TSTP Solution File: GRP123-7.003 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GRP123-7.003 : TPTP v8.1.0. Released v1.2.0.
% 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 07:35:01 EDT 2022
% Result : Unsatisfiable 0.43s 1.11s
% Output : Refutation 0.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : GRP123-7.003 : TPTP v8.1.0. Released v1.2.0.
% 0.08/0.13 % 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 : Mon Jun 13 13:23:36 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.43/1.11 *** allocated 10000 integers for termspace/termends
% 0.43/1.11 *** allocated 10000 integers for clauses
% 0.43/1.11 *** allocated 10000 integers for justifications
% 0.43/1.11 Bliksem 1.12
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 Automatic Strategy Selection
% 0.43/1.11
% 0.43/1.11 Clauses:
% 0.43/1.11 [
% 0.43/1.11 [ next( 'e_1', 'e_2' ) ],
% 0.43/1.11 [ next( 'e_2', 'e_3' ) ],
% 0.43/1.11 [ greater( 'e_2', 'e_1' ) ],
% 0.43/1.11 [ greater( 'e_3', 'e_1' ) ],
% 0.43/1.11 [ greater( 'e_3', 'e_2' ) ],
% 0.43/1.11 [ ~( product( X, 'e_1', Y ) ), ~( next( X, Z ) ), ~( greater( Y, Z ) ) ]
% 0.43/1.11 ,
% 0.43/1.11 [ 'group_element'( 'e_1' ) ],
% 0.43/1.11 [ 'group_element'( 'e_2' ) ],
% 0.43/1.11 [ 'group_element'( 'e_3' ) ],
% 0.43/1.11 [ ~( equalish( 'e_1', 'e_2' ) ) ],
% 0.43/1.11 [ ~( equalish( 'e_1', 'e_3' ) ) ],
% 0.43/1.11 [ ~( equalish( 'e_2', 'e_1' ) ) ],
% 0.43/1.11 [ ~( equalish( 'e_2', 'e_3' ) ) ],
% 0.43/1.11 [ ~( equalish( 'e_3', 'e_1' ) ) ],
% 0.43/1.11 [ ~( equalish( 'e_3', 'e_2' ) ) ],
% 0.43/1.11 [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ), product1( X, Y,
% 0.43/1.11 'e_1' ), product1( X, Y, 'e_2' ), product1( X, Y, 'e_3' ) ],
% 0.43/1.11 [ ~( product1( X, Y, Z ) ), ~( product1( X, Y, T ) ), equalish( Z, T ) ]
% 0.43/1.11 ,
% 0.43/1.11 [ ~( product1( X, Y, Z ) ), ~( product1( X, T, Z ) ), equalish( Y, T ) ]
% 0.43/1.11 ,
% 0.43/1.11 [ ~( product1( X, Y, Z ) ), ~( product1( T, Y, Z ) ), equalish( X, T ) ]
% 0.43/1.11 ,
% 0.43/1.11 [ product1( X, X, X ) ],
% 0.43/1.11 [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ), product2( X, Y,
% 0.43/1.11 'e_1' ), product2( X, Y, 'e_2' ), product2( X, Y, 'e_3' ) ],
% 0.43/1.11 [ ~( product2( X, Y, Z ) ), ~( product2( X, Y, T ) ), equalish( Z, T ) ]
% 0.43/1.11 ,
% 0.43/1.11 [ ~( product2( X, Y, Z ) ), ~( product2( X, T, Z ) ), equalish( Y, T ) ]
% 0.43/1.11 ,
% 0.43/1.11 [ ~( product2( X, Y, Z ) ), ~( product2( T, Y, Z ) ), equalish( X, T ) ]
% 0.43/1.11 ,
% 0.43/1.11 [ product2( X, X, X ) ],
% 0.43/1.11 [ ~( product1( X, Y, Z ) ), ~( product1( Z, Y, T ) ), product2( T, X, Y
% 0.43/1.11 ) ]
% 0.43/1.11 ] .
