TSTP Solution File: GRP128-4.003 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GRP128-4.003 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n026.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 07:35:20 EDT 2022
% Result : Unsatisfiable 0.82s 1.22s
% Output : Refutation 0.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP128-4.003 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.10/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n026.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 : Tue Jun 14 12:52:36 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.82/1.22 *** allocated 10000 integers for termspace/termends
% 0.82/1.22 *** allocated 10000 integers for clauses
% 0.82/1.22 *** allocated 10000 integers for justifications
% 0.82/1.22 Bliksem 1.12
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 Automatic Strategy Selection
% 0.82/1.22
% 0.82/1.22 Clauses:
% 0.82/1.22 [
% 0.82/1.22 [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ), product( 'e_1',
% 0.82/1.22 X, Y ), product( 'e_2', X, Y ), product( 'e_3', X, Y ) ],
% 0.82/1.22 [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ), product( X,
% 0.82/1.22 'e_1', Y ), product( X, 'e_2', Y ), product( X, 'e_3', Y ) ],
% 0.82/1.22 [ product( X, Y, Z ), ~( product( X, Z, T ) ), ~( product( Z, Y, T ) ) ]
% 0.82/1.22 ,
% 0.82/1.22 [ product( X, Y, Z ), ~( product( T, X, Z ) ), ~( product( T, Y, X ) ) ]
% 0.82/1.22 ,
% 0.82/1.22 [ 'group_element'( 'e_1' ) ],
% 0.82/1.22 [ 'group_element'( 'e_2' ) ],
% 0.82/1.22 [ 'group_element'( 'e_3' ) ],
% 0.82/1.22 [ ~( equalish( 'e_1', 'e_2' ) ) ],
% 0.82/1.22 [ ~( equalish( 'e_1', 'e_3' ) ) ],
% 0.82/1.22 [ ~( equalish( 'e_2', 'e_1' ) ) ],
% 0.82/1.22 [ ~( equalish( 'e_2', 'e_3' ) ) ],
% 0.82/1.22 [ ~( equalish( 'e_3', 'e_1' ) ) ],
% 0.82/1.22 [ ~( equalish( 'e_3', 'e_2' ) ) ],
% 0.82/1.22 [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ), product( X, Y,
% 0.82/1.22 'e_1' ), product( X, Y, 'e_2' ), product( X, Y, 'e_3' ) ],
% 0.82/1.22 [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), equalish( Z, T ) ]
% 0.82/1.22 ,
% 0.82/1.22 [ ~( product( X, Y, Z ) ), ~( product( X, T, Z ) ), equalish( Y, T ) ]
% 0.82/1.22 ,
% 0.82/1.22 [ ~( product( X, Y, Z ) ), ~( product( T, Y, Z ) ), equalish( X, T ) ]
% 0.82/1.22 ,
% 0.82/1.22 [ ~( product( X, Y, Z ) ), ~( product( Z, Y, T ) ), product( X, Z, T ) ]
% 0.82/1.22
% 0.82/1.22 ] .
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 percentage equality = 0.000000, percentage horn = 0.833333
% 0.82/1.22 This a non-horn, non-equality problem
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 Options Used:
% 0.82/1.22
% 0.82/1.22 useres = 1
% 0.82/1.22 useparamod = 0
% 0.82/1.22 useeqrefl = 0
% 0.82/1.22 useeqfact = 0
% 0.82/1.22 usefactor = 1
% 0.82/1.22 usesimpsplitting = 0
% 0.82/1.22 usesimpdemod = 0
% 0.82/1.22 usesimpres = 3
% 0.82/1.22
% 0.82/1.22 resimpinuse = 1000
% 0.82/1.22 resimpclauses = 20000
% 0.82/1.22 substype = standard
% 0.82/1.22 backwardsubs = 1
% 0.82/1.22 selectoldest = 5
% 0.82/1.22
% 0.82/1.22 litorderings [0] = split
% 0.82/1.22 litorderings [1] = liftord
% 0.82/1.22
% 0.82/1.22 termordering = none
% 0.82/1.22
% 0.82/1.22 litapriori = 1
% 0.82/1.22 termapriori = 0
% 0.82/1.22 litaposteriori = 0
% 0.82/1.22 termaposteriori = 0
% 0.82/1.22 demodaposteriori = 0
% 0.82/1.22 ordereqreflfact = 0
