TSTP Solution File: GRP025-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GRP025-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Sat Jul 16 07:34:22 EDT 2022
% Result : Unsatisfiable 49.17s 49.65s
% Output : Refutation 49.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP025-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.06/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Mon Jun 13 05:24:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 49.17/49.65 *** allocated 10000 integers for termspace/termends
% 49.17/49.65 *** allocated 10000 integers for clauses
% 49.17/49.65 *** allocated 10000 integers for justifications
% 49.17/49.65 Bliksem 1.12
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 Automatic Strategy Selection
% 49.17/49.65
% 49.17/49.65 Clauses:
% 49.17/49.65 [
% 49.17/49.65 [ 'group_member'( 'identity_for'( X ), X ) ],
% 49.17/49.65 [ product( X, 'identity_for'( X ), Y, Y ) ],
% 49.17/49.65 [ product( X, Y, 'identity_for'( X ), Y ) ],
% 49.17/49.65 [ ~( 'group_member'( X, Y ) ), 'group_member'( inverse( Y, X ), Y ) ]
% 49.17/49.65 ,
% 49.17/49.65 [ product( X, inverse( X, Y ), Y, 'identity_for'( X ) ) ],
% 49.17/49.65 [ product( X, Y, inverse( X, Y ), 'identity_for'( X ) ) ],
% 49.17/49.65 [ ~( 'group_member'( X, Y ) ), ~( 'group_member'( Z, Y ) ), product( Y,
% 49.17/49.65 X, Z, multiply( Y, X, Z ) ) ],
% 49.17/49.65 [ ~( 'group_member'( X, Y ) ), ~( 'group_member'( Z, Y ) ),
% 49.17/49.65 'group_member'( multiply( Y, X, Z ), Y ) ],
% 49.17/49.65 [ ~( product( X, Y, Z, T ) ), ~( product( X, Y, Z, U ) ), =( U, T ) ]
% 49.17/49.65 ,
% 49.17/49.65 [ ~( product( X, Y, Z, T ) ), ~( product( X, Z, U, W ) ), ~( product( X
% 49.17/49.65 , T, U, V0 ) ), product( X, Y, W, V0 ) ],
% 49.17/49.65 [ ~( product( X, Y, Z, T ) ), ~( product( X, Z, U, W ) ), ~( product( X
% 49.17/49.65 , Y, W, V0 ) ), product( X, T, U, V0 ) ],
% 49.17/49.65 [ 'group_member'( a, g1 ) ],
% 49.17/49.65 [ 'group_member'( b, g1 ) ],
% 49.17/49.65 [ 'group_member'( c, g2 ) ],
% 49.17/49.65 [ 'group_member'( d, g2 ) ],
% 49.17/49.65 [ ~( 'group_member'( X, g1 ) ), =( X, a ), =( X, b ) ],
% 49.17/49.65 [ ~( 'group_member'( X, g2 ) ), =( X, c ), =( X, d ) ],
% 49.17/49.65 [ product( g1, a, a, a ) ],
% 49.17/49.65 [ product( g1, a, b, b ) ],
% 49.17/49.65 [ product( g1, b, a, b ) ],
% 49.17/49.65 [ product( g1, b, b, a ) ],
% 49.17/49.65 [ product( g2, c, c, c ) ],
% 49.17/49.65 [ product( g2, c, d, d ) ],
% 49.17/49.65 [ product( g2, d, c, d ) ],
% 49.17/49.65 [ product( g2, d, d, c ) ],
% 49.17/49.65 [ =( 'an_isomorphism'( a ), c ) ],
% 49.17/49.65 [ =( 'an_isomorphism'( b ), d ) ],
% 49.17/49.65 [ 'group_member'( d1, g1 ) ],
% 49.17/49.65 [ 'group_member'( d2, g1 ) ],
% 49.17/49.65 [ 'group_member'( d3, g1 ) ],
% 49.17/49.65 [ product( g1, d1, d2, d3 ) ],
% 49.17/49.65 [ ~( product( g2, 'an_isomorphism'( d1 ), 'an_isomorphism'( d2 ),
% 49.17/49.65 'an_isomorphism'( d3 ) ) ) ]
% 49.17/49.65 ] .
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 percentage equality = 0.142857, percentage horn = 0.937500
% 49.17/49.65 This is a problem with some equality
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 Options Used:
% 49.17/49.65
% 49.17/49.65 useres = 1
% 49.17/49.65 useparamod = 1
% 49.17/49.65 useeqrefl = 1
% 49.17/49.65 useeqfact = 1
% 49.17/49.65 usefactor = 1
% 49.17/49.65 usesimpsplitting = 0
% 49.17/49.65 usesimpdemod = 5
% 49.17/49.65 usesimpres = 3
% 49.17/49.65
% 49.17/49.65 resimpinuse = 1000
% 49.17/49.65 resimpclauses = 20000
% 49.17/49.65 substype = eqrewr
% 49.17/49.65 backwardsubs = 1
% 49.17/49.65 selectoldest = 5
% 49.17/49.65
% 49.17/49.65 litorderings [0] = split
% 49.17/49.65 litorderings [1] = extend the termordering, first sorting on arguments
% 49.17/49.65
% 49.17/49.65 termordering = kbo
% 49.17/49.65
% 49.17/49.65 litapriori = 0
% 49.17/49.65 termapriori = 1
% 49.17/49.65 litaposteriori = 0
% 49.17/49.65 termaposteriori = 0
% 49.17/49.65 demodaposteriori = 0
% 49.17/49.65 ordereqreflfact = 0
% 49.17/49.65
% 49.17/49.65 litselect = negord
% 49.17/49.65
% 49.17/49.65 maxweight = 15
% 49.17/49.65 maxdepth = 30000
% 49.17/49.65 maxlength = 115
% 49.17/49.65 maxnrvars = 195
% 49.17/49.65 excuselevel = 1
% 49.17/49.65 increasemaxweight = 1
% 49.17/49.65
% 49.17/49.65 maxselected = 10000000
% 49.17/49.65 maxnrclauses = 10000000
% 49.17/49.65
% 49.17/49.65 showgenerated = 0
% 49.17/49.65 showkept = 0
% 49.17/49.65 showselected = 0
% 49.17/49.65 showdeleted = 0
% 49.17/49.65 showresimp = 1
% 49.17/49.65 showstatus = 2000
% 49.17/49.65
% 49.17/49.65 prologoutput = 1
% 49.17/49.65 nrgoals = 5000000
% 49.17/49.65 totalproof = 1
% 49.17/49.65
% 49.17/49.65 Symbols occurring in the translation:
% 49.17/49.65
% 49.17/49.65 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 49.17/49.65 . [1, 2] (w:1, o:33, a:1, s:1, b:0),
% 49.17/49.65 ! [4, 1] (w:0, o:26, a:1, s:1, b:0),
% 49.17/49.65 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 49.17/49.65 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 49.17/49.65 'identity_for' [40, 1] (w:1, o:31, a:1, s:1, b:0),
% 49.17/49.65 'group_member' [41, 2] (w:1, o:58, a:1, s:1, b:0),
% 49.17/49.65 product [43, 4] (w:1, o:61, a:1, s:1, b:0),
% 49.17/49.65 inverse [44, 2] (w:1, o:59, a:1, s:1, b:0),
% 49.17/49.65 multiply [46, 3] (w:1, o:60, a:1, s:1, b:0),
% 49.17/49.65 a [52, 0] (w:1, o:17, a:1, s:1, b:0),
% 49.17/49.65 g1 [53, 0] (w:1, o:18, a:1, s:1, b:0),
% 49.17/49.65 b [54, 0] (w:1, o:19, a:1, s:1, b:0),
% 49.17/49.65 c [55, 0] (w:1, o:20, a:1, s:1, b:0),
% 49.17/49.65 g2 [56, 0] (w:1, o:21, a:1, s:1, b:0),
% 49.17/49.65 d [57, 0] (w:1, o:22, a:1, s:1, b:0),
% 49.17/49.65 'an_isomorphism' [58, 1] (w:1, o:32, a:1, s:1, b:0),
% 49.17/49.65 d1 [59, 0] (w:1, o:23, a:1, s:1, b:0),
% 49.17/49.65 d2 [60, 0] (w:1, o:24, a:1, s:1, b:0),
% 49.17/49.65 d3 [61, 0] (w:1, o:25, a:1, s:1, b:0).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 Starting Search:
% 49.17/49.65
