TSTP Solution File: ITP115^1 by Lash---1.13

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%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ITP115^1 : 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 : n027.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 04:02:11 EDT 2023

% Result   : Theorem 0.19s 0.45s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_a,type,
    a: $tType ).

thf(ty_b,type,
    b: $tType ).

thf(ty_set_b,type,
    set_b: $tType ).

thf(ty_thesis,type,
    thesis: $o ).

thf(ty_eigen__0,type,
    eigen__0: set_b ).

thf(ty_a2,type,
    a2: b ).

thf(ty_f,type,
    f: a > b ).

thf(ty_eigen__1,type,
    eigen__1: set_b ).

thf(ty_member_b,type,
    member_b: b > set_b > $o ).

thf(ty_x0,type,
    x0: a ).

thf(ty_inf_inf_set_b,type,
    inf_inf_set_b: set_b > set_b > set_b ).

thf(ty_bot_bot_set_b,type,
    bot_bot_set_b: set_b ).

thf(ty_topolo1276428102open_b,type,
    topolo1276428102open_b: set_b > $o ).

thf(sP1,plain,
    ( sP1
  <=> ( ( inf_inf_set_b @ eigen__0 @ eigen__1 )
      = bot_bot_set_b ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: set_b,X2: set_b] :
        ( ~ ( ~ ( ~ ( ~ ( ( topolo1276428102open_b @ X1 )
                       => ~ ( topolo1276428102open_b @ X2 ) )
                   => ~ ( member_b @ ( f @ x0 ) @ X1 ) )
               => ~ ( member_b @ a2 @ X2 ) )
           => ( ( inf_inf_set_b @ X1 @ X2 )
             != bot_bot_set_b ) )
       => thesis ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ( topolo1276428102open_b @ eigen__0 )
     => ~ ( topolo1276428102open_b @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ~ ( ~ sP3
         => ~ ( member_b @ ( f @ x0 ) @ eigen__0 ) )
     => ~ ( member_b @ a2 @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( topolo1276428102open_b @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

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

thf(sP7,plain,
    ( sP7
  <=> ( topolo1276428102open_b @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( ~ sP3
     => ~ ( member_b @ ( f @ x0 ) @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( ~ sP4
     => ~ sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( member_b @ a2 @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ! [X1: set_b] :
        ( ~ ( ~ ( ~ ( ~ ( sP7
                       => ~ ( topolo1276428102open_b @ X1 ) )
                   => ~ ( member_b @ ( f @ x0 ) @ eigen__0 ) )
               => ~ ( member_b @ a2 @ X1 ) )
           => ( ( inf_inf_set_b @ eigen__0 @ X1 )
             != bot_bot_set_b ) )
       => sP6 ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( a2
      = ( f @ x0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( ( f @ x0 )
      = a2 ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ( ~ sP9
     => sP6 ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ( member_b @ ( f @ x0 ) @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(conj_1,conjecture,
    sP6 ).

thf(h0,negated_conjecture,
    ~ sP6,
    inference(assume_negation,[status(cth)],[conj_1]) ).

thf(h1,assumption,
    sP13,
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ! [X1: set_b,X2: set_b] :
        ( ~ ( ~ ( ~ ( ( topolo1276428102open_b @ X1 )
                   => ~ ( topolo1276428102open_b @ X2 ) )
               => ~ ( member_b @ ( f @ x0 ) @ X1 ) )
           => ~ ( member_b @ a2 @ X2 ) )
       => ( ( inf_inf_set_b @ X1 @ X2 )
         != bot_bot_set_b ) ),
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP13
    | sP12 ),
    inference(symeq,[status(thm)],]) ).

thf(fact_0__092_060open_062A_A_092_060noteq_062_Af_Ax0_092_060close_062,axiom,
    ~ sP12 ).

thf(2,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,h1,fact_0__092_060open_062A_A_092_060noteq_062_Af_Ax0_092_060close_062]) ).

