%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV727-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 09:09:00 AM UTC 2026
% Result : Unsatisfiable 16.13s 2.91s
% Output : CNFRefutation 16.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 27 ( 15 unt; 0 def)
% Number of atoms : 44 ( 5 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 31 ( 14 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 9 con; 0-3 aty)
% Number of variables : 20 ( 1 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_6,axiom,
( c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Event_Oused(v_evsf),tc_Message_Omsg)
| ~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_nat) ),
file('theBenchmark.p',cls_conjecture_6) ).
cnf(c_91,plain,
( c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Event_Oused(v_evsf),tc_Message_Omsg)
| ~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_nat) ),
inference(clausify,[status(thm)],[cls_conjecture_6]) ).
fof(cls_conjecture_5,axiom,
c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg))),tc_nat),
file('theBenchmark.p',cls_conjecture_5) ).
cnf(c_92,plain,
c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_Message_Omsg))),tc_nat),
inference(clausify,[status(thm)],[cls_conjecture_5]) ).
fof(cls_conjecture_4,axiom,
~ c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Event_Oused(v_evsf),tc_Message_Omsg),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(c_93,plain,
~ c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Event_Oused(v_evsf),tc_Message_Omsg),
inference(clausify,[status(thm)],[cls_conjecture_4]) ).
fof(cls_conjecture_2,axiom,
c_in(v_X,c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_95,plain,
c_in(v_X,c_Message_Osynth(c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_Message_Omsg),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_0,axiom,
c_in(v_K,c_Message_OsymKeys,tc_nat),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_97,plain,
c_in(v_K,c_Message_OsymKeys,tc_nat),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_usedI_0,axiom,
! [VAR_0,VAR_1] :
( ~ c_in(VAR_0,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,VAR_1)),tc_Message_Omsg)
| c_in(VAR_0,c_Event_Oused(VAR_1),tc_Message_Omsg) ),
file('theBenchmark.p',cls_usedI_0) ).
cnf(c_134,plain,
( ~ c_in(A,c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,B)),tc_Message_Omsg)
| c_in(A,c_Event_Oused(B),tc_Message_Omsg) ),
inference(clausify,[status(thm)],[cls_usedI_0]) ).
fof(cls_keysFor__parts__insert_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ c_in(VAR_0,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(VAR_3,VAR_2,tc_Message_Omsg))),tc_nat)
| ~ c_in(VAR_3,c_Message_Osynth(c_Message_Oanalz(VAR_1)),tc_Message_Omsg)
| c_in(VAR_0,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(VAR_2,VAR_1,tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat)
| c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(VAR_0)),c_Message_Oparts(VAR_1),tc_Message_Omsg) ),
file('theBenchmark.p',cls_keysFor__parts__insert_0) ).
cnf(c_169,plain,
( ~ c_in(A,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(D,C,tc_Message_Omsg))),tc_nat)
| ~ c_in(D,c_Message_Osynth(c_Message_Oanalz(B)),tc_Message_Omsg)
| c_in(A,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(C,B,tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat)
| c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(A)),c_Message_Oparts(B),tc_Message_Omsg) ),
inference(clausify,[status(thm)],[cls_keysFor__parts__insert_0]) ).
fof(cls_Un__absorb_0,axiom,
! [VAR_0,VAR_1] : c_Lattices_Oupper__semilattice__class_Osup(VAR_0,VAR_0,tc_fun(VAR_1,tc_bool)) = VAR_0,
file('theBenchmark.p',cls_Un__absorb_0) ).
cnf(c_240,plain,
c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_fun(B,tc_bool)) = A,
inference(clausify,[status(thm)],[cls_Un__absorb_0]) ).
fof(cls_invKey__K_0,axiom,
! [VAR_0] :
( ~ c_in(VAR_0,c_Message_OsymKeys,tc_nat)
| c_Message_OinvKey(VAR_0) = VAR_0 ),
file('theBenchmark.p',cls_invKey__K_0) ).
cnf(c_272,plain,
( ~ c_in(A,c_Message_OsymKeys,tc_nat)
| c_Message_OinvKey(A) = A ),
inference(clausify,[status(thm)],[cls_invKey__K_0]) ).
cnf(c_530,plain,
~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_nat),
inference(resolve,[status(thm)],[c_93,c_91]) ).
cnf(c_661,plain,
( ~ c_in(A,c_Message_OkeysFor(c_Message_Oparts(c_Set_Oinsert(v_X,B,tc_Message_Omsg))),tc_nat)
| c_in(A,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(B,c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat)
| c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(A)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg) ),
inference(resolve,[status(thm)],[c_169,c_95]) ).
cnf(c_861,plain,
c_Message_OinvKey(v_K) = v_K,
inference(resolve,[status(thm)],[c_272,c_97]) ).
cnf(c_11724,plain,
( c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat)
| c_in(hAPP(c_Message_Omsg_OKey,c_Message_OinvKey(v_K)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg) ),
inference(resolve,[status(thm)],[c_661,c_92]) ).
cnf(c_11725,plain,
( c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf),tc_fun(tc_Message_Omsg,tc_bool)))),tc_nat)
| c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg) ),
inference(paramod,[status(thm)],[c_861,c_11724]) ).
cnf(c_11726,plain,
( c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf))),tc_nat)
| c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg) ),
inference(paramod,[status(thm)],[c_240,c_11725]) ).
cnf(c_9957,plain,
c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evsf)),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_530,c_11726]) ).
cnf(c_11727,plain,
c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Event_Oused(v_evsf),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_9957,c_134]) ).
cnf(c_11723,plain,
$false,
inference(resolve,[status(thm)],[c_93,c_11727]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV727-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n018.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 14:53:22 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 699738 was started by sandbox2 on n018,
% 0.09/0.36 % Sat Sep 26 14:53:22 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.38
% 0.13/0.38 % From the command line: assign(max_seconds, 300).
% 16.13/2.91
% 16.13/2.91 % given #500 (T,wt=17): 2469 c_in(v_evsf,c_Set_Oinsert(A,c_NS__Shared__Mirabelle_Ons__shared,B),B). [resolve(2452,a,148,b)].
% 16.13/2.91
% 16.13/2.91 % given #1000 (A,wt=41): 619 c_Set_Oinsert(hAPP(c_Message_Omsg_OKey,A),c_Message_Oanalz(B),tc_Message_Omsg) = c_Message_Oanalz(c_Set_Oinsert(hAPP(c_Message_Omsg_OKey,A),B,tc_Message_Omsg)) | hBOOL(hAPP(c_Message_OkeysFor(c_Message_Oanalz(B)),A)). [resolve(143,b,113,b)].
% 16.13/2.91
% 16.13/2.91 % given #1500 (T,wt=24): 8197 c_in(c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Oagent_OSpy),c_Message_Oagent_OSpy),c_Message_Oparts(c_Message_Osynth(c_Event_Obad)),tc_Message_Omsg). [resolve(4779,a,147,b)].
% 16.13/2.91
% 16.13/2.91 % SZS status Unsatisfiable for theBenchmark
% 16.13/2.91
% 16.13/2.91 % Proof 1 at 1.79 (+ 0.46) seconds.
% 16.13/2.91 % Length of proof is 14.
% 16.13/2.91 % Level of proof is 3.
% 16.13/2.91 % Maximum clause weight is 59.000.
% 16.13/2.91 % Given clauses 1515.
% 16.13/2.91
% 16.13/2.91 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------