%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SWV014+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n022.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 : 300s
% DateTime : Fri Jul 25 04:45:56 PM UTC 2025
% Result : Theorem 2.04s 0.63s
% Output : CNFRefutation 2.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 14
% Syntax : Number of formulae : 63 ( 22 unt; 0 def)
% Number of atoms : 136 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 126 ( 53 ~; 50 |; 14 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-1 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 54 ( 7 sgn 23 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,plain,
? [U] :
( intruder_holds(key(U,b))
& b_holds(key(U,a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(co1_negated,plain,
~ ? [U] :
( intruder_holds(key(U,b))
& b_holds(key(U,a)) ),
inference(negate_conjecture,[status(cth)],[co1]) ).
cnf(37,plain,
( ~ b_holds(key(X0,a))
| ~ intruder_holds(key(X0,b)) ),
inference(cnf,[status(esa)],[co1_negated]) ).
cnf(l0,plain,
( ~ b_holds(key(an_a_nonce,a))
| ~ intruder_holds(key(an_a_nonce,b)) ),
inference(instantiation,[status(thm)],[37]) ).
fof(intruder_holds_key,plain,
! [V,W] :
( ( intruder_message(V)
& party_of_protocol(W) )
=> intruder_holds(key(V,W)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_holds_key) ).
cnf(31,plain,
( ~ party_of_protocol(X0)
| ~ intruder_message(X1)
| intruder_holds(key(X1,X0)) ),
inference(cnf,[status(esa)],[intruder_holds_key]) ).
cnf(l2,plain,
( ~ party_of_protocol(b)
| ~ intruder_message(an_a_nonce)
| intruder_holds(key(an_a_nonce,b)) ),
inference(instantiation,[status(thm)],[31]) ).
fof(b_accepts_secure_session_key,plain,
! [V,X,Y] :
( ( message(sent(X,b,pair(encrypt(triple(X,V,generate_expiration_time(Y)),bt),encrypt(generate_b_nonce(Y),V))))
& b_stored(pair(X,Y)) )
=> b_holds(key(V,X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_accepts_secure_session_key) ).
cnf(11,plain,
( ~ message(sent(X0,b,pair(encrypt(triple(X0,X1,generate_expiration_time(X2)),bt),encrypt(generate_b_nonce(X2),X1))))
| ~ b_stored(pair(X0,X2))
| b_holds(key(X1,X0)) ),
inference(cnf,[status(esa)],[b_accepts_secure_session_key]) ).
cnf(l1,plain,
( ~ message(sent(a,b,pair(encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt),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(instantiation,[status(thm)],[11]) ).
fof(b_is_party_of_protocol,plain,
party_of_protocol(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_party_of_protocol) ).
cnf(7,plain,
party_of_protocol(b),
inference(cnf,[status(esa)],[b_is_party_of_protocol]) ).
cnf(l14,plain,
party_of_protocol(b),
inference(instantiation,[status(thm)],[7]) ).
fof(b_creates_freash_nonces_in_time,plain,
! [U,V] :
( ( message(sent(U,b,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))))
& b_stored(pair(U,V)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_creates_freash_nonces_in_time) ).
cnf(10,plain,
( ~ fresh_to_b(X0)
| ~ message(sent(X1,b,pair(X1,X0)))
| b_stored(pair(X1,X0)) ),
inference(cnf,[status(esa)],[b_creates_freash_nonces_in_time]) ).
cnf(l4,plain,
( ~ fresh_to_b(an_a_nonce)
| ~ message(sent(a,b,pair(a,an_a_nonce)))
| b_stored(pair(a,an_a_nonce)) ),
inference(instantiation,[status(thm)],[10]) ).
fof(nonce_a_is_fresh_to_b,plain,
fresh_to_b(an_a_nonce),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonce_a_is_fresh_to_b) ).
cnf(8,plain,
fresh_to_b(an_a_nonce),
inference(cnf,[status(esa)],[nonce_a_is_fresh_to_b]) ).
cnf(l8,plain,
fresh_to_b(an_a_nonce),
inference(instantiation,[status(thm)],[8]) ).
fof(a_sent_message_i_to_b,plain,
message(sent(a,b,pair(a,an_a_nonce))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_sent_message_i_to_b) ).
cnf(2,plain,
message(sent(a,b,pair(a,an_a_nonce))),
inference(cnf,[status(esa)],[a_sent_message_i_to_b]) ).
