TPTP Problem File: SWV718_5.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SWV718_5 : TPTP v8.2.0. Released v6.0.0.
% Domain : Software Verification
% Problem : Needham-Schroeder shared-key protocol line 96
% Version : Especial.
% English :
% Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% : [Bla13] Blanchette (2011), Email to Geoff Sutcliffe
% Source : [Bla13]
% Names : ns_96 [Bla13]
% Status : Unknown
% Rating : 1.00 v6.4.0
% Syntax : Number of formulae : 149 ( 63 unt; 43 typ; 0 def)
% Number of atoms : 198 ( 93 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 152 ( 60 ~; 1 |; 13 &)
% ( 15 <=>; 63 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 56 ( 28 >; 28 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 0 prp; 1-3 aty)
% Number of functors : 33 ( 33 usr; 9 con; 0-5 aty)
% Number of variables : 373 ( 352 !; 6 ?; 373 :)
% ( 15 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_UNK_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-12-13 16:13:54
%------------------------------------------------------------------------------
%----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 (36)
tff(sy_c_Event_Oevent_OGets,type,
gets: ( agent * msg ) > event ).
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_Oevent_Oevent__case,type,
event_case:
!>[T: $tType] : ( ( fun(agent,fun(agent,fun(msg,T))) * fun(agent,fun(msg,T)) * fun(agent,fun(msg,T)) * event ) > T ) ).
tff(sy_c_Event_Oevent_Oevent__rec,type,
event_rec:
!>[T: $tType] : ( ( fun(agent,fun(agent,fun(msg,T))) * fun(agent,fun(msg,T)) * fun(agent,fun(msg,T)) * event ) > T ) ).
tff(sy_c_Event_OinitState,type,
initState: agent > fun(msg,bool) ).
tff(sy_c_Event_Oused,type,
used: list(event) > fun(msg,bool) ).
tff(sy_c_List_Oinsert,type,
insert:
!>[A: $tType] : ( ( A * list(A) ) > list(A) ) ).
tff(sy_c_List_Olist_OCons,type,
cons:
!>[A: $tType] : ( ( A * list(A) ) > list(A) ) ).
tff(sy_c_List_Olist_ONil,type,
nil:
!>[A: $tType] : list(A) ).
tff(sy_c_List_Olist_Olist__case,type,
list_case:
!>[T: $tType,A: $tType] : ( ( T * fun(A,fun(list(A),T)) * list(A) ) > T ) ).
tff(sy_c_List_Olist__ex1,type,
list_ex1:
!>[A: $tType] : ( ( fun(A,bool) * list(A) ) > $o ) ).
tff(sy_c_List_Oset,type,
set:
!>[A: $tType] : ( list(A) > fun(A,bool) ) ).
tff(sy_c_List_Osplice,type,
splice:
!>[A: $tType] : ( ( list(A) * list(A) ) > list(A) ) ).
tff(sy_c_Message_Oagent_OServer,type,
server: agent ).
tff(sy_c_Message_Oagent_OSpy,type,
spy: agent ).
tff(sy_c_Message_Oagent_Oagent__case,type,
agent_case:
!>[T: $tType] : ( ( T * fun(nat,T) * T * agent ) > T ) ).
tff(sy_c_Message_Oagent_Oagent__rec,type,
agent_rec:
!>[T: $tType] : ( ( T * fun(nat,T) * T * agent ) > T ) ).
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_OsymKeys,type,
symKeys: fun(nat,bool) ).
tff(sy_c_Message_Osynthp,type,
synthp: ( fun(msg,bool) * msg ) > $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:
!>[A: $tType,B: $tType] : ( ( fun(A,B) * A ) > B ) ).
tff(sy_c_fFalse,type,
fFalse: bool ).
tff(sy_c_fTrue,type,
fTrue: bool ).
tff(sy_c_member,type,
member:
!>[A: $tType] : ( ( A * fun(A,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 ).
