TSTP Solution File: FLD018-3 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : FLD018-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n029.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 01:50:59 EDT 2022
% Result : Unsatisfiable 0.88s 1.31s
% Output : Refutation 0.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : FLD018-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n029.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 : Mon Jun 6 23:16:50 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.88/1.31 *** allocated 10000 integers for termspace/termends
% 0.88/1.31 *** allocated 10000 integers for clauses
% 0.88/1.31 *** allocated 10000 integers for justifications
% 0.88/1.31 Bliksem 1.12
% 0.88/1.31
% 0.88/1.31
% 0.88/1.31 Automatic Strategy Selection
% 0.88/1.31
% 0.88/1.31 Clauses:
% 0.88/1.31 [
% 0.88/1.31 [ sum( X, Y, Z ), ~( sum( X, T, U ) ), ~( sum( T, W, Y ) ), ~( sum( U, W
% 0.88/1.31 , Z ) ) ],
% 0.88/1.31 [ sum( X, Y, Z ), ~( sum( T, U, X ) ), ~( sum( U, Y, W ) ), ~( sum( T, W
% 0.88/1.31 , Z ) ) ],
% 0.88/1.31 [ sum( 'additive_identity', X, X ), ~( defined( X ) ) ],
% 0.88/1.31 [ sum( 'additive_inverse'( X ), X, 'additive_identity' ), ~( defined( X
% 0.88/1.31 ) ) ],
% 0.88/1.31 [ sum( X, Y, Z ), ~( sum( Y, X, Z ) ) ],
% 0.88/1.31 [ product( X, Y, Z ), ~( product( X, T, U ) ), ~( product( T, W, Y ) ),
% 0.88/1.31 ~( product( U, W, Z ) ) ],
% 0.88/1.31 [ product( X, Y, Z ), ~( product( T, U, X ) ), ~( product( U, Y, W ) ),
% 0.88/1.31 ~( product( T, W, Z ) ) ],
% 0.88/1.31 [ product( 'multiplicative_identity', X, X ), ~( defined( X ) ) ],
% 0.88/1.31 [ product( 'multiplicative_inverse'( X ), X, 'multiplicative_identity' )
% 0.88/1.31 , sum( 'additive_identity', X, 'additive_identity' ), ~( defined( X ) ) ]
% 0.88/1.31 ,
% 0.88/1.31 [ product( X, Y, Z ), ~( product( Y, X, Z ) ) ],
% 0.88/1.31 [ sum( X, Y, Z ), ~( sum( T, U, W ) ), ~( product( W, V0, Z ) ), ~(
% 0.88/1.31 product( T, V0, X ) ), ~( product( U, V0, Y ) ) ],
% 0.88/1.31 [ product( X, Y, Z ), ~( sum( T, U, X ) ), ~( product( T, Y, W ) ), ~(
% 0.88/1.31 product( U, Y, V0 ) ), ~( sum( W, V0, Z ) ) ],
% 0.88/1.31 [ defined( add( X, Y ) ), ~( defined( X ) ), ~( defined( Y ) ) ],
% 0.88/1.31 [ defined( 'additive_identity' ) ],
% 0.88/1.31 [ defined( 'additive_inverse'( X ) ), ~( defined( X ) ) ],
% 0.88/1.31 [ defined( multiply( X, Y ) ), ~( defined( X ) ), ~( defined( Y ) ) ]
% 0.88/1.31 ,
% 0.88/1.31 [ defined( 'multiplicative_identity' ) ],
% 0.88/1.31 [ defined( 'multiplicative_inverse'( X ) ), ~( defined( X ) ), sum(
% 0.88/1.31 'additive_identity', X, 'additive_identity' ) ],
% 0.88/1.31 [ sum( X, Y, add( X, Y ) ), ~( defined( X ) ), ~( defined( Y ) ) ],
% 0.88/1.31 [ product( X, Y, multiply( X, Y ) ), ~( defined( X ) ), ~( defined( Y )
% 0.88/1.31 ) ],
% 0.88/1.31 [ sum( 'additive_identity', X, Y ), ~( 'less_or_equal'( X, Y ) ), ~(
% 0.88/1.31 'less_or_equal'( Y, X ) ) ],
% 0.88/1.31 [ 'less_or_equal'( X, Y ), ~( 'less_or_equal'( X, Z ) ), ~(
% 0.88/1.31 'less_or_equal'( Z, Y ) ) ],
% 0.88/1.31 [ 'less_or_equal'( X, Y ), 'less_or_equal'( Y, X ), ~( defined( X ) ),
% 0.88/1.31 ~( defined( Y ) ) ],
% 0.88/1.31 [ 'less_or_equal'( X, Y ), ~( 'less_or_equal'( Z, T ) ), ~( sum( Z, U, X
% 0.88/1.31 ) ), ~( sum( T, U, Y ) ) ],
% 0.88/1.31 [ 'less_or_equal'( 'additive_identity', X ), ~( 'less_or_equal'(
% 0.88/1.31 'additive_identity', Y ) ), ~( 'less_or_equal'( 'additive_identity', Z )
% 0.88/1.31 ), ~( product( Y, Z, X ) ) ],
% 0.88/1.31 [ ~( sum( 'additive_identity', 'additive_identity',
% 0.88/1.31 'multiplicative_identity' ) ) ],
% 0.88/1.31 [ defined( a ) ],
% 0.88/1.31 [ sum( 'additive_identity', a, 'additive_identity' ) ],
% 0.88/1.31 [ ~( sum( 'additive_identity', 'additive_inverse'( a ),
% 0.88/1.31 'additive_identity' ) ) ]
% 0.88/1.31 ] .