% 0.82/1.22
% 0.82/1.22 litselect = none
% 0.82/1.22
% 0.82/1.22 maxweight = 15
% 0.82/1.22 maxdepth = 30000
% 0.82/1.22 maxlength = 115
% 0.82/1.22 maxnrvars = 195
% 0.82/1.22 excuselevel = 1
% 0.82/1.22 increasemaxweight = 1
% 0.82/1.22
% 0.82/1.22 maxselected = 10000000
% 0.82/1.22 maxnrclauses = 10000000
% 0.82/1.22
% 0.82/1.22 showgenerated = 0
% 0.82/1.22 showkept = 0
% 0.82/1.22 showselected = 0
% 0.82/1.22 showdeleted = 0
% 0.82/1.22 showresimp = 1
% 0.82/1.22 showstatus = 2000
% 0.82/1.22
% 0.82/1.22 prologoutput = 1
% 0.82/1.22 nrgoals = 5000000
% 0.82/1.22 totalproof = 1
% 0.82/1.22
% 0.82/1.22 Symbols occurring in the translation:
% 0.82/1.22
% 0.82/1.22 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.82/1.22 . [1, 2] (w:1, o:24, a:1, s:1, b:0),
% 0.82/1.22 ! [4, 1] (w:0, o:18, a:1, s:1, b:0),
% 0.82/1.22 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.82/1.22 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.82/1.22 'group_element' [40, 1] (w:1, o:23, a:1, s:1, b:0),
% 0.82/1.22 'e_1' [42, 0] (w:1, o:12, a:1, s:1, b:0),
% 0.82/1.22 product [43, 3] (w:1, o:50, a:1, s:1, b:0),
% 0.82/1.22 'e_2' [44, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.82/1.22 'e_3' [45, 0] (w:1, o:14, a:1, s:1, b:0),
% 0.82/1.22 equalish [48, 2] (w:1, o:49, a:1, s:1, b:0).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 Starting Search:
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 Bliksems!, er is een bewijs:
% 0.82/1.22 % SZS status Unsatisfiable
% 0.82/1.22 % SZS output start Refutation
% 0.82/1.22
% 0.82/1.22 clause( 3, [ ~( product( T, X, Z ) ), ~( product( T, Y, X ) ), product( X,
% 0.82/1.22 Y, Z ) ] )
% 0.82/1.22 .
% 0.82/1.22 clause( 4, [ 'group_element'( 'e_1' ) ] )
% 0.82/1.22 .
% 0.82/1.22 clause( 5, [ 'group_element'( 'e_2' ) ] )
% 0.82/1.22 .
% 0.82/1.22 clause( 6, [ 'group_element'( 'e_3' ) ] )
% 0.82/1.22 .
% 0.82/1.22 clause( 7, [ ~( equalish( 'e_1', 'e_2' ) ) ] )
% 0.82/1.22 .
% 0.82/1.22 clause( 8, [ ~( equalish( 'e_1', 'e_3' ) ) ] )
% 0.82/1.22 .
% 0.82/1.22 clause( 9, [ ~( equalish( 'e_2', 'e_1' ) ) ] )
% 0.82/1.22 .
% 0.82/1.22 clause( 10, [ ~( equalish( 'e_2', 'e_3' ) ) ] )
% 0.82/1.22 .
% 0.82/1.22 clause( 13, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ), product(
% 0.82/1.22 X, Y, 'e_1' ), product( X, Y, 'e_2' ), product( X, Y, 'e_3' ) ] )
% 0.82/1.22 .
% 0.82/1.22 clause( 15, [ equalish( Y, T ), ~( product( X, Y, Z ) ), ~( product( X, T,
% 0.82/1.22 Z ) ) ] )
% 0.82/1.22 .
% 0.82/1.22 clause( 16, [ equalish( X, T ), ~( product( X, Y, Z ) ), ~( product( T, Y,
% 0.82/1.22 Z ) ) ] )
% 0.82/1.22 .
% 0.82/1.22 clause( 17, [ ~( product( Z, Y, T ) ), product( X, Z, T ), ~( product( X, Y
% 0.82/1.22 , Z ) ) ] )
% 0.82/1.22 .
% 0.82/1.22 clause( 21, [ product( Y, Y, Y ), ~( product( X, Y, Y ) ) ] )
% 0.82/1.22 .
% 0.82/1.22 clause( 26, [ product( X, X, X ), ~( product( X, Y, X ) ) ] )
% 0.82/1.22 .
% 0.82/1.22 clause( 98, [ equalish( X, Y ), ~( product( Z, X, X ) ), ~( product( Y, X,
% 0.82/1.22 X ) ) ] )
% 0.82/1.22 .
% 0.82/1.22 clause( 109, [ equalish( X, Y ), ~( product( Y, X, X ) ) ] )
% 0.82/1.22 .
% 0.82/1.22 clause( 111, [ equalish( X, Y ), ~( product( Z, X, Y ) ), ~( product( Z, Y
% 0.82/1.22 , X ) ) ] )
% 0.82/1.22 .
% 0.82/1.22 clause( 155, [ equalish( X, Y ), ~( product( Y, Z, Y ) ), ~( product( Y, X
% 0.82/1.22 , Y ) ) ] )
% 0.82/1.22 .
