TSTP Solution File: SWV235+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV235+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n010.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 16:23:02 EDT 2022
% Result : Theorem 10.48s 10.92s
% Output : Refutation 10.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV235+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Tue Jun 14 19:40:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 10.48/10.92 *** allocated 10000 integers for termspace/termends
% 10.48/10.92 *** allocated 10000 integers for clauses
% 10.48/10.92 *** allocated 10000 integers for justifications
% 10.48/10.92 Bliksem 1.12
% 10.48/10.92
% 10.48/10.92
% 10.48/10.92 Automatic Strategy Selection
% 10.48/10.92
% 10.48/10.92
% 10.48/10.92 Clauses:
% 10.48/10.92
% 10.48/10.92 { xor( X, Y ) = xor( Y, X ) }.
% 10.48/10.92 { xor( X, xor( Y, Z ) ) = xor( xor( X, Y ), Z ) }.
% 10.48/10.92 { decrypt( X, crypt( X, Y ) ) = Y }.
% 10.48/10.92 { xor( X, id ) = X }.
% 10.48/10.92 { xor( X, X ) = id }.
% 10.48/10.92 { ! p( crypt( xor( X, Y ), Z ) ), ! p( T ), ! p( crypt( xor( km, imp ), U )
% 10.48/10.92 ), p( crypt( xor( km, T ), decrypt( xor( U, T ), crypt( xor( X, Y ), Z )
% 10.48/10.92 ) ) ) }.
% 10.48/10.92 { ! p( crypt( xor( km, X ), Y ) ), ! p( X ), ! p( crypt( xor( km, exp ), Z
% 10.48/10.92 ) ), p( crypt( xor( Z, X ), Y ) ) }.
% 10.48/10.92 { ! p( X ), ! p( Y ), p( crypt( xor( km, xor( kp, Y ) ), X ) ) }.
% 10.48/10.92 { ! p( X ), ! p( crypt( xor( km, xor( kp, Y ) ), Z ) ), ! p( Y ), p( crypt
% 10.48/10.92 ( xor( km, xor( Y, kp ) ), xor( X, Z ) ) ) }.
% 10.48/10.92 { ! p( X ), ! p( crypt( xor( km, xor( Y, kp ) ), Z ) ), ! p( Y ), p( crypt
% 10.48/10.92 ( xor( km, Y ), xor( Z, X ) ) ) }.
% 10.48/10.92 { ! p( X ), ! p( crypt( xor( km, data ), Y ) ), p( crypt( Y, X ) ) }.
% 10.48/10.92 { ! p( X ), ! p( crypt( xor( km, data ), Y ) ), p( decrypt( Y, X ) ) }.
% 10.48/10.92 { ! p( crypt( X, Y ) ), ! p( Z ), ! p( crypt( xor( km, imp ), T ) ), ! p(
% 10.48/10.92 crypt( xor( km, exp ), U ) ), p( crypt( xor( U, W ), decrypt( xor( Z, T )
% 10.48/10.92 , crypt( X, Y ) ) ) ) }.
% 10.48/10.92 { ! p( X ), ! p( Y ), p( xor( X, Y ) ) }.
% 10.48/10.92 { ! p( crypt( Y, X ) ), ! p( Y ), p( X ) }.
% 10.48/10.92 { ! p( Y ), ! p( X ), p( crypt( X, Y ) ) }.
% 10.48/10.92 { p( kp ) }.
% 10.48/10.92 { p( imp ) }.
% 10.48/10.92 { p( data ) }.
% 10.48/10.92 { p( id ) }.
% 10.48/10.92 { p( pin ) }.
% 10.48/10.92 { p( crypt( xor( km, pin ), pp ) ) }.
% 10.48/10.92 { p( crypt( xor( km, imp ), xor( rand, xor( imp, exp ) ) ) ) }.
% 10.48/10.92 { p( crypt( xor( km, imp ), rand ) ) }.
% 10.48/10.92 { p( crypt( xor( km, xor( imp, kp ) ), kek ) ) }.
% 10.48/10.92 { p( crypt( xor( rand, imp ), kek ) ) }.
% 10.48/10.92 { p( exp ) }.
% 10.48/10.92 { p( a ) }.
% 10.48/10.92 { ! p( crypt( pp, a ) ) }.
% 10.48/10.92
% 10.48/10.92 percentage equality = 0.087719, percentage horn = 1.000000
% 10.48/10.92 This is a problem with some equality
% 10.48/10.92
% 10.48/10.92
% 10.48/10.92
% 10.48/10.92 Options Used:
% 10.48/10.92
% 10.48/10.92 useres = 1
% 10.48/10.92 useparamod = 1
% 10.48/10.92 useeqrefl = 1
% 10.48/10.92 useeqfact = 1
% 10.48/10.92 usefactor = 1
% 10.48/10.92 usesimpsplitting = 0
% 10.48/10.92 usesimpdemod = 5
% 10.48/10.92 usesimpres = 3
% 10.48/10.92
% 10.48/10.92 resimpinuse = 1000
% 10.48/10.92 resimpclauses = 20000
% 10.48/10.92 substype = eqrewr
% 10.48/10.92 backwardsubs = 1
% 10.48/10.92 selectoldest = 5
% 10.48/10.92
% 10.48/10.92 litorderings [0] = split
% 10.48/10.92 litorderings [1] = extend the termordering, first sorting on arguments
% 10.48/10.92
% 10.48/10.92 termordering = kbo
% 10.48/10.92
% 10.48/10.92 litapriori = 0
% 10.48/10.92 termapriori = 1
% 10.48/10.92 litaposteriori = 0
% 10.48/10.92 termaposteriori = 0
% 10.48/10.92 demodaposteriori = 0
% 10.48/10.92 ordereqreflfact = 0
% 10.48/10.92
% 10.48/10.92 litselect = negord
% 10.48/10.92
% 10.48/10.92 maxweight = 15
% 10.48/10.92 maxdepth = 30000
% 10.48/10.92 maxlength = 115
% 10.48/10.92 maxnrvars = 195
% 10.48/10.92 excuselevel = 1
% 10.48/10.92 increasemaxweight = 1
% 10.48/10.92
% 10.48/10.92 maxselected = 10000000
% 10.48/10.92 maxnrclauses = 10000000
% 10.48/10.92
% 10.48/10.92 showgenerated = 0
% 10.48/10.92 showkept = 0
% 10.48/10.92 showselected = 0
% 10.48/10.92 showdeleted = 0
% 10.48/10.92 showresimp = 1
% 10.48/10.92 showstatus = 2000
% 10.48/10.92
% 10.48/10.92 prologoutput = 0
% 10.48/10.92 nrgoals = 5000000
% 10.48/10.92 totalproof = 1
% 10.48/10.92
% 10.48/10.92 Symbols occurring in the translation:
% 10.48/10.92
% 10.48/10.92 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 10.48/10.92 . [1, 2] (w:1, o:34, a:1, s:1, b:0),
% 10.48/10.92 ! [4, 1] (w:0, o:28, a:1, s:1, b:0),
% 10.48/10.92 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 10.48/10.92 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 10.48/10.92 xor [37, 2] (w:1, o:58, a:1, s:1, b:0),
% 10.48/10.92 crypt [39, 2] (w:1, o:59, a:1, s:1, b:0),
% 10.48/10.92 decrypt [40, 2] (w:1, o:60, a:1, s:1, b:0),
% 10.48/10.92 id [41, 0] (w:1, o:9, a:1, s:1, b:0),
% 10.48/10.92 p [47, 1] (w:1, o:33, a:1, s:1, b:0),
% 10.48/10.92 km [48, 0] (w:1, o:15, a:1, s:1, b:0),
% 10.48/10.92 imp [49, 0] (w:1, o:16, a:1, s:1, b:0),
% 10.48/10.92 exp [51, 0] (w:1, o:19, a:1, s:1, b:0),
% 10.48/10.92 kp [53, 0] (w:1, o:21, a:1, s:1, b:0),
% 10.48/10.92 data [55, 0] (w:1, o:18, a:1, s:1, b:0),
% 10.48/10.92 pin [56, 0] (w:1, o:23, a:1, s:1, b:0),
% 10.48/10.92 pp [57, 0] (w:1, o:24, a:1, s:1, b:0),
% 10.48/10.92 rand [58, 0] (w:1, o:25, a:1, s:1, b:0),
% 10.48/10.92 kek [59, 0] (w:1, o:26, a:1, s:1, b:0),
% 10.48/10.92 a [60, 0] (w:1, o:27, a:1, s:1, b:0).
