TSTP Solution File: SWV354-2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWV354-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Wed Jul 20 21:42:28 EDT 2022
% Result : Unsatisfiable 0.18s 0.41s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of clauses : 30 ( 14 unt; 7 nHn; 30 RR)
% Number of literals : 63 ( 0 equ; 31 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 43 ( 43 usr; 29 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ c_in(u,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Message_Omsg_ONonce(v),c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(w),c_Event_Oknows(c_Message_Oagent_OSpy,u),tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,x,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(x),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(y),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(w),c_Message_Omsg_OMPair(z,c_Message_Omsg_ONonce(x1))))),x2)),c_List_Oset(u,tc_Event_Oevent),tc_Event_Oevent)
| equal(v,x1)
| equal(c_Public_OshrK(v_sko__2VY(w)),w)
| c_in(c_Message_Omsg_ONonce(v),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,u)),tc_Message_Omsg) ),
file('SWV354-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ c_in(u,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(w),c_Message_Omsg_OMPair(x,c_Message_Omsg_OMPair(y,z)))),x1)),c_List_Oset(u,tc_Event_Oevent),tc_Event_Oevent)
| c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(w),c_Message_Omsg_OCrypt(c_Public_OshrK(w),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v),c_Message_Omsg_OMPair(y,z))))),c_List_Oset(u,tc_Event_Oevent),tc_Event_Oevent) ),
file('SWV354-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ c_in(u,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OGets(v,c_Message_Omsg_OMPair(w,c_Message_Omsg_OCrypt(c_Public_OshrK(x),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(y),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(z),x1))))),c_List_Oset(u,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(x2,x3,c_Message_Omsg_OMPair(x4,c_Message_Omsg_OCrypt(c_Public_OshrK(x5),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(x6),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(x7),x1))))),c_List_Oset(u,tc_Event_Oevent),tc_Event_Oevent)
| equal(z,x7)
| c_in(x1,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,u)),tc_Message_Omsg) ),
file('SWV354-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ c_in(u,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(w),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(c_Public_OshrK(x)),c_Message_Omsg_OMPair(y,z)))),x1)),c_List_Oset(u,tc_Event_Oevent),tc_Event_Oevent) ),
file('SWV354-2.p',unknown),
[] ).
cnf(5,axiom,
c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)),
file('SWV354-2.p',unknown),
[] ).
cnf(6,axiom,
c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_ONonce(v_NBa))))),v_X)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent),
file('SWV354-2.p',unknown),
[] ).
cnf(7,axiom,
c_in(c_Event_Oevent_OSays(v_B,c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent),
file('SWV354-2.p',unknown),
[] ).
cnf(8,axiom,
~ c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg),
file('SWV354-2.p',unknown),
[] ).
cnf(9,axiom,
c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(v_K),c_Event_Oknows(c_Message_Oagent_OSpy,v_evso),tc_Message_Omsg)),tc_Message_Omsg),
file('SWV354-2.p',unknown),
[] ).
cnf(10,axiom,
( ~ equal(u,c_Message_Omsg_OKey(v_K))
| ~ equal(v_NA,v_NAa)
| ~ equal(v_NB,v_NBa) ),
file('SWV354-2.p',unknown),
[] ).
cnf(11,plain,
( ~ equal(v_NB,v_NBa)
| ~ equal(v_NA,v_NAa) ),
inference(aed,[status(thm),theory(equality)],[10]),
[iquote('0:AED:10.0')] ).
cnf(12,plain,
( ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_ONonce(v_NBa)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ),
inference(res,[status(thm),theory(equality)],[6,2]),
[iquote('0:Res:6.0,2.1')] ).
cnf(13,plain,
c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_ONonce(v_NBa)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent),
inference(mrr,[status(thm)],[12,5]),
[iquote('0:MRR:12.0,5.0')] ).
cnf(14,plain,
( ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OGets(u,c_Message_Omsg_OMPair(v,c_Message_Omsg_OCrypt(c_Public_OshrK(w),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(x),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(y),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| equal(y,v_NA)
| c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg) ),
inference(res,[status(thm),theory(equality)],[7,3]),
[iquote('0:Res:7.0,3.2')] ).
cnf(15,plain,
( ~ c_in(c_Event_Oevent_OGets(u,c_Message_Omsg_OMPair(v,c_Message_Omsg_OCrypt(c_Public_OshrK(w),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(x),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(y),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| equal(y,v_NA) ),
inference(mrr,[status(thm)],[14,5,8]),
[iquote('0:MRR:14.0,14.3,5.0,8.0')] ).
cnf(16,plain,
( ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Message_Omsg_ONonce(u),c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(v_K),c_Event_Oknows(c_Message_Oagent_OSpy,v_evso),tc_Message_Omsg)),tc_Message_Omsg)
| equal(u,v_NBa)
| equal(c_Public_OshrK(v_sko__2VY(v_K)),v_K)
| c_in(c_Message_Omsg_ONonce(u),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg) ),
inference(res,[status(thm),theory(equality)],[6,1]),
[iquote('0:Res:6.0,1.2')] ).
