%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV792-1 : 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 05:36:06 AM UTC 2025
% Result : Unsatisfiable 0.70s 0.88s
% Output : Proof 0.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 32
% Syntax : Number of formulae : 75 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 314 ( 108 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 382 ( 161 ~; 185 |; 0 &)
% ( 36 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 18 ( 18 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 : 28 ( 28 usr; 18 con; 0-3 aty)
% Number of variables : 276 ( 249 !; 0 ?; 276 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Message_Omsg_OCrypt_type,type,
c_Message_Omsg_OCrypt: ( $i * $i ) > $i ).
tff(c_Message_Omsg_ONonce_type,type,
c_Message_Omsg_ONonce: $i > $i ).
tff(v_Nb_type,type,
v_Nb: $i ).
tff(v_K_type,type,
v_K: $i ).
tff(c_Message_Omsg_OMPair_type,type,
c_Message_Omsg_OMPair: ( $i * $i ) > $i ).
tff(c_Message_Omsg_OAgent_type,type,
c_Message_Omsg_OAgent: $i > $i ).
tff(v_Aa_type,type,
v_Aa: $i ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(v_Ka_type,type,
v_Ka: $i ).
tff(c_Message_Omsg_OKey_type,type,
c_Message_Omsg_OKey: $i ).
tff(v_Ba_type,type,
v_Ba: $i ).
tff(c_Public_OshrK_type,type,
c_Public_OshrK: $i ).
tff(v_X_type,type,
v_X: $i ).
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(tc_Message_Omsg_type,type,
tc_Message_Omsg: $i ).
tff(c_Message_Oparts_type,type,
c_Message_Oparts: $i > $i ).
tff(c_Event_Oknows_type,type,
c_Event_Oknows: ( $i * $i ) > $i ).
tff(v_evs3_type,type,
v_evs3: $i ).
tff(c_Message_Oagent_OSpy_type,type,
c_Message_Oagent_OSpy: $i ).
tff(v_NA_type,type,
v_NA: $i ).
tff(tc_Event_Oevent_type,type,
tc_Event_Oevent: $i ).
tff(c_List_Oset_type,type,
c_List_Oset: ( $i * $i ) > $i ).
tff(c_Event_Oevent_OSays_type,type,
c_Event_Oevent_OSays: ( $i * $i * $i ) > $i ).
tff(v_S_type,type,
v_S: $i ).
tff(tc_Message_Oagent_type,type,
tc_Message_Oagent: $i ).
tff(c_Event_Obad_type,type,
c_Event_Obad: $i ).
tff(v_B_type,type,
v_B: $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(1,plain,
( ( c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_Nb)) = v_X )
<=> ( c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_Nb)) = v_X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_Nb)) = v_X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_9) ).
tff(3,plain,
c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_Nb)) = v_X,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
v_X = c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_Nb)),
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( 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_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),c_List_Oset(v_evs3,tc_Event_Oevent),tc_Event_Oevent)
<=> 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_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),c_List_Oset(v_evs3,tc_Event_Oevent),tc_Event_Oevent) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
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_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),c_List_Oset(v_evs3,tc_Event_Oevent),tc_Event_Oevent),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
tff(7,plain,
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_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),c_List_Oset(v_evs3,tc_Event_Oevent),tc_Event_Oevent),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
^ [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
refl(( ( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
<=> ( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
<=> ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
<=> ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,plain,
^ [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
rewrite(( ( c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) )
<=> ( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) )
<=> ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,axiom,
! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Says__imp__parts__knows__Spy_0) ).
tff(14,plain,
! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[14,10]) ).
tff(16,plain,
! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[16,9]) ).
tff(18,plain,
( ( ~ ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
| ~ 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_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),c_List_Oset(v_evs3,tc_Event_Oevent),tc_Event_Oevent)
| c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) )
<=> ( ~ ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
| ~ 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_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),c_List_Oset(v_evs3,tc_Event_Oevent),tc_Event_Oevent)
| c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
| ~ 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_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),c_List_Oset(v_evs3,tc_Event_Oevent),tc_Event_Oevent)
| c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],[]) ).
tff(20,plain,
( ~ ! [V_X: $i,V_B: $i,V_A: $i,V_evs: $i] :
( ~ c_in(c_Event_Oevent_OSays(V_A,V_B,V_X),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_X,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
| ~ 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_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X))))),c_List_Oset(v_evs3,tc_Event_Oevent),tc_Event_Oevent)
| c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[20,17,7]) ).
