%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GRP040-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n018.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 07:34:32 EDT 2022
% Result : Unsatisfiable 18.49s 18.89s
% Output : Refutation 18.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP040-4 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : bliksem %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Mon Jun 13 23:04:28 EDT 2022
% 0.13/0.34 % CPUTime :
% 18.49/18.89 *** allocated 10000 integers for termspace/termends
% 18.49/18.89 *** allocated 10000 integers for clauses
% 18.49/18.89 *** allocated 10000 integers for justifications
% 18.49/18.89 Bliksem 1.12
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 Automatic Strategy Selection
% 18.49/18.89
% 18.49/18.89 Clauses:
% 18.49/18.89 [
% 18.49/18.89 [ product( identity, X, X ) ],
% 18.49/18.89 [ product( X, identity, X ) ],
% 18.49/18.89 [ product( inverse( X ), X, identity ) ],
% 18.49/18.89 [ product( X, inverse( X ), identity ) ],
% 18.49/18.89 [ product( X, Y, multiply( X, Y ) ) ],
% 18.49/18.89 [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z, T ) ],
% 18.49/18.89 [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~( product( Z, T, W
% 18.49/18.89 ) ), product( X, U, W ) ],
% 18.49/18.89 [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~( product( X, U, W
% 18.49/18.89 ) ), product( Z, T, W ) ],
% 18.49/18.89 [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( Y ) ), ~( product(
% 18.49/18.89 X, inverse( Y ), Z ) ), 'subgroup_member'( Z ) ],
% 18.49/18.89 [ 'subgroup_member'( identity ) ],
% 18.49/18.89 [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( inverse( X ) ) ],
% 18.49/18.89 [ ~( product( X, Y, Z ) ), ~( product( X, T, Z ) ), =( T, Y ) ],
% 18.49/18.89 [ ~( product( X, Y, Z ) ), ~( product( T, Y, Z ) ), =( T, X ) ],
% 18.49/18.89 [ 'subgroup_member'( 'element_in_O2'( X, Y ) ), 'subgroup_member'( Y ),
% 18.49/18.89 'subgroup_member'( X ) ],
% 18.49/18.89 [ product( X, 'element_in_O2'( X, Y ), Y ), 'subgroup_member'( Y ),
% 18.49/18.89 'subgroup_member'( X ) ],
% 18.49/18.89 [ ~( 'subgroup_member'( a ) ) ],
% 18.49/18.89 [ 'subgroup_member'( b ) ],
% 18.49/18.89 [ ~( 'subgroup_member'( d ) ) ],
% 18.49/18.89 [ product( b, inverse( a ), c ) ],
% 18.49/18.89 [ product( a, c, d ) ],
% 18.49/18.89 [ =( inverse( inverse( X ) ), X ) ]
% 18.49/18.89 ] .
