82
% 246.44/246.82 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 246.44/246.82
% 246.44/246.82 initialclauses(
% 246.44/246.82 [ clause( 100574, [ =( multiply( identity, X ), X ) ] )
% 246.44/246.82 , clause( 100575, [ =( multiply( inverse( X ), X ), identity ) ] )
% 246.44/246.82 , clause( 100576, [ =( multiply( multiply( X, Y ), Z ), multiply( X,
% 246.44/246.82 multiply( Y, Z ) ) ) ] )
% 246.44/246.82 , clause( 100577, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( inverse(
% 246.44/246.82 X ) ) ] )
% 246.44/246.82 , clause( 100578, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( Y )
% 246.44/246.82 ), ~( =( multiply( X, Y ), Z ) ), 'subgroup_member'( Z ) ] )
% 246.44/246.82 , clause( 100579, [ =( multiply( X, identity ), X ) ] )
% 246.44/246.82 , clause( 100580, [ =( multiply( X, inverse( X ) ), identity ) ] )
% 246.44/246.82 , clause( 100581, [ 'subgroup_member'( identity ) ] )
% 246.44/246.82 , clause( 100582, [ 'subgroup_member'( X ), 'subgroup_member'( Y ),
% 246.44/246.82 'subgroup_member'( 'element_in_O2'( X, Y ) ) ] )
% 246.44/246.82 , clause( 100583, [ 'subgroup_member'( X ), 'subgroup_member'( Y ), =(
% 246.44/246.82 multiply( X, 'element_in_O2'( X, Y ) ), Y ) ] )
% 246.44/246.82 , clause( 100584, [ 'subgroup_member'( b ) ] )
% 246.44/246.82 , clause( 100585, [ =( multiply( b, inverse( a ) ), c ) ] )
% 246.44/246.82 , clause( 100586, [ =( multiply( a, c ), d ) ] )
% 246.44/246.82 , clause( 100587, [ ~( 'subgroup_member'( d ) ) ] )
% 246.44/246.82 ] ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 0, [ =( multiply( identity, X ), X ) ] )
% 246.44/246.82 , clause( 100574, [ =( multiply( identity, X ), X ) ] )
% 246.44/246.82 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 246.44/246.82 , clause( 100575, [ =( multiply( inverse( X ), X ), identity ) ] )
% 246.44/246.82 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 eqswap(
% 246.44/246.82 clause( 100593, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X
% 246.44/246.82 , Y ), Z ) ) ] )
% 246.44/246.82 , clause( 100576, [ =( multiply( multiply( X, Y ), Z ), multiply( X,
% 246.44/246.82 multiply( Y, Z ) ) ) ] )
% 246.44/246.82 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y )
% 246.44/246.82 , Z ) ) ] )
% 246.44/246.82 , clause( 100593, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply(
% 246.44/246.82 X, Y ), Z ) ) ] )
% 246.44/246.82 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 246.44/246.82 permutation( 0, [ ==>( 0, 0 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 3, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( inverse( X ) )
% 246.44/246.82 ] )
% 246.44/246.82 , clause( 100577, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( inverse(
% 246.44/246.82 X ) ) ] )
% 246.44/246.82 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 246.44/246.82 1 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 4, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( Y ) ), ~(
% 246.44/246.82 =( multiply( X, Y ), Z ) ), 'subgroup_member'( Z ) ] )
% 246.44/246.82 , clause( 100578, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( Y )
% 246.44/246.82 ), ~( =( multiply( X, Y ), Z ) ), 'subgroup_member'( Z ) ] )
% 246.44/246.82 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 246.44/246.82 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 ), ==>( 3, 3 )] )
% 246.44/246.82 ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 5, [ =( multiply( X, identity ), X ) ] )
% 246.44/246.82 , clause( 100579, [ =( multiply( X, identity ), X ) ] )
% 246.44/246.82 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 6, [ =( multiply( X, inverse( X ) ), identity ) ] )
% 246.44/246.82 , clause( 100580, [ =( multiply( X, inverse( X ) ), identity ) ] )
% 246.44/246.82 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 8, [ 'subgroup_member'( X ), 'subgroup_member'( Y ),
% 246.44/246.82 'subgroup_member'( 'element_in_O2'( X, Y ) ) ] )
% 246.44/246.82 , clause( 100582, [ 'subgroup_member'( X ), 'subgroup_member'( Y ),
% 246.44/246.82 'subgroup_member'( 'element_in_O2'( X, Y ) ) ] )
% 246.44/246.82 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 246.44/246.82 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 9, [ 'subgroup_member'( X ), 'subgroup_member'( Y ), =( multiply( X
% 246.44/246.82 , 'element_in_O2'( X, Y ) ), Y ) ] )
% 246.44/246.82 , clause( 100583, [ 'subgroup_member'( X ), 'subgroup_member'( Y ), =(
% 246.44/246.82 multiply( X, 'element_in_O2'( X, Y ) ), Y ) ] )
% 246.44/246.82 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 246.44/246.82 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 10, [ 'subgroup_member'( b ) ] )
% 246.44/246.82 , clause( 100584, [ 'subgroup_member'( b ) ] )
% 246.44/246.82 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 11, [ =( multiply( b, inverse( a ) ), c ) ] )
% 246.44/246.82 , clause( 100585, [ =( multiply( b, inverse( a ) ), c ) ] )
% 246.44/246.82 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 12, [ =( multiply( a, c ), d ) ] )
% 246.44/246.82 , clause( 100586, [ =( multiply( a, c ), d ) ] )
% 246.44/246.82 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 13, [ ~( 'subgroup_member'( d ) ) ] )
% 246.44/246.82 , clause( 100587, [ ~( 'subgroup_member'( d ) ) ] )
% 246.44/246.82 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 eqswap(
% 246.44/246.82 clause( 100692, [ ~( =( Z, multiply( X, Y ) ) ), ~( 'subgroup_member'( X )
% 246.44/246.82 ), ~( 'subgroup_member'( Y ) ), 'subgroup_member'( Z ) ] )
% 246.44/246.82 , clause( 4, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( Y ) ),
% 246.44/246.82 ~( =( multiply( X, Y ), Z ) ), 'subgroup_member'( Z ) ] )
% 246.44/246.82 , 2, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 eqrefl(
% 246.44/246.82 clause( 100693, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( Y ) )
% 246.44/246.82 , 'subgroup_member'( multiply( X, Y ) ) ] )
% 246.44/246.82 , clause( 100692, [ ~( =( Z, multiply( X, Y ) ) ), ~( 'subgroup_member'( X
% 246.44/246.82 ) ), ~( 'subgroup_member'( Y ) ), 'subgroup_member'( Z ) ] )
% 246.44/246.82 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, multiply( X, Y ) )] )
% 246.44/246.82 ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 15, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( Y ) ),
% 246.44/246.82 'subgroup_member'( multiply( X, Y ) ) ] )
% 246.44/246.82 , clause( 100693, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( Y )
% 246.44/246.82 ), 'subgroup_member'( multiply( X, Y ) ) ] )
% 246.44/246.82 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 246.44/246.82 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 factor(
% 246.44/246.82 clause( 100695, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( multiply(
% 246.44/246.82 X, X ) ) ] )
% 246.44/246.82 , clause( 15, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( Y ) ),
% 246.44/246.82 'subgroup_member'( multiply( X, Y ) ) ] )
% 246.44/246.82 , 0, 1, substitution( 0, [ :=( X, X ), :=( Y, X )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 16, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( multiply( X,
% 246.44/246.82 X ) ) ] )
% 246.44/246.82 , clause( 100695, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'(
% 246.44/246.82 multiply( X, X ) ) ] )
% 246.44/246.82 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 246.44/246.82 1 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 resolution(
% 246.44/246.82 clause( 100696, [ 'subgroup_member'( inverse( b ) ) ] )
% 246.44/246.82 , clause( 3, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( inverse( X )
% 246.44/246.82 ) ] )
% 246.44/246.82 , 0, clause( 10, [ 'subgroup_member'( b ) ] )
% 246.44/246.82 , 0, substitution( 0, [ :=( X, b )] ), substitution( 1, [] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 21, [ 'subgroup_member'( inverse( b ) ) ] )
% 246.44/246.82 , clause( 100696, [ 'subgroup_member'( inverse( b ) ) ] )
% 246.44/246.82 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 eqswap(
% 246.44/246.82 clause( 100698, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 246.44/246.82 Y, Z ) ) ) ] )
% 246.44/246.82 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 246.44/246.82 ), Z ) ) ] )
% 246.44/246.82 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 paramod(
% 246.44/246.82 clause( 100700, [ =( multiply( multiply( X, a ), c ), multiply( X, d ) ) ]
% 246.44/246.82 )
% 246.44/246.82 , clause( 12, [ =( multiply( a, c ), d ) ] )
% 246.44/246.82 , 0, clause( 100698, [ =( multiply( multiply( X, Y ), Z ), multiply( X,
% 246.44/246.82 multiply( Y, Z ) ) ) ] )
% 246.44/246.82 , 0, 8, substitution( 0, [] ), substitution( 1, [ :=( X, X ), :=( Y, a ),
% 246.44/246.82 :=( Z, c )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 23, [ =( multiply( multiply( X, a ), c ), multiply( X, d ) ) ] )
% 246.44/246.82 , clause( 100700, [ =( multiply( multiply( X, a ), c ), multiply( X, d ) )
% 246.44/246.82 ] )
% 246.44/246.82 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 eqswap(
% 246.44/246.82 clause( 100704, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 246.44/246.82 Y, Z ) ) ) ] )
