TSTP Solution File: SWV815_5 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWV815_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% 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 May 19 12:18:42 EDT 2023
% Result : Theorem 58.48s 22.07s
% Output : Refutation 58.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 165
% Syntax : Number of formulae : 284 ( 96 unt; 48 typ; 0 def)
% Number of atoms : 620 ( 187 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 4029 ( 159 ~; 25 |; 47 &;3532 @)
% ( 18 <=>; 248 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 9 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 48 ( 45 usr; 25 con; 0-5 aty)
% Number of variables : 732 ( 0 ^; 714 !; 4 ?; 732 :)
% ( 14 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(event_type,type,
event: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(agent1_type,type,
agent1: $tType ).
thf(msg_type,type,
msg: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(combb_type,type,
combb:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ TB ) > ( fun @ TA @ TC ) > ( fun @ TA @ TB ) ) ).
thf(combc_type,type,
combc:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > TB > ( fun @ TC @ TA ) ) ).
thf(bad_type,type,
bad: fun @ agent1 @ bool ).
thf(notes_type,type,
notes: agent1 > msg > event ).
thf(says_type,type,
says: agent1 > agent1 > msg > event ).
thf(knows_type,type,
knows: agent1 > ( list @ event ) > ( fun @ msg @ bool ) ).
thf(cons_type,type,
cons:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(rev_type,type,
rev:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) ) ).
thf(set_type,type,
set:
!>[TA: $tType] : ( ( list @ TA ) > ( fun @ TA @ bool ) ) ).
thf(takeWhile_type,type,
takeWhile:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( list @ TA ) > ( list @ TA ) ) ).
thf(server_type,type,
server: agent1 ).
thf(spy_type,type,
spy: agent1 ).
thf(analz_type,type,
analz: ( fun @ msg @ bool ) > ( fun @ msg @ bool ) ).
thf(agent_type,type,
agent: agent1 > msg ).
thf(crypt_type,type,
crypt: nat > msg > msg ).
thf(key_type,type,
key: nat > msg ).
thf(mPair_type,type,
mPair: msg > msg > msg ).
thf(nonce_type,type,
nonce: nat > msg ).
thf(parts_type,type,
parts: ( fun @ msg @ bool ) > ( fun @ msg @ bool ) ).
thf(symKeys_type,type,
symKeys: fun @ nat @ bool ).
thf(nS_Sha512322870Issues_type,type,
nS_Sha512322870Issues: agent1 > agent1 > msg > ( list @ event ) > $o ).
thf(nS_Sha254967238shared_type,type,
nS_Sha254967238shared: fun @ ( list @ event ) @ bool ).
thf(shrK_type,type,
shrK: agent1 > nat ).
thf(aa1_type,type,
aa1:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).
thf(fFalse_type,type,
fFalse: bool ).
thf(fNot_type,type,
fNot: fun @ bool @ bool ).
thf(fTrue_type,type,
fTrue: bool ).
thf(fequal_type,type,
fequal:
!>[TA: $tType] : ( fun @ TA @ ( fun @ TA @ bool ) ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( fun @ TA @ bool ) > $o ) ).
thf(pp_type,type,
pp: bool > $o ).
thf(a_type,type,
a: agent1 ).
thf(aa_type,type,
aa: agent1 ).
thf(b_type,type,
b: agent1 ).
thf(b1_type,type,
b1: agent1 ).
thf(ba_type,type,
ba: agent1 ).
thf(k_type,type,
k: nat ).
thf(ka_type,type,
ka: nat ).
thf(na_type,type,
na: nat ).
thf(nb_type,type,
nb: nat ).
thf(nBa_type,type,
nBa: nat ).
thf(s_type,type,
s: agent1 ).
thf(x_type,type,
x: msg ).
thf(evs5_type,type,
evs5: list @ event ).
thf(58,axiom,
! [A: msg,B: agent1,C: msg,D: agent1,E: list @ event,F: nat,G: nat] :
( ( member @ msg @ ( crypt @ G @ ( nonce @ F ) ) @ ( parts @ ( knows @ spy @ E ) ) )
=> ( ( member @ msg @ ( crypt @ ( shrK @ D ) @ ( mPair @ C @ ( mPair @ ( agent @ B ) @ ( mPair @ ( key @ G ) @ A ) ) ) ) @ ( parts @ ( knows @ spy @ E ) ) )
=> ( ! [H: msg] :
~ ( member @ event @ ( notes @ spy @ ( mPair @ C @ ( mPair @ H @ ( key @ G ) ) ) ) @ ( set @ event @ E ) )
=> ( ~ ( member @ agent1 @ D @ bad )
=> ( ~ ( member @ agent1 @ B @ bad )
=> ( ( member @ ( list @ event ) @ E @ nS_Sha254967238shared )
=> ( member @ event @ ( says @ B @ D @ ( crypt @ G @ ( nonce @ F ) ) ) @ ( set @ event @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_A__trusts__NS4) ).
thf(333,plain,
! [A: msg,B: agent1,C: msg,D: agent1,E: list @ event,F: nat,G: nat] :
( ( member @ msg @ ( crypt @ G @ ( nonce @ F ) ) @ ( parts @ ( knows @ spy @ E ) ) )
=> ( ( member @ msg @ ( crypt @ ( shrK @ D ) @ ( mPair @ C @ ( mPair @ ( agent @ B ) @ ( mPair @ ( key @ G ) @ A ) ) ) ) @ ( parts @ ( knows @ spy @ E ) ) )
=> ( ! [H: msg] :
~ ( member @ event @ ( notes @ spy @ ( mPair @ C @ ( mPair @ H @ ( key @ G ) ) ) ) @ ( set @ event @ E ) )
=> ( ~ ( member @ agent1 @ D @ bad )
=> ( ~ ( member @ agent1 @ B @ bad )
=> ( ( member @ ( list @ event ) @ E @ nS_Sha254967238shared )
=> ( member @ event @ ( says @ B @ D @ ( crypt @ G @ ( nonce @ F ) ) ) @ ( set @ event @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(62,axiom,
~ ( member @ msg @ ( key @ k ) @ ( analz @ ( knows @ spy @ evs5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_6) ).
thf(344,plain,
~ ( member @ msg @ ( key @ k ) @ ( analz @ ( knows @ spy @ evs5 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(3,axiom,
! [A: fun @ msg @ bool] :
( ( analz @ ( analz @ A ) )
= ( analz @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_analz__idem) ).
thf(129,plain,
! [A: fun @ msg @ bool] :
( ( analz @ ( analz @ A ) )
= ( analz @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(106,axiom,
member @ ( list @ event ) @ evs5 @ nS_Sha254967238shared,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
thf(477,plain,
member @ ( list @ event ) @ evs5 @ nS_Sha254967238shared,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(82,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( rev @ TA @ B )
= ( rev @ TA @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_rev__is__rev__conv) ).
thf(409,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( ( rev @ TA @ B )
= ( rev @ TA @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( rev @ TA @ B )
= ( rev @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(116,axiom,
! [A: msg,B: agent1,C: agent1,D: msg,E: agent1,F: agent1] :
( ( ( says @ F @ E @ D )
= ( says @ C @ B @ A ) )
<=> ( ( F = C )
& ( E = B )
& ( D = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_event_Osimps_I1_J) ).
thf(517,plain,
! [A: msg,B: agent1,C: agent1,D: msg,E: agent1,F: agent1] :
( ( ( ( says @ F @ E @ D )
= ( says @ C @ B @ A ) )
=> ( ( F = C )
& ( E = B )
& ( D = A ) ) )
& ( ( ( F = C )
& ( E = B )
& ( D = A ) )
=> ( ( says @ F @ E @ D )
= ( says @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(33,axiom,
member @ nat @ ka @ symKeys,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
thf(247,plain,
member @ nat @ ka @ symKeys,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(93,axiom,
spy != server,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_agent_Osimps_I5_J) ).
thf(440,plain,
spy != server,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(75,axiom,
! [A: fun @ msg @ bool,B: msg] :
( ( ( member @ msg @ B @ ( analz @ A ) )
& ( member @ msg @ B @ ( parts @ A ) ) )
<=> ( member @ msg @ B @ ( analz @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_analz__conj__parts) ).
thf(385,plain,
! [A: fun @ msg @ bool,B: msg] :
( ( ( ( member @ msg @ B @ ( analz @ A ) )
& ( member @ msg @ B @ ( parts @ A ) ) )
=> ( member @ msg @ B @ ( analz @ A ) ) )
& ( ( member @ msg @ B @ ( analz @ A ) )
=> ( ( member @ msg @ B @ ( analz @ A ) )
& ( member @ msg @ B @ ( parts @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(118,axiom,
! [A: msg,B: msg,C: nat] :
( ( key @ C )
!= ( mPair @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_msg_Osimps_I40_J) ).
thf(533,plain,
! [A: msg,B: msg,C: nat] :
( ( key @ C )
!= ( mPair @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(84,axiom,
! [A: fun @ msg @ bool,B: msg] :
( ( member @ msg @ B @ A )
=> ( member @ msg @ B @ ( parts @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_parts_OInj) ).
thf(417,plain,
! [A: fun @ msg @ bool,B: msg] :
( ( member @ msg @ B @ A )
=> ( member @ msg @ B @ ( parts @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(37,axiom,
! [A: list @ event,B: msg,C: agent1] :
( ( member @ event @ ( notes @ C @ B ) @ ( set @ event @ A ) )
=> ( member @ msg @ B @ ( knows @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_Notes__imp__knows) ).
thf(257,plain,
! [A: list @ event,B: msg,C: agent1] :
( ( member @ event @ ( notes @ C @ B ) @ ( set @ event @ A ) )
=> ( member @ msg @ B @ ( knows @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(14,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_not__Cons__self2) ).
thf(189,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(86,axiom,
! [A: list @ event] :
( ( knows @ spy @ A )
= ( knows @ spy @ ( rev @ event @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_spies__evs__rev) ).
thf(421,plain,
! [A: list @ event] :
( ( knows @ spy @ A )
= ( knows @ spy @ ( rev @ event @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(55,axiom,
! [A: agent1,B: msg,C: msg] :
( ( mPair @ C @ B )
!= ( agent @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_msg_Osimps_I17_J) ).
