TSTP Solution File: GRP123-6.003 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GRP123-6.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n025.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 0.46s 1.14s
% Output : Refutation 0.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP123-6.003 : TPTP v8.1.0. Released v1.2.0.
% 0.07/0.14 % Command : bliksem %s
% 0.13/0.35 % Computer : n025.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % DateTime : Mon Jun 13 15:38:54 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.46/1.14 *** allocated 10000 integers for termspace/termends
% 0.46/1.14 *** allocated 10000 integers for clauses
% 0.46/1.14 *** allocated 10000 integers for justifications
% 0.46/1.14 Bliksem 1.12
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 Automatic Strategy Selection
% 0.46/1.14
% 0.46/1.14 Clauses:
% 0.46/1.14 [
% 0.46/1.14 [ 'group_element'( 'e_1' ) ],
% 0.46/1.14 [ 'group_element'( 'e_2' ) ],
% 0.46/1.14 [ 'group_element'( 'e_3' ) ],
% 0.46/1.14 [ ~( equalish( 'e_1', 'e_2' ) ) ],
% 0.46/1.14 [ ~( equalish( 'e_1', 'e_3' ) ) ],
% 0.46/1.14 [ ~( equalish( 'e_2', 'e_1' ) ) ],
% 0.46/1.14 [ ~( equalish( 'e_2', 'e_3' ) ) ],
% 0.46/1.14 [ ~( equalish( 'e_3', 'e_1' ) ) ],
% 0.46/1.14 [ ~( equalish( 'e_3', 'e_2' ) ) ],
% 0.46/1.14 [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ), product1( X, Y,
% 0.46/1.14 'e_1' ), product1( X, Y, 'e_2' ), product1( X, Y, 'e_3' ) ],
% 0.46/1.14 [ ~( product1( X, Y, Z ) ), ~( product1( X, Y, T ) ), equalish( Z, T ) ]
% 0.46/1.14 ,
% 0.46/1.14 [ ~( product1( X, Y, Z ) ), ~( product1( X, T, Z ) ), equalish( Y, T ) ]
% 0.46/1.14 ,
% 0.46/1.14 [ ~( product1( X, Y, Z ) ), ~( product1( T, Y, Z ) ), equalish( X, T ) ]
% 0.46/1.14 ,
% 0.46/1.14 [ product1( X, X, X ) ],
% 0.46/1.14 [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ), product2( X, Y,
% 0.46/1.14 'e_1' ), product2( X, Y, 'e_2' ), product2( X, Y, 'e_3' ) ],
% 0.46/1.14 [ ~( product2( X, Y, Z ) ), ~( product2( X, Y, T ) ), equalish( Z, T ) ]
% 0.46/1.14 ,
% 0.46/1.14 [ ~( product2( X, Y, Z ) ), ~( product2( X, T, Z ) ), equalish( Y, T ) ]
% 0.46/1.14 ,
% 0.46/1.14 [ ~( product2( X, Y, Z ) ), ~( product2( T, Y, Z ) ), equalish( X, T ) ]
% 0.46/1.14 ,
% 0.46/1.14 [ product2( X, X, X ) ],
% 0.46/1.14 [ ~( product1( X, Y, Z ) ), ~( product1( Z, Y, T ) ), product2( T, X, Y
% 0.46/1.14 ) ]
% 0.46/1.14 ] .
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 percentage equality = 0.000000, percentage horn = 0.900000
% 0.46/1.14 This is a near-Horn, non-equality problem
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 Options Used:
% 0.46/1.14
% 0.46/1.14 useres = 1
% 0.46/1.14 useparamod = 0
% 0.46/1.14 useeqrefl = 0
% 0.46/1.14 useeqfact = 0
% 0.46/1.14 usefactor = 1
% 0.46/1.14 usesimpsplitting = 0
% 0.46/1.14 usesimpdemod = 0
% 0.46/1.14 usesimpres = 4
% 0.46/1.14
% 0.46/1.14 resimpinuse = 1000
% 0.46/1.14 resimpclauses = 20000
% 0.46/1.14 substype = standard
% 0.46/1.14 backwardsubs = 1
% 0.46/1.14 selectoldest = 5
% 0.46/1.14
% 0.46/1.14 litorderings [0] = split
% 0.46/1.14 litorderings [1] = liftord
% 0.46/1.14
% 0.46/1.14 termordering = none
% 0.46/1.14
% 0.46/1.14 litapriori = 1
% 0.46/1.14 termapriori = 0
% 0.46/1.14 litaposteriori = 0
% 0.46/1.14 termaposteriori = 0
% 0.46/1.14 demodaposteriori = 0
% 0.46/1.14 ordereqreflfact = 0
% 0.46/1.14
% 0.46/1.14 litselect = negative
% 0.46/1.14
