TSTP Solution File: GRP047-2 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GRP047-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Sat Jul 16 07:34:34 EDT 2022
% Result : Unsatisfiable 2.31s 2.68s
% Output : Refutation 2.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP047-2 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Mon Jun 13 12:06:35 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.31/2.68 *** allocated 10000 integers for termspace/termends
% 2.31/2.68 *** allocated 10000 integers for clauses
% 2.31/2.68 *** allocated 10000 integers for justifications
% 2.31/2.68 Bliksem 1.12
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 Automatic Strategy Selection
% 2.31/2.68
% 2.31/2.68 Clauses:
% 2.31/2.68 [
% 2.31/2.68 [ product( identity, X, X ) ],
% 2.31/2.68 [ product( inverse( X ), X, identity ) ],
% 2.31/2.68 [ product( X, Y, multiply( X, Y ) ) ],
% 2.31/2.68 [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), equalish( Z, T ) ]
% 2.31/2.68 ,
% 2.31/2.68 [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~( product( Z, T, W
% 2.31/2.68 ) ), product( X, U, W ) ],
% 2.31/2.68 [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~( product( X, U, W
% 2.31/2.68 ) ), product( Z, T, W ) ],
% 2.31/2.68 [ ~( equalish( X, Y ) ), ~( product( Z, T, X ) ), product( Z, T, Y ) ]
% 2.31/2.68 ,
% 2.31/2.68 [ equalish( a, b ) ],
% 2.31/2.68 [ ~( equalish( multiply( c, a ), multiply( c, b ) ) ) ]
% 2.31/2.68 ] .
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 percentage equality = 0.000000, percentage horn = 1.000000
% 2.31/2.68 This is a near-Horn, non-equality problem
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 Options Used:
% 2.31/2.68
% 2.31/2.68 useres = 1
% 2.31/2.68 useparamod = 0
% 2.31/2.68 useeqrefl = 0
% 2.31/2.68 useeqfact = 0
% 2.31/2.68 usefactor = 1
% 2.31/2.68 usesimpsplitting = 0
% 2.31/2.68 usesimpdemod = 0
% 2.31/2.68 usesimpres = 4
% 2.31/2.68
% 2.31/2.68 resimpinuse = 1000
% 2.31/2.68 resimpclauses = 20000
% 2.31/2.68 substype = standard
% 2.31/2.68 backwardsubs = 1
% 2.31/2.68 selectoldest = 5
% 2.31/2.68
% 2.31/2.68 litorderings [0] = split
% 2.31/2.68 litorderings [1] = liftord
% 2.31/2.68
% 2.31/2.68 termordering = none
% 2.31/2.68
% 2.31/2.68 litapriori = 1
% 2.31/2.68 termapriori = 0
% 2.31/2.68 litaposteriori = 0
% 2.31/2.68 termaposteriori = 0
% 2.31/2.68 demodaposteriori = 0
% 2.31/2.68 ordereqreflfact = 0
% 2.31/2.68
% 2.31/2.68 litselect = negative
% 2.31/2.68
% 2.31/2.68 maxweight = 30000
% 2.31/2.68 maxdepth = 30000
% 2.31/2.68 maxlength = 115
% 2.31/2.68 maxnrvars = 195
% 2.31/2.68 excuselevel = 0
% 2.31/2.68 increasemaxweight = 0
% 2.31/2.68
% 2.31/2.68 maxselected = 10000000
% 2.31/2.68 maxnrclauses = 10000000
% 2.31/2.68
% 2.31/2.68 showgenerated = 0
% 2.31/2.68 showkept = 0
% 2.31/2.68 showselected = 0
% 2.31/2.68 showdeleted = 0
% 2.31/2.68 showresimp = 1
% 2.31/2.68 showstatus = 2000
% 2.31/2.68
% 2.31/2.68 prologoutput = 1
% 2.31/2.68 nrgoals = 5000000
% 2.31/2.68 totalproof = 1
% 2.31/2.68
% 2.31/2.68 Symbols occurring in the translation:
% 2.31/2.68
% 2.31/2.68 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 2.31/2.68 . [1, 2] (w:1, o:25, a:1, s:1, b:0),
% 2.31/2.68 ! [4, 1] (w:1, o:19, a:1, s:1, b:0),
% 2.31/2.68 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.31/2.68 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 2.31/2.68 identity [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 2.31/2.68 product [41, 3] (w:1, o:52, a:1, s:1, b:0),
