TPTP Problem File: SWV747_5.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SWV747_5 : TPTP v8.2.0. Released v6.0.0.
% Domain : Software Verification
% Problem : Needham-Schroeder shared-key protocol line 271
% Version : Especial.
% English :
% Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% : [Bla13] Blanchette (2011), Email to Geoff Sutcliffe
% Source : [Bla13]
% Names : ns_271 [Bla13]
% Status : Unknown
% Rating : 1.00 v6.4.0
% Syntax : Number of formulae : 147 ( 45 unt; 39 typ; 0 def)
% Number of atoms : 217 ( 66 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 152 ( 43 ~; 5 |; 14 &)
% ( 20 <=>; 70 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 32 ( 21 >; 11 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 0 prp; 1-3 aty)
% Number of functors : 31 ( 31 usr; 13 con; 0-4 aty)
% Number of variables : 302 ( 295 !; 1 ?; 302 :)
% ( 6 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_UNK_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-12-13 16:18:10
%------------------------------------------------------------------------------
%----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,
agent1: $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 (32)
tff(sy_c_Event_Obad,type,
bad: fun(agent1,bool) ).
tff(sy_c_Event_Oevent_ONotes,type,
notes: ( agent1 * msg ) > event ).
tff(sy_c_Event_Oevent_OSays,type,
says: ( agent1 * agent1 * msg ) > event ).
tff(sy_c_Event_Oknows,type,
knows: ( agent1 * 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: agent1 ).
tff(sy_c_Message_Oagent_OSpy,type,
spy: agent1 ).
tff(sy_c_Message_Oanalz,type,
analz: fun(msg,bool) > fun(msg,bool) ).
tff(sy_c_Message_Omsg_OAgent,type,
agent: agent1 > 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_Osynth,type,
synth: fun(msg,bool) > fun(msg,bool) ).
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: agent1 > nat ).
tff(sy_c_Set_Oinsert,type,
insert:
!>[A1: $tType] : ( ( A1 * fun(A1,bool) ) > fun(A1,bool) ) ).
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: agent1 ).
tff(sy_v_B,type,
b: agent1 ).
tff(sy_v_Ba,type,
ba: agent1 ).
tff(sy_v_K,type,
k: nat ).
tff(sy_v_NA,type,
na: msg ).
tff(sy_v_X,type,
x: msg ).
tff(sy_v_evsf,type,
evsf: list(event) ).
%----Relevant facts (100)
tff(fact_0_Spy__analz__shrK,axiom,
! [Aa: agent1,Evsa: list(event)] :
( member(list(event),Evsa,nS_Sha254967238shared)
=> ( member(msg,key(shrK(Aa)),analz(knows(spy,Evsa)))
<=> member(agent1,Aa,bad) ) ) ).
tff(fact_1_ns__shared_OFake,axiom,
! [Ba: agent1,X: msg,Evsf: list(event)] :
( member(list(event),Evsf,nS_Sha254967238shared)
=> ( member(msg,X,synth(analz(knows(spy,Evsf))))
=> member(list(event),cons(event,says(spy,Ba,X),Evsf),nS_Sha254967238shared) ) ) ).
tff(fact_2_unique__session__keys,axiom,
! [X2: msg,B: agent1,NA: msg,A3: agent1,Evsa: list(event),X: msg,Ka: nat,Ba: agent1,NAa: msg,Aa: agent1] :
( member(event,says(server,Aa,crypt(shrK(Aa),mPair(NAa,mPair(agent(Ba),mPair(key(Ka),X))))),set(event,Evsa))
=> ( member(event,says(server,A3,crypt(shrK(A3),mPair(NA,mPair(agent(B),mPair(key(Ka),X2))))),set(event,Evsa))
=> ( member(list(event),Evsa,nS_Sha254967238shared)
=> ( ( Aa = A3 )
& ( NAa = NA )
& ( Ba = B )
& ( X = X2 ) ) ) ) ) ).
tff(fact_3_Spy__spies__bad__shrK,axiom,
! [Evsa: list(event),Aa: agent1] :
( member(agent1,Aa,bad)
=> member(msg,key(shrK(Aa)),knows(spy,Evsa)) ) ).
tff(fact_4_shrK__in__knows,axiom,
! [Evsa: list(event),Aa: agent1] : member(msg,key(shrK(Aa)),knows(Aa,Evsa)) ).