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 percentage equality = 0.097561, percentage horn = 0.904762
% 18.49/18.89 This is a problem with some equality
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 Options Used:
% 18.49/18.89
% 18.49/18.89 useres = 1
% 18.49/18.89 useparamod = 1
% 18.49/18.89 useeqrefl = 1
% 18.49/18.89 useeqfact = 1
% 18.49/18.89 usefactor = 1
% 18.49/18.89 usesimpsplitting = 0
% 18.49/18.89 usesimpdemod = 5
% 18.49/18.89 usesimpres = 3
% 18.49/18.89
% 18.49/18.89 resimpinuse = 1000
% 18.49/18.89 resimpclauses = 20000
% 18.49/18.89 substype = eqrewr
% 18.49/18.89 backwardsubs = 1
% 18.49/18.89 selectoldest = 5
% 18.49/18.89
% 18.49/18.89 litorderings [0] = split
% 18.49/18.89 litorderings [1] = extend the termordering, first sorting on arguments
% 18.49/18.89
% 18.49/18.89 termordering = kbo
% 18.49/18.89
% 18.49/18.89 litapriori = 0
% 18.49/18.89 termapriori = 1
% 18.49/18.89 litaposteriori = 0
% 18.49/18.89 termaposteriori = 0
% 18.49/18.89 demodaposteriori = 0
% 18.49/18.89 ordereqreflfact = 0
% 18.49/18.89
% 18.49/18.89 litselect = negord
% 18.49/18.89
% 18.49/18.89 maxweight = 15
% 18.49/18.89 maxdepth = 30000
% 18.49/18.89 maxlength = 115
% 18.49/18.89 maxnrvars = 195
% 18.49/18.89 excuselevel = 1
% 18.49/18.89 increasemaxweight = 1
% 18.49/18.89
% 18.49/18.89 maxselected = 10000000
% 18.49/18.89 maxnrclauses = 10000000
% 18.49/18.89
% 18.49/18.89 showgenerated = 0
% 18.49/18.89 showkept = 0
% 18.49/18.89 showselected = 0
% 18.49/18.89 showdeleted = 0
% 18.49/18.89 showresimp = 1
% 18.49/18.89 showstatus = 2000
% 18.49/18.89
% 18.49/18.89 prologoutput = 1
% 18.49/18.89 nrgoals = 5000000
% 18.49/18.89 totalproof = 1
% 18.49/18.89
% 18.49/18.89 Symbols occurring in the translation:
% 18.49/18.89
% 18.49/18.89 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 18.49/18.89 . [1, 2] (w:1, o:31, a:1, s:1, b:0),
% 18.49/18.89 ! [4, 1] (w:0, o:24, a:1, s:1, b:0),
% 18.49/18.89 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 18.49/18.89 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 18.49/18.89 identity [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 18.49/18.89 product [41, 3] (w:1, o:58, a:1, s:1, b:0),
% 18.49/18.89 inverse [42, 1] (w:1, o:29, a:1, s:1, b:0),
% 18.49/18.89 multiply [44, 2] (w:1, o:56, a:1, s:1, b:0),
% 18.49/18.89 'subgroup_member' [50, 1] (w:1, o:30, a:1, s:1, b:0),
% 18.49/18.89 'element_in_O2' [54, 2] (w:1, o:57, a:1, s:1, b:0),
% 18.49/18.89 a [55, 0] (w:1, o:20, a:1, s:1, b:0),
% 18.49/18.89 b [56, 0] (w:1, o:21, a:1, s:1, b:0),
% 18.49/18.89 d [57, 0] (w:1, o:23, a:1, s:1, b:0),
% 18.49/18.89 c [58, 0] (w:1, o:22, a:1, s:1, b:0).
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 Starting Search:
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 Intermediate Status:
% 18.49/18.89 Generated: 5307
% 18.49/18.89 Kept: 2021
% 18.49/18.89 Inuse: 100
% 18.49/18.89 Deleted: 1
% 18.49/18.89 Deletedinuse: 1
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 Intermediate Status:
% 18.49/18.89 Generated: 10047
% 18.49/18.89 Kept: 4036
% 18.49/18.89 Inuse: 129
% 18.49/18.89 Deleted: 4
% 18.49/18.89 Deletedinuse: 2
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 Intermediate Status:
% 18.49/18.89 Generated: 16745
% 18.49/18.89 Kept: 6067
% 18.49/18.89 Inuse: 187
