TSTP Solution File: BOO017-10 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : BOO017-10 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n024.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 : Thu Jul 14 23:30:40 EDT 2022
% Result : Unsatisfiable 4.10s 4.47s
% Output : Refutation 4.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : BOO017-10 : TPTP v8.1.0. Released v7.5.0.
% 0.03/0.12 % Command : bliksem %s
% 0.13/0.33 % Computer : n024.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 : Wed Jun 1 21:26:36 EDT 2022
% 0.13/0.33 % CPUTime :
% 4.10/4.47 *** allocated 10000 integers for termspace/termends
% 4.10/4.47 *** allocated 10000 integers for clauses
% 4.10/4.47 *** allocated 10000 integers for justifications
% 4.10/4.47 Bliksem 1.12
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 Automatic Strategy Selection
% 4.10/4.47
% 4.10/4.47 Clauses:
% 4.10/4.47 [
% 4.10/4.47 [ =( ifeq2( X, X, Y, Z ), Y ) ],
% 4.10/4.47 [ =( ifeq( X, X, Y, Z ), Y ) ],
% 4.10/4.47 [ =( sum( X, Y, add( X, Y ) ), true ) ],
% 4.10/4.47 [ =( product( X, Y, multiply( X, Y ) ), true ) ],
% 4.10/4.47 [ =( ifeq( sum( X, Y, Z ), true, sum( Y, X, Z ), true ), true ) ],
% 4.10/4.47 [ =( ifeq( product( X, Y, Z ), true, product( Y, X, Z ), true ), true )
% 4.10/4.47 ],
% 4.10/4.47 [ =( sum( 'additive_identity', X, X ), true ) ],
% 4.10/4.47 [ =( sum( X, 'additive_identity', X ), true ) ],
% 4.10/4.47 [ =( product( 'multiplicative_identity', X, X ), true ) ],
% 4.10/4.47 [ =( product( X, 'multiplicative_identity', X ), true ) ],
% 4.10/4.47 [ =( ifeq( product( X, Y, Z ), true, ifeq( product( X, T, U ), true,
% 4.10/4.47 ifeq( product( X, W, V0 ), true, ifeq( sum( W, T, Y ), true, sum( V0, U,
% 4.10/4.47 Z ), true ), true ), true ), true ), true ) ],
% 4.10/4.47 [ =( ifeq( product( X, Y, Z ), true, ifeq( product( X, T, U ), true,
% 4.10/4.47 ifeq( sum( U, Z, W ), true, ifeq( sum( T, Y, V0 ), true, product( X, V0,
% 4.10/4.47 W ), true ), true ), true ), true ), true ) ],
% 4.10/4.47 [ =( ifeq( product( X, Y, Z ), true, ifeq( product( T, Y, U ), true,
% 4.10/4.47 ifeq( product( W, Y, V0 ), true, ifeq( sum( W, T, X ), true, sum( V0, U,
% 4.10/4.47 Z ), true ), true ), true ), true ), true ) ],
% 4.10/4.47 [ =( ifeq( product( X, Y, Z ), true, ifeq( product( T, Y, U ), true,
% 4.10/4.47 ifeq( sum( U, Z, W ), true, ifeq( sum( T, X, V0 ), true, product( V0, Y,
% 4.10/4.47 W ), true ), true ), true ), true ), true ) ],
% 4.10/4.47 [ =( ifeq( product( X, Y, Z ), true, ifeq( sum( T, Z, U ), true, ifeq(
% 4.10/4.47 sum( T, Y, W ), true, ifeq( sum( T, X, V0 ), true, product( V0, W, U ),
% 4.10/4.47 true ), true ), true ), true ), true ) ],
% 4.10/4.47 [ =( ifeq( product( X, Y, Z ), true, ifeq( product( T, U, W ), true,
% 4.10/4.47 ifeq( sum( V0, U, Y ), true, ifeq( sum( V0, T, X ), true, sum( V0, W, Z )
% 4.10/4.47 , true ), true ), true ), true ), true ) ],
% 4.10/4.47 [ =( ifeq( product( X, Y, Z ), true, ifeq( sum( Z, T, U ), true, ifeq(
% 4.10/4.47 sum( Y, T, W ), true, ifeq( sum( X, T, V0 ), true, product( V0, W, U ),
% 4.10/4.47 true ), true ), true ), true ), true ) ],
% 4.10/4.47 [ =( ifeq( product( X, Y, Z ), true, ifeq( product( T, U, W ), true,
% 4.10/4.47 ifeq( sum( U, V0, Y ), true, ifeq( sum( T, V0, X ), true, sum( W, V0, Z )
% 4.10/4.47 , true ), true ), true ), true ), true ) ],
% 4.10/4.47 [ =( sum( inverse( X ), X, 'multiplicative_identity' ), true ) ],
% 4.10/4.47 [ =( sum( X, inverse( X ), 'multiplicative_identity' ), true ) ],
% 4.10/4.47 [ =( product( inverse( X ), X, 'additive_identity' ), true ) ],
% 4.10/4.47 [ =( product( X, inverse( X ), 'additive_identity' ), true ) ],
% 4.10/4.47 [ =( ifeq2( sum( X, Y, Z ), true, ifeq2( sum( X, Y, T ), true, T, Z ), Z
% 4.10/4.47 ), Z ) ],
% 4.10/4.47 [ =( ifeq2( product( X, Y, Z ), true, ifeq2( product( X, Y, T ), true, T
% 4.10/4.47 , Z ), Z ), Z ) ],
% 4.10/4.47 [ =( sum( x, y, z ), true ) ],
% 4.10/4.47 [ ~( =( product( x, z, x ), true ) ) ]
% 4.10/4.47 ] .
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 percentage equality = 1.000000, percentage horn = 1.000000
% 4.10/4.47 This is a pure equality problem
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 Options Used:
% 4.10/4.47
% 4.10/4.47 useres = 1
% 4.10/4.47 useparamod = 1
% 4.10/4.47 useeqrefl = 1
% 4.10/4.47 useeqfact = 1
% 4.10/4.47 usefactor = 1
% 4.10/4.47 usesimpsplitting = 0
% 4.10/4.47 usesimpdemod = 5
% 4.10/4.47 usesimpres = 3
% 4.10/4.47
% 4.10/4.47 resimpinuse = 1000
% 4.10/4.47 resimpclauses = 20000
% 4.10/4.47 substype = eqrewr
% 4.10/4.47 backwardsubs = 1
% 4.10/4.47 selectoldest = 5
% 4.10/4.47
% 4.10/4.47 litorderings [0] = split
% 4.10/4.47 litorderings [1] = extend the termordering, first sorting on arguments
% 4.10/4.47
% 4.10/4.47 termordering = kbo
% 4.10/4.47
% 4.10/4.47 litapriori = 0
% 4.10/4.47 termapriori = 1
% 4.10/4.47 litaposteriori = 0
% 4.10/4.47 termaposteriori = 0
% 4.10/4.47 demodaposteriori = 0
% 4.10/4.47 ordereqreflfact = 0
% 4.10/4.47
% 4.10/4.47 litselect = negord
% 4.10/4.47
% 4.10/4.47 maxweight = 15
% 4.10/4.47 maxdepth = 30000
% 4.10/4.47 maxlength = 115
% 4.10/4.47 maxnrvars = 195
% 4.10/4.47 excuselevel = 1
% 4.10/4.47 increasemaxweight = 1
% 4.10/4.47
% 4.10/4.47 maxselected = 10000000
% 4.10/4.47 maxnrclauses = 10000000
% 4.10/4.47
% 4.10/4.47 showgenerated = 0
% 4.10/4.47 showkept = 0
% 4.10/4.47 showselected = 0
% 4.10/4.47 showdeleted = 0
% 4.10/4.47 showresimp = 1
% 4.10/4.47 showstatus = 2000
% 4.10/4.47
% 4.10/4.47 prologoutput = 1
% 4.10/4.47 nrgoals = 5000000
% 4.10/4.47 totalproof = 1
% 4.10/4.47
% 4.10/4.47 Symbols occurring in the translation:
% 4.10/4.47
% 4.10/4.47 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 4.10/4.47 . [1, 2] (w:1, o:33, a:1, s:1, b:0),
% 4.10/4.47 ! [4, 1] (w:0, o:27, a:1, s:1, b:0),
% 4.10/4.47 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 4.10/4.47 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 4.10/4.47 ifeq2 [42, 4] (w:1, o:62, a:1, s:1, b:0),
% 4.10/4.47 ifeq [43, 4] (w:1, o:63, a:1, s:1, b:0),
% 4.10/4.47 add [46, 2] (w:1, o:58, a:1, s:1, b:0),
% 4.10/4.47 sum [47, 3] (w:1, o:60, a:1, s:1, b:0),
% 4.10/4.47 true [48, 0] (w:1, o:14, a:1, s:1, b:0),
% 4.10/4.47 multiply [49, 2] (w:1, o:59, a:1, s:1, b:0),
% 4.10/4.47 product [50, 3] (w:1, o:61, a:1, s:1, b:0),
% 4.10/4.47 'additive_identity' [52, 0] (w:1, o:16, a:1, s:1, b:0),
% 4.10/4.47 'multiplicative_identity' [53, 0] (w:1, o:17, a:1, s:1, b:0),
% 4.10/4.47 inverse [58, 1] (w:1, o:32, a:1, s:1, b:0),
% 4.10/4.47 x [61, 0] (w:1, o:24, a:1, s:1, b:0),
% 4.10/4.47 y [62, 0] (w:1, o:25, a:1, s:1, b:0),
% 4.10/4.47 z [63, 0] (w:1, o:26, a:1, s:1, b:0).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 Starting Search:
% 4.10/4.47
% 4.10/4.47 Resimplifying inuse:
% 4.10/4.47 Done
% 4.10/4.47
% 4.10/4.47 Failed to find proof!
