TSTP Solution File: CAT009-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : CAT009-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n017.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 : Thu Jul 14 23:54:11 EDT 2022
% Result : Unsatisfiable 27.15s 27.59s
% Output : Refutation 27.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : CAT009-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Sun May 29 18:49:39 EDT 2022
% 0.12/0.34 % CPUTime :
% 27.15/27.59 *** allocated 10000 integers for termspace/termends
% 27.15/27.59 *** allocated 10000 integers for clauses
% 27.15/27.59 *** allocated 10000 integers for justifications
% 27.15/27.59 Bliksem 1.12
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 Automatic Strategy Selection
% 27.15/27.59
% 27.15/27.59 Clauses:
% 27.15/27.59 [
% 27.15/27.59 [ ~( defined( X, Y ) ), product( X, Y, compose( X, Y ) ) ],
% 27.15/27.59 [ ~( product( X, Y, Z ) ), defined( X, Y ) ],
% 27.15/27.59 [ ~( product( X, Y, Z ) ), ~( defined( Z, T ) ), defined( Y, T ) ],
% 27.15/27.59 [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~( defined( Z, T ) )
% 27.15/27.59 , defined( X, U ) ],
% 27.15/27.59 [ ~( product( X, Y, Z ) ), ~( product( Z, T, U ) ), ~( product( Y, T, W
% 27.15/27.59 ) ), product( X, W, U ) ],
% 27.15/27.59 [ ~( product( X, Y, Z ) ), ~( defined( T, Z ) ), defined( T, X ) ],
% 27.15/27.59 [ ~( product( X, Y, Z ) ), ~( product( T, X, U ) ), ~( defined( T, Z ) )
% 27.15/27.59 , defined( U, Y ) ],
% 27.15/27.59 [ ~( product( X, Y, Z ) ), ~( product( T, Z, U ) ), ~( product( T, X, W
% 27.15/27.59 ) ), product( W, Y, U ) ],
% 27.15/27.59 [ ~( defined( X, Y ) ), ~( defined( Y, Z ) ), ~( 'identity_map'( Y ) ),
% 27.15/27.59 defined( X, Z ) ],
% 27.15/27.59 [ 'identity_map'( domain( X ) ) ],
% 27.15/27.59 [ 'identity_map'( codomain( X ) ) ],
% 27.15/27.59 [ defined( X, domain( X ) ) ],
% 27.15/27.59 [ defined( codomain( X ), X ) ],
% 27.15/27.59 [ product( X, domain( X ), X ) ],
% 27.15/27.59 [ product( codomain( X ), X, X ) ],
% 27.15/27.59 [ ~( defined( X, Y ) ), ~( 'identity_map'( X ) ), product( X, Y, Y ) ]
% 27.15/27.59 ,
% 27.15/27.59 [ ~( defined( X, Y ) ), ~( 'identity_map'( Y ) ), product( X, Y, X ) ]
% 27.15/27.59 ,
% 27.15/27.59 [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z, T ) ],
% 27.15/27.59 [ defined( b, a ) ],
% 27.15/27.59 [ ~( =( domain( compose( b, a ) ), domain( a ) ) ) ]
% 27.15/27.59 ] .
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 percentage equality = 0.042553, percentage horn = 1.000000
% 27.15/27.59 This is a problem with some equality
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 Options Used:
% 27.15/27.59
% 27.15/27.59 useres = 1
% 27.15/27.59 useparamod = 1
% 27.15/27.59 useeqrefl = 1
% 27.15/27.59 useeqfact = 1
% 27.15/27.59 usefactor = 1
% 27.15/27.59 usesimpsplitting = 0
% 27.15/27.59 usesimpdemod = 5
% 27.15/27.59 usesimpres = 3
% 27.15/27.59
% 27.15/27.59 resimpinuse = 1000
% 27.15/27.59 resimpclauses = 20000
% 27.15/27.59 substype = eqrewr
% 27.15/27.59 backwardsubs = 1
% 27.15/27.59 selectoldest = 5
% 27.15/27.59
% 27.15/27.59 litorderings [0] = split
% 27.15/27.59 litorderings [1] = extend the termordering, first sorting on arguments
% 27.15/27.59
% 27.15/27.59 termordering = kbo
% 27.15/27.59
% 27.15/27.59 litapriori = 0
% 27.15/27.59 termapriori = 1
% 27.15/27.59 litaposteriori = 0
% 27.15/27.59 termaposteriori = 0
% 27.15/27.59 demodaposteriori = 0
% 27.15/27.59 ordereqreflfact = 0
% 27.15/27.59
% 27.15/27.59 litselect = negord
% 27.15/27.59
% 27.15/27.59 maxweight = 15
% 27.15/27.59 maxdepth = 30000
% 27.15/27.59 maxlength = 115
% 27.15/27.59 maxnrvars = 195
% 27.15/27.59 excuselevel = 1
% 27.15/27.59 increasemaxweight = 1
% 27.15/27.59
% 27.15/27.59 maxselected = 10000000
% 27.15/27.59 maxnrclauses = 10000000
% 27.15/27.59
% 27.15/27.59 showgenerated = 0
% 27.15/27.59 showkept = 0
% 27.15/27.59 showselected = 0
% 27.15/27.59 showdeleted = 0
% 27.15/27.59 showresimp = 1
% 27.15/27.59 showstatus = 2000
% 27.15/27.59
% 27.15/27.59 prologoutput = 1
% 27.15/27.59 nrgoals = 5000000
% 27.15/27.59 totalproof = 1
% 27.15/27.59
% 27.15/27.59 Symbols occurring in the translation:
% 27.15/27.59
% 27.15/27.59 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 27.15/27.59 . [1, 2] (w:1, o:26, a:1, s:1, b:0),
% 27.15/27.59 ! [4, 1] (w:0, o:18, a:1, s:1, b:0),
% 27.15/27.59 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 27.15/27.59 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 27.15/27.59 defined [41, 2] (w:1, o:52, a:1, s:1, b:0),
% 27.15/27.59 compose [42, 2] (w:1, o:51, a:1, s:1, b:0),
% 27.15/27.59 product [43, 3] (w:1, o:53, a:1, s:1, b:0),
% 27.15/27.59 'identity_map' [48, 1] (w:1, o:23, a:1, s:1, b:0),
% 27.15/27.59 domain [49, 1] (w:1, o:25, a:1, s:1, b:0),
% 27.15/27.59 codomain [50, 1] (w:1, o:24, a:1, s:1, b:0),
% 27.15/27.59 b [52, 0] (w:1, o:17, a:1, s:1, b:0),
% 27.15/27.59 a [53, 0] (w:1, o:16, a:1, s:1, b:0).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 Starting Search:
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 Intermediate Status:
% 27.15/27.59 Generated: 4742
% 27.15/27.59 Kept: 2002
% 27.15/27.59 Inuse: 130
% 27.15/27.59 Deleted: 0
% 27.15/27.59 Deletedinuse: 0
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 Intermediate Status:
% 27.15/27.59 Generated: 10673
% 27.15/27.59 Kept: 4058
% 27.15/27.59 Inuse: 224
% 27.15/27.59 Deleted: 8
% 27.15/27.59 Deletedinuse: 6
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 Intermediate Status:
% 27.15/27.59 Generated: 17007
% 27.15/27.59 Kept: 6081
% 27.15/27.59 Inuse: 302
% 27.15/27.59 Deleted: 15
% 27.15/27.59 Deletedinuse: 6
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 Intermediate Status:
% 27.15/27.59 Generated: 23728
% 27.15/27.59 Kept: 8087
% 27.15/27.59 Inuse: 363
% 27.15/27.59 Deleted: 41
% 27.15/27.59 Deletedinuse: 29
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 Intermediate Status:
% 27.15/27.59 Generated: 32056
% 27.15/27.59 Kept: 11373
% 27.15/27.59 Inuse: 408
% 27.15/27.59 Deleted: 59
% 27.15/27.59 Deletedinuse: 45
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 Intermediate Status:
% 27.15/27.59 Generated: 41047
% 27.15/27.59 Kept: 13393
% 27.15/27.59 Inuse: 451
% 27.15/27.59 Deleted: 207
% 27.15/27.59 Deletedinuse: 186
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 Intermediate Status:
% 27.15/27.59 Generated: 49431
% 27.15/27.59 Kept: 15395
% 27.15/27.59 Inuse: 501
% 27.15/27.59 Deleted: 254
% 27.15/27.59 Deletedinuse: 228