%----Relevant facts (100)
tff(fact_0_ns__shared_ONil,axiom,
member(list(event),nil(event),nS_Sha254967238shared) ).
tff(fact_1_MPair__used,axiom,
! [H: list(event),Y3: msg,X2: msg] :
( member(msg,mPair(X2,Y3),used(H))
=> ~ ( member(msg,X2,used(H))
=> ~ member(msg,Y3,used(H)) ) ) ).
tff(fact_2_Nonce__notin__used__empty,axiom,
! [N2: nat] : ~ member(msg,nonce(N2),used(nil(event))) ).
tff(fact_3_Crypt__notin__used__empty,axiom,
! [X2: msg,Ka: nat] : ~ member(msg,crypt(Ka,X2),used(nil(event))) ).
tff(fact_4_Says__imp__used,axiom,
! [Evs: list(event),X2: msg,Ba: agent,Aa: agent] :
( member(event,says(Aa,Ba,X2),set(event,Evs))
=> member(msg,X2,used(Evs)) ) ).
tff(fact_5_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_6_msg_Osimps_I3_J,axiom,
! [Nat3: nat,Nat2: nat] :
( ( nonce(Nat2) = nonce(Nat3) )
<=> ( Nat2 = Nat3 ) ) ).
tff(fact_7_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_8_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_9_msg_Osimps_I4_J,axiom,
! [Nat3: nat,Nat2: nat] :
( ( key(Nat2) = key(Nat3) )
<=> ( Nat2 = Nat3 ) ) ).
tff(fact_10_MPair__used__D,axiom,
! [H: list(event),Y3: msg,X2: msg] :
( member(msg,mPair(X2,Y3),used(H))
=> ( member(msg,X2,used(H))
& member(msg,Y3,used(H)) ) ) ).
tff(fact_11_msg_Osimps_I36_J,axiom,
! [Msg: msg,Nat: nat,Nat1: nat] : nonce(Nat1) != crypt(Nat,Msg) ).
tff(fact_12_msg_Osimps_I37_J,axiom,
! [Nat1: nat,Msg: msg,Nat: nat] : crypt(Nat,Msg) != nonce(Nat1) ).
tff(fact_13_symKeys__neq__imp__neq,axiom,
! [K: nat,Ka: nat] :
( ~ ( member(nat,Ka,symKeys)
<=> member(nat,K,symKeys) )
=> ( Ka != K ) ) ).
tff(fact_14_msg_Osimps_I41_J,axiom,
! [Nat1: nat,Msg21: msg,Msg11: msg] : mPair(Msg11,Msg21) != key(Nat1) ).
tff(fact_15_msg_Osimps_I40_J,axiom,
! [Msg21: msg,Msg11: msg,Nat1: nat] : key(Nat1) != mPair(Msg11,Msg21) ).
tff(fact_16_msg_Osimps_I43_J,axiom,
! [Nat1: nat,Msg: msg,Nat: nat] : crypt(Nat,Msg) != key(Nat1) ).
tff(fact_17_msg_Osimps_I42_J,axiom,
! [Msg: msg,Nat: nat,Nat1: nat] : key(Nat1) != crypt(Nat,Msg) ).
tff(fact_18_msg_Osimps_I48_J,axiom,
! [Msg: msg,Nat: nat,Msg22: msg,Msg12: msg] : mPair(Msg12,Msg22) != crypt(Nat,Msg) ).
tff(fact_19_msg_Osimps_I49_J,axiom,
! [Msg22: msg,Msg12: msg,Msg: msg,Nat: nat] : crypt(Nat,Msg) != mPair(Msg12,Msg22) ).
tff(fact_20_msg_Osimps_I30_J,axiom,
! [Nat: nat,Nat1: nat] : nonce(Nat1) != key(Nat) ).
tff(fact_21_msg_Osimps_I31_J,axiom,
! [Nat1: nat,Nat: nat] : key(Nat) != nonce(Nat1) ).
tff(fact_22_msg_Osimps_I35_J,axiom,
! [Nat1: nat,Msg21: msg,Msg11: msg] : mPair(Msg11,Msg21) != nonce(Nat1) ).
