TSTP Solution File: GRP123-2.003 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GRP123-2.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n022.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 07:34:59 EDT 2022
% Result : Unsatisfiable 0.42s 1.05s
% Output : Refutation 0.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP123-2.003 : TPTP v8.1.0. Released v1.2.0.
% 0.03/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n022.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 Jun 13 06:43:18 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.42/1.05 *** allocated 10000 integers for termspace/termends
% 0.42/1.05 *** allocated 10000 integers for clauses
% 0.42/1.05 *** allocated 10000 integers for justifications
% 0.42/1.05 Bliksem 1.12
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 Automatic Strategy Selection
% 0.42/1.05
% 0.42/1.05 Clauses:
% 0.42/1.05 [
% 0.42/1.05 [ next( 'e_1', 'e_2' ) ],
% 0.42/1.05 [ next( 'e_2', 'e_3' ) ],
% 0.42/1.05 [ greater( 'e_2', 'e_1' ) ],
% 0.42/1.05 [ greater( 'e_3', 'e_1' ) ],
% 0.42/1.05 [ greater( 'e_3', 'e_2' ) ],
% 0.42/1.05 [ ~( product( X, 'e_1', Y ) ), ~( next( X, Z ) ), ~( greater( Y, Z ) ) ]
% 0.42/1.05 ,
% 0.42/1.05 [ 'group_element'( 'e_1' ) ],
% 0.42/1.05 [ 'group_element'( 'e_2' ) ],
% 0.42/1.05 [ 'group_element'( 'e_3' ) ],
% 0.42/1.05 [ ~( equalish( 'e_1', 'e_2' ) ) ],
% 0.42/1.05 [ ~( equalish( 'e_1', 'e_3' ) ) ],
% 0.42/1.05 [ ~( equalish( 'e_2', 'e_1' ) ) ],
% 0.42/1.05 [ ~( equalish( 'e_2', 'e_3' ) ) ],
% 0.42/1.05 [ ~( equalish( 'e_3', 'e_1' ) ) ],
% 0.42/1.05 [ ~( equalish( 'e_3', 'e_2' ) ) ],
% 0.42/1.05 [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ), product( X, Y,
% 0.42/1.05 'e_1' ), product( X, Y, 'e_2' ), product( X, Y, 'e_3' ) ],
% 0.42/1.05 [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), equalish( Z, T ) ]
% 0.42/1.05 ,
% 0.42/1.05 [ ~( product( X, Y, Z ) ), ~( product( X, T, Z ) ), equalish( Y, T ) ]
% 0.42/1.05 ,
% 0.42/1.05 [ ~( product( X, Y, Z ) ), ~( product( T, Y, Z ) ), equalish( X, T ) ]
% 0.42/1.05 ,
% 0.42/1.05 [ product( X, X, X ) ],
% 0.42/1.05 [ ~( product( X, Y, Z ) ), ~( product( T, U, Z ) ), ~( product( W, Y, X
% 0.42/1.05 ) ), ~( product( W, U, T ) ), equalish( X, T ) ],
% 0.42/1.05 [ ~( product( X, Y, Z ) ), ~( product( T, U, Z ) ), ~( product( W, Y, X
% 0.42/1.05 ) ), ~( product( W, U, T ) ), equalish( Y, U ) ]
% 0.42/1.05 ] .
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 percentage equality = 0.000000, percentage horn = 0.954545
% 0.42/1.05 This is a near-Horn, non-equality problem
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 Options Used:
% 0.42/1.05
% 0.42/1.05 useres = 1
% 0.42/1.05 useparamod = 0
% 0.42/1.05 useeqrefl = 0
% 0.42/1.05 useeqfact = 0
% 0.42/1.05 usefactor = 1
% 0.42/1.05 usesimpsplitting = 0
% 0.42/1.05 usesimpdemod = 0
% 0.42/1.05 usesimpres = 4
% 0.42/1.05
% 0.42/1.05 resimpinuse = 1000
% 0.42/1.05 resimpclauses = 20000
% 0.42/1.05 substype = standard
% 0.42/1.05 backwardsubs = 1
% 0.42/1.05 selectoldest = 5
% 0.42/1.05
% 0.42/1.05 litorderings [0] = split
% 0.42/1.05 litorderings [1] = liftord
% 0.42/1.05
% 0.42/1.05 termordering = none
% 0.42/1.05
% 0.42/1.05 litapriori = 1
% 0.42/1.05 termapriori = 0
% 0.42/1.05 litaposteriori = 0
% 0.42/1.05 termaposteriori = 0