% 10.48/10.92
% 10.48/10.92
% 10.48/10.92 Starting Search:
% 10.48/10.92
% 10.48/10.92 *** allocated 15000 integers for clauses
% 10.48/10.92 *** allocated 22500 integers for clauses
% 10.48/10.92 *** allocated 33750 integers for clauses
% 10.48/10.92 *** allocated 15000 integers for termspace/termends
% 10.48/10.92 *** allocated 50625 integers for clauses
% 10.48/10.92 *** allocated 75937 integers for clauses
% 10.48/10.92 *** allocated 22500 integers for termspace/termends
% 10.48/10.92 Resimplifying inuse:
% 10.48/10.92 Done
% 10.48/10.92
% 10.48/10.92 *** allocated 113905 integers for clauses
% 10.48/10.92 *** allocated 33750 integers for termspace/termends
% 10.48/10.92
% 10.48/10.92 Intermediate Status:
% 10.48/10.92 Generated: 5022
% 10.48/10.92 Kept: 2015
% 10.48/10.92 Inuse: 132
% 10.48/10.92 Deleted: 1
% 10.48/10.92 Deletedinuse: 1
% 10.48/10.92
% 10.48/10.92 Resimplifying inuse:
% 10.48/10.92 Done
% 10.48/10.92
% 10.48/10.92 *** allocated 170857 integers for clauses
% 10.48/10.92 *** allocated 50625 integers for termspace/termends
% 10.48/10.92 Resimplifying inuse:
% 10.48/10.92 Done
% 10.48/10.92
% 10.48/10.92 *** allocated 256285 integers for clauses
% 10.48/10.92
% 10.48/10.92 Intermediate Status:
% 10.48/10.92 Generated: 9189
% 10.48/10.92 Kept: 4063
% 10.48/10.92 Inuse: 173
% 10.48/10.92 Deleted: 2
% 10.48/10.92 Deletedinuse: 2
% 10.48/10.92
% 10.48/10.92 Resimplifying inuse:
% 10.48/10.92 Done
% 10.48/10.92
% 10.48/10.92 *** allocated 75937 integers for termspace/termends
% 10.48/10.92 *** allocated 384427 integers for clauses
% 10.48/10.92 Resimplifying inuse:
% 10.48/10.92 Done
% 10.48/10.92
% 10.48/10.92
% 10.48/10.92 Intermediate Status:
% 10.48/10.92 Generated: 14118
% 10.48/10.92 Kept: 6082
% 10.48/10.92 Inuse: 217
% 10.48/10.92 Deleted: 2
% 10.48/10.92 Deletedinuse: 2
% 10.48/10.92
% 10.48/10.92 Resimplifying inuse:
% 10.48/10.92 Done
% 10.48/10.92
% 10.48/10.92 Resimplifying inuse:
% 10.48/10.92 Done
% 10.48/10.92
% 10.48/10.92 *** allocated 113905 integers for termspace/termends
% 10.48/10.92 *** allocated 576640 integers for clauses
% 10.48/10.92
% 10.48/10.92 Intermediate Status:
% 10.48/10.92 Generated: 19239
% 10.48/10.92 Kept: 8129
% 10.48/10.92 Inuse: 253
% 10.48/10.92 Deleted: 2
% 10.48/10.92 Deletedinuse: 2
% 10.48/10.92
% 10.48/10.92 Resimplifying inuse:
% 10.48/10.92 Done
% 10.48/10.92
% 10.48/10.92 Resimplifying inuse:
% 10.48/10.92 Done
% 10.48/10.92
% 10.48/10.92
% 10.48/10.92 Intermediate Status:
% 10.48/10.92 Generated: 25498
% 10.48/10.92 Kept: 10170
% 10.48/10.92 Inuse: 299
% 10.48/10.92 Deleted: 10
% 10.48/10.92 Deletedinuse: 2
% 10.48/10.92
% 10.48/10.92 Resimplifying inuse:
% 10.48/10.92 Done
% 10.48/10.92
% 10.48/10.92 Resimplifying inuse:
% 10.48/10.92 Done
% 10.48/10.92
% 10.48/10.92 *** allocated 170857 integers for termspace/termends
% 10.48/10.92 *** allocated 864960 integers for clauses
% 10.48/10.92
% 10.48/10.92 Intermediate Status:
% 10.48/10.92 Generated: 34091
% 10.48/10.92 Kept: 12181
% 10.48/10.92 Inuse: 371
% 10.48/10.92 Deleted: 13
% 10.48/10.92 Deletedinuse: 2
% 10.48/10.92
% 10.48/10.92 Resimplifying inuse:
% 10.48/10.92 Done
% 10.48/10.92
% 10.48/10.92 Resimplifying inuse:
% 10.48/10.92 Done
% 10.48/10.92
% 10.48/10.92
% 10.48/10.92 Intermediate Status:
% 10.48/10.92 Generated: 42537
% 10.48/10.92 Kept: 14195
% 10.48/10.92 Inuse: 479
% 10.48/10.92 Deleted: 16
% 10.48/10.92 Deletedinuse: 2
% 10.48/10.92
% 10.48/10.92 Resimplifying inuse:
% 10.48/10.92 Done
% 10.48/10.92
% 10.48/10.92 Resimplifying inuse:
% 10.48/10.92 Done
% 10.48/10.92
% 10.48/10.92
% 10.48/10.92 Intermediate Status:
% 10.48/10.92 Generated: 49026