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 percentage equality = 0.000000, percentage horn = 0.923077
% 0.43/1.11 This is a near-Horn, non-equality problem
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 Options Used:
% 0.43/1.11
% 0.43/1.11 useres = 1
% 0.43/1.11 useparamod = 0
% 0.43/1.11 useeqrefl = 0
% 0.43/1.11 useeqfact = 0
% 0.43/1.11 usefactor = 1
% 0.43/1.11 usesimpsplitting = 0
% 0.43/1.11 usesimpdemod = 0
% 0.43/1.11 usesimpres = 4
% 0.43/1.11
% 0.43/1.11 resimpinuse = 1000
% 0.43/1.11 resimpclauses = 20000
% 0.43/1.11 substype = standard
% 0.43/1.11 backwardsubs = 1
% 0.43/1.11 selectoldest = 5
% 0.43/1.11
% 0.43/1.11 litorderings [0] = split
% 0.43/1.11 litorderings [1] = liftord
% 0.43/1.11
% 0.43/1.11 termordering = none
% 0.43/1.11
% 0.43/1.11 litapriori = 1
% 0.43/1.11 termapriori = 0
% 0.43/1.11 litaposteriori = 0
% 0.43/1.11 termaposteriori = 0
% 0.43/1.11 demodaposteriori = 0
% 0.43/1.11 ordereqreflfact = 0
% 0.43/1.11
% 0.43/1.11 litselect = negative
% 0.43/1.11
% 0.43/1.11 maxweight = 30000
% 0.43/1.11 maxdepth = 30000
% 0.43/1.11 maxlength = 115
% 0.43/1.11 maxnrvars = 195
% 0.43/1.11 excuselevel = 0
% 0.43/1.11 increasemaxweight = 0
% 0.43/1.11
% 0.43/1.11 maxselected = 10000000
% 0.43/1.11 maxnrclauses = 10000000
% 0.43/1.11
% 0.43/1.11 showgenerated = 0
% 0.43/1.11 showkept = 0
% 0.43/1.11 showselected = 0
% 0.43/1.11 showdeleted = 0
% 0.43/1.11 showresimp = 1
% 0.43/1.11 showstatus = 2000
% 0.43/1.11
% 0.43/1.11 prologoutput = 1
% 0.43/1.11 nrgoals = 5000000
% 0.43/1.11 totalproof = 1
% 0.43/1.11
% 0.43/1.11 Symbols occurring in the translation:
% 0.43/1.11
% 0.43/1.11 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.43/1.11 . [1, 2] (w:1, o:25, a:1, s:1, b:0),
% 0.43/1.11 ! [4, 1] (w:1, o:19, a:1, s:1, b:0),
% 0.43/1.11 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.43/1.11 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.43/1.11 'e_1' [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.43/1.11 'e_2' [40, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.43/1.11 next [41, 2] (w:1, o:50, a:1, s:1, b:0),
% 0.43/1.11 'e_3' [42, 0] (w:1, o:11, a:1, s:1, b:0),
% 0.43/1.11 greater [43, 2] (w:1, o:51, a:1, s:1, b:0),
% 0.43/1.11 product [46, 3] (w:1, o:53, a:1, s:1, b:0),
% 0.43/1.11 'group_element' [48, 1] (w:1, o:24, a:1, s:1, b:0),
% 0.43/1.11 equalish [49, 2] (w:1, o:52, a:1, s:1, b:0),
% 0.43/1.11 product1 [50, 3] (w:1, o:54, a:1, s:1, b:0),
% 0.43/1.11 product2 [53, 3] (w:1, o:55, a:1, s:1, b:0).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 Starting Search:
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 Bliksems!, er is een bewijs:
% 0.43/1.11 % SZS status Unsatisfiable
% 0.43/1.11 % SZS output start Refutation
% 0.43/1.11
% 0.43/1.11 clause( 6, [ 'group_element'( 'e_1' ) ] )
% 0.43/1.11 .
% 0.43/1.11 clause( 7, [ 'group_element'( 'e_2' ) ] )
% 0.43/1.11 .
% 0.43/1.11 clause( 8, [ 'group_element'( 'e_3' ) ] )
% 0.43/1.11 .
% 0.43/1.11 clause( 9, [ ~( equalish( 'e_1', 'e_2' ) ) ] )
% 0.43/1.11 .
% 0.43/1.11 clause( 11, [ ~( equalish( 'e_2', 'e_1' ) ) ] )
% 0.43/1.11 .
% 0.43/1.11 clause( 12, [ ~( equalish( 'e_2', 'e_3' ) ) ] )
% 0.43/1.11 .
% 0.43/1.11 clause( 14, [ ~( equalish( 'e_3', 'e_2' ) ) ] )
% 0.43/1.11 .
% 0.43/1.11 clause( 15, [ ~( 'group_element'( X ) ), product1( X, Y, 'e_3' ), product1(
% 0.43/1.11 X, Y, 'e_1' ), product1( X, Y, 'e_2' ), ~( 'group_element'( Y ) ) ] )
% 0.43/1.11 .
% 0.43/1.11 clause( 17, [ equalish( Y, T ), ~( product1( X, Y, Z ) ), ~( product1( X, T
% 0.43/1.11 , Z ) ) ] )
% 0.43/1.11 .
% 0.43/1.11 clause( 18, [ equalish( X, T ), ~( product1( X, Y, Z ) ), ~( product1( T, Y
% 0.43/1.11 , Z ) ) ] )
% 0.43/1.11 .
% 0.43/1.11 clause( 19, [ product1( X, X, X ) ] )
% 0.43/1.11 .
% 0.43/1.11 clause( 21, [ equalish( Z, T ), ~( product2( X, Y, Z ) ), ~( product2( X, Y
% 0.43/1.11 , T ) ) ] )
% 0.43/1.11 .
% 0.43/1.11 clause( 24, [ product2( X, X, X ) ] )
% 0.43/1.11 .
% 0.43/1.11 clause( 25, [ ~( product1( X, Y, Z ) ), product2( T, X, Y ), ~( product1( Z
% 0.43/1.11 , Y, T ) ) ] )
% 0.43/1.11 .
