TSTP Solution File: GRP135-1.002 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GRP135-1.002 : 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 07:35:31 EDT 2022
% Result : Unsatisfiable 0.76s 1.16s
% Output : Refutation 0.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GRP135-1.002 : TPTP v8.1.0. Released v1.2.0.
% 0.04/0.14 % Command : bliksem %s
% 0.15/0.35 % Computer : n025.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % DateTime : Mon Jun 13 20:56:39 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.76/1.16 *** allocated 10000 integers for termspace/termends
% 0.76/1.16 *** allocated 10000 integers for clauses
% 0.76/1.16 *** allocated 10000 integers for justifications
% 0.76/1.16 Bliksem 1.12
% 0.76/1.16
% 0.76/1.16
% 0.76/1.16 Automatic Strategy Selection
% 0.76/1.16
% 0.76/1.16 Clauses:
% 0.76/1.16 [
% 0.76/1.16 [ 'group_element'( 'e_1' ) ],
% 0.76/1.16 [ 'group_element'( 'e_2' ) ],
% 0.76/1.16 [ ~( equalish( 'e_1', 'e_2' ) ) ],
% 0.76/1.16 [ ~( equalish( 'e_2', 'e_1' ) ) ],
% 0.76/1.16 [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ), product( X, Y,
% 0.76/1.16 'e_1' ), product( X, Y, 'e_2' ) ],
% 0.76/1.16 [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), equalish( Z, T ) ]
% 0.76/1.16 ,
% 0.76/1.16 [ ~( product( X, Y, Z ) ), ~( product( X, T, Z ) ), equalish( Y, T ) ]
% 0.76/1.16 ,
% 0.76/1.16 [ ~( product( X, Y, Z ) ), ~( product( T, Y, Z ) ), equalish( X, T ) ]
% 0.76/1.16 ,
% 0.76/1.16 [ ~( product( X, Y, Z ) ), ~( product( Z, X, T ) ), product( T, X, Y ) ]
% 0.76/1.16
% 0.76/1.16 ] .
% 0.76/1.16
% 0.76/1.16
% 0.76/1.16 percentage equality = 0.000000, percentage horn = 0.888889
% 0.76/1.16 This a non-horn, non-equality problem
% 0.76/1.16
% 0.76/1.16
% 0.76/1.16 Options Used:
% 0.76/1.16
% 0.76/1.16 useres = 1
% 0.76/1.16 useparamod = 0
% 0.76/1.16 useeqrefl = 0
% 0.76/1.16 useeqfact = 0
% 0.76/1.16 usefactor = 1
% 0.76/1.16 usesimpsplitting = 0
% 0.76/1.16 usesimpdemod = 0
% 0.76/1.16 usesimpres = 3
% 0.76/1.16
% 0.76/1.16 resimpinuse = 1000
% 0.76/1.16 resimpclauses = 20000
% 0.76/1.16 substype = standard
% 0.76/1.16 backwardsubs = 1
% 0.76/1.16 selectoldest = 5
% 0.76/1.16
% 0.76/1.16 litorderings [0] = split
% 0.76/1.16 litorderings [1] = liftord
% 0.76/1.16
% 0.76/1.16 termordering = none
% 0.76/1.16
% 0.76/1.16 litapriori = 1
% 0.76/1.16 termapriori = 0
% 0.76/1.16 litaposteriori = 0
% 0.76/1.16 termaposteriori = 0
% 0.76/1.16 demodaposteriori = 0
% 0.76/1.16 ordereqreflfact = 0
% 0.76/1.16
% 0.76/1.16 litselect = none
% 0.76/1.16
% 0.76/1.16 maxweight = 15
% 0.76/1.16 maxdepth = 30000
% 0.76/1.16 maxlength = 115
% 0.76/1.16 maxnrvars = 195
% 0.76/1.16 excuselevel = 1
% 0.76/1.16 increasemaxweight = 1
% 0.76/1.16
% 0.76/1.16 maxselected = 10000000
% 0.76/1.16 maxnrclauses = 10000000
% 0.76/1.16
% 0.76/1.16 showgenerated = 0
% 0.76/1.16 showkept = 0
% 0.76/1.16 showselected = 0
% 0.76/1.16 showdeleted = 0
% 0.76/1.16 showresimp = 1
% 0.76/1.16 showstatus = 2000
% 0.76/1.16
% 0.76/1.16 prologoutput = 1
% 0.76/1.16 nrgoals = 5000000
% 0.76/1.16 totalproof = 1
% 0.76/1.16
% 0.76/1.16 Symbols occurring in the translation:
% 0.76/1.16
% 0.76/1.16 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.76/1.16 . [1, 2] (w:1, o:23, a:1, s:1, b:0),
% 0.76/1.16 ! [4, 1] (w:0, o:17, a:1, s:1, b:0),
% 0.76/1.16 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.76/1.16 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.76/1.16 'e_1' [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.76/1.16 'group_element' [40, 1] (w:1, o:22, a:1, s:1, b:0),
% 0.76/1.16 'e_2' [41, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.76/1.16 equalish [42, 2] (w:1, o:48, a:1, s:1, b:0),
% 0.76/1.16 product [45, 3] (w:1, o:49, a:1, s:1, b:0).
% 0.76/1.16
% 0.76/1.16
% 0.76/1.16 Starting Search:
% 0.76/1.16
% 0.76/1.16
% 0.76/1.16 Bliksems!, er is een bewijs:
% 0.76/1.16 % SZS status Unsatisfiable
% 0.76/1.16 % SZS output start Refutation
% 0.76/1.16
% 0.76/1.16 clause( 0, [ 'group_element'( 'e_1' ) ] )
% 0.76/1.16 .
% 0.76/1.16 clause( 1, [ 'group_element'( 'e_2' ) ] )
% 0.76/1.16 .
% 0.76/1.16 clause( 2, [ ~( equalish( 'e_1', 'e_2' ) ) ] )
% 0.76/1.16 .
% 0.76/1.16 clause( 3, [ ~( equalish( 'e_2', 'e_1' ) ) ] )
% 0.76/1.16 .
% 0.76/1.16 clause( 4, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ), product(
% 0.76/1.16 X, Y, 'e_1' ), product( X, Y, 'e_2' ) ] )
% 0.76/1.16 .
% 0.76/1.16 clause( 7, [ equalish( X, T ), ~( product( X, Y, Z ) ), ~( product( T, Y, Z
% 0.76/1.16 ) ) ] )
% 0.76/1.16 .
