%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV803-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:36:08 AM UTC 2025
% Result : Unsatisfiable 281.76s 282.19s
% Output : Proof 282.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 90
% Syntax : Number of formulae : 263 ( 93 unt; 0 typ; 0 def)
% Number of atoms : 1292 ( 246 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 1693 ( 735 ~; 836 |; 0 &)
% ( 122 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of FOOLs : 71 ( 71 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 : 37 ( 37 usr; 23 con; 0-3 aty)
% Number of variables : 1041 ( 948 !; 0 ?;1041 :)
% 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_A_type,type,
v_A: $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_NA_type,type,
v_NA: $i ).
tff(c_Message_Oagent_OServer_type,type,
c_Message_Oagent_OServer: $i ).
tff(c_List_Olist_OCons_type,type,
c_List_Olist_OCons: ( $i * $i * $i ) > $i ).
tff(v_NBa_type,type,
v_NBa: $i ).
tff(v_Aa_type,type,
v_Aa: $i ).
tff(v_B_H_type,type,
v_B_H: $i ).
tff(v_X_type,type,
v_X: $i ).
tff(v_K_type,type,
v_K: $i ).
tff(c_Set_Oinsert_type,type,
c_Set_Oinsert: ( $i * $i * $i ) > $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(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(tc_Message_Oagent_type,type,
tc_Message_Oagent: $i ).
tff(c_Event_Obad_type,type,
c_Event_Obad: $i ).
tff(v_NAa_type,type,
v_NAa: $i ).
tff(v_Xa_type,type,
v_Xa: $i ).
tff(v_S_type,type,
v_S: $i ).
tff(c_Message_Oanalz_type,type,
c_Message_Oanalz: $i > $i ).
tff(1,plain,
^ [V_x: $i,V_xs: $i,T_a: $i] :
refl(( ( c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_Set_Oinsert(V_x,c_List_Oset(V_xs,T_a),T_a) )
<=> ( c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_Set_Oinsert(V_x,c_List_Oset(V_xs,T_a),T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [V_x: $i,V_xs: $i,T_a: $i] : ( c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_Set_Oinsert(V_x,c_List_Oset(V_xs,T_a),T_a) )
<=> ! [V_x: $i,V_xs: $i,T_a: $i] : ( c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_Set_Oinsert(V_x,c_List_Oset(V_xs,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_x: $i,V_xs: $i,T_a: $i] : ( c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_Set_Oinsert(V_x,c_List_Oset(V_xs,T_a),T_a) )
<=> ! [V_x: $i,V_xs: $i,T_a: $i] : ( c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_Set_Oinsert(V_x,c_List_Oset(V_xs,T_a),T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] : ( c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_Set_Oinsert(V_x,c_List_Oset(V_xs,T_a),T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset_Osimps_I2_J_0) ).
tff(5,plain,
! [V_x: $i,V_xs: $i,T_a: $i] : ( c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_Set_Oinsert(V_x,c_List_Oset(V_xs,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V_x: $i,V_xs: $i,T_a: $i] : ( c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_Set_Oinsert(V_x,c_List_Oset(V_xs,T_a),T_a) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V_x: $i,V_xs: $i,T_a: $i] : ( c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_Set_Oinsert(V_x,c_List_Oset(V_xs,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V_x: $i,V_xs: $i,T_a: $i] : ( c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_Set_Oinsert(V_x,c_List_Oset(V_xs,T_a),T_a) )
| ( c_List_Oset(c_List_Olist_OCons(c_Event_Oevent_OSays(v_B_H,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NBa))),v_evs5,tc_Event_Oevent),tc_Event_Oevent) = c_Set_Oinsert(c_Event_Oevent_OSays(v_B_H,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NBa))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
c_List_Oset(c_List_Olist_OCons(c_Event_Oevent_OSays(v_B_H,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NBa))),v_evs5,tc_Event_Oevent),tc_Event_Oevent) = c_Set_Oinsert(c_Event_Oevent_OSays(v_B_H,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NBa))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
c_Set_Oinsert(c_Event_Oevent_OSays(v_B_H,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NBa))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent) = c_List_Oset(c_List_Olist_OCons(c_Event_Oevent_OSays(v_B_H,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NBa))),v_evs5,tc_Event_Oevent),tc_Event_Oevent),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( hBOOL(c_in(c_Event_Oevent_OSays(v_B_H,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NBa))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent))
<=> hBOOL(c_in(c_Event_Oevent_OSays(v_B_H,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NBa))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
hBOOL(c_in(c_Event_Oevent_OSays(v_B_H,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NBa))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
tff(13,plain,
hBOOL(c_in(c_Event_Oevent_OSays(v_B_H,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NBa))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
^ [V_a: $i,T_a: $i,V_A: $i] :
refl(( ( ~ hBOOL(c_in(V_a,V_A,T_a))
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
<=> ( ~ hBOOL(c_in(V_a,V_A,T_a))
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ) )),
inference(bind,[status(th)],[]) ).