% 2.31/2.68 inverse [42, 1] (w:1, o:24, a:1, s:1, b:0),
% 2.31/2.68 multiply [44, 2] (w:1, o:50, a:1, s:1, b:0),
% 2.31/2.68 equalish [47, 2] (w:1, o:51, a:1, s:1, b:0),
% 2.31/2.68 a [50, 0] (w:1, o:16, a:1, s:1, b:0),
% 2.31/2.68 b [51, 0] (w:1, o:17, a:1, s:1, b:0),
% 2.31/2.68 c [52, 0] (w:1, o:18, a:1, s:1, b:0).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 Starting Search:
% 2.31/2.68
% 2.31/2.68 Resimplifying inuse:
% 2.31/2.68 Done
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 Intermediate Status:
% 2.31/2.68 Generated: 2999
% 2.31/2.68 Kept: 2013
% 2.31/2.68 Inuse: 278
% 2.31/2.68 Deleted: 13
% 2.31/2.68 Deletedinuse: 5
% 2.31/2.68
% 2.31/2.68 Resimplifying inuse:
% 2.31/2.68 Done
% 2.31/2.68
% 2.31/2.68 Resimplifying inuse:
% 2.31/2.68 Done
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 Intermediate Status:
% 2.31/2.68 Generated: 5998
% 2.31/2.68 Kept: 4022
% 2.31/2.68 Inuse: 440
% 2.31/2.68 Deleted: 57
% 2.31/2.68 Deletedinuse: 34
% 2.31/2.68
% 2.31/2.68 Resimplifying inuse:
% 2.31/2.68 Done
% 2.31/2.68
% 2.31/2.68 Resimplifying inuse:
% 2.31/2.68 Done
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 Intermediate Status:
% 2.31/2.68 Generated: 9009
% 2.31/2.68 Kept: 6025
% 2.31/2.68 Inuse: 566
% 2.31/2.68 Deleted: 91
% 2.31/2.68 Deletedinuse: 55
% 2.31/2.68
% 2.31/2.68 Resimplifying inuse:
% 2.31/2.68 Done
% 2.31/2.68
% 2.31/2.68 Resimplifying inuse:
% 2.31/2.68 Done
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 Intermediate Status:
% 2.31/2.68 Generated: 11866
% 2.31/2.68 Kept: 8080
% 2.31/2.68 Inuse: 662
% 2.31/2.68 Deleted: 128
% 2.31/2.68 Deletedinuse: 84
% 2.31/2.68
% 2.31/2.68 Resimplifying inuse:
% 2.31/2.68 Done
% 2.31/2.68
% 2.31/2.68 Resimplifying inuse:
% 2.31/2.68 Done
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 Intermediate Status:
% 2.31/2.68 Generated: 14943
% 2.31/2.68 Kept: 10138
% 2.31/2.68 Inuse: 759
% 2.31/2.68 Deleted: 144
% 2.31/2.68 Deletedinuse: 92
% 2.31/2.68
% 2.31/2.68 Resimplifying inuse:
% 2.31/2.68 Done
% 2.31/2.68
% 2.31/2.68 Resimplifying inuse:
% 2.31/2.68 Done
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 Intermediate Status:
% 2.31/2.68 Generated: 17818
% 2.31/2.68 Kept: 12138
% 2.31/2.68 Inuse: 832
% 2.31/2.68 Deleted: 152
% 2.31/2.68 Deletedinuse: 92
% 2.31/2.68
% 2.31/2.68 Resimplifying inuse:
% 2.31/2.68 Done
% 2.31/2.68
% 2.31/2.68 Resimplifying inuse:
% 2.31/2.68 Done
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 Intermediate Status:
% 2.31/2.68 Generated: 20532
% 2.31/2.68 Kept: 14151
% 2.31/2.68 Inuse: 905
% 2.31/2.68 Deleted: 166
% 2.31/2.68 Deletedinuse: 92
% 2.31/2.68
% 2.31/2.68 Resimplifying inuse:
% 2.31/2.68 Done
% 2.31/2.68
% 2.31/2.68 Resimplifying inuse:
% 2.31/2.68 Done
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 Intermediate Status:
% 2.31/2.68 Generated: 23334
% 2.31/2.68 Kept: 16162
% 2.31/2.68 Inuse: 1001
% 2.31/2.68 Deleted: 183
% 2.31/2.68 Deletedinuse: 94
% 2.31/2.68
% 2.31/2.68 Resimplifying inuse:
% 2.31/2.68 Done
% 2.31/2.68
% 2.31/2.68 Resimplifying inuse:
% 2.31/2.68 Done
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 Intermediate Status:
% 2.31/2.68 Generated: 26649
% 2.31/2.68 Kept: 18163
% 2.31/2.68 Inuse: 1068
% 2.31/2.68 Deleted: 217
% 2.31/2.68 Deletedinuse: 125
% 2.31/2.68
% 2.31/2.68 Resimplifying inuse:
% 2.31/2.68 Done
% 2.31/2.68
% 2.31/2.68 Resimplifying inuse:
% 2.31/2.68 Done
% 2.31/2.68
% 2.31/2.68 Resimplifying clauses:
% 2.31/2.68 Done
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 Intermediate Status:
% 2.31/2.68 Generated: 29891
% 2.31/2.68 Kept: 20572
% 2.31/2.68 Inuse: 1130
% 2.31/2.68 Deleted: 2000
% 2.31/2.68 Deletedinuse: 130
% 2.31/2.68
% 2.31/2.68 Resimplifying inuse:
% 2.31/2.68 Done
% 2.31/2.68
% 2.31/2.68 Resimplifying inuse:
% 2.31/2.68 Done
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 Intermediate Status:
% 2.31/2.68 Generated: 32548
% 2.31/2.68 Kept: 22600
% 2.31/2.68 Inuse: 1182
% 2.31/2.68 Deleted: 2002
% 2.31/2.68 Deletedinuse: 132
% 2.31/2.68
% 2.31/2.68 Resimplifying inuse:
% 2.31/2.68 Done
% 2.31/2.68
% 2.31/2.68 Resimplifying inuse:
% 2.31/2.68 Done
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 Intermediate Status:
% 2.31/2.68 Generated: 35430
% 2.31/2.68 Kept: 24621
% 2.31/2.68 Inuse: 1227
% 2.31/2.68 Deleted: 2002
% 2.31/2.68 Deletedinuse: 132
% 2.31/2.68
% 2.31/2.68 Resimplifying inuse:
% 2.31/2.68 Done
% 2.31/2.68
% 2.31/2.68 Resimplifying inuse:
% 2.31/2.68 Done
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 Intermediate Status:
% 2.31/2.68 Generated: 38387
% 2.31/2.68 Kept: 26683
% 2.31/2.68 Inuse: 1288
% 2.31/2.68 Deleted: 2004
% 2.31/2.68 Deletedinuse: 134
% 2.31/2.68
% 2.31/2.68 Resimplifying inuse:
% 2.31/2.68 Done
% 2.31/2.68
% 2.31/2.68 Resimplifying inuse:
% 2.31/2.68 Done
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 Intermediate Status:
% 2.31/2.68 Generated: 41687
% 2.31/2.68 Kept: 28702
% 2.31/2.68 Inuse: 1371
% 2.31/2.68 Deleted: 2010
% 2.31/2.68 Deletedinuse: 138
% 2.31/2.68
% 2.31/2.68 Resimplifying inuse:
% 2.31/2.68 Done
% 2.31/2.68
% 2.31/2.68 Resimplifying inuse:
% 2.31/2.68 Done
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 Intermediate Status:
% 2.31/2.68 Generated: 44999
% 2.31/2.68 Kept: 30720
% 2.31/2.68 Inuse: 1453
% 2.31/2.68 Deleted: 2011
% 2.31/2.68 Deletedinuse: 138
% 2.31/2.68
% 2.31/2.68 Resimplifying inuse:
% 2.31/2.68 Done
% 2.31/2.68
% 2.31/2.68 Resimplifying inuse:
% 2.31/2.68 Done
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 Intermediate Status:
% 2.31/2.68 Generated: 48526
% 2.31/2.68 Kept: 32788
% 2.31/2.68 Inuse: 1569
% 2.31/2.68 Deleted: 2013
% 2.31/2.68 Deletedinuse: 138
% 2.31/2.68
% 2.31/2.68 Resimplifying inuse:
% 2.31/2.68 Done
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 Bliksems!, er is een bewijs:
% 2.31/2.68 % SZS status Unsatisfiable
% 2.31/2.68 % SZS output start Refutation
% 2.31/2.68
% 2.31/2.68 clause( 0, [ product( identity, X, X ) ] )
% 2.31/2.68 .
% 2.31/2.68 clause( 1, [ product( inverse( X ), X, identity ) ] )
% 2.31/2.68 .
% 2.31/2.68 clause( 2, [ product( X, Y, multiply( X, Y ) ) ] )
% 2.31/2.68 .
% 2.31/2.68 clause( 3, [ equalish( Z, T ), ~( product( X, Y, Z ) ), ~( product( X, Y, T
% 2.31/2.68 ) ) ] )
% 2.31/2.68 .
% 2.31/2.68 clause( 4, [ ~( product( Y, T, U ) ), ~( product( X, Y, Z ) ), product( X,
% 2.31/2.68 U, W ), ~( product( Z, T, W ) ) ] )
% 2.31/2.68 .
% 2.31/2.68 clause( 5, [ ~( product( X, Y, Z ) ), ~( product( X, U, W ) ), product( Z,
% 2.31/2.68 T, W ), ~( product( Y, T, U ) ) ] )
% 2.31/2.68 .
% 2.31/2.68 clause( 6, [ ~( equalish( X, Y ) ), product( Z, T, Y ), ~( product( Z, T, X
% 2.31/2.68 ) ) ] )
% 2.31/2.68 .
% 2.31/2.68 clause( 7, [ equalish( a, b ) ] )
% 2.31/2.68 .