tff(fact_5_synth__simps_I5_J,axiom,
! [H: fun(msg,bool),X: msg,Ka: nat] :
( member(msg,crypt(Ka,X),synth(H))
<=> ( member(msg,crypt(Ka,X),H)
| ( member(msg,X,synth(H))
& member(msg,key(Ka),H) ) ) ) ).
tff(fact_6_synth_OCrypt,axiom,
! [Ka: nat,H: fun(msg,bool),X: msg] :
( member(msg,X,synth(H))
=> ( member(msg,key(Ka),H)
=> member(msg,crypt(Ka,X),synth(H)) ) ) ).
tff(fact_7_MPair__synth__analz,axiom,
! [H: fun(msg,bool),Y: msg,X: msg] :
( member(msg,mPair(X,Y),synth(analz(H)))
<=> ( member(msg,X,synth(analz(H)))
& member(msg,Y,synth(analz(H))) ) ) ).
tff(fact_8_Crypt__Spy__analz__bad,axiom,
! [Evsa: list(event),X: msg,Aa: agent1] :
( member(msg,crypt(shrK(Aa),X),analz(knows(spy,Evsa)))
=> ( member(agent1,Aa,bad)
=> member(msg,X,analz(knows(spy,Evsa))) ) ) ).
tff(fact_9_Spy__in__bad,axiom,
member(agent1,spy,bad) ).
tff(fact_10_Notes__imp__knows__Spy,axiom,
! [Evsa: list(event),X: msg,Aa: agent1] :
( member(event,notes(Aa,X),set(event,Evsa))
=> ( member(agent1,Aa,bad)
=> member(msg,X,knows(spy,Evsa)) ) ) ).
tff(fact_11_analz__mono__contra_I2_J,axiom,
! [Evsa: list(event),X: msg,Aa: agent1,C: msg] :
( ~ member(msg,C,analz(knows(spy,cons(event,notes(Aa,X),Evsa))))
=> ~ member(msg,C,analz(knows(spy,Evsa))) ) ).
tff(fact_12_analz__mono__contra_I1_J,axiom,
! [Evsa: list(event),X: msg,Ba: agent1,Aa: agent1,C: msg] :
( ~ member(msg,C,analz(knows(spy,cons(event,says(Aa,Ba,X),Evsa))))
=> ~ member(msg,C,analz(knows(spy,Evsa))) ) ).
tff(fact_13_Says__imp__analz__Spy,axiom,
! [Evsa: list(event),X: msg,Ba: agent1,Aa: agent1] :
( member(event,says(Aa,Ba,X),set(event,Evsa))
=> member(msg,X,analz(knows(spy,Evsa))) ) ).
tff(fact_14_synth_OAgent,axiom,
! [H: fun(msg,bool),Agt: agent1] : member(msg,agent(Agt),synth(H)) ).
tff(fact_15_analz_OInj,axiom,
! [H: fun(msg,bool),X: msg] :
( member(msg,X,H)
=> member(msg,X,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,
! [Msg23: msg,Msg14: msg,Msg22: msg,Msg13: msg] :
( ( mPair(Msg13,Msg22) = mPair(Msg14,Msg23) )
<=> ( ( Msg13 = Msg14 )
& ( Msg22 = Msg23 ) ) ) ).
tff(fact_18_msg_Osimps_I4_J,axiom,
! [Nat3: nat,Nat2: nat] :
( ( key(Nat2) = key(Nat3) )
<=> ( Nat2 = Nat3 ) ) ).
tff(fact_19_msg_Osimps_I7_J,axiom,
! [Msg4: msg,Nat3: nat,Msg3: msg,Nat2: nat] :
( ( crypt(Nat2,Msg3) = crypt(Nat3,Msg4) )
<=> ( ( Nat2 = Nat3 )
& ( Msg3 = Msg4 ) ) ) ).
tff(fact_20_synth_OInj,axiom,
! [H: fun(msg,bool),X: msg] :
( member(msg,X,H)
=> member(msg,X,synth(H)) ) ).
tff(fact_21_msg_Osimps_I1_J,axiom,
! [Agent5: agent1,Agent4: agent1] :
( ( agent(Agent4) = agent(Agent5) )
<=> ( Agent4 = Agent5 ) ) ).