% 0.76/1.16 clause( 8, [ ~( product( Z, X, T ) ), product( T, X, Y ), ~( product( X, Y
% 0.76/1.16 , Z ) ) ] )
% 0.76/1.16 .
% 0.76/1.16 clause( 9, [ ~( 'group_element'( X ) ), product( X, X, 'e_1' ), product( X
% 0.76/1.16 , X, 'e_2' ) ] )
% 0.76/1.16 .
% 0.76/1.16 clause( 56, [ ~( 'group_element'( Z ) ), ~( 'group_element'( X ) ), ~(
% 0.76/1.16 product( X, Y, Z ) ), product( Z, X, 'e_1' ), product( 'e_2', X, Y ) ] )
% 0.76/1.16 .
% 0.76/1.16 clause( 57, [ ~( 'group_element'( X ) ), ~( 'group_element'( Z ) ), product(
% 0.76/1.16 Y, X, Z ), product( X, Z, 'e_1' ), ~( product( 'e_2', X, Y ) ) ] )
% 0.76/1.16 .
% 0.76/1.16 clause( 58, [ product( 'e_1', 'e_1', 'e_1' ), ~( product( 'e_2', 'e_1',
% 0.76/1.16 'e_1' ) ) ] )
% 0.76/1.16 .
% 0.76/1.16 clause( 59, [ ~( 'group_element'( X ) ), product( 'e_2', X, 'e_1' ), ~(
% 0.76/1.16 product( X, 'e_1', 'e_2' ) ) ] )
% 0.76/1.16 .
% 0.76/1.16 clause( 78, [ product( 'e_1', 'e_1', 'e_1' ), product( 'e_2', 'e_1', 'e_1'
% 0.76/1.16 ) ] )
% 0.76/1.16 .
% 0.76/1.16 clause( 79, [ ~( 'group_element'( X ) ), product( X, 'e_1', 'e_1' ),
% 0.76/1.16 product( 'e_2', X, 'e_1' ) ] )
% 0.76/1.16 .
% 0.76/1.16 clause( 80, [ product( 'e_1', 'e_1', 'e_1' ) ] )
% 0.76/1.16 .
% 0.76/1.16 clause( 81, [ ~( product( 'e_1', X, 'e_1' ) ), product( 'e_1', 'e_1', X ) ]
% 0.76/1.16 )
% 0.76/1.16 .
% 0.76/1.16 clause( 86, [ equalish( X, 'e_1' ), ~( product( X, 'e_1', 'e_1' ) ) ] )
% 0.76/1.16 .
% 0.76/1.16 clause( 110, [ product( X, 'e_1', Y ), ~( product( 'e_1', Y, 'e_1' ) ), ~(
% 0.76/1.16 product( 'e_1', X, 'e_1' ) ) ] )
% 0.76/1.16 .
% 0.76/1.16 clause( 119, [ ~( product( 'e_1', X, 'e_1' ) ), product( X, 'e_1', X ) ] )
% 0.76/1.16 .
% 0.76/1.16 clause( 122, [ ~( product( 'e_1', 'e_2', 'e_1' ) ), product( 'e_2', 'e_2',
% 0.76/1.16 'e_1' ) ] )
% 0.76/1.16 .
% 0.76/1.16 clause( 158, [ equalish( X, 'e_2' ), ~( product( X, 'e_2', 'e_1' ) ), ~(
% 0.76/1.16 product( 'e_1', 'e_2', 'e_1' ) ) ] )
% 0.76/1.16 .
% 0.76/1.16 clause( 161, [ ~( product( 'e_1', 'e_2', 'e_1' ) ) ] )
% 0.76/1.16 .
% 0.76/1.16 clause( 164, [ ~( product( 'e_2', 'e_1', X ) ), ~( product( X, 'e_2', 'e_1'
% 0.76/1.16 ) ) ] )
% 0.76/1.16 .
% 0.76/1.16 clause( 171, [ ~( 'group_element'( 'e_1' ) ), ~( 'group_element'( 'e_2' ) )
% 0.76/1.16 , product( 'e_2', 'e_1', 'e_1' ) ] )
% 0.76/1.16 .
% 0.76/1.16 clause( 175, [ product( 'e_2', 'e_1', 'e_1' ) ] )
% 0.76/1.16 .
% 0.76/1.16 clause( 176, [] )
% 0.76/1.16 .
% 0.76/1.16
% 0.76/1.16
% 0.76/1.16 % SZS output end Refutation
% 0.76/1.16 found a proof!
% 0.76/1.16
% 0.76/1.16 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.76/1.16
% 0.76/1.16 initialclauses(
% 0.76/1.16 [ clause( 178, [ 'group_element'( 'e_1' ) ] )
% 0.76/1.16 , clause( 179, [ 'group_element'( 'e_2' ) ] )
% 0.76/1.16 , clause( 180, [ ~( equalish( 'e_1', 'e_2' ) ) ] )
% 0.76/1.16 , clause( 181, [ ~( equalish( 'e_2', 'e_1' ) ) ] )
% 0.76/1.16 , clause( 182, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ),
% 0.76/1.16 product( X, Y, 'e_1' ), product( X, Y, 'e_2' ) ] )
% 0.76/1.16 , clause( 183, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), equalish(
% 0.76/1.16 Z, T ) ] )
% 0.76/1.16 , clause( 184, [ ~( product( X, Y, Z ) ), ~( product( X, T, Z ) ), equalish(
% 0.76/1.16 Y, T ) ] )
% 0.76/1.16 , clause( 185, [ ~( product( X, Y, Z ) ), ~( product( T, Y, Z ) ), equalish(
% 0.76/1.16 X, T ) ] )
% 0.76/1.16 , clause( 186, [ ~( product( X, Y, Z ) ), ~( product( Z, X, T ) ), product(
% 0.76/1.16 T, X, Y ) ] )
% 0.76/1.16 ] ).
