%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWX186-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n028.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 06:56:45 PM UTC 2026
% Result : Unsatisfiable 0.66s 1.08s
% Output : Refutation 0.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWX186-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : bliksem %s
% 0.14/0.33 % Computer : n028.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % DateTime : Tue May 5 09:38:45 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.66/1.08 *** allocated 10000 integers for termspace/termends
% 0.66/1.08 *** allocated 10000 integers for clauses
% 0.66/1.08 *** allocated 10000 integers for justifications
% 0.66/1.08 Bliksem 1.12
% 0.66/1.08
% 0.66/1.08
% 0.66/1.08 Automatic Strategy Selection
% 0.66/1.08
% 0.66/1.08 Clauses:
% 0.66/1.08 [
% 0.66/1.08 [ =( impl( btrue, X ), X ) ],
% 0.66/1.08 [ =( impl( bfalse, X ), btrue ) ],
% 0.66/1.08 [ =( drop( s( X ), nil ), nil ) ],
% 0.66/1.08 [ =( drop( s( X ), cons( Y, Z ) ), drop( X, Z ) ) ],
% 0.66/1.08 [ =( drop( z, X ), X ) ],
% 0.66/1.08 [ =( 'prop_drop_inj2'( X, Y, Z ), impl( eq( drop( X, Y ), drop( X, Z ) )
% 0.66/1.08 , eq( Y, Z ) ) ) ],
% 0.66/1.08 [ =( eq3( bfalse, btrue ), bfalse ) ],
% 0.66/1.08 [ =( eq3( btrue, bfalse ), bfalse ) ],
% 0.66/1.08 [ =( eq2( s( X ), s( Y ) ), eq2( X, Y ) ) ],
% 0.66/1.08 [ =( eq2( s( X ), z ), bfalse ) ],
% 0.66/1.08 [ =( eq2( z, s( X ) ), bfalse ) ],
% 0.66/1.08 [ =( eq( X, X ), btrue ) ],
% 0.66/1.08 [ =( eq2( X, X ), btrue ) ],
% 0.66/1.08 [ =( eq3( X, X ), btrue ) ],
% 0.66/1.08 [ ~( =( eq2( X, Y ), bfalse ) ), =( eq( cons( X, Z ), cons( Y, T ) ),
% 0.66/1.08 bfalse ) ],
% 0.66/1.08 [ ~( =( eq2( X, Y ), btrue ) ), =( eq( cons( X, Z ), cons( Y, T ) ), eq(
% 0.66/1.08 Z, T ) ) ],
% 0.66/1.08 [ =( eq( nil, cons( X, Y ) ), bfalse ) ],
% 0.66/1.08 [ =( eq( cons( X, Y ), nil ), bfalse ) ],
% 0.66/1.08 [ ~( =( eq3( 'prop_drop_inj2'( X, Y, Z ), bfalse ), btrue ) ) ]
% 0.66/1.08 ] .
% 0.66/1.08
% 0.66/1.08
% 0.66/1.08 percentage equality = 1.000000, percentage horn = 1.000000
% 0.66/1.08 This is a pure equality problem
% 0.66/1.08
% 0.66/1.08
% 0.66/1.08
% 0.66/1.08 Options Used:
% 0.66/1.08
% 0.66/1.08 useres = 1
% 0.66/1.08 useparamod = 1
% 0.66/1.08 useeqrefl = 1
% 0.66/1.08 useeqfact = 1
% 0.66/1.08 usefactor = 1
% 0.66/1.08 usesimpsplitting = 0
% 0.66/1.08 usesimpdemod = 5
% 0.66/1.08 usesimpres = 3
% 0.66/1.08
% 0.66/1.08 resimpinuse = 1000
% 0.66/1.08 resimpclauses = 20000
% 0.66/1.08 substype = eqrewr
% 0.66/1.08 backwardsubs = 1
% 0.66/1.08 selectoldest = 5
% 0.66/1.08
% 0.66/1.08 litorderings [0] = split
% 0.66/1.08 litorderings [1] = extend the termordering, first sorting on arguments
% 0.66/1.08
