TSTP Solution File: RNG001-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : RNG001-1 : 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 20:16:02 EDT 2022
% Result : Unsatisfiable 0.75s 1.16s
% Output : Refutation 0.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : RNG001-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Mon May 30 16:05:10 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.75/1.16 *** allocated 10000 integers for termspace/termends
% 0.75/1.16 *** allocated 10000 integers for clauses
% 0.75/1.16 *** allocated 10000 integers for justifications
% 0.75/1.16 Bliksem 1.12
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 Automatic Strategy Selection
% 0.75/1.16
% 0.75/1.16 Clauses:
% 0.75/1.16 [
% 0.75/1.16 [ sum( 'additive_identity', X, X ) ],
% 0.75/1.16 [ sum( X, 'additive_identity', X ) ],
% 0.75/1.16 [ product( X, Y, multiply( X, Y ) ) ],
% 0.75/1.16 [ sum( X, Y, add( X, Y ) ) ],
% 0.75/1.16 [ sum( 'additive_inverse'( X ), X, 'additive_identity' ) ],
% 0.75/1.16 [ sum( X, 'additive_inverse'( X ), 'additive_identity' ) ],
% 0.75/1.16 [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( Z, T, W ) ), sum( X
% 0.75/1.16 , U, W ) ],
% 0.75/1.16 [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( X, U, W ) ), sum( Z
% 0.75/1.16 , T, W ) ],
% 0.75/1.16 [ ~( sum( X, Y, Z ) ), sum( Y, X, Z ) ],
% 0.75/1.16 [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~( product( Z, T, W
% 0.75/1.16 ) ), product( X, U, W ) ],
% 0.75/1.16 [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~( product( X, U, W
% 0.75/1.16 ) ), product( Z, T, W ) ],
% 0.75/1.16 [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum( Y, T, W ) )
% 0.75/1.16 , ~( product( X, W, V0 ) ), sum( Z, U, V0 ) ],
% 0.75/1.16 [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum( Y, T, W ) )
% 0.75/1.16 , ~( sum( Z, U, V0 ) ), product( X, W, V0 ) ],
% 0.75/1.16 [ ~( product( X, Y, Z ) ), ~( product( T, Y, U ) ), ~( sum( X, T, W ) )
% 0.75/1.16 , ~( product( W, Y, V0 ) ), sum( Z, U, V0 ) ],
% 0.75/1.16 [ ~( product( X, Y, Z ) ), ~( product( T, Y, U ) ), ~( sum( X, T, W ) )
% 0.75/1.16 , ~( sum( Z, U, V0 ) ), product( W, Y, V0 ) ],
% 0.75/1.16 [ ~( sum( X, Y, Z ) ), ~( sum( X, Y, T ) ), =( Z, T ) ],
% 0.75/1.16 [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z, T ) ],
% 0.75/1.16 [ ~( product( a, 'additive_identity', 'additive_identity' ) ) ]
% 0.75/1.16 ] .
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 percentage equality = 0.039216, percentage horn = 1.000000
% 0.75/1.16 This is a problem with some equality
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 Options Used:
% 0.75/1.16
% 0.75/1.16 useres = 1
% 0.75/1.16 useparamod = 1
% 0.75/1.16 useeqrefl = 1
% 0.75/1.16 useeqfact = 1
% 0.75/1.16 usefactor = 1
% 0.75/1.16 usesimpsplitting = 0
% 0.75/1.16 usesimpdemod = 5
% 0.75/1.16 usesimpres = 3
% 0.75/1.16
% 0.75/1.16 resimpinuse = 1000
% 0.75/1.16 resimpclauses = 20000
% 0.75/1.16 substype = eqrewr
% 0.75/1.16 backwardsubs = 1
% 0.75/1.16 selectoldest = 5
% 0.75/1.16
% 0.75/1.16 litorderings [0] = split
% 0.75/1.16 litorderings [1] = extend the termordering, first sorting on arguments
% 0.75/1.16
% 0.75/1.16 termordering = kbo
% 0.75/1.16
% 0.75/1.16 litapriori = 0
% 0.75/1.16 termapriori = 1
