%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWX206-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Tue May 5 06:56:48 PM UTC 2026
% Result : Unsatisfiable 0.68s 1.08s
% Output : Refutation 0.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX206-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : bliksem %s
% 0.15/0.33 % Computer : n013.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % DateTime : Tue May 5 11:33:40 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.68/1.08 *** allocated 10000 integers for termspace/termends
% 0.68/1.08 *** allocated 10000 integers for clauses
% 0.68/1.08 *** allocated 10000 integers for justifications
% 0.68/1.08 Bliksem 1.12
% 0.68/1.08
% 0.68/1.08
% 0.68/1.08 Automatic Strategy Selection
% 0.68/1.08
% 0.68/1.08 Clauses:
% 0.68/1.08 [
% 0.68/1.08 [ =( impl( btrue, X ), X ) ],
% 0.68/1.08 [ =( impl( bfalse, X ), btrue ) ],
% 0.68/1.08 [ =( x2( z, X ), X ) ],
% 0.68/1.08 [ =( x2( s( X ), Y ), s( x2( X, Y ) ) ) ],
% 0.68/1.08 [ =( 'plus_not_idem'( X ), impl( eq( x2( X, X ), X ), eq2( btrue, bfalse
% 0.68/1.08 ) ) ) ],
% 0.68/1.08 [ =( eq2( bfalse, btrue ), bfalse ) ],
% 0.68/1.08 [ =( eq2( btrue, bfalse ), bfalse ) ],
% 0.68/1.08 [ =( eq( s( X ), s( Y ) ), eq( X, Y ) ) ],
% 0.68/1.08 [ =( eq( z, s( X ) ), bfalse ) ],
% 0.68/1.08 [ =( eq( s( X ), z ), bfalse ) ],
% 0.68/1.08 [ =( eq( X, X ), btrue ) ],
% 0.68/1.08 [ =( eq2( X, X ), btrue ) ],
% 0.68/1.08 [ ~( =( eq2( 'plus_not_idem'( X ), bfalse ), btrue ) ) ]
% 0.68/1.08 ] .
% 0.68/1.08
% 0.68/1.08
% 0.68/1.08 percentage equality = 1.000000, percentage horn = 1.000000
% 0.68/1.08 This is a pure equality problem
% 0.68/1.08
% 0.68/1.08
% 0.68/1.08
% 0.68/1.08 Options Used:
% 0.68/1.08
% 0.68/1.08 useres = 1
% 0.68/1.08 useparamod = 1
% 0.68/1.08 useeqrefl = 1
% 0.68/1.08 useeqfact = 1
% 0.68/1.08 usefactor = 1
% 0.68/1.08 usesimpsplitting = 0
% 0.68/1.08 usesimpdemod = 5
% 0.68/1.08 usesimpres = 3
% 0.68/1.08
% 0.68/1.08 resimpinuse = 1000
% 0.68/1.08 resimpclauses = 20000
% 0.68/1.08 substype = eqrewr
% 0.68/1.08 backwardsubs = 1
% 0.68/1.08 selectoldest = 5
% 0.68/1.08
% 0.68/1.08 litorderings [0] = split
% 0.68/1.08 litorderings [1] = extend the termordering, first sorting on arguments
% 0.68/1.08
% 0.68/1.08 termordering = kbo
% 0.68/1.08
% 0.68/1.08 litapriori = 0
% 0.68/1.08 termapriori = 1
% 0.68/1.08 litaposteriori = 0
% 0.68/1.08 termaposteriori = 0
% 0.68/1.08 demodaposteriori = 0
% 0.68/1.08 ordereqreflfact = 0
% 0.68/1.08
% 0.68/1.08 litselect = negord