tff(15,plain,
( ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_in(V_a,V_A,T_a))
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
<=> ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_in(V_a,V_A,T_a))
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
( ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_in(V_a,V_A,T_a))
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
<=> ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_in(V_a,V_A,T_a))
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,plain,
^ [V_a: $i,T_a: $i,V_A: $i] :
rewrite(( ( ( c_Set_Oinsert(V_a,V_A,T_a) = V_A )
| ~ hBOOL(c_in(V_a,V_A,T_a)) )
<=> ( ~ hBOOL(c_in(V_a,V_A,T_a))
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ) )),
inference(bind,[status(th)],[]) ).
tff(18,plain,
( ! [V_a: $i,T_a: $i,V_A: $i] :
( ( c_Set_Oinsert(V_a,V_A,T_a) = V_A )
| ~ hBOOL(c_in(V_a,V_A,T_a)) )
<=> ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_in(V_a,V_A,T_a))
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,axiom,
! [V_a: $i,T_a: $i,V_A: $i] :
( ( c_Set_Oinsert(V_a,V_A,T_a) = V_A )
| ~ hBOOL(c_in(V_a,V_A,T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
tff(20,plain,
! [V_a: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_in(V_a,V_A,T_a))
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
! [V_a: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_in(V_a,V_A,T_a))
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
! [V_a: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_in(V_a,V_A,T_a))
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ),
inference(skolemize,[status(sab)],[21]) ).
tff(23,plain,
! [V_a: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_in(V_a,V_A,T_a))
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ),
inference(modus_ponens,[status(thm)],[22,15]) ).
tff(24,plain,
( ( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_in(V_a,V_A,T_a))
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
| ~ hBOOL(c_in(c_Event_Oevent_OSays(v_B_H,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NBa))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent))
| ( c_Set_Oinsert(c_Event_Oevent_OSays(v_B_H,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NBa))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent) = c_List_Oset(v_evs5,tc_Event_Oevent) ) )
<=> ( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_in(V_a,V_A,T_a))
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
| ~ hBOOL(c_in(c_Event_Oevent_OSays(v_B_H,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NBa))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent))
| ( c_Set_Oinsert(c_Event_Oevent_OSays(v_B_H,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NBa))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent) = c_List_Oset(v_evs5,tc_Event_Oevent) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_in(V_a,V_A,T_a))
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
| ~ hBOOL(c_in(c_Event_Oevent_OSays(v_B_H,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NBa))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent))
| ( c_Set_Oinsert(c_Event_Oevent_OSays(v_B_H,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NBa))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent) = c_List_Oset(v_evs5,tc_Event_Oevent) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(26,plain,
( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_in(V_a,V_A,T_a))
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
| ~ hBOOL(c_in(c_Event_Oevent_OSays(v_B_H,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NBa))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent))
| ( c_Set_Oinsert(c_Event_Oevent_OSays(v_B_H,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NBa))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent) = c_List_Oset(v_evs5,tc_Event_Oevent) ) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
c_Set_Oinsert(c_Event_Oevent_OSays(v_B_H,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NBa))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent) = c_List_Oset(v_evs5,tc_Event_Oevent),
inference(unit_resolution,[status(thm)],[26,23,13]) ).
tff(28,plain,
c_List_Oset(v_evs5,tc_Event_Oevent) = c_Set_Oinsert(c_Event_Oevent_OSays(v_B_H,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NBa))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent),
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
c_List_Oset(v_evs5,tc_Event_Oevent) = c_List_Oset(c_List_Olist_OCons(c_Event_Oevent_OSays(v_B_H,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NBa))),v_evs5,tc_Event_Oevent),tc_Event_Oevent),
inference(transitivity,[status(thm)],[28,10]) ).
