TSTP Solution File: SWV815-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV815-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 15:24:36 EDT 2022
% Result : Unsatisfiable 0.20s 0.60s
% Output : Proof 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 96
% Syntax : Number of formulae : 168 ( 44 unt; 42 typ; 0 def)
% Number of atoms : 648 ( 40 equ)
% Maximal formula atoms : 28 ( 5 avg)
% Number of connectives : 782 ( 299 ~; 413 |; 0 &)
% ( 70 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of FOOLs : 39 ( 39 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 45 ( 20 >; 25 *; 0 +; 0 <<)
% Number of predicates : 9 ( 6 usr; 2 prp; 0-3 aty)
% Number of functors : 40 ( 40 usr; 22 con; 0-5 aty)
% Number of variables : 348 ( 313 !; 0 ?; 348 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(tc_fun_type,type,
tc_fun: ( $i * $i ) > $i ).
tff(tc_bool_type,type,
tc_bool: $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(v_evs5_type,type,
v_evs5: $i ).
tff(c_Message_Oagent_OSpy_type,type,
c_Message_Oagent_OSpy: $i ).
tff(c_Set_Oinsert_type,type,
c_Set_Oinsert: ( $i * $i * $i ) > $i ).
tff(c_List_OtakeWhile_type,type,
c_List_OtakeWhile: ( $i * $i * $i ) > $i ).
tff(tc_Event_Oevent_type,type,
tc_Event_Oevent: $i ).
tff(c_List_Orev_type,type,
c_List_Orev: ( $i * $i ) > $i ).
tff(c_COMBB_type,type,
c_COMBB: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_COMBC_type,type,
c_COMBC: ( $i * $i * $i * $i * $i ) > $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_ONonce_type,type,
c_Message_Omsg_ONonce: $i > $i ).
tff(v_NBa_type,type,
v_NBa: $i ).
tff(v_Ka_type,type,
v_Ka: $i ).
tff(v_Ba_type,type,
v_Ba: $i ).
tff(v_Aa_type,type,
v_Aa: $i ).
tff(c_fequal_type,type,
c_fequal: $i > $i ).
tff(c_Not_type,type,
c_Not: $i ).
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(v_X_type,type,
v_X: $i ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(c_Message_Omsg_OKey_type,type,
c_Message_Omsg_OKey: $i ).
tff(c_Message_Omsg_OAgent_type,type,
c_Message_Omsg_OAgent: $i > $i ).
tff(v_NA_type,type,
v_NA: $i ).
tff(c_Public_OshrK_type,type,
c_Public_OshrK: $i ).
tff(c_List_Oset_type,type,
c_List_Oset: ( $i * $i ) > $i ).
tff(v_S_type,type,
v_S: $i ).
tff(v_NB_type,type,
v_NB: $i ).
tff(v_K_type,type,
v_K: $i ).
tff(v_B_type,type,
v_B: $i ).
tff(v_A_type,type,
v_A: $i ).
tff(c_Message_Oanalz_type,type,
c_Message_Oanalz: $i > $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(1,plain,
^ [V_evs: $i] :
refl(
( ( c_Event_Oknows(c_Message_Oagent_OSpy,V_evs) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Orev(V_evs,tc_Event_Oevent)) )
<=> ( c_Event_Oknows(c_Message_Oagent_OSpy,V_evs) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Orev(V_evs,tc_Event_Oevent)) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [V_evs: $i] : ( c_Event_Oknows(c_Message_Oagent_OSpy,V_evs) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Orev(V_evs,tc_Event_Oevent)) )
<=> ! [V_evs: $i] : ( c_Event_Oknows(c_Message_Oagent_OSpy,V_evs) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Orev(V_evs,tc_Event_Oevent)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_evs: $i] : ( c_Event_Oknows(c_Message_Oagent_OSpy,V_evs) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Orev(V_evs,tc_Event_Oevent)) )
<=> ! [V_evs: $i] : ( c_Event_Oknows(c_Message_Oagent_OSpy,V_evs) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Orev(V_evs,tc_Event_Oevent)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [V_evs: $i] : ( c_Event_Oknows(c_Message_Oagent_OSpy,V_evs) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Orev(V_evs,tc_Event_Oevent)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_spies__evs__rev_0) ).
