%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV769-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 : Sat Jun 21 05:36:03 AM UTC 2025
% Result : Unsatisfiable 19.81s 20.00s
% Output : Proof 20.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 67
% Syntax : Number of formulae : 184 ( 54 unt; 0 typ; 0 def)
% Number of atoms : 1015 ( 157 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 1361 ( 598 ~; 667 |; 0 &)
% ( 96 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of FOOLs : 68 ( 68 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 32 ( 32 usr; 20 con; 0-3 aty)
% Number of variables : 849 ( 765 !; 0 ?; 849 :)
% Comments :
%------------------------------------------------------------------------------
tff(v_Ba_type,type,
v_Ba: $i ).
tff(v_B_type,type,
v_B: $i ).
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(c_in_type,type,
c_in: ( $i * $i * $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(v_evs5_type,type,
v_evs5: $i ).
tff(c_Event_Oevent_OSays_type,type,
c_Event_Oevent_OSays: ( $i * $i * $i ) > $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_OAgent_type,type,
c_Message_Omsg_OAgent: $i > $i ).
tff(v_Aa_type,type,
v_Aa: $i ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(v_Ka_type,type,
v_Ka: $i ).
tff(c_Message_Omsg_OKey_type,type,
c_Message_Omsg_OKey: $i ).
tff(c_Public_OshrK_type,type,
c_Public_OshrK: $i ).
tff(c_Message_Omsg_ONonce_type,type,
c_Message_Omsg_ONonce: $i > $i ).
tff(v_NAa_type,type,
v_NAa: $i ).
tff(c_Message_Oagent_OServer_type,type,
c_Message_Oagent_OServer: $i ).
tff(v_X_type,type,
v_X: $i ).
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(c_Message_Oagent_OSpy_type,type,
c_Message_Oagent_OSpy: $i ).
tff(v_S_type,type,
v_S: $i ).
tff(tc_Message_Oagent_type,type,
tc_Message_Oagent: $i ).
tff(c_Event_Obad_type,type,
c_Event_Obad: $i ).
tff(c_Message_Oanalz_type,type,
c_Message_Oanalz: $i > $i ).
tff(v_K_type,type,
v_K: $i ).
tff(tc_List_Olist_type,type,
tc_List_Olist: $i > $i ).
tff(c_NS__Shared__Mirabelle_Ons__shared_type,type,
c_NS__Shared__Mirabelle_Ons__shared: $i ).
tff(v_A_type,type,
v_A: $i ).
tff(v_NA_type,type,
v_NA: $i ).
tff(1,plain,
( hBOOL(c_in(c_Event_Oevent_OSays(v_S,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent))
<=> hBOOL(c_in(c_Event_Oevent_OSays(v_S,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
hBOOL(c_in(c_Event_Oevent_OSays(v_S,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
tff(3,plain,
hBOOL(c_in(c_Event_Oevent_OSays(v_S,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
refl(( ( hBOOL(c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) )
<=> ( hBOOL(c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( hBOOL(c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) )
<=> ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( hBOOL(c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( hBOOL(c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) )
<=> ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( hBOOL(c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( hBOOL(c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Says__imp__parts__knows__Spy_0) ).
tff(8,plain,
! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( hBOOL(c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( hBOOL(c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( hBOOL(c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( hBOOL(c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) )
| hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(v_S,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)) )
<=> ( ~ ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( hBOOL(c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) )
| hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(v_S,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( hBOOL(c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) )
| hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(v_S,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( hBOOL(c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) )
| hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(v_S,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
^ [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
refl(( ( hBOOL(c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) )
<=> ( hBOOL(c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( hBOOL(c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) )
<=> ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( hBOOL(c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( hBOOL(c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) )
<=> ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( hBOOL(c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( hBOOL(c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Says__imp__analz__Spy_0) ).
tff(19,plain,
! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( hBOOL(c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( hBOOL(c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( hBOOL(c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
( ( ~ ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( hBOOL(c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) )
| hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(v_S,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)) )
<=> ( ~ ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( hBOOL(c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) )
| hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(v_S,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
( ~ ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( hBOOL(c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) )
| hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(v_S,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
( ~ ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( hBOOL(c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) )
| hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(v_S,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)),
inference(unit_resolution,[status(thm)],[24,21,3]) ).
