%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : COL002-4 : TPTP v8.1.0. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n032.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 : Fri Jul 15 00:12:19 EDT 2022
% Result : Unsatisfiable 0.42s 0.84s
% Output : Refutation 0.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.08 % Problem : COL002-4 : TPTP v8.1.0. Bugfixed v3.1.0.
% 0.06/0.08 % Command : bliksem %s
% 0.07/0.27 % Computer : n032.cluster.edu
% 0.07/0.27 % Model : x86_64 x86_64
% 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27 % Memory : 8042.1875MB
% 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27 % CPULimit : 300
% 0.07/0.27 % DateTime : Tue May 31 07:57:43 EDT 2022
% 0.07/0.27 % CPUTime :
% 0.42/0.84 *** allocated 10000 integers for termspace/termends
% 0.42/0.84 *** allocated 10000 integers for clauses
% 0.42/0.84 *** allocated 10000 integers for justifications
% 0.42/0.84 Bliksem 1.12
% 0.42/0.84
% 0.42/0.84
% 0.42/0.84 Automatic Strategy Selection
% 0.42/0.84
% 0.42/0.84 Clauses:
% 0.42/0.84 [
% 0.42/0.84 [ =( apply( apply( apply( s, X ), Y ), Z ), apply( apply( X, Z ), apply(
% 0.42/0.84 Y, Z ) ) ) ],
% 0.42/0.84 [ =( apply( apply( apply( b, X ), Y ), Z ), apply( X, apply( Y, Z ) ) )
% 0.42/0.84 ],
% 0.42/0.84 [ =( apply( apply( apply( c, X ), Y ), Z ), apply( apply( X, Z ), Y ) )
% 0.42/0.84 ],
% 0.42/0.84 [ =( apply( i, X ), X ) ],
% 0.42/0.84 [ =( 'weak_fixed_point'( X ), apply( apply( apply( s, apply( b, X ) ), i
% 0.42/0.84 ), apply( apply( s, apply( b, X ) ), i ) ) ) ],
% 0.42/0.84 [ ~( =( 'weak_fixed_point'( 'fixed_pt' ), apply( 'fixed_pt',
% 0.42/0.84 'weak_fixed_point'( 'fixed_pt' ) ) ) ) ]
% 0.42/0.84 ] .
% 0.42/0.84
% 0.42/0.84
% 0.42/0.84 percentage equality = 1.000000, percentage horn = 1.000000
% 0.42/0.84 This is a pure equality problem
% 0.42/0.84
% 0.42/0.84
% 0.42/0.84
% 0.42/0.84 Options Used:
% 0.42/0.84
% 0.42/0.84 useres = 1
% 0.42/0.84 useparamod = 1
% 0.42/0.84 useeqrefl = 1
% 0.42/0.84 useeqfact = 1
% 0.42/0.84 usefactor = 1
% 0.42/0.84 usesimpsplitting = 0
% 0.42/0.84 usesimpdemod = 5
% 0.42/0.84 usesimpres = 3
% 0.42/0.84
% 0.42/0.84 resimpinuse = 1000
% 0.42/0.84 resimpclauses = 20000
% 0.42/0.84 substype = eqrewr
% 0.42/0.84 backwardsubs = 1
% 0.42/0.84 selectoldest = 5
% 0.42/0.84
% 0.42/0.84 litorderings [0] = split
% 0.42/0.84 litorderings [1] = extend the termordering, first sorting on arguments
% 0.42/0.84
% 0.42/0.84 termordering = kbo
% 0.42/0.84
% 0.42/0.84 litapriori = 0
% 0.42/0.84 termapriori = 1
% 0.42/0.84 litaposteriori = 0
% 0.42/0.84 termaposteriori = 0
% 0.42/0.84 demodaposteriori = 0
% 0.42/0.84 ordereqreflfact = 0
% 0.42/0.84
% 0.42/0.84 litselect = negord
% 0.42/0.84
% 0.42/0.84 maxweight = 15
% 0.42/0.84 maxdepth = 30000
% 0.42/0.84 maxlength = 115
% 0.42/0.84 maxnrvars = 195
% 0.42/0.84 excuselevel = 1
% 0.42/0.84 increasemaxweight = 1
% 0.42/0.84
% 0.42/0.84 maxselected = 10000000
% 0.42/0.84 maxnrclauses = 10000000
% 0.42/0.84