thf(325,plain,
! [A: agent1,B: msg,C: msg] :
( ( mPair @ C @ B )
!= ( agent @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(39,axiom,
! [A: fun @ msg @ bool,B: msg,C: msg] :
( ( member @ msg @ ( mPair @ C @ B ) @ ( parts @ A ) )
=> ( member @ msg @ B @ ( parts @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_parts_OSnd) ).
thf(261,plain,
! [A: fun @ msg @ bool,B: msg,C: msg] :
( ( member @ msg @ ( mPair @ C @ B ) @ ( parts @ A ) )
=> ( member @ msg @ B @ ( parts @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(105,axiom,
! [A: list @ event,B: agent1,C: nat,D: agent1] :
( ( member @ msg @ ( crypt @ ( shrK @ D ) @ ( mPair @ ( key @ C ) @ ( agent @ B ) ) ) @ ( parts @ ( knows @ spy @ A ) ) )
=> ( ~ ( member @ agent1 @ D @ bad )
=> ( ( member @ ( list @ event ) @ A @ nS_Sha254967238shared )
=> ? [E: msg] : ( member @ event @ ( says @ server @ B @ ( crypt @ ( shrK @ B ) @ ( mPair @ E @ ( mPair @ ( agent @ D ) @ ( mPair @ ( key @ C ) @ ( crypt @ ( shrK @ D ) @ ( mPair @ ( key @ C ) @ ( agent @ B ) ) ) ) ) ) ) ) @ ( set @ event @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_B__trusts__NS3) ).
thf(475,plain,
! [A: list @ event,B: agent1,C: nat,D: agent1] :
( ( member @ msg @ ( crypt @ ( shrK @ D ) @ ( mPair @ ( key @ C ) @ ( agent @ B ) ) ) @ ( parts @ ( knows @ spy @ A ) ) )
=> ( ~ ( member @ agent1 @ D @ bad )
=> ( ( member @ ( list @ event ) @ A @ nS_Sha254967238shared )
=> ? [E: msg] : ( member @ event @ ( says @ server @ B @ ( crypt @ ( shrK @ B ) @ ( mPair @ E @ ( mPair @ ( agent @ D ) @ ( mPair @ ( key @ C ) @ ( crypt @ ( shrK @ D ) @ ( mPair @ ( key @ C ) @ ( agent @ B ) ) ) ) ) ) ) ) @ ( set @ event @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(9,axiom,
! [A: nat,B: agent1] :
( ( agent @ B )
!= ( key @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_msg_Osimps_I12_J) ).
thf(164,plain,
! [A: nat,B: agent1] :
( ( agent @ B )
!= ( key @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(12,axiom,
! [A: agent1,B: agent1] :
( ( ( shrK @ B )
= ( shrK @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_shrK__injective) ).
thf(179,plain,
! [A: agent1,B: agent1] :
( ( ( ( shrK @ B )
= ( shrK @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( shrK @ B )
= ( shrK @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(94,axiom,
! [TA: $tType,A: list @ TA,B: fun @ TA @ bool] :
( ( ( takeWhile @ TA @ B @ A )
= A )
<=> ! [C: TA] :
( ( member @ TA @ C @ ( set @ TA @ A ) )
=> ( pp @ ( aa1 @ TA @ bool @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_takeWhile__eq__all__conv) ).
thf(443,plain,
! [TA: $tType,A: list @ TA,B: fun @ TA @ bool] :
( ( ( ( takeWhile @ TA @ B @ A )
= A )
=> ! [C: TA] :
( ( member @ TA @ C @ ( set @ TA @ A ) )
=> ( pp @ ( aa1 @ TA @ bool @ B @ C ) ) ) )
& ( ! [C: TA] :
( ( member @ TA @ C @ ( set @ TA @ A ) )
=> ( pp @ ( aa1 @ TA @ bool @ B @ C ) ) )
=> ( ( takeWhile @ TA @ B @ A )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(53,axiom,
! [A: fun @ msg @ bool] :
( ( analz @ ( parts @ A ) )
= ( parts @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_analz__parts) ).
thf(321,plain,
! [A: fun @ msg @ bool] :
( ( analz @ ( parts @ A ) )
= ( parts @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(71,axiom,
! [A: agent1] : ( member @ nat @ ( shrK @ A ) @ symKeys ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_sym__shrK) ).
thf(376,plain,
! [A: agent1] : ( member @ nat @ ( shrK @ A ) @ symKeys ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(36,axiom,
! [A: nat,B: agent1] :
( ( agent @ B )
!= ( nonce @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_msg_Osimps_I10_J) ).
thf(253,plain,
! [A: nat,B: agent1] :
( ( agent @ B )
!= ( nonce @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(108,axiom,
! [TA: $tType,A: list @ TA,B: fun @ TA @ bool,C: TA] :
( ( member @ TA @ C @ ( set @ TA @ ( takeWhile @ TA @ B @ A ) ) )
=> ( ( member @ TA @ C @ ( set @ TA @ A ) )
& ( pp @ ( aa1 @ TA @ bool @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_set__takeWhileD) ).
thf(485,plain,
! [TA: $tType,A: list @ TA,B: fun @ TA @ bool,C: TA] :
( ( member @ TA @ C @ ( set @ TA @ ( takeWhile @ TA @ B @ A ) ) )
=> ( ( member @ TA @ C @ ( set @ TA @ A ) )
& ( pp @ ( aa1 @ TA @ bool @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(30,axiom,
! [A: list @ event,B: msg,C: agent1,D: agent1] :
( ( member @ event @ ( says @ D @ C @ B ) @ ( set @ event @ A ) )
=> ( member @ msg @ B @ ( analz @ ( knows @ spy @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_Says__imp__analz__Spy) ).
thf(238,plain,
! [A: list @ event,B: msg,C: agent1,D: agent1] :
( ( member @ event @ ( says @ D @ C @ B ) @ ( set @ event @ A ) )
=> ( member @ msg @ B @ ( analz @ ( knows @ spy @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(64,axiom,
! [A: fun @ msg @ bool,B: msg] :
( ~ ( member @ msg @ B @ ( parts @ A ) )
=> ~ ( member @ msg @ B @ ( analz @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_not__parts__not__analz) ).
thf(348,plain,
! [A: fun @ msg @ bool,B: msg] :
( ~ ( member @ msg @ B @ ( parts @ A ) )
=> ~ ( member @ msg @ B @ ( analz @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(66,axiom,
! [A: bool] :
( ( pp @ A )
| ( pp @ ( aa1 @ bool @ bool @ fNot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
thf(353,plain,
! [A: bool] :
( ( pp @ A )
| ( pp @ ( aa1 @ bool @ bool @ fNot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(45,axiom,
! [TA: $tType,A: list @ TA] :
( ( set @ TA @ ( rev @ TA @ A ) )
= ( set @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_set__rev) ).
thf(280,plain,
! [TA: $tType,A: list @ TA] :
( ( set @ TA @ ( rev @ TA @ A ) )
= ( set @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(4,axiom,
! [A: agent1,B: nat] :
( ( key @ B )
!= ( agent @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_msg_Osimps_I13_J) ).
thf(132,plain,
! [A: agent1,B: nat] :
( ( key @ B )
!= ( agent @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(48,axiom,
! [A: nat,B: nat] :
( ( nonce @ B )
!= ( key @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_msg_Osimps_I30_J) ).
thf(292,plain,
! [A: nat,B: nat] :
( ( nonce @ B )
!= ( key @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(34,axiom,
! [A: nat,B: msg,C: msg] :
( ( mPair @ C @ B )
!= ( nonce @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_msg_Osimps_I35_J) ).
thf(248,plain,
! [A: nat,B: msg,C: msg] :
( ( mPair @ C @ B )
!= ( nonce @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(42,axiom,
! [TA: $tType,A: TA,B: TA] :
( ~ ( pp @ ( aa1 @ TA @ bool @ ( aa1 @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
thf(270,plain,
! [TA: $tType,A: TA,B: TA] :
( ~ ( pp @ ( aa1 @ TA @ bool @ ( aa1 @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(73,axiom,
! [A: nat,B: msg,C: agent1,D: msg,E: agent1,F: nat,G: list @ event] :
( ( member @ ( list @ event ) @ G @ nS_Sha254967238shared )
=> ( ~ ( member @ msg @ ( key @ F ) @ ( analz @ ( knows @ spy @ G ) ) )
=> ( ( member @ event @ ( says @ server @ E @ ( crypt @ ( shrK @ E ) @ ( mPair @ D @ ( mPair @ ( agent @ C ) @ ( mPair @ ( key @ F ) @ B ) ) ) ) ) @ ( set @ event @ G ) )
=> ( ( member @ msg @ ( crypt @ F @ ( nonce @ A ) ) @ ( parts @ ( knows @ spy @ G ) ) )
=> ? [H: agent1] : ( member @ event @ ( says @ H @ C @ B ) @ ( set @ event @ G ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_NS4__implies__NS3) ).
thf(381,plain,
! [A: nat,B: msg,C: agent1,D: msg,E: agent1,F: nat,G: list @ event] :
( ( member @ ( list @ event ) @ G @ nS_Sha254967238shared )
=> ( ~ ( member @ msg @ ( key @ F ) @ ( analz @ ( knows @ spy @ G ) ) )
=> ( ( member @ event @ ( says @ server @ E @ ( crypt @ ( shrK @ E ) @ ( mPair @ D @ ( mPair @ ( agent @ C ) @ ( mPair @ ( key @ F ) @ B ) ) ) ) ) @ ( set @ event @ G ) )
=> ( ( member @ msg @ ( crypt @ F @ ( nonce @ A ) ) @ ( parts @ ( knows @ spy @ G ) ) )
=> ? [H: agent1] : ( member @ event @ ( says @ H @ C @ B ) @ ( set @ event @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(24,axiom,
! [A: msg,B: nat,C: nat] :
( ( key @ C )
!= ( crypt @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_msg_Osimps_I42_J) ).
