%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWX228-1 : 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 06:56:51 PM UTC 2026
% Result : Unsatisfiable 0.73s 1.15s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX228-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : bliksem %s
% 0.15/0.33 % Computer : n003.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
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % DateTime : Tue May 5 12:55:26 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.73/1.15 *** allocated 10000 integers for termspace/termends
% 0.73/1.15 *** allocated 10000 integers for clauses
% 0.73/1.15 *** allocated 10000 integers for justifications
% 0.73/1.15 Bliksem 1.12
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 Automatic Strategy Selection
% 0.73/1.15
% 0.73/1.15 Clauses:
% 0.73/1.15 [
% 0.73/1.15 [ =( aux( X, Y, Z, btrue ), union( Z, X ) ) ],
% 0.73/1.15 [ =( aux( X, Y, Z, bfalse ), cons( Y, union( Z, X ) ) ) ],
% 0.73/1.15 [ =( barbar( btrue, X ), btrue ) ],
% 0.73/1.15 [ =( barbar( bfalse, X ), X ) ],
% 0.73/1.15 [ =( eqNat( s( X ), s( Y ) ), eqNat( X, Y ) ) ],
% 0.73/1.15 [ =( eqNat( s( X ), z ), bfalse ) ],
% 0.73/1.15 [ =( eqNat( z, s( X ) ), bfalse ) ],
% 0.73/1.15 [ =( eqNat( z, z ), btrue ) ],
% 0.73/1.15 [ =( elem( X, nil ), bfalse ) ],
% 0.73/1.15 [ =( elem( X, cons( Y, Z ) ), barbar( eqNat( X, Y ), elem( X, Z ) ) ) ]
% 0.73/1.15 ,
% 0.73/1.15 [ =( union( nil, X ), X ) ],
% 0.73/1.15 [ =( union( cons( X, Y ), Z ), aux( Z, X, Y, elem( X, Z ) ) ) ],
% 0.73/1.15 [ =( 'prop_union_comm'( X, Y ), eq( union( X, Y ), union( Y, X ) ) ) ]
% 0.73/1.15 ,
% 0.73/1.15 [ =( eq3( bfalse, btrue ), bfalse ) ],
% 0.73/1.15 [ =( eq3( btrue, bfalse ), bfalse ) ],
% 0.73/1.15 [ =( eq2( s( X ), s( Y ) ), eq2( X, Y ) ) ],
% 0.73/1.15 [ =( eq2( s( X ), z ), bfalse ) ],
% 0.73/1.15 [ =( eq2( z, s( X ) ), bfalse ) ],
% 0.73/1.15 [ =( eq( X, X ), btrue ) ],
% 0.73/1.15 [ =( eq2( X, X ), btrue ) ],
% 0.73/1.15 [ =( eq3( X, X ), btrue ) ],
% 0.73/1.15 [ ~( =( eq2( X, Y ), bfalse ) ), =( eq( cons( X, Z ), cons( Y, T ) ),
% 0.73/1.15 bfalse ) ],
% 0.73/1.15 [ ~( =( eq2( X, Y ), btrue ) ), =( eq( cons( X, Z ), cons( Y, T ) ), eq(
% 0.73/1.15 Z, T ) ) ],
% 0.73/1.15 [ =( eq( nil, cons( X, Y ) ), bfalse ) ],
% 0.73/1.15 [ =( eq( cons( X, Y ), nil ), bfalse ) ],
% 0.73/1.15 [ ~( =( eq3( 'prop_union_comm'( X, Y ), bfalse ), btrue ) ) ]
% 0.73/1.15 ] .
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 percentage equality = 1.000000, percentage horn = 1.000000
% 0.73/1.15 This is a pure equality problem
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 Options Used:
% 0.73/1.15
% 0.73/1.15 useres = 1
% 0.73/1.15 useparamod = 1
% 0.73/1.15 useeqrefl = 1
% 0.73/1.15 useeqfact = 1
% 0.73/1.15 usefactor = 1
% 0.73/1.15 usesimpsplitting = 0
% 0.73/1.15 usesimpdemod = 5
% 0.73/1.15 usesimpres = 3
% 0.73/1.15
% 0.73/1.15 resimpinuse = 1000
% 0.73/1.15 resimpclauses = 20000
% 0.73/1.15 substype = eqrewr
% 0.73/1.15 backwardsubs = 1
% 0.73/1.15 selectoldest = 5
% 0.73/1.15
% 0.73/1.15 litorderings [0] = split
% 0.73/1.15 litorderings [1] = extend the termordering, first sorting on arguments
% 0.73/1.15
% 0.73/1.15 termordering = kbo
% 0.73/1.15
% 0.73/1.15 litapriori = 0
% 0.73/1.15 termapriori = 1
% 0.73/1.15 litaposteriori = 0
% 0.73/1.15 termaposteriori = 0
% 0.73/1.15 demodaposteriori = 0
% 0.73/1.15 ordereqreflfact = 0
% 0.73/1.15
% 0.73/1.15 litselect = negord
% 0.73/1.15
% 0.73/1.15 maxweight = 15
% 0.73/1.15 maxdepth = 30000
% 0.73/1.15 maxlength = 115
% 0.73/1.15 maxnrvars = 195
% 0.73/1.15 excuselevel = 1
% 0.73/1.15 increasemaxweight = 1
% 0.73/1.15
% 0.73/1.15 maxselected = 10000000
% 0.73/1.15 maxnrclauses = 10000000
% 0.73/1.15
% 0.73/1.15 showgenerated = 0
% 0.73/1.15 showkept = 0
% 0.73/1.15 showselected = 0
% 0.73/1.15 showdeleted = 0
% 0.73/1.15 showresimp = 1
% 0.73/1.15 showstatus = 2000
% 0.73/1.15
% 0.73/1.15 prologoutput = 1
% 0.73/1.15 nrgoals = 5000000
% 0.73/1.15 totalproof = 1
% 0.73/1.15
% 0.73/1.15 Symbols occurring in the translation:
% 0.73/1.15
% 0.73/1.15 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.73/1.15 . [1, 2] (w:1, o:25, a:1, s:1, b:0),
% 0.73/1.15 ! [4, 1] (w:0, o:19, a:1, s:1, b:0),
% 0.73/1.15 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.73/1.15 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.73/1.15 btrue [42, 0] (w:1, o:15, a:1, s:1, b:0),
% 0.73/1.15 aux [43, 4] (w:1, o:59, a:1, s:1, b:0),
% 0.73/1.15 union [44, 2] (w:1, o:50, a:1, s:1, b:0),
% 0.73/1.15 bfalse [45, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.73/1.15 cons [46, 2] (w:1, o:52, a:1, s:1, b:0),
% 0.73/1.15 barbar [47, 2] (w:1, o:51, a:1, s:1, b:0),
% 0.73/1.15 s [48, 1] (w:1, o:24, a:1, s:1, b:0),
% 0.73/1.15 eqNat [50, 2] (w:1, o:53, a:1, s:1, b:0),
% 0.73/1.15 z [51, 0] (w:1, o:17, a:1, s:1, b:0),
% 0.73/1.15 nil [54, 0] (w:1, o:18, a:1, s:1, b:0),
% 0.73/1.15 elem [55, 2] (w:1, o:54, a:1, s:1, b:0),
% 0.73/1.15 'prop_union_comm' [56, 2] (w:1, o:55, a:1, s:1, b:0),
% 0.73/1.15 eq [57, 2] (w:1, o:56, a:1, s:1, b:0),
% 0.73/1.15 eq3 [58, 2] (w:1, o:58, a:1, s:1, b:0),
% 0.73/1.15 eq2 [59, 2] (w:1, o:57, a:1, s:1, b:0).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 Starting Search:
% 0.73/1.15
% 0.73/1.15 Resimplifying inuse:
% 0.73/1.15 Done
% 0.73/1.15
% 0.73/1.15 Failed to find proof!
