TSTP Solution File: GRP123-4.003 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GRP123-4.003 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n017.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 07:35:00 EDT 2022
% Result : Unsatisfiable 0.71s 1.11s
% Output : Refutation 0.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP123-4.003 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n017.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 13 17:59:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.71/1.11 *** allocated 10000 integers for termspace/termends
% 0.71/1.11 *** allocated 10000 integers for clauses
% 0.71/1.11 *** allocated 10000 integers for justifications
% 0.71/1.11 Bliksem 1.12
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 Automatic Strategy Selection
% 0.71/1.11
% 0.71/1.11 Clauses:
% 0.71/1.11 [
% 0.71/1.11 [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ), product( 'e_1',
% 0.71/1.11 X, Y ), product( 'e_2', X, Y ), product( 'e_3', X, Y ) ],
% 0.71/1.11 [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ), product( X,
% 0.71/1.11 'e_1', Y ), product( X, 'e_2', Y ), product( X, 'e_3', Y ) ],
% 0.71/1.11 [ 'group_element'( 'e_1' ) ],
% 0.71/1.11 [ 'group_element'( 'e_2' ) ],
% 0.71/1.11 [ 'group_element'( 'e_3' ) ],
% 0.71/1.11 [ ~( equalish( 'e_1', 'e_2' ) ) ],
% 0.71/1.11 [ ~( equalish( 'e_1', 'e_3' ) ) ],
% 0.71/1.11 [ ~( equalish( 'e_2', 'e_1' ) ) ],
% 0.71/1.11 [ ~( equalish( 'e_2', 'e_3' ) ) ],
% 0.71/1.11 [ ~( equalish( 'e_3', 'e_1' ) ) ],
% 0.71/1.11 [ ~( equalish( 'e_3', 'e_2' ) ) ],
% 0.71/1.11 [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ), product( X, Y,
% 0.71/1.11 'e_1' ), product( X, Y, 'e_2' ), product( X, Y, 'e_3' ) ],
% 0.71/1.11 [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), equalish( Z, T ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ ~( product( X, Y, Z ) ), ~( product( X, T, Z ) ), equalish( Y, T ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ ~( product( X, Y, Z ) ), ~( product( T, Y, Z ) ), equalish( X, T ) ]
% 0.71/1.11 ,
% 0.71/1.11 [ product( X, X, X ) ],
% 0.71/1.11 [ ~( product( X, Y, Z ) ), ~( product( T, U, Z ) ), ~( product( W, Y, X
% 0.71/1.11 ) ), ~( product( W, U, T ) ), equalish( X, T ) ],
% 0.71/1.11 [ ~( product( X, Y, Z ) ), ~( product( T, U, Z ) ), ~( product( W, Y, X
% 0.71/1.11 ) ), ~( product( W, U, T ) ), equalish( Y, U ) ]
% 0.71/1.11 ] .
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 percentage equality = 0.000000, percentage horn = 0.833333
% 0.71/1.11 This a non-horn, non-equality problem
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 Options Used:
% 0.71/1.11
% 0.71/1.11 useres = 1
% 0.71/1.11 useparamod = 0
% 0.71/1.11 useeqrefl = 0
% 0.71/1.11 useeqfact = 0
% 0.71/1.11 usefactor = 1
% 0.71/1.11 usesimpsplitting = 0
% 0.71/1.11 usesimpdemod = 0
% 0.71/1.11 usesimpres = 3
% 0.71/1.11
% 0.71/1.11 resimpinuse = 1000
% 0.71/1.11 resimpclauses = 20000
% 0.71/1.11 substype = standard
% 0.71/1.11 backwardsubs = 1
% 0.71/1.11 selectoldest = 5
% 0.71/1.11
% 0.71/1.11 litorderings [0] = split
% 0.71/1.11 litorderings [1] = liftord
% 0.71/1.11
% 0.71/1.11 termordering = none
% 0.71/1.11
% 0.71/1.11 litapriori = 1
% 0.71/1.11 termapriori = 0
% 0.71/1.11 litaposteriori = 0
% 0.71/1.11 termaposteriori = 0
% 0.71/1.11 demodaposteriori = 0
% 0.71/1.11 ordereqreflfact = 0
% 0.71/1.11
% 0.71/1.11 litselect = none
% 0.71/1.11
