%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV750-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 09:09:03 AM UTC 2026
% Result : Unsatisfiable 20.05s 3.41s
% Output : CNFRefutation 20.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 23 ( 14 unt; 0 def)
% Number of atoms : 38 ( 19 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 35 ( 20 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 14 con; 0-3 aty)
% Number of variables : 32 ( 10 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_10,axiom,
( v_NA != c_Message_Omsg_ONonce(v_NAa)
| v_K != v_Ka ),
file('theBenchmark.p',cls_conjecture_10) ).
cnf(c_96,plain,
( v_NA != c_Message_Omsg_ONonce(v_NAa)
| v_K != v_Ka ),
inference(clausify,[status(thm)],[cls_conjecture_10]) ).
cnf(c_12786,plain,
( v_NA != c_Message_Omsg_ONonce(v_NAa)
| v_Ka != v_K ),
inference(copy,[status(thm)],[c_96]) ).
cnf(c_97,plain,
( c_Message_Omsg_ONonce(v_NAa) != v_NA
| v_Ka != v_K ),
inference(copy,[status(thm)],[c_12786]) ).
fof(cls_conjecture_9,axiom,
v_K = v_Ka,
file('theBenchmark.p',cls_conjecture_9) ).
cnf(c_98,plain,
v_K = v_Ka,
inference(clausify,[status(thm)],[cls_conjecture_9]) ).
cnf(c_99,plain,
v_Ka = v_K,
inference(copy,[status(thm)],[c_98]) ).
fof(cls_conjecture_7,axiom,
hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)),
file('theBenchmark.p',cls_conjecture_7) ).
cnf(c_101,plain,
hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_A),c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OAgent(v_A)))))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)),
inference(clausify,[status(thm)],[cls_conjecture_7]) ).
fof(cls_conjecture_4,axiom,
hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa)))))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(c_106,plain,
hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa)))))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)),
inference(clausify,[status(thm)],[cls_conjecture_4]) ).
fof(cls_conjecture_2,axiom,
hBOOL(c_in(v_evso,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_108,plain,
hBOOL(c_in(v_evso,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_unique__session__keys_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7,VAR_8,VAR_9] :
( ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,VAR_7,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,VAR_7),c_Message_Omsg_OMPair(VAR_0,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(VAR_8),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,VAR_5),VAR_9))))),c_List_Oset(VAR_2,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,VAR_3,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,VAR_3),c_Message_Omsg_OMPair(VAR_1,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(VAR_4),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,VAR_5),VAR_6))))),c_List_Oset(VAR_2,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(VAR_2,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| VAR_0 = VAR_1 ),
file('theBenchmark.p',cls_unique__session__keys_1) ).
cnf(c_154,plain,
( ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V7,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,V7),c_Message_Omsg_OMPair(A,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V8),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,F),V9))))),c_List_Oset(C,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,D,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,D),c_Message_Omsg_OMPair(B,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(E),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,F),V6))))),c_List_Oset(C,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(C,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| A = B ),
inference(clausify,[status(thm)],[cls_unique__session__keys_1]) ).
cnf(c_745,plain,
c_Message_Omsg_ONonce(v_NAa) != v_NA,
inference(resolve,[status(thm)],[c_99,c_97]) ).
cnf(c_870,plain,
hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,v_Ba),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_Ka),c_Message_Omsg_OAgent(v_Aa)))))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)),
inference(paramod,[status(thm)],[c_99,c_106]) ).
cnf(c_12787,plain,
( ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,B,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,B),c_Message_Omsg_OMPair(A,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(C),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),D))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(v_evso,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| A = v_NA ),
inference(resolve,[status(thm)],[c_154,c_101]) ).
cnf(c_12788,plain,
( ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,B,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,B),c_Message_Omsg_OMPair(A,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(C),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),D))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent))
| ~ hBOOL(c_in(v_evso,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| v_NA = A ),
inference(copy,[status(thm)],[c_12787]) ).
cnf(c_895,plain,
( ~ hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,B,c_Message_Omsg_OCrypt(hAPP(c_Public_OshrK,B),c_Message_Omsg_OMPair(A,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(C),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),D))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent))
| v_NA = A ),
inference(resolve,[status(thm)],[c_108,c_12788]) ).
cnf(c_12789,plain,
v_NA = c_Message_Omsg_ONonce(v_NAa),
inference(resolve,[status(thm)],[c_895,c_870]) ).
cnf(c_12790,plain,
c_Message_Omsg_ONonce(v_NAa) = v_NA,
inference(copy,[status(thm)],[c_12789]) ).
cnf(c_12785,plain,
$false,
inference(resolve,[status(thm)],[c_745,c_12790]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV750-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n003.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sat Sep 26 14:55:40 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.45 % Process 3141065 was started by sandbox on n003,
% 0.17/0.45 % Sat Sep 26 14:55:40 2026
% 0.17/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.49
% 0.17/0.49 % From the command line: assign(max_seconds, 300).
% 20.05/3.41
% 20.05/3.41 % given #500 (I,wt=19): 659 -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,A),A) # tptp_name(cls_inf__sup__ord_I3_J_0) # clausal_fof(1). [assumption].
% 20.05/3.41
% 20.05/3.41 % given #1000 (T,wt=23): 7280 c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,c_Orderings_Obot__class_Obot(tc_nat),tc_nat),A,tc_nat). [resolve(3466,b,3162,a)].
% 20.05/3.41
% 20.05/3.41 % SZS status Unsatisfiable for theBenchmark
% 20.05/3.41
% 20.05/3.41 % Proof 1 at 2.12 (+ 0.72) seconds.
% 20.05/3.41 % Length of proof is 12.
% 20.05/3.41 % Level of proof is 3.
% 20.05/3.41 % Maximum clause weight is 95.000.
% 20.05/3.41 % Given clauses 1046.
% 20.05/3.41
% 20.05/3.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------