% 10.48/10.92 Kept: 16261
% 10.48/10.92 Inuse: 537
% 10.48/10.92 Deleted: 16
% 10.48/10.92 Deletedinuse: 2
% 10.48/10.92
% 10.48/10.92 Resimplifying inuse:
% 10.48/10.92 Done
% 10.48/10.92
% 10.48/10.92 *** allocated 256285 integers for termspace/termends
% 10.48/10.92 *** allocated 1297440 integers for clauses
% 10.48/10.92 Resimplifying inuse:
% 10.48/10.92 Done
% 10.48/10.92
% 10.48/10.92
% 10.48/10.92 Intermediate Status:
% 10.48/10.92 Generated: 52974
% 10.48/10.92 Kept: 18394
% 10.48/10.92 Inuse: 572
% 10.48/10.92 Deleted: 16
% 10.48/10.92 Deletedinuse: 2
% 10.48/10.92
% 10.48/10.92 Resimplifying inuse:
% 10.48/10.92 Done
% 10.48/10.92
% 10.48/10.92 Resimplifying clauses:
% 10.48/10.92 Done
% 10.48/10.92
% 10.48/10.92 Resimplifying inuse:
% 10.48/10.92 Done
% 10.48/10.92
% 10.48/10.92
% 10.48/10.92 Intermediate Status:
% 10.48/10.92 Generated: 56990
% 10.48/10.92 Kept: 20421
% 10.48/10.92 Inuse: 600
% 10.48/10.92 Deleted: 144
% 10.48/10.92 Deletedinuse: 2
% 10.48/10.92
% 10.48/10.92 Resimplifying inuse:
% 10.48/10.92 Done
% 10.48/10.92
% 10.48/10.92 Resimplifying inuse:
% 10.48/10.92 Done
% 10.48/10.92
% 10.48/10.92
% 10.48/10.92 Intermediate Status:
% 10.48/10.92 Generated: 62369
% 10.48/10.92 Kept: 22435
% 10.48/10.92 Inuse: 625
% 10.48/10.92 Deleted: 144
% 10.48/10.92 Deletedinuse: 2
% 10.48/10.92
% 10.48/10.92
% 10.48/10.92 Bliksems!, er is een bewijs:
% 10.48/10.92 % SZS status Theorem
% 10.48/10.92 % SZS output start Refutation
% 10.48/10.92
% 10.48/10.92 (1) {G0,W11,D4,L1,V3,M1} I { xor( X, xor( Y, Z ) ) ==> xor( xor( X, Y ), Z
% 10.48/10.92 ) }.
% 10.48/10.92 (3) {G0,W5,D3,L1,V1,M1} I { xor( X, id ) ==> X }.
% 10.48/10.92 (4) {G0,W5,D3,L1,V1,M1} I { xor( X, X ) ==> id }.
% 10.48/10.92 (6) {G0,W20,D4,L4,V3,M4} I { ! p( crypt( xor( km, X ), Y ) ), ! p( X ), ! p
% 10.48/10.92 ( crypt( xor( km, exp ), Z ) ), p( crypt( xor( Z, X ), Y ) ) }.
% 10.48/10.92 (7) {G1,W12,D5,L3,V2,M3} I;d(1) { ! p( X ), ! p( Y ), p( crypt( xor( xor(
% 10.48/10.92 km, kp ), Y ), X ) ) }.
% 10.48/10.92 (13) {G0,W8,D3,L3,V2,M3} I { ! p( X ), ! p( Y ), p( xor( X, Y ) ) }.
% 10.48/10.92 (14) {G0,W8,D3,L3,V2,M3} I { ! p( crypt( Y, X ) ), ! p( Y ), p( X ) }.
% 10.48/10.92 (15) {G0,W8,D3,L3,V2,M3} I { ! p( Y ), ! p( X ), p( crypt( X, Y ) ) }.
% 10.48/10.92 (16) {G0,W2,D2,L1,V0,M1} I { p( kp ) }.
% 10.48/10.92 (20) {G0,W2,D2,L1,V0,M1} I { p( pin ) }.
% 10.48/10.92 (21) {G0,W6,D4,L1,V0,M1} I { p( crypt( xor( km, pin ), pp ) ) }.
% 10.48/10.92 (26) {G0,W2,D2,L1,V0,M1} I { p( exp ) }.
% 10.48/10.92 (27) {G0,W2,D2,L1,V0,M1} I { p( a ) }.
% 10.48/10.92 (28) {G0,W4,D3,L1,V0,M1} I { ! p( crypt( pp, a ) ) }.
% 10.48/10.92 (44) {G1,W7,D4,L1,V2,M1} P(4,1);d(3) { xor( xor( Y, X ), X ) ==> Y }.
% 10.48/10.92 (116) {G1,W12,D4,L2,V1,M2} R(21,6);r(20) { ! p( crypt( xor( km, exp ), X )
% 10.48/10.92 ), p( crypt( xor( X, pin ), pp ) ) }.
% 10.48/10.92 (151) {G2,W10,D5,L2,V1,M2} R(7,16) { ! p( X ), p( crypt( xor( xor( km, kp )
% 10.48/10.92 , X ), kp ) ) }.
% 10.48/10.92 (566) {G1,W6,D3,L2,V1,M2} R(13,16) { ! p( X ), p( xor( kp, X ) ) }.
% 10.48/10.92 (636) {G2,W4,D3,L1,V0,M1} R(566,20) { p( xor( kp, pin ) ) }.
% 10.48/10.92 (637) {G2,W4,D3,L1,V0,M1} R(566,26) { p( xor( kp, exp ) ) }.
% 10.48/10.92 (931) {G1,W2,D2,L1,V0,M1} R(15,28);r(27) { ! p( pp ) }.
% 10.48/10.92 (973) {G2,W6,D3,L2,V1,M2} R(931,14) { ! p( crypt( X, pp ) ), ! p( X ) }.
% 10.48/10.92 (1028) {G3,W6,D4,L1,V0,M1} R(973,636) { ! p( crypt( xor( kp, pin ), pp ) )
% 10.48/10.92 }.
% 10.48/10.92 (22214) {G3,W6,D4,L1,V0,M1} R(151,637);d(1);d(44) { p( crypt( xor( km, exp
% 10.48/10.92 ), kp ) ) }.
% 10.48/10.92 (22450) {G4,W0,D0,L0,V0,M0} R(22214,116);r(1028) { }.
