%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV346-1 : 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 : n005.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 51.42s 18.04s
% Output : CNFRefutation 51.42s
% 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_2,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_9 = VAR_4
| ~ 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_2) ).
cnf(c_2334,plain,
( V9 = E
| ~ 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_2]) ).
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_2338,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_2339,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_2340,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_na != c_Message_Omsg_ONonce(v_NA),
file('theBenchmark.p',cls_conjecture_7) ).
cnf(c_2343,plain,
v_na != c_Message_Omsg_ONonce(v_NA),
inference(clausify,[status(thm)],[cls_conjecture_7]) ).
cnf(c_2344,plain,
c_Message_Omsg_ONonce(v_NA) != v_na,
inference(copy,[status(thm)],[c_2343]) ).
cnf(c_11302,plain,
( V8 = D
| ~ 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_2334,c_2338]) ).
cnf(c_11303,plain,
( C = c_Message_Omsg_ONonce(v_NA)
| ~ 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_11302,c_2339]) ).
cnf(c_11304,plain,
v_na = c_Message_Omsg_ONonce(v_NA),
inference(resolve,[status(thm)],[c_11303,c_2340]) ).
cnf(c_11305,plain,
c_Message_Omsg_ONonce(v_NA) = v_na,
inference(copy,[status(thm)],[c_11304]) ).
cnf(c_11301,plain,
$false,
inference(resolve,[status(thm)],[c_2344,c_11305]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV346-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/10.52 % Computer : n005.cluster.edu
% 0.10/10.52 % Model : x86_64 x86_64
% 0.10/10.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.52 % Memory : 8046.5625MB
% 0.10/10.52 % OS : Linux 6.8.0-71-generic
% 0.10/10.52 % CPULimit : 300
% 0.10/10.52 % WCLimit : 300
% 0.10/10.52 % DateTime : Sat Sep 26 13:35:27 UTC 2026
% 0.10/10.53 % CPUTime :
% 0.10/10.53 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/10.53 % Process 2279509 was started by sandbox on n005,
% 0.10/10.53 % Sat Sep 26 13:35:27 2026
% 0.10/10.53 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/10.60
% 0.12/10.60 % From the command line: assign(max_seconds, 300).
% 51.42/18.04
% 51.42/18.04 % given #500 (I,wt=24): 955 c_List_Oset(c_List_Oremdups(A,B),B) = c_List_Oset(A,B) # tptp_name(cls_List_Oset__remdups_0) # clausal_fof(1). [assumption].
% 51.42/18.04
% 51.42/18.04 % given #1000 (I,wt=24): 1635 c_Pair(A,B,C,D) != c_Pair(E,F,C,D) | B = F # tptp_name(cls_Product__Type_OPair__eq_1) # clausal_fof(1). [assumption].
% 51.42/18.04
% 51.42/18.04 % SZS status Unsatisfiable for theBenchmark
% 51.42/18.04
% 51.42/18.04 % Proof 1 at 6.83 (+ 0.45) seconds.
% 51.42/18.04 % Length of proof is 7.
% 51.42/18.04 % Level of proof is 2.
% 51.42/18.04 % Maximum clause weight is 107.000.
% 51.42/18.04 % Given clauses 1497.
% 51.42/18.04
% 51.42/18.04 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------