TSTP Solution File: SWV236+1 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV236+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 16:23:03 EDT 2022
% Result : Theorem 0.88s 1.32s
% Output : Refutation 0.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SWV236+1 : TPTP v8.1.0. Released v3.2.0.
% 0.00/0.10 % Command : bliksem %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % DateTime : Tue Jun 14 22:16:58 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.88/1.32 *** allocated 10000 integers for termspace/termends
% 0.88/1.32 *** allocated 10000 integers for clauses
% 0.88/1.32 *** allocated 10000 integers for justifications
% 0.88/1.32 Bliksem 1.12
% 0.88/1.32
% 0.88/1.32
% 0.88/1.32 Automatic Strategy Selection
% 0.88/1.32
% 0.88/1.32
% 0.88/1.32 Clauses:
% 0.88/1.32
% 0.88/1.32 { xor( X, Y ) = xor( Y, X ) }.
% 0.88/1.32 { xor( X, xor( Y, Z ) ) = xor( xor( X, Y ), Z ) }.
% 0.88/1.32 { decrypt( X, crypt( X, Y ) ) = Y }.
% 0.88/1.32 { xor( X, id ) = X }.
% 0.88/1.32 { xor( X, X ) = id }.
% 0.88/1.32 { ! p( crypt( xor( X, Y ), Z ) ), ! p( T ), ! p( crypt( xor( km, imp ), U )
% 0.88/1.32 ), p( crypt( xor( km, T ), decrypt( xor( U, T ), crypt( xor( X, Y ), Z )
% 0.88/1.32 ) ) ) }.
% 0.88/1.32 { ! p( crypt( xor( km, X ), Y ) ), ! p( X ), ! p( crypt( xor( km, exp ), Z
% 0.88/1.32 ) ), p( crypt( xor( Z, X ), Y ) ) }.
% 0.88/1.32 { ! p( X ), ! p( Y ), p( crypt( xor( km, xor( kp, Y ) ), X ) ) }.
% 0.88/1.32 { ! p( X ), ! p( crypt( xor( km, xor( kp, Y ) ), Z ) ), ! p( Y ), p( crypt
% 0.88/1.32 ( xor( km, xor( Y, kp ) ), xor( X, Z ) ) ) }.
% 0.88/1.32 { ! p( X ), ! p( crypt( xor( km, xor( Y, kp ) ), Z ) ), ! p( Y ), p( crypt
% 0.88/1.32 ( xor( km, Y ), xor( Z, X ) ) ) }.
% 0.88/1.32 { ! p( X ), ! p( crypt( xor( km, data ), Y ) ), p( crypt( Y, X ) ) }.
% 0.88/1.32 { ! p( X ), ! p( crypt( xor( km, data ), Y ) ), p( decrypt( Y, X ) ) }.
% 0.88/1.32 { ! p( crypt( X, Y ) ), ! p( Z ), ! p( crypt( xor( km, imp ), T ) ), ! p(
% 0.88/1.32 crypt( xor( km, exp ), U ) ), p( crypt( xor( U, W ), decrypt( xor( Z, T )
% 0.88/1.32 , crypt( X, Y ) ) ) ) }.
% 0.88/1.32 { ! p( X ), ! p( Y ), p( xor( X, Y ) ) }.
% 0.88/1.32 { ! p( crypt( Y, X ) ), ! p( Y ), p( X ) }.
% 0.88/1.32 { ! p( Y ), ! p( X ), p( crypt( X, Y ) ) }.
% 0.88/1.32 { ! p( crypt( xor( X, data ), Y ) ), p( crypt( X, Y ) ) }.
% 0.88/1.32 { p( kp ) }.
% 0.88/1.32 { p( imp ) }.
% 0.88/1.32 { p( data ) }.
% 0.88/1.32 { p( id ) }.
% 0.88/1.32 { p( pin ) }.
% 0.88/1.32 { p( crypt( xor( km, pin ), pp ) ) }.
% 0.88/1.32 { p( crypt( xor( km, exp ), eurk ) ) }.
% 0.88/1.32 { p( crypt( xor( km, data ), eurk ) ) }.
% 0.88/1.32 { p( exp ) }.
% 0.88/1.32 { p( a ) }.
% 0.88/1.32 { ! p( crypt( xor( km, exp ), X ) ), ! p( X ) }.