% 0.71/1.11 maxweight = 15
% 0.71/1.11 maxdepth = 30000
% 0.71/1.11 maxlength = 115
% 0.71/1.11 maxnrvars = 195
% 0.71/1.11 excuselevel = 1
% 0.71/1.11 increasemaxweight = 1
% 0.71/1.11
% 0.71/1.11 maxselected = 10000000
% 0.71/1.11 maxnrclauses = 10000000
% 0.71/1.11
% 0.71/1.11 showgenerated = 0
% 0.71/1.11 showkept = 0
% 0.71/1.11 showselected = 0
% 0.71/1.11 showdeleted = 0
% 0.71/1.11 showresimp = 1
% 0.71/1.11 showstatus = 2000
% 0.71/1.11
% 0.71/1.11 prologoutput = 1
% 0.71/1.11 nrgoals = 5000000
% 0.71/1.11 totalproof = 1
% 0.71/1.11
% 0.71/1.11 Symbols occurring in the translation:
% 0.71/1.11
% 0.71/1.11 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.71/1.11 . [1, 2] (w:1, o:28, a:1, s:1, b:0),
% 0.71/1.11 ! [4, 1] (w:0, o:22, a:1, s:1, b:0),
% 0.71/1.11 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.71/1.11 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.71/1.11 'group_element' [40, 1] (w:1, o:27, a:1, s:1, b:0),
% 0.71/1.11 'e_1' [42, 0] (w:1, o:14, a:1, s:1, b:0),
% 0.71/1.11 product [43, 3] (w:1, o:54, a:1, s:1, b:0),
% 0.71/1.11 'e_2' [44, 0] (w:1, o:15, a:1, s:1, b:0),
% 0.71/1.11 'e_3' [45, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.71/1.11 equalish [46, 2] (w:1, o:53, a:1, s:1, b:0).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 Starting Search:
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 Bliksems!, er is een bewijs:
% 0.71/1.11 % SZS status Unsatisfiable
% 0.71/1.11 % SZS output start Refutation
% 0.71/1.11
% 0.71/1.11 clause( 2, [ 'group_element'( 'e_1' ) ] )
% 0.71/1.11 .
% 0.71/1.11 clause( 3, [ 'group_element'( 'e_2' ) ] )
% 0.71/1.11 .
% 0.71/1.11 clause( 4, [ 'group_element'( 'e_3' ) ] )
% 0.71/1.11 .
% 0.71/1.11 clause( 5, [ ~( equalish( 'e_1', 'e_2' ) ) ] )
% 0.71/1.11 .
% 0.71/1.11 clause( 8, [ ~( equalish( 'e_2', 'e_3' ) ) ] )
% 0.71/1.11 .
% 0.71/1.11 clause( 9, [ ~( equalish( 'e_3', 'e_1' ) ) ] )
% 0.71/1.11 .
% 0.71/1.11 clause( 11, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ), product(
% 0.71/1.11 X, Y, 'e_1' ), product( X, Y, 'e_2' ), product( X, Y, 'e_3' ) ] )
% 0.71/1.11 .
% 0.71/1.11 clause( 13, [ equalish( Y, T ), ~( product( X, Y, Z ) ), ~( product( X, T,
% 0.71/1.11 Z ) ) ] )
% 0.71/1.11 .
% 0.71/1.11 clause( 14, [ equalish( X, T ), ~( product( X, Y, Z ) ), ~( product( T, Y,
% 0.71/1.11 Z ) ) ] )
% 0.71/1.11 .
% 0.71/1.11 clause( 15, [ product( X, X, X ) ] )
% 0.71/1.11 .
% 0.71/1.11 clause( 16, [ equalish( X, T ), ~( product( W, Y, X ) ), ~( product( W, U,
% 0.71/1.11 T ) ), ~( product( X, Y, Z ) ), ~( product( T, U, Z ) ) ] )
% 0.71/1.11 .
% 0.71/1.11 clause( 31, [ equalish( X, Y ), ~( product( Y, X, X ) ) ] )
% 0.71/1.11 .
% 0.71/1.11 clause( 32, [ equalish( X, Y ), ~( product( X, Y, Y ) ) ] )
% 0.71/1.11 .
% 0.71/1.11 clause( 59, [ equalish( X, Y ), ~( product( X, Y, X ) ) ] )
% 0.71/1.11 .
% 0.71/1.11 clause( 60, [ equalish( X, Y ), ~( product( Y, X, Y ) ) ] )
% 0.71/1.11 .
% 0.71/1.11 clause( 84, [ ~( 'group_element'( X ) ), equalish( X, 'e_3' ), product(
% 0.71/1.11 'e_3', X, 'e_1' ), product( 'e_3', X, 'e_2' ) ] )
% 0.71/1.11 .
% 0.71/1.11 clause( 88, [ equalish( 'e_2', 'e_3' ), product( 'e_3', 'e_2', 'e_1' ) ] )
% 0.71/1.11 .
% 0.71/1.11 clause( 89, [ product( 'e_3', 'e_2', 'e_1' ) ] )
% 0.71/1.11 .
% 0.71/1.11 clause( 91, [ equalish( X, 'e_1' ), ~( product( X, Y, Z ) ), ~( product(
% 0.71/1.11 'e_1', 'e_2', Z ) ), ~( product( 'e_3', Y, X ) ) ] )
% 0.71/1.11 .