% 0.46/1.14 maxweight = 30000
% 0.46/1.14 maxdepth = 30000
% 0.46/1.14 maxlength = 115
% 0.46/1.14 maxnrvars = 195
% 0.46/1.14 excuselevel = 0
% 0.46/1.14 increasemaxweight = 0
% 0.46/1.14
% 0.46/1.14 maxselected = 10000000
% 0.46/1.14 maxnrclauses = 10000000
% 0.46/1.14
% 0.46/1.14 showgenerated = 0
% 0.46/1.14 showkept = 0
% 0.46/1.14 showselected = 0
% 0.46/1.14 showdeleted = 0
% 0.46/1.14 showresimp = 1
% 0.46/1.14 showstatus = 2000
% 0.46/1.14
% 0.46/1.14 prologoutput = 1
% 0.46/1.14 nrgoals = 5000000
% 0.46/1.14 totalproof = 1
% 0.46/1.14
% 0.46/1.14 Symbols occurring in the translation:
% 0.46/1.14
% 0.46/1.14 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.46/1.14 . [1, 2] (w:1, o:24, a:1, s:1, b:0),
% 0.46/1.14 ! [4, 1] (w:1, o:18, a:1, s:1, b:0),
% 0.46/1.14 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.46/1.14 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.46/1.14 'e_1' [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.46/1.14 'group_element' [40, 1] (w:1, o:23, a:1, s:1, b:0),
% 0.46/1.14 'e_2' [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.46/1.14 'e_3' [42, 0] (w:1, o:11, a:1, s:1, b:0),
% 0.46/1.14 equalish [43, 2] (w:1, o:49, a:1, s:1, b:0),
% 0.46/1.14 product1 [46, 3] (w:1, o:50, a:1, s:1, b:0),
% 0.46/1.14 product2 [49, 3] (w:1, o:51, a:1, s:1, b:0).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 Starting Search:
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 Bliksems!, er is een bewijs:
% 0.46/1.14 % SZS status Unsatisfiable
% 0.46/1.14 % SZS output start Refutation
% 0.46/1.14
% 0.46/1.14 clause( 0, [ 'group_element'( 'e_1' ) ] )
% 0.46/1.14 .
% 0.46/1.14 clause( 1, [ 'group_element'( 'e_2' ) ] )
% 0.46/1.14 .
% 0.46/1.14 clause( 2, [ 'group_element'( 'e_3' ) ] )
% 0.46/1.14 .
% 0.46/1.14 clause( 3, [ ~( equalish( 'e_1', 'e_2' ) ) ] )
% 0.46/1.14 .
% 0.46/1.14 clause( 4, [ ~( equalish( 'e_1', 'e_3' ) ) ] )
% 0.46/1.14 .
% 0.46/1.14 clause( 5, [ ~( equalish( 'e_2', 'e_1' ) ) ] )
% 0.46/1.14 .
% 0.46/1.14 clause( 7, [ ~( equalish( 'e_3', 'e_1' ) ) ] )
% 0.46/1.14 .
% 0.46/1.14 clause( 9, [ ~( 'group_element'( X ) ), product1( X, Y, 'e_3' ), product1(
% 0.46/1.14 X, Y, 'e_1' ), product1( X, Y, 'e_2' ), ~( 'group_element'( Y ) ) ] )
% 0.46/1.14 .
% 0.46/1.14 clause( 11, [ equalish( Y, T ), ~( product1( X, Y, Z ) ), ~( product1( X, T
% 0.46/1.14 , Z ) ) ] )
% 0.46/1.14 .
% 0.46/1.14 clause( 12, [ equalish( X, T ), ~( product1( X, Y, Z ) ), ~( product1( T, Y
% 0.46/1.14 , Z ) ) ] )
% 0.46/1.14 .
% 0.46/1.14 clause( 13, [ product1( X, X, X ) ] )
% 0.46/1.14 .
% 0.46/1.14 clause( 15, [ equalish( Z, T ), ~( product2( X, Y, Z ) ), ~( product2( X, Y
% 0.46/1.14 , T ) ) ] )
% 0.46/1.14 .
% 0.46/1.14 clause( 18, [ product2( X, X, X ) ] )
% 0.46/1.14 .
% 0.46/1.14 clause( 19, [ ~( product1( X, Y, Z ) ), product2( T, X, Y ), ~( product1( Z
% 0.46/1.14 , Y, T ) ) ] )
% 0.46/1.14 .
% 0.46/1.14 clause( 28, [ product2( X, X, Y ), ~( product1( X, Y, X ) ) ] )
% 0.46/1.14 .
% 0.46/1.14 clause( 30, [ product1( X, 'e_1', 'e_3' ), product1( X, 'e_1', 'e_1' ),
% 0.46/1.14 product1( X, 'e_1', 'e_2' ), ~( 'group_element'( X ) ) ] )
% 0.46/1.14 .
% 0.46/1.14 clause( 36, [ equalish( X, Y ), ~( product1( Y, X, Y ) ) ] )
% 0.46/1.14 .
% 0.46/1.14 clause( 37, [ equalish( X, Y ), ~( product2( Y, Y, X ) ) ] )
% 0.46/1.14 .
% 0.46/1.14 clause( 38, [ equalish( X, Y ), ~( product1( X, Y, Y ) ) ] )
% 0.46/1.14 .