% 246.44/246.82 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 246.44/246.82 ), Z ) ) ] )
% 246.44/246.82 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 paramod(
% 246.44/246.82 clause( 100709, [ =( multiply( multiply( X, inverse( Y ) ), Y ), multiply(
% 246.44/246.82 X, identity ) ) ] )
% 246.44/246.82 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 246.44/246.82 , 0, clause( 100704, [ =( multiply( multiply( X, Y ), Z ), multiply( X,
% 246.44/246.82 multiply( Y, Z ) ) ) ] )
% 246.44/246.82 , 0, 9, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 246.44/246.82 :=( Y, inverse( Y ) ), :=( Z, Y )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 paramod(
% 246.44/246.82 clause( 100710, [ =( multiply( multiply( X, inverse( Y ) ), Y ), X ) ] )
% 246.44/246.82 , clause( 5, [ =( multiply( X, identity ), X ) ] )
% 246.44/246.82 , 0, clause( 100709, [ =( multiply( multiply( X, inverse( Y ) ), Y ),
% 246.44/246.82 multiply( X, identity ) ) ] )
% 246.44/246.82 , 0, 7, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 246.44/246.82 :=( Y, Y )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 25, [ =( multiply( multiply( Y, inverse( X ) ), X ), Y ) ] )
% 246.44/246.82 , clause( 100710, [ =( multiply( multiply( X, inverse( Y ) ), Y ), X ) ] )
% 246.44/246.82 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 246.44/246.82 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 eqswap(
% 246.44/246.82 clause( 100712, [ ~( =( Z, multiply( X, Y ) ) ), ~( 'subgroup_member'( X )
% 246.44/246.82 ), ~( 'subgroup_member'( Y ) ), 'subgroup_member'( Z ) ] )
% 246.44/246.82 , clause( 4, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( Y ) ),
% 246.44/246.82 ~( =( multiply( X, Y ), Z ) ), 'subgroup_member'( Z ) ] )
% 246.44/246.82 , 2, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 resolution(
% 246.44/246.82 clause( 100713, [ ~( =( X, multiply( inverse( b ), Y ) ) ), ~(
% 246.44/246.82 'subgroup_member'( Y ) ), 'subgroup_member'( X ) ] )
% 246.44/246.82 , clause( 100712, [ ~( =( Z, multiply( X, Y ) ) ), ~( 'subgroup_member'( X
% 246.44/246.82 ) ), ~( 'subgroup_member'( Y ) ), 'subgroup_member'( Z ) ] )
% 246.44/246.82 , 1, clause( 21, [ 'subgroup_member'( inverse( b ) ) ] )
% 246.44/246.82 , 0, substitution( 0, [ :=( X, inverse( b ) ), :=( Y, Y ), :=( Z, X )] ),
% 246.44/246.82 substitution( 1, [] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 eqswap(
% 246.44/246.82 clause( 100716, [ ~( =( multiply( inverse( b ), Y ), X ) ), ~(
% 246.44/246.82 'subgroup_member'( Y ) ), 'subgroup_member'( X ) ] )
% 246.44/246.82 , clause( 100713, [ ~( =( X, multiply( inverse( b ), Y ) ) ), ~(
% 246.44/246.82 'subgroup_member'( Y ) ), 'subgroup_member'( X ) ] )
% 246.44/246.82 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 44, [ ~( 'subgroup_member'( X ) ), ~( =( multiply( inverse( b ), X
% 246.44/246.82 ), Y ) ), 'subgroup_member'( Y ) ] )
% 246.44/246.82 , clause( 100716, [ ~( =( multiply( inverse( b ), Y ), X ) ), ~(
% 246.44/246.82 'subgroup_member'( Y ) ), 'subgroup_member'( X ) ] )
% 246.44/246.82 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 1
% 246.44/246.82 ), ==>( 1, 0 ), ==>( 2, 2 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 eqswap(
% 246.44/246.82 clause( 100717, [ ~( =( Z, multiply( X, Y ) ) ), ~( 'subgroup_member'( X )
% 246.44/246.82 ), ~( 'subgroup_member'( Y ) ), 'subgroup_member'( Z ) ] )
% 246.44/246.82 , clause( 4, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( Y ) ),
% 246.44/246.82 ~( =( multiply( X, Y ), Z ) ), 'subgroup_member'( Z ) ] )
% 246.44/246.82 , 2, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 resolution(
% 246.44/246.82 clause( 100719, [ ~( =( X, multiply( Y, inverse( Z ) ) ) ), ~(
% 246.44/246.82 'subgroup_member'( Y ) ), 'subgroup_member'( X ), ~( 'subgroup_member'( Z
% 246.44/246.82 ) ) ] )
% 246.44/246.82 , clause( 100717, [ ~( =( Z, multiply( X, Y ) ) ), ~( 'subgroup_member'( X
% 246.44/246.82 ) ), ~( 'subgroup_member'( Y ) ), 'subgroup_member'( Z ) ] )
% 246.44/246.82 , 2, clause( 3, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( inverse(
% 246.44/246.82 X ) ) ] )
% 246.44/246.82 , 1, substitution( 0, [ :=( X, Y ), :=( Y, inverse( Z ) ), :=( Z, X )] ),
% 246.44/246.82 substitution( 1, [ :=( X, Z )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 eqswap(
% 246.44/246.82 clause( 100720, [ ~( =( multiply( Y, inverse( Z ) ), X ) ), ~(
% 246.44/246.82 'subgroup_member'( Y ) ), 'subgroup_member'( X ), ~( 'subgroup_member'( Z
% 246.44/246.82 ) ) ] )
% 246.44/246.82 , clause( 100719, [ ~( =( X, multiply( Y, inverse( Z ) ) ) ), ~(
% 246.44/246.82 'subgroup_member'( Y ) ), 'subgroup_member'( X ), ~( 'subgroup_member'( Z
% 246.44/246.82 ) ) ] )
% 246.44/246.82 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 47, [ ~( 'subgroup_member'( X ) ), ~( =( multiply( X, inverse( Y )
% 246.44/246.82 ), Z ) ), 'subgroup_member'( Z ), ~( 'subgroup_member'( Y ) ) ] )
% 246.44/246.82 , clause( 100720, [ ~( =( multiply( Y, inverse( Z ) ), X ) ), ~(
% 246.44/246.82 'subgroup_member'( Y ) ), 'subgroup_member'( X ), ~( 'subgroup_member'( Z
% 246.44/246.82 ) ) ] )
% 246.44/246.82 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 246.44/246.82 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 ), ==>( 2, 2 ), ==>( 3, 3 )] )
% 246.44/246.82 ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 eqswap(
% 246.44/246.82 clause( 100726, [ ~( =( Z, multiply( X, Y ) ) ), ~( 'subgroup_member'( X )
% 246.44/246.82 ), ~( 'subgroup_member'( Y ) ), 'subgroup_member'( Z ) ] )
% 246.44/246.82 , clause( 4, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( Y ) ),
% 246.44/246.82 ~( =( multiply( X, Y ), Z ) ), 'subgroup_member'( Z ) ] )
% 246.44/246.82 , 2, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 resolution(
% 246.44/246.82 clause( 100727, [ ~( =( X, multiply( b, Y ) ) ), ~( 'subgroup_member'( Y )
% 246.44/246.82 ), 'subgroup_member'( X ) ] )
% 246.44/246.82 , clause( 100726, [ ~( =( Z, multiply( X, Y ) ) ), ~( 'subgroup_member'( X
% 246.44/246.82 ) ), ~( 'subgroup_member'( Y ) ), 'subgroup_member'( Z ) ] )
% 246.44/246.82 , 1, clause( 10, [ 'subgroup_member'( b ) ] )
% 246.44/246.82 , 0, substitution( 0, [ :=( X, b ), :=( Y, Y ), :=( Z, X )] ),
% 246.44/246.82 substitution( 1, [] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 eqswap(
% 246.44/246.82 clause( 100730, [ ~( =( multiply( b, Y ), X ) ), ~( 'subgroup_member'( Y )
% 246.44/246.82 ), 'subgroup_member'( X ) ] )
% 246.44/246.82 , clause( 100727, [ ~( =( X, multiply( b, Y ) ) ), ~( 'subgroup_member'( Y
% 246.44/246.82 ) ), 'subgroup_member'( X ) ] )
% 246.44/246.82 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 50, [ ~( 'subgroup_member'( X ) ), ~( =( multiply( b, X ), Y ) ),
% 246.44/246.82 'subgroup_member'( Y ) ] )
% 246.44/246.82 , clause( 100730, [ ~( =( multiply( b, Y ), X ) ), ~( 'subgroup_member'( Y
% 246.44/246.82 ) ), 'subgroup_member'( X ) ] )
% 246.44/246.82 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 1
% 246.44/246.82 ), ==>( 1, 0 ), ==>( 2, 2 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 eqswap(
% 246.44/246.82 clause( 100732, [ ~( =( Z, multiply( X, Y ) ) ), ~( 'subgroup_member'( X )
% 246.44/246.82 ), ~( 'subgroup_member'( Y ) ), 'subgroup_member'( Z ) ] )
% 246.44/246.82 , clause( 4, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( Y ) ),
% 246.44/246.82 ~( =( multiply( X, Y ), Z ) ), 'subgroup_member'( Z ) ] )
% 246.44/246.82 , 2, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 paramod(
% 246.44/246.82 clause( 100733, [ ~( =( X, d ) ), ~( 'subgroup_member'( a ) ), ~(
% 246.44/246.82 'subgroup_member'( c ) ), 'subgroup_member'( X ) ] )
% 246.44/246.82 , clause( 12, [ =( multiply( a, c ), d ) ] )
% 246.44/246.82 , 0, clause( 100732, [ ~( =( Z, multiply( X, Y ) ) ), ~( 'subgroup_member'(
% 246.44/246.82 X ) ), ~( 'subgroup_member'( Y ) ), 'subgroup_member'( Z ) ] )
% 246.44/246.82 , 0, 3, substitution( 0, [] ), substitution( 1, [ :=( X, a ), :=( Y, c ),
% 246.44/246.82 :=( Z, X )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 eqswap(
% 246.44/246.82 clause( 100734, [ ~( =( d, X ) ), ~( 'subgroup_member'( a ) ), ~(
% 246.44/246.82 'subgroup_member'( c ) ), 'subgroup_member'( X ) ] )
% 246.44/246.82 , clause( 100733, [ ~( =( X, d ) ), ~( 'subgroup_member'( a ) ), ~(
% 246.44/246.82 'subgroup_member'( c ) ), 'subgroup_member'( X ) ] )
% 246.44/246.82 , 0, substitution( 0, [ :=( X, X )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 54, [ ~( 'subgroup_member'( a ) ), ~( 'subgroup_member'( c ) ), ~(
% 246.44/246.82 =( d, X ) ), 'subgroup_member'( X ) ] )
% 246.44/246.82 , clause( 100734, [ ~( =( d, X ) ), ~( 'subgroup_member'( a ) ), ~(
% 246.44/246.82 'subgroup_member'( c ) ), 'subgroup_member'( X ) ] )
% 246.44/246.82 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 2 ), ==>( 1,
% 246.44/246.82 0 ), ==>( 2, 1 ), ==>( 3, 3 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 eqswap(
% 246.44/246.82 clause( 100735, [ ~( =( X, d ) ), ~( 'subgroup_member'( a ) ), ~(
% 246.44/246.82 'subgroup_member'( c ) ), 'subgroup_member'( X ) ] )
% 246.44/246.82 , clause( 54, [ ~( 'subgroup_member'( a ) ), ~( 'subgroup_member'( c ) ),
