TSTP Solution File: GRP012-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GRP012-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n013.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 07:34:17 EDT 2022
% Result : Unsatisfiable 1.87s 2.28s
% Output : Refutation 1.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP012-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : bliksem %s
% 0.13/0.33 % Computer : n013.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % DateTime : Tue Jun 14 04:14:58 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.87/2.28 *** allocated 10000 integers for termspace/termends
% 1.87/2.28 *** allocated 10000 integers for clauses
% 1.87/2.28 *** allocated 10000 integers for justifications
% 1.87/2.28 Bliksem 1.12
% 1.87/2.28
% 1.87/2.28
% 1.87/2.28 Automatic Strategy Selection
% 1.87/2.28
% 1.87/2.28 Clauses:
% 1.87/2.28 [
% 1.87/2.28 [ product( identity, X, X ) ],
% 1.87/2.28 [ product( X, identity, X ) ],
% 1.87/2.28 [ product( inverse( X ), X, identity ) ],
% 1.87/2.28 [ product( X, inverse( X ), identity ) ],
% 1.87/2.28 [ product( X, Y, multiply( X, Y ) ) ],
% 1.87/2.28 [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z, T ) ],
% 1.87/2.28 [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~( product( Z, T, W
% 1.87/2.28 ) ), product( X, U, W ) ],
% 1.87/2.28 [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~( product( X, U, W
% 1.87/2.28 ) ), product( Z, T, W ) ],
% 1.87/2.28 [ product( a, b, c ) ],
% 1.87/2.28 [ product( inverse( b ), inverse( a ), d ) ],
% 1.87/2.28 [ ~( product( c, d, identity ) ) ]
% 1.87/2.28 ] .
% 1.87/2.28
% 1.87/2.28
% 1.87/2.28 percentage equality = 0.052632, percentage horn = 1.000000
% 1.87/2.28 This is a problem with some equality
% 1.87/2.28
% 1.87/2.28
% 1.87/2.28
% 1.87/2.28 Options Used:
% 1.87/2.28
% 1.87/2.28 useres = 1
% 1.87/2.28 useparamod = 1
% 1.87/2.28 useeqrefl = 1
% 1.87/2.28 useeqfact = 1
% 1.87/2.28 usefactor = 1
% 1.87/2.28 usesimpsplitting = 0
% 1.87/2.28 usesimpdemod = 5
% 1.87/2.28 usesimpres = 3
% 1.87/2.28
% 1.87/2.28 resimpinuse = 1000
% 1.87/2.28 resimpclauses = 20000
% 1.87/2.28 substype = eqrewr
% 1.87/2.28 backwardsubs = 1
% 1.87/2.28 selectoldest = 5
% 1.87/2.28
% 1.87/2.28 litorderings [0] = split
% 1.87/2.28 litorderings [1] = extend the termordering, first sorting on arguments
% 1.87/2.28
% 1.87/2.28 termordering = kbo
% 1.87/2.28
% 1.87/2.28 litapriori = 0
% 1.87/2.28 termapriori = 1
% 1.87/2.28 litaposteriori = 0
% 1.87/2.28 termaposteriori = 0
% 1.87/2.28 demodaposteriori = 0
% 1.87/2.28 ordereqreflfact = 0
% 1.87/2.28
% 1.87/2.28 litselect = negord
% 1.87/2.28
% 1.87/2.28 maxweight = 15
% 1.87/2.28 maxdepth = 30000
% 1.87/2.28 maxlength = 115
% 1.87/2.28 maxnrvars = 195
% 1.87/2.28 excuselevel = 1
% 1.87/2.28 increasemaxweight = 1
% 1.87/2.28
% 1.87/2.28 maxselected = 10000000
% 1.87/2.28 maxnrclauses = 10000000
% 1.87/2.28
% 1.87/2.28 showgenerated = 0
% 1.87/2.28 showkept = 0
% 1.87/2.28 showselected = 0
% 1.87/2.28 showdeleted = 0
% 1.87/2.28 showresimp = 1
