%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWV354-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n016.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 : Fri Sep 25 03:13:03 PM UTC 2026
% Result : Unsatisfiable 4.60s 1.07s
% Output : Proof 4.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 56 ( 25 unt; 0 def)
% Number of atoms : 132 ( 44 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 148 ( 72 ~; 76 |; 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 : 187 ( 68 sgn 72 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f2,axiom,
( V_NA_H = V_NA
| c_in(V_nb,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(V_C,V_S,c_Message_Omsg_OMPair(V_X,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),V_nb))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OGets(V_S_H,c_Message_Omsg_OMPair(V_X_H,c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H),V_nb))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Yahalom_OSays__unique__NB_0) ).
fof(f2_nnf,plain,
! [V_evs,V_S_H,V_X_H,V_B_H,V_A_H,V_NA_H,V_nb,V_C,V_S,V_X,V_B,V_A,V_NA] :
( V_NA_H = V_NA
| c_in(V_nb,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(V_C,V_S,c_Message_Omsg_OMPair(V_X,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),V_nb))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OGets(V_S_H,c_Message_Omsg_OMPair(V_X_H,c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H),V_nb))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [V_evs,V_S_H,V_X_H,V_B_H,V_A_H,V_NA_H,V_nb,V_C,V_S,V_X,V_B,V_A,V_NA] :
( V_NA_H = V_NA
| c_in(V_nb,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(V_C,V_S,c_Message_Omsg_OMPair(V_X,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),V_nb))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OGets(V_S_H,c_Message_Omsg_OMPair(V_X_H,c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H),V_nb))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( X5 = X12
| c_in(X6,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X0)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(X7,X8,c_Message_Omsg_OMPair(X9,c_Message_Omsg_OCrypt(c_Public_OshrK(X10),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X11),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(X12),X6))))),c_List_Oset(X0,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OGets(X1,c_Message_Omsg_OMPair(X2,c_Message_Omsg_OCrypt(c_Public_OshrK(X3),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X4),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(X5),X6))))),c_List_Oset(X0,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(X0,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(f4,negated_conjecture,
c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f4_nnf,plain,
c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)),
inference(nnf_transformation,[status(thm)],[f4]) ).
cnf(c4,plain,
c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)),
inference(cnf_transformation,[status(esa)],[f4_nnf]) ).
cnf(p25,plain,
( X4 = X11
| c_in(X5,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(X6,X7,c_Message_Omsg_OMPair(X8,c_Message_Omsg_OCrypt(c_Public_OshrK(X9),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X10),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(X11),X5))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OGets(X0,c_Message_Omsg_OMPair(X1,c_Message_Omsg_OCrypt(c_Public_OshrK(X2),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X3),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(X4),X5))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ),
inference(resolution,[status(thm)],[c2,c4]) ).
cnf(f1,axiom,
( c_in(c_Event_Oevent_OGets(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(V_na,V_nb))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(V_k,c_Message_Omsg_OMPair(V_na,V_nb)))),V_X)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Yahalom_OSays__Server__imp__YM2_0) ).
fof(f1_nnf,plain,
! [V_evs,V_A,V_B,V_k,V_na,V_nb,V_X] :
( c_in(c_Event_Oevent_OGets(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(V_na,V_nb))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(V_k,c_Message_Omsg_OMPair(V_na,V_nb)))),V_X)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [V_evs,V_A,V_B,V_k,V_na,V_nb,V_X] :
( c_in(c_Event_Oevent_OGets(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(V_na,V_nb))))),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(V_k,c_Message_Omsg_OMPair(V_na,V_nb)))),V_X)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X2),c_Message_Omsg_OCrypt(c_Public_OshrK(X2),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X1),c_Message_Omsg_OMPair(X4,X5))))),c_List_Oset(X0,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X1,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X1),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X2),c_Message_Omsg_OMPair(X3,c_Message_Omsg_OMPair(X4,X5)))),X6)),c_List_Oset(X0,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(X0,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p19,plain,
( c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X1),c_Message_Omsg_OCrypt(c_Public_OshrK(X1),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X0),c_Message_Omsg_OMPair(X3,X4))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X0,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X0),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X1),c_Message_Omsg_OMPair(X2,c_Message_Omsg_OMPair(X3,X4)))),X5)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ),
inference(resolution,[status(thm)],[c1,c4]) ).