% 0.75/1.16 litaposteriori = 0
% 0.75/1.16 termaposteriori = 0
% 0.75/1.16 demodaposteriori = 0
% 0.75/1.16 ordereqreflfact = 0
% 0.75/1.16
% 0.75/1.16 litselect = negord
% 0.75/1.16
% 0.75/1.16 maxweight = 15
% 0.75/1.16 maxdepth = 30000
% 0.75/1.16 maxlength = 115
% 0.75/1.16 maxnrvars = 195
% 0.75/1.16 excuselevel = 1
% 0.75/1.16 increasemaxweight = 1
% 0.75/1.16
% 0.75/1.16 maxselected = 10000000
% 0.75/1.16 maxnrclauses = 10000000
% 0.75/1.16
% 0.75/1.16 showgenerated = 0
% 0.75/1.16 showkept = 0
% 0.75/1.16 showselected = 0
% 0.75/1.16 showdeleted = 0
% 0.75/1.16 showresimp = 1
% 0.75/1.16 showstatus = 2000
% 0.75/1.16
% 0.75/1.16 prologoutput = 1
% 0.75/1.16 nrgoals = 5000000
% 0.75/1.16 totalproof = 1
% 0.75/1.16
% 0.75/1.16 Symbols occurring in the translation:
% 0.75/1.16
% 0.75/1.16 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.75/1.16 . [1, 2] (w:1, o:27, a:1, s:1, b:0),
% 0.75/1.16 ! [4, 1] (w:0, o:21, a:1, s:1, b:0),
% 0.75/1.16 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.75/1.16 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.75/1.16 'additive_identity' [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.75/1.16 sum [41, 3] (w:1, o:54, a:1, s:1, b:0),
% 0.75/1.16 multiply [43, 2] (w:1, o:52, a:1, s:1, b:0),
% 0.75/1.16 product [44, 3] (w:1, o:55, a:1, s:1, b:0),
% 0.75/1.16 add [45, 2] (w:1, o:53, a:1, s:1, b:0),
% 0.75/1.16 'additive_inverse' [46, 1] (w:1, o:26, a:1, s:1, b:0),
% 0.75/1.16 a [55, 0] (w:1, o:20, a:1, s:1, b:0).
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 Starting Search:
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 Bliksems!, er is een bewijs:
% 0.75/1.16 % SZS status Unsatisfiable
% 0.75/1.16 % SZS output start Refutation
% 0.75/1.16
% 0.75/1.16 clause( 0, [ sum( 'additive_identity', X, X ) ] )
% 0.75/1.16 .
% 0.75/1.16 clause( 1, [ sum( X, 'additive_identity', X ) ] )
% 0.75/1.16 .
% 0.75/1.16 clause( 2, [ product( X, Y, multiply( X, Y ) ) ] )
% 0.75/1.16 .
% 0.75/1.16 clause( 5, [ sum( X, 'additive_inverse'( X ), 'additive_identity' ) ] )
% 0.75/1.16 .
% 0.75/1.16 clause( 6, [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( Z, T, W ) )
% 0.75/1.16 , sum( X, U, W ) ] )
% 0.75/1.16 .
% 0.75/1.16 clause( 11, [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum( Y,
% 0.75/1.16 T, W ) ), ~( product( X, W, V0 ) ), sum( Z, U, V0 ) ] )
% 0.75/1.16 .
% 0.75/1.16 clause( 12, [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum( Y,
% 0.75/1.16 T, W ) ), ~( sum( Z, U, V0 ) ), product( X, W, V0 ) ] )
% 0.75/1.16 .
% 0.75/1.16 clause( 15, [ ~( sum( X, Y, Z ) ), ~( sum( X, Y, T ) ), =( Z, T ) ] )
% 0.75/1.16 .
% 0.75/1.16 clause( 17, [ ~( product( a, 'additive_identity', 'additive_identity' ) ) ]
% 0.75/1.16 )
% 0.75/1.16 .
% 0.75/1.16 clause( 19, [ ~( sum( X, Y, Y ) ), ~( sum( Y, Z, T ) ), sum( X, T, T ) ] )
% 0.75/1.16 .
% 0.75/1.16 clause( 228, [ ~( product( X, Y, Z ) ), ~( product( X, 'additive_identity'
% 0.75/1.16 , T ) ), ~( product( X, Y, U ) ), sum( Z, T, U ) ] )
% 0.75/1.16 .
% 0.75/1.16 clause( 231, [ ~( product( X, 'additive_identity', Y ) ), ~( product( X,
% 0.75/1.16 'additive_identity', Z ) ), sum( Y, Z, Z ) ] )
% 0.75/1.16 .
% 0.75/1.16 clause( 232, [ ~( product( X, 'additive_identity', Y ) ), sum( Y, Y, Y ) ]
% 0.75/1.16 )
% 0.75/1.16 .
