%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV768-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:36:03 AM UTC 2025
% Result : Unsatisfiable 0.43s 0.60s
% Output : Proof 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 22
% Syntax : Number of formulae : 46 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 297 ( 0 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 454 ( 219 ~; 207 |; 0 &)
% ( 28 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 16 ( 16 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 10 con; 0-3 aty)
% Number of variables : 105 ( 95 !; 0 ?; 105 :)
% Comments :
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $i ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(c_Message_OkeysFor_type,type,
c_Message_OkeysFor: $i > $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_evs2_type,type,
v_evs2: $i ).
tff(c_Message_Oagent_OSpy_type,type,
c_Message_Oagent_OSpy: $i ).
tff(v_KAB_type,type,
v_KAB: $i ).
tff(tc_Message_Omsg_type,type,
tc_Message_Omsg: $i ).
tff(c_Message_Omsg_OCrypt_type,type,
c_Message_Omsg_OCrypt: ( $i * $i ) > $i ).
tff(c_Message_Omsg_OMPair_type,type,
c_Message_Omsg_OMPair: ( $i * $i ) > $i ).
tff(c_Message_Omsg_ONonce_type,type,
c_Message_Omsg_ONonce: $i > $i ).
tff(v_NB_type,type,
v_NB: $i ).
tff(c_Message_OsymKeys_type,type,
c_Message_OsymKeys: $i ).
tff(c_Event_Oused_type,type,
c_Event_Oused: $i > $i ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(c_Message_Omsg_OKey_type,type,
c_Message_Omsg_OKey: $i ).
tff(tc_List_Olist_type,type,
tc_List_Olist: $i > $i ).
tff(tc_Event_Oevent_type,type,
tc_Event_Oevent: $i ).
tff(c_NS__Shared__Mirabelle_Ons__shared_type,type,
c_NS__Shared__Mirabelle_Ons__shared: $i ).
tff(1,plain,
( hBOOL(c_in(c_Message_Omsg_OCrypt(v_KAB,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2)),tc_Message_Omsg))
<=> hBOOL(c_in(c_Message_Omsg_OCrypt(v_KAB,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2)),tc_Message_Omsg)) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
hBOOL(c_in(c_Message_Omsg_OCrypt(v_KAB,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2)),tc_Message_Omsg)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_13) ).
tff(3,plain,
hBOOL(c_in(c_Message_Omsg_OCrypt(v_KAB,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2)),tc_Message_Omsg)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( hBOOL(c_in(v_KAB,c_Message_OsymKeys,tc_nat))
<=> hBOOL(c_in(v_KAB,c_Message_OsymKeys,tc_nat)) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
hBOOL(c_in(v_KAB,c_Message_OsymKeys,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(6,plain,
hBOOL(c_in(v_KAB,c_Message_OsymKeys,tc_nat)),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [V_H: $i,V_X: $i,V_K: $i] :
refl(( ( ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg))
| hBOOL(c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)) )
<=> ( ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg))
| hBOOL(c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [V_H: $i,V_X: $i,V_K: $i] :
( ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg))
| hBOOL(c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)) )
<=> ! [V_H: $i,V_X: $i,V_K: $i] :
( ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg))
| hBOOL(c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [V_H: $i,V_X: $i,V_K: $i] :
( ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg))
| hBOOL(c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)) )
<=> ! [V_H: $i,V_X: $i,V_K: $i] :
( ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg))
| hBOOL(c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,plain,
^ [V_H: $i,V_X: $i,V_K: $i] :
rewrite(( ( hBOOL(c_in(V_K,c_Message_OkeysFor(V_H),tc_nat))
| ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)) )
<=> ( ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg))
| hBOOL(c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [V_H: $i,V_X: $i,V_K: $i] :
( hBOOL(c_in(V_K,c_Message_OkeysFor(V_H),tc_nat))
| ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)) )
<=> ! [V_H: $i,V_X: $i,V_K: $i] :
( ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg))
| hBOOL(c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [V_H: $i,V_X: $i,V_K: $i] :
( hBOOL(c_in(V_K,c_Message_OkeysFor(V_H),tc_nat))
| ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Crypt__imp__keysFor_0) ).