tff(fact_23_msg_Osimps_I34_J,axiom,
! [Msg21: msg,Msg11: msg,Nat1: nat] : nonce(Nat1) != mPair(Msg11,Msg21) ).
tff(fact_24_Nonce__supply1,axiom,
! [Evs: list(event)] :
? [N1: nat] : ~ member(msg,nonce(N1),used(Evs)) ).
tff(fact_25_synthp_OCrypt,axiom,
! [Ka: nat,X2: msg,H: fun(msg,bool)] :
( synthp(H,X2)
=> ( pp(aa(msg,bool,H,key(Ka)))
=> synthp(H,crypt(Ka,X2)) ) ) ).
tff(fact_26_agent_Osimps_I8_J,axiom,
! [A: $tType,F3: A,F2: fun(nat,A),F1: A] : agent_case(A,F1,F2,F3,server) = F1 ).
tff(fact_27_agent_Orecs_I1_J,axiom,
! [A: $tType,F3: A,F2: fun(nat,A),F1: A] : agent_rec(A,F1,F2,F3,server) = F1 ).
tff(fact_28_event_Osimps_I10_J,axiom,
! [A: $tType,Msg2: msg,Agent21: agent,Agent11: agent,F3: fun(agent,fun(msg,A)),F2: fun(agent,fun(msg,A)),F1: fun(agent,fun(agent,fun(msg,A)))] : event_case(A,F1,F2,F3,says(Agent11,Agent21,Msg2)) = aa(msg,A,aa(agent,fun(msg,A),aa(agent,fun(agent,fun(msg,A)),F1,Agent11),Agent21),Msg2) ).
tff(fact_29_event_Orecs_I1_J,axiom,
! [A: $tType,Msg2: msg,Agent21: agent,Agent11: agent,F3: fun(agent,fun(msg,A)),F2: fun(agent,fun(msg,A)),F1: fun(agent,fun(agent,fun(msg,A)))] : event_rec(A,F1,F2,F3,says(Agent11,Agent21,Msg2)) = aa(msg,A,aa(agent,fun(msg,A),aa(agent,fun(agent,fun(msg,A)),F1,Agent11),Agent21),Msg2) ).
tff(fact_30_ns__shared_ONS2,axiom,
! [NA: nat,Ba: agent,Aa: agent,A5: 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(A5,server,mPair(agent1(Aa),mPair(agent1(Ba),nonce(NA)))),set(event,Evs2))
=> member(list(event),cons(event,says(server,Aa,crypt(shrK(Aa),mPair(nonce(NA),mPair(agent1(Ba),mPair(key(KAB),crypt(shrK(Ba),mPair(key(KAB),agent1(Aa)))))))),Evs2),nS_Sha254967238shared) ) ) ) ) ).
tff(fact_31_ns__shared_ONS4,axiom,
! [Aa: agent,Ba: agent,A5: agent,Ka: nat,NB: nat,Evs4: list(event)] :
( member(list(event),Evs4,nS_Sha254967238shared)
=> ( ~ member(msg,nonce(NB),used(Evs4))
=> ( member(nat,Ka,symKeys)
=> ( member(event,says(A5,Ba,crypt(shrK(Ba),mPair(key(Ka),agent1(Aa)))),set(event,Evs4))
=> member(list(event),cons(event,says(Ba,Aa,crypt(Ka,nonce(NB))),Evs4),nS_Sha254967238shared) ) ) ) ) ).
tff(fact_32_ns__shared_ONS1,axiom,
! [Ba: agent,Aa: agent,NA: nat,Evs1: list(event)] :
( member(list(event),Evs1,nS_Sha254967238shared)
=> ( ~ member(msg,nonce(NA),used(Evs1))
=> member(list(event),cons(event,says(Aa,server,mPair(agent1(Aa),mPair(agent1(Ba),nonce(NA)))),Evs1),nS_Sha254967238shared) ) ) ).
tff(fact_33_msg_Osimps_I1_J,axiom,
! [Agent5: agent,Agent4: agent] :
( ( agent1(Agent4) = agent1(Agent5) )
<=> ( Agent4 = Agent5 ) ) ).
