%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWX213-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n012.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 06:56:49 PM UTC 2026
% Result : Timeout 299.59s 300.01s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SWX213-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.06 % Command : bliksem %s
% 0.07/0.25 % Computer : n012.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % DateTime : Tue May 5 12:00:45 EDT 2026
% 0.07/0.25 % CPUTime :
% 0.60/1.09 *** allocated 10000 integers for termspace/termends
% 0.60/1.09 *** allocated 10000 integers for clauses
% 0.60/1.09 *** allocated 10000 integers for justifications
% 0.60/1.09 Bliksem 1.12
% 0.60/1.09
% 0.60/1.09
% 0.60/1.09 Automatic Strategy Selection
% 0.60/1.09
% 0.60/1.09 Clauses:
% 0.60/1.09 [
% 0.60/1.09 [ =( aux( X, Y, btrue ), eps ) ],
% 0.60/1.09 [ =( aux( X, Y, bfalse ), nil2 ) ],
% 0.60/1.09 [ =( aux2( X, Y, Z, btrue ), x( y( step( Y, X ), Z ), step( Z, X ) ) ) ]
% 0.60/1.09 ,
% 0.60/1.09 [ =( aux2( X, Y, Z, bfalse ), x( y( step( Y, X ), Z ), nil2 ) ) ],
% 0.60/1.09 [ =( z( nil2, X ), nil2 ) ],
% 0.60/1.09 [ =( z( eps, X ), X ) ],
% 0.60/1.09 [ =( z( atom( X ), nil2 ), nil2 ) ],
% 0.60/1.09 [ =( z( atom( X ), eps ), atom( X ) ) ],
% 0.60/1.09 [ =( z( atom( X ), atom( Y ) ), y( atom( X ), atom( Y ) ) ) ],
% 0.60/1.09 [ =( z( atom( X ), x( Y, Z ) ), y( atom( X ), x( Y, Z ) ) ) ],
% 0.60/1.09 [ =( z( atom( X ), y( Y, Z ) ), y( atom( X ), y( Y, Z ) ) ) ],
% 0.60/1.09 [ =( z( atom( X ), star( Y ) ), y( atom( X ), star( Y ) ) ) ],
% 0.60/1.09 [ =( z( x( X, Y ), nil2 ), nil2 ) ],
% 0.60/1.09 [ =( z( x( X, Y ), eps ), x( X, Y ) ) ],
% 0.60/1.09 [ =( z( x( X, Y ), atom( Z ) ), y( x( X, Y ), atom( Z ) ) ) ],
% 0.60/1.09 [ =( z( x( X, Y ), x( Z, T ) ), y( x( X, Y ), x( Z, T ) ) ) ],
% 0.60/1.09 [ =( z( x( X, Y ), y( Z, T ) ), y( x( X, Y ), y( Z, T ) ) ) ],
% 0.60/1.09 [ =( z( x( X, Y ), star( Z ) ), y( x( X, Y ), star( Z ) ) ) ],
% 0.60/1.09 [ =( z( y( X, Y ), nil2 ), nil2 ) ],
% 0.60/1.09 [ =( z( y( X, Y ), eps ), y( X, Y ) ) ],
% 0.60/1.09 [ =( z( y( X, Y ), atom( Z ) ), y( y( X, Y ), atom( Z ) ) ) ],
% 0.60/1.09 [ =( z( y( X, Y ), x( Z, T ) ), y( y( X, Y ), x( Z, T ) ) ) ],
% 0.60/1.09 [ =( z( y( X, Y ), y( Z, T ) ), y( y( X, Y ), y( Z, T ) ) ) ],
% 0.60/1.09 [ =( z( y( X, Y ), star( Z ) ), y( y( X, Y ), star( Z ) ) ) ],
% 0.60/1.09 [ =( z( star( X ), nil2 ), nil2 ) ],
% 0.60/1.09 [ =( z( star( X ), eps ), star( X ) ) ],
% 0.60/1.09 [ =( z( star( X ), atom( Y ) ), y( star( X ), atom( Y ) ) ) ],
% 0.60/1.09 [ =( z( star( X ), x( Y, Z ) ), y( star( X ), x( Y, Z ) ) ) ],
% 0.60/1.09 [ =( z( star( X ), y( Y, Z ) ), y( star( X ), y( Y, Z ) ) ) ],
% 0.60/1.09 [ =( z( star( X ), star( Y ) ), y( star( X ), star( Y ) ) ) ],
% 0.60/1.09 [ =( x2( nil2, X ), X ) ],
