%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV014-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 : Wed Oct 7 10:54:27 AM UTC 2026
% Result : Unsatisfiable 0.54s 0.33s
% Output : CNFRefutation 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 35
% Syntax : Number of formulae : 272 ( 162 unt; 0 typ; 0 def)
% Number of atoms : 1561 ( 403 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 3528 ( 407 ~; 483 |; 0 &;2638 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 25 usr; 8 con; 0-4 aty)
% Number of variables : 793 ( 0 ^; 793 !; 0 ?; 793 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_a_nonce,type,
a_nonce: $i > $o ).
thf(tp_a_stored,type,
a_stored: $i > $o ).
thf(tp_an_a_nonce,type,
an_a_nonce: $i ).
thf(tp_at,type,
at: $i ).
thf(tp_b,type,
b: $i ).
thf(tp_b_holds,type,
b_holds: $i > $o ).
thf(tp_b_stored,type,
b_stored: $i > $o ).
thf(tp_bt,type,
bt: $i ).
thf(tp_encrypt,type,
encrypt: $i > $i > $i ).
thf(tp_fresh_to_b,type,
fresh_to_b: $i > $o ).
thf(tp_generate_b_nonce,type,
generate_b_nonce: $i > $i ).
thf(tp_generate_expiration_time,type,
generate_expiration_time: $i > $i ).
thf(tp_generate_key,type,
generate_key: $i > $i ).
thf(tp_intruder_holds,type,
intruder_holds: $i > $o ).
thf(tp_intruder_message,type,
intruder_message: $i > $o ).
thf(tp_key,type,
key: $i > $i > $i ).
thf(tp_message,type,
message: $i > $o ).
thf(tp_pair,type,
pair: $i > $i > $i ).
thf(tp_party_of_protocol,type,
party_of_protocol: $i > $o ).
thf(tp_quadruple,type,
quadruple: $i > $i > $i > $i > $i ).
thf(tp_sent,type,
sent: $i > $i > $i > $i ).
thf(tp_t,type,
t: $i ).
thf(tp_t_holds,type,
t_holds: $i > $o ).
thf(tp_triple,type,
triple: $i > $i > $i > $i ).
thf(1,axiom,
! [A: $i] : ( a_nonce @ ( generate_b_nonce @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',generated_times_and_nonces_are_nonces_37) ).
thf(2,axiom,
! [A: $i] : ( a_nonce @ ( generate_expiration_time @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',generated_times_and_nonces_are_nonces_36) ).
thf(3,axiom,
a_nonce @ an_a_nonce,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',an_a_nonce_is_a_nonce_34) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( intruder_message @ ( encrypt @ A @ B ) )
| ~ ( intruder_holds @ ( key @ B @ C ) )
| ~ ( intruder_message @ A )
| ~ ( party_of_protocol @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_key_encrypts_33) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( intruder_holds @ ( key @ A @ B ) )
| ~ ( intruder_message @ A )
| ~ ( party_of_protocol @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_holds_key_32) ).
thf(6,axiom,
! [B: $i,C: $i,A: $i] :
( ( message @ ( sent @ B @ C @ A ) )
| ~ ( intruder_message @ A )
| ~ ( party_of_protocol @ C )
| ~ ( party_of_protocol @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_message_sent_31) ).
thf(7,axiom,
! [B: $i,C: $i,A: $i] :
( ( intruder_message @ B )
| ~ ( intruder_holds @ ( key @ B @ C ) )
| ~ ( intruder_message @ ( encrypt @ A @ B ) )
| ~ ( party_of_protocol @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_interception_30) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( intruder_message @ ( quadruple @ A @ B @ C @ D ) )
| ~ ( intruder_message @ D )
| ~ ( intruder_message @ C )
| ~ ( intruder_message @ B )
| ~ ( intruder_message @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_composes_quadruples_29) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( intruder_message @ ( triple @ A @ B @ C ) )
| ~ ( intruder_message @ C )
| ~ ( intruder_message @ B )
| ~ ( intruder_message @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_composes_triples_28) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( intruder_message @ ( pair @ A @ B ) )
| ~ ( intruder_message @ B )
| ~ ( intruder_message @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_composes_pairs_27) ).
thf(11,axiom,
! [D: $i,A: $i,B: $i,C: $i] :
( ( intruder_message @ D )
| ~ ( intruder_message @ ( quadruple @ A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_decomposes_quadruples_26) ).
thf(12,axiom,
! [C: $i,A: $i,B: $i,D: $i] :
( ( intruder_message @ C )
| ~ ( intruder_message @ ( quadruple @ A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_decomposes_quadruples_25) ).
thf(13,axiom,
! [B: $i,A: $i,C: $i,D: $i] :
( ( intruder_message @ B )
| ~ ( intruder_message @ ( quadruple @ A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_decomposes_quadruples_24) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( intruder_message @ A )
| ~ ( intruder_message @ ( quadruple @ A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_decomposes_quadruples_23) ).
thf(15,axiom,
! [C: $i,A: $i,B: $i] :
( ( intruder_message @ C )
| ~ ( intruder_message @ ( triple @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_decomposes_triples_22) ).
thf(16,axiom,
! [B: $i,A: $i,C: $i] :
( ( intruder_message @ B )
| ~ ( intruder_message @ ( triple @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_decomposes_triples_21) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( intruder_message @ A )
| ~ ( intruder_message @ ( triple @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_decomposes_triples_20) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ( intruder_message @ B )
| ~ ( intruder_message @ ( pair @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_decomposes_pairs_19) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( intruder_message @ A )
| ~ ( intruder_message @ ( pair @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_decomposes_pairs_18) ).
thf(20,axiom,
! [C: $i,A: $i,B: $i] :
( ( intruder_message @ C )
| ~ ( message @ ( sent @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_can_record_17) ).
thf(21,axiom,
! [C: $i,A: $i,D: $i,E: $i,G: $i,F: $i,B: $i] :
( ( message @ ( sent @ t @ C @ ( triple @ ( encrypt @ ( quadruple @ A @ D @ ( generate_key @ D ) @ E ) @ G ) @ ( encrypt @ ( triple @ C @ ( generate_key @ D ) @ E ) @ F ) @ B ) ) )
| ~ ( a_nonce @ D )
| ~ ( message @ ( sent @ A @ t @ ( triple @ A @ B @ ( encrypt @ ( triple @ C @ D @ E ) @ F ) ) ) )
| ~ ( t_holds @ ( key @ G @ C ) )
| ~ ( t_holds @ ( key @ F @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',server_t_generates_key_16) ).
thf(22,axiom,
party_of_protocol @ t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t_is_party_of_protocol_15) ).
thf(23,axiom,
t_holds @ ( key @ bt @ b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t_holds_key_bt_for_b_14) ).
thf(24,axiom,
t_holds @ ( key @ at @ a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t_holds_key_at_for_a_13) ).
thf(25,axiom,
! [B: $i,A: $i,C: $i] :
( ( b_holds @ ( key @ B @ A ) )
| ~ ( b_stored @ ( pair @ A @ C ) )
| ~ ( message @ ( sent @ A @ b @ ( pair @ ( encrypt @ ( triple @ A @ B @ ( generate_expiration_time @ C ) ) @ bt ) @ ( encrypt @ ( generate_b_nonce @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_accepts_secure_session_key_12) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( b_stored @ ( pair @ A @ B ) )
| ~ ( fresh_to_b @ B )
| ~ ( message @ ( sent @ A @ b @ ( pair @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_creates_freash_nonces_in_time_11) ).
thf(27,axiom,
! [B: $i,A: $i] :
( ( message @ ( sent @ b @ t @ ( triple @ b @ ( generate_b_nonce @ B ) @ ( encrypt @ ( triple @ A @ B @ ( generate_expiration_time @ B ) ) @ bt ) ) ) )
| ~ ( fresh_to_b @ B )
| ~ ( message @ ( sent @ A @ b @ ( pair @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_creates_freash_nonces_in_time_10) ).
thf(28,axiom,
fresh_to_b @ an_a_nonce,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonce_a_is_fresh_to_b_9) ).
thf(29,axiom,
party_of_protocol @ b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_party_of_protocol_8) ).
thf(30,axiom,
! [A: $i,E: $i,F: $i,C: $i,B: $i,D: $i] :
( ( message @ ( sent @ a @ A @ ( pair @ E @ ( encrypt @ F @ C ) ) ) )
| ~ ( a_stored @ ( pair @ A @ B ) )
| ~ ( message @ ( sent @ t @ a @ ( triple @ ( encrypt @ ( quadruple @ A @ B @ C @ D ) @ at ) @ E @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_forwards_secure_5) ).
thf(31,axiom,
a_stored @ ( pair @ b @ an_a_nonce ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_stored_message_i_4) ).
thf(32,axiom,
message @ ( sent @ a @ b @ ( pair @ a @ an_a_nonce ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_sent_message_i_to_b_3) ).
thf(33,axiom,
party_of_protocol @ a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_party_of_protocol_2) ).
thf(34,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(35,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[34]) ).
thf(36,negated_conjecture,
! [A: $i] :
( ~ ( b_holds @ ( key @ A @ a ) )
| ~ ( intruder_holds @ ( key @ A @ b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_38) ).
thf(37,plain,
$false = $false,
inference(unfold_def,[status(thm)],[35]) ).
