%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWV353-2 : 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/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n004.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 2.85s 1.65s
% Output : CNFRefutation 2.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 21 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 41 ( 9 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 40 ( 20 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 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 : 27 ( 27 usr; 15 con; 0-3 aty)
% Number of variables : 56 ( 56 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_in > c_Event_Oevent_OSays > c_Message_Omsg_OMPair > c_Message_Omsg_OCrypt > c_List_Oset > c_Event_Oknows > c_Event_Oevent_OGets > #nlpp > 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_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(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(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_Yahalom_Oyahalom,type,
c_Yahalom_Oyahalom: $i ).
tff(c_Message_Omsg_OKey,type,
c_Message_Omsg_OKey: $i > $i ).
tff(f_36,axiom,
! [V_U] :
( ( V_U != c_Message_Omsg_OKey(v_K) )
| ( v_NA != v_NAa ) ),
file(unknown,unknown) ).
tff(f_26,axiom,
c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)),
file(unknown,unknown) ).
tff(f_27,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_NB))))),v_X)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent),
file(unknown,unknown) ).
tff(f_44,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_30,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_28,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_57,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_10,plain,
v_NAa != v_NA,
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_2,plain,
c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)),
inference(cnfTransformation,[status(thm)],[f_26]) ).
tff(c_4,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_NB))))),v_X)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent),
inference(cnfTransformation,[status(thm)],[f_27]) ).
tff(c_15,plain,
! [V_na_22,V_nb_23,V_B_27,V_evs_26,V_k_28,V_X_25,V_A_24] :
( c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_27),c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_27),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_24),c_Message_Omsg_OMPair(V_na_22,V_nb_23))))),c_List_Oset(V_evs_26,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_24,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_24),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_27),c_Message_Omsg_OMPair(V_k_28,c_Message_Omsg_OMPair(V_na_22,V_nb_23)))),V_X_25)),c_List_Oset(V_evs_26,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs_26,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_17,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)
| ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(resolution,[status(thm)],[c_4,c_15]) ).
tff(c_20,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_2,c_17]) ).
tff(c_8,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_30]) ).
tff(c_6,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_28]) ).
tff(c_21,plain,
! [V_X_30,V_S_H_41,V_NA_39,V_B_H_31,V_B_29,V_nb_33,V_evs_38,V_S_32,V_X_H_35,V_C_37,V_A_34,V_A_H_40,V_NA_H_36] :
( ( V_NA_H_36 = V_NA_39 )
| c_in(V_nb_33,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs_38)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(V_C_37,V_S_32,c_Message_Omsg_OMPair(V_X_30,c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_29),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_34),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_39),V_nb_33))))),c_List_Oset(V_evs_38,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OGets(V_S_H_41,c_Message_Omsg_OMPair(V_X_H_35,c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H_31),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H_40),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H_36),V_nb_33))))),c_List_Oset(V_evs_38,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs_38,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_23,plain,
! [V_S_H_41,V_B_H_31,V_X_H_35,V_A_H_40,V_NA_H_36] :
( ( v_NA = V_NA_H_36 )
| 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_41,c_Message_Omsg_OMPair(V_X_H_35,c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H_31),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H_40),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H_36),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_6,c_21]) ).
tff(c_26,plain,
! [V_S_H_41,V_B_H_31,V_X_H_35,V_A_H_40,V_NA_H_36] :
( ( v_NA = V_NA_H_36 )
| 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_41,c_Message_Omsg_OMPair(V_X_H_35,c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H_31),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H_40),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H_36),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_23]) ).
tff(c_28,plain,
! [V_S_H_45,V_A_H_43,V_X_H_44,V_B_H_46,V_NA_H_42] :
( ( v_NA = V_NA_H_42 )
| ~ c_in(c_Event_Oevent_OGets(V_S_H_45,c_Message_Omsg_OMPair(V_X_H_44,c_Message_Omsg_OCrypt(c_Public_OshrK(V_B_H_46),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_A_H_43),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V_NA_H_42),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ),
inference(negUnitSimplification,[status(thm)],[c_8,c_26]) ).
tff(c_31,plain,
v_NAa = v_NA,
inference(resolution,[status(thm)],[c_20,c_28]) ).
tff(c_35,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_10,c_31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWV353-2 : TPTP v9.0.0. Released v3.2.0.
% 0.13/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.15/0.35 % Computer : n004.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Wed Apr 9 03:06:37 EDT 2025
% 0.21/0.35 % CPUTime :
% 2.85/1.65 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.85/1.65
% 2.85/1.65 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------