%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV802-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 09:09:08 AM UTC 2026
% Result : Unsatisfiable 6.36s 1.26s
% Output : CNFRefutation 6.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 21 ( 14 unt; 0 def)
% Number of atoms : 30 ( 3 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 13 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 28 ( 28 usr; 18 con; 0-3 aty)
% Number of variables : 20 ( 6 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_parts__cut__eq_0,axiom,
! [VAR_0,VAR_1] :
( ~ c_in(VAR_0,c_Message_Oparts(VAR_1),tc_Message_Omsg)
| c_Message_Oparts(c_Set_Oinsert(VAR_0,VAR_1,tc_Message_Omsg)) = c_Message_Oparts(VAR_1) ),
file('theBenchmark.p',cls_parts__cut__eq_0) ).
cnf(c_546,plain,
( ~ c_in(A,c_Message_Oparts(B),tc_Message_Omsg)
| c_Message_Oparts(c_Set_Oinsert(A,B,tc_Message_Omsg)) = c_Message_Oparts(B) ),
inference(clausify,[status(thm)],[cls_parts__cut__eq_0]) ).
fof(cls_NS3__msg__in__parts__spies_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7] :
( ~ c_in(c_Event_Oevent_OSays(VAR_2,VAR_3,c_Message_Omsg_OCrypt(VAR_4,c_Message_Omsg_OMPair(VAR_5,c_Message_Omsg_OMPair(VAR_6,c_Message_Omsg_OMPair(VAR_7,VAR_0))))),c_List_Oset(VAR_1,tc_Event_Oevent),tc_Event_Oevent)
| c_in(VAR_0,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,VAR_1)),tc_Message_Omsg) ),
file('theBenchmark.p',cls_NS3__msg__in__parts__spies_0) ).
cnf(c_547,plain,
( ~ c_in(c_Event_Oevent_OSays(C,D,c_Message_Omsg_OCrypt(E,c_Message_Omsg_OMPair(F,c_Message_Omsg_OMPair(V6,c_Message_Omsg_OMPair(V7,A))))),c_List_Oset(B,tc_Event_Oevent),tc_Event_Oevent)
| c_in(A,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,B)),tc_Message_Omsg) ),
inference(clausify,[status(thm)],[cls_NS3__msg__in__parts__spies_0]) ).
fof(cls_conjecture_4,axiom,
c_in(c_Event_Oevent_OSays(v_S,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_Xa))))),c_List_Oset(v_evs3,tc_Event_Oevent),tc_Event_Oevent),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(c_642,plain,
c_in(c_Event_Oevent_OSays(v_S,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),v_Xa))))),c_List_Oset(v_evs3,tc_Event_Oevent),tc_Event_Oevent),
inference(clausify,[status(thm)],[cls_conjecture_4]) ).
fof(cls_conjecture_7,axiom,
c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X)))),c_Message_Oparts(c_Set_Oinsert(v_Xa,c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3),tc_Message_Omsg)),tc_Message_Omsg),
file('theBenchmark.p',cls_conjecture_7) ).
cnf(c_645,plain,
c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X)))),c_Message_Oparts(c_Set_Oinsert(v_Xa,c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3),tc_Message_Omsg)),tc_Message_Omsg),
inference(clausify,[status(thm)],[cls_conjecture_7]) ).
fof(cls_conjecture_8,axiom,
c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Set_Oinsert(v_Xa,c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3),tc_Message_Omsg)),tc_Message_Omsg),
file('theBenchmark.p',cls_conjecture_8) ).
cnf(c_646,plain,
c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Set_Oinsert(v_Xa,c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3),tc_Message_Omsg)),tc_Message_Omsg),
inference(clausify,[status(thm)],[cls_conjecture_8]) ).
fof(cls_conjecture_9,axiom,
~ 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_evs3,tc_Event_Oevent),tc_Event_Oevent),
file('theBenchmark.p',cls_conjecture_9) ).
cnf(c_647,plain,
~ c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evs3,tc_Event_Oevent),tc_Event_Oevent),
inference(clausify,[status(thm)],[cls_conjecture_9]) ).
fof(cls_conjecture_10,axiom,
( ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
| c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evs3,tc_Event_Oevent),tc_Event_Oevent) ),
file('theBenchmark.p',cls_conjecture_10) ).
cnf(c_648,plain,
( ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
| c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB)))),c_List_Oset(v_evs3,tc_Event_Oevent),tc_Event_Oevent) ),
inference(clausify,[status(thm)],[cls_conjecture_10]) ).
cnf(c_649,plain,
( ~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
inference(resolve,[status(thm)],[c_647,c_648]) ).
cnf(c_2037,plain,
c_in(v_Xa,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_642,c_547]) ).
cnf(c_3932,plain,
c_Message_Oparts(c_Set_Oinsert(v_Xa,c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3),tc_Message_Omsg)) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),
inference(resolve,[status(thm)],[c_2037,c_546]) ).
cnf(c_3975,plain,
c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg),
inference(paramod,[status(thm)],[c_3932,c_646]) ).
cnf(c_3976,plain,
c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg),
inference(paramod,[status(thm)],[c_3932,c_645]) ).
cnf(c_3978,plain,
~ c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_3975,c_649]) ).
cnf(c_3977,plain,
$false,
inference(resolve,[status(thm)],[c_3976,c_3978]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV802-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n005.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 14:58:46 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 2408863 was started by sandbox on n005,
% 0.09/0.36 % Sat Sep 26 14:58:46 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.38
% 0.13/0.38 % From the command line: assign(max_seconds, 300).
% 6.36/1.26
% 6.36/1.26 % given #500 (I,wt=98): 730 c_in(c_Event_Oevent_OSays(A,A,c_Message_Omsg_OCrypt(B,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(C),c_Message_Omsg_ONonce(C)))),c_List_Oset(D,tc_Event_Oevent),tc_Event_Oevent) | -c_in(D,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)) | c_in(A,c_Event_Obad,tc_Message_Oagent) | c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(v_sko__NS__Shared__Mirabelle__XB__trusts__NS5__1(B,D),c_Message_Omsg_OMPair(v_sko__NS__Shared__Mirabelle__XB__trusts__NS5__2(B,D),hAPP(c_Message_Omsg_OKey,B)))),c_List_Oset(D,tc_Event_Oevent),tc_Event_Oevent) | -c_in(c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,A),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,B),c_Message_Omsg_OAgent(A))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,D)),tc_Message_Omsg) | -c_in(c_Message_Omsg_OCrypt(B,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(C),c_Message_Omsg_ONonce(C))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,D)),tc_Message_Omsg). [factor(505,c,d)].
% 6.36/1.26
% 6.36/1.26 % SZS status Unsatisfiable for theBenchmark
% 6.36/1.26
% 6.36/1.26 % Proof 1 at 0.63 (+ 0.15) seconds.
% 6.36/1.26 % Length of proof is 13.
% 6.36/1.26 % Level of proof is 4.
% 6.36/1.26 % Maximum clause weight is 68.000.
% 6.36/1.26 % Given clauses 778.
% 6.36/1.26
% 6.36/1.26 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------