TSTP Solution File: SWV803_5 by Leo-III---1.7.7

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SWV803_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n005.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 12:18:39 EDT 2023

% Result   : Theorem 53.10s 19.95s
% Output   : Refutation 53.35s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  157
% Syntax   : Number of formulae    :  270 (  84 unt;  46 typ;   0 def)
%            Number of atoms       :  636 ( 149 equ;   0 cnn)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives : 4307 ( 159   ~;  15   |;  42   &;3785   @)
%                                         (  15 <=>; 291  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (   9 avg)
%            Number of types       :    6 (   5 usr)
%            Number of type conns  :   31 (  31   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   46 (  43 usr;  26 con; 0-4 aty)
%            Number of variables   :  724 (   0   ^; 715   !;   4   ?; 724   :)
%                                         (   5  !>;   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(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(used_type,type,
    used: ( list @ event ) > ( fun @ msg @ bool ) ).

thf(cons_type,type,
    cons: 
      !>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).

thf(set_type,type,
    set: 
      !>[TA: $tType] : ( ( list @ TA ) > ( fun @ TA @ bool ) ) ).

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(nS_Sha993195050haredp_type,type,
    nS_Sha993195050haredp: ( list @ event ) > $o ).

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(fTrue_type,type,
    fTrue: 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(nAa_type,type,
    nAa: 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(xa_type,type,
    xa: msg ).

thf(evs5_type,type,
    evs5: list @ event ).

thf(48,axiom,
    ! [A: nat,B: agent1,C: agent1,D: agent1,E: nat,F: list @ event] :
      ( ( nS_Sha993195050haredp @ F )
     => ( ~ ( member @ msg @ ( key @ E ) @ ( used @ F ) )
       => ( ( member @ nat @ E @ symKeys )
         => ( ( member @ event @ ( says @ D @ server @ ( mPair @ ( agent @ C ) @ ( mPair @ ( agent @ B ) @ ( nonce @ A ) ) ) ) @ ( set @ event @ F ) )
           => ( nS_Sha993195050haredp @ ( cons @ event @ ( says @ server @ C @ ( crypt @ ( shrK @ C ) @ ( mPair @ ( nonce @ A ) @ ( mPair @ ( agent @ B ) @ ( mPair @ ( key @ E ) @ ( crypt @ ( shrK @ B ) @ ( mPair @ ( key @ E ) @ ( agent @ C ) ) ) ) ) ) ) ) @ F ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_ns__sharedp_ONS2) ).

thf(284,plain,
    ! [A: nat,B: agent1,C: agent1,D: agent1,E: nat,F: list @ event] :
      ( ( nS_Sha993195050haredp @ F )
     => ( ~ ( member @ msg @ ( key @ E ) @ ( used @ F ) )
       => ( ( member @ nat @ E @ symKeys )
         => ( ( member @ event @ ( says @ D @ server @ ( mPair @ ( agent @ C ) @ ( mPair @ ( agent @ B ) @ ( nonce @ A ) ) ) ) @ ( set @ event @ F ) )
           => ( nS_Sha993195050haredp @ ( cons @ event @ ( says @ server @ C @ ( crypt @ ( shrK @ C ) @ ( mPair @ ( nonce @ A ) @ ( mPair @ ( agent @ B ) @ ( mPair @ ( key @ E ) @ ( crypt @ ( shrK @ B ) @ ( mPair @ ( key @ E ) @ ( agent @ C ) ) ) ) ) ) ) ) @ F ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(41,axiom,
    member @ agent1 @ spy @ bad,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_Spy__in__bad) ).

thf(266,plain,
    member @ agent1 @ spy @ bad,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(91,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/sandbox2/benchmark/theBenchmark.p',fact_24_event_Osimps_I1_J) ).

thf(409,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)],[91]) ).

thf(78,axiom,
    ! [A: list @ event,B: nat,C: agent1,D: msg,E: agent1] :
      ( ( member @ event @ ( says @ server @ E @ ( crypt @ ( shrK @ E ) @ ( mPair @ D @ ( mPair @ ( agent @ C ) @ ( mPair @ ( key @ B ) @ ( crypt @ ( shrK @ C ) @ ( mPair @ ( key @ B ) @ ( agent @ E ) ) ) ) ) ) ) ) @ ( set @ event @ A ) )
     => ( ~ ( member @ agent1 @ E @ bad )
       => ( ~ ( member @ agent1 @ C @ bad )
         => ( ( member @ ( list @ event ) @ A @ nS_Sha254967238shared )
           => ( ! [F: msg] :
                  ~ ( member @ event @ ( notes @ spy @ ( mPair @ D @ ( mPair @ F @ ( key @ B ) ) ) ) @ ( set @ event @ A ) )
             => ~ ( member @ msg @ ( key @ B ) @ ( analz @ ( knows @ spy @ A ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_secrecy__lemma) ).

thf(368,plain,
    ! [A: list @ event,B: nat,C: agent1,D: msg,E: agent1] :
      ( ( member @ event @ ( says @ server @ E @ ( crypt @ ( shrK @ E ) @ ( mPair @ D @ ( mPair @ ( agent @ C ) @ ( mPair @ ( key @ B ) @ ( crypt @ ( shrK @ C ) @ ( mPair @ ( key @ B ) @ ( agent @ E ) ) ) ) ) ) ) ) @ ( set @ event @ A ) )
     => ( ~ ( member @ agent1 @ E @ bad )
       => ( ~ ( member @ agent1 @ C @ bad )
         => ( ( member @ ( list @ event ) @ A @ nS_Sha254967238shared )
           => ( ! [F: msg] :
                  ~ ( member @ event @ ( notes @ spy @ ( mPair @ D @ ( mPair @ F @ ( key @ B ) ) ) ) @ ( set @ event @ A ) )
             => ~ ( member @ msg @ ( key @ B ) @ ( analz @ ( knows @ spy @ A ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(77,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/sandbox2/benchmark/theBenchmark.p',fact_0_Spy__analz__shrK) ).

