%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV014+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 : Tue Sep 29 01:07:54 PM UTC 2026
% Result : Theorem 1.09s 0.62s
% Output : Refutation 2.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 28
% Syntax : Number of formulae : 141 ( 32 unt; 14 def)
% Number of atoms : 346 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 382 ( 177 ~; 163 |; 19 &)
% ( 14 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 22 ( 21 usr; 15 prp; 0-1 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 125 ( 0 sgn 123 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
party_of_protocol(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_party_of_protocol) ).
fof(f3,axiom,
message(sent(a,b,pair(a,an_a_nonce))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_sent_message_i_to_b) ).
fof(f7,axiom,
party_of_protocol(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_party_of_protocol) ).
fof(f8,axiom,
fresh_to_b(an_a_nonce),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonce_a_is_fresh_to_b) ).
fof(f9,axiom,
! [X0,X1] :
( ( message(sent(X0,b,pair(X0,X1)))
& fresh_to_b(X1) )
=> ( message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X0,X1,generate_expiration_time(X1)),bt))))
& b_stored(pair(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_creates_freash_nonces_in_time) ).
fof(f10,axiom,
! [X0,X1,X2] :
( ( message(sent(X1,b,pair(encrypt(triple(X1,X0,generate_expiration_time(X2)),bt),encrypt(generate_b_nonce(X2),X0))))
& b_stored(pair(X1,X2)) )
=> b_holds(key(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_accepts_secure_session_key) ).
fof(f15,axiom,
! [X0,X1,X2] :
( message(sent(X0,X1,X2))
=> intruder_message(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intruder_can_record) ).
fof(f16,axiom,
! [X0,X1] :
( intruder_message(pair(X0,X1))
=> ( intruder_message(X0)
& intruder_message(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intruder_decomposes_pairs) ).
fof(f17,axiom,
! [X0,X1,X2] :
( intruder_message(triple(X0,X1,X2))
=> ( intruder_message(X0)
& intruder_message(X1)
& intruder_message(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intruder_decomposes_triples) ).
fof(f19,axiom,
! [X0,X1] :
( ( intruder_message(X0)
& intruder_message(X1) )
=> intruder_message(pair(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intruder_composes_pairs) ).
fof(f23,axiom,
! [X0,X1,X2] :
( ( intruder_message(X0)
& party_of_protocol(X1)
& party_of_protocol(X2) )
=> message(sent(X1,X2,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intruder_message_sent) ).
fof(f24,axiom,
! [X0,X1] :
( ( intruder_message(X0)
& party_of_protocol(X1) )
=> intruder_holds(key(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intruder_holds_key) ).
fof(f25,axiom,
! [X0,X1,X2] :
( ( intruder_message(X0)
& intruder_holds(key(X1,X2))
& party_of_protocol(X2) )
=> intruder_message(encrypt(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intruder_key_encrypts) ).
fof(f29,conjecture,
? [X0] :
( intruder_holds(key(X0,b))
& b_holds(key(X0,a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f30,negated_conjecture,
~ ? [X0] :
( intruder_holds(key(X0,b))
& b_holds(key(X0,a)) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f35,plain,
! [X0,X1] :
( ( message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X0,X1,generate_expiration_time(X1)),bt))))
& b_stored(pair(X0,X1)) )
| ~ message(sent(X0,b,pair(X0,X1)))
| ~ fresh_to_b(X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f36,plain,
! [X0,X1] :
( ( message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X0,X1,generate_expiration_time(X1)),bt))))
& b_stored(pair(X0,X1)) )
| ~ message(sent(X0,b,pair(X0,X1)))
| ~ fresh_to_b(X1) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
! [X0,X1,X2] :
( b_holds(key(X0,X1))
| ~ message(sent(X1,b,pair(encrypt(triple(X1,X0,generate_expiration_time(X2)),bt),encrypt(generate_b_nonce(X2),X0))))
| ~ b_stored(pair(X1,X2)) ),
inference(ennf_transformation,[],[f10]) ).