% 0.75/1.16 clause( 240, [ sum( multiply( X, 'additive_identity' ), multiply( X,
% 0.75/1.16 'additive_identity' ), multiply( X, 'additive_identity' ) ) ] )
% 0.75/1.16 .
% 0.75/1.16 clause( 281, [ ~( product( a, X, Y ) ), ~( product( a, Z, T ) ), ~( sum( X
% 0.75/1.16 , Z, 'additive_identity' ) ), ~( sum( Y, T, 'additive_identity' ) ) ] )
% 0.75/1.16 .
% 0.75/1.16 clause( 289, [ ~( product( a, X, X ) ), ~( product( a, Y, Y ) ), ~( sum( X
% 0.75/1.16 , Y, 'additive_identity' ) ) ] )
% 0.75/1.16 .
% 0.75/1.16 clause( 290, [ ~( product( a, X, X ) ), ~( sum( X, X, 'additive_identity' )
% 0.75/1.16 ) ] )
% 0.75/1.16 .
% 0.75/1.16 clause( 466, [ ~( sum( X, 'additive_identity', Y ) ), =( X, Y ) ] )
% 0.75/1.16 .
% 0.75/1.16 clause( 716, [ ~( sum( X, Y, Y ) ), sum( X, 'additive_identity',
% 0.75/1.16 'additive_identity' ) ] )
% 0.75/1.16 .
% 0.75/1.16 clause( 726, [ sum( multiply( X, 'additive_identity' ), 'additive_identity'
% 0.75/1.16 , 'additive_identity' ) ] )
% 0.75/1.16 .
% 0.75/1.16 clause( 806, [ =( multiply( X, 'additive_identity' ), 'additive_identity' )
% 0.75/1.16 ] )
% 0.75/1.16 .
% 0.75/1.16 clause( 824, [ product( X, 'additive_identity', 'additive_identity' ) ] )
% 0.75/1.16 .
% 0.75/1.16 clause( 825, [] )
% 0.75/1.16 .
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 % SZS output end Refutation
% 0.75/1.16 found a proof!
% 0.75/1.16
% 0.75/1.16 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.75/1.16
% 0.75/1.16 initialclauses(
% 0.75/1.16 [ clause( 827, [ sum( 'additive_identity', X, X ) ] )
% 0.75/1.16 , clause( 828, [ sum( X, 'additive_identity', X ) ] )
% 0.75/1.16 , clause( 829, [ product( X, Y, multiply( X, Y ) ) ] )
% 0.75/1.16 , clause( 830, [ sum( X, Y, add( X, Y ) ) ] )
% 0.75/1.16 , clause( 831, [ sum( 'additive_inverse'( X ), X, 'additive_identity' ) ]
% 0.75/1.16 )
% 0.75/1.16 , clause( 832, [ sum( X, 'additive_inverse'( X ), 'additive_identity' ) ]
% 0.75/1.16 )
% 0.75/1.16 , clause( 833, [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( Z, T, W
% 0.75/1.16 ) ), sum( X, U, W ) ] )
% 0.75/1.16 , clause( 834, [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( X, U, W
% 0.75/1.16 ) ), sum( Z, T, W ) ] )
% 0.75/1.16 , clause( 835, [ ~( sum( X, Y, Z ) ), sum( Y, X, Z ) ] )
% 0.75/1.16 , clause( 836, [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~(
% 0.75/1.16 product( Z, T, W ) ), product( X, U, W ) ] )
% 0.75/1.16 , clause( 837, [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~(
% 0.75/1.16 product( X, U, W ) ), product( Z, T, W ) ] )
% 0.75/1.16 , clause( 838, [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum(
% 0.75/1.16 Y, T, W ) ), ~( product( X, W, V0 ) ), sum( Z, U, V0 ) ] )
% 0.75/1.16 , clause( 839, [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum(
% 0.75/1.16 Y, T, W ) ), ~( sum( Z, U, V0 ) ), product( X, W, V0 ) ] )
% 0.75/1.16 , clause( 840, [ ~( product( X, Y, Z ) ), ~( product( T, Y, U ) ), ~( sum(
% 0.75/1.16 X, T, W ) ), ~( product( W, Y, V0 ) ), sum( Z, U, V0 ) ] )
% 0.75/1.16 , clause( 841, [ ~( product( X, Y, Z ) ), ~( product( T, Y, U ) ), ~( sum(
% 0.75/1.16 X, T, W ) ), ~( sum( Z, U, V0 ) ), product( W, Y, V0 ) ] )
% 0.75/1.16 , clause( 842, [ ~( sum( X, Y, Z ) ), ~( sum( X, Y, T ) ), =( Z, T ) ] )
% 0.75/1.16 , clause( 843, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z, T
% 0.75/1.16 ) ] )
% 0.75/1.16 , clause( 844, [ ~( product( a, 'additive_identity', 'additive_identity' )
% 0.75/1.16 ) ] )
% 0.75/1.16 ] ).