% 49.17/49.65 Resimplifying inuse:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 Intermediate Status:
% 49.17/49.65 Generated: 5798
% 49.17/49.65 Kept: 2179
% 49.17/49.65 Inuse: 86
% 49.17/49.65 Deleted: 5
% 49.17/49.65 Deletedinuse: 1
% 49.17/49.65
% 49.17/49.65 Resimplifying inuse:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65 Resimplifying inuse:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 Intermediate Status:
% 49.17/49.65 Generated: 10619
% 49.17/49.65 Kept: 4223
% 49.17/49.65 Inuse: 117
% 49.17/49.65 Deleted: 12
% 49.17/49.65 Deletedinuse: 6
% 49.17/49.65
% 49.17/49.65 Resimplifying inuse:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65 Resimplifying inuse:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 Intermediate Status:
% 49.17/49.65 Generated: 18093
% 49.17/49.65 Kept: 6236
% 49.17/49.65 Inuse: 172
% 49.17/49.65 Deleted: 12
% 49.17/49.65 Deletedinuse: 6
% 49.17/49.65
% 49.17/49.65 Resimplifying inuse:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65 Resimplifying inuse:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 Intermediate Status:
% 49.17/49.65 Generated: 26336
% 49.17/49.65 Kept: 8264
% 49.17/49.65 Inuse: 227
% 49.17/49.65 Deleted: 33
% 49.17/49.65 Deletedinuse: 6
% 49.17/49.65
% 49.17/49.65 Resimplifying inuse:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65 Resimplifying inuse:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 Intermediate Status:
% 49.17/49.65 Generated: 37322
% 49.17/49.65 Kept: 10655
% 49.17/49.65 Inuse: 281
% 49.17/49.65 Deleted: 45
% 49.17/49.65 Deletedinuse: 8
% 49.17/49.65
% 49.17/49.65 Resimplifying inuse:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65 Resimplifying inuse:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 Intermediate Status:
% 49.17/49.65 Generated: 47686
% 49.17/49.65 Kept: 12662
% 49.17/49.65 Inuse: 319
% 49.17/49.65 Deleted: 45
% 49.17/49.65 Deletedinuse: 8
% 49.17/49.65
% 49.17/49.65 Resimplifying inuse:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65 Resimplifying inuse:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 Intermediate Status:
% 49.17/49.65 Generated: 56110
% 49.17/49.65 Kept: 14671
% 49.17/49.65 Inuse: 350
% 49.17/49.65 Deleted: 45
% 49.17/49.65 Deletedinuse: 8
% 49.17/49.65
% 49.17/49.65 Resimplifying inuse:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65 Resimplifying inuse:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 Intermediate Status:
% 49.17/49.65 Generated: 64956
% 49.17/49.65 Kept: 16737
% 49.17/49.65 Inuse: 375
% 49.17/49.65 Deleted: 45
% 49.17/49.65 Deletedinuse: 8
% 49.17/49.65
% 49.17/49.65 Resimplifying inuse:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65 Resimplifying inuse:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 Intermediate Status:
% 49.17/49.65 Generated: 71183
% 49.17/49.65 Kept: 18741
% 49.17/49.65 Inuse: 394
% 49.17/49.65 Deleted: 45
% 49.17/49.65 Deletedinuse: 8
% 49.17/49.65
% 49.17/49.65 Resimplifying inuse:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65 Resimplifying clauses:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65 Resimplifying inuse:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 Intermediate Status:
% 49.17/49.65 Generated: 82818
% 49.17/49.65 Kept: 22816
% 49.17/49.65 Inuse: 421
% 49.17/49.65 Deleted: 1482
% 49.17/49.65 Deletedinuse: 10
% 49.17/49.65
% 49.17/49.65 Resimplifying inuse:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 Intermediate Status:
% 49.17/49.65 Generated: 87790
% 49.17/49.65 Kept: 25116
% 49.17/49.65 Inuse: 426
% 49.17/49.65 Deleted: 1527
% 49.17/49.65 Deletedinuse: 55
% 49.17/49.65
% 49.17/49.65 Resimplifying inuse:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65 Resimplifying inuse:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 Intermediate Status:
% 49.17/49.65 Generated: 93332
% 49.17/49.65 Kept: 27194
% 49.17/49.65 Inuse: 451
% 49.17/49.65 Deleted: 1544
% 49.17/49.65 Deletedinuse: 70
% 49.17/49.65
% 49.17/49.65 Resimplifying inuse:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65 Resimplifying inuse:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 Intermediate Status:
% 49.17/49.65 Generated: 100021
% 49.17/49.65 Kept: 29279
% 49.17/49.65 Inuse: 476
% 49.17/49.65 Deleted: 1544
% 49.17/49.65 Deletedinuse: 70
% 49.17/49.65
% 49.17/49.65 Resimplifying inuse:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65 Resimplifying inuse:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 Intermediate Status:
% 49.17/49.65 Generated: 105698
% 49.17/49.65 Kept: 31360
% 49.17/49.65 Inuse: 498
% 49.17/49.65 Deleted: 1544
% 49.17/49.65 Deletedinuse: 70
% 49.17/49.65
% 49.17/49.65 Resimplifying inuse:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65 Resimplifying inuse:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 Intermediate Status:
% 49.17/49.65 Generated: 110913
% 49.17/49.65 Kept: 33404
% 49.17/49.65 Inuse: 519
% 49.17/49.65 Deleted: 1546
% 49.17/49.65 Deletedinuse: 70
% 49.17/49.65
% 49.17/49.65 Resimplifying inuse:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65 Resimplifying inuse:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 Intermediate Status:
% 49.17/49.65 Generated: 116108
% 49.17/49.65 Kept: 35411
% 49.17/49.65 Inuse: 540
% 49.17/49.65 Deleted: 1546
% 49.17/49.65 Deletedinuse: 70
% 49.17/49.65
% 49.17/49.65 Resimplifying inuse:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65 Resimplifying inuse:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 Intermediate Status:
% 49.17/49.65 Generated: 121768
% 49.17/49.65 Kept: 37454
% 49.17/49.65 Inuse: 563
% 49.17/49.65 Deleted: 1546
% 49.17/49.65 Deletedinuse: 70
% 49.17/49.65
% 49.17/49.65 Resimplifying inuse:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65 Resimplifying inuse:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 Intermediate Status:
% 49.17/49.65 Generated: 128950
% 49.17/49.65 Kept: 39494
% 49.17/49.65 Inuse: 584
% 49.17/49.65 Deleted: 1546