% 0.88/1.31
% 0.88/1.31
% 0.88/1.31 percentage equality = 0.000000, percentage horn = 0.896552
% 0.88/1.31 This a non-horn, non-equality problem
% 0.88/1.31
% 0.88/1.31
% 0.88/1.31 Options Used:
% 0.88/1.31
% 0.88/1.31 useres = 1
% 0.88/1.31 useparamod = 0
% 0.88/1.31 useeqrefl = 0
% 0.88/1.31 useeqfact = 0
% 0.88/1.31 usefactor = 1
% 0.88/1.31 usesimpsplitting = 0
% 0.88/1.31 usesimpdemod = 0
% 0.88/1.31 usesimpres = 3
% 0.88/1.31
% 0.88/1.31 resimpinuse = 1000
% 0.88/1.31 resimpclauses = 20000
% 0.88/1.31 substype = standard
% 0.88/1.31 backwardsubs = 1
% 0.88/1.31 selectoldest = 5
% 0.88/1.31
% 0.88/1.31 litorderings [0] = split
% 0.88/1.31 litorderings [1] = liftord
% 0.88/1.31
% 0.88/1.31 termordering = none
% 0.88/1.31
% 0.88/1.31 litapriori = 1
% 0.88/1.31 termapriori = 0
% 0.88/1.31 litaposteriori = 0
% 0.88/1.31 termaposteriori = 0
% 0.88/1.31 demodaposteriori = 0
% 0.88/1.31 ordereqreflfact = 0
% 0.88/1.31
% 0.88/1.31 litselect = none
% 0.88/1.31
% 0.88/1.31 maxweight = 15
% 0.88/1.31 maxdepth = 30000
% 0.88/1.31 maxlength = 115
% 0.88/1.31 maxnrvars = 195
% 0.88/1.31 excuselevel = 1
% 0.88/1.31 increasemaxweight = 1
% 0.88/1.31
% 0.88/1.31 maxselected = 10000000
% 0.88/1.31 maxnrclauses = 10000000
% 0.88/1.31
% 0.88/1.31 showgenerated = 0
% 0.88/1.31 showkept = 0
% 0.88/1.31 showselected = 0
% 0.88/1.31 showdeleted = 0
% 0.88/1.31 showresimp = 1
% 0.88/1.31 showstatus = 2000
% 0.88/1.31
% 0.88/1.31 prologoutput = 1
% 0.88/1.31 nrgoals = 5000000
% 0.88/1.31 totalproof = 1
% 0.88/1.31
% 0.88/1.31 Symbols occurring in the translation:
% 0.88/1.31
% 0.88/1.31 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.88/1.31 . [1, 2] (w:1, o:30, a:1, s:1, b:0),
% 0.88/1.31 ! [4, 1] (w:0, o:22, a:1, s:1, b:0),
% 0.88/1.31 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.88/1.31 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.88/1.31 sum [42, 3] (w:1, o:58, a:1, s:1, b:0),
% 0.88/1.31 'additive_identity' [46, 0] (w:1, o:15, a:1, s:1, b:0),
% 0.88/1.31 defined [47, 1] (w:1, o:27, a:1, s:1, b:0),
% 0.88/1.31 'additive_inverse' [48, 1] (w:1, o:28, a:1, s:1, b:0),
% 0.88/1.31 product [49, 3] (w:1, o:59, a:1, s:1, b:0),
% 0.88/1.31 'multiplicative_identity' [50, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.88/1.31 'multiplicative_inverse' [51, 1] (w:1, o:29, a:1, s:1, b:0),
% 0.88/1.31 add [56, 2] (w:1, o:55, a:1, s:1, b:0),
% 0.88/1.31 multiply [57, 2] (w:1, o:57, a:1, s:1, b:0),
% 0.88/1.31 'less_or_equal' [58, 2] (w:1, o:56, a:1, s:1, b:0),
% 0.88/1.31 a [59, 0] (w:1, o:21, a:1, s:1, b:0).
% 0.88/1.31
% 0.88/1.31
% 0.88/1.31 Starting Search:
% 0.88/1.31
% 0.88/1.31 Resimplifying inuse:
% 0.88/1.31 Done
% 0.88/1.31
% 0.88/1.31
% 0.88/1.31 Intermediate Status:
% 0.88/1.31 Generated: 2925
% 0.88/1.31 Kept: 2025
% 0.88/1.31 Inuse: 130
% 0.88/1.31 Deleted: 0
% 0.88/1.31 Deletedinuse: 0
% 0.88/1.31
% 0.88/1.31 Resimplifying inuse:
% 0.88/1.31 Done
% 0.88/1.31
% 0.88/1.31 Resimplifying inuse:
% 0.88/1.31 Done
% 0.88/1.31
% 0.88/1.31
% 0.88/1.31 Intermediate Status:
% 0.88/1.31 Generated: 5864
% 0.88/1.31 Kept: 4025
% 0.88/1.31 Inuse: 235
% 0.88/1.31 Deleted: 1
% 0.88/1.31 Deletedinuse: 0
% 0.88/1.31
% 0.88/1.31 Resimplifying inuse:
% 0.88/1.31 Done
% 0.88/1.31
% 0.88/1.31 Resimplifying inuse:
% 0.88/1.31 Done
% 0.88/1.31
% 0.88/1.31
% 0.88/1.31 Bliksems!, er is een bewijs:
% 0.88/1.31 % SZS status Unsatisfiable
% 0.88/1.31 % SZS output start Refutation
% 0.88/1.31
% 0.88/1.31 clause( 0, [ ~( sum( X, T, U ) ), ~( sum( T, W, Y ) ), ~( sum( U, W, Z ) )
% 0.88/1.31 , sum( X, Y, Z ) ] )
% 0.88/1.31 .