% 0.42/0.84 showgenerated = 0
% 0.42/0.84 showkept = 0
% 0.42/0.84 showselected = 0
% 0.42/0.84 showdeleted = 0
% 0.42/0.84 showresimp = 1
% 0.42/0.84 showstatus = 2000
% 0.42/0.84
% 0.42/0.84 prologoutput = 1
% 0.42/0.84 nrgoals = 5000000
% 0.42/0.84 totalproof = 1
% 0.42/0.84
% 0.42/0.84 Symbols occurring in the translation:
% 0.42/0.84
% 0.42/0.84 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.42/0.84 . [1, 2] (w:1, o:23, a:1, s:1, b:0),
% 0.42/0.84 ! [4, 1] (w:0, o:17, a:1, s:1, b:0),
% 0.42/0.84 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.42/0.84 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.42/0.84 s [39, 0] (w:1, o:5, a:1, s:1, b:0),
% 0.42/0.84 apply [41, 2] (w:1, o:48, a:1, s:1, b:0),
% 0.42/0.84 b [44, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.42/0.84 c [45, 0] (w:1, o:14, a:1, s:1, b:0),
% 0.42/0.84 i [46, 0] (w:1, o:15, a:1, s:1, b:0),
% 0.42/0.84 'weak_fixed_point' [47, 1] (w:1, o:22, a:1, s:1, b:0),
% 0.42/0.84 'fixed_pt' [48, 0] (w:1, o:16, a:1, s:1, b:0).
% 0.42/0.84
% 0.42/0.84
% 0.42/0.84 Starting Search:
% 0.42/0.84
% 0.42/0.84
% 0.42/0.84 Bliksems!, er is een bewijs:
% 0.42/0.84 % SZS status Unsatisfiable
% 0.42/0.84 % SZS output start Refutation
% 0.42/0.84
% 0.42/0.84 clause( 0, [ =( apply( apply( apply( s, X ), Y ), Z ), apply( apply( X, Z )
% 0.42/0.84 , apply( Y, Z ) ) ) ] )
% 0.42/0.84 .
% 0.42/0.84 clause( 1, [ =( apply( apply( apply( b, X ), Y ), Z ), apply( X, apply( Y,
% 0.42/0.84 Z ) ) ) ] )
% 0.42/0.84 .
% 0.42/0.84 clause( 3, [ =( apply( i, X ), X ) ] )
% 0.42/0.84 .
% 0.42/0.84 clause( 4, [ =( apply( apply( apply( s, apply( b, X ) ), i ), apply( apply(
% 0.42/0.84 s, apply( b, X ) ), i ) ), 'weak_fixed_point'( X ) ) ] )
% 0.42/0.84 .
% 0.42/0.84 clause( 5, [ ~( =( apply( 'fixed_pt', 'weak_fixed_point'( 'fixed_pt' ) ),
% 0.42/0.84 'weak_fixed_point'( 'fixed_pt' ) ) ) ] )
% 0.42/0.84 .
% 0.42/0.84 clause( 22, [ =( apply( X, 'weak_fixed_point'( X ) ), 'weak_fixed_point'( X
% 0.42/0.84 ) ) ] )
% 0.42/0.84 .
% 0.42/0.84 clause( 26, [] )
% 0.42/0.84 .
% 0.42/0.84
% 0.42/0.84
% 0.42/0.84 % SZS output end Refutation
% 0.42/0.84 found a proof!
% 0.42/0.84
% 0.42/0.84 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.42/0.84
% 0.42/0.84 initialclauses(
% 0.42/0.84 [ clause( 28, [ =( apply( apply( apply( s, X ), Y ), Z ), apply( apply( X,
% 0.42/0.84 Z ), apply( Y, Z ) ) ) ] )
% 0.42/0.84 , clause( 29, [ =( apply( apply( apply( b, X ), Y ), Z ), apply( X, apply(
% 0.42/0.84 Y, Z ) ) ) ] )
% 0.42/0.84 , clause( 30, [ =( apply( apply( apply( c, X ), Y ), Z ), apply( apply( X,
% 0.42/0.84 Z ), Y ) ) ] )
% 0.42/0.84 , clause( 31, [ =( apply( i, X ), X ) ] )
% 0.42/0.84 , clause( 32, [ =( 'weak_fixed_point'( X ), apply( apply( apply( s, apply(
% 0.42/0.84 b, X ) ), i ), apply( apply( s, apply( b, X ) ), i ) ) ) ] )
% 0.42/0.84 , clause( 33, [ ~( =( 'weak_fixed_point'( 'fixed_pt' ), apply( 'fixed_pt',
% 0.42/0.84 'weak_fixed_point'( 'fixed_pt' ) ) ) ) ] )
% 0.42/0.84 ] ).
