TSTP Solution File: SWV276-2 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV276-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n027.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 : Wed Jul 20 16:23:31 EDT 2022
% Result : Unsatisfiable 1.87s 2.24s
% Output : Refutation 1.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SWV276-2 : TPTP v8.1.0. Released v3.2.0.
% 0.14/0.14 % Command : bliksem %s
% 0.15/0.36 % Computer : n027.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % DateTime : Thu Jun 16 01:23:50 EDT 2022
% 0.15/0.36 % CPUTime :
% 1.87/2.24 *** allocated 10000 integers for termspace/termends
% 1.87/2.24 *** allocated 10000 integers for clauses
% 1.87/2.24 *** allocated 10000 integers for justifications
% 1.87/2.24 Bliksem 1.12
% 1.87/2.24
% 1.87/2.24
% 1.87/2.24 Automatic Strategy Selection
% 1.87/2.24
% 1.87/2.24 Clauses:
% 1.87/2.24 [
% 1.87/2.24 [ ~( 'c_in'( X, 'c_Message_OkeysFor'( 'c_Message_Osynth'( Y ) ),
% 1.87/2.24 'tc_nat' ) ), 'c_in'( X, 'c_Message_OkeysFor'( Y ), 'tc_nat' ), 'c_in'(
% 1.87/2.24 'c_Message_Omsg_OKey'( 'v_sko__uhi'( Y, X ) ), Y, 'tc_Message_Omsg' ) ]
% 1.87/2.24 ,
% 1.87/2.24 [ ~( 'c_in'( X, 'c_Message_OkeysFor'( 'c_Message_Osynth'( Y ) ),
% 1.87/2.24 'tc_nat' ) ), 'c_in'( X, 'c_Message_OkeysFor'( Y ), 'tc_nat' ), =( X,
% 1.87/2.24 'c_Message_OinvKey'( 'v_sko__uhi'( Y, X ) ) ) ],
% 1.87/2.24 [ ~( 'c_in'( X, 'c_Message_Oanalz'( Y ), 'tc_Message_Omsg' ) ), 'c_in'(
% 1.87/2.24 X, 'c_Message_Oparts'( Y ), 'tc_Message_Omsg' ) ],
% 1.87/2.24 [ 'c_lessequals'( 'c_Message_Oanalz'( X ), 'c_Message_Oparts'( X ),
% 1.87/2.24 'tc_set'( 'tc_Message_Omsg' ) ) ],
% 1.87/2.24 [ =( 'c_Message_OinvKey'( 'c_Message_OinvKey'( X ) ), X ) ],
% 1.87/2.24 [ ~( 'c_lessequals'( X, Y, 'tc_set'( 'tc_Message_Omsg' ) ) ),
% 1.87/2.24 'c_lessequals'( 'c_Message_OkeysFor'( X ), 'c_Message_OkeysFor'( Y ),
% 1.87/2.24 'tc_set'( 'tc_nat' ) ) ],
% 1.87/2.24 [ =( 'c_Message_OkeysFor'( 'c_union'( X, Y, 'tc_Message_Omsg' ) ),
% 1.87/2.24 'c_union'( 'c_Message_OkeysFor'( X ), 'c_Message_OkeysFor'( Y ), 'tc_nat'
% 1.87/2.24 ) ) ],
% 1.87/2.24 [ =( 'c_Message_Oparts'( 'c_Message_Oanalz'( X ) ), 'c_Message_Oparts'(
% 1.87/2.24 X ) ) ],
% 1.87/2.24 [ ~( 'c_in'( X, Y, 'tc_Message_Omsg' ) ), 'c_lessequals'(
% 1.87/2.24 'c_Message_Oparts'( 'c_insert'( X, Z, 'tc_Message_Omsg' ) ), 'c_union'(
% 1.87/2.24 'c_Message_Oparts'( Y ), 'c_Message_Oparts'( Z ), 'tc_Message_Omsg' ),
% 1.87/2.24 'tc_set'( 'tc_Message_Omsg' ) ) ],
% 1.87/2.24 [ =( 'c_Message_Oparts'( 'c_Message_Osynth'( X ) ), 'c_union'(
% 1.87/2.24 'c_Message_Oparts'( X ), 'c_Message_Osynth'( X ), 'tc_Message_Omsg' ) ) ]
% 1.87/2.24 ,
% 1.87/2.24 [ =( 'c_Message_Oparts'( 'c_union'( X, Y, 'tc_Message_Omsg' ) ),
% 1.87/2.24 'c_union'( 'c_Message_Oparts'( X ), 'c_Message_Oparts'( Y ),
% 1.87/2.24 'tc_Message_Omsg' ) ) ],
% 1.87/2.24 [ ~( 'c_in'( X, Y, Z ) ), ~( 'c_lessequals'( Y, T, 'tc_set'( Z ) ) ),
% 1.87/2.24 'c_in'( X, T, Z ) ],
% 1.87/2.24 [ ~( 'c_in'( X, 'c_union'( Y, Z, T ), T ) ), 'c_in'( X, Z, T ), 'c_in'(
% 1.87/2.24 X, Y, T ) ],
% 1.87/2.24 [ ~( 'c_in'( X, Y, Z ) ), 'c_in'( X, 'c_union'( Y, T, Z ), Z ) ],
% 1.87/2.24 [ ~( 'c_in'( X, Y, Z ) ), 'c_in'( X, 'c_union'( T, Y, Z ), Z ) ],
% 1.87/2.24 [ 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_Message_Oparts'( 'c_insert'(
% 1.87/2.24 'v_X', 'v_G', 'tc_Message_Omsg' ) ) ), 'tc_nat' ) ],
% 1.87/2.24 [ 'c_in'( 'v_X', 'c_Message_Osynth'( 'c_Message_Oanalz'( 'v_H' ) ),
% 1.87/2.24 'tc_Message_Omsg' ) ],
% 1.87/2.24 [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_Message_Oparts'( 'c_union'(
% 1.87/2.24 'v_G', 'v_H', 'tc_Message_Omsg' ) ) ), 'tc_nat' ) ) ],
% 1.87/2.24 [ ~( 'c_in'( 'c_Message_Omsg_OKey'( 'c_Message_OinvKey'( 'v_K' ) ),
% 1.87/2.24 'c_Message_Oparts'( 'v_H' ), 'tc_Message_Omsg' ) ) ]
% 1.87/2.24 ] .
% 1.87/2.24
% 1.87/2.24
% 1.87/2.24 percentage equality = 0.187500, percentage horn = 0.842105
% 1.87/2.24 This is a problem with some equality
% 1.87/2.24
% 1.87/2.24
% 1.87/2.24
% 1.87/2.24 Options Used:
% 1.87/2.24
% 1.87/2.24 useres = 1
% 1.87/2.24 useparamod = 1
% 1.87/2.24 useeqrefl = 1
% 1.87/2.24 useeqfact = 1
% 1.87/2.24 usefactor = 1
% 1.87/2.24 usesimpsplitting = 0
% 1.87/2.24 usesimpdemod = 5
% 1.87/2.24 usesimpres = 3
% 1.87/2.24
% 1.87/2.24 resimpinuse = 1000
% 1.87/2.24 resimpclauses = 20000
% 1.87/2.24 substype = eqrewr
% 1.87/2.24 backwardsubs = 1
% 1.87/2.24 selectoldest = 5
% 1.87/2.24
% 1.87/2.24 litorderings [0] = split
% 1.87/2.24 litorderings [1] = extend the termordering, first sorting on arguments
% 1.87/2.24
% 1.87/2.24 termordering = kbo
% 1.87/2.24
% 1.87/2.24 litapriori = 0
% 1.87/2.24 termapriori = 1
% 1.87/2.24 litaposteriori = 0
% 1.87/2.24 termaposteriori = 0
% 1.87/2.24 demodaposteriori = 0
% 1.87/2.24 ordereqreflfact = 0
% 1.87/2.24
% 1.87/2.24 litselect = negord
% 1.87/2.24
% 1.87/2.24 maxweight = 15
% 1.87/2.24 maxdepth = 30000
% 1.87/2.24 maxlength = 115
% 1.87/2.24 maxnrvars = 195
% 1.87/2.24 excuselevel = 1
% 1.87/2.24 increasemaxweight = 1
% 1.87/2.24
% 1.87/2.24 maxselected = 10000000
% 1.87/2.24 maxnrclauses = 10000000
% 1.87/2.24
% 1.87/2.24 showgenerated = 0
% 1.87/2.24 showkept = 0
% 1.87/2.24 showselected = 0
% 1.87/2.24 showdeleted = 0
% 1.87/2.24 showresimp = 1
% 1.87/2.24 showstatus = 2000
% 1.87/2.24
% 1.87/2.24 prologoutput = 1
% 1.87/2.24 nrgoals = 5000000
% 1.87/2.24 totalproof = 1
% 1.87/2.24
% 1.87/2.24 Symbols occurring in the translation:
% 1.87/2.24
% 1.87/2.24 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.87/2.24 . [1, 2] (w:1, o:37, a:1, s:1, b:0),
% 1.87/2.24 ! [4, 1] (w:0, o:25, a:1, s:1, b:0),
% 1.87/2.24 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.87/2.24 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.87/2.24 'c_Message_Osynth' [41, 1] (w:1, o:30, a:1, s:1, b:0),
% 1.87/2.24 'c_Message_OkeysFor' [42, 1] (w:1, o:31, a:1, s:1, b:0),
% 1.87/2.24 'tc_nat' [43, 0] (w:1, o:12, a:1, s:1, b:0),
% 1.87/2.24 'c_in' [44, 3] (w:1, o:63, a:1, s:1, b:0),
% 1.87/2.24 'v_sko__uhi' [45, 2] (w:1, o:62, a:1, s:1, b:0),
% 1.87/2.24 'c_Message_Omsg_OKey' [46, 1] (w:1, o:32, a:1, s:1, b:0),
% 1.87/2.24 'tc_Message_Omsg' [47, 0] (w:1, o:13, a:1, s:1, b:0),
% 1.87/2.24 'c_Message_OinvKey' [48, 1] (w:1, o:33, a:1, s:1, b:0),
% 1.87/2.24 'c_Message_Oanalz' [50, 1] (w:1, o:34, a:1, s:1, b:0),
% 1.87/2.24 'c_Message_Oparts' [51, 1] (w:1, o:35, a:1, s:1, b:0),
% 1.87/2.24 'tc_set' [52, 1] (w:1, o:36, a:1, s:1, b:0),
% 1.87/2.24 'c_lessequals' [53, 3] (w:1, o:64, a:1, s:1, b:0),
% 1.87/2.24 'c_union' [57, 3] (w:1, o:65, a:1, s:1, b:0),
% 1.87/2.24 'c_insert' [58, 3] (w:1, o:66, a:1, s:1, b:0),
% 1.87/2.24 'v_K' [63, 0] (w:1, o:21, a:1, s:1, b:0),
% 1.87/2.24 'v_X' [64, 0] (w:1, o:22, a:1, s:1, b:0),
% 1.87/2.24 'v_G' [65, 0] (w:1, o:23, a:1, s:1, b:0),
% 1.87/2.24 'v_H' [66, 0] (w:1, o:24, a:1, s:1, b:0).
% 1.87/2.24
% 1.87/2.24
% 1.87/2.24 Starting Search:
% 1.87/2.24
% 1.87/2.24 Resimplifying inuse:
% 1.87/2.24 Done
% 1.87/2.24
% 1.87/2.24
% 1.87/2.24 Intermediate Status:
% 1.87/2.24 Generated: 7949
% 1.87/2.24 Kept: 2076
% 1.87/2.24 Inuse: 312
% 1.87/2.24 Deleted: 3
% 1.87/2.24 Deletedinuse: 2
% 1.87/2.24
% 1.87/2.24 Resimplifying inuse:
% 1.87/2.24 Done
% 1.87/2.24
% 1.87/2.24 Resimplifying inuse:
% 1.87/2.24 Done
% 1.87/2.24
% 1.87/2.24
% 1.87/2.24 Intermediate Status:
% 1.87/2.24 Generated: 44557
% 1.87/2.24 Kept: 4079
% 1.87/2.24 Inuse: 883
% 1.87/2.24 Deleted: 3
% 1.87/2.24 Deletedinuse: 2
% 1.87/2.24
% 1.87/2.24 Resimplifying inuse:
% 1.87/2.24 Done
% 1.87/2.24
% 1.87/2.24 Resimplifying inuse:
% 1.87/2.24 Done
% 1.87/2.24
% 1.87/2.24
% 1.87/2.24 Intermediate Status:
% 1.87/2.24 Generated: 111835
% 1.87/2.24 Kept: 6798
% 1.87/2.24 Inuse: 1821
% 1.87/2.24 Deleted: 8
% 1.87/2.24 Deletedinuse: 4
% 1.87/2.24
% 1.87/2.24 Resimplifying inuse:
% 1.87/2.24 Done
% 1.87/2.24
% 1.87/2.24 Resimplifying inuse:
% 1.87/2.24 Done
% 1.87/2.24
% 1.87/2.24
% 1.87/2.24 Intermediate Status:
% 1.87/2.24 Generated: 116140
% 1.87/2.24 Kept: 9069
% 1.87/2.24 Inuse: 1848
% 1.87/2.24 Deleted: 9
% 1.87/2.24 Deletedinuse: 5
% 1.87/2.24
% 1.87/2.24 Resimplifying inuse:
% 1.87/2.24 Done
% 1.87/2.24
% 1.87/2.24 Resimplifying inuse:
% 1.87/2.24 Done
% 1.87/2.24
% 1.87/2.24
% 1.87/2.24 Intermediate Status:
% 1.87/2.24 Generated: 141551
% 1.87/2.24 Kept: 11071
% 1.87/2.24 Inuse: 2119
% 1.87/2.24 Deleted: 11
% 1.87/2.24 Deletedinuse: 7
% 1.87/2.24
% 1.87/2.24 Resimplifying inuse:
% 1.87/2.24 Done
% 1.87/2.24
% 1.87/2.24 Resimplifying inuse:
% 1.87/2.24 Done
% 1.87/2.24
% 1.87/2.24
% 1.87/2.24 Bliksems!, er is een bewijs:
% 1.87/2.24 % SZS status Unsatisfiable
% 1.87/2.24 % SZS output start Refutation
% 1.87/2.24
% 1.87/2.24 clause( 0, [ ~( 'c_in'( X, 'c_Message_OkeysFor'( 'c_Message_Osynth'( Y ) )
% 1.87/2.24 , 'tc_nat' ) ), 'c_in'( X, 'c_Message_OkeysFor'( Y ), 'tc_nat' ), 'c_in'(
% 1.87/2.24 'c_Message_Omsg_OKey'( 'v_sko__uhi'( Y, X ) ), Y, 'tc_Message_Omsg' ) ]
% 1.87/2.24 )
% 1.87/2.24 .