% 0.73/1.15 maxweight = 15
% 0.73/1.15 maxnrclauses = 10000000
% 0.73/1.15 Generated: 687
% 0.73/1.15 Kept: 99
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 The strategy used was not complete!
% 0.73/1.15
% 0.73/1.15 Increased maxweight to 16
% 0.73/1.15
% 0.73/1.15 Starting Search:
% 0.73/1.15
% 0.73/1.15 Resimplifying inuse:
% 0.73/1.15 Done
% 0.73/1.15
% 0.73/1.15 Failed to find proof!
% 0.73/1.15 maxweight = 16
% 0.73/1.15 maxnrclauses = 10000000
% 0.73/1.15 Generated: 882
% 0.73/1.15 Kept: 118
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 The strategy used was not complete!
% 0.73/1.15
% 0.73/1.15 Increased maxweight to 17
% 0.73/1.15
% 0.73/1.15 Starting Search:
% 0.73/1.15
% 0.73/1.15 Resimplifying inuse:
% 0.73/1.15 Done
% 0.73/1.15
% 0.73/1.15 Failed to find proof!
% 0.73/1.15 maxweight = 17
% 0.73/1.15 maxnrclauses = 10000000
% 0.73/1.15 Generated: 1054
% 0.73/1.15 Kept: 131
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 The strategy used was not complete!
% 0.73/1.15
% 0.73/1.15 Increased maxweight to 18
% 0.73/1.15
% 0.73/1.15 Starting Search:
% 0.73/1.15
% 0.73/1.15 Resimplifying inuse:
% 0.73/1.15 Done
% 0.73/1.15
% 0.73/1.15 Failed to find proof!
% 0.73/1.15 maxweight = 18
% 0.73/1.15 maxnrclauses = 10000000
% 0.73/1.15 Generated: 1618
% 0.73/1.15 Kept: 174
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 The strategy used was not complete!
% 0.73/1.15
% 0.73/1.15 Increased maxweight to 19
% 0.73/1.15
% 0.73/1.15 Starting Search:
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 Bliksems!, er is een bewijs:
% 0.73/1.15 % SZS status Unsatisfiable
% 0.73/1.15 % SZS output start Refutation
% 0.73/1.15
% 0.73/1.15 clause( 0, [ =( aux( X, Y, Z, btrue ), union( Z, X ) ) ] )
% 0.73/1.15 .
% 0.73/1.15 clause( 1, [ =( aux( X, Y, Z, bfalse ), cons( Y, union( Z, X ) ) ) ] )
% 0.73/1.15 .
% 0.73/1.15 clause( 2, [ =( barbar( btrue, X ), btrue ) ] )
% 0.73/1.15 .
% 0.73/1.15 clause( 3, [ =( barbar( bfalse, X ), X ) ] )
% 0.73/1.15 .
% 0.73/1.15 clause( 5, [ =( eqNat( s( X ), z ), bfalse ) ] )
% 0.73/1.15 .
% 0.73/1.15 clause( 7, [ =( eqNat( z, z ), btrue ) ] )
% 0.73/1.15 .
% 0.73/1.15 clause( 8, [ =( elem( X, nil ), bfalse ) ] )
% 0.73/1.15 .
% 0.73/1.15 clause( 9, [ =( barbar( eqNat( X, Y ), elem( X, Z ) ), elem( X, cons( Y, Z
% 0.73/1.15 ) ) ) ] )
% 0.73/1.15 .
% 0.73/1.15 clause( 10, [ =( union( nil, X ), X ) ] )
% 0.73/1.15 .
% 0.73/1.15 clause( 11, [ =( aux( Z, X, Y, elem( X, Z ) ), union( cons( X, Y ), Z ) ) ]
% 0.73/1.15 )
% 0.73/1.15 .
% 0.73/1.15 clause( 12, [ =( eq( union( X, Y ), union( Y, X ) ), 'prop_union_comm'( X,
% 0.73/1.15 Y ) ) ] )
% 0.73/1.15 .
% 0.73/1.15 clause( 16, [ =( eq2( s( X ), z ), bfalse ) ] )
% 0.73/1.15 .
% 0.73/1.15 clause( 20, [ =( eq3( X, X ), btrue ) ] )
% 0.73/1.15 .
% 0.73/1.15 clause( 21, [ ~( =( eq2( X, Y ), bfalse ) ), =( eq( cons( X, Z ), cons( Y,
% 0.73/1.15 T ) ), bfalse ) ] )
% 0.73/1.15 .
% 0.73/1.15 clause( 25, [ ~( =( eq3( 'prop_union_comm'( X, Y ), bfalse ), btrue ) ) ]
% 0.73/1.15 )
% 0.73/1.15 .
% 0.73/1.15 clause( 29, [ =( elem( z, cons( z, X ) ), btrue ) ] )
% 0.73/1.15 .