% 0.68/1.08
% 0.68/1.08 maxweight = 15
% 0.68/1.08 maxdepth = 30000
% 0.68/1.08 maxlength = 115
% 0.68/1.08 maxnrvars = 195
% 0.68/1.08 excuselevel = 1
% 0.68/1.08 increasemaxweight = 1
% 0.68/1.08
% 0.68/1.08 maxselected = 10000000
% 0.68/1.08 maxnrclauses = 10000000
% 0.68/1.08
% 0.68/1.08 showgenerated = 0
% 0.68/1.08 showkept = 0
% 0.68/1.08 showselected = 0
% 0.68/1.08 showdeleted = 0
% 0.68/1.08 showresimp = 1
% 0.68/1.08 showstatus = 2000
% 0.68/1.08
% 0.68/1.08 prologoutput = 1
% 0.68/1.08 nrgoals = 5000000
% 0.68/1.08 totalproof = 1
% 0.68/1.08
% 0.68/1.08 Symbols occurring in the translation:
% 0.68/1.08
% 0.68/1.08 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.68/1.08 . [1, 2] (w:1, o:23, a:1, s:1, b:0),
% 0.68/1.08 ! [4, 1] (w:0, o:16, a:1, s:1, b:0),
% 0.68/1.08 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.68/1.08 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.68/1.08 btrue [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.68/1.08 impl [41, 2] (w:1, o:48, a:1, s:1, b:0),
% 0.68/1.08 bfalse [42, 0] (w:1, o:11, a:1, s:1, b:0),
% 0.68/1.08 z [43, 0] (w:1, o:12, a:1, s:1, b:0),
% 0.68/1.08 x2 [45, 2] (w:1, o:49, a:1, s:1, b:0),
% 0.68/1.08 s [47, 1] (w:1, o:21, a:1, s:1, b:0),
% 0.68/1.08 'plus_not_idem' [49, 1] (w:1, o:22, a:1, s:1, b:0),
% 0.68/1.08 eq [50, 2] (w:1, o:50, a:1, s:1, b:0),
% 0.68/1.08 eq2 [51, 2] (w:1, o:51, a:1, s:1, b:0).
% 0.68/1.08
% 0.68/1.08
% 0.68/1.08 Starting Search:
% 0.68/1.08
% 0.68/1.08
% 0.68/1.08 Bliksems!, er is een bewijs:
% 0.68/1.08 % SZS status Unsatisfiable
% 0.68/1.08 % SZS output start Refutation
% 0.68/1.08
% 0.68/1.08 clause( 0, [ =( impl( btrue, X ), X ) ] )
% 0.68/1.08 .
% 0.68/1.08 clause( 2, [ =( x2( z, X ), X ) ] )
% 0.68/1.08 .
% 0.68/1.08 clause( 4, [ =( impl( eq( x2( X, X ), X ), eq2( btrue, bfalse ) ),
% 0.68/1.08 'plus_not_idem'( X ) ) ] )
% 0.68/1.08 .
% 0.68/1.08 clause( 6, [ =( eq2( btrue, bfalse ), bfalse ) ] )
% 0.68/1.08 .
% 0.68/1.08 clause( 10, [ =( eq( X, X ), btrue ) ] )
% 0.68/1.08 .
% 0.68/1.08 clause( 11, [ =( eq2( X, X ), btrue ) ] )
% 0.68/1.08 .
% 0.68/1.08 clause( 12, [ ~( =( eq2( 'plus_not_idem'( X ), bfalse ), btrue ) ) ] )
% 0.68/1.08 .
% 0.68/1.08 clause( 13, [ =( impl( eq( x2( X, X ), X ), bfalse ), 'plus_not_idem'( X )
% 0.68/1.08 ) ] )
% 0.68/1.08 .
% 0.68/1.08 clause( 15, [ =( 'plus_not_idem'( z ), bfalse ) ] )
% 0.68/1.08 .
% 0.68/1.08 clause( 16, [] )
% 0.68/1.08 .
% 0.68/1.08
% 0.68/1.08
% 0.68/1.08 % SZS output end Refutation
% 0.68/1.08 found a proof!