% 0.46/1.14 clause( 40, [ product1( 'e_2', 'e_1', 'e_1' ), product1( 'e_2', 'e_1',
% 0.46/1.14 'e_2' ), product1( 'e_2', 'e_1', 'e_3' ) ] )
% 0.46/1.14 .
% 0.46/1.14 clause( 41, [ product1( 'e_3', 'e_1', 'e_1' ), product1( 'e_3', 'e_1',
% 0.46/1.14 'e_2' ), product1( 'e_3', 'e_1', 'e_3' ) ] )
% 0.46/1.14 .
% 0.46/1.14 clause( 51, [ product1( 'e_3', 'e_1', 'e_1' ), product1( 'e_3', 'e_1',
% 0.46/1.14 'e_2' ) ] )
% 0.46/1.14 .
% 0.46/1.14 clause( 52, [ product1( 'e_3', 'e_1', 'e_1' ), product2( 'e_2', X, 'e_1' )
% 0.46/1.14 , ~( product1( X, 'e_1', 'e_3' ) ) ] )
% 0.46/1.14 .
% 0.46/1.14 clause( 56, [ product1( 'e_3', 'e_1', 'e_1' ), product1( 'e_2', 'e_1',
% 0.46/1.14 'e_1' ), product2( 'e_2', 'e_2', 'e_1' ) ] )
% 0.46/1.14 .
% 0.46/1.14 clause( 57, [ product1( 'e_2', 'e_1', 'e_1' ), product1( 'e_3', 'e_1',
% 0.46/1.14 'e_1' ) ] )
% 0.46/1.14 .
% 0.46/1.14 clause( 60, [ product1( 'e_2', 'e_1', 'e_1' ) ] )
% 0.46/1.14 .
% 0.46/1.14 clause( 63, [] )
% 0.46/1.14 .
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 % SZS output end Refutation
% 0.46/1.14 found a proof!
% 0.46/1.14
% 0.46/1.14 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.46/1.14
% 0.46/1.14 initialclauses(
% 0.46/1.14 [ clause( 65, [ 'group_element'( 'e_1' ) ] )
% 0.46/1.14 , clause( 66, [ 'group_element'( 'e_2' ) ] )
% 0.46/1.14 , clause( 67, [ 'group_element'( 'e_3' ) ] )
% 0.46/1.14 , clause( 68, [ ~( equalish( 'e_1', 'e_2' ) ) ] )
% 0.46/1.14 , clause( 69, [ ~( equalish( 'e_1', 'e_3' ) ) ] )
% 0.46/1.14 , clause( 70, [ ~( equalish( 'e_2', 'e_1' ) ) ] )
% 0.46/1.14 , clause( 71, [ ~( equalish( 'e_2', 'e_3' ) ) ] )
% 0.46/1.14 , clause( 72, [ ~( equalish( 'e_3', 'e_1' ) ) ] )
% 0.46/1.14 , clause( 73, [ ~( equalish( 'e_3', 'e_2' ) ) ] )
% 0.46/1.14 , clause( 74, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ),
% 0.46/1.14 product1( X, Y, 'e_1' ), product1( X, Y, 'e_2' ), product1( X, Y, 'e_3' )
% 0.46/1.14 ] )
% 0.46/1.14 , clause( 75, [ ~( product1( X, Y, Z ) ), ~( product1( X, Y, T ) ),
% 0.46/1.14 equalish( Z, T ) ] )
% 0.46/1.14 , clause( 76, [ ~( product1( X, Y, Z ) ), ~( product1( X, T, Z ) ),
% 0.46/1.14 equalish( Y, T ) ] )
% 0.46/1.14 , clause( 77, [ ~( product1( X, Y, Z ) ), ~( product1( T, Y, Z ) ),
% 0.46/1.14 equalish( X, T ) ] )
% 0.46/1.14 , clause( 78, [ product1( X, X, X ) ] )
% 0.46/1.14 , clause( 79, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ),
% 0.46/1.14 product2( X, Y, 'e_1' ), product2( X, Y, 'e_2' ), product2( X, Y, 'e_3' )
% 0.46/1.14 ] )
% 0.46/1.14 , clause( 80, [ ~( product2( X, Y, Z ) ), ~( product2( X, Y, T ) ),
% 0.46/1.14 equalish( Z, T ) ] )
% 0.46/1.14 , clause( 81, [ ~( product2( X, Y, Z ) ), ~( product2( X, T, Z ) ),
% 0.46/1.14 equalish( Y, T ) ] )
% 0.46/1.14 , clause( 82, [ ~( product2( X, Y, Z ) ), ~( product2( T, Y, Z ) ),
% 0.46/1.14 equalish( X, T ) ] )
% 0.46/1.14 , clause( 83, [ product2( X, X, X ) ] )
% 0.46/1.14 , clause( 84, [ ~( product1( X, Y, Z ) ), ~( product1( Z, Y, T ) ),
% 0.46/1.14 product2( T, X, Y ) ] )
% 0.46/1.14 ] ).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 subsumption(
% 0.46/1.14 clause( 0, [ 'group_element'( 'e_1' ) ] )
% 0.46/1.14 , clause( 65, [ 'group_element'( 'e_1' ) ] )
% 0.46/1.14 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 subsumption(
% 0.46/1.14 clause( 1, [ 'group_element'( 'e_2' ) ] )
% 0.46/1.14 , clause( 66, [ 'group_element'( 'e_2' ) ] )
% 0.46/1.14 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 subsumption(
% 0.46/1.14 clause( 2, [ 'group_element'( 'e_3' ) ] )