% 246.44/246.82 ~( =( d, X ) ), 'subgroup_member'( X ) ] )
% 246.44/246.82 , 2, substitution( 0, [ :=( X, X )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 eqrefl(
% 246.44/246.82 clause( 100736, [ ~( 'subgroup_member'( a ) ), ~( 'subgroup_member'( c ) )
% 246.44/246.82 , 'subgroup_member'( d ) ] )
% 246.44/246.82 , clause( 100735, [ ~( =( X, d ) ), ~( 'subgroup_member'( a ) ), ~(
% 246.44/246.82 'subgroup_member'( c ) ), 'subgroup_member'( X ) ] )
% 246.44/246.82 , 0, substitution( 0, [ :=( X, d )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 resolution(
% 246.44/246.82 clause( 100737, [ ~( 'subgroup_member'( a ) ), ~( 'subgroup_member'( c ) )
% 246.44/246.82 ] )
% 246.44/246.82 , clause( 13, [ ~( 'subgroup_member'( d ) ) ] )
% 246.44/246.82 , 0, clause( 100736, [ ~( 'subgroup_member'( a ) ), ~( 'subgroup_member'( c
% 246.44/246.82 ) ), 'subgroup_member'( d ) ] )
% 246.44/246.82 , 2, substitution( 0, [] ), substitution( 1, [] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 56, [ ~( 'subgroup_member'( a ) ), ~( 'subgroup_member'( c ) ) ] )
% 246.44/246.82 , clause( 100737, [ ~( 'subgroup_member'( a ) ), ~( 'subgroup_member'( c )
% 246.44/246.82 ) ] )
% 246.44/246.82 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] )
% 246.44/246.82 ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 eqswap(
% 246.44/246.82 clause( 100738, [ ~( =( Y, multiply( b, X ) ) ), ~( 'subgroup_member'( X )
% 246.44/246.82 ), 'subgroup_member'( Y ) ] )
% 246.44/246.82 , clause( 50, [ ~( 'subgroup_member'( X ) ), ~( =( multiply( b, X ), Y ) )
% 246.44/246.82 , 'subgroup_member'( Y ) ] )
% 246.44/246.82 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 eqrefl(
% 246.44/246.82 clause( 100739, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( multiply(
% 246.44/246.82 b, X ) ) ] )
% 246.44/246.82 , clause( 100738, [ ~( =( Y, multiply( b, X ) ) ), ~( 'subgroup_member'( X
% 246.44/246.82 ) ), 'subgroup_member'( Y ) ] )
% 246.44/246.82 , 0, substitution( 0, [ :=( X, X ), :=( Y, multiply( b, X ) )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 62, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( multiply( b,
% 246.44/246.82 X ) ) ] )
% 246.44/246.82 , clause( 100739, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'(
% 246.44/246.82 multiply( b, X ) ) ] )
% 246.44/246.82 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 246.44/246.82 1 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 eqswap(
% 246.44/246.82 clause( 100740, [ ~( =( Y, multiply( inverse( b ), X ) ) ), ~(
% 246.44/246.82 'subgroup_member'( X ) ), 'subgroup_member'( Y ) ] )
% 246.44/246.82 , clause( 44, [ ~( 'subgroup_member'( X ) ), ~( =( multiply( inverse( b ),
% 246.44/246.82 X ), Y ) ), 'subgroup_member'( Y ) ] )
% 246.44/246.82 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 eqrefl(
% 246.44/246.82 clause( 100741, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( multiply(
% 246.44/246.82 inverse( b ), X ) ) ] )
% 246.44/246.82 , clause( 100740, [ ~( =( Y, multiply( inverse( b ), X ) ) ), ~(
% 246.44/246.82 'subgroup_member'( X ) ), 'subgroup_member'( Y ) ] )
% 246.44/246.82 , 0, substitution( 0, [ :=( X, X ), :=( Y, multiply( inverse( b ), X ) )] )
% 246.44/246.82 ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 69, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( multiply(
% 246.44/246.82 inverse( b ), X ) ) ] )
% 246.44/246.82 , clause( 100741, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'(
% 246.44/246.82 multiply( inverse( b ), X ) ) ] )
% 246.44/246.82 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 246.44/246.82 1 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 paramod(
% 246.44/246.82 clause( 100743, [ 'subgroup_member'( multiply( multiply( b, X ), Y ) ), ~(
% 246.44/246.82 'subgroup_member'( multiply( X, Y ) ) ) ] )
% 246.44/246.82 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 246.44/246.82 ), Z ) ) ] )
% 246.44/246.82 , 0, clause( 62, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( multiply(
% 246.44/246.82 b, X ) ) ] )
% 246.44/246.82 , 1, 1, substitution( 0, [ :=( X, b ), :=( Y, X ), :=( Z, Y )] ),
% 246.44/246.82 substitution( 1, [ :=( X, multiply( X, Y ) )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 134, [ ~( 'subgroup_member'( multiply( X, Y ) ) ),
% 246.44/246.82 'subgroup_member'( multiply( multiply( b, X ), Y ) ) ] )
% 246.44/246.82 , clause( 100743, [ 'subgroup_member'( multiply( multiply( b, X ), Y ) ),
% 246.44/246.82 ~( 'subgroup_member'( multiply( X, Y ) ) ) ] )
% 246.44/246.82 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 1
% 246.44/246.82 ), ==>( 1, 0 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 eqswap(
% 246.44/246.82 clause( 100744, [ ~( =( Z, multiply( X, Y ) ) ), ~( 'subgroup_member'( X )
% 246.44/246.82 ), ~( 'subgroup_member'( Y ) ), 'subgroup_member'( Z ) ] )
% 246.44/246.82 , clause( 4, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( Y ) ),
% 246.44/246.82 ~( =( multiply( X, Y ), Z ) ), 'subgroup_member'( Z ) ] )
% 246.44/246.82 , 2, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 resolution(
% 246.44/246.82 clause( 100745, [ ~( =( X, multiply( Y, Z ) ) ), ~( 'subgroup_member'( Z )
% 246.44/246.82 ), 'subgroup_member'( X ), 'subgroup_member'( T ), 'subgroup_member'(
% 246.44/246.82 'element_in_O2'( Y, T ) ) ] )
% 246.44/246.82 , clause( 100744, [ ~( =( Z, multiply( X, Y ) ) ), ~( 'subgroup_member'( X
% 246.44/246.82 ) ), ~( 'subgroup_member'( Y ) ), 'subgroup_member'( Z ) ] )
% 246.44/246.82 , 1, clause( 8, [ 'subgroup_member'( X ), 'subgroup_member'( Y ),
% 246.44/246.82 'subgroup_member'( 'element_in_O2'( X, Y ) ) ] )
% 246.44/246.82 , 0, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] ),
% 246.44/246.82 substitution( 1, [ :=( X, Y ), :=( Y, T )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 eqswap(
% 246.44/246.82 clause( 100756, [ ~( =( multiply( Y, Z ), X ) ), ~( 'subgroup_member'( Z )
% 246.44/246.82 ), 'subgroup_member'( X ), 'subgroup_member'( T ), 'subgroup_member'(
% 246.44/246.82 'element_in_O2'( Y, T ) ) ] )
% 246.44/246.82 , clause( 100745, [ ~( =( X, multiply( Y, Z ) ) ), ~( 'subgroup_member'( Z
% 246.44/246.82 ) ), 'subgroup_member'( X ), 'subgroup_member'( T ), 'subgroup_member'(
% 246.44/246.82 'element_in_O2'( Y, T ) ) ] )
% 246.44/246.82 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 246.44/246.82 ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 216, [ 'subgroup_member'( X ), 'subgroup_member'( 'element_in_O2'(
% 246.44/246.82 Y, X ) ), ~( 'subgroup_member'( Z ) ), ~( =( multiply( Y, Z ), T ) ),
% 246.44/246.82 'subgroup_member'( T ) ] )
% 246.44/246.82 , clause( 100756, [ ~( =( multiply( Y, Z ), X ) ), ~( 'subgroup_member'( Z
% 246.44/246.82 ) ), 'subgroup_member'( X ), 'subgroup_member'( T ), 'subgroup_member'(
% 246.44/246.82 'element_in_O2'( Y, T ) ) ] )
% 246.44/246.82 , substitution( 0, [ :=( X, T ), :=( Y, Y ), :=( Z, Z ), :=( T, X )] ),
% 246.44/246.82 permutation( 0, [ ==>( 0, 3 ), ==>( 1, 2 ), ==>( 2, 4 ), ==>( 3, 0 ),
% 246.44/246.82 ==>( 4, 1 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 resolution(
% 246.44/246.82 clause( 100790, [ 'subgroup_member'( inverse( X ) ), 'subgroup_member'( Y )
% 246.44/246.82 , 'subgroup_member'( 'element_in_O2'( Y, X ) ) ] )
% 246.44/246.82 , clause( 3, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( inverse( X )
% 246.44/246.82 ) ] )
% 246.44/246.82 , 0, clause( 8, [ 'subgroup_member'( X ), 'subgroup_member'( Y ),
% 246.44/246.82 'subgroup_member'( 'element_in_O2'( X, Y ) ) ] )
% 246.44/246.82 , 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, Y ), :=( Y
% 246.44/246.82 , X )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 223, [ 'subgroup_member'( X ), 'subgroup_member'( 'element_in_O2'(
% 246.44/246.82 X, Y ) ), 'subgroup_member'( inverse( Y ) ) ] )
% 246.44/246.82 , clause( 100790, [ 'subgroup_member'( inverse( X ) ), 'subgroup_member'( Y
% 246.44/246.82 ), 'subgroup_member'( 'element_in_O2'( Y, X ) ) ] )
% 246.44/246.82 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 2
% 246.44/246.82 ), ==>( 1, 0 ), ==>( 2, 1 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 resolution(
% 246.44/246.82 clause( 100795, [ 'subgroup_member'( X ), 'subgroup_member'(
% 246.44/246.82 'element_in_O2'( d, X ) ) ] )
% 246.44/246.82 , clause( 13, [ ~( 'subgroup_member'( d ) ) ] )
% 246.44/246.82 , 0, clause( 8, [ 'subgroup_member'( X ), 'subgroup_member'( Y ),
% 246.44/246.82 'subgroup_member'( 'element_in_O2'( X, Y ) ) ] )
% 246.44/246.82 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, d ), :=( Y, X )] )
% 246.44/246.82 ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 225, [ 'subgroup_member'( X ), 'subgroup_member'( 'element_in_O2'(
% 246.44/246.82 d, X ) ) ] )
% 246.44/246.82 , clause( 100795, [ 'subgroup_member'( X ), 'subgroup_member'(
% 246.44/246.82 'element_in_O2'( d, X ) ) ] )
% 246.44/246.82 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 246.44/246.82 1 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 factor(
% 246.44/246.82 clause( 100798, [ 'subgroup_member'( X ), 'subgroup_member'(
% 246.44/246.82 'element_in_O2'( Y, X ) ), ~( 'subgroup_member'( Z ) ), ~( =( multiply( Y