thf(365,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)],[77]) ).

thf(107,axiom,
    ! [A: fun @ msg @ bool,B: msg,C: msg] :
      ( ( member @ msg @ ( mPair @ C @ B ) @ ( analz @ A ) )
     => ( member @ msg @ C @ ( analz @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_analz_OFst) ).

thf(481,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)],[107]) ).

thf(99,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/sandbox2/benchmark/theBenchmark.p',fact_85_ns__shared_ONS3) ).

thf(449,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)],[99]) ).

thf(43,axiom,
    ! [A: msg,B: nat,C: nat] :
      ( ( key @ C )
     != ( crypt @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_msg_Osimps_I42_J) ).

thf(269,plain,
    ! [A: msg,B: nat,C: nat] :
      ( ( key @ C )
     != ( crypt @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(83,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/sandbox2/benchmark/theBenchmark.p',fact_70_NS4__implies__NS3) ).

thf(385,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)],[83]) ).

thf(8,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/sandbox2/benchmark/theBenchmark.p',fact_2_NS3__msg__in__parts__spies) ).

thf(142,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)],[8]) ).

thf(105,axiom,
    member @ ( list @ event ) @ evs5 @ nS_Sha254967238shared,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).

thf(472,plain,
    member @ ( list @ event ) @ evs5 @ nS_Sha254967238shared,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(68,axiom,
    ! [A: agent1] : ( member @ nat @ ( shrK @ A ) @ symKeys ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_sym__shrK) ).

thf(340,plain,
    ! [A: agent1] : ( member @ nat @ ( shrK @ A ) @ symKeys ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(50,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/sandbox2/benchmark/theBenchmark.p',fact_68_B__trusts__NS5) ).

thf(288,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)],[50]) ).

thf(56,axiom,
    ! [A: agent1,B: msg,C: msg] :
      ( ( mPair @ C @ B )
     != ( agent @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_msg_Osimps_I17_J) ).

thf(301,plain,
    ! [A: agent1,B: msg,C: msg] :
      ( ( mPair @ C @ B )
     != ( agent @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(37,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/sandbox2/benchmark/theBenchmark.p',fact_81_analz__mono__contra_I2_J) ).

thf(257,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)],[37]) ).

thf(4,axiom,
    pp @ fTrue,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).

thf(125,plain,
    pp @ fTrue,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(75,axiom,
    ! [A: msg,B: msg,C: nat] :
      ( ( key @ C )
     != ( mPair @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_msg_Osimps_I40_J) ).

thf(357,plain,
    ! [A: msg,B: msg,C: nat] :
      ( ( key @ C )
     != ( mPair @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(12,axiom,
    ! [A: msg,B: nat,C: agent1,D: nat,E: agent1,F: agent1,G: list @ event] :
      ( ( nS_Sha993195050haredp @ G )
     => ( ( 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 ) )
           => ( nS_Sha993195050haredp @ ( cons @ event @ ( says @ F @ C @ A ) @ G ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_ns__sharedp_ONS3) ).

thf(157,plain,
    ! [A: msg,B: nat,C: agent1,D: nat,E: agent1,F: agent1,G: list @ event] :
      ( ( nS_Sha993195050haredp @ G )
     => ( ( 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 ) )
           => ( nS_Sha993195050haredp @ ( cons @ event @ ( says @ F @ C @ A ) @ G ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(63,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( ( member @ nat @ B @ symKeys )
        <=> ( member @ nat @ A @ symKeys ) )
     => ( B != A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_symKeys__neq__imp__neq) ).

thf(321,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)],[63]) ).

thf(35,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/sandbox2/benchmark/theBenchmark.p',fact_61_Says__imp__knows) ).

thf(253,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)],[35]) ).

thf(71,axiom,
    ~ ( member @ agent1 @ a @ bad ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(348,plain,
    ~ ( member @ agent1 @ a @ bad ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(73,axiom,
    ! [A: list @ event,B: agent1] :
      ( ( member @ agent1 @ B @ bad )
     => ( member @ msg @ ( key @ ( shrK @ B ) ) @ ( knows @ spy @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_Spy__spies__bad__shrK) ).

thf(353,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)],[73]) ).

thf(112,axiom,
    ! [A: fun @ msg @ bool,B: msg] :
      ( ( member @ msg @ B @ ( parts @ ( parts @ A ) ) )
     => ( member @ msg @ B @ ( parts @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_parts__partsD) ).

thf(492,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)],[112]) ).

thf(14,axiom,
    ! [A: list @ event,B: msg,C: nat,D: agent1,E: msg,F: nat,G: agent1] :
      ( ( member @ event @ ( says @ server @ G @ ( crypt @ F @ ( mPair @ E @ ( mPair @ ( agent @ D ) @ ( mPair @ ( key @ C ) @ B ) ) ) ) ) @ ( set @ event @ A ) )
     => ( ! [H: msg] :
            ~ ( member @ event @ ( notes @ spy @ ( mPair @ E @ ( mPair @ H @ ( key @ C ) ) ) ) @ ( set @ event @ A ) )
       => ( ~ ( member @ agent1 @ G @ bad )
         => ( ~ ( member @ agent1 @ D @ bad )
           => ( ( member @ ( list @ event ) @ A @ nS_Sha254967238shared )
             => ~ ( member @ msg @ ( key @ C ) @ ( analz @ ( knows @ spy @ A ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_Spy__not__see__encrypted__key) ).