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 Intermediate Status:
% 27.15/27.59 Generated: 58737
% 27.15/27.59 Kept: 17397
% 27.15/27.59 Inuse: 542
% 27.15/27.59 Deleted: 266
% 27.15/27.59 Deletedinuse: 230
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 Intermediate Status:
% 27.15/27.59 Generated: 68270
% 27.15/27.59 Kept: 19446
% 27.15/27.59 Inuse: 598
% 27.15/27.59 Deleted: 402
% 27.15/27.59 Deletedinuse: 269
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59 Resimplifying clauses:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 Intermediate Status:
% 27.15/27.59 Generated: 86701
% 27.15/27.59 Kept: 21513
% 27.15/27.59 Inuse: 642
% 27.15/27.59 Deleted: 10336
% 27.15/27.59 Deletedinuse: 273
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 Intermediate Status:
% 27.15/27.59 Generated: 101069
% 27.15/27.59 Kept: 23523
% 27.15/27.59 Inuse: 701
% 27.15/27.59 Deleted: 10349
% 27.15/27.59 Deletedinuse: 286
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 Intermediate Status:
% 27.15/27.59 Generated: 111780
% 27.15/27.59 Kept: 25631
% 27.15/27.59 Inuse: 748
% 27.15/27.59 Deleted: 10405
% 27.15/27.59 Deletedinuse: 339
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 Intermediate Status:
% 27.15/27.59 Generated: 120767
% 27.15/27.59 Kept: 27644
% 27.15/27.59 Inuse: 803
% 27.15/27.59 Deleted: 10424
% 27.15/27.59 Deletedinuse: 346
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 Intermediate Status:
% 27.15/27.59 Generated: 133380
% 27.15/27.59 Kept: 29682
% 27.15/27.59 Inuse: 866
% 27.15/27.59 Deleted: 10457
% 27.15/27.59 Deletedinuse: 365
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 Intermediate Status:
% 27.15/27.59 Generated: 152409
% 27.15/27.59 Kept: 31706
% 27.15/27.59 Inuse: 914
% 27.15/27.59 Deleted: 10488
% 27.15/27.59 Deletedinuse: 365
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 Intermediate Status:
% 27.15/27.59 Generated: 172841
% 27.15/27.59 Kept: 33934
% 27.15/27.59 Inuse: 960
% 27.15/27.59 Deleted: 10498
% 27.15/27.59 Deletedinuse: 365
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 Intermediate Status:
% 27.15/27.59 Generated: 187299
% 27.15/27.59 Kept: 36187
% 27.15/27.59 Inuse: 995
% 27.15/27.59 Deleted: 10521
% 27.15/27.59 Deletedinuse: 366
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 Intermediate Status:
% 27.15/27.59 Generated: 199691
% 27.15/27.59 Kept: 38217
% 27.15/27.59 Inuse: 1030
% 27.15/27.59 Deleted: 10533
% 27.15/27.59 Deletedinuse: 366
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59 Resimplifying clauses:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 Intermediate Status:
% 27.15/27.59 Generated: 212697
% 27.15/27.59 Kept: 40377
% 27.15/27.59 Inuse: 1055
% 27.15/27.59 Deleted: 17107
% 27.15/27.59 Deletedinuse: 367
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 Intermediate Status:
% 27.15/27.59 Generated: 228239
% 27.15/27.59 Kept: 42384
% 27.15/27.59 Inuse: 1093
% 27.15/27.59 Deleted: 17109
% 27.15/27.59 Deletedinuse: 367
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 Intermediate Status:
% 27.15/27.59 Generated: 243996
% 27.15/27.59 Kept: 44529
% 27.15/27.59 Inuse: 1128
% 27.15/27.59 Deleted: 17116
% 27.15/27.59 Deletedinuse: 371
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 Intermediate Status:
% 27.15/27.59 Generated: 256937
% 27.15/27.59 Kept: 46538
% 27.15/27.59 Inuse: 1157
% 27.15/27.59 Deleted: 17126
% 27.15/27.59 Deletedinuse: 378
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 Intermediate Status:
% 27.15/27.59 Generated: 277183
% 27.15/27.59 Kept: 48563
% 27.15/27.59 Inuse: 1196
% 27.15/27.59 Deleted: 17126
% 27.15/27.59 Deletedinuse: 378
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 Intermediate Status:
% 27.15/27.59 Generated: 294268
% 27.15/27.59 Kept: 52444
% 27.15/27.59 Inuse: 1221
% 27.15/27.59 Deleted: 17126
% 27.15/27.59 Deletedinuse: 378
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 Intermediate Status:
% 27.15/27.59 Generated: 299172
% 27.15/27.59 Kept: 55117
% 27.15/27.59 Inuse: 1222
% 27.15/27.59 Deleted: 17130
% 27.15/27.59 Deletedinuse: 382
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 Intermediate Status:
% 27.15/27.59 Generated: 311814
% 27.15/27.59 Kept: 58566
% 27.15/27.59 Inuse: 1238
% 27.15/27.59 Deleted: 17146
% 27.15/27.59 Deletedinuse: 397
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59 Done
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 Intermediate Status:
% 27.15/27.59 Generated: 332443
% 27.15/27.59 Kept: 60750
% 27.15/27.59 Inuse: 1267
% 27.15/27.59 Deleted: 17153
% 27.15/27.59 Deletedinuse: 400
% 27.15/27.59
% 27.15/27.59 Resimplifying inuse:
% 27.15/27.59
% 27.15/27.59 Bliksems!, er is een bewijs:
% 27.15/27.59 % SZS status Unsatisfiable
% 27.15/27.59 % SZS output start Refutation
% 27.15/27.59
% 27.15/27.59 clause( 0, [ ~( defined( X, Y ) ), product( X, Y, compose( X, Y ) ) ] )
% 27.15/27.59 .
% 27.15/27.59 clause( 1, [ ~( product( X, Y, Z ) ), defined( X, Y ) ] )
% 27.15/27.59 .
% 27.15/27.59 clause( 2, [ ~( product( X, Y, Z ) ), ~( defined( Z, T ) ), defined( Y, T )
% 27.15/27.59 ] )
% 27.15/27.59 .
% 27.15/27.59 clause( 5, [ ~( product( X, Y, Z ) ), ~( defined( T, Z ) ), defined( T, X )
% 27.15/27.59 ] )
% 27.15/27.59 .
% 27.15/27.59 clause( 8, [ ~( defined( X, Y ) ), ~( defined( Y, Z ) ), ~( 'identity_map'(
% 27.15/27.59 Y ) ), defined( X, Z ) ] )
% 27.15/27.59 .
% 27.15/27.59 clause( 9, [ 'identity_map'( domain( X ) ) ] )
% 27.15/27.59 .
% 27.15/27.59 clause( 10, [ 'identity_map'( codomain( X ) ) ] )
% 27.15/27.59 .
% 27.15/27.59 clause( 11, [ defined( X, domain( X ) ) ] )
% 27.15/27.59 .
% 27.15/27.59 clause( 12, [ defined( codomain( X ), X ) ] )
% 27.15/27.59 .
% 27.15/27.59 clause( 13, [ product( X, domain( X ), X ) ] )
% 27.15/27.59 .
% 27.15/27.59 clause( 14, [ product( codomain( X ), X, X ) ] )
% 27.15/27.59 .
% 27.15/27.59 clause( 15, [ ~( defined( X, Y ) ), ~( 'identity_map'( X ) ), product( X, Y
% 27.15/27.59 , Y ) ] )
% 27.15/27.59 .
% 27.15/27.59 clause( 16, [ ~( defined( X, Y ) ), ~( 'identity_map'( Y ) ), product( X, Y
% 27.15/27.59 , X ) ] )
% 27.15/27.59 .
% 27.15/27.59 clause( 17, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z, T ) ]
% 27.15/27.59 )
% 27.15/27.59 .
% 27.15/27.59 clause( 18, [ defined( b, a ) ] )
% 27.15/27.59 .
% 27.15/27.59 clause( 19, [ ~( =( domain( compose( b, a ) ), domain( a ) ) ) ] )
% 27.15/27.59 .
% 27.15/27.59 clause( 30, [ product( b, a, compose( b, a ) ) ] )
% 27.15/27.59 .
% 27.15/27.59 clause( 34, [ ~( defined( compose( b, a ), X ) ), defined( a, X ) ] )
% 27.15/27.59 .
