%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GRP123-8.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n015.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 0.44s 1.12s
% Output : Refutation 0.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP123-8.003 : TPTP v8.1.0. Released v1.2.0.
% 0.07/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % DateTime : Mon Jun 13 05:22:22 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.44/1.12 *** allocated 10000 integers for termspace/termends
% 0.44/1.12 *** allocated 10000 integers for clauses
% 0.44/1.12 *** allocated 10000 integers for justifications
% 0.44/1.12 Bliksem 1.12
% 0.44/1.12
% 0.44/1.12
% 0.44/1.12 Automatic Strategy Selection
% 0.44/1.12
% 0.44/1.12 Clauses:
% 0.44/1.12 [
% 0.44/1.12 [ next( 'e_0', 'e_1' ) ],
% 0.44/1.12 [ next( 'e_1', 'e_2' ) ],
% 0.44/1.12 [ next( 'e_2', 'e_3' ) ],
% 0.44/1.12 [ greater( 'e_1', 'e_0' ) ],
% 0.44/1.12 [ greater( 'e_2', 'e_0' ) ],
% 0.44/1.12 [ greater( 'e_3', 'e_0' ) ],
% 0.44/1.12 [ greater( 'e_2', 'e_1' ) ],
% 0.44/1.12 [ greater( 'e_3', 'e_1' ) ],
% 0.44/1.12 [ greater( 'e_3', 'e_2' ) ],
% 0.44/1.12 [ ~( cycle( X, Y ) ), ~( cycle( X, Z ) ), equalish( Y, Z ) ],
% 0.44/1.12 [ ~( 'group_element'( X ) ), cycle( X, 'e_0' ), cycle( X, 'e_1' ), cycle(
% 0.44/1.12 X, 'e_2' ) ],
% 0.44/1.12 [ cycle( 'e_3', 'e_0' ) ],
% 0.44/1.12 [ ~( cycle( X, Y ) ), ~( cycle( Z, T ) ), ~( next( X, Z ) ), ~( greater(
% 0.44/1.12 Y, 'e_0' ) ), ~( next( T, U ) ), equalish( Y, U ) ],
% 0.44/1.12 [ ~( cycle( X, Y ) ), ~( cycle( Z, 'e_0' ) ), ~( cycle( T, U ) ), ~(
% 0.44/1.12 next( Z, T ) ), ~( greater( Z, X ) ), ~( greater( Y, U ) ) ],
% 0.44/1.12 [ ~( cycle( X, 'e_0' ) ), ~( product( X, 'e_1', Y ) ), ~( greater( Y, X
% 0.44/1.12 ) ) ],
% 0.44/1.12 [ ~( cycle( X, Y ) ), ~( product( X, 'e_1', Z ) ), ~( greater( Y, 'e_0'
% 0.44/1.12 ) ), ~( next( X, T ) ), equalish( Z, T ) ],
% 0.44/1.12 [ 'group_element'( 'e_1' ) ],
% 0.44/1.12 [ 'group_element'( 'e_2' ) ],
% 0.44/1.12 [ 'group_element'( 'e_3' ) ],
% 0.44/1.12 [ ~( equalish( 'e_1', 'e_2' ) ) ],
% 0.44/1.12 [ ~( equalish( 'e_1', 'e_3' ) ) ],
% 0.44/1.12 [ ~( equalish( 'e_2', 'e_1' ) ) ],
% 0.44/1.12 [ ~( equalish( 'e_2', 'e_3' ) ) ],
% 0.44/1.12 [ ~( equalish( 'e_3', 'e_1' ) ) ],
% 0.44/1.12 [ ~( equalish( 'e_3', 'e_2' ) ) ],
% 0.44/1.12 [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ), product1( X, Y,
% 0.44/1.12 'e_1' ), product1( X, Y, 'e_2' ), product1( X, Y, 'e_3' ) ],
% 0.44/1.12 [ ~( product1( X, Y, Z ) ), ~( product1( X, Y, T ) ), equalish( Z, T ) ]
% 0.44/1.12 ,
% 0.44/1.12 [ ~( product1( X, Y, Z ) ), ~( product1( X, T, Z ) ), equalish( Y, T ) ]
% 0.44/1.12 ,
% 0.44/1.12 [ ~( product1( X, Y, Z ) ), ~( product1( T, Y, Z ) ), equalish( X, T ) ]
% 0.44/1.12 ,
% 0.44/1.12 [ product1( X, X, X ) ],
% 0.44/1.12 [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ), product2( X, Y,
% 0.44/1.12 'e_1' ), product2( X, Y, 'e_2' ), product2( X, Y, 'e_3' ) ],
% 0.44/1.12 [ ~( product2( X, Y, Z ) ), ~( product2( X, Y, T ) ), equalish( Z, T ) ]
% 0.44/1.12 ,
% 0.44/1.12 [ ~( product2( X, Y, Z ) ), ~( product2( X, T, Z ) ), equalish( Y, T ) ]
% 0.44/1.12 ,
% 0.44/1.12 [ ~( product2( X, Y, Z ) ), ~( product2( T, Y, Z ) ), equalish( X, T ) ]
% 0.44/1.12 ,
% 0.44/1.12 [ product2( X, X, X ) ],
% 0.44/1.12 [ ~( product1( X, Y, Z ) ), ~( product1( Z, Y, T ) ), product2( T, X, Y
% 0.44/1.12 ) ]
% 0.44/1.12 ] .