tff(30,plain,
( ( v_K = v_Ka )
<=> ( v_K = v_Ka ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,axiom,
v_K = v_Ka,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_8) ).
tff(32,plain,
v_K = v_Ka,
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
hAPP(c_Message_Omsg_OKey,v_K) = hAPP(c_Message_Omsg_OKey,v_Ka),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
hAPP(c_Message_Omsg_OKey,v_Ka) = hAPP(c_Message_Omsg_OKey,v_K),
inference(symmetry,[status(thm)],[33]) ).
tff(35,plain,
c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X) = c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)) = c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X)),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))) = c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(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))),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,plain,
c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))) = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(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)))),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(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_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),
inference(symmetry,[status(thm)],[38]) ).
tff(40,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(c_Message_Omsg_ONonce(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_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,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(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))) = c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(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))))),
inference(symmetry,[status(thm)],[40]) ).
tff(42,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(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),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(c_Message_Omsg_ONonce(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(c_List_Olist_OCons(c_Event_Oevent_OSays(v_B_H,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NBa))),v_evs5,tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent),
inference(monotonicity,[status(thm)],[41,29]) ).
tff(43,plain,
c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),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) = c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(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_evs5)),tc_Message_Omsg),
inference(monotonicity,[status(thm)],[38]) ).
tff(44,plain,
( hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),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_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(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_evs5)),tc_Message_Omsg)) ),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
( hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(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_evs5)),tc_Message_Omsg))
<=> hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),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(symmetry,[status(thm)],[44]) ).
tff(46,plain,
( hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(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_evs5)),tc_Message_Omsg))
<=> hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(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_evs5)),tc_Message_Omsg)) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,axiom,
hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(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_evs5)),tc_Message_Omsg)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_7) ).
tff(48,plain,
hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(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_evs5)),tc_Message_Omsg)),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),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(modus_ponens,[status(thm)],[48,45]) ).
tff(50,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(51,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_2) ).
tff(52,plain,
hBOOL(c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
( ~ hBOOL(c_in(v_A,c_Event_Obad,tc_Message_Oagent))
<=> ~ hBOOL(c_in(v_A,c_Event_Obad,tc_Message_Oagent)) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,axiom,
~ hBOOL(c_in(v_A,c_Event_Obad,tc_Message_Oagent)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(55,plain,
~ hBOOL(c_in(v_A,c_Event_Obad,tc_Message_Oagent)),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,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(57,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)],[56]) ).
tff(58,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(59,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(60,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)],[59]) ).
tff(61,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(62,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)],[61,60]) ).
tff(63,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)],[62,58]) ).
tff(64,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)],[63]) ).
tff(65,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)],[64,57]) ).
tff(66,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_A,c_Event_Obad,tc_Message_Oagent))
| ~ 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_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),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_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),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))) ) )
| hBOOL(c_in(v_A,c_Event_Obad,tc_Message_Oagent))
| ~ 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_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),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_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_A))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,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_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),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_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_Ka),c_Message_Omsg_OAgent(v_A))) ) )
<=> ( hBOOL(c_in(v_A,c_Event_Obad,tc_Message_Oagent))
| ~ 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_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),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_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_A))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,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_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),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_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_Ka),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))) ) )
| hBOOL(c_in(v_A,c_Event_Obad,tc_Message_Oagent))
| ~ 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_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),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_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_A))) ) ) ),
inference(monotonicity,[status(thm)],[67]) ).
tff(69,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_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),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_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_Ka),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))) ) )
| hBOOL(c_in(v_A,c_Event_Obad,tc_Message_Oagent))
| ~ 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_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),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_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_A))) ) ) ),
inference(transitivity,[status(thm)],[68,66]) ).
tff(70,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_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),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_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_Ka),c_Message_Omsg_OAgent(v_A))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(71,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_A,c_Event_Obad,tc_Message_Oagent))
| ~ 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_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),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_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_A))) ) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
( ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),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_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_A))) ) ),
inference(unit_resolution,[status(thm)],[71,65,55,52]) ).
tff(73,plain,
v_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_A))),
inference(unit_resolution,[status(thm)],[72,49]) ).
tff(74,plain,
c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_A))) = v_X,
inference(symmetry,[status(thm)],[73]) ).
tff(75,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_Ka),c_Message_Omsg_OAgent(v_A)))) = c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X),
inference(monotonicity,[status(thm)],[34,74]) ).
