TPTP Problem File: SWV795_5.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SWV795_5 : TPTP v8.2.0. Released v6.0.0.
% Domain : Software Verification
% Problem : Needham-Schroeder shared-key protocol line 468
% Version : Especial.
% English :
% Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% : [Bla13] Blanchette (2011), Email to Geoff Sutcliffe
% Source : [Bla13]
% Names : ns_468 [Bla13]
% Status : Unknown
% Rating : 1.00 v6.4.0
% Syntax : Number of formulae : 149 ( 42 unt; 40 typ; 0 def)
% Number of atoms : 264 ( 58 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 230 ( 75 ~; 1 |; 9 &)
% ( 15 <=>; 130 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 34 ( 21 >; 13 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 0 prp; 1-4 aty)
% Number of functors : 31 ( 31 usr; 14 con; 0-4 aty)
% Number of variables : 366 ( 359 !; 2 ?; 366 :)
% ( 5 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_UNK_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-12-13 16:27:38
%------------------------------------------------------------------------------
%----Should-be-implicit typings (7)
tff(ty_tc_Event_Oevent,type,
event: $tType ).
tff(ty_tc_HOL_Obool,type,
bool: $tType ).
tff(ty_tc_List_Olist,type,
list: $tType > $tType ).
tff(ty_tc_Message_Oagent,type,
agent: $tType ).
tff(ty_tc_Message_Omsg,type,
msg: $tType ).
tff(ty_tc_Nat_Onat,type,
nat: $tType ).
tff(ty_tc_fun,type,
fun: ( $tType * $tType ) > $tType ).
%----Explicit typings (33)
tff(sy_c_Event_Obad,type,
bad: fun(agent,bool) ).
tff(sy_c_Event_Oevent_ONotes,type,
notes: ( agent * msg ) > event ).
tff(sy_c_Event_Oevent_OSays,type,
says: ( agent * agent * msg ) > event ).
tff(sy_c_Event_Oknows,type,
knows: ( agent * list(event) ) > fun(msg,bool) ).
tff(sy_c_Event_Oused,type,
used: list(event) > fun(msg,bool) ).
tff(sy_c_List_Olist_OCons,type,
cons:
!>[A1: $tType] : ( ( A1 * list(A1) ) > list(A1) ) ).
tff(sy_c_List_Oset,type,
set:
!>[A1: $tType] : ( list(A1) > fun(A1,bool) ) ).
tff(sy_c_Message_Oagent_OServer,type,
server: agent ).
tff(sy_c_Message_Oagent_OSpy,type,
spy: agent ).
tff(sy_c_Message_Oanalz,type,
analz: fun(msg,bool) > fun(msg,bool) ).
tff(sy_c_Message_Omsg_OAgent,type,
agent1: agent > msg ).
tff(sy_c_Message_Omsg_OCrypt,type,
crypt: ( nat * msg ) > msg ).
tff(sy_c_Message_Omsg_OKey,type,
key: nat > msg ).
tff(sy_c_Message_Omsg_OMPair,type,
mPair: ( msg * msg ) > msg ).
tff(sy_c_Message_Omsg_ONonce,type,
nonce: nat > msg ).
tff(sy_c_Message_Oparts,type,
parts: fun(msg,bool) > fun(msg,bool) ).
tff(sy_c_Message_OsymKeys,type,
symKeys: fun(nat,bool) ).
tff(sy_c_NS__Shared__Mirabelle__iywubrjwsc_OIssues,type,
nS_Sha512322870Issues: ( agent * agent * msg * list(event) ) > $o ).
tff(sy_c_NS__Shared__Mirabelle__iywubrjwsc_Ons__shared,type,
nS_Sha254967238shared: fun(list(event),bool) ).
tff(sy_c_NS__Shared__Mirabelle__iywubrjwsc_Ons__sharedp,type,
nS_Sha993195050haredp: list(event) > $o ).
tff(sy_c_Public_OshrK,type,
shrK: agent > nat ).
tff(sy_c_aa,type,
aa:
!>[A1: $tType,B1: $tType] : ( ( fun(A1,B1) * A1 ) > B1 ) ).
tff(sy_c_fFalse,type,
fFalse: bool ).
tff(sy_c_fTrue,type,
fTrue: bool ).
tff(sy_c_member,type,
member:
!>[A1: $tType] : ( ( A1 * fun(A1,bool) ) > $o ) ).
tff(sy_c_pp,type,
pp: bool > $o ).
tff(sy_v_A,type,
a: agent ).
tff(sy_v_B,type,
b: agent ).
tff(sy_v_K,type,
k: nat ).
tff(sy_v_NA,type,
na: nat ).
tff(sy_v_NB,type,
nb: nat ).
tff(sy_v_X,type,
x: msg ).
tff(sy_v_evs,type,
evs: list(event) ).
