%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWV354-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Apr 9 09:30:18 PM UTC 2025
% Result : Unsatisfiable 3.54s 1.85s
% Output : CNFRefutation 3.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 52 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 113 ( 38 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 114 ( 53 ~; 61 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% 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 : 146 ( 146 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_in > c_insert > c_Event_Oevent_OSays > c_Message_Omsg_OMPair > c_Message_Omsg_OCrypt > c_List_Oset > c_Event_Oknows > c_Event_Oevent_OGets > #nlpp > v_sko__2VY > tc_List_Olist > c_Public_OshrK > c_Message_Omsg_ONonce > c_Message_Omsg_OKey > c_Message_Omsg_OAgent > c_Message_Oanalz > v_evso > v_X > v_NBa > v_NB > v_NAa > v_NA > v_K > v_Ba > v_B > v_Aa > v_A > tc_Message_Omsg > tc_Event_Oevent > c_Yahalom_Oyahalom > c_Message_Oagent_OSpy > c_Message_Oagent_OServer
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(c_Message_Omsg_OMPair,type,
c_Message_Omsg_OMPair: ( $i * $i ) > $i ).
tff(c_Event_Oknows,type,
c_Event_Oknows: ( $i * $i ) > $i ).
tff(v_K,type,
v_K: $i ).
tff(v_X,type,
v_X: $i ).
tff(c_Public_OshrK,type,
c_Public_OshrK: $i > $i ).
tff(c_Message_Oanalz,type,
c_Message_Oanalz: $i > $i ).
tff(v_NAa,type,
v_NAa: $i ).
tff(c_Message_Oagent_OSpy,type,
c_Message_Oagent_OSpy: $i ).
tff(tc_Event_Oevent,type,
tc_Event_Oevent: $i ).
tff(v_evso,type,
v_evso: $i ).
tff(v_NA,type,
v_NA: $i ).
tff(v_NB,type,
v_NB: $i ).
tff(v_NBa,type,
v_NBa: $i ).
tff(c_List_Oset,type,
c_List_Oset: ( $i * $i ) > $i ).
tff(v_Aa,type,
v_Aa: $i ).
tff(c_Message_Omsg_OAgent,type,
c_Message_Omsg_OAgent: $i > $i ).
tff(tc_List_Olist,type,
tc_List_Olist: $i > $i ).
tff(c_in,type,
c_in: ( $i * $i * $i ) > $o ).
tff(v_sko__2VY,type,
v_sko__2VY: $i > $i ).
tff(tc_Message_Omsg,type,
tc_Message_Omsg: $i ).
tff(c_Message_Omsg_OCrypt,type,
c_Message_Omsg_OCrypt: ( $i * $i ) > $i ).
tff(v_B,type,
v_B: $i ).
tff(c_Message_Oagent_OServer,type,
c_Message_Oagent_OServer: $i ).
tff(v_Ba,type,
v_Ba: $i ).
tff(c_Event_Oevent_OGets,type,
c_Event_Oevent_OGets: ( $i * $i ) > $i ).
tff(c_Message_Omsg_ONonce,type,
c_Message_Omsg_ONonce: $i > $i ).
tff(v_A,type,
v_A: $i ).
tff(c_Event_Oevent_OSays,type,
c_Event_Oevent_OSays: ( $i * $i * $i ) > $i ).
tff(c_insert,type,
c_insert: ( $i * $i * $i ) > $i ).
tff(c_Yahalom_Oyahalom,type,
c_Yahalom_Oyahalom: $i ).
tff(c_Message_Omsg_OKey,type,
c_Message_Omsg_OKey: $i > $i ).
tff(f_82,axiom,
! [V_U] :
( ( V_U != c_Message_Omsg_OKey(v_K) )
| ( v_NA != v_NAa )
| ( v_NB != v_NBa ) ),
file(unknown,unknown) ).
tff(f_69,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(unknown,unknown) ).
tff(f_68,axiom,
c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)),
file(unknown,unknown) ).
tff(f_72,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(unknown,unknown) ).
tff(f_73,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(unknown,unknown) ).