% 0.46/1.14 , clause( 67, [ 'group_element'( 'e_3' ) ] )
% 0.46/1.14 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 subsumption(
% 0.46/1.14 clause( 3, [ ~( equalish( 'e_1', 'e_2' ) ) ] )
% 0.46/1.14 , clause( 68, [ ~( equalish( 'e_1', 'e_2' ) ) ] )
% 0.46/1.14 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 subsumption(
% 0.46/1.14 clause( 4, [ ~( equalish( 'e_1', 'e_3' ) ) ] )
% 0.46/1.14 , clause( 69, [ ~( equalish( 'e_1', 'e_3' ) ) ] )
% 0.46/1.14 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 subsumption(
% 0.46/1.14 clause( 5, [ ~( equalish( 'e_2', 'e_1' ) ) ] )
% 0.46/1.14 , clause( 70, [ ~( equalish( 'e_2', 'e_1' ) ) ] )
% 0.46/1.14 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 subsumption(
% 0.46/1.14 clause( 7, [ ~( equalish( 'e_3', 'e_1' ) ) ] )
% 0.46/1.14 , clause( 72, [ ~( equalish( 'e_3', 'e_1' ) ) ] )
% 0.46/1.14 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 subsumption(
% 0.46/1.14 clause( 9, [ ~( 'group_element'( X ) ), product1( X, Y, 'e_3' ), product1(
% 0.46/1.14 X, Y, 'e_1' ), product1( X, Y, 'e_2' ), ~( 'group_element'( Y ) ) ] )
% 0.46/1.14 , clause( 74, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ),
% 0.46/1.14 product1( X, Y, 'e_1' ), product1( X, Y, 'e_2' ), product1( X, Y, 'e_3' )
% 0.46/1.14 ] )
% 0.46/1.14 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.46/1.14 ), ==>( 1, 4 ), ==>( 2, 2 ), ==>( 3, 3 ), ==>( 4, 1 )] ) ).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 subsumption(
% 0.46/1.14 clause( 11, [ equalish( Y, T ), ~( product1( X, Y, Z ) ), ~( product1( X, T
% 0.46/1.14 , Z ) ) ] )
% 0.46/1.14 , clause( 76, [ ~( product1( X, Y, Z ) ), ~( product1( X, T, Z ) ),
% 0.46/1.14 equalish( Y, T ) ] )
% 0.46/1.14 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.46/1.14 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 2 ), ==>( 2, 0 )] ) ).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 subsumption(
% 0.46/1.14 clause( 12, [ equalish( X, T ), ~( product1( X, Y, Z ) ), ~( product1( T, Y
% 0.46/1.14 , Z ) ) ] )
% 0.46/1.14 , clause( 77, [ ~( product1( X, Y, Z ) ), ~( product1( T, Y, Z ) ),
% 0.46/1.14 equalish( X, T ) ] )
% 0.46/1.14 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.46/1.14 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 2 ), ==>( 2, 0 )] ) ).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 subsumption(
% 0.46/1.14 clause( 13, [ product1( X, X, X ) ] )
% 0.46/1.14 , clause( 78, [ product1( X, X, X ) ] )
% 0.46/1.14 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 subsumption(
% 0.46/1.14 clause( 15, [ equalish( Z, T ), ~( product2( X, Y, Z ) ), ~( product2( X, Y
% 0.46/1.14 , T ) ) ] )
% 0.46/1.14 , clause( 80, [ ~( product2( X, Y, Z ) ), ~( product2( X, Y, T ) ),
% 0.46/1.14 equalish( Z, T ) ] )
% 0.46/1.14 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.46/1.14 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 2 ), ==>( 2, 0 )] ) ).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 subsumption(
% 0.46/1.14 clause( 18, [ product2( X, X, X ) ] )
% 0.46/1.14 , clause( 83, [ product2( X, X, X ) ] )
% 0.46/1.14 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 subsumption(
% 0.46/1.14 clause( 19, [ ~( product1( X, Y, Z ) ), product2( T, X, Y ), ~( product1( Z
% 0.46/1.14 , Y, T ) ) ] )
% 0.46/1.14 , clause( 84, [ ~( product1( X, Y, Z ) ), ~( product1( Z, Y, T ) ),
% 0.46/1.14 product2( T, X, Y ) ] )
% 0.46/1.14 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.46/1.14 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 2 ), ==>( 2, 1 )] ) ).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 factor(