thf(38,plain,
( ( ! [A: $i] : ( a_nonce @ ( generate_b_nonce @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(39,plain,
( ( ! [A: $i] : ( a_nonce @ ( generate_expiration_time @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(40,plain,
( ( a_nonce @ an_a_nonce )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(41,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( intruder_message @ ( encrypt @ A @ B ) )
| ~ ( intruder_holds @ ( key @ B @ C ) )
| ~ ( intruder_message @ A )
| ~ ( party_of_protocol @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(42,plain,
( ( ! [A: $i,B: $i] :
( ( intruder_holds @ ( key @ A @ B ) )
| ~ ( intruder_message @ A )
| ~ ( party_of_protocol @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(43,plain,
( ( ! [B: $i,C: $i,A: $i] :
( ( message @ ( sent @ B @ C @ A ) )
| ~ ( intruder_message @ A )
| ~ ( party_of_protocol @ C )
| ~ ( party_of_protocol @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(44,plain,
( ( ! [B: $i,C: $i,A: $i] :
( ( intruder_message @ B )
| ~ ( intruder_holds @ ( key @ B @ C ) )
| ~ ( intruder_message @ ( encrypt @ A @ B ) )
| ~ ( party_of_protocol @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(45,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( intruder_message @ ( quadruple @ A @ B @ C @ D ) )
| ~ ( intruder_message @ D )
| ~ ( intruder_message @ C )
| ~ ( intruder_message @ B )
| ~ ( intruder_message @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(46,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( intruder_message @ ( triple @ A @ B @ C ) )
| ~ ( intruder_message @ C )
| ~ ( intruder_message @ B )
| ~ ( intruder_message @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(47,plain,
( ( ! [A: $i,B: $i] :
( ( intruder_message @ ( pair @ A @ B ) )
| ~ ( intruder_message @ B )
| ~ ( intruder_message @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(48,plain,
( ( ! [D: $i,A: $i,B: $i,C: $i] :
( ( intruder_message @ D )
| ~ ( intruder_message @ ( quadruple @ A @ B @ C @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(49,plain,
( ( ! [C: $i,A: $i,B: $i,D: $i] :
( ( intruder_message @ C )
| ~ ( intruder_message @ ( quadruple @ A @ B @ C @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(50,plain,
( ( ! [B: $i,A: $i,C: $i,D: $i] :
( ( intruder_message @ B )
| ~ ( intruder_message @ ( quadruple @ A @ B @ C @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(51,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( intruder_message @ A )
| ~ ( intruder_message @ ( quadruple @ A @ B @ C @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(52,plain,
( ( ! [C: $i,A: $i,B: $i] :
( ( intruder_message @ C )
| ~ ( intruder_message @ ( triple @ A @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(53,plain,
( ( ! [B: $i,A: $i,C: $i] :
( ( intruder_message @ B )
| ~ ( intruder_message @ ( triple @ A @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(54,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( intruder_message @ A )
| ~ ( intruder_message @ ( triple @ A @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(55,plain,
( ( ! [B: $i,A: $i] :
( ( intruder_message @ B )
| ~ ( intruder_message @ ( pair @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(56,plain,
( ( ! [A: $i,B: $i] :
( ( intruder_message @ A )
| ~ ( intruder_message @ ( pair @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(57,plain,
( ( ! [C: $i,A: $i,B: $i] :
( ( intruder_message @ C )
| ~ ( message @ ( sent @ A @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(58,plain,
( ( ! [C: $i,A: $i,D: $i,E: $i,G: $i,F: $i,B: $i] :
( ( message @ ( sent @ t @ C @ ( triple @ ( encrypt @ ( quadruple @ A @ D @ ( generate_key @ D ) @ E ) @ G ) @ ( encrypt @ ( triple @ C @ ( generate_key @ D ) @ E ) @ F ) @ B ) ) )
| ~ ( a_nonce @ D )
| ~ ( message @ ( sent @ A @ t @ ( triple @ A @ B @ ( encrypt @ ( triple @ C @ D @ E ) @ F ) ) ) )
| ~ ( t_holds @ ( key @ G @ C ) )
| ~ ( t_holds @ ( key @ F @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(59,plain,
( ( party_of_protocol @ t )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(60,plain,
( ( t_holds @ ( key @ bt @ b ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(61,plain,
( ( t_holds @ ( key @ at @ a ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(62,plain,
( ( ! [B: $i,A: $i,C: $i] :
( ( b_holds @ ( key @ B @ A ) )
| ~ ( b_stored @ ( pair @ A @ C ) )
| ~ ( message @ ( sent @ A @ b @ ( pair @ ( encrypt @ ( triple @ A @ B @ ( generate_expiration_time @ C ) ) @ bt ) @ ( encrypt @ ( generate_b_nonce @ C ) @ B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(63,plain,
( ( ! [A: $i,B: $i] :
( ( b_stored @ ( pair @ A @ B ) )
| ~ ( fresh_to_b @ B )
| ~ ( message @ ( sent @ A @ b @ ( pair @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(64,plain,
( ( ! [B: $i,A: $i] :
( ( message @ ( sent @ b @ t @ ( triple @ b @ ( generate_b_nonce @ B ) @ ( encrypt @ ( triple @ A @ B @ ( generate_expiration_time @ B ) ) @ bt ) ) ) )
| ~ ( fresh_to_b @ B )
| ~ ( message @ ( sent @ A @ b @ ( pair @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(65,plain,
( ( fresh_to_b @ an_a_nonce )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(66,plain,
( ( party_of_protocol @ b )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(67,plain,
( ( ! [A: $i,E: $i,F: $i,C: $i,B: $i,D: $i] :
( ( message @ ( sent @ a @ A @ ( pair @ E @ ( encrypt @ F @ C ) ) ) )
| ~ ( a_stored @ ( pair @ A @ B ) )
| ~ ( message @ ( sent @ t @ a @ ( triple @ ( encrypt @ ( quadruple @ A @ B @ C @ D ) @ at ) @ E @ F ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(68,plain,
( ( a_stored @ ( pair @ b @ an_a_nonce ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(69,plain,
( ( message @ ( sent @ a @ b @ ( pair @ a @ an_a_nonce ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(70,plain,
( ( party_of_protocol @ a )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(71,plain,
( ( ! [A: $i] :
( ~ ( b_holds @ ( key @ A @ a ) )
| ~ ( intruder_holds @ ( key @ A @ b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(72,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[37]) ).
thf(73,plain,
( ( ! [A: $i] :
( ~ ( b_holds @ ( key @ A @ a ) )
| ~ ( intruder_holds @ ( key @ A @ b ) ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(74,plain,
( ( party_of_protocol @ a )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(75,plain,
( ( message @ ( sent @ a @ b @ ( pair @ a @ an_a_nonce ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(76,plain,
( ( a_stored @ ( pair @ b @ an_a_nonce ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(77,plain,
( ( ! [A: $i,E: $i,F: $i,C: $i,B: $i,D: $i] :
( ( message @ ( sent @ a @ A @ ( pair @ E @ ( encrypt @ F @ C ) ) ) )
| ~ ( a_stored @ ( pair @ A @ B ) )
| ~ ( message @ ( sent @ t @ a @ ( triple @ ( encrypt @ ( quadruple @ A @ B @ C @ D ) @ at ) @ E @ F ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(78,plain,
( ( party_of_protocol @ b )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(79,plain,
( ( fresh_to_b @ an_a_nonce )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(80,plain,
( ( ! [B: $i,A: $i] :
( ( message @ ( sent @ b @ t @ ( triple @ b @ ( generate_b_nonce @ B ) @ ( encrypt @ ( triple @ A @ B @ ( generate_expiration_time @ B ) ) @ bt ) ) ) )
| ~ ( fresh_to_b @ B )
| ~ ( message @ ( sent @ A @ b @ ( pair @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(81,plain,
( ( ! [A: $i,B: $i] :
( ( b_stored @ ( pair @ A @ B ) )
| ~ ( fresh_to_b @ B )
| ~ ( message @ ( sent @ A @ b @ ( pair @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(82,plain,
( ( ! [B: $i,A: $i,C: $i] :
( ( b_holds @ ( key @ B @ A ) )
| ~ ( b_stored @ ( pair @ A @ C ) )
| ~ ( message @ ( sent @ A @ b @ ( pair @ ( encrypt @ ( triple @ A @ B @ ( generate_expiration_time @ C ) ) @ bt ) @ ( encrypt @ ( generate_b_nonce @ C ) @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(83,plain,
( ( t_holds @ ( key @ at @ a ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(84,plain,
( ( t_holds @ ( key @ bt @ b ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(85,plain,
( ( party_of_protocol @ t )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(86,plain,
( ( ! [C: $i,A: $i,D: $i,E: $i,G: $i,F: $i,B: $i] :
( ( message @ ( sent @ t @ C @ ( triple @ ( encrypt @ ( quadruple @ A @ D @ ( generate_key @ D ) @ E ) @ G ) @ ( encrypt @ ( triple @ C @ ( generate_key @ D ) @ E ) @ F ) @ B ) ) )
| ~ ( a_nonce @ D )
| ~ ( message @ ( sent @ A @ t @ ( triple @ A @ B @ ( encrypt @ ( triple @ C @ D @ E ) @ F ) ) ) )
| ~ ( t_holds @ ( key @ G @ C ) )
| ~ ( t_holds @ ( key @ F @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(87,plain,
( ( ! [C: $i,A: $i,B: $i] :
( ( intruder_message @ C )
| ~ ( message @ ( sent @ A @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(88,plain,
( ( ! [A: $i,B: $i] :
( ( intruder_message @ A )
| ~ ( intruder_message @ ( pair @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(89,plain,
( ( ! [B: $i,A: $i] :
( ( intruder_message @ B )
| ~ ( intruder_message @ ( pair @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(90,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( intruder_message @ A )
| ~ ( intruder_message @ ( triple @ A @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(91,plain,
( ( ! [B: $i,A: $i,C: $i] :
( ( intruder_message @ B )
| ~ ( intruder_message @ ( triple @ A @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(92,plain,
( ( ! [C: $i,A: $i,B: $i] :
( ( intruder_message @ C )
| ~ ( intruder_message @ ( triple @ A @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(93,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( intruder_message @ A )
| ~ ( intruder_message @ ( quadruple @ A @ B @ C @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(94,plain,
( ( ! [B: $i,A: $i,C: $i,D: $i] :
( ( intruder_message @ B )
| ~ ( intruder_message @ ( quadruple @ A @ B @ C @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(95,plain,
( ( ! [C: $i,A: $i,B: $i,D: $i] :
( ( intruder_message @ C )
| ~ ( intruder_message @ ( quadruple @ A @ B @ C @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(96,plain,
( ( ! [D: $i,A: $i,B: $i,C: $i] :
( ( intruder_message @ D )
| ~ ( intruder_message @ ( quadruple @ A @ B @ C @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(97,plain,
( ( ! [A: $i,B: $i] :
( ( intruder_message @ ( pair @ A @ B ) )
| ~ ( intruder_message @ B )
| ~ ( intruder_message @ A ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(98,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( intruder_message @ ( triple @ A @ B @ C ) )
| ~ ( intruder_message @ C )
| ~ ( intruder_message @ B )
| ~ ( intruder_message @ A ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(99,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( intruder_message @ ( quadruple @ A @ B @ C @ D ) )
| ~ ( intruder_message @ D )
| ~ ( intruder_message @ C )
| ~ ( intruder_message @ B )
| ~ ( intruder_message @ A ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(100,plain,
( ( ! [B: $i,C: $i,A: $i] :
( ( intruder_message @ B )
| ~ ( intruder_holds @ ( key @ B @ C ) )
| ~ ( intruder_message @ ( encrypt @ A @ B ) )
| ~ ( party_of_protocol @ C ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(101,plain,
( ( ! [B: $i,C: $i,A: $i] :
( ( message @ ( sent @ B @ C @ A ) )
| ~ ( intruder_message @ A )
| ~ ( party_of_protocol @ C )
| ~ ( party_of_protocol @ B ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(102,plain,
( ( ! [A: $i,B: $i] :
( ( intruder_holds @ ( key @ A @ B ) )
| ~ ( intruder_message @ A )
| ~ ( party_of_protocol @ B ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(103,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( intruder_message @ ( encrypt @ A @ B ) )
| ~ ( intruder_holds @ ( key @ B @ C ) )
| ~ ( intruder_message @ A )
| ~ ( party_of_protocol @ C ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(104,plain,
( ( a_nonce @ an_a_nonce )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(105,plain,
( ( ! [A: $i] : ( a_nonce @ ( generate_expiration_time @ A ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(106,plain,
( ( ! [A: $i] : ( a_nonce @ ( generate_b_nonce @ A ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(107,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[72]) ).