% 2.31/2.68 clause( 8, [ ~( equalish( multiply( c, a ), multiply( c, b ) ) ) ] )
% 2.31/2.68 .
% 2.31/2.68 clause( 19, [ equalish( X, multiply( Y, Z ) ), ~( product( Y, Z, X ) ) ] )
% 2.31/2.68 .
% 2.31/2.68 clause( 21, [ equalish( X, Y ), ~( product( identity, Y, X ) ) ] )
% 2.31/2.68 .
% 2.31/2.68 clause( 25, [ ~( product( X, Y, Z ) ), product( T, Z, Y ), ~( product( T, X
% 2.31/2.68 , identity ) ) ] )
% 2.31/2.68 .
% 2.31/2.68 clause( 32, [ ~( product( X, identity, Y ) ), product( Y, Z, T ), ~(
% 2.31/2.68 product( X, Z, T ) ) ] )
% 2.31/2.68 .
% 2.31/2.68 clause( 33, [ product( Y, identity, Y ), ~( product( X, identity, Y ) ) ]
% 2.31/2.68 )
% 2.31/2.68 .
% 2.31/2.68 clause( 45, [ product( identity, X, Y ), ~( equalish( X, Y ) ) ] )
% 2.31/2.68 .
% 2.31/2.68 clause( 49, [ product( identity, a, b ) ] )
% 2.31/2.68 .
% 2.31/2.68 clause( 54, [ equalish( b, a ) ] )
% 2.31/2.68 .
% 2.31/2.68 clause( 57, [ product( identity, b, a ) ] )
% 2.31/2.68 .
% 2.31/2.68 clause( 61, [ ~( product( X, a, Z ) ), product( Y, b, Z ), ~( product( X,
% 2.31/2.68 identity, Y ) ) ] )
% 2.31/2.68 .
% 2.31/2.68 clause( 213, [ product( inverse( X ), Z, Y ), ~( product( X, Y, Z ) ) ] )
% 2.31/2.68 .
% 2.31/2.68 clause( 2572, [ product( inverse( inverse( X ) ), identity, X ) ] )
% 2.31/2.68 .
% 2.31/2.68 clause( 2761, [ product( X, identity, X ) ] )
% 2.31/2.68 .
% 2.31/2.68 clause( 2772, [ product( X, b, Y ), ~( product( X, a, Y ) ) ] )
% 2.31/2.68 .
% 2.31/2.68 clause( 33984, [ product( X, b, multiply( X, a ) ) ] )
% 2.31/2.68 .
% 2.31/2.68 clause( 34122, [ equalish( multiply( X, a ), multiply( X, b ) ) ] )
% 2.31/2.68 .
% 2.31/2.68 clause( 34265, [] )
% 2.31/2.68 .
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 % SZS output end Refutation
% 2.31/2.68 found a proof!
% 2.31/2.68
% 2.31/2.68 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 2.31/2.68
% 2.31/2.68 initialclauses(
% 2.31/2.68 [ clause( 34267, [ product( identity, X, X ) ] )
% 2.31/2.68 , clause( 34268, [ product( inverse( X ), X, identity ) ] )
% 2.31/2.68 , clause( 34269, [ product( X, Y, multiply( X, Y ) ) ] )
% 2.31/2.68 , clause( 34270, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ),
% 2.31/2.68 equalish( Z, T ) ] )
% 2.31/2.68 , clause( 34271, [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~(
% 2.31/2.68 product( Z, T, W ) ), product( X, U, W ) ] )
% 2.31/2.68 , clause( 34272, [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~(
% 2.31/2.68 product( X, U, W ) ), product( Z, T, W ) ] )
% 2.31/2.68 , clause( 34273, [ ~( equalish( X, Y ) ), ~( product( Z, T, X ) ), product(
% 2.31/2.68 Z, T, Y ) ] )
% 2.31/2.68 , clause( 34274, [ equalish( a, b ) ] )
% 2.31/2.68 , clause( 34275, [ ~( equalish( multiply( c, a ), multiply( c, b ) ) ) ] )
% 2.31/2.68 ] ).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 subsumption(
% 2.31/2.68 clause( 0, [ product( identity, X, X ) ] )
% 2.31/2.68 , clause( 34267, [ product( identity, X, X ) ] )
% 2.31/2.68 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 subsumption(
% 2.31/2.68 clause( 1, [ product( inverse( X ), X, identity ) ] )
% 2.31/2.68 , clause( 34268, [ product( inverse( X ), X, identity ) ] )
% 2.31/2.68 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 subsumption(
% 2.31/2.68 clause( 2, [ product( X, Y, multiply( X, Y ) ) ] )
% 2.31/2.68 , clause( 34269, [ product( X, Y, multiply( X, Y ) ) ] )
% 2.31/2.68 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.31/2.68 )] ) ).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 subsumption(
% 2.31/2.68 clause( 3, [ equalish( Z, T ), ~( product( X, Y, Z ) ), ~( product( X, Y, T
% 2.31/2.68 ) ) ] )
% 2.31/2.68 , clause( 34270, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ),
% 2.31/2.68 equalish( Z, T ) ] )