% 0.42/1.05 demodaposteriori = 0
% 0.42/1.05 ordereqreflfact = 0
% 0.42/1.05
% 0.42/1.05 litselect = negative
% 0.42/1.05
% 0.42/1.05 maxweight = 30000
% 0.42/1.05 maxdepth = 30000
% 0.42/1.05 maxlength = 115
% 0.42/1.05 maxnrvars = 195
% 0.42/1.05 excuselevel = 0
% 0.42/1.05 increasemaxweight = 0
% 0.42/1.05
% 0.42/1.05 maxselected = 10000000
% 0.42/1.05 maxnrclauses = 10000000
% 0.42/1.05
% 0.42/1.05 showgenerated = 0
% 0.42/1.05 showkept = 0
% 0.42/1.05 showselected = 0
% 0.42/1.05 showdeleted = 0
% 0.42/1.05 showresimp = 1
% 0.42/1.05 showstatus = 2000
% 0.42/1.05
% 0.42/1.05 prologoutput = 1
% 0.42/1.05 nrgoals = 5000000
% 0.42/1.05 totalproof = 1
% 0.42/1.05
% 0.42/1.05 Symbols occurring in the translation:
% 0.42/1.05
% 0.42/1.05 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.42/1.05 . [1, 2] (w:1, o:28, a:1, s:1, b:0),
% 0.42/1.05 ! [4, 1] (w:1, o:22, a:1, s:1, b:0),
% 0.42/1.05 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.42/1.05 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.42/1.05 'e_1' [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.42/1.05 'e_2' [40, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.42/1.05 next [41, 2] (w:1, o:53, a:1, s:1, b:0),
% 0.42/1.05 'e_3' [42, 0] (w:1, o:11, a:1, s:1, b:0),
% 0.42/1.05 greater [43, 2] (w:1, o:54, a:1, s:1, b:0),
% 0.42/1.05 product [46, 3] (w:1, o:56, a:1, s:1, b:0),
% 0.42/1.05 'group_element' [48, 1] (w:1, o:27, a:1, s:1, b:0),
% 0.42/1.05 equalish [49, 2] (w:1, o:55, a:1, s:1, b:0).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 Starting Search:
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 Bliksems!, er is een bewijs:
% 0.42/1.05 % SZS status Unsatisfiable
% 0.42/1.05 % SZS output start Refutation
% 0.42/1.05
% 0.42/1.05 clause( 6, [ 'group_element'( 'e_1' ) ] )
% 0.42/1.05 .
% 0.42/1.05 clause( 7, [ 'group_element'( 'e_2' ) ] )
% 0.42/1.05 .
% 0.42/1.05 clause( 8, [ 'group_element'( 'e_3' ) ] )
% 0.42/1.05 .
% 0.42/1.05 clause( 9, [ ~( equalish( 'e_1', 'e_2' ) ) ] )
% 0.42/1.05 .
% 0.42/1.05 clause( 10, [ ~( equalish( 'e_1', 'e_3' ) ) ] )
% 0.42/1.05 .
% 0.42/1.05 clause( 12, [ ~( equalish( 'e_2', 'e_3' ) ) ] )
% 0.42/1.05 .
% 0.42/1.05 clause( 14, [ ~( equalish( 'e_3', 'e_2' ) ) ] )
% 0.42/1.05 .
% 0.42/1.05 clause( 15, [ ~( 'group_element'( X ) ), product( X, Y, 'e_3' ), product( X
% 0.42/1.05 , Y, 'e_1' ), product( X, Y, 'e_2' ), ~( 'group_element'( Y ) ) ] )
% 0.42/1.05 .
% 0.42/1.05 clause( 17, [ equalish( Y, T ), ~( product( X, Y, Z ) ), ~( product( X, T,
% 0.42/1.05 Z ) ) ] )
% 0.42/1.05 .
% 0.42/1.05 clause( 18, [ equalish( X, T ), ~( product( X, Y, Z ) ), ~( product( T, Y,
% 0.42/1.05 Z ) ) ] )
% 0.42/1.05 .
% 0.42/1.05 clause( 19, [ product( X, X, X ) ] )
% 0.42/1.05 .
% 0.42/1.05 clause( 20, [ equalish( X, T ), ~( product( W, Y, X ) ), ~( product( T, U,
% 0.42/1.05 Z ) ), ~( product( X, Y, Z ) ), ~( product( W, U, T ) ) ] )
% 0.42/1.05 .
% 0.42/1.05 clause( 26, [ equalish( X, Y ), ~( product( X, Z, X ) ), ~( product( X, T,
% 0.42/1.05 Y ) ), ~( product( Y, T, X ) ) ] )
% 0.42/1.05 .
% 0.42/1.05 clause( 34, [ product( X, 'e_2', 'e_3' ), product( X, 'e_2', 'e_1' ),
% 0.42/1.05 product( X, 'e_2', 'e_2' ), ~( 'group_element'( X ) ) ] )
% 0.42/1.05 .
% 0.42/1.05 clause( 37, [ equalish( X, Y ), ~( product( X, Y, Y ) ) ] )
% 0.42/1.05 .