% 0.82/1.22 clause( 160, [ equalish( X, Y ), ~( product( Y, X, Y ) ) ] )
% 0.82/1.22 .
% 0.82/1.22 clause( 165, [ ~( 'group_element'( X ) ), equalish( X, 'e_3' ), product(
% 0.82/1.22 'e_3', X, 'e_1' ), product( 'e_3', X, 'e_2' ) ] )
% 0.82/1.22 .
% 0.82/1.22 clause( 283, [ equalish( 'e_2', 'e_3' ), product( 'e_3', 'e_2', 'e_1' ) ]
% 0.82/1.22 )
% 0.82/1.22 .
% 0.82/1.22 clause( 284, [ product( 'e_3', 'e_2', 'e_1' ) ] )
% 0.82/1.22 .
% 0.82/1.22 clause( 304, [ ~( product( 'e_3', 'e_1', 'e_2' ) ) ] )
% 0.82/1.22 .
% 0.82/1.22 clause( 310, [ equalish( X, 'e_2' ), ~( product( 'e_3', X, 'e_1' ) ) ] )
% 0.82/1.22 .
% 0.82/1.22 clause( 326, [ equalish( 'e_1', 'e_3' ), product( 'e_3', 'e_1', 'e_1' ) ]
% 0.82/1.22 )
% 0.82/1.22 .
% 0.82/1.22 clause( 416, [ product( 'e_3', 'e_1', 'e_1' ) ] )
% 0.82/1.22 .
% 0.82/1.22 clause( 417, [] )
% 0.82/1.22 .
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 % SZS output end Refutation
% 0.82/1.22 found a proof!
% 0.82/1.22
% 0.82/1.22 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.82/1.22
% 0.82/1.22 initialclauses(
% 0.82/1.22 [ clause( 419, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ),
% 0.82/1.22 product( 'e_1', X, Y ), product( 'e_2', X, Y ), product( 'e_3', X, Y ) ]
% 0.82/1.22 )
% 0.82/1.22 , clause( 420, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ),
% 0.82/1.22 product( X, 'e_1', Y ), product( X, 'e_2', Y ), product( X, 'e_3', Y ) ]
% 0.82/1.22 )
% 0.82/1.22 , clause( 421, [ product( X, Y, Z ), ~( product( X, Z, T ) ), ~( product( Z
% 0.82/1.22 , Y, T ) ) ] )
% 0.82/1.22 , clause( 422, [ product( X, Y, Z ), ~( product( T, X, Z ) ), ~( product( T
% 0.82/1.22 , Y, X ) ) ] )
% 0.82/1.22 , clause( 423, [ 'group_element'( 'e_1' ) ] )
% 0.82/1.22 , clause( 424, [ 'group_element'( 'e_2' ) ] )
% 0.82/1.22 , clause( 425, [ 'group_element'( 'e_3' ) ] )
% 0.82/1.22 , clause( 426, [ ~( equalish( 'e_1', 'e_2' ) ) ] )
% 0.82/1.22 , clause( 427, [ ~( equalish( 'e_1', 'e_3' ) ) ] )
% 0.82/1.22 , clause( 428, [ ~( equalish( 'e_2', 'e_1' ) ) ] )
% 0.82/1.22 , clause( 429, [ ~( equalish( 'e_2', 'e_3' ) ) ] )
% 0.82/1.22 , clause( 430, [ ~( equalish( 'e_3', 'e_1' ) ) ] )
% 0.82/1.22 , clause( 431, [ ~( equalish( 'e_3', 'e_2' ) ) ] )
% 0.82/1.22 , clause( 432, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ),
% 0.82/1.22 product( X, Y, 'e_1' ), product( X, Y, 'e_2' ), product( X, Y, 'e_3' ) ]
% 0.82/1.22 )
% 0.82/1.22 , clause( 433, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), equalish(
% 0.82/1.22 Z, T ) ] )
% 0.82/1.22 , clause( 434, [ ~( product( X, Y, Z ) ), ~( product( X, T, Z ) ), equalish(
% 0.82/1.22 Y, T ) ] )
% 0.82/1.22 , clause( 435, [ ~( product( X, Y, Z ) ), ~( product( T, Y, Z ) ), equalish(
% 0.82/1.22 X, T ) ] )
% 0.82/1.22 , clause( 436, [ ~( product( X, Y, Z ) ), ~( product( Z, Y, T ) ), product(
% 0.82/1.22 X, Z, T ) ] )
% 0.82/1.22 ] ).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 subsumption(
% 0.82/1.22 clause( 3, [ ~( product( T, X, Z ) ), ~( product( T, Y, X ) ), product( X,
% 0.82/1.22 Y, Z ) ] )
% 0.82/1.22 , clause( 422, [ product( X, Y, Z ), ~( product( T, X, Z ) ), ~( product( T
% 0.82/1.22 , Y, X ) ) ] )
% 0.82/1.22 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.82/1.22 permutation( 0, [ ==>( 0, 2 ), ==>( 1, 0 ), ==>( 2, 1 )] ) ).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 subsumption(
% 0.82/1.22 clause( 4, [ 'group_element'( 'e_1' ) ] )
% 0.82/1.22 , clause( 423, [ 'group_element'( 'e_1' ) ] )