tff(13,plain,
! [V_H: $i,V_X: $i,V_K: $i] :
( ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg))
| hBOOL(c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [V_H: $i,V_X: $i,V_K: $i] :
( ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg))
| hBOOL(c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [V_H: $i,V_X: $i,V_K: $i] :
( ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg))
| hBOOL(c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [V_H: $i,V_X: $i,V_K: $i] :
( ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg))
| hBOOL(c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [V_H: $i,V_X: $i,V_K: $i] :
( ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg))
| hBOOL(c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)) )
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(v_KAB,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2)),tc_Message_Omsg))
| ~ hBOOL(c_in(v_KAB,c_Message_OsymKeys,tc_nat))
| hBOOL(c_in(v_KAB,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2))),tc_nat)) )
<=> ( ~ ! [V_H: $i,V_X: $i,V_K: $i] :
( ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg))
| hBOOL(c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)) )
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(v_KAB,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2)),tc_Message_Omsg))
| ~ hBOOL(c_in(v_KAB,c_Message_OsymKeys,tc_nat))
| hBOOL(c_in(v_KAB,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2))),tc_nat)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ( ~ hBOOL(c_in(v_KAB,c_Message_OsymKeys,tc_nat))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(v_KAB,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2)),tc_Message_Omsg))
| hBOOL(c_in(v_KAB,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2))),tc_nat)) )
<=> ( ~ hBOOL(c_in(c_Message_Omsg_OCrypt(v_KAB,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2)),tc_Message_Omsg))
| ~ hBOOL(c_in(v_KAB,c_Message_OsymKeys,tc_nat))
| hBOOL(c_in(v_KAB,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2))),tc_nat)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ( ~ ! [V_H: $i,V_X: $i,V_K: $i] :
( ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg))
| hBOOL(c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)) )
| ~ hBOOL(c_in(v_KAB,c_Message_OsymKeys,tc_nat))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(v_KAB,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2)),tc_Message_Omsg))
| hBOOL(c_in(v_KAB,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2))),tc_nat)) )
<=> ( ~ ! [V_H: $i,V_X: $i,V_K: $i] :
( ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg))
| hBOOL(c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)) )
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(v_KAB,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2)),tc_Message_Omsg))
| ~ hBOOL(c_in(v_KAB,c_Message_OsymKeys,tc_nat))
| hBOOL(c_in(v_KAB,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2))),tc_nat)) ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ( ~ ! [V_H: $i,V_X: $i,V_K: $i] :
( ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg))
| hBOOL(c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)) )
| ~ hBOOL(c_in(v_KAB,c_Message_OsymKeys,tc_nat))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(v_KAB,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2)),tc_Message_Omsg))
| hBOOL(c_in(v_KAB,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2))),tc_nat)) )
<=> ( ~ ! [V_H: $i,V_X: $i,V_K: $i] :
( ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg))
| hBOOL(c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)) )
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(v_KAB,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2)),tc_Message_Omsg))
| ~ hBOOL(c_in(v_KAB,c_Message_OsymKeys,tc_nat))
| hBOOL(c_in(v_KAB,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2))),tc_nat)) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
( ~ ! [V_H: $i,V_X: $i,V_K: $i] :
( ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg))
| hBOOL(c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)) )
| ~ hBOOL(c_in(v_KAB,c_Message_OsymKeys,tc_nat))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(v_KAB,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2)),tc_Message_Omsg))
| hBOOL(c_in(v_KAB,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2))),tc_nat)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [V_H: $i,V_X: $i,V_K: $i] :
( ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg))
| hBOOL(c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)) )
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(v_KAB,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2)),tc_Message_Omsg))
| ~ hBOOL(c_in(v_KAB,c_Message_OsymKeys,tc_nat))
| hBOOL(c_in(v_KAB,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2))),tc_nat)) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
hBOOL(c_in(v_KAB,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2))),tc_nat)),
inference(unit_resolution,[status(thm)],[22,16,6,3]) ).