% 0.46/1.14 clause( 120, [ ~( product1( X, Y, X ) ), product2( X, X, Y ) ] )
% 0.46/1.14 , clause( 19, [ ~( product1( X, Y, Z ) ), product2( T, X, Y ), ~( product1(
% 0.46/1.14 Z, Y, T ) ) ] )
% 0.46/1.14 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, X ), :=( T, X )] )
% 0.46/1.14 ).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 subsumption(
% 0.46/1.14 clause( 28, [ product2( X, X, Y ), ~( product1( X, Y, X ) ) ] )
% 0.46/1.14 , clause( 120, [ ~( product1( X, Y, X ) ), product2( X, X, Y ) ] )
% 0.46/1.14 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 1
% 0.46/1.14 ), ==>( 1, 0 )] ) ).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 resolution(
% 0.46/1.14 clause( 122, [ ~( 'group_element'( X ) ), product1( X, 'e_1', 'e_3' ),
% 0.46/1.14 product1( X, 'e_1', 'e_1' ), product1( X, 'e_1', 'e_2' ) ] )
% 0.46/1.14 , clause( 9, [ ~( 'group_element'( X ) ), product1( X, Y, 'e_3' ), product1(
% 0.46/1.14 X, Y, 'e_1' ), product1( X, Y, 'e_2' ), ~( 'group_element'( Y ) ) ] )
% 0.46/1.14 , 4, clause( 0, [ 'group_element'( 'e_1' ) ] )
% 0.46/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, 'e_1' )] ), substitution( 1, [] )
% 0.46/1.14 ).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 subsumption(
% 0.46/1.14 clause( 30, [ product1( X, 'e_1', 'e_3' ), product1( X, 'e_1', 'e_1' ),
% 0.46/1.14 product1( X, 'e_1', 'e_2' ), ~( 'group_element'( X ) ) ] )
% 0.46/1.14 , clause( 122, [ ~( 'group_element'( X ) ), product1( X, 'e_1', 'e_3' ),
% 0.46/1.14 product1( X, 'e_1', 'e_1' ), product1( X, 'e_1', 'e_2' ) ] )
% 0.46/1.14 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 3 ), ==>( 1,
% 0.46/1.14 0 ), ==>( 2, 1 ), ==>( 3, 2 )] ) ).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 resolution(
% 0.46/1.14 clause( 124, [ equalish( X, Y ), ~( product1( Y, X, Y ) ) ] )
% 0.46/1.14 , clause( 11, [ equalish( Y, T ), ~( product1( X, Y, Z ) ), ~( product1( X
% 0.46/1.14 , T, Z ) ) ] )
% 0.46/1.14 , 2, clause( 13, [ product1( X, X, X ) ] )
% 0.46/1.14 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Y ), :=( T, Y )] ),
% 0.46/1.14 substitution( 1, [ :=( X, Y )] )).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 subsumption(
% 0.46/1.14 clause( 36, [ equalish( X, Y ), ~( product1( Y, X, Y ) ) ] )
% 0.46/1.14 , clause( 124, [ equalish( X, Y ), ~( product1( Y, X, Y ) ) ] )
% 0.46/1.14 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.46/1.14 ), ==>( 1, 1 )] ) ).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 resolution(
% 0.46/1.14 clause( 126, [ equalish( X, Y ), ~( product2( Y, Y, X ) ) ] )
% 0.46/1.14 , clause( 15, [ equalish( Z, T ), ~( product2( X, Y, Z ) ), ~( product2( X
% 0.46/1.14 , Y, T ) ) ] )
% 0.46/1.14 , 2, clause( 18, [ product2( X, X, X ) ] )
% 0.46/1.14 , 0, substitution( 0, [ :=( X, Y ), :=( Y, Y ), :=( Z, X ), :=( T, Y )] ),
% 0.46/1.14 substitution( 1, [ :=( X, Y )] )).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 subsumption(
% 0.46/1.14 clause( 37, [ equalish( X, Y ), ~( product2( Y, Y, X ) ) ] )
% 0.46/1.14 , clause( 126, [ equalish( X, Y ), ~( product2( Y, Y, X ) ) ] )
% 0.46/1.14 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.46/1.14 ), ==>( 1, 1 )] ) ).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 resolution(
% 0.46/1.14 clause( 128, [ equalish( X, Y ), ~( product1( X, Y, Y ) ) ] )
% 0.46/1.14 , clause( 12, [ equalish( X, T ), ~( product1( X, Y, Z ) ), ~( product1( T
% 0.46/1.14 , Y, Z ) ) ] )
% 0.46/1.14 , 2, clause( 13, [ product1( X, X, X ) ] )
