%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SYO348^5 : TPTP v8.1.2. Released v4.0.0.
% 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 : Fri Sep  1 04:46:21 EDT 2023

% Result   : Theorem 0.21s 0.40s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

thf(ty_eigen__0,type,
    eigen__0: $o > $o ).

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

thf(ty_eigen__1,type,
    eigen__1: $o > $o ).

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

thf(sP2,plain,
    ( sP2
  <=> ( eigen__1 @ a ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( a = b ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( eigen__1 @ b ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

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

thf(sP6,plain,
    ( sP6
  <=> ( eigen__0 @ sP5 ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> a ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(cE1EXT,conjecture,
    ( sP3
   => ! [X1: $o > $o] :
        ( ( X1 @ sP7 )
       => ( X1 @ sP5 ) ) ) ).

thf(h0,negated_conjecture,
    ~ ( sP3
     => ! [X1: $o > $o] :
          ( ( X1 @ sP7 )
         => ( X1 @ sP5 ) ) ),
    inference(assume_negation,[status(cth)],[cE1EXT]) ).

thf(h1,assumption,
    sP3,
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ! [X1: $o > $o] :
        ( ( X1 @ sP7 )
       => ( X1 @ sP5 ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    sP7,
    introduced(assumption,[]) ).

thf(h4,assumption,
    sP5,
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ sP7,
    introduced(assumption,[]) ).

thf(h6,assumption,
    ~ sP5,
    introduced(assumption,[]) ).

thf(h7,assumption,
    ~ ( sP1
     => sP6 ),
    introduced(assumption,[]) ).

thf(h8,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h9,assumption,
    ~ sP6,
    introduced(assumption,[]) ).

thf(1,plain,
    ( sP3
    | ~ sP7
    | ~ sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP1
    | sP6
    | ~ sP3 ),
    inference(mating_rule,[status(thm)],]) ).

thf(3,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h8,h9,h7,h3,h4,h1,h2,h0])],[1,2,h3,h4,h8,h9]) ).

thf(4,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h7,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h8,h9])],[h7,3,h8,h9]) ).

thf(5,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__0)],[h2,4,h7]) ).

thf(h10,assumption,
    ~ ( sP2
     => sP4 ),
    introduced(assumption,[]) ).

thf(h11,assumption,
    sP2,
    introduced(assumption,[]) ).

thf(h12,assumption,
    ~ sP4,
    introduced(assumption,[]) ).

thf(6,plain,
    ( sP3
    | sP7
    | sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP2
    | sP4
    | ~ sP3 ),
    inference(mating_rule,[status(thm)],]) ).

thf(8,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h11,h12,h10,h5,h6,h1,h2,h0])],[6,7,h5,h6,h11,h12]) ).

thf(9,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h10,h5,h6,h1,h2,h0]),tab_negimp(discharge,[h11,h12])],[h10,8,h11,h12]) ).

thf(10,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h5,h6,h1,h2,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__1)],[h2,9,h10]) ).

thf(11,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h1,h2,h0]),tab_bq(discharge,[h3,h4]),tab_bq(discharge,[h5,h6])],[h1,5,10,h3,h4,h5,h6]) ).

thf(12,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,11,h1,h2]) ).

thf(0,theorem,
    ( sP3
   => ! [X1: $o > $o] :
        ( ( X1 @ sP7 )
       => ( X1 @ sP5 ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[12,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SYO348^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35  % Computer : n027.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 Aug 26 05:19:49 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.21/0.40  % SZS status Theorem
% 0.21/0.40  % Mode: cade22grackle2xfee4
% 0.21/0.40  % Steps: 20
% 0.21/0.40  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------