%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWX204-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Tue May 5 06:56:48 PM UTC 2026
% Result : Unsatisfiable 0.82s 1.19s
% Output : Refutation 0.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX204-1 : TPTP v9.3.0. Released v9.3.0.
% 0.13/0.13 % Command : bliksem %s
% 0.18/0.34 % Computer : n015.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % DateTime : Tue May 5 11:29:31 EDT 2026
% 0.18/0.35 % CPUTime :
% 0.82/1.19 *** allocated 10000 integers for termspace/termends
% 0.82/1.19 *** allocated 10000 integers for clauses
% 0.82/1.19 *** allocated 10000 integers for justifications
% 0.82/1.19 Bliksem 1.12
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 Automatic Strategy Selection
% 0.82/1.19
% 0.82/1.19 Clauses:
% 0.82/1.19 [
% 0.82/1.19 [ =( x2( z, X ), X ) ],
% 0.82/1.19 [ =( x2( s( X ), Y ), s( x2( X, Y ) ) ) ],
% 0.82/1.19 [ =( x22( z, X ), z ) ],
% 0.82/1.19 [ =( x22( s( X ), Y ), x2( Y, x22( X, Y ) ) ) ],
% 0.82/1.19 [ =( 'mul_idem'( X ), eq( x22( X, X ), X ) ) ],
% 0.82/1.19 [ =( eq2( bfalse, btrue ), bfalse ) ],
% 0.82/1.19 [ =( eq2( btrue, bfalse ), bfalse ) ],
% 0.82/1.19 [ =( eq( s( X ), s( Y ) ), eq( X, Y ) ) ],
% 0.82/1.19 [ =( eq( z, s( X ) ), bfalse ) ],
% 0.82/1.19 [ =( eq( s( X ), z ), bfalse ) ],
% 0.82/1.19 [ =( eq( X, X ), btrue ) ],
% 0.82/1.19 [ =( eq2( X, X ), btrue ) ],
% 0.82/1.19 [ ~( =( eq2( 'mul_idem'( X ), bfalse ), btrue ) ) ]
% 0.82/1.19 ] .
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 percentage equality = 1.000000, percentage horn = 1.000000
% 0.82/1.19 This is a pure equality problem
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 Options Used:
% 0.82/1.19
% 0.82/1.19 useres = 1
% 0.82/1.19 useparamod = 1
% 0.82/1.19 useeqrefl = 1
% 0.82/1.19 useeqfact = 1
% 0.82/1.19 usefactor = 1
% 0.82/1.19 usesimpsplitting = 0
% 0.82/1.19 usesimpdemod = 5
% 0.82/1.19 usesimpres = 3
% 0.82/1.19
% 0.82/1.19 resimpinuse = 1000
% 0.82/1.19 resimpclauses = 20000
% 0.82/1.19 substype = eqrewr
% 0.82/1.19 backwardsubs = 1
% 0.82/1.19 selectoldest = 5
% 0.82/1.19
% 0.82/1.19 litorderings [0] = split
% 0.82/1.19 litorderings [1] = extend the termordering, first sorting on arguments
% 0.82/1.19
% 0.82/1.19 termordering = kbo
% 0.82/1.19
% 0.82/1.19 litapriori = 0
% 0.82/1.19 termapriori = 1
% 0.82/1.19 litaposteriori = 0
% 0.82/1.19 termaposteriori = 0
% 0.82/1.19 demodaposteriori = 0
% 0.82/1.19 ordereqreflfact = 0
% 0.82/1.19
% 0.82/1.19 litselect = negord
% 0.82/1.19
% 0.82/1.19 maxweight = 15
% 0.82/1.19 maxdepth = 30000
% 0.82/1.19 maxlength = 115
% 0.82/1.19 maxnrvars = 195
% 0.82/1.19 excuselevel = 1
% 0.82/1.19 increasemaxweight = 1
% 0.82/1.19
% 0.82/1.19 maxselected = 10000000
% 0.82/1.19 maxnrclauses = 10000000
% 0.82/1.19
% 0.82/1.19 showgenerated = 0
% 0.82/1.19 showkept = 0
% 0.82/1.19 showselected = 0
% 0.82/1.19 showdeleted = 0
% 0.82/1.19 showresimp = 1
% 0.82/1.19 showstatus = 2000
% 0.82/1.19
% 0.82/1.19 prologoutput = 1
% 0.82/1.19 nrgoals = 5000000
% 0.82/1.19 totalproof = 1
% 0.82/1.19
% 0.82/1.19 Symbols occurring in the translation:
% 0.82/1.19
% 0.82/1.19 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.82/1.19 . [1, 2] (w:1, o:22, a:1, s:1, b:0),
% 0.82/1.19 ! [4, 1] (w:0, o:15, a:1, s:1, b:0),
% 0.82/1.19 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.82/1.19 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.82/1.19 z [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.82/1.19 x2 [41, 2] (w:1, o:47, a:1, s:1, b:0),
% 0.82/1.19 s [43, 1] (w:1, o:20, a:1, s:1, b:0),
% 0.82/1.19 x22 [44, 2] (w:1, o:48, a:1, s:1, b:0),
% 0.82/1.19 'mul_idem' [46, 1] (w:1, o:21, a:1, s:1, b:0),
% 0.82/1.19 eq [47, 2] (w:1, o:49, a:1, s:1, b:0),
% 0.82/1.19 bfalse [48, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.82/1.19 btrue [49, 0] (w:1, o:14, a:1, s:1, b:0),
% 0.82/1.19 eq2 [50, 2] (w:1, o:50, a:1, s:1, b:0).