fof(f38,plain,
! [X0,X1,X2] :
( b_holds(key(X0,X1))
| ~ message(sent(X1,b,pair(encrypt(triple(X1,X0,generate_expiration_time(X2)),bt),encrypt(generate_b_nonce(X2),X0))))
| ~ b_stored(pair(X1,X2)) ),
inference(flattening,[],[f37]) ).
fof(f41,plain,
! [X0,X1,X2] :
( intruder_message(X2)
| ~ message(sent(X0,X1,X2)) ),
inference(ennf_transformation,[],[f15]) ).
fof(f42,plain,
! [X0,X1] :
( ( intruder_message(X0)
& intruder_message(X1) )
| ~ intruder_message(pair(X0,X1)) ),
inference(ennf_transformation,[],[f16]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ( intruder_message(X0)
& intruder_message(X1)
& intruder_message(X2) )
| ~ intruder_message(triple(X0,X1,X2)) ),
inference(ennf_transformation,[],[f17]) ).
fof(f45,plain,
! [X0,X1] :
( intruder_message(pair(X0,X1))
| ~ intruder_message(X0)
| ~ intruder_message(X1) ),
inference(ennf_transformation,[],[f19]) ).
fof(f46,plain,
! [X0,X1] :
( intruder_message(pair(X0,X1))
| ~ intruder_message(X0)
| ~ intruder_message(X1) ),
inference(flattening,[],[f45]) ).
fof(f53,plain,
! [X0,X1,X2] :
( message(sent(X1,X2,X0))
| ~ intruder_message(X0)
| ~ party_of_protocol(X1)
| ~ party_of_protocol(X2) ),
inference(ennf_transformation,[],[f23]) ).
fof(f54,plain,
! [X0,X1,X2] :
( message(sent(X1,X2,X0))
| ~ intruder_message(X0)
| ~ party_of_protocol(X1)
| ~ party_of_protocol(X2) ),
inference(flattening,[],[f53]) ).
fof(f55,plain,
! [X0,X1] :
( intruder_holds(key(X0,X1))
| ~ intruder_message(X0)
| ~ party_of_protocol(X1) ),
inference(ennf_transformation,[],[f24]) ).
fof(f56,plain,
! [X0,X1] :
( intruder_holds(key(X0,X1))
| ~ intruder_message(X0)
| ~ party_of_protocol(X1) ),
inference(flattening,[],[f55]) ).
fof(f57,plain,
! [X0,X1,X2] :
( intruder_message(encrypt(X0,X1))
| ~ intruder_message(X0)
| ~ intruder_holds(key(X1,X2))
| ~ party_of_protocol(X2) ),
inference(ennf_transformation,[],[f25]) ).
fof(f58,plain,
! [X0,X1,X2] :
( intruder_message(encrypt(X0,X1))
| ~ intruder_message(X0)
| ~ intruder_holds(key(X1,X2))
| ~ party_of_protocol(X2) ),
inference(flattening,[],[f57]) ).
fof(f59,plain,
! [X0] :
( ~ intruder_holds(key(X0,b))
| ~ b_holds(key(X0,a)) ),
inference(ennf_transformation,[],[f30]) ).
fof(f60,plain,
party_of_protocol(a),
inference(cnf_transformation,[],[f2]) ).
fof(f61,plain,
message(sent(a,b,pair(a,an_a_nonce))),
inference(cnf_transformation,[],[f3]) ).
fof(f65,plain,
party_of_protocol(b),
inference(cnf_transformation,[],[f7]) ).
fof(f66,plain,
fresh_to_b(an_a_nonce),
inference(cnf_transformation,[],[f8]) ).
fof(f67,plain,
! [X0,X1] :
( b_stored(pair(X0,X1))
| ~ message(sent(X0,b,pair(X0,X1)))
| ~ fresh_to_b(X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f68,plain,
! [X0,X1] :
( ~ fresh_to_b(X1)
| ~ message(sent(X0,b,pair(X0,X1)))
| message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X0,X1,generate_expiration_time(X1)),bt)))) ),
inference(cnf_transformation,[],[f36]) ).