%----Relevant facts (100)
tff(fact_0_Spy__analz__shrK,axiom,
! [Aa: agent,Evsa: list(event)] :
( member(list(event),Evsa,nS_Sha254967238shared)
=> ( member(msg,key(shrK(Aa)),analz(knows(spy,Evsa)))
<=> member(agent,Aa,bad) ) ) ).
tff(fact_1_Spy__see__shrK,axiom,
! [Aa: agent,Evsa: list(event)] :
( member(list(event),Evsa,nS_Sha254967238shared)
=> ( member(msg,key(shrK(Aa)),parts(knows(spy,Evsa)))
<=> member(agent,Aa,bad) ) ) ).
tff(fact_2_NS3__msg__in__parts__spies,axiom,
! [Evsa: list(event),Xa: msg,Ka: msg,Ba: msg,N: msg,KA: nat,Aa: agent,S: agent] :
( member(event,says(S,Aa,crypt(KA,mPair(N,mPair(Ba,mPair(Ka,Xa))))),set(event,Evsa))
=> member(msg,Xa,parts(knows(spy,Evsa))) ) ).
tff(fact_3_Spy__spies__bad__shrK,axiom,
! [Evsa: list(event),Aa: agent] :
( member(agent,Aa,bad)
=> member(msg,key(shrK(Aa)),knows(spy,Evsa)) ) ).
tff(fact_4_A__authenticates__and__keydist__to__B,axiom,
! [Xa: msg,Ba: agent,NAa: msg,Aa: agent,Evsa: list(event),NBa: nat,Ka: nat] :
( member(msg,crypt(Ka,nonce(NBa)),parts(knows(spy,Evsa)))
=> ( member(msg,crypt(shrK(Aa),mPair(NAa,mPair(agent1(Ba),mPair(key(Ka),Xa)))),parts(knows(spy,Evsa)))
=> ( ~ member(msg,key(Ka),analz(knows(spy,Evsa)))
=> ( ~ member(agent,Aa,bad)
=> ( ~ member(agent,Ba,bad)
=> ( member(list(event),Evsa,nS_Sha254967238shared)
=> nS_Sha512322870Issues(Ba,Aa,crypt(Ka,nonce(NBa)),Evsa) ) ) ) ) ) ) ).
tff(fact_5_B__Issues__A,axiom,
! [Evsa: list(event),Nb: nat,Ka: nat,Aa: agent,Ba: agent] :
( member(event,says(Ba,Aa,crypt(Ka,nonce(Nb))),set(event,Evsa))
=> ( ~ member(msg,key(Ka),analz(knows(spy,Evsa)))
=> ( ~ member(agent,Aa,bad)
=> ( ~ member(agent,Ba,bad)
=> ( member(list(event),Evsa,nS_Sha254967238shared)
=> nS_Sha512322870Issues(Ba,Aa,crypt(Ka,nonce(Nb)),Evsa) ) ) ) ) ) ).
tff(fact_6_shrK__in__knows,axiom,
! [Evsa: list(event),Aa: agent] : member(msg,key(shrK(Aa)),knows(Aa,Evsa)) ).
tff(fact_7_Crypt__Spy__analz__bad,axiom,
! [Evsa: list(event),Xa: msg,Aa: agent] :
( member(msg,crypt(shrK(Aa),Xa),analz(knows(spy,Evsa)))
=> ( member(agent,Aa,bad)
=> member(msg,Xa,analz(knows(spy,Evsa))) ) ) ).
tff(fact_8_Spy__in__bad,axiom,
member(agent,spy,bad) ).
tff(fact_9_Says__imp__parts__knows__Spy,axiom,
! [Evsa: list(event),Xa: msg,Ba: agent,Aa: agent] :
( member(event,says(Aa,Ba,Xa),set(event,Evsa))
=> member(msg,Xa,parts(knows(spy,Evsa))) ) ).
tff(fact_10_Says__imp__analz__Spy,axiom,
! [Evsa: list(event),Xa: msg,Ba: agent,Aa: agent] :
( member(event,says(Aa,Ba,Xa),set(event,Evsa))
=> member(msg,Xa,analz(knows(spy,Evsa))) ) ).
tff(fact_11_MPair__parts,axiom,
! [H: fun(msg,bool),Y: msg,Xa: msg] :
( member(msg,mPair(Xa,Y),parts(H))
=> ~ ( member(msg,Xa,parts(H))
=> ~ member(msg,Y,parts(H)) ) ) ).
tff(fact_12_analz__parts,axiom,
! [H: fun(msg,bool)] : analz(parts(H)) = parts(H) ).
tff(fact_13_parts__analz,axiom,
! [H: fun(msg,bool)] : parts(analz(H)) = parts(H) ).
tff(fact_14_analz__conj__parts,axiom,
! [H: fun(msg,bool),Xa: msg] :
( ( member(msg,Xa,analz(H))
& member(msg,Xa,parts(H)) )
<=> member(msg,Xa,analz(H)) ) ).
tff(fact_15_analz_OInj,axiom,
! [H: fun(msg,bool),Xa: msg] :
( member(msg,Xa,H)
=> member(msg,Xa,analz(H)) ) ).
tff(fact_16_analz__idem,axiom,
! [H: fun(msg,bool)] : analz(analz(H)) = analz(H) ).