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 Starting Search:
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 Bliksems!, er is een bewijs:
% 0.82/1.19 % SZS status Unsatisfiable
% 0.82/1.19 % SZS output start Refutation
% 0.82/1.19
% 0.82/1.19 clause( 0, [ =( x2( z, X ), X ) ] )
% 0.82/1.19 .
% 0.82/1.19 clause( 1, [ =( x2( s( X ), Y ), s( x2( X, Y ) ) ) ] )
% 0.82/1.19 .
% 0.82/1.19 clause( 2, [ =( x22( z, X ), z ) ] )
% 0.82/1.19 .
% 0.82/1.19 clause( 3, [ =( x2( Y, x22( X, Y ) ), x22( s( X ), Y ) ) ] )
% 0.82/1.19 .
% 0.82/1.19 clause( 4, [ =( eq( x22( X, X ), X ), 'mul_idem'( X ) ) ] )
% 0.82/1.19 .
% 0.82/1.19 clause( 7, [ =( eq( s( X ), s( Y ) ), eq( X, Y ) ) ] )
% 0.82/1.19 .
% 0.82/1.19 clause( 9, [ =( eq( s( X ), z ), bfalse ) ] )
% 0.82/1.19 .
% 0.82/1.19 clause( 11, [ =( eq2( X, X ), btrue ) ] )
% 0.82/1.19 .
% 0.82/1.19 clause( 12, [ ~( =( eq2( 'mul_idem'( X ), bfalse ), btrue ) ) ] )
% 0.82/1.19 .
% 0.82/1.19 clause( 15, [ =( x22( s( z ), X ), x2( X, z ) ) ] )
% 0.82/1.19 .
% 0.82/1.19 clause( 16, [ =( x2( X, x2( X, z ) ), x22( s( s( z ) ), X ) ) ] )
% 0.82/1.19 .
% 0.82/1.19 clause( 20, [ =( 'mul_idem'( s( s( z ) ) ), bfalse ) ] )
% 0.82/1.19 .
% 0.82/1.19 clause( 23, [] )
% 0.82/1.19 .
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 % SZS output end Refutation
% 0.82/1.19 found a proof!
% 0.82/1.19
% 0.82/1.19 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.82/1.19
% 0.82/1.19 initialclauses(
% 0.82/1.19 [ clause( 25, [ =( x2( z, X ), X ) ] )
% 0.82/1.19 , clause( 26, [ =( x2( s( X ), Y ), s( x2( X, Y ) ) ) ] )
% 0.82/1.19 , clause( 27, [ =( x22( z, X ), z ) ] )
% 0.82/1.19 , clause( 28, [ =( x22( s( X ), Y ), x2( Y, x22( X, Y ) ) ) ] )
% 0.82/1.19 , clause( 29, [ =( 'mul_idem'( X ), eq( x22( X, X ), X ) ) ] )
% 0.82/1.19 , clause( 30, [ =( eq2( bfalse, btrue ), bfalse ) ] )
% 0.82/1.19 , clause( 31, [ =( eq2( btrue, bfalse ), bfalse ) ] )
% 0.82/1.19 , clause( 32, [ =( eq( s( X ), s( Y ) ), eq( X, Y ) ) ] )
% 0.82/1.19 , clause( 33, [ =( eq( z, s( X ) ), bfalse ) ] )
% 0.82/1.19 , clause( 34, [ =( eq( s( X ), z ), bfalse ) ] )
% 0.82/1.19 , clause( 35, [ =( eq( X, X ), btrue ) ] )
% 0.82/1.19 , clause( 36, [ =( eq2( X, X ), btrue ) ] )
% 0.82/1.19 , clause( 37, [ ~( =( eq2( 'mul_idem'( X ), bfalse ), btrue ) ) ] )
% 0.82/1.19 ] ).