% 4.10/4.47 maxweight = 15
% 4.10/4.47 maxnrclauses = 10000000
% 4.10/4.47 Generated: 8387
% 4.10/4.47 Kept: 311
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 The strategy used was not complete!
% 4.10/4.47
% 4.10/4.47 Increased maxweight to 16
% 4.10/4.47
% 4.10/4.47 Starting Search:
% 4.10/4.47
% 4.10/4.47 Resimplifying inuse:
% 4.10/4.47 Done
% 4.10/4.47
% 4.10/4.47 Failed to find proof!
% 4.10/4.47 maxweight = 16
% 4.10/4.47 maxnrclauses = 10000000
% 4.10/4.47 Generated: 8387
% 4.10/4.47 Kept: 311
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 The strategy used was not complete!
% 4.10/4.47
% 4.10/4.47 Increased maxweight to 17
% 4.10/4.47
% 4.10/4.47 Starting Search:
% 4.10/4.47
% 4.10/4.47 Resimplifying inuse:
% 4.10/4.47 Done
% 4.10/4.47
% 4.10/4.47 Failed to find proof!
% 4.10/4.47 maxweight = 17
% 4.10/4.47 maxnrclauses = 10000000
% 4.10/4.47 Generated: 10127
% 4.10/4.47 Kept: 375
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 The strategy used was not complete!
% 4.10/4.47
% 4.10/4.47 Increased maxweight to 18
% 4.10/4.47
% 4.10/4.47 Starting Search:
% 4.10/4.47
% 4.10/4.47 Resimplifying inuse:
% 4.10/4.47 Done
% 4.10/4.47
% 4.10/4.47 Failed to find proof!
% 4.10/4.47 maxweight = 18
% 4.10/4.47 maxnrclauses = 10000000
% 4.10/4.47 Generated: 10407
% 4.10/4.47 Kept: 386
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 The strategy used was not complete!
% 4.10/4.47
% 4.10/4.47 Increased maxweight to 19
% 4.10/4.47
% 4.10/4.47 Starting Search:
% 4.10/4.47
% 4.10/4.47 Resimplifying inuse:
% 4.10/4.47 Done
% 4.10/4.47
% 4.10/4.47 Failed to find proof!
% 4.10/4.47 maxweight = 19
% 4.10/4.47 maxnrclauses = 10000000
% 4.10/4.47 Generated: 34701
% 4.10/4.47 Kept: 745
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 The strategy used was not complete!
% 4.10/4.47
% 4.10/4.47 Increased maxweight to 20
% 4.10/4.47
% 4.10/4.47 Starting Search:
% 4.10/4.47
% 4.10/4.47 Resimplifying inuse:
% 4.10/4.47 Done
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 Intermediate Status:
% 4.10/4.47 Generated: 26220
% 4.10/4.47 Kept: 2009
% 4.10/4.47 Inuse: 968
% 4.10/4.47 Deleted: 436
% 4.10/4.47 Deletedinuse: 189
% 4.10/4.47
% 4.10/4.47 Resimplifying inuse:
% 4.10/4.47 Done
% 4.10/4.47
% 4.10/4.47 Resimplifying inuse:
% 4.10/4.47 Done
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 Intermediate Status:
% 4.10/4.47 Generated: 78304
% 4.10/4.47 Kept: 4082
% 4.10/4.47 Inuse: 1216
% 4.10/4.47 Deleted: 1062
% 4.10/4.47 Deletedinuse: 681
% 4.10/4.47
% 4.10/4.47 Resimplifying inuse:
% 4.10/4.47 Done
% 4.10/4.47
% 4.10/4.47 Resimplifying inuse:
% 4.10/4.47 Done
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 Bliksems!, er is een bewijs:
% 4.10/4.47 % SZS status Unsatisfiable
% 4.10/4.47 % SZS output start Refutation
% 4.10/4.47
% 4.10/4.47 clause( 0, [ =( ifeq2( X, X, Y, Z ), Y ) ] )
% 4.10/4.47 .
% 4.10/4.47 clause( 1, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 4.10/4.47 .
% 4.10/4.47 clause( 3, [ =( product( X, Y, multiply( X, Y ) ), true ) ] )
% 4.10/4.47 .
% 4.10/4.47 clause( 5, [ =( ifeq( product( X, Y, Z ), true, product( Y, X, Z ), true )
% 4.10/4.47 , true ) ] )
% 4.10/4.47 .
% 4.10/4.47 clause( 6, [ =( sum( 'additive_identity', X, X ), true ) ] )
% 4.10/4.47 .
% 4.10/4.47 clause( 7, [ =( sum( X, 'additive_identity', X ), true ) ] )
% 4.10/4.47 .
% 4.10/4.47 clause( 11, [ =( ifeq( product( X, Y, Z ), true, ifeq( product( X, T, U ),
% 4.10/4.47 true, ifeq( sum( U, Z, W ), true, ifeq( sum( T, Y, V0 ), true, product( X
% 4.10/4.47 , V0, W ), true ), true ), true ), true ), true ) ] )
% 4.10/4.47 .
% 4.10/4.47 clause( 14, [ =( ifeq( product( X, Y, Z ), true, ifeq( sum( T, Z, U ), true
% 4.10/4.47 , ifeq( sum( T, Y, W ), true, ifeq( sum( T, X, V0 ), true, product( V0, W
% 4.10/4.47 , U ), true ), true ), true ), true ), true ) ] )
% 4.10/4.47 .
% 4.10/4.47 clause( 20, [ =( product( inverse( X ), X, 'additive_identity' ), true ) ]
% 4.10/4.47 )
% 4.10/4.47 .
% 4.10/4.47 clause( 21, [ =( product( X, inverse( X ), 'additive_identity' ), true ) ]
% 4.10/4.47 )
% 4.10/4.47 .
% 4.10/4.47 clause( 23, [ =( ifeq2( product( X, Y, Z ), true, ifeq2( product( X, Y, T )
% 4.10/4.47 , true, T, Z ), Z ), Z ) ] )
% 4.10/4.47 .
% 4.10/4.47 clause( 24, [ =( sum( x, y, z ), true ) ] )
% 4.10/4.47 .
% 4.10/4.47 clause( 25, [ ~( =( product( x, z, x ), true ) ) ] )
% 4.10/4.47 .
% 4.10/4.47 clause( 26, [ =( product( Y, X, multiply( X, Y ) ), true ) ] )
% 4.10/4.47 .
% 4.10/4.47 clause( 31, [ =( ifeq2( product( X, Y, Z ), true, Z, multiply( X, Y ) ),
% 4.10/4.47 multiply( X, Y ) ) ] )
% 4.10/4.47 .
% 4.10/4.47 clause( 33, [ =( ifeq2( product( inverse( X ), X, Y ), true, Y,
% 4.10/4.47 'additive_identity' ), 'additive_identity' ) ] )
% 4.10/4.47 .
% 4.10/4.47 clause( 89, [ =( ifeq( product( Y, Z, X ), true, ifeq( product( Y, T,
% 4.10/4.47 'additive_identity' ), true, ifeq( sum( T, Z, U ), true, product( Y, U, X
% 4.10/4.47 ), true ), true ), true ), true ) ] )
% 4.10/4.47 .
% 4.10/4.47 clause( 99, [ =( multiply( X, inverse( X ) ), 'additive_identity' ) ] )
% 4.10/4.47 .
% 4.10/4.47 clause( 173, [ =( ifeq( product( X, y, Y ), true, ifeq( sum( x, Y, Z ),
% 4.10/4.47 true, ifeq( sum( x, X, T ), true, product( T, z, Z ), true ), true ),
% 4.10/4.47 true ), true ) ] )
% 4.10/4.47 .
% 4.10/4.47 clause( 673, [ =( ifeq( product( Y, 'additive_identity', Z ), true, ifeq(
% 4.10/4.47 product( Y, X, 'additive_identity' ), true, product( Y, X, Z ), true ),
% 4.10/4.47 true ), true ) ] )
% 4.10/4.47 .
% 4.10/4.47 clause( 1171, [ =( ifeq( product( X, y, 'additive_identity' ), true, ifeq(
% 4.10/4.47 sum( x, X, Y ), true, product( Y, z, x ), true ), true ), true ) ] )
% 4.10/4.47 .
% 4.10/4.47 clause( 4805, [ =( ifeq( product( X, 'additive_identity', Y ), true,
% 4.10/4.47 product( X, inverse( X ), Y ), true ), true ) ] )
% 4.10/4.47 .