thf(164,plain,
    ! [A: list @ event,B: msg,C: nat,D: agent1,E: msg,F: nat,G: agent1] :
      ( ( member @ event @ ( says @ server @ G @ ( crypt @ F @ ( mPair @ E @ ( mPair @ ( agent @ D ) @ ( mPair @ ( key @ C ) @ B ) ) ) ) ) @ ( set @ event @ A ) )
     => ( ! [H: msg] :
            ~ ( member @ event @ ( notes @ spy @ ( mPair @ E @ ( mPair @ H @ ( key @ C ) ) ) ) @ ( set @ event @ A ) )
       => ( ~ ( member @ agent1 @ G @ bad )
         => ( ~ ( member @ agent1 @ D @ bad )
           => ( ( member @ ( list @ event ) @ A @ nS_Sha254967238shared )
             => ~ ( member @ msg @ ( key @ C ) @ ( analz @ ( knows @ spy @ A ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(10,axiom,
    ! [A: fun @ msg @ bool,B: msg,C: msg] :
      ( ( member @ msg @ ( mPair @ C @ B ) @ ( parts @ A ) )
     => ( member @ msg @ C @ ( parts @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_parts_OFst) ).

thf(147,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)],[10]) ).

thf(87,axiom,
    ! [A: agent1,B: nat] :
      ( ( key @ B )
     != ( agent @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_msg_Osimps_I13_J) ).

thf(396,plain,
    ! [A: agent1,B: nat] :
      ( ( key @ B )
     != ( agent @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(33,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/sandbox2/benchmark/theBenchmark.p',fact_66_A__trusts__NS4__lemma) ).

thf(243,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)],[33]) ).

thf(58,axiom,
    ~ ( member @ msg @ ( key @ k ) @ ( analz @ ( knows @ spy @ evs5 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_6) ).

thf(307,plain,
    ~ ( member @ msg @ ( key @ k ) @ ( analz @ ( knows @ spy @ evs5 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(100,axiom,
    ! [A: fun @ msg @ bool,B: msg] :
      ( ( member @ msg @ B @ ( analz @ A ) )
     => ( member @ msg @ B @ ( parts @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_analz__into__parts) ).

thf(452,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)],[100]) ).

thf(82,axiom,
    ! [A: agent1,B: nat] :
      ( ( nonce @ B )
     != ( agent @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_msg_Osimps_I11_J) ).

thf(381,plain,
    ! [A: agent1,B: nat] :
      ( ( nonce @ B )
     != ( agent @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(28,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/sandbox2/benchmark/theBenchmark.p',fact_88_unique__session__keys) ).

thf(220,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)],[28]) ).

thf(13,axiom,
    ! [A: msg,B: agent1,C: agent1,D: msg,E: agent1] :
      ( ( notes @ E @ D )
     != ( says @ C @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_event_Osimps_I7_J) ).

thf(160,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)],[13]) ).

thf(54,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/sandbox2/benchmark/theBenchmark.p',fact_82_Notes__imp__knows) ).

thf(297,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)],[54]) ).

thf(90,axiom,
    ! [A: fun @ msg @ bool,B: msg] :
      ( ( member @ msg @ B @ A )
     => ( member @ msg @ B @ ( analz @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_analz_OInj) ).

thf(407,plain,
    ! [A: fun @ msg @ bool,B: msg] :
      ( ( member @ msg @ B @ A )
     => ( member @ msg @ B @ ( analz @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(45,axiom,
    ! [A: agent1,B: msg,C: nat] :
      ( ( crypt @ C @ B )
     != ( agent @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_msg_Osimps_I19_J) ).

thf(275,plain,
    ! [A: agent1,B: msg,C: nat] :
      ( ( crypt @ C @ B )
     != ( agent @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(103,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/sandbox2/benchmark/theBenchmark.p',fact_65_B__trusts__NS5__lemma) ).

thf(467,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)],[103]) ).

thf(29,axiom,
    member @ event @ ( says @ s @ aa @ ( crypt @ ( shrK @ aa ) @ ( mPair @ ( nonce @ nAa ) @ ( mPair @ ( agent @ ba ) @ ( mPair @ ( key @ ka ) @ xa ) ) ) ) ) @ ( set @ event @ evs5 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_5) ).

thf(229,plain,
    member @ event @ ( says @ s @ aa @ ( crypt @ ( shrK @ aa ) @ ( mPair @ ( nonce @ nAa ) @ ( mPair @ ( agent @ ba ) @ ( mPair @ ( key @ ka ) @ xa ) ) ) ) ) @ ( set @ event @ evs5 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(24,axiom,
    ! [A: msg,B: nat,C: msg,D: nat] :
      ( ( ( crypt @ D @ C )
        = ( crypt @ B @ A ) )
    <=> ( ( D = B )
        & ( C = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_msg_Osimps_I7_J) ).

thf(197,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)],[24]) ).

thf(76,axiom,
    ! [A: nat,B: agent1] :
      ( ( agent @ B )
     != ( nonce @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_msg_Osimps_I10_J) ).

thf(361,plain,
    ! [A: nat,B: agent1] :
      ( ( agent @ B )
     != ( nonce @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(102,axiom,
    ! [A: msg,B: msg,C: msg,D: msg] :
      ( ( ( mPair @ D @ C )
        = ( mPair @ B @ A ) )
    <=> ( ( D = B )
        & ( C = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_msg_Osimps_I6_J) ).

thf(456,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)],[102]) ).

thf(89,axiom,
    ! [A: nat,B: nat] :
      ( ( key @ B )
     != ( nonce @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_msg_Osimps_I31_J) ).

thf(403,plain,
    ! [A: nat,B: nat] :
      ( ( key @ B )
     != ( nonce @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(16,axiom,
    ! [A: msg,B: agent1,C: msg,D: agent1,E: agent1] :
      ( ( says @ E @ D @ C )
     != ( notes @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_event_Osimps_I6_J) ).

thf(169,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)],[16]) ).

thf(64,axiom,
    ! [A: nat,B: msg,C: msg] :
      ( ( mPair @ C @ B )
     != ( key @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_msg_Osimps_I41_J) ).