tff(26,plain,
( ( v_K = v_Ka )
<=> ( v_K = v_Ka ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,axiom,
v_K = v_Ka,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_7) ).
tff(28,plain,
v_K = v_Ka,
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
hAPP(c_Message_Omsg_OKey,v_K) = hAPP(c_Message_Omsg_OKey,v_Ka),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
hAPP(c_Message_Omsg_OKey,v_Ka) = hAPP(c_Message_Omsg_OKey,v_K),
inference(symmetry,[status(thm)],[29]) ).
tff(31,plain,
c_in(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg) = c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
<=> hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) ),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
( hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
<=> hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) ),
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
( ~ hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
<=> ~ hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) ),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,plain,
( ~ hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
<=> ~ hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,axiom,
~ hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
tff(37,plain,
~ hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
~ hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)),
inference(modus_ponens,[status(thm)],[37,34]) ).
tff(39,plain,
^ [V_Y: $i,V_H: $i,V_X: $i] :
refl(( ( hBOOL(c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)) )
<=> ( hBOOL(c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)) ) )),
inference(bind,[status(th)],[]) ).
tff(40,plain,
( ! [V_Y: $i,V_H: $i,V_X: $i] :
( hBOOL(c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)) )
<=> ! [V_Y: $i,V_H: $i,V_X: $i] :
( hBOOL(c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [V_Y: $i,V_H: $i,V_X: $i] :
( hBOOL(c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)) )
<=> ! [V_Y: $i,V_H: $i,V_X: $i] :
( hBOOL(c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,axiom,
! [V_Y: $i,V_H: $i,V_X: $i] :
( hBOOL(c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz_OFst_0) ).
tff(43,plain,
! [V_Y: $i,V_H: $i,V_X: $i] :
( hBOOL(c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
! [V_Y: $i,V_H: $i,V_X: $i] :
( hBOOL(c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)) ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [V_Y: $i,V_H: $i,V_X: $i] :
( hBOOL(c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
( ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( hBOOL(c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)) )
| hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) )
<=> ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( hBOOL(c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)) )
| hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( hBOOL(c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)) )
| hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( hBOOL(c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)) )
| hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
( hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) ),
inference(unit_resolution,[status(thm)],[48,45]) ).
tff(50,plain,
~ hBOOL(c_in(c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)),
inference(unit_resolution,[status(thm)],[49,38]) ).
tff(51,plain,
^ [V_Y: $i,V_H: $i,V_X: $i] :
refl(( ( hBOOL(c_in(V_Y,c_Message_Oanalz(V_H),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)) )
<=> ( hBOOL(c_in(V_Y,c_Message_Oanalz(V_H),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)) ) )),
inference(bind,[status(th)],[]) ).
tff(52,plain,
( ! [V_Y: $i,V_H: $i,V_X: $i] :
( hBOOL(c_in(V_Y,c_Message_Oanalz(V_H),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)) )
<=> ! [V_Y: $i,V_H: $i,V_X: $i] :
( hBOOL(c_in(V_Y,c_Message_Oanalz(V_H),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
( ! [V_Y: $i,V_H: $i,V_X: $i] :
( hBOOL(c_in(V_Y,c_Message_Oanalz(V_H),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)) )
<=> ! [V_Y: $i,V_H: $i,V_X: $i] :
( hBOOL(c_in(V_Y,c_Message_Oanalz(V_H),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,axiom,
! [V_Y: $i,V_H: $i,V_X: $i] :
( hBOOL(c_in(V_Y,c_Message_Oanalz(V_H),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_analz_OSnd_0) ).
tff(55,plain,
! [V_Y: $i,V_H: $i,V_X: $i] :
( hBOOL(c_in(V_Y,c_Message_Oanalz(V_H),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
! [V_Y: $i,V_H: $i,V_X: $i] :
( hBOOL(c_in(V_Y,c_Message_Oanalz(V_H),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)) ),
inference(skolemize,[status(sab)],[55]) ).
tff(57,plain,
! [V_Y: $i,V_H: $i,V_X: $i] :
( hBOOL(c_in(V_Y,c_Message_Oanalz(V_H),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[56,52]) ).