tff(5,plain,
! [V_evs: $i] : ( c_Event_Oknows(c_Message_Oagent_OSpy,V_evs) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Orev(V_evs,tc_Event_Oevent)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V_evs: $i] : ( c_Event_Oknows(c_Message_Oagent_OSpy,V_evs) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Orev(V_evs,tc_Event_Oevent)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V_evs: $i] : ( c_Event_Oknows(c_Message_Oagent_OSpy,V_evs) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Orev(V_evs,tc_Event_Oevent)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V_evs: $i] : ( c_Event_Oknows(c_Message_Oagent_OSpy,V_evs) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Orev(V_evs,tc_Event_Oevent)) )
| ( c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Orev(v_evs5,tc_Event_Oevent)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5) = c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Orev(v_evs5,tc_Event_Oevent)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Orev(v_evs5,tc_Event_Oevent)) = c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Orev(v_evs5,tc_Event_Oevent))) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Orev(v_evs5,tc_Event_Oevent))),
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
( c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg)
<=> c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_11) ).
tff(15,plain,
c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
^ [V_a: $i,T_a: $i,V_A: $i] :
refl(
( ( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
<=> ( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ) )),
inference(bind,[status(th)],]) ).
tff(17,plain,
( ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ 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] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
( ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ 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] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
^ [V_a: $i,T_a: $i,V_A: $i] :
rewrite(
( ( ( c_Set_Oinsert(V_a,V_A,T_a) = V_A )
| ~ c_in(V_a,V_A,T_a) )
<=> ( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [V_a: $i,T_a: $i,V_A: $i] :
( ( c_Set_Oinsert(V_a,V_A,T_a) = V_A )
| ~ c_in(V_a,V_A,T_a) )
<=> ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,axiom,
! [V_a: $i,T_a: $i,V_A: $i] :
( ( c_Set_Oinsert(V_a,V_A,T_a) = V_A )
| ~ c_in(V_a,V_A,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
tff(22,plain,
! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ),
inference(modus_ponens,[status(thm)],[22,18]) ).
tff(24,plain,
! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) ),
inference(modus_ponens,[status(thm)],[24,17]) ).
tff(26,plain,
( ( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
| ~ c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg)
| ( c_Set_Oinsert(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))) ) )
<=> ( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
| ~ c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg)
| ( c_Set_Oinsert(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
| ~ c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg)
| ( c_Set_Oinsert(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
( ~ ! [V_a: $i,T_a: $i,V_A: $i] :
( ~ c_in(V_a,V_A,T_a)
| ( c_Set_Oinsert(V_a,V_A,T_a) = V_A ) )
| ~ c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg)
| ( c_Set_Oinsert(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))) ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
c_Set_Oinsert(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),
inference(unit_resolution,[status(thm)],[28,25,15]) ).
tff(30,plain,
( c_lessequals(c_Set_Oinsert(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_fun(tc_Message_Omsg,tc_bool))
<=> c_lessequals(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Orev(v_evs5,tc_Event_Oevent))),tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(monotonicity,[status(thm)],[29,12]) ).
tff(31,plain,
( c_lessequals(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Orev(v_evs5,tc_Event_Oevent))),tc_fun(tc_Message_Omsg,tc_bool))
<=> c_lessequals(c_Set_Oinsert(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(symmetry,[status(thm)],[30]) ).
tff(32,plain,
^ [V_P: $i,V_evs: $i] :
refl(
( c_lessequals(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(V_P,V_evs,tc_Event_Oevent))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_fun(tc_Message_Omsg,tc_bool))
<=> c_lessequals(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(V_P,V_evs,tc_Event_Oevent))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_fun(tc_Message_Omsg,tc_bool)) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [V_P: $i,V_evs: $i] : c_lessequals(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(V_P,V_evs,tc_Event_Oevent))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_fun(tc_Message_Omsg,tc_bool))
<=> ! [V_P: $i,V_evs: $i] : c_lessequals(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(V_P,V_evs,tc_Event_Oevent))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [V_P: $i,V_evs: $i] : c_lessequals(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(V_P,V_evs,tc_Event_Oevent))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_fun(tc_Message_Omsg,tc_bool))
<=> ! [V_P: $i,V_evs: $i] : c_lessequals(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(V_P,V_evs,tc_Event_Oevent))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(rewrite,[status(thm)],]) ).
tff(35,axiom,
! [V_P: $i,V_evs: $i] : c_lessequals(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(V_P,V_evs,tc_Event_Oevent))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_fun(tc_Message_Omsg,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_parts__spies__takeWhile__mono_0) ).