% 0.43/1.11 clause( 34, [ product2( X, X, Y ), ~( product1( X, Y, X ) ) ] )
% 0.43/1.11 .
% 0.43/1.11 clause( 39, [ product1( X, 'e_2', 'e_3' ), product1( X, 'e_2', 'e_1' ),
% 0.43/1.11 product1( X, 'e_2', 'e_2' ), ~( 'group_element'( X ) ) ] )
% 0.43/1.11 .
% 0.43/1.11 clause( 43, [ equalish( X, Y ), ~( product1( Y, X, Y ) ) ] )
% 0.43/1.11 .
% 0.43/1.11 clause( 45, [ equalish( X, Y ), ~( product1( X, Y, Y ) ) ] )
% 0.43/1.11 .
% 0.43/1.11 clause( 47, [ equalish( X, Y ), ~( product2( Y, Y, X ) ) ] )
% 0.43/1.11 .
% 0.43/1.11 clause( 80, [ product1( 'e_1', 'e_2', 'e_1' ), product1( 'e_1', 'e_2',
% 0.43/1.11 'e_2' ), product1( 'e_1', 'e_2', 'e_3' ) ] )
% 0.43/1.11 .
% 0.43/1.11 clause( 81, [ product1( 'e_3', 'e_2', 'e_1' ), product1( 'e_3', 'e_2',
% 0.43/1.11 'e_2' ), product1( 'e_3', 'e_2', 'e_3' ) ] )
% 0.43/1.11 .
% 0.43/1.11 clause( 88, [ product1( 'e_3', 'e_2', 'e_1' ), product1( 'e_3', 'e_2',
% 0.43/1.11 'e_2' ) ] )
% 0.43/1.11 .
% 0.43/1.11 clause( 94, [ product1( 'e_3', 'e_2', 'e_1' ) ] )
% 0.43/1.11 .
% 0.43/1.11 clause( 95, [ product2( 'e_1', X, 'e_2' ), ~( product1( X, 'e_2', 'e_3' ) )
% 0.43/1.11 ] )
% 0.43/1.11 .
% 0.43/1.11 clause( 101, [ product1( 'e_1', 'e_2', 'e_2' ), product2( 'e_1', 'e_1',
% 0.43/1.11 'e_2' ) ] )
% 0.43/1.11 .
% 0.43/1.11 clause( 103, [ product1( 'e_1', 'e_2', 'e_2' ) ] )
% 0.43/1.11 .
% 0.43/1.11 clause( 106, [] )
% 0.43/1.11 .
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 % SZS output end Refutation
% 0.43/1.11 found a proof!
% 0.43/1.11
% 0.43/1.11 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.43/1.11
% 0.43/1.11 initialclauses(
% 0.43/1.11 [ clause( 108, [ next( 'e_1', 'e_2' ) ] )
% 0.43/1.11 , clause( 109, [ next( 'e_2', 'e_3' ) ] )
% 0.43/1.11 , clause( 110, [ greater( 'e_2', 'e_1' ) ] )
% 0.43/1.11 , clause( 111, [ greater( 'e_3', 'e_1' ) ] )
% 0.43/1.11 , clause( 112, [ greater( 'e_3', 'e_2' ) ] )
% 0.43/1.11 , clause( 113, [ ~( product( X, 'e_1', Y ) ), ~( next( X, Z ) ), ~( greater(
% 0.43/1.11 Y, Z ) ) ] )
% 0.43/1.11 , clause( 114, [ 'group_element'( 'e_1' ) ] )
% 0.43/1.11 , clause( 115, [ 'group_element'( 'e_2' ) ] )
% 0.43/1.11 , clause( 116, [ 'group_element'( 'e_3' ) ] )
% 0.43/1.11 , clause( 117, [ ~( equalish( 'e_1', 'e_2' ) ) ] )
% 0.43/1.11 , clause( 118, [ ~( equalish( 'e_1', 'e_3' ) ) ] )
% 0.43/1.11 , clause( 119, [ ~( equalish( 'e_2', 'e_1' ) ) ] )
% 0.43/1.11 , clause( 120, [ ~( equalish( 'e_2', 'e_3' ) ) ] )
% 0.43/1.11 , clause( 121, [ ~( equalish( 'e_3', 'e_1' ) ) ] )
% 0.43/1.11 , clause( 122, [ ~( equalish( 'e_3', 'e_2' ) ) ] )
% 0.43/1.11 , clause( 123, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ),
% 0.43/1.11 product1( X, Y, 'e_1' ), product1( X, Y, 'e_2' ), product1( X, Y, 'e_3' )
% 0.43/1.11 ] )
% 0.43/1.11 , clause( 124, [ ~( product1( X, Y, Z ) ), ~( product1( X, Y, T ) ),
% 0.43/1.11 equalish( Z, T ) ] )
% 0.43/1.11 , clause( 125, [ ~( product1( X, Y, Z ) ), ~( product1( X, T, Z ) ),
% 0.43/1.11 equalish( Y, T ) ] )
% 0.43/1.11 , clause( 126, [ ~( product1( X, Y, Z ) ), ~( product1( T, Y, Z ) ),
% 0.43/1.11 equalish( X, T ) ] )
% 0.43/1.11 , clause( 127, [ product1( X, X, X ) ] )
% 0.43/1.11 , clause( 128, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ),
% 0.43/1.11 product2( X, Y, 'e_1' ), product2( X, Y, 'e_2' ), product2( X, Y, 'e_3' )
% 0.43/1.11 ] )
% 0.43/1.11 , clause( 129, [ ~( product2( X, Y, Z ) ), ~( product2( X, Y, T ) ),
% 0.43/1.11 equalish( Z, T ) ] )
% 0.43/1.11 , clause( 130, [ ~( product2( X, Y, Z ) ), ~( product2( X, T, Z ) ),
% 0.43/1.11 equalish( Y, T ) ] )