thf(h3,assumption,
    ~ ! [X1: set_b] :
        ( ~ ( ~ ( ~ ( sP7
                   => ~ ( topolo1276428102open_b @ X1 ) )
               => ~ sP15 )
           => ~ ( member_b @ a2 @ X1 ) )
       => ( ( inf_inf_set_b @ eigen__0 @ X1 )
         != bot_bot_set_b ) ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ sP9,
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ sP4,
    introduced(assumption,[]) ).

thf(h6,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h7,assumption,
    ~ sP8,
    introduced(assumption,[]) ).

thf(h8,assumption,
    sP10,
    introduced(assumption,[]) ).

thf(h9,assumption,
    ~ sP3,
    introduced(assumption,[]) ).

thf(h10,assumption,
    sP15,
    introduced(assumption,[]) ).

thf(h11,assumption,
    sP7,
    introduced(assumption,[]) ).

thf(h12,assumption,
    sP5,
    introduced(assumption,[]) ).

thf(3,plain,
    ( ~ sP8
    | sP3
    | ~ sP15 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP4
    | sP8
    | ~ sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP3
    | ~ sP7
    | ~ sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP9
    | sP4
    | ~ sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP14
    | sP9
    | sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP11
    | sP14 ),
    inference(all_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP2
    | sP11 ),
    inference(all_rule,[status(thm)],]) ).

thf(conj_0,axiom,
    sP2 ).

thf(10,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h11,h12,h9,h10,h7,h8,h5,h6,h4,h3,h2,h0])],[3,4,5,6,7,8,9,h0,conj_0,h11,h12,h10,h8,h6]) ).

thf(11,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h4,h3,h2,h0]),tab_negimp(discharge,[h11,h12])],[h9,10,h11,h12]) ).

thf(12,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h4,h3,h2,h0]),tab_negimp(discharge,[h9,h10])],[h7,11,h9,h10]) ).

thf(13,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h5,h6,h4,h3,h2,h0]),tab_negimp(discharge,[h7,h8])],[h5,12,h7,h8]) ).

thf(14,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h4,h3,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,13,h5,h6]) ).

thf(15,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h3,h2,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,14,h4]) ).

thf(16,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h2,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,15,h3]) ).

thf(fact_1__092_060open_062f_Ax0_A_092_060noteq_062_AA_A_092_060Longrightarrow_062_A_092_060exists_062U_AV_O_Aopen_AU_A_092_060and_062_Aopen_AV_A_092_060and_062_Af_Ax0_A_092_060in_062_AU_A_092_060and_062_AA_A_092_060in_062_AV_A_092_060and_062_AU_A_092_060inter_062_AV_A_061_A_123_125_092_060close_062,axiom,
    ( ~ sP13
   => ~ ! [X1: set_b,X2: set_b] :
          ( ~ ( ~ ( ~ ( ( topolo1276428102open_b @ X1 )
                     => ~ ( topolo1276428102open_b @ X2 ) )
                 => ~ ( member_b @ ( f @ x0 ) @ X1 ) )
             => ~ ( member_b @ a2 @ X2 ) )
         => ( ( inf_inf_set_b @ X1 @ X2 )
           != bot_bot_set_b ) ) ) ).

thf(17,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h2])],[fact_1__092_060open_062f_Ax0_A_092_060noteq_062_AA_A_092_060Longrightarrow_062_A_092_060exists_062U_AV_O_Aopen_AU_A_092_060and_062_Aopen_AV_A_092_060and_062_Af_Ax0_A_092_060in_062_AU_A_092_060and_062_AA_A_092_060in_062_AV_A_092_060and_062_AU_A_092_060inter_062_AV_A_061_A_123_125_092_060close_062,2,16,h1,h2]) ).

thf(0,theorem,
    sP6,
    inference(contra,[status(thm),contra(discharge,[h0])],[17,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ITP115^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n027.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Sun Aug 27 11:48:36 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.45  % SZS status Theorem
% 0.19/0.45  % Mode: cade22sinegrackle2x6978
% 0.19/0.45  % Steps: 339
% 0.19/0.45  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------