% 0.42/1.05 clause( 39, [ equalish( X, Y ), ~( product( Y, X, Y ) ) ] )
% 0.42/1.05 .
% 0.42/1.05 clause( 59, [ product( 'e_1', 'e_2', 'e_1' ), product( 'e_1', 'e_2', 'e_2'
% 0.42/1.05 ), product( 'e_1', 'e_2', 'e_3' ) ] )
% 0.42/1.05 .
% 0.42/1.05 clause( 60, [ product( 'e_3', 'e_2', 'e_1' ), product( 'e_3', 'e_2', 'e_2'
% 0.42/1.05 ), product( 'e_3', 'e_2', 'e_3' ) ] )
% 0.42/1.05 .
% 0.42/1.05 clause( 69, [ product( 'e_3', 'e_2', 'e_1' ), product( 'e_3', 'e_2', 'e_2'
% 0.42/1.05 ) ] )
% 0.42/1.05 .
% 0.42/1.05 clause( 74, [ product( 'e_3', 'e_2', 'e_1' ) ] )
% 0.42/1.05 .
% 0.42/1.05 clause( 78, [ ~( product( 'e_1', 'e_2', 'e_3' ) ), ~( product( 'e_1', X,
% 0.42/1.05 'e_1' ) ) ] )
% 0.42/1.05 .
% 0.42/1.05 clause( 83, [ equalish( X, 'e_3' ), ~( product( X, 'e_2', 'e_1' ) ) ] )
% 0.42/1.05 .
% 0.42/1.05 clause( 86, [ ~( product( 'e_1', 'e_2', 'e_3' ) ) ] )
% 0.42/1.05 .
% 0.42/1.05 clause( 87, [ product( 'e_1', 'e_2', 'e_1' ), product( 'e_1', 'e_2', 'e_2'
% 0.42/1.05 ) ] )
% 0.42/1.05 .
% 0.42/1.05 clause( 92, [ product( 'e_1', 'e_2', 'e_1' ) ] )
% 0.42/1.05 .
% 0.42/1.05 clause( 94, [] )
% 0.42/1.05 .
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 % SZS output end Refutation
% 0.42/1.05 found a proof!
% 0.42/1.05
% 0.42/1.05 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.42/1.05
% 0.42/1.05 initialclauses(
% 0.42/1.05 [ clause( 96, [ next( 'e_1', 'e_2' ) ] )
% 0.42/1.05 , clause( 97, [ next( 'e_2', 'e_3' ) ] )
% 0.42/1.05 , clause( 98, [ greater( 'e_2', 'e_1' ) ] )
% 0.42/1.05 , clause( 99, [ greater( 'e_3', 'e_1' ) ] )
% 0.42/1.05 , clause( 100, [ greater( 'e_3', 'e_2' ) ] )
% 0.42/1.05 , clause( 101, [ ~( product( X, 'e_1', Y ) ), ~( next( X, Z ) ), ~( greater(
% 0.42/1.05 Y, Z ) ) ] )
% 0.42/1.05 , clause( 102, [ 'group_element'( 'e_1' ) ] )
% 0.42/1.05 , clause( 103, [ 'group_element'( 'e_2' ) ] )
% 0.42/1.05 , clause( 104, [ 'group_element'( 'e_3' ) ] )
% 0.42/1.05 , clause( 105, [ ~( equalish( 'e_1', 'e_2' ) ) ] )
% 0.42/1.05 , clause( 106, [ ~( equalish( 'e_1', 'e_3' ) ) ] )
% 0.42/1.05 , clause( 107, [ ~( equalish( 'e_2', 'e_1' ) ) ] )
% 0.42/1.05 , clause( 108, [ ~( equalish( 'e_2', 'e_3' ) ) ] )
% 0.42/1.05 , clause( 109, [ ~( equalish( 'e_3', 'e_1' ) ) ] )
% 0.42/1.05 , clause( 110, [ ~( equalish( 'e_3', 'e_2' ) ) ] )
% 0.42/1.05 , clause( 111, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ),
% 0.42/1.05 product( X, Y, 'e_1' ), product( X, Y, 'e_2' ), product( X, Y, 'e_3' ) ]
% 0.42/1.05 )
% 0.42/1.05 , clause( 112, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), equalish(
% 0.42/1.05 Z, T ) ] )
% 0.42/1.05 , clause( 113, [ ~( product( X, Y, Z ) ), ~( product( X, T, Z ) ), equalish(
% 0.42/1.05 Y, T ) ] )
% 0.42/1.05 , clause( 114, [ ~( product( X, Y, Z ) ), ~( product( T, Y, Z ) ), equalish(
% 0.42/1.05 X, T ) ] )
% 0.42/1.05 , clause( 115, [ product( X, X, X ) ] )
% 0.42/1.05 , clause( 116, [ ~( product( X, Y, Z ) ), ~( product( T, U, Z ) ), ~(
% 0.42/1.05 product( W, Y, X ) ), ~( product( W, U, T ) ), equalish( X, T ) ] )
% 0.42/1.05 , clause( 117, [ ~( product( X, Y, Z ) ), ~( product( T, U, Z ) ), ~(
% 0.42/1.05 product( W, Y, X ) ), ~( product( W, U, T ) ), equalish( Y, U ) ] )
% 0.42/1.05 ] ).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 subsumption(
% 0.42/1.05 clause( 6, [ 'group_element'( 'e_1' ) ] )
% 0.42/1.05 , clause( 102, [ 'group_element'( 'e_1' ) ] )