% 0.44/1.12
% 0.44/1.12
% 0.44/1.12 percentage equality = 0.000000, percentage horn = 0.916667
% 0.44/1.12 This is a near-Horn, non-equality problem
% 0.44/1.12
% 0.44/1.12
% 0.44/1.12 Options Used:
% 0.44/1.12
% 0.44/1.12 useres = 1
% 0.44/1.12 useparamod = 0
% 0.44/1.12 useeqrefl = 0
% 0.44/1.12 useeqfact = 0
% 0.44/1.12 usefactor = 1
% 0.44/1.12 usesimpsplitting = 0
% 0.44/1.12 usesimpdemod = 0
% 0.44/1.12 usesimpres = 4
% 0.44/1.12
% 0.44/1.12 resimpinuse = 1000
% 0.44/1.12 resimpclauses = 20000
% 0.44/1.12 substype = standard
% 0.44/1.12 backwardsubs = 1
% 0.44/1.12 selectoldest = 5
% 0.44/1.12
% 0.44/1.12 litorderings [0] = split
% 0.44/1.12 litorderings [1] = liftord
% 0.44/1.12
% 0.44/1.12 termordering = none
% 0.44/1.12
% 0.44/1.12 litapriori = 1
% 0.44/1.12 termapriori = 0
% 0.44/1.12 litaposteriori = 0
% 0.44/1.12 termaposteriori = 0
% 0.44/1.12 demodaposteriori = 0
% 0.44/1.12 ordereqreflfact = 0
% 0.44/1.12
% 0.44/1.12 litselect = negative
% 0.44/1.12
% 0.44/1.12 maxweight = 30000
% 0.44/1.12 maxdepth = 30000
% 0.44/1.12 maxlength = 115
% 0.44/1.12 maxnrvars = 195
% 0.44/1.12 excuselevel = 0
% 0.44/1.12 increasemaxweight = 0
% 0.44/1.12
% 0.44/1.12 maxselected = 10000000
% 0.44/1.12 maxnrclauses = 10000000
% 0.44/1.12
% 0.44/1.12 showgenerated = 0
% 0.44/1.12 showkept = 0
% 0.44/1.12 showselected = 0
% 0.44/1.12 showdeleted = 0
% 0.44/1.12 showresimp = 1
% 0.44/1.12 showstatus = 2000
% 0.44/1.12
% 0.44/1.12 prologoutput = 1
% 0.44/1.12 nrgoals = 5000000
% 0.44/1.12 totalproof = 1
% 0.44/1.12
% 0.44/1.12 Symbols occurring in the translation:
% 0.44/1.12
% 0.44/1.12 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.44/1.12 . [1, 2] (w:1, o:26, a:1, s:1, b:0),
% 0.44/1.12 ! [4, 1] (w:1, o:20, a:1, s:1, b:0),
% 0.44/1.12 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.44/1.12 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.44/1.12 'e_0' [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.44/1.12 'e_1' [40, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.44/1.12 next [41, 2] (w:1, o:51, a:1, s:1, b:0),
% 0.44/1.12 'e_2' [42, 0] (w:1, o:11, a:1, s:1, b:0),
% 0.44/1.12 'e_3' [43, 0] (w:1, o:12, a:1, s:1, b:0),
% 0.44/1.12 greater [44, 2] (w:1, o:52, a:1, s:1, b:0),
% 0.44/1.12 cycle [47, 2] (w:1, o:53, a:1, s:1, b:0),
% 0.44/1.12 equalish [49, 2] (w:1, o:54, a:1, s:1, b:0),
% 0.44/1.12 'group_element' [50, 1] (w:1, o:25, a:1, s:1, b:0),
% 0.44/1.12 product [54, 3] (w:1, o:55, a:1, s:1, b:0),
% 0.44/1.12 product1 [56, 3] (w:1, o:56, a:1, s:1, b:0),
% 0.44/1.12 product2 [57, 3] (w:1, o:57, a:1, s:1, b:0).
% 0.44/1.12
% 0.44/1.12
% 0.44/1.12 Starting Search:
% 0.44/1.12
% 0.44/1.12
% 0.44/1.12 Bliksems!, er is een bewijs:
% 0.44/1.12 % SZS status Unsatisfiable
% 0.44/1.12 % SZS output start Refutation
% 0.44/1.12
% 0.44/1.12 clause( 16, [ 'group_element'( 'e_1' ) ] )
% 0.44/1.12 .
% 0.44/1.12 clause( 17, [ 'group_element'( 'e_2' ) ] )
% 0.44/1.12 .
% 0.44/1.12 clause( 18, [ 'group_element'( 'e_3' ) ] )
% 0.44/1.12 .
% 0.44/1.12 clause( 20, [ ~( equalish( 'e_1', 'e_3' ) ) ] )
% 0.44/1.12 .
% 0.44/1.12 clause( 21, [ ~( equalish( 'e_2', 'e_1' ) ) ] )
% 0.44/1.12 .
% 0.44/1.12 clause( 22, [ ~( equalish( 'e_2', 'e_3' ) ) ] )
% 0.44/1.12 .
% 0.44/1.12 clause( 23, [ ~( equalish( 'e_3', 'e_1' ) ) ] )
% 0.44/1.12 .
% 0.44/1.12 clause( 24, [ ~( equalish( 'e_3', 'e_2' ) ) ] )
% 0.44/1.12 .
% 0.44/1.12 clause( 25, [ ~( 'group_element'( X ) ), product1( X, Y, 'e_3' ), product1(
% 0.44/1.12 X, Y, 'e_1' ), product1( X, Y, 'e_2' ), ~( 'group_element'( Y ) ) ] )
% 0.44/1.12 .
% 0.44/1.12 clause( 27, [ equalish( Y, T ), ~( product1( X, Y, Z ) ), ~( product1( X, T
% 0.44/1.12 , Z ) ) ] )
% 0.44/1.12 .
% 0.44/1.12 clause( 28, [ equalish( X, T ), ~( product1( X, Y, Z ) ), ~( product1( T, Y
% 0.44/1.12 , Z ) ) ] )
% 0.44/1.12 .
% 0.44/1.12 clause( 29, [ product1( X, X, X ) ] )
% 0.44/1.12 .
% 0.44/1.12 clause( 30, [ ~( 'group_element'( X ) ), product2( X, Y, 'e_3' ), product2(
% 0.44/1.12 X, Y, 'e_1' ), product2( X, Y, 'e_2' ), ~( 'group_element'( Y ) ) ] )
% 0.44/1.12 .
% 0.44/1.12 clause( 32, [ equalish( Y, T ), ~( product2( X, Y, Z ) ), ~( product2( X, T
% 0.44/1.12 , Z ) ) ] )
% 0.44/1.12 .
% 0.44/1.12 clause( 33, [ equalish( X, T ), ~( product2( X, Y, Z ) ), ~( product2( T, Y
% 0.44/1.12 , Z ) ) ] )
% 0.44/1.12 .
% 0.44/1.12 clause( 34, [ product2( X, X, X ) ] )
% 0.44/1.12 .
% 0.44/1.12 clause( 35, [ ~( product1( X, Y, Z ) ), product2( T, X, Y ), ~( product1( Z
% 0.44/1.12 , Y, T ) ) ] )
% 0.44/1.12 .
% 0.44/1.12 clause( 56, [ product2( X, X, Y ), ~( product1( X, Y, X ) ) ] )
% 0.44/1.12 .
% 0.44/1.12 clause( 91, [ product1( X, 'e_1', 'e_3' ), product1( X, 'e_1', 'e_1' ),
% 0.44/1.12 product1( X, 'e_1', 'e_2' ), ~( 'group_element'( X ) ) ] )
% 0.44/1.12 .
% 0.44/1.12 clause( 98, [ equalish( X, Y ), ~( product1( Y, X, Y ) ) ] )
% 0.44/1.12 .
% 0.44/1.12 clause( 99, [ equalish( X, Y ), ~( product2( X, Y, Y ) ) ] )
% 0.44/1.12 .
% 0.44/1.12 clause( 100, [ equalish( X, Y ), ~( product2( Y, X, Y ) ) ] )
% 0.44/1.12 .
% 0.44/1.12 clause( 101, [ equalish( X, Y ), ~( product1( X, Y, Y ) ) ] )
% 0.44/1.12 .
% 0.44/1.12 clause( 105, [ product2( X, 'e_3', 'e_3' ), product2( X, 'e_3', 'e_1' ),
% 0.44/1.12 product2( X, 'e_3', 'e_2' ), ~( 'group_element'( X ) ) ] )
% 0.44/1.12 .
% 0.44/1.12 clause( 142, [ product2( 'e_2', 'e_3', 'e_1' ), product2( 'e_2', 'e_3',
% 0.44/1.12 'e_2' ), product2( 'e_2', 'e_3', 'e_3' ) ] )
% 0.44/1.12 .
