TSTP Solution File: ITP091^2 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : ITP091^2 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n009.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 : Mon May 20 22:22:49 EDT 2024

% Result   : Theorem 33.69s 19.28s
% Output   : Refutation 34.51s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  322
% Syntax   : Number of formulae    :  584 ( 182 unt;  62 typ;   0 def)
%            Number of atoms       : 2464 ( 534 equ;   8 cnn)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives : 8858 ( 437   ~;  72   |; 180   &;7109   @)
%                                         (   0 <=>;1060  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   8 avg)
%            Number of types       :    8 (   7 usr)
%            Number of type conns  :  172 ( 172   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   60 (  57 usr;   9 con; 0-4 aty)
%            Number of variables   : 1804 (  90   ^1638   !;  58   ?;1804   :)
%                                         (  18  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(secrecy_Expression_type,type,
    secrecy_Expression: $tType ).

thf(secrecy_Secrets_type,type,
    secrecy_Secrets: $tType ).

thf(secrecy_specID_type,type,
    secrecy_specID: $tType ).

thf(secrecy_chanID_type,type,
    secrecy_chanID: $tType ).

thf(secrecy_Keys_type,type,
    secrecy_Keys: $tType ).

thf(secrecy_KS_type,type,
    secrecy_KS: $tType ).

thf(nat_type,type,
    nat: $tType ).

thf(bounded_lattice_type,type,
    bounded_lattice: 
      !>[TA: $tType] : $o ).

thf(bot_type,type,
    bot: 
      !>[TA: $tType] : $o ).

thf(ord_type,type,
    ord: 
      !>[TA: $tType] : $o ).

thf(linorder_type,type,
    linorder: 
      !>[TA: $tType] : $o ).

thf(preorder_type,type,
    preorder: 
      !>[TA: $tType] : $o ).

thf(bounde1808546759up_bot_type,type,
    bounde1808546759up_bot: 
      !>[TA: $tType] : $o ).

thf(localSecrets_type,type,
    localSecrets: secrecy_specID > ( set @ secrecy_KS ) ).

thf(knowle1667810483orrect_type,type,
    knowle1667810483orrect: secrecy_specID > secrecy_KS > $o ).

thf(knowle1437066798e_know_type,type,
    knowle1437066798e_know: secrecy_specID > secrecy_KS > $o ).

thf(sup_sup_type,type,
    sup_sup: 
      !>[TA: $tType] : ( TA > TA > TA ) ).

thf(mem_type,type,
    mem: 
      !>[TA: $tType] : ( TA > ( list @ TA ) > $o ) ).

thf(bot_bot_type,type,
    bot_bot: 
      !>[TA: $tType] : TA ).

thf(ord_less_eq_type,type,
    ord_less_eq: 
      !>[TA: $tType] : ( TA > TA > $o ) ).

thf(correctCompositionKS_type,type,
    correctCompositionKS: secrecy_specID > $o ).

thf(eout_type,type,
    eout: secrecy_specID > secrecy_Expression > $o ).

thf(eoutM_type,type,
    eoutM: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).

thf(exprChannel_type,type,
    exprChannel: secrecy_chanID > secrecy_Expression > $o ).

thf(ine_type,type,
    ine: secrecy_specID > secrecy_Expression > $o ).

thf(ineM_type,type,
    ineM: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).

thf(ine_exprChannelSet_type,type,
    ine_exprChannelSet: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).

thf(ine_ex1303305700Single_type,type,
    ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).

thf(notSpe1586871396tsExpr_type,type,
    notSpe1586871396tsExpr: secrecy_specID > ( list @ secrecy_Expression ) > $o ).

thf(out_exprChannelSet_type,type,
    out_exprChannelSet: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).

thf(out_ex985543062Single_type,type,
    out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).

thf(specKeys_type,type,
    specKeys: secrecy_specID > ( set @ secrecy_Keys ) ).

thf(specKeysSecrets_type,type,
    specKeysSecrets: secrecy_specID > ( set @ secrecy_KS ) ).

thf(specSecrets_type,type,
    specSecrets: secrecy_specID > ( set @ secrecy_Secrets ) ).

thf(secrecy_kE_type,type,
    secrecy_kE: secrecy_Keys > secrecy_Expression ).

thf(secrecy_sE_type,type,
    secrecy_sE: secrecy_Secrets > secrecy_Expression ).

thf(secrec1016742679ession_type,type,
    secrec1016742679ession: secrecy_KS > secrecy_Expression ).

thf(secrecy_case_KS_type,type,
    secrecy_case_KS: 
      !>[TA: $tType] : ( ( secrecy_Keys > TA ) > ( secrecy_Secrets > TA ) > secrecy_KS > TA ) ).

thf(secrecy_kKS_type,type,
    secrecy_kKS: secrecy_Keys > secrecy_KS ).

thf(secrecy_rec_KS_type,type,
    secrecy_rec_KS: 
      !>[TA: $tType] : ( ( secrecy_Keys > TA ) > ( secrecy_Secrets > TA ) > secrecy_KS > TA ) ).

thf(secrecy_sKS_type,type,
    secrecy_sKS: secrecy_Secrets > secrecy_KS ).

thf(collect_type,type,
    collect: 
      !>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).

thf(insert_type,type,
    insert: 
      !>[TA: $tType] : ( TA > ( set @ TA ) > ( set @ TA ) ) ).

thf(is_empty_type,type,
    is_empty: 
      !>[TA: $tType] : ( ( set @ TA ) > $o ) ).

thf(is_singleton_type,type,
    is_singleton: 
      !>[TA: $tType] : ( ( set @ TA ) > $o ) ).

thf(the_elem_type,type,
    the_elem: 
      !>[TA: $tType] : ( ( set @ TA ) > TA ) ).

thf(correctCompositionIn_type,type,
    correctCompositionIn: secrecy_specID > $o ).

thf(correc965049635ionLoc_type,type,
    correc965049635ionLoc: secrecy_specID > $o ).

thf(correc990227761ionOut_type,type,
    correc990227761ionOut: secrecy_specID > $o ).

thf(inStream_type,type,
    inStream: secrecy_specID > ( set @ secrecy_chanID ) > $o ).

thf(ins_type,type,
    ins: secrecy_specID > ( set @ secrecy_chanID ) ).

thf(loc_type,type,
    loc: secrecy_specID > ( set @ secrecy_chanID ) ).

thf(locStream_type,type,
    locStream: secrecy_specID > ( set @ secrecy_chanID ) > $o ).

thf(out_type,type,
    out: secrecy_specID > ( set @ secrecy_chanID ) ).

thf(outStream_type,type,
    outStream: secrecy_specID > ( set @ secrecy_chanID ) > $o ).

thf(subcomponents_type,type,
    subcomponents: secrecy_specID > ( set @ secrecy_specID ) ).

thf(member_type,type,
    member: 
      !>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).

thf(p_type,type,
    p: secrecy_specID ).

thf(pq_type,type,
    pq: secrecy_specID ).

thf(q_type,type,
    q: secrecy_specID ).

thf(m_type,type,
    m: secrecy_KS ).

thf(secret_type,type,
    secret: secrecy_Secrets ).

thf(174,axiom,
    ! [TA: $tType] :
      ( ( bot_bot @ ( TA > $o ) )
      = ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_bot__empty__eq) ).

thf(809,plain,
    ! [TA: $tType] :
      ( ( bot_bot @ ( TA > $o ) )
      = ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(75,axiom,
    ! [TA: $tType] :
      ( ( bounde1808546759up_bot @ TA )
     => ! [A: TA] :
          ( ( sup_sup @ TA @ A @ ( bot_bot @ TA ) )
          = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_sup__bot__right) ).

thf(479,plain,
    ! [TA: $tType] :
      ( ( bounde1808546759up_bot @ TA )
     => ! [A: TA] :
          ( ( sup_sup @ TA @ A @ ( bot_bot @ TA ) )
          = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(28,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB )
     => ( ( ord_less_eq @ ( TA > TB ) )
        = ( ^ [A: TA > TB,B: TA > TB] :
            ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_le__fun__def) ).

thf(347,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB )
     => ( ( ord_less_eq @ ( TA > TB ) )
        = ( ^ [A: TA > TB,B: TA > TB] :
            ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(182,axiom,
    ! [TA: $tType] :
      ( ( ord_less_eq @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
          ! [C: TA] :
            ( ( member @ TA @ C @ A )
           => ( member @ TA @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_subset__iff) ).

thf(846,plain,
    ! [TA: $tType] :
      ( ( ord_less_eq @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
          ! [C: TA] :
            ( ( member @ TA @ C @ A )
           => ( member @ TA @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(197,axiom,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ( ine @ A @ B )
     => ( ~ ( ine @ C @ B )
       => ( ( ( subcomponents @ D )
            = ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
         => ( ( correctCompositionIn @ D )
           => ( ? [E: secrecy_chanID] :
                  ( ( ine_ex1303305700Single @ A @ E @ B )
                  & ( member @ secrecy_chanID @ E @ ( loc @ D ) ) )
             => ~ ( ine @ D @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_TBtheorem4a__notP1) ).

thf(909,plain,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ( ine @ A @ B )
     => ( ~ ( ine @ C @ B )
       => ( ( ( subcomponents @ D )
            = ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
         => ( ( correctCompositionIn @ D )
           => ( ? [E: secrecy_chanID] :
                  ( ( ine_ex1303305700Single @ A @ E @ B )
                  & ( member @ secrecy_chanID @ E @ ( loc @ D ) ) )
             => ~ ( ine @ D @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(194,axiom,
    ! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
      ( ( eoutM @ A @ B @ C )
     => ( ~ ( eoutM @ D @ B @ C )
       => ( ( ( subcomponents @ E )
            = ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
         => ( ( correc990227761ionOut @ E )
           => ( ? [F: secrecy_chanID] :
                  ( ( out_ex985543062Single @ A @ F @ C )
                  & ( member @ secrecy_chanID @ F @ B )
                  & ( member @ secrecy_chanID @ F @ ( loc @ E ) ) )
             => ~ ( eoutM @ E @ B @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_TBtheorem5b__notP1) ).

thf(893,plain,
    ! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
      ( ( eoutM @ A @ B @ C )
     => ( ~ ( eoutM @ D @ B @ C )
       => ( ( ( subcomponents @ E )
            = ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
         => ( ( correc990227761ionOut @ E )
           => ( ? [F: secrecy_chanID] :
                  ( ( out_ex985543062Single @ A @ F @ C )
                  & ( member @ secrecy_chanID @ F @ B )
                  & ( member @ secrecy_chanID @ F @ ( loc @ E ) ) )
             => ~ ( eoutM @ E @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(209,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correc965049635ionLoc @ A )
       => ( ( correctCompositionKS @ A )
         => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ B ) )
           => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ C ) )
             => ( ~ ( ine @ B @ ( secrecy_kE @ D ) )
               => ( ~ ( ine @ C @ ( secrecy_kE @ D ) )
                 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( sup_sup @ ( set @ secrecy_KS ) @ ( localSecrets @ B ) @ ( localSecrets @ C ) ) )
                   => ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_LocalSecretsComposition__neg__k) ).

thf(962,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correc965049635ionLoc @ A )
       => ( ( correctCompositionKS @ A )
         => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ B ) )
           => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ C ) )
             => ( ~ ( ine @ B @ ( secrecy_kE @ D ) )
               => ( ~ ( ine @ C @ ( secrecy_kE @ D ) )
                 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( sup_sup @ ( set @ secrecy_KS ) @ ( localSecrets @ B ) @ ( localSecrets @ C ) ) )
                   => ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(69,axiom,
    ! [A: secrecy_specID,B: secrecy_Keys] :
      ( ~ ( knowle1437066798e_know @ A @ ( secrecy_kKS @ B ) )
     => ~ ( ine @ A @ ( secrecy_kE @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_not__know__k__not__ine) ).

thf(468,plain,
    ! [A: secrecy_specID,B: secrecy_Keys] :
      ( ~ ( knowle1437066798e_know @ A @ ( secrecy_kKS @ B ) )
     => ~ ( ine @ A @ ( secrecy_kE @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(222,axiom,
    ! [A: secrecy_specID,B: secrecy_Secrets] :
      ( ( knowle1437066798e_know @ A @ ( secrecy_sKS @ B ) )
      = ( ( ine @ A @ ( secrecy_sE @ B ) )
        | ( member @ secrecy_KS @ ( secrecy_sKS @ B ) @ ( localSecrets @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_know_Osimps_I2_J) ).

thf(1005,plain,
    ! [A: secrecy_specID,B: secrecy_Secrets] :
      ( ( knowle1437066798e_know @ A @ ( secrecy_sKS @ B ) )
      = ( ( ine @ A @ ( secrecy_sE @ B ) )
        | ( member @ secrecy_KS @ ( secrecy_sKS @ B ) @ ( localSecrets @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(140,axiom,
    ! [TA: $tType,A: TA] : ( member @ TA @ A @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_singletonI) ).

thf(683,plain,
    ! [TA: $tType,A: TA] : ( member @ TA @ A @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(240,axiom,
    ! [TA: $tType,A: TA,B: set @ TA] :
      ( ( member @ TA @ A @ B )
     => ( ( insert @ TA @ A @ B )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_insert__absorb) ).

thf(1073,plain,
    ! [TA: $tType,A: TA,B: set @ TA] :
      ( ( member @ TA @ A @ B )
     => ( ( insert @ TA @ A @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(40,axiom,
    ! [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
      ( ( out_ex985543062Single @ A @ B @ C )
     => ( out_exprChannelSet @ A @ ( insert @ secrecy_chanID @ B @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_out__exprChannelSingle__Set) ).

thf(379,plain,
    ! [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
      ( ( out_ex985543062Single @ A @ B @ C )
     => ( out_exprChannelSet @ A @ ( insert @ secrecy_chanID @ B @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(132,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_chanID,E: secrecy_Expression] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correctCompositionIn @ A )
       => ( ( member @ secrecy_chanID @ D @ ( ins @ B ) )
         => ( ( exprChannel @ D @ E )
           => ( ! [F: secrecy_chanID] :
                  ( ( member @ secrecy_chanID @ F @ ( ins @ A ) )
                 => ~ ( exprChannel @ F @ E ) )
             => ( member @ secrecy_chanID @ D @ ( loc @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_correctCompositionInLoc__exprChannel) ).

thf(655,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_chanID,E: secrecy_Expression] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correctCompositionIn @ A )
       => ( ( member @ secrecy_chanID @ D @ ( ins @ B ) )
         => ( ( exprChannel @ D @ E )
           => ( ! [F: secrecy_chanID] :
                  ( ( member @ secrecy_chanID @ F @ ( ins @ A ) )
                 => ~ ( exprChannel @ F @ E ) )
             => ( member @ secrecy_chanID @ D @ ( loc @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(121,axiom,
    ! [TA: $tType] :
      ( ( (=) @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
            ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
            & ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_set__eq__subset) ).

thf(614,plain,
    ! [TA: $tType] :
      ( ( (=) @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
            ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
            & ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(5,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB )
     => ! [A: TA > TB,B: TA > TB] :
          ( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
         => ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_le__funI) ).

thf(269,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB )
     => ! [A: TA > TB,B: TA > TB] :
          ( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
         => ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(138,axiom,
    ! [A: secrecy_Keys,B: secrecy_specID] :
      ( ~ ( member @ secrecy_Keys @ A @ ( specKeys @ B ) )
     => ( ( eout @ B @ ( secrecy_kE @ A ) )
       => ( ( knowle1667810483orrect @ B @ ( secrecy_kKS @ A ) )
         => ( knowle1437066798e_know @ B @ ( secrecy_kKS @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_eout__know__nonKS__k) ).

thf(677,plain,
    ! [A: secrecy_Keys,B: secrecy_specID] :
      ( ~ ( member @ secrecy_Keys @ A @ ( specKeys @ B ) )
     => ( ( eout @ B @ ( secrecy_kE @ A ) )
       => ( ( knowle1667810483orrect @ B @ ( secrecy_kKS @ A ) )
         => ( knowle1437066798e_know @ B @ ( secrecy_kKS @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(42,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( A = B )
     => ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_equalityD1) ).

thf(384,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( A = B )
     => ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(100,axiom,
    ! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
      ( ( ineM @ A @ B @ C )
     => ( ( ( subcomponents @ A )
          = ( insert @ secrecy_specID @ D @ ( insert @ secrecy_specID @ E @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correctCompositionIn @ A )
         => ( ( ineM @ D @ B @ C )
            | ( ineM @ E @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_TBtheorem1b) ).

thf(550,plain,
    ! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
      ( ( ineM @ A @ B @ C )
     => ( ( ( subcomponents @ A )
          = ( insert @ secrecy_specID @ D @ ( insert @ secrecy_specID @ E @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correctCompositionIn @ A )
         => ( ( ineM @ D @ B @ C )
            | ( ineM @ E @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(198,axiom,
    ! [TA: $tType,A: TA,B: set @ TA] :
      ( ( member @ TA @ A @ B )
     => ~ ! [C: set @ TA] :
            ( ( B
              = ( insert @ TA @ A @ C ) )
           => ( member @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_Set_Oset__insert) ).

thf(913,plain,
    ! [TA: $tType,A: TA,B: set @ TA] :
      ( ( member @ TA @ A @ B )
     => ~ ! [C: set @ TA] :
            ( ( B
              = ( insert @ TA @ A @ C ) )
           => ( member @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(205,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets,E: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) )
         => ( ( member @ secrecy_chanID @ E @ ( ins @ B ) )
           => ( ( exprChannel @ E @ ( secrecy_sE @ D ) )
             => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ A ) )
               => ( ( correctCompositionIn @ A )
                 => ( ( member @ secrecy_chanID @ E @ ( ins @ A ) )
                    & ( exprChannel @ E @ ( secrecy_sE @ D ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_correctCompositionKS__exprChannel__s__P) ).

thf(945,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets,E: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) )
         => ( ( member @ secrecy_chanID @ E @ ( ins @ B ) )
           => ( ( exprChannel @ E @ ( secrecy_sE @ D ) )
             => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ A ) )
               => ( ( correctCompositionIn @ A )
                 => ( ( member @ secrecy_chanID @ E @ ( ins @ A ) )
                    & ( exprChannel @ E @ ( secrecy_sE @ D ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(237,axiom,
    ! [A: secrecy_Secrets,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
      ( ( member @ secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ B ) )
     => ( ( ( subcomponents @ B )
          = ( insert @ secrecy_specID @ C @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correc965049635ionLoc @ B )
         => ( ~ ( ine @ D @ ( secrecy_sE @ A ) )
           => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ C ) )
             => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ D ) )
               => ( ine @ C @ ( secrecy_sE @ A ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_LocalSecretsComposition__ine1__s) ).

thf(1063,plain,
    ! [A: secrecy_Secrets,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
      ( ( member @ secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ B ) )
     => ( ( ( subcomponents @ B )
          = ( insert @ secrecy_specID @ C @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correc965049635ionLoc @ B )
         => ( ~ ( ine @ D @ ( secrecy_sE @ A ) )
           => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ C ) )
             => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ D ) )
               => ( ine @ C @ ( secrecy_sE @ A ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(95,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( ( sup_sup @ ( set @ TA ) @ A @ B )
        = ( bot_bot @ ( set @ TA ) ) )
      = ( ( A
          = ( bot_bot @ ( set @ TA ) ) )
        & ( B
          = ( bot_bot @ ( set @ TA ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_Un__empty) ).

thf(538,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( ( sup_sup @ ( set @ TA ) @ A @ B )
        = ( bot_bot @ ( set @ TA ) ) )
      = ( ( A
          = ( bot_bot @ ( set @ TA ) ) )
        & ( B
          = ( bot_bot @ ( set @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(171,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: set @ secrecy_chanID,E: secrecy_Expression,F: set @ secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correc990227761ionOut @ A )
       => ( ( out_exprChannelSet @ B @ D @ E )
         => ( ( out_exprChannelSet @ C @ F @ E )
           => ( ! [G: secrecy_chanID] :
                  ( ( member @ secrecy_chanID @ G @ D )
                 => ( member @ secrecy_chanID @ G @ ( loc @ A ) ) )
             => ( ! [G: secrecy_chanID] :
                    ( ( member @ secrecy_chanID @ G @ F )
                   => ( member @ secrecy_chanID @ G @ ( loc @ A ) ) )
               => ~ ( eout @ A @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_TBtheorem5a__notPQ) ).