tff(fact_17_msg_Osimps_I6_J,axiom,
! [Msg24: msg,Msg14: msg,Msg23: msg,Msg13: msg] :
( ( mPair(Msg13,Msg23) = mPair(Msg14,Msg24) )
<=> ( ( Msg13 = Msg14 )
& ( Msg23 = Msg24 ) ) ) ).
tff(fact_18_msg_Osimps_I4_J,axiom,
! [Nat3: nat,Nat2: nat] :
( ( key(Nat2) = key(Nat3) )
<=> ( Nat2 = Nat3 ) ) ).
tff(fact_19_parts_OInj,axiom,
! [H: fun(msg,bool),Xa: msg] :
( member(msg,Xa,H)
=> member(msg,Xa,parts(H)) ) ).
tff(fact_20_parts__idem,axiom,
! [H: fun(msg,bool)] : parts(parts(H)) = parts(H) ).
tff(fact_21_msg_Osimps_I7_J,axiom,
! [Msg3: msg,Nat3: nat,Msg2: msg,Nat2: nat] :
( ( crypt(Nat2,Msg2) = crypt(Nat3,Msg3) )
<=> ( ( Nat2 = Nat3 )
& ( Msg2 = Msg3 ) ) ) ).
tff(fact_22_msg_Osimps_I3_J,axiom,
! [Nat3: nat,Nat2: nat] :
( ( nonce(Nat2) = nonce(Nat3) )
<=> ( Nat2 = Nat3 ) ) ).
tff(fact_23_msg_Osimps_I1_J,axiom,
! [Agent4: agent,Agent3: agent] :
( ( agent1(Agent3) = agent1(Agent4) )
<=> ( Agent3 = Agent4 ) ) ).
tff(fact_24_event_Osimps_I1_J,axiom,
! [Msg3: msg,Agent22: agent,Agent12: agent,Msg2: msg,Agent21: agent,Agent11: agent] :
( ( says(Agent11,Agent21,Msg2) = says(Agent12,Agent22,Msg3) )
<=> ( ( Agent11 = Agent12 )
& ( Agent21 = Agent22 )
& ( Msg2 = Msg3 ) ) ) ).
tff(fact_25_shrK__injective,axiom,
! [Y1: agent,X1: agent] :
( ( shrK(X1) = shrK(Y1) )
<=> ( X1 = Y1 ) ) ).
tff(fact_26_MPair__analz,axiom,
! [H: fun(msg,bool),Y: msg,Xa: msg] :
( member(msg,mPair(Xa,Y),analz(H))
=> ~ ( member(msg,Xa,analz(H))
=> ~ member(msg,Y,analz(H)) ) ) ).
tff(fact_27_analz__disj__parts,axiom,
! [H: fun(msg,bool),Xa: msg] :
( ( member(msg,Xa,analz(H))
| member(msg,Xa,parts(H)) )
<=> member(msg,Xa,parts(H)) ) ).
tff(fact_28_analz__analzD,axiom,
! [H: fun(msg,bool),Xa: msg] :
( member(msg,Xa,analz(analz(H)))
=> member(msg,Xa,analz(H)) ) ).
tff(fact_29_parts__partsD,axiom,
! [H: fun(msg,bool),Xa: msg] :
( member(msg,Xa,parts(parts(H)))
=> member(msg,Xa,parts(H)) ) ).
tff(fact_30_analz_OSnd,axiom,
! [H: fun(msg,bool),Y: msg,Xa: msg] :
( member(msg,mPair(Xa,Y),analz(H))
=> member(msg,Y,analz(H)) ) ).
tff(fact_31_analz_OFst,axiom,
! [H: fun(msg,bool),Y: msg,Xa: msg] :
( member(msg,mPair(Xa,Y),analz(H))
=> member(msg,Xa,analz(H)) ) ).
tff(fact_32_analz__into__parts,axiom,
! [H: fun(msg,bool),C: msg] :
( member(msg,C,analz(H))
=> member(msg,C,parts(H)) ) ).
tff(fact_33_not__parts__not__analz,axiom,
! [H: fun(msg,bool),C: msg] :
( ~ member(msg,C,parts(H))
=> ~ member(msg,C,analz(H)) ) ).
tff(fact_34_msg_Osimps_I41_J,axiom,
! [Nat1: nat,Msg21: msg,Msg11: msg] : mPair(Msg11,Msg21) != key(Nat1) ).
tff(fact_35_msg_Osimps_I40_J,axiom,
! [Msg21: msg,Msg11: msg,Nat1: nat] : key(Nat1) != mPair(Msg11,Msg21) ).
tff(fact_36_parts_OSnd,axiom,
! [H: fun(msg,bool),Y: msg,Xa: msg] :
( member(msg,mPair(Xa,Y),parts(H))
=> member(msg,Y,parts(H)) ) ).
tff(fact_37_parts_OFst,axiom,
! [H: fun(msg,bool),Y: msg,Xa: msg] :
( member(msg,mPair(Xa,Y),parts(H))
=> member(msg,Xa,parts(H)) ) ).
tff(fact_38_msg_Osimps_I48_J,axiom,
! [Msg1: msg,Nat: nat,Msg22: msg,Msg12: msg] : mPair(Msg12,Msg22) != crypt(Nat,Msg1) ).