thf(220,plain,
! [A: msg,B: nat,C: nat] :
( ( key @ C )
!= ( crypt @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(28,axiom,
! [A: fun @ msg @ bool,B: msg] :
( ( member @ msg @ B @ ( analz @ A ) )
=> ( member @ msg @ B @ ( parts @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_analz__into__parts) ).
thf(233,plain,
! [A: fun @ msg @ bool,B: msg] :
( ( member @ msg @ B @ ( analz @ A ) )
=> ( member @ msg @ B @ ( parts @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(96,axiom,
! [A: msg,B: agent1,C: agent1,D: msg,E: agent1] :
( ( notes @ E @ D )
!= ( says @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_event_Osimps_I7_J) ).
thf(452,plain,
! [A: msg,B: agent1,C: agent1,D: msg,E: agent1] :
( ( notes @ E @ D )
!= ( says @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(76,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa1 @ TC @ TB @ ( combc @ TC @ TA @ TB @ C @ B ) @ A )
= ( aa1 @ TA @ TB @ ( aa1 @ TC @ ( fun @ TA @ TB ) @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
thf(392,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa1 @ TC @ TB @ ( combc @ TC @ TA @ TB @ C @ B ) @ A )
= ( aa1 @ TA @ TB @ ( aa1 @ TC @ ( fun @ TA @ TB ) @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(87,axiom,
! [A: list @ event,B: msg,C: nat,D: agent1,E: msg,F: agent1] :
( ( member @ msg @ ( crypt @ ( shrK @ F ) @ ( mPair @ E @ ( mPair @ ( agent @ D ) @ ( mPair @ ( key @ C ) @ B ) ) ) ) @ ( parts @ ( knows @ spy @ A ) ) )
=> ( ~ ( member @ agent1 @ F @ bad )
=> ( ( member @ ( list @ event ) @ A @ nS_Sha254967238shared )
=> ( member @ event @ ( says @ server @ F @ ( crypt @ ( shrK @ F ) @ ( mPair @ E @ ( mPair @ ( agent @ D ) @ ( mPair @ ( key @ C ) @ B ) ) ) ) ) @ ( set @ event @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_A__trusts__NS2) ).
thf(424,plain,
! [A: list @ event,B: msg,C: nat,D: agent1,E: msg,F: agent1] :
( ( member @ msg @ ( crypt @ ( shrK @ F ) @ ( mPair @ E @ ( mPair @ ( agent @ D ) @ ( mPair @ ( key @ C ) @ B ) ) ) ) @ ( parts @ ( knows @ spy @ A ) ) )
=> ( ~ ( member @ agent1 @ F @ bad )
=> ( ( member @ ( list @ event ) @ A @ nS_Sha254967238shared )
=> ( member @ event @ ( says @ server @ F @ ( crypt @ ( shrK @ F ) @ ( mPair @ E @ ( mPair @ ( agent @ D ) @ ( mPair @ ( key @ C ) @ B ) ) ) ) ) @ ( set @ event @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(89,axiom,
! [A: list @ event,B: msg,C: agent1,D: msg] :
( ~ ( member @ msg @ D @ ( analz @ ( knows @ spy @ ( cons @ event @ ( notes @ C @ B ) @ A ) ) ) )
=> ~ ( member @ msg @ D @ ( analz @ ( knows @ spy @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_analz__mono__contra_I2_J) ).
thf(429,plain,
! [A: list @ event,B: msg,C: agent1,D: msg] :
( ~ ( member @ msg @ D @ ( analz @ ( knows @ spy @ ( cons @ event @ ( notes @ C @ B ) @ A ) ) ) )
=> ~ ( member @ msg @ D @ ( analz @ ( knows @ spy @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(15,axiom,
! [A: list @ event,B: msg,C: agent1] :
( ( member @ msg @ ( crypt @ ( shrK @ C ) @ B ) @ ( analz @ ( knows @ spy @ A ) ) )
=> ( ( member @ agent1 @ C @ bad )
=> ( member @ msg @ B @ ( analz @ ( knows @ spy @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_Crypt__Spy__analz__bad) ).
thf(192,plain,
! [A: list @ event,B: msg,C: agent1] :
( ( member @ msg @ ( crypt @ ( shrK @ C ) @ B ) @ ( analz @ ( knows @ spy @ A ) ) )
=> ( ( member @ agent1 @ C @ bad )
=> ( member @ msg @ B @ ( analz @ ( knows @ spy @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(81,axiom,
! [A: list @ event,B: msg,C: agent1] :
( ( member @ event @ ( notes @ C @ B ) @ ( set @ event @ A ) )
=> ( ( member @ agent1 @ C @ bad )
=> ( member @ msg @ B @ ( knows @ spy @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_Notes__imp__knows__Spy) ).
thf(407,plain,
! [A: list @ event,B: msg,C: agent1] :
( ( member @ event @ ( notes @ C @ B ) @ ( set @ event @ A ) )
=> ( ( member @ agent1 @ C @ bad )
=> ( member @ msg @ B @ ( knows @ spy @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(103,axiom,
! [A: nat,B: msg,C: msg] :
( ( mPair @ C @ B )
!= ( key @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_msg_Osimps_I41_J) ).
thf(467,plain,
! [A: nat,B: msg,C: msg] :
( ( mPair @ C @ B )
!= ( key @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(35,axiom,
member @ agent1 @ spy @ bad,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_Spy__in__bad) ).
thf(252,plain,
member @ agent1 @ spy @ bad,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(17,axiom,
! [A: list @ event,B: msg,C: msg,D: msg,E: msg,F: agent1] :
( ( member @ event @ ( says @ server @ F @ ( crypt @ ( shrK @ F ) @ ( mPair @ E @ ( mPair @ D @ ( mPair @ C @ B ) ) ) ) ) @ ( set @ event @ A ) )
=> ( member @ msg @ C @ ( parts @ ( knows @ spy @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_Oops__parts__spies) ).
thf(197,plain,
! [A: list @ event,B: msg,C: msg,D: msg,E: msg,F: agent1] :
( ( member @ event @ ( says @ server @ F @ ( crypt @ ( shrK @ F ) @ ( mPair @ E @ ( mPair @ D @ ( mPair @ C @ B ) ) ) ) ) @ ( set @ event @ A ) )
=> ( member @ msg @ C @ ( parts @ ( knows @ spy @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(68,axiom,
! [A: msg,B: agent1,C: msg,D: agent1,E: list @ event,F: msg,G: nat,H: agent1,I: msg,J: agent1] :
( ( member @ event @ ( says @ server @ J @ ( crypt @ ( shrK @ J ) @ ( mPair @ I @ ( mPair @ ( agent @ H ) @ ( mPair @ ( key @ G ) @ F ) ) ) ) ) @ ( set @ event @ E ) )
=> ( ( member @ event @ ( says @ server @ D @ ( crypt @ ( shrK @ D ) @ ( mPair @ C @ ( mPair @ ( agent @ B ) @ ( mPair @ ( key @ G ) @ A ) ) ) ) ) @ ( set @ event @ E ) )
=> ( ( member @ ( list @ event ) @ E @ nS_Sha254967238shared )
=> ( ( J = D )
& ( I = C )
& ( H = B )
& ( F = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_unique__session__keys) ).
thf(361,plain,
! [A: msg,B: agent1,C: msg,D: agent1,E: list @ event,F: msg,G: nat,H: agent1,I: msg,J: agent1] :
( ( member @ event @ ( says @ server @ J @ ( crypt @ ( shrK @ J ) @ ( mPair @ I @ ( mPair @ ( agent @ H ) @ ( mPair @ ( key @ G ) @ F ) ) ) ) ) @ ( set @ event @ E ) )
=> ( ( member @ event @ ( says @ server @ D @ ( crypt @ ( shrK @ D ) @ ( mPair @ C @ ( mPair @ ( agent @ B ) @ ( mPair @ ( key @ G ) @ A ) ) ) ) ) @ ( set @ event @ E ) )
=> ( ( member @ ( list @ event ) @ E @ nS_Sha254967238shared )
=> ( ( J = D )
& ( I = C )
& ( H = B )
& ( F = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(56,axiom,
! [A: fun @ msg @ bool,B: msg,C: agent1] :
( ( member @ msg @ ( crypt @ ( shrK @ C ) @ B ) @ ( analz @ A ) )
=> ( ( member @ msg @ ( key @ ( shrK @ C ) ) @ ( analz @ A ) )
=> ( member @ msg @ B @ ( analz @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_analz__shrK__Decrypt) ).
thf(329,plain,
! [A: fun @ msg @ bool,B: msg,C: agent1] :
( ( member @ msg @ ( crypt @ ( shrK @ C ) @ B ) @ ( analz @ A ) )
=> ( ( member @ msg @ ( key @ ( shrK @ C ) ) @ ( analz @ A ) )
=> ( member @ msg @ B @ ( analz @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(100,axiom,
! [A: bool] :
( ~ ( pp @ ( aa1 @ bool @ bool @ fNot @ A ) )
| ~ ( pp @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
thf(461,plain,
! [A: bool] :
( ~ ( pp @ ( aa1 @ bool @ bool @ fNot @ A ) )
| ~ ( pp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(111,axiom,
! [A: msg,B: msg,C: agent1] :
( ( agent @ C )
!= ( mPair @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_msg_Osimps_I16_J) ).
thf(493,plain,
! [A: msg,B: msg,C: agent1] :
( ( agent @ C )
!= ( mPair @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(97,axiom,
( ( member @ event @ ( says @ a @ b @ ( crypt @ k @ ( mPair @ ( nonce @ nb ) @ ( nonce @ nb ) ) ) ) @ ( set @ event @ evs5 ) )
=> ~ ( member @ msg @ ( crypt @ k @ ( mPair @ ( nonce @ nb ) @ ( nonce @ nb ) ) ) @ ( parts @ ( knows @ spy @ ( takeWhile @ event @ ( combb @ bool @ bool @ event @ fNot @ ( combc @ event @ event @ bool @ ( fequal @ event ) @ ( says @ a @ b @ ( crypt @ k @ ( mPair @ ( nonce @ nb ) @ ( nonce @ nb ) ) ) ) ) ) @ ( rev @ event @ evs5 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_7) ).
