%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV354-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 09:07:31 AM UTC 2026
% Result : Unsatisfiable 0.16s 5.40s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 45 ( 18 unt; 0 def)
% Number of atoms : 111 ( 46 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 125 ( 59 ~; 66 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 30 ( 30 usr; 16 con; 0-3 aty)
% Number of variables : 117 ( 51 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_Yahalom_Osingle__Nonce__secrecy_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7] :
( VAR_3 = c_Public_OshrK(v_sko__2VY(VAR_3))
| VAR_7 = VAR_5
| c_in(c_Message_Omsg_ONonce(VAR_7),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,VAR_0)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_ONonce(VAR_7),c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(VAR_3),c_Event_Oknows(c_Message_Oagent_OSpy,VAR_0),tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,VAR_1,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(VAR_1),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(VAR_2),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(VAR_3),c_Message_Omsg_OMPair(VAR_4,c_Message_Omsg_ONonce(VAR_5))))),VAR_6)),c_List_Oset(VAR_0,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(VAR_0,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
file('theBenchmark.p',cls_Yahalom_Osingle__Nonce__secrecy_0) ).
cnf(c_1,plain,
( D = c_Public_OshrK(v_sko__2VY(D))
| V7 = F
| c_in(c_Message_Omsg_ONonce(V7),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,A)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_ONonce(V7),c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(D),c_Event_Oknows(c_Message_Oagent_OSpy,A),tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,B,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(C),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(D),c_Message_Omsg_OMPair(E,c_Message_Omsg_ONonce(F))))),V6)),c_List_Oset(A,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(A,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(clausify,[status(thm)],[cls_Yahalom_Osingle__Nonce__secrecy_0]) ).
cnf(c_2,plain,
( c_Public_OshrK(v_sko__2VY(D)) = D
| V7 = F
| c_in(c_Message_Omsg_ONonce(V7),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,A)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_ONonce(V7),c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(D),c_Event_Oknows(c_Message_Oagent_OSpy,A),tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,B,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(C),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(D),c_Message_Omsg_OMPair(E,c_Message_Omsg_ONonce(F))))),V6)),c_List_Oset(A,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(A,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(copy,[status(thm)],[c_1]) ).
fof(cls_Yahalom_OSays__Server__imp__YM2_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] :
( c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(VAR_2),c_Message_Omsg_OCrypt(c_Public_OshrK(VAR_2),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(VAR_1),c_Message_Omsg_OMPair(VAR_4,VAR_5))))),c_List_Oset(VAR_0,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,VAR_1,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(VAR_1),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(VAR_2),c_Message_Omsg_OMPair(VAR_3,c_Message_Omsg_OMPair(VAR_4,VAR_5)))),VAR_6)),c_List_Oset(VAR_0,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(VAR_0,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
file('theBenchmark.p',cls_Yahalom_OSays__Server__imp__YM2_0) ).
cnf(c_3,plain,
( c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(C),c_Message_Omsg_OCrypt(c_Public_OshrK(C),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(B),c_Message_Omsg_OMPair(E,F))))),c_List_Oset(A,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,B,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(C),c_Message_Omsg_OMPair(D,c_Message_Omsg_OMPair(E,F)))),V6)),c_List_Oset(A,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(A,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(clausify,[status(thm)],[cls_Yahalom_OSays__Server__imp__YM2_0]) ).
fof(cls_Yahalom_OSays__unique__NB_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7,VAR_8,VAR_9,VAR_10,VAR_11,VAR_12] :
( VAR_5 = VAR_12
| c_in(VAR_6,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,VAR_0)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(VAR_7,VAR_8,c_Message_Omsg_OMPair(VAR_9,c_Message_Omsg_OCrypt(c_Public_OshrK(VAR_10),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(VAR_11),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(VAR_12),VAR_6))))),c_List_Oset(VAR_0,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OGets(VAR_1,c_Message_Omsg_OMPair(VAR_2,c_Message_Omsg_OCrypt(c_Public_OshrK(VAR_3),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(VAR_4),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(VAR_5),VAR_6))))),c_List_Oset(VAR_0,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(VAR_0,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
file('theBenchmark.p',cls_Yahalom_OSays__unique__NB_0) ).