thf(328,plain,
    ! [A: nat,B: msg,C: msg] :
      ( ( mPair @ C @ B )
     != ( key @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(110,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/sandbox2/benchmark/theBenchmark.p',fact_69_A__trusts__NS4) ).

thf(488,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)],[110]) ).

thf(86,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/sandbox2/benchmark/theBenchmark.p',fact_87_Oops__parts__spies) ).

thf(393,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)],[86]) ).

thf(17,axiom,
    ! [A: nat,B: msg,C: msg] :
      ( ( mPair @ C @ B )
     != ( nonce @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_msg_Osimps_I35_J) ).

thf(173,plain,
    ! [A: nat,B: msg,C: msg] :
      ( ( mPair @ C @ B )
     != ( nonce @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(6,axiom,
    ~ ( pp @ fFalse ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).

thf(129,plain,
    ~ ( pp @ fFalse ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(79,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/sandbox2/benchmark/theBenchmark.p',fact_10_Says__imp__parts__knows__Spy) ).

thf(371,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)],[79]) ).

thf(40,axiom,
    ~ ( member @ agent1 @ server @ bad ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_Server__not__bad) ).

thf(264,plain,
    ~ ( member @ agent1 @ server @ bad ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(46,axiom,
    ! [A: nat,B: agent1,C: agent1,D: agent1,E: nat,F: list @ event] :
      ( ( member @ ( list @ event ) @ F @ nS_Sha254967238shared )
     => ( ~ ( member @ msg @ ( key @ E ) @ ( used @ F ) )
       => ( ( member @ nat @ E @ symKeys )
         => ( ( member @ event @ ( says @ D @ server @ ( mPair @ ( agent @ C ) @ ( mPair @ ( agent @ B ) @ ( nonce @ A ) ) ) ) @ ( set @ event @ F ) )
           => ( member @ ( list @ event ) @ ( cons @ event @ ( says @ server @ C @ ( crypt @ ( shrK @ C ) @ ( mPair @ ( nonce @ A ) @ ( mPair @ ( agent @ B ) @ ( mPair @ ( key @ E ) @ ( crypt @ ( shrK @ B ) @ ( mPair @ ( key @ E ) @ ( agent @ C ) ) ) ) ) ) ) ) @ F ) @ nS_Sha254967238shared ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_ns__shared_ONS2) ).

thf(279,plain,
    ! [A: nat,B: agent1,C: agent1,D: agent1,E: nat,F: list @ event] :
      ( ( member @ ( list @ event ) @ F @ nS_Sha254967238shared )
     => ( ~ ( member @ msg @ ( key @ E ) @ ( used @ F ) )
       => ( ( member @ nat @ E @ symKeys )
         => ( ( member @ event @ ( says @ D @ server @ ( mPair @ ( agent @ C ) @ ( mPair @ ( agent @ B ) @ ( nonce @ A ) ) ) ) @ ( set @ event @ F ) )
           => ( member @ ( list @ event ) @ ( cons @ event @ ( says @ server @ C @ ( crypt @ ( shrK @ C ) @ ( mPair @ ( nonce @ A ) @ ( mPair @ ( agent @ B ) @ ( mPair @ ( key @ E ) @ ( crypt @ ( shrK @ B ) @ ( mPair @ ( key @ E ) @ ( agent @ C ) ) ) ) ) ) ) ) @ F ) @ nS_Sha254967238shared ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(53,axiom,
    member @ event @ ( says @ b1 @ aa @ ( crypt @ ka @ ( nonce @ nBa ) ) ) @ ( set @ event @ evs5 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).

thf(296,plain,
    member @ event @ ( says @ b1 @ aa @ ( crypt @ ka @ ( nonce @ nBa ) ) ) @ ( set @ event @ evs5 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(11,axiom,
    ! [A: nat,B: nat] :
      ( ( ( nonce @ B )
        = ( nonce @ A ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_msg_Osimps_I3_J) ).

thf(149,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)],[11]) ).

thf(92,axiom,
    ! [A: msg,B: nat,C: nat] :
      ( ( nonce @ C )
     != ( crypt @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_msg_Osimps_I36_J) ).

thf(423,plain,
    ! [A: msg,B: nat,C: nat] :
      ( ( nonce @ C )
     != ( crypt @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(22,axiom,
    ! [A: msg,B: msg,C: msg,D: nat] :
      ( ( crypt @ D @ C )
     != ( mPair @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_msg_Osimps_I49_J) ).

thf(191,plain,
    ! [A: msg,B: msg,C: msg,D: nat] :
      ( ( crypt @ D @ C )
     != ( mPair @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(49,axiom,
    ! [A: fun @ msg @ bool,B: msg] :
      ( ( member @ msg @ B @ A )
     => ( member @ msg @ B @ ( parts @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_parts_OInj) ).

thf(286,plain,
    ! [A: fun @ msg @ bool,B: msg] :
      ( ( member @ msg @ B @ A )
     => ( member @ msg @ B @ ( parts @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(51,axiom,
    ! [TA: $tType,A: fun @ TA @ bool,B: TA] :
      ( ( member @ TA @ B @ A )
    <=> ( pp @ ( aa1 @ TA @ bool @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_mem__def) ).

thf(291,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)],[51]) ).

thf(47,axiom,
    ! [A: fun @ msg @ bool] :
      ( ( analz @ ( parts @ A ) )
      = ( parts @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_analz__parts) ).

thf(281,plain,
    ! [A: fun @ msg @ bool] :
      ( ( analz @ ( parts @ A ) )
      = ( parts @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(38,axiom,
    ! [A: fun @ msg @ bool,B: msg,C: nat] :
      ( ( member @ msg @ ( crypt @ C @ B ) @ ( parts @ A ) )
     => ( member @ msg @ B @ ( parts @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_parts_OBody) ).

thf(259,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)],[38]) ).