% 0.73/1.15 clause( 30, [ =( elem( X, cons( Y, nil ) ), barbar( eqNat( X, Y ), bfalse )
% 0.73/1.15 ) ] )
% 0.73/1.15 .
% 0.73/1.15 clause( 35, [ =( union( cons( z, Y ), cons( z, X ) ), union( Y, cons( z, X
% 0.73/1.15 ) ) ) ] )
% 0.73/1.15 .
% 0.73/1.15 clause( 52, [ =( eq( cons( s( X ), Y ), cons( z, Z ) ), bfalse ) ] )
% 0.73/1.15 .
% 0.73/1.15 clause( 69, [ =( aux( cons( Y, nil ), X, Z, barbar( eqNat( X, Y ), bfalse )
% 0.73/1.15 ), union( cons( X, Z ), cons( Y, nil ) ) ) ] )
% 0.73/1.15 .
% 0.73/1.15 clause( 95, [ =( eq( union( X, cons( z, Y ) ), union( Y, cons( z, X ) ) ),
% 0.73/1.15 'prop_union_comm'( cons( z, X ), cons( z, Y ) ) ) ] )
% 0.73/1.15 .
% 0.73/1.15 clause( 161, [ =( cons( s( X ), union( Y, cons( z, nil ) ) ), union( cons(
% 0.73/1.15 s( X ), Y ), cons( z, nil ) ) ) ] )
% 0.73/1.15 .
% 0.73/1.15 clause( 231, [ =( union( cons( s( X ), nil ), cons( z, nil ) ), cons( s( X
% 0.73/1.15 ), cons( z, nil ) ) ) ] )
% 0.73/1.15 .
% 0.73/1.15 clause( 260, [ =( 'prop_union_comm'( cons( z, cons( s( X ), nil ) ), cons(
% 0.73/1.15 z, nil ) ), bfalse ) ] )
% 0.73/1.15 .
% 0.73/1.15 clause( 264, [] )
% 0.73/1.15 .
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 % SZS output end Refutation
% 0.73/1.15 found a proof!
% 0.73/1.15
% 0.73/1.15 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.73/1.15
% 0.73/1.15 initialclauses(
% 0.73/1.15 [ clause( 266, [ =( aux( X, Y, Z, btrue ), union( Z, X ) ) ] )
% 0.73/1.15 , clause( 267, [ =( aux( X, Y, Z, bfalse ), cons( Y, union( Z, X ) ) ) ] )
% 0.73/1.15 , clause( 268, [ =( barbar( btrue, X ), btrue ) ] )
% 0.73/1.15 , clause( 269, [ =( barbar( bfalse, X ), X ) ] )
% 0.73/1.15 , clause( 270, [ =( eqNat( s( X ), s( Y ) ), eqNat( X, Y ) ) ] )
% 0.73/1.15 , clause( 271, [ =( eqNat( s( X ), z ), bfalse ) ] )
% 0.73/1.15 , clause( 272, [ =( eqNat( z, s( X ) ), bfalse ) ] )
% 0.73/1.15 , clause( 273, [ =( eqNat( z, z ), btrue ) ] )
% 0.73/1.15 , clause( 274, [ =( elem( X, nil ), bfalse ) ] )
% 0.73/1.15 , clause( 275, [ =( elem( X, cons( Y, Z ) ), barbar( eqNat( X, Y ), elem( X
% 0.73/1.15 , Z ) ) ) ] )
% 0.73/1.15 , clause( 276, [ =( union( nil, X ), X ) ] )
% 0.73/1.15 , clause( 277, [ =( union( cons( X, Y ), Z ), aux( Z, X, Y, elem( X, Z ) )
% 0.73/1.15 ) ] )
% 0.73/1.15 , clause( 278, [ =( 'prop_union_comm'( X, Y ), eq( union( X, Y ), union( Y
% 0.73/1.15 , X ) ) ) ] )
% 0.73/1.15 , clause( 279, [ =( eq3( bfalse, btrue ), bfalse ) ] )
% 0.73/1.15 , clause( 280, [ =( eq3( btrue, bfalse ), bfalse ) ] )
% 0.73/1.15 , clause( 281, [ =( eq2( s( X ), s( Y ) ), eq2( X, Y ) ) ] )
% 0.73/1.15 , clause( 282, [ =( eq2( s( X ), z ), bfalse ) ] )
% 0.73/1.15 , clause( 283, [ =( eq2( z, s( X ) ), bfalse ) ] )
% 0.73/1.15 , clause( 284, [ =( eq( X, X ), btrue ) ] )
% 0.73/1.15 , clause( 285, [ =( eq2( X, X ), btrue ) ] )
% 0.73/1.15 , clause( 286, [ =( eq3( X, X ), btrue ) ] )
% 0.73/1.15 , clause( 287, [ ~( =( eq2( X, Y ), bfalse ) ), =( eq( cons( X, Z ), cons(
% 0.73/1.15 Y, T ) ), bfalse ) ] )
% 0.73/1.15 , clause( 288, [ ~( =( eq2( X, Y ), btrue ) ), =( eq( cons( X, Z ), cons( Y
% 0.73/1.15 , T ) ), eq( Z, T ) ) ] )
% 0.73/1.15 , clause( 289, [ =( eq( nil, cons( X, Y ) ), bfalse ) ] )
% 0.73/1.15 , clause( 290, [ =( eq( cons( X, Y ), nil ), bfalse ) ] )
% 0.73/1.15 , clause( 291, [ ~( =( eq3( 'prop_union_comm'( X, Y ), bfalse ), btrue ) )
% 0.73/1.15 ] )
% 0.73/1.15 ] ).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 subsumption(
% 0.73/1.15 clause( 0, [ =( aux( X, Y, Z, btrue ), union( Z, X ) ) ] )
% 0.73/1.15 , clause( 266, [ =( aux( X, Y, Z, btrue ), union( Z, X ) ) ] )
% 0.73/1.15 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.73/1.15 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 subsumption(
% 0.73/1.15 clause( 1, [ =( aux( X, Y, Z, bfalse ), cons( Y, union( Z, X ) ) ) ] )
% 0.73/1.15 , clause( 267, [ =( aux( X, Y, Z, bfalse ), cons( Y, union( Z, X ) ) ) ] )
% 0.73/1.15 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.73/1.15 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 subsumption(
% 0.73/1.15 clause( 2, [ =( barbar( btrue, X ), btrue ) ] )
% 0.73/1.15 , clause( 268, [ =( barbar( btrue, X ), btrue ) ] )
% 0.73/1.15 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 subsumption(
% 0.73/1.15 clause( 3, [ =( barbar( bfalse, X ), X ) ] )
% 0.73/1.15 , clause( 269, [ =( barbar( bfalse, X ), X ) ] )
% 0.73/1.15 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 subsumption(
% 0.73/1.15 clause( 5, [ =( eqNat( s( X ), z ), bfalse ) ] )
