TSTP Solution File: RNG006-3 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : RNG006-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n019.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 : Mon Jul 18 20:16:04 EDT 2022
% Result : Unsatisfiable 15.17s 15.54s
% Output : Refutation 15.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : RNG006-3 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.14 % Command : bliksem %s
% 0.15/0.36 % Computer : n019.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % DateTime : Mon May 30 19:00:40 EDT 2022
% 0.15/0.36 % CPUTime :
% 14.16/14.50 *** allocated 10000 integers for termspace/termends
% 14.16/14.50 *** allocated 10000 integers for clauses
% 14.16/14.50 *** allocated 10000 integers for justifications
% 14.16/14.50 Bliksem 1.12
% 14.16/14.50
% 14.16/14.50
% 14.16/14.50 Automatic Strategy Selection
% 14.16/14.50
% 14.16/14.50 Clauses:
% 14.16/14.50 [
% 14.16/14.50 [ sum( 'additive_identity', X, X ) ],
% 14.16/14.50 [ sum( X, 'additive_identity', X ) ],
% 14.16/14.50 [ product( X, Y, multiply( X, Y ) ) ],
% 14.16/14.50 [ sum( X, Y, add( X, Y ) ) ],
% 14.16/14.50 [ sum( 'additive_inverse'( X ), X, 'additive_identity' ) ],
% 14.16/14.50 [ sum( X, 'additive_inverse'( X ), 'additive_identity' ) ],
% 14.16/14.50 [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( Z, T, W ) ), sum( X
% 14.16/14.50 , U, W ) ],
% 14.16/14.50 [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( X, U, W ) ), sum( Z
% 14.16/14.50 , T, W ) ],
% 14.16/14.50 [ ~( sum( X, Y, Z ) ), sum( Y, X, Z ) ],
% 14.16/14.50 [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~( product( Z, T, W
% 14.16/14.50 ) ), product( X, U, W ) ],
% 14.16/14.50 [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~( product( X, U, W
% 14.16/14.50 ) ), product( Z, T, W ) ],
% 14.16/14.50 [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum( Y, T, W ) )
% 14.16/14.50 , ~( product( X, W, V0 ) ), sum( Z, U, V0 ) ],
% 14.16/14.50 [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum( Y, T, W ) )
% 14.16/14.50 , ~( sum( Z, U, V0 ) ), product( X, W, V0 ) ],
% 14.16/14.50 [ ~( product( X, Y, Z ) ), ~( product( T, Y, U ) ), ~( sum( X, T, W ) )
% 14.16/14.50 , ~( product( W, Y, V0 ) ), sum( Z, U, V0 ) ],
% 14.16/14.50 [ ~( product( X, Y, Z ) ), ~( product( T, Y, U ) ), ~( sum( X, T, W ) )
% 14.16/14.50 , ~( sum( Z, U, V0 ) ), product( W, Y, V0 ) ],
% 14.16/14.50 [ ~( sum( X, Y, Z ) ), ~( sum( X, Y, T ) ), =( Z, T ) ],
% 14.16/14.50 [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z, T ) ],
% 14.16/14.50 [ sum( b, 'additive_inverse'( c ), 'bS_Ic' ) ],
% 14.16/14.50 [ product( a, b, aPb ) ],
% 14.16/14.50 [ product( a, c, aPc ) ],
% 14.16/14.50 [ sum( aPb, 'additive_inverse'( aPc ), 'aPb_S_IaPc' ) ],
% 14.16/14.50 [ ~( product( a, 'bS_Ic', 'aPb_S_IaPc' ) ) ]
% 14.16/14.50 ] .
% 14.16/14.50
% 14.16/14.50
% 14.16/14.50 percentage equality = 0.036364, percentage horn = 1.000000
% 14.16/14.50 This is a problem with some equality
% 14.16/14.50
% 14.16/14.50
% 14.16/14.50
% 14.16/14.50 Options Used:
% 14.16/14.50
% 14.16/14.50 useres = 1
% 14.16/14.50 useparamod = 1
% 14.16/14.50 useeqrefl = 1
% 14.16/14.50 useeqfact = 1
% 14.16/14.50 usefactor = 1
% 14.16/14.50 usesimpsplitting = 0
% 14.16/14.50 usesimpdemod = 5
% 14.16/14.50 usesimpres = 3
% 14.16/14.50
% 14.16/14.50 resimpinuse = 1000
% 14.16/14.50 resimpclauses = 20000
% 14.16/14.50 substype = eqrewr
% 14.16/14.50 backwardsubs = 1
% 14.16/14.50 selectoldest = 5
% 14.16/14.50
% 14.16/14.50 litorderings [0] = split
% 14.16/14.50 litorderings [1] = extend the termordering, first sorting on arguments
% 14.16/14.50
% 14.16/14.50 termordering = kbo
% 14.16/14.50
% 14.16/14.50 litapriori = 0
% 14.16/14.50 termapriori = 1
% 14.16/14.50 litaposteriori = 0
% 14.16/14.50 termaposteriori = 0
% 14.16/14.50 demodaposteriori = 0
% 14.16/14.50 ordereqreflfact = 0
% 14.16/14.50
% 14.16/14.50 litselect = negord
% 14.16/14.50
% 14.16/14.50 maxweight = 15
% 14.16/14.50 maxdepth = 30000
% 14.16/14.50 maxlength = 115
% 14.16/14.50 maxnrvars = 195
% 14.16/14.50 excuselevel = 1
% 14.16/14.50 increasemaxweight = 1
% 14.16/14.50
% 14.16/14.50 maxselected = 10000000
% 14.16/14.50 maxnrclauses = 10000000
% 14.16/14.50
% 14.16/14.50 showgenerated = 0
% 14.16/14.50 showkept = 0
% 14.16/14.50 showselected = 0
% 14.16/14.50 showdeleted = 0
% 14.16/14.50 showresimp = 1
% 14.16/14.50 showstatus = 2000
% 14.16/14.50
% 14.16/14.50 prologoutput = 1
% 14.16/14.50 nrgoals = 5000000
% 14.16/14.50 totalproof = 1
% 14.16/14.50
% 14.16/14.50 Symbols occurring in the translation:
% 14.16/14.50
% 14.16/14.50 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 14.16/14.50 . [1, 2] (w:1, o:33, a:1, s:1, b:0),
% 14.16/14.50 ! [4, 1] (w:0, o:27, a:1, s:1, b:0),
% 14.16/14.50 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 14.16/14.50 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 14.16/14.50 'additive_identity' [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 14.16/14.50 sum [41, 3] (w:1, o:60, a:1, s:1, b:0),
% 14.16/14.50 multiply [43, 2] (w:1, o:58, a:1, s:1, b:0),
% 14.16/14.50 product [44, 3] (w:1, o:61, a:1, s:1, b:0),
% 14.16/14.50 add [45, 2] (w:1, o:59, a:1, s:1, b:0),
% 14.16/14.50 'additive_inverse' [46, 1] (w:1, o:32, a:1, s:1, b:0),
% 14.16/14.50 b [55, 0] (w:1, o:24, a:1, s:1, b:0),
% 14.16/14.50 c [56, 0] (w:1, o:26, a:1, s:1, b:0),
% 14.16/14.50 'bS_Ic' [57, 0] (w:1, o:25, a:1, s:1, b:0),
% 14.16/14.50 a [58, 0] (w:1, o:20, a:1, s:1, b:0),
% 14.16/14.50 aPb [59, 0] (w:1, o:21, a:1, s:1, b:0),
% 14.16/14.50 aPc [60, 0] (w:1, o:23, a:1, s:1, b:0),
% 14.16/14.50 'aPb_S_IaPc' [61, 0] (w:1, o:22, a:1, s:1, b:0).