% 0.82/1.22 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 subsumption(
% 0.82/1.22 clause( 5, [ 'group_element'( 'e_2' ) ] )
% 0.82/1.22 , clause( 424, [ 'group_element'( 'e_2' ) ] )
% 0.82/1.22 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 subsumption(
% 0.82/1.22 clause( 6, [ 'group_element'( 'e_3' ) ] )
% 0.82/1.22 , clause( 425, [ 'group_element'( 'e_3' ) ] )
% 0.82/1.22 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 subsumption(
% 0.82/1.22 clause( 7, [ ~( equalish( 'e_1', 'e_2' ) ) ] )
% 0.82/1.22 , clause( 426, [ ~( equalish( 'e_1', 'e_2' ) ) ] )
% 0.82/1.22 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 subsumption(
% 0.82/1.22 clause( 8, [ ~( equalish( 'e_1', 'e_3' ) ) ] )
% 0.82/1.22 , clause( 427, [ ~( equalish( 'e_1', 'e_3' ) ) ] )
% 0.82/1.22 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 subsumption(
% 0.82/1.22 clause( 9, [ ~( equalish( 'e_2', 'e_1' ) ) ] )
% 0.82/1.22 , clause( 428, [ ~( equalish( 'e_2', 'e_1' ) ) ] )
% 0.82/1.22 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 subsumption(
% 0.82/1.22 clause( 10, [ ~( equalish( 'e_2', 'e_3' ) ) ] )
% 0.82/1.22 , clause( 429, [ ~( equalish( 'e_2', 'e_3' ) ) ] )
% 0.82/1.22 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 subsumption(
% 0.82/1.22 clause( 13, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ), product(
% 0.82/1.22 X, Y, 'e_1' ), product( X, Y, 'e_2' ), product( X, Y, 'e_3' ) ] )
% 0.82/1.22 , clause( 432, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ),
% 0.82/1.22 product( X, Y, 'e_1' ), product( X, Y, 'e_2' ), product( X, Y, 'e_3' ) ]
% 0.82/1.22 )
% 0.82/1.22 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.82/1.22 ), ==>( 1, 1 ), ==>( 2, 2 ), ==>( 3, 3 ), ==>( 4, 4 )] ) ).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 subsumption(
% 0.82/1.22 clause( 15, [ equalish( Y, T ), ~( product( X, Y, Z ) ), ~( product( X, T,
% 0.82/1.22 Z ) ) ] )
% 0.82/1.22 , clause( 434, [ ~( product( X, Y, Z ) ), ~( product( X, T, Z ) ), equalish(
% 0.82/1.22 Y, T ) ] )
% 0.82/1.22 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.82/1.22 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 2 ), ==>( 2, 0 )] ) ).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 subsumption(
% 0.82/1.22 clause( 16, [ equalish( X, T ), ~( product( X, Y, Z ) ), ~( product( T, Y,
% 0.82/1.22 Z ) ) ] )
% 0.82/1.22 , clause( 435, [ ~( product( X, Y, Z ) ), ~( product( T, Y, Z ) ), equalish(
% 0.82/1.22 X, T ) ] )
% 0.82/1.22 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.82/1.22 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 2 ), ==>( 2, 0 )] ) ).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 subsumption(
% 0.82/1.22 clause( 17, [ ~( product( Z, Y, T ) ), product( X, Z, T ), ~( product( X, Y
% 0.82/1.22 , Z ) ) ] )
% 0.82/1.22 , clause( 436, [ ~( product( X, Y, Z ) ), ~( product( Z, Y, T ) ), product(
% 0.82/1.22 X, Z, T ) ] )
% 0.82/1.22 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.82/1.22 permutation( 0, [ ==>( 0, 2 ), ==>( 1, 0 ), ==>( 2, 1 )] ) ).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 factor(
% 0.82/1.22 clause( 498, [ ~( product( X, Y, Y ) ), product( Y, Y, Y ) ] )
% 0.82/1.22 , clause( 3, [ ~( product( T, X, Z ) ), ~( product( T, Y, X ) ), product( X
% 0.82/1.22 , Y, Z ) ] )
% 0.82/1.22 , 0, 1, substitution( 0, [ :=( X, Y ), :=( Y, Y ), :=( Z, Y ), :=( T, X )] )
% 0.82/1.22 ).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 subsumption(