% 246.44/246.82 , Z ), X ) ) ] )
% 246.44/246.82 , clause( 216, [ 'subgroup_member'( X ), 'subgroup_member'( 'element_in_O2'(
% 246.44/246.82 Y, X ) ), ~( 'subgroup_member'( Z ) ), ~( =( multiply( Y, Z ), T ) ),
% 246.44/246.82 'subgroup_member'( T ) ] )
% 246.44/246.82 , 0, 4, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, X )] )
% 246.44/246.82 ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 247, [ 'subgroup_member'( X ), 'subgroup_member'( 'element_in_O2'(
% 246.44/246.82 Y, X ) ), ~( 'subgroup_member'( Z ) ), ~( =( multiply( Y, Z ), X ) ) ] )
% 246.44/246.82 , clause( 100798, [ 'subgroup_member'( X ), 'subgroup_member'(
% 246.44/246.82 'element_in_O2'( Y, X ) ), ~( 'subgroup_member'( Z ) ), ~( =( multiply( Y
% 246.44/246.82 , Z ), X ) ) ] )
% 246.44/246.82 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 246.44/246.82 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 ), ==>( 3, 3 )] )
% 246.44/246.82 ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 eqswap(
% 246.44/246.82 clause( 100802, [ =( Y, multiply( X, 'element_in_O2'( X, Y ) ) ),
% 246.44/246.82 'subgroup_member'( X ), 'subgroup_member'( Y ) ] )
% 246.44/246.82 , clause( 9, [ 'subgroup_member'( X ), 'subgroup_member'( Y ), =( multiply(
% 246.44/246.82 X, 'element_in_O2'( X, Y ) ), Y ) ] )
% 246.44/246.82 , 2, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 resolution(
% 246.44/246.82 clause( 100804, [ 'subgroup_member'( inverse( X ) ), =( X, multiply( Y,
% 246.44/246.82 'element_in_O2'( Y, X ) ) ), 'subgroup_member'( Y ) ] )
% 246.44/246.82 , clause( 3, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( inverse( X )
% 246.44/246.82 ) ] )
% 246.44/246.82 , 0, clause( 100802, [ =( Y, multiply( X, 'element_in_O2'( X, Y ) ) ),
% 246.44/246.82 'subgroup_member'( X ), 'subgroup_member'( Y ) ] )
% 246.44/246.82 , 2, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, Y ), :=( Y
% 246.44/246.82 , X )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 eqswap(
% 246.44/246.82 clause( 100805, [ =( multiply( Y, 'element_in_O2'( Y, X ) ), X ),
% 246.44/246.82 'subgroup_member'( inverse( X ) ), 'subgroup_member'( Y ) ] )
% 246.44/246.82 , clause( 100804, [ 'subgroup_member'( inverse( X ) ), =( X, multiply( Y,
% 246.44/246.82 'element_in_O2'( Y, X ) ) ), 'subgroup_member'( Y ) ] )
% 246.44/246.82 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 366, [ 'subgroup_member'( X ), =( multiply( X, 'element_in_O2'( X,
% 246.44/246.82 Y ) ), Y ), 'subgroup_member'( inverse( Y ) ) ] )
% 246.44/246.82 , clause( 100805, [ =( multiply( Y, 'element_in_O2'( Y, X ) ), X ),
% 246.44/246.82 'subgroup_member'( inverse( X ) ), 'subgroup_member'( Y ) ] )
% 246.44/246.82 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 1
% 246.44/246.82 ), ==>( 1, 2 ), ==>( 2, 0 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 eqswap(
% 246.44/246.82 clause( 100812, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 246.44/246.82 Y, Z ) ) ) ] )
% 246.44/246.82 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 246.44/246.82 ), Z ) ) ] )
% 246.44/246.82 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 paramod(
% 246.44/246.82 clause( 100815, [ =( multiply( multiply( X, Y ), 'element_in_O2'( Y, Z ) )
% 246.44/246.82 , multiply( X, Z ) ), 'subgroup_member'( Y ), 'subgroup_member'( Z ) ] )
% 246.44/246.82 , clause( 9, [ 'subgroup_member'( X ), 'subgroup_member'( Y ), =( multiply(
% 246.44/246.82 X, 'element_in_O2'( X, Y ) ), Y ) ] )
% 246.44/246.82 , 2, clause( 100812, [ =( multiply( multiply( X, Y ), Z ), multiply( X,
% 246.44/246.82 multiply( Y, Z ) ) ) ] )
% 246.44/246.82 , 0, 10, substitution( 0, [ :=( X, Y ), :=( Y, Z )] ), substitution( 1, [
% 246.44/246.82 :=( X, X ), :=( Y, Y ), :=( Z, 'element_in_O2'( Y, Z ) )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 369, [ =( multiply( multiply( Z, X ), 'element_in_O2'( X, Y ) ),
% 246.44/246.82 multiply( Z, Y ) ), 'subgroup_member'( X ), 'subgroup_member'( Y ) ] )
% 246.44/246.82 , clause( 100815, [ =( multiply( multiply( X, Y ), 'element_in_O2'( Y, Z )
% 246.44/246.82 ), multiply( X, Z ) ), 'subgroup_member'( Y ), 'subgroup_member'( Z ) ]
% 246.44/246.82 )
% 246.44/246.82 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 246.44/246.82 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 factor(
% 246.44/246.82 clause( 100826, [ 'subgroup_member'( inverse( X ) ), =( multiply( inverse(
% 246.44/246.82 X ), 'element_in_O2'( inverse( X ), X ) ), X ) ] )
% 246.44/246.82 , clause( 366, [ 'subgroup_member'( X ), =( multiply( X, 'element_in_O2'( X
% 246.44/246.82 , Y ) ), Y ), 'subgroup_member'( inverse( Y ) ) ] )
% 246.44/246.82 , 0, 2, substitution( 0, [ :=( X, inverse( X ) ), :=( Y, X )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 371, [ 'subgroup_member'( inverse( X ) ), =( multiply( inverse( X )
% 246.44/246.82 , 'element_in_O2'( inverse( X ), X ) ), X ) ] )
% 246.44/246.82 , clause( 100826, [ 'subgroup_member'( inverse( X ) ), =( multiply( inverse(
% 246.44/246.82 X ), 'element_in_O2'( inverse( X ), X ) ), X ) ] )
% 246.44/246.82 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 246.44/246.82 1 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 paramod(
% 246.44/246.82 clause( 100829, [ 'subgroup_member'( c ), ~( 'subgroup_member'( inverse( a
% 246.44/246.82 ) ) ) ] )
% 246.44/246.82 , clause( 11, [ =( multiply( b, inverse( a ) ), c ) ] )
% 246.44/246.82 , 0, clause( 62, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( multiply(
% 246.44/246.82 b, X ) ) ] )
% 246.44/246.82 , 1, 1, substitution( 0, [] ), substitution( 1, [ :=( X, inverse( a ) )] )
% 246.44/246.82 ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 463, [ ~( 'subgroup_member'( inverse( a ) ) ), 'subgroup_member'( c
% 246.44/246.82 ) ] )
% 246.44/246.82 , clause( 100829, [ 'subgroup_member'( c ), ~( 'subgroup_member'( inverse(
% 246.44/246.82 a ) ) ) ] )
% 246.44/246.82 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] )
% 246.44/246.82 ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 eqswap(
% 246.44/246.82 clause( 100831, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 246.44/246.82 Y, Z ) ) ) ] )
% 246.44/246.82 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 246.44/246.82 ), Z ) ) ] )
% 246.44/246.82 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 paramod(
% 246.44/246.82 clause( 100833, [ =( multiply( multiply( X, b ), inverse( a ) ), multiply(
% 246.44/246.82 X, c ) ) ] )
% 246.44/246.82 , clause( 11, [ =( multiply( b, inverse( a ) ), c ) ] )
% 246.44/246.82 , 0, clause( 100831, [ =( multiply( multiply( X, Y ), Z ), multiply( X,
% 246.44/246.82 multiply( Y, Z ) ) ) ] )
% 246.44/246.82 , 0, 9, substitution( 0, [] ), substitution( 1, [ :=( X, X ), :=( Y, b ),
% 246.44/246.82 :=( Z, inverse( a ) )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 465, [ =( multiply( multiply( X, b ), inverse( a ) ), multiply( X,
% 246.44/246.82 c ) ) ] )
% 246.44/246.82 , clause( 100833, [ =( multiply( multiply( X, b ), inverse( a ) ), multiply(
% 246.44/246.82 X, c ) ) ] )
% 246.44/246.82 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 resolution(
% 246.44/246.82 clause( 100836, [ ~( 'subgroup_member'( a ) ), ~( 'subgroup_member'(
% 246.44/246.82 inverse( a ) ) ) ] )
% 246.44/246.82 , clause( 56, [ ~( 'subgroup_member'( a ) ), ~( 'subgroup_member'( c ) ) ]
% 246.44/246.82 )
% 246.44/246.82 , 1, clause( 463, [ ~( 'subgroup_member'( inverse( a ) ) ),
% 246.44/246.82 'subgroup_member'( c ) ] )
% 246.44/246.82 , 1, substitution( 0, [] ), substitution( 1, [] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 resolution(
% 246.44/246.82 clause( 100837, [ ~( 'subgroup_member'( a ) ), ~( 'subgroup_member'( a ) )
% 246.44/246.82 ] )
% 246.44/246.82 , clause( 100836, [ ~( 'subgroup_member'( a ) ), ~( 'subgroup_member'(
% 246.44/246.82 inverse( a ) ) ) ] )
% 246.44/246.82 , 1, clause( 3, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( inverse(
% 246.44/246.82 X ) ) ] )
% 246.44/246.82 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, a )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 factor(
% 246.44/246.82 clause( 100838, [ ~( 'subgroup_member'( a ) ) ] )
% 246.44/246.82 , clause( 100837, [ ~( 'subgroup_member'( a ) ), ~( 'subgroup_member'( a )
% 246.44/246.82 ) ] )
% 246.44/246.82 , 0, 1, substitution( 0, [] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 478, [ ~( 'subgroup_member'( a ) ) ] )
% 246.44/246.82 , clause( 100838, [ ~( 'subgroup_member'( a ) ) ] )
% 246.44/246.82 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 eqswap(
% 246.44/246.82 clause( 100840, [ =( multiply( X, d ), multiply( multiply( X, a ), c ) ) ]
% 246.44/246.82 )
% 246.44/246.82 , clause( 23, [ =( multiply( multiply( X, a ), c ), multiply( X, d ) ) ] )
% 246.44/246.82 , 0, substitution( 0, [ :=( X, X )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 paramod(
% 246.44/246.82 clause( 100843, [ =( multiply( inverse( a ), d ), multiply( identity, c ) )
% 246.44/246.82 ] )
% 246.44/246.82 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 246.44/246.82 , 0, clause( 100840, [ =( multiply( X, d ), multiply( multiply( X, a ), c )
% 246.44/246.82 ) ] )