% 14.16/14.50
% 14.16/14.50
% 14.16/14.50 Starting Search:
% 14.16/14.50
% 14.16/14.50 Resimplifying inuse:
% 14.16/14.50 Done
% 14.16/14.50
% 14.16/14.50
% 14.16/14.50 Intermediate Status:
% 14.16/14.50 Generated: 6656
% 14.16/14.50 Kept: 2024
% 14.16/14.50 Inuse: 91
% 14.16/14.50 Deleted: 15
% 14.16/14.50 Deletedinuse: 7
% 14.16/14.50
% 14.16/14.50 Resimplifying inuse:
% 14.16/14.50 Done
% 14.16/14.50
% 14.16/14.50 Resimplifying inuse:
% 14.16/14.50 Done
% 14.16/14.50
% 14.16/14.50
% 14.16/14.50 Intermediate Status:
% 14.16/14.50 Generated: 17829
% 14.16/14.50 Kept: 4049
% 14.16/14.50 Inuse: 185
% 14.16/14.50 Deleted: 64
% 14.16/14.50 Deletedinuse: 38
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 Intermediate Status:
% 15.17/15.54 Generated: 24549
% 15.17/15.54 Kept: 6174
% 15.17/15.54 Inuse: 224
% 15.17/15.54 Deleted: 70
% 15.17/15.54 Deletedinuse: 44
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 Intermediate Status:
% 15.17/15.54 Generated: 33219
% 15.17/15.54 Kept: 8231
% 15.17/15.54 Inuse: 273
% 15.17/15.54 Deleted: 100
% 15.17/15.54 Deletedinuse: 67
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 Intermediate Status:
% 15.17/15.54 Generated: 40589
% 15.17/15.54 Kept: 10292
% 15.17/15.54 Inuse: 315
% 15.17/15.54 Deleted: 103
% 15.17/15.54 Deletedinuse: 67
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 Intermediate Status:
% 15.17/15.54 Generated: 49817
% 15.17/15.54 Kept: 12333
% 15.17/15.54 Inuse: 358
% 15.17/15.54 Deleted: 112
% 15.17/15.54 Deletedinuse: 67
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 Intermediate Status:
% 15.17/15.54 Generated: 56674
% 15.17/15.54 Kept: 14356
% 15.17/15.54 Inuse: 387
% 15.17/15.54 Deleted: 118
% 15.17/15.54 Deletedinuse: 68
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 Intermediate Status:
% 15.17/15.54 Generated: 63294
% 15.17/15.54 Kept: 16555
% 15.17/15.54 Inuse: 413
% 15.17/15.54 Deleted: 123
% 15.17/15.54 Deletedinuse: 68
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 Intermediate Status:
% 15.17/15.54 Generated: 73378
% 15.17/15.54 Kept: 18596
% 15.17/15.54 Inuse: 441
% 15.17/15.54 Deleted: 126
% 15.17/15.54 Deletedinuse: 70
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54 Resimplifying clauses:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 Intermediate Status:
% 15.17/15.54 Generated: 80852
% 15.17/15.54 Kept: 20738
% 15.17/15.54 Inuse: 465
% 15.17/15.54 Deleted: 2672
% 15.17/15.54 Deletedinuse: 70
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 Intermediate Status:
% 15.17/15.54 Generated: 87179
% 15.17/15.54 Kept: 22771
% 15.17/15.54 Inuse: 479
% 15.17/15.54 Deleted: 2674
% 15.17/15.54 Deletedinuse: 72
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 Intermediate Status:
% 15.17/15.54 Generated: 93701
% 15.17/15.54 Kept: 24845
% 15.17/15.54 Inuse: 500
% 15.17/15.54 Deleted: 2674
% 15.17/15.54 Deletedinuse: 72
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 Intermediate Status:
% 15.17/15.54 Generated: 100539
% 15.17/15.54 Kept: 26865
% 15.17/15.54 Inuse: 524
% 15.17/15.54 Deleted: 2674
% 15.17/15.54 Deletedinuse: 72
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 Intermediate Status:
% 15.17/15.54 Generated: 104686
% 15.17/15.54 Kept: 28875
% 15.17/15.54 Inuse: 532
% 15.17/15.54 Deleted: 2676
% 15.17/15.54 Deletedinuse: 72
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 Intermediate Status:
% 15.17/15.54 Generated: 110757
% 15.17/15.54 Kept: 30903
% 15.17/15.54 Inuse: 553
% 15.17/15.54 Deleted: 2720
% 15.17/15.54 Deletedinuse: 110
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 Intermediate Status:
% 15.17/15.54 Generated: 115774
% 15.17/15.54 Kept: 32947
% 15.17/15.54 Inuse: 566
% 15.17/15.54 Deleted: 2723
% 15.17/15.54 Deletedinuse: 110
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 Intermediate Status:
% 15.17/15.54 Generated: 125515
% 15.17/15.54 Kept: 34991
% 15.17/15.54 Inuse: 595