% 0.82/1.22 clause( 21, [ product( Y, Y, Y ), ~( product( X, Y, Y ) ) ] )
% 0.82/1.22 , clause( 498, [ ~( product( X, Y, Y ) ), product( Y, Y, Y ) ] )
% 0.82/1.22 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 1
% 0.82/1.22 ), ==>( 1, 0 )] ) ).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 factor(
% 0.82/1.22 clause( 499, [ ~( product( X, Y, X ) ), product( X, X, X ) ] )
% 0.82/1.22 , clause( 17, [ ~( product( Z, Y, T ) ), product( X, Z, T ), ~( product( X
% 0.82/1.22 , Y, Z ) ) ] )
% 0.82/1.22 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, X ), :=( T, X )] )
% 0.82/1.22 ).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 subsumption(
% 0.82/1.22 clause( 26, [ product( X, X, X ), ~( product( X, Y, X ) ) ] )
% 0.82/1.22 , clause( 499, [ ~( product( X, Y, X ) ), product( X, X, X ) ] )
% 0.82/1.22 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 1
% 0.82/1.22 ), ==>( 1, 0 )] ) ).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 resolution(
% 0.82/1.22 clause( 500, [ equalish( X, Y ), ~( product( Y, X, X ) ), ~( product( Z, X
% 0.82/1.22 , X ) ) ] )
% 0.82/1.22 , clause( 16, [ equalish( X, T ), ~( product( X, Y, Z ) ), ~( product( T, Y
% 0.82/1.22 , Z ) ) ] )
% 0.82/1.22 , 1, clause( 21, [ product( Y, Y, Y ), ~( product( X, Y, Y ) ) ] )
% 0.82/1.22 , 0, substitution( 0, [ :=( X, X ), :=( Y, X ), :=( Z, X ), :=( T, Y )] ),
% 0.82/1.22 substitution( 1, [ :=( X, Z ), :=( Y, X )] )).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 subsumption(
% 0.82/1.22 clause( 98, [ equalish( X, Y ), ~( product( Z, X, X ) ), ~( product( Y, X,
% 0.82/1.22 X ) ) ] )
% 0.82/1.22 , clause( 500, [ equalish( X, Y ), ~( product( Y, X, X ) ), ~( product( Z,
% 0.82/1.22 X, X ) ) ] )
% 0.82/1.22 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.82/1.22 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 2 ), ==>( 2, 1 )] ) ).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 factor(
% 0.82/1.22 clause( 504, [ equalish( X, Y ), ~( product( Y, X, X ) ) ] )
% 0.82/1.22 , clause( 98, [ equalish( X, Y ), ~( product( Z, X, X ) ), ~( product( Y, X
% 0.82/1.22 , X ) ) ] )
% 0.82/1.22 , 1, 2, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Y )] )).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 subsumption(
% 0.82/1.22 clause( 109, [ equalish( X, Y ), ~( product( Y, X, X ) ) ] )
% 0.82/1.22 , clause( 504, [ equalish( X, Y ), ~( product( Y, X, X ) ) ] )
% 0.82/1.22 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.82/1.22 ), ==>( 1, 1 )] ) ).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 resolution(
% 0.82/1.22 clause( 505, [ equalish( X, Y ), ~( product( Z, Y, X ) ), ~( product( Z, X
% 0.82/1.22 , Y ) ) ] )
% 0.82/1.22 , clause( 109, [ equalish( X, Y ), ~( product( Y, X, X ) ) ] )
% 0.82/1.22 , 1, clause( 3, [ ~( product( T, X, Z ) ), ~( product( T, Y, X ) ), product(
% 0.82/1.22 X, Y, Z ) ] )
% 0.82/1.22 , 2, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [ :=( X
% 0.82/1.22 , Y ), :=( Y, X ), :=( Z, X ), :=( T, Z )] )).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 subsumption(
% 0.82/1.22 clause( 111, [ equalish( X, Y ), ~( product( Z, X, Y ) ), ~( product( Z, Y
% 0.82/1.22 , X ) ) ] )
% 0.82/1.22 , clause( 505, [ equalish( X, Y ), ~( product( Z, Y, X ) ), ~( product( Z,
% 0.82/1.22 X, Y ) ) ] )
% 0.82/1.22 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.82/1.22 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 2 ), ==>( 2, 1 )] ) ).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 resolution(