% 246.44/246.82 , 0, 6, substitution( 0, [ :=( X, a )] ), substitution( 1, [ :=( X, inverse(
% 246.44/246.82 a ) )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 paramod(
% 246.44/246.82 clause( 100844, [ =( multiply( inverse( a ), d ), c ) ] )
% 246.44/246.82 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 246.44/246.82 , 0, clause( 100843, [ =( multiply( inverse( a ), d ), multiply( identity,
% 246.44/246.82 c ) ) ] )
% 246.44/246.82 , 0, 5, substitution( 0, [ :=( X, c )] ), substitution( 1, [] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 803, [ =( multiply( inverse( a ), d ), c ) ] )
% 246.44/246.82 , clause( 100844, [ =( multiply( inverse( a ), d ), c ) ] )
% 246.44/246.82 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 eqswap(
% 246.44/246.82 clause( 100846, [ =( X, multiply( multiply( X, inverse( Y ) ), Y ) ) ] )
% 246.44/246.82 , clause( 25, [ =( multiply( multiply( Y, inverse( X ) ), X ), Y ) ] )
% 246.44/246.82 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 paramod(
% 246.44/246.82 clause( 100849, [ =( multiply( X, inverse( inverse( Y ) ) ), multiply( X, Y
% 246.44/246.82 ) ) ] )
% 246.44/246.82 , clause( 25, [ =( multiply( multiply( Y, inverse( X ) ), X ), Y ) ] )
% 246.44/246.82 , 0, clause( 100846, [ =( X, multiply( multiply( X, inverse( Y ) ), Y ) ) ]
% 246.44/246.82 )
% 246.44/246.82 , 0, 7, substitution( 0, [ :=( X, inverse( Y ) ), :=( Y, X )] ),
% 246.44/246.82 substitution( 1, [ :=( X, multiply( X, inverse( inverse( Y ) ) ) ), :=( Y
% 246.44/246.82 , Y )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 872, [ =( multiply( X, inverse( inverse( Y ) ) ), multiply( X, Y )
% 246.44/246.82 ) ] )
% 246.44/246.82 , clause( 100849, [ =( multiply( X, inverse( inverse( Y ) ) ), multiply( X
% 246.44/246.82 , Y ) ) ] )
% 246.44/246.82 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 246.44/246.82 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 eqswap(
% 246.44/246.82 clause( 100852, [ =( X, multiply( multiply( X, inverse( Y ) ), Y ) ) ] )
% 246.44/246.82 , clause( 25, [ =( multiply( multiply( Y, inverse( X ) ), X ), Y ) ] )
% 246.44/246.82 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 paramod(
% 246.44/246.82 clause( 100854, [ =( inverse( inverse( X ) ), multiply( identity, X ) ) ]
% 246.44/246.82 )
% 246.44/246.82 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 246.44/246.82 , 0, clause( 100852, [ =( X, multiply( multiply( X, inverse( Y ) ), Y ) ) ]
% 246.44/246.82 )
% 246.44/246.82 , 0, 5, substitution( 0, [ :=( X, inverse( X ) )] ), substitution( 1, [
% 246.44/246.82 :=( X, inverse( inverse( X ) ) ), :=( Y, X )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 paramod(
% 246.44/246.82 clause( 100855, [ =( inverse( inverse( X ) ), X ) ] )
% 246.44/246.82 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 246.44/246.82 , 0, clause( 100854, [ =( inverse( inverse( X ) ), multiply( identity, X )
% 246.44/246.82 ) ] )
% 246.44/246.82 , 0, 4, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 246.44/246.82 ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 878, [ =( inverse( inverse( X ) ), X ) ] )
% 246.44/246.82 , clause( 100855, [ =( inverse( inverse( X ) ), X ) ] )
% 246.44/246.82 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 paramod(
% 246.44/246.82 clause( 100858, [ 'subgroup_member'( X ), ~( 'subgroup_member'( inverse( X
% 246.44/246.82 ) ) ) ] )
% 246.44/246.82 , clause( 878, [ =( inverse( inverse( X ) ), X ) ] )
% 246.44/246.82 , 0, clause( 3, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( inverse(
% 246.44/246.82 X ) ) ] )
% 246.44/246.82 , 1, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, inverse(
% 246.44/246.82 X ) )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 883, [ ~( 'subgroup_member'( inverse( X ) ) ), 'subgroup_member'( X
% 246.44/246.82 ) ] )
% 246.44/246.82 , clause( 100858, [ 'subgroup_member'( X ), ~( 'subgroup_member'( inverse(
% 246.44/246.82 X ) ) ) ] )
% 246.44/246.82 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1,
% 246.44/246.82 0 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 resolution(
% 246.44/246.82 clause( 100859, [ ~( 'subgroup_member'( inverse( a ) ) ) ] )
% 246.44/246.82 , clause( 478, [ ~( 'subgroup_member'( a ) ) ] )
% 246.44/246.82 , 0, clause( 883, [ ~( 'subgroup_member'( inverse( X ) ) ),
% 246.44/246.82 'subgroup_member'( X ) ] )
% 246.44/246.82 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, a )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 891, [ ~( 'subgroup_member'( inverse( a ) ) ) ] )
% 246.44/246.82 , clause( 100859, [ ~( 'subgroup_member'( inverse( a ) ) ) ] )
% 246.44/246.82 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 resolution(
% 246.44/246.82 clause( 100860, [ 'subgroup_member'( multiply( X, X ) ), ~(
% 246.44/246.82 'subgroup_member'( inverse( X ) ) ) ] )
% 246.44/246.82 , clause( 16, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( multiply( X
% 246.44/246.82 , X ) ) ] )
% 246.44/246.82 , 0, clause( 883, [ ~( 'subgroup_member'( inverse( X ) ) ),
% 246.44/246.82 'subgroup_member'( X ) ] )
% 246.44/246.82 , 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 246.44/246.82 ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 898, [ ~( 'subgroup_member'( inverse( X ) ) ), 'subgroup_member'(
% 246.44/246.82 multiply( X, X ) ) ] )
% 246.44/246.82 , clause( 100860, [ 'subgroup_member'( multiply( X, X ) ), ~(
% 246.44/246.82 'subgroup_member'( inverse( X ) ) ) ] )
% 246.44/246.82 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1,
% 246.44/246.82 0 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 eqswap(
% 246.44/246.82 clause( 100862, [ ~( =( Z, multiply( X, inverse( Y ) ) ) ), ~(
% 246.44/246.82 'subgroup_member'( X ) ), 'subgroup_member'( Z ), ~( 'subgroup_member'( Y
% 246.44/246.82 ) ) ] )
% 246.44/246.82 , clause( 47, [ ~( 'subgroup_member'( X ) ), ~( =( multiply( X, inverse( Y
% 246.44/246.82 ) ), Z ) ), 'subgroup_member'( Z ), ~( 'subgroup_member'( Y ) ) ] )
% 246.44/246.82 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 paramod(
% 246.44/246.82 clause( 100864, [ ~( =( X, Y ) ), ~( 'subgroup_member'( multiply( Y,
% 246.44/246.82 inverse( inverse( Z ) ) ) ) ), 'subgroup_member'( X ), ~(
% 246.44/246.82 'subgroup_member'( Z ) ) ] )
% 246.44/246.82 , clause( 25, [ =( multiply( multiply( Y, inverse( X ) ), X ), Y ) ] )
% 246.44/246.82 , 0, clause( 100862, [ ~( =( Z, multiply( X, inverse( Y ) ) ) ), ~(
% 246.44/246.82 'subgroup_member'( X ) ), 'subgroup_member'( Z ), ~( 'subgroup_member'( Y
% 246.44/246.82 ) ) ] )
% 246.44/246.82 , 0, 3, substitution( 0, [ :=( X, inverse( Z ) ), :=( Y, Y )] ),
% 246.44/246.82 substitution( 1, [ :=( X, multiply( Y, inverse( inverse( Z ) ) ) ), :=( Y
% 246.44/246.82 , Z ), :=( Z, X )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 paramod(
% 246.44/246.82 clause( 100865, [ ~( 'subgroup_member'( multiply( X, Y ) ) ), ~( =( Z, X )
% 246.44/246.82 ), 'subgroup_member'( Z ), ~( 'subgroup_member'( Y ) ) ] )
% 246.44/246.82 , clause( 872, [ =( multiply( X, inverse( inverse( Y ) ) ), multiply( X, Y
% 246.44/246.82 ) ) ] )
% 246.44/246.82 , 0, clause( 100864, [ ~( =( X, Y ) ), ~( 'subgroup_member'( multiply( Y,
% 246.44/246.82 inverse( inverse( Z ) ) ) ) ), 'subgroup_member'( X ), ~(
% 246.44/246.82 'subgroup_member'( Z ) ) ] )
% 246.44/246.82 , 1, 2, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 246.44/246.82 :=( X, Z ), :=( Y, X ), :=( Z, Y )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 eqswap(
% 246.44/246.82 clause( 100866, [ ~( =( Y, X ) ), ~( 'subgroup_member'( multiply( Y, Z ) )
% 246.44/246.82 ), 'subgroup_member'( X ), ~( 'subgroup_member'( Z ) ) ] )
% 246.44/246.82 , clause( 100865, [ ~( 'subgroup_member'( multiply( X, Y ) ) ), ~( =( Z, X
% 246.44/246.82 ) ), 'subgroup_member'( Z ), ~( 'subgroup_member'( Y ) ) ] )
% 246.44/246.82 , 1, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 3777, [ ~( =( X, Z ) ), 'subgroup_member'( Z ), ~(
% 246.44/246.82 'subgroup_member'( Y ) ), ~( 'subgroup_member'( multiply( X, Y ) ) ) ] )
% 246.44/246.82 , clause( 100866, [ ~( =( Y, X ) ), ~( 'subgroup_member'( multiply( Y, Z )
% 246.44/246.82 ) ), 'subgroup_member'( X ), ~( 'subgroup_member'( Z ) ) ] )
% 246.44/246.82 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 246.44/246.82 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 3 ), ==>( 2, 1 ), ==>( 3, 2 )] )
% 246.44/246.82 ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 eqswap(
% 246.44/246.82 clause( 100867, [ ~( =( Y, X ) ), 'subgroup_member'( Y ), ~(
% 246.44/246.82 'subgroup_member'( Z ) ), ~( 'subgroup_member'( multiply( X, Z ) ) ) ] )
% 246.44/246.82 , clause( 3777, [ ~( =( X, Z ) ), 'subgroup_member'( Z ), ~(
% 246.44/246.82 'subgroup_member'( Y ) ), ~( 'subgroup_member'( multiply( X, Y ) ) ) ] )
% 246.44/246.82 , 0, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 eqrefl(
% 246.44/246.82 clause( 100868, [ 'subgroup_member'( X ), ~( 'subgroup_member'( Y ) ), ~(
% 246.44/246.82 'subgroup_member'( multiply( X, Y ) ) ) ] )
% 246.44/246.82 , clause( 100867, [ ~( =( Y, X ) ), 'subgroup_member'( Y ), ~(
% 246.44/246.82 'subgroup_member'( Z ) ), ~( 'subgroup_member'( multiply( X, Z ) ) ) ] )