% 4.10/4.47 clause( 4806, [ =( product( X, inverse( X ), multiply( 'additive_identity'
% 4.10/4.47 , X ) ), true ) ] )
% 4.10/4.47 .
% 4.10/4.47 clause( 4809, [ =( multiply( 'additive_identity', X ), 'additive_identity'
% 4.10/4.47 ) ] )
% 4.10/4.47 .
% 4.10/4.47 clause( 4819, [ =( product( 'additive_identity', X, 'additive_identity' ),
% 4.10/4.47 true ) ] )
% 4.10/4.47 .
% 4.10/4.47 clause( 6070, [] )
% 4.10/4.47 .
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 % SZS output end Refutation
% 4.10/4.47 found a proof!
% 4.10/4.47
% 4.10/4.47 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 4.10/4.47
% 4.10/4.47 initialclauses(
% 4.10/4.47 [ clause( 6072, [ =( ifeq2( X, X, Y, Z ), Y ) ] )
% 4.10/4.47 , clause( 6073, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 4.10/4.47 , clause( 6074, [ =( sum( X, Y, add( X, Y ) ), true ) ] )
% 4.10/4.47 , clause( 6075, [ =( product( X, Y, multiply( X, Y ) ), true ) ] )
% 4.10/4.47 , clause( 6076, [ =( ifeq( sum( X, Y, Z ), true, sum( Y, X, Z ), true ),
% 4.10/4.47 true ) ] )
% 4.10/4.47 , clause( 6077, [ =( ifeq( product( X, Y, Z ), true, product( Y, X, Z ),
% 4.10/4.47 true ), true ) ] )
% 4.10/4.47 , clause( 6078, [ =( sum( 'additive_identity', X, X ), true ) ] )
% 4.10/4.47 , clause( 6079, [ =( sum( X, 'additive_identity', X ), true ) ] )
% 4.10/4.47 , clause( 6080, [ =( product( 'multiplicative_identity', X, X ), true ) ]
% 4.10/4.47 )
% 4.10/4.47 , clause( 6081, [ =( product( X, 'multiplicative_identity', X ), true ) ]
% 4.10/4.47 )
% 4.10/4.47 , clause( 6082, [ =( ifeq( product( X, Y, Z ), true, ifeq( product( X, T, U
% 4.10/4.47 ), true, ifeq( product( X, W, V0 ), true, ifeq( sum( W, T, Y ), true,
% 4.10/4.47 sum( V0, U, Z ), true ), true ), true ), true ), true ) ] )
% 4.10/4.47 , clause( 6083, [ =( ifeq( product( X, Y, Z ), true, ifeq( product( X, T, U
% 4.10/4.47 ), true, ifeq( sum( U, Z, W ), true, ifeq( sum( T, Y, V0 ), true,
% 4.10/4.47 product( X, V0, W ), true ), true ), true ), true ), true ) ] )
% 4.10/4.47 , clause( 6084, [ =( ifeq( product( X, Y, Z ), true, ifeq( product( T, Y, U
% 4.10/4.47 ), true, ifeq( product( W, Y, V0 ), true, ifeq( sum( W, T, X ), true,
% 4.10/4.47 sum( V0, U, Z ), true ), true ), true ), true ), true ) ] )
% 4.10/4.47 , clause( 6085, [ =( ifeq( product( X, Y, Z ), true, ifeq( product( T, Y, U
% 4.10/4.47 ), true, ifeq( sum( U, Z, W ), true, ifeq( sum( T, X, V0 ), true,
% 4.10/4.47 product( V0, Y, W ), true ), true ), true ), true ), true ) ] )
% 4.10/4.47 , clause( 6086, [ =( ifeq( product( X, Y, Z ), true, ifeq( sum( T, Z, U ),
% 4.10/4.47 true, ifeq( sum( T, Y, W ), true, ifeq( sum( T, X, V0 ), true, product(
% 4.10/4.47 V0, W, U ), true ), true ), true ), true ), true ) ] )
% 4.10/4.47 , clause( 6087, [ =( ifeq( product( X, Y, Z ), true, ifeq( product( T, U, W
% 4.10/4.47 ), true, ifeq( sum( V0, U, Y ), true, ifeq( sum( V0, T, X ), true, sum(
% 4.10/4.47 V0, W, Z ), true ), true ), true ), true ), true ) ] )
% 4.10/4.47 , clause( 6088, [ =( ifeq( product( X, Y, Z ), true, ifeq( sum( Z, T, U ),
% 4.10/4.47 true, ifeq( sum( Y, T, W ), true, ifeq( sum( X, T, V0 ), true, product(
% 4.10/4.47 V0, W, U ), true ), true ), true ), true ), true ) ] )
% 4.10/4.47 , clause( 6089, [ =( ifeq( product( X, Y, Z ), true, ifeq( product( T, U, W
% 4.10/4.47 ), true, ifeq( sum( U, V0, Y ), true, ifeq( sum( T, V0, X ), true, sum(
% 4.10/4.47 W, V0, Z ), true ), true ), true ), true ), true ) ] )
% 4.10/4.47 , clause( 6090, [ =( sum( inverse( X ), X, 'multiplicative_identity' ),
% 4.10/4.47 true ) ] )
% 4.10/4.47 , clause( 6091, [ =( sum( X, inverse( X ), 'multiplicative_identity' ),
% 4.10/4.47 true ) ] )
% 4.10/4.47 , clause( 6092, [ =( product( inverse( X ), X, 'additive_identity' ), true
% 4.10/4.47 ) ] )
% 4.10/4.47 , clause( 6093, [ =( product( X, inverse( X ), 'additive_identity' ), true
% 4.10/4.47 ) ] )
% 4.10/4.47 , clause( 6094, [ =( ifeq2( sum( X, Y, Z ), true, ifeq2( sum( X, Y, T ),
% 4.10/4.47 true, T, Z ), Z ), Z ) ] )
% 4.10/4.47 , clause( 6095, [ =( ifeq2( product( X, Y, Z ), true, ifeq2( product( X, Y
% 4.10/4.47 , T ), true, T, Z ), Z ), Z ) ] )
% 4.10/4.47 , clause( 6096, [ =( sum( x, y, z ), true ) ] )
% 4.10/4.47 , clause( 6097, [ ~( =( product( x, z, x ), true ) ) ] )
% 4.10/4.47 ] ).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 subsumption(
% 4.10/4.47 clause( 0, [ =( ifeq2( X, X, Y, Z ), Y ) ] )
% 4.10/4.47 , clause( 6072, [ =( ifeq2( X, X, Y, Z ), Y ) ] )
% 4.10/4.47 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 4.10/4.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 subsumption(
% 4.10/4.47 clause( 1, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 4.10/4.47 , clause( 6073, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 4.10/4.47 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 4.10/4.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 subsumption(
% 4.10/4.47 clause( 3, [ =( product( X, Y, multiply( X, Y ) ), true ) ] )
% 4.10/4.47 , clause( 6075, [ =( product( X, Y, multiply( X, Y ) ), true ) ] )
% 4.10/4.47 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 4.10/4.47 )] ) ).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 subsumption(
% 4.10/4.47 clause( 5, [ =( ifeq( product( X, Y, Z ), true, product( Y, X, Z ), true )
% 4.10/4.47 , true ) ] )
% 4.10/4.47 , clause( 6077, [ =( ifeq( product( X, Y, Z ), true, product( Y, X, Z ),
% 4.10/4.47 true ), true ) ] )
% 4.10/4.47 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 4.10/4.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 subsumption(
% 4.10/4.47 clause( 6, [ =( sum( 'additive_identity', X, X ), true ) ] )
% 4.10/4.47 , clause( 6078, [ =( sum( 'additive_identity', X, X ), true ) ] )
% 4.10/4.47 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 subsumption(
% 4.10/4.47 clause( 7, [ =( sum( X, 'additive_identity', X ), true ) ] )
% 4.10/4.47 , clause( 6079, [ =( sum( X, 'additive_identity', X ), true ) ] )
% 4.10/4.47 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 subsumption(
% 4.10/4.47 clause( 11, [ =( ifeq( product( X, Y, Z ), true, ifeq( product( X, T, U ),
% 4.10/4.47 true, ifeq( sum( U, Z, W ), true, ifeq( sum( T, Y, V0 ), true, product( X
% 4.10/4.47 , V0, W ), true ), true ), true ), true ), true ) ] )
% 4.10/4.47 , clause( 6083, [ =( ifeq( product( X, Y, Z ), true, ifeq( product( X, T, U
% 4.10/4.47 ), true, ifeq( sum( U, Z, W ), true, ifeq( sum( T, Y, V0 ), true,
% 4.10/4.47 product( X, V0, W ), true ), true ), true ), true ), true ) ] )
% 4.10/4.47 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 4.10/4.47 , U ), :=( W, W ), :=( V0, V0 )] ), permutation( 0, [ ==>( 0, 0 )] )
% 4.10/4.47 ).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 subsumption(
% 4.10/4.47 clause( 14, [ =( ifeq( product( X, Y, Z ), true, ifeq( sum( T, Z, U ), true
% 4.10/4.47 , ifeq( sum( T, Y, W ), true, ifeq( sum( T, X, V0 ), true, product( V0, W
% 4.10/4.47 , U ), true ), true ), true ), true ), true ) ] )
% 4.10/4.47 , clause( 6086, [ =( ifeq( product( X, Y, Z ), true, ifeq( sum( T, Z, U ),
% 4.10/4.47 true, ifeq( sum( T, Y, W ), true, ifeq( sum( T, X, V0 ), true, product(
% 4.10/4.47 V0, W, U ), true ), true ), true ), true ), true ) ] )
