TSTP Solution File: SWV731-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV731-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 15:24:17 EDT 2022
% Result : Unsatisfiable 0.69s 0.75s
% Output : Proof 0.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 60
% Syntax : Number of formulae : 102 ( 16 unt; 31 typ; 0 def)
% Number of atoms : 437 ( 51 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 639 ( 297 ~; 302 |; 0 &)
% ( 40 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 24 ( 24 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 25 ( 14 >; 11 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 30 ( 30 usr; 17 con; 0-4 aty)
% Number of variables : 420 ( 380 !; 0 ?; 420 :)
% Comments :
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(c_Set_Oimage_type,type,
c_Set_Oimage: ( $i * $i * $i * $i ) > $i ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(tc_Message_Oagent_type,type,
tc_Message_Oagent: $i ).
tff(c_Orderings_Otop__class_Otop_type,type,
c_Orderings_Otop__class_Otop: $i > $i ).
tff(tc_fun_type,type,
tc_fun: ( $i * $i ) > $i ).
tff(tc_bool_type,type,
tc_bool: $i ).
tff(c_Public_OshrK_type,type,
c_Public_OshrK: $i ).
tff(v_K_type,type,
v_K: $i ).
tff(c_in_type,type,
c_in: $i > $i ).
tff(c_List_Oset_type,type,
c_List_Oset: ( $i * $i ) > $i ).
tff(tc_Event_Oevent_type,type,
tc_Event_Oevent: $i ).
tff(v_evs_type,type,
v_evs: $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(v_X_type,type,
v_X: $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_B_type,type,
v_B: $i ).
tff(v_NA_type,type,
v_NA: $i ).
tff(v_A_type,type,
v_A: $i ).
tff(c_Message_Oagent_OServer_type,type,
c_Message_Oagent_OServer: $i ).
tff(c_NS__Shared__Mirabelle_Ons__shared_type,type,
c_NS__Shared__Mirabelle_Ons__shared: $i ).
tff(tc_List_Olist_type,type,
tc_List_Olist: $i > $i ).
tff(c_Event_Obad_type,type,
c_Event_Obad: $i ).
tff(c_Message_Oparts_type,type,
c_Message_Oparts: $i > $i ).
tff(c_Event_Oknows_type,type,
c_Event_Oknows: ( $i * $i ) > $i ).
tff(c_Message_Oagent_OSpy_type,type,
c_Message_Oagent_OSpy: $i ).
tff(tc_Message_Omsg_type,type,
tc_Message_Omsg: $i ).
tff(1,plain,
( hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),v_evs),c_NS__Shared__Mirabelle_Ons__shared))
<=> hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),v_evs),c_NS__Shared__Mirabelle_Ons__shared)) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),v_evs),c_NS__Shared__Mirabelle_Ons__shared)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(3,plain,
hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),v_evs),c_NS__Shared__Mirabelle_Ons__shared)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),v_A),c_Event_Obad))
<=> ~ hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),v_A),c_Event_Obad)) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
~ hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),v_A),c_Event_Obad)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(6,plain,
~ hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),v_A),c_Event_Obad)),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( hBOOL(hAPP(hAPP(c_in(tc_Message_Omsg),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,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))))
<=> hBOOL(hAPP(hAPP(c_in(tc_Message_Omsg),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,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)))) ),
inference(rewrite,[status(thm)],]) ).