% 1.87/2.24 clause( 1, [ ~( 'c_in'( X, 'c_Message_OkeysFor'( 'c_Message_Osynth'( Y ) )
% 1.87/2.24 , 'tc_nat' ) ), 'c_in'( X, 'c_Message_OkeysFor'( Y ), 'tc_nat' ), =(
% 1.87/2.24 'c_Message_OinvKey'( 'v_sko__uhi'( Y, X ) ), X ) ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 2, [ ~( 'c_in'( X, 'c_Message_Oanalz'( Y ), 'tc_Message_Omsg' ) ),
% 1.87/2.24 'c_in'( X, 'c_Message_Oparts'( Y ), 'tc_Message_Omsg' ) ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 3, [ 'c_lessequals'( 'c_Message_Oanalz'( X ), 'c_Message_Oparts'( X
% 1.87/2.24 ), 'tc_set'( 'tc_Message_Omsg' ) ) ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 4, [ =( 'c_Message_OinvKey'( 'c_Message_OinvKey'( X ) ), X ) ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 5, [ ~( 'c_lessequals'( X, Y, 'tc_set'( 'tc_Message_Omsg' ) ) ),
% 1.87/2.24 'c_lessequals'( 'c_Message_OkeysFor'( X ), 'c_Message_OkeysFor'( Y ),
% 1.87/2.24 'tc_set'( 'tc_nat' ) ) ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 6, [ =( 'c_union'( 'c_Message_OkeysFor'( X ), 'c_Message_OkeysFor'(
% 1.87/2.24 Y ), 'tc_nat' ), 'c_Message_OkeysFor'( 'c_union'( X, Y, 'tc_Message_Omsg'
% 1.87/2.24 ) ) ) ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 7, [ =( 'c_Message_Oparts'( 'c_Message_Oanalz'( X ) ),
% 1.87/2.24 'c_Message_Oparts'( X ) ) ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 8, [ ~( 'c_in'( X, Y, 'tc_Message_Omsg' ) ), 'c_lessequals'(
% 1.87/2.24 'c_Message_Oparts'( 'c_insert'( X, Z, 'tc_Message_Omsg' ) ), 'c_union'(
% 1.87/2.24 'c_Message_Oparts'( Y ), 'c_Message_Oparts'( Z ), 'tc_Message_Omsg' ),
% 1.87/2.24 'tc_set'( 'tc_Message_Omsg' ) ) ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 9, [ =( 'c_union'( 'c_Message_Oparts'( X ), 'c_Message_Osynth'( X )
% 1.87/2.24 , 'tc_Message_Omsg' ), 'c_Message_Oparts'( 'c_Message_Osynth'( X ) ) ) ]
% 1.87/2.24 )
% 1.87/2.24 .
% 1.87/2.24 clause( 10, [ =( 'c_union'( 'c_Message_Oparts'( X ), 'c_Message_Oparts'( Y
% 1.87/2.24 ), 'tc_Message_Omsg' ), 'c_Message_Oparts'( 'c_union'( X, Y,
% 1.87/2.24 'tc_Message_Omsg' ) ) ) ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 11, [ ~( 'c_in'( X, Y, Z ) ), ~( 'c_lessequals'( Y, T, 'tc_set'( Z
% 1.87/2.24 ) ) ), 'c_in'( X, T, Z ) ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 12, [ ~( 'c_in'( X, 'c_union'( Y, Z, T ), T ) ), 'c_in'( X, Z, T )
% 1.87/2.24 , 'c_in'( X, Y, T ) ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 13, [ ~( 'c_in'( X, Y, Z ) ), 'c_in'( X, 'c_union'( Y, T, Z ), Z )
% 1.87/2.24 ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 14, [ ~( 'c_in'( X, Y, Z ) ), 'c_in'( X, 'c_union'( T, Y, Z ), Z )
% 1.87/2.24 ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 15, [ 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.24 'c_insert'( 'v_X', 'v_G', 'tc_Message_Omsg' ) ) ), 'tc_nat' ) ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 16, [ 'c_in'( 'v_X', 'c_Message_Osynth'( 'c_Message_Oanalz'( 'v_H'
% 1.87/2.24 ) ), 'tc_Message_Omsg' ) ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 17, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.24 'c_union'( 'v_G', 'v_H', 'tc_Message_Omsg' ) ) ), 'tc_nat' ) ) ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 18, [ ~( 'c_in'( 'c_Message_Omsg_OKey'( 'c_Message_OinvKey'( 'v_K'
% 1.87/2.24 ) ), 'c_Message_Oparts'( 'v_H' ), 'tc_Message_Omsg' ) ) ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 29, [ =( 'v_sko__uhi'( X, Y ), 'c_Message_OinvKey'( Y ) ), ~(
% 1.87/2.24 'c_in'( Y, 'c_Message_OkeysFor'( 'c_Message_Osynth'( X ) ), 'tc_nat' ) )
% 1.87/2.24 , 'c_in'( Y, 'c_Message_OkeysFor'( X ), 'tc_nat' ) ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 30, [ ~( 'c_in'( 'c_Message_Omsg_OKey'( 'c_Message_OinvKey'( 'v_K'
% 1.87/2.24 ) ), 'c_Message_Oanalz'( 'v_H' ), 'tc_Message_Omsg' ) ) ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 32, [ =( 'c_union'( 'c_Message_Oparts'( X ), 'c_Message_Osynth'(
% 1.87/2.24 'c_Message_Oanalz'( X ) ), 'tc_Message_Omsg' ), 'c_Message_Oparts'(
% 1.87/2.24 'c_Message_Osynth'( 'c_Message_Oanalz'( X ) ) ) ) ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 37, [ 'c_lessequals'( 'c_Message_OkeysFor'( 'c_Message_Oanalz'( X )
% 1.87/2.24 ), 'c_Message_OkeysFor'( 'c_Message_Oparts'( X ) ), 'tc_set'( 'tc_nat' )
% 1.87/2.24 ) ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 42, [ 'c_in'( X, 'c_union'( Y, 'c_Message_OkeysFor'( Z ), 'tc_nat'
% 1.87/2.24 ), 'tc_nat' ), ~( 'c_in'( X, 'c_Message_OkeysFor'( 'c_Message_Osynth'( Z
% 1.87/2.24 ) ), 'tc_nat' ) ), 'c_in'( 'c_Message_Omsg_OKey'( 'v_sko__uhi'( Z, X ) )
% 1.87/2.24 , Z, 'tc_Message_Omsg' ) ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 47, [ ~( 'c_in'( Z, 'c_Message_OkeysFor'( Y ), 'tc_nat' ) ), 'c_in'(
% 1.87/2.24 Z, 'c_Message_OkeysFor'( 'c_union'( X, Y, 'tc_Message_Omsg' ) ), 'tc_nat'
% 1.87/2.24 ) ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 60, [ 'c_in'( 'v_X', 'c_union'( 'c_Message_Osynth'(
% 1.87/2.24 'c_Message_Oanalz'( 'v_H' ) ), X, 'tc_Message_Omsg' ), 'tc_Message_Omsg'
% 1.87/2.24 ) ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 61, [ ~( 'c_in'( Z, 'c_Message_OkeysFor'( X ), 'tc_nat' ) ), 'c_in'(
% 1.87/2.24 Z, 'c_Message_OkeysFor'( 'c_union'( X, Y, 'tc_Message_Omsg' ) ), 'tc_nat'
% 1.87/2.24 ) ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 65, [ ~( 'c_in'( X, Y, 'tc_Message_Omsg' ) ), 'c_lessequals'(
% 1.87/2.24 'c_Message_Oparts'( 'c_insert'( X, Z, 'tc_Message_Omsg' ) ),
% 1.87/2.24 'c_Message_Oparts'( 'c_union'( Y, Z, 'tc_Message_Omsg' ) ), 'tc_set'(
% 1.87/2.24 'tc_Message_Omsg' ) ) ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 110, [ ~( 'c_in'( X, 'c_Message_OkeysFor'( 'c_Message_Oanalz'( Y )
% 1.87/2.24 ), 'tc_nat' ) ), 'c_in'( X, 'c_Message_OkeysFor'( 'c_Message_Oparts'( Y
% 1.87/2.24 ) ), 'tc_nat' ) ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 111, [ ~( 'c_in'( X, 'c_Message_OkeysFor'( Y ), 'tc_nat' ) ),
% 1.87/2.24 'c_in'( X, 'c_Message_OkeysFor'( Z ), 'tc_nat' ), ~( 'c_lessequals'( Y, Z
% 1.87/2.24 , 'tc_set'( 'tc_Message_Omsg' ) ) ) ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 156, [ ~( 'c_in'( 'v_K', 'c_union'( X, 'c_Message_OkeysFor'(
% 1.87/2.24 'c_Message_Oparts'( 'c_union'( 'v_G', 'v_H', 'tc_Message_Omsg' ) ) ),
% 1.87/2.24 'tc_nat' ), 'tc_nat' ) ), 'c_in'( 'v_K', X, 'tc_nat' ) ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 486, [ ~( 'c_in'( Z, 'c_Message_OkeysFor'( 'c_Message_Oparts'( Y )
% 1.87/2.24 ), 'tc_nat' ) ), 'c_in'( Z, 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.24 'c_union'( X, Y, 'tc_Message_Omsg' ) ) ), 'tc_nat' ) ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 665, [ ~( 'c_in'( Z, 'c_Message_OkeysFor'( 'c_Message_Oparts'( X )
% 1.87/2.24 ), 'tc_nat' ) ), 'c_in'( Z, 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.24 'c_union'( X, Y, 'tc_Message_Omsg' ) ) ), 'tc_nat' ) ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 2300, [ 'c_in'( 'v_K', 'c_Message_OkeysFor'( X ), 'tc_nat' ), ~(
% 1.87/2.24 'c_lessequals'( 'c_Message_Oparts'( 'c_insert'( 'v_X', 'v_G',
% 1.87/2.24 'tc_Message_Omsg' ) ), X, 'tc_set'( 'tc_Message_Omsg' ) ) ) ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 3549, [ 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.24 'c_union'( X, 'v_G', 'tc_Message_Omsg' ) ) ), 'tc_nat' ), ~( 'c_in'(
% 1.87/2.24 'v_X', X, 'tc_Message_Omsg' ) ) ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 3575, [ 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.24 'c_union'( 'c_union'( 'c_Message_Osynth'( 'c_Message_Oanalz'( 'v_H' ) ),
% 1.87/2.24 X, 'tc_Message_Omsg' ), 'v_G', 'tc_Message_Omsg' ) ) ), 'tc_nat' ) ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 4512, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.24 'v_H' ) ), 'tc_nat' ) ) ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 4527, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_Message_Oanalz'(
% 1.87/2.24 'v_H' ) ), 'tc_nat' ) ) ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 4530, [ ~( 'c_in'( 'v_K', 'c_union'( 'c_Message_OkeysFor'(
% 1.87/2.24 'c_Message_Oparts'( 'v_H' ) ), X, 'tc_nat' ), 'tc_nat' ) ), 'c_in'( 'v_K'
% 1.87/2.24 , X, 'tc_nat' ) ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 4542, [ =( 'v_sko__uhi'( 'c_Message_Oanalz'( 'v_H' ), 'v_K' ),
% 1.87/2.24 'c_Message_OinvKey'( 'v_K' ) ), ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'(
% 1.87/2.24 'c_Message_Osynth'( 'c_Message_Oanalz'( 'v_H' ) ) ), 'tc_nat' ) ) ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 4543, [ ~( 'c_in'( 'v_K', 'c_union'( X, 'c_Message_OkeysFor'(
% 1.87/2.24 'c_Message_Oanalz'( 'v_H' ) ), 'tc_nat' ), 'tc_nat' ) ), 'c_in'( 'v_K', X
% 1.87/2.24 , 'tc_nat' ) ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 4923, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_union'(
% 1.87/2.24 'c_Message_Oparts'( 'v_H' ), 'c_Message_Oanalz'( 'v_H' ),
% 1.87/2.24 'tc_Message_Omsg' ) ), 'tc_nat' ) ) ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 4930, [ 'c_in'( 'v_K', X, 'tc_nat' ), ~( 'c_in'( 'v_K',
% 1.87/2.24 'c_Message_OkeysFor'( 'c_Message_Osynth'( 'c_Message_Oanalz'( 'v_H' ) ) )
% 1.87/2.24 , 'tc_nat' ) ) ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 4936, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_Message_Osynth'(
% 1.87/2.24 'c_Message_Oanalz'( 'v_H' ) ) ), 'tc_nat' ) ) ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 5195, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.24 'c_Message_Osynth'( 'c_Message_Oanalz'( 'v_H' ) ) ) ), 'tc_nat' ) ) ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 5227, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.24 'c_union'( 'c_Message_Osynth'( 'c_Message_Oanalz'( 'v_H' ) ), 'c_union'(
% 1.87/2.24 'v_G', 'v_H', 'tc_Message_Omsg' ), 'tc_Message_Omsg' ) ) ), 'tc_nat' ) )
% 1.87/2.24 ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 5620, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.24 'v_G' ) ), 'tc_nat' ) ) ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 5647, [ ~( 'c_in'( 'v_K', 'c_union'( X, 'c_Message_OkeysFor'(
% 1.87/2.24 'c_Message_Oparts'( 'v_G' ) ), 'tc_nat' ), 'tc_nat' ) ), 'c_in'( 'v_K', X
% 1.87/2.24 , 'tc_nat' ) ] )
% 1.87/2.24 .
% 1.87/2.24 clause( 12818, [] )
% 1.87/2.24 .
% 1.87/2.24
% 1.87/2.24
% 1.87/2.24 % SZS output end Refutation
% 1.87/2.24 found a proof!
% 1.87/2.24
% 1.87/2.24 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.87/2.24
% 1.87/2.24 initialclauses(
% 1.87/2.24 [ clause( 12820, [ ~( 'c_in'( X, 'c_Message_OkeysFor'( 'c_Message_Osynth'(
% 1.87/2.24 Y ) ), 'tc_nat' ) ), 'c_in'( X, 'c_Message_OkeysFor'( Y ), 'tc_nat' ),
% 1.87/2.24 'c_in'( 'c_Message_Omsg_OKey'( 'v_sko__uhi'( Y, X ) ), Y,
% 1.87/2.24 'tc_Message_Omsg' ) ] )
% 1.87/2.24 , clause( 12821, [ ~( 'c_in'( X, 'c_Message_OkeysFor'( 'c_Message_Osynth'(
% 1.87/2.24 Y ) ), 'tc_nat' ) ), 'c_in'( X, 'c_Message_OkeysFor'( Y ), 'tc_nat' ),
% 1.87/2.24 =( X, 'c_Message_OinvKey'( 'v_sko__uhi'( Y, X ) ) ) ] )
% 1.87/2.24 , clause( 12822, [ ~( 'c_in'( X, 'c_Message_Oanalz'( Y ), 'tc_Message_Omsg'
% 1.87/2.24 ) ), 'c_in'( X, 'c_Message_Oparts'( Y ), 'tc_Message_Omsg' ) ] )
% 1.87/2.24 , clause( 12823, [ 'c_lessequals'( 'c_Message_Oanalz'( X ),
% 1.87/2.24 'c_Message_Oparts'( X ), 'tc_set'( 'tc_Message_Omsg' ) ) ] )
% 1.87/2.24 , clause( 12824, [ =( 'c_Message_OinvKey'( 'c_Message_OinvKey'( X ) ), X )
% 1.87/2.24 ] )
% 1.87/2.24 , clause( 12825, [ ~( 'c_lessequals'( X, Y, 'tc_set'( 'tc_Message_Omsg' ) )
% 1.87/2.24 ), 'c_lessequals'( 'c_Message_OkeysFor'( X ), 'c_Message_OkeysFor'( Y )
% 1.87/2.24 , 'tc_set'( 'tc_nat' ) ) ] )
% 1.87/2.24 , clause( 12826, [ =( 'c_Message_OkeysFor'( 'c_union'( X, Y,
% 1.87/2.24 'tc_Message_Omsg' ) ), 'c_union'( 'c_Message_OkeysFor'( X ),
% 1.87/2.24 'c_Message_OkeysFor'( Y ), 'tc_nat' ) ) ] )
% 1.87/2.24 , clause( 12827, [ =( 'c_Message_Oparts'( 'c_Message_Oanalz'( X ) ),
% 1.87/2.24 'c_Message_Oparts'( X ) ) ] )
% 1.87/2.24 , clause( 12828, [ ~( 'c_in'( X, Y, 'tc_Message_Omsg' ) ), 'c_lessequals'(
% 1.87/2.24 'c_Message_Oparts'( 'c_insert'( X, Z, 'tc_Message_Omsg' ) ), 'c_union'(
% 1.87/2.24 'c_Message_Oparts'( Y ), 'c_Message_Oparts'( Z ), 'tc_Message_Omsg' ),
% 1.87/2.24 'tc_set'( 'tc_Message_Omsg' ) ) ] )
% 1.87/2.24 , clause( 12829, [ =( 'c_Message_Oparts'( 'c_Message_Osynth'( X ) ),
% 1.87/2.24 'c_union'( 'c_Message_Oparts'( X ), 'c_Message_Osynth'( X ),
% 1.87/2.24 'tc_Message_Omsg' ) ) ] )
% 1.87/2.24 , clause( 12830, [ =( 'c_Message_Oparts'( 'c_union'( X, Y,
% 1.87/2.24 'tc_Message_Omsg' ) ), 'c_union'( 'c_Message_Oparts'( X ),
% 1.87/2.24 'c_Message_Oparts'( Y ), 'tc_Message_Omsg' ) ) ] )
% 1.87/2.24 , clause( 12831, [ ~( 'c_in'( X, Y, Z ) ), ~( 'c_lessequals'( Y, T,
% 1.87/2.24 'tc_set'( Z ) ) ), 'c_in'( X, T, Z ) ] )
% 1.87/2.24 , clause( 12832, [ ~( 'c_in'( X, 'c_union'( Y, Z, T ), T ) ), 'c_in'( X, Z
% 1.87/2.24 , T ), 'c_in'( X, Y, T ) ] )
% 1.87/2.24 , clause( 12833, [ ~( 'c_in'( X, Y, Z ) ), 'c_in'( X, 'c_union'( Y, T, Z )
% 1.87/2.24 , Z ) ] )
% 1.87/2.24 , clause( 12834, [ ~( 'c_in'( X, Y, Z ) ), 'c_in'( X, 'c_union'( T, Y, Z )
% 1.87/2.24 , Z ) ] )
% 1.87/2.24 , clause( 12835, [ 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.24 'c_insert'( 'v_X', 'v_G', 'tc_Message_Omsg' ) ) ), 'tc_nat' ) ] )
% 1.87/2.24 , clause( 12836, [ 'c_in'( 'v_X', 'c_Message_Osynth'( 'c_Message_Oanalz'(
% 1.87/2.24 'v_H' ) ), 'tc_Message_Omsg' ) ] )
% 1.87/2.24 , clause( 12837, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'(
% 1.87/2.24 'c_Message_Oparts'( 'c_union'( 'v_G', 'v_H', 'tc_Message_Omsg' ) ) ),
% 1.87/2.24 'tc_nat' ) ) ] )
% 1.87/2.24 , clause( 12838, [ ~( 'c_in'( 'c_Message_Omsg_OKey'( 'c_Message_OinvKey'(
% 1.87/2.24 'v_K' ) ), 'c_Message_Oparts'( 'v_H' ), 'tc_Message_Omsg' ) ) ] )
% 1.87/2.24 ] ).