thf(108,plain,
! [SV1: $i] :
( ( ~ ( b_holds @ ( key @ SV1 @ a ) )
| ~ ( intruder_holds @ ( key @ SV1 @ b ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(109,plain,
! [SV2: $i] :
( ( ! [SY75: $i,SY76: $i,SY77: $i,SY78: $i,SY79: $i] :
( ( message @ ( sent @ a @ SV2 @ ( pair @ SY75 @ ( encrypt @ SY76 @ SY77 ) ) ) )
| ~ ( a_stored @ ( pair @ SV2 @ SY78 ) )
| ~ ( message @ ( sent @ t @ a @ ( triple @ ( encrypt @ ( quadruple @ SV2 @ SY78 @ SY77 @ SY79 ) @ at ) @ SY75 @ SY76 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(110,plain,
! [SV3: $i] :
( ( ! [SY80: $i] :
( ( message @ ( sent @ b @ t @ ( triple @ b @ ( generate_b_nonce @ SV3 ) @ ( encrypt @ ( triple @ SY80 @ SV3 @ ( generate_expiration_time @ SV3 ) ) @ bt ) ) ) )
| ~ ( fresh_to_b @ SV3 )
| ~ ( message @ ( sent @ SY80 @ b @ ( pair @ SY80 @ SV3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(111,plain,
! [SV4: $i] :
( ( ! [SY81: $i] :
( ( b_stored @ ( pair @ SV4 @ SY81 ) )
| ~ ( fresh_to_b @ SY81 )
| ~ ( message @ ( sent @ SV4 @ b @ ( pair @ SV4 @ SY81 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(112,plain,
! [SV5: $i] :
( ( ! [SY82: $i,SY83: $i] :
( ( b_holds @ ( key @ SV5 @ SY82 ) )
| ~ ( b_stored @ ( pair @ SY82 @ SY83 ) )
| ~ ( message @ ( sent @ SY82 @ b @ ( pair @ ( encrypt @ ( triple @ SY82 @ SV5 @ ( generate_expiration_time @ SY83 ) ) @ bt ) @ ( encrypt @ ( generate_b_nonce @ SY83 ) @ SV5 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(113,plain,
! [SV6: $i] :
( ( ! [SY84: $i,SY85: $i,SY86: $i,SY87: $i,SY88: $i,SY89: $i] :
( ( message @ ( sent @ t @ SV6 @ ( triple @ ( encrypt @ ( quadruple @ SY84 @ SY85 @ ( generate_key @ SY85 ) @ SY86 ) @ SY87 ) @ ( encrypt @ ( triple @ SV6 @ ( generate_key @ SY85 ) @ SY86 ) @ SY88 ) @ SY89 ) ) )
| ~ ( a_nonce @ SY85 )
| ~ ( message @ ( sent @ SY84 @ t @ ( triple @ SY84 @ SY89 @ ( encrypt @ ( triple @ SV6 @ SY85 @ SY86 ) @ SY88 ) ) ) )
| ~ ( t_holds @ ( key @ SY87 @ SV6 ) )
| ~ ( t_holds @ ( key @ SY88 @ SY84 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(114,plain,
! [SV7: $i] :
( ( ! [SY90: $i,SY91: $i] :
( ( intruder_message @ SV7 )
| ~ ( message @ ( sent @ SY90 @ SY91 @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(115,plain,
! [SV8: $i] :
( ( ! [SY92: $i] :
( ( intruder_message @ SV8 )
| ~ ( intruder_message @ ( pair @ SV8 @ SY92 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(116,plain,
! [SV9: $i] :
( ( ! [SY93: $i] :
( ( intruder_message @ SV9 )
| ~ ( intruder_message @ ( pair @ SY93 @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(117,plain,
! [SV10: $i] :
( ( ! [SY94: $i,SY95: $i] :
( ( intruder_message @ SV10 )
| ~ ( intruder_message @ ( triple @ SV10 @ SY94 @ SY95 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(118,plain,
! [SV11: $i] :
( ( ! [SY96: $i,SY97: $i] :
( ( intruder_message @ SV11 )
| ~ ( intruder_message @ ( triple @ SY96 @ SV11 @ SY97 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(119,plain,
! [SV12: $i] :
( ( ! [SY98: $i,SY99: $i] :
( ( intruder_message @ SV12 )
| ~ ( intruder_message @ ( triple @ SY98 @ SY99 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(120,plain,
! [SV13: $i] :
( ( ! [SY100: $i,SY101: $i,SY102: $i] :
( ( intruder_message @ SV13 )
| ~ ( intruder_message @ ( quadruple @ SV13 @ SY100 @ SY101 @ SY102 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(121,plain,
! [SV14: $i] :
( ( ! [SY103: $i,SY104: $i,SY105: $i] :
( ( intruder_message @ SV14 )
| ~ ( intruder_message @ ( quadruple @ SY103 @ SV14 @ SY104 @ SY105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(122,plain,
! [SV15: $i] :
( ( ! [SY106: $i,SY107: $i,SY108: $i] :
( ( intruder_message @ SV15 )
| ~ ( intruder_message @ ( quadruple @ SY106 @ SY107 @ SV15 @ SY108 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(123,plain,
! [SV16: $i] :
( ( ! [SY109: $i,SY110: $i,SY111: $i] :
( ( intruder_message @ SV16 )
| ~ ( intruder_message @ ( quadruple @ SY109 @ SY110 @ SY111 @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(124,plain,
! [SV17: $i] :
( ( ! [SY112: $i] :
( ( intruder_message @ ( pair @ SV17 @ SY112 ) )
| ~ ( intruder_message @ SY112 )
| ~ ( intruder_message @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(125,plain,
! [SV18: $i] :
( ( ! [SY113: $i,SY114: $i] :
( ( intruder_message @ ( triple @ SV18 @ SY113 @ SY114 ) )
| ~ ( intruder_message @ SY114 )
| ~ ( intruder_message @ SY113 )
| ~ ( intruder_message @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(126,plain,
! [SV19: $i] :
( ( ! [SY115: $i,SY116: $i,SY117: $i] :
( ( intruder_message @ ( quadruple @ SV19 @ SY115 @ SY116 @ SY117 ) )
| ~ ( intruder_message @ SY117 )
| ~ ( intruder_message @ SY116 )
| ~ ( intruder_message @ SY115 )
| ~ ( intruder_message @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(127,plain,
! [SV20: $i] :
( ( ! [SY118: $i,SY119: $i] :
( ( intruder_message @ SV20 )
| ~ ( intruder_holds @ ( key @ SV20 @ SY118 ) )
| ~ ( intruder_message @ ( encrypt @ SY119 @ SV20 ) )
| ~ ( party_of_protocol @ SY118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(128,plain,
! [SV21: $i] :
( ( ! [SY120: $i,SY121: $i] :
( ( message @ ( sent @ SV21 @ SY120 @ SY121 ) )
| ~ ( intruder_message @ SY121 )
| ~ ( party_of_protocol @ SY120 )
| ~ ( party_of_protocol @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(129,plain,
! [SV22: $i] :
( ( ! [SY122: $i] :
( ( intruder_holds @ ( key @ SV22 @ SY122 ) )
| ~ ( intruder_message @ SV22 )
| ~ ( party_of_protocol @ SY122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(130,plain,
! [SV23: $i] :
( ( ! [SY123: $i,SY124: $i] :
( ( intruder_message @ ( encrypt @ SV23 @ SY123 ) )
| ~ ( intruder_holds @ ( key @ SY123 @ SY124 ) )
| ~ ( intruder_message @ SV23 )
| ~ ( party_of_protocol @ SY124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(131,plain,
! [SV24: $i] :
( ( a_nonce @ ( generate_expiration_time @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(132,plain,
! [SV25: $i] :
( ( a_nonce @ ( generate_b_nonce @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(133,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(134,plain,
! [SV1: $i] :
( ( ( ~ ( b_holds @ ( key @ SV1 @ a ) ) )
= $true )
| ( ( ~ ( intruder_holds @ ( key @ SV1 @ b ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(135,plain,
! [SV26: $i,SV2: $i] :
( ( ! [SY125: $i,SY126: $i,SY127: $i,SY128: $i] :
( ( message @ ( sent @ a @ SV2 @ ( pair @ SV26 @ ( encrypt @ SY125 @ SY126 ) ) ) )
| ~ ( a_stored @ ( pair @ SV2 @ SY127 ) )
| ~ ( message @ ( sent @ t @ a @ ( triple @ ( encrypt @ ( quadruple @ SV2 @ SY127 @ SY126 @ SY128 ) @ at ) @ SV26 @ SY125 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(136,plain,
! [SV27: $i,SV3: $i] :
( ( ( message @ ( sent @ b @ t @ ( triple @ b @ ( generate_b_nonce @ SV3 ) @ ( encrypt @ ( triple @ SV27 @ SV3 @ ( generate_expiration_time @ SV3 ) ) @ bt ) ) ) )
| ~ ( fresh_to_b @ SV3 )
| ~ ( message @ ( sent @ SV27 @ b @ ( pair @ SV27 @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(137,plain,
! [SV28: $i,SV4: $i] :
( ( ( b_stored @ ( pair @ SV4 @ SV28 ) )
| ~ ( fresh_to_b @ SV28 )
| ~ ( message @ ( sent @ SV4 @ b @ ( pair @ SV4 @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(138,plain,
! [SV29: $i,SV5: $i] :
( ( ! [SY129: $i] :
( ( b_holds @ ( key @ SV5 @ SV29 ) )
| ~ ( b_stored @ ( pair @ SV29 @ SY129 ) )
| ~ ( message @ ( sent @ SV29 @ b @ ( pair @ ( encrypt @ ( triple @ SV29 @ SV5 @ ( generate_expiration_time @ SY129 ) ) @ bt ) @ ( encrypt @ ( generate_b_nonce @ SY129 ) @ SV5 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(139,plain,
! [SV30: $i,SV6: $i] :
( ( ! [SY130: $i,SY131: $i,SY132: $i,SY133: $i,SY134: $i] :
( ( message @ ( sent @ t @ SV6 @ ( triple @ ( encrypt @ ( quadruple @ SV30 @ SY130 @ ( generate_key @ SY130 ) @ SY131 ) @ SY132 ) @ ( encrypt @ ( triple @ SV6 @ ( generate_key @ SY130 ) @ SY131 ) @ SY133 ) @ SY134 ) ) )