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 subsumption(
% 0.75/1.16 clause( 0, [ sum( 'additive_identity', X, X ) ] )
% 0.75/1.16 , clause( 827, [ sum( 'additive_identity', X, X ) ] )
% 0.75/1.16 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 subsumption(
% 0.75/1.16 clause( 1, [ sum( X, 'additive_identity', X ) ] )
% 0.75/1.16 , clause( 828, [ sum( X, 'additive_identity', X ) ] )
% 0.75/1.16 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 subsumption(
% 0.75/1.16 clause( 2, [ product( X, Y, multiply( X, Y ) ) ] )
% 0.75/1.16 , clause( 829, [ product( X, Y, multiply( X, Y ) ) ] )
% 0.75/1.16 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.75/1.16 )] ) ).
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 subsumption(
% 0.75/1.16 clause( 5, [ sum( X, 'additive_inverse'( X ), 'additive_identity' ) ] )
% 0.75/1.16 , clause( 832, [ sum( X, 'additive_inverse'( X ), 'additive_identity' ) ]
% 0.75/1.16 )
% 0.75/1.16 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 subsumption(
% 0.75/1.16 clause( 6, [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( Z, T, W ) )
% 0.75/1.16 , sum( X, U, W ) ] )
% 0.75/1.16 , clause( 833, [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( Z, T, W
% 0.75/1.16 ) ), sum( X, U, W ) ] )
% 0.75/1.16 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.75/1.16 , U ), :=( W, W )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2
% 0.75/1.16 , 2 ), ==>( 3, 3 )] ) ).
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 subsumption(
% 0.75/1.16 clause( 11, [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum( Y,
% 0.75/1.16 T, W ) ), ~( product( X, W, V0 ) ), sum( Z, U, V0 ) ] )
% 0.75/1.16 , clause( 838, [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum(
% 0.75/1.16 Y, T, W ) ), ~( product( X, W, V0 ) ), sum( Z, U, V0 ) ] )
% 0.75/1.16 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.75/1.16 , U ), :=( W, W ), :=( V0, V0 )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1
% 0.75/1.16 , 1 ), ==>( 2, 2 ), ==>( 3, 3 ), ==>( 4, 4 )] ) ).
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 subsumption(
% 0.75/1.16 clause( 12, [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum( Y,
% 0.75/1.16 T, W ) ), ~( sum( Z, U, V0 ) ), product( X, W, V0 ) ] )
% 0.75/1.16 , clause( 839, [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum(
% 0.75/1.16 Y, T, W ) ), ~( sum( Z, U, V0 ) ), product( X, W, V0 ) ] )
% 0.75/1.16 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.75/1.16 , U ), :=( W, W ), :=( V0, V0 )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1
% 0.75/1.16 , 1 ), ==>( 2, 2 ), ==>( 3, 3 ), ==>( 4, 4 )] ) ).
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 subsumption(
% 0.75/1.16 clause( 15, [ ~( sum( X, Y, Z ) ), ~( sum( X, Y, T ) ), =( Z, T ) ] )
% 0.75/1.16 , clause( 842, [ ~( sum( X, Y, Z ) ), ~( sum( X, Y, T ) ), =( Z, T ) ] )
% 0.75/1.16 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.75/1.16 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 subsumption(
% 0.75/1.16 clause( 17, [ ~( product( a, 'additive_identity', 'additive_identity' ) ) ]
% 0.75/1.16 )
% 0.75/1.16 , clause( 844, [ ~( product( a, 'additive_identity', 'additive_identity' )
% 0.75/1.16 ) ] )
% 0.75/1.16 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 factor(
% 0.75/1.16 clause( 957, [ ~( sum( X, Y, Y ) ), ~( sum( Y, Z, T ) ), sum( X, T, T ) ]
% 0.75/1.16 )
% 0.75/1.16 , clause( 6, [ ~( sum( X, Y, Z ) ), ~( sum( Y, T, U ) ), ~( sum( Z, T, W )
% 0.75/1.16 ), sum( X, U, W ) ] )
% 0.75/1.16 , 1, 2, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Y ), :=( T, Z ),
% 0.75/1.16 :=( U, T ), :=( W, T )] )).