cnf(c_4,plain,
( F = V12
| c_in(V6,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,A)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(V7,V8,c_Message_Omsg_OMPair(V9,c_Message_Omsg_OCrypt(c_Public_OshrK(V10),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V11),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V12),V6))))),c_List_Oset(A,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OGets(B,c_Message_Omsg_OMPair(C,c_Message_Omsg_OCrypt(c_Public_OshrK(D),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(E),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(F),V6))))),c_List_Oset(A,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(A,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(clausify,[status(thm)],[cls_Yahalom_OSays__unique__NB_0]) ).
fof(cls_Yahalom_OSays__Server__not__shrK_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] :
( ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,VAR_1,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(VAR_1),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(VAR_2),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(c_Public_OshrK(VAR_3)),c_Message_Omsg_OMPair(VAR_4,VAR_5)))),VAR_6)),c_List_Oset(VAR_0,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(VAR_0,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
file('theBenchmark.p',cls_Yahalom_OSays__Server__not__shrK_0) ).
cnf(c_5,plain,
( ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,B,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(C),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(c_Public_OshrK(D)),c_Message_Omsg_OMPair(E,F)))),V6)),c_List_Oset(A,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(A,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(clausify,[status(thm)],[cls_Yahalom_OSays__Server__not__shrK_0]) ).
fof(cls_conjecture_2,axiom,
c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_6,plain,
c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_3,axiom,
c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_ONonce(v_NBa))))),v_X)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_7,plain,
c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_ONonce(v_NBa))))),v_X)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
fof(cls_conjecture_5,axiom,
c_in(c_Event_Oevent_OSays(v_B,c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent),
file('theBenchmark.p',cls_conjecture_5) ).
cnf(c_8,plain,
c_in(c_Event_Oevent_OSays(v_B,c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent),
inference(clausify,[status(thm)],[cls_conjecture_5]) ).
fof(cls_conjecture_6,axiom,
~ c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg),
file('theBenchmark.p',cls_conjecture_6) ).
cnf(c_9,plain,
~ c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg),
inference(clausify,[status(thm)],[cls_conjecture_6]) ).
fof(cls_conjecture_7,axiom,
c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(v_K),c_Event_Oknows(c_Message_Oagent_OSpy,v_evso),tc_Message_Omsg)),tc_Message_Omsg),
file('theBenchmark.p',cls_conjecture_7) ).
cnf(c_10,plain,
c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(v_K),c_Event_Oknows(c_Message_Oagent_OSpy,v_evso),tc_Message_Omsg)),tc_Message_Omsg),
inference(clausify,[status(thm)],[cls_conjecture_7]) ).
fof(cls_conjecture_9,axiom,
! [VAR_0] :
( v_NB != v_NBa
| v_NA != v_NAa
| VAR_0 != c_Message_Omsg_OKey(v_K) ),
file('theBenchmark.p',cls_conjecture_9) ).
cnf(c_11,plain,
( v_NB != v_NBa
| v_NA != v_NAa
| A != c_Message_Omsg_OKey(v_K) ),
inference(clausify,[status(thm)],[cls_conjecture_9]) ).
cnf(c_49,plain,
( v_NB != v_NBa
| v_NA != v_NAa
| c_Message_Omsg_OKey(v_K) != A ),
inference(copy,[status(thm)],[c_11]) ).
cnf(c_50,plain,
( v_NB != v_NBa
| v_NAa != v_NA
| c_Message_Omsg_OKey(v_K) != A ),
inference(copy,[status(thm)],[c_49]) ).
cnf(c_51,plain,
( v_NBa != v_NB
| v_NAa != v_NA
| c_Message_Omsg_OKey(v_K) != A ),
inference(copy,[status(thm)],[c_50]) ).
cnf(c_12,plain,
( v_NBa != v_NB
| v_NAa != v_NA ),
inference(copy,[status(thm)],[c_51]) ).
cnf(c_14,plain,
~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(B),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(c_Public_OshrK(C)),c_Message_Omsg_OMPair(D,E)))),F)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_52,plain,
( c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_ONonce(v_NBa)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(resolve,[status(thm)],[c_7,c_3]) ).
cnf(c_19,plain,
c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_ONonce(v_NBa)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent),
inference(resolve,[status(thm)],[c_6,c_52]) ).