% 0.76/1.16
% 0.76/1.16
% 0.76/1.16
% 0.76/1.16 subsumption(
% 0.76/1.16 clause( 0, [ 'group_element'( 'e_1' ) ] )
% 0.76/1.16 , clause( 178, [ 'group_element'( 'e_1' ) ] )
% 0.76/1.16 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.76/1.16
% 0.76/1.16
% 0.76/1.16 subsumption(
% 0.76/1.16 clause( 1, [ 'group_element'( 'e_2' ) ] )
% 0.76/1.16 , clause( 179, [ 'group_element'( 'e_2' ) ] )
% 0.76/1.16 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.76/1.16
% 0.76/1.16
% 0.76/1.16 subsumption(
% 0.76/1.16 clause( 2, [ ~( equalish( 'e_1', 'e_2' ) ) ] )
% 0.76/1.16 , clause( 180, [ ~( equalish( 'e_1', 'e_2' ) ) ] )
% 0.76/1.16 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.76/1.16
% 0.76/1.16
% 0.76/1.16 subsumption(
% 0.76/1.16 clause( 3, [ ~( equalish( 'e_2', 'e_1' ) ) ] )
% 0.76/1.16 , clause( 181, [ ~( equalish( 'e_2', 'e_1' ) ) ] )
% 0.76/1.16 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.76/1.16
% 0.76/1.16
% 0.76/1.16 subsumption(
% 0.76/1.16 clause( 4, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ), product(
% 0.76/1.16 X, Y, 'e_1' ), product( X, Y, 'e_2' ) ] )
% 0.76/1.16 , clause( 182, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ),
% 0.76/1.16 product( X, Y, 'e_1' ), product( X, Y, 'e_2' ) ] )
% 0.76/1.16 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.76/1.16 ), ==>( 1, 1 ), ==>( 2, 2 ), ==>( 3, 3 )] ) ).
% 0.76/1.16
% 0.76/1.16
% 0.76/1.16 subsumption(
% 0.76/1.16 clause( 7, [ equalish( X, T ), ~( product( X, Y, Z ) ), ~( product( T, Y, Z
% 0.76/1.16 ) ) ] )
% 0.76/1.16 , clause( 185, [ ~( product( X, Y, Z ) ), ~( product( T, Y, Z ) ), equalish(
% 0.76/1.16 X, T ) ] )
% 0.76/1.16 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.76/1.16 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 2 ), ==>( 2, 0 )] ) ).
% 0.76/1.16
% 0.76/1.16
% 0.76/1.16 subsumption(
% 0.76/1.16 clause( 8, [ ~( product( Z, X, T ) ), product( T, X, Y ), ~( product( X, Y
% 0.76/1.16 , Z ) ) ] )
% 0.76/1.16 , clause( 186, [ ~( product( X, Y, Z ) ), ~( product( Z, X, T ) ), product(
% 0.76/1.16 T, X, Y ) ] )
% 0.76/1.16 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.76/1.16 permutation( 0, [ ==>( 0, 2 ), ==>( 1, 0 ), ==>( 2, 1 )] ) ).
% 0.76/1.16
% 0.76/1.16
% 0.76/1.16 factor(
% 0.76/1.16 clause( 197, [ ~( 'group_element'( X ) ), product( X, X, 'e_1' ), product(
% 0.76/1.16 X, X, 'e_2' ) ] )
% 0.76/1.16 , clause( 4, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ),
% 0.76/1.16 product( X, Y, 'e_1' ), product( X, Y, 'e_2' ) ] )
% 0.76/1.16 , 0, 1, substitution( 0, [ :=( X, X ), :=( Y, X )] )).
% 0.76/1.16
% 0.76/1.16
% 0.76/1.16 subsumption(
% 0.76/1.16 clause( 9, [ ~( 'group_element'( X ) ), product( X, X, 'e_1' ), product( X
% 0.76/1.16 , X, 'e_2' ) ] )
% 0.76/1.16 , clause( 197, [ ~( 'group_element'( X ) ), product( X, X, 'e_1' ), product(
% 0.76/1.16 X, X, 'e_2' ) ] )
% 0.76/1.16 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 0.76/1.16 1 ), ==>( 2, 2 )] ) ).
% 0.76/1.16
% 0.76/1.16
% 0.76/1.16 resolution(
% 0.76/1.16 clause( 199, [ product( 'e_2', Y, Z ), ~( product( Y, Z, X ) ), ~(
% 0.76/1.16 'group_element'( X ) ), ~( 'group_element'( Y ) ), product( X, Y, 'e_1' )
% 0.76/1.16 ] )
% 0.76/1.16 , clause( 8, [ ~( product( Z, X, T ) ), product( T, X, Y ), ~( product( X,
% 0.76/1.16 Y, Z ) ) ] )
% 0.76/1.16 , 0, clause( 4, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ),
% 0.76/1.16 product( X, Y, 'e_1' ), product( X, Y, 'e_2' ) ] )
% 0.76/1.16 , 3, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X ), :=( T, 'e_2' )] )
% 0.76/1.16 , substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 0.76/1.16
% 0.76/1.16
% 0.76/1.16 subsumption(
% 0.76/1.16 clause( 56, [ ~( 'group_element'( Z ) ), ~( 'group_element'( X ) ), ~(
% 0.76/1.16 product( X, Y, Z ) ), product( Z, X, 'e_1' ), product( 'e_2', X, Y ) ] )
% 0.76/1.16 , clause( 199, [ product( 'e_2', Y, Z ), ~( product( Y, Z, X ) ), ~(
% 0.76/1.16 'group_element'( X ) ), ~( 'group_element'( Y ) ), product( X, Y, 'e_1' )
% 0.76/1.16 ] )
% 0.76/1.16 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 0.76/1.16 permutation( 0, [ ==>( 0, 4 ), ==>( 1, 2 ), ==>( 2, 0 ), ==>( 3, 1 ),
% 0.76/1.16 ==>( 4, 3 )] ) ).
% 0.76/1.16
% 0.76/1.16
% 0.76/1.16 resolution(
% 0.76/1.16 clause( 217, [ ~( product( 'e_2', X, Y ) ), product( Y, X, Z ), ~(
% 0.76/1.16 'group_element'( X ) ), ~( 'group_element'( Z ) ), product( X, Z, 'e_1' )
% 0.76/1.16 ] )
% 0.76/1.16 , clause( 8, [ ~( product( Z, X, T ) ), product( T, X, Y ), ~( product( X,
% 0.76/1.16 Y, Z ) ) ] )
% 0.76/1.16 , 2, clause( 4, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ),
% 0.76/1.16 product( X, Y, 'e_1' ), product( X, Y, 'e_2' ) ] )
% 0.76/1.16 , 3, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, 'e_2' ), :=( T, Y )] )
% 0.76/1.16 , substitution( 1, [ :=( X, X ), :=( Y, Z )] )).
% 0.76/1.16
% 0.76/1.16
% 0.76/1.16 subsumption(
% 0.76/1.16 clause( 57, [ ~( 'group_element'( X ) ), ~( 'group_element'( Z ) ), product(
% 0.76/1.16 Y, X, Z ), product( X, Z, 'e_1' ), ~( product( 'e_2', X, Y ) ) ] )
% 0.76/1.16 , clause( 217, [ ~( product( 'e_2', X, Y ) ), product( Y, X, Z ), ~(
% 0.76/1.16 'group_element'( X ) ), ~( 'group_element'( Z ) ), product( X, Z, 'e_1' )
% 0.76/1.16 ] )
% 0.76/1.16 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.76/1.16 permutation( 0, [ ==>( 0, 4 ), ==>( 1, 2 ), ==>( 2, 0 ), ==>( 3, 1 ),
% 0.76/1.16 ==>( 4, 3 )] ) ).