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 subsumption(
% 0.75/1.16 clause( 19, [ ~( sum( X, Y, Y ) ), ~( sum( Y, Z, T ) ), sum( X, T, T ) ] )
% 0.75/1.16 , clause( 957, [ ~( sum( X, Y, Y ) ), ~( sum( Y, Z, T ) ), sum( X, T, T ) ]
% 0.75/1.16 )
% 0.75/1.16 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.75/1.16 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 resolution(
% 0.75/1.16 clause( 959, [ ~( product( X, Y, Z ) ), ~( product( X, 'additive_identity'
% 0.75/1.16 , T ) ), ~( product( X, Y, U ) ), sum( Z, T, U ) ] )
% 0.75/1.16 , clause( 11, [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum( Y
% 0.75/1.16 , T, W ) ), ~( product( X, W, V0 ) ), sum( Z, U, V0 ) ] )
% 0.75/1.16 , 2, clause( 1, [ sum( X, 'additive_identity', X ) ] )
% 0.75/1.16 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T,
% 0.75/1.16 'additive_identity' ), :=( U, T ), :=( W, Y ), :=( V0, U )] ),
% 0.75/1.16 substitution( 1, [ :=( X, Y )] )).
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 subsumption(
% 0.75/1.16 clause( 228, [ ~( product( X, Y, Z ) ), ~( product( X, 'additive_identity'
% 0.75/1.16 , T ) ), ~( product( X, Y, U ) ), sum( Z, T, U ) ] )
% 0.75/1.16 , clause( 959, [ ~( product( X, Y, Z ) ), ~( product( X,
% 0.75/1.16 'additive_identity', T ) ), ~( product( X, Y, U ) ), sum( Z, T, U ) ] )
% 0.75/1.16 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.75/1.16 , U )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 ), ==>( 3
% 0.75/1.16 , 3 )] ) ).
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 factor(
% 0.75/1.16 clause( 966, [ ~( product( X, 'additive_identity', Y ) ), ~( product( X,
% 0.75/1.16 'additive_identity', Z ) ), sum( Y, Z, Z ) ] )
% 0.75/1.16 , clause( 228, [ ~( product( X, Y, Z ) ), ~( product( X,
% 0.75/1.16 'additive_identity', T ) ), ~( product( X, Y, U ) ), sum( Z, T, U ) ] )
% 0.75/1.16 , 1, 2, substitution( 0, [ :=( X, X ), :=( Y, 'additive_identity' ), :=( Z
% 0.75/1.16 , Y ), :=( T, Z ), :=( U, Z )] )).
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 subsumption(
% 0.75/1.16 clause( 231, [ ~( product( X, 'additive_identity', Y ) ), ~( product( X,
% 0.75/1.16 'additive_identity', Z ) ), sum( Y, Z, Z ) ] )
% 0.75/1.16 , clause( 966, [ ~( product( X, 'additive_identity', Y ) ), ~( product( X,
% 0.75/1.16 'additive_identity', Z ) ), sum( Y, Z, Z ) ] )
% 0.75/1.16 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.75/1.16 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 factor(
% 0.75/1.16 clause( 968, [ ~( product( X, 'additive_identity', Y ) ), sum( Y, Y, Y ) ]
% 0.75/1.16 )
% 0.75/1.16 , clause( 231, [ ~( product( X, 'additive_identity', Y ) ), ~( product( X,
% 0.75/1.16 'additive_identity', Z ) ), sum( Y, Z, Z ) ] )
% 0.75/1.16 , 0, 1, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Y )] )).
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 subsumption(
% 0.75/1.16 clause( 232, [ ~( product( X, 'additive_identity', Y ) ), sum( Y, Y, Y ) ]
% 0.75/1.16 )
% 0.75/1.16 , clause( 968, [ ~( product( X, 'additive_identity', Y ) ), sum( Y, Y, Y )
% 0.75/1.16 ] )
% 0.75/1.16 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.75/1.16 ), ==>( 1, 1 )] ) ).
