TSTP Solution File: GRP131-1.002 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GRP131-1.002 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n006.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 07:35:26 EDT 2022
% Result : Unsatisfiable 0.69s 1.09s
% Output : Refutation 0.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP131-1.002 : TPTP v8.1.0. Released v1.2.0.
% 0.11/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Tue Jun 14 09:55:26 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.69/1.09 *** allocated 10000 integers for termspace/termends
% 0.69/1.09 *** allocated 10000 integers for clauses
% 0.69/1.09 *** allocated 10000 integers for justifications
% 0.69/1.09 Bliksem 1.12
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 Automatic Strategy Selection
% 0.69/1.09
% 0.69/1.09 Clauses:
% 0.69/1.09 [
% 0.69/1.09 [ 'group_element'( 'e_1' ) ],
% 0.69/1.09 [ 'group_element'( 'e_2' ) ],
% 0.69/1.09 [ ~( equalish( 'e_1', 'e_2' ) ) ],
% 0.69/1.09 [ ~( equalish( 'e_2', 'e_1' ) ) ],
% 0.69/1.09 [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ), product( X, Y,
% 0.69/1.09 'e_1' ), product( X, Y, 'e_2' ) ],
% 0.69/1.09 [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), equalish( Z, T ) ]
% 0.69/1.09 ,
% 0.69/1.09 [ ~( product( X, Y, Z ) ), ~( product( X, T, Z ) ), equalish( Y, T ) ]
% 0.69/1.09 ,
% 0.69/1.09 [ ~( product( X, Y, Z ) ), ~( product( T, Y, Z ) ), equalish( X, T ) ]
% 0.69/1.09 ,
% 0.69/1.09 [ ~( product( X, Y, Z ) ), ~( product( T, U, Z ) ), ~( product( W, Y, X
% 0.69/1.09 ) ), ~( product( W, U, T ) ), equalish( X, T ) ],
% 0.69/1.09 [ ~( product( X, Y, Z ) ), ~( product( T, U, Z ) ), ~( product( W, Y, X
% 0.69/1.09 ) ), ~( product( W, U, T ) ), equalish( Y, U ) ]
% 0.69/1.09 ] .
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 percentage equality = 0.000000, percentage horn = 0.900000
% 0.69/1.09 This is a near-Horn, non-equality problem
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 Options Used:
% 0.69/1.09
% 0.69/1.09 useres = 1
% 0.69/1.09 useparamod = 0
% 0.69/1.09 useeqrefl = 0
% 0.69/1.09 useeqfact = 0
% 0.69/1.09 usefactor = 1
% 0.69/1.09 usesimpsplitting = 0
% 0.69/1.09 usesimpdemod = 0
% 0.69/1.09 usesimpres = 4
% 0.69/1.09
% 0.69/1.09 resimpinuse = 1000
% 0.69/1.09 resimpclauses = 20000
% 0.69/1.09 substype = standard
% 0.69/1.09 backwardsubs = 1
% 0.69/1.09 selectoldest = 5
% 0.69/1.09
% 0.69/1.09 litorderings [0] = split
% 0.69/1.09 litorderings [1] = liftord
% 0.69/1.09
% 0.69/1.09 termordering = none
% 0.69/1.09
% 0.69/1.09 litapriori = 1
% 0.69/1.09 termapriori = 0
% 0.69/1.09 litaposteriori = 0
% 0.69/1.09 termaposteriori = 0
% 0.69/1.09 demodaposteriori = 0
% 0.69/1.09 ordereqreflfact = 0
% 0.69/1.09
% 0.69/1.09 litselect = negative
% 0.69/1.09
% 0.69/1.09 maxweight = 30000
% 0.69/1.09 maxdepth = 30000
% 0.69/1.09 maxlength = 115
% 0.69/1.09 maxnrvars = 195
% 0.69/1.09 excuselevel = 0
% 0.69/1.09 increasemaxweight = 0
% 0.69/1.09
% 0.69/1.09 maxselected = 10000000
% 0.69/1.09 maxnrclauses = 10000000
% 0.69/1.09
% 0.69/1.09 showgenerated = 0
% 0.69/1.09 showkept = 0
% 0.69/1.09 showselected = 0
% 0.69/1.09 showdeleted = 0
% 0.69/1.09 showresimp = 1
% 0.69/1.09 showstatus = 2000
% 0.69/1.09
% 0.69/1.09 prologoutput = 1
% 0.69/1.09 nrgoals = 5000000
% 0.69/1.09 totalproof = 1
% 0.69/1.09
% 0.69/1.09 Symbols occurring in the translation:
% 0.69/1.09
% 0.69/1.09 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.69/1.09 . [1, 2] (w:1, o:27, a:1, s:1, b:0),
% 0.69/1.09 ! [4, 1] (w:1, o:21, a:1, s:1, b:0),
% 0.69/1.09 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.69/1.09 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.69/1.09 'e_1' [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.69/1.09 'group_element' [40, 1] (w:1, o:26, a:1, s:1, b:0),
% 0.69/1.09 'e_2' [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.69/1.09 equalish [42, 2] (w:1, o:52, a:1, s:1, b:0),
% 0.69/1.09 product [45, 3] (w:1, o:53, a:1, s:1, b:0).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 Starting Search:
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 Bliksems!, er is een bewijs:
% 0.69/1.09 % SZS status Unsatisfiable
% 0.69/1.09 % SZS output start Refutation
% 0.69/1.09
% 0.69/1.09 clause( 0, [ 'group_element'( 'e_1' ) ] )
% 0.69/1.09 .
% 0.69/1.09 clause( 1, [ 'group_element'( 'e_2' ) ] )
% 0.69/1.09 .
% 0.69/1.09 clause( 2, [ ~( equalish( 'e_1', 'e_2' ) ) ] )
% 0.69/1.09 .
% 0.69/1.09 clause( 3, [ ~( equalish( 'e_2', 'e_1' ) ) ] )
% 0.69/1.09 .
% 0.69/1.09 clause( 4, [ ~( 'group_element'( X ) ), product( X, Y, 'e_2' ), product( X
% 0.69/1.09 , Y, 'e_1' ), ~( 'group_element'( Y ) ) ] )
% 0.69/1.09 .
% 0.69/1.09 clause( 6, [ equalish( Y, T ), ~( product( X, Y, Z ) ), ~( product( X, T, Z
% 0.69/1.09 ) ) ] )
% 0.69/1.09 .
% 0.69/1.09 clause( 7, [ equalish( X, T ), ~( product( X, Y, Z ) ), ~( product( T, Y, Z
% 0.69/1.09 ) ) ] )
% 0.69/1.09 .