% 0.42/1.05 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 subsumption(
% 0.42/1.05 clause( 7, [ 'group_element'( 'e_2' ) ] )
% 0.42/1.05 , clause( 103, [ 'group_element'( 'e_2' ) ] )
% 0.42/1.05 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 subsumption(
% 0.42/1.05 clause( 8, [ 'group_element'( 'e_3' ) ] )
% 0.42/1.05 , clause( 104, [ 'group_element'( 'e_3' ) ] )
% 0.42/1.05 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 subsumption(
% 0.42/1.05 clause( 9, [ ~( equalish( 'e_1', 'e_2' ) ) ] )
% 0.42/1.05 , clause( 105, [ ~( equalish( 'e_1', 'e_2' ) ) ] )
% 0.42/1.05 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 subsumption(
% 0.42/1.05 clause( 10, [ ~( equalish( 'e_1', 'e_3' ) ) ] )
% 0.42/1.05 , clause( 106, [ ~( equalish( 'e_1', 'e_3' ) ) ] )
% 0.42/1.05 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 subsumption(
% 0.42/1.05 clause( 12, [ ~( equalish( 'e_2', 'e_3' ) ) ] )
% 0.42/1.05 , clause( 108, [ ~( equalish( 'e_2', 'e_3' ) ) ] )
% 0.42/1.05 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 subsumption(
% 0.42/1.05 clause( 14, [ ~( equalish( 'e_3', 'e_2' ) ) ] )
% 0.42/1.05 , clause( 110, [ ~( equalish( 'e_3', 'e_2' ) ) ] )
% 0.42/1.05 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 subsumption(
% 0.42/1.05 clause( 15, [ ~( 'group_element'( X ) ), product( X, Y, 'e_3' ), product( X
% 0.42/1.05 , Y, 'e_1' ), product( X, Y, 'e_2' ), ~( 'group_element'( Y ) ) ] )
% 0.42/1.05 , clause( 111, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ),
% 0.42/1.05 product( X, Y, 'e_1' ), product( X, Y, 'e_2' ), product( X, Y, 'e_3' ) ]
% 0.42/1.05 )
% 0.42/1.05 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.42/1.05 ), ==>( 1, 4 ), ==>( 2, 2 ), ==>( 3, 3 ), ==>( 4, 1 )] ) ).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 subsumption(
% 0.42/1.05 clause( 17, [ equalish( Y, T ), ~( product( X, Y, Z ) ), ~( product( X, T,
% 0.42/1.05 Z ) ) ] )
% 0.42/1.05 , clause( 113, [ ~( product( X, Y, Z ) ), ~( product( X, T, Z ) ), equalish(
% 0.42/1.05 Y, T ) ] )
% 0.42/1.05 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.42/1.05 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 2 ), ==>( 2, 0 )] ) ).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 subsumption(
% 0.42/1.05 clause( 18, [ equalish( X, T ), ~( product( X, Y, Z ) ), ~( product( T, Y,
% 0.42/1.05 Z ) ) ] )
% 0.42/1.05 , clause( 114, [ ~( product( X, Y, Z ) ), ~( product( T, Y, Z ) ), equalish(
% 0.42/1.05 X, T ) ] )
% 0.42/1.05 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.42/1.05 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 2 ), ==>( 2, 0 )] ) ).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 subsumption(
% 0.42/1.05 clause( 19, [ product( X, X, X ) ] )
% 0.42/1.05 , clause( 115, [ product( X, X, X ) ] )
% 0.42/1.05 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 subsumption(
% 0.42/1.05 clause( 20, [ equalish( X, T ), ~( product( W, Y, X ) ), ~( product( T, U,
% 0.42/1.05 Z ) ), ~( product( X, Y, Z ) ), ~( product( W, U, T ) ) ] )
% 0.42/1.05 , clause( 116, [ ~( product( X, Y, Z ) ), ~( product( T, U, Z ) ), ~(
% 0.42/1.05 product( W, Y, X ) ), ~( product( W, U, T ) ), equalish( X, T ) ] )
% 0.42/1.05 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.42/1.05 , U ), :=( W, W )] ), permutation( 0, [ ==>( 0, 3 ), ==>( 1, 2 ), ==>( 2
% 0.42/1.05 , 1 ), ==>( 3, 4 ), ==>( 4, 0 )] ) ).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 factor(