% 2.31/2.68 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 2.31/2.68 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 2 ), ==>( 2, 0 )] ) ).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 subsumption(
% 2.31/2.68 clause( 4, [ ~( product( Y, T, U ) ), ~( product( X, Y, Z ) ), product( X,
% 2.31/2.68 U, W ), ~( product( Z, T, W ) ) ] )
% 2.31/2.68 , clause( 34271, [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~(
% 2.31/2.68 product( Z, T, W ) ), product( X, U, W ) ] )
% 2.31/2.68 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 2.31/2.68 , U ), :=( W, W )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 ), ==>( 2
% 2.31/2.68 , 3 ), ==>( 3, 2 )] ) ).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 subsumption(
% 2.31/2.68 clause( 5, [ ~( product( X, Y, Z ) ), ~( product( X, U, W ) ), product( Z,
% 2.31/2.68 T, W ), ~( product( Y, T, U ) ) ] )
% 2.31/2.68 , clause( 34272, [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~(
% 2.31/2.68 product( X, U, W ) ), product( Z, T, W ) ] )
% 2.31/2.68 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 2.31/2.68 , U ), :=( W, W )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 3 ), ==>( 2
% 2.31/2.68 , 1 ), ==>( 3, 2 )] ) ).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 subsumption(
% 2.31/2.68 clause( 6, [ ~( equalish( X, Y ) ), product( Z, T, Y ), ~( product( Z, T, X
% 2.31/2.68 ) ) ] )
% 2.31/2.68 , clause( 34273, [ ~( equalish( X, Y ) ), ~( product( Z, T, X ) ), product(
% 2.31/2.68 Z, T, Y ) ] )
% 2.31/2.68 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 2.31/2.68 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 2 ), ==>( 2, 1 )] ) ).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 subsumption(
% 2.31/2.68 clause( 7, [ equalish( a, b ) ] )
% 2.31/2.68 , clause( 34274, [ equalish( a, b ) ] )
% 2.31/2.68 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 subsumption(
% 2.31/2.68 clause( 8, [ ~( equalish( multiply( c, a ), multiply( c, b ) ) ) ] )
% 2.31/2.68 , clause( 34275, [ ~( equalish( multiply( c, a ), multiply( c, b ) ) ) ] )
% 2.31/2.68 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 resolution(
% 2.31/2.68 clause( 34319, [ equalish( X, multiply( Y, Z ) ), ~( product( Y, Z, X ) ) ]
% 2.31/2.68 )
% 2.31/2.68 , clause( 3, [ equalish( Z, T ), ~( product( X, Y, Z ) ), ~( product( X, Y
% 2.31/2.68 , T ) ) ] )
% 2.31/2.68 , 2, clause( 2, [ product( X, Y, multiply( X, Y ) ) ] )
% 2.31/2.68 , 0, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X ), :=( T, multiply(
% 2.31/2.68 Y, Z ) )] ), substitution( 1, [ :=( X, Y ), :=( Y, Z )] )).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 subsumption(
% 2.31/2.68 clause( 19, [ equalish( X, multiply( Y, Z ) ), ~( product( Y, Z, X ) ) ] )
% 2.31/2.68 , clause( 34319, [ equalish( X, multiply( Y, Z ) ), ~( product( Y, Z, X ) )
% 2.31/2.68 ] )
% 2.31/2.68 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 2.31/2.68 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 resolution(
% 2.31/2.68 clause( 34321, [ equalish( X, Y ), ~( product( identity, Y, X ) ) ] )
% 2.31/2.68 , clause( 3, [ equalish( Z, T ), ~( product( X, Y, Z ) ), ~( product( X, Y
% 2.31/2.68 , T ) ) ] )
% 2.31/2.68 , 2, clause( 0, [ product( identity, X, X ) ] )
% 2.31/2.68 , 0, substitution( 0, [ :=( X, identity ), :=( Y, Y ), :=( Z, X ), :=( T, Y
% 2.31/2.68 )] ), substitution( 1, [ :=( X, Y )] )).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 subsumption(
% 2.31/2.68 clause( 21, [ equalish( X, Y ), ~( product( identity, Y, X ) ) ] )
% 2.31/2.68 , clause( 34321, [ equalish( X, Y ), ~( product( identity, Y, X ) ) ] )
% 2.31/2.68 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.31/2.68 ), ==>( 1, 1 )] ) ).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 resolution(
% 2.31/2.68 clause( 34324, [ ~( product( X, Y, Z ) ), ~( product( T, X, identity ) ),
% 2.31/2.68 product( T, Z, Y ) ] )
% 2.31/2.68 , clause( 4, [ ~( product( Y, T, U ) ), ~( product( X, Y, Z ) ), product( X