% 0.73/1.15 , clause( 271, [ =( eqNat( s( X ), z ), bfalse ) ] )
% 0.73/1.15 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 subsumption(
% 0.73/1.15 clause( 7, [ =( eqNat( z, z ), btrue ) ] )
% 0.73/1.15 , clause( 273, [ =( eqNat( z, z ), btrue ) ] )
% 0.73/1.15 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 subsumption(
% 0.73/1.15 clause( 8, [ =( elem( X, nil ), bfalse ) ] )
% 0.73/1.15 , clause( 274, [ =( elem( X, nil ), bfalse ) ] )
% 0.73/1.15 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 eqswap(
% 0.73/1.15 clause( 334, [ =( barbar( eqNat( X, Y ), elem( X, Z ) ), elem( X, cons( Y,
% 0.73/1.15 Z ) ) ) ] )
% 0.73/1.15 , clause( 275, [ =( elem( X, cons( Y, Z ) ), barbar( eqNat( X, Y ), elem( X
% 0.73/1.15 , Z ) ) ) ] )
% 0.73/1.15 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 subsumption(
% 0.73/1.15 clause( 9, [ =( barbar( eqNat( X, Y ), elem( X, Z ) ), elem( X, cons( Y, Z
% 0.73/1.15 ) ) ) ] )
% 0.73/1.15 , clause( 334, [ =( barbar( eqNat( X, Y ), elem( X, Z ) ), elem( X, cons( Y
% 0.73/1.15 , Z ) ) ) ] )
% 0.73/1.15 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.73/1.15 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 subsumption(
% 0.73/1.15 clause( 10, [ =( union( nil, X ), X ) ] )
% 0.73/1.15 , clause( 276, [ =( union( nil, X ), X ) ] )
% 0.73/1.15 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 eqswap(
% 0.73/1.15 clause( 357, [ =( aux( Z, X, Y, elem( X, Z ) ), union( cons( X, Y ), Z ) )
% 0.73/1.15 ] )
% 0.73/1.15 , clause( 277, [ =( union( cons( X, Y ), Z ), aux( Z, X, Y, elem( X, Z ) )
% 0.73/1.15 ) ] )
% 0.73/1.15 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 subsumption(
% 0.73/1.15 clause( 11, [ =( aux( Z, X, Y, elem( X, Z ) ), union( cons( X, Y ), Z ) ) ]
% 0.73/1.15 )
% 0.73/1.15 , clause( 357, [ =( aux( Z, X, Y, elem( X, Z ) ), union( cons( X, Y ), Z )
% 0.73/1.15 ) ] )
% 0.73/1.15 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.73/1.15 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 eqswap(
% 0.73/1.15 clause( 370, [ =( eq( union( X, Y ), union( Y, X ) ), 'prop_union_comm'( X
% 0.73/1.15 , Y ) ) ] )
% 0.73/1.15 , clause( 278, [ =( 'prop_union_comm'( X, Y ), eq( union( X, Y ), union( Y
% 0.73/1.15 , X ) ) ) ] )
% 0.73/1.15 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 subsumption(
% 0.73/1.15 clause( 12, [ =( eq( union( X, Y ), union( Y, X ) ), 'prop_union_comm'( X,
% 0.73/1.15 Y ) ) ] )
% 0.73/1.15 , clause( 370, [ =( eq( union( X, Y ), union( Y, X ) ), 'prop_union_comm'(
% 0.73/1.15 X, Y ) ) ] )
% 0.73/1.15 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.15 )] ) ).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 subsumption(
% 0.73/1.15 clause( 16, [ =( eq2( s( X ), z ), bfalse ) ] )
% 0.73/1.15 , clause( 282, [ =( eq2( s( X ), z ), bfalse ) ] )
% 0.73/1.15 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 subsumption(
% 0.73/1.15 clause( 20, [ =( eq3( X, X ), btrue ) ] )
% 0.73/1.15 , clause( 286, [ =( eq3( X, X ), btrue ) ] )
% 0.73/1.15 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 subsumption(
% 0.73/1.15 clause( 21, [ ~( =( eq2( X, Y ), bfalse ) ), =( eq( cons( X, Z ), cons( Y,
% 0.73/1.15 T ) ), bfalse ) ] )
% 0.73/1.15 , clause( 287, [ ~( =( eq2( X, Y ), bfalse ) ), =( eq( cons( X, Z ), cons(
% 0.73/1.15 Y, T ) ), bfalse ) ] )
% 0.73/1.15 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 0.73/1.15 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 subsumption(
% 0.73/1.15 clause( 25, [ ~( =( eq3( 'prop_union_comm'( X, Y ), bfalse ), btrue ) ) ]
% 0.73/1.15 )
% 0.73/1.15 , clause( 291, [ ~( =( eq3( 'prop_union_comm'( X, Y ), bfalse ), btrue ) )
% 0.73/1.15 ] )
% 0.73/1.15 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.15 )] ) ).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 eqswap(
% 0.73/1.15 clause( 464, [ =( elem( X, cons( Y, Z ) ), barbar( eqNat( X, Y ), elem( X,
% 0.73/1.15 Z ) ) ) ] )
% 0.73/1.15 , clause( 9, [ =( barbar( eqNat( X, Y ), elem( X, Z ) ), elem( X, cons( Y,
% 0.73/1.15 Z ) ) ) ] )
% 0.73/1.15 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 paramod(
% 0.73/1.15 clause( 466, [ =( elem( z, cons( z, X ) ), barbar( btrue, elem( z, X ) ) )
% 0.73/1.15 ] )
% 0.73/1.15 , clause( 7, [ =( eqNat( z, z ), btrue ) ] )
% 0.73/1.15 , 0, clause( 464, [ =( elem( X, cons( Y, Z ) ), barbar( eqNat( X, Y ), elem(
% 0.73/1.15 X, Z ) ) ) ] )
% 0.73/1.15 , 0, 7, substitution( 0, [] ), substitution( 1, [ :=( X, z ), :=( Y, z ),