% 27.15/27.59 clause( 35, [ ~( defined( X, Y ) ), defined( domain( X ), Y ) ] )
% 27.15/27.59 .
% 27.15/27.59 clause( 38, [ ~( product( X, Y, Z ) ), defined( Y, domain( Z ) ) ] )
% 27.15/27.59 .
% 27.15/27.59 clause( 172, [ ~( defined( X, Y ) ), defined( X, codomain( Y ) ) ] )
% 27.15/27.59 .
% 27.15/27.59 clause( 437, [ ~( defined( domain( X ), Y ) ), defined( X, Y ) ] )
% 27.15/27.59 .
% 27.15/27.59 clause( 525, [ ~( 'identity_map'( X ) ), product( X, Y, Y ), ~( product( X
% 27.15/27.59 , Y, Z ) ) ] )
% 27.15/27.59 .
% 27.15/27.59 clause( 591, [ product( Y, codomain( X ), Y ), ~( defined( Y, X ) ) ] )
% 27.15/27.59 .
% 27.15/27.59 clause( 680, [ ~( product( X, domain( X ), Y ) ), =( X, Y ) ] )
% 27.15/27.59 .
% 27.15/27.59 clause( 681, [ ~( product( codomain( X ), X, Y ) ), =( X, Y ) ] )
% 27.15/27.59 .
% 27.15/27.59 clause( 1233, [ defined( X, codomain( Y ) ), ~( defined( domain( X ), Y ) )
% 27.15/27.59 ] )
% 27.15/27.59 .
% 27.15/27.59 clause( 1936, [ defined( a, domain( compose( b, a ) ) ) ] )
% 27.15/27.59 .
% 27.15/27.59 clause( 1943, [ defined( domain( a ), domain( compose( b, a ) ) ) ] )
% 27.15/27.59 .
% 27.15/27.59 clause( 9666, [ ~( defined( domain( X ), Y ) ), product( X, codomain( Y ),
% 27.15/27.59 X ) ] )
% 27.15/27.59 .
% 27.15/27.59 clause( 9758, [ =( domain( X ), X ), ~( 'identity_map'( X ) ) ] )
% 27.15/27.59 .
% 27.15/27.59 clause( 11373, [ =( domain( domain( X ) ), domain( X ) ) ] )
% 27.15/27.59 .
% 27.15/27.59 clause( 11374, [ =( domain( codomain( X ) ), codomain( X ) ) ] )
% 27.15/27.59 .
% 27.15/27.59 clause( 11577, [ =( codomain( X ), X ), ~( 'identity_map'( X ) ) ] )
% 27.15/27.59 .
% 27.15/27.59 clause( 12491, [ =( codomain( domain( X ) ), domain( X ) ) ] )
% 27.15/27.59 .
% 27.15/27.59 clause( 12679, [ ~( defined( X, Y ) ), defined( codomain( Y ), domain( X )
% 27.15/27.59 ) ] )
% 27.15/27.59 .
% 27.15/27.59 clause( 49623, [ ~( 'identity_map'( X ) ), ~( product( X, Y, Z ) ), ~(
% 27.15/27.59 product( X, Y, T ) ), =( Y, T ) ] )
% 27.15/27.59 .
% 27.15/27.59 clause( 49624, [ ~( 'identity_map'( X ) ), ~( product( X, Y, Z ) ), =( Y, Z
% 27.15/27.59 ) ] )
% 27.15/27.59 .
% 27.15/27.59 clause( 49671, [ ~( product( codomain( X ), Y, Z ) ), =( Y, Z ) ] )
% 27.15/27.59 .
% 27.15/27.59 clause( 56197, [ =( codomain( X ), codomain( Y ) ), ~( defined( codomain( Y
% 27.15/27.59 ), X ) ) ] )
% 27.15/27.59 .
% 27.15/27.59 clause( 59853, [ ~( defined( X, Y ) ), =( domain( X ), codomain( Y ) ) ] )
% 27.15/27.59 .
% 27.15/27.59 clause( 60467, [ =( domain( compose( b, a ) ), domain( a ) ) ] )
% 27.15/27.59 .
% 27.15/27.59 clause( 60751, [] )
% 27.15/27.59 .
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 % SZS output end Refutation
% 27.15/27.59 found a proof!
% 27.15/27.59
% 27.15/27.59 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 27.15/27.59
% 27.15/27.59 initialclauses(
% 27.15/27.59 [ clause( 60753, [ ~( defined( X, Y ) ), product( X, Y, compose( X, Y ) ) ]
% 27.15/27.59 )
% 27.15/27.59 , clause( 60754, [ ~( product( X, Y, Z ) ), defined( X, Y ) ] )
% 27.15/27.59 , clause( 60755, [ ~( product( X, Y, Z ) ), ~( defined( Z, T ) ), defined(
% 27.15/27.59 Y, T ) ] )
% 27.15/27.59 , clause( 60756, [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~(
% 27.15/27.59 defined( Z, T ) ), defined( X, U ) ] )
% 27.15/27.59 , clause( 60757, [ ~( product( X, Y, Z ) ), ~( product( Z, T, U ) ), ~(
% 27.15/27.59 product( Y, T, W ) ), product( X, W, U ) ] )
% 27.15/27.59 , clause( 60758, [ ~( product( X, Y, Z ) ), ~( defined( T, Z ) ), defined(
% 27.15/27.59 T, X ) ] )
% 27.15/27.59 , clause( 60759, [ ~( product( X, Y, Z ) ), ~( product( T, X, U ) ), ~(
% 27.15/27.59 defined( T, Z ) ), defined( U, Y ) ] )
% 27.15/27.59 , clause( 60760, [ ~( product( X, Y, Z ) ), ~( product( T, Z, U ) ), ~(
% 27.15/27.59 product( T, X, W ) ), product( W, Y, U ) ] )
% 27.15/27.59 , clause( 60761, [ ~( defined( X, Y ) ), ~( defined( Y, Z ) ), ~(
% 27.15/27.59 'identity_map'( Y ) ), defined( X, Z ) ] )
% 27.15/27.59 , clause( 60762, [ 'identity_map'( domain( X ) ) ] )
% 27.15/27.59 , clause( 60763, [ 'identity_map'( codomain( X ) ) ] )
% 27.15/27.59 , clause( 60764, [ defined( X, domain( X ) ) ] )
% 27.15/27.59 , clause( 60765, [ defined( codomain( X ), X ) ] )
% 27.15/27.59 , clause( 60766, [ product( X, domain( X ), X ) ] )
% 27.15/27.59 , clause( 60767, [ product( codomain( X ), X, X ) ] )
% 27.15/27.59 , clause( 60768, [ ~( defined( X, Y ) ), ~( 'identity_map'( X ) ), product(
% 27.15/27.59 X, Y, Y ) ] )
% 27.15/27.59 , clause( 60769, [ ~( defined( X, Y ) ), ~( 'identity_map'( Y ) ), product(
% 27.15/27.59 X, Y, X ) ] )
% 27.15/27.59 , clause( 60770, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z,
% 27.15/27.59 T ) ] )
% 27.15/27.59 , clause( 60771, [ defined( b, a ) ] )
% 27.15/27.59 , clause( 60772, [ ~( =( domain( compose( b, a ) ), domain( a ) ) ) ] )
% 27.15/27.59 ] ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 subsumption(
% 27.15/27.59 clause( 0, [ ~( defined( X, Y ) ), product( X, Y, compose( X, Y ) ) ] )
% 27.15/27.59 , clause( 60753, [ ~( defined( X, Y ) ), product( X, Y, compose( X, Y ) ) ]
% 27.15/27.59 )
% 27.15/27.59 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 27.15/27.59 ), ==>( 1, 1 )] ) ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 subsumption(
% 27.15/27.59 clause( 1, [ ~( product( X, Y, Z ) ), defined( X, Y ) ] )
% 27.15/27.59 , clause( 60754, [ ~( product( X, Y, Z ) ), defined( X, Y ) ] )
% 27.15/27.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 27.15/27.59 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 subsumption(
% 27.15/27.59 clause( 2, [ ~( product( X, Y, Z ) ), ~( defined( Z, T ) ), defined( Y, T )
% 27.15/27.59 ] )
% 27.15/27.59 , clause( 60755, [ ~( product( X, Y, Z ) ), ~( defined( Z, T ) ), defined(
% 27.15/27.59 Y, T ) ] )
% 27.15/27.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 27.15/27.59 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 subsumption(
% 27.15/27.59 clause( 5, [ ~( product( X, Y, Z ) ), ~( defined( T, Z ) ), defined( T, X )
% 27.15/27.59 ] )
% 27.15/27.59 , clause( 60758, [ ~( product( X, Y, Z ) ), ~( defined( T, Z ) ), defined(
% 27.15/27.59 T, X ) ] )
% 27.15/27.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 27.15/27.59 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 subsumption(
% 27.15/27.59 clause( 8, [ ~( defined( X, Y ) ), ~( defined( Y, Z ) ), ~( 'identity_map'(
% 27.15/27.59 Y ) ), defined( X, Z ) ] )
% 27.15/27.59 , clause( 60761, [ ~( defined( X, Y ) ), ~( defined( Y, Z ) ), ~(
% 27.15/27.59 'identity_map'( Y ) ), defined( X, Z ) ] )
% 27.15/27.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 27.15/27.59 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 ), ==>( 3, 3 )] )