fof(f69,plain,
! [X2,X0,X1] :
( ~ b_stored(pair(X1,X2))
| ~ message(sent(X1,b,pair(encrypt(triple(X1,X0,generate_expiration_time(X2)),bt),encrypt(generate_b_nonce(X2),X0))))
| b_holds(key(X0,X1)) ),
inference(cnf_transformation,[],[f38]) ).
fof(f74,plain,
! [X2,X0,X1] :
( ~ message(sent(X0,X1,X2))
| intruder_message(X2) ),
inference(cnf_transformation,[],[f41]) ).
fof(f75,plain,
! [X0,X1] :
( ~ intruder_message(pair(X0,X1))
| intruder_message(X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f77,plain,
! [X2,X0,X1] :
( ~ intruder_message(triple(X0,X1,X2))
| intruder_message(X2) ),
inference(cnf_transformation,[],[f43]) ).
fof(f78,plain,
! [X2,X0,X1] :
( ~ intruder_message(triple(X0,X1,X2))
| intruder_message(X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f84,plain,
! [X0,X1] :
( intruder_message(pair(X0,X1))
| ~ intruder_message(X0)
| ~ intruder_message(X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f88,plain,
! [X2,X0,X1] :
( message(sent(X1,X2,X0))
| ~ intruder_message(X0)
| ~ party_of_protocol(X1)
| ~ party_of_protocol(X2) ),
inference(cnf_transformation,[],[f54]) ).
fof(f89,plain,
! [X0,X1] :
( intruder_holds(key(X0,X1))
| ~ intruder_message(X0)
| ~ party_of_protocol(X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f90,plain,
! [X2,X0,X1] :
( ~ intruder_holds(key(X1,X2))
| ~ intruder_message(X0)
| intruder_message(encrypt(X0,X1))
| ~ party_of_protocol(X2) ),
inference(cnf_transformation,[],[f58]) ).
fof(f95,plain,
! [X0] :
( ~ b_holds(key(X0,a))
| ~ intruder_holds(key(X0,b)) ),
inference(cnf_transformation,[],[f59]) ).
fof(f96,plain,
intruder_message(pair(a,an_a_nonce)),
inference(resolution,[],[f74,f61]) ).
fof(f98,plain,
intruder_message(an_a_nonce),
inference(resolution,[],[f96,f75]) ).
fof(f107,plain,
! [X2,X0,X1] :
( ~ intruder_message(X0)
| intruder_message(encrypt(X0,X1))
| ~ party_of_protocol(X2)
| ~ intruder_message(X1)
| ~ party_of_protocol(X2) ),
inference(resolution,[],[f90,f89]) ).
fof(f108,plain,
! [X2,X0,X1] :
( ~ intruder_message(X0)
| intruder_message(encrypt(X0,X1))
| ~ party_of_protocol(X2)
| ~ intruder_message(X1) ),
inference(duplicate_literal_removal,[],[f107]) ).
fof(f110,definition,
( spl0_1
<=> ! [X2] : ~ party_of_protocol(X2) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f111,plain,
( ! [X2] : ~ party_of_protocol(X2)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f113,definition,
( spl0_2
<=> ! [X0,X1] :
( ~ intruder_message(X0)
| ~ intruder_message(X1)
| intruder_message(encrypt(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f114,plain,
( ! [X0,X1] :
( intruder_message(encrypt(X0,X1))
| ~ intruder_message(X1)
| ~ intruder_message(X0) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f115,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f108,f113,f110]) ).
fof(f120,plain,
! [X0] :
( message(sent(b,t,triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(X0,an_a_nonce,generate_expiration_time(an_a_nonce)),bt))))
| ~ message(sent(X0,b,pair(X0,an_a_nonce))) ),
inference(resolution,[],[f68,f66]) ).
fof(f121,plain,
! [X0] :
( ~ message(sent(X0,b,pair(X0,an_a_nonce)))
| intruder_message(triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(X0,an_a_nonce,generate_expiration_time(an_a_nonce)),bt))) ),
inference(resolution,[],[f120,f74]) ).
