%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV768-1 : 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 : n007.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 09:09:04 AM UTC 2026
% Result : Unsatisfiable 13.09s 2.19s
% Output : CNFRefutation 13.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 33 ( 21 unt; 0 def)
% Number of atoms : 50 ( 6 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 37 ( 20 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 11 con; 0-3 aty)
% Number of variables : 26 ( 4 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_13,axiom,
hBOOL(c_in(c_Message_Omsg_OCrypt(v_KAB,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2)),tc_Message_Omsg)),
file('theBenchmark.p',cls_conjecture_13) ).
cnf(c_94,plain,
hBOOL(c_in(c_Message_Omsg_OCrypt(v_KAB,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2)),tc_Message_Omsg)),
inference(clausify,[status(thm)],[cls_conjecture_13]) ).
fof(cls_conjecture_11,axiom,
v_K = v_KAB,
file('theBenchmark.p',cls_conjecture_11) ).
cnf(c_97,plain,
v_K = v_KAB,
inference(clausify,[status(thm)],[cls_conjecture_11]) ).
cnf(c_98,plain,
v_KAB = v_K,
inference(copy,[status(thm)],[c_97]) ).
fof(cls_conjecture_3,axiom,
hBOOL(c_in(v_KAB,c_Message_OsymKeys,tc_nat)),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_109,plain,
hBOOL(c_in(v_KAB,c_Message_OsymKeys,tc_nat)),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
cnf(c_110,plain,
hBOOL(c_in(v_K,c_Message_OsymKeys,tc_nat)),
inference(paramod,[status(thm)],[c_98,c_109]) ).
fof(cls_conjecture_2,axiom,
~ hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_KAB),c_Event_Oused(v_evs2),tc_Message_Omsg)),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_111,plain,
~ hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_KAB),c_Event_Oused(v_evs2),tc_Message_Omsg)),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
cnf(c_112,plain,
~ hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Event_Oused(v_evs2),tc_Message_Omsg)),
inference(paramod,[status(thm)],[c_98,c_111]) ).
fof(cls_conjecture_1,axiom,
hBOOL(c_in(v_evs2,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_113,plain,
hBOOL(c_in(v_evs2,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_mem__def_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ hBOOL(c_in(VAR_1,VAR_0,VAR_2))
| hBOOL(hAPP(VAR_0,VAR_1)) ),
file('theBenchmark.p',cls_mem__def_0) ).
cnf(c_141,plain,
( ~ hBOOL(c_in(B,A,C))
| hBOOL(hAPP(A,B)) ),
inference(clausify,[status(thm)],[cls_mem__def_0]) ).
fof(cls_mem__def_1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ hBOOL(hAPP(VAR_1,VAR_0))
| hBOOL(c_in(VAR_0,VAR_1,VAR_2)) ),
file('theBenchmark.p',cls_mem__def_1) ).
cnf(c_142,plain,
( ~ hBOOL(hAPP(B,A))
| hBOOL(c_in(A,B,C)) ),
inference(clausify,[status(thm)],[cls_mem__def_1]) ).
fof(cls_new__keys__not__used_0,axiom,
! [VAR_0,VAR_1] :
( hBOOL(c_in(hAPP(c_Message_Omsg_OKey,VAR_0),c_Event_Oused(VAR_1),tc_Message_Omsg))
| ~ hBOOL(c_in(VAR_0,c_Message_OsymKeys,tc_nat))
| ~ hBOOL(c_in(VAR_1,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(VAR_0,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,VAR_1))),tc_nat)) ),
file('theBenchmark.p',cls_new__keys__not__used_0) ).
cnf(c_208,plain,
( hBOOL(c_in(hAPP(c_Message_Omsg_OKey,A),c_Event_Oused(B),tc_Message_Omsg))
| ~ hBOOL(c_in(A,c_Message_OsymKeys,tc_nat))
| ~ hBOOL(c_in(B,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent)))
| ~ hBOOL(c_in(A,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,B))),tc_nat)) ),
inference(clausify,[status(thm)],[cls_new__keys__not__used_0]) ).