% 0.66/1.08 termordering = kbo
% 0.66/1.08
% 0.66/1.08 litapriori = 0
% 0.66/1.08 termapriori = 1
% 0.66/1.08 litaposteriori = 0
% 0.66/1.08 termaposteriori = 0
% 0.66/1.08 demodaposteriori = 0
% 0.66/1.08 ordereqreflfact = 0
% 0.66/1.08
% 0.66/1.08 litselect = negord
% 0.66/1.08
% 0.66/1.08 maxweight = 15
% 0.66/1.08 maxdepth = 30000
% 0.66/1.08 maxlength = 115
% 0.66/1.08 maxnrvars = 195
% 0.66/1.08 excuselevel = 1
% 0.66/1.08 increasemaxweight = 1
% 0.66/1.08
% 0.66/1.08 maxselected = 10000000
% 0.66/1.08 maxnrclauses = 10000000
% 0.66/1.08
% 0.66/1.08 showgenerated = 0
% 0.66/1.08 showkept = 0
% 0.66/1.08 showselected = 0
% 0.66/1.08 showdeleted = 0
% 0.66/1.08 showresimp = 1
% 0.66/1.08 showstatus = 2000
% 0.66/1.08
% 0.66/1.08 prologoutput = 1
% 0.66/1.08 nrgoals = 5000000
% 0.66/1.08 totalproof = 1
% 0.66/1.08
% 0.66/1.08 Symbols occurring in the translation:
% 0.66/1.08
% 0.66/1.08 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.66/1.08 . [1, 2] (w:1, o:25, a:1, s:1, b:0),
% 0.66/1.08 ! [4, 1] (w:0, o:19, a:1, s:1, b:0),
% 0.66/1.08 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.66/1.08 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.66/1.08 btrue [39, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.66/1.08 impl [41, 2] (w:1, o:50, a:1, s:1, b:0),
% 0.66/1.08 bfalse [42, 0] (w:1, o:11, a:1, s:1, b:0),
% 0.66/1.08 s [44, 1] (w:1, o:24, a:1, s:1, b:0),
% 0.66/1.08 nil [45, 0] (w:1, o:15, a:1, s:1, b:0),
% 0.66/1.08 drop [46, 2] (w:1, o:52, a:1, s:1, b:0),
% 0.66/1.08 cons [49, 2] (w:1, o:51, a:1, s:1, b:0),
% 0.66/1.08 z [50, 0] (w:1, o:18, a:1, s:1, b:0),
% 0.66/1.08 'prop_drop_inj2' [53, 3] (w:1, o:56, a:1, s:1, b:0),
% 0.66/1.08 eq [54, 2] (w:1, o:53, a:1, s:1, b:0),
% 0.66/1.08 eq3 [55, 2] (w:1, o:55, a:1, s:1, b:0),
% 0.66/1.08 eq2 [56, 2] (w:1, o:54, a:1, s:1, b:0).
% 0.66/1.08
% 0.66/1.08
% 0.66/1.08 Starting Search:
% 0.66/1.08
% 0.66/1.08
% 0.66/1.08 Bliksems!, er is een bewijs:
% 0.66/1.08 % SZS status Unsatisfiable
% 0.66/1.08 % SZS output start Refutation
% 0.66/1.08
% 0.66/1.08 clause( 0, [ =( impl( btrue, X ), X ) ] )
% 0.66/1.08 .
% 0.66/1.08 clause( 2, [ =( drop( s( X ), nil ), nil ) ] )
% 0.66/1.08 .
% 0.66/1.08 clause( 3, [ =( drop( s( X ), cons( Y, Z ) ), drop( X, Z ) ) ] )
% 0.66/1.08 .
% 0.66/1.08 clause( 5, [ =( impl( eq( drop( X, Y ), drop( X, Z ) ), eq( Y, Z ) ),
% 0.66/1.08 'prop_drop_inj2'( X, Y, Z ) ) ] )
% 0.66/1.08 .
% 0.66/1.08 clause( 11, [ =( eq( X, X ), btrue ) ] )
% 0.66/1.08 .
% 0.66/1.08 clause( 13, [ =( eq3( X, X ), btrue ) ] )
% 0.66/1.08 .
% 0.66/1.08 clause( 16, [ =( eq( nil, cons( X, Y ) ), bfalse ) ] )
% 0.66/1.08 .
% 0.66/1.08 clause( 18, [ ~( =( eq3( 'prop_drop_inj2'( X, Y, Z ), bfalse ), btrue ) ) ]
% 0.66/1.08 )
% 0.66/1.08 .