% 49.17/49.65 Deletedinuse: 70
% 49.17/49.65
% 49.17/49.65 Resimplifying inuse:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65 Resimplifying clauses:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65 Resimplifying inuse:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 Intermediate Status:
% 49.17/49.65 Generated: 140027
% 49.17/49.65 Kept: 41531
% 49.17/49.65 Inuse: 611
% 49.17/49.65 Deleted: 8784
% 49.17/49.65 Deletedinuse: 70
% 49.17/49.65
% 49.17/49.65 Resimplifying inuse:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65 Resimplifying inuse:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 Intermediate Status:
% 49.17/49.65 Generated: 152057
% 49.17/49.65 Kept: 43584
% 49.17/49.65 Inuse: 641
% 49.17/49.65 Deleted: 8784
% 49.17/49.65 Deletedinuse: 70
% 49.17/49.65
% 49.17/49.65 Resimplifying inuse:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65 Resimplifying inuse:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 Intermediate Status:
% 49.17/49.65 Generated: 168977
% 49.17/49.65 Kept: 49296
% 49.17/49.65 Inuse: 664
% 49.17/49.65 Deleted: 8784
% 49.17/49.65 Deletedinuse: 70
% 49.17/49.65
% 49.17/49.65 Resimplifying inuse:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 Intermediate Status:
% 49.17/49.65 Generated: 178957
% 49.17/49.65 Kept: 53127
% 49.17/49.65 Inuse: 682
% 49.17/49.65 Deleted: 8812
% 49.17/49.65 Deletedinuse: 93
% 49.17/49.65
% 49.17/49.65 Resimplifying inuse:
% 49.17/49.65 Done
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 Bliksems!, er is een bewijs:
% 49.17/49.65 % SZS status Unsatisfiable
% 49.17/49.65 % SZS output start Refutation
% 49.17/49.65
% 49.17/49.65 clause( 0, [ 'group_member'( 'identity_for'( X ), X ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 1, [ product( X, 'identity_for'( X ), Y, Y ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 2, [ product( X, Y, 'identity_for'( X ), Y ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 8, [ ~( product( X, Y, Z, T ) ), ~( product( X, Y, Z, U ) ), =( U,
% 49.17/49.65 T ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 11, [ 'group_member'( a, g1 ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 12, [ 'group_member'( b, g1 ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 13, [ 'group_member'( c, g2 ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 15, [ ~( 'group_member'( X, g1 ) ), =( X, a ), =( X, b ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 16, [ ~( 'group_member'( X, g2 ) ), =( X, c ), =( X, d ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 17, [ product( g1, a, a, a ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 20, [ product( g1, b, b, a ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 21, [ product( g2, c, c, c ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 24, [ product( g2, d, d, c ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 25, [ =( 'an_isomorphism'( a ), c ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 26, [ =( 'an_isomorphism'( b ), d ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 27, [ 'group_member'( d1, g1 ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 28, [ 'group_member'( d2, g1 ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 29, [ 'group_member'( d3, g1 ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 30, [ product( g1, d1, d2, d3 ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 31, [ ~( product( g2, 'an_isomorphism'( d1 ), 'an_isomorphism'( d2
% 49.17/49.65 ), 'an_isomorphism'( d3 ) ) ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 42, [ ~( =( d, c ) ), ~( 'group_member'( X, g2 ) ), =( X, d ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 177, [ ~( =( d, c ) ), =( 'identity_for'( g2 ), d ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 178, [ ~( =( d, c ) ), =( d, c ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 274, [ ~( product( g1, a, a, X ) ), =( X, a ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 277, [ ~( product( g1, b, b, X ) ), =( X, a ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 279, [ ~( product( X, Y, 'identity_for'( X ), Z ) ), =( Z, Y ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 282, [ ~( product( g2, d, d, X ) ), =( X, c ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 283, [ ~( product( g1, d1, d2, X ) ), =( X, d3 ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 366, [ ~( =( d, c ) ), =( 'identity_for'( g2 ), c ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 956, [ =( 'identity_for'( g1 ), a ), =( 'identity_for'( g1 ), b ) ]
% 49.17/49.65 )
% 49.17/49.65 .
% 49.17/49.65 clause( 957, [ =( d1, a ), =( d1, b ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 958, [ =( d2, a ), =( d2, b ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 959, [ =( d3, a ), =( d3, b ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 1148, [ product( g1, a, d2, d3 ), =( d1, b ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 1152, [ product( g1, b, d2, d3 ), =( d1, a ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 1153, [ product( g1, d1, b, d3 ), =( d2, a ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 1251, [ ~( =( b, a ) ), =( d3, b ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 1252, [ ~( =( b, a ) ), =( b, a ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 1253, [ ~( =( b, a ) ), =( d2, a ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 1254, [ ~( =( b, a ) ), =( d1, a ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 1281, [ =( 'identity_for'( g2 ), c ), =( 'identity_for'( g2 ), d )
% 49.17/49.65 ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 1647, [ ~( =( b, a ) ), =( d3, a ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 1654, [ ~( =( b, a ) ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 1659, [ ~( product( g1, b, b, b ) ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 2848, [ =( 'identity_for'( g2 ), c ), ~( product( g2, d, d, d ) ) ]
% 49.17/49.65 )
% 49.17/49.65 .