tff(24,plain,
( ~ hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_KAB),c_Event_Oused(v_evs2),tc_Message_Omsg))
<=> ~ hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_KAB),c_Event_Oused(v_evs2),tc_Message_Omsg)) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,axiom,
~ hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_KAB),c_Event_Oused(v_evs2),tc_Message_Omsg)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(26,plain,
~ hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_KAB),c_Event_Oused(v_evs2),tc_Message_Omsg)),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
( hBOOL(c_in(v_evs2,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
<=> hBOOL(c_in(v_evs2,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,axiom,
hBOOL(c_in(v_evs2,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(29,plain,
hBOOL(c_in(v_evs2,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
^ [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(hAPP(c_Message_Omsg_OKey,V_K),c_Event_Oused(V_evs),tc_Message_Omsg))
| ~ hBOOL(c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat))
| ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat)) )
<=> ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Event_Oused(V_evs),tc_Message_Omsg))
| ~ hBOOL(c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat))
| ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat)) ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [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(hAPP(c_Message_Omsg_OKey,V_K),c_Event_Oused(V_evs),tc_Message_Omsg))
| ~ hBOOL(c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat))
| ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat)) )
<=> ! [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(hAPP(c_Message_Omsg_OKey,V_K),c_Event_Oused(V_evs),tc_Message_Omsg))
| ~ hBOOL(c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat))
| ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat)) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [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(hAPP(c_Message_Omsg_OKey,V_K),c_Event_Oused(V_evs),tc_Message_Omsg))
| ~ hBOOL(c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat))
| ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat)) )
<=> ! [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(hAPP(c_Message_Omsg_OKey,V_K),c_Event_Oused(V_evs),tc_Message_Omsg))
| ~ hBOOL(c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat))
| ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
^ [V_K: $i,V_evs: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ~ hBOOL(c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat))
| ~ 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(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat)) ) )),
( ( ~ hBOOL(c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat))
| ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat)) )
<=> ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat))
| ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat)) ) )),
rewrite(( ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat))
| ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat)) )
<=> ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat))
| ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat)) ) )),
( ( ~ hBOOL(c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat))
| ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat)) )
<=> ( ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat))
| ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat)) ) )),
( ( ~ hBOOL(c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat))
| ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat))
| hBOOL(c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Event_Oused(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_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat))
| ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat))
| hBOOL(c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Event_Oused(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_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat))
| ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat))
| hBOOL(c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Event_Oused(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(hAPP(c_Message_Omsg_OKey,V_K),c_Event_Oused(V_evs),tc_Message_Omsg))
| ~ hBOOL(c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat))
| ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat)) ) )),
( ( ~ hBOOL(c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat))
| ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat))
| hBOOL(c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Event_Oused(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(hAPP(c_Message_Omsg_OKey,V_K),c_Event_Oused(V_evs),tc_Message_Omsg))
| ~ hBOOL(c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat))
| ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat)) ) )),
inference(bind,[status(th)],[]) ).
tff(34,plain,
( ! [V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat))
| ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat))
| hBOOL(c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Event_Oused(V_evs),tc_Message_Omsg)) )
<=> ! [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(hAPP(c_Message_Omsg_OKey,V_K),c_Event_Oused(V_evs),tc_Message_Omsg))
| ~ hBOOL(c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat))
| ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat)) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,axiom,
! [V_K: $i,V_evs: $i] :
( ~ hBOOL(c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat))
| ~ hBOOL(c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat))
| hBOOL(c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Event_Oused(V_evs),tc_Message_Omsg)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_new__keys__not__used_0) ).
tff(36,plain,
! [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(hAPP(c_Message_Omsg_OKey,V_K),c_Event_Oused(V_evs),tc_Message_Omsg))
| ~ hBOOL(c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat))
| ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat)) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [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(hAPP(c_Message_Omsg_OKey,V_K),c_Event_Oused(V_evs),tc_Message_Omsg))
| ~ hBOOL(c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat))
| ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat)) ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
! [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(hAPP(c_Message_Omsg_OKey,V_K),c_Event_Oused(V_evs),tc_Message_Omsg))
| ~ hBOOL(c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat))
| ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat)) ),
inference(skolemize,[status(sab)],[37]) ).
tff(39,plain,
! [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(hAPP(c_Message_Omsg_OKey,V_K),c_Event_Oused(V_evs),tc_Message_Omsg))
| ~ hBOOL(c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat))
| ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat)) ),
inference(modus_ponens,[status(thm)],[38,31]) ).
