TSTP Solution File: SWV352-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV352-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 : 300s
% DateTime : Thu Sep 29 15:11:23 EDT 2022
% Result : Unsatisfiable 0.55s 0.58s
% Output : Proof 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 81
% Syntax : Number of formulae : 147 ( 34 unt; 29 typ; 0 def)
% Number of atoms : 568 ( 14 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 809 ( 381 ~; 372 |; 0 &)
% ( 56 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 22 ( 22 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 23 ( 14 >; 9 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 28 ( 28 usr; 15 con; 0-3 aty)
% Number of variables : 525 ( 479 !; 0 ?; 525 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(tc_Message_Omsg_type,type,
tc_Message_Omsg: $i ).
tff(c_Message_Oparts_type,type,
c_Message_Oparts: $i > $i ).
tff(c_Event_Oknows_type,type,
c_Event_Oknows: ( $i * $i ) > $i ).
tff(v_evso_type,type,
v_evso: $i ).
tff(c_Message_Oagent_OSpy_type,type,
c_Message_Oagent_OSpy: $i ).
tff(c_Message_Omsg_OCrypt_type,type,
c_Message_Omsg_OCrypt: ( $i * $i ) > $i ).
tff(c_Message_Omsg_OMPair_type,type,
c_Message_Omsg_OMPair: ( $i * $i ) > $i ).
tff(c_Message_Omsg_ONonce_type,type,
c_Message_Omsg_ONonce: $i > $i ).
tff(v_NBa_type,type,
v_NBa: $i ).
tff(v_NB_type,type,
v_NB: $i ).
tff(c_Message_Omsg_OAgent_type,type,
c_Message_Omsg_OAgent: $i > $i ).
tff(v_Aa_type,type,
v_Aa: $i ).
tff(c_Public_OshrK_type,type,
c_Public_OshrK: $i > $i ).
tff(v_Ba_type,type,
v_Ba: $i ).
tff(c_Message_Oanalz_type,type,
c_Message_Oanalz: $i > $i ).
tff(tc_Event_Oevent_type,type,
tc_Event_Oevent: $i ).
tff(c_List_Oset_type,type,
c_List_Oset: ( $i * $i ) > $i ).
tff(c_Event_Oevent_OGets_type,type,
c_Event_Oevent_OGets: ( $i * $i ) > $i ).
tff(c_Message_Oagent_OServer_type,type,
c_Message_Oagent_OServer: $i ).
tff(c_Event_Oevent_OSays_type,type,
c_Event_Oevent_OSays: ( $i * $i * $i ) > $i ).
tff(tc_List_Olist_type,type,
tc_List_Olist: $i > $i ).
tff(c_Yahalom_Oyahalom_type,type,
c_Yahalom_Oyahalom: $i ).
tff(v_X_type,type,
v_X: $i ).
tff(c_Message_Omsg_OKey_type,type,
c_Message_Omsg_OKey: $i > $i ).
tff(v_K_type,type,
v_K: $i ).
tff(v_NA_type,type,
v_NA: $i ).
tff(v_A_type,type,
v_A: $i ).
tff(v_B_type,type,
v_B: $i ).
tff(1,plain,
^ [V_H: $i] :
refl(
( ( c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H) )
<=> ( c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [V_H: $i] : ( c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H) )
<=> ! [V_H: $i] : ( c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_H: $i] : ( c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H) )
<=> ! [V_H: $i] : ( c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [V_H: $i] : ( c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__analz_0) ).