% 4.10/4.47 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 4.10/4.47 , U ), :=( W, W ), :=( V0, V0 )] ), permutation( 0, [ ==>( 0, 0 )] )
% 4.10/4.47 ).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 subsumption(
% 4.10/4.47 clause( 20, [ =( product( inverse( X ), X, 'additive_identity' ), true ) ]
% 4.10/4.47 )
% 4.10/4.47 , clause( 6092, [ =( product( inverse( X ), X, 'additive_identity' ), true
% 4.10/4.47 ) ] )
% 4.10/4.47 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 subsumption(
% 4.10/4.47 clause( 21, [ =( product( X, inverse( X ), 'additive_identity' ), true ) ]
% 4.10/4.47 )
% 4.10/4.47 , clause( 6093, [ =( product( X, inverse( X ), 'additive_identity' ), true
% 4.10/4.47 ) ] )
% 4.10/4.47 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 subsumption(
% 4.10/4.47 clause( 23, [ =( ifeq2( product( X, Y, Z ), true, ifeq2( product( X, Y, T )
% 4.10/4.47 , true, T, Z ), Z ), Z ) ] )
% 4.10/4.47 , clause( 6095, [ =( ifeq2( product( X, Y, Z ), true, ifeq2( product( X, Y
% 4.10/4.47 , T ), true, T, Z ), Z ), Z ) ] )
% 4.10/4.47 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 4.10/4.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 subsumption(
% 4.10/4.47 clause( 24, [ =( sum( x, y, z ), true ) ] )
% 4.10/4.47 , clause( 6096, [ =( sum( x, y, z ), true ) ] )
% 4.10/4.47 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 subsumption(
% 4.10/4.47 clause( 25, [ ~( =( product( x, z, x ), true ) ) ] )
% 4.10/4.47 , clause( 6097, [ ~( =( product( x, z, x ), true ) ) ] )
% 4.10/4.47 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 eqswap(
% 4.10/4.47 clause( 6272, [ =( true, ifeq( product( X, Y, Z ), true, product( Y, X, Z )
% 4.10/4.47 , true ) ) ] )
% 4.10/4.47 , clause( 5, [ =( ifeq( product( X, Y, Z ), true, product( Y, X, Z ), true
% 4.10/4.47 ), true ) ] )
% 4.10/4.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 paramod(
% 4.10/4.47 clause( 6274, [ =( true, ifeq( true, true, product( Y, X, multiply( X, Y )
% 4.10/4.47 ), true ) ) ] )
% 4.10/4.47 , clause( 3, [ =( product( X, Y, multiply( X, Y ) ), true ) ] )
% 4.10/4.47 , 0, clause( 6272, [ =( true, ifeq( product( X, Y, Z ), true, product( Y, X
% 4.10/4.47 , Z ), true ) ) ] )
% 4.10/4.47 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 4.10/4.47 :=( X, X ), :=( Y, Y ), :=( Z, multiply( X, Y ) )] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 paramod(
% 4.10/4.47 clause( 6276, [ =( true, product( X, Y, multiply( Y, X ) ) ) ] )
% 4.10/4.47 , clause( 1, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 4.10/4.47 , 0, clause( 6274, [ =( true, ifeq( true, true, product( Y, X, multiply( X
% 4.10/4.47 , Y ) ), true ) ) ] )
% 4.10/4.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, product( X, Y, multiply( Y
% 4.10/4.47 , X ) ) ), :=( Z, true )] ), substitution( 1, [ :=( X, Y ), :=( Y, X )] )
% 4.10/4.47 ).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 eqswap(
% 4.10/4.47 clause( 6277, [ =( product( X, Y, multiply( Y, X ) ), true ) ] )
% 4.10/4.47 , clause( 6276, [ =( true, product( X, Y, multiply( Y, X ) ) ) ] )
% 4.10/4.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 subsumption(
% 4.10/4.47 clause( 26, [ =( product( Y, X, multiply( X, Y ) ), true ) ] )
% 4.10/4.47 , clause( 6277, [ =( product( X, Y, multiply( Y, X ) ), true ) ] )
% 4.10/4.47 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 4.10/4.47 )] ) ).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 eqswap(
% 4.10/4.47 clause( 6279, [ =( Z, ifeq2( product( X, Y, Z ), true, ifeq2( product( X, Y
% 4.10/4.47 , T ), true, T, Z ), Z ) ) ] )
% 4.10/4.47 , clause( 23, [ =( ifeq2( product( X, Y, Z ), true, ifeq2( product( X, Y, T
% 4.10/4.47 ), true, T, Z ), Z ), Z ) ] )
% 4.10/4.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 4.10/4.47 ).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 paramod(
% 4.10/4.47 clause( 6281, [ =( multiply( X, Y ), ifeq2( true, true, ifeq2( product( X,
% 4.10/4.47 Y, Z ), true, Z, multiply( X, Y ) ), multiply( X, Y ) ) ) ] )
% 4.10/4.47 , clause( 3, [ =( product( X, Y, multiply( X, Y ) ), true ) ] )
% 4.10/4.47 , 0, clause( 6279, [ =( Z, ifeq2( product( X, Y, Z ), true, ifeq2( product(
% 4.10/4.47 X, Y, T ), true, T, Z ), Z ) ) ] )
% 4.10/4.47 , 0, 5, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 4.10/4.47 :=( X, X ), :=( Y, Y ), :=( Z, multiply( X, Y ) ), :=( T, Z )] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 paramod(
% 4.10/4.47 clause( 6285, [ =( multiply( X, Y ), ifeq2( product( X, Y, Z ), true, Z,
% 4.10/4.47 multiply( X, Y ) ) ) ] )
% 4.10/4.47 , clause( 0, [ =( ifeq2( X, X, Y, Z ), Y ) ] )
% 4.10/4.47 , 0, clause( 6281, [ =( multiply( X, Y ), ifeq2( true, true, ifeq2( product(
% 4.10/4.47 X, Y, Z ), true, Z, multiply( X, Y ) ), multiply( X, Y ) ) ) ] )
% 4.10/4.47 , 0, 4, substitution( 0, [ :=( X, true ), :=( Y, ifeq2( product( X, Y, Z )
% 4.10/4.47 , true, Z, multiply( X, Y ) ) ), :=( Z, multiply( X, Y ) )] ),
% 4.10/4.47 substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 eqswap(
% 4.10/4.47 clause( 6286, [ =( ifeq2( product( X, Y, Z ), true, Z, multiply( X, Y ) ),
% 4.10/4.47 multiply( X, Y ) ) ] )
% 4.10/4.47 , clause( 6285, [ =( multiply( X, Y ), ifeq2( product( X, Y, Z ), true, Z,
% 4.10/4.47 multiply( X, Y ) ) ) ] )
% 4.10/4.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 subsumption(
% 4.10/4.47 clause( 31, [ =( ifeq2( product( X, Y, Z ), true, Z, multiply( X, Y ) ),
% 4.10/4.47 multiply( X, Y ) ) ] )
% 4.10/4.47 , clause( 6286, [ =( ifeq2( product( X, Y, Z ), true, Z, multiply( X, Y ) )
% 4.10/4.47 , multiply( X, Y ) ) ] )
% 4.10/4.47 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 4.10/4.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 eqswap(
% 4.10/4.47 clause( 6288, [ =( Z, ifeq2( product( X, Y, Z ), true, ifeq2( product( X, Y
% 4.10/4.47 , T ), true, T, Z ), Z ) ) ] )
% 4.10/4.47 , clause( 23, [ =( ifeq2( product( X, Y, Z ), true, ifeq2( product( X, Y, T
% 4.10/4.47 ), true, T, Z ), Z ), Z ) ] )
% 4.10/4.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 4.10/4.47 ).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 paramod(
% 4.10/4.47 clause( 6290, [ =( 'additive_identity', ifeq2( true, true, ifeq2( product(
% 4.10/4.47 inverse( X ), X, Y ), true, Y, 'additive_identity' ), 'additive_identity'
% 4.10/4.47 ) ) ] )
% 4.10/4.47 , clause( 20, [ =( product( inverse( X ), X, 'additive_identity' ), true )
% 4.10/4.47 ] )
% 4.10/4.47 , 0, clause( 6288, [ =( Z, ifeq2( product( X, Y, Z ), true, ifeq2( product(
% 4.10/4.47 X, Y, T ), true, T, Z ), Z ) ) ] )
% 4.10/4.47 , 0, 3, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, inverse(
% 4.10/4.47 X ) ), :=( Y, X ), :=( Z, 'additive_identity' ), :=( T, Y )] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 paramod(
% 4.10/4.47 clause( 6294, [ =( 'additive_identity', ifeq2( product( inverse( X ), X, Y
% 4.10/4.47 ), true, Y, 'additive_identity' ) ) ] )
% 4.10/4.47 , clause( 0, [ =( ifeq2( X, X, Y, Z ), Y ) ] )
% 4.10/4.47 , 0, clause( 6290, [ =( 'additive_identity', ifeq2( true, true, ifeq2(
% 4.10/4.47 product( inverse( X ), X, Y ), true, Y, 'additive_identity' ),