thf(782,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: set @ secrecy_chanID,E: secrecy_Expression,F: set @ secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correc990227761ionOut @ A )
       => ( ( out_exprChannelSet @ B @ D @ E )
         => ( ( out_exprChannelSet @ C @ F @ E )
           => ( ! [G: secrecy_chanID] :
                  ( ( member @ secrecy_chanID @ G @ D )
                 => ( member @ secrecy_chanID @ G @ ( loc @ A ) ) )
             => ( ! [G: secrecy_chanID] :
                    ( ( member @ secrecy_chanID @ G @ F )
                   => ( member @ secrecy_chanID @ G @ ( loc @ A ) ) )
               => ~ ( eout @ A @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(149,axiom,
    ! [A: secrecy_Secrets,B: secrecy_specID,C: secrecy_chanID] :
      ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ B ) )
     => ( ( exprChannel @ C @ ( secrecy_sE @ A ) )
       => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ A ) @ ( specKeysSecrets @ B ) )
         => ~ ( member @ secrecy_chanID @ C @ ( loc @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_LocalSecretsComposition__neg__loc__s) ).

thf(709,plain,
    ! [A: secrecy_Secrets,B: secrecy_specID,C: secrecy_chanID] :
      ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ B ) )
     => ( ( exprChannel @ C @ ( secrecy_sE @ A ) )
       => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ A ) @ ( specKeysSecrets @ B ) )
         => ~ ( member @ secrecy_chanID @ C @ ( loc @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(180,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
      ( ( ? [D: TA] :
            ( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
            & ( C @ D ) ) )
      = ( ? [D: TA] :
            ( ( member @ TA @ D @ A )
            & ( C @ D ) )
        | ? [D: TA] :
            ( ( member @ TA @ D @ B )
            & ( C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_bex__Un) ).

thf(841,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
      ( ( ? [D: TA] :
            ( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
            & ( C @ D ) ) )
      = ( ? [D: TA] :
            ( ( member @ TA @ D @ A )
            & ( C @ D ) )
        | ? [D: TA] :
            ( ( member @ TA @ D @ B )
            & ( C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(192,axiom,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID,E: set @ secrecy_chanID] :
      ( ~ ( eout @ A @ B )
     => ( ( ( subcomponents @ C )
          = ( insert @ secrecy_specID @ D @ ( insert @ secrecy_specID @ A @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correc990227761ionOut @ C )
         => ( ( out_exprChannelSet @ D @ E @ B )
           => ( ! [F: secrecy_chanID] :
                  ( ( member @ secrecy_chanID @ F @ E )
                 => ( member @ secrecy_chanID @ F @ ( loc @ C ) ) )
             => ~ ( eout @ C @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_TBtheorem5a__notP2) ).

thf(885,plain,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID,E: set @ secrecy_chanID] :
      ( ~ ( eout @ A @ B )
     => ( ( ( subcomponents @ C )
          = ( insert @ secrecy_specID @ D @ ( insert @ secrecy_specID @ A @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correc990227761ionOut @ C )
         => ( ( out_exprChannelSet @ D @ E @ B )
           => ( ! [F: secrecy_chanID] :
                  ( ( member @ secrecy_chanID @ F @ E )
                 => ( member @ secrecy_chanID @ F @ ( loc @ C ) ) )
             => ~ ( eout @ C @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(12,axiom,
    ! [TA: $tType] :
      ( ( preorder @ TA )
     => ! [A: TA,B: TA] :
          ( ( A = B )
         => ( ord_less_eq @ TA @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_eq__refl) ).

thf(288,plain,
    ! [TA: $tType] :
      ( ( preorder @ TA )
     => ! [A: TA,B: TA] :
          ( ( A = B )
         => ( ord_less_eq @ TA @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(152,axiom,
    ! [TA: $tType,A: TA] :
      ~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_empty__iff) ).

thf(719,plain,
    ! [TA: $tType,A: TA] :
      ~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(37,axiom,
    ( inStream
    = ( ^ [A: secrecy_specID] : ( (=) @ ( set @ secrecy_chanID ) @ ( ins @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_inStream__def) ).

thf(372,plain,
    ( inStream
    = ( ^ [A: secrecy_specID] : ( (=) @ ( set @ secrecy_chanID ) @ ( ins @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(83,axiom,
    ! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
      ( ( sup_sup @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
      = ( insert @ TA @ B @ ( sup_sup @ ( set @ TA ) @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_Un__insert__right) ).

thf(504,plain,
    ! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
      ( ( sup_sup @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
      = ( insert @ TA @ B @ ( sup_sup @ ( set @ TA ) @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(253,axiom,
    ! [TA: $tType,A: set @ TA] :
      ( ! [B: TA] :
          ~ ( member @ TA @ B @ A )
     => ( A
        = ( bot_bot @ ( set @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_equals0I) ).

thf(1132,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ! [B: TA] :
          ~ ( member @ TA @ B @ A )
     => ( A
        = ( bot_bot @ ( set @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(97,axiom,
    ! [TA: $tType] :
      ( ( sup_sup @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] : ( sup_sup @ ( set @ TA ) @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_Un__commute) ).

thf(542,plain,
    ! [TA: $tType] :
      ( ( sup_sup @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] : ( sup_sup @ ( set @ TA ) @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(112,axiom,
    ! [TA: $tType,A: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
      = ( A
        = ( bot_bot @ ( set @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_subset__empty) ).

thf(587,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
      = ( A
        = ( bot_bot @ ( set @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(179,axiom,
    ! [A: secrecy_Secrets,B: secrecy_Secrets] :
      ( ( ( secrecy_sKS @ A )
        = ( secrecy_sKS @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_KS_Oinject_I2_J) ).

thf(838,plain,
    ! [A: secrecy_Secrets,B: secrecy_Secrets] :
      ( ( ( secrecy_sKS @ A )
        = ( secrecy_sKS @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(199,axiom,
    ! [TA: $tType,A: TA,B: set @ TA] :
      ( ( member @ TA @ A @ B )
     => ? [C: set @ TA] :
          ( ( B
            = ( insert @ TA @ A @ C ) )
          & ~ ( member @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_mk__disjoint__insert) ).

thf(917,plain,
    ! [TA: $tType,A: TA,B: set @ TA] :
      ( ( member @ TA @ A @ B )
     => ? [C: set @ TA] :
          ( ( B
            = ( insert @ TA @ A @ C ) )
          & ~ ( member @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(146,axiom,
    ( out_ex985543062Single
    = ( ^ [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
          ( ( member @ secrecy_chanID @ B @ ( out @ A ) )
          & ( exprChannel @ B @ C )
          & ! [D: secrecy_chanID,E: nat] :
              ( ( ( member @ secrecy_chanID @ D @ ( out @ A ) )
                & ( D != B ) )
             => ~ ( exprChannel @ D @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_out__exprChannelSingle__def) ).

thf(702,plain,
    ( out_ex985543062Single
    = ( ^ [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
          ( ( member @ secrecy_chanID @ B @ ( out @ A ) )
          & ( exprChannel @ B @ C )
          & ! [D: secrecy_chanID] :
              ( ( ( member @ secrecy_chanID @ D @ ( out @ A ) )
                & ( D != B ) )
             => ~ ( exprChannel @ D @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(103,axiom,
    correctCompositionIn @ pq,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_cCompI) ).

thf(559,plain,
    correctCompositionIn @ pq,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(184,axiom,
    ! [TA: $tType,A: TA] :
      ~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_emptyE) ).

thf(853,plain,
    ! [TA: $tType,A: TA] :
      ~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(54,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( A = B )
     => ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
         => ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_equalityE) ).

thf(421,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( A = B )
     => ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
         => ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(118,axiom,
    ! [TA: $tType,A: set @ TA,B: TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_subset__insertI) ).

thf(606,plain,
    ! [TA: $tType,A: set @ TA,B: TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(52,axiom,
    ! [TA: $tType,A: set @ TA,B: TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
     => ( ( A
          = ( bot_bot @ ( set @ TA ) ) )
        | ( A
          = ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_subset__singletonD) ).

thf(416,plain,
    ! [TA: $tType,A: set @ TA,B: TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
     => ( ( A
          = ( bot_bot @ ( set @ TA ) ) )
        | ( A
          = ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(23,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TA )
     => ( ord @ ( TB > TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).

thf(325,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TA )
     => ( ord @ ( TB > TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(63,axiom,
    ! [A: secrecy_specID,B: secrecy_KS,C: secrecy_specID,D: secrecy_specID] :
      ( ~ ( knowle1437066798e_know @ A @ B )
     => ( ~ ( knowle1437066798e_know @ C @ B )
       => ( ( ( subcomponents @ D )
            = ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
         => ( ( correc965049635ionLoc @ D )
           => ( ( correctCompositionIn @ D )
             => ~ ( knowle1437066798e_know @ D @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_know__composition__neg1) ).

thf(448,plain,
    ! [A: secrecy_specID,B: secrecy_KS,C: secrecy_specID,D: secrecy_specID] :
      ( ~ ( knowle1437066798e_know @ A @ B )
     => ( ~ ( knowle1437066798e_know @ C @ B )
       => ( ( ( subcomponents @ D )
            = ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
         => ( ( correc965049635ionLoc @ D )
           => ( ( correctCompositionIn @ D )
             => ~ ( knowle1437066798e_know @ D @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(10,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ~ ( ord_less_eq @ TA @ A @ B )
         => ( ord_less_eq @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_le__cases) ).

thf(284,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ~ ( ord_less_eq @ TA @ A @ B )
         => ( ord_less_eq @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(167,axiom,
    ~ ( knowle1437066798e_know @ q @ m ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_not__knowQm) ).

thf(770,plain,
    ~ ( knowle1437066798e_know @ q @ m ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(73,axiom,
    preorder @ $o,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_13) ).

thf(475,plain,
    preorder @ $o,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(61,axiom,
    ! [A: secrecy_specID,B: secrecy_Expression,C: set @ secrecy_chanID] :
      ( ~ ( ine @ A @ B )
     => ~ ( ineM @ A @ C @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_not__ine__ineM) ).

thf(443,plain,
    ! [A: secrecy_specID,B: secrecy_Expression,C: set @ secrecy_chanID] :
      ( ~ ( ine @ A @ B )
     => ~ ( ineM @ A @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(39,axiom,
    ! [TA: $tType] :
      ( ( bounde1808546759up_bot @ TA )
     => ! [A: TA] :
          ( ( sup_sup @ TA @ ( bot_bot @ TA ) @ A )
          = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_sup__bot_Oleft__neutral) ).

thf(376,plain,
    ! [TA: $tType] :
      ( ( bounde1808546759up_bot @ TA )
     => ! [A: TA] :
          ( ( sup_sup @ TA @ ( bot_bot @ TA ) @ A )
          = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(124,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
       => ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_subset__trans) ).

thf(623,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
       => ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(78,axiom,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ( ( eout @ A @ B )
        | ( eout @ C @ B ) )
     => ( ( ( subcomponents @ D )
          = ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correc990227761ionOut @ D )
         => ( ( ( loc @ D )
              = ( bot_bot @ ( set @ secrecy_chanID ) ) )
           => ( eout @ D @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_TBtheorem5a__empty) ).

thf(485,plain,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ( ( eout @ A @ B )
        | ( eout @ C @ B ) )
     => ( ( ( subcomponents @ D )
          = ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correc990227761ionOut @ D )
         => ( ( ( loc @ D )
              = ( bot_bot @ ( set @ secrecy_chanID ) ) )
           => ( eout @ D @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(173,axiom,
    ! [A: secrecy_specID,B: secrecy_Keys] :
      ( ( knowle1437066798e_know @ A @ ( secrecy_kKS @ B ) )
      = ( ( ine @ A @ ( secrecy_kE @ B ) )
        | ( member @ secrecy_KS @ ( secrecy_kKS @ B ) @ ( localSecrets @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_know_Osimps_I1_J) ).

thf(806,plain,
    ! [A: secrecy_specID,B: secrecy_Keys] :
      ( ( knowle1437066798e_know @ A @ ( secrecy_kKS @ B ) )
      = ( ( ine @ A @ ( secrecy_kE @ B ) )
        | ( member @ secrecy_KS @ ( secrecy_kKS @ B ) @ ( localSecrets @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(233,axiom,
    ! [TA: $tType,A: TA,B: set @ TA] : ( member @ TA @ A @ ( insert @ TA @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_insertI1) ).

thf(1051,plain,
    ! [TA: $tType,A: TA,B: set @ TA] : ( member @ TA @ A @ ( insert @ TA @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(30,axiom,
    ! [TA: $tType] :
      ( ( bounde1808546759up_bot @ TA )
     => ! [A: TA] :
          ( ( sup_sup @ TA @ A @ ( bot_bot @ TA ) )
          = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_sup__bot_Oright__neutral) ).

thf(353,plain,
    ! [TA: $tType] :
      ( ( bounde1808546759up_bot @ TA )
     => ! [A: TA] :
          ( ( sup_sup @ TA @ A @ ( bot_bot @ TA ) )
          = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(210,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys,E: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) )
         => ( ( member @ secrecy_chanID @ E @ ( ins @ B ) )
           => ( ( exprChannel @ E @ ( secrecy_kE @ D ) )
             => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ A ) )
               => ( ( correctCompositionIn @ A )
                 => ( ( member @ secrecy_chanID @ E @ ( ins @ A ) )
                    & ( exprChannel @ E @ ( secrecy_kE @ D ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_correctCompositionKS__exprChannel__k__P) ).

thf(966,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys,E: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) )
         => ( ( member @ secrecy_chanID @ E @ ( ins @ B ) )
           => ( ( exprChannel @ E @ ( secrecy_kE @ D ) )
             => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ A ) )
               => ( ( correctCompositionIn @ A )
                 => ( ( member @ secrecy_chanID @ E @ ( ins @ A ) )
                    & ( exprChannel @ E @ ( secrecy_kE @ D ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(169,axiom,
    ! [A: secrecy_Secrets,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
      ( ( member @ secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ B ) )
     => ( ( ( subcomponents @ B )
          = ( insert @ secrecy_specID @ C @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correc965049635ionLoc @ B )
         => ( ~ ( ine @ C @ ( secrecy_sE @ A ) )
           => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ C ) )
             => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ D ) )
               => ( ine @ D @ ( secrecy_sE @ A ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_LocalSecretsComposition__ine2__s) ).

thf(774,plain,
    ! [A: secrecy_Secrets,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
      ( ( member @ secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ B ) )
     => ( ( ( subcomponents @ B )
          = ( insert @ secrecy_specID @ C @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correc965049635ionLoc @ B )
         => ( ~ ( ine @ C @ ( secrecy_sE @ A ) )
           => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ C ) )
             => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ A ) @ ( localSecrets @ D ) )
               => ( ine @ D @ ( secrecy_sE @ A ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(46,axiom,
    ! [TA: $tType,A: TA] :
      ( ( the_elem @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_the__elem__eq) ).

thf(396,plain,
    ! [TA: $tType,A: TA] :
      ( ( the_elem @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(55,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
        = ( sup_sup @ ( set @ TA ) @ B @ C ) )
      = ( ( ( B
            = ( bot_bot @ ( set @ TA ) ) )
          & ( C
            = ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) )
        | ( ( B
            = ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
          & ( C
            = ( bot_bot @ ( set @ TA ) ) ) )
        | ( ( B
            = ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
          & ( C
            = ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_singleton__Un__iff) ).

thf(428,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
        = ( sup_sup @ ( set @ TA ) @ B @ C ) )
      = ( ( ( B
            = ( bot_bot @ ( set @ TA ) ) )
          & ( C
            = ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) )
        | ( ( B
            = ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
          & ( C
            = ( bot_bot @ ( set @ TA ) ) ) )
        | ( ( B
            = ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
          & ( C
            = ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(84,axiom,
    ! [TA: $tType,A: TA,B: set @ TA] :
      ( ( insert @ TA @ A @ ( insert @ TA @ A @ B ) )
      = ( insert @ TA @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_insert__absorb2) ).

thf(507,plain,
    ! [TA: $tType,A: TA,B: set @ TA] :
      ( ( insert @ TA @ A @ ( insert @ TA @ A @ B ) )
      = ( insert @ TA @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(248,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: set @ secrecy_chanID,E: secrecy_Expression,F: set @ secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correctCompositionIn @ A )
       => ( ( ine_exprChannelSet @ B @ D @ E )
         => ( ( ine_exprChannelSet @ C @ F @ E )
           => ( ! [G: secrecy_chanID] :
                  ( ( member @ secrecy_chanID @ G @ D )
                 => ( member @ secrecy_chanID @ G @ ( loc @ A ) ) )
             => ( ! [G: secrecy_chanID] :
                    ( ( member @ secrecy_chanID @ G @ F )
                   => ( member @ secrecy_chanID @ G @ ( loc @ A ) ) )
               => ~ ( ine @ A @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_TBtheorem4a__notPQ) ).

thf(1104,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: set @ secrecy_chanID,E: secrecy_Expression,F: set @ secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correctCompositionIn @ A )
       => ( ( ine_exprChannelSet @ B @ D @ E )
         => ( ( ine_exprChannelSet @ C @ F @ E )
           => ( ! [G: secrecy_chanID] :
                  ( ( member @ secrecy_chanID @ G @ D )
                 => ( member @ secrecy_chanID @ G @ ( loc @ A ) ) )
             => ( ! [G: secrecy_chanID] :
                    ( ( member @ secrecy_chanID @ G @ F )
                   => ( member @ secrecy_chanID @ G @ ( loc @ A ) ) )
               => ~ ( ine @ A @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(183,axiom,
    ! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
      ( ( eoutM @ A @ B @ C )
     => ( ( ( subcomponents @ D )
          = ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ E @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correc990227761ionOut @ D )
         => ( ? [F: secrecy_chanID] :
                ( ( member @ secrecy_chanID @ F @ ( out @ E ) )
                & ( exprChannel @ F @ C )
                & ~ ( member @ secrecy_chanID @ F @ ( loc @ D ) )
                & ( member @ secrecy_chanID @ F @ B ) )
           => ( eoutM @ D @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_TBtheore54b__P) ).

thf(849,plain,
    ! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
      ( ( eoutM @ A @ B @ C )
     => ( ( ( subcomponents @ D )
          = ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ E @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correc990227761ionOut @ D )
         => ( ? [F: secrecy_chanID] :
                ( ( member @ secrecy_chanID @ F @ ( out @ E ) )
                & ( exprChannel @ F @ C )
                & ~ ( member @ secrecy_chanID @ F @ ( loc @ D ) )
                & ( member @ secrecy_chanID @ F @ B ) )
           => ( eoutM @ D @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(13,axiom,
    ! [TA: $tType] :
      ( ( ord @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( B = C )
           => ( ord_less_eq @ TA @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_ord__le__eq__trans) ).

thf(292,plain,
    ! [TA: $tType] :
      ( ( ord @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( B = C )
           => ( ord_less_eq @ TA @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(64,axiom,
    ! [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
      ( ( ine_exprChannelSet @ A @ ( insert @ secrecy_chanID @ B @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ C )
     => ( ine_ex1303305700Single @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_ine__exprChannelSet__Single) ).

thf(452,plain,
    ! [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
      ( ( ine_exprChannelSet @ A @ ( insert @ secrecy_chanID @ B @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ C )
     => ( ine_ex1303305700Single @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(91,axiom,
    ! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression] :
      ( ( ine_exprChannelSet @ A @ B @ C )
     => ( ( B
         != ( bot_bot @ ( set @ secrecy_chanID ) ) )
       => ( ine @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_ine__nonempty__exprChannelSet) ).

thf(529,plain,
    ! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression] :
      ( ( ine_exprChannelSet @ A @ B @ C )
     => ( ( B
         != ( bot_bot @ ( set @ secrecy_chanID ) ) )
       => ( ine @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(133,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
      = ( ( member @ TA @ A @ C )
        & ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_insert__subset) ).

thf(661,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
      = ( ( member @ TA @ A @ C )
        & ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(201,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correctCompositionIn @ A )
       => ( ( member @ secrecy_chanID @ D @ ( ins @ A ) )
         => ( ( member @ secrecy_chanID @ D @ ( ins @ B ) )
            | ( member @ secrecy_chanID @ D @ ( ins @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_correctCompositionIn__prop1) ).

