%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV337-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:07:27 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 33 ( 17 unt; 0 def)
% Number of atoms : 58 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 54 ( 29 ~; 25 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 27 ( 27 usr; 14 con; 0-3 aty)
% Number of variables : 57 ( 10 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
c_in(v_evs4,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1,plain,
c_in(v_evs4,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_conjecture_3,axiom,
c_in(c_Event_Oevent_OGets(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_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),v_X)),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_2,plain,
c_in(c_Event_Oevent_OGets(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_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),v_X)),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
fof(cls_conjecture_6,axiom,
~ c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg),
file('theBenchmark.p',cls_conjecture_6) ).
cnf(c_3,plain,
~ c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg),
inference(clausify,[status(thm)],[cls_conjecture_6]) ).
fof(cls_conjecture_8,axiom,
! [VAR_0,VAR_1,VAR_2] : ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,VAR_0,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(VAR_0),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(VAR_1),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(VAR_2),c_Message_Omsg_ONonce(v_NB))))),c_Message_Omsg_OCrypt(c_Public_OshrK(VAR_1),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(VAR_0),c_Message_Omsg_OKey(v_K))))),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent),
file('theBenchmark.p',cls_conjecture_8) ).
cnf(c_4,plain,
~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(B),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(C),c_Message_Omsg_ONonce(v_NB))))),c_Message_Omsg_OCrypt(c_Public_OshrK(B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(A),c_Message_Omsg_OKey(v_K))))),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent),
inference(clausify,[status(thm)],[cls_conjecture_8]) ).
fof(cls_Message_OMPair__analz_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_in(VAR_1,c_Message_Oanalz(VAR_2),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(VAR_0,VAR_1),c_Message_Oanalz(VAR_2),tc_Message_Omsg) ),
file('theBenchmark.p',cls_Message_OMPair__analz_0) ).
cnf(c_5,plain,
( c_in(B,c_Message_Oanalz(C),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(A,B),c_Message_Oanalz(C),tc_Message_Omsg) ),
inference(clausify,[status(thm)],[cls_Message_OMPair__analz_0]) ).
fof(cls_Message_OMPair__analz_1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_in(VAR_0,c_Message_Oanalz(VAR_2),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(VAR_0,VAR_1),c_Message_Oanalz(VAR_2),tc_Message_Omsg) ),
file('theBenchmark.p',cls_Message_OMPair__analz_1) ).
cnf(c_6,plain,
( c_in(A,c_Message_Oanalz(C),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(A,B),c_Message_Oanalz(C),tc_Message_Omsg) ),
inference(clausify,[status(thm)],[cls_Message_OMPair__analz_1]) ).
fof(cls_Message_Oanalz__into__parts__dest_0,axiom,
! [VAR_0,VAR_1] :
( c_in(VAR_0,c_Message_Oparts(VAR_1),tc_Message_Omsg)
| ~ c_in(VAR_0,c_Message_Oanalz(VAR_1),tc_Message_Omsg) ),
file('theBenchmark.p',cls_Message_Oanalz__into__parts__dest_0) ).
cnf(c_7,plain,
( c_in(A,c_Message_Oparts(B),tc_Message_Omsg)
| ~ c_in(A,c_Message_Oanalz(B),tc_Message_Omsg) ),
inference(clausify,[status(thm)],[cls_Message_Oanalz__into__parts__dest_0]) ).
fof(cls_Public_OCrypt__Spy__analz__bad_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_in(VAR_1,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,VAR_2)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(VAR_0),VAR_1),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,VAR_2)),tc_Message_Omsg)
| ~ c_in(VAR_0,c_Event_Obad,tc_Message_Oagent) ),
file('theBenchmark.p',cls_Public_OCrypt__Spy__analz__bad_0) ).
cnf(c_8,plain,
( c_in(B,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,C)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(A),B),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,C)),tc_Message_Omsg)
| ~ c_in(A,c_Event_Obad,tc_Message_Oagent) ),
inference(clausify,[status(thm)],[cls_Public_OCrypt__Spy__analz__bad_0]) ).