% 10.48/10.92
% 10.48/10.92
% 10.48/10.92 % SZS output end Refutation
% 10.48/10.92 found a proof!
% 10.48/10.92
% 10.48/10.92
% 10.48/10.92 Unprocessed initial clauses:
% 10.48/10.92
% 10.48/10.92 (22452) {G0,W7,D3,L1,V2,M1} { xor( X, Y ) = xor( Y, X ) }.
% 10.48/10.92 (22453) {G0,W11,D4,L1,V3,M1} { xor( X, xor( Y, Z ) ) = xor( xor( X, Y ), Z
% 10.48/10.92 ) }.
% 10.48/10.92 (22454) {G0,W7,D4,L1,V2,M1} { decrypt( X, crypt( X, Y ) ) = Y }.
% 10.48/10.92 (22455) {G0,W5,D3,L1,V1,M1} { xor( X, id ) = X }.
% 10.48/10.92 (22456) {G0,W5,D3,L1,V1,M1} { xor( X, X ) = id }.
% 10.48/10.92 (22457) {G0,W28,D6,L4,V5,M4} { ! p( crypt( xor( X, Y ), Z ) ), ! p( T ), !
% 10.48/10.92 p( crypt( xor( km, imp ), U ) ), p( crypt( xor( km, T ), decrypt( xor( U
% 10.48/10.92 , T ), crypt( xor( X, Y ), Z ) ) ) ) }.
% 10.48/10.92 (22458) {G0,W20,D4,L4,V3,M4} { ! p( crypt( xor( km, X ), Y ) ), ! p( X ),
% 10.48/10.92 ! p( crypt( xor( km, exp ), Z ) ), p( crypt( xor( Z, X ), Y ) ) }.
% 10.48/10.92 (22459) {G0,W12,D5,L3,V2,M3} { ! p( X ), ! p( Y ), p( crypt( xor( km, xor
% 10.48/10.92 ( kp, Y ) ), X ) ) }.
% 10.48/10.92 (22460) {G0,W22,D5,L4,V3,M4} { ! p( X ), ! p( crypt( xor( km, xor( kp, Y )
% 10.48/10.92 ), Z ) ), ! p( Y ), p( crypt( xor( km, xor( Y, kp ) ), xor( X, Z ) ) )
% 10.48/10.92 }.
% 10.48/10.92 (22461) {G0,W20,D5,L4,V3,M4} { ! p( X ), ! p( crypt( xor( km, xor( Y, kp )
% 10.48/10.92 ), Z ) ), ! p( Y ), p( crypt( xor( km, Y ), xor( Z, X ) ) ) }.
% 10.48/10.92 (22462) {G0,W12,D4,L3,V2,M3} { ! p( X ), ! p( crypt( xor( km, data ), Y )
% 10.48/10.92 ), p( crypt( Y, X ) ) }.
% 10.48/10.92 (22463) {G0,W12,D4,L3,V2,M3} { ! p( X ), ! p( crypt( xor( km, data ), Y )
% 10.48/10.92 ), p( decrypt( Y, X ) ) }.
% 10.48/10.92 (22464) {G0,W30,D5,L5,V6,M5} { ! p( crypt( X, Y ) ), ! p( Z ), ! p( crypt
% 10.48/10.92 ( xor( km, imp ), T ) ), ! p( crypt( xor( km, exp ), U ) ), p( crypt( xor
% 10.48/10.92 ( U, W ), decrypt( xor( Z, T ), crypt( X, Y ) ) ) ) }.
% 10.48/10.92 (22465) {G0,W8,D3,L3,V2,M3} { ! p( X ), ! p( Y ), p( xor( X, Y ) ) }.
% 10.48/10.92 (22466) {G0,W8,D3,L3,V2,M3} { ! p( crypt( Y, X ) ), ! p( Y ), p( X ) }.
% 10.48/10.92 (22467) {G0,W8,D3,L3,V2,M3} { ! p( Y ), ! p( X ), p( crypt( X, Y ) ) }.
% 10.48/10.92 (22468) {G0,W2,D2,L1,V0,M1} { p( kp ) }.
% 10.48/10.92 (22469) {G0,W2,D2,L1,V0,M1} { p( imp ) }.
% 10.48/10.92 (22470) {G0,W2,D2,L1,V0,M1} { p( data ) }.
% 10.48/10.92 (22471) {G0,W2,D2,L1,V0,M1} { p( id ) }.
% 10.48/10.92 (22472) {G0,W2,D2,L1,V0,M1} { p( pin ) }.
% 10.48/10.92 (22473) {G0,W6,D4,L1,V0,M1} { p( crypt( xor( km, pin ), pp ) ) }.
% 10.48/10.92 (22474) {G0,W10,D5,L1,V0,M1} { p( crypt( xor( km, imp ), xor( rand, xor(
% 10.48/10.92 imp, exp ) ) ) ) }.
% 10.48/10.92 (22475) {G0,W6,D4,L1,V0,M1} { p( crypt( xor( km, imp ), rand ) ) }.
% 10.48/10.92 (22476) {G0,W8,D5,L1,V0,M1} { p( crypt( xor( km, xor( imp, kp ) ), kek ) )
% 10.48/10.92 }.
% 10.48/10.92 (22477) {G0,W6,D4,L1,V0,M1} { p( crypt( xor( rand, imp ), kek ) ) }.
% 10.48/10.92 (22478) {G0,W2,D2,L1,V0,M1} { p( exp ) }.
% 10.48/10.92 (22479) {G0,W2,D2,L1,V0,M1} { p( a ) }.
% 10.48/10.92 (22480) {G0,W4,D3,L1,V0,M1} { ! p( crypt( pp, a ) ) }.
% 10.48/10.92
% 10.48/10.92
% 10.48/10.92 Total Proof:
% 10.48/10.92
% 10.48/10.92 subsumption: (1) {G0,W11,D4,L1,V3,M1} I { xor( X, xor( Y, Z ) ) ==> xor(
% 10.48/10.92 xor( X, Y ), Z ) }.
% 10.48/10.92 parent0: (22453) {G0,W11,D4,L1,V3,M1} { xor( X, xor( Y, Z ) ) = xor( xor(
% 10.48/10.92 X, Y ), Z ) }.
% 10.48/10.92 substitution0:
% 10.48/10.92 X := X
% 10.48/10.92 Y := Y
% 10.48/10.92 Z := Z
% 10.48/10.92 end
% 10.48/10.92 permutation0:
% 10.48/10.92 0 ==> 0
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 subsumption: (3) {G0,W5,D3,L1,V1,M1} I { xor( X, id ) ==> X }.
% 10.48/10.92 parent0: (22455) {G0,W5,D3,L1,V1,M1} { xor( X, id ) = X }.