| ~ ( a_nonce @ SY130 )
| ~ ( message @ ( sent @ SV30 @ t @ ( triple @ SV30 @ SY134 @ ( encrypt @ ( triple @ SV6 @ SY130 @ SY131 ) @ SY133 ) ) ) )
| ~ ( t_holds @ ( key @ SY132 @ SV6 ) )
| ~ ( t_holds @ ( key @ SY133 @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(140,plain,
! [SV31: $i,SV7: $i] :
( ( ! [SY135: $i] :
( ( intruder_message @ SV7 )
| ~ ( message @ ( sent @ SV31 @ SY135 @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(141,plain,
! [SV32: $i,SV8: $i] :
( ( ( intruder_message @ SV8 )
| ~ ( intruder_message @ ( pair @ SV8 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(142,plain,
! [SV33: $i,SV9: $i] :
( ( ( intruder_message @ SV9 )
| ~ ( intruder_message @ ( pair @ SV33 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(143,plain,
! [SV34: $i,SV10: $i] :
( ( ! [SY136: $i] :
( ( intruder_message @ SV10 )
| ~ ( intruder_message @ ( triple @ SV10 @ SV34 @ SY136 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(144,plain,
! [SV35: $i,SV11: $i] :
( ( ! [SY137: $i] :
( ( intruder_message @ SV11 )
| ~ ( intruder_message @ ( triple @ SV35 @ SV11 @ SY137 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(145,plain,
! [SV36: $i,SV12: $i] :
( ( ! [SY138: $i] :
( ( intruder_message @ SV12 )
| ~ ( intruder_message @ ( triple @ SV36 @ SY138 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(146,plain,
! [SV37: $i,SV13: $i] :
( ( ! [SY139: $i,SY140: $i] :
( ( intruder_message @ SV13 )
| ~ ( intruder_message @ ( quadruple @ SV13 @ SV37 @ SY139 @ SY140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(147,plain,
! [SV38: $i,SV14: $i] :
( ( ! [SY141: $i,SY142: $i] :
( ( intruder_message @ SV14 )
| ~ ( intruder_message @ ( quadruple @ SV38 @ SV14 @ SY141 @ SY142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(148,plain,
! [SV39: $i,SV15: $i] :
( ( ! [SY143: $i,SY144: $i] :
( ( intruder_message @ SV15 )
| ~ ( intruder_message @ ( quadruple @ SV39 @ SY143 @ SV15 @ SY144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(149,plain,
! [SV40: $i,SV16: $i] :
( ( ! [SY145: $i,SY146: $i] :
( ( intruder_message @ SV16 )
| ~ ( intruder_message @ ( quadruple @ SV40 @ SY145 @ SY146 @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(150,plain,
! [SV41: $i,SV17: $i] :
( ( ( intruder_message @ ( pair @ SV17 @ SV41 ) )
| ~ ( intruder_message @ SV41 )
| ~ ( intruder_message @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(151,plain,
! [SV42: $i,SV18: $i] :
( ( ! [SY147: $i] :
( ( intruder_message @ ( triple @ SV18 @ SV42 @ SY147 ) )
| ~ ( intruder_message @ SY147 )
| ~ ( intruder_message @ SV42 )
| ~ ( intruder_message @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(152,plain,
! [SV43: $i,SV19: $i] :
( ( ! [SY148: $i,SY149: $i] :
( ( intruder_message @ ( quadruple @ SV19 @ SV43 @ SY148 @ SY149 ) )
| ~ ( intruder_message @ SY149 )
| ~ ( intruder_message @ SY148 )
| ~ ( intruder_message @ SV43 )
| ~ ( intruder_message @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(153,plain,
! [SV44: $i,SV20: $i] :
( ( ! [SY150: $i] :
( ( intruder_message @ SV20 )
| ~ ( intruder_holds @ ( key @ SV20 @ SV44 ) )
| ~ ( intruder_message @ ( encrypt @ SY150 @ SV20 ) )
| ~ ( party_of_protocol @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(154,plain,
! [SV45: $i,SV21: $i] :
( ( ! [SY151: $i] :
( ( message @ ( sent @ SV21 @ SV45 @ SY151 ) )
| ~ ( intruder_message @ SY151 )
| ~ ( party_of_protocol @ SV45 )
| ~ ( party_of_protocol @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(155,plain,
! [SV46: $i,SV22: $i] :
( ( ( intruder_holds @ ( key @ SV22 @ SV46 ) )
| ~ ( intruder_message @ SV22 )
| ~ ( party_of_protocol @ SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(156,plain,
! [SV47: $i,SV23: $i] :
( ( ! [SY152: $i] :
( ( intruder_message @ ( encrypt @ SV23 @ SV47 ) )
| ~ ( intruder_holds @ ( key @ SV47 @ SY152 ) )
| ~ ( intruder_message @ SV23 )
| ~ ( party_of_protocol @ SY152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(157,plain,
! [SV1: $i] :
( ( ( b_holds @ ( key @ SV1 @ a ) )
= $false )
| ( ( ~ ( intruder_holds @ ( key @ SV1 @ b ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(158,plain,
! [SV48: $i,SV26: $i,SV2: $i] :
( ( ! [SY153: $i,SY154: $i,SY155: $i] :
( ( message @ ( sent @ a @ SV2 @ ( pair @ SV26 @ ( encrypt @ SV48 @ SY153 ) ) ) )
| ~ ( a_stored @ ( pair @ SV2 @ SY154 ) )
| ~ ( message @ ( sent @ t @ a @ ( triple @ ( encrypt @ ( quadruple @ SV2 @ SY154 @ SY153 @ SY155 ) @ at ) @ SV26 @ SV48 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(159,plain,
! [SV27: $i,SV3: $i] :
( ( ( message @ ( sent @ b @ t @ ( triple @ b @ ( generate_b_nonce @ SV3 ) @ ( encrypt @ ( triple @ SV27 @ SV3 @ ( generate_expiration_time @ SV3 ) ) @ bt ) ) ) )
= $true )
| ( ( ~ ( fresh_to_b @ SV3 )
| ~ ( message @ ( sent @ SV27 @ b @ ( pair @ SV27 @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(160,plain,
! [SV28: $i,SV4: $i] :
( ( ( b_stored @ ( pair @ SV4 @ SV28 ) )
= $true )
| ( ( ~ ( fresh_to_b @ SV28 )
| ~ ( message @ ( sent @ SV4 @ b @ ( pair @ SV4 @ SV28 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(161,plain,
! [SV49: $i,SV29: $i,SV5: $i] :
( ( ( b_holds @ ( key @ SV5 @ SV29 ) )
| ~ ( b_stored @ ( pair @ SV29 @ SV49 ) )
| ~ ( message @ ( sent @ SV29 @ b @ ( pair @ ( encrypt @ ( triple @ SV29 @ SV5 @ ( generate_expiration_time @ SV49 ) ) @ bt ) @ ( encrypt @ ( generate_b_nonce @ SV49 ) @ SV5 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(162,plain,
! [SV50: $i,SV30: $i,SV6: $i] :
( ( ! [SY156: $i,SY157: $i,SY158: $i,SY159: $i] :
( ( message @ ( sent @ t @ SV6 @ ( triple @ ( encrypt @ ( quadruple @ SV30 @ SV50 @ ( generate_key @ SV50 ) @ SY156 ) @ SY157 ) @ ( encrypt @ ( triple @ SV6 @ ( generate_key @ SV50 ) @ SY156 ) @ SY158 ) @ SY159 ) ) )
| ~ ( a_nonce @ SV50 )
| ~ ( message @ ( sent @ SV30 @ t @ ( triple @ SV30 @ SY159 @ ( encrypt @ ( triple @ SV6 @ SV50 @ SY156 ) @ SY158 ) ) ) )
| ~ ( t_holds @ ( key @ SY157 @ SV6 ) )
| ~ ( t_holds @ ( key @ SY158 @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(163,plain,
! [SV51: $i,SV31: $i,SV7: $i] :
( ( ( intruder_message @ SV7 )
| ~ ( message @ ( sent @ SV31 @ SV51 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(164,plain,
! [SV32: $i,SV8: $i] :
( ( ( intruder_message @ SV8 )
= $true )
| ( ( ~ ( intruder_message @ ( pair @ SV8 @ SV32 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(165,plain,
! [SV33: $i,SV9: $i] :
( ( ( intruder_message @ SV9 )
= $true )
| ( ( ~ ( intruder_message @ ( pair @ SV33 @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(166,plain,
! [SV52: $i,SV34: $i,SV10: $i] :
( ( ( intruder_message @ SV10 )
| ~ ( intruder_message @ ( triple @ SV10 @ SV34 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(167,plain,
! [SV53: $i,SV35: $i,SV11: $i] :
( ( ( intruder_message @ SV11 )
| ~ ( intruder_message @ ( triple @ SV35 @ SV11 @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(168,plain,
! [SV54: $i,SV36: $i,SV12: $i] :
( ( ( intruder_message @ SV12 )
| ~ ( intruder_message @ ( triple @ SV36 @ SV54 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(169,plain,
! [SV55: $i,SV37: $i,SV13: $i] :
( ( ! [SY160: $i] :
( ( intruder_message @ SV13 )
| ~ ( intruder_message @ ( quadruple @ SV13 @ SV37 @ SV55 @ SY160 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(170,plain,
! [SV56: $i,SV38: $i,SV14: $i] :
( ( ! [SY161: $i] :
( ( intruder_message @ SV14 )
| ~ ( intruder_message @ ( quadruple @ SV38 @ SV14 @ SV56 @ SY161 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(171,plain,
! [SV57: $i,SV39: $i,SV15: $i] :
( ( ! [SY162: $i] :
( ( intruder_message @ SV15 )
| ~ ( intruder_message @ ( quadruple @ SV39 @ SV57 @ SV15 @ SY162 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(172,plain,