% 4.10/4.47 'additive_identity' ) ) ] )
% 4.10/4.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq2( product( inverse( X
% 4.10/4.47 ), X, Y ), true, Y, 'additive_identity' ) ), :=( Z, 'additive_identity'
% 4.10/4.47 )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 eqswap(
% 4.10/4.47 clause( 6295, [ =( ifeq2( product( inverse( X ), X, Y ), true, Y,
% 4.10/4.47 'additive_identity' ), 'additive_identity' ) ] )
% 4.10/4.47 , clause( 6294, [ =( 'additive_identity', ifeq2( product( inverse( X ), X,
% 4.10/4.47 Y ), true, Y, 'additive_identity' ) ) ] )
% 4.10/4.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 subsumption(
% 4.10/4.47 clause( 33, [ =( ifeq2( product( inverse( X ), X, Y ), true, Y,
% 4.10/4.47 'additive_identity' ), 'additive_identity' ) ] )
% 4.10/4.47 , clause( 6295, [ =( ifeq2( product( inverse( X ), X, Y ), true, Y,
% 4.10/4.47 'additive_identity' ), 'additive_identity' ) ] )
% 4.10/4.47 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 4.10/4.47 )] ) ).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 eqswap(
% 4.10/4.47 clause( 6297, [ =( true, ifeq( product( X, Y, Z ), true, ifeq( product( X,
% 4.10/4.47 T, U ), true, ifeq( sum( U, Z, W ), true, ifeq( sum( T, Y, V0 ), true,
% 4.10/4.47 product( X, V0, W ), true ), true ), true ), true ) ) ] )
% 4.10/4.47 , clause( 11, [ =( ifeq( product( X, Y, Z ), true, ifeq( product( X, T, U )
% 4.10/4.47 , true, ifeq( sum( U, Z, W ), true, ifeq( sum( T, Y, V0 ), true, product(
% 4.10/4.47 X, V0, W ), true ), true ), true ), true ), true ) ] )
% 4.10/4.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 4.10/4.47 :=( U, U ), :=( W, W ), :=( V0, V0 )] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 paramod(
% 4.10/4.47 clause( 6299, [ =( true, ifeq( product( X, Y, Z ), true, ifeq( product( X,
% 4.10/4.47 T, 'additive_identity' ), true, ifeq( true, true, ifeq( sum( T, Y, U ),
% 4.10/4.47 true, product( X, U, Z ), true ), true ), true ), true ) ) ] )
% 4.10/4.47 , clause( 6, [ =( sum( 'additive_identity', X, X ), true ) ] )
% 4.10/4.47 , 0, clause( 6297, [ =( true, ifeq( product( X, Y, Z ), true, ifeq( product(
% 4.10/4.47 X, T, U ), true, ifeq( sum( U, Z, W ), true, ifeq( sum( T, Y, V0 ), true
% 4.10/4.47 , product( X, V0, W ), true ), true ), true ), true ) ) ] )
% 4.10/4.47 , 0, 15, substitution( 0, [ :=( X, Z )] ), substitution( 1, [ :=( X, X ),
% 4.10/4.47 :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U, 'additive_identity' ), :=( W,
% 4.10/4.47 Z ), :=( V0, U )] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 paramod(
% 4.10/4.47 clause( 6303, [ =( true, ifeq( product( X, Y, Z ), true, ifeq( product( X,
% 4.10/4.47 T, 'additive_identity' ), true, ifeq( sum( T, Y, U ), true, product( X, U
% 4.10/4.47 , Z ), true ), true ), true ) ) ] )
% 4.10/4.47 , clause( 1, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 4.10/4.47 , 0, clause( 6299, [ =( true, ifeq( product( X, Y, Z ), true, ifeq( product(
% 4.10/4.47 X, T, 'additive_identity' ), true, ifeq( true, true, ifeq( sum( T, Y, U )
% 4.10/4.47 , true, product( X, U, Z ), true ), true ), true ), true ) ) ] )
% 4.10/4.47 , 0, 14, substitution( 0, [ :=( X, true ), :=( Y, ifeq( sum( T, Y, U ),
% 4.10/4.47 true, product( X, U, Z ), true ) ), :=( Z, true )] ), substitution( 1, [
% 4.10/4.47 :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U, U )] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 eqswap(
% 4.10/4.47 clause( 6304, [ =( ifeq( product( X, Y, Z ), true, ifeq( product( X, T,
% 4.10/4.47 'additive_identity' ), true, ifeq( sum( T, Y, U ), true, product( X, U, Z
% 4.10/4.47 ), true ), true ), true ), true ) ] )
% 4.10/4.47 , clause( 6303, [ =( true, ifeq( product( X, Y, Z ), true, ifeq( product( X
% 4.10/4.47 , T, 'additive_identity' ), true, ifeq( sum( T, Y, U ), true, product( X
% 4.10/4.47 , U, Z ), true ), true ), true ) ) ] )
% 4.10/4.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 4.10/4.47 :=( U, U )] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 subsumption(
% 4.10/4.47 clause( 89, [ =( ifeq( product( Y, Z, X ), true, ifeq( product( Y, T,
% 4.10/4.47 'additive_identity' ), true, ifeq( sum( T, Z, U ), true, product( Y, U, X
% 4.10/4.47 ), true ), true ), true ), true ) ] )
% 4.10/4.47 , clause( 6304, [ =( ifeq( product( X, Y, Z ), true, ifeq( product( X, T,
% 4.10/4.47 'additive_identity' ), true, ifeq( sum( T, Y, U ), true, product( X, U, Z
% 4.10/4.47 ), true ), true ), true ), true ) ] )
% 4.10/4.47 , substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X ), :=( T, T ), :=( U
% 4.10/4.47 , U )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 eqswap(
% 4.10/4.47 clause( 6306, [ =( 'additive_identity', ifeq2( product( inverse( X ), X, Y
% 4.10/4.47 ), true, Y, 'additive_identity' ) ) ] )
% 4.10/4.47 , clause( 33, [ =( ifeq2( product( inverse( X ), X, Y ), true, Y,
% 4.10/4.47 'additive_identity' ), 'additive_identity' ) ] )
% 4.10/4.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 paramod(
% 4.10/4.47 clause( 6308, [ =( 'additive_identity', ifeq2( true, true, multiply( X,
% 4.10/4.47 inverse( X ) ), 'additive_identity' ) ) ] )
% 4.10/4.47 , clause( 26, [ =( product( Y, X, multiply( X, Y ) ), true ) ] )
% 4.10/4.47 , 0, clause( 6306, [ =( 'additive_identity', ifeq2( product( inverse( X ),
% 4.10/4.47 X, Y ), true, Y, 'additive_identity' ) ) ] )
% 4.10/4.47 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, inverse( X ) )] ),
% 4.10/4.47 substitution( 1, [ :=( X, X ), :=( Y, multiply( X, inverse( X ) ) )] )
% 4.10/4.47 ).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 paramod(
% 4.10/4.47 clause( 6309, [ =( 'additive_identity', multiply( X, inverse( X ) ) ) ] )
% 4.10/4.47 , clause( 0, [ =( ifeq2( X, X, Y, Z ), Y ) ] )
% 4.10/4.47 , 0, clause( 6308, [ =( 'additive_identity', ifeq2( true, true, multiply( X
% 4.10/4.47 , inverse( X ) ), 'additive_identity' ) ) ] )
% 4.10/4.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, multiply( X, inverse( X )
% 4.10/4.47 ) ), :=( Z, 'additive_identity' )] ), substitution( 1, [ :=( X, X )] )
% 4.10/4.47 ).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 eqswap(
% 4.10/4.47 clause( 6310, [ =( multiply( X, inverse( X ) ), 'additive_identity' ) ] )
% 4.10/4.47 , clause( 6309, [ =( 'additive_identity', multiply( X, inverse( X ) ) ) ]
% 4.10/4.47 )
% 4.10/4.47 , 0, substitution( 0, [ :=( X, X )] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 subsumption(
% 4.10/4.47 clause( 99, [ =( multiply( X, inverse( X ) ), 'additive_identity' ) ] )
% 4.10/4.47 , clause( 6310, [ =( multiply( X, inverse( X ) ), 'additive_identity' ) ]
% 4.10/4.47 )
% 4.10/4.47 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 eqswap(
% 4.10/4.47 clause( 6312, [ =( true, ifeq( product( X, Y, Z ), true, ifeq( sum( T, Z, U
% 4.10/4.47 ), true, ifeq( sum( T, Y, W ), true, ifeq( sum( T, X, V0 ), true,
% 4.10/4.47 product( V0, W, U ), true ), true ), true ), true ) ) ] )
% 4.10/4.47 , clause( 14, [ =( ifeq( product( X, Y, Z ), true, ifeq( sum( T, Z, U ),
% 4.10/4.47 true, ifeq( sum( T, Y, W ), true, ifeq( sum( T, X, V0 ), true, product(
% 4.10/4.47 V0, W, U ), true ), true ), true ), true ), true ) ] )
% 4.10/4.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ),