% 15.17/15.54 Deleted: 2775
% 15.17/15.54 Deletedinuse: 153
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 Intermediate Status:
% 15.17/15.54 Generated: 131557
% 15.17/15.54 Kept: 37054
% 15.17/15.54 Inuse: 622
% 15.17/15.54 Deleted: 2777
% 15.17/15.54 Deletedinuse: 154
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 Intermediate Status:
% 15.17/15.54 Generated: 139355
% 15.17/15.54 Kept: 39083
% 15.17/15.54 Inuse: 651
% 15.17/15.54 Deleted: 2778
% 15.17/15.54 Deletedinuse: 155
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54 Resimplifying clauses:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 Intermediate Status:
% 15.17/15.54 Generated: 149124
% 15.17/15.54 Kept: 41137
% 15.17/15.54 Inuse: 680
% 15.17/15.54 Deleted: 10678
% 15.17/15.54 Deletedinuse: 156
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 Intermediate Status:
% 15.17/15.54 Generated: 159520
% 15.17/15.54 Kept: 43198
% 15.17/15.54 Inuse: 713
% 15.17/15.54 Deleted: 10683
% 15.17/15.54 Deletedinuse: 160
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 Intermediate Status:
% 15.17/15.54 Generated: 166785
% 15.17/15.54 Kept: 45274
% 15.17/15.54 Inuse: 737
% 15.17/15.54 Deleted: 10687
% 15.17/15.54 Deletedinuse: 164
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 Intermediate Status:
% 15.17/15.54 Generated: 179668
% 15.17/15.54 Kept: 47346
% 15.17/15.54 Inuse: 768
% 15.17/15.54 Deleted: 10688
% 15.17/15.54 Deletedinuse: 164
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 Intermediate Status:
% 15.17/15.54 Generated: 193932
% 15.17/15.54 Kept: 49399
% 15.17/15.54 Inuse: 799
% 15.17/15.54 Deleted: 10688
% 15.17/15.54 Deletedinuse: 164
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 Intermediate Status:
% 15.17/15.54 Generated: 210802
% 15.17/15.54 Kept: 51478
% 15.17/15.54 Inuse: 829
% 15.17/15.54 Deleted: 10688
% 15.17/15.54 Deletedinuse: 164
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 Intermediate Status:
% 15.17/15.54 Generated: 227263
% 15.17/15.54 Kept: 53514
% 15.17/15.54 Inuse: 861
% 15.17/15.54 Deleted: 10688
% 15.17/15.54 Deletedinuse: 164
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54 Resimplifying inuse:
% 15.17/15.54 Done
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 Intermediate Status:
% 15.17/15.54 Generated: 238905
% 15.17/15.54 Kept: 55580
% 15.17/15.54 Inuse: 889
% 15.17/15.54 Deleted: 10688
% 15.17/15.54 Deletedinuse: 164
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 Bliksems!, er is een bewijs:
% 15.17/15.54 % SZS status Unsatisfiable
% 15.17/15.54 % SZS output start Refutation
% 15.17/15.54
% 15.17/15.54 clause( 0, [ sum( 'additive_identity', X, X ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 2, [ product( X, Y, multiply( X, Y ) ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 3, [ sum( X, Y, add( X, Y ) ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 4, [ sum( 'additive_inverse'( X ), X, 'additive_identity' ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 5, [ sum( X, 'additive_inverse'( X ), 'additive_identity' ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 6, [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( Z, T, W ) )
% 15.17/15.54 , sum( X, U, W ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 7, [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( X, U, W ) )
% 15.17/15.54 , sum( Z, T, W ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 8, [ ~( sum( X, Y, Z ) ), sum( Y, X, Z ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 11, [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum( Y,
% 15.17/15.54 T, W ) ), ~( product( X, W, V0 ) ), sum( Z, U, V0 ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 15, [ ~( sum( X, Y, Z ) ), ~( sum( X, Y, T ) ), =( Z, T ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 16, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z, T ) ]
% 15.17/15.54 )
% 15.17/15.54 .