% 0.71/1.11 clause( 101, [ ~( product( 'e_1', 'e_2', 'e_3' ) ), ~( product( 'e_3', X,
% 0.71/1.11 'e_3' ) ) ] )
% 0.71/1.11 .
% 0.71/1.11 clause( 129, [ ~( product( 'e_1', 'e_2', 'e_3' ) ) ] )
% 0.71/1.11 .
% 0.71/1.11 clause( 130, [ ~( 'group_element'( 'e_2' ) ), product( 'e_1', 'e_2', 'e_1'
% 0.71/1.11 ), product( 'e_1', 'e_2', 'e_2' ) ] )
% 0.71/1.11 .
% 0.71/1.11 clause( 131, [ product( 'e_1', 'e_2', 'e_1' ), product( 'e_1', 'e_2', 'e_2'
% 0.71/1.11 ) ] )
% 0.71/1.11 .
% 0.71/1.11 clause( 136, [ equalish( 'e_1', 'e_2' ) ] )
% 0.71/1.11 .
% 0.71/1.11 clause( 140, [] )
% 0.71/1.11 .
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 % SZS output end Refutation
% 0.71/1.11 found a proof!
% 0.71/1.11
% 0.71/1.11 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.71/1.11
% 0.71/1.11 initialclauses(
% 0.71/1.11 [ clause( 142, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ),
% 0.71/1.11 product( 'e_1', X, Y ), product( 'e_2', X, Y ), product( 'e_3', X, Y ) ]
% 0.71/1.11 )
% 0.71/1.11 , clause( 143, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ),
% 0.71/1.11 product( X, 'e_1', Y ), product( X, 'e_2', Y ), product( X, 'e_3', Y ) ]
% 0.71/1.11 )
% 0.71/1.11 , clause( 144, [ 'group_element'( 'e_1' ) ] )
% 0.71/1.11 , clause( 145, [ 'group_element'( 'e_2' ) ] )
% 0.71/1.11 , clause( 146, [ 'group_element'( 'e_3' ) ] )
% 0.71/1.11 , clause( 147, [ ~( equalish( 'e_1', 'e_2' ) ) ] )
% 0.71/1.11 , clause( 148, [ ~( equalish( 'e_1', 'e_3' ) ) ] )
% 0.71/1.11 , clause( 149, [ ~( equalish( 'e_2', 'e_1' ) ) ] )
% 0.71/1.11 , clause( 150, [ ~( equalish( 'e_2', 'e_3' ) ) ] )
% 0.71/1.11 , clause( 151, [ ~( equalish( 'e_3', 'e_1' ) ) ] )
% 0.71/1.11 , clause( 152, [ ~( equalish( 'e_3', 'e_2' ) ) ] )
% 0.71/1.11 , clause( 153, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ),
% 0.71/1.11 product( X, Y, 'e_1' ), product( X, Y, 'e_2' ), product( X, Y, 'e_3' ) ]
% 0.71/1.11 )
% 0.71/1.11 , clause( 154, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), equalish(
% 0.71/1.11 Z, T ) ] )
% 0.71/1.11 , clause( 155, [ ~( product( X, Y, Z ) ), ~( product( X, T, Z ) ), equalish(
% 0.71/1.11 Y, T ) ] )
% 0.71/1.11 , clause( 156, [ ~( product( X, Y, Z ) ), ~( product( T, Y, Z ) ), equalish(
% 0.71/1.11 X, T ) ] )
% 0.71/1.11 , clause( 157, [ product( X, X, X ) ] )
% 0.71/1.11 , clause( 158, [ ~( product( X, Y, Z ) ), ~( product( T, U, Z ) ), ~(
% 0.71/1.11 product( W, Y, X ) ), ~( product( W, U, T ) ), equalish( X, T ) ] )
% 0.71/1.11 , clause( 159, [ ~( product( X, Y, Z ) ), ~( product( T, U, Z ) ), ~(
% 0.71/1.11 product( W, Y, X ) ), ~( product( W, U, T ) ), equalish( Y, U ) ] )
% 0.71/1.11 ] ).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 subsumption(
% 0.71/1.11 clause( 2, [ 'group_element'( 'e_1' ) ] )
% 0.71/1.11 , clause( 144, [ 'group_element'( 'e_1' ) ] )
% 0.71/1.11 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 subsumption(
% 0.71/1.11 clause( 3, [ 'group_element'( 'e_2' ) ] )
% 0.71/1.11 , clause( 145, [ 'group_element'( 'e_2' ) ] )
% 0.71/1.11 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 subsumption(
% 0.71/1.11 clause( 4, [ 'group_element'( 'e_3' ) ] )
% 0.71/1.11 , clause( 146, [ 'group_element'( 'e_3' ) ] )
% 0.71/1.11 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 subsumption(
% 0.71/1.11 clause( 5, [ ~( equalish( 'e_1', 'e_2' ) ) ] )
% 0.71/1.11 , clause( 147, [ ~( equalish( 'e_1', 'e_2' ) ) ] )