% 49.17/49.65 clause( 3100, [ ~( =( d3, a ) ), ~( product( g1, d1, d2, b ) ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 9561, [ product( g2, d, X, X ), =( 'identity_for'( g2 ), c ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 20069, [ =( 'identity_for'( g2 ), c ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 20196, [ product( g2, X, c, X ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 20197, [ product( g2, c, X, X ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 49051, [ ~( product( g1, X, X, Y ) ), =( Y, X ), ~( product( Z, X,
% 49.17/49.65 'identity_for'( Z ), a ) ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 49223, [ =( 'identity_for'( g1 ), a ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 49329, [ product( g1, X, a, X ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 49330, [ product( g1, a, X, X ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 49392, [ ~( product( g1, a, X, Y ) ), =( Y, X ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 49908, [ =( d3, d2 ), =( d1, b ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 53129, [ product( g1, b, d2, d3 ), =( d3, d2 ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 53140, [ ~( product( g1, b, d2, X ) ), =( X, d3 ), =( d3, d2 ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 53142, [ =( d1, b ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 53144, [ ~( =( d3, d2 ) ), =( d3, d2 ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 53267, [ =( d2, a ), ~( =( d3, b ) ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 53279, [ =( d2, a ), =( d3, a ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 53296, [ =( d3, a ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 53297, [ =( d2, a ) ] )
% 49.17/49.65 .
% 49.17/49.65 clause( 53298, [] )
% 49.17/49.65 .
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 % SZS output end Refutation
% 49.17/49.65 found a proof!
% 49.17/49.65
% 49.17/49.65 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 49.17/49.65
% 49.17/49.65 initialclauses(
% 49.17/49.65 [ clause( 53300, [ 'group_member'( 'identity_for'( X ), X ) ] )
% 49.17/49.65 , clause( 53301, [ product( X, 'identity_for'( X ), Y, Y ) ] )
% 49.17/49.65 , clause( 53302, [ product( X, Y, 'identity_for'( X ), Y ) ] )
% 49.17/49.65 , clause( 53303, [ ~( 'group_member'( X, Y ) ), 'group_member'( inverse( Y
% 49.17/49.65 , X ), Y ) ] )
% 49.17/49.65 , clause( 53304, [ product( X, inverse( X, Y ), Y, 'identity_for'( X ) ) ]
% 49.17/49.65 )
% 49.17/49.65 , clause( 53305, [ product( X, Y, inverse( X, Y ), 'identity_for'( X ) ) ]
% 49.17/49.65 )
% 49.17/49.65 , clause( 53306, [ ~( 'group_member'( X, Y ) ), ~( 'group_member'( Z, Y ) )
% 49.17/49.65 , product( Y, X, Z, multiply( Y, X, Z ) ) ] )
% 49.17/49.65 , clause( 53307, [ ~( 'group_member'( X, Y ) ), ~( 'group_member'( Z, Y ) )
% 49.17/49.65 , 'group_member'( multiply( Y, X, Z ), Y ) ] )
% 49.17/49.65 , clause( 53308, [ ~( product( X, Y, Z, T ) ), ~( product( X, Y, Z, U ) ),
% 49.17/49.65 =( U, T ) ] )
% 49.17/49.65 , clause( 53309, [ ~( product( X, Y, Z, T ) ), ~( product( X, Z, U, W ) ),
% 49.17/49.65 ~( product( X, T, U, V0 ) ), product( X, Y, W, V0 ) ] )
% 49.17/49.65 , clause( 53310, [ ~( product( X, Y, Z, T ) ), ~( product( X, Z, U, W ) ),
% 49.17/49.65 ~( product( X, Y, W, V0 ) ), product( X, T, U, V0 ) ] )
% 49.17/49.65 , clause( 53311, [ 'group_member'( a, g1 ) ] )
% 49.17/49.65 , clause( 53312, [ 'group_member'( b, g1 ) ] )
% 49.17/49.65 , clause( 53313, [ 'group_member'( c, g2 ) ] )
% 49.17/49.65 , clause( 53314, [ 'group_member'( d, g2 ) ] )
% 49.17/49.65 , clause( 53315, [ ~( 'group_member'( X, g1 ) ), =( X, a ), =( X, b ) ] )
% 49.17/49.65 , clause( 53316, [ ~( 'group_member'( X, g2 ) ), =( X, c ), =( X, d ) ] )
% 49.17/49.65 , clause( 53317, [ product( g1, a, a, a ) ] )
% 49.17/49.65 , clause( 53318, [ product( g1, a, b, b ) ] )
% 49.17/49.65 , clause( 53319, [ product( g1, b, a, b ) ] )
% 49.17/49.65 , clause( 53320, [ product( g1, b, b, a ) ] )
% 49.17/49.65 , clause( 53321, [ product( g2, c, c, c ) ] )
% 49.17/49.65 , clause( 53322, [ product( g2, c, d, d ) ] )
% 49.17/49.65 , clause( 53323, [ product( g2, d, c, d ) ] )
% 49.17/49.65 , clause( 53324, [ product( g2, d, d, c ) ] )
% 49.17/49.65 , clause( 53325, [ =( 'an_isomorphism'( a ), c ) ] )
% 49.17/49.65 , clause( 53326, [ =( 'an_isomorphism'( b ), d ) ] )
% 49.17/49.65 , clause( 53327, [ 'group_member'( d1, g1 ) ] )
% 49.17/49.65 , clause( 53328, [ 'group_member'( d2, g1 ) ] )
% 49.17/49.65 , clause( 53329, [ 'group_member'( d3, g1 ) ] )
% 49.17/49.65 , clause( 53330, [ product( g1, d1, d2, d3 ) ] )
% 49.17/49.65 , clause( 53331, [ ~( product( g2, 'an_isomorphism'( d1 ), 'an_isomorphism'(
% 49.17/49.65 d2 ), 'an_isomorphism'( d3 ) ) ) ] )
% 49.17/49.65 ] ).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 subsumption(
% 49.17/49.65 clause( 0, [ 'group_member'( 'identity_for'( X ), X ) ] )
% 49.17/49.65 , clause( 53300, [ 'group_member'( 'identity_for'( X ), X ) ] )
% 49.17/49.65 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 subsumption(
% 49.17/49.65 clause( 1, [ product( X, 'identity_for'( X ), Y, Y ) ] )
% 49.17/49.65 , clause( 53301, [ product( X, 'identity_for'( X ), Y, Y ) ] )
% 49.17/49.65 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 49.17/49.65 )] ) ).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 subsumption(