% 0.66/1.08 clause( 34, [ =( impl( eq( drop( s( X ), T ), drop( X, Z ) ), eq( T, cons(
% 0.66/1.08 Y, Z ) ) ), 'prop_drop_inj2'( s( X ), T, cons( Y, Z ) ) ) ] )
% 0.66/1.08 .
% 0.66/1.08 clause( 58, [ =( impl( eq( nil, drop( Z, Y ) ), bfalse ), 'prop_drop_inj2'(
% 0.66/1.08 s( Z ), nil, cons( X, Y ) ) ) ] )
% 0.66/1.08 .
% 0.66/1.08 clause( 61, [ =( 'prop_drop_inj2'( s( s( X ) ), nil, cons( Y, nil ) ),
% 0.66/1.08 bfalse ) ] )
% 0.66/1.08 .
% 0.66/1.08 clause( 63, [] )
% 0.66/1.08 .
% 0.66/1.08
% 0.66/1.08
% 0.66/1.08 % SZS output end Refutation
% 0.66/1.08 found a proof!
% 0.66/1.08
% 0.66/1.08 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.66/1.08
% 0.66/1.08 initialclauses(
% 0.66/1.08 [ clause( 65, [ =( impl( btrue, X ), X ) ] )
% 0.66/1.08 , clause( 66, [ =( impl( bfalse, X ), btrue ) ] )
% 0.66/1.08 , clause( 67, [ =( drop( s( X ), nil ), nil ) ] )
% 0.66/1.08 , clause( 68, [ =( drop( s( X ), cons( Y, Z ) ), drop( X, Z ) ) ] )
% 0.66/1.08 , clause( 69, [ =( drop( z, X ), X ) ] )
% 0.66/1.08 , clause( 70, [ =( 'prop_drop_inj2'( X, Y, Z ), impl( eq( drop( X, Y ),
% 0.66/1.08 drop( X, Z ) ), eq( Y, Z ) ) ) ] )
% 0.66/1.08 , clause( 71, [ =( eq3( bfalse, btrue ), bfalse ) ] )
% 0.66/1.08 , clause( 72, [ =( eq3( btrue, bfalse ), bfalse ) ] )
% 0.66/1.08 , clause( 73, [ =( eq2( s( X ), s( Y ) ), eq2( X, Y ) ) ] )
% 0.66/1.08 , clause( 74, [ =( eq2( s( X ), z ), bfalse ) ] )
% 0.66/1.08 , clause( 75, [ =( eq2( z, s( X ) ), bfalse ) ] )
% 0.66/1.08 , clause( 76, [ =( eq( X, X ), btrue ) ] )
% 0.66/1.08 , clause( 77, [ =( eq2( X, X ), btrue ) ] )
% 0.66/1.08 , clause( 78, [ =( eq3( X, X ), btrue ) ] )
% 0.66/1.08 , clause( 79, [ ~( =( eq2( X, Y ), bfalse ) ), =( eq( cons( X, Z ), cons( Y
% 0.66/1.08 , T ) ), bfalse ) ] )
% 0.66/1.08 , clause( 80, [ ~( =( eq2( X, Y ), btrue ) ), =( eq( cons( X, Z ), cons( Y
% 0.66/1.08 , T ) ), eq( Z, T ) ) ] )
% 0.66/1.08 , clause( 81, [ =( eq( nil, cons( X, Y ) ), bfalse ) ] )
% 0.66/1.08 , clause( 82, [ =( eq( cons( X, Y ), nil ), bfalse ) ] )
% 0.66/1.08 , clause( 83, [ ~( =( eq3( 'prop_drop_inj2'( X, Y, Z ), bfalse ), btrue ) )
% 0.66/1.08 ] )
% 0.66/1.08 ] ).