% 0.71/1.11 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 subsumption(
% 0.71/1.11 clause( 8, [ ~( equalish( 'e_2', 'e_3' ) ) ] )
% 0.71/1.11 , clause( 150, [ ~( equalish( 'e_2', 'e_3' ) ) ] )
% 0.71/1.11 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 subsumption(
% 0.71/1.11 clause( 9, [ ~( equalish( 'e_3', 'e_1' ) ) ] )
% 0.71/1.11 , clause( 151, [ ~( equalish( 'e_3', 'e_1' ) ) ] )
% 0.71/1.11 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 subsumption(
% 0.71/1.11 clause( 11, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ), product(
% 0.71/1.11 X, Y, 'e_1' ), product( X, Y, 'e_2' ), product( X, Y, 'e_3' ) ] )
% 0.71/1.11 , clause( 153, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ),
% 0.71/1.11 product( X, Y, 'e_1' ), product( X, Y, 'e_2' ), product( X, Y, 'e_3' ) ]
% 0.71/1.11 )
% 0.71/1.11 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.71/1.11 ), ==>( 1, 1 ), ==>( 2, 2 ), ==>( 3, 3 ), ==>( 4, 4 )] ) ).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 subsumption(
% 0.71/1.11 clause( 13, [ equalish( Y, T ), ~( product( X, Y, Z ) ), ~( product( X, T,
% 0.71/1.11 Z ) ) ] )
% 0.71/1.11 , clause( 155, [ ~( product( X, Y, Z ) ), ~( product( X, T, Z ) ), equalish(
% 0.71/1.11 Y, T ) ] )
% 0.71/1.11 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.71/1.11 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 2 ), ==>( 2, 0 )] ) ).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 subsumption(
% 0.71/1.11 clause( 14, [ equalish( X, T ), ~( product( X, Y, Z ) ), ~( product( T, Y,
% 0.71/1.11 Z ) ) ] )
% 0.71/1.11 , clause( 156, [ ~( product( X, Y, Z ) ), ~( product( T, Y, Z ) ), equalish(
% 0.71/1.11 X, T ) ] )
% 0.71/1.11 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.71/1.11 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 2 ), ==>( 2, 0 )] ) ).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 subsumption(
% 0.71/1.11 clause( 15, [ product( X, X, X ) ] )
% 0.71/1.11 , clause( 157, [ product( X, X, X ) ] )
% 0.71/1.11 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 subsumption(
% 0.71/1.11 clause( 16, [ equalish( X, T ), ~( product( W, Y, X ) ), ~( product( W, U,
% 0.71/1.11 T ) ), ~( product( X, Y, Z ) ), ~( product( T, U, Z ) ) ] )
% 0.71/1.11 , clause( 158, [ ~( product( X, Y, Z ) ), ~( product( T, U, Z ) ), ~(
% 0.71/1.11 product( W, Y, X ) ), ~( product( W, U, T ) ), equalish( X, T ) ] )
% 0.71/1.11 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.71/1.11 , U ), :=( W, W )] ), permutation( 0, [ ==>( 0, 3 ), ==>( 1, 4 ), ==>( 2
% 0.71/1.11 , 1 ), ==>( 3, 2 ), ==>( 4, 0 )] ) ).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 resolution(
% 0.71/1.11 clause( 206, [ equalish( X, Y ), ~( product( Y, X, X ) ) ] )
% 0.71/1.11 , clause( 14, [ equalish( X, T ), ~( product( X, Y, Z ) ), ~( product( T, Y
% 0.71/1.11 , Z ) ) ] )
% 0.71/1.11 , 1, clause( 15, [ product( X, X, X ) ] )
% 0.71/1.11 , 0, substitution( 0, [ :=( X, X ), :=( Y, X ), :=( Z, X ), :=( T, Y )] ),
% 0.71/1.11 substitution( 1, [ :=( X, X )] )).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 subsumption(
% 0.71/1.11 clause( 31, [ equalish( X, Y ), ~( product( Y, X, X ) ) ] )
% 0.71/1.11 , clause( 206, [ equalish( X, Y ), ~( product( Y, X, X ) ) ] )
% 0.71/1.11 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.71/1.11 ), ==>( 1, 1 )] ) ).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 resolution(
% 0.71/1.11 clause( 209, [ equalish( X, Y ), ~( product( X, Y, Y ) ) ] )
