TSTP Solution File: SWV014+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWV014+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 21:40:57 EDT 2022
% Result : Theorem 0.19s 0.47s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 20
% Syntax : Number of clauses : 48 ( 17 unt; 0 nHn; 48 RR)
% Number of literals : 119 ( 0 equ; 74 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-1 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
party_of_protocol(a),
file('SWV014+1.p',unknown),
[] ).
cnf(2,axiom,
party_of_protocol(b),
file('SWV014+1.p',unknown),
[] ).
cnf(3,axiom,
fresh_to_b(an_a_nonce),
file('SWV014+1.p',unknown),
[] ).
cnf(5,axiom,
a_nonce(an_a_nonce),
file('SWV014+1.p',unknown),
[] ).
cnf(7,axiom,
a_nonce(generate_b_nonce(u)),
file('SWV014+1.p',unknown),
[] ).
cnf(14,axiom,
message(sent(a,b,pair(a,an_a_nonce))),
file('SWV014+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ intruder_message(pair(u,v))
| intruder_message(u) ),
file('SWV014+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ intruder_message(pair(u,v))
| intruder_message(v) ),
file('SWV014+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ message(sent(u,v,w))
| intruder_message(w) ),
file('SWV014+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ intruder_message(triple(u,v,w))
| intruder_message(u) ),
file('SWV014+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ intruder_message(triple(u,v,w))
| intruder_message(v) ),
file('SWV014+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ intruder_message(triple(u,v,w))
| intruder_message(w) ),
file('SWV014+1.p',unknown),
[] ).
cnf(25,axiom,
( ~ b_holds(key(u,a))
| ~ intruder_holds(key(u,b)) ),
file('SWV014+1.p',unknown),
[] ).
cnf(26,axiom,
( ~ intruder_message(u)
| ~ intruder_message(v)
| intruder_message(pair(v,u)) ),
file('SWV014+1.p',unknown),
[] ).
cnf(27,axiom,
( ~ party_of_protocol(u)
| ~ intruder_message(v)
| intruder_holds(key(v,u)) ),
file('SWV014+1.p',unknown),
[] ).
cnf(29,axiom,
( ~ party_of_protocol(u)
| ~ party_of_protocol(v)
| ~ intruder_message(w)
| message(sent(v,u,w)) ),
file('SWV014+1.p',unknown),
[] ).
cnf(30,axiom,
( ~ fresh_to_b(u)
| ~ message(sent(v,b,pair(v,u)))
| b_stored(pair(v,u)) ),
file('SWV014+1.p',unknown),
[] ).
cnf(32,axiom,
( ~ party_of_protocol(u)
| ~ intruder_message(v)
| ~ intruder_holds(key(w,u))
| intruder_message(encrypt(v,w)) ),
file('SWV014+1.p',unknown),
[] ).
cnf(35,axiom,
( ~ b_stored(pair(u,v))
| ~ message(sent(u,b,pair(encrypt(triple(u,w,generate_expiration_time(v)),bt),encrypt(generate_b_nonce(v),w))))
| b_holds(key(w,u)) ),
file('SWV014+1.p',unknown),
[] ).
cnf(36,axiom,
( ~ fresh_to_b(u)
| ~ message(sent(v,b,pair(v,u)))
| message(sent(b,t,triple(b,generate_b_nonce(u),encrypt(triple(v,u,generate_expiration_time(u)),bt)))) ),
file('SWV014+1.p',unknown),
[] ).
cnf(75,plain,
intruder_message(pair(a,an_a_nonce)),
inference(res,[status(thm),theory(equality)],[14,17]),
[iquote('0:Res:14.0,17.0')] ).
cnf(76,plain,
intruder_message(a),
inference(res,[status(thm),theory(equality)],[75,15]),
[iquote('0:Res:75.0,15.0')] ).
cnf(77,plain,
intruder_message(an_a_nonce),
inference(res,[status(thm),theory(equality)],[75,16]),
[iquote('0:Res:75.0,16.0')] ).
cnf(84,plain,
( ~ fresh_to_b(an_a_nonce)
| b_stored(pair(a,an_a_nonce)) ),
inference(res,[status(thm),theory(equality)],[14,30]),
[iquote('0:Res:14.0,30.1')] ).
cnf(86,plain,
b_stored(pair(a,an_a_nonce)),
inference(ssi,[status(thm)],[84,3,5,77]),
[iquote('0:SSi:84.0,3.0,5.0,77.0')] ).