tff(fact_34_shrK__injective,axiom,
! [Y2: agent,X3: agent] :
( ( shrK(X3) = shrK(Y2) )
<=> ( X3 = Y2 ) ) ).
tff(fact_35_synthp_OInj,axiom,
! [X2: msg,H: fun(msg,bool)] :
( pp(aa(msg,bool,H,X2))
=> synthp(H,X2) ) ).
tff(fact_36_synthp_OMPair,axiom,
! [Y3: msg,X2: msg,H: fun(msg,bool)] :
( synthp(H,X2)
=> ( synthp(H,Y3)
=> synthp(H,mPair(X2,Y3)) ) ) ).
tff(fact_37_synthp_OAgent,axiom,
! [Agt: agent,H: fun(msg,bool)] : synthp(H,agent1(Agt)) ).
tff(fact_38_sym__shrK,axiom,
! [X2: agent] : member(nat,shrK(X2),symKeys) ).
tff(fact_39_shrK__in__used,axiom,
! [Evs: list(event),Aa: agent] : member(msg,key(shrK(Aa)),used(Evs)) ).
tff(fact_40_msg_Osimps_I13_J,axiom,
! [Agent3: agent,Nat: nat] : key(Nat) != agent1(Agent3) ).
tff(fact_41_msg_Osimps_I12_J,axiom,
! [Nat: nat,Agent3: agent] : agent1(Agent3) != key(Nat) ).
tff(fact_42_msg_Osimps_I16_J,axiom,
! [Msg21: msg,Msg11: msg,Agent3: agent] : agent1(Agent3) != mPair(Msg11,Msg21) ).
tff(fact_43_msg_Osimps_I17_J,axiom,
! [Agent3: agent,Msg21: msg,Msg11: msg] : mPair(Msg11,Msg21) != agent1(Agent3) ).
tff(fact_44_msg_Osimps_I18_J,axiom,
! [Msg: msg,Nat: nat,Agent3: agent] : agent1(Agent3) != crypt(Nat,Msg) ).
tff(fact_45_msg_Osimps_I19_J,axiom,
! [Agent3: agent,Msg: msg,Nat: nat] : crypt(Nat,Msg) != agent1(Agent3) ).
tff(fact_46_msg_Osimps_I10_J,axiom,
! [Nat: nat,Agent3: agent] : agent1(Agent3) != nonce(Nat) ).
tff(fact_47_msg_Osimps_I11_J,axiom,
! [Agent3: agent,Nat: nat] : nonce(Nat) != agent1(Agent3) ).
tff(fact_48_neq__shrK,axiom,
! [Ba: agent,Evs: list(event),S1: nat] :
( ~ member(msg,key(S1),used(Evs))
=> ( S1 != shrK(Ba) ) ) ).
tff(fact_49_shrK__neq,axiom,
! [Ba: agent,Evs: list(event),Ka: nat] :
( ~ member(msg,key(Ka),used(Evs))
=> ( shrK(Ba) != Ka ) ) ).
tff(fact_50_ns__shared_ONS3,axiom,
! [X2: msg,Ka: nat,Ba: agent,NA: 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(NA),mPair(agent1(Ba),mPair(key(Ka),X2))))),set(event,Evs3))
=> ( member(event,says(Aa,server,mPair(agent1(Aa),mPair(agent1(Ba),nonce(NA)))),set(event,Evs3))
=> member(list(event),cons(event,says(Aa,Ba,X2),Evs3),nS_Sha254967238shared) ) ) ) ) ).
