TSTP Solution File: GRP037-3 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GRP037-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n004.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 07:34:29 EDT 2022
% Result : Unsatisfiable 1.41s 1.79s
% Output : Refutation 1.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP037-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Tue Jun 14 14:06:09 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.41/1.79 *** allocated 10000 integers for termspace/termends
% 1.41/1.79 *** allocated 10000 integers for clauses
% 1.41/1.79 *** allocated 10000 integers for justifications
% 1.41/1.79 Bliksem 1.12
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 Automatic Strategy Selection
% 1.41/1.79
% 1.41/1.79 Clauses:
% 1.41/1.79 [
% 1.41/1.79 [ product( identity, X, X ) ],
% 1.41/1.79 [ product( X, identity, X ) ],
% 1.41/1.79 [ product( inverse( X ), X, identity ) ],
% 1.41/1.79 [ product( X, inverse( X ), identity ) ],
% 1.41/1.79 [ product( X, Y, multiply( X, Y ) ) ],
% 1.41/1.79 [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z, T ) ],
% 1.41/1.79 [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~( product( Z, T, W
% 1.41/1.79 ) ), product( X, U, W ) ],
% 1.41/1.79 [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~( product( X, U, W
% 1.41/1.79 ) ), product( Z, T, W ) ],
% 1.41/1.79 [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( Y ) ), ~( product(
% 1.41/1.79 X, inverse( Y ), Z ) ), 'subgroup_member'( Z ) ],
% 1.41/1.79 [ ~( 'subgroup_member'( X ) ), product( 'another_identity', X, X ) ]
% 1.41/1.79 ,
% 1.41/1.79 [ ~( 'subgroup_member'( X ) ), product( X, 'another_identity', X ) ]
% 1.41/1.79 ,
% 1.41/1.79 [ ~( 'subgroup_member'( X ) ), product( X, 'another_inverse'( X ),
% 1.41/1.79 'another_identity' ) ],
% 1.41/1.79 [ ~( 'subgroup_member'( X ) ), product( 'another_inverse'( X ), X,
% 1.41/1.79 'another_identity' ) ],
% 1.41/1.79 [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( 'another_inverse'( X )
% 1.41/1.79 ) ],
% 1.41/1.79 [ ~( product( X, Y, Z ) ), ~( product( X, T, Z ) ), =( T, Y ) ],
% 1.41/1.79 [ ~( product( X, Y, Z ) ), ~( product( T, Y, Z ) ), =( T, X ) ],
% 1.41/1.79 [ 'subgroup_member'( a ) ],
% 1.41/1.79 [ 'subgroup_member'( 'another_identity' ) ],
% 1.41/1.79 [ ~( =( inverse( a ), 'another_inverse'( a ) ) ) ]
% 1.41/1.79 ] .
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 percentage equality = 0.102564, percentage horn = 1.000000
% 1.41/1.79 This is a problem with some equality
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 Options Used:
% 1.41/1.79
% 1.41/1.79 useres = 1
% 1.41/1.79 useparamod = 1
% 1.41/1.79 useeqrefl = 1
% 1.41/1.79 useeqfact = 1
% 1.41/1.79 usefactor = 1
% 1.41/1.79 usesimpsplitting = 0
% 1.41/1.79 usesimpdemod = 5
% 1.41/1.79 usesimpres = 3
% 1.41/1.79
% 1.41/1.79 resimpinuse = 1000
% 1.41/1.79 resimpclauses = 20000
% 1.41/1.79 substype = eqrewr
% 1.41/1.79 backwardsubs = 1
% 1.41/1.79 selectoldest = 5
% 1.41/1.79
% 1.41/1.79 litorderings [0] = split
% 1.41/1.79 litorderings [1] = extend the termordering, first sorting on arguments
% 1.41/1.79
% 1.41/1.79 termordering = kbo
% 1.41/1.79
% 1.41/1.79 litapriori = 0
% 1.41/1.79 termapriori = 1
% 1.41/1.79 litaposteriori = 0
% 1.41/1.79 termaposteriori = 0
% 1.41/1.79 demodaposteriori = 0
% 1.41/1.79 ordereqreflfact = 0
% 1.41/1.79
% 1.41/1.79 litselect = negord
% 1.41/1.79
% 1.41/1.79 maxweight = 15
% 1.41/1.79 maxdepth = 30000
% 1.41/1.79 maxlength = 115
% 1.41/1.79 maxnrvars = 195
% 1.41/1.79 excuselevel = 1
% 1.41/1.79 increasemaxweight = 1
% 1.41/1.79
% 1.41/1.79 maxselected = 10000000
% 1.41/1.79 maxnrclauses = 10000000
% 1.41/1.79
% 1.41/1.79 showgenerated = 0
% 1.41/1.79 showkept = 0
% 1.41/1.79 showselected = 0
% 1.41/1.79 showdeleted = 0
% 1.41/1.79 showresimp = 1
% 1.41/1.79 showstatus = 2000