tff(8,axiom,
hBOOL(hAPP(hAPP(c_in(tc_Message_Omsg),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,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)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(9,plain,
hBOOL(hAPP(hAPP(c_in(tc_Message_Omsg),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,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)))),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
^ [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
refl(
( ( ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Message_Omsg),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,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))))
| hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),V_A),c_Event_Obad))
| hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent))) )
<=> ( ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Message_Omsg),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,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))))
| hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),V_A),c_Event_Obad))
| hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent))) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Message_Omsg),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,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))))
| hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),V_A),c_Event_Obad))
| hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent))) )
<=> ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Message_Omsg),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,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))))
| hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),V_A),c_Event_Obad))
| hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent))) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Message_Omsg),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,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))))
| hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),V_A),c_Event_Obad))
| hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent))) )
<=> ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Message_Omsg),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,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))))
| hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),V_A),c_Event_Obad))
| hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
^ [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared)) )
<=> ( ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent))) ) )),
( ( hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),V_A),c_Event_Obad)) )
<=> ( ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),V_A),c_Event_Obad)) ) )),
rewrite(
( ( ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),V_A),c_Event_Obad)) )
<=> ( ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),V_A),c_Event_Obad))
| hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent))) ) )),
( ( hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),V_A),c_Event_Obad)) )
<=> ( ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),V_A),c_Event_Obad))
| hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent))) ) )),
( ( hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),V_A),c_Event_Obad))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Message_Omsg),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,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)))) )
<=> ( ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),V_A),c_Event_Obad))
| hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Message_Omsg),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,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)))) ) )),
rewrite(
( ( ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),V_A),c_Event_Obad))
| hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Message_Omsg),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,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)))) )
<=> ( ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Message_Omsg),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,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))))
| hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),V_A),c_Event_Obad))
| hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent))) ) )),
( ( hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),V_A),c_Event_Obad))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Message_Omsg),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,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)))) )
<=> ( ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Message_Omsg),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,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))))
| hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),V_A),c_Event_Obad))
| hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent))) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),V_A),c_Event_Obad))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Message_Omsg),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,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)))) )
<=> ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Message_Omsg),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,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))))
| hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),V_A),c_Event_Obad))
| hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent))) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),V_A),c_Event_Obad))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Message_Omsg),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,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)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_A__trusts__NS2_0) ).
tff(16,plain,
! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Message_Omsg),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,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))))
| hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),V_A),c_Event_Obad))
| hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent))) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Message_Omsg),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,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))))
| hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),V_A),c_Event_Obad))
| hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent))) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Message_Omsg),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,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))))
| hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),V_A),c_Event_Obad))
| hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent))) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Message_Omsg),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,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))))
| hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),V_A),c_Event_Obad))
| hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent))) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( ( ~ ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Message_Omsg),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,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))))
| hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),V_A),c_Event_Obad))
| hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent))) )
| hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),v_A),c_Event_Obad))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Message_Omsg),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,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))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),v_evs),c_NS__Shared__Mirabelle_Ons__shared))
| hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X)))))),c_List_Oset(v_evs,tc_Event_Oevent))) )
<=> ( ~ ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Message_Omsg),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,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))))
| hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),V_A),c_Event_Obad))
| hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent))) )
| hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),v_A),c_Event_Obad))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Message_Omsg),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,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))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),v_evs),c_NS__Shared__Mirabelle_Ons__shared))
| hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X)))))),c_List_Oset(v_evs,tc_Event_Oevent))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
( ( ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),v_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Message_Omsg),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,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))))
| hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),v_A),c_Event_Obad))
| hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X)))))),c_List_Oset(v_evs,tc_Event_Oevent))) )
<=> ( hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),v_A),c_Event_Obad))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Message_Omsg),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,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))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),v_evs),c_NS__Shared__Mirabelle_Ons__shared))
| hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X)))))),c_List_Oset(v_evs,tc_Event_Oevent))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
( ( ~ ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Message_Omsg),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,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))))
| hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),V_A),c_Event_Obad))
| hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent))) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),v_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Message_Omsg),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,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))))
| hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),v_A),c_Event_Obad))
| hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X)))))),c_List_Oset(v_evs,tc_Event_Oevent))) )
<=> ( ~ ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Message_Omsg),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,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))))
| hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),V_A),c_Event_Obad))
| hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent))) )
| hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),v_A),c_Event_Obad))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Message_Omsg),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,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))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),v_evs),c_NS__Shared__Mirabelle_Ons__shared))
| hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X)))))),c_List_Oset(v_evs,tc_Event_Oevent))) ) ),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
( ( ~ ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Message_Omsg),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,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))))
| hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),V_A),c_Event_Obad))
| hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent))) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),v_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Message_Omsg),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,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))))
| hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),v_A),c_Event_Obad))
| hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X)))))),c_List_Oset(v_evs,tc_Event_Oevent))) )
<=> ( ~ ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Message_Omsg),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,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))))
| hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),V_A),c_Event_Obad))
| hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent))) )
| hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),v_A),c_Event_Obad))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Message_Omsg),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,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))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),v_evs),c_NS__Shared__Mirabelle_Ons__shared))
| hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X)))))),c_List_Oset(v_evs,tc_Event_Oevent))) ) ),
inference(transitivity,[status(thm)],[22,20]) ).
