%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV348-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 : Tue Sep 29 01:08:57 PM UTC 2026
% Result : Unsatisfiable 3.04s 1.08s
% Output : Refutation 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 22
% Syntax : Number of formulae : 68 ( 18 unt; 2 def)
% Number of atoms : 167 ( 11 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 168 ( 69 ~; 97 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-3 aty)
% Number of functors : 31 ( 31 usr; 17 con; 0-3 aty)
% Number of variables : 124 ( 0 sgn 124 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ c_in(c_Message_Omsg_OMPair(X0,X1),c_Message_Oparts(X2),tc_Message_Omsg)
| c_in(X0,c_Message_Oparts(X2),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__parts_1) ).
fof(f2,axiom,
! [X0,X1] :
( c_in(X0,c_Message_Oparts(X1),tc_Message_Omsg)
| ~ c_in(X0,X1,tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts_OInj_0) ).
fof(f3,axiom,
! [X0] : c_Message_Oparts(c_Message_Oanalz(X0)) = c_Message_Oparts(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__analz_0) ).
fof(f4,axiom,
! [X2,X0,X1] :
( ~ c_in(c_Message_Omsg_OMPair(X0,X1),c_Message_Oanalz(X2),tc_Message_Omsg)
| c_in(X1,c_Message_Oanalz(X2),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__analz_0) ).
fof(f5,axiom,
! [X2,X0,X1] :
( ~ c_in(c_Message_Omsg_OMPair(X0,X1),c_Message_Oanalz(X2),tc_Message_Omsg)
| c_in(X0,c_Message_Oanalz(X2),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__analz_1) ).
fof(f6,axiom,
! [X0,X1] :
( c_in(c_Message_Omsg_OKey(c_Public_OshrK(X0)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X1)),tc_Message_Omsg)
| ~ c_in(X1,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(X0,c_Event_Obad,tc_Message_Oagent) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Yahalom_OSpy__analz__shrK_1) ).
fof(f7,axiom,
! [X2,X0,X1] :
( ~ c_in(c_Event_Oevent_OGets(X1,X2),c_List_Oset(X0,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(X0,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(X2,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X0)),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Yahalom_OGets__imp__analz__Spy__dest_0) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ 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))
| 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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Yahalom_OSays__Server__imp__YM2_0) ).
fof(f9,axiom,
! [X2,X0,X1] :
( ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(X0),X1),c_Message_Oanalz(X2),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OKey(c_Public_OshrK(X0)),c_Message_Oanalz(X2),tc_Message_Omsg)
| c_in(X1,c_Message_Oanalz(X2),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_Oanalz__shrK__Decrypt_0) ).
fof(f10,axiom,
! [X2,X3,X0,X1,X4,X5] :
( 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,X5)))),c_Message_Omsg_OCrypt(c_Public_OshrK(X2),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X1),c_Message_Omsg_OKey(X3))))),c_List_Oset(X0,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(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,X5)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X0)),tc_Message_Omsg)
| c_in(X1,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(X0,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Yahalom_OA__trusts__YM3_0) ).
fof(f11,axiom,
! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X4,X5,X12] :
( ~ 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))
| c_in(X6,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X0)),tc_Message_Omsg)
| X5 = X12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Yahalom_OSays__unique__NB_0) ).
fof(f12,axiom,
! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X4,X5,X12] :
( ~ 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))
| c_in(X6,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X0)),tc_Message_Omsg)
| X3 = X10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Yahalom_OSays__unique__NB_2) ).
fof(f13,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ 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,X5)))),c_Message_Omsg_OCrypt(c_Public_OshrK(X2),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X1),c_Message_Omsg_OKey(X3))))),c_List_Oset(X0,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(X0,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Message_Omsg_OKey(X3),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X0)),tc_Message_Omsg)
| c_in(X2,c_Event_Obad,tc_Message_Oagent)
| c_in(X1,c_Event_Obad,tc_Message_Oagent)
| c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(X4,c_Message_Omsg_OMPair(X5,c_Message_Omsg_OKey(X3)))),c_List_Oset(X0,tc_Event_Oevent),tc_Event_Oevent) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Yahalom_OSpy__not__see__encrypted__key_0) ).