% 0.60/1.09 [ =( x2( eps, nil2 ), eps ) ],
% 0.60/1.09 [ =( x2( eps, eps ), x( eps, eps ) ) ],
% 0.60/1.09 [ =( x2( eps, atom( X ) ), x( eps, atom( X ) ) ) ],
% 0.60/1.09 [ =( x2( eps, x( X, Y ) ), x( eps, x( X, Y ) ) ) ],
% 0.60/1.09 [ =( x2( eps, y( X, Y ) ), x( eps, y( X, Y ) ) ) ],
% 0.60/1.09 [ =( x2( eps, star( X ) ), x( eps, star( X ) ) ) ],
% 0.60/1.09 [ =( x2( atom( X ), nil2 ), atom( X ) ) ],
% 0.60/1.09 [ =( x2( atom( X ), eps ), x( atom( X ), eps ) ) ],
% 0.60/1.09 [ =( x2( atom( X ), atom( Y ) ), x( atom( X ), atom( Y ) ) ) ],
% 0.60/1.09 [ =( x2( atom( X ), x( Y, Z ) ), x( atom( X ), x( Y, Z ) ) ) ],
% 0.60/1.09 [ =( x2( atom( X ), y( Y, Z ) ), x( atom( X ), y( Y, Z ) ) ) ],
% 0.60/1.09 [ =( x2( atom( X ), star( Y ) ), x( atom( X ), star( Y ) ) ) ],
% 0.60/1.09 [ =( x2( x( X, Y ), nil2 ), x( X, Y ) ) ],
% 0.60/1.09 [ =( x2( x( X, Y ), eps ), x( x( X, Y ), eps ) ) ],
% 0.60/1.09 [ =( x2( x( X, Y ), atom( Z ) ), x( x( X, Y ), atom( Z ) ) ) ],
% 0.60/1.09 [ =( x2( x( X, Y ), x( Z, T ) ), x( x( X, Y ), x( Z, T ) ) ) ],
% 0.60/1.09 [ =( x2( x( X, Y ), y( Z, T ) ), x( x( X, Y ), y( Z, T ) ) ) ],
% 0.60/1.09 [ =( x2( x( X, Y ), star( Z ) ), x( x( X, Y ), star( Z ) ) ) ],
% 0.60/1.09 [ =( x2( y( X, Y ), nil2 ), y( X, Y ) ) ],
% 0.60/1.09 [ =( x2( y( X, Y ), eps ), x( y( X, Y ), eps ) ) ],
% 0.60/1.09 [ =( x2( y( X, Y ), atom( Z ) ), x( y( X, Y ), atom( Z ) ) ) ],
% 0.60/1.09 [ =( x2( y( X, Y ), x( Z, T ) ), x( y( X, Y ), x( Z, T ) ) ) ],
% 0.60/1.09 [ =( x2( y( X, Y ), y( Z, T ) ), x( y( X, Y ), y( Z, T ) ) ) ],
% 0.60/1.09 [ =( x2( y( X, Y ), star( Z ) ), x( y( X, Y ), star( Z ) ) ) ],
% 0.60/1.09 [ =( x2( star( X ), nil2 ), star( X ) ) ],
% 0.60/1.09 [ =( x2( star( X ), eps ), x( star( X ), eps ) ) ],
% 0.60/1.09 [ =( x2( star( X ), atom( Y ) ), x( star( X ), atom( Y ) ) ) ],
% 0.60/1.09 [ =( x2( star( X ), x( Y, Z ) ), x( star( X ), x( Y, Z ) ) ) ],
% 0.60/1.09 [ =( x2( star( X ), y( Y, Z ) ), x( star( X ), y( Y, Z ) ) ) ],
% 0.60/1.09 [ =( x2( star( X ), star( Y ) ), x( star( X ), star( Y ) ) ) ],
% 0.60/1.09 [ =( orb( btrue, X ), btrue ) ],
% 0.60/1.09 [ =( orb( bfalse, X ), X ) ],
% 0.60/1.09 [ =( impl( btrue, X ), X ) ],
% 0.60/1.09 [ =( impl( bfalse, X ), btrue ) ],
% 0.60/1.09 [ =( andb( btrue, X ), X ) ],
% 0.60/1.09 [ =( andb( bfalse, X ), bfalse ) ],
% 0.60/1.09 [ =( eps2( eps ), btrue ) ],
% 0.60/1.09 [ =( eps2( x( X, Y ) ), orb( eps2( X ), eps2( Y ) ) ) ],
% 0.60/1.09 [ =( eps2( y( X, Y ) ), andb( eps2( X ), eps2( Y ) ) ) ],
% 0.60/1.09 [ =( eps2( star( X ) ), btrue ) ],
% 0.60/1.09 [ =( eps2( nil2 ), bfalse ) ],
% 58.88/59.31 [ =( eps2( atom( X ) ), bfalse ) ],
% 58.88/59.31 [ =( step( atom( X ), Y ), aux( Y, X, eq( X, Y ) ) ) ],
% 58.88/59.31 [ =( step( x( X, Y ), Z ), x( step( X, Z ), step( Y, Z ) ) ) ],