% 15.17/15.54 clause( 17, [ sum( b, 'additive_inverse'( c ), 'bS_Ic' ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 18, [ product( a, b, aPb ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 19, [ product( a, c, aPc ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 20, [ sum( aPb, 'additive_inverse'( aPc ), 'aPb_S_IaPc' ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 21, [ ~( product( a, 'bS_Ic', 'aPb_S_IaPc' ) ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 48, [ sum( 'additive_inverse'( aPc ), aPb, 'aPb_S_IaPc' ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 56, [ ~( sum( X, 'additive_inverse'( aPc ), Y ) ), ~( sum( Y, aPb,
% 15.17/15.54 Z ) ), sum( X, 'aPb_S_IaPc', Z ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 74, [ ~( sum( X, Y, Z ) ), ~( sum( 'additive_identity', Y, T ) ),
% 15.17/15.54 sum( 'additive_inverse'( X ), Z, T ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 79, [ ~( sum( X, Y, Z ) ), ~( sum( Y, 'additive_inverse'( Z ), T )
% 15.17/15.54 ), sum( X, T, 'additive_identity' ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 82, [ ~( sum( X, Y, 'additive_identity' ) ), ~( sum( Y, Z, T ) ),
% 15.17/15.54 sum( X, T, Z ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 86, [ ~( sum( 'additive_identity', X, Y ) ), sum(
% 15.17/15.54 'additive_inverse'( 'additive_identity' ), Y, Y ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 97, [ sum( 'additive_inverse'( 'additive_identity' ), X, X ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 125, [ ~( sum( 'additive_inverse'( aPc ), X, Y ) ), ~( sum( X, Z,
% 15.17/15.54 aPb ) ), sum( Y, Z, 'aPb_S_IaPc' ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 133, [ ~( sum( X, Y, Z ) ), ~( sum( T, Z, U ) ), sum( add( T, X ),
% 15.17/15.54 Y, U ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 136, [ ~( sum( 'additive_inverse'( c ), X, Y ) ), ~( sum( b, Y, Z )
% 15.17/15.54 ), sum( 'bS_Ic', X, Z ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 154, [ ~( sum( X, Y, Y ) ), sum( add( X, X ), Y, Y ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 162, [ sum( add( 'additive_inverse'( 'additive_identity' ),
% 15.17/15.54 'additive_inverse'( 'additive_identity' ) ), X, X ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 248, [ ~( product( a, X, Y ) ), ~( product( a, Z, T ) ), ~( sum( X
% 15.17/15.54 , Z, b ) ), sum( Y, T, aPb ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 274, [ sum( X, add( 'additive_inverse'( 'additive_identity' ),
% 15.17/15.54 'additive_inverse'( 'additive_identity' ) ), X ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 490, [ ~( sum( 'additive_identity', X, Y ) ), =( X, Y ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 545, [ =( add( 'additive_inverse'( 'additive_identity' ),
% 15.17/15.54 'additive_inverse'( 'additive_identity' ) ), 'additive_identity' ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 593, [ sum( Y, X, Y ), ~( sum( 'additive_identity',
% 15.17/15.54 'additive_identity', X ) ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 599, [ sum( X, Y, Y ), ~( sum( 'additive_identity',
% 15.17/15.54 'additive_identity', X ) ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 737, [ ~( product( a, c, X ) ), =( aPc, X ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 4350, [ ~( sum( 'additive_identity', aPb, X ) ), sum( aPc,
% 15.17/15.54 'aPb_S_IaPc', X ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 4385, [ sum( aPc, 'aPb_S_IaPc', aPb ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 4483, [ sum( 'aPb_S_IaPc', aPc, aPb ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 10228, [ ~( sum( X, 'aPb_S_IaPc', 'additive_identity' ) ), sum( X,
% 15.17/15.54 aPb, aPc ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 12929, [ sum( 'additive_inverse'( 'aPb_S_IaPc' ), aPb, aPc ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 13022, [ sum( aPb, 'additive_inverse'( 'aPb_S_IaPc' ), aPc ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 13094, [ ~( sum( X, aPb, 'aPb_S_IaPc' ) ), sum( X, aPc,
% 15.17/15.54 'additive_identity' ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 13239, [ sum( X, aPc, 'additive_identity' ), ~( sum( aPb, X,
% 15.17/15.54 'aPb_S_IaPc' ) ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 21475, [ ~( sum( aPc, X, aPb ) ), sum( 'additive_identity', X,
% 15.17/15.54 'aPb_S_IaPc' ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 21728, [ ~( sum( aPc, X, aPb ) ), =( X, 'aPb_S_IaPc' ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 21816, [ =( X, 'aPb_S_IaPc' ), ~( sum( X, aPc, aPb ) ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 22663, [ ~( product( a, 'bS_Ic', X ) ), ~( sum( X, aPc, aPb ) ) ]
% 15.17/15.54 )
% 15.17/15.54 .
% 15.17/15.54 clause( 22750, [ ~( product( a, 'bS_Ic', Y ) ), ~( sum( Y, X, aPb ) ), ~(
% 15.17/15.54 product( a, c, X ) ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 27388, [ ~( sum( b, 'additive_identity', X ) ), sum( 'bS_Ic', c, X
% 15.17/15.54 ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 27500, [ sum( 'bS_Ic', c, b ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 55615, [ ~( product( a, 'bS_Ic', X ) ), ~( product( a, c, Y ) ) ]
% 15.17/15.54 )
% 15.17/15.54 .
% 15.17/15.54 clause( 55686, [ ~( product( a, c, X ) ) ] )
% 15.17/15.54 .
% 15.17/15.54 clause( 55721, [] )
% 15.17/15.54 .
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 % SZS output end Refutation
% 15.17/15.54 found a proof!