tff(f_40,axiom,
! [V_B,V_NB,V_A,V_X,V_KAB,V_NB_H,V_na,V_evs] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(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(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(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_Message_Omsg_ONonce(V_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ( V_NB = V_NB_H )
| ( V_KAB = c_Public_OshrK(v_sko__2VY(V_KAB)) ) ),
file(unknown,unknown) ).
tff(f_67,axiom,
! [V_B,V_nb,V_A,V_X,V_na,V_x,V_evs] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(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(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) ),
file(unknown,unknown) ).
tff(f_48,axiom,
! [V_B,V_nb,V_k,V_A,V_X,V_na,V_evs] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(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(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) ),
file(unknown,unknown) ).
tff(f_70,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(unknown,unknown) ).
tff(f_61,axiom,
! [V_B,V_S_H,V_nb,V_NA,V_A_H,V_S,V_X_H,V_A,V_X,V_NA_H,V_C,V_B_H,V_evs] :
( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(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(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(V_nb,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs)),tc_Message_Omsg)
| ( V_NA_H = V_NA ) ),
file(unknown,unknown) ).
tff(c_20,plain,
( ( v_NBa != v_NB )
| ( v_NAa != v_NA ) ),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_21,plain,
v_NAa != v_NA,
inference(splitLeft,[status(thm)],[c_20]) ).
tff(c_12,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(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_10,plain,
c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_16,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(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_18,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(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_37,plain,
! [V_evs_74,V_KAB_76,V_A_73,V_NB_70,V_B_75,V_na_71,V_NB_H_69,V_X_72] :
( ( c_Public_OshrK(v_sko__2VY(V_KAB_76)) = V_KAB_76 )
| ( V_NB_H_69 = V_NB_70 )
| c_in(c_Message_Omsg_ONonce(V_NB_70),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs_74)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_ONonce(V_NB_70),c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB_76),c_Event_Oknows(c_Message_Oagent_OSpy,V_evs_74),tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_73,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_73),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_75),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB_76),c_Message_Omsg_OMPair(V_na_71,c_Message_Omsg_ONonce(V_NB_H_69))))),V_X_72)),c_List_Oset(V_evs_74,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs_74,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_39,plain,
! [V_A_73,V_B_75,V_na_71,V_NB_H_69,V_X_72] :
( ( c_Public_OshrK(v_sko__2VY(v_K)) = v_K )
| ( v_NB = V_NB_H_69 )
| 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_OSays(c_Message_Oagent_OServer,V_A_73,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_73),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_75),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(V_na_71,c_Message_Omsg_ONonce(V_NB_H_69))))),V_X_72)),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(resolution,[status(thm)],[c_18,c_37]) ).
tff(c_42,plain,
! [V_A_73,V_B_75,V_na_71,V_NB_H_69,V_X_72] :
( ( c_Public_OshrK(v_sko__2VY(v_K)) = v_K )
| ( v_NB = V_NB_H_69 )
| 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_OSays(c_Message_Oagent_OServer,V_A_73,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_73),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_75),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(V_na_71,c_Message_Omsg_ONonce(V_NB_H_69))))),V_X_72)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_39]) ).
tff(c_43,plain,
! [V_A_73,V_B_75,V_na_71,V_NB_H_69,V_X_72] :
( ( c_Public_OshrK(v_sko__2VY(v_K)) = v_K )
| ( v_NB = V_NB_H_69 )
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_73,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_73),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_75),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(V_na_71,c_Message_Omsg_ONonce(V_NB_H_69))))),V_X_72)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ),
inference(negUnitSimplification,[status(thm)],[c_16,c_42]) ).
tff(c_44,plain,
c_Public_OshrK(v_sko__2VY(v_K)) = v_K,
inference(splitLeft,[status(thm)],[c_43]) ).