tff(76,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_Ka),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),v_X)),
inference(monotonicity,[status(thm)],[75]) ).
tff(77,plain,
c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(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_Ka),c_Message_Omsg_OAgent(v_A)))))) = c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(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))),
inference(monotonicity,[status(thm)],[76]) ).
tff(78,plain,
c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(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_Ka),c_Message_Omsg_OAgent(v_A))))))) = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(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)))),
inference(monotonicity,[status(thm)],[77]) ).
tff(79,plain,
c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(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_Ka),c_Message_Omsg_OAgent(v_A))))))) = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),
inference(transitivity,[status(thm)],[78,39]) ).
tff(80,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(c_Message_Omsg_ONonce(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_Ka),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(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,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(c_Message_Omsg_ONonce(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_Ka),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(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),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)],[80]) ).
tff(82,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(c_Message_Omsg_ONonce(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_Ka),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(c_Message_Omsg_ONonce(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(c_List_Olist_OCons(c_Event_Oevent_OSays(v_B_H,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NBa))),v_evs5,tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent),
inference(transitivity,[status(thm)],[81,42]) ).
tff(83,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(c_Message_Omsg_ONonce(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_Ka),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(c_Message_Omsg_ONonce(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(c_List_Olist_OCons(c_Event_Oevent_OSays(v_B_H,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NBa))),v_evs5,tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent)) ),
inference(monotonicity,[status(thm)],[82]) ).
tff(84,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(c_Message_Omsg_ONonce(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(c_List_Olist_OCons(c_Event_Oevent_OSays(v_B_H,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NBa))),v_evs5,tc_Event_Oevent),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(c_Message_Omsg_ONonce(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_Ka),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)) ),
inference(symmetry,[status(thm)],[83]) ).
tff(85,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(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),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_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(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(c_List_Olist_OCons(c_Event_Oevent_OSays(v_B_H,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NBa))),v_evs5,tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent)) ),
inference(monotonicity,[status(thm)],[42]) ).
tff(86,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(87,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)],[86]) ).
tff(88,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(89,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(90,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)],[89]) ).
tff(91,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(92,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)],[91,90]) ).
tff(93,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)],[92,88]) ).
tff(94,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)],[93]) ).
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))
| 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)],[94,87]) ).
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))
| 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_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_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),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_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),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_A,c_Event_Obad,tc_Message_Oagent))
| ~ 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_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),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_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),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(97,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_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),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_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(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),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_A,c_Event_Obad,tc_Message_Oagent))
| ~ 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_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),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_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),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(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))
| 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_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),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_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(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),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_A,c_Event_Obad,tc_Message_Oagent))
| ~ 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_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),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_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),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)],[97]) ).
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))
| 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_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),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_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(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),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_A,c_Event_Obad,tc_Message_Oagent))
| ~ 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_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),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_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),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)],[98,96]) ).
tff(100,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_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),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_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(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),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(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))
| 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_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_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),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_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),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)],[100,99]) ).
tff(102,plain,
( ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),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_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),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)],[101,95,55,52]) ).
tff(103,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(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),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)],[102,49]) ).
tff(104,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(c_Message_Omsg_ONonce(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(c_List_Olist_OCons(c_Event_Oevent_OSays(v_B_H,v_Aa,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_ONonce(v_NBa))),v_evs5,tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent)),
inference(modus_ponens,[status(thm)],[103,85]) ).
tff(105,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(c_Message_Omsg_ONonce(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_Ka),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)),
inference(modus_ponens,[status(thm)],[104,84]) ).
tff(106,plain,
( ~ ! [V_x: $i,V_xs: $i,T_a: $i] : ( c_List_Oset(c_List_Olist_OCons(V_x,V_xs,T_a),T_a) = c_Set_Oinsert(V_x,c_List_Oset(V_xs,T_a),T_a) )
| ( c_List_Oset(c_List_Olist_OCons(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_Xa))))),v_evs5,tc_Event_Oevent),tc_Event_Oevent) = c_Set_Oinsert(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_Xa))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(107,plain,
c_List_Oset(c_List_Olist_OCons(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_Xa))))),v_evs5,tc_Event_Oevent),tc_Event_Oevent) = c_Set_Oinsert(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_Xa))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent),
inference(unit_resolution,[status(thm)],[106,7]) ).
