%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : GRP175-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n017.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 07:35:47 EDT 2022
% Result : Unsatisfiable 0.72s 1.18s
% Output : Refutation 0.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP175-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Mon Jun 13 11:01:37 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.72/1.18 *** allocated 10000 integers for termspace/termends
% 0.72/1.18 *** allocated 10000 integers for clauses
% 0.72/1.18 *** allocated 10000 integers for justifications
% 0.72/1.18 Bliksem 1.12
% 0.72/1.18
% 0.72/1.18
% 0.72/1.18 Automatic Strategy Selection
% 0.72/1.18
% 0.72/1.18 Clauses:
% 0.72/1.18 [
% 0.72/1.18 [ =( multiply( identity, X ), X ) ],
% 0.72/1.18 [ =( multiply( inverse( X ), X ), identity ) ],
% 0.72/1.18 [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply( Y, Z ) ) )
% 0.72/1.18 ],
% 0.72/1.18 [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y, X ) ) ]
% 0.72/1.18 ,
% 0.72/1.18 [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) ) ],
% 0.72/1.18 [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y, Z ) ),
% 0.72/1.18 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ],
% 0.72/1.18 [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) ),
% 0.72/1.18 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ],
% 0.72/1.18 [ =( 'least_upper_bound'( X, X ), X ) ],
% 0.72/1.18 [ =( 'greatest_lower_bound'( X, X ), X ) ],
% 0.72/1.18 [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) ), X ) ]
% 0.72/1.18 ,
% 0.72/1.18 [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) ), X ) ]
% 0.72/1.18 ,
% 0.72/1.18 [ =( multiply( X, 'least_upper_bound'( Y, Z ) ), 'least_upper_bound'(
% 0.72/1.18 multiply( X, Y ), multiply( X, Z ) ) ) ],
% 0.72/1.18 [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ),
% 0.72/1.18 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ],
% 0.72/1.18 [ =( multiply( 'least_upper_bound'( X, Y ), Z ), 'least_upper_bound'(
% 0.72/1.18 multiply( X, Z ), multiply( Y, Z ) ) ) ],
% 0.72/1.18 [ =( multiply( 'greatest_lower_bound'( X, Y ), Z ),
% 0.72/1.18 'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ],
% 0.72/1.18 [ =( 'least_upper_bound'( identity, b ), b ) ],
% 0.72/1.18 [ ~( =( 'least_upper_bound'( identity, multiply( inverse( a ), multiply(
% 0.72/1.18 b, a ) ) ), multiply( inverse( a ), multiply( b, a ) ) ) ) ]
% 0.72/1.18 ] .
% 0.72/1.18
% 0.72/1.18
% 0.72/1.18 percentage equality = 1.000000, percentage horn = 1.000000
% 0.72/1.18 This is a pure equality problem
% 0.72/1.18
% 0.72/1.18
% 0.72/1.18
% 0.72/1.18 Options Used:
% 0.72/1.18
% 0.72/1.18 useres = 1
% 0.72/1.18 useparamod = 1
% 0.72/1.18 useeqrefl = 1
% 0.72/1.18 useeqfact = 1
% 0.72/1.18 usefactor = 1
% 0.72/1.18 usesimpsplitting = 0
% 0.72/1.18 usesimpdemod = 5
% 0.72/1.18 usesimpres = 3
% 0.72/1.18
% 0.72/1.18 resimpinuse = 1000
% 0.72/1.18 resimpclauses = 20000
% 0.72/1.18 substype = eqrewr
% 0.72/1.18 backwardsubs = 1
% 0.72/1.18 selectoldest = 5
% 0.72/1.18
% 0.72/1.18 litorderings [0] = split
% 0.72/1.18 litorderings [1] = extend the termordering, first sorting on arguments
% 0.72/1.18
% 0.72/1.18 termordering = kbo
% 0.72/1.18
% 0.72/1.18 litapriori = 0
% 0.72/1.18 termapriori = 1
% 0.72/1.18 litaposteriori = 0
% 0.72/1.18 termaposteriori = 0
% 0.72/1.18 demodaposteriori = 0
% 0.72/1.18 ordereqreflfact = 0
% 0.72/1.18
% 0.72/1.18 litselect = negord
% 0.72/1.18
% 0.72/1.18 maxweight = 15
% 0.72/1.18 maxdepth = 30000
% 0.72/1.18 maxlength = 115
% 0.72/1.18 maxnrvars = 195
% 0.72/1.18 excuselevel = 1
% 0.72/1.18 increasemaxweight = 1
% 0.72/1.18
% 0.72/1.18 maxselected = 10000000
% 0.72/1.18 maxnrclauses = 10000000
% 0.72/1.18
% 0.72/1.18 showgenerated = 0
% 0.72/1.18 showkept = 0
% 0.72/1.18 showselected = 0
% 0.72/1.18 showdeleted = 0
% 0.72/1.18 showresimp = 1
% 0.72/1.18 showstatus = 2000
% 0.72/1.18
% 0.72/1.18 prologoutput = 1
% 0.72/1.18 nrgoals = 5000000
% 0.72/1.18 totalproof = 1
% 0.72/1.18
% 0.72/1.18 Symbols occurring in the translation:
% 0.72/1.18
% 0.72/1.18 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.72/1.18 . [1, 2] (w:1, o:21, a:1, s:1, b:0),
% 0.72/1.18 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 0.72/1.18 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.72/1.18 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.72/1.18 identity [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.72/1.18 multiply [41, 2] (w:1, o:47, a:1, s:1, b:0),
% 0.72/1.18 inverse [42, 1] (w:1, o:20, a:1, s:1, b:0),
% 0.72/1.18 'greatest_lower_bound' [45, 2] (w:1, o:48, a:1, s:1, b:0),
% 0.72/1.18 'least_upper_bound' [46, 2] (w:1, o:46, a:1, s:1, b:0),
% 0.72/1.18 b [47, 0] (w:1, o:14, a:1, s:1, b:0),
% 0.72/1.18 a [48, 0] (w:1, o:13, a:1, s:1, b:0).
