%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV756-1 : 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 9.04s 1.64s
% Output : CNFRefutation 9.04s
% 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 : 21 ( 21 usr; 12 con; 0-3 aty)
% Number of variables : 26 ( 4 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_10,axiom,
hBOOL(c_in(c_Message_Omsg_OCrypt(v_KAB,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_10) ).
cnf(c_104,plain,
hBOOL(c_in(c_Message_Omsg_OCrypt(v_KAB,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_10]) ).
fof(cls_conjecture_8,axiom,
v_K = v_KAB,
file('theBenchmark.p',cls_conjecture_8) ).
cnf(c_107,plain,
v_K = v_KAB,
inference(clausify,[status(thm)],[cls_conjecture_8]) ).
cnf(c_108,plain,
v_KAB = v_K,
inference(copy,[status(thm)],[c_107]) ).
fof(cls_conjecture_2,axiom,
hBOOL(c_in(v_KAB,c_Message_OsymKeys,tc_nat)),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_118,plain,
hBOOL(c_in(v_KAB,c_Message_OsymKeys,tc_nat)),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
cnf(c_119,plain,
hBOOL(c_in(v_K,c_Message_OsymKeys,tc_nat)),
inference(paramod,[status(thm)],[c_108,c_118]) ).
fof(cls_conjecture_1,axiom,
~ hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_KAB),c_Event_Oused(v_evs2),tc_Message_Omsg)),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_120,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_1]) ).
cnf(c_121,plain,
~ hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Event_Oused(v_evs2),tc_Message_Omsg)),
inference(paramod,[status(thm)],[c_108,c_120]) ).
fof(cls_conjecture_0,axiom,
hBOOL(c_in(v_evs2,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_122,plain,
hBOOL(c_in(v_evs2,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
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_146,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_147,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_202,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(hAPP(c_Message_OinvKey,VAR_0),c_Message_OkeysFor(VAR_1),tc_nat)) ),
file('theBenchmark.p',cls_Crypt__imp__invKey__keysFor_0) ).
cnf(c_390,plain,
( ~ hBOOL(c_in(c_Message_Omsg_OCrypt(A,C),B,tc_Message_Omsg))
| hBOOL(c_in(hAPP(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))
| hAPP(c_Message_OinvKey,VAR_0) = VAR_0 ),
file('theBenchmark.p',cls_invKey__K_0) ).
cnf(c_418,plain,
( ~ hBOOL(c_in(A,c_Message_OsymKeys,tc_nat))
| hAPP(c_Message_OinvKey,A) = A ),
inference(clausify,[status(thm)],[cls_invKey__K_0]) ).
cnf(c_648,plain,
hBOOL(c_in(c_Message_Omsg_OCrypt(v_K,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_108,c_104]) ).
cnf(c_771,plain,
hBOOL(hAPP(c_Message_OsymKeys,v_K)),
inference(resolve,[status(thm)],[c_146,c_119]) ).
cnf(c_791,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_202,c_122]) ).
cnf(c_1485,plain,
hAPP(c_Message_OinvKey,v_K) = v_K,
inference(resolve,[status(thm)],[c_418,c_119]) ).
cnf(c_4652,plain,
hBOOL(c_in(hAPP(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_648,c_390]) ).
cnf(c_2593,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_1485,c_4652]) ).
cnf(c_2978,plain,
hBOOL(c_in(v_K,c_Message_OsymKeys,A)),
inference(resolve,[status(thm)],[c_771,c_147]) ).
cnf(c_4653,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_791,c_2978]) ).
cnf(c_4654,plain,
hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Event_Oused(v_evs2),tc_Message_Omsg)),
inference(resolve,[status(thm)],[c_2593,c_4653]) ).
cnf(c_4651,plain,
$false,
inference(resolve,[status(thm)],[c_121,c_4654]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV756-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n003.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 14:56:09 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 3142616 was started by sandbox on n003,
% 0.10/0.37 % Sat Sep 26 14:56:09 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.40
% 0.10/0.40 % From the command line: assign(max_seconds, 300).
% 9.04/1.64
% 9.04/1.64 % given #500 (W,wt=14): 752 class_Orderings_Obot(tc_fun(A,tc_nat)). [resolve(95,b,89,a)].
% 9.04/1.64
% 9.04/1.64 % SZS status Unsatisfiable for theBenchmark
% 9.04/1.64
% 9.04/1.64 % Proof 1 at 0.98 (+ 0.22) seconds.
% 9.04/1.64 % Length of proof is 20.
% 9.04/1.64 % Level of proof is 5.
% 9.04/1.64 % Maximum clause weight is 53.000.
% 9.04/1.64 % Given clauses 828.
% 9.04/1.64
% 9.04/1.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------