%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWX233-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n003.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 06:56:52 PM UTC 2026
% Result : Unsatisfiable 0.65s 1.06s
% Output : Refutation 0.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX233-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : bliksem %s
% 0.13/0.32 % Computer : n003.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % DateTime : Tue May 5 13:06:26 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.65/1.06 *** allocated 10000 integers for termspace/termends
% 0.65/1.06 *** allocated 10000 integers for clauses
% 0.65/1.06 *** allocated 10000 integers for justifications
% 0.65/1.06 Bliksem 1.12
% 0.65/1.06
% 0.65/1.06
% 0.65/1.06 Automatic Strategy Selection
% 0.65/1.06
% 0.65/1.06 Clauses:
% 0.65/1.06 [
% 0.65/1.06 [ =( aux( X, btrue ), bfalse ) ],
% 0.65/1.06 [ =( aux( X, bfalse ), btrue ) ],
% 0.65/1.06 [ =( h( nil ), nil ) ],
% 0.65/1.06 [ =( h( cons( X, Y ) ), Y ) ],
% 0.65/1.06 [ =( g( btrue ), bfalse ) ],
% 0.65/1.06 [ =( g( bfalse ), btrue ) ],
% 0.65/1.06 [ =( f( nil ), btrue ) ],
% 0.65/1.06 [ =( f( cons( X, Y ) ), aux( Y, f( Y ) ) ) ],
% 0.65/1.06 [ =( prop1( X ), eq( f( X ), bfalse ) ) ],
% 0.65/1.06 [ =( eq( bfalse, btrue ), bfalse ) ],
% 0.65/1.06 [ =( eq( btrue, bfalse ), bfalse ) ],
% 0.65/1.06 [ =( eq( X, X ), btrue ) ],
% 0.65/1.06 [ ~( =( eq( prop1( X ), bfalse ), btrue ) ) ]
% 0.65/1.06 ] .
% 0.65/1.06
% 0.65/1.06
% 0.65/1.06 percentage equality = 1.000000, percentage horn = 1.000000
% 0.65/1.06 This is a pure equality problem
% 0.65/1.06
% 0.65/1.06
% 0.65/1.06
% 0.65/1.06 Options Used:
% 0.65/1.06
% 0.65/1.06 useres = 1
% 0.65/1.06 useparamod = 1
% 0.65/1.06 useeqrefl = 1
% 0.65/1.06 useeqfact = 1
% 0.65/1.06 usefactor = 1
% 0.65/1.06 usesimpsplitting = 0
% 0.65/1.06 usesimpdemod = 5
% 0.65/1.06 usesimpres = 3
% 0.65/1.06
% 0.65/1.06 resimpinuse = 1000
% 0.65/1.06 resimpclauses = 20000
% 0.65/1.06 substype = eqrewr
% 0.65/1.06 backwardsubs = 1
% 0.65/1.06 selectoldest = 5
% 0.65/1.06
% 0.65/1.06 litorderings [0] = split
% 0.65/1.06 litorderings [1] = extend the termordering, first sorting on arguments
% 0.65/1.06
% 0.65/1.06 termordering = kbo
% 0.65/1.06
% 0.65/1.06 litapriori = 0
% 0.65/1.06 termapriori = 1
% 0.65/1.06 litaposteriori = 0