tff(5,plain,
! [V_H: $i] : ( c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V_H: $i] : ( c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V_H: $i] : ( c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V_H: $i] : ( c_Message_Oparts(c_Message_Oanalz(V_H)) = c_Message_Oparts(V_H) )
| ( c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso))) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso))) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)) = c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso))),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
<=> c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa)))),c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso))),tc_Message_Omsg) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa)))),c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso))),tc_Message_Omsg)
<=> c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg) ),
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
^ [V_nb: $i,V_na: $i,V_X: $i,V_B: $i,V_A: $i,V_k: $i,V_evs: $i] :
refl(
( ( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,V_nb))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(V_k,c_Message_Omsg_OMPair(V_na,V_nb)))),V_X)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) )
<=> ( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,V_nb))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(V_k,c_Message_Omsg_OMPair(V_na,V_nb)))),V_X)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [V_nb: $i,V_na: $i,V_X: $i,V_B: $i,V_A: $i,V_k: $i,V_evs: $i] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,V_nb))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(V_k,c_Message_Omsg_OMPair(V_na,V_nb)))),V_X)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) )
<=> ! [V_nb: $i,V_na: $i,V_X: $i,V_B: $i,V_A: $i,V_k: $i,V_evs: $i] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,V_nb))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(V_k,c_Message_Omsg_OMPair(V_na,V_nb)))),V_X)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [V_nb: $i,V_na: $i,V_X: $i,V_B: $i,V_A: $i,V_k: $i,V_evs: $i] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,V_nb))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(V_k,c_Message_Omsg_OMPair(V_na,V_nb)))),V_X)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) )
<=> ! [V_nb: $i,V_na: $i,V_X: $i,V_B: $i,V_A: $i,V_k: $i,V_evs: $i] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,V_nb))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(V_k,c_Message_Omsg_OMPair(V_na,V_nb)))),V_X)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ) ),
inference(rewrite,[status(thm)],]) ).
tff(16,plain,
^ [V_nb: $i,V_na: $i,V_X: $i,V_B: $i,V_A: $i,V_k: $i,V_evs: $i] :
rewrite(
( ( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(V_k,c_Message_Omsg_OMPair(V_na,V_nb)))),V_X)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,V_nb))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) )
<=> ( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,V_nb))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(V_k,c_Message_Omsg_OMPair(V_na,V_nb)))),V_X)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ) )),
inference(bind,[status(th)],]) ).
tff(17,plain,
( ! [V_nb: $i,V_na: $i,V_X: $i,V_B: $i,V_A: $i,V_k: $i,V_evs: $i] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(V_k,c_Message_Omsg_OMPair(V_na,V_nb)))),V_X)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,V_nb))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) )
<=> ! [V_nb: $i,V_na: $i,V_X: $i,V_B: $i,V_A: $i,V_k: $i,V_evs: $i] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,V_nb))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(V_k,c_Message_Omsg_OMPair(V_na,V_nb)))),V_X)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,axiom,
! [V_nb: $i,V_na: $i,V_X: $i,V_B: $i,V_A: $i,V_k: $i,V_evs: $i] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(V_k,c_Message_Omsg_OMPair(V_na,V_nb)))),V_X)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,V_nb))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OSays__Server__imp__YM2_0) ).
tff(19,plain,
! [V_nb: $i,V_na: $i,V_X: $i,V_B: $i,V_A: $i,V_k: $i,V_evs: $i] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,V_nb))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(V_k,c_Message_Omsg_OMPair(V_na,V_nb)))),V_X)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [V_nb: $i,V_na: $i,V_X: $i,V_B: $i,V_A: $i,V_k: $i,V_evs: $i] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,V_nb))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(V_k,c_Message_Omsg_OMPair(V_na,V_nb)))),V_X)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
! [V_nb: $i,V_na: $i,V_X: $i,V_B: $i,V_A: $i,V_k: $i,V_evs: $i] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,V_nb))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(V_k,c_Message_Omsg_OMPair(V_na,V_nb)))),V_X)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [V_nb: $i,V_na: $i,V_X: $i,V_B: $i,V_A: $i,V_k: $i,V_evs: $i] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,V_nb))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(V_k,c_Message_Omsg_OMPair(V_na,V_nb)))),V_X)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ),
inference(modus_ponens,[status(thm)],[21,14]) ).
tff(23,plain,
( c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa))))),v_X)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
<=> c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa))))),v_X)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ),
inference(rewrite,[status(thm)],]) ).
tff(24,axiom,
c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa))))),v_X)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(25,plain,
c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa))))),v_X)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
( c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
<=> c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(rewrite,[status(thm)],]) ).