fof(cls_Crypt__imp__invKey__keysFor_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ hBOOL(c_in(c_Message_Omsg_OCrypt(VAR_0,VAR_2),VAR_1,tc_Message_Omsg))
| hBOOL(c_in(c_Message_OinvKey(VAR_0),c_Message_OkeysFor(VAR_1),tc_nat)) ),
file('theBenchmark.p',cls_Crypt__imp__invKey__keysFor_0) ).
cnf(c_263,plain,
( ~ hBOOL(c_in(c_Message_Omsg_OCrypt(A,C),B,tc_Message_Omsg))
| hBOOL(c_in(c_Message_OinvKey(A),c_Message_OkeysFor(B),tc_nat)) ),
inference(clausify,[status(thm)],[cls_Crypt__imp__invKey__keysFor_0]) ).
fof(cls_invKey__K_0,axiom,
! [VAR_0] :
( ~ hBOOL(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_316,plain,
( ~ hBOOL(c_in(A,c_Message_OsymKeys,tc_nat))
| c_Message_OinvKey(A) = A ),
inference(clausify,[status(thm)],[cls_invKey__K_0]) ).
cnf(c_639,plain,
hBOOL(c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NB),c_Message_Omsg_ONonce(v_NB))),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2)),tc_Message_Omsg)),
inference(paramod,[status(thm)],[c_98,c_94]) ).
cnf(c_742,plain,
hBOOL(hAPP(c_Message_OsymKeys,v_K)),
inference(resolve,[status(thm)],[c_141,c_110]) ).
cnf(c_771,plain,
( hBOOL(c_in(hAPP(c_Message_Omsg_OKey,A),c_Event_Oused(v_evs2),tc_Message_Omsg))
| ~ hBOOL(c_in(A,c_Message_OsymKeys,tc_nat))
| ~ hBOOL(c_in(A,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2))),tc_nat)) ),
inference(resolve,[status(thm)],[c_208,c_113]) ).
cnf(c_956,plain,
c_Message_OinvKey(v_K) = v_K,
inference(resolve,[status(thm)],[c_316,c_110]) ).
cnf(c_4660,plain,
hBOOL(c_in(c_Message_OinvKey(v_K),c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2))),tc_nat)),
inference(resolve,[status(thm)],[c_639,c_263]) ).
cnf(c_2569,plain,
hBOOL(c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2))),tc_nat)),
inference(paramod,[status(thm)],[c_956,c_4660]) ).
cnf(c_2791,plain,
hBOOL(c_in(v_K,c_Message_OsymKeys,A)),
inference(resolve,[status(thm)],[c_742,c_142]) ).
cnf(c_4661,plain,
( hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Event_Oused(v_evs2),tc_Message_Omsg))
| ~ hBOOL(c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2))),tc_nat)) ),
inference(resolve,[status(thm)],[c_771,c_2791]) ).
cnf(c_4662,plain,
hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Event_Oused(v_evs2),tc_Message_Omsg)),
inference(resolve,[status(thm)],[c_2569,c_4661]) ).
cnf(c_4659,plain,
$false,
inference(resolve,[status(thm)],[c_112,c_4662]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV768-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n007.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sat Sep 26 14:53:39 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 4000315 was started by sandbox2 on n007,
% 0.16/0.43 % Sat Sep 26 14:53:39 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.47
% 0.16/0.47 % From the command line: assign(max_seconds, 300).
% 13.09/2.19
% 13.09/2.19 % given #500 (A,wt=34): 666 c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) != c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_bool) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_bool),tc_bool). [para(36(a,1),32(a,1))].
% 13.09/2.19
% 13.09/2.19 % SZS status Unsatisfiable for theBenchmark
% 13.09/2.19
% 13.09/2.19 % Proof 1 at 1.35 (+ 0.33) seconds.
% 13.09/2.19 % Length of proof is 20.
% 13.09/2.19 % Level of proof is 5.
% 13.09/2.19 % Maximum clause weight is 53.000.
% 13.09/2.19 % Given clauses 839.
% 13.09/2.19
% 13.09/2.19 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------