tff(fact_39_msg_Osimps_I49_J,axiom,
! [Msg22: msg,Msg12: msg,Msg1: msg,Nat: nat] : crypt(Nat,Msg1) != mPair(Msg12,Msg22) ).
tff(fact_40_msg_Osimps_I43_J,axiom,
! [Nat1: nat,Msg1: msg,Nat: nat] : crypt(Nat,Msg1) != key(Nat1) ).
tff(fact_41_msg_Osimps_I42_J,axiom,
! [Msg1: msg,Nat: nat,Nat1: nat] : key(Nat1) != crypt(Nat,Msg1) ).
tff(fact_42_spies__partsEs_I2_J,axiom,
! [H: fun(msg,bool),Xa: msg,Ka: nat] :
( member(msg,crypt(Ka,Xa),parts(H))
=> member(msg,Xa,parts(H)) ) ).
tff(fact_43_parts_OBody,axiom,
! [H: fun(msg,bool),Xa: msg,Ka: nat] :
( member(msg,crypt(Ka,Xa),parts(H))
=> member(msg,Xa,parts(H)) ) ).
tff(fact_44_msg_Osimps_I35_J,axiom,
! [Nat1: nat,Msg21: msg,Msg11: msg] : mPair(Msg11,Msg21) != nonce(Nat1) ).
tff(fact_45_msg_Osimps_I34_J,axiom,
! [Msg21: msg,Msg11: msg,Nat1: nat] : nonce(Nat1) != mPair(Msg11,Msg21) ).
tff(fact_46_msg_Osimps_I30_J,axiom,
! [Nat: nat,Nat1: nat] : nonce(Nat1) != key(Nat) ).
tff(fact_47_msg_Osimps_I31_J,axiom,
! [Nat1: nat,Nat: nat] : key(Nat) != nonce(Nat1) ).
tff(fact_48_msg_Osimps_I17_J,axiom,
! [Agent5: agent,Msg21: msg,Msg11: msg] : mPair(Msg11,Msg21) != agent1(Agent5) ).
tff(fact_49_msg_Osimps_I16_J,axiom,
! [Msg21: msg,Msg11: msg,Agent5: agent] : agent1(Agent5) != mPair(Msg11,Msg21) ).
tff(fact_50_msg_Osimps_I12_J,axiom,
! [Nat: nat,Agent5: agent] : agent1(Agent5) != key(Nat) ).
tff(fact_51_msg_Osimps_I13_J,axiom,
! [Agent5: agent,Nat: nat] : key(Nat) != agent1(Agent5) ).
tff(fact_52_msg_Osimps_I37_J,axiom,
! [Nat1: nat,Msg1: msg,Nat: nat] : crypt(Nat,Msg1) != nonce(Nat1) ).
tff(fact_53_msg_Osimps_I36_J,axiom,
! [Msg1: msg,Nat: nat,Nat1: nat] : nonce(Nat1) != crypt(Nat,Msg1) ).
tff(fact_54_msg_Osimps_I19_J,axiom,
! [Agent5: agent,Msg1: msg,Nat: nat] : crypt(Nat,Msg1) != agent1(Agent5) ).
tff(fact_55_msg_Osimps_I18_J,axiom,
! [Msg1: msg,Nat: nat,Agent5: agent] : agent1(Agent5) != crypt(Nat,Msg1) ).
tff(fact_56_msg_Osimps_I11_J,axiom,
! [Agent5: agent,Nat: nat] : nonce(Nat) != agent1(Agent5) ).
tff(fact_57_msg_Osimps_I10_J,axiom,
! [Nat: nat,Agent5: agent] : agent1(Agent5) != nonce(Nat) ).
tff(fact_58_analz__impI,axiom,
! [Q: bool,Evsa: list(event),Y: msg] :
( ( ~ member(msg,Y,analz(knows(spy,Evsa)))
=> pp(Q) )
=> ( ~ member(msg,Y,analz(knows(spy,Evsa)))
=> pp(Q) ) ) ).
tff(fact_59_Says__imp__knows,axiom,
! [Evsa: list(event),Xa: msg,Ba: agent,Aa: agent] :
( member(event,says(Aa,Ba,Xa),set(event,Evsa))
=> member(msg,Xa,knows(Aa,Evsa)) ) ).
tff(fact_60_analz__shrK__Decrypt,axiom,
! [H: fun(msg,bool),Xa: msg,Aa: agent] :
( member(msg,crypt(shrK(Aa),Xa),analz(H))
=> ( member(msg,key(shrK(Aa)),analz(H))
=> member(msg,Xa,analz(H)) ) ) ).
tff(fact_61_Says__imp__spies,axiom,
! [Evsa: list(event),Xa: msg,Ba: agent,Aa: agent] :
( member(event,says(Aa,Ba,Xa),set(event,Evsa))
=> member(msg,Xa,knows(spy,Evsa)) ) ).