% 15.17/15.54
% 15.17/15.54 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 15.17/15.54
% 15.17/15.54 initialclauses(
% 15.17/15.54 [ clause( 55723, [ sum( 'additive_identity', X, X ) ] )
% 15.17/15.54 , clause( 55724, [ sum( X, 'additive_identity', X ) ] )
% 15.17/15.54 , clause( 55725, [ product( X, Y, multiply( X, Y ) ) ] )
% 15.17/15.54 , clause( 55726, [ sum( X, Y, add( X, Y ) ) ] )
% 15.17/15.54 , clause( 55727, [ sum( 'additive_inverse'( X ), X, 'additive_identity' ) ]
% 15.17/15.54 )
% 15.17/15.54 , clause( 55728, [ sum( X, 'additive_inverse'( X ), 'additive_identity' ) ]
% 15.17/15.54 )
% 15.17/15.54 , clause( 55729, [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( Z, T,
% 15.17/15.54 W ) ), sum( X, U, W ) ] )
% 15.17/15.54 , clause( 55730, [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( X, U,
% 15.17/15.54 W ) ), sum( Z, T, W ) ] )
% 15.17/15.54 , clause( 55731, [ ~( sum( X, Y, Z ) ), sum( Y, X, Z ) ] )
% 15.17/15.54 , clause( 55732, [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~(
% 15.17/15.54 product( Z, T, W ) ), product( X, U, W ) ] )
% 15.17/15.54 , clause( 55733, [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~(
% 15.17/15.54 product( X, U, W ) ), product( Z, T, W ) ] )
% 15.17/15.54 , clause( 55734, [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum(
% 15.17/15.54 Y, T, W ) ), ~( product( X, W, V0 ) ), sum( Z, U, V0 ) ] )
% 15.17/15.54 , clause( 55735, [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum(
% 15.17/15.54 Y, T, W ) ), ~( sum( Z, U, V0 ) ), product( X, W, V0 ) ] )
% 15.17/15.54 , clause( 55736, [ ~( product( X, Y, Z ) ), ~( product( T, Y, U ) ), ~( sum(
% 15.17/15.54 X, T, W ) ), ~( product( W, Y, V0 ) ), sum( Z, U, V0 ) ] )
% 15.17/15.54 , clause( 55737, [ ~( product( X, Y, Z ) ), ~( product( T, Y, U ) ), ~( sum(
% 15.17/15.54 X, T, W ) ), ~( sum( Z, U, V0 ) ), product( W, Y, V0 ) ] )
% 15.17/15.54 , clause( 55738, [ ~( sum( X, Y, Z ) ), ~( sum( X, Y, T ) ), =( Z, T ) ] )
% 15.17/15.54 , clause( 55739, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z,
% 15.17/15.54 T ) ] )
% 15.17/15.54 , clause( 55740, [ sum( b, 'additive_inverse'( c ), 'bS_Ic' ) ] )
% 15.17/15.54 , clause( 55741, [ product( a, b, aPb ) ] )
% 15.17/15.54 , clause( 55742, [ product( a, c, aPc ) ] )
% 15.17/15.54 , clause( 55743, [ sum( aPb, 'additive_inverse'( aPc ), 'aPb_S_IaPc' ) ] )
% 15.17/15.54 , clause( 55744, [ ~( product( a, 'bS_Ic', 'aPb_S_IaPc' ) ) ] )
% 15.17/15.54 ] ).
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 subsumption(
% 15.17/15.54 clause( 0, [ sum( 'additive_identity', X, X ) ] )
% 15.17/15.54 , clause( 55723, [ sum( 'additive_identity', X, X ) ] )
% 15.17/15.54 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 subsumption(
% 15.17/15.54 clause( 2, [ product( X, Y, multiply( X, Y ) ) ] )
% 15.17/15.54 , clause( 55725, [ product( X, Y, multiply( X, Y ) ) ] )
% 15.17/15.54 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 15.17/15.54 )] ) ).
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 subsumption(
% 15.17/15.54 clause( 3, [ sum( X, Y, add( X, Y ) ) ] )
% 15.17/15.54 , clause( 55726, [ sum( X, Y, add( X, Y ) ) ] )
% 15.17/15.54 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 15.17/15.54 )] ) ).
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 subsumption(
% 15.17/15.54 clause( 4, [ sum( 'additive_inverse'( X ), X, 'additive_identity' ) ] )
% 15.17/15.54 , clause( 55727, [ sum( 'additive_inverse'( X ), X, 'additive_identity' ) ]
% 15.17/15.54 )
% 15.17/15.54 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 subsumption(
% 15.17/15.54 clause( 5, [ sum( X, 'additive_inverse'( X ), 'additive_identity' ) ] )
% 15.17/15.54 , clause( 55728, [ sum( X, 'additive_inverse'( X ), 'additive_identity' ) ]
% 15.17/15.54 )
% 15.17/15.54 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 subsumption(
% 15.17/15.54 clause( 6, [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( Z, T, W ) )
% 15.17/15.54 , sum( X, U, W ) ] )
% 15.17/15.54 , clause( 55729, [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( Z, T,
% 15.17/15.54 W ) ), sum( X, U, W ) ] )
% 15.17/15.54 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 15.17/15.54 , U ), :=( W, W )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2
% 15.17/15.54 , 2 ), ==>( 3, 3 )] ) ).
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 subsumption(
% 15.17/15.54 clause( 7, [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( X, U, W ) )
% 15.17/15.54 , sum( Z, T, W ) ] )
% 15.17/15.54 , clause( 55730, [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( X, U,
% 15.17/15.54 W ) ), sum( Z, T, W ) ] )
% 15.17/15.54 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 15.17/15.54 , U ), :=( W, W )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2
% 15.17/15.54 , 2 ), ==>( 3, 3 )] ) ).
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 subsumption(
% 15.17/15.54 clause( 8, [ ~( sum( X, Y, Z ) ), sum( Y, X, Z ) ] )
% 15.17/15.54 , clause( 55731, [ ~( sum( X, Y, Z ) ), sum( Y, X, Z ) ] )
% 15.17/15.54 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 15.17/15.54 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 subsumption(
% 15.17/15.54 clause( 11, [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum( Y,
% 15.17/15.54 T, W ) ), ~( product( X, W, V0 ) ), sum( Z, U, V0 ) ] )
% 15.17/15.54 , clause( 55734, [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum(
% 15.17/15.54 Y, T, W ) ), ~( product( X, W, V0 ) ), sum( Z, U, V0 ) ] )
% 15.17/15.54 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 15.17/15.54 , U ), :=( W, W ), :=( V0, V0 )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1
% 15.17/15.54 , 1 ), ==>( 2, 2 ), ==>( 3, 3 ), ==>( 4, 4 )] ) ).