% 0.88/1.32
% 0.88/1.32 percentage equality = 0.086207, percentage horn = 1.000000
% 0.88/1.32 This is a problem with some equality
% 0.88/1.32
% 0.88/1.32
% 0.88/1.32
% 0.88/1.32 Options Used:
% 0.88/1.32
% 0.88/1.32 useres = 1
% 0.88/1.32 useparamod = 1
% 0.88/1.32 useeqrefl = 1
% 0.88/1.32 useeqfact = 1
% 0.88/1.32 usefactor = 1
% 0.88/1.32 usesimpsplitting = 0
% 0.88/1.32 usesimpdemod = 5
% 0.88/1.32 usesimpres = 3
% 0.88/1.32
% 0.88/1.32 resimpinuse = 1000
% 0.88/1.32 resimpclauses = 20000
% 0.88/1.32 substype = eqrewr
% 0.88/1.32 backwardsubs = 1
% 0.88/1.32 selectoldest = 5
% 0.88/1.32
% 0.88/1.32 litorderings [0] = split
% 0.88/1.32 litorderings [1] = extend the termordering, first sorting on arguments
% 0.88/1.32
% 0.88/1.32 termordering = kbo
% 0.88/1.32
% 0.88/1.32 litapriori = 0
% 0.88/1.32 termapriori = 1
% 0.88/1.32 litaposteriori = 0
% 0.88/1.32 termaposteriori = 0
% 0.88/1.32 demodaposteriori = 0
% 0.88/1.32 ordereqreflfact = 0
% 0.88/1.32
% 0.88/1.32 litselect = negord
% 0.88/1.32
% 0.88/1.32 maxweight = 15
% 0.88/1.32 maxdepth = 30000
% 0.88/1.32 maxlength = 115
% 0.88/1.32 maxnrvars = 195
% 0.88/1.32 excuselevel = 1
% 0.88/1.32 increasemaxweight = 1
% 0.88/1.32
% 0.88/1.32 maxselected = 10000000
% 0.88/1.32 maxnrclauses = 10000000
% 0.88/1.32
% 0.88/1.32 showgenerated = 0
% 0.88/1.32 showkept = 0
% 0.88/1.32 showselected = 0
% 0.88/1.32 showdeleted = 0
% 0.88/1.32 showresimp = 1
% 0.88/1.32 showstatus = 2000
% 0.88/1.32
% 0.88/1.32 prologoutput = 0
% 0.88/1.32 nrgoals = 5000000
% 0.88/1.32 totalproof = 1
% 0.88/1.32
% 0.88/1.32 Symbols occurring in the translation:
% 0.88/1.32
% 0.88/1.32 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.88/1.32 . [1, 2] (w:1, o:34, a:1, s:1, b:0),
% 0.88/1.32 ! [4, 1] (w:0, o:28, a:1, s:1, b:0),
% 0.88/1.32 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.88/1.32 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.88/1.32 xor [37, 2] (w:1, o:58, a:1, s:1, b:0),
% 0.88/1.32 crypt [39, 2] (w:1, o:59, a:1, s:1, b:0),
% 0.88/1.32 decrypt [40, 2] (w:1, o:60, a:1, s:1, b:0),
% 0.88/1.32 id [41, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.88/1.32 p [47, 1] (w:1, o:33, a:1, s:1, b:0),
% 0.88/1.32 km [48, 0] (w:1, o:15, a:1, s:1, b:0),
% 0.88/1.32 imp [49, 0] (w:1, o:16, a:1, s:1, b:0),
% 0.88/1.32 exp [51, 0] (w:1, o:19, a:1, s:1, b:0),
% 0.88/1.32 kp [53, 0] (w:1, o:21, a:1, s:1, b:0),
% 0.88/1.32 data [55, 0] (w:1, o:18, a:1, s:1, b:0),
% 0.88/1.32 pin [56, 0] (w:1, o:23, a:1, s:1, b:0),
% 0.88/1.32 pp [57, 0] (w:1, o:24, a:1, s:1, b:0),
% 0.88/1.32 eurk [58, 0] (w:1, o:25, a:1, s:1, b:0),
% 0.88/1.32 a [59, 0] (w:1, o:26, a:1, s:1, b:0).