% 1.41/1.79
% 1.41/1.79 prologoutput = 1
% 1.41/1.79 nrgoals = 5000000
% 1.41/1.79 totalproof = 1
% 1.41/1.79
% 1.41/1.79 Symbols occurring in the translation:
% 1.41/1.79
% 1.41/1.79 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.41/1.79 . [1, 2] (w:1, o:30, a:1, s:1, b:0),
% 1.41/1.79 ! [4, 1] (w:0, o:22, a:1, s:1, b:0),
% 1.41/1.79 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.41/1.79 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.41/1.79 identity [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 1.41/1.79 product [41, 3] (w:1, o:56, a:1, s:1, b:0),
% 1.41/1.79 inverse [42, 1] (w:1, o:27, a:1, s:1, b:0),
% 1.41/1.79 multiply [44, 2] (w:1, o:55, a:1, s:1, b:0),
% 1.41/1.79 'subgroup_member' [50, 1] (w:1, o:28, a:1, s:1, b:0),
% 1.41/1.79 'another_identity' [53, 0] (w:1, o:19, a:1, s:1, b:0),
% 1.41/1.79 'another_inverse' [54, 1] (w:1, o:29, a:1, s:1, b:0),
% 1.41/1.79 a [56, 0] (w:1, o:21, a:1, s:1, b:0).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 Starting Search:
% 1.41/1.79
% 1.41/1.79 Resimplifying inuse:
% 1.41/1.79 Done
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 Intermediate Status:
% 1.41/1.79 Generated: 6037
% 1.41/1.79 Kept: 2016
% 1.41/1.79 Inuse: 107
% 1.41/1.79 Deleted: 62
% 1.41/1.79 Deletedinuse: 37
% 1.41/1.79
% 1.41/1.79 Resimplifying inuse:
% 1.41/1.79 Done
% 1.41/1.79
% 1.41/1.79 Resimplifying inuse:
% 1.41/1.79 Done
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 Intermediate Status:
% 1.41/1.79 Generated: 11500
% 1.41/1.79 Kept: 4029
% 1.41/1.79 Inuse: 168
% 1.41/1.79 Deleted: 72
% 1.41/1.79 Deletedinuse: 40
% 1.41/1.79
% 1.41/1.79 Resimplifying inuse:
% 1.41/1.79 Done
% 1.41/1.79
% 1.41/1.79 Resimplifying inuse:
% 1.41/1.79 Done
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 Intermediate Status:
% 1.41/1.79 Generated: 17433
% 1.41/1.79 Kept: 6046
% 1.41/1.79 Inuse: 213
% 1.41/1.79 Deleted: 82
% 1.41/1.79 Deletedinuse: 40
% 1.41/1.79
% 1.41/1.79 Resimplifying inuse:
% 1.41/1.79 Done
% 1.41/1.79
% 1.41/1.79 Resimplifying inuse:
% 1.41/1.79 Done
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 Intermediate Status:
% 1.41/1.79 Generated: 22366
% 1.41/1.79 Kept: 8069
% 1.41/1.79 Inuse: 256
% 1.41/1.79 Deleted: 96
% 1.41/1.79 Deletedinuse: 40
% 1.41/1.79
% 1.41/1.79 Resimplifying inuse:
% 1.41/1.79 Done
% 1.41/1.79
% 1.41/1.79 Resimplifying inuse:
% 1.41/1.79 Done
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 Intermediate Status:
% 1.41/1.79 Generated: 35511
% 1.41/1.79 Kept: 10154
% 1.41/1.79 Inuse: 330
% 1.41/1.79 Deleted: 143
% 1.41/1.79 Deletedinuse: 42
% 1.41/1.79
% 1.41/1.79 Resimplifying inuse:
% 1.41/1.79 Done
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 Bliksems!, er is een bewijs:
% 1.41/1.79 % SZS status Unsatisfiable
% 1.41/1.79 % SZS output start Refutation
% 1.41/1.79
% 1.41/1.79 clause( 0, [ product( identity, X, X ) ] )
% 1.41/1.79 .
% 1.41/1.79 clause( 1, [ product( X, identity, X ) ] )
% 1.41/1.79 .
% 1.41/1.79 clause( 2, [ product( inverse( X ), X, identity ) ] )
% 1.41/1.79 .
% 1.41/1.79 clause( 3, [ product( X, inverse( X ), identity ) ] )
% 1.41/1.79 .
% 1.41/1.79 clause( 5, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z, T ) ]
% 1.41/1.79 )
% 1.41/1.79 .
% 1.41/1.79 clause( 6, [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~( product(
% 1.41/1.79 Z, T, W ) ), product( X, U, W ) ] )
% 1.41/1.79 .
% 1.41/1.79 clause( 7, [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~( product(
% 1.41/1.79 X, U, W ) ), product( Z, T, W ) ] )
% 1.41/1.79 .
% 1.41/1.79 clause( 8, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( Y ) ), ~(
% 1.41/1.79 product( X, inverse( Y ), Z ) ), 'subgroup_member'( Z ) ] )
% 1.41/1.79 .
% 1.41/1.79 clause( 9, [ ~( 'subgroup_member'( X ) ), product( 'another_identity', X, X
% 1.41/1.79 ) ] )
% 1.41/1.79 .