tff(36,plain,
! [V_P: $i,V_evs: $i] : c_lessequals(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(V_P,V_evs,tc_Event_Oevent))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_fun(tc_Message_Omsg,tc_bool)),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [V_P: $i,V_evs: $i] : c_lessequals(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(V_P,V_evs,tc_Event_Oevent))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_fun(tc_Message_Omsg,tc_bool)),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [V_P: $i,V_evs: $i] : c_lessequals(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(V_P,V_evs,tc_Event_Oevent))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_fun(tc_Message_Omsg,tc_bool)),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
( ~ ! [V_P: $i,V_evs: $i] : c_lessequals(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(V_P,V_evs,tc_Event_Oevent))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_fun(tc_Message_Omsg,tc_bool))
| c_lessequals(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Orev(v_evs5,tc_Event_Oevent))),tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,plain,
c_lessequals(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Orev(v_evs5,tc_Event_Oevent))),tc_fun(tc_Message_Omsg,tc_bool)),
inference(unit_resolution,[status(thm)],[39,38]) ).
tff(41,plain,
c_lessequals(c_Set_Oinsert(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_fun(tc_Message_Omsg,tc_bool)),
inference(modus_ponens,[status(thm)],[40,31]) ).
tff(42,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_evs5,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_evs5,tc_Event_Oevent),tc_Event_Oevent) ),
inference(rewrite,[status(thm)],]) ).
tff(43,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_evs5,tc_Event_Oevent),tc_Event_Oevent),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
tff(44,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_evs5,tc_Event_Oevent),tc_Event_Oevent),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,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(46,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)],[45]) ).
tff(47,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(48,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(49,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)],[48]) ).
tff(50,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/sandbox/benchmark/theBenchmark.p',cls_Says__imp__parts__knows__Spy_0) ).
tff(51,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)],[50,49]) ).
tff(52,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)],[51,47]) ).
tff(53,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)],[52]) ).
tff(54,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)],[53,46]) ).
tff(55,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_evs5,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_evs5)),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_evs5,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_evs5)),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(56,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_evs5,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_evs5)),tc_Message_Omsg) ),
inference(quant_inst,[status(thm)],]) ).
tff(57,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_evs5,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_evs5)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,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_evs5)),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[57,54,44]) ).
tff(59,plain,
( ( $false
| ~ c_in(c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent) )
<=> ~ c_in(c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent) ),
inference(rewrite,[status(thm)],]) ).
tff(60,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
( c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg)
<=> $true ),
inference(iff_true,[status(thm)],[15]) ).
tff(62,plain,
( ~ c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
( ~ c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg)
<=> $false ),
inference(transitivity,[status(thm)],[62,60]) ).
tff(64,plain,
( ( ~ c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent) )
<=> ( $false
| ~ c_in(c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent) ) ),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,plain,
( ( ~ c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent) )
<=> ~ c_in(c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent) ),
inference(transitivity,[status(thm)],[64,59]) ).
tff(66,plain,
( ( ~ c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent) )
<=> ( ~ c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent) ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,plain,
( ~ c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)
<=> ~ c_in(c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent) ),
inference(rewrite,[status(thm)],]) ).
tff(68,plain,
( ~ c_in(c_Message_Omsg_OCrypt(v_K,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,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg)
<=> ~ c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
( ( ~ c_in(c_Message_Omsg_OCrypt(v_K,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,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent) )
<=> ( ~ c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent) ) ),
inference(monotonicity,[status(thm)],[68,67]) ).
tff(70,plain,
( ( ~ c_in(c_Message_Omsg_OCrypt(v_K,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,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent) )
<=> ( ~ c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent) ) ),
inference(transitivity,[status(thm)],[69,66]) ).
tff(71,plain,
( ( ~ c_in(c_Message_Omsg_OCrypt(v_K,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,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent) )
<=> ( ~ c_in(c_Message_Omsg_OCrypt(v_K,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,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent) ) ),
inference(rewrite,[status(thm)],]) ).
tff(72,axiom,
( ~ c_in(c_Message_Omsg_OCrypt(v_K,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,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_12) ).
tff(73,plain,
( ~ c_in(c_Message_Omsg_OCrypt(v_K,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,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
( ~ c_in(c_Message_Omsg_OCrypt(v_K,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,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent) ),
inference(modus_ponens,[status(thm)],[73,71]) ).
tff(75,plain,
( ~ c_in(c_Message_Omsg_OCrypt(v_K,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,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent) ),
inference(modus_ponens,[status(thm)],[74,71]) ).