tff(22,plain,
( ( v_B = v_Aa )
<=> ( v_B = v_Aa ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
v_B = v_Aa,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_7) ).
tff(24,plain,
v_B = v_Aa,
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
v_Aa = v_B,
inference(symmetry,[status(thm)],[24]) ).
tff(26,plain,
( c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)
<=> c_in(v_B,c_Event_Obad,tc_Message_Oagent) ),
inference(monotonicity,[status(thm)],[25]) ).
tff(27,plain,
( c_in(v_B,c_Event_Obad,tc_Message_Oagent)
<=> c_in(v_Aa,c_Event_Obad,tc_Message_Oagent) ),
inference(symmetry,[status(thm)],[26]) ).
tff(28,plain,
( ~ c_in(v_B,c_Event_Obad,tc_Message_Oagent)
<=> ~ c_in(v_Aa,c_Event_Obad,tc_Message_Oagent) ),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,plain,
( ~ c_in(v_B,c_Event_Obad,tc_Message_Oagent)
<=> ~ c_in(v_B,c_Event_Obad,tc_Message_Oagent) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
~ c_in(v_B,c_Event_Obad,tc_Message_Oagent),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(31,plain,
~ c_in(v_B,c_Event_Obad,tc_Message_Oagent),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
~ c_in(v_Aa,c_Event_Obad,tc_Message_Oagent),
inference(modus_ponens,[status(thm)],[31,28]) ).
tff(33,plain,
( c_in(v_evs3,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
<=> c_in(v_evs3,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,axiom,
c_in(v_evs3,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(35,plain,
c_in(v_evs3,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
^ [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
refl(( ( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| ~ 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)
| 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))) ) )
<=> ( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| ~ 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)
| 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(37,plain,
( ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| ~ 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)
| 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] :
( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| ~ 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)
| 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)],[36]) ).
tff(38,plain,
( ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| ~ 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)
| 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] :
( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| ~ 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)
| 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(39,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))) )
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)) )
<=> ( ~ 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))) )
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(V_A,c_Event_Obad,tc_Message_Oagent) )
<=> ( ~ 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))) )
| c_in(V_A,c_Event_Obad,tc_Message_Oagent) ) )),
rewrite(( ( ~ 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))) )
| c_in(V_A,c_Event_Obad,tc_Message_Oagent) )
<=> ( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| 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))) )
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(V_A,c_Event_Obad,tc_Message_Oagent) )
<=> ( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| 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))) )
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| ~ 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) )
<=> ( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| 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))) )
| ~ 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(( ( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| 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))) )
| ~ 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) )
<=> ( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| ~ 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)
| 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))) )
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| ~ 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) )
<=> ( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| ~ 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)
| 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(40,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))) )
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| ~ 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] :
( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| ~ 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)
| 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)],[39]) ).
tff(41,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))) )
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| ~ 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(42,plain,
! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| ~ 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)
| 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)],[41,40]) ).
tff(43,plain,
! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| ~ 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)
| 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)],[42,38]) ).
tff(44,plain,
! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| ~ 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)
| 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)],[43]) ).
tff(45,plain,
! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| ~ 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)
| 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)],[44,37]) ).
tff(46,plain,
( ( ~ ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| ~ 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)
| 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))) ) )
| c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(v_evs3,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
| ( v_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa))) ) )
<=> ( ~ ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| ~ 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)
| 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))) ) )
| c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(v_evs3,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
| ( v_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
( ( ~ c_in(v_evs3,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
| c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)
| ( v_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa))) ) )
<=> ( c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(v_evs3,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
| ( v_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,plain,
( ( ~ ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| ~ 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)
| 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))) ) )
| ~ c_in(v_evs3,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
| c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)
| ( v_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa))) ) )
<=> ( ~ ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| ~ 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)
| 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))) ) )
| c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(v_evs3,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
| ( v_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa))) ) ) ),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
( ( ~ ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| ~ 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)
| 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))) ) )
| ~ c_in(v_evs3,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
| c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)
| ( v_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa))) ) )
<=> ( ~ ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| ~ 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)
| 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))) ) )
| c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(v_evs3,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
| ( v_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa))) ) ) ),
inference(transitivity,[status(thm)],[48,46]) ).
tff(50,plain,
( ~ ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| ~ 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)
| 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))) ) )
| ~ c_in(v_evs3,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
| c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)
| ( v_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(51,plain,
( ~ ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| ~ 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)
| 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))) ) )
| c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(v_evs3,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
| ( v_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa))) ) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
( c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
| ( v_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa))) ) ),
inference(unit_resolution,[status(thm)],[51,45,35]) ).