fof(f122,plain,
! [X2,X0,X1] :
( ~ fresh_to_b(X2)
| b_holds(key(X1,X0))
| ~ message(sent(X0,b,pair(X0,X2)))
| ~ message(sent(X0,b,pair(encrypt(triple(X0,X1,generate_expiration_time(X2)),bt),encrypt(generate_b_nonce(X2),X1)))) ),
inference(resolution,[],[f69,f67]) ).
fof(f124,plain,
! [X0] :
( intruder_message(triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(X0,an_a_nonce,generate_expiration_time(an_a_nonce)),bt)))
| ~ intruder_message(pair(X0,an_a_nonce))
| ~ party_of_protocol(X0)
| ~ party_of_protocol(b) ),
inference(resolution,[],[f121,f88]) ).
fof(f126,definition,
( spl0_3
<=> party_of_protocol(b) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f127,plain,
( ~ party_of_protocol(b)
| spl0_3 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f129,definition,
( spl0_4
<=> ! [X0] :
( intruder_message(triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(X0,an_a_nonce,generate_expiration_time(an_a_nonce)),bt)))
| ~ party_of_protocol(X0)
| ~ intruder_message(pair(X0,an_a_nonce)) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f130,plain,
( ! [X0] :
( ~ party_of_protocol(X0)
| intruder_message(triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(X0,an_a_nonce,generate_expiration_time(an_a_nonce)),bt)))
| ~ intruder_message(pair(X0,an_a_nonce)) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f131,plain,
( ~ spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f124,f129,f126]) ).
fof(f132,plain,
( $false
| spl0_3 ),
inference(resolution,[],[f127,f65]) ).
fof(f133,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f132]) ).
fof(f134,plain,
( intruder_message(triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt)))
| ~ intruder_message(pair(a,an_a_nonce))
| ~ spl0_4 ),
inference(resolution,[],[f130,f60]) ).
fof(f152,definition,
( spl0_9
<=> intruder_message(pair(a,an_a_nonce)) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f153,plain,
( ~ intruder_message(pair(a,an_a_nonce))
| spl0_9 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f155,definition,
( spl0_10
<=> intruder_message(triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt))) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f156,plain,
( intruder_message(triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt)))
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f157,plain,
( ~ spl0_9
| spl0_10
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f134,f129,f155,f152]) ).
fof(f160,definition,
( spl0_11
<=> intruder_message(an_a_nonce) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f161,plain,
( ~ intruder_message(an_a_nonce)
| spl0_11 ),
inference(avatar_component_clause,[],[f160]) ).
fof(f166,plain,
( $false
| spl0_11 ),
inference(resolution,[],[f161,f98]) ).
fof(f167,plain,
spl0_11,
inference(avatar_contradiction_clause,[],[f166]) ).
fof(f173,plain,
( $false
| spl0_9 ),
inference(resolution,[],[f153,f96]) ).
fof(f175,plain,
spl0_9,
inference(avatar_contradiction_clause,[],[f173]) ).
fof(f181,plain,
( intruder_message(generate_b_nonce(an_a_nonce))
| ~ spl0_10 ),
inference(resolution,[],[f156,f78]) ).
fof(f182,plain,
( intruder_message(encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt))
| ~ spl0_10 ),
inference(resolution,[],[f156,f77]) ).
fof(f193,definition,
( spl0_15
<=> party_of_protocol(a) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f194,plain,
( ~ party_of_protocol(a)
| spl0_15 ),
inference(avatar_component_clause,[],[f193]) ).
fof(f212,plain,
( $false
| spl0_15 ),
inference(resolution,[],[f194,f60]) ).
fof(f213,plain,
spl0_15,
inference(avatar_contradiction_clause,[],[f212]) ).
fof(f233,plain,
! [X0,X1] :
( b_holds(key(X0,X1))
| ~ message(sent(X1,b,pair(X1,an_a_nonce)))
| ~ message(sent(X1,b,pair(encrypt(triple(X1,X0,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),X0)))) ),
inference(resolution,[],[f122,f66]) ).
