%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWV014+1 : TPTP v9.2.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n028.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 : Tue May 5 05:20:36 PM UTC 2026
% Result : Theorem 1.26s 1.73s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 58 ( 18 unt; 0 def)
% Number of atoms : 143 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 147 ( 62 ~; 58 |; 18 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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 : 88 ( 8 sgn 47 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(b_creates_freash_nonces_in_time,axiom,
! [X1,X2] :
( ( message(sent(X1,b,pair(X1,X2)))
& fresh_to_b(X2) )
=> ( message(sent(b,t,triple(b,generate_b_nonce(X2),encrypt(triple(X1,X2,generate_expiration_time(X2)),bt))))
& b_stored(pair(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_creates_freash_nonces_in_time) ).
fof(b_accepts_secure_session_key,axiom,
! [X2,X4,X5] :
( ( message(sent(X4,b,pair(encrypt(triple(X4,X2,generate_expiration_time(X5)),bt),encrypt(generate_b_nonce(X5),X2))))
& b_stored(pair(X4,X5)) )
=> b_holds(key(X2,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_accepts_secure_session_key) ).
fof(a_sent_message_i_to_b,axiom,
message(sent(a,b,pair(a,an_a_nonce))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_sent_message_i_to_b) ).
fof(nonce_a_is_fresh_to_b,axiom,
fresh_to_b(an_a_nonce),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonce_a_is_fresh_to_b) ).
fof(intruder_message_sent,axiom,
! [X1,X2,X3] :
( ( intruder_message(X1)
& party_of_protocol(X2)
& party_of_protocol(X3) )
=> message(sent(X2,X3,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_message_sent) ).
fof(intruder_key_encrypts,axiom,
! [X1,X2,X3] :
( ( intruder_message(X1)
& intruder_holds(key(X2,X3))
& party_of_protocol(X3) )
=> intruder_message(encrypt(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_key_encrypts) ).
fof(intruder_holds_key,axiom,
! [X2,X3] :
( ( intruder_message(X2)
& party_of_protocol(X3) )
=> intruder_holds(key(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_holds_key) ).
fof(b_is_party_of_protocol,axiom,
party_of_protocol(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_party_of_protocol) ).
fof(a_is_party_of_protocol,axiom,
party_of_protocol(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_party_of_protocol) ).
fof(intruder_composes_pairs,axiom,
! [X1,X2] :
( ( intruder_message(X1)
& intruder_message(X2) )
=> intruder_message(pair(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_composes_pairs) ).
fof(intruder_can_record,axiom,
! [X1,X2,X3] :
( message(sent(X1,X2,X3))
=> intruder_message(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_can_record) ).
fof(intruder_decomposes_triples,axiom,
! [X1,X2,X3] :
( intruder_message(triple(X1,X2,X3))
=> ( intruder_message(X1)
& intruder_message(X2)
& intruder_message(X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_decomposes_triples) ).
fof(intruder_decomposes_pairs,axiom,
! [X1,X2] :
( intruder_message(pair(X1,X2))
=> ( intruder_message(X1)
& intruder_message(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_decomposes_pairs) ).
fof(co1,conjecture,
? [X1] :
( intruder_holds(key(X1,b))
& b_holds(key(X1,a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(c_0_14,plain,
! [X67,X68] :
( ( message(sent(b,t,triple(b,generate_b_nonce(X68),encrypt(triple(X67,X68,generate_expiration_time(X68)),bt))))
| ~ message(sent(X67,b,pair(X67,X68)))
| ~ fresh_to_b(X68) )
& ( b_stored(pair(X67,X68))
| ~ message(sent(X67,b,pair(X67,X68)))
| ~ fresh_to_b(X68) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[b_creates_freash_nonces_in_time])])]) ).
fof(c_0_15,plain,
! [X69,X70,X71] :
( ~ message(sent(X70,b,pair(encrypt(triple(X70,X69,generate_expiration_time(X71)),bt),encrypt(generate_b_nonce(X71),X69))))
| ~ b_stored(pair(X70,X71))
| b_holds(key(X69,X70)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[b_accepts_secure_session_key])]) ).
cnf(c_0_16,plain,
( b_stored(pair(X1,X2))
| ~ message(sent(X1,b,pair(X1,X2)))
| ~ fresh_to_b(X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_17,plain,
message(sent(a,b,pair(a,an_a_nonce))),
inference(split_conjunct,[status(thm)],[a_sent_message_i_to_b]) ).
cnf(c_0_18,plain,
fresh_to_b(an_a_nonce),
inference(split_conjunct,[status(thm)],[nonce_a_is_fresh_to_b]) ).
cnf(c_0_19,plain,
( b_holds(key(X2,X1))
| ~ message(sent(X1,b,pair(encrypt(triple(X1,X2,generate_expiration_time(X3)),bt),encrypt(generate_b_nonce(X3),X2))))
| ~ b_stored(pair(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
b_stored(pair(a,an_a_nonce)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]) ).
fof(c_0_21,plain,
! [X103,X104,X105] :
( ~ intruder_message(X103)
| ~ party_of_protocol(X104)
| ~ party_of_protocol(X105)
| message(sent(X104,X105,X103)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intruder_message_sent])]) ).
fof(c_0_22,plain,
! [X108,X109,X110] :
( ~ intruder_message(X108)
| ~ intruder_holds(key(X109,X110))
| ~ party_of_protocol(X110)
| intruder_message(encrypt(X108,X109)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intruder_key_encrypts])]) ).