% 0.76/1.16
% 0.76/1.16
% 0.76/1.16 factor(
% 0.76/1.16 clause( 231, [ ~( 'group_element'( 'e_1' ) ), ~( 'group_element'( 'e_1' ) )
% 0.76/1.16 , product( 'e_1', 'e_1', 'e_1' ), ~( product( 'e_2', 'e_1', 'e_1' ) ) ]
% 0.76/1.16 )
% 0.76/1.16 , clause( 57, [ ~( 'group_element'( X ) ), ~( 'group_element'( Z ) ),
% 0.76/1.16 product( Y, X, Z ), product( X, Z, 'e_1' ), ~( product( 'e_2', X, Y ) ) ]
% 0.76/1.16 )
% 0.76/1.16 , 2, 3, substitution( 0, [ :=( X, 'e_1' ), :=( Y, 'e_1' ), :=( Z, 'e_1' )] )
% 0.76/1.16 ).
% 0.76/1.16
% 0.76/1.16
% 0.76/1.16 factor(
% 0.76/1.16 clause( 232, [ ~( 'group_element'( 'e_1' ) ), product( 'e_1', 'e_1', 'e_1'
% 0.76/1.16 ), ~( product( 'e_2', 'e_1', 'e_1' ) ) ] )
% 0.76/1.16 , clause( 231, [ ~( 'group_element'( 'e_1' ) ), ~( 'group_element'( 'e_1' )
% 0.76/1.16 ), product( 'e_1', 'e_1', 'e_1' ), ~( product( 'e_2', 'e_1', 'e_1' ) ) ]
% 0.76/1.16 )
% 0.76/1.16 , 0, 1, substitution( 0, [] )).
% 0.76/1.16
% 0.76/1.16
% 0.76/1.16 resolution(
% 0.76/1.16 clause( 234, [ product( 'e_1', 'e_1', 'e_1' ), ~( product( 'e_2', 'e_1',
% 0.76/1.16 'e_1' ) ) ] )
% 0.76/1.16 , clause( 232, [ ~( 'group_element'( 'e_1' ) ), product( 'e_1', 'e_1',
% 0.76/1.16 'e_1' ), ~( product( 'e_2', 'e_1', 'e_1' ) ) ] )
% 0.76/1.16 , 0, clause( 0, [ 'group_element'( 'e_1' ) ] )
% 0.76/1.16 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.76/1.16
% 0.76/1.16
% 0.76/1.16 subsumption(
% 0.76/1.16 clause( 58, [ product( 'e_1', 'e_1', 'e_1' ), ~( product( 'e_2', 'e_1',
% 0.76/1.16 'e_1' ) ) ] )
% 0.76/1.16 , clause( 234, [ product( 'e_1', 'e_1', 'e_1' ), ~( product( 'e_2', 'e_1',
% 0.76/1.16 'e_1' ) ) ] )
% 0.76/1.16 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] )
% 0.76/1.16 ).
% 0.76/1.16
% 0.76/1.16
% 0.76/1.16 factor(
% 0.76/1.16 clause( 236, [ ~( 'group_element'( 'e_2' ) ), ~( 'group_element'( X ) ),
% 0.76/1.16 ~( product( X, 'e_1', 'e_2' ) ), product( 'e_2', X, 'e_1' ) ] )
% 0.76/1.16 , clause( 56, [ ~( 'group_element'( Z ) ), ~( 'group_element'( X ) ), ~(
% 0.76/1.16 product( X, Y, Z ) ), product( Z, X, 'e_1' ), product( 'e_2', X, Y ) ] )
% 0.76/1.16 , 3, 4, substitution( 0, [ :=( X, X ), :=( Y, 'e_1' ), :=( Z, 'e_2' )] )
% 0.76/1.16 ).
% 0.76/1.16
% 0.76/1.16
% 0.76/1.16 resolution(
% 0.76/1.16 clause( 239, [ ~( 'group_element'( X ) ), ~( product( X, 'e_1', 'e_2' ) ),
% 0.76/1.16 product( 'e_2', X, 'e_1' ) ] )
% 0.76/1.16 , clause( 236, [ ~( 'group_element'( 'e_2' ) ), ~( 'group_element'( X ) ),
% 0.76/1.16 ~( product( X, 'e_1', 'e_2' ) ), product( 'e_2', X, 'e_1' ) ] )
% 0.76/1.16 , 0, clause( 1, [ 'group_element'( 'e_2' ) ] )
% 0.76/1.16 , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [] )).
% 0.76/1.16
% 0.76/1.16
% 0.76/1.16 subsumption(
% 0.76/1.16 clause( 59, [ ~( 'group_element'( X ) ), product( 'e_2', X, 'e_1' ), ~(
% 0.76/1.16 product( X, 'e_1', 'e_2' ) ) ] )
% 0.76/1.16 , clause( 239, [ ~( 'group_element'( X ) ), ~( product( X, 'e_1', 'e_2' ) )
% 0.76/1.16 , product( 'e_2', X, 'e_1' ) ] )
% 0.76/1.16 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 0.76/1.16 2 ), ==>( 2, 1 )] ) ).
% 0.76/1.16
% 0.76/1.16
% 0.76/1.16 resolution(
% 0.76/1.16 clause( 240, [ ~( 'group_element'( 'e_1' ) ), product( 'e_2', 'e_1', 'e_1'
% 0.76/1.16 ), ~( 'group_element'( 'e_1' ) ), product( 'e_1', 'e_1', 'e_1' ) ] )
% 0.76/1.17 , clause( 59, [ ~( 'group_element'( X ) ), product( 'e_2', X, 'e_1' ), ~(
% 0.76/1.17 product( X, 'e_1', 'e_2' ) ) ] )
% 0.76/1.17 , 2, clause( 9, [ ~( 'group_element'( X ) ), product( X, X, 'e_1' ),
% 0.76/1.17 product( X, X, 'e_2' ) ] )
% 0.76/1.17 , 2, substitution( 0, [ :=( X, 'e_1' )] ), substitution( 1, [ :=( X, 'e_1'
% 0.76/1.17 )] )).