% 2.31/2.68 , U, W ), ~( product( Z, T, W ) ) ] )
% 2.31/2.68 , 3, clause( 0, [ product( identity, X, X ) ] )
% 2.31/2.68 , 0, substitution( 0, [ :=( X, T ), :=( Y, X ), :=( Z, identity ), :=( T, Y
% 2.31/2.68 ), :=( U, Z ), :=( W, Y )] ), substitution( 1, [ :=( X, Y )] )).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 subsumption(
% 2.31/2.68 clause( 25, [ ~( product( X, Y, Z ) ), product( T, Z, Y ), ~( product( T, X
% 2.31/2.68 , identity ) ) ] )
% 2.31/2.68 , clause( 34324, [ ~( product( X, Y, Z ) ), ~( product( T, X, identity ) )
% 2.31/2.68 , product( T, Z, Y ) ] )
% 2.31/2.68 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 2.31/2.68 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 2 ), ==>( 2, 1 )] ) ).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 resolution(
% 2.31/2.68 clause( 34330, [ ~( product( X, identity, Y ) ), ~( product( X, Z, T ) ),
% 2.31/2.68 product( Y, Z, T ) ] )
% 2.31/2.68 , clause( 5, [ ~( product( X, Y, Z ) ), ~( product( X, U, W ) ), product( Z
% 2.31/2.68 , T, W ), ~( product( Y, T, U ) ) ] )
% 2.31/2.68 , 3, clause( 0, [ product( identity, X, X ) ] )
% 2.31/2.68 , 0, substitution( 0, [ :=( X, X ), :=( Y, identity ), :=( Z, Y ), :=( T, Z
% 2.31/2.68 ), :=( U, Z ), :=( W, T )] ), substitution( 1, [ :=( X, Z )] )).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 subsumption(
% 2.31/2.68 clause( 32, [ ~( product( X, identity, Y ) ), product( Y, Z, T ), ~(
% 2.31/2.68 product( X, Z, T ) ) ] )
% 2.31/2.68 , clause( 34330, [ ~( product( X, identity, Y ) ), ~( product( X, Z, T ) )
% 2.31/2.68 , product( Y, Z, T ) ] )
% 2.31/2.68 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 2.31/2.68 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 2 ), ==>( 2, 1 )] ) ).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 factor(
% 2.31/2.68 clause( 34334, [ ~( product( X, identity, Y ) ), product( Y, identity, Y )
% 2.31/2.68 ] )
% 2.31/2.68 , clause( 32, [ ~( product( X, identity, Y ) ), product( Y, Z, T ), ~(
% 2.31/2.68 product( X, Z, T ) ) ] )
% 2.31/2.68 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, identity ), :=( T
% 2.31/2.68 , Y )] )).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 subsumption(
% 2.31/2.68 clause( 33, [ product( Y, identity, Y ), ~( product( X, identity, Y ) ) ]
% 2.31/2.68 )
% 2.31/2.68 , clause( 34334, [ ~( product( X, identity, Y ) ), product( Y, identity, Y
% 2.31/2.68 ) ] )
% 2.31/2.68 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 1
% 2.31/2.68 ), ==>( 1, 0 )] ) ).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 resolution(
% 2.31/2.68 clause( 34335, [ ~( equalish( X, Y ) ), product( identity, X, Y ) ] )
% 2.31/2.68 , clause( 6, [ ~( equalish( X, Y ) ), product( Z, T, Y ), ~( product( Z, T
% 2.31/2.68 , X ) ) ] )
% 2.31/2.68 , 2, clause( 0, [ product( identity, X, X ) ] )
% 2.31/2.68 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, identity ), :=( T, X
% 2.31/2.68 )] ), substitution( 1, [ :=( X, X )] )).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 subsumption(
% 2.31/2.68 clause( 45, [ product( identity, X, Y ), ~( equalish( X, Y ) ) ] )
% 2.31/2.68 , clause( 34335, [ ~( equalish( X, Y ) ), product( identity, X, Y ) ] )
% 2.31/2.68 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 1
% 2.31/2.68 ), ==>( 1, 0 )] ) ).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 resolution(
% 2.31/2.68 clause( 34336, [ product( identity, a, b ) ] )
% 2.31/2.68 , clause( 45, [ product( identity, X, Y ), ~( equalish( X, Y ) ) ] )
% 2.31/2.68 , 1, clause( 7, [ equalish( a, b ) ] )
% 2.31/2.68 , 0, substitution( 0, [ :=( X, a ), :=( Y, b )] ), substitution( 1, [] )
% 2.31/2.68 ).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 subsumption(
% 2.31/2.68 clause( 49, [ product( identity, a, b ) ] )
% 2.31/2.68 , clause( 34336, [ product( identity, a, b ) ] )