tff(fact_62_B__trusts__NS5__lemma,axiom,
! [NBa: nat,NAa: msg,Aa: agent,Ka: nat,Evsa: list(event),Ba: agent] :
( ~ member(agent,Ba,bad)
=> ( member(list(event),Evsa,nS_Sha254967238shared)
=> ( ~ member(msg,key(Ka),analz(knows(spy,Evsa)))
=> ( member(event,says(server,Aa,crypt(shrK(Aa),mPair(NAa,mPair(agent1(Ba),mPair(key(Ka),crypt(shrK(Ba),mPair(key(Ka),agent1(Aa)))))))),set(event,Evsa))
=> ( member(msg,crypt(Ka,mPair(nonce(NBa),nonce(NBa))),parts(knows(spy,Evsa)))
=> member(event,says(Aa,Ba,crypt(Ka,mPair(nonce(NBa),nonce(NBa)))),set(event,Evsa)) ) ) ) ) ) ).
tff(fact_63_A__trusts__NS4__lemma,axiom,
! [NBa: nat,Xa: msg,Ba: agent,NAa: msg,Aa: agent,Ka: nat,Evsa: list(event)] :
( member(list(event),Evsa,nS_Sha254967238shared)
=> ( ~ member(msg,key(Ka),analz(knows(spy,Evsa)))
=> ( member(event,says(server,Aa,crypt(shrK(Aa),mPair(NAa,mPair(agent1(Ba),mPair(key(Ka),Xa))))),set(event,Evsa))
=> ( member(msg,crypt(Ka,nonce(NBa)),parts(knows(spy,Evsa)))
=> member(event,says(Ba,Aa,crypt(Ka,nonce(NBa))),set(event,Evsa)) ) ) ) ) ).
tff(fact_64_A__trusts__NS2,axiom,
! [Evsa: list(event),Xa: msg,Ka: nat,Ba: agent,NAa: msg,Aa: agent] :
( member(msg,crypt(shrK(Aa),mPair(NAa,mPair(agent1(Ba),mPair(key(Ka),Xa)))),parts(knows(spy,Evsa)))
=> ( ~ member(agent,Aa,bad)
=> ( member(list(event),Evsa,nS_Sha254967238shared)
=> member(event,says(server,Aa,crypt(shrK(Aa),mPair(NAa,mPair(agent1(Ba),mPair(key(Ka),Xa))))),set(event,Evsa)) ) ) ) ).
tff(fact_65_B__trusts__NS5,axiom,
! [Aa: agent,Ba: agent,Evsa: list(event),NBa: nat,Ka: nat] :
( member(msg,crypt(Ka,mPair(nonce(NBa),nonce(NBa))),parts(knows(spy,Evsa)))
=> ( member(msg,crypt(shrK(Ba),mPair(key(Ka),agent1(Aa))),parts(knows(spy,Evsa)))
=> ( ! [NA1: msg,NB: msg] : ~ member(event,notes(spy,mPair(NA1,mPair(NB,key(Ka)))),set(event,Evsa))
=> ( ~ member(agent,Aa,bad)
=> ( ~ member(agent,Ba,bad)
=> ( member(list(event),Evsa,nS_Sha254967238shared)
=> member(event,says(Aa,Ba,crypt(Ka,mPair(nonce(NBa),nonce(NBa)))),set(event,Evsa)) ) ) ) ) ) ) ).
tff(fact_66_A__trusts__NS4,axiom,
! [Xa: msg,Ba: agent,NAa: msg,Aa: agent,Evsa: list(event),NBa: nat,Ka: nat] :
( member(msg,crypt(Ka,nonce(NBa)),parts(knows(spy,Evsa)))
=> ( member(msg,crypt(shrK(Aa),mPair(NAa,mPair(agent1(Ba),mPair(key(Ka),Xa)))),parts(knows(spy,Evsa)))
=> ( ! [NB: msg] : ~ member(event,notes(spy,mPair(NAa,mPair(NB,key(Ka)))),set(event,Evsa))
=> ( ~ member(agent,Aa,bad)
=> ( ~ member(agent,Ba,bad)
=> ( member(list(event),Evsa,nS_Sha254967238shared)
=> member(event,says(Ba,Aa,crypt(Ka,nonce(NBa))),set(event,Evsa)) ) ) ) ) ) ) ).
tff(fact_67_NS4__implies__NS3,axiom,
! [NBa: nat,Xa: msg,Ba: agent,NAa: msg,Aa: agent,Ka: nat,Evsa: list(event)] :
( member(list(event),Evsa,nS_Sha254967238shared)
=> ( ~ member(msg,key(Ka),analz(knows(spy,Evsa)))
=> ( member(event,says(server,Aa,crypt(shrK(Aa),mPair(NAa,mPair(agent1(Ba),mPair(key(Ka),Xa))))),set(event,Evsa))
=> ( member(msg,crypt(Ka,nonce(NBa)),parts(knows(spy,Evsa)))
=> ? [A2: agent] : member(event,says(A2,Ba,Xa),set(event,Evsa)) ) ) ) ) ).