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 resolution(
% 0.75/1.16 clause( 969, [ sum( multiply( X, 'additive_identity' ), multiply( X,
% 0.75/1.16 'additive_identity' ), multiply( X, 'additive_identity' ) ) ] )
% 0.75/1.16 , clause( 232, [ ~( product( X, 'additive_identity', Y ) ), sum( Y, Y, Y )
% 0.75/1.16 ] )
% 0.75/1.16 , 0, clause( 2, [ product( X, Y, multiply( X, Y ) ) ] )
% 0.75/1.16 , 0, substitution( 0, [ :=( X, X ), :=( Y, multiply( X, 'additive_identity'
% 0.75/1.16 ) )] ), substitution( 1, [ :=( X, X ), :=( Y, 'additive_identity' )] )
% 0.75/1.16 ).
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 subsumption(
% 0.75/1.16 clause( 240, [ sum( multiply( X, 'additive_identity' ), multiply( X,
% 0.75/1.16 'additive_identity' ), multiply( X, 'additive_identity' ) ) ] )
% 0.75/1.16 , clause( 969, [ sum( multiply( X, 'additive_identity' ), multiply( X,
% 0.75/1.16 'additive_identity' ), multiply( X, 'additive_identity' ) ) ] )
% 0.75/1.16 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 resolution(
% 0.75/1.16 clause( 970, [ ~( product( a, X, Y ) ), ~( product( a, Z, T ) ), ~( sum( X
% 0.75/1.16 , Z, 'additive_identity' ) ), ~( sum( Y, T, 'additive_identity' ) ) ] )
% 0.75/1.16 , clause( 17, [ ~( product( a, 'additive_identity', 'additive_identity' ) )
% 0.75/1.16 ] )
% 0.75/1.16 , 0, clause( 12, [ ~( product( X, Y, Z ) ), ~( product( X, T, U ) ), ~( sum(
% 0.75/1.16 Y, T, W ) ), ~( sum( Z, U, V0 ) ), product( X, W, V0 ) ] )
% 0.75/1.16 , 4, substitution( 0, [] ), substitution( 1, [ :=( X, a ), :=( Y, X ), :=(
% 0.75/1.16 Z, Y ), :=( T, Z ), :=( U, T ), :=( W, 'additive_identity' ), :=( V0,
% 0.75/1.16 'additive_identity' )] )).
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 subsumption(
% 0.75/1.16 clause( 281, [ ~( product( a, X, Y ) ), ~( product( a, Z, T ) ), ~( sum( X
% 0.75/1.16 , Z, 'additive_identity' ) ), ~( sum( Y, T, 'additive_identity' ) ) ] )
% 0.75/1.16 , clause( 970, [ ~( product( a, X, Y ) ), ~( product( a, Z, T ) ), ~( sum(
% 0.75/1.16 X, Z, 'additive_identity' ) ), ~( sum( Y, T, 'additive_identity' ) ) ] )
% 0.75/1.16 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.75/1.16 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 ), ==>( 3, 3 )] )
% 0.75/1.16 ).
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 factor(
% 0.75/1.16 clause( 975, [ ~( product( a, X, X ) ), ~( product( a, Y, Y ) ), ~( sum( X
% 0.75/1.16 , Y, 'additive_identity' ) ) ] )
% 0.75/1.16 , clause( 281, [ ~( product( a, X, Y ) ), ~( product( a, Z, T ) ), ~( sum(
% 0.75/1.16 X, Z, 'additive_identity' ) ), ~( sum( Y, T, 'additive_identity' ) ) ] )
% 0.75/1.16 , 2, 3, substitution( 0, [ :=( X, X ), :=( Y, X ), :=( Z, Y ), :=( T, Y )] )
% 0.75/1.16 ).
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 subsumption(
% 0.75/1.16 clause( 289, [ ~( product( a, X, X ) ), ~( product( a, Y, Y ) ), ~( sum( X
% 0.75/1.16 , Y, 'additive_identity' ) ) ] )
% 0.75/1.16 , clause( 975, [ ~( product( a, X, X ) ), ~( product( a, Y, Y ) ), ~( sum(
% 0.75/1.16 X, Y, 'additive_identity' ) ) ] )
% 0.75/1.16 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.75/1.16 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 factor(
% 0.75/1.16 clause( 977, [ ~( product( a, X, X ) ), ~( sum( X, X, 'additive_identity' )
% 0.75/1.16 ) ] )
% 0.75/1.16 , clause( 289, [ ~( product( a, X, X ) ), ~( product( a, Y, Y ) ), ~( sum(
% 0.75/1.16 X, Y, 'additive_identity' ) ) ] )
% 0.75/1.16 , 0, 1, substitution( 0, [ :=( X, X ), :=( Y, X )] )).