% 1.41/1.79 clause( 11, [ ~( 'subgroup_member'( X ) ), product( X, 'another_inverse'( X
% 1.41/1.79 ), 'another_identity' ) ] )
% 1.41/1.79 .
% 1.41/1.79 clause( 13, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'(
% 1.41/1.79 'another_inverse'( X ) ) ] )
% 1.41/1.79 .
% 1.41/1.79 clause( 15, [ ~( product( X, Y, Z ) ), ~( product( T, Y, Z ) ), =( T, X ) ]
% 1.41/1.79 )
% 1.41/1.79 .
% 1.41/1.79 clause( 16, [ 'subgroup_member'( a ) ] )
% 1.41/1.79 .
% 1.41/1.79 clause( 18, [ ~( =( 'another_inverse'( a ), inverse( a ) ) ) ] )
% 1.41/1.79 .
% 1.41/1.79 clause( 24, [ ~( product( X, X, Y ) ), ~( product( X, Z, Z ) ), product( Y
% 1.41/1.79 , Z, Z ) ] )
% 1.41/1.79 .
% 1.41/1.79 clause( 27, [ 'subgroup_member'( 'another_inverse'( a ) ) ] )
% 1.41/1.79 .
% 1.41/1.79 clause( 29, [ 'subgroup_member'( 'another_inverse'( 'another_inverse'( a )
% 1.41/1.79 ) ) ] )
% 1.41/1.79 .
% 1.41/1.79 clause( 32, [ 'subgroup_member'( 'another_inverse'( 'another_inverse'(
% 1.41/1.79 'another_inverse'( a ) ) ) ) ] )
% 1.41/1.79 .
% 1.41/1.79 clause( 33, [ 'subgroup_member'( 'another_inverse'( 'another_inverse'(
% 1.41/1.79 'another_inverse'( 'another_inverse'( a ) ) ) ) ) ] )
% 1.41/1.79 .
% 1.41/1.79 clause( 38, [ ~( product( identity, X, Y ) ), =( X, Y ) ] )
% 1.41/1.79 .
% 1.41/1.79 clause( 39, [ ~( product( X, identity, Y ) ), =( X, Y ) ] )
% 1.41/1.79 .
% 1.41/1.79 clause( 116, [ ~( product( X, Y, Z ) ), ~( product( identity, Y, T ) ),
% 1.41/1.79 product( inverse( X ), Z, T ) ] )
% 1.41/1.79 .
% 1.41/1.79 clause( 285, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( identity ) ]
% 1.41/1.79 )
% 1.41/1.79 .
% 1.41/1.79 clause( 305, [ 'subgroup_member'( identity ) ] )
% 1.41/1.79 .
% 1.41/1.79 clause( 316, [ 'subgroup_member'( 'another_inverse'( identity ) ) ] )
% 1.41/1.79 .
% 1.41/1.79 clause( 321, [ product( 'another_identity', 'another_inverse'( identity ),
% 1.41/1.79 'another_inverse'( identity ) ) ] )
% 1.41/1.79 .
% 1.41/1.79 clause( 355, [ product( a, 'another_inverse'( a ), 'another_identity' ) ]
% 1.41/1.79 )
% 1.41/1.79 .
% 1.41/1.79 clause( 649, [ ~( product( X, Y, Y ) ), =( X, identity ) ] )
% 1.41/1.79 .
% 1.41/1.79 clause( 934, [ =( 'another_identity', identity ) ] )
% 1.41/1.79 .
% 1.41/1.79 clause( 954, [ product( a, 'another_inverse'( a ), identity ) ] )
% 1.41/1.79 .
% 1.41/1.79 clause( 1129, [ ~( product( identity, identity, X ) ), product( X, Y, Y ) ]
% 1.41/1.79 )
% 1.41/1.79 .
% 1.41/1.79 clause( 1166, [ product( a, X, identity ), ~( product( identity, X,
% 1.41/1.79 'another_inverse'( a ) ) ) ] )
% 1.41/1.79 .
% 1.41/1.79 clause( 1850, [ ~( =( X, inverse( a ) ) ), ~( product( X, identity,
% 1.41/1.79 'another_inverse'( a ) ) ) ] )
% 1.41/1.79 .
% 1.41/1.79 clause( 1859, [ ~( product( inverse( a ), identity, 'another_inverse'( a )
% 1.41/1.79 ) ) ] )
% 1.41/1.79 .
% 1.41/1.79 clause( 10719, [ ~( product( identity, X, 'another_inverse'( a ) ) ) ] )
% 1.41/1.79 .
% 1.41/1.79 clause( 10733, [] )
% 1.41/1.79 .
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 % SZS output end Refutation
% 1.41/1.79 found a proof!