thf(97,axiom,
    ! [A: list @ event,B: agent1] : ( member @ msg @ ( key @ ( shrK @ B ) ) @ ( used @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_shrK__in__used) ).

thf(445,plain,
    ! [A: list @ event,B: agent1] : ( member @ msg @ ( key @ ( shrK @ B ) ) @ ( used @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(60,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/sandbox2/benchmark/theBenchmark.p',fact_71_B__trusts__NS3) ).

thf(313,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)],[60]) ).

thf(66,axiom,
    spy != server,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_agent_Osimps_I5_J) ).

thf(335,plain,
    spy != server,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(31,axiom,
    ! [A: nat,B: msg,C: nat] :
      ( ( crypt @ C @ B )
     != ( key @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_msg_Osimps_I43_J) ).

thf(236,plain,
    ! [A: nat,B: msg,C: nat] :
      ( ( crypt @ C @ B )
     != ( key @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(72,axiom,
    server != spy,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_agent_Osimps_I4_J) ).

thf(350,plain,
    server != spy,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(1,conjecture,
    ( ~ ( member @ msg @ ( crypt @ ( shrK @ a ) @ ( mPair @ ( nonce @ na ) @ ( mPair @ ( agent @ b ) @ ( mPair @ ( key @ k ) @ x ) ) ) ) @ ( parts @ ( knows @ spy @ evs5 ) ) )
    | ( k != ka )
    | ( nb != nBa )
    | ( ( a = aa )
      & ( b = ba ) )
    | ( member @ event @ ( says @ a @ b @ ( crypt @ ka @ ( mPair @ ( nonce @ nBa ) @ ( nonce @ nBa ) ) ) ) @ ( set @ event @ evs5 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_8) ).

thf(2,negated_conjecture,
    ~ ( ~ ( member @ msg @ ( crypt @ ( shrK @ a ) @ ( mPair @ ( nonce @ na ) @ ( mPair @ ( agent @ b ) @ ( mPair @ ( key @ k ) @ x ) ) ) ) @ ( parts @ ( knows @ spy @ evs5 ) ) )
      | ( k != ka )
      | ( nb != nBa )
      | ( ( a = aa )
        & ( b = ba ) )
      | ( member @ event @ ( says @ a @ b @ ( crypt @ ka @ ( mPair @ ( nonce @ nBa ) @ ( nonce @ nBa ) ) ) ) @ ( set @ event @ evs5 ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(113,plain,
    ~ ( ~ ( member @ msg @ ( crypt @ ( shrK @ a ) @ ( mPair @ ( nonce @ na ) @ ( mPair @ ( agent @ b ) @ ( mPair @ ( key @ k ) @ x ) ) ) ) @ ( parts @ ( knows @ spy @ evs5 ) ) )
      | ( k != ka )
      | ( nb != nBa )
      | ( ( a = aa )
        & ( b = ba ) )
      | ( member @ event @ ( says @ a @ b @ ( crypt @ ka @ ( mPair @ ( nonce @ nBa ) @ ( nonce @ nBa ) ) ) ) @ ( set @ event @ evs5 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(81,axiom,
    ! [A: nat,B: msg,C: nat] :
      ( ( crypt @ C @ B )
     != ( nonce @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_msg_Osimps_I37_J) ).

thf(377,plain,
    ! [A: nat,B: msg,C: nat] :
      ( ( crypt @ C @ B )
     != ( nonce @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(30,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/sandbox2/benchmark/theBenchmark.p',fact_27_analz__disj__parts) ).

thf(230,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)],[30]) ).

thf(34,axiom,
    ! [A: agent1,B: agent1] :
      ( ( ( shrK @ B )
        = ( shrK @ A ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_shrK__injective) ).

thf(245,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)],[34]) ).

thf(62,axiom,
    ! [A: fun @ msg @ bool,B: msg,C: nat] :
      ( ( member @ msg @ ( crypt @ C @ B ) @ ( parts @ A ) )
     => ( member @ msg @ B @ ( parts @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_spies__partsEs_I2_J) ).

thf(318,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)],[62]) ).

thf(25,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/sandbox2/benchmark/theBenchmark.p',fact_5_B__Issues__A) ).

thf(208,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)],[25]) ).

thf(84,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/sandbox2/benchmark/theBenchmark.p',fact_1_Spy__see__shrK) ).

thf(387,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)],[84]) ).

thf(27,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/sandbox2/benchmark/theBenchmark.p',fact_28_analz__conj__parts) ).

thf(213,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)],[27]) ).

thf(108,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/sandbox2/benchmark/theBenchmark.p',fact_12_MPair__parts) ).

thf(483,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)],[108]) ).

thf(32,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/sandbox2/benchmark/theBenchmark.p',fact_26_MPair__analz) ).

thf(240,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)],[32]) ).

thf(55,axiom,
    ! [A: fun @ msg @ bool,B: msg] :
      ( ( member @ msg @ B @ ( analz @ ( analz @ A ) ) )
     => ( member @ msg @ B @ ( analz @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_analz__analzD) ).

thf(299,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)],[55]) ).

thf(42,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/sandbox2/benchmark/theBenchmark.p',fact_84_analz__mono__contra_I1_J) ).

thf(267,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)],[42]) ).

thf(94,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/sandbox2/benchmark/theBenchmark.p',fact_4_A__authenticates__and__keydist__to__B) ).

thf(431,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)],[94]) ).

thf(15,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/sandbox2/benchmark/theBenchmark.p',fact_83_ns__shared_OOops) ).

thf(167,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)],[15]) ).

thf(106,axiom,
    ! [A: agent1,B: agent1] :
      ( ( ( agent @ B )
        = ( agent @ A ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_msg_Osimps_I1_J) ).

thf(473,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)],[106]) ).

thf(80,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/sandbox2/benchmark/theBenchmark.p',fact_63_Says__imp__spies) ).

thf(374,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)],[80]) ).

