%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV314-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:32:05 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 18
% Syntax : Number of formulae : 32 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 258 ( 0 equ)
% Maximal formula atoms : 24 ( 8 avg)
% Number of connectives : 345 ( 139 ~; 185 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 20 ( 20 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 13 con; 0-3 aty)
% Number of variables : 102 ( 90 !; 0 ?; 102 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(tc_List_Olist_type,type,
tc_List_Olist: $i > $i ).
tff(tc_Event_Oevent_type,type,
tc_Event_Oevent: $i ).
tff(c_OtwayRees_Ootway_type,type,
c_OtwayRees_Ootway: $i ).
tff(c_List_Oset_type,type,
c_List_Oset: ( $i * $i ) > $i ).
tff(c_Event_Oevent_OSays_type,type,
c_Event_Oevent_OSays: ( $i * $i * $i ) > $i ).
tff(c_Message_Omsg_OMPair_type,type,
c_Message_Omsg_OMPair: ( $i * $i ) > $i ).
tff(c_Message_Omsg_OCrypt_type,type,
c_Message_Omsg_OCrypt: ( $i * $i ) > $i ).
tff(c_Message_Omsg_OKey_type,type,
c_Message_Omsg_OKey: $i > $i ).
tff(c_Public_OshrK_type,type,
c_Public_OshrK: $i > $i ).
tff(c_Message_Oagent_OServer_type,type,
c_Message_Oagent_OServer: $i ).
tff(tc_Message_Omsg_type,type,
tc_Message_Omsg: $i ).
tff(c_Message_Oanalz_type,type,
c_Message_Oanalz: $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_Oagent_type,type,
tc_Message_Oagent: $i ).
tff(c_Event_Obad_type,type,
c_Event_Obad: $i ).
tff(c_Event_Oevent_ONotes_type,type,
c_Event_Oevent_ONotes: ( $i * $i ) > $i ).
tff(v_evs_type,type,
v_evs: $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(v_NB_type,type,
v_NB: $i ).
tff(v_NA_type,type,
v_NA: $i ).
tff(1,plain,
^ [V_NA: $i,V_NB: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
refl(( ( c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),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(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(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) )
<=> ( c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),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(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(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [V_NA: $i,V_NB: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),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(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(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) )
<=> ! [V_NA: $i,V_NB: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),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(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(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_NA: $i,V_NB: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),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(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(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) )
<=> ! [V_NA: $i,V_NB: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),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(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(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
^ [V_NA: $i,V_NB: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(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_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ) )),
( ( ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| c_in(V_B,c_Event_Obad,tc_Message_Oagent) )
<=> ( ~ c_in(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(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent))
| c_in(V_B,c_Event_Obad,tc_Message_Oagent) ) )),
rewrite(( ( ~ c_in(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(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_OtwayRees_Ootway,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(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(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ) )),
( ( ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| c_in(V_B,c_Event_Obad,tc_Message_Oagent) )
<=> ( c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(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(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ) )),
( ( ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| 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(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(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(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(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(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(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(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(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ) )),
( ( ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| 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(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(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ) )),
( ( ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),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(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(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ) )),
rewrite(( ( c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(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(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) )
<=> ( c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),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(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(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ) )),
( ( ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) )
<=> ( c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),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(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(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [V_NA: $i,V_NB: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) )
<=> ! [V_NA: $i,V_NB: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),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(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(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [V_NA: $i,V_NB: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Message_Omsg_OKey(V_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| c_in(V_B,c_Event_Obad,tc_Message_Oagent)
| c_in(V_A,c_Event_Obad,tc_Message_Oagent)
| c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OtwayRees_Osecrecy__lemma__dest_0) ).
tff(7,plain,
! [V_NA: $i,V_NB: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),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(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(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [V_NA: $i,V_NB: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),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(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(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [V_NA: $i,V_NB: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),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(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(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [V_NA: $i,V_NB: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),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(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(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( c_in(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_OKey(v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
c_in(c_Message_Omsg_OKey(v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
tff(13,plain,
c_in(c_Message_Omsg_OKey(v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( c_in(v_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent))
<=> c_in(v_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
c_in(v_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
tff(16,plain,
c_in(v_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,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(18,axiom,
~ c_in(v_B,c_Event_Obad,tc_Message_Oagent),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(19,plain,
~ c_in(v_B,c_Event_Obad,tc_Message_Oagent),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,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(21,axiom,
~ c_in(v_A,c_Event_Obad,tc_Message_Oagent),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(22,plain,
~ c_in(v_A,c_Event_Obad,tc_Message_Oagent),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
( ~ c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_NB,c_Message_Omsg_OKey(v_K)))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)
<=> ~ c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_NB,c_Message_Omsg_OKey(v_K)))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
~ c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_NB,c_Message_Omsg_OKey(v_K)))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(25,plain,
~ c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_NB,c_Message_Omsg_OKey(v_K)))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
( c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_B,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OKey(v_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(v_NB,c_Message_Omsg_OKey(v_K)))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)
<=> c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_B,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OKey(v_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(v_NB,c_Message_Omsg_OKey(v_K)))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,axiom,
c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_B,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OKey(v_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(v_NB,c_Message_Omsg_OKey(v_K)))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(28,plain,
c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_B,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OKey(v_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(v_NB,c_Message_Omsg_OKey(v_K)))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
( ( ~ ! [V_NA: $i,V_NB: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),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(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(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) )
| c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_NB,c_Message_Omsg_OKey(v_K)))),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(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(c_Message_Oagent_OServer,v_B,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OKey(v_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(v_NB,c_Message_Omsg_OKey(v_K)))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(v_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) )
<=> ( ~ ! [V_NA: $i,V_NB: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),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(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(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) )
| c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_NB,c_Message_Omsg_OKey(v_K)))),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(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(c_Message_Oagent_OServer,v_B,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OKey(v_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(v_NB,c_Message_Omsg_OKey(v_K)))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(v_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,plain,
( ~ ! [V_NA: $i,V_NB: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),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(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(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) )
| c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_NB,c_Message_Omsg_OKey(v_K)))),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(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(c_Message_Oagent_OServer,v_B,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OKey(v_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(v_NB,c_Message_Omsg_OKey(v_K)))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(v_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(31,plain,
( ~ ! [V_NA: $i,V_NB: $i,V_B: $i,V_A: $i,V_K: $i,V_evs: $i] :
( c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))),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(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(c_Message_Oagent_OServer,V_B,c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(V_NA,c_Message_Omsg_OKey(V_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B),c_Message_Omsg_OMPair(V_NB,c_Message_Omsg_OKey(V_K)))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) )
| c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_NB,c_Message_Omsg_OKey(v_K)))),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(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(c_Message_Oagent_OServer,v_B,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OKey(v_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(v_NB,c_Message_Omsg_OKey(v_K)))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(v_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
$false,
inference(unit_resolution,[status(thm)],[31,28,25,22,19,16,13,10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWV314-2 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n006.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 : Fri Jun 20 09:40:35 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.20/0.38 % SZS status Unsatisfiable
% 0.20/0.38 % SZS output start Proof
% See solution above
% 0.20/0.40 % E exiting
%------------------------------------------------------------------------------