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 subsumption(
% 0.82/1.19 clause( 0, [ =( x2( z, X ), X ) ] )
% 0.82/1.19 , clause( 25, [ =( x2( z, X ), X ) ] )
% 0.82/1.19 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 subsumption(
% 0.82/1.19 clause( 1, [ =( x2( s( X ), Y ), s( x2( X, Y ) ) ) ] )
% 0.82/1.19 , clause( 26, [ =( x2( s( X ), Y ), s( x2( X, Y ) ) ) ] )
% 0.82/1.19 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.82/1.19 )] ) ).
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 subsumption(
% 0.82/1.19 clause( 2, [ =( x22( z, X ), z ) ] )
% 0.82/1.19 , clause( 27, [ =( x22( z, X ), z ) ] )
% 0.82/1.19 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 eqswap(
% 0.82/1.19 clause( 47, [ =( x2( Y, x22( X, Y ) ), x22( s( X ), Y ) ) ] )
% 0.82/1.19 , clause( 28, [ =( x22( s( X ), Y ), x2( Y, x22( X, Y ) ) ) ] )
% 0.82/1.19 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 subsumption(
% 0.82/1.19 clause( 3, [ =( x2( Y, x22( X, Y ) ), x22( s( X ), Y ) ) ] )
% 0.82/1.19 , clause( 47, [ =( x2( Y, x22( X, Y ) ), x22( s( X ), Y ) ) ] )
% 0.82/1.19 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.82/1.19 )] ) ).
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 eqswap(
% 0.82/1.19 clause( 52, [ =( eq( x22( X, X ), X ), 'mul_idem'( X ) ) ] )
% 0.82/1.19 , clause( 29, [ =( 'mul_idem'( X ), eq( x22( X, X ), X ) ) ] )
% 0.82/1.19 , 0, substitution( 0, [ :=( X, X )] )).
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 subsumption(
% 0.82/1.19 clause( 4, [ =( eq( x22( X, X ), X ), 'mul_idem'( X ) ) ] )
% 0.82/1.19 , clause( 52, [ =( eq( x22( X, X ), X ), 'mul_idem'( X ) ) ] )
% 0.82/1.19 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 subsumption(
% 0.82/1.19 clause( 7, [ =( eq( s( X ), s( Y ) ), eq( X, Y ) ) ] )
% 0.82/1.19 , clause( 32, [ =( eq( s( X ), s( Y ) ), eq( X, Y ) ) ] )
% 0.82/1.19 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.82/1.19 )] ) ).
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 subsumption(
% 0.82/1.19 clause( 9, [ =( eq( s( X ), z ), bfalse ) ] )
% 0.82/1.19 , clause( 34, [ =( eq( s( X ), z ), bfalse ) ] )
% 0.82/1.19 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 subsumption(
% 0.82/1.19 clause( 11, [ =( eq2( X, X ), btrue ) ] )
% 0.82/1.19 , clause( 36, [ =( eq2( X, X ), btrue ) ] )
% 0.82/1.19 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 subsumption(
% 0.82/1.19 clause( 12, [ ~( =( eq2( 'mul_idem'( X ), bfalse ), btrue ) ) ] )
% 0.82/1.19 , clause( 37, [ ~( =( eq2( 'mul_idem'( X ), bfalse ), btrue ) ) ] )
% 0.82/1.19 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 eqswap(
% 0.82/1.19 clause( 97, [ =( x22( s( Y ), X ), x2( X, x22( Y, X ) ) ) ] )
% 0.82/1.19 , clause( 3, [ =( x2( Y, x22( X, Y ) ), x22( s( X ), Y ) ) ] )
% 0.82/1.19 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 paramod(
% 0.82/1.19 clause( 98, [ =( x22( s( z ), X ), x2( X, z ) ) ] )
% 0.82/1.19 , clause( 2, [ =( x22( z, X ), z ) ] )
% 0.82/1.19 , 0, clause( 97, [ =( x22( s( Y ), X ), x2( X, x22( Y, X ) ) ) ] )
% 0.82/1.19 , 0, 7, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 0.82/1.19 :=( Y, z )] )).
