%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ITP116^1 : 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 : n004.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 04:02:12 EDT 2023

% Result   : Theorem 21.31s 21.50s
% Output   : Proof 21.31s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_set_Fi1058188332real_n,type,
    set_Fi1058188332real_n: $tType ).

thf(ty_finite1489363574real_n,type,
    finite1489363574real_n: $tType ).

thf(ty_sigma_1466784463real_n,type,
    sigma_1466784463real_n: $tType ).

thf(ty_finite964658038_int_n,type,
    finite964658038_int_n: $tType ).

thf(ty_sigma_346513458real_n,type,
    sigma_346513458real_n: sigma_1466784463real_n > set_Fi1058188332real_n > sigma_1466784463real_n ).

thf(ty_inf_in1974387902real_n,type,
    inf_in1974387902real_n: set_Fi1058188332real_n > set_Fi1058188332real_n > set_Fi1058188332real_n ).

thf(ty_sigma_476185326real_n,type,
    sigma_476185326real_n: sigma_1466784463real_n > set_Fi1058188332real_n ).

thf(ty_plus_p585657087real_n,type,
    plus_p585657087real_n: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n ).

thf(ty_a,type,
    a: finite964658038_int_n ).

thf(ty_lebesg260170249real_n,type,
    lebesg260170249real_n: sigma_1466784463real_n ).

thf(ty_t2,type,
    t2: finite964658038_int_n > set_Fi1058188332real_n ).

thf(ty_comple230862828real_n,type,
    comple230862828real_n: sigma_1466784463real_n > sigma_1466784463real_n ).

thf(ty_vimage1233683625real_n,type,
    vimage1233683625real_n: ( finite1489363574real_n > finite1489363574real_n ) > set_Fi1058188332real_n > set_Fi1058188332real_n ).

thf(ty_sigma_1235138647real_n,type,
    sigma_1235138647real_n: sigma_1466784463real_n > set_se2111327970real_n ).

thf(ty_minkow1134813771n_real,type,
    minkow1134813771n_real: finite964658038_int_n > finite1489363574real_n ).

thf(ty_member223413699real_n,type,
    member223413699real_n: set_Fi1058188332real_n > set_se2111327970real_n > $o ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: finite964658038_int_n] :
        ( ( member223413699real_n @ ( t2 @ X1 ) @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
       => ( member223413699real_n
          @ ( inf_in1974387902real_n
            @ ( vimage1233683625real_n
              @ ^ [X2: finite1489363574real_n] : ( plus_p585657087real_n @ X2 @ ( minkow1134813771n_real @ X1 ) )
              @ ( t2 @ X1 ) )
            @ ( sigma_476185326real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
          @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: set_Fi1058188332real_n] :
        ( ( sigma_476185326real_n @ ( sigma_346513458real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ X1 ) )
        = X1 ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: sigma_1466784463real_n,X2: set_Fi1058188332real_n] :
        ( ( sigma_476185326real_n @ ( sigma_346513458real_n @ X1 @ X2 ) )
        = ( inf_in1974387902real_n @ X2 @ ( sigma_476185326real_n @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( member223413699real_n @ ( t2 @ a ) @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> $false ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( member223413699real_n
      @ ( vimage1233683625real_n
        @ ^ [X1: finite1489363574real_n] : ( plus_p585657087real_n @ X1 @ ( minkow1134813771n_real @ a ) )
        @ ( t2 @ a ) )
      @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ( sigma_476185326real_n
        @ ( sigma_346513458real_n @ ( comple230862828real_n @ lebesg260170249real_n )
          @ ( vimage1233683625real_n
            @ ^ [X1: finite1489363574real_n] : ( plus_p585657087real_n @ X1 @ ( minkow1134813771n_real @ a ) )
            @ ( t2 @ a ) ) ) )
      = ( inf_in1974387902real_n
        @ ( vimage1233683625real_n
          @ ^ [X1: finite1489363574real_n] : ( plus_p585657087real_n @ X1 @ ( minkow1134813771n_real @ a ) )
          @ ( t2 @ a ) )
        @ ( sigma_476185326real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ! [X1: set_Fi1058188332real_n] :
        ( ( sigma_476185326real_n @ ( sigma_346513458real_n @ ( comple230862828real_n @ lebesg260170249real_n ) @ X1 ) )
        = ( inf_in1974387902real_n @ X1 @ ( sigma_476185326real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( ( inf_in1974387902real_n
        @ ( vimage1233683625real_n
          @ ^ [X1: finite1489363574real_n] : ( plus_p585657087real_n @ X1 @ ( minkow1134813771n_real @ a ) )
          @ ( t2 @ a ) )
        @ ( sigma_476185326real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
      = ( vimage1233683625real_n
        @ ^ [X1: finite1489363574real_n] : ( plus_p585657087real_n @ X1 @ ( minkow1134813771n_real @ a ) )
        @ ( t2 @ a ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ! [X1: finite964658038_int_n] : ( member223413699real_n @ ( t2 @ X1 ) @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( member223413699real_n
      @ ( inf_in1974387902real_n
        @ ( vimage1233683625real_n
          @ ^ [X1: finite1489363574real_n] : ( plus_p585657087real_n @ X1 @ ( minkow1134813771n_real @ a ) )
          @ ( t2 @ a ) )
        @ ( sigma_476185326real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) )
      @ ( sigma_1235138647real_n @ ( comple230862828real_n @ lebesg260170249real_n ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( sP4
     => sP11 ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( ( sigma_476185326real_n
        @ ( sigma_346513458real_n @ ( comple230862828real_n @ lebesg260170249real_n )
          @ ( vimage1233683625real_n
            @ ^ [X1: finite1489363574real_n] : ( plus_p585657087real_n @ X1 @ ( minkow1134813771n_real @ a ) )
            @ ( t2 @ a ) ) ) )
      = ( vimage1233683625real_n
        @ ^ [X1: finite1489363574real_n] : ( plus_p585657087real_n @ X1 @ ( minkow1134813771n_real @ a ) )
        @ ( t2 @ a ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(conj_0,conjecture,
    sP6 ).