% 0.69/1.09 clause( 9, [ equalish( Y, U ), ~( product( W, Y, X ) ), ~( product( T, U, Z
% 0.69/1.09 ) ), ~( product( X, Y, Z ) ), ~( product( W, U, T ) ) ] )
% 0.69/1.09 .
% 0.69/1.09 clause( 18, [ product( X, 'e_1', 'e_2' ), product( X, 'e_1', 'e_1' ), ~(
% 0.69/1.09 'group_element'( X ) ) ] )
% 0.69/1.09 .
% 0.69/1.09 clause( 19, [ product( X, 'e_2', 'e_2' ), product( X, 'e_2', 'e_1' ), ~(
% 0.69/1.09 'group_element'( X ) ) ] )
% 0.69/1.09 .
% 0.69/1.09 clause( 20, [ product( 'e_1', 'e_1', 'e_1' ), product( 'e_1', 'e_1', 'e_2'
% 0.69/1.09 ) ] )
% 0.69/1.09 .
% 0.69/1.09 clause( 21, [ product( 'e_2', 'e_1', 'e_1' ), product( 'e_2', 'e_1', 'e_2'
% 0.69/1.09 ) ] )
% 0.69/1.09 .
% 0.69/1.09 clause( 30, [ product( 'e_1', 'e_2', 'e_1' ), product( 'e_1', 'e_2', 'e_2'
% 0.69/1.09 ) ] )
% 0.69/1.09 .
% 0.69/1.09 clause( 31, [ product( 'e_2', 'e_2', 'e_1' ), product( 'e_2', 'e_2', 'e_2'
% 0.69/1.09 ) ] )
% 0.69/1.09 .
% 0.69/1.09 clause( 36, [ equalish( X, 'e_2' ), product( 'e_2', 'e_2', 'e_1' ), ~(
% 0.69/1.09 product( X, 'e_2', 'e_2' ) ) ] )
% 0.69/1.09 .
% 0.69/1.09 clause( 38, [ equalish( X, 'e_2' ), product( 'e_2', 'e_1', 'e_1' ), ~(
% 0.69/1.09 product( X, 'e_1', 'e_2' ) ) ] )
% 0.69/1.09 .
% 0.69/1.09 clause( 40, [ product( 'e_1', 'e_2', 'e_1' ), product( 'e_2', 'e_2', 'e_1'
% 0.69/1.09 ) ] )
% 0.69/1.09 .
% 0.69/1.09 clause( 42, [ equalish( X, 'e_2' ), product( 'e_1', 'e_2', 'e_1' ), ~(
% 0.69/1.09 product( 'e_2', X, 'e_1' ) ) ] )
% 0.69/1.09 .
% 0.69/1.09 clause( 52, [ product( 'e_1', 'e_1', 'e_1' ), product( 'e_2', 'e_1', 'e_1'
% 0.69/1.09 ) ] )
% 0.69/1.09 .
% 0.69/1.09 clause( 55, [ equalish( X, 'e_2' ), ~( product( 'e_2', 'e_2', Z ) ), ~(
% 0.69/1.09 product( 'e_1', X, Y ) ), product( 'e_1', 'e_2', 'e_1' ), ~( product( Y,
% 0.69/1.09 X, Z ) ) ] )
% 0.69/1.09 .
% 0.69/1.09 clause( 59, [ equalish( X, 'e_2' ), product( 'e_1', 'e_2', 'e_1' ), ~(
% 0.69/1.09 product( 'e_1', X, 'e_1' ) ) ] )
% 0.69/1.09 .
% 0.69/1.09 clause( 61, [ equalish( X, 'e_1' ), ~( product( 'e_2', X, Y ) ), ~( product(
% 0.69/1.09 'e_1', 'e_1', Z ) ), product( 'e_1', 'e_1', 'e_1' ), ~( product( Y, X, Z
% 0.69/1.09 ) ) ] )
% 0.69/1.09 .
% 0.69/1.09 clause( 62, [ equalish( 'e_1', 'e_2' ), product( 'e_1', 'e_2', 'e_1' ) ] )
% 0.69/1.09 .
% 0.69/1.09 clause( 68, [ equalish( X, 'e_1' ), product( 'e_1', 'e_1', 'e_1' ), ~(
% 0.69/1.09 product( 'e_2', X, 'e_2' ) ) ] )
% 0.69/1.09 .
% 0.69/1.09 clause( 69, [ product( 'e_1', 'e_2', 'e_1' ) ] )
% 0.69/1.09 .
% 0.69/1.09 clause( 72, [ equalish( X, 'e_1' ), ~( product( X, 'e_2', 'e_1' ) ) ] )
% 0.69/1.09 .
% 0.69/1.09 clause( 73, [ equalish( X, 'e_2' ), ~( product( 'e_1', X, 'e_1' ) ) ] )
% 0.69/1.09 .
% 0.69/1.09 clause( 77, [ product( 'e_1', 'e_1', 'e_1' ), product( 'e_2', 'e_2', 'e_1'
% 0.69/1.09 ) ] )
% 0.69/1.09 .
% 0.69/1.09 clause( 79, [ product( 'e_1', 'e_1', 'e_1' ) ] )
% 0.69/1.09 .
% 0.69/1.09 clause( 83, [] )
% 0.69/1.09 .
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 % SZS output end Refutation
% 0.69/1.09 found a proof!