% 58.88/59.31 [ =( step( y( X, Y ), Z ), aux2( Z, X, Y, eps2( X ) ) ) ],
% 58.88/59.31 [ =( step( star( X ), Y ), y( step( X, Y ), star( X ) ) ) ],
% 58.88/59.31 [ =( step( nil2, X ), nil2 ) ],
% 58.88/59.31 [ =( step( eps, X ), nil2 ) ],
% 58.88/59.31 [ =( rec( X, nil ), eps2( X ) ) ],
% 58.88/59.31 [ =( rec( X, cons( Y, Z ) ), rec( step( X, Y ), Z ) ) ],
% 58.88/59.31 [ =( 'prop_star_plus_1'( X, Y, Z ), impl( eq2( rec( star( x( X, Y ) ), Z
% 58.88/59.31 ), btrue ), eq2( rec( x( star( X ), star( Y ) ), Z ), btrue ) ) ) ],
% 58.88/59.31 [ =( eq( a, b ), bfalse ) ],
% 58.88/59.31 [ =( eq( a, c ), bfalse ) ],
% 58.88/59.31 [ =( eq( b, a ), bfalse ) ],
% 58.88/59.31 [ =( eq( b, c ), bfalse ) ],
% 58.88/59.31 [ =( eq( c, a ), bfalse ) ],
% 58.88/59.31 [ =( eq( c, b ), bfalse ) ],
% 58.88/59.31 [ =( eq2( bfalse, btrue ), bfalse ) ],
% 58.88/59.31 [ =( eq2( btrue, bfalse ), bfalse ) ],
% 58.88/59.31 [ =( eq( X, X ), btrue ) ],
% 58.88/59.31 [ =( eq2( X, X ), btrue ) ],
% 58.88/59.31 [ ~( =( eq2( 'prop_star_plus_1'( X, Y, Z ), bfalse ), btrue ) ) ]
% 58.88/59.31 ] .
% 58.88/59.31
% 58.88/59.31
% 58.88/59.31 percentage equality = 1.000000, percentage horn = 1.000000
% 58.88/59.31 This is a pure equality problem
% 58.88/59.31
% 58.88/59.31
% 58.88/59.31
% 58.88/59.31 Options Used:
% 58.88/59.31
% 58.88/59.31 useres = 1
% 58.88/59.31 useparamod = 1
% 58.88/59.31 useeqrefl = 1
% 58.88/59.31 useeqfact = 1
% 58.88/59.31 usefactor = 1
% 58.88/59.31 usesimpsplitting = 0
% 58.88/59.31 usesimpdemod = 5
% 58.88/59.31 usesimpres = 3
% 58.88/59.31
% 58.88/59.31 resimpinuse = 1000
% 58.88/59.31 resimpclauses = 20000
% 58.88/59.31 substype = eqrewr
% 58.88/59.31 backwardsubs = 1
% 58.88/59.31 selectoldest = 5
% 58.88/59.31
% 58.88/59.31 litorderings [0] = split
% 58.88/59.31 litorderings [1] = extend the termordering, first sorting on arguments
% 58.88/59.31
% 58.88/59.31 termordering = kbo
% 58.88/59.31
% 58.88/59.31 litapriori = 0
% 58.88/59.31 termapriori = 1
% 58.88/59.31 litaposteriori = 0
% 58.88/59.31 termaposteriori = 0
% 58.88/59.31 demodaposteriori = 0
% 58.88/59.31 ordereqreflfact = 0
% 58.88/59.31
% 58.88/59.31 litselect = negord
% 58.88/59.31
% 58.88/59.31 maxweight = 15
% 58.88/59.31 maxdepth = 30000
% 58.88/59.31 maxlength = 115
% 58.88/59.31 maxnrvars = 195
% 58.88/59.31 excuselevel = 1
% 58.88/59.31 increasemaxweight = 1
% 58.88/59.31
% 58.88/59.31 maxselected = 10000000
% 58.88/59.31 maxnrclauses = 10000000
% 58.88/59.31
% 58.88/59.31 showgenerated = 0
% 58.88/59.31 showkept = 0
% 58.88/59.31 showselected = 0
% 58.88/59.31 showdeleted = 0
% 58.88/59.31 showresimp = 1
% 58.88/59.31 showstatus = 2000
% 58.88/59.31
% 58.88/59.31 prologoutput = 1
% 58.88/59.31 nrgoals = 5000000
% 58.88/59.31 totalproof = 1
% 58.88/59.31
% 58.88/59.31 Symbols occurring in the translation:
% 58.88/59.31
% 58.88/59.31 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 58.88/59.31 . [1, 2] (w:1, o:38, a:1, s:1, b:0),
% 58.88/59.31 ! [4, 1] (w:0, o:30, a:1, s:1, b:0),
% 58.88/59.31 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 58.88/59.31 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 58.88/59.31 btrue [41, 0] (w:1, o:17, a:1, s:1, b:0),
% 58.88/59.31 aux [42, 3] (w:1, o:75, a:1, s:1, b:0),
% 58.88/59.31 eps [43, 0] (w:1, o:18, a:1, s:1, b:0),
% 58.88/59.31 bfalse [44, 0] (w:1, o:19, a:1, s:1, b:0),
% 58.88/59.31 nil2 [45, 0] (w:1, o:20, a:1, s:1, b:0),
% 58.88/59.31 aux2 [48, 4] (w:1, o:77, a:1, s:1, b:0),
% 58.88/59.31 step [49, 2] (w:1, o:64, a:1, s:1, b:0),
% 58.88/59.31 y [50, 2] (w:1, o:67, a:1, s:1, b:0),
% 58.88/59.31 x [51, 2] (w:1, o:65, a:1, s:1, b:0),
% 58.88/59.31 z [52, 2] (w:1, o:68, a:1, s:1, b:0),
% 58.88/59.31 atom [54, 1] (w:1, o:35, a:1, s:1, b:0),
% 58.88/59.31 star [57, 1] (w:1, o:36, a:1, s:1, b:0),
% 58.88/59.31 x2 [59, 2] (w:1, o:66, a:1, s:1, b:0),
% 58.88/59.31 orb [61, 2] (w:1, o:69, a:1, s:1, b:0),
% 58.88/59.31 impl [62, 2] (w:1, o:70, a:1, s:1, b:0),
% 58.88/59.31 andb [63, 2] (w:1, o:71, a:1, s:1, b:0),
% 58.88/59.31 eps2 [64, 1] (w:1, o:37, a:1, s:1, b:0),
% 58.88/59.31 eq [66, 2] (w:1, o:72, a:1, s:1, b:0),
% 58.88/59.31 nil [68, 0] (w:1, o:26, a:1, s:1, b:0),
% 58.88/59.31 rec [69, 2] (w:1, o:63, a:1, s:1, b:0),
% 58.88/59.31 cons [72, 2] (w:1, o:73, a:1, s:1, b:0),
% 58.88/59.31 'prop_star_plus_1' [73, 3] (w:1, o:76, a:1, s:1, b:0),
% 58.88/59.31 eq2 [74, 2] (w:1, o:74, a:1, s:1, b:0),
% 58.88/59.31 a [75, 0] (w:1, o:16, a:1, s:1, b:0),
% 58.88/59.31 b [76, 0] (w:1, o:28, a:1, s:1, b:0),
% 58.88/59.31 c [77, 0] (w:1, o:29, a:1, s:1, b:0).
% 58.88/59.31
% 58.88/59.31
% 58.88/59.31 Starting Search:
% 58.88/59.31
% 58.88/59.31 Resimplifying inuse:
% 58.88/59.31 Done
% 58.88/59.31
% 58.88/59.31
% 58.88/59.31 Intermediate Status:
% 58.88/59.31 Generated: 6438
% 58.88/59.31 Kept: 2005
% 58.88/59.31 Inuse: 399
% 58.88/59.31 Deleted: 133
% 58.88/59.31 Deletedinuse: 23
% 58.88/59.31
% 58.88/59.31 Resimplifying inuse:
% 58.88/59.31 Done
% 58.88/59.31
% 58.88/59.31 Resimplifying inuse:
% 58.88/59.31 Done
% 58.88/59.31
% 58.88/59.31
% 58.88/59.31 Intermediate Status:
% 58.88/59.31 Generated: 22971
% 58.88/59.31 Kept: 4007
% 58.88/59.31 Inuse: 849
% 58.88/59.31 Deleted: 460
% 58.88/59.31 Deletedinuse: 45
% 58.88/59.31
% 58.88/59.31 Resimplifying inuse:
% 58.88/59.31 Done
% 58.88/59.31
% 58.88/59.31 Resimplifying inuse:
% 58.88/59.31 Done
% 58.88/59.31
% 58.88/59.31
% 58.88/59.31 Intermediate Status:
% 58.88/59.31 Generated: 35310
% 58.88/59.31 Kept: 6008
% 58.88/59.31 Inuse: 1173
% 58.88/59.31 DTerminated
% 299.59/300.01 Bliksem ended
%------------------------------------------------------------------------------