tff(108,plain,
c_Set_Oinsert(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_Xa))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent) = c_List_Oset(c_List_Olist_OCons(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_Xa))))),v_evs5,tc_Event_Oevent),tc_Event_Oevent),
inference(symmetry,[status(thm)],[107]) ).
tff(109,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_Xa))))),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_Xa))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)) ),
inference(rewrite,[status(thm)],[]) ).
tff(110,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_Xa))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
tff(111,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_Xa))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
( ( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_in(V_a,V_A,T_a))
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
| ~ 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_Xa))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent))
| ( c_Set_Oinsert(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_Xa))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent) = c_List_Oset(v_evs5,tc_Event_Oevent) ) )
<=> ( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_in(V_a,V_A,T_a))
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
| ~ 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_Xa))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent))
| ( c_Set_Oinsert(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_Xa))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent) = c_List_Oset(v_evs5,tc_Event_Oevent) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(113,plain,
( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_in(V_a,V_A,T_a))
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
| ~ 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_Xa))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent))
| ( c_Set_Oinsert(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_Xa))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent) = c_List_Oset(v_evs5,tc_Event_Oevent) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(114,plain,
( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ hBOOL(c_in(V_a,V_A,T_a))
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
| ~ 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_Xa))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent))
| ( c_Set_Oinsert(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_Xa))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent) = c_List_Oset(v_evs5,tc_Event_Oevent) ) ),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
c_Set_Oinsert(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_Xa))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent) = c_List_Oset(v_evs5,tc_Event_Oevent),
inference(unit_resolution,[status(thm)],[114,23,111]) ).
tff(116,plain,
c_List_Oset(v_evs5,tc_Event_Oevent) = c_Set_Oinsert(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_Xa))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent),
inference(symmetry,[status(thm)],[115]) ).
tff(117,plain,
c_List_Oset(v_evs5,tc_Event_Oevent) = c_List_Oset(c_List_Olist_OCons(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_Xa))))),v_evs5,tc_Event_Oevent),tc_Event_Oevent),
inference(transitivity,[status(thm)],[116,108]) ).
tff(118,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),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(c_List_Olist_OCons(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_Xa))))),v_evs5,tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent),
inference(monotonicity,[status(thm)],[117]) ).
tff(119,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),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(c_List_Olist_OCons(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_Xa))))),v_evs5,tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent)) ),
inference(monotonicity,[status(thm)],[118]) ).
tff(120,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(c_List_Olist_OCons(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_Xa))))),v_evs5,tc_Event_Oevent),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)],[119]) ).
tff(121,plain,
c_List_Oset(c_List_Olist_OCons(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_Xa))))),v_evs5,tc_Event_Oevent),tc_Event_Oevent) = c_List_Oset(v_evs5,tc_Event_Oevent),
inference(transitivity,[status(thm)],[107,115]) ).
tff(122,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(123,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)],[122]) ).
tff(124,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(125,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(126,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)],[125,124]) ).
tff(127,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)],[126]) ).
tff(128,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)],[127,123]) ).
tff(129,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_Xa)))),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_Xa))))),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_Xa)))),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_Xa))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(130,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_Xa)))),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_Xa))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(131,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_Xa)))),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_Xa))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)) ),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,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_Xa)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)),
inference(unit_resolution,[status(thm)],[131,128,111]) ).
tff(133,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(134,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)],[133]) ).
tff(135,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(136,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(137,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)],[136,135]) ).
tff(138,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)],[137]) ).
tff(139,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)],[138,134]) ).
tff(140,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_Xa)))),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_Xa))))),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_Xa)))),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_Xa))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(141,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_Xa)))),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_Xa))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(142,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_Xa)))),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_Xa))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)) ),
inference(modus_ponens,[status(thm)],[141,140]) ).
tff(143,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_Xa)))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)),
inference(unit_resolution,[status(thm)],[142,139,111]) ).
tff(144,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)],[34]) ).
tff(145,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)],[144]) ).
tff(146,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)],[145]) ).
tff(147,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)],[146]) ).
tff(148,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(149,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_6) ).
tff(150,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)],[149,148]) ).
tff(151,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)],[150,147]) ).
tff(152,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(153,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)],[152]) ).
tff(154,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(155,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(156,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)],[155,154]) ).
tff(157,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)],[156]) ).
tff(158,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)],[157,153]) ).