% 0.66/1.08
% 0.66/1.08
% 0.66/1.08
% 0.66/1.08 subsumption(
% 0.66/1.08 clause( 0, [ =( impl( btrue, X ), X ) ] )
% 0.66/1.08 , clause( 65, [ =( impl( btrue, X ), X ) ] )
% 0.66/1.08 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.66/1.08
% 0.66/1.08
% 0.66/1.08 subsumption(
% 0.66/1.08 clause( 2, [ =( drop( s( X ), nil ), nil ) ] )
% 0.66/1.08 , clause( 67, [ =( drop( s( X ), nil ), nil ) ] )
% 0.66/1.08 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.66/1.08
% 0.66/1.08
% 0.66/1.08 subsumption(
% 0.66/1.08 clause( 3, [ =( drop( s( X ), cons( Y, Z ) ), drop( X, Z ) ) ] )
% 0.66/1.08 , clause( 68, [ =( drop( s( X ), cons( Y, Z ) ), drop( X, Z ) ) ] )
% 0.66/1.08 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.66/1.08 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.66/1.08
% 0.66/1.08
% 0.66/1.08 eqswap(
% 0.66/1.08 clause( 97, [ =( impl( eq( drop( X, Y ), drop( X, Z ) ), eq( Y, Z ) ),
% 0.66/1.08 'prop_drop_inj2'( X, Y, Z ) ) ] )
% 0.66/1.08 , clause( 70, [ =( 'prop_drop_inj2'( X, Y, Z ), impl( eq( drop( X, Y ),
% 0.66/1.08 drop( X, Z ) ), eq( Y, Z ) ) ) ] )
% 0.66/1.08 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.66/1.08
% 0.66/1.08
% 0.66/1.08 subsumption(
% 0.66/1.08 clause( 5, [ =( impl( eq( drop( X, Y ), drop( X, Z ) ), eq( Y, Z ) ),
% 0.66/1.08 'prop_drop_inj2'( X, Y, Z ) ) ] )
% 0.66/1.08 , clause( 97, [ =( impl( eq( drop( X, Y ), drop( X, Z ) ), eq( Y, Z ) ),
% 0.66/1.08 'prop_drop_inj2'( X, Y, Z ) ) ] )
% 0.66/1.08 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.66/1.08 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.66/1.08
% 0.66/1.08
% 0.66/1.08 subsumption(
% 0.66/1.08 clause( 11, [ =( eq( X, X ), btrue ) ] )
% 0.66/1.08 , clause( 76, [ =( eq( X, X ), btrue ) ] )
% 0.66/1.08 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.66/1.08
% 0.66/1.08
% 0.66/1.08 subsumption(
% 0.66/1.08 clause( 13, [ =( eq3( X, X ), btrue ) ] )
% 0.66/1.08 , clause( 78, [ =( eq3( X, X ), btrue ) ] )
% 0.66/1.08 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.66/1.08
% 0.66/1.08
% 0.66/1.08 subsumption(
% 0.66/1.08 clause( 16, [ =( eq( nil, cons( X, Y ) ), bfalse ) ] )
% 0.66/1.08 , clause( 81, [ =( eq( nil, cons( X, Y ) ), bfalse ) ] )
% 0.66/1.08 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.66/1.08 )] ) ).
% 0.66/1.08
% 0.66/1.08
% 0.66/1.08 subsumption(
% 0.66/1.08 clause( 18, [ ~( =( eq3( 'prop_drop_inj2'( X, Y, Z ), bfalse ), btrue ) ) ]
% 0.66/1.08 )
% 0.66/1.08 , clause( 83, [ ~( =( eq3( 'prop_drop_inj2'( X, Y, Z ), bfalse ), btrue ) )
% 0.66/1.08 ] )
% 0.66/1.08 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.66/1.08 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.66/1.08
% 0.66/1.08
% 0.66/1.08 eqswap(
% 0.66/1.08 clause( 169, [ =( 'prop_drop_inj2'( X, Y, Z ), impl( eq( drop( X, Y ), drop(
% 0.66/1.08 X, Z ) ), eq( Y, Z ) ) ) ] )
% 0.66/1.08 , clause( 5, [ =( impl( eq( drop( X, Y ), drop( X, Z ) ), eq( Y, Z ) ),
% 0.66/1.08 'prop_drop_inj2'( X, Y, Z ) ) ] )
% 0.66/1.08 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.66/1.08
% 0.66/1.08
% 0.66/1.08 paramod(
% 0.66/1.08 clause( 171, [ =( 'prop_drop_inj2'( s( X ), Y, cons( Z, T ) ), impl( eq(
% 0.66/1.08 drop( s( X ), Y ), drop( X, T ) ), eq( Y, cons( Z, T ) ) ) ) ] )
% 0.66/1.08 , clause( 3, [ =( drop( s( X ), cons( Y, Z ) ), drop( X, Z ) ) ] )
% 0.66/1.08 , 0, clause( 169, [ =( 'prop_drop_inj2'( X, Y, Z ), impl( eq( drop( X, Y )
% 0.66/1.08 , drop( X, Z ) ), eq( Y, Z ) ) ) ] )
% 0.66/1.08 , 0, 14, substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, T )] ),
% 0.66/1.08 substitution( 1, [ :=( X, s( X ) ), :=( Y, Y ), :=( Z, cons( Z, T ) )] )
% 0.66/1.08 ).
