%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV286-2 : 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 : n002.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 09:07:16 AM UTC 2026
% Result : Unsatisfiable 0.15s 10.41s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 24 ( 15 unt; 0 def)
% Number of atoms : 47 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 47 ( 24 ~; 23 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 21 ( 21 usr; 11 con; 0-5 aty)
% Number of variables : 47 ( 9 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_OtwayRees_OA__trusts__OR4__dest_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_5,c_Message_Omsg_OMPair(VAR_3,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(VAR_2),c_Message_Omsg_OMPair(VAR_3,c_Message_Omsg_OKey(VAR_4))),c_Message_Omsg_OCrypt(c_Public_OshrK(VAR_5),c_Message_Omsg_OMPair(v_sko__u8o(VAR_2,VAR_5,VAR_4,VAR_3,VAR_0),c_Message_Omsg_OKey(VAR_4)))))),c_List_Oset(VAR_0,tc_Event_Oevent),tc_Event_Oevent)
| c_in(VAR_2,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(c_Event_Oevent_OSays(VAR_2,VAR_5,c_Message_Omsg_OMPair(VAR_3,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(VAR_2),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(VAR_5),c_Message_Omsg_OCrypt(c_Public_OshrK(VAR_2),c_Message_Omsg_OMPair(VAR_3,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(VAR_2),c_Message_Omsg_OAgent(VAR_5)))))))),c_List_Oset(VAR_0,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(VAR_1,VAR_2,c_Message_Omsg_OMPair(VAR_3,c_Message_Omsg_OCrypt(c_Public_OshrK(VAR_2),c_Message_Omsg_OMPair(VAR_3,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_OA__trusts__OR4__dest_0) ).
cnf(c_1,plain,
( c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,F,c_Message_Omsg_OMPair(D,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(C),c_Message_Omsg_OMPair(D,c_Message_Omsg_OKey(E))),c_Message_Omsg_OCrypt(c_Public_OshrK(F),c_Message_Omsg_OMPair(v_sko__u8o(C,F,E,D,A),c_Message_Omsg_OKey(E)))))),c_List_Oset(A,tc_Event_Oevent),tc_Event_Oevent)
| c_in(C,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(c_Event_Oevent_OSays(C,F,c_Message_Omsg_OMPair(D,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(C),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(F),c_Message_Omsg_OCrypt(c_Public_OshrK(C),c_Message_Omsg_OMPair(D,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(C),c_Message_Omsg_OAgent(F)))))))),c_List_Oset(A,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(B,C,c_Message_Omsg_OMPair(D,c_Message_Omsg_OCrypt(c_Public_OshrK(C),c_Message_Omsg_OMPair(D,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_OA__trusts__OR4__dest_0]) ).
fof(cls_OtwayRees_OOR3__imp__OR2__dest_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( c_in(c_Event_Oevent_OSays(VAR_1,c_Message_Oagent_OServer,c_Message_Omsg_OMPair(VAR_2,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(VAR_3),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(VAR_1),c_Message_Omsg_OMPair(v_sko__vEb(VAR_3,VAR_1,VAR_2,VAR_5,VAR_0),c_Message_Omsg_OCrypt(c_Public_OshrK(VAR_1),c_Message_Omsg_OMPair(VAR_2,c_Message_Omsg_OMPair(VAR_5,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(VAR_3),c_Message_Omsg_OAgent(VAR_1)))))))))),c_List_Oset(VAR_0,tc_Event_Oevent),tc_Event_Oevent)
| c_in(VAR_1,c_Event_Obad,tc_Message_Oagent)
| ~ 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_OOR3__imp__OR2__dest_0) ).
cnf(c_2,plain,
( c_in(c_Event_Oevent_OSays(B,c_Message_Oagent_OServer,c_Message_Omsg_OMPair(C,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(D),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(B),c_Message_Omsg_OMPair(v_sko__vEb(D,B,C,F,A),c_Message_Omsg_OCrypt(c_Public_OshrK(B),c_Message_Omsg_OMPair(C,c_Message_Omsg_OMPair(F,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(D),c_Message_Omsg_OAgent(B)))))))))),c_List_Oset(A,tc_Event_Oevent),tc_Event_Oevent)
| c_in(B,c_Event_Obad,tc_Message_Oagent)
| ~ 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_OOR3__imp__OR2__dest_0]) ).
fof(cls_conjecture_0,axiom,
c_in(c_Event_Oevent_OSays(v_B_H,v_A,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,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_3,plain,
c_in(c_Event_Oevent_OSays(v_B_H,v_A,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,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_conjecture_1,axiom,
c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B)))))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_4,plain,
c_in(c_Event_Oevent_OSays(v_A,v_B,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B)))))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_2,axiom,
~ c_in(v_A,c_Event_Obad,tc_Message_Oagent),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_5,plain,
~ c_in(v_A,c_Event_Obad,tc_Message_Oagent),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_3,axiom,
~ c_in(v_B,c_Event_Obad,tc_Message_Oagent),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_6,plain,
~ c_in(v_B,c_Event_Obad,tc_Message_Oagent),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
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_7,plain,
c_in(v_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)),
inference(clausify,[status(thm)],[cls_conjecture_4]) ).