tff(40,plain,
( ( ~ ! [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(hAPP(c_Message_Omsg_OKey,V_K),c_Event_Oused(V_evs),tc_Message_Omsg))
| ~ hBOOL(c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat))
| ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat)) )
| hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_KAB),c_Event_Oused(v_evs2),tc_Message_Omsg))
| ~ hBOOL(c_in(v_KAB,c_Message_OsymKeys,tc_nat))
| ~ hBOOL(c_in(v_evs2,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(v_KAB,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2))),tc_nat)) )
<=> ( ~ ! [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(hAPP(c_Message_Omsg_OKey,V_K),c_Event_Oused(V_evs),tc_Message_Omsg))
| ~ hBOOL(c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat))
| ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat)) )
| hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_KAB),c_Event_Oused(v_evs2),tc_Message_Omsg))
| ~ hBOOL(c_in(v_KAB,c_Message_OsymKeys,tc_nat))
| ~ hBOOL(c_in(v_evs2,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(v_KAB,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2))),tc_nat)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
( ( ~ hBOOL(c_in(v_evs2,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_KAB),c_Event_Oused(v_evs2),tc_Message_Omsg))
| ~ hBOOL(c_in(v_KAB,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2))),tc_nat))
| ~ hBOOL(c_in(v_KAB,c_Message_OsymKeys,tc_nat)) )
<=> ( hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_KAB),c_Event_Oused(v_evs2),tc_Message_Omsg))
| ~ hBOOL(c_in(v_KAB,c_Message_OsymKeys,tc_nat))
| ~ hBOOL(c_in(v_evs2,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(v_KAB,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2))),tc_nat)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
( ( ~ ! [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(hAPP(c_Message_Omsg_OKey,V_K),c_Event_Oused(V_evs),tc_Message_Omsg))
| ~ hBOOL(c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat))
| ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat)) )
| ~ hBOOL(c_in(v_evs2,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_KAB),c_Event_Oused(v_evs2),tc_Message_Omsg))
| ~ hBOOL(c_in(v_KAB,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2))),tc_nat))
| ~ hBOOL(c_in(v_KAB,c_Message_OsymKeys,tc_nat)) )
<=> ( ~ ! [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(hAPP(c_Message_Omsg_OKey,V_K),c_Event_Oused(V_evs),tc_Message_Omsg))
| ~ hBOOL(c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat))
| ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat)) )
| hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_KAB),c_Event_Oused(v_evs2),tc_Message_Omsg))
| ~ hBOOL(c_in(v_KAB,c_Message_OsymKeys,tc_nat))
| ~ hBOOL(c_in(v_evs2,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(v_KAB,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2))),tc_nat)) ) ),
inference(monotonicity,[status(thm)],[41]) ).
tff(43,plain,
( ( ~ ! [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(hAPP(c_Message_Omsg_OKey,V_K),c_Event_Oused(V_evs),tc_Message_Omsg))
| ~ hBOOL(c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat))
| ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat)) )
| ~ hBOOL(c_in(v_evs2,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_KAB),c_Event_Oused(v_evs2),tc_Message_Omsg))
| ~ hBOOL(c_in(v_KAB,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2))),tc_nat))
| ~ hBOOL(c_in(v_KAB,c_Message_OsymKeys,tc_nat)) )
<=> ( ~ ! [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(hAPP(c_Message_Omsg_OKey,V_K),c_Event_Oused(V_evs),tc_Message_Omsg))
| ~ hBOOL(c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat))
| ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat)) )
| hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_KAB),c_Event_Oused(v_evs2),tc_Message_Omsg))
| ~ hBOOL(c_in(v_KAB,c_Message_OsymKeys,tc_nat))
| ~ hBOOL(c_in(v_evs2,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(v_KAB,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2))),tc_nat)) ) ),
inference(transitivity,[status(thm)],[42,40]) ).
tff(44,plain,
( ~ ! [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(hAPP(c_Message_Omsg_OKey,V_K),c_Event_Oused(V_evs),tc_Message_Omsg))
| ~ hBOOL(c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat))
| ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat)) )
| ~ hBOOL(c_in(v_evs2,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_KAB),c_Event_Oused(v_evs2),tc_Message_Omsg))
| ~ hBOOL(c_in(v_KAB,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2))),tc_nat))
| ~ hBOOL(c_in(v_KAB,c_Message_OsymKeys,tc_nat)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(45,plain,
( ~ ! [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(hAPP(c_Message_Omsg_OKey,V_K),c_Event_Oused(V_evs),tc_Message_Omsg))
| ~ hBOOL(c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat))
| ~ hBOOL(c_in(V_K,c_Message_OsymKeys,tc_nat)) )
| hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_KAB),c_Event_Oused(v_evs2),tc_Message_Omsg))
| ~ hBOOL(c_in(v_KAB,c_Message_OsymKeys,tc_nat))
| ~ hBOOL(c_in(v_evs2,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(v_KAB,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2))),tc_nat)) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
$false,
inference(unit_resolution,[status(thm)],[45,39,29,26,6,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.15 % Problem : SWV768-1 : TPTP v9.0.0. Released v4.1.0.
% 0.08/0.15 % Command : run_E %s %d THM
% 0.14/0.37 % Computer : n015.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Fri Jun 20 10:50:25 EDT 2025
% 0.14/0.37 % CPUTime :
% 0.43/0.60 % SZS status Unsatisfiable
% 0.43/0.60 % SZS output start Proof
% See solution above
% 0.45/0.64 % E exiting
%------------------------------------------------------------------------------