tff(58,plain,
( ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( hBOOL(c_in(V_Y,c_Message_Oanalz(V_H),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)) )
| hBOOL(c_in(c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) )
<=> ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( hBOOL(c_in(V_Y,c_Message_Oanalz(V_H),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)) )
| hBOOL(c_in(c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,plain,
( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( hBOOL(c_in(V_Y,c_Message_Oanalz(V_H),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)) )
| hBOOL(c_in(c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(60,plain,
( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( hBOOL(c_in(V_Y,c_Message_Oanalz(V_H),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)) )
| hBOOL(c_in(c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
( hBOOL(c_in(c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) ),
inference(unit_resolution,[status(thm)],[60,57]) ).
tff(62,plain,
~ hBOOL(c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)),
inference(unit_resolution,[status(thm)],[61,50]) ).
tff(63,plain,
( ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( hBOOL(c_in(V_Y,c_Message_Oanalz(V_H),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)) )
| hBOOL(c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) )
<=> ( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( hBOOL(c_in(V_Y,c_Message_Oanalz(V_H),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)) )
| hBOOL(c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,plain,
( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( hBOOL(c_in(V_Y,c_Message_Oanalz(V_H),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)) )
| hBOOL(c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(65,plain,
( ~ ! [V_Y: $i,V_H: $i,V_X: $i] :
( hBOOL(c_in(V_Y,c_Message_Oanalz(V_H),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oanalz(V_H),tc_Message_Omsg)) )
| hBOOL(c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
( hBOOL(c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) ),
inference(unit_resolution,[status(thm)],[65,57]) ).
tff(67,plain,
~ hBOOL(c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)),
inference(unit_resolution,[status(thm)],[66,62]) ).
tff(68,plain,
^ [V_X: $i,V_A: $i,V_evs: $i] :
refl(( ( ~ hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),V_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)) )
<=> ( ~ hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),V_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)) ) )),
inference(bind,[status(th)],[]) ).
tff(69,plain,
( ! [V_X: $i,V_A: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),V_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)) )
<=> ! [V_X: $i,V_A: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),V_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)) ) ),
inference(quant_intro,[status(thm)],[68]) ).
tff(70,plain,
( ! [V_X: $i,V_A: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),V_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)) )
<=> ! [V_X: $i,V_A: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),V_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,plain,
^ [V_X: $i,V_A: $i,V_evs: $i] :
trans(monotonicity(rewrite(( ( hBOOL(c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| ~ hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent)) )
<=> ( ~ hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)) ) )),
( ( hBOOL(c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| ~ hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),V_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)) )
<=> ( ~ hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),V_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)) ) )),
rewrite(( ( ~ hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),V_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)) )
<=> ( ~ hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),V_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)) ) )),
( ( hBOOL(c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| ~ hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),V_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)) )
<=> ( ~ hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),V_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)) ) )),
inference(bind,[status(th)],[]) ).
tff(72,plain,
( ! [V_X: $i,V_A: $i,V_evs: $i] :
( hBOOL(c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| ~ hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),V_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)) )
<=> ! [V_X: $i,V_A: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),V_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,axiom,
! [V_X: $i,V_A: $i,V_evs: $i] :
( hBOOL(c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| ~ hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),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_Crypt__Spy__analz__bad_0) ).
tff(74,plain,
! [V_X: $i,V_A: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),V_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
! [V_X: $i,V_A: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),V_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[74,70]) ).
tff(76,plain,
! [V_X: $i,V_A: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),V_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)) ),
inference(skolemize,[status(sab)],[75]) ).
tff(77,plain,
! [V_X: $i,V_A: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),V_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[76,69]) ).
tff(78,plain,
( ( ~ ! [V_X: $i,V_A: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),V_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)) )
| ~ hBOOL(c_in(v_Aa,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) )
<=> ( ~ ! [V_X: $i,V_A: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),V_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)) )
| ~ hBOOL(c_in(v_Aa,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(79,plain,
( ( ~ hBOOL(c_in(v_Aa,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| hBOOL(c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) )
<=> ( ~ hBOOL(c_in(v_Aa,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(80,plain,
( ( ~ ! [V_X: $i,V_A: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),V_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)) )
| ~ hBOOL(c_in(v_Aa,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| hBOOL(c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) )
<=> ( ~ ! [V_X: $i,V_A: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),V_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)) )
| ~ hBOOL(c_in(v_Aa,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) ) ),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
( ( ~ ! [V_X: $i,V_A: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),V_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)) )
| ~ hBOOL(c_in(v_Aa,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| hBOOL(c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) )
<=> ( ~ ! [V_X: $i,V_A: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),V_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)) )
| ~ hBOOL(c_in(v_Aa,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) ) ),
inference(transitivity,[status(thm)],[80,78]) ).