fof(cls_conjecture_5,axiom,
! [VAR_0,VAR_1] : ~ c_in(c_Event_Oevent_OSays(v_B,c_Message_Oagent_OServer,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(VAR_0,c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(VAR_1,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B)))))))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent),
file('theBenchmark.p',cls_conjecture_5) ).
cnf(c_8,plain,
~ c_in(c_Event_Oevent_OSays(v_B,c_Message_Oagent_OServer,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(A,c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(B,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OAgent(v_B)))))))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent),
inference(clausify,[status(thm)],[cls_conjecture_5]) ).
cnf(c_16,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(B))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(v_sko__u8o(v_A,v_B,B,v_NA,v_evs),c_Message_Omsg_OKey(B)))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(v_A,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(c_Event_Oevent_OSays(A,v_A,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OKey(B))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(v_evs,c_OtwayRees_Ootway,tc_List_Olist(tc_Event_Oevent)) ),
inference(resolve,[status(thm)],[c_4,c_1]) ).
cnf(c_17,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(B))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(v_sko__u8o(v_A,v_B,B,v_NA,v_evs),c_Message_Omsg_OKey(B)))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(v_A,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(c_Event_Oevent_OSays(A,v_A,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OKey(B))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent) ),
inference(resolve,[status(thm)],[c_7,c_16]) ).
cnf(c_10,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(B))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(v_sko__u8o(v_A,v_B,B,v_NA,v_evs),c_Message_Omsg_OKey(B)))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(A,v_A,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OKey(B))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent) ),
inference(resolve,[status(thm)],[c_5,c_17]) ).
cnf(c_18,plain,
( c_in(c_Event_Oevent_OSays(A,c_Message_Oagent_OServer,c_Message_Omsg_OMPair(B,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(C),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(A),c_Message_Omsg_OMPair(v_sko__vEb(C,A,B,E,v_evs),c_Message_Omsg_OCrypt(c_Public_OshrK(A),c_Message_Omsg_OMPair(B,c_Message_Omsg_OMPair(E,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(C),c_Message_Omsg_OAgent(A)))))))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)
| c_in(A,c_Event_Obad,tc_Message_Oagent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,A,c_Message_Omsg_OMPair(B,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(C),c_Message_Omsg_OMPair(B,c_Message_Omsg_OKey(D))),c_Message_Omsg_OCrypt(c_Public_OshrK(A),c_Message_Omsg_OMPair(E,c_Message_Omsg_OKey(D)))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent) ),
inference(resolve,[status(thm)],[c_2,c_7]) ).
cnf(c_19,plain,
( c_in(c_Event_Oevent_OSays(v_B,c_Message_Oagent_OServer,c_Message_Omsg_OMPair(A,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(v_sko__vEb(B,v_B,A,D,v_evs),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(A,c_Message_Omsg_OMPair(D,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(B),c_Message_Omsg_OAgent(v_B)))))))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_B,c_Message_Omsg_OMPair(A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(B),c_Message_Omsg_OMPair(A,c_Message_Omsg_OKey(C))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(D,c_Message_Omsg_OKey(C)))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent) ),
inference(resolve,[status(thm)],[c_18,c_6]) ).
cnf(c_13,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(A))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(B,c_Message_Omsg_OKey(A)))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent),
inference(resolve,[status(thm)],[c_19,c_8]) ).
cnf(c_14,plain,
~ c_in(c_Event_Oevent_OSays(A,v_A,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OKey(B))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent),
inference(resolve,[status(thm)],[c_13,c_10]) ).
cnf(c_15,plain,
$false,
inference(resolve,[status(thm)],[c_14,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV286-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/10.39 % Computer : n002.cluster.edu
% 0.11/10.39 % Model : x86_64 x86_64
% 0.11/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.39 % Memory : 8046.5625MB
% 0.11/10.39 % OS : Linux 6.8.0-71-generic
% 0.11/10.39 % CPULimit : 300
% 0.11/10.39 % WCLimit : 300
% 0.11/10.39 % DateTime : Sat Sep 26 13:30:45 UTC 2026
% 0.11/10.39 % CPUTime :
% 0.11/10.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/10.40 % Process 1843668 was started by sandbox2 on n002,
% 0.11/10.40 % Sat Sep 26 13:30:45 2026
% 0.11/10.40 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/10.40
% 0.15/10.40 % From the command line: assign(max_seconds, 300).
% 0.15/10.41
% 0.15/10.41 % SZS status Unsatisfiable for theBenchmark
% 0.15/10.41
% 0.15/10.41 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.15/10.41 % Length of proof is 12.
% 0.15/10.41 % Level of proof is 3.
% 0.15/10.41 % Maximum clause weight is 82.000.
% 0.15/10.41 % Given clauses 8.
% 0.15/10.41
% 0.15/10.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------