% 0.66/1.08
% 0.66/1.08
% 0.66/1.08 eqswap(
% 0.66/1.08 clause( 173, [ =( impl( eq( drop( s( X ), Y ), drop( X, T ) ), eq( Y, cons(
% 0.66/1.08 Z, T ) ) ), 'prop_drop_inj2'( s( X ), Y, cons( Z, T ) ) ) ] )
% 0.66/1.08 , clause( 171, [ =( 'prop_drop_inj2'( s( X ), Y, cons( Z, T ) ), impl( eq(
% 0.66/1.08 drop( s( X ), Y ), drop( X, T ) ), eq( Y, cons( Z, T ) ) ) ) ] )
% 0.66/1.08 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 0.66/1.08 ).
% 0.66/1.08
% 0.66/1.08
% 0.66/1.08 subsumption(
% 0.66/1.08 clause( 34, [ =( impl( eq( drop( s( X ), T ), drop( X, Z ) ), eq( T, cons(
% 0.66/1.08 Y, Z ) ) ), 'prop_drop_inj2'( s( X ), T, cons( Y, Z ) ) ) ] )
% 0.66/1.08 , clause( 173, [ =( impl( eq( drop( s( X ), Y ), drop( X, T ) ), eq( Y,
% 0.66/1.08 cons( Z, T ) ) ), 'prop_drop_inj2'( s( X ), Y, cons( Z, T ) ) ) ] )
% 0.66/1.08 , substitution( 0, [ :=( X, X ), :=( Y, T ), :=( Z, Y ), :=( T, Z )] ),
% 0.66/1.08 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.66/1.08
% 0.66/1.08
% 0.66/1.08 eqswap(
% 0.66/1.08 clause( 175, [ =( 'prop_drop_inj2'( s( X ), Y, cons( T, Z ) ), impl( eq(
% 0.66/1.08 drop( s( X ), Y ), drop( X, Z ) ), eq( Y, cons( T, Z ) ) ) ) ] )
% 0.66/1.08 , clause( 34, [ =( impl( eq( drop( s( X ), T ), drop( X, Z ) ), eq( T, cons(
% 0.66/1.08 Y, Z ) ) ), 'prop_drop_inj2'( s( X ), T, cons( Y, Z ) ) ) ] )
% 0.66/1.08 , 0, substitution( 0, [ :=( X, X ), :=( Y, T ), :=( Z, Z ), :=( T, Y )] )
% 0.66/1.08 ).
% 0.66/1.08
% 0.66/1.08
% 0.66/1.08 paramod(
% 0.66/1.08 clause( 177, [ =( 'prop_drop_inj2'( s( X ), nil, cons( Y, Z ) ), impl( eq(
% 0.66/1.08 drop( s( X ), nil ), drop( X, Z ) ), bfalse ) ) ] )
% 0.66/1.08 , clause( 16, [ =( eq( nil, cons( X, Y ) ), bfalse ) ] )
% 0.66/1.08 , 0, clause( 175, [ =( 'prop_drop_inj2'( s( X ), Y, cons( T, Z ) ), impl(
% 0.66/1.08 eq( drop( s( X ), Y ), drop( X, Z ) ), eq( Y, cons( T, Z ) ) ) ) ] )
% 0.66/1.08 , 0, 17, substitution( 0, [ :=( X, Y ), :=( Y, Z )] ), substitution( 1, [
% 0.66/1.08 :=( X, X ), :=( Y, nil ), :=( Z, Z ), :=( T, Y )] )).
% 0.66/1.08
% 0.66/1.08
% 0.66/1.08 paramod(
% 0.66/1.08 clause( 178, [ =( 'prop_drop_inj2'( s( X ), nil, cons( Y, Z ) ), impl( eq(
% 0.66/1.08 nil, drop( X, Z ) ), bfalse ) ) ] )
% 0.66/1.08 , clause( 2, [ =( drop( s( X ), nil ), nil ) ] )
% 0.66/1.08 , 0, clause( 177, [ =( 'prop_drop_inj2'( s( X ), nil, cons( Y, Z ) ), impl(
% 0.66/1.08 eq( drop( s( X ), nil ), drop( X, Z ) ), bfalse ) ) ] )
% 0.66/1.08 , 0, 10, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 0.66/1.08 :=( Y, Y ), :=( Z, Z )] )).