tff(fact_51_ns__shared_ONS5,axiom,
! [X2: msg,Ba: agent,NA: nat,S: agent,NB: nat,Aa: agent,B1: agent,Ka: nat,Evs5: list(event)] :
( member(list(event),Evs5,nS_Sha254967238shared)
=> ( member(nat,Ka,symKeys)
=> ( member(event,says(B1,Aa,crypt(Ka,nonce(NB))),set(event,Evs5))
=> ( member(event,says(S,Aa,crypt(shrK(Aa),mPair(nonce(NA),mPair(agent1(Ba),mPair(key(Ka),X2))))),set(event,Evs5))
=> member(list(event),cons(event,says(Aa,Ba,crypt(Ka,mPair(nonce(NB),nonce(NB)))),Evs5),nS_Sha254967238shared) ) ) ) ) ).
tff(fact_52_ns__sharedp_ONS2,axiom,
! [NA: nat,Ba: agent,Aa: agent,A5: agent,KAB: nat,Evs2: list(event)] :
( nS_Sha993195050haredp(Evs2)
=> ( ~ member(msg,key(KAB),used(Evs2))
=> ( member(nat,KAB,symKeys)
=> ( member(event,says(A5,server,mPair(agent1(Aa),mPair(agent1(Ba),nonce(NA)))),set(event,Evs2))
=> nS_Sha993195050haredp(cons(event,says(server,Aa,crypt(shrK(Aa),mPair(nonce(NA),mPair(agent1(Ba),mPair(key(KAB),crypt(shrK(Ba),mPair(key(KAB),agent1(Aa)))))))),Evs2)) ) ) ) ) ).
tff(fact_53_ns__sharedp_ONS4,axiom,
! [Aa: agent,Ba: agent,A5: agent,Ka: nat,NB: nat,Evs4: list(event)] :
( nS_Sha993195050haredp(Evs4)
=> ( ~ member(msg,nonce(NB),used(Evs4))
=> ( member(nat,Ka,symKeys)
=> ( member(event,says(A5,Ba,crypt(shrK(Ba),mPair(key(Ka),agent1(Aa)))),set(event,Evs4))
=> nS_Sha993195050haredp(cons(event,says(Ba,Aa,crypt(Ka,nonce(NB))),Evs4)) ) ) ) ) ).
tff(fact_54_ns__sharedp_ONS5,axiom,
! [X2: msg,Ba: agent,NA: nat,S: agent,NB: nat,Aa: agent,B1: agent,Ka: nat,Evs5: list(event)] :
( nS_Sha993195050haredp(Evs5)
=> ( member(nat,Ka,symKeys)
=> ( member(event,says(B1,Aa,crypt(Ka,nonce(NB))),set(event,Evs5))
=> ( member(event,says(S,Aa,crypt(shrK(Aa),mPair(nonce(NA),mPair(agent1(Ba),mPair(key(Ka),X2))))),set(event,Evs5))
=> nS_Sha993195050haredp(cons(event,says(Aa,Ba,crypt(Ka,mPair(nonce(NB),nonce(NB)))),Evs5)) ) ) ) ) ).
tff(fact_55_ns__sharedp_ONS3,axiom,
! [X2: msg,Ka: nat,Ba: agent,NA: nat,S: agent,Aa: agent,Evs3: list(event)] :
( nS_Sha993195050haredp(Evs3)
=> ( ( Aa != server )
=> ( member(event,says(S,Aa,crypt(shrK(Aa),mPair(nonce(NA),mPair(agent1(Ba),mPair(key(Ka),X2))))),set(event,Evs3))
=> ( member(event,says(Aa,server,mPair(agent1(Aa),mPair(agent1(Ba),nonce(NA)))),set(event,Evs3))
=> nS_Sha993195050haredp(cons(event,says(Aa,Ba,X2),Evs3)) ) ) ) ) ).
tff(fact_56_ns__sharedp_ONS1,axiom,
! [Ba: agent,Aa: agent,NA: nat,Evs1: list(event)] :
( nS_Sha993195050haredp(Evs1)
=> ( ~ member(msg,nonce(NA),used(Evs1))
=> nS_Sha993195050haredp(cons(event,says(Aa,server,mPair(agent1(Aa),mPair(agent1(Ba),nonce(NA)))),Evs1)) ) ) ).