% 0.72/1.18
% 0.72/1.18
% 0.72/1.18 Starting Search:
% 0.72/1.18
% 0.72/1.18 Resimplifying inuse:
% 0.72/1.18 Done
% 0.72/1.18
% 0.72/1.18
% 0.72/1.18 Intermediate Status:
% 0.72/1.18 Generated: 26708
% 0.72/1.18 Kept: 2013
% 0.72/1.18 Inuse: 249
% 0.72/1.18 Deleted: 18
% 0.72/1.18 Deletedinuse: 6
% 0.72/1.18
% 0.72/1.18 Resimplifying inuse:
% 0.72/1.18
% 0.72/1.18 Bliksems!, er is een bewijs:
% 0.72/1.18 % SZS status Unsatisfiable
% 0.72/1.18 % SZS output start Refutation
% 0.72/1.18
% 0.72/1.18 clause( 0, [ =( multiply( identity, X ), X ) ] )
% 0.72/1.18 .
% 0.72/1.18 clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.72/1.18 .
% 0.72/1.18 clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y )
% 0.72/1.18 , Z ) ) ] )
% 0.72/1.18 .
% 0.72/1.18 clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y,
% 0.72/1.18 X ) ) ] )
% 0.72/1.18 .
% 0.72/1.18 clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) )
% 0.72/1.18 ] )
% 0.72/1.18 .
% 0.72/1.18 clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) ), X
% 0.72/1.18 ) ] )
% 0.72/1.18 .
% 0.72/1.18 clause( 10, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) ),
% 0.72/1.18 X ) ] )
% 0.72/1.18 .
% 0.72/1.18 clause( 12, [ =( 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z )
% 0.72/1.18 ), multiply( X, 'greatest_lower_bound'( Y, Z ) ) ) ] )
% 0.72/1.18 .
% 0.72/1.18 clause( 13, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z ) )
% 0.72/1.18 , multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 0.72/1.18 .
% 0.72/1.18 clause( 15, [ =( 'least_upper_bound'( identity, b ), b ) ] )
% 0.72/1.18 .
% 0.72/1.18 clause( 16, [ ~( =( 'least_upper_bound'( identity, multiply( multiply(
% 0.72/1.18 inverse( a ), b ), a ) ), multiply( multiply( inverse( a ), b ), a ) ) )
% 0.72/1.18 ] )
% 0.72/1.18 .
% 0.72/1.18 clause( 18, [ =( multiply( multiply( Y, inverse( X ) ), X ), multiply( Y,
% 0.72/1.18 identity ) ) ] )
% 0.72/1.18 .
% 0.72/1.18 clause( 19, [ =( multiply( multiply( Y, identity ), X ), multiply( Y, X ) )
% 0.72/1.18 ] )
% 0.72/1.18 .
% 0.72/1.18 clause( 23, [ =( 'greatest_lower_bound'( identity, b ), identity ) ] )
% 0.72/1.18 .
% 0.72/1.18 clause( 52, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X ) ),
% 0.72/1.18 X ) ] )
% 0.72/1.18 .
% 0.72/1.18 clause( 56, [ =( 'least_upper_bound'( 'greatest_lower_bound'( Y, X ), X ),
% 0.72/1.18 X ) ] )
% 0.72/1.18 .
% 0.72/1.18 clause( 93, [ =( multiply( 'least_upper_bound'( inverse( X ), Y ), X ),
% 0.72/1.18 'least_upper_bound'( identity, multiply( Y, X ) ) ) ] )
% 0.72/1.18 .
% 0.72/1.18 clause( 159, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 0.72/1.18 .
% 0.72/1.18 clause( 164, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y )
% 0.72/1.18 ) ] )
% 0.72/1.18 .
% 0.72/1.18 clause( 165, [ =( 'greatest_lower_bound'( X, multiply( X, Y ) ), multiply(
% 0.72/1.18 X, 'greatest_lower_bound'( identity, Y ) ) ) ] )
% 0.72/1.18 .
% 0.72/1.18 clause( 280, [ =( multiply( X, identity ), X ) ] )
% 0.72/1.18 .
% 0.72/1.18 clause( 778, [ =( 'greatest_lower_bound'( X, multiply( X, b ) ), X ) ] )
% 0.72/1.18 .
% 0.72/1.18 clause( 817, [ =( 'least_upper_bound'( X, multiply( X, b ) ), multiply( X,
% 0.72/1.18 b ) ) ] )
% 0.72/1.18 .
% 0.72/1.18 clause( 1933, [ =( 'least_upper_bound'( identity, multiply( multiply(
% 0.72/1.18 inverse( X ), b ), X ) ), multiply( multiply( inverse( X ), b ), X ) ) ]
% 0.72/1.18 )
% 0.72/1.18 .
% 0.72/1.18 clause( 2013, [] )
% 0.72/1.18 .
% 0.72/1.18
% 0.72/1.18
% 0.72/1.18 % SZS output end Refutation
% 0.72/1.18 found a proof!