tff(159,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_Xa),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_Xa),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(160,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_Xa),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(161,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_Xa),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[160,159]) ).
tff(162,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_Xa),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) ),
inference(unit_resolution,[status(thm)],[161,158]) ).
tff(163,plain,
~ hBOOL(c_in(c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_Xa),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)),
inference(unit_resolution,[status(thm)],[162,151]) ).
tff(164,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(165,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)],[164]) ).
tff(166,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(167,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(168,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)],[167,166]) ).
tff(169,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)],[168]) ).
tff(170,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)],[169,165]) ).
tff(171,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_Xa),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_Xa)),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_Xa),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_Xa)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(172,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_Xa),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_Xa)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(173,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_Xa),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_Xa)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[172,171]) ).
tff(174,plain,
( hBOOL(c_in(c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_Xa),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_Xa)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) ),
inference(unit_resolution,[status(thm)],[173,170]) ).
tff(175,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_Xa)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)),
inference(unit_resolution,[status(thm)],[174,163]) ).
tff(176,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_Xa)),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_Xa))),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_Xa)),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_Xa))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(177,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_Xa)),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_Xa))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(178,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_Xa)),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_Xa))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[177,176]) ).
tff(179,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_Xa)),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_Xa))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) ),
inference(unit_resolution,[status(thm)],[178,170]) ).
tff(180,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_Xa))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)),
inference(unit_resolution,[status(thm)],[179,175]) ).
tff(181,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(182,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)],[181]) ).
tff(183,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(184,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(185,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)],[184]) ).
tff(186,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(187,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)],[186,185]) ).
tff(188,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)],[187,183]) ).
tff(189,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)],[188]) ).
tff(190,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)],[189,182]) ).
tff(191,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_Xa))),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_Xa)))),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_Xa))),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_Xa)))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(192,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_Xa)))),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_Xa))),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_Xa))),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_Xa)))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(193,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_Xa)))),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_Xa))),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_Xa))),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_Xa)))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) ) ),
inference(monotonicity,[status(thm)],[192]) ).
tff(194,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_Xa)))),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_Xa))),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_Xa))),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_Xa)))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) ) ),
inference(transitivity,[status(thm)],[193,191]) ).
tff(195,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_Xa)))),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_Xa))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(196,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_Xa))),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_Xa)))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) ),
inference(modus_ponens,[status(thm)],[195,194]) ).
tff(197,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_Xa))),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_Xa)))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)) ),
inference(unit_resolution,[status(thm)],[196,190]) ).
tff(198,plain,
~ hBOOL(c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)),
inference(unit_resolution,[status(thm)],[197,180,143]) ).
tff(199,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_Xa)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ( v_Xa = 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_Xa)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ( v_Xa = 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(200,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_Xa)))),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_Xa = 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_Xa)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ( v_Xa = 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(201,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_Xa)))),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_Xa = 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_Xa)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ( v_Xa = 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)],[200]) ).
tff(202,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_Xa)))),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_Xa = 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_Xa)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ( v_Xa = 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)],[201,199]) ).
tff(203,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_Xa)))),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_Xa = 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(204,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_Xa)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ( v_Xa = 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)],[203,202]) ).
tff(205,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_Xa)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg))
| ( v_Xa = 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)],[204,65,52]) ).
tff(206,plain,
v_Xa = 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)],[205,198,132]) ).
tff(207,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_Xa,
inference(symmetry,[status(thm)],[206]) ).
tff(208,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_Xa),
inference(monotonicity,[status(thm)],[207]) ).
tff(209,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_Xa)),
inference(monotonicity,[status(thm)],[208]) ).
tff(210,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_Xa))),
inference(monotonicity,[status(thm)],[209]) ).
tff(211,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_Xa)))),
inference(monotonicity,[status(thm)],[210]) ).
tff(212,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_Xa))))),
inference(monotonicity,[status(thm)],[211]) ).
tff(213,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(c_List_Olist_OCons(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_Xa))))),v_evs5,tc_Event_Oevent),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_Xa))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent),
inference(monotonicity,[status(thm)],[212,121]) ).
tff(214,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(c_List_Olist_OCons(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_Xa))))),v_evs5,tc_Event_Oevent),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_Xa))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)) ),
inference(monotonicity,[status(thm)],[213]) ).
tff(215,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_Xa))))),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(c_List_Olist_OCons(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_Xa))))),v_evs5,tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent)) ),
inference(symmetry,[status(thm)],[214]) ).