% 0.65/1.06 termaposteriori = 0
% 0.65/1.06 demodaposteriori = 0
% 0.65/1.06 ordereqreflfact = 0
% 0.65/1.06
% 0.65/1.06 litselect = negord
% 0.65/1.06
% 0.65/1.06 maxweight = 15
% 0.65/1.06 maxdepth = 30000
% 0.65/1.06 maxlength = 115
% 0.65/1.06 maxnrvars = 195
% 0.65/1.06 excuselevel = 1
% 0.65/1.06 increasemaxweight = 1
% 0.65/1.06
% 0.65/1.06 maxselected = 10000000
% 0.65/1.06 maxnrclauses = 10000000
% 0.65/1.06
% 0.65/1.06 showgenerated = 0
% 0.65/1.06 showkept = 0
% 0.65/1.06 showselected = 0
% 0.65/1.06 showdeleted = 0
% 0.65/1.06 showresimp = 1
% 0.65/1.06 showstatus = 2000
% 0.65/1.06
% 0.65/1.06 prologoutput = 1
% 0.65/1.06 nrgoals = 5000000
% 0.65/1.06 totalproof = 1
% 0.65/1.06
% 0.65/1.06 Symbols occurring in the translation:
% 0.65/1.06
% 0.65/1.06 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.65/1.06 . [1, 2] (w:1, o:25, a:1, s:1, b:0),
% 0.65/1.06 ! [4, 1] (w:0, o:16, a:1, s:1, b:0),
% 0.65/1.06 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.65/1.06 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.65/1.06 btrue [40, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.65/1.06 aux [41, 2] (w:1, o:50, a:1, s:1, b:0),
% 0.65/1.06 bfalse [42, 0] (w:1, o:14, a:1, s:1, b:0),
% 0.65/1.06 nil [43, 0] (w:1, o:15, a:1, s:1, b:0),
% 0.65/1.06 h [44, 1] (w:1, o:23, a:1, s:1, b:0),
% 0.65/1.06 cons [47, 2] (w:1, o:51, a:1, s:1, b:0),
% 0.65/1.06 g [48, 1] (w:1, o:22, a:1, s:1, b:0),
% 0.65/1.06 f [49, 1] (w:1, o:21, a:1, s:1, b:0),
% 0.65/1.06 prop1 [51, 1] (w:1, o:24, a:1, s:1, b:0),
% 0.65/1.06 eq [52, 2] (w:1, o:52, a:1, s:1, b:0).
% 0.65/1.06
% 0.65/1.06
% 0.65/1.06 Starting Search:
% 0.65/1.06
% 0.65/1.06
% 0.65/1.06 Bliksems!, er is een bewijs:
% 0.65/1.06 % SZS status Unsatisfiable
% 0.65/1.06 % SZS output start Refutation
% 0.65/1.06
% 0.65/1.06 clause( 6, [ =( f( nil ), btrue ) ] )
% 0.65/1.06 .
% 0.65/1.06 clause( 8, [ =( eq( f( X ), bfalse ), prop1( X ) ) ] )
% 0.65/1.06 .
% 0.65/1.06 clause( 10, [ =( eq( btrue, bfalse ), bfalse ) ] )
% 0.65/1.06 .
% 0.65/1.06 clause( 11, [ =( eq( X, X ), btrue ) ] )
% 0.65/1.06 .
% 0.65/1.06 clause( 12, [ ~( =( eq( prop1( X ), bfalse ), btrue ) ) ] )
% 0.65/1.06 .
% 0.65/1.06 clause( 19, [ =( prop1( nil ), bfalse ) ] )
% 0.65/1.06 .
% 0.65/1.06 clause( 20, [] )
% 0.65/1.06 .
% 0.65/1.06
% 0.65/1.06
% 0.65/1.06 % SZS output end Refutation
% 0.65/1.06 found a proof!