% 0.68/1.08
% 0.68/1.08 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.68/1.08
% 0.68/1.08 initialclauses(
% 0.68/1.08 [ clause( 18, [ =( impl( btrue, X ), X ) ] )
% 0.68/1.08 , clause( 19, [ =( impl( bfalse, X ), btrue ) ] )
% 0.68/1.08 , clause( 20, [ =( x2( z, X ), X ) ] )
% 0.68/1.08 , clause( 21, [ =( x2( s( X ), Y ), s( x2( X, Y ) ) ) ] )
% 0.68/1.08 , clause( 22, [ =( 'plus_not_idem'( X ), impl( eq( x2( X, X ), X ), eq2(
% 0.68/1.08 btrue, bfalse ) ) ) ] )
% 0.68/1.08 , clause( 23, [ =( eq2( bfalse, btrue ), bfalse ) ] )
% 0.68/1.08 , clause( 24, [ =( eq2( btrue, bfalse ), bfalse ) ] )
% 0.68/1.08 , clause( 25, [ =( eq( s( X ), s( Y ) ), eq( X, Y ) ) ] )
% 0.68/1.08 , clause( 26, [ =( eq( z, s( X ) ), bfalse ) ] )
% 0.68/1.08 , clause( 27, [ =( eq( s( X ), z ), bfalse ) ] )
% 0.68/1.08 , clause( 28, [ =( eq( X, X ), btrue ) ] )
% 0.68/1.08 , clause( 29, [ =( eq2( X, X ), btrue ) ] )
% 0.68/1.08 , clause( 30, [ ~( =( eq2( 'plus_not_idem'( X ), bfalse ), btrue ) ) ] )
% 0.68/1.08 ] ).
% 0.68/1.08
% 0.68/1.08
% 0.68/1.08
% 0.68/1.08 subsumption(
% 0.68/1.08 clause( 0, [ =( impl( btrue, X ), X ) ] )
% 0.68/1.08 , clause( 18, [ =( impl( btrue, X ), X ) ] )
% 0.68/1.08 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.68/1.08
% 0.68/1.08
% 0.68/1.08 subsumption(
% 0.68/1.08 clause( 2, [ =( x2( z, X ), X ) ] )
% 0.68/1.08 , clause( 20, [ =( x2( z, X ), X ) ] )
% 0.68/1.08 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.68/1.08
% 0.68/1.08
% 0.68/1.08 eqswap(
% 0.68/1.08 clause( 39, [ =( impl( eq( x2( X, X ), X ), eq2( btrue, bfalse ) ),
% 0.68/1.08 'plus_not_idem'( X ) ) ] )
% 0.68/1.08 , clause( 22, [ =( 'plus_not_idem'( X ), impl( eq( x2( X, X ), X ), eq2(
% 0.68/1.08 btrue, bfalse ) ) ) ] )
% 0.68/1.08 , 0, substitution( 0, [ :=( X, X )] )).