tff(fact_57_list_Oinject,axiom,
! [A: $tType,List3: list(A),A4: A,List: list(A),A1: A] :
( ( cons(A,A1,List) = cons(A,A4,List3) )
<=> ( ( A1 = A4 )
& ( List = List3 ) ) ) ).
tff(fact_58_ns__sharedp__ns__shared__eq,axiom,
! [X: list(event)] :
( nS_Sha993195050haredp(X)
<=> member(list(event),X,nS_Sha254967238shared) ) ).
tff(fact_59_ns__sharedp_ONil,axiom,
nS_Sha993195050haredp(nil(event)) ).
tff(fact_60_not__Cons__self,axiom,
! [A: $tType,X4: A,Xs1: list(A)] : Xs1 != cons(A,X4,Xs1) ).
tff(fact_61_not__Cons__self2,axiom,
! [A: $tType,Xs1: list(A),X4: A] : cons(A,X4,Xs1) != Xs1 ).
tff(fact_62_set__ConsD,axiom,
! [A: $tType,Xs: list(A),X3: A,Y2: A] :
( member(A,Y2,set(A,cons(A,X3,Xs)))
=> ( ( Y2 = X3 )
| member(A,Y2,set(A,Xs)) ) ) ).
tff(fact_63_list_Osimps_I2_J,axiom,
! [A: $tType,List2: list(A),A3: A] : nil(A) != cons(A,A3,List2) ).
tff(fact_64_list_Osimps_I3_J,axiom,
! [A: $tType,List2: list(A),A3: A] : cons(A,A3,List2) != nil(A) ).
tff(fact_65_neq__Nil__conv,axiom,
! [A: $tType,Xs: list(A)] :
( ( Xs != nil(A) )
<=> ? [Y: A,Ys1: list(A)] : Xs = cons(A,Y,Ys1) ) ).
tff(fact_66_list_Oexhaust,axiom,
! [A: $tType,Y1: list(A)] :
( ( Y1 != nil(A) )
=> ~ ! [A2: A,List1: list(A)] : Y1 != cons(A,A2,List1) ) ).
tff(fact_67_ns__sharedp_OOops,axiom,
! [X2: msg,NA: nat,NB: nat,Ka: nat,Aa: agent,Ba: agent,Evso: list(event)] :
( nS_Sha993195050haredp(Evso)
=> ( member(event,says(Ba,Aa,crypt(Ka,nonce(NB))),set(event,Evso))
=> ( member(event,says(server,Aa,crypt(shrK(Aa),mPair(nonce(NA),mPair(agent1(Ba),mPair(key(Ka),X2))))),set(event,Evso))
=> nS_Sha993195050haredp(cons(event,notes(spy,mPair(nonce(NA),mPair(nonce(NB),key(Ka)))),Evso)) ) ) ) ).
tff(fact_68_event_Osimps_I3_J,axiom,
! [Msg3: msg,Agent5: agent,Msg2: msg,Agent4: agent] :
( ( notes(Agent4,Msg2) = notes(Agent5,Msg3) )
<=> ( ( Agent4 = Agent5 )
& ( Msg2 = Msg3 ) ) ) ).
tff(fact_69_agent_Osimps_I4_J,axiom,
server != spy ).
tff(fact_70_agent_Osimps_I5_J,axiom,
spy != server ).
tff(fact_71_event_Osimps_I7_J,axiom,
! [Msg1: msg,Agent2: agent,Agent1: agent,Msg: msg,Agent: agent] : notes(Agent,Msg) != says(Agent1,Agent2,Msg1) ).
tff(fact_72_event_Osimps_I6_J,axiom,
! [Msg: msg,Agent: agent,Msg1: msg,Agent2: agent,Agent1: agent] : says(Agent1,Agent2,Msg1) != notes(Agent,Msg) ).
tff(fact_73_agent_Orecs_I3_J,axiom,
! [A: $tType,F3: A,F2: fun(nat,A),F1: A] : agent_rec(A,F1,F2,F3,spy) = F3 ).
tff(fact_74_agent_Osimps_I10_J,axiom,
! [A: $tType,F3: A,F2: fun(nat,A),F1: A] : agent_case(A,F1,F2,F3,spy) = F3 ).