% 0.88/1.32
% 0.88/1.32
% 0.88/1.32 Starting Search:
% 0.88/1.32
% 0.88/1.32 *** allocated 15000 integers for clauses
% 0.88/1.32 *** allocated 22500 integers for clauses
% 0.88/1.32 *** allocated 33750 integers for clauses
% 0.88/1.32 *** allocated 15000 integers for termspace/termends
% 0.88/1.32 *** allocated 50625 integers for clauses
% 0.88/1.32 *** allocated 75937 integers for clauses
% 0.88/1.32 *** allocated 22500 integers for termspace/termends
% 0.88/1.32 Resimplifying inuse:
% 0.88/1.32 Done
% 0.88/1.32
% 0.88/1.32 *** allocated 113905 integers for clauses
% 0.88/1.32 *** allocated 33750 integers for termspace/termends
% 0.88/1.32
% 0.88/1.32 Intermediate Status:
% 0.88/1.32 Generated: 4699
% 0.88/1.32 Kept: 2000
% 0.88/1.32 Inuse: 121
% 0.88/1.32 Deleted: 1
% 0.88/1.32 Deletedinuse: 1
% 0.88/1.32
% 0.88/1.32 Resimplifying inuse:
% 0.88/1.32 Done
% 0.88/1.32
% 0.88/1.32 *** allocated 170857 integers for clauses
% 0.88/1.32 *** allocated 50625 integers for termspace/termends
% 0.88/1.32 Resimplifying inuse:
% 0.88/1.32 Done
% 0.88/1.32
% 0.88/1.32 *** allocated 256285 integers for clauses
% 0.88/1.32
% 0.88/1.32 Intermediate Status:
% 0.88/1.32 Generated: 9091
% 0.88/1.32 Kept: 4000
% 0.88/1.32 Inuse: 169
% 0.88/1.32 Deleted: 3
% 0.88/1.32 Deletedinuse: 2
% 0.88/1.32
% 0.88/1.32 Resimplifying inuse:
% 0.88/1.32 Done
% 0.88/1.32
% 0.88/1.32 *** allocated 75937 integers for termspace/termends
% 0.88/1.32
% 0.88/1.32 Bliksems!, er is een bewijs:
% 0.88/1.32 % SZS status Theorem
% 0.88/1.32 % SZS output start Refutation
% 0.88/1.32
% 0.88/1.32 (1) {G0,W11,D4,L1,V3,M1} I { xor( X, xor( Y, Z ) ) ==> xor( xor( X, Y ), Z
% 0.88/1.32 ) }.
% 0.88/1.32 (3) {G0,W5,D3,L1,V1,M1} I { xor( X, id ) ==> X }.
% 0.88/1.32 (4) {G0,W5,D3,L1,V1,M1} I { xor( X, X ) ==> id }.
% 0.88/1.32 (7) {G1,W12,D5,L3,V2,M3} I;d(1) { ! p( X ), ! p( Y ), p( crypt( xor( xor(
% 0.88/1.32 km, kp ), Y ), X ) ) }.
% 0.88/1.32 (13) {G0,W8,D3,L3,V2,M3} I { ! p( X ), ! p( Y ), p( xor( X, Y ) ) }.
% 0.88/1.32 (17) {G0,W2,D2,L1,V0,M1} I { p( kp ) }.
% 0.88/1.32 (25) {G0,W2,D2,L1,V0,M1} I { p( exp ) }.
% 0.88/1.32 (27) {G0,W8,D4,L2,V1,M2} I { ! p( crypt( xor( km, exp ), X ) ), ! p( X )
% 0.88/1.32 }.
% 0.88/1.32 (33) {G2,W10,D5,L2,V1,M2} F(7) { ! p( X ), p( crypt( xor( xor( km, kp ), X
% 0.88/1.32 ), X ) ) }.
% 0.88/1.32 (44) {G1,W7,D4,L1,V2,M1} P(4,1);d(3) { xor( xor( Y, X ), X ) ==> Y }.
% 0.88/1.32 (679) {G1,W6,D3,L2,V1,M2} R(13,17) { ! p( X ), p( xor( kp, X ) ) }.
% 0.88/1.32 (4731) {G2,W4,D3,L1,V0,M1} R(679,25) { p( xor( kp, exp ) ) }.
% 0.88/1.32 (4988) {G3,W8,D4,L1,V0,M1} R(4731,33);d(1);d(44) { p( crypt( xor( km, exp )
% 0.88/1.32 , xor( kp, exp ) ) ) }.
