%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV770-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:09:04 AM UTC 2026
% Result : Unsatisfiable 16.06s 2.73s
% Output : CNFRefutation 16.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 40 ( 20 unt; 0 def)
% Number of atoms : 93 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 88 ( 35 ~; 53 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 29 ( 29 usr; 14 con; 0-4 aty)
% Number of variables : 57 ( 10 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_6,axiom,
~ hBOOL(c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)),
file('theBenchmark.p',cls_conjecture_6) ).
cnf(c_95,plain,
~ hBOOL(c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)),
inference(clausify,[status(thm)],[cls_conjecture_6]) ).
fof(cls_conjecture_5,axiom,
hBOOL(c_in(v_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))),
file('theBenchmark.p',cls_conjecture_5) ).
cnf(c_96,plain,
hBOOL(c_in(v_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))),
inference(clausify,[status(thm)],[cls_conjecture_5]) ).
fof(cls_conjecture_4,axiom,
~ hBOOL(c_in(v_B,c_Event_Obad,tc_Message_Oagent)),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(c_97,plain,
~ hBOOL(c_in(v_B,c_Event_Obad,tc_Message_Oagent)),
inference(clausify,[status(thm)],[cls_conjecture_4]) ).
fof(cls_conjecture_3,axiom,
~ hBOOL(c_in(v_A,c_Event_Obad,tc_Message_Oagent)),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_98,plain,
~ hBOOL(c_in(v_A,c_Event_Obad,tc_Message_Oagent)),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
fof(cls_conjecture_2,axiom,
! [VAR_0,VAR_1] : ~ hBOOL(c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(VAR_0,c_Message_Omsg_OMPair(VAR_1,hAPP(c_Message_Omsg_OKey,v_K)))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_99,plain,
~ hBOOL(c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(A,c_Message_Omsg_OMPair(B,hAPP(c_Message_Omsg_OKey,v_K)))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_1,axiom,
hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_100,plain,
hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_0,axiom,
hBOOL(c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_101,plain,
hBOOL(c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_mem__def_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ hBOOL(c_in(VAR_1,VAR_0,VAR_2))
| hBOOL(hAPP(VAR_0,VAR_1)) ),
file('theBenchmark.p',cls_mem__def_0) ).
cnf(c_120,plain,
( ~ hBOOL(c_in(B,A,C))
| hBOOL(hAPP(A,B)) ),
inference(clausify,[status(thm)],[cls_mem__def_0]) ).
fof(cls_mem__def_1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ hBOOL(hAPP(VAR_1,VAR_0))
| hBOOL(c_in(VAR_0,VAR_1,VAR_2)) ),
file('theBenchmark.p',cls_mem__def_1) ).
cnf(c_121,plain,
( ~ hBOOL(hAPP(B,A))
| hBOOL(c_in(A,B,C)) ),
inference(clausify,[status(thm)],[cls_mem__def_1]) ).
fof(cls_B__trusts__NS5__lemma_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( hBOOL(c_in(VAR_1,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(VAR_4,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(hAPP(c_Message_Omsg_OKey,VAR_2),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,VAR_4)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,VAR_0,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,VAR_0),c_Message_Omsg_OMPair(VAR_5,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(VAR_1),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,VAR_2),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,VAR_1),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,VAR_2),c_Message_Omsg_OAgent(VAR_0)))))))),c_List_Oset(VAR_4,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(VAR_2,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(VAR_3),c_Message_Omsg_ONonce(VAR_3))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,VAR_4)),tc_Message_Omsg))
| hBOOL(c_in(c_Event_Oevent_OSays(VAR_0,VAR_1,c_Message_Omsg_OCrypt(VAR_2,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(VAR_3),c_Message_Omsg_ONonce(VAR_3)))),c_List_Oset(VAR_4,tc_Event_Oevent),tc_Event_Oevent)) ),
file('theBenchmark.p',cls_B__trusts__NS5__lemma_0) ).
cnf(c_173,plain,
( hBOOL(c_in(B,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(E,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(hAPP(c_Message_Omsg_OKey,C),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,E)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,A),c_Message_Omsg_OMPair(F,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,C),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,C),c_Message_Omsg_OAgent(A)))))))),c_List_Oset(E,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Message_Omsg_OCrypt(C,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(D),c_Message_Omsg_ONonce(D))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,E)),tc_Message_Omsg))
| hBOOL(c_in(c_Event_Oevent_OSays(A,B,c_Message_Omsg_OCrypt(C,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(D),c_Message_Omsg_ONonce(D)))),c_List_Oset(E,tc_Event_Oevent),tc_Event_Oevent)) ),
inference(clausify,[status(thm)],[cls_B__trusts__NS5__lemma_0]) ).