% 27.15/27.59 ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 subsumption(
% 27.15/27.59 clause( 9, [ 'identity_map'( domain( X ) ) ] )
% 27.15/27.59 , clause( 60762, [ 'identity_map'( domain( X ) ) ] )
% 27.15/27.59 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 subsumption(
% 27.15/27.59 clause( 10, [ 'identity_map'( codomain( X ) ) ] )
% 27.15/27.59 , clause( 60763, [ 'identity_map'( codomain( X ) ) ] )
% 27.15/27.59 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 subsumption(
% 27.15/27.59 clause( 11, [ defined( X, domain( X ) ) ] )
% 27.15/27.59 , clause( 60764, [ defined( X, domain( X ) ) ] )
% 27.15/27.59 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 subsumption(
% 27.15/27.59 clause( 12, [ defined( codomain( X ), X ) ] )
% 27.15/27.59 , clause( 60765, [ defined( codomain( X ), X ) ] )
% 27.15/27.59 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 subsumption(
% 27.15/27.59 clause( 13, [ product( X, domain( X ), X ) ] )
% 27.15/27.59 , clause( 60766, [ product( X, domain( X ), X ) ] )
% 27.15/27.59 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 subsumption(
% 27.15/27.59 clause( 14, [ product( codomain( X ), X, X ) ] )
% 27.15/27.59 , clause( 60767, [ product( codomain( X ), X, X ) ] )
% 27.15/27.59 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 subsumption(
% 27.15/27.59 clause( 15, [ ~( defined( X, Y ) ), ~( 'identity_map'( X ) ), product( X, Y
% 27.15/27.59 , Y ) ] )
% 27.15/27.59 , clause( 60768, [ ~( defined( X, Y ) ), ~( 'identity_map'( X ) ), product(
% 27.15/27.59 X, Y, Y ) ] )
% 27.15/27.59 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 27.15/27.59 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 subsumption(
% 27.15/27.59 clause( 16, [ ~( defined( X, Y ) ), ~( 'identity_map'( Y ) ), product( X, Y
% 27.15/27.59 , X ) ] )
% 27.15/27.59 , clause( 60769, [ ~( defined( X, Y ) ), ~( 'identity_map'( Y ) ), product(
% 27.15/27.59 X, Y, X ) ] )
% 27.15/27.59 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 27.15/27.59 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 subsumption(
% 27.15/27.59 clause( 17, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z, T ) ]
% 27.15/27.59 )
% 27.15/27.59 , clause( 60770, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z,
% 27.15/27.59 T ) ] )
% 27.15/27.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 27.15/27.59 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 subsumption(
% 27.15/27.59 clause( 18, [ defined( b, a ) ] )
% 27.15/27.59 , clause( 60771, [ defined( b, a ) ] )
% 27.15/27.59 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 subsumption(
% 27.15/27.59 clause( 19, [ ~( =( domain( compose( b, a ) ), domain( a ) ) ) ] )
% 27.15/27.59 , clause( 60772, [ ~( =( domain( compose( b, a ) ), domain( a ) ) ) ] )
% 27.15/27.59 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 resolution(
% 27.15/27.59 clause( 60914, [ product( b, a, compose( b, a ) ) ] )
% 27.15/27.59 , clause( 0, [ ~( defined( X, Y ) ), product( X, Y, compose( X, Y ) ) ] )
% 27.15/27.59 , 0, clause( 18, [ defined( b, a ) ] )
% 27.15/27.59 , 0, substitution( 0, [ :=( X, b ), :=( Y, a )] ), substitution( 1, [] )
% 27.15/27.59 ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 subsumption(
% 27.15/27.59 clause( 30, [ product( b, a, compose( b, a ) ) ] )
% 27.15/27.59 , clause( 60914, [ product( b, a, compose( b, a ) ) ] )
% 27.15/27.59 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 resolution(
% 27.15/27.59 clause( 60915, [ ~( defined( compose( b, a ), X ) ), defined( a, X ) ] )
% 27.15/27.59 , clause( 2, [ ~( product( X, Y, Z ) ), ~( defined( Z, T ) ), defined( Y, T
% 27.15/27.59 ) ] )
% 27.15/27.59 , 0, clause( 30, [ product( b, a, compose( b, a ) ) ] )
% 27.15/27.59 , 0, substitution( 0, [ :=( X, b ), :=( Y, a ), :=( Z, compose( b, a ) ),
% 27.15/27.59 :=( T, X )] ), substitution( 1, [] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 subsumption(
% 27.15/27.59 clause( 34, [ ~( defined( compose( b, a ), X ) ), defined( a, X ) ] )
% 27.15/27.59 , clause( 60915, [ ~( defined( compose( b, a ), X ) ), defined( a, X ) ] )
% 27.15/27.59 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 27.15/27.59 1 )] ) ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 resolution(
% 27.15/27.59 clause( 60916, [ ~( defined( X, Y ) ), defined( domain( X ), Y ) ] )
% 27.15/27.59 , clause( 2, [ ~( product( X, Y, Z ) ), ~( defined( Z, T ) ), defined( Y, T
% 27.15/27.59 ) ] )
% 27.15/27.59 , 0, clause( 13, [ product( X, domain( X ), X ) ] )
% 27.15/27.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, domain( X ) ), :=( Z, X ), :=( T
% 27.15/27.59 , Y )] ), substitution( 1, [ :=( X, X )] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 subsumption(
% 27.15/27.59 clause( 35, [ ~( defined( X, Y ) ), defined( domain( X ), Y ) ] )
% 27.15/27.59 , clause( 60916, [ ~( defined( X, Y ) ), defined( domain( X ), Y ) ] )
% 27.15/27.59 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 27.15/27.59 ), ==>( 1, 1 )] ) ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 resolution(
% 27.15/27.59 clause( 60917, [ ~( product( X, Y, Z ) ), defined( Y, domain( Z ) ) ] )
% 27.15/27.59 , clause( 2, [ ~( product( X, Y, Z ) ), ~( defined( Z, T ) ), defined( Y, T
% 27.15/27.59 ) ] )
% 27.15/27.59 , 1, clause( 11, [ defined( X, domain( X ) ) ] )
% 27.15/27.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, domain(
% 27.15/27.59 Z ) )] ), substitution( 1, [ :=( X, Z )] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 subsumption(
% 27.15/27.59 clause( 38, [ ~( product( X, Y, Z ) ), defined( Y, domain( Z ) ) ] )
% 27.15/27.59 , clause( 60917, [ ~( product( X, Y, Z ) ), defined( Y, domain( Z ) ) ] )
% 27.15/27.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 27.15/27.59 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 resolution(
% 27.15/27.59 clause( 60918, [ ~( defined( Y, X ) ), defined( Y, codomain( X ) ) ] )
% 27.15/27.59 , clause( 5, [ ~( product( X, Y, Z ) ), ~( defined( T, Z ) ), defined( T, X
% 27.15/27.59 ) ] )
% 27.15/27.59 , 0, clause( 14, [ product( codomain( X ), X, X ) ] )
% 27.15/27.59 , 0, substitution( 0, [ :=( X, codomain( X ) ), :=( Y, X ), :=( Z, X ),
% 27.15/27.59 :=( T, Y )] ), substitution( 1, [ :=( X, X )] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 subsumption(
% 27.15/27.59 clause( 172, [ ~( defined( X, Y ) ), defined( X, codomain( Y ) ) ] )
% 27.15/27.59 , clause( 60918, [ ~( defined( Y, X ) ), defined( Y, codomain( X ) ) ] )
% 27.15/27.59 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 27.15/27.59 ), ==>( 1, 1 )] ) ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 resolution(
% 27.15/27.59 clause( 60919, [ ~( defined( domain( X ), Y ) ), ~( 'identity_map'( domain(