tff(82,plain,
( ~ ! [V_X: $i,V_A: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),V_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)) )
| ~ hBOOL(c_in(v_Aa,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| hBOOL(c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(83,plain,
( ~ ! [V_X: $i,V_A: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),V_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_X,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)) )
| ~ hBOOL(c_in(v_Aa,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
( ~ hBOOL(c_in(v_Aa,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) ),
inference(unit_resolution,[status(thm)],[83,77]) ).
tff(85,plain,
~ hBOOL(c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)),
inference(unit_resolution,[status(thm)],[84,67,25]) ).
tff(86,plain,
( hBOOL(c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
<=> hBOOL(c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))) ),
inference(rewrite,[status(thm)],[]) ).
tff(87,axiom,
hBOOL(c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(88,plain,
hBOOL(c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
^ [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
refl(( ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) )
<=> ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) ) )),
inference(bind,[status(th)],[]) ).
tff(90,plain,
( ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) )
<=> ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
( ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) )
<=> ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(92,plain,
^ [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) )
| ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))) )
<=> ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) ) )),
( ( ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) )
| ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent)) )
<=> ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) )
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent)) ) )),
rewrite(( ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) )
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent)) )
<=> ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) ) )),
( ( ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) )
| ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent)) )
<=> ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) ) )),
( ( ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) )
| ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)) )
<=> ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) )
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)) ) )),
rewrite(( ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) )
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)) )
<=> ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) ) )),
( ( ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) )
| ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)) )
<=> ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) ) )),
inference(bind,[status(th)],[]) ).
tff(93,plain,
( ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) )
| ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)) )
<=> ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,axiom,
! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) )
| ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cert__A__form_1) ).
tff(95,plain,
! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) ),
inference(modus_ponens,[status(thm)],[95,91]) ).
tff(97,plain,
! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) ),
inference(skolemize,[status(sab)],[96]) ).
tff(98,plain,
! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) ),
inference(modus_ponens,[status(thm)],[97,90]) ).
tff(99,plain,
( ( ~ ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) )
| ~ hBOOL(c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(v_Aa,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ( v_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa))) ) )
<=> ( ~ ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) )
| ~ hBOOL(c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(v_Aa,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ( v_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(100,plain,
( ( ~ hBOOL(c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| hBOOL(c_in(v_Aa,c_Event_Obad,tc_Message_Oagent))
| ( v_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa))) ) )
<=> ( ~ hBOOL(c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(v_Aa,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ( v_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(101,plain,
( ( ~ ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) )
| ~ hBOOL(c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| hBOOL(c_in(v_Aa,c_Event_Obad,tc_Message_Oagent))
| ( v_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa))) ) )
<=> ( ~ ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) )
| ~ hBOOL(c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(v_Aa,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ( v_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa))) ) ) ),
inference(monotonicity,[status(thm)],[100]) ).
tff(102,plain,
( ( ~ ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) )
| ~ hBOOL(c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| hBOOL(c_in(v_Aa,c_Event_Obad,tc_Message_Oagent))
| ( v_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa))) ) )
<=> ( ~ ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) )
| ~ hBOOL(c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(v_Aa,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ( v_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa))) ) ) ),
inference(transitivity,[status(thm)],[101,99]) ).
tff(103,plain,
( ~ ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) )
| ~ hBOOL(c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| hBOOL(c_in(v_Aa,c_Event_Obad,tc_Message_Oagent))
| ( v_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(104,plain,
( ~ ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) )
| ~ hBOOL(c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(v_Aa,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ( v_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa))) ) ),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
( hBOOL(c_in(v_Aa,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ( v_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa))) ) ),
inference(unit_resolution,[status(thm)],[104,98,88]) ).
tff(106,plain,
v_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa))),
inference(unit_resolution,[status(thm)],[105,85,14]) ).
tff(107,plain,
c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa))) = v_X,
inference(symmetry,[status(thm)],[106]) ).
tff(108,plain,
c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa)))) = c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X),
inference(monotonicity,[status(thm)],[107]) ).