% 0.88/1.32 (4991) {G4,W0,D0,L0,V0,M0} R(4731,27);r(4988) { }.
% 0.88/1.32
% 0.88/1.32
% 0.88/1.32 % SZS output end Refutation
% 0.88/1.32 found a proof!
% 0.88/1.32
% 0.88/1.32
% 0.88/1.32 Unprocessed initial clauses:
% 0.88/1.32
% 0.88/1.32 (4993) {G0,W7,D3,L1,V2,M1} { xor( X, Y ) = xor( Y, X ) }.
% 0.88/1.32 (4994) {G0,W11,D4,L1,V3,M1} { xor( X, xor( Y, Z ) ) = xor( xor( X, Y ), Z
% 0.88/1.32 ) }.
% 0.88/1.32 (4995) {G0,W7,D4,L1,V2,M1} { decrypt( X, crypt( X, Y ) ) = Y }.
% 0.88/1.32 (4996) {G0,W5,D3,L1,V1,M1} { xor( X, id ) = X }.
% 0.88/1.32 (4997) {G0,W5,D3,L1,V1,M1} { xor( X, X ) = id }.
% 0.88/1.32 (4998) {G0,W28,D6,L4,V5,M4} { ! p( crypt( xor( X, Y ), Z ) ), ! p( T ), !
% 0.88/1.32 p( crypt( xor( km, imp ), U ) ), p( crypt( xor( km, T ), decrypt( xor( U
% 0.88/1.32 , T ), crypt( xor( X, Y ), Z ) ) ) ) }.
% 0.88/1.32 (4999) {G0,W20,D4,L4,V3,M4} { ! p( crypt( xor( km, X ), Y ) ), ! p( X ), !
% 0.88/1.32 p( crypt( xor( km, exp ), Z ) ), p( crypt( xor( Z, X ), Y ) ) }.
% 0.88/1.32 (5000) {G0,W12,D5,L3,V2,M3} { ! p( X ), ! p( Y ), p( crypt( xor( km, xor(
% 0.88/1.32 kp, Y ) ), X ) ) }.
% 0.88/1.32 (5001) {G0,W22,D5,L4,V3,M4} { ! p( X ), ! p( crypt( xor( km, xor( kp, Y )
% 0.88/1.32 ), Z ) ), ! p( Y ), p( crypt( xor( km, xor( Y, kp ) ), xor( X, Z ) ) )
% 0.88/1.32 }.
% 0.88/1.32 (5002) {G0,W20,D5,L4,V3,M4} { ! p( X ), ! p( crypt( xor( km, xor( Y, kp )
% 0.88/1.32 ), Z ) ), ! p( Y ), p( crypt( xor( km, Y ), xor( Z, X ) ) ) }.
% 0.88/1.32 (5003) {G0,W12,D4,L3,V2,M3} { ! p( X ), ! p( crypt( xor( km, data ), Y ) )
% 0.88/1.32 , p( crypt( Y, X ) ) }.
% 0.88/1.32 (5004) {G0,W12,D4,L3,V2,M3} { ! p( X ), ! p( crypt( xor( km, data ), Y ) )
% 0.88/1.32 , p( decrypt( Y, X ) ) }.
% 0.88/1.32 (5005) {G0,W30,D5,L5,V6,M5} { ! p( crypt( X, Y ) ), ! p( Z ), ! p( crypt(
% 0.88/1.32 xor( km, imp ), T ) ), ! p( crypt( xor( km, exp ), U ) ), p( crypt( xor(
% 0.88/1.32 U, W ), decrypt( xor( Z, T ), crypt( X, Y ) ) ) ) }.
% 0.88/1.32 (5006) {G0,W8,D3,L3,V2,M3} { ! p( X ), ! p( Y ), p( xor( X, Y ) ) }.
% 0.88/1.32 (5007) {G0,W8,D3,L3,V2,M3} { ! p( crypt( Y, X ) ), ! p( Y ), p( X ) }.
% 0.88/1.32 (5008) {G0,W8,D3,L3,V2,M3} { ! p( Y ), ! p( X ), p( crypt( X, Y ) ) }.