% 0.72/1.18
% 0.72/1.18 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.72/1.18
% 0.72/1.18 initialclauses(
% 0.72/1.18 [ clause( 2015, [ =( multiply( identity, X ), X ) ] )
% 0.72/1.18 , clause( 2016, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.72/1.18 , clause( 2017, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 0.72/1.18 Y, Z ) ) ) ] )
% 0.72/1.18 , clause( 2018, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'(
% 0.72/1.18 Y, X ) ) ] )
% 0.72/1.18 , clause( 2019, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X
% 0.72/1.18 ) ) ] )
% 0.72/1.18 , clause( 2020, [ =( 'greatest_lower_bound'( X, 'greatest_lower_bound'( Y,
% 0.72/1.18 Z ) ), 'greatest_lower_bound'( 'greatest_lower_bound'( X, Y ), Z ) ) ] )
% 0.72/1.18 , clause( 2021, [ =( 'least_upper_bound'( X, 'least_upper_bound'( Y, Z ) )
% 0.72/1.18 , 'least_upper_bound'( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 0.72/1.18 , clause( 2022, [ =( 'least_upper_bound'( X, X ), X ) ] )
% 0.72/1.18 , clause( 2023, [ =( 'greatest_lower_bound'( X, X ), X ) ] )
% 0.72/1.18 , clause( 2024, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y )
% 0.72/1.18 ), X ) ] )
% 0.72/1.18 , clause( 2025, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y )
% 0.72/1.18 ), X ) ] )
% 0.72/1.18 , clause( 2026, [ =( multiply( X, 'least_upper_bound'( Y, Z ) ),
% 0.72/1.18 'least_upper_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 0.72/1.18 , clause( 2027, [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ),
% 0.72/1.18 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 0.72/1.18 , clause( 2028, [ =( multiply( 'least_upper_bound'( X, Y ), Z ),
% 0.72/1.18 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ] )
% 0.72/1.18 , clause( 2029, [ =( multiply( 'greatest_lower_bound'( X, Y ), Z ),
% 0.72/1.18 'greatest_lower_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ] )
% 0.72/1.18 , clause( 2030, [ =( 'least_upper_bound'( identity, b ), b ) ] )
% 0.72/1.18 , clause( 2031, [ ~( =( 'least_upper_bound'( identity, multiply( inverse( a
% 0.72/1.18 ), multiply( b, a ) ) ), multiply( inverse( a ), multiply( b, a ) ) ) )
% 0.72/1.18 ] )
% 0.72/1.18 ] ).
% 0.72/1.18
% 0.72/1.18
% 0.72/1.18
% 0.72/1.18 subsumption(
% 0.72/1.18 clause( 0, [ =( multiply( identity, X ), X ) ] )
% 0.72/1.18 , clause( 2015, [ =( multiply( identity, X ), X ) ] )
% 0.72/1.18 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.72/1.18
% 0.72/1.18
% 0.72/1.18 subsumption(
% 0.72/1.18 clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.72/1.18 , clause( 2016, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.72/1.18 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.72/1.18
% 0.72/1.18
% 0.72/1.18 eqswap(
% 0.72/1.18 clause( 2037, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X,
% 0.72/1.18 Y ), Z ) ) ] )
% 0.72/1.18 , clause( 2017, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 0.72/1.18 Y, Z ) ) ) ] )
% 0.72/1.18 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.72/1.18
% 0.72/1.18
% 0.72/1.18 subsumption(
% 0.72/1.18 clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y )
% 0.72/1.18 , Z ) ) ] )
% 0.72/1.18 , clause( 2037, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X
% 0.72/1.18 , Y ), Z ) ) ] )
% 0.72/1.18 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.72/1.18 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.72/1.18
% 0.72/1.18
% 0.72/1.18 subsumption(
% 0.72/1.18 clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y,
% 0.72/1.18 X ) ) ] )
% 0.72/1.18 , clause( 2018, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'(
% 0.72/1.18 Y, X ) ) ] )
% 0.72/1.18 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.72/1.18 )] ) ).
% 0.72/1.18
% 0.72/1.18
% 0.72/1.18 subsumption(
% 0.72/1.18 clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X ) )
% 0.72/1.18 ] )
% 0.72/1.18 , clause( 2019, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X
% 0.72/1.18 ) ) ] )
% 0.72/1.18 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.72/1.18 )] ) ).
% 0.72/1.18
% 0.72/1.18
% 0.72/1.18 subsumption(
% 0.72/1.18 clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) ), X
% 0.72/1.18 ) ] )
% 0.72/1.18 , clause( 2024, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y )
% 0.72/1.18 ), X ) ] )
% 0.72/1.18 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.72/1.18 )] ) ).
% 0.72/1.18
% 0.72/1.18
% 0.72/1.18 subsumption(
% 0.72/1.18 clause( 10, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) ),
% 0.72/1.18 X ) ] )
% 0.72/1.18 , clause( 2025, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y )
% 0.72/1.18 ), X ) ] )
% 0.72/1.18 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.72/1.18 )] ) ).