% 49.17/49.65 clause( 2, [ product( X, Y, 'identity_for'( X ), Y ) ] )
% 49.17/49.65 , clause( 53302, [ product( X, Y, 'identity_for'( X ), Y ) ] )
% 49.17/49.65 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 49.17/49.65 )] ) ).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 subsumption(
% 49.17/49.65 clause( 8, [ ~( product( X, Y, Z, T ) ), ~( product( X, Y, Z, U ) ), =( U,
% 49.17/49.65 T ) ] )
% 49.17/49.65 , clause( 53308, [ ~( product( X, Y, Z, T ) ), ~( product( X, Y, Z, U ) ),
% 49.17/49.65 =( U, T ) ] )
% 49.17/49.65 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 49.17/49.65 , U )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] )
% 49.17/49.65 ).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 subsumption(
% 49.17/49.65 clause( 11, [ 'group_member'( a, g1 ) ] )
% 49.17/49.65 , clause( 53311, [ 'group_member'( a, g1 ) ] )
% 49.17/49.65 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 subsumption(
% 49.17/49.65 clause( 12, [ 'group_member'( b, g1 ) ] )
% 49.17/49.65 , clause( 53312, [ 'group_member'( b, g1 ) ] )
% 49.17/49.65 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 subsumption(
% 49.17/49.65 clause( 13, [ 'group_member'( c, g2 ) ] )
% 49.17/49.65 , clause( 53313, [ 'group_member'( c, g2 ) ] )
% 49.17/49.65 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 subsumption(
% 49.17/49.65 clause( 15, [ ~( 'group_member'( X, g1 ) ), =( X, a ), =( X, b ) ] )
% 49.17/49.65 , clause( 53315, [ ~( 'group_member'( X, g1 ) ), =( X, a ), =( X, b ) ] )
% 49.17/49.65 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 49.17/49.65 1 ), ==>( 2, 2 )] ) ).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 subsumption(
% 49.17/49.65 clause( 16, [ ~( 'group_member'( X, g2 ) ), =( X, c ), =( X, d ) ] )
% 49.17/49.65 , clause( 53316, [ ~( 'group_member'( X, g2 ) ), =( X, c ), =( X, d ) ] )
% 49.17/49.65 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 49.17/49.65 1 ), ==>( 2, 2 )] ) ).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 subsumption(
% 49.17/49.65 clause( 17, [ product( g1, a, a, a ) ] )
% 49.17/49.65 , clause( 53317, [ product( g1, a, a, a ) ] )
% 49.17/49.65 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 subsumption(
% 49.17/49.65 clause( 20, [ product( g1, b, b, a ) ] )
% 49.17/49.65 , clause( 53320, [ product( g1, b, b, a ) ] )
% 49.17/49.65 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 subsumption(
% 49.17/49.65 clause( 21, [ product( g2, c, c, c ) ] )
% 49.17/49.65 , clause( 53321, [ product( g2, c, c, c ) ] )
% 49.17/49.65 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 subsumption(
% 49.17/49.65 clause( 24, [ product( g2, d, d, c ) ] )
% 49.17/49.65 , clause( 53324, [ product( g2, d, d, c ) ] )
% 49.17/49.65 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 subsumption(
% 49.17/49.65 clause( 25, [ =( 'an_isomorphism'( a ), c ) ] )
% 49.17/49.65 , clause( 53325, [ =( 'an_isomorphism'( a ), c ) ] )
% 49.17/49.65 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 subsumption(
% 49.17/49.65 clause( 26, [ =( 'an_isomorphism'( b ), d ) ] )
% 49.17/49.65 , clause( 53326, [ =( 'an_isomorphism'( b ), d ) ] )
% 49.17/49.65 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 subsumption(
% 49.17/49.65 clause( 27, [ 'group_member'( d1, g1 ) ] )
% 49.17/49.65 , clause( 53327, [ 'group_member'( d1, g1 ) ] )
% 49.17/49.65 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 subsumption(
% 49.17/49.65 clause( 28, [ 'group_member'( d2, g1 ) ] )
% 49.17/49.65 , clause( 53328, [ 'group_member'( d2, g1 ) ] )
% 49.17/49.65 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 subsumption(
% 49.17/49.65 clause( 29, [ 'group_member'( d3, g1 ) ] )
% 49.17/49.65 , clause( 53329, [ 'group_member'( d3, g1 ) ] )
% 49.17/49.65 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 subsumption(
% 49.17/49.65 clause( 30, [ product( g1, d1, d2, d3 ) ] )
% 49.17/49.65 , clause( 53330, [ product( g1, d1, d2, d3 ) ] )
% 49.17/49.65 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 subsumption(
% 49.17/49.65 clause( 31, [ ~( product( g2, 'an_isomorphism'( d1 ), 'an_isomorphism'( d2
% 49.17/49.65 ), 'an_isomorphism'( d3 ) ) ) ] )
% 49.17/49.65 , clause( 53331, [ ~( product( g2, 'an_isomorphism'( d1 ), 'an_isomorphism'(
% 49.17/49.65 d2 ), 'an_isomorphism'( d3 ) ) ) ] )
% 49.17/49.65 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 eqfact(
% 49.17/49.65 clause( 53614, [ ~( =( c, d ) ), ~( 'group_member'( X, g2 ) ), =( X, d ) ]
% 49.17/49.65 )
% 49.17/49.65 , clause( 16, [ ~( 'group_member'( X, g2 ) ), =( X, c ), =( X, d ) ] )
% 49.17/49.65 , 1, 2, substitution( 0, [ :=( X, X )] )).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 eqswap(
% 49.17/49.65 clause( 53619, [ ~( =( d, c ) ), ~( 'group_member'( X, g2 ) ), =( X, d ) ]
% 49.17/49.65 )
% 49.17/49.65 , clause( 53614, [ ~( =( c, d ) ), ~( 'group_member'( X, g2 ) ), =( X, d )
% 49.17/49.65 ] )
% 49.17/49.65 , 0, substitution( 0, [ :=( X, X )] )).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 subsumption(
% 49.17/49.65 clause( 42, [ ~( =( d, c ) ), ~( 'group_member'( X, g2 ) ), =( X, d ) ] )
% 49.17/49.65 , clause( 53619, [ ~( =( d, c ) ), ~( 'group_member'( X, g2 ) ), =( X, d )
% 49.17/49.65 ] )