tff(fact_22_event_Osimps_I1_J,axiom,
! [Msg4: msg,Agent22: agent1,Agent12: agent1,Msg3: msg,Agent21: agent1,Agent11: agent1] :
( ( says(Agent11,Agent21,Msg3) = says(Agent12,Agent22,Msg4) )
<=> ( ( Agent11 = Agent12 )
& ( Agent21 = Agent22 )
& ( Msg3 = Msg4 ) ) ) ).
tff(fact_23_shrK__injective,axiom,
! [Y1: agent1,X1: agent1] :
( ( shrK(X1) = shrK(Y1) )
<=> ( X1 = Y1 ) ) ).
tff(fact_24_event_Osimps_I3_J,axiom,
! [Msg4: msg,Agent5: agent1,Msg3: msg,Agent4: agent1] :
( ( notes(Agent4,Msg3) = notes(Agent5,Msg4) )
<=> ( ( Agent4 = Agent5 )
& ( Msg3 = Msg4 ) ) ) ).
tff(fact_25_MPair__analz,axiom,
! [H: fun(msg,bool),Y: msg,X: msg] :
( member(msg,mPair(X,Y),analz(H))
=> ~ ( member(msg,X,analz(H))
=> ~ member(msg,Y,analz(H)) ) ) ).
tff(fact_26_synth_OMPair,axiom,
! [Y: msg,H: fun(msg,bool),X: msg] :
( member(msg,X,synth(H))
=> ( member(msg,Y,synth(H))
=> member(msg,mPair(X,Y),synth(H)) ) ) ).
tff(fact_27_synth__simps_I4_J,axiom,
! [H: fun(msg,bool),Y: msg,X: msg] :
( member(msg,mPair(X,Y),synth(H))
<=> ( member(msg,mPair(X,Y),H)
| ( member(msg,X,synth(H))
& member(msg,Y,synth(H)) ) ) ) ).
tff(fact_28_Key__synth__eq,axiom,
! [H: fun(msg,bool),Ka: nat] :
( member(msg,key(Ka),synth(H))
<=> member(msg,key(Ka),H) ) ).
tff(fact_29_analz__analzD,axiom,
! [H: fun(msg,bool),X: msg] :
( member(msg,X,analz(analz(H)))
=> member(msg,X,analz(H)) ) ).
tff(fact_30_synth__synthD,axiom,
! [H: fun(msg,bool),X: msg] :
( member(msg,X,synth(synth(H)))
=> member(msg,X,synth(H)) ) ).
tff(fact_31_synth__idem,axiom,
! [H: fun(msg,bool)] : synth(synth(H)) = synth(H) ).
tff(fact_32_analz_OSnd,axiom,
! [H: fun(msg,bool),Y: msg,X: msg] :
( member(msg,mPair(X,Y),analz(H))
=> member(msg,Y,analz(H)) ) ).
tff(fact_33_analz_OFst,axiom,
! [H: fun(msg,bool),Y: msg,X: msg] :
( member(msg,mPair(X,Y),analz(H))
=> member(msg,X,analz(H)) ) ).
tff(fact_34_msg_Osimps_I41_J,axiom,
! [Nat1: nat,Msg2: msg,Msg11: msg] : mPair(Msg11,Msg2) != key(Nat1) ).
tff(fact_35_msg_Osimps_I40_J,axiom,
! [Msg2: msg,Msg11: msg,Nat1: nat] : key(Nat1) != mPair(Msg11,Msg2) ).
tff(fact_36_msg_Osimps_I48_J,axiom,
! [Msg: msg,Nat: nat,Msg21: msg,Msg12: msg] : mPair(Msg12,Msg21) != crypt(Nat,Msg) ).
tff(fact_37_msg_Osimps_I49_J,axiom,
! [Msg21: msg,Msg12: msg,Msg: msg,Nat: nat] : crypt(Nat,Msg) != mPair(Msg12,Msg21) ).
tff(fact_38_msg_Osimps_I43_J,axiom,
! [Nat1: nat,Msg: msg,Nat: nat] : crypt(Nat,Msg) != key(Nat1) ).
tff(fact_39_msg_Osimps_I42_J,axiom,
! [Msg: msg,Nat: nat,Nat1: nat] : key(Nat1) != crypt(Nat,Msg) ).