% 0.76/1.17
% 0.76/1.17
% 0.76/1.17 factor(
% 0.76/1.17 clause( 241, [ ~( 'group_element'( 'e_1' ) ), product( 'e_2', 'e_1', 'e_1'
% 0.76/1.17 ), product( 'e_1', 'e_1', 'e_1' ) ] )
% 0.76/1.17 , clause( 240, [ ~( 'group_element'( 'e_1' ) ), product( 'e_2', 'e_1',
% 0.76/1.17 'e_1' ), ~( 'group_element'( 'e_1' ) ), product( 'e_1', 'e_1', 'e_1' ) ]
% 0.76/1.17 )
% 0.76/1.17 , 0, 2, substitution( 0, [] )).
% 0.76/1.17
% 0.76/1.17
% 0.76/1.17 resolution(
% 0.76/1.17 clause( 243, [ product( 'e_2', 'e_1', 'e_1' ), product( 'e_1', 'e_1', 'e_1'
% 0.76/1.17 ) ] )
% 0.76/1.17 , clause( 241, [ ~( 'group_element'( 'e_1' ) ), product( 'e_2', 'e_1',
% 0.76/1.17 'e_1' ), product( 'e_1', 'e_1', 'e_1' ) ] )
% 0.76/1.17 , 0, clause( 0, [ 'group_element'( 'e_1' ) ] )
% 0.76/1.17 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.76/1.17
% 0.76/1.17
% 0.76/1.17 subsumption(
% 0.76/1.17 clause( 78, [ product( 'e_1', 'e_1', 'e_1' ), product( 'e_2', 'e_1', 'e_1'
% 0.76/1.17 ) ] )
% 0.76/1.17 , clause( 243, [ product( 'e_2', 'e_1', 'e_1' ), product( 'e_1', 'e_1',
% 0.76/1.17 'e_1' ) ] )
% 0.76/1.17 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] )
% 0.76/1.17 ).
% 0.76/1.17
% 0.76/1.17
% 0.76/1.17 resolution(
% 0.76/1.17 clause( 244, [ ~( 'group_element'( X ) ), product( 'e_2', X, 'e_1' ), ~(
% 0.76/1.17 'group_element'( X ) ), ~( 'group_element'( 'e_1' ) ), product( X, 'e_1'
% 0.76/1.17 , 'e_1' ) ] )
% 0.76/1.17 , clause( 59, [ ~( 'group_element'( X ) ), product( 'e_2', X, 'e_1' ), ~(
% 0.76/1.17 product( X, 'e_1', 'e_2' ) ) ] )
% 0.76/1.17 , 2, clause( 4, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ),
% 0.76/1.17 product( X, Y, 'e_1' ), product( X, Y, 'e_2' ) ] )
% 0.76/1.17 , 3, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ), :=( Y
% 0.76/1.17 , 'e_1' )] )).
% 0.76/1.17
% 0.76/1.17
% 0.76/1.17 resolution(
% 0.76/1.17 clause( 247, [ ~( 'group_element'( X ) ), product( 'e_2', X, 'e_1' ), ~(
% 0.76/1.17 'group_element'( X ) ), product( X, 'e_1', 'e_1' ) ] )
% 0.76/1.17 , clause( 244, [ ~( 'group_element'( X ) ), product( 'e_2', X, 'e_1' ), ~(
% 0.76/1.17 'group_element'( X ) ), ~( 'group_element'( 'e_1' ) ), product( X, 'e_1'
% 0.76/1.17 , 'e_1' ) ] )
% 0.76/1.17 , 3, clause( 0, [ 'group_element'( 'e_1' ) ] )
% 0.76/1.17 , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [] )).
% 0.76/1.17
% 0.76/1.17
% 0.76/1.17 factor(
% 0.76/1.17 clause( 248, [ ~( 'group_element'( X ) ), product( 'e_2', X, 'e_1' ),
% 0.76/1.17 product( X, 'e_1', 'e_1' ) ] )
% 0.76/1.17 , clause( 247, [ ~( 'group_element'( X ) ), product( 'e_2', X, 'e_1' ), ~(
% 0.76/1.17 'group_element'( X ) ), product( X, 'e_1', 'e_1' ) ] )
% 0.76/1.17 , 0, 2, substitution( 0, [ :=( X, X )] )).
% 0.76/1.17
% 0.76/1.17
% 0.76/1.17 subsumption(
% 0.76/1.17 clause( 79, [ ~( 'group_element'( X ) ), product( X, 'e_1', 'e_1' ),
% 0.76/1.17 product( 'e_2', X, 'e_1' ) ] )
% 0.76/1.17 , clause( 248, [ ~( 'group_element'( X ) ), product( 'e_2', X, 'e_1' ),
% 0.76/1.17 product( X, 'e_1', 'e_1' ) ] )
% 0.76/1.17 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 0.76/1.17 2 ), ==>( 2, 1 )] ) ).
% 0.76/1.17
% 0.76/1.17
% 0.76/1.17 resolution(
% 0.76/1.17 clause( 249, [ product( 'e_1', 'e_1', 'e_1' ), product( 'e_1', 'e_1', 'e_1'
% 0.76/1.17 ) ] )
% 0.76/1.17 , clause( 58, [ product( 'e_1', 'e_1', 'e_1' ), ~( product( 'e_2', 'e_1',
% 0.76/1.17 'e_1' ) ) ] )
% 0.76/1.17 , 1, clause( 78, [ product( 'e_1', 'e_1', 'e_1' ), product( 'e_2', 'e_1',
% 0.76/1.17 'e_1' ) ] )
% 0.76/1.17 , 1, substitution( 0, [] ), substitution( 1, [] )).
% 0.76/1.17
% 0.76/1.17
% 0.76/1.17 factor(
% 0.76/1.17 clause( 250, [ product( 'e_1', 'e_1', 'e_1' ) ] )
% 0.76/1.17 , clause( 249, [ product( 'e_1', 'e_1', 'e_1' ), product( 'e_1', 'e_1',
% 0.76/1.17 'e_1' ) ] )
% 0.76/1.17 , 0, 1, substitution( 0, [] )).