thf(925,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correctCompositionIn @ A )
       => ( ( member @ secrecy_chanID @ D @ ( ins @ A ) )
         => ( ( member @ secrecy_chanID @ D @ ( ins @ B ) )
            | ( member @ secrecy_chanID @ D @ ( ins @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(41,axiom,
    ! [TA: $tType,A: TA,B: set @ TA] :
      ( ( insert @ TA @ A @ B )
     != ( bot_bot @ ( set @ TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_insert__not__empty) ).

thf(381,plain,
    ! [TA: $tType,A: TA,B: set @ TA] :
      ( ( insert @ TA @ A @ B )
     != ( bot_bot @ ( set @ TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(93,axiom,
    bounde1808546759up_bot @ $o,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_12) ).

thf(534,plain,
    bounde1808546759up_bot @ $o,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(238,axiom,
    ! [A: secrecy_KS,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
      ( ( member @ secrecy_KS @ A @ ( localSecrets @ B ) )
     => ( ( ( subcomponents @ C )
          = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( member @ secrecy_KS @ A @ ( localSecrets @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_LocalSecretsComposition1) ).

thf(1067,plain,
    ! [A: secrecy_KS,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
      ( ( member @ secrecy_KS @ A @ ( localSecrets @ B ) )
     => ( ( ( subcomponents @ C )
          = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( member @ secrecy_KS @ A @ ( localSecrets @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(235,axiom,
    ! [TA: $tType] :
      ( ( ord_less_eq @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
          ! [C: TA] :
            ( ( member @ TA @ C @ A )
           => ( member @ TA @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_subset__eq) ).

thf(1057,plain,
    ! [TA: $tType] :
      ( ( ord_less_eq @ ( set @ TA ) )
      = ( ^ [A: set @ TA,B: set @ TA] :
          ! [C: TA] :
            ( ( member @ TA @ C @ A )
           => ( member @ TA @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(260,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_Keys] :
      ( ( correctCompositionKS @ A )
     => ( ( member @ secrecy_specID @ B @ ( subcomponents @ A ) )
       => ( ( member @ secrecy_Keys @ C @ ( specKeys @ B ) )
         => ( member @ secrecy_Keys @ C @ ( specKeys @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_correctCompositionKS__subcomp3) ).

thf(1153,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_Keys] :
      ( ( correctCompositionKS @ A )
     => ( ( member @ secrecy_specID @ B @ ( subcomponents @ A ) )
       => ( ( member @ secrecy_Keys @ C @ ( specKeys @ B ) )
         => ( member @ secrecy_Keys @ C @ ( specKeys @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(163,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( ~ ( member @ TA @ A @ B )
       => ( member @ TA @ A @ C ) )
     => ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_UnCI) ).

thf(761,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( ~ ( member @ TA @ A @ B )
       => ( member @ TA @ A @ C ) )
     => ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(158,axiom,
    ! [TA: $tType,A: secrecy_Keys > TA,B: secrecy_Secrets > TA,C: secrecy_Secrets] :
      ( ( secrecy_rec_KS @ TA @ A @ B @ ( secrecy_sKS @ C ) )
      = ( B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_KS_Osimps_I8_J) ).

thf(746,plain,
    ! [TA: $tType,A: secrecy_Keys > TA,B: secrecy_Secrets > TA,C: secrecy_Secrets] :
      ( ( secrecy_rec_KS @ TA @ A @ B @ ( secrecy_sKS @ C ) )
      = ( B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(170,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correc965049635ionLoc @ A )
       => ( ( correctCompositionKS @ A )
         => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ B ) )
           => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ C ) )
             => ( ~ ( ine @ B @ ( secrecy_sE @ D ) )
               => ( ~ ( ine @ C @ ( secrecy_sE @ D ) )
                 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( sup_sup @ ( set @ secrecy_KS ) @ ( localSecrets @ B ) @ ( localSecrets @ C ) ) )
                   => ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_LocalSecretsComposition__neg__s) ).

thf(778,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correc965049635ionLoc @ A )
       => ( ( correctCompositionKS @ A )
         => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ B ) )
           => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ C ) )
             => ( ~ ( ine @ B @ ( secrecy_sE @ D ) )
               => ( ~ ( ine @ C @ ( secrecy_sE @ D ) )
                 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( sup_sup @ ( set @ secrecy_KS ) @ ( localSecrets @ B ) @ ( localSecrets @ C ) ) )
                   => ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(231,axiom,
    ( ine_exprChannelSet
    = ( ^ [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression] :
          ( ! [D: secrecy_chanID] :
              ( ( member @ secrecy_chanID @ D @ B )
             => ( ( member @ secrecy_chanID @ D @ ( ins @ A ) )
                & ( exprChannel @ D @ C ) ) )
          & ! [D: secrecy_chanID] :
              ( ( ~ ( member @ secrecy_chanID @ D @ B )
                & ( member @ secrecy_chanID @ D @ ( ins @ A ) ) )
             => ~ ( exprChannel @ D @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_ine__exprChannelSet__def) ).

thf(1042,plain,
    ( ine_exprChannelSet
    = ( ^ [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression] :
          ( ! [D: secrecy_chanID] :
              ( ( member @ secrecy_chanID @ D @ B )
             => ( ( member @ secrecy_chanID @ D @ ( ins @ A ) )
                & ( exprChannel @ D @ C ) ) )
          & ! [D: secrecy_chanID] :
              ( ( ~ ( member @ secrecy_chanID @ D @ B )
                & ( member @ secrecy_chanID @ D @ ( ins @ A ) ) )
             => ~ ( exprChannel @ D @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(17,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( preorder @ TA )
     => ( preorder @ ( TB > TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder) ).

thf(302,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( preorder @ TA )
     => ( preorder @ ( TB > TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(127,axiom,
    ! [TA: $tType,A: TA > $o] :
      ( ( ( collect @ TA @ A )
        = ( bot_bot @ ( set @ TA ) ) )
      = ( A
        = ( bot_bot @ ( TA > $o ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_Collect__empty__eq__bot) ).

thf(630,plain,
    ! [TA: $tType,A: TA > $o] :
      ( ( ( collect @ TA @ A )
        = ( bot_bot @ ( set @ TA ) ) )
      = ( A
        = ( bot_bot @ ( TA > $o ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(125,axiom,
    ! [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
      ( ( out_exprChannelSet @ A @ ( insert @ secrecy_chanID @ B @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ C )
     => ( out_ex985543062Single @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_out__exprChannelSet__Single) ).

thf(625,plain,
    ! [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
      ( ( out_exprChannelSet @ A @ ( insert @ secrecy_chanID @ B @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ C )
     => ( out_ex985543062Single @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(190,axiom,
    ! [A: secrecy_KS > $o,B: secrecy_KS] :
      ( ! [C: secrecy_Keys] : ( A @ ( secrecy_kKS @ C ) )
     => ( ! [C: secrecy_Secrets] : ( A @ ( secrecy_sKS @ C ) )
       => ( A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_KS_Oinduct) ).

thf(879,plain,
    ! [A: secrecy_KS > $o,B: secrecy_KS] :
      ( ! [C: secrecy_Keys] : ( A @ ( secrecy_kKS @ C ) )
     => ( ! [C: secrecy_Secrets] : ( A @ ( secrecy_sKS @ C ) )
       => ( A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(25,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB )
     => ! [A: TA > TB,B: TA > TB,C: TA] :
          ( ( ord_less_eq @ ( TA > TB ) @ A @ B )
         => ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_le__funE) ).

thf(329,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB )
     => ! [A: TA > TB,B: TA > TB,C: TA] :
          ( ( ord_less_eq @ ( TA > TB ) @ A @ B )
         => ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(89,axiom,
    ! [A: secrecy_Keys,B: secrecy_Keys] :
      ( ( ( secrecy_kE @ A )
        = ( secrecy_kE @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_Expression_Oinject_I1_J) ).

thf(522,plain,
    ! [A: secrecy_Keys,B: secrecy_Keys] :
      ( ( ( secrecy_kE @ A )
        = ( secrecy_kE @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(161,axiom,
    ( m
    = ( secrecy_sKS @ secret ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_a2) ).

thf(757,plain,
    ( m
    = ( secrecy_sKS @ secret ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(66,axiom,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
      = ( ! [C: TA] :
            ( ( A @ C )
           => ( B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_Collect__mono__iff) ).

thf(456,plain,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
      = ( ! [C: TA] :
            ( ( A @ C )
           => ( B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(225,axiom,
    ! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
      ( ( ( ineM @ A @ B @ C )
        | ( ineM @ D @ B @ C ) )
     => ( ( ( subcomponents @ E )
          = ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correctCompositionIn @ E )
         => ( ? [F: secrecy_chanID] :
                ( ( ( member @ secrecy_chanID @ F @ ( ins @ A ) )
                  | ( member @ secrecy_chanID @ F @ ( ins @ D ) ) )
                & ( member @ secrecy_chanID @ F @ B )
                & ( exprChannel @ F @ C )
                & ~ ( member @ secrecy_chanID @ F @ ( loc @ E ) ) )
           => ( ineM @ E @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_TBtheorem4b__PQ) ).

thf(1012,plain,
    ! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
      ( ( ( ineM @ A @ B @ C )
        | ( ineM @ D @ B @ C ) )
     => ( ( ( subcomponents @ E )
          = ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correctCompositionIn @ E )
         => ( ? [F: secrecy_chanID] :
                ( ( ( member @ secrecy_chanID @ F @ ( ins @ A ) )
                  | ( member @ secrecy_chanID @ F @ ( ins @ D ) ) )
                & ( member @ secrecy_chanID @ F @ B )
                & ( exprChannel @ F @ C )
                & ~ ( member @ secrecy_chanID @ F @ ( loc @ E ) ) )
           => ( ineM @ E @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(106,axiom,
    ! [TA: $tType,A: TA > $o] :
      ( ( ( bot_bot @ ( set @ TA ) )
        = ( collect @ TA @ A ) )
      = ( ! [B: TA] :
            ~ ( A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_empty__Collect__eq) ).

thf(566,plain,
    ! [TA: $tType,A: TA > $o] :
      ( ( ( bot_bot @ ( set @ TA ) )
        = ( collect @ TA @ A ) )
      = ( ! [B: TA] :
            ~ ( A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(77,axiom,
    knowle1437066798e_know @ pq @ m,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_knowPQ) ).

thf(484,plain,
    knowle1437066798e_know @ pq @ m,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(88,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
      ( ( sup_sup @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
      = ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_Un__assoc) ).

thf(519,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
      ( ( sup_sup @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
      = ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(257,axiom,
    ! [A: secrecy_Secrets,B: secrecy_specID] :
      ( ~ ( member @ secrecy_Secrets @ A @ ( specSecrets @ B ) )
     => ( ~ ( knowle1437066798e_know @ B @ ( secrecy_sKS @ A ) )
       => ( ( knowle1667810483orrect @ B @ ( secrecy_sKS @ A ) )
         => ~ ( eout @ B @ ( secrecy_sE @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_not__know__s__not__eout) ).

thf(1143,plain,
    ! [A: secrecy_Secrets,B: secrecy_specID] :
      ( ~ ( member @ secrecy_Secrets @ A @ ( specSecrets @ B ) )
     => ( ~ ( knowle1437066798e_know @ B @ ( secrecy_sKS @ A ) )
       => ( ( knowle1667810483orrect @ B @ ( secrecy_sKS @ A ) )
         => ~ ( eout @ B @ ( secrecy_sE @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(48,axiom,
    ! [TA: $tType] :
      ( ( bounde1808546759up_bot @ TA )
     => ! [A: TA,B: TA] :
          ( ( ( sup_sup @ TA @ A @ B )
            = ( bot_bot @ TA ) )
          = ( ( A
              = ( bot_bot @ TA ) )
            & ( B
              = ( bot_bot @ TA ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_sup__eq__bot__iff) ).

thf(403,plain,
    ! [TA: $tType] :
      ( ( bounde1808546759up_bot @ TA )
     => ! [A: TA,B: TA] :
          ( ( ( sup_sup @ TA @ A @ B )
            = ( bot_bot @ TA ) )
          = ( ( A
              = ( bot_bot @ TA ) )
            & ( B
              = ( bot_bot @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(43,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_subset__insertI2) ).

thf(388,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(31,axiom,
    ! [A: secrecy_Secrets,B: secrecy_Secrets] :
      ( ( ( secrecy_sE @ A )
        = ( secrecy_sE @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_Expression_Oinject_I2_J) ).

thf(356,plain,
    ! [A: secrecy_Secrets,B: secrecy_Secrets] :
      ( ( ( secrecy_sE @ A )
        = ( secrecy_sE @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(114,axiom,
    ! [TA: $tType,A: secrecy_Keys > TA,B: secrecy_Secrets > TA,C: secrecy_Keys] :
      ( ( secrecy_rec_KS @ TA @ A @ B @ ( secrecy_kKS @ C ) )
      = ( A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_KS_Osimps_I7_J) ).

thf(593,plain,
    ! [TA: $tType,A: secrecy_Keys > TA,B: secrecy_Secrets > TA,C: secrecy_Keys] :
      ( ( secrecy_rec_KS @ TA @ A @ B @ ( secrecy_kKS @ C ) )
      = ( A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(243,axiom,
    ( eout
    = ( ^ [A: secrecy_specID,B: secrecy_Expression] :
        ? [C: secrecy_chanID] :
          ( ( member @ secrecy_chanID @ C @ ( out @ A ) )
          & ( exprChannel @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_eout__def) ).

thf(1082,plain,
    ( eout
    = ( ^ [A: secrecy_specID,B: secrecy_Expression] :
        ? [C: secrecy_chanID] :
          ( ( member @ secrecy_chanID @ C @ ( out @ A ) )
          & ( exprChannel @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(74,axiom,
    ! [TA: $tType] :
      ( ( bot_bot @ ( set @ TA ) )
      = ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_bot__set__def) ).

thf(476,plain,
    ! [TA: $tType] :
      ( ( bot_bot @ ( set @ TA ) )
      = ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(113,axiom,
    ! [A: secrecy_Keys,B: secrecy_Keys] :
      ( ( ( secrecy_kKS @ A )
        = ( secrecy_kKS @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_KS_Oinject_I1_J) ).

thf(590,plain,
    ! [A: secrecy_Keys,B: secrecy_Keys] :
      ( ( ( secrecy_kKS @ A )
        = ( secrecy_kKS @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(148,axiom,
    ! [A: secrecy_Secrets] :
      ( ( secrec1016742679ession @ ( secrecy_sKS @ A ) )
      = ( secrecy_sE @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_KS2Expression_Osimps_I2_J) ).

thf(706,plain,
    ! [A: secrecy_Secrets] :
      ( ( secrec1016742679ession @ ( secrecy_sKS @ A ) )
      = ( secrecy_sE @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(101,axiom,
    ! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression] :
      ( ( ineM @ A @ B @ C )
     => ( ine @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_ineM__ine) ).

thf(554,plain,
    ! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression] :
      ( ( ineM @ A @ B @ C )
     => ( ine @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(160,axiom,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ( eout @ A @ B )
     => ( ~ ( eout @ C @ B )
       => ( ( ( subcomponents @ D )
            = ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
         => ( ( correc990227761ionOut @ D )
           => ( ? [E: secrecy_chanID] :
                  ( ( out_ex985543062Single @ A @ E @ B )
                  & ( member @ secrecy_chanID @ E @ ( loc @ D ) ) )
             => ~ ( eout @ D @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_TBtheorem5a__notP1) ).

thf(753,plain,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ( eout @ A @ B )
     => ( ~ ( eout @ C @ B )
       => ( ( ( subcomponents @ D )
            = ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
         => ( ( correc990227761ionOut @ D )
           => ( ? [E: secrecy_chanID] :
                  ( ( out_ex985543062Single @ A @ E @ B )
                  & ( member @ secrecy_chanID @ E @ ( loc @ D ) ) )
             => ~ ( eout @ D @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(139,axiom,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ( ine @ A @ B )
     => ( ( ( subcomponents @ C )
          = ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correctCompositionIn @ C )
         => ( ? [E: secrecy_chanID] :
                ( ( member @ secrecy_chanID @ E @ ( ins @ A ) )
                & ( exprChannel @ E @ B )
                & ~ ( member @ secrecy_chanID @ E @ ( loc @ C ) ) )
           => ( ine @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_TBtheorem4a__P) ).

thf(679,plain,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ( ine @ A @ B )
     => ( ( ( subcomponents @ C )
          = ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correctCompositionIn @ C )
         => ( ? [E: secrecy_chanID] :
                ( ( member @ secrecy_chanID @ E @ ( ins @ A ) )
                & ( exprChannel @ E @ B )
                & ~ ( member @ secrecy_chanID @ E @ ( loc @ C ) ) )
           => ( ine @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(230,axiom,
    ! [A: secrecy_specID,B: secrecy_Keys] :
      ( ( knowle1667810483orrect @ A @ ( secrecy_kKS @ B ) )
      = ( ( eout @ A @ ( secrecy_kE @ B ) )
        = ( ( member @ secrecy_Keys @ B @ ( specKeys @ A ) )
          | ( knowle1437066798e_know @ A @ ( secrecy_kKS @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_eout__know__k) ).

thf(1039,plain,
    ! [A: secrecy_specID,B: secrecy_Keys] :
      ( ( knowle1667810483orrect @ A @ ( secrecy_kKS @ B ) )
      = ( ( eout @ A @ ( secrecy_kE @ B ) )
        = ( ( member @ secrecy_Keys @ B @ ( specKeys @ A ) )
          | ( knowle1437066798e_know @ A @ ( secrecy_kKS @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(219,axiom,
    ! [TA: $tType,A: secrecy_Keys > TA,B: secrecy_Secrets > TA,C: secrecy_Secrets] :
      ( ( secrecy_case_KS @ TA @ A @ B @ ( secrecy_sKS @ C ) )
      = ( B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_KS_Osimps_I6_J) ).

thf(997,plain,
    ! [TA: $tType,A: secrecy_Keys > TA,B: secrecy_Secrets > TA,C: secrecy_Secrets] :
      ( ( secrecy_case_KS @ TA @ A @ B @ ( secrecy_sKS @ C ) )
      = ( B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(156,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( member @ TA @ A @ B )
     => ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_UnI2) ).

thf(738,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( member @ TA @ A @ B )
     => ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(236,axiom,
    ! [TA: $tType,A: TA,B: TA > $o] :
      ( ( member @ TA @ A @ ( collect @ TA @ B ) )
      = ( B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_mem__Collect__eq) ).

thf(1060,plain,
    ! [TA: $tType,A: TA,B: TA > $o] :
      ( ( member @ TA @ A @ ( collect @ TA @ B ) )
      = ( B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(153,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: set @ secrecy_chanID,E: secrecy_Expression,F: set @ secrecy_chanID,G: set @ secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correctCompositionIn @ A )
       => ( ( ine_exprChannelSet @ B @ D @ E )
         => ( ( ine_exprChannelSet @ C @ F @ E )
           => ( ! [H: secrecy_chanID] :
                  ( ( member @ secrecy_chanID @ H @ D )
                 => ( member @ secrecy_chanID @ H @ ( loc @ A ) ) )
             => ( ! [H: secrecy_chanID] :
                    ( ( member @ secrecy_chanID @ H @ F )
                   => ( member @ secrecy_chanID @ H @ ( loc @ A ) ) )
               => ~ ( ineM @ A @ G @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_TBtheorem4b__notPQ) ).

thf(721,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: set @ secrecy_chanID,E: secrecy_Expression,F: set @ secrecy_chanID,G: set @ secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correctCompositionIn @ A )
       => ( ( ine_exprChannelSet @ B @ D @ E )
         => ( ( ine_exprChannelSet @ C @ F @ E )
           => ( ! [H: secrecy_chanID] :
                  ( ( member @ secrecy_chanID @ H @ D )
                 => ( member @ secrecy_chanID @ H @ ( loc @ A ) ) )
             => ( ! [H: secrecy_chanID] :
                    ( ( member @ secrecy_chanID @ H @ F )
                   => ( member @ secrecy_chanID @ H @ ( loc @ A ) ) )
               => ~ ( ineM @ A @ G @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(107,axiom,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ( ine @ A @ B )
     => ( ( ( subcomponents @ A )
          = ( insert @ secrecy_specID @ C @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correctCompositionIn @ A )
         => ( ( ine @ C @ B )
            | ( ine @ D @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_TBtheorem1a) ).

thf(569,plain,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ( ine @ A @ B )
     => ( ( ( subcomponents @ A )
          = ( insert @ secrecy_specID @ C @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correctCompositionIn @ A )
         => ( ( ine @ C @ B )
            | ( ine @ D @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(45,axiom,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ! [C: TA] :
          ( ( A @ C )
          = ( B @ C ) )
     => ( ( collect @ TA @ A )
        = ( collect @ TA @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_Collect__cong) ).