% 0.69/1.09
% 0.69/1.09 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.69/1.09
% 0.69/1.09 initialclauses(
% 0.69/1.09 [ clause( 85, [ 'group_element'( 'e_1' ) ] )
% 0.69/1.09 , clause( 86, [ 'group_element'( 'e_2' ) ] )
% 0.69/1.09 , clause( 87, [ ~( equalish( 'e_1', 'e_2' ) ) ] )
% 0.69/1.09 , clause( 88, [ ~( equalish( 'e_2', 'e_1' ) ) ] )
% 0.69/1.09 , clause( 89, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ),
% 0.69/1.09 product( X, Y, 'e_1' ), product( X, Y, 'e_2' ) ] )
% 0.69/1.09 , clause( 90, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), equalish(
% 0.69/1.09 Z, T ) ] )
% 0.69/1.09 , clause( 91, [ ~( product( X, Y, Z ) ), ~( product( X, T, Z ) ), equalish(
% 0.69/1.09 Y, T ) ] )
% 0.69/1.09 , clause( 92, [ ~( product( X, Y, Z ) ), ~( product( T, Y, Z ) ), equalish(
% 0.69/1.09 X, T ) ] )
% 0.69/1.09 , clause( 93, [ ~( product( X, Y, Z ) ), ~( product( T, U, Z ) ), ~(
% 0.69/1.09 product( W, Y, X ) ), ~( product( W, U, T ) ), equalish( X, T ) ] )
% 0.69/1.09 , clause( 94, [ ~( product( X, Y, Z ) ), ~( product( T, U, Z ) ), ~(
% 0.69/1.09 product( W, Y, X ) ), ~( product( W, U, T ) ), equalish( Y, U ) ] )
% 0.69/1.09 ] ).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 subsumption(
% 0.69/1.09 clause( 0, [ 'group_element'( 'e_1' ) ] )
% 0.69/1.09 , clause( 85, [ 'group_element'( 'e_1' ) ] )
% 0.69/1.09 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 subsumption(
% 0.69/1.09 clause( 1, [ 'group_element'( 'e_2' ) ] )
% 0.69/1.09 , clause( 86, [ 'group_element'( 'e_2' ) ] )
% 0.69/1.09 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 subsumption(
% 0.69/1.09 clause( 2, [ ~( equalish( 'e_1', 'e_2' ) ) ] )
% 0.69/1.09 , clause( 87, [ ~( equalish( 'e_1', 'e_2' ) ) ] )
% 0.69/1.09 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 subsumption(
% 0.69/1.09 clause( 3, [ ~( equalish( 'e_2', 'e_1' ) ) ] )
% 0.69/1.09 , clause( 88, [ ~( equalish( 'e_2', 'e_1' ) ) ] )
% 0.69/1.09 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 subsumption(
% 0.69/1.09 clause( 4, [ ~( 'group_element'( X ) ), product( X, Y, 'e_2' ), product( X
% 0.69/1.09 , Y, 'e_1' ), ~( 'group_element'( Y ) ) ] )
% 0.69/1.09 , clause( 89, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ),
% 0.69/1.09 product( X, Y, 'e_1' ), product( X, Y, 'e_2' ) ] )
% 0.69/1.09 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.69/1.09 ), ==>( 1, 3 ), ==>( 2, 2 ), ==>( 3, 1 )] ) ).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 subsumption(
% 0.69/1.09 clause( 6, [ equalish( Y, T ), ~( product( X, Y, Z ) ), ~( product( X, T, Z
% 0.69/1.09 ) ) ] )
% 0.69/1.09 , clause( 91, [ ~( product( X, Y, Z ) ), ~( product( X, T, Z ) ), equalish(
% 0.69/1.09 Y, T ) ] )
% 0.69/1.09 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.69/1.09 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 2 ), ==>( 2, 0 )] ) ).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 subsumption(
% 0.69/1.09 clause( 7, [ equalish( X, T ), ~( product( X, Y, Z ) ), ~( product( T, Y, Z
% 0.69/1.09 ) ) ] )
% 0.69/1.09 , clause( 92, [ ~( product( X, Y, Z ) ), ~( product( T, Y, Z ) ), equalish(
% 0.69/1.09 X, T ) ] )
% 0.69/1.09 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.69/1.09 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 2 ), ==>( 2, 0 )] ) ).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 subsumption(
% 0.69/1.09 clause( 9, [ equalish( Y, U ), ~( product( W, Y, X ) ), ~( product( T, U, Z
% 0.69/1.09 ) ), ~( product( X, Y, Z ) ), ~( product( W, U, T ) ) ] )
% 0.69/1.09 , clause( 94, [ ~( product( X, Y, Z ) ), ~( product( T, U, Z ) ), ~(
% 0.69/1.09 product( W, Y, X ) ), ~( product( W, U, T ) ), equalish( Y, U ) ] )
% 0.69/1.09 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 0.69/1.09 , U ), :=( W, W )] ), permutation( 0, [ ==>( 0, 3 ), ==>( 1, 2 ), ==>( 2
% 0.69/1.09 , 1 ), ==>( 3, 4 ), ==>( 4, 0 )] ) ).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 resolution(
% 0.69/1.09 clause( 123, [ ~( 'group_element'( X ) ), product( X, 'e_1', 'e_2' ),
% 0.69/1.09 product( X, 'e_1', 'e_1' ) ] )
% 0.69/1.09 , clause( 4, [ ~( 'group_element'( X ) ), product( X, Y, 'e_2' ), product(
% 0.69/1.09 X, Y, 'e_1' ), ~( 'group_element'( Y ) ) ] )
% 0.69/1.09 , 3, clause( 0, [ 'group_element'( 'e_1' ) ] )
% 0.69/1.09 , 0, substitution( 0, [ :=( X, X ), :=( Y, 'e_1' )] ), substitution( 1, [] )
% 0.69/1.09 ).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 subsumption(
% 0.69/1.09 clause( 18, [ product( X, 'e_1', 'e_2' ), product( X, 'e_1', 'e_1' ), ~(
% 0.69/1.09 'group_element'( X ) ) ] )
% 0.69/1.09 , clause( 123, [ ~( 'group_element'( X ) ), product( X, 'e_1', 'e_2' ),
% 0.69/1.09 product( X, 'e_1', 'e_1' ) ] )
% 0.69/1.09 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 2 ), ==>( 1,
% 0.69/1.09 0 ), ==>( 2, 1 )] ) ).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 resolution(