% 0.72/1.18
% 0.72/1.18
% 0.72/1.18 eqswap(
% 0.72/1.18 clause( 2071, [ =( 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z
% 0.72/1.18 ) ), multiply( X, 'greatest_lower_bound'( Y, Z ) ) ) ] )
% 0.72/1.18 , clause( 2027, [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ),
% 0.72/1.18 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 0.72/1.18 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.72/1.18
% 0.72/1.18
% 0.72/1.18 subsumption(
% 0.72/1.18 clause( 12, [ =( 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z )
% 0.72/1.18 ), multiply( X, 'greatest_lower_bound'( Y, Z ) ) ) ] )
% 0.72/1.18 , clause( 2071, [ =( 'greatest_lower_bound'( multiply( X, Y ), multiply( X
% 0.72/1.18 , Z ) ), multiply( X, 'greatest_lower_bound'( Y, Z ) ) ) ] )
% 0.72/1.18 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.72/1.18 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.72/1.18
% 0.72/1.18
% 0.72/1.18 eqswap(
% 0.72/1.18 clause( 2083, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z )
% 0.72/1.18 ), multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 0.72/1.18 , clause( 2028, [ =( multiply( 'least_upper_bound'( X, Y ), Z ),
% 0.72/1.18 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z ) ) ) ] )
% 0.72/1.18 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.72/1.18
% 0.72/1.18
% 0.72/1.18 subsumption(
% 0.72/1.18 clause( 13, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z ) )
% 0.72/1.18 , multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 0.72/1.18 , clause( 2083, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z
% 0.72/1.18 ) ), multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 0.72/1.18 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.72/1.18 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.72/1.18
% 0.72/1.18
% 0.72/1.18 subsumption(
% 0.72/1.18 clause( 15, [ =( 'least_upper_bound'( identity, b ), b ) ] )
% 0.72/1.18 , clause( 2030, [ =( 'least_upper_bound'( identity, b ), b ) ] )
% 0.72/1.18 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.72/1.18
% 0.72/1.18
% 0.72/1.18 paramod(
% 0.72/1.18 clause( 2133, [ ~( =( 'least_upper_bound'( identity, multiply( inverse( a )
% 0.72/1.18 , multiply( b, a ) ) ), multiply( multiply( inverse( a ), b ), a ) ) ) ]
% 0.72/1.18 )
% 0.72/1.18 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 0.72/1.18 ), Z ) ) ] )
% 0.72/1.18 , 0, clause( 2031, [ ~( =( 'least_upper_bound'( identity, multiply( inverse(
% 0.72/1.18 a ), multiply( b, a ) ) ), multiply( inverse( a ), multiply( b, a ) ) ) )
% 0.72/1.18 ] )
% 0.72/1.18 , 0, 10, substitution( 0, [ :=( X, inverse( a ) ), :=( Y, b ), :=( Z, a )] )
% 0.72/1.18 , substitution( 1, [] )).
% 0.72/1.18
% 0.72/1.18
% 0.72/1.18 paramod(
% 0.72/1.18 clause( 2134, [ ~( =( 'least_upper_bound'( identity, multiply( multiply(
% 0.72/1.18 inverse( a ), b ), a ) ), multiply( multiply( inverse( a ), b ), a ) ) )
% 0.72/1.18 ] )
% 0.72/1.18 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 0.84/1.18 ), Z ) ) ] )
% 0.84/1.18 , 0, clause( 2133, [ ~( =( 'least_upper_bound'( identity, multiply( inverse(
% 0.84/1.18 a ), multiply( b, a ) ) ), multiply( multiply( inverse( a ), b ), a ) ) )
% 0.84/1.18 ] )
% 0.84/1.18 , 0, 4, substitution( 0, [ :=( X, inverse( a ) ), :=( Y, b ), :=( Z, a )] )
% 0.84/1.18 , substitution( 1, [] )).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 subsumption(
% 0.84/1.18 clause( 16, [ ~( =( 'least_upper_bound'( identity, multiply( multiply(
% 0.84/1.18 inverse( a ), b ), a ) ), multiply( multiply( inverse( a ), b ), a ) ) )
% 0.84/1.18 ] )
% 0.84/1.18 , clause( 2134, [ ~( =( 'least_upper_bound'( identity, multiply( multiply(
% 0.84/1.18 inverse( a ), b ), a ) ), multiply( multiply( inverse( a ), b ), a ) ) )
% 0.84/1.18 ] )
% 0.84/1.18 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 eqswap(
% 0.84/1.18 clause( 2139, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 0.84/1.18 Y, Z ) ) ) ] )
% 0.84/1.18 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 0.84/1.18 ), Z ) ) ] )
% 0.84/1.18 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 paramod(
% 0.84/1.18 clause( 2144, [ =( multiply( multiply( X, inverse( Y ) ), Y ), multiply( X
% 0.84/1.18 , identity ) ) ] )
% 0.84/1.18 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.84/1.18 , 0, clause( 2139, [ =( multiply( multiply( X, Y ), Z ), multiply( X,
% 0.84/1.18 multiply( Y, Z ) ) ) ] )
% 0.84/1.18 , 0, 9, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 0.84/1.18 :=( Y, inverse( Y ) ), :=( Z, Y )] )).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 subsumption(
% 0.84/1.18 clause( 18, [ =( multiply( multiply( Y, inverse( X ) ), X ), multiply( Y,
% 0.84/1.18 identity ) ) ] )
% 0.84/1.18 , clause( 2144, [ =( multiply( multiply( X, inverse( Y ) ), Y ), multiply(
% 0.84/1.18 X, identity ) ) ] )
% 0.84/1.18 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 0.84/1.18 )] ) ).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 eqswap(