thf(393,plain,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ! [C: TA] :
          ( ( A @ C )
          = ( B @ C ) )
     => ( ( collect @ TA @ A )
        = ( collect @ TA @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(249,axiom,
    ! [A: secrecy_specID,B: secrecy_Keys] :
      ( ( knowle1667810483orrect @ A @ ( secrecy_kKS @ B ) )
     => ( ( eout @ A @ ( secrecy_kE @ B ) )
       => ( ( member @ secrecy_Keys @ B @ ( specKeys @ A ) )
          | ( knowle1437066798e_know @ A @ ( secrecy_kKS @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_eoutKnowCorrect__L1k) ).

thf(1114,plain,
    ! [A: secrecy_specID,B: secrecy_Keys] :
      ( ( knowle1667810483orrect @ A @ ( secrecy_kKS @ B ) )
     => ( ( eout @ A @ ( secrecy_kE @ B ) )
       => ( ( member @ secrecy_Keys @ B @ ( specKeys @ A ) )
          | ( knowle1437066798e_know @ A @ ( secrecy_kKS @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(172,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: set @ secrecy_chanID,E: secrecy_Expression,F: set @ secrecy_chanID,G: set @ secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correc990227761ionOut @ A )
       => ( ( out_exprChannelSet @ B @ D @ E )
         => ( ( out_exprChannelSet @ C @ F @ E )
           => ( ( G
                = ( sup_sup @ ( set @ secrecy_chanID ) @ D @ F ) )
             => ( ! [H: secrecy_chanID] :
                    ( ( member @ secrecy_chanID @ H @ D )
                   => ( member @ secrecy_chanID @ H @ ( loc @ A ) ) )
               => ( ! [H: secrecy_chanID] :
                      ( ( member @ secrecy_chanID @ H @ F )
                     => ( member @ secrecy_chanID @ H @ ( loc @ A ) ) )
                 => ~ ( eoutM @ A @ G @ E ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_TBtheorem5b__notPQ) ).

thf(792,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: set @ secrecy_chanID,E: secrecy_Expression,F: set @ secrecy_chanID,G: set @ secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correc990227761ionOut @ A )
       => ( ( out_exprChannelSet @ B @ D @ E )
         => ( ( out_exprChannelSet @ C @ F @ E )
           => ( ( G
                = ( sup_sup @ ( set @ secrecy_chanID ) @ D @ F ) )
             => ( ! [H: secrecy_chanID] :
                    ( ( member @ secrecy_chanID @ H @ D )
                   => ( member @ secrecy_chanID @ H @ ( loc @ A ) ) )
               => ( ! [H: secrecy_chanID] :
                      ( ( member @ secrecy_chanID @ H @ F )
                     => ( member @ secrecy_chanID @ H @ ( loc @ A ) ) )
                 => ~ ( eoutM @ A @ G @ E ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(4,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( bot @ TB )
     => ( ( bot_bot @ ( TA > TB ) )
        = ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_bot__apply) ).

thf(266,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( bot @ TB )
     => ( ( bot_bot @ ( TA > TB ) )
        = ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(128,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys,E: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) )
         => ( ( member @ secrecy_chanID @ E @ ( ins @ B ) )
           => ( ( exprChannel @ E @ ( secrecy_kE @ D ) )
             => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ A ) )
               => ( ( correctCompositionIn @ A )
                 => ? [F: secrecy_chanID] :
                      ( ( member @ secrecy_chanID @ F @ ( ins @ A ) )
                      & ( exprChannel @ F @ ( secrecy_kE @ D ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_correctCompositionKS__exprChannel__k__Pex) ).

thf(633,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys,E: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) )
         => ( ( member @ secrecy_chanID @ E @ ( ins @ B ) )
           => ( ( exprChannel @ E @ ( secrecy_kE @ D ) )
             => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ A ) )
               => ( ( correctCompositionIn @ A )
                 => ? [F: secrecy_chanID] :
                      ( ( member @ secrecy_chanID @ F @ ( ins @ A ) )
                      & ( exprChannel @ F @ ( secrecy_kE @ D ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(19,axiom,
    ! [TA: $tType] : ( bounde1808546759up_bot @ ( set @ TA ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_7) ).

thf(311,plain,
    ! [TA: $tType] : ( bounde1808546759up_bot @ ( set @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(200,axiom,
    ! [A: secrecy_KS,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
      ( ~ ( member @ secrecy_KS @ A @ ( specKeysSecrets @ B ) )
     => ( ~ ( member @ secrecy_KS @ A @ ( specKeysSecrets @ C ) )
       => ( ( knowle1437066798e_know @ C @ A )
         => ( ( ( subcomponents @ D )
              = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
           => ( ( correctCompositionIn @ D )
             => ( ( correctCompositionKS @ D )
               => ( knowle1437066798e_know @ D @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_know__composition2) ).

thf(921,plain,
    ! [A: secrecy_KS,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
      ( ~ ( member @ secrecy_KS @ A @ ( specKeysSecrets @ B ) )
     => ( ~ ( member @ secrecy_KS @ A @ ( specKeysSecrets @ C ) )
       => ( ( knowle1437066798e_know @ C @ A )
         => ( ( ( subcomponents @ D )
              = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
           => ( ( correctCompositionIn @ D )
             => ( ( correctCompositionKS @ D )
               => ( knowle1437066798e_know @ D @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(96,axiom,
    ord @ $o,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_16) ).

thf(541,plain,
    ord @ $o,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(165,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_Secrets] :
      ( ( ord_less_eq @ ( set @ secrecy_chanID ) @ ( out @ A ) @ ( ins @ B ) )
     => ( ~ ( knowle1437066798e_know @ B @ ( secrecy_sKS @ C ) )
       => ~ ( eout @ A @ ( secrecy_sE @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_adv__not__know2) ).

thf(765,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_Secrets] :
      ( ( ord_less_eq @ ( set @ secrecy_chanID ) @ ( out @ A ) @ ( ins @ B ) )
     => ( ~ ( knowle1437066798e_know @ B @ ( secrecy_sKS @ C ) )
       => ~ ( eout @ A @ ( secrecy_sE @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(229,axiom,
    ! [A: secrecy_KS] :
      ( ! [B: secrecy_Keys] :
          ( A
         != ( secrecy_kKS @ B ) )
     => ~ ! [B: secrecy_Secrets] :
            ( A
           != ( secrecy_sKS @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_KS_Oexhaust) ).

thf(1035,plain,
    ! [A: secrecy_KS] :
      ( ! [B: secrecy_Keys] :
          ( A
         != ( secrecy_kKS @ B ) )
     => ~ ! [B: secrecy_Secrets] :
            ( A
           != ( secrecy_sKS @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(239,axiom,
    ( ine
    = ( ^ [A: secrecy_specID,B: secrecy_Expression] :
        ? [C: secrecy_chanID] :
          ( ( member @ secrecy_chanID @ C @ ( ins @ A ) )
          & ( exprChannel @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_ine__def) ).

thf(1071,plain,
    ( ine
    = ( ^ [A: secrecy_specID,B: secrecy_Expression] :
        ? [C: secrecy_chanID] :
          ( ( member @ secrecy_chanID @ C @ ( ins @ A ) )
          & ( exprChannel @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(137,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ~ ( member @ TA @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
        = ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_subset__insert) ).

thf(674,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ~ ( member @ TA @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
        = ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(227,axiom,
    ! [A: secrecy_Keys,B: secrecy_specID,C: secrecy_chanID] :
      ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ B ) )
     => ( ( exprChannel @ C @ ( secrecy_kE @ A ) )
       => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ A ) @ ( specKeysSecrets @ B ) )
         => ~ ( member @ secrecy_chanID @ C @ ( loc @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_LocalSecretsComposition__neg__loc__k) ).

thf(1026,plain,
    ! [A: secrecy_Keys,B: secrecy_specID,C: secrecy_chanID] :
      ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ B ) )
     => ( ( exprChannel @ C @ ( secrecy_kE @ A ) )
       => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ A ) @ ( specKeysSecrets @ B ) )
         => ~ ( member @ secrecy_chanID @ C @ ( loc @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(15,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB )
     => ! [A: TA > TB,B: TA > TB,C: TA] :
          ( ( ord_less_eq @ ( TA > TB ) @ A @ B )
         => ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_le__funD) ).

thf(298,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ord @ TB )
     => ! [A: TA > TB,B: TA > TB,C: TA] :
          ( ( ord_less_eq @ ( TA > TB ) @ A @ B )
         => ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(254,axiom,
    ! [A: secrecy_chanID,B: secrecy_Secrets,C: secrecy_specID,D: secrecy_specID] :
      ( ( exprChannel @ A @ ( secrecy_sE @ B ) )
     => ( ~ ( ine @ C @ ( secrecy_sE @ B ) )
       => ( ~ ( ine @ D @ ( secrecy_sE @ B ) )
         => ( ~ ( member @ secrecy_chanID @ A @ ( ins @ C ) )
            & ~ ( member @ secrecy_chanID @ A @ ( ins @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_LocalSecretsComposition__exprChannel__s) ).

thf(1135,plain,
    ! [A: secrecy_chanID,B: secrecy_Secrets,C: secrecy_specID,D: secrecy_specID] :
      ( ( exprChannel @ A @ ( secrecy_sE @ B ) )
     => ( ~ ( ine @ C @ ( secrecy_sE @ B ) )
       => ( ~ ( ine @ D @ ( secrecy_sE @ B ) )
         => ( ~ ( member @ secrecy_chanID @ A @ ( ins @ C ) )
            & ~ ( member @ secrecy_chanID @ A @ ( ins @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(86,axiom,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ! [C: TA] :
          ( ( A @ C )
         => ( B @ C ) )
     => ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_Collect__mono) ).

thf(513,plain,
    ! [TA: $tType,A: TA > $o,B: TA > $o] :
      ( ! [C: TA] :
          ( ( A @ C )
         => ( B @ C ) )
     => ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(3,axiom,
    ! [TA: $tType] :
      ( ( preorder @ TA )
     => ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_order__refl) ).

thf(264,plain,
    ! [TA: $tType] :
      ( ( preorder @ TA )
     => ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(108,axiom,
    ! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
      ( ( eoutM @ A @ B @ C )
     => ( ( ( subcomponents @ A )
          = ( insert @ secrecy_specID @ D @ ( insert @ secrecy_specID @ E @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correc990227761ionOut @ A )
         => ( ( eoutM @ D @ B @ C )
            | ( eoutM @ E @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_TBtheorem2b) ).

thf(573,plain,
    ! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
      ( ( eoutM @ A @ B @ C )
     => ( ( ( subcomponents @ A )
          = ( insert @ secrecy_specID @ D @ ( insert @ secrecy_specID @ E @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correc990227761ionOut @ A )
         => ( ( eoutM @ D @ B @ C )
            | ( eoutM @ E @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(14,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( bot @ TA )
     => ( bot @ ( TB > TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Obot) ).

thf(296,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( bot @ TA )
     => ( bot @ ( TB > TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(111,axiom,
    ! [TA: $tType,A: set @ TA] :
      ( ( sup_sup @ ( set @ TA ) @ A @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_Un__absorb) ).

thf(584,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ( sup_sup @ ( set @ TA ) @ A @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(144,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: TA] :
      ( ( ~ ( member @ TA @ A @ B )
       => ( A = C ) )
     => ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_insertCI) ).

thf(694,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: TA] :
      ( ( ~ ( member @ TA @ A @ B )
       => ( A = C ) )
     => ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(168,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: TA] :
      ( ( member @ TA @ A @ B )
     => ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_insertI2) ).

thf(772,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: TA] :
      ( ( member @ TA @ A @ B )
     => ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(11,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( bounded_lattice @ TA )
     => ( bounde1808546759up_bot @ ( TB > TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Obounded__semilattice__sup__bot) ).

thf(286,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( bounded_lattice @ TA )
     => ( bounde1808546759up_bot @ ( TB > TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(208,axiom,
    ! [TA: $tType,A: set @ TA,B: TA] :
      ( ( A
        = ( bot_bot @ ( set @ TA ) ) )
     => ~ ( member @ TA @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_equals0D) ).

thf(958,plain,
    ! [TA: $tType,A: set @ TA,B: TA] :
      ( ( A
        = ( bot_bot @ ( set @ TA ) ) )
     => ~ ( member @ TA @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(98,axiom,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ~ ( ine @ A @ B )
     => ( ~ ( ine @ C @ B )
       => ( ( ( subcomponents @ D )
            = ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
         => ( ( correctCompositionIn @ D )
           => ~ ( ine @ D @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_TBtheorem3a) ).

thf(545,plain,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ~ ( ine @ A @ B )
     => ( ~ ( ine @ C @ B )
       => ( ( ( subcomponents @ D )
            = ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
         => ( ( correctCompositionIn @ D )
           => ~ ( ine @ D @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(51,axiom,
    ! [TA: $tType,A: set @ TA,B: TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
      = ( ( A
          = ( bot_bot @ ( set @ TA ) ) )
        | ( A
          = ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_subset__singleton__iff) ).

thf(413,plain,
    ! [TA: $tType,A: set @ TA,B: TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
      = ( ( A
          = ( bot_bot @ ( set @ TA ) ) )
        | ( A
          = ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(189,axiom,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ( eout @ A @ B )
     => ( ( ( subcomponents @ C )
          = ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correc990227761ionOut @ C )
         => ( ? [E: secrecy_chanID] :
                ( ( member @ secrecy_chanID @ E @ ( out @ A ) )
                & ( exprChannel @ E @ B )
                & ~ ( member @ secrecy_chanID @ E @ ( loc @ C ) ) )
           => ( eout @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_TBtheorem45a__P) ).

thf(875,plain,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ( eout @ A @ B )
     => ( ( ( subcomponents @ C )
          = ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correc990227761ionOut @ C )
         => ( ? [E: secrecy_chanID] :
                ( ( member @ secrecy_chanID @ E @ ( out @ A ) )
                & ( exprChannel @ E @ B )
                & ~ ( member @ secrecy_chanID @ E @ ( loc @ C ) ) )
           => ( eout @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(177,axiom,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ( ( eout @ A @ B )
        | ( eout @ C @ B ) )
     => ( ( ( subcomponents @ D )
          = ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correc990227761ionOut @ D )
         => ( ? [E: secrecy_chanID] :
                ( ( ( member @ secrecy_chanID @ E @ ( out @ A ) )
                  | ( member @ secrecy_chanID @ E @ ( out @ C ) ) )
                & ( exprChannel @ E @ B )
                & ~ ( member @ secrecy_chanID @ E @ ( loc @ D ) ) )
           => ( eout @ D @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_TBtheorem5a__PQ) ).

thf(826,plain,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ( ( eout @ A @ B )
        | ( eout @ C @ B ) )
     => ( ( ( subcomponents @ D )
          = ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correc990227761ionOut @ D )
         => ( ? [E: secrecy_chanID] :
                ( ( ( member @ secrecy_chanID @ E @ ( out @ A ) )
                  | ( member @ secrecy_chanID @ E @ ( out @ C ) ) )
                & ( exprChannel @ E @ B )
                & ~ ( member @ secrecy_chanID @ E @ ( loc @ D ) ) )
           => ( eout @ D @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(109,axiom,
    ! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression,D: set @ secrecy_chanID] :
      ( ( ineM @ A @ B @ C )
     => ( ineM @ A @ ( sup_sup @ ( set @ secrecy_chanID ) @ B @ D ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_ineM__Un1) ).

thf(577,plain,
    ! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression,D: set @ secrecy_chanID] :
      ( ( ineM @ A @ B @ C )
     => ( ineM @ A @ ( sup_sup @ ( set @ secrecy_chanID ) @ B @ D ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(255,axiom,
    ! [A: secrecy_specID,B: secrecy_Secrets] :
      ( ~ ( knowle1437066798e_know @ A @ ( secrecy_sKS @ B ) )
     => ~ ( ine @ A @ ( secrecy_sE @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_not__know__s__not__ine) ).

thf(1139,plain,
    ! [A: secrecy_specID,B: secrecy_Secrets] :
      ( ~ ( knowle1437066798e_know @ A @ ( secrecy_sKS @ B ) )
     => ~ ( ine @ A @ ( secrecy_sE @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(20,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( bounded_lattice @ TA )
     => ( bounded_lattice @ ( TB > TA ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Obounded__lattice_2) ).

thf(313,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( bounded_lattice @ TA )
     => ( bounded_lattice @ ( TB > TA ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(120,axiom,
    ! [TA: $tType,A: secrecy_Keys > TA,B: secrecy_Secrets > TA,C: secrecy_Keys] :
      ( ( secrecy_case_KS @ TA @ A @ B @ ( secrecy_kKS @ C ) )
      = ( A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_KS_Osimps_I5_J) ).

thf(611,plain,
    ! [TA: $tType,A: secrecy_Keys > TA,B: secrecy_Secrets > TA,C: secrecy_Keys] :
      ( ( secrecy_case_KS @ TA @ A @ B @ ( secrecy_kKS @ C ) )
      = ( A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(245,axiom,
    ! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
      ( ( ineM @ A @ B @ C )
     => ( ( ( subcomponents @ D )
          = ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ E @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correctCompositionIn @ D )
         => ( ? [F: secrecy_chanID] :
                ( ( member @ secrecy_chanID @ F @ ( ins @ E ) )
                & ( exprChannel @ F @ C )
                & ~ ( member @ secrecy_chanID @ F @ ( loc @ D ) )
                & ( member @ secrecy_chanID @ F @ B ) )
           => ( ineM @ D @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_TBtheorem4b__P) ).

thf(1090,plain,
    ! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
      ( ( ineM @ A @ B @ C )
     => ( ( ( subcomponents @ D )
          = ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ E @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correctCompositionIn @ D )
         => ( ? [F: secrecy_chanID] :
                ( ( member @ secrecy_chanID @ F @ ( ins @ E ) )
                & ( exprChannel @ F @ C )
                & ~ ( member @ secrecy_chanID @ F @ ( loc @ D ) )
                & ( member @ secrecy_chanID @ F @ B ) )
           => ( ineM @ D @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(147,axiom,
    ( ineM
    = ( ^ [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression] :
        ? [D: secrecy_chanID] :
          ( ( member @ secrecy_chanID @ D @ ( ins @ A ) )
          & ( member @ secrecy_chanID @ D @ B )
          & ( exprChannel @ D @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_ineM__def) ).

thf(704,plain,
    ( ineM
    = ( ^ [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression] :
        ? [D: secrecy_chanID] :
          ( ( member @ secrecy_chanID @ D @ ( ins @ A ) )
          & ( member @ secrecy_chanID @ D @ B )
          & ( exprChannel @ D @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(29,axiom,
    ! [TA: $tType] :
      ( ( bounde1808546759up_bot @ TA )
     => ! [A: TA,B: TA] :
          ( ( ( sup_sup @ TA @ A @ B )
            = ( bot_bot @ TA ) )
          = ( ( A
              = ( bot_bot @ TA ) )
            & ( B
              = ( bot_bot @ TA ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_sup__bot_Oeq__neutr__iff) ).

thf(350,plain,
    ! [TA: $tType] :
      ( ( bounde1808546759up_bot @ TA )
     => ! [A: TA,B: TA] :
          ( ( ( sup_sup @ TA @ A @ B )
            = ( bot_bot @ TA ) )
          = ( ( A
              = ( bot_bot @ TA ) )
            & ( B
              = ( bot_bot @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(49,axiom,
    ! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
      ( ~ ( ineM @ A @ B @ C )
     => ( ~ ( ineM @ D @ B @ C )
       => ( ( ( subcomponents @ E )
            = ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
         => ( ( correctCompositionIn @ E )
           => ~ ( ineM @ E @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_TBtheorem3b) ).

thf(406,plain,
    ! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
      ( ~ ( ineM @ A @ B @ C )
     => ( ~ ( ineM @ D @ B @ C )
       => ( ( ( subcomponents @ E )
            = ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
         => ( ( correctCompositionIn @ E )
           => ~ ( ineM @ E @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(53,axiom,
    ! [TA: $tType] : ( bounded_lattice @ ( set @ TA ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Obounded__lattice_1) ).