% 49.17/49.65 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 49.17/49.65 1 ), ==>( 2, 2 )] ) ).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 eqswap(
% 49.17/49.65 clause( 53622, [ ~( =( c, d ) ), ~( 'group_member'( X, g2 ) ), =( X, d ) ]
% 49.17/49.65 )
% 49.17/49.65 , clause( 42, [ ~( =( d, c ) ), ~( 'group_member'( X, g2 ) ), =( X, d ) ]
% 49.17/49.65 )
% 49.17/49.65 , 0, substitution( 0, [ :=( X, X )] )).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 resolution(
% 49.17/49.65 clause( 53625, [ ~( =( c, d ) ), =( 'identity_for'( g2 ), d ) ] )
% 49.17/49.65 , clause( 53622, [ ~( =( c, d ) ), ~( 'group_member'( X, g2 ) ), =( X, d )
% 49.17/49.65 ] )
% 49.17/49.65 , 1, clause( 0, [ 'group_member'( 'identity_for'( X ), X ) ] )
% 49.17/49.65 , 0, substitution( 0, [ :=( X, 'identity_for'( g2 ) )] ), substitution( 1
% 49.17/49.65 , [ :=( X, g2 )] )).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 eqswap(
% 49.17/49.65 clause( 53626, [ ~( =( d, c ) ), =( 'identity_for'( g2 ), d ) ] )
% 49.17/49.65 , clause( 53625, [ ~( =( c, d ) ), =( 'identity_for'( g2 ), d ) ] )
% 49.17/49.65 , 0, substitution( 0, [] )).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 subsumption(
% 49.17/49.65 clause( 177, [ ~( =( d, c ) ), =( 'identity_for'( g2 ), d ) ] )
% 49.17/49.65 , clause( 53626, [ ~( =( d, c ) ), =( 'identity_for'( g2 ), d ) ] )
% 49.17/49.65 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] )
% 49.17/49.65 ).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 eqswap(
% 49.17/49.65 clause( 53629, [ ~( =( c, d ) ), ~( 'group_member'( X, g2 ) ), =( X, d ) ]
% 49.17/49.65 )
% 49.17/49.65 , clause( 42, [ ~( =( d, c ) ), ~( 'group_member'( X, g2 ) ), =( X, d ) ]
% 49.17/49.65 )
% 49.17/49.65 , 0, substitution( 0, [ :=( X, X )] )).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 resolution(
% 49.17/49.65 clause( 53632, [ ~( =( c, d ) ), =( c, d ) ] )
% 49.17/49.65 , clause( 53629, [ ~( =( c, d ) ), ~( 'group_member'( X, g2 ) ), =( X, d )
% 49.17/49.65 ] )
% 49.17/49.65 , 1, clause( 13, [ 'group_member'( c, g2 ) ] )
% 49.17/49.65 , 0, substitution( 0, [ :=( X, c )] ), substitution( 1, [] )).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 eqswap(
% 49.17/49.65 clause( 53634, [ =( d, c ), ~( =( c, d ) ) ] )
% 49.17/49.65 , clause( 53632, [ ~( =( c, d ) ), =( c, d ) ] )
% 49.17/49.65 , 1, substitution( 0, [] )).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 eqswap(
% 49.17/49.65 clause( 53635, [ ~( =( d, c ) ), =( d, c ) ] )
% 49.17/49.65 , clause( 53634, [ =( d, c ), ~( =( c, d ) ) ] )
% 49.17/49.65 , 1, substitution( 0, [] )).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 subsumption(
% 49.17/49.65 clause( 178, [ ~( =( d, c ) ), =( d, c ) ] )
% 49.17/49.65 , clause( 53635, [ ~( =( d, c ) ), =( d, c ) ] )
% 49.17/49.65 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] )
% 49.17/49.65 ).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 resolution(
% 49.17/49.65 clause( 53636, [ ~( product( g1, a, a, X ) ), =( X, a ) ] )
% 49.17/49.65 , clause( 8, [ ~( product( X, Y, Z, T ) ), ~( product( X, Y, Z, U ) ), =( U
% 49.17/49.65 , T ) ] )
% 49.17/49.65 , 0, clause( 17, [ product( g1, a, a, a ) ] )
% 49.17/49.65 , 0, substitution( 0, [ :=( X, g1 ), :=( Y, a ), :=( Z, a ), :=( T, a ),
% 49.17/49.65 :=( U, X )] ), substitution( 1, [] )).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 subsumption(
% 49.17/49.65 clause( 274, [ ~( product( g1, a, a, X ) ), =( X, a ) ] )
% 49.17/49.65 , clause( 53636, [ ~( product( g1, a, a, X ) ), =( X, a ) ] )
% 49.17/49.65 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 49.17/49.65 1 )] ) ).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 resolution(
% 49.17/49.65 clause( 53638, [ ~( product( g1, b, b, X ) ), =( X, a ) ] )
% 49.17/49.65 , clause( 8, [ ~( product( X, Y, Z, T ) ), ~( product( X, Y, Z, U ) ), =( U
% 49.17/49.65 , T ) ] )
% 49.17/49.65 , 0, clause( 20, [ product( g1, b, b, a ) ] )
% 49.17/49.65 , 0, substitution( 0, [ :=( X, g1 ), :=( Y, b ), :=( Z, b ), :=( T, a ),
% 49.17/49.65 :=( U, X )] ), substitution( 1, [] )).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 subsumption(
% 49.17/49.65 clause( 277, [ ~( product( g1, b, b, X ) ), =( X, a ) ] )
% 49.17/49.65 , clause( 53638, [ ~( product( g1, b, b, X ) ), =( X, a ) ] )
% 49.17/49.65 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 49.17/49.65 1 )] ) ).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 resolution(
% 49.17/49.65 clause( 53640, [ ~( product( X, Y, 'identity_for'( X ), Z ) ), =( Z, Y ) ]
% 49.17/49.65 )
% 49.17/49.65 , clause( 8, [ ~( product( X, Y, Z, T ) ), ~( product( X, Y, Z, U ) ), =( U
% 49.17/49.65 , T ) ] )
% 49.17/49.65 , 0, clause( 2, [ product( X, Y, 'identity_for'( X ), Y ) ] )
% 49.17/49.65 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, 'identity_for'( X )
% 49.17/49.65 ), :=( T, Y ), :=( U, Z )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )
% 49.17/49.65 ).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 subsumption(
% 49.17/49.65 clause( 279, [ ~( product( X, Y, 'identity_for'( X ), Z ) ), =( Z, Y ) ] )
% 49.17/49.65 , clause( 53640, [ ~( product( X, Y, 'identity_for'( X ), Z ) ), =( Z, Y )
% 49.17/49.65 ] )
% 49.17/49.65 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 49.17/49.65 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 resolution(