% 0.42/1.05 clause( 143, [ equalish( X, Y ), ~( product( X, Z, X ) ), ~( product( Y, T
% 0.42/1.05 , X ) ), ~( product( X, T, Y ) ) ] )
% 0.42/1.05 , clause( 20, [ equalish( X, T ), ~( product( W, Y, X ) ), ~( product( T, U
% 0.42/1.05 , Z ) ), ~( product( X, Y, Z ) ), ~( product( W, U, T ) ) ] )
% 0.42/1.05 , 1, 3, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, X ), :=( T, Y ),
% 0.42/1.05 :=( U, T ), :=( W, X )] )).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 subsumption(
% 0.42/1.05 clause( 26, [ equalish( X, Y ), ~( product( X, Z, X ) ), ~( product( X, T,
% 0.42/1.05 Y ) ), ~( product( Y, T, X ) ) ] )
% 0.42/1.05 , clause( 143, [ equalish( X, Y ), ~( product( X, Z, X ) ), ~( product( Y,
% 0.42/1.05 T, X ) ), ~( product( X, T, Y ) ) ] )
% 0.42/1.05 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.42/1.05 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 3 ), ==>( 3, 2 )] )
% 0.42/1.05 ).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 resolution(
% 0.42/1.05 clause( 151, [ ~( 'group_element'( X ) ), product( X, 'e_2', 'e_3' ),
% 0.42/1.05 product( X, 'e_2', 'e_1' ), product( X, 'e_2', 'e_2' ) ] )
% 0.42/1.05 , clause( 15, [ ~( 'group_element'( X ) ), product( X, Y, 'e_3' ), product(
% 0.42/1.05 X, Y, 'e_1' ), product( X, Y, 'e_2' ), ~( 'group_element'( Y ) ) ] )
% 0.42/1.05 , 4, clause( 7, [ 'group_element'( 'e_2' ) ] )
% 0.42/1.05 , 0, substitution( 0, [ :=( X, X ), :=( Y, 'e_2' )] ), substitution( 1, [] )
% 0.42/1.05 ).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 subsumption(
% 0.42/1.05 clause( 34, [ product( X, 'e_2', 'e_3' ), product( X, 'e_2', 'e_1' ),
% 0.42/1.05 product( X, 'e_2', 'e_2' ), ~( 'group_element'( X ) ) ] )
% 0.42/1.05 , clause( 151, [ ~( 'group_element'( X ) ), product( X, 'e_2', 'e_3' ),
% 0.42/1.05 product( X, 'e_2', 'e_1' ), product( X, 'e_2', 'e_2' ) ] )
% 0.42/1.05 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 3 ), ==>( 1,
% 0.42/1.05 0 ), ==>( 2, 1 ), ==>( 3, 2 )] ) ).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 resolution(
% 0.42/1.05 clause( 153, [ equalish( X, Y ), ~( product( X, Y, Y ) ) ] )
% 0.42/1.05 , clause( 18, [ equalish( X, T ), ~( product( X, Y, Z ) ), ~( product( T, Y
% 0.42/1.05 , Z ) ) ] )
% 0.42/1.05 , 2, clause( 19, [ product( X, X, X ) ] )
% 0.42/1.05 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Y ), :=( T, Y )] ),
% 0.42/1.05 substitution( 1, [ :=( X, Y )] )).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 subsumption(
% 0.42/1.05 clause( 37, [ equalish( X, Y ), ~( product( X, Y, Y ) ) ] )
% 0.42/1.05 , clause( 153, [ equalish( X, Y ), ~( product( X, Y, Y ) ) ] )
% 0.42/1.05 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.42/1.05 ), ==>( 1, 1 )] ) ).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 resolution(
% 0.42/1.05 clause( 155, [ equalish( X, Y ), ~( product( Y, X, Y ) ) ] )
% 0.42/1.05 , clause( 17, [ equalish( Y, T ), ~( product( X, Y, Z ) ), ~( product( X, T
% 0.42/1.05 , Z ) ) ] )
% 0.42/1.05 , 2, clause( 19, [ product( X, X, X ) ] )
% 0.42/1.05 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Y ), :=( T, Y )] ),
% 0.42/1.05 substitution( 1, [ :=( X, Y )] )).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 subsumption(
% 0.42/1.05 clause( 39, [ equalish( X, Y ), ~( product( Y, X, Y ) ) ] )
% 0.42/1.05 , clause( 155, [ equalish( X, Y ), ~( product( Y, X, Y ) ) ] )