% 1.87/2.24
% 1.87/2.24
% 1.87/2.24
% 1.87/2.24 subsumption(
% 1.87/2.24 clause( 0, [ ~( 'c_in'( X, 'c_Message_OkeysFor'( 'c_Message_Osynth'( Y ) )
% 1.87/2.24 , 'tc_nat' ) ), 'c_in'( X, 'c_Message_OkeysFor'( Y ), 'tc_nat' ), 'c_in'(
% 1.87/2.24 'c_Message_Omsg_OKey'( 'v_sko__uhi'( Y, X ) ), Y, 'tc_Message_Omsg' ) ]
% 1.87/2.24 )
% 1.87/2.24 , clause( 12820, [ ~( 'c_in'( X, 'c_Message_OkeysFor'( 'c_Message_Osynth'(
% 1.87/2.24 Y ) ), 'tc_nat' ) ), 'c_in'( X, 'c_Message_OkeysFor'( Y ), 'tc_nat' ),
% 1.87/2.24 'c_in'( 'c_Message_Omsg_OKey'( 'v_sko__uhi'( Y, X ) ), Y,
% 1.87/2.24 'tc_Message_Omsg' ) ] )
% 1.87/2.24 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.87/2.24 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 1.87/2.24
% 1.87/2.24
% 1.87/2.24 eqswap(
% 1.87/2.24 clause( 12839, [ =( 'c_Message_OinvKey'( 'v_sko__uhi'( Y, X ) ), X ), ~(
% 1.87/2.24 'c_in'( X, 'c_Message_OkeysFor'( 'c_Message_Osynth'( Y ) ), 'tc_nat' ) )
% 1.87/2.24 , 'c_in'( X, 'c_Message_OkeysFor'( Y ), 'tc_nat' ) ] )
% 1.87/2.24 , clause( 12821, [ ~( 'c_in'( X, 'c_Message_OkeysFor'( 'c_Message_Osynth'(
% 1.87/2.24 Y ) ), 'tc_nat' ) ), 'c_in'( X, 'c_Message_OkeysFor'( Y ), 'tc_nat' ),
% 1.87/2.24 =( X, 'c_Message_OinvKey'( 'v_sko__uhi'( Y, X ) ) ) ] )
% 1.87/2.24 , 2, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.87/2.24
% 1.87/2.24
% 1.87/2.24 subsumption(
% 1.87/2.24 clause( 1, [ ~( 'c_in'( X, 'c_Message_OkeysFor'( 'c_Message_Osynth'( Y ) )
% 1.87/2.24 , 'tc_nat' ) ), 'c_in'( X, 'c_Message_OkeysFor'( Y ), 'tc_nat' ), =(
% 1.87/2.24 'c_Message_OinvKey'( 'v_sko__uhi'( Y, X ) ), X ) ] )
% 1.87/2.24 , clause( 12839, [ =( 'c_Message_OinvKey'( 'v_sko__uhi'( Y, X ) ), X ), ~(
% 1.87/2.24 'c_in'( X, 'c_Message_OkeysFor'( 'c_Message_Osynth'( Y ) ), 'tc_nat' ) )
% 1.87/2.24 , 'c_in'( X, 'c_Message_OkeysFor'( Y ), 'tc_nat' ) ] )
% 1.87/2.24 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 2
% 1.87/2.24 ), ==>( 1, 0 ), ==>( 2, 1 )] ) ).
% 1.87/2.24
% 1.87/2.24
% 1.87/2.24 subsumption(
% 1.87/2.24 clause( 2, [ ~( 'c_in'( X, 'c_Message_Oanalz'( Y ), 'tc_Message_Omsg' ) ),
% 1.87/2.24 'c_in'( X, 'c_Message_Oparts'( Y ), 'tc_Message_Omsg' ) ] )
% 1.87/2.24 , clause( 12822, [ ~( 'c_in'( X, 'c_Message_Oanalz'( Y ), 'tc_Message_Omsg'
% 1.87/2.24 ) ), 'c_in'( X, 'c_Message_Oparts'( Y ), 'tc_Message_Omsg' ) ] )
% 1.87/2.24 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.87/2.24 ), ==>( 1, 1 )] ) ).
% 1.87/2.24
% 1.87/2.24
% 1.87/2.24 subsumption(
% 1.87/2.24 clause( 3, [ 'c_lessequals'( 'c_Message_Oanalz'( X ), 'c_Message_Oparts'( X
% 1.87/2.24 ), 'tc_set'( 'tc_Message_Omsg' ) ) ] )
% 1.87/2.24 , clause( 12823, [ 'c_lessequals'( 'c_Message_Oanalz'( X ),
% 1.87/2.24 'c_Message_Oparts'( X ), 'tc_set'( 'tc_Message_Omsg' ) ) ] )
% 1.87/2.24 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.87/2.24
% 1.87/2.24
% 1.87/2.24 subsumption(
% 1.87/2.24 clause( 4, [ =( 'c_Message_OinvKey'( 'c_Message_OinvKey'( X ) ), X ) ] )
% 1.87/2.24 , clause( 12824, [ =( 'c_Message_OinvKey'( 'c_Message_OinvKey'( X ) ), X )
% 1.87/2.24 ] )
% 1.87/2.24 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.87/2.24
% 1.87/2.24
% 1.87/2.24 subsumption(
% 1.87/2.24 clause( 5, [ ~( 'c_lessequals'( X, Y, 'tc_set'( 'tc_Message_Omsg' ) ) ),
% 1.87/2.24 'c_lessequals'( 'c_Message_OkeysFor'( X ), 'c_Message_OkeysFor'( Y ),
% 1.87/2.24 'tc_set'( 'tc_nat' ) ) ] )
% 1.87/2.24 , clause( 12825, [ ~( 'c_lessequals'( X, Y, 'tc_set'( 'tc_Message_Omsg' ) )
% 1.87/2.24 ), 'c_lessequals'( 'c_Message_OkeysFor'( X ), 'c_Message_OkeysFor'( Y )
% 1.87/2.24 , 'tc_set'( 'tc_nat' ) ) ] )
% 1.87/2.24 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.87/2.24 ), ==>( 1, 1 )] ) ).
% 1.87/2.24
% 1.87/2.24
% 1.87/2.24 eqswap(
% 1.87/2.24 clause( 12848, [ =( 'c_union'( 'c_Message_OkeysFor'( X ),
% 1.87/2.24 'c_Message_OkeysFor'( Y ), 'tc_nat' ), 'c_Message_OkeysFor'( 'c_union'( X
% 1.87/2.24 , Y, 'tc_Message_Omsg' ) ) ) ] )
% 1.87/2.24 , clause( 12826, [ =( 'c_Message_OkeysFor'( 'c_union'( X, Y,
% 1.87/2.24 'tc_Message_Omsg' ) ), 'c_union'( 'c_Message_OkeysFor'( X ),
% 1.87/2.24 'c_Message_OkeysFor'( Y ), 'tc_nat' ) ) ] )
% 1.87/2.24 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.87/2.24
% 1.87/2.24
% 1.87/2.24 subsumption(
% 1.87/2.24 clause( 6, [ =( 'c_union'( 'c_Message_OkeysFor'( X ), 'c_Message_OkeysFor'(
% 1.87/2.24 Y ), 'tc_nat' ), 'c_Message_OkeysFor'( 'c_union'( X, Y, 'tc_Message_Omsg'
% 1.87/2.24 ) ) ) ] )
% 1.87/2.24 , clause( 12848, [ =( 'c_union'( 'c_Message_OkeysFor'( X ),
% 1.87/2.24 'c_Message_OkeysFor'( Y ), 'tc_nat' ), 'c_Message_OkeysFor'( 'c_union'( X
% 1.87/2.24 , Y, 'tc_Message_Omsg' ) ) ) ] )
% 1.87/2.24 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.87/2.24 )] ) ).
% 1.87/2.24
% 1.87/2.24
% 1.87/2.24 subsumption(
% 1.87/2.24 clause( 7, [ =( 'c_Message_Oparts'( 'c_Message_Oanalz'( X ) ),
% 1.87/2.24 'c_Message_Oparts'( X ) ) ] )
% 1.87/2.24 , clause( 12827, [ =( 'c_Message_Oparts'( 'c_Message_Oanalz'( X ) ),
% 1.87/2.24 'c_Message_Oparts'( X ) ) ] )
% 1.87/2.24 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.87/2.24
% 1.87/2.24
% 1.87/2.24 subsumption(
% 1.87/2.24 clause( 8, [ ~( 'c_in'( X, Y, 'tc_Message_Omsg' ) ), 'c_lessequals'(
% 1.87/2.24 'c_Message_Oparts'( 'c_insert'( X, Z, 'tc_Message_Omsg' ) ), 'c_union'(
% 1.87/2.24 'c_Message_Oparts'( Y ), 'c_Message_Oparts'( Z ), 'tc_Message_Omsg' ),
% 1.87/2.24 'tc_set'( 'tc_Message_Omsg' ) ) ] )
% 1.87/2.24 , clause( 12828, [ ~( 'c_in'( X, Y, 'tc_Message_Omsg' ) ), 'c_lessequals'(
% 1.87/2.24 'c_Message_Oparts'( 'c_insert'( X, Z, 'tc_Message_Omsg' ) ), 'c_union'(
% 1.87/2.24 'c_Message_Oparts'( Y ), 'c_Message_Oparts'( Z ), 'tc_Message_Omsg' ),
% 1.87/2.24 'tc_set'( 'tc_Message_Omsg' ) ) ] )
% 1.87/2.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.87/2.24 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 1.87/2.24
% 1.87/2.24
% 1.87/2.24 eqswap(
% 1.87/2.24 clause( 12861, [ =( 'c_union'( 'c_Message_Oparts'( X ), 'c_Message_Osynth'(
% 1.87/2.24 X ), 'tc_Message_Omsg' ), 'c_Message_Oparts'( 'c_Message_Osynth'( X ) ) )
% 1.87/2.24 ] )
% 1.87/2.24 , clause( 12829, [ =( 'c_Message_Oparts'( 'c_Message_Osynth'( X ) ),
% 1.87/2.24 'c_union'( 'c_Message_Oparts'( X ), 'c_Message_Osynth'( X ),
% 1.87/2.24 'tc_Message_Omsg' ) ) ] )
% 1.87/2.24 , 0, substitution( 0, [ :=( X, X )] )).
% 1.87/2.24
% 1.87/2.24
% 1.87/2.24 subsumption(
% 1.87/2.24 clause( 9, [ =( 'c_union'( 'c_Message_Oparts'( X ), 'c_Message_Osynth'( X )
% 1.87/2.24 , 'tc_Message_Omsg' ), 'c_Message_Oparts'( 'c_Message_Osynth'( X ) ) ) ]
% 1.87/2.24 )
% 1.87/2.24 , clause( 12861, [ =( 'c_union'( 'c_Message_Oparts'( X ),
% 1.87/2.24 'c_Message_Osynth'( X ), 'tc_Message_Omsg' ), 'c_Message_Oparts'(
% 1.87/2.24 'c_Message_Osynth'( X ) ) ) ] )
% 1.87/2.24 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.87/2.24
% 1.87/2.24
% 1.87/2.24 eqswap(
% 1.87/2.24 clause( 12867, [ =( 'c_union'( 'c_Message_Oparts'( X ), 'c_Message_Oparts'(
% 1.87/2.24 Y ), 'tc_Message_Omsg' ), 'c_Message_Oparts'( 'c_union'( X, Y,
% 1.87/2.24 'tc_Message_Omsg' ) ) ) ] )
% 1.87/2.24 , clause( 12830, [ =( 'c_Message_Oparts'( 'c_union'( X, Y,
% 1.87/2.24 'tc_Message_Omsg' ) ), 'c_union'( 'c_Message_Oparts'( X ),
% 1.87/2.24 'c_Message_Oparts'( Y ), 'tc_Message_Omsg' ) ) ] )
% 1.87/2.24 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.87/2.24
% 1.87/2.24
% 1.87/2.24 subsumption(
% 1.87/2.24 clause( 10, [ =( 'c_union'( 'c_Message_Oparts'( X ), 'c_Message_Oparts'( Y
% 1.87/2.24 ), 'tc_Message_Omsg' ), 'c_Message_Oparts'( 'c_union'( X, Y,
% 1.87/2.24 'tc_Message_Omsg' ) ) ) ] )
% 1.87/2.24 , clause( 12867, [ =( 'c_union'( 'c_Message_Oparts'( X ),
% 1.87/2.24 'c_Message_Oparts'( Y ), 'tc_Message_Omsg' ), 'c_Message_Oparts'(
% 1.87/2.24 'c_union'( X, Y, 'tc_Message_Omsg' ) ) ) ] )
% 1.87/2.24 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.87/2.24 )] ) ).