thf(419,plain,
    ! [TA: $tType] : ( bounded_lattice @ ( set @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(216,axiom,
    ! [A: secrecy_chanID,B: set @ secrecy_chanID,C: secrecy_specID,D: secrecy_Expression] :
      ( ( member @ secrecy_chanID @ A @ B )
     => ( ( member @ secrecy_chanID @ A @ ( ins @ C ) )
       => ( ( exprChannel @ A @ D )
         => ( ineM @ C @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_ineM__L1) ).

thf(990,plain,
    ! [A: secrecy_chanID,B: set @ secrecy_chanID,C: secrecy_specID,D: secrecy_Expression] :
      ( ( member @ secrecy_chanID @ A @ B )
     => ( ( member @ secrecy_chanID @ A @ ( ins @ C ) )
       => ( ( exprChannel @ A @ D )
         => ( ineM @ C @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(33,axiom,
    ! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_empty__subsetI) ).

thf(362,plain,
    ! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(57,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
      = ( sup_sup @ ( set @ TA ) @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_Un__left__absorb) ).

thf(434,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
      = ( sup_sup @ ( set @ TA ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(252,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correc965049635ionLoc @ A )
       => ( ( correctCompositionKS @ A )
         => ( ~ ( member @ secrecy_KS @ D @ ( specKeysSecrets @ B ) )
           => ( ~ ( member @ secrecy_KS @ D @ ( specKeysSecrets @ C ) )
             => ( ! [E: secrecy_Keys] :
                    ( ( D
                      = ( secrecy_kKS @ E ) )
                   => ( ~ ( ine @ B @ ( secrecy_kE @ E ) )
                      & ~ ( ine @ C @ ( secrecy_kE @ E ) ) ) )
               => ( ! [E: secrecy_Secrets] :
                      ( ( D
                        = ( secrecy_sKS @ E ) )
                     => ( ~ ( ine @ B @ ( secrecy_sE @ E ) )
                        & ~ ( ine @ C @ ( secrecy_sE @ E ) ) ) )
                 => ( ~ ( member @ secrecy_KS @ D @ ( sup_sup @ ( set @ secrecy_KS ) @ ( localSecrets @ B ) @ ( localSecrets @ C ) ) )
                   => ~ ( member @ secrecy_KS @ D @ ( localSecrets @ A ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_LocalSecretsComposition__neg) ).

thf(1122,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correc965049635ionLoc @ A )
       => ( ( correctCompositionKS @ A )
         => ( ~ ( member @ secrecy_KS @ D @ ( specKeysSecrets @ B ) )
           => ( ~ ( member @ secrecy_KS @ D @ ( specKeysSecrets @ C ) )
             => ( ! [E: secrecy_Keys] :
                    ( ( D
                      = ( secrecy_kKS @ E ) )
                   => ( ~ ( ine @ B @ ( secrecy_kE @ E ) )
                      & ~ ( ine @ C @ ( secrecy_kE @ E ) ) ) )
               => ( ! [E: secrecy_Secrets] :
                      ( ( D
                        = ( secrecy_sKS @ E ) )
                     => ( ~ ( ine @ B @ ( secrecy_sE @ E ) )
                        & ~ ( ine @ C @ ( secrecy_sE @ E ) ) ) )
                 => ( ~ ( member @ secrecy_KS @ D @ ( sup_sup @ ( set @ secrecy_KS ) @ ( localSecrets @ B ) @ ( localSecrets @ C ) ) )
                   => ~ ( member @ secrecy_KS @ D @ ( localSecrets @ A ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(6,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
          | ( ord_less_eq @ TA @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_linear) ).

thf(271,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
          | ( ord_less_eq @ TA @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(164,axiom,
    member @ secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ pq ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_sg5) ).

thf(764,plain,
    member @ secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ pq ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(213,axiom,
    ! [A: secrecy_Keys,B: secrecy_Secrets] :
      ( ( secrecy_kKS @ A )
     != ( secrecy_sKS @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_KS_Odistinct_I1_J) ).

thf(979,plain,
    ! [A: secrecy_Keys,B: secrecy_Secrets] :
      ( ( secrecy_kKS @ A )
     != ( secrecy_sKS @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(94,axiom,
    ! [TA: $tType] :
      ( ( is_singleton @ TA )
      = ( ^ [A: set @ TA] :
            ( A
            = ( insert @ TA @ ( the_elem @ TA @ A ) @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_is__singleton__the__elem) ).

thf(535,plain,
    ! [TA: $tType] :
      ( ( is_singleton @ TA )
      = ( ^ [A: set @ TA] :
            ( A
            = ( insert @ TA @ ( the_elem @ TA @ A ) @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(176,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correc965049635ionLoc @ A )
       => ( ! [E: secrecy_Keys] :
              ( ( D
                = ( secrecy_kKS @ E ) )
             => ( ~ ( ine @ B @ ( secrecy_kE @ E ) )
                & ~ ( ine @ C @ ( secrecy_kE @ E ) ) ) )
         => ( ! [E: secrecy_Secrets] :
                ( ( D
                  = ( secrecy_sKS @ E ) )
               => ( ~ ( ine @ B @ ( secrecy_sE @ E ) )
                  & ~ ( ine @ C @ ( secrecy_sE @ E ) ) ) )
           => ( ~ ( member @ secrecy_KS @ D @ ( localSecrets @ B ) )
             => ( ~ ( member @ secrecy_KS @ D @ ( localSecrets @ C ) )
               => ~ ( member @ secrecy_KS @ D @ ( localSecrets @ A ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_LocalSecretsComposition__neg1) ).

thf(816,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correc965049635ionLoc @ A )
       => ( ! [E: secrecy_Keys] :
              ( ( D
                = ( secrecy_kKS @ E ) )
             => ( ~ ( ine @ B @ ( secrecy_kE @ E ) )
                & ~ ( ine @ C @ ( secrecy_kE @ E ) ) ) )
         => ( ! [E: secrecy_Secrets] :
                ( ( D
                  = ( secrecy_sKS @ E ) )
               => ( ~ ( ine @ B @ ( secrecy_sE @ E ) )
                  & ~ ( ine @ C @ ( secrecy_sE @ E ) ) ) )
           => ( ~ ( member @ secrecy_KS @ D @ ( localSecrets @ B ) )
             => ( ~ ( member @ secrecy_KS @ D @ ( localSecrets @ C ) )
               => ~ ( member @ secrecy_KS @ D @ ( localSecrets @ A ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(228,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets,E: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) )
         => ( ( member @ secrecy_chanID @ E @ ( ins @ C ) )
           => ( ( exprChannel @ E @ ( secrecy_sE @ D ) )
             => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ A ) )
               => ( ( correctCompositionIn @ A )
                 => ? [F: secrecy_chanID] :
                      ( ( member @ secrecy_chanID @ F @ ( ins @ A ) )
                      & ( exprChannel @ F @ ( secrecy_sE @ D ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_correctCompositionKS__exprChannel__s__Qex) ).

thf(1029,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets,E: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) )
         => ( ( member @ secrecy_chanID @ E @ ( ins @ C ) )
           => ( ( exprChannel @ E @ ( secrecy_sE @ D ) )
             => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ A ) )
               => ( ( correctCompositionIn @ A )
                 => ? [F: secrecy_chanID] :
                      ( ( member @ secrecy_chanID @ F @ ( ins @ A ) )
                      & ( exprChannel @ F @ ( secrecy_sE @ D ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(259,axiom,
    ! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID,F: secrecy_chanID] :
      ( ~ ( ineM @ A @ B @ C )
     => ( ~ ( ineM @ D @ B @ C )
       => ( ( ( subcomponents @ E )
            = ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
         => ( ( correctCompositionIn @ E )
           => ( ( member @ secrecy_chanID @ F @ B )
             => ( ( member @ secrecy_chanID @ F @ ( ins @ E ) )
               => ~ ( exprChannel @ F @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_TBlemma3b) ).

thf(1149,plain,
    ! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID,F: secrecy_chanID] :
      ( ~ ( ineM @ A @ B @ C )
     => ( ~ ( ineM @ D @ B @ C )
       => ( ( ( subcomponents @ E )
            = ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
         => ( ( correctCompositionIn @ E )
           => ( ( member @ secrecy_chanID @ F @ B )
             => ( ( member @ secrecy_chanID @ F @ ( ins @ E ) )
               => ~ ( exprChannel @ F @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(226,axiom,
    ! [A: secrecy_KS,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
      ( ~ ( member @ secrecy_KS @ A @ ( specKeysSecrets @ B ) )
     => ( ~ ( member @ secrecy_KS @ A @ ( specKeysSecrets @ C ) )
       => ( ( knowle1437066798e_know @ B @ A )
         => ( ( ( subcomponents @ D )
              = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
           => ( ( correctCompositionIn @ D )
             => ( ( correctCompositionKS @ D )
               => ( knowle1437066798e_know @ D @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_know__composition1) ).

thf(1022,plain,
    ! [A: secrecy_KS,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
      ( ~ ( member @ secrecy_KS @ A @ ( specKeysSecrets @ B ) )
     => ( ~ ( member @ secrecy_KS @ A @ ( specKeysSecrets @ C ) )
       => ( ( knowle1437066798e_know @ B @ A )
         => ( ( ( subcomponents @ D )
              = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
           => ( ( correctCompositionIn @ D )
             => ( ( correctCompositionKS @ D )
               => ( knowle1437066798e_know @ D @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(68,axiom,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ( ( ine @ A @ B )
        | ( ine @ C @ B ) )
     => ( ( ( subcomponents @ D )
          = ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correctCompositionIn @ D )
         => ( ( ( loc @ D )
              = ( bot_bot @ ( set @ secrecy_chanID ) ) )
           => ( ine @ D @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_TBtheorem4a__empty) ).

thf(462,plain,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ( ( ine @ A @ B )
        | ( ine @ C @ B ) )
     => ( ( ( subcomponents @ D )
          = ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correctCompositionIn @ D )
         => ( ( ( loc @ D )
              = ( bot_bot @ ( set @ secrecy_chanID ) ) )
           => ( ine @ D @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(80,axiom,
    ! [TA: $tType] :
      ( ( bounde1808546759up_bot @ TA )
     => ! [A: TA,B: TA] :
          ( ( ( bot_bot @ TA )
            = ( sup_sup @ TA @ A @ B ) )
          = ( ( A
              = ( bot_bot @ TA ) )
            & ( B
              = ( bot_bot @ TA ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_bot__eq__sup__iff) ).

thf(494,plain,
    ! [TA: $tType] :
      ( ( bounde1808546759up_bot @ TA )
     => ! [A: TA,B: TA] :
          ( ( ( bot_bot @ TA )
            = ( sup_sup @ TA @ A @ B ) )
          = ( ( A
              = ( bot_bot @ TA ) )
            & ( B
              = ( bot_bot @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(242,axiom,
    ( out_exprChannelSet
    = ( ^ [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression] :
          ( ! [D: secrecy_chanID] :
              ( ( member @ secrecy_chanID @ D @ B )
             => ( ( member @ secrecy_chanID @ D @ ( out @ A ) )
                & ( exprChannel @ D @ C ) ) )
          & ! [D: secrecy_chanID] :
              ( ( ~ ( member @ secrecy_chanID @ D @ B )
                & ( member @ secrecy_chanID @ D @ ( out @ A ) ) )
             => ~ ( exprChannel @ D @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_out__exprChannelSet__def) ).

thf(1080,plain,
    ( out_exprChannelSet
    = ( ^ [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression] :
          ( ! [D: secrecy_chanID] :
              ( ( member @ secrecy_chanID @ D @ B )
             => ( ( member @ secrecy_chanID @ D @ ( out @ A ) )
                & ( exprChannel @ D @ C ) ) )
          & ! [D: secrecy_chanID] :
              ( ( ~ ( member @ secrecy_chanID @ D @ B )
                & ( member @ secrecy_chanID @ D @ ( out @ A ) ) )
             => ~ ( exprChannel @ D @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(27,axiom,
    ! [TA: $tType] : ( bot @ ( set @ TA ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Obot_11) ).

thf(345,plain,
    ! [TA: $tType] : ( bot @ ( set @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(186,axiom,
    ! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
      ( ( ( eoutM @ A @ B @ C )
        | ( eoutM @ D @ B @ C ) )
     => ( ( ( subcomponents @ E )
          = ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correc990227761ionOut @ E )
         => ( ? [F: secrecy_chanID] :
                ( ( ( member @ secrecy_chanID @ F @ ( out @ A ) )
                  | ( member @ secrecy_chanID @ F @ ( out @ D ) ) )
                & ( member @ secrecy_chanID @ F @ B )
                & ( exprChannel @ F @ C )
                & ~ ( member @ secrecy_chanID @ F @ ( loc @ E ) ) )
           => ( eoutM @ E @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_TBtheorem5b__PQ) ).

thf(858,plain,
    ! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
      ( ( ( eoutM @ A @ B @ C )
        | ( eoutM @ D @ B @ C ) )
     => ( ( ( subcomponents @ E )
          = ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correc990227761ionOut @ E )
         => ( ? [F: secrecy_chanID] :
                ( ( ( member @ secrecy_chanID @ F @ ( out @ A ) )
                  | ( member @ secrecy_chanID @ F @ ( out @ D ) ) )
                & ( member @ secrecy_chanID @ F @ B )
                & ( exprChannel @ F @ C )
                & ~ ( member @ secrecy_chanID @ F @ ( loc @ E ) ) )
           => ( eoutM @ E @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(35,axiom,
    ! [TA: $tType,A: TA] : ( is_singleton @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_is__singletonI) ).

thf(367,plain,
    ! [TA: $tType,A: TA] : ( is_singleton @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(141,axiom,
    ! [TA: $tType,A: TA,B: TA,C: set @ TA] :
      ( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
      = ( ( A = B )
        | ( member @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_insert__iff) ).

thf(685,plain,
    ! [TA: $tType,A: TA,B: TA,C: set @ TA] :
      ( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
      = ( ( A = B )
        | ( member @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(214,axiom,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_chanID] :
      ( ~ ( ine @ A @ B )
     => ( ( exprChannel @ C @ B )
       => ~ ( member @ secrecy_chanID @ C @ ( ins @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_ine__ins__neg1) ).

thf(983,plain,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_chanID] :
      ( ~ ( ine @ A @ B )
     => ( ( exprChannel @ C @ B )
       => ~ ( member @ secrecy_chanID @ C @ ( ins @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(47,axiom,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ( eout @ A @ B )
     => ( ( ( subcomponents @ A )
          = ( insert @ secrecy_specID @ C @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correc990227761ionOut @ A )
         => ( ( eout @ C @ B )
            | ( eout @ D @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_TBtheorem2a) ).

thf(399,plain,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ( eout @ A @ B )
     => ( ( ( subcomponents @ A )
          = ( insert @ secrecy_specID @ C @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correc990227761ionOut @ A )
         => ( ( eout @ C @ B )
            | ( eout @ D @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(166,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
     => ( ~ ( member @ TA @ A @ B )
       => ( member @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_UnE) ).

thf(768,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
     => ( ~ ( member @ TA @ A @ B )
       => ( member @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(232,axiom,
    ! [TA: $tType,A: set @ TA] :
      ( ( A
       != ( bot_bot @ ( set @ TA ) ) )
     => ( ! [B: TA,C: TA] :
            ( ( member @ TA @ B @ A )
           => ( ( member @ TA @ C @ A )
             => ( B = C ) ) )
       => ( is_singleton @ TA @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_is__singletonI_H) ).

thf(1044,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ( A
       != ( bot_bot @ ( set @ TA ) ) )
     => ( ! [B: TA,C: TA] :
            ( ( member @ TA @ B @ A )
           => ( ( member @ TA @ C @ A )
             => ( B = C ) ) )
       => ( is_singleton @ TA @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(119,axiom,
    ! [TA: $tType] :
      ( ( insert @ TA )
      = ( ^ [A: TA] : ( sup_sup @ ( set @ TA ) @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_insert__is__Un) ).

thf(608,plain,
    ! [TA: $tType] :
      ( ( insert @ TA )
      = ( ^ [A: TA] : ( sup_sup @ ( set @ TA ) @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(215,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correc965049635ionLoc @ A )
       => ( ~ ( ine @ B @ ( secrecy_sE @ D ) )
         => ( ~ ( ine @ C @ ( secrecy_sE @ D ) )
           => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ B ) )
             => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ C ) )
               => ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_LocalSecretsComposition__neg1__s) ).

thf(986,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correc965049635ionLoc @ A )
       => ( ~ ( ine @ B @ ( secrecy_sE @ D ) )
         => ( ~ ( ine @ C @ ( secrecy_sE @ D ) )
           => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ B ) )
             => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ C ) )
               => ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(105,axiom,
    ! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
      ( ( ( insert @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
        = ( insert @ TA @ C @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
      = ( ( ( A = C )
          & ( B = D ) )
        | ( ( A = D )
          & ( B = C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_doubleton__eq__iff) ).

thf(563,plain,
    ! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
      ( ( ( insert @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
        = ( insert @ TA @ C @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
      = ( ( ( A = C )
          & ( B = D ) )
        | ( ( A = D )
          & ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(220,axiom,
    ! [TA: $tType,A: set @ TA] :
      ( ( collect @ TA
        @ ^ [B: TA] : ( member @ TA @ B @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_Collect__mem__eq) ).

thf(1000,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ( collect @ TA
        @ ^ [B: TA] : ( member @ TA @ B @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(59,axiom,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
        = ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_singleton__inject) ).

thf(438,plain,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
        = ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(56,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_subset__antisym) ).

thf(431,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(131,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( member @ TA @ A @ B )
     => ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_UnI1) ).

thf(653,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( member @ TA @ A @ B )
     => ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(8,axiom,
    ! [TA: $tType] :
      ( ( ord @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( A = B )
         => ( ( ord_less_eq @ TA @ B @ C )
           => ( ord_less_eq @ TA @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_ord__eq__le__trans) ).

thf(278,plain,
    ! [TA: $tType] :
      ( ( ord @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( A = B )
         => ( ( ord_less_eq @ TA @ B @ C )
           => ( ord_less_eq @ TA @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(187,axiom,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_singletonD) ).

thf(868,plain,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(38,axiom,
    ! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_subset__refl) ).

thf(374,plain,
    ! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(175,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correctCompositionIn @ A )
       => ( ( member @ secrecy_chanID @ D @ ( ins @ A ) )
         => ( ( member @ secrecy_chanID @ D @ ( ins @ B ) )
            | ( member @ secrecy_chanID @ D @ ( ins @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_correctCompositionIn__L2) ).

thf(812,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correctCompositionIn @ A )
       => ( ( member @ secrecy_chanID @ D @ ( ins @ A ) )
         => ( ( member @ secrecy_chanID @ D @ ( ins @ B ) )
            | ( member @ secrecy_chanID @ D @ ( ins @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(159,axiom,
    ! [A: secrecy_Keys,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
      ( ( member @ secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ B ) )
     => ( ( ( subcomponents @ B )
          = ( insert @ secrecy_specID @ C @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correc965049635ionLoc @ B )
         => ( ~ ( ine @ D @ ( secrecy_kE @ A ) )
           => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ C ) )
             => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ D ) )
               => ( ine @ C @ ( secrecy_kE @ A ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_LocalSecretsComposition__ine1__k) ).

thf(749,plain,
    ! [A: secrecy_Keys,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
      ( ( member @ secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ B ) )
     => ( ( ( subcomponents @ B )
          = ( insert @ secrecy_specID @ C @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correc965049635ionLoc @ B )
         => ( ~ ( ine @ D @ ( secrecy_kE @ A ) )
           => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ C ) )
             => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ D ) )
               => ( ine @ C @ ( secrecy_kE @ A ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(204,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets,E: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) )
         => ( ( member @ secrecy_chanID @ E @ ( ins @ C ) )
           => ( ( exprChannel @ E @ ( secrecy_sE @ D ) )
             => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ A ) )
               => ( ( correctCompositionIn @ A )
                 => ( ( member @ secrecy_chanID @ E @ ( ins @ A ) )
                    & ( exprChannel @ E @ ( secrecy_sE @ D ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_correctCompositionKS__exprChannel__s__Q) ).