tff(fact_40_msg_Osimps_I17_J,axiom,
! [Agent3: agent1,Msg2: msg,Msg11: msg] : mPair(Msg11,Msg2) != agent(Agent3) ).
tff(fact_41_msg_Osimps_I16_J,axiom,
! [Msg2: msg,Msg11: msg,Agent3: agent1] : agent(Agent3) != mPair(Msg11,Msg2) ).
tff(fact_42_msg_Osimps_I12_J,axiom,
! [Nat: nat,Agent3: agent1] : agent(Agent3) != key(Nat) ).
tff(fact_43_msg_Osimps_I13_J,axiom,
! [Agent3: agent1,Nat: nat] : key(Nat) != agent(Agent3) ).
tff(fact_44_msg_Osimps_I19_J,axiom,
! [Agent3: agent1,Msg: msg,Nat: nat] : crypt(Nat,Msg) != agent(Agent3) ).
tff(fact_45_msg_Osimps_I18_J,axiom,
! [Msg: msg,Nat: nat,Agent3: agent1] : agent(Agent3) != crypt(Nat,Msg) ).
tff(fact_46_Agent__synth,axiom,
! [H: fun(msg,bool),Aa: agent1] : member(msg,agent(Aa),synth(H)) ).
tff(fact_47_agent_Osimps_I4_J,axiom,
server != spy ).
tff(fact_48_agent_Osimps_I5_J,axiom,
spy != server ).
tff(fact_49_event_Osimps_I6_J,axiom,
! [Msg: msg,Agent: agent1,Msg1: msg,Agent2: agent1,Agent1: agent1] : says(Agent1,Agent2,Msg1) != notes(Agent,Msg) ).
tff(fact_50_event_Osimps_I7_J,axiom,
! [Msg1: msg,Agent2: agent1,Agent1: agent1,Msg: msg,Agent: agent1] : notes(Agent,Msg) != says(Agent1,Agent2,Msg1) ).
tff(fact_51_Server__not__bad,axiom,
~ member(agent1,server,bad) ).
tff(fact_52_Crypt__synth__eq,axiom,
! [X: msg,H: fun(msg,bool),Ka: nat] :
( ~ member(msg,key(Ka),H)
=> ( member(msg,crypt(Ka,X),synth(H))
<=> member(msg,crypt(Ka,X),H) ) ) ).
tff(fact_53_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_54_Says__imp__knows,axiom,
! [Evsa: list(event),X: msg,Ba: agent1,Aa: agent1] :
( member(event,says(Aa,Ba,X),set(event,Evsa))
=> member(msg,X,knows(Aa,Evsa)) ) ).
tff(fact_55_Notes__imp__knows,axiom,
! [Evsa: list(event),X: msg,Aa: agent1] :
( member(event,notes(Aa,X),set(event,Evsa))
=> member(msg,X,knows(Aa,Evsa)) ) ).
tff(fact_56_analz__shrK__Decrypt,axiom,
! [H: fun(msg,bool),X: msg,Aa: agent1] :
( member(msg,crypt(shrK(Aa),X),analz(H))
=> ( member(msg,key(shrK(Aa)),analz(H))
=> member(msg,X,analz(H)) ) ) ).
tff(fact_57_syan__impI,axiom,
! [Q: bool,Evsa: list(event),Y: msg] :
( ( ~ member(msg,Y,synth(analz(knows(spy,Evsa))))
=> pp(Q) )
=> ( ~ member(msg,Y,synth(analz(knows(spy,Evsa))))
=> pp(Q) ) ) ).
tff(fact_58_Says__imp__spies,axiom,
! [Evsa: list(event),X: msg,Ba: agent1,Aa: agent1] :
( member(event,says(Aa,Ba,X),set(event,Evsa))
=> member(msg,X,knows(spy,Evsa)) ) ).
tff(fact_59_ns__shared_OOops,axiom,
! [X: msg,NAa: nat,NB2: nat,Ka: nat,Aa: agent1,Ba: agent1,Evso: list(event)] :
( member(list(event),Evso,nS_Sha254967238shared)
=> ( member(event,says(Ba,Aa,crypt(Ka,nonce(NB2))),set(event,Evso))
=> ( member(event,says(server,Aa,crypt(shrK(Aa),mPair(nonce(NAa),mPair(agent(Ba),mPair(key(Ka),X))))),set(event,Evso))
=> member(list(event),cons(event,notes(spy,mPair(nonce(NAa),mPair(nonce(NB2),key(Ka)))),Evso),nS_Sha254967238shared) ) ) ) ).