% 0.71/1.11 , clause( 14, [ equalish( X, T ), ~( product( X, Y, Z ) ), ~( product( T, Y
% 0.71/1.11 , Z ) ) ] )
% 0.71/1.11 , 2, clause( 15, [ product( X, X, X ) ] )
% 0.71/1.11 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Y ), :=( T, Y )] ),
% 0.71/1.11 substitution( 1, [ :=( X, Y )] )).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 subsumption(
% 0.71/1.11 clause( 32, [ equalish( X, Y ), ~( product( X, Y, Y ) ) ] )
% 0.71/1.11 , clause( 209, [ equalish( X, Y ), ~( product( X, Y, Y ) ) ] )
% 0.71/1.11 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.71/1.11 ), ==>( 1, 1 )] ) ).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 resolution(
% 0.71/1.11 clause( 210, [ equalish( X, Y ), ~( product( X, Y, X ) ) ] )
% 0.71/1.11 , clause( 13, [ equalish( Y, T ), ~( product( X, Y, Z ) ), ~( product( X, T
% 0.71/1.11 , Z ) ) ] )
% 0.71/1.11 , 1, clause( 15, [ product( X, X, X ) ] )
% 0.71/1.11 , 0, substitution( 0, [ :=( X, X ), :=( Y, X ), :=( Z, X ), :=( T, Y )] ),
% 0.71/1.11 substitution( 1, [ :=( X, X )] )).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 subsumption(
% 0.71/1.11 clause( 59, [ equalish( X, Y ), ~( product( X, Y, X ) ) ] )
% 0.71/1.11 , clause( 210, [ equalish( X, Y ), ~( product( X, Y, X ) ) ] )
% 0.71/1.11 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.71/1.11 ), ==>( 1, 1 )] ) ).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 resolution(
% 0.71/1.11 clause( 213, [ equalish( X, Y ), ~( product( Y, X, Y ) ) ] )
% 0.71/1.11 , clause( 13, [ equalish( Y, T ), ~( product( X, Y, Z ) ), ~( product( X, T
% 0.71/1.11 , Z ) ) ] )
% 0.71/1.11 , 2, clause( 15, [ product( X, X, X ) ] )
% 0.71/1.11 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Y ), :=( T, Y )] ),
% 0.71/1.11 substitution( 1, [ :=( X, Y )] )).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 subsumption(
% 0.71/1.11 clause( 60, [ equalish( X, Y ), ~( product( Y, X, Y ) ) ] )
% 0.71/1.11 , clause( 213, [ equalish( X, Y ), ~( product( Y, X, Y ) ) ] )
% 0.71/1.11 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.71/1.11 ), ==>( 1, 1 )] ) ).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 resolution(
% 0.71/1.11 clause( 216, [ equalish( X, 'e_3' ), ~( 'group_element'( 'e_3' ) ), ~(
% 0.71/1.11 'group_element'( X ) ), product( 'e_3', X, 'e_1' ), product( 'e_3', X,
% 0.71/1.11 'e_2' ) ] )
% 0.71/1.11 , clause( 60, [ equalish( X, Y ), ~( product( Y, X, Y ) ) ] )
% 0.71/1.11 , 1, clause( 11, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ),
% 0.71/1.11 product( X, Y, 'e_1' ), product( X, Y, 'e_2' ), product( X, Y, 'e_3' ) ]
% 0.71/1.11 )
% 0.71/1.11 , 4, substitution( 0, [ :=( X, X ), :=( Y, 'e_3' )] ), substitution( 1, [
% 0.71/1.11 :=( X, 'e_3' ), :=( Y, X )] )).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 resolution(
% 0.71/1.11 clause( 221, [ equalish( X, 'e_3' ), ~( 'group_element'( X ) ), product(
% 0.71/1.11 'e_3', X, 'e_1' ), product( 'e_3', X, 'e_2' ) ] )
% 0.71/1.11 , clause( 216, [ equalish( X, 'e_3' ), ~( 'group_element'( 'e_3' ) ), ~(
% 0.71/1.11 'group_element'( X ) ), product( 'e_3', X, 'e_1' ), product( 'e_3', X,
% 0.71/1.11 'e_2' ) ] )
% 0.71/1.11 , 1, clause( 4, [ 'group_element'( 'e_3' ) ] )
% 0.71/1.11 , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [] )).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 subsumption(
% 0.71/1.11 clause( 84, [ ~( 'group_element'( X ) ), equalish( X, 'e_3' ), product(