% 18.49/18.89 Deleted: 5
% 18.49/18.89 Deletedinuse: 2
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 Intermediate Status:
% 18.49/18.89 Generated: 25453
% 18.49/18.89 Kept: 8292
% 18.49/18.89 Inuse: 238
% 18.49/18.89 Deleted: 15
% 18.49/18.89 Deletedinuse: 11
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 Intermediate Status:
% 18.49/18.89 Generated: 32456
% 18.49/18.89 Kept: 10343
% 18.49/18.89 Inuse: 283
% 18.49/18.89 Deleted: 66
% 18.49/18.89 Deletedinuse: 51
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 Intermediate Status:
% 18.49/18.89 Generated: 42400
% 18.49/18.89 Kept: 12364
% 18.49/18.89 Inuse: 326
% 18.49/18.89 Deleted: 72
% 18.49/18.89 Deletedinuse: 51
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 Intermediate Status:
% 18.49/18.89 Generated: 51950
% 18.49/18.89 Kept: 14488
% 18.49/18.89 Inuse: 377
% 18.49/18.89 Deleted: 99
% 18.49/18.89 Deletedinuse: 75
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 Intermediate Status:
% 18.49/18.89 Generated: 65630
% 18.49/18.89 Kept: 16507
% 18.49/18.89 Inuse: 427
% 18.49/18.89 Deleted: 111
% 18.49/18.89 Deletedinuse: 76
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 Intermediate Status:
% 18.49/18.89 Generated: 77291
% 18.49/18.89 Kept: 18533
% 18.49/18.89 Inuse: 469
% 18.49/18.89 Deleted: 117
% 18.49/18.89 Deletedinuse: 76
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89 Resimplifying clauses:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 Intermediate Status:
% 18.49/18.89 Generated: 95061
% 18.49/18.89 Kept: 20550
% 18.49/18.89 Inuse: 514
% 18.49/18.89 Deleted: 4441
% 18.49/18.89 Deletedinuse: 76
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 Intermediate Status:
% 18.49/18.89 Generated: 103649
% 18.49/18.89 Kept: 22552
% 18.49/18.89 Inuse: 544
% 18.49/18.89 Deleted: 4441
% 18.49/18.89 Deletedinuse: 76
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 Intermediate Status:
% 18.49/18.89 Generated: 111749
% 18.49/18.89 Kept: 24569
% 18.49/18.89 Inuse: 573
% 18.49/18.89 Deleted: 4441
% 18.49/18.89 Deletedinuse: 76
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 Intermediate Status:
% 18.49/18.89 Generated: 124031
% 18.49/18.89 Kept: 26633
% 18.49/18.89 Inuse: 609
% 18.49/18.89 Deleted: 4446
% 18.49/18.89 Deletedinuse: 81
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 Intermediate Status:
% 18.49/18.89 Generated: 132745
% 18.49/18.89 Kept: 28685
% 18.49/18.89 Inuse: 650
% 18.49/18.89 Deleted: 4455
% 18.49/18.89 Deletedinuse: 87
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 Intermediate Status:
% 18.49/18.89 Generated: 148026
% 18.49/18.89 Kept: 32007
% 18.49/18.89 Inuse: 661
% 18.49/18.89 Deleted: 4455
% 18.49/18.89 Deletedinuse: 87
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 Intermediate Status:
% 18.49/18.89 Generated: 159452
% 18.49/18.89 Kept: 34140
% 18.49/18.89 Inuse: 681
% 18.49/18.89 Deleted: 4455
% 18.49/18.89 Deletedinuse: 87
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 Intermediate Status:
% 18.49/18.89 Generated: 166195
% 18.49/18.89 Kept: 36156
% 18.49/18.89 Inuse: 695
% 18.49/18.89 Deleted: 4455
% 18.49/18.89 Deletedinuse: 87
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 Intermediate Status:
% 18.49/18.89 Generated: 174646
% 18.49/18.89 Kept: 38219
% 18.49/18.89 Inuse: 721