tff(24,plain,
( ~ ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Message_Omsg),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,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))))
| hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),V_A),c_Event_Obad))
| hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent))) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),v_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Message_Omsg),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,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))))
| hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),v_A),c_Event_Obad))
| hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X)))))),c_List_Oset(v_evs,tc_Event_Oevent))) ),
inference(quant_inst,[status(thm)],]) ).
tff(25,plain,
( ~ ! [V_NA: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Message_Omsg),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,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))))
| hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),V_A),c_Event_Obad))
| hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent))) )
| hBOOL(hAPP(hAPP(c_in(tc_Message_Oagent),v_A),c_Event_Obad))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Message_Omsg),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,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))))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),v_evs),c_NS__Shared__Mirabelle_Ons__shared))
| hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X)))))),c_List_Oset(v_evs,tc_Event_Oevent))) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X)))))),c_List_Oset(v_evs,tc_Event_Oevent))),
inference(unit_resolution,[status(thm)],[25,19,9,6,3]) ).
tff(27,plain,
^ [V_N: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_K_H: $i,V_evs: $i] :
refl(
( ( ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_nat),V_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat))) )
<=> ( ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_nat),V_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat))) ) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [V_N: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_K_H: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_nat),V_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat))) )
<=> ! [V_N: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_K_H: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_nat),V_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat))) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [V_N: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_K_H: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_nat),V_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat))) )
<=> ! [V_N: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_K_H: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_nat),V_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
^ [V_N: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_K_H: $i,V_evs: $i] :
rewrite(
( ( ~ hBOOL(hAPP(hAPP(c_in(tc_nat),V_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent))) )
<=> ( ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_nat),V_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat))) ) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [V_N: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_K_H: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_nat),V_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent))) )
<=> ! [V_N: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_K_H: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_nat),V_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat))) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,axiom,
! [V_N: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_K_H: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_nat),V_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Says__Server__message__form_0) ).
tff(33,plain,
! [V_N: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_K_H: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_nat),V_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat))) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [V_N: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_K_H: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_nat),V_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat))) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
! [V_N: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_K_H: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_nat),V_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat))) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [V_N: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_K_H: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_nat),V_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat))) ),
inference(modus_ponens,[status(thm)],[35,28]) ).
tff(37,plain,
( ( ~ ! [V_N: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_K_H: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_nat),V_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat))) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),v_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X)))))),c_List_Oset(v_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_nat),v_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat))) )
<=> ( ~ ! [V_N: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_K_H: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_nat),V_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat))) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),v_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X)))))),c_List_Oset(v_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_nat),v_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
( ( ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X)))))),c_List_Oset(v_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),v_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_nat),v_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat))) )
<=> ( ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),v_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X)))))),c_List_Oset(v_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_nat),v_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
( ( ~ ! [V_N: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_K_H: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_nat),V_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat))) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X)))))),c_List_Oset(v_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),v_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_nat),v_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat))) )
<=> ( ~ ! [V_N: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_K_H: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_nat),V_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat))) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),v_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X)))))),c_List_Oset(v_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_nat),v_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat))) ) ),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
( ( ~ ! [V_N: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_K_H: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_nat),V_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat))) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X)))))),c_List_Oset(v_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),v_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_nat),v_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat))) )
<=> ( ~ ! [V_N: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_K_H: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_nat),V_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat))) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),v_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X)))))),c_List_Oset(v_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_nat),v_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat))) ) ),
inference(transitivity,[status(thm)],[39,37]) ).