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 subsumption(
% 0.82/1.19 clause( 15, [ =( x22( s( z ), X ), x2( X, z ) ) ] )
% 0.82/1.19 , clause( 98, [ =( x22( s( z ), X ), x2( X, z ) ) ] )
% 0.82/1.19 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 eqswap(
% 0.82/1.19 clause( 101, [ =( x22( s( Y ), X ), x2( X, x22( Y, X ) ) ) ] )
% 0.82/1.19 , clause( 3, [ =( x2( Y, x22( X, Y ) ), x22( s( X ), Y ) ) ] )
% 0.82/1.19 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X )] )).
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 paramod(
% 0.82/1.19 clause( 103, [ =( x22( s( s( z ) ), X ), x2( X, x2( X, z ) ) ) ] )
% 0.82/1.19 , clause( 15, [ =( x22( s( z ), X ), x2( X, z ) ) ] )
% 0.82/1.19 , 0, clause( 101, [ =( x22( s( Y ), X ), x2( X, x22( Y, X ) ) ) ] )
% 0.82/1.19 , 0, 8, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 0.82/1.19 :=( Y, s( z ) )] )).
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 eqswap(
% 0.82/1.19 clause( 105, [ =( x2( X, x2( X, z ) ), x22( s( s( z ) ), X ) ) ] )
% 0.82/1.19 , clause( 103, [ =( x22( s( s( z ) ), X ), x2( X, x2( X, z ) ) ) ] )
% 0.82/1.19 , 0, substitution( 0, [ :=( X, X )] )).
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 subsumption(
% 0.82/1.19 clause( 16, [ =( x2( X, x2( X, z ) ), x22( s( s( z ) ), X ) ) ] )
% 0.82/1.19 , clause( 105, [ =( x2( X, x2( X, z ) ), x22( s( s( z ) ), X ) ) ] )
% 0.82/1.19 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 eqswap(
% 0.82/1.19 clause( 106, [ =( x22( s( s( z ) ), X ), x2( X, x2( X, z ) ) ) ] )
% 0.82/1.19 , clause( 16, [ =( x2( X, x2( X, z ) ), x22( s( s( z ) ), X ) ) ] )
% 0.82/1.19 , 0, substitution( 0, [ :=( X, X )] )).
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 eqswap(
% 0.82/1.19 clause( 107, [ =( 'mul_idem'( X ), eq( x22( X, X ), X ) ) ] )
% 0.82/1.19 , clause( 4, [ =( eq( x22( X, X ), X ), 'mul_idem'( X ) ) ] )
% 0.82/1.19 , 0, substitution( 0, [ :=( X, X )] )).
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 paramod(
% 0.82/1.19 clause( 115, [ =( 'mul_idem'( s( s( z ) ) ), eq( x2( s( s( z ) ), x2( s( s(
% 0.82/1.19 z ) ), z ) ), s( s( z ) ) ) ) ] )
% 0.82/1.19 , clause( 106, [ =( x22( s( s( z ) ), X ), x2( X, x2( X, z ) ) ) ] )
% 0.82/1.19 , 0, clause( 107, [ =( 'mul_idem'( X ), eq( x22( X, X ), X ) ) ] )
% 0.82/1.19 , 0, 6, substitution( 0, [ :=( X, s( s( z ) ) )] ), substitution( 1, [ :=(
% 0.82/1.19 X, s( s( z ) ) )] )).
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 paramod(
% 0.82/1.19 clause( 117, [ =( 'mul_idem'( s( s( z ) ) ), eq( x2( s( s( z ) ), s( x2( s(
% 0.82/1.19 z ), z ) ) ), s( s( z ) ) ) ) ] )
% 0.82/1.19 , clause( 1, [ =( x2( s( X ), Y ), s( x2( X, Y ) ) ) ] )
% 0.82/1.19 , 0, clause( 115, [ =( 'mul_idem'( s( s( z ) ) ), eq( x2( s( s( z ) ), x2(
% 0.82/1.19 s( s( z ) ), z ) ), s( s( z ) ) ) ) ] )
% 0.82/1.19 , 0, 10, substitution( 0, [ :=( X, s( z ) ), :=( Y, z )] ), substitution( 1
% 0.82/1.19 , [] )).