% 0.43/1.11 , clause( 131, [ ~( product2( X, Y, Z ) ), ~( product2( T, Y, Z ) ),
% 0.43/1.11 equalish( X, T ) ] )
% 0.43/1.11 , clause( 132, [ product2( X, X, X ) ] )
% 0.43/1.11 , clause( 133, [ ~( product1( X, Y, Z ) ), ~( product1( Z, Y, T ) ),
% 0.43/1.11 product2( T, X, Y ) ] )
% 0.43/1.11 ] ).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 subsumption(
% 0.43/1.11 clause( 6, [ 'group_element'( 'e_1' ) ] )
% 0.43/1.11 , clause( 114, [ 'group_element'( 'e_1' ) ] )
% 0.43/1.11 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 subsumption(
% 0.43/1.11 clause( 7, [ 'group_element'( 'e_2' ) ] )
% 0.43/1.11 , clause( 115, [ 'group_element'( 'e_2' ) ] )
% 0.43/1.11 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 subsumption(
% 0.43/1.11 clause( 8, [ 'group_element'( 'e_3' ) ] )
% 0.43/1.11 , clause( 116, [ 'group_element'( 'e_3' ) ] )
% 0.43/1.11 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 subsumption(
% 0.43/1.11 clause( 9, [ ~( equalish( 'e_1', 'e_2' ) ) ] )
% 0.43/1.11 , clause( 117, [ ~( equalish( 'e_1', 'e_2' ) ) ] )
% 0.43/1.11 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 subsumption(
% 0.43/1.11 clause( 11, [ ~( equalish( 'e_2', 'e_1' ) ) ] )
% 0.43/1.11 , clause( 119, [ ~( equalish( 'e_2', 'e_1' ) ) ] )
% 0.43/1.11 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 subsumption(
% 0.43/1.11 clause( 12, [ ~( equalish( 'e_2', 'e_3' ) ) ] )
% 0.43/1.11 , clause( 120, [ ~( equalish( 'e_2', 'e_3' ) ) ] )
% 0.43/1.11 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 subsumption(
% 0.43/1.11 clause( 14, [ ~( equalish( 'e_3', 'e_2' ) ) ] )
% 0.43/1.11 , clause( 122, [ ~( equalish( 'e_3', 'e_2' ) ) ] )
% 0.43/1.11 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 subsumption(
% 0.43/1.11 clause( 15, [ ~( 'group_element'( X ) ), product1( X, Y, 'e_3' ), product1(
% 0.43/1.11 X, Y, 'e_1' ), product1( X, Y, 'e_2' ), ~( 'group_element'( Y ) ) ] )
% 0.43/1.11 , clause( 123, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ),
% 0.43/1.11 product1( X, Y, 'e_1' ), product1( X, Y, 'e_2' ), product1( X, Y, 'e_3' )
% 0.43/1.11 ] )
% 0.43/1.11 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.43/1.11 ), ==>( 1, 4 ), ==>( 2, 2 ), ==>( 3, 3 ), ==>( 4, 1 )] ) ).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 subsumption(
% 0.43/1.11 clause( 17, [ equalish( Y, T ), ~( product1( X, Y, Z ) ), ~( product1( X, T
% 0.43/1.11 , Z ) ) ] )
% 0.43/1.11 , clause( 125, [ ~( product1( X, Y, Z ) ), ~( product1( X, T, Z ) ),
% 0.43/1.11 equalish( Y, T ) ] )
% 0.43/1.11 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.43/1.11 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 2 ), ==>( 2, 0 )] ) ).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 subsumption(
% 0.43/1.11 clause( 18, [ equalish( X, T ), ~( product1( X, Y, Z ) ), ~( product1( T, Y
% 0.43/1.11 , Z ) ) ] )
% 0.43/1.11 , clause( 126, [ ~( product1( X, Y, Z ) ), ~( product1( T, Y, Z ) ),
% 0.43/1.11 equalish( X, T ) ] )
% 0.43/1.11 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.43/1.11 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 2 ), ==>( 2, 0 )] ) ).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 subsumption(
% 0.43/1.11 clause( 19, [ product1( X, X, X ) ] )
% 0.43/1.11 , clause( 127, [ product1( X, X, X ) ] )
% 0.43/1.11 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 subsumption(
% 0.43/1.11 clause( 21, [ equalish( Z, T ), ~( product2( X, Y, Z ) ), ~( product2( X, Y
% 0.43/1.11 , T ) ) ] )
% 0.43/1.11 , clause( 129, [ ~( product2( X, Y, Z ) ), ~( product2( X, Y, T ) ),