% 10.48/10.92 substitution0:
% 10.48/10.92 X := X
% 10.48/10.92 end
% 10.48/10.92 permutation0:
% 10.48/10.92 0 ==> 0
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 subsumption: (4) {G0,W5,D3,L1,V1,M1} I { xor( X, X ) ==> id }.
% 10.48/10.92 parent0: (22456) {G0,W5,D3,L1,V1,M1} { xor( X, X ) = id }.
% 10.48/10.92 substitution0:
% 10.48/10.92 X := X
% 10.48/10.92 end
% 10.48/10.92 permutation0:
% 10.48/10.92 0 ==> 0
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 subsumption: (6) {G0,W20,D4,L4,V3,M4} I { ! p( crypt( xor( km, X ), Y ) ),
% 10.48/10.92 ! p( X ), ! p( crypt( xor( km, exp ), Z ) ), p( crypt( xor( Z, X ), Y ) )
% 10.48/10.92 }.
% 10.48/10.92 parent0: (22458) {G0,W20,D4,L4,V3,M4} { ! p( crypt( xor( km, X ), Y ) ), !
% 10.48/10.92 p( X ), ! p( crypt( xor( km, exp ), Z ) ), p( crypt( xor( Z, X ), Y ) )
% 10.48/10.92 }.
% 10.48/10.92 substitution0:
% 10.48/10.92 X := X
% 10.48/10.92 Y := Y
% 10.48/10.92 Z := Z
% 10.48/10.92 end
% 10.48/10.92 permutation0:
% 10.48/10.92 0 ==> 0
% 10.48/10.92 1 ==> 1
% 10.48/10.92 2 ==> 2
% 10.48/10.92 3 ==> 3
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 paramod: (22521) {G1,W12,D5,L3,V2,M3} { p( crypt( xor( xor( km, kp ), X )
% 10.48/10.92 , Y ) ), ! p( Y ), ! p( X ) }.
% 10.48/10.92 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { xor( X, xor( Y, Z ) ) ==> xor( xor
% 10.48/10.92 ( X, Y ), Z ) }.
% 10.48/10.92 parent1[2; 2]: (22459) {G0,W12,D5,L3,V2,M3} { ! p( X ), ! p( Y ), p( crypt
% 10.48/10.92 ( xor( km, xor( kp, Y ) ), X ) ) }.
% 10.48/10.92 substitution0:
% 10.48/10.92 X := km
% 10.48/10.92 Y := kp
% 10.48/10.92 Z := X
% 10.48/10.92 end
% 10.48/10.92 substitution1:
% 10.48/10.92 X := Y
% 10.48/10.92 Y := X
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 subsumption: (7) {G1,W12,D5,L3,V2,M3} I;d(1) { ! p( X ), ! p( Y ), p( crypt
% 10.48/10.92 ( xor( xor( km, kp ), Y ), X ) ) }.
% 10.48/10.92 parent0: (22521) {G1,W12,D5,L3,V2,M3} { p( crypt( xor( xor( km, kp ), X )
% 10.48/10.92 , Y ) ), ! p( Y ), ! p( X ) }.
% 10.48/10.92 substitution0:
% 10.48/10.92 X := Y
% 10.48/10.92 Y := X
% 10.48/10.92 end
% 10.48/10.92 permutation0:
% 10.48/10.92 0 ==> 2
% 10.48/10.92 1 ==> 0
% 10.48/10.92 2 ==> 1
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 subsumption: (13) {G0,W8,D3,L3,V2,M3} I { ! p( X ), ! p( Y ), p( xor( X, Y
% 10.48/10.92 ) ) }.
% 10.48/10.92 parent0: (22465) {G0,W8,D3,L3,V2,M3} { ! p( X ), ! p( Y ), p( xor( X, Y )
% 10.48/10.92 ) }.
% 10.48/10.92 substitution0:
% 10.48/10.92 X := X
% 10.48/10.92 Y := Y
% 10.48/10.92 end
% 10.48/10.92 permutation0:
% 10.48/10.92 0 ==> 0
% 10.48/10.92 1 ==> 1
% 10.48/10.92 2 ==> 2
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 subsumption: (14) {G0,W8,D3,L3,V2,M3} I { ! p( crypt( Y, X ) ), ! p( Y ), p
% 10.48/10.92 ( X ) }.
% 10.48/10.92 parent0: (22466) {G0,W8,D3,L3,V2,M3} { ! p( crypt( Y, X ) ), ! p( Y ), p(
% 10.48/10.92 X ) }.
% 10.48/10.92 substitution0:
% 10.48/10.92 X := X
% 10.48/10.92 Y := Y
% 10.48/10.92 end
% 10.48/10.92 permutation0:
% 10.48/10.92 0 ==> 0
% 10.48/10.92 1 ==> 1
% 10.48/10.92 2 ==> 2
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 subsumption: (15) {G0,W8,D3,L3,V2,M3} I { ! p( Y ), ! p( X ), p( crypt( X,
% 10.48/10.92 Y ) ) }.
% 10.48/10.92 parent0: (22467) {G0,W8,D3,L3,V2,M3} { ! p( Y ), ! p( X ), p( crypt( X, Y
% 10.48/10.92 ) ) }.
% 10.48/10.92 substitution0:
% 10.48/10.92 X := X
% 10.48/10.92 Y := Y
% 10.48/10.92 end
% 10.48/10.92 permutation0:
% 10.48/10.92 0 ==> 0
% 10.48/10.92 1 ==> 1
% 10.48/10.92 2 ==> 2
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 subsumption: (16) {G0,W2,D2,L1,V0,M1} I { p( kp ) }.
% 10.48/10.92 parent0: (22468) {G0,W2,D2,L1,V0,M1} { p( kp ) }.
% 10.48/10.92 substitution0:
% 10.48/10.92 end
% 10.48/10.92 permutation0:
% 10.48/10.92 0 ==> 0
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 subsumption: (20) {G0,W2,D2,L1,V0,M1} I { p( pin ) }.
% 10.48/10.92 parent0: (22472) {G0,W2,D2,L1,V0,M1} { p( pin ) }.
% 10.48/10.92 substitution0:
% 10.48/10.92 end
% 10.48/10.92 permutation0:
% 10.48/10.92 0 ==> 0
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 subsumption: (21) {G0,W6,D4,L1,V0,M1} I { p( crypt( xor( km, pin ), pp ) )
% 10.48/10.92 }.
% 10.48/10.92 parent0: (22473) {G0,W6,D4,L1,V0,M1} { p( crypt( xor( km, pin ), pp ) )
% 10.48/10.92 }.
% 10.48/10.92 substitution0:
% 10.48/10.92 end
% 10.48/10.92 permutation0:
% 10.48/10.92 0 ==> 0
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 subsumption: (26) {G0,W2,D2,L1,V0,M1} I { p( exp ) }.