% 0.88/1.31 clause( 1, [ ~( sum( T, U, X ) ), ~( sum( U, Y, W ) ), ~( sum( T, W, Z ) )
% 0.88/1.31 , sum( X, Y, Z ) ] )
% 0.88/1.31 .
% 0.88/1.31 clause( 2, [ ~( defined( X ) ), sum( 'additive_identity', X, X ) ] )
% 0.88/1.31 .
% 0.88/1.31 clause( 3, [ ~( defined( X ) ), sum( 'additive_inverse'( X ), X,
% 0.88/1.31 'additive_identity' ) ] )
% 0.88/1.31 .
% 0.88/1.31 clause( 4, [ ~( sum( Y, X, Z ) ), sum( X, Y, Z ) ] )
% 0.88/1.31 .
% 0.88/1.31 clause( 13, [ defined( 'additive_identity' ) ] )
% 0.88/1.31 .
% 0.88/1.31 clause( 26, [ defined( a ) ] )
% 0.88/1.31 .
% 0.88/1.31 clause( 27, [ sum( 'additive_identity', a, 'additive_identity' ) ] )
% 0.88/1.31 .
% 0.88/1.31 clause( 28, [ ~( sum( 'additive_identity', 'additive_inverse'( a ),
% 0.88/1.31 'additive_identity' ) ) ] )
% 0.88/1.31 .
% 0.88/1.31 clause( 56, [ ~( sum( 'additive_identity', X, Z ) ), sum(
% 0.88/1.31 'additive_identity', Y, Z ), ~( sum( a, X, Y ) ) ] )
% 0.88/1.31 .
% 0.88/1.31 clause( 71, [ ~( sum( Y, 'additive_inverse'( a ), Z ) ), ~( sum( X, Z,
% 0.88/1.31 'additive_identity' ) ), ~( sum( X, Y, 'additive_identity' ) ) ] )
% 0.88/1.31 .
% 0.88/1.31 clause( 79, [ ~( sum( 'additive_identity', Y, Z ) ), sum(
% 0.88/1.31 'additive_identity', X, Z ), ~( sum( a, X, Y ) ) ] )
% 0.88/1.31 .
% 0.88/1.31 clause( 85, [ ~( sum( Y, X, 'additive_identity' ) ), ~( sum( X,
% 0.88/1.31 'additive_inverse'( a ), X ) ) ] )
% 0.88/1.31 .
% 0.88/1.31 clause( 133, [ ~( defined( X ) ), sum( X, 'additive_identity', X ) ] )
% 0.88/1.31 .
% 0.88/1.31 clause( 5443, [ sum( 'additive_identity', X, 'additive_identity' ), ~( sum(
% 0.88/1.31 a, X, 'additive_identity' ) ) ] )
% 0.88/1.31 .
% 0.88/1.31 clause( 5966, [ ~( sum( 'additive_identity', Y, 'additive_identity' ) ),
% 0.88/1.31 ~( sum( a, Y, X ) ), ~( sum( X, 'additive_inverse'( a ), X ) ) ] )
% 0.88/1.31 .
% 0.88/1.31 clause( 5974, [ ~( sum( a, 'additive_inverse'( a ), 'additive_identity' ) )
% 0.88/1.31 ] )
% 0.88/1.31 .
% 0.88/1.31 clause( 5976, [ ~( sum( 'additive_inverse'( a ), a, 'additive_identity' ) )
% 0.88/1.31 ] )
% 0.88/1.31 .
% 0.88/1.31 clause( 5981, [] )
% 0.88/1.31 .
% 0.88/1.31
% 0.88/1.31
% 0.88/1.31 % SZS output end Refutation
% 0.88/1.31 found a proof!