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 subsumption(
% 0.75/1.16 clause( 290, [ ~( product( a, X, X ) ), ~( sum( X, X, 'additive_identity' )
% 0.75/1.16 ) ] )
% 0.75/1.16 , clause( 977, [ ~( product( a, X, X ) ), ~( sum( X, X, 'additive_identity'
% 0.75/1.16 ) ) ] )
% 0.75/1.16 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 0.75/1.16 1 )] ) ).
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 resolution(
% 0.75/1.16 clause( 978, [ ~( sum( X, 'additive_identity', Y ) ), =( X, Y ) ] )
% 0.75/1.16 , clause( 15, [ ~( sum( X, Y, Z ) ), ~( sum( X, Y, T ) ), =( Z, T ) ] )
% 0.75/1.16 , 0, clause( 1, [ sum( X, 'additive_identity', X ) ] )
% 0.75/1.16 , 0, substitution( 0, [ :=( X, X ), :=( Y, 'additive_identity' ), :=( Z, X
% 0.75/1.16 ), :=( T, Y )] ), substitution( 1, [ :=( X, X )] )).
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 subsumption(
% 0.75/1.16 clause( 466, [ ~( sum( X, 'additive_identity', Y ) ), =( X, Y ) ] )
% 0.75/1.16 , clause( 978, [ ~( sum( X, 'additive_identity', Y ) ), =( X, Y ) ] )
% 0.75/1.16 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.75/1.16 ), ==>( 1, 1 )] ) ).
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 resolution(
% 0.75/1.16 clause( 980, [ ~( sum( X, Y, Y ) ), sum( X, 'additive_identity',
% 0.75/1.16 'additive_identity' ) ] )
% 0.75/1.16 , clause( 19, [ ~( sum( X, Y, Y ) ), ~( sum( Y, Z, T ) ), sum( X, T, T ) ]
% 0.75/1.16 )
% 0.75/1.16 , 1, clause( 5, [ sum( X, 'additive_inverse'( X ), 'additive_identity' ) ]
% 0.75/1.16 )
% 0.75/1.16 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, 'additive_inverse'(
% 0.75/1.16 Y ) ), :=( T, 'additive_identity' )] ), substitution( 1, [ :=( X, Y )] )
% 0.75/1.16 ).
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 subsumption(
% 0.75/1.16 clause( 716, [ ~( sum( X, Y, Y ) ), sum( X, 'additive_identity',
% 0.75/1.16 'additive_identity' ) ] )
% 0.75/1.16 , clause( 980, [ ~( sum( X, Y, Y ) ), sum( X, 'additive_identity',
% 0.75/1.16 'additive_identity' ) ] )
% 0.75/1.16 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.75/1.16 ), ==>( 1, 1 )] ) ).
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 resolution(
% 0.75/1.16 clause( 981, [ sum( multiply( X, 'additive_identity' ), 'additive_identity'
% 0.75/1.16 , 'additive_identity' ) ] )
% 0.75/1.16 , clause( 716, [ ~( sum( X, Y, Y ) ), sum( X, 'additive_identity',
% 0.75/1.16 'additive_identity' ) ] )
% 0.75/1.16 , 0, clause( 240, [ sum( multiply( X, 'additive_identity' ), multiply( X,
% 0.75/1.16 'additive_identity' ), multiply( X, 'additive_identity' ) ) ] )
% 0.75/1.16 , 0, substitution( 0, [ :=( X, multiply( X, 'additive_identity' ) ), :=( Y
% 0.75/1.16 , multiply( X, 'additive_identity' ) )] ), substitution( 1, [ :=( X, X )] )
% 0.75/1.16 ).
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 subsumption(
% 0.75/1.16 clause( 726, [ sum( multiply( X, 'additive_identity' ), 'additive_identity'
% 0.75/1.16 , 'additive_identity' ) ] )
% 0.75/1.16 , clause( 981, [ sum( multiply( X, 'additive_identity' ),
% 0.75/1.16 'additive_identity', 'additive_identity' ) ] )
% 0.75/1.16 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 eqswap(
% 0.75/1.16 clause( 982, [ =( Y, X ), ~( sum( X, 'additive_identity', Y ) ) ] )
% 0.75/1.16 , clause( 466, [ ~( sum( X, 'additive_identity', Y ) ), =( X, Y ) ] )
% 0.75/1.16 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 resolution(
% 0.75/1.16 clause( 983, [ =( 'additive_identity', multiply( X, 'additive_identity' ) )
% 0.75/1.16 ] )
% 0.75/1.16 , clause( 982, [ =( Y, X ), ~( sum( X, 'additive_identity', Y ) ) ] )
% 0.75/1.16 , 1, clause( 726, [ sum( multiply( X, 'additive_identity' ),
% 0.75/1.16 'additive_identity', 'additive_identity' ) ] )
% 0.75/1.16 , 0, substitution( 0, [ :=( X, multiply( X, 'additive_identity' ) ), :=( Y
% 0.75/1.16 , 'additive_identity' )] ), substitution( 1, [ :=( X, X )] )).