% 0.73/1.15 :=( Z, X )] )).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 paramod(
% 0.73/1.15 clause( 467, [ =( elem( z, cons( z, X ) ), btrue ) ] )
% 0.73/1.15 , clause( 2, [ =( barbar( btrue, X ), btrue ) ] )
% 0.73/1.15 , 0, clause( 466, [ =( elem( z, cons( z, X ) ), barbar( btrue, elem( z, X )
% 0.73/1.15 ) ) ] )
% 0.73/1.15 , 0, 6, substitution( 0, [ :=( X, elem( z, X ) )] ), substitution( 1, [
% 0.73/1.15 :=( X, X )] )).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 subsumption(
% 0.73/1.15 clause( 29, [ =( elem( z, cons( z, X ) ), btrue ) ] )
% 0.73/1.15 , clause( 467, [ =( elem( z, cons( z, X ) ), btrue ) ] )
% 0.73/1.15 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 eqswap(
% 0.73/1.15 clause( 470, [ =( elem( X, cons( Y, Z ) ), barbar( eqNat( X, Y ), elem( X,
% 0.73/1.15 Z ) ) ) ] )
% 0.73/1.15 , clause( 9, [ =( barbar( eqNat( X, Y ), elem( X, Z ) ), elem( X, cons( Y,
% 0.73/1.15 Z ) ) ) ] )
% 0.73/1.15 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 paramod(
% 0.73/1.15 clause( 471, [ =( elem( X, cons( Y, nil ) ), barbar( eqNat( X, Y ), bfalse
% 0.73/1.15 ) ) ] )
% 0.73/1.15 , clause( 8, [ =( elem( X, nil ), bfalse ) ] )
% 0.73/1.15 , 0, clause( 470, [ =( elem( X, cons( Y, Z ) ), barbar( eqNat( X, Y ), elem(
% 0.73/1.15 X, Z ) ) ) ] )
% 0.73/1.15 , 0, 10, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, X ),
% 0.73/1.15 :=( Y, Y ), :=( Z, nil )] )).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 subsumption(
% 0.73/1.15 clause( 30, [ =( elem( X, cons( Y, nil ) ), barbar( eqNat( X, Y ), bfalse )
% 0.73/1.15 ) ] )
% 0.73/1.15 , clause( 471, [ =( elem( X, cons( Y, nil ) ), barbar( eqNat( X, Y ),
% 0.73/1.15 bfalse ) ) ] )
% 0.73/1.15 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.15 )] ) ).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 eqswap(
% 0.73/1.15 clause( 474, [ =( union( cons( Y, Z ), X ), aux( X, Y, Z, elem( Y, X ) ) )
% 0.73/1.15 ] )
% 0.73/1.15 , clause( 11, [ =( aux( Z, X, Y, elem( X, Z ) ), union( cons( X, Y ), Z ) )
% 0.73/1.15 ] )
% 0.73/1.15 , 0, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] )).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 paramod(
% 0.73/1.15 clause( 476, [ =( union( cons( z, X ), cons( z, Y ) ), aux( cons( z, Y ), z
% 0.73/1.15 , X, btrue ) ) ] )
% 0.73/1.15 , clause( 29, [ =( elem( z, cons( z, X ) ), btrue ) ] )
% 0.73/1.15 , 0, clause( 474, [ =( union( cons( Y, Z ), X ), aux( X, Y, Z, elem( Y, X )
% 0.73/1.15 ) ) ] )
% 0.73/1.15 , 0, 14, substitution( 0, [ :=( X, Y )] ), substitution( 1, [ :=( X, cons(
% 0.73/1.15 z, Y ) ), :=( Y, z ), :=( Z, X )] )).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 paramod(
% 0.73/1.15 clause( 477, [ =( union( cons( z, X ), cons( z, Y ) ), union( X, cons( z, Y
% 0.73/1.15 ) ) ) ] )
% 0.73/1.15 , clause( 0, [ =( aux( X, Y, Z, btrue ), union( Z, X ) ) ] )
% 0.73/1.15 , 0, clause( 476, [ =( union( cons( z, X ), cons( z, Y ) ), aux( cons( z, Y
% 0.73/1.15 ), z, X, btrue ) ) ] )
% 0.73/1.15 , 0, 8, substitution( 0, [ :=( X, cons( z, Y ) ), :=( Y, z ), :=( Z, X )] )
% 0.73/1.15 , substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 subsumption(
% 0.73/1.15 clause( 35, [ =( union( cons( z, Y ), cons( z, X ) ), union( Y, cons( z, X
% 0.73/1.15 ) ) ) ] )
% 0.73/1.15 , clause( 477, [ =( union( cons( z, X ), cons( z, Y ) ), union( X, cons( z
% 0.73/1.15 , Y ) ) ) ] )
% 0.73/1.15 , substitution( 0, [ :=( X, Y ), :=( Y, X )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.15 )] ) ).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 eqswap(
% 0.73/1.15 clause( 479, [ ~( =( bfalse, eq2( X, Y ) ) ), =( eq( cons( X, Z ), cons( Y
% 0.73/1.15 , T ) ), bfalse ) ] )
% 0.73/1.15 , clause( 21, [ ~( =( eq2( X, Y ), bfalse ) ), =( eq( cons( X, Z ), cons( Y
% 0.73/1.15 , T ) ), bfalse ) ] )
% 0.73/1.15 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] )
% 0.73/1.15 ).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 eqswap(
% 0.73/1.15 clause( 482, [ =( bfalse, eq2( s( X ), z ) ) ] )
% 0.73/1.15 , clause( 16, [ =( eq2( s( X ), z ), bfalse ) ] )
% 0.73/1.15 , 0, substitution( 0, [ :=( X, X )] )).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 resolution(
% 0.73/1.15 clause( 483, [ =( eq( cons( s( X ), Y ), cons( z, Z ) ), bfalse ) ] )
% 0.73/1.15 , clause( 479, [ ~( =( bfalse, eq2( X, Y ) ) ), =( eq( cons( X, Z ), cons(
% 0.73/1.15 Y, T ) ), bfalse ) ] )
% 0.73/1.15 , 0, clause( 482, [ =( bfalse, eq2( s( X ), z ) ) ] )
% 0.73/1.15 , 0, substitution( 0, [ :=( X, s( X ) ), :=( Y, z ), :=( Z, Y ), :=( T, Z )] )