% 18.49/18.89 Deleted: 4455
% 18.49/18.89 Deletedinuse: 87
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89 Resimplifying clauses:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 Intermediate Status:
% 18.49/18.89 Generated: 182584
% 18.49/18.89 Kept: 40289
% 18.49/18.89 Inuse: 748
% 18.49/18.89 Deleted: 5932
% 18.49/18.89 Deletedinuse: 87
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 Intermediate Status:
% 18.49/18.89 Generated: 191853
% 18.49/18.89 Kept: 42306
% 18.49/18.89 Inuse: 777
% 18.49/18.89 Deleted: 5933
% 18.49/18.89 Deletedinuse: 88
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 Intermediate Status:
% 18.49/18.89 Generated: 200072
% 18.49/18.89 Kept: 44372
% 18.49/18.89 Inuse: 804
% 18.49/18.89 Deleted: 5934
% 18.49/18.89 Deletedinuse: 88
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 Intermediate Status:
% 18.49/18.89 Generated: 216467
% 18.49/18.89 Kept: 46456
% 18.49/18.89 Inuse: 834
% 18.49/18.89 Deleted: 5944
% 18.49/18.89 Deletedinuse: 89
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 Intermediate Status:
% 18.49/18.89 Generated: 223583
% 18.49/18.89 Kept: 48530
% 18.49/18.89 Inuse: 854
% 18.49/18.89 Deleted: 5946
% 18.49/18.89 Deletedinuse: 89
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89 Done
% 18.49/18.89
% 18.49/18.89 Resimplifying inuse:
% 18.49/18.89
% 18.49/18.89 Bliksems!, er is een bewijs:
% 18.49/18.89 % SZS status Unsatisfiable
% 18.49/18.89 % SZS output start Refutation
% 18.49/18.89
% 18.49/18.89 clause( 0, [ product( identity, X, X ) ] )
% 18.49/18.89 .
% 18.49/18.89 clause( 2, [ product( inverse( X ), X, identity ) ] )
% 18.49/18.89 .
% 18.49/18.89 clause( 5, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z, T ) ]
% 18.49/18.89 )
% 18.49/18.89 .
% 18.49/18.89 clause( 6, [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~( product(
% 18.49/18.89 Z, T, W ) ), product( X, U, W ) ] )
% 18.49/18.89 .
% 18.49/18.89 clause( 8, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( Y ) ), ~(
% 18.49/18.89 product( X, inverse( Y ), Z ) ), 'subgroup_member'( Z ) ] )
% 18.49/18.89 .
% 18.49/18.89 clause( 10, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( inverse( X )
% 18.49/18.89 ) ] )
% 18.49/18.89 .
% 18.49/18.89 clause( 11, [ ~( product( X, Y, Z ) ), ~( product( X, T, Z ) ), =( T, Y ) ]
% 18.49/18.89 )
% 18.49/18.89 .
% 18.49/18.89 clause( 13, [ 'subgroup_member'( 'element_in_O2'( X, Y ) ),
% 18.49/18.89 'subgroup_member'( Y ), 'subgroup_member'( X ) ] )
% 18.49/18.89 .
% 18.49/18.89 clause( 14, [ product( X, 'element_in_O2'( X, Y ), Y ), 'subgroup_member'(
% 18.49/18.89 Y ), 'subgroup_member'( X ) ] )
% 18.49/18.89 .
% 18.49/18.89 clause( 15, [ ~( 'subgroup_member'( a ) ) ] )
% 18.49/18.89 .
% 18.49/18.89 clause( 16, [ 'subgroup_member'( b ) ] )
% 18.49/18.89 .
% 18.49/18.89 clause( 17, [ ~( 'subgroup_member'( d ) ) ] )
% 18.49/18.89 .
% 18.49/18.89 clause( 18, [ product( b, inverse( a ), c ) ] )
% 18.49/18.89 .
% 18.49/18.89 clause( 19, [ product( a, c, d ) ] )
% 18.49/18.89 .
% 18.49/18.89 clause( 20, [ =( inverse( inverse( X ) ), X ) ] )
% 18.49/18.89 .
% 18.49/18.89 clause( 31, [ 'subgroup_member'( inverse( b ) ) ] )
% 18.49/18.89 .
% 18.49/18.89 clause( 32, [ ~( 'subgroup_member'( inverse( X ) ) ), 'subgroup_member'( X
% 18.49/18.89 ) ] )
% 18.49/18.89 .
