%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV345-2 : 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 : n013.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 09:07:29 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.81s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 16 ( 12 unt; 0 def)
% Number of atoms : 25 ( 9 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 21 ( 12 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 14 con; 0-3 aty)
% Number of variables : 40 ( 15 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_Yahalom_Ounique__session__keys__dest_3,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7,VAR_8,VAR_9,VAR_10,VAR_11] :
( VAR_10 = VAR_5
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,VAR_7,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(VAR_7),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(VAR_8),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(VAR_3),c_Message_Omsg_OMPair(VAR_9,VAR_10)))),VAR_11)),c_List_Oset(VAR_0,tc_Event_Oevent),tc_Event_Oevent)
| ~ 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)))),VAR_6)),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_Ounique__session__keys__dest_3) ).
cnf(c_1,plain,
( V10 = F
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V7,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V7),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V8),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(D),c_Message_Omsg_OMPair(V9,V10)))),V11)),c_List_Oset(A,tc_Event_Oevent),tc_Event_Oevent)
| ~ 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)))),V6)),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_Ounique__session__keys__dest_3]) ).
fof(cls_conjecture_2,axiom,
c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_2,plain,
c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_3,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_NA),c_Message_Omsg_ONonce(v_NB))))),v_X)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_3,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_NB))))),v_X)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
fof(cls_conjecture_4,axiom,
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(v_na,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_evso,tc_Event_Oevent),tc_Event_Oevent),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(c_4,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(v_na,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_evso,tc_Event_Oevent),tc_Event_Oevent),
inference(clausify,[status(thm)],[cls_conjecture_4]) ).
fof(cls_conjecture_7,axiom,
v_nb != c_Message_Omsg_ONonce(v_NB),
file('theBenchmark.p',cls_conjecture_7) ).
cnf(c_5,plain,
v_nb != c_Message_Omsg_ONonce(v_NB),
inference(clausify,[status(thm)],[cls_conjecture_7]) ).
cnf(c_6,plain,
c_Message_Omsg_ONonce(v_NB) != v_nb,
inference(copy,[status(thm)],[c_5]) ).
cnf(c_9,plain,
( V9 = E
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V6,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V6),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V7),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(C),c_Message_Omsg_OMPair(V8,V9)))),V10)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| ~ 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)))),F)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_10,plain,
( D = c_Message_Omsg_ONonce(v_NB)
| ~ 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,D)))),E)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ),
inference(resolve,[status(thm)],[c_9,c_3]) ).
cnf(c_11,plain,
v_nb = c_Message_Omsg_ONonce(v_NB),
inference(resolve,[status(thm)],[c_10,c_4]) ).
cnf(c_7,plain,
c_Message_Omsg_ONonce(v_NB) = v_nb,
inference(copy,[status(thm)],[c_11]) ).
cnf(c_8,plain,
$false,
inference(resolve,[status(thm)],[c_7,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV345-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.79 % Computer : n013.cluster.edu
% 0.11/0.79 % Model : x86_64 x86_64
% 0.11/0.79 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.79 % Memory : 8046.5625MB
% 0.11/0.79 % OS : Linux 6.8.0-71-generic
% 0.11/0.79 % CPULimit : 300
% 0.11/0.79 % WCLimit : 300
% 0.11/0.79 % DateTime : Sat Sep 26 13:35:12 UTC 2026
% 0.11/0.79 % CPUTime :
% 0.11/0.80 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.80 % Process 2856800 was started by sandbox on n013,
% 0.11/0.80 % Sat Sep 26 13:35:12 2026
% 0.11/0.80 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.80
% 0.15/0.80 % From the command line: assign(max_seconds, 300).
% 0.15/0.81
% 0.15/0.81 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.81
% 0.15/0.81 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.15/0.81 % Length of proof is 8.
% 0.15/0.81 % Level of proof is 2.
% 0.15/0.81 % Maximum clause weight is 52.000.
% 0.15/0.81 % Given clauses 4.
% 0.15/0.81
% 0.15/0.81 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------