tff(fact_60_A__trusts__NS2,axiom,
! [Evsa: list(event),X: msg,Ka: nat,Ba: agent1,NAa: msg,Aa: agent1] :
( member(msg,crypt(shrK(Aa),mPair(NAa,mPair(agent(Ba),mPair(key(Ka),X)))),parts(knows(spy,Evsa)))
=> ( ~ member(agent1,Aa,bad)
=> ( member(list(event),Evsa,nS_Sha254967238shared)
=> member(event,says(server,Aa,crypt(shrK(Aa),mPair(NAa,mPair(agent(Ba),mPair(key(Ka),X))))),set(event,Evsa)) ) ) ) ).
tff(fact_61_ns__shared_ONS3,axiom,
! [X: msg,Ka: nat,Ba: agent1,NAa: nat,S: agent1,Aa: agent1,Evs3: list(event)] :
( member(list(event),Evs3,nS_Sha254967238shared)
=> ( ( Aa != server )
=> ( member(event,says(S,Aa,crypt(shrK(Aa),mPair(nonce(NAa),mPair(agent(Ba),mPair(key(Ka),X))))),set(event,Evs3))
=> ( member(event,says(Aa,server,mPair(agent(Aa),mPair(agent(Ba),nonce(NAa)))),set(event,Evs3))
=> member(list(event),cons(event,says(Aa,Ba,X),Evs3),nS_Sha254967238shared) ) ) ) ) ).
tff(fact_62_ns__sharedp_OFake,axiom,
! [Ba: agent1,X: msg,Evsf: list(event)] :
( nS_Sha993195050haredp(Evsf)
=> ( member(msg,X,synth(analz(knows(spy,Evsf))))
=> nS_Sha993195050haredp(cons(event,says(spy,Ba,X),Evsf)) ) ) ).
tff(fact_63_list_Oinject,axiom,
! [A1: $tType,List1: list(A1),A2: A1,List: list(A1),A: A1] :
( ( cons(A1,A,List) = cons(A1,A2,List1) )
<=> ( ( A = A2 )
& ( List = List1 ) ) ) ).
tff(fact_64_Oops__parts__spies,axiom,
! [Evsa: list(event),X: msg,Ka: msg,Ba: msg,NAa: msg,Aa: agent1] :
( member(event,says(server,Aa,crypt(shrK(Aa),mPair(NAa,mPair(Ba,mPair(Ka,X))))),set(event,Evsa))
=> member(msg,Ka,parts(knows(spy,Evsa))) ) ).
tff(fact_65_ns__sharedp_OOops,axiom,
! [X: msg,NAa: nat,NB2: nat,Ka: nat,Aa: agent1,Ba: agent1,Evso: list(event)] :
( nS_Sha993195050haredp(Evso)
=> ( member(event,says(Ba,Aa,crypt(Ka,nonce(NB2))),set(event,Evso))
=> ( member(event,says(server,Aa,crypt(shrK(Aa),mPair(nonce(NAa),mPair(agent(Ba),mPair(key(Ka),X))))),set(event,Evso))
=> nS_Sha993195050haredp(cons(event,notes(spy,mPair(nonce(NAa),mPair(nonce(NB2),key(Ka)))),Evso)) ) ) ) ).
tff(fact_66_knows__Spy__Notes,axiom,
! [Evsa: list(event),X: msg,Aa: agent1] :
( ( member(agent1,Aa,bad)
=> ( knows(spy,cons(event,notes(Aa,X),Evsa)) = insert(msg,X,knows(spy,Evsa)) ) )
& ( ~ member(agent1,Aa,bad)
=> ( knows(spy,cons(event,notes(Aa,X),Evsa)) = knows(spy,Evsa) ) ) ) ).
tff(fact_67_parts__idem,axiom,
! [H: fun(msg,bool)] : parts(parts(H)) = parts(H) ).
tff(fact_68_parts_OInj,axiom,
! [H: fun(msg,bool),X: msg] :
( member(msg,X,H)
=> member(msg,X,parts(H)) ) ).