! [SV58: $i,SV40: $i,SV16: $i] :
( ( ! [SY163: $i] :
( ( intruder_message @ SV16 )
| ~ ( intruder_message @ ( quadruple @ SV40 @ SV58 @ SY163 @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(173,plain,
! [SV41: $i,SV17: $i] :
( ( ( intruder_message @ ( pair @ SV17 @ SV41 ) )
= $true )
| ( ( ~ ( intruder_message @ SV41 )
| ~ ( intruder_message @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(174,plain,
! [SV59: $i,SV42: $i,SV18: $i] :
( ( ( intruder_message @ ( triple @ SV18 @ SV42 @ SV59 ) )
| ~ ( intruder_message @ SV59 )
| ~ ( intruder_message @ SV42 )
| ~ ( intruder_message @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(175,plain,
! [SV60: $i,SV43: $i,SV19: $i] :
( ( ! [SY164: $i] :
( ( intruder_message @ ( quadruple @ SV19 @ SV43 @ SV60 @ SY164 ) )
| ~ ( intruder_message @ SY164 )
| ~ ( intruder_message @ SV60 )
| ~ ( intruder_message @ SV43 )
| ~ ( intruder_message @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(176,plain,
! [SV61: $i,SV44: $i,SV20: $i] :
( ( ( intruder_message @ SV20 )
| ~ ( intruder_holds @ ( key @ SV20 @ SV44 ) )
| ~ ( intruder_message @ ( encrypt @ SV61 @ SV20 ) )
| ~ ( party_of_protocol @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(177,plain,
! [SV62: $i,SV45: $i,SV21: $i] :
( ( ( message @ ( sent @ SV21 @ SV45 @ SV62 ) )
| ~ ( intruder_message @ SV62 )
| ~ ( party_of_protocol @ SV45 )
| ~ ( party_of_protocol @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(178,plain,
! [SV46: $i,SV22: $i] :
( ( ( intruder_holds @ ( key @ SV22 @ SV46 ) )
= $true )
| ( ( ~ ( intruder_message @ SV22 )
| ~ ( party_of_protocol @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(179,plain,
! [SV63: $i,SV47: $i,SV23: $i] :
( ( ( intruder_message @ ( encrypt @ SV23 @ SV47 ) )
| ~ ( intruder_holds @ ( key @ SV47 @ SV63 ) )
| ~ ( intruder_message @ SV23 )
| ~ ( party_of_protocol @ SV63 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(180,plain,
! [SV1: $i] :
( ( ( intruder_holds @ ( key @ SV1 @ b ) )
= $false )
| ( ( b_holds @ ( key @ SV1 @ a ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(181,plain,
! [SV64: $i,SV48: $i,SV26: $i,SV2: $i] :
( ( ! [SY165: $i,SY166: $i] :
( ( message @ ( sent @ a @ SV2 @ ( pair @ SV26 @ ( encrypt @ SV48 @ SV64 ) ) ) )
| ~ ( a_stored @ ( pair @ SV2 @ SY165 ) )
| ~ ( message @ ( sent @ t @ a @ ( triple @ ( encrypt @ ( quadruple @ SV2 @ SY165 @ SV64 @ SY166 ) @ at ) @ SV26 @ SV48 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(182,plain,
! [SV27: $i,SV3: $i] :
( ( ( ~ ( fresh_to_b @ SV3 ) )
= $true )
| ( ( ~ ( message @ ( sent @ SV27 @ b @ ( pair @ SV27 @ SV3 ) ) ) )
= $true )
| ( ( message @ ( sent @ b @ t @ ( triple @ b @ ( generate_b_nonce @ SV3 ) @ ( encrypt @ ( triple @ SV27 @ SV3 @ ( generate_expiration_time @ SV3 ) ) @ bt ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(183,plain,
! [SV4: $i,SV28: $i] :
( ( ( ~ ( fresh_to_b @ SV28 ) )
= $true )
| ( ( ~ ( message @ ( sent @ SV4 @ b @ ( pair @ SV4 @ SV28 ) ) ) )
= $true )
| ( ( b_stored @ ( pair @ SV4 @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(184,plain,
! [SV49: $i,SV29: $i,SV5: $i] :
( ( ( b_holds @ ( key @ SV5 @ SV29 ) )
= $true )
| ( ( ~ ( b_stored @ ( pair @ SV29 @ SV49 ) )
| ~ ( message @ ( sent @ SV29 @ b @ ( pair @ ( encrypt @ ( triple @ SV29 @ SV5 @ ( generate_expiration_time @ SV49 ) ) @ bt ) @ ( encrypt @ ( generate_b_nonce @ SV49 ) @ SV5 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(185,plain,
! [SV65: $i,SV50: $i,SV30: $i,SV6: $i] :
( ( ! [SY167: $i,SY168: $i,SY169: $i] :
( ( message @ ( sent @ t @ SV6 @ ( triple @ ( encrypt @ ( quadruple @ SV30 @ SV50 @ ( generate_key @ SV50 ) @ SV65 ) @ SY167 ) @ ( encrypt @ ( triple @ SV6 @ ( generate_key @ SV50 ) @ SV65 ) @ SY168 ) @ SY169 ) ) )
| ~ ( a_nonce @ SV50 )
| ~ ( message @ ( sent @ SV30 @ t @ ( triple @ SV30 @ SY169 @ ( encrypt @ ( triple @ SV6 @ SV50 @ SV65 ) @ SY168 ) ) ) )
| ~ ( t_holds @ ( key @ SY167 @ SV6 ) )
| ~ ( t_holds @ ( key @ SY168 @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(186,plain,
! [SV51: $i,SV31: $i,SV7: $i] :
( ( ( intruder_message @ SV7 )
= $true )
| ( ( ~ ( message @ ( sent @ SV31 @ SV51 @ SV7 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(187,plain,
! [SV32: $i,SV8: $i] :
( ( ( intruder_message @ ( pair @ SV8 @ SV32 ) )
= $false )
| ( ( intruder_message @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(188,plain,
! [SV9: $i,SV33: $i] :
( ( ( intruder_message @ ( pair @ SV33 @ SV9 ) )
= $false )
| ( ( intruder_message @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(189,plain,
! [SV52: $i,SV34: $i,SV10: $i] :
( ( ( intruder_message @ SV10 )
= $true )
| ( ( ~ ( intruder_message @ ( triple @ SV10 @ SV34 @ SV52 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(190,plain,
! [SV53: $i,SV35: $i,SV11: $i] :
( ( ( intruder_message @ SV11 )
= $true )
| ( ( ~ ( intruder_message @ ( triple @ SV35 @ SV11 @ SV53 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(191,plain,
! [SV54: $i,SV36: $i,SV12: $i] :
( ( ( intruder_message @ SV12 )
= $true )
| ( ( ~ ( intruder_message @ ( triple @ SV36 @ SV54 @ SV12 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(192,plain,
! [SV66: $i,SV55: $i,SV37: $i,SV13: $i] :
( ( ( intruder_message @ SV13 )
| ~ ( intruder_message @ ( quadruple @ SV13 @ SV37 @ SV55 @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(193,plain,
! [SV67: $i,SV56: $i,SV38: $i,SV14: $i] :
( ( ( intruder_message @ SV14 )
| ~ ( intruder_message @ ( quadruple @ SV38 @ SV14 @ SV56 @ SV67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(194,plain,
! [SV68: $i,SV57: $i,SV39: $i,SV15: $i] :
( ( ( intruder_message @ SV15 )
| ~ ( intruder_message @ ( quadruple @ SV39 @ SV57 @ SV15 @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(195,plain,
! [SV69: $i,SV58: $i,SV40: $i,SV16: $i] :
( ( ( intruder_message @ SV16 )
| ~ ( intruder_message @ ( quadruple @ SV40 @ SV58 @ SV69 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(196,plain,
! [SV17: $i,SV41: $i] :
( ( ( ~ ( intruder_message @ SV41 ) )
= $true )
| ( ( ~ ( intruder_message @ SV17 ) )
= $true )
| ( ( intruder_message @ ( pair @ SV17 @ SV41 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(197,plain,
! [SV59: $i,SV42: $i,SV18: $i] :
( ( ( intruder_message @ ( triple @ SV18 @ SV42 @ SV59 ) )
= $true )
| ( ( ~ ( intruder_message @ SV59 )
| ~ ( intruder_message @ SV42 )
| ~ ( intruder_message @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(198,plain,
! [SV70: $i,SV60: $i,SV43: $i,SV19: $i] :
( ( ( intruder_message @ ( quadruple @ SV19 @ SV43 @ SV60 @ SV70 ) )
| ~ ( intruder_message @ SV70 )
| ~ ( intruder_message @ SV60 )
| ~ ( intruder_message @ SV43 )
| ~ ( intruder_message @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(199,plain,
! [SV61: $i,SV44: $i,SV20: $i] :
( ( ( intruder_message @ SV20 )
= $true )
| ( ( ~ ( intruder_holds @ ( key @ SV20 @ SV44 ) )
| ~ ( intruder_message @ ( encrypt @ SV61 @ SV20 ) )
| ~ ( party_of_protocol @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(200,plain,
! [SV62: $i,SV45: $i,SV21: $i] :
( ( ( message @ ( sent @ SV21 @ SV45 @ SV62 ) )
= $true )
| ( ( ~ ( intruder_message @ SV62 )
| ~ ( party_of_protocol @ SV45 )
| ~ ( party_of_protocol @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(201,plain,
! [SV46: $i,SV22: $i] :
( ( ( ~ ( intruder_message @ SV22 ) )
= $true )
| ( ( ~ ( party_of_protocol @ SV46 ) )
= $true )
| ( ( intruder_holds @ ( key @ SV22 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(202,plain,
! [SV63: $i,SV47: $i,SV23: $i] :
( ( ( intruder_message @ ( encrypt @ SV23 @ SV47 ) )
= $true )
| ( ( ~ ( intruder_holds @ ( key @ SV47 @ SV63 ) )
| ~ ( intruder_message @ SV23 )
| ~ ( party_of_protocol @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[179]) ).