tff(27,axiom,
c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(28,plain,
c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
( ( ~ ! [V_nb: $i,V_na: $i,V_X: $i,V_B: $i,V_A: $i,V_k: $i,V_evs: $i] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,V_nb))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(V_k,c_Message_Omsg_OMPair(V_na,V_nb)))),V_X)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) )
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa))))),v_X)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) )
<=> ( ~ ! [V_nb: $i,V_na: $i,V_X: $i,V_B: $i,V_A: $i,V_k: $i,V_evs: $i] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,V_nb))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(V_k,c_Message_Omsg_OMPair(V_na,V_nb)))),V_X)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) )
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa))))),v_X)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ( ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa))))),v_X)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) )
<=> ( ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa))))),v_X)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
( ( ~ ! [V_nb: $i,V_na: $i,V_X: $i,V_B: $i,V_A: $i,V_k: $i,V_evs: $i] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,V_nb))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(V_k,c_Message_Omsg_OMPair(V_na,V_nb)))),V_X)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) )
| ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa))))),v_X)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) )
<=> ( ~ ! [V_nb: $i,V_na: $i,V_X: $i,V_B: $i,V_A: $i,V_k: $i,V_evs: $i] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,V_nb))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(V_k,c_Message_Omsg_OMPair(V_na,V_nb)))),V_X)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) )
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa))))),v_X)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ) ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( ( ~ ! [V_nb: $i,V_na: $i,V_X: $i,V_B: $i,V_A: $i,V_k: $i,V_evs: $i] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,V_nb))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(V_k,c_Message_Omsg_OMPair(V_na,V_nb)))),V_X)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) )
| ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa))))),v_X)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) )
<=> ( ~ ! [V_nb: $i,V_na: $i,V_X: $i,V_B: $i,V_A: $i,V_k: $i,V_evs: $i] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,V_nb))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(V_k,c_Message_Omsg_OMPair(V_na,V_nb)))),V_X)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) )
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa))))),v_X)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ) ),
inference(transitivity,[status(thm)],[31,29]) ).
tff(33,plain,
( ~ ! [V_nb: $i,V_na: $i,V_X: $i,V_B: $i,V_A: $i,V_k: $i,V_evs: $i] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,V_nb))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(V_k,c_Message_Omsg_OMPair(V_na,V_nb)))),V_X)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) )
| ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa))))),v_X)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
( ~ ! [V_nb: $i,V_na: $i,V_X: $i,V_B: $i,V_A: $i,V_k: $i,V_evs: $i] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,V_nb))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(V_k,c_Message_Omsg_OMPair(V_na,V_nb)))),V_X)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) )
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa))))),v_X)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent),
inference(unit_resolution,[status(thm)],[34,28,25,22]) ).
tff(36,plain,
^ [V_X: $i,V_B: $i,V_evs: $i] :
refl(
( ( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) )
<=> ( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ) )),
inference(bind,[status(th)],]) ).
tff(37,plain,
( ! [V_X: $i,V_B: $i,V_evs: $i] :
( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) )
<=> ! [V_X: $i,V_B: $i,V_evs: $i] :
( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [V_X: $i,V_B: $i,V_evs: $i] :
( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) )
<=> ! [V_X: $i,V_B: $i,V_evs: $i] :
( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
^ [V_X: $i,V_B: $i,V_evs: $i] :
trans(
monotonicity(
rewrite(
( ( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) )
<=> ( ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ) )),
( ( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
<=> ( ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) )),
rewrite(
( ( ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
<=> ( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ) )),
( ( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
<=> ( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ) )),
inference(bind,[status(th)],]) ).
tff(40,plain,
( ! [V_X: $i,V_B: $i,V_evs: $i] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
<=> ! [V_X: $i,V_B: $i,V_evs: $i] :
( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,axiom,
! [V_X: $i,V_B: $i,V_evs: $i] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OGets__imp__analz__Spy__dest_0) ).
tff(42,plain,
! [V_X: $i,V_B: $i,V_evs: $i] :
( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [V_X: $i,V_B: $i,V_evs: $i] :
( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
! [V_X: $i,V_B: $i,V_evs: $i] :
( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [V_X: $i,V_B: $i,V_evs: $i] :
( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(modus_ponens,[status(thm)],[44,37]) ).
tff(46,plain,
( ( ~ ! [V_X: $i,V_B: $i,V_evs: $i] :
( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) )
| ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa))))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) )
<=> ( ~ ! [V_X: $i,V_B: $i,V_evs: $i] :
( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) )
| ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa))))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ) ),
inference(rewrite,[status(thm)],]) ).
tff(47,plain,
( ( c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa))))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) )
<=> ( ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa))))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ) ),
inference(rewrite,[status(thm)],]) ).