% 0.71/1.11 'e_3', X, 'e_1' ), product( 'e_3', X, 'e_2' ) ] )
% 0.71/1.11 , clause( 221, [ equalish( X, 'e_3' ), ~( 'group_element'( X ) ), product(
% 0.71/1.11 'e_3', X, 'e_1' ), product( 'e_3', X, 'e_2' ) ] )
% 0.71/1.11 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1,
% 0.71/1.11 0 ), ==>( 2, 2 ), ==>( 3, 3 )] ) ).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 resolution(
% 0.71/1.11 clause( 223, [ equalish( 'e_2', 'e_3' ), ~( 'group_element'( 'e_2' ) ),
% 0.71/1.11 equalish( 'e_2', 'e_3' ), product( 'e_3', 'e_2', 'e_1' ) ] )
% 0.71/1.11 , clause( 31, [ equalish( X, Y ), ~( product( Y, X, X ) ) ] )
% 0.71/1.11 , 1, clause( 84, [ ~( 'group_element'( X ) ), equalish( X, 'e_3' ), product(
% 0.71/1.11 'e_3', X, 'e_1' ), product( 'e_3', X, 'e_2' ) ] )
% 0.71/1.11 , 3, substitution( 0, [ :=( X, 'e_2' ), :=( Y, 'e_3' )] ), substitution( 1
% 0.71/1.11 , [ :=( X, 'e_2' )] )).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 resolution(
% 0.71/1.11 clause( 226, [ equalish( 'e_2', 'e_3' ), equalish( 'e_2', 'e_3' ), product(
% 0.71/1.11 'e_3', 'e_2', 'e_1' ) ] )
% 0.71/1.11 , clause( 223, [ equalish( 'e_2', 'e_3' ), ~( 'group_element'( 'e_2' ) ),
% 0.71/1.11 equalish( 'e_2', 'e_3' ), product( 'e_3', 'e_2', 'e_1' ) ] )
% 0.71/1.11 , 1, clause( 3, [ 'group_element'( 'e_2' ) ] )
% 0.71/1.11 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 factor(
% 0.71/1.11 clause( 227, [ equalish( 'e_2', 'e_3' ), product( 'e_3', 'e_2', 'e_1' ) ]
% 0.71/1.11 )
% 0.71/1.11 , clause( 226, [ equalish( 'e_2', 'e_3' ), equalish( 'e_2', 'e_3' ),
% 0.71/1.11 product( 'e_3', 'e_2', 'e_1' ) ] )
% 0.71/1.11 , 0, 1, substitution( 0, [] )).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 subsumption(
% 0.71/1.11 clause( 88, [ equalish( 'e_2', 'e_3' ), product( 'e_3', 'e_2', 'e_1' ) ] )
% 0.71/1.11 , clause( 227, [ equalish( 'e_2', 'e_3' ), product( 'e_3', 'e_2', 'e_1' ) ]
% 0.71/1.11 )
% 0.71/1.11 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] )
% 0.71/1.11 ).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 resolution(
% 0.71/1.11 clause( 228, [ product( 'e_3', 'e_2', 'e_1' ) ] )
% 0.71/1.11 , clause( 8, [ ~( equalish( 'e_2', 'e_3' ) ) ] )
% 0.71/1.11 , 0, clause( 88, [ equalish( 'e_2', 'e_3' ), product( 'e_3', 'e_2', 'e_1' )
% 0.71/1.11 ] )
% 0.71/1.11 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 subsumption(
% 0.71/1.11 clause( 89, [ product( 'e_3', 'e_2', 'e_1' ) ] )
% 0.71/1.11 , clause( 228, [ product( 'e_3', 'e_2', 'e_1' ) ] )
% 0.71/1.11 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 resolution(
% 0.71/1.11 clause( 230, [ equalish( X, 'e_1' ), ~( product( 'e_3', Y, X ) ), ~(
% 0.71/1.11 product( X, Y, Z ) ), ~( product( 'e_1', 'e_2', Z ) ) ] )
% 0.71/1.11 , clause( 16, [ equalish( X, T ), ~( product( W, Y, X ) ), ~( product( W, U
% 0.71/1.11 , T ) ), ~( product( X, Y, Z ) ), ~( product( T, U, Z ) ) ] )
% 0.71/1.11 , 2, clause( 89, [ product( 'e_3', 'e_2', 'e_1' ) ] )
% 0.71/1.11 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, 'e_1' )
% 0.71/1.11 , :=( U, 'e_2' ), :=( W, 'e_3' )] ), substitution( 1, [] )).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 subsumption(
% 0.71/1.11 clause( 91, [ equalish( X, 'e_1' ), ~( product( X, Y, Z ) ), ~( product(
% 0.71/1.11 'e_1', 'e_2', Z ) ), ~( product( 'e_3', Y, X ) ) ] )
% 0.71/1.11 , clause( 230, [ equalish( X, 'e_1' ), ~( product( 'e_3', Y, X ) ), ~(