% 0.73/1.15 , substitution( 1, [ :=( X, X )] )).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 subsumption(
% 0.73/1.15 clause( 52, [ =( eq( cons( s( X ), Y ), cons( z, Z ) ), bfalse ) ] )
% 0.73/1.15 , clause( 483, [ =( eq( cons( s( X ), Y ), cons( z, Z ) ), bfalse ) ] )
% 0.73/1.15 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 0.73/1.15 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 eqswap(
% 0.73/1.15 clause( 486, [ =( union( cons( Y, Z ), X ), aux( X, Y, Z, elem( Y, X ) ) )
% 0.73/1.15 ] )
% 0.73/1.15 , clause( 11, [ =( aux( Z, X, Y, elem( X, Z ) ), union( cons( X, Y ), Z ) )
% 0.73/1.15 ] )
% 0.73/1.15 , 0, substitution( 0, [ :=( X, Y ), :=( Y, Z ), :=( Z, X )] )).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 paramod(
% 0.73/1.15 clause( 487, [ =( union( cons( X, Y ), cons( Z, nil ) ), aux( cons( Z, nil
% 0.73/1.15 ), X, Y, barbar( eqNat( X, Z ), bfalse ) ) ) ] )
% 0.73/1.15 , clause( 30, [ =( elem( X, cons( Y, nil ) ), barbar( eqNat( X, Y ), bfalse
% 0.73/1.15 ) ) ] )
% 0.73/1.15 , 0, clause( 486, [ =( union( cons( Y, Z ), X ), aux( X, Y, Z, elem( Y, X )
% 0.73/1.15 ) ) ] )
% 0.73/1.15 , 0, 14, substitution( 0, [ :=( X, X ), :=( Y, Z )] ), substitution( 1, [
% 0.73/1.15 :=( X, cons( Z, nil ) ), :=( Y, X ), :=( Z, Y )] )).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 eqswap(
% 0.73/1.15 clause( 488, [ =( aux( cons( Z, nil ), X, Y, barbar( eqNat( X, Z ), bfalse
% 0.73/1.15 ) ), union( cons( X, Y ), cons( Z, nil ) ) ) ] )
% 0.73/1.15 , clause( 487, [ =( union( cons( X, Y ), cons( Z, nil ) ), aux( cons( Z,
% 0.73/1.15 nil ), X, Y, barbar( eqNat( X, Z ), bfalse ) ) ) ] )
% 0.73/1.15 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] )).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 subsumption(
% 0.73/1.15 clause( 69, [ =( aux( cons( Y, nil ), X, Z, barbar( eqNat( X, Y ), bfalse )
% 0.73/1.15 ), union( cons( X, Z ), cons( Y, nil ) ) ) ] )
% 0.73/1.15 , clause( 488, [ =( aux( cons( Z, nil ), X, Y, barbar( eqNat( X, Z ),
% 0.73/1.15 bfalse ) ), union( cons( X, Y ), cons( Z, nil ) ) ) ] )
% 0.73/1.15 , substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] ),
% 0.73/1.15 permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 eqswap(
% 0.73/1.15 clause( 490, [ =( 'prop_union_comm'( X, Y ), eq( union( X, Y ), union( Y, X
% 0.73/1.15 ) ) ) ] )
% 0.73/1.15 , clause( 12, [ =( eq( union( X, Y ), union( Y, X ) ), 'prop_union_comm'( X
% 0.73/1.15 , Y ) ) ] )
% 0.73/1.15 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 paramod(
% 0.73/1.15 clause( 493, [ =( 'prop_union_comm'( cons( z, X ), cons( z, Y ) ), eq(
% 0.73/1.15 union( cons( z, X ), cons( z, Y ) ), union( Y, cons( z, X ) ) ) ) ] )
% 0.73/1.15 , clause( 35, [ =( union( cons( z, Y ), cons( z, X ) ), union( Y, cons( z,
% 0.73/1.15 X ) ) ) ] )
% 0.73/1.15 , 0, clause( 490, [ =( 'prop_union_comm'( X, Y ), eq( union( X, Y ), union(
% 0.73/1.15 Y, X ) ) ) ] )
% 0.73/1.15 , 0, 16, substitution( 0, [ :=( X, X ), :=( Y, Y )] ), substitution( 1, [
% 0.73/1.15 :=( X, cons( z, X ) ), :=( Y, cons( z, Y ) )] )).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 paramod(
% 0.73/1.15 clause( 495, [ =( 'prop_union_comm'( cons( z, X ), cons( z, Y ) ), eq(
% 0.73/1.15 union( X, cons( z, Y ) ), union( Y, cons( z, X ) ) ) ) ] )
% 0.73/1.15 , clause( 35, [ =( union( cons( z, Y ), cons( z, X ) ), union( Y, cons( z,
% 0.73/1.15 X ) ) ) ] )
% 0.73/1.15 , 0, clause( 493, [ =( 'prop_union_comm'( cons( z, X ), cons( z, Y ) ), eq(
% 0.73/1.15 union( cons( z, X ), cons( z, Y ) ), union( Y, cons( z, X ) ) ) ) ] )
% 0.73/1.15 , 0, 9, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 0.73/1.15 :=( X, X ), :=( Y, Y )] )).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 eqswap(
% 0.73/1.15 clause( 496, [ =( eq( union( X, cons( z, Y ) ), union( Y, cons( z, X ) ) )
% 0.73/1.15 , 'prop_union_comm'( cons( z, X ), cons( z, Y ) ) ) ] )
% 0.73/1.15 , clause( 495, [ =( 'prop_union_comm'( cons( z, X ), cons( z, Y ) ), eq(
% 0.73/1.15 union( X, cons( z, Y ) ), union( Y, cons( z, X ) ) ) ) ] )
% 0.73/1.15 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 subsumption(
% 0.73/1.15 clause( 95, [ =( eq( union( X, cons( z, Y ) ), union( Y, cons( z, X ) ) ),
% 0.73/1.15 'prop_union_comm'( cons( z, X ), cons( z, Y ) ) ) ] )
% 0.73/1.15 , clause( 496, [ =( eq( union( X, cons( z, Y ) ), union( Y, cons( z, X ) )
% 0.73/1.15 ), 'prop_union_comm'( cons( z, X ), cons( z, Y ) ) ) ] )