% 4.10/4.47 :=( U, U ), :=( W, W ), :=( V0, V0 )] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 paramod(
% 4.10/4.47 clause( 6315, [ =( true, ifeq( product( X, y, Y ), true, ifeq( sum( x, Y, Z
% 4.10/4.47 ), true, ifeq( true, true, ifeq( sum( x, X, T ), true, product( T, z, Z
% 4.10/4.47 ), true ), true ), true ), true ) ) ] )
% 4.10/4.47 , clause( 24, [ =( sum( x, y, z ), true ) ] )
% 4.10/4.47 , 0, clause( 6312, [ =( true, ifeq( product( X, Y, Z ), true, ifeq( sum( T
% 4.10/4.47 , Z, U ), true, ifeq( sum( T, Y, W ), true, ifeq( sum( T, X, V0 ), true,
% 4.10/4.47 product( V0, W, U ), true ), true ), true ), true ) ) ] )
% 4.10/4.47 , 0, 15, substitution( 0, [] ), substitution( 1, [ :=( X, X ), :=( Y, y ),
% 4.10/4.47 :=( Z, Y ), :=( T, x ), :=( U, Z ), :=( W, z ), :=( V0, T )] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 paramod(
% 4.10/4.47 clause( 6319, [ =( true, ifeq( product( X, y, Y ), true, ifeq( sum( x, Y, Z
% 4.10/4.47 ), true, ifeq( sum( x, X, T ), true, product( T, z, Z ), true ), true )
% 4.10/4.47 , true ) ) ] )
% 4.10/4.47 , clause( 1, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 4.10/4.47 , 0, clause( 6315, [ =( true, ifeq( product( X, y, Y ), true, ifeq( sum( x
% 4.10/4.47 , Y, Z ), true, ifeq( true, true, ifeq( sum( x, X, T ), true, product( T
% 4.10/4.47 , z, Z ), true ), true ), true ), true ) ) ] )
% 4.10/4.47 , 0, 14, substitution( 0, [ :=( X, true ), :=( Y, ifeq( sum( x, X, T ),
% 4.10/4.47 true, product( T, z, Z ), true ) ), :=( Z, true )] ), substitution( 1, [
% 4.10/4.47 :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 eqswap(
% 4.10/4.47 clause( 6320, [ =( ifeq( product( X, y, Y ), true, ifeq( sum( x, Y, Z ),
% 4.10/4.47 true, ifeq( sum( x, X, T ), true, product( T, z, Z ), true ), true ),
% 4.10/4.47 true ), true ) ] )
% 4.10/4.47 , clause( 6319, [ =( true, ifeq( product( X, y, Y ), true, ifeq( sum( x, Y
% 4.10/4.47 , Z ), true, ifeq( sum( x, X, T ), true, product( T, z, Z ), true ), true
% 4.10/4.47 ), true ) ) ] )
% 4.10/4.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 4.10/4.47 ).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 subsumption(
% 4.10/4.47 clause( 173, [ =( ifeq( product( X, y, Y ), true, ifeq( sum( x, Y, Z ),
% 4.10/4.47 true, ifeq( sum( x, X, T ), true, product( T, z, Z ), true ), true ),
% 4.10/4.47 true ), true ) ] )
% 4.10/4.47 , clause( 6320, [ =( ifeq( product( X, y, Y ), true, ifeq( sum( x, Y, Z ),
% 4.10/4.47 true, ifeq( sum( x, X, T ), true, product( T, z, Z ), true ), true ),
% 4.10/4.47 true ), true ) ] )
% 4.10/4.47 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 4.10/4.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 eqswap(
% 4.10/4.47 clause( 6322, [ =( true, ifeq( product( X, Y, Z ), true, ifeq( product( X,
% 4.10/4.47 T, 'additive_identity' ), true, ifeq( sum( T, Y, U ), true, product( X, U
% 4.10/4.47 , Z ), true ), true ), true ) ) ] )
% 4.10/4.47 , clause( 89, [ =( ifeq( product( Y, Z, X ), true, ifeq( product( Y, T,
% 4.10/4.47 'additive_identity' ), true, ifeq( sum( T, Z, U ), true, product( Y, U, X
% 4.10/4.47 ), true ), true ), true ), true ) ] )
% 4.10/4.47 , 0, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y ), :=( T, T ),
% 4.10/4.47 :=( U, U )] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 paramod(
% 4.10/4.47 clause( 6324, [ =( true, ifeq( product( X, 'additive_identity', Y ), true,
% 4.10/4.47 ifeq( product( X, Z, 'additive_identity' ), true, ifeq( true, true,
% 4.10/4.47 product( X, Z, Y ), true ), true ), true ) ) ] )
% 4.10/4.47 , clause( 7, [ =( sum( X, 'additive_identity', X ), true ) ] )
% 4.10/4.47 , 0, clause( 6322, [ =( true, ifeq( product( X, Y, Z ), true, ifeq( product(
% 4.10/4.47 X, T, 'additive_identity' ), true, ifeq( sum( T, Y, U ), true, product( X
% 4.10/4.47 , U, Z ), true ), true ), true ) ) ] )
% 4.10/4.47 , 0, 15, substitution( 0, [ :=( X, Z )] ), substitution( 1, [ :=( X, X ),
% 4.10/4.47 :=( Y, 'additive_identity' ), :=( Z, Y ), :=( T, Z ), :=( U, Z )] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 paramod(
% 4.10/4.47 clause( 6325, [ =( true, ifeq( product( X, 'additive_identity', Y ), true,
% 4.10/4.47 ifeq( product( X, Z, 'additive_identity' ), true, product( X, Z, Y ),
% 4.10/4.47 true ), true ) ) ] )
% 4.10/4.47 , clause( 1, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 4.10/4.47 , 0, clause( 6324, [ =( true, ifeq( product( X, 'additive_identity', Y ),
% 4.10/4.47 true, ifeq( product( X, Z, 'additive_identity' ), true, ifeq( true, true
% 4.10/4.47 , product( X, Z, Y ), true ), true ), true ) ) ] )
% 4.10/4.47 , 0, 14, substitution( 0, [ :=( X, true ), :=( Y, product( X, Z, Y ) ),
% 4.10/4.47 :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )
% 4.10/4.47 ).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 eqswap(
% 4.10/4.47 clause( 6326, [ =( ifeq( product( X, 'additive_identity', Y ), true, ifeq(
% 4.10/4.47 product( X, Z, 'additive_identity' ), true, product( X, Z, Y ), true ),
% 4.10/4.47 true ), true ) ] )
% 4.10/4.47 , clause( 6325, [ =( true, ifeq( product( X, 'additive_identity', Y ), true
% 4.10/4.47 , ifeq( product( X, Z, 'additive_identity' ), true, product( X, Z, Y ),
% 4.10/4.47 true ), true ) ) ] )
% 4.10/4.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 subsumption(
% 4.10/4.47 clause( 673, [ =( ifeq( product( Y, 'additive_identity', Z ), true, ifeq(
% 4.10/4.47 product( Y, X, 'additive_identity' ), true, product( Y, X, Z ), true ),
% 4.10/4.47 true ), true ) ] )
% 4.10/4.47 , clause( 6326, [ =( ifeq( product( X, 'additive_identity', Y ), true, ifeq(
% 4.10/4.47 product( X, Z, 'additive_identity' ), true, product( X, Z, Y ), true ),
% 4.10/4.47 true ), true ) ] )
% 4.10/4.47 , substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] ),
% 4.10/4.47 permutation( 0, [ ==>( 0, 0 )] ) ).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 eqswap(
% 4.10/4.47 clause( 6328, [ =( true, ifeq( product( X, y, Y ), true, ifeq( sum( x, Y, Z
% 4.10/4.47 ), true, ifeq( sum( x, X, T ), true, product( T, z, Z ), true ), true )
% 4.10/4.47 , true ) ) ] )
% 4.10/4.47 , clause( 173, [ =( ifeq( product( X, y, Y ), true, ifeq( sum( x, Y, Z ),
% 4.10/4.47 true, ifeq( sum( x, X, T ), true, product( T, z, Z ), true ), true ),
% 4.10/4.47 true ), true ) ] )
% 4.10/4.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 4.10/4.47 ).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 paramod(
% 4.10/4.47 clause( 6330, [ =( true, ifeq( product( X, y, 'additive_identity' ), true,
% 4.10/4.47 ifeq( true, true, ifeq( sum( x, X, Y ), true, product( Y, z, x ), true )
% 4.10/4.47 , true ), true ) ) ] )
% 4.10/4.47 , clause( 7, [ =( sum( X, 'additive_identity', X ), true ) ] )
% 4.10/4.47 , 0, clause( 6328, [ =( true, ifeq( product( X, y, Y ), true, ifeq( sum( x
% 4.10/4.47 , Y, Z ), true, ifeq( sum( x, X, T ), true, product( T, z, Z ), true ),
% 4.10/4.47 true ), true ) ) ] )
% 4.10/4.47 , 0, 9, substitution( 0, [ :=( X, x )] ), substitution( 1, [ :=( X, X ),
% 4.10/4.47 :=( Y, 'additive_identity' ), :=( Z, x ), :=( T, Y )] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 paramod(
% 4.10/4.47 clause( 6334, [ =( true, ifeq( product( X, y, 'additive_identity' ), true,