thf(h0,negated_conjecture,
    ~ sP6,
    inference(assume_negation,[status(cth)],[conj_0]) ).

thf(1,plain,
    ( ~ sP7
    | sP9
    | ~ sP7
    | ~ sP13 ),
    inference(confrontation_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP11
    | sP6
    | sP5
    | ~ sP9 ),
    inference(mating_rule,[status(thm)],]) ).

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

thf(4,plain,
    ( ~ sP12
    | ~ sP4
    | sP11 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP8
    | sP7 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP1
    | sP12 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP10
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP2
    | sP13 ),
    inference(all_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP3
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(fact_275_space__lebesgue__on,axiom,
    sP2 ).

thf(fact_268_space__restrict__space,axiom,
    sP3 ).

thf(fact_3__092_060open_062_092_060And_062a_O_AT_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062,axiom,
    sP10 ).

thf(fact_2__092_060open_062_092_060And_062a_O_AT_Aa_A_092_060in_062_Asets_Alebesgue_A_092_060Longrightarrow_062_A_I_092_060lambda_062x_O_Ax_A_L_Aof__int__vec_Aa_J_A_N_096_AT_Aa_A_092_060inter_062_Aspace_Alebesgue_A_092_060in_062_Asets_Alebesgue_092_060close_062,axiom,
    sP1 ).

thf(10,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,h0,fact_275_space__lebesgue__on,fact_268_space__restrict__space,fact_3__092_060open_062_092_060And_062a_O_AT_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062,fact_2__092_060open_062_092_060And_062a_O_AT_Aa_A_092_060in_062_Asets_Alebesgue_A_092_060Longrightarrow_062_A_I_092_060lambda_062x_O_Ax_A_L_Aof__int__vec_Aa_J_A_N_096_AT_Aa_A_092_060inter_062_Aspace_Alebesgue_A_092_060in_062_Asets_Alebesgue_092_060close_062]) ).

thf(0,theorem,
    sP6,
    inference(contra,[status(thm),contra(discharge,[h0])],[10,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : ITP116^1 : TPTP v8.1.2. Released v7.5.0.
% 0.14/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35  % Computer : n004.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 : Sun Aug 27 16:18:52 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 21.31/21.50  % SZS status Theorem
% 21.31/21.50  % Mode: cade22sinegrackle2xfaf3
% 21.31/21.50  % Steps: 12357
% 21.31/21.50  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------