tff(fact_68_B__trusts__NS3,axiom,
! [Evsa: list(event),Aa: agent,Ka: nat,Ba: agent] :
( member(msg,crypt(shrK(Ba),mPair(key(Ka),agent1(Aa))),parts(knows(spy,Evsa)))
=> ( ~ member(agent,Ba,bad)
=> ( member(list(event),Evsa,nS_Sha254967238shared)
=> ? [NA1: msg] : member(event,says(server,Aa,crypt(shrK(Aa),mPair(NA1,mPair(agent1(Ba),mPair(key(Ka),crypt(shrK(Ba),mPair(key(Ka),agent1(Aa)))))))),set(event,Evsa)) ) ) ) ).
tff(fact_69_unique__session__keys,axiom,
! [X3: msg,B: agent,NA: msg,A: agent,Evsa: list(event),Xa: msg,Ka: nat,Ba: agent,NAa: msg,Aa: agent] :
( member(event,says(server,Aa,crypt(shrK(Aa),mPair(NAa,mPair(agent1(Ba),mPair(key(Ka),Xa))))),set(event,Evsa))
=> ( member(event,says(server,A,crypt(shrK(A),mPair(NA,mPair(agent1(B),mPair(key(Ka),X3))))),set(event,Evsa))
=> ( member(list(event),Evsa,nS_Sha254967238shared)
=> ( ( Aa = A )
& ( NAa = NA )
& ( Ba = B )
& ( Xa = X3 ) ) ) ) ) ).
tff(fact_70_event_Osimps_I3_J,axiom,
! [Msg3: msg,Agent4: agent,Msg2: msg,Agent3: agent] :
( ( notes(Agent3,Msg2) = notes(Agent4,Msg3) )
<=> ( ( Agent3 = Agent4 )
& ( Msg2 = Msg3 ) ) ) ).
tff(fact_71_agent_Osimps_I5_J,axiom,
spy != server ).
tff(fact_72_agent_Osimps_I4_J,axiom,
server != spy ).
tff(fact_73_event_Osimps_I7_J,axiom,
! [Msg: msg,Agent2: agent,Agent1: agent,Msg1: msg,Agent: agent] : notes(Agent,Msg1) != says(Agent1,Agent2,Msg) ).
tff(fact_74_event_Osimps_I6_J,axiom,
! [Msg1: msg,Agent: agent,Msg: msg,Agent2: agent,Agent1: agent] : says(Agent1,Agent2,Msg) != notes(Agent,Msg1) ).
tff(fact_75_ext,axiom,
! [B1: $tType,A1: $tType,G: fun(A1,B1),F: fun(A1,B1)] :
( ! [X2: A1] : aa(A1,B1,F,X2) = aa(A1,B1,G,X2)
=> ( F = G ) ) ).
tff(fact_76_mem__def,axiom,
! [A1: $tType,Aa: fun(A1,bool),X1: A1] :
( member(A1,X1,Aa)
<=> pp(aa(A1,bool,Aa,X1)) ) ).
tff(fact_77_Server__not__bad,axiom,
~ member(agent,server,bad) ).
tff(fact_78_Notes__imp__knows,axiom,
! [Evsa: list(event),Xa: msg,Aa: agent] :
( member(event,notes(Aa,Xa),set(event,Evsa))
=> member(msg,Xa,knows(Aa,Evsa)) ) ).
tff(fact_79_Notes__imp__knows__Spy,axiom,
! [Evsa: list(event),Xa: msg,Aa: agent] :
( member(event,notes(Aa,Xa),set(event,Evsa))
=> ( member(agent,Aa,bad)
=> member(msg,Xa,knows(spy,Evsa)) ) ) ).
tff(fact_80_Oops__parts__spies,axiom,
! [Evsa: list(event),Xa: msg,Ka: msg,Ba: msg,NAa: msg,Aa: agent] :
( member(event,says(server,Aa,crypt(shrK(Aa),mPair(NAa,mPair(Ba,mPair(Ka,Xa))))),set(event,Evsa))
=> member(msg,Ka,parts(knows(spy,Evsa))) ) ).
tff(fact_81_secrecy__lemma,axiom,
! [Evsa: list(event),Ka: nat,Ba: agent,NAa: msg,Aa: agent] :
( member(event,says(server,Aa,crypt(shrK(Aa),mPair(NAa,mPair(agent1(Ba),mPair(key(Ka),crypt(shrK(Ba),mPair(key(Ka),agent1(Aa)))))))),set(event,Evsa))
=> ( ~ member(agent,Aa,bad)
=> ( ~ member(agent,Ba,bad)
=> ( member(list(event),Evsa,nS_Sha254967238shared)
=> ( ! [NB: msg] : ~ member(event,notes(spy,mPair(NAa,mPair(NB,key(Ka)))),set(event,Evsa))
=> ~ member(msg,key(Ka),analz(knows(spy,Evsa))) ) ) ) ) ) ).