% 0.71/1.11 product( X, Y, Z ) ), ~( product( 'e_1', 'e_2', Z ) ) ] )
% 0.71/1.11 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.71/1.11 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 3 ), ==>( 2, 1 ), ==>( 3, 2 )] )
% 0.71/1.11 ).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 factor(
% 0.71/1.11 clause( 240, [ equalish( 'e_3', 'e_1' ), ~( product( 'e_3', X, 'e_3' ) ),
% 0.71/1.11 ~( product( 'e_1', 'e_2', 'e_3' ) ) ] )
% 0.71/1.11 , clause( 91, [ equalish( X, 'e_1' ), ~( product( X, Y, Z ) ), ~( product(
% 0.71/1.11 'e_1', 'e_2', Z ) ), ~( product( 'e_3', Y, X ) ) ] )
% 0.71/1.11 , 1, 3, substitution( 0, [ :=( X, 'e_3' ), :=( Y, X ), :=( Z, 'e_3' )] )
% 0.71/1.11 ).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 resolution(
% 0.71/1.11 clause( 241, [ ~( product( 'e_3', X, 'e_3' ) ), ~( product( 'e_1', 'e_2',
% 0.71/1.11 'e_3' ) ) ] )
% 0.71/1.11 , clause( 9, [ ~( equalish( 'e_3', 'e_1' ) ) ] )
% 0.71/1.11 , 0, clause( 240, [ equalish( 'e_3', 'e_1' ), ~( product( 'e_3', X, 'e_3' )
% 0.71/1.11 ), ~( product( 'e_1', 'e_2', 'e_3' ) ) ] )
% 0.71/1.11 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, X )] )).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 subsumption(
% 0.71/1.11 clause( 101, [ ~( product( 'e_1', 'e_2', 'e_3' ) ), ~( product( 'e_3', X,
% 0.71/1.11 'e_3' ) ) ] )
% 0.71/1.11 , clause( 241, [ ~( product( 'e_3', X, 'e_3' ) ), ~( product( 'e_1', 'e_2'
% 0.71/1.11 , 'e_3' ) ) ] )
% 0.71/1.11 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1,
% 0.71/1.11 0 )] ) ).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 resolution(
% 0.71/1.11 clause( 242, [ ~( product( 'e_1', 'e_2', 'e_3' ) ) ] )
% 0.71/1.11 , clause( 101, [ ~( product( 'e_1', 'e_2', 'e_3' ) ), ~( product( 'e_3', X
% 0.71/1.11 , 'e_3' ) ) ] )
% 0.71/1.11 , 1, clause( 15, [ product( X, X, X ) ] )
% 0.71/1.11 , 0, substitution( 0, [ :=( X, 'e_3' )] ), substitution( 1, [ :=( X, 'e_3'
% 0.71/1.11 )] )).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 subsumption(
% 0.71/1.11 clause( 129, [ ~( product( 'e_1', 'e_2', 'e_3' ) ) ] )
% 0.71/1.11 , clause( 242, [ ~( product( 'e_1', 'e_2', 'e_3' ) ) ] )
% 0.71/1.11 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 resolution(
% 0.71/1.11 clause( 243, [ ~( 'group_element'( 'e_1' ) ), ~( 'group_element'( 'e_2' ) )
% 0.71/1.11 , product( 'e_1', 'e_2', 'e_1' ), product( 'e_1', 'e_2', 'e_2' ) ] )
% 0.71/1.11 , clause( 129, [ ~( product( 'e_1', 'e_2', 'e_3' ) ) ] )
% 0.71/1.11 , 0, clause( 11, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ),
% 0.71/1.11 product( X, Y, 'e_1' ), product( X, Y, 'e_2' ), product( X, Y, 'e_3' ) ]
% 0.71/1.11 )
% 0.71/1.11 , 4, substitution( 0, [] ), substitution( 1, [ :=( X, 'e_1' ), :=( Y, 'e_2'
% 0.71/1.11 )] )).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 resolution(
% 0.71/1.11 clause( 244, [ ~( 'group_element'( 'e_2' ) ), product( 'e_1', 'e_2', 'e_1'
% 0.71/1.11 ), product( 'e_1', 'e_2', 'e_2' ) ] )
% 0.71/1.11 , clause( 243, [ ~( 'group_element'( 'e_1' ) ), ~( 'group_element'( 'e_2' )
% 0.71/1.11 ), product( 'e_1', 'e_2', 'e_1' ), product( 'e_1', 'e_2', 'e_2' ) ] )
% 0.71/1.11 , 0, clause( 2, [ 'group_element'( 'e_1' ) ] )
% 0.71/1.11 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 subsumption(
% 0.71/1.11 clause( 130, [ ~( 'group_element'( 'e_2' ) ), product( 'e_1', 'e_2', 'e_1'
% 0.71/1.11 ), product( 'e_1', 'e_2', 'e_2' ) ] )