% 0.43/1.11 equalish( Z, T ) ] )
% 0.43/1.11 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.43/1.11 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 2 ), ==>( 2, 0 )] ) ).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 subsumption(
% 0.43/1.11 clause( 24, [ product2( X, X, X ) ] )
% 0.43/1.11 , clause( 132, [ product2( X, X, X ) ] )
% 0.43/1.11 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 subsumption(
% 0.43/1.11 clause( 25, [ ~( product1( X, Y, Z ) ), product2( T, X, Y ), ~( product1( Z
% 0.43/1.11 , Y, T ) ) ] )
% 0.43/1.11 , clause( 133, [ ~( product1( X, Y, Z ) ), ~( product1( Z, Y, T ) ),
% 0.43/1.11 product2( T, X, Y ) ] )
% 0.43/1.11 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.43/1.11 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 2 ), ==>( 2, 1 )] ) ).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 factor(
% 0.43/1.11 clause( 169, [ ~( product1( X, Y, X ) ), product2( X, X, Y ) ] )
% 0.43/1.11 , clause( 25, [ ~( product1( X, Y, Z ) ), product2( T, X, Y ), ~( product1(
% 0.43/1.11 Z, Y, T ) ) ] )
% 0.43/1.11 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, X ), :=( T, X )] )
% 0.43/1.11 ).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 subsumption(
% 0.43/1.11 clause( 34, [ product2( X, X, Y ), ~( product1( X, Y, X ) ) ] )
% 0.43/1.11 , clause( 169, [ ~( product1( X, Y, X ) ), product2( X, X, Y ) ] )
% 0.43/1.11 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 1
% 0.43/1.11 ), ==>( 1, 0 )] ) ).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 resolution(
% 0.43/1.11 clause( 171, [ ~( 'group_element'( X ) ), product1( X, 'e_2', 'e_3' ),
% 0.43/1.11 product1( X, 'e_2', 'e_1' ), product1( X, 'e_2', 'e_2' ) ] )
% 0.43/1.11 , clause( 15, [ ~( 'group_element'( X ) ), product1( X, Y, 'e_3' ),
% 0.43/1.11 product1( X, Y, 'e_1' ), product1( X, Y, 'e_2' ), ~( 'group_element'( Y )
% 0.43/1.11 ) ] )
% 0.43/1.11 , 4, clause( 7, [ 'group_element'( 'e_2' ) ] )
% 0.43/1.11 , 0, substitution( 0, [ :=( X, X ), :=( Y, 'e_2' )] ), substitution( 1, [] )
% 0.43/1.11 ).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 subsumption(
% 0.43/1.11 clause( 39, [ product1( X, 'e_2', 'e_3' ), product1( X, 'e_2', 'e_1' ),
% 0.43/1.11 product1( X, 'e_2', 'e_2' ), ~( 'group_element'( X ) ) ] )
% 0.43/1.11 , clause( 171, [ ~( 'group_element'( X ) ), product1( X, 'e_2', 'e_3' ),
% 0.43/1.11 product1( X, 'e_2', 'e_1' ), product1( X, 'e_2', 'e_2' ) ] )
% 0.43/1.11 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 3 ), ==>( 1,
% 0.43/1.11 0 ), ==>( 2, 1 ), ==>( 3, 2 )] ) ).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 resolution(
% 0.43/1.11 clause( 173, [ equalish( X, Y ), ~( product1( Y, X, Y ) ) ] )
% 0.43/1.11 , clause( 17, [ equalish( Y, T ), ~( product1( X, Y, Z ) ), ~( product1( X
% 0.43/1.11 , T, Z ) ) ] )
% 0.43/1.11 , 2, clause( 19, [ product1( X, X, X ) ] )
% 0.43/1.11 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Y ), :=( T, Y )] ),
% 0.43/1.11 substitution( 1, [ :=( X, Y )] )).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 subsumption(
% 0.43/1.11 clause( 43, [ equalish( X, Y ), ~( product1( Y, X, Y ) ) ] )
% 0.43/1.11 , clause( 173, [ equalish( X, Y ), ~( product1( Y, X, Y ) ) ] )
% 0.43/1.11 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.43/1.11 ), ==>( 1, 1 )] ) ).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 resolution(
% 0.43/1.11 clause( 175, [ equalish( X, Y ), ~( product1( X, Y, Y ) ) ] )
% 0.43/1.11 , clause( 18, [ equalish( X, T ), ~( product1( X, Y, Z ) ), ~( product1( T