% 0.66/1.08
% 0.66/1.08
% 0.66/1.08 eqswap(
% 0.66/1.08 clause( 179, [ =( impl( eq( nil, drop( X, Z ) ), bfalse ), 'prop_drop_inj2'(
% 0.66/1.08 s( X ), nil, cons( Y, Z ) ) ) ] )
% 0.66/1.08 , clause( 178, [ =( 'prop_drop_inj2'( s( X ), nil, cons( Y, Z ) ), impl( eq(
% 0.66/1.08 nil, drop( X, Z ) ), bfalse ) ) ] )
% 0.66/1.08 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.66/1.08
% 0.66/1.08
% 0.66/1.08 subsumption(
% 0.66/1.08 clause( 58, [ =( impl( eq( nil, drop( Z, Y ) ), bfalse ), 'prop_drop_inj2'(
% 0.66/1.08 s( Z ), nil, cons( X, Y ) ) ) ] )
% 0.66/1.08 , clause( 179, [ =( impl( eq( nil, drop( X, Z ) ), bfalse ),
% 0.66/1.08 'prop_drop_inj2'( s( X ), nil, cons( Y, Z ) ) ) ] )
% 0.66/1.08 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 0.66/1.08 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.66/1.08
% 0.66/1.08
% 0.66/1.08 eqswap(
% 0.66/1.08 clause( 181, [ =( 'prop_drop_inj2'( s( X ), nil, cons( Z, Y ) ), impl( eq(
% 0.66/1.08 nil, drop( X, Y ) ), bfalse ) ) ] )
% 0.66/1.08 , clause( 58, [ =( impl( eq( nil, drop( Z, Y ) ), bfalse ),
% 0.66/1.08 'prop_drop_inj2'( s( Z ), nil, cons( X, Y ) ) ) ] )
% 0.66/1.08 , 0, substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, X )] )).
% 0.66/1.08
% 0.66/1.08
% 0.66/1.08 paramod(
% 0.66/1.08 clause( 184, [ =( 'prop_drop_inj2'( s( s( X ) ), nil, cons( Y, nil ) ),
% 0.66/1.08 impl( eq( nil, nil ), bfalse ) ) ] )
% 0.66/1.08 , clause( 2, [ =( drop( s( X ), nil ), nil ) ] )
% 0.66/1.08 , 0, clause( 181, [ =( 'prop_drop_inj2'( s( X ), nil, cons( Z, Y ) ), impl(
% 0.66/1.08 eq( nil, drop( X, Y ) ), bfalse ) ) ] )
% 0.66/1.08 , 0, 12, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, s( X )
% 0.66/1.08 ), :=( Y, nil ), :=( Z, Y )] )).
% 0.66/1.08
% 0.66/1.08
% 0.66/1.08 paramod(
% 0.66/1.08 clause( 185, [ =( 'prop_drop_inj2'( s( s( X ) ), nil, cons( Y, nil ) ),
% 0.66/1.08 impl( btrue, bfalse ) ) ] )
% 0.66/1.08 , clause( 11, [ =( eq( X, X ), btrue ) ] )
% 0.66/1.08 , 0, clause( 184, [ =( 'prop_drop_inj2'( s( s( X ) ), nil, cons( Y, nil ) )
% 0.66/1.08 , impl( eq( nil, nil ), bfalse ) ) ] )
% 0.66/1.08 , 0, 10, substitution( 0, [ :=( X, nil )] ), substitution( 1, [ :=( X, X )
% 0.66/1.08 , :=( Y, Y )] )).
% 0.66/1.08
% 0.66/1.08
% 0.66/1.08 paramod(
% 0.66/1.08 clause( 186, [ =( 'prop_drop_inj2'( s( s( X ) ), nil, cons( Y, nil ) ),
% 0.66/1.08 bfalse ) ] )
% 0.66/1.08 , clause( 0, [ =( impl( btrue, X ), X ) ] )
% 0.66/1.08 , 0, clause( 185, [ =( 'prop_drop_inj2'( s( s( X ) ), nil, cons( Y, nil ) )
% 0.66/1.08 , impl( btrue, bfalse ) ) ] )
% 0.66/1.08 , 0, 9, substitution( 0, [ :=( X, bfalse )] ), substitution( 1, [ :=( X, X
% 0.66/1.08 ), :=( Y, Y )] )).