% 0.76/1.17
% 0.76/1.17
% 0.76/1.17 subsumption(
% 0.76/1.17 clause( 80, [ product( 'e_1', 'e_1', 'e_1' ) ] )
% 0.76/1.17 , clause( 250, [ product( 'e_1', 'e_1', 'e_1' ) ] )
% 0.76/1.17 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.76/1.17
% 0.76/1.17
% 0.76/1.17 resolution(
% 0.76/1.17 clause( 251, [ product( 'e_1', 'e_1', X ), ~( product( 'e_1', X, 'e_1' ) )
% 0.76/1.17 ] )
% 0.76/1.17 , clause( 8, [ ~( product( Z, X, T ) ), product( T, X, Y ), ~( product( X,
% 0.76/1.17 Y, Z ) ) ] )
% 0.76/1.17 , 0, clause( 80, [ product( 'e_1', 'e_1', 'e_1' ) ] )
% 0.76/1.17 , 0, substitution( 0, [ :=( X, 'e_1' ), :=( Y, X ), :=( Z, 'e_1' ), :=( T,
% 0.76/1.17 'e_1' )] ), substitution( 1, [] )).
% 0.76/1.17
% 0.76/1.17
% 0.76/1.17 subsumption(
% 0.76/1.17 clause( 81, [ ~( product( 'e_1', X, 'e_1' ) ), product( 'e_1', 'e_1', X ) ]
% 0.76/1.17 )
% 0.76/1.17 , clause( 251, [ product( 'e_1', 'e_1', X ), ~( product( 'e_1', X, 'e_1' )
% 0.76/1.17 ) ] )
% 0.76/1.17 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1,
% 0.76/1.17 0 )] ) ).
% 0.76/1.17
% 0.76/1.17
% 0.76/1.17 resolution(
% 0.76/1.17 clause( 254, [ equalish( X, 'e_1' ), ~( product( X, 'e_1', 'e_1' ) ) ] )
% 0.76/1.17 , clause( 7, [ equalish( X, T ), ~( product( X, Y, Z ) ), ~( product( T, Y
% 0.76/1.17 , Z ) ) ] )
% 0.76/1.17 , 2, clause( 80, [ product( 'e_1', 'e_1', 'e_1' ) ] )
% 0.76/1.17 , 0, substitution( 0, [ :=( X, X ), :=( Y, 'e_1' ), :=( Z, 'e_1' ), :=( T,
% 0.76/1.17 'e_1' )] ), substitution( 1, [] )).
% 0.76/1.17
% 0.76/1.17
% 0.76/1.17 subsumption(
% 0.76/1.17 clause( 86, [ equalish( X, 'e_1' ), ~( product( X, 'e_1', 'e_1' ) ) ] )
% 0.76/1.17 , clause( 254, [ equalish( X, 'e_1' ), ~( product( X, 'e_1', 'e_1' ) ) ] )
% 0.76/1.17 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 0.76/1.17 1 )] ) ).
% 0.76/1.17
% 0.76/1.17
% 0.76/1.17 resolution(
% 0.76/1.17 clause( 257, [ product( X, 'e_1', Y ), ~( product( 'e_1', Y, 'e_1' ) ), ~(
% 0.76/1.17 product( 'e_1', X, 'e_1' ) ) ] )
% 0.76/1.17 , clause( 8, [ ~( product( Z, X, T ) ), product( T, X, Y ), ~( product( X,
% 0.76/1.17 Y, Z ) ) ] )
% 0.76/1.17 , 0, clause( 81, [ ~( product( 'e_1', X, 'e_1' ) ), product( 'e_1', 'e_1',
% 0.76/1.17 X ) ] )
% 0.76/1.17 , 1, substitution( 0, [ :=( X, 'e_1' ), :=( Y, Y ), :=( Z, 'e_1' ), :=( T,
% 0.76/1.17 X )] ), substitution( 1, [ :=( X, X )] )).
% 0.76/1.17
% 0.76/1.17
% 0.76/1.17 subsumption(
% 0.76/1.17 clause( 110, [ product( X, 'e_1', Y ), ~( product( 'e_1', Y, 'e_1' ) ), ~(
% 0.76/1.17 product( 'e_1', X, 'e_1' ) ) ] )
% 0.76/1.17 , clause( 257, [ product( X, 'e_1', Y ), ~( product( 'e_1', Y, 'e_1' ) ),
% 0.76/1.17 ~( product( 'e_1', X, 'e_1' ) ) ] )
% 0.76/1.17 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.76/1.17 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 0.76/1.17
% 0.76/1.17
% 0.76/1.17 factor(
% 0.76/1.17 clause( 260, [ product( X, 'e_1', X ), ~( product( 'e_1', X, 'e_1' ) ) ] )
% 0.76/1.17 , clause( 110, [ product( X, 'e_1', Y ), ~( product( 'e_1', Y, 'e_1' ) ),
% 0.76/1.17 ~( product( 'e_1', X, 'e_1' ) ) ] )
% 0.76/1.17 , 1, 2, substitution( 0, [ :=( X, X ), :=( Y, X )] )).
% 0.76/1.17
% 0.76/1.17
% 0.76/1.17 subsumption(
% 0.76/1.17 clause( 119, [ ~( product( 'e_1', X, 'e_1' ) ), product( X, 'e_1', X ) ] )
% 0.76/1.17 , clause( 260, [ product( X, 'e_1', X ), ~( product( 'e_1', X, 'e_1' ) ) ]
% 0.76/1.17 )
% 0.76/1.17 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1,
% 0.76/1.17 0 )] ) ).
% 0.76/1.17
% 0.76/1.17
% 0.76/1.17 resolution(
% 0.76/1.17 clause( 261, [ ~( 'group_element'( 'e_2' ) ), product( 'e_2', 'e_2', 'e_1'
% 0.76/1.17 ), ~( product( 'e_1', 'e_2', 'e_1' ) ) ] )
% 0.76/1.17 , clause( 59, [ ~( 'group_element'( X ) ), product( 'e_2', X, 'e_1' ), ~(
% 0.76/1.17 product( X, 'e_1', 'e_2' ) ) ] )
% 0.76/1.17 , 2, clause( 119, [ ~( product( 'e_1', X, 'e_1' ) ), product( X, 'e_1', X )
% 0.76/1.17 ] )
% 0.76/1.17 , 1, substitution( 0, [ :=( X, 'e_2' )] ), substitution( 1, [ :=( X, 'e_2'
% 0.76/1.17 )] )).