fof(f14,negated_conjecture,
~ c_in(v_B,c_Event_Obad,tc_Message_Oagent),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f15,negated_conjecture,
c_in(v_evs4,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f16,negated_conjecture,
c_in(c_Event_Oevent_OGets(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_NB))))),v_X)),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f17,negated_conjecture,
! [X0] : ~ c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),X0))),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_8) ).
fof(f18,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_evs4,tc_Event_Oevent),tc_Event_Oevent),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_9) ).
fof(f19,negated_conjecture,
~ c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_10) ).
fof(f20,negated_conjecture,
c_in(c_Message_Omsg_OKey(v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_11) ).
fof(f22,plain,
! [X2,X0,X1] :
( ~ c_in(c_Message_Omsg_OMPair(X0,X2),X1,tc_Message_Omsg)
| c_in(X0,c_Message_Oparts(X1),tc_Message_Omsg) ),
inference(resolution,[],[f1,f2]) ).
fof(f28,plain,
( ~ c_in(v_evs4,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(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_NB))))),v_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg) ),
inference(resolution,[],[f7,f16]) ).
fof(f29,plain,
c_in(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_NB))))),v_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg),
inference(forward_subsumption_resolution,[],[f28,f15]) ).
fof(f30,plain,
c_in(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_NB))))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg),
inference(resolution,[],[f29,f5]) ).
fof(f33,plain,
c_in(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_NB))))),c_Message_Oparts(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4))),tc_Message_Omsg),
inference(resolution,[],[f29,f22]) ).
fof(f35,plain,
c_in(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_NB))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg),
inference(forward_demodulation,[],[f33,f3]) ).
fof(f38,plain,
! [X2,X3,X0,X1,X4] :
( ~ 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),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(v_evs4,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg)
| v_NA = X4 ),
inference(resolution,[],[f11,f18]) ).
fof(f39,plain,
! [X2,X3,X0,X1,X4] :
( ~ 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),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent)
| c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg)
| v_NA = X4 ),
inference(forward_subsumption_resolution,[],[f38,f15]) ).
fof(f40,plain,
! [X2,X3,X0,X1,X4] :
( ~ 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),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent)
| v_NA = X4 ),
inference(forward_subsumption_resolution,[],[f39,f19]) ).
fof(f41,plain,
( ~ c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_Aa)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg)
| c_in(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_NB)))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg) ),
inference(resolution,[],[f30,f9]) ).
fof(f44,definition,
( spl0_1
<=> c_in(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_NB)))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f46,plain,
( c_in(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_NB)))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f48,definition,
( spl0_2
<=> c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_Aa)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f50,plain,
( ~ c_in(c_Message_Omsg_OKey(c_Public_OshrK(v_Aa)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg)
| spl0_2 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f51,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f41,f48,f44]) ).
fof(f52,plain,
! [X2,X3,X0,X1,X4] :
( ~ 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),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(v_evs4,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg)
| v_B = X2 ),
inference(resolution,[],[f12,f18]) ).
fof(f53,plain,
! [X2,X3,X0,X1,X4] :
( ~ 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),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent)
| c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg)
| v_B = X2 ),
inference(forward_subsumption_resolution,[],[f52,f15]) ).
fof(f54,plain,
! [X2,X3,X0,X1,X4] :
( ~ 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),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent)
| v_B = X2 ),
inference(forward_subsumption_resolution,[],[f53,f19]) ).
fof(f55,plain,
( ~ c_in(v_evs4,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)
| spl0_2 ),
inference(resolution,[],[f50,f6]) ).
fof(f56,plain,
( ~ c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f55,f15]) ).