% 1.41/1.79
% 1.41/1.79 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.41/1.79
% 1.41/1.79 initialclauses(
% 1.41/1.79 [ clause( 10735, [ product( identity, X, X ) ] )
% 1.41/1.79 , clause( 10736, [ product( X, identity, X ) ] )
% 1.41/1.79 , clause( 10737, [ product( inverse( X ), X, identity ) ] )
% 1.41/1.79 , clause( 10738, [ product( X, inverse( X ), identity ) ] )
% 1.41/1.79 , clause( 10739, [ product( X, Y, multiply( X, Y ) ) ] )
% 1.41/1.79 , clause( 10740, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z,
% 1.41/1.79 T ) ] )
% 1.41/1.79 , clause( 10741, [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~(
% 1.41/1.79 product( Z, T, W ) ), product( X, U, W ) ] )
% 1.41/1.79 , clause( 10742, [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~(
% 1.41/1.79 product( X, U, W ) ), product( Z, T, W ) ] )
% 1.41/1.79 , clause( 10743, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( Y ) )
% 1.41/1.79 , ~( product( X, inverse( Y ), Z ) ), 'subgroup_member'( Z ) ] )
% 1.41/1.79 , clause( 10744, [ ~( 'subgroup_member'( X ) ), product( 'another_identity'
% 1.41/1.79 , X, X ) ] )
% 1.41/1.79 , clause( 10745, [ ~( 'subgroup_member'( X ) ), product( X,
% 1.41/1.79 'another_identity', X ) ] )
% 1.41/1.79 , clause( 10746, [ ~( 'subgroup_member'( X ) ), product( X,
% 1.41/1.79 'another_inverse'( X ), 'another_identity' ) ] )
% 1.41/1.79 , clause( 10747, [ ~( 'subgroup_member'( X ) ), product( 'another_inverse'(
% 1.41/1.79 X ), X, 'another_identity' ) ] )
% 1.41/1.79 , clause( 10748, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'(
% 1.41/1.79 'another_inverse'( X ) ) ] )
% 1.41/1.79 , clause( 10749, [ ~( product( X, Y, Z ) ), ~( product( X, T, Z ) ), =( T,
% 1.41/1.79 Y ) ] )
% 1.41/1.79 , clause( 10750, [ ~( product( X, Y, Z ) ), ~( product( T, Y, Z ) ), =( T,
% 1.41/1.79 X ) ] )
% 1.41/1.79 , clause( 10751, [ 'subgroup_member'( a ) ] )
% 1.41/1.79 , clause( 10752, [ 'subgroup_member'( 'another_identity' ) ] )
% 1.41/1.79 , clause( 10753, [ ~( =( inverse( a ), 'another_inverse'( a ) ) ) ] )
% 1.41/1.79 ] ).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 subsumption(
% 1.41/1.79 clause( 0, [ product( identity, X, X ) ] )
% 1.41/1.79 , clause( 10735, [ product( identity, X, X ) ] )
% 1.41/1.79 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 subsumption(
% 1.41/1.79 clause( 1, [ product( X, identity, X ) ] )
% 1.41/1.79 , clause( 10736, [ product( X, identity, X ) ] )
% 1.41/1.79 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 subsumption(
% 1.41/1.79 clause( 2, [ product( inverse( X ), X, identity ) ] )
% 1.41/1.79 , clause( 10737, [ product( inverse( X ), X, identity ) ] )
% 1.41/1.79 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 subsumption(
% 1.41/1.79 clause( 3, [ product( X, inverse( X ), identity ) ] )
% 1.41/1.79 , clause( 10738, [ product( X, inverse( X ), identity ) ] )
% 1.41/1.79 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 subsumption(
% 1.41/1.79 clause( 5, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z, T ) ]
% 1.41/1.79 )
% 1.41/1.79 , clause( 10740, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z,
% 1.41/1.79 T ) ] )
% 1.41/1.79 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 1.41/1.79 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 subsumption(
% 1.41/1.79 clause( 6, [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~( product(
% 1.41/1.79 Z, T, W ) ), product( X, U, W ) ] )
% 1.41/1.79 , clause( 10741, [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~(
% 1.41/1.79 product( Z, T, W ) ), product( X, U, W ) ] )
% 1.41/1.79 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 1.41/1.79 , U ), :=( W, W )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2
% 1.41/1.79 , 2 ), ==>( 3, 3 )] ) ).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 subsumption(
% 1.41/1.79 clause( 7, [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~( product(
% 1.41/1.79 X, U, W ) ), product( Z, T, W ) ] )
% 1.41/1.79 , clause( 10742, [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~(
% 1.41/1.79 product( X, U, W ) ), product( Z, T, W ) ] )
% 1.41/1.79 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 1.41/1.79 , U ), :=( W, W )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2
% 1.41/1.79 , 2 ), ==>( 3, 3 )] ) ).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 subsumption(
% 1.41/1.79 clause( 8, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( Y ) ), ~(