% 0.44/1.12 clause( 151, [ product2( 'e_2', 'e_3', 'e_1' ), product2( 'e_2', 'e_3',
% 0.44/1.12 'e_2' ) ] )
% 0.44/1.12 .
% 0.44/1.12 clause( 154, [ product2( 'e_2', 'e_3', 'e_1' ) ] )
% 0.44/1.12 .
% 0.44/1.12 clause( 156, [ equalish( X, 'e_3' ), ~( product2( 'e_2', X, 'e_1' ) ) ] )
% 0.44/1.12 .
% 0.44/1.12 clause( 158, [ product1( 'e_2', 'e_1', 'e_1' ), product1( 'e_2', 'e_1',
% 0.44/1.12 'e_2' ), product1( 'e_2', 'e_1', 'e_3' ) ] )
% 0.44/1.12 .
% 0.44/1.12 clause( 159, [ product1( 'e_3', 'e_1', 'e_1' ), product1( 'e_3', 'e_1',
% 0.44/1.12 'e_2' ), product1( 'e_3', 'e_1', 'e_3' ) ] )
% 0.44/1.12 .
% 0.44/1.12 clause( 166, [ product1( 'e_3', 'e_1', 'e_1' ), product1( 'e_3', 'e_1',
% 0.44/1.12 'e_2' ) ] )
% 0.44/1.12 .
% 0.44/1.12 clause( 167, [ product1( 'e_3', 'e_1', 'e_1' ), product2( 'e_2', X, 'e_1' )
% 0.44/1.12 , ~( product1( X, 'e_1', 'e_3' ) ) ] )
% 0.44/1.12 .
% 0.44/1.12 clause( 173, [ product1( 'e_3', 'e_1', 'e_1' ), product1( 'e_2', 'e_1',
% 0.44/1.12 'e_1' ), product2( 'e_2', 'e_2', 'e_1' ) ] )
% 0.44/1.12 .
% 0.44/1.12 clause( 174, [ product1( 'e_2', 'e_1', 'e_1' ), product1( 'e_3', 'e_1',
% 0.44/1.12 'e_1' ) ] )
% 0.44/1.12 .
% 0.44/1.12 clause( 177, [ product1( 'e_2', 'e_1', 'e_1' ) ] )
% 0.44/1.12 .
% 0.44/1.12 clause( 182, [] )
% 0.44/1.12 .
% 0.44/1.12
% 0.44/1.12
% 0.44/1.12 % SZS output end Refutation
% 0.44/1.12 found a proof!
% 0.44/1.12
% 0.44/1.12 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.44/1.12
% 0.44/1.12 initialclauses(
% 0.44/1.12 [ clause( 184, [ next( 'e_0', 'e_1' ) ] )
% 0.44/1.12 , clause( 185, [ next( 'e_1', 'e_2' ) ] )
% 0.44/1.12 , clause( 186, [ next( 'e_2', 'e_3' ) ] )
% 0.44/1.12 , clause( 187, [ greater( 'e_1', 'e_0' ) ] )
% 0.44/1.12 , clause( 188, [ greater( 'e_2', 'e_0' ) ] )
% 0.44/1.12 , clause( 189, [ greater( 'e_3', 'e_0' ) ] )
% 0.44/1.12 , clause( 190, [ greater( 'e_2', 'e_1' ) ] )
% 0.44/1.12 , clause( 191, [ greater( 'e_3', 'e_1' ) ] )
% 0.44/1.12 , clause( 192, [ greater( 'e_3', 'e_2' ) ] )
% 0.44/1.12 , clause( 193, [ ~( cycle( X, Y ) ), ~( cycle( X, Z ) ), equalish( Y, Z ) ]
% 0.44/1.12 )
% 0.44/1.12 , clause( 194, [ ~( 'group_element'( X ) ), cycle( X, 'e_0' ), cycle( X,
% 0.44/1.12 'e_1' ), cycle( X, 'e_2' ) ] )
% 0.44/1.12 , clause( 195, [ cycle( 'e_3', 'e_0' ) ] )
% 0.44/1.12 , clause( 196, [ ~( cycle( X, Y ) ), ~( cycle( Z, T ) ), ~( next( X, Z ) )
% 0.44/1.12 , ~( greater( Y, 'e_0' ) ), ~( next( T, U ) ), equalish( Y, U ) ] )
% 0.44/1.12 , clause( 197, [ ~( cycle( X, Y ) ), ~( cycle( Z, 'e_0' ) ), ~( cycle( T, U
% 0.44/1.12 ) ), ~( next( Z, T ) ), ~( greater( Z, X ) ), ~( greater( Y, U ) ) ] )
% 0.44/1.12 , clause( 198, [ ~( cycle( X, 'e_0' ) ), ~( product( X, 'e_1', Y ) ), ~(
% 0.44/1.12 greater( Y, X ) ) ] )
% 0.44/1.12 , clause( 199, [ ~( cycle( X, Y ) ), ~( product( X, 'e_1', Z ) ), ~(
% 0.44/1.12 greater( Y, 'e_0' ) ), ~( next( X, T ) ), equalish( Z, T ) ] )
% 0.44/1.12 , clause( 200, [ 'group_element'( 'e_1' ) ] )
% 0.44/1.12 , clause( 201, [ 'group_element'( 'e_2' ) ] )
% 0.44/1.12 , clause( 202, [ 'group_element'( 'e_3' ) ] )
% 0.44/1.12 , clause( 203, [ ~( equalish( 'e_1', 'e_2' ) ) ] )
% 0.44/1.12 , clause( 204, [ ~( equalish( 'e_1', 'e_3' ) ) ] )
% 0.44/1.12 , clause( 205, [ ~( equalish( 'e_2', 'e_1' ) ) ] )
% 0.44/1.12 , clause( 206, [ ~( equalish( 'e_2', 'e_3' ) ) ] )
% 0.44/1.12 , clause( 207, [ ~( equalish( 'e_3', 'e_1' ) ) ] )
% 0.44/1.12 , clause( 208, [ ~( equalish( 'e_3', 'e_2' ) ) ] )
% 0.44/1.12 , clause( 209, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ),
% 0.44/1.12 product1( X, Y, 'e_1' ), product1( X, Y, 'e_2' ), product1( X, Y, 'e_3' )
% 0.44/1.12 ] )
% 0.44/1.12 , clause( 210, [ ~( product1( X, Y, Z ) ), ~( product1( X, Y, T ) ),
% 0.44/1.12 equalish( Z, T ) ] )
% 0.44/1.12 , clause( 211, [ ~( product1( X, Y, Z ) ), ~( product1( X, T, Z ) ),
% 0.44/1.12 equalish( Y, T ) ] )
% 0.44/1.12 , clause( 212, [ ~( product1( X, Y, Z ) ), ~( product1( T, Y, Z ) ),
% 0.44/1.12 equalish( X, T ) ] )
% 0.44/1.12 , clause( 213, [ product1( X, X, X ) ] )
% 0.44/1.12 , clause( 214, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ),
% 0.44/1.12 product2( X, Y, 'e_1' ), product2( X, Y, 'e_2' ), product2( X, Y, 'e_3' )
% 0.44/1.12 ] )
% 0.44/1.12 , clause( 215, [ ~( product2( X, Y, Z ) ), ~( product2( X, Y, T ) ),
% 0.44/1.12 equalish( Z, T ) ] )
% 0.44/1.12 , clause( 216, [ ~( product2( X, Y, Z ) ), ~( product2( X, T, Z ) ),
% 0.44/1.12 equalish( Y, T ) ] )
% 0.44/1.12 , clause( 217, [ ~( product2( X, Y, Z ) ), ~( product2( T, Y, Z ) ),
% 0.44/1.12 equalish( X, T ) ] )
% 0.44/1.12 , clause( 218, [ product2( X, X, X ) ] )
% 0.44/1.12 , clause( 219, [ ~( product1( X, Y, Z ) ), ~( product1( Z, Y, T ) ),
% 0.44/1.12 product2( T, X, Y ) ] )
% 0.44/1.12 ] ).