cnf(c_53,plain,
( c_Public_OshrK(v_sko__2VY(v_K)) = v_K
| A = v_NBa
| c_in(c_Message_Omsg_ONonce(A),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_ONonce(A),c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(v_K),c_Event_Oknows(c_Message_Oagent_OSpy,v_evso),tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(resolve,[status(thm)],[c_7,c_2]) ).
cnf(c_54,plain,
( c_Public_OshrK(v_sko__2VY(v_K)) = v_K
| v_NBa = A
| c_in(c_Message_Omsg_ONonce(A),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_ONonce(A),c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(v_K),c_Event_Oknows(c_Message_Oagent_OSpy,v_evso),tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(copy,[status(thm)],[c_53]) ).
cnf(c_20,plain,
( c_Public_OshrK(v_sko__2VY(v_K)) = v_K
| v_NBa = A
| c_in(c_Message_Omsg_ONonce(A),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_ONonce(A),c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(v_K),c_Event_Oknows(c_Message_Oagent_OSpy,v_evso),tc_Message_Omsg)),tc_Message_Omsg) ),
inference(resolve,[status(thm)],[c_6,c_54]) ).
cnf(c_55,plain,
( E = v_NA
| c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(A,c_Message_Omsg_OMPair(B,c_Message_Omsg_OCrypt(c_Public_OshrK(C),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(D),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(E),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(resolve,[status(thm)],[c_8,c_4]) ).
cnf(c_56,plain,
( v_NA = E
| c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(A,c_Message_Omsg_OMPair(B,c_Message_Omsg_OCrypt(c_Public_OshrK(C),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(D),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(E),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(copy,[status(thm)],[c_55]) ).
cnf(c_57,plain,
( v_NA = E
| c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(A,c_Message_Omsg_OMPair(B,c_Message_Omsg_OCrypt(c_Public_OshrK(C),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(D),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(E),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ),
inference(resolve,[status(thm)],[c_6,c_56]) ).
cnf(c_21,plain,
( v_NA = E
| ~ c_in(c_Event_Oevent_OGets(A,c_Message_Omsg_OMPair(B,c_Message_Omsg_OCrypt(c_Public_OshrK(C),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(D),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(E),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ),
inference(resolve,[status(thm)],[c_9,c_57]) ).
cnf(c_58,plain,
( c_Public_OshrK(v_sko__2VY(v_K)) = v_K
| v_NBa = v_NB
| c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg) ),
inference(resolve,[status(thm)],[c_20,c_10]) ).
cnf(c_24,plain,
( c_Public_OshrK(v_sko__2VY(v_K)) = v_K
| v_NBa = v_NB ),
inference(resolve,[status(thm)],[c_9,c_58]) ).
cnf(c_33,plain,
( ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(B),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(C,D)))),E)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| v_NBa = v_NB ),
inference(paramod,[status(thm)],[c_24,c_14]) ).
cnf(c_42,plain,
v_NBa = v_NB,
inference(resolve,[status(thm)],[c_33,c_7]) ).
cnf(c_45,plain,
c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent),
inference(paramod,[status(thm)],[c_42,c_19]) ).
cnf(c_59,plain,
( v_NB != v_NB
| v_NAa != v_NA ),
inference(paramod,[status(thm)],[c_42,c_12]) ).
cnf(c_46,plain,
v_NAa != v_NA,
inference(copy,[status(thm)],[c_59]) ).
cnf(c_60,plain,
v_NA = v_NAa,
inference(resolve,[status(thm)],[c_45,c_21]) ).
cnf(c_61,plain,
v_NAa = v_NA,
inference(copy,[status(thm)],[c_60]) ).
cnf(c_48,plain,
$false,
inference(resolve,[status(thm)],[c_46,c_61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV354-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.38 % Computer : n005.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Sat Sep 26 13:36:22 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.39 % Process 2282030 was started by sandbox2 on n005,
% 0.11/5.39 % Sat Sep 26 13:36:22 2026
% 0.11/5.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/5.39
% 0.11/5.39 % From the command line: assign(max_seconds, 300).
% 0.16/5.40
% 0.16/5.40 % SZS status Unsatisfiable for theBenchmark
% 0.16/5.40
% 0.16/5.40 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.16/5.40 % Length of proof is 22.
% 0.16/5.40 % Level of proof is 7.
% 0.16/5.40 % Maximum clause weight is 56.000.
% 0.16/5.40 % Given clauses 20.
% 0.16/5.40
% 0.16/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------