thf(203,plain,
! [SV71: $i,SV64: $i,SV48: $i,SV26: $i,SV2: $i] :
( ( ! [SY170: $i] :
( ( message @ ( sent @ a @ SV2 @ ( pair @ SV26 @ ( encrypt @ SV48 @ SV64 ) ) ) )
| ~ ( a_stored @ ( pair @ SV2 @ SV71 ) )
| ~ ( message @ ( sent @ t @ a @ ( triple @ ( encrypt @ ( quadruple @ SV2 @ SV71 @ SV64 @ SY170 ) @ at ) @ SV26 @ SV48 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(204,plain,
! [SV27: $i,SV3: $i] :
( ( ( fresh_to_b @ SV3 )
= $false )
| ( ( ~ ( message @ ( sent @ SV27 @ b @ ( pair @ SV27 @ SV3 ) ) ) )
= $true )
| ( ( message @ ( sent @ b @ t @ ( triple @ b @ ( generate_b_nonce @ SV3 ) @ ( encrypt @ ( triple @ SV27 @ SV3 @ ( generate_expiration_time @ SV3 ) ) @ bt ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(205,plain,
! [SV4: $i,SV28: $i] :
( ( ( fresh_to_b @ SV28 )
= $false )
| ( ( ~ ( message @ ( sent @ SV4 @ b @ ( pair @ SV4 @ SV28 ) ) ) )
= $true )
| ( ( b_stored @ ( pair @ SV4 @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(206,plain,
! [SV5: $i,SV49: $i,SV29: $i] :
( ( ( ~ ( b_stored @ ( pair @ SV29 @ SV49 ) ) )
= $true )
| ( ( ~ ( message @ ( sent @ SV29 @ b @ ( pair @ ( encrypt @ ( triple @ SV29 @ SV5 @ ( generate_expiration_time @ SV49 ) ) @ bt ) @ ( encrypt @ ( generate_b_nonce @ SV49 ) @ SV5 ) ) ) ) )
= $true )
| ( ( b_holds @ ( key @ SV5 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(207,plain,
! [SV72: $i,SV65: $i,SV50: $i,SV30: $i,SV6: $i] :
( ( ! [SY171: $i,SY172: $i] :
( ( message @ ( sent @ t @ SV6 @ ( triple @ ( encrypt @ ( quadruple @ SV30 @ SV50 @ ( generate_key @ SV50 ) @ SV65 ) @ SV72 ) @ ( encrypt @ ( triple @ SV6 @ ( generate_key @ SV50 ) @ SV65 ) @ SY171 ) @ SY172 ) ) )
| ~ ( a_nonce @ SV50 )
| ~ ( message @ ( sent @ SV30 @ t @ ( triple @ SV30 @ SY172 @ ( encrypt @ ( triple @ SV6 @ SV50 @ SV65 ) @ SY171 ) ) ) )
| ~ ( t_holds @ ( key @ SV72 @ SV6 ) )
| ~ ( t_holds @ ( key @ SY171 @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(208,plain,
! [SV7: $i,SV51: $i,SV31: $i] :
( ( ( message @ ( sent @ SV31 @ SV51 @ SV7 ) )
= $false )
| ( ( intruder_message @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(209,plain,
! [SV52: $i,SV34: $i,SV10: $i] :
( ( ( intruder_message @ ( triple @ SV10 @ SV34 @ SV52 ) )
= $false )
| ( ( intruder_message @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(210,plain,
! [SV53: $i,SV11: $i,SV35: $i] :
( ( ( intruder_message @ ( triple @ SV35 @ SV11 @ SV53 ) )
= $false )
| ( ( intruder_message @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(211,plain,
! [SV12: $i,SV54: $i,SV36: $i] :
( ( ( intruder_message @ ( triple @ SV36 @ SV54 @ SV12 ) )
= $false )
| ( ( intruder_message @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(212,plain,
! [SV66: $i,SV55: $i,SV37: $i,SV13: $i] :
( ( ( intruder_message @ SV13 )
= $true )
| ( ( ~ ( intruder_message @ ( quadruple @ SV13 @ SV37 @ SV55 @ SV66 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(213,plain,
! [SV67: $i,SV56: $i,SV38: $i,SV14: $i] :
( ( ( intruder_message @ SV14 )
= $true )
| ( ( ~ ( intruder_message @ ( quadruple @ SV38 @ SV14 @ SV56 @ SV67 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(214,plain,
! [SV68: $i,SV57: $i,SV39: $i,SV15: $i] :
( ( ( intruder_message @ SV15 )
= $true )
| ( ( ~ ( intruder_message @ ( quadruple @ SV39 @ SV57 @ SV15 @ SV68 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[194]) ).
thf(215,plain,
! [SV69: $i,SV58: $i,SV40: $i,SV16: $i] :
( ( ( intruder_message @ SV16 )
= $true )
| ( ( ~ ( intruder_message @ ( quadruple @ SV40 @ SV58 @ SV69 @ SV16 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(216,plain,
! [SV17: $i,SV41: $i] :
( ( ( intruder_message @ SV41 )
= $false )
| ( ( ~ ( intruder_message @ SV17 ) )
= $true )
| ( ( intruder_message @ ( pair @ SV17 @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(217,plain,
! [SV18: $i,SV42: $i,SV59: $i] :
( ( ( ~ ( intruder_message @ SV59 ) )
= $true )
| ( ( ~ ( intruder_message @ SV42 )
| ~ ( intruder_message @ SV18 ) )
= $true )
| ( ( intruder_message @ ( triple @ SV18 @ SV42 @ SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(218,plain,
! [SV70: $i,SV60: $i,SV43: $i,SV19: $i] :
( ( ( intruder_message @ ( quadruple @ SV19 @ SV43 @ SV60 @ SV70 ) )
= $true )
| ( ( ~ ( intruder_message @ SV70 )
| ~ ( intruder_message @ SV60 )
| ~ ( intruder_message @ SV43 )
| ~ ( intruder_message @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(219,plain,
! [SV61: $i,SV44: $i,SV20: $i] :
( ( ( ~ ( intruder_holds @ ( key @ SV20 @ SV44 ) ) )
= $true )
| ( ( ~ ( intruder_message @ ( encrypt @ SV61 @ SV20 ) )
| ~ ( party_of_protocol @ SV44 ) )
= $true )
| ( ( intruder_message @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[199]) ).
thf(220,plain,
! [SV21: $i,SV45: $i,SV62: $i] :
( ( ( ~ ( intruder_message @ SV62 ) )
= $true )
| ( ( ~ ( party_of_protocol @ SV45 )
| ~ ( party_of_protocol @ SV21 ) )
= $true )
| ( ( message @ ( sent @ SV21 @ SV45 @ SV62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[200]) ).
thf(221,plain,
! [SV46: $i,SV22: $i] :
( ( ( intruder_message @ SV22 )
= $false )
| ( ( ~ ( party_of_protocol @ SV46 ) )
= $true )
| ( ( intruder_holds @ ( key @ SV22 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(222,plain,
! [SV23: $i,SV63: $i,SV47: $i] :
( ( ( ~ ( intruder_holds @ ( key @ SV47 @ SV63 ) ) )
= $true )
| ( ( ~ ( intruder_message @ SV23 )
| ~ ( party_of_protocol @ SV63 ) )
= $true )
| ( ( intruder_message @ ( encrypt @ SV23 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(223,plain,
! [SV73: $i,SV71: $i,SV64: $i,SV48: $i,SV26: $i,SV2: $i] :
( ( ( message @ ( sent @ a @ SV2 @ ( pair @ SV26 @ ( encrypt @ SV48 @ SV64 ) ) ) )
| ~ ( a_stored @ ( pair @ SV2 @ SV71 ) )
| ~ ( message @ ( sent @ t @ a @ ( triple @ ( encrypt @ ( quadruple @ SV2 @ SV71 @ SV64 @ SV73 ) @ at ) @ SV26 @ SV48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(224,plain,
! [SV3: $i,SV27: $i] :
( ( ( message @ ( sent @ SV27 @ b @ ( pair @ SV27 @ SV3 ) ) )
= $false )
| ( ( fresh_to_b @ SV3 )
= $false )
| ( ( message @ ( sent @ b @ t @ ( triple @ b @ ( generate_b_nonce @ SV3 ) @ ( encrypt @ ( triple @ SV27 @ SV3 @ ( generate_expiration_time @ SV3 ) ) @ bt ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(225,plain,
! [SV28: $i,SV4: $i] :
( ( ( message @ ( sent @ SV4 @ b @ ( pair @ SV4 @ SV28 ) ) )
= $false )
| ( ( fresh_to_b @ SV28 )
= $false )
| ( ( b_stored @ ( pair @ SV4 @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(226,plain,
! [SV5: $i,SV49: $i,SV29: $i] :
( ( ( b_stored @ ( pair @ SV29 @ SV49 ) )
= $false )
| ( ( ~ ( message @ ( sent @ SV29 @ b @ ( pair @ ( encrypt @ ( triple @ SV29 @ SV5 @ ( generate_expiration_time @ SV49 ) ) @ bt ) @ ( encrypt @ ( generate_b_nonce @ SV49 ) @ SV5 ) ) ) ) )
= $true )
| ( ( b_holds @ ( key @ SV5 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(227,plain,
! [SV74: $i,SV72: $i,SV65: $i,SV50: $i,SV30: $i,SV6: $i] :
( ( ! [SY173: $i] :
( ( message @ ( sent @ t @ SV6 @ ( triple @ ( encrypt @ ( quadruple @ SV30 @ SV50 @ ( generate_key @ SV50 ) @ SV65 ) @ SV72 ) @ ( encrypt @ ( triple @ SV6 @ ( generate_key @ SV50 ) @ SV65 ) @ SV74 ) @ SY173 ) ) )
| ~ ( a_nonce @ SV50 )
| ~ ( message @ ( sent @ SV30 @ t @ ( triple @ SV30 @ SY173 @ ( encrypt @ ( triple @ SV6 @ SV50 @ SV65 ) @ SV74 ) ) ) )
| ~ ( t_holds @ ( key @ SV72 @ SV6 ) )
| ~ ( t_holds @ ( key @ SV74 @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(228,plain,
! [SV66: $i,SV55: $i,SV37: $i,SV13: $i] :
( ( ( intruder_message @ ( quadruple @ SV13 @ SV37 @ SV55 @ SV66 ) )
= $false )
| ( ( intruder_message @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(229,plain,
! [SV67: $i,SV56: $i,SV14: $i,SV38: $i] :
( ( ( intruder_message @ ( quadruple @ SV38 @ SV14 @ SV56 @ SV67 ) )
= $false )
| ( ( intruder_message @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(230,plain,
! [SV68: $i,SV15: $i,SV57: $i,SV39: $i] :
( ( ( intruder_message @ ( quadruple @ SV39 @ SV57 @ SV15 @ SV68 ) )
= $false )
| ( ( intruder_message @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(231,plain,
! [SV16: $i,SV69: $i,SV58: $i,SV40: $i] :
( ( ( intruder_message @ ( quadruple @ SV40 @ SV58 @ SV69 @ SV16 ) )
= $false )
| ( ( intruder_message @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(232,plain,