% 246.44/246.82 , 0, substitution( 0, [ :=( X, X ), :=( Y, X ), :=( Z, Y )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 3778, [ 'subgroup_member'( X ), ~( 'subgroup_member'( Y ) ), ~(
% 246.44/246.82 'subgroup_member'( multiply( X, Y ) ) ) ] )
% 246.44/246.82 , clause( 100868, [ 'subgroup_member'( X ), ~( 'subgroup_member'( Y ) ),
% 246.44/246.82 ~( 'subgroup_member'( multiply( X, Y ) ) ) ] )
% 246.44/246.82 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 246.44/246.82 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 resolution(
% 246.44/246.82 clause( 100869, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'(
% 246.44/246.82 multiply( inverse( a ), X ) ) ) ] )
% 246.44/246.82 , clause( 891, [ ~( 'subgroup_member'( inverse( a ) ) ) ] )
% 246.44/246.82 , 0, clause( 3778, [ 'subgroup_member'( X ), ~( 'subgroup_member'( Y ) ),
% 246.44/246.82 ~( 'subgroup_member'( multiply( X, Y ) ) ) ] )
% 246.44/246.82 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, inverse( a ) ), :=( Y
% 246.44/246.82 , X )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 59229, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'(
% 246.44/246.82 multiply( inverse( a ), X ) ) ) ] )
% 246.44/246.82 , clause( 100869, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'(
% 246.44/246.82 multiply( inverse( a ), X ) ) ) ] )
% 246.44/246.82 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 246.44/246.82 1 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 eqswap(
% 246.44/246.82 clause( 100871, [ =( multiply( X, Z ), multiply( multiply( X, Y ),
% 246.44/246.82 'element_in_O2'( Y, Z ) ) ), 'subgroup_member'( Y ), 'subgroup_member'( Z
% 246.44/246.82 ) ] )
% 246.44/246.82 , clause( 369, [ =( multiply( multiply( Z, X ), 'element_in_O2'( X, Y ) ),
% 246.44/246.82 multiply( Z, Y ) ), 'subgroup_member'( X ), 'subgroup_member'( Y ) ] )
% 246.44/246.82 , 0, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 paramod(
% 246.44/246.82 clause( 100873, [ =( multiply( inverse( a ), X ), multiply( c,
% 246.44/246.82 'element_in_O2'( d, X ) ) ), 'subgroup_member'( d ), 'subgroup_member'( X
% 246.44/246.82 ) ] )
% 246.44/246.82 , clause( 803, [ =( multiply( inverse( a ), d ), c ) ] )
% 246.44/246.82 , 0, clause( 100871, [ =( multiply( X, Z ), multiply( multiply( X, Y ),
% 246.44/246.82 'element_in_O2'( Y, Z ) ) ), 'subgroup_member'( Y ), 'subgroup_member'( Z
% 246.44/246.82 ) ] )
% 246.44/246.82 , 0, 6, substitution( 0, [] ), substitution( 1, [ :=( X, inverse( a ) ),
% 246.44/246.82 :=( Y, d ), :=( Z, X )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 resolution(
% 246.44/246.82 clause( 100878, [ =( multiply( inverse( a ), X ), multiply( c,
% 246.44/246.82 'element_in_O2'( d, X ) ) ), 'subgroup_member'( X ) ] )
% 246.44/246.82 , clause( 13, [ ~( 'subgroup_member'( d ) ) ] )
% 246.44/246.82 , 0, clause( 100873, [ =( multiply( inverse( a ), X ), multiply( c,
% 246.44/246.82 'element_in_O2'( d, X ) ) ), 'subgroup_member'( d ), 'subgroup_member'( X
% 246.44/246.82 ) ] )
% 246.44/246.82 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, X )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 eqswap(
% 246.44/246.82 clause( 100879, [ =( multiply( c, 'element_in_O2'( d, X ) ), multiply(
% 246.44/246.82 inverse( a ), X ) ), 'subgroup_member'( X ) ] )
% 246.44/246.82 , clause( 100878, [ =( multiply( inverse( a ), X ), multiply( c,
% 246.44/246.82 'element_in_O2'( d, X ) ) ), 'subgroup_member'( X ) ] )
% 246.44/246.82 , 0, substitution( 0, [ :=( X, X )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 84265, [ =( multiply( c, 'element_in_O2'( d, X ) ), multiply(
% 246.44/246.82 inverse( a ), X ) ), 'subgroup_member'( X ) ] )
% 246.44/246.82 , clause( 100879, [ =( multiply( c, 'element_in_O2'( d, X ) ), multiply(
% 246.44/246.82 inverse( a ), X ) ), 'subgroup_member'( X ) ] )
% 246.44/246.82 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 246.44/246.82 1 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 eqswap(
% 246.44/246.82 clause( 100881, [ =( multiply( X, Z ), multiply( multiply( X, Y ),
% 246.44/246.82 'element_in_O2'( Y, Z ) ) ), 'subgroup_member'( Y ), 'subgroup_member'( Z
% 246.44/246.82 ) ] )
% 246.44/246.82 , clause( 369, [ =( multiply( multiply( Z, X ), 'element_in_O2'( X, Y ) ),
% 246.44/246.82 multiply( Z, Y ) ), 'subgroup_member'( X ), 'subgroup_member'( Y ) ] )
% 246.44/246.82 , 0, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 paramod(
% 246.44/246.82 clause( 100884, [ =( multiply( X, Y ), multiply( identity, 'element_in_O2'(
% 246.44/246.82 inverse( X ), Y ) ) ), 'subgroup_member'( inverse( X ) ),
% 246.44/246.82 'subgroup_member'( Y ) ] )
% 246.44/246.82 , clause( 6, [ =( multiply( X, inverse( X ) ), identity ) ] )
% 246.44/246.82 , 0, clause( 100881, [ =( multiply( X, Z ), multiply( multiply( X, Y ),
% 246.44/246.82 'element_in_O2'( Y, Z ) ) ), 'subgroup_member'( Y ), 'subgroup_member'( Z
% 246.44/246.82 ) ] )
% 246.44/246.82 , 0, 5, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 246.44/246.82 :=( Y, inverse( X ) ), :=( Z, Y )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 paramod(
% 246.44/246.82 clause( 100889, [ =( multiply( X, Y ), 'element_in_O2'( inverse( X ), Y ) )
% 246.44/246.82 , 'subgroup_member'( inverse( X ) ), 'subgroup_member'( Y ) ] )
% 246.44/246.82 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 246.44/246.82 , 0, clause( 100884, [ =( multiply( X, Y ), multiply( identity,
% 246.44/246.82 'element_in_O2'( inverse( X ), Y ) ) ), 'subgroup_member'( inverse( X ) )
% 246.44/246.82 , 'subgroup_member'( Y ) ] )
% 246.44/246.82 , 0, 4, substitution( 0, [ :=( X, 'element_in_O2'( inverse( X ), Y ) )] ),
% 246.44/246.82 substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 eqswap(
% 246.44/246.82 clause( 100890, [ =( 'element_in_O2'( inverse( X ), Y ), multiply( X, Y ) )
% 246.44/246.82 , 'subgroup_member'( inverse( X ) ), 'subgroup_member'( Y ) ] )
% 246.44/246.82 , clause( 100889, [ =( multiply( X, Y ), 'element_in_O2'( inverse( X ), Y )
% 246.44/246.82 ), 'subgroup_member'( inverse( X ) ), 'subgroup_member'( Y ) ] )
% 246.44/246.82 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 84267, [ 'subgroup_member'( inverse( X ) ), 'subgroup_member'( Y )
% 246.44/246.82 , =( 'element_in_O2'( inverse( X ), Y ), multiply( X, Y ) ) ] )
% 246.44/246.82 , clause( 100890, [ =( 'element_in_O2'( inverse( X ), Y ), multiply( X, Y )
% 246.44/246.82 ), 'subgroup_member'( inverse( X ) ), 'subgroup_member'( Y ) ] )
% 246.44/246.82 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 2
% 246.44/246.82 ), ==>( 1, 0 ), ==>( 2, 1 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 eqswap(
% 246.44/246.82 clause( 100894, [ ~( =( Z, multiply( X, Y ) ) ), 'subgroup_member'( Z ),
% 246.44/246.82 'subgroup_member'( 'element_in_O2'( X, Z ) ), ~( 'subgroup_member'( Y ) )
% 246.44/246.82 ] )
% 246.44/246.82 , clause( 247, [ 'subgroup_member'( X ), 'subgroup_member'( 'element_in_O2'(
% 246.44/246.82 Y, X ) ), ~( 'subgroup_member'( Z ) ), ~( =( multiply( Y, Z ), X ) ) ] )
% 246.44/246.82 , 3, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 paramod(
% 246.44/246.82 clause( 100896, [ ~( =( X, Y ) ), 'subgroup_member'( inverse( Y ) ),
% 246.44/246.82 'subgroup_member'( X ), 'subgroup_member'( 'element_in_O2'( inverse( Y )
% 246.44/246.82 , X ) ), ~( 'subgroup_member'( 'element_in_O2'( inverse( Y ), Y ) ) ) ]
% 246.44/246.82 )
% 246.44/246.82 , clause( 371, [ 'subgroup_member'( inverse( X ) ), =( multiply( inverse( X
% 246.44/246.82 ), 'element_in_O2'( inverse( X ), X ) ), X ) ] )
% 246.44/246.82 , 1, clause( 100894, [ ~( =( Z, multiply( X, Y ) ) ), 'subgroup_member'( Z
% 246.44/246.82 ), 'subgroup_member'( 'element_in_O2'( X, Z ) ), ~( 'subgroup_member'( Y
% 246.44/246.82 ) ) ] )
% 246.44/246.82 , 0, 3, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, inverse(
% 246.44/246.82 Y ) ), :=( Y, 'element_in_O2'( inverse( Y ), Y ) ), :=( Z, X )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 paramod(
% 246.44/246.82 clause( 100990, [ 'subgroup_member'( multiply( X, Y ) ), 'subgroup_member'(
% 246.44/246.82 inverse( X ) ), 'subgroup_member'( Y ), ~( =( Y, X ) ), 'subgroup_member'(
% 246.44/246.82 inverse( X ) ), 'subgroup_member'( Y ), ~( 'subgroup_member'(
% 246.44/246.82 'element_in_O2'( inverse( X ), X ) ) ) ] )
% 246.44/246.82 , clause( 84267, [ 'subgroup_member'( inverse( X ) ), 'subgroup_member'( Y
% 246.44/246.82 ), =( 'element_in_O2'( inverse( X ), Y ), multiply( X, Y ) ) ] )
% 246.44/246.82 , 2, clause( 100896, [ ~( =( X, Y ) ), 'subgroup_member'( inverse( Y ) ),
% 246.44/246.82 'subgroup_member'( X ), 'subgroup_member'( 'element_in_O2'( inverse( Y )
% 246.44/246.82 , X ) ), ~( 'subgroup_member'( 'element_in_O2'( inverse( Y ), Y ) ) ) ]
% 246.44/246.82 )
% 246.44/246.82 , 3, 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 246.44/246.82 :=( X, Y ), :=( Y, X )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 factor(
% 246.44/246.82 clause( 100994, [ 'subgroup_member'( multiply( X, Y ) ), 'subgroup_member'(
% 246.44/246.82 inverse( X ) ), 'subgroup_member'( Y ), ~( =( Y, X ) ), 'subgroup_member'(
% 246.44/246.82 Y ), ~( 'subgroup_member'( 'element_in_O2'( inverse( X ), X ) ) ) ] )