cnf(17,plain,
( ~ c_in(c_Message_Omsg_ONonce(u),c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(v_K),c_Event_Oknows(c_Message_Oagent_OSpy,v_evso),tc_Message_Omsg)),tc_Message_Omsg)
| equal(u,v_NBa)
| equal(c_Public_OshrK(v_sko__2VY(v_K)),v_K)
| c_in(c_Message_Omsg_ONonce(u),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg) ),
inference(mrr,[status(thm)],[16,5]),
[iquote('0:MRR:16.0,5.0')] ).
cnf(18,plain,
( equal(v_NB,v_NBa)
| equal(c_Public_OshrK(v_sko__2VY(v_K)),v_K)
| c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg) ),
inference(res,[status(thm),theory(equality)],[9,17]),
[iquote('0:Res:9.0,17.0')] ).
cnf(19,plain,
( equal(v_NB,v_NBa)
| equal(c_Public_OshrK(v_sko__2VY(v_K)),v_K) ),
inference(mrr,[status(thm)],[18,8]),
[iquote('0:MRR:18.2,8.0')] ).
cnf(20,plain,
equal(v_NB,v_NBa),
inference(spt,[spt(split,[position(s1)])],[19]),
[iquote('1:Spt:19.0')] ).
cnf(21,plain,
( ~ equal(v_NBa,v_NBa)
| ~ equal(v_NA,v_NAa) ),
inference(rew,[status(thm),theory(equality)],[20,11]),
[iquote('1:Rew:20.0,11.0')] ).
cnf(25,plain,
( ~ c_in(c_Event_Oevent_OGets(u,c_Message_Omsg_OMPair(v,c_Message_Omsg_OCrypt(c_Public_OshrK(w),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(x),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(y),c_Message_Omsg_ONonce(v_NBa)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| equal(y,v_NA) ),
inference(rew,[status(thm),theory(equality)],[20,15]),
[iquote('1:Rew:20.0,15.0')] ).
cnf(26,plain,
~ equal(v_NA,v_NAa),
inference(obv,[status(thm),theory(equality)],[21]),
[iquote('1:Obv:21.0')] ).
cnf(30,plain,
equal(v_NA,v_NAa),
inference(res,[status(thm),theory(equality)],[13,25]),
[iquote('1:Res:13.0,25.0')] ).
cnf(31,plain,
$false,
inference(mrr,[status(thm)],[30,26]),
[iquote('1:MRR:30.0,26.0')] ).
cnf(32,plain,
~ equal(v_NB,v_NBa),
inference(spt,[spt(split,[position(sa)])],[31,20]),
[iquote('1:Spt:31.0,19.0,20.0')] ).
cnf(33,plain,
equal(c_Public_OshrK(v_sko__2VY(v_K)),v_K),
inference(spt,[spt(split,[position(s2)])],[19]),
[iquote('1:Spt:31.0,19.1')] ).
cnf(35,plain,
( ~ c_in(u,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(w),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(x,y)))),z)),c_List_Oset(u,tc_Event_Oevent),tc_Event_Oevent) ),
inference(spl,[status(thm),theory(equality)],[33,4]),
[iquote('1:SpL:33.0,4.1')] ).
cnf(43,plain,
~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)),
inference(res,[status(thm),theory(equality)],[6,35]),
[iquote('1:Res:6.0,35.1')] ).
cnf(44,plain,
$false,
inference(mrr,[status(thm)],[43,5]),
[iquote('1:MRR:43.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV354-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n012.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Wed Jun 15 17:11:24 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.18/0.41
% 0.18/0.41 SPASS V 3.9
% 0.18/0.41 SPASS beiseite: Proof found.
% 0.18/0.41 % SZS status Theorem
% 0.18/0.41 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.41 SPASS derived 24 clauses, backtracked 7 clauses, performed 1 splits and kept 35 clauses.
% 0.18/0.41 SPASS allocated 63251 KBytes.
% 0.18/0.41 SPASS spent 0:00:00.07 on the problem.
% 0.18/0.41 0:00:00.04 for the input.
% 0.18/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.41 0:00:00.00 for inferences.
% 0.18/0.41 0:00:00.00 for the backtracking.
% 0.18/0.41 0:00:00.01 for the reduction.
% 0.18/0.41
% 0.18/0.41
% 0.18/0.41 Here is a proof with depth 5, length 30 :
% 0.18/0.41 % SZS output start Refutation
% See solution above
% 0.18/0.41 Formulae used in the proof : cls_Yahalom_Osingle__Nonce__secrecy_0 cls_Yahalom_OSays__Server__imp__YM2_0 cls_Yahalom_OSays__unique__NB_0 cls_Yahalom_OSays__Server__not__shrK_0 cls_conjecture_2 cls_conjecture_3 cls_conjecture_5 cls_conjecture_6 cls_conjecture_7 cls_conjecture_9
% 0.18/0.42
%------------------------------------------------------------------------------