tff(fact_75_ext,axiom,
! [B: $tType,A: $tType,G: fun(A,B),F: fun(A,B)] :
( ! [X5: A] : aa(A,B,F,X5) = aa(A,B,G,X5)
=> ( F = G ) ) ).
tff(fact_76_mem__def,axiom,
! [A: $tType,Aa: fun(A,bool),X3: A] :
( member(A,X3,Aa)
<=> pp(aa(A,bool,Aa,X3)) ) ).
tff(fact_77_event_Osimps_I12_J,axiom,
! [A: $tType,Msg2: msg,Agent4: agent,F3: fun(agent,fun(msg,A)),F2: fun(agent,fun(msg,A)),F1: fun(agent,fun(agent,fun(msg,A)))] : event_case(A,F1,F2,F3,notes(Agent4,Msg2)) = aa(msg,A,aa(agent,fun(msg,A),F3,Agent4),Msg2) ).
tff(fact_78_event_Orecs_I3_J,axiom,
! [A: $tType,Msg2: msg,Agent4: agent,F3: fun(agent,fun(msg,A)),F2: fun(agent,fun(msg,A)),F1: fun(agent,fun(agent,fun(msg,A)))] : event_rec(A,F1,F2,F3,notes(Agent4,Msg2)) = aa(msg,A,aa(agent,fun(msg,A),F3,Agent4),Msg2) ).
tff(fact_79_Notes__imp__used,axiom,
! [Evs: list(event),X2: msg,Aa: agent] :
( member(event,notes(Aa,X2),set(event,Evs))
=> member(msg,X2,used(Evs)) ) ).
tff(fact_80_ns__shared_OOops,axiom,
! [X2: msg,NA: nat,NB: nat,Ka: nat,Aa: agent,Ba: agent,Evso: list(event)] :
( member(list(event),Evso,nS_Sha254967238shared)
=> ( member(event,says(Ba,Aa,crypt(Ka,nonce(NB))),set(event,Evso))
=> ( member(event,says(server,Aa,crypt(shrK(Aa),mPair(nonce(NA),mPair(agent1(Ba),mPair(key(Ka),X2))))),set(event,Evso))
=> member(list(event),cons(event,notes(spy,mPair(nonce(NA),mPair(nonce(NB),key(Ka)))),Evso),nS_Sha254967238shared) ) ) ) ).
tff(fact_81_insert__Nil,axiom,
! [A: $tType,X4: A] : insert(A,X4,nil(A)) = cons(A,X4,nil(A)) ).
tff(fact_82_shrK__in__initState,axiom,
! [Aa: agent] : member(msg,key(shrK(Aa)),initState(Aa)) ).
tff(fact_83_splice_Osimps_I2_J,axiom,
! [A: $tType,Va: list(A),V: A] : splice(A,cons(A,V,Va),nil(A)) = cons(A,V,Va) ).
tff(fact_84_splice_Osimps_I3_J,axiom,
! [A: $tType,Ys: list(A),Y1: A,Xs1: list(A),X4: A] : splice(A,cons(A,X4,Xs1),cons(A,Y1,Ys)) = cons(A,X4,cons(A,Y1,splice(A,Xs1,Ys))) ).
tff(fact_85_in__set__insert,axiom,
! [A: $tType,Xs: list(A),X3: A] :
( member(A,X3,set(A,Xs))
=> ( insert(A,X3,Xs) = Xs ) ) ).
tff(fact_86_splice__Nil2,axiom,
! [A: $tType,Xs1: list(A)] : splice(A,Xs1,nil(A)) = Xs1 ).
tff(fact_87_splice_Osimps_I1_J,axiom,
! [A: $tType,Ys: list(A)] : splice(A,nil(A),Ys) = Ys ).
tff(fact_88_List_Oinsert__def,axiom,
! [A: $tType,Xs: list(A),X3: A] :
( ( member(A,X3,set(A,Xs))
=> ( insert(A,X3,Xs) = Xs ) )
& ( ~ member(A,X3,set(A,Xs))
=> ( insert(A,X3,Xs) = cons(A,X3,Xs) ) ) ) ).
