%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ITP090^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n013.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 : Thu Aug 31 04:01:58 EDT 2023

% Result   : Theorem 0.22s 0.51s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_secrecy_specID,type,
    secrecy_specID: $tType ).

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

thf(ty_member_Secrecy_KS,type,
    member_Secrecy_KS: secrecy_KS > set_Secrecy_KS > $o ).

thf(ty_q,type,
    q: secrecy_specID ).

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

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

thf(ty_knowle945212990e_know,type,
    knowle945212990e_know: secrecy_specID > secrecy_KS > $o ).

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

thf(ty_key,type,
    key: secrecy_Keys ).

thf(ty_localSecrets,type,
    localSecrets: secrecy_specID > set_Secrecy_KS ).

thf(sP1,plain,
    ( sP1
  <=> ( m
      = ( secrecy_kKS @ key ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ( secrecy_kKS @ key )
      = m ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( knowle945212990e_know @ q @ ( secrecy_kKS @ key ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> $false ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( member_Secrecy_KS @ ( secrecy_kKS @ key ) @ ( localSecrets @ q ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( ~ ( ine @ q @ ( secrecy_kE @ key ) )
     => sP5 ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: secrecy_specID,X2: secrecy_Keys] :
        ( ( knowle945212990e_know @ X1 @ ( secrecy_kKS @ X2 ) )
        = ( ~ ( ine @ X1 @ ( secrecy_kE @ X2 ) )
         => ( member_Secrecy_KS @ ( secrecy_kKS @ X2 ) @ ( localSecrets @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( sP3 = sP6 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( knowle945212990e_know @ q @ m ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ! [X1: secrecy_Keys] :
        ( ( knowle945212990e_know @ q @ ( secrecy_kKS @ X1 ) )
        = ( ~ ( ine @ q @ ( secrecy_kE @ X1 ) )
         => ( member_Secrecy_KS @ ( secrecy_kKS @ X1 ) @ ( localSecrets @ q ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(conj_0,conjecture,
    ~ sP5 ).

thf(h0,negated_conjecture,
    sP5,
    inference(assume_negation,[status(cth)],[conj_0]) ).

thf(1,plain,
    ( ~ sP3
    | sP9
    | ~ sP2
    | sP4 ),
    inference(mating_rule,[status(thm)],]) ).

thf(2,plain,
    ~ sP4,
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP6
    | ~ sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP8
    | sP3
    | ~ sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP10
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP7
    | sP10 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP1
    | sP2 ),
    inference(symeq,[status(thm)],]) ).

thf(fact_8_know_Osimps_I1_J,axiom,
    sP7 ).

thf(fact_1_a1,axiom,
    sP1 ).

thf(fact_0_not__knowQm,axiom,
    ~ sP9 ).

thf(8,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,h0,fact_8_know_Osimps_I1_J,fact_1_a1,fact_0_not__knowQm]) ).

thf(0,theorem,
    ~ sP5,
    inference(contra,[status(thm),contra(discharge,[h0])],[8,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.16  % Problem  : ITP090^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.17  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.15/0.39  % Computer : n013.cluster.edu
% 0.15/0.39  % Model    : x86_64 x86_64
% 0.15/0.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.39  % Memory   : 8042.1875MB
% 0.15/0.39  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.39  % CPULimit : 300
% 0.15/0.39  % WCLimit  : 300
% 0.15/0.39  % DateTime : Sun Aug 27 12:58:47 EDT 2023
% 0.15/0.39  % CPUTime  : 
% 0.22/0.51  % SZS status Theorem
% 0.22/0.51  % Mode: cade22sinegrackle2x6978
% 0.22/0.51  % Steps: 1303
% 0.22/0.51  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------