% 2.31/2.68 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 resolution(
% 2.31/2.68 clause( 34337, [ equalish( b, a ) ] )
% 2.31/2.68 , clause( 21, [ equalish( X, Y ), ~( product( identity, Y, X ) ) ] )
% 2.31/2.68 , 1, clause( 49, [ product( identity, a, b ) ] )
% 2.31/2.68 , 0, substitution( 0, [ :=( X, b ), :=( Y, a )] ), substitution( 1, [] )
% 2.31/2.68 ).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 subsumption(
% 2.31/2.68 clause( 54, [ equalish( b, a ) ] )
% 2.31/2.68 , clause( 34337, [ equalish( b, a ) ] )
% 2.31/2.68 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 resolution(
% 2.31/2.68 clause( 34338, [ product( identity, b, a ) ] )
% 2.31/2.68 , clause( 45, [ product( identity, X, Y ), ~( equalish( X, Y ) ) ] )
% 2.31/2.68 , 1, clause( 54, [ equalish( b, a ) ] )
% 2.31/2.68 , 0, substitution( 0, [ :=( X, b ), :=( Y, a )] ), substitution( 1, [] )
% 2.31/2.68 ).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 subsumption(
% 2.31/2.68 clause( 57, [ product( identity, b, a ) ] )
% 2.31/2.68 , clause( 34338, [ product( identity, b, a ) ] )
% 2.31/2.68 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 resolution(
% 2.31/2.68 clause( 34341, [ ~( product( X, identity, Y ) ), ~( product( X, a, Z ) ),
% 2.31/2.68 product( Y, b, Z ) ] )
% 2.31/2.68 , clause( 5, [ ~( product( X, Y, Z ) ), ~( product( X, U, W ) ), product( Z
% 2.31/2.68 , T, W ), ~( product( Y, T, U ) ) ] )
% 2.31/2.68 , 3, clause( 57, [ product( identity, b, a ) ] )
% 2.31/2.68 , 0, substitution( 0, [ :=( X, X ), :=( Y, identity ), :=( Z, Y ), :=( T, b
% 2.31/2.68 ), :=( U, a ), :=( W, Z )] ), substitution( 1, [] )).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 subsumption(
% 2.31/2.68 clause( 61, [ ~( product( X, a, Z ) ), product( Y, b, Z ), ~( product( X,
% 2.31/2.68 identity, Y ) ) ] )
% 2.31/2.68 , clause( 34341, [ ~( product( X, identity, Y ) ), ~( product( X, a, Z ) )
% 2.31/2.68 , product( Y, b, Z ) ] )
% 2.31/2.68 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 2.31/2.68 permutation( 0, [ ==>( 0, 2 ), ==>( 1, 0 ), ==>( 2, 1 )] ) ).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 resolution(
% 2.31/2.68 clause( 34344, [ ~( product( X, Y, Z ) ), product( inverse( X ), Z, Y ) ]
% 2.31/2.68 )
% 2.31/2.68 , clause( 25, [ ~( product( X, Y, Z ) ), product( T, Z, Y ), ~( product( T
% 2.31/2.68 , X, identity ) ) ] )
% 2.31/2.68 , 2, clause( 1, [ product( inverse( X ), X, identity ) ] )
% 2.31/2.68 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, inverse(
% 2.31/2.68 X ) )] ), substitution( 1, [ :=( X, X )] )).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 subsumption(
% 2.31/2.68 clause( 213, [ product( inverse( X ), Z, Y ), ~( product( X, Y, Z ) ) ] )
% 2.31/2.68 , clause( 34344, [ ~( product( X, Y, Z ) ), product( inverse( X ), Z, Y ) ]
% 2.31/2.68 )
% 2.31/2.68 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 2.31/2.68 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 resolution(
% 2.31/2.68 clause( 34345, [ product( inverse( inverse( X ) ), identity, X ) ] )
% 2.31/2.68 , clause( 213, [ product( inverse( X ), Z, Y ), ~( product( X, Y, Z ) ) ]
% 2.31/2.68 )
% 2.31/2.68 , 1, clause( 1, [ product( inverse( X ), X, identity ) ] )
% 2.31/2.68 , 0, substitution( 0, [ :=( X, inverse( X ) ), :=( Y, X ), :=( Z, identity
% 2.31/2.68 )] ), substitution( 1, [ :=( X, X )] )).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 subsumption(
% 2.31/2.68 clause( 2572, [ product( inverse( inverse( X ) ), identity, X ) ] )
% 2.31/2.68 , clause( 34345, [ product( inverse( inverse( X ) ), identity, X ) ] )
% 2.31/2.68 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 resolution(
% 2.31/2.68 clause( 34346, [ product( X, identity, X ) ] )
% 2.31/2.68 , clause( 33, [ product( Y, identity, Y ), ~( product( X, identity, Y ) ) ]
% 2.31/2.68 )