% 0.73/1.15 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.15 )] ) ).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 eqswap(
% 0.73/1.15 clause( 498, [ =( union( cons( Y, Z ), cons( X, nil ) ), aux( cons( X, nil
% 0.73/1.15 ), Y, Z, barbar( eqNat( Y, X ), bfalse ) ) ) ] )
% 0.73/1.15 , clause( 69, [ =( aux( cons( Y, nil ), X, Z, barbar( eqNat( X, Y ), bfalse
% 0.73/1.15 ) ), union( cons( X, Z ), cons( Y, nil ) ) ) ] )
% 0.73/1.15 , 0, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, Z )] )).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 paramod(
% 0.73/1.15 clause( 501, [ =( union( cons( s( X ), Y ), cons( z, nil ) ), aux( cons( z
% 0.73/1.15 , nil ), s( X ), Y, barbar( bfalse, bfalse ) ) ) ] )
% 0.73/1.15 , clause( 5, [ =( eqNat( s( X ), z ), bfalse ) ] )
% 0.73/1.15 , 0, clause( 498, [ =( union( cons( Y, Z ), cons( X, nil ) ), aux( cons( X
% 0.73/1.15 , nil ), Y, Z, barbar( eqNat( Y, X ), bfalse ) ) ) ] )
% 0.73/1.15 , 0, 17, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, z ),
% 0.73/1.15 :=( Y, s( X ) ), :=( Z, Y )] )).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 paramod(
% 0.73/1.15 clause( 502, [ =( union( cons( s( X ), Y ), cons( z, nil ) ), aux( cons( z
% 0.73/1.15 , nil ), s( X ), Y, bfalse ) ) ] )
% 0.73/1.15 , clause( 3, [ =( barbar( bfalse, X ), X ) ] )
% 0.73/1.15 , 0, clause( 501, [ =( union( cons( s( X ), Y ), cons( z, nil ) ), aux(
% 0.73/1.15 cons( z, nil ), s( X ), Y, barbar( bfalse, bfalse ) ) ) ] )
% 0.73/1.15 , 0, 16, substitution( 0, [ :=( X, bfalse )] ), substitution( 1, [ :=( X, X
% 0.73/1.15 ), :=( Y, Y )] )).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 paramod(
% 0.73/1.15 clause( 503, [ =( union( cons( s( X ), Y ), cons( z, nil ) ), cons( s( X )
% 0.73/1.15 , union( Y, cons( z, nil ) ) ) ) ] )
% 0.73/1.15 , clause( 1, [ =( aux( X, Y, Z, bfalse ), cons( Y, union( Z, X ) ) ) ] )
% 0.73/1.15 , 0, clause( 502, [ =( union( cons( s( X ), Y ), cons( z, nil ) ), aux(
% 0.73/1.15 cons( z, nil ), s( X ), Y, bfalse ) ) ] )
% 0.73/1.15 , 0, 9, substitution( 0, [ :=( X, cons( z, nil ) ), :=( Y, s( X ) ), :=( Z
% 0.73/1.15 , Y )] ), substitution( 1, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 eqswap(
% 0.73/1.15 clause( 504, [ =( cons( s( X ), union( Y, cons( z, nil ) ) ), union( cons(
% 0.73/1.15 s( X ), Y ), cons( z, nil ) ) ) ] )
% 0.73/1.15 , clause( 503, [ =( union( cons( s( X ), Y ), cons( z, nil ) ), cons( s( X
% 0.73/1.15 ), union( Y, cons( z, nil ) ) ) ) ] )
% 0.73/1.15 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 subsumption(
% 0.73/1.15 clause( 161, [ =( cons( s( X ), union( Y, cons( z, nil ) ) ), union( cons(
% 0.73/1.15 s( X ), Y ), cons( z, nil ) ) ) ] )
% 0.73/1.15 , clause( 504, [ =( cons( s( X ), union( Y, cons( z, nil ) ) ), union( cons(
% 0.73/1.15 s( X ), Y ), cons( z, nil ) ) ) ] )
% 0.73/1.15 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 0.73/1.15 )] ) ).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 eqswap(
% 0.73/1.15 clause( 506, [ =( union( cons( s( X ), Y ), cons( z, nil ) ), cons( s( X )
% 0.73/1.15 , union( Y, cons( z, nil ) ) ) ) ] )
% 0.73/1.15 , clause( 161, [ =( cons( s( X ), union( Y, cons( z, nil ) ) ), union( cons(
% 0.73/1.15 s( X ), Y ), cons( z, nil ) ) ) ] )
% 0.73/1.15 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 paramod(
% 0.73/1.15 clause( 507, [ =( union( cons( s( X ), nil ), cons( z, nil ) ), cons( s( X
% 0.73/1.15 ), cons( z, nil ) ) ) ] )
% 0.73/1.15 , clause( 10, [ =( union( nil, X ), X ) ] )
% 0.73/1.15 , 0, clause( 506, [ =( union( cons( s( X ), Y ), cons( z, nil ) ), cons( s(
% 0.73/1.15 X ), union( Y, cons( z, nil ) ) ) ) ] )
% 0.73/1.15 , 0, 12, substitution( 0, [ :=( X, cons( z, nil ) )] ), substitution( 1, [
% 0.73/1.15 :=( X, X ), :=( Y, nil )] )).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 subsumption(
% 0.73/1.15 clause( 231, [ =( union( cons( s( X ), nil ), cons( z, nil ) ), cons( s( X
% 0.73/1.15 ), cons( z, nil ) ) ) ] )
% 0.73/1.15 , clause( 507, [ =( union( cons( s( X ), nil ), cons( z, nil ) ), cons( s(
% 0.73/1.15 X ), cons( z, nil ) ) ) ] )
% 0.73/1.15 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 eqswap(
% 0.73/1.15 clause( 510, [ =( 'prop_union_comm'( cons( z, X ), cons( z, Y ) ), eq(
% 0.73/1.15 union( X, cons( z, Y ) ), union( Y, cons( z, X ) ) ) ) ] )
% 0.73/1.15 , clause( 95, [ =( eq( union( X, cons( z, Y ) ), union( Y, cons( z, X ) ) )
% 0.73/1.15 , 'prop_union_comm'( cons( z, X ), cons( z, Y ) ) ) ] )
% 0.73/1.15 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 paramod(