% 1.41/1.79 product( X, inverse( Y ), Z ) ), 'subgroup_member'( Z ) ] )
% 1.41/1.79 , clause( 10743, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( Y ) )
% 1.41/1.79 , ~( product( X, inverse( Y ), Z ) ), 'subgroup_member'( Z ) ] )
% 1.41/1.79 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.41/1.79 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 ), ==>( 3, 3 )] )
% 1.41/1.79 ).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 subsumption(
% 1.41/1.79 clause( 9, [ ~( 'subgroup_member'( X ) ), product( 'another_identity', X, X
% 1.41/1.79 ) ] )
% 1.41/1.79 , clause( 10744, [ ~( 'subgroup_member'( X ) ), product( 'another_identity'
% 1.41/1.79 , X, X ) ] )
% 1.41/1.79 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 1.41/1.79 1 )] ) ).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 subsumption(
% 1.41/1.79 clause( 11, [ ~( 'subgroup_member'( X ) ), product( X, 'another_inverse'( X
% 1.41/1.79 ), 'another_identity' ) ] )
% 1.41/1.79 , clause( 10746, [ ~( 'subgroup_member'( X ) ), product( X,
% 1.41/1.79 'another_inverse'( X ), 'another_identity' ) ] )
% 1.41/1.79 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 1.41/1.79 1 )] ) ).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 subsumption(
% 1.41/1.79 clause( 13, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'(
% 1.41/1.79 'another_inverse'( X ) ) ] )
% 1.41/1.79 , clause( 10748, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'(
% 1.41/1.79 'another_inverse'( X ) ) ] )
% 1.41/1.79 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 1.41/1.79 1 )] ) ).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 subsumption(
% 1.41/1.79 clause( 15, [ ~( product( X, Y, Z ) ), ~( product( T, Y, Z ) ), =( T, X ) ]
% 1.41/1.79 )
% 1.41/1.79 , clause( 10750, [ ~( product( X, Y, Z ) ), ~( product( T, Y, Z ) ), =( T,
% 1.41/1.79 X ) ] )
% 1.41/1.79 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 1.41/1.79 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 subsumption(
% 1.41/1.79 clause( 16, [ 'subgroup_member'( a ) ] )
% 1.41/1.79 , clause( 10751, [ 'subgroup_member'( a ) ] )
% 1.41/1.79 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 eqswap(
% 1.41/1.79 clause( 10845, [ ~( =( 'another_inverse'( a ), inverse( a ) ) ) ] )
% 1.41/1.79 , clause( 10753, [ ~( =( inverse( a ), 'another_inverse'( a ) ) ) ] )
% 1.41/1.79 , 0, substitution( 0, [] )).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 subsumption(
% 1.41/1.79 clause( 18, [ ~( =( 'another_inverse'( a ), inverse( a ) ) ) ] )
% 1.41/1.79 , clause( 10845, [ ~( =( 'another_inverse'( a ), inverse( a ) ) ) ] )
% 1.41/1.79 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 factor(
% 1.41/1.79 clause( 10848, [ ~( product( X, X, Y ) ), ~( product( X, Z, Z ) ), product(
% 1.41/1.79 Y, Z, Z ) ] )
% 1.41/1.79 , clause( 7, [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~( product(
% 1.41/1.79 X, U, W ) ), product( Z, T, W ) ] )
% 1.41/1.79 , 1, 2, substitution( 0, [ :=( X, X ), :=( Y, X ), :=( Z, Y ), :=( T, Z ),
% 1.41/1.79 :=( U, Z ), :=( W, Z )] )).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 subsumption(
% 1.41/1.79 clause( 24, [ ~( product( X, X, Y ) ), ~( product( X, Z, Z ) ), product( Y
% 1.41/1.79 , Z, Z ) ] )
% 1.41/1.79 , clause( 10848, [ ~( product( X, X, Y ) ), ~( product( X, Z, Z ) ),
% 1.41/1.79 product( Y, Z, Z ) ] )
% 1.41/1.79 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.41/1.79 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 resolution(
% 1.41/1.79 clause( 10850, [ 'subgroup_member'( 'another_inverse'( a ) ) ] )
% 1.41/1.79 , clause( 13, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'(
% 1.41/1.79 'another_inverse'( X ) ) ] )
% 1.41/1.79 , 0, clause( 16, [ 'subgroup_member'( a ) ] )
% 1.41/1.79 , 0, substitution( 0, [ :=( X, a )] ), substitution( 1, [] )).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 subsumption(
% 1.41/1.79 clause( 27, [ 'subgroup_member'( 'another_inverse'( a ) ) ] )
% 1.41/1.79 , clause( 10850, [ 'subgroup_member'( 'another_inverse'( a ) ) ] )
% 1.41/1.79 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 resolution(
% 1.41/1.79 clause( 10851, [ 'subgroup_member'( 'another_inverse'( 'another_inverse'( a
% 1.41/1.79 ) ) ) ] )
% 1.41/1.79 , clause( 13, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'(
% 1.41/1.79 'another_inverse'( X ) ) ] )