% 18.49/18.89 clause( 38, [ ~( product( identity, X, Y ) ), =( X, Y ) ] )
% 18.49/18.89 .
% 18.49/18.89 clause( 64, [ ~( 'subgroup_member'( inverse( a ) ) ) ] )
% 18.49/18.89 .
% 18.49/18.89 clause( 67, [ ~( 'subgroup_member'( X ) ), ~( product( Y, Z, inverse( a ) )
% 18.49/18.89 ), ~( product( Y, Z, X ) ) ] )
% 18.49/18.89 .
% 18.49/18.89 clause( 90, [ ~( product( X, Y, Z ) ), ~( product( identity, Y, T ) ),
% 18.49/18.89 product( inverse( X ), Z, T ) ] )
% 18.49/18.89 .
% 18.49/18.89 clause( 237, [ product( b, X, c ), ~( product( identity, inverse( a ), X )
% 18.49/18.89 ) ] )
% 18.49/18.89 .
% 18.49/18.89 clause( 301, [ ~( 'subgroup_member'( X ) ), ~( product( inverse( b ),
% 18.49/18.89 inverse( X ), Y ) ), 'subgroup_member'( Y ) ] )
% 18.49/18.89 .
% 18.49/18.89 clause( 372, [ ~( product( a, X, d ) ), =( X, c ) ] )
% 18.49/18.89 .
% 18.49/18.89 clause( 686, [ 'subgroup_member'( 'element_in_O2'( a, X ) ),
% 18.49/18.89 'subgroup_member'( X ) ] )
% 18.49/18.89 .
% 18.49/18.89 clause( 2303, [ 'subgroup_member'( 'element_in_O2'( a, d ) ) ] )
% 18.49/18.89 .
% 18.49/18.89 clause( 2336, [ 'subgroup_member'( inverse( 'element_in_O2'( a, d ) ) ) ]
% 18.49/18.89 )
% 18.49/18.89 .
% 18.49/18.89 clause( 7960, [ =( 'element_in_O2'( a, d ), c ), 'subgroup_member'( a ) ]
% 18.49/18.89 )
% 18.49/18.89 .
% 18.49/18.89 clause( 12958, [ =( 'element_in_O2'( a, d ), c ) ] )
% 18.49/18.89 .
% 18.49/18.89 clause( 12984, [ 'subgroup_member'( inverse( c ) ) ] )
% 18.49/18.89 .
% 18.49/18.89 clause( 38179, [ ~( product( identity, inverse( a ), X ) ), ~( product(
% 18.49/18.89 identity, X, Y ) ), product( inverse( b ), c, Y ) ] )
% 18.49/18.89 .
% 18.49/18.89 clause( 38218, [ product( inverse( b ), c, inverse( a ) ) ] )
% 18.49/18.89 .
% 18.49/18.89 clause( 38259, [ ~( 'subgroup_member'( X ) ), ~( product( inverse( b ), c,
% 18.49/18.89 X ) ) ] )
% 18.49/18.89 .
% 18.49/18.89 clause( 50141, [ ~( product( inverse( b ), c, X ) ) ] )
% 18.49/18.89 .
% 18.49/18.89 clause( 50288, [] )
% 18.49/18.89 .
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 % SZS output end Refutation
% 18.49/18.89 found a proof!