% 10.48/10.92 parent0: (22478) {G0,W2,D2,L1,V0,M1} { p( exp ) }.
% 10.48/10.92 substitution0:
% 10.48/10.92 end
% 10.48/10.92 permutation0:
% 10.48/10.92 0 ==> 0
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 subsumption: (27) {G0,W2,D2,L1,V0,M1} I { p( a ) }.
% 10.48/10.92 parent0: (22479) {G0,W2,D2,L1,V0,M1} { p( a ) }.
% 10.48/10.92 substitution0:
% 10.48/10.92 end
% 10.48/10.92 permutation0:
% 10.48/10.92 0 ==> 0
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 subsumption: (28) {G0,W4,D3,L1,V0,M1} I { ! p( crypt( pp, a ) ) }.
% 10.48/10.92 parent0: (22480) {G0,W4,D3,L1,V0,M1} { ! p( crypt( pp, a ) ) }.
% 10.48/10.92 substitution0:
% 10.48/10.92 end
% 10.48/10.92 permutation0:
% 10.48/10.92 0 ==> 0
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 eqswap: (22774) {G0,W11,D4,L1,V3,M1} { xor( xor( X, Y ), Z ) ==> xor( X,
% 10.48/10.92 xor( Y, Z ) ) }.
% 10.48/10.92 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { xor( X, xor( Y, Z ) ) ==> xor( xor
% 10.48/10.92 ( X, Y ), Z ) }.
% 10.48/10.92 substitution0:
% 10.48/10.92 X := X
% 10.48/10.92 Y := Y
% 10.48/10.92 Z := Z
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 paramod: (22780) {G1,W9,D4,L1,V2,M1} { xor( xor( X, Y ), Y ) ==> xor( X,
% 10.48/10.92 id ) }.
% 10.48/10.92 parent0[0]: (4) {G0,W5,D3,L1,V1,M1} I { xor( X, X ) ==> id }.
% 10.48/10.92 parent1[0; 8]: (22774) {G0,W11,D4,L1,V3,M1} { xor( xor( X, Y ), Z ) ==>
% 10.48/10.92 xor( X, xor( Y, Z ) ) }.
% 10.48/10.92 substitution0:
% 10.48/10.92 X := Y
% 10.48/10.92 end
% 10.48/10.92 substitution1:
% 10.48/10.92 X := X
% 10.48/10.92 Y := Y
% 10.48/10.92 Z := Y
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 paramod: (22781) {G1,W7,D4,L1,V2,M1} { xor( xor( X, Y ), Y ) ==> X }.
% 10.48/10.92 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { xor( X, id ) ==> X }.
% 10.48/10.92 parent1[0; 6]: (22780) {G1,W9,D4,L1,V2,M1} { xor( xor( X, Y ), Y ) ==> xor
% 10.48/10.92 ( X, id ) }.
% 10.48/10.92 substitution0:
% 10.48/10.92 X := X
% 10.48/10.92 end
% 10.48/10.92 substitution1:
% 10.48/10.92 X := X
% 10.48/10.92 Y := Y
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 subsumption: (44) {G1,W7,D4,L1,V2,M1} P(4,1);d(3) { xor( xor( Y, X ), X )
% 10.48/10.92 ==> Y }.
% 10.48/10.92 parent0: (22781) {G1,W7,D4,L1,V2,M1} { xor( xor( X, Y ), Y ) ==> X }.
% 10.48/10.92 substitution0:
% 10.48/10.92 X := Y
% 10.48/10.92 Y := X
% 10.48/10.92 end
% 10.48/10.92 permutation0:
% 10.48/10.92 0 ==> 0
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 resolution: (22783) {G1,W14,D4,L3,V1,M3} { ! p( pin ), ! p( crypt( xor( km
% 10.48/10.92 , exp ), X ) ), p( crypt( xor( X, pin ), pp ) ) }.
% 10.48/10.92 parent0[0]: (6) {G0,W20,D4,L4,V3,M4} I { ! p( crypt( xor( km, X ), Y ) ), !
% 10.48/10.92 p( X ), ! p( crypt( xor( km, exp ), Z ) ), p( crypt( xor( Z, X ), Y ) )
% 10.48/10.92 }.
% 10.48/10.92 parent1[0]: (21) {G0,W6,D4,L1,V0,M1} I { p( crypt( xor( km, pin ), pp ) )
% 10.48/10.92 }.
% 10.48/10.92 substitution0:
% 10.48/10.92 X := pin
% 10.48/10.92 Y := pp
% 10.48/10.92 Z := X
% 10.48/10.92 end
% 10.48/10.92 substitution1:
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 resolution: (22785) {G1,W12,D4,L2,V1,M2} { ! p( crypt( xor( km, exp ), X )
% 10.48/10.92 ), p( crypt( xor( X, pin ), pp ) ) }.
% 10.48/10.92 parent0[0]: (22783) {G1,W14,D4,L3,V1,M3} { ! p( pin ), ! p( crypt( xor( km
% 10.48/10.92 , exp ), X ) ), p( crypt( xor( X, pin ), pp ) ) }.
% 10.48/10.92 parent1[0]: (20) {G0,W2,D2,L1,V0,M1} I { p( pin ) }.
% 10.48/10.92 substitution0:
% 10.48/10.92 X := X
% 10.48/10.92 end
% 10.48/10.92 substitution1:
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 subsumption: (116) {G1,W12,D4,L2,V1,M2} R(21,6);r(20) { ! p( crypt( xor( km
% 10.48/10.92 , exp ), X ) ), p( crypt( xor( X, pin ), pp ) ) }.
% 10.48/10.92 parent0: (22785) {G1,W12,D4,L2,V1,M2} { ! p( crypt( xor( km, exp ), X ) )
% 10.48/10.92 , p( crypt( xor( X, pin ), pp ) ) }.
% 10.48/10.92 substitution0:
% 10.48/10.92 X := X
% 10.48/10.92 end
% 10.48/10.92 permutation0:
% 10.48/10.92 0 ==> 0
% 10.48/10.92 1 ==> 1
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 resolution: (22786) {G1,W10,D5,L2,V1,M2} { ! p( X ), p( crypt( xor( xor(
% 10.48/10.92 km, kp ), X ), kp ) ) }.
% 10.48/10.92 parent0[0]: (7) {G1,W12,D5,L3,V2,M3} I;d(1) { ! p( X ), ! p( Y ), p( crypt
% 10.48/10.92 ( xor( xor( km, kp ), Y ), X ) ) }.
% 10.48/10.92 parent1[0]: (16) {G0,W2,D2,L1,V0,M1} I { p( kp ) }.