% 0.69/1.09 clause( 125, [ ~( 'group_element'( X ) ), product( X, 'e_2', 'e_2' ),
% 0.69/1.09 product( X, 'e_2', 'e_1' ) ] )
% 0.69/1.09 , clause( 4, [ ~( 'group_element'( X ) ), product( X, Y, 'e_2' ), product(
% 0.69/1.09 X, Y, 'e_1' ), ~( 'group_element'( Y ) ) ] )
% 0.69/1.09 , 3, clause( 1, [ 'group_element'( 'e_2' ) ] )
% 0.69/1.09 , 0, substitution( 0, [ :=( X, X ), :=( Y, 'e_2' )] ), substitution( 1, [] )
% 0.69/1.09 ).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 subsumption(
% 0.69/1.09 clause( 19, [ product( X, 'e_2', 'e_2' ), product( X, 'e_2', 'e_1' ), ~(
% 0.69/1.09 'group_element'( X ) ) ] )
% 0.69/1.09 , clause( 125, [ ~( 'group_element'( X ) ), product( X, 'e_2', 'e_2' ),
% 0.69/1.09 product( X, 'e_2', 'e_1' ) ] )
% 0.69/1.09 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 2 ), ==>( 1,
% 0.69/1.09 0 ), ==>( 2, 1 )] ) ).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 resolution(
% 0.69/1.09 clause( 126, [ product( 'e_1', 'e_1', 'e_2' ), product( 'e_1', 'e_1', 'e_1'
% 0.69/1.09 ) ] )
% 0.69/1.09 , clause( 18, [ product( X, 'e_1', 'e_2' ), product( X, 'e_1', 'e_1' ), ~(
% 0.69/1.09 'group_element'( X ) ) ] )
% 0.69/1.09 , 2, clause( 0, [ 'group_element'( 'e_1' ) ] )
% 0.69/1.09 , 0, substitution( 0, [ :=( X, 'e_1' )] ), substitution( 1, [] )).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 subsumption(
% 0.69/1.09 clause( 20, [ product( 'e_1', 'e_1', 'e_1' ), product( 'e_1', 'e_1', 'e_2'
% 0.69/1.09 ) ] )
% 0.69/1.09 , clause( 126, [ product( 'e_1', 'e_1', 'e_2' ), product( 'e_1', 'e_1',
% 0.69/1.09 'e_1' ) ] )
% 0.69/1.09 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] )
% 0.69/1.09 ).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 resolution(
% 0.69/1.09 clause( 127, [ product( 'e_2', 'e_1', 'e_2' ), product( 'e_2', 'e_1', 'e_1'
% 0.69/1.09 ) ] )
% 0.69/1.09 , clause( 18, [ product( X, 'e_1', 'e_2' ), product( X, 'e_1', 'e_1' ), ~(
% 0.69/1.09 'group_element'( X ) ) ] )
% 0.69/1.09 , 2, clause( 1, [ 'group_element'( 'e_2' ) ] )
% 0.69/1.09 , 0, substitution( 0, [ :=( X, 'e_2' )] ), substitution( 1, [] )).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 subsumption(
% 0.69/1.09 clause( 21, [ product( 'e_2', 'e_1', 'e_1' ), product( 'e_2', 'e_1', 'e_2'
% 0.69/1.09 ) ] )
% 0.69/1.09 , clause( 127, [ product( 'e_2', 'e_1', 'e_2' ), product( 'e_2', 'e_1',
% 0.69/1.09 'e_1' ) ] )
% 0.69/1.09 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] )
% 0.69/1.09 ).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 resolution(
% 0.69/1.09 clause( 128, [ product( 'e_1', 'e_2', 'e_2' ), product( 'e_1', 'e_2', 'e_1'
% 0.69/1.09 ) ] )
% 0.69/1.09 , clause( 19, [ product( X, 'e_2', 'e_2' ), product( X, 'e_2', 'e_1' ), ~(
% 0.69/1.09 'group_element'( X ) ) ] )
% 0.69/1.09 , 2, clause( 0, [ 'group_element'( 'e_1' ) ] )
% 0.69/1.09 , 0, substitution( 0, [ :=( X, 'e_1' )] ), substitution( 1, [] )).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 subsumption(
% 0.69/1.09 clause( 30, [ product( 'e_1', 'e_2', 'e_1' ), product( 'e_1', 'e_2', 'e_2'
% 0.69/1.09 ) ] )
% 0.69/1.09 , clause( 128, [ product( 'e_1', 'e_2', 'e_2' ), product( 'e_1', 'e_2',
% 0.69/1.09 'e_1' ) ] )
% 0.69/1.09 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] )
% 0.69/1.09 ).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 resolution(
% 0.69/1.09 clause( 129, [ product( 'e_2', 'e_2', 'e_2' ), product( 'e_2', 'e_2', 'e_1'
% 0.69/1.09 ) ] )
% 0.69/1.09 , clause( 19, [ product( X, 'e_2', 'e_2' ), product( X, 'e_2', 'e_1' ), ~(
% 0.69/1.09 'group_element'( X ) ) ] )
% 0.69/1.09 , 2, clause( 1, [ 'group_element'( 'e_2' ) ] )
% 0.69/1.09 , 0, substitution( 0, [ :=( X, 'e_2' )] ), substitution( 1, [] )).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 subsumption(
% 0.69/1.09 clause( 31, [ product( 'e_2', 'e_2', 'e_1' ), product( 'e_2', 'e_2', 'e_2'
% 0.69/1.09 ) ] )
% 0.69/1.09 , clause( 129, [ product( 'e_2', 'e_2', 'e_2' ), product( 'e_2', 'e_2',
% 0.69/1.09 'e_1' ) ] )
% 0.69/1.09 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] )
% 0.69/1.09 ).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 resolution(
% 0.69/1.09 clause( 133, [ equalish( X, 'e_2' ), ~( product( X, 'e_2', 'e_2' ) ),
% 0.69/1.09 product( 'e_2', 'e_2', 'e_1' ) ] )
% 0.69/1.09 , clause( 7, [ equalish( X, T ), ~( product( X, Y, Z ) ), ~( product( T, Y
% 0.69/1.09 , Z ) ) ] )
% 0.69/1.09 , 2, clause( 31, [ product( 'e_2', 'e_2', 'e_1' ), product( 'e_2', 'e_2',
% 0.69/1.09 'e_2' ) ] )
% 0.69/1.09 , 1, substitution( 0, [ :=( X, X ), :=( Y, 'e_2' ), :=( Z, 'e_2' ), :=( T,
% 0.69/1.09 'e_2' )] ), substitution( 1, [] )).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 subsumption(
% 0.69/1.09 clause( 36, [ equalish( X, 'e_2' ), product( 'e_2', 'e_2', 'e_1' ), ~(
% 0.69/1.09 product( X, 'e_2', 'e_2' ) ) ] )
% 0.69/1.09 , clause( 133, [ equalish( X, 'e_2' ), ~( product( X, 'e_2', 'e_2' ) ),