thf(36,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/sandbox2/benchmark/theBenchmark.p',fact_72_ns__shared_ONS5) ).

thf(255,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)],[36]) ).

thf(69,axiom,
    ! [A: nat,B: agent1] :
      ( ( agent @ B )
     != ( key @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_msg_Osimps_I12_J) ).

thf(342,plain,
    ! [A: nat,B: agent1] :
      ( ( agent @ B )
     != ( key @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(74,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/sandbox2/benchmark/theBenchmark.p',fact_64_analz__Decrypt_H) ).

thf(355,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)],[74]) ).

thf(9,axiom,
    ! [A: msg,B: agent1,C: nat,D: agent1,E: nat,F: agent1,G: agent1,H: nat,I: list @ event] :
      ( ( nS_Sha993195050haredp @ I )
     => ( ( 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 ) )
           => ( nS_Sha993195050haredp @ ( cons @ event @ ( says @ F @ B @ ( crypt @ H @ ( mPair @ ( nonce @ E ) @ ( nonce @ E ) ) ) ) @ I ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_ns__sharedp_ONS5) ).

thf(145,plain,
    ! [A: msg,B: agent1,C: nat,D: agent1,E: nat,F: agent1,G: agent1,H: nat,I: list @ event] :
      ( ( nS_Sha993195050haredp @ I )
     => ( ( 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 ) )
           => ( nS_Sha993195050haredp @ ( cons @ event @ ( says @ F @ B @ ( crypt @ H @ ( mPair @ ( nonce @ E ) @ ( nonce @ E ) ) ) ) @ I ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(67,axiom,
    ! [A: fun @ msg @ bool,B: msg] :
      ( ~ ( member @ msg @ B @ ( parts @ A ) )
     => ~ ( member @ msg @ B @ ( analz @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_not__parts__not__analz) ).

thf(338,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)],[67]) ).

thf(18,axiom,
    ! [A: list @ event] :
      ( ( nS_Sha993195050haredp @ A )
    <=> ( member @ ( list @ event ) @ A @ nS_Sha254967238shared ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_ns__sharedp__ns__shared__eq) ).

thf(177,plain,
    ! [A: list @ event] :
      ( ( ( nS_Sha993195050haredp @ A )
       => ( member @ ( list @ event ) @ A @ nS_Sha254967238shared ) )
      & ( ( member @ ( list @ event ) @ A @ nS_Sha254967238shared )
       => ( nS_Sha993195050haredp @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(19,axiom,
    ! [A: nat,B: nat] :
      ( ( nonce @ B )
     != ( key @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_msg_Osimps_I30_J) ).

thf(182,plain,
    ! [A: nat,B: nat] :
      ( ( nonce @ B )
     != ( key @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(85,axiom,
    ! [A: fun @ msg @ bool,B: msg,C: msg] :
      ( ( member @ msg @ ( mPair @ C @ B ) @ ( parts @ A ) )
     => ( member @ msg @ B @ ( parts @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_parts_OSnd) ).

thf(390,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)],[85]) ).

thf(20,axiom,
    ! [A: msg,B: msg,C: agent1] :
      ( ( agent @ C )
     != ( mPair @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_msg_Osimps_I16_J) ).

thf(186,plain,
    ! [A: msg,B: msg,C: agent1] :
      ( ( agent @ C )
     != ( mPair @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(95,axiom,
    ! [A: msg,B: nat,C: agent1] :
      ( ( agent @ C )
     != ( crypt @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_msg_Osimps_I18_J) ).

thf(433,plain,
    ! [A: msg,B: nat,C: agent1] :
      ( ( agent @ C )
     != ( crypt @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(70,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/sandbox2/benchmark/theBenchmark.p',fact_86_Notes__imp__knows__Spy) ).

thf(346,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)],[70]) ).

thf(98,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/sandbox2/benchmark/theBenchmark.p',fact_67_A__trusts__NS2) ).

thf(447,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)],[98]) ).

thf(61,axiom,
    ! [A: fun @ msg @ bool,B: msg,C: msg] :
      ( ( member @ msg @ ( mPair @ C @ B ) @ ( analz @ A ) )
     => ( member @ msg @ B @ ( analz @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_analz_OSnd) ).

thf(315,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)],[61]) ).

thf(39,axiom,
    ! [A: msg,B: nat,C: nat,D: nat,E: agent1,F: agent1,G: list @ event] :
      ( ( nS_Sha993195050haredp @ G )
     => ( ( 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 ) )
         => ( nS_Sha993195050haredp @ ( cons @ event @ ( notes @ spy @ ( mPair @ ( nonce @ B ) @ ( mPair @ ( nonce @ C ) @ ( key @ D ) ) ) ) @ G ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_ns__sharedp_OOops) ).

thf(262,plain,
    ! [A: msg,B: nat,C: nat,D: nat,E: agent1,F: agent1,G: list @ event] :
      ( ( nS_Sha993195050haredp @ G )
     => ( ( 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 ) )
         => ( nS_Sha993195050haredp @ ( cons @ event @ ( notes @ spy @ ( mPair @ ( nonce @ B ) @ ( mPair @ ( nonce @ C ) @ ( key @ D ) ) ) ) @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(21,axiom,
    member @ nat @ ka @ symKeys,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3) ).

thf(190,plain,
    member @ nat @ ka @ symKeys,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(44,axiom,
    ! [A: list @ event,B: msg] :
      ( ( member @ msg @ B @ ( parts @ ( knows @ spy @ A ) ) )
     => ( member @ msg @ B @ ( used @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_usedI) ).