% 0.44/1.12
% 0.44/1.12
% 0.44/1.12
% 0.44/1.12 subsumption(
% 0.44/1.12 clause( 16, [ 'group_element'( 'e_1' ) ] )
% 0.44/1.12 , clause( 200, [ 'group_element'( 'e_1' ) ] )
% 0.44/1.12 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.44/1.12
% 0.44/1.12
% 0.44/1.12 subsumption(
% 0.44/1.12 clause( 17, [ 'group_element'( 'e_2' ) ] )
% 0.44/1.13 , clause( 201, [ 'group_element'( 'e_2' ) ] )
% 0.44/1.13 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 subsumption(
% 0.44/1.13 clause( 18, [ 'group_element'( 'e_3' ) ] )
% 0.44/1.13 , clause( 202, [ 'group_element'( 'e_3' ) ] )
% 0.44/1.13 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 subsumption(
% 0.44/1.13 clause( 20, [ ~( equalish( 'e_1', 'e_3' ) ) ] )
% 0.44/1.13 , clause( 204, [ ~( equalish( 'e_1', 'e_3' ) ) ] )
% 0.44/1.13 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 subsumption(
% 0.44/1.13 clause( 21, [ ~( equalish( 'e_2', 'e_1' ) ) ] )
% 0.44/1.13 , clause( 205, [ ~( equalish( 'e_2', 'e_1' ) ) ] )
% 0.44/1.13 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 subsumption(
% 0.44/1.13 clause( 22, [ ~( equalish( 'e_2', 'e_3' ) ) ] )
% 0.44/1.13 , clause( 206, [ ~( equalish( 'e_2', 'e_3' ) ) ] )
% 0.44/1.13 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 subsumption(
% 0.44/1.13 clause( 23, [ ~( equalish( 'e_3', 'e_1' ) ) ] )
% 0.44/1.13 , clause( 207, [ ~( equalish( 'e_3', 'e_1' ) ) ] )
% 0.44/1.13 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 subsumption(
% 0.44/1.13 clause( 24, [ ~( equalish( 'e_3', 'e_2' ) ) ] )
% 0.44/1.13 , clause( 208, [ ~( equalish( 'e_3', 'e_2' ) ) ] )
% 0.44/1.13 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 subsumption(
% 0.44/1.13 clause( 25, [ ~( 'group_element'( X ) ), product1( X, Y, 'e_3' ), product1(
% 0.44/1.13 X, Y, 'e_1' ), product1( X, Y, 'e_2' ), ~( 'group_element'( Y ) ) ] )
% 0.44/1.13 , clause( 209, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ),
% 0.44/1.13 product1( X, Y, 'e_1' ), product1( X, Y, 'e_2' ), product1( X, Y, 'e_3' )
% 0.44/1.13 ] )
% 0.44/1.13 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.44/1.13 ), ==>( 1, 4 ), ==>( 2, 2 ), ==>( 3, 3 ), ==>( 4, 1 )] ) ).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 subsumption(
% 0.44/1.13 clause( 27, [ equalish( Y, T ), ~( product1( X, Y, Z ) ), ~( product1( X, T
% 0.44/1.13 , Z ) ) ] )
% 0.44/1.13 , clause( 211, [ ~( product1( X, Y, Z ) ), ~( product1( X, T, Z ) ),
% 0.44/1.13 equalish( Y, T ) ] )
% 0.44/1.13 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.44/1.13 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 2 ), ==>( 2, 0 )] ) ).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 subsumption(
% 0.44/1.13 clause( 28, [ equalish( X, T ), ~( product1( X, Y, Z ) ), ~( product1( T, Y
% 0.44/1.13 , Z ) ) ] )
% 0.44/1.13 , clause( 212, [ ~( product1( X, Y, Z ) ), ~( product1( T, Y, Z ) ),
% 0.44/1.13 equalish( X, T ) ] )
% 0.44/1.13 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.44/1.13 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 2 ), ==>( 2, 0 )] ) ).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 subsumption(
% 0.44/1.13 clause( 29, [ product1( X, X, X ) ] )
% 0.44/1.13 , clause( 213, [ product1( X, X, X ) ] )
% 0.44/1.13 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 subsumption(
% 0.44/1.13 clause( 30, [ ~( 'group_element'( X ) ), product2( X, Y, 'e_3' ), product2(
% 0.44/1.13 X, Y, 'e_1' ), product2( X, Y, 'e_2' ), ~( 'group_element'( Y ) ) ] )
% 0.44/1.13 , clause( 214, [ ~( 'group_element'( X ) ), ~( 'group_element'( Y ) ),
% 0.44/1.13 product2( X, Y, 'e_1' ), product2( X, Y, 'e_2' ), product2( X, Y, 'e_3' )
% 0.44/1.13 ] )
% 0.44/1.13 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.44/1.13 ), ==>( 1, 4 ), ==>( 2, 2 ), ==>( 3, 3 ), ==>( 4, 1 )] ) ).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 subsumption(
% 0.44/1.13 clause( 32, [ equalish( Y, T ), ~( product2( X, Y, Z ) ), ~( product2( X, T
% 0.44/1.13 , Z ) ) ] )
% 0.44/1.13 , clause( 216, [ ~( product2( X, Y, Z ) ), ~( product2( X, T, Z ) ),
% 0.44/1.13 equalish( Y, T ) ] )
% 0.44/1.13 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.44/1.13 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 2 ), ==>( 2, 0 )] ) ).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 subsumption(
% 0.44/1.13 clause( 33, [ equalish( X, T ), ~( product2( X, Y, Z ) ), ~( product2( T, Y
% 0.44/1.13 , Z ) ) ] )
% 0.44/1.13 , clause( 217, [ ~( product2( X, Y, Z ) ), ~( product2( T, Y, Z ) ),
% 0.44/1.13 equalish( X, T ) ] )
% 0.44/1.13 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.44/1.13 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 2 ), ==>( 2, 0 )] ) ).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 subsumption(
% 0.44/1.13 clause( 34, [ product2( X, X, X ) ] )
% 0.44/1.13 , clause( 218, [ product2( X, X, X ) ] )
% 0.44/1.13 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 subsumption(
% 0.44/1.13 clause( 35, [ ~( product1( X, Y, Z ) ), product2( T, X, Y ), ~( product1( Z
% 0.44/1.13 , Y, T ) ) ] )