tff(48,plain,
( ( ~ ! [V_X: $i,V_B: $i,V_evs: $i] :
( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) )
| c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa))))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) )
<=> ( ~ ! [V_X: $i,V_B: $i,V_evs: $i] :
( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) )
| ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa))))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ) ),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
( ( ~ ! [V_X: $i,V_B: $i,V_evs: $i] :
( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) )
| c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa))))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) )
<=> ( ~ ! [V_X: $i,V_B: $i,V_evs: $i] :
( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) )
| ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa))))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ) ),
inference(transitivity,[status(thm)],[48,46]) ).
tff(50,plain,
( ~ ! [V_X: $i,V_B: $i,V_evs: $i] :
( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) )
| c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa))))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(quant_inst,[status(thm)],]) ).
tff(51,plain,
( ~ ! [V_X: $i,V_B: $i,V_evs: $i] :
( c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) )
| ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa))))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa))))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[51,28,45,35]) ).
tff(53,plain,
^ [V_H: $i,V_X: $i] :
refl(
( ( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
<=> ( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ) )),
inference(bind,[status(th)],]) ).
tff(54,plain,
( ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
<=> ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,plain,
( ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
<=> ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(56,axiom,
! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts_OInj_0) ).
tff(57,plain,
! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ),
inference(skolemize,[status(sab)],[57]) ).
tff(59,plain,
! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[58,54]) ).
tff(60,plain,
( ( ~ ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa))))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa))))),c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso))),tc_Message_Omsg) )
<=> ( ~ ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa))))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa))))),c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso))),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
( ~ ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa))))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa))))),c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso))),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],]) ).
tff(62,plain,
( ~ ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa))))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa))))),c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso))),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa))))),c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso))),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[62,59,52]) ).
tff(64,plain,
^ [V_Y: $i,V_H: $i,V_X: $i] :
refl(
( ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
| c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) )
<=> ( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
| c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) ) )),
inference(bind,[status(th)],]) ).
tff(65,plain,
( ! [V_Y: $i,V_H: $i,V_X: $i] :
( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
| c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) )
<=> ! [V_Y: $i,V_H: $i,V_X: $i] :
( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
| c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,plain,
( ! [V_Y: $i,V_H: $i,V_X: $i] :
( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
| c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) )
<=> ! [V_Y: $i,V_H: $i,V_X: $i] :
( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
| c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,axiom,
! [V_Y: $i,V_H: $i,V_X: $i] :
( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
| c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__parts_0) ).
tff(68,plain,
! [V_Y: $i,V_H: $i,V_X: $i] :
( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
| c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [V_Y: $i,V_H: $i,V_X: $i] :
( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
| c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) ),
inference(skolemize,[status(sab)],[68]) ).
tff(70,plain,
! [V_Y: $i,V_H: $i,V_X: $i] :
( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
| c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,plain,
( ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
| c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa))))),c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso))),tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa)))),c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso))),tc_Message_Omsg) )
<=> ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
| c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa))))),c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso))),tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa)))),c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso))),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
| c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa))))),c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso))),tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa)))),c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso))),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],]) ).
tff(73,plain,
( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
| c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa))))),c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso))),tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa)))),c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso))),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa)))),c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso))),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[73,70,63]) ).
tff(75,plain,
c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[74,12]) ).
tff(76,plain,
^ [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
refl(
( ( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) )
<=> ( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) ) )),
inference(bind,[status(th)],]) ).
tff(77,plain,
( ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) )
<=> ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) ) ),
inference(quant_intro,[status(thm)],[76]) ).
tff(78,plain,
( ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) )
<=> ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(79,axiom,
! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_OSays__imp__spies_0) ).
tff(80,plain,
! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) ),
inference(skolemize,[status(sab)],[80]) ).
tff(82,plain,
! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[81,77]) ).
tff(83,plain,
( c_in(c_Event_Oevent_OSays(v_B,c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
<=> c_in(c_Event_Oevent_OSays(v_B,c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ),
inference(rewrite,[status(thm)],]) ).
tff(84,axiom,
c_in(c_Event_Oevent_OSays(v_B,c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
tff(85,plain,
c_in(c_Event_Oevent_OSays(v_B,c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
( ( ~ ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) )
| ~ c_in(c_Event_Oevent_OSays(v_B,c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),c_Event_Oknows(c_Message_Oagent_OSpy,v_evso),tc_Message_Omsg) )
<=> ( ~ ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) )
| ~ c_in(c_Event_Oevent_OSays(v_B,c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),c_Event_Oknows(c_Message_Oagent_OSpy,v_evso),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(87,plain,
( ~ ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) )
| ~ c_in(c_Event_Oevent_OSays(v_B,c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),c_Event_Oknows(c_Message_Oagent_OSpy,v_evso),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],]) ).