thf(456,plain,
( ( member @ event @ ( says @ a @ b @ ( crypt @ k @ ( mPair @ ( nonce @ nb ) @ ( nonce @ nb ) ) ) ) @ ( set @ event @ evs5 ) )
=> ~ ( member @ msg @ ( crypt @ k @ ( mPair @ ( nonce @ nb ) @ ( nonce @ nb ) ) ) @ ( parts @ ( knows @ spy @ ( takeWhile @ event @ ( combb @ bool @ bool @ event @ fNot @ ( combc @ event @ event @ bool @ ( fequal @ event ) @ ( says @ a @ b @ ( crypt @ k @ ( mPair @ ( nonce @ nb ) @ ( nonce @ nb ) ) ) ) ) ) @ ( rev @ event @ evs5 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(54,axiom,
member @ event @ ( says @ b1 @ aa @ ( crypt @ ka @ ( nonce @ nBa ) ) ) @ ( set @ event @ evs5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).
thf(324,plain,
member @ event @ ( says @ b1 @ aa @ ( crypt @ ka @ ( nonce @ nBa ) ) ) @ ( set @ event @ evs5 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(25,axiom,
! [A: list @ event,B: agent1] :
( ( member @ agent1 @ B @ bad )
=> ( member @ msg @ ( key @ ( shrK @ B ) ) @ ( knows @ spy @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_Spy__spies__bad__shrK) ).
thf(224,plain,
! [A: list @ event,B: agent1] :
( ( member @ agent1 @ B @ bad )
=> ( member @ msg @ ( key @ ( shrK @ B ) ) @ ( knows @ spy @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(52,axiom,
! [A: nat,B: nat] :
( ( key @ B )
!= ( nonce @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_msg_Osimps_I31_J) ).
thf(317,plain,
! [A: nat,B: nat] :
( ( key @ B )
!= ( nonce @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(8,axiom,
! [A: nat,B: nat] :
( ( ( key @ B )
= ( key @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_msg_Osimps_I4_J) ).
thf(156,plain,
! [A: nat,B: nat] :
( ( ( ( key @ B )
= ( key @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( key @ B )
= ( key @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(80,axiom,
! [A: agent1,B: nat] :
( ( nonce @ B )
!= ( agent @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_msg_Osimps_I11_J) ).
thf(403,plain,
! [A: agent1,B: nat] :
( ( nonce @ B )
!= ( agent @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(104,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( B != A )
| ( pp @ ( aa1 @ TA @ bool @ ( aa1 @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
thf(471,plain,
! [TA: $tType,A: TA,B: TA] :
( ( B != A )
| ( pp @ ( aa1 @ TA @ bool @ ( aa1 @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(109,axiom,
! [A: bool,B: list @ event,C: msg] :
( ( ~ ( member @ msg @ C @ ( analz @ ( knows @ spy @ B ) ) )
=> ( pp @ A ) )
=> ( ~ ( member @ msg @ C @ ( analz @ ( knows @ spy @ B ) ) )
=> ( pp @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_analz__impI) ).
thf(488,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(60,axiom,
! [A: fun @ msg @ bool,B: msg,C: nat] :
( ( member @ msg @ ( crypt @ C @ B ) @ ( analz @ A ) )
=> ( ( member @ nat @ C @ symKeys )
=> ( ( member @ msg @ ( key @ C ) @ ( analz @ A ) )
=> ( member @ msg @ B @ ( analz @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_analz__Decrypt_H) ).
thf(339,plain,
! [A: fun @ msg @ bool,B: msg,C: nat] :
( ( member @ msg @ ( crypt @ C @ B ) @ ( analz @ A ) )
=> ( ( member @ nat @ C @ symKeys )
=> ( ( member @ msg @ ( key @ C ) @ ( analz @ A ) )
=> ( member @ msg @ B @ ( analz @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(110,axiom,
! [A: nat,B: msg,C: nat] :
( ( crypt @ C @ B )
!= ( nonce @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_msg_Osimps_I37_J) ).
thf(489,plain,
! [A: nat,B: msg,C: nat] :
( ( crypt @ C @ B )
!= ( nonce @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(32,axiom,
! [A: fun @ msg @ bool] :
( ( parts @ ( parts @ A ) )
= ( parts @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_parts__idem) ).
thf(244,plain,
! [A: fun @ msg @ bool] :
( ( parts @ ( parts @ A ) )
= ( parts @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(113,axiom,
! [A: fun @ msg @ bool,B: msg,C: msg] :
( ( member @ msg @ ( mPair @ C @ B ) @ ( analz @ A ) )
=> ( member @ msg @ C @ ( analz @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_analz_OFst) ).
thf(508,plain,
! [A: fun @ msg @ bool,B: msg,C: msg] :
( ( member @ msg @ ( mPair @ C @ B ) @ ( analz @ A ) )
=> ( member @ msg @ C @ ( analz @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(78,axiom,
! [A: msg,B: agent1,C: nat,D: agent1,E: nat,F: agent1,G: agent1,H: nat,I: list @ event] :
( ( member @ ( list @ event ) @ I @ nS_Sha254967238shared )
=> ( ( member @ nat @ H @ symKeys )
=> ( ( member @ event @ ( says @ G @ F @ ( crypt @ H @ ( nonce @ E ) ) ) @ ( set @ event @ I ) )
=> ( ( member @ event @ ( says @ D @ F @ ( crypt @ ( shrK @ F ) @ ( mPair @ ( nonce @ C ) @ ( mPair @ ( agent @ B ) @ ( mPair @ ( key @ H ) @ A ) ) ) ) ) @ ( set @ event @ I ) )
=> ( member @ ( list @ event ) @ ( cons @ event @ ( says @ F @ B @ ( crypt @ H @ ( mPair @ ( nonce @ E ) @ ( nonce @ E ) ) ) ) @ I ) @ nS_Sha254967238shared ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_ns__shared_ONS5) ).
thf(398,plain,
! [A: msg,B: agent1,C: nat,D: agent1,E: nat,F: agent1,G: agent1,H: nat,I: list @ event] :
( ( member @ ( list @ event ) @ I @ nS_Sha254967238shared )
=> ( ( member @ nat @ H @ symKeys )
=> ( ( member @ event @ ( says @ G @ F @ ( crypt @ H @ ( nonce @ E ) ) ) @ ( set @ event @ I ) )
=> ( ( member @ event @ ( says @ D @ F @ ( crypt @ ( shrK @ F ) @ ( mPair @ ( nonce @ C ) @ ( mPair @ ( agent @ B ) @ ( mPair @ ( key @ H ) @ A ) ) ) ) ) @ ( set @ event @ I ) )
=> ( member @ ( list @ event ) @ ( cons @ event @ ( says @ F @ B @ ( crypt @ H @ ( mPair @ ( nonce @ E ) @ ( nonce @ E ) ) ) ) @ I ) @ nS_Sha254967238shared ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(50,axiom,
! [A: nat,B: nat] :
( ( ( nonce @ B )
= ( nonce @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_msg_Osimps_I3_J) ).
thf(298,plain,
! [A: nat,B: nat] :
( ( ( ( nonce @ B )
= ( nonce @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( nonce @ B )
= ( nonce @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(115,axiom,
! [A: msg,B: nat,C: agent1] :
( ( agent @ C )
!= ( crypt @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_msg_Osimps_I18_J) ).
thf(513,plain,
! [A: msg,B: nat,C: agent1] :
( ( agent @ C )
!= ( crypt @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(40,axiom,
! [A: fun @ msg @ bool,B: msg,C: msg] :
( ( member @ msg @ ( mPair @ C @ B ) @ ( analz @ A ) )
=> ( member @ msg @ B @ ( analz @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_analz_OSnd) ).
thf(264,plain,
! [A: fun @ msg @ bool,B: msg,C: msg] :
( ( member @ msg @ ( mPair @ C @ B ) @ ( analz @ A ) )
=> ( member @ msg @ B @ ( analz @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(49,axiom,
! [A: fun @ msg @ bool,B: msg] :
( ( member @ msg @ B @ ( analz @ ( analz @ A ) ) )
=> ( member @ msg @ B @ ( analz @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_analz__analzD) ).
thf(296,plain,
! [A: fun @ msg @ bool,B: msg] :
( ( member @ msg @ B @ ( analz @ ( analz @ A ) ) )
=> ( member @ msg @ B @ ( analz @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(11,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( B
!= ( cons @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_not__Cons__self) ).
thf(176,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( B
!= ( cons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(38,axiom,
~ ( member @ agent1 @ b @ bad ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(259,plain,
~ ( member @ agent1 @ b @ bad ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(6,axiom,
pp @ fTrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(144,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(65,axiom,
! [A: list @ event,B: msg,C: msg,D: msg,E: msg,F: nat,G: agent1,H: agent1] :
( ( member @ event @ ( says @ H @ G @ ( crypt @ F @ ( mPair @ E @ ( mPair @ D @ ( mPair @ C @ B ) ) ) ) ) @ ( set @ event @ A ) )
=> ( member @ msg @ B @ ( parts @ ( knows @ spy @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_NS3__msg__in__parts__spies) ).
thf(350,plain,
! [A: list @ event,B: msg,C: msg,D: msg,E: msg,F: nat,G: agent1,H: agent1] :
( ( member @ event @ ( says @ H @ G @ ( crypt @ F @ ( mPair @ E @ ( mPair @ D @ ( mPair @ C @ B ) ) ) ) ) @ ( set @ event @ A ) )
=> ( member @ msg @ B @ ( parts @ ( knows @ spy @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(13,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(187,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(85,axiom,
~ ( member @ agent1 @ server @ bad ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_Server__not__bad) ).