% 27.15/27.59 X ) ) ), defined( X, Y ) ] )
% 27.15/27.59 , clause( 8, [ ~( defined( X, Y ) ), ~( defined( Y, Z ) ), ~(
% 27.15/27.59 'identity_map'( Y ) ), defined( X, Z ) ] )
% 27.15/27.59 , 0, clause( 11, [ defined( X, domain( X ) ) ] )
% 27.15/27.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, domain( X ) ), :=( Z, Y )] ),
% 27.15/27.59 substitution( 1, [ :=( X, X )] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 resolution(
% 27.15/27.59 clause( 60921, [ ~( defined( domain( X ), Y ) ), defined( X, Y ) ] )
% 27.15/27.59 , clause( 60919, [ ~( defined( domain( X ), Y ) ), ~( 'identity_map'(
% 27.15/27.59 domain( X ) ) ), defined( X, Y ) ] )
% 27.15/27.59 , 1, clause( 9, [ 'identity_map'( domain( X ) ) ] )
% 27.15/27.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [ :=( X
% 27.15/27.59 , X )] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 subsumption(
% 27.15/27.59 clause( 437, [ ~( defined( domain( X ), Y ) ), defined( X, Y ) ] )
% 27.15/27.59 , clause( 60921, [ ~( defined( domain( X ), Y ) ), defined( X, Y ) ] )
% 27.15/27.59 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 27.15/27.59 ), ==>( 1, 1 )] ) ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 resolution(
% 27.15/27.59 clause( 60922, [ ~( 'identity_map'( X ) ), product( X, Y, Y ), ~( product(
% 27.15/27.59 X, Y, Z ) ) ] )
% 27.15/27.59 , clause( 15, [ ~( defined( X, Y ) ), ~( 'identity_map'( X ) ), product( X
% 27.15/27.59 , Y, Y ) ] )
% 27.15/27.59 , 0, clause( 1, [ ~( product( X, Y, Z ) ), defined( X, Y ) ] )
% 27.15/27.59 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [ :=( X
% 27.15/27.59 , X ), :=( Y, Y ), :=( Z, Z )] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 subsumption(
% 27.15/27.59 clause( 525, [ ~( 'identity_map'( X ) ), product( X, Y, Y ), ~( product( X
% 27.15/27.59 , Y, Z ) ) ] )
% 27.15/27.59 , clause( 60922, [ ~( 'identity_map'( X ) ), product( X, Y, Y ), ~( product(
% 27.15/27.59 X, Y, Z ) ) ] )
% 27.15/27.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 27.15/27.59 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 resolution(
% 27.15/27.59 clause( 60923, [ ~( 'identity_map'( codomain( Y ) ) ), product( X, codomain(
% 27.15/27.59 Y ), X ), ~( defined( X, Y ) ) ] )
% 27.15/27.59 , clause( 16, [ ~( defined( X, Y ) ), ~( 'identity_map'( Y ) ), product( X
% 27.15/27.59 , Y, X ) ] )
% 27.15/27.59 , 0, clause( 172, [ ~( defined( X, Y ) ), defined( X, codomain( Y ) ) ] )
% 27.15/27.59 , 1, substitution( 0, [ :=( X, X ), :=( Y, codomain( Y ) )] ),
% 27.15/27.59 substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 resolution(
% 27.15/27.59 clause( 60924, [ product( Y, codomain( X ), Y ), ~( defined( Y, X ) ) ] )
% 27.15/27.59 , clause( 60923, [ ~( 'identity_map'( codomain( Y ) ) ), product( X,
% 27.15/27.59 codomain( Y ), X ), ~( defined( X, Y ) ) ] )
% 27.15/27.59 , 0, clause( 10, [ 'identity_map'( codomain( X ) ) ] )
% 27.15/27.59 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [ :=( X
% 27.15/27.59 , X )] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 subsumption(
% 27.15/27.59 clause( 591, [ product( Y, codomain( X ), Y ), ~( defined( Y, X ) ) ] )
% 27.15/27.59 , clause( 60924, [ product( Y, codomain( X ), Y ), ~( defined( Y, X ) ) ]
% 27.15/27.59 )
% 27.15/27.59 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 27.15/27.59 ), ==>( 1, 1 )] ) ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 resolution(
% 27.15/27.59 clause( 60925, [ ~( product( X, domain( X ), Y ) ), =( X, Y ) ] )
% 27.15/27.59 , clause( 17, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z, T )
% 27.15/27.59 ] )
% 27.15/27.59 , 0, clause( 13, [ product( X, domain( X ), X ) ] )
% 27.15/27.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, domain( X ) ), :=( Z, X ), :=( T
% 27.15/27.59 , Y )] ), substitution( 1, [ :=( X, X )] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 subsumption(
% 27.15/27.59 clause( 680, [ ~( product( X, domain( X ), Y ) ), =( X, Y ) ] )
% 27.15/27.59 , clause( 60925, [ ~( product( X, domain( X ), Y ) ), =( X, Y ) ] )
% 27.15/27.59 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 27.15/27.59 ), ==>( 1, 1 )] ) ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 resolution(
% 27.15/27.59 clause( 60927, [ ~( product( codomain( X ), X, Y ) ), =( X, Y ) ] )
% 27.15/27.59 , clause( 17, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z, T )
% 27.15/27.59 ] )
% 27.15/27.59 , 0, clause( 14, [ product( codomain( X ), X, X ) ] )
% 27.15/27.59 , 0, substitution( 0, [ :=( X, codomain( X ) ), :=( Y, X ), :=( Z, X ),
% 27.15/27.59 :=( T, Y )] ), substitution( 1, [ :=( X, X )] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 subsumption(
% 27.15/27.59 clause( 681, [ ~( product( codomain( X ), X, Y ) ), =( X, Y ) ] )
% 27.15/27.59 , clause( 60927, [ ~( product( codomain( X ), X, Y ) ), =( X, Y ) ] )
% 27.15/27.59 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 27.15/27.59 ), ==>( 1, 1 )] ) ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 resolution(
% 27.15/27.59 clause( 60929, [ defined( X, codomain( Y ) ), ~( defined( domain( X ), Y )
% 27.15/27.59 ) ] )
% 27.15/27.59 , clause( 437, [ ~( defined( domain( X ), Y ) ), defined( X, Y ) ] )
% 27.15/27.59 , 0, clause( 172, [ ~( defined( X, Y ) ), defined( X, codomain( Y ) ) ] )
% 27.15/27.59 , 1, substitution( 0, [ :=( X, X ), :=( Y, codomain( Y ) )] ),
% 27.15/27.59 substitution( 1, [ :=( X, domain( X ) ), :=( Y, Y )] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 subsumption(
% 27.15/27.59 clause( 1233, [ defined( X, codomain( Y ) ), ~( defined( domain( X ), Y ) )
% 27.15/27.59 ] )
% 27.15/27.59 , clause( 60929, [ defined( X, codomain( Y ) ), ~( defined( domain( X ), Y
% 27.15/27.59 ) ) ] )
% 27.15/27.59 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 27.15/27.59 ), ==>( 1, 1 )] ) ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 resolution(
% 27.15/27.59 clause( 60930, [ defined( a, domain( compose( b, a ) ) ) ] )
% 27.15/27.59 , clause( 34, [ ~( defined( compose( b, a ), X ) ), defined( a, X ) ] )
% 27.15/27.59 , 0, clause( 11, [ defined( X, domain( X ) ) ] )
% 27.15/27.59 , 0, substitution( 0, [ :=( X, domain( compose( b, a ) ) )] ),
% 27.15/27.59 substitution( 1, [ :=( X, compose( b, a ) )] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 subsumption(
% 27.15/27.59 clause( 1936, [ defined( a, domain( compose( b, a ) ) ) ] )
% 27.15/27.59 , clause( 60930, [ defined( a, domain( compose( b, a ) ) ) ] )
% 27.15/27.59 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 resolution(
% 27.15/27.59 clause( 60931, [ defined( domain( a ), domain( compose( b, a ) ) ) ] )
% 27.15/27.59 , clause( 35, [ ~( defined( X, Y ) ), defined( domain( X ), Y ) ] )