tff(c_8,plain,
! [V_na_33,V_B_29,V_A_31,V_evs_35,V_X_32,V_nb_30,V_x_34] :
( ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_31,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_31),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_29),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(c_Public_OshrK(V_x_34)),c_Message_Omsg_OMPair(V_na_33,V_nb_30)))),V_X_32)),c_List_Oset(V_evs_35,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs_35,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_60,plain,
! [V_nb_85,V_A_81,V_na_82,V_evs_83,V_B_86,V_X_84] :
( ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_81,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_81),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_86),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(V_na_82,V_nb_85)))),V_X_84)),c_List_Oset(V_evs_83,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs_83,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(superposition,[status(thm),theory(equality)],[c_44,c_8]) ).
tff(c_66,plain,
~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)),
inference(resolution,[status(thm)],[c_12,c_60]) ).
tff(c_70,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_10,c_66]) ).
tff(c_73,plain,
! [V_X_90,V_A_87,V_B_88,V_NB_H_91,V_na_89] :
( ( v_NB = V_NB_H_91 )
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_87,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_87),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_88),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(V_na_89,c_Message_Omsg_ONonce(V_NB_H_91))))),V_X_90)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ),
inference(splitRight,[status(thm)],[c_43]) ).
tff(c_77,plain,
v_NBa = v_NB,
inference(resolution,[status(thm)],[c_12,c_73]) ).
tff(c_23,plain,
! [V_evs_48,V_A_45,V_B_44,V_nb_50,V_X_47,V_na_49,V_k_46] :
( c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_44),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_44),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_45),c_Message_Omsg_OMPair(V_na_49,V_nb_50))))),c_List_Oset(V_evs_48,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_45,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_45),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_44),c_Message_Omsg_OMPair(V_k_46,c_Message_Omsg_OMPair(V_na_49,V_nb_50)))),V_X_47)),c_List_Oset(V_evs_48,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs_48,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_25,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(resolution,[status(thm)],[c_12,c_23]) ).
tff(c_28,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(demodulation,[status(thm),theory(equality)],[c_10,c_25]) ).
tff(c_78,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(demodulation,[status(thm),theory(equality)],[c_77,c_28]) ).
tff(c_14,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(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_29,plain,
! [V_S_H_55,V_X_63,V_B_62,V_C_61,V_X_H_56,V_NA_53,V_NA_H_59,V_B_H_57,V_A_60,V_nb_52,V_evs_54,V_A_H_51,V_S_58] :
( ( V_NA_H_59 = V_NA_53 )
| c_in(V_nb_52,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs_54)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(V_C_61,V_S_58,c_Message_Omsg_OMPair(V_X_63,c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_62),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_60),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_53),V_nb_52))))),c_List_Oset(V_evs_54,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OGets(V_S_H_55,c_Message_Omsg_OMPair(V_X_H_56,c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H_57),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H_51),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H_59),V_nb_52))))),c_List_Oset(V_evs_54,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs_54,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_31,plain,
! [V_S_H_55,V_X_H_56,V_NA_H_59,V_B_H_57,V_A_H_51] :
( ( v_NA = V_NA_H_59 )
| 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(V_S_H_55,c_Message_Omsg_OMPair(V_X_H_56,c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H_57),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H_51),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H_59),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(resolution,[status(thm)],[c_14,c_29]) ).
tff(c_34,plain,
! [V_S_H_55,V_X_H_56,V_NA_H_59,V_B_H_57,V_A_H_51] :
( ( v_NA = V_NA_H_59 )
| 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(V_S_H_55,c_Message_Omsg_OMPair(V_X_H_56,c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H_57),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H_51),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H_59),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_31]) ).
tff(c_35,plain,
! [V_S_H_55,V_X_H_56,V_NA_H_59,V_B_H_57,V_A_H_51] :
( ( v_NA = V_NA_H_59 )
| ~ c_in(c_Event_Oevent_OGets(V_S_H_55,c_Message_Omsg_OMPair(V_X_H_56,c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H_57),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H_51),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H_59),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ),
inference(negUnitSimplification,[status(thm)],[c_16,c_34]) ).
tff(c_86,plain,
v_NAa = v_NA,
inference(resolution,[status(thm)],[c_78,c_35]) ).
tff(c_90,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_21,c_86]) ).