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 paramod(
% 0.82/1.19 clause( 118, [ =( 'mul_idem'( s( s( z ) ) ), eq( s( x2( s( z ), s( x2( s( z
% 0.82/1.19 ), z ) ) ) ), s( s( z ) ) ) ) ] )
% 0.82/1.19 , clause( 1, [ =( x2( s( X ), Y ), s( x2( X, Y ) ) ) ] )
% 0.82/1.19 , 0, clause( 117, [ =( 'mul_idem'( s( s( z ) ) ), eq( x2( s( s( z ) ), s(
% 0.82/1.19 x2( s( z ), z ) ) ), s( s( z ) ) ) ) ] )
% 0.82/1.19 , 0, 6, substitution( 0, [ :=( X, s( z ) ), :=( Y, s( x2( s( z ), z ) ) )] )
% 0.82/1.19 , substitution( 1, [] )).
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 paramod(
% 0.82/1.19 clause( 132, [ =( 'mul_idem'( s( s( z ) ) ), eq( x2( s( z ), s( x2( s( z )
% 0.82/1.19 , z ) ) ), s( z ) ) ) ] )
% 0.82/1.19 , clause( 7, [ =( eq( s( X ), s( Y ) ), eq( X, Y ) ) ] )
% 0.82/1.19 , 0, clause( 118, [ =( 'mul_idem'( s( s( z ) ) ), eq( s( x2( s( z ), s( x2(
% 0.82/1.19 s( z ), z ) ) ) ), s( s( z ) ) ) ) ] )
% 0.82/1.19 , 0, 5, substitution( 0, [ :=( X, x2( s( z ), s( x2( s( z ), z ) ) ) ),
% 0.82/1.19 :=( Y, s( z ) )] ), substitution( 1, [] )).
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 paramod(
% 0.82/1.19 clause( 133, [ =( 'mul_idem'( s( s( z ) ) ), eq( s( x2( z, s( x2( s( z ), z
% 0.82/1.19 ) ) ) ), s( z ) ) ) ] )
% 0.82/1.19 , clause( 1, [ =( x2( s( X ), Y ), s( x2( X, Y ) ) ) ] )
% 0.82/1.19 , 0, clause( 132, [ =( 'mul_idem'( s( s( z ) ) ), eq( x2( s( z ), s( x2( s(
% 0.82/1.19 z ), z ) ) ), s( z ) ) ) ] )
% 0.82/1.19 , 0, 6, substitution( 0, [ :=( X, z ), :=( Y, s( x2( s( z ), z ) ) )] ),
% 0.82/1.19 substitution( 1, [] )).
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 paramod(
% 0.82/1.19 clause( 140, [ =( 'mul_idem'( s( s( z ) ) ), eq( x2( z, s( x2( s( z ), z )
% 0.82/1.19 ) ), z ) ) ] )
% 0.82/1.19 , clause( 7, [ =( eq( s( X ), s( Y ) ), eq( X, Y ) ) ] )
% 0.82/1.19 , 0, clause( 133, [ =( 'mul_idem'( s( s( z ) ) ), eq( s( x2( z, s( x2( s( z
% 0.82/1.19 ), z ) ) ) ), s( z ) ) ) ] )
% 0.82/1.19 , 0, 5, substitution( 0, [ :=( X, x2( z, s( x2( s( z ), z ) ) ) ), :=( Y, z
% 0.82/1.19 )] ), substitution( 1, [] )).
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 paramod(
% 0.82/1.19 clause( 141, [ =( 'mul_idem'( s( s( z ) ) ), eq( s( x2( s( z ), z ) ), z )
% 0.82/1.19 ) ] )
% 0.82/1.19 , clause( 0, [ =( x2( z, X ), X ) ] )
% 0.82/1.19 , 0, clause( 140, [ =( 'mul_idem'( s( s( z ) ) ), eq( x2( z, s( x2( s( z )
% 0.82/1.19 , z ) ) ), z ) ) ] )
% 0.82/1.19 , 0, 6, substitution( 0, [ :=( X, s( x2( s( z ), z ) ) )] ), substitution(
% 0.82/1.19 1, [] )).