% 0.44/1.13 , clause( 219, [ ~( product1( X, Y, Z ) ), ~( product1( Z, Y, T ) ),
% 0.44/1.13 product2( T, X, Y ) ] )
% 0.44/1.13 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.44/1.13 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 2 ), ==>( 2, 1 )] ) ).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 factor(
% 0.44/1.13 clause( 490, [ ~( product1( X, Y, X ) ), product2( X, X, Y ) ] )
% 0.44/1.13 , clause( 35, [ ~( product1( X, Y, Z ) ), product2( T, X, Y ), ~( product1(
% 0.44/1.13 Z, Y, T ) ) ] )
% 0.44/1.13 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, X ), :=( T, X )] )
% 0.44/1.13 ).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 subsumption(
% 0.44/1.13 clause( 56, [ product2( X, X, Y ), ~( product1( X, Y, X ) ) ] )
% 0.44/1.13 , clause( 490, [ ~( product1( X, Y, X ) ), product2( X, X, Y ) ] )
% 0.44/1.13 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 1
% 0.44/1.13 ), ==>( 1, 0 )] ) ).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 resolution(
% 0.44/1.13 clause( 492, [ ~( 'group_element'( X ) ), product1( X, 'e_1', 'e_3' ),
% 0.44/1.13 product1( X, 'e_1', 'e_1' ), product1( X, 'e_1', 'e_2' ) ] )
% 0.44/1.13 , clause( 25, [ ~( 'group_element'( X ) ), product1( X, Y, 'e_3' ),
% 0.44/1.13 product1( X, Y, 'e_1' ), product1( X, Y, 'e_2' ), ~( 'group_element'( Y )
% 0.44/1.13 ) ] )
% 0.44/1.13 , 4, clause( 16, [ 'group_element'( 'e_1' ) ] )
% 0.44/1.13 , 0, substitution( 0, [ :=( X, X ), :=( Y, 'e_1' )] ), substitution( 1, [] )
% 0.44/1.13 ).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 subsumption(
% 0.44/1.13 clause( 91, [ product1( X, 'e_1', 'e_3' ), product1( X, 'e_1', 'e_1' ),
% 0.44/1.13 product1( X, 'e_1', 'e_2' ), ~( 'group_element'( X ) ) ] )
% 0.44/1.13 , clause( 492, [ ~( 'group_element'( X ) ), product1( X, 'e_1', 'e_3' ),
% 0.44/1.13 product1( X, 'e_1', 'e_1' ), product1( X, 'e_1', 'e_2' ) ] )
% 0.44/1.13 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 3 ), ==>( 1,
% 0.44/1.13 0 ), ==>( 2, 1 ), ==>( 3, 2 )] ) ).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 resolution(
% 0.44/1.13 clause( 494, [ equalish( X, Y ), ~( product1( Y, X, Y ) ) ] )
% 0.44/1.13 , clause( 27, [ equalish( Y, T ), ~( product1( X, Y, Z ) ), ~( product1( X
% 0.44/1.13 , T, Z ) ) ] )
% 0.44/1.13 , 2, clause( 29, [ product1( X, X, X ) ] )
% 0.44/1.13 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Y ), :=( T, Y )] ),
% 0.44/1.13 substitution( 1, [ :=( X, Y )] )).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 subsumption(
% 0.44/1.13 clause( 98, [ equalish( X, Y ), ~( product1( Y, X, Y ) ) ] )
% 0.44/1.13 , clause( 494, [ equalish( X, Y ), ~( product1( Y, X, Y ) ) ] )
% 0.44/1.13 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.44/1.13 ), ==>( 1, 1 )] ) ).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 resolution(
% 0.44/1.13 clause( 496, [ equalish( X, Y ), ~( product2( X, Y, Y ) ) ] )
% 0.44/1.13 , clause( 33, [ equalish( X, T ), ~( product2( X, Y, Z ) ), ~( product2( T
% 0.44/1.13 , Y, Z ) ) ] )
% 0.44/1.13 , 2, clause( 34, [ product2( X, X, X ) ] )
% 0.44/1.13 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Y ), :=( T, Y )] ),
% 0.44/1.13 substitution( 1, [ :=( X, Y )] )).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 subsumption(
% 0.44/1.13 clause( 99, [ equalish( X, Y ), ~( product2( X, Y, Y ) ) ] )
% 0.44/1.13 , clause( 496, [ equalish( X, Y ), ~( product2( X, Y, Y ) ) ] )
% 0.44/1.13 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.44/1.13 ), ==>( 1, 1 )] ) ).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 resolution(
% 0.44/1.13 clause( 498, [ equalish( X, Y ), ~( product2( Y, X, Y ) ) ] )
% 0.44/1.13 , clause( 32, [ equalish( Y, T ), ~( product2( X, Y, Z ) ), ~( product2( X
% 0.44/1.13 , T, Z ) ) ] )
% 0.44/1.13 , 2, clause( 34, [ product2( X, X, X ) ] )
% 0.44/1.13 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Y ), :=( T, Y )] ),
% 0.44/1.13 substitution( 1, [ :=( X, Y )] )).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 subsumption(
% 0.44/1.13 clause( 100, [ equalish( X, Y ), ~( product2( Y, X, Y ) ) ] )
% 0.44/1.13 , clause( 498, [ equalish( X, Y ), ~( product2( Y, X, Y ) ) ] )
% 0.44/1.13 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.44/1.13 ), ==>( 1, 1 )] ) ).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 resolution(
% 0.44/1.13 clause( 500, [ equalish( X, Y ), ~( product1( X, Y, Y ) ) ] )
% 0.44/1.13 , clause( 28, [ equalish( X, T ), ~( product1( X, Y, Z ) ), ~( product1( T
% 0.44/1.13 , Y, Z ) ) ] )
% 0.44/1.13 , 2, clause( 29, [ product1( X, X, X ) ] )
% 0.44/1.13 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Y ), :=( T, Y )] ),
% 0.44/1.13 substitution( 1, [ :=( X, Y )] )).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 subsumption(
% 0.44/1.13 clause( 101, [ equalish( X, Y ), ~( product1( X, Y, Y ) ) ] )
% 0.44/1.13 , clause( 500, [ equalish( X, Y ), ~( product1( X, Y, Y ) ) ] )
% 0.44/1.13 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.44/1.13 ), ==>( 1, 1 )] ) ).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 resolution(