% 0.42/0.84
% 0.42/0.84
% 0.42/0.84
% 0.42/0.84 subsumption(
% 0.42/0.84 clause( 0, [ =( apply( apply( apply( s, X ), Y ), Z ), apply( apply( X, Z )
% 0.42/0.84 , apply( Y, Z ) ) ) ] )
% 0.42/0.84 , clause( 28, [ =( apply( apply( apply( s, X ), Y ), Z ), apply( apply( X,
% 0.42/0.84 Z ), apply( Y, Z ) ) ) ] )
% 0.42/0.84 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.42/0.84 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.42/0.84
% 0.42/0.84
% 0.42/0.84 subsumption(
% 0.42/0.84 clause( 1, [ =( apply( apply( apply( b, X ), Y ), Z ), apply( X, apply( Y,
% 0.42/0.84 Z ) ) ) ] )
% 0.42/0.84 , clause( 29, [ =( apply( apply( apply( b, X ), Y ), Z ), apply( X, apply(
% 0.42/0.84 Y, Z ) ) ) ] )
% 0.42/0.84 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.42/0.84 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.42/0.84
% 0.42/0.84
% 0.42/0.84 subsumption(
% 0.42/0.84 clause( 3, [ =( apply( i, X ), X ) ] )
% 0.42/0.84 , clause( 31, [ =( apply( i, X ), X ) ] )
% 0.42/0.84 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.42/0.84
% 0.42/0.84
% 0.42/0.84 eqswap(
% 0.42/0.84 clause( 45, [ =( apply( apply( apply( s, apply( b, X ) ), i ), apply( apply(
% 0.42/0.84 s, apply( b, X ) ), i ) ), 'weak_fixed_point'( X ) ) ] )
% 0.42/0.84 , clause( 32, [ =( 'weak_fixed_point'( X ), apply( apply( apply( s, apply(
% 0.42/0.84 b, X ) ), i ), apply( apply( s, apply( b, X ) ), i ) ) ) ] )
% 0.42/0.84 , 0, substitution( 0, [ :=( X, X )] )).
% 0.42/0.84
% 0.42/0.84
% 0.42/0.84 subsumption(
% 0.42/0.84 clause( 4, [ =( apply( apply( apply( s, apply( b, X ) ), i ), apply( apply(
% 0.42/0.84 s, apply( b, X ) ), i ) ), 'weak_fixed_point'( X ) ) ] )
% 0.42/0.84 , clause( 45, [ =( apply( apply( apply( s, apply( b, X ) ), i ), apply(
% 0.42/0.84 apply( s, apply( b, X ) ), i ) ), 'weak_fixed_point'( X ) ) ] )
% 0.42/0.84 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.42/0.84
% 0.42/0.84
% 0.42/0.84 eqswap(
% 0.42/0.84 clause( 51, [ ~( =( apply( 'fixed_pt', 'weak_fixed_point'( 'fixed_pt' ) ),
% 0.42/0.84 'weak_fixed_point'( 'fixed_pt' ) ) ) ] )
% 0.42/0.84 , clause( 33, [ ~( =( 'weak_fixed_point'( 'fixed_pt' ), apply( 'fixed_pt',
% 0.42/0.84 'weak_fixed_point'( 'fixed_pt' ) ) ) ) ] )
% 0.42/0.84 , 0, substitution( 0, [] )).
% 0.42/0.84
% 0.42/0.84
% 0.42/0.84 subsumption(
% 0.42/0.84 clause( 5, [ ~( =( apply( 'fixed_pt', 'weak_fixed_point'( 'fixed_pt' ) ),
% 0.42/0.84 'weak_fixed_point'( 'fixed_pt' ) ) ) ] )
% 0.42/0.84 , clause( 51, [ ~( =( apply( 'fixed_pt', 'weak_fixed_point'( 'fixed_pt' ) )
% 0.42/0.84 , 'weak_fixed_point'( 'fixed_pt' ) ) ) ] )
% 0.42/0.84 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.42/0.84
% 0.42/0.84
% 0.42/0.84 eqswap(
% 0.42/0.84 clause( 52, [ =( 'weak_fixed_point'( X ), apply( apply( apply( s, apply( b
% 0.42/0.84 , X ) ), i ), apply( apply( s, apply( b, X ) ), i ) ) ) ] )
% 0.42/0.84 , clause( 4, [ =( apply( apply( apply( s, apply( b, X ) ), i ), apply(
% 0.42/0.84 apply( s, apply( b, X ) ), i ) ), 'weak_fixed_point'( X ) ) ] )
% 0.42/0.84 , 0, substitution( 0, [ :=( X, X )] )).