% 0.66/1.08
% 0.66/1.08
% 0.66/1.08 subsumption(
% 0.66/1.08 clause( 61, [ =( 'prop_drop_inj2'( s( s( X ) ), nil, cons( Y, nil ) ),
% 0.66/1.08 bfalse ) ] )
% 0.66/1.08 , clause( 186, [ =( 'prop_drop_inj2'( s( s( X ) ), nil, cons( Y, nil ) ),
% 0.66/1.08 bfalse ) ] )
% 0.66/1.08 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.66/1.08 )] ) ).
% 0.66/1.08
% 0.66/1.08
% 0.66/1.08 eqswap(
% 0.66/1.08 clause( 189, [ ~( =( btrue, eq3( 'prop_drop_inj2'( X, Y, Z ), bfalse ) ) )
% 0.66/1.08 ] )
% 0.66/1.08 , clause( 18, [ ~( =( eq3( 'prop_drop_inj2'( X, Y, Z ), bfalse ), btrue ) )
% 0.66/1.08 ] )
% 0.66/1.08 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.66/1.08
% 0.66/1.08
% 0.66/1.08 paramod(
% 0.66/1.08 clause( 191, [ ~( =( btrue, eq3( bfalse, bfalse ) ) ) ] )
% 0.66/1.08 , clause( 61, [ =( 'prop_drop_inj2'( s( s( X ) ), nil, cons( Y, nil ) ),
% 0.66/1.08 bfalse ) ] )
% 0.66/1.08 , 0, clause( 189, [ ~( =( btrue, eq3( 'prop_drop_inj2'( X, Y, Z ), bfalse )
% 0.66/1.08 ) ) ] )
% 0.66/1.08 , 0, 4, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 0.66/1.08 :=( X, s( s( X ) ) ), :=( Y, nil ), :=( Z, cons( Y, nil ) )] )).
% 0.66/1.08
% 0.66/1.08
% 0.66/1.08 paramod(
% 0.66/1.08 clause( 192, [ ~( =( btrue, btrue ) ) ] )
% 0.66/1.08 , clause( 13, [ =( eq3( X, X ), btrue ) ] )
% 0.66/1.08 , 0, clause( 191, [ ~( =( btrue, eq3( bfalse, bfalse ) ) ) ] )
% 0.66/1.08 , 0, 3, substitution( 0, [ :=( X, bfalse )] ), substitution( 1, [] )).
% 0.66/1.08
% 0.66/1.08
% 0.66/1.08 eqrefl(
% 0.66/1.08 clause( 193, [] )
% 0.66/1.08 , clause( 192, [ ~( =( btrue, btrue ) ) ] )
% 0.66/1.08 , 0, substitution( 0, [] )).
% 0.66/1.08
% 0.66/1.08
% 0.66/1.08 subsumption(
% 0.66/1.08 clause( 63, [] )
% 0.66/1.08 , clause( 193, [] )
% 0.66/1.08 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.66/1.08
% 0.66/1.08
% 0.66/1.08 end.
% 0.66/1.08
% 0.66/1.08 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.66/1.08
% 0.66/1.08 Memory use:
% 0.66/1.08
% 0.66/1.08 space for terms: 1130
% 0.66/1.08 space for clauses: 7003
% 0.66/1.08
% 0.66/1.08
% 0.66/1.08 clauses generated: 545
% 0.66/1.08 clauses kept: 64
% 0.66/1.08 clauses selected: 46
% 0.66/1.08 clauses deleted: 7
% 0.66/1.08 clauses inuse deleted: 0
% 0.66/1.08
% 0.66/1.08 subsentry: 827
% 0.66/1.08 literals s-matched: 466
% 0.66/1.08 literals matched: 466
% 0.66/1.08 full subsumption: 0
% 0.66/1.08
% 0.66/1.08 checksum: -1082807309
% 0.66/1.08
% 0.66/1.08
% 0.66/1.08 Bliksem ended
%------------------------------------------------------------------------------