% 0.73/1.15 clause( 513, [ =( 'prop_union_comm'( cons( z, cons( s( X ), nil ) ), cons(
% 0.73/1.15 z, nil ) ), eq( cons( s( X ), cons( z, nil ) ), union( nil, cons( z, cons(
% 0.73/1.15 s( X ), nil ) ) ) ) ) ] )
% 0.73/1.15 , clause( 231, [ =( union( cons( s( X ), nil ), cons( z, nil ) ), cons( s(
% 0.73/1.15 X ), cons( z, nil ) ) ) ] )
% 0.73/1.15 , 0, clause( 510, [ =( 'prop_union_comm'( cons( z, X ), cons( z, Y ) ), eq(
% 0.73/1.15 union( X, cons( z, Y ) ), union( Y, cons( z, X ) ) ) ) ] )
% 0.73/1.15 , 0, 12, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, cons(
% 0.73/1.15 s( X ), nil ) ), :=( Y, nil )] )).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 paramod(
% 0.73/1.15 clause( 516, [ =( 'prop_union_comm'( cons( z, cons( s( X ), nil ) ), cons(
% 0.73/1.15 z, nil ) ), eq( cons( s( X ), cons( z, nil ) ), cons( z, cons( s( X ),
% 0.73/1.15 nil ) ) ) ) ] )
% 0.73/1.15 , clause( 10, [ =( union( nil, X ), X ) ] )
% 0.73/1.15 , 0, clause( 513, [ =( 'prop_union_comm'( cons( z, cons( s( X ), nil ) ),
% 0.73/1.15 cons( z, nil ) ), eq( cons( s( X ), cons( z, nil ) ), union( nil, cons( z
% 0.73/1.15 , cons( s( X ), nil ) ) ) ) ) ] )
% 0.73/1.15 , 0, 18, substitution( 0, [ :=( X, cons( z, cons( s( X ), nil ) ) )] ),
% 0.73/1.15 substitution( 1, [ :=( X, X )] )).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 paramod(
% 0.73/1.15 clause( 517, [ =( 'prop_union_comm'( cons( z, cons( s( X ), nil ) ), cons(
% 0.73/1.15 z, nil ) ), bfalse ) ] )
% 0.73/1.15 , clause( 52, [ =( eq( cons( s( X ), Y ), cons( z, Z ) ), bfalse ) ] )
% 0.73/1.15 , 0, clause( 516, [ =( 'prop_union_comm'( cons( z, cons( s( X ), nil ) ),
% 0.73/1.15 cons( z, nil ) ), eq( cons( s( X ), cons( z, nil ) ), cons( z, cons( s( X
% 0.73/1.15 ), nil ) ) ) ) ] )
% 0.73/1.15 , 0, 11, substitution( 0, [ :=( X, X ), :=( Y, cons( z, nil ) ), :=( Z,
% 0.73/1.15 cons( s( X ), nil ) )] ), substitution( 1, [ :=( X, X )] )).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 subsumption(
% 0.73/1.15 clause( 260, [ =( 'prop_union_comm'( cons( z, cons( s( X ), nil ) ), cons(
% 0.73/1.15 z, nil ) ), bfalse ) ] )
% 0.73/1.15 , clause( 517, [ =( 'prop_union_comm'( cons( z, cons( s( X ), nil ) ), cons(
% 0.73/1.15 z, nil ) ), bfalse ) ] )
% 0.73/1.15 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 eqswap(
% 0.73/1.15 clause( 520, [ ~( =( btrue, eq3( 'prop_union_comm'( X, Y ), bfalse ) ) ) ]
% 0.73/1.15 )
% 0.73/1.15 , clause( 25, [ ~( =( eq3( 'prop_union_comm'( X, Y ), bfalse ), btrue ) ) ]
% 0.73/1.15 )
% 0.73/1.15 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 paramod(
% 0.73/1.15 clause( 522, [ ~( =( btrue, eq3( bfalse, bfalse ) ) ) ] )
% 0.73/1.15 , clause( 260, [ =( 'prop_union_comm'( cons( z, cons( s( X ), nil ) ), cons(
% 0.73/1.15 z, nil ) ), bfalse ) ] )
% 0.73/1.15 , 0, clause( 520, [ ~( =( btrue, eq3( 'prop_union_comm'( X, Y ), bfalse ) )
% 0.73/1.15 ) ] )
% 0.73/1.15 , 0, 4, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, cons( z
% 0.73/1.15 , cons( s( X ), nil ) ) ), :=( Y, cons( z, nil ) )] )).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 paramod(
% 0.73/1.15 clause( 523, [ ~( =( btrue, btrue ) ) ] )
% 0.73/1.15 , clause( 20, [ =( eq3( X, X ), btrue ) ] )
% 0.73/1.15 , 0, clause( 522, [ ~( =( btrue, eq3( bfalse, bfalse ) ) ) ] )
% 0.73/1.15 , 0, 3, substitution( 0, [ :=( X, bfalse )] ), substitution( 1, [] )).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 eqrefl(
% 0.73/1.15 clause( 524, [] )
% 0.73/1.15 , clause( 523, [ ~( =( btrue, btrue ) ) ] )
% 0.73/1.15 , 0, substitution( 0, [] )).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 subsumption(
% 0.73/1.15 clause( 264, [] )
% 0.73/1.15 , clause( 524, [] )
% 0.73/1.15 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 end.
% 0.73/1.15
% 0.73/1.15 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.73/1.15
% 0.73/1.15 Memory use:
% 0.73/1.15
% 0.73/1.15 space for terms: 4444
% 0.73/1.15 space for clauses: 33335
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 clauses generated: 1296
% 0.73/1.15 clauses kept: 265
% 0.73/1.15 clauses selected: 147
% 0.73/1.15 clauses deleted: 5
% 0.73/1.15 clauses inuse deleted: 0
% 0.73/1.15
% 0.73/1.15 subsentry: 1318
% 0.73/1.15 literals s-matched: 666
% 0.73/1.15 literals matched: 666
% 0.73/1.15 full subsumption: 0
% 0.73/1.15
% 0.73/1.15 checksum: 421320205
% 0.73/1.15
% 0.73/1.15
% 0.73/1.15 Bliksem ended
%------------------------------------------------------------------------------