% 0.43/1.11 , Y, Z ) ) ] )
% 0.43/1.11 , 2, clause( 19, [ product1( X, X, X ) ] )
% 0.43/1.11 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Y ), :=( T, Y )] ),
% 0.43/1.11 substitution( 1, [ :=( X, Y )] )).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 subsumption(
% 0.43/1.11 clause( 45, [ equalish( X, Y ), ~( product1( X, Y, Y ) ) ] )
% 0.43/1.11 , clause( 175, [ equalish( X, Y ), ~( product1( X, Y, Y ) ) ] )
% 0.43/1.11 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.43/1.11 ), ==>( 1, 1 )] ) ).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 resolution(
% 0.43/1.11 clause( 177, [ equalish( X, Y ), ~( product2( Y, Y, X ) ) ] )
% 0.43/1.11 , clause( 21, [ equalish( Z, T ), ~( product2( X, Y, Z ) ), ~( product2( X
% 0.43/1.11 , Y, T ) ) ] )
% 0.43/1.11 , 2, clause( 24, [ product2( X, X, X ) ] )
% 0.43/1.11 , 0, substitution( 0, [ :=( X, Y ), :=( Y, Y ), :=( Z, X ), :=( T, Y )] ),
% 0.43/1.11 substitution( 1, [ :=( X, Y )] )).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 subsumption(
% 0.43/1.11 clause( 47, [ equalish( X, Y ), ~( product2( Y, Y, X ) ) ] )
% 0.43/1.11 , clause( 177, [ equalish( X, Y ), ~( product2( Y, Y, X ) ) ] )
% 0.43/1.11 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.43/1.11 ), ==>( 1, 1 )] ) ).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 resolution(
% 0.43/1.11 clause( 178, [ product1( 'e_1', 'e_2', 'e_3' ), product1( 'e_1', 'e_2',
% 0.43/1.11 'e_1' ), product1( 'e_1', 'e_2', 'e_2' ) ] )
% 0.43/1.11 , clause( 39, [ product1( X, 'e_2', 'e_3' ), product1( X, 'e_2', 'e_1' ),
% 0.43/1.11 product1( X, 'e_2', 'e_2' ), ~( 'group_element'( X ) ) ] )
% 0.43/1.11 , 3, clause( 6, [ 'group_element'( 'e_1' ) ] )
% 0.43/1.11 , 0, substitution( 0, [ :=( X, 'e_1' )] ), substitution( 1, [] )).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 subsumption(
% 0.43/1.11 clause( 80, [ product1( 'e_1', 'e_2', 'e_1' ), product1( 'e_1', 'e_2',
% 0.43/1.11 'e_2' ), product1( 'e_1', 'e_2', 'e_3' ) ] )
% 0.43/1.11 , clause( 178, [ product1( 'e_1', 'e_2', 'e_3' ), product1( 'e_1', 'e_2',
% 0.43/1.11 'e_1' ), product1( 'e_1', 'e_2', 'e_2' ) ] )
% 0.43/1.11 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 2 ), ==>( 1, 0 ), ==>( 2
% 0.43/1.11 , 1 )] ) ).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 resolution(
% 0.43/1.11 clause( 179, [ product1( 'e_3', 'e_2', 'e_3' ), product1( 'e_3', 'e_2',
% 0.43/1.11 'e_1' ), product1( 'e_3', 'e_2', 'e_2' ) ] )
% 0.43/1.11 , clause( 39, [ product1( X, 'e_2', 'e_3' ), product1( X, 'e_2', 'e_1' ),
% 0.43/1.11 product1( X, 'e_2', 'e_2' ), ~( 'group_element'( X ) ) ] )
% 0.43/1.11 , 3, clause( 8, [ 'group_element'( 'e_3' ) ] )
% 0.43/1.11 , 0, substitution( 0, [ :=( X, 'e_3' )] ), substitution( 1, [] )).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 subsumption(
% 0.43/1.11 clause( 81, [ product1( 'e_3', 'e_2', 'e_1' ), product1( 'e_3', 'e_2',
% 0.43/1.11 'e_2' ), product1( 'e_3', 'e_2', 'e_3' ) ] )
% 0.43/1.11 , clause( 179, [ product1( 'e_3', 'e_2', 'e_3' ), product1( 'e_3', 'e_2',
% 0.43/1.11 'e_1' ), product1( 'e_3', 'e_2', 'e_2' ) ] )
% 0.43/1.11 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 2 ), ==>( 1, 0 ), ==>( 2
% 0.43/1.11 , 1 )] ) ).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 resolution(
% 0.43/1.11 clause( 180, [ equalish( 'e_2', 'e_3' ), product1( 'e_3', 'e_2', 'e_1' ),
% 0.43/1.11 product1( 'e_3', 'e_2', 'e_2' ) ] )
% 0.43/1.11 , clause( 43, [ equalish( X, Y ), ~( product1( Y, X, Y ) ) ] )
% 0.43/1.11 , 1, clause( 81, [ product1( 'e_3', 'e_2', 'e_1' ), product1( 'e_3', 'e_2'