% 0.42/0.84
% 0.42/0.84
% 0.42/0.84 paramod(
% 0.42/0.84 clause( 58, [ =( 'weak_fixed_point'( X ), apply( apply( apply( b, X ),
% 0.42/0.84 apply( apply( s, apply( b, X ) ), i ) ), apply( i, apply( apply( s, apply(
% 0.42/0.84 b, X ) ), i ) ) ) ) ] )
% 0.42/0.84 , clause( 0, [ =( apply( apply( apply( s, X ), Y ), Z ), apply( apply( X, Z
% 0.42/0.84 ), apply( Y, Z ) ) ) ] )
% 0.42/0.84 , 0, clause( 52, [ =( 'weak_fixed_point'( X ), apply( apply( apply( s,
% 0.42/0.84 apply( b, X ) ), i ), apply( apply( s, apply( b, X ) ), i ) ) ) ] )
% 0.42/0.84 , 0, 3, substitution( 0, [ :=( X, apply( b, X ) ), :=( Y, i ), :=( Z, apply(
% 0.42/0.84 apply( s, apply( b, X ) ), i ) )] ), substitution( 1, [ :=( X, X )] )
% 0.42/0.84 ).
% 0.42/0.84
% 0.42/0.84
% 0.42/0.84 paramod(
% 0.42/0.84 clause( 59, [ =( 'weak_fixed_point'( X ), apply( X, apply( apply( apply( s
% 0.42/0.84 , apply( b, X ) ), i ), apply( i, apply( apply( s, apply( b, X ) ), i ) )
% 0.42/0.84 ) ) ) ] )
% 0.42/0.84 , clause( 1, [ =( apply( apply( apply( b, X ), Y ), Z ), apply( X, apply( Y
% 0.42/0.84 , Z ) ) ) ] )
% 0.42/0.84 , 0, clause( 58, [ =( 'weak_fixed_point'( X ), apply( apply( apply( b, X )
% 0.42/0.84 , apply( apply( s, apply( b, X ) ), i ) ), apply( i, apply( apply( s,
% 0.42/0.84 apply( b, X ) ), i ) ) ) ) ] )
% 0.42/0.84 , 0, 3, substitution( 0, [ :=( X, X ), :=( Y, apply( apply( s, apply( b, X
% 0.42/0.84 ) ), i ) ), :=( Z, apply( i, apply( apply( s, apply( b, X ) ), i ) ) )] )
% 0.42/0.84 , substitution( 1, [ :=( X, X )] )).
% 0.42/0.84
% 0.42/0.84
% 0.42/0.84 paramod(
% 0.42/0.84 clause( 60, [ =( 'weak_fixed_point'( X ), apply( X, apply( apply( apply( s
% 0.42/0.84 , apply( b, X ) ), i ), apply( apply( s, apply( b, X ) ), i ) ) ) ) ] )
% 0.42/0.84 , clause( 3, [ =( apply( i, X ), X ) ] )
% 0.42/0.84 , 0, clause( 59, [ =( 'weak_fixed_point'( X ), apply( X, apply( apply(
% 0.42/0.84 apply( s, apply( b, X ) ), i ), apply( i, apply( apply( s, apply( b, X )
% 0.42/0.84 ), i ) ) ) ) ) ] )
% 0.42/0.84 , 0, 13, substitution( 0, [ :=( X, apply( apply( s, apply( b, X ) ), i ) )] )
% 0.42/0.84 , substitution( 1, [ :=( X, X )] )).
% 0.42/0.84
% 0.42/0.84
% 0.42/0.84 paramod(
% 0.42/0.84 clause( 61, [ =( 'weak_fixed_point'( X ), apply( X, 'weak_fixed_point'( X )
% 0.42/0.84 ) ) ] )
% 0.42/0.84 , clause( 4, [ =( apply( apply( apply( s, apply( b, X ) ), i ), apply(
% 0.42/0.84 apply( s, apply( b, X ) ), i ) ), 'weak_fixed_point'( X ) ) ] )
% 0.42/0.84 , 0, clause( 60, [ =( 'weak_fixed_point'( X ), apply( X, apply( apply(
% 0.42/0.84 apply( s, apply( b, X ) ), i ), apply( apply( s, apply( b, X ) ), i ) ) )
% 0.42/0.84 ) ] )
% 0.42/0.84 , 0, 5, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X )] )
% 0.42/0.84 ).