% 0.71/1.11 , clause( 244, [ ~( 'group_element'( 'e_2' ) ), product( 'e_1', 'e_2',
% 0.71/1.11 'e_1' ), product( 'e_1', 'e_2', 'e_2' ) ] )
% 0.71/1.11 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2
% 0.71/1.11 , 2 )] ) ).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 resolution(
% 0.71/1.11 clause( 245, [ product( 'e_1', 'e_2', 'e_1' ), product( 'e_1', 'e_2', 'e_2'
% 0.71/1.11 ) ] )
% 0.71/1.11 , clause( 130, [ ~( 'group_element'( 'e_2' ) ), product( 'e_1', 'e_2',
% 0.71/1.11 'e_1' ), product( 'e_1', 'e_2', 'e_2' ) ] )
% 0.71/1.11 , 0, clause( 3, [ 'group_element'( 'e_2' ) ] )
% 0.71/1.11 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 subsumption(
% 0.71/1.11 clause( 131, [ product( 'e_1', 'e_2', 'e_1' ), product( 'e_1', 'e_2', 'e_2'
% 0.71/1.11 ) ] )
% 0.71/1.11 , clause( 245, [ product( 'e_1', 'e_2', 'e_1' ), product( 'e_1', 'e_2',
% 0.71/1.11 'e_2' ) ] )
% 0.71/1.11 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] )
% 0.71/1.11 ).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 resolution(
% 0.71/1.11 clause( 246, [ equalish( 'e_1', 'e_2' ), product( 'e_1', 'e_2', 'e_1' ) ]
% 0.71/1.11 )
% 0.71/1.11 , clause( 32, [ equalish( X, Y ), ~( product( X, Y, Y ) ) ] )
% 0.71/1.11 , 1, clause( 131, [ product( 'e_1', 'e_2', 'e_1' ), product( 'e_1', 'e_2',
% 0.71/1.11 'e_2' ) ] )
% 0.71/1.11 , 1, substitution( 0, [ :=( X, 'e_1' ), :=( Y, 'e_2' )] ), substitution( 1
% 0.71/1.11 , [] )).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 resolution(
% 0.71/1.11 clause( 247, [ equalish( 'e_1', 'e_2' ), equalish( 'e_1', 'e_2' ) ] )
% 0.71/1.11 , clause( 59, [ equalish( X, Y ), ~( product( X, Y, X ) ) ] )
% 0.71/1.11 , 1, clause( 246, [ equalish( 'e_1', 'e_2' ), product( 'e_1', 'e_2', 'e_1'
% 0.71/1.11 ) ] )
% 0.71/1.11 , 1, substitution( 0, [ :=( X, 'e_1' ), :=( Y, 'e_2' )] ), substitution( 1
% 0.71/1.11 , [] )).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 factor(
% 0.71/1.11 clause( 248, [ equalish( 'e_1', 'e_2' ) ] )
% 0.71/1.11 , clause( 247, [ equalish( 'e_1', 'e_2' ), equalish( 'e_1', 'e_2' ) ] )
% 0.71/1.11 , 0, 1, substitution( 0, [] )).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 subsumption(
% 0.71/1.11 clause( 136, [ equalish( 'e_1', 'e_2' ) ] )
% 0.71/1.11 , clause( 248, [ equalish( 'e_1', 'e_2' ) ] )
% 0.71/1.11 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 resolution(
% 0.71/1.11 clause( 249, [] )
% 0.71/1.11 , clause( 5, [ ~( equalish( 'e_1', 'e_2' ) ) ] )
% 0.71/1.11 , 0, clause( 136, [ equalish( 'e_1', 'e_2' ) ] )
% 0.71/1.11 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 subsumption(
% 0.71/1.11 clause( 140, [] )
% 0.71/1.11 , clause( 249, [] )
% 0.71/1.11 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 end.
% 0.71/1.11
% 0.71/1.11 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.71/1.11
% 0.71/1.11 Memory use:
% 0.71/1.11
% 0.71/1.11 space for terms: 2838
% 0.71/1.11 space for clauses: 5664
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 clauses generated: 412
% 0.71/1.11 clauses kept: 141
% 0.71/1.11 clauses selected: 39
% 0.71/1.11 clauses deleted: 6
% 0.71/1.11 clauses inuse deleted: 0
% 0.71/1.11
% 0.71/1.11 subsentry: 1883
% 0.71/1.11 literals s-matched: 1344
% 0.71/1.11 literals matched: 1106
% 0.71/1.11 full subsumption: 826
% 0.71/1.11
% 0.71/1.11 checksum: -936099619
% 0.71/1.11
% 0.71/1.11
% 0.71/1.11 Bliksem ended
%------------------------------------------------------------------------------