% 0.68/1.08
% 0.68/1.08
% 0.68/1.08 subsumption(
% 0.68/1.08 clause( 4, [ =( impl( eq( x2( X, X ), X ), eq2( btrue, bfalse ) ),
% 0.68/1.08 'plus_not_idem'( X ) ) ] )
% 0.68/1.08 , clause( 39, [ =( impl( eq( x2( X, X ), X ), eq2( btrue, bfalse ) ),
% 0.68/1.08 'plus_not_idem'( X ) ) ] )
% 0.68/1.08 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.68/1.08
% 0.68/1.08
% 0.68/1.08 subsumption(
% 0.68/1.08 clause( 6, [ =( eq2( btrue, bfalse ), bfalse ) ] )
% 0.68/1.08 , clause( 24, [ =( eq2( btrue, bfalse ), bfalse ) ] )
% 0.68/1.08 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.68/1.08
% 0.68/1.08
% 0.68/1.08 subsumption(
% 0.68/1.08 clause( 10, [ =( eq( X, X ), btrue ) ] )
% 0.68/1.08 , clause( 28, [ =( eq( X, X ), btrue ) ] )
% 0.68/1.08 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.68/1.08
% 0.68/1.08
% 0.68/1.08 subsumption(
% 0.68/1.08 clause( 11, [ =( eq2( X, X ), btrue ) ] )
% 0.68/1.08 , clause( 29, [ =( eq2( X, X ), btrue ) ] )
% 0.68/1.08 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.68/1.08
% 0.68/1.08
% 0.68/1.08 subsumption(
% 0.68/1.08 clause( 12, [ ~( =( eq2( 'plus_not_idem'( X ), bfalse ), btrue ) ) ] )
% 0.68/1.08 , clause( 30, [ ~( =( eq2( 'plus_not_idem'( X ), bfalse ), btrue ) ) ] )
% 0.68/1.08 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.68/1.08
% 0.68/1.08
% 0.68/1.08 paramod(
% 0.68/1.08 clause( 85, [ =( impl( eq( x2( X, X ), X ), bfalse ), 'plus_not_idem'( X )
% 0.68/1.08 ) ] )
% 0.68/1.08 , clause( 6, [ =( eq2( btrue, bfalse ), bfalse ) ] )
% 0.68/1.08 , 0, clause( 4, [ =( impl( eq( x2( X, X ), X ), eq2( btrue, bfalse ) ),
% 0.68/1.08 'plus_not_idem'( X ) ) ] )
% 0.68/1.08 , 0, 7, substitution( 0, [] ), substitution( 1, [ :=( X, X )] )).
% 0.68/1.08
% 0.68/1.08
% 0.68/1.08 subsumption(
% 0.68/1.08 clause( 13, [ =( impl( eq( x2( X, X ), X ), bfalse ), 'plus_not_idem'( X )
% 0.68/1.08 ) ] )
% 0.68/1.08 , clause( 85, [ =( impl( eq( x2( X, X ), X ), bfalse ), 'plus_not_idem'( X
% 0.68/1.08 ) ) ] )
% 0.68/1.08 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.68/1.08
% 0.68/1.08
% 0.68/1.08 eqswap(
% 0.68/1.08 clause( 88, [ =( 'plus_not_idem'( X ), impl( eq( x2( X, X ), X ), bfalse )
% 0.68/1.08 ) ] )
% 0.68/1.08 , clause( 13, [ =( impl( eq( x2( X, X ), X ), bfalse ), 'plus_not_idem'( X
% 0.68/1.08 ) ) ] )
% 0.68/1.08 , 0, substitution( 0, [ :=( X, X )] )).
% 0.68/1.08
% 0.68/1.08
% 0.68/1.08 paramod(
% 0.68/1.08 clause( 91, [ =( 'plus_not_idem'( z ), impl( eq( z, z ), bfalse ) ) ] )
% 0.68/1.08 , clause( 2, [ =( x2( z, X ), X ) ] )
% 0.68/1.08 , 0, clause( 88, [ =( 'plus_not_idem'( X ), impl( eq( x2( X, X ), X ),
% 0.68/1.08 bfalse ) ) ] )
% 0.68/1.08 , 0, 5, substitution( 0, [ :=( X, z )] ), substitution( 1, [ :=( X, z )] )
% 0.68/1.08 ).
% 0.68/1.08
% 0.68/1.08
% 0.68/1.08 paramod(
% 0.68/1.08 clause( 92, [ =( 'plus_not_idem'( z ), impl( btrue, bfalse ) ) ] )
% 0.68/1.08 , clause( 10, [ =( eq( X, X ), btrue ) ] )
% 0.68/1.08 , 0, clause( 91, [ =( 'plus_not_idem'( z ), impl( eq( z, z ), bfalse ) ) ]
% 0.68/1.08 )
% 0.68/1.08 , 0, 4, substitution( 0, [ :=( X, z )] ), substitution( 1, [] )).