tff(fact_69_msg_Osimps_I3_J,axiom,
! [Nat3: nat,Nat2: nat] :
( ( nonce(Nat2) = nonce(Nat3) )
<=> ( Nat2 = Nat3 ) ) ).
tff(fact_70_analz__parts,axiom,
! [H: fun(msg,bool)] : analz(parts(H)) = parts(H) ).
tff(fact_71_parts__analz,axiom,
! [H: fun(msg,bool)] : parts(analz(H)) = parts(H) ).
tff(fact_72_analz__conj__parts,axiom,
! [H: fun(msg,bool),X: msg] :
( ( member(msg,X,analz(H))
& member(msg,X,parts(H)) )
<=> member(msg,X,analz(H)) ) ).
tff(fact_73_analz__disj__parts,axiom,
! [H: fun(msg,bool),X: msg] :
( ( member(msg,X,analz(H))
| member(msg,X,parts(H)) )
<=> member(msg,X,parts(H)) ) ).
tff(fact_74_MPair__parts,axiom,
! [H: fun(msg,bool),Y: msg,X: msg] :
( member(msg,mPair(X,Y),parts(H))
=> ~ ( member(msg,X,parts(H))
=> ~ member(msg,Y,parts(H)) ) ) ).
tff(fact_75_mem__def,axiom,
! [A1: $tType,Aa: fun(A1,bool),X1: A1] :
( member(A1,X1,Aa)
<=> pp(aa(A1,bool,Aa,X1)) ) ).
tff(fact_76_Nonce__synth__eq,axiom,
! [H: fun(msg,bool),N: nat] :
( member(msg,nonce(N),synth(H))
<=> member(msg,nonce(N),H) ) ).
tff(fact_77_synth__simps_I1_J,axiom,
! [H: fun(msg,bool),N1: nat] :
( member(msg,nonce(N1),synth(H))
<=> member(msg,nonce(N1),H) ) ).
tff(fact_78_List_Oset_Osimps_I2_J,axiom,
! [A1: $tType,Xs: list(A1),X1: A1] : set(A1,cons(A1,X1,Xs)) = insert(A1,X1,set(A1,Xs)) ).
tff(fact_79_analz__insert__MPair,axiom,
! [H: fun(msg,bool),Y: msg,X: msg] : analz(insert(msg,mPair(X,Y),H)) = insert(msg,mPair(X,Y),analz(insert(msg,X,insert(msg,Y,H)))) ).
tff(fact_80_parts__insert__Key,axiom,
! [H: fun(msg,bool),Ka: nat] : parts(insert(msg,key(Ka),H)) = insert(msg,key(Ka),parts(H)) ).
tff(fact_81_parts__insert__MPair,axiom,
! [H: fun(msg,bool),Y: msg,X: msg] : parts(insert(msg,mPair(X,Y),H)) = insert(msg,mPair(X,Y),parts(insert(msg,X,insert(msg,Y,H)))) ).
tff(fact_82_parts__insert__Crypt,axiom,
! [H: fun(msg,bool),X: msg,Ka: nat] : parts(insert(msg,crypt(Ka,X),H)) = insert(msg,crypt(Ka,X),parts(insert(msg,X,H))) ).
tff(fact_83_analz__insert__Nonce,axiom,
! [H: fun(msg,bool),N: nat] : analz(insert(msg,nonce(N),H)) = insert(msg,nonce(N),analz(H)) ).
tff(fact_84_analz__insert__Agent,axiom,
! [H: fun(msg,bool),Agt: agent1] : analz(insert(msg,agent(Agt),H)) = insert(msg,agent(Agt),analz(H)) ).
tff(fact_85_parts__insert__Nonce,axiom,
! [H: fun(msg,bool),N: nat] : parts(insert(msg,nonce(N),H)) = insert(msg,nonce(N),parts(H)) ).
tff(fact_86_parts__insert__Agent,axiom,
! [H: fun(msg,bool),Agt: agent1] : parts(insert(msg,agent(Agt),H)) = insert(msg,agent(Agt),parts(H)) ).
tff(fact_87_knows__Spy__Says,axiom,
! [Evsa: list(event),X: msg,Ba: agent1,Aa: agent1] : knows(spy,cons(event,says(Aa,Ba,X),Evsa)) = insert(msg,X,knows(spy,Evsa)) ).