% 0.88/1.31
% 0.88/1.31 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.88/1.31
% 0.88/1.31 initialclauses(
% 0.88/1.31 [ clause( 5983, [ sum( X, Y, Z ), ~( sum( X, T, U ) ), ~( sum( T, W, Y ) )
% 0.88/1.31 , ~( sum( U, W, Z ) ) ] )
% 0.88/1.31 , clause( 5984, [ sum( X, Y, Z ), ~( sum( T, U, X ) ), ~( sum( U, Y, W ) )
% 0.88/1.31 , ~( sum( T, W, Z ) ) ] )
% 0.88/1.31 , clause( 5985, [ sum( 'additive_identity', X, X ), ~( defined( X ) ) ] )
% 0.88/1.31 , clause( 5986, [ sum( 'additive_inverse'( X ), X, 'additive_identity' ),
% 0.88/1.31 ~( defined( X ) ) ] )
% 0.88/1.31 , clause( 5987, [ sum( X, Y, Z ), ~( sum( Y, X, Z ) ) ] )
% 0.88/1.31 , clause( 5988, [ product( X, Y, Z ), ~( product( X, T, U ) ), ~( product(
% 0.88/1.31 T, W, Y ) ), ~( product( U, W, Z ) ) ] )
% 0.88/1.31 , clause( 5989, [ product( X, Y, Z ), ~( product( T, U, X ) ), ~( product(
% 0.88/1.31 U, Y, W ) ), ~( product( T, W, Z ) ) ] )
% 0.88/1.31 , clause( 5990, [ product( 'multiplicative_identity', X, X ), ~( defined( X
% 0.88/1.31 ) ) ] )
% 0.88/1.31 , clause( 5991, [ product( 'multiplicative_inverse'( X ), X,
% 0.88/1.31 'multiplicative_identity' ), sum( 'additive_identity', X,
% 0.88/1.31 'additive_identity' ), ~( defined( X ) ) ] )
% 0.88/1.31 , clause( 5992, [ product( X, Y, Z ), ~( product( Y, X, Z ) ) ] )
% 0.88/1.31 , clause( 5993, [ sum( X, Y, Z ), ~( sum( T, U, W ) ), ~( product( W, V0, Z
% 0.88/1.31 ) ), ~( product( T, V0, X ) ), ~( product( U, V0, Y ) ) ] )
% 0.88/1.31 , clause( 5994, [ product( X, Y, Z ), ~( sum( T, U, X ) ), ~( product( T, Y
% 0.88/1.31 , W ) ), ~( product( U, Y, V0 ) ), ~( sum( W, V0, Z ) ) ] )
% 0.88/1.31 , clause( 5995, [ defined( add( X, Y ) ), ~( defined( X ) ), ~( defined( Y
% 0.88/1.31 ) ) ] )
% 0.88/1.31 , clause( 5996, [ defined( 'additive_identity' ) ] )
% 0.88/1.31 , clause( 5997, [ defined( 'additive_inverse'( X ) ), ~( defined( X ) ) ]
% 0.88/1.31 )
% 0.88/1.31 , clause( 5998, [ defined( multiply( X, Y ) ), ~( defined( X ) ), ~(
% 0.88/1.31 defined( Y ) ) ] )
% 0.88/1.31 , clause( 5999, [ defined( 'multiplicative_identity' ) ] )
% 0.88/1.31 , clause( 6000, [ defined( 'multiplicative_inverse'( X ) ), ~( defined( X )
% 0.88/1.31 ), sum( 'additive_identity', X, 'additive_identity' ) ] )
% 0.88/1.31 , clause( 6001, [ sum( X, Y, add( X, Y ) ), ~( defined( X ) ), ~( defined(
% 0.88/1.31 Y ) ) ] )
% 0.88/1.31 , clause( 6002, [ product( X, Y, multiply( X, Y ) ), ~( defined( X ) ), ~(
% 0.88/1.31 defined( Y ) ) ] )
% 0.88/1.31 , clause( 6003, [ sum( 'additive_identity', X, Y ), ~( 'less_or_equal'( X,
% 0.88/1.31 Y ) ), ~( 'less_or_equal'( Y, X ) ) ] )
% 0.88/1.31 , clause( 6004, [ 'less_or_equal'( X, Y ), ~( 'less_or_equal'( X, Z ) ),
% 0.88/1.31 ~( 'less_or_equal'( Z, Y ) ) ] )
% 0.88/1.31 , clause( 6005, [ 'less_or_equal'( X, Y ), 'less_or_equal'( Y, X ), ~(
% 0.88/1.31 defined( X ) ), ~( defined( Y ) ) ] )
% 0.88/1.31 , clause( 6006, [ 'less_or_equal'( X, Y ), ~( 'less_or_equal'( Z, T ) ),
% 0.88/1.31 ~( sum( Z, U, X ) ), ~( sum( T, U, Y ) ) ] )
% 0.88/1.31 , clause( 6007, [ 'less_or_equal'( 'additive_identity', X ), ~(
% 0.88/1.31 'less_or_equal'( 'additive_identity', Y ) ), ~( 'less_or_equal'(
% 0.88/1.31 'additive_identity', Z ) ), ~( product( Y, Z, X ) ) ] )
% 0.88/1.31 , clause( 6008, [ ~( sum( 'additive_identity', 'additive_identity',
% 0.88/1.31 'multiplicative_identity' ) ) ] )
% 0.88/1.31 , clause( 6009, [ defined( a ) ] )
% 0.88/1.31 , clause( 6010, [ sum( 'additive_identity', a, 'additive_identity' ) ] )
% 0.88/1.31 , clause( 6011, [ ~( sum( 'additive_identity', 'additive_inverse'( a ),
% 0.88/1.31 'additive_identity' ) ) ] )
% 0.88/1.31 ] ).
% 0.88/1.31
% 0.88/1.31
% 0.88/1.31
% 0.88/1.31 subsumption(
% 0.88/1.31 clause( 0, [ ~( sum( X, T, U ) ), ~( sum( T, W, Y ) ), ~( sum( U, W, Z ) )
% 0.88/1.31 , sum( X, Y, Z ) ] )
% 0.88/1.31 , clause( 5983, [ sum( X, Y, Z ), ~( sum( X, T, U ) ), ~( sum( T, W, Y ) )
% 0.88/1.31 , ~( sum( U, W, Z ) ) ] )
% 0.88/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.88/1.31 , U ), :=( W, W )] ), permutation( 0, [ ==>( 0, 3 ), ==>( 1, 0 ), ==>( 2
% 0.88/1.31 , 1 ), ==>( 3, 2 )] ) ).