tff(76,plain,
( ~ c_in(c_Message_Omsg_OCrypt(v_K,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,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent) ),
inference(modus_ponens,[status(thm)],[75,71]) ).
tff(77,plain,
( ~ c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent) ),
inference(modus_ponens,[status(thm)],[76,70]) ).
tff(78,plain,
( ~ c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent) ),
inference(modus_ponens,[status(thm)],[77,66]) ).
tff(79,plain,
~ c_in(c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent),
inference(modus_ponens,[status(thm)],[78,65]) ).
tff(80,plain,
( ~ c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)
<=> ~ 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(rewrite,[status(thm)],]) ).
tff(81,plain,
( ~ c_in(hAPP(c_Message_Omsg_OKey,v_K),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(rewrite,[status(thm)],]) ).
tff(82,axiom,
~ 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/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
tff(83,plain,
~ 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)],[82,81]) ).
tff(84,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),
inference(modus_ponens,[status(thm)],[83,80]) ).
tff(85,plain,
( c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
<=> c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)) ),
inference(rewrite,[status(thm)],]) ).
tff(86,axiom,
c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(87,plain,
c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
( ~ c_in(v_B,c_Event_Obad,tc_Message_Oagent)
<=> ~ c_in(v_Ba,c_Event_Obad,tc_Message_Oagent) ),
inference(rewrite,[status(thm)],]) ).
tff(89,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(90,axiom,
~ c_in(v_B,c_Event_Obad,tc_Message_Oagent),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(91,plain,
~ c_in(v_B,c_Event_Obad,tc_Message_Oagent),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
~ c_in(v_Ba,c_Event_Obad,tc_Message_Oagent),
inference(modus_ponens,[status(thm)],[91,88]) ).
tff(93,plain,
( ~ c_in(v_A,c_Event_Obad,tc_Message_Oagent)
<=> ~ c_in(v_Aa,c_Event_Obad,tc_Message_Oagent) ),
inference(rewrite,[status(thm)],]) ).
tff(94,plain,
( ~ c_in(v_A,c_Event_Obad,tc_Message_Oagent)
<=> ~ c_in(v_A,c_Event_Obad,tc_Message_Oagent) ),
inference(rewrite,[status(thm)],]) ).
tff(95,axiom,
~ c_in(v_A,c_Event_Obad,tc_Message_Oagent),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(96,plain,
~ c_in(v_A,c_Event_Obad,tc_Message_Oagent),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
~ c_in(v_Aa,c_Event_Obad,tc_Message_Oagent),
inference(modus_ponens,[status(thm)],[96,93]) ).
tff(98,plain,
^ [V_NA: $i,V_NB: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
refl(
( ( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,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_evs)),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_evs)),tc_Message_Omsg)
| c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) )
<=> ( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,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_evs)),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_evs)),tc_Message_Omsg)
| c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ) )),
inference(bind,[status(th)],]) ).
tff(99,plain,
( ! [V_NA: $i,V_NB: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,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_evs)),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_evs)),tc_Message_Omsg)
| c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) )
<=> ! [V_NA: $i,V_NB: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,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_evs)),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_evs)),tc_Message_Omsg)
| c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ) ),
inference(quant_intro,[status(thm)],[98]) ).
tff(100,plain,
( ! [V_NA: $i,V_NB: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,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_evs)),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_evs)),tc_Message_Omsg)
| c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) )
<=> ! [V_NA: $i,V_NB: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,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_evs)),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_evs)),tc_Message_Omsg)
| c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ) ),
inference(rewrite,[status(thm)],]) ).