tff(fact_88_pushes_I2_J,axiom,
! [Aa: fun(msg,bool),N: nat,Ka: nat] : insert(msg,key(Ka),insert(msg,nonce(N),Aa)) = insert(msg,nonce(N),insert(msg,key(Ka),Aa)) ).
tff(fact_89_pushes_I9_J,axiom,
! [Aa: fun(msg,bool),N: nat,Ka: msg,X: nat] : insert(msg,crypt(X,Ka),insert(msg,nonce(N),Aa)) = insert(msg,nonce(N),insert(msg,crypt(X,Ka),Aa)) ).
tff(fact_90_parts__insertI,axiom,
! [A: msg,G: fun(msg,bool),C: msg] :
( member(msg,C,parts(G))
=> member(msg,C,parts(insert(msg,A,G))) ) ).
tff(fact_91_parts__cut__eq,axiom,
! [H: fun(msg,bool),X: msg] :
( member(msg,X,parts(H))
=> ( parts(insert(msg,X,H)) = parts(H) ) ) ).
tff(fact_92_parts__partsD,axiom,
! [H: fun(msg,bool),X: msg] :
( member(msg,X,parts(parts(H)))
=> member(msg,X,parts(H)) ) ).
tff(fact_93_not__parts__not__analz,axiom,
! [H: fun(msg,bool),C: msg] :
( ~ member(msg,C,parts(H))
=> ~ member(msg,C,analz(H)) ) ).
tff(fact_94_analz__into__parts,axiom,
! [H: fun(msg,bool),C: msg] :
( member(msg,C,analz(H))
=> member(msg,C,parts(H)) ) ).
tff(fact_95_parts_OFst,axiom,
! [H: fun(msg,bool),Y: msg,X: msg] :
( member(msg,mPair(X,Y),parts(H))
=> member(msg,X,parts(H)) ) ).
tff(fact_96_parts_OSnd,axiom,
! [H: fun(msg,bool),Y: msg,X: msg] :
( member(msg,mPair(X,Y),parts(H))
=> member(msg,Y,parts(H)) ) ).
tff(fact_97_parts_OBody,axiom,
! [H: fun(msg,bool),X: msg,Ka: nat] :
( member(msg,crypt(Ka,X),parts(H))
=> member(msg,X,parts(H)) ) ).
tff(fact_98_spies__partsEs_I2_J,axiom,
! [H: fun(msg,bool),X: msg,Ka: nat] :
( member(msg,crypt(Ka,X),parts(H))
=> member(msg,X,parts(H)) ) ).
tff(fact_99_msg_Osimps_I31_J,axiom,
! [Nat1: nat,Nat: nat] : key(Nat) != nonce(Nat1) ).
%----Helper facts (2)
tff(help_pp_1_1_U,axiom,
~ pp(fFalse) ).
tff(help_pp_2_1_U,axiom,
pp(fTrue) ).
%----Conjectures (6)
tff(conj_0,hypothesis,
~ member(agent1,a,bad) ).
tff(conj_1,hypothesis,
~ member(agent1,b,bad) ).
tff(conj_2,hypothesis,
member(list(event),evsf,nS_Sha254967238shared) ).
tff(conj_3,hypothesis,
( member(event,says(server,a,crypt(shrK(a),mPair(na,mPair(agent(b),mPair(key(k),crypt(shrK(b),mPair(key(k),agent(a)))))))),set(event,evsf))
=> ( ! [NB1: msg] : ~ member(event,notes(spy,mPair(na,mPair(NB1,key(k)))),set(event,evsf))
=> ~ member(msg,key(k),analz(knows(spy,evsf))) ) ) ).
tff(conj_4,hypothesis,
member(msg,x,synth(analz(knows(spy,evsf)))) ).
tff(conj_5,conjecture,
( ~ member(event,says(server,a,crypt(shrK(a),mPair(na,mPair(agent(b),mPair(key(k),crypt(shrK(b),mPair(key(k),agent(a)))))))),set(event,cons(event,says(spy,ba,x),evsf)))
| ? [NB: msg] : member(event,notes(spy,mPair(na,mPair(NB,key(k)))),set(event,cons(event,says(spy,ba,x),evsf)))
| ~ member(msg,key(k),analz(knows(spy,cons(event,says(spy,ba,x),evsf)))) ) ).
%------------------------------------------------------------------------------