% 0.44/1.13 clause( 502, [ ~( 'group_element'( X ) ), product2( X, 'e_3', 'e_3' ),
% 0.44/1.13 product2( X, 'e_3', 'e_1' ), product2( X, 'e_3', 'e_2' ) ] )
% 0.44/1.13 , clause( 30, [ ~( 'group_element'( X ) ), product2( X, Y, 'e_3' ),
% 0.44/1.13 product2( X, Y, 'e_1' ), product2( X, Y, 'e_2' ), ~( 'group_element'( Y )
% 0.44/1.13 ) ] )
% 0.44/1.13 , 4, clause( 18, [ 'group_element'( 'e_3' ) ] )
% 0.44/1.13 , 0, substitution( 0, [ :=( X, X ), :=( Y, 'e_3' )] ), substitution( 1, [] )
% 0.44/1.13 ).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 subsumption(
% 0.44/1.13 clause( 105, [ product2( X, 'e_3', 'e_3' ), product2( X, 'e_3', 'e_1' ),
% 0.44/1.13 product2( X, 'e_3', 'e_2' ), ~( 'group_element'( X ) ) ] )
% 0.44/1.13 , clause( 502, [ ~( 'group_element'( X ) ), product2( X, 'e_3', 'e_3' ),
% 0.44/1.13 product2( X, 'e_3', 'e_1' ), product2( X, 'e_3', 'e_2' ) ] )
% 0.44/1.13 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 3 ), ==>( 1,
% 0.44/1.13 0 ), ==>( 2, 1 ), ==>( 3, 2 )] ) ).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 resolution(
% 0.44/1.13 clause( 503, [ product2( 'e_2', 'e_3', 'e_3' ), product2( 'e_2', 'e_3',
% 0.44/1.13 'e_1' ), product2( 'e_2', 'e_3', 'e_2' ) ] )
% 0.44/1.13 , clause( 105, [ product2( X, 'e_3', 'e_3' ), product2( X, 'e_3', 'e_1' ),
% 0.44/1.13 product2( X, 'e_3', 'e_2' ), ~( 'group_element'( X ) ) ] )
% 0.44/1.13 , 3, clause( 17, [ 'group_element'( 'e_2' ) ] )
% 0.44/1.13 , 0, substitution( 0, [ :=( X, 'e_2' )] ), substitution( 1, [] )).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 subsumption(
% 0.44/1.13 clause( 142, [ product2( 'e_2', 'e_3', 'e_1' ), product2( 'e_2', 'e_3',
% 0.44/1.13 'e_2' ), product2( 'e_2', 'e_3', 'e_3' ) ] )
% 0.44/1.13 , clause( 503, [ product2( 'e_2', 'e_3', 'e_3' ), product2( 'e_2', 'e_3',
% 0.44/1.13 'e_1' ), product2( 'e_2', 'e_3', 'e_2' ) ] )
% 0.44/1.13 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 2 ), ==>( 1, 0 ), ==>( 2
% 0.44/1.13 , 1 )] ) ).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 resolution(
% 0.44/1.13 clause( 504, [ equalish( 'e_2', 'e_3' ), product2( 'e_2', 'e_3', 'e_1' ),
% 0.44/1.13 product2( 'e_2', 'e_3', 'e_2' ) ] )
% 0.44/1.13 , clause( 99, [ equalish( X, Y ), ~( product2( X, Y, Y ) ) ] )
% 0.44/1.13 , 1, clause( 142, [ product2( 'e_2', 'e_3', 'e_1' ), product2( 'e_2', 'e_3'
% 0.44/1.13 , 'e_2' ), product2( 'e_2', 'e_3', 'e_3' ) ] )
% 0.44/1.13 , 2, substitution( 0, [ :=( X, 'e_2' ), :=( Y, 'e_3' )] ), substitution( 1
% 0.44/1.13 , [] )).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 resolution(
% 0.44/1.13 clause( 505, [ product2( 'e_2', 'e_3', 'e_1' ), product2( 'e_2', 'e_3',
% 0.44/1.13 'e_2' ) ] )
% 0.44/1.13 , clause( 22, [ ~( equalish( 'e_2', 'e_3' ) ) ] )
% 0.44/1.13 , 0, clause( 504, [ equalish( 'e_2', 'e_3' ), product2( 'e_2', 'e_3', 'e_1'
% 0.44/1.13 ), product2( 'e_2', 'e_3', 'e_2' ) ] )
% 0.44/1.13 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 subsumption(
% 0.44/1.13 clause( 151, [ product2( 'e_2', 'e_3', 'e_1' ), product2( 'e_2', 'e_3',
% 0.44/1.13 'e_2' ) ] )
% 0.44/1.13 , clause( 505, [ product2( 'e_2', 'e_3', 'e_1' ), product2( 'e_2', 'e_3',
% 0.44/1.13 'e_2' ) ] )
% 0.44/1.13 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] )
% 0.44/1.13 ).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 resolution(
% 0.44/1.13 clause( 506, [ equalish( 'e_3', 'e_2' ), product2( 'e_2', 'e_3', 'e_1' ) ]
% 0.44/1.13 )
% 0.44/1.13 , clause( 100, [ equalish( X, Y ), ~( product2( Y, X, Y ) ) ] )
% 0.44/1.13 , 1, clause( 151, [ product2( 'e_2', 'e_3', 'e_1' ), product2( 'e_2', 'e_3'
% 0.44/1.13 , 'e_2' ) ] )
% 0.44/1.13 , 1, substitution( 0, [ :=( X, 'e_3' ), :=( Y, 'e_2' )] ), substitution( 1
% 0.44/1.13 , [] )).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 resolution(
% 0.44/1.13 clause( 507, [ product2( 'e_2', 'e_3', 'e_1' ) ] )
% 0.44/1.13 , clause( 24, [ ~( equalish( 'e_3', 'e_2' ) ) ] )
% 0.44/1.13 , 0, clause( 506, [ equalish( 'e_3', 'e_2' ), product2( 'e_2', 'e_3', 'e_1'
% 0.44/1.13 ) ] )
% 0.44/1.13 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 subsumption(
% 0.44/1.13 clause( 154, [ product2( 'e_2', 'e_3', 'e_1' ) ] )
% 0.44/1.13 , clause( 507, [ product2( 'e_2', 'e_3', 'e_1' ) ] )
% 0.44/1.13 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 resolution(
% 0.44/1.13 clause( 509, [ equalish( X, 'e_3' ), ~( product2( 'e_2', X, 'e_1' ) ) ] )
% 0.44/1.13 , clause( 32, [ equalish( Y, T ), ~( product2( X, Y, Z ) ), ~( product2( X
% 0.44/1.13 , T, Z ) ) ] )
% 0.44/1.13 , 2, clause( 154, [ product2( 'e_2', 'e_3', 'e_1' ) ] )
% 0.44/1.13 , 0, substitution( 0, [ :=( X, 'e_2' ), :=( Y, X ), :=( Z, 'e_1' ), :=( T,
% 0.44/1.13 'e_3' )] ), substitution( 1, [] )).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 subsumption(
% 0.44/1.13 clause( 156, [ equalish( X, 'e_3' ), ~( product2( 'e_2', X, 'e_1' ) ) ] )
% 0.44/1.13 , clause( 509, [ equalish( X, 'e_3' ), ~( product2( 'e_2', X, 'e_1' ) ) ]
% 0.44/1.13 )
% 0.44/1.13 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 0.44/1.13 1 )] ) ).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 resolution(