% 0.69/1.09 product( 'e_2', 'e_2', 'e_1' ) ] )
% 0.69/1.09 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 0.69/1.09 2 ), ==>( 2, 1 )] ) ).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 resolution(
% 0.69/1.09 clause( 137, [ equalish( X, 'e_2' ), ~( product( X, 'e_1', 'e_2' ) ),
% 0.69/1.09 product( 'e_2', 'e_1', 'e_1' ) ] )
% 0.69/1.09 , clause( 7, [ equalish( X, T ), ~( product( X, Y, Z ) ), ~( product( T, Y
% 0.69/1.09 , Z ) ) ] )
% 0.69/1.09 , 2, clause( 21, [ product( 'e_2', 'e_1', 'e_1' ), product( 'e_2', 'e_1',
% 0.69/1.09 'e_2' ) ] )
% 0.69/1.09 , 1, substitution( 0, [ :=( X, X ), :=( Y, 'e_1' ), :=( Z, 'e_2' ), :=( T,
% 0.69/1.09 'e_2' )] ), substitution( 1, [] )).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 subsumption(
% 0.69/1.09 clause( 38, [ equalish( X, 'e_2' ), product( 'e_2', 'e_1', 'e_1' ), ~(
% 0.69/1.09 product( X, 'e_1', 'e_2' ) ) ] )
% 0.69/1.09 , clause( 137, [ equalish( X, 'e_2' ), ~( product( X, 'e_1', 'e_2' ) ),
% 0.69/1.09 product( 'e_2', 'e_1', 'e_1' ) ] )
% 0.69/1.09 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 0.69/1.09 2 ), ==>( 2, 1 )] ) ).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 resolution(
% 0.69/1.09 clause( 138, [ equalish( 'e_1', 'e_2' ), product( 'e_2', 'e_2', 'e_1' ),
% 0.69/1.09 product( 'e_1', 'e_2', 'e_1' ) ] )
% 0.69/1.09 , clause( 36, [ equalish( X, 'e_2' ), product( 'e_2', 'e_2', 'e_1' ), ~(
% 0.69/1.09 product( X, 'e_2', 'e_2' ) ) ] )
% 0.69/1.09 , 2, clause( 30, [ product( 'e_1', 'e_2', 'e_1' ), product( 'e_1', 'e_2',
% 0.69/1.09 'e_2' ) ] )
% 0.69/1.09 , 1, substitution( 0, [ :=( X, 'e_1' )] ), substitution( 1, [] )).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 resolution(
% 0.69/1.09 clause( 139, [ product( 'e_2', 'e_2', 'e_1' ), product( 'e_1', 'e_2', 'e_1'
% 0.69/1.09 ) ] )
% 0.69/1.09 , clause( 2, [ ~( equalish( 'e_1', 'e_2' ) ) ] )
% 0.69/1.09 , 0, clause( 138, [ equalish( 'e_1', 'e_2' ), product( 'e_2', 'e_2', 'e_1'
% 0.69/1.09 ), product( 'e_1', 'e_2', 'e_1' ) ] )
% 0.69/1.09 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 subsumption(
% 0.69/1.09 clause( 40, [ product( 'e_1', 'e_2', 'e_1' ), product( 'e_2', 'e_2', 'e_1'
% 0.69/1.09 ) ] )
% 0.69/1.09 , clause( 139, [ product( 'e_2', 'e_2', 'e_1' ), product( 'e_1', 'e_2',
% 0.69/1.09 'e_1' ) ] )
% 0.69/1.09 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] )
% 0.69/1.09 ).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 resolution(
% 0.69/1.09 clause( 143, [ equalish( X, 'e_2' ), ~( product( 'e_2', X, 'e_1' ) ),
% 0.69/1.09 product( 'e_1', 'e_2', 'e_1' ) ] )
% 0.69/1.09 , clause( 6, [ equalish( Y, T ), ~( product( X, Y, Z ) ), ~( product( X, T
% 0.69/1.09 , Z ) ) ] )
% 0.69/1.09 , 2, clause( 40, [ product( 'e_1', 'e_2', 'e_1' ), product( 'e_2', 'e_2',
% 0.69/1.09 'e_1' ) ] )
% 0.69/1.09 , 1, substitution( 0, [ :=( X, 'e_2' ), :=( Y, X ), :=( Z, 'e_1' ), :=( T,
% 0.69/1.09 'e_2' )] ), substitution( 1, [] )).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 subsumption(
% 0.69/1.09 clause( 42, [ equalish( X, 'e_2' ), product( 'e_1', 'e_2', 'e_1' ), ~(
% 0.69/1.09 product( 'e_2', X, 'e_1' ) ) ] )
% 0.69/1.09 , clause( 143, [ equalish( X, 'e_2' ), ~( product( 'e_2', X, 'e_1' ) ),
% 0.69/1.09 product( 'e_1', 'e_2', 'e_1' ) ] )
% 0.69/1.09 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 0.69/1.09 2 ), ==>( 2, 1 )] ) ).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 resolution(
% 0.69/1.09 clause( 144, [ equalish( 'e_1', 'e_2' ), product( 'e_2', 'e_1', 'e_1' ),
% 0.69/1.09 product( 'e_1', 'e_1', 'e_1' ) ] )
% 0.69/1.09 , clause( 38, [ equalish( X, 'e_2' ), product( 'e_2', 'e_1', 'e_1' ), ~(
% 0.69/1.09 product( X, 'e_1', 'e_2' ) ) ] )
% 0.69/1.09 , 2, clause( 20, [ product( 'e_1', 'e_1', 'e_1' ), product( 'e_1', 'e_1',
% 0.69/1.09 'e_2' ) ] )
% 0.69/1.09 , 1, substitution( 0, [ :=( X, 'e_1' )] ), substitution( 1, [] )).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 resolution(
% 0.69/1.09 clause( 145, [ product( 'e_2', 'e_1', 'e_1' ), product( 'e_1', 'e_1', 'e_1'
% 0.69/1.09 ) ] )
% 0.69/1.09 , clause( 2, [ ~( equalish( 'e_1', 'e_2' ) ) ] )
% 0.69/1.09 , 0, clause( 144, [ equalish( 'e_1', 'e_2' ), product( 'e_2', 'e_1', 'e_1'
% 0.69/1.09 ), product( 'e_1', 'e_1', 'e_1' ) ] )
% 0.69/1.09 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 subsumption(
% 0.69/1.09 clause( 52, [ product( 'e_1', 'e_1', 'e_1' ), product( 'e_2', 'e_1', 'e_1'
% 0.69/1.09 ) ] )
% 0.69/1.09 , clause( 145, [ product( 'e_2', 'e_1', 'e_1' ), product( 'e_1', 'e_1',
% 0.69/1.09 'e_1' ) ] )
% 0.69/1.09 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] )
% 0.69/1.09 ).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 resolution(
% 0.69/1.09 clause( 153, [ equalish( X, 'e_2' ), ~( product( 'e_1', X, Y ) ), ~(
% 0.69/1.09 product( 'e_2', 'e_2', Z ) ), ~( product( Y, X, Z ) ), product( 'e_1',