% 0.84/1.18 clause( 2149, [ =( multiply( multiply( X, Y ), Z ), multiply( X, multiply(
% 0.84/1.18 Y, Z ) ) ) ] )
% 0.84/1.18 , clause( 2, [ =( multiply( X, multiply( Y, Z ) ), multiply( multiply( X, Y
% 0.84/1.18 ), Z ) ) ] )
% 0.84/1.18 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 paramod(
% 0.84/1.18 clause( 2154, [ =( multiply( multiply( X, identity ), Y ), multiply( X, Y )
% 0.84/1.18 ) ] )
% 0.84/1.18 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 0.84/1.18 , 0, clause( 2149, [ =( multiply( multiply( X, Y ), Z ), multiply( X,
% 0.84/1.18 multiply( Y, Z ) ) ) ] )
% 0.84/1.18 , 0, 8, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, X ),
% 0.84/1.18 :=( Y, identity ), :=( Z, Y )] )).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 subsumption(
% 0.84/1.18 clause( 19, [ =( multiply( multiply( Y, identity ), X ), multiply( Y, X ) )
% 0.84/1.18 ] )
% 0.84/1.18 , clause( 2154, [ =( multiply( multiply( X, identity ), Y ), multiply( X, Y
% 0.84/1.18 ) ) ] )
% 0.84/1.18 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 0.84/1.18 )] ) ).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 eqswap(
% 0.84/1.18 clause( 2160, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y
% 0.84/1.18 ) ) ) ] )
% 0.84/1.18 , clause( 10, [ =( 'greatest_lower_bound'( X, 'least_upper_bound'( X, Y ) )
% 0.84/1.18 , X ) ] )
% 0.84/1.18 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 paramod(
% 0.84/1.18 clause( 2161, [ =( identity, 'greatest_lower_bound'( identity, b ) ) ] )
% 0.84/1.18 , clause( 15, [ =( 'least_upper_bound'( identity, b ), b ) ] )
% 0.84/1.18 , 0, clause( 2160, [ =( X, 'greatest_lower_bound'( X, 'least_upper_bound'(
% 0.84/1.18 X, Y ) ) ) ] )
% 0.84/1.18 , 0, 4, substitution( 0, [] ), substitution( 1, [ :=( X, identity ), :=( Y
% 0.84/1.18 , b )] )).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 eqswap(
% 0.84/1.18 clause( 2162, [ =( 'greatest_lower_bound'( identity, b ), identity ) ] )
% 0.84/1.18 , clause( 2161, [ =( identity, 'greatest_lower_bound'( identity, b ) ) ] )
% 0.84/1.18 , 0, substitution( 0, [] )).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 subsumption(
% 0.84/1.18 clause( 23, [ =( 'greatest_lower_bound'( identity, b ), identity ) ] )
% 0.84/1.18 , clause( 2162, [ =( 'greatest_lower_bound'( identity, b ), identity ) ] )
% 0.84/1.18 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 eqswap(
% 0.84/1.18 clause( 2163, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y
% 0.84/1.18 ) ) ) ] )
% 0.84/1.18 , clause( 9, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( X, Y ) )
% 0.84/1.18 , X ) ] )
% 0.84/1.18 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 paramod(
% 0.84/1.18 clause( 2164, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X
% 0.84/1.18 ) ) ) ] )
% 0.84/1.18 , clause( 3, [ =( 'greatest_lower_bound'( X, Y ), 'greatest_lower_bound'( Y
% 0.84/1.18 , X ) ) ] )
% 0.84/1.18 , 0, clause( 2163, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'(
% 0.84/1.18 X, Y ) ) ) ] )
% 0.84/1.18 , 0, 4, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 0.84/1.18 :=( X, X ), :=( Y, Y )] )).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 eqswap(
% 0.84/1.18 clause( 2167, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X ) )
% 0.84/1.18 , X ) ] )
% 0.84/1.18 , clause( 2164, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( Y,
% 0.84/1.18 X ) ) ) ] )
% 0.84/1.18 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 subsumption(
% 0.84/1.18 clause( 52, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X ) ),
% 0.84/1.18 X ) ] )
% 0.84/1.18 , clause( 2167, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X )
% 0.84/1.18 ), X ) ] )
% 0.84/1.18 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.84/1.18 )] ) ).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 eqswap(
% 0.84/1.18 clause( 2168, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X
% 0.84/1.18 ) ) ) ] )
% 0.84/1.18 , clause( 52, [ =( 'least_upper_bound'( X, 'greatest_lower_bound'( Y, X ) )
% 0.84/1.18 , X ) ] )
% 0.84/1.18 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 paramod(
% 0.84/1.18 clause( 2169, [ =( X, 'least_upper_bound'( 'greatest_lower_bound'( Y, X ),
% 0.84/1.18 X ) ) ] )
% 0.84/1.18 , clause( 4, [ =( 'least_upper_bound'( X, Y ), 'least_upper_bound'( Y, X )
% 0.84/1.18 ) ] )
% 0.84/1.18 , 0, clause( 2168, [ =( X, 'least_upper_bound'( X, 'greatest_lower_bound'(
% 0.84/1.18 Y, X ) ) ) ] )
% 0.84/1.18 , 0, 2, substitution( 0, [ :=( X, X ), :=( Y, 'greatest_lower_bound'( Y, X
% 0.84/1.18 ) )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 eqswap(
% 0.84/1.18 clause( 2172, [ =( 'least_upper_bound'( 'greatest_lower_bound'( Y, X ), X )
% 0.84/1.18 , X ) ] )
% 0.84/1.18 , clause( 2169, [ =( X, 'least_upper_bound'( 'greatest_lower_bound'( Y, X )
% 0.84/1.18 , X ) ) ] )
% 0.84/1.18 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 subsumption(
% 0.84/1.18 clause( 56, [ =( 'least_upper_bound'( 'greatest_lower_bound'( Y, X ), X ),
% 0.84/1.18 X ) ] )