% 49.17/49.65 clause( 53642, [ ~( product( g2, d, d, X ) ), =( X, c ) ] )
% 49.17/49.65 , clause( 8, [ ~( product( X, Y, Z, T ) ), ~( product( X, Y, Z, U ) ), =( U
% 49.17/49.65 , T ) ] )
% 49.17/49.65 , 0, clause( 24, [ product( g2, d, d, c ) ] )
% 49.17/49.65 , 0, substitution( 0, [ :=( X, g2 ), :=( Y, d ), :=( Z, d ), :=( T, c ),
% 49.17/49.65 :=( U, X )] ), substitution( 1, [] )).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 subsumption(
% 49.17/49.65 clause( 282, [ ~( product( g2, d, d, X ) ), =( X, c ) ] )
% 49.17/49.65 , clause( 53642, [ ~( product( g2, d, d, X ) ), =( X, c ) ] )
% 49.17/49.65 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 49.17/49.65 1 )] ) ).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 resolution(
% 49.17/49.65 clause( 53644, [ ~( product( g1, d1, d2, X ) ), =( X, d3 ) ] )
% 49.17/49.65 , clause( 8, [ ~( product( X, Y, Z, T ) ), ~( product( X, Y, Z, U ) ), =( U
% 49.17/49.65 , T ) ] )
% 49.17/49.65 , 0, clause( 30, [ product( g1, d1, d2, d3 ) ] )
% 49.17/49.65 , 0, substitution( 0, [ :=( X, g1 ), :=( Y, d1 ), :=( Z, d2 ), :=( T, d3 )
% 49.17/49.65 , :=( U, X )] ), substitution( 1, [] )).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 subsumption(
% 49.17/49.65 clause( 283, [ ~( product( g1, d1, d2, X ) ), =( X, d3 ) ] )
% 49.17/49.65 , clause( 53644, [ ~( product( g1, d1, d2, X ) ), =( X, d3 ) ] )
% 49.17/49.65 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 49.17/49.65 1 )] ) ).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 eqswap(
% 49.17/49.65 clause( 53649, [ ~( =( c, d ) ), =( d, c ) ] )
% 49.17/49.65 , clause( 178, [ ~( =( d, c ) ), =( d, c ) ] )
% 49.17/49.65 , 0, substitution( 0, [] )).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 paramod(
% 49.17/49.65 clause( 53653, [ =( 'identity_for'( g2 ), c ), ~( =( c, d ) ), ~( =( d, c )
% 49.17/49.65 ) ] )
% 49.17/49.65 , clause( 53649, [ ~( =( c, d ) ), =( d, c ) ] )
% 49.17/49.65 , 1, clause( 177, [ ~( =( d, c ) ), =( 'identity_for'( g2 ), d ) ] )
% 49.17/49.65 , 1, 3, substitution( 0, [] ), substitution( 1, [] )).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 eqswap(
% 49.17/49.65 clause( 53682, [ ~( =( d, c ) ), =( 'identity_for'( g2 ), c ), ~( =( d, c )
% 49.17/49.65 ) ] )
% 49.17/49.65 , clause( 53653, [ =( 'identity_for'( g2 ), c ), ~( =( c, d ) ), ~( =( d, c
% 49.17/49.65 ) ) ] )
% 49.17/49.65 , 1, substitution( 0, [] )).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 factor(
% 49.17/49.65 clause( 53687, [ ~( =( d, c ) ), =( 'identity_for'( g2 ), c ) ] )
% 49.17/49.65 , clause( 53682, [ ~( =( d, c ) ), =( 'identity_for'( g2 ), c ), ~( =( d, c
% 49.17/49.65 ) ) ] )
% 49.17/49.65 , 0, 2, substitution( 0, [] )).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 subsumption(
% 49.17/49.65 clause( 366, [ ~( =( d, c ) ), =( 'identity_for'( g2 ), c ) ] )
% 49.17/49.65 , clause( 53687, [ ~( =( d, c ) ), =( 'identity_for'( g2 ), c ) ] )
% 49.17/49.65 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] )
% 49.17/49.65 ).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 eqswap(
% 49.17/49.65 clause( 53690, [ =( a, X ), ~( 'group_member'( X, g1 ) ), =( X, b ) ] )
% 49.17/49.65 , clause( 15, [ ~( 'group_member'( X, g1 ) ), =( X, a ), =( X, b ) ] )
% 49.17/49.65 , 1, substitution( 0, [ :=( X, X )] )).
% 49.17/49.65
% 49.17/49.65
% 49.17/49.65 resolution(
% 49.17/49.65 clause( 53693, [ =( a, 'identity_for'( g1 ) ), =( 'identity_for'( g1 ), b )
% 49.17/49.65 ] )
% 49.17/49.65 , clause( 53690, [ =( a, X ), ~( 'group_member'( X, g1 ) ), =( X, b ) ] )
% 49.17/49.65 , 1, clause( 0, [ 'group_member'( 'identity_for'( X ), X ) ] )
% 266.66/267.17 , 0, substitution( 0, [ :=( X, 'identity_for'( g1 ) )] ), substitution( 1
% 266.66/267.17 , [ :=( X, g1 )] )).
% 266.66/267.17
% 266.66/267.17
% 266.66/267.17 eqswap(
% 266.66/267.17 clause( 53694, [ =( 'identity_for'( g1 ), a ), =( 'identity_for'( g1 ), b )
% 266.66/267.17 ] )
% 266.66/267.17 , clause( 53693, [ =( a, 'identity_for'( g1 ) ), =( 'identity_for'( g1 ), b
% 266.66/267.17 ) ] )
% 266.66/267.17 , 0, substitution( 0, [] )).
% 266.66/267.17
% 266.66/267.17
% 266.66/267.17 subsumption(
% 266.66/267.17 clause( 956, [ =( 'identity_for'( g1 ), a ), =( 'identity_for'( g1 ), b ) ]
% 266.66/267.17 )
% 266.66/267.17 , clause( 53694, [ =( 'identity_for'( g1 ), a ), =( 'identity_for'( g1 ), b
% 266.66/267.17 ) ] )
% 266.66/267.17 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] )
% 266.66/267.17 ).
% 266.66/267.17
% 266.66/267.17
% 266.66/267.17 eqswap(
% 266.66/267.17 clause( 53697, [ =( a, X ), ~( 'group_member'( X, g1 ) ), =( X, b ) ] )
% 266.66/267.17 , clause( 15, [ ~( 'group_member'( X, g1 ) ), =( X, a ), =( X, b ) ] )
% 266.66/267.17 , 1, substitution( 0, [ :=( X, X )] )).
% 266.66/267.17
% 266.66/267.17
% 266.66/267.17 resolution(
% 266.66/267.17 clause( 53700, [ =( a, d1 ), =( d1, b ) ] )
% 266.66/267.17 , clause( 53697, [ =( a, X ), ~( 'group_member'( X, g1 ) ), =( X, b ) ] )
% 266.66/267.17 , 1, clause( 27, [ 'group_member'( d1, g1 ) ] )
% 266.66/267.17 , 0, substitution( 0, [ :=( X, d1 )] ), substitution( 1, [] )).
% 266.66/267.17
% 266.66/267.17
% 266.66/267.17 eqswap(
% 266.66/267.17 clause( 53701, [ =( d1, a ), =( d1, b ) ] )
% 266.66/267.17 , clause( 53700, [ =( a, d1 ), =( d1, b ) ] )
% 266.66/267.17 , 0, substitution( 0, [] )).