% 27.15/27.59 , 0, clause( 1936, [ defined( a, domain( compose( b, a ) ) ) ] )
% 27.15/27.59 , 0, substitution( 0, [ :=( X, a ), :=( Y, domain( compose( b, a ) ) )] ),
% 27.15/27.59 substitution( 1, [] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 subsumption(
% 27.15/27.59 clause( 1943, [ defined( domain( a ), domain( compose( b, a ) ) ) ] )
% 27.15/27.59 , clause( 60931, [ defined( domain( a ), domain( compose( b, a ) ) ) ] )
% 27.15/27.59 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 resolution(
% 27.15/27.59 clause( 60932, [ ~( 'identity_map'( codomain( Y ) ) ), product( X, codomain(
% 27.15/27.59 Y ), X ), ~( defined( domain( X ), Y ) ) ] )
% 27.15/27.59 , clause( 16, [ ~( defined( X, Y ) ), ~( 'identity_map'( Y ) ), product( X
% 27.15/27.59 , Y, X ) ] )
% 27.15/27.59 , 0, clause( 1233, [ defined( X, codomain( Y ) ), ~( defined( domain( X ),
% 27.15/27.59 Y ) ) ] )
% 27.15/27.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, codomain( Y ) )] ),
% 27.15/27.59 substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 resolution(
% 27.15/27.59 clause( 60933, [ product( Y, codomain( X ), Y ), ~( defined( domain( Y ), X
% 27.15/27.59 ) ) ] )
% 27.15/27.59 , clause( 60932, [ ~( 'identity_map'( codomain( Y ) ) ), product( X,
% 27.15/27.59 codomain( Y ), X ), ~( defined( domain( X ), Y ) ) ] )
% 27.15/27.59 , 0, clause( 10, [ 'identity_map'( codomain( X ) ) ] )
% 27.15/27.59 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [ :=( X
% 27.15/27.59 , X )] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 subsumption(
% 27.15/27.59 clause( 9666, [ ~( defined( domain( X ), Y ) ), product( X, codomain( Y ),
% 27.15/27.59 X ) ] )
% 27.15/27.59 , clause( 60933, [ product( Y, codomain( X ), Y ), ~( defined( domain( Y )
% 27.15/27.59 , X ) ) ] )
% 27.15/27.59 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 1
% 27.15/27.59 ), ==>( 1, 0 )] ) ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 eqswap(
% 27.15/27.59 clause( 60934, [ =( Y, X ), ~( product( X, domain( X ), Y ) ) ] )
% 27.15/27.59 , clause( 680, [ ~( product( X, domain( X ), Y ) ), =( X, Y ) ] )
% 27.15/27.59 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 resolution(
% 27.15/27.59 clause( 60935, [ =( domain( X ), X ), ~( defined( X, domain( X ) ) ), ~(
% 27.15/27.59 'identity_map'( X ) ) ] )
% 27.15/27.59 , clause( 60934, [ =( Y, X ), ~( product( X, domain( X ), Y ) ) ] )
% 27.15/27.59 , 1, clause( 15, [ ~( defined( X, Y ) ), ~( 'identity_map'( X ) ), product(
% 27.15/27.59 X, Y, Y ) ] )
% 27.15/27.59 , 2, substitution( 0, [ :=( X, X ), :=( Y, domain( X ) )] ), substitution(
% 27.15/27.59 1, [ :=( X, X ), :=( Y, domain( X ) )] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 resolution(
% 27.15/27.59 clause( 60936, [ =( domain( X ), X ), ~( 'identity_map'( X ) ) ] )
% 27.15/27.59 , clause( 60935, [ =( domain( X ), X ), ~( defined( X, domain( X ) ) ), ~(
% 27.15/27.59 'identity_map'( X ) ) ] )
% 27.15/27.59 , 1, clause( 11, [ defined( X, domain( X ) ) ] )
% 27.15/27.59 , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 27.15/27.59 ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 subsumption(
% 27.15/27.59 clause( 9758, [ =( domain( X ), X ), ~( 'identity_map'( X ) ) ] )
% 27.15/27.59 , clause( 60936, [ =( domain( X ), X ), ~( 'identity_map'( X ) ) ] )
% 27.15/27.59 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 27.15/27.59 1 )] ) ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 eqswap(
% 27.15/27.59 clause( 60938, [ =( X, domain( X ) ), ~( 'identity_map'( X ) ) ] )
% 27.15/27.59 , clause( 9758, [ =( domain( X ), X ), ~( 'identity_map'( X ) ) ] )
% 27.15/27.59 , 0, substitution( 0, [ :=( X, X )] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 resolution(
% 27.15/27.59 clause( 60939, [ =( domain( X ), domain( domain( X ) ) ) ] )
% 27.15/27.59 , clause( 60938, [ =( X, domain( X ) ), ~( 'identity_map'( X ) ) ] )
% 27.15/27.59 , 1, clause( 9, [ 'identity_map'( domain( X ) ) ] )
% 27.15/27.59 , 0, substitution( 0, [ :=( X, domain( X ) )] ), substitution( 1, [ :=( X,
% 27.15/27.59 X )] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 eqswap(
% 27.15/27.59 clause( 60940, [ =( domain( domain( X ) ), domain( X ) ) ] )
% 27.15/27.59 , clause( 60939, [ =( domain( X ), domain( domain( X ) ) ) ] )
% 27.15/27.59 , 0, substitution( 0, [ :=( X, X )] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 subsumption(
% 27.15/27.59 clause( 11373, [ =( domain( domain( X ) ), domain( X ) ) ] )
% 27.15/27.59 , clause( 60940, [ =( domain( domain( X ) ), domain( X ) ) ] )
% 27.15/27.59 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 eqswap(
% 27.15/27.59 clause( 60941, [ =( X, domain( X ) ), ~( 'identity_map'( X ) ) ] )
% 27.15/27.59 , clause( 9758, [ =( domain( X ), X ), ~( 'identity_map'( X ) ) ] )
% 27.15/27.59 , 0, substitution( 0, [ :=( X, X )] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 resolution(
% 27.15/27.59 clause( 60942, [ =( codomain( X ), domain( codomain( X ) ) ) ] )
% 27.15/27.59 , clause( 60941, [ =( X, domain( X ) ), ~( 'identity_map'( X ) ) ] )
% 27.15/27.59 , 1, clause( 10, [ 'identity_map'( codomain( X ) ) ] )
% 27.15/27.59 , 0, substitution( 0, [ :=( X, codomain( X ) )] ), substitution( 1, [ :=( X
% 27.15/27.59 , X )] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 eqswap(
% 27.15/27.59 clause( 60943, [ =( domain( codomain( X ) ), codomain( X ) ) ] )
% 27.15/27.59 , clause( 60942, [ =( codomain( X ), domain( codomain( X ) ) ) ] )
% 27.15/27.59 , 0, substitution( 0, [ :=( X, X )] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 subsumption(
% 27.15/27.59 clause( 11374, [ =( domain( codomain( X ) ), codomain( X ) ) ] )
% 27.15/27.59 , clause( 60943, [ =( domain( codomain( X ) ), codomain( X ) ) ] )
% 27.15/27.59 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 eqswap(
% 27.15/27.59 clause( 60944, [ =( Y, X ), ~( product( codomain( X ), X, Y ) ) ] )
% 27.15/27.59 , clause( 681, [ ~( product( codomain( X ), X, Y ) ), =( X, Y ) ] )
% 27.15/27.59 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 resolution(
% 27.15/27.59 clause( 60945, [ =( codomain( X ), X ), ~( defined( codomain( X ), X ) ),
% 27.15/27.59 ~( 'identity_map'( X ) ) ] )
% 27.15/27.59 , clause( 60944, [ =( Y, X ), ~( product( codomain( X ), X, Y ) ) ] )
% 27.15/27.59 , 1, clause( 16, [ ~( defined( X, Y ) ), ~( 'identity_map'( Y ) ), product(
% 27.15/27.59 X, Y, X ) ] )
% 27.15/27.59 , 2, substitution( 0, [ :=( X, X ), :=( Y, codomain( X ) )] ),
% 27.15/27.59 substitution( 1, [ :=( X, codomain( X ) ), :=( Y, X )] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 resolution(
% 27.15/27.59 clause( 60946, [ =( codomain( X ), X ), ~( 'identity_map'( X ) ) ] )