% 0.84/1.18 , clause( 2172, [ =( 'least_upper_bound'( 'greatest_lower_bound'( Y, X ), X
% 0.84/1.18 ), X ) ] )
% 0.84/1.18 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.84/1.18 )] ) ).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 eqswap(
% 0.84/1.18 clause( 2174, [ =( multiply( 'least_upper_bound'( X, Z ), Y ),
% 0.84/1.18 'least_upper_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 0.84/1.18 , clause( 13, [ =( 'least_upper_bound'( multiply( X, Z ), multiply( Y, Z )
% 0.84/1.18 ), multiply( 'least_upper_bound'( X, Y ), Z ) ) ] )
% 0.84/1.18 , 0, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] )).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 paramod(
% 0.84/1.18 clause( 2175, [ =( multiply( 'least_upper_bound'( inverse( X ), Y ), X ),
% 0.84/1.18 'least_upper_bound'( identity, multiply( Y, X ) ) ) ] )
% 0.84/1.18 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.84/1.18 , 0, clause( 2174, [ =( multiply( 'least_upper_bound'( X, Z ), Y ),
% 0.84/1.18 'least_upper_bound'( multiply( X, Y ), multiply( Z, Y ) ) ) ] )
% 0.84/1.18 , 0, 8, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, inverse(
% 0.84/1.18 X ) ), :=( Y, X ), :=( Z, Y )] )).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 subsumption(
% 0.84/1.18 clause( 93, [ =( multiply( 'least_upper_bound'( inverse( X ), Y ), X ),
% 0.84/1.18 'least_upper_bound'( identity, multiply( Y, X ) ) ) ] )
% 0.84/1.18 , clause( 2175, [ =( multiply( 'least_upper_bound'( inverse( X ), Y ), X )
% 0.84/1.18 , 'least_upper_bound'( identity, multiply( Y, X ) ) ) ] )
% 0.84/1.18 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.84/1.18 )] ) ).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 eqswap(
% 0.84/1.18 clause( 2180, [ =( multiply( X, identity ), multiply( multiply( X, inverse(
% 0.84/1.18 Y ) ), Y ) ) ] )
% 0.84/1.18 , clause( 18, [ =( multiply( multiply( Y, inverse( X ) ), X ), multiply( Y
% 0.84/1.18 , identity ) ) ] )
% 0.84/1.18 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 paramod(
% 0.84/1.18 clause( 2183, [ =( multiply( inverse( inverse( X ) ), identity ), multiply(
% 0.84/1.18 identity, X ) ) ] )
% 0.84/1.18 , clause( 1, [ =( multiply( inverse( X ), X ), identity ) ] )
% 0.84/1.18 , 0, clause( 2180, [ =( multiply( X, identity ), multiply( multiply( X,
% 0.84/1.18 inverse( Y ) ), Y ) ) ] )
% 0.84/1.18 , 0, 7, substitution( 0, [ :=( X, inverse( X ) )] ), substitution( 1, [
% 0.84/1.18 :=( X, inverse( inverse( X ) ) ), :=( Y, X )] )).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 paramod(
% 0.84/1.18 clause( 2184, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 0.84/1.18 , clause( 0, [ =( multiply( identity, X ), X ) ] )
% 0.84/1.18 , 0, clause( 2183, [ =( multiply( inverse( inverse( X ) ), identity ),
% 0.84/1.18 multiply( identity, X ) ) ] )
% 0.84/1.18 , 0, 6, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 0.84/1.18 ).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 subsumption(
% 0.84/1.18 clause( 159, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 0.84/1.18 , clause( 2184, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ]
% 0.84/1.18 )
% 0.84/1.18 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 eqswap(
% 0.84/1.18 clause( 2187, [ =( multiply( X, Y ), multiply( multiply( X, identity ), Y )
% 0.84/1.18 ) ] )
% 0.84/1.18 , clause( 19, [ =( multiply( multiply( Y, identity ), X ), multiply( Y, X )
% 0.84/1.18 ) ] )
% 0.84/1.18 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 paramod(
% 0.84/1.18 clause( 2190, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y )
% 0.84/1.18 ) ] )
% 0.84/1.18 , clause( 159, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 0.84/1.18 , 0, clause( 2187, [ =( multiply( X, Y ), multiply( multiply( X, identity )
% 0.84/1.18 , Y ) ) ] )
% 0.84/1.18 , 0, 7, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, inverse(
% 0.84/1.18 inverse( X ) ) ), :=( Y, Y )] )).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 subsumption(
% 0.84/1.18 clause( 164, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y )
% 0.84/1.18 ) ] )
% 0.84/1.18 , clause( 2190, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 0.84/1.18 ) ) ] )
% 0.84/1.18 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.84/1.18 )] ) ).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 eqswap(
% 0.84/1.18 clause( 2197, [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ),
% 0.84/1.18 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 0.84/1.18 , clause( 12, [ =( 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z
% 0.84/1.18 ) ), multiply( X, 'greatest_lower_bound'( Y, Z ) ) ) ] )
% 0.84/1.18 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 paramod(
% 0.84/1.18 clause( 2200, [ =( multiply( inverse( inverse( X ) ),
% 0.84/1.18 'greatest_lower_bound'( identity, Y ) ), 'greatest_lower_bound'( X,
% 0.84/1.18 multiply( inverse( inverse( X ) ), Y ) ) ) ] )