% 1.87/2.28 showstatus = 2000
% 1.87/2.28
% 1.87/2.28 prologoutput = 1
% 1.87/2.28 nrgoals = 5000000
% 1.87/2.28 totalproof = 1
% 1.87/2.28
% 1.87/2.28 Symbols occurring in the translation:
% 1.87/2.28
% 1.87/2.28 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.87/2.28 . [1, 2] (w:1, o:26, a:1, s:1, b:0),
% 1.87/2.28 ! [4, 1] (w:0, o:20, a:1, s:1, b:0),
% 1.87/2.28 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.87/2.28 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.87/2.28 identity [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 1.87/2.28 product [41, 3] (w:1, o:52, a:1, s:1, b:0),
% 1.87/2.28 inverse [42, 1] (w:1, o:25, a:1, s:1, b:0),
% 1.87/2.28 multiply [44, 2] (w:1, o:51, a:1, s:1, b:0),
% 1.87/2.28 a [49, 0] (w:1, o:16, a:1, s:1, b:0),
% 1.87/2.28 b [50, 0] (w:1, o:17, a:1, s:1, b:0),
% 1.87/2.28 c [51, 0] (w:1, o:18, a:1, s:1, b:0),
% 1.87/2.28 d [52, 0] (w:1, o:19, a:1, s:1, b:0).
% 1.87/2.28
% 1.87/2.28
% 1.87/2.28 Starting Search:
% 1.87/2.28
% 1.87/2.28 Resimplifying inuse:
% 1.87/2.28 Done
% 1.87/2.28
% 1.87/2.28
% 1.87/2.28 Intermediate Status:
% 1.87/2.28 Generated: 5971
% 1.87/2.28 Kept: 2013
% 1.87/2.28 Inuse: 85
% 1.87/2.28 Deleted: 15
% 1.87/2.28 Deletedinuse: 13
% 1.87/2.28
% 1.87/2.28 Resimplifying inuse:
% 1.87/2.28 Done
% 1.87/2.28
% 1.87/2.28 Resimplifying inuse:
% 1.87/2.28 Done
% 1.87/2.28
% 1.87/2.28
% 1.87/2.28 Intermediate Status:
% 1.87/2.28 Generated: 12614
% 1.87/2.28 Kept: 4047
% 1.87/2.28 Inuse: 142
% 1.87/2.28 Deleted: 25
% 1.87/2.28 Deletedinuse: 13
% 1.87/2.28
% 1.87/2.28 Resimplifying inuse:
% 1.87/2.28 Done
% 1.87/2.28
% 1.87/2.28 Resimplifying inuse:
% 1.87/2.28 Done
% 1.87/2.28
% 1.87/2.28
% 1.87/2.28 Intermediate Status:
% 1.87/2.28 Generated: 19805
% 1.87/2.28 Kept: 6048
% 1.87/2.28 Inuse: 195
% 1.87/2.28 Deleted: 50
% 1.87/2.28 Deletedinuse: 35
% 1.87/2.28
% 1.87/2.28 Resimplifying inuse:
% 1.87/2.28 Done
% 1.87/2.28
% 1.87/2.28 Resimplifying inuse:
% 1.87/2.28 Done
% 1.87/2.28
% 1.87/2.28
% 1.87/2.28 Intermediate Status:
% 1.87/2.28 Generated: 26039
% 1.87/2.28 Kept: 8070
% 1.87/2.28 Inuse: 245
% 1.87/2.28 Deleted: 50
% 1.87/2.28 Deletedinuse: 35
% 1.87/2.28
% 1.87/2.28 Resimplifying inuse:
% 1.87/2.28 Done
% 1.87/2.28
% 1.87/2.28 Resimplifying inuse:
% 1.87/2.28 Done
% 1.87/2.28
% 1.87/2.28
% 1.87/2.28 Intermediate Status:
% 1.87/2.28 Generated: 42427
% 1.87/2.28 Kept: 10082
% 1.87/2.28 Inuse: 336
% 1.87/2.28 Deleted: 61
% 1.87/2.28 Deletedinuse: 35
% 1.87/2.28
% 1.87/2.28 Resimplifying inuse:
% 1.87/2.28 Done
% 1.87/2.28
% 1.87/2.28 Resimplifying inuse:
% 1.87/2.28 Done
% 1.87/2.28
% 1.87/2.28
% 1.87/2.28 Intermediate Status:
% 1.87/2.28 Generated: 55204
% 1.87/2.28 Kept: 12375
% 1.87/2.28 Inuse: 372
% 1.87/2.28 Deleted: 70
% 1.87/2.28 Deletedinuse: 36
% 1.87/2.28
% 1.87/2.28 Resimplifying inuse:
% 1.87/2.28 Done
% 1.87/2.28
% 1.87/2.28
% 1.87/2.28 Bliksems!, er is een bewijs:
% 1.87/2.28 % SZS status Unsatisfiable
% 1.87/2.28 % SZS output start Refutation
% 1.87/2.28
% 1.87/2.28 clause( 0, [ product( identity, X, X ) ] )
% 1.87/2.28 .