% 18.49/18.89
% 18.49/18.89 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 18.49/18.89
% 18.49/18.89 initialclauses(
% 18.49/18.89 [ clause( 50290, [ product( identity, X, X ) ] )
% 18.49/18.89 , clause( 50291, [ product( X, identity, X ) ] )
% 18.49/18.89 , clause( 50292, [ product( inverse( X ), X, identity ) ] )
% 18.49/18.89 , clause( 50293, [ product( X, inverse( X ), identity ) ] )
% 18.49/18.89 , clause( 50294, [ product( X, Y, multiply( X, Y ) ) ] )
% 18.49/18.89 , clause( 50295, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z,
% 18.49/18.89 T ) ] )
% 18.49/18.89 , clause( 50296, [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~(
% 18.49/18.89 product( Z, T, W ) ), product( X, U, W ) ] )
% 18.49/18.89 , clause( 50297, [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~(
% 18.49/18.89 product( X, U, W ) ), product( Z, T, W ) ] )
% 18.49/18.89 , clause( 50298, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( Y ) )
% 18.49/18.89 , ~( product( X, inverse( Y ), Z ) ), 'subgroup_member'( Z ) ] )
% 18.49/18.89 , clause( 50299, [ 'subgroup_member'( identity ) ] )
% 18.49/18.89 , clause( 50300, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( inverse(
% 18.49/18.89 X ) ) ] )
% 18.49/18.89 , clause( 50301, [ ~( product( X, Y, Z ) ), ~( product( X, T, Z ) ), =( T,
% 18.49/18.89 Y ) ] )
% 18.49/18.89 , clause( 50302, [ ~( product( X, Y, Z ) ), ~( product( T, Y, Z ) ), =( T,
% 18.49/18.89 X ) ] )
% 18.49/18.89 , clause( 50303, [ 'subgroup_member'( 'element_in_O2'( X, Y ) ),
% 18.49/18.89 'subgroup_member'( Y ), 'subgroup_member'( X ) ] )
% 18.49/18.89 , clause( 50304, [ product( X, 'element_in_O2'( X, Y ), Y ),
% 18.49/18.89 'subgroup_member'( Y ), 'subgroup_member'( X ) ] )
% 18.49/18.89 , clause( 50305, [ ~( 'subgroup_member'( a ) ) ] )
% 18.49/18.89 , clause( 50306, [ 'subgroup_member'( b ) ] )
% 18.49/18.89 , clause( 50307, [ ~( 'subgroup_member'( d ) ) ] )
% 18.49/18.89 , clause( 50308, [ product( b, inverse( a ), c ) ] )
% 18.49/18.89 , clause( 50309, [ product( a, c, d ) ] )
% 18.49/18.89 , clause( 50310, [ =( inverse( inverse( X ) ), X ) ] )
% 18.49/18.89 ] ).
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 subsumption(
% 18.49/18.89 clause( 0, [ product( identity, X, X ) ] )
% 18.49/18.89 , clause( 50290, [ product( identity, X, X ) ] )
% 18.49/18.89 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 subsumption(
% 18.49/18.89 clause( 2, [ product( inverse( X ), X, identity ) ] )
% 18.49/18.89 , clause( 50292, [ product( inverse( X ), X, identity ) ] )
% 18.49/18.89 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 subsumption(
% 18.49/18.89 clause( 5, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z, T ) ]
% 18.49/18.89 )
% 18.49/18.89 , clause( 50295, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z,
% 18.49/18.89 T ) ] )
% 18.49/18.89 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 18.49/18.89 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 subsumption(
% 18.49/18.89 clause( 6, [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~( product(
% 18.49/18.89 Z, T, W ) ), product( X, U, W ) ] )
% 18.49/18.89 , clause( 50296, [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~(
% 18.49/18.89 product( Z, T, W ) ), product( X, U, W ) ] )
% 18.49/18.89 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 18.49/18.89 , U ), :=( W, W )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2
% 18.49/18.89 , 2 ), ==>( 3, 3 )] ) ).
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 subsumption(
% 18.49/18.89 clause( 8, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( Y ) ), ~(
% 18.49/18.89 product( X, inverse( Y ), Z ) ), 'subgroup_member'( Z ) ] )
% 18.49/18.89 , clause( 50298, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( Y ) )
% 18.49/18.89 , ~( product( X, inverse( Y ), Z ) ), 'subgroup_member'( Z ) ] )
% 18.49/18.89 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 18.49/18.89 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 ), ==>( 3, 3 )] )
% 18.49/18.89 ).