cnf(88,plain,
( ~ party_of_protocol(u)
| ~ intruder_message(v)
| ~ party_of_protocol(u)
| ~ intruder_message(w)
| intruder_message(encrypt(w,v)) ),
inference(res,[status(thm),theory(equality)],[27,32]),
[iquote('0:Res:27.2,32.2')] ).
cnf(89,plain,
( ~ intruder_message(u)
| ~ party_of_protocol(v)
| ~ intruder_message(w)
| intruder_message(encrypt(w,u)) ),
inference(obv,[status(thm),theory(equality)],[88]),
[iquote('0:Obv:88.0')] ).
cnf(90,plain,
( ~ intruder_message(u)
| ~ intruder_message(v)
| intruder_message(encrypt(v,u)) ),
inference(ems,[status(thm)],[89,1]),
[iquote('0:EmS:89.1,1.0')] ).
cnf(106,plain,
( ~ fresh_to_b(an_a_nonce)
| message(sent(b,t,triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt)))) ),
inference(res,[status(thm),theory(equality)],[14,36]),
[iquote('0:Res:14.0,36.1')] ).
cnf(107,plain,
( ~ party_of_protocol(b)
| ~ party_of_protocol(u)
| ~ intruder_message(pair(u,v))
| ~ fresh_to_b(v)
| message(sent(b,t,triple(b,generate_b_nonce(v),encrypt(triple(u,v,generate_expiration_time(v)),bt)))) ),
inference(res,[status(thm),theory(equality)],[29,36]),
[iquote('0:Res:29.3,36.1')] ).
cnf(108,plain,
message(sent(b,t,triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt)))),
inference(ssi,[status(thm)],[106,3,5,77]),
[iquote('0:SSi:106.0,3.0,5.0,77.0')] ).
cnf(109,plain,
( ~ party_of_protocol(u)
| ~ intruder_message(pair(u,v))
| ~ fresh_to_b(v)
| message(sent(b,t,triple(b,generate_b_nonce(v),encrypt(triple(u,v,generate_expiration_time(v)),bt)))) ),
inference(ssi,[status(thm)],[107,2]),
[iquote('0:SSi:107.0,2.0')] ).
cnf(110,plain,
intruder_message(triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt))),
inference(res,[status(thm),theory(equality)],[108,17]),
[iquote('0:Res:108.0,17.0')] ).
cnf(111,plain,
intruder_message(b),
inference(res,[status(thm),theory(equality)],[110,18]),
[iquote('0:Res:110.0,18.0')] ).
cnf(113,plain,
intruder_message(encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt)),
inference(res,[status(thm),theory(equality)],[110,20]),
[iquote('0:Res:110.0,20.0')] ).
cnf(114,plain,
( ~ party_of_protocol(b)
| ~ party_of_protocol(u)
| ~ intruder_message(pair(encrypt(triple(u,v,generate_expiration_time(w)),bt),encrypt(generate_b_nonce(w),v)))
| ~ b_stored(pair(u,w))
| b_holds(key(v,u)) ),
inference(res,[status(thm),theory(equality)],[29,35]),
[iquote('0:Res:29.3,35.1')] ).
cnf(115,plain,
( ~ party_of_protocol(u)
| ~ intruder_message(pair(encrypt(triple(u,v,generate_expiration_time(w)),bt),encrypt(generate_b_nonce(w),v)))
| ~ b_stored(pair(u,w))
| b_holds(key(v,u)) ),
inference(ssi,[status(thm)],[114,2,111]),
[iquote('0:SSi:114.0,2.0,111.0')] ).
cnf(124,plain,
( ~ party_of_protocol(u)
| ~ fresh_to_b(v)
| ~ intruder_message(u)
| ~ intruder_message(v)
| message(sent(b,t,triple(b,generate_b_nonce(v),encrypt(triple(u,v,generate_expiration_time(v)),bt)))) ),
inference(sor,[status(thm)],[109,26]),
[iquote('0:SoR:109.1,26.2')] ).
cnf(135,plain,
( ~ party_of_protocol(u)
| ~ intruder_message(encrypt(triple(u,v,generate_expiration_time(w)),bt))
| ~ intruder_message(encrypt(generate_b_nonce(w),v))
| ~ b_stored(pair(u,w))
| b_holds(key(v,u)) ),
inference(sor,[status(thm)],[115,26]),
[iquote('0:SoR:115.1,26.2')] ).