% 0.82/1.22 clause( 508, [ equalish( X, Y ), ~( product( Y, X, Y ) ), ~( product( Y, Z
% 0.82/1.22 , Y ) ) ] )
% 0.82/1.22 , clause( 15, [ equalish( Y, T ), ~( product( X, Y, Z ) ), ~( product( X, T
% 0.82/1.22 , Z ) ) ] )
% 0.82/1.22 , 2, clause( 26, [ product( X, X, X ), ~( product( X, Y, X ) ) ] )
% 0.82/1.22 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Y ), :=( T, Y )] ),
% 0.82/1.22 substitution( 1, [ :=( X, Y ), :=( Y, Z )] )).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 subsumption(
% 0.82/1.22 clause( 155, [ equalish( X, Y ), ~( product( Y, Z, Y ) ), ~( product( Y, X
% 0.82/1.22 , Y ) ) ] )
% 0.82/1.22 , clause( 508, [ equalish( X, Y ), ~( product( Y, X, Y ) ), ~( product( Y,
% 0.82/1.22 Z, Y ) ) ] )
% 0.82/1.22 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.82/1.22 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 2 ), ==>( 2, 1 )] ) ).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 factor(
% 0.82/1.22 clause( 511, [ equalish( X, Y ), ~( product( Y, X, Y ) ) ] )
% 0.82/1.22 , clause( 155, [ equalish( X, Y ), ~( product( Y, Z, Y ) ), ~( product( Y,
% 0.82/1.22 X, Y ) ) ] )
% 0.82/1.22 , 1, 2, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, X )] )).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 subsumption(
% 0.82/1.22 clause( 160, [ equalish( X, Y ), ~( product( Y, X, Y ) ) ] )
% 0.82/1.22 , clause( 511, [ equalish( X, Y ), ~( product( Y, X, Y ) ) ] )
% 0.82/1.22 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.82/1.22 ), ==>( 1, 1 )] ) ).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 resolution(
% 0.82/1.22 clause( 514, [ equalish( X, 'e_3' ), ~( 'group_element'( 'e_3' ) ), ~(
% 0.82/1.22 'group_element'( X ) ), product( 'e_3', X, 'e_1' ), product( 'e_3', X,
% 0.82/1.22 'e_2' ) ] )
% 0.82/1.22 , clause( 160, [ equalish( X, Y ), ~( product( Y, X, Y ) ) ] )
% 0.82/1.22 , 1, clause( 13, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ),
% 0.82/1.22 product( X, Y, 'e_1' ), product( X, Y, 'e_2' ), product( X, Y, 'e_3' ) ]
% 0.82/1.22 )
% 0.82/1.22 , 4, substitution( 0, [ :=( X, X ), :=( Y, 'e_3' )] ), substitution( 1, [
% 0.82/1.22 :=( X, 'e_3' ), :=( Y, X )] )).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 resolution(
% 0.82/1.22 clause( 519, [ equalish( X, 'e_3' ), ~( 'group_element'( X ) ), product(
% 0.82/1.22 'e_3', X, 'e_1' ), product( 'e_3', X, 'e_2' ) ] )
% 0.82/1.22 , clause( 514, [ equalish( X, 'e_3' ), ~( 'group_element'( 'e_3' ) ), ~(
% 0.82/1.22 'group_element'( X ) ), product( 'e_3', X, 'e_1' ), product( 'e_3', X,
% 0.82/1.22 'e_2' ) ] )
% 0.82/1.22 , 1, clause( 6, [ 'group_element'( 'e_3' ) ] )
% 0.82/1.22 , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [] )).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 subsumption(
% 0.82/1.22 clause( 165, [ ~( 'group_element'( X ) ), equalish( X, 'e_3' ), product(
% 0.82/1.22 'e_3', X, 'e_1' ), product( 'e_3', X, 'e_2' ) ] )
% 0.82/1.22 , clause( 519, [ equalish( X, 'e_3' ), ~( 'group_element'( X ) ), product(
% 0.82/1.22 'e_3', X, 'e_1' ), product( 'e_3', X, 'e_2' ) ] )
% 0.82/1.22 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1,
% 0.82/1.22 0 ), ==>( 2, 2 ), ==>( 3, 3 )] ) ).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 resolution(
% 0.82/1.22 clause( 521, [ equalish( 'e_2', 'e_3' ), ~( 'group_element'( 'e_2' ) ),
% 0.82/1.22 equalish( 'e_2', 'e_3' ), product( 'e_3', 'e_2', 'e_1' ) ] )
% 0.82/1.22 , clause( 109, [ equalish( X, Y ), ~( product( Y, X, X ) ) ] )