tff(101,plain,
^ [V_NA: $i,V_NB: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ 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))
| c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ) )),
( ( c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(V_B,c_Event_Obad,tc_Message_Oagent) )
<=> ( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_B,c_Event_Obad,tc_Message_Oagent) ) )),
rewrite(
( ( ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_B,c_Event_Obad,tc_Message_Oagent) )
<=> ( c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ) )),
( ( c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(V_B,c_Event_Obad,tc_Message_Oagent) )
<=> ( c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ) )),
( ( c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| c_in(V_A,c_Event_Obad,tc_Message_Oagent) )
<=> ( c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_A,c_Event_Obad,tc_Message_Oagent) ) )),
rewrite(
( ( c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(V_A,c_Event_Obad,tc_Message_Oagent) )
<=> ( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ) )),
( ( c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| c_in(V_A,c_Event_Obad,tc_Message_Oagent) )
<=> ( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ) )),
( ( c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
<=> ( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) ) )),
rewrite(
( ( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
<=> ( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ) )),
( ( c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg) )
<=> ( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ) )),
( ( c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),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_evs)),tc_Message_Omsg) )
<=> ( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ 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_evs)),tc_Message_Omsg) ) )),
rewrite(
( ( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ 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_evs)),tc_Message_Omsg) )
<=> ( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),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_evs)),tc_Message_Omsg)
| c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ) )),
( ( c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),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_evs)),tc_Message_Omsg) )
<=> ( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),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_evs)),tc_Message_Omsg)
| c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ) )),
( ( c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),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_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,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_evs)),tc_Message_Omsg) )
<=> ( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),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_evs)),tc_Message_Omsg)
| c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,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_evs)),tc_Message_Omsg) ) )),
rewrite(
( ( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),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_evs)),tc_Message_Omsg)
| c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,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_evs)),tc_Message_Omsg) )
<=> ( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,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_evs)),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_evs)),tc_Message_Omsg)
| c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ) )),
( ( c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),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_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,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_evs)),tc_Message_Omsg) )
<=> ( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,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_evs)),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_evs)),tc_Message_Omsg)
| c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ) )),
inference(bind,[status(th)],]) ).
tff(102,plain,
( ! [V_NA: $i,V_NB: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),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_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,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_evs)),tc_Message_Omsg) )
<=> ! [V_NA: $i,V_NB: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,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_evs)),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_evs)),tc_Message_Omsg)
| c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ) ),
inference(quant_intro,[status(thm)],[101]) ).
tff(103,axiom,
! [V_NA: $i,V_NB: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),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_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,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_evs)),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_A__trusts__NS5_0) ).
tff(104,plain,
! [V_NA: $i,V_NB: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,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_evs)),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_evs)),tc_Message_Omsg)
| c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
! [V_NA: $i,V_NB: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,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_evs)),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_evs)),tc_Message_Omsg)
| c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ),
inference(modus_ponens,[status(thm)],[104,100]) ).
tff(106,plain,
! [V_NA: $i,V_NB: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,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_evs)),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_evs)),tc_Message_Omsg)
| c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ),
inference(skolemize,[status(sab)],[105]) ).
tff(107,plain,
! [V_NA: $i,V_NB: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,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_evs)),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_evs)),tc_Message_Omsg)
| c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ),
inference(modus_ponens,[status(thm)],[106,99]) ).
tff(108,plain,
( ( ~ ! [V_NA: $i,V_NB: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,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_evs)),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_evs)),tc_Message_Omsg)
| c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) )
| c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)
| c_in(v_Ba,c_Event_Obad,tc_Message_Oagent)
| 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(c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),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_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_evs5)),tc_Message_Omsg) )
<=> ( ~ ! [V_NA: $i,V_NB: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,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_evs)),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_evs)),tc_Message_Omsg)
| c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) )
| c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)
| c_in(v_Ba,c_Event_Obad,tc_Message_Oagent)
| 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(c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),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_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_evs5)),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(109,plain,
( ( c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)
| c_in(v_Ba,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| 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(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),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_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_evs5)),tc_Message_Omsg)
| c_in(c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent) )
<=> ( c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)
| c_in(v_Ba,c_Event_Obad,tc_Message_Oagent)
| 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(c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),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_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_evs5)),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(110,plain,
( ( ~ ! [V_NA: $i,V_NB: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,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_evs)),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_evs)),tc_Message_Omsg)
| c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) )
| c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)
| c_in(v_Ba,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| 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(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),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_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_evs5)),tc_Message_Omsg)
| c_in(c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent) )
<=> ( ~ ! [V_NA: $i,V_NB: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,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_evs)),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_evs)),tc_Message_Omsg)
| c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) )
| c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)
| c_in(v_Ba,c_Event_Obad,tc_Message_Oagent)
| 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(c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),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_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_evs5)),tc_Message_Omsg) ) ),
inference(monotonicity,[status(thm)],[109]) ).
tff(111,plain,
( ( ~ ! [V_NA: $i,V_NB: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,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_evs)),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_evs)),tc_Message_Omsg)
| c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) )
| c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)
| c_in(v_Ba,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| 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(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),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_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_evs5)),tc_Message_Omsg)
| c_in(c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent) )
<=> ( ~ ! [V_NA: $i,V_NB: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,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_evs)),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_evs)),tc_Message_Omsg)
| c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) )
| c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)
| c_in(v_Ba,c_Event_Obad,tc_Message_Oagent)
| 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(c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),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_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_evs5)),tc_Message_Omsg) ) ),
inference(transitivity,[status(thm)],[110,108]) ).