tff(109,plain,
c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa))))) = c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)),
inference(monotonicity,[status(thm)],[108]) ).
tff(110,plain,
c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa)))))) = c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))),
inference(monotonicity,[status(thm)],[109]) ).
tff(111,plain,
c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa))))))) = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),
inference(monotonicity,[status(thm)],[110]) ).
tff(112,plain,
c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa)))))))) = c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),
inference(monotonicity,[status(thm)],[111]) ).
tff(113,plain,
c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa)))))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent) = c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent),
inference(monotonicity,[status(thm)],[112]) ).
tff(114,plain,
( hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa)))))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent))
<=> hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)) ),
inference(monotonicity,[status(thm)],[113]) ).
tff(115,plain,
( hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent))
<=> hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa)))))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)) ),
inference(symmetry,[status(thm)],[114]) ).
tff(116,plain,
^ [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
refl(( ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) )
<=> ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) ) )),
inference(bind,[status(th)],[]) ).
tff(117,plain,
( ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) )
<=> ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) ) ),
inference(quant_intro,[status(thm)],[116]) ).
tff(118,plain,
( ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) )
<=> ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(119,plain,
^ [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))) )
<=> ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) ) )),
( ( hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent)) )
<=> ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent)) ) )),
rewrite(( ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent)) )
<=> ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) ) )),
( ( hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent)) )
<=> ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) ) )),
( ( hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)) )
<=> ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)) ) )),
rewrite(( ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)) )
<=> ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) ) )),
( ( hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)) )
<=> ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) ) )),
inference(bind,[status(th)],[]) ).
tff(120,plain,
( ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)) )
<=> ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) ) ),
inference(quant_intro,[status(thm)],[119]) ).
tff(121,axiom,
! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_A__trusts__NS2_0) ).
tff(122,plain,
! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) ),
inference(modus_ponens,[status(thm)],[122,118]) ).
tff(124,plain,
! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) ),
inference(skolemize,[status(sab)],[123]) ).
tff(125,plain,
! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) ),
inference(modus_ponens,[status(thm)],[124,117]) ).
tff(126,plain,
( ( ~ ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) )
| ~ hBOOL(c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(v_Aa,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)) )
<=> ( ~ ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) )
| ~ hBOOL(c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(v_Aa,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(127,plain,
( ( ~ hBOOL(c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| hBOOL(c_in(v_Aa,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)) )
<=> ( ~ hBOOL(c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(v_Aa,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(128,plain,
( ( ~ ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) )
| ~ hBOOL(c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| hBOOL(c_in(v_Aa,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)) )
<=> ( ~ ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) )
| ~ hBOOL(c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(v_Aa,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)) ) ),
inference(monotonicity,[status(thm)],[127]) ).
tff(129,plain,
( ( ~ ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) )
| ~ hBOOL(c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| hBOOL(c_in(v_Aa,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)) )
<=> ( ~ ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) )
| ~ hBOOL(c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(v_Aa,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)) ) ),
inference(transitivity,[status(thm)],[128,126]) ).
tff(130,plain,
( ~ ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) )
| ~ hBOOL(c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| hBOOL(c_in(v_Aa,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(131,plain,
( ~ ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg))
| hBOOL(c_in(V_A,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) )
| ~ hBOOL(c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(v_Aa,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)) ),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
( hBOOL(c_in(v_Aa,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)) ),
inference(unit_resolution,[status(thm)],[131,125,88]) ).
tff(133,plain,
hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)),
inference(unit_resolution,[status(thm)],[132,85,14]) ).
tff(134,plain,
hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa)))))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)),
inference(modus_ponens,[status(thm)],[133,115]) ).
tff(135,plain,
c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))) = c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))),
inference(monotonicity,[status(thm)],[30]) ).
tff(136,plain,
c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A))))) = c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A))))),
inference(monotonicity,[status(thm)],[135]) ).
tff(137,plain,
c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))) = c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))),
inference(monotonicity,[status(thm)],[136]) ).
tff(138,plain,
c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A))))))) = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A))))))),
inference(monotonicity,[status(thm)],[137]) ).
tff(139,plain,
c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))) = c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),
inference(monotonicity,[status(thm)],[138]) ).
tff(140,plain,
c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent) = c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent),
inference(monotonicity,[status(thm)],[139]) ).