% 0.76/1.17
% 0.76/1.17
% 0.76/1.17 resolution(
% 0.76/1.17 clause( 262, [ product( 'e_2', 'e_2', 'e_1' ), ~( product( 'e_1', 'e_2',
% 0.76/1.17 'e_1' ) ) ] )
% 0.76/1.17 , clause( 261, [ ~( 'group_element'( 'e_2' ) ), product( 'e_2', 'e_2',
% 0.76/1.17 'e_1' ), ~( product( 'e_1', 'e_2', 'e_1' ) ) ] )
% 0.76/1.17 , 0, clause( 1, [ 'group_element'( 'e_2' ) ] )
% 0.76/1.17 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.76/1.17
% 0.76/1.17
% 0.76/1.17 subsumption(
% 0.76/1.17 clause( 122, [ ~( product( 'e_1', 'e_2', 'e_1' ) ), product( 'e_2', 'e_2',
% 0.76/1.17 'e_1' ) ] )
% 0.76/1.17 , clause( 262, [ product( 'e_2', 'e_2', 'e_1' ), ~( product( 'e_1', 'e_2',
% 0.76/1.17 'e_1' ) ) ] )
% 0.76/1.17 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] )
% 0.76/1.17 ).
% 0.76/1.17
% 0.76/1.17
% 0.76/1.17 resolution(
% 0.76/1.17 clause( 264, [ equalish( X, 'e_2' ), ~( product( X, 'e_2', 'e_1' ) ), ~(
% 0.76/1.17 product( 'e_1', 'e_2', 'e_1' ) ) ] )
% 0.76/1.17 , clause( 7, [ equalish( X, T ), ~( product( X, Y, Z ) ), ~( product( T, Y
% 0.76/1.17 , Z ) ) ] )
% 0.76/1.17 , 2, clause( 122, [ ~( product( 'e_1', 'e_2', 'e_1' ) ), product( 'e_2',
% 0.76/1.17 'e_2', 'e_1' ) ] )
% 0.76/1.17 , 1, substitution( 0, [ :=( X, X ), :=( Y, 'e_2' ), :=( Z, 'e_1' ), :=( T,
% 0.76/1.17 'e_2' )] ), substitution( 1, [] )).
% 0.76/1.17
% 0.76/1.17
% 0.76/1.17 subsumption(
% 0.76/1.17 clause( 158, [ equalish( X, 'e_2' ), ~( product( X, 'e_2', 'e_1' ) ), ~(
% 0.76/1.17 product( 'e_1', 'e_2', 'e_1' ) ) ] )
% 0.76/1.17 , clause( 264, [ equalish( X, 'e_2' ), ~( product( X, 'e_2', 'e_1' ) ), ~(
% 0.76/1.17 product( 'e_1', 'e_2', 'e_1' ) ) ] )
% 0.76/1.17 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 0.76/1.17 1 ), ==>( 2, 2 )] ) ).
% 0.76/1.17
% 0.76/1.17
% 0.76/1.17 factor(
% 0.76/1.17 clause( 267, [ equalish( 'e_1', 'e_2' ), ~( product( 'e_1', 'e_2', 'e_1' )
% 0.76/1.17 ) ] )
% 0.76/1.17 , clause( 158, [ equalish( X, 'e_2' ), ~( product( X, 'e_2', 'e_1' ) ), ~(
% 0.76/1.17 product( 'e_1', 'e_2', 'e_1' ) ) ] )
% 0.76/1.17 , 1, 2, substitution( 0, [ :=( X, 'e_1' )] )).
% 0.76/1.17
% 0.76/1.17
% 0.76/1.17 resolution(
% 0.76/1.17 clause( 268, [ ~( product( 'e_1', 'e_2', 'e_1' ) ) ] )
% 0.76/1.17 , clause( 2, [ ~( equalish( 'e_1', 'e_2' ) ) ] )
% 0.76/1.17 , 0, clause( 267, [ equalish( 'e_1', 'e_2' ), ~( product( 'e_1', 'e_2',
% 0.76/1.17 'e_1' ) ) ] )
% 0.76/1.17 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.76/1.17
% 0.76/1.17
% 0.76/1.17 subsumption(
% 0.76/1.17 clause( 161, [ ~( product( 'e_1', 'e_2', 'e_1' ) ) ] )
% 0.76/1.17 , clause( 268, [ ~( product( 'e_1', 'e_2', 'e_1' ) ) ] )
% 0.76/1.17 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.76/1.17
% 0.76/1.17
% 0.76/1.17 resolution(
% 0.76/1.17 clause( 269, [ ~( product( X, 'e_2', 'e_1' ) ), ~( product( 'e_2', 'e_1', X
% 0.76/1.17 ) ) ] )
% 0.76/1.17 , clause( 161, [ ~( product( 'e_1', 'e_2', 'e_1' ) ) ] )
% 0.76/1.17 , 0, clause( 8, [ ~( product( Z, X, T ) ), product( T, X, Y ), ~( product(
% 0.76/1.17 X, Y, Z ) ) ] )
% 0.76/1.17 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, 'e_2' ), :=( Y, 'e_1'
% 0.76/1.17 ), :=( Z, X ), :=( T, 'e_1' )] )).
% 0.76/1.17
% 0.76/1.17
% 0.76/1.17 subsumption(
% 0.76/1.17 clause( 164, [ ~( product( 'e_2', 'e_1', X ) ), ~( product( X, 'e_2', 'e_1'
% 0.76/1.17 ) ) ] )
% 0.76/1.17 , clause( 269, [ ~( product( X, 'e_2', 'e_1' ) ), ~( product( 'e_2', 'e_1'
% 0.76/1.17 , X ) ) ] )
% 0.76/1.17 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1,
% 0.76/1.17 0 )] ) ).
% 0.76/1.17
% 0.76/1.17
% 0.76/1.17 resolution(
% 0.76/1.17 clause( 271, [ ~( product( 'e_2', 'e_2', 'e_1' ) ), ~( 'group_element'(
% 0.76/1.17 'e_2' ) ), ~( 'group_element'( 'e_1' ) ), product( 'e_2', 'e_1', 'e_1' )
% 0.76/1.17 ] )
% 0.76/1.17 , clause( 164, [ ~( product( 'e_2', 'e_1', X ) ), ~( product( X, 'e_2',
% 0.76/1.17 'e_1' ) ) ] )
% 0.76/1.17 , 0, clause( 4, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ),
% 0.76/1.17 product( X, Y, 'e_1' ), product( X, Y, 'e_2' ) ] )
% 0.76/1.17 , 3, substitution( 0, [ :=( X, 'e_2' )] ), substitution( 1, [ :=( X, 'e_2'
% 0.76/1.17 ), :=( Y, 'e_1' )] )).