thf(419,plain,
~ ( member @ agent1 @ server @ bad ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(27,axiom,
! [A: agent1,B: agent1,C: list @ event,D: nat,E: nat] :
( ( member @ msg @ ( crypt @ E @ ( mPair @ ( nonce @ D ) @ ( nonce @ D ) ) ) @ ( parts @ ( knows @ spy @ C ) ) )
=> ( ( member @ msg @ ( crypt @ ( shrK @ B ) @ ( mPair @ ( key @ E ) @ ( agent @ A ) ) ) @ ( parts @ ( knows @ spy @ C ) ) )
=> ( ! [F: msg,G: msg] :
~ ( member @ event @ ( notes @ spy @ ( mPair @ F @ ( mPair @ G @ ( key @ E ) ) ) ) @ ( set @ event @ C ) )
=> ( ~ ( member @ agent1 @ A @ bad )
=> ( ~ ( member @ agent1 @ B @ bad )
=> ( ( member @ ( list @ event ) @ C @ nS_Sha254967238shared )
=> ( member @ event @ ( says @ A @ B @ ( crypt @ E @ ( mPair @ ( nonce @ D ) @ ( nonce @ D ) ) ) ) @ ( set @ event @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_B__trusts__NS5) ).
thf(230,plain,
! [A: agent1,B: agent1,C: list @ event,D: nat,E: nat] :
( ( member @ msg @ ( crypt @ E @ ( mPair @ ( nonce @ D ) @ ( nonce @ D ) ) ) @ ( parts @ ( knows @ spy @ C ) ) )
=> ( ( member @ msg @ ( crypt @ ( shrK @ B ) @ ( mPair @ ( key @ E ) @ ( agent @ A ) ) ) @ ( parts @ ( knows @ spy @ C ) ) )
=> ( ! [F: msg,G: msg] :
~ ( member @ event @ ( notes @ spy @ ( mPair @ F @ ( mPair @ G @ ( key @ E ) ) ) ) @ ( set @ event @ C ) )
=> ( ~ ( member @ agent1 @ A @ bad )
=> ( ~ ( member @ agent1 @ B @ bad )
=> ( ( member @ ( list @ event ) @ C @ nS_Sha254967238shared )
=> ( member @ event @ ( says @ A @ B @ ( crypt @ E @ ( mPair @ ( nonce @ D ) @ ( nonce @ D ) ) ) ) @ ( set @ event @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(91,axiom,
! [A: nat,B: msg,C: nat] :
( ( crypt @ C @ B )
!= ( key @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_msg_Osimps_I43_J) ).
thf(434,plain,
! [A: nat,B: msg,C: nat] :
( ( crypt @ C @ B )
!= ( key @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(51,axiom,
! [A: msg,B: msg,C: msg,D: msg] :
( ( ( mPair @ D @ C )
= ( mPair @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_msg_Osimps_I6_J) ).
thf(306,plain,
! [A: msg,B: msg,C: msg,D: msg] :
( ( ( ( mPair @ D @ C )
= ( mPair @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( mPair @ D @ C )
= ( mPair @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(26,axiom,
! [A: msg,B: agent1,C: msg,D: agent1,E: agent1] :
( ( says @ E @ D @ C )
!= ( notes @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_event_Osimps_I6_J) ).
thf(226,plain,
! [A: msg,B: agent1,C: msg,D: agent1,E: agent1] :
( ( says @ E @ D @ C )
!= ( notes @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(41,axiom,
! [A: fun @ msg @ bool,B: msg,C: nat] :
( ( member @ msg @ ( crypt @ C @ B ) @ ( parts @ A ) )
=> ( member @ msg @ B @ ( parts @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_parts_OBody) ).
thf(267,plain,
! [A: fun @ msg @ bool,B: msg,C: nat] :
( ( member @ msg @ ( crypt @ C @ B ) @ ( parts @ A ) )
=> ( member @ msg @ B @ ( parts @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(92,axiom,
! [A: list @ event,B: nat,C: nat,D: agent1,E: agent1] :
( ( member @ event @ ( says @ E @ D @ ( crypt @ C @ ( nonce @ B ) ) ) @ ( set @ event @ A ) )
=> ( ~ ( member @ msg @ ( key @ C ) @ ( analz @ ( knows @ spy @ A ) ) )
=> ( ~ ( member @ agent1 @ D @ bad )
=> ( ~ ( member @ agent1 @ E @ bad )
=> ( ( member @ ( list @ event ) @ A @ nS_Sha254967238shared )
=> ( nS_Sha512322870Issues @ E @ D @ ( crypt @ C @ ( nonce @ B ) ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_B__Issues__A) ).
thf(438,plain,
! [A: list @ event,B: nat,C: nat,D: agent1,E: agent1] :
( ( member @ event @ ( says @ E @ D @ ( crypt @ C @ ( nonce @ B ) ) ) @ ( set @ event @ A ) )
=> ( ~ ( member @ msg @ ( key @ C ) @ ( analz @ ( knows @ spy @ A ) ) )
=> ( ~ ( member @ agent1 @ D @ bad )
=> ( ~ ( member @ agent1 @ E @ bad )
=> ( ( member @ ( list @ event ) @ A @ nS_Sha254967238shared )
=> ( nS_Sha512322870Issues @ E @ D @ ( crypt @ C @ ( nonce @ B ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(90,axiom,
! [A: list @ event,B: msg,C: agent1,D: agent1] :
( ( member @ event @ ( says @ D @ C @ B ) @ ( set @ event @ A ) )
=> ( member @ msg @ B @ ( parts @ ( knows @ spy @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_Says__imp__parts__knows__Spy) ).
thf(431,plain,
! [A: list @ event,B: msg,C: agent1,D: agent1] :
( ( member @ event @ ( says @ D @ C @ B ) @ ( set @ event @ A ) )
=> ( member @ msg @ B @ ( parts @ ( knows @ spy @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(31,axiom,
! [A: fun @ msg @ bool,B: msg,C: nat] :
( ( member @ msg @ ( crypt @ C @ B ) @ ( parts @ A ) )
=> ( member @ msg @ B @ ( parts @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_spies__partsEs_I2_J) ).
thf(241,plain,
! [A: fun @ msg @ bool,B: msg,C: nat] :
( ( member @ msg @ ( crypt @ C @ B ) @ ( parts @ A ) )
=> ( member @ msg @ B @ ( parts @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(88,axiom,
server != spy,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_agent_Osimps_I4_J) ).
thf(426,plain,
server != spy,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(117,axiom,
! [A: list @ event,B: msg,C: agent1,D: agent1,E: msg] :
( ~ ( member @ msg @ E @ ( analz @ ( knows @ spy @ ( cons @ event @ ( says @ D @ C @ B ) @ A ) ) ) )
=> ~ ( member @ msg @ E @ ( analz @ ( knows @ spy @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_analz__mono__contra_I1_J) ).
thf(531,plain,
! [A: list @ event,B: msg,C: agent1,D: agent1,E: msg] :
( ~ ( member @ msg @ E @ ( analz @ ( knows @ spy @ ( cons @ event @ ( says @ D @ C @ B ) @ A ) ) ) )
=> ~ ( member @ msg @ E @ ( analz @ ( knows @ spy @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(70,axiom,
! [A: nat,B: msg,C: agent1,D: msg,E: agent1,F: nat,G: list @ event] :
( ( member @ ( list @ event ) @ G @ nS_Sha254967238shared )
=> ( ~ ( member @ msg @ ( key @ F ) @ ( analz @ ( knows @ spy @ G ) ) )
=> ( ( member @ event @ ( says @ server @ E @ ( crypt @ ( shrK @ E ) @ ( mPair @ D @ ( mPair @ ( agent @ C ) @ ( mPair @ ( key @ F ) @ B ) ) ) ) ) @ ( set @ event @ G ) )
=> ( ( member @ msg @ ( crypt @ F @ ( nonce @ A ) ) @ ( parts @ ( knows @ spy @ G ) ) )
=> ( member @ event @ ( says @ C @ E @ ( crypt @ F @ ( nonce @ A ) ) ) @ ( set @ event @ G ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_A__trusts__NS4__lemma) ).
thf(374,plain,
! [A: nat,B: msg,C: agent1,D: msg,E: agent1,F: nat,G: list @ event] :
( ( member @ ( list @ event ) @ G @ nS_Sha254967238shared )
=> ( ~ ( member @ msg @ ( key @ F ) @ ( analz @ ( knows @ spy @ G ) ) )
=> ( ( member @ event @ ( says @ server @ E @ ( crypt @ ( shrK @ E ) @ ( mPair @ D @ ( mPair @ ( agent @ C ) @ ( mPair @ ( key @ F ) @ B ) ) ) ) ) @ ( set @ event @ G ) )
=> ( ( member @ msg @ ( crypt @ F @ ( nonce @ A ) ) @ ( parts @ ( knows @ spy @ G ) ) )
=> ( member @ event @ ( says @ C @ E @ ( crypt @ F @ ( nonce @ A ) ) ) @ ( set @ event @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(67,axiom,
! [A: fun @ msg @ bool,B: msg] :
( ( ( member @ msg @ B @ ( analz @ A ) )
| ( member @ msg @ B @ ( parts @ A ) ) )
<=> ( member @ msg @ B @ ( parts @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_analz__disj__parts) ).
thf(355,plain,
! [A: fun @ msg @ bool,B: msg] :
( ( ( ( member @ msg @ B @ ( analz @ A ) )
| ( member @ msg @ B @ ( parts @ A ) ) )
=> ( member @ msg @ B @ ( parts @ A ) ) )
& ( ( member @ msg @ B @ ( parts @ A ) )
=> ( ( member @ msg @ B @ ( analz @ A ) )
| ( member @ msg @ B @ ( parts @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(98,axiom,
member @ event @ ( says @ s @ aa @ ( crypt @ ( shrK @ aa ) @ ( mPair @ ( nonce @ na ) @ ( mPair @ ( agent @ ba ) @ ( mPair @ ( key @ ka ) @ x ) ) ) ) ) @ ( set @ event @ evs5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_5) ).