% 1.41/1.79 , 0, clause( 27, [ 'subgroup_member'( 'another_inverse'( a ) ) ] )
% 1.41/1.79 , 0, substitution( 0, [ :=( X, 'another_inverse'( a ) )] ), substitution( 1
% 1.41/1.79 , [] )).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 subsumption(
% 1.41/1.79 clause( 29, [ 'subgroup_member'( 'another_inverse'( 'another_inverse'( a )
% 1.41/1.79 ) ) ] )
% 1.41/1.79 , clause( 10851, [ 'subgroup_member'( 'another_inverse'( 'another_inverse'(
% 1.41/1.79 a ) ) ) ] )
% 1.41/1.79 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 resolution(
% 1.41/1.79 clause( 10852, [ 'subgroup_member'( 'another_inverse'( 'another_inverse'(
% 1.41/1.79 'another_inverse'( a ) ) ) ) ] )
% 1.41/1.79 , clause( 13, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'(
% 1.41/1.79 'another_inverse'( X ) ) ] )
% 1.41/1.79 , 0, clause( 29, [ 'subgroup_member'( 'another_inverse'( 'another_inverse'(
% 1.41/1.79 a ) ) ) ] )
% 1.41/1.79 , 0, substitution( 0, [ :=( X, 'another_inverse'( 'another_inverse'( a ) )
% 1.41/1.79 )] ), substitution( 1, [] )).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 subsumption(
% 1.41/1.79 clause( 32, [ 'subgroup_member'( 'another_inverse'( 'another_inverse'(
% 1.41/1.79 'another_inverse'( a ) ) ) ) ] )
% 1.41/1.79 , clause( 10852, [ 'subgroup_member'( 'another_inverse'( 'another_inverse'(
% 1.41/1.79 'another_inverse'( a ) ) ) ) ] )
% 1.41/1.79 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 resolution(
% 1.41/1.79 clause( 10853, [ 'subgroup_member'( 'another_inverse'( 'another_inverse'(
% 1.41/1.79 'another_inverse'( 'another_inverse'( a ) ) ) ) ) ] )
% 1.41/1.79 , clause( 13, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'(
% 1.41/1.79 'another_inverse'( X ) ) ] )
% 1.41/1.79 , 0, clause( 32, [ 'subgroup_member'( 'another_inverse'( 'another_inverse'(
% 1.41/1.79 'another_inverse'( a ) ) ) ) ] )
% 1.41/1.79 , 0, substitution( 0, [ :=( X, 'another_inverse'( 'another_inverse'(
% 1.41/1.79 'another_inverse'( a ) ) ) )] ), substitution( 1, [] )).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 subsumption(
% 1.41/1.79 clause( 33, [ 'subgroup_member'( 'another_inverse'( 'another_inverse'(
% 1.41/1.79 'another_inverse'( 'another_inverse'( a ) ) ) ) ) ] )
% 1.41/1.79 , clause( 10853, [ 'subgroup_member'( 'another_inverse'( 'another_inverse'(
% 1.41/1.79 'another_inverse'( 'another_inverse'( a ) ) ) ) ) ] )
% 1.41/1.79 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 resolution(
% 1.41/1.79 clause( 10854, [ ~( product( identity, X, Y ) ), =( X, Y ) ] )
% 1.41/1.79 , clause( 5, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z, T )
% 1.41/1.79 ] )
% 1.41/1.79 , 0, clause( 0, [ product( identity, X, X ) ] )
% 1.41/1.79 , 0, substitution( 0, [ :=( X, identity ), :=( Y, X ), :=( Z, X ), :=( T, Y
% 1.41/1.79 )] ), substitution( 1, [ :=( X, X )] )).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 subsumption(
% 1.41/1.79 clause( 38, [ ~( product( identity, X, Y ) ), =( X, Y ) ] )
% 1.41/1.79 , clause( 10854, [ ~( product( identity, X, Y ) ), =( X, Y ) ] )
% 1.41/1.79 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.41/1.79 ), ==>( 1, 1 )] ) ).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 resolution(
% 1.41/1.79 clause( 10856, [ ~( product( X, identity, Y ) ), =( X, Y ) ] )
% 1.41/1.79 , clause( 5, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z, T )
% 1.41/1.79 ] )
% 1.41/1.79 , 0, clause( 1, [ product( X, identity, X ) ] )
% 1.41/1.79 , 0, substitution( 0, [ :=( X, X ), :=( Y, identity ), :=( Z, X ), :=( T, Y
% 1.41/1.79 )] ), substitution( 1, [ :=( X, X )] )).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 subsumption(
% 1.41/1.79 clause( 39, [ ~( product( X, identity, Y ) ), =( X, Y ) ] )
% 1.41/1.79 , clause( 10856, [ ~( product( X, identity, Y ) ), =( X, Y ) ] )
% 1.41/1.79 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.41/1.79 ), ==>( 1, 1 )] ) ).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 resolution(
% 1.41/1.79 clause( 10858, [ ~( product( X, Y, Z ) ), ~( product( identity, Y, T ) ),
% 1.41/1.79 product( inverse( X ), Z, T ) ] )
% 1.41/1.79 , clause( 6, [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~( product(
% 1.41/1.79 Z, T, W ) ), product( X, U, W ) ] )
% 1.41/1.79 , 0, clause( 2, [ product( inverse( X ), X, identity ) ] )
% 1.41/1.79 , 0, substitution( 0, [ :=( X, inverse( X ) ), :=( Y, X ), :=( Z, identity