fof(f241,definition,
( spl0_24
<=> message(sent(a,b,pair(a,an_a_nonce))) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f242,plain,
( ~ message(sent(a,b,pair(a,an_a_nonce)))
| spl0_24 ),
inference(avatar_component_clause,[],[f241]) ).
fof(f270,plain,
( $false
| spl0_24 ),
inference(resolution,[],[f242,f61]) ).
fof(f272,plain,
spl0_24,
inference(avatar_contradiction_clause,[],[f270]) ).
fof(f308,plain,
! [X0] :
( ~ message(sent(a,b,pair(a,an_a_nonce)))
| ~ message(sent(a,b,pair(encrypt(triple(a,X0,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),X0))))
| ~ intruder_holds(key(X0,b)) ),
inference(resolution,[],[f233,f95]) ).
fof(f310,definition,
( spl0_32
<=> ! [X0] :
( ~ message(sent(a,b,pair(encrypt(triple(a,X0,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),X0))))
| ~ intruder_holds(key(X0,b)) ) ),
introduced(definition,[new_symbols(definition,[spl0_32])],[avatar_definition]) ).
fof(f311,plain,
( ! [X0] :
( ~ intruder_holds(key(X0,b))
| ~ message(sent(a,b,pair(encrypt(triple(a,X0,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),X0)))) )
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f310]) ).
fof(f312,plain,
( spl0_32
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f308,f241,f310]) ).
fof(f313,plain,
( ! [X0] :
( ~ message(sent(a,b,pair(encrypt(triple(a,X0,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),X0))))
| ~ intruder_message(X0)
| ~ party_of_protocol(b) )
| ~ spl0_32 ),
inference(resolution,[],[f311,f89]) ).
fof(f315,definition,
( spl0_33
<=> ! [X0] :
( ~ message(sent(a,b,pair(encrypt(triple(a,X0,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),X0))))
| ~ intruder_message(X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_33])],[avatar_definition]) ).
fof(f316,plain,
( ! [X0] :
( ~ message(sent(a,b,pair(encrypt(triple(a,X0,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),X0))))
| ~ intruder_message(X0) )
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f315]) ).
fof(f317,plain,
( ~ spl0_3
| spl0_33
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f313,f310,f315,f126]) ).
fof(f320,plain,
( ! [X0] :
( ~ intruder_message(X0)
| ~ intruder_message(pair(encrypt(triple(a,X0,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),X0)))
| ~ party_of_protocol(a)
| ~ party_of_protocol(b) )
| ~ spl0_33 ),
inference(resolution,[],[f316,f88]) ).
fof(f322,definition,
( spl0_34
<=> ! [X0] :
( ~ intruder_message(X0)
| ~ intruder_message(pair(encrypt(triple(a,X0,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),X0))) ) ),
introduced(definition,[new_symbols(definition,[spl0_34])],[avatar_definition]) ).
fof(f323,plain,
( ! [X0] :
( ~ intruder_message(pair(encrypt(triple(a,X0,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),X0)))
| ~ intruder_message(X0) )
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f322]) ).
fof(f324,plain,
( ~ spl0_3
| ~ spl0_15
| spl0_34
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f320,f315,f322,f193,f126]) ).
fof(f343,plain,
( ! [X0] :
( ~ intruder_message(encrypt(triple(a,X0,generate_expiration_time(an_a_nonce)),bt))
| ~ intruder_message(X0)
| ~ intruder_message(encrypt(generate_b_nonce(an_a_nonce),X0)) )
| ~ spl0_34 ),
inference(resolution,[],[f323,f84]) ).
fof(f345,definition,
( spl0_38
<=> intruder_message(generate_b_nonce(an_a_nonce)) ),
introduced(definition,[new_symbols(definition,[spl0_38])],[avatar_definition]) ).
fof(f346,plain,
( ~ intruder_message(generate_b_nonce(an_a_nonce))
| spl0_38 ),
inference(avatar_component_clause,[],[f345]) ).
fof(f365,plain,
( $false
| ~ spl0_10
| spl0_38 ),
inference(resolution,[],[f346,f181]) ).