% 0.46/1.14 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Y ), :=( T, Y )] ),
% 0.46/1.14 substitution( 1, [ :=( X, Y )] )).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 subsumption(
% 0.46/1.14 clause( 38, [ equalish( X, Y ), ~( product1( X, Y, Y ) ) ] )
% 0.46/1.14 , clause( 128, [ equalish( X, Y ), ~( product1( X, Y, Y ) ) ] )
% 0.46/1.14 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.46/1.14 ), ==>( 1, 1 )] ) ).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 resolution(
% 0.46/1.14 clause( 129, [ product1( 'e_2', 'e_1', 'e_3' ), product1( 'e_2', 'e_1',
% 0.46/1.14 'e_1' ), product1( 'e_2', 'e_1', 'e_2' ) ] )
% 0.46/1.14 , clause( 30, [ product1( X, 'e_1', 'e_3' ), product1( X, 'e_1', 'e_1' ),
% 0.46/1.14 product1( X, 'e_1', 'e_2' ), ~( 'group_element'( X ) ) ] )
% 0.46/1.14 , 3, clause( 1, [ 'group_element'( 'e_2' ) ] )
% 0.46/1.14 , 0, substitution( 0, [ :=( X, 'e_2' )] ), substitution( 1, [] )).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 subsumption(
% 0.46/1.14 clause( 40, [ product1( 'e_2', 'e_1', 'e_1' ), product1( 'e_2', 'e_1',
% 0.46/1.14 'e_2' ), product1( 'e_2', 'e_1', 'e_3' ) ] )
% 0.46/1.14 , clause( 129, [ product1( 'e_2', 'e_1', 'e_3' ), product1( 'e_2', 'e_1',
% 0.46/1.14 'e_1' ), product1( 'e_2', 'e_1', 'e_2' ) ] )
% 0.46/1.14 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 2 ), ==>( 1, 0 ), ==>( 2
% 0.46/1.14 , 1 )] ) ).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 resolution(
% 0.46/1.14 clause( 130, [ product1( 'e_3', 'e_1', 'e_3' ), product1( 'e_3', 'e_1',
% 0.46/1.14 'e_1' ), product1( 'e_3', 'e_1', 'e_2' ) ] )
% 0.46/1.14 , clause( 30, [ product1( X, 'e_1', 'e_3' ), product1( X, 'e_1', 'e_1' ),
% 0.46/1.14 product1( X, 'e_1', 'e_2' ), ~( 'group_element'( X ) ) ] )
% 0.46/1.14 , 3, clause( 2, [ 'group_element'( 'e_3' ) ] )
% 0.46/1.14 , 0, substitution( 0, [ :=( X, 'e_3' )] ), substitution( 1, [] )).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 subsumption(
% 0.46/1.14 clause( 41, [ product1( 'e_3', 'e_1', 'e_1' ), product1( 'e_3', 'e_1',
% 0.46/1.14 'e_2' ), product1( 'e_3', 'e_1', 'e_3' ) ] )
% 0.46/1.14 , clause( 130, [ product1( 'e_3', 'e_1', 'e_3' ), product1( 'e_3', 'e_1',
% 0.46/1.14 'e_1' ), product1( 'e_3', 'e_1', 'e_2' ) ] )
% 0.46/1.14 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 2 ), ==>( 1, 0 ), ==>( 2
% 0.46/1.14 , 1 )] ) ).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 resolution(
% 0.46/1.14 clause( 131, [ equalish( 'e_1', 'e_3' ), product1( 'e_3', 'e_1', 'e_1' ),
% 0.46/1.14 product1( 'e_3', 'e_1', 'e_2' ) ] )
% 0.46/1.14 , clause( 36, [ equalish( X, Y ), ~( product1( Y, X, Y ) ) ] )
% 0.46/1.14 , 1, clause( 41, [ product1( 'e_3', 'e_1', 'e_1' ), product1( 'e_3', 'e_1'
% 0.46/1.14 , 'e_2' ), product1( 'e_3', 'e_1', 'e_3' ) ] )
% 0.46/1.14 , 2, substitution( 0, [ :=( X, 'e_1' ), :=( Y, 'e_3' )] ), substitution( 1
% 0.46/1.14 , [] )).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 resolution(
% 0.46/1.14 clause( 132, [ product1( 'e_3', 'e_1', 'e_1' ), product1( 'e_3', 'e_1',
% 0.46/1.14 'e_2' ) ] )
% 0.46/1.14 , clause( 4, [ ~( equalish( 'e_1', 'e_3' ) ) ] )
% 0.46/1.14 , 0, clause( 131, [ equalish( 'e_1', 'e_3' ), product1( 'e_3', 'e_1', 'e_1'
% 0.46/1.14 ), product1( 'e_3', 'e_1', 'e_2' ) ] )
% 0.46/1.14 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 subsumption(
% 0.46/1.14 clause( 51, [ product1( 'e_3', 'e_1', 'e_1' ), product1( 'e_3', 'e_1',
% 0.46/1.14 'e_2' ) ] )
% 0.46/1.14 , clause( 132, [ product1( 'e_3', 'e_1', 'e_1' ), product1( 'e_3', 'e_1',