fof(cls_B__trusts__NS3_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,VAR_1),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,VAR_2),c_Message_Omsg_OAgent(VAR_0))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,VAR_3)),tc_Message_Omsg))
| hBOOL(c_in(VAR_1,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(VAR_3,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,VAR_0,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,VAR_0),c_Message_Omsg_OMPair(v_sko__NS__Shared__Mirabelle__XB__trusts__NS3__1(VAR_0,VAR_1,VAR_2,VAR_3),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(VAR_1),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,VAR_2),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,VAR_1),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,VAR_2),c_Message_Omsg_OAgent(VAR_0)))))))),c_List_Oset(VAR_3,tc_Event_Oevent),tc_Event_Oevent)) ),
file('theBenchmark.p',cls_B__trusts__NS3_0) ).
cnf(c_174,plain,
( ~ hBOOL(c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,C),c_Message_Omsg_OAgent(A))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,D)),tc_Message_Omsg))
| hBOOL(c_in(B,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(D,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,A),c_Message_Omsg_OMPair(v_sko__NS__Shared__Mirabelle__XB__trusts__NS3__1(A,B,C,D),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,C),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,C),c_Message_Omsg_OAgent(A)))))))),c_List_Oset(D,tc_Event_Oevent),tc_Event_Oevent)) ),
inference(clausify,[status(thm)],[cls_B__trusts__NS3_0]) ).
fof(cls_Spy__not__see__encrypted__key_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] :
( ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,VAR_3,c_Message_Omsg_OCrypt(VAR_5,c_Message_Omsg_OMPair(VAR_4,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(VAR_2),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,VAR_0),VAR_6))))),c_List_Oset(VAR_1,tc_Event_Oevent),tc_Event_Oevent))
| hBOOL(c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(VAR_4,c_Message_Omsg_OMPair(v_sko__NS__Shared__Mirabelle__XSpy__not__see__encrypted__key__1(VAR_0,VAR_4,VAR_1),hAPP(c_Message_Omsg_OKey,VAR_0)))),c_List_Oset(VAR_1,tc_Event_Oevent),tc_Event_Oevent))
| hBOOL(c_in(VAR_3,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(VAR_2,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(VAR_1,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(hAPP(c_Message_Omsg_OKey,VAR_0),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,VAR_1)),tc_Message_Omsg)) ),
file('theBenchmark.p',cls_Spy__not__see__encrypted__key_0) ).
cnf(c_183,plain,
( ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,D,c_Message_Omsg_OCrypt(F,c_Message_Omsg_OMPair(E,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(C),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,A),V6))))),c_List_Oset(B,tc_Event_Oevent),tc_Event_Oevent))
| hBOOL(c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(E,c_Message_Omsg_OMPair(v_sko__NS__Shared__Mirabelle__XSpy__not__see__encrypted__key__1(A,E,B),hAPP(c_Message_Omsg_OKey,A)))),c_List_Oset(B,tc_Event_Oevent),tc_Event_Oevent))
| hBOOL(c_in(D,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(C,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(B,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(hAPP(c_Message_Omsg_OKey,A),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,B)),tc_Message_Omsg)) ),
inference(clausify,[status(thm)],[cls_Spy__not__see__encrypted__key_0]) ).
cnf(c_876,plain,
hBOOL(hAPP(c_NS__Shared__Mirabelle_Ons__shared,v_evs)),
inference(resolve,[status(thm)],[c_120,c_96]) ).
cnf(c_6227,plain,
( hBOOL(c_in(B,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(v_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,A),c_Message_Omsg_OMPair(C,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(A)))))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent))
| hBOOL(c_in(c_Event_Oevent_OSays(A,B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)) ),
inference(resolve,[status(thm)],[c_173,c_101]) ).
cnf(c_899,plain,
( hBOOL(c_in(B,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,A),c_Message_Omsg_OMPair(C,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(A)))))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent))
| hBOOL(c_in(c_Event_Oevent_OSays(A,B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)) ),
inference(resolve,[status(thm)],[c_96,c_6227]) ).
cnf(c_6228,plain,
( hBOOL(c_in(v_B,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(v_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| hBOOL(c_in(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_sko__NS__Shared__Mirabelle__XB__trusts__NS3__1(v_A,v_B,v_K,v_evs),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)) ),
inference(resolve,[status(thm)],[c_174,c_100]) ).
cnf(c_6229,plain,
( hBOOL(c_in(v_B,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(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_sko__NS__Shared__Mirabelle__XB__trusts__NS3__1(v_A,v_B,v_K,v_evs),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)) ),
inference(resolve,[status(thm)],[c_96,c_6228]) ).
cnf(c_902,plain,
hBOOL(c_in(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_sko__NS__Shared__Mirabelle__XB__trusts__NS3__1(v_A,v_B,v_K,v_evs),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)),
inference(resolve,[status(thm)],[c_97,c_6229]) ).
cnf(c_3477,plain,
hBOOL(c_in(v_evs,c_NS__Shared__Mirabelle_Ons__shared,A)),
inference(resolve,[status(thm)],[c_876,c_121]) ).
cnf(c_6230,plain,
( hBOOL(c_in(v_B,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg))
| hBOOL(c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)) ),
inference(resolve,[status(thm)],[c_902,c_899]) ).
cnf(c_6231,plain,
( hBOOL(c_in(v_B,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)) ),
inference(resolve,[status(thm)],[c_95,c_6230]) ).
