%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SYO236^5 : 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 : n028.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 04:45:59 EDT 2023

% Result   : Theorem 20.21s 20.41s
% Output   : Proof 20.21s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

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

thf(ty_eigen__0,type,
    eigen__0: b ).

thf(ty_eigen__1,type,
    eigen__1: b ).

thf(ty_g,type,
    g: b > a ).

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

thf(sP1,plain,
    ( sP1
  <=> ! [X1: b] :
        ( ( f @ X1 )
        = ( g @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( f = g ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ( f @ eigen__0 )
      = ( g @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

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

thf(cTHM504,conjecture,
    ( ( ~ ! [X1: ( b > a ) > $o] :
            ( ( X1 @ f )
           => ( X1 @ g ) )
     => sP1 )
   => sP2 ) ).

thf(h0,negated_conjecture,
    ~ ( ( ~ ! [X1: ( b > a ) > $o] :
              ( ( X1 @ f )
             => ( X1 @ g ) )
       => sP1 )
     => sP2 ),
    inference(assume_negation,[status(cth)],[cTHM504]) ).

thf(h1,assumption,
    ( ~ ! [X1: ( b > a ) > $o] :
          ( ( X1 @ f )
         => ( X1 @ g ) )
   => sP1 ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ sP2,
    introduced(assumption,[]) ).

thf(h3,assumption,
    ! [X1: ( b > a ) > $o] :
      ( ( X1 @ f )
     => ( X1 @ g ) ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ sP1,
    introduced(assumption,[]) ).

thf(h6,assumption,
    ~ sP4,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP1
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP2
    | sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h6,h5,h3,h3,h1,h2,h0])],[1,2,h3,h6]) ).

thf(4,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h5,h3,h3,h1,h2,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[h5,3,h6]) ).

thf(5,plain,
    $false,
    inference(tab_fe,[status(thm),assumptions([h3,h3,h1,h2,h0]),tab_fe(discharge,[h5])],[h2,4,h5]) ).

thf(h7,assumption,
    ~ sP3,
    introduced(assumption,[]) ).

thf(6,plain,
    ( ~ sP1
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h7,h5,h4,h1,h2,h0])],[6,h4,h7]) ).

thf(8,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h5,h4,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__0)],[h5,7,h7]) ).

thf(9,plain,
    $false,
    inference(tab_fe,[status(thm),assumptions([h4,h1,h2,h0]),tab_fe(discharge,[h5])],[h2,8,h5]) ).

thf(10,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h1,h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[h1,5,9,h3,h4]) ).

thf(11,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,10,h1,h2]) ).

thf(0,theorem,
    ( ( ~ ! [X1: ( b > a ) > $o] :
            ( ( X1 @ f )
           => ( X1 @ g ) )
     => sP1 )
   => sP2 ),
    inference(contra,[status(thm),contra(discharge,[h0])],[11,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SYO236^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.17/0.33  % Computer : n028.cluster.edu
% 0.17/0.33  % Model    : x86_64 x86_64
% 0.17/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33  % Memory   : 8042.1875MB
% 0.17/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33  % CPULimit : 300
% 0.17/0.33  % WCLimit  : 300
% 0.17/0.33  % DateTime : Sat Aug 26 02:11:37 EDT 2023
% 0.17/0.34  % CPUTime  : 
% 20.21/20.41  % SZS status Theorem
% 20.21/20.41  % Mode: cade22grackle2x798d
% 20.21/20.41  % Steps: 24
% 20.21/20.41  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------