% 0.46/1.14 'e_2' ) ] )
% 0.46/1.14 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] )
% 0.46/1.14 ).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 resolution(
% 0.46/1.14 clause( 136, [ ~( product1( X, 'e_1', 'e_3' ) ), product2( 'e_2', X, 'e_1'
% 0.46/1.14 ), product1( 'e_3', 'e_1', 'e_1' ) ] )
% 0.46/1.14 , clause( 19, [ ~( product1( X, Y, Z ) ), product2( T, X, Y ), ~( product1(
% 0.46/1.14 Z, Y, T ) ) ] )
% 0.46/1.14 , 2, clause( 51, [ product1( 'e_3', 'e_1', 'e_1' ), product1( 'e_3', 'e_1'
% 0.46/1.14 , 'e_2' ) ] )
% 0.46/1.14 , 1, substitution( 0, [ :=( X, X ), :=( Y, 'e_1' ), :=( Z, 'e_3' ), :=( T,
% 0.46/1.14 'e_2' )] ), substitution( 1, [] )).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 subsumption(
% 0.46/1.14 clause( 52, [ product1( 'e_3', 'e_1', 'e_1' ), product2( 'e_2', X, 'e_1' )
% 0.46/1.14 , ~( product1( X, 'e_1', 'e_3' ) ) ] )
% 0.46/1.14 , clause( 136, [ ~( product1( X, 'e_1', 'e_3' ) ), product2( 'e_2', X,
% 0.46/1.14 'e_1' ), product1( 'e_3', 'e_1', 'e_1' ) ] )
% 0.46/1.14 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 2 ), ==>( 1,
% 0.46/1.14 1 ), ==>( 2, 0 )] ) ).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 resolution(
% 0.46/1.14 clause( 137, [ product1( 'e_3', 'e_1', 'e_1' ), product2( 'e_2', 'e_2',
% 0.46/1.14 'e_1' ), product1( 'e_2', 'e_1', 'e_1' ), product1( 'e_2', 'e_1', 'e_2' )
% 0.46/1.14 ] )
% 0.46/1.14 , clause( 52, [ product1( 'e_3', 'e_1', 'e_1' ), product2( 'e_2', X, 'e_1'
% 0.46/1.14 ), ~( product1( X, 'e_1', 'e_3' ) ) ] )
% 0.46/1.14 , 2, clause( 40, [ product1( 'e_2', 'e_1', 'e_1' ), product1( 'e_2', 'e_1'
% 0.46/1.14 , 'e_2' ), product1( 'e_2', 'e_1', 'e_3' ) ] )
% 0.46/1.14 , 2, substitution( 0, [ :=( X, 'e_2' )] ), substitution( 1, [] )).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 resolution(
% 0.46/1.14 clause( 138, [ product2( 'e_2', 'e_2', 'e_1' ), product1( 'e_3', 'e_1',
% 0.46/1.14 'e_1' ), product2( 'e_2', 'e_2', 'e_1' ), product1( 'e_2', 'e_1', 'e_1' )
% 0.46/1.14 ] )
% 0.46/1.14 , clause( 28, [ product2( X, X, Y ), ~( product1( X, Y, X ) ) ] )
% 0.46/1.14 , 1, clause( 137, [ product1( 'e_3', 'e_1', 'e_1' ), product2( 'e_2', 'e_2'
% 0.46/1.14 , 'e_1' ), product1( 'e_2', 'e_1', 'e_1' ), product1( 'e_2', 'e_1', 'e_2'
% 0.46/1.14 ) ] )
% 0.46/1.14 , 3, substitution( 0, [ :=( X, 'e_2' ), :=( Y, 'e_1' )] ), substitution( 1
% 0.46/1.14 , [] )).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 factor(
% 0.46/1.14 clause( 139, [ product2( 'e_2', 'e_2', 'e_1' ), product1( 'e_3', 'e_1',
% 0.46/1.14 'e_1' ), product1( 'e_2', 'e_1', 'e_1' ) ] )
% 0.46/1.14 , clause( 138, [ product2( 'e_2', 'e_2', 'e_1' ), product1( 'e_3', 'e_1',
% 0.46/1.14 'e_1' ), product2( 'e_2', 'e_2', 'e_1' ), product1( 'e_2', 'e_1', 'e_1' )
% 0.46/1.14 ] )
% 0.46/1.14 , 0, 2, substitution( 0, [] )).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 subsumption(
% 0.46/1.14 clause( 56, [ product1( 'e_3', 'e_1', 'e_1' ), product1( 'e_2', 'e_1',
% 0.46/1.14 'e_1' ), product2( 'e_2', 'e_2', 'e_1' ) ] )
% 0.46/1.14 , clause( 139, [ product2( 'e_2', 'e_2', 'e_1' ), product1( 'e_3', 'e_1',
% 0.46/1.14 'e_1' ), product1( 'e_2', 'e_1', 'e_1' ) ] )
% 0.46/1.14 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 2 ), ==>( 1, 0 ), ==>( 2
% 0.46/1.14 , 1 )] ) ).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 resolution(
% 0.46/1.14 clause( 140, [ equalish( 'e_1', 'e_2' ), product1( 'e_3', 'e_1', 'e_1' ),
% 0.46/1.14 product1( 'e_2', 'e_1', 'e_1' ) ] )
% 0.46/1.14 , clause( 37, [ equalish( X, Y ), ~( product2( Y, Y, X ) ) ] )