% 0.43/1.11 , 'e_2' ), product1( 'e_3', 'e_2', 'e_3' ) ] )
% 0.43/1.11 , 2, substitution( 0, [ :=( X, 'e_2' ), :=( Y, 'e_3' )] ), substitution( 1
% 0.43/1.11 , [] )).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 resolution(
% 0.43/1.11 clause( 181, [ product1( 'e_3', 'e_2', 'e_1' ), product1( 'e_3', 'e_2',
% 0.43/1.11 'e_2' ) ] )
% 0.43/1.11 , clause( 12, [ ~( equalish( 'e_2', 'e_3' ) ) ] )
% 0.43/1.11 , 0, clause( 180, [ equalish( 'e_2', 'e_3' ), product1( 'e_3', 'e_2', 'e_1'
% 0.43/1.11 ), product1( 'e_3', 'e_2', 'e_2' ) ] )
% 0.43/1.11 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 subsumption(
% 0.43/1.11 clause( 88, [ product1( 'e_3', 'e_2', 'e_1' ), product1( 'e_3', 'e_2',
% 0.43/1.11 'e_2' ) ] )
% 0.43/1.11 , clause( 181, [ product1( 'e_3', 'e_2', 'e_1' ), product1( 'e_3', 'e_2',
% 0.43/1.11 'e_2' ) ] )
% 0.43/1.11 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] )
% 0.43/1.11 ).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 resolution(
% 0.43/1.11 clause( 182, [ equalish( 'e_3', 'e_2' ), product1( 'e_3', 'e_2', 'e_1' ) ]
% 0.43/1.11 )
% 0.43/1.11 , clause( 45, [ equalish( X, Y ), ~( product1( X, Y, Y ) ) ] )
% 0.43/1.11 , 1, clause( 88, [ product1( 'e_3', 'e_2', 'e_1' ), product1( 'e_3', 'e_2'
% 0.43/1.11 , 'e_2' ) ] )
% 0.43/1.11 , 1, substitution( 0, [ :=( X, 'e_3' ), :=( Y, 'e_2' )] ), substitution( 1
% 0.43/1.11 , [] )).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 resolution(
% 0.43/1.11 clause( 183, [ product1( 'e_3', 'e_2', 'e_1' ) ] )
% 0.43/1.11 , clause( 14, [ ~( equalish( 'e_3', 'e_2' ) ) ] )
% 0.43/1.11 , 0, clause( 182, [ equalish( 'e_3', 'e_2' ), product1( 'e_3', 'e_2', 'e_1'
% 0.43/1.11 ) ] )
% 0.43/1.11 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 subsumption(
% 0.43/1.11 clause( 94, [ product1( 'e_3', 'e_2', 'e_1' ) ] )
% 0.43/1.11 , clause( 183, [ product1( 'e_3', 'e_2', 'e_1' ) ] )
% 0.43/1.11 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 resolution(
% 0.43/1.11 clause( 185, [ ~( product1( X, 'e_2', 'e_3' ) ), product2( 'e_1', X, 'e_2'
% 0.43/1.11 ) ] )
% 0.43/1.11 , clause( 25, [ ~( product1( X, Y, Z ) ), product2( T, X, Y ), ~( product1(
% 0.43/1.11 Z, Y, T ) ) ] )
% 0.43/1.11 , 2, clause( 94, [ product1( 'e_3', 'e_2', 'e_1' ) ] )
% 0.43/1.11 , 0, substitution( 0, [ :=( X, X ), :=( Y, 'e_2' ), :=( Z, 'e_3' ), :=( T,
% 0.43/1.11 'e_1' )] ), substitution( 1, [] )).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 subsumption(
% 0.43/1.11 clause( 95, [ product2( 'e_1', X, 'e_2' ), ~( product1( X, 'e_2', 'e_3' ) )
% 0.43/1.11 ] )
% 0.43/1.11 , clause( 185, [ ~( product1( X, 'e_2', 'e_3' ) ), product2( 'e_1', X,
% 0.43/1.11 'e_2' ) ] )
% 0.43/1.11 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1,
% 0.43/1.11 0 )] ) ).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 resolution(
% 0.43/1.11 clause( 186, [ product2( 'e_1', 'e_1', 'e_2' ), product1( 'e_1', 'e_2',
% 0.43/1.11 'e_1' ), product1( 'e_1', 'e_2', 'e_2' ) ] )
% 0.43/1.11 , clause( 95, [ product2( 'e_1', X, 'e_2' ), ~( product1( X, 'e_2', 'e_3' )
% 0.43/1.11 ) ] )
% 0.43/1.11 , 1, clause( 80, [ product1( 'e_1', 'e_2', 'e_1' ), product1( 'e_1', 'e_2'
% 0.43/1.11 , 'e_2' ), product1( 'e_1', 'e_2', 'e_3' ) ] )
% 0.43/1.11 , 2, substitution( 0, [ :=( X, 'e_1' )] ), substitution( 1, [] )).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 resolution(
% 0.43/1.11 clause( 187, [ product2( 'e_1', 'e_1', 'e_2' ), product2( 'e_1', 'e_1',
% 0.43/1.11 'e_2' ), product1( 'e_1', 'e_2', 'e_2' ) ] )