% 0.69/1.09 'e_2', 'e_1' ) ] )
% 0.69/1.09 , clause( 9, [ equalish( Y, U ), ~( product( W, Y, X ) ), ~( product( T, U
% 0.69/1.09 , Z ) ), ~( product( X, Y, Z ) ), ~( product( W, U, T ) ) ] )
% 0.69/1.09 , 4, clause( 30, [ product( 'e_1', 'e_2', 'e_1' ), product( 'e_1', 'e_2',
% 0.69/1.09 'e_2' ) ] )
% 0.69/1.09 , 1, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z ), :=( T, 'e_2' )
% 0.69/1.09 , :=( U, 'e_2' ), :=( W, 'e_1' )] ), substitution( 1, [] )).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 subsumption(
% 0.69/1.09 clause( 55, [ equalish( X, 'e_2' ), ~( product( 'e_2', 'e_2', Z ) ), ~(
% 0.69/1.09 product( 'e_1', X, Y ) ), product( 'e_1', 'e_2', 'e_1' ), ~( product( Y,
% 0.69/1.09 X, Z ) ) ] )
% 0.69/1.09 , clause( 153, [ equalish( X, 'e_2' ), ~( product( 'e_1', X, Y ) ), ~(
% 0.69/1.09 product( 'e_2', 'e_2', Z ) ), ~( product( Y, X, Z ) ), product( 'e_1',
% 0.69/1.09 'e_2', 'e_1' ) ] )
% 0.69/1.09 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.69/1.09 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 2 ), ==>( 2, 1 ), ==>( 3, 4 ),
% 0.69/1.09 ==>( 4, 3 )] ) ).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 factor(
% 0.69/1.09 clause( 167, [ equalish( X, 'e_2' ), ~( product( 'e_2', 'e_2', 'e_1' ) ),
% 0.69/1.09 ~( product( 'e_1', X, 'e_1' ) ), product( 'e_1', 'e_2', 'e_1' ) ] )
% 0.69/1.09 , clause( 55, [ equalish( X, 'e_2' ), ~( product( 'e_2', 'e_2', Z ) ), ~(
% 0.69/1.09 product( 'e_1', X, Y ) ), product( 'e_1', 'e_2', 'e_1' ), ~( product( Y,
% 0.69/1.09 X, Z ) ) ] )
% 0.69/1.09 , 2, 4, substitution( 0, [ :=( X, X ), :=( Y, 'e_1' ), :=( Z, 'e_1' )] )
% 0.69/1.09 ).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 resolution(
% 0.69/1.09 clause( 168, [ equalish( X, 'e_2' ), ~( product( 'e_1', X, 'e_1' ) ),
% 0.69/1.09 product( 'e_1', 'e_2', 'e_1' ), product( 'e_1', 'e_2', 'e_1' ) ] )
% 0.69/1.09 , clause( 167, [ equalish( X, 'e_2' ), ~( product( 'e_2', 'e_2', 'e_1' ) )
% 0.69/1.09 , ~( product( 'e_1', X, 'e_1' ) ), product( 'e_1', 'e_2', 'e_1' ) ] )
% 0.69/1.09 , 1, clause( 40, [ product( 'e_1', 'e_2', 'e_1' ), product( 'e_2', 'e_2',
% 0.69/1.09 'e_1' ) ] )
% 0.69/1.09 , 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [] )).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 factor(
% 0.69/1.09 clause( 169, [ equalish( X, 'e_2' ), ~( product( 'e_1', X, 'e_1' ) ),
% 0.69/1.09 product( 'e_1', 'e_2', 'e_1' ) ] )
% 0.69/1.09 , clause( 168, [ equalish( X, 'e_2' ), ~( product( 'e_1', X, 'e_1' ) ),
% 0.69/1.09 product( 'e_1', 'e_2', 'e_1' ), product( 'e_1', 'e_2', 'e_1' ) ] )
% 0.69/1.09 , 2, 3, substitution( 0, [ :=( X, X )] )).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 subsumption(
% 0.69/1.09 clause( 59, [ equalish( X, 'e_2' ), product( 'e_1', 'e_2', 'e_1' ), ~(
% 0.69/1.09 product( 'e_1', X, 'e_1' ) ) ] )
% 0.69/1.09 , clause( 169, [ equalish( X, 'e_2' ), ~( product( 'e_1', X, 'e_1' ) ),
% 0.69/1.09 product( 'e_1', 'e_2', 'e_1' ) ] )
% 0.69/1.09 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 0.69/1.09 2 ), ==>( 2, 1 )] ) ).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 resolution(
% 0.69/1.09 clause( 177, [ equalish( X, 'e_1' ), ~( product( 'e_2', X, Y ) ), ~(
% 0.69/1.09 product( 'e_1', 'e_1', Z ) ), ~( product( Y, X, Z ) ), product( 'e_1',
% 0.69/1.09 'e_1', 'e_1' ) ] )
% 0.69/1.09 , clause( 9, [ equalish( Y, U ), ~( product( W, Y, X ) ), ~( product( T, U
% 0.69/1.09 , Z ) ), ~( product( X, Y, Z ) ), ~( product( W, U, T ) ) ] )
% 0.69/1.09 , 4, clause( 52, [ product( 'e_1', 'e_1', 'e_1' ), product( 'e_2', 'e_1',
% 0.69/1.09 'e_1' ) ] )
% 0.69/1.09 , 1, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z ), :=( T, 'e_1' )
% 0.69/1.09 , :=( U, 'e_1' ), :=( W, 'e_2' )] ), substitution( 1, [] )).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 subsumption(
% 0.69/1.09 clause( 61, [ equalish( X, 'e_1' ), ~( product( 'e_2', X, Y ) ), ~( product(
% 0.69/1.09 'e_1', 'e_1', Z ) ), product( 'e_1', 'e_1', 'e_1' ), ~( product( Y, X, Z
% 0.69/1.09 ) ) ] )
% 0.69/1.09 , clause( 177, [ equalish( X, 'e_1' ), ~( product( 'e_2', X, Y ) ), ~(
% 0.69/1.09 product( 'e_1', 'e_1', Z ) ), ~( product( Y, X, Z ) ), product( 'e_1',
% 0.69/1.09 'e_1', 'e_1' ) ] )
% 0.69/1.09 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.69/1.09 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 ), ==>( 3, 4 ),
% 0.69/1.09 ==>( 4, 3 )] ) ).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 resolution(
% 0.69/1.09 clause( 190, [ equalish( 'e_1', 'e_2' ), product( 'e_1', 'e_2', 'e_1' ),
% 0.69/1.09 product( 'e_1', 'e_1', 'e_1' ) ] )
% 0.69/1.09 , clause( 42, [ equalish( X, 'e_2' ), product( 'e_1', 'e_2', 'e_1' ), ~(
% 0.69/1.09 product( 'e_2', X, 'e_1' ) ) ] )
% 0.69/1.09 , 2, clause( 52, [ product( 'e_1', 'e_1', 'e_1' ), product( 'e_2', 'e_1',
% 0.69/1.09 'e_1' ) ] )
% 0.69/1.09 , 1, substitution( 0, [ :=( X, 'e_1' )] ), substitution( 1, [] )).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 resolution(