thf(939,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets,E: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) )
         => ( ( member @ secrecy_chanID @ E @ ( ins @ C ) )
           => ( ( exprChannel @ E @ ( secrecy_sE @ D ) )
             => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ A ) )
               => ( ( correctCompositionIn @ A )
                 => ( ( member @ secrecy_chanID @ E @ ( ins @ A ) )
                    & ( exprChannel @ E @ ( secrecy_sE @ D ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(258,axiom,
    ! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
      ( ( ineM @ A @ B @ C )
     => ( ~ ( ineM @ D @ B @ C )
       => ( ( ( subcomponents @ E )
            = ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
         => ( ( correctCompositionIn @ E )
           => ( ? [F: secrecy_chanID] :
                  ( ( ine_ex1303305700Single @ A @ F @ C )
                  & ( member @ secrecy_chanID @ F @ B )
                  & ( member @ secrecy_chanID @ F @ ( loc @ E ) ) )
             => ~ ( ineM @ E @ B @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_TBtheorem4b__notP1) ).

thf(1145,plain,
    ! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID] :
      ( ( ineM @ A @ B @ C )
     => ( ~ ( ineM @ D @ B @ C )
       => ( ( ( subcomponents @ E )
            = ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
         => ( ( correctCompositionIn @ E )
           => ( ? [F: secrecy_chanID] :
                  ( ( ine_ex1303305700Single @ A @ F @ C )
                  & ( member @ secrecy_chanID @ F @ B )
                  & ( member @ secrecy_chanID @ F @ ( loc @ E ) ) )
             => ~ ( ineM @ E @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(178,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( member @ TA @ C @ A )
       => ( member @ TA @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_subsetD) ).

thf(836,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( member @ TA @ C @ A )
       => ( member @ TA @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(71,axiom,
    bot @ $o,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Obot_17) ).

thf(473,plain,
    bot @ $o,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(241,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correctCompositionIn @ A )
       => ( ~ ( member @ secrecy_chanID @ D @ ( loc @ A ) )
         => ( ( member @ secrecy_chanID @ D @ ( ins @ B ) )
           => ( member @ secrecy_chanID @ D @ ( ins @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_correctCompositionIn__L1) ).

thf(1076,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correctCompositionIn @ A )
       => ( ~ ( member @ secrecy_chanID @ D @ ( loc @ A ) )
         => ( ( member @ secrecy_chanID @ D @ ( ins @ B ) )
           => ( member @ secrecy_chanID @ D @ ( ins @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(122,axiom,
    ! [TA: $tType,A: set @ TA] :
      ( ( sup_sup @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_Un__empty__left) ).

thf(617,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ( sup_sup @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(87,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
      ( ( ( sup_sup @ ( set @ TA ) @ A @ B )
        = ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
      = ( ( ( A
            = ( bot_bot @ ( set @ TA ) ) )
          & ( B
            = ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) )
        | ( ( A
            = ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
          & ( B
            = ( bot_bot @ ( set @ TA ) ) ) )
        | ( ( A
            = ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
          & ( B
            = ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_Un__singleton__iff) ).

thf(516,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
      ( ( ( sup_sup @ ( set @ TA ) @ A @ B )
        = ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
      = ( ( ( A
            = ( bot_bot @ ( set @ TA ) ) )
          & ( B
            = ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) )
        | ( ( A
            = ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
          & ( B
            = ( bot_bot @ ( set @ TA ) ) ) )
        | ( ( A
            = ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
          & ( B
            = ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(90,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( A = B )
     => ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_equalityD2) ).

thf(525,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ( A = B )
     => ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(24,axiom,
    ! [TA: $tType] : ( preorder @ ( set @ TA ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Opreorder_8) ).

thf(327,plain,
    ! [TA: $tType] : ( preorder @ ( set @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(247,axiom,
    ! [A: secrecy_KS,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
      ( ~ ( member @ secrecy_KS @ A @ ( specKeysSecrets @ B ) )
     => ( ~ ( member @ secrecy_KS @ A @ ( specKeysSecrets @ C ) )
       => ( ( ( knowle1437066798e_know @ B @ A )
            | ( knowle1437066798e_know @ C @ A ) )
         => ( ( ( subcomponents @ D )
              = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
           => ( ( correctCompositionIn @ D )
             => ( ( correctCompositionKS @ D )
               => ( knowle1437066798e_know @ D @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_know__composition) ).

thf(1098,plain,
    ! [A: secrecy_KS,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
      ( ~ ( member @ secrecy_KS @ A @ ( specKeysSecrets @ B ) )
     => ( ~ ( member @ secrecy_KS @ A @ ( specKeysSecrets @ C ) )
       => ( ( ( knowle1437066798e_know @ B @ A )
            | ( knowle1437066798e_know @ C @ A ) )
         => ( ( ( subcomponents @ D )
              = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
           => ( ( correctCompositionIn @ D )
             => ( ( correctCompositionKS @ D )
               => ( knowle1437066798e_know @ D @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(217,axiom,
    ( eoutM
    = ( ^ [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression] :
        ? [D: secrecy_chanID] :
          ( ( member @ secrecy_chanID @ D @ ( out @ A ) )
          & ( member @ secrecy_chanID @ D @ B )
          & ( exprChannel @ D @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_eoutM__def) ).

thf(993,plain,
    ( eoutM
    = ( ^ [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression] :
        ? [D: secrecy_chanID] :
          ( ( member @ secrecy_chanID @ D @ ( out @ A ) )
          & ( member @ secrecy_chanID @ D @ B )
          & ( exprChannel @ D @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(150,axiom,
    ! [A: secrecy_specID,B: secrecy_Secrets,C: secrecy_specID,D: secrecy_specID] :
      ( ~ ( knowle1437066798e_know @ A @ ( secrecy_sKS @ B ) )
     => ( ~ ( knowle1437066798e_know @ C @ ( secrecy_sKS @ B ) )
       => ( ( ( subcomponents @ D )
            = ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
         => ( ( correctCompositionIn @ D )
           => ~ ( ine @ D @ ( secrecy_sE @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_know__composition__neg__ine__s) ).

thf(712,plain,
    ! [A: secrecy_specID,B: secrecy_Secrets,C: secrecy_specID,D: secrecy_specID] :
      ( ~ ( knowle1437066798e_know @ A @ ( secrecy_sKS @ B ) )
     => ( ~ ( knowle1437066798e_know @ C @ ( secrecy_sKS @ B ) )
       => ( ( ( subcomponents @ D )
            = ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
         => ( ( correctCompositionIn @ D )
           => ~ ( ine @ D @ ( secrecy_sE @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(221,axiom,
    ! [A: secrecy_Keys,B: secrecy_specID] :
      ( ~ ( member @ secrecy_Keys @ A @ ( specKeys @ B ) )
     => ( ~ ( knowle1437066798e_know @ B @ ( secrecy_kKS @ A ) )
       => ( ( knowle1667810483orrect @ B @ ( secrecy_kKS @ A ) )
         => ~ ( eout @ B @ ( secrecy_kE @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_not__know__k__not__eout) ).

thf(1003,plain,
    ! [A: secrecy_Keys,B: secrecy_specID] :
      ( ~ ( member @ secrecy_Keys @ A @ ( specKeys @ B ) )
     => ( ~ ( knowle1437066798e_know @ B @ ( secrecy_kKS @ A ) )
       => ( ( knowle1667810483orrect @ B @ ( secrecy_kKS @ A ) )
         => ~ ( eout @ B @ ( secrecy_kE @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(110,axiom,
    ! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression] :
      ( ( ine_exprChannelSet @ A @ B @ C )
     => ( ( B
          = ( bot_bot @ ( set @ secrecy_chanID ) ) )
       => ~ ( ine @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_ine__empty__exprChannelSet) ).

thf(580,plain,
    ! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression] :
      ( ( ine_exprChannelSet @ A @ B @ C )
     => ( ( B
          = ( bot_bot @ ( set @ secrecy_chanID ) ) )
       => ~ ( ine @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(185,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
      = ( ( member @ TA @ A @ B )
        | ( member @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_Un__iff) ).

thf(855,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
      = ( ( member @ TA @ A @ B )
        | ( member @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(9,axiom,
    ! [TA: $tType] :
      ( ( preorder @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ B @ C )
           => ( ord_less_eq @ TA @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_order__trans) ).

thf(282,plain,
    ! [TA: $tType] :
      ( ( preorder @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ord_less_eq @ TA @ A @ B )
         => ( ( ord_less_eq @ TA @ B @ C )
           => ( ord_less_eq @ TA @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(261,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys,E: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) )
         => ( ( member @ secrecy_chanID @ E @ ( ins @ C ) )
           => ( ( exprChannel @ E @ ( secrecy_kE @ D ) )
             => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ A ) )
               => ( ( correctCompositionIn @ A )
                 => ( ( member @ secrecy_chanID @ E @ ( ins @ A ) )
                    & ( exprChannel @ E @ ( secrecy_kE @ D ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_correctCompositionKS__exprChannel__k__Q) ).

thf(1156,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys,E: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) )
         => ( ( member @ secrecy_chanID @ E @ ( ins @ C ) )
           => ( ( exprChannel @ E @ ( secrecy_kE @ D ) )
             => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ A ) )
               => ( ( correctCompositionIn @ A )
                 => ( ( member @ secrecy_chanID @ E @ ( ins @ A ) )
                    & ( exprChannel @ E @ ( secrecy_kE @ D ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(234,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correc965049635ionLoc @ A )
       => ( ~ ( ine @ B @ ( secrecy_kE @ D ) )
         => ( ~ ( ine @ C @ ( secrecy_kE @ D ) )
           => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ B ) )
             => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ C ) )
               => ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_LocalSecretsComposition__neg1__k) ).

thf(1053,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correc965049635ionLoc @ A )
       => ( ~ ( ine @ B @ ( secrecy_kE @ D ) )
         => ( ~ ( ine @ C @ ( secrecy_kE @ D ) )
           => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ B ) )
             => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ C ) )
               => ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(26,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( ord_less_eq @ TA @ A @ B )
           => ~ ( ord_less_eq @ TA @ B @ C ) )
         => ( ( ( ord_less_eq @ TA @ B @ A )
             => ~ ( ord_less_eq @ TA @ A @ C ) )
           => ( ( ( ord_less_eq @ TA @ A @ C )
               => ~ ( ord_less_eq @ TA @ C @ B ) )
             => ( ( ( ord_less_eq @ TA @ C @ B )
                 => ~ ( ord_less_eq @ TA @ B @ A ) )
               => ( ( ( ord_less_eq @ TA @ B @ C )
                   => ~ ( ord_less_eq @ TA @ C @ A ) )
                 => ~ ( ( ord_less_eq @ TA @ C @ A )
                     => ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_le__cases3) ).

thf(331,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA,B: TA,C: TA] :
          ( ( ( ord_less_eq @ TA @ A @ B )
           => ~ ( ord_less_eq @ TA @ B @ C ) )
         => ( ( ( ord_less_eq @ TA @ B @ A )
             => ~ ( ord_less_eq @ TA @ A @ C ) )
           => ( ( ( ord_less_eq @ TA @ A @ C )
               => ~ ( ord_less_eq @ TA @ C @ B ) )
             => ( ( ( ord_less_eq @ TA @ C @ B )
                 => ~ ( ord_less_eq @ TA @ B @ A ) )
               => ( ( ( ord_less_eq @ TA @ B @ C )
                   => ~ ( ord_less_eq @ TA @ C @ A ) )
                 => ~ ( ( ord_less_eq @ TA @ C @ A )
                     => ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(60,axiom,
    ( locStream
    = ( ^ [A: secrecy_specID] : ( (=) @ ( set @ secrecy_chanID ) @ ( loc @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_locStream__def) ).

thf(441,plain,
    ( locStream
    = ( ^ [A: secrecy_specID] : ( (=) @ ( set @ secrecy_chanID ) @ ( loc @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(70,axiom,
    ! [TA: $tType,A: TA > $o] :
      ( ( ( collect @ TA @ A )
        = ( bot_bot @ ( set @ TA ) ) )
      = ( ! [B: TA] :
            ~ ( A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_Collect__empty__eq) ).

thf(470,plain,
    ! [TA: $tType,A: TA > $o] :
      ( ( ( collect @ TA @ A )
        = ( bot_bot @ ( set @ TA ) ) )
      = ( ! [B: TA] :
            ~ ( A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(206,axiom,
    ! [A: secrecy_chanID,B: secrecy_Keys,C: secrecy_specID,D: secrecy_specID] :
      ( ( exprChannel @ A @ ( secrecy_kE @ B ) )
     => ( ~ ( ine @ C @ ( secrecy_kE @ B ) )
       => ( ~ ( ine @ D @ ( secrecy_kE @ B ) )
         => ( ~ ( member @ secrecy_chanID @ A @ ( ins @ C ) )
            & ~ ( member @ secrecy_chanID @ A @ ( ins @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_LocalSecretsComposition__exprChannel__k) ).

thf(951,plain,
    ! [A: secrecy_chanID,B: secrecy_Keys,C: secrecy_specID,D: secrecy_specID] :
      ( ( exprChannel @ A @ ( secrecy_kE @ B ) )
     => ( ~ ( ine @ C @ ( secrecy_kE @ B ) )
       => ( ~ ( ine @ D @ ( secrecy_kE @ B ) )
         => ( ~ ( member @ secrecy_chanID @ A @ ( ins @ C ) )
            & ~ ( member @ secrecy_chanID @ A @ ( ins @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(32,axiom,
    ! [TA: $tType] :
      ( ( bounde1808546759up_bot @ TA )
     => ! [A: TA,B: TA] :
          ( ( ( bot_bot @ TA )
            = ( sup_sup @ TA @ A @ B ) )
          = ( ( A
              = ( bot_bot @ TA ) )
            & ( B
              = ( bot_bot @ TA ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_sup__bot_Oneutr__eq__iff) ).

thf(359,plain,
    ! [TA: $tType] :
      ( ( bounde1808546759up_bot @ TA )
     => ! [A: TA,B: TA] :
          ( ( ( bot_bot @ TA )
            = ( sup_sup @ TA @ A @ B ) )
          = ( ( A
              = ( bot_bot @ TA ) )
            & ( B
              = ( bot_bot @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(130,axiom,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ( ( ine @ A @ B )
        | ( ine @ C @ B ) )
     => ( ( ( subcomponents @ D )
          = ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correctCompositionIn @ D )
         => ( ? [E: secrecy_chanID] :
                ( ( ( member @ secrecy_chanID @ E @ ( ins @ A ) )
                  | ( member @ secrecy_chanID @ E @ ( ins @ C ) ) )
                & ( exprChannel @ E @ B )
                & ~ ( member @ secrecy_chanID @ E @ ( loc @ D ) ) )
           => ( ine @ D @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_TBtheorem4a__PQ) ).

thf(643,plain,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID] :
      ( ( ( ine @ A @ B )
        | ( ine @ C @ B ) )
     => ( ( ( subcomponents @ D )
          = ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correctCompositionIn @ D )
         => ( ? [E: secrecy_chanID] :
                ( ( ( member @ secrecy_chanID @ E @ ( ins @ A ) )
                  | ( member @ secrecy_chanID @ E @ ( ins @ C ) ) )
                & ( exprChannel @ E @ B )
                & ~ ( member @ secrecy_chanID @ E @ ( loc @ D ) ) )
           => ( ine @ D @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(256,axiom,
    ~ ( ine @ q @ ( secrecy_sE @ secret ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_sg6a) ).

thf(1141,plain,
    ~ ( ine @ q @ ( secrecy_sE @ secret ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(116,axiom,
    ! [TA: $tType] :
      ( ( bounde1808546759up_bot @ TA )
     => ! [A: TA] :
          ( ( sup_sup @ TA @ ( bot_bot @ TA ) @ A )
          = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_sup__bot__left) ).

thf(600,plain,
    ! [TA: $tType] :
      ( ( bounde1808546759up_bot @ TA )
     => ! [A: TA] :
          ( ( sup_sup @ TA @ ( bot_bot @ TA ) @ A )
          = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(246,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member @ secrecy_KS @ D @ ( specKeysSecrets @ A ) )
         => ~ ( member @ secrecy_KS @ D @ ( specKeysSecrets @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_correctCompositionKS__negP) ).

thf(1094,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member @ secrecy_KS @ D @ ( specKeysSecrets @ A ) )
         => ~ ( member @ secrecy_KS @ D @ ( specKeysSecrets @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(223,axiom,
    ( ( subcomponents @ pq )
    = ( insert @ secrecy_specID @ p @ ( insert @ secrecy_specID @ q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_subPQ) ).

thf(1008,plain,
    ( ( subcomponents @ pq )
    = ( insert @ secrecy_specID @ p @ ( insert @ secrecy_specID @ q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(62,axiom,
    ( outStream
    = ( ^ [A: secrecy_specID] : ( (=) @ ( set @ secrecy_chanID ) @ ( out @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_outStream__def) ).

thf(446,plain,
    ( outStream
    = ( ^ [A: secrecy_specID] : ( (=) @ ( set @ secrecy_chanID ) @ ( out @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(81,axiom,
    ! [A: secrecy_Keys,B: secrecy_Secrets] :
      ( ( secrecy_kE @ A )
     != ( secrecy_sE @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_Expression_Odistinct_I1_J) ).

thf(497,plain,
    ! [A: secrecy_Keys,B: secrecy_Secrets] :
      ( ( secrecy_kE @ A )
     != ( secrecy_sE @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(126,axiom,
    ! [TA: $tType,A: set @ TA] :
      ( ( sup_sup @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_Un__empty__right) ).

thf(627,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ( sup_sup @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(244,axiom,
    ! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID,F: set @ secrecy_chanID] :
      ( ~ ( ineM @ A @ B @ C )
     => ( ( ( subcomponents @ D )
          = ( insert @ secrecy_specID @ E @ ( insert @ secrecy_specID @ A @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correctCompositionIn @ D )
         => ( ( ine_exprChannelSet @ E @ F @ C )
           => ( ! [G: secrecy_chanID] :
                  ( ( member @ secrecy_chanID @ G @ F )
                 => ( member @ secrecy_chanID @ G @ ( loc @ D ) ) )
             => ~ ( ineM @ D @ B @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_TBtheorem4b__notP2) ).

thf(1084,plain,
    ! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID,F: set @ secrecy_chanID] :
      ( ~ ( ineM @ A @ B @ C )
     => ( ( ( subcomponents @ D )
          = ( insert @ secrecy_specID @ E @ ( insert @ secrecy_specID @ A @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correctCompositionIn @ D )
         => ( ( ine_exprChannelSet @ E @ F @ C )
           => ( ! [G: secrecy_chanID] :
                  ( ( member @ secrecy_chanID @ G @ F )
                 => ( member @ secrecy_chanID @ G @ ( loc @ D ) ) )
             => ~ ( ineM @ D @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(102,axiom,
    ! [TA: $tType,A: set @ TA] :
      ( ( is_singleton @ TA @ A )
     => ~ ! [B: TA] :
            ( A
           != ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_is__singletonE) ).

thf(556,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ( is_singleton @ TA @ A )
     => ~ ! [B: TA] :
            ( A
           != ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(76,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ C @ A ) @ ( insert @ TA @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_insert__mono) ).

thf(482,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ C @ A ) @ ( insert @ TA @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(136,axiom,
    ! [TA: $tType,A: TA,B: TA,C: set @ TA] :
      ( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
     => ( ( A != B )
       => ( member @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_insertE) ).

thf(671,plain,
    ! [TA: $tType,A: TA,B: TA,C: set @ TA] :
      ( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
     => ( ( A != B )
       => ( member @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(162,axiom,
    ~ ( ine @ pq @ ( secrecy_sE @ secret ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_a22) ).

thf(759,plain,
    ~ ( ine @ pq @ ( secrecy_sE @ secret ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(193,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( member @ TA @ C @ A )
       => ( member @ TA @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_in__mono) ).

thf(891,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
     => ( ( member @ TA @ C @ A )
       => ( member @ TA @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(224,axiom,
    ( notSpe1586871396tsExpr
    = ( ^ [A: secrecy_specID,B: list @ secrecy_Expression] :
          ( ! [C: secrecy_Keys] :
              ( ( mem @ secrecy_Expression @ ( secrecy_kE @ C ) @ B )
             => ~ ( member @ secrecy_KS @ ( secrecy_kKS @ C ) @ ( specKeysSecrets @ A ) ) )
          & ! [C: secrecy_Secrets] :
              ( ( mem @ secrecy_Expression @ ( secrecy_sE @ C ) @ B )
             => ~ ( member @ secrecy_KS @ ( secrecy_sKS @ C ) @ ( specKeysSecrets @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_notSpecKeysSecretsExpr__def) ).