cnf(l7,plain,
message(sent(a,b,pair(a,an_a_nonce))),
inference(instantiation,[status(thm)],[2]) ).
fof(intruder_message_sent,plain,
! [U,V,W] :
( ( intruder_message(U)
& party_of_protocol(V)
& party_of_protocol(W) )
=> message(sent(V,W,U)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_message_sent) ).
cnf(30,plain,
( ~ party_of_protocol(X0)
| ~ party_of_protocol(X1)
| ~ intruder_message(X2)
| message(sent(X0,X1,X2)) ),
inference(cnf,[status(esa)],[intruder_message_sent]) ).
cnf(l6,plain,
( ~ party_of_protocol(a)
| ~ party_of_protocol(b)
| ~ intruder_message(pair(encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),an_a_nonce)))
| message(sent(a,b,pair(encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),an_a_nonce)))) ),
inference(instantiation,[status(thm)],[30]) ).
fof(a_is_party_of_protocol,plain,
party_of_protocol(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_party_of_protocol) ).
cnf(1,plain,
party_of_protocol(a),
inference(cnf,[status(esa)],[a_is_party_of_protocol]) ).
cnf(l15,plain,
party_of_protocol(a),
inference(instantiation,[status(thm)],[1]) ).
fof(intruder_composes_pairs,plain,
! [U,V] :
( ( intruder_message(U)
& intruder_message(V) )
=> intruder_message(pair(U,V)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_composes_pairs) ).
cnf(26,plain,
( ~ intruder_message(X0)
| ~ intruder_message(X1)
| intruder_message(pair(X0,X1)) ),
inference(cnf,[status(esa)],[intruder_composes_pairs]) ).
cnf(l13,plain,
( ~ intruder_message(encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt))
| ~ intruder_message(encrypt(generate_b_nonce(an_a_nonce),an_a_nonce))
| intruder_message(pair(encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),an_a_nonce))) ),
inference(instantiation,[status(thm)],[26]) ).
cnf(l9,plain,
party_of_protocol(b),
inference(instantiation,[status(thm)],[7]) ).
fof(intruder_decomposes_triples,plain,
! [U,V,W] :
( intruder_message(triple(U,V,W))
=> ( intruder_message(U)
& intruder_message(V)
& intruder_message(W) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_decomposes_triples) ).
cnf(21,plain,
( ~ intruder_message(triple(X0,X1,X2))
| intruder_message(X2) ),
inference(cnf,[status(esa)],[intruder_decomposes_triples]) ).
cnf(l21,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(encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt)) ),
inference(instantiation,[status(thm)],[21]) ).
fof(intruder_can_record,plain,
! [U,V,W] :
( message(sent(U,V,W))
=> intruder_message(W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_can_record) ).
cnf(16,plain,
( ~ message(sent(X0,X1,X2))
| intruder_message(X2) ),
inference(cnf,[status(esa)],[intruder_can_record]) ).
cnf(l23,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))))
| intruder_message(triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt))) ),
inference(instantiation,[status(thm)],[16]) ).
cnf(9,plain,
( ~ fresh_to_b(X0)
| ~ message(sent(X1,b,pair(X1,X0)))
| message(sent(b,t,triple(b,generate_b_nonce(X0),encrypt(triple(X1,X0,generate_expiration_time(X0)),bt)))) ),
inference(cnf,[status(esa)],[b_creates_freash_nonces_in_time]) ).
cnf(l28,plain,
( ~ fresh_to_b(an_a_nonce)
| ~ message(sent(a,b,pair(a,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(instantiation,[status(thm)],[9]) ).
cnf(l42,plain,
message(sent(a,b,pair(a,an_a_nonce))),
inference(instantiation,[status(thm)],[2]) ).
fof(intruder_decomposes_pairs,plain,
! [U,V] :
( intruder_message(pair(U,V))
=> ( intruder_message(U)
& intruder_message(V) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_decomposes_pairs) ).
cnf(18,plain,
( ~ intruder_message(pair(X0,X1))
| intruder_message(X1) ),
inference(cnf,[status(esa)],[intruder_decomposes_pairs]) ).
cnf(l3,plain,
( ~ intruder_message(pair(a,an_a_nonce))
| intruder_message(an_a_nonce) ),
inference(instantiation,[status(thm)],[18]) ).
cnf(l31,plain,
fresh_to_b(an_a_nonce),
inference(instantiation,[status(thm)],[8]) ).