tff(88,plain,
( ~ ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg) )
| ~ c_in(c_Event_Oevent_OSays(v_B,c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),c_Event_Oknows(c_Message_Oagent_OSpy,v_evso),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),c_Event_Oknows(c_Message_Oagent_OSpy,v_evso),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[88,85,82]) ).
tff(90,plain,
( ( ~ ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),c_Event_Oknows(c_Message_Oagent_OSpy,v_evso),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg) )
<=> ( ~ ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),c_Event_Oknows(c_Message_Oagent_OSpy,v_evso),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(91,plain,
( ~ ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),c_Event_Oknows(c_Message_Oagent_OSpy,v_evso),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],]) ).
tff(92,plain,
( ~ ! [V_H: $i,V_X: $i] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),c_Event_Oknows(c_Message_Oagent_OSpy,v_evso),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[92,59,89]) ).
tff(94,plain,
( ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
| c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg) )
<=> ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
| c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(95,plain,
( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
| c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],]) ).
tff(96,plain,
( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg)
| c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg) )
| ~ c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[96,70,93]) ).
tff(98,plain,
^ [V_B_H: $i,V_A_H: $i,V_nb_H: $i,V_NB: $i,V_na: $i,V_B: $i,V_A: $i,V_evs: $i] :
refl(
( ( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Message_Omsg_ONonce(V_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),V_nb_H))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,c_Message_Omsg_ONonce(V_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
<=> ( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Message_Omsg_ONonce(V_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),V_nb_H))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,c_Message_Omsg_ONonce(V_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) )),
inference(bind,[status(th)],]) ).
tff(99,plain,
( ! [V_B_H: $i,V_A_H: $i,V_nb_H: $i,V_NB: $i,V_na: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Message_Omsg_ONonce(V_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),V_nb_H))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,c_Message_Omsg_ONonce(V_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
<=> ! [V_B_H: $i,V_A_H: $i,V_nb_H: $i,V_NB: $i,V_na: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Message_Omsg_ONonce(V_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),V_nb_H))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,c_Message_Omsg_ONonce(V_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) ),
inference(quant_intro,[status(thm)],[98]) ).
tff(100,plain,
( ! [V_B_H: $i,V_A_H: $i,V_nb_H: $i,V_NB: $i,V_na: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Message_Omsg_ONonce(V_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),V_nb_H))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,c_Message_Omsg_ONonce(V_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
<=> ! [V_B_H: $i,V_A_H: $i,V_nb_H: $i,V_NB: $i,V_na: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Message_Omsg_ONonce(V_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),V_nb_H))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,c_Message_Omsg_ONonce(V_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(101,plain,
^ [V_B_H: $i,V_A_H: $i,V_nb_H: $i,V_NB: $i,V_na: $i,V_B: $i,V_A: $i,V_evs: $i] :
trans(
monotonicity(
rewrite(
( ( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,c_Message_Omsg_ONonce(V_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),V_nb_H))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
<=> ( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),V_nb_H))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,c_Message_Omsg_ONonce(V_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) )),
( ( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,c_Message_Omsg_ONonce(V_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),V_nb_H))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(V_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
<=> ( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),V_nb_H))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,c_Message_Omsg_ONonce(V_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(V_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) )),
rewrite(
( ( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),V_nb_H))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,c_Message_Omsg_ONonce(V_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(V_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
<=> ( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Message_Omsg_ONonce(V_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),V_nb_H))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,c_Message_Omsg_ONonce(V_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) )),
( ( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,c_Message_Omsg_ONonce(V_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),V_nb_H))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(V_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
<=> ( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Message_Omsg_ONonce(V_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),V_nb_H))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,c_Message_Omsg_ONonce(V_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) )),
inference(bind,[status(th)],]) ).
tff(102,plain,
( ! [V_B_H: $i,V_A_H: $i,V_nb_H: $i,V_NB: $i,V_na: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,c_Message_Omsg_ONonce(V_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),V_nb_H))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(V_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
<=> ! [V_B_H: $i,V_A_H: $i,V_nb_H: $i,V_NB: $i,V_na: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Message_Omsg_ONonce(V_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),V_nb_H))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,c_Message_Omsg_ONonce(V_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) ),
inference(quant_intro,[status(thm)],[101]) ).