% 0.44/1.13 clause( 510, [ product1( 'e_2', 'e_1', 'e_3' ), product1( 'e_2', 'e_1',
% 0.44/1.13 'e_1' ), product1( 'e_2', 'e_1', 'e_2' ) ] )
% 0.44/1.13 , clause( 91, [ product1( X, 'e_1', 'e_3' ), product1( X, 'e_1', 'e_1' ),
% 0.44/1.13 product1( X, 'e_1', 'e_2' ), ~( 'group_element'( X ) ) ] )
% 0.44/1.13 , 3, clause( 17, [ 'group_element'( 'e_2' ) ] )
% 0.44/1.13 , 0, substitution( 0, [ :=( X, 'e_2' )] ), substitution( 1, [] )).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 subsumption(
% 0.44/1.13 clause( 158, [ product1( 'e_2', 'e_1', 'e_1' ), product1( 'e_2', 'e_1',
% 0.44/1.13 'e_2' ), product1( 'e_2', 'e_1', 'e_3' ) ] )
% 0.44/1.13 , clause( 510, [ product1( 'e_2', 'e_1', 'e_3' ), product1( 'e_2', 'e_1',
% 0.44/1.13 'e_1' ), product1( 'e_2', 'e_1', 'e_2' ) ] )
% 0.44/1.13 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 2 ), ==>( 1, 0 ), ==>( 2
% 0.44/1.13 , 1 )] ) ).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 resolution(
% 0.44/1.13 clause( 511, [ product1( 'e_3', 'e_1', 'e_3' ), product1( 'e_3', 'e_1',
% 0.44/1.13 'e_1' ), product1( 'e_3', 'e_1', 'e_2' ) ] )
% 0.44/1.13 , clause( 91, [ product1( X, 'e_1', 'e_3' ), product1( X, 'e_1', 'e_1' ),
% 0.44/1.13 product1( X, 'e_1', 'e_2' ), ~( 'group_element'( X ) ) ] )
% 0.44/1.13 , 3, clause( 18, [ 'group_element'( 'e_3' ) ] )
% 0.44/1.13 , 0, substitution( 0, [ :=( X, 'e_3' )] ), substitution( 1, [] )).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 subsumption(
% 0.44/1.13 clause( 159, [ product1( 'e_3', 'e_1', 'e_1' ), product1( 'e_3', 'e_1',
% 0.44/1.13 'e_2' ), product1( 'e_3', 'e_1', 'e_3' ) ] )
% 0.44/1.13 , clause( 511, [ product1( 'e_3', 'e_1', 'e_3' ), product1( 'e_3', 'e_1',
% 0.44/1.13 'e_1' ), product1( 'e_3', 'e_1', 'e_2' ) ] )
% 0.44/1.13 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 2 ), ==>( 1, 0 ), ==>( 2
% 0.44/1.13 , 1 )] ) ).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 resolution(
% 0.44/1.13 clause( 512, [ equalish( 'e_1', 'e_3' ), product1( 'e_3', 'e_1', 'e_1' ),
% 0.44/1.13 product1( 'e_3', 'e_1', 'e_2' ) ] )
% 0.44/1.13 , clause( 98, [ equalish( X, Y ), ~( product1( Y, X, Y ) ) ] )
% 0.44/1.13 , 1, clause( 159, [ product1( 'e_3', 'e_1', 'e_1' ), product1( 'e_3', 'e_1'
% 0.44/1.13 , 'e_2' ), product1( 'e_3', 'e_1', 'e_3' ) ] )
% 0.44/1.13 , 2, substitution( 0, [ :=( X, 'e_1' ), :=( Y, 'e_3' )] ), substitution( 1
% 0.44/1.13 , [] )).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 resolution(
% 0.44/1.13 clause( 513, [ product1( 'e_3', 'e_1', 'e_1' ), product1( 'e_3', 'e_1',
% 0.44/1.13 'e_2' ) ] )
% 0.44/1.13 , clause( 20, [ ~( equalish( 'e_1', 'e_3' ) ) ] )
% 0.44/1.13 , 0, clause( 512, [ equalish( 'e_1', 'e_3' ), product1( 'e_3', 'e_1', 'e_1'
% 0.44/1.13 ), product1( 'e_3', 'e_1', 'e_2' ) ] )
% 0.44/1.13 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 subsumption(
% 0.44/1.13 clause( 166, [ product1( 'e_3', 'e_1', 'e_1' ), product1( 'e_3', 'e_1',
% 0.44/1.13 'e_2' ) ] )
% 0.44/1.13 , clause( 513, [ product1( 'e_3', 'e_1', 'e_1' ), product1( 'e_3', 'e_1',
% 0.44/1.13 'e_2' ) ] )
% 0.44/1.13 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] )
% 0.44/1.13 ).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 resolution(
% 0.44/1.13 clause( 517, [ ~( product1( X, 'e_1', 'e_3' ) ), product2( 'e_2', X, 'e_1'
% 0.44/1.13 ), product1( 'e_3', 'e_1', 'e_1' ) ] )
% 0.44/1.13 , clause( 35, [ ~( product1( X, Y, Z ) ), product2( T, X, Y ), ~( product1(
% 0.44/1.13 Z, Y, T ) ) ] )
% 0.44/1.13 , 2, clause( 166, [ product1( 'e_3', 'e_1', 'e_1' ), product1( 'e_3', 'e_1'
% 0.44/1.13 , 'e_2' ) ] )
% 0.44/1.13 , 1, substitution( 0, [ :=( X, X ), :=( Y, 'e_1' ), :=( Z, 'e_3' ), :=( T,
% 0.44/1.13 'e_2' )] ), substitution( 1, [] )).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 subsumption(
% 0.44/1.13 clause( 167, [ product1( 'e_3', 'e_1', 'e_1' ), product2( 'e_2', X, 'e_1' )
% 0.44/1.13 , ~( product1( X, 'e_1', 'e_3' ) ) ] )
% 0.44/1.13 , clause( 517, [ ~( product1( X, 'e_1', 'e_3' ) ), product2( 'e_2', X,
% 0.44/1.13 'e_1' ), product1( 'e_3', 'e_1', 'e_1' ) ] )
% 0.44/1.13 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 2 ), ==>( 1,
% 0.44/1.13 1 ), ==>( 2, 0 )] ) ).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 resolution(
% 0.44/1.13 clause( 518, [ product1( 'e_3', 'e_1', 'e_1' ), product2( 'e_2', 'e_2',
% 0.44/1.13 'e_1' ), product1( 'e_2', 'e_1', 'e_1' ), product1( 'e_2', 'e_1', 'e_2' )
% 0.44/1.13 ] )
% 0.44/1.13 , clause( 167, [ product1( 'e_3', 'e_1', 'e_1' ), product2( 'e_2', X, 'e_1'
% 0.44/1.13 ), ~( product1( X, 'e_1', 'e_3' ) ) ] )
% 0.44/1.13 , 2, clause( 158, [ product1( 'e_2', 'e_1', 'e_1' ), product1( 'e_2', 'e_1'
% 0.44/1.13 , 'e_2' ), product1( 'e_2', 'e_1', 'e_3' ) ] )
% 0.44/1.13 , 2, substitution( 0, [ :=( X, 'e_2' )] ), substitution( 1, [] )).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 resolution(
% 0.44/1.13 clause( 519, [ product2( 'e_2', 'e_2', 'e_1' ), product1( 'e_3', 'e_1',
% 0.44/1.13 'e_1' ), product2( 'e_2', 'e_2', 'e_1' ), product1( 'e_2', 'e_1', 'e_1' )