fof(c_0_23,plain,
! [X106,X107] :
( ~ intruder_message(X106)
| ~ party_of_protocol(X107)
| intruder_holds(key(X106,X107)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intruder_holds_key])]) ).
cnf(c_0_24,plain,
( b_holds(key(X1,a))
| ~ message(sent(a,b,pair(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),X1)))) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
( message(sent(X2,X3,X1))
| ~ intruder_message(X1)
| ~ party_of_protocol(X2)
| ~ party_of_protocol(X3) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_26,plain,
party_of_protocol(b),
inference(split_conjunct,[status(thm)],[b_is_party_of_protocol]) ).
cnf(c_0_27,plain,
party_of_protocol(a),
inference(split_conjunct,[status(thm)],[a_is_party_of_protocol]) ).
fof(c_0_28,plain,
! [X91,X92] :
( ~ intruder_message(X91)
| ~ intruder_message(X92)
| intruder_message(pair(X91,X92)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intruder_composes_pairs])]) ).
cnf(c_0_29,plain,
( intruder_message(encrypt(X1,X2))
| ~ intruder_message(X1)
| ~ intruder_holds(key(X2,X3))
| ~ party_of_protocol(X3) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,plain,
( intruder_holds(key(X1,X2))
| ~ intruder_message(X1)
| ~ party_of_protocol(X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_31,plain,
! [X79,X80,X81] :
( ~ message(sent(X79,X80,X81))
| intruder_message(X81) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intruder_can_record])]) ).
cnf(c_0_32,plain,
( message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt))))
| ~ message(sent(X2,b,pair(X2,X1)))
| ~ fresh_to_b(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_33,plain,
( b_holds(key(X1,a))
| ~ intruder_message(pair(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),X1))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_27])]) ).
cnf(c_0_34,plain,
( intruder_message(pair(X1,X2))
| ~ intruder_message(X1)
| ~ intruder_message(X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,plain,
( intruder_message(encrypt(X1,X2))
| ~ intruder_message(X1)
| ~ intruder_message(X2)
| ~ party_of_protocol(X3) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
fof(c_0_36,plain,
! [X84,X85,X86] :
( ( intruder_message(X84)
| ~ intruder_message(triple(X84,X85,X86)) )
& ( intruder_message(X85)
| ~ intruder_message(triple(X84,X85,X86)) )
& ( intruder_message(X86)
| ~ intruder_message(triple(X84,X85,X86)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intruder_decomposes_triples])])]) ).
cnf(c_0_37,plain,
( intruder_message(X3)
| ~ message(sent(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_38,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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_17]),c_0_18])]) ).
cnf(c_0_39,plain,
( b_holds(key(X1,a))
| ~ intruder_message(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt))
| ~ intruder_message(encrypt(generate_b_nonce(an_a_nonce),X1)) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_40,plain,
( intruder_message(encrypt(X1,X2))
| ~ intruder_message(X1)
| ~ intruder_message(X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_26]) ).
cnf(c_0_41,plain,
( intruder_message(X1)
| ~ intruder_message(triple(X2,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_42,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(spm,[status(thm)],[c_0_37,c_0_38]) ).
fof(c_0_43,plain,
! [X82,X83] :
( ( intruder_message(X82)
| ~ intruder_message(pair(X82,X83)) )
& ( intruder_message(X83)
| ~ intruder_message(pair(X82,X83)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intruder_decomposes_pairs])])]) ).
fof(c_0_44,negated_conjecture,
~ ? [X1] :
( intruder_holds(key(X1,b))
& b_holds(key(X1,a)) ),
inference(assume_negation,[status(cth)],[co1]) ).
cnf(c_0_45,plain,
( b_holds(key(X1,a))
| ~ intruder_message(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt))
| ~ intruder_message(generate_b_nonce(an_a_nonce))
| ~ intruder_message(X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_46,plain,
intruder_message(generate_b_nonce(an_a_nonce)),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_47,plain,
( intruder_message(X1)
| ~ intruder_message(triple(X2,X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_48,plain,
( intruder_message(X1)
| ~ intruder_message(pair(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_49,plain,
intruder_message(pair(a,an_a_nonce)),
inference(spm,[status(thm)],[c_0_37,c_0_17]) ).
fof(c_0_50,negated_conjecture,
! [X113] :
( ~ intruder_holds(key(X113,b))
| ~ b_holds(key(X113,a)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])]) ).
cnf(c_0_51,plain,
( b_holds(key(X1,a))
| ~ intruder_message(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt))
| ~ intruder_message(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46])]) ).
cnf(c_0_52,plain,
intruder_message(encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt)),
inference(spm,[status(thm)],[c_0_47,c_0_42]) ).
cnf(c_0_53,plain,
intruder_message(an_a_nonce),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_54,negated_conjecture,
( ~ intruder_holds(key(X1,b))
| ~ b_holds(key(X1,a)) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_55,plain,
b_holds(key(an_a_nonce,a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53])]) ).
cnf(c_0_56,negated_conjecture,
~ intruder_holds(key(an_a_nonce,b)),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_57,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_30]),c_0_53]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV014+1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n028.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 04:53:30 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.26/1.73 % Version : CSE_E---1.7
% 1.26/1.73 % Problem : theBenchmark.p
% 1.26/1.73 % SZS status Theorem for theBenchmark.p
% 1.26/1.73 % SZS output start CNFRefutation
% See solution above
% 1.26/1.73 % Total time : 1.374s
%------------------------------------------------------------------------------