fof(f57,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_in(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,X4)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X5)),tc_Message_Omsg)
| c_in(X0,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(X5,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(X5,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| 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(X5,tc_Event_Oevent),tc_Event_Oevent) ),
inference(resolution,[],[f10,f8]) ).
fof(f58,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_in(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,X4)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X5)),tc_Message_Omsg)
| c_in(X0,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(X5,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| 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(X5,tc_Event_Oevent),tc_Event_Oevent) ),
inference(duplicate_literal_removal,[],[f57]) ).
fof(f59,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_in(X0,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Message_Omsg_OKey(X1),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X0)),tc_Message_Omsg)
| c_in(X2,c_Event_Obad,tc_Message_Oagent)
| c_in(X3,c_Event_Obad,tc_Message_Oagent)
| c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(X4,c_Message_Omsg_OMPair(X5,c_Message_Omsg_OKey(X1)))),c_List_Oset(X0,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(X3),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X2),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X1),c_Message_Omsg_OMPair(X4,X5)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X0)),tc_Message_Omsg)
| c_in(X3,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(X0,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(resolution,[],[f13,f10]) ).
fof(f60,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(X3),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X2),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X1),c_Message_Omsg_OMPair(X4,X5)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X0)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OKey(X1),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,X0)),tc_Message_Omsg)
| c_in(X2,c_Event_Obad,tc_Message_Oagent)
| c_in(X3,c_Event_Obad,tc_Message_Oagent)
| c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(X4,c_Message_Omsg_OMPair(X5,c_Message_Omsg_OKey(X1)))),c_List_Oset(X0,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(X0,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(duplicate_literal_removal,[],[f59]) ).
fof(f64,plain,
( c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(v_evs4,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| 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_evs4,tc_Event_Oevent),tc_Event_Oevent) ),
inference(resolution,[],[f58,f35]) ).
fof(f66,plain,
( ~ c_in(v_evs4,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| 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_evs4,tc_Event_Oevent),tc_Event_Oevent)
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f64,f56]) ).
fof(f67,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_evs4,tc_Event_Oevent),tc_Event_Oevent)
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f66,f15]) ).
fof(f68,plain,
( v_B = v_Ba
| spl0_2 ),
inference(resolution,[],[f67,f54]) ).
fof(f69,plain,
( v_NAa = v_NA
| spl0_2 ),
inference(resolution,[],[f67,f40]) ).
fof(f73,plain,
( ~ c_in(c_Message_Omsg_OKey(v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg)
| c_in(v_Ba,c_Event_Obad,tc_Message_Oagent)
| c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)
| c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OKey(v_K)))),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(v_evs4,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(resolution,[],[f60,f35]) ).
fof(f75,plain,
( c_in(v_Ba,c_Event_Obad,tc_Message_Oagent)
| c_in(v_Aa,c_Event_Obad,tc_Message_Oagent)
| c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OKey(v_K)))),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(v_evs4,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(forward_subsumption_resolution,[],[f73,f20]) ).
fof(f76,plain,
( c_in(v_Ba,c_Event_Obad,tc_Message_Oagent)
| c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OKey(v_K)))),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(v_evs4,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f75,f56]) ).
fof(f77,plain,
( c_in(v_Ba,c_Event_Obad,tc_Message_Oagent)
| c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OKey(v_K)))),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent)
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f76,f15]) ).
fof(f78,plain,
( c_in(v_B,c_Event_Obad,tc_Message_Oagent)
| c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OKey(v_K)))),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent)
| spl0_2 ),
inference(forward_demodulation,[],[f77,f68]) ).
fof(f79,plain,
( c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_OKey(v_K)))),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent)
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f78,f14]) ).
fof(f88,plain,
( ! [X0] : ~ c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),X0))),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent)
| spl0_2 ),
inference(superposition,[],[f17,f69]) ).
fof(f89,plain,
( $false
| spl0_2 ),
inference(resolution,[],[f79,f88]) ).
fof(f90,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f89]) ).