% 0.84/1.18 , clause( 159, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 0.84/1.18 , 0, clause( 2197, [ =( multiply( X, 'greatest_lower_bound'( Y, Z ) ),
% 0.84/1.18 'greatest_lower_bound'( multiply( X, Y ), multiply( X, Z ) ) ) ] )
% 0.84/1.18 , 0, 9, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, inverse(
% 0.84/1.18 inverse( X ) ) ), :=( Y, identity ), :=( Z, Y )] )).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 paramod(
% 0.84/1.18 clause( 2210, [ =( multiply( inverse( inverse( X ) ),
% 0.84/1.18 'greatest_lower_bound'( identity, Y ) ), 'greatest_lower_bound'( X,
% 0.84/1.18 multiply( X, Y ) ) ) ] )
% 0.84/1.18 , clause( 164, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 0.84/1.18 ) ) ] )
% 0.84/1.18 , 0, clause( 2200, [ =( multiply( inverse( inverse( X ) ),
% 0.84/1.18 'greatest_lower_bound'( identity, Y ) ), 'greatest_lower_bound'( X,
% 0.84/1.18 multiply( inverse( inverse( X ) ), Y ) ) ) ] )
% 0.84/1.18 , 0, 10, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 0.84/1.18 :=( X, X ), :=( Y, Y )] )).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 paramod(
% 0.84/1.18 clause( 2212, [ =( multiply( X, 'greatest_lower_bound'( identity, Y ) ),
% 0.84/1.18 'greatest_lower_bound'( X, multiply( X, Y ) ) ) ] )
% 0.84/1.18 , clause( 164, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 0.84/1.18 ) ) ] )
% 0.84/1.18 , 0, clause( 2210, [ =( multiply( inverse( inverse( X ) ),
% 0.84/1.18 'greatest_lower_bound'( identity, Y ) ), 'greatest_lower_bound'( X,
% 0.84/1.18 multiply( X, Y ) ) ) ] )
% 0.84/1.18 , 0, 1, substitution( 0, [ :=( X, X ), :=( Y, 'greatest_lower_bound'(
% 0.84/1.18 identity, Y ) )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 eqswap(
% 0.84/1.18 clause( 2213, [ =( 'greatest_lower_bound'( X, multiply( X, Y ) ), multiply(
% 0.84/1.18 X, 'greatest_lower_bound'( identity, Y ) ) ) ] )
% 0.84/1.18 , clause( 2212, [ =( multiply( X, 'greatest_lower_bound'( identity, Y ) ),
% 0.84/1.18 'greatest_lower_bound'( X, multiply( X, Y ) ) ) ] )
% 0.84/1.18 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 subsumption(
% 0.84/1.18 clause( 165, [ =( 'greatest_lower_bound'( X, multiply( X, Y ) ), multiply(
% 0.84/1.18 X, 'greatest_lower_bound'( identity, Y ) ) ) ] )
% 0.84/1.18 , clause( 2213, [ =( 'greatest_lower_bound'( X, multiply( X, Y ) ),
% 0.84/1.18 multiply( X, 'greatest_lower_bound'( identity, Y ) ) ) ] )
% 0.84/1.18 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.84/1.18 )] ) ).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 eqswap(
% 0.84/1.18 clause( 2214, [ =( multiply( X, Y ), multiply( inverse( inverse( X ) ), Y )
% 0.84/1.18 ) ] )
% 0.84/1.18 , clause( 164, [ =( multiply( inverse( inverse( X ) ), Y ), multiply( X, Y
% 0.84/1.18 ) ) ] )
% 0.84/1.18 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 paramod(
% 0.84/1.18 clause( 2217, [ =( multiply( X, identity ), X ) ] )
% 0.84/1.18 , clause( 159, [ =( multiply( inverse( inverse( X ) ), identity ), X ) ] )
% 0.84/1.18 , 0, clause( 2214, [ =( multiply( X, Y ), multiply( inverse( inverse( X ) )
% 0.84/1.18 , Y ) ) ] )
% 0.84/1.18 , 0, 4, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 0.84/1.18 :=( Y, identity )] )).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 subsumption(
% 0.84/1.18 clause( 280, [ =( multiply( X, identity ), X ) ] )
% 0.84/1.18 , clause( 2217, [ =( multiply( X, identity ), X ) ] )
% 0.84/1.18 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 eqswap(
% 0.84/1.18 clause( 2223, [ =( multiply( X, 'greatest_lower_bound'( identity, Y ) ),
% 0.84/1.18 'greatest_lower_bound'( X, multiply( X, Y ) ) ) ] )
% 0.84/1.18 , clause( 165, [ =( 'greatest_lower_bound'( X, multiply( X, Y ) ), multiply(
% 0.84/1.18 X, 'greatest_lower_bound'( identity, Y ) ) ) ] )
% 0.84/1.18 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 paramod(
% 0.84/1.18 clause( 2225, [ =( multiply( X, identity ), 'greatest_lower_bound'( X,
% 0.84/1.18 multiply( X, b ) ) ) ] )
% 0.84/1.18 , clause( 23, [ =( 'greatest_lower_bound'( identity, b ), identity ) ] )
% 0.84/1.18 , 0, clause( 2223, [ =( multiply( X, 'greatest_lower_bound'( identity, Y )
% 0.84/1.18 ), 'greatest_lower_bound'( X, multiply( X, Y ) ) ) ] )
% 0.84/1.18 , 0, 3, substitution( 0, [] ), substitution( 1, [ :=( X, X ), :=( Y, b )] )
% 0.84/1.18 ).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 paramod(
% 0.84/1.18 clause( 2226, [ =( X, 'greatest_lower_bound'( X, multiply( X, b ) ) ) ] )
% 0.84/1.18 , clause( 280, [ =( multiply( X, identity ), X ) ] )
% 0.84/1.18 , 0, clause( 2225, [ =( multiply( X, identity ), 'greatest_lower_bound'( X
% 0.84/1.18 , multiply( X, b ) ) ) ] )
% 0.84/1.18 , 0, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 0.84/1.18 ).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 eqswap(
% 0.84/1.18 clause( 2227, [ =( 'greatest_lower_bound'( X, multiply( X, b ) ), X ) ] )
% 0.84/1.18 , clause( 2226, [ =( X, 'greatest_lower_bound'( X, multiply( X, b ) ) ) ]
% 0.84/1.18 )
% 0.84/1.18 , 0, substitution( 0, [ :=( X, X )] )).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 subsumption(