tff(216,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_Xa))))),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(transitivity,[status(thm)],[215,120]) ).
tff(217,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_Xa)))),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_Xa))))),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_Xa)))),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_Xa))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(218,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_Xa)))),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_Xa))))),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_Xa)))),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_Xa))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(219,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_Xa)))),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_Xa))))),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_Xa)))),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_Xa))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)) ) ),
inference(monotonicity,[status(thm)],[218]) ).
tff(220,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_Xa)))),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_Xa))))),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_Xa)))),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_Xa))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)) ) ),
inference(transitivity,[status(thm)],[219,217]) ).
tff(221,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_Xa)))),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_Xa))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(222,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_Xa)))),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_Xa))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)) ),
inference(modus_ponens,[status(thm)],[221,220]) ).
tff(223,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_Xa)))),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_Xa))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)) ),
inference(unit_resolution,[status(thm)],[222,95,52]) ).
tff(224,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_Xa))))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)),
inference(unit_resolution,[status(thm)],[223,198,132]) ).
tff(225,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)],[224,216]) ).
tff(226,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(227,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)],[226]) ).
tff(228,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(229,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(230,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)],[229]) ).
tff(231,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(232,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)],[231,230]) ).
tff(233,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)],[232,228]) ).
tff(234,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)],[233]) ).
tff(235,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)],[234,227]) ).
tff(236,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(c_Message_Omsg_ONonce(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_Ka),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(c_Message_Omsg_ONonce(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_Ka),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(237,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(c_Message_Omsg_ONonce(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_Ka),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(238,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(c_Message_Omsg_ONonce(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_Ka),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)],[237,236]) ).
tff(239,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(c_Message_Omsg_ONonce(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_Ka),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(unit_resolution,[status(thm)],[238,235,52]) ).
tff(240,plain,
v_B = v_Ba,
inference(unit_resolution,[status(thm)],[239,225,105]) ).
tff(241,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(242,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)],[241]) ).
tff(243,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(244,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(245,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)],[244]) ).
tff(246,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(247,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)],[246,245]) ).
tff(248,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)],[247,243]) ).
tff(249,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)],[248]) ).
tff(250,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)],[249,242]) ).
tff(251,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(c_Message_Omsg_ONonce(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_Ka),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(c_Message_Omsg_ONonce(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_Ka),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(252,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(c_Message_Omsg_ONonce(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_Ka),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(253,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(c_Message_Omsg_ONonce(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_Ka),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)],[252,251]) ).
tff(254,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(c_Message_Omsg_ONonce(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_Ka),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(unit_resolution,[status(thm)],[253,250,52]) ).
tff(255,plain,
v_A = v_Aa,
inference(unit_resolution,[status(thm)],[254,225,105]) ).
tff(256,plain,
( ( ( v_B != v_Ba )
| ( v_A != v_Aa ) )
<=> ( ( v_B != v_Ba )
| ( v_A != v_Aa ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(257,axiom,
( ( v_B != v_Ba )
| ( v_A != v_Aa ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_11) ).
tff(258,plain,
( ( v_B != v_Ba )
| ( v_A != v_Aa ) ),
inference(modus_ponens,[status(thm)],[257,256]) ).
tff(259,plain,
( ( v_B != v_Ba )
| ( v_A != v_Aa ) ),
inference(modus_ponens,[status(thm)],[258,256]) ).
tff(260,plain,
( ( v_B != v_Ba )
| ( v_A != v_Aa ) ),
inference(modus_ponens,[status(thm)],[259,256]) ).
tff(261,plain,
( ( v_B != v_Ba )
| ( v_A != v_Aa ) ),
inference(modus_ponens,[status(thm)],[260,256]) ).
tff(262,plain,
( ( v_B != v_Ba )
| ( v_A != v_Aa ) ),
inference(modus_ponens,[status(thm)],[261,256]) ).
tff(263,plain,
$false,
inference(unit_resolution,[status(thm)],[262,255,240]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV803-1 : TPTP v9.0.0. Released v4.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 10:54:20 EDT 2025
% 0.12/0.34 % CPUTime :
% 281.76/282.19 % SZS status Unsatisfiable
% 281.76/282.19 % SZS output start Proof
% See solution above
% 282.86/283.30 % E exiting
%------------------------------------------------------------------------------