! [SV41: $i,SV17: $i] :
( ( ( intruder_message @ SV17 )
= $false )
| ( ( intruder_message @ SV41 )
= $false )
| ( ( intruder_message @ ( pair @ SV17 @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(233,plain,
! [SV18: $i,SV42: $i,SV59: $i] :
( ( ( intruder_message @ SV59 )
= $false )
| ( ( ~ ( intruder_message @ SV42 )
| ~ ( intruder_message @ SV18 ) )
= $true )
| ( ( intruder_message @ ( triple @ SV18 @ SV42 @ SV59 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(234,plain,
! [SV19: $i,SV43: $i,SV60: $i,SV70: $i] :
( ( ( ~ ( intruder_message @ SV70 ) )
= $true )
| ( ( ~ ( intruder_message @ SV60 )
| ~ ( intruder_message @ SV43 )
| ~ ( intruder_message @ SV19 ) )
= $true )
| ( ( intruder_message @ ( quadruple @ SV19 @ SV43 @ SV60 @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(235,plain,
! [SV61: $i,SV44: $i,SV20: $i] :
( ( ( intruder_holds @ ( key @ SV20 @ SV44 ) )
= $false )
| ( ( ~ ( intruder_message @ ( encrypt @ SV61 @ SV20 ) )
| ~ ( party_of_protocol @ SV44 ) )
= $true )
| ( ( intruder_message @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(236,plain,
! [SV21: $i,SV45: $i,SV62: $i] :
( ( ( intruder_message @ SV62 )
= $false )
| ( ( ~ ( party_of_protocol @ SV45 )
| ~ ( party_of_protocol @ SV21 ) )
= $true )
| ( ( message @ ( sent @ SV21 @ SV45 @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(237,plain,
! [SV22: $i,SV46: $i] :
( ( ( party_of_protocol @ SV46 )
= $false )
| ( ( intruder_message @ SV22 )
= $false )
| ( ( intruder_holds @ ( key @ SV22 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(238,plain,
! [SV23: $i,SV63: $i,SV47: $i] :
( ( ( intruder_holds @ ( key @ SV47 @ SV63 ) )
= $false )
| ( ( ~ ( intruder_message @ SV23 )
| ~ ( party_of_protocol @ SV63 ) )
= $true )
| ( ( intruder_message @ ( encrypt @ SV23 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(239,plain,
! [SV73: $i,SV71: $i,SV64: $i,SV48: $i,SV26: $i,SV2: $i] :
( ( ( message @ ( sent @ a @ SV2 @ ( pair @ SV26 @ ( encrypt @ SV48 @ SV64 ) ) ) )
= $true )
| ( ( ~ ( a_stored @ ( pair @ SV2 @ SV71 ) )
| ~ ( message @ ( sent @ t @ a @ ( triple @ ( encrypt @ ( quadruple @ SV2 @ SV71 @ SV64 @ SV73 ) @ at ) @ SV26 @ SV48 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(240,plain,
! [SV49: $i,SV5: $i,SV29: $i] :
( ( ( message @ ( sent @ SV29 @ b @ ( pair @ ( encrypt @ ( triple @ SV29 @ SV5 @ ( generate_expiration_time @ SV49 ) ) @ bt ) @ ( encrypt @ ( generate_b_nonce @ SV49 ) @ SV5 ) ) ) )
= $false )
| ( ( b_stored @ ( pair @ SV29 @ SV49 ) )
= $false )
| ( ( b_holds @ ( key @ SV5 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(241,plain,
! [SV75: $i,SV74: $i,SV72: $i,SV65: $i,SV50: $i,SV30: $i,SV6: $i] :
( ( ( message @ ( sent @ t @ SV6 @ ( triple @ ( encrypt @ ( quadruple @ SV30 @ SV50 @ ( generate_key @ SV50 ) @ SV65 ) @ SV72 ) @ ( encrypt @ ( triple @ SV6 @ ( generate_key @ SV50 ) @ SV65 ) @ SV74 ) @ SV75 ) ) )
| ~ ( a_nonce @ SV50 )
| ~ ( message @ ( sent @ SV30 @ t @ ( triple @ SV30 @ SV75 @ ( encrypt @ ( triple @ SV6 @ SV50 @ SV65 ) @ SV74 ) ) ) )
| ~ ( t_holds @ ( key @ SV72 @ SV6 ) )
| ~ ( t_holds @ ( key @ SV74 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(242,plain,
! [SV59: $i,SV18: $i,SV42: $i] :
( ( ( ~ ( intruder_message @ SV42 ) )
= $true )
| ( ( ~ ( intruder_message @ SV18 ) )
= $true )
| ( ( intruder_message @ SV59 )
= $false )
| ( ( intruder_message @ ( triple @ SV18 @ SV42 @ SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[233]) ).
thf(243,plain,
! [SV19: $i,SV43: $i,SV60: $i,SV70: $i] :
( ( ( intruder_message @ SV70 )
= $false )
| ( ( ~ ( intruder_message @ SV60 )
| ~ ( intruder_message @ SV43 )
| ~ ( intruder_message @ SV19 ) )
= $true )
| ( ( intruder_message @ ( quadruple @ SV19 @ SV43 @ SV60 @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(244,plain,
! [SV44: $i,SV20: $i,SV61: $i] :
( ( ( ~ ( intruder_message @ ( encrypt @ SV61 @ SV20 ) ) )
= $true )
| ( ( ~ ( party_of_protocol @ SV44 ) )
= $true )
| ( ( intruder_holds @ ( key @ SV20 @ SV44 ) )
= $false )
| ( ( intruder_message @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[235]) ).
thf(245,plain,
! [SV62: $i,SV21: $i,SV45: $i] :
( ( ( ~ ( party_of_protocol @ SV45 ) )
= $true )
| ( ( ~ ( party_of_protocol @ SV21 ) )
= $true )
| ( ( intruder_message @ SV62 )
= $false )
| ( ( message @ ( sent @ SV21 @ SV45 @ SV62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(246,plain,
! [SV47: $i,SV63: $i,SV23: $i] :
( ( ( ~ ( intruder_message @ SV23 ) )
= $true )
| ( ( ~ ( party_of_protocol @ SV63 ) )
= $true )
| ( ( intruder_holds @ ( key @ SV47 @ SV63 ) )
= $false )
| ( ( intruder_message @ ( encrypt @ SV23 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[238]) ).
thf(247,plain,
! [SV48: $i,SV26: $i,SV73: $i,SV64: $i,SV71: $i,SV2: $i] :
( ( ( ~ ( a_stored @ ( pair @ SV2 @ SV71 ) ) )
= $true )
| ( ( ~ ( message @ ( sent @ t @ a @ ( triple @ ( encrypt @ ( quadruple @ SV2 @ SV71 @ SV64 @ SV73 ) @ at ) @ SV26 @ SV48 ) ) ) )
= $true )
| ( ( message @ ( sent @ a @ SV2 @ ( pair @ SV26 @ ( encrypt @ SV48 @ SV64 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(248,plain,
! [SV75: $i,SV74: $i,SV72: $i,SV65: $i,SV50: $i,SV30: $i,SV6: $i] :
( ( ( message @ ( sent @ t @ SV6 @ ( triple @ ( encrypt @ ( quadruple @ SV30 @ SV50 @ ( generate_key @ SV50 ) @ SV65 ) @ SV72 ) @ ( encrypt @ ( triple @ SV6 @ ( generate_key @ SV50 ) @ SV65 ) @ SV74 ) @ SV75 ) ) )
= $true )
| ( ( ~ ( a_nonce @ SV50 )
| ~ ( message @ ( sent @ SV30 @ t @ ( triple @ SV30 @ SV75 @ ( encrypt @ ( triple @ SV6 @ SV50 @ SV65 ) @ SV74 ) ) ) )
| ~ ( t_holds @ ( key @ SV72 @ SV6 ) )
| ~ ( t_holds @ ( key @ SV74 @ SV30 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[241]) ).
thf(249,plain,
! [SV59: $i,SV18: $i,SV42: $i] :
( ( ( intruder_message @ SV42 )
= $false )
| ( ( ~ ( intruder_message @ SV18 ) )
= $true )
| ( ( intruder_message @ SV59 )
= $false )
| ( ( intruder_message @ ( triple @ SV18 @ SV42 @ SV59 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(250,plain,
! [SV70: $i,SV19: $i,SV43: $i,SV60: $i] :
( ( ( ~ ( intruder_message @ SV60 ) )
= $true )
| ( ( ~ ( intruder_message @ SV43 )
| ~ ( intruder_message @ SV19 ) )
= $true )
| ( ( intruder_message @ SV70 )
= $false )
| ( ( intruder_message @ ( quadruple @ SV19 @ SV43 @ SV60 @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[243]) ).
thf(251,plain,
! [SV44: $i,SV20: $i,SV61: $i] :
( ( ( intruder_message @ ( encrypt @ SV61 @ SV20 ) )
= $false )
| ( ( ~ ( party_of_protocol @ SV44 ) )
= $true )
| ( ( intruder_holds @ ( key @ SV20 @ SV44 ) )
= $false )
| ( ( intruder_message @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(252,plain,
! [SV62: $i,SV21: $i,SV45: $i] :
( ( ( party_of_protocol @ SV45 )
= $false )
| ( ( ~ ( party_of_protocol @ SV21 ) )
= $true )
| ( ( intruder_message @ SV62 )
= $false )
| ( ( message @ ( sent @ SV21 @ SV45 @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(253,plain,
! [SV47: $i,SV63: $i,SV23: $i] :
( ( ( intruder_message @ SV23 )
= $false )
| ( ( ~ ( party_of_protocol @ SV63 ) )
= $true )
| ( ( intruder_holds @ ( key @ SV47 @ SV63 ) )
= $false )
| ( ( intruder_message @ ( encrypt @ SV23 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(254,plain,
! [SV48: $i,SV26: $i,SV73: $i,SV64: $i,SV71: $i,SV2: $i] :
( ( ( a_stored @ ( pair @ SV2 @ SV71 ) )
= $false )
| ( ( ~ ( message @ ( sent @ t @ a @ ( triple @ ( encrypt @ ( quadruple @ SV2 @ SV71 @ SV64 @ SV73 ) @ at ) @ SV26 @ SV48 ) ) ) )
= $true )
| ( ( message @ ( sent @ a @ SV2 @ ( pair @ SV26 @ ( encrypt @ SV48 @ SV64 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(255,plain,
! [SV72: $i,SV74: $i,SV65: $i,SV6: $i,SV75: $i,SV30: $i,SV50: $i] :
( ( ( ~ ( a_nonce @ SV50 ) )
= $true )
| ( ( ~ ( message @ ( sent @ SV30 @ t @ ( triple @ SV30 @ SV75 @ ( encrypt @ ( triple @ SV6 @ SV50 @ SV65 ) @ SV74 ) ) ) )
| ~ ( t_holds @ ( key @ SV72 @ SV6 ) )
| ~ ( t_holds @ ( key @ SV74 @ SV30 ) ) )
= $true )
| ( ( message @ ( sent @ t @ SV6 @ ( triple @ ( encrypt @ ( quadruple @ SV30 @ SV50 @ ( generate_key @ SV50 ) @ SV65 ) @ SV72 ) @ ( encrypt @ ( triple @ SV6 @ ( generate_key @ SV50 ) @ SV65 ) @ SV74 ) @ SV75 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[248]) ).