% 0.65/1.06
% 0.65/1.06 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.65/1.06
% 0.65/1.06 initialclauses(
% 0.65/1.06 [ clause( 22, [ =( aux( X, btrue ), bfalse ) ] )
% 0.65/1.06 , clause( 23, [ =( aux( X, bfalse ), btrue ) ] )
% 0.65/1.06 , clause( 24, [ =( h( nil ), nil ) ] )
% 0.65/1.06 , clause( 25, [ =( h( cons( X, Y ) ), Y ) ] )
% 0.65/1.06 , clause( 26, [ =( g( btrue ), bfalse ) ] )
% 0.65/1.06 , clause( 27, [ =( g( bfalse ), btrue ) ] )
% 0.65/1.06 , clause( 28, [ =( f( nil ), btrue ) ] )
% 0.65/1.06 , clause( 29, [ =( f( cons( X, Y ) ), aux( Y, f( Y ) ) ) ] )
% 0.65/1.06 , clause( 30, [ =( prop1( X ), eq( f( X ), bfalse ) ) ] )
% 0.65/1.06 , clause( 31, [ =( eq( bfalse, btrue ), bfalse ) ] )
% 0.65/1.06 , clause( 32, [ =( eq( btrue, bfalse ), bfalse ) ] )
% 0.65/1.06 , clause( 33, [ =( eq( X, X ), btrue ) ] )
% 0.65/1.06 , clause( 34, [ ~( =( eq( prop1( X ), bfalse ), btrue ) ) ] )
% 0.65/1.06 ] ).
% 0.65/1.06
% 0.65/1.06
% 0.65/1.06
% 0.65/1.06 subsumption(
% 0.65/1.06 clause( 6, [ =( f( nil ), btrue ) ] )
% 0.65/1.06 , clause( 28, [ =( f( nil ), btrue ) ] )
% 0.65/1.06 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.65/1.06
% 0.65/1.06
% 0.65/1.06 eqswap(
% 0.65/1.06 clause( 50, [ =( eq( f( X ), bfalse ), prop1( X ) ) ] )
% 0.65/1.06 , clause( 30, [ =( prop1( X ), eq( f( X ), bfalse ) ) ] )
% 0.65/1.06 , 0, substitution( 0, [ :=( X, X )] )).
% 0.65/1.06
% 0.65/1.06
% 0.65/1.06 subsumption(
% 0.65/1.06 clause( 8, [ =( eq( f( X ), bfalse ), prop1( X ) ) ] )
% 0.65/1.06 , clause( 50, [ =( eq( f( X ), bfalse ), prop1( X ) ) ] )
% 0.65/1.06 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.65/1.06
% 0.65/1.06
% 0.65/1.06 subsumption(
% 0.65/1.06 clause( 10, [ =( eq( btrue, bfalse ), bfalse ) ] )
% 0.65/1.06 , clause( 32, [ =( eq( btrue, bfalse ), bfalse ) ] )
% 0.65/1.06 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.65/1.06
% 0.65/1.06
% 0.65/1.06 subsumption(
% 0.65/1.06 clause( 11, [ =( eq( X, X ), btrue ) ] )
% 0.65/1.06 , clause( 33, [ =( eq( X, X ), btrue ) ] )
% 0.65/1.06 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.65/1.06
% 0.65/1.06
% 0.65/1.06 subsumption(
% 0.65/1.06 clause( 12, [ ~( =( eq( prop1( X ), bfalse ), btrue ) ) ] )
% 0.65/1.06 , clause( 34, [ ~( =( eq( prop1( X ), bfalse ), btrue ) ) ] )
% 0.65/1.06 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.65/1.06
% 0.65/1.06
% 0.65/1.06 eqswap(
% 0.65/1.06 clause( 88, [ =( prop1( X ), eq( f( X ), bfalse ) ) ] )
% 0.65/1.06 , clause( 8, [ =( eq( f( X ), bfalse ), prop1( X ) ) ] )
% 0.65/1.06 , 0, substitution( 0, [ :=( X, X )] )).
% 0.65/1.06
% 0.65/1.06
% 0.65/1.06 paramod(
% 0.65/1.06 clause( 90, [ =( prop1( nil ), eq( btrue, bfalse ) ) ] )
% 0.65/1.06 , clause( 6, [ =( f( nil ), btrue ) ] )
% 0.65/1.06 , 0, clause( 88, [ =( prop1( X ), eq( f( X ), bfalse ) ) ] )
% 0.65/1.06 , 0, 4, substitution( 0, [] ), substitution( 1, [ :=( X, nil )] )).