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 subsumption(
% 18.49/18.89 clause( 10, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( inverse( X )
% 18.49/18.89 ) ] )
% 18.49/18.89 , clause( 50300, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( inverse(
% 18.49/18.89 X ) ) ] )
% 18.49/18.89 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 18.49/18.89 1 )] ) ).
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 subsumption(
% 18.49/18.89 clause( 11, [ ~( product( X, Y, Z ) ), ~( product( X, T, Z ) ), =( T, Y ) ]
% 18.49/18.89 )
% 18.49/18.89 , clause( 50301, [ ~( product( X, Y, Z ) ), ~( product( X, T, Z ) ), =( T,
% 18.49/18.89 Y ) ] )
% 18.49/18.89 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 18.49/18.89 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 subsumption(
% 18.49/18.89 clause( 13, [ 'subgroup_member'( 'element_in_O2'( X, Y ) ),
% 18.49/18.89 'subgroup_member'( Y ), 'subgroup_member'( X ) ] )
% 18.49/18.89 , clause( 50303, [ 'subgroup_member'( 'element_in_O2'( X, Y ) ),
% 18.49/18.89 'subgroup_member'( Y ), 'subgroup_member'( X ) ] )
% 18.49/18.89 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 18.49/18.89 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 subsumption(
% 18.49/18.89 clause( 14, [ product( X, 'element_in_O2'( X, Y ), Y ), 'subgroup_member'(
% 18.49/18.89 Y ), 'subgroup_member'( X ) ] )
% 18.49/18.89 , clause( 50304, [ product( X, 'element_in_O2'( X, Y ), Y ),
% 18.49/18.89 'subgroup_member'( Y ), 'subgroup_member'( X ) ] )
% 18.49/18.89 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 18.49/18.89 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 subsumption(
% 18.49/18.89 clause( 15, [ ~( 'subgroup_member'( a ) ) ] )
% 18.49/18.89 , clause( 50305, [ ~( 'subgroup_member'( a ) ) ] )
% 18.49/18.89 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 subsumption(
% 18.49/18.89 clause( 16, [ 'subgroup_member'( b ) ] )
% 18.49/18.89 , clause( 50306, [ 'subgroup_member'( b ) ] )
% 18.49/18.89 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 subsumption(
% 18.49/18.89 clause( 17, [ ~( 'subgroup_member'( d ) ) ] )
% 18.49/18.89 , clause( 50307, [ ~( 'subgroup_member'( d ) ) ] )
% 18.49/18.89 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 subsumption(
% 18.49/18.89 clause( 18, [ product( b, inverse( a ), c ) ] )
% 18.49/18.89 , clause( 50308, [ product( b, inverse( a ), c ) ] )
% 18.49/18.89 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 subsumption(
% 18.49/18.89 clause( 19, [ product( a, c, d ) ] )
% 18.49/18.89 , clause( 50309, [ product( a, c, d ) ] )
% 18.49/18.89 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 subsumption(
% 18.49/18.89 clause( 20, [ =( inverse( inverse( X ) ), X ) ] )
% 18.49/18.89 , clause( 50310, [ =( inverse( inverse( X ) ), X ) ] )
% 18.49/18.89 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 resolution(
% 18.49/18.89 clause( 50460, [ 'subgroup_member'( inverse( b ) ) ] )
% 18.49/18.89 , clause( 10, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( inverse( X
% 18.49/18.89 ) ) ] )
% 18.49/18.89 , 0, clause( 16, [ 'subgroup_member'( b ) ] )
% 18.49/18.89 , 0, substitution( 0, [ :=( X, b )] ), substitution( 1, [] )).