% 1.87/2.24
% 1.87/2.24
% 1.87/2.24 subsumption(
% 1.87/2.24 clause( 11, [ ~( 'c_in'( X, Y, Z ) ), ~( 'c_lessequals'( Y, T, 'tc_set'( Z
% 1.87/2.24 ) ) ), 'c_in'( X, T, Z ) ] )
% 1.87/2.24 , clause( 12831, [ ~( 'c_in'( X, Y, Z ) ), ~( 'c_lessequals'( Y, T,
% 1.87/2.24 'tc_set'( Z ) ) ), 'c_in'( X, T, Z ) ] )
% 1.87/2.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 1.87/2.24 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 1.87/2.24
% 1.87/2.24
% 1.87/2.24 subsumption(
% 1.87/2.24 clause( 12, [ ~( 'c_in'( X, 'c_union'( Y, Z, T ), T ) ), 'c_in'( X, Z, T )
% 1.87/2.24 , 'c_in'( X, Y, T ) ] )
% 1.87/2.24 , clause( 12832, [ ~( 'c_in'( X, 'c_union'( Y, Z, T ), T ) ), 'c_in'( X, Z
% 1.87/2.24 , T ), 'c_in'( X, Y, T ) ] )
% 1.87/2.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 1.87/2.24 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 1.87/2.24
% 1.87/2.24
% 1.87/2.24 subsumption(
% 1.87/2.24 clause( 13, [ ~( 'c_in'( X, Y, Z ) ), 'c_in'( X, 'c_union'( Y, T, Z ), Z )
% 1.87/2.24 ] )
% 1.87/2.24 , clause( 12833, [ ~( 'c_in'( X, Y, Z ) ), 'c_in'( X, 'c_union'( Y, T, Z )
% 1.87/2.24 , Z ) ] )
% 1.87/2.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 1.87/2.24 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 1.87/2.24
% 1.87/2.24
% 1.87/2.24 subsumption(
% 1.87/2.24 clause( 14, [ ~( 'c_in'( X, Y, Z ) ), 'c_in'( X, 'c_union'( T, Y, Z ), Z )
% 1.87/2.24 ] )
% 1.87/2.24 , clause( 12834, [ ~( 'c_in'( X, Y, Z ) ), 'c_in'( X, 'c_union'( T, Y, Z )
% 1.87/2.24 , Z ) ] )
% 1.87/2.24 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T )] ),
% 1.87/2.25 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 subsumption(
% 1.87/2.25 clause( 15, [ 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.25 'c_insert'( 'v_X', 'v_G', 'tc_Message_Omsg' ) ) ), 'tc_nat' ) ] )
% 1.87/2.25 , clause( 12835, [ 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.25 'c_insert'( 'v_X', 'v_G', 'tc_Message_Omsg' ) ) ), 'tc_nat' ) ] )
% 1.87/2.25 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 subsumption(
% 1.87/2.25 clause( 16, [ 'c_in'( 'v_X', 'c_Message_Osynth'( 'c_Message_Oanalz'( 'v_H'
% 1.87/2.25 ) ), 'tc_Message_Omsg' ) ] )
% 1.87/2.25 , clause( 12836, [ 'c_in'( 'v_X', 'c_Message_Osynth'( 'c_Message_Oanalz'(
% 1.87/2.25 'v_H' ) ), 'tc_Message_Omsg' ) ] )
% 1.87/2.25 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 subsumption(
% 1.87/2.25 clause( 17, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.25 'c_union'( 'v_G', 'v_H', 'tc_Message_Omsg' ) ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , clause( 12837, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oparts'( 'c_union'( 'v_G', 'v_H', 'tc_Message_Omsg' ) ) ),
% 1.87/2.25 'tc_nat' ) ) ] )
% 1.87/2.25 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 subsumption(
% 1.87/2.25 clause( 18, [ ~( 'c_in'( 'c_Message_Omsg_OKey'( 'c_Message_OinvKey'( 'v_K'
% 1.87/2.25 ) ), 'c_Message_Oparts'( 'v_H' ), 'tc_Message_Omsg' ) ) ] )
% 1.87/2.25 , clause( 12838, [ ~( 'c_in'( 'c_Message_Omsg_OKey'( 'c_Message_OinvKey'(
% 1.87/2.25 'v_K' ) ), 'c_Message_Oparts'( 'v_H' ), 'tc_Message_Omsg' ) ) ] )
% 1.87/2.25 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 eqswap(
% 1.87/2.25 clause( 12924, [ =( X, 'c_Message_OinvKey'( 'c_Message_OinvKey'( X ) ) ) ]
% 1.87/2.25 )
% 1.87/2.25 , clause( 4, [ =( 'c_Message_OinvKey'( 'c_Message_OinvKey'( X ) ), X ) ] )
% 1.87/2.25 , 0, substitution( 0, [ :=( X, X )] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 paramod(
% 1.87/2.25 clause( 12925, [ =( 'v_sko__uhi'( X, Y ), 'c_Message_OinvKey'( Y ) ), ~(
% 1.87/2.25 'c_in'( Y, 'c_Message_OkeysFor'( 'c_Message_Osynth'( X ) ), 'tc_nat' ) )
% 1.87/2.25 , 'c_in'( Y, 'c_Message_OkeysFor'( X ), 'tc_nat' ) ] )
% 1.87/2.25 , clause( 1, [ ~( 'c_in'( X, 'c_Message_OkeysFor'( 'c_Message_Osynth'( Y )
% 1.87/2.25 ), 'tc_nat' ) ), 'c_in'( X, 'c_Message_OkeysFor'( Y ), 'tc_nat' ), =(
% 1.87/2.25 'c_Message_OinvKey'( 'v_sko__uhi'( Y, X ) ), X ) ] )
% 1.87/2.25 , 2, clause( 12924, [ =( X, 'c_Message_OinvKey'( 'c_Message_OinvKey'( X ) )
% 1.87/2.25 ) ] )
% 1.87/2.25 , 0, 5, substitution( 0, [ :=( X, Y ), :=( Y, X )] ), substitution( 1, [
% 1.87/2.25 :=( X, 'v_sko__uhi'( X, Y ) )] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 subsumption(
% 1.87/2.25 clause( 29, [ =( 'v_sko__uhi'( X, Y ), 'c_Message_OinvKey'( Y ) ), ~(
% 1.87/2.25 'c_in'( Y, 'c_Message_OkeysFor'( 'c_Message_Osynth'( X ) ), 'tc_nat' ) )
% 1.87/2.25 , 'c_in'( Y, 'c_Message_OkeysFor'( X ), 'tc_nat' ) ] )
% 1.87/2.25 , clause( 12925, [ =( 'v_sko__uhi'( X, Y ), 'c_Message_OinvKey'( Y ) ), ~(
% 1.87/2.25 'c_in'( Y, 'c_Message_OkeysFor'( 'c_Message_Osynth'( X ) ), 'tc_nat' ) )
% 1.87/2.25 , 'c_in'( Y, 'c_Message_OkeysFor'( X ), 'tc_nat' ) ] )
% 1.87/2.25 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.87/2.25 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 resolution(
% 1.87/2.25 clause( 12927, [ ~( 'c_in'( 'c_Message_Omsg_OKey'( 'c_Message_OinvKey'(
% 1.87/2.25 'v_K' ) ), 'c_Message_Oanalz'( 'v_H' ), 'tc_Message_Omsg' ) ) ] )
% 1.87/2.25 , clause( 18, [ ~( 'c_in'( 'c_Message_Omsg_OKey'( 'c_Message_OinvKey'(
% 1.87/2.25 'v_K' ) ), 'c_Message_Oparts'( 'v_H' ), 'tc_Message_Omsg' ) ) ] )
% 1.87/2.25 , 0, clause( 2, [ ~( 'c_in'( X, 'c_Message_Oanalz'( Y ), 'tc_Message_Omsg'
% 1.87/2.25 ) ), 'c_in'( X, 'c_Message_Oparts'( Y ), 'tc_Message_Omsg' ) ] )
% 1.87/2.25 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, 'c_Message_Omsg_OKey'(
% 1.87/2.25 'c_Message_OinvKey'( 'v_K' ) ) ), :=( Y, 'v_H' )] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 subsumption(
% 1.87/2.25 clause( 30, [ ~( 'c_in'( 'c_Message_Omsg_OKey'( 'c_Message_OinvKey'( 'v_K'
% 1.87/2.25 ) ), 'c_Message_Oanalz'( 'v_H' ), 'tc_Message_Omsg' ) ) ] )
% 1.87/2.25 , clause( 12927, [ ~( 'c_in'( 'c_Message_Omsg_OKey'( 'c_Message_OinvKey'(
% 1.87/2.25 'v_K' ) ), 'c_Message_Oanalz'( 'v_H' ), 'tc_Message_Omsg' ) ) ] )
% 1.87/2.25 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 eqswap(
% 1.87/2.25 clause( 12929, [ =( 'c_Message_Oparts'( 'c_Message_Osynth'( X ) ),
% 1.87/2.25 'c_union'( 'c_Message_Oparts'( X ), 'c_Message_Osynth'( X ),
% 1.87/2.25 'tc_Message_Omsg' ) ) ] )
% 1.87/2.25 , clause( 9, [ =( 'c_union'( 'c_Message_Oparts'( X ), 'c_Message_Osynth'( X
% 1.87/2.25 ), 'tc_Message_Omsg' ), 'c_Message_Oparts'( 'c_Message_Osynth'( X ) ) )
% 1.87/2.25 ] )
% 1.87/2.25 , 0, substitution( 0, [ :=( X, X )] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 paramod(
% 1.87/2.25 clause( 12930, [ =( 'c_Message_Oparts'( 'c_Message_Osynth'(
% 1.87/2.25 'c_Message_Oanalz'( X ) ) ), 'c_union'( 'c_Message_Oparts'( X ),
% 1.87/2.25 'c_Message_Osynth'( 'c_Message_Oanalz'( X ) ), 'tc_Message_Omsg' ) ) ] )
% 1.87/2.25 , clause( 7, [ =( 'c_Message_Oparts'( 'c_Message_Oanalz'( X ) ),
% 1.87/2.25 'c_Message_Oparts'( X ) ) ] )
% 1.87/2.25 , 0, clause( 12929, [ =( 'c_Message_Oparts'( 'c_Message_Osynth'( X ) ),
% 1.87/2.25 'c_union'( 'c_Message_Oparts'( X ), 'c_Message_Osynth'( X ),
% 1.87/2.25 'tc_Message_Omsg' ) ) ] )
% 1.87/2.25 , 0, 6, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X,
% 1.87/2.25 'c_Message_Oanalz'( X ) )] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 eqswap(
% 1.87/2.25 clause( 12931, [ =( 'c_union'( 'c_Message_Oparts'( X ), 'c_Message_Osynth'(
% 1.87/2.25 'c_Message_Oanalz'( X ) ), 'tc_Message_Omsg' ), 'c_Message_Oparts'(
% 1.87/2.25 'c_Message_Osynth'( 'c_Message_Oanalz'( X ) ) ) ) ] )
% 1.87/2.25 , clause( 12930, [ =( 'c_Message_Oparts'( 'c_Message_Osynth'(
% 1.87/2.25 'c_Message_Oanalz'( X ) ) ), 'c_union'( 'c_Message_Oparts'( X ),
% 1.87/2.25 'c_Message_Osynth'( 'c_Message_Oanalz'( X ) ), 'tc_Message_Omsg' ) ) ] )
% 1.87/2.25 , 0, substitution( 0, [ :=( X, X )] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 subsumption(
% 1.87/2.25 clause( 32, [ =( 'c_union'( 'c_Message_Oparts'( X ), 'c_Message_Osynth'(
% 1.87/2.25 'c_Message_Oanalz'( X ) ), 'tc_Message_Omsg' ), 'c_Message_Oparts'(
% 1.87/2.25 'c_Message_Osynth'( 'c_Message_Oanalz'( X ) ) ) ) ] )
% 1.87/2.25 , clause( 12931, [ =( 'c_union'( 'c_Message_Oparts'( X ),
% 1.87/2.25 'c_Message_Osynth'( 'c_Message_Oanalz'( X ) ), 'tc_Message_Omsg' ),
% 1.87/2.25 'c_Message_Oparts'( 'c_Message_Osynth'( 'c_Message_Oanalz'( X ) ) ) ) ]
% 1.87/2.25 )
% 1.87/2.25 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 resolution(
% 1.87/2.25 clause( 12932, [ 'c_lessequals'( 'c_Message_OkeysFor'( 'c_Message_Oanalz'(
% 1.87/2.25 X ) ), 'c_Message_OkeysFor'( 'c_Message_Oparts'( X ) ), 'tc_set'(
% 1.87/2.25 'tc_nat' ) ) ] )
% 1.87/2.25 , clause( 5, [ ~( 'c_lessequals'( X, Y, 'tc_set'( 'tc_Message_Omsg' ) ) ),
% 1.87/2.25 'c_lessequals'( 'c_Message_OkeysFor'( X ), 'c_Message_OkeysFor'( Y ),
% 1.87/2.25 'tc_set'( 'tc_nat' ) ) ] )
% 1.87/2.25 , 0, clause( 3, [ 'c_lessequals'( 'c_Message_Oanalz'( X ),
% 1.87/2.25 'c_Message_Oparts'( X ), 'tc_set'( 'tc_Message_Omsg' ) ) ] )
% 1.87/2.25 , 0, substitution( 0, [ :=( X, 'c_Message_Oanalz'( X ) ), :=( Y,
% 1.87/2.25 'c_Message_Oparts'( X ) )] ), substitution( 1, [ :=( X, X )] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 subsumption(
% 1.87/2.25 clause( 37, [ 'c_lessequals'( 'c_Message_OkeysFor'( 'c_Message_Oanalz'( X )
% 1.87/2.25 ), 'c_Message_OkeysFor'( 'c_Message_Oparts'( X ) ), 'tc_set'( 'tc_nat' )
% 1.87/2.25 ) ] )
% 1.87/2.25 , clause( 12932, [ 'c_lessequals'( 'c_Message_OkeysFor'( 'c_Message_Oanalz'(
% 1.87/2.25 X ) ), 'c_Message_OkeysFor'( 'c_Message_Oparts'( X ) ), 'tc_set'(
% 1.87/2.25 'tc_nat' ) ) ] )
% 1.87/2.25 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 resolution(
% 1.87/2.25 clause( 12933, [ 'c_in'( X, 'c_union'( Z, 'c_Message_OkeysFor'( Y ),
% 1.87/2.25 'tc_nat' ), 'tc_nat' ), ~( 'c_in'( X, 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Osynth'( Y ) ), 'tc_nat' ) ), 'c_in'( 'c_Message_Omsg_OKey'(
% 1.87/2.25 'v_sko__uhi'( Y, X ) ), Y, 'tc_Message_Omsg' ) ] )
% 1.87/2.25 , clause( 14, [ ~( 'c_in'( X, Y, Z ) ), 'c_in'( X, 'c_union'( T, Y, Z ), Z
% 1.87/2.25 ) ] )
% 1.87/2.25 , 0, clause( 0, [ ~( 'c_in'( X, 'c_Message_OkeysFor'( 'c_Message_Osynth'( Y
% 1.87/2.25 ) ), 'tc_nat' ) ), 'c_in'( X, 'c_Message_OkeysFor'( Y ), 'tc_nat' ),
% 1.87/2.25 'c_in'( 'c_Message_Omsg_OKey'( 'v_sko__uhi'( Y, X ) ), Y,
% 1.87/2.25 'tc_Message_Omsg' ) ] )
% 1.87/2.25 , 1, substitution( 0, [ :=( X, X ), :=( Y, 'c_Message_OkeysFor'( Y ) ),
% 1.87/2.25 :=( Z, 'tc_nat' ), :=( T, Z )] ), substitution( 1, [ :=( X, X ), :=( Y, Y
% 1.87/2.25 )] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 subsumption(
% 1.87/2.25 clause( 42, [ 'c_in'( X, 'c_union'( Y, 'c_Message_OkeysFor'( Z ), 'tc_nat'
% 1.87/2.25 ), 'tc_nat' ), ~( 'c_in'( X, 'c_Message_OkeysFor'( 'c_Message_Osynth'( Z
% 1.87/2.25 ) ), 'tc_nat' ) ), 'c_in'( 'c_Message_Omsg_OKey'( 'v_sko__uhi'( Z, X ) )
% 1.87/2.25 , Z, 'tc_Message_Omsg' ) ] )
% 1.87/2.25 , clause( 12933, [ 'c_in'( X, 'c_union'( Z, 'c_Message_OkeysFor'( Y ),
% 1.87/2.25 'tc_nat' ), 'tc_nat' ), ~( 'c_in'( X, 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Osynth'( Y ) ), 'tc_nat' ) ), 'c_in'( 'c_Message_Omsg_OKey'(
% 1.87/2.25 'v_sko__uhi'( Y, X ) ), Y, 'tc_Message_Omsg' ) ] )
% 1.87/2.25 , substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] ),
% 1.87/2.25 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 paramod(
% 1.87/2.25 clause( 12936, [ 'c_in'( X, 'c_Message_OkeysFor'( 'c_union'( Y, Z,
% 1.87/2.25 'tc_Message_Omsg' ) ), 'tc_nat' ), ~( 'c_in'( X, 'c_Message_OkeysFor'( Z
% 1.87/2.25 ), 'tc_nat' ) ) ] )
% 1.87/2.25 , clause( 6, [ =( 'c_union'( 'c_Message_OkeysFor'( X ),
% 1.87/2.25 'c_Message_OkeysFor'( Y ), 'tc_nat' ), 'c_Message_OkeysFor'( 'c_union'( X
% 1.87/2.25 , Y, 'tc_Message_Omsg' ) ) ) ] )