% 27.15/27.59 , clause( 60945, [ =( codomain( X ), X ), ~( defined( codomain( X ), X ) )
% 27.15/27.59 , ~( 'identity_map'( X ) ) ] )
% 27.15/27.59 , 1, clause( 12, [ defined( codomain( X ), X ) ] )
% 27.15/27.59 , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 27.15/27.59 ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 subsumption(
% 27.15/27.59 clause( 11577, [ =( codomain( X ), X ), ~( 'identity_map'( X ) ) ] )
% 27.15/27.59 , clause( 60946, [ =( codomain( X ), X ), ~( 'identity_map'( X ) ) ] )
% 27.15/27.59 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 27.15/27.59 1 )] ) ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 eqswap(
% 27.15/27.59 clause( 60948, [ =( X, codomain( X ) ), ~( 'identity_map'( X ) ) ] )
% 27.15/27.59 , clause( 11577, [ =( codomain( X ), X ), ~( 'identity_map'( X ) ) ] )
% 27.15/27.59 , 0, substitution( 0, [ :=( X, X )] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 resolution(
% 27.15/27.59 clause( 60949, [ =( domain( X ), codomain( domain( X ) ) ) ] )
% 27.15/27.59 , clause( 60948, [ =( X, codomain( X ) ), ~( 'identity_map'( X ) ) ] )
% 27.15/27.59 , 1, clause( 9, [ 'identity_map'( domain( X ) ) ] )
% 27.15/27.59 , 0, substitution( 0, [ :=( X, domain( X ) )] ), substitution( 1, [ :=( X,
% 27.15/27.59 X )] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 eqswap(
% 27.15/27.59 clause( 60950, [ =( codomain( domain( X ) ), domain( X ) ) ] )
% 27.15/27.59 , clause( 60949, [ =( domain( X ), codomain( domain( X ) ) ) ] )
% 27.15/27.59 , 0, substitution( 0, [ :=( X, X )] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 subsumption(
% 27.15/27.59 clause( 12491, [ =( codomain( domain( X ) ), domain( X ) ) ] )
% 27.15/27.59 , clause( 60950, [ =( codomain( domain( X ) ), domain( X ) ) ] )
% 27.15/27.59 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 resolution(
% 27.15/27.59 clause( 60952, [ defined( codomain( Y ), domain( X ) ), ~( defined( X, Y )
% 27.15/27.59 ) ] )
% 27.15/27.59 , clause( 38, [ ~( product( X, Y, Z ) ), defined( Y, domain( Z ) ) ] )
% 27.15/27.59 , 0, clause( 591, [ product( Y, codomain( X ), Y ), ~( defined( Y, X ) ) ]
% 27.15/27.59 )
% 27.15/27.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, codomain( Y ) ), :=( Z, X )] ),
% 27.15/27.59 substitution( 1, [ :=( X, Y ), :=( Y, X )] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 subsumption(
% 27.15/27.59 clause( 12679, [ ~( defined( X, Y ) ), defined( codomain( Y ), domain( X )
% 27.15/27.59 ) ] )
% 27.15/27.59 , clause( 60952, [ defined( codomain( Y ), domain( X ) ), ~( defined( X, Y
% 27.15/27.59 ) ) ] )
% 27.15/27.59 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 1
% 27.15/27.59 ), ==>( 1, 0 )] ) ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 resolution(
% 27.15/27.59 clause( 60953, [ ~( product( X, Y, Z ) ), =( Y, Z ), ~( 'identity_map'( X )
% 27.15/27.59 ), ~( product( X, Y, T ) ) ] )
% 27.15/27.59 , clause( 17, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z, T )
% 27.15/27.59 ] )
% 27.15/27.59 , 0, clause( 525, [ ~( 'identity_map'( X ) ), product( X, Y, Y ), ~(
% 27.15/27.59 product( X, Y, Z ) ) ] )
% 27.15/27.59 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Y ), :=( T, Z )] ),
% 27.15/27.59 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, T )] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 subsumption(
% 27.15/27.59 clause( 49623, [ ~( 'identity_map'( X ) ), ~( product( X, Y, Z ) ), ~(
% 27.15/27.59 product( X, Y, T ) ), =( Y, T ) ] )
% 27.15/27.59 , clause( 60953, [ ~( product( X, Y, Z ) ), =( Y, Z ), ~( 'identity_map'( X
% 27.15/27.59 ) ), ~( product( X, Y, T ) ) ] )
% 27.15/27.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, T ), :=( T, Z )] ),
% 27.15/27.59 permutation( 0, [ ==>( 0, 2 ), ==>( 1, 3 ), ==>( 2, 0 ), ==>( 3, 1 )] )
% 27.15/27.59 ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 factor(
% 27.15/27.59 clause( 60958, [ ~( 'identity_map'( X ) ), ~( product( X, Y, Z ) ), =( Y, Z
% 27.15/27.59 ) ] )
% 27.15/27.59 , clause( 49623, [ ~( 'identity_map'( X ) ), ~( product( X, Y, Z ) ), ~(
% 27.15/27.59 product( X, Y, T ) ), =( Y, T ) ] )
% 27.15/27.59 , 1, 2, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, Z )] )
% 27.15/27.59 ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 subsumption(
% 27.15/27.59 clause( 49624, [ ~( 'identity_map'( X ) ), ~( product( X, Y, Z ) ), =( Y, Z
% 27.15/27.59 ) ] )
% 27.15/27.59 , clause( 60958, [ ~( 'identity_map'( X ) ), ~( product( X, Y, Z ) ), =( Y
% 27.15/27.59 , Z ) ] )
% 27.15/27.59 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 27.15/27.59 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 eqswap(
% 27.15/27.59 clause( 60960, [ =( Y, X ), ~( 'identity_map'( Z ) ), ~( product( Z, X, Y )
% 27.15/27.59 ) ] )
% 27.15/27.59 , clause( 49624, [ ~( 'identity_map'( X ) ), ~( product( X, Y, Z ) ), =( Y
% 27.15/27.59 , Z ) ] )
% 27.15/27.59 , 2, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 resolution(
% 27.15/27.59 clause( 60961, [ =( X, Y ), ~( product( codomain( Z ), Y, X ) ) ] )
% 27.15/27.59 , clause( 60960, [ =( Y, X ), ~( 'identity_map'( Z ) ), ~( product( Z, X, Y
% 27.15/27.59 ) ) ] )
% 27.15/27.59 , 1, clause( 10, [ 'identity_map'( codomain( X ) ) ] )
% 27.15/27.59 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, codomain( Z ) )] ),
% 27.15/27.59 substitution( 1, [ :=( X, Z )] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 eqswap(
% 27.15/27.59 clause( 60962, [ =( Y, X ), ~( product( codomain( Z ), Y, X ) ) ] )
% 27.15/27.59 , clause( 60961, [ =( X, Y ), ~( product( codomain( Z ), Y, X ) ) ] )
% 27.15/27.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 subsumption(
% 27.15/27.59 clause( 49671, [ ~( product( codomain( X ), Y, Z ) ), =( Y, Z ) ] )
% 27.15/27.59 , clause( 60962, [ =( Y, X ), ~( product( codomain( Z ), Y, X ) ) ] )
% 27.15/27.59 , substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, X )] ),
% 27.15/27.59 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 eqswap(
% 27.15/27.59 clause( 60963, [ =( Y, X ), ~( product( codomain( Z ), X, Y ) ) ] )
% 27.15/27.59 , clause( 49671, [ ~( product( codomain( X ), Y, Z ) ), =( Y, Z ) ] )
% 27.15/27.59 , 1, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 resolution(
% 27.15/27.59 clause( 60965, [ =( codomain( X ), codomain( Y ) ), ~( defined( domain(
% 27.15/27.59 codomain( X ) ), Y ) ) ] )
% 27.15/27.59 , clause( 60963, [ =( Y, X ), ~( product( codomain( Z ), X, Y ) ) ] )
% 27.15/27.59 , 1, clause( 9666, [ ~( defined( domain( X ), Y ) ), product( X, codomain(
% 27.15/27.59 Y ), X ) ] )
% 27.15/27.59 , 1, substitution( 0, [ :=( X, codomain( Y ) ), :=( Y, codomain( X ) ),
% 27.15/27.59 :=( Z, X )] ), substitution( 1, [ :=( X, codomain( X ) ), :=( Y, Y )] )