% 246.44/246.82 , clause( 100990, [ 'subgroup_member'( multiply( X, Y ) ),
% 246.44/246.82 'subgroup_member'( inverse( X ) ), 'subgroup_member'( Y ), ~( =( Y, X ) )
% 246.44/246.82 , 'subgroup_member'( inverse( X ) ), 'subgroup_member'( Y ), ~(
% 246.44/246.82 'subgroup_member'( 'element_in_O2'( inverse( X ), X ) ) ) ] )
% 246.44/246.82 , 1, 4, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 factor(
% 246.44/246.82 clause( 100996, [ 'subgroup_member'( multiply( X, Y ) ), 'subgroup_member'(
% 246.44/246.82 inverse( X ) ), 'subgroup_member'( Y ), ~( =( Y, X ) ), ~(
% 246.44/246.82 'subgroup_member'( 'element_in_O2'( inverse( X ), X ) ) ) ] )
% 246.44/246.82 , clause( 100994, [ 'subgroup_member'( multiply( X, Y ) ),
% 246.44/246.82 'subgroup_member'( inverse( X ) ), 'subgroup_member'( Y ), ~( =( Y, X ) )
% 246.44/246.82 , 'subgroup_member'( Y ), ~( 'subgroup_member'( 'element_in_O2'( inverse(
% 246.44/246.82 X ), X ) ) ) ] )
% 246.44/246.82 , 2, 4, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 resolution(
% 246.44/246.82 clause( 101270, [ 'subgroup_member'( multiply( X, Y ) ), 'subgroup_member'(
% 246.44/246.82 inverse( X ) ), 'subgroup_member'( Y ), ~( =( Y, X ) ), 'subgroup_member'(
% 246.44/246.82 inverse( X ) ), 'subgroup_member'( inverse( X ) ) ] )
% 246.44/246.82 , clause( 100996, [ 'subgroup_member'( multiply( X, Y ) ),
% 246.44/246.82 'subgroup_member'( inverse( X ) ), 'subgroup_member'( Y ), ~( =( Y, X ) )
% 246.44/246.82 , ~( 'subgroup_member'( 'element_in_O2'( inverse( X ), X ) ) ) ] )
% 246.44/246.82 , 4, clause( 223, [ 'subgroup_member'( X ), 'subgroup_member'(
% 246.44/246.82 'element_in_O2'( X, Y ) ), 'subgroup_member'( inverse( Y ) ) ] )
% 246.44/246.82 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [ :=( X
% 246.44/246.82 , inverse( X ) ), :=( Y, X )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 eqswap(
% 246.44/246.82 clause( 101271, [ ~( =( Y, X ) ), 'subgroup_member'( multiply( Y, X ) ),
% 246.44/246.82 'subgroup_member'( inverse( Y ) ), 'subgroup_member'( X ),
% 246.44/246.82 'subgroup_member'( inverse( Y ) ), 'subgroup_member'( inverse( Y ) ) ] )
% 246.44/246.82 , clause( 101270, [ 'subgroup_member'( multiply( X, Y ) ),
% 246.44/246.82 'subgroup_member'( inverse( X ) ), 'subgroup_member'( Y ), ~( =( Y, X ) )
% 246.44/246.82 , 'subgroup_member'( inverse( X ) ), 'subgroup_member'( inverse( X ) ) ]
% 246.44/246.82 )
% 246.44/246.82 , 3, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 factor(
% 246.44/246.82 clause( 101279, [ ~( =( X, Y ) ), 'subgroup_member'( multiply( X, Y ) ),
% 246.44/246.82 'subgroup_member'( inverse( X ) ), 'subgroup_member'( Y ),
% 246.44/246.82 'subgroup_member'( inverse( X ) ) ] )
% 246.44/246.82 , clause( 101271, [ ~( =( Y, X ) ), 'subgroup_member'( multiply( Y, X ) ),
% 246.44/246.82 'subgroup_member'( inverse( Y ) ), 'subgroup_member'( X ),
% 246.44/246.82 'subgroup_member'( inverse( Y ) ), 'subgroup_member'( inverse( Y ) ) ] )
% 246.44/246.82 , 2, 4, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 factor(
% 246.44/246.82 clause( 101281, [ ~( =( X, Y ) ), 'subgroup_member'( multiply( X, Y ) ),
% 246.44/246.82 'subgroup_member'( inverse( X ) ), 'subgroup_member'( Y ) ] )
% 246.44/246.82 , clause( 101279, [ ~( =( X, Y ) ), 'subgroup_member'( multiply( X, Y ) ),
% 246.44/246.82 'subgroup_member'( inverse( X ) ), 'subgroup_member'( Y ),
% 246.44/246.82 'subgroup_member'( inverse( X ) ) ] )
% 246.44/246.82 , 2, 4, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 84709, [ 'subgroup_member'( Y ), ~( =( X, Y ) ), 'subgroup_member'(
% 246.44/246.82 inverse( X ) ), 'subgroup_member'( multiply( X, Y ) ) ] )
% 246.44/246.82 , clause( 101281, [ ~( =( X, Y ) ), 'subgroup_member'( multiply( X, Y ) ),
% 246.44/246.82 'subgroup_member'( inverse( X ) ), 'subgroup_member'( Y ) ] )
% 246.44/246.82 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 1
% 246.44/246.82 ), ==>( 1, 3 ), ==>( 2, 2 ), ==>( 3, 0 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 eqswap(
% 246.44/246.82 clause( 101288, [ ~( =( Y, X ) ), 'subgroup_member'( Y ), 'subgroup_member'(
% 246.44/246.82 inverse( X ) ), 'subgroup_member'( multiply( X, Y ) ) ] )
% 246.44/246.82 , clause( 84709, [ 'subgroup_member'( Y ), ~( =( X, Y ) ),
% 246.44/246.82 'subgroup_member'( inverse( X ) ), 'subgroup_member'( multiply( X, Y ) )
% 246.44/246.82 ] )
% 246.44/246.82 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 eqrefl(
% 246.44/246.82 clause( 101289, [ 'subgroup_member'( X ), 'subgroup_member'( inverse( X ) )
% 246.44/246.82 , 'subgroup_member'( multiply( X, X ) ) ] )
% 246.44/246.82 , clause( 101288, [ ~( =( Y, X ) ), 'subgroup_member'( Y ),
% 246.44/246.82 'subgroup_member'( inverse( X ) ), 'subgroup_member'( multiply( X, Y ) )
% 246.44/246.82 ] )
% 246.44/246.82 , 0, substitution( 0, [ :=( X, X ), :=( Y, X )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 resolution(
% 246.44/246.82 clause( 101290, [ 'subgroup_member'( inverse( X ) ), 'subgroup_member'(
% 246.44/246.82 inverse( X ) ), 'subgroup_member'( multiply( X, X ) ) ] )
% 246.44/246.82 , clause( 3, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( inverse( X )
% 246.44/246.82 ) ] )
% 246.44/246.82 , 0, clause( 101289, [ 'subgroup_member'( X ), 'subgroup_member'( inverse(
% 246.44/246.82 X ) ), 'subgroup_member'( multiply( X, X ) ) ] )
% 246.44/246.82 , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 246.44/246.82 ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 factor(
% 246.44/246.82 clause( 101293, [ 'subgroup_member'( inverse( X ) ), 'subgroup_member'(
% 246.44/246.82 multiply( X, X ) ) ] )
% 246.44/246.82 , clause( 101290, [ 'subgroup_member'( inverse( X ) ), 'subgroup_member'(
% 246.44/246.82 inverse( X ) ), 'subgroup_member'( multiply( X, X ) ) ] )
% 246.44/246.82 , 0, 1, substitution( 0, [ :=( X, X )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 84713, [ 'subgroup_member'( inverse( X ) ), 'subgroup_member'(
% 246.44/246.82 multiply( X, X ) ) ] )
% 246.44/246.82 , clause( 101293, [ 'subgroup_member'( inverse( X ) ), 'subgroup_member'(
% 246.44/246.82 multiply( X, X ) ) ] )
% 246.44/246.82 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 246.44/246.82 1 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 resolution(
% 246.44/246.82 clause( 101294, [ 'subgroup_member'( multiply( X, X ) ), 'subgroup_member'(
% 246.44/246.82 multiply( X, X ) ) ] )
% 246.44/246.82 , clause( 898, [ ~( 'subgroup_member'( inverse( X ) ) ), 'subgroup_member'(
% 246.44/246.82 multiply( X, X ) ) ] )
% 246.44/246.82 , 0, clause( 84713, [ 'subgroup_member'( inverse( X ) ), 'subgroup_member'(
% 246.44/246.82 multiply( X, X ) ) ] )
% 246.44/246.82 , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 246.44/246.82 ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 factor(
% 246.44/246.82 clause( 101295, [ 'subgroup_member'( multiply( X, X ) ) ] )
% 246.44/246.82 , clause( 101294, [ 'subgroup_member'( multiply( X, X ) ),
% 246.44/246.82 'subgroup_member'( multiply( X, X ) ) ] )
% 246.44/246.82 , 0, 1, substitution( 0, [ :=( X, X )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 84715, [ 'subgroup_member'( multiply( X, X ) ) ] )
% 246.44/246.82 , clause( 101295, [ 'subgroup_member'( multiply( X, X ) ) ] )
% 246.44/246.82 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 resolution(
% 246.44/246.82 clause( 101296, [ 'subgroup_member'( multiply( multiply( b, X ), X ) ) ] )
% 246.44/246.82 , clause( 134, [ ~( 'subgroup_member'( multiply( X, Y ) ) ),
% 246.44/246.82 'subgroup_member'( multiply( multiply( b, X ), Y ) ) ] )
% 246.44/246.82 , 0, clause( 84715, [ 'subgroup_member'( multiply( X, X ) ) ] )
% 246.44/246.82 , 0, substitution( 0, [ :=( X, X ), :=( Y, X )] ), substitution( 1, [ :=( X
% 246.44/246.82 , X )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 84826, [ 'subgroup_member'( multiply( multiply( b, X ), X ) ) ] )
% 246.44/246.82 , clause( 101296, [ 'subgroup_member'( multiply( multiply( b, X ), X ) ) ]
% 246.44/246.82 )
% 246.44/246.82 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 paramod(
% 246.44/246.82 clause( 101298, [ 'subgroup_member'( multiply( c, inverse( a ) ) ) ] )
% 246.44/246.82 , clause( 11, [ =( multiply( b, inverse( a ) ), c ) ] )
% 246.44/246.82 , 0, clause( 84826, [ 'subgroup_member'( multiply( multiply( b, X ), X ) )
% 246.44/246.82 ] )
% 246.44/246.82 , 0, 2, substitution( 0, [] ), substitution( 1, [ :=( X, inverse( a ) )] )
% 246.44/246.82 ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 85719, [ 'subgroup_member'( multiply( c, inverse( a ) ) ) ] )
% 246.44/246.82 , clause( 101298, [ 'subgroup_member'( multiply( c, inverse( a ) ) ) ] )
% 246.44/246.82 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 resolution(
% 246.44/246.82 clause( 101300, [ 'subgroup_member'( multiply( inverse( b ), multiply( c,
% 246.44/246.82 inverse( a ) ) ) ) ] )
% 246.44/246.82 , clause( 69, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( multiply(
% 246.44/246.82 inverse( b ), X ) ) ] )
% 246.44/246.82 , 0, clause( 85719, [ 'subgroup_member'( multiply( c, inverse( a ) ) ) ] )
% 246.44/246.82 , 0, substitution( 0, [ :=( X, multiply( c, inverse( a ) ) )] ),