% 10.48/10.92 substitution0:
% 10.48/10.92 X := kp
% 10.48/10.92 Y := X
% 10.48/10.92 end
% 10.48/10.92 substitution1:
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 subsumption: (151) {G2,W10,D5,L2,V1,M2} R(7,16) { ! p( X ), p( crypt( xor(
% 10.48/10.92 xor( km, kp ), X ), kp ) ) }.
% 10.48/10.92 parent0: (22786) {G1,W10,D5,L2,V1,M2} { ! p( X ), p( crypt( xor( xor( km,
% 10.48/10.92 kp ), X ), kp ) ) }.
% 10.48/10.92 substitution0:
% 10.48/10.92 X := X
% 10.48/10.92 end
% 10.48/10.92 permutation0:
% 10.48/10.92 0 ==> 0
% 10.48/10.92 1 ==> 1
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 resolution: (22788) {G1,W6,D3,L2,V1,M2} { ! p( X ), p( xor( kp, X ) ) }.
% 10.48/10.92 parent0[0]: (13) {G0,W8,D3,L3,V2,M3} I { ! p( X ), ! p( Y ), p( xor( X, Y )
% 10.48/10.92 ) }.
% 10.48/10.92 parent1[0]: (16) {G0,W2,D2,L1,V0,M1} I { p( kp ) }.
% 10.48/10.92 substitution0:
% 10.48/10.92 X := kp
% 10.48/10.92 Y := X
% 10.48/10.92 end
% 10.48/10.92 substitution1:
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 subsumption: (566) {G1,W6,D3,L2,V1,M2} R(13,16) { ! p( X ), p( xor( kp, X )
% 10.48/10.92 ) }.
% 10.48/10.92 parent0: (22788) {G1,W6,D3,L2,V1,M2} { ! p( X ), p( xor( kp, X ) ) }.
% 10.48/10.92 substitution0:
% 10.48/10.92 X := X
% 10.48/10.92 end
% 10.48/10.92 permutation0:
% 10.48/10.92 0 ==> 0
% 10.48/10.92 1 ==> 1
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 resolution: (22790) {G1,W4,D3,L1,V0,M1} { p( xor( kp, pin ) ) }.
% 10.48/10.92 parent0[0]: (566) {G1,W6,D3,L2,V1,M2} R(13,16) { ! p( X ), p( xor( kp, X )
% 10.48/10.92 ) }.
% 10.48/10.92 parent1[0]: (20) {G0,W2,D2,L1,V0,M1} I { p( pin ) }.
% 10.48/10.92 substitution0:
% 10.48/10.92 X := pin
% 10.48/10.92 end
% 10.48/10.92 substitution1:
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 subsumption: (636) {G2,W4,D3,L1,V0,M1} R(566,20) { p( xor( kp, pin ) ) }.
% 10.48/10.92 parent0: (22790) {G1,W4,D3,L1,V0,M1} { p( xor( kp, pin ) ) }.
% 10.48/10.92 substitution0:
% 10.48/10.92 end
% 10.48/10.92 permutation0:
% 10.48/10.92 0 ==> 0
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 resolution: (22791) {G1,W4,D3,L1,V0,M1} { p( xor( kp, exp ) ) }.
% 10.48/10.92 parent0[0]: (566) {G1,W6,D3,L2,V1,M2} R(13,16) { ! p( X ), p( xor( kp, X )
% 10.48/10.92 ) }.
% 10.48/10.92 parent1[0]: (26) {G0,W2,D2,L1,V0,M1} I { p( exp ) }.
% 10.48/10.92 substitution0:
% 10.48/10.92 X := exp
% 10.48/10.92 end
% 10.48/10.92 substitution1:
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 subsumption: (637) {G2,W4,D3,L1,V0,M1} R(566,26) { p( xor( kp, exp ) ) }.
% 10.48/10.92 parent0: (22791) {G1,W4,D3,L1,V0,M1} { p( xor( kp, exp ) ) }.
% 10.48/10.92 substitution0:
% 10.48/10.92 end
% 10.48/10.92 permutation0:
% 10.48/10.92 0 ==> 0
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 resolution: (22792) {G1,W4,D2,L2,V0,M2} { ! p( a ), ! p( pp ) }.
% 10.48/10.92 parent0[0]: (28) {G0,W4,D3,L1,V0,M1} I { ! p( crypt( pp, a ) ) }.
% 10.48/10.92 parent1[2]: (15) {G0,W8,D3,L3,V2,M3} I { ! p( Y ), ! p( X ), p( crypt( X, Y
% 10.48/10.92 ) ) }.
% 10.48/10.92 substitution0:
% 10.48/10.92 end
% 10.48/10.92 substitution1:
% 10.48/10.92 X := pp
% 10.48/10.92 Y := a
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 resolution: (22793) {G1,W2,D2,L1,V0,M1} { ! p( pp ) }.
% 10.48/10.92 parent0[0]: (22792) {G1,W4,D2,L2,V0,M2} { ! p( a ), ! p( pp ) }.
% 10.48/10.92 parent1[0]: (27) {G0,W2,D2,L1,V0,M1} I { p( a ) }.
% 10.48/10.92 substitution0:
% 10.48/10.92 end
% 10.48/10.92 substitution1:
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 subsumption: (931) {G1,W2,D2,L1,V0,M1} R(15,28);r(27) { ! p( pp ) }.
% 10.48/10.92 parent0: (22793) {G1,W2,D2,L1,V0,M1} { ! p( pp ) }.
% 10.48/10.92 substitution0:
% 10.48/10.92 end
% 10.48/10.92 permutation0:
% 10.48/10.92 0 ==> 0
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 resolution: (22794) {G1,W6,D3,L2,V1,M2} { ! p( crypt( X, pp ) ), ! p( X )
% 10.48/10.92 }.
% 10.48/10.92 parent0[0]: (931) {G1,W2,D2,L1,V0,M1} R(15,28);r(27) { ! p( pp ) }.
% 10.48/10.92 parent1[2]: (14) {G0,W8,D3,L3,V2,M3} I { ! p( crypt( Y, X ) ), ! p( Y ), p
% 10.48/10.92 ( X ) }.
% 10.48/10.92 substitution0:
% 10.48/10.92 end
% 10.48/10.92 substitution1:
% 10.48/10.92 X := pp
% 10.48/10.92 Y := X
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 subsumption: (973) {G2,W6,D3,L2,V1,M2} R(931,14) { ! p( crypt( X, pp ) ), !
% 10.48/10.92 p( X ) }.
% 10.48/10.92 parent0: (22794) {G1,W6,D3,L2,V1,M2} { ! p( crypt( X, pp ) ), ! p( X ) }.
% 10.48/10.92 substitution0:
% 10.48/10.92 X := X
% 10.48/10.92 end
% 10.48/10.92 permutation0:
% 10.48/10.92 0 ==> 0
% 10.48/10.92 1 ==> 1
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 resolution: (22795) {G3,W6,D4,L1,V0,M1} { ! p( crypt( xor( kp, pin ), pp )
% 10.48/10.92 ) }.