tff(53,plain,
v_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa))),
inference(unit_resolution,[status(thm)],[52,32,21]) ).
tff(54,plain,
c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa))) = v_X,
inference(symmetry,[status(thm)],[53]) ).
tff(55,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))) = c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_Nb)),
inference(transitivity,[status(thm)],[54,4]) ).
tff(56,plain,
^ [V_msg1_H: $i,V_nat: $i,V_msg2_H: $i] :
refl(( ( c_Message_Omsg_OMPair(V_msg1_H,V_msg2_H) != c_Message_Omsg_ONonce(V_nat) )
<=> ( c_Message_Omsg_OMPair(V_msg1_H,V_msg2_H) != c_Message_Omsg_ONonce(V_nat) ) )),
inference(bind,[status(th)],[]) ).
tff(57,plain,
( ! [V_msg1_H: $i,V_nat: $i,V_msg2_H: $i] : ( c_Message_Omsg_OMPair(V_msg1_H,V_msg2_H) != c_Message_Omsg_ONonce(V_nat) )
<=> ! [V_msg1_H: $i,V_nat: $i,V_msg2_H: $i] : ( c_Message_Omsg_OMPair(V_msg1_H,V_msg2_H) != c_Message_Omsg_ONonce(V_nat) ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,plain,
( ! [V_msg1_H: $i,V_nat: $i,V_msg2_H: $i] : ( c_Message_Omsg_OMPair(V_msg1_H,V_msg2_H) != c_Message_Omsg_ONonce(V_nat) )
<=> ! [V_msg1_H: $i,V_nat: $i,V_msg2_H: $i] : ( c_Message_Omsg_OMPair(V_msg1_H,V_msg2_H) != c_Message_Omsg_ONonce(V_nat) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,axiom,
! [V_msg1_H: $i,V_nat: $i,V_msg2_H: $i] : ( c_Message_Omsg_OMPair(V_msg1_H,V_msg2_H) != c_Message_Omsg_ONonce(V_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I35_J_0) ).
tff(60,plain,
! [V_msg1_H: $i,V_nat: $i,V_msg2_H: $i] : ( c_Message_Omsg_OMPair(V_msg1_H,V_msg2_H) != c_Message_Omsg_ONonce(V_nat) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
! [V_msg1_H: $i,V_nat: $i,V_msg2_H: $i] : ( c_Message_Omsg_OMPair(V_msg1_H,V_msg2_H) != c_Message_Omsg_ONonce(V_nat) ),
inference(skolemize,[status(sab)],[60]) ).
tff(62,plain,
! [V_msg1_H: $i,V_nat: $i,V_msg2_H: $i] : ( c_Message_Omsg_OMPair(V_msg1_H,V_msg2_H) != c_Message_Omsg_ONonce(V_nat) ),
inference(modus_ponens,[status(thm)],[61,57]) ).
tff(63,plain,
( ~ ! [V_msg1_H: $i,V_nat: $i,V_msg2_H: $i] : ( c_Message_Omsg_OMPair(V_msg1_H,V_msg2_H) != c_Message_Omsg_ONonce(V_nat) )
| ( c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa)) != c_Message_Omsg_ONonce(v_Nb) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(64,plain,
c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa)) != c_Message_Omsg_ONonce(v_Nb),
inference(unit_resolution,[status(thm)],[63,62]) ).
tff(65,plain,
^ [V_nat_H: $i,V_nat: $i,V_msg_H: $i,V_msg: $i] :
refl(( ( ( c_Message_Omsg_OCrypt(V_nat,V_msg) != c_Message_Omsg_OCrypt(V_nat_H,V_msg_H) )
| ( V_msg = V_msg_H ) )
<=> ( ( c_Message_Omsg_OCrypt(V_nat,V_msg) != c_Message_Omsg_OCrypt(V_nat_H,V_msg_H) )
| ( V_msg = V_msg_H ) ) )),
inference(bind,[status(th)],[]) ).