tff(fact_82_Spy__not__see__encrypted__key,axiom,
! [Evsa: list(event),Xa: msg,Ka: nat,Ba: agent,NAa: msg,K: nat,Aa: agent] :
( member(event,says(server,Aa,crypt(K,mPair(NAa,mPair(agent1(Ba),mPair(key(Ka),Xa))))),set(event,Evsa))
=> ( ! [NB: msg] : ~ member(event,notes(spy,mPair(NAa,mPair(NB,key(Ka)))),set(event,Evsa))
=> ( ~ member(agent,Aa,bad)
=> ( ~ member(agent,Ba,bad)
=> ( member(list(event),Evsa,nS_Sha254967238shared)
=> ~ member(msg,key(Ka),analz(knows(spy,Evsa))) ) ) ) ) ) ).
tff(fact_83_ns__shared_OOops,axiom,
! [Xa: msg,NAa: nat,NBa: nat,Ka: nat,Aa: agent,Ba: agent,Evso: list(event)] :
( member(list(event),Evso,nS_Sha254967238shared)
=> ( member(event,says(Ba,Aa,crypt(Ka,nonce(NBa))),set(event,Evso))
=> ( member(event,says(server,Aa,crypt(shrK(Aa),mPair(nonce(NAa),mPair(agent1(Ba),mPair(key(Ka),Xa))))),set(event,Evso))
=> member(list(event),cons(event,notes(spy,mPair(nonce(NAa),mPair(nonce(NBa),key(Ka)))),Evso),nS_Sha254967238shared) ) ) ) ).
tff(fact_84_analz__mono__contra_I1_J,axiom,
! [Evsa: list(event),Xa: msg,Ba: agent,Aa: agent,C: msg] :
( ~ member(msg,C,analz(knows(spy,cons(event,says(Aa,Ba,Xa),Evsa))))
=> ~ member(msg,C,analz(knows(spy,Evsa))) ) ).
tff(fact_85_analz__mono__contra_I2_J,axiom,
! [Evsa: list(event),Xa: msg,Aa: agent,C: msg] :
( ~ member(msg,C,analz(knows(spy,cons(event,notes(Aa,Xa),Evsa))))
=> ~ member(msg,C,analz(knows(spy,Evsa))) ) ).
tff(fact_86_ns__shared_ONS3,axiom,
! [Xa: msg,Ka: nat,Ba: agent,NAa: nat,S: agent,Aa: agent,Evs3: list(event)] :
( member(list(event),Evs3,nS_Sha254967238shared)
=> ( ( Aa != server )
=> ( member(event,says(S,Aa,crypt(shrK(Aa),mPair(nonce(NAa),mPair(agent1(Ba),mPair(key(Ka),Xa))))),set(event,Evs3))
=> ( member(event,says(Aa,server,mPair(agent1(Aa),mPair(agent1(Ba),nonce(NAa)))),set(event,Evs3))
=> member(list(event),cons(event,says(Aa,Ba,Xa),Evs3),nS_Sha254967238shared) ) ) ) ) ).
tff(fact_87_ns__sharedp_OOops,axiom,
! [Xa: msg,NAa: nat,NBa: nat,Ka: nat,Aa: agent,Ba: agent,Evso: list(event)] :
( nS_Sha993195050haredp(Evso)
=> ( member(event,says(Ba,Aa,crypt(Ka,nonce(NBa))),set(event,Evso))
=> ( member(event,says(server,Aa,crypt(shrK(Aa),mPair(nonce(NAa),mPair(agent1(Ba),mPair(key(Ka),Xa))))),set(event,Evso))
=> nS_Sha993195050haredp(cons(event,notes(spy,mPair(nonce(NAa),mPair(nonce(NBa),key(Ka)))),Evso)) ) ) ) ).
tff(fact_88_ns__sharedp_ONS3,axiom,
! [Xa: msg,Ka: nat,Ba: agent,NAa: nat,S: agent,Aa: agent,Evs3: list(event)] :
( nS_Sha993195050haredp(Evs3)
=> ( ( Aa != server )
=> ( member(event,says(S,Aa,crypt(shrK(Aa),mPair(nonce(NAa),mPair(agent1(Ba),mPair(key(Ka),Xa))))),set(event,Evs3))
=> ( member(event,says(Aa,server,mPair(agent1(Aa),mPair(agent1(Ba),nonce(NAa)))),set(event,Evs3))
=> nS_Sha993195050haredp(cons(event,says(Aa,Ba,Xa),Evs3)) ) ) ) ) ).
tff(fact_89_ns__sharedp__ns__shared__eq,axiom,
! [X: list(event)] :
( nS_Sha993195050haredp(X)
<=> member(list(event),X,nS_Sha254967238shared) ) ).
tff(fact_90_ns__sharedp_ONS5,axiom,
! [Xa: msg,Ba: agent,NAa: nat,S: agent,NBa: nat,Aa: agent,B: agent,Ka: nat,Evs5: list(event)] :
( nS_Sha993195050haredp(Evs5)
=> ( member(nat,Ka,symKeys)
=> ( member(event,says(B,Aa,crypt(Ka,nonce(NBa))),set(event,Evs5))
=> ( member(event,says(S,Aa,crypt(shrK(Aa),mPair(nonce(NAa),mPair(agent1(Ba),mPair(key(Ka),Xa))))),set(event,Evs5))
=> nS_Sha993195050haredp(cons(event,says(Aa,Ba,crypt(Ka,mPair(nonce(NBa),nonce(NBa)))),Evs5)) ) ) ) ) ).