% 0.88/1.32 (5009) {G0,W10,D4,L2,V2,M2} { ! p( crypt( xor( X, data ), Y ) ), p( crypt
% 0.88/1.32 ( X, Y ) ) }.
% 0.88/1.32 (5010) {G0,W2,D2,L1,V0,M1} { p( kp ) }.
% 0.88/1.32 (5011) {G0,W2,D2,L1,V0,M1} { p( imp ) }.
% 0.88/1.32 (5012) {G0,W2,D2,L1,V0,M1} { p( data ) }.
% 0.88/1.32 (5013) {G0,W2,D2,L1,V0,M1} { p( id ) }.
% 0.88/1.32 (5014) {G0,W2,D2,L1,V0,M1} { p( pin ) }.
% 0.88/1.32 (5015) {G0,W6,D4,L1,V0,M1} { p( crypt( xor( km, pin ), pp ) ) }.
% 0.88/1.32 (5016) {G0,W6,D4,L1,V0,M1} { p( crypt( xor( km, exp ), eurk ) ) }.
% 0.88/1.32 (5017) {G0,W6,D4,L1,V0,M1} { p( crypt( xor( km, data ), eurk ) ) }.
% 0.88/1.32 (5018) {G0,W2,D2,L1,V0,M1} { p( exp ) }.
% 0.88/1.32 (5019) {G0,W2,D2,L1,V0,M1} { p( a ) }.
% 0.88/1.32 (5020) {G0,W8,D4,L2,V1,M2} { ! p( crypt( xor( km, exp ), X ) ), ! p( X )
% 0.88/1.32 }.
% 0.88/1.32
% 0.88/1.32
% 0.88/1.32 Total Proof:
% 0.88/1.32
% 0.88/1.32 subsumption: (1) {G0,W11,D4,L1,V3,M1} I { xor( X, xor( Y, Z ) ) ==> xor(
% 0.88/1.32 xor( X, Y ), Z ) }.
% 0.88/1.32 parent0: (4994) {G0,W11,D4,L1,V3,M1} { xor( X, xor( Y, Z ) ) = xor( xor( X
% 0.88/1.32 , Y ), Z ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := X
% 0.88/1.32 Y := Y
% 0.88/1.32 Z := Z
% 0.88/1.32 end
% 0.88/1.32 permutation0:
% 0.88/1.32 0 ==> 0
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 subsumption: (3) {G0,W5,D3,L1,V1,M1} I { xor( X, id ) ==> X }.
% 0.88/1.32 parent0: (4996) {G0,W5,D3,L1,V1,M1} { xor( X, id ) = X }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := X
% 0.88/1.32 end
% 0.88/1.32 permutation0:
% 0.88/1.32 0 ==> 0
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 subsumption: (4) {G0,W5,D3,L1,V1,M1} I { xor( X, X ) ==> id }.
% 0.88/1.32 parent0: (4997) {G0,W5,D3,L1,V1,M1} { xor( X, X ) = id }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := X
% 0.88/1.32 end
% 0.88/1.32 permutation0:
% 0.88/1.32 0 ==> 0
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 paramod: (5051) {G1,W12,D5,L3,V2,M3} { p( crypt( xor( xor( km, kp ), X ),
% 0.88/1.32 Y ) ), ! p( Y ), ! p( X ) }.
% 0.88/1.32 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { xor( X, xor( Y, Z ) ) ==> xor( xor
% 0.88/1.32 ( X, Y ), Z ) }.
% 0.88/1.32 parent1[2; 2]: (5000) {G0,W12,D5,L3,V2,M3} { ! p( X ), ! p( Y ), p( crypt
% 0.88/1.32 ( xor( km, xor( kp, Y ) ), X ) ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := km
% 0.88/1.32 Y := kp
% 0.88/1.32 Z := X
% 0.88/1.32 end
% 0.88/1.32 substitution1:
% 0.88/1.32 X := Y
% 0.88/1.32 Y := X
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 subsumption: (7) {G1,W12,D5,L3,V2,M3} I;d(1) { ! p( X ), ! p( Y ), p( crypt
% 0.88/1.32 ( xor( xor( km, kp ), Y ), X ) ) }.