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 subsumption(
% 15.17/15.54 clause( 15, [ ~( sum( X, Y, Z ) ), ~( sum( X, Y, T ) ), =( Z, T ) ] )
% 15.17/15.54 , clause( 55738, [ ~( sum( X, Y, Z ) ), ~( sum( X, Y, T ) ), =( Z, T ) ] )
% 15.17/15.54 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 15.17/15.54 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 subsumption(
% 15.17/15.54 clause( 16, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z, T ) ]
% 15.17/15.54 )
% 15.17/15.54 , clause( 55739, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z,
% 15.17/15.54 T ) ] )
% 15.17/15.54 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 15.17/15.54 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 subsumption(
% 15.17/15.54 clause( 17, [ sum( b, 'additive_inverse'( c ), 'bS_Ic' ) ] )
% 15.17/15.54 , clause( 55740, [ sum( b, 'additive_inverse'( c ), 'bS_Ic' ) ] )
% 15.17/15.54 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 subsumption(
% 15.17/15.54 clause( 18, [ product( a, b, aPb ) ] )
% 15.17/15.54 , clause( 55741, [ product( a, b, aPb ) ] )
% 15.17/15.54 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 subsumption(
% 15.17/15.54 clause( 19, [ product( a, c, aPc ) ] )
% 15.17/15.54 , clause( 55742, [ product( a, c, aPc ) ] )
% 15.17/15.54 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 subsumption(
% 15.17/15.54 clause( 20, [ sum( aPb, 'additive_inverse'( aPc ), 'aPb_S_IaPc' ) ] )
% 15.17/15.54 , clause( 55743, [ sum( aPb, 'additive_inverse'( aPc ), 'aPb_S_IaPc' ) ] )
% 15.17/15.54 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 subsumption(
% 15.17/15.54 clause( 21, [ ~( product( a, 'bS_Ic', 'aPb_S_IaPc' ) ) ] )
% 15.17/15.54 , clause( 55744, [ ~( product( a, 'bS_Ic', 'aPb_S_IaPc' ) ) ] )
% 15.17/15.54 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 resolution(
% 15.17/15.54 clause( 56008, [ sum( 'additive_inverse'( aPc ), aPb, 'aPb_S_IaPc' ) ] )
% 15.17/15.54 , clause( 8, [ ~( sum( X, Y, Z ) ), sum( Y, X, Z ) ] )
% 15.17/15.54 , 0, clause( 20, [ sum( aPb, 'additive_inverse'( aPc ), 'aPb_S_IaPc' ) ] )
% 15.17/15.54 , 0, substitution( 0, [ :=( X, aPb ), :=( Y, 'additive_inverse'( aPc ) ),
% 15.17/15.54 :=( Z, 'aPb_S_IaPc' )] ), substitution( 1, [] )).
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 subsumption(
% 15.17/15.54 clause( 48, [ sum( 'additive_inverse'( aPc ), aPb, 'aPb_S_IaPc' ) ] )
% 15.17/15.54 , clause( 56008, [ sum( 'additive_inverse'( aPc ), aPb, 'aPb_S_IaPc' ) ] )
% 15.17/15.54 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 resolution(
% 15.17/15.54 clause( 56010, [ ~( sum( X, 'additive_inverse'( aPc ), Y ) ), ~( sum( Y,
% 15.17/15.54 aPb, Z ) ), sum( X, 'aPb_S_IaPc', Z ) ] )
% 15.17/15.54 , clause( 6, [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( Z, T, W )
% 15.17/15.54 ), sum( X, U, W ) ] )
% 15.17/15.54 , 1, clause( 48, [ sum( 'additive_inverse'( aPc ), aPb, 'aPb_S_IaPc' ) ] )
% 15.17/15.54 , 0, substitution( 0, [ :=( X, X ), :=( Y, 'additive_inverse'( aPc ) ),
% 15.17/15.54 :=( Z, Y ), :=( T, aPb ), :=( U, 'aPb_S_IaPc' ), :=( W, Z )] ),
% 15.17/15.54 substitution( 1, [] )).
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 subsumption(
% 15.17/15.54 clause( 56, [ ~( sum( X, 'additive_inverse'( aPc ), Y ) ), ~( sum( Y, aPb,
% 15.17/15.54 Z ) ), sum( X, 'aPb_S_IaPc', Z ) ] )
% 15.17/15.54 , clause( 56010, [ ~( sum( X, 'additive_inverse'( aPc ), Y ) ), ~( sum( Y,
% 15.17/15.54 aPb, Z ) ), sum( X, 'aPb_S_IaPc', Z ) ] )
% 15.17/15.54 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 15.17/15.54 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 resolution(
% 15.17/15.54 clause( 56013, [ ~( sum( X, Y, Z ) ), ~( sum( 'additive_identity', Y, T ) )
% 15.17/15.54 , sum( 'additive_inverse'( X ), Z, T ) ] )
% 15.17/15.54 , clause( 6, [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( Z, T, W )
% 15.17/15.54 ), sum( X, U, W ) ] )
% 15.17/15.54 , 0, clause( 4, [ sum( 'additive_inverse'( X ), X, 'additive_identity' ) ]
% 15.17/15.54 )
% 15.17/15.54 , 0, substitution( 0, [ :=( X, 'additive_inverse'( X ) ), :=( Y, X ), :=( Z
% 15.17/15.54 , 'additive_identity' ), :=( T, Y ), :=( U, Z ), :=( W, T )] ),
% 15.17/15.54 substitution( 1, [ :=( X, X )] )).
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 subsumption(
% 15.17/15.54 clause( 74, [ ~( sum( X, Y, Z ) ), ~( sum( 'additive_identity', Y, T ) ),
% 15.17/15.54 sum( 'additive_inverse'( X ), Z, T ) ] )
% 15.17/15.54 , clause( 56013, [ ~( sum( X, Y, Z ) ), ~( sum( 'additive_identity', Y, T )
% 15.17/15.54 ), sum( 'additive_inverse'( X ), Z, T ) ] )
% 15.17/15.54 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 15.17/15.54 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 resolution(
% 15.17/15.54 clause( 56020, [ ~( sum( X, Y, Z ) ), ~( sum( Y, 'additive_inverse'( Z ), T
% 15.17/15.54 ) ), sum( X, T, 'additive_identity' ) ] )
% 15.17/15.54 , clause( 6, [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( Z, T, W )
% 15.17/15.54 ), sum( X, U, W ) ] )
% 15.17/15.54 , 2, clause( 5, [ sum( X, 'additive_inverse'( X ), 'additive_identity' ) ]
% 15.17/15.54 )
% 15.17/15.54 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T,
% 15.17/15.54 'additive_inverse'( Z ) ), :=( U, T ), :=( W, 'additive_identity' )] ),
% 15.17/15.54 substitution( 1, [ :=( X, Z )] )).