tff(41,plain,
( ~ ! [V_N: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_K_H: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_nat),V_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat))) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X)))))),c_List_Oset(v_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),v_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_nat),v_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat))) ),
inference(quant_inst,[status(thm)],]) ).
tff(42,plain,
( ~ ! [V_N: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_K_H: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_nat),V_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat))) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),v_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X)))))),c_List_Oset(v_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_nat),v_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat))) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
~ hBOOL(hAPP(hAPP(c_in(tc_nat),v_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat))),
inference(unit_resolution,[status(thm)],[42,36,3,26]) ).
tff(44,plain,
^ [V_N: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_K_H: $i,V_evs: $i] :
refl(
( ( ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) )
<=> ( ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) ) )),
inference(bind,[status(th)],]) ).
tff(45,plain,
( ! [V_N: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_K_H: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) )
<=> ! [V_N: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_K_H: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,plain,
( ! [V_N: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_K_H: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) )
<=> ! [V_N: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_K_H: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(47,plain,
^ [V_N: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_K_H: $i,V_evs: $i] :
trans(
monotonicity(
rewrite(
( ( ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared)) )
<=> ( ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) ) )),
( ( ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent))) )
<=> ( ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent))) ) )),
rewrite(
( ( ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent))) )
<=> ( ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) ) )),
( ( ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent))) )
<=> ( ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) ) )),
inference(bind,[status(th)],]) ).
tff(48,plain,
( ! [V_N: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_K_H: $i,V_evs: $i] :
( ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent))) )
<=> ! [V_N: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_K_H: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,axiom,
! [V_N: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_K_H: $i,V_evs: $i] :
( ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Says__Server__message__form_1) ).
tff(50,plain,
! [V_N: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_K_H: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [V_N: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_K_H: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) ),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
! [V_N: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_K_H: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) ),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [V_N: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_K_H: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) ),
inference(modus_ponens,[status(thm)],[52,45]) ).
tff(54,plain,
( ( ~ ! [V_N: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_K_H: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) )
| ( v_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A))) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),v_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X)))))),c_List_Oset(v_evs,tc_Event_Oevent))) )
<=> ( ~ ! [V_N: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_K_H: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) )
| ( v_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A))) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),v_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X)))))),c_List_Oset(v_evs,tc_Event_Oevent))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(55,plain,
( ( ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X)))))),c_List_Oset(v_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),v_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ( v_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A))) ) )
<=> ( ( v_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A))) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),v_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X)))))),c_List_Oset(v_evs,tc_Event_Oevent))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(56,plain,
( ( ~ ! [V_N: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_K_H: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X)))))),c_List_Oset(v_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),v_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ( v_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A))) ) )
<=> ( ~ ! [V_N: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_K_H: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) )
| ( v_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A))) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),v_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X)))))),c_List_Oset(v_evs,tc_Event_Oevent))) ) ),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
( ( ~ ! [V_N: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_K_H: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X)))))),c_List_Oset(v_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),v_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ( v_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A))) ) )
<=> ( ~ ! [V_N: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_K_H: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) )
| ( v_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A))) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),v_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X)))))),c_List_Oset(v_evs,tc_Event_Oevent))) ) ),
inference(transitivity,[status(thm)],[56,54]) ).