% 0.65/1.06
% 0.65/1.06
% 0.65/1.06 paramod(
% 0.65/1.06 clause( 91, [ =( prop1( nil ), bfalse ) ] )
% 0.65/1.06 , clause( 10, [ =( eq( btrue, bfalse ), bfalse ) ] )
% 0.65/1.06 , 0, clause( 90, [ =( prop1( nil ), eq( btrue, bfalse ) ) ] )
% 0.65/1.06 , 0, 3, substitution( 0, [] ), substitution( 1, [] )).
% 0.65/1.06
% 0.65/1.06
% 0.65/1.06 subsumption(
% 0.65/1.06 clause( 19, [ =( prop1( nil ), bfalse ) ] )
% 0.65/1.06 , clause( 91, [ =( prop1( nil ), bfalse ) ] )
% 0.65/1.06 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.65/1.06
% 0.65/1.06
% 0.65/1.06 eqswap(
% 0.65/1.06 clause( 94, [ ~( =( btrue, eq( prop1( X ), bfalse ) ) ) ] )
% 0.65/1.06 , clause( 12, [ ~( =( eq( prop1( X ), bfalse ), btrue ) ) ] )
% 0.65/1.06 , 0, substitution( 0, [ :=( X, X )] )).
% 0.65/1.06
% 0.65/1.06
% 0.65/1.06 paramod(
% 0.65/1.06 clause( 96, [ ~( =( btrue, eq( bfalse, bfalse ) ) ) ] )
% 0.65/1.06 , clause( 19, [ =( prop1( nil ), bfalse ) ] )
% 0.65/1.06 , 0, clause( 94, [ ~( =( btrue, eq( prop1( X ), bfalse ) ) ) ] )
% 0.65/1.06 , 0, 4, substitution( 0, [] ), substitution( 1, [ :=( X, nil )] )).
% 0.65/1.06
% 0.65/1.06
% 0.65/1.06 paramod(
% 0.65/1.06 clause( 97, [ ~( =( btrue, btrue ) ) ] )
% 0.65/1.06 , clause( 11, [ =( eq( X, X ), btrue ) ] )
% 0.65/1.06 , 0, clause( 96, [ ~( =( btrue, eq( bfalse, bfalse ) ) ) ] )
% 0.65/1.06 , 0, 3, substitution( 0, [ :=( X, bfalse )] ), substitution( 1, [] )).
% 0.65/1.06
% 0.65/1.06
% 0.65/1.06 eqrefl(
% 0.65/1.06 clause( 98, [] )
% 0.65/1.06 , clause( 97, [ ~( =( btrue, btrue ) ) ] )
% 0.65/1.06 , 0, substitution( 0, [] )).
% 0.65/1.06
% 0.65/1.06
% 0.65/1.06 subsumption(
% 0.65/1.06 clause( 20, [] )
% 0.65/1.06 , clause( 98, [] )
% 0.65/1.06 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.65/1.06
% 0.65/1.06
% 0.65/1.06 end.
% 0.65/1.06
% 0.65/1.06 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.65/1.06
% 0.65/1.06 Memory use:
% 0.65/1.06
% 0.65/1.06 space for terms: 328
% 0.65/1.06 space for clauses: 1674
% 0.65/1.06
% 0.65/1.06
% 0.65/1.06 clauses generated: 53
% 0.65/1.06 clauses kept: 21
% 0.65/1.06 clauses selected: 15
% 0.65/1.06 clauses deleted: 0
% 0.65/1.06 clauses inuse deleted: 0
% 0.65/1.06
% 0.65/1.06 subsentry: 335
% 0.65/1.06 literals s-matched: 165
% 0.65/1.06 literals matched: 165
% 0.65/1.06 full subsumption: 0
% 0.65/1.06
% 0.65/1.06 checksum: 1846755677
% 0.65/1.06
% 0.65/1.06
% 0.65/1.06 Bliksem ended
%------------------------------------------------------------------------------