tff(141,plain,
( hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent))
<=> hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)) ),
inference(monotonicity,[status(thm)],[140]) ).
tff(142,plain,
( hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent))
<=> hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)) ),
inference(symmetry,[status(thm)],[141]) ).
tff(143,plain,
( hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent))
<=> hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)) ),
inference(rewrite,[status(thm)],[]) ).
tff(144,axiom,
hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
tff(145,plain,
hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)),
inference(modus_ponens,[status(thm)],[144,143]) ).
tff(146,plain,
hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)),
inference(modus_ponens,[status(thm)],[145,142]) ).
tff(147,plain,
^ [V_B_H: $i,V_A_H: $i,V_X_H: $i,V_NA: $i,V_X: $i,V_NA_H: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
refl(( ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ( V_B = V_B_H ) )
<=> ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ( V_B = V_B_H ) ) )),
inference(bind,[status(th)],[]) ).
tff(148,plain,
( ! [V_B_H: $i,V_A_H: $i,V_X_H: $i,V_NA: $i,V_X: $i,V_NA_H: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ( V_B = V_B_H ) )
<=> ! [V_B_H: $i,V_A_H: $i,V_X_H: $i,V_NA: $i,V_X: $i,V_NA_H: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ( V_B = V_B_H ) ) ),
inference(quant_intro,[status(thm)],[147]) ).
tff(149,plain,
( ! [V_B_H: $i,V_A_H: $i,V_X_H: $i,V_NA: $i,V_X: $i,V_NA_H: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ( V_B = V_B_H ) )
<=> ! [V_B_H: $i,V_A_H: $i,V_X_H: $i,V_NA: $i,V_X: $i,V_NA_H: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ( V_B = V_B_H ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(150,plain,
^ [V_B_H: $i,V_A_H: $i,V_X_H: $i,V_NA: $i,V_X: $i,V_NA_H: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ( V_B = V_B_H )
| ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))) )
<=> ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ( V_B = V_B_H ) ) )),
( ( ( V_B = V_B_H )
| ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) )
<=> ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ( V_B = V_B_H )
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) ) )),
rewrite(( ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ( V_B = V_B_H )
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) )
<=> ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ( V_B = V_B_H ) ) )),
( ( ( V_B = V_B_H )
| ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) )
<=> ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ( V_B = V_B_H ) ) )),
( ( ( V_B = V_B_H )
| ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) )
<=> ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ( V_B = V_B_H )
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) ) )),
rewrite(( ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ( V_B = V_B_H )
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) )
<=> ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ( V_B = V_B_H ) ) )),
( ( ( V_B = V_B_H )
| ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) )
<=> ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ( V_B = V_B_H ) ) )),
inference(bind,[status(th)],[]) ).
tff(151,plain,
( ! [V_B_H: $i,V_A_H: $i,V_X_H: $i,V_NA: $i,V_X: $i,V_NA_H: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ( V_B = V_B_H )
| ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) )
<=> ! [V_B_H: $i,V_A_H: $i,V_X_H: $i,V_NA: $i,V_X: $i,V_NA_H: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ( V_B = V_B_H ) ) ),
inference(quant_intro,[status(thm)],[150]) ).
tff(152,axiom,
! [V_B_H: $i,V_A_H: $i,V_X_H: $i,V_NA: $i,V_X: $i,V_NA_H: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ( V_B = V_B_H )
| ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_unique__session__keys_2) ).
tff(153,plain,
! [V_B_H: $i,V_A_H: $i,V_X_H: $i,V_NA: $i,V_X: $i,V_NA_H: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ( V_B = V_B_H ) ),
inference(modus_ponens,[status(thm)],[152,151]) ).
tff(154,plain,
! [V_B_H: $i,V_A_H: $i,V_X_H: $i,V_NA: $i,V_X: $i,V_NA_H: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ( V_B = V_B_H ) ),
inference(modus_ponens,[status(thm)],[153,149]) ).
tff(155,plain,
! [V_B_H: $i,V_A_H: $i,V_X_H: $i,V_NA: $i,V_X: $i,V_NA_H: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ( V_B = V_B_H ) ),
inference(skolemize,[status(sab)],[154]) ).
tff(156,plain,
! [V_B_H: $i,V_A_H: $i,V_X_H: $i,V_NA: $i,V_X: $i,V_NA_H: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ( V_B = V_B_H ) ),
inference(modus_ponens,[status(thm)],[155,148]) ).