tff(103,axiom,
! [V_B_H: $i,V_A_H: $i,V_nb_H: $i,V_NB: $i,V_na: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,c_Message_Omsg_ONonce(V_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),V_nb_H))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(V_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_Ono__nonce__YM1__YM2_0) ).
tff(104,plain,
! [V_B_H: $i,V_A_H: $i,V_nb_H: $i,V_NB: $i,V_na: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Message_Omsg_ONonce(V_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),V_nb_H))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,c_Message_Omsg_ONonce(V_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
! [V_B_H: $i,V_A_H: $i,V_nb_H: $i,V_NB: $i,V_na: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Message_Omsg_ONonce(V_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),V_nb_H))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,c_Message_Omsg_ONonce(V_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[104,100]) ).
tff(106,plain,
! [V_B_H: $i,V_A_H: $i,V_nb_H: $i,V_NB: $i,V_na: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Message_Omsg_ONonce(V_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),V_nb_H))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,c_Message_Omsg_ONonce(V_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ),
inference(skolemize,[status(sab)],[105]) ).
tff(107,plain,
! [V_B_H: $i,V_A_H: $i,V_nb_H: $i,V_NB: $i,V_na: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Message_Omsg_ONonce(V_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),V_nb_H))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,c_Message_Omsg_ONonce(V_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[106,99]) ).
tff(108,plain,
( ~ c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
<=> ~ c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg) ),
inference(rewrite,[status(thm)],]) ).
tff(109,axiom,
~ c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
tff(110,plain,
~ c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
( ( ~ ! [V_B_H: $i,V_A_H: $i,V_nb_H: $i,V_NB: $i,V_na: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Message_Omsg_ONonce(V_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),V_nb_H))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,c_Message_Omsg_ONonce(V_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
| c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg) )
<=> ( ~ ! [V_B_H: $i,V_A_H: $i,V_nb_H: $i,V_NB: $i,V_na: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Message_Omsg_ONonce(V_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),V_nb_H))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,c_Message_Omsg_ONonce(V_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
| c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(112,plain,
( ( ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg) )
<=> ( c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(113,plain,
( ( ~ ! [V_B_H: $i,V_A_H: $i,V_nb_H: $i,V_NB: $i,V_na: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Message_Omsg_ONonce(V_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),V_nb_H))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,c_Message_Omsg_ONonce(V_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
| ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg) )
<=> ( ~ ! [V_B_H: $i,V_A_H: $i,V_nb_H: $i,V_NB: $i,V_na: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Message_Omsg_ONonce(V_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),V_nb_H))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,c_Message_Omsg_ONonce(V_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
| c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg) ) ),
inference(monotonicity,[status(thm)],[112]) ).
tff(114,plain,
( ( ~ ! [V_B_H: $i,V_A_H: $i,V_nb_H: $i,V_NB: $i,V_na: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Message_Omsg_ONonce(V_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),V_nb_H))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,c_Message_Omsg_ONonce(V_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
| ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg) )
<=> ( ~ ! [V_B_H: $i,V_A_H: $i,V_nb_H: $i,V_NB: $i,V_na: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Message_Omsg_ONonce(V_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),V_nb_H))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,c_Message_Omsg_ONonce(V_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
| c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg) ) ),
inference(transitivity,[status(thm)],[113,111]) ).
tff(115,plain,
( ~ ! [V_B_H: $i,V_A_H: $i,V_nb_H: $i,V_NB: $i,V_na: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Message_Omsg_ONonce(V_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),V_nb_H))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,c_Message_Omsg_ONonce(V_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
| ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],]) ).
tff(116,plain,
( ~ ! [V_B_H: $i,V_A_H: $i,V_nb_H: $i,V_NB: $i,V_na: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Message_Omsg_ONonce(V_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),V_nb_H))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A),c_Message_Omsg_OMPair(V_na,c_Message_Omsg_ONonce(V_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
| c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,plain,
~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NBa)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[116,28,110,107,97]) ).
tff(118,plain,
$false,
inference(unit_resolution,[status(thm)],[117,75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV352-2 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n001.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 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Sep 4 02:58:42 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.55/0.58 % SZS status Unsatisfiable
% 0.55/0.58 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------