% 0.68/1.08
% 0.68/1.08
% 0.68/1.08 paramod(
% 0.68/1.08 clause( 93, [ =( 'plus_not_idem'( z ), bfalse ) ] )
% 0.68/1.08 , clause( 0, [ =( impl( btrue, X ), X ) ] )
% 0.68/1.08 , 0, clause( 92, [ =( 'plus_not_idem'( z ), impl( btrue, bfalse ) ) ] )
% 0.68/1.08 , 0, 3, substitution( 0, [ :=( X, bfalse )] ), substitution( 1, [] )).
% 0.68/1.08
% 0.68/1.08
% 0.68/1.08 subsumption(
% 0.68/1.08 clause( 15, [ =( 'plus_not_idem'( z ), bfalse ) ] )
% 0.68/1.08 , clause( 93, [ =( 'plus_not_idem'( z ), bfalse ) ] )
% 0.68/1.08 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.68/1.08
% 0.68/1.08
% 0.68/1.08 eqswap(
% 0.68/1.08 clause( 96, [ ~( =( btrue, eq2( 'plus_not_idem'( X ), bfalse ) ) ) ] )
% 0.68/1.08 , clause( 12, [ ~( =( eq2( 'plus_not_idem'( X ), bfalse ), btrue ) ) ] )
% 0.68/1.08 , 0, substitution( 0, [ :=( X, X )] )).
% 0.68/1.08
% 0.68/1.08
% 0.68/1.08 paramod(
% 0.68/1.08 clause( 98, [ ~( =( btrue, eq2( bfalse, bfalse ) ) ) ] )
% 0.68/1.08 , clause( 15, [ =( 'plus_not_idem'( z ), bfalse ) ] )
% 0.68/1.08 , 0, clause( 96, [ ~( =( btrue, eq2( 'plus_not_idem'( X ), bfalse ) ) ) ]
% 0.68/1.08 )
% 0.68/1.08 , 0, 4, substitution( 0, [] ), substitution( 1, [ :=( X, z )] )).
% 0.68/1.08
% 0.68/1.08
% 0.68/1.08 paramod(
% 0.68/1.08 clause( 99, [ ~( =( btrue, btrue ) ) ] )
% 0.68/1.08 , clause( 11, [ =( eq2( X, X ), btrue ) ] )
% 0.68/1.08 , 0, clause( 98, [ ~( =( btrue, eq2( bfalse, bfalse ) ) ) ] )
% 0.68/1.08 , 0, 3, substitution( 0, [ :=( X, bfalse )] ), substitution( 1, [] )).
% 0.68/1.08
% 0.68/1.08
% 0.68/1.08 eqrefl(
% 0.68/1.08 clause( 100, [] )
% 0.68/1.08 , clause( 99, [ ~( =( btrue, btrue ) ) ] )
% 0.68/1.08 , 0, substitution( 0, [] )).
% 0.68/1.08
% 0.68/1.08
% 0.68/1.08 subsumption(
% 0.68/1.08 clause( 16, [] )
% 0.68/1.08 , clause( 100, [] )
% 0.68/1.08 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.68/1.08
% 0.68/1.08
% 0.68/1.08 end.
% 0.68/1.08
% 0.68/1.08 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.68/1.08
% 0.68/1.08 Memory use:
% 0.68/1.08
% 0.68/1.08 space for terms: 337
% 0.68/1.08 space for clauses: 1493
% 0.68/1.08
% 0.68/1.08
% 0.68/1.08 clauses generated: 45
% 0.68/1.08 clauses kept: 17
% 0.68/1.08 clauses selected: 14
% 0.68/1.08 clauses deleted: 1
% 0.68/1.08 clauses inuse deleted: 0
% 0.68/1.08
% 0.68/1.08 subsentry: 345
% 0.68/1.08 literals s-matched: 167
% 0.68/1.08 literals matched: 167
% 0.68/1.08 full subsumption: 0
% 0.68/1.08
% 0.68/1.08 checksum: 206307777
% 0.68/1.08
% 0.68/1.08
% 0.68/1.08 Bliksem ended
%------------------------------------------------------------------------------