tff(157,plain,
( ( ~ ! [V_B_H: $i,V_A_H: $i,V_X_H: $i,V_NA: $i,V_X: $i,V_NA_H: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ( V_B = V_B_H ) )
| ~ hBOOL(c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa)))))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent))
| ( v_B = v_Ba ) )
<=> ( ~ ! [V_B_H: $i,V_A_H: $i,V_X_H: $i,V_NA: $i,V_X: $i,V_NA_H: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ( V_B = V_B_H ) )
| ~ hBOOL(c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa)))))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent))
| ( v_B = v_Ba ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(158,plain,
( ~ ! [V_B_H: $i,V_A_H: $i,V_X_H: $i,V_NA: $i,V_X: $i,V_NA_H: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ( V_B = V_B_H ) )
| ~ hBOOL(c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa)))))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent))
| ( v_B = v_Ba ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(159,plain,
( ~ ! [V_B_H: $i,V_A_H: $i,V_X_H: $i,V_NA: $i,V_X: $i,V_NA_H: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ( V_B = V_B_H ) )
| ~ hBOOL(c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa)))))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent))
| ( v_B = v_Ba ) ),
inference(modus_ponens,[status(thm)],[158,157]) ).
tff(160,plain,
( ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa)))))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent))
| ( v_B = v_Ba ) ),
inference(unit_resolution,[status(thm)],[159,156,88,146]) ).
tff(161,plain,
v_B = v_Ba,
inference(unit_resolution,[status(thm)],[160,134]) ).
tff(162,plain,
^ [V_B_H: $i,V_A_H: $i,V_X_H: $i,V_NA: $i,V_X: $i,V_NA_H: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
refl(( ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ( V_A = V_A_H ) )
<=> ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ( V_A = V_A_H ) ) )),
inference(bind,[status(th)],[]) ).
tff(163,plain,
( ! [V_B_H: $i,V_A_H: $i,V_X_H: $i,V_NA: $i,V_X: $i,V_NA_H: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ( V_A = V_A_H ) )
<=> ! [V_B_H: $i,V_A_H: $i,V_X_H: $i,V_NA: $i,V_X: $i,V_NA_H: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ( V_A = V_A_H ) ) ),
inference(quant_intro,[status(thm)],[162]) ).
tff(164,plain,
( ! [V_B_H: $i,V_A_H: $i,V_X_H: $i,V_NA: $i,V_X: $i,V_NA_H: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ( V_A = V_A_H ) )
<=> ! [V_B_H: $i,V_A_H: $i,V_X_H: $i,V_NA: $i,V_X: $i,V_NA_H: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ( V_A = V_A_H ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(165,plain,
^ [V_B_H: $i,V_A_H: $i,V_X_H: $i,V_NA: $i,V_X: $i,V_NA_H: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ( V_A = V_A_H )
| ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))) )
<=> ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ( V_A = V_A_H ) ) )),
( ( ( V_A = V_A_H )
| ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) )
<=> ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ( V_A = V_A_H )
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) ) )),
rewrite(( ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ( V_A = V_A_H )
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) )
<=> ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ( V_A = V_A_H ) ) )),
( ( ( V_A = V_A_H )
| ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) )
<=> ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ( V_A = V_A_H ) ) )),
( ( ( V_A = V_A_H )
| ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) )
<=> ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ( V_A = V_A_H )
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) ) )),
rewrite(( ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ( V_A = V_A_H )
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) )
<=> ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ( V_A = V_A_H ) ) )),
( ( ( V_A = V_A_H )
| ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) )
<=> ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ( V_A = V_A_H ) ) )),
inference(bind,[status(th)],[]) ).
tff(166,plain,
( ! [V_B_H: $i,V_A_H: $i,V_X_H: $i,V_NA: $i,V_X: $i,V_NA_H: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ( V_A = V_A_H )
| ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) )
<=> ! [V_B_H: $i,V_A_H: $i,V_X_H: $i,V_NA: $i,V_X: $i,V_NA_H: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ( V_A = V_A_H ) ) ),
inference(quant_intro,[status(thm)],[165]) ).
tff(167,axiom,
! [V_B_H: $i,V_A_H: $i,V_X_H: $i,V_NA: $i,V_X: $i,V_NA_H: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ( V_A = V_A_H )
| ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_unique__session__keys_0) ).