% 0.69/1.09 clause( 192, [ equalish( 'e_1', 'e_2' ), product( 'e_1', 'e_2', 'e_1' ),
% 0.69/1.09 equalish( 'e_1', 'e_2' ), product( 'e_1', 'e_2', 'e_1' ) ] )
% 0.69/1.09 , clause( 59, [ equalish( X, 'e_2' ), product( 'e_1', 'e_2', 'e_1' ), ~(
% 0.69/1.09 product( 'e_1', X, 'e_1' ) ) ] )
% 0.69/1.09 , 2, clause( 190, [ equalish( 'e_1', 'e_2' ), product( 'e_1', 'e_2', 'e_1'
% 0.69/1.09 ), product( 'e_1', 'e_1', 'e_1' ) ] )
% 0.69/1.09 , 2, substitution( 0, [ :=( X, 'e_1' )] ), substitution( 1, [] )).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 factor(
% 0.69/1.09 clause( 194, [ equalish( 'e_1', 'e_2' ), product( 'e_1', 'e_2', 'e_1' ),
% 0.69/1.09 equalish( 'e_1', 'e_2' ) ] )
% 0.69/1.09 , clause( 192, [ equalish( 'e_1', 'e_2' ), product( 'e_1', 'e_2', 'e_1' ),
% 0.69/1.09 equalish( 'e_1', 'e_2' ), product( 'e_1', 'e_2', 'e_1' ) ] )
% 0.69/1.09 , 1, 3, substitution( 0, [] )).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 factor(
% 0.69/1.09 clause( 195, [ equalish( 'e_1', 'e_2' ), product( 'e_1', 'e_2', 'e_1' ) ]
% 0.69/1.09 )
% 0.69/1.09 , clause( 194, [ equalish( 'e_1', 'e_2' ), product( 'e_1', 'e_2', 'e_1' ),
% 0.69/1.09 equalish( 'e_1', 'e_2' ) ] )
% 0.69/1.09 , 0, 2, substitution( 0, [] )).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 subsumption(
% 0.69/1.09 clause( 62, [ equalish( 'e_1', 'e_2' ), product( 'e_1', 'e_2', 'e_1' ) ] )
% 0.69/1.09 , clause( 195, [ equalish( 'e_1', 'e_2' ), product( 'e_1', 'e_2', 'e_1' ) ]
% 0.69/1.09 )
% 0.69/1.09 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] )
% 0.69/1.09 ).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 factor(
% 0.69/1.09 clause( 196, [ equalish( X, 'e_1' ), ~( product( 'e_2', X, 'e_2' ) ), ~(
% 0.69/1.09 product( 'e_1', 'e_1', 'e_2' ) ), product( 'e_1', 'e_1', 'e_1' ) ] )
% 0.69/1.09 , clause( 61, [ equalish( X, 'e_1' ), ~( product( 'e_2', X, Y ) ), ~(
% 0.69/1.09 product( 'e_1', 'e_1', Z ) ), product( 'e_1', 'e_1', 'e_1' ), ~( product(
% 0.69/1.09 Y, X, Z ) ) ] )
% 0.69/1.09 , 1, 4, substitution( 0, [ :=( X, X ), :=( Y, 'e_2' ), :=( Z, 'e_2' )] )
% 0.69/1.09 ).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 resolution(
% 0.69/1.09 clause( 198, [ equalish( X, 'e_1' ), ~( product( 'e_2', X, 'e_2' ) ),
% 0.69/1.09 product( 'e_1', 'e_1', 'e_1' ), product( 'e_1', 'e_1', 'e_1' ) ] )
% 0.69/1.09 , clause( 196, [ equalish( X, 'e_1' ), ~( product( 'e_2', X, 'e_2' ) ), ~(
% 0.69/1.09 product( 'e_1', 'e_1', 'e_2' ) ), product( 'e_1', 'e_1', 'e_1' ) ] )
% 0.69/1.09 , 2, clause( 20, [ product( 'e_1', 'e_1', 'e_1' ), product( 'e_1', 'e_1',
% 0.69/1.09 'e_2' ) ] )
% 0.69/1.09 , 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [] )).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 factor(
% 0.69/1.09 clause( 199, [ equalish( X, 'e_1' ), ~( product( 'e_2', X, 'e_2' ) ),
% 0.69/1.09 product( 'e_1', 'e_1', 'e_1' ) ] )
% 0.69/1.09 , clause( 198, [ equalish( X, 'e_1' ), ~( product( 'e_2', X, 'e_2' ) ),
% 0.69/1.09 product( 'e_1', 'e_1', 'e_1' ), product( 'e_1', 'e_1', 'e_1' ) ] )
% 0.69/1.09 , 2, 3, substitution( 0, [ :=( X, X )] )).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 subsumption(
% 0.69/1.09 clause( 68, [ equalish( X, 'e_1' ), product( 'e_1', 'e_1', 'e_1' ), ~(
% 0.69/1.09 product( 'e_2', X, 'e_2' ) ) ] )
% 0.69/1.09 , clause( 199, [ equalish( X, 'e_1' ), ~( product( 'e_2', X, 'e_2' ) ),
% 0.69/1.09 product( 'e_1', 'e_1', 'e_1' ) ] )
% 0.69/1.09 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 0.69/1.09 2 ), ==>( 2, 1 )] ) ).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 resolution(
% 0.69/1.09 clause( 200, [ product( 'e_1', 'e_2', 'e_1' ) ] )
% 0.69/1.09 , clause( 2, [ ~( equalish( 'e_1', 'e_2' ) ) ] )
% 0.69/1.09 , 0, clause( 62, [ equalish( 'e_1', 'e_2' ), product( 'e_1', 'e_2', 'e_1' )
% 0.69/1.09 ] )
% 0.69/1.09 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 subsumption(
% 0.69/1.09 clause( 69, [ product( 'e_1', 'e_2', 'e_1' ) ] )
% 0.69/1.09 , clause( 200, [ product( 'e_1', 'e_2', 'e_1' ) ] )
% 0.69/1.09 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.69/1.09
% 0.69/1.09
% 0.69/1.09 resolution(
% 0.69/1.09 clause( 202, [ equalish( X, 'e_1' ), ~( product( X, 'e_2', 'e_1' ) ) ] )
% 0.69/1.09 , clause( 7, [ equalish( X, T ), ~( product( X, Y, Z ) ), ~( product( T, Y
% 0.69/1.10 , Z ) ) ] )
% 0.69/1.10 , 2, clause( 69, [ product( 'e_1', 'e_2', 'e_1' ) ] )
% 0.69/1.10 , 0, substitution( 0, [ :=( X, X ), :=( Y, 'e_2' ), :=( Z, 'e_1' ), :=( T,
% 0.69/1.10 'e_1' )] ), substitution( 1, [] )).
% 0.69/1.10
% 0.69/1.10
% 0.69/1.10 subsumption(
% 0.69/1.10 clause( 72, [ equalish( X, 'e_1' ), ~( product( X, 'e_2', 'e_1' ) ) ] )
% 0.69/1.10 , clause( 202, [ equalish( X, 'e_1' ), ~( product( X, 'e_2', 'e_1' ) ) ] )
% 0.69/1.10 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 0.69/1.10 1 )] ) ).