% 1.87/2.25 , 0, clause( 14, [ ~( 'c_in'( X, Y, Z ) ), 'c_in'( X, 'c_union'( T, Y, Z )
% 1.87/2.25 , Z ) ] )
% 1.87/2.25 , 1, 2, substitution( 0, [ :=( X, Y ), :=( Y, Z )] ), substitution( 1, [
% 1.87/2.25 :=( X, X ), :=( Y, 'c_Message_OkeysFor'( Z ) ), :=( Z, 'tc_nat' ), :=( T
% 1.87/2.25 , 'c_Message_OkeysFor'( Y ) )] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 subsumption(
% 1.87/2.25 clause( 47, [ ~( 'c_in'( Z, 'c_Message_OkeysFor'( Y ), 'tc_nat' ) ), 'c_in'(
% 1.87/2.25 Z, 'c_Message_OkeysFor'( 'c_union'( X, Y, 'tc_Message_Omsg' ) ), 'tc_nat'
% 1.87/2.25 ) ] )
% 1.87/2.25 , clause( 12936, [ 'c_in'( X, 'c_Message_OkeysFor'( 'c_union'( Y, Z,
% 1.87/2.25 'tc_Message_Omsg' ) ), 'tc_nat' ), ~( 'c_in'( X, 'c_Message_OkeysFor'( Z
% 1.87/2.25 ), 'tc_nat' ) ) ] )
% 1.87/2.25 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 1.87/2.25 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 resolution(
% 1.87/2.25 clause( 12937, [ 'c_in'( 'v_X', 'c_union'( 'c_Message_Osynth'(
% 1.87/2.25 'c_Message_Oanalz'( 'v_H' ) ), X, 'tc_Message_Omsg' ), 'tc_Message_Omsg'
% 1.87/2.25 ) ] )
% 1.87/2.25 , clause( 13, [ ~( 'c_in'( X, Y, Z ) ), 'c_in'( X, 'c_union'( Y, T, Z ), Z
% 1.87/2.25 ) ] )
% 1.87/2.25 , 0, clause( 16, [ 'c_in'( 'v_X', 'c_Message_Osynth'( 'c_Message_Oanalz'(
% 1.87/2.25 'v_H' ) ), 'tc_Message_Omsg' ) ] )
% 1.87/2.25 , 0, substitution( 0, [ :=( X, 'v_X' ), :=( Y, 'c_Message_Osynth'(
% 1.87/2.25 'c_Message_Oanalz'( 'v_H' ) ) ), :=( Z, 'tc_Message_Omsg' ), :=( T, X )] )
% 1.87/2.25 , substitution( 1, [] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 subsumption(
% 1.87/2.25 clause( 60, [ 'c_in'( 'v_X', 'c_union'( 'c_Message_Osynth'(
% 1.87/2.25 'c_Message_Oanalz'( 'v_H' ) ), X, 'tc_Message_Omsg' ), 'tc_Message_Omsg'
% 1.87/2.25 ) ] )
% 1.87/2.25 , clause( 12937, [ 'c_in'( 'v_X', 'c_union'( 'c_Message_Osynth'(
% 1.87/2.25 'c_Message_Oanalz'( 'v_H' ) ), X, 'tc_Message_Omsg' ), 'tc_Message_Omsg'
% 1.87/2.25 ) ] )
% 1.87/2.25 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 paramod(
% 1.87/2.25 clause( 12939, [ 'c_in'( X, 'c_Message_OkeysFor'( 'c_union'( Y, Z,
% 1.87/2.25 'tc_Message_Omsg' ) ), 'tc_nat' ), ~( 'c_in'( X, 'c_Message_OkeysFor'( Y
% 1.87/2.25 ), 'tc_nat' ) ) ] )
% 1.87/2.25 , clause( 6, [ =( 'c_union'( 'c_Message_OkeysFor'( X ),
% 1.87/2.25 'c_Message_OkeysFor'( Y ), 'tc_nat' ), 'c_Message_OkeysFor'( 'c_union'( X
% 1.87/2.25 , Y, 'tc_Message_Omsg' ) ) ) ] )
% 1.87/2.25 , 0, clause( 13, [ ~( 'c_in'( X, Y, Z ) ), 'c_in'( X, 'c_union'( Y, T, Z )
% 1.87/2.25 , Z ) ] )
% 1.87/2.25 , 1, 2, substitution( 0, [ :=( X, Y ), :=( Y, Z )] ), substitution( 1, [
% 1.87/2.25 :=( X, X ), :=( Y, 'c_Message_OkeysFor'( Y ) ), :=( Z, 'tc_nat' ), :=( T
% 1.87/2.25 , 'c_Message_OkeysFor'( Z ) )] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 subsumption(
% 1.87/2.25 clause( 61, [ ~( 'c_in'( Z, 'c_Message_OkeysFor'( X ), 'tc_nat' ) ), 'c_in'(
% 1.87/2.25 Z, 'c_Message_OkeysFor'( 'c_union'( X, Y, 'tc_Message_Omsg' ) ), 'tc_nat'
% 1.87/2.25 ) ] )
% 1.87/2.25 , clause( 12939, [ 'c_in'( X, 'c_Message_OkeysFor'( 'c_union'( Y, Z,
% 1.87/2.25 'tc_Message_Omsg' ) ), 'tc_nat' ), ~( 'c_in'( X, 'c_Message_OkeysFor'( Y
% 1.87/2.25 ), 'tc_nat' ) ) ] )
% 1.87/2.25 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 1.87/2.25 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 paramod(
% 1.87/2.25 clause( 12941, [ 'c_lessequals'( 'c_Message_Oparts'( 'c_insert'( X, Y,
% 1.87/2.25 'tc_Message_Omsg' ) ), 'c_Message_Oparts'( 'c_union'( Z, Y,
% 1.87/2.25 'tc_Message_Omsg' ) ), 'tc_set'( 'tc_Message_Omsg' ) ), ~( 'c_in'( X, Z,
% 1.87/2.25 'tc_Message_Omsg' ) ) ] )
% 1.87/2.25 , clause( 10, [ =( 'c_union'( 'c_Message_Oparts'( X ), 'c_Message_Oparts'(
% 1.87/2.25 Y ), 'tc_Message_Omsg' ), 'c_Message_Oparts'( 'c_union'( X, Y,
% 1.87/2.25 'tc_Message_Omsg' ) ) ) ] )
% 1.87/2.25 , 0, clause( 8, [ ~( 'c_in'( X, Y, 'tc_Message_Omsg' ) ), 'c_lessequals'(
% 1.87/2.25 'c_Message_Oparts'( 'c_insert'( X, Z, 'tc_Message_Omsg' ) ), 'c_union'(
% 1.87/2.25 'c_Message_Oparts'( Y ), 'c_Message_Oparts'( Z ), 'tc_Message_Omsg' ),
% 1.87/2.25 'tc_set'( 'tc_Message_Omsg' ) ) ] )
% 1.87/2.25 , 1, 6, substitution( 0, [ :=( X, Z ), :=( Y, Y )] ), substitution( 1, [
% 1.87/2.25 :=( X, X ), :=( Y, Z ), :=( Z, Y )] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 subsumption(
% 1.87/2.25 clause( 65, [ ~( 'c_in'( X, Y, 'tc_Message_Omsg' ) ), 'c_lessequals'(
% 1.87/2.25 'c_Message_Oparts'( 'c_insert'( X, Z, 'tc_Message_Omsg' ) ),
% 1.87/2.25 'c_Message_Oparts'( 'c_union'( Y, Z, 'tc_Message_Omsg' ) ), 'tc_set'(
% 1.87/2.25 'tc_Message_Omsg' ) ) ] )
% 1.87/2.25 , clause( 12941, [ 'c_lessequals'( 'c_Message_Oparts'( 'c_insert'( X, Y,
% 1.87/2.25 'tc_Message_Omsg' ) ), 'c_Message_Oparts'( 'c_union'( Z, Y,
% 1.87/2.25 'tc_Message_Omsg' ) ), 'tc_set'( 'tc_Message_Omsg' ) ), ~( 'c_in'( X, Z,
% 1.87/2.25 'tc_Message_Omsg' ) ) ] )
% 1.87/2.25 , substitution( 0, [ :=( X, X ), :=( Y, Z ), :=( Z, Y )] ),
% 1.87/2.25 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 resolution(
% 1.87/2.25 clause( 12942, [ ~( 'c_in'( X, 'c_Message_OkeysFor'( 'c_Message_Oanalz'( Y
% 1.87/2.25 ) ), 'tc_nat' ) ), 'c_in'( X, 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.25 Y ) ), 'tc_nat' ) ] )
% 1.87/2.25 , clause( 11, [ ~( 'c_in'( X, Y, Z ) ), ~( 'c_lessequals'( Y, T, 'tc_set'(
% 1.87/2.25 Z ) ) ), 'c_in'( X, T, Z ) ] )
% 1.87/2.25 , 1, clause( 37, [ 'c_lessequals'( 'c_Message_OkeysFor'( 'c_Message_Oanalz'(
% 1.87/2.25 X ) ), 'c_Message_OkeysFor'( 'c_Message_Oparts'( X ) ), 'tc_set'(
% 1.87/2.25 'tc_nat' ) ) ] )
% 1.87/2.25 , 0, substitution( 0, [ :=( X, X ), :=( Y, 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oanalz'( Y ) ) ), :=( Z, 'tc_nat' ), :=( T,
% 1.87/2.25 'c_Message_OkeysFor'( 'c_Message_Oparts'( Y ) ) )] ), substitution( 1, [
% 1.87/2.25 :=( X, Y )] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 subsumption(
% 1.87/2.25 clause( 110, [ ~( 'c_in'( X, 'c_Message_OkeysFor'( 'c_Message_Oanalz'( Y )
% 1.87/2.25 ), 'tc_nat' ) ), 'c_in'( X, 'c_Message_OkeysFor'( 'c_Message_Oparts'( Y
% 1.87/2.25 ) ), 'tc_nat' ) ] )
% 1.87/2.25 , clause( 12942, [ ~( 'c_in'( X, 'c_Message_OkeysFor'( 'c_Message_Oanalz'(
% 1.87/2.25 Y ) ), 'tc_nat' ) ), 'c_in'( X, 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.25 Y ) ), 'tc_nat' ) ] )
% 1.87/2.25 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.87/2.25 ), ==>( 1, 1 )] ) ).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 resolution(
% 1.87/2.25 clause( 12943, [ ~( 'c_in'( X, 'c_Message_OkeysFor'( Y ), 'tc_nat' ) ),
% 1.87/2.25 'c_in'( X, 'c_Message_OkeysFor'( Z ), 'tc_nat' ), ~( 'c_lessequals'( Y, Z
% 1.87/2.25 , 'tc_set'( 'tc_Message_Omsg' ) ) ) ] )
% 1.87/2.25 , clause( 11, [ ~( 'c_in'( X, Y, Z ) ), ~( 'c_lessequals'( Y, T, 'tc_set'(
% 1.87/2.25 Z ) ) ), 'c_in'( X, T, Z ) ] )
% 1.87/2.25 , 1, clause( 5, [ ~( 'c_lessequals'( X, Y, 'tc_set'( 'tc_Message_Omsg' ) )
% 1.87/2.25 ), 'c_lessequals'( 'c_Message_OkeysFor'( X ), 'c_Message_OkeysFor'( Y )
% 1.87/2.25 , 'tc_set'( 'tc_nat' ) ) ] )
% 1.87/2.25 , 1, substitution( 0, [ :=( X, X ), :=( Y, 'c_Message_OkeysFor'( Y ) ),
% 1.87/2.25 :=( Z, 'tc_nat' ), :=( T, 'c_Message_OkeysFor'( Z ) )] ), substitution( 1
% 1.87/2.25 , [ :=( X, Y ), :=( Y, Z )] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 subsumption(
% 1.87/2.25 clause( 111, [ ~( 'c_in'( X, 'c_Message_OkeysFor'( Y ), 'tc_nat' ) ),
% 1.87/2.25 'c_in'( X, 'c_Message_OkeysFor'( Z ), 'tc_nat' ), ~( 'c_lessequals'( Y, Z
% 1.87/2.25 , 'tc_set'( 'tc_Message_Omsg' ) ) ) ] )
% 1.87/2.25 , clause( 12943, [ ~( 'c_in'( X, 'c_Message_OkeysFor'( Y ), 'tc_nat' ) ),
% 1.87/2.25 'c_in'( X, 'c_Message_OkeysFor'( Z ), 'tc_nat' ), ~( 'c_lessequals'( Y, Z
% 1.87/2.25 , 'tc_set'( 'tc_Message_Omsg' ) ) ) ] )
% 1.87/2.25 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 1.87/2.25 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] ) ).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 resolution(
% 1.87/2.25 clause( 12944, [ ~( 'c_in'( 'v_K', 'c_union'( X, 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oparts'( 'c_union'( 'v_G', 'v_H', 'tc_Message_Omsg' ) ) ),
% 1.87/2.25 'tc_nat' ), 'tc_nat' ) ), 'c_in'( 'v_K', X, 'tc_nat' ) ] )
% 1.87/2.25 , clause( 17, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.25 'c_union'( 'v_G', 'v_H', 'tc_Message_Omsg' ) ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , 0, clause( 12, [ ~( 'c_in'( X, 'c_union'( Y, Z, T ), T ) ), 'c_in'( X, Z
% 1.87/2.25 , T ), 'c_in'( X, Y, T ) ] )
% 1.87/2.25 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, 'v_K' ), :=( Y, X ),
% 1.87/2.25 :=( Z, 'c_Message_OkeysFor'( 'c_Message_Oparts'( 'c_union'( 'v_G', 'v_H'
% 1.87/2.25 , 'tc_Message_Omsg' ) ) ) ), :=( T, 'tc_nat' )] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 subsumption(
% 1.87/2.25 clause( 156, [ ~( 'c_in'( 'v_K', 'c_union'( X, 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oparts'( 'c_union'( 'v_G', 'v_H', 'tc_Message_Omsg' ) ) ),
% 1.87/2.25 'tc_nat' ), 'tc_nat' ) ), 'c_in'( 'v_K', X, 'tc_nat' ) ] )
% 1.87/2.25 , clause( 12944, [ ~( 'c_in'( 'v_K', 'c_union'( X, 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oparts'( 'c_union'( 'v_G', 'v_H', 'tc_Message_Omsg' ) ) ),
% 1.87/2.25 'tc_nat' ), 'tc_nat' ) ), 'c_in'( 'v_K', X, 'tc_nat' ) ] )
% 1.87/2.25 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 1.87/2.25 1 )] ) ).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 paramod(
% 1.87/2.25 clause( 12947, [ 'c_in'( X, 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.25 'c_union'( Y, Z, 'tc_Message_Omsg' ) ) ), 'tc_nat' ), ~( 'c_in'( X,
% 1.87/2.25 'c_Message_OkeysFor'( 'c_Message_Oparts'( Z ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , clause( 10, [ =( 'c_union'( 'c_Message_Oparts'( X ), 'c_Message_Oparts'(
% 1.87/2.25 Y ), 'tc_Message_Omsg' ), 'c_Message_Oparts'( 'c_union'( X, Y,
% 1.87/2.25 'tc_Message_Omsg' ) ) ) ] )
% 1.87/2.25 , 0, clause( 47, [ ~( 'c_in'( Z, 'c_Message_OkeysFor'( Y ), 'tc_nat' ) ),
% 1.87/2.25 'c_in'( Z, 'c_Message_OkeysFor'( 'c_union'( X, Y, 'tc_Message_Omsg' ) ),
% 1.87/2.25 'tc_nat' ) ] )
% 1.87/2.25 , 1, 3, substitution( 0, [ :=( X, Y ), :=( Y, Z )] ), substitution( 1, [
% 1.87/2.25 :=( X, 'c_Message_Oparts'( Y ) ), :=( Y, 'c_Message_Oparts'( Z ) ), :=( Z
% 1.87/2.25 , X )] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 subsumption(
% 1.87/2.25 clause( 486, [ ~( 'c_in'( Z, 'c_Message_OkeysFor'( 'c_Message_Oparts'( Y )
% 1.87/2.25 ), 'tc_nat' ) ), 'c_in'( Z, 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.25 'c_union'( X, Y, 'tc_Message_Omsg' ) ) ), 'tc_nat' ) ] )
% 1.87/2.25 , clause( 12947, [ 'c_in'( X, 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.25 'c_union'( Y, Z, 'tc_Message_Omsg' ) ) ), 'tc_nat' ), ~( 'c_in'( X,
% 1.87/2.25 'c_Message_OkeysFor'( 'c_Message_Oparts'( Z ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 1.87/2.25 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 paramod(
% 1.87/2.25 clause( 12949, [ 'c_in'( X, 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.25 'c_union'( Y, Z, 'tc_Message_Omsg' ) ) ), 'tc_nat' ), ~( 'c_in'( X,
% 1.87/2.25 'c_Message_OkeysFor'( 'c_Message_Oparts'( Y ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , clause( 10, [ =( 'c_union'( 'c_Message_Oparts'( X ), 'c_Message_Oparts'(
% 1.87/2.25 Y ), 'tc_Message_Omsg' ), 'c_Message_Oparts'( 'c_union'( X, Y,
% 1.87/2.25 'tc_Message_Omsg' ) ) ) ] )
% 1.87/2.25 , 0, clause( 61, [ ~( 'c_in'( Z, 'c_Message_OkeysFor'( X ), 'tc_nat' ) ),
% 1.87/2.25 'c_in'( Z, 'c_Message_OkeysFor'( 'c_union'( X, Y, 'tc_Message_Omsg' ) ),
% 1.87/2.25 'tc_nat' ) ] )
% 1.87/2.25 , 1, 3, substitution( 0, [ :=( X, Y ), :=( Y, Z )] ), substitution( 1, [