tff(fact_91_ns__shared_ONS5,axiom,
! [Xa: msg,Ba: agent,NAa: nat,S: agent,NBa: nat,Aa: agent,B: agent,Ka: nat,Evs5: list(event)] :
( member(list(event),Evs5,nS_Sha254967238shared)
=> ( member(nat,Ka,symKeys)
=> ( member(event,says(B,Aa,crypt(Ka,nonce(NBa))),set(event,Evs5))
=> ( member(event,says(S,Aa,crypt(shrK(Aa),mPair(nonce(NAa),mPair(agent1(Ba),mPair(key(Ka),Xa))))),set(event,Evs5))
=> member(list(event),cons(event,says(Aa,Ba,crypt(Ka,mPair(nonce(NBa),nonce(NBa)))),Evs5),nS_Sha254967238shared) ) ) ) ) ).
tff(fact_92_sym__shrK,axiom,
! [Xa: agent] : member(nat,shrK(Xa),symKeys) ).
tff(fact_93_symKeys__neq__imp__neq,axiom,
! [K: nat,Ka: nat] :
( ~ ( member(nat,Ka,symKeys)
<=> member(nat,K,symKeys) )
=> ( Ka != K ) ) ).
tff(fact_94_analz__Decrypt_H,axiom,
! [H: fun(msg,bool),Xa: msg,Ka: nat] :
( member(msg,crypt(Ka,Xa),analz(H))
=> ( member(nat,Ka,symKeys)
=> ( member(msg,key(Ka),analz(H))
=> member(msg,Xa,analz(H)) ) ) ) ).
tff(fact_95_ns__sharedp_ONS2,axiom,
! [NAa: nat,Ba: agent,Aa: agent,A: agent,KAB: nat,Evs2: list(event)] :
( nS_Sha993195050haredp(Evs2)
=> ( ~ member(msg,key(KAB),used(Evs2))
=> ( member(nat,KAB,symKeys)
=> ( member(event,says(A,server,mPair(agent1(Aa),mPair(agent1(Ba),nonce(NAa)))),set(event,Evs2))
=> nS_Sha993195050haredp(cons(event,says(server,Aa,crypt(shrK(Aa),mPair(nonce(NAa),mPair(agent1(Ba),mPair(key(KAB),crypt(shrK(Ba),mPair(key(KAB),agent1(Aa)))))))),Evs2)) ) ) ) ) ).
tff(fact_96_ns__shared_ONS2,axiom,
! [NAa: nat,Ba: agent,Aa: agent,A: agent,KAB: nat,Evs2: list(event)] :
( member(list(event),Evs2,nS_Sha254967238shared)
=> ( ~ member(msg,key(KAB),used(Evs2))
=> ( member(nat,KAB,symKeys)
=> ( member(event,says(A,server,mPair(agent1(Aa),mPair(agent1(Ba),nonce(NAa)))),set(event,Evs2))
=> member(list(event),cons(event,says(server,Aa,crypt(shrK(Aa),mPair(nonce(NAa),mPair(agent1(Ba),mPair(key(KAB),crypt(shrK(Ba),mPair(key(KAB),agent1(Aa)))))))),Evs2),nS_Sha254967238shared) ) ) ) ) ).
tff(fact_97_MPair__used,axiom,
! [H: list(event),Y: msg,Xa: msg] :
( member(msg,mPair(Xa,Y),used(H))
=> ~ ( member(msg,Xa,used(H))
=> ~ member(msg,Y,used(H)) ) ) ).
tff(fact_98_shrK__in__used,axiom,
! [Evsa: list(event),Aa: agent] : member(msg,key(shrK(Aa)),used(Evsa)) ).
tff(fact_99_usedI,axiom,
! [Evsa: list(event),C: msg] :
( member(msg,C,parts(knows(spy,Evsa)))
=> member(msg,C,used(Evsa)) ) ).
%----Helper facts (2)
tff(help_pp_1_1_U,axiom,
~ pp(fFalse) ).
tff(help_pp_2_1_U,axiom,
pp(fTrue) ).
%----Conjectures (7)
tff(conj_0,hypothesis,
member(msg,crypt(k,mPair(nonce(nb),nonce(nb))),parts(knows(spy,evs))) ).
tff(conj_1,hypothesis,
member(msg,crypt(shrK(a),mPair(nonce(na),mPair(agent1(b),mPair(key(k),x)))),parts(knows(spy,evs))) ).
tff(conj_2,hypothesis,
~ member(msg,key(k),analz(knows(spy,evs))) ).
tff(conj_3,hypothesis,
~ member(agent,a,bad) ).
tff(conj_4,hypothesis,
~ member(agent,b,bad) ).
tff(conj_5,hypothesis,
member(list(event),evs,nS_Sha254967238shared) ).
tff(conj_6,conjecture,
member(event,says(a,b,crypt(k,mPair(nonce(nb),nonce(nb)))),set(event,evs)) ).
%------------------------------------------------------------------------------