% 1.41/1.79 ), :=( T, Y ), :=( U, Z ), :=( W, T )] ), substitution( 1, [ :=( X, X )] )
% 1.41/1.79 ).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 subsumption(
% 1.41/1.79 clause( 116, [ ~( product( X, Y, Z ) ), ~( product( identity, Y, T ) ),
% 1.41/1.79 product( inverse( X ), Z, T ) ] )
% 1.41/1.79 , clause( 10858, [ ~( product( X, Y, Z ) ), ~( product( identity, Y, T ) )
% 1.41/1.79 , product( inverse( X ), Z, T ) ] )
% 1.41/1.79 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 1.41/1.79 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 resolution(
% 1.41/1.79 clause( 10863, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( X ) ),
% 1.41/1.79 'subgroup_member'( identity ) ] )
% 1.41/1.79 , clause( 8, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( Y ) ),
% 1.41/1.79 ~( product( X, inverse( Y ), Z ) ), 'subgroup_member'( Z ) ] )
% 1.41/1.79 , 2, clause( 3, [ product( X, inverse( X ), identity ) ] )
% 1.41/1.79 , 0, substitution( 0, [ :=( X, X ), :=( Y, X ), :=( Z, identity )] ),
% 1.41/1.79 substitution( 1, [ :=( X, X )] )).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 factor(
% 1.41/1.79 clause( 10864, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( identity )
% 1.41/1.79 ] )
% 1.41/1.79 , clause( 10863, [ ~( 'subgroup_member'( X ) ), ~( 'subgroup_member'( X ) )
% 1.41/1.79 , 'subgroup_member'( identity ) ] )
% 1.41/1.79 , 0, 1, substitution( 0, [ :=( X, X )] )).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 subsumption(
% 1.41/1.79 clause( 285, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( identity ) ]
% 1.41/1.79 )
% 1.41/1.79 , clause( 10864, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( identity
% 1.41/1.79 ) ] )
% 1.41/1.79 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 1.41/1.79 1 )] ) ).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 resolution(
% 1.41/1.79 clause( 10865, [ 'subgroup_member'( identity ) ] )
% 1.41/1.79 , clause( 285, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'( identity )
% 1.41/1.79 ] )
% 1.41/1.79 , 0, clause( 33, [ 'subgroup_member'( 'another_inverse'( 'another_inverse'(
% 1.41/1.79 'another_inverse'( 'another_inverse'( a ) ) ) ) ) ] )
% 1.41/1.79 , 0, substitution( 0, [ :=( X, 'another_inverse'( 'another_inverse'(
% 1.41/1.79 'another_inverse'( 'another_inverse'( a ) ) ) ) )] ), substitution( 1, [] )
% 1.41/1.79 ).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 subsumption(
% 1.41/1.79 clause( 305, [ 'subgroup_member'( identity ) ] )
% 1.41/1.79 , clause( 10865, [ 'subgroup_member'( identity ) ] )
% 1.41/1.79 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 resolution(
% 1.41/1.79 clause( 10866, [ 'subgroup_member'( 'another_inverse'( identity ) ) ] )
% 1.41/1.79 , clause( 13, [ ~( 'subgroup_member'( X ) ), 'subgroup_member'(
% 1.41/1.79 'another_inverse'( X ) ) ] )
% 1.41/1.79 , 0, clause( 305, [ 'subgroup_member'( identity ) ] )
% 1.41/1.79 , 0, substitution( 0, [ :=( X, identity )] ), substitution( 1, [] )).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 subsumption(
% 1.41/1.79 clause( 316, [ 'subgroup_member'( 'another_inverse'( identity ) ) ] )
% 1.41/1.79 , clause( 10866, [ 'subgroup_member'( 'another_inverse'( identity ) ) ] )
% 1.41/1.79 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 resolution(
% 1.41/1.79 clause( 10867, [ product( 'another_identity', 'another_inverse'( identity )
% 1.41/1.79 , 'another_inverse'( identity ) ) ] )
% 1.41/1.79 , clause( 9, [ ~( 'subgroup_member'( X ) ), product( 'another_identity', X
% 1.41/1.79 , X ) ] )
% 1.41/1.79 , 0, clause( 316, [ 'subgroup_member'( 'another_inverse'( identity ) ) ] )
% 1.41/1.79 , 0, substitution( 0, [ :=( X, 'another_inverse'( identity ) )] ),
% 1.41/1.79 substitution( 1, [] )).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 subsumption(
% 1.41/1.79 clause( 321, [ product( 'another_identity', 'another_inverse'( identity ),
% 1.41/1.79 'another_inverse'( identity ) ) ] )
% 1.41/1.79 , clause( 10867, [ product( 'another_identity', 'another_inverse'( identity
% 1.41/1.79 ), 'another_inverse'( identity ) ) ] )
% 1.41/1.79 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 resolution(
% 1.41/1.79 clause( 10868, [ product( a, 'another_inverse'( a ), 'another_identity' ) ]
% 1.41/1.79 )
% 1.41/1.79 , clause( 11, [ ~( 'subgroup_member'( X ) ), product( X, 'another_inverse'(
% 1.41/1.79 X ), 'another_identity' ) ] )
% 1.41/1.79 , 0, clause( 16, [ 'subgroup_member'( a ) ] )