tff(58,plain,
( ~ ! [V_N: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_K_H: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X)))))),c_List_Oset(v_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),v_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ( v_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(59,plain,
( ~ ! [V_N: $i,V_X: $i,V_B: $i,V_A: $i,V_K: $i,V_K_H: $i,V_evs: $i] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OCrypt(V_K_H,c_Message_Omsg_OMPair(V_N,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),V_X)))))),c_List_Oset(V_evs,tc_Event_Oevent)))
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),V_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ( V_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,V_K),c_Message_Omsg_OAgent(V_A))) ) )
| ( v_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A))) )
| ~ hBOOL(hAPP(hAPP(c_in(tc_List_Olist(tc_Event_Oevent)),v_evs),c_NS__Shared__Mirabelle_Ons__shared))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Event_Oevent),c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X)))))),c_List_Oset(v_evs,tc_Event_Oevent))) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
v_X = c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A))),
inference(unit_resolution,[status(thm)],[59,53,3,26]) ).
tff(61,plain,
( ( ( v_X != c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A))) )
| hBOOL(hAPP(hAPP(c_in(tc_nat),v_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat))) )
<=> ( ( v_X != c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A))) )
| hBOOL(hAPP(hAPP(c_in(tc_nat),v_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(62,axiom,
( ( v_X != c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A))) )
| hBOOL(hAPP(hAPP(c_in(tc_nat),v_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(63,plain,
( ( v_X != c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A))) )
| hBOOL(hAPP(hAPP(c_in(tc_nat),v_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat))) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
( ( v_X != c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A))) )
| hBOOL(hAPP(hAPP(c_in(tc_nat),v_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat))) ),
inference(modus_ponens,[status(thm)],[63,61]) ).
tff(65,plain,
( ( v_X != c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A))) )
| hBOOL(hAPP(hAPP(c_in(tc_nat),v_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat))) ),
inference(modus_ponens,[status(thm)],[64,61]) ).
tff(66,plain,
( ( v_X != c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A))) )
| hBOOL(hAPP(hAPP(c_in(tc_nat),v_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat))) ),
inference(modus_ponens,[status(thm)],[65,61]) ).
tff(67,plain,
( ( v_X != c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A))) )
| hBOOL(hAPP(hAPP(c_in(tc_nat),v_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat))) ),
inference(modus_ponens,[status(thm)],[66,61]) ).
tff(68,plain,
( ( v_X != c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A))) )
| hBOOL(hAPP(hAPP(c_in(tc_nat),v_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat))) ),
inference(modus_ponens,[status(thm)],[67,61]) ).
tff(69,plain,
( ( v_X != c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A))) )
| hBOOL(hAPP(hAPP(c_in(tc_nat),v_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat))) ),
inference(modus_ponens,[status(thm)],[68,61]) ).
tff(70,plain,
( ( v_X != c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A))) )
| hBOOL(hAPP(hAPP(c_in(tc_nat),v_K),c_Set_Oimage(c_Public_OshrK,c_Orderings_Otop__class_Otop(tc_fun(tc_Message_Oagent,tc_bool)),tc_Message_Oagent,tc_nat))) ),
inference(modus_ponens,[status(thm)],[69,61]) ).
tff(71,plain,
$false,
inference(unit_resolution,[status(thm)],[70,60,43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : SWV731-1 : TPTP v8.1.0. Released v4.1.0.
% 0.09/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.31 % Computer : n020.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sun Sep 4 07:26:59 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.32 Usage: tptp [options] [-file:]file
% 0.11/0.32 -h, -? prints this message.
% 0.11/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.32 -m, -model generate model.
% 0.11/0.32 -p, -proof generate proof.
% 0.11/0.32 -c, -core generate unsat core of named formulas.
% 0.11/0.32 -st, -statistics display statistics.
% 0.11/0.32 -t:timeout set timeout (in second).
% 0.11/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.32 -<param>:<value> configuration parameter and value.
% 0.11/0.32 -o:<output-file> file to place output in.
% 0.69/0.75 % SZS status Unsatisfiable
% 0.69/0.75 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------