% 1.87/2.28 clause( 1, [ product( X, identity, X ) ] )
% 1.87/2.28 .
% 1.87/2.28 clause( 2, [ product( inverse( X ), X, identity ) ] )
% 1.87/2.28 .
% 1.87/2.28 clause( 3, [ product( X, inverse( X ), identity ) ] )
% 1.87/2.28 .
% 1.87/2.28 clause( 4, [ product( X, Y, multiply( X, Y ) ) ] )
% 1.87/2.28 .
% 1.87/2.28 clause( 5, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z, T ) ]
% 1.87/2.28 )
% 1.87/2.28 .
% 1.87/2.28 clause( 6, [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~( product(
% 1.87/2.28 Z, T, W ) ), product( X, U, W ) ] )
% 1.87/2.28 .
% 1.87/2.28 clause( 7, [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~( product(
% 1.87/2.28 X, U, W ) ), product( Z, T, W ) ] )
% 1.87/2.28 .
% 1.87/2.28 clause( 8, [ product( a, b, c ) ] )
% 1.87/2.28 .
% 1.87/2.28 clause( 9, [ product( inverse( b ), inverse( a ), d ) ] )
% 1.87/2.28 .
% 1.87/2.28 clause( 10, [ ~( product( c, d, identity ) ) ] )
% 1.87/2.28 .
% 1.87/2.28 clause( 13, [ ~( product( X, Y, Y ) ), ~( product( Y, Z, T ) ), product( X
% 1.87/2.28 , T, T ) ] )
% 1.87/2.28 .
% 1.87/2.28 clause( 15, [ ~( product( X, Y, Z ) ), ~( product( Y, T, Y ) ), product( Z
% 1.87/2.28 , T, Z ) ] )
% 1.87/2.28 .
% 1.87/2.28 clause( 19, [ ~( product( inverse( X ), X, Y ) ), =( identity, Y ) ] )
% 1.87/2.28 .
% 1.87/2.28 clause( 22, [ ~( product( identity, X, Y ) ), =( X, Y ) ] )
% 1.87/2.28 .
% 1.87/2.28 clause( 23, [ ~( product( X, identity, Y ) ), =( X, Y ) ] )
% 1.87/2.28 .
% 1.87/2.28 clause( 71, [ product( a, X, c ), ~( product( identity, b, X ) ) ] )
% 1.87/2.28 .
% 1.87/2.28 clause( 82, [ product( X, Y, Y ), ~( product( identity, X, identity ) ) ]
% 1.87/2.28 )
% 1.87/2.28 .
% 1.87/2.28 clause( 92, [ ~( product( inverse( a ), X, Y ) ), ~( product( d, X, Z ) ),
% 1.87/2.28 product( inverse( b ), Y, Z ) ] )
% 1.87/2.28 .
% 1.87/2.28 clause( 96, [ ~( product( X, Y, Z ) ), ~( product( Z, T, U ) ), product( X
% 1.87/2.28 , multiply( Y, T ), U ) ] )
% 1.87/2.28 .
% 1.87/2.28 clause( 98, [ ~( product( X, Y, Z ) ), ~( product( identity, Y, T ) ),
% 1.87/2.28 product( inverse( X ), Z, T ) ] )
% 1.87/2.28 .