thf(256,plain,
! [SV59: $i,SV42: $i,SV18: $i] :
( ( ( intruder_message @ SV18 )
= $false )
| ( ( intruder_message @ SV42 )
= $false )
| ( ( intruder_message @ SV59 )
= $false )
| ( ( intruder_message @ ( triple @ SV18 @ SV42 @ SV59 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(257,plain,
! [SV70: $i,SV19: $i,SV43: $i,SV60: $i] :
( ( ( intruder_message @ SV60 )
= $false )
| ( ( ~ ( intruder_message @ SV43 )
| ~ ( intruder_message @ SV19 ) )
= $true )
| ( ( intruder_message @ SV70 )
= $false )
| ( ( intruder_message @ ( quadruple @ SV19 @ SV43 @ SV60 @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(258,plain,
! [SV20: $i,SV61: $i,SV44: $i] :
( ( ( party_of_protocol @ SV44 )
= $false )
| ( ( intruder_message @ ( encrypt @ SV61 @ SV20 ) )
= $false )
| ( ( intruder_holds @ ( key @ SV20 @ SV44 ) )
= $false )
| ( ( intruder_message @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(259,plain,
! [SV62: $i,SV45: $i,SV21: $i] :
( ( ( party_of_protocol @ SV21 )
= $false )
| ( ( party_of_protocol @ SV45 )
= $false )
| ( ( intruder_message @ SV62 )
= $false )
| ( ( message @ ( sent @ SV21 @ SV45 @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(260,plain,
! [SV47: $i,SV23: $i,SV63: $i] :
( ( ( party_of_protocol @ SV63 )
= $false )
| ( ( intruder_message @ SV23 )
= $false )
| ( ( intruder_holds @ ( key @ SV47 @ SV63 ) )
= $false )
| ( ( intruder_message @ ( encrypt @ SV23 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(261,plain,
! [SV48: $i,SV26: $i,SV73: $i,SV64: $i,SV71: $i,SV2: $i] :
( ( ( message @ ( sent @ t @ a @ ( triple @ ( encrypt @ ( quadruple @ SV2 @ SV71 @ SV64 @ SV73 ) @ at ) @ SV26 @ SV48 ) ) )
= $false )
| ( ( a_stored @ ( pair @ SV2 @ SV71 ) )
= $false )
| ( ( message @ ( sent @ a @ SV2 @ ( pair @ SV26 @ ( encrypt @ SV48 @ SV64 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(262,plain,
! [SV72: $i,SV74: $i,SV65: $i,SV6: $i,SV75: $i,SV30: $i,SV50: $i] :
( ( ( a_nonce @ SV50 )
= $false )
| ( ( ~ ( message @ ( sent @ SV30 @ t @ ( triple @ SV30 @ SV75 @ ( encrypt @ ( triple @ SV6 @ SV50 @ SV65 ) @ SV74 ) ) ) )
| ~ ( t_holds @ ( key @ SV72 @ SV6 ) )
| ~ ( t_holds @ ( key @ SV74 @ SV30 ) ) )
= $true )
| ( ( message @ ( sent @ t @ SV6 @ ( triple @ ( encrypt @ ( quadruple @ SV30 @ SV50 @ ( generate_key @ SV50 ) @ SV65 ) @ SV72 ) @ ( encrypt @ ( triple @ SV6 @ ( generate_key @ SV50 ) @ SV65 ) @ SV74 ) @ SV75 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(263,plain,
! [SV70: $i,SV60: $i,SV19: $i,SV43: $i] :
( ( ( ~ ( intruder_message @ SV43 ) )
= $true )
| ( ( ~ ( intruder_message @ SV19 ) )
= $true )
| ( ( intruder_message @ SV60 )
= $false )
| ( ( intruder_message @ SV70 )
= $false )
| ( ( intruder_message @ ( quadruple @ SV19 @ SV43 @ SV60 @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[257]) ).
thf(264,plain,
! [SV72: $i,SV74: $i,SV65: $i,SV50: $i,SV6: $i,SV75: $i,SV30: $i] :
( ( ( ~ ( message @ ( sent @ SV30 @ t @ ( triple @ SV30 @ SV75 @ ( encrypt @ ( triple @ SV6 @ SV50 @ SV65 ) @ SV74 ) ) ) ) )
= $true )
| ( ( ~ ( t_holds @ ( key @ SV72 @ SV6 ) )
| ~ ( t_holds @ ( key @ SV74 @ SV30 ) ) )
= $true )
| ( ( a_nonce @ SV50 )
= $false )
| ( ( message @ ( sent @ t @ SV6 @ ( triple @ ( encrypt @ ( quadruple @ SV30 @ SV50 @ ( generate_key @ SV50 ) @ SV65 ) @ SV72 ) @ ( encrypt @ ( triple @ SV6 @ ( generate_key @ SV50 ) @ SV65 ) @ SV74 ) @ SV75 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[262]) ).
thf(265,plain,
! [SV70: $i,SV60: $i,SV19: $i,SV43: $i] :
( ( ( intruder_message @ SV43 )
= $false )
| ( ( ~ ( intruder_message @ SV19 ) )
= $true )
| ( ( intruder_message @ SV60 )
= $false )
| ( ( intruder_message @ SV70 )
= $false )
| ( ( intruder_message @ ( quadruple @ SV19 @ SV43 @ SV60 @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(266,plain,
! [SV72: $i,SV74: $i,SV65: $i,SV50: $i,SV6: $i,SV75: $i,SV30: $i] :
( ( ( message @ ( sent @ SV30 @ t @ ( triple @ SV30 @ SV75 @ ( encrypt @ ( triple @ SV6 @ SV50 @ SV65 ) @ SV74 ) ) ) )
= $false )
| ( ( ~ ( t_holds @ ( key @ SV72 @ SV6 ) )
| ~ ( t_holds @ ( key @ SV74 @ SV30 ) ) )
= $true )
| ( ( a_nonce @ SV50 )
= $false )
| ( ( message @ ( sent @ t @ SV6 @ ( triple @ ( encrypt @ ( quadruple @ SV30 @ SV50 @ ( generate_key @ SV50 ) @ SV65 ) @ SV72 ) @ ( encrypt @ ( triple @ SV6 @ ( generate_key @ SV50 ) @ SV65 ) @ SV74 ) @ SV75 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(267,plain,
! [SV70: $i,SV60: $i,SV43: $i,SV19: $i] :
( ( ( intruder_message @ SV19 )
= $false )
| ( ( intruder_message @ SV43 )
= $false )
| ( ( intruder_message @ SV60 )
= $false )
| ( ( intruder_message @ SV70 )
= $false )
| ( ( intruder_message @ ( quadruple @ SV19 @ SV43 @ SV60 @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(268,plain,
! [SV65: $i,SV50: $i,SV75: $i,SV30: $i,SV74: $i,SV6: $i,SV72: $i] :
( ( ( ~ ( t_holds @ ( key @ SV72 @ SV6 ) ) )
= $true )
| ( ( ~ ( t_holds @ ( key @ SV74 @ SV30 ) ) )
= $true )
| ( ( message @ ( sent @ SV30 @ t @ ( triple @ SV30 @ SV75 @ ( encrypt @ ( triple @ SV6 @ SV50 @ SV65 ) @ SV74 ) ) ) )
= $false )
| ( ( a_nonce @ SV50 )
= $false )
| ( ( message @ ( sent @ t @ SV6 @ ( triple @ ( encrypt @ ( quadruple @ SV30 @ SV50 @ ( generate_key @ SV50 ) @ SV65 ) @ SV72 ) @ ( encrypt @ ( triple @ SV6 @ ( generate_key @ SV50 ) @ SV65 ) @ SV74 ) @ SV75 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(269,plain,
! [SV65: $i,SV50: $i,SV75: $i,SV30: $i,SV74: $i,SV6: $i,SV72: $i] :
( ( ( t_holds @ ( key @ SV72 @ SV6 ) )
= $false )
| ( ( ~ ( t_holds @ ( key @ SV74 @ SV30 ) ) )
= $true )
| ( ( message @ ( sent @ SV30 @ t @ ( triple @ SV30 @ SV75 @ ( encrypt @ ( triple @ SV6 @ SV50 @ SV65 ) @ SV74 ) ) ) )
= $false )
| ( ( a_nonce @ SV50 )
= $false )
| ( ( message @ ( sent @ t @ SV6 @ ( triple @ ( encrypt @ ( quadruple @ SV30 @ SV50 @ ( generate_key @ SV50 ) @ SV65 ) @ SV72 ) @ ( encrypt @ ( triple @ SV6 @ ( generate_key @ SV50 ) @ SV65 ) @ SV74 ) @ SV75 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(270,plain,
! [SV65: $i,SV50: $i,SV75: $i,SV6: $i,SV72: $i,SV30: $i,SV74: $i] :
( ( ( t_holds @ ( key @ SV74 @ SV30 ) )
= $false )
| ( ( t_holds @ ( key @ SV72 @ SV6 ) )
= $false )
| ( ( message @ ( sent @ SV30 @ t @ ( triple @ SV30 @ SV75 @ ( encrypt @ ( triple @ SV6 @ SV50 @ SV65 ) @ SV74 ) ) ) )
= $false )
| ( ( a_nonce @ SV50 )
= $false )
| ( ( message @ ( sent @ t @ SV6 @ ( triple @ ( encrypt @ ( quadruple @ SV30 @ SV50 @ ( generate_key @ SV50 ) @ SV65 ) @ SV72 ) @ ( encrypt @ ( triple @ SV6 @ ( generate_key @ SV50 ) @ SV65 ) @ SV74 ) @ SV75 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(271,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[74,270,267,261,260,259,258,256,240,237,232,231,230,229,228,225,224,211,210,209,208,188,187,180,133,132,131,104,85,84,83,79,78,76,75]) ).
thf(272,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[271]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV014-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.19 % Computer : n017.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 16:12:24 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.54/0.33
% 0.54/0.33 No.of.Axioms: 34
% 0.54/0.33
% 0.54/0.33 Length.of.Defs: 0
% 0.54/0.33
% 0.54/0.33 Contains.Choice.Funs: false
% 0.54/0.33 .......
% 0.54/0.33
% 0.54/0.33 ********************************
% 0.54/0.33 * All subproblems solved! *
% 0.54/0.33 ********************************
% 0.54/0.33 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:34,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:271,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.54/0.33
% 0.54/0.33 %**** Beginning of derivation protocol ****
% 0.54/0.33 % SZS output start CNFRefutation
% See solution above
% 0.54/0.34
% 0.54/0.34 %**** End of derivation protocol ****
% 0.54/0.34 %**** no. of clauses in derivation: 272 ****
% 0.54/0.34 %**** clause counter: 271 ****
% 0.54/0.34
% 0.54/0.34 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:34,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:271,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------