% 0.88/1.31
% 0.88/1.31
% 0.88/1.31 subsumption(
% 0.88/1.31 clause( 1, [ ~( sum( T, U, X ) ), ~( sum( U, Y, W ) ), ~( sum( T, W, Z ) )
% 0.88/1.31 , sum( X, Y, Z ) ] )
% 0.88/1.31 , clause( 5984, [ sum( X, Y, Z ), ~( sum( T, U, X ) ), ~( sum( U, Y, W ) )
% 0.88/1.31 , ~( sum( T, W, Z ) ) ] )
% 0.88/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.88/1.31 , U ), :=( W, W )] ), permutation( 0, [ ==>( 0, 3 ), ==>( 1, 0 ), ==>( 2
% 0.88/1.31 , 1 ), ==>( 3, 2 )] ) ).
% 0.88/1.31
% 0.88/1.31
% 0.88/1.31 subsumption(
% 0.88/1.31 clause( 2, [ ~( defined( X ) ), sum( 'additive_identity', X, X ) ] )
% 0.88/1.31 , clause( 5985, [ sum( 'additive_identity', X, X ), ~( defined( X ) ) ] )
% 0.88/1.31 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1,
% 0.88/1.31 0 )] ) ).
% 0.88/1.31
% 0.88/1.31
% 0.88/1.31 subsumption(
% 0.88/1.31 clause( 3, [ ~( defined( X ) ), sum( 'additive_inverse'( X ), X,
% 0.88/1.31 'additive_identity' ) ] )
% 0.88/1.31 , clause( 5986, [ sum( 'additive_inverse'( X ), X, 'additive_identity' ),
% 0.88/1.31 ~( defined( X ) ) ] )
% 0.88/1.31 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1,
% 0.88/1.31 0 )] ) ).
% 0.88/1.31
% 0.88/1.31
% 0.88/1.31 subsumption(
% 0.88/1.31 clause( 4, [ ~( sum( Y, X, Z ) ), sum( X, Y, Z ) ] )
% 0.88/1.31 , clause( 5987, [ sum( X, Y, Z ), ~( sum( Y, X, Z ) ) ] )
% 0.88/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.88/1.31 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 0.88/1.31
% 0.88/1.31
% 0.88/1.31 subsumption(
% 0.88/1.31 clause( 13, [ defined( 'additive_identity' ) ] )
% 0.88/1.31 , clause( 5996, [ defined( 'additive_identity' ) ] )
% 0.88/1.31 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.31
% 0.88/1.31
% 0.88/1.31 subsumption(
% 0.88/1.31 clause( 26, [ defined( a ) ] )
% 0.88/1.31 , clause( 6009, [ defined( a ) ] )
% 0.88/1.31 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.31
% 0.88/1.31
% 0.88/1.31 subsumption(
% 0.88/1.31 clause( 27, [ sum( 'additive_identity', a, 'additive_identity' ) ] )
% 0.88/1.31 , clause( 6010, [ sum( 'additive_identity', a, 'additive_identity' ) ] )
% 0.88/1.31 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.31
% 0.88/1.31
% 0.88/1.31 subsumption(
% 0.88/1.31 clause( 28, [ ~( sum( 'additive_identity', 'additive_inverse'( a ),
% 0.88/1.31 'additive_identity' ) ) ] )
% 0.88/1.31 , clause( 6011, [ ~( sum( 'additive_identity', 'additive_inverse'( a ),
% 0.88/1.31 'additive_identity' ) ) ] )
% 0.88/1.31 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.31
% 0.88/1.31
% 0.88/1.31 resolution(
% 0.88/1.31 clause( 6171, [ ~( sum( a, X, Y ) ), ~( sum( 'additive_identity', X, Z ) )
% 0.88/1.31 , sum( 'additive_identity', Y, Z ) ] )
% 0.88/1.31 , clause( 0, [ ~( sum( X, T, U ) ), ~( sum( T, W, Y ) ), ~( sum( U, W, Z )
% 0.88/1.31 ), sum( X, Y, Z ) ] )
% 0.88/1.31 , 0, clause( 27, [ sum( 'additive_identity', a, 'additive_identity' ) ] )
% 0.88/1.31 , 0, substitution( 0, [ :=( X, 'additive_identity' ), :=( Y, Y ), :=( Z, Z
% 0.88/1.31 ), :=( T, a ), :=( U, 'additive_identity' ), :=( W, X )] ),
% 0.88/1.31 substitution( 1, [] )).
% 0.88/1.31
% 0.88/1.31
% 0.88/1.31 subsumption(
% 0.88/1.31 clause( 56, [ ~( sum( 'additive_identity', X, Z ) ), sum(
% 0.88/1.31 'additive_identity', Y, Z ), ~( sum( a, X, Y ) ) ] )
% 0.88/1.31 , clause( 6171, [ ~( sum( a, X, Y ) ), ~( sum( 'additive_identity', X, Z )
% 0.88/1.31 ), sum( 'additive_identity', Y, Z ) ] )
% 0.88/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.88/1.31 permutation( 0, [ ==>( 0, 2 ), ==>( 1, 0 ), ==>( 2, 1 )] ) ).