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 subsumption(
% 15.17/15.54 clause( 79, [ ~( sum( X, Y, Z ) ), ~( sum( Y, 'additive_inverse'( Z ), T )
% 15.17/15.54 ), sum( X, T, 'additive_identity' ) ] )
% 15.17/15.54 , clause( 56020, [ ~( sum( X, Y, Z ) ), ~( sum( Y, 'additive_inverse'( Z )
% 15.17/15.54 , T ) ), sum( X, T, 'additive_identity' ) ] )
% 15.17/15.54 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 15.17/15.54 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 resolution(
% 15.17/15.54 clause( 56024, [ ~( sum( X, Y, 'additive_identity' ) ), ~( sum( Y, Z, T ) )
% 15.17/15.54 , sum( X, T, Z ) ] )
% 15.17/15.54 , clause( 6, [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( Z, T, W )
% 15.17/15.54 ), sum( X, U, W ) ] )
% 15.17/15.54 , 2, clause( 0, [ sum( 'additive_identity', X, X ) ] )
% 15.17/15.54 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, 'additive_identity'
% 15.17/15.54 ), :=( T, Z ), :=( U, T ), :=( W, Z )] ), substitution( 1, [ :=( X, Z )] )
% 15.17/15.54 ).
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 subsumption(
% 15.17/15.54 clause( 82, [ ~( sum( X, Y, 'additive_identity' ) ), ~( sum( Y, Z, T ) ),
% 15.17/15.54 sum( X, T, Z ) ] )
% 15.17/15.54 , clause( 56024, [ ~( sum( X, Y, 'additive_identity' ) ), ~( sum( Y, Z, T )
% 15.17/15.54 ), sum( X, T, Z ) ] )
% 15.17/15.54 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 15.17/15.54 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 factor(
% 15.17/15.54 clause( 56028, [ ~( sum( 'additive_identity', X, Y ) ), sum(
% 15.17/15.54 'additive_inverse'( 'additive_identity' ), Y, Y ) ] )
% 15.17/15.54 , clause( 74, [ ~( sum( X, Y, Z ) ), ~( sum( 'additive_identity', Y, T ) )
% 15.17/15.54 , sum( 'additive_inverse'( X ), Z, T ) ] )
% 15.17/15.54 , 0, 1, substitution( 0, [ :=( X, 'additive_identity' ), :=( Y, X ), :=( Z
% 15.17/15.54 , Y ), :=( T, Y )] )).
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 subsumption(
% 15.17/15.54 clause( 86, [ ~( sum( 'additive_identity', X, Y ) ), sum(
% 15.17/15.54 'additive_inverse'( 'additive_identity' ), Y, Y ) ] )
% 15.17/15.54 , clause( 56028, [ ~( sum( 'additive_identity', X, Y ) ), sum(
% 15.17/15.54 'additive_inverse'( 'additive_identity' ), Y, Y ) ] )
% 15.17/15.54 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 15.17/15.54 ), ==>( 1, 1 )] ) ).
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 resolution(
% 15.17/15.54 clause( 56029, [ sum( 'additive_inverse'( 'additive_identity' ), X, X ) ]
% 15.17/15.54 )
% 15.17/15.54 , clause( 86, [ ~( sum( 'additive_identity', X, Y ) ), sum(
% 15.17/15.54 'additive_inverse'( 'additive_identity' ), Y, Y ) ] )
% 15.17/15.54 , 0, clause( 0, [ sum( 'additive_identity', X, X ) ] )
% 15.17/15.54 , 0, substitution( 0, [ :=( X, X ), :=( Y, X )] ), substitution( 1, [ :=( X
% 15.17/15.54 , X )] )).
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 subsumption(
% 15.17/15.54 clause( 97, [ sum( 'additive_inverse'( 'additive_identity' ), X, X ) ] )
% 15.17/15.54 , clause( 56029, [ sum( 'additive_inverse'( 'additive_identity' ), X, X ) ]
% 15.17/15.54 )
% 15.17/15.54 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 resolution(
% 15.17/15.54 clause( 56032, [ ~( sum( 'additive_inverse'( aPc ), X, Y ) ), ~( sum( X, Z
% 15.17/15.54 , aPb ) ), sum( Y, Z, 'aPb_S_IaPc' ) ] )
% 15.17/15.54 , clause( 7, [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( X, U, W )
% 15.17/15.54 ), sum( Z, T, W ) ] )
% 15.17/15.54 , 2, clause( 48, [ sum( 'additive_inverse'( aPc ), aPb, 'aPb_S_IaPc' ) ] )
% 15.17/15.54 , 0, substitution( 0, [ :=( X, 'additive_inverse'( aPc ) ), :=( Y, X ),
% 15.17/15.54 :=( Z, Y ), :=( T, Z ), :=( U, aPb ), :=( W, 'aPb_S_IaPc' )] ),
% 15.17/15.54 substitution( 1, [] )).
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 subsumption(
% 15.17/15.54 clause( 125, [ ~( sum( 'additive_inverse'( aPc ), X, Y ) ), ~( sum( X, Z,
% 15.17/15.54 aPb ) ), sum( Y, Z, 'aPb_S_IaPc' ) ] )
% 15.17/15.54 , clause( 56032, [ ~( sum( 'additive_inverse'( aPc ), X, Y ) ), ~( sum( X,
% 15.17/15.54 Z, aPb ) ), sum( Y, Z, 'aPb_S_IaPc' ) ] )
% 15.17/15.54 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 15.17/15.54 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 resolution(
% 15.17/15.54 clause( 56034, [ ~( sum( Y, Z, T ) ), ~( sum( X, T, U ) ), sum( add( X, Y )
% 15.17/15.54 , Z, U ) ] )
% 15.17/15.54 , clause( 7, [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( X, U, W )
% 15.17/15.54 ), sum( Z, T, W ) ] )
% 15.17/15.54 , 0, clause( 3, [ sum( X, Y, add( X, Y ) ) ] )
% 15.17/15.54 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, add( X, Y ) ), :=( T
% 15.17/15.54 , Z ), :=( U, T ), :=( W, U )] ), substitution( 1, [ :=( X, X ), :=( Y, Y
% 15.17/15.54 )] )).