fof(f366,plain,
( ~ spl0_10
| spl0_38 ),
inference(avatar_contradiction_clause,[],[f365]) ).
fof(f370,plain,
( ~ intruder_message(an_a_nonce)
| ~ intruder_message(encrypt(generate_b_nonce(an_a_nonce),an_a_nonce))
| ~ spl0_10
| ~ spl0_34 ),
inference(resolution,[],[f343,f182]) ).
fof(f381,definition,
( spl0_42
<=> intruder_message(encrypt(generate_b_nonce(an_a_nonce),an_a_nonce)) ),
introduced(definition,[new_symbols(definition,[spl0_42])],[avatar_definition]) ).
fof(f382,plain,
( ~ intruder_message(encrypt(generate_b_nonce(an_a_nonce),an_a_nonce))
| spl0_42 ),
inference(avatar_component_clause,[],[f381]) ).
fof(f383,plain,
( ~ spl0_42
| ~ spl0_11
| ~ spl0_10
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f370,f322,f155,f160,f381]) ).
fof(f385,plain,
( ~ intruder_message(an_a_nonce)
| ~ intruder_message(generate_b_nonce(an_a_nonce))
| ~ spl0_2
| spl0_42 ),
inference(resolution,[],[f382,f114]) ).
fof(f386,plain,
( ~ spl0_38
| ~ spl0_11
| ~ spl0_2
| spl0_42 ),
inference(avatar_split_clause,[],[f385,f381,f113,f160,f345]) ).
fof(f391,plain,
( $false
| ~ spl0_1 ),
inference(resolution,[],[f111,f60]) ).
fof(f396,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f391]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f115]) ).
cnf(s2,plain,
( ~ spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f131]) ).
cnf(s3,plain,
spl0_3,
inference(sat_conversion,[],[f133]) ).
cnf(s6,plain,
( ~ spl0_4
| ~ spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f157]) ).
cnf(s8,plain,
spl0_11,
inference(sat_conversion,[],[f167]) ).
cnf(s10,plain,
spl0_9,
inference(sat_conversion,[],[f175]) ).
cnf(s15,plain,
spl0_15,
inference(sat_conversion,[],[f213]) ).
cnf(s31,plain,
spl0_24,
inference(sat_conversion,[],[f272]) ).
cnf(s38,plain,
( ~ spl0_24
| spl0_32 ),
inference(sat_conversion,[],[f312]) ).
cnf(s39,plain,
( ~ spl0_3
| ~ spl0_32
| spl0_33 ),
inference(sat_conversion,[],[f317]) ).
cnf(s40,plain,
( ~ spl0_3
| ~ spl0_15
| ~ spl0_33
| spl0_34 ),
inference(sat_conversion,[],[f324]) ).
cnf(s49,plain,
( ~ spl0_10
| spl0_38 ),
inference(sat_conversion,[],[f366]) ).
cnf(s53,plain,
( ~ spl0_10
| ~ spl0_11
| ~ spl0_34
| ~ spl0_42 ),
inference(sat_conversion,[],[f383]) ).
cnf(s54,plain,
( ~ spl0_2
| ~ spl0_11
| ~ spl0_38
| spl0_42 ),
inference(sat_conversion,[],[f386]) ).
cnf(s58,plain,
~ spl0_1,
inference(sat_conversion,[],[f396]) ).
cnf(s60,plain,
spl0_32,
inference(rat,[],[s38,s31]) ).
cnf(s69,plain,
( ~ spl0_4
| spl0_10 ),
inference(rat,[],[s6,s10]) ).
cnf(s70,plain,
spl0_33,
inference(rat,[],[s39,s60,s3]) ).
cnf(s73,plain,
spl0_34,
inference(rat,[],[s40,s3,s15,s70]) ).
cnf(s74,plain,
spl0_4,
inference(rat,[],[s2,s3]) ).
cnf(s75,plain,
spl0_10,
inference(rat,[],[s69,s74]) ).
cnf(s76,plain,
~ spl0_42,
inference(rat,[],[s53,s73,s8,s75]) ).
cnf(s77,plain,
spl0_38,
inference(rat,[],[s49,s75]) ).
cnf(s82,plain,
~ spl0_2,
inference(rat,[],[s54,s76,s8,s77]) ).
cnf(s87,plain,
$false,
inference(rat,[],[s1,s82,s58]) ).
fof(f397,plain,
$false,
inference(avatar_sat_refutation,[],[s87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWV014+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Mon Sep 28 09:42:19 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.13 Running first-order theorem proving
% 0.09/0.13 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.09/0.62 % (3269026)Detected formulas, will run a generic FOF schedule.
