%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SEV227^5 : 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 : n006.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 19:33:02 EDT 2023

% Result   : Theorem 0.20s 0.42s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

thf(ty_y,type,
    y: a > $o ).

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

thf(ty_x,type,
    x: a > $o ).

thf(ty_eigen__0,type,
    eigen__0: a ).

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

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

thf(sP3,plain,
    ( sP3
  <=> ! [X1: a] :
        ( ( eigen__1 @ X1 )
        = ( y @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( eigen__1 @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ~ sP2
     => ( eigen__1 = y ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: a] :
        ( ( eigen__1 @ X1 )
        = ( x @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( sP4
      = ( y @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( x @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ! [X1: a > $o] :
        ( ( ( X1 != x )
         => ( X1 = y ) )
       => ~ ( X1 @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

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

thf(sP11,plain,
    ( sP11
  <=> ( sP4 = sP8 ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( y @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(cX5200_pme,conjecture,
    ( ( ^ [X1: a] :
          ( ~ ( x @ X1 )
         => ( y @ X1 ) ) )
    = ( ^ [X1: a] :
          ~ ! [X2: a > $o] :
              ( ( ( X2 != x )
               => ( X2 = y ) )
             => ~ ( X2 @ X1 ) ) ) ) ).

thf(h0,negated_conjecture,
    ( ( ^ [X1: a] :
          ( ~ ( x @ X1 )
         => ( y @ X1 ) ) )
   != ( ^ [X1: a] :
          ~ ! [X2: a > $o] :
              ( ( ( X2 != x )
               => ( X2 = y ) )
             => ~ ( X2 @ X1 ) ) ) ),
    inference(assume_negation,[status(cth)],[cX5200_pme]) ).

thf(h1,assumption,
    ~ ! [X1: a] :
        ( ( ~ ( x @ X1 )
         => ( y @ X1 ) )
        = ( ~ ! [X2: a > $o] :
                ( ( ( X2 != x )
                 => ( X2 = y ) )
               => ~ ( X2 @ X1 ) ) ) ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ( sP1 != ~ sP9 ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    sP1,
    introduced(assumption,[]) ).

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

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

thf(h6,assumption,
    sP9,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP9
    | ~ sP12 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP9
    | ~ sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP1
    | sP8
    | sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h3,h4,h2,h1,h0])],[1,2,3,h3,h4]) ).

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

thf(h8,assumption,
    ~ sP12,
    introduced(assumption,[]) ).

thf(h9,assumption,
    ~ ( sP5
     => ~ sP4 ),
    introduced(assumption,[]) ).

thf(h10,assumption,
    sP5,
    introduced(assumption,[]) ).

thf(h11,assumption,
    sP4,
    introduced(assumption,[]) ).

thf(5,plain,
    ( ~ sP11
    | ~ sP4
    | sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP7
    | ~ sP4
    | sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP6
    | sP11 ),
    inference(all_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP3
    | sP7 ),
    inference(all_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP10
    | sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP2
    | sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP5
    | sP2
    | sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(12,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h10,h11,h9,h7,h8,h5,h6,h2,h1,h0])],[5,6,7,8,9,10,11,h7,h8,h10,h11]) ).

thf(13,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h9,h7,h8,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,12,h10,h11]) ).

thf(14,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h7,h8,h5,h6,h2,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__1)],[h6,13,h9]) ).

thf(15,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h5,h6,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h5,14,h7,h8]) ).

thf(16,plain,
    $false,
    inference(tab_be,[status(thm),assumptions([h2,h1,h0]),tab_be(discharge,[h3,h4]),tab_be(discharge,[h5,h6])],[h2,4,15,h3,h4,h5,h6]) ).

thf(17,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,16,h2]) ).

thf(18,plain,
    $false,
    inference(tab_fe,[status(thm),assumptions([h0]),tab_fe(discharge,[h1])],[h0,17,h1]) ).

thf(0,theorem,
    ( ( ^ [X1: a] :
          ( ~ ( x @ X1 )
         => ( y @ X1 ) ) )
    = ( ^ [X1: a] :
          ~ ! [X2: a > $o] :
              ( ( ( X2 != x )
               => ( X2 = y ) )
             => ~ ( X2 @ X1 ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[18,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEV227^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n006.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 : Thu Aug 24 03:38:23 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.42  % SZS status Theorem
% 0.20/0.42  % Mode: cade22grackle2xfee4
% 0.20/0.42  % Steps: 24
% 0.20/0.42  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------