% 1.87/2.28 clause( 415, [ ~( product( X, Y, Y ) ), product( X, identity, identity ) ]
% 1.87/2.28 )
% 1.87/2.28 .
% 1.87/2.28 clause( 424, [ ~( product( X, Y, Y ) ), =( X, identity ) ] )
% 1.87/2.28 .
% 1.87/2.28 clause( 464, [ ~( product( c, d, X ) ), ~( product( X, Y, Y ) ) ] )
% 1.87/2.28 .
% 1.87/2.28 clause( 527, [ ~( product( multiply( c, d ), X, X ) ) ] )
% 1.87/2.28 .
% 1.87/2.28 clause( 566, [ ~( product( identity, multiply( c, d ), identity ) ) ] )
% 1.87/2.28 .
% 1.87/2.28 clause( 612, [ ~( product( X, Y, X ) ), product( identity, Y, identity ) ]
% 1.87/2.28 )
% 1.87/2.28 .
% 1.87/2.28 clause( 678, [ ~( product( X, multiply( c, d ), X ) ) ] )
% 1.87/2.28 .
% 1.87/2.28 clause( 11772, [ ~( product( X, c, Y ) ), ~( product( Y, d, X ) ) ] )
% 1.87/2.28 .
% 1.87/2.28 clause( 11896, [ ~( product( d, c, identity ) ) ] )
% 1.87/2.28 .
% 1.87/2.28 clause( 11936, [ ~( product( d, c, X ) ), ~( product( inverse( Y ), Y, X )
% 1.87/2.28 ) ] )
% 1.87/2.28 .
% 1.87/2.28 clause( 12557, [ ~( product( identity, X, Y ) ), product( inverse( a ), c,
% 1.87/2.28 Y ), ~( product( identity, b, X ) ) ] )
% 1.87/2.28 .
% 1.87/2.28 clause( 12689, [ product( inverse( a ), c, b ) ] )
% 1.87/2.28 .
% 1.87/2.28 clause( 12699, [ ~( product( d, c, X ) ) ] )
% 1.87/2.28 .
% 1.87/2.28 clause( 12778, [] )
% 1.87/2.28 .
% 1.87/2.28
% 1.87/2.28
% 1.87/2.28 % SZS output end Refutation
% 1.87/2.28 found a proof!
% 1.87/2.28
% 1.87/2.28 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.87/2.28
% 1.87/2.28 initialclauses(
% 1.87/2.28 [ clause( 12780, [ product( identity, X, X ) ] )
% 1.87/2.28 , clause( 12781, [ product( X, identity, X ) ] )
% 1.87/2.28 , clause( 12782, [ product( inverse( X ), X, identity ) ] )
% 1.87/2.28 , clause( 12783, [ product( X, inverse( X ), identity ) ] )
% 1.87/2.28 , clause( 12784, [ product( X, Y, multiply( X, Y ) ) ] )
% 1.87/2.28 , clause( 12785, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z,
% 1.87/2.28 T ) ] )
% 1.87/2.28 , clause( 12786, [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~(
% 1.87/2.28 product( Z, T, W ) ), product( X, U, W ) ] )
% 1.87/2.28 , clause( 12787, [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~(
% 1.87/2.28 product( X, U, W ) ), product( Z, T, W ) ] )
% 1.87/2.28 , clause( 12788, [ product( a, b, c ) ] )
% 1.87/2.28 , clause( 12789, [ product( inverse( b ), inverse( a ), d ) ] )
% 1.87/2.28 , clause( 12790, [ ~( product( c, d, identity ) ) ] )
% 1.87/2.28 ] ).