cnf(l5,plain,
( ~ message(sent(a,b,pair(a,an_a_nonce)))
| intruder_message(pair(a,an_a_nonce)) ),
inference(instantiation,[status(thm)],[16]) ).
cnf(l10,plain,
message(sent(a,b,pair(a,an_a_nonce))),
inference(instantiation,[status(thm)],[2]) ).
fof(intruder_key_encrypts,plain,
! [U,V,W] :
( ( intruder_message(U)
& intruder_holds(key(V,W))
& party_of_protocol(W) )
=> intruder_message(encrypt(U,V)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_key_encrypts) ).
cnf(32,plain,
( ~ party_of_protocol(X0)
| ~ intruder_holds(key(X1,X0))
| ~ intruder_message(X2)
| intruder_message(encrypt(X2,X1)) ),
inference(cnf,[status(esa)],[intruder_key_encrypts]) ).
cnf(l242,plain,
( ~ party_of_protocol(b)
| ~ intruder_holds(key(an_a_nonce,b))
| ~ intruder_message(generate_b_nonce(an_a_nonce))
| intruder_message(encrypt(generate_b_nonce(an_a_nonce),an_a_nonce)) ),
inference(instantiation,[status(thm)],[32]) ).
cnf(l248,plain,
party_of_protocol(b),
inference(instantiation,[status(thm)],[7]) ).
cnf(l315,plain,
( ~ party_of_protocol(b)
| ~ intruder_message(an_a_nonce)
| intruder_holds(key(an_a_nonce,b)) ),
inference(instantiation,[status(thm)],[31]) ).
cnf(l316,plain,
party_of_protocol(b),
inference(instantiation,[status(thm)],[7]) ).
cnf(l317,plain,
( ~ intruder_message(pair(a,an_a_nonce))
| intruder_message(an_a_nonce) ),
inference(instantiation,[status(thm)],[18]) ).
cnf(l318,plain,
( ~ message(sent(a,b,pair(a,an_a_nonce)))
| intruder_message(pair(a,an_a_nonce)) ),
inference(instantiation,[status(thm)],[16]) ).
cnf(l321,plain,
message(sent(a,b,pair(a,an_a_nonce))),
inference(instantiation,[status(thm)],[2]) ).
cnf(20,plain,
( ~ intruder_message(triple(X0,X1,X2))
| intruder_message(X1) ),
inference(cnf,[status(esa)],[intruder_decomposes_triples]) ).
cnf(l285,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(generate_b_nonce(an_a_nonce)) ),
inference(instantiation,[status(thm)],[20]) ).
cnf(l319,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))))
| intruder_message(triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt))) ),
inference(instantiation,[status(thm)],[16]) ).
cnf(l320,plain,
( ~ fresh_to_b(an_a_nonce)
| ~ message(sent(a,b,pair(a,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(instantiation,[status(thm)],[9]) ).
cnf(l338,plain,
message(sent(a,b,pair(a,an_a_nonce))),
inference(instantiation,[status(thm)],[2]) ).
cnf(l322,plain,
fresh_to_b(an_a_nonce),
inference(instantiation,[status(thm)],[8]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l2,l1,l14,l4,l8,l7,l6,l15,l13,l9,l21,l23,l28,l42,l3,l31,l5,l10,l242,l248,l315,l316,l317,l318,l321,l285,l319,l320,l338,l322]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV014+1 : TPTP v9.0.0. Released v2.4.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34 % Computer : n022.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 : 300
% 0.13/0.34 % DateTime : Tue Jul 22 07:59:19 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % launching worker at depth: 6
% 0.13/0.35 % launching worker at depth: 7
% 0.13/0.35 % launching worker at depth: 4
% 0.13/0.35 % launching worker at depth: 2
% 0.13/0.35 % launching worker at depth: 1
% 0.13/0.35 % launching worker at depth: 3
% 0.13/0.35 % launching worker at depth: 8
% 0.13/0.35 % launching worker at depth: 5
% 0.13/0.35 % launching worker at depth: 9
% 0.13/0.35 % launching worker at depth: 10
% 0.13/0.35 % launching worker at depth: 11
% 0.13/0.36 % launching worker at depth: 12
% 0.13/0.37 % launching worker at depth: 13
% 0.19/0.42 % launching worker at depth: 14
% 2.04/0.62 % launching worker at depth: 15
% 2.04/0.63 % SZS status Theorem for theBenchmark
% 2.04/0.63 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------