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 paramod(
% 0.82/1.19 clause( 142, [ =( 'mul_idem'( s( s( z ) ) ), eq( s( s( x2( z, z ) ) ), z )
% 0.82/1.19 ) ] )
% 0.82/1.19 , clause( 1, [ =( x2( s( X ), Y ), s( x2( X, Y ) ) ) ] )
% 0.82/1.19 , 0, clause( 141, [ =( 'mul_idem'( s( s( z ) ) ), eq( s( x2( s( z ), z ) )
% 0.82/1.19 , z ) ) ] )
% 0.82/1.19 , 0, 7, substitution( 0, [ :=( X, z ), :=( Y, z )] ), substitution( 1, [] )
% 0.82/1.19 ).
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 paramod(
% 0.82/1.19 clause( 143, [ =( 'mul_idem'( s( s( z ) ) ), bfalse ) ] )
% 0.82/1.19 , clause( 9, [ =( eq( s( X ), z ), bfalse ) ] )
% 0.82/1.19 , 0, clause( 142, [ =( 'mul_idem'( s( s( z ) ) ), eq( s( s( x2( z, z ) ) )
% 0.82/1.19 , z ) ) ] )
% 0.82/1.19 , 0, 5, substitution( 0, [ :=( X, s( x2( z, z ) ) )] ), substitution( 1, [] )
% 0.82/1.19 ).
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 subsumption(
% 0.82/1.19 clause( 20, [ =( 'mul_idem'( s( s( z ) ) ), bfalse ) ] )
% 0.82/1.19 , clause( 143, [ =( 'mul_idem'( s( s( z ) ) ), bfalse ) ] )
% 0.82/1.19 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 eqswap(
% 0.82/1.19 clause( 146, [ ~( =( btrue, eq2( 'mul_idem'( X ), bfalse ) ) ) ] )
% 0.82/1.19 , clause( 12, [ ~( =( eq2( 'mul_idem'( X ), bfalse ), btrue ) ) ] )
% 0.82/1.19 , 0, substitution( 0, [ :=( X, X )] )).
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 paramod(
% 0.82/1.19 clause( 148, [ ~( =( btrue, eq2( bfalse, bfalse ) ) ) ] )
% 0.82/1.19 , clause( 20, [ =( 'mul_idem'( s( s( z ) ) ), bfalse ) ] )
% 0.82/1.19 , 0, clause( 146, [ ~( =( btrue, eq2( 'mul_idem'( X ), bfalse ) ) ) ] )
% 0.82/1.19 , 0, 4, substitution( 0, [] ), substitution( 1, [ :=( X, s( s( z ) ) )] )
% 0.82/1.19 ).
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 paramod(
% 0.82/1.19 clause( 149, [ ~( =( btrue, btrue ) ) ] )
% 0.82/1.19 , clause( 11, [ =( eq2( X, X ), btrue ) ] )
% 0.82/1.19 , 0, clause( 148, [ ~( =( btrue, eq2( bfalse, bfalse ) ) ) ] )
% 0.82/1.19 , 0, 3, substitution( 0, [ :=( X, bfalse )] ), substitution( 1, [] )).
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 eqrefl(
% 0.82/1.19 clause( 150, [] )
% 0.82/1.19 , clause( 149, [ ~( =( btrue, btrue ) ) ] )
% 0.82/1.19 , 0, substitution( 0, [] )).
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 subsumption(
% 0.82/1.19 clause( 23, [] )
% 0.82/1.19 , clause( 150, [] )
% 0.82/1.19 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 end.
% 0.82/1.19
% 0.82/1.19 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.82/1.19
% 0.82/1.19 Memory use:
% 0.82/1.19
% 0.82/1.19 space for terms: 401
% 0.82/1.19 space for clauses: 2231
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 clauses generated: 77
% 0.82/1.19 clauses kept: 24
% 0.82/1.19 clauses selected: 20
% 0.82/1.19 clauses deleted: 0
% 0.82/1.19 clauses inuse deleted: 0
% 0.82/1.19
% 0.82/1.19 subsentry: 470
% 0.82/1.19 literals s-matched: 202
% 0.82/1.19 literals matched: 202
% 0.82/1.19 full subsumption: 0
% 0.82/1.19
% 0.82/1.19 checksum: 457710951
% 0.82/1.19
% 0.82/1.19
% 0.82/1.19 Bliksem ended
%------------------------------------------------------------------------------