% 4.10/4.47 ifeq( sum( x, X, Y ), true, product( Y, z, x ), true ), true ) ) ] )
% 4.10/4.47 , clause( 1, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 4.10/4.47 , 0, clause( 6330, [ =( true, ifeq( product( X, y, 'additive_identity' ),
% 4.10/4.47 true, ifeq( true, true, ifeq( sum( x, X, Y ), true, product( Y, z, x ),
% 4.10/4.47 true ), true ), true ) ) ] )
% 4.10/4.47 , 0, 8, substitution( 0, [ :=( X, true ), :=( Y, ifeq( sum( x, X, Y ), true
% 4.10/4.47 , product( Y, z, x ), true ) ), :=( Z, true )] ), substitution( 1, [ :=(
% 4.10/4.47 X, X ), :=( Y, Y )] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 eqswap(
% 4.10/4.47 clause( 6335, [ =( ifeq( product( X, y, 'additive_identity' ), true, ifeq(
% 4.10/4.47 sum( x, X, Y ), true, product( Y, z, x ), true ), true ), true ) ] )
% 4.10/4.47 , clause( 6334, [ =( true, ifeq( product( X, y, 'additive_identity' ), true
% 4.10/4.47 , ifeq( sum( x, X, Y ), true, product( Y, z, x ), true ), true ) ) ] )
% 4.10/4.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 subsumption(
% 4.10/4.47 clause( 1171, [ =( ifeq( product( X, y, 'additive_identity' ), true, ifeq(
% 4.10/4.47 sum( x, X, Y ), true, product( Y, z, x ), true ), true ), true ) ] )
% 4.10/4.47 , clause( 6335, [ =( ifeq( product( X, y, 'additive_identity' ), true, ifeq(
% 4.10/4.47 sum( x, X, Y ), true, product( Y, z, x ), true ), true ), true ) ] )
% 4.10/4.47 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 4.10/4.47 )] ) ).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 eqswap(
% 4.10/4.47 clause( 6337, [ =( true, ifeq( product( X, 'additive_identity', Y ), true,
% 4.10/4.47 ifeq( product( X, Z, 'additive_identity' ), true, product( X, Z, Y ),
% 4.10/4.47 true ), true ) ) ] )
% 4.10/4.47 , clause( 673, [ =( ifeq( product( Y, 'additive_identity', Z ), true, ifeq(
% 4.10/4.47 product( Y, X, 'additive_identity' ), true, product( Y, X, Z ), true ),
% 4.10/4.47 true ), true ) ] )
% 4.10/4.47 , 0, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 paramod(
% 4.10/4.47 clause( 6339, [ =( true, ifeq( product( X, 'additive_identity', Y ), true,
% 4.10/4.47 ifeq( true, true, product( X, inverse( X ), Y ), true ), true ) ) ] )
% 4.10/4.47 , clause( 21, [ =( product( X, inverse( X ), 'additive_identity' ), true )
% 4.10/4.47 ] )
% 4.10/4.47 , 0, clause( 6337, [ =( true, ifeq( product( X, 'additive_identity', Y ),
% 4.10/4.47 true, ifeq( product( X, Z, 'additive_identity' ), true, product( X, Z, Y
% 4.10/4.47 ), true ), true ) ) ] )
% 4.10/4.47 , 0, 9, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 4.10/4.47 :=( Y, Y ), :=( Z, inverse( X ) )] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 paramod(
% 4.10/4.47 clause( 6344, [ =( true, ifeq( product( X, 'additive_identity', Y ), true,
% 4.10/4.47 product( X, inverse( X ), Y ), true ) ) ] )
% 4.10/4.47 , clause( 1, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 4.10/4.47 , 0, clause( 6339, [ =( true, ifeq( product( X, 'additive_identity', Y ),
% 4.10/4.47 true, ifeq( true, true, product( X, inverse( X ), Y ), true ), true ) ) ]
% 4.10/4.47 )
% 4.10/4.47 , 0, 8, substitution( 0, [ :=( X, true ), :=( Y, product( X, inverse( X ),
% 4.10/4.47 Y ) ), :=( Z, true )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )
% 4.10/4.47 ).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 eqswap(
% 4.10/4.47 clause( 6345, [ =( ifeq( product( X, 'additive_identity', Y ), true,
% 4.10/4.47 product( X, inverse( X ), Y ), true ), true ) ] )
% 4.10/4.47 , clause( 6344, [ =( true, ifeq( product( X, 'additive_identity', Y ), true
% 4.10/4.47 , product( X, inverse( X ), Y ), true ) ) ] )
% 4.10/4.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 subsumption(
% 4.10/4.47 clause( 4805, [ =( ifeq( product( X, 'additive_identity', Y ), true,
% 4.10/4.47 product( X, inverse( X ), Y ), true ), true ) ] )
% 4.10/4.47 , clause( 6345, [ =( ifeq( product( X, 'additive_identity', Y ), true,
% 4.10/4.47 product( X, inverse( X ), Y ), true ), true ) ] )
% 4.10/4.47 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 4.10/4.47 )] ) ).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 eqswap(
% 4.10/4.47 clause( 6347, [ =( true, ifeq( product( X, 'additive_identity', Y ), true,
% 4.10/4.47 product( X, inverse( X ), Y ), true ) ) ] )
% 4.10/4.47 , clause( 4805, [ =( ifeq( product( X, 'additive_identity', Y ), true,
% 4.10/4.47 product( X, inverse( X ), Y ), true ), true ) ] )
% 4.10/4.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 paramod(
% 4.10/4.47 clause( 6349, [ =( true, ifeq( true, true, product( X, inverse( X ),
% 4.10/4.47 multiply( 'additive_identity', X ) ), true ) ) ] )
% 4.10/4.47 , clause( 26, [ =( product( Y, X, multiply( X, Y ) ), true ) ] )
% 4.10/4.47 , 0, clause( 6347, [ =( true, ifeq( product( X, 'additive_identity', Y ),
% 4.10/4.47 true, product( X, inverse( X ), Y ), true ) ) ] )
% 4.10/4.47 , 0, 3, substitution( 0, [ :=( X, 'additive_identity' ), :=( Y, X )] ),
% 4.10/4.47 substitution( 1, [ :=( X, X ), :=( Y, multiply( 'additive_identity', X )
% 4.10/4.47 )] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 paramod(
% 4.10/4.47 clause( 6351, [ =( true, product( X, inverse( X ), multiply(
% 4.10/4.47 'additive_identity', X ) ) ) ] )
% 4.10/4.47 , clause( 1, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 4.10/4.47 , 0, clause( 6349, [ =( true, ifeq( true, true, product( X, inverse( X ),
% 4.10/4.47 multiply( 'additive_identity', X ) ), true ) ) ] )
% 4.10/4.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, product( X, inverse( X ),
% 4.10/4.47 multiply( 'additive_identity', X ) ) ), :=( Z, true )] ), substitution( 1
% 4.10/4.47 , [ :=( X, X )] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 eqswap(
% 4.10/4.47 clause( 6352, [ =( product( X, inverse( X ), multiply( 'additive_identity'
% 4.10/4.47 , X ) ), true ) ] )
% 4.10/4.47 , clause( 6351, [ =( true, product( X, inverse( X ), multiply(
% 4.10/4.47 'additive_identity', X ) ) ) ] )
% 4.10/4.47 , 0, substitution( 0, [ :=( X, X )] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 subsumption(
% 4.10/4.47 clause( 4806, [ =( product( X, inverse( X ), multiply( 'additive_identity'
% 4.10/4.47 , X ) ), true ) ] )
% 4.10/4.47 , clause( 6352, [ =( product( X, inverse( X ), multiply(
% 4.10/4.47 'additive_identity', X ) ), true ) ] )
% 4.10/4.47 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 eqswap(
% 4.10/4.47 clause( 6354, [ =( multiply( X, Y ), ifeq2( product( X, Y, Z ), true, Z,
% 4.10/4.47 multiply( X, Y ) ) ) ] )
% 4.10/4.47 , clause( 31, [ =( ifeq2( product( X, Y, Z ), true, Z, multiply( X, Y ) ),
% 4.10/4.47 multiply( X, Y ) ) ] )
% 4.10/4.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 paramod(
% 4.10/4.47 clause( 6357, [ =( multiply( X, inverse( X ) ), ifeq2( true, true, multiply(
% 4.10/4.47 'additive_identity', X ), multiply( X, inverse( X ) ) ) ) ] )
% 4.10/4.47 , clause( 4806, [ =( product( X, inverse( X ), multiply(
% 4.10/4.47 'additive_identity', X ) ), true ) ] )
% 4.10/4.47 , 0, clause( 6354, [ =( multiply( X, Y ), ifeq2( product( X, Y, Z ), true,
% 4.10/4.47 Z, multiply( X, Y ) ) ) ] )