% 0.46/1.14 , 1, clause( 56, [ product1( 'e_3', 'e_1', 'e_1' ), product1( 'e_2', 'e_1'
% 0.46/1.14 , 'e_1' ), product2( 'e_2', 'e_2', 'e_1' ) ] )
% 0.46/1.14 , 2, substitution( 0, [ :=( X, 'e_1' ), :=( Y, 'e_2' )] ), substitution( 1
% 0.46/1.14 , [] )).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 resolution(
% 0.46/1.14 clause( 141, [ product1( 'e_3', 'e_1', 'e_1' ), product1( 'e_2', 'e_1',
% 0.46/1.14 'e_1' ) ] )
% 0.46/1.14 , clause( 3, [ ~( equalish( 'e_1', 'e_2' ) ) ] )
% 0.46/1.14 , 0, clause( 140, [ equalish( 'e_1', 'e_2' ), product1( 'e_3', 'e_1', 'e_1'
% 0.46/1.14 ), product1( 'e_2', 'e_1', 'e_1' ) ] )
% 0.46/1.14 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 subsumption(
% 0.46/1.14 clause( 57, [ product1( 'e_2', 'e_1', 'e_1' ), product1( 'e_3', 'e_1',
% 0.46/1.14 'e_1' ) ] )
% 0.46/1.14 , clause( 141, [ product1( 'e_3', 'e_1', 'e_1' ), product1( 'e_2', 'e_1',
% 0.46/1.14 'e_1' ) ] )
% 0.46/1.14 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] )
% 0.46/1.14 ).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 resolution(
% 0.46/1.14 clause( 143, [ equalish( 'e_3', 'e_1' ), product1( 'e_2', 'e_1', 'e_1' ) ]
% 0.46/1.14 )
% 0.46/1.14 , clause( 38, [ equalish( X, Y ), ~( product1( X, Y, Y ) ) ] )
% 0.46/1.14 , 1, clause( 57, [ product1( 'e_2', 'e_1', 'e_1' ), product1( 'e_3', 'e_1'
% 0.46/1.14 , 'e_1' ) ] )
% 0.46/1.14 , 1, substitution( 0, [ :=( X, 'e_3' ), :=( Y, 'e_1' )] ), substitution( 1
% 0.46/1.14 , [] )).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 resolution(
% 0.46/1.14 clause( 144, [ product1( 'e_2', 'e_1', 'e_1' ) ] )
% 0.46/1.14 , clause( 7, [ ~( equalish( 'e_3', 'e_1' ) ) ] )
% 0.46/1.14 , 0, clause( 143, [ equalish( 'e_3', 'e_1' ), product1( 'e_2', 'e_1', 'e_1'
% 0.46/1.14 ) ] )
% 0.46/1.14 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 subsumption(
% 0.46/1.14 clause( 60, [ product1( 'e_2', 'e_1', 'e_1' ) ] )
% 0.46/1.14 , clause( 144, [ product1( 'e_2', 'e_1', 'e_1' ) ] )
% 0.46/1.14 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 resolution(
% 0.46/1.14 clause( 145, [ equalish( 'e_2', 'e_1' ) ] )
% 0.46/1.14 , clause( 38, [ equalish( X, Y ), ~( product1( X, Y, Y ) ) ] )
% 0.46/1.14 , 1, clause( 60, [ product1( 'e_2', 'e_1', 'e_1' ) ] )
% 0.46/1.14 , 0, substitution( 0, [ :=( X, 'e_2' ), :=( Y, 'e_1' )] ), substitution( 1
% 0.46/1.14 , [] )).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 resolution(
% 0.46/1.14 clause( 146, [] )
% 0.46/1.14 , clause( 5, [ ~( equalish( 'e_2', 'e_1' ) ) ] )
% 0.46/1.14 , 0, clause( 145, [ equalish( 'e_2', 'e_1' ) ] )
% 0.46/1.14 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 subsumption(
% 0.46/1.14 clause( 63, [] )
% 0.46/1.14 , clause( 146, [] )
% 0.46/1.14 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 end.
% 0.46/1.14
% 0.46/1.14 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.46/1.14
% 0.46/1.14 Memory use:
% 0.46/1.14
% 0.46/1.14 space for terms: 1103
% 0.46/1.14 space for clauses: 3371
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 clauses generated: 95
% 0.46/1.14 clauses kept: 64
% 0.46/1.14 clauses selected: 43
% 0.46/1.14 clauses deleted: 5
% 0.46/1.14 clauses inuse deleted: 0
% 0.46/1.14
% 0.46/1.14 subsentry: 211
% 0.46/1.14 literals s-matched: 109
% 0.46/1.14 literals matched: 97
% 0.46/1.14 full subsumption: 36
% 0.46/1.14
% 0.46/1.14 checksum: -270879484
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 Bliksem ended
%------------------------------------------------------------------------------