thf(458,plain,
member @ event @ ( says @ s @ aa @ ( crypt @ ( shrK @ aa ) @ ( mPair @ ( nonce @ na ) @ ( mPair @ ( agent @ ba ) @ ( mPair @ ( key @ ka ) @ x ) ) ) ) ) @ ( set @ event @ evs5 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(16,axiom,
! [A: fun @ msg @ bool,B: msg,C: msg] :
( ( member @ msg @ ( mPair @ C @ B ) @ ( parts @ A ) )
=> ~ ( ( member @ msg @ C @ ( parts @ A ) )
=> ~ ( member @ msg @ B @ ( parts @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_MPair__parts) ).
thf(194,plain,
! [A: fun @ msg @ bool,B: msg,C: msg] :
( ( member @ msg @ ( mPair @ C @ B ) @ ( parts @ A ) )
=> ~ ( ( member @ msg @ C @ ( parts @ A ) )
=> ~ ( member @ msg @ B @ ( parts @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(7,axiom,
! [A: msg,B: agent1,C: msg,D: agent1] :
( ( ( notes @ D @ C )
= ( notes @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_event_Osimps_I3_J) ).
thf(145,plain,
! [A: msg,B: agent1,C: msg,D: agent1] :
( ( ( ( notes @ D @ C )
= ( notes @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( notes @ D @ C )
= ( notes @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(57,axiom,
! [A: fun @ msg @ bool,B: msg,C: msg] :
( ( member @ msg @ ( mPair @ C @ B ) @ ( parts @ A ) )
=> ( member @ msg @ C @ ( parts @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_parts_OFst) ).
thf(331,plain,
! [A: fun @ msg @ bool,B: msg,C: msg] :
( ( member @ msg @ ( mPair @ C @ B ) @ ( parts @ A ) )
=> ( member @ msg @ C @ ( parts @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(69,axiom,
! [A: msg,B: nat,C: msg,D: msg] :
( ( mPair @ D @ C )
!= ( crypt @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_msg_Osimps_I48_J) ).
thf(370,plain,
! [A: msg,B: nat,C: msg,D: msg] :
( ( mPair @ D @ C )
!= ( crypt @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(101,axiom,
! [A: fun @ msg @ bool,B: msg] :
( ( member @ msg @ B @ ( parts @ ( parts @ A ) ) )
=> ( member @ msg @ B @ ( parts @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_parts__partsD) ).
thf(463,plain,
! [A: fun @ msg @ bool,B: msg] :
( ( member @ msg @ B @ ( parts @ ( parts @ A ) ) )
=> ( member @ msg @ B @ ( parts @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(59,axiom,
! [TA: $tType,A: list @ TA] :
( ( rev @ TA @ ( rev @ TA @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_rev__rev__ident) ).
thf(336,plain,
! [TA: $tType,A: list @ TA] :
( ( rev @ TA @ ( rev @ TA @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(112,axiom,
! [A: msg,B: nat,C: msg,D: nat] :
( ( ( crypt @ D @ C )
= ( crypt @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_msg_Osimps_I7_J) ).
thf(497,plain,
! [A: msg,B: nat,C: msg,D: nat] :
( ( ( ( crypt @ D @ C )
= ( crypt @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( crypt @ D @ C )
= ( crypt @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(102,axiom,
! [A: nat,B: msg,C: agent1,D: nat,E: list @ event,F: agent1] :
( ~ ( member @ agent1 @ F @ bad )
=> ( ( member @ ( list @ event ) @ E @ nS_Sha254967238shared )
=> ( ~ ( member @ msg @ ( key @ D ) @ ( analz @ ( knows @ spy @ E ) ) )
=> ( ( member @ event @ ( says @ server @ C @ ( crypt @ ( shrK @ C ) @ ( mPair @ B @ ( mPair @ ( agent @ F ) @ ( mPair @ ( key @ D ) @ ( crypt @ ( shrK @ F ) @ ( mPair @ ( key @ D ) @ ( agent @ C ) ) ) ) ) ) ) ) @ ( set @ event @ E ) )
=> ( ( member @ msg @ ( crypt @ D @ ( mPair @ ( nonce @ A ) @ ( nonce @ A ) ) ) @ ( parts @ ( knows @ spy @ E ) ) )
=> ( member @ event @ ( says @ C @ F @ ( crypt @ D @ ( mPair @ ( nonce @ A ) @ ( nonce @ A ) ) ) ) @ ( set @ event @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_B__trusts__NS5__lemma) ).
thf(465,plain,
! [A: nat,B: msg,C: agent1,D: nat,E: list @ event,F: agent1] :
( ~ ( member @ agent1 @ F @ bad )
=> ( ( member @ ( list @ event ) @ E @ nS_Sha254967238shared )
=> ( ~ ( member @ msg @ ( key @ D ) @ ( analz @ ( knows @ spy @ E ) ) )
=> ( ( member @ event @ ( says @ server @ C @ ( crypt @ ( shrK @ C ) @ ( mPair @ B @ ( mPair @ ( agent @ F ) @ ( mPair @ ( key @ D ) @ ( crypt @ ( shrK @ F ) @ ( mPair @ ( key @ D ) @ ( agent @ C ) ) ) ) ) ) ) ) @ ( set @ event @ E ) )
=> ( ( member @ msg @ ( crypt @ D @ ( mPair @ ( nonce @ A ) @ ( nonce @ A ) ) ) @ ( parts @ ( knows @ spy @ E ) ) )
=> ( member @ event @ ( says @ C @ F @ ( crypt @ D @ ( mPair @ ( nonce @ A ) @ ( nonce @ A ) ) ) ) @ ( set @ event @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(95,axiom,
! [A: list @ event,B: agent1] : ( member @ msg @ ( key @ ( shrK @ B ) ) @ ( knows @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_shrK__in__knows) ).
thf(450,plain,
! [A: list @ event,B: agent1] : ( member @ msg @ ( key @ ( shrK @ B ) ) @ ( knows @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(19,axiom,
! [A: msg,B: msg,C: msg,D: nat] :
( ( crypt @ D @ C )
!= ( mPair @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_msg_Osimps_I49_J) ).
thf(203,plain,
! [A: msg,B: msg,C: msg,D: nat] :
( ( crypt @ D @ C )
!= ( mPair @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(23,axiom,
! [A: msg,B: agent1,C: nat,D: agent1,E: list @ event,F: nat,G: nat] :
( ( member @ msg @ ( crypt @ G @ ( mPair @ ( nonce @ F ) @ ( nonce @ F ) ) ) @ ( parts @ ( knows @ spy @ E ) ) )
=> ( ( member @ msg @ ( crypt @ ( shrK @ D ) @ ( mPair @ ( nonce @ C ) @ ( mPair @ ( agent @ B ) @ ( mPair @ ( key @ G ) @ A ) ) ) ) @ ( parts @ ( knows @ spy @ E ) ) )
=> ( ~ ( member @ msg @ ( key @ G ) @ ( analz @ ( knows @ spy @ E ) ) )
=> ( ~ ( member @ agent1 @ D @ bad )
=> ( ~ ( member @ agent1 @ B @ bad )
=> ( ( member @ ( list @ event ) @ E @ nS_Sha254967238shared )
=> ( member @ event @ ( says @ D @ B @ ( crypt @ G @ ( mPair @ ( nonce @ F ) @ ( nonce @ F ) ) ) ) @ ( set @ event @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_A__trusts__NS5) ).
thf(218,plain,
! [A: msg,B: agent1,C: nat,D: agent1,E: list @ event,F: nat,G: nat] :
( ( member @ msg @ ( crypt @ G @ ( mPair @ ( nonce @ F ) @ ( nonce @ F ) ) ) @ ( parts @ ( knows @ spy @ E ) ) )
=> ( ( member @ msg @ ( crypt @ ( shrK @ D ) @ ( mPair @ ( nonce @ C ) @ ( mPair @ ( agent @ B ) @ ( mPair @ ( key @ G ) @ A ) ) ) ) @ ( parts @ ( knows @ spy @ E ) ) )
=> ( ~ ( member @ msg @ ( key @ G ) @ ( analz @ ( knows @ spy @ E ) ) )
=> ( ~ ( member @ agent1 @ D @ bad )
=> ( ~ ( member @ agent1 @ B @ bad )
=> ( ( member @ ( list @ event ) @ E @ nS_Sha254967238shared )
=> ( member @ event @ ( says @ D @ B @ ( crypt @ G @ ( mPair @ ( nonce @ F ) @ ( nonce @ F ) ) ) ) @ ( set @ event @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(29,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
( ( aa1 @ TA @ TC @ ( combb @ TB @ TC @ TA @ C @ B ) @ A )
= ( aa1 @ TB @ TC @ C @ ( aa1 @ TA @ TB @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(235,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
( ( aa1 @ TA @ TC @ ( combb @ TB @ TC @ TA @ C @ B ) @ A )
= ( aa1 @ TB @ TC @ C @ ( aa1 @ TA @ TB @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(114,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: TA] :
( ( member @ TA @ C @ ( set @ TA @ ( cons @ TA @ B @ A ) ) )
=> ( ( C = B )
| ( member @ TA @ C @ ( set @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_set__ConsD) ).
thf(510,plain,
! [TA: $tType,A: list @ TA,B: TA,C: TA] :
( ( member @ TA @ C @ ( set @ TA @ ( cons @ TA @ B @ A ) ) )
=> ( ( C = B )
| ( member @ TA @ C @ ( set @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(20,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( member @ TA @ B @ A )
<=> ( pp @ ( aa1 @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_mem__def) ).
thf(207,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( ( member @ TA @ B @ A )
=> ( pp @ ( aa1 @ TA @ bool @ A @ B ) ) )
& ( ( pp @ ( aa1 @ TA @ bool @ A @ B ) )
=> ( member @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(107,axiom,
! [A: nat,B: nat] :
( ~ ( ( member @ nat @ B @ symKeys )
<=> ( member @ nat @ A @ symKeys ) )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_symKeys__neq__imp__neq) ).
thf(478,plain,
! [A: nat,B: nat] :
( ~ ( ( ( member @ nat @ B @ symKeys )
=> ( member @ nat @ A @ symKeys ) )
& ( ( member @ nat @ A @ symKeys )
=> ( member @ nat @ B @ symKeys ) ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(74,axiom,
~ ( member @ agent1 @ a @ bad ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(383,plain,
~ ( member @ agent1 @ a @ bad ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(63,axiom,
! [A: list @ event,B: msg,C: agent1,D: agent1] :
( ( member @ event @ ( says @ D @ C @ B ) @ ( set @ event @ A ) )
=> ( member @ msg @ B @ ( knows @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_Says__imp__knows) ).