% 0.44/1.13 ] )
% 0.44/1.13 , clause( 56, [ product2( X, X, Y ), ~( product1( X, Y, X ) ) ] )
% 0.44/1.13 , 1, clause( 518, [ product1( 'e_3', 'e_1', 'e_1' ), product2( 'e_2', 'e_2'
% 0.44/1.13 , 'e_1' ), product1( 'e_2', 'e_1', 'e_1' ), product1( 'e_2', 'e_1', 'e_2'
% 0.44/1.13 ) ] )
% 0.44/1.13 , 3, substitution( 0, [ :=( X, 'e_2' ), :=( Y, 'e_1' )] ), substitution( 1
% 0.44/1.13 , [] )).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 factor(
% 0.44/1.13 clause( 520, [ product2( 'e_2', 'e_2', 'e_1' ), product1( 'e_3', 'e_1',
% 0.44/1.13 'e_1' ), product1( 'e_2', 'e_1', 'e_1' ) ] )
% 0.44/1.13 , clause( 519, [ product2( 'e_2', 'e_2', 'e_1' ), product1( 'e_3', 'e_1',
% 0.44/1.13 'e_1' ), product2( 'e_2', 'e_2', 'e_1' ), product1( 'e_2', 'e_1', 'e_1' )
% 0.44/1.13 ] )
% 0.44/1.13 , 0, 2, substitution( 0, [] )).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 subsumption(
% 0.44/1.13 clause( 173, [ product1( 'e_3', 'e_1', 'e_1' ), product1( 'e_2', 'e_1',
% 0.44/1.13 'e_1' ), product2( 'e_2', 'e_2', 'e_1' ) ] )
% 0.44/1.13 , clause( 520, [ product2( 'e_2', 'e_2', 'e_1' ), product1( 'e_3', 'e_1',
% 0.44/1.13 'e_1' ), product1( 'e_2', 'e_1', 'e_1' ) ] )
% 0.44/1.13 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 2 ), ==>( 1, 0 ), ==>( 2
% 0.44/1.13 , 1 )] ) ).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 resolution(
% 0.44/1.13 clause( 521, [ equalish( 'e_2', 'e_3' ), product1( 'e_3', 'e_1', 'e_1' ),
% 0.44/1.13 product1( 'e_2', 'e_1', 'e_1' ) ] )
% 0.44/1.13 , clause( 156, [ equalish( X, 'e_3' ), ~( product2( 'e_2', X, 'e_1' ) ) ]
% 0.44/1.13 )
% 0.44/1.13 , 1, clause( 173, [ product1( 'e_3', 'e_1', 'e_1' ), product1( 'e_2', 'e_1'
% 0.44/1.13 , 'e_1' ), product2( 'e_2', 'e_2', 'e_1' ) ] )
% 0.44/1.13 , 2, substitution( 0, [ :=( X, 'e_2' )] ), substitution( 1, [] )).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 resolution(
% 0.44/1.13 clause( 522, [ product1( 'e_3', 'e_1', 'e_1' ), product1( 'e_2', 'e_1',
% 0.44/1.13 'e_1' ) ] )
% 0.44/1.13 , clause( 22, [ ~( equalish( 'e_2', 'e_3' ) ) ] )
% 0.44/1.13 , 0, clause( 521, [ equalish( 'e_2', 'e_3' ), product1( 'e_3', 'e_1', 'e_1'
% 0.44/1.13 ), product1( 'e_2', 'e_1', 'e_1' ) ] )
% 0.44/1.13 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 subsumption(
% 0.44/1.13 clause( 174, [ product1( 'e_2', 'e_1', 'e_1' ), product1( 'e_3', 'e_1',
% 0.44/1.13 'e_1' ) ] )
% 0.44/1.13 , clause( 522, [ product1( 'e_3', 'e_1', 'e_1' ), product1( 'e_2', 'e_1',
% 0.44/1.13 'e_1' ) ] )
% 0.44/1.13 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] )
% 0.44/1.13 ).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 resolution(
% 0.44/1.13 clause( 524, [ equalish( 'e_3', 'e_1' ), product1( 'e_2', 'e_1', 'e_1' ) ]
% 0.44/1.13 )
% 0.44/1.13 , clause( 101, [ equalish( X, Y ), ~( product1( X, Y, Y ) ) ] )
% 0.44/1.13 , 1, clause( 174, [ product1( 'e_2', 'e_1', 'e_1' ), product1( 'e_3', 'e_1'
% 0.44/1.13 , 'e_1' ) ] )
% 0.44/1.13 , 1, substitution( 0, [ :=( X, 'e_3' ), :=( Y, 'e_1' )] ), substitution( 1
% 0.44/1.13 , [] )).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 resolution(
% 0.44/1.13 clause( 525, [ product1( 'e_2', 'e_1', 'e_1' ) ] )
% 0.44/1.13 , clause( 23, [ ~( equalish( 'e_3', 'e_1' ) ) ] )
% 0.44/1.13 , 0, clause( 524, [ equalish( 'e_3', 'e_1' ), product1( 'e_2', 'e_1', 'e_1'
% 0.44/1.13 ) ] )
% 0.44/1.13 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 subsumption(
% 0.44/1.13 clause( 177, [ product1( 'e_2', 'e_1', 'e_1' ) ] )
% 0.44/1.13 , clause( 525, [ product1( 'e_2', 'e_1', 'e_1' ) ] )
% 0.44/1.13 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 resolution(
% 0.44/1.13 clause( 526, [ equalish( 'e_2', 'e_1' ) ] )
% 0.44/1.13 , clause( 101, [ equalish( X, Y ), ~( product1( X, Y, Y ) ) ] )
% 0.44/1.13 , 1, clause( 177, [ product1( 'e_2', 'e_1', 'e_1' ) ] )
% 0.44/1.13 , 0, substitution( 0, [ :=( X, 'e_2' ), :=( Y, 'e_1' )] ), substitution( 1
% 0.44/1.13 , [] )).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 resolution(
% 0.44/1.13 clause( 527, [] )
% 0.44/1.13 , clause( 21, [ ~( equalish( 'e_2', 'e_1' ) ) ] )
% 0.44/1.13 , 0, clause( 526, [ equalish( 'e_2', 'e_1' ) ] )
% 0.44/1.13 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 subsumption(
% 0.44/1.13 clause( 182, [] )
% 0.44/1.13 , clause( 527, [] )
% 0.44/1.13 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 end.
% 0.44/1.13
% 0.44/1.13 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.44/1.13
% 0.44/1.13 Memory use:
% 0.44/1.13
% 0.44/1.13 space for terms: 2929
% 0.44/1.13 space for clauses: 9309
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 clauses generated: 293
% 0.44/1.13 clauses kept: 183
% 0.44/1.13 clauses selected: 125
% 0.44/1.13 clauses deleted: 12
% 0.44/1.13 clauses inuse deleted: 0
% 0.44/1.13
% 0.44/1.13 subsentry: 1243
% 0.44/1.13 literals s-matched: 685
% 0.44/1.13 literals matched: 441
% 0.44/1.13 full subsumption: 111
% 0.44/1.13
% 0.44/1.13 checksum: 1950511196
% 0.44/1.13
% 0.44/1.13
% 0.44/1.13 Bliksem ended
%------------------------------------------------------------------------------