% 0.88/1.31
% 0.88/1.31
% 0.88/1.31 resolution(
% 0.88/1.31 clause( 6175, [ ~( sum( X, Y, 'additive_identity' ) ), ~( sum( Y,
% 0.88/1.31 'additive_inverse'( a ), Z ) ), ~( sum( X, Z, 'additive_identity' ) ) ]
% 0.88/1.31 )
% 0.88/1.31 , clause( 28, [ ~( sum( 'additive_identity', 'additive_inverse'( a ),
% 0.88/1.31 'additive_identity' ) ) ] )
% 0.88/1.31 , 0, clause( 1, [ ~( sum( T, U, X ) ), ~( sum( U, Y, W ) ), ~( sum( T, W, Z
% 0.88/1.31 ) ), sum( X, Y, Z ) ] )
% 0.88/1.31 , 3, substitution( 0, [] ), substitution( 1, [ :=( X, 'additive_identity' )
% 0.88/1.31 , :=( Y, 'additive_inverse'( a ) ), :=( Z, 'additive_identity' ), :=( T,
% 0.88/1.31 X ), :=( U, Y ), :=( W, Z )] )).
% 0.88/1.31
% 0.88/1.31
% 0.88/1.31 subsumption(
% 0.88/1.31 clause( 71, [ ~( sum( Y, 'additive_inverse'( a ), Z ) ), ~( sum( X, Z,
% 0.88/1.31 'additive_identity' ) ), ~( sum( X, Y, 'additive_identity' ) ) ] )
% 0.88/1.31 , clause( 6175, [ ~( sum( X, Y, 'additive_identity' ) ), ~( sum( Y,
% 0.88/1.31 'additive_inverse'( a ), Z ) ), ~( sum( X, Z, 'additive_identity' ) ) ]
% 0.88/1.31 )
% 0.88/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.88/1.31 permutation( 0, [ ==>( 0, 2 ), ==>( 1, 0 ), ==>( 2, 1 )] ) ).
% 0.88/1.31
% 0.88/1.31
% 0.88/1.31 resolution(
% 0.88/1.31 clause( 6178, [ ~( sum( a, X, Y ) ), ~( sum( 'additive_identity', Y, Z ) )
% 0.88/1.31 , sum( 'additive_identity', X, Z ) ] )
% 0.88/1.31 , clause( 1, [ ~( sum( T, U, X ) ), ~( sum( U, Y, W ) ), ~( sum( T, W, Z )
% 0.88/1.31 ), sum( X, Y, Z ) ] )
% 0.88/1.31 , 0, clause( 27, [ sum( 'additive_identity', a, 'additive_identity' ) ] )
% 0.88/1.31 , 0, substitution( 0, [ :=( X, 'additive_identity' ), :=( Y, X ), :=( Z, Z
% 0.88/1.31 ), :=( T, 'additive_identity' ), :=( U, a ), :=( W, Y )] ),
% 0.88/1.31 substitution( 1, [] )).
% 0.88/1.31
% 0.88/1.31
% 0.88/1.31 subsumption(
% 0.88/1.31 clause( 79, [ ~( sum( 'additive_identity', Y, Z ) ), sum(
% 0.88/1.31 'additive_identity', X, Z ), ~( sum( a, X, Y ) ) ] )
% 0.88/1.31 , clause( 6178, [ ~( sum( a, X, Y ) ), ~( sum( 'additive_identity', Y, Z )
% 0.88/1.31 ), sum( 'additive_identity', X, Z ) ] )
% 0.88/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.88/1.31 permutation( 0, [ ==>( 0, 2 ), ==>( 1, 0 ), ==>( 2, 1 )] ) ).
% 0.88/1.31
% 0.88/1.31
% 0.88/1.31 factor(
% 0.88/1.31 clause( 6184, [ ~( sum( X, 'additive_inverse'( a ), X ) ), ~( sum( Y, X,
% 0.88/1.31 'additive_identity' ) ) ] )
% 0.88/1.31 , clause( 71, [ ~( sum( Y, 'additive_inverse'( a ), Z ) ), ~( sum( X, Z,
% 0.88/1.31 'additive_identity' ) ), ~( sum( X, Y, 'additive_identity' ) ) ] )
% 0.88/1.31 , 1, 2, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, X )] )).
% 0.88/1.31
% 0.88/1.31
% 0.88/1.31 subsumption(
% 0.88/1.31 clause( 85, [ ~( sum( Y, X, 'additive_identity' ) ), ~( sum( X,
% 0.88/1.31 'additive_inverse'( a ), X ) ) ] )
% 0.88/1.31 , clause( 6184, [ ~( sum( X, 'additive_inverse'( a ), X ) ), ~( sum( Y, X,
% 0.88/1.31 'additive_identity' ) ) ] )
% 0.88/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 1
% 0.88/1.31 ), ==>( 1, 0 )] ) ).
% 0.88/1.31
% 0.88/1.31
% 0.88/1.31 resolution(
% 0.88/1.31 clause( 6185, [ sum( X, 'additive_identity', X ), ~( defined( X ) ) ] )
% 0.88/1.31 , clause( 4, [ ~( sum( Y, X, Z ) ), sum( X, Y, Z ) ] )
% 0.88/1.31 , 0, clause( 2, [ ~( defined( X ) ), sum( 'additive_identity', X, X ) ] )
% 0.88/1.31 , 1, substitution( 0, [ :=( X, X ), :=( Y, 'additive_identity' ), :=( Z, X
% 0.88/1.31 )] ), substitution( 1, [ :=( X, X )] )).