% 0.82/1.22 , 1, clause( 165, [ ~( 'group_element'( X ) ), equalish( X, 'e_3' ),
% 0.82/1.22 product( 'e_3', X, 'e_1' ), product( 'e_3', X, 'e_2' ) ] )
% 0.82/1.22 , 3, substitution( 0, [ :=( X, 'e_2' ), :=( Y, 'e_3' )] ), substitution( 1
% 0.82/1.22 , [ :=( X, 'e_2' )] )).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 resolution(
% 0.82/1.22 clause( 524, [ equalish( 'e_2', 'e_3' ), equalish( 'e_2', 'e_3' ), product(
% 0.82/1.22 'e_3', 'e_2', 'e_1' ) ] )
% 0.82/1.22 , clause( 521, [ equalish( 'e_2', 'e_3' ), ~( 'group_element'( 'e_2' ) ),
% 0.82/1.22 equalish( 'e_2', 'e_3' ), product( 'e_3', 'e_2', 'e_1' ) ] )
% 0.82/1.22 , 1, clause( 5, [ 'group_element'( 'e_2' ) ] )
% 0.82/1.22 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 factor(
% 0.82/1.22 clause( 525, [ equalish( 'e_2', 'e_3' ), product( 'e_3', 'e_2', 'e_1' ) ]
% 0.82/1.22 )
% 0.82/1.22 , clause( 524, [ equalish( 'e_2', 'e_3' ), equalish( 'e_2', 'e_3' ),
% 0.82/1.22 product( 'e_3', 'e_2', 'e_1' ) ] )
% 0.82/1.22 , 0, 1, substitution( 0, [] )).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 subsumption(
% 0.82/1.22 clause( 283, [ equalish( 'e_2', 'e_3' ), product( 'e_3', 'e_2', 'e_1' ) ]
% 0.82/1.22 )
% 0.82/1.22 , clause( 525, [ equalish( 'e_2', 'e_3' ), product( 'e_3', 'e_2', 'e_1' ) ]
% 0.82/1.22 )
% 0.82/1.22 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] )
% 0.82/1.22 ).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 resolution(
% 0.82/1.22 clause( 526, [ product( 'e_3', 'e_2', 'e_1' ) ] )
% 0.82/1.22 , clause( 10, [ ~( equalish( 'e_2', 'e_3' ) ) ] )
% 0.82/1.22 , 0, clause( 283, [ equalish( 'e_2', 'e_3' ), product( 'e_3', 'e_2', 'e_1'
% 0.82/1.22 ) ] )
% 0.82/1.22 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 subsumption(
% 0.82/1.22 clause( 284, [ product( 'e_3', 'e_2', 'e_1' ) ] )
% 0.82/1.22 , clause( 526, [ product( 'e_3', 'e_2', 'e_1' ) ] )
% 0.82/1.22 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 resolution(
% 0.82/1.22 clause( 527, [ equalish( 'e_2', 'e_1' ), ~( product( 'e_3', 'e_1', 'e_2' )
% 0.82/1.22 ) ] )
% 0.82/1.22 , clause( 111, [ equalish( X, Y ), ~( product( Z, X, Y ) ), ~( product( Z,
% 0.82/1.22 Y, X ) ) ] )
% 0.82/1.22 , 1, clause( 284, [ product( 'e_3', 'e_2', 'e_1' ) ] )
% 0.82/1.22 , 0, substitution( 0, [ :=( X, 'e_2' ), :=( Y, 'e_1' ), :=( Z, 'e_3' )] ),
% 0.82/1.22 substitution( 1, [] )).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 resolution(
% 0.82/1.22 clause( 529, [ ~( product( 'e_3', 'e_1', 'e_2' ) ) ] )
% 0.82/1.22 , clause( 9, [ ~( equalish( 'e_2', 'e_1' ) ) ] )
% 0.82/1.22 , 0, clause( 527, [ equalish( 'e_2', 'e_1' ), ~( product( 'e_3', 'e_1',
% 0.82/1.22 'e_2' ) ) ] )
% 0.82/1.22 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 subsumption(
% 0.82/1.22 clause( 304, [ ~( product( 'e_3', 'e_1', 'e_2' ) ) ] )
% 0.82/1.22 , clause( 529, [ ~( product( 'e_3', 'e_1', 'e_2' ) ) ] )
% 0.82/1.22 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 resolution(
% 0.82/1.22 clause( 531, [ equalish( X, 'e_2' ), ~( product( 'e_3', X, 'e_1' ) ) ] )
% 0.82/1.22 , clause( 15, [ equalish( Y, T ), ~( product( X, Y, Z ) ), ~( product( X, T
% 0.82/1.22 , Z ) ) ] )
% 0.82/1.22 , 2, clause( 284, [ product( 'e_3', 'e_2', 'e_1' ) ] )
% 0.82/1.22 , 0, substitution( 0, [ :=( X, 'e_3' ), :=( Y, X ), :=( Z, 'e_1' ), :=( T,
% 0.82/1.22 'e_2' )] ), substitution( 1, [] )).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 subsumption(