% 0.76/1.17
% 0.76/1.17
% 0.76/1.17 resolution(
% 0.76/1.17 clause( 274, [ ~( 'group_element'( 'e_2' ) ), ~( 'group_element'( 'e_1' ) )
% 0.76/1.17 , product( 'e_2', 'e_1', 'e_1' ), ~( 'group_element'( 'e_2' ) ), product(
% 0.76/1.17 'e_2', 'e_1', 'e_1' ) ] )
% 0.76/1.17 , clause( 271, [ ~( product( 'e_2', 'e_2', 'e_1' ) ), ~( 'group_element'(
% 0.76/1.17 'e_2' ) ), ~( 'group_element'( 'e_1' ) ), product( 'e_2', 'e_1', 'e_1' )
% 0.76/1.17 ] )
% 0.76/1.17 , 0, clause( 79, [ ~( 'group_element'( X ) ), product( X, 'e_1', 'e_1' ),
% 0.76/1.17 product( 'e_2', X, 'e_1' ) ] )
% 0.76/1.17 , 2, substitution( 0, [] ), substitution( 1, [ :=( X, 'e_2' )] )).
% 0.76/1.17
% 0.76/1.17
% 0.76/1.17 factor(
% 0.76/1.17 clause( 276, [ ~( 'group_element'( 'e_2' ) ), ~( 'group_element'( 'e_1' ) )
% 0.76/1.17 , product( 'e_2', 'e_1', 'e_1' ), ~( 'group_element'( 'e_2' ) ) ] )
% 0.76/1.17 , clause( 274, [ ~( 'group_element'( 'e_2' ) ), ~( 'group_element'( 'e_1' )
% 0.76/1.17 ), product( 'e_2', 'e_1', 'e_1' ), ~( 'group_element'( 'e_2' ) ),
% 0.76/1.17 product( 'e_2', 'e_1', 'e_1' ) ] )
% 0.76/1.17 , 2, 4, substitution( 0, [] )).
% 0.76/1.17
% 0.76/1.17
% 0.76/1.17 factor(
% 0.76/1.17 clause( 277, [ ~( 'group_element'( 'e_2' ) ), ~( 'group_element'( 'e_1' ) )
% 0.76/1.17 , product( 'e_2', 'e_1', 'e_1' ) ] )
% 0.76/1.17 , clause( 276, [ ~( 'group_element'( 'e_2' ) ), ~( 'group_element'( 'e_1' )
% 0.76/1.17 ), product( 'e_2', 'e_1', 'e_1' ), ~( 'group_element'( 'e_2' ) ) ] )
% 0.76/1.17 , 0, 3, substitution( 0, [] )).
% 0.76/1.17
% 0.76/1.17
% 0.76/1.17 subsumption(
% 0.76/1.17 clause( 171, [ ~( 'group_element'( 'e_1' ) ), ~( 'group_element'( 'e_2' ) )
% 0.76/1.17 , product( 'e_2', 'e_1', 'e_1' ) ] )
% 0.76/1.17 , clause( 277, [ ~( 'group_element'( 'e_2' ) ), ~( 'group_element'( 'e_1' )
% 0.76/1.17 ), product( 'e_2', 'e_1', 'e_1' ) ] )
% 0.76/1.17 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 ), ==>( 2
% 0.76/1.17 , 2 )] ) ).
% 0.76/1.17
% 0.76/1.17
% 0.76/1.17 resolution(
% 0.76/1.17 clause( 278, [ ~( 'group_element'( 'e_2' ) ), product( 'e_2', 'e_1', 'e_1'
% 0.76/1.17 ) ] )
% 0.76/1.17 , clause( 171, [ ~( 'group_element'( 'e_1' ) ), ~( 'group_element'( 'e_2' )
% 0.76/1.17 ), product( 'e_2', 'e_1', 'e_1' ) ] )
% 0.76/1.17 , 0, clause( 0, [ 'group_element'( 'e_1' ) ] )
% 0.76/1.17 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.76/1.17
% 0.76/1.17
% 0.76/1.17 resolution(
% 0.76/1.17 clause( 279, [ product( 'e_2', 'e_1', 'e_1' ) ] )
% 0.76/1.17 , clause( 278, [ ~( 'group_element'( 'e_2' ) ), product( 'e_2', 'e_1',
% 0.76/1.17 'e_1' ) ] )
% 0.76/1.17 , 0, clause( 1, [ 'group_element'( 'e_2' ) ] )
% 0.76/1.17 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.76/1.17
% 0.76/1.17
% 0.76/1.17 subsumption(
% 0.76/1.17 clause( 175, [ product( 'e_2', 'e_1', 'e_1' ) ] )
% 0.76/1.17 , clause( 279, [ product( 'e_2', 'e_1', 'e_1' ) ] )
% 0.76/1.17 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.76/1.17
% 0.76/1.17
% 0.76/1.17 resolution(
% 0.76/1.17 clause( 280, [ equalish( 'e_2', 'e_1' ) ] )
% 0.76/1.17 , clause( 86, [ equalish( X, 'e_1' ), ~( product( X, 'e_1', 'e_1' ) ) ] )
% 0.76/1.17 , 1, clause( 175, [ product( 'e_2', 'e_1', 'e_1' ) ] )
% 0.76/1.17 , 0, substitution( 0, [ :=( X, 'e_2' )] ), substitution( 1, [] )).
% 0.76/1.17
% 0.76/1.17
% 0.76/1.17 resolution(
% 0.76/1.17 clause( 281, [] )
% 0.76/1.17 , clause( 3, [ ~( equalish( 'e_2', 'e_1' ) ) ] )
% 0.76/1.17 , 0, clause( 280, [ equalish( 'e_2', 'e_1' ) ] )
% 0.76/1.17 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.76/1.17
% 0.76/1.17
% 0.76/1.17 subsumption(
% 0.76/1.17 clause( 176, [] )
% 0.76/1.17 , clause( 281, [] )
% 0.76/1.17 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.76/1.17
% 0.76/1.17
% 0.76/1.17 end.
% 0.76/1.17
% 0.76/1.17 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.76/1.17
% 0.76/1.17 Memory use:
% 0.76/1.17
% 0.76/1.17 space for terms: 2509
% 0.76/1.17 space for clauses: 7380
% 0.76/1.17
% 0.76/1.17
% 0.76/1.17 clauses generated: 563
% 0.76/1.17 clauses kept: 177
% 0.76/1.17 clauses selected: 46
% 0.76/1.17 clauses deleted: 4
% 0.76/1.17 clauses inuse deleted: 0
% 0.76/1.17
% 0.76/1.17 subsentry: 4783
% 0.76/1.17 literals s-matched: 2751
% 0.76/1.17 literals matched: 1935
% 0.76/1.17 full subsumption: 954
% 0.76/1.17
% 0.76/1.17 checksum: -2793573
% 0.76/1.17
% 0.76/1.17
% 0.76/1.17 Bliksem ended
%------------------------------------------------------------------------------