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 subsumption(
% 15.17/15.54 clause( 133, [ ~( sum( X, Y, Z ) ), ~( sum( T, Z, U ) ), sum( add( T, X ),
% 15.17/15.54 Y, U ) ] )
% 15.17/15.54 , clause( 56034, [ ~( sum( Y, Z, T ) ), ~( sum( X, T, U ) ), sum( add( X, Y
% 15.17/15.54 ), Z, U ) ] )
% 15.17/15.54 , substitution( 0, [ :=( X, T ), :=( Y, X ), :=( Z, Y ), :=( T, Z ), :=( U
% 15.17/15.54 , U )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] )
% 15.17/15.54 ).
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 resolution(
% 15.17/15.54 clause( 56039, [ ~( sum( 'additive_inverse'( c ), X, Y ) ), ~( sum( b, Y, Z
% 15.17/15.54 ) ), sum( 'bS_Ic', X, Z ) ] )
% 15.17/15.54 , clause( 7, [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( X, U, W )
% 15.17/15.54 ), sum( Z, T, W ) ] )
% 15.17/15.54 , 0, clause( 17, [ sum( b, 'additive_inverse'( c ), 'bS_Ic' ) ] )
% 15.17/15.54 , 0, substitution( 0, [ :=( X, b ), :=( Y, 'additive_inverse'( c ) ), :=( Z
% 15.17/15.54 , 'bS_Ic' ), :=( T, X ), :=( U, Y ), :=( W, Z )] ), substitution( 1, [] )
% 15.17/15.54 ).
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 subsumption(
% 15.17/15.54 clause( 136, [ ~( sum( 'additive_inverse'( c ), X, Y ) ), ~( sum( b, Y, Z )
% 15.17/15.54 ), sum( 'bS_Ic', X, Z ) ] )
% 15.17/15.54 , clause( 56039, [ ~( sum( 'additive_inverse'( c ), X, Y ) ), ~( sum( b, Y
% 15.17/15.54 , Z ) ), sum( 'bS_Ic', X, Z ) ] )
% 15.17/15.54 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 15.17/15.54 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 factor(
% 15.17/15.54 clause( 56043, [ ~( sum( X, Y, Y ) ), sum( add( X, X ), Y, Y ) ] )
% 15.17/15.54 , clause( 133, [ ~( sum( X, Y, Z ) ), ~( sum( T, Z, U ) ), sum( add( T, X )
% 15.17/15.54 , Y, U ) ] )
% 15.17/15.54 , 0, 1, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Y ), :=( T, X ),
% 15.17/15.54 :=( U, Y )] )).
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 subsumption(
% 15.17/15.54 clause( 154, [ ~( sum( X, Y, Y ) ), sum( add( X, X ), Y, Y ) ] )
% 15.17/15.54 , clause( 56043, [ ~( sum( X, Y, Y ) ), sum( add( X, X ), Y, Y ) ] )
% 15.17/15.54 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 15.17/15.54 ), ==>( 1, 1 )] ) ).
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 resolution(
% 15.17/15.54 clause( 56044, [ sum( add( 'additive_inverse'( 'additive_identity' ),
% 15.17/15.54 'additive_inverse'( 'additive_identity' ) ), X, X ) ] )
% 15.17/15.54 , clause( 154, [ ~( sum( X, Y, Y ) ), sum( add( X, X ), Y, Y ) ] )
% 15.17/15.54 , 0, clause( 97, [ sum( 'additive_inverse'( 'additive_identity' ), X, X ) ]
% 15.17/15.54 )
% 15.17/15.54 , 0, substitution( 0, [ :=( X, 'additive_inverse'( 'additive_identity' ) )
% 15.17/15.54 , :=( Y, X )] ), substitution( 1, [ :=( X, X )] )).
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 subsumption(
% 15.17/15.54 clause( 162, [ sum( add( 'additive_inverse'( 'additive_identity' ),
% 15.17/15.54 'additive_inverse'( 'additive_identity' ) ), X, X ) ] )
% 15.17/15.54 , clause( 56044, [ sum( add( 'additive_inverse'( 'additive_identity' ),
% 15.17/15.54 'additive_inverse'( 'additive_identity' ) ), X, X ) ] )
% 15.17/15.54 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 resolution(
% 15.17/15.54 clause( 56047, [ ~( product( a, X, Y ) ), ~( product( a, Z, T ) ), ~( sum(
% 15.17/15.54 X, Z, b ) ), sum( Y, T, aPb ) ] )
% 15.17/15.54 , clause( 11, [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum( Y
% 15.17/15.54 , T, W ) ), ~( product( X, W, V0 ) ), sum( Z, U, V0 ) ] )
% 15.17/15.54 , 3, clause( 18, [ product( a, b, aPb ) ] )
% 15.17/15.54 , 0, substitution( 0, [ :=( X, a ), :=( Y, X ), :=( Z, Y ), :=( T, Z ),
% 15.17/15.54 :=( U, T ), :=( W, b ), :=( V0, aPb )] ), substitution( 1, [] )).
% 15.17/15.54
% 15.17/15.54
% 15.17/15.54 subsumption(
% 15.17/15.54 clause( 248, [ ~( product( a, X, Y ) ), ~( product( a, Z, T ) ), ~( sum( X
% 15.17/15.54 , Z, b ) ), sum( Y, T, aPb ) ] )
% 15.17/15.54 , clause( 56047, [ ~( product( a, X, Y ) ), ~( product( a, Z, T ) ), ~( sum(
% 15.17/15.54 X, Z, b ) ), sum( Y, T, aPb ) ] )
% 15.17/15.54 , substitCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------