tff(fact_89_not__in__set__insert,axiom,
! [A: $tType,Xs: list(A),X3: A] :
( ~ member(A,X3,set(A,Xs))
=> ( insert(A,X3,Xs) = cons(A,X3,Xs) ) ) ).
tff(fact_90_list_Osimps_I4_J,axiom,
! [B: $tType,A: $tType,F2: fun(B,fun(list(B),A)),F1: A] : list_case(A,B,F1,F2,nil(B)) = F1 ).
tff(fact_91_list_Osimps_I5_J,axiom,
! [A: $tType,B: $tType,List: list(B),A1: B,F2: fun(B,fun(list(B),A)),F1: A] : list_case(A,B,F1,F2,cons(B,A1,List)) = aa(list(B),A,aa(B,fun(list(B),A),F2,A1),List) ).
tff(fact_92_used__Gets,axiom,
! [Evs: list(event),X2: msg,Aa: agent] : used(cons(event,gets(Aa,X2),Evs)) = used(Evs) ).
tff(fact_93_list__ex1__simps_I1_J,axiom,
! [A: $tType,P: fun(A,bool)] : ~ list_ex1(A,P,nil(A)) ).
tff(fact_94_event_Osimps_I2_J,axiom,
! [Msg3: msg,Agent5: agent,Msg2: msg,Agent4: agent] :
( ( gets(Agent4,Msg2) = gets(Agent5,Msg3) )
<=> ( ( Agent4 = Agent5 )
& ( Msg2 = Msg3 ) ) ) ).
tff(fact_95_list__ex1__iff,axiom,
! [A: $tType,Xs: list(A),P: fun(A,bool)] :
( list_ex1(A,P,Xs)
<=> ? [X1: A] :
( member(A,X1,set(A,Xs))
& pp(aa(A,bool,P,X1))
& ! [Y: A] :
( ( member(A,Y,set(A,Xs))
& pp(aa(A,bool,P,Y)) )
=> ( Y = X1 ) ) ) ) ).
tff(fact_96_event_Orecs_I2_J,axiom,
! [A: $tType,Msg2: msg,Agent4: agent,F3: fun(agent,fun(msg,A)),F2: fun(agent,fun(msg,A)),F1: fun(agent,fun(agent,fun(msg,A)))] : event_rec(A,F1,F2,F3,gets(Agent4,Msg2)) = aa(msg,A,aa(agent,fun(msg,A),F2,Agent4),Msg2) ).
tff(fact_97_event_Osimps_I8_J,axiom,
! [Msg: msg,Agent: agent,Msg1: msg,Agent3: agent] : gets(Agent3,Msg1) != notes(Agent,Msg) ).
tff(fact_98_event_Osimps_I9_J,axiom,
! [Msg1: msg,Agent3: agent,Msg: msg,Agent: agent] : notes(Agent,Msg) != gets(Agent3,Msg1) ).
tff(fact_99_event_Osimps_I5_J,axiom,
! [Msg1: msg,Agent2: agent,Agent1: agent,Msg: msg,Agent: agent] : gets(Agent,Msg) != says(Agent1,Agent2,Msg1) ).
%----Helper facts (2)
tff(help_pp_1_1_U,axiom,
~ pp(fFalse) ).
tff(help_pp_2_1_U,axiom,
pp(fTrue) ).
%----Conjectures (4)
tff(conj_0,hypothesis,
a != server ).
tff(conj_1,hypothesis,
~ member(msg,key(k),used(nil(event))) ).
tff(conj_2,hypothesis,
member(nat,k,symKeys) ).
tff(conj_3,conjecture,
? [N: nat,X: list(event)] :
( member(list(event),X,nS_Sha254967238shared)
& member(event,says(a,b,crypt(k,mPair(nonce(N),nonce(N)))),set(event,X)) ) ).
%------------------------------------------------------------------------------