thf(346,plain,
! [A: list @ event,B: msg,C: agent1,D: agent1] :
( ( member @ event @ ( says @ D @ C @ B ) @ ( set @ event @ A ) )
=> ( member @ msg @ B @ ( knows @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(22,axiom,
! [A: msg,B: msg,C: nat] :
( ( nonce @ C )
!= ( mPair @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_msg_Osimps_I34_J) ).
thf(214,plain,
! [A: msg,B: msg,C: nat] :
( ( nonce @ C )
!= ( mPair @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(47,axiom,
! [A: msg,B: nat,C: nat,D: nat,E: agent1,F: agent1,G: list @ event] :
( ( member @ ( list @ event ) @ G @ nS_Sha254967238shared )
=> ( ( member @ event @ ( says @ F @ E @ ( crypt @ D @ ( nonce @ C ) ) ) @ ( set @ event @ G ) )
=> ( ( member @ event @ ( says @ server @ E @ ( crypt @ ( shrK @ E ) @ ( mPair @ ( nonce @ B ) @ ( mPair @ ( agent @ F ) @ ( mPair @ ( key @ D ) @ A ) ) ) ) ) @ ( set @ event @ G ) )
=> ( member @ ( list @ event ) @ ( cons @ event @ ( notes @ spy @ ( mPair @ ( nonce @ B ) @ ( mPair @ ( nonce @ C ) @ ( key @ D ) ) ) ) @ G ) @ nS_Sha254967238shared ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_ns__shared_OOops) ).
thf(290,plain,
! [A: msg,B: nat,C: nat,D: nat,E: agent1,F: agent1,G: list @ event] :
( ( member @ ( list @ event ) @ G @ nS_Sha254967238shared )
=> ( ( member @ event @ ( says @ F @ E @ ( crypt @ D @ ( nonce @ C ) ) ) @ ( set @ event @ G ) )
=> ( ( member @ event @ ( says @ server @ E @ ( crypt @ ( shrK @ E ) @ ( mPair @ ( nonce @ B ) @ ( mPair @ ( agent @ F ) @ ( mPair @ ( key @ D ) @ A ) ) ) ) ) @ ( set @ event @ G ) )
=> ( member @ ( list @ event ) @ ( cons @ event @ ( notes @ spy @ ( mPair @ ( nonce @ B ) @ ( mPair @ ( nonce @ C ) @ ( key @ D ) ) ) ) @ G ) @ nS_Sha254967238shared ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(1,conjecture,
( ( a != aa )
| ( b != ba )
| ( k != ka )
| ( nb != nBa )
| ~ ( member @ msg @ ( crypt @ ka @ ( mPair @ ( nonce @ nBa ) @ ( nonce @ nBa ) ) ) @ ( parts @ ( knows @ spy @ ( takeWhile @ event @ ( combb @ bool @ bool @ event @ fNot @ ( combc @ event @ event @ bool @ ( fequal @ event ) @ ( says @ aa @ ba @ ( crypt @ ka @ ( mPair @ ( nonce @ nBa ) @ ( nonce @ nBa ) ) ) ) ) ) @ ( rev @ event @ evs5 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_8) ).
thf(2,negated_conjecture,
~ ( ( a != aa )
| ( b != ba )
| ( k != ka )
| ( nb != nBa )
| ~ ( member @ msg @ ( crypt @ ka @ ( mPair @ ( nonce @ nBa ) @ ( nonce @ nBa ) ) ) @ ( parts @ ( knows @ spy @ ( takeWhile @ event @ ( combb @ bool @ bool @ event @ fNot @ ( combc @ event @ event @ bool @ ( fequal @ event ) @ ( says @ aa @ ba @ ( crypt @ ka @ ( mPair @ ( nonce @ nBa ) @ ( nonce @ nBa ) ) ) ) ) ) @ ( rev @ event @ evs5 ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(119,plain,
~ ( ( a != aa )
| ( b != ba )
| ( k != ka )
| ( nb != nBa )
| ~ ( member @ msg @ ( crypt @ ka @ ( mPair @ ( nonce @ nBa ) @ ( nonce @ nBa ) ) ) @ ( parts @ ( knows @ spy @ ( takeWhile @ event @ ( combb @ bool @ bool @ event @ fNot @ ( combc @ event @ event @ bool @ ( fequal @ event ) @ ( says @ aa @ ba @ ( crypt @ ka @ ( mPair @ ( nonce @ nBa ) @ ( nonce @ nBa ) ) ) ) ) ) @ ( rev @ event @ evs5 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(72,axiom,
! [A: agent1,B: list @ event] :
( ( member @ ( list @ event ) @ B @ nS_Sha254967238shared )
=> ( ( member @ msg @ ( key @ ( shrK @ A ) ) @ ( parts @ ( knows @ spy @ B ) ) )
<=> ( member @ agent1 @ A @ bad ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_Spy__see__shrK) ).
thf(378,plain,
! [A: agent1,B: list @ event] :
( ( member @ ( list @ event ) @ B @ nS_Sha254967238shared )
=> ( ( ( member @ msg @ ( key @ ( shrK @ A ) ) @ ( parts @ ( knows @ spy @ B ) ) )
=> ( member @ agent1 @ A @ bad ) )
& ( ( member @ agent1 @ A @ bad )
=> ( member @ msg @ ( key @ ( shrK @ A ) ) @ ( parts @ ( knows @ spy @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(10,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( ( cons @ TA @ D @ C )
= ( cons @ TA @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_list_Oinject) ).
thf(168,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( ( ( cons @ TA @ D @ C )
= ( cons @ TA @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( cons @ TA @ D @ C )
= ( cons @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(43,axiom,
! [A: agent1,B: msg,C: nat] :
( ( crypt @ C @ B )
!= ( agent @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_msg_Osimps_I19_J) ).
thf(273,plain,
! [A: agent1,B: msg,C: nat] :
( ( crypt @ C @ B )
!= ( agent @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(21,axiom,
! [A: msg,B: nat,C: nat] :
( ( nonce @ C )
!= ( crypt @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_msg_Osimps_I36_J) ).
thf(210,plain,
! [A: msg,B: nat,C: nat] :
( ( nonce @ C )
!= ( crypt @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(5,axiom,
! [A: agent1,B: agent1] :
( ( ( agent @ B )
= ( agent @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_msg_Osimps_I1_J) ).
thf(136,plain,
! [A: agent1,B: agent1] :
( ( ( ( agent @ B )
= ( agent @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( agent @ B )
= ( agent @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(61,axiom,
! [A: fun @ msg @ bool,B: msg,C: msg] :
( ( member @ msg @ ( mPair @ C @ B ) @ ( analz @ A ) )
=> ~ ( ( member @ msg @ C @ ( analz @ A ) )
=> ~ ( member @ msg @ B @ ( analz @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_MPair__analz) ).
thf(341,plain,
! [A: fun @ msg @ bool,B: msg,C: msg] :
( ( member @ msg @ ( mPair @ C @ B ) @ ( analz @ A ) )
=> ~ ( ( member @ msg @ C @ ( analz @ A ) )
=> ~ ( member @ msg @ B @ ( analz @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(79,axiom,
! [A: agent1,B: list @ event] :
( ( member @ ( list @ event ) @ B @ nS_Sha254967238shared )
=> ( ( member @ msg @ ( key @ ( shrK @ A ) ) @ ( analz @ ( knows @ spy @ B ) ) )
<=> ( member @ agent1 @ A @ bad ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_Spy__analz__shrK) ).
thf(400,plain,
! [A: agent1,B: list @ event] :
( ( member @ ( list @ event ) @ B @ nS_Sha254967238shared )
=> ( ( ( member @ msg @ ( key @ ( shrK @ A ) ) @ ( analz @ ( knows @ spy @ B ) ) )
=> ( member @ agent1 @ A @ bad ) )
& ( ( member @ agent1 @ A @ bad )
=> ( member @ msg @ ( key @ ( shrK @ A ) ) @ ( analz @ ( knows @ spy @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(46,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( rev @ TA @ B )
= A )
<=> ( B
= ( rev @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_rev__swap) ).
thf(283,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( ( rev @ TA @ B )
= A )
=> ( B
= ( rev @ TA @ A ) ) )
& ( ( B
= ( rev @ TA @ A ) )
=> ( ( rev @ TA @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(83,axiom,
! [A: msg,B: agent1,C: msg,D: agent1,E: list @ event,F: nat,G: nat] :
( ( member @ msg @ ( crypt @ G @ ( nonce @ F ) ) @ ( parts @ ( knows @ spy @ E ) ) )
=> ( ( member @ msg @ ( crypt @ ( shrK @ D ) @ ( mPair @ C @ ( mPair @ ( agent @ B ) @ ( mPair @ ( key @ G ) @ A ) ) ) ) @ ( parts @ ( knows @ spy @ E ) ) )
=> ( ~ ( member @ msg @ ( key @ G ) @ ( analz @ ( knows @ spy @ E ) ) )
=> ( ~ ( member @ agent1 @ D @ bad )
=> ( ~ ( member @ agent1 @ B @ bad )
=> ( ( member @ ( list @ event ) @ E @ nS_Sha254967238shared )
=> ( nS_Sha512322870Issues @ B @ D @ ( crypt @ G @ ( nonce @ F ) ) @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_A__authenticates__and__keydist__to__B) ).