% 0.88/1.32 parent0: (5051) {G1,W12,D5,L3,V2,M3} { p( crypt( xor( xor( km, kp ), X ),
% 0.88/1.32 Y ) ), ! p( Y ), ! p( X ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := Y
% 0.88/1.32 Y := X
% 0.88/1.32 end
% 0.88/1.32 permutation0:
% 0.88/1.32 0 ==> 2
% 0.88/1.32 1 ==> 0
% 0.88/1.32 2 ==> 1
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 subsumption: (13) {G0,W8,D3,L3,V2,M3} I { ! p( X ), ! p( Y ), p( xor( X, Y
% 0.88/1.32 ) ) }.
% 0.88/1.32 parent0: (5006) {G0,W8,D3,L3,V2,M3} { ! p( X ), ! p( Y ), p( xor( X, Y ) )
% 0.88/1.32 }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := X
% 0.88/1.32 Y := Y
% 0.88/1.32 end
% 0.88/1.32 permutation0:
% 0.88/1.32 0 ==> 0
% 0.88/1.32 1 ==> 1
% 0.88/1.32 2 ==> 2
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 subsumption: (17) {G0,W2,D2,L1,V0,M1} I { p( kp ) }.
% 0.88/1.32 parent0: (5010) {G0,W2,D2,L1,V0,M1} { p( kp ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 end
% 0.88/1.32 permutation0:
% 0.88/1.32 0 ==> 0
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 subsumption: (25) {G0,W2,D2,L1,V0,M1} I { p( exp ) }.
% 0.88/1.32 parent0: (5018) {G0,W2,D2,L1,V0,M1} { p( exp ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 end
% 0.88/1.32 permutation0:
% 0.88/1.32 0 ==> 0
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 subsumption: (27) {G0,W8,D4,L2,V1,M2} I { ! p( crypt( xor( km, exp ), X ) )
% 0.88/1.32 , ! p( X ) }.
% 0.88/1.32 parent0: (5020) {G0,W8,D4,L2,V1,M2} { ! p( crypt( xor( km, exp ), X ) ), !
% 0.88/1.32 p( X ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := X
% 0.88/1.32 end
% 0.88/1.32 permutation0:
% 0.88/1.32 0 ==> 0
% 0.88/1.32 1 ==> 1
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 factor: (5164) {G1,W10,D5,L2,V1,M2} { ! p( X ), p( crypt( xor( xor( km, kp
% 0.88/1.32 ), X ), X ) ) }.
% 0.88/1.32 parent0[0, 1]: (7) {G1,W12,D5,L3,V2,M3} I;d(1) { ! p( X ), ! p( Y ), p(
% 0.88/1.32 crypt( xor( xor( km, kp ), Y ), X ) ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := X
% 0.88/1.32 Y := X
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 subsumption: (33) {G2,W10,D5,L2,V1,M2} F(7) { ! p( X ), p( crypt( xor( xor
% 0.88/1.32 ( km, kp ), X ), X ) ) }.
% 0.88/1.32 parent0: (5164) {G1,W10,D5,L2,V1,M2} { ! p( X ), p( crypt( xor( xor( km,
% 0.88/1.32 kp ), X ), X ) ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := X
% 0.88/1.32 end
% 0.88/1.32 permutation0:
% 0.88/1.32 0 ==> 0
% 0.88/1.32 1 ==> 1
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 eqswap: (5166) {G0,W11,D4,L1,V3,M1} { xor( xor( X, Y ), Z ) ==> xor( X,
% 0.88/1.32 xor( Y, Z ) ) }.
% 0.88/1.32 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { xor( X, xor( Y, Z ) ) ==> xor( xor
% 0.88/1.32 ( X, Y ), Z ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := X
% 0.88/1.32 Y := Y
% 0.88/1.32 Z := Z
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 paramod: (5172) {G1,W9,D4,L1,V2,M1} { xor( xor( X, Y ), Y ) ==> xor( X, id
% 0.88/1.32 ) }.
% 0.88/1.32 parent0[0]: (4) {G0,W5,D3,L1,V1,M1} I { xor( X, X ) ==> id }.
% 0.88/1.32 parent1[0; 8]: (5166) {G0,W11,D4,L1,V3,M1} { xor( xor( X, Y ), Z ) ==> xor
% 0.88/1.32 ( X, xor( Y, Z ) ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := Y
% 0.88/1.32 end
% 0.88/1.32 substitution1:
% 0.88/1.32 X := X
% 0.88/1.32 Y := Y
% 0.88/1.32 Z := Y
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 paramod: (5173) {G1,W7,D4,L1,V2,M1} { xor( xor( X, Y ), Y ) ==> X }.