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 eqswap(
% 0.75/1.16 clause( 984, [ =( multiply( X, 'additive_identity' ), 'additive_identity' )
% 0.75/1.16 ] )
% 0.75/1.16 , clause( 983, [ =( 'additive_identity', multiply( X, 'additive_identity' )
% 0.75/1.16 ) ] )
% 0.75/1.16 , 0, substitution( 0, [ :=( X, X )] )).
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 subsumption(
% 0.75/1.16 clause( 806, [ =( multiply( X, 'additive_identity' ), 'additive_identity' )
% 0.75/1.16 ] )
% 0.75/1.16 , clause( 984, [ =( multiply( X, 'additive_identity' ), 'additive_identity'
% 0.75/1.16 ) ] )
% 0.75/1.16 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 paramod(
% 0.75/1.16 clause( 986, [ product( X, 'additive_identity', 'additive_identity' ) ] )
% 0.75/1.16 , clause( 806, [ =( multiply( X, 'additive_identity' ), 'additive_identity'
% 0.75/1.16 ) ] )
% 0.75/1.16 , 0, clause( 2, [ product( X, Y, multiply( X, Y ) ) ] )
% 0.75/1.16 , 0, 3, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 0.75/1.16 :=( Y, 'additive_identity' )] )).
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 subsumption(
% 0.75/1.16 clause( 824, [ product( X, 'additive_identity', 'additive_identity' ) ] )
% 0.75/1.16 , clause( 986, [ product( X, 'additive_identity', 'additive_identity' ) ]
% 0.75/1.16 )
% 0.75/1.16 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 resolution(
% 0.75/1.16 clause( 987, [ ~( sum( 'additive_identity', 'additive_identity',
% 0.75/1.16 'additive_identity' ) ) ] )
% 0.75/1.16 , clause( 290, [ ~( product( a, X, X ) ), ~( sum( X, X, 'additive_identity'
% 0.75/1.16 ) ) ] )
% 0.75/1.16 , 0, clause( 824, [ product( X, 'additive_identity', 'additive_identity' )
% 0.75/1.16 ] )
% 0.75/1.16 , 0, substitution( 0, [ :=( X, 'additive_identity' )] ), substitution( 1, [
% 0.75/1.16 :=( X, a )] )).
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 resolution(
% 0.75/1.16 clause( 988, [] )
% 0.75/1.16 , clause( 987, [ ~( sum( 'additive_identity', 'additive_identity',
% 0.75/1.16 'additive_identity' ) ) ] )
% 0.75/1.16 , 0, clause( 0, [ sum( 'additive_identity', X, X ) ] )
% 0.75/1.16 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, 'additive_identity' )] )
% 0.75/1.16 ).
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 subsumption(
% 0.75/1.16 clause( 825, [] )
% 0.75/1.16 , clause( 988, [] )
% 0.75/1.16 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 end.
% 0.75/1.16
% 0.75/1.16 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.75/1.16
% 0.75/1.16 Memory use:
% 0.75/1.16
% 0.75/1.16 space for terms: 14478
% 0.75/1.16 space for clauses: 36101
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 clauses generated: 3922
% 0.75/1.16 clauses kept: 826
% 0.75/1.16 clauses selected: 65
% 0.75/1.16 clauses deleted: 8
% 0.75/1.16 clauses inuse deleted: 0
% 0.75/1.16
% 0.75/1.16 subsentry: 46098
% 0.75/1.16 literals s-matched: 17508
% 0.75/1.16 literals matched: 16628
% 0.75/1.16 full subsumption: 14219
% 0.75/1.16
% 0.75/1.16 checksum: -1109926917
% 0.75/1.16
% 0.75/1.16
% 0.75/1.16 Bliksem ended
%------------------------------------------------------------------------------