% 0.82/1.22 clause( 310, [ equalish( X, 'e_2' ), ~( product( 'e_3', X, 'e_1' ) ) ] )
% 0.82/1.22 , clause( 531, [ equalish( X, 'e_2' ), ~( product( 'e_3', X, 'e_1' ) ) ] )
% 0.82/1.22 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 0.82/1.22 1 )] ) ).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 resolution(
% 0.82/1.22 clause( 532, [ ~( 'group_element'( 'e_1' ) ), equalish( 'e_1', 'e_3' ),
% 0.82/1.22 product( 'e_3', 'e_1', 'e_1' ) ] )
% 0.82/1.22 , clause( 304, [ ~( product( 'e_3', 'e_1', 'e_2' ) ) ] )
% 0.82/1.22 , 0, clause( 165, [ ~( 'group_element'( X ) ), equalish( X, 'e_3' ),
% 0.82/1.22 product( 'e_3', X, 'e_1' ), product( 'e_3', X, 'e_2' ) ] )
% 0.82/1.22 , 3, substitution( 0, [] ), substitution( 1, [ :=( X, 'e_1' )] )).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 resolution(
% 0.82/1.22 clause( 533, [ equalish( 'e_1', 'e_3' ), product( 'e_3', 'e_1', 'e_1' ) ]
% 0.82/1.22 )
% 0.82/1.22 , clause( 532, [ ~( 'group_element'( 'e_1' ) ), equalish( 'e_1', 'e_3' ),
% 0.82/1.22 product( 'e_3', 'e_1', 'e_1' ) ] )
% 0.82/1.22 , 0, clause( 4, [ 'group_element'( 'e_1' ) ] )
% 0.82/1.22 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 subsumption(
% 0.82/1.22 clause( 326, [ equalish( 'e_1', 'e_3' ), product( 'e_3', 'e_1', 'e_1' ) ]
% 0.82/1.22 )
% 0.82/1.22 , clause( 533, [ equalish( 'e_1', 'e_3' ), product( 'e_3', 'e_1', 'e_1' ) ]
% 0.82/1.22 )
% 0.82/1.22 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] )
% 0.82/1.22 ).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 resolution(
% 0.82/1.22 clause( 534, [ product( 'e_3', 'e_1', 'e_1' ) ] )
% 0.82/1.22 , clause( 8, [ ~( equalish( 'e_1', 'e_3' ) ) ] )
% 0.82/1.22 , 0, clause( 326, [ equalish( 'e_1', 'e_3' ), product( 'e_3', 'e_1', 'e_1'
% 0.82/1.22 ) ] )
% 0.82/1.22 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 subsumption(
% 0.82/1.22 clause( 416, [ product( 'e_3', 'e_1', 'e_1' ) ] )
% 0.82/1.22 , clause( 534, [ product( 'e_3', 'e_1', 'e_1' ) ] )
% 0.82/1.22 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 resolution(
% 0.82/1.22 clause( 535, [ equalish( 'e_1', 'e_2' ) ] )
% 0.82/1.22 , clause( 310, [ equalish( X, 'e_2' ), ~( product( 'e_3', X, 'e_1' ) ) ] )
% 0.82/1.22 , 1, clause( 416, [ product( 'e_3', 'e_1', 'e_1' ) ] )
% 0.82/1.22 , 0, substitution( 0, [ :=( X, 'e_1' )] ), substitution( 1, [] )).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 resolution(
% 0.82/1.22 clause( 536, [] )
% 0.82/1.22 , clause( 7, [ ~( equalish( 'e_1', 'e_2' ) ) ] )
% 0.82/1.22 , 0, clause( 535, [ equalish( 'e_1', 'e_2' ) ] )
% 0.82/1.22 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 subsumption(
% 0.82/1.22 clause( 417, [] )
% 0.82/1.22 , clause( 536, [] )
% 0.82/1.22 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 end.
% 0.82/1.22
% 0.82/1.22 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.82/1.22
% 0.82/1.22 Memory use:
% 0.82/1.22
% 0.82/1.22 space for terms: 6485
% 0.82/1.22 space for clauses: 16620
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 clauses generated: 3795
% 0.82/1.22 clauses kept: 418
% 0.82/1.22 clauses selected: 80
% 0.82/1.22 clauses deleted: 50
% 0.82/1.22 clauses inuse deleted: 0
% 0.82/1.22
% 0.82/1.22 subsentry: 26950
% 0.82/1.22 literals s-matched: 16378
% 0.82/1.22 literals matched: 13588
% 0.82/1.22 full subsumption: 11965
% 0.82/1.22
% 0.82/1.22 checksum: -880058521
% 0.82/1.22
% 0.82/1.22
% 0.82/1.22 Bliksem ended
%------------------------------------------------------------------------------