% 246.44/246.82 substitution( 1, [] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 paramod(
% 246.44/246.82 clause( 101301, [ 'subgroup_member'( multiply( multiply( inverse( b ), c )
% 246.44/246.82 , inverse( a ) ) ) ] )
% 246.44/246.82 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 246.44/246.82 ), Z ) ) ] )
% 246.44/246.82 , 0, clause( 101300, [ 'subgroup_member'( multiply( inverse( b ), multiply(
% 246.44/246.82 c, inverse( a ) ) ) ) ] )
% 246.44/246.82 , 0, 1, substitution( 0, [ :=( X, inverse( b ) ), :=( Y, c ), :=( Z,
% 246.44/246.82 inverse( a ) )] ), substitution( 1, [] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 85839, [ 'subgroup_member'( multiply( multiply( inverse( b ), c ),
% 246.44/246.82 inverse( a ) ) ) ] )
% 246.44/246.82 , clause( 101301, [ 'subgroup_member'( multiply( multiply( inverse( b ), c
% 246.44/246.82 ), inverse( a ) ) ) ] )
% 246.44/246.82 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 eqswap(
% 246.44/246.82 clause( 101303, [ =( multiply( X, c ), multiply( multiply( X, b ), inverse(
% 246.44/246.82 a ) ) ) ] )
% 246.44/246.82 , clause( 465, [ =( multiply( multiply( X, b ), inverse( a ) ), multiply( X
% 246.44/246.82 , c ) ) ] )
% 246.44/246.82 , 0, substitution( 0, [ :=( X, X )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 paramod(
% 246.44/246.82 clause( 101306, [ =( multiply( inverse( b ), c ), multiply( identity,
% 246.44/246.82 inverse( a ) ) ) ] )
% 246.44/246.82 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 246.44/246.82 , 0, clause( 101303, [ =( multiply( X, c ), multiply( multiply( X, b ),
% 246.44/246.82 inverse( a ) ) ) ] )
% 246.44/246.82 , 0, 6, substitution( 0, [ :=( X, b )] ), substitution( 1, [ :=( X, inverse(
% 246.44/246.82 b ) )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 paramod(
% 246.44/246.82 clause( 101307, [ =( multiply( inverse( b ), c ), inverse( a ) ) ] )
% 246.44/246.82 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 246.44/246.82 , 0, clause( 101306, [ =( multiply( inverse( b ), c ), multiply( identity,
% 246.44/246.82 inverse( a ) ) ) ] )
% 246.44/246.82 , 0, 5, substitution( 0, [ :=( X, inverse( a ) )] ), substitution( 1, [] )
% 246.44/246.82 ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 89068, [ =( multiply( inverse( b ), c ), inverse( a ) ) ] )
% 246.44/246.82 , clause( 101307, [ =( multiply( inverse( b ), c ), inverse( a ) ) ] )
% 246.44/246.82 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 paramod(
% 246.44/246.82 clause( 101310, [ 'subgroup_member'( inverse( a ) ), ~( 'subgroup_member'(
% 246.44/246.82 c ) ) ] )
% 246.44/246.82 , clause( 89068, [ =( multiply( inverse( b ), c ), inverse( a ) ) ] )
% 246.44/246.82 , 0, clause( 69, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( multiply(
% 246.44/246.82 inverse( b ), X ) ) ] )
% 246.44/246.82 , 1, 1, substitution( 0, [] ), substitution( 1, [ :=( X, c )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 resolution(
% 246.44/246.82 clause( 101311, [ ~( 'subgroup_member'( c ) ) ] )
% 246.44/246.82 , clause( 891, [ ~( 'subgroup_member'( inverse( a ) ) ) ] )
% 246.44/246.82 , 0, clause( 101310, [ 'subgroup_member'( inverse( a ) ), ~(
% 246.44/246.82 'subgroup_member'( c ) ) ] )
% 246.44/246.82 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 89127, [ ~( 'subgroup_member'( c ) ) ] )
% 246.44/246.82 , clause( 101311, [ ~( 'subgroup_member'( c ) ) ] )
% 246.44/246.82 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 resolution(
% 246.44/246.82 clause( 101312, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'(
% 246.44/246.82 multiply( c, X ) ) ) ] )
% 246.44/246.82 , clause( 89127, [ ~( 'subgroup_member'( c ) ) ] )
% 246.44/246.82 , 0, clause( 3778, [ 'subgroup_member'( X ), ~( 'subgroup_member'( Y ) ),
% 246.44/246.82 ~( 'subgroup_member'( multiply( X, Y ) ) ) ] )
% 246.44/246.82 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, c ), :=( Y, X )] )
% 246.44/246.82 ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 89200, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'(
% 246.44/246.82 multiply( c, X ) ) ) ] )
% 246.44/246.82 , clause( 101312, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'(
% 246.44/246.82 multiply( c, X ) ) ) ] )
% 246.44/246.82 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 246.44/246.82 1 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 resolution(
% 246.44/246.82 clause( 101315, [ ~( 'subgroup_member'( multiply( c, 'element_in_O2'( d, X
% 246.44/246.82 ) ) ) ), 'subgroup_member'( X ) ] )
% 246.44/246.82 , clause( 89200, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'(
% 246.44/246.82 multiply( c, X ) ) ) ] )
% 246.44/246.82 , 0, clause( 225, [ 'subgroup_member'( X ), 'subgroup_member'(
% 246.44/246.82 'element_in_O2'( d, X ) ) ] )
% 246.44/246.82 , 1, substitution( 0, [ :=( X, 'element_in_O2'( d, X ) )] ), substitution(
% 246.44/246.82 1, [ :=( X, X )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 paramod(
% 246.44/246.82 clause( 101317, [ ~( 'subgroup_member'( multiply( inverse( a ), X ) ) ),
% 246.44/246.82 'subgroup_member'( X ), 'subgroup_member'( X ) ] )
% 246.44/246.82 , clause( 84265, [ =( multiply( c, 'element_in_O2'( d, X ) ), multiply(
% 246.44/246.82 inverse( a ), X ) ), 'subgroup_member'( X ) ] )
% 246.44/246.82 , 0, clause( 101315, [ ~( 'subgroup_member'( multiply( c, 'element_in_O2'(
% 246.44/246.82 d, X ) ) ) ), 'subgroup_member'( X ) ] )
% 246.44/246.82 , 0, 2, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 246.44/246.82 ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 factor(
% 246.44/246.82 clause( 101318, [ ~( 'subgroup_member'( multiply( inverse( a ), X ) ) ),
% 246.44/246.82 'subgroup_member'( X ) ] )
% 246.44/246.82 , clause( 101317, [ ~( 'subgroup_member'( multiply( inverse( a ), X ) ) ),
% 246.44/246.82 'subgroup_member'( X ), 'subgroup_member'( X ) ] )
% 246.44/246.82 , 1, 2, substitution( 0, [ :=( X, X )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 resolution(
% 246.44/246.82 clause( 101319, [ ~( 'subgroup_member'( multiply( inverse( a ), X ) ) ),
% 246.44/246.82 ~( 'subgroup_member'( multiply( inverse( a ), X ) ) ) ] )
% 246.44/246.82 , clause( 59229, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'(
% 246.44/246.82 multiply( inverse( a ), X ) ) ) ] )
% 246.44/246.82 , 0, clause( 101318, [ ~( 'subgroup_member'( multiply( inverse( a ), X ) )
% 246.44/246.82 ), 'subgroup_member'( X ) ] )
% 246.44/246.82 , 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 246.44/246.82 ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 factor(
% 246.44/246.82 clause( 101320, [ ~( 'subgroup_member'( multiply( inverse( a ), X ) ) ) ]
% 246.44/246.82 )
% 246.44/246.82 , clause( 101319, [ ~( 'subgroup_member'( multiply( inverse( a ), X ) ) ),
% 246.44/246.82 ~( 'subgroup_member'( multiply( inverse( a ), X ) ) ) ] )
% 246.44/246.82 , 0, 1, substitution( 0, [ :=( X, X )] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 100398, [ ~( 'subgroup_member'( multiply( inverse( a ), X ) ) ) ]
% 246.44/246.82 )
% 246.44/246.82 , clause( 101320, [ ~( 'subgroup_member'( multiply( inverse( a ), X ) ) ) ]
% 246.44/246.82 )
% 246.44/246.82 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 paramod(
% 246.44/246.82 clause( 101322, [ 'subgroup_member'( multiply( inverse( a ), inverse( a ) )
% 246.44/246.82 ) ] )
% 246.44/246.82 , clause( 89068, [ =( multiply( inverse( b ), c ), inverse( a ) ) ] )
% 246.44/246.82 , 0, clause( 85839, [ 'subgroup_member'( multiply( multiply( inverse( b ),
% 246.44/246.82 c ), inverse( a ) ) ) ] )
% 246.44/246.82 , 0, 2, substitution( 0, [] ), substitution( 1, [] )).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 resolution(
% 246.44/246.82 clause( 101323, [] )
% 246.44/246.82 , clause( 100398, [ ~( 'subgroup_member'( multiply( inverse( a ), X ) ) ) ]
% 246.44/246.82 )
% 246.44/246.82 , 0, clause( 101322, [ 'subgroup_member'( multiply( inverse( a ), inverse(
% 246.44/246.82 a ) ) ) ] )
% 246.44/246.82 , 0, substitution( 0, [ :=( X, inverse( a ) )] ), substitution( 1, [] )
% 246.44/246.82 ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 subsumption(
% 246.44/246.82 clause( 100572, [] )
% 246.44/246.82 , clause( 101323, [] )
% 246.44/246.82 , substitution( 0, [] ), permutation( 0, [] ) ).
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 end.
% 246.44/246.82
% 246.44/246.82 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 246.44/246.82
% 246.44/246.82 Memory use:
% 246.44/246.82
% 246.44/246.82 space for terms: 1376369
% 246.44/246.82 space for clauses: 4738433
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 clauses generated: 309304
% 246.44/246.82 clauses kept: 100573
% 246.44/246.82 clauses selected: 1315
% 246.44/246.82 clauses deleted: 2916
% 246.44/246.82 clauses inuse deleted: 249
% 246.44/246.82
% 246.44/246.82 subsentry: 6826073
% 246.44/246.82 literals s-matched: 2458021
% 246.44/246.82 literals matched: 2038931
% 246.44/246.82 full subsumption: 1141486
% 246.44/246.82
% 246.44/246.82 checksum: -893148307
% 246.44/246.82
% 246.44/246.82
% 246.44/246.82 Bliksem ended
%------------------------------------------------------------------------------