thf(1010,plain,
    ( notSpe1586871396tsExpr
    = ( ^ [A: secrecy_specID,B: list @ secrecy_Expression] :
          ( ! [C: secrecy_Keys] :
              ( ( mem @ secrecy_Expression @ ( secrecy_kE @ C ) @ B )
             => ~ ( member @ secrecy_KS @ ( secrecy_kKS @ C ) @ ( specKeysSecrets @ A ) ) )
          & ! [C: secrecy_Secrets] :
              ( ( mem @ secrecy_Expression @ ( secrecy_sE @ C ) @ B )
             => ~ ( member @ secrecy_KS @ ( secrecy_sKS @ C ) @ ( specKeysSecrets @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(181,axiom,
    ( ine_ex1303305700Single
    = ( ^ [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
          ( ( member @ secrecy_chanID @ B @ ( ins @ A ) )
          & ( exprChannel @ B @ C )
          & ! [D: secrecy_chanID,E: nat] :
              ( ( ( member @ secrecy_chanID @ D @ ( ins @ A ) )
                & ( D != B ) )
             => ~ ( exprChannel @ D @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_ine__exprChannelSingle__def) ).

thf(844,plain,
    ( ine_ex1303305700Single
    = ( ^ [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
          ( ( member @ secrecy_chanID @ B @ ( ins @ A ) )
          & ( exprChannel @ B @ C )
          & ! [D: secrecy_chanID] :
              ( ( ( member @ secrecy_chanID @ D @ ( ins @ A ) )
                & ( D != B ) )
             => ~ ( exprChannel @ D @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(212,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
      ( ( ! [D: TA] :
            ( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
           => ( C @ D ) ) )
      = ( ! [D: TA] :
            ( ( member @ TA @ D @ A )
           => ( C @ D ) )
        & ! [D: TA] :
            ( ( member @ TA @ D @ B )
           => ( C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_ball__Un) ).

thf(976,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
      ( ( ! [D: TA] :
            ( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
           => ( C @ D ) ) )
      = ( ! [D: TA] :
            ( ( member @ TA @ D @ A )
           => ( C @ D ) )
        & ! [D: TA] :
            ( ( member @ TA @ D @ B )
           => ( C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(142,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_Secrets] :
      ( ( correctCompositionKS @ A )
     => ( ( member @ secrecy_specID @ B @ ( subcomponents @ A ) )
       => ( ( member @ secrecy_Secrets @ C @ ( specSecrets @ B ) )
         => ( member @ secrecy_Secrets @ C @ ( specSecrets @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_correctCompositionKS__subcomp4) ).

thf(688,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_Secrets] :
      ( ( correctCompositionKS @ A )
     => ( ( member @ secrecy_specID @ B @ ( subcomponents @ A ) )
       => ( ( member @ secrecy_Secrets @ C @ ( specSecrets @ B ) )
         => ( member @ secrecy_Secrets @ C @ ( specSecrets @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(196,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets,E: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) )
         => ( ( member @ secrecy_chanID @ E @ ( ins @ B ) )
           => ( ( exprChannel @ E @ ( secrecy_sE @ D ) )
             => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ A ) )
               => ( ( correctCompositionIn @ A )
                 => ? [F: secrecy_chanID] :
                      ( ( member @ secrecy_chanID @ F @ ( ins @ A ) )
                      & ( exprChannel @ F @ ( secrecy_sE @ D ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_correctCompositionKS__exprChannel__s__Pex) ).

thf(903,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Secrets,E: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( localSecrets @ A ) )
         => ( ( member @ secrecy_chanID @ E @ ( ins @ B ) )
           => ( ( exprChannel @ E @ ( secrecy_sE @ D ) )
             => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ D ) @ ( specKeysSecrets @ A ) )
               => ( ( correctCompositionIn @ A )
                 => ? [F: secrecy_chanID] :
                      ( ( member @ secrecy_chanID @ F @ ( ins @ A ) )
                      & ( exprChannel @ F @ ( secrecy_sE @ D ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(145,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ! [C: TA] :
          ( ( member @ TA @ C @ A )
         => ( member @ TA @ C @ B ) )
     => ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_subsetI) ).

thf(699,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA] :
      ( ! [C: TA] :
          ( ( member @ TA @ C @ A )
         => ( member @ TA @ C @ B ) )
     => ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(18,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ord @ TA )
        & ( ord @ TB ) )
     => ! [A: TB,B: TB,C: TB > TA,D: TA] :
          ( ( ord_less_eq @ TB @ A @ B )
         => ( ( ( C @ B )
              = D )
           => ( ! [E: TB,F: TB] :
                  ( ( ord_less_eq @ TB @ E @ F )
                 => ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
             => ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_ord__le__eq__subst) ).

thf(304,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ord @ TA )
        & ( ord @ TB ) )
     => ! [A: TB,B: TB,C: TB > TA,D: TA] :
          ( ( ord_less_eq @ TB @ A @ B )
         => ( ( ( C @ B )
              = D )
           => ( ! [E: TB,F: TB] :
                  ( ( ord_less_eq @ TB @ E @ F )
                 => ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
             => ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(44,axiom,
    ! [A: secrecy_specID,B: secrecy_Expression,C: set @ secrecy_chanID] :
      ( ~ ( eout @ A @ B )
     => ~ ( eoutM @ A @ C @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_not__eout__eoutM) ).

thf(390,plain,
    ! [A: secrecy_specID,B: secrecy_Expression,C: set @ secrecy_chanID] :
      ( ~ ( eout @ A @ B )
     => ~ ( eoutM @ A @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(154,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member @ secrecy_KS @ D @ ( specKeysSecrets @ A ) )
         => ~ ( member @ secrecy_KS @ D @ ( specKeysSecrets @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_correctCompositionKS__negQ) ).

thf(731,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member @ secrecy_KS @ D @ ( specKeysSecrets @ A ) )
         => ~ ( member @ secrecy_KS @ D @ ( specKeysSecrets @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(218,axiom,
    ! [A: secrecy_Secrets,B: secrecy_specID] :
      ( ~ ( member @ secrecy_Secrets @ A @ ( specSecrets @ B ) )
     => ( ( eout @ B @ ( secrecy_sE @ A ) )
       => ( ( knowle1667810483orrect @ B @ ( secrecy_sKS @ A ) )
         => ( knowle1437066798e_know @ B @ ( secrecy_sKS @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_eout__know__nonKS__s) ).

thf(995,plain,
    ! [A: secrecy_Secrets,B: secrecy_specID] :
      ( ~ ( member @ secrecy_Secrets @ A @ ( specSecrets @ B ) )
     => ( ( eout @ B @ ( secrecy_sE @ A ) )
       => ( ( knowle1667810483orrect @ B @ ( secrecy_sKS @ A ) )
         => ( knowle1437066798e_know @ B @ ( secrecy_sKS @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(85,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
      ( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
      = ( sup_sup @ ( set @ TA ) @ B @ ( sup_sup @ ( set @ TA ) @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_Un__left__commute) ).

thf(510,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
      ( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
      = ( sup_sup @ ( set @ TA ) @ B @ ( sup_sup @ ( set @ TA ) @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(135,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ( member @ secrecy_KS @ D @ ( specKeysSecrets @ A ) )
         => ( ( member @ secrecy_KS @ D @ ( specKeysSecrets @ B ) )
            | ( member @ secrecy_KS @ D @ ( specKeysSecrets @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_correctCompositionKS__PQ) ).

thf(667,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ( member @ secrecy_KS @ D @ ( specKeysSecrets @ A ) )
         => ( ( member @ secrecy_KS @ D @ ( specKeysSecrets @ B ) )
            | ( member @ secrecy_KS @ D @ ( specKeysSecrets @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(202,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys,E: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) )
         => ( ( member @ secrecy_chanID @ E @ ( ins @ C ) )
           => ( ( exprChannel @ E @ ( secrecy_kE @ D ) )
             => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ A ) )
               => ( ( correctCompositionIn @ A )
                 => ? [F: secrecy_chanID] :
                      ( ( member @ secrecy_chanID @ F @ ( ins @ A ) )
                      & ( exprChannel @ F @ ( secrecy_kE @ D ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_correctCompositionKS__exprChannel__k__Qex) ).

thf(929,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_Keys,E: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( localSecrets @ A ) )
         => ( ( member @ secrecy_chanID @ E @ ( ins @ C ) )
           => ( ( exprChannel @ E @ ( secrecy_kE @ D ) )
             => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ D ) @ ( specKeysSecrets @ A ) )
               => ( ( correctCompositionIn @ A )
                 => ? [F: secrecy_chanID] :
                      ( ( member @ secrecy_chanID @ F @ ( ins @ A ) )
                      & ( exprChannel @ F @ ( secrecy_kE @ D ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(99,axiom,
    linorder @ $o,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder_14) ).

thf(549,plain,
    linorder @ $o,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(151,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: TA,D: set @ TA] :
      ( ~ ( member @ TA @ A @ B )
     => ( ~ ( member @ TA @ C @ D )
       => ( ( ( insert @ TA @ A @ B )
            = ( insert @ TA @ C @ D ) )
          = ( ( ( A = C )
             => ( B = D ) )
            & ( ( A != C )
             => ? [E: set @ TA] :
                  ( ( B
                    = ( insert @ TA @ C @ E ) )
                  & ~ ( member @ TA @ C @ E )
                  & ( D
                    = ( insert @ TA @ A @ E ) )
                  & ~ ( member @ TA @ A @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_insert__eq__iff) ).

thf(716,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: TA,D: set @ TA] :
      ( ~ ( member @ TA @ A @ B )
     => ( ~ ( member @ TA @ C @ D )
       => ( ( ( insert @ TA @ A @ B )
            = ( insert @ TA @ C @ D ) )
          = ( ( ( A = C )
             => ( B = D ) )
            & ( ( A != C )
             => ? [E: set @ TA] :
                  ( ( B
                    = ( insert @ TA @ C @ E ) )
                  & ~ ( member @ TA @ C @ E )
                  & ( D
                    = ( insert @ TA @ A @ E ) )
                  & ~ ( member @ TA @ A @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(250,axiom,
    ! [A: secrecy_Keys,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
      ( ( member @ secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ B ) )
     => ( ( ( subcomponents @ B )
          = ( insert @ secrecy_specID @ C @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correc965049635ionLoc @ B )
         => ( ~ ( ine @ C @ ( secrecy_kE @ A ) )
           => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ C ) )
             => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ D ) )
               => ( ine @ D @ ( secrecy_kE @ A ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_LocalSecretsComposition__ine2__k) ).

thf(1116,plain,
    ! [A: secrecy_Keys,B: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
      ( ( member @ secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ B ) )
     => ( ( ( subcomponents @ B )
          = ( insert @ secrecy_specID @ C @ ( insert @ secrecy_specID @ D @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correc965049635ionLoc @ B )
         => ( ~ ( ine @ C @ ( secrecy_kE @ A ) )
           => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ C ) )
             => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ A ) @ ( localSecrets @ D ) )
               => ( ine @ D @ ( secrecy_kE @ A ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(16,axiom,
    ! [TA: $tType] : ( ord @ ( set @ TA ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_10) ).

thf(300,plain,
    ! [TA: $tType] : ( ord @ ( set @ TA ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(123,axiom,
    ! [TA: $tType,A: TA,B: TA,C: set @ TA] :
      ( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
        = ( insert @ TA @ B @ C ) )
      = ( ( B = A )
        & ( ord_less_eq @ ( set @ TA ) @ C @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_singleton__insert__inj__eq) ).

thf(620,plain,
    ! [TA: $tType,A: TA,B: TA,C: set @ TA] :
      ( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
        = ( insert @ TA @ B @ C ) )
      = ( ( B = A )
        & ( ord_less_eq @ ( set @ TA ) @ C @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(21,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ord @ TA )
        & ( ord @ TB ) )
     => ! [A: TB,B: TA > TB,C: TA,D: TA] :
          ( ( A
            = ( B @ C ) )
         => ( ( ord_less_eq @ TA @ C @ D )
           => ( ! [E: TA,F: TA] :
                  ( ( ord_less_eq @ TA @ E @ F )
                 => ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
             => ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_ord__eq__le__subst) ).

thf(315,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( ( ord @ TA )
        & ( ord @ TB ) )
     => ! [A: TB,B: TA > TB,C: TA,D: TA] :
          ( ( A
            = ( B @ C ) )
         => ( ( ord_less_eq @ TA @ C @ D )
           => ( ! [E: TA,F: TA] :
                  ( ( ord_less_eq @ TA @ E @ F )
                 => ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
             => ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(50,axiom,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
      = ( ( ord_less_eq @ ( set @ TA ) @ A @ C )
        & ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_Un__subset__iff) ).

thf(410,plain,
    ! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
      ( ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
      = ( ( ord_less_eq @ ( set @ TA ) @ A @ C )
        & ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(1,conjecture,
    ~ ( member @ secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ q ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ~ ~ ( member @ secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ q ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(262,plain,
    ~ ~ ( member @ secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ q ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(7,axiom,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA > TA > $o,B: TA,C: TA] :
          ( ! [D: TA,E: TA] :
              ( ( ord_less_eq @ TA @ D @ E )
             => ( A @ D @ E ) )
         => ( ! [D: TA,E: TA] :
                ( ( A @ E @ D )
               => ( A @ D @ E ) )
           => ( A @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_linorder__wlog) ).

thf(273,plain,
    ! [TA: $tType] :
      ( ( linorder @ TA )
     => ! [A: TA > TA > $o,B: TA,C: TA] :
          ( ! [D: TA,E: TA] :
              ( ( ord_less_eq @ TA @ D @ E )
             => ( A @ D @ E ) )
         => ( ! [D: TA,E: TA] :
                ( ( A @ E @ D )
               => ( A @ D @ E ) )
           => ( A @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(117,axiom,
    ! [A: secrecy_Keys] :
      ( ( secrec1016742679ession @ ( secrecy_kKS @ A ) )
      = ( secrecy_kE @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_KS2Expression_Osimps_I1_J) ).

thf(603,plain,
    ! [A: secrecy_Keys] :
      ( ( secrec1016742679ession @ ( secrecy_kKS @ A ) )
      = ( secrecy_kE @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(155,axiom,
    ! [A: secrecy_specID,B: secrecy_Secrets] :
      ( ( knowle1667810483orrect @ A @ ( secrecy_sKS @ B ) )
      = ( ( eout @ A @ ( secrecy_sE @ B ) )
        = ( ( member @ secrecy_Secrets @ B @ ( specSecrets @ A ) )
          | ( knowle1437066798e_know @ A @ ( secrecy_sKS @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_eout__know__s) ).

thf(735,plain,
    ! [A: secrecy_specID,B: secrecy_Secrets] :
      ( ( knowle1667810483orrect @ A @ ( secrecy_sKS @ B ) )
      = ( ( eout @ A @ ( secrecy_sE @ B ) )
        = ( ( member @ secrecy_Secrets @ B @ ( specSecrets @ A ) )
          | ( knowle1437066798e_know @ A @ ( secrecy_sKS @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(58,axiom,
    bounded_lattice @ $o,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Obounded__lattice) ).

thf(437,plain,
    bounded_lattice @ $o,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(134,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ~ ( member @ TA @ A @ B )
     => ( ~ ( member @ TA @ A @ C )
       => ( ( ( insert @ TA @ A @ B )
            = ( insert @ TA @ A @ C ) )
          = ( B = C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_insert__ident) ).

thf(664,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ~ ( member @ TA @ A @ B )
     => ( ~ ( member @ TA @ A @ C )
       => ( ( ( insert @ TA @ A @ B )
            = ( insert @ TA @ A @ C ) )
          = ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(92,axiom,
    ! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression] :
      ( ( eoutM @ A @ B @ C )
     => ( eout @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_eoutM__eout) ).

thf(532,plain,
    ! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression] :
      ( ( eoutM @ A @ B @ C )
     => ( eout @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(207,axiom,
    ! [TA: $tType,A: set @ TA] :
      ( ( ? [B: TA] : ( member @ TA @ B @ A ) )
      = ( A
       != ( bot_bot @ ( set @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_ex__in__conv) ).

thf(955,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ( ? [B: TA] : ( member @ TA @ B @ A ) )
      = ( A
       != ( bot_bot @ ( set @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(195,axiom,
    ! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID,F: set @ secrecy_chanID] :
      ( ~ ( eoutM @ A @ B @ C )
     => ( ( ( subcomponents @ D )
          = ( insert @ secrecy_specID @ E @ ( insert @ secrecy_specID @ A @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correc990227761ionOut @ D )
         => ( ( out_exprChannelSet @ E @ F @ C )
           => ( ! [G: secrecy_chanID] :
                  ( ( member @ secrecy_chanID @ G @ F )
                 => ( member @ secrecy_chanID @ G @ ( loc @ D ) ) )
             => ~ ( eoutM @ D @ B @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_TBtheorem5b__notP2) ).

thf(897,plain,
    ! [A: secrecy_specID,B: set @ secrecy_chanID,C: secrecy_Expression,D: secrecy_specID,E: secrecy_specID,F: set @ secrecy_chanID] :
      ( ~ ( eoutM @ A @ B @ C )
     => ( ( ( subcomponents @ D )
          = ( insert @ secrecy_specID @ E @ ( insert @ secrecy_specID @ A @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correc990227761ionOut @ D )
         => ( ( out_exprChannelSet @ E @ F @ C )
           => ( ! [G: secrecy_chanID] :
                  ( ( member @ secrecy_chanID @ G @ F )
                 => ( member @ secrecy_chanID @ G @ ( loc @ D ) ) )
             => ~ ( eoutM @ D @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(72,axiom,
    correc965049635ionLoc @ pq,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_cCompLoc) ).

thf(474,plain,
    correc965049635ionLoc @ pq,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(157,axiom,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID,E: set @ secrecy_chanID] :
      ( ~ ( ine @ A @ B )
     => ( ( ( subcomponents @ C )
          = ( insert @ secrecy_specID @ D @ ( insert @ secrecy_specID @ A @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correctCompositionIn @ C )
         => ( ( ine_exprChannelSet @ D @ E @ B )
           => ( ! [F: secrecy_chanID] :
                  ( ( member @ secrecy_chanID @ F @ E )
                 => ( member @ secrecy_chanID @ F @ ( loc @ C ) ) )
             => ~ ( ine @ C @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_TBtheorem4a__notP2) ).

thf(740,plain,
    ! [A: secrecy_specID,B: secrecy_Expression,C: secrecy_specID,D: secrecy_specID,E: set @ secrecy_chanID] :
      ( ~ ( ine @ A @ B )
     => ( ( ( subcomponents @ C )
          = ( insert @ secrecy_specID @ D @ ( insert @ secrecy_specID @ A @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
       => ( ( correctCompositionIn @ C )
         => ( ( ine_exprChannelSet @ D @ E @ B )
           => ( ! [F: secrecy_chanID] :
                  ( ( member @ secrecy_chanID @ F @ E )
                 => ( member @ secrecy_chanID @ F @ ( loc @ C ) ) )
             => ~ ( ine @ C @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(115,axiom,
    ! [A: secrecy_specID,B: secrecy_Keys,C: secrecy_specID,D: secrecy_specID] :
      ( ~ ( knowle1437066798e_know @ A @ ( secrecy_kKS @ B ) )
     => ( ~ ( knowle1437066798e_know @ C @ ( secrecy_kKS @ B ) )
       => ( ( ( subcomponents @ D )
            = ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
         => ( ( correctCompositionIn @ D )
           => ~ ( ine @ D @ ( secrecy_kE @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_know__composition__neg__ine__k) ).

thf(596,plain,
    ! [A: secrecy_specID,B: secrecy_Keys,C: secrecy_specID,D: secrecy_specID] :
      ( ~ ( knowle1437066798e_know @ A @ ( secrecy_kKS @ B ) )
     => ( ~ ( knowle1437066798e_know @ C @ ( secrecy_kKS @ B ) )
       => ( ( ( subcomponents @ D )
            = ( insert @ secrecy_specID @ A @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
         => ( ( correctCompositionIn @ D )
           => ~ ( ine @ D @ ( secrecy_kE @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(67,axiom,
    ! [TA: $tType,A: TA,B: TA,C: set @ TA] :
      ( ( insert @ TA @ A @ ( insert @ TA @ B @ C ) )
      = ( insert @ TA @ B @ ( insert @ TA @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_insert__commute) ).

thf(459,plain,
    ! [TA: $tType,A: TA,B: TA,C: set @ TA] :
      ( ( insert @ TA @ A @ ( insert @ TA @ B @ C ) )
      = ( insert @ TA @ B @ ( insert @ TA @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(143,axiom,
    ! [TA: $tType,A: set @ TA] :
      ( ( ! [B: TA] :
            ~ ( member @ TA @ B @ A ) )
      = ( A
        = ( bot_bot @ ( set @ TA ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_all__not__in__conv) ).