tff(168,plain,
! [V_B_H: $i,V_A_H: $i,V_X_H: $i,V_NA: $i,V_X: $i,V_NA_H: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ( V_A = V_A_H ) ),
inference(modus_ponens,[status(thm)],[167,166]) ).
tff(169,plain,
! [V_B_H: $i,V_A_H: $i,V_X_H: $i,V_NA: $i,V_X: $i,V_NA_H: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ( V_A = V_A_H ) ),
inference(modus_ponens,[status(thm)],[168,164]) ).
tff(170,plain,
! [V_B_H: $i,V_A_H: $i,V_X_H: $i,V_NA: $i,V_X: $i,V_NA_H: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ( V_A = V_A_H ) ),
inference(skolemize,[status(sab)],[169]) ).
tff(171,plain,
! [V_B_H: $i,V_A_H: $i,V_X_H: $i,V_NA: $i,V_X: $i,V_NA_H: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ( V_A = V_A_H ) ),
inference(modus_ponens,[status(thm)],[170,163]) ).
tff(172,plain,
( ( ~ ! [V_B_H: $i,V_A_H: $i,V_X_H: $i,V_NA: $i,V_X: $i,V_NA_H: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ( V_A = V_A_H ) )
| ~ hBOOL(c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa)))))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent))
| ( v_A = v_Aa ) )
<=> ( ~ ! [V_B_H: $i,V_A_H: $i,V_X_H: $i,V_NA: $i,V_X: $i,V_NA_H: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ( V_A = V_A_H ) )
| ~ hBOOL(c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa)))))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent))
| ( v_A = v_Aa ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(173,plain,
( ~ ! [V_B_H: $i,V_A_H: $i,V_X_H: $i,V_NA: $i,V_X: $i,V_NA_H: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ( V_A = V_A_H ) )
| ~ hBOOL(c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa)))))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent))
| ( v_A = v_Aa ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(174,plain,
( ~ ! [V_B_H: $i,V_A_H: $i,V_X_H: $i,V_NA: $i,V_X: $i,V_NA_H: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A_H),c_Message_Omsg_OMPair(V_NA_H,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X_H))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent))
| ( V_A = V_A_H ) )
| ~ hBOOL(c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa)))))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent))
| ( v_A = v_Aa ) ),
inference(modus_ponens,[status(thm)],[173,172]) ).
tff(175,plain,
( ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa)))))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent))
| ( v_A = v_Aa ) ),
inference(unit_resolution,[status(thm)],[174,171,88,146]) ).
tff(176,plain,
v_A = v_Aa,
inference(unit_resolution,[status(thm)],[175,134]) ).
tff(177,plain,
( ( ( v_B != v_Ba )
| ( v_A != v_Aa ) )
<=> ( ( v_B != v_Ba )
| ( v_A != v_Aa ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(178,axiom,
( ( v_B != v_Ba )
| ( v_A != v_Aa ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_10) ).
tff(179,plain,
( ( v_B != v_Ba )
| ( v_A != v_Aa ) ),
inference(modus_ponens,[status(thm)],[178,177]) ).
tff(180,plain,
( ( v_B != v_Ba )
| ( v_A != v_Aa ) ),
inference(modus_ponens,[status(thm)],[179,177]) ).
tff(181,plain,
( ( v_B != v_Ba )
| ( v_A != v_Aa ) ),
inference(modus_ponens,[status(thm)],[180,177]) ).
tff(182,plain,
( ( v_B != v_Ba )
| ( v_A != v_Aa ) ),
inference(modus_ponens,[status(thm)],[181,177]) ).
tff(183,plain,
( ( v_B != v_Ba )
| ( v_A != v_Aa ) ),
inference(modus_ponens,[status(thm)],[182,177]) ).
tff(184,plain,
$false,
inference(unit_resolution,[status(thm)],[183,176,161]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SWV769-1 : TPTP v9.0.0. Released v4.1.0.
% 0.04/0.14 % Command : run_E %s %d THM
% 0.16/0.36 % Computer : n011.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Fri Jun 20 10:50:26 EDT 2025
% 0.16/0.36 % CPUTime :
% 19.81/20.00 % SZS status Unsatisfiable
% 19.81/20.00 % SZS output start Proof
% See solution above
% 20.00/20.14 % E exiting
%------------------------------------------------------------------------------