% 1.87/2.25 :=( X, 'c_Message_Oparts'( Y ) ), :=( Y, 'c_Message_Oparts'( Z ) ), :=( Z
% 1.87/2.25 , X )] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 subsumption(
% 1.87/2.25 clause( 665, [ ~( 'c_in'( Z, 'c_Message_OkeysFor'( 'c_Message_Oparts'( X )
% 1.87/2.25 ), 'tc_nat' ) ), 'c_in'( Z, 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.25 'c_union'( X, Y, 'tc_Message_Omsg' ) ) ), 'tc_nat' ) ] )
% 1.87/2.25 , clause( 12949, [ 'c_in'( X, 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.25 'c_union'( Y, Z, 'tc_Message_Omsg' ) ) ), 'tc_nat' ), ~( 'c_in'( X,
% 1.87/2.25 'c_Message_OkeysFor'( 'c_Message_Oparts'( Y ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, Y )] ),
% 1.87/2.25 permutation( 0, [ ==>( 0, 1 ), ==>( 1, 0 )] ) ).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 resolution(
% 1.87/2.25 clause( 12950, [ 'c_in'( 'v_K', 'c_Message_OkeysFor'( X ), 'tc_nat' ), ~(
% 1.87/2.25 'c_lessequals'( 'c_Message_Oparts'( 'c_insert'( 'v_X', 'v_G',
% 1.87/2.25 'tc_Message_Omsg' ) ), X, 'tc_set'( 'tc_Message_Omsg' ) ) ) ] )
% 1.87/2.25 , clause( 111, [ ~( 'c_in'( X, 'c_Message_OkeysFor'( Y ), 'tc_nat' ) ),
% 1.87/2.25 'c_in'( X, 'c_Message_OkeysFor'( Z ), 'tc_nat' ), ~( 'c_lessequals'( Y, Z
% 1.87/2.25 , 'tc_set'( 'tc_Message_Omsg' ) ) ) ] )
% 1.87/2.25 , 0, clause( 15, [ 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.25 'c_insert'( 'v_X', 'v_G', 'tc_Message_Omsg' ) ) ), 'tc_nat' ) ] )
% 1.87/2.25 , 0, substitution( 0, [ :=( X, 'v_K' ), :=( Y, 'c_Message_Oparts'(
% 1.87/2.25 'c_insert'( 'v_X', 'v_G', 'tc_Message_Omsg' ) ) ), :=( Z, X )] ),
% 1.87/2.25 substitution( 1, [] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 subsumption(
% 1.87/2.25 clause( 2300, [ 'c_in'( 'v_K', 'c_Message_OkeysFor'( X ), 'tc_nat' ), ~(
% 1.87/2.25 'c_lessequals'( 'c_Message_Oparts'( 'c_insert'( 'v_X', 'v_G',
% 1.87/2.25 'tc_Message_Omsg' ) ), X, 'tc_set'( 'tc_Message_Omsg' ) ) ) ] )
% 1.87/2.25 , clause( 12950, [ 'c_in'( 'v_K', 'c_Message_OkeysFor'( X ), 'tc_nat' ),
% 1.87/2.25 ~( 'c_lessequals'( 'c_Message_Oparts'( 'c_insert'( 'v_X', 'v_G',
% 1.87/2.25 'tc_Message_Omsg' ) ), X, 'tc_set'( 'tc_Message_Omsg' ) ) ) ] )
% 1.87/2.25 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 1.87/2.25 1 )] ) ).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 resolution(
% 1.87/2.25 clause( 12951, [ 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.25 'c_union'( X, 'v_G', 'tc_Message_Omsg' ) ) ), 'tc_nat' ), ~( 'c_in'(
% 1.87/2.25 'v_X', X, 'tc_Message_Omsg' ) ) ] )
% 1.87/2.25 , clause( 2300, [ 'c_in'( 'v_K', 'c_Message_OkeysFor'( X ), 'tc_nat' ), ~(
% 1.87/2.25 'c_lessequals'( 'c_Message_Oparts'( 'c_insert'( 'v_X', 'v_G',
% 1.87/2.25 'tc_Message_Omsg' ) ), X, 'tc_set'( 'tc_Message_Omsg' ) ) ) ] )
% 1.87/2.25 , 1, clause( 65, [ ~( 'c_in'( X, Y, 'tc_Message_Omsg' ) ), 'c_lessequals'(
% 1.87/2.25 'c_Message_Oparts'( 'c_insert'( X, Z, 'tc_Message_Omsg' ) ),
% 1.87/2.25 'c_Message_Oparts'( 'c_union'( Y, Z, 'tc_Message_Omsg' ) ), 'tc_set'(
% 1.87/2.25 'tc_Message_Omsg' ) ) ] )
% 1.87/2.25 , 1, substitution( 0, [ :=( X, 'c_Message_Oparts'( 'c_union'( X, 'v_G',
% 1.87/2.25 'tc_Message_Omsg' ) ) )] ), substitution( 1, [ :=( X, 'v_X' ), :=( Y, X )
% 1.87/2.25 , :=( Z, 'v_G' )] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 subsumption(
% 1.87/2.25 clause( 3549, [ 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.25 'c_union'( X, 'v_G', 'tc_Message_Omsg' ) ) ), 'tc_nat' ), ~( 'c_in'(
% 1.87/2.25 'v_X', X, 'tc_Message_Omsg' ) ) ] )
% 1.87/2.25 , clause( 12951, [ 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.25 'c_union'( X, 'v_G', 'tc_Message_Omsg' ) ) ), 'tc_nat' ), ~( 'c_in'(
% 1.87/2.25 'v_X', X, 'tc_Message_Omsg' ) ) ] )
% 1.87/2.25 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 1.87/2.25 1 )] ) ).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 resolution(
% 1.87/2.25 clause( 12952, [ 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.25 'c_union'( 'c_union'( 'c_Message_Osynth'( 'c_Message_Oanalz'( 'v_H' ) ),
% 1.87/2.25 X, 'tc_Message_Omsg' ), 'v_G', 'tc_Message_Omsg' ) ) ), 'tc_nat' ) ] )
% 1.87/2.25 , clause( 3549, [ 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.25 'c_union'( X, 'v_G', 'tc_Message_Omsg' ) ) ), 'tc_nat' ), ~( 'c_in'(
% 1.87/2.25 'v_X', X, 'tc_Message_Omsg' ) ) ] )
% 1.87/2.25 , 1, clause( 60, [ 'c_in'( 'v_X', 'c_union'( 'c_Message_Osynth'(
% 1.87/2.25 'c_Message_Oanalz'( 'v_H' ) ), X, 'tc_Message_Omsg' ), 'tc_Message_Omsg'
% 1.87/2.25 ) ] )
% 1.87/2.25 , 0, substitution( 0, [ :=( X, 'c_union'( 'c_Message_Osynth'(
% 1.87/2.25 'c_Message_Oanalz'( 'v_H' ) ), X, 'tc_Message_Omsg' ) )] ),
% 1.87/2.25 substitution( 1, [ :=( X, X )] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 subsumption(
% 1.87/2.25 clause( 3575, [ 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.25 'c_union'( 'c_union'( 'c_Message_Osynth'( 'c_Message_Oanalz'( 'v_H' ) ),
% 1.87/2.25 X, 'tc_Message_Omsg' ), 'v_G', 'tc_Message_Omsg' ) ) ), 'tc_nat' ) ] )
% 1.87/2.25 , clause( 12952, [ 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.25 'c_union'( 'c_union'( 'c_Message_Osynth'( 'c_Message_Oanalz'( 'v_H' ) ),
% 1.87/2.25 X, 'tc_Message_Omsg' ), 'v_G', 'tc_Message_Omsg' ) ) ), 'tc_nat' ) ] )
% 1.87/2.25 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 resolution(
% 1.87/2.25 clause( 12953, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.25 'v_H' ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , clause( 17, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.25 'c_union'( 'v_G', 'v_H', 'tc_Message_Omsg' ) ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , 0, clause( 486, [ ~( 'c_in'( Z, 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.25 Y ) ), 'tc_nat' ) ), 'c_in'( Z, 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.25 'c_union'( X, Y, 'tc_Message_Omsg' ) ) ), 'tc_nat' ) ] )
% 1.87/2.25 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, 'v_G' ), :=( Y, 'v_H'
% 1.87/2.25 ), :=( Z, 'v_K' )] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 subsumption(
% 1.87/2.25 clause( 4512, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.25 'v_H' ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , clause( 12953, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oparts'( 'v_H' ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 resolution(
% 1.87/2.25 clause( 12954, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_Message_Oanalz'(
% 1.87/2.25 'v_H' ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , clause( 4512, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oparts'( 'v_H' ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , 0, clause( 110, [ ~( 'c_in'( X, 'c_Message_OkeysFor'( 'c_Message_Oanalz'(
% 1.87/2.25 Y ) ), 'tc_nat' ) ), 'c_in'( X, 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.25 Y ) ), 'tc_nat' ) ] )
% 1.87/2.25 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, 'v_K' ), :=( Y, 'v_H'
% 1.87/2.25 )] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 subsumption(
% 1.87/2.25 clause( 4527, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_Message_Oanalz'(
% 1.87/2.25 'v_H' ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , clause( 12954, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oanalz'( 'v_H' ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 resolution(
% 1.87/2.25 clause( 12956, [ ~( 'c_in'( 'v_K', 'c_union'( 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oparts'( 'v_H' ) ), X, 'tc_nat' ), 'tc_nat' ) ), 'c_in'( 'v_K'
% 1.87/2.25 , X, 'tc_nat' ) ] )
% 1.87/2.25 , clause( 4512, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oparts'( 'v_H' ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , 0, clause( 12, [ ~( 'c_in'( X, 'c_union'( Y, Z, T ), T ) ), 'c_in'( X, Z
% 1.87/2.25 , T ), 'c_in'( X, Y, T ) ] )
% 1.87/2.25 , 2, substitution( 0, [] ), substitution( 1, [ :=( X, 'v_K' ), :=( Y,
% 1.87/2.25 'c_Message_OkeysFor'( 'c_Message_Oparts'( 'v_H' ) ) ), :=( Z, X ), :=( T
% 1.87/2.25 , 'tc_nat' )] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 subsumption(
% 1.87/2.25 clause( 4530, [ ~( 'c_in'( 'v_K', 'c_union'( 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oparts'( 'v_H' ) ), X, 'tc_nat' ), 'tc_nat' ) ), 'c_in'( 'v_K'
% 1.87/2.25 , X, 'tc_nat' ) ] )
% 1.87/2.25 , clause( 12956, [ ~( 'c_in'( 'v_K', 'c_union'( 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oparts'( 'v_H' ) ), X, 'tc_nat' ), 'tc_nat' ) ), 'c_in'( 'v_K'
% 1.87/2.25 , X, 'tc_nat' ) ] )
% 1.87/2.25 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 1.87/2.25 1 )] ) ).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 eqswap(
% 1.87/2.25 clause( 12957, [ =( 'c_Message_OinvKey'( Y ), 'v_sko__uhi'( X, Y ) ), ~(
% 1.87/2.25 'c_in'( Y, 'c_Message_OkeysFor'( 'c_Message_Osynth'( X ) ), 'tc_nat' ) )
% 1.87/2.25 , 'c_in'( Y, 'c_Message_OkeysFor'( X ), 'tc_nat' ) ] )
% 1.87/2.25 , clause( 29, [ =( 'v_sko__uhi'( X, Y ), 'c_Message_OinvKey'( Y ) ), ~(
% 1.87/2.25 'c_in'( Y, 'c_Message_OkeysFor'( 'c_Message_Osynth'( X ) ), 'tc_nat' ) )
% 1.87/2.25 , 'c_in'( Y, 'c_Message_OkeysFor'( X ), 'tc_nat' ) ] )
% 1.87/2.25 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 resolution(
% 1.87/2.25 clause( 12958, [ =( 'c_Message_OinvKey'( 'v_K' ), 'v_sko__uhi'(
% 1.87/2.25 'c_Message_Oanalz'( 'v_H' ), 'v_K' ) ), ~( 'c_in'( 'v_K',
% 1.87/2.25 'c_Message_OkeysFor'( 'c_Message_Osynth'( 'c_Message_Oanalz'( 'v_H' ) ) )
% 1.87/2.25 , 'tc_nat' ) ) ] )
% 1.87/2.25 , clause( 4527, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oanalz'( 'v_H' ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , 0, clause( 12957, [ =( 'c_Message_OinvKey'( Y ), 'v_sko__uhi'( X, Y ) ),
% 1.87/2.25 ~( 'c_in'( Y, 'c_Message_OkeysFor'( 'c_Message_Osynth'( X ) ), 'tc_nat' )
% 1.87/2.25 ), 'c_in'( Y, 'c_Message_OkeysFor'( X ), 'tc_nat' ) ] )
% 1.87/2.25 , 2, substitution( 0, [] ), substitution( 1, [ :=( X, 'c_Message_Oanalz'(
% 1.87/2.25 'v_H' ) ), :=( Y, 'v_K' )] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 eqswap(
% 1.87/2.25 clause( 12959, [ =( 'v_sko__uhi'( 'c_Message_Oanalz'( 'v_H' ), 'v_K' ),
% 1.87/2.25 'c_Message_OinvKey'( 'v_K' ) ), ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Osynth'( 'c_Message_Oanalz'( 'v_H' ) ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , clause( 12958, [ =( 'c_Message_OinvKey'( 'v_K' ), 'v_sko__uhi'(
% 1.87/2.25 'c_Message_Oanalz'( 'v_H' ), 'v_K' ) ), ~( 'c_in'( 'v_K',
% 1.87/2.25 'c_Message_OkeysFor'( 'c_Message_Osynth'( 'c_Message_Oanalz'( 'v_H' ) ) )
% 1.87/2.25 , 'tc_nat' ) ) ] )
% 1.87/2.25 , 0, substitution( 0, [] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 subsumption(
% 1.87/2.25 clause( 4542, [ =( 'v_sko__uhi'( 'c_Message_Oanalz'( 'v_H' ), 'v_K' ),
% 1.87/2.25 'c_Message_OinvKey'( 'v_K' ) ), ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Osynth'( 'c_Message_Oanalz'( 'v_H' ) ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , clause( 12959, [ =( 'v_sko__uhi'( 'c_Message_Oanalz'( 'v_H' ), 'v_K' ),
% 1.87/2.25 'c_Message_OinvKey'( 'v_K' ) ), ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Osynth'( 'c_Message_Oanalz'( 'v_H' ) ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] )
% 1.87/2.25 ).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 resolution(
% 1.87/2.25 clause( 12960, [ ~( 'c_in'( 'v_K', 'c_union'( X, 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oanalz'( 'v_H' ) ), 'tc_nat' ), 'tc_nat' ) ), 'c_in'( 'v_K', X
% 1.87/2.25 , 'tc_nat' ) ] )
% 1.87/2.25 , clause( 4527, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oanalz'( 'v_H' ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , 0, clause( 12, [ ~( 'c_in'( X, 'c_union'( Y, Z, T ), T ) ), 'c_in'( X, Z