% 0.69/1.10
% 0.69/1.10
% 0.69/1.10 resolution(
% 0.69/1.10 clause( 204, [ equalish( X, 'e_2' ), ~( product( 'e_1', X, 'e_1' ) ) ] )
% 0.69/1.10 , clause( 6, [ equalish( Y, T ), ~( product( X, Y, Z ) ), ~( product( X, T
% 0.69/1.10 , Z ) ) ] )
% 0.69/1.10 , 2, clause( 69, [ product( 'e_1', 'e_2', 'e_1' ) ] )
% 0.69/1.10 , 0, substitution( 0, [ :=( X, 'e_1' ), :=( Y, X ), :=( Z, 'e_1' ), :=( T,
% 0.69/1.10 'e_2' )] ), substitution( 1, [] )).
% 0.69/1.10
% 0.69/1.10
% 0.69/1.10 subsumption(
% 0.69/1.10 clause( 73, [ equalish( X, 'e_2' ), ~( product( 'e_1', X, 'e_1' ) ) ] )
% 0.69/1.10 , clause( 204, [ equalish( X, 'e_2' ), ~( product( 'e_1', X, 'e_1' ) ) ] )
% 0.69/1.10 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 0.69/1.10 1 )] ) ).
% 0.69/1.10
% 0.69/1.10
% 0.69/1.10 resolution(
% 0.69/1.10 clause( 205, [ equalish( 'e_2', 'e_1' ), product( 'e_1', 'e_1', 'e_1' ),
% 0.69/1.10 product( 'e_2', 'e_2', 'e_1' ) ] )
% 0.69/1.10 , clause( 68, [ equalish( X, 'e_1' ), product( 'e_1', 'e_1', 'e_1' ), ~(
% 0.69/1.10 product( 'e_2', X, 'e_2' ) ) ] )
% 0.69/1.10 , 2, clause( 31, [ product( 'e_2', 'e_2', 'e_1' ), product( 'e_2', 'e_2',
% 0.69/1.10 'e_2' ) ] )
% 0.69/1.10 , 1, substitution( 0, [ :=( X, 'e_2' )] ), substitution( 1, [] )).
% 0.69/1.10
% 0.69/1.10
% 0.69/1.10 resolution(
% 0.69/1.10 clause( 206, [ product( 'e_1', 'e_1', 'e_1' ), product( 'e_2', 'e_2', 'e_1'
% 0.69/1.10 ) ] )
% 0.69/1.10 , clause( 3, [ ~( equalish( 'e_2', 'e_1' ) ) ] )
% 0.69/1.10 , 0, clause( 205, [ equalish( 'e_2', 'e_1' ), product( 'e_1', 'e_1', 'e_1'
% 0.69/1.10 ), product( 'e_2', 'e_2', 'e_1' ) ] )
% 0.69/1.10 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.69/1.10
% 0.69/1.10
% 0.69/1.10 subsumption(
% 0.69/1.10 clause( 77, [ product( 'e_1', 'e_1', 'e_1' ), product( 'e_2', 'e_2', 'e_1'
% 0.69/1.10 ) ] )
% 0.69/1.10 , clause( 206, [ product( 'e_1', 'e_1', 'e_1' ), product( 'e_2', 'e_2',
% 0.69/1.10 'e_1' ) ] )
% 0.69/1.10 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] )
% 0.69/1.10 ).
% 0.69/1.10
% 0.69/1.10
% 0.69/1.10 resolution(
% 0.69/1.10 clause( 207, [ equalish( 'e_2', 'e_1' ), product( 'e_1', 'e_1', 'e_1' ) ]
% 0.69/1.10 )
% 0.69/1.10 , clause( 72, [ equalish( X, 'e_1' ), ~( product( X, 'e_2', 'e_1' ) ) ] )
% 0.69/1.10 , 1, clause( 77, [ product( 'e_1', 'e_1', 'e_1' ), product( 'e_2', 'e_2',
% 0.69/1.10 'e_1' ) ] )
% 0.69/1.10 , 1, substitution( 0, [ :=( X, 'e_2' )] ), substitution( 1, [] )).
% 0.69/1.10
% 0.69/1.10
% 0.69/1.10 resolution(
% 0.69/1.10 clause( 208, [ product( 'e_1', 'e_1', 'e_1' ) ] )
% 0.69/1.10 , clause( 3, [ ~( equalish( 'e_2', 'e_1' ) ) ] )
% 0.69/1.10 , 0, clause( 207, [ equalish( 'e_2', 'e_1' ), product( 'e_1', 'e_1', 'e_1'
% 0.69/1.10 ) ] )
% 0.69/1.10 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.69/1.10
% 0.69/1.10
% 0.69/1.10 subsumption(
% 0.69/1.10 clause( 79, [ product( 'e_1', 'e_1', 'e_1' ) ] )
% 0.69/1.10 , clause( 208, [ product( 'e_1', 'e_1', 'e_1' ) ] )
% 0.69/1.10 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.69/1.10
% 0.69/1.10
% 0.69/1.10 resolution(
% 0.69/1.10 clause( 209, [ equalish( 'e_1', 'e_2' ) ] )
% 0.69/1.10 , clause( 73, [ equalish( X, 'e_2' ), ~( product( 'e_1', X, 'e_1' ) ) ] )
% 0.69/1.10 , 1, clause( 79, [ product( 'e_1', 'e_1', 'e_1' ) ] )
% 0.69/1.10 , 0, substitution( 0, [ :=( X, 'e_1' )] ), substitution( 1, [] )).
% 0.69/1.10
% 0.69/1.10
% 0.69/1.10 resolution(
% 0.69/1.10 clause( 210, [] )
% 0.69/1.10 , clause( 2, [ ~( equalish( 'e_1', 'e_2' ) ) ] )
% 0.69/1.10 , 0, clause( 209, [ equalish( 'e_1', 'e_2' ) ] )
% 0.69/1.10 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.69/1.10
% 0.69/1.10
% 0.69/1.10 subsumption(
% 0.69/1.10 clause( 83, [] )
% 0.69/1.10 , clause( 210, [] )
% 0.69/1.10 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.69/1.10
% 0.69/1.10
% 0.69/1.10 end.
% 0.69/1.10
% 0.69/1.10 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.69/1.10
% 0.69/1.10 Memory use:
% 0.69/1.10
% 0.69/1.10 space for terms: 1370
% 0.69/1.10 space for clauses: 3814
% 0.69/1.10
% 0.69/1.10
% 0.69/1.10 clauses generated: 195
% 0.69/1.10 clauses kept: 84
% 0.69/1.10 clauses selected: 40
% 0.69/1.10 clauses deleted: 2
% 0.69/1.10 clauses inuse deleted: 0
% 0.69/1.10
% 0.69/1.10 subsentry: 1714
% 0.69/1.10 literals s-matched: 933
% 0.69/1.10 literals matched: 553
% 0.69/1.10 full subsumption: 374
% 0.69/1.10
% 0.69/1.10 checksum: 350781
% 0.69/1.10
% 0.69/1.10
% 0.69/1.10 Bliksem ended
%------------------------------------------------------------------------------