fof(cls_Yahalom_OA__trusts__YM3_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,VAR_1,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(VAR_1),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(VAR_2),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(VAR_3),c_Message_Omsg_OMPair(VAR_4,VAR_5)))),c_Message_Omsg_OCrypt(c_Public_OshrK(VAR_2),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(VAR_1),c_Message_Omsg_OKey(VAR_3))))),c_List_Oset(VAR_0,tc_Event_Oevent),tc_Event_Oevent)
| c_in(VAR_1,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(VAR_1),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(VAR_2),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(VAR_3),c_Message_Omsg_OMPair(VAR_4,VAR_5)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,VAR_0)),tc_Message_Omsg)
| ~ c_in(VAR_0,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
file('theBenchmark.p',cls_Yahalom_OA__trusts__YM3_0) ).
cnf(c_9,plain,
( c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,B,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(C),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(D),c_Message_Omsg_OMPair(E,F)))),c_Message_Omsg_OCrypt(c_Public_OshrK(C),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(B),c_Message_Omsg_OKey(D))))),c_List_Oset(A,tc_Event_Oevent),tc_Event_Oevent)
| c_in(B,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(C),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(D),c_Message_Omsg_OMPair(E,F)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,A)),tc_Message_Omsg)
| ~ c_in(A,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(clausify,[status(thm)],[cls_Yahalom_OA__trusts__YM3_0]) ).
fof(cls_Yahalom_OGets__imp__analz__Spy__dest_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_in(VAR_2,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,VAR_0)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(VAR_1,VAR_2),c_List_Oset(VAR_0,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(VAR_0,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
file('theBenchmark.p',cls_Yahalom_OGets__imp__analz__Spy__dest_0) ).
cnf(c_10,plain,
( c_in(C,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,A)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(B,C),c_List_Oset(A,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(A,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(clausify,[status(thm)],[cls_Yahalom_OGets__imp__analz__Spy__dest_0]) ).
cnf(c_11,plain,
~ c_in(c_Message_Omsg_OMPair(A,c_Message_Omsg_ONonce(v_NB)),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_5,c_3]) ).
cnf(c_13,plain,
( c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(B),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(C),c_Message_Omsg_OMPair(D,E)))),c_Message_Omsg_OCrypt(c_Public_OshrK(B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(A),c_Message_Omsg_OKey(C))))),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent)
| c_in(A,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(c_Message_Omsg_OCrypt(c_Public_OshrK(A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(B),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(C),c_Message_Omsg_OMPair(D,E)))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg) ),
inference(resolve,[status(thm)],[c_9,c_1]) ).
cnf(c_42,plain,
( c_in(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_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),v_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg)
| ~ c_in(v_evs4,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(resolve,[status(thm)],[c_10,c_2]) ).
cnf(c_15,plain,
c_in(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_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),v_X),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_1,c_42]) ).
cnf(c_19,plain,
~ c_in(c_Message_Omsg_OMPair(A,c_Message_Omsg_OMPair(B,c_Message_Omsg_ONonce(v_NB))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_5,c_11]) ).
cnf(c_24,plain,
c_in(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_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_15,c_6]) ).
cnf(c_32,plain,
~ c_in(c_Message_Omsg_OMPair(A,c_Message_Omsg_OMPair(B,c_Message_Omsg_OMPair(C,c_Message_Omsg_ONonce(v_NB)))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_5,c_19]) ).
cnf(c_43,plain,
( c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),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_NB)))),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg)
| ~ c_in(v_A,c_Event_Obad,tc_Message_Oagent) ),
inference(resolve,[status(thm)],[c_24,c_8]) ).
cnf(c_39,plain,
~ c_in(v_A,c_Event_Obad,tc_Message_Oagent),
inference(resolve,[status(thm)],[c_32,c_43]) ).
cnf(c_40,plain,
c_in(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_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs4)),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_24,c_7]) ).
cnf(c_44,plain,
( 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_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OKey(v_K))))),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent)
| c_in(v_A,c_Event_Obad,tc_Message_Oagent) ),
inference(resolve,[status(thm)],[c_40,c_13]) ).
cnf(c_45,plain,
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_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OKey(v_K))))),c_List_Oset(v_evs4,tc_Event_Oevent),tc_Event_Oevent),
inference(resolve,[status(thm)],[c_39,c_44]) ).
cnf(c_41,plain,
$false,
inference(resolve,[status(thm)],[c_4,c_45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV337-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 13:32:39 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 3853427 was started by sandbox on n007,
% 0.09/0.37 % Sat Sep 26 13:32:39 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.38
% 0.13/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.38
% 0.13/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.38 % Length of proof is 19.
% 0.13/0.38 % Level of proof is 5.
% 0.13/0.38 % Maximum clause weight is 56.000.
% 0.13/0.38 % Given clauses 26.
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------