% 1.87/2.28
% 1.87/2.28
% 1.87/2.28
% 1.87/2.28 subsumption(
% 1.87/2.28 clause( 0, [ product( identity, X, X ) ] )
% 1.87/2.28 , clause( 12780, [ product( identity, X, X ) ] )
% 1.87/2.28 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.87/2.28
% 1.87/2.28
% 1.87/2.28 subsumption(
% 1.87/2.28 clause( 1, [ product( X, identity, X ) ] )
% 1.87/2.28 , clause( 12781, [ product( X, identity, X ) ] )
% 1.87/2.28 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.87/2.28
% 1.87/2.28
% 1.87/2.28 subsumption(
% 1.87/2.28 clause( 2, [ product( inverse( X ), X, identity ) ] )
% 1.87/2.28 , clause( 12782, [ product( inverse( X ), X, identity ) ] )
% 1.87/2.28 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.87/2.28
% 1.87/2.28
% 1.87/2.28 subsumption(
% 1.87/2.28 clause( 3, [ product( X, inverse( X ), identity ) ] )
% 1.87/2.28 , clause( 12783, [ product( X, inverse( X ), identity ) ] )
% 1.87/2.28 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.87/2.28
% 1.87/2.28
% 1.87/2.28 subsumption(
% 1.87/2.28 clause( 4, [ product( X, Y, multiply( X, Y ) ) ] )
% 1.87/2.28 , clause( 12784, [ product( X, Y, multiply( X, Y ) ) ] )
% 1.87/2.28 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.87/2.28 )] ) ).
% 1.87/2.28
% 1.87/2.28
% 1.87/2.28 subsumption(
% 1.87/2.28 clause( 5, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z, T ) ]
% 1.87/2.28 )
% 1.87/2.28 , clause( 12785, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z,
% 1.87/2.28 T ) ] )
% 1.87/2.28 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 1.87/2.28 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 1.87/2.28
% 1.87/2.28
% 1.87/2.28 subsumption(
% 1.87/2.28 clause( 6, [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~( product(
% 1.87/2.28 Z, T, W ) ), product( X, U, W ) ] )
% 1.87/2.28 , clause( 12786, [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~(
% 1.87/2.28 product( Z, T, W ) ), product( X, U, W ) ] )
% 1.87/2.28 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 1.87/2.28 , U ), :=( W, W )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2
% 1.87/2.28 , 2 ), ==>( 3, 3 )] ) ).
% 1.87/2.28
% 1.87/2.28
% 1.87/2.28 subsumption(
% 1.87/2.28 clause( 7, [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~( product(
% 1.87/2.28 X, U, W ) ), product( Z, T, W ) ] )
% 1.87/2.28 , clause( 12787, [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~(
% 1.87/2.28 product( X, U, W ) ), product( Z, T, W ) ] )
% 1.87/2.28 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 1.87/2.28 , U ), :=( W, W )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2
% 1.87/2.28 , 2 ), ==>( 3, 3 )] ) ).
% 1.87/2.28
% 1.87/2.28
% 1.87/2.28 subsumption(
% 1.87/2.28 clause( 8, [ product( a, b, c ) ] )
% 1.87/2.28 , clause( 12788, [ product( a, b, c ) ] )
% 1.87/2.28 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.87/2.28
% 1.87/2.28
% 1.87/2.28 subsumption(
% 1.87/2.28 clause( 9, [ product( inverse( b ), inverse( a ), d ) ] )
% 1.87/2.28 , clause( 12789, [ product( inverse( b ), inverse( a ), d ) ] )
% 1.87/2.28 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.87/2.28
% 1.87/2.28
% 1.87/2.28 subsumption(
% 1.87/2.28 clause( 10, [ ~( product( c, d, identity ) ) ] )
% 1.87/2.28 , clause( 12790, [ ~( product( c, d, identity ) ) ] )
% 1.87/2.28 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.87/2.28
% 1.87/2.28
% 1.87/2.28 factor(
% 1.87/2.28 clause( 12835, [ ~( product( X, Y, Y ) ), ~( product( Y, Z, T ) ), product(
% 1.87/2.28 X, T, T ) ] )
% 1.87/2.28 , clause( 6, [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~( product(
% 1.87/2.28 Z, T, W ) ), product( X, U, W ) ] )
% 1.87/2.28 , 1, 2, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Y ), :=( T, Z ),
% 1.87/2.28 :=( U, T ), :=( W, T )] )).