thf(691,plain,
    ! [TA: $tType,A: set @ TA] :
      ( ( ! [B: TA] :
            ~ ( member @ TA @ B @ A ) )
      = ( A
        = ( bot_bot @ ( set @ TA ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(188,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correc990227761ionOut @ A )
       => ( ( member @ secrecy_chanID @ D @ ( out @ A ) )
         => ( ( member @ secrecy_chanID @ D @ ( out @ B ) )
            | ( member @ secrecy_chanID @ D @ ( out @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_correctCompositionOut__prop1) ).

thf(871,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_chanID] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correc990227761ionOut @ A )
       => ( ( member @ secrecy_chanID @ D @ ( out @ A ) )
         => ( ( member @ secrecy_chanID @ D @ ( out @ B ) )
            | ( member @ secrecy_chanID @ D @ ( out @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(251,axiom,
    ! [A: secrecy_specID,B: secrecy_Secrets] :
      ( ( knowle1667810483orrect @ A @ ( secrecy_sKS @ B ) )
     => ( ( eout @ A @ ( secrecy_sE @ B ) )
       => ( ( member @ secrecy_Secrets @ B @ ( specSecrets @ A ) )
          | ( knowle1437066798e_know @ A @ ( secrecy_sKS @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_eoutKnowCorrect__L1s) ).

thf(1120,plain,
    ! [A: secrecy_specID,B: secrecy_Secrets] :
      ( ( knowle1667810483orrect @ A @ ( secrecy_sKS @ B ) )
     => ( ( eout @ A @ ( secrecy_sE @ B ) )
       => ( ( member @ secrecy_Secrets @ B @ ( specSecrets @ A ) )
          | ( knowle1437066798e_know @ A @ ( secrecy_sKS @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(82,axiom,
    ! [TA: $tType] :
      ( ( is_singleton @ TA )
      = ( ^ [A: set @ TA] :
          ? [B: TA] :
            ( A
            = ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_is__singleton__def) ).

thf(501,plain,
    ! [TA: $tType] :
      ( ( is_singleton @ TA )
      = ( ^ [A: set @ TA] :
          ? [B: TA] :
            ( A
            = ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(36,axiom,
    ! [TA: $tType] :
      ( ( is_empty @ TA )
      = ( ^ [A: set @ TA] :
            ( A
            = ( bot_bot @ ( set @ TA ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_Set_Ois__empty__def) ).

thf(369,plain,
    ! [TA: $tType] :
      ( ( is_empty @ TA )
      = ( ^ [A: set @ TA] :
            ( A
            = ( bot_bot @ ( set @ TA ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(22,axiom,
    ! [TA: $tType,TB: $tType] :
      ( ( bot @ TB )
     => ( ( bot_bot @ ( TA > TB ) )
        = ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_bot__fun__def) ).

thf(322,plain,
    ! [TA: $tType,TB: $tType] :
      ( ( bot @ TB )
     => ( ( bot_bot @ ( TA > TB ) )
        = ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(203,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_Secrets] :
      ( ( correctCompositionKS @ A )
     => ( ( member @ secrecy_specID @ B @ ( subcomponents @ A ) )
       => ( ( member @ secrecy_Secrets @ C @ ( specSecrets @ A ) )
         => ? [D: secrecy_specID] :
              ( ( member @ secrecy_specID @ D @ ( subcomponents @ A ) )
              & ( member @ secrecy_Secrets @ C @ ( specSecrets @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_correctCompositionKS__subcomp2) ).

thf(935,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_Secrets] :
      ( ( correctCompositionKS @ A )
     => ( ( member @ secrecy_specID @ B @ ( subcomponents @ A ) )
       => ( ( member @ secrecy_Secrets @ C @ ( specSecrets @ A ) )
         => ? [D: secrecy_specID] :
              ( ( member @ secrecy_specID @ D @ ( subcomponents @ A ) )
              & ( member @ secrecy_Secrets @ C @ ( specSecrets @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(104,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: TA] :
      ( ( ( insert @ TA @ A @ B )
        = ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
      = ( ( A = C )
        & ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_singleton__insert__inj__eq_H) ).

thf(560,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: TA] :
      ( ( ( insert @ TA @ A @ B )
        = ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
      = ( ( A = C )
        & ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(129,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member @ secrecy_KS @ D @ ( specKeysSecrets @ B ) )
         => ( ~ ( member @ secrecy_KS @ D @ ( specKeysSecrets @ C ) )
           => ~ ( member @ secrecy_KS @ D @ ( specKeysSecrets @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_correctCompositionKS__neg1) ).

thf(639,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_specID,D: secrecy_KS] :
      ( ( ( subcomponents @ A )
        = ( insert @ secrecy_specID @ B @ ( insert @ secrecy_specID @ C @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
     => ( ( correctCompositionKS @ A )
       => ( ~ ( member @ secrecy_KS @ D @ ( specKeysSecrets @ B ) )
         => ( ~ ( member @ secrecy_KS @ D @ ( specKeysSecrets @ C ) )
           => ~ ( member @ secrecy_KS @ D @ ( specKeysSecrets @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(79,axiom,
    ! [A: secrecy_specID] :
      ( ( correc965049635ionLoc @ A )
     => ( ( ( subcomponents @ A )
          = ( bot_bot @ ( set @ secrecy_specID ) ) )
       => ( ( loc @ A )
          = ( bot_bot @ ( set @ secrecy_chanID ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_subcomponents__loc) ).

thf(491,plain,
    ! [A: secrecy_specID] :
      ( ( correc965049635ionLoc @ A )
     => ( ( ( subcomponents @ A )
          = ( bot_bot @ ( set @ secrecy_specID ) ) )
       => ( ( loc @ A )
          = ( bot_bot @ ( set @ secrecy_chanID ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(65,axiom,
    ! [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
      ( ( ine_ex1303305700Single @ A @ B @ C )
     => ( ine_exprChannelSet @ A @ ( insert @ secrecy_chanID @ B @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_ine__exprChannelSingle__Set) ).

thf(454,plain,
    ! [A: secrecy_specID,B: secrecy_chanID,C: secrecy_Expression] :
      ( ( ine_ex1303305700Single @ A @ B @ C )
     => ( ine_exprChannelSet @ A @ ( insert @ secrecy_chanID @ B @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(34,axiom,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( sup_sup @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
      = ( insert @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_Un__insert__left) ).

thf(364,plain,
    ! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
      ( ( sup_sup @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
      = ( insert @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(191,axiom,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_singleton__iff) ).

thf(882,plain,
    ! [TA: $tType,A: TA,B: TA] :
      ( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(211,axiom,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_Keys] :
      ( ( correctCompositionKS @ A )
     => ( ( member @ secrecy_specID @ B @ ( subcomponents @ A ) )
       => ( ( member @ secrecy_Keys @ C @ ( specKeys @ A ) )
         => ? [D: secrecy_specID] :
              ( ( member @ secrecy_specID @ D @ ( subcomponents @ A ) )
              & ( member @ secrecy_Keys @ C @ ( specKeys @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_correctCompositionKS__subcomp1) ).

thf(972,plain,
    ! [A: secrecy_specID,B: secrecy_specID,C: secrecy_Keys] :
      ( ( correctCompositionKS @ A )
     => ( ( member @ secrecy_specID @ B @ ( subcomponents @ A ) )
       => ( ( member @ secrecy_Keys @ C @ ( specKeys @ A ) )
         => ? [D: secrecy_specID] :
              ( ( member @ secrecy_specID @ D @ ( subcomponents @ A ) )
              & ( member @ secrecy_Keys @ C @ ( specKeys @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(1162,plain,
    $false,
    inference(e,[status(thm)],[809,479,347,846,909,893,962,468,1005,683,1073,379,655,614,269,677,384,550,913,945,1063,538,782,709,841,885,288,719,372,504,1132,542,587,838,917,702,559,853,421,606,416,325,448,284,770,475,443,376,623,485,806,1051,353,966,774,396,428,507,1104,849,292,452,529,661,925,381,534,1067,1057,1153,761,746,778,1042,302,630,625,879,329,522,757,456,1012,566,484,519,1143,403,388,356,593,1082,476,590,706,554,753,679,1039,997,738,1060,721,569,393,1114,792,266,633,311,921,541,765,1035,1071,674,1026,298,1135,513,264,573,296,584,694,772,286,958,545,413,875,826,577,1139,313,611,1090,704,350,406,419,990,362,434,1122,271,764,979,535,816,1029,1149,1022,462,494,1080,345,858,367,685,983,399,768,1044,608,986,563,1000,438,431,653,278,868,374,812,749,939,1145,836,473,1076,617,516,525,327,1098,993,712,1003,580,855,282,1156,1053,331,441,470,951,359,643,1141,600,1094,1008,446,497,627,1084,556,482,671,759,891,1010,844,976,688,903,699,304,390,731,995,510,667,929,549,716,1116,300,620,315,410,262,273,603,735,437,664,532,955,897,474,740,596,459,691,871,1120,501,369,322,935,560,639,491,454,364,882,972]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : ITP091^2 : TPTP v8.2.0. Released v7.5.0.
% 0.13/0.14  % Command  : run_Leo-III %s %d
% 0.14/0.35  % Computer : n009.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Sat May 18 17:57:39 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.84/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.88/1.08  % [INFO] 	 Parsing done (234ms). 
% 1.88/1.09  % [INFO] 	 Running in sequential loop mode. 
% 2.50/1.29  % [INFO] 	 eprover registered as external prover. 
% 2.50/1.30  % [INFO] 	 cvc4 registered as external prover. 
% 2.50/1.30  % [INFO] 	 Scanning for conjecture ... 
% 2.80/1.40  % [INFO] 	 Found a conjecture (or negated_conjecture) and 280 axioms. Running axiom selection ... 
% 3.16/1.49  % [INFO] 	 Axiom selection finished. Selected 259 axioms (removed 21 axioms). 
% 3.95/1.68  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 3.95/1.70  % [INFO] 	 Type checking passed. 
% 3.95/1.70  % [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 ... 
% 33.69/19.27  % External prover 'e' found a proof!
% 33.69/19.27  % [INFO] 	 Killing All external provers ... 
% 33.69/19.28  % Time passed: 18768ms (effective reasoning time: 18183ms)
% 33.69/19.28  % 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)>
% 33.69/19.28  % Axioms used in derivation (259): fact_185_TBtheorem5b__notP1, tcon_fun___Orderings_Obot, fact_212_subset__singletonD, tcon_Set_Oset___Orderings_Oord_10, fact_69_KS2Expression_Osimps_I1_J, fact_136_LocalSecretsComposition__neg__k, fact_249_subset__trans, fact_226_le__cases, fact_6_cCompLoc, fact_161_sup__bot_Oeq__neutr__iff, fact_70_bot__set__def, fact_12_cCompI, tcon_HOL_Obool___Orderings_Oord_16, fact_8_KS_Osimps_I8_J, fact_201_outStream__def, fact_119_correctCompositionKS__exprChannel__s__Qex, fact_188_not__know__k__not__eout, fact_24_LocalSecretsComposition__ine2__s, tcon_HOL_Obool___Orderings_Olinorder_14, fact_36_empty__iff, fact_133_correctCompositionKS__exprChannel__k__Qex, fact_139_Un__iff, fact_61_bot__apply, fact_132_correctCompositionKS__exprChannel__k__Pex, fact_81_TBtheorem3b, tcon_Set_Oset___Orderings_Opreorder_8, fact_130_correctCompositionKS__exprChannel__k__P, fact_205_subset__antisym, fact_253_subset__insert, fact_14_KS_Oinduct, fact_146_bex__Un, fact_202_adv__not__know2, fact_59_LocalSecretsComposition__neg1, fact_31_insert__iff, fact_206_subset__empty, fact_184_TBtheorem5b__notP2, fact_10_know_Osimps_I2_J, fact_169_correctCompositionKS__subcomp2, fact_166_ineM__Un1, fact_23_LocalSecretsComposition__ine1__s, fact_141_Un__insert__right, fact_17_KS_Osimps_I7_J, fact_224_linear, tcon_fun___Orderings_Oord, fact_28_singletonI, fact_173_TBtheorem5a__notP1, fact_149_Un__absorb, fact_67_KS2Expression_Osimps_I2_J, fact_228_le__cases3, fact_151_Un__left__absorb, fact_217_le__fun__def, fact_108_correctCompositionInLoc__exprChannel, fact_51_insertI2, fact_84_correctCompositionIn__prop1, fact_171_correctCompositionKS__subcomp4, fact_236_linorder__wlog, fact_37_ex__in__conv, fact_153_Un__empty__left, fact_41_mk__disjoint__insert, fact_193_TBtheorem5b__PQ, fact_243_subset__eq, fact_126_correctCompositionKS__negQ, tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_7, fact_246_subset__iff, fact_80_TBtheorem1b, fact_197_out__exprChannelSet__def, tcon_fun___Lattices_Obounded__semilattice__sup__bot, fact_116_bot__empty__eq, fact_200_TBtheorem5a__PQ, fact_245_equalityD2, fact_251_Collect__mono__iff, fact_29_LocalSecretsComposition1, fact_152_Un__left__commute, fact_16_Expression_Oinject_I2_J, fact_121_correctCompositionKS__exprChannel__s__Q, fact_155_singleton__Un__iff, fact_50_Set_Oset__insert, fact_118_LocalSecretsComposition__neg__loc__k, fact_125_correctCompositionKS__negP, fact_46_Collect__mem__eq, fact_179_eout__know__s, fact_44_insert__absorb, fact_53_insertE, fact_34_Collect__empty__eq, fact_191_eoutKnowCorrect__L1s, fact_88_TBtheorem4b__notP1, fact_244_equalityD1, fact_162_sup__bot__left, fact_94_TBtheorem4a__notP2, fact_89_correctCompositionIn__L1, fact_145_UnI2, fact_56_doubleton__eq__iff, fact_180_not__know__s__not__eout, fact_76_is__singletonE, fact_98_ine__ins__neg1, fact_158_sup__bot_Oright__neutral, fact_18_KS_Osimps_I5_J, fact_213_subset__singleton__iff, fact_42_insert__commute, fact_5_sg6a, fact_199_correctCompositionOut__prop1, fact_111_TBtheorem4a__PQ, tcon_fun___Lattices_Obounded__lattice_2, fact_113_locStream__def, fact_190_eout__know__nonKS__s, fact_115_Collect__empty__eq__bot, fact_214_le__funD, fact_0_not__knowQm, fact_128_know__composition1, fact_140_Un__empty, fact_99_ineM__def, fact_210_singleton__insert__inj__eq_H, fact_90_subcomponents__loc, tcon_Set_Oset___Orderings_Obot_11, fact_79_TBtheorem4a__empty, fact_55_insert__not__empty, fact_255_subset__insertI2, fact_25_LocalSecretsComposition__neg1__s, fact_163_sup__bot__right, fact_192_TBtheore54b__P, fact_19_know__composition__neg1, fact_183_TBtheorem2b, fact_20_know__composition__neg__ine__s, fact_250_set__eq__subset, fact_77_is__singleton__def, fact_105_ine__empty__exprChannelSet, fact_102_LocalSecretsComposition__exprChannel__s, fact_112_TBtheorem4b__P, fact_168_correctCompositionKS__subcomp1, fact_177_out__exprChannelSet__Single, fact_72_is__singleton__the__elem, fact_78_know_Osimps_I1_J, fact_109_TBlemma3b, fact_181_not__eout__eoutM, fact_21_not__know__s__not__ine, fact_208_insert__subset, fact_247_subset__refl, fact_91_TBtheorem4b__notPQ, fact_248_Collect__mono, fact_64_LocalSecretsComposition__ine1__k, fact_252_insert__mono, fact_58_singletonD, fact_45_mem__Collect__eq, fact_66_is__singletonI, fact_54_singleton__inject, fact_215_le__funE, fact_172_correctCompositionKS__subcomp3, fact_86_not__ine__ineM, fact_194_TBtheorem45a__P, fact_123_correctCompositionKS__PQ, fact_231_ord__eq__le__trans, fact_170_TBtheorem2a, fact_4_KS_Oinject_I2_J, fact_85_TBtheorem4a__notP1, fact_138_UnCI, fact_30_insertCI, fact_187_eoutKnowCorrect__L1k, fact_241_subsetD, fact_142_Un__insert__left, fact_3_sg5, fact_49_insert__ident, fact_65_know__composition__neg__ine__k, fact_204_subsetI, fact_221_ord__le__eq__subst, fact_40_emptyE, fact_143_UnE, fact_9_KS_Osimps_I6_J, fact_240_in__mono, fact_176_out__exprChannelSingle__Set, fact_32_insert__absorb2, fact_101_ine__exprChannelSingle__def, fact_82_Set_Ois__empty__def, fact_22_KS_Oexhaust, fact_73_is__singletonI_H, fact_43_insert__eq__iff, fact_189_eout__know__k, fact_87_ineM__ine, fact_47_Collect__cong, fact_93_TBtheorem4a__notPQ, fact_39_equals0D, fact_254_subset__insertI, fact_165_sup__eq__bot__iff, fact_13_KS_Odistinct_I1_J, tcon_Set_Oset___Lattices_Obounded__lattice_1, fact_150_Un__commute, fact_234_order__trans, fact_120_correctCompositionKS__exprChannel__s__Pex, fact_26_TBtheorem1a, fact_122_correctCompositionKS__exprChannel__s__P, fact_33_empty__Collect__eq, fact_62_LocalSecretsComposition__neg1__k, fact_52_insertI1, fact_167_TBtheorem5a__empty, tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_12, fact_110_TBtheorem4a__P, fact_83_correctCompositionIn__L2, fact_175_TBtheorem5a__notP2, fact_27_TBtheorem3a, fact_186_eout__know__nonKS__k, fact_203_order__refl, fact_100_ineM__L1, fact_164_bot__eq__sup__iff, fact_92_TBtheorem4b__notP2, tcon_fun___Orderings_Opreorder, fact_2_knowPQ, fact_95_TBtheorem4b__PQ, fact_207_empty__subsetI, fact_106_ine__exprChannelSingle__Set, fact_174_TBtheorem5a__notPQ, fact_57_singleton__iff, fact_211_singleton__insert__inj__eq, fact_147_ball__Un, fact_216_le__funI, fact_35_all__not__in__conv, fact_117_LocalSecretsComposition__neg__loc__s, fact_159_sup__bot_Oneutr__eq__iff, fact_71_Expression_Odistinct_I1_J, fact_63_LocalSecretsComposition__ine2__k, fact_1_a2, fact_137_notSpecKeysSecretsExpr__def, fact_104_ine__nonempty__exprChannelSet, fact_144_UnI1, fact_196_eoutM__def, fact_195_eout__def, fact_225_eq__refl, fact_75_not__know__k__not__ine, fact_60_the__elem__eq, fact_7_a22, fact_160_sup__bot_Oleft__neutral, fact_209_Un__subset__iff, fact_242_equalityE, fact_97_ine__def, fact_131_correctCompositionKS__exprChannel__k__Q, fact_232_ord__le__eq__trans, tcon_HOL_Obool___Lattices_Obounded__lattice, fact_135_LocalSecretsComposition__neg__s, tcon_HOL_Obool___Orderings_Opreorder_13, fact_154_Un__empty__right, fact_220_ord__eq__le__subst, fact_178_TBtheorem5b__notPQ, fact_38_equals0I, fact_103_LocalSecretsComposition__exprChannel__k, tcon_HOL_Obool___Orderings_Obot_17, fact_107_ine__exprChannelSet__Single, fact_68_Expression_Oinject_I1_J, fact_96_ine__exprChannelSet__def, fact_127_know__composition, fact_156_Un__singleton__iff, fact_157_insert__is__Un, fact_198_out__exprChannelSingle__def, fact_114_inStream__def, fact_11_subPQ, fact_134_LocalSecretsComposition__neg, fact_148_Un__assoc, fact_124_correctCompositionKS__neg1, fact_182_eoutM__eout, fact_129_know__composition2, fact_15_KS_Oinject_I1_J, fact_74_bot__fun__def
% 33.69/19.28  % No. of inferences in proof: 522
% 33.69/19.28  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 18768 ms resp. 18183 ms w/o parsing
% 34.51/19.44  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 34.51/19.44  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------