% 4.10/4.47 , 0, 6, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 4.10/4.47 :=( Y, inverse( X ) ), :=( Z, multiply( 'additive_identity', X ) )] )
% 4.10/4.47 ).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 paramod(
% 4.10/4.47 clause( 6358, [ =( multiply( X, inverse( X ) ), multiply(
% 4.10/4.47 'additive_identity', X ) ) ] )
% 4.10/4.47 , clause( 0, [ =( ifeq2( X, X, Y, Z ), Y ) ] )
% 4.10/4.47 , 0, clause( 6357, [ =( multiply( X, inverse( X ) ), ifeq2( true, true,
% 4.10/4.47 multiply( 'additive_identity', X ), multiply( X, inverse( X ) ) ) ) ] )
% 4.10/4.47 , 0, 5, substitution( 0, [ :=( X, true ), :=( Y, multiply(
% 4.10/4.47 'additive_identity', X ) ), :=( Z, multiply( X, inverse( X ) ) )] ),
% 4.10/4.47 substitution( 1, [ :=( X, X )] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 paramod(
% 4.10/4.47 clause( 6359, [ =( 'additive_identity', multiply( 'additive_identity', X )
% 4.10/4.47 ) ] )
% 4.10/4.47 , clause( 99, [ =( multiply( X, inverse( X ) ), 'additive_identity' ) ] )
% 4.10/4.47 , 0, clause( 6358, [ =( multiply( X, inverse( X ) ), multiply(
% 4.10/4.47 'additive_identity', X ) ) ] )
% 4.10/4.47 , 0, 1, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 4.10/4.47 ).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 eqswap(
% 4.10/4.47 clause( 6360, [ =( multiply( 'additive_identity', X ), 'additive_identity'
% 4.10/4.47 ) ] )
% 4.10/4.47 , clause( 6359, [ =( 'additive_identity', multiply( 'additive_identity', X
% 4.10/4.47 ) ) ] )
% 4.10/4.47 , 0, substitution( 0, [ :=( X, X )] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 subsumption(
% 4.10/4.47 clause( 4809, [ =( multiply( 'additive_identity', X ), 'additive_identity'
% 4.10/4.47 ) ] )
% 4.10/4.47 , clause( 6360, [ =( multiply( 'additive_identity', X ),
% 4.10/4.47 'additive_identity' ) ] )
% 4.10/4.47 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 eqswap(
% 4.10/4.47 clause( 6362, [ =( true, product( X, Y, multiply( X, Y ) ) ) ] )
% 4.10/4.47 , clause( 3, [ =( product( X, Y, multiply( X, Y ) ), true ) ] )
% 4.10/4.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 paramod(
% 4.10/4.47 clause( 6363, [ =( true, product( 'additive_identity', X,
% 4.10/4.47 'additive_identity' ) ) ] )
% 4.10/4.47 , clause( 4809, [ =( multiply( 'additive_identity', X ),
% 4.10/4.47 'additive_identity' ) ] )
% 4.10/4.47 , 0, clause( 6362, [ =( true, product( X, Y, multiply( X, Y ) ) ) ] )
% 4.10/4.47 , 0, 5, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X,
% 4.10/4.47 'additive_identity' ), :=( Y, X )] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 eqswap(
% 4.10/4.47 clause( 6364, [ =( product( 'additive_identity', X, 'additive_identity' ),
% 4.10/4.47 true ) ] )
% 4.10/4.47 , clause( 6363, [ =( true, product( 'additive_identity', X,
% 4.10/4.47 'additive_identity' ) ) ] )
% 4.10/4.47 , 0, substitution( 0, [ :=( X, X )] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 subsumption(
% 4.10/4.47 clause( 4819, [ =( product( 'additive_identity', X, 'additive_identity' ),
% 4.10/4.47 true ) ] )
% 4.10/4.47 , clause( 6364, [ =( product( 'additive_identity', X, 'additive_identity' )
% 4.10/4.47 , true ) ] )
% 4.10/4.47 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 eqswap(
% 4.10/4.47 clause( 6366, [ =( true, ifeq( product( X, y, 'additive_identity' ), true,
% 4.10/4.47 ifeq( sum( x, X, Y ), true, product( Y, z, x ), true ), true ) ) ] )
% 4.10/4.47 , clause( 1171, [ =( ifeq( product( X, y, 'additive_identity' ), true, ifeq(
% 4.10/4.47 sum( x, X, Y ), true, product( Y, z, x ), true ), true ), true ) ] )
% 4.10/4.47 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 eqswap(
% 4.10/4.47 clause( 6370, [ ~( =( true, product( x, z, x ) ) ) ] )
% 4.10/4.47 , clause( 25, [ ~( =( product( x, z, x ), true ) ) ] )
% 4.10/4.47 , 0, substitution( 0, [] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 paramod(
% 4.10/4.47 clause( 6371, [ =( true, ifeq( product( 'additive_identity', y,
% 4.10/4.47 'additive_identity' ), true, ifeq( true, true, product( x, z, x ), true )
% 4.10/4.47 , true ) ) ] )
% 4.10/4.47 , clause( 7, [ =( sum( X, 'additive_identity', X ), true ) ] )
% 4.10/4.47 , 0, clause( 6366, [ =( true, ifeq( product( X, y, 'additive_identity' ),
% 4.10/4.47 true, ifeq( sum( x, X, Y ), true, product( Y, z, x ), true ), true ) ) ]
% 4.10/4.47 )
% 4.10/4.47 , 0, 9, substitution( 0, [ :=( X, x )] ), substitution( 1, [ :=( X,
% 4.10/4.47 'additive_identity' ), :=( Y, x )] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 paramod(
% 4.10/4.47 clause( 6372, [ =( true, ifeq( true, true, ifeq( true, true, product( x, z
% 4.10/4.47 , x ), true ), true ) ) ] )
% 4.10/4.47 , clause( 4819, [ =( product( 'additive_identity', X, 'additive_identity' )
% 4.10/4.47 , true ) ] )
% 4.10/4.47 , 0, clause( 6371, [ =( true, ifeq( product( 'additive_identity', y,
% 4.10/4.47 'additive_identity' ), true, ifeq( true, true, product( x, z, x ), true )
% 4.10/4.47 , true ) ) ] )
% 4.10/4.47 , 0, 3, substitution( 0, [ :=( X, y )] ), substitution( 1, [] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 paramod(
% 4.10/4.47 clause( 6373, [ =( true, ifeq( true, true, product( x, z, x ), true ) ) ]
% 4.10/4.47 )
% 4.10/4.47 , clause( 1, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 4.10/4.47 , 0, clause( 6372, [ =( true, ifeq( true, true, ifeq( true, true, product(
% 4.10/4.47 x, z, x ), true ), true ) ) ] )
% 4.10/4.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, ifeq( true, true, product(
% 4.10/4.47 x, z, x ), true ) ), :=( Z, true )] ), substitution( 1, [] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 paramod(
% 4.10/4.47 clause( 6375, [ =( true, product( x, z, x ) ) ] )
% 4.10/4.47 , clause( 1, [ =( ifeq( X, X, Y, Z ), Y ) ] )
% 4.10/4.47 , 0, clause( 6373, [ =( true, ifeq( true, true, product( x, z, x ), true )
% 4.10/4.47 ) ] )
% 4.10/4.47 , 0, 2, substitution( 0, [ :=( X, true ), :=( Y, product( x, z, x ) ), :=(
% 4.10/4.47 Z, true )] ), substitution( 1, [] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 resolution(
% 4.10/4.47 clause( 6376, [] )
% 4.10/4.47 , clause( 6370, [ ~( =( true, product( x, z, x ) ) ) ] )
% 4.10/4.47 , 0, clause( 6375, [ =( true, product( x, z, x ) ) ] )
% 4.10/4.47 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 subsumption(
% 4.10/4.47 clause( 6070, [] )
% 4.10/4.47 , clause( 6376, [] )
% 4.10/4.47 , substitution( 0, [] ), permutation( 0, [] ) ).
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 end.
% 4.10/4.47
% 4.10/4.47 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 4.10/4.47
% 4.10/4.47 Memory use:
% 4.10/4.47
% 4.10/4.47 space for terms: 110935
% 4.10/4.47 space for clauses: 855546
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 clauses generated: 667284
% 4.10/4.47 clauses kept: 6071
% 4.10/4.47 clauses selected: 2317
% 4.10/4.47 clauses deleted: 1442
% 4.10/4.47 clauses inuse deleted: 798
% 4.10/4.47
% 4.10/4.47 subsentry: 21971
% 4.10/4.47 literals s-matched: 21319
% 4.10/4.47 literals matched: 21319
% 4.10/4.47 full subsumption: 0
% 4.10/4.47
% 4.10/4.47 checksum: -971404362
% 4.10/4.47
% 4.10/4.47
% 4.10/4.47 Bliksem ended
%------------------------------------------------------------------------------