% 0.88/1.31
% 0.88/1.31
% 0.88/1.31 subsumption(
% 0.88/1.31 clause( 133, [ ~( defined( X ) ), sum( X, 'additive_identity', X ) ] )
% 0.88/1.31 , clause( 6185, [ sum( X, 'additive_identity', X ), ~( defined( X ) ) ] )
% 0.88/1.31 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1,
% 0.88/1.31 0 )] ) ).
% 0.88/1.31
% 0.88/1.31
% 0.88/1.31 resolution(
% 0.88/1.31 clause( 6186, [ sum( 'additive_identity', X, 'additive_identity' ), ~( sum(
% 0.88/1.31 a, X, 'additive_identity' ) ), ~( defined( 'additive_identity' ) ) ] )
% 0.88/1.31 , clause( 79, [ ~( sum( 'additive_identity', Y, Z ) ), sum(
% 0.88/1.31 'additive_identity', X, Z ), ~( sum( a, X, Y ) ) ] )
% 0.88/1.31 , 0, clause( 133, [ ~( defined( X ) ), sum( X, 'additive_identity', X ) ]
% 0.88/1.31 )
% 0.88/1.31 , 1, substitution( 0, [ :=( X, X ), :=( Y, 'additive_identity' ), :=( Z,
% 0.88/1.31 'additive_identity' )] ), substitution( 1, [ :=( X, 'additive_identity' )] )
% 0.88/1.31 ).
% 0.88/1.31
% 0.88/1.31
% 0.88/1.31 resolution(
% 0.88/1.31 clause( 6188, [ sum( 'additive_identity', X, 'additive_identity' ), ~( sum(
% 0.88/1.31 a, X, 'additive_identity' ) ) ] )
% 0.88/1.31 , clause( 6186, [ sum( 'additive_identity', X, 'additive_identity' ), ~(
% 0.88/1.31 sum( a, X, 'additive_identity' ) ), ~( defined( 'additive_identity' ) ) ]
% 0.88/1.31 )
% 0.88/1.31 , 2, clause( 13, [ defined( 'additive_identity' ) ] )
% 0.88/1.31 , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [] )).
% 0.88/1.31
% 0.88/1.31
% 0.88/1.31 subsumption(
% 0.88/1.31 clause( 5443, [ sum( 'additive_identity', X, 'additive_identity' ), ~( sum(
% 0.88/1.31 a, X, 'additive_identity' ) ) ] )
% 0.88/1.31 , clause( 6188, [ sum( 'additive_identity', X, 'additive_identity' ), ~(
% 0.88/1.31 sum( a, X, 'additive_identity' ) ) ] )
% 0.88/1.31 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 0.88/1.31 1 )] ) ).
% 0.88/1.31
% 0.88/1.31
% 0.88/1.31 resolution(
% 0.88/1.31 clause( 6189, [ ~( sum( X, 'additive_inverse'( a ), X ) ), ~( sum(
% 0.88/1.31 'additive_identity', Y, 'additive_identity' ) ), ~( sum( a, Y, X ) ) ] )
% 0.88/1.31 , clause( 85, [ ~( sum( Y, X, 'additive_identity' ) ), ~( sum( X,
% 0.88/1.31 'additive_inverse'( a ), X ) ) ] )
% 0.88/1.31 , 0, clause( 56, [ ~( sum( 'additive_identity', X, Z ) ), sum(
% 0.88/1.31 'additive_identity', Y, Z ), ~( sum( a, X, Y ) ) ] )
% 0.88/1.31 , 1, substitution( 0, [ :=( X, X ), :=( Y, 'additive_identity' )] ),
% 0.88/1.31 substitution( 1, [ :=( X, Y ), :=( Y, X ), :=( Z, 'additive_identity' )] )
% 0.88/1.31 ).
% 0.88/1.31
% 0.88/1.31
% 0.88/1.31 subsumption(
% 0.88/1.31 clause( 5966, [ ~( sum( 'additive_identity', Y, 'additive_identity' ) ),
% 0.88/1.31 ~( sum( a, Y, X ) ), ~( sum( X, 'additive_inverse'( a ), X ) ) ] )
% 0.88/1.31 , clause( 6189, [ ~( sum( X, 'additive_inverse'( a ), X ) ), ~( sum(
% 0.88/1.31 'additive_identity', Y, 'additive_identity' ) ), ~( sum( a, Y, X ) ) ] )
% 0.88/1.31 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 2
% 0.88/1.31 ), ==>( 1, 0 ), ==>( 2, 1 )] ) ).
% 0.88/1.31
% 0.88/1.31
% 0.88/1.31 factor(
% 0.88/1.31 clause( 6194, [ ~( sum( 'additive_identity', 'additive_inverse'( a ),
% 0.88/1.31 'additive_identity' ) ), ~( sum( a, 'additive_inverse'( a ),
% 0.88/1.32 'additive_identity' ) ) ] )
% 0.88/1.32 , clause( 5966, [ ~( sum( 'additive_identity', Y, 'additive_identity' ) ),
% 0.88/1.32 ~( sum( a, Y, X ) ), ~( sum( X, 'additive_inverse'( a ), X ) ) ] )
% 0.88/1.32 , 0, 2, substitution( 0, [ :=( X, 'additive_identity' ), :=( Y,
% 0.88/1.32 'additive_inverse'( a ) )] )).