% 0.42/0.84
% 0.42/0.84
% 0.42/0.84 eqswap(
% 0.42/0.84 clause( 62, [ =( apply( X, 'weak_fixed_point'( X ) ), 'weak_fixed_point'( X
% 0.42/0.84 ) ) ] )
% 0.42/0.84 , clause( 61, [ =( 'weak_fixed_point'( X ), apply( X, 'weak_fixed_point'( X
% 0.42/0.84 ) ) ) ] )
% 0.42/0.84 , 0, substitution( 0, [ :=( X, X )] )).
% 0.42/0.84
% 0.42/0.84
% 0.42/0.84 subsumption(
% 0.42/0.84 clause( 22, [ =( apply( X, 'weak_fixed_point'( X ) ), 'weak_fixed_point'( X
% 0.42/0.84 ) ) ] )
% 0.42/0.84 , clause( 62, [ =( apply( X, 'weak_fixed_point'( X ) ), 'weak_fixed_point'(
% 0.42/0.84 X ) ) ] )
% 0.42/0.84 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.42/0.84
% 0.42/0.84
% 0.42/0.84 eqswap(
% 0.42/0.84 clause( 63, [ =( 'weak_fixed_point'( X ), apply( X, 'weak_fixed_point'( X )
% 0.42/0.84 ) ) ] )
% 0.42/0.84 , clause( 22, [ =( apply( X, 'weak_fixed_point'( X ) ), 'weak_fixed_point'(
% 0.42/0.84 X ) ) ] )
% 0.42/0.84 , 0, substitution( 0, [ :=( X, X )] )).
% 0.42/0.84
% 0.42/0.84
% 0.42/0.84 eqswap(
% 0.42/0.84 clause( 64, [ ~( =( 'weak_fixed_point'( 'fixed_pt' ), apply( 'fixed_pt',
% 0.42/0.84 'weak_fixed_point'( 'fixed_pt' ) ) ) ) ] )
% 0.42/0.84 , clause( 5, [ ~( =( apply( 'fixed_pt', 'weak_fixed_point'( 'fixed_pt' ) )
% 0.42/0.84 , 'weak_fixed_point'( 'fixed_pt' ) ) ) ] )
% 0.42/0.84 , 0, substitution( 0, [] )).
% 0.42/0.84
% 0.42/0.84
% 0.42/0.84 resolution(
% 0.42/0.84 clause( 65, [] )
% 0.42/0.84 , clause( 64, [ ~( =( 'weak_fixed_point'( 'fixed_pt' ), apply( 'fixed_pt',
% 0.42/0.84 'weak_fixed_point'( 'fixed_pt' ) ) ) ) ] )
% 0.42/0.84 , 0, clause( 63, [ =( 'weak_fixed_point'( X ), apply( X, 'weak_fixed_point'(
% 0.42/0.84 X ) ) ) ] )
% 0.42/0.84 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, 'fixed_pt' )] )).
% 0.42/0.84
% 0.42/0.84
% 0.42/0.84 subsumption(
% 0.42/0.84 clause( 26, [] )
% 0.42/0.84 , clause( 65, [] )
% 0.42/0.84 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.42/0.84
% 0.42/0.84
% 0.42/0.84 end.
% 0.42/0.84
% 0.42/0.84 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.42/0.84
% 0.42/0.84 Memory use:
% 0.42/0.84
% 0.42/0.84 space for terms: 650
% 0.42/0.84 space for clauses: 4268
% 0.42/0.84
% 0.42/0.84
% 0.42/0.84 clauses generated: 51
% 0.42/0.84 clauses kept: 27
% 0.42/0.84 clauses selected: 7
% 0.42/0.84 clauses deleted: 0
% 0.42/0.84 clauses inuse deleted: 0
% 0.42/0.84
% 0.42/0.84 subsentry: 137
% 0.42/0.84 literals s-matched: 67
% 0.42/0.84 literals matched: 67
% 0.42/0.84 full subsumption: 0
% 0.42/0.84
% 0.42/0.84 checksum: 1741426967
% 0.42/0.84
% 0.42/0.84
% 0.42/0.84 Bliksem ended
%------------------------------------------------------------------------------