%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SEV241^5 : 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 : n009.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 19:33:05 EDT 2023

% Result   : Theorem 0.13s 0.38s
% Output   : Proof 0.13s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

thf(ty_cW,type,
    cW: a > $o ).

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

thf(ty_cU,type,
    cU: a > $o ).

thf(ty_eigen__0,type,
    eigen__0: a ).

thf(sP1,plain,
    ( sP1
  <=> ( ( eigen__1 != cU )
     => ( eigen__1 = cW ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: a] :
        ( ( eigen__1 @ X1 )
        = ( cU @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

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

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

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

thf(sP6,plain,
    ( sP6
  <=> ( ( eigen__1 @ eigen__0 )
      = ( cW @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

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

thf(sP8,plain,
    ( sP8
  <=> ( eigen__1 @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ! [X1: a] :
        ( ( eigen__1 @ X1 )
        = ( cW @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( cU @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(cX5201A_pme,conjecture,
    ! [X1: a] :
      ( ~ ( ( cU @ X1 )
         => ~ ( cW @ X1 ) )
     => ! [X2: a > $o] :
          ( ( ( X2 != cU )
           => ( X2 = cW ) )
         => ( X2 @ X1 ) ) ) ).

thf(h0,negated_conjecture,
    ~ ! [X1: a] :
        ( ~ ( ( cU @ X1 )
           => ~ ( cW @ X1 ) )
       => ! [X2: a > $o] :
            ( ( ( X2 != cU )
             => ( X2 = cW ) )
           => ( X2 @ X1 ) ) ),
    inference(assume_negation,[status(cth)],[cX5201A_pme]) ).

thf(h1,assumption,
    ~ ( ~ ( sP10
         => ~ sP7 )
     => ! [X1: a > $o] :
          ( ( ( X1 != cU )
           => ( X1 = cW ) )
         => ( X1 @ eigen__0 ) ) ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ( sP10
     => ~ sP7 ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ ! [X1: a > $o] :
        ( ( ( X1 != cU )
         => ( X1 = cW ) )
       => ( X1 @ eigen__0 ) ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    sP10,
    introduced(assumption,[]) ).

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

thf(h6,assumption,
    ~ ( sP1
     => sP8 ),
    introduced(assumption,[]) ).

thf(h7,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h8,assumption,
    ~ sP8,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP3
    | sP8
    | ~ sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP6
    | sP8
    | ~ sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP2
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP9
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP5
    | sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP4
    | sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP1
    | sP4
    | sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h7,h8,h6,h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,6,7,h4,h5,h7,h8]) ).

thf(9,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,8,h7,h8]) ).

thf(10,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[h3,9,h6]) ).

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

thf(12,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,11,h2,h3]) ).

thf(13,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,12,h1]) ).

thf(0,theorem,
    ! [X1: a] :
      ( ~ ( ( cU @ X1 )
         => ~ ( cW @ X1 ) )
     => ! [X2: a > $o] :
          ( ( ( X2 != cU )
           => ( X2 = cW ) )
         => ( X2 @ X1 ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[13,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SEV241^5 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.12  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33  % Computer : n009.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Thu Aug 24 03:03:21 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 0.13/0.38  % SZS status Theorem
% 0.13/0.38  % Mode: cade22grackle2xfee4
% 0.13/0.38  % Steps: 15
% 0.13/0.38  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------