% 1.09/0.62 % (3269093)dis-21_1_sil=8000:lcm=predicate:random_seed=2449802628:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_3000 on theBenchmark for (3000ds/129Mi)
% 1.09/0.62 % (3269092)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=564529786:s2a=on:i=139:gtg=position_3000 on theBenchmark for (3000ds/139Mi)
% 1.09/0.62 % (3269086)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3319530127:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/134677Mi)
% 1.09/0.62 % (3269087)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1289674936:i=141695:sd=1:nm=32:gsp=on:ss=included_3000 on theBenchmark for (3000ds/141695Mi)
% 1.09/0.62 % (3269090)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=205115865:i=119:av=off:ss=axioms_3000 on theBenchmark for (3000ds/119Mi)
% 1.09/0.62 % (3269089)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2515519748:i=109:sd=1:ins=1:gsp=on:ss=axioms_3000 on theBenchmark for (3000ds/109Mi)
% 1.09/0.62 % (3269084)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2040994063:i=141193_3000 on theBenchmark for (3000ds/141193Mi)
% 1.09/0.62 % (3269089)Refutation not found, incomplete strategy
% 1.09/0.62 % (3269089)------------------------------
% 1.09/0.62 % (3269089)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.09/0.62 % (3269089)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.09/0.62 % (3269090)Refutation not found, incomplete strategy
% 1.09/0.62 % (3269090)------------------------------
% 1.09/0.62 % (3269090)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.09/0.62 % (3269089)CaDiCaL version: 2.1.3
% 1.09/0.62 % (3269090)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.09/0.62 % (3269089)Termination reason: Refutation not found, incomplete strategy
% 1.09/0.62 % (3269089)Time elapsed: 0.0000 s
% 1.09/0.62 % (3269089)Peak memory usage: 87 MB
% 1.09/0.62 % (3269090)CaDiCaL version: 2.1.3
% 1.09/0.62 % (3269090)Termination reason: Refutation not found, incomplete strategy
% 1.09/0.62 % (3269090)Time elapsed: 0.001 s
% 1.09/0.62 % (3269090)Peak memory usage: 87 MB
% 1.09/0.62 % (3269093)First to succeed.
% 1.09/0.62 % (3269093)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3269026"
% 1.09/0.62 % (3269092)Also succeeded, but the first one will report.
% 1.09/0.62 % (3269090)------------------------------
% 1.09/0.62 % (3269090)------------------------------
% 1.09/0.62 % (3269089)------------------------------
% 1.09/0.62 % (3269089)------------------------------
% 1.09/0.62 % (3269093)Refutation found. Thanks to Tanya!
% 1.09/0.62 % SZS status Theorem for theBenchmark
% 1.09/0.62 % SZS output start Proof for theBenchmark
% See solution above
% 2.28/0.72 % (3269093)------------------------------
% 2.28/0.72 % (3269093)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.28/0.72 % (3269093)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.28/0.72 % (3269093)CaDiCaL version: 2.1.3
% 2.28/0.72 % (3269093)Termination reason: Refutation
% 2.28/0.72 % (3269093)Time elapsed: 0.004 s
% 2.28/0.72 % (3269093)Peak memory usage: 89 MB
% 2.28/0.72 % (3269093)Instructions burned: 9 (million)
% 2.28/0.72 % (3269093)------------------------------
% 2.28/0.72 % (3269093)------------------------------
% 2.28/0.72 % (3269026)Success in time 0.278 s
% 2.28/0.72 % Vampire exiting
%------------------------------------------------------------------------------