tff(66,plain,
( ! [V_nat_H: $i,V_nat: $i,V_msg_H: $i,V_msg: $i] :
( ( c_Message_Omsg_OCrypt(V_nat,V_msg) != c_Message_Omsg_OCrypt(V_nat_H,V_msg_H) )
| ( V_msg = V_msg_H ) )
<=> ! [V_nat_H: $i,V_nat: $i,V_msg_H: $i,V_msg: $i] :
( ( c_Message_Omsg_OCrypt(V_nat,V_msg) != c_Message_Omsg_OCrypt(V_nat_H,V_msg_H) )
| ( V_msg = V_msg_H ) ) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,plain,
( ! [V_nat_H: $i,V_nat: $i,V_msg_H: $i,V_msg: $i] :
( ( c_Message_Omsg_OCrypt(V_nat,V_msg) != c_Message_Omsg_OCrypt(V_nat_H,V_msg_H) )
| ( V_msg = V_msg_H ) )
<=> ! [V_nat_H: $i,V_nat: $i,V_msg_H: $i,V_msg: $i] :
( ( c_Message_Omsg_OCrypt(V_nat,V_msg) != c_Message_Omsg_OCrypt(V_nat_H,V_msg_H) )
| ( V_msg = V_msg_H ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,axiom,
! [V_nat_H: $i,V_nat: $i,V_msg_H: $i,V_msg: $i] :
( ( c_Message_Omsg_OCrypt(V_nat,V_msg) != c_Message_Omsg_OCrypt(V_nat_H,V_msg_H) )
| ( V_msg = V_msg_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_msg_Osimps_I7_J_1) ).
tff(69,plain,
! [V_nat_H: $i,V_nat: $i,V_msg_H: $i,V_msg: $i] :
( ( c_Message_Omsg_OCrypt(V_nat,V_msg) != c_Message_Omsg_OCrypt(V_nat_H,V_msg_H) )
| ( V_msg = V_msg_H ) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
! [V_nat_H: $i,V_nat: $i,V_msg_H: $i,V_msg: $i] :
( ( c_Message_Omsg_OCrypt(V_nat,V_msg) != c_Message_Omsg_OCrypt(V_nat_H,V_msg_H) )
| ( V_msg = V_msg_H ) ),
inference(skolemize,[status(sab)],[69]) ).
tff(71,plain,
! [V_nat_H: $i,V_nat: $i,V_msg_H: $i,V_msg: $i] :
( ( c_Message_Omsg_OCrypt(V_nat,V_msg) != c_Message_Omsg_OCrypt(V_nat_H,V_msg_H) )
| ( V_msg = V_msg_H ) ),
inference(modus_ponens,[status(thm)],[70,66]) ).
tff(72,plain,
( ( ~ ! [V_nat_H: $i,V_nat: $i,V_msg_H: $i,V_msg: $i] :
( ( c_Message_Omsg_OCrypt(V_nat,V_msg) != c_Message_Omsg_OCrypt(V_nat_H,V_msg_H) )
| ( V_msg = V_msg_H ) )
| ( 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(v_K,c_Message_Omsg_ONonce(v_Nb)) )
| ( c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa)) = c_Message_Omsg_ONonce(v_Nb) ) )
<=> ( ~ ! [V_nat_H: $i,V_nat: $i,V_msg_H: $i,V_msg: $i] :
( ( c_Message_Omsg_OCrypt(V_nat,V_msg) != c_Message_Omsg_OCrypt(V_nat_H,V_msg_H) )
| ( V_msg = V_msg_H ) )
| ( 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(v_K,c_Message_Omsg_ONonce(v_Nb)) )
| ( c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa)) = c_Message_Omsg_ONonce(v_Nb) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,plain,
( ~ ! [V_nat_H: $i,V_nat: $i,V_msg_H: $i,V_msg: $i] :
( ( c_Message_Omsg_OCrypt(V_nat,V_msg) != c_Message_Omsg_OCrypt(V_nat_H,V_msg_H) )
| ( V_msg = V_msg_H ) )
| ( 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(v_K,c_Message_Omsg_ONonce(v_Nb)) )
| ( c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa)) = c_Message_Omsg_ONonce(v_Nb) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(74,plain,
( ~ ! [V_nat_H: $i,V_nat: $i,V_msg_H: $i,V_msg: $i] :
( ( c_Message_Omsg_OCrypt(V_nat,V_msg) != c_Message_Omsg_OCrypt(V_nat_H,V_msg_H) )
| ( V_msg = V_msg_H ) )
| ( 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(v_K,c_Message_Omsg_ONonce(v_Nb)) )
| ( c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa)) = c_Message_Omsg_ONonce(v_Nb) ) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
$false,
inference(unit_resolution,[status(thm)],[74,71,64,55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWV792-1 : TPTP v9.0.0. Released v4.1.0.
% 0.08/0.13 % 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 10:53:35 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.70/0.88 % SZS status Unsatisfiable
% 0.70/0.88 % SZS output start Proof
% See solution above
% 0.73/0.92 % E exiting
%------------------------------------------------------------------------------