thf(273,plain,
    ! [A: list @ event,B: msg] :
      ( ( member @ msg @ B @ ( parts @ ( knows @ spy @ A ) ) )
     => ( member @ msg @ B @ ( used @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(57,axiom,
    ( ( member @ msg @ ( crypt @ ( shrK @ a ) @ ( mPair @ ( nonce @ na ) @ ( mPair @ ( agent @ b ) @ ( mPair @ ( key @ k ) @ x ) ) ) ) @ ( parts @ ( knows @ spy @ evs5 ) ) )
   => ( ( member @ msg @ ( crypt @ k @ ( mPair @ ( nonce @ nb ) @ ( nonce @ nb ) ) ) @ ( parts @ ( knows @ spy @ evs5 ) ) )
     => ( member @ event @ ( says @ a @ b @ ( crypt @ k @ ( mPair @ ( nonce @ nb ) @ ( nonce @ nb ) ) ) ) @ ( set @ event @ evs5 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_7) ).

thf(305,plain,
    ( ( member @ msg @ ( crypt @ ( shrK @ a ) @ ( mPair @ ( nonce @ na ) @ ( mPair @ ( agent @ b ) @ ( mPair @ ( key @ k ) @ x ) ) ) ) @ ( parts @ ( knows @ spy @ evs5 ) ) )
   => ( ( member @ msg @ ( crypt @ k @ ( mPair @ ( nonce @ nb ) @ ( nonce @ nb ) ) ) @ ( parts @ ( knows @ spy @ evs5 ) ) )
     => ( member @ event @ ( says @ a @ b @ ( crypt @ k @ ( mPair @ ( nonce @ nb ) @ ( nonce @ nb ) ) ) ) @ ( set @ event @ evs5 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(26,axiom,
    ! [A: fun @ msg @ bool] :
      ( ( parts @ ( analz @ A ) )
      = ( parts @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_parts__analz) ).

thf(210,plain,
    ! [A: fun @ msg @ bool] :
      ( ( parts @ ( analz @ A ) )
      = ( parts @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(23,axiom,
    ~ ( member @ agent1 @ b @ bad ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).

thf(195,plain,
    ~ ( member @ agent1 @ b @ bad ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(96,axiom,
    ! [A: nat,B: nat] :
      ( ( ( key @ B )
        = ( key @ A ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_msg_Osimps_I4_J) ).

thf(437,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)],[96]) ).

thf(88,axiom,
    ! [A: list @ event,B: msg,C: msg] :
      ( ( member @ msg @ ( mPair @ C @ B ) @ ( used @ A ) )
     => ~ ( ( member @ msg @ C @ ( used @ A ) )
         => ~ ( member @ msg @ B @ ( used @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_MPair__used) ).

thf(400,plain,
    ! [A: list @ event,B: msg,C: msg] :
      ( ( member @ msg @ ( mPair @ C @ B ) @ ( used @ A ) )
     => ~ ( ( member @ msg @ C @ ( used @ A ) )
         => ~ ( member @ msg @ B @ ( used @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(52,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/sandbox2/benchmark/theBenchmark.p',fact_7_Crypt__Spy__analz__bad) ).

thf(294,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)],[52]) ).

thf(5,axiom,
    ! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
      ( ! [C: TA] :
          ( ( aa1 @ TA @ TB @ B @ C )
          = ( aa1 @ TA @ TB @ A @ C ) )
     => ( B = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_ext) ).

thf(126,plain,
    ! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
      ( ! [C: TA] :
          ( ( aa1 @ TA @ TB @ B @ C )
          = ( aa1 @ TA @ TB @ A @ C ) )
     => ( B = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(65,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/sandbox2/benchmark/theBenchmark.p',fact_11_Says__imp__analz__Spy) ).

thf(332,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)],[65]) ).

thf(93,axiom,
    ! [A: msg,B: nat,C: msg,D: msg] :
      ( ( mPair @ D @ C )
     != ( crypt @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_msg_Osimps_I48_J) ).

thf(427,plain,
    ! [A: msg,B: nat,C: msg,D: msg] :
      ( ( mPair @ D @ C )
     != ( crypt @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(7,axiom,
    ! [A: msg,B: agent1,C: msg,D: agent1] :
      ( ( ( notes @ D @ C )
        = ( notes @ B @ A ) )
    <=> ( ( D = B )
        & ( C = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_event_Osimps_I3_J) ).

thf(131,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(109,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/sandbox2/benchmark/theBenchmark.p',fact_62_analz__shrK__Decrypt) ).

thf(486,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)],[109]) ).

thf(3,axiom,
    ! [A: fun @ msg @ bool] :
      ( ( analz @ ( analz @ A ) )
      = ( analz @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_analz__idem) ).

thf(122,plain,
    ! [A: fun @ msg @ bool] :
      ( ( analz @ ( analz @ A ) )
      = ( analz @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(104,axiom,
    ! [A: fun @ msg @ bool] :
      ( ( parts @ ( parts @ A ) )
      = ( parts @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_parts__idem) ).

thf(469,plain,
    ! [A: fun @ msg @ bool] :
      ( ( parts @ ( parts @ A ) )
      = ( parts @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(59,axiom,
    ! [A: msg,B: msg,C: nat] :
      ( ( nonce @ C )
     != ( mPair @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_msg_Osimps_I34_J) ).

thf(309,plain,
    ! [A: msg,B: msg,C: nat] :
      ( ( nonce @ C )
     != ( mPair @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(111,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/sandbox2/benchmark/theBenchmark.p',fact_60_analz__impI) ).

thf(491,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(101,axiom,
    ! [A: list @ event,B: agent1] : ( member @ msg @ ( key @ ( shrK @ B ) ) @ ( knows @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_shrK__in__knows) ).