% 266.66/267.17
% 266.66/267.17
% 266.66/267.17 subsumption(
% 266.66/267.17 clause( 957, [ =( d1, a ), =( d1, b ) ] )
% 266.66/267.17 , clause( 53701, [ =( d1, a ), =( d1, b ) ] )
% 266.66/267.17 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] )
% 266.66/267.17 ).
% 266.66/267.17
% 266.66/267.17
% 266.66/267.17 eqswap(
% 266.66/267.17 clause( 53704, [ =( a, X ), ~( 'group_member'( X, g1 ) ), =( X, b ) ] )
% 266.66/267.17 , clause( 15, [ ~( 'group_member'( X, g1 ) ), =( X, a ), =( X, b ) ] )
% 266.66/267.17 , 1, substitution( 0, [ :=( X, X )] )).
% 266.66/267.17
% 266.66/267.17
% 266.66/267.17 resolution(
% 266.66/267.17 clause( 53707, [ =( a, d2 ), =( d2, b ) ] )
% 266.66/267.17 , clause( 53704, [ =( a, X ), ~( 'group_member'( X, g1 ) ), =( X, b ) ] )
% 266.66/267.17 , 1, clause( 28, [ 'group_member'( d2, g1 ) ] )
% 266.66/267.17 , 0, substitution( 0, [ :=( X, d2 )] ), substitution( 1, [] )).
% 266.66/267.17
% 266.66/267.17
% 266.66/267.17 eqswap(
% 266.66/267.17 clause( 53708, [ =( d2, a ), =( d2, b ) ] )
% 266.66/267.17 , clause( 53707, [ =( a, d2 ), =( d2, b ) ] )
% 266.66/267.17 , 0, substitution( 0, [] )).
% 266.66/267.17
% 266.66/267.17
% 266.66/267.17 subsumption(
% 266.66/267.17 clause( 958, [ =( d2, a ), =( d2, b ) ] )
% 266.66/267.17 , clause( 53708, [ =( d2, a ), =( d2, b ) ] )
% 266.66/267.17 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] )
% 266.66/267.17 ).
% 266.66/267.17
% 266.66/267.17
% 266.66/267.17 eqswap(
% 266.66/267.17 clause( 53711, [ =( a, X ), ~( 'group_member'( X, g1 ) ), =( X, b ) ] )
% 266.66/267.17 , clause( 15, [ ~( 'group_member'( X, g1 ) ), =( X, a ), =( X, b ) ] )
% 266.66/267.17 , 1, substitution( 0, [ :=( X, X )] )).
% 266.66/267.17
% 266.66/267.17
% 266.66/267.17 resolution(
% 266.66/267.17 clause( 53714, [ =( a, d3 ), =( d3, b ) ] )
% 266.66/267.17 , clause( 53711, [ =( a, X ), ~( 'group_member'( X, g1 ) ), =( X, b ) ] )
% 266.66/267.17 , 1, clause( 29, [ 'group_member'( d3, g1 ) ] )
% 266.66/267.17 , 0, substitution( 0, [ :=( X, d3 )] ), substitution( 1, [] )).
% 266.66/267.17
% 266.66/267.17
% 266.66/267.17 eqswap(
% 266.66/267.17 clause( 53715, [ =( d3, a ), =( d3, b ) ] )
% 266.66/267.17 , clause( 53714, [ =( a, d3 ), =( d3, b ) ] )
% 266.66/267.17 , 0, substitution( 0, [] )).
% 266.66/267.17
% 266.66/267.17
% 266.66/267.17 subsumption(
% 266.66/267.17 clause( 959, [ =( d3, a ), =( d3, b ) ] )
% 266.66/267.17 , clause( 53715, [ =( d3, a ), =( d3, b ) ] )
% 266.66/267.17 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] )
% 266.66/267.17 ).
% 266.66/267.17
% 266.66/267.17
% 266.66/267.17 eqswap(
% 266.66/267.17 clause( 53719, [ =( b, X ), ~( 'group_member'( X, g1 ) ), =( X, a ) ] )
% 266.66/267.17 , clause( 15, [ ~( 'group_member'( X, g1 ) ), =( X, a ), =( X, b ) ] )
% 266.66/267.17 , 2, substitution( 0, [ :=( X, X )] )).
% 266.66/267.17
% 266.66/267.17
% 266.66/267.17 eqswap(
% 266.66/267.17 clause( 53722, [ =( b, d1 ), =( d1, a ) ] )
% 266.66/267.17 , clause( 957, [ =( d1, a ), =( d1, b ) ] )
% 266.66/267.17 , 1, substitution( 0, [] )).
% 266.66/267.17
% 266.66/267.17
% 266.66/267.17 paramod(
% 266.66/267.17 clause( 3894893, [ product( g1, a, d2, d3 ), =( b, d1 ), ~( 'group_member'(
% 266.66/267.17 d1, g1 ) ) ] )
% 266.66/267.17 , clause( 53719, [ =( b, X ), ~( 'group_member'( X, g1 ) ), =( X, a ) ] )
% 266.66/267.17 , 2, clause( 30, [ product( g1, d1, d2, d3 ) ] )
% 266.66/267.17 , 0, 2, substitution( 0, [ :=( X, d1 )] ), substitution( 1, [] )).
% 266.66/267.17
% 266.66/267.17
% 266.66/267.17 paramod(
% 266.66/267.17 clause( 5013399, [ ~( 'group_member'( a, g1 ) ), =( b, d1 ), product( g1, a
% 266.66/267.17 , d2, d3 ), =( b, d1 ) ] )
% 266.66/267.17 , clause( 53722, [ =( b, d1 ), =( d1, a ) ] )
% 266.66/267.17 , 1, clause( 3894893, [ product( g1, a, d2, d3 ), =( b, d1 ), ~(
% 266.66/267.17 'group_member'( d1, g1 ) ) ] )
% 266.66/267.17 , 2, 2, substitution( 0, [] ), substitution( 1, [] )).
% 266.66/267.17
% 266.66/267.17
% 266.66/267.17 factor(
% 266.66/267.17 clause( 5013422, [ ~( 'group_member'( a, g1 ) ), =( b, d1 ), product( g1, a
% 266.66/267.17 , d2, d3 ) ] )
% 266.66/267.17 , clause( 5013399, [ ~( 'group_member'( a, g1 ) ), =( b, d1 ), product( g1
% 266.66/267.17 , a, d2, d3 ), =( b, d1 ) ] )
% 266.66/267.17 , 1, 3, substitution( 0, [] )).
% 266.66/267.17
% 266.66/267.17
% 266.66/267.17 resolution(
% 266.66/267.17 clause( 5013423, [ =( b, d1 ), product( g1, a, d2, d3 ) ] )
% 266.66/267.17 , clause( 501Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------