cnf(f5,negated_conjecture,
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('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f5_nnf,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(nnf_transformation,[status(thm)],[f5]) ).
cnf(c5,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(cnf_transformation,[status(esa)],[f5_nnf]) ).
cnf(p26,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(resolution,[status(thm)],[p19,c5]) ).
cnf(p37,plain,
( v_NAa = X5
| c_in(c_Message_Omsg_ONonce(v_NBa),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(X0,X1,c_Message_Omsg_OMPair(X2,c_Message_Omsg_OCrypt(c_Public_OshrK(X3),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X4),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(X5),c_Message_Omsg_ONonce(v_NBa)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ),
inference(resolution,[status(thm)],[p25,p26]) ).
cnf(f0,axiom,
( V_KAB = c_Public_OshrK(v_sko__2VY(V_KAB))
| V_NB = V_NB_H
| c_in(c_Message_Omsg_ONonce(V_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_ONonce(V_NB),c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB),c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB),c_Message_Omsg_OMPair(V_na,c_Message_Omsg_ONonce(V_NB_H))))),V_X)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Yahalom_Osingle__Nonce__secrecy_0) ).
fof(f0_nnf,plain,
! [V_evs,V_A,V_B,V_KAB,V_na,V_NB_H,V_X,V_NB] :
( V_KAB = c_Public_OshrK(v_sko__2VY(V_KAB))
| V_NB = V_NB_H
| c_in(c_Message_Omsg_ONonce(V_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_ONonce(V_NB),c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB),c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB),c_Message_Omsg_OMPair(V_na,c_Message_Omsg_ONonce(V_NB_H))))),V_X)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [V_evs,V_A,V_B,V_KAB,V_na,V_NB_H,V_X,V_NB] :
( V_KAB = c_Public_OshrK(v_sko__2VY(V_KAB))
| V_NB = V_NB_H
| c_in(c_Message_Omsg_ONonce(V_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_ONonce(V_NB),c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB),c_Event_Oknows(c_Message_Oagent_OSpy,V_evs),tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB),c_Message_Omsg_OMPair(V_na,c_Message_Omsg_ONonce(V_NB_H))))),V_X)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( X3 = c_Public_OshrK(v_sko__2VY(X3))
| X7 = X5
| c_in(c_Message_Omsg_ONonce(X7),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X0)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_ONonce(X7),c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(X3),c_Event_Oknows(c_Message_Oagent_OSpy,X0),tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X1,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X1),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X2),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X3),c_Message_Omsg_OMPair(X4,c_Message_Omsg_ONonce(X5))))),X6)),c_List_Oset(X0,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(X0,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p14,plain,
( X2 = c_Public_OshrK(v_sko__2VY(X2))
| X6 = X4
| c_in(c_Message_Omsg_ONonce(X6),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_ONonce(X6),c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(X2),c_Event_Oknows(c_Message_Oagent_OSpy,v_evso),tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X0,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X0),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X1),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X2),c_Message_Omsg_OMPair(X3,c_Message_Omsg_ONonce(X4))))),X5)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ),
inference(resolution,[status(thm)],[c0,c4]) ).
cnf(p18,plain,
( v_K = c_Public_OshrK(v_sko__2VY(v_K))
| X0 = v_NBa
| c_in(c_Message_Omsg_ONonce(X0),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_ONonce(X0),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(resolution,[status(thm)],[p14,c5]) ).
cnf(f8,negated_conjecture,
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('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_7) ).
fof(f8_nnf,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(nnf_transformation,[status(thm)],[f8]) ).
cnf(c8,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(cnf_transformation,[status(esa)],[f8_nnf]) ).