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 subsumption(
% 18.49/18.89 clause( 31, [ 'subgroup_member'( inverse( b ) ) ] )
% 18.49/18.89 , clause( 50460, [ 'subgroup_member'( inverse( b ) ) ] )
% 18.49/18.89 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 18.49/18.89
% 18.49/18.89
% 18.49/18.89 paramod(
% 18.49/18.89 clause( 50462, [ 'subgroup_member'( X ), ~( 'subgroup_member'( inverse( X )
% 18.49/18.89 ) ) ] )
% 18.49/18.89 , clause( 20, [ =( inverse( inverse( X ) ), X ) ] )
% 18.49/18.89 , 0, clause( 10, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( inverse(
% 18.49/18.89 X ) ) ] )
% 18.49/18.89 , 1, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, inverse(
% 18.49/18.92 X ) )] )).
% 18.49/18.92
% 18.49/18.92
% 18.49/18.92 subsumption(
% 18.49/18.92 clause( 32, [ ~( 'subgroup_member'( inverse( X ) ) ), 'subgroup_member'( X
% 18.49/18.92 ) ] )
% 18.49/18.92 , clause( 50462, [ 'subgroup_member'( X ), ~( 'subgroup_member'( inverse( X
% 18.49/18.92 ) ) ) ] )
% 18.49/18.92 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1,
% 18.49/18.92 0 )] ) ).
% 18.49/18.92
% 18.49/18.92
% 18.49/18.92 resolution(
% 18.49/18.92 clause( 50463, [ ~( product( identity, X, Y ) ), =( X, Y ) ] )
% 18.49/18.92 , clause( 5, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z, T )
% 18.49/18.92 ] )
% 18.49/18.92 , 0, clause( 0, [ product( identity, X, X ) ] )
% 18.49/18.92 , 0, substitution( 0, [ :=( X, identity ), :=( Y, X ), :=( Z, X ), :=( T, Y
% 18.49/18.92 )] ), substitution( 1, [ :=( X, X )] )).
% 18.49/18.92
% 18.49/18.92
% 18.49/18.92 subsumption(
% 18.49/18.92 clause( 38, [ ~( product( identity, X, Y ) ), =( X, Y ) ] )
% 18.49/18.92 , clause( 50463, [ ~( product( identity, X, Y ) ), =( X, Y ) ] )
% 18.49/18.92 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 18.49/18.92 ), ==>( 1, 1 )] ) ).
% 18.49/18.92
% 18.49/18.92
% 18.49/18.92 resolution(
% 18.49/18.92 clause( 50465, [ ~( 'subgroup_member'( inverse( a ) ) ) ] )
% 18.49/18.92 , clause( 15, [ ~( 'subgroup_member'( a ) ) ] )
% 18.49/18.92 , 0, clause( 32, [ ~( 'subgroup_member'( inverse( X ) ) ),
% 18.49/18.92 'subgroup_member'( X ) ] )
% 18.49/18.92 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, a )] )).
% 18.49/18.92
% 18.49/18.92
% 18.49/18.92 subsumption(
% 18.49/18.92 clause( 64, [ ~( 'subgroup_member'( inverse( a ) ) ) ] )
% 18.49/18.92 , clause( 50465, [ ~( 'subgroup_member'( inverse( a ) ) ) ] )
% 18.49/18.92 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 18.49/18.92
% 18.49/18.92
% 18.49/18.92 assignments is full
% 18.49/18.92
% 18.49/18.92 Memory use:
% 18.49/18.92
% 18.49/18.92 space for terms: 724669
% 18.49/18.92 space for clauses: 2099660
% 18.49/18.92
% 18.49/18.92
% 18.49/18.92 clauses generated: 228359
% 18.49/18.92 clauses kept: 50289
% 18.49/18.92 clauses selected: 869
% 18.49/18.92 clauses deleted: 5953
% 18.49/18.92 clauses inuse deleted: 96
% 18.49/18.92
% 18.49/18.92 subsentry: 5602619
% 18.49/18.92 literals s-matched: 2248351
% 18.49/18.92 literals matched: 1455783
% 18.49/18.92 full subsumption: 853746
% 18.49/18.92
% 18.49/18.92 checksum: -1667642875
% 18.49/18.92
% 18.49/18.92
% 18.49/18.92 Bliksem ended
%------------------------------------------------------------------------------