% 0.84/1.18 clause( 778, [ =( 'greatest_lower_bound'( X, multiply( X, b ) ), X ) ] )
% 0.84/1.18 , clause( 2227, [ =( 'greatest_lower_bound'( X, multiply( X, b ) ), X ) ]
% 0.84/1.18 )
% 0.84/1.18 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 eqswap(
% 0.84/1.18 clause( 2229, [ =( Y, 'least_upper_bound'( 'greatest_lower_bound'( X, Y ),
% 0.84/1.18 Y ) ) ] )
% 0.84/1.18 , clause( 56, [ =( 'least_upper_bound'( 'greatest_lower_bound'( Y, X ), X )
% 0.84/1.18 , X ) ] )
% 0.84/1.18 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 paramod(
% 0.84/1.18 clause( 2230, [ =( multiply( X, b ), 'least_upper_bound'( X, multiply( X, b
% 0.84/1.18 ) ) ) ] )
% 0.84/1.18 , clause( 778, [ =( 'greatest_lower_bound'( X, multiply( X, b ) ), X ) ] )
% 0.84/1.18 , 0, clause( 2229, [ =( Y, 'least_upper_bound'( 'greatest_lower_bound'( X,
% 0.84/1.18 Y ), Y ) ) ] )
% 0.84/1.18 , 0, 5, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 0.84/1.18 :=( Y, multiply( X, b ) )] )).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 eqswap(
% 0.84/1.18 clause( 2231, [ =( 'least_upper_bound'( X, multiply( X, b ) ), multiply( X
% 0.84/1.18 , b ) ) ] )
% 0.84/1.18 , clause( 2230, [ =( multiply( X, b ), 'least_upper_bound'( X, multiply( X
% 0.84/1.18 , b ) ) ) ] )
% 0.84/1.18 , 0, substitution( 0, [ :=( X, X )] )).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 subsumption(
% 0.84/1.18 clause( 817, [ =( 'least_upper_bound'( X, multiply( X, b ) ), multiply( X,
% 0.84/1.18 b ) ) ] )
% 0.84/1.18 , clause( 2231, [ =( 'least_upper_bound'( X, multiply( X, b ) ), multiply(
% 0.84/1.18 X, b ) ) ] )
% 0.84/1.18 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 eqswap(
% 0.84/1.18 clause( 2233, [ =( 'least_upper_bound'( identity, multiply( Y, X ) ),
% 0.84/1.18 multiply( 'least_upper_bound'( inverse( X ), Y ), X ) ) ] )
% 0.84/1.18 , clause( 93, [ =( multiply( 'least_upper_bound'( inverse( X ), Y ), X ),
% 0.84/1.18 'least_upper_bound'( identity, multiply( Y, X ) ) ) ] )
% 0.84/1.18 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 paramod(
% 0.84/1.18 clause( 2241, [ =( 'least_upper_bound'( identity, multiply( multiply(
% 0.84/1.18 inverse( X ), b ), X ) ), multiply( multiply( inverse( X ), b ), X ) ) ]
% 0.84/1.18 )
% 0.84/1.18 , clause( 817, [ =( 'least_upper_bound'( X, multiply( X, b ) ), multiply( X
% 0.84/1.18 , b ) ) ] )
% 0.84/1.18 , 0, clause( 2233, [ =( 'least_upper_bound'( identity, multiply( Y, X ) ),
% 0.84/1.18 multiply( 'least_upper_bound'( inverse( X ), Y ), X ) ) ] )
% 0.84/1.18 , 0, 10, substitution( 0, [ :=( X, inverse( X ) )] ), substitution( 1, [
% 0.84/1.18 :=( X, X ), :=( Y, multiply( inverse( X ), b ) )] )).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 subsumption(
% 0.84/1.18 clause( 1933, [ =( 'least_upper_bound'( identity, multiply( multiply(
% 0.84/1.18 inverse( X ), b ), X ) ), multiply( multiply( inverse( X ), b ), X ) ) ]
% 0.84/1.18 )
% 0.84/1.18 , clause( 2241, [ =( 'least_upper_bound'( identity, multiply( multiply(
% 0.84/1.18 inverse( X ), b ), X ) ), multiply( multiply( inverse( X ), b ), X ) ) ]
% 0.84/1.18 )
% 0.84/1.18 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 paramod(
% 0.84/1.18 clause( 2246, [ ~( =( multiply( multiply( inverse( a ), b ), a ), multiply(
% 0.84/1.18 multiply( inverse( a ), b ), a ) ) ) ] )
% 0.84/1.18 , clause( 1933, [ =( 'least_upper_bound'( identity, multiply( multiply(
% 0.84/1.18 inverse( X ), b ), X ) ), multiply( multiply( inverse( X ), b ), X ) ) ]
% 0.84/1.18 )
% 0.84/1.18 , 0, clause( 16, [ ~( =( 'least_upper_bound'( identity, multiply( multiply(
% 0.84/1.18 inverse( a ), b ), a ) ), multiply( multiply( inverse( a ), b ), a ) ) )
% 0.84/1.18 ] )
% 0.84/1.18 , 0, 2, substitution( 0, [ :=( X, a )] ), substitution( 1, [] )).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 eqrefl(
% 0.84/1.18 clause( 2247, [] )
% 0.84/1.18 , clause( 2246, [ ~( =( multiply( multiply( inverse( a ), b ), a ),
% 0.84/1.18 multiply( multiply( inverse( a ), b ), a ) ) ) ] )
% 0.84/1.18 , 0, substitution( 0, [] )).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 subsumption(
% 0.84/1.18 clause( 2013, [] )
% 0.84/1.18 , clause( 2247, [] )
% 0.84/1.18 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 end.
% 0.84/1.18
% 0.84/1.18 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.84/1.18
% 0.84/1.18 Memory use:
% 0.84/1.18
% 0.84/1.18 space for terms: 26091
% 0.84/1.18 space for clauses: 216207
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 clauses generated: 26709
% 0.84/1.18 clauses kept: 2014
% 0.84/1.18 clauses selected: 249
% 0.84/1.18 clauses deleted: 19
% 0.84/1.18 clauses inuse deleted: 7
% 0.84/1.18
% 0.84/1.18 subsentry: 4308
% 0.84/1.18 literals s-matched: 3776
% 0.84/1.18 literals matched: 3764
% 0.84/1.18 full subsumption: 0
% 0.84/1.18
% 0.84/1.18 checksum: -270335241
% 0.84/1.18
% 0.84/1.18
% 0.84/1.18 Bliksem ended
%------------------------------------------------------------------------------