tff(c_91,plain,
v_NBa != v_NB,
inference(splitRight,[status(thm)],[c_20]) ).
tff(c_92,plain,
v_NAa = v_NA,
inference(splitRight,[status(thm)],[c_20]) ).
tff(c_97,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_NA),c_Message_Omsg_ONonce(v_NBa))))),v_X)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent),
inference(demodulation,[status(thm),theory(equality)],[c_92,c_12]) ).
tff(c_113,plain,
! [V_NB_H_124,V_evs_129,V_NB_125,V_X_127,V_KAB_131,V_na_126,V_A_128,V_B_130] :
( ( c_Public_OshrK(v_sko__2VY(V_KAB_131)) = V_KAB_131 )
| ( V_NB_H_124 = V_NB_125 )
| c_in(c_Message_Omsg_ONonce(V_NB_125),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs_129)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_ONonce(V_NB_125),c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(V_KAB_131),c_Event_Oknows(c_Message_Oagent_OSpy,V_evs_129),tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_128,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_128),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_130),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_KAB_131),c_Message_Omsg_OMPair(V_na_126,c_Message_Omsg_ONonce(V_NB_H_124))))),V_X_127)),c_List_Oset(V_evs_129,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs_129,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_115,plain,
! [V_NB_H_124,V_X_127,V_na_126,V_A_128,V_B_130] :
( ( c_Public_OshrK(v_sko__2VY(v_K)) = v_K )
| ( v_NB = V_NB_H_124 )
| 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_OSays(c_Message_Oagent_OServer,V_A_128,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_128),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_130),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(V_na_126,c_Message_Omsg_ONonce(V_NB_H_124))))),V_X_127)),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(resolution,[status(thm)],[c_18,c_113]) ).
tff(c_118,plain,
! [V_NB_H_124,V_X_127,V_na_126,V_A_128,V_B_130] :
( ( c_Public_OshrK(v_sko__2VY(v_K)) = v_K )
| ( v_NB = V_NB_H_124 )
| 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_OSays(c_Message_Oagent_OServer,V_A_128,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_128),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_130),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(V_na_126,c_Message_Omsg_ONonce(V_NB_H_124))))),V_X_127)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_115]) ).
tff(c_119,plain,
! [V_NB_H_124,V_X_127,V_na_126,V_A_128,V_B_130] :
( ( c_Public_OshrK(v_sko__2VY(v_K)) = v_K )
| ( v_NB = V_NB_H_124 )
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_128,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_128),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_130),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(V_na_126,c_Message_Omsg_ONonce(V_NB_H_124))))),V_X_127)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ),
inference(negUnitSimplification,[status(thm)],[c_16,c_118]) ).
tff(c_120,plain,
c_Public_OshrK(v_sko__2VY(v_K)) = v_K,
inference(splitLeft,[status(thm)],[c_119]) ).
tff(c_136,plain,
! [V_nb_140,V_B_141,V_X_139,V_na_137,V_evs_138,V_A_136] :
( ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_136,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_136),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_141),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(V_na_137,V_nb_140)))),V_X_139)),c_List_Oset(V_evs_138,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs_138,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(superposition,[status(thm),theory(equality)],[c_120,c_8]) ).
tff(c_142,plain,
~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)),
inference(resolution,[status(thm)],[c_97,c_136]) ).
tff(c_146,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_10,c_142]) ).
tff(c_149,plain,
! [V_na_144,V_B_142,V_NB_H_146,V_X_145,V_A_143] :
( ( v_NB = V_NB_H_146 )
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_143,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_143),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_142),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(V_na_144,c_Message_Omsg_ONonce(V_NB_H_146))))),V_X_145)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ),
inference(splitRight,[status(thm)],[c_119]) ).
tff(c_152,plain,
v_NBa = v_NB,
inference(resolution,[status(thm)],[c_97,c_149]) ).
tff(c_156,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_91,c_152]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV354-2 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Apr 9 03:06:35 EDT 2025
% 0.13/0.34 % CPUTime :
% 3.54/1.85 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.54/1.86
% 3.54/1.86 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------