% 27.15/27.59 ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 paramod(
% 27.15/27.59 clause( 60966, [ ~( defined( codomain( X ), Y ) ), =( codomain( X ),
% 27.15/27.59 codomain( Y ) ) ] )
% 27.15/27.59 , clause( 11374, [ =( domain( codomain( X ) ), codomain( X ) ) ] )
% 27.15/27.59 , 0, clause( 60965, [ =( codomain( X ), codomain( Y ) ), ~( defined( domain(
% 27.15/27.59 codomain( X ) ), Y ) ) ] )
% 27.15/27.59 , 1, 2, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 27.15/27.59 :=( Y, Y )] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 eqswap(
% 27.15/27.59 clause( 60967, [ =( codomain( Y ), codomain( X ) ), ~( defined( codomain( X
% 27.15/27.59 ), Y ) ) ] )
% 27.15/27.59 , clause( 60966, [ ~( defined( codomain( X ), Y ) ), =( codomain( X ),
% 27.15/27.59 codomain( Y ) ) ] )
% 27.15/27.59 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 subsumption(
% 27.15/27.59 clause( 56197, [ =( codomain( X ), codomain( Y ) ), ~( defined( codomain( Y
% 27.15/27.59 ), X ) ) ] )
% 27.15/27.59 , clause( 60967, [ =( codomain( Y ), codomain( X ) ), ~( defined( codomain(
% 27.15/27.59 X ), Y ) ) ] )
% 27.15/27.59 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 27.15/27.59 ), ==>( 1, 1 )] ) ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 eqswap(
% 27.15/27.59 clause( 60968, [ =( codomain( Y ), codomain( X ) ), ~( defined( codomain( Y
% 27.15/27.59 ), X ) ) ] )
% 27.15/27.59 , clause( 56197, [ =( codomain( X ), codomain( Y ) ), ~( defined( codomain(
% 27.15/27.59 Y ), X ) ) ] )
% 27.15/27.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 resolution(
% 27.15/27.59 clause( 60970, [ =( codomain( X ), codomain( domain( Y ) ) ), ~( defined( Y
% 27.15/27.59 , X ) ) ] )
% 27.15/27.59 , clause( 60968, [ =( codomain( Y ), codomain( X ) ), ~( defined( codomain(
% 27.15/27.59 Y ), X ) ) ] )
% 27.15/27.59 , 1, clause( 12679, [ ~( defined( X, Y ) ), defined( codomain( Y ), domain(
% 27.15/27.59 X ) ) ] )
% 27.15/27.59 , 1, substitution( 0, [ :=( X, domain( Y ) ), :=( Y, X )] ), substitution(
% 27.15/27.59 1, [ :=( X, Y ), :=( Y, X )] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 paramod(
% 27.15/27.59 clause( 60971, [ =( codomain( X ), domain( Y ) ), ~( defined( Y, X ) ) ] )
% 27.15/27.59 , clause( 12491, [ =( codomain( domain( X ) ), domain( X ) ) ] )
% 27.15/27.59 , 0, clause( 60970, [ =( codomain( X ), codomain( domain( Y ) ) ), ~(
% 27.15/27.59 defined( Y, X ) ) ] )
% 27.15/27.59 , 0, 3, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 27.15/27.59 :=( Y, Y )] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 eqswap(
% 27.15/27.59 clause( 60972, [ =( domain( Y ), codomain( X ) ), ~( defined( Y, X ) ) ] )
% 27.15/27.59 , clause( 60971, [ =( codomain( X ), domain( Y ) ), ~( defined( Y, X ) ) ]
% 27.15/27.59 )
% 27.15/27.59 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 subsumption(
% 27.15/27.59 clause( 59853, [ ~( defined( X, Y ) ), =( domain( X ), codomain( Y ) ) ] )
% 27.15/27.59 , clause( 60972, [ =( domain( Y ), codomain( X ) ), ~( defined( Y, X ) ) ]
% 27.15/27.59 )
% 27.15/27.59 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 1
% 27.15/27.59 ), ==>( 1, 0 )] ) ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 eqswap(
% 27.15/27.59 clause( 60973, [ =( codomain( Y ), domain( X ) ), ~( defined( X, Y ) ) ] )
% 27.15/27.59 , clause( 59853, [ ~( defined( X, Y ) ), =( domain( X ), codomain( Y ) ) ]
% 27.15/27.59 )
% 27.15/27.59 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 resolution(
% 27.15/27.59 clause( 60976, [ =( codomain( domain( compose( b, a ) ) ), domain( domain(
% 27.15/27.59 a ) ) ) ] )
% 27.15/27.59 , clause( 60973, [ =( codomain( Y ), domain( X ) ), ~( defined( X, Y ) ) ]
% 27.15/27.59 )
% 27.15/27.59 , 1, clause( 1943, [ defined( domain( a ), domain( compose( b, a ) ) ) ] )
% 27.15/27.59 , 0, substitution( 0, [ :=( X, domain( a ) ), :=( Y, domain( compose( b, a
% 27.15/27.59 ) ) )] ), substitution( 1, [] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 paramod(
% 27.15/27.59 clause( 60977, [ =( codomain( domain( compose( b, a ) ) ), domain( a ) ) ]
% 27.15/27.59 )
% 27.15/27.59 , clause( 11373, [ =( domain( domain( X ) ), domain( X ) ) ] )
% 27.15/27.59 , 0, clause( 60976, [ =( codomain( domain( compose( b, a ) ) ), domain(
% 27.15/27.59 domain( a ) ) ) ] )
% 27.15/27.59 , 0, 6, substitution( 0, [ :=( X, a )] ), substitution( 1, [] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 paramod(
% 27.15/27.59 clause( 60978, [ =( domain( compose( b, a ) ), domain( a ) ) ] )
% 27.15/27.59 , clause( 12491, [ =( codomain( domain( X ) ), domain( X ) ) ] )
% 27.15/27.59 , 0, clause( 60977, [ =( codomain( domain( compose( b, a ) ) ), domain( a )
% 27.15/27.59 ) ] )
% 27.15/27.59 , 0, 1, substitution( 0, [ :=( X, compose( b, a ) )] ), substitution( 1, [] )
% 27.15/27.59 ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 subsumption(
% 27.15/27.59 clause( 60467, [ =( domain( compose( b, a ) ), domain( a ) ) ] )
% 27.15/27.59 , clause( 60978, [ =( domain( compose( b, a ) ), domain( a ) ) ] )
% 27.15/27.59 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 paramod(
% 27.15/27.59 clause( 60982, [ ~( =( domain( a ), domain( a ) ) ) ] )
% 27.15/27.59 , clause( 60467, [ =( domain( compose( b, a ) ), domain( a ) ) ] )
% 27.15/27.59 , 0, clause( 19, [ ~( =( domain( compose( b, a ) ), domain( a ) ) ) ] )
% 27.15/27.59 , 0, 2, substitution( 0, [] ), substitution( 1, [] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 eqrefl(
% 27.15/27.59 clause( 60983, [] )
% 27.15/27.59 , clause( 60982, [ ~( =( domain( a ), domain( a ) ) ) ] )
% 27.15/27.59 , 0, substitution( 0, [] )).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 subsumption(
% 27.15/27.59 clause( 60751, [] )
% 27.15/27.59 , clause( 60983, [] )
% 27.15/27.59 , substitution( 0, [] ), permutation( 0, [] ) ).
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 end.
% 27.15/27.59
% 27.15/27.59 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 27.15/27.59
% 27.15/27.59 Memory use:
% 27.15/27.59
% 27.15/27.59 space for terms: 909742
% 27.15/27.59 space for clauses: 2384921
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 clauses generated: 332461
% 27.15/27.59 clauses kept: 60752
% 27.15/27.59 clauses selected: 1267
% 27.15/27.59 clauses deleted: 17173
% 27.15/27.59 clauses inuse deleted: 420
% 27.15/27.59
% 27.15/27.59 subsentry: 16014741
% 27.15/27.59 literals s-matched: 6563383
% 27.15/27.59 literals matched: 4665189
% 27.15/27.59 full subsumption: 2712849
% 27.15/27.59
% 27.15/27.59 checksum: -295300344
% 27.15/27.59
% 27.15/27.59
% 27.15/27.59 Bliksem ended
%------------------------------------------------------------------------------