% 1.41/1.79 , 0, substitution( 0, [ :=( X, a )] ), substitution( 1, [] )).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 subsumption(
% 1.41/1.79 clause( 355, [ product( a, 'another_inverse'( a ), 'another_identity' ) ]
% 1.41/1.79 )
% 1.41/1.79 , clause( 10868, [ product( a, 'another_inverse'( a ), 'another_identity' )
% 1.41/1.79 ] )
% 1.41/1.79 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 resolution(
% 1.41/1.79 clause( 10869, [ ~( product( Y, X, X ) ), =( Y, identity ) ] )
% 1.41/1.79 , clause( 15, [ ~( product( X, Y, Z ) ), ~( product( T, Y, Z ) ), =( T, X )
% 1.41/1.79 ] )
% 1.41/1.79 , 0, clause( 0, [ product( identity, X, X ) ] )
% 1.41/1.79 , 0, substitution( 0, [ :=( X, identity ), :=( Y, X ), :=( Z, X ), :=( T, Y
% 1.41/1.79 )] ), substitution( 1, [ :=( X, X )] )).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 subsumption(
% 1.41/1.79 clause( 649, [ ~( product( X, Y, Y ) ), =( X, identity ) ] )
% 1.41/1.79 , clause( 10869, [ ~( product( Y, X, X ) ), =( Y, identity ) ] )
% 1.41/1.79 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 1.41/1.79 ), ==>( 1, 1 )] ) ).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 eqswap(
% 1.41/1.79 clause( 10871, [ =( identity, X ), ~( product( X, Y, Y ) ) ] )
% 1.41/1.79 , clause( 649, [ ~( product( X, Y, Y ) ), =( X, identity ) ] )
% 1.41/1.79 , 1, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 resolution(
% 1.41/1.79 clause( 10872, [ =( identity, 'another_identity' ) ] )
% 1.41/1.79 , clause( 10871, [ =( identity, X ), ~( product( X, Y, Y ) ) ] )
% 1.41/1.79 , 1, clause( 321, [ product( 'another_identity', 'another_inverse'(
% 1.41/1.79 identity ), 'another_inverse'( identity ) ) ] )
% 1.41/1.79 , 0, substitution( 0, [ :=( X, 'another_identity' ), :=( Y,
% 1.41/1.79 'another_inverse'( identity ) )] ), substitution( 1, [] )).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 eqswap(
% 1.41/1.79 clause( 10873, [ =( 'another_identity', identity ) ] )
% 1.41/1.79 , clause( 10872, [ =( identity, 'another_identity' ) ] )
% 1.41/1.79 , 0, substitution( 0, [] )).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 subsumption(
% 1.41/1.79 clause( 934, [ =( 'another_identity', identity ) ] )
% 1.41/1.79 , clause( 10873, [ =( 'another_identity', identity ) ] )
% 1.41/1.79 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 paramod(
% 1.41/1.79 clause( 10879, [ product( a, 'another_inverse'( a ), identity ), ~( product(
% 1.41/1.79 'another_identity', X, X ) ) ] )
% 1.41/1.79 , clause( 649, [ ~( product( X, Y, Y ) ), =( X, identity ) ] )
% 1.41/1.79 , 1, clause( 355, [ product( a, 'another_inverse'( a ), 'another_identity'
% 1.41/1.79 ) ] )
% 1.41/1.79 , 0, 4, substitution( 0, [ :=( X, 'another_identity' ), :=( Y, X )] ),
% 1.41/1.79 substitution( 1, [] )).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 paramod(
% 1.41/1.79 clause( 10920, [ ~( product( identity, X, X ) ), product( a,
% 1.41/1.79 'another_inverse'( a ), identity ) ] )
% 1.41/1.79 , clause( 934, [ =( 'another_identity', identity ) ] )
% 1.41/1.79 , 0, clause( 10879, [ product( a, 'another_inverse'( a ), identity ), ~(
% 1.41/1.79 product( 'another_identity', X, X ) ) ] )
% 1.41/1.79 , 1, 2, substitution( 0, [] ), substitution( 1, [ :=( X, X )] )).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 resolution(
% 1.41/1.79 clause( 10921, [ product( a, 'another_inverse'( a ), identity ) ] )
% 1.41/1.79 , clause( 10920, [ ~( product( identity, X, X ) ), product( a,
% 1.41/1.79 'another_inverse'( a ), identity ) ] )
% 1.41/1.79 , 0, clause( 0, [ product( identity, X, X ) ] )
% 1.41/1.79 , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 1.41/1.79 ).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 subsumption(
% 1.41/1.79 clause( 954, [ product( a, 'another_inverse'( a ), identity ) ] )
% 1.41/1.79 , clause( 10921, [ product( a, 'another_inverse'( a ), identity ) ] )
% 1.41/1.79 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.41/1.79
% 1.41/1.79
% 1.41/1.79 resolution(
% 1.41/1.79 clause( 10923, [ ~( product( identity, identity, X ) ), product( X, Y, Y )
% 1.41/1.79 ] )
% 1.41/1.79 , clause( 24, [ ~( product( X, X, Y ) ), ~( product( X, Z, Z ) ), product(
% 1.41/1.79 Y, Z, Z ) ] )
% 1.41/1.79 , 1, clause( 0, [ product( identity, X, X ) ] )
% 1.41/1.79 , 0, substitution( 0, [ :=( X, identity )Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------