cnf(p22,plain,
( v_K = c_Public_OshrK(v_sko__2VY(v_K))
| v_NB = v_NBa
| c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg) ),
inference(resolution,[status(thm)],[p18,c8]) ).
cnf(f7,negated_conjecture,
~ c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
fof(f7_nnf,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(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,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(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,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(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p23,plain,
( v_K = c_Public_OshrK(v_sko__2VY(v_K))
| v_NB = v_NBa ),
inference(resolution,[status(thm)],[p22,c7]) ).
cnf(f3,axiom,
( ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(c_Public_OshrK(V_x)),c_Message_Omsg_OMPair(V_na,V_nb)))),V_X)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Yahalom_OSays__Server__not__shrK_0) ).
fof(f3_nnf,plain,
! [V_evs,V_A,V_B,V_x,V_na,V_nb,V_X] :
( ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(c_Public_OshrK(V_x)),c_Message_Omsg_OMPair(V_na,V_nb)))),V_X)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [V_evs,V_A,V_B,V_x,V_na,V_nb,V_X] :
( ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(c_Public_OshrK(V_x)),c_Message_Omsg_OMPair(V_na,V_nb)))),V_X)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X1,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X1),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X2),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(c_Public_OshrK(X3)),c_Message_Omsg_OMPair(X4,X5)))),X6)),c_List_Oset(X0,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(X0,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p28,plain,
~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X0,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X0),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X1),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(c_Public_OshrK(X2)),c_Message_Omsg_OMPair(X3,X4)))),X5)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent),
inference(resolution,[status(thm)],[c3,c4]) ).
cnf(p30,plain,
( ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X0,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X0),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X1),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(X2,X3)))),X4)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| v_NB = v_NBa ),
inference(superposition,[status(thm)],[p23,p28]) ).
cnf(p31,plain,
v_NB = v_NBa,
inference(resolution,[status(thm)],[p30,c5]) ).
cnf(f6,negated_conjecture,
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('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f6_nnf,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(nnf_transformation,[status(thm)],[f6]) ).
cnf(c6,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(cnf_transformation,[status(esa)],[f6_nnf]) ).
cnf(p32,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_NBa)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent),
inference(demodulation,[status(thm)],[p31,c6]) ).
cnf(p38,plain,
( v_NAa = v_NA
| c_in(c_Message_Omsg_ONonce(v_NBa),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg) ),
inference(resolution,[status(thm)],[p37,p32]) ).
cnf(p33,plain,
~ c_in(c_Message_Omsg_ONonce(v_NBa),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg),
inference(demodulation,[status(thm)],[p31,c7]) ).
cnf(p39,plain,
v_NAa = v_NA,
inference(resolution,[status(thm)],[p38,p33]) ).
cnf(f9,negated_conjecture,
( v_NB != v_NBa
| v_NA != v_NAa
| V_U != c_Message_Omsg_OKey(v_K) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_9) ).
fof(f9_nnf,plain,
! [V_U] :
( v_NB != v_NBa
| v_NA != v_NAa
| V_U != c_Message_Omsg_OKey(v_K) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [V_U] :
( v_NB != v_NBa
| v_NA != v_NAa
| V_U != c_Message_Omsg_OKey(v_K) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( v_NB != v_NBa
| v_NA != v_NAa
| X0 != c_Message_Omsg_OKey(v_K) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p10,plain,
( v_NB != v_NBa
| v_NA != v_NAa ),
inference(equality_resolution,[status(thm)],[c9]) ).
cnf(p35,plain,
( v_NBa != v_NBa
| v_NA != v_NAa ),
inference(demodulation,[status(thm)],[p31,p10]) ).
cnf(p36,plain,
v_NA != v_NAa,
inference(equality_resolution,[status(thm)],[p35]) ).
cnf(p40,plain,
v_NAa != v_NAa,
inference(superposition,[status(thm)],[p39,p36]) ).
cnf(p42,plain,
$false,
inference(equality_resolution,[status(thm)],[p40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV354-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n016.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 19:25:27 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.60/1.07 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.60/1.07 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------