%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV331-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 09:07:26 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 11 unt; 0 def)
% Number of atoms : 32 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 30 ( 16 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-2 aty)
% Number of variables : 12 ( 2 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
c_in(v_evs3,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1,plain,
c_in(v_evs3,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_conjecture_1,axiom,
~ c_in(c_Message_Omsg_OKey(v_K),c_Event_Oused(v_evs3),tc_Message_Omsg),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_2,plain,
~ c_in(c_Message_Omsg_OKey(v_K),c_Event_Oused(v_evs3),tc_Message_Omsg),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_2,axiom,
c_in(v_K,c_Message_OsymKeys,tc_nat),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_3,plain,
c_in(v_K,c_Message_OsymKeys,tc_nat),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_5,axiom,
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_evs3)),tc_Message_Omsg),
file('theBenchmark.p',cls_conjecture_5) ).
cnf(c_4,plain,
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_evs3)),tc_Message_Omsg),
inference(clausify,[status(thm)],[cls_conjecture_5]) ).
fof(cls_Public_OCrypt__imp__keysFor_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_in(VAR_0,c_Message_OkeysFor(VAR_2),tc_nat)
| ~ c_in(c_Message_Omsg_OCrypt(VAR_0,VAR_1),VAR_2,tc_Message_Omsg)
| ~ c_in(VAR_0,c_Message_OsymKeys,tc_nat) ),
file('theBenchmark.p',cls_Public_OCrypt__imp__keysFor_0) ).
cnf(c_5,plain,
( c_in(A,c_Message_OkeysFor(C),tc_nat)
| ~ c_in(c_Message_Omsg_OCrypt(A,B),C,tc_Message_Omsg)
| ~ c_in(A,c_Message_OsymKeys,tc_nat) ),
inference(clausify,[status(thm)],[cls_Public_OCrypt__imp__keysFor_0]) ).
fof(cls_Yahalom_Onew__keys__not__used_0,axiom,
! [VAR_0,VAR_1] :
( c_in(c_Message_Omsg_OKey(VAR_0),c_Event_Oused(VAR_1),tc_Message_Omsg)
| ~ c_in(VAR_1,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(VAR_0,c_Message_OsymKeys,tc_nat)
| ~ 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_Yahalom_Onew__keys__not__used_0) ).
cnf(c_6,plain,
( c_in(c_Message_Omsg_OKey(A),c_Event_Oused(B),tc_Message_Omsg)
| ~ c_in(B,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(A,c_Message_OsymKeys,tc_nat)
| ~ c_in(A,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,B))),tc_nat) ),
inference(clausify,[status(thm)],[cls_Yahalom_Onew__keys__not__used_0]) ).
cnf(c_10,plain,
( c_in(v_K,c_Message_OkeysFor(B),tc_nat)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,A),B,tc_Message_Omsg) ),
inference(resolve,[status(thm)],[c_5,c_3]) ).
cnf(c_7,plain,
c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3))),tc_nat),
inference(resolve,[status(thm)],[c_10,c_4]) ).
cnf(c_11,plain,
( c_in(c_Message_Omsg_OKey(v_K),c_Event_Oused(v_evs3),tc_Message_Omsg)
| ~ c_in(v_evs3,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(v_K,c_Message_OsymKeys,tc_nat) ),
inference(resolve,[status(thm)],[c_6,c_7]) ).
cnf(c_12,plain,
( c_in(c_Message_Omsg_OKey(v_K),c_Event_Oused(v_evs3),tc_Message_Omsg)
| ~ c_in(v_evs3,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(resolve,[status(thm)],[c_11,c_3]) ).
cnf(c_8,plain,
c_in(c_Message_Omsg_OKey(v_K),c_Event_Oused(v_evs3),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_12,c_1]) ).
cnf(c_9,plain,
$false,
inference(resolve,[status(thm)],[c_8,c_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV331-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n001.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 13:38:58 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 1924289 was started by sandbox on n001,
% 0.10/0.38 % Sat Sep 26 13:38:58 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.10/0.39
% 0.10/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.39
% 0.10/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.39 % Length of proof is 9.
% 0.10/0.39 % Level of proof is 3.
% 0.10/0.39 % Maximum clause weight is 23.000.
% 0.10/0.39 % Given clauses 7.
% 0.10/0.39
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------