thf(415,plain,
! [A: msg,B: agent1,C: msg,D: agent1,E: list @ event,F: nat,G: nat] :
( ( member @ msg @ ( crypt @ G @ ( nonce @ F ) ) @ ( parts @ ( knows @ spy @ E ) ) )
=> ( ( member @ msg @ ( crypt @ ( shrK @ D ) @ ( mPair @ C @ ( mPair @ ( agent @ B ) @ ( mPair @ ( key @ G ) @ A ) ) ) ) @ ( parts @ ( knows @ spy @ E ) ) )
=> ( ~ ( member @ msg @ ( key @ G ) @ ( analz @ ( knows @ spy @ E ) ) )
=> ( ~ ( member @ agent1 @ D @ bad )
=> ( ~ ( member @ agent1 @ B @ bad )
=> ( ( member @ ( list @ event ) @ E @ nS_Sha254967238shared )
=> ( nS_Sha512322870Issues @ B @ D @ ( crypt @ G @ ( nonce @ F ) ) @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(77,axiom,
! [A: fun @ msg @ bool] :
( ( parts @ ( analz @ A ) )
= ( parts @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_parts__analz) ).
thf(395,plain,
! [A: fun @ msg @ bool] :
( ( parts @ ( analz @ A ) )
= ( parts @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(99,axiom,
! [A: fun @ msg @ bool,B: msg] :
( ( member @ msg @ B @ A )
=> ( member @ msg @ B @ ( analz @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_analz_OInj) ).
thf(459,plain,
! [A: fun @ msg @ bool,B: msg] :
( ( member @ msg @ B @ A )
=> ( member @ msg @ B @ ( analz @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(18,axiom,
! [A: list @ event,B: msg,C: agent1,D: agent1] :
( ( member @ event @ ( says @ D @ C @ B ) @ ( set @ event @ A ) )
=> ( member @ msg @ B @ ( knows @ spy @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_Says__imp__spies) ).
thf(200,plain,
! [A: list @ event,B: msg,C: agent1,D: agent1] :
( ( member @ event @ ( says @ D @ C @ B ) @ ( set @ event @ A ) )
=> ( member @ msg @ B @ ( knows @ spy @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(44,axiom,
! [A: msg,B: nat,C: agent1,D: nat,E: agent1,F: agent1,G: list @ event] :
( ( member @ ( list @ event ) @ G @ nS_Sha254967238shared )
=> ( ( F != server )
=> ( ( member @ event @ ( says @ E @ F @ ( crypt @ ( shrK @ F ) @ ( mPair @ ( nonce @ D ) @ ( mPair @ ( agent @ C ) @ ( mPair @ ( key @ B ) @ A ) ) ) ) ) @ ( set @ event @ G ) )
=> ( ( member @ event @ ( says @ F @ server @ ( mPair @ ( agent @ F ) @ ( mPair @ ( agent @ C ) @ ( nonce @ D ) ) ) ) @ ( set @ event @ G ) )
=> ( member @ ( list @ event ) @ ( cons @ event @ ( says @ F @ C @ A ) @ G ) @ nS_Sha254967238shared ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_ns__shared_ONS3) ).
thf(277,plain,
! [A: msg,B: nat,C: agent1,D: nat,E: agent1,F: agent1,G: list @ event] :
( ( member @ ( list @ event ) @ G @ nS_Sha254967238shared )
=> ( ( F != server )
=> ( ( member @ event @ ( says @ E @ F @ ( crypt @ ( shrK @ F ) @ ( mPair @ ( nonce @ D ) @ ( mPair @ ( agent @ C ) @ ( mPair @ ( key @ B ) @ A ) ) ) ) ) @ ( set @ event @ G ) )
=> ( ( member @ event @ ( says @ F @ server @ ( mPair @ ( agent @ F ) @ ( mPair @ ( agent @ C ) @ ( nonce @ D ) ) ) ) @ ( set @ event @ G ) )
=> ( member @ ( list @ event ) @ ( cons @ event @ ( says @ F @ C @ A ) @ G ) @ nS_Sha254967238shared ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(27035,plain,
$false,
inference(cvc4,[status(thm)],[333,344,129,477,409,517,247,440,385,533,417,257,189,421,325,261,475,164,179,443,321,376,253,485,238,348,353,280,132,292,248,270,381,220,233,452,392,424,429,192,407,467,252,197,361,329,461,493,456,324,224,317,156,403,471,488,339,489,244,508,398,298,513,264,296,176,259,144,350,187,419,230,434,306,226,267,438,431,241,426,531,374,355,458,194,145,331,370,463,336,497,465,450,203,218,235,510,207,478,383,346,214,290,119,378,168,273,210,136,341,400,283,415,395,459,200,277]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SWV815_5 : TPTP v8.1.2. Released v6.0.0.
% 0.08/0.17 % Command : run_Leo-III %s %d
% 0.18/0.39 % Computer : n022.cluster.edu
% 0.18/0.39 % Model : x86_64 x86_64
% 0.18/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.39 % Memory : 8042.1875MB
% 0.18/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.39 % CPULimit : 300
% 0.18/0.39 % WCLimit : 300
% 0.18/0.39 % DateTime : Fri May 19 02:34:47 EDT 2023
% 0.18/0.39 % CPUTime :
% 1.07/0.94 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.43/1.15 % [INFO] Parsing done (212ms).
% 1.43/1.16 % [INFO] Running in sequential loop mode.
% 2.27/1.37 % [INFO] eprover registered as external prover.
% 2.27/1.37 % [INFO] cvc4 registered as external prover.
% 2.27/1.37 % [INFO] Scanning for conjecture ...
% 2.73/1.49 % [INFO] Found a conjecture and 116 axioms. Running axiom selection ...
% 3.01/1.58 % [INFO] Axiom selection finished. Selected 116 axioms (removed 0 axioms).
% 3.52/1.73 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.52/1.75 % [INFO] Type checking passed.
% 3.52/1.75 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 58.48/22.06 % External prover 'cvc4' found a proof!
% 58.48/22.06 % [INFO] Killing All external provers ...
% 58.48/22.06 % Time passed: 21508ms (effective reasoning time: 20900ms)
% 58.48/22.06 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 58.48/22.07 % Axioms used in derivation (116): help_fNot_2_1_U, fact_55_msg_Osimps_I30_J, fact_9_Crypt__Spy__analz__bad, fact_25_msg_Osimps_I1_J, fact_48_msg_Osimps_I49_J, fact_95_analz__mono__contra_I1_J, fact_67_msg_Osimps_I10_J, fact_82_list_Oinject, fact_8_shrK__in__knows, fact_21_parts_OInj, fact_86_set__ConsD, fact_47_msg_Osimps_I48_J, fact_36_rev__swap, fact_53_msg_Osimps_I35_J, fact_17_analz_OInj, fact_24_msg_Osimps_I3_J, fact_37_rev__rev__ident, conj_3, fact_93_Notes__imp__knows, fact_13_Says__imp__analz__Spy, fact_65_set__takeWhileD, fact_58_msg_Osimps_I16_J, fact_90_event_Osimps_I6_J, fact_26_event_Osimps_I1_J, fact_84_not__Cons__self, fact_16_MPair__parts, fact_35_parts__partsD, fact_33_analz__parts, fact_10_sym__shrK, fact_0_spies__evs__rev, fact_40_analz_OFst, fact_75_mem__def, fact_72_analz__Decrypt_H, fact_71_Says__imp__spies, fact_96_ns__shared_ONS3, fact_1_Spy__analz__shrK, help_fNot_1_1_U, fact_69_Says__imp__knows, fact_43_analz__into__parts, fact_88_agent_Osimps_I4_J, fact_80_B__trusts__NS3, fact_29_MPair__analz, fact_20_msg_Osimps_I4_J, fact_12_Says__imp__parts__knows__Spy, help_COMBB_1_1_U, conj_2, fact_56_msg_Osimps_I31_J, fact_34_analz__analzD, conj_7, fact_5_Spy__spies__bad__shrK, fact_31_analz__conj__parts, fact_50_msg_Osimps_I42_J, fact_14_takeWhile__eq__all__conv, fact_52_parts_OBody, fact_44_not__parts__not__analz, fact_39_analz_OSnd, fact_22_parts__idem, fact_94_ns__shared_OOops, fact_27_shrK__injective, fact_2_Spy__see__shrK, fact_91_Server__not__bad, help_fequal_1_1_T, fact_59_msg_Osimps_I12_J, fact_7_B__Issues__A, fact_3_A__trusts__NS5, fact_63_msg_Osimps_I19_J, fact_79_NS4__implies__NS3, fact_46_parts_OFst, help_COMBC_1_1_U, conj_6, fact_76_A__trusts__NS2, conj_1, help_fequal_2_1_T, fact_61_msg_Osimps_I37_J, fact_19_msg_Osimps_I6_J, fact_4_NS3__msg__in__parts__spies, fact_85_not__Cons__self2, fact_18_analz__idem, fact_81_ns__shared_ONS5, fact_49_msg_Osimps_I43_J, fact_73_B__trusts__NS5__lemma, fact_57_msg_Osimps_I17_J, fact_99_unique__session__keys, fact_89_event_Osimps_I7_J, fact_54_msg_Osimps_I34_J, fact_41_msg_Osimps_I41_J, fact_15_set__rev, help_pp_1_1_U, fact_38_symKeys__neq__imp__neq, fact_30_analz__disj__parts, fact_68_analz__impI, conj_4, fact_23_msg_Osimps_I7_J, fact_62_msg_Osimps_I36_J, fact_66_msg_Osimps_I11_J, fact_28_rev__is__rev__conv, fact_51_spies__partsEs_I2_J, fact_92_analz__mono__contra_I2_J, fact_11_Spy__in__bad, fact_64_msg_Osimps_I18_J, fact_74_A__trusts__NS4__lemma, fact_78_A__trusts__NS4, conj_5, fact_70_analz__shrK__Decrypt, conj_0, fact_60_msg_Osimps_I13_J, help_pp_2_1_U, fact_45_parts_OSnd, fact_83_event_Osimps_I3_J, fact_87_agent_Osimps_I5_J, fact_98_Oops__parts__spies, fact_6_A__authenticates__and__keydist__to__B, fact_97_Notes__imp__knows__Spy, fact_42_msg_Osimps_I40_J, fact_32_parts__analz, fact_77_B__trusts__NS5
% 58.48/22.07 % No. of inferences in proof: 236
% 58.48/22.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 21508 ms resp. 20900 ms w/o parsing
% 58.99/22.19 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 58.99/22.19 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------