cnf(137,plain,
( ~ party_of_protocol(u)
| ~ fresh_to_b(v)
| ~ intruder_message(u)
| ~ intruder_message(v)
| intruder_message(triple(b,generate_b_nonce(v),encrypt(triple(u,v,generate_expiration_time(v)),bt))) ),
inference(res,[status(thm),theory(equality)],[124,17]),
[iquote('0:Res:124.4,17.0')] ).
cnf(144,plain,
( ~ party_of_protocol(u)
| ~ fresh_to_b(v)
| ~ intruder_message(u)
| ~ intruder_message(v)
| intruder_message(generate_b_nonce(v)) ),
inference(res,[status(thm),theory(equality)],[137,19]),
[iquote('0:Res:137.4,19.0')] ).
cnf(146,plain,
( ~ intruder_message(u)
| ~ fresh_to_b(u)
| intruder_message(generate_b_nonce(u)) ),
inference(ems,[status(thm)],[144,2,111]),
[iquote('0:EmS:144.0,144.2,2.0,111.0')] ).
cnf(150,plain,
( ~ party_of_protocol(a)
| ~ intruder_message(encrypt(generate_b_nonce(an_a_nonce),an_a_nonce))
| ~ b_stored(pair(a,an_a_nonce))
| b_holds(key(an_a_nonce,a)) ),
inference(sor,[status(thm)],[135,113]),
[iquote('0:SoR:135.1,113.0')] ).
cnf(153,plain,
( ~ b_stored(pair(a,an_a_nonce))
| b_holds(key(an_a_nonce,a)) ),
inference(ssi,[status(thm)],[150,90,7,3,5,77,146,1,76]),
[iquote('0:SSi:150.1,150.0,90.0,7.0,3.0,5.0,77.0,146.0,3.0,5.0,77.2,3.0,5.0,77.0,1.0,76.2')] ).
cnf(154,plain,
b_holds(key(an_a_nonce,a)),
inference(mrr,[status(thm)],[153,86]),
[iquote('0:MRR:153.0,86.0')] ).
cnf(158,plain,
~ intruder_holds(key(an_a_nonce,b)),
inference(res,[status(thm),theory(equality)],[154,25]),
[iquote('0:Res:154.0,25.0')] ).
cnf(159,plain,
( ~ party_of_protocol(b)
| ~ intruder_message(an_a_nonce) ),
inference(res,[status(thm),theory(equality)],[27,158]),
[iquote('0:Res:27.2,158.0')] ).
cnf(160,plain,
$false,
inference(ssi,[status(thm)],[159,3,5,77,2,111]),
[iquote('0:SSi:159.1,159.0,3.0,5.0,77.0,2.0,111.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV014+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 15 09:20:33 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.47
% 0.19/0.47 SPASS V 3.9
% 0.19/0.47 SPASS beiseite: Proof found.
% 0.19/0.47 % SZS status Theorem
% 0.19/0.47 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.47 SPASS derived 63 clauses, backtracked 0 clauses, performed 0 splits and kept 80 clauses.
% 0.19/0.47 SPASS allocated 97879 KBytes.
% 0.19/0.47 SPASS spent 0:00:00.11 on the problem.
% 0.19/0.47 0:00:00.03 for the input.
% 0.19/0.47 0:00:00.04 for the FLOTTER CNF translation.
% 0.19/0.47 0:00:00.00 for inferences.
% 0.19/0.47 0:00:00.00 for the backtracking.
% 0.19/0.47 0:00:00.01 for the reduction.
% 0.19/0.47
% 0.19/0.47
% 0.19/0.47 Here is a proof with depth 6, length 48 :
% 0.19/0.47 % SZS output start Refutation
% See solution above
% 0.19/0.47 Formulae used in the proof : a_is_party_of_protocol b_is_party_of_protocol nonce_a_is_fresh_to_b an_a_nonce_is_a_nonce generated_times_and_nonces_are_nonces a_sent_message_i_to_b intruder_decomposes_pairs intruder_can_record intruder_decomposes_triples co1 intruder_composes_pairs intruder_holds_key intruder_message_sent b_creates_freash_nonces_in_time intruder_key_encrypts b_accepts_secure_session_key
% 0.19/0.47
%------------------------------------------------------------------------------