% 2.31/2.68 , 1, clause( 2572, [ product( inverse( inverse( X ) ), identity, X ) ] )
% 2.31/2.68 , 0, substitution( 0, [ :=( X, inverse( inverse( X ) ) ), :=( Y, X )] ),
% 2.31/2.68 substitution( 1, [ :=( X, X )] )).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 subsumption(
% 2.31/2.68 clause( 2761, [ product( X, identity, X ) ] )
% 2.31/2.68 , clause( 34346, [ product( X, identity, X ) ] )
% 2.31/2.68 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 resolution(
% 2.31/2.68 clause( 34347, [ ~( product( X, a, Y ) ), product( X, b, Y ) ] )
% 2.31/2.68 , clause( 61, [ ~( product( X, a, Z ) ), product( Y, b, Z ), ~( product( X
% 2.31/2.68 , identity, Y ) ) ] )
% 2.31/2.68 , 2, clause( 2761, [ product( X, identity, X ) ] )
% 2.31/2.68 , 0, substitution( 0, [ :=( X, X ), :=( Y, X ), :=( Z, Y )] ),
% 2.31/2.68 substitution( 1, [ :=( X, X )] )).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 subsumption(
% 2.31/2.68 clause( 2772, [ product( X, b, Y ), ~( product( X, a, Y ) ) ] )
% 2.31/2.68 , clause( 34347, [ ~( product( X, a, Y ) ), product( X, b, Y ) ] )
% 2.31/2.68 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 1
% 2.31/2.68 ), ==>( 1, 0 )] ) ).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 resolution(
% 2.31/2.68 clause( 34348, [ product( X, b, multiply( X, a ) ) ] )
% 2.31/2.68 , clause( 2772, [ product( X, b, Y ), ~( product( X, a, Y ) ) ] )
% 2.31/2.68 , 1, clause( 2, [ product( X, Y, multiply( X, Y ) ) ] )
% 2.31/2.68 , 0, substitution( 0, [ :=( X, X ), :=( Y, multiply( X, a ) )] ),
% 2.31/2.68 substitution( 1, [ :=( X, X ), :=( Y, a )] )).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 subsumption(
% 2.31/2.68 clause( 33984, [ product( X, b, multiply( X, a ) ) ] )
% 2.31/2.68 , clause( 34348, [ product( X, b, multiply( X, a ) ) ] )
% 2.31/2.68 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 resolution(
% 2.31/2.68 clause( 34349, [ equalish( multiply( X, a ), multiply( X, b ) ) ] )
% 2.31/2.68 , clause( 19, [ equalish( X, multiply( Y, Z ) ), ~( product( Y, Z, X ) ) ]
% 2.31/2.68 )
% 2.31/2.68 , 1, clause( 33984, [ product( X, b, multiply( X, a ) ) ] )
% 2.31/2.68 , 0, substitution( 0, [ :=( X, multiply( X, a ) ), :=( Y, X ), :=( Z, b )] )
% 2.31/2.68 , substitution( 1, [ :=( X, X )] )).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 subsumption(
% 2.31/2.68 clause( 34122, [ equalish( multiply( X, a ), multiply( X, b ) ) ] )
% 2.31/2.68 , clause( 34349, [ equalish( multiply( X, a ), multiply( X, b ) ) ] )
% 2.31/2.68 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 resolution(
% 2.31/2.68 clause( 34350, [] )
% 2.31/2.68 , clause( 8, [ ~( equalish( multiply( c, a ), multiply( c, b ) ) ) ] )
% 2.31/2.68 , 0, clause( 34122, [ equalish( multiply( X, a ), multiply( X, b ) ) ] )
% 2.31/2.68 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, c )] )).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 subsumption(
% 2.31/2.68 clause( 34265, [] )
% 2.31/2.68 , clause( 34350, [] )
% 2.31/2.68 , substitution( 0, [] ), permutation( 0, [] ) ).
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 end.
% 2.31/2.68
% 2.31/2.68 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 2.31/2.68
% 2.31/2.68 Memory use:
% 2.31/2.68
% 2.31/2.68 space for terms: 467207
% 2.31/2.68 space for clauses: 1829241
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 clauses generated: 51143
% 2.31/2.68 clauses kept: 34266
% 2.31/2.68 clauses selected: 1632
% 2.31/2.68 clauses deleted: 2019
% 2.31/2.68 clauses inuse deleted: 140
% 2.31/2.68
% 2.31/2.68 subsentry: 365260
% 2.31/2.68 literals s-matched: 161898
% 2.31/2.68 literals matched: 145739
% 2.31/2.68 full subsumption: 12190
% 2.31/2.68
% 2.31/2.68 checksum: 815925529
% 2.31/2.68
% 2.31/2.68
% 2.31/2.68 Bliksem ended
%------------------------------------------------------------------------------