% 1.87/2.25 , T ), 'c_in'( X, Y, T ) ] )
% 1.87/2.25 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, 'v_K' ), :=( Y, X ),
% 1.87/2.25 :=( Z, 'c_Message_OkeysFor'( 'c_Message_Oanalz'( 'v_H' ) ) ), :=( T,
% 1.87/2.25 'tc_nat' )] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 subsumption(
% 1.87/2.25 clause( 4543, [ ~( 'c_in'( 'v_K', 'c_union'( X, 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oanalz'( 'v_H' ) ), 'tc_nat' ), 'tc_nat' ) ), 'c_in'( 'v_K', X
% 1.87/2.25 , 'tc_nat' ) ] )
% 1.87/2.25 , clause( 12960, [ ~( 'c_in'( 'v_K', 'c_union'( X, 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oanalz'( 'v_H' ) ), 'tc_nat' ), 'tc_nat' ) ), 'c_in'( 'v_K', X
% 1.87/2.25 , 'tc_nat' ) ] )
% 1.87/2.25 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 1.87/2.25 1 )] ) ).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 resolution(
% 1.87/2.25 clause( 12963, [ ~( 'c_in'( 'v_K', 'c_union'( 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oparts'( 'v_H' ) ), 'c_Message_OkeysFor'( 'c_Message_Oanalz'(
% 1.87/2.25 'v_H' ) ), 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.87/2.25 , clause( 4512, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oparts'( 'v_H' ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , 0, clause( 4543, [ ~( 'c_in'( 'v_K', 'c_union'( X, 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oanalz'( 'v_H' ) ), 'tc_nat' ), 'tc_nat' ) ), 'c_in'( 'v_K', X
% 1.87/2.25 , 'tc_nat' ) ] )
% 1.87/2.25 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oparts'( 'v_H' ) ) )] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 paramod(
% 1.87/2.25 clause( 12964, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_union'(
% 1.87/2.25 'c_Message_Oparts'( 'v_H' ), 'c_Message_Oanalz'( 'v_H' ),
% 1.87/2.25 'tc_Message_Omsg' ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , clause( 6, [ =( 'c_union'( 'c_Message_OkeysFor'( X ),
% 1.87/2.25 'c_Message_OkeysFor'( Y ), 'tc_nat' ), 'c_Message_OkeysFor'( 'c_union'( X
% 1.87/2.25 , Y, 'tc_Message_Omsg' ) ) ) ] )
% 1.87/2.25 , 0, clause( 12963, [ ~( 'c_in'( 'v_K', 'c_union'( 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oparts'( 'v_H' ) ), 'c_Message_OkeysFor'( 'c_Message_Oanalz'(
% 1.87/2.25 'v_H' ) ), 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.87/2.25 , 0, 3, substitution( 0, [ :=( X, 'c_Message_Oparts'( 'v_H' ) ), :=( Y,
% 1.87/2.25 'c_Message_Oanalz'( 'v_H' ) )] ), substitution( 1, [] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 subsumption(
% 1.87/2.25 clause( 4923, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_union'(
% 1.87/2.25 'c_Message_Oparts'( 'v_H' ), 'c_Message_Oanalz'( 'v_H' ),
% 1.87/2.25 'tc_Message_Omsg' ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , clause( 12964, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_union'(
% 1.87/2.25 'c_Message_Oparts'( 'v_H' ), 'c_Message_Oanalz'( 'v_H' ),
% 1.87/2.25 'tc_Message_Omsg' ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 resolution(
% 1.87/2.25 clause( 12966, [ 'c_in'( 'v_K', X, 'tc_nat' ), ~( 'c_in'( 'v_K',
% 1.87/2.25 'c_Message_OkeysFor'( 'c_Message_Osynth'( 'c_Message_Oanalz'( 'v_H' ) ) )
% 1.87/2.25 , 'tc_nat' ) ), 'c_in'( 'c_Message_Omsg_OKey'( 'v_sko__uhi'(
% 1.87/2.25 'c_Message_Oanalz'( 'v_H' ), 'v_K' ) ), 'c_Message_Oanalz'( 'v_H' ),
% 1.87/2.25 'tc_Message_Omsg' ) ] )
% 1.87/2.25 , clause( 4543, [ ~( 'c_in'( 'v_K', 'c_union'( X, 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oanalz'( 'v_H' ) ), 'tc_nat' ), 'tc_nat' ) ), 'c_in'( 'v_K', X
% 1.87/2.25 , 'tc_nat' ) ] )
% 1.87/2.25 , 0, clause( 42, [ 'c_in'( X, 'c_union'( Y, 'c_Message_OkeysFor'( Z ),
% 1.87/2.25 'tc_nat' ), 'tc_nat' ), ~( 'c_in'( X, 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Osynth'( Z ) ), 'tc_nat' ) ), 'c_in'( 'c_Message_Omsg_OKey'(
% 1.87/2.25 'v_sko__uhi'( Z, X ) ), Z, 'tc_Message_Omsg' ) ] )
% 1.87/2.25 , 0, substitution( 0, [ :=( X, X )] ), substitution( 1, [ :=( X, 'v_K' ),
% 1.87/2.25 :=( Y, X ), :=( Z, 'c_Message_Oanalz'( 'v_H' ) )] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 paramod(
% 1.87/2.25 clause( 12967, [ 'c_in'( 'c_Message_Omsg_OKey'( 'c_Message_OinvKey'( 'v_K'
% 1.87/2.25 ) ), 'c_Message_Oanalz'( 'v_H' ), 'tc_Message_Omsg' ), ~( 'c_in'( 'v_K'
% 1.87/2.25 , 'c_Message_OkeysFor'( 'c_Message_Osynth'( 'c_Message_Oanalz'( 'v_H' ) )
% 1.87/2.25 ), 'tc_nat' ) ), 'c_in'( 'v_K', X, 'tc_nat' ), ~( 'c_in'( 'v_K',
% 1.87/2.25 'c_Message_OkeysFor'( 'c_Message_Osynth'( 'c_Message_Oanalz'( 'v_H' ) ) )
% 1.87/2.25 , 'tc_nat' ) ) ] )
% 1.87/2.25 , clause( 4542, [ =( 'v_sko__uhi'( 'c_Message_Oanalz'( 'v_H' ), 'v_K' ),
% 1.87/2.25 'c_Message_OinvKey'( 'v_K' ) ), ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Osynth'( 'c_Message_Oanalz'( 'v_H' ) ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , 0, clause( 12966, [ 'c_in'( 'v_K', X, 'tc_nat' ), ~( 'c_in'( 'v_K',
% 1.87/2.25 'c_Message_OkeysFor'( 'c_Message_Osynth'( 'c_Message_Oanalz'( 'v_H' ) ) )
% 1.87/2.25 , 'tc_nat' ) ), 'c_in'( 'c_Message_Omsg_OKey'( 'v_sko__uhi'(
% 1.87/2.25 'c_Message_Oanalz'( 'v_H' ), 'v_K' ) ), 'c_Message_Oanalz'( 'v_H' ),
% 1.87/2.25 'tc_Message_Omsg' ) ] )
% 1.87/2.25 , 2, 2, substitution( 0, [] ), substitution( 1, [ :=( X, X )] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 factor(
% 1.87/2.25 clause( 12968, [ 'c_in'( 'c_Message_Omsg_OKey'( 'c_Message_OinvKey'( 'v_K'
% 1.87/2.25 ) ), 'c_Message_Oanalz'( 'v_H' ), 'tc_Message_Omsg' ), ~( 'c_in'( 'v_K'
% 1.87/2.25 , 'c_Message_OkeysFor'( 'c_Message_Osynth'( 'c_Message_Oanalz'( 'v_H' ) )
% 1.87/2.25 ), 'tc_nat' ) ), 'c_in'( 'v_K', X, 'tc_nat' ) ] )
% 1.87/2.25 , clause( 12967, [ 'c_in'( 'c_Message_Omsg_OKey'( 'c_Message_OinvKey'(
% 1.87/2.25 'v_K' ) ), 'c_Message_Oanalz'( 'v_H' ), 'tc_Message_Omsg' ), ~( 'c_in'(
% 1.87/2.25 'v_K', 'c_Message_OkeysFor'( 'c_Message_Osynth'( 'c_Message_Oanalz'(
% 1.87/2.25 'v_H' ) ) ), 'tc_nat' ) ), 'c_in'( 'v_K', X, 'tc_nat' ), ~( 'c_in'( 'v_K'
% 1.87/2.25 , 'c_Message_OkeysFor'( 'c_Message_Osynth'( 'c_Message_Oanalz'( 'v_H' ) )
% 1.87/2.25 ), 'tc_nat' ) ) ] )
% 1.87/2.25 , 1, 3, substitution( 0, [ :=( X, X )] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 resolution(
% 1.87/2.25 clause( 12969, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_Message_Osynth'(
% 1.87/2.25 'c_Message_Oanalz'( 'v_H' ) ) ), 'tc_nat' ) ), 'c_in'( 'v_K', X, 'tc_nat'
% 1.87/2.25 ) ] )
% 1.87/2.25 , clause( 30, [ ~( 'c_in'( 'c_Message_Omsg_OKey'( 'c_Message_OinvKey'(
% 1.87/2.25 'v_K' ) ), 'c_Message_Oanalz'( 'v_H' ), 'tc_Message_Omsg' ) ) ] )
% 1.87/2.25 , 0, clause( 12968, [ 'c_in'( 'c_Message_Omsg_OKey'( 'c_Message_OinvKey'(
% 1.87/2.25 'v_K' ) ), 'c_Message_Oanalz'( 'v_H' ), 'tc_Message_Omsg' ), ~( 'c_in'(
% 1.87/2.25 'v_K', 'c_Message_OkeysFor'( 'c_Message_Osynth'( 'c_Message_Oanalz'(
% 1.87/2.25 'v_H' ) ) ), 'tc_nat' ) ), 'c_in'( 'v_K', X, 'tc_nat' ) ] )
% 1.87/2.25 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, X )] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 subsumption(
% 1.87/2.25 clause( 4930, [ 'c_in'( 'v_K', X, 'tc_nat' ), ~( 'c_in'( 'v_K',
% 1.87/2.25 'c_Message_OkeysFor'( 'c_Message_Osynth'( 'c_Message_Oanalz'( 'v_H' ) ) )
% 1.87/2.25 , 'tc_nat' ) ) ] )
% 1.87/2.25 , clause( 12969, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Osynth'( 'c_Message_Oanalz'( 'v_H' ) ) ), 'tc_nat' ) ), 'c_in'(
% 1.87/2.25 'v_K', X, 'tc_nat' ) ] )
% 1.87/2.25 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 1 ), ==>( 1,
% 1.87/2.25 0 )] ) ).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 resolution(
% 1.87/2.25 clause( 12970, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_Message_Osynth'(
% 1.87/2.25 'c_Message_Oanalz'( 'v_H' ) ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , clause( 4923, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_union'(
% 1.87/2.25 'c_Message_Oparts'( 'v_H' ), 'c_Message_Oanalz'( 'v_H' ),
% 1.87/2.25 'tc_Message_Omsg' ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , 0, clause( 4930, [ 'c_in'( 'v_K', X, 'tc_nat' ), ~( 'c_in'( 'v_K',
% 1.87/2.25 'c_Message_OkeysFor'( 'c_Message_Osynth'( 'c_Message_Oanalz'( 'v_H' ) ) )
% 1.87/2.25 , 'tc_nat' ) ) ] )
% 1.87/2.25 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, 'c_Message_OkeysFor'(
% 1.87/2.25 'c_union'( 'c_Message_Oparts'( 'v_H' ), 'c_Message_Oanalz'( 'v_H' ),
% 1.87/2.25 'tc_Message_Omsg' ) ) )] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 subsumption(
% 1.87/2.25 clause( 4936, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_Message_Osynth'(
% 1.87/2.25 'c_Message_Oanalz'( 'v_H' ) ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , clause( 12970, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Osynth'( 'c_Message_Oanalz'( 'v_H' ) ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 resolution(
% 1.87/2.25 clause( 12973, [ ~( 'c_in'( 'v_K', 'c_union'( 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oparts'( 'v_H' ) ), 'c_Message_OkeysFor'( 'c_Message_Osynth'(
% 1.87/2.25 'c_Message_Oanalz'( 'v_H' ) ) ), 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.87/2.25 , clause( 4936, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Osynth'( 'c_Message_Oanalz'( 'v_H' ) ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , 0, clause( 4530, [ ~( 'c_in'( 'v_K', 'c_union'( 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oparts'( 'v_H' ) ), X, 'tc_nat' ), 'tc_nat' ) ), 'c_in'( 'v_K'
% 1.87/2.25 , X, 'tc_nat' ) ] )
% 1.87/2.25 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Osynth'( 'c_Message_Oanalz'( 'v_H' ) ) ) )] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 paramod(
% 1.87/2.25 clause( 12974, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_union'(
% 1.87/2.25 'c_Message_Oparts'( 'v_H' ), 'c_Message_Osynth'( 'c_Message_Oanalz'(
% 1.87/2.25 'v_H' ) ), 'tc_Message_Omsg' ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , clause( 6, [ =( 'c_union'( 'c_Message_OkeysFor'( X ),
% 1.87/2.25 'c_Message_OkeysFor'( Y ), 'tc_nat' ), 'c_Message_OkeysFor'( 'c_union'( X
% 1.87/2.25 , Y, 'tc_Message_Omsg' ) ) ) ] )
% 1.87/2.25 , 0, clause( 12973, [ ~( 'c_in'( 'v_K', 'c_union'( 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oparts'( 'v_H' ) ), 'c_Message_OkeysFor'( 'c_Message_Osynth'(
% 1.87/2.25 'c_Message_Oanalz'( 'v_H' ) ) ), 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.87/2.25 , 0, 3, substitution( 0, [ :=( X, 'c_Message_Oparts'( 'v_H' ) ), :=( Y,
% 1.87/2.25 'c_Message_Osynth'( 'c_Message_Oanalz'( 'v_H' ) ) )] ), substitution( 1
% 1.87/2.25 , [] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 paramod(
% 1.87/2.25 clause( 12975, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.25 'c_Message_Osynth'( 'c_Message_Oanalz'( 'v_H' ) ) ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , clause( 32, [ =( 'c_union'( 'c_Message_Oparts'( X ), 'c_Message_Osynth'(
% 1.87/2.25 'c_Message_Oanalz'( X ) ), 'tc_Message_Omsg' ), 'c_Message_Oparts'(
% 1.87/2.25 'c_Message_Osynth'( 'c_Message_Oanalz'( X ) ) ) ) ] )
% 1.87/2.25 , 0, clause( 12974, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_union'(
% 1.87/2.25 'c_Message_Oparts'( 'v_H' ), 'c_Message_Osynth'( 'c_Message_Oanalz'(
% 1.87/2.25 'v_H' ) ), 'tc_Message_Omsg' ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , 0, 4, substitution( 0, [ :=( X, 'v_H' )] ), substitution( 1, [] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 subsumption(
% 1.87/2.25 clause( 5195, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.25 'c_Message_Osynth'( 'c_Message_Oanalz'( 'v_H' ) ) ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , clause( 12975, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oparts'( 'c_Message_Osynth'( 'c_Message_Oanalz'( 'v_H' ) ) ) )