tff(112,plain,
( ~ ! [V_NA: $i,V_NB: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,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_evs)),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_evs)),tc_Message_Omsg)
| c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) )
| c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)
| c_in(v_Ba,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| 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(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),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_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_evs5)),tc_Message_Omsg)
| c_in(c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent) ),
inference(quant_inst,[status(thm)],]) ).
tff(113,plain,
( ~ ! [V_NA: $i,V_NB: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(V_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| c_in(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,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_evs)),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_evs)),tc_Message_Omsg)
| c_in(c_Event_Oevent_OSays(V_A,V_B,c_Message_Omsg_OCrypt(V_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NB),c_Message_Omsg_ONonce(V_NB)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) )
| c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)
| c_in(v_Ba,c_Event_Obad,tc_Message_Oagent)
| 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(c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),c_List_Oset(v_evs5,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(v_evs5,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),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_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_evs5)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[112,111]) ).
tff(114,plain,
~ c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg),
inference(unit_resolution,[status(thm)],[113,107,97,92,87,84,79,58]) ).
tff(115,plain,
^ [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
refl(
( ( c_in(V_x,V_B,T_a)
| ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) )
<=> ( c_in(V_x,V_B,T_a)
| ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) ) )),
inference(bind,[status(th)],]) ).
tff(116,plain,
( ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_x,V_B,T_a)
| ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) )
<=> ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_x,V_B,T_a)
| ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) ) ),
inference(quant_intro,[status(thm)],[115]) ).
tff(117,plain,
( ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_x,V_B,T_a)
| ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) )
<=> ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_x,V_B,T_a)
| ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(118,axiom,
! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_x,V_B,T_a)
| ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).
tff(119,plain,
! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_x,V_B,T_a)
| ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) ),
inference(modus_ponens,[status(thm)],[118,117]) ).
tff(120,plain,
! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_x,V_B,T_a)
| ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) ),
inference(skolemize,[status(sab)],[119]) ).
tff(121,plain,
! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_x,V_B,T_a)
| ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) ),
inference(modus_ponens,[status(thm)],[120,116]) ).
tff(122,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_x,V_B,T_a)
| ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) )
| c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)
| ~ c_lessequals(c_Set_Oinsert(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_fun(tc_Message_Omsg,tc_bool)) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_x,V_B,T_a)
| ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) )
| c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)
| ~ c_lessequals(c_Set_Oinsert(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_fun(tc_Message_Omsg,tc_bool)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(123,plain,
( ~ ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_x,V_B,T_a)
| ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) )
| c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)
| ~ c_lessequals(c_Set_Oinsert(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(quant_inst,[status(thm)],]) ).
tff(124,plain,
( ~ ! [V_x: $i,T_a: $i,V_B: $i,V_A: $i] :
( c_in(V_x,V_B,T_a)
| ~ c_lessequals(c_Set_Oinsert(V_x,V_A,T_a),V_B,tc_fun(T_a,tc_bool)) )
| c_in(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_Message_Omsg)
| ~ c_lessequals(c_Set_Oinsert(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_fun(tc_Message_Omsg,tc_bool)) ),
inference(modus_ponens,[status(thm)],[123,122]) ).
tff(125,plain,
~ c_lessequals(c_Set_Oinsert(c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,c_List_OtakeWhile(c_COMBB(c_Not,c_COMBC(c_fequal(tc_Event_Oevent),c_Event_Oevent_OSays(v_Aa,v_Ba,c_Message_Omsg_OCrypt(v_Ka,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NBa),c_Message_Omsg_ONonce(v_NBa)))),tc_Event_Oevent,tc_Event_Oevent,tc_bool),tc_bool,tc_bool,tc_Event_Oevent),c_List_Orev(v_evs5,tc_Event_Oevent),tc_Event_Oevent))),tc_Message_Omsg),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs5)),tc_fun(tc_Message_Omsg,tc_bool)),
inference(unit_resolution,[status(thm)],[124,121,114]) ).
tff(126,plain,
$false,
inference(unit_resolution,[status(thm)],[125,41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV815-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Sep 4 08:25:45 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.60 % SZS status Unsatisfiable
% 0.20/0.60 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------