% 0.42/1.05 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.42/1.05 ), ==>( 1, 1 )] ) ).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 resolution(
% 0.42/1.05 clause( 156, [ product( 'e_1', 'e_2', 'e_3' ), product( 'e_1', 'e_2', 'e_1'
% 0.42/1.05 ), product( 'e_1', 'e_2', 'e_2' ) ] )
% 0.42/1.05 , clause( 34, [ product( X, 'e_2', 'e_3' ), product( X, 'e_2', 'e_1' ),
% 0.42/1.05 product( X, 'e_2', 'e_2' ), ~( 'group_element'( X ) ) ] )
% 0.42/1.05 , 3, clause( 6, [ 'group_element'( 'e_1' ) ] )
% 0.42/1.05 , 0, substitution( 0, [ :=( X, 'e_1' )] ), substitution( 1, [] )).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 subsumption(
% 0.42/1.05 clause( 59, [ product( 'e_1', 'e_2', 'e_1' ), product( 'e_1', 'e_2', 'e_2'
% 0.42/1.05 ), product( 'e_1', 'e_2', 'e_3' ) ] )
% 0.42/1.05 , clause( 156, [ product( 'e_1', 'e_2', 'e_3' ), product( 'e_1', 'e_2',
% 0.42/1.05 'e_1' ), product( 'e_1', 'e_2', 'e_2' ) ] )
% 0.42/1.05 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 2 ), ==>( 1, 0 ), ==>( 2
% 0.42/1.05 , 1 )] ) ).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 resolution(
% 0.42/1.05 clause( 157, [ product( 'e_3', 'e_2', 'e_3' ), product( 'e_3', 'e_2', 'e_1'
% 0.42/1.05 ), product( 'e_3', 'e_2', 'e_2' ) ] )
% 0.42/1.05 , clause( 34, [ product( X, 'e_2', 'e_3' ), product( X, 'e_2', 'e_1' ),
% 0.42/1.05 product( X, 'e_2', 'e_2' ), ~( 'group_element'( X ) ) ] )
% 0.42/1.05 , 3, clause( 8, [ 'group_element'( 'e_3' ) ] )
% 0.42/1.05 , 0, substitution( 0, [ :=( X, 'e_3' )] ), substitution( 1, [] )).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 subsumption(
% 0.42/1.05 clause( 60, [ product( 'e_3', 'e_2', 'e_1' ), product( 'e_3', 'e_2', 'e_2'
% 0.42/1.05 ), product( 'e_3', 'e_2', 'e_3' ) ] )
% 0.42/1.05 , clause( 157, [ product( 'e_3', 'e_2', 'e_3' ), product( 'e_3', 'e_2',
% 0.42/1.05 'e_1' ), product( 'e_3', 'e_2', 'e_2' ) ] )
% 0.42/1.05 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 2 ), ==>( 1, 0 ), ==>( 2
% 0.42/1.05 , 1 )] ) ).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 resolution(
% 0.42/1.05 clause( 158, [ equalish( 'e_2', 'e_3' ), product( 'e_3', 'e_2', 'e_1' ),
% 0.42/1.05 product( 'e_3', 'e_2', 'e_2' ) ] )
% 0.42/1.05 , clause( 39, [ equalish( X, Y ), ~( product( Y, X, Y ) ) ] )
% 0.42/1.05 , 1, clause( 60, [ product( 'e_3', 'e_2', 'e_1' ), product( 'e_3', 'e_2',
% 0.42/1.05 'e_2' ), product( 'e_3', 'e_2', 'e_3' ) ] )
% 0.42/1.05 , 2, substitution( 0, [ :=( X, 'e_2' ), :=( Y, 'e_3' )] ), substitution( 1
% 0.42/1.05 , [] )).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 resolution(
% 0.42/1.05 clause( 159, [ product( 'e_3', 'e_2', 'e_1' ), product( 'e_3', 'e_2', 'e_2'
% 0.42/1.05 ) ] )
% 0.42/1.05 , clause( 12, [ ~( equalish( 'e_2', 'e_3' ) ) ] )
% 0.42/1.05 , 0, clause( 158, [ equalish( 'e_2', 'e_3' ), product( 'e_3', 'e_2', 'e_1'
% 0.42/1.05 ), product( 'e_3', 'e_2', 'e_2' ) ] )
% 0.42/1.05 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 subsumption(
% 0.42/1.05 clause( 69, [ product( 'e_3', 'e_2', 'e_1' ), product( 'e_3', 'e_2', 'e_2'
% 0.42/1.05 ) ] )
% 0.42/1.05 , clause( 159, [ product( 'e_3', 'e_2', 'e_1' ), product( 'e_3', 'e_2',
% 0.42/1.05 'e_2' ) ] )
% 0.42/1.05 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] )
% 0.42/1.05 ).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 resolution(
% 0.42/1.05 clause( 160, [ equalish( 'e_3', 'e_2' ), product( 'e_3', 'e_2', 'e_1' ) ]
% 0.42/1.05 )