cnf(c_6210,plain,
hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)),
inference(resolve,[status(thm)],[c_97,c_6231]) ).
cnf(c_6232,plain,
( hBOOL(c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(v_sko__NS__Shared__Mirabelle__XB__trusts__NS3__1(v_A,v_B,v_K,v_evs),c_Message_Omsg_OMPair(v_sko__NS__Shared__Mirabelle__XSpy__not__see__encrypted__key__1(v_K,v_sko__NS__Shared__Mirabelle__XB__trusts__NS3__1(v_A,v_B,v_K,v_evs),v_evs),hAPP(c_Message_Omsg_OKey,v_K)))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent))
| hBOOL(c_in(v_A,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(v_B,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(v_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)) ),
inference(resolve,[status(thm)],[c_902,c_183]) ).
cnf(c_6233,plain,
( hBOOL(c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(v_sko__NS__Shared__Mirabelle__XB__trusts__NS3__1(v_A,v_B,v_K,v_evs),c_Message_Omsg_OMPair(v_sko__NS__Shared__Mirabelle__XSpy__not__see__encrypted__key__1(v_K,v_sko__NS__Shared__Mirabelle__XB__trusts__NS3__1(v_A,v_B,v_K,v_evs),v_evs),hAPP(c_Message_Omsg_OKey,v_K)))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent))
| hBOOL(c_in(v_A,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(v_B,c_Event_Obad,tc_Message_Oagent))
| ~ hBOOL(c_in(v_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))) ),
inference(resolve,[status(thm)],[c_6210,c_6232]) ).
cnf(c_6234,plain,
( hBOOL(c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(v_sko__NS__Shared__Mirabelle__XB__trusts__NS3__1(v_A,v_B,v_K,v_evs),c_Message_Omsg_OMPair(v_sko__NS__Shared__Mirabelle__XSpy__not__see__encrypted__key__1(v_K,v_sko__NS__Shared__Mirabelle__XB__trusts__NS3__1(v_A,v_B,v_K,v_evs),v_evs),hAPP(c_Message_Omsg_OKey,v_K)))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent))
| hBOOL(c_in(v_A,c_Event_Obad,tc_Message_Oagent))
| hBOOL(c_in(v_B,c_Event_Obad,tc_Message_Oagent)) ),
inference(resolve,[status(thm)],[c_3477,c_6233]) ).
cnf(c_6235,plain,
( hBOOL(c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(v_sko__NS__Shared__Mirabelle__XB__trusts__NS3__1(v_A,v_B,v_K,v_evs),c_Message_Omsg_OMPair(v_sko__NS__Shared__Mirabelle__XSpy__not__see__encrypted__key__1(v_K,v_sko__NS__Shared__Mirabelle__XB__trusts__NS3__1(v_A,v_B,v_K,v_evs),v_evs),hAPP(c_Message_Omsg_OKey,v_K)))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent))
| hBOOL(c_in(v_A,c_Event_Obad,tc_Message_Oagent)) ),
inference(resolve,[status(thm)],[c_97,c_6234]) ).
cnf(c_6236,plain,
hBOOL(c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(v_sko__NS__Shared__Mirabelle__XB__trusts__NS3__1(v_A,v_B,v_K,v_evs),c_Message_Omsg_OMPair(v_sko__NS__Shared__Mirabelle__XSpy__not__see__encrypted__key__1(v_K,v_sko__NS__Shared__Mirabelle__XB__trusts__NS3__1(v_A,v_B,v_K,v_evs),v_evs),hAPP(c_Message_Omsg_OKey,v_K)))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)),
inference(resolve,[status(thm)],[c_98,c_6235]) ).
cnf(c_6226,plain,
$false,
inference(resolve,[status(thm)],[c_99,c_6236]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV770-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n007.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 14:53:25 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 3999913 was started by sandbox2 on n007,
% 0.10/0.36 % Sat Sep 26 14:53:25 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 16.06/2.73
% 16.06/2.73 % given #500 (I,wt=23): 753 c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_OSays(A,B,C),D,tc_Event_Oevent)) = c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)),c_Event_Oused(D),tc_fun(tc_Message_Omsg,tc_bool)) # tptp_name(cls_used__Says_0) # clausal_fof(1). [assumption].
% 16.06/2.73
% 16.06/2.73 % given #1000 (T,wt=8): 3995 c_Set_Oinsert(v_evs,c_Message_Oanalz(c_NS__Shared__Mirabelle_Ons__shared),A) = c_Message_Oanalz(c_NS__Shared__Mirabelle_Ons__shared). [resolve(3817,a,508,b)].
% 16.06/2.73
% 16.06/2.73 % SZS status Unsatisfiable for theBenchmark
% 16.06/2.73
% 16.06/2.73 % Proof 1 at 1.86 (+ 0.42) seconds.
% 16.06/2.73 % Length of proof is 18.
% 16.06/2.73 % Level of proof is 3.
% 16.06/2.73 % Maximum clause weight is 83.000.
% 16.06/2.73 % Given clauses 1200.
% 16.06/2.73
% 16.06/2.73 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------