% 1.87/2.25 , 'tc_nat' ) ) ] )
% 1.87/2.25 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 resolution(
% 1.87/2.25 clause( 12978, [ ~( 'c_in'( 'v_K', 'c_union'( 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oparts'( 'c_Message_Osynth'( 'c_Message_Oanalz'( 'v_H' ) ) ) )
% 1.87/2.25 , 'c_Message_OkeysFor'( 'c_Message_Oparts'( 'c_union'( 'v_G', 'v_H',
% 1.87/2.25 'tc_Message_Omsg' ) ) ), 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.87/2.25 , clause( 5195, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oparts'( 'c_Message_Osynth'( 'c_Message_Oanalz'( 'v_H' ) ) ) )
% 1.87/2.25 , 'tc_nat' ) ) ] )
% 1.87/2.25 , 0, clause( 156, [ ~( 'c_in'( 'v_K', 'c_union'( X, 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oparts'( 'c_union'( 'v_G', 'v_H', 'tc_Message_Omsg' ) ) ),
% 1.87/2.25 'tc_nat' ), 'tc_nat' ) ), 'c_in'( 'v_K', X, 'tc_nat' ) ] )
% 1.87/2.25 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oparts'( 'c_Message_Osynth'( 'c_Message_Oanalz'( 'v_H' ) ) ) )
% 1.87/2.25 )] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 paramod(
% 1.87/2.25 clause( 12979, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_union'(
% 1.87/2.25 'c_Message_Oparts'( 'c_Message_Osynth'( 'c_Message_Oanalz'( 'v_H' ) ) ),
% 1.87/2.25 'c_Message_Oparts'( 'c_union'( 'v_G', 'v_H', 'tc_Message_Omsg' ) ),
% 1.87/2.25 'tc_Message_Omsg' ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , clause( 6, [ =( 'c_union'( 'c_Message_OkeysFor'( X ),
% 1.87/2.25 'c_Message_OkeysFor'( Y ), 'tc_nat' ), 'c_Message_OkeysFor'( 'c_union'( X
% 1.87/2.25 , Y, 'tc_Message_Omsg' ) ) ) ] )
% 1.87/2.25 , 0, clause( 12978, [ ~( 'c_in'( 'v_K', 'c_union'( 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oparts'( 'c_Message_Osynth'( 'c_Message_Oanalz'( 'v_H' ) ) ) )
% 1.87/2.25 , 'c_Message_OkeysFor'( 'c_Message_Oparts'( 'c_union'( 'v_G', 'v_H',
% 1.87/2.25 'tc_Message_Omsg' ) ) ), 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.87/2.25 , 0, 3, substitution( 0, [ :=( X, 'c_Message_Oparts'( 'c_Message_Osynth'(
% 1.87/2.25 'c_Message_Oanalz'( 'v_H' ) ) ) ), :=( Y, 'c_Message_Oparts'( 'c_union'(
% 1.87/2.25 'v_G', 'v_H', 'tc_Message_Omsg' ) ) )] ), substitution( 1, [] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 paramod(
% 1.87/2.25 clause( 12980, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.25 'c_union'( 'c_Message_Osynth'( 'c_Message_Oanalz'( 'v_H' ) ), 'c_union'(
% 1.87/2.25 'v_G', 'v_H', 'tc_Message_Omsg' ), 'tc_Message_Omsg' ) ) ), 'tc_nat' ) )
% 1.87/2.25 ] )
% 1.87/2.25 , clause( 10, [ =( 'c_union'( 'c_Message_Oparts'( X ), 'c_Message_Oparts'(
% 1.87/2.25 Y ), 'tc_Message_Omsg' ), 'c_Message_Oparts'( 'c_union'( X, Y,
% 1.87/2.25 'tc_Message_Omsg' ) ) ) ] )
% 1.87/2.25 , 0, clause( 12979, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_union'(
% 1.87/2.25 'c_Message_Oparts'( 'c_Message_Osynth'( 'c_Message_Oanalz'( 'v_H' ) ) ),
% 1.87/2.25 'c_Message_Oparts'( 'c_union'( 'v_G', 'v_H', 'tc_Message_Omsg' ) ),
% 1.87/2.25 'tc_Message_Omsg' ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , 0, 4, substitution( 0, [ :=( X, 'c_Message_Osynth'( 'c_Message_Oanalz'(
% 1.87/2.25 'v_H' ) ) ), :=( Y, 'c_union'( 'v_G', 'v_H', 'tc_Message_Omsg' ) )] ),
% 1.87/2.25 substitution( 1, [] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 subsumption(
% 1.87/2.25 clause( 5227, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.25 'c_union'( 'c_Message_Osynth'( 'c_Message_Oanalz'( 'v_H' ) ), 'c_union'(
% 1.87/2.25 'v_G', 'v_H', 'tc_Message_Omsg' ), 'tc_Message_Omsg' ) ) ), 'tc_nat' ) )
% 1.87/2.25 ] )
% 1.87/2.25 , clause( 12980, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oparts'( 'c_union'( 'c_Message_Osynth'( 'c_Message_Oanalz'(
% 1.87/2.25 'v_H' ) ), 'c_union'( 'v_G', 'v_H', 'tc_Message_Omsg' ),
% 1.87/2.25 'tc_Message_Omsg' ) ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 resolution(
% 1.87/2.25 clause( 12981, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.25 'v_G' ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , clause( 17, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.25 'c_union'( 'v_G', 'v_H', 'tc_Message_Omsg' ) ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , 0, clause( 665, [ ~( 'c_in'( Z, 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.25 X ) ), 'tc_nat' ) ), 'c_in'( Z, 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.25 'c_union'( X, Y, 'tc_Message_Omsg' ) ) ), 'tc_nat' ) ] )
% 1.87/2.25 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, 'v_G' ), :=( Y, 'v_H'
% 1.87/2.25 ), :=( Z, 'v_K' )] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 subsumption(
% 1.87/2.25 clause( 5620, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.25 'v_G' ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , clause( 12981, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oparts'( 'v_G' ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 resolution(
% 1.87/2.25 clause( 12982, [ ~( 'c_in'( 'v_K', 'c_union'( X, 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oparts'( 'v_G' ) ), 'tc_nat' ), 'tc_nat' ) ), 'c_in'( 'v_K', X
% 1.87/2.25 , 'tc_nat' ) ] )
% 1.87/2.25 , clause( 5620, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oparts'( 'v_G' ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , 0, clause( 12, [ ~( 'c_in'( X, 'c_union'( Y, Z, T ), T ) ), 'c_in'( X, Z
% 1.87/2.25 , T ), 'c_in'( X, Y, T ) ] )
% 1.87/2.25 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, 'v_K' ), :=( Y, X ),
% 1.87/2.25 :=( Z, 'c_Message_OkeysFor'( 'c_Message_Oparts'( 'v_G' ) ) ), :=( T,
% 1.87/2.25 'tc_nat' )] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 subsumption(
% 1.87/2.25 clause( 5647, [ ~( 'c_in'( 'v_K', 'c_union'( X, 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oparts'( 'v_G' ) ), 'tc_nat' ), 'tc_nat' ) ), 'c_in'( 'v_K', X
% 1.87/2.25 , 'tc_nat' ) ] )
% 1.87/2.25 , clause( 12982, [ ~( 'c_in'( 'v_K', 'c_union'( X, 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oparts'( 'v_G' ) ), 'tc_nat' ), 'tc_nat' ) ), 'c_in'( 'v_K', X
% 1.87/2.25 , 'tc_nat' ) ] )
% 1.87/2.25 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 1.87/2.25 1 )] ) ).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 resolution(
% 1.87/2.25 clause( 12986, [ ~( 'c_in'( 'v_K', 'c_union'( 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oparts'( 'c_union'( 'c_Message_Osynth'( 'c_Message_Oanalz'(
% 1.87/2.25 'v_H' ) ), 'c_union'( 'v_G', 'v_H', 'tc_Message_Omsg' ),
% 1.87/2.25 'tc_Message_Omsg' ) ) ), 'c_Message_OkeysFor'( 'c_Message_Oparts'( 'v_G'
% 1.87/2.25 ) ), 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.87/2.25 , clause( 5227, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oparts'( 'c_union'( 'c_Message_Osynth'( 'c_Message_Oanalz'(
% 1.87/2.25 'v_H' ) ), 'c_union'( 'v_G', 'v_H', 'tc_Message_Omsg' ),
% 1.87/2.25 'tc_Message_Omsg' ) ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , 0, clause( 5647, [ ~( 'c_in'( 'v_K', 'c_union'( X, 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oparts'( 'v_G' ) ), 'tc_nat' ), 'tc_nat' ) ), 'c_in'( 'v_K', X
% 1.87/2.25 , 'tc_nat' ) ] )
% 1.87/2.25 , 1, substitution( 0, [] ), substitution( 1, [ :=( X, 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oparts'( 'c_union'( 'c_Message_Osynth'( 'c_Message_Oanalz'(
% 1.87/2.25 'v_H' ) ), 'c_union'( 'v_G', 'v_H', 'tc_Message_Omsg' ),
% 1.87/2.25 'tc_Message_Omsg' ) ) ) )] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 paramod(
% 1.87/2.25 clause( 12987, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_union'(
% 1.87/2.25 'c_Message_Oparts'( 'c_union'( 'c_Message_Osynth'( 'c_Message_Oanalz'(
% 1.87/2.25 'v_H' ) ), 'c_union'( 'v_G', 'v_H', 'tc_Message_Omsg' ),
% 1.87/2.25 'tc_Message_Omsg' ) ), 'c_Message_Oparts'( 'v_G' ), 'tc_Message_Omsg' ) )
% 1.87/2.25 , 'tc_nat' ) ) ] )
% 1.87/2.25 , clause( 6, [ =( 'c_union'( 'c_Message_OkeysFor'( X ),
% 1.87/2.25 'c_Message_OkeysFor'( Y ), 'tc_nat' ), 'c_Message_OkeysFor'( 'c_union'( X
% 1.87/2.25 , Y, 'tc_Message_Omsg' ) ) ) ] )
% 1.87/2.25 , 0, clause( 12986, [ ~( 'c_in'( 'v_K', 'c_union'( 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oparts'( 'c_union'( 'c_Message_Osynth'( 'c_Message_Oanalz'(
% 1.87/2.25 'v_H' ) ), 'c_union'( 'v_G', 'v_H', 'tc_Message_Omsg' ),
% 1.87/2.25 'tc_Message_Omsg' ) ) ), 'c_Message_OkeysFor'( 'c_Message_Oparts'( 'v_G'
% 1.87/2.25 ) ), 'tc_nat' ), 'tc_nat' ) ) ] )
% 1.87/2.25 , 0, 3, substitution( 0, [ :=( X, 'c_Message_Oparts'( 'c_union'(
% 1.87/2.25 'c_Message_Osynth'( 'c_Message_Oanalz'( 'v_H' ) ), 'c_union'( 'v_G',
% 1.87/2.25 'v_H', 'tc_Message_Omsg' ), 'tc_Message_Omsg' ) ) ), :=( Y,
% 1.87/2.25 'c_Message_Oparts'( 'v_G' ) )] ), substitution( 1, [] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 paramod(
% 1.87/2.25 clause( 12988, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_Message_Oparts'(
% 1.87/2.25 'c_union'( 'c_union'( 'c_Message_Osynth'( 'c_Message_Oanalz'( 'v_H' ) ),
% 1.87/2.25 'c_union'( 'v_G', 'v_H', 'tc_Message_Omsg' ), 'tc_Message_Omsg' ), 'v_G'
% 1.87/2.25 , 'tc_Message_Omsg' ) ) ), 'tc_nat' ) ) ] )
% 1.87/2.25 , clause( 10, [ =( 'c_union'( 'c_Message_Oparts'( X ), 'c_Message_Oparts'(
% 1.87/2.25 Y ), 'tc_Message_Omsg' ), 'c_Message_Oparts'( 'c_union'( X, Y,
% 1.87/2.25 'tc_Message_Omsg' ) ) ) ] )
% 1.87/2.25 , 0, clause( 12987, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'( 'c_union'(
% 1.87/2.25 'c_Message_Oparts'( 'c_union'( 'c_Message_Osynth'( 'c_Message_Oanalz'(
% 1.87/2.25 'v_H' ) ), 'c_union'( 'v_G', 'v_H', 'tc_Message_Omsg' ),
% 1.87/2.25 'tc_Message_Omsg' ) ), 'c_Message_Oparts'( 'v_G' ), 'tc_Message_Omsg' ) )
% 1.87/2.25 , 'tc_nat' ) ) ] )
% 1.87/2.25 , 0, 4, substitution( 0, [ :=( X, 'c_union'( 'c_Message_Osynth'(
% 1.87/2.25 'c_Message_Oanalz'( 'v_H' ) ), 'c_union'( 'v_G', 'v_H', 'tc_Message_Omsg'
% 1.87/2.25 ), 'tc_Message_Omsg' ) ), :=( Y, 'v_G' )] ), substitution( 1, [] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 resolution(
% 1.87/2.25 clause( 12989, [] )
% 1.87/2.25 , clause( 12988, [ ~( 'c_in'( 'v_K', 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oparts'( 'c_union'( 'c_union'( 'c_Message_Osynth'(
% 1.87/2.25 'c_Message_Oanalz'( 'v_H' ) ), 'c_union'( 'v_G', 'v_H', 'tc_Message_Omsg'
% 1.87/2.25 ), 'tc_Message_Omsg' ), 'v_G', 'tc_Message_Omsg' ) ) ), 'tc_nat' ) ) ]
% 1.87/2.25 )
% 1.87/2.25 , 0, clause( 3575, [ 'c_in'( 'v_K', 'c_Message_OkeysFor'(
% 1.87/2.25 'c_Message_Oparts'( 'c_union'( 'c_union'( 'c_Message_Osynth'(
% 1.87/2.25 'c_Message_Oanalz'( 'v_H' ) ), X, 'tc_Message_Omsg' ), 'v_G',
% 1.87/2.25 'tc_Message_Omsg' ) ) ), 'tc_nat' ) ] )
% 1.87/2.25 , 0, substitution( 0, [] ), substitution( 1, [ :=( X, 'c_union'( 'v_G',
% 1.87/2.25 'v_H', 'tc_Message_Omsg' ) )] )).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 subsumption(
% 1.87/2.25 clause( 12818, [] )
% 1.87/2.25 , clause( 12989, [] )
% 1.87/2.25 , substitution( 0, [] ), permutation( 0, [] ) ).
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 end.
% 1.87/2.25
% 1.87/2.25 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.87/2.25
% 1.87/2.25 Memory use:
% 1.87/2.25
% 1.87/2.25 space for terms: 193855
% 1.87/2.25 space for clauses: 910068
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 clauses generated: 200807
% 1.87/2.25 clauses kept: 12819
% 1.87/2.25 clauses selected: 2711
% 1.87/2.25 clauses deleted: 11
% 1.87/2.25 clauses inuse deleted: 7
% 1.87/2.25
% 1.87/2.25 subsentry: 41169
% 1.87/2.25 literals s-matched: 35558
% 1.87/2.25 literals matched: 35526
% 1.87/2.25 full subsumption: 604
% 1.87/2.25
% 1.87/2.25 checksum: -1095612317
% 1.87/2.25
% 1.87/2.25
% 1.87/2.25 Bliksem ended
%------------------------------------------------------------------------------