% 1.87/2.28
% 1.87/2.28
% 1.87/2.28 subsumption(
% 1.87/2.28 clause( 13, [ ~( product( X, Y, Y ) ), ~( product( Y, Z, T ) ), product( X
% 1.87/2.28 , T, T ) ] )
% 1.87/2.28 , clause( 12835, [ ~( product( X, Y, Y ) ), ~( product( Y, Z, T ) ),
% 1.87/2.28 product( X, T, T ) ] )
% 1.87/2.28 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 1.87/2.28 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 1.87/2.28
% 1.87/2.28
% 1.87/2.28 factor(
% 1.87/2.28 clause( 12838, [ ~( product( X, Y, Z ) ), ~( product( Y, T, Y ) ), product(
% 1.87/2.28 Z, T, Z ) ] )
% 1.87/2.28 , clause( 7, [ ~( product( X, Y, Z ) ), ~( product( Y, T, U ) ), ~( product(
% 1.87/2.28 X, U, W ) ), product( Z, T, W ) ] )
% 1.87/2.28 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 1.87/2.28 :=( U, Y ), :=( W, Z )] )).
% 1.87/2.28
% 1.87/2.28
% 1.87/2.28 subsumption(
% 1.87/2.28 clause( 15, [ ~( product( X, Y, Z ) ), ~( product( Y, T, Y ) ), product( Z
% 1.87/2.28 , T, Z ) ] )
% 1.87/2.28 , clause( 12838, [ ~( product( X, Y, Z ) ), ~( product( Y, T, Y ) ),
% 1.87/2.28 product( Z, T, Z ) ] )
% 1.87/2.28 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 1.87/2.28 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 1.87/2.28
% 1.87/2.28
% 1.87/2.28 resolution(
% 1.87/2.28 clause( 12841, [ ~( product( inverse( X ), X, Y ) ), =( identity, Y ) ] )
% 1.87/2.28 , clause( 5, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z, T )
% 1.87/2.28 ] )
% 1.87/2.28 , 0, clause( 2, [ product( inverse( X ), X, identity ) ] )
% 1.87/2.28 , 0, substitution( 0, [ :=( X, inverse( X ) ), :=( Y, X ), :=( Z, identity
% 1.87/2.28 ), :=( T, Y )] ), substitution( 1, [ :=( X, X )] )).
% 1.87/2.28
% 1.87/2.28
% 1.87/2.28 subsumption(
% 1.87/2.28 clause( 19, [ ~( product( inverse( X ), X, Y ) ), =( identity, Y ) ] )
% 1.87/2.28 , clause( 12841, [ ~( product( inverse( X ), X, Y ) ), =( identity, Y ) ]
% 1.87/2.28 )
% 1.87/2.28 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.87/2.28 ), ==>( 1, 1 )] ) ).
% 1.87/2.28
% 1.87/2.28
% 1.87/2.28 resolution(
% 1.87/2.28 clause( 12843, [ ~( product( identity, X, Y ) ), =( X, Y ) ] )
% 1.87/2.28 , clause( 5, [ ~( product( X, Y, Z ) ), ~( product( X, Y, T ) ), =( Z, T )
% 1.87/2.28 ] )
% 1.87/2.28 , 0, clause( 0, [ product( identity, X, X ) ] )
% 1.87/2.28 , 0, substitution( 0, [ :=( X, identity ), :=( Y, X ), :=( Z, X ), :=( T, Y
% 1.87/2.28 )] ), substitution( 1, [ :=( X, X )] )).
% 1.87/2.28
% 1.87/2.28
% 1.87/2.28 subsumption(
% 1.87/2.28 clause( 22, [ ~( product( identity, X, Y ) ), =( X, Y ) ] )
% 1.87/2.28 , clause( 12843, [ ~( product( identity, X, Y ) ), =( X, Y ) ] )
% 1.87/2.28 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.87/2.28 ), ==>( 1, 1 )] ) ).
% 1.87/2.28
% 1.87/2.28
% 1.87/2.28 resolution(
% 1.87/2.28 clause( 12845, [ ~( product( X, identity, Y )Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------