% 0.43/1.11 , clause( 34, [ product2( X, X, Y ), ~( product1( X, Y, X ) ) ] )
% 0.43/1.11 , 1, clause( 186, [ product2( 'e_1', 'e_1', 'e_2' ), product1( 'e_1', 'e_2'
% 0.43/1.11 , 'e_1' ), product1( 'e_1', 'e_2', 'e_2' ) ] )
% 0.43/1.11 , 1, substitution( 0, [ :=( X, 'e_1' ), :=( Y, 'e_2' )] ), substitution( 1
% 0.43/1.11 , [] )).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 factor(
% 0.43/1.11 clause( 188, [ product2( 'e_1', 'e_1', 'e_2' ), product1( 'e_1', 'e_2',
% 0.43/1.11 'e_2' ) ] )
% 0.43/1.11 , clause( 187, [ product2( 'e_1', 'e_1', 'e_2' ), product2( 'e_1', 'e_1',
% 0.43/1.11 'e_2' ), product1( 'e_1', 'e_2', 'e_2' ) ] )
% 0.43/1.11 , 0, 1, substitution( 0, [] )).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 subsumption(
% 0.43/1.11 clause( 101, [ product1( 'e_1', 'e_2', 'e_2' ), product2( 'e_1', 'e_1',
% 0.43/1.11 'e_2' ) ] )
% 0.43/1.11 , clause( 188, [ product2( 'e_1', 'e_1', 'e_2' ), product1( 'e_1', 'e_2',
% 0.43/1.11 'e_2' ) ] )
% 0.43/1.11 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] )
% 0.43/1.11 ).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 resolution(
% 0.43/1.11 clause( 189, [ equalish( 'e_2', 'e_1' ), product1( 'e_1', 'e_2', 'e_2' ) ]
% 0.43/1.11 )
% 0.43/1.11 , clause( 47, [ equalish( X, Y ), ~( product2( Y, Y, X ) ) ] )
% 0.43/1.11 , 1, clause( 101, [ product1( 'e_1', 'e_2', 'e_2' ), product2( 'e_1', 'e_1'
% 0.43/1.11 , 'e_2' ) ] )
% 0.43/1.11 , 1, substitution( 0, [ :=( X, 'e_2' ), :=( Y, 'e_1' )] ), substitution( 1
% 0.43/1.11 , [] )).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 resolution(
% 0.43/1.11 clause( 190, [ product1( 'e_1', 'e_2', 'e_2' ) ] )
% 0.43/1.11 , clause( 11, [ ~( equalish( 'e_2', 'e_1' ) ) ] )
% 0.43/1.11 , 0, clause( 189, [ equalish( 'e_2', 'e_1' ), product1( 'e_1', 'e_2', 'e_2'
% 0.43/1.11 ) ] )
% 0.43/1.11 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 subsumption(
% 0.43/1.11 clause( 103, [ product1( 'e_1', 'e_2', 'e_2' ) ] )
% 0.43/1.11 , clause( 190, [ product1( 'e_1', 'e_2', 'e_2' ) ] )
% 0.43/1.11 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 resolution(
% 0.43/1.11 clause( 191, [ equalish( 'e_1', 'e_2' ) ] )
% 0.43/1.11 , clause( 45, [ equalish( X, Y ), ~( product1( X, Y, Y ) ) ] )
% 0.43/1.11 , 1, clause( 103, [ product1( 'e_1', 'e_2', 'e_2' ) ] )
% 0.43/1.11 , 0, substitution( 0, [ :=( X, 'e_1' ), :=( Y, 'e_2' )] ), substitution( 1
% 0.43/1.11 , [] )).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 resolution(
% 0.43/1.11 clause( 192, [] )
% 0.43/1.11 , clause( 9, [ ~( equalish( 'e_1', 'e_2' ) ) ] )
% 0.43/1.11 , 0, clause( 191, [ equalish( 'e_1', 'e_2' ) ] )
% 0.43/1.11 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 subsumption(
% 0.43/1.11 clause( 106, [] )
% 0.43/1.11 , clause( 192, [] )
% 0.43/1.11 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 end.
% 0.43/1.11
% 0.43/1.11 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.43/1.11
% 0.43/1.11 Memory use:
% 0.43/1.11
% 0.43/1.11 space for terms: 1661
% 0.43/1.11 space for clauses: 5820
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 clauses generated: 161
% 0.43/1.11 clauses kept: 107
% 0.43/1.11 clauses selected: 71
% 0.43/1.11 clauses deleted: 7
% 0.43/1.11 clauses inuse deleted: 0
% 0.43/1.11
% 0.43/1.11 subsentry: 324
% 0.43/1.11 literals s-matched: 186
% 0.43/1.11 literals matched: 160
% 0.43/1.11 full subsumption: 36
% 0.43/1.11
% 0.43/1.11 checksum: 1128168011
% 0.43/1.11
% 0.43/1.11
% 0.43/1.11 Bliksem ended
%------------------------------------------------------------------------------