% 0.42/1.05 , clause( 37, [ equalish( X, Y ), ~( product( X, Y, Y ) ) ] )
% 0.42/1.05 , 1, clause( 69, [ product( 'e_3', 'e_2', 'e_1' ), product( 'e_3', 'e_2',
% 0.42/1.05 'e_2' ) ] )
% 0.42/1.05 , 1, substitution( 0, [ :=( X, 'e_3' ), :=( Y, 'e_2' )] ), substitution( 1
% 0.42/1.05 , [] )).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 resolution(
% 0.42/1.05 clause( 161, [ product( 'e_3', 'e_2', 'e_1' ) ] )
% 0.42/1.05 , clause( 14, [ ~( equalish( 'e_3', 'e_2' ) ) ] )
% 0.42/1.05 , 0, clause( 160, [ equalish( 'e_3', 'e_2' ), product( 'e_3', 'e_2', 'e_1'
% 0.42/1.05 ) ] )
% 0.42/1.05 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 subsumption(
% 0.42/1.05 clause( 74, [ product( 'e_3', 'e_2', 'e_1' ) ] )
% 0.42/1.05 , clause( 161, [ product( 'e_3', 'e_2', 'e_1' ) ] )
% 0.42/1.05 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 resolution(
% 0.42/1.05 clause( 163, [ equalish( 'e_1', 'e_3' ), ~( product( 'e_1', X, 'e_1' ) ),
% 0.42/1.05 ~( product( 'e_1', 'e_2', 'e_3' ) ) ] )
% 0.42/1.05 , clause( 26, [ equalish( X, Y ), ~( product( X, Z, X ) ), ~( product( X, T
% 0.42/1.05 , Y ) ), ~( product( Y, T, X ) ) ] )
% 0.42/1.05 , 3, clause( 74, [ product( 'e_3', 'e_2', 'e_1' ) ] )
% 0.42/1.05 , 0, substitution( 0, [ :=( X, 'e_1' ), :=( Y, 'e_3' ), :=( Z, X ), :=( T,
% 0.42/1.05 'e_2' )] ), substitution( 1, [] )).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 resolution(
% 0.42/1.05 clause( 164, [ ~( product( 'e_1', X, 'e_1' ) ), ~( product( 'e_1', 'e_2',
% 0.42/1.05 'e_3' ) ) ] )
% 0.42/1.05 , clause( 10, [ ~( equalish( 'e_1', 'e_3' ) ) ] )
% 0.42/1.05 , 0, clause( 163, [ equalish( 'e_1', 'e_3' ), ~( product( 'e_1', X, 'e_1' )
% 0.42/1.05 ), ~( product( 'e_1', 'e_2', 'e_3' ) ) ] )
% 0.42/1.05 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, X )] )).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 subsumption(
% 0.42/1.05 clause( 78, [ ~( product( 'e_1', 'e_2', 'e_3' ) ), ~( product( 'e_1', X,
% 0.42/1.05 'e_1' ) ) ] )
% 0.42/1.05 , clause( 164, [ ~( product( 'e_1', X, 'e_1' ) ), ~( product( 'e_1', 'e_2'
% 0.42/1.05 , 'e_3' ) ) ] )
% 0.42/1.05 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1,
% 0.42/1.05 0 )] ) ).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 resolution(
% 0.42/1.05 clause( 166, [ equalish( X, 'e_3' ), ~( product( X, 'e_2', 'e_1' ) ) ] )
% 0.42/1.05 , clause( 18, [ equalish( X, T ), ~( product( X, Y, Z ) ), ~( product( T, Y
% 0.42/1.05 , Z ) ) ] )
% 0.42/1.05 , 2, clause( 74, [ product( 'e_3', 'e_2', 'e_1' ) ] )
% 0.42/1.05 , 0, substitution( 0, [ :=( X, X ), :=( Y, 'e_2' ), :=( Z, 'e_1' ), :=( T,
% 0.42/1.05 'e_3' )] ), substitution( 1, [] )).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 subsumption(
% 0.42/1.05 clause( 83, [ equalish( X, 'e_3' ), ~( product( X, 'e_2', 'e_1' ) ) ] )
% 0.42/1.05 , clause( 166, [ equalish( X, 'e_3' ), ~( product( X, 'e_2', 'e_1' ) ) ] )
% 0.42/1.05 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 0.42/1.05 1 )] ) ).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 resolution(
% 0.42/1.05 clause( 167, [ ~( product( 'e_1', 'e_2', 'e_3' ) ) ] )
% 0.42/1.05 , clause( 78, [ ~( product( 'e_1', 'e_2', 'e_3' ) ), ~( product( 'e_1', X,
% 0.42/1.05 'e_1' ) ) ] )
% 0.42/1.05 , 1, clause( 19, [ product( X, X, X ) ] )
% 0.42/1.05 , 0, substitution( 0, [ :=( X, 'e_1' )] ), substitution( 1, [ :=( X, 'e_1'
% 0.42/1.05 )] )).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 subsumption(