% 0.88/1.32 parent0[0]: (3) {G0,W5,D3,L1,V1,M1} I { xor( X, id ) ==> X }.
% 0.88/1.32 parent1[0; 6]: (5172) {G1,W9,D4,L1,V2,M1} { xor( xor( X, Y ), Y ) ==> xor
% 0.88/1.32 ( X, id ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := X
% 0.88/1.32 end
% 0.88/1.32 substitution1:
% 0.88/1.32 X := X
% 0.88/1.32 Y := Y
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 subsumption: (44) {G1,W7,D4,L1,V2,M1} P(4,1);d(3) { xor( xor( Y, X ), X )
% 0.88/1.32 ==> Y }.
% 0.88/1.32 parent0: (5173) {G1,W7,D4,L1,V2,M1} { xor( xor( X, Y ), Y ) ==> X }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := Y
% 0.88/1.32 Y := X
% 0.88/1.32 end
% 0.88/1.32 permutation0:
% 0.88/1.32 0 ==> 0
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 resolution: (5175) {G1,W6,D3,L2,V1,M2} { ! p( X ), p( xor( kp, X ) ) }.
% 0.88/1.32 parent0[0]: (13) {G0,W8,D3,L3,V2,M3} I { ! p( X ), ! p( Y ), p( xor( X, Y )
% 0.88/1.32 ) }.
% 0.88/1.32 parent1[0]: (17) {G0,W2,D2,L1,V0,M1} I { p( kp ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := kp
% 0.88/1.32 Y := X
% 0.88/1.32 end
% 0.88/1.32 substitution1:
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 subsumption: (679) {G1,W6,D3,L2,V1,M2} R(13,17) { ! p( X ), p( xor( kp, X )
% 0.88/1.32 ) }.
% 0.88/1.32 parent0: (5175) {G1,W6,D3,L2,V1,M2} { ! p( X ), p( xor( kp, X ) ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := X
% 0.88/1.32 end
% 0.88/1.32 permutation0:
% 0.88/1.32 0 ==> 0
% 0.88/1.32 1 ==> 1
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 resolution: (5177) {G1,W4,D3,L1,V0,M1} { p( xor( kp, exp ) ) }.
% 0.88/1.32 parent0[0]: (679) {G1,W6,D3,L2,V1,M2} R(13,17) { ! p( X ), p( xor( kp, X )
% 0.88/1.32 ) }.
% 0.88/1.32 parent1[0]: (25) {G0,W2,D2,L1,V0,M1} I { p( exp ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := exp
% 0.88/1.32 end
% 0.88/1.32 substitution1:
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 subsumption: (4731) {G2,W4,D3,L1,V0,M1} R(679,25) { p( xor( kp, exp ) ) }.
% 0.88/1.32 parent0: (5177) {G1,W4,D3,L1,V0,M1} { p( xor( kp, exp ) ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 end
% 0.88/1.32 permutation0:
% 0.88/1.32 0 ==> 0
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 resolution: (5180) {G3,W12,D5,L1,V0,M1} { p( crypt( xor( xor( km, kp ),
% 0.88/1.32 xor( kp, exp ) ), xor( kp, exp ) ) ) }.
% 0.88/1.32 parent0[0]: (33) {G2,W10,D5,L2,V1,M2} F(7) { ! p( X ), p( crypt( xor( xor(
% 0.88/1.32 km, kp ), X ), X ) ) }.
% 0.88/1.32 parent1[0]: (4731) {G2,W4,D3,L1,V0,M1} R(679,25) { p( xor( kp, exp ) ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := xor( kp, exp )
% 0.88/1.32 end
% 0.88/1.32 substitution1:
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 paramod: (5181) {G1,W12,D6,L1,V0,M1} { p( crypt( xor( xor( xor( km, kp ),
% 0.88/1.32 kp ), exp ), xor( kp, exp ) ) ) }.
% 0.88/1.32 parent0[0]: (1) {G0,W11,D4,L1,V3,M1} I { xor( X, xor( Y, Z ) ) ==> xor( xor
% 0.88/1.32 ( X, Y ), Z ) }.
