%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV313-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 09:07:22 AM UTC 2026
% Result : Unsatisfiable 16.31s 2.76s
% Output : CNFRefutation 16.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 23 ( 15 unt; 0 def)
% Number of atoms : 45 ( 0 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 42 ( 20 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 13 con; 0-3 aty)
% Number of variables : 16 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_5,axiom,
c_in(c_Message_Omsg_OKey(v_K),c_Event_Oknows(c_Message_Oagent_OSpy,v_evs),tc_Message_Omsg),
file('theBenchmark.p',cls_conjecture_5) ).
cnf(c_2265,plain,
c_in(c_Message_Omsg_OKey(v_K),c_Event_Oknows(c_Message_Oagent_OSpy,v_evs),tc_Message_Omsg),
inference(clausify,[status(thm)],[cls_conjecture_5]) ).
fof(cls_conjecture_4,axiom,
c_in(v_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(c_2266,plain,
c_in(v_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)),
inference(clausify,[status(thm)],[cls_conjecture_4]) ).
fof(cls_conjecture_3,axiom,
~ c_in(v_B,c_Event_Obad,tc_Message_Oagent),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_2267,plain,
~ c_in(v_B,c_Event_Obad,tc_Message_Oagent),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
fof(cls_conjecture_2,axiom,
~ c_in(v_A,c_Event_Obad,tc_Message_Oagent),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_2268,plain,
~ c_in(v_A,c_Event_Obad,tc_Message_Oagent),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_1,axiom,
~ c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_NB,c_Message_Omsg_OKey(v_K)))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_2269,plain,
~ c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_NB,c_Message_Omsg_OKey(v_K)))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_0,axiom,
c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_B,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OKey(v_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(v_NB,c_Message_Omsg_OKey(v_K)))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_2270,plain,
c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_B,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OKey(v_K))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(v_NB,c_Message_Omsg_OKey(v_K)))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_OtwayRees_Osecrecy__lemma__dest_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(VAR_2,c_Message_Omsg_OMPair(VAR_5,c_Message_Omsg_OKey(VAR_4)))),c_List_Oset(VAR_0,tc_Event_Oevent),tc_Event_Oevent)
| c_in(VAR_3,c_Event_Obad,tc_Message_Oagent)
| c_in(VAR_1,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(c_Message_Omsg_OKey(VAR_4),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,VAR_0)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,VAR_1,c_Message_Omsg_OMPair(VAR_2,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(VAR_3),c_Message_Omsg_OMPair(VAR_2,c_Message_Omsg_OKey(VAR_4))),c_Message_Omsg_OCrypt(c_Public_OshrK(VAR_1),c_Message_Omsg_OMPair(VAR_5,c_Message_Omsg_OKey(VAR_4)))))),c_List_Oset(VAR_0,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(VAR_0,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ),
file('theBenchmark.p',cls_OtwayRees_Osecrecy__lemma__dest_0) ).
cnf(c_2271,plain,
( c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(C,c_Message_Omsg_OMPair(F,c_Message_Omsg_OKey(E)))),c_List_Oset(A,tc_Event_Oevent),tc_Event_Oevent)
| c_in(D,c_Event_Obad,tc_Message_Oagent)
| c_in(B,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(c_Message_Omsg_OKey(E),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,A)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,B,c_Message_Omsg_OMPair(C,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(D),c_Message_Omsg_OMPair(C,c_Message_Omsg_OKey(E))),c_Message_Omsg_OCrypt(c_Public_OshrK(B),c_Message_Omsg_OMPair(F,c_Message_Omsg_OKey(E)))))),c_List_Oset(A,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(A,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ),
inference(clausify,[status(thm)],[cls_OtwayRees_Osecrecy__lemma__dest_0]) ).
fof(cls_Message_Oanalz_OInj_0,axiom,
! [VAR_0,VAR_1] :
( c_in(VAR_0,c_Message_Oanalz(VAR_1),tc_Message_Omsg)
| ~ c_in(VAR_0,VAR_1,tc_Message_Omsg) ),
file('theBenchmark.p',cls_Message_Oanalz_OInj_0) ).
cnf(c_2328,plain,
( c_in(A,c_Message_Oanalz(B),tc_Message_Omsg)
| ~ c_in(A,B,tc_Message_Omsg) ),
inference(clausify,[status(thm)],[cls_Message_Oanalz_OInj_0]) ).
cnf(c_2832,plain,
( c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_NB,c_Message_Omsg_OKey(v_K)))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(v_A,c_Event_Obad,tc_Message_Oagent)
| c_in(v_B,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(c_Message_Omsg_OKey(v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg)
| ~ c_in(v_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ),
inference(resolve,[status(thm)],[c_2271,c_2270]) ).
cnf(c_2833,plain,
( c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_NB,c_Message_Omsg_OKey(v_K)))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(v_A,c_Event_Obad,tc_Message_Oagent)
| c_in(v_B,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(c_Message_Omsg_OKey(v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) ),
inference(resolve,[status(thm)],[c_2266,c_2832]) ).
cnf(c_2834,plain,
( c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_NB,c_Message_Omsg_OKey(v_K)))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(v_A,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(c_Message_Omsg_OKey(v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) ),
inference(resolve,[status(thm)],[c_2267,c_2833]) ).
cnf(c_2835,plain,
( c_in(c_Event_Oevent_ONotes(c_Message_Oagent_OSpy,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(v_NB,c_Message_Omsg_OKey(v_K)))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Message_Omsg_OKey(v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg) ),
inference(resolve,[status(thm)],[c_2268,c_2834]) ).
cnf(c_2773,plain,
~ c_in(c_Message_Omsg_OKey(v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_2269,c_2835]) ).
cnf(c_2836,plain,
c_in(c_Message_Omsg_OKey(v_K),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs)),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_2328,c_2265]) ).
cnf(c_2831,plain,
$false,
inference(resolve,[status(thm)],[c_2773,c_2836]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV313-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n008.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 13:32:25 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 3781656 was started by sandbox2 on n008,
% 0.09/0.37 % Sat Sep 26 13:32:25 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.41
% 0.09/0.41 % From the command line: assign(max_seconds, 300).
% 16.31/2.76
% 16.31/2.76 % SZS status Unsatisfiable for theBenchmark
% 16.31/2.76
% 16.31/2.76 % Proof 1 at 2.27 (+ 0.01) seconds.
% 16.31/2.76 % Length of proof is 10.
% 16.31/2.76 % Level of proof is 2.
% 16.31/2.76 % Maximum clause weight is 98.000.
% 16.31/2.76 % Given clauses 112.
% 16.31/2.76
% 16.31/2.76 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------