% 10.48/10.92 parent0[1]: (973) {G2,W6,D3,L2,V1,M2} R(931,14) { ! p( crypt( X, pp ) ), !
% 10.48/10.92 p( X ) }.
% 10.48/10.92 parent1[0]: (636) {G2,W4,D3,L1,V0,M1} R(566,20) { p( xor( kp, pin ) ) }.
% 10.48/10.92 substitution0:
% 10.48/10.92 X := xor( kp, pin )
% 10.48/10.92 end
% 10.48/10.92 substitution1:
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 subsumption: (1028) {G3,W6,D4,L1,V0,M1} R(973,636) { ! p( crypt( xor( kp,
% 10.48/10.92 pin ), pp ) ) }.
% 10.48/10.92 parent0: (22795) {G3,W6,D4,L1,V0,M1} { ! p( crypt( xor( kp, pin ), pp ) )
% 10.48/10.92 }.
% 10.48/10.92 substitution0:
% 10.48/10.92 end
% 10.48/10.92 permutation0:
% 10.48/10.92 0 ==> 0
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 resolution: (22798) {G3,W10,D5,L1,V0,M1} { p( crypt( xor( xor( km, kp ),
% 10.48/10.92 xor( kp, exp ) ), kp ) ) }.
% 10.48/10.92 parent0[0]: (151) {G2,W10,D5,L2,V1,M2} R(7,16) { ! p( X ), p( crypt( xor(
% 10.48/10.92 xor( km, kp ), X ), kp ) ) }.
% 10.48/10.92 parent1[0]: (637) {G2,W4,D3,L1,V0,M1} R(566,26) { p( xor( kp, exp ) ) }.
% 10.48/10.92 substitution0:
% 10.48/10.92 X := xor( kp, exp )
% 10.48/10.92 end
% 10.48/10.92 substitution1:
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 paramod: (22799) {G1,W10,D6,L1,V0,M1} { p( crypt( xor( xor( xor( km, kp )
% 10.48/10.92 , kp ), exp ), kp ) ) }.
% 10.48/10.92 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { xor( X, xor( Y, Z ) ) ==> xor( xor
% 10.48/10.92 ( X, Y ), Z ) }.
% 10.48/10.92 parent1[0; 2]: (22798) {G3,W10,D5,L1,V0,M1} { p( crypt( xor( xor( km, kp )
% 10.48/10.92 , xor( kp, exp ) ), kp ) ) }.
% 10.48/10.92 substitution0:
% 10.48/10.92 X := xor( km, kp )
% 10.48/10.92 Y := kp
% 10.48/10.92 Z := exp
% 10.48/10.92 end
% 10.48/10.92 substitution1:
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 paramod: (22800) {G2,W6,D4,L1,V0,M1} { p( crypt( xor( km, exp ), kp ) )
% 10.48/10.92 }.
% 10.48/10.92 parent0[0]: (44) {G1,W7,D4,L1,V2,M1} P(4,1);d(3) { xor( xor( Y, X ), X )
% 10.48/10.92 ==> Y }.
% 10.48/10.92 parent1[0; 3]: (22799) {G1,W10,D6,L1,V0,M1} { p( crypt( xor( xor( xor( km
% 10.48/10.92 , kp ), kp ), exp ), kp ) ) }.
% 10.48/10.92 substitution0:
% 10.48/10.92 X := kp
% 10.48/10.92 Y := km
% 10.48/10.92 end
% 10.48/10.92 substitution1:
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 subsumption: (22214) {G3,W6,D4,L1,V0,M1} R(151,637);d(1);d(44) { p( crypt(
% 10.48/10.92 xor( km, exp ), kp ) ) }.
% 10.48/10.92 parent0: (22800) {G2,W6,D4,L1,V0,M1} { p( crypt( xor( km, exp ), kp ) )
% 10.48/10.92 }.
% 10.48/10.92 substitution0:
% 10.48/10.92 end
% 10.48/10.92 permutation0:
% 10.48/10.92 0 ==> 0
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 resolution: (22801) {G2,W6,D4,L1,V0,M1} { p( crypt( xor( kp, pin ), pp ) )
% 10.48/10.92 }.
% 10.48/10.92 parent0[0]: (116) {G1,W12,D4,L2,V1,M2} R(21,6);r(20) { ! p( crypt( xor( km
% 10.48/10.92 , exp ), X ) ), p( crypt( xor( X, pin ), pp ) ) }.
% 10.48/10.92 parent1[0]: (22214) {G3,W6,D4,L1,V0,M1} R(151,637);d(1);d(44) { p( crypt(
% 10.48/10.92 xor( km, exp ), kp ) ) }.
% 10.48/10.92 substitution0:
% 10.48/10.92 X := kp
% 10.48/10.92 end
% 10.48/10.92 substitution1:
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 resolution: (22802) {G3,W0,D0,L0,V0,M0} { }.
% 10.48/10.92 parent0[0]: (1028) {G3,W6,D4,L1,V0,M1} R(973,636) { ! p( crypt( xor( kp,
% 10.48/10.92 pin ), pp ) ) }.
% 10.48/10.92 parent1[0]: (22801) {G2,W6,D4,L1,V0,M1} { p( crypt( xor( kp, pin ), pp ) )
% 10.48/10.92 }.
% 10.48/10.92 substitution0:
% 10.48/10.92 end
% 10.48/10.92 substitution1:
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 subsumption: (22450) {G4,W0,D0,L0,V0,M0} R(22214,116);r(1028) { }.
% 10.48/10.92 parent0: (22802) {G3,W0,D0,L0,V0,M0} { }.
% 10.48/10.92 substitution0:
% 10.48/10.92 end
% 10.48/10.92 permutation0:
% 10.48/10.92 end
% 10.48/10.92
% 10.48/10.92 Proof check complete!
% 10.48/10.92
% 10.48/10.92 Memory use:
% 10.48/10.92
% 10.48/10.92 space for terms: 238477
% 10.48/10.92 space for clauses: 1082701
% 10.48/10.92
% 10.48/10.92
% 10.48/10.92 clauses generated: 62404
% 10.48/10.92 clauses kept: 22451
% 10.48/10.92 clauses selected: 626
% 10.48/10.92 clauses deleted: 144
% 10.48/10.92 clauses inuse deleted: 2
% 10.48/10.92
% 10.48/10.92 subsentry: 211765
% 10.48/10.92 literals s-matched: 64753
% 10.48/10.92 literals matched: 58479
% 10.48/10.92 full subsumption: 27578
% 10.48/10.92
% 10.48/10.92 checksum: -414443183
% 10.48/10.92
% 10.48/10.92
% 10.48/10.92 Bliksem ended
%------------------------------------------------------------------------------