% 0.88/1.32 parent1[0; 2]: (5180) {G3,W12,D5,L1,V0,M1} { p( crypt( xor( xor( km, kp )
% 0.88/1.32 , xor( kp, exp ) ), xor( kp, exp ) ) ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := xor( km, kp )
% 0.88/1.32 Y := kp
% 0.88/1.32 Z := exp
% 0.88/1.32 end
% 0.88/1.32 substitution1:
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 paramod: (5182) {G2,W8,D4,L1,V0,M1} { p( crypt( xor( km, exp ), xor( kp,
% 0.88/1.32 exp ) ) ) }.
% 0.88/1.32 parent0[0]: (44) {G1,W7,D4,L1,V2,M1} P(4,1);d(3) { xor( xor( Y, X ), X )
% 0.88/1.32 ==> Y }.
% 0.88/1.32 parent1[0; 3]: (5181) {G1,W12,D6,L1,V0,M1} { p( crypt( xor( xor( xor( km,
% 0.88/1.32 kp ), kp ), exp ), xor( kp, exp ) ) ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := kp
% 0.88/1.32 Y := km
% 0.88/1.32 end
% 0.88/1.32 substitution1:
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 subsumption: (4988) {G3,W8,D4,L1,V0,M1} R(4731,33);d(1);d(44) { p( crypt(
% 0.88/1.32 xor( km, exp ), xor( kp, exp ) ) ) }.
% 0.88/1.32 parent0: (5182) {G2,W8,D4,L1,V0,M1} { p( crypt( xor( km, exp ), xor( kp,
% 0.88/1.32 exp ) ) ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 end
% 0.88/1.32 permutation0:
% 0.88/1.32 0 ==> 0
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 resolution: (5183) {G1,W8,D4,L1,V0,M1} { ! p( crypt( xor( km, exp ), xor(
% 0.88/1.32 kp, exp ) ) ) }.
% 0.88/1.32 parent0[1]: (27) {G0,W8,D4,L2,V1,M2} I { ! p( crypt( xor( km, exp ), X ) )
% 0.88/1.32 , ! p( X ) }.
% 0.88/1.32 parent1[0]: (4731) {G2,W4,D3,L1,V0,M1} R(679,25) { p( xor( kp, exp ) ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 X := xor( kp, exp )
% 0.88/1.32 end
% 0.88/1.32 substitution1:
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 resolution: (5184) {G2,W0,D0,L0,V0,M0} { }.
% 0.88/1.32 parent0[0]: (5183) {G1,W8,D4,L1,V0,M1} { ! p( crypt( xor( km, exp ), xor(
% 0.88/1.32 kp, exp ) ) ) }.
% 0.88/1.32 parent1[0]: (4988) {G3,W8,D4,L1,V0,M1} R(4731,33);d(1);d(44) { p( crypt(
% 0.88/1.32 xor( km, exp ), xor( kp, exp ) ) ) }.
% 0.88/1.32 substitution0:
% 0.88/1.32 end
% 0.88/1.32 substitution1:
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 subsumption: (4991) {G4,W0,D0,L0,V0,M0} R(4731,27);r(4988) { }.
% 0.88/1.32 parent0: (5184) {G2,W0,D0,L0,V0,M0} { }.
% 0.88/1.32 substitution0:
% 0.88/1.32 end
% 0.88/1.32 permutation0:
% 0.88/1.32 end
% 0.88/1.32
% 0.88/1.32 Proof check complete!
% 0.88/1.32
% 0.88/1.32 Memory use:
% 0.88/1.32
% 0.88/1.32 space for terms: 50660
% 0.88/1.32 space for clauses: 242233
% 0.88/1.32
% 0.88/1.32
% 0.88/1.32 clauses generated: 10612
% 0.88/1.32 clauses kept: 4992
% 0.88/1.32 clauses selected: 186
% 0.88/1.32 clauses deleted: 3
% 0.88/1.32 clauses inuse deleted: 2
% 0.88/1.32
% 0.88/1.32 subsentry: 21014
% 0.88/1.32 literals s-matched: 7153
% 0.88/1.32 literals matched: 6602
% 0.88/1.32 full subsumption: 4115
% 0.88/1.32
% 0.88/1.32 checksum: -1771058159
% 0.88/1.32
% 0.88/1.32
% 0.88/1.32 Bliksem ended
%------------------------------------------------------------------------------