fof(f113,plain,
( c_in(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_NB))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg)
| ~ spl0_1 ),
inference(resolution,[],[f46,f4]) ).
fof(f127,plain,
( c_in(c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_ONonce(v_NB)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg)
| ~ spl0_1 ),
inference(resolution,[],[f113,f4]) ).
fof(f140,plain,
( c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg)
| ~ spl0_1 ),
inference(resolution,[],[f127,f4]) ).
fof(f148,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f140,f19]) ).
fof(f149,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f148]) ).
cnf(s1,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f51]) ).
cnf(s2,plain,
spl0_2,
inference(sat_conversion,[],[f90]) ).
cnf(s5,plain,
~ spl0_1,
inference(sat_conversion,[],[f149]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s2,s5]) ).
fof(f150,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV348-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n019.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 10:40:34 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.04/1.08 % (3924171)Input is clausal, will run a generic CNF schedule.
% 3.04/1.08 % (3924176)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3855861203:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.04/1.08 % (3924178)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=665918338:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.04/1.08 % (3924181)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2236415869:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.04/1.08 % (3924177)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3582708969:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.04/1.08 % (3924179)lrs+10_1_sil=8000:sp=occurrence:random_seed=932935055:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.04/1.08 % (3924180)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4201627950:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.04/1.08 % (3924182)dis-21_1_sil=8000:lcm=predicate:random_seed=1732572324:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.04/1.08 % (3924179)First to succeed.
% 3.04/1.08 % (3924180)Also succeeded, but the first one will report.
% 3.04/1.08 % (3924179)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3924171"
% 3.04/1.08 % (3924181)Also succeeded, but the first one will report.
% 3.04/1.08 % (3924182)Instruction limit reached!
% 3.04/1.08 % (3924182)------------------------------
% 3.04/1.08 % (3924182)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.04/1.08 % (3924182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.04/1.08 % (3924182)CaDiCaL version: 2.1.3
% 3.04/1.08 % (3924182)Termination reason: Instruction limit
% 3.04/1.08 % (3924182)Termination phase: Saturation
% 3.04/1.08 % (3924182)Time elapsed: 0.054 s
% 3.04/1.08 % (3924182)Peak memory usage: 88 MB
% 3.04/1.08 % (3924182)Instructions burned: 118 (million)
% 3.04/1.08 % (3924190)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=2422884334:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.04/1.08 % (3924190)Refutation not found, incomplete strategy
% 3.04/1.08 % (3924190)------------------------------
% 3.04/1.08 % (3924190)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.04/1.08 % (3924190)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.04/1.08 % (3924190)CaDiCaL version: 2.1.3
% 3.04/1.08 % (3924190)Termination reason: Refutation not found, incomplete strategy
% 3.04/1.08 % (3924190)Time elapsed: 0.003 s
% 3.04/1.08 % (3924190)Peak memory usage: 88 MB
% 3.04/1.08 % (3924190)Instructions burned: 4 (million)
% 3.04/1.08 % (3924179)Refutation found. Thanks to Tanya!
% 3.04/1.08 % SZS status Unsatisfiable for theBenchmark
% 3.04/1.08 % SZS output start Proof for theBenchmark
% See solution above
% 3.55/1.27 % (3924179)------------------------------
% 3.55/1.27 % (3924179)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.27 % (3924179)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.27 % (3924179)CaDiCaL version: 2.1.3
% 3.55/1.27 % (3924179)Termination reason: Refutation
% 3.55/1.27 % (3924179)Time elapsed: 0.009 s
% 3.55/1.27 % (3924179)Peak memory usage: 89 MB
% 3.55/1.27 % (3924179)Instructions burned: 13 (million)
% 3.55/1.27 % (3924179)------------------------------
% 3.55/1.27 % (3924179)------------------------------
% 3.55/1.27 % (3924171)Success in time 0.418 s
% 3.55/1.27 % Vampire exiting
%------------------------------------------------------------------------------