thf(454,plain,
    ! [A: list @ event,B: agent1] : ( member @ msg @ ( key @ ( shrK @ B ) ) @ ( knows @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(31713,plain,
    $false,
    inference(cvc4,[status(thm)],[284,266,409,368,365,481,449,269,385,142,472,340,288,301,257,125,357,157,321,253,348,353,492,164,147,396,243,307,452,381,220,160,297,407,275,467,229,197,361,456,403,169,328,488,393,173,129,371,264,279,296,149,423,191,286,291,281,259,445,313,335,236,350,113,377,230,245,318,208,387,213,483,240,299,267,431,167,473,374,255,342,355,145,338,177,182,390,186,433,346,447,315,262,190,273,305,210,195,437,400,294,126,332,427,131,486,122,469,309,491,454]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWV803_5 : TPTP v8.1.2. Released v6.0.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.35  % Computer : n005.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Fri May 19 02:41:54 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.93/0.83  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.39/1.03  % [INFO] 	 Parsing done (200ms). 
% 1.39/1.04  % [INFO] 	 Running in sequential loop mode. 
% 2.22/1.24  % [INFO] 	 eprover registered as external prover. 
% 2.22/1.24  % [INFO] 	 cvc4 registered as external prover. 
% 2.22/1.24  % [INFO] 	 Scanning for conjecture ... 
% 2.57/1.35  % [INFO] 	 Found a conjecture and 110 axioms. Running axiom selection ... 
% 2.99/1.44  % [INFO] 	 Axiom selection finished. Selected 110 axioms (removed 0 axioms). 
% 3.37/1.59  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 3.37/1.61  % [INFO] 	 Type checking passed. 
% 3.37/1.61  % [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 ... 
% 53.10/19.94  % External prover 'cvc4' found a proof!
% 53.10/19.95  % [INFO] 	 Killing All external provers ... 
% 53.10/19.95  % Time passed: 19435ms (effective reasoning time: 18904ms)
% 53.10/19.95  % 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)>
% 53.10/19.95  % Axioms used in derivation (110): fact_57_msg_Osimps_I18_J, fact_62_analz__shrK__Decrypt, fact_74_agent_Osimps_I5_J, fact_92_ns__sharedp_ONS5, fact_81_analz__mono__contra_I2_J, fact_73_event_Osimps_I3_J, fact_15_analz_OInj, fact_18_msg_Osimps_I4_J, fact_29_analz__analzD, fact_38_parts_OSnd, fact_99_usedI, fact_17_msg_Osimps_I6_J, fact_68_B__trusts__NS5, fact_46_msg_Osimps_I35_J, fact_52_msg_Osimps_I12_J, fact_1_Spy__see__shrK, fact_26_MPair__analz, fact_97_MPair__used, fact_94_ns__sharedp_ONS3, fact_7_Crypt__Spy__analz__bad, conj_3, fact_33_analz_OFst, fact_72_ns__shared_ONS5, fact_19_parts_OInj, fact_63_Says__imp__spies, fact_51_msg_Osimps_I16_J, fact_21_msg_Osimps_I7_J, fact_79_event_Osimps_I6_J, fact_12_MPair__parts, fact_93_ns__sharedp__ns__shared__eq, fact_49_msg_Osimps_I31_J, fact_95_ns__sharedp_ONS2, fact_54_msg_Osimps_I37_J, fact_16_analz__idem, fact_71_B__trusts__NS3, fact_85_ns__shared_ONS3, fact_40_msg_Osimps_I48_J, fact_83_ns__shared_OOops, fact_42_msg_Osimps_I43_J, fact_96_ns__shared_ONS2, fact_24_event_Osimps_I1_J, fact_28_analz__conj__parts, fact_88_unique__session__keys, fact_82_Notes__imp__knows, fact_48_msg_Osimps_I30_J, fact_45_parts_OBody, conj_2, fact_11_Says__imp__analz__Spy, fact_50_msg_Osimps_I17_J, fact_36_msg_Osimps_I41_J, fact_61_Says__imp__knows, fact_27_analz__disj__parts, fact_80_Server__not__bad, conj_7, fact_30_parts__partsD, fact_53_msg_Osimps_I13_J, fact_55_msg_Osimps_I36_J, fact_65_B__trusts__NS5__lemma, fact_35_not__parts__not__analz, fact_59_msg_Osimps_I10_J, fact_66_A__trusts__NS4__lemma, fact_10_Says__imp__parts__knows__Spy, fact_60_analz__impI, fact_5_B__Issues__A, fact_58_msg_Osimps_I11_J, fact_98_shrK__in__used, fact_39_parts_OFst, fact_84_analz__mono__contra_I1_J, fact_76_mem__def, fact_37_msg_Osimps_I40_J, fact_32_analz_OSnd, fact_13_analz__parts, fact_34_analz__into__parts, conj_6, fact_70_NS4__implies__NS3, fact_77_agent_Osimps_I4_J, fact_9_Spy__in__bad, conj_1, fact_23_msg_Osimps_I1_J, fact_89_secrecy__lemma, fact_69_A__trusts__NS4, fact_2_NS3__msg__in__parts__spies, fact_14_parts__analz, fact_90_Spy__not__see__encrypted__key, fact_64_analz__Decrypt_H, fact_78_event_Osimps_I7_J, help_pp_1_1_U, fact_56_msg_Osimps_I19_J, fact_8_sym__shrK, conj_4, fact_41_msg_Osimps_I49_J, fact_86_Notes__imp__knows__Spy, fact_6_shrK__in__knows, fact_67_A__trusts__NS2, fact_75_ext, fact_31_symKeys__neq__imp__neq, conj_5, fact_20_parts__idem, fact_44_spies__partsEs_I2_J, fact_47_msg_Osimps_I34_J, help_pp_2_1_U, fact_0_Spy__analz__shrK, fact_43_msg_Osimps_I42_J, conj_0, fact_3_Spy__spies__bad__shrK, fact_87_Oops__parts__spies, fact_91_ns__sharedp_OOops, fact_25_shrK__injective, fact_22_msg_Osimps_I3_J, fact_4_A__authenticates__and__keydist__to__B
% 53.10/19.95  % No. of inferences in proof: 224
% 53.10/19.95  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 19435 ms resp. 18904 ms w/o parsing
% 53.35/20.02  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 53.35/20.02  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------