% 0.88/1.32
% 0.88/1.32
% 0.88/1.32 resolution(
% 0.88/1.32 clause( 6196, [ ~( sum( a, 'additive_inverse'( a ), 'additive_identity' ) )
% 0.88/1.32 , ~( sum( a, 'additive_inverse'( a ), 'additive_identity' ) ) ] )
% 0.88/1.32 , clause( 6194, [ ~( sum( 'additive_identity', 'additive_inverse'( a ),
% 0.88/1.32 'additive_identity' ) ), ~( sum( a, 'additive_inverse'( a ),
% 0.88/1.32 'additive_identity' ) ) ] )
% 0.88/1.32 , 0, clause( 5443, [ sum( 'additive_identity', X, 'additive_identity' ),
% 0.88/1.32 ~( sum( a, X, 'additive_identity' ) ) ] )
% 0.88/1.32 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, 'additive_inverse'( a
% 0.88/1.32 ) )] )).
% 0.88/1.32
% 0.88/1.32
% 0.88/1.32 factor(
% 0.88/1.32 clause( 6197, [ ~( sum( a, 'additive_inverse'( a ), 'additive_identity' ) )
% 0.88/1.32 ] )
% 0.88/1.32 , clause( 6196, [ ~( sum( a, 'additive_inverse'( a ), 'additive_identity' )
% 0.88/1.32 ), ~( sum( a, 'additive_inverse'( a ), 'additive_identity' ) ) ] )
% 0.88/1.32 , 0, 1, substitution( 0, [] )).
% 0.88/1.32
% 0.88/1.32
% 0.88/1.32 subsumption(
% 0.88/1.32 clause( 5974, [ ~( sum( a, 'additive_inverse'( a ), 'additive_identity' ) )
% 0.88/1.32 ] )
% 0.88/1.32 , clause( 6197, [ ~( sum( a, 'additive_inverse'( a ), 'additive_identity' )
% 0.88/1.32 ) ] )
% 0.88/1.32 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.32
% 0.88/1.32
% 0.88/1.32 resolution(
% 0.88/1.32 clause( 6198, [ ~( sum( 'additive_inverse'( a ), a, 'additive_identity' ) )
% 0.88/1.32 ] )
% 0.88/1.32 , clause( 5974, [ ~( sum( a, 'additive_inverse'( a ), 'additive_identity' )
% 0.88/1.32 ) ] )
% 0.88/1.32 , 0, clause( 4, [ ~( sum( Y, X, Z ) ), sum( X, Y, Z ) ] )
% 0.88/1.32 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, a ), :=( Y,
% 0.88/1.32 'additive_inverse'( a ) ), :=( Z, 'additive_identity' )] )).
% 0.88/1.32
% 0.88/1.32
% 0.88/1.32 subsumption(
% 0.88/1.32 clause( 5976, [ ~( sum( 'additive_inverse'( a ), a, 'additive_identity' ) )
% 0.88/1.32 ] )
% 0.88/1.32 , clause( 6198, [ ~( sum( 'additive_inverse'( a ), a, 'additive_identity' )
% 0.88/1.32 ) ] )
% 0.88/1.32 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.88/1.32
% 0.88/1.32
% 0.88/1.32 resolution(
% 0.88/1.32 clause( 6199, [ ~( defined( a ) ) ] )
% 0.88/1.32 , clause( 5976, [ ~( sum( 'additive_inverse'( a ), a, 'additive_identity' )
% 0.88/1.32 ) ] )
% 0.88/1.32 , 0, clause( 3, [ ~( defined( X ) ), sum( 'additive_inverse'( X ), X,
% 0.88/1.32 'additive_identity' ) ] )
% 0.88/1.32 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, a )] )).
% 0.88/1.32
% 0.88/1.32
% 0.88/1.32 resolution(
% 0.88/1.32 clause( 6200, [] )
% 0.88/1.32 , clause( 6199, [ ~( defined( a ) ) ] )
% 0.88/1.32 , 0, clause( 26, [ defined( a ) ] )
% 0.88/1.32 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.88/1.32
% 0.88/1.32
% 0.88/1.32 subsumption(
% 0.88/1.32 clause( 5981, [] )
% 0.88/1.32 , clause( 6200, [] )
% 0.88/1.32 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.88/1.32
% 0.88/1.32
% 0.88/1.32 end.
% 0.88/1.32
% 0.88/1.32 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.88/1.32
% 0.88/1.32 Memory use:
% 0.88/1.32
% 0.88/1.32 space for terms: 56485
% 0.88/1.32 space for clauses: 291438
% 0.88/1.32
% 0.88/1.32
% 0.88/1.32 clauses generated: 10409
% 0.88/1.32 clauses kept: 5982
% 0.88/1.32 clauses selected: 348
% 0.88/1.32 clauses deleted: 6
% 0.88/1.32 clauses inuse deleted: 1
% 0.88/1.32
% 0.88/1.32 subsentry: 33719
% 0.88/1.32 literals s-matched: 11734
% 0.88/1.32 literals matched: 10906
% 0.88/1.32 full subsumption: 8698
% 0.88/1.32
% 0.88/1.32 checksum: -607895072
% 0.88/1.32
% 0.88/1.32
% 0.88/1.32 Bliksem ended
%------------------------------------------------------------------------------