% 0.42/1.05 clause( 86, [ ~( product( 'e_1', 'e_2', 'e_3' ) ) ] )
% 0.42/1.05 , clause( 167, [ ~( product( 'e_1', 'e_2', 'e_3' ) ) ] )
% 0.42/1.05 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 resolution(
% 0.42/1.05 clause( 168, [ product( 'e_1', 'e_2', 'e_1' ), product( 'e_1', 'e_2', 'e_2'
% 0.42/1.05 ) ] )
% 0.42/1.05 , clause( 86, [ ~( product( 'e_1', 'e_2', 'e_3' ) ) ] )
% 0.42/1.05 , 0, clause( 59, [ product( 'e_1', 'e_2', 'e_1' ), product( 'e_1', 'e_2',
% 0.42/1.05 'e_2' ), product( 'e_1', 'e_2', 'e_3' ) ] )
% 0.42/1.05 , 2, substitution( 0, [] ), substitution( 1, [] )).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 subsumption(
% 0.42/1.05 clause( 87, [ product( 'e_1', 'e_2', 'e_1' ), product( 'e_1', 'e_2', 'e_2'
% 0.42/1.05 ) ] )
% 0.42/1.05 , clause( 168, [ product( 'e_1', 'e_2', 'e_1' ), product( 'e_1', 'e_2',
% 0.42/1.05 'e_2' ) ] )
% 0.42/1.05 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] )
% 0.42/1.05 ).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 resolution(
% 0.42/1.05 clause( 169, [ equalish( 'e_1', 'e_2' ), product( 'e_1', 'e_2', 'e_1' ) ]
% 0.42/1.05 )
% 0.42/1.05 , clause( 37, [ equalish( X, Y ), ~( product( X, Y, Y ) ) ] )
% 0.42/1.05 , 1, clause( 87, [ product( 'e_1', 'e_2', 'e_1' ), product( 'e_1', 'e_2',
% 0.42/1.05 'e_2' ) ] )
% 0.42/1.05 , 1, substitution( 0, [ :=( X, 'e_1' ), :=( Y, 'e_2' )] ), substitution( 1
% 0.42/1.05 , [] )).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 resolution(
% 0.42/1.05 clause( 170, [ product( 'e_1', 'e_2', 'e_1' ) ] )
% 0.42/1.05 , clause( 9, [ ~( equalish( 'e_1', 'e_2' ) ) ] )
% 0.42/1.05 , 0, clause( 169, [ equalish( 'e_1', 'e_2' ), product( 'e_1', 'e_2', 'e_1'
% 0.42/1.05 ) ] )
% 0.42/1.05 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 subsumption(
% 0.42/1.05 clause( 92, [ product( 'e_1', 'e_2', 'e_1' ) ] )
% 0.42/1.05 , clause( 170, [ product( 'e_1', 'e_2', 'e_1' ) ] )
% 0.42/1.05 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 resolution(
% 0.42/1.05 clause( 171, [ equalish( 'e_1', 'e_3' ) ] )
% 0.42/1.05 , clause( 83, [ equalish( X, 'e_3' ), ~( product( X, 'e_2', 'e_1' ) ) ] )
% 0.42/1.05 , 1, clause( 92, [ product( 'e_1', 'e_2', 'e_1' ) ] )
% 0.42/1.05 , 0, substitution( 0, [ :=( X, 'e_1' )] ), substitution( 1, [] )).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 resolution(
% 0.42/1.05 clause( 172, [] )
% 0.42/1.05 , clause( 10, [ ~( equalish( 'e_1', 'e_3' ) ) ] )
% 0.42/1.05 , 0, clause( 171, [ equalish( 'e_1', 'e_3' ) ] )
% 0.42/1.05 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 subsumption(
% 0.42/1.05 clause( 94, [] )
% 0.42/1.05 , clause( 172, [] )
% 0.42/1.05 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 end.
% 0.42/1.05
% 0.42/1.05 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.42/1.05
% 0.42/1.05 Memory use:
% 0.42/1.05
% 0.42/1.05 space for terms: 1666
% 0.42/1.05 space for clauses: 4430
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 clauses generated: 204
% 0.42/1.05 clauses kept: 95
% 0.42/1.05 clauses selected: 54
% 0.42/1.05 clauses deleted: 3
% 0.42/1.05 clauses inuse deleted: 0
% 0.42/1.05
% 0.42/1.05 subsentry: 1355
% 0.42/1.05 literals s-matched: 904
% 0.42/1.05 literals matched: 718
% 0.42/1.05 full subsumption: 519
% 0.42/1.05
% 0.42/1